TSTP Solution File: NUM530+1 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : NUM530+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n027.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 : 600s
% DateTime : Mon Jul 18 11:52:09 EDT 2022
% Result : Theorem 0.47s 0.65s
% Output : CNFRefutation 0.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 60
% Syntax : Number of formulae : 724 ( 338 unt; 16 typ; 0 def)
% Number of atoms : 7039 (2784 equ; 0 cnn)
% Maximal formula atoms : 10 ( 9 avg)
% Number of connectives : 10913 (2167 ~;2680 |; 203 &;5751 @)
% ( 0 <=>; 112 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 17 ( 17 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 8 con; 0-2 aty)
% Number of variables : 1649 ( 0 ^1647 !; 2 ?;1649 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_aNaturalNumber0,type,
aNaturalNumber0: $i > $o ).
thf(tp_doDivides0,type,
doDivides0: $i > $i > $o ).
thf(tp_iLess0,type,
iLess0: $i > $i > $o ).
thf(tp_isPrime0,type,
isPrime0: $i > $o ).
thf(tp_sK1_W1,type,
sK1_W1: $i > $i ).
thf(tp_sdtasdt0,type,
sdtasdt0: $i > $i > $i ).
thf(tp_sdtlseqdt0,type,
sdtlseqdt0: $i > $i > $o ).
thf(tp_sdtmndt0,type,
sdtmndt0: $i > $i > $i ).
thf(tp_sdtpldt0,type,
sdtpldt0: $i > $i > $i ).
thf(tp_sdtsldt0,type,
sdtsldt0: $i > $i > $i ).
thf(tp_sz00,type,
sz00: $i ).
thf(tp_sz10,type,
sz10: $i ).
thf(tp_xm,type,
xm: $i ).
thf(tp_xn,type,
xn: $i ).
thf(tp_xp,type,
xp: $i ).
thf(tp_xq,type,
xq: $i ).
thf(1,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 )
& ( aNaturalNumber0 @ W2 ) )
=> ( ( ( isPrime0 @ W2 )
& ( doDivides0 @ W2 @ ( sdtasdt0 @ W0 @ W1 ) ) )
=> ( ( doDivides0 @ W2 @ W0 )
| ( doDivides0 @ W2 @ W1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mPDP) ).
thf(2,axiom,
! [W0: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( W0 != sz00 )
& ( W0 != sz10 ) )
=> ? [W1: $i] :
( ( aNaturalNumber0 @ W1 )
& ( doDivides0 @ W1 @ W0 )
& ( isPrime0 @ W1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mPrimDiv) ).
thf(3,axiom,
! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( ( W0 != sz00 )
& ( doDivides0 @ W0 @ W1 ) )
=> ! [W2: $i] :
( ( aNaturalNumber0 @ W2 )
=> ( ( sdtasdt0 @ W2 @ ( sdtsldt0 @ W1 @ W0 ) )
= ( sdtsldt0 @ ( sdtasdt0 @ W2 @ W1 ) @ W0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivAsso) ).
thf(4,axiom,
! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( ( doDivides0 @ W0 @ W1 )
& ( W1 != sz00 ) )
=> ( sdtlseqdt0 @ W0 @ W1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivLE) ).
thf(5,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 )
& ( aNaturalNumber0 @ W2 ) )
=> ( ( ( doDivides0 @ W0 @ W1 )
& ( doDivides0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) ) )
=> ( doDivides0 @ W0 @ W2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivMin) ).
thf(6,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 )
& ( aNaturalNumber0 @ W2 ) )
=> ( ( ( doDivides0 @ W0 @ W1 )
& ( doDivides0 @ W0 @ W2 ) )
=> ( doDivides0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivSum) ).
thf(7,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 )
& ( aNaturalNumber0 @ W2 ) )
=> ( ( ( doDivides0 @ W0 @ W1 )
& ( doDivides0 @ W1 @ W2 ) )
=> ( doDivides0 @ W0 @ W2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivTrans) ).
thf(8,axiom,
! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( ( W0 != W1 )
& ( sdtlseqdt0 @ W0 @ W1 ) )
=> ( iLess0 @ W0 @ W1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIH_03) ).
thf(9,axiom,
! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( iLess0 @ W0 @ W1 )
=> $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIH) ).
thf(10,axiom,
! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( W0 != sz00 )
=> ( sdtlseqdt0 @ W1 @ ( sdtasdt0 @ W1 @ W0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMonMul2) ).
thf(11,axiom,
! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> ( ( W0 = sz00 )
| ( W0 = sz10 )
| ( ( sz10 != W0 )
& ( sdtlseqdt0 @ sz10 @ W0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLENTr) ).
thf(12,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 )
& ( aNaturalNumber0 @ W2 ) )
=> ( ( ( W0 != sz00 )
& ( W1 != W2 )
& ( sdtlseqdt0 @ W1 @ W2 ) )
=> ( ( ( sdtasdt0 @ W0 @ W1 )
!= ( sdtasdt0 @ W0 @ W2 ) )
& ( sdtlseqdt0 @ ( sdtasdt0 @ W0 @ W1 ) @ ( sdtasdt0 @ W0 @ W2 ) )
& ( ( sdtasdt0 @ W1 @ W0 )
!= ( sdtasdt0 @ W2 @ W0 ) )
& ( sdtlseqdt0 @ ( sdtasdt0 @ W1 @ W0 ) @ ( sdtasdt0 @ W2 @ W0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMonMul) ).
thf(13,axiom,
! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( ( W0 != W1 )
& ( sdtlseqdt0 @ W0 @ W1 ) )
=> ! [W2: $i] :
( ( aNaturalNumber0 @ W2 )
=> ( ( ( sdtpldt0 @ W2 @ W0 )
!= ( sdtpldt0 @ W2 @ W1 ) )
& ( sdtlseqdt0 @ ( sdtpldt0 @ W2 @ W0 ) @ ( sdtpldt0 @ W2 @ W1 ) )
& ( ( sdtpldt0 @ W0 @ W2 )
!= ( sdtpldt0 @ W1 @ W2 ) )
& ( sdtlseqdt0 @ ( sdtpldt0 @ W0 @ W2 ) @ ( sdtpldt0 @ W1 @ W2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMonAdd) ).
thf(14,axiom,
! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( sdtlseqdt0 @ W0 @ W1 )
| ( ( W1 != W0 )
& ( sdtlseqdt0 @ W1 @ W0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETotal) ).
thf(15,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 )
& ( aNaturalNumber0 @ W2 ) )
=> ( ( ( sdtlseqdt0 @ W0 @ W1 )
& ( sdtlseqdt0 @ W1 @ W2 ) )
=> ( sdtlseqdt0 @ W0 @ W2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETran) ).
thf(16,axiom,
! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( ( sdtlseqdt0 @ W0 @ W1 )
& ( sdtlseqdt0 @ W1 @ W0 ) )
=> ( W0 = W1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLEAsym) ).
thf(17,axiom,
! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> ( sdtlseqdt0 @ W0 @ W0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLERefl) ).
thf(18,axiom,
! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( ( sdtasdt0 @ W0 @ W1 )
= sz00 )
=> ( ( W0 = sz00 )
| ( W1 = sz00 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroMul) ).
thf(19,axiom,
! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( ( sdtpldt0 @ W0 @ W1 )
= sz00 )
=> ( ( W0 = sz00 )
& ( W1 = sz00 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroAdd) ).
thf(20,axiom,
! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> ( ( W0 != sz00 )
=> ! [W1: $i,W2: $i] :
( ( ( aNaturalNumber0 @ W1 )
& ( aNaturalNumber0 @ W2 ) )
=> ( ( ( ( sdtasdt0 @ W0 @ W1 )
= ( sdtasdt0 @ W0 @ W2 ) )
| ( ( sdtasdt0 @ W1 @ W0 )
= ( sdtasdt0 @ W2 @ W0 ) ) )
=> ( W1 = W2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulCanc) ).
thf(21,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 )
& ( aNaturalNumber0 @ W2 ) )
=> ( ( ( ( sdtpldt0 @ W0 @ W1 )
= ( sdtpldt0 @ W0 @ W2 ) )
| ( ( sdtpldt0 @ W1 @ W0 )
= ( sdtpldt0 @ W2 @ W0 ) ) )
=> ( W1 = W2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddCanc) ).
thf(22,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 )
& ( aNaturalNumber0 @ W2 ) )
=> ( ( ( sdtasdt0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ W0 @ W1 ) @ ( sdtasdt0 @ W0 @ W2 ) ) )
& ( ( sdtasdt0 @ ( sdtpldt0 @ W1 @ W2 ) @ W0 )
= ( sdtpldt0 @ ( sdtasdt0 @ W1 @ W0 ) @ ( sdtasdt0 @ W2 @ W0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAMDistr) ).
thf(23,axiom,
! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> ( ( ( sdtasdt0 @ W0 @ sz00 )
= sz00 )
& ( sz00
= ( sdtasdt0 @ sz00 @ W0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulZero) ).
thf(24,axiom,
! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> ( ( ( sdtasdt0 @ W0 @ sz10 )
= W0 )
& ( W0
= ( sdtasdt0 @ sz10 @ W0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulUnit) ).
thf(25,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 )
& ( aNaturalNumber0 @ W2 ) )
=> ( ( sdtasdt0 @ ( sdtasdt0 @ W0 @ W1 ) @ W2 )
= ( sdtasdt0 @ W0 @ ( sdtasdt0 @ W1 @ W2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulAsso) ).
thf(26,axiom,
! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( sdtasdt0 @ W0 @ W1 )
= ( sdtasdt0 @ W1 @ W0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
thf(27,axiom,
! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> ( ( ( sdtpldt0 @ W0 @ sz00 )
= W0 )
& ( W0
= ( sdtpldt0 @ sz00 @ W0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_AddZero) ).
thf(28,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 )
& ( aNaturalNumber0 @ W2 ) )
=> ( ( sdtpldt0 @ ( sdtpldt0 @ W0 @ W1 ) @ W2 )
= ( sdtpldt0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddAsso) ).
thf(29,axiom,
! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( sdtpldt0 @ W0 @ W1 )
= ( sdtpldt0 @ W1 @ W0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
thf(30,axiom,
! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( aNaturalNumber0 @ ( sdtasdt0 @ W0 @ W1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
thf(31,axiom,
! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( aNaturalNumber0 @ ( sdtpldt0 @ W0 @ W1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
thf(32,axiom,
( ( aNaturalNumber0 @ sz10 )
& ( sz10 != sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
thf(33,axiom,
aNaturalNumber0 @ sz00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
thf(34,axiom,
! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNatSort) ).
thf(35,axiom,
~ ( isPrime0 @ xp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3161) ).
thf(36,axiom,
( ( xm != xn )
& ( sdtlseqdt0 @ xm @ xn ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3124) ).
thf(37,axiom,
( ( sdtasdt0 @ xm @ xm )
= ( sdtasdt0 @ xp @ ( sdtasdt0 @ xq @ xq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3082) ).
thf(38,axiom,
( xq
= ( sdtsldt0 @ xn @ xp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3059) ).
thf(39,axiom,
( ( doDivides0 @ xp @ ( sdtasdt0 @ xn @ xn ) )
& ( doDivides0 @ xp @ xn ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3046) ).
thf(40,axiom,
isPrime0 @ xp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3025) ).
thf(41,axiom,
( ( sdtasdt0 @ xp @ ( sdtasdt0 @ xm @ xm ) )
= ( sdtasdt0 @ xn @ xn ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3014) ).
thf(42,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 )
& ( aNaturalNumber0 @ W2 )
& ( W0 != sz00 )
& ( W1 != sz00 )
& ( W2 != sz00 ) )
=> ( ( ( sdtasdt0 @ W2 @ ( sdtasdt0 @ W1 @ W1 ) )
= ( sdtasdt0 @ W0 @ W0 ) )
=> ( ( iLess0 @ W0 @ xn )
=> ~ ( isPrime0 @ W2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2963) ).
thf(43,axiom,
( ( aNaturalNumber0 @ xn )
& ( aNaturalNumber0 @ xm )
& ( aNaturalNumber0 @ xp )
& ( xn != sz00 )
& ( xm != sz00 )
& ( xp != sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2987) ).
thf(44,conjecture,
$false,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
thf(45,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[44]) ).
thf(46,plain,
$false = $false,
inference(unfold_def,[status(thm)],[45]) ).
thf(47,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 )
& ( aNaturalNumber0 @ W2 ) )
=> ( ( ( isPrime0 @ W2 )
& ( doDivides0 @ W2 @ ( sdtasdt0 @ W0 @ W1 ) ) )
=> ( ( doDivides0 @ W2 @ W0 )
| ( doDivides0 @ W2 @ W1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(48,plain,
( ( ! [W0: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( W0 != sz00 )
& ( W0 != sz10 ) )
=> ? [W1: $i] :
( ( aNaturalNumber0 @ W1 )
& ( doDivides0 @ W1 @ W0 )
& ( isPrime0 @ W1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(49,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( ( W0 != sz00 )
& ( doDivides0 @ W0 @ W1 ) )
=> ! [W2: $i] :
( ( aNaturalNumber0 @ W2 )
=> ( ( sdtasdt0 @ W2 @ ( sdtsldt0 @ W1 @ W0 ) )
= ( sdtsldt0 @ ( sdtasdt0 @ W2 @ W1 ) @ W0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(50,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( ( doDivides0 @ W0 @ W1 )
& ( W1 != sz00 ) )
=> ( sdtlseqdt0 @ W0 @ W1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(51,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 )
& ( aNaturalNumber0 @ W2 ) )
=> ( ( ( doDivides0 @ W0 @ W1 )
& ( doDivides0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) ) )
=> ( doDivides0 @ W0 @ W2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(52,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 )
& ( aNaturalNumber0 @ W2 ) )
=> ( ( ( doDivides0 @ W0 @ W1 )
& ( doDivides0 @ W0 @ W2 ) )
=> ( doDivides0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(53,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 )
& ( aNaturalNumber0 @ W2 ) )
=> ( ( ( doDivides0 @ W0 @ W1 )
& ( doDivides0 @ W1 @ W2 ) )
=> ( doDivides0 @ W0 @ W2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(54,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( ( W0 != W1 )
& ( sdtlseqdt0 @ W0 @ W1 ) )
=> ( iLess0 @ W0 @ W1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(55,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( iLess0 @ W0 @ W1 )
=> $true ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(56,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( W0 != sz00 )
=> ( sdtlseqdt0 @ W1 @ ( sdtasdt0 @ W1 @ W0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(57,plain,
( ( ! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> ( ( W0 = sz00 )
| ( W0 = sz10 )
| ( ( sz10 != W0 )
& ( sdtlseqdt0 @ sz10 @ W0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(58,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 )
& ( aNaturalNumber0 @ W2 ) )
=> ( ( ( W0 != sz00 )
& ( W1 != W2 )
& ( sdtlseqdt0 @ W1 @ W2 ) )
=> ( ( ( sdtasdt0 @ W0 @ W1 )
!= ( sdtasdt0 @ W0 @ W2 ) )
& ( sdtlseqdt0 @ ( sdtasdt0 @ W0 @ W1 ) @ ( sdtasdt0 @ W0 @ W2 ) )
& ( ( sdtasdt0 @ W1 @ W0 )
!= ( sdtasdt0 @ W2 @ W0 ) )
& ( sdtlseqdt0 @ ( sdtasdt0 @ W1 @ W0 ) @ ( sdtasdt0 @ W2 @ W0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(59,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( ( W0 != W1 )
& ( sdtlseqdt0 @ W0 @ W1 ) )
=> ! [W2: $i] :
( ( aNaturalNumber0 @ W2 )
=> ( ( ( sdtpldt0 @ W2 @ W0 )
!= ( sdtpldt0 @ W2 @ W1 ) )
& ( sdtlseqdt0 @ ( sdtpldt0 @ W2 @ W0 ) @ ( sdtpldt0 @ W2 @ W1 ) )
& ( ( sdtpldt0 @ W0 @ W2 )
!= ( sdtpldt0 @ W1 @ W2 ) )
& ( sdtlseqdt0 @ ( sdtpldt0 @ W0 @ W2 ) @ ( sdtpldt0 @ W1 @ W2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(60,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( sdtlseqdt0 @ W0 @ W1 )
| ( ( W1 != W0 )
& ( sdtlseqdt0 @ W1 @ W0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(61,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 )
& ( aNaturalNumber0 @ W2 ) )
=> ( ( ( sdtlseqdt0 @ W0 @ W1 )
& ( sdtlseqdt0 @ W1 @ W2 ) )
=> ( sdtlseqdt0 @ W0 @ W2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(62,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( ( sdtlseqdt0 @ W0 @ W1 )
& ( sdtlseqdt0 @ W1 @ W0 ) )
=> ( W0 = W1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(63,plain,
( ( ! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> ( sdtlseqdt0 @ W0 @ W0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(64,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( ( sdtasdt0 @ W0 @ W1 )
= sz00 )
=> ( ( W0 = sz00 )
| ( W1 = sz00 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(65,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( ( sdtpldt0 @ W0 @ W1 )
= sz00 )
=> ( ( W0 = sz00 )
& ( W1 = sz00 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(66,plain,
( ( ! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> ( ( W0 != sz00 )
=> ! [W1: $i,W2: $i] :
( ( ( aNaturalNumber0 @ W1 )
& ( aNaturalNumber0 @ W2 ) )
=> ( ( ( ( sdtasdt0 @ W0 @ W1 )
= ( sdtasdt0 @ W0 @ W2 ) )
| ( ( sdtasdt0 @ W1 @ W0 )
= ( sdtasdt0 @ W2 @ W0 ) ) )
=> ( W1 = W2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(67,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 )
& ( aNaturalNumber0 @ W2 ) )
=> ( ( ( ( sdtpldt0 @ W0 @ W1 )
= ( sdtpldt0 @ W0 @ W2 ) )
| ( ( sdtpldt0 @ W1 @ W0 )
= ( sdtpldt0 @ W2 @ W0 ) ) )
=> ( W1 = W2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(68,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 )
& ( aNaturalNumber0 @ W2 ) )
=> ( ( ( sdtasdt0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ W0 @ W1 ) @ ( sdtasdt0 @ W0 @ W2 ) ) )
& ( ( sdtasdt0 @ ( sdtpldt0 @ W1 @ W2 ) @ W0 )
= ( sdtpldt0 @ ( sdtasdt0 @ W1 @ W0 ) @ ( sdtasdt0 @ W2 @ W0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(69,plain,
( ( ! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> ( ( ( sdtasdt0 @ W0 @ sz00 )
= sz00 )
& ( sz00
= ( sdtasdt0 @ sz00 @ W0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(70,plain,
( ( ! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> ( ( ( sdtasdt0 @ W0 @ sz10 )
= W0 )
& ( W0
= ( sdtasdt0 @ sz10 @ W0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(71,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 )
& ( aNaturalNumber0 @ W2 ) )
=> ( ( sdtasdt0 @ ( sdtasdt0 @ W0 @ W1 ) @ W2 )
= ( sdtasdt0 @ W0 @ ( sdtasdt0 @ W1 @ W2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(72,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( sdtasdt0 @ W0 @ W1 )
= ( sdtasdt0 @ W1 @ W0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(73,plain,
( ( ! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> ( ( ( sdtpldt0 @ W0 @ sz00 )
= W0 )
& ( W0
= ( sdtpldt0 @ sz00 @ W0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(74,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 )
& ( aNaturalNumber0 @ W2 ) )
=> ( ( sdtpldt0 @ ( sdtpldt0 @ W0 @ W1 ) @ W2 )
= ( sdtpldt0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(75,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( sdtpldt0 @ W0 @ W1 )
= ( sdtpldt0 @ W1 @ W0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(76,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( aNaturalNumber0 @ ( sdtasdt0 @ W0 @ W1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(77,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( aNaturalNumber0 @ ( sdtpldt0 @ W0 @ W1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(78,plain,
( ( ( aNaturalNumber0 @ sz10 )
& ( sz10 != sz00 ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(79,plain,
( ( aNaturalNumber0 @ sz00 )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(80,plain,
( ( ! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> $true ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(81,plain,
( ( ~ ( isPrime0 @ xp ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(82,plain,
( ( ( xm != xn )
& ( sdtlseqdt0 @ xm @ xn ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(83,plain,
( ( ( sdtasdt0 @ xm @ xm )
= ( sdtasdt0 @ xp @ ( sdtasdt0 @ xq @ xq ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(84,plain,
( ( xq
= ( sdtsldt0 @ xn @ xp ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(85,plain,
( ( ( doDivides0 @ xp @ ( sdtasdt0 @ xn @ xn ) )
& ( doDivides0 @ xp @ xn ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(86,plain,
( ( isPrime0 @ xp )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(87,plain,
( ( ( sdtasdt0 @ xp @ ( sdtasdt0 @ xm @ xm ) )
= ( sdtasdt0 @ xn @ xn ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(88,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 )
& ( aNaturalNumber0 @ W2 )
& ( W0 != sz00 )
& ( W1 != sz00 )
& ( W2 != sz00 ) )
=> ( ( ( sdtasdt0 @ W2 @ ( sdtasdt0 @ W1 @ W1 ) )
= ( sdtasdt0 @ W0 @ W0 ) )
=> ( ( iLess0 @ W0 @ xn )
=> ~ ( isPrime0 @ W2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(89,plain,
( ( ( aNaturalNumber0 @ xn )
& ( aNaturalNumber0 @ xm )
& ( aNaturalNumber0 @ xp )
& ( xn != sz00 )
& ( xm != sz00 )
& ( xp != sz00 ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(90,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[46]) ).
thf(91,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ~ ( aNaturalNumber0 @ W2 )
| ~ ( doDivides0 @ W2 @ ( sdtasdt0 @ W0 @ W1 ) )
| ~ ( isPrime0 @ W2 )
| ( doDivides0 @ W2 @ W0 )
| ( doDivides0 @ W2 @ W1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[47]) ).
thf(92,plain,
( ( ! [W0: $i] :
( ( W0 = sz10 )
| ( W0 = sz00 )
| ~ ( aNaturalNumber0 @ W0 )
| ( ( aNaturalNumber0 @ ( sK1_W1 @ W0 ) )
& ( doDivides0 @ ( sK1_W1 @ W0 ) @ W0 )
& ( isPrime0 @ ( sK1_W1 @ W0 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[48]) ).
thf(93,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ( W0 = sz00 )
| ~ ( doDivides0 @ W0 @ W1 )
| ! [W2: $i] :
( ~ ( aNaturalNumber0 @ W2 )
| ( ( sdtasdt0 @ W2 @ ( sdtsldt0 @ W1 @ W0 ) )
= ( sdtsldt0 @ ( sdtasdt0 @ W2 @ W1 ) @ W0 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[49]) ).
thf(94,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ( W1 = sz00 )
| ~ ( doDivides0 @ W0 @ W1 )
| ( sdtlseqdt0 @ W0 @ W1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[50]) ).
thf(95,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ~ ( aNaturalNumber0 @ W2 )
| ~ ( doDivides0 @ W0 @ W1 )
| ~ ( doDivides0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) )
| ( doDivides0 @ W0 @ W2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[51]) ).
thf(96,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ~ ( aNaturalNumber0 @ W2 )
| ~ ( doDivides0 @ W0 @ W1 )
| ~ ( doDivides0 @ W0 @ W2 )
| ( doDivides0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[52]) ).
thf(97,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ~ ( aNaturalNumber0 @ W2 )
| ~ ( doDivides0 @ W0 @ W1 )
| ~ ( doDivides0 @ W1 @ W2 )
| ( doDivides0 @ W0 @ W2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[53]) ).
thf(98,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ( W0 = W1 )
| ~ ( sdtlseqdt0 @ W0 @ W1 )
| ( iLess0 @ W0 @ W1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[54]) ).
thf(99,plain,
( ( ! [W0: $i] :
~ ( aNaturalNumber0 @ W0 )
| ! [W1: $i] :
~ ( aNaturalNumber0 @ W1 )
| $true )
= $true ),
inference(extcnf_combined,[status(esa)],[55]) ).
thf(100,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ( W0 = sz00 )
| ( sdtlseqdt0 @ W1 @ ( sdtasdt0 @ W1 @ W0 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[56]) ).
thf(101,plain,
( ( ! [W0: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ( sz10 != W0 )
| ( W0 = sz00 )
| ( W0 = sz10 ) )
& ! [W0: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ( sdtlseqdt0 @ sz10 @ W0 )
| ( W0 = sz00 )
| ( W0 = sz10 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[57]) ).
thf(102,plain,
( ( ! [W0: $i] :
( ! [W1: $i,W2: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ~ ( aNaturalNumber0 @ W2 )
| ( W0 = sz00 )
| ( W1 = W2 )
| ~ ( sdtlseqdt0 @ W1 @ W2 )
| ( ( sdtasdt0 @ W1 @ W0 )
!= ( sdtasdt0 @ W2 @ W0 ) ) )
& ! [W1: $i,W2: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ~ ( aNaturalNumber0 @ W2 )
| ( W0 = sz00 )
| ( W1 = W2 )
| ~ ( sdtlseqdt0 @ W1 @ W2 )
| ( ( sdtasdt0 @ W0 @ W1 )
!= ( sdtasdt0 @ W0 @ W2 ) ) )
& ! [W1: $i,W2: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ~ ( aNaturalNumber0 @ W2 )
| ( W0 = sz00 )
| ( W1 = W2 )
| ~ ( sdtlseqdt0 @ W1 @ W2 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ W0 @ W1 ) @ ( sdtasdt0 @ W0 @ W2 ) ) )
& ! [W1: $i,W2: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ~ ( aNaturalNumber0 @ W2 )
| ( W0 = sz00 )
| ( W1 = W2 )
| ~ ( sdtlseqdt0 @ W1 @ W2 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ W1 @ W0 ) @ ( sdtasdt0 @ W2 @ W0 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[58]) ).
thf(103,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ( W0 = W1 )
| ~ ( sdtlseqdt0 @ W0 @ W1 )
| ( ! [W2: $i] :
( ~ ( aNaturalNumber0 @ W2 )
| ( ( sdtpldt0 @ W0 @ W2 )
!= ( sdtpldt0 @ W1 @ W2 ) ) )
& ! [W2: $i] :
( ~ ( aNaturalNumber0 @ W2 )
| ( ( sdtpldt0 @ W2 @ W0 )
!= ( sdtpldt0 @ W2 @ W1 ) ) )
& ! [W2: $i] :
( ~ ( aNaturalNumber0 @ W2 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ W2 @ W0 ) @ ( sdtpldt0 @ W2 @ W1 ) ) )
& ! [W2: $i] :
( ~ ( aNaturalNumber0 @ W2 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ W0 @ W2 ) @ ( sdtpldt0 @ W1 @ W2 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[59]) ).
thf(104,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ( W1 != W0 )
| ( sdtlseqdt0 @ W0 @ W1 ) )
& ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ( sdtlseqdt0 @ W1 @ W0 )
| ( sdtlseqdt0 @ W0 @ W1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[60]) ).
thf(105,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ~ ( aNaturalNumber0 @ W2 )
| ~ ( sdtlseqdt0 @ W0 @ W1 )
| ~ ( sdtlseqdt0 @ W1 @ W2 )
| ( sdtlseqdt0 @ W0 @ W2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[61]) ).
thf(106,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ~ ( sdtlseqdt0 @ W0 @ W1 )
| ~ ( sdtlseqdt0 @ W1 @ W0 )
| ( W0 = W1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[62]) ).
thf(107,plain,
( ( ! [W0: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ( sdtlseqdt0 @ W0 @ W0 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[63]) ).
thf(108,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ( ( sdtasdt0 @ W0 @ W1 )
!= sz00 )
| ( W0 = sz00 )
| ( W1 = sz00 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[64]) ).
thf(109,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ( ( sdtpldt0 @ W0 @ W1 )
!= sz00 )
| ( W0 = sz00 ) )
& ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ( ( sdtpldt0 @ W0 @ W1 )
!= sz00 )
| ( W1 = sz00 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[65]) ).
thf(110,plain,
( ( ! [W0: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ( W0 = sz00 )
| ( ! [W1: $i,W2: $i] :
( ~ ( aNaturalNumber0 @ W1 )
| ~ ( aNaturalNumber0 @ W2 )
| ( ( sdtasdt0 @ W0 @ W1 )
!= ( sdtasdt0 @ W0 @ W2 ) )
| ( W1 = W2 ) )
& ! [W1: $i,W2: $i] :
( ~ ( aNaturalNumber0 @ W1 )
| ~ ( aNaturalNumber0 @ W2 )
| ( ( sdtasdt0 @ W1 @ W0 )
!= ( sdtasdt0 @ W2 @ W0 ) )
| ( W1 = W2 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[66]) ).
thf(111,plain,
( ( ! [W0: $i] :
( ! [W1: $i,W2: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ~ ( aNaturalNumber0 @ W2 )
| ( ( sdtpldt0 @ W0 @ W1 )
!= ( sdtpldt0 @ W0 @ W2 ) )
| ( W1 = W2 ) )
& ! [W1: $i,W2: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ~ ( aNaturalNumber0 @ W2 )
| ( ( sdtpldt0 @ W1 @ W0 )
!= ( sdtpldt0 @ W2 @ W0 ) )
| ( W1 = W2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[67]) ).
thf(112,plain,
( ( ! [W0: $i] :
( ! [W1: $i,W2: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ~ ( aNaturalNumber0 @ W2 )
| ( ( sdtasdt0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ W0 @ W1 ) @ ( sdtasdt0 @ W0 @ W2 ) ) ) )
& ! [W1: $i,W2: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ~ ( aNaturalNumber0 @ W2 )
| ( ( sdtasdt0 @ ( sdtpldt0 @ W1 @ W2 ) @ W0 )
= ( sdtpldt0 @ ( sdtasdt0 @ W1 @ W0 ) @ ( sdtasdt0 @ W2 @ W0 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[68]) ).
thf(113,plain,
( ( ! [W0: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ( ( sdtasdt0 @ W0 @ sz00 )
= sz00 ) )
& ! [W0: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ( sz00
= ( sdtasdt0 @ sz00 @ W0 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[69]) ).
thf(114,plain,
( ( ! [W0: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ( ( sdtasdt0 @ W0 @ sz10 )
= W0 ) )
& ! [W0: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ( W0
= ( sdtasdt0 @ sz10 @ W0 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[70]) ).
thf(115,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ~ ( aNaturalNumber0 @ W2 )
| ( ( sdtasdt0 @ ( sdtasdt0 @ W0 @ W1 ) @ W2 )
= ( sdtasdt0 @ W0 @ ( sdtasdt0 @ W1 @ W2 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[71]) ).
thf(116,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ( ( sdtasdt0 @ W0 @ W1 )
= ( sdtasdt0 @ W1 @ W0 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[72]) ).
thf(117,plain,
( ( ! [W0: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ( ( sdtpldt0 @ W0 @ sz00 )
= W0 ) )
& ! [W0: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ( W0
= ( sdtpldt0 @ sz00 @ W0 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[73]) ).
thf(118,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ~ ( aNaturalNumber0 @ W2 )
| ( ( sdtpldt0 @ ( sdtpldt0 @ W0 @ W1 ) @ W2 )
= ( sdtpldt0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[74]) ).
thf(119,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ( ( sdtpldt0 @ W0 @ W1 )
= ( sdtpldt0 @ W1 @ W0 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[75]) ).
thf(120,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ( aNaturalNumber0 @ ( sdtasdt0 @ W0 @ W1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[76]) ).
thf(121,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ( aNaturalNumber0 @ ( sdtpldt0 @ W0 @ W1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[77]) ).
thf(122,plain,
( ( ( sz10 != sz00 )
& ( aNaturalNumber0 @ sz10 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[78]) ).
thf(123,plain,
( ( ! [W0: $i] : $true )
= $true ),
inference(extcnf_combined,[status(esa)],[80]) ).
thf(124,plain,
( ( ( xm != xn )
& ( sdtlseqdt0 @ xm @ xn ) )
= $true ),
inference(extcnf_combined,[status(esa)],[82]) ).
thf(125,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ( W2 = sz00 )
| ( W1 = sz00 )
| ( W0 = sz00 )
| ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ~ ( aNaturalNumber0 @ W2 )
| ( ( sdtasdt0 @ W2 @ ( sdtasdt0 @ W1 @ W1 ) )
!= ( sdtasdt0 @ W0 @ W0 ) )
| ~ ( iLess0 @ W0 @ xn )
| ~ ( isPrime0 @ W2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[88]) ).
thf(126,plain,
( ( ( xp != sz00 )
& ( xm != sz00 )
& ( xn != sz00 )
& ( aNaturalNumber0 @ xn )
& ( aNaturalNumber0 @ xm )
& ( aNaturalNumber0 @ xp ) )
= $true ),
inference(extcnf_combined,[status(esa)],[89]) ).
thf(127,plain,
( ( ( xp != sz00 )
& ( xm != sz00 )
& ( xn != sz00 )
& ( aNaturalNumber0 @ xn )
& ( aNaturalNumber0 @ xm )
& ( aNaturalNumber0 @ xp ) )
= $true ),
inference(copy,[status(thm)],[126]) ).
thf(128,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ( W2 = sz00 )
| ( W1 = sz00 )
| ( W0 = sz00 )
| ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ~ ( aNaturalNumber0 @ W2 )
| ( ( sdtasdt0 @ W2 @ ( sdtasdt0 @ W1 @ W1 ) )
!= ( sdtasdt0 @ W0 @ W0 ) )
| ~ ( iLess0 @ W0 @ xn )
| ~ ( isPrime0 @ W2 ) ) )
= $true ),
inference(copy,[status(thm)],[125]) ).
thf(129,plain,
( ( ( sdtasdt0 @ xp @ ( sdtasdt0 @ xm @ xm ) )
= ( sdtasdt0 @ xn @ xn ) )
= $true ),
inference(copy,[status(thm)],[87]) ).
thf(130,plain,
( ( isPrime0 @ xp )
= $true ),
inference(copy,[status(thm)],[86]) ).
thf(131,plain,
( ( ( doDivides0 @ xp @ ( sdtasdt0 @ xn @ xn ) )
& ( doDivides0 @ xp @ xn ) )
= $true ),
inference(copy,[status(thm)],[85]) ).
thf(132,plain,
( ( xq
= ( sdtsldt0 @ xn @ xp ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(133,plain,
( ( ( sdtasdt0 @ xm @ xm )
= ( sdtasdt0 @ xp @ ( sdtasdt0 @ xq @ xq ) ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(134,plain,
( ( ( xm != xn )
& ( sdtlseqdt0 @ xm @ xn ) )
= $true ),
inference(copy,[status(thm)],[124]) ).
thf(135,plain,
( ( ~ ( isPrime0 @ xp ) )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(136,plain,
( ( ! [W0: $i] : $true )
= $true ),
inference(copy,[status(thm)],[123]) ).
thf(137,plain,
( ( aNaturalNumber0 @ sz00 )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(138,plain,
( ( ( sz10 != sz00 )
& ( aNaturalNumber0 @ sz10 ) )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(139,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ( aNaturalNumber0 @ ( sdtpldt0 @ W0 @ W1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[121]) ).
thf(140,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ( aNaturalNumber0 @ ( sdtasdt0 @ W0 @ W1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[120]) ).
thf(141,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ( ( sdtpldt0 @ W0 @ W1 )
= ( sdtpldt0 @ W1 @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[119]) ).
thf(142,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ~ ( aNaturalNumber0 @ W2 )
| ( ( sdtpldt0 @ ( sdtpldt0 @ W0 @ W1 ) @ W2 )
= ( sdtpldt0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(143,plain,
( ( ! [W0: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ( ( sdtpldt0 @ W0 @ sz00 )
= W0 ) )
& ! [W0: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ( W0
= ( sdtpldt0 @ sz00 @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(144,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ( ( sdtasdt0 @ W0 @ W1 )
= ( sdtasdt0 @ W1 @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(145,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ~ ( aNaturalNumber0 @ W2 )
| ( ( sdtasdt0 @ ( sdtasdt0 @ W0 @ W1 ) @ W2 )
= ( sdtasdt0 @ W0 @ ( sdtasdt0 @ W1 @ W2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[115]) ).
thf(146,plain,
( ( ! [W0: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ( ( sdtasdt0 @ W0 @ sz10 )
= W0 ) )
& ! [W0: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ( W0
= ( sdtasdt0 @ sz10 @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(147,plain,
( ( ! [W0: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ( ( sdtasdt0 @ W0 @ sz00 )
= sz00 ) )
& ! [W0: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ( sz00
= ( sdtasdt0 @ sz00 @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(148,plain,
( ( ! [W0: $i] :
( ! [W1: $i,W2: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ~ ( aNaturalNumber0 @ W2 )
| ( ( sdtasdt0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ W0 @ W1 ) @ ( sdtasdt0 @ W0 @ W2 ) ) ) )
& ! [W1: $i,W2: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ~ ( aNaturalNumber0 @ W2 )
| ( ( sdtasdt0 @ ( sdtpldt0 @ W1 @ W2 ) @ W0 )
= ( sdtpldt0 @ ( sdtasdt0 @ W1 @ W0 ) @ ( sdtasdt0 @ W2 @ W0 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(149,plain,
( ( ! [W0: $i] :
( ! [W1: $i,W2: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ~ ( aNaturalNumber0 @ W2 )
| ( ( sdtpldt0 @ W0 @ W1 )
!= ( sdtpldt0 @ W0 @ W2 ) )
| ( W1 = W2 ) )
& ! [W1: $i,W2: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ~ ( aNaturalNumber0 @ W2 )
| ( ( sdtpldt0 @ W1 @ W0 )
!= ( sdtpldt0 @ W2 @ W0 ) )
| ( W1 = W2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(150,plain,
( ( ! [W0: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ( W0 = sz00 )
| ( ! [W1: $i,W2: $i] :
( ~ ( aNaturalNumber0 @ W1 )
| ~ ( aNaturalNumber0 @ W2 )
| ( ( sdtasdt0 @ W0 @ W1 )
!= ( sdtasdt0 @ W0 @ W2 ) )
| ( W1 = W2 ) )
& ! [W1: $i,W2: $i] :
( ~ ( aNaturalNumber0 @ W1 )
| ~ ( aNaturalNumber0 @ W2 )
| ( ( sdtasdt0 @ W1 @ W0 )
!= ( sdtasdt0 @ W2 @ W0 ) )
| ( W1 = W2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(151,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ( ( sdtpldt0 @ W0 @ W1 )
!= sz00 )
| ( W0 = sz00 ) )
& ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ( ( sdtpldt0 @ W0 @ W1 )
!= sz00 )
| ( W1 = sz00 ) ) )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(152,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ( ( sdtasdt0 @ W0 @ W1 )
!= sz00 )
| ( W0 = sz00 )
| ( W1 = sz00 ) ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(153,plain,
( ( ! [W0: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ( sdtlseqdt0 @ W0 @ W0 ) ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(154,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ~ ( sdtlseqdt0 @ W0 @ W1 )
| ~ ( sdtlseqdt0 @ W1 @ W0 )
| ( W0 = W1 ) ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(155,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ~ ( aNaturalNumber0 @ W2 )
| ~ ( sdtlseqdt0 @ W0 @ W1 )
| ~ ( sdtlseqdt0 @ W1 @ W2 )
| ( sdtlseqdt0 @ W0 @ W2 ) ) )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(156,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ( W1 != W0 )
| ( sdtlseqdt0 @ W0 @ W1 ) )
& ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ( sdtlseqdt0 @ W1 @ W0 )
| ( sdtlseqdt0 @ W0 @ W1 ) ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(157,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ( W0 = W1 )
| ~ ( sdtlseqdt0 @ W0 @ W1 )
| ( ! [W2: $i] :
( ~ ( aNaturalNumber0 @ W2 )
| ( ( sdtpldt0 @ W0 @ W2 )
!= ( sdtpldt0 @ W1 @ W2 ) ) )
& ! [W2: $i] :
( ~ ( aNaturalNumber0 @ W2 )
| ( ( sdtpldt0 @ W2 @ W0 )
!= ( sdtpldt0 @ W2 @ W1 ) ) )
& ! [W2: $i] :
( ~ ( aNaturalNumber0 @ W2 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ W2 @ W0 ) @ ( sdtpldt0 @ W2 @ W1 ) ) )
& ! [W2: $i] :
( ~ ( aNaturalNumber0 @ W2 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ W0 @ W2 ) @ ( sdtpldt0 @ W1 @ W2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(158,plain,
( ( ! [W0: $i] :
( ! [W1: $i,W2: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ~ ( aNaturalNumber0 @ W2 )
| ( W0 = sz00 )
| ( W1 = W2 )
| ~ ( sdtlseqdt0 @ W1 @ W2 )
| ( ( sdtasdt0 @ W1 @ W0 )
!= ( sdtasdt0 @ W2 @ W0 ) ) )
& ! [W1: $i,W2: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ~ ( aNaturalNumber0 @ W2 )
| ( W0 = sz00 )
| ( W1 = W2 )
| ~ ( sdtlseqdt0 @ W1 @ W2 )
| ( ( sdtasdt0 @ W0 @ W1 )
!= ( sdtasdt0 @ W0 @ W2 ) ) )
& ! [W1: $i,W2: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ~ ( aNaturalNumber0 @ W2 )
| ( W0 = sz00 )
| ( W1 = W2 )
| ~ ( sdtlseqdt0 @ W1 @ W2 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ W0 @ W1 ) @ ( sdtasdt0 @ W0 @ W2 ) ) )
& ! [W1: $i,W2: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ~ ( aNaturalNumber0 @ W2 )
| ( W0 = sz00 )
| ( W1 = W2 )
| ~ ( sdtlseqdt0 @ W1 @ W2 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ W1 @ W0 ) @ ( sdtasdt0 @ W2 @ W0 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(159,plain,
( ( ! [W0: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ( sz10 != W0 )
| ( W0 = sz00 )
| ( W0 = sz10 ) )
& ! [W0: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ( sdtlseqdt0 @ sz10 @ W0 )
| ( W0 = sz00 )
| ( W0 = sz10 ) ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(160,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ( W0 = sz00 )
| ( sdtlseqdt0 @ W1 @ ( sdtasdt0 @ W1 @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(161,plain,
( ( ! [W0: $i] :
~ ( aNaturalNumber0 @ W0 )
| ! [W1: $i] :
~ ( aNaturalNumber0 @ W1 )
| $true )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(162,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ( W0 = W1 )
| ~ ( sdtlseqdt0 @ W0 @ W1 )
| ( iLess0 @ W0 @ W1 ) ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(163,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ~ ( aNaturalNumber0 @ W2 )
| ~ ( doDivides0 @ W0 @ W1 )
| ~ ( doDivides0 @ W1 @ W2 )
| ( doDivides0 @ W0 @ W2 ) ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(164,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ~ ( aNaturalNumber0 @ W2 )
| ~ ( doDivides0 @ W0 @ W1 )
| ~ ( doDivides0 @ W0 @ W2 )
| ( doDivides0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[96]) ).
thf(165,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ~ ( aNaturalNumber0 @ W2 )
| ~ ( doDivides0 @ W0 @ W1 )
| ~ ( doDivides0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) )
| ( doDivides0 @ W0 @ W2 ) ) )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(166,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ( W1 = sz00 )
| ~ ( doDivides0 @ W0 @ W1 )
| ( sdtlseqdt0 @ W0 @ W1 ) ) )
= $true ),
inference(copy,[status(thm)],[94]) ).
thf(167,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ( W0 = sz00 )
| ~ ( doDivides0 @ W0 @ W1 )
| ! [W2: $i] :
( ~ ( aNaturalNumber0 @ W2 )
| ( ( sdtasdt0 @ W2 @ ( sdtsldt0 @ W1 @ W0 ) )
= ( sdtsldt0 @ ( sdtasdt0 @ W2 @ W1 ) @ W0 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[93]) ).
thf(168,plain,
( ( ! [W0: $i] :
( ( W0 = sz10 )
| ( W0 = sz00 )
| ~ ( aNaturalNumber0 @ W0 )
| ( ( aNaturalNumber0 @ ( sK1_W1 @ W0 ) )
& ( doDivides0 @ ( sK1_W1 @ W0 ) @ W0 )
& ( isPrime0 @ ( sK1_W1 @ W0 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(169,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ~ ( aNaturalNumber0 @ W2 )
| ~ ( doDivides0 @ W2 @ ( sdtasdt0 @ W0 @ W1 ) )
| ~ ( isPrime0 @ W2 )
| ( doDivides0 @ W2 @ W0 )
| ( doDivides0 @ W2 @ W1 ) ) )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(170,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(171,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 )
| ~ ( aNaturalNumber0 @ SX2 )
| ( ( sdtpldt0 @ SX0 @ SX1 )
!= ( sdtpldt0 @ SX0 @ SX2 ) )
| ( SX1 = SX2 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 )
| ~ ( aNaturalNumber0 @ SX2 )
| ( ( sdtpldt0 @ SX1 @ SX0 )
!= ( sdtpldt0 @ SX2 @ SX0 ) )
| ( SX1 = SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[149]) ).
thf(172,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( ( sdtasdt0 @ SX0 @ sz00 )
= sz00 ) )
| ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( sz00
= ( sdtasdt0 @ sz00 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[147]) ).
thf(173,plain,
( ( ~ ( ~ ( ( sz10 != sz00 ) )
| ~ ( aNaturalNumber0 @ sz10 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[138]) ).
thf(174,plain,
( ( ! [SX0: $i] :
~ ( ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 )
| ~ ( aNaturalNumber0 @ SX2 )
| ( SX0 = sz00 )
| ( SX1 = SX2 )
| ~ ( sdtlseqdt0 @ SX1 @ SX2 )
| ( ( sdtasdt0 @ SX1 @ SX0 )
!= ( sdtasdt0 @ SX2 @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 )
| ~ ( aNaturalNumber0 @ SX2 )
| ( SX0 = sz00 )
| ( SX1 = SX2 )
| ~ ( sdtlseqdt0 @ SX1 @ SX2 )
| ( ( sdtasdt0 @ SX0 @ SX1 )
!= ( sdtasdt0 @ SX0 @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 )
| ~ ( aNaturalNumber0 @ SX2 )
| ( SX0 = sz00 )
| ( SX1 = SX2 )
| ~ ( sdtlseqdt0 @ SX1 @ SX2 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SX0 @ SX1 ) @ ( sdtasdt0 @ SX0 @ SX2 ) ) ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 )
| ~ ( aNaturalNumber0 @ SX2 )
| ( SX0 = sz00 )
| ( SX1 = SX2 )
| ~ ( sdtlseqdt0 @ SX1 @ SX2 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ ( sdtasdt0 @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[158]) ).
thf(175,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 )
| ( ( sdtpldt0 @ SX0 @ SX1 )
!= sz00 )
| ( SX0 = sz00 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 )
| ( ( sdtpldt0 @ SX0 @ SX1 )
!= sz00 )
| ( SX1 = sz00 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[151]) ).
thf(176,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( ( sdtasdt0 @ SX0 @ sz10 )
= SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( SX0
= ( sdtasdt0 @ sz10 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[146]) ).
thf(177,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 )
| ( SX1 != SX0 )
| ( sdtlseqdt0 @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 )
| ( sdtlseqdt0 @ SX1 @ SX0 )
| ( sdtlseqdt0 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[156]) ).
thf(178,plain,
( ( ~ ( ~ ( ( xm != xn ) )
| ~ ( sdtlseqdt0 @ xm @ xn ) ) )
= $true ),
inference(unfold_def,[status(thm)],[134]) ).
thf(179,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 )
| ~ ( aNaturalNumber0 @ SX2 )
| ( ( sdtasdt0 @ SX0 @ ( sdtpldt0 @ SX1 @ SX2 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SX0 @ SX1 ) @ ( sdtasdt0 @ SX0 @ SX2 ) ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 )
| ~ ( aNaturalNumber0 @ SX2 )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SX1 @ SX2 ) @ SX0 )
= ( sdtpldt0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ ( sdtasdt0 @ SX2 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[148]) ).
thf(180,plain,
( ( ~ ( ~ ( ( xp != sz00 ) )
| ~ ~ ( ~ ( ( xm != sz00 ) )
| ~ ~ ( ~ ( ( xn != sz00 ) )
| ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ xn )
| ~ ( aNaturalNumber0 @ xm ) )
| ~ ( aNaturalNumber0 @ xp ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[127]) ).
thf(181,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 )
| ( SX0 = SX1 )
| ~ ( sdtlseqdt0 @ SX0 @ SX1 )
| ~ ( ~ ~ ( ~ ! [SX2: $i] :
( ~ ( aNaturalNumber0 @ SX2 )
| ( ( sdtpldt0 @ SX0 @ SX2 )
!= ( sdtpldt0 @ SX1 @ SX2 ) ) )
| ~ ~ ( ~ ! [SX2: $i] :
( ~ ( aNaturalNumber0 @ SX2 )
| ( ( sdtpldt0 @ SX2 @ SX0 )
!= ( sdtpldt0 @ SX2 @ SX1 ) ) )
| ~ ! [SX2: $i] :
( ~ ( aNaturalNumber0 @ SX2 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SX2 @ SX0 ) @ ( sdtpldt0 @ SX2 @ SX1 ) ) ) ) )
| ~ ! [SX2: $i] :
( ~ ( aNaturalNumber0 @ SX2 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SX0 @ SX2 ) @ ( sdtpldt0 @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[157]) ).
thf(182,plain,
( ( ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( SX0 = sz00 )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( aNaturalNumber0 @ SX1 )
| ~ ( aNaturalNumber0 @ SX2 )
| ( ( sdtasdt0 @ SX0 @ SX1 )
!= ( sdtasdt0 @ SX0 @ SX2 ) )
| ( SX1 = SX2 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( aNaturalNumber0 @ SX1 )
| ~ ( aNaturalNumber0 @ SX2 )
| ( ( sdtasdt0 @ SX1 @ SX0 )
!= ( sdtasdt0 @ SX2 @ SX0 ) )
| ( SX1 = SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[150]) ).
thf(183,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( ( sdtpldt0 @ SX0 @ sz00 )
= SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( SX0
= ( sdtpldt0 @ sz00 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[143]) ).
thf(184,plain,
( ( ~ ( ~ ( doDivides0 @ xp @ ( sdtasdt0 @ xn @ xn ) )
| ~ ( doDivides0 @ xp @ xn ) ) )
= $true ),
inference(unfold_def,[status(thm)],[131]) ).
thf(185,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( sz10 != SX0 )
| ( SX0 = sz00 )
| ( SX0 = sz10 ) )
| ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( sdtlseqdt0 @ sz10 @ SX0 )
| ( SX0 = sz00 )
| ( SX0 = sz10 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[159]) ).
thf(186,plain,
( ( ! [SX0: $i] :
( ( SX0 = sz10 )
| ( SX0 = sz00 )
| ~ ( aNaturalNumber0 @ SX0 )
| ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ ( sK1_W1 @ SX0 ) )
| ~ ( doDivides0 @ ( sK1_W1 @ SX0 ) @ SX0 ) )
| ~ ( isPrime0 @ ( sK1_W1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[168]) ).
thf(187,plain,
! [SV1: $i] :
( ( ! [SY74: $i,SY75: $i] :
( ( SY75 = sz00 )
| ( SY74 = sz00 )
| ( SV1 = sz00 )
| ~ ( aNaturalNumber0 @ SV1 )
| ~ ( aNaturalNumber0 @ SY74 )
| ~ ( aNaturalNumber0 @ SY75 )
| ( ( sdtasdt0 @ SY75 @ ( sdtasdt0 @ SY74 @ SY74 ) )
!= ( sdtasdt0 @ SV1 @ SV1 ) )
| ~ ( iLess0 @ SV1 @ xn )
| ~ ( isPrime0 @ SY75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(188,plain,
( ( isPrime0 @ xp )
= $false ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(189,plain,
$true = $true,
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(190,plain,
! [SV3: $i] :
( ( ! [SY76: $i] :
( ~ ( aNaturalNumber0 @ SV3 )
| ~ ( aNaturalNumber0 @ SY76 )
| ( aNaturalNumber0 @ ( sdtpldt0 @ SV3 @ SY76 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(191,plain,
! [SV4: $i] :
( ( ! [SY77: $i] :
( ~ ( aNaturalNumber0 @ SV4 )
| ~ ( aNaturalNumber0 @ SY77 )
| ( aNaturalNumber0 @ ( sdtasdt0 @ SV4 @ SY77 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(192,plain,
! [SV5: $i] :
( ( ! [SY78: $i] :
( ~ ( aNaturalNumber0 @ SV5 )
| ~ ( aNaturalNumber0 @ SY78 )
| ( ( sdtpldt0 @ SV5 @ SY78 )
= ( sdtpldt0 @ SY78 @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(193,plain,
! [SV6: $i] :
( ( ! [SY79: $i,SY80: $i] :
( ~ ( aNaturalNumber0 @ SV6 )
| ~ ( aNaturalNumber0 @ SY79 )
| ~ ( aNaturalNumber0 @ SY80 )
| ( ( sdtpldt0 @ ( sdtpldt0 @ SV6 @ SY79 ) @ SY80 )
= ( sdtpldt0 @ SV6 @ ( sdtpldt0 @ SY79 @ SY80 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(194,plain,
! [SV7: $i] :
( ( ! [SY81: $i] :
( ~ ( aNaturalNumber0 @ SV7 )
| ~ ( aNaturalNumber0 @ SY81 )
| ( ( sdtasdt0 @ SV7 @ SY81 )
= ( sdtasdt0 @ SY81 @ SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(195,plain,
! [SV8: $i] :
( ( ! [SY82: $i,SY83: $i] :
( ~ ( aNaturalNumber0 @ SV8 )
| ~ ( aNaturalNumber0 @ SY82 )
| ~ ( aNaturalNumber0 @ SY83 )
| ( ( sdtasdt0 @ ( sdtasdt0 @ SV8 @ SY82 ) @ SY83 )
= ( sdtasdt0 @ SV8 @ ( sdtasdt0 @ SY82 @ SY83 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(196,plain,
! [SV9: $i] :
( ( ! [SY84: $i] :
( ~ ( aNaturalNumber0 @ SV9 )
| ~ ( aNaturalNumber0 @ SY84 )
| ( ( sdtasdt0 @ SV9 @ SY84 )
!= sz00 )
| ( SV9 = sz00 )
| ( SY84 = sz00 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(197,plain,
! [SV10: $i] :
( ( ~ ( aNaturalNumber0 @ SV10 )
| ( sdtlseqdt0 @ SV10 @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(198,plain,
! [SV11: $i] :
( ( ! [SY85: $i] :
( ~ ( aNaturalNumber0 @ SV11 )
| ~ ( aNaturalNumber0 @ SY85 )
| ~ ( sdtlseqdt0 @ SV11 @ SY85 )
| ~ ( sdtlseqdt0 @ SY85 @ SV11 )
| ( SV11 = SY85 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(199,plain,
! [SV12: $i] :
( ( ! [SY86: $i,SY87: $i] :
( ~ ( aNaturalNumber0 @ SV12 )
| ~ ( aNaturalNumber0 @ SY86 )
| ~ ( aNaturalNumber0 @ SY87 )
| ~ ( sdtlseqdt0 @ SV12 @ SY86 )
| ~ ( sdtlseqdt0 @ SY86 @ SY87 )
| ( sdtlseqdt0 @ SV12 @ SY87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(200,plain,
! [SV13: $i] :
( ( ! [SY88: $i] :
( ~ ( aNaturalNumber0 @ SV13 )
| ~ ( aNaturalNumber0 @ SY88 )
| ( SV13 = sz00 )
| ( sdtlseqdt0 @ SY88 @ ( sdtasdt0 @ SY88 @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(201,plain,
( ( ( ! [W0: $i] :
~ ( aNaturalNumber0 @ W0 )
| ! [W1: $i] :
~ ( aNaturalNumber0 @ W1 ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[161]) ).
thf(202,plain,
! [SV14: $i] :
( ( ! [SY89: $i] :
( ~ ( aNaturalNumber0 @ SV14 )
| ~ ( aNaturalNumber0 @ SY89 )
| ( SV14 = SY89 )
| ~ ( sdtlseqdt0 @ SV14 @ SY89 )
| ( iLess0 @ SV14 @ SY89 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(203,plain,
! [SV15: $i] :
( ( ! [SY90: $i,SY91: $i] :
( ~ ( aNaturalNumber0 @ SV15 )
| ~ ( aNaturalNumber0 @ SY90 )
| ~ ( aNaturalNumber0 @ SY91 )
| ~ ( doDivides0 @ SV15 @ SY90 )
| ~ ( doDivides0 @ SY90 @ SY91 )
| ( doDivides0 @ SV15 @ SY91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(204,plain,
! [SV16: $i] :
( ( ! [SY92: $i,SY93: $i] :
( ~ ( aNaturalNumber0 @ SV16 )
| ~ ( aNaturalNumber0 @ SY92 )
| ~ ( aNaturalNumber0 @ SY93 )
| ~ ( doDivides0 @ SV16 @ SY92 )
| ~ ( doDivides0 @ SV16 @ SY93 )
| ( doDivides0 @ SV16 @ ( sdtpldt0 @ SY92 @ SY93 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(205,plain,
! [SV17: $i] :
( ( ! [SY94: $i,SY95: $i] :
( ~ ( aNaturalNumber0 @ SV17 )
| ~ ( aNaturalNumber0 @ SY94 )
| ~ ( aNaturalNumber0 @ SY95 )
| ~ ( doDivides0 @ SV17 @ SY94 )
| ~ ( doDivides0 @ SV17 @ ( sdtpldt0 @ SY94 @ SY95 ) )
| ( doDivides0 @ SV17 @ SY95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(206,plain,
! [SV18: $i] :
( ( ! [SY96: $i] :
( ~ ( aNaturalNumber0 @ SV18 )
| ~ ( aNaturalNumber0 @ SY96 )
| ( SY96 = sz00 )
| ~ ( doDivides0 @ SV18 @ SY96 )
| ( sdtlseqdt0 @ SV18 @ SY96 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(207,plain,
! [SV19: $i] :
( ( ! [SY97: $i] :
( ~ ( aNaturalNumber0 @ SV19 )
| ~ ( aNaturalNumber0 @ SY97 )
| ( SV19 = sz00 )
| ~ ( doDivides0 @ SV19 @ SY97 )
| ! [SY98: $i] :
( ~ ( aNaturalNumber0 @ SY98 )
| ( ( sdtasdt0 @ SY98 @ ( sdtsldt0 @ SY97 @ SV19 ) )
= ( sdtsldt0 @ ( sdtasdt0 @ SY98 @ SY97 ) @ SV19 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(208,plain,
! [SV20: $i] :
( ( ! [SY99: $i,SY100: $i] :
( ~ ( aNaturalNumber0 @ SV20 )
| ~ ( aNaturalNumber0 @ SY99 )
| ~ ( aNaturalNumber0 @ SY100 )
| ~ ( doDivides0 @ SY100 @ ( sdtasdt0 @ SV20 @ SY99 ) )
| ~ ( isPrime0 @ SY100 )
| ( doDivides0 @ SY100 @ SV20 )
| ( doDivides0 @ SY100 @ SY99 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(209,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(210,plain,
! [SV21: $i] :
( ( ~ ( ~ ! [SY101: $i,SY102: $i] :
( ~ ( aNaturalNumber0 @ SV21 )
| ~ ( aNaturalNumber0 @ SY101 )
| ~ ( aNaturalNumber0 @ SY102 )
| ( ( sdtpldt0 @ SV21 @ SY101 )
!= ( sdtpldt0 @ SV21 @ SY102 ) )
| ( SY101 = SY102 ) )
| ~ ! [SY103: $i,SY104: $i] :
( ~ ( aNaturalNumber0 @ SV21 )
| ~ ( aNaturalNumber0 @ SY103 )
| ~ ( aNaturalNumber0 @ SY104 )
| ( ( sdtpldt0 @ SY103 @ SV21 )
!= ( sdtpldt0 @ SY104 @ SV21 ) )
| ( SY103 = SY104 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(211,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( ( sdtasdt0 @ SX0 @ sz00 )
= sz00 ) )
| ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( sz00
= ( sdtasdt0 @ sz00 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(212,plain,
( ( ~ ( ( sz10 != sz00 ) )
| ~ ( aNaturalNumber0 @ sz10 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(213,plain,
! [SV22: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY105: $i,SY106: $i] :
( ~ ( aNaturalNumber0 @ SV22 )
| ~ ( aNaturalNumber0 @ SY105 )
| ~ ( aNaturalNumber0 @ SY106 )
| ( SV22 = sz00 )
| ( SY105 = SY106 )
| ~ ( sdtlseqdt0 @ SY105 @ SY106 )
| ( ( sdtasdt0 @ SY105 @ SV22 )
!= ( sdtasdt0 @ SY106 @ SV22 ) ) )
| ~ ~ ( ~ ! [SY107: $i,SY108: $i] :
( ~ ( aNaturalNumber0 @ SV22 )
| ~ ( aNaturalNumber0 @ SY107 )
| ~ ( aNaturalNumber0 @ SY108 )
| ( SV22 = sz00 )
| ( SY107 = SY108 )
| ~ ( sdtlseqdt0 @ SY107 @ SY108 )
| ( ( sdtasdt0 @ SV22 @ SY107 )
!= ( sdtasdt0 @ SV22 @ SY108 ) ) )
| ~ ! [SY109: $i,SY110: $i] :
( ~ ( aNaturalNumber0 @ SV22 )
| ~ ( aNaturalNumber0 @ SY109 )
| ~ ( aNaturalNumber0 @ SY110 )
| ( SV22 = sz00 )
| ( SY109 = SY110 )
| ~ ( sdtlseqdt0 @ SY109 @ SY110 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV22 @ SY109 ) @ ( sdtasdt0 @ SV22 @ SY110 ) ) ) ) )
| ~ ! [SY111: $i,SY112: $i] :
( ~ ( aNaturalNumber0 @ SV22 )
| ~ ( aNaturalNumber0 @ SY111 )
| ~ ( aNaturalNumber0 @ SY112 )
| ( SV22 = sz00 )
| ( SY111 = SY112 )
| ~ ( sdtlseqdt0 @ SY111 @ SY112 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SY111 @ SV22 ) @ ( sdtasdt0 @ SY112 @ SV22 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(214,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 )
| ( ( sdtpldt0 @ SX0 @ SX1 )
!= sz00 )
| ( SX0 = sz00 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 )
| ( ( sdtpldt0 @ SX0 @ SX1 )
!= sz00 )
| ( SX1 = sz00 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[175]) ).
thf(215,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( ( sdtasdt0 @ SX0 @ sz10 )
= SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( SX0
= ( sdtasdt0 @ sz10 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(216,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 )
| ( SX1 != SX0 )
| ( sdtlseqdt0 @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 )
| ( sdtlseqdt0 @ SX1 @ SX0 )
| ( sdtlseqdt0 @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(217,plain,
( ( ~ ( ( xm != xn ) )
| ~ ( sdtlseqdt0 @ xm @ xn ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(218,plain,
! [SV23: $i] :
( ( ~ ( ~ ! [SY113: $i,SY114: $i] :
( ~ ( aNaturalNumber0 @ SV23 )
| ~ ( aNaturalNumber0 @ SY113 )
| ~ ( aNaturalNumber0 @ SY114 )
| ( ( sdtasdt0 @ SV23 @ ( sdtpldt0 @ SY113 @ SY114 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV23 @ SY113 ) @ ( sdtasdt0 @ SV23 @ SY114 ) ) ) )
| ~ ! [SY115: $i,SY116: $i] :
( ~ ( aNaturalNumber0 @ SV23 )
| ~ ( aNaturalNumber0 @ SY115 )
| ~ ( aNaturalNumber0 @ SY116 )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SY115 @ SY116 ) @ SV23 )
= ( sdtpldt0 @ ( sdtasdt0 @ SY115 @ SV23 ) @ ( sdtasdt0 @ SY116 @ SV23 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(219,plain,
( ( ~ ( ( xp != sz00 ) )
| ~ ~ ( ~ ( ( xm != sz00 ) )
| ~ ~ ( ~ ( ( xn != sz00 ) )
| ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ xn )
| ~ ( aNaturalNumber0 @ xm ) )
| ~ ( aNaturalNumber0 @ xp ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(220,plain,
! [SV24: $i] :
( ( ! [SY117: $i] :
( ~ ( aNaturalNumber0 @ SV24 )
| ~ ( aNaturalNumber0 @ SY117 )
| ( SV24 = SY117 )
| ~ ( sdtlseqdt0 @ SV24 @ SY117 )
| ~ ( ~ ~ ( ~ ! [SY118: $i] :
( ~ ( aNaturalNumber0 @ SY118 )
| ( ( sdtpldt0 @ SV24 @ SY118 )
!= ( sdtpldt0 @ SY117 @ SY118 ) ) )
| ~ ~ ( ~ ! [SY119: $i] :
( ~ ( aNaturalNumber0 @ SY119 )
| ( ( sdtpldt0 @ SY119 @ SV24 )
!= ( sdtpldt0 @ SY119 @ SY117 ) ) )
| ~ ! [SY120: $i] :
( ~ ( aNaturalNumber0 @ SY120 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SY120 @ SV24 ) @ ( sdtpldt0 @ SY120 @ SY117 ) ) ) ) )
| ~ ! [SY121: $i] :
( ~ ( aNaturalNumber0 @ SY121 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SV24 @ SY121 ) @ ( sdtpldt0 @ SY117 @ SY121 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(221,plain,
! [SV25: $i] :
( ( ~ ( aNaturalNumber0 @ SV25 )
| ( SV25 = sz00 )
| ~ ( ~ ! [SY122: $i,SY123: $i] :
( ~ ( aNaturalNumber0 @ SY122 )
| ~ ( aNaturalNumber0 @ SY123 )
| ( ( sdtasdt0 @ SV25 @ SY122 )
!= ( sdtasdt0 @ SV25 @ SY123 ) )
| ( SY122 = SY123 ) )
| ~ ! [SY124: $i,SY125: $i] :
( ~ ( aNaturalNumber0 @ SY124 )
| ~ ( aNaturalNumber0 @ SY125 )
| ( ( sdtasdt0 @ SY124 @ SV25 )
!= ( sdtasdt0 @ SY125 @ SV25 ) )
| ( SY124 = SY125 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(222,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( ( sdtpldt0 @ SX0 @ sz00 )
= SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( SX0
= ( sdtpldt0 @ sz00 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[183]) ).
thf(223,plain,
( ( ~ ( doDivides0 @ xp @ ( sdtasdt0 @ xn @ xn ) )
| ~ ( doDivides0 @ xp @ xn ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[184]) ).
thf(224,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( sz10 != SX0 )
| ( SX0 = sz00 )
| ( SX0 = sz10 ) )
| ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( sdtlseqdt0 @ sz10 @ SX0 )
| ( SX0 = sz00 )
| ( SX0 = sz10 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(225,plain,
! [SV26: $i] :
( ( ( SV26 = sz10 )
| ( SV26 = sz00 )
| ~ ( aNaturalNumber0 @ SV26 )
| ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ ( sK1_W1 @ SV26 ) )
| ~ ( doDivides0 @ ( sK1_W1 @ SV26 ) @ SV26 ) )
| ~ ( isPrime0 @ ( sK1_W1 @ SV26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(226,plain,
! [SV1: $i,SV27: $i] :
( ( ! [SY126: $i] :
( ( SY126 = sz00 )
| ( SV27 = sz00 )
| ( SV1 = sz00 )
| ~ ( aNaturalNumber0 @ SV1 )
| ~ ( aNaturalNumber0 @ SV27 )
| ~ ( aNaturalNumber0 @ SY126 )
| ( ( sdtasdt0 @ SY126 @ ( sdtasdt0 @ SV27 @ SV27 ) )
!= ( sdtasdt0 @ SV1 @ SV1 ) )
| ~ ( iLess0 @ SV1 @ xn )
| ~ ( isPrime0 @ SY126 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(227,plain,
! [SV28: $i,SV3: $i] :
( ( ~ ( aNaturalNumber0 @ SV3 )
| ~ ( aNaturalNumber0 @ SV28 )
| ( aNaturalNumber0 @ ( sdtpldt0 @ SV3 @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(228,plain,
! [SV29: $i,SV4: $i] :
( ( ~ ( aNaturalNumber0 @ SV4 )
| ~ ( aNaturalNumber0 @ SV29 )
| ( aNaturalNumber0 @ ( sdtasdt0 @ SV4 @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[191]) ).
thf(229,plain,
! [SV30: $i,SV5: $i] :
( ( ~ ( aNaturalNumber0 @ SV5 )
| ~ ( aNaturalNumber0 @ SV30 )
| ( ( sdtpldt0 @ SV5 @ SV30 )
= ( sdtpldt0 @ SV30 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[192]) ).
thf(230,plain,
! [SV31: $i,SV6: $i] :
( ( ! [SY127: $i] :
( ~ ( aNaturalNumber0 @ SV6 )
| ~ ( aNaturalNumber0 @ SV31 )
| ~ ( aNaturalNumber0 @ SY127 )
| ( ( sdtpldt0 @ ( sdtpldt0 @ SV6 @ SV31 ) @ SY127 )
= ( sdtpldt0 @ SV6 @ ( sdtpldt0 @ SV31 @ SY127 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[193]) ).
thf(231,plain,
! [SV32: $i,SV7: $i] :
( ( ~ ( aNaturalNumber0 @ SV7 )
| ~ ( aNaturalNumber0 @ SV32 )
| ( ( sdtasdt0 @ SV7 @ SV32 )
= ( sdtasdt0 @ SV32 @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(232,plain,
! [SV33: $i,SV8: $i] :
( ( ! [SY128: $i] :
( ~ ( aNaturalNumber0 @ SV8 )
| ~ ( aNaturalNumber0 @ SV33 )
| ~ ( aNaturalNumber0 @ SY128 )
| ( ( sdtasdt0 @ ( sdtasdt0 @ SV8 @ SV33 ) @ SY128 )
= ( sdtasdt0 @ SV8 @ ( sdtasdt0 @ SV33 @ SY128 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[195]) ).
thf(233,plain,
! [SV34: $i,SV9: $i] :
( ( ~ ( aNaturalNumber0 @ SV9 )
| ~ ( aNaturalNumber0 @ SV34 )
| ( ( sdtasdt0 @ SV9 @ SV34 )
!= sz00 )
| ( SV9 = sz00 )
| ( SV34 = sz00 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(234,plain,
! [SV10: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV10 ) )
= $true )
| ( ( sdtlseqdt0 @ SV10 @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[197]) ).
thf(235,plain,
! [SV35: $i,SV11: $i] :
( ( ~ ( aNaturalNumber0 @ SV11 )
| ~ ( aNaturalNumber0 @ SV35 )
| ~ ( sdtlseqdt0 @ SV11 @ SV35 )
| ~ ( sdtlseqdt0 @ SV35 @ SV11 )
| ( SV11 = SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(236,plain,
! [SV36: $i,SV12: $i] :
( ( ! [SY129: $i] :
( ~ ( aNaturalNumber0 @ SV12 )
| ~ ( aNaturalNumber0 @ SV36 )
| ~ ( aNaturalNumber0 @ SY129 )
| ~ ( sdtlseqdt0 @ SV12 @ SV36 )
| ~ ( sdtlseqdt0 @ SV36 @ SY129 )
| ( sdtlseqdt0 @ SV12 @ SY129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[199]) ).
thf(237,plain,
! [SV37: $i,SV13: $i] :
( ( ~ ( aNaturalNumber0 @ SV13 )
| ~ ( aNaturalNumber0 @ SV37 )
| ( SV13 = sz00 )
| ( sdtlseqdt0 @ SV37 @ ( sdtasdt0 @ SV37 @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[200]) ).
thf(238,plain,
( ( ( ! [W0: $i] :
~ ( aNaturalNumber0 @ W0 ) )
= $true )
| ( ( ! [W1: $i] :
~ ( aNaturalNumber0 @ W1 ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[201]) ).
thf(239,plain,
! [SV38: $i,SV14: $i] :
( ( ~ ( aNaturalNumber0 @ SV14 )
| ~ ( aNaturalNumber0 @ SV38 )
| ( SV14 = SV38 )
| ~ ( sdtlseqdt0 @ SV14 @ SV38 )
| ( iLess0 @ SV14 @ SV38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[202]) ).
thf(240,plain,
! [SV39: $i,SV15: $i] :
( ( ! [SY130: $i] :
( ~ ( aNaturalNumber0 @ SV15 )
| ~ ( aNaturalNumber0 @ SV39 )
| ~ ( aNaturalNumber0 @ SY130 )
| ~ ( doDivides0 @ SV15 @ SV39 )
| ~ ( doDivides0 @ SV39 @ SY130 )
| ( doDivides0 @ SV15 @ SY130 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[203]) ).
thf(241,plain,
! [SV40: $i,SV16: $i] :
( ( ! [SY131: $i] :
( ~ ( aNaturalNumber0 @ SV16 )
| ~ ( aNaturalNumber0 @ SV40 )
| ~ ( aNaturalNumber0 @ SY131 )
| ~ ( doDivides0 @ SV16 @ SV40 )
| ~ ( doDivides0 @ SV16 @ SY131 )
| ( doDivides0 @ SV16 @ ( sdtpldt0 @ SV40 @ SY131 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(242,plain,
! [SV41: $i,SV17: $i] :
( ( ! [SY132: $i] :
( ~ ( aNaturalNumber0 @ SV17 )
| ~ ( aNaturalNumber0 @ SV41 )
| ~ ( aNaturalNumber0 @ SY132 )
| ~ ( doDivides0 @ SV17 @ SV41 )
| ~ ( doDivides0 @ SV17 @ ( sdtpldt0 @ SV41 @ SY132 ) )
| ( doDivides0 @ SV17 @ SY132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(243,plain,
! [SV42: $i,SV18: $i] :
( ( ~ ( aNaturalNumber0 @ SV18 )
| ~ ( aNaturalNumber0 @ SV42 )
| ( SV42 = sz00 )
| ~ ( doDivides0 @ SV18 @ SV42 )
| ( sdtlseqdt0 @ SV18 @ SV42 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(244,plain,
! [SV43: $i,SV19: $i] :
( ( ~ ( aNaturalNumber0 @ SV19 )
| ~ ( aNaturalNumber0 @ SV43 )
| ( SV19 = sz00 )
| ~ ( doDivides0 @ SV19 @ SV43 )
| ! [SY133: $i] :
( ~ ( aNaturalNumber0 @ SY133 )
| ( ( sdtasdt0 @ SY133 @ ( sdtsldt0 @ SV43 @ SV19 ) )
= ( sdtsldt0 @ ( sdtasdt0 @ SY133 @ SV43 ) @ SV19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(245,plain,
! [SV44: $i,SV20: $i] :
( ( ! [SY134: $i] :
( ~ ( aNaturalNumber0 @ SV20 )
| ~ ( aNaturalNumber0 @ SV44 )
| ~ ( aNaturalNumber0 @ SY134 )
| ~ ( doDivides0 @ SY134 @ ( sdtasdt0 @ SV20 @ SV44 ) )
| ~ ( isPrime0 @ SY134 )
| ( doDivides0 @ SY134 @ SV20 )
| ( doDivides0 @ SY134 @ SV44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(246,plain,
! [SV21: $i] :
( ( ~ ! [SY101: $i,SY102: $i] :
( ~ ( aNaturalNumber0 @ SV21 )
| ~ ( aNaturalNumber0 @ SY101 )
| ~ ( aNaturalNumber0 @ SY102 )
| ( ( sdtpldt0 @ SV21 @ SY101 )
!= ( sdtpldt0 @ SV21 @ SY102 ) )
| ( SY101 = SY102 ) )
| ~ ! [SY103: $i,SY104: $i] :
( ~ ( aNaturalNumber0 @ SV21 )
| ~ ( aNaturalNumber0 @ SY103 )
| ~ ( aNaturalNumber0 @ SY104 )
| ( ( sdtpldt0 @ SY103 @ SV21 )
!= ( sdtpldt0 @ SY104 @ SV21 ) )
| ( SY103 = SY104 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(247,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( ( sdtasdt0 @ SX0 @ sz00 )
= sz00 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[211]) ).
thf(248,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( sz00
= ( sdtasdt0 @ sz00 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[211]) ).
thf(249,plain,
( ( ~ ( ( sz10 != sz00 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[212]) ).
thf(250,plain,
( ( ~ ( aNaturalNumber0 @ sz10 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[212]) ).
thf(251,plain,
! [SV22: $i] :
( ( ~ ~ ( ~ ! [SY105: $i,SY106: $i] :
( ~ ( aNaturalNumber0 @ SV22 )
| ~ ( aNaturalNumber0 @ SY105 )
| ~ ( aNaturalNumber0 @ SY106 )
| ( SV22 = sz00 )
| ( SY105 = SY106 )
| ~ ( sdtlseqdt0 @ SY105 @ SY106 )
| ( ( sdtasdt0 @ SY105 @ SV22 )
!= ( sdtasdt0 @ SY106 @ SV22 ) ) )
| ~ ~ ( ~ ! [SY107: $i,SY108: $i] :
( ~ ( aNaturalNumber0 @ SV22 )
| ~ ( aNaturalNumber0 @ SY107 )
| ~ ( aNaturalNumber0 @ SY108 )
| ( SV22 = sz00 )
| ( SY107 = SY108 )
| ~ ( sdtlseqdt0 @ SY107 @ SY108 )
| ( ( sdtasdt0 @ SV22 @ SY107 )
!= ( sdtasdt0 @ SV22 @ SY108 ) ) )
| ~ ! [SY109: $i,SY110: $i] :
( ~ ( aNaturalNumber0 @ SV22 )
| ~ ( aNaturalNumber0 @ SY109 )
| ~ ( aNaturalNumber0 @ SY110 )
| ( SV22 = sz00 )
| ( SY109 = SY110 )
| ~ ( sdtlseqdt0 @ SY109 @ SY110 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV22 @ SY109 ) @ ( sdtasdt0 @ SV22 @ SY110 ) ) ) ) )
| ~ ! [SY111: $i,SY112: $i] :
( ~ ( aNaturalNumber0 @ SV22 )
| ~ ( aNaturalNumber0 @ SY111 )
| ~ ( aNaturalNumber0 @ SY112 )
| ( SV22 = sz00 )
| ( SY111 = SY112 )
| ~ ( sdtlseqdt0 @ SY111 @ SY112 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SY111 @ SV22 ) @ ( sdtasdt0 @ SY112 @ SV22 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[213]) ).
thf(252,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 )
| ( ( sdtpldt0 @ SX0 @ SX1 )
!= sz00 )
| ( SX0 = sz00 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[214]) ).
thf(253,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 )
| ( ( sdtpldt0 @ SX0 @ SX1 )
!= sz00 )
| ( SX1 = sz00 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[214]) ).
thf(254,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( ( sdtasdt0 @ SX0 @ sz10 )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[215]) ).
thf(255,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( SX0
= ( sdtasdt0 @ sz10 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[215]) ).
thf(256,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 )
| ( SX1 != SX0 )
| ( sdtlseqdt0 @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[216]) ).
thf(257,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 )
| ( sdtlseqdt0 @ SX1 @ SX0 )
| ( sdtlseqdt0 @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[216]) ).
thf(258,plain,
( ( ~ ( ( xm != xn ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[217]) ).
thf(259,plain,
( ( ~ ( sdtlseqdt0 @ xm @ xn ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[217]) ).
thf(260,plain,
! [SV23: $i] :
( ( ~ ! [SY113: $i,SY114: $i] :
( ~ ( aNaturalNumber0 @ SV23 )
| ~ ( aNaturalNumber0 @ SY113 )
| ~ ( aNaturalNumber0 @ SY114 )
| ( ( sdtasdt0 @ SV23 @ ( sdtpldt0 @ SY113 @ SY114 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV23 @ SY113 ) @ ( sdtasdt0 @ SV23 @ SY114 ) ) ) )
| ~ ! [SY115: $i,SY116: $i] :
( ~ ( aNaturalNumber0 @ SV23 )
| ~ ( aNaturalNumber0 @ SY115 )
| ~ ( aNaturalNumber0 @ SY116 )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SY115 @ SY116 ) @ SV23 )
= ( sdtpldt0 @ ( sdtasdt0 @ SY115 @ SV23 ) @ ( sdtasdt0 @ SY116 @ SV23 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[218]) ).
thf(261,plain,
( ( ~ ( ( xp != sz00 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[219]) ).
thf(262,plain,
( ( ~ ~ ( ~ ( ( xm != sz00 ) )
| ~ ~ ( ~ ( ( xn != sz00 ) )
| ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ xn )
| ~ ( aNaturalNumber0 @ xm ) )
| ~ ( aNaturalNumber0 @ xp ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[219]) ).
thf(263,plain,
! [SV45: $i,SV24: $i] :
( ( ~ ( aNaturalNumber0 @ SV24 )
| ~ ( aNaturalNumber0 @ SV45 )
| ( SV24 = SV45 )
| ~ ( sdtlseqdt0 @ SV24 @ SV45 )
| ~ ( ~ ~ ( ~ ! [SY135: $i] :
( ~ ( aNaturalNumber0 @ SY135 )
| ( ( sdtpldt0 @ SV24 @ SY135 )
!= ( sdtpldt0 @ SV45 @ SY135 ) ) )
| ~ ~ ( ~ ! [SY136: $i] :
( ~ ( aNaturalNumber0 @ SY136 )
| ( ( sdtpldt0 @ SY136 @ SV24 )
!= ( sdtpldt0 @ SY136 @ SV45 ) ) )
| ~ ! [SY137: $i] :
( ~ ( aNaturalNumber0 @ SY137 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SY137 @ SV24 ) @ ( sdtpldt0 @ SY137 @ SV45 ) ) ) ) )
| ~ ! [SY138: $i] :
( ~ ( aNaturalNumber0 @ SY138 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SV24 @ SY138 ) @ ( sdtpldt0 @ SV45 @ SY138 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[220]) ).
thf(264,plain,
! [SV25: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV25 ) )
= $true )
| ( ( ( SV25 = sz00 )
| ~ ( ~ ! [SY122: $i,SY123: $i] :
( ~ ( aNaturalNumber0 @ SY122 )
| ~ ( aNaturalNumber0 @ SY123 )
| ( ( sdtasdt0 @ SV25 @ SY122 )
!= ( sdtasdt0 @ SV25 @ SY123 ) )
| ( SY122 = SY123 ) )
| ~ ! [SY124: $i,SY125: $i] :
( ~ ( aNaturalNumber0 @ SY124 )
| ~ ( aNaturalNumber0 @ SY125 )
| ( ( sdtasdt0 @ SY124 @ SV25 )
!= ( sdtasdt0 @ SY125 @ SV25 ) )
| ( SY124 = SY125 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[221]) ).
thf(265,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( ( sdtpldt0 @ SX0 @ sz00 )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[222]) ).
thf(266,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( SX0
= ( sdtpldt0 @ sz00 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[222]) ).
thf(267,plain,
( ( ~ ( doDivides0 @ xp @ ( sdtasdt0 @ xn @ xn ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[223]) ).
thf(268,plain,
( ( ~ ( doDivides0 @ xp @ xn ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[223]) ).
thf(269,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( sz10 != SX0 )
| ( SX0 = sz00 )
| ( SX0 = sz10 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[224]) ).
thf(270,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( sdtlseqdt0 @ sz10 @ SX0 )
| ( SX0 = sz00 )
| ( SX0 = sz10 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[224]) ).
thf(271,plain,
! [SV26: $i] :
( ( ( ( SV26 = sz10 )
| ( SV26 = sz00 )
| ~ ( aNaturalNumber0 @ SV26 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ ( sK1_W1 @ SV26 ) )
| ~ ( doDivides0 @ ( sK1_W1 @ SV26 ) @ SV26 ) )
| ~ ( isPrime0 @ ( sK1_W1 @ SV26 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[225]) ).
thf(272,plain,
! [SV1: $i,SV27: $i,SV46: $i] :
( ( ( SV46 = sz00 )
| ( SV27 = sz00 )
| ( SV1 = sz00 )
| ~ ( aNaturalNumber0 @ SV1 )
| ~ ( aNaturalNumber0 @ SV27 )
| ~ ( aNaturalNumber0 @ SV46 )
| ( ( sdtasdt0 @ SV46 @ ( sdtasdt0 @ SV27 @ SV27 ) )
!= ( sdtasdt0 @ SV1 @ SV1 ) )
| ~ ( iLess0 @ SV1 @ xn )
| ~ ( isPrime0 @ SV46 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[226]) ).
thf(273,plain,
! [SV28: $i,SV3: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV3 )
| ~ ( aNaturalNumber0 @ SV28 ) )
= $true )
| ( ( aNaturalNumber0 @ ( sdtpldt0 @ SV3 @ SV28 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[227]) ).
thf(274,plain,
! [SV29: $i,SV4: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV4 )
| ~ ( aNaturalNumber0 @ SV29 ) )
= $true )
| ( ( aNaturalNumber0 @ ( sdtasdt0 @ SV4 @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[228]) ).
thf(275,plain,
! [SV30: $i,SV5: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV5 )
| ~ ( aNaturalNumber0 @ SV30 ) )
= $true )
| ( ( ( sdtpldt0 @ SV5 @ SV30 )
= ( sdtpldt0 @ SV30 @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[229]) ).
thf(276,plain,
! [SV47: $i,SV31: $i,SV6: $i] :
( ( ~ ( aNaturalNumber0 @ SV6 )
| ~ ( aNaturalNumber0 @ SV31 )
| ~ ( aNaturalNumber0 @ SV47 )
| ( ( sdtpldt0 @ ( sdtpldt0 @ SV6 @ SV31 ) @ SV47 )
= ( sdtpldt0 @ SV6 @ ( sdtpldt0 @ SV31 @ SV47 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[230]) ).
thf(277,plain,
! [SV32: $i,SV7: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV7 )
| ~ ( aNaturalNumber0 @ SV32 ) )
= $true )
| ( ( ( sdtasdt0 @ SV7 @ SV32 )
= ( sdtasdt0 @ SV32 @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[231]) ).
thf(278,plain,
! [SV48: $i,SV33: $i,SV8: $i] :
( ( ~ ( aNaturalNumber0 @ SV8 )
| ~ ( aNaturalNumber0 @ SV33 )
| ~ ( aNaturalNumber0 @ SV48 )
| ( ( sdtasdt0 @ ( sdtasdt0 @ SV8 @ SV33 ) @ SV48 )
= ( sdtasdt0 @ SV8 @ ( sdtasdt0 @ SV33 @ SV48 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[232]) ).
thf(279,plain,
! [SV34: $i,SV9: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV9 )
| ~ ( aNaturalNumber0 @ SV34 ) )
= $true )
| ( ( ( ( sdtasdt0 @ SV9 @ SV34 )
!= sz00 )
| ( SV9 = sz00 )
| ( SV34 = sz00 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[233]) ).
thf(280,plain,
! [SV10: $i] :
( ( ( aNaturalNumber0 @ SV10 )
= $false )
| ( ( sdtlseqdt0 @ SV10 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[234]) ).
thf(281,plain,
! [SV35: $i,SV11: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV11 )
| ~ ( aNaturalNumber0 @ SV35 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV11 @ SV35 )
| ~ ( sdtlseqdt0 @ SV35 @ SV11 )
| ( SV11 = SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[235]) ).
thf(282,plain,
! [SV49: $i,SV36: $i,SV12: $i] :
( ( ~ ( aNaturalNumber0 @ SV12 )
| ~ ( aNaturalNumber0 @ SV36 )
| ~ ( aNaturalNumber0 @ SV49 )
| ~ ( sdtlseqdt0 @ SV12 @ SV36 )
| ~ ( sdtlseqdt0 @ SV36 @ SV49 )
| ( sdtlseqdt0 @ SV12 @ SV49 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[236]) ).
thf(283,plain,
! [SV37: $i,SV13: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV13 )
| ~ ( aNaturalNumber0 @ SV37 ) )
= $true )
| ( ( ( SV13 = sz00 )
| ( sdtlseqdt0 @ SV37 @ ( sdtasdt0 @ SV37 @ SV13 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[237]) ).
thf(284,plain,
! [SV50: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV50 ) )
= $true )
| ( ( ! [W1: $i] :
~ ( aNaturalNumber0 @ W1 ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[238]) ).
thf(285,plain,
! [SV38: $i,SV14: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV14 )
| ~ ( aNaturalNumber0 @ SV38 ) )
= $true )
| ( ( ( SV14 = SV38 )
| ~ ( sdtlseqdt0 @ SV14 @ SV38 )
| ( iLess0 @ SV14 @ SV38 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[239]) ).
thf(286,plain,
! [SV51: $i,SV39: $i,SV15: $i] :
( ( ~ ( aNaturalNumber0 @ SV15 )
| ~ ( aNaturalNumber0 @ SV39 )
| ~ ( aNaturalNumber0 @ SV51 )
| ~ ( doDivides0 @ SV15 @ SV39 )
| ~ ( doDivides0 @ SV39 @ SV51 )
| ( doDivides0 @ SV15 @ SV51 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[240]) ).
thf(287,plain,
! [SV52: $i,SV40: $i,SV16: $i] :
( ( ~ ( aNaturalNumber0 @ SV16 )
| ~ ( aNaturalNumber0 @ SV40 )
| ~ ( aNaturalNumber0 @ SV52 )
| ~ ( doDivides0 @ SV16 @ SV40 )
| ~ ( doDivides0 @ SV16 @ SV52 )
| ( doDivides0 @ SV16 @ ( sdtpldt0 @ SV40 @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[241]) ).
thf(288,plain,
! [SV53: $i,SV41: $i,SV17: $i] :
( ( ~ ( aNaturalNumber0 @ SV17 )
| ~ ( aNaturalNumber0 @ SV41 )
| ~ ( aNaturalNumber0 @ SV53 )
| ~ ( doDivides0 @ SV17 @ SV41 )
| ~ ( doDivides0 @ SV17 @ ( sdtpldt0 @ SV41 @ SV53 ) )
| ( doDivides0 @ SV17 @ SV53 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[242]) ).
thf(289,plain,
! [SV42: $i,SV18: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV18 )
| ~ ( aNaturalNumber0 @ SV42 ) )
= $true )
| ( ( ( SV42 = sz00 )
| ~ ( doDivides0 @ SV18 @ SV42 )
| ( sdtlseqdt0 @ SV18 @ SV42 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[243]) ).
thf(290,plain,
! [SV43: $i,SV19: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV19 )
| ~ ( aNaturalNumber0 @ SV43 ) )
= $true )
| ( ( ( SV19 = sz00 )
| ~ ( doDivides0 @ SV19 @ SV43 )
| ! [SY133: $i] :
( ~ ( aNaturalNumber0 @ SY133 )
| ( ( sdtasdt0 @ SY133 @ ( sdtsldt0 @ SV43 @ SV19 ) )
= ( sdtsldt0 @ ( sdtasdt0 @ SY133 @ SV43 ) @ SV19 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[244]) ).
thf(291,plain,
! [SV54: $i,SV44: $i,SV20: $i] :
( ( ~ ( aNaturalNumber0 @ SV20 )
| ~ ( aNaturalNumber0 @ SV44 )
| ~ ( aNaturalNumber0 @ SV54 )
| ~ ( doDivides0 @ SV54 @ ( sdtasdt0 @ SV20 @ SV44 ) )
| ~ ( isPrime0 @ SV54 )
| ( doDivides0 @ SV54 @ SV20 )
| ( doDivides0 @ SV54 @ SV44 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[245]) ).
thf(292,plain,
! [SV21: $i] :
( ( ~ ! [SY101: $i,SY102: $i] :
( ~ ( aNaturalNumber0 @ SV21 )
| ~ ( aNaturalNumber0 @ SY101 )
| ~ ( aNaturalNumber0 @ SY102 )
| ( ( sdtpldt0 @ SV21 @ SY101 )
!= ( sdtpldt0 @ SV21 @ SY102 ) )
| ( SY101 = SY102 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[246]) ).
thf(293,plain,
! [SV21: $i] :
( ( ~ ! [SY103: $i,SY104: $i] :
( ~ ( aNaturalNumber0 @ SV21 )
| ~ ( aNaturalNumber0 @ SY103 )
| ~ ( aNaturalNumber0 @ SY104 )
| ( ( sdtpldt0 @ SY103 @ SV21 )
!= ( sdtpldt0 @ SY104 @ SV21 ) )
| ( SY103 = SY104 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[246]) ).
thf(294,plain,
( ( ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( ( sdtasdt0 @ SX0 @ sz00 )
= sz00 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[247]) ).
thf(295,plain,
( ( ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( sz00
= ( sdtasdt0 @ sz00 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[248]) ).
thf(296,plain,
( ( ( sz10 != sz00 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[249]) ).
thf(297,plain,
( ( aNaturalNumber0 @ sz10 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[250]) ).
thf(298,plain,
! [SV22: $i] :
( ( ~ ~ ( ~ ! [SY105: $i,SY106: $i] :
( ~ ( aNaturalNumber0 @ SV22 )
| ~ ( aNaturalNumber0 @ SY105 )
| ~ ( aNaturalNumber0 @ SY106 )
| ( SV22 = sz00 )
| ( SY105 = SY106 )
| ~ ( sdtlseqdt0 @ SY105 @ SY106 )
| ( ( sdtasdt0 @ SY105 @ SV22 )
!= ( sdtasdt0 @ SY106 @ SV22 ) ) )
| ~ ~ ( ~ ! [SY107: $i,SY108: $i] :
( ~ ( aNaturalNumber0 @ SV22 )
| ~ ( aNaturalNumber0 @ SY107 )
| ~ ( aNaturalNumber0 @ SY108 )
| ( SV22 = sz00 )
| ( SY107 = SY108 )
| ~ ( sdtlseqdt0 @ SY107 @ SY108 )
| ( ( sdtasdt0 @ SV22 @ SY107 )
!= ( sdtasdt0 @ SV22 @ SY108 ) ) )
| ~ ! [SY109: $i,SY110: $i] :
( ~ ( aNaturalNumber0 @ SV22 )
| ~ ( aNaturalNumber0 @ SY109 )
| ~ ( aNaturalNumber0 @ SY110 )
| ( SV22 = sz00 )
| ( SY109 = SY110 )
| ~ ( sdtlseqdt0 @ SY109 @ SY110 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV22 @ SY109 ) @ ( sdtasdt0 @ SV22 @ SY110 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[251]) ).
thf(299,plain,
! [SV22: $i] :
( ( ~ ! [SY111: $i,SY112: $i] :
( ~ ( aNaturalNumber0 @ SV22 )
| ~ ( aNaturalNumber0 @ SY111 )
| ~ ( aNaturalNumber0 @ SY112 )
| ( SV22 = sz00 )
| ( SY111 = SY112 )
| ~ ( sdtlseqdt0 @ SY111 @ SY112 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SY111 @ SV22 ) @ ( sdtasdt0 @ SY112 @ SV22 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[251]) ).
thf(300,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 )
| ( ( sdtpldt0 @ SX0 @ SX1 )
!= sz00 )
| ( SX0 = sz00 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[252]) ).
thf(301,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 )
| ( ( sdtpldt0 @ SX0 @ SX1 )
!= sz00 )
| ( SX1 = sz00 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[253]) ).
thf(302,plain,
( ( ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( ( sdtasdt0 @ SX0 @ sz10 )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[254]) ).
thf(303,plain,
( ( ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( SX0
= ( sdtasdt0 @ sz10 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[255]) ).
thf(304,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 )
| ( SX1 != SX0 )
| ( sdtlseqdt0 @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[256]) ).
thf(305,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 )
| ( sdtlseqdt0 @ SX1 @ SX0 )
| ( sdtlseqdt0 @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[257]) ).
thf(306,plain,
( ( ( xm != xn ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[258]) ).
thf(307,plain,
( ( sdtlseqdt0 @ xm @ xn )
= $true ),
inference(extcnf_not_neg,[status(thm)],[259]) ).
thf(308,plain,
! [SV23: $i] :
( ( ~ ! [SY113: $i,SY114: $i] :
( ~ ( aNaturalNumber0 @ SV23 )
| ~ ( aNaturalNumber0 @ SY113 )
| ~ ( aNaturalNumber0 @ SY114 )
| ( ( sdtasdt0 @ SV23 @ ( sdtpldt0 @ SY113 @ SY114 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV23 @ SY113 ) @ ( sdtasdt0 @ SV23 @ SY114 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[260]) ).
thf(309,plain,
! [SV23: $i] :
( ( ~ ! [SY115: $i,SY116: $i] :
( ~ ( aNaturalNumber0 @ SV23 )
| ~ ( aNaturalNumber0 @ SY115 )
| ~ ( aNaturalNumber0 @ SY116 )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SY115 @ SY116 ) @ SV23 )
= ( sdtpldt0 @ ( sdtasdt0 @ SY115 @ SV23 ) @ ( sdtasdt0 @ SY116 @ SV23 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[260]) ).
thf(310,plain,
( ( ( xp != sz00 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[261]) ).
thf(311,plain,
( ( ~ ( ~ ( ( xm != sz00 ) )
| ~ ~ ( ~ ( ( xn != sz00 ) )
| ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ xn )
| ~ ( aNaturalNumber0 @ xm ) )
| ~ ( aNaturalNumber0 @ xp ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[262]) ).
thf(312,plain,
! [SV45: $i,SV24: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV24 )
| ~ ( aNaturalNumber0 @ SV45 ) )
= $true )
| ( ( ( SV24 = SV45 )
| ~ ( sdtlseqdt0 @ SV24 @ SV45 )
| ~ ( ~ ~ ( ~ ! [SY135: $i] :
( ~ ( aNaturalNumber0 @ SY135 )
| ( ( sdtpldt0 @ SV24 @ SY135 )
!= ( sdtpldt0 @ SV45 @ SY135 ) ) )
| ~ ~ ( ~ ! [SY136: $i] :
( ~ ( aNaturalNumber0 @ SY136 )
| ( ( sdtpldt0 @ SY136 @ SV24 )
!= ( sdtpldt0 @ SY136 @ SV45 ) ) )
| ~ ! [SY137: $i] :
( ~ ( aNaturalNumber0 @ SY137 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SY137 @ SV24 ) @ ( sdtpldt0 @ SY137 @ SV45 ) ) ) ) )
| ~ ! [SY138: $i] :
( ~ ( aNaturalNumber0 @ SY138 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SV24 @ SY138 ) @ ( sdtpldt0 @ SV45 @ SY138 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[263]) ).
thf(313,plain,
! [SV25: $i] :
( ( ( aNaturalNumber0 @ SV25 )
= $false )
| ( ( ( SV25 = sz00 )
| ~ ( ~ ! [SY122: $i,SY123: $i] :
( ~ ( aNaturalNumber0 @ SY122 )
| ~ ( aNaturalNumber0 @ SY123 )
| ( ( sdtasdt0 @ SV25 @ SY122 )
!= ( sdtasdt0 @ SV25 @ SY123 ) )
| ( SY122 = SY123 ) )
| ~ ! [SY124: $i,SY125: $i] :
( ~ ( aNaturalNumber0 @ SY124 )
| ~ ( aNaturalNumber0 @ SY125 )
| ( ( sdtasdt0 @ SY124 @ SV25 )
!= ( sdtasdt0 @ SY125 @ SV25 ) )
| ( SY124 = SY125 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[264]) ).
thf(314,plain,
( ( ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( ( sdtpldt0 @ SX0 @ sz00 )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[265]) ).
thf(315,plain,
( ( ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( SX0
= ( sdtpldt0 @ sz00 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[266]) ).
thf(316,plain,
( ( doDivides0 @ xp @ ( sdtasdt0 @ xn @ xn ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[267]) ).
thf(317,plain,
( ( doDivides0 @ xp @ xn )
= $true ),
inference(extcnf_not_neg,[status(thm)],[268]) ).
thf(318,plain,
( ( ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( sz10 != SX0 )
| ( SX0 = sz00 )
| ( SX0 = sz10 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[269]) ).
thf(319,plain,
( ( ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( sdtlseqdt0 @ sz10 @ SX0 )
| ( SX0 = sz00 )
| ( SX0 = sz10 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[270]) ).
thf(320,plain,
! [SV26: $i] :
( ( ( SV26 = sz10 )
= $true )
| ( ( ( SV26 = sz00 )
| ~ ( aNaturalNumber0 @ SV26 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ ( sK1_W1 @ SV26 ) )
| ~ ( doDivides0 @ ( sK1_W1 @ SV26 ) @ SV26 ) )
| ~ ( isPrime0 @ ( sK1_W1 @ SV26 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[271]) ).
thf(321,plain,
! [SV1: $i,SV27: $i,SV46: $i] :
( ( ( ( SV46 = sz00 )
| ( SV27 = sz00 )
| ( SV1 = sz00 )
| ~ ( aNaturalNumber0 @ SV1 )
| ~ ( aNaturalNumber0 @ SV27 )
| ~ ( aNaturalNumber0 @ SV46 ) )
= $true )
| ( ( ( ( sdtasdt0 @ SV46 @ ( sdtasdt0 @ SV27 @ SV27 ) )
!= ( sdtasdt0 @ SV1 @ SV1 ) )
| ~ ( iLess0 @ SV1 @ xn )
| ~ ( isPrime0 @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[272]) ).
thf(322,plain,
! [SV28: $i,SV3: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV3 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV28 ) )
= $true )
| ( ( aNaturalNumber0 @ ( sdtpldt0 @ SV3 @ SV28 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[273]) ).
thf(323,plain,
! [SV29: $i,SV4: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV4 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV29 ) )
= $true )
| ( ( aNaturalNumber0 @ ( sdtasdt0 @ SV4 @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[274]) ).
thf(324,plain,
! [SV30: $i,SV5: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV5 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV30 ) )
= $true )
| ( ( ( sdtpldt0 @ SV5 @ SV30 )
= ( sdtpldt0 @ SV30 @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[275]) ).
thf(325,plain,
! [SV47: $i,SV31: $i,SV6: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV6 )
| ~ ( aNaturalNumber0 @ SV31 )
| ~ ( aNaturalNumber0 @ SV47 ) )
= $true )
| ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV6 @ SV31 ) @ SV47 )
= ( sdtpldt0 @ SV6 @ ( sdtpldt0 @ SV31 @ SV47 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[276]) ).
thf(326,plain,
! [SV32: $i,SV7: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV7 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV32 ) )
= $true )
| ( ( ( sdtasdt0 @ SV7 @ SV32 )
= ( sdtasdt0 @ SV32 @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[277]) ).
thf(327,plain,
! [SV48: $i,SV33: $i,SV8: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV8 )
| ~ ( aNaturalNumber0 @ SV33 )
| ~ ( aNaturalNumber0 @ SV48 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV8 @ SV33 ) @ SV48 )
= ( sdtasdt0 @ SV8 @ ( sdtasdt0 @ SV33 @ SV48 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[278]) ).
thf(328,plain,
! [SV34: $i,SV9: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV9 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV34 ) )
= $true )
| ( ( ( ( sdtasdt0 @ SV9 @ SV34 )
!= sz00 )
| ( SV9 = sz00 )
| ( SV34 = sz00 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[279]) ).
thf(329,plain,
! [SV35: $i,SV11: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV11 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV35 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV11 @ SV35 )
| ~ ( sdtlseqdt0 @ SV35 @ SV11 )
| ( SV11 = SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[281]) ).
thf(330,plain,
! [SV49: $i,SV36: $i,SV12: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV12 )
| ~ ( aNaturalNumber0 @ SV36 )
| ~ ( aNaturalNumber0 @ SV49 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV12 @ SV36 )
| ~ ( sdtlseqdt0 @ SV36 @ SV49 )
| ( sdtlseqdt0 @ SV12 @ SV49 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[282]) ).
thf(331,plain,
! [SV37: $i,SV13: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV13 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV37 ) )
= $true )
| ( ( ( SV13 = sz00 )
| ( sdtlseqdt0 @ SV37 @ ( sdtasdt0 @ SV37 @ SV13 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[283]) ).
thf(332,plain,
! [SV50: $i] :
( ( ( aNaturalNumber0 @ SV50 )
= $false )
| ( ( ! [W1: $i] :
~ ( aNaturalNumber0 @ W1 ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[284]) ).
thf(333,plain,
! [SV38: $i,SV14: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV14 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV38 ) )
= $true )
| ( ( ( SV14 = SV38 )
| ~ ( sdtlseqdt0 @ SV14 @ SV38 )
| ( iLess0 @ SV14 @ SV38 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[285]) ).
thf(334,plain,
! [SV51: $i,SV39: $i,SV15: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV15 )
| ~ ( aNaturalNumber0 @ SV39 )
| ~ ( aNaturalNumber0 @ SV51 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV15 @ SV39 )
| ~ ( doDivides0 @ SV39 @ SV51 )
| ( doDivides0 @ SV15 @ SV51 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[286]) ).
thf(335,plain,
! [SV52: $i,SV40: $i,SV16: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV16 )
| ~ ( aNaturalNumber0 @ SV40 )
| ~ ( aNaturalNumber0 @ SV52 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV16 @ SV40 )
| ~ ( doDivides0 @ SV16 @ SV52 )
| ( doDivides0 @ SV16 @ ( sdtpldt0 @ SV40 @ SV52 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[287]) ).
thf(336,plain,
! [SV53: $i,SV41: $i,SV17: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV17 )
| ~ ( aNaturalNumber0 @ SV41 )
| ~ ( aNaturalNumber0 @ SV53 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV17 @ SV41 )
| ~ ( doDivides0 @ SV17 @ ( sdtpldt0 @ SV41 @ SV53 ) )
| ( doDivides0 @ SV17 @ SV53 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[288]) ).
thf(337,plain,
! [SV42: $i,SV18: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV18 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV42 ) )
= $true )
| ( ( ( SV42 = sz00 )
| ~ ( doDivides0 @ SV18 @ SV42 )
| ( sdtlseqdt0 @ SV18 @ SV42 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[289]) ).
thf(338,plain,
! [SV43: $i,SV19: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV19 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV43 ) )
= $true )
| ( ( ( SV19 = sz00 )
| ~ ( doDivides0 @ SV19 @ SV43 )
| ! [SY133: $i] :
( ~ ( aNaturalNumber0 @ SY133 )
| ( ( sdtasdt0 @ SY133 @ ( sdtsldt0 @ SV43 @ SV19 ) )
= ( sdtsldt0 @ ( sdtasdt0 @ SY133 @ SV43 ) @ SV19 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[290]) ).
thf(339,plain,
! [SV54: $i,SV44: $i,SV20: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV20 )
| ~ ( aNaturalNumber0 @ SV44 )
| ~ ( aNaturalNumber0 @ SV54 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV54 @ ( sdtasdt0 @ SV20 @ SV44 ) )
| ~ ( isPrime0 @ SV54 )
| ( doDivides0 @ SV54 @ SV20 )
| ( doDivides0 @ SV54 @ SV44 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[291]) ).
thf(340,plain,
! [SV21: $i] :
( ( ! [SY101: $i,SY102: $i] :
( ~ ( aNaturalNumber0 @ SV21 )
| ~ ( aNaturalNumber0 @ SY101 )
| ~ ( aNaturalNumber0 @ SY102 )
| ( ( sdtpldt0 @ SV21 @ SY101 )
!= ( sdtpldt0 @ SV21 @ SY102 ) )
| ( SY101 = SY102 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[292]) ).
thf(341,plain,
! [SV21: $i] :
( ( ! [SY103: $i,SY104: $i] :
( ~ ( aNaturalNumber0 @ SV21 )
| ~ ( aNaturalNumber0 @ SY103 )
| ~ ( aNaturalNumber0 @ SY104 )
| ( ( sdtpldt0 @ SY103 @ SV21 )
!= ( sdtpldt0 @ SY104 @ SV21 ) )
| ( SY103 = SY104 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[293]) ).
thf(342,plain,
! [SV55: $i] :
( ( ~ ( aNaturalNumber0 @ SV55 )
| ( ( sdtasdt0 @ SV55 @ sz00 )
= sz00 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[294]) ).
thf(343,plain,
! [SV56: $i] :
( ( ~ ( aNaturalNumber0 @ SV56 )
| ( sz00
= ( sdtasdt0 @ sz00 @ SV56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[295]) ).
thf(344,plain,
( ( sz10 = sz00 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[296]) ).
thf(345,plain,
! [SV22: $i] :
( ( ~ ( ~ ! [SY105: $i,SY106: $i] :
( ~ ( aNaturalNumber0 @ SV22 )
| ~ ( aNaturalNumber0 @ SY105 )
| ~ ( aNaturalNumber0 @ SY106 )
| ( SV22 = sz00 )
| ( SY105 = SY106 )
| ~ ( sdtlseqdt0 @ SY105 @ SY106 )
| ( ( sdtasdt0 @ SY105 @ SV22 )
!= ( sdtasdt0 @ SY106 @ SV22 ) ) )
| ~ ~ ( ~ ! [SY107: $i,SY108: $i] :
( ~ ( aNaturalNumber0 @ SV22 )
| ~ ( aNaturalNumber0 @ SY107 )
| ~ ( aNaturalNumber0 @ SY108 )
| ( SV22 = sz00 )
| ( SY107 = SY108 )
| ~ ( sdtlseqdt0 @ SY107 @ SY108 )
| ( ( sdtasdt0 @ SV22 @ SY107 )
!= ( sdtasdt0 @ SV22 @ SY108 ) ) )
| ~ ! [SY109: $i,SY110: $i] :
( ~ ( aNaturalNumber0 @ SV22 )
| ~ ( aNaturalNumber0 @ SY109 )
| ~ ( aNaturalNumber0 @ SY110 )
| ( SV22 = sz00 )
| ( SY109 = SY110 )
| ~ ( sdtlseqdt0 @ SY109 @ SY110 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV22 @ SY109 ) @ ( sdtasdt0 @ SV22 @ SY110 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[298]) ).
thf(346,plain,
! [SV22: $i] :
( ( ! [SY111: $i,SY112: $i] :
( ~ ( aNaturalNumber0 @ SV22 )
| ~ ( aNaturalNumber0 @ SY111 )
| ~ ( aNaturalNumber0 @ SY112 )
| ( SV22 = sz00 )
| ( SY111 = SY112 )
| ~ ( sdtlseqdt0 @ SY111 @ SY112 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SY111 @ SV22 ) @ ( sdtasdt0 @ SY112 @ SV22 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[299]) ).
thf(347,plain,
! [SV57: $i] :
( ( ! [SY139: $i] :
( ~ ( aNaturalNumber0 @ SV57 )
| ~ ( aNaturalNumber0 @ SY139 )
| ( ( sdtpldt0 @ SV57 @ SY139 )
!= sz00 )
| ( SV57 = sz00 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[300]) ).
thf(348,plain,
! [SV58: $i] :
( ( ! [SY140: $i] :
( ~ ( aNaturalNumber0 @ SV58 )
| ~ ( aNaturalNumber0 @ SY140 )
| ( ( sdtpldt0 @ SV58 @ SY140 )
!= sz00 )
| ( SY140 = sz00 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[301]) ).
thf(349,plain,
! [SV59: $i] :
( ( ~ ( aNaturalNumber0 @ SV59 )
| ( ( sdtasdt0 @ SV59 @ sz10 )
= SV59 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[302]) ).
thf(350,plain,
! [SV60: $i] :
( ( ~ ( aNaturalNumber0 @ SV60 )
| ( SV60
= ( sdtasdt0 @ sz10 @ SV60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[303]) ).
thf(351,plain,
! [SV61: $i] :
( ( ! [SY141: $i] :
( ~ ( aNaturalNumber0 @ SV61 )
| ~ ( aNaturalNumber0 @ SY141 )
| ( SY141 != SV61 )
| ( sdtlseqdt0 @ SV61 @ SY141 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[304]) ).
thf(352,plain,
! [SV62: $i] :
( ( ! [SY142: $i] :
( ~ ( aNaturalNumber0 @ SV62 )
| ~ ( aNaturalNumber0 @ SY142 )
| ( sdtlseqdt0 @ SY142 @ SV62 )
| ( sdtlseqdt0 @ SV62 @ SY142 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[305]) ).
thf(353,plain,
( ( xm = xn )
= $false ),
inference(extcnf_not_pos,[status(thm)],[306]) ).
thf(354,plain,
! [SV23: $i] :
( ( ! [SY113: $i,SY114: $i] :
( ~ ( aNaturalNumber0 @ SV23 )
| ~ ( aNaturalNumber0 @ SY113 )
| ~ ( aNaturalNumber0 @ SY114 )
| ( ( sdtasdt0 @ SV23 @ ( sdtpldt0 @ SY113 @ SY114 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV23 @ SY113 ) @ ( sdtasdt0 @ SV23 @ SY114 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[308]) ).
thf(355,plain,
! [SV23: $i] :
( ( ! [SY115: $i,SY116: $i] :
( ~ ( aNaturalNumber0 @ SV23 )
| ~ ( aNaturalNumber0 @ SY115 )
| ~ ( aNaturalNumber0 @ SY116 )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SY115 @ SY116 ) @ SV23 )
= ( sdtpldt0 @ ( sdtasdt0 @ SY115 @ SV23 ) @ ( sdtasdt0 @ SY116 @ SV23 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[309]) ).
thf(356,plain,
( ( xp = sz00 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[310]) ).
thf(357,plain,
( ( ~ ( ( xm != sz00 ) )
| ~ ~ ( ~ ( ( xn != sz00 ) )
| ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ xn )
| ~ ( aNaturalNumber0 @ xm ) )
| ~ ( aNaturalNumber0 @ xp ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[311]) ).
thf(358,plain,
! [SV45: $i,SV24: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV24 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV45 ) )
= $true )
| ( ( ( SV24 = SV45 )
| ~ ( sdtlseqdt0 @ SV24 @ SV45 )
| ~ ( ~ ~ ( ~ ! [SY135: $i] :
( ~ ( aNaturalNumber0 @ SY135 )
| ( ( sdtpldt0 @ SV24 @ SY135 )
!= ( sdtpldt0 @ SV45 @ SY135 ) ) )
| ~ ~ ( ~ ! [SY136: $i] :
( ~ ( aNaturalNumber0 @ SY136 )
| ( ( sdtpldt0 @ SY136 @ SV24 )
!= ( sdtpldt0 @ SY136 @ SV45 ) ) )
| ~ ! [SY137: $i] :
( ~ ( aNaturalNumber0 @ SY137 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SY137 @ SV24 ) @ ( sdtpldt0 @ SY137 @ SV45 ) ) ) ) )
| ~ ! [SY138: $i] :
( ~ ( aNaturalNumber0 @ SY138 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SV24 @ SY138 ) @ ( sdtpldt0 @ SV45 @ SY138 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[312]) ).
thf(359,plain,
! [SV25: $i] :
( ( ( SV25 = sz00 )
= $true )
| ( ( ~ ( ~ ! [SY122: $i,SY123: $i] :
( ~ ( aNaturalNumber0 @ SY122 )
| ~ ( aNaturalNumber0 @ SY123 )
| ( ( sdtasdt0 @ SV25 @ SY122 )
!= ( sdtasdt0 @ SV25 @ SY123 ) )
| ( SY122 = SY123 ) )
| ~ ! [SY124: $i,SY125: $i] :
( ~ ( aNaturalNumber0 @ SY124 )
| ~ ( aNaturalNumber0 @ SY125 )
| ( ( sdtasdt0 @ SY124 @ SV25 )
!= ( sdtasdt0 @ SY125 @ SV25 ) )
| ( SY124 = SY125 ) ) ) )
= $true )
| ( ( aNaturalNumber0 @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[313]) ).
thf(360,plain,
! [SV63: $i] :
( ( ~ ( aNaturalNumber0 @ SV63 )
| ( ( sdtpldt0 @ SV63 @ sz00 )
= SV63 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[314]) ).
thf(361,plain,
! [SV64: $i] :
( ( ~ ( aNaturalNumber0 @ SV64 )
| ( SV64
= ( sdtpldt0 @ sz00 @ SV64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[315]) ).
thf(362,plain,
! [SV65: $i] :
( ( ~ ( aNaturalNumber0 @ SV65 )
| ( sz10 != SV65 )
| ( SV65 = sz00 )
| ( SV65 = sz10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[318]) ).
thf(363,plain,
! [SV66: $i] :
( ( ~ ( aNaturalNumber0 @ SV66 )
| ( sdtlseqdt0 @ sz10 @ SV66 )
| ( SV66 = sz00 )
| ( SV66 = sz10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[319]) ).
thf(364,plain,
! [SV26: $i] :
( ( ( SV26 = sz00 )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV26 ) )
= $true )
| ( ( SV26 = sz10 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ ( sK1_W1 @ SV26 ) )
| ~ ( doDivides0 @ ( sK1_W1 @ SV26 ) @ SV26 ) )
| ~ ( isPrime0 @ ( sK1_W1 @ SV26 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[320]) ).
thf(365,plain,
! [SV1: $i,SV27: $i,SV46: $i] :
( ( ( SV46 = sz00 )
= $true )
| ( ( ( SV27 = sz00 )
| ( SV1 = sz00 )
| ~ ( aNaturalNumber0 @ SV1 )
| ~ ( aNaturalNumber0 @ SV27 )
| ~ ( aNaturalNumber0 @ SV46 ) )
= $true )
| ( ( ( ( sdtasdt0 @ SV46 @ ( sdtasdt0 @ SV27 @ SV27 ) )
!= ( sdtasdt0 @ SV1 @ SV1 ) )
| ~ ( iLess0 @ SV1 @ xn )
| ~ ( isPrime0 @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[321]) ).
thf(366,plain,
! [SV28: $i,SV3: $i] :
( ( ( aNaturalNumber0 @ SV3 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV28 ) )
= $true )
| ( ( aNaturalNumber0 @ ( sdtpldt0 @ SV3 @ SV28 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[322]) ).
thf(367,plain,
! [SV29: $i,SV4: $i] :
( ( ( aNaturalNumber0 @ SV4 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV29 ) )
= $true )
| ( ( aNaturalNumber0 @ ( sdtasdt0 @ SV4 @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[323]) ).
thf(368,plain,
! [SV30: $i,SV5: $i] :
( ( ( aNaturalNumber0 @ SV5 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV30 ) )
= $true )
| ( ( ( sdtpldt0 @ SV5 @ SV30 )
= ( sdtpldt0 @ SV30 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[324]) ).
thf(369,plain,
! [SV47: $i,SV31: $i,SV6: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV6 )
| ~ ( aNaturalNumber0 @ SV31 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV47 ) )
= $true )
| ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV6 @ SV31 ) @ SV47 )
= ( sdtpldt0 @ SV6 @ ( sdtpldt0 @ SV31 @ SV47 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[325]) ).
thf(370,plain,
! [SV32: $i,SV7: $i] :
( ( ( aNaturalNumber0 @ SV7 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV32 ) )
= $true )
| ( ( ( sdtasdt0 @ SV7 @ SV32 )
= ( sdtasdt0 @ SV32 @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[326]) ).
thf(371,plain,
! [SV48: $i,SV33: $i,SV8: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV8 )
| ~ ( aNaturalNumber0 @ SV33 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV48 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV8 @ SV33 ) @ SV48 )
= ( sdtasdt0 @ SV8 @ ( sdtasdt0 @ SV33 @ SV48 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[327]) ).
thf(372,plain,
! [SV34: $i,SV9: $i] :
( ( ( aNaturalNumber0 @ SV9 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV34 ) )
= $true )
| ( ( ( ( sdtasdt0 @ SV9 @ SV34 )
!= sz00 )
| ( SV9 = sz00 )
| ( SV34 = sz00 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[328]) ).
thf(373,plain,
! [SV35: $i,SV11: $i] :
( ( ( aNaturalNumber0 @ SV11 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV35 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV11 @ SV35 )
| ~ ( sdtlseqdt0 @ SV35 @ SV11 )
| ( SV11 = SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[329]) ).
thf(374,plain,
! [SV49: $i,SV36: $i,SV12: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV12 )
| ~ ( aNaturalNumber0 @ SV36 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV49 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV12 @ SV36 )
| ~ ( sdtlseqdt0 @ SV36 @ SV49 )
| ( sdtlseqdt0 @ SV12 @ SV49 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[330]) ).
thf(375,plain,
! [SV37: $i,SV13: $i] :
( ( ( aNaturalNumber0 @ SV13 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV37 ) )
= $true )
| ( ( ( SV13 = sz00 )
| ( sdtlseqdt0 @ SV37 @ ( sdtasdt0 @ SV37 @ SV13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[331]) ).
thf(376,plain,
! [SV50: $i,SV67: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV67 ) )
= $true )
| ( ( aNaturalNumber0 @ SV50 )
= $false )
| ( $true = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[332]) ).
thf(377,plain,
! [SV38: $i,SV14: $i] :
( ( ( aNaturalNumber0 @ SV14 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV38 ) )
= $true )
| ( ( ( SV14 = SV38 )
| ~ ( sdtlseqdt0 @ SV14 @ SV38 )
| ( iLess0 @ SV14 @ SV38 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[333]) ).
thf(378,plain,
! [SV51: $i,SV39: $i,SV15: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV15 )
| ~ ( aNaturalNumber0 @ SV39 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV51 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV15 @ SV39 )
| ~ ( doDivides0 @ SV39 @ SV51 )
| ( doDivides0 @ SV15 @ SV51 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[334]) ).
thf(379,plain,
! [SV52: $i,SV40: $i,SV16: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV16 )
| ~ ( aNaturalNumber0 @ SV40 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV52 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV16 @ SV40 )
| ~ ( doDivides0 @ SV16 @ SV52 )
| ( doDivides0 @ SV16 @ ( sdtpldt0 @ SV40 @ SV52 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[335]) ).
thf(380,plain,
! [SV53: $i,SV41: $i,SV17: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV17 )
| ~ ( aNaturalNumber0 @ SV41 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV53 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV17 @ SV41 )
| ~ ( doDivides0 @ SV17 @ ( sdtpldt0 @ SV41 @ SV53 ) )
| ( doDivides0 @ SV17 @ SV53 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[336]) ).
thf(381,plain,
! [SV42: $i,SV18: $i] :
( ( ( aNaturalNumber0 @ SV18 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV42 ) )
= $true )
| ( ( ( SV42 = sz00 )
| ~ ( doDivides0 @ SV18 @ SV42 )
| ( sdtlseqdt0 @ SV18 @ SV42 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[337]) ).
thf(382,plain,
! [SV43: $i,SV19: $i] :
( ( ( aNaturalNumber0 @ SV19 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV43 ) )
= $true )
| ( ( ( SV19 = sz00 )
| ~ ( doDivides0 @ SV19 @ SV43 )
| ! [SY133: $i] :
( ~ ( aNaturalNumber0 @ SY133 )
| ( ( sdtasdt0 @ SY133 @ ( sdtsldt0 @ SV43 @ SV19 ) )
= ( sdtsldt0 @ ( sdtasdt0 @ SY133 @ SV43 ) @ SV19 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[338]) ).
thf(383,plain,
! [SV54: $i,SV44: $i,SV20: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV20 )
| ~ ( aNaturalNumber0 @ SV44 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV54 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV54 @ ( sdtasdt0 @ SV20 @ SV44 ) )
| ~ ( isPrime0 @ SV54 )
| ( doDivides0 @ SV54 @ SV20 )
| ( doDivides0 @ SV54 @ SV44 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[339]) ).
thf(384,plain,
! [SV68: $i,SV21: $i] :
( ( ! [SY143: $i] :
( ~ ( aNaturalNumber0 @ SV21 )
| ~ ( aNaturalNumber0 @ SV68 )
| ~ ( aNaturalNumber0 @ SY143 )
| ( ( sdtpldt0 @ SV21 @ SV68 )
!= ( sdtpldt0 @ SV21 @ SY143 ) )
| ( SV68 = SY143 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[340]) ).
thf(385,plain,
! [SV69: $i,SV21: $i] :
( ( ! [SY144: $i] :
( ~ ( aNaturalNumber0 @ SV21 )
| ~ ( aNaturalNumber0 @ SV69 )
| ~ ( aNaturalNumber0 @ SY144 )
| ( ( sdtpldt0 @ SV69 @ SV21 )
!= ( sdtpldt0 @ SY144 @ SV21 ) )
| ( SV69 = SY144 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[341]) ).
thf(386,plain,
! [SV55: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV55 ) )
= $true )
| ( ( ( sdtasdt0 @ SV55 @ sz00 )
= sz00 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[342]) ).
thf(387,plain,
! [SV56: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV56 ) )
= $true )
| ( ( sz00
= ( sdtasdt0 @ sz00 @ SV56 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[343]) ).
thf(388,plain,
! [SV22: $i] :
( ( ~ ! [SY105: $i,SY106: $i] :
( ~ ( aNaturalNumber0 @ SV22 )
| ~ ( aNaturalNumber0 @ SY105 )
| ~ ( aNaturalNumber0 @ SY106 )
| ( SV22 = sz00 )
| ( SY105 = SY106 )
| ~ ( sdtlseqdt0 @ SY105 @ SY106 )
| ( ( sdtasdt0 @ SY105 @ SV22 )
!= ( sdtasdt0 @ SY106 @ SV22 ) ) )
| ~ ~ ( ~ ! [SY107: $i,SY108: $i] :
( ~ ( aNaturalNumber0 @ SV22 )
| ~ ( aNaturalNumber0 @ SY107 )
| ~ ( aNaturalNumber0 @ SY108 )
| ( SV22 = sz00 )
| ( SY107 = SY108 )
| ~ ( sdtlseqdt0 @ SY107 @ SY108 )
| ( ( sdtasdt0 @ SV22 @ SY107 )
!= ( sdtasdt0 @ SV22 @ SY108 ) ) )
| ~ ! [SY109: $i,SY110: $i] :
( ~ ( aNaturalNumber0 @ SV22 )
| ~ ( aNaturalNumber0 @ SY109 )
| ~ ( aNaturalNumber0 @ SY110 )
| ( SV22 = sz00 )
| ( SY109 = SY110 )
| ~ ( sdtlseqdt0 @ SY109 @ SY110 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV22 @ SY109 ) @ ( sdtasdt0 @ SV22 @ SY110 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[345]) ).
thf(389,plain,
! [SV70: $i,SV22: $i] :
( ( ! [SY145: $i] :
( ~ ( aNaturalNumber0 @ SV22 )
| ~ ( aNaturalNumber0 @ SV70 )
| ~ ( aNaturalNumber0 @ SY145 )
| ( SV22 = sz00 )
| ( SV70 = SY145 )
| ~ ( sdtlseqdt0 @ SV70 @ SY145 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV70 @ SV22 ) @ ( sdtasdt0 @ SY145 @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[346]) ).
thf(390,plain,
! [SV71: $i,SV57: $i] :
( ( ~ ( aNaturalNumber0 @ SV57 )
| ~ ( aNaturalNumber0 @ SV71 )
| ( ( sdtpldt0 @ SV57 @ SV71 )
!= sz00 )
| ( SV57 = sz00 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[347]) ).
thf(391,plain,
! [SV72: $i,SV58: $i] :
( ( ~ ( aNaturalNumber0 @ SV58 )
| ~ ( aNaturalNumber0 @ SV72 )
| ( ( sdtpldt0 @ SV58 @ SV72 )
!= sz00 )
| ( SV72 = sz00 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[348]) ).
thf(392,plain,
! [SV59: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV59 ) )
= $true )
| ( ( ( sdtasdt0 @ SV59 @ sz10 )
= SV59 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[349]) ).
thf(393,plain,
! [SV60: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV60 ) )
= $true )
| ( ( SV60
= ( sdtasdt0 @ sz10 @ SV60 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[350]) ).
thf(394,plain,
! [SV73: $i,SV61: $i] :
( ( ~ ( aNaturalNumber0 @ SV61 )
| ~ ( aNaturalNumber0 @ SV73 )
| ( SV73 != SV61 )
| ( sdtlseqdt0 @ SV61 @ SV73 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[351]) ).
thf(395,plain,
! [SV74: $i,SV62: $i] :
( ( ~ ( aNaturalNumber0 @ SV62 )
| ~ ( aNaturalNumber0 @ SV74 )
| ( sdtlseqdt0 @ SV74 @ SV62 )
| ( sdtlseqdt0 @ SV62 @ SV74 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[352]) ).
thf(396,plain,
! [SV75: $i,SV23: $i] :
( ( ! [SY146: $i] :
( ~ ( aNaturalNumber0 @ SV23 )
| ~ ( aNaturalNumber0 @ SV75 )
| ~ ( aNaturalNumber0 @ SY146 )
| ( ( sdtasdt0 @ SV23 @ ( sdtpldt0 @ SV75 @ SY146 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV23 @ SV75 ) @ ( sdtasdt0 @ SV23 @ SY146 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[354]) ).
thf(397,plain,
! [SV76: $i,SV23: $i] :
( ( ! [SY147: $i] :
( ~ ( aNaturalNumber0 @ SV23 )
| ~ ( aNaturalNumber0 @ SV76 )
| ~ ( aNaturalNumber0 @ SY147 )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SV76 @ SY147 ) @ SV23 )
= ( sdtpldt0 @ ( sdtasdt0 @ SV76 @ SV23 ) @ ( sdtasdt0 @ SY147 @ SV23 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[355]) ).
thf(398,plain,
( ( ~ ( ( xm != sz00 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[357]) ).
thf(399,plain,
( ( ~ ~ ( ~ ( ( xn != sz00 ) )
| ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ xn )
| ~ ( aNaturalNumber0 @ xm ) )
| ~ ( aNaturalNumber0 @ xp ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[357]) ).
thf(400,plain,
! [SV45: $i,SV24: $i] :
( ( ( aNaturalNumber0 @ SV24 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV45 ) )
= $true )
| ( ( ( SV24 = SV45 )
| ~ ( sdtlseqdt0 @ SV24 @ SV45 )
| ~ ( ~ ~ ( ~ ! [SY135: $i] :
( ~ ( aNaturalNumber0 @ SY135 )
| ( ( sdtpldt0 @ SV24 @ SY135 )
!= ( sdtpldt0 @ SV45 @ SY135 ) ) )
| ~ ~ ( ~ ! [SY136: $i] :
( ~ ( aNaturalNumber0 @ SY136 )
| ( ( sdtpldt0 @ SY136 @ SV24 )
!= ( sdtpldt0 @ SY136 @ SV45 ) ) )
| ~ ! [SY137: $i] :
( ~ ( aNaturalNumber0 @ SY137 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SY137 @ SV24 ) @ ( sdtpldt0 @ SY137 @ SV45 ) ) ) ) )
| ~ ! [SY138: $i] :
( ~ ( aNaturalNumber0 @ SY138 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SV24 @ SY138 ) @ ( sdtpldt0 @ SV45 @ SY138 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[358]) ).
thf(401,plain,
! [SV25: $i] :
( ( ( ~ ! [SY122: $i,SY123: $i] :
( ~ ( aNaturalNumber0 @ SY122 )
| ~ ( aNaturalNumber0 @ SY123 )
| ( ( sdtasdt0 @ SV25 @ SY122 )
!= ( sdtasdt0 @ SV25 @ SY123 ) )
| ( SY122 = SY123 ) )
| ~ ! [SY124: $i,SY125: $i] :
( ~ ( aNaturalNumber0 @ SY124 )
| ~ ( aNaturalNumber0 @ SY125 )
| ( ( sdtasdt0 @ SY124 @ SV25 )
!= ( sdtasdt0 @ SY125 @ SV25 ) )
| ( SY124 = SY125 ) ) )
= $false )
| ( ( SV25 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[359]) ).
thf(402,plain,
! [SV63: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV63 ) )
= $true )
| ( ( ( sdtpldt0 @ SV63 @ sz00 )
= SV63 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[360]) ).
thf(403,plain,
! [SV64: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV64 ) )
= $true )
| ( ( SV64
= ( sdtpldt0 @ sz00 @ SV64 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[361]) ).
thf(404,plain,
! [SV65: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV65 ) )
= $true )
| ( ( ( sz10 != SV65 )
| ( SV65 = sz00 )
| ( SV65 = sz10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[362]) ).
thf(405,plain,
! [SV66: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV66 ) )
= $true )
| ( ( ( sdtlseqdt0 @ sz10 @ SV66 )
| ( SV66 = sz00 )
| ( SV66 = sz10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[363]) ).
thf(406,plain,
! [SV26: $i] :
( ( ( aNaturalNumber0 @ SV26 )
= $false )
| ( ( SV26 = sz00 )
= $true )
| ( ( SV26 = sz10 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ ( sK1_W1 @ SV26 ) )
| ~ ( doDivides0 @ ( sK1_W1 @ SV26 ) @ SV26 ) )
| ~ ( isPrime0 @ ( sK1_W1 @ SV26 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[364]) ).
thf(407,plain,
! [SV46: $i,SV1: $i,SV27: $i] :
( ( ( SV27 = sz00 )
= $true )
| ( ( ( SV1 = sz00 )
| ~ ( aNaturalNumber0 @ SV1 )
| ~ ( aNaturalNumber0 @ SV27 )
| ~ ( aNaturalNumber0 @ SV46 ) )
= $true )
| ( ( SV46 = sz00 )
= $true )
| ( ( ( ( sdtasdt0 @ SV46 @ ( sdtasdt0 @ SV27 @ SV27 ) )
!= ( sdtasdt0 @ SV1 @ SV1 ) )
| ~ ( iLess0 @ SV1 @ xn )
| ~ ( isPrime0 @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[365]) ).
thf(408,plain,
! [SV3: $i,SV28: $i] :
( ( ( aNaturalNumber0 @ SV28 )
= $false )
| ( ( aNaturalNumber0 @ SV3 )
= $false )
| ( ( aNaturalNumber0 @ ( sdtpldt0 @ SV3 @ SV28 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[366]) ).
thf(409,plain,
! [SV4: $i,SV29: $i] :
( ( ( aNaturalNumber0 @ SV29 )
= $false )
| ( ( aNaturalNumber0 @ SV4 )
= $false )
| ( ( aNaturalNumber0 @ ( sdtasdt0 @ SV4 @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[367]) ).
thf(410,plain,
! [SV5: $i,SV30: $i] :
( ( ( aNaturalNumber0 @ SV30 )
= $false )
| ( ( aNaturalNumber0 @ SV5 )
= $false )
| ( ( ( sdtpldt0 @ SV5 @ SV30 )
= ( sdtpldt0 @ SV30 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[368]) ).
thf(411,plain,
! [SV47: $i,SV31: $i,SV6: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV6 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV31 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV47 ) )
= $true )
| ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV6 @ SV31 ) @ SV47 )
= ( sdtpldt0 @ SV6 @ ( sdtpldt0 @ SV31 @ SV47 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[369]) ).
thf(412,plain,
! [SV7: $i,SV32: $i] :
( ( ( aNaturalNumber0 @ SV32 )
= $false )
| ( ( aNaturalNumber0 @ SV7 )
= $false )
| ( ( ( sdtasdt0 @ SV7 @ SV32 )
= ( sdtasdt0 @ SV32 @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[370]) ).
thf(413,plain,
! [SV48: $i,SV33: $i,SV8: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV8 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV33 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV48 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV8 @ SV33 ) @ SV48 )
= ( sdtasdt0 @ SV8 @ ( sdtasdt0 @ SV33 @ SV48 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[371]) ).
thf(414,plain,
! [SV9: $i,SV34: $i] :
( ( ( aNaturalNumber0 @ SV34 )
= $false )
| ( ( aNaturalNumber0 @ SV9 )
= $false )
| ( ( ( ( sdtasdt0 @ SV9 @ SV34 )
!= sz00 )
| ( SV9 = sz00 )
| ( SV34 = sz00 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[372]) ).
thf(415,plain,
! [SV11: $i,SV35: $i] :
( ( ( aNaturalNumber0 @ SV35 )
= $false )
| ( ( aNaturalNumber0 @ SV11 )
= $false )
| ( ( ~ ( sdtlseqdt0 @ SV11 @ SV35 )
| ~ ( sdtlseqdt0 @ SV35 @ SV11 )
| ( SV11 = SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[373]) ).
thf(416,plain,
! [SV49: $i,SV36: $i,SV12: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV12 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV36 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV49 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV12 @ SV36 )
| ~ ( sdtlseqdt0 @ SV36 @ SV49 )
| ( sdtlseqdt0 @ SV12 @ SV49 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[374]) ).
thf(417,plain,
! [SV13: $i,SV37: $i] :
( ( ( aNaturalNumber0 @ SV37 )
= $false )
| ( ( aNaturalNumber0 @ SV13 )
= $false )
| ( ( ( SV13 = sz00 )
| ( sdtlseqdt0 @ SV37 @ ( sdtasdt0 @ SV37 @ SV13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[375]) ).
thf(418,plain,
! [SV50: $i,SV67: $i] :
( ( ( aNaturalNumber0 @ SV67 )
= $false )
| ( ( aNaturalNumber0 @ SV50 )
= $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[376]) ).
thf(419,plain,
! [SV14: $i,SV38: $i] :
( ( ( aNaturalNumber0 @ SV38 )
= $false )
| ( ( aNaturalNumber0 @ SV14 )
= $false )
| ( ( ( SV14 = SV38 )
| ~ ( sdtlseqdt0 @ SV14 @ SV38 )
| ( iLess0 @ SV14 @ SV38 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[377]) ).
thf(420,plain,
! [SV51: $i,SV39: $i,SV15: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV15 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV39 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV51 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV15 @ SV39 )
| ~ ( doDivides0 @ SV39 @ SV51 )
| ( doDivides0 @ SV15 @ SV51 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[378]) ).
thf(421,plain,
! [SV52: $i,SV40: $i,SV16: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV16 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV40 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV52 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV16 @ SV40 )
| ~ ( doDivides0 @ SV16 @ SV52 )
| ( doDivides0 @ SV16 @ ( sdtpldt0 @ SV40 @ SV52 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[379]) ).
thf(422,plain,
! [SV53: $i,SV41: $i,SV17: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV17 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV41 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV53 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV17 @ SV41 )
| ~ ( doDivides0 @ SV17 @ ( sdtpldt0 @ SV41 @ SV53 ) )
| ( doDivides0 @ SV17 @ SV53 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[380]) ).
thf(423,plain,
! [SV18: $i,SV42: $i] :
( ( ( aNaturalNumber0 @ SV42 )
= $false )
| ( ( aNaturalNumber0 @ SV18 )
= $false )
| ( ( ( SV42 = sz00 )
| ~ ( doDivides0 @ SV18 @ SV42 )
| ( sdtlseqdt0 @ SV18 @ SV42 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[381]) ).
thf(424,plain,
! [SV19: $i,SV43: $i] :
( ( ( aNaturalNumber0 @ SV43 )
= $false )
| ( ( aNaturalNumber0 @ SV19 )
= $false )
| ( ( ( SV19 = sz00 )
| ~ ( doDivides0 @ SV19 @ SV43 )
| ! [SY133: $i] :
( ~ ( aNaturalNumber0 @ SY133 )
| ( ( sdtasdt0 @ SY133 @ ( sdtsldt0 @ SV43 @ SV19 ) )
= ( sdtsldt0 @ ( sdtasdt0 @ SY133 @ SV43 ) @ SV19 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[382]) ).
thf(425,plain,
! [SV54: $i,SV44: $i,SV20: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV20 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV44 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV54 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV54 @ ( sdtasdt0 @ SV20 @ SV44 ) )
| ~ ( isPrime0 @ SV54 )
| ( doDivides0 @ SV54 @ SV20 )
| ( doDivides0 @ SV54 @ SV44 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[383]) ).
thf(426,plain,
! [SV77: $i,SV68: $i,SV21: $i] :
( ( ~ ( aNaturalNumber0 @ SV21 )
| ~ ( aNaturalNumber0 @ SV68 )
| ~ ( aNaturalNumber0 @ SV77 )
| ( ( sdtpldt0 @ SV21 @ SV68 )
!= ( sdtpldt0 @ SV21 @ SV77 ) )
| ( SV68 = SV77 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[384]) ).
thf(427,plain,
! [SV78: $i,SV69: $i,SV21: $i] :
( ( ~ ( aNaturalNumber0 @ SV21 )
| ~ ( aNaturalNumber0 @ SV69 )
| ~ ( aNaturalNumber0 @ SV78 )
| ( ( sdtpldt0 @ SV69 @ SV21 )
!= ( sdtpldt0 @ SV78 @ SV21 ) )
| ( SV69 = SV78 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[385]) ).
thf(428,plain,
! [SV55: $i] :
( ( ( aNaturalNumber0 @ SV55 )
= $false )
| ( ( ( sdtasdt0 @ SV55 @ sz00 )
= sz00 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[386]) ).
thf(429,plain,
! [SV56: $i] :
( ( ( aNaturalNumber0 @ SV56 )
= $false )
| ( ( sz00
= ( sdtasdt0 @ sz00 @ SV56 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[387]) ).
thf(430,plain,
! [SV22: $i] :
( ( ~ ! [SY105: $i,SY106: $i] :
( ~ ( aNaturalNumber0 @ SV22 )
| ~ ( aNaturalNumber0 @ SY105 )
| ~ ( aNaturalNumber0 @ SY106 )
| ( SV22 = sz00 )
| ( SY105 = SY106 )
| ~ ( sdtlseqdt0 @ SY105 @ SY106 )
| ( ( sdtasdt0 @ SY105 @ SV22 )
!= ( sdtasdt0 @ SY106 @ SV22 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[388]) ).
thf(431,plain,
! [SV22: $i] :
( ( ~ ~ ( ~ ! [SY107: $i,SY108: $i] :
( ~ ( aNaturalNumber0 @ SV22 )
| ~ ( aNaturalNumber0 @ SY107 )
| ~ ( aNaturalNumber0 @ SY108 )
| ( SV22 = sz00 )
| ( SY107 = SY108 )
| ~ ( sdtlseqdt0 @ SY107 @ SY108 )
| ( ( sdtasdt0 @ SV22 @ SY107 )
!= ( sdtasdt0 @ SV22 @ SY108 ) ) )
| ~ ! [SY109: $i,SY110: $i] :
( ~ ( aNaturalNumber0 @ SV22 )
| ~ ( aNaturalNumber0 @ SY109 )
| ~ ( aNaturalNumber0 @ SY110 )
| ( SV22 = sz00 )
| ( SY109 = SY110 )
| ~ ( sdtlseqdt0 @ SY109 @ SY110 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV22 @ SY109 ) @ ( sdtasdt0 @ SV22 @ SY110 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[388]) ).
thf(432,plain,
! [SV79: $i,SV70: $i,SV22: $i] :
( ( ~ ( aNaturalNumber0 @ SV22 )
| ~ ( aNaturalNumber0 @ SV70 )
| ~ ( aNaturalNumber0 @ SV79 )
| ( SV22 = sz00 )
| ( SV70 = SV79 )
| ~ ( sdtlseqdt0 @ SV70 @ SV79 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV70 @ SV22 ) @ ( sdtasdt0 @ SV79 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[389]) ).
thf(433,plain,
! [SV71: $i,SV57: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV57 )
| ~ ( aNaturalNumber0 @ SV71 ) )
= $true )
| ( ( ( ( sdtpldt0 @ SV57 @ SV71 )
!= sz00 )
| ( SV57 = sz00 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[390]) ).
thf(434,plain,
! [SV72: $i,SV58: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV58 )
| ~ ( aNaturalNumber0 @ SV72 ) )
= $true )
| ( ( ( ( sdtpldt0 @ SV58 @ SV72 )
!= sz00 )
| ( SV72 = sz00 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[391]) ).
thf(435,plain,
! [SV59: $i] :
( ( ( aNaturalNumber0 @ SV59 )
= $false )
| ( ( ( sdtasdt0 @ SV59 @ sz10 )
= SV59 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[392]) ).
thf(436,plain,
! [SV60: $i] :
( ( ( aNaturalNumber0 @ SV60 )
= $false )
| ( ( SV60
= ( sdtasdt0 @ sz10 @ SV60 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[393]) ).
thf(437,plain,
! [SV73: $i,SV61: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV61 )
| ~ ( aNaturalNumber0 @ SV73 ) )
= $true )
| ( ( ( SV73 != SV61 )
| ( sdtlseqdt0 @ SV61 @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[394]) ).
thf(438,plain,
! [SV74: $i,SV62: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV62 )
| ~ ( aNaturalNumber0 @ SV74 ) )
= $true )
| ( ( ( sdtlseqdt0 @ SV74 @ SV62 )
| ( sdtlseqdt0 @ SV62 @ SV74 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[395]) ).
thf(439,plain,
! [SV80: $i,SV75: $i,SV23: $i] :
( ( ~ ( aNaturalNumber0 @ SV23 )
| ~ ( aNaturalNumber0 @ SV75 )
| ~ ( aNaturalNumber0 @ SV80 )
| ( ( sdtasdt0 @ SV23 @ ( sdtpldt0 @ SV75 @ SV80 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV23 @ SV75 ) @ ( sdtasdt0 @ SV23 @ SV80 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[396]) ).
thf(440,plain,
! [SV81: $i,SV76: $i,SV23: $i] :
( ( ~ ( aNaturalNumber0 @ SV23 )
| ~ ( aNaturalNumber0 @ SV76 )
| ~ ( aNaturalNumber0 @ SV81 )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SV76 @ SV81 ) @ SV23 )
= ( sdtpldt0 @ ( sdtasdt0 @ SV76 @ SV23 ) @ ( sdtasdt0 @ SV81 @ SV23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[397]) ).
thf(441,plain,
( ( ( xm != sz00 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[398]) ).
thf(442,plain,
( ( ~ ( ~ ( ( xn != sz00 ) )
| ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ xn )
| ~ ( aNaturalNumber0 @ xm ) )
| ~ ( aNaturalNumber0 @ xp ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[399]) ).
thf(443,plain,
! [SV24: $i,SV45: $i] :
( ( ( aNaturalNumber0 @ SV45 )
= $false )
| ( ( aNaturalNumber0 @ SV24 )
= $false )
| ( ( ( SV24 = SV45 )
| ~ ( sdtlseqdt0 @ SV24 @ SV45 )
| ~ ( ~ ~ ( ~ ! [SY135: $i] :
( ~ ( aNaturalNumber0 @ SY135 )
| ( ( sdtpldt0 @ SV24 @ SY135 )
!= ( sdtpldt0 @ SV45 @ SY135 ) ) )
| ~ ~ ( ~ ! [SY136: $i] :
( ~ ( aNaturalNumber0 @ SY136 )
| ( ( sdtpldt0 @ SY136 @ SV24 )
!= ( sdtpldt0 @ SY136 @ SV45 ) ) )
| ~ ! [SY137: $i] :
( ~ ( aNaturalNumber0 @ SY137 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SY137 @ SV24 ) @ ( sdtpldt0 @ SY137 @ SV45 ) ) ) ) )
| ~ ! [SY138: $i] :
( ~ ( aNaturalNumber0 @ SY138 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SV24 @ SY138 ) @ ( sdtpldt0 @ SV45 @ SY138 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[400]) ).
thf(444,plain,
! [SV25: $i] :
( ( ( ~ ! [SY122: $i,SY123: $i] :
( ~ ( aNaturalNumber0 @ SY122 )
| ~ ( aNaturalNumber0 @ SY123 )
| ( ( sdtasdt0 @ SV25 @ SY122 )
!= ( sdtasdt0 @ SV25 @ SY123 ) )
| ( SY122 = SY123 ) ) )
= $false )
| ( ( SV25 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV25 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[401]) ).
thf(445,plain,
! [SV25: $i] :
( ( ( ~ ! [SY124: $i,SY125: $i] :
( ~ ( aNaturalNumber0 @ SY124 )
| ~ ( aNaturalNumber0 @ SY125 )
| ( ( sdtasdt0 @ SY124 @ SV25 )
!= ( sdtasdt0 @ SY125 @ SV25 ) )
| ( SY124 = SY125 ) ) )
= $false )
| ( ( SV25 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV25 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[401]) ).
thf(446,plain,
! [SV63: $i] :
( ( ( aNaturalNumber0 @ SV63 )
= $false )
| ( ( ( sdtpldt0 @ SV63 @ sz00 )
= SV63 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[402]) ).
thf(447,plain,
! [SV64: $i] :
( ( ( aNaturalNumber0 @ SV64 )
= $false )
| ( ( SV64
= ( sdtpldt0 @ sz00 @ SV64 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[403]) ).
thf(448,plain,
! [SV65: $i] :
( ( ( aNaturalNumber0 @ SV65 )
= $false )
| ( ( ( sz10 != SV65 )
| ( SV65 = sz00 )
| ( SV65 = sz10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[404]) ).
thf(449,plain,
! [SV66: $i] :
( ( ( aNaturalNumber0 @ SV66 )
= $false )
| ( ( ( sdtlseqdt0 @ sz10 @ SV66 )
| ( SV66 = sz00 )
| ( SV66 = sz10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[405]) ).
thf(450,plain,
! [SV26: $i] :
( ( ( ~ ~ ( ~ ( aNaturalNumber0 @ ( sK1_W1 @ SV26 ) )
| ~ ( doDivides0 @ ( sK1_W1 @ SV26 ) @ SV26 ) )
| ~ ( isPrime0 @ ( sK1_W1 @ SV26 ) ) )
= $false )
| ( ( SV26 = sz10 )
= $true )
| ( ( SV26 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[406]) ).
thf(451,plain,
! [SV46: $i,SV27: $i,SV1: $i] :
( ( ( SV1 = sz00 )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV1 )
| ~ ( aNaturalNumber0 @ SV27 )
| ~ ( aNaturalNumber0 @ SV46 ) )
= $true )
| ( ( SV27 = sz00 )
= $true )
| ( ( SV46 = sz00 )
= $true )
| ( ( ( ( sdtasdt0 @ SV46 @ ( sdtasdt0 @ SV27 @ SV27 ) )
!= ( sdtasdt0 @ SV1 @ SV1 ) )
| ~ ( iLess0 @ SV1 @ xn )
| ~ ( isPrime0 @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[407]) ).
thf(452,plain,
! [SV47: $i,SV31: $i,SV6: $i] :
( ( ( aNaturalNumber0 @ SV6 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV31 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV47 ) )
= $true )
| ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV6 @ SV31 ) @ SV47 )
= ( sdtpldt0 @ SV6 @ ( sdtpldt0 @ SV31 @ SV47 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[411]) ).
thf(453,plain,
! [SV48: $i,SV33: $i,SV8: $i] :
( ( ( aNaturalNumber0 @ SV8 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV33 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV48 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV8 @ SV33 ) @ SV48 )
= ( sdtasdt0 @ SV8 @ ( sdtasdt0 @ SV33 @ SV48 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[413]) ).
thf(454,plain,
! [SV34: $i,SV9: $i] :
( ( ( ( ( sdtasdt0 @ SV9 @ SV34 )
!= sz00 ) )
= $true )
| ( ( ( SV9 = sz00 )
| ( SV34 = sz00 ) )
= $true )
| ( ( aNaturalNumber0 @ SV9 )
= $false )
| ( ( aNaturalNumber0 @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[414]) ).
thf(455,plain,
! [SV35: $i,SV11: $i] :
( ( ( ~ ( sdtlseqdt0 @ SV11 @ SV35 )
| ~ ( sdtlseqdt0 @ SV35 @ SV11 ) )
= $true )
| ( ( SV11 = SV35 )
= $true )
| ( ( aNaturalNumber0 @ SV11 )
= $false )
| ( ( aNaturalNumber0 @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[415]) ).
thf(456,plain,
! [SV49: $i,SV36: $i,SV12: $i] :
( ( ( aNaturalNumber0 @ SV12 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV36 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV49 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV12 @ SV36 )
| ~ ( sdtlseqdt0 @ SV36 @ SV49 )
| ( sdtlseqdt0 @ SV12 @ SV49 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[416]) ).
thf(457,plain,
! [SV37: $i,SV13: $i] :
( ( ( SV13 = sz00 )
= $true )
| ( ( sdtlseqdt0 @ SV37 @ ( sdtasdt0 @ SV37 @ SV13 ) )
= $true )
| ( ( aNaturalNumber0 @ SV13 )
= $false )
| ( ( aNaturalNumber0 @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[417]) ).
thf(458,plain,
! [SV38: $i,SV14: $i] :
( ( ( ( SV14 = SV38 )
| ~ ( sdtlseqdt0 @ SV14 @ SV38 ) )
= $true )
| ( ( iLess0 @ SV14 @ SV38 )
= $true )
| ( ( aNaturalNumber0 @ SV14 )
= $false )
| ( ( aNaturalNumber0 @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[419]) ).
thf(459,plain,
! [SV51: $i,SV39: $i,SV15: $i] :
( ( ( aNaturalNumber0 @ SV15 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV39 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV51 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV15 @ SV39 )
| ~ ( doDivides0 @ SV39 @ SV51 )
| ( doDivides0 @ SV15 @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[420]) ).
thf(460,plain,
! [SV52: $i,SV40: $i,SV16: $i] :
( ( ( aNaturalNumber0 @ SV16 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV40 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV52 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV16 @ SV40 )
| ~ ( doDivides0 @ SV16 @ SV52 )
| ( doDivides0 @ SV16 @ ( sdtpldt0 @ SV40 @ SV52 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[421]) ).
thf(461,plain,
! [SV53: $i,SV41: $i,SV17: $i] :
( ( ( aNaturalNumber0 @ SV17 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV41 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV53 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV17 @ SV41 )
| ~ ( doDivides0 @ SV17 @ ( sdtpldt0 @ SV41 @ SV53 ) )
| ( doDivides0 @ SV17 @ SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[422]) ).
thf(462,plain,
! [SV18: $i,SV42: $i] :
( ( ( ( SV42 = sz00 )
| ~ ( doDivides0 @ SV18 @ SV42 ) )
= $true )
| ( ( sdtlseqdt0 @ SV18 @ SV42 )
= $true )
| ( ( aNaturalNumber0 @ SV18 )
= $false )
| ( ( aNaturalNumber0 @ SV42 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[423]) ).
thf(463,plain,
! [SV43: $i,SV19: $i] :
( ( ( ( SV19 = sz00 )
| ~ ( doDivides0 @ SV19 @ SV43 ) )
= $true )
| ( ( ! [SY133: $i] :
( ~ ( aNaturalNumber0 @ SY133 )
| ( ( sdtasdt0 @ SY133 @ ( sdtsldt0 @ SV43 @ SV19 ) )
= ( sdtsldt0 @ ( sdtasdt0 @ SY133 @ SV43 ) @ SV19 ) ) ) )
= $true )
| ( ( aNaturalNumber0 @ SV19 )
= $false )
| ( ( aNaturalNumber0 @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[424]) ).
thf(464,plain,
! [SV54: $i,SV44: $i,SV20: $i] :
( ( ( aNaturalNumber0 @ SV20 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV44 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV54 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV54 @ ( sdtasdt0 @ SV20 @ SV44 ) )
| ~ ( isPrime0 @ SV54 )
| ( doDivides0 @ SV54 @ SV20 )
| ( doDivides0 @ SV54 @ SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[425]) ).
thf(465,plain,
! [SV77: $i,SV68: $i,SV21: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV21 )
| ~ ( aNaturalNumber0 @ SV68 )
| ~ ( aNaturalNumber0 @ SV77 ) )
= $true )
| ( ( ( ( sdtpldt0 @ SV21 @ SV68 )
!= ( sdtpldt0 @ SV21 @ SV77 ) )
| ( SV68 = SV77 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[426]) ).
thf(466,plain,
! [SV78: $i,SV69: $i,SV21: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV21 )
| ~ ( aNaturalNumber0 @ SV69 )
| ~ ( aNaturalNumber0 @ SV78 ) )
= $true )
| ( ( ( ( sdtpldt0 @ SV69 @ SV21 )
!= ( sdtpldt0 @ SV78 @ SV21 ) )
| ( SV69 = SV78 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[427]) ).
thf(467,plain,
! [SV22: $i] :
( ( ! [SY105: $i,SY106: $i] :
( ~ ( aNaturalNumber0 @ SV22 )
| ~ ( aNaturalNumber0 @ SY105 )
| ~ ( aNaturalNumber0 @ SY106 )
| ( SV22 = sz00 )
| ( SY105 = SY106 )
| ~ ( sdtlseqdt0 @ SY105 @ SY106 )
| ( ( sdtasdt0 @ SY105 @ SV22 )
!= ( sdtasdt0 @ SY106 @ SV22 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[430]) ).
thf(468,plain,
! [SV22: $i] :
( ( ~ ( ~ ! [SY107: $i,SY108: $i] :
( ~ ( aNaturalNumber0 @ SV22 )
| ~ ( aNaturalNumber0 @ SY107 )
| ~ ( aNaturalNumber0 @ SY108 )
| ( SV22 = sz00 )
| ( SY107 = SY108 )
| ~ ( sdtlseqdt0 @ SY107 @ SY108 )
| ( ( sdtasdt0 @ SV22 @ SY107 )
!= ( sdtasdt0 @ SV22 @ SY108 ) ) )
| ~ ! [SY109: $i,SY110: $i] :
( ~ ( aNaturalNumber0 @ SV22 )
| ~ ( aNaturalNumber0 @ SY109 )
| ~ ( aNaturalNumber0 @ SY110 )
| ( SV22 = sz00 )
| ( SY109 = SY110 )
| ~ ( sdtlseqdt0 @ SY109 @ SY110 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV22 @ SY109 ) @ ( sdtasdt0 @ SV22 @ SY110 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[431]) ).
thf(469,plain,
! [SV79: $i,SV70: $i,SV22: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV22 )
| ~ ( aNaturalNumber0 @ SV70 )
| ~ ( aNaturalNumber0 @ SV79 ) )
= $true )
| ( ( ( SV22 = sz00 )
| ( SV70 = SV79 )
| ~ ( sdtlseqdt0 @ SV70 @ SV79 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV70 @ SV22 ) @ ( sdtasdt0 @ SV79 @ SV22 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[432]) ).
thf(470,plain,
! [SV71: $i,SV57: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV57 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV71 ) )
= $true )
| ( ( ( ( sdtpldt0 @ SV57 @ SV71 )
!= sz00 )
| ( SV57 = sz00 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[433]) ).
thf(471,plain,
! [SV72: $i,SV58: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV58 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV72 ) )
= $true )
| ( ( ( ( sdtpldt0 @ SV58 @ SV72 )
!= sz00 )
| ( SV72 = sz00 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[434]) ).
thf(472,plain,
! [SV73: $i,SV61: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV61 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV73 ) )
= $true )
| ( ( ( SV73 != SV61 )
| ( sdtlseqdt0 @ SV61 @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[437]) ).
thf(473,plain,
! [SV74: $i,SV62: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV62 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV74 ) )
= $true )
| ( ( ( sdtlseqdt0 @ SV74 @ SV62 )
| ( sdtlseqdt0 @ SV62 @ SV74 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[438]) ).
thf(474,plain,
! [SV80: $i,SV75: $i,SV23: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV23 )
| ~ ( aNaturalNumber0 @ SV75 )
| ~ ( aNaturalNumber0 @ SV80 ) )
= $true )
| ( ( ( sdtasdt0 @ SV23 @ ( sdtpldt0 @ SV75 @ SV80 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV23 @ SV75 ) @ ( sdtasdt0 @ SV23 @ SV80 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[439]) ).
thf(475,plain,
! [SV81: $i,SV76: $i,SV23: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV23 )
| ~ ( aNaturalNumber0 @ SV76 )
| ~ ( aNaturalNumber0 @ SV81 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV76 @ SV81 ) @ SV23 )
= ( sdtpldt0 @ ( sdtasdt0 @ SV76 @ SV23 ) @ ( sdtasdt0 @ SV81 @ SV23 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[440]) ).
thf(476,plain,
( ( xm = sz00 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[441]) ).
thf(477,plain,
( ( ~ ( ( xn != sz00 ) )
| ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ xn )
| ~ ( aNaturalNumber0 @ xm ) )
| ~ ( aNaturalNumber0 @ xp ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[442]) ).
thf(478,plain,
! [SV45: $i,SV24: $i] :
( ( ( ( SV24 = SV45 )
| ~ ( sdtlseqdt0 @ SV24 @ SV45 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY135: $i] :
( ~ ( aNaturalNumber0 @ SY135 )
| ( ( sdtpldt0 @ SV24 @ SY135 )
!= ( sdtpldt0 @ SV45 @ SY135 ) ) )
| ~ ~ ( ~ ! [SY136: $i] :
( ~ ( aNaturalNumber0 @ SY136 )
| ( ( sdtpldt0 @ SY136 @ SV24 )
!= ( sdtpldt0 @ SY136 @ SV45 ) ) )
| ~ ! [SY137: $i] :
( ~ ( aNaturalNumber0 @ SY137 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SY137 @ SV24 ) @ ( sdtpldt0 @ SY137 @ SV45 ) ) ) ) )
| ~ ! [SY138: $i] :
( ~ ( aNaturalNumber0 @ SY138 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SV24 @ SY138 ) @ ( sdtpldt0 @ SV45 @ SY138 ) ) ) ) )
= $true )
| ( ( aNaturalNumber0 @ SV24 )
= $false )
| ( ( aNaturalNumber0 @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[443]) ).
thf(479,plain,
! [SV25: $i] :
( ( ( ! [SY122: $i,SY123: $i] :
( ~ ( aNaturalNumber0 @ SY122 )
| ~ ( aNaturalNumber0 @ SY123 )
| ( ( sdtasdt0 @ SV25 @ SY122 )
!= ( sdtasdt0 @ SV25 @ SY123 ) )
| ( SY122 = SY123 ) ) )
= $true )
| ( ( SV25 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[444]) ).
thf(480,plain,
! [SV25: $i] :
( ( ( ! [SY124: $i,SY125: $i] :
( ~ ( aNaturalNumber0 @ SY124 )
| ~ ( aNaturalNumber0 @ SY125 )
| ( ( sdtasdt0 @ SY124 @ SV25 )
!= ( sdtasdt0 @ SY125 @ SV25 ) )
| ( SY124 = SY125 ) ) )
= $true )
| ( ( SV25 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[445]) ).
thf(481,plain,
! [SV65: $i] :
( ( ( ( sz10 != SV65 ) )
= $true )
| ( ( ( SV65 = sz00 )
| ( SV65 = sz10 ) )
= $true )
| ( ( aNaturalNumber0 @ SV65 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[448]) ).
thf(482,plain,
! [SV66: $i] :
( ( ( sdtlseqdt0 @ sz10 @ SV66 )
= $true )
| ( ( ( SV66 = sz00 )
| ( SV66 = sz10 ) )
= $true )
| ( ( aNaturalNumber0 @ SV66 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[449]) ).
thf(483,plain,
! [SV26: $i] :
( ( ( ~ ~ ( ~ ( aNaturalNumber0 @ ( sK1_W1 @ SV26 ) )
| ~ ( doDivides0 @ ( sK1_W1 @ SV26 ) @ SV26 ) ) )
= $false )
| ( ( SV26 = sz10 )
= $true )
| ( ( SV26 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV26 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[450]) ).
thf(484,plain,
! [SV26: $i] :
( ( ( ~ ( isPrime0 @ ( sK1_W1 @ SV26 ) ) )
= $false )
| ( ( SV26 = sz10 )
= $true )
| ( ( SV26 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV26 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[450]) ).
thf(485,plain,
! [SV46: $i,SV27: $i,SV1: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV1 )
| ~ ( aNaturalNumber0 @ SV27 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV46 ) )
= $true )
| ( ( SV1 = sz00 )
= $true )
| ( ( SV27 = sz00 )
= $true )
| ( ( SV46 = sz00 )
= $true )
| ( ( ( ( sdtasdt0 @ SV46 @ ( sdtasdt0 @ SV27 @ SV27 ) )
!= ( sdtasdt0 @ SV1 @ SV1 ) )
| ~ ( iLess0 @ SV1 @ xn )
| ~ ( isPrime0 @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[451]) ).
thf(486,plain,
! [SV47: $i,SV6: $i,SV31: $i] :
( ( ( aNaturalNumber0 @ SV31 )
= $false )
| ( ( aNaturalNumber0 @ SV6 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV47 ) )
= $true )
| ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV6 @ SV31 ) @ SV47 )
= ( sdtpldt0 @ SV6 @ ( sdtpldt0 @ SV31 @ SV47 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[452]) ).
thf(487,plain,
! [SV48: $i,SV8: $i,SV33: $i] :
( ( ( aNaturalNumber0 @ SV33 )
= $false )
| ( ( aNaturalNumber0 @ SV8 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV48 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV8 @ SV33 ) @ SV48 )
= ( sdtasdt0 @ SV8 @ ( sdtasdt0 @ SV33 @ SV48 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[453]) ).
thf(488,plain,
! [SV34: $i,SV9: $i] :
( ( ( ( sdtasdt0 @ SV9 @ SV34 )
= sz00 )
= $false )
| ( ( ( SV9 = sz00 )
| ( SV34 = sz00 ) )
= $true )
| ( ( aNaturalNumber0 @ SV9 )
= $false )
| ( ( aNaturalNumber0 @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[454]) ).
thf(489,plain,
! [SV35: $i,SV11: $i] :
( ( ( ~ ( sdtlseqdt0 @ SV11 @ SV35 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV35 @ SV11 ) )
= $true )
| ( ( SV11 = SV35 )
= $true )
| ( ( aNaturalNumber0 @ SV11 )
= $false )
| ( ( aNaturalNumber0 @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[455]) ).
thf(490,plain,
! [SV49: $i,SV12: $i,SV36: $i] :
( ( ( aNaturalNumber0 @ SV36 )
= $false )
| ( ( aNaturalNumber0 @ SV12 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV49 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV12 @ SV36 )
| ~ ( sdtlseqdt0 @ SV36 @ SV49 )
| ( sdtlseqdt0 @ SV12 @ SV49 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[456]) ).
thf(491,plain,
! [SV38: $i,SV14: $i] :
( ( ( SV14 = SV38 )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV14 @ SV38 ) )
= $true )
| ( ( iLess0 @ SV14 @ SV38 )
= $true )
| ( ( aNaturalNumber0 @ SV14 )
= $false )
| ( ( aNaturalNumber0 @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[458]) ).
thf(492,plain,
! [SV51: $i,SV15: $i,SV39: $i] :
( ( ( aNaturalNumber0 @ SV39 )
= $false )
| ( ( aNaturalNumber0 @ SV15 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV51 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV15 @ SV39 )
| ~ ( doDivides0 @ SV39 @ SV51 )
| ( doDivides0 @ SV15 @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[459]) ).
thf(493,plain,
! [SV52: $i,SV16: $i,SV40: $i] :
( ( ( aNaturalNumber0 @ SV40 )
= $false )
| ( ( aNaturalNumber0 @ SV16 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV52 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV16 @ SV40 )
| ~ ( doDivides0 @ SV16 @ SV52 )
| ( doDivides0 @ SV16 @ ( sdtpldt0 @ SV40 @ SV52 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[460]) ).
thf(494,plain,
! [SV53: $i,SV17: $i,SV41: $i] :
( ( ( aNaturalNumber0 @ SV41 )
= $false )
| ( ( aNaturalNumber0 @ SV17 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV53 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV17 @ SV41 )
| ~ ( doDivides0 @ SV17 @ ( sdtpldt0 @ SV41 @ SV53 ) )
| ( doDivides0 @ SV17 @ SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[461]) ).
thf(495,plain,
! [SV18: $i,SV42: $i] :
( ( ( SV42 = sz00 )
= $true )
| ( ( ~ ( doDivides0 @ SV18 @ SV42 ) )
= $true )
| ( ( sdtlseqdt0 @ SV18 @ SV42 )
= $true )
| ( ( aNaturalNumber0 @ SV18 )
= $false )
| ( ( aNaturalNumber0 @ SV42 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[462]) ).
thf(496,plain,
! [SV43: $i,SV19: $i] :
( ( ( SV19 = sz00 )
= $true )
| ( ( ~ ( doDivides0 @ SV19 @ SV43 ) )
= $true )
| ( ( ! [SY133: $i] :
( ~ ( aNaturalNumber0 @ SY133 )
| ( ( sdtasdt0 @ SY133 @ ( sdtsldt0 @ SV43 @ SV19 ) )
= ( sdtsldt0 @ ( sdtasdt0 @ SY133 @ SV43 ) @ SV19 ) ) ) )
= $true )
| ( ( aNaturalNumber0 @ SV19 )
= $false )
| ( ( aNaturalNumber0 @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[463]) ).
thf(497,plain,
! [SV54: $i,SV20: $i,SV44: $i] :
( ( ( aNaturalNumber0 @ SV44 )
= $false )
| ( ( aNaturalNumber0 @ SV20 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV54 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV54 @ ( sdtasdt0 @ SV20 @ SV44 ) )
| ~ ( isPrime0 @ SV54 )
| ( doDivides0 @ SV54 @ SV20 )
| ( doDivides0 @ SV54 @ SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[464]) ).
thf(498,plain,
! [SV77: $i,SV68: $i,SV21: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV21 )
| ~ ( aNaturalNumber0 @ SV68 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV77 ) )
= $true )
| ( ( ( ( sdtpldt0 @ SV21 @ SV68 )
!= ( sdtpldt0 @ SV21 @ SV77 ) )
| ( SV68 = SV77 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[465]) ).
thf(499,plain,
! [SV78: $i,SV69: $i,SV21: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV21 )
| ~ ( aNaturalNumber0 @ SV69 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV78 ) )
= $true )
| ( ( ( ( sdtpldt0 @ SV69 @ SV21 )
!= ( sdtpldt0 @ SV78 @ SV21 ) )
| ( SV69 = SV78 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[466]) ).
thf(500,plain,
! [SV82: $i,SV22: $i] :
( ( ! [SY148: $i] :
( ~ ( aNaturalNumber0 @ SV22 )
| ~ ( aNaturalNumber0 @ SV82 )
| ~ ( aNaturalNumber0 @ SY148 )
| ( SV22 = sz00 )
| ( SV82 = SY148 )
| ~ ( sdtlseqdt0 @ SV82 @ SY148 )
| ( ( sdtasdt0 @ SV82 @ SV22 )
!= ( sdtasdt0 @ SY148 @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[467]) ).
thf(501,plain,
! [SV22: $i] :
( ( ~ ! [SY107: $i,SY108: $i] :
( ~ ( aNaturalNumber0 @ SV22 )
| ~ ( aNaturalNumber0 @ SY107 )
| ~ ( aNaturalNumber0 @ SY108 )
| ( SV22 = sz00 )
| ( SY107 = SY108 )
| ~ ( sdtlseqdt0 @ SY107 @ SY108 )
| ( ( sdtasdt0 @ SV22 @ SY107 )
!= ( sdtasdt0 @ SV22 @ SY108 ) ) )
| ~ ! [SY109: $i,SY110: $i] :
( ~ ( aNaturalNumber0 @ SV22 )
| ~ ( aNaturalNumber0 @ SY109 )
| ~ ( aNaturalNumber0 @ SY110 )
| ( SV22 = sz00 )
| ( SY109 = SY110 )
| ~ ( sdtlseqdt0 @ SY109 @ SY110 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV22 @ SY109 ) @ ( sdtasdt0 @ SV22 @ SY110 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[468]) ).
thf(502,plain,
! [SV79: $i,SV70: $i,SV22: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV22 )
| ~ ( aNaturalNumber0 @ SV70 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV79 ) )
= $true )
| ( ( ( SV22 = sz00 )
| ( SV70 = SV79 )
| ~ ( sdtlseqdt0 @ SV70 @ SV79 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV70 @ SV22 ) @ ( sdtasdt0 @ SV79 @ SV22 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[469]) ).
thf(503,plain,
! [SV71: $i,SV57: $i] :
( ( ( aNaturalNumber0 @ SV57 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV71 ) )
= $true )
| ( ( ( ( sdtpldt0 @ SV57 @ SV71 )
!= sz00 )
| ( SV57 = sz00 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[470]) ).
thf(504,plain,
! [SV72: $i,SV58: $i] :
( ( ( aNaturalNumber0 @ SV58 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV72 ) )
= $true )
| ( ( ( ( sdtpldt0 @ SV58 @ SV72 )
!= sz00 )
| ( SV72 = sz00 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[471]) ).
thf(505,plain,
! [SV73: $i,SV61: $i] :
( ( ( aNaturalNumber0 @ SV61 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV73 ) )
= $true )
| ( ( ( SV73 != SV61 )
| ( sdtlseqdt0 @ SV61 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[472]) ).
thf(506,plain,
! [SV74: $i,SV62: $i] :
( ( ( aNaturalNumber0 @ SV62 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV74 ) )
= $true )
| ( ( ( sdtlseqdt0 @ SV74 @ SV62 )
| ( sdtlseqdt0 @ SV62 @ SV74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[473]) ).
thf(507,plain,
! [SV80: $i,SV75: $i,SV23: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV23 )
| ~ ( aNaturalNumber0 @ SV75 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV80 ) )
= $true )
| ( ( ( sdtasdt0 @ SV23 @ ( sdtpldt0 @ SV75 @ SV80 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV23 @ SV75 ) @ ( sdtasdt0 @ SV23 @ SV80 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[474]) ).
thf(508,plain,
! [SV81: $i,SV76: $i,SV23: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV23 )
| ~ ( aNaturalNumber0 @ SV76 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV81 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV76 @ SV81 ) @ SV23 )
= ( sdtpldt0 @ ( sdtasdt0 @ SV76 @ SV23 ) @ ( sdtasdt0 @ SV81 @ SV23 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[475]) ).
thf(509,plain,
( ( ~ ( ( xn != sz00 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[477]) ).
thf(510,plain,
( ( ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ xn )
| ~ ( aNaturalNumber0 @ xm ) )
| ~ ( aNaturalNumber0 @ xp ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[477]) ).
thf(511,plain,
! [SV45: $i,SV24: $i] :
( ( ( SV24 = SV45 )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV24 @ SV45 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY135: $i] :
( ~ ( aNaturalNumber0 @ SY135 )
| ( ( sdtpldt0 @ SV24 @ SY135 )
!= ( sdtpldt0 @ SV45 @ SY135 ) ) )
| ~ ~ ( ~ ! [SY136: $i] :
( ~ ( aNaturalNumber0 @ SY136 )
| ( ( sdtpldt0 @ SY136 @ SV24 )
!= ( sdtpldt0 @ SY136 @ SV45 ) ) )
| ~ ! [SY137: $i] :
( ~ ( aNaturalNumber0 @ SY137 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SY137 @ SV24 ) @ ( sdtpldt0 @ SY137 @ SV45 ) ) ) ) )
| ~ ! [SY138: $i] :
( ~ ( aNaturalNumber0 @ SY138 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SV24 @ SY138 ) @ ( sdtpldt0 @ SV45 @ SY138 ) ) ) ) )
= $true )
| ( ( aNaturalNumber0 @ SV24 )
= $false )
| ( ( aNaturalNumber0 @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[478]) ).
thf(512,plain,
! [SV25: $i,SV83: $i] :
( ( ( ! [SY149: $i] :
( ~ ( aNaturalNumber0 @ SV83 )
| ~ ( aNaturalNumber0 @ SY149 )
| ( ( sdtasdt0 @ SV25 @ SV83 )
!= ( sdtasdt0 @ SV25 @ SY149 ) )
| ( SV83 = SY149 ) ) )
= $true )
| ( ( SV25 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV25 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[479]) ).
thf(513,plain,
! [SV25: $i,SV84: $i] :
( ( ( ! [SY150: $i] :
( ~ ( aNaturalNumber0 @ SV84 )
| ~ ( aNaturalNumber0 @ SY150 )
| ( ( sdtasdt0 @ SV84 @ SV25 )
!= ( sdtasdt0 @ SY150 @ SV25 ) )
| ( SV84 = SY150 ) ) )
= $true )
| ( ( SV25 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV25 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[480]) ).
thf(514,plain,
! [SV65: $i] :
( ( ( sz10 = SV65 )
= $false )
| ( ( ( SV65 = sz00 )
| ( SV65 = sz10 ) )
= $true )
| ( ( aNaturalNumber0 @ SV65 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[481]) ).
thf(515,plain,
! [SV66: $i] :
( ( ( SV66 = sz00 )
= $true )
| ( ( SV66 = sz10 )
= $true )
| ( ( sdtlseqdt0 @ sz10 @ SV66 )
= $true )
| ( ( aNaturalNumber0 @ SV66 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[482]) ).
thf(516,plain,
! [SV26: $i] :
( ( ( ~ ( ~ ( aNaturalNumber0 @ ( sK1_W1 @ SV26 ) )
| ~ ( doDivides0 @ ( sK1_W1 @ SV26 ) @ SV26 ) ) )
= $true )
| ( ( SV26 = sz10 )
= $true )
| ( ( SV26 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV26 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[483]) ).
thf(517,plain,
! [SV26: $i] :
( ( ( isPrime0 @ ( sK1_W1 @ SV26 ) )
= $true )
| ( ( SV26 = sz10 )
= $true )
| ( ( SV26 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV26 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[484]) ).
thf(518,plain,
! [SV46: $i,SV27: $i,SV1: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV1 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV27 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV46 ) )
= $true )
| ( ( SV1 = sz00 )
= $true )
| ( ( SV27 = sz00 )
= $true )
| ( ( SV46 = sz00 )
= $true )
| ( ( ( ( sdtasdt0 @ SV46 @ ( sdtasdt0 @ SV27 @ SV27 ) )
!= ( sdtasdt0 @ SV1 @ SV1 ) )
| ~ ( iLess0 @ SV1 @ xn )
| ~ ( isPrime0 @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[485]) ).
thf(519,plain,
! [SV31: $i,SV6: $i,SV47: $i] :
( ( ( aNaturalNumber0 @ SV47 )
= $false )
| ( ( aNaturalNumber0 @ SV6 )
= $false )
| ( ( aNaturalNumber0 @ SV31 )
= $false )
| ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV6 @ SV31 ) @ SV47 )
= ( sdtpldt0 @ SV6 @ ( sdtpldt0 @ SV31 @ SV47 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[486]) ).
thf(520,plain,
! [SV33: $i,SV8: $i,SV48: $i] :
( ( ( aNaturalNumber0 @ SV48 )
= $false )
| ( ( aNaturalNumber0 @ SV8 )
= $false )
| ( ( aNaturalNumber0 @ SV33 )
= $false )
| ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV8 @ SV33 ) @ SV48 )
= ( sdtasdt0 @ SV8 @ ( sdtasdt0 @ SV33 @ SV48 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[487]) ).
thf(521,plain,
! [SV34: $i,SV9: $i] :
( ( ( SV9 = sz00 )
= $true )
| ( ( SV34 = sz00 )
= $true )
| ( ( ( sdtasdt0 @ SV9 @ SV34 )
= sz00 )
= $false )
| ( ( aNaturalNumber0 @ SV9 )
= $false )
| ( ( aNaturalNumber0 @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[488]) ).
thf(522,plain,
! [SV35: $i,SV11: $i] :
( ( ( sdtlseqdt0 @ SV11 @ SV35 )
= $false )
| ( ( ~ ( sdtlseqdt0 @ SV35 @ SV11 ) )
= $true )
| ( ( SV11 = SV35 )
= $true )
| ( ( aNaturalNumber0 @ SV11 )
= $false )
| ( ( aNaturalNumber0 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[489]) ).
thf(523,plain,
! [SV36: $i,SV12: $i,SV49: $i] :
( ( ( aNaturalNumber0 @ SV49 )
= $false )
| ( ( aNaturalNumber0 @ SV12 )
= $false )
| ( ( aNaturalNumber0 @ SV36 )
= $false )
| ( ( ~ ( sdtlseqdt0 @ SV12 @ SV36 )
| ~ ( sdtlseqdt0 @ SV36 @ SV49 )
| ( sdtlseqdt0 @ SV12 @ SV49 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[490]) ).
thf(524,plain,
! [SV38: $i,SV14: $i] :
( ( ( sdtlseqdt0 @ SV14 @ SV38 )
= $false )
| ( ( SV14 = SV38 )
= $true )
| ( ( iLess0 @ SV14 @ SV38 )
= $true )
| ( ( aNaturalNumber0 @ SV14 )
= $false )
| ( ( aNaturalNumber0 @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[491]) ).
thf(525,plain,
! [SV39: $i,SV15: $i,SV51: $i] :
( ( ( aNaturalNumber0 @ SV51 )
= $false )
| ( ( aNaturalNumber0 @ SV15 )
= $false )
| ( ( aNaturalNumber0 @ SV39 )
= $false )
| ( ( ~ ( doDivides0 @ SV15 @ SV39 )
| ~ ( doDivides0 @ SV39 @ SV51 )
| ( doDivides0 @ SV15 @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[492]) ).
thf(526,plain,
! [SV40: $i,SV16: $i,SV52: $i] :
( ( ( aNaturalNumber0 @ SV52 )
= $false )
| ( ( aNaturalNumber0 @ SV16 )
= $false )
| ( ( aNaturalNumber0 @ SV40 )
= $false )
| ( ( ~ ( doDivides0 @ SV16 @ SV40 )
| ~ ( doDivides0 @ SV16 @ SV52 )
| ( doDivides0 @ SV16 @ ( sdtpldt0 @ SV40 @ SV52 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[493]) ).
thf(527,plain,
! [SV41: $i,SV17: $i,SV53: $i] :
( ( ( aNaturalNumber0 @ SV53 )
= $false )
| ( ( aNaturalNumber0 @ SV17 )
= $false )
| ( ( aNaturalNumber0 @ SV41 )
= $false )
| ( ( ~ ( doDivides0 @ SV17 @ SV41 )
| ~ ( doDivides0 @ SV17 @ ( sdtpldt0 @ SV41 @ SV53 ) )
| ( doDivides0 @ SV17 @ SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[494]) ).
thf(528,plain,
! [SV42: $i,SV18: $i] :
( ( ( doDivides0 @ SV18 @ SV42 )
= $false )
| ( ( SV42 = sz00 )
= $true )
| ( ( sdtlseqdt0 @ SV18 @ SV42 )
= $true )
| ( ( aNaturalNumber0 @ SV18 )
= $false )
| ( ( aNaturalNumber0 @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[495]) ).
thf(529,plain,
! [SV43: $i,SV19: $i] :
( ( ( doDivides0 @ SV19 @ SV43 )
= $false )
| ( ( SV19 = sz00 )
= $true )
| ( ( ! [SY133: $i] :
( ~ ( aNaturalNumber0 @ SY133 )
| ( ( sdtasdt0 @ SY133 @ ( sdtsldt0 @ SV43 @ SV19 ) )
= ( sdtsldt0 @ ( sdtasdt0 @ SY133 @ SV43 ) @ SV19 ) ) ) )
= $true )
| ( ( aNaturalNumber0 @ SV19 )
= $false )
| ( ( aNaturalNumber0 @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[496]) ).
thf(530,plain,
! [SV44: $i,SV20: $i,SV54: $i] :
( ( ( aNaturalNumber0 @ SV54 )
= $false )
| ( ( aNaturalNumber0 @ SV20 )
= $false )
| ( ( aNaturalNumber0 @ SV44 )
= $false )
| ( ( ~ ( doDivides0 @ SV54 @ ( sdtasdt0 @ SV20 @ SV44 ) )
| ~ ( isPrime0 @ SV54 )
| ( doDivides0 @ SV54 @ SV20 )
| ( doDivides0 @ SV54 @ SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[497]) ).
thf(531,plain,
! [SV77: $i,SV68: $i,SV21: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV21 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV68 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV77 ) )
= $true )
| ( ( ( ( sdtpldt0 @ SV21 @ SV68 )
!= ( sdtpldt0 @ SV21 @ SV77 ) )
| ( SV68 = SV77 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[498]) ).
thf(532,plain,
! [SV78: $i,SV69: $i,SV21: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV21 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV69 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV78 ) )
= $true )
| ( ( ( ( sdtpldt0 @ SV69 @ SV21 )
!= ( sdtpldt0 @ SV78 @ SV21 ) )
| ( SV69 = SV78 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[499]) ).
thf(533,plain,
! [SV85: $i,SV82: $i,SV22: $i] :
( ( ~ ( aNaturalNumber0 @ SV22 )
| ~ ( aNaturalNumber0 @ SV82 )
| ~ ( aNaturalNumber0 @ SV85 )
| ( SV22 = sz00 )
| ( SV82 = SV85 )
| ~ ( sdtlseqdt0 @ SV82 @ SV85 )
| ( ( sdtasdt0 @ SV82 @ SV22 )
!= ( sdtasdt0 @ SV85 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[500]) ).
thf(534,plain,
! [SV22: $i] :
( ( ~ ! [SY107: $i,SY108: $i] :
( ~ ( aNaturalNumber0 @ SV22 )
| ~ ( aNaturalNumber0 @ SY107 )
| ~ ( aNaturalNumber0 @ SY108 )
| ( SV22 = sz00 )
| ( SY107 = SY108 )
| ~ ( sdtlseqdt0 @ SY107 @ SY108 )
| ( ( sdtasdt0 @ SV22 @ SY107 )
!= ( sdtasdt0 @ SV22 @ SY108 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[501]) ).
thf(535,plain,
! [SV22: $i] :
( ( ~ ! [SY109: $i,SY110: $i] :
( ~ ( aNaturalNumber0 @ SV22 )
| ~ ( aNaturalNumber0 @ SY109 )
| ~ ( aNaturalNumber0 @ SY110 )
| ( SV22 = sz00 )
| ( SY109 = SY110 )
| ~ ( sdtlseqdt0 @ SY109 @ SY110 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV22 @ SY109 ) @ ( sdtasdt0 @ SV22 @ SY110 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[501]) ).
thf(536,plain,
! [SV79: $i,SV70: $i,SV22: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV22 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV70 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV79 ) )
= $true )
| ( ( ( SV22 = sz00 )
| ( SV70 = SV79 )
| ~ ( sdtlseqdt0 @ SV70 @ SV79 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV70 @ SV22 ) @ ( sdtasdt0 @ SV79 @ SV22 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[502]) ).
thf(537,plain,
! [SV57: $i,SV71: $i] :
( ( ( aNaturalNumber0 @ SV71 )
= $false )
| ( ( aNaturalNumber0 @ SV57 )
= $false )
| ( ( ( ( sdtpldt0 @ SV57 @ SV71 )
!= sz00 )
| ( SV57 = sz00 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[503]) ).
thf(538,plain,
! [SV58: $i,SV72: $i] :
( ( ( aNaturalNumber0 @ SV72 )
= $false )
| ( ( aNaturalNumber0 @ SV58 )
= $false )
| ( ( ( ( sdtpldt0 @ SV58 @ SV72 )
!= sz00 )
| ( SV72 = sz00 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[504]) ).
thf(539,plain,
! [SV61: $i,SV73: $i] :
( ( ( aNaturalNumber0 @ SV73 )
= $false )
| ( ( aNaturalNumber0 @ SV61 )
= $false )
| ( ( ( SV73 != SV61 )
| ( sdtlseqdt0 @ SV61 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[505]) ).
thf(540,plain,
! [SV62: $i,SV74: $i] :
( ( ( aNaturalNumber0 @ SV74 )
= $false )
| ( ( aNaturalNumber0 @ SV62 )
= $false )
| ( ( ( sdtlseqdt0 @ SV74 @ SV62 )
| ( sdtlseqdt0 @ SV62 @ SV74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[506]) ).
thf(541,plain,
! [SV80: $i,SV75: $i,SV23: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV23 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV75 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV80 ) )
= $true )
| ( ( ( sdtasdt0 @ SV23 @ ( sdtpldt0 @ SV75 @ SV80 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV23 @ SV75 ) @ ( sdtasdt0 @ SV23 @ SV80 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[507]) ).
thf(542,plain,
! [SV81: $i,SV76: $i,SV23: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV23 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV76 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV81 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV76 @ SV81 ) @ SV23 )
= ( sdtpldt0 @ ( sdtasdt0 @ SV76 @ SV23 ) @ ( sdtasdt0 @ SV81 @ SV23 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[508]) ).
thf(543,plain,
( ( ( xn != sz00 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[509]) ).
thf(544,plain,
( ( ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ xn )
| ~ ( aNaturalNumber0 @ xm ) )
| ~ ( aNaturalNumber0 @ xp ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[510]) ).
thf(545,plain,
! [SV45: $i,SV24: $i] :
( ( ( sdtlseqdt0 @ SV24 @ SV45 )
= $false )
| ( ( SV24 = SV45 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY135: $i] :
( ~ ( aNaturalNumber0 @ SY135 )
| ( ( sdtpldt0 @ SV24 @ SY135 )
!= ( sdtpldt0 @ SV45 @ SY135 ) ) )
| ~ ~ ( ~ ! [SY136: $i] :
( ~ ( aNaturalNumber0 @ SY136 )
| ( ( sdtpldt0 @ SY136 @ SV24 )
!= ( sdtpldt0 @ SY136 @ SV45 ) ) )
| ~ ! [SY137: $i] :
( ~ ( aNaturalNumber0 @ SY137 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SY137 @ SV24 ) @ ( sdtpldt0 @ SY137 @ SV45 ) ) ) ) )
| ~ ! [SY138: $i] :
( ~ ( aNaturalNumber0 @ SY138 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SV24 @ SY138 ) @ ( sdtpldt0 @ SV45 @ SY138 ) ) ) ) )
= $true )
| ( ( aNaturalNumber0 @ SV24 )
= $false )
| ( ( aNaturalNumber0 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[511]) ).
thf(546,plain,
! [SV25: $i,SV86: $i,SV83: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV83 )
| ~ ( aNaturalNumber0 @ SV86 )
| ( ( sdtasdt0 @ SV25 @ SV83 )
!= ( sdtasdt0 @ SV25 @ SV86 ) )
| ( SV83 = SV86 ) )
= $true )
| ( ( SV25 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV25 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[512]) ).
thf(547,plain,
! [SV25: $i,SV87: $i,SV84: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV84 )
| ~ ( aNaturalNumber0 @ SV87 )
| ( ( sdtasdt0 @ SV84 @ SV25 )
!= ( sdtasdt0 @ SV87 @ SV25 ) )
| ( SV84 = SV87 ) )
= $true )
| ( ( SV25 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV25 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[513]) ).
thf(548,plain,
! [SV65: $i] :
( ( ( SV65 = sz00 )
= $true )
| ( ( SV65 = sz10 )
= $true )
| ( ( sz10 = SV65 )
= $false )
| ( ( aNaturalNumber0 @ SV65 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[514]) ).
thf(549,plain,
! [SV26: $i] :
( ( ( ~ ( aNaturalNumber0 @ ( sK1_W1 @ SV26 ) )
| ~ ( doDivides0 @ ( sK1_W1 @ SV26 ) @ SV26 ) )
= $false )
| ( ( SV26 = sz10 )
= $true )
| ( ( SV26 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[516]) ).
thf(550,plain,
! [SV46: $i,SV27: $i,SV1: $i] :
( ( ( aNaturalNumber0 @ SV1 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV27 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV46 ) )
= $true )
| ( ( SV1 = sz00 )
= $true )
| ( ( SV27 = sz00 )
= $true )
| ( ( SV46 = sz00 )
= $true )
| ( ( ( ( sdtasdt0 @ SV46 @ ( sdtasdt0 @ SV27 @ SV27 ) )
!= ( sdtasdt0 @ SV1 @ SV1 ) )
| ~ ( iLess0 @ SV1 @ xn )
| ~ ( isPrime0 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[518]) ).
thf(551,plain,
! [SV11: $i,SV35: $i] :
( ( ( sdtlseqdt0 @ SV35 @ SV11 )
= $false )
| ( ( sdtlseqdt0 @ SV11 @ SV35 )
= $false )
| ( ( SV11 = SV35 )
= $true )
| ( ( aNaturalNumber0 @ SV11 )
= $false )
| ( ( aNaturalNumber0 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[522]) ).
thf(552,plain,
! [SV49: $i,SV36: $i,SV12: $i] :
( ( ( ~ ( sdtlseqdt0 @ SV12 @ SV36 )
| ~ ( sdtlseqdt0 @ SV36 @ SV49 ) )
= $true )
| ( ( sdtlseqdt0 @ SV12 @ SV49 )
= $true )
| ( ( aNaturalNumber0 @ SV36 )
= $false )
| ( ( aNaturalNumber0 @ SV12 )
= $false )
| ( ( aNaturalNumber0 @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[523]) ).
thf(553,plain,
! [SV51: $i,SV39: $i,SV15: $i] :
( ( ( ~ ( doDivides0 @ SV15 @ SV39 )
| ~ ( doDivides0 @ SV39 @ SV51 ) )
= $true )
| ( ( doDivides0 @ SV15 @ SV51 )
= $true )
| ( ( aNaturalNumber0 @ SV39 )
= $false )
| ( ( aNaturalNumber0 @ SV15 )
= $false )
| ( ( aNaturalNumber0 @ SV51 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[525]) ).
thf(554,plain,
! [SV52: $i,SV40: $i,SV16: $i] :
( ( ( ~ ( doDivides0 @ SV16 @ SV40 )
| ~ ( doDivides0 @ SV16 @ SV52 ) )
= $true )
| ( ( doDivides0 @ SV16 @ ( sdtpldt0 @ SV40 @ SV52 ) )
= $true )
| ( ( aNaturalNumber0 @ SV40 )
= $false )
| ( ( aNaturalNumber0 @ SV16 )
= $false )
| ( ( aNaturalNumber0 @ SV52 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[526]) ).
thf(555,plain,
! [SV53: $i,SV41: $i,SV17: $i] :
( ( ( ~ ( doDivides0 @ SV17 @ SV41 )
| ~ ( doDivides0 @ SV17 @ ( sdtpldt0 @ SV41 @ SV53 ) ) )
= $true )
| ( ( doDivides0 @ SV17 @ SV53 )
= $true )
| ( ( aNaturalNumber0 @ SV41 )
= $false )
| ( ( aNaturalNumber0 @ SV17 )
= $false )
| ( ( aNaturalNumber0 @ SV53 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[527]) ).
thf(556,plain,
! [SV19: $i,SV43: $i,SV88: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV88 )
| ( ( sdtasdt0 @ SV88 @ ( sdtsldt0 @ SV43 @ SV19 ) )
= ( sdtsldt0 @ ( sdtasdt0 @ SV88 @ SV43 ) @ SV19 ) ) )
= $true )
| ( ( SV19 = sz00 )
= $true )
| ( ( doDivides0 @ SV19 @ SV43 )
= $false )
| ( ( aNaturalNumber0 @ SV19 )
= $false )
| ( ( aNaturalNumber0 @ SV43 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[529]) ).
thf(557,plain,
! [SV44: $i,SV20: $i,SV54: $i] :
( ( ( ~ ( doDivides0 @ SV54 @ ( sdtasdt0 @ SV20 @ SV44 ) )
| ~ ( isPrime0 @ SV54 ) )
= $true )
| ( ( ( doDivides0 @ SV54 @ SV20 )
| ( doDivides0 @ SV54 @ SV44 ) )
= $true )
| ( ( aNaturalNumber0 @ SV44 )
= $false )
| ( ( aNaturalNumber0 @ SV20 )
= $false )
| ( ( aNaturalNumber0 @ SV54 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[530]) ).
thf(558,plain,
! [SV77: $i,SV68: $i,SV21: $i] :
( ( ( aNaturalNumber0 @ SV21 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV68 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV77 ) )
= $true )
| ( ( ( ( sdtpldt0 @ SV21 @ SV68 )
!= ( sdtpldt0 @ SV21 @ SV77 ) )
| ( SV68 = SV77 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[531]) ).
thf(559,plain,
! [SV78: $i,SV69: $i,SV21: $i] :
( ( ( aNaturalNumber0 @ SV21 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV69 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV78 ) )
= $true )
| ( ( ( ( sdtpldt0 @ SV69 @ SV21 )
!= ( sdtpldt0 @ SV78 @ SV21 ) )
| ( SV69 = SV78 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[532]) ).
thf(560,plain,
! [SV85: $i,SV82: $i,SV22: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV22 )
| ~ ( aNaturalNumber0 @ SV82 )
| ~ ( aNaturalNumber0 @ SV85 ) )
= $true )
| ( ( ( SV22 = sz00 )
| ( SV82 = SV85 )
| ~ ( sdtlseqdt0 @ SV82 @ SV85 )
| ( ( sdtasdt0 @ SV82 @ SV22 )
!= ( sdtasdt0 @ SV85 @ SV22 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[533]) ).
thf(561,plain,
! [SV22: $i] :
( ( ! [SY107: $i,SY108: $i] :
( ~ ( aNaturalNumber0 @ SV22 )
| ~ ( aNaturalNumber0 @ SY107 )
| ~ ( aNaturalNumber0 @ SY108 )
| ( SV22 = sz00 )
| ( SY107 = SY108 )
| ~ ( sdtlseqdt0 @ SY107 @ SY108 )
| ( ( sdtasdt0 @ SV22 @ SY107 )
!= ( sdtasdt0 @ SV22 @ SY108 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[534]) ).
thf(562,plain,
! [SV22: $i] :
( ( ! [SY109: $i,SY110: $i] :
( ~ ( aNaturalNumber0 @ SV22 )
| ~ ( aNaturalNumber0 @ SY109 )
| ~ ( aNaturalNumber0 @ SY110 )
| ( SV22 = sz00 )
| ( SY109 = SY110 )
| ~ ( sdtlseqdt0 @ SY109 @ SY110 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV22 @ SY109 ) @ ( sdtasdt0 @ SV22 @ SY110 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[535]) ).
thf(563,plain,
! [SV79: $i,SV70: $i,SV22: $i] :
( ( ( aNaturalNumber0 @ SV22 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV70 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV79 ) )
= $true )
| ( ( ( SV22 = sz00 )
| ( SV70 = SV79 )
| ~ ( sdtlseqdt0 @ SV70 @ SV79 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV70 @ SV22 ) @ ( sdtasdt0 @ SV79 @ SV22 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[536]) ).
thf(564,plain,
! [SV71: $i,SV57: $i] :
( ( ( ( ( sdtpldt0 @ SV57 @ SV71 )
!= sz00 ) )
= $true )
| ( ( SV57 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV57 )
= $false )
| ( ( aNaturalNumber0 @ SV71 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[537]) ).
thf(565,plain,
! [SV72: $i,SV58: $i] :
( ( ( ( ( sdtpldt0 @ SV58 @ SV72 )
!= sz00 ) )
= $true )
| ( ( SV72 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV58 )
= $false )
| ( ( aNaturalNumber0 @ SV72 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[538]) ).
thf(566,plain,
! [SV61: $i,SV73: $i] :
( ( ( ( SV73 != SV61 ) )
= $true )
| ( ( sdtlseqdt0 @ SV61 @ SV73 )
= $true )
| ( ( aNaturalNumber0 @ SV61 )
= $false )
| ( ( aNaturalNumber0 @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[539]) ).
thf(567,plain,
! [SV62: $i,SV74: $i] :
( ( ( sdtlseqdt0 @ SV74 @ SV62 )
= $true )
| ( ( sdtlseqdt0 @ SV62 @ SV74 )
= $true )
| ( ( aNaturalNumber0 @ SV62 )
= $false )
| ( ( aNaturalNumber0 @ SV74 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[540]) ).
thf(568,plain,
! [SV80: $i,SV75: $i,SV23: $i] :
( ( ( aNaturalNumber0 @ SV23 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV75 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV80 ) )
= $true )
| ( ( ( sdtasdt0 @ SV23 @ ( sdtpldt0 @ SV75 @ SV80 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV23 @ SV75 ) @ ( sdtasdt0 @ SV23 @ SV80 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[541]) ).
thf(569,plain,
! [SV81: $i,SV76: $i,SV23: $i] :
( ( ( aNaturalNumber0 @ SV23 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV76 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV81 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV76 @ SV81 ) @ SV23 )
= ( sdtpldt0 @ ( sdtasdt0 @ SV76 @ SV23 ) @ ( sdtasdt0 @ SV81 @ SV23 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[542]) ).
thf(570,plain,
( ( xn = sz00 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[543]) ).
thf(571,plain,
( ( ~ ~ ( ~ ( aNaturalNumber0 @ xn )
| ~ ( aNaturalNumber0 @ xm ) )
| ~ ( aNaturalNumber0 @ xp ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[544]) ).
thf(572,plain,
! [SV45: $i,SV24: $i] :
( ( ( ~ ~ ( ~ ! [SY135: $i] :
( ~ ( aNaturalNumber0 @ SY135 )
| ( ( sdtpldt0 @ SV24 @ SY135 )
!= ( sdtpldt0 @ SV45 @ SY135 ) ) )
| ~ ~ ( ~ ! [SY136: $i] :
( ~ ( aNaturalNumber0 @ SY136 )
| ( ( sdtpldt0 @ SY136 @ SV24 )
!= ( sdtpldt0 @ SY136 @ SV45 ) ) )
| ~ ! [SY137: $i] :
( ~ ( aNaturalNumber0 @ SY137 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SY137 @ SV24 ) @ ( sdtpldt0 @ SY137 @ SV45 ) ) ) ) )
| ~ ! [SY138: $i] :
( ~ ( aNaturalNumber0 @ SY138 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SV24 @ SY138 ) @ ( sdtpldt0 @ SV45 @ SY138 ) ) ) )
= $false )
| ( ( SV24 = SV45 )
= $true )
| ( ( sdtlseqdt0 @ SV24 @ SV45 )
= $false )
| ( ( aNaturalNumber0 @ SV24 )
= $false )
| ( ( aNaturalNumber0 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[545]) ).
thf(573,plain,
! [SV25: $i,SV86: $i,SV83: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV83 )
| ~ ( aNaturalNumber0 @ SV86 ) )
= $true )
| ( ( ( ( sdtasdt0 @ SV25 @ SV83 )
!= ( sdtasdt0 @ SV25 @ SV86 ) )
| ( SV83 = SV86 ) )
= $true )
| ( ( SV25 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[546]) ).
thf(574,plain,
! [SV25: $i,SV87: $i,SV84: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV84 )
| ~ ( aNaturalNumber0 @ SV87 ) )
= $true )
| ( ( ( ( sdtasdt0 @ SV84 @ SV25 )
!= ( sdtasdt0 @ SV87 @ SV25 ) )
| ( SV84 = SV87 ) )
= $true )
| ( ( SV25 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[547]) ).
thf(575,plain,
! [SV26: $i] :
( ( ( ~ ( aNaturalNumber0 @ ( sK1_W1 @ SV26 ) ) )
= $false )
| ( ( SV26 = sz10 )
= $true )
| ( ( SV26 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV26 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[549]) ).
thf(576,plain,
! [SV26: $i] :
( ( ( ~ ( doDivides0 @ ( sK1_W1 @ SV26 ) @ SV26 ) )
= $false )
| ( ( SV26 = sz10 )
= $true )
| ( ( SV26 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV26 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[549]) ).
thf(577,plain,
! [SV46: $i,SV1: $i,SV27: $i] :
( ( ( aNaturalNumber0 @ SV27 )
= $false )
| ( ( aNaturalNumber0 @ SV1 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV46 ) )
= $true )
| ( ( SV1 = sz00 )
= $true )
| ( ( SV27 = sz00 )
= $true )
| ( ( SV46 = sz00 )
= $true )
| ( ( ( ( sdtasdt0 @ SV46 @ ( sdtasdt0 @ SV27 @ SV27 ) )
!= ( sdtasdt0 @ SV1 @ SV1 ) )
| ~ ( iLess0 @ SV1 @ xn )
| ~ ( isPrime0 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[550]) ).
thf(578,plain,
! [SV49: $i,SV36: $i,SV12: $i] :
( ( ( ~ ( sdtlseqdt0 @ SV12 @ SV36 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV36 @ SV49 ) )
= $true )
| ( ( sdtlseqdt0 @ SV12 @ SV49 )
= $true )
| ( ( aNaturalNumber0 @ SV36 )
= $false )
| ( ( aNaturalNumber0 @ SV12 )
= $false )
| ( ( aNaturalNumber0 @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[552]) ).
thf(579,plain,
! [SV51: $i,SV39: $i,SV15: $i] :
( ( ( ~ ( doDivides0 @ SV15 @ SV39 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV39 @ SV51 ) )
= $true )
| ( ( doDivides0 @ SV15 @ SV51 )
= $true )
| ( ( aNaturalNumber0 @ SV39 )
= $false )
| ( ( aNaturalNumber0 @ SV15 )
= $false )
| ( ( aNaturalNumber0 @ SV51 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[553]) ).
thf(580,plain,
! [SV52: $i,SV40: $i,SV16: $i] :
( ( ( ~ ( doDivides0 @ SV16 @ SV40 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV16 @ SV52 ) )
= $true )
| ( ( doDivides0 @ SV16 @ ( sdtpldt0 @ SV40 @ SV52 ) )
= $true )
| ( ( aNaturalNumber0 @ SV40 )
= $false )
| ( ( aNaturalNumber0 @ SV16 )
= $false )
| ( ( aNaturalNumber0 @ SV52 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[554]) ).
thf(581,plain,
! [SV53: $i,SV41: $i,SV17: $i] :
( ( ( ~ ( doDivides0 @ SV17 @ SV41 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV17 @ ( sdtpldt0 @ SV41 @ SV53 ) ) )
= $true )
| ( ( doDivides0 @ SV17 @ SV53 )
= $true )
| ( ( aNaturalNumber0 @ SV41 )
= $false )
| ( ( aNaturalNumber0 @ SV17 )
= $false )
| ( ( aNaturalNumber0 @ SV53 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[555]) ).
thf(582,plain,
! [SV19: $i,SV43: $i,SV88: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV88 ) )
= $true )
| ( ( ( sdtasdt0 @ SV88 @ ( sdtsldt0 @ SV43 @ SV19 ) )
= ( sdtsldt0 @ ( sdtasdt0 @ SV88 @ SV43 ) @ SV19 ) )
= $true )
| ( ( SV19 = sz00 )
= $true )
| ( ( doDivides0 @ SV19 @ SV43 )
= $false )
| ( ( aNaturalNumber0 @ SV19 )
= $false )
| ( ( aNaturalNumber0 @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[556]) ).
thf(583,plain,
! [SV44: $i,SV20: $i,SV54: $i] :
( ( ( ~ ( doDivides0 @ SV54 @ ( sdtasdt0 @ SV20 @ SV44 ) ) )
= $true )
| ( ( ~ ( isPrime0 @ SV54 ) )
= $true )
| ( ( ( doDivides0 @ SV54 @ SV20 )
| ( doDivides0 @ SV54 @ SV44 ) )
= $true )
| ( ( aNaturalNumber0 @ SV44 )
= $false )
| ( ( aNaturalNumber0 @ SV20 )
= $false )
| ( ( aNaturalNumber0 @ SV54 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[557]) ).
thf(584,plain,
! [SV77: $i,SV21: $i,SV68: $i] :
( ( ( aNaturalNumber0 @ SV68 )
= $false )
| ( ( aNaturalNumber0 @ SV21 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV77 ) )
= $true )
| ( ( ( ( sdtpldt0 @ SV21 @ SV68 )
!= ( sdtpldt0 @ SV21 @ SV77 ) )
| ( SV68 = SV77 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[558]) ).
thf(585,plain,
! [SV78: $i,SV21: $i,SV69: $i] :
( ( ( aNaturalNumber0 @ SV69 )
= $false )
| ( ( aNaturalNumber0 @ SV21 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV78 ) )
= $true )
| ( ( ( ( sdtpldt0 @ SV69 @ SV21 )
!= ( sdtpldt0 @ SV78 @ SV21 ) )
| ( SV69 = SV78 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[559]) ).
thf(586,plain,
! [SV85: $i,SV82: $i,SV22: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV22 )
| ~ ( aNaturalNumber0 @ SV82 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV85 ) )
= $true )
| ( ( ( SV22 = sz00 )
| ( SV82 = SV85 )
| ~ ( sdtlseqdt0 @ SV82 @ SV85 )
| ( ( sdtasdt0 @ SV82 @ SV22 )
!= ( sdtasdt0 @ SV85 @ SV22 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[560]) ).
thf(587,plain,
! [SV89: $i,SV22: $i] :
( ( ! [SY151: $i] :
( ~ ( aNaturalNumber0 @ SV22 )
| ~ ( aNaturalNumber0 @ SV89 )
| ~ ( aNaturalNumber0 @ SY151 )
| ( SV22 = sz00 )
| ( SV89 = SY151 )
| ~ ( sdtlseqdt0 @ SV89 @ SY151 )
| ( ( sdtasdt0 @ SV22 @ SV89 )
!= ( sdtasdt0 @ SV22 @ SY151 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[561]) ).
thf(588,plain,
! [SV90: $i,SV22: $i] :
( ( ! [SY152: $i] :
( ~ ( aNaturalNumber0 @ SV22 )
| ~ ( aNaturalNumber0 @ SV90 )
| ~ ( aNaturalNumber0 @ SY152 )
| ( SV22 = sz00 )
| ( SV90 = SY152 )
| ~ ( sdtlseqdt0 @ SV90 @ SY152 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV22 @ SV90 ) @ ( sdtasdt0 @ SV22 @ SY152 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[562]) ).
thf(589,plain,
! [SV79: $i,SV22: $i,SV70: $i] :
( ( ( aNaturalNumber0 @ SV70 )
= $false )
| ( ( aNaturalNumber0 @ SV22 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV79 ) )
= $true )
| ( ( ( SV22 = sz00 )
| ( SV70 = SV79 )
| ~ ( sdtlseqdt0 @ SV70 @ SV79 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV70 @ SV22 ) @ ( sdtasdt0 @ SV79 @ SV22 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[563]) ).
thf(590,plain,
! [SV71: $i,SV57: $i] :
( ( ( ( sdtpldt0 @ SV57 @ SV71 )
= sz00 )
= $false )
| ( ( SV57 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV57 )
= $false )
| ( ( aNaturalNumber0 @ SV71 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[564]) ).
thf(591,plain,
! [SV72: $i,SV58: $i] :
( ( ( ( sdtpldt0 @ SV58 @ SV72 )
= sz00 )
= $false )
| ( ( SV72 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV58 )
= $false )
| ( ( aNaturalNumber0 @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[565]) ).
thf(592,plain,
! [SV61: $i,SV73: $i] :
( ( ( SV73 = SV61 )
= $false )
| ( ( sdtlseqdt0 @ SV61 @ SV73 )
= $true )
| ( ( aNaturalNumber0 @ SV61 )
= $false )
| ( ( aNaturalNumber0 @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[566]) ).
thf(593,plain,
! [SV80: $i,SV23: $i,SV75: $i] :
( ( ( aNaturalNumber0 @ SV75 )
= $false )
| ( ( aNaturalNumber0 @ SV23 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV80 ) )
= $true )
| ( ( ( sdtasdt0 @ SV23 @ ( sdtpldt0 @ SV75 @ SV80 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV23 @ SV75 ) @ ( sdtasdt0 @ SV23 @ SV80 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[568]) ).
thf(594,plain,
! [SV81: $i,SV23: $i,SV76: $i] :
( ( ( aNaturalNumber0 @ SV76 )
= $false )
| ( ( aNaturalNumber0 @ SV23 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV81 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV76 @ SV81 ) @ SV23 )
= ( sdtpldt0 @ ( sdtasdt0 @ SV76 @ SV23 ) @ ( sdtasdt0 @ SV81 @ SV23 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[569]) ).
thf(595,plain,
( ( ~ ~ ( ~ ( aNaturalNumber0 @ xn )
| ~ ( aNaturalNumber0 @ xm ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[571]) ).
thf(596,plain,
( ( ~ ( aNaturalNumber0 @ xp ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[571]) ).
thf(597,plain,
! [SV45: $i,SV24: $i] :
( ( ( ~ ~ ( ~ ! [SY135: $i] :
( ~ ( aNaturalNumber0 @ SY135 )
| ( ( sdtpldt0 @ SV24 @ SY135 )
!= ( sdtpldt0 @ SV45 @ SY135 ) ) )
| ~ ~ ( ~ ! [SY136: $i] :
( ~ ( aNaturalNumber0 @ SY136 )
| ( ( sdtpldt0 @ SY136 @ SV24 )
!= ( sdtpldt0 @ SY136 @ SV45 ) ) )
| ~ ! [SY137: $i] :
( ~ ( aNaturalNumber0 @ SY137 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SY137 @ SV24 ) @ ( sdtpldt0 @ SY137 @ SV45 ) ) ) ) ) )
= $false )
| ( ( SV24 = SV45 )
= $true )
| ( ( sdtlseqdt0 @ SV24 @ SV45 )
= $false )
| ( ( aNaturalNumber0 @ SV24 )
= $false )
| ( ( aNaturalNumber0 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[572]) ).
thf(598,plain,
! [SV45: $i,SV24: $i] :
( ( ( ~ ! [SY138: $i] :
( ~ ( aNaturalNumber0 @ SY138 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SV24 @ SY138 ) @ ( sdtpldt0 @ SV45 @ SY138 ) ) ) )
= $false )
| ( ( SV24 = SV45 )
= $true )
| ( ( sdtlseqdt0 @ SV24 @ SV45 )
= $false )
| ( ( aNaturalNumber0 @ SV24 )
= $false )
| ( ( aNaturalNumber0 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[572]) ).
thf(599,plain,
! [SV25: $i,SV86: $i,SV83: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV83 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV86 ) )
= $true )
| ( ( ( ( sdtasdt0 @ SV25 @ SV83 )
!= ( sdtasdt0 @ SV25 @ SV86 ) )
| ( SV83 = SV86 ) )
= $true )
| ( ( SV25 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[573]) ).
thf(600,plain,
! [SV25: $i,SV87: $i,SV84: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV84 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV87 ) )
= $true )
| ( ( ( ( sdtasdt0 @ SV84 @ SV25 )
!= ( sdtasdt0 @ SV87 @ SV25 ) )
| ( SV84 = SV87 ) )
= $true )
| ( ( SV25 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[574]) ).
thf(601,plain,
! [SV26: $i] :
( ( ( aNaturalNumber0 @ ( sK1_W1 @ SV26 ) )
= $true )
| ( ( SV26 = sz10 )
= $true )
| ( ( SV26 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV26 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[575]) ).
thf(602,plain,
! [SV26: $i] :
( ( ( doDivides0 @ ( sK1_W1 @ SV26 ) @ SV26 )
= $true )
| ( ( SV26 = sz10 )
= $true )
| ( ( SV26 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV26 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[576]) ).
thf(603,plain,
! [SV27: $i,SV1: $i,SV46: $i] :
( ( ( aNaturalNumber0 @ SV46 )
= $false )
| ( ( aNaturalNumber0 @ SV1 )
= $false )
| ( ( aNaturalNumber0 @ SV27 )
= $false )
| ( ( SV1 = sz00 )
= $true )
| ( ( SV27 = sz00 )
= $true )
| ( ( SV46 = sz00 )
= $true )
| ( ( ( ( sdtasdt0 @ SV46 @ ( sdtasdt0 @ SV27 @ SV27 ) )
!= ( sdtasdt0 @ SV1 @ SV1 ) )
| ~ ( iLess0 @ SV1 @ xn )
| ~ ( isPrime0 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[577]) ).
thf(604,plain,
! [SV49: $i,SV36: $i,SV12: $i] :
( ( ( sdtlseqdt0 @ SV12 @ SV36 )
= $false )
| ( ( ~ ( sdtlseqdt0 @ SV36 @ SV49 ) )
= $true )
| ( ( sdtlseqdt0 @ SV12 @ SV49 )
= $true )
| ( ( aNaturalNumber0 @ SV36 )
= $false )
| ( ( aNaturalNumber0 @ SV12 )
= $false )
| ( ( aNaturalNumber0 @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[578]) ).
thf(605,plain,
! [SV51: $i,SV39: $i,SV15: $i] :
( ( ( doDivides0 @ SV15 @ SV39 )
= $false )
| ( ( ~ ( doDivides0 @ SV39 @ SV51 ) )
= $true )
| ( ( doDivides0 @ SV15 @ SV51 )
= $true )
| ( ( aNaturalNumber0 @ SV39 )
= $false )
| ( ( aNaturalNumber0 @ SV15 )
= $false )
| ( ( aNaturalNumber0 @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[579]) ).
thf(606,plain,
! [SV52: $i,SV40: $i,SV16: $i] :
( ( ( doDivides0 @ SV16 @ SV40 )
= $false )
| ( ( ~ ( doDivides0 @ SV16 @ SV52 ) )
= $true )
| ( ( doDivides0 @ SV16 @ ( sdtpldt0 @ SV40 @ SV52 ) )
= $true )
| ( ( aNaturalNumber0 @ SV40 )
= $false )
| ( ( aNaturalNumber0 @ SV16 )
= $false )
| ( ( aNaturalNumber0 @ SV52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[580]) ).
thf(607,plain,
! [SV53: $i,SV41: $i,SV17: $i] :
( ( ( doDivides0 @ SV17 @ SV41 )
= $false )
| ( ( ~ ( doDivides0 @ SV17 @ ( sdtpldt0 @ SV41 @ SV53 ) ) )
= $true )
| ( ( doDivides0 @ SV17 @ SV53 )
= $true )
| ( ( aNaturalNumber0 @ SV41 )
= $false )
| ( ( aNaturalNumber0 @ SV17 )
= $false )
| ( ( aNaturalNumber0 @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[581]) ).
thf(608,plain,
! [SV19: $i,SV43: $i,SV88: $i] :
( ( ( aNaturalNumber0 @ SV88 )
= $false )
| ( ( ( sdtasdt0 @ SV88 @ ( sdtsldt0 @ SV43 @ SV19 ) )
= ( sdtsldt0 @ ( sdtasdt0 @ SV88 @ SV43 ) @ SV19 ) )
= $true )
| ( ( SV19 = sz00 )
= $true )
| ( ( doDivides0 @ SV19 @ SV43 )
= $false )
| ( ( aNaturalNumber0 @ SV19 )
= $false )
| ( ( aNaturalNumber0 @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[582]) ).
thf(609,plain,
! [SV44: $i,SV20: $i,SV54: $i] :
( ( ( doDivides0 @ SV54 @ ( sdtasdt0 @ SV20 @ SV44 ) )
= $false )
| ( ( ~ ( isPrime0 @ SV54 ) )
= $true )
| ( ( ( doDivides0 @ SV54 @ SV20 )
| ( doDivides0 @ SV54 @ SV44 ) )
= $true )
| ( ( aNaturalNumber0 @ SV44 )
= $false )
| ( ( aNaturalNumber0 @ SV20 )
= $false )
| ( ( aNaturalNumber0 @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[583]) ).
thf(610,plain,
! [SV68: $i,SV21: $i,SV77: $i] :
( ( ( aNaturalNumber0 @ SV77 )
= $false )
| ( ( aNaturalNumber0 @ SV21 )
= $false )
| ( ( aNaturalNumber0 @ SV68 )
= $false )
| ( ( ( ( sdtpldt0 @ SV21 @ SV68 )
!= ( sdtpldt0 @ SV21 @ SV77 ) )
| ( SV68 = SV77 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[584]) ).
thf(611,plain,
! [SV69: $i,SV21: $i,SV78: $i] :
( ( ( aNaturalNumber0 @ SV78 )
= $false )
| ( ( aNaturalNumber0 @ SV21 )
= $false )
| ( ( aNaturalNumber0 @ SV69 )
= $false )
| ( ( ( ( sdtpldt0 @ SV69 @ SV21 )
!= ( sdtpldt0 @ SV78 @ SV21 ) )
| ( SV69 = SV78 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[585]) ).
thf(612,plain,
! [SV85: $i,SV82: $i,SV22: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV22 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV82 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV85 ) )
= $true )
| ( ( ( SV22 = sz00 )
| ( SV82 = SV85 )
| ~ ( sdtlseqdt0 @ SV82 @ SV85 )
| ( ( sdtasdt0 @ SV82 @ SV22 )
!= ( sdtasdt0 @ SV85 @ SV22 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[586]) ).
thf(613,plain,
! [SV91: $i,SV89: $i,SV22: $i] :
( ( ~ ( aNaturalNumber0 @ SV22 )
| ~ ( aNaturalNumber0 @ SV89 )
| ~ ( aNaturalNumber0 @ SV91 )
| ( SV22 = sz00 )
| ( SV89 = SV91 )
| ~ ( sdtlseqdt0 @ SV89 @ SV91 )
| ( ( sdtasdt0 @ SV22 @ SV89 )
!= ( sdtasdt0 @ SV22 @ SV91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[587]) ).
thf(614,plain,
! [SV92: $i,SV90: $i,SV22: $i] :
( ( ~ ( aNaturalNumber0 @ SV22 )
| ~ ( aNaturalNumber0 @ SV90 )
| ~ ( aNaturalNumber0 @ SV92 )
| ( SV22 = sz00 )
| ( SV90 = SV92 )
| ~ ( sdtlseqdt0 @ SV90 @ SV92 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV22 @ SV90 ) @ ( sdtasdt0 @ SV22 @ SV92 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[588]) ).
thf(615,plain,
! [SV70: $i,SV22: $i,SV79: $i] :
( ( ( aNaturalNumber0 @ SV79 )
= $false )
| ( ( aNaturalNumber0 @ SV22 )
= $false )
| ( ( aNaturalNumber0 @ SV70 )
= $false )
| ( ( ( SV22 = sz00 )
| ( SV70 = SV79 )
| ~ ( sdtlseqdt0 @ SV70 @ SV79 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV70 @ SV22 ) @ ( sdtasdt0 @ SV79 @ SV22 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[589]) ).
thf(616,plain,
! [SV75: $i,SV23: $i,SV80: $i] :
( ( ( aNaturalNumber0 @ SV80 )
= $false )
| ( ( aNaturalNumber0 @ SV23 )
= $false )
| ( ( aNaturalNumber0 @ SV75 )
= $false )
| ( ( ( sdtasdt0 @ SV23 @ ( sdtpldt0 @ SV75 @ SV80 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV23 @ SV75 ) @ ( sdtasdt0 @ SV23 @ SV80 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[593]) ).
thf(617,plain,
! [SV76: $i,SV23: $i,SV81: $i] :
( ( ( aNaturalNumber0 @ SV81 )
= $false )
| ( ( aNaturalNumber0 @ SV23 )
= $false )
| ( ( aNaturalNumber0 @ SV76 )
= $false )
| ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV76 @ SV81 ) @ SV23 )
= ( sdtpldt0 @ ( sdtasdt0 @ SV76 @ SV23 ) @ ( sdtasdt0 @ SV81 @ SV23 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[594]) ).
thf(618,plain,
( ( ~ ( ~ ( aNaturalNumber0 @ xn )
| ~ ( aNaturalNumber0 @ xm ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[595]) ).
thf(619,plain,
( ( aNaturalNumber0 @ xp )
= $true ),
inference(extcnf_not_neg,[status(thm)],[596]) ).
thf(620,plain,
! [SV45: $i,SV24: $i] :
( ( ( ~ ( ~ ! [SY135: $i] :
( ~ ( aNaturalNumber0 @ SY135 )
| ( ( sdtpldt0 @ SV24 @ SY135 )
!= ( sdtpldt0 @ SV45 @ SY135 ) ) )
| ~ ~ ( ~ ! [SY136: $i] :
( ~ ( aNaturalNumber0 @ SY136 )
| ( ( sdtpldt0 @ SY136 @ SV24 )
!= ( sdtpldt0 @ SY136 @ SV45 ) ) )
| ~ ! [SY137: $i] :
( ~ ( aNaturalNumber0 @ SY137 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SY137 @ SV24 ) @ ( sdtpldt0 @ SY137 @ SV45 ) ) ) ) ) )
= $true )
| ( ( SV24 = SV45 )
= $true )
| ( ( sdtlseqdt0 @ SV24 @ SV45 )
= $false )
| ( ( aNaturalNumber0 @ SV24 )
= $false )
| ( ( aNaturalNumber0 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[597]) ).
thf(621,plain,
! [SV45: $i,SV24: $i] :
( ( ( ! [SY138: $i] :
( ~ ( aNaturalNumber0 @ SY138 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SV24 @ SY138 ) @ ( sdtpldt0 @ SV45 @ SY138 ) ) ) )
= $true )
| ( ( SV24 = SV45 )
= $true )
| ( ( sdtlseqdt0 @ SV24 @ SV45 )
= $false )
| ( ( aNaturalNumber0 @ SV24 )
= $false )
| ( ( aNaturalNumber0 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[598]) ).
thf(622,plain,
! [SV25: $i,SV86: $i,SV83: $i] :
( ( ( aNaturalNumber0 @ SV83 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV86 ) )
= $true )
| ( ( ( ( sdtasdt0 @ SV25 @ SV83 )
!= ( sdtasdt0 @ SV25 @ SV86 ) )
| ( SV83 = SV86 ) )
= $true )
| ( ( SV25 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[599]) ).
thf(623,plain,
! [SV25: $i,SV87: $i,SV84: $i] :
( ( ( aNaturalNumber0 @ SV84 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV87 ) )
= $true )
| ( ( ( ( sdtasdt0 @ SV84 @ SV25 )
!= ( sdtasdt0 @ SV87 @ SV25 ) )
| ( SV84 = SV87 ) )
= $true )
| ( ( SV25 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[600]) ).
thf(624,plain,
! [SV1: $i,SV27: $i,SV46: $i] :
( ( ( ( ( sdtasdt0 @ SV46 @ ( sdtasdt0 @ SV27 @ SV27 ) )
!= ( sdtasdt0 @ SV1 @ SV1 ) ) )
= $true )
| ( ( ~ ( iLess0 @ SV1 @ xn )
| ~ ( isPrime0 @ SV46 ) )
= $true )
| ( ( SV46 = sz00 )
= $true )
| ( ( SV27 = sz00 )
= $true )
| ( ( SV1 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV27 )
= $false )
| ( ( aNaturalNumber0 @ SV1 )
= $false )
| ( ( aNaturalNumber0 @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[603]) ).
thf(625,plain,
! [SV12: $i,SV49: $i,SV36: $i] :
( ( ( sdtlseqdt0 @ SV36 @ SV49 )
= $false )
| ( ( sdtlseqdt0 @ SV12 @ SV36 )
= $false )
| ( ( sdtlseqdt0 @ SV12 @ SV49 )
= $true )
| ( ( aNaturalNumber0 @ SV36 )
= $false )
| ( ( aNaturalNumber0 @ SV12 )
= $false )
| ( ( aNaturalNumber0 @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[604]) ).
thf(626,plain,
! [SV15: $i,SV51: $i,SV39: $i] :
( ( ( doDivides0 @ SV39 @ SV51 )
= $false )
| ( ( doDivides0 @ SV15 @ SV39 )
= $false )
| ( ( doDivides0 @ SV15 @ SV51 )
= $true )
| ( ( aNaturalNumber0 @ SV39 )
= $false )
| ( ( aNaturalNumber0 @ SV15 )
= $false )
| ( ( aNaturalNumber0 @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[605]) ).
thf(627,plain,
! [SV40: $i,SV52: $i,SV16: $i] :
( ( ( doDivides0 @ SV16 @ SV52 )
= $false )
| ( ( doDivides0 @ SV16 @ SV40 )
= $false )
| ( ( doDivides0 @ SV16 @ ( sdtpldt0 @ SV40 @ SV52 ) )
= $true )
| ( ( aNaturalNumber0 @ SV40 )
= $false )
| ( ( aNaturalNumber0 @ SV16 )
= $false )
| ( ( aNaturalNumber0 @ SV52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[606]) ).
thf(628,plain,
! [SV53: $i,SV41: $i,SV17: $i] :
( ( ( doDivides0 @ SV17 @ ( sdtpldt0 @ SV41 @ SV53 ) )
= $false )
| ( ( doDivides0 @ SV17 @ SV41 )
= $false )
| ( ( doDivides0 @ SV17 @ SV53 )
= $true )
| ( ( aNaturalNumber0 @ SV41 )
= $false )
| ( ( aNaturalNumber0 @ SV17 )
= $false )
| ( ( aNaturalNumber0 @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[607]) ).
thf(629,plain,
! [SV44: $i,SV20: $i,SV54: $i] :
( ( ( isPrime0 @ SV54 )
= $false )
| ( ( doDivides0 @ SV54 @ ( sdtasdt0 @ SV20 @ SV44 ) )
= $false )
| ( ( ( doDivides0 @ SV54 @ SV20 )
| ( doDivides0 @ SV54 @ SV44 ) )
= $true )
| ( ( aNaturalNumber0 @ SV44 )
= $false )
| ( ( aNaturalNumber0 @ SV20 )
= $false )
| ( ( aNaturalNumber0 @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[609]) ).
thf(630,plain,
! [SV77: $i,SV68: $i,SV21: $i] :
( ( ( ( ( sdtpldt0 @ SV21 @ SV68 )
!= ( sdtpldt0 @ SV21 @ SV77 ) ) )
= $true )
| ( ( SV68 = SV77 )
= $true )
| ( ( aNaturalNumber0 @ SV68 )
= $false )
| ( ( aNaturalNumber0 @ SV21 )
= $false )
| ( ( aNaturalNumber0 @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[610]) ).
thf(631,plain,
! [SV78: $i,SV21: $i,SV69: $i] :
( ( ( ( ( sdtpldt0 @ SV69 @ SV21 )
!= ( sdtpldt0 @ SV78 @ SV21 ) ) )
= $true )
| ( ( SV69 = SV78 )
= $true )
| ( ( aNaturalNumber0 @ SV69 )
= $false )
| ( ( aNaturalNumber0 @ SV21 )
= $false )
| ( ( aNaturalNumber0 @ SV78 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[611]) ).
thf(632,plain,
! [SV85: $i,SV82: $i,SV22: $i] :
( ( ( aNaturalNumber0 @ SV22 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV82 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV85 ) )
= $true )
| ( ( ( SV22 = sz00 )
| ( SV82 = SV85 )
| ~ ( sdtlseqdt0 @ SV82 @ SV85 )
| ( ( sdtasdt0 @ SV82 @ SV22 )
!= ( sdtasdt0 @ SV85 @ SV22 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[612]) ).
thf(633,plain,
! [SV91: $i,SV89: $i,SV22: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV22 )
| ~ ( aNaturalNumber0 @ SV89 )
| ~ ( aNaturalNumber0 @ SV91 ) )
= $true )
| ( ( ( SV22 = sz00 )
| ( SV89 = SV91 )
| ~ ( sdtlseqdt0 @ SV89 @ SV91 )
| ( ( sdtasdt0 @ SV22 @ SV89 )
!= ( sdtasdt0 @ SV22 @ SV91 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[613]) ).
thf(634,plain,
! [SV92: $i,SV90: $i,SV22: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV22 )
| ~ ( aNaturalNumber0 @ SV90 )
| ~ ( aNaturalNumber0 @ SV92 ) )
= $true )
| ( ( ( SV22 = sz00 )
| ( SV90 = SV92 )
| ~ ( sdtlseqdt0 @ SV90 @ SV92 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV22 @ SV90 ) @ ( sdtasdt0 @ SV22 @ SV92 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[614]) ).
thf(635,plain,
! [SV79: $i,SV70: $i,SV22: $i] :
( ( ( ( SV22 = sz00 )
| ( SV70 = SV79 )
| ~ ( sdtlseqdt0 @ SV70 @ SV79 ) )
= $true )
| ( ( sdtlseqdt0 @ ( sdtasdt0 @ SV70 @ SV22 ) @ ( sdtasdt0 @ SV79 @ SV22 ) )
= $true )
| ( ( aNaturalNumber0 @ SV70 )
= $false )
| ( ( aNaturalNumber0 @ SV22 )
= $false )
| ( ( aNaturalNumber0 @ SV79 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[615]) ).
thf(636,plain,
( ( ~ ( aNaturalNumber0 @ xn )
| ~ ( aNaturalNumber0 @ xm ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[618]) ).
thf(637,plain,
! [SV45: $i,SV24: $i] :
( ( ( ~ ! [SY135: $i] :
( ~ ( aNaturalNumber0 @ SY135 )
| ( ( sdtpldt0 @ SV24 @ SY135 )
!= ( sdtpldt0 @ SV45 @ SY135 ) ) )
| ~ ~ ( ~ ! [SY136: $i] :
( ~ ( aNaturalNumber0 @ SY136 )
| ( ( sdtpldt0 @ SY136 @ SV24 )
!= ( sdtpldt0 @ SY136 @ SV45 ) ) )
| ~ ! [SY137: $i] :
( ~ ( aNaturalNumber0 @ SY137 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SY137 @ SV24 ) @ ( sdtpldt0 @ SY137 @ SV45 ) ) ) ) )
= $false )
| ( ( SV24 = SV45 )
= $true )
| ( ( sdtlseqdt0 @ SV24 @ SV45 )
= $false )
| ( ( aNaturalNumber0 @ SV24 )
= $false )
| ( ( aNaturalNumber0 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[620]) ).
thf(638,plain,
! [SV45: $i,SV24: $i,SV93: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV93 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SV24 @ SV93 ) @ ( sdtpldt0 @ SV45 @ SV93 ) ) )
= $true )
| ( ( SV24 = SV45 )
= $true )
| ( ( sdtlseqdt0 @ SV24 @ SV45 )
= $false )
| ( ( aNaturalNumber0 @ SV24 )
= $false )
| ( ( aNaturalNumber0 @ SV45 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[621]) ).
thf(639,plain,
! [SV25: $i,SV83: $i,SV86: $i] :
( ( ( aNaturalNumber0 @ SV86 )
= $false )
| ( ( aNaturalNumber0 @ SV83 )
= $false )
| ( ( ( ( sdtasdt0 @ SV25 @ SV83 )
!= ( sdtasdt0 @ SV25 @ SV86 ) )
| ( SV83 = SV86 ) )
= $true )
| ( ( SV25 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[622]) ).
thf(640,plain,
! [SV25: $i,SV84: $i,SV87: $i] :
( ( ( aNaturalNumber0 @ SV87 )
= $false )
| ( ( aNaturalNumber0 @ SV84 )
= $false )
| ( ( ( ( sdtasdt0 @ SV84 @ SV25 )
!= ( sdtasdt0 @ SV87 @ SV25 ) )
| ( SV84 = SV87 ) )
= $true )
| ( ( SV25 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[623]) ).
thf(641,plain,
! [SV1: $i,SV27: $i,SV46: $i] :
( ( ( ( sdtasdt0 @ SV46 @ ( sdtasdt0 @ SV27 @ SV27 ) )
= ( sdtasdt0 @ SV1 @ SV1 ) )
= $false )
| ( ( ~ ( iLess0 @ SV1 @ xn )
| ~ ( isPrime0 @ SV46 ) )
= $true )
| ( ( SV46 = sz00 )
= $true )
| ( ( SV27 = sz00 )
= $true )
| ( ( SV1 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV27 )
= $false )
| ( ( aNaturalNumber0 @ SV1 )
= $false )
| ( ( aNaturalNumber0 @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[624]) ).
thf(642,plain,
! [SV44: $i,SV20: $i,SV54: $i] :
( ( ( doDivides0 @ SV54 @ SV20 )
= $true )
| ( ( doDivides0 @ SV54 @ SV44 )
= $true )
| ( ( doDivides0 @ SV54 @ ( sdtasdt0 @ SV20 @ SV44 ) )
= $false )
| ( ( isPrime0 @ SV54 )
= $false )
| ( ( aNaturalNumber0 @ SV44 )
= $false )
| ( ( aNaturalNumber0 @ SV20 )
= $false )
| ( ( aNaturalNumber0 @ SV54 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[629]) ).
thf(643,plain,
! [SV77: $i,SV68: $i,SV21: $i] :
( ( ( ( sdtpldt0 @ SV21 @ SV68 )
= ( sdtpldt0 @ SV21 @ SV77 ) )
= $false )
| ( ( SV68 = SV77 )
= $true )
| ( ( aNaturalNumber0 @ SV68 )
= $false )
| ( ( aNaturalNumber0 @ SV21 )
= $false )
| ( ( aNaturalNumber0 @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[630]) ).
thf(644,plain,
! [SV78: $i,SV21: $i,SV69: $i] :
( ( ( ( sdtpldt0 @ SV69 @ SV21 )
= ( sdtpldt0 @ SV78 @ SV21 ) )
= $false )
| ( ( SV69 = SV78 )
= $true )
| ( ( aNaturalNumber0 @ SV69 )
= $false )
| ( ( aNaturalNumber0 @ SV21 )
= $false )
| ( ( aNaturalNumber0 @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[631]) ).
thf(645,plain,
! [SV85: $i,SV22: $i,SV82: $i] :
( ( ( aNaturalNumber0 @ SV82 )
= $false )
| ( ( aNaturalNumber0 @ SV22 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV85 ) )
= $true )
| ( ( ( SV22 = sz00 )
| ( SV82 = SV85 )
| ~ ( sdtlseqdt0 @ SV82 @ SV85 )
| ( ( sdtasdt0 @ SV82 @ SV22 )
!= ( sdtasdt0 @ SV85 @ SV22 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[632]) ).
thf(646,plain,
! [SV91: $i,SV89: $i,SV22: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV22 )
| ~ ( aNaturalNumber0 @ SV89 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV91 ) )
= $true )
| ( ( ( SV22 = sz00 )
| ( SV89 = SV91 )
| ~ ( sdtlseqdt0 @ SV89 @ SV91 )
| ( ( sdtasdt0 @ SV22 @ SV89 )
!= ( sdtasdt0 @ SV22 @ SV91 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[633]) ).
thf(647,plain,
! [SV92: $i,SV90: $i,SV22: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV22 )
| ~ ( aNaturalNumber0 @ SV90 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV92 ) )
= $true )
| ( ( ( SV22 = sz00 )
| ( SV90 = SV92 )
| ~ ( sdtlseqdt0 @ SV90 @ SV92 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV22 @ SV90 ) @ ( sdtasdt0 @ SV22 @ SV92 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[634]) ).
thf(648,plain,
! [SV79: $i,SV70: $i,SV22: $i] :
( ( ( ( SV22 = sz00 )
| ( SV70 = SV79 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV70 @ SV79 ) )
= $true )
| ( ( sdtlseqdt0 @ ( sdtasdt0 @ SV70 @ SV22 ) @ ( sdtasdt0 @ SV79 @ SV22 ) )
= $true )
| ( ( aNaturalNumber0 @ SV70 )
= $false )
| ( ( aNaturalNumber0 @ SV22 )
= $false )
| ( ( aNaturalNumber0 @ SV79 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[635]) ).
thf(649,plain,
( ( ~ ( aNaturalNumber0 @ xn ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[636]) ).
thf(650,plain,
( ( ~ ( aNaturalNumber0 @ xm ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[636]) ).
thf(651,plain,
! [SV45: $i,SV24: $i] :
( ( ( ~ ! [SY135: $i] :
( ~ ( aNaturalNumber0 @ SY135 )
| ( ( sdtpldt0 @ SV24 @ SY135 )
!= ( sdtpldt0 @ SV45 @ SY135 ) ) ) )
= $false )
| ( ( SV24 = SV45 )
= $true )
| ( ( sdtlseqdt0 @ SV24 @ SV45 )
= $false )
| ( ( aNaturalNumber0 @ SV24 )
= $false )
| ( ( aNaturalNumber0 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[637]) ).
thf(652,plain,
! [SV45: $i,SV24: $i] :
( ( ( ~ ~ ( ~ ! [SY136: $i] :
( ~ ( aNaturalNumber0 @ SY136 )
| ( ( sdtpldt0 @ SY136 @ SV24 )
!= ( sdtpldt0 @ SY136 @ SV45 ) ) )
| ~ ! [SY137: $i] :
( ~ ( aNaturalNumber0 @ SY137 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SY137 @ SV24 ) @ ( sdtpldt0 @ SY137 @ SV45 ) ) ) ) )
= $false )
| ( ( SV24 = SV45 )
= $true )
| ( ( sdtlseqdt0 @ SV24 @ SV45 )
= $false )
| ( ( aNaturalNumber0 @ SV24 )
= $false )
| ( ( aNaturalNumber0 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[637]) ).
thf(653,plain,
! [SV45: $i,SV24: $i,SV93: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV93 ) )
= $true )
| ( ( sdtlseqdt0 @ ( sdtpldt0 @ SV24 @ SV93 ) @ ( sdtpldt0 @ SV45 @ SV93 ) )
= $true )
| ( ( SV24 = SV45 )
= $true )
| ( ( sdtlseqdt0 @ SV24 @ SV45 )
= $false )
| ( ( aNaturalNumber0 @ SV24 )
= $false )
| ( ( aNaturalNumber0 @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[638]) ).
thf(654,plain,
! [SV86: $i,SV83: $i,SV25: $i] :
( ( ( ( ( sdtasdt0 @ SV25 @ SV83 )
!= ( sdtasdt0 @ SV25 @ SV86 ) ) )
= $true )
| ( ( SV83 = SV86 )
= $true )
| ( ( aNaturalNumber0 @ SV83 )
= $false )
| ( ( aNaturalNumber0 @ SV86 )
= $false )
| ( ( SV25 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[639]) ).
thf(655,plain,
! [SV87: $i,SV25: $i,SV84: $i] :
( ( ( ( ( sdtasdt0 @ SV84 @ SV25 )
!= ( sdtasdt0 @ SV87 @ SV25 ) ) )
= $true )
| ( ( SV84 = SV87 )
= $true )
| ( ( aNaturalNumber0 @ SV84 )
= $false )
| ( ( aNaturalNumber0 @ SV87 )
= $false )
| ( ( SV25 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[640]) ).
thf(656,plain,
! [SV27: $i,SV46: $i,SV1: $i] :
( ( ( ~ ( iLess0 @ SV1 @ xn ) )
= $true )
| ( ( ~ ( isPrime0 @ SV46 ) )
= $true )
| ( ( ( sdtasdt0 @ SV46 @ ( sdtasdt0 @ SV27 @ SV27 ) )
= ( sdtasdt0 @ SV1 @ SV1 ) )
= $false )
| ( ( SV46 = sz00 )
= $true )
| ( ( SV27 = sz00 )
= $true )
| ( ( SV1 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV27 )
= $false )
| ( ( aNaturalNumber0 @ SV1 )
= $false )
| ( ( aNaturalNumber0 @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[641]) ).
thf(657,plain,
! [SV82: $i,SV22: $i,SV85: $i] :
( ( ( aNaturalNumber0 @ SV85 )
= $false )
| ( ( aNaturalNumber0 @ SV22 )
= $false )
| ( ( aNaturalNumber0 @ SV82 )
= $false )
| ( ( ( SV22 = sz00 )
| ( SV82 = SV85 )
| ~ ( sdtlseqdt0 @ SV82 @ SV85 )
| ( ( sdtasdt0 @ SV82 @ SV22 )
!= ( sdtasdt0 @ SV85 @ SV22 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[645]) ).
thf(658,plain,
! [SV91: $i,SV89: $i,SV22: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV22 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV89 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV91 ) )
= $true )
| ( ( ( SV22 = sz00 )
| ( SV89 = SV91 )
| ~ ( sdtlseqdt0 @ SV89 @ SV91 )
| ( ( sdtasdt0 @ SV22 @ SV89 )
!= ( sdtasdt0 @ SV22 @ SV91 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[646]) ).
thf(659,plain,
! [SV92: $i,SV90: $i,SV22: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV22 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV90 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV92 ) )
= $true )
| ( ( ( SV22 = sz00 )
| ( SV90 = SV92 )
| ~ ( sdtlseqdt0 @ SV90 @ SV92 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV22 @ SV90 ) @ ( sdtasdt0 @ SV22 @ SV92 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[647]) ).
thf(660,plain,
! [SV79: $i,SV70: $i,SV22: $i] :
( ( ( SV22 = sz00 )
= $true )
| ( ( SV70 = SV79 )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV70 @ SV79 ) )
= $true )
| ( ( sdtlseqdt0 @ ( sdtasdt0 @ SV70 @ SV22 ) @ ( sdtasdt0 @ SV79 @ SV22 ) )
= $true )
| ( ( aNaturalNumber0 @ SV70 )
= $false )
| ( ( aNaturalNumber0 @ SV22 )
= $false )
| ( ( aNaturalNumber0 @ SV79 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[648]) ).
thf(661,plain,
( ( aNaturalNumber0 @ xn )
= $true ),
inference(extcnf_not_neg,[status(thm)],[649]) ).
thf(662,plain,
( ( aNaturalNumber0 @ xm )
= $true ),
inference(extcnf_not_neg,[status(thm)],[650]) ).
thf(663,plain,
! [SV45: $i,SV24: $i] :
( ( ( ! [SY135: $i] :
( ~ ( aNaturalNumber0 @ SY135 )
| ( ( sdtpldt0 @ SV24 @ SY135 )
!= ( sdtpldt0 @ SV45 @ SY135 ) ) ) )
= $true )
| ( ( SV24 = SV45 )
= $true )
| ( ( sdtlseqdt0 @ SV24 @ SV45 )
= $false )
| ( ( aNaturalNumber0 @ SV24 )
= $false )
| ( ( aNaturalNumber0 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[651]) ).
thf(664,plain,
! [SV45: $i,SV24: $i] :
( ( ( ~ ( ~ ! [SY136: $i] :
( ~ ( aNaturalNumber0 @ SY136 )
| ( ( sdtpldt0 @ SY136 @ SV24 )
!= ( sdtpldt0 @ SY136 @ SV45 ) ) )
| ~ ! [SY137: $i] :
( ~ ( aNaturalNumber0 @ SY137 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SY137 @ SV24 ) @ ( sdtpldt0 @ SY137 @ SV45 ) ) ) ) )
= $true )
| ( ( SV24 = SV45 )
= $true )
| ( ( sdtlseqdt0 @ SV24 @ SV45 )
= $false )
| ( ( aNaturalNumber0 @ SV24 )
= $false )
| ( ( aNaturalNumber0 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[652]) ).
thf(665,plain,
! [SV45: $i,SV24: $i,SV93: $i] :
( ( ( aNaturalNumber0 @ SV93 )
= $false )
| ( ( sdtlseqdt0 @ ( sdtpldt0 @ SV24 @ SV93 ) @ ( sdtpldt0 @ SV45 @ SV93 ) )
= $true )
| ( ( SV24 = SV45 )
= $true )
| ( ( sdtlseqdt0 @ SV24 @ SV45 )
= $false )
| ( ( aNaturalNumber0 @ SV24 )
= $false )
| ( ( aNaturalNumber0 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[653]) ).
thf(666,plain,
! [SV86: $i,SV83: $i,SV25: $i] :
( ( ( ( sdtasdt0 @ SV25 @ SV83 )
= ( sdtasdt0 @ SV25 @ SV86 ) )
= $false )
| ( ( SV83 = SV86 )
= $true )
| ( ( aNaturalNumber0 @ SV83 )
= $false )
| ( ( aNaturalNumber0 @ SV86 )
= $false )
| ( ( SV25 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[654]) ).
thf(667,plain,
! [SV87: $i,SV25: $i,SV84: $i] :
( ( ( ( sdtasdt0 @ SV84 @ SV25 )
= ( sdtasdt0 @ SV87 @ SV25 ) )
= $false )
| ( ( SV84 = SV87 )
= $true )
| ( ( aNaturalNumber0 @ SV84 )
= $false )
| ( ( aNaturalNumber0 @ SV87 )
= $false )
| ( ( SV25 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[655]) ).
thf(668,plain,
! [SV27: $i,SV46: $i,SV1: $i] :
( ( ( iLess0 @ SV1 @ xn )
= $false )
| ( ( ~ ( isPrime0 @ SV46 ) )
= $true )
| ( ( ( sdtasdt0 @ SV46 @ ( sdtasdt0 @ SV27 @ SV27 ) )
= ( sdtasdt0 @ SV1 @ SV1 ) )
= $false )
| ( ( SV46 = sz00 )
= $true )
| ( ( SV27 = sz00 )
= $true )
| ( ( SV1 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV27 )
= $false )
| ( ( aNaturalNumber0 @ SV1 )
= $false )
| ( ( aNaturalNumber0 @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[656]) ).
thf(669,plain,
! [SV85: $i,SV82: $i,SV22: $i] :
( ( ( ( SV22 = sz00 )
| ( SV82 = SV85 )
| ~ ( sdtlseqdt0 @ SV82 @ SV85 ) )
= $true )
| ( ( ( ( sdtasdt0 @ SV82 @ SV22 )
!= ( sdtasdt0 @ SV85 @ SV22 ) ) )
= $true )
| ( ( aNaturalNumber0 @ SV82 )
= $false )
| ( ( aNaturalNumber0 @ SV22 )
= $false )
| ( ( aNaturalNumber0 @ SV85 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[657]) ).
thf(670,plain,
! [SV91: $i,SV89: $i,SV22: $i] :
( ( ( aNaturalNumber0 @ SV22 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV89 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV91 ) )
= $true )
| ( ( ( SV22 = sz00 )
| ( SV89 = SV91 )
| ~ ( sdtlseqdt0 @ SV89 @ SV91 )
| ( ( sdtasdt0 @ SV22 @ SV89 )
!= ( sdtasdt0 @ SV22 @ SV91 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[658]) ).
thf(671,plain,
! [SV92: $i,SV90: $i,SV22: $i] :
( ( ( aNaturalNumber0 @ SV22 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV90 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV92 ) )
= $true )
| ( ( ( SV22 = sz00 )
| ( SV90 = SV92 )
| ~ ( sdtlseqdt0 @ SV90 @ SV92 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV22 @ SV90 ) @ ( sdtasdt0 @ SV22 @ SV92 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[659]) ).
thf(672,plain,
! [SV22: $i,SV79: $i,SV70: $i] :
( ( ( sdtlseqdt0 @ SV70 @ SV79 )
= $false )
| ( ( SV70 = SV79 )
= $true )
| ( ( SV22 = sz00 )
= $true )
| ( ( sdtlseqdt0 @ ( sdtasdt0 @ SV70 @ SV22 ) @ ( sdtasdt0 @ SV79 @ SV22 ) )
= $true )
| ( ( aNaturalNumber0 @ SV70 )
= $false )
| ( ( aNaturalNumber0 @ SV22 )
= $false )
| ( ( aNaturalNumber0 @ SV79 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[660]) ).
thf(673,plain,
! [SV45: $i,SV24: $i,SV94: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV94 )
| ( ( sdtpldt0 @ SV24 @ SV94 )
!= ( sdtpldt0 @ SV45 @ SV94 ) ) )
= $true )
| ( ( SV24 = SV45 )
= $true )
| ( ( sdtlseqdt0 @ SV24 @ SV45 )
= $false )
| ( ( aNaturalNumber0 @ SV24 )
= $false )
| ( ( aNaturalNumber0 @ SV45 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[663]) ).
thf(674,plain,
! [SV45: $i,SV24: $i] :
( ( ( ~ ! [SY136: $i] :
( ~ ( aNaturalNumber0 @ SY136 )
| ( ( sdtpldt0 @ SY136 @ SV24 )
!= ( sdtpldt0 @ SY136 @ SV45 ) ) )
| ~ ! [SY137: $i] :
( ~ ( aNaturalNumber0 @ SY137 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SY137 @ SV24 ) @ ( sdtpldt0 @ SY137 @ SV45 ) ) ) )
= $false )
| ( ( SV24 = SV45 )
= $true )
| ( ( sdtlseqdt0 @ SV24 @ SV45 )
= $false )
| ( ( aNaturalNumber0 @ SV24 )
= $false )
| ( ( aNaturalNumber0 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[664]) ).
thf(675,plain,
! [SV27: $i,SV1: $i,SV46: $i] :
( ( ( isPrime0 @ SV46 )
= $false )
| ( ( iLess0 @ SV1 @ xn )
= $false )
| ( ( ( sdtasdt0 @ SV46 @ ( sdtasdt0 @ SV27 @ SV27 ) )
= ( sdtasdt0 @ SV1 @ SV1 ) )
= $false )
| ( ( SV46 = sz00 )
= $true )
| ( ( SV27 = sz00 )
= $true )
| ( ( SV1 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV27 )
= $false )
| ( ( aNaturalNumber0 @ SV1 )
= $false )
| ( ( aNaturalNumber0 @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[668]) ).
thf(676,plain,
! [SV85: $i,SV82: $i,SV22: $i] :
( ( ( ( SV22 = sz00 )
| ( SV82 = SV85 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV82 @ SV85 ) )
= $true )
| ( ( ( ( sdtasdt0 @ SV82 @ SV22 )
!= ( sdtasdt0 @ SV85 @ SV22 ) ) )
= $true )
| ( ( aNaturalNumber0 @ SV82 )
= $false )
| ( ( aNaturalNumber0 @ SV22 )
= $false )
| ( ( aNaturalNumber0 @ SV85 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[669]) ).
thf(677,plain,
! [SV91: $i,SV22: $i,SV89: $i] :
( ( ( aNaturalNumber0 @ SV89 )
= $false )
| ( ( aNaturalNumber0 @ SV22 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV91 ) )
= $true )
| ( ( ( SV22 = sz00 )
| ( SV89 = SV91 )
| ~ ( sdtlseqdt0 @ SV89 @ SV91 )
| ( ( sdtasdt0 @ SV22 @ SV89 )
!= ( sdtasdt0 @ SV22 @ SV91 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[670]) ).
thf(678,plain,
! [SV92: $i,SV22: $i,SV90: $i] :
( ( ( aNaturalNumber0 @ SV90 )
= $false )
| ( ( aNaturalNumber0 @ SV22 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV92 ) )
= $true )
| ( ( ( SV22 = sz00 )
| ( SV90 = SV92 )
| ~ ( sdtlseqdt0 @ SV90 @ SV92 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV22 @ SV90 ) @ ( sdtasdt0 @ SV22 @ SV92 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[671]) ).
thf(679,plain,
! [SV45: $i,SV24: $i,SV94: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV94 ) )
= $true )
| ( ( ( ( sdtpldt0 @ SV24 @ SV94 )
!= ( sdtpldt0 @ SV45 @ SV94 ) ) )
= $true )
| ( ( SV24 = SV45 )
= $true )
| ( ( sdtlseqdt0 @ SV24 @ SV45 )
= $false )
| ( ( aNaturalNumber0 @ SV24 )
= $false )
| ( ( aNaturalNumber0 @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[673]) ).
thf(680,plain,
! [SV45: $i,SV24: $i] :
( ( ( ~ ! [SY136: $i] :
( ~ ( aNaturalNumber0 @ SY136 )
| ( ( sdtpldt0 @ SY136 @ SV24 )
!= ( sdtpldt0 @ SY136 @ SV45 ) ) ) )
= $false )
| ( ( SV24 = SV45 )
= $true )
| ( ( sdtlseqdt0 @ SV24 @ SV45 )
= $false )
| ( ( aNaturalNumber0 @ SV24 )
= $false )
| ( ( aNaturalNumber0 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[674]) ).
thf(681,plain,
! [SV45: $i,SV24: $i] :
( ( ( ~ ! [SY137: $i] :
( ~ ( aNaturalNumber0 @ SY137 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SY137 @ SV24 ) @ ( sdtpldt0 @ SY137 @ SV45 ) ) ) )
= $false )
| ( ( SV24 = SV45 )
= $true )
| ( ( sdtlseqdt0 @ SV24 @ SV45 )
= $false )
| ( ( aNaturalNumber0 @ SV24 )
= $false )
| ( ( aNaturalNumber0 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[674]) ).
thf(682,plain,
! [SV85: $i,SV82: $i,SV22: $i] :
( ( ( SV22 = sz00 )
= $true )
| ( ( SV82 = SV85 )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV82 @ SV85 ) )
= $true )
| ( ( ( ( sdtasdt0 @ SV82 @ SV22 )
!= ( sdtasdt0 @ SV85 @ SV22 ) ) )
= $true )
| ( ( aNaturalNumber0 @ SV82 )
= $false )
| ( ( aNaturalNumber0 @ SV22 )
= $false )
| ( ( aNaturalNumber0 @ SV85 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[676]) ).
thf(683,plain,
! [SV89: $i,SV22: $i,SV91: $i] :
( ( ( aNaturalNumber0 @ SV91 )
= $false )
| ( ( aNaturalNumber0 @ SV22 )
= $false )
| ( ( aNaturalNumber0 @ SV89 )
= $false )
| ( ( ( SV22 = sz00 )
| ( SV89 = SV91 )
| ~ ( sdtlseqdt0 @ SV89 @ SV91 )
| ( ( sdtasdt0 @ SV22 @ SV89 )
!= ( sdtasdt0 @ SV22 @ SV91 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[677]) ).
thf(684,plain,
! [SV90: $i,SV22: $i,SV92: $i] :
( ( ( aNaturalNumber0 @ SV92 )
= $false )
| ( ( aNaturalNumber0 @ SV22 )
= $false )
| ( ( aNaturalNumber0 @ SV90 )
= $false )
| ( ( ( SV22 = sz00 )
| ( SV90 = SV92 )
| ~ ( sdtlseqdt0 @ SV90 @ SV92 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV22 @ SV90 ) @ ( sdtasdt0 @ SV22 @ SV92 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[678]) ).
thf(685,plain,
! [SV45: $i,SV24: $i,SV94: $i] :
( ( ( aNaturalNumber0 @ SV94 )
= $false )
| ( ( ( ( sdtpldt0 @ SV24 @ SV94 )
!= ( sdtpldt0 @ SV45 @ SV94 ) ) )
= $true )
| ( ( SV24 = SV45 )
= $true )
| ( ( sdtlseqdt0 @ SV24 @ SV45 )
= $false )
| ( ( aNaturalNumber0 @ SV24 )
= $false )
| ( ( aNaturalNumber0 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[679]) ).
thf(686,plain,
! [SV45: $i,SV24: $i] :
( ( ( ! [SY136: $i] :
( ~ ( aNaturalNumber0 @ SY136 )
| ( ( sdtpldt0 @ SY136 @ SV24 )
!= ( sdtpldt0 @ SY136 @ SV45 ) ) ) )
= $true )
| ( ( SV24 = SV45 )
= $true )
| ( ( sdtlseqdt0 @ SV24 @ SV45 )
= $false )
| ( ( aNaturalNumber0 @ SV24 )
= $false )
| ( ( aNaturalNumber0 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[680]) ).
thf(687,plain,
! [SV45: $i,SV24: $i] :
( ( ( ! [SY137: $i] :
( ~ ( aNaturalNumber0 @ SY137 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SY137 @ SV24 ) @ ( sdtpldt0 @ SY137 @ SV45 ) ) ) )
= $true )
| ( ( SV24 = SV45 )
= $true )
| ( ( sdtlseqdt0 @ SV24 @ SV45 )
= $false )
| ( ( aNaturalNumber0 @ SV24 )
= $false )
| ( ( aNaturalNumber0 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[681]) ).
thf(688,plain,
! [SV22: $i,SV85: $i,SV82: $i] :
( ( ( sdtlseqdt0 @ SV82 @ SV85 )
= $false )
| ( ( SV82 = SV85 )
= $true )
| ( ( SV22 = sz00 )
= $true )
| ( ( ( ( sdtasdt0 @ SV82 @ SV22 )
!= ( sdtasdt0 @ SV85 @ SV22 ) ) )
= $true )
| ( ( aNaturalNumber0 @ SV82 )
= $false )
| ( ( aNaturalNumber0 @ SV22 )
= $false )
| ( ( aNaturalNumber0 @ SV85 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[682]) ).
thf(689,plain,
! [SV91: $i,SV89: $i,SV22: $i] :
( ( ( ( SV22 = sz00 )
| ( SV89 = SV91 )
| ~ ( sdtlseqdt0 @ SV89 @ SV91 ) )
= $true )
| ( ( ( ( sdtasdt0 @ SV22 @ SV89 )
!= ( sdtasdt0 @ SV22 @ SV91 ) ) )
= $true )
| ( ( aNaturalNumber0 @ SV89 )
= $false )
| ( ( aNaturalNumber0 @ SV22 )
= $false )
| ( ( aNaturalNumber0 @ SV91 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[683]) ).
thf(690,plain,
! [SV92: $i,SV90: $i,SV22: $i] :
( ( ( ( SV22 = sz00 )
| ( SV90 = SV92 )
| ~ ( sdtlseqdt0 @ SV90 @ SV92 ) )
= $true )
| ( ( sdtlseqdt0 @ ( sdtasdt0 @ SV22 @ SV90 ) @ ( sdtasdt0 @ SV22 @ SV92 ) )
= $true )
| ( ( aNaturalNumber0 @ SV90 )
= $false )
| ( ( aNaturalNumber0 @ SV22 )
= $false )
| ( ( aNaturalNumber0 @ SV92 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[684]) ).
thf(691,plain,
! [SV45: $i,SV94: $i,SV24: $i] :
( ( ( ( sdtpldt0 @ SV24 @ SV94 )
= ( sdtpldt0 @ SV45 @ SV94 ) )
= $false )
| ( ( aNaturalNumber0 @ SV94 )
= $false )
| ( ( SV24 = SV45 )
= $true )
| ( ( sdtlseqdt0 @ SV24 @ SV45 )
= $false )
| ( ( aNaturalNumber0 @ SV24 )
= $false )
| ( ( aNaturalNumber0 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[685]) ).
thf(692,plain,
! [SV45: $i,SV24: $i,SV95: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV95 )
| ( ( sdtpldt0 @ SV95 @ SV24 )
!= ( sdtpldt0 @ SV95 @ SV45 ) ) )
= $true )
| ( ( SV24 = SV45 )
= $true )
| ( ( sdtlseqdt0 @ SV24 @ SV45 )
= $false )
| ( ( aNaturalNumber0 @ SV24 )
= $false )
| ( ( aNaturalNumber0 @ SV45 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[686]) ).
thf(693,plain,
! [SV45: $i,SV24: $i,SV96: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV96 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SV96 @ SV24 ) @ ( sdtpldt0 @ SV96 @ SV45 ) ) )
= $true )
| ( ( SV24 = SV45 )
= $true )
| ( ( sdtlseqdt0 @ SV24 @ SV45 )
= $false )
| ( ( aNaturalNumber0 @ SV24 )
= $false )
| ( ( aNaturalNumber0 @ SV45 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[687]) ).
thf(694,plain,
! [SV85: $i,SV22: $i,SV82: $i] :
( ( ( ( sdtasdt0 @ SV82 @ SV22 )
= ( sdtasdt0 @ SV85 @ SV22 ) )
= $false )
| ( ( SV22 = sz00 )
= $true )
| ( ( SV82 = SV85 )
= $true )
| ( ( sdtlseqdt0 @ SV82 @ SV85 )
= $false )
| ( ( aNaturalNumber0 @ SV82 )
= $false )
| ( ( aNaturalNumber0 @ SV22 )
= $false )
| ( ( aNaturalNumber0 @ SV85 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[688]) ).
thf(695,plain,
! [SV91: $i,SV89: $i,SV22: $i] :
( ( ( ( SV22 = sz00 )
| ( SV89 = SV91 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV89 @ SV91 ) )
= $true )
| ( ( ( ( sdtasdt0 @ SV22 @ SV89 )
!= ( sdtasdt0 @ SV22 @ SV91 ) ) )
= $true )
| ( ( aNaturalNumber0 @ SV89 )
= $false )
| ( ( aNaturalNumber0 @ SV22 )
= $false )
| ( ( aNaturalNumber0 @ SV91 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[689]) ).
thf(696,plain,
! [SV92: $i,SV90: $i,SV22: $i] :
( ( ( ( SV22 = sz00 )
| ( SV90 = SV92 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV90 @ SV92 ) )
= $true )
| ( ( sdtlseqdt0 @ ( sdtasdt0 @ SV22 @ SV90 ) @ ( sdtasdt0 @ SV22 @ SV92 ) )
= $true )
| ( ( aNaturalNumber0 @ SV90 )
= $false )
| ( ( aNaturalNumber0 @ SV22 )
= $false )
| ( ( aNaturalNumber0 @ SV92 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[690]) ).
thf(697,plain,
! [SV45: $i,SV24: $i,SV95: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV95 ) )
= $true )
| ( ( ( ( sdtpldt0 @ SV95 @ SV24 )
!= ( sdtpldt0 @ SV95 @ SV45 ) ) )
= $true )
| ( ( SV24 = SV45 )
= $true )
| ( ( sdtlseqdt0 @ SV24 @ SV45 )
= $false )
| ( ( aNaturalNumber0 @ SV24 )
= $false )
| ( ( aNaturalNumber0 @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[692]) ).
thf(698,plain,
! [SV45: $i,SV24: $i,SV96: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV96 ) )
= $true )
| ( ( sdtlseqdt0 @ ( sdtpldt0 @ SV96 @ SV24 ) @ ( sdtpldt0 @ SV96 @ SV45 ) )
= $true )
| ( ( SV24 = SV45 )
= $true )
| ( ( sdtlseqdt0 @ SV24 @ SV45 )
= $false )
| ( ( aNaturalNumber0 @ SV24 )
= $false )
| ( ( aNaturalNumber0 @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[693]) ).
thf(699,plain,
! [SV91: $i,SV89: $i,SV22: $i] :
( ( ( SV22 = sz00 )
= $true )
| ( ( SV89 = SV91 )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV89 @ SV91 ) )
= $true )
| ( ( ( ( sdtasdt0 @ SV22 @ SV89 )
!= ( sdtasdt0 @ SV22 @ SV91 ) ) )
= $true )
| ( ( aNaturalNumber0 @ SV89 )
= $false )
| ( ( aNaturalNumber0 @ SV22 )
= $false )
| ( ( aNaturalNumber0 @ SV91 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[695]) ).
thf(700,plain,
! [SV92: $i,SV90: $i,SV22: $i] :
( ( ( SV22 = sz00 )
= $true )
| ( ( SV90 = SV92 )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV90 @ SV92 ) )
= $true )
| ( ( sdtlseqdt0 @ ( sdtasdt0 @ SV22 @ SV90 ) @ ( sdtasdt0 @ SV22 @ SV92 ) )
= $true )
| ( ( aNaturalNumber0 @ SV90 )
= $false )
| ( ( aNaturalNumber0 @ SV22 )
= $false )
| ( ( aNaturalNumber0 @ SV92 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[696]) ).
thf(701,plain,
! [SV45: $i,SV24: $i,SV95: $i] :
( ( ( aNaturalNumber0 @ SV95 )
= $false )
| ( ( ( ( sdtpldt0 @ SV95 @ SV24 )
!= ( sdtpldt0 @ SV95 @ SV45 ) ) )
= $true )
| ( ( SV24 = SV45 )
= $true )
| ( ( sdtlseqdt0 @ SV24 @ SV45 )
= $false )
| ( ( aNaturalNumber0 @ SV24 )
= $false )
| ( ( aNaturalNumber0 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[697]) ).
thf(702,plain,
! [SV45: $i,SV24: $i,SV96: $i] :
( ( ( aNaturalNumber0 @ SV96 )
= $false )
| ( ( sdtlseqdt0 @ ( sdtpldt0 @ SV96 @ SV24 ) @ ( sdtpldt0 @ SV96 @ SV45 ) )
= $true )
| ( ( SV24 = SV45 )
= $true )
| ( ( sdtlseqdt0 @ SV24 @ SV45 )
= $false )
| ( ( aNaturalNumber0 @ SV24 )
= $false )
| ( ( aNaturalNumber0 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[698]) ).
thf(703,plain,
! [SV22: $i,SV91: $i,SV89: $i] :
( ( ( sdtlseqdt0 @ SV89 @ SV91 )
= $false )
| ( ( SV89 = SV91 )
= $true )
| ( ( SV22 = sz00 )
= $true )
| ( ( ( ( sdtasdt0 @ SV22 @ SV89 )
!= ( sdtasdt0 @ SV22 @ SV91 ) ) )
= $true )
| ( ( aNaturalNumber0 @ SV89 )
= $false )
| ( ( aNaturalNumber0 @ SV22 )
= $false )
| ( ( aNaturalNumber0 @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[699]) ).
thf(704,plain,
! [SV22: $i,SV92: $i,SV90: $i] :
( ( ( sdtlseqdt0 @ SV90 @ SV92 )
= $false )
| ( ( SV90 = SV92 )
= $true )
| ( ( SV22 = sz00 )
= $true )
| ( ( sdtlseqdt0 @ ( sdtasdt0 @ SV22 @ SV90 ) @ ( sdtasdt0 @ SV22 @ SV92 ) )
= $true )
| ( ( aNaturalNumber0 @ SV90 )
= $false )
| ( ( aNaturalNumber0 @ SV22 )
= $false )
| ( ( aNaturalNumber0 @ SV92 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[700]) ).
thf(705,plain,
! [SV45: $i,SV24: $i,SV95: $i] :
( ( ( ( sdtpldt0 @ SV95 @ SV24 )
= ( sdtpldt0 @ SV95 @ SV45 ) )
= $false )
| ( ( aNaturalNumber0 @ SV95 )
= $false )
| ( ( SV24 = SV45 )
= $true )
| ( ( sdtlseqdt0 @ SV24 @ SV45 )
= $false )
| ( ( aNaturalNumber0 @ SV24 )
= $false )
| ( ( aNaturalNumber0 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[701]) ).
thf(706,plain,
! [SV91: $i,SV89: $i,SV22: $i] :
( ( ( ( sdtasdt0 @ SV22 @ SV89 )
= ( sdtasdt0 @ SV22 @ SV91 ) )
= $false )
| ( ( SV22 = sz00 )
= $true )
| ( ( SV89 = SV91 )
= $true )
| ( ( sdtlseqdt0 @ SV89 @ SV91 )
= $false )
| ( ( aNaturalNumber0 @ SV89 )
= $false )
| ( ( aNaturalNumber0 @ SV22 )
= $false )
| ( ( aNaturalNumber0 @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[703]) ).
thf(707,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[129,706,705,704,702,694,691,675,672,667,666,665,662,661,644,643,642,628,627,626,625,619,617,616,608,602,601,592,591,590,570,567,551,548,528,524,521,520,519,517,515,476,457,447,446,436,435,429,428,418,412,410,409,408,356,353,344,317,316,307,297,280,209,189,188,137,133,132,130]) ).
thf(708,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[707]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM530+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n027.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 : 600
% 0.13/0.34 % DateTime : Tue Jul 5 18:54:42 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.39
% 0.13/0.39 No.of.Axioms: 43
% 0.13/0.39
% 0.13/0.39 Length.of.Defs: 0
% 0.13/0.39
% 0.13/0.39 Contains.Choice.Funs: false
% 0.20/0.41 .
% 0.20/0.43 (rf:0,axioms:43,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:45,loop_count:0,foatp_calls:0,translation:fof_full).....................................
% 0.47/0.65
% 0.47/0.65 ********************************
% 0.47/0.65 * All subproblems solved! *
% 0.47/0.65 ********************************
% 0.47/0.65 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:43,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:707,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.67/0.85
% 0.67/0.85 %**** Beginning of derivation protocol ****
% 0.67/0.85 % SZS output start CNFRefutation
% See solution above
% 0.67/0.86
% 0.67/0.86 %**** End of derivation protocol ****
% 0.67/0.86 %**** no. of clauses in derivation: 708 ****
% 0.67/0.86 %**** clause counter: 707 ****
% 0.67/0.86
% 0.67/0.86 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:43,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:707,loop_count:0,foatp_calls:1,translation:fof_full)
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