%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM526+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:34:18 AM UTC 2026
% Result : Theorem 192.43s 32.34s
% Output : CNFRefutation 192.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 42
% Syntax : Number of formulae : 1505 ( 689 unt; 0 typ; 0 def)
% Number of atoms : 17093 (7266 equ; 0 cnn)
% Maximal formula atoms : 16 ( 11 avg)
% Number of connectives : 27197 (5816 ~;6811 |; 307 &;14147 @)
% ( 0 <=>; 116 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 20 usr; 10 con; 0-3 aty)
% Number of variables : 3510 ( 0 ^;3495 !; 15 ?;3510 :)
% 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_sK2_W0,type,
sK2_W0: $i ).
thf(tp_sK3_W0,type,
sK3_W0: $i ).
thf(tp_sK4_W3,type,
sK4_W3: $i > $i > $i > $i ).
thf(tp_sK5_SY81,type,
sK5_SY81: $i > $i > $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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mIH_03) ).
thf(9,axiom,
! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( iLess0 @ W0 @ W1 )
=> $true ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mMonMul2) ).
thf(11,axiom,
! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> ( ( W0 = sz00 )
| ( W0 = sz10 )
| ( ( sz10 != W0 )
& ( sdtlseqdt0 @ sz10 @ W0 ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mLEAsym) ).
thf(17,axiom,
! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> ( sdtlseqdt0 @ W0 @ W0 ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mAMDistr) ).
thf(23,axiom,
! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> ( ( ( sdtasdt0 @ W0 @ sz00 )
= sz00 )
& ( sz00
= ( sdtasdt0 @ sz00 @ W0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulZero) ).
thf(24,axiom,
! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> ( ( ( sdtasdt0 @ W0 @ sz10 )
= W0 )
& ( W0
= ( sdtasdt0 @ sz10 @ W0 ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mMulAsso) ).
thf(26,axiom,
! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( sdtasdt0 @ W0 @ W1 )
= ( sdtasdt0 @ W1 @ W0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
thf(27,axiom,
! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> ( ( ( sdtpldt0 @ W0 @ sz00 )
= W0 )
& ( W0
= ( sdtpldt0 @ sz00 @ W0 ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mAddAsso) ).
thf(29,axiom,
! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( sdtpldt0 @ W0 @ W1 )
= ( sdtpldt0 @ W1 @ W0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
thf(30,axiom,
! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( aNaturalNumber0 @ ( sdtasdt0 @ W0 @ W1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
thf(31,axiom,
! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( aNaturalNumber0 @ ( sdtpldt0 @ W0 @ W1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
thf(32,axiom,
( ( aNaturalNumber0 @ sz10 )
& ( sz10 != sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
thf(33,axiom,
aNaturalNumber0 @ sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
thf(34,axiom,
! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNatSort) ).
thf(35,axiom,
( ( sdtasdt0 @ xm @ xm )
= ( sdtasdt0 @ xp @ ( sdtasdt0 @ xq @ xq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3082) ).
thf(36,axiom,
( ( aNaturalNumber0 @ xq )
& ( xn
= ( sdtasdt0 @ xp @ xq ) )
& ( xq
= ( sdtsldt0 @ xn @ xp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3059) ).
thf(37,axiom,
( ? [W0: $i] :
( ( aNaturalNumber0 @ W0 )
& ( ( sdtasdt0 @ xn @ xn )
= ( sdtasdt0 @ xp @ W0 ) ) )
& ( doDivides0 @ xp @ ( sdtasdt0 @ xn @ xn ) )
& ? [W0: $i] :
( ( aNaturalNumber0 @ W0 )
& ( xn
= ( sdtasdt0 @ xp @ W0 ) ) )
& ( doDivides0 @ xp @ xn ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3046) ).
thf(38,axiom,
( ( xp != sz10 )
& ! [W0: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( ? [W1: $i] :
( ( aNaturalNumber0 @ W1 )
& ( xp
= ( sdtasdt0 @ W0 @ W1 ) ) )
| ( doDivides0 @ W0 @ xp ) ) )
=> ( ( W0 = sz10 )
| ( W0 = xp ) ) )
& ( isPrime0 @ xp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3025) ).
thf(39,axiom,
( ( sdtasdt0 @ xp @ ( sdtasdt0 @ xm @ xm ) )
= ( sdtasdt0 @ xn @ xn ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3014) ).
thf(40,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 )
=> ~ ( ( ( W2 != sz10 )
& ! [W3: $i] :
( ( ( aNaturalNumber0 @ W3 )
& ? [W4: $i] :
( ( aNaturalNumber0 @ W4 )
& ( W2
= ( sdtasdt0 @ W3 @ W4 ) ) )
& ( doDivides0 @ W3 @ W2 ) )
=> ( ( W3 = sz10 )
| ( W3 = W2 ) ) ) )
| ( isPrime0 @ W2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2963) ).
thf(41,axiom,
( ( aNaturalNumber0 @ xn )
& ( aNaturalNumber0 @ xm )
& ( aNaturalNumber0 @ xp )
& ( xn != sz00 )
& ( xm != sz00 )
& ( xp != sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2987) ).
thf(42,conjecture,
( ( xm != xn )
& ( ? [W0: $i] :
( ( aNaturalNumber0 @ W0 )
& ( ( sdtpldt0 @ xm @ W0 )
= xn ) )
| ( sdtlseqdt0 @ xm @ xn ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(43,negated_conjecture,
( ( ( xm != xn )
& ( ? [W0: $i] :
( ( aNaturalNumber0 @ W0 )
& ( ( sdtpldt0 @ xm @ W0 )
= xn ) )
| ( sdtlseqdt0 @ xm @ xn ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[42]) ).
thf(44,plain,
( ( ( xm != xn )
& ( ? [W0: $i] :
( ( aNaturalNumber0 @ W0 )
& ( ( sdtpldt0 @ xm @ W0 )
= xn ) )
| ( sdtlseqdt0 @ xm @ xn ) ) )
= $false ),
inference(unfold_def,[status(thm)],[43]) ).
thf(45,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(46,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(47,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(48,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(49,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(50,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(51,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(52,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(53,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( iLess0 @ W0 @ W1 )
=> $true ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(54,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( W0 != sz00 )
=> ( sdtlseqdt0 @ W1 @ ( sdtasdt0 @ W1 @ W0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(55,plain,
( ( ! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> ( ( W0 = sz00 )
| ( W0 = sz10 )
| ( ( sz10 != W0 )
& ( sdtlseqdt0 @ sz10 @ W0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(56,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(57,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(58,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(59,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(60,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(61,plain,
( ( ! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> ( sdtlseqdt0 @ W0 @ W0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(62,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(63,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(64,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(65,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(66,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(67,plain,
( ( ! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> ( ( ( sdtasdt0 @ W0 @ sz00 )
= sz00 )
& ( sz00
= ( sdtasdt0 @ sz00 @ W0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(68,plain,
( ( ! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> ( ( ( sdtasdt0 @ W0 @ sz10 )
= W0 )
& ( W0
= ( sdtasdt0 @ sz10 @ W0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(69,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(70,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( sdtasdt0 @ W0 @ W1 )
= ( sdtasdt0 @ W1 @ W0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(71,plain,
( ( ! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> ( ( ( sdtpldt0 @ W0 @ sz00 )
= W0 )
& ( W0
= ( sdtpldt0 @ sz00 @ W0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(72,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(73,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( sdtpldt0 @ W0 @ W1 )
= ( sdtpldt0 @ W1 @ W0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(74,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( aNaturalNumber0 @ ( sdtasdt0 @ W0 @ W1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(75,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( aNaturalNumber0 @ ( sdtpldt0 @ W0 @ W1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(76,plain,
( ( ( aNaturalNumber0 @ sz10 )
& ( sz10 != sz00 ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(77,plain,
( ( aNaturalNumber0 @ sz00 )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(78,plain,
( ( ! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> $true ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(79,plain,
( ( ( sdtasdt0 @ xm @ xm )
= ( sdtasdt0 @ xp @ ( sdtasdt0 @ xq @ xq ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(80,plain,
( ( ( aNaturalNumber0 @ xq )
& ( xn
= ( sdtasdt0 @ xp @ xq ) )
& ( xq
= ( sdtsldt0 @ xn @ xp ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(81,plain,
( ( ? [W0: $i] :
( ( aNaturalNumber0 @ W0 )
& ( ( sdtasdt0 @ xn @ xn )
= ( sdtasdt0 @ xp @ W0 ) ) )
& ( doDivides0 @ xp @ ( sdtasdt0 @ xn @ xn ) )
& ? [W0: $i] :
( ( aNaturalNumber0 @ W0 )
& ( xn
= ( sdtasdt0 @ xp @ W0 ) ) )
& ( doDivides0 @ xp @ xn ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(82,plain,
( ( ( xp != sz10 )
& ! [W0: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( ? [W1: $i] :
( ( aNaturalNumber0 @ W1 )
& ( xp
= ( sdtasdt0 @ W0 @ W1 ) ) )
| ( doDivides0 @ W0 @ xp ) ) )
=> ( ( W0 = sz10 )
| ( W0 = xp ) ) )
& ( isPrime0 @ xp ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(83,plain,
( ( ( sdtasdt0 @ xp @ ( sdtasdt0 @ xm @ xm ) )
= ( sdtasdt0 @ xn @ xn ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(84,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 )
=> ~ ( ( ( W2 != sz10 )
& ! [W3: $i] :
( ( ( aNaturalNumber0 @ W3 )
& ? [W4: $i] :
( ( aNaturalNumber0 @ W4 )
& ( W2
= ( sdtasdt0 @ W3 @ W4 ) ) )
& ( doDivides0 @ W3 @ W2 ) )
=> ( ( W3 = sz10 )
| ( W3 = W2 ) ) ) )
| ( isPrime0 @ W2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(85,plain,
( ( ( aNaturalNumber0 @ xn )
& ( aNaturalNumber0 @ xm )
& ( aNaturalNumber0 @ xp )
& ( xn != sz00 )
& ( xm != sz00 )
& ( xp != sz00 ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(86,plain,
( ( xm != xn )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[44]) ).
thf(87,plain,
( ( ? [W0: $i] :
( ( aNaturalNumber0 @ W0 )
& ( ( sdtpldt0 @ xm @ W0 )
= xn ) )
| ( sdtlseqdt0 @ xm @ xn ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[44]) ).
thf(88,plain,
( ( ~ ( ( xm != xn ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[86]) ).
thf(89,plain,
( ( ~ ( ? [W0: $i] :
( ( aNaturalNumber0 @ W0 )
& ( ( sdtpldt0 @ xm @ W0 )
= xn ) )
| ( sdtlseqdt0 @ xm @ xn ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[87]) ).
thf(90,plain,
( ( xm = xn )
= $true ),
inference(extcnf_combined,[status(esa)],[88]) ).
thf(91,plain,
( ( ! [W0: $i] :
( ( ( sdtpldt0 @ xm @ W0 )
!= xn )
| ~ ( aNaturalNumber0 @ W0 ) )
& ~ ( sdtlseqdt0 @ xm @ xn ) )
= $true ),
inference(extcnf_combined,[status(esa)],[89]) ).
thf(92,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)],[45]) ).
thf(93,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)],[46]) ).
thf(94,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)],[47]) ).
thf(95,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ( W1 = sz00 )
| ~ ( doDivides0 @ W0 @ W1 )
| ( sdtlseqdt0 @ W0 @ W1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[48]) ).
thf(96,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)],[49]) ).
thf(97,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)],[50]) ).
thf(98,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)],[51]) ).
thf(99,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ( W0 = W1 )
| ~ ( sdtlseqdt0 @ W0 @ W1 )
| ( iLess0 @ W0 @ W1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[52]) ).
thf(100,plain,
( ( ! [W0: $i] :
~ ( aNaturalNumber0 @ W0 )
| ! [W1: $i] :
~ ( aNaturalNumber0 @ W1 )
| $true )
= $true ),
inference(extcnf_combined,[status(esa)],[53]) ).
thf(101,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ( W0 = sz00 )
| ( sdtlseqdt0 @ W1 @ ( sdtasdt0 @ W1 @ W0 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[54]) ).
thf(102,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)],[55]) ).
thf(103,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)],[56]) ).
thf(104,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)],[57]) ).
thf(105,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)],[58]) ).
thf(106,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)],[59]) ).
thf(107,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ~ ( sdtlseqdt0 @ W0 @ W1 )
| ~ ( sdtlseqdt0 @ W1 @ W0 )
| ( W0 = W1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[60]) ).
thf(108,plain,
( ( ! [W0: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ( sdtlseqdt0 @ W0 @ W0 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[61]) ).
thf(109,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ( ( sdtasdt0 @ W0 @ W1 )
!= sz00 )
| ( W0 = sz00 )
| ( W1 = sz00 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[62]) ).
thf(110,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)],[63]) ).
thf(111,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)],[64]) ).
thf(112,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)],[65]) ).
thf(113,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)],[66]) ).
thf(114,plain,
( ( ! [W0: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ( ( sdtasdt0 @ W0 @ sz00 )
= sz00 ) )
& ! [W0: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ( sz00
= ( sdtasdt0 @ sz00 @ W0 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[67]) ).
thf(115,plain,
( ( ! [W0: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ( ( sdtasdt0 @ W0 @ sz10 )
= W0 ) )
& ! [W0: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ( W0
= ( sdtasdt0 @ sz10 @ W0 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[68]) ).
thf(116,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)],[69]) ).
thf(117,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ( ( sdtasdt0 @ W0 @ W1 )
= ( sdtasdt0 @ W1 @ W0 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[70]) ).
thf(118,plain,
( ( ! [W0: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ( ( sdtpldt0 @ W0 @ sz00 )
= W0 ) )
& ! [W0: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ( W0
= ( sdtpldt0 @ sz00 @ W0 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[71]) ).
thf(119,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)],[72]) ).
thf(120,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ( ( sdtpldt0 @ W0 @ W1 )
= ( sdtpldt0 @ W1 @ W0 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[73]) ).
thf(121,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ( aNaturalNumber0 @ ( sdtasdt0 @ W0 @ W1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[74]) ).
thf(122,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ( aNaturalNumber0 @ ( sdtpldt0 @ W0 @ W1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[75]) ).
thf(123,plain,
( ( ( sz10 != sz00 )
& ( aNaturalNumber0 @ sz10 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[76]) ).
thf(124,plain,
( ( ! [W0: $i] : $true )
= $true ),
inference(extcnf_combined,[status(esa)],[78]) ).
thf(125,plain,
( ( ( xn
= ( sdtasdt0 @ xp @ xq ) )
& ( aNaturalNumber0 @ xq )
& ( xq
= ( sdtsldt0 @ xn @ xp ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[80]) ).
thf(126,plain,
( ( ( ( sdtasdt0 @ xn @ xn )
= ( sdtasdt0 @ xp @ sK3_W0 ) )
& ( aNaturalNumber0 @ sK3_W0 )
& ( doDivides0 @ xp @ ( sdtasdt0 @ xn @ xn ) )
& ( xn
= ( sdtasdt0 @ xp @ sK2_W0 ) )
& ( aNaturalNumber0 @ sK2_W0 )
& ( doDivides0 @ xp @ xn ) )
= $true ),
inference(extcnf_combined,[status(esa)],[81]) ).
thf(127,plain,
( ( ! [W0: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ! [W1: $i] :
( ( xp
!= ( sdtasdt0 @ W0 @ W1 ) )
| ~ ( aNaturalNumber0 @ W1 ) )
| ( W0 = sz10 )
| ( W0 = xp ) )
& ! [W0: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( doDivides0 @ W0 @ xp )
| ( W0 = sz10 )
| ( W0 = xp ) )
& ( xp != sz10 )
& ( isPrime0 @ xp ) )
= $true ),
inference(extcnf_combined,[status(esa)],[82]) ).
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 )
| ( ( W2
= ( sdtasdt0 @ ( sK4_W3 @ W2 @ W1 @ W0 ) @ ( sK5_SY81 @ W2 @ W1 @ W0 ) ) )
& ( aNaturalNumber0 @ ( sK5_SY81 @ W2 @ W1 @ W0 ) )
& ( aNaturalNumber0 @ ( sK4_W3 @ W2 @ W1 @ W0 ) )
& ( doDivides0 @ ( sK4_W3 @ W2 @ W1 @ W0 ) @ W2 )
& ( ( sK4_W3 @ W2 @ W1 @ W0 )
!= sz10 )
& ( ( sK4_W3 @ W2 @ W1 @ W0 )
!= W2 ) )
| ( W2 = sz10 ) )
& ! [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)],[84]) ).
thf(129,plain,
( ( ( xp != sz00 )
& ( xm != sz00 )
& ( xn != sz00 )
& ( aNaturalNumber0 @ xn )
& ( aNaturalNumber0 @ xm )
& ( aNaturalNumber0 @ xp ) )
= $true ),
inference(extcnf_combined,[status(esa)],[85]) ).
thf(130,plain,
( ( ( xp != sz00 )
& ( xm != sz00 )
& ( xn != sz00 )
& ( aNaturalNumber0 @ xn )
& ( aNaturalNumber0 @ xm )
& ( aNaturalNumber0 @ xp ) )
= $true ),
inference(copy,[status(thm)],[129]) ).
thf(131,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 )
| ( ( W2
= ( sdtasdt0 @ ( sK4_W3 @ W2 @ W1 @ W0 ) @ ( sK5_SY81 @ W2 @ W1 @ W0 ) ) )
& ( aNaturalNumber0 @ ( sK5_SY81 @ W2 @ W1 @ W0 ) )
& ( aNaturalNumber0 @ ( sK4_W3 @ W2 @ W1 @ W0 ) )
& ( doDivides0 @ ( sK4_W3 @ W2 @ W1 @ W0 ) @ W2 )
& ( ( sK4_W3 @ W2 @ W1 @ W0 )
!= sz10 )
& ( ( sK4_W3 @ W2 @ W1 @ W0 )
!= W2 ) )
| ( W2 = sz10 ) )
& ! [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)],[128]) ).
thf(132,plain,
( ( ( sdtasdt0 @ xp @ ( sdtasdt0 @ xm @ xm ) )
= ( sdtasdt0 @ xn @ xn ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(133,plain,
( ( ! [W0: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ! [W1: $i] :
( ( xp
!= ( sdtasdt0 @ W0 @ W1 ) )
| ~ ( aNaturalNumber0 @ W1 ) )
| ( W0 = sz10 )
| ( W0 = xp ) )
& ! [W0: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( doDivides0 @ W0 @ xp )
| ( W0 = sz10 )
| ( W0 = xp ) )
& ( xp != sz10 )
& ( isPrime0 @ xp ) )
= $true ),
inference(copy,[status(thm)],[127]) ).
thf(134,plain,
( ( ( ( sdtasdt0 @ xn @ xn )
= ( sdtasdt0 @ xp @ sK3_W0 ) )
& ( aNaturalNumber0 @ sK3_W0 )
& ( doDivides0 @ xp @ ( sdtasdt0 @ xn @ xn ) )
& ( xn
= ( sdtasdt0 @ xp @ sK2_W0 ) )
& ( aNaturalNumber0 @ sK2_W0 )
& ( doDivides0 @ xp @ xn ) )
= $true ),
inference(copy,[status(thm)],[126]) ).
thf(135,plain,
( ( ( xn
= ( sdtasdt0 @ xp @ xq ) )
& ( aNaturalNumber0 @ xq )
& ( xq
= ( sdtsldt0 @ xn @ xp ) ) )
= $true ),
inference(copy,[status(thm)],[125]) ).
thf(136,plain,
( ( ( sdtasdt0 @ xm @ xm )
= ( sdtasdt0 @ xp @ ( sdtasdt0 @ xq @ xq ) ) )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(137,plain,
( ( ! [W0: $i] : $true )
= $true ),
inference(copy,[status(thm)],[124]) ).
thf(138,plain,
( ( aNaturalNumber0 @ sz00 )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(139,plain,
( ( ( sz10 != sz00 )
& ( aNaturalNumber0 @ sz10 ) )
= $true ),
inference(copy,[status(thm)],[123]) ).
thf(140,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ( aNaturalNumber0 @ ( sdtpldt0 @ W0 @ W1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(141,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ( aNaturalNumber0 @ ( sdtasdt0 @ W0 @ W1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[121]) ).
thf(142,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ( ( sdtpldt0 @ W0 @ W1 )
= ( sdtpldt0 @ W1 @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[120]) ).
thf(143,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)],[119]) ).
thf(144,plain,
( ( ! [W0: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ( ( sdtpldt0 @ W0 @ sz00 )
= W0 ) )
& ! [W0: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ( W0
= ( sdtpldt0 @ sz00 @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(145,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ( ( sdtasdt0 @ W0 @ W1 )
= ( sdtasdt0 @ W1 @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(146,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)],[116]) ).
thf(147,plain,
( ( ! [W0: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ( ( sdtasdt0 @ W0 @ sz10 )
= W0 ) )
& ! [W0: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ( W0
= ( sdtasdt0 @ sz10 @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[115]) ).
thf(148,plain,
( ( ! [W0: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ( ( sdtasdt0 @ W0 @ sz00 )
= sz00 ) )
& ! [W0: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ( sz00
= ( sdtasdt0 @ sz00 @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(149,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)],[113]) ).
thf(150,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)],[112]) ).
thf(151,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)],[111]) ).
thf(152,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)],[110]) ).
thf(153,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ( ( sdtasdt0 @ W0 @ W1 )
!= sz00 )
| ( W0 = sz00 )
| ( W1 = sz00 ) ) )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(154,plain,
( ( ! [W0: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ( sdtlseqdt0 @ W0 @ W0 ) ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(155,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ~ ( sdtlseqdt0 @ W0 @ W1 )
| ~ ( sdtlseqdt0 @ W1 @ W0 )
| ( W0 = W1 ) ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(156,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)],[106]) ).
thf(157,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)],[105]) ).
thf(158,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)],[104]) ).
thf(159,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)],[103]) ).
thf(160,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)],[102]) ).
thf(161,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ( W0 = sz00 )
| ( sdtlseqdt0 @ W1 @ ( sdtasdt0 @ W1 @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(162,plain,
( ( ! [W0: $i] :
~ ( aNaturalNumber0 @ W0 )
| ! [W1: $i] :
~ ( aNaturalNumber0 @ W1 )
| $true )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(163,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ( W0 = W1 )
| ~ ( sdtlseqdt0 @ W0 @ W1 )
| ( iLess0 @ W0 @ W1 ) ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(164,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)],[98]) ).
thf(165,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)],[97]) ).
thf(166,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)],[96]) ).
thf(167,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ( W1 = sz00 )
| ~ ( doDivides0 @ W0 @ W1 )
| ( sdtlseqdt0 @ W0 @ W1 ) ) )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(168,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)],[94]) ).
thf(169,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)],[93]) ).
thf(170,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)],[92]) ).
thf(171,plain,
( ( xm = xn )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(172,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)],[149]) ).
thf(173,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( ( sdtasdt0 @ SX0 @ sz10 )
= SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( SX0
= ( sdtasdt0 @ sz10 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[147]) ).
thf(174,plain,
( ( ~ ( ~ ( ( sz10 != sz00 ) )
| ~ ( aNaturalNumber0 @ sz10 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[139]) ).
thf(175,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)],[158]) ).
thf(176,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)],[151]) ).
thf(177,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xn @ xn )
!= ( sdtasdt0 @ xp @ sK3_W0 ) )
| ~ ( aNaturalNumber0 @ sK3_W0 ) )
| ~ ( doDivides0 @ xp @ ( sdtasdt0 @ xn @ xn ) ) )
| ~ ~ ( ( xn
!= ( sdtasdt0 @ xp @ sK2_W0 ) )
| ~ ( aNaturalNumber0 @ sK2_W0 ) ) )
| ~ ( doDivides0 @ xp @ xn ) ) )
= $true ),
inference(unfold_def,[status(thm)],[134]) ).
thf(178,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ! [SX1: $i] :
( ( xp
!= ( sdtasdt0 @ SX0 @ SX1 ) )
| ~ ( aNaturalNumber0 @ SX1 ) )
| ( SX0 = sz10 )
| ( SX0 = xp ) )
| ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( doDivides0 @ SX0 @ xp )
| ( SX0 = sz10 )
| ( SX0 = xp ) ) )
| ~ ( ( xp != sz10 ) ) )
| ~ ( isPrime0 @ xp ) ) )
= $true ),
inference(unfold_def,[status(thm)],[133]) ).
thf(179,plain,
( ( ~ ( ~ ( ( xp != sz00 ) )
| ~ ~ ( ~ ( ( xm != sz00 ) )
| ~ ~ ( ~ ( ( xn != sz00 ) )
| ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ xn )
| ~ ( aNaturalNumber0 @ xm ) )
| ~ ( aNaturalNumber0 @ xp ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[130]) ).
thf(180,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( ( sdtasdt0 @ SX0 @ sz00 )
= sz00 ) )
| ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( sz00
= ( sdtasdt0 @ sz00 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[148]) ).
thf(181,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)],[169]) ).
thf(182,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)],[157]) ).
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)],[144]) ).
thf(184,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)],[150]) ).
thf(185,plain,
( ( ~ ( ~ ~ ( ( xn
!= ( sdtasdt0 @ xp @ xq ) )
| ~ ( aNaturalNumber0 @ xq ) )
| ( xq
!= ( sdtsldt0 @ xn @ xp ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[135]) ).
thf(186,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ( SX2 = sz00 )
| ( SX1 = sz00 )
| ( SX0 = sz00 )
| ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 )
| ~ ( aNaturalNumber0 @ SX2 )
| ( ( sdtasdt0 @ SX2 @ ( sdtasdt0 @ SX1 @ SX1 ) )
!= ( sdtasdt0 @ SX0 @ SX0 ) )
| ~ ( iLess0 @ SX0 @ xn )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( SX2
!= ( sdtasdt0 @ ( sK4_W3 @ SX2 @ SX1 @ SX0 ) @ ( sK5_SY81 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( aNaturalNumber0 @ ( sK5_SY81 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( aNaturalNumber0 @ ( sK4_W3 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( doDivides0 @ ( sK4_W3 @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ~ ( ~ ( ( ( sK4_W3 @ SX2 @ SX1 @ SX0 )
!= sz10 ) )
| ~ ( ( ( sK4_W3 @ SX2 @ SX1 @ SX0 )
!= SX2 ) ) ) )
| ( SX2 = sz10 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2 = sz00 )
| ( SX1 = sz00 )
| ( SX0 = sz00 )
| ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 )
| ~ ( aNaturalNumber0 @ SX2 )
| ( ( sdtasdt0 @ SX2 @ ( sdtasdt0 @ SX1 @ SX1 ) )
!= ( sdtasdt0 @ SX0 @ SX0 ) )
| ~ ( iLess0 @ SX0 @ xn )
| ~ ( isPrime0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[131]) ).
thf(187,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)],[159]) ).
thf(188,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)],[160]) ).
thf(189,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)],[152]) ).
thf(190,plain,
$true = $true,
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(191,plain,
! [SV2: $i] :
( ( ! [SY82: $i] :
( ~ ( aNaturalNumber0 @ SV2 )
| ~ ( aNaturalNumber0 @ SY82 )
| ( aNaturalNumber0 @ ( sdtpldt0 @ SV2 @ SY82 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(192,plain,
! [SV3: $i] :
( ( ! [SY83: $i] :
( ~ ( aNaturalNumber0 @ SV3 )
| ~ ( aNaturalNumber0 @ SY83 )
| ( aNaturalNumber0 @ ( sdtasdt0 @ SV3 @ SY83 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(193,plain,
! [SV4: $i] :
( ( ! [SY84: $i] :
( ~ ( aNaturalNumber0 @ SV4 )
| ~ ( aNaturalNumber0 @ SY84 )
| ( ( sdtpldt0 @ SV4 @ SY84 )
= ( sdtpldt0 @ SY84 @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(194,plain,
! [SV5: $i] :
( ( ! [SY85: $i,SY86: $i] :
( ~ ( aNaturalNumber0 @ SV5 )
| ~ ( aNaturalNumber0 @ SY85 )
| ~ ( aNaturalNumber0 @ SY86 )
| ( ( sdtpldt0 @ ( sdtpldt0 @ SV5 @ SY85 ) @ SY86 )
= ( sdtpldt0 @ SV5 @ ( sdtpldt0 @ SY85 @ SY86 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(195,plain,
! [SV6: $i] :
( ( ! [SY87: $i] :
( ~ ( aNaturalNumber0 @ SV6 )
| ~ ( aNaturalNumber0 @ SY87 )
| ( ( sdtasdt0 @ SV6 @ SY87 )
= ( sdtasdt0 @ SY87 @ SV6 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(196,plain,
! [SV7: $i] :
( ( ! [SY88: $i,SY89: $i] :
( ~ ( aNaturalNumber0 @ SV7 )
| ~ ( aNaturalNumber0 @ SY88 )
| ~ ( aNaturalNumber0 @ SY89 )
| ( ( sdtasdt0 @ ( sdtasdt0 @ SV7 @ SY88 ) @ SY89 )
= ( sdtasdt0 @ SV7 @ ( sdtasdt0 @ SY88 @ SY89 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(197,plain,
! [SV8: $i] :
( ( ! [SY90: $i] :
( ~ ( aNaturalNumber0 @ SV8 )
| ~ ( aNaturalNumber0 @ SY90 )
| ( ( sdtasdt0 @ SV8 @ SY90 )
!= sz00 )
| ( SV8 = sz00 )
| ( SY90 = sz00 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(198,plain,
! [SV9: $i] :
( ( ~ ( aNaturalNumber0 @ SV9 )
| ( sdtlseqdt0 @ SV9 @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(199,plain,
! [SV10: $i] :
( ( ! [SY91: $i] :
( ~ ( aNaturalNumber0 @ SV10 )
| ~ ( aNaturalNumber0 @ SY91 )
| ~ ( sdtlseqdt0 @ SV10 @ SY91 )
| ~ ( sdtlseqdt0 @ SY91 @ SV10 )
| ( SV10 = SY91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(200,plain,
! [SV11: $i] :
( ( ! [SY92: $i,SY93: $i] :
( ~ ( aNaturalNumber0 @ SV11 )
| ~ ( aNaturalNumber0 @ SY92 )
| ~ ( aNaturalNumber0 @ SY93 )
| ~ ( sdtlseqdt0 @ SV11 @ SY92 )
| ~ ( sdtlseqdt0 @ SY92 @ SY93 )
| ( sdtlseqdt0 @ SV11 @ SY93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(201,plain,
! [SV12: $i] :
( ( ! [SY94: $i] :
( ~ ( aNaturalNumber0 @ SV12 )
| ~ ( aNaturalNumber0 @ SY94 )
| ( SV12 = sz00 )
| ( sdtlseqdt0 @ SY94 @ ( sdtasdt0 @ SY94 @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(202,plain,
( ( ( ! [W0: $i] :
~ ( aNaturalNumber0 @ W0 )
| ! [W1: $i] :
~ ( aNaturalNumber0 @ W1 ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[162]) ).
thf(203,plain,
! [SV13: $i] :
( ( ! [SY95: $i] :
( ~ ( aNaturalNumber0 @ SV13 )
| ~ ( aNaturalNumber0 @ SY95 )
| ( SV13 = SY95 )
| ~ ( sdtlseqdt0 @ SV13 @ SY95 )
| ( iLess0 @ SV13 @ SY95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(204,plain,
! [SV14: $i] :
( ( ! [SY96: $i,SY97: $i] :
( ~ ( aNaturalNumber0 @ SV14 )
| ~ ( aNaturalNumber0 @ SY96 )
| ~ ( aNaturalNumber0 @ SY97 )
| ~ ( doDivides0 @ SV14 @ SY96 )
| ~ ( doDivides0 @ SY96 @ SY97 )
| ( doDivides0 @ SV14 @ SY97 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(205,plain,
! [SV15: $i] :
( ( ! [SY98: $i,SY99: $i] :
( ~ ( aNaturalNumber0 @ SV15 )
| ~ ( aNaturalNumber0 @ SY98 )
| ~ ( aNaturalNumber0 @ SY99 )
| ~ ( doDivides0 @ SV15 @ SY98 )
| ~ ( doDivides0 @ SV15 @ SY99 )
| ( doDivides0 @ SV15 @ ( sdtpldt0 @ SY98 @ SY99 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(206,plain,
! [SV16: $i] :
( ( ! [SY100: $i,SY101: $i] :
( ~ ( aNaturalNumber0 @ SV16 )
| ~ ( aNaturalNumber0 @ SY100 )
| ~ ( aNaturalNumber0 @ SY101 )
| ~ ( doDivides0 @ SV16 @ SY100 )
| ~ ( doDivides0 @ SV16 @ ( sdtpldt0 @ SY100 @ SY101 ) )
| ( doDivides0 @ SV16 @ SY101 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(207,plain,
! [SV17: $i] :
( ( ! [SY102: $i] :
( ~ ( aNaturalNumber0 @ SV17 )
| ~ ( aNaturalNumber0 @ SY102 )
| ( SY102 = sz00 )
| ~ ( doDivides0 @ SV17 @ SY102 )
| ( sdtlseqdt0 @ SV17 @ SY102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(208,plain,
! [SV18: $i] :
( ( ! [SY103: $i] :
( ~ ( aNaturalNumber0 @ SV18 )
| ~ ( aNaturalNumber0 @ SY103 )
| ( SV18 = sz00 )
| ~ ( doDivides0 @ SV18 @ SY103 )
| ! [SY104: $i] :
( ~ ( aNaturalNumber0 @ SY104 )
| ( ( sdtasdt0 @ SY104 @ ( sdtsldt0 @ SY103 @ SV18 ) )
= ( sdtsldt0 @ ( sdtasdt0 @ SY104 @ SY103 ) @ SV18 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(209,plain,
! [SV19: $i] :
( ( ! [SY105: $i,SY106: $i] :
( ~ ( aNaturalNumber0 @ SV19 )
| ~ ( aNaturalNumber0 @ SY105 )
| ~ ( aNaturalNumber0 @ SY106 )
| ~ ( doDivides0 @ SY106 @ ( sdtasdt0 @ SV19 @ SY105 ) )
| ~ ( isPrime0 @ SY106 )
| ( doDivides0 @ SY106 @ SV19 )
| ( doDivides0 @ SY106 @ SY105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(210,plain,
! [SV20: $i] :
( ( ~ ( ~ ! [SY107: $i,SY108: $i] :
( ~ ( aNaturalNumber0 @ SV20 )
| ~ ( aNaturalNumber0 @ SY107 )
| ~ ( aNaturalNumber0 @ SY108 )
| ( ( sdtasdt0 @ SV20 @ ( sdtpldt0 @ SY107 @ SY108 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV20 @ SY107 ) @ ( sdtasdt0 @ SV20 @ SY108 ) ) ) )
| ~ ! [SY109: $i,SY110: $i] :
( ~ ( aNaturalNumber0 @ SV20 )
| ~ ( aNaturalNumber0 @ SY109 )
| ~ ( aNaturalNumber0 @ SY110 )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SY109 @ SY110 ) @ SV20 )
= ( sdtpldt0 @ ( sdtasdt0 @ SY109 @ SV20 ) @ ( sdtasdt0 @ SY110 @ SV20 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(211,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( ( sdtasdt0 @ SX0 @ sz10 )
= SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( SX0
= ( sdtasdt0 @ sz10 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(212,plain,
( ( ~ ( ( sz10 != sz00 ) )
| ~ ( aNaturalNumber0 @ sz10 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(213,plain,
! [SV21: $i] :
( ( ! [SY111: $i] :
( ~ ( aNaturalNumber0 @ SV21 )
| ~ ( aNaturalNumber0 @ SY111 )
| ( SV21 = SY111 )
| ~ ( sdtlseqdt0 @ SV21 @ SY111 )
| ~ ( ~ ~ ( ~ ! [SY112: $i] :
( ~ ( aNaturalNumber0 @ SY112 )
| ( ( sdtpldt0 @ SV21 @ SY112 )
!= ( sdtpldt0 @ SY111 @ SY112 ) ) )
| ~ ~ ( ~ ! [SY113: $i] :
( ~ ( aNaturalNumber0 @ SY113 )
| ( ( sdtpldt0 @ SY113 @ SV21 )
!= ( sdtpldt0 @ SY113 @ SY111 ) ) )
| ~ ! [SY114: $i] :
( ~ ( aNaturalNumber0 @ SY114 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SY114 @ SV21 ) @ ( sdtpldt0 @ SY114 @ SY111 ) ) ) ) )
| ~ ! [SY115: $i] :
( ~ ( aNaturalNumber0 @ SY115 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SV21 @ SY115 ) @ ( sdtpldt0 @ SY111 @ SY115 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(214,plain,
! [SV22: $i] :
( ( ~ ( aNaturalNumber0 @ SV22 )
| ( SV22 = sz00 )
| ~ ( ~ ! [SY116: $i,SY117: $i] :
( ~ ( aNaturalNumber0 @ SY116 )
| ~ ( aNaturalNumber0 @ SY117 )
| ( ( sdtasdt0 @ SV22 @ SY116 )
!= ( sdtasdt0 @ SV22 @ SY117 ) )
| ( SY116 = SY117 ) )
| ~ ! [SY118: $i,SY119: $i] :
( ~ ( aNaturalNumber0 @ SY118 )
| ~ ( aNaturalNumber0 @ SY119 )
| ( ( sdtasdt0 @ SY118 @ SV22 )
!= ( sdtasdt0 @ SY119 @ SV22 ) )
| ( SY118 = SY119 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(215,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xn @ xn )
!= ( sdtasdt0 @ xp @ sK3_W0 ) )
| ~ ( aNaturalNumber0 @ sK3_W0 ) )
| ~ ( doDivides0 @ xp @ ( sdtasdt0 @ xn @ xn ) ) )
| ~ ~ ( ( xn
!= ( sdtasdt0 @ xp @ sK2_W0 ) )
| ~ ( aNaturalNumber0 @ sK2_W0 ) ) )
| ~ ( doDivides0 @ xp @ xn ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(216,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ! [SX1: $i] :
( ( xp
!= ( sdtasdt0 @ SX0 @ SX1 ) )
| ~ ( aNaturalNumber0 @ SX1 ) )
| ( SX0 = sz10 )
| ( SX0 = xp ) )
| ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( doDivides0 @ SX0 @ xp )
| ( SX0 = sz10 )
| ( SX0 = xp ) ) )
| ~ ( ( xp != sz10 ) ) )
| ~ ( isPrime0 @ xp ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(217,plain,
( ( ~ ( ( xp != sz00 ) )
| ~ ~ ( ~ ( ( xm != sz00 ) )
| ~ ~ ( ~ ( ( xn != sz00 ) )
| ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ xn )
| ~ ( aNaturalNumber0 @ xm ) )
| ~ ( aNaturalNumber0 @ xp ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(218,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( ( sdtasdt0 @ SX0 @ sz00 )
= sz00 ) )
| ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( sz00
= ( sdtasdt0 @ sz00 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(219,plain,
! [SV23: $i] :
( ( ( SV23 = sz10 )
| ( SV23 = sz00 )
| ~ ( aNaturalNumber0 @ SV23 )
| ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ ( sK1_W1 @ SV23 ) )
| ~ ( doDivides0 @ ( sK1_W1 @ SV23 ) @ SV23 ) )
| ~ ( isPrime0 @ ( sK1_W1 @ SV23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(220,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)],[182]) ).
thf(221,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(222,plain,
! [SV24: $i] :
( ( ~ ( ~ ! [SY120: $i,SY121: $i] :
( ~ ( aNaturalNumber0 @ SV24 )
| ~ ( aNaturalNumber0 @ SY120 )
| ~ ( aNaturalNumber0 @ SY121 )
| ( ( sdtpldt0 @ SV24 @ SY120 )
!= ( sdtpldt0 @ SV24 @ SY121 ) )
| ( SY120 = SY121 ) )
| ~ ! [SY122: $i,SY123: $i] :
( ~ ( aNaturalNumber0 @ SV24 )
| ~ ( aNaturalNumber0 @ SY122 )
| ~ ( aNaturalNumber0 @ SY123 )
| ( ( sdtpldt0 @ SY122 @ SV24 )
!= ( sdtpldt0 @ SY123 @ SV24 ) )
| ( SY122 = SY123 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(223,plain,
( ( ~ ~ ( ( xn
!= ( sdtasdt0 @ xp @ xq ) )
| ~ ( aNaturalNumber0 @ xq ) )
| ( xq
!= ( sdtsldt0 @ xn @ xp ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(224,plain,
! [SV25: $i] :
( ( ~ ( ~ ! [SY124: $i,SY125: $i] :
( ( SY125 = sz00 )
| ( SY124 = sz00 )
| ( SV25 = sz00 )
| ~ ( aNaturalNumber0 @ SV25 )
| ~ ( aNaturalNumber0 @ SY124 )
| ~ ( aNaturalNumber0 @ SY125 )
| ( ( sdtasdt0 @ SY125 @ ( sdtasdt0 @ SY124 @ SY124 ) )
!= ( sdtasdt0 @ SV25 @ SV25 ) )
| ~ ( iLess0 @ SV25 @ xn )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( SY125
!= ( sdtasdt0 @ ( sK4_W3 @ SY125 @ SY124 @ SV25 ) @ ( sK5_SY81 @ SY125 @ SY124 @ SV25 ) ) )
| ~ ( aNaturalNumber0 @ ( sK5_SY81 @ SY125 @ SY124 @ SV25 ) ) )
| ~ ( aNaturalNumber0 @ ( sK4_W3 @ SY125 @ SY124 @ SV25 ) ) )
| ~ ( doDivides0 @ ( sK4_W3 @ SY125 @ SY124 @ SV25 ) @ SY125 ) )
| ~ ~ ( ~ ( ( ( sK4_W3 @ SY125 @ SY124 @ SV25 )
!= sz10 ) )
| ~ ( ( ( sK4_W3 @ SY125 @ SY124 @ SV25 )
!= SY125 ) ) ) )
| ( SY125 = sz10 ) )
| ~ ! [SY126: $i,SY127: $i] :
( ( SY127 = sz00 )
| ( SY126 = sz00 )
| ( SV25 = sz00 )
| ~ ( aNaturalNumber0 @ SV25 )
| ~ ( aNaturalNumber0 @ SY126 )
| ~ ( aNaturalNumber0 @ SY127 )
| ( ( sdtasdt0 @ SY127 @ ( sdtasdt0 @ SY126 @ SY126 ) )
!= ( sdtasdt0 @ SV25 @ SV25 ) )
| ~ ( iLess0 @ SV25 @ xn )
| ~ ( isPrime0 @ SY127 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(225,plain,
! [SV26: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY128: $i,SY129: $i] :
( ~ ( aNaturalNumber0 @ SV26 )
| ~ ( aNaturalNumber0 @ SY128 )
| ~ ( aNaturalNumber0 @ SY129 )
| ( SV26 = sz00 )
| ( SY128 = SY129 )
| ~ ( sdtlseqdt0 @ SY128 @ SY129 )
| ( ( sdtasdt0 @ SY128 @ SV26 )
!= ( sdtasdt0 @ SY129 @ SV26 ) ) )
| ~ ~ ( ~ ! [SY130: $i,SY131: $i] :
( ~ ( aNaturalNumber0 @ SV26 )
| ~ ( aNaturalNumber0 @ SY130 )
| ~ ( aNaturalNumber0 @ SY131 )
| ( SV26 = sz00 )
| ( SY130 = SY131 )
| ~ ( sdtlseqdt0 @ SY130 @ SY131 )
| ( ( sdtasdt0 @ SV26 @ SY130 )
!= ( sdtasdt0 @ SV26 @ SY131 ) ) )
| ~ ! [SY132: $i,SY133: $i] :
( ~ ( aNaturalNumber0 @ SV26 )
| ~ ( aNaturalNumber0 @ SY132 )
| ~ ( aNaturalNumber0 @ SY133 )
| ( SV26 = sz00 )
| ( SY132 = SY133 )
| ~ ( sdtlseqdt0 @ SY132 @ SY133 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV26 @ SY132 ) @ ( sdtasdt0 @ SV26 @ SY133 ) ) ) ) )
| ~ ! [SY134: $i,SY135: $i] :
( ~ ( aNaturalNumber0 @ SV26 )
| ~ ( aNaturalNumber0 @ SY134 )
| ~ ( aNaturalNumber0 @ SY135 )
| ( SV26 = sz00 )
| ( SY134 = SY135 )
| ~ ( sdtlseqdt0 @ SY134 @ SY135 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SY134 @ SV26 ) @ ( sdtasdt0 @ SY135 @ SV26 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(226,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)],[188]) ).
thf(227,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)],[189]) ).
thf(228,plain,
! [SV27: $i,SV2: $i] :
( ( ~ ( aNaturalNumber0 @ SV2 )
| ~ ( aNaturalNumber0 @ SV27 )
| ( aNaturalNumber0 @ ( sdtpldt0 @ SV2 @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[191]) ).
thf(229,plain,
! [SV28: $i,SV3: $i] :
( ( ~ ( aNaturalNumber0 @ SV3 )
| ~ ( aNaturalNumber0 @ SV28 )
| ( aNaturalNumber0 @ ( sdtasdt0 @ SV3 @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[192]) ).
thf(230,plain,
! [SV29: $i,SV4: $i] :
( ( ~ ( aNaturalNumber0 @ SV4 )
| ~ ( aNaturalNumber0 @ SV29 )
| ( ( sdtpldt0 @ SV4 @ SV29 )
= ( sdtpldt0 @ SV29 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[193]) ).
thf(231,plain,
! [SV30: $i,SV5: $i] :
( ( ! [SY136: $i] :
( ~ ( aNaturalNumber0 @ SV5 )
| ~ ( aNaturalNumber0 @ SV30 )
| ~ ( aNaturalNumber0 @ SY136 )
| ( ( sdtpldt0 @ ( sdtpldt0 @ SV5 @ SV30 ) @ SY136 )
= ( sdtpldt0 @ SV5 @ ( sdtpldt0 @ SV30 @ SY136 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(232,plain,
! [SV31: $i,SV6: $i] :
( ( ~ ( aNaturalNumber0 @ SV6 )
| ~ ( aNaturalNumber0 @ SV31 )
| ( ( sdtasdt0 @ SV6 @ SV31 )
= ( sdtasdt0 @ SV31 @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[195]) ).
thf(233,plain,
! [SV32: $i,SV7: $i] :
( ( ! [SY137: $i] :
( ~ ( aNaturalNumber0 @ SV7 )
| ~ ( aNaturalNumber0 @ SV32 )
| ~ ( aNaturalNumber0 @ SY137 )
| ( ( sdtasdt0 @ ( sdtasdt0 @ SV7 @ SV32 ) @ SY137 )
= ( sdtasdt0 @ SV7 @ ( sdtasdt0 @ SV32 @ SY137 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(234,plain,
! [SV33: $i,SV8: $i] :
( ( ~ ( aNaturalNumber0 @ SV8 )
| ~ ( aNaturalNumber0 @ SV33 )
| ( ( sdtasdt0 @ SV8 @ SV33 )
!= sz00 )
| ( SV8 = sz00 )
| ( SV33 = sz00 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(235,plain,
! [SV9: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV9 ) )
= $true )
| ( ( sdtlseqdt0 @ SV9 @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[198]) ).
thf(236,plain,
! [SV34: $i,SV10: $i] :
( ( ~ ( aNaturalNumber0 @ SV10 )
| ~ ( aNaturalNumber0 @ SV34 )
| ~ ( sdtlseqdt0 @ SV10 @ SV34 )
| ~ ( sdtlseqdt0 @ SV34 @ SV10 )
| ( SV10 = SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[199]) ).
thf(237,plain,
! [SV35: $i,SV11: $i] :
( ( ! [SY138: $i] :
( ~ ( aNaturalNumber0 @ SV11 )
| ~ ( aNaturalNumber0 @ SV35 )
| ~ ( aNaturalNumber0 @ SY138 )
| ~ ( sdtlseqdt0 @ SV11 @ SV35 )
| ~ ( sdtlseqdt0 @ SV35 @ SY138 )
| ( sdtlseqdt0 @ SV11 @ SY138 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[200]) ).
thf(238,plain,
! [SV36: $i,SV12: $i] :
( ( ~ ( aNaturalNumber0 @ SV12 )
| ~ ( aNaturalNumber0 @ SV36 )
| ( SV12 = sz00 )
| ( sdtlseqdt0 @ SV36 @ ( sdtasdt0 @ SV36 @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[201]) ).
thf(239,plain,
( ( ( ! [W0: $i] :
~ ( aNaturalNumber0 @ W0 ) )
= $true )
| ( ( ! [W1: $i] :
~ ( aNaturalNumber0 @ W1 ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[202]) ).
thf(240,plain,
! [SV37: $i,SV13: $i] :
( ( ~ ( aNaturalNumber0 @ SV13 )
| ~ ( aNaturalNumber0 @ SV37 )
| ( SV13 = SV37 )
| ~ ( sdtlseqdt0 @ SV13 @ SV37 )
| ( iLess0 @ SV13 @ SV37 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[203]) ).
thf(241,plain,
! [SV38: $i,SV14: $i] :
( ( ! [SY139: $i] :
( ~ ( aNaturalNumber0 @ SV14 )
| ~ ( aNaturalNumber0 @ SV38 )
| ~ ( aNaturalNumber0 @ SY139 )
| ~ ( doDivides0 @ SV14 @ SV38 )
| ~ ( doDivides0 @ SV38 @ SY139 )
| ( doDivides0 @ SV14 @ SY139 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(242,plain,
! [SV39: $i,SV15: $i] :
( ( ! [SY140: $i] :
( ~ ( aNaturalNumber0 @ SV15 )
| ~ ( aNaturalNumber0 @ SV39 )
| ~ ( aNaturalNumber0 @ SY140 )
| ~ ( doDivides0 @ SV15 @ SV39 )
| ~ ( doDivides0 @ SV15 @ SY140 )
| ( doDivides0 @ SV15 @ ( sdtpldt0 @ SV39 @ SY140 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(243,plain,
! [SV40: $i,SV16: $i] :
( ( ! [SY141: $i] :
( ~ ( aNaturalNumber0 @ SV16 )
| ~ ( aNaturalNumber0 @ SV40 )
| ~ ( aNaturalNumber0 @ SY141 )
| ~ ( doDivides0 @ SV16 @ SV40 )
| ~ ( doDivides0 @ SV16 @ ( sdtpldt0 @ SV40 @ SY141 ) )
| ( doDivides0 @ SV16 @ SY141 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(244,plain,
! [SV41: $i,SV17: $i] :
( ( ~ ( aNaturalNumber0 @ SV17 )
| ~ ( aNaturalNumber0 @ SV41 )
| ( SV41 = sz00 )
| ~ ( doDivides0 @ SV17 @ SV41 )
| ( sdtlseqdt0 @ SV17 @ SV41 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(245,plain,
! [SV42: $i,SV18: $i] :
( ( ~ ( aNaturalNumber0 @ SV18 )
| ~ ( aNaturalNumber0 @ SV42 )
| ( SV18 = sz00 )
| ~ ( doDivides0 @ SV18 @ SV42 )
| ! [SY142: $i] :
( ~ ( aNaturalNumber0 @ SY142 )
| ( ( sdtasdt0 @ SY142 @ ( sdtsldt0 @ SV42 @ SV18 ) )
= ( sdtsldt0 @ ( sdtasdt0 @ SY142 @ SV42 ) @ SV18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(246,plain,
! [SV43: $i,SV19: $i] :
( ( ! [SY143: $i] :
( ~ ( aNaturalNumber0 @ SV19 )
| ~ ( aNaturalNumber0 @ SV43 )
| ~ ( aNaturalNumber0 @ SY143 )
| ~ ( doDivides0 @ SY143 @ ( sdtasdt0 @ SV19 @ SV43 ) )
| ~ ( isPrime0 @ SY143 )
| ( doDivides0 @ SY143 @ SV19 )
| ( doDivides0 @ SY143 @ SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[209]) ).
thf(247,plain,
! [SV20: $i] :
( ( ~ ! [SY107: $i,SY108: $i] :
( ~ ( aNaturalNumber0 @ SV20 )
| ~ ( aNaturalNumber0 @ SY107 )
| ~ ( aNaturalNumber0 @ SY108 )
| ( ( sdtasdt0 @ SV20 @ ( sdtpldt0 @ SY107 @ SY108 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV20 @ SY107 ) @ ( sdtasdt0 @ SV20 @ SY108 ) ) ) )
| ~ ! [SY109: $i,SY110: $i] :
( ~ ( aNaturalNumber0 @ SV20 )
| ~ ( aNaturalNumber0 @ SY109 )
| ~ ( aNaturalNumber0 @ SY110 )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SY109 @ SY110 ) @ SV20 )
= ( sdtpldt0 @ ( sdtasdt0 @ SY109 @ SV20 ) @ ( sdtasdt0 @ SY110 @ SV20 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(248,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( ( sdtasdt0 @ SX0 @ sz10 )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[211]) ).
thf(249,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( SX0
= ( sdtasdt0 @ sz10 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[211]) ).
thf(250,plain,
( ( ~ ( ( sz10 != sz00 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[212]) ).
thf(251,plain,
( ( ~ ( aNaturalNumber0 @ sz10 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[212]) ).
thf(252,plain,
! [SV44: $i,SV21: $i] :
( ( ~ ( aNaturalNumber0 @ SV21 )
| ~ ( aNaturalNumber0 @ SV44 )
| ( SV21 = SV44 )
| ~ ( sdtlseqdt0 @ SV21 @ SV44 )
| ~ ( ~ ~ ( ~ ! [SY144: $i] :
( ~ ( aNaturalNumber0 @ SY144 )
| ( ( sdtpldt0 @ SV21 @ SY144 )
!= ( sdtpldt0 @ SV44 @ SY144 ) ) )
| ~ ~ ( ~ ! [SY145: $i] :
( ~ ( aNaturalNumber0 @ SY145 )
| ( ( sdtpldt0 @ SY145 @ SV21 )
!= ( sdtpldt0 @ SY145 @ SV44 ) ) )
| ~ ! [SY146: $i] :
( ~ ( aNaturalNumber0 @ SY146 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SY146 @ SV21 ) @ ( sdtpldt0 @ SY146 @ SV44 ) ) ) ) )
| ~ ! [SY147: $i] :
( ~ ( aNaturalNumber0 @ SY147 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SV21 @ SY147 ) @ ( sdtpldt0 @ SV44 @ SY147 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[213]) ).
thf(253,plain,
! [SV22: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV22 ) )
= $true )
| ( ( ( SV22 = sz00 )
| ~ ( ~ ! [SY116: $i,SY117: $i] :
( ~ ( aNaturalNumber0 @ SY116 )
| ~ ( aNaturalNumber0 @ SY117 )
| ( ( sdtasdt0 @ SV22 @ SY116 )
!= ( sdtasdt0 @ SV22 @ SY117 ) )
| ( SY116 = SY117 ) )
| ~ ! [SY118: $i,SY119: $i] :
( ~ ( aNaturalNumber0 @ SY118 )
| ~ ( aNaturalNumber0 @ SY119 )
| ( ( sdtasdt0 @ SY118 @ SV22 )
!= ( sdtasdt0 @ SY119 @ SV22 ) )
| ( SY118 = SY119 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[214]) ).
thf(254,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xn @ xn )
!= ( sdtasdt0 @ xp @ sK3_W0 ) )
| ~ ( aNaturalNumber0 @ sK3_W0 ) )
| ~ ( doDivides0 @ xp @ ( sdtasdt0 @ xn @ xn ) ) )
| ~ ~ ( ( xn
!= ( sdtasdt0 @ xp @ sK2_W0 ) )
| ~ ( aNaturalNumber0 @ sK2_W0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[215]) ).
thf(255,plain,
( ( ~ ( doDivides0 @ xp @ xn ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[215]) ).
thf(256,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ! [SX1: $i] :
( ( xp
!= ( sdtasdt0 @ SX0 @ SX1 ) )
| ~ ( aNaturalNumber0 @ SX1 ) )
| ( SX0 = sz10 )
| ( SX0 = xp ) )
| ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( doDivides0 @ SX0 @ xp )
| ( SX0 = sz10 )
| ( SX0 = xp ) ) )
| ~ ( ( xp != sz10 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[216]) ).
thf(257,plain,
( ( ~ ( isPrime0 @ xp ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[216]) ).
thf(258,plain,
( ( ~ ( ( xp != sz00 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[217]) ).
thf(259,plain,
( ( ~ ~ ( ~ ( ( xm != sz00 ) )
| ~ ~ ( ~ ( ( xn != sz00 ) )
| ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ xn )
| ~ ( aNaturalNumber0 @ xm ) )
| ~ ( aNaturalNumber0 @ xp ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[217]) ).
thf(260,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( ( sdtasdt0 @ SX0 @ sz00 )
= sz00 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[218]) ).
thf(261,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( sz00
= ( sdtasdt0 @ sz00 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[218]) ).
thf(262,plain,
! [SV23: $i] :
( ( ( ( SV23 = sz10 )
| ( SV23 = sz00 )
| ~ ( aNaturalNumber0 @ SV23 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ ( sK1_W1 @ SV23 ) )
| ~ ( doDivides0 @ ( sK1_W1 @ SV23 ) @ SV23 ) )
| ~ ( isPrime0 @ ( sK1_W1 @ SV23 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[219]) ).
thf(263,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 )
| ( SX1 != SX0 )
| ( sdtlseqdt0 @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[220]) ).
thf(264,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 )
| ( sdtlseqdt0 @ SX1 @ SX0 )
| ( sdtlseqdt0 @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[220]) ).
thf(265,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( ( sdtpldt0 @ SX0 @ sz00 )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[221]) ).
thf(266,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( SX0
= ( sdtpldt0 @ sz00 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[221]) ).
thf(267,plain,
! [SV24: $i] :
( ( ~ ! [SY120: $i,SY121: $i] :
( ~ ( aNaturalNumber0 @ SV24 )
| ~ ( aNaturalNumber0 @ SY120 )
| ~ ( aNaturalNumber0 @ SY121 )
| ( ( sdtpldt0 @ SV24 @ SY120 )
!= ( sdtpldt0 @ SV24 @ SY121 ) )
| ( SY120 = SY121 ) )
| ~ ! [SY122: $i,SY123: $i] :
( ~ ( aNaturalNumber0 @ SV24 )
| ~ ( aNaturalNumber0 @ SY122 )
| ~ ( aNaturalNumber0 @ SY123 )
| ( ( sdtpldt0 @ SY122 @ SV24 )
!= ( sdtpldt0 @ SY123 @ SV24 ) )
| ( SY122 = SY123 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[222]) ).
thf(268,plain,
( ( ~ ~ ( ( xn
!= ( sdtasdt0 @ xp @ xq ) )
| ~ ( aNaturalNumber0 @ xq ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[223]) ).
thf(269,plain,
( ( xq
!= ( sdtsldt0 @ xn @ xp ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[223]) ).
thf(270,plain,
! [SV25: $i] :
( ( ~ ! [SY124: $i,SY125: $i] :
( ( SY125 = sz00 )
| ( SY124 = sz00 )
| ( SV25 = sz00 )
| ~ ( aNaturalNumber0 @ SV25 )
| ~ ( aNaturalNumber0 @ SY124 )
| ~ ( aNaturalNumber0 @ SY125 )
| ( ( sdtasdt0 @ SY125 @ ( sdtasdt0 @ SY124 @ SY124 ) )
!= ( sdtasdt0 @ SV25 @ SV25 ) )
| ~ ( iLess0 @ SV25 @ xn )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( SY125
!= ( sdtasdt0 @ ( sK4_W3 @ SY125 @ SY124 @ SV25 ) @ ( sK5_SY81 @ SY125 @ SY124 @ SV25 ) ) )
| ~ ( aNaturalNumber0 @ ( sK5_SY81 @ SY125 @ SY124 @ SV25 ) ) )
| ~ ( aNaturalNumber0 @ ( sK4_W3 @ SY125 @ SY124 @ SV25 ) ) )
| ~ ( doDivides0 @ ( sK4_W3 @ SY125 @ SY124 @ SV25 ) @ SY125 ) )
| ~ ~ ( ~ ( ( ( sK4_W3 @ SY125 @ SY124 @ SV25 )
!= sz10 ) )
| ~ ( ( ( sK4_W3 @ SY125 @ SY124 @ SV25 )
!= SY125 ) ) ) )
| ( SY125 = sz10 ) )
| ~ ! [SY126: $i,SY127: $i] :
( ( SY127 = sz00 )
| ( SY126 = sz00 )
| ( SV25 = sz00 )
| ~ ( aNaturalNumber0 @ SV25 )
| ~ ( aNaturalNumber0 @ SY126 )
| ~ ( aNaturalNumber0 @ SY127 )
| ( ( sdtasdt0 @ SY127 @ ( sdtasdt0 @ SY126 @ SY126 ) )
!= ( sdtasdt0 @ SV25 @ SV25 ) )
| ~ ( iLess0 @ SV25 @ xn )
| ~ ( isPrime0 @ SY127 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[224]) ).
thf(271,plain,
! [SV26: $i] :
( ( ~ ~ ( ~ ! [SY128: $i,SY129: $i] :
( ~ ( aNaturalNumber0 @ SV26 )
| ~ ( aNaturalNumber0 @ SY128 )
| ~ ( aNaturalNumber0 @ SY129 )
| ( SV26 = sz00 )
| ( SY128 = SY129 )
| ~ ( sdtlseqdt0 @ SY128 @ SY129 )
| ( ( sdtasdt0 @ SY128 @ SV26 )
!= ( sdtasdt0 @ SY129 @ SV26 ) ) )
| ~ ~ ( ~ ! [SY130: $i,SY131: $i] :
( ~ ( aNaturalNumber0 @ SV26 )
| ~ ( aNaturalNumber0 @ SY130 )
| ~ ( aNaturalNumber0 @ SY131 )
| ( SV26 = sz00 )
| ( SY130 = SY131 )
| ~ ( sdtlseqdt0 @ SY130 @ SY131 )
| ( ( sdtasdt0 @ SV26 @ SY130 )
!= ( sdtasdt0 @ SV26 @ SY131 ) ) )
| ~ ! [SY132: $i,SY133: $i] :
( ~ ( aNaturalNumber0 @ SV26 )
| ~ ( aNaturalNumber0 @ SY132 )
| ~ ( aNaturalNumber0 @ SY133 )
| ( SV26 = sz00 )
| ( SY132 = SY133 )
| ~ ( sdtlseqdt0 @ SY132 @ SY133 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV26 @ SY132 ) @ ( sdtasdt0 @ SV26 @ SY133 ) ) ) ) )
| ~ ! [SY134: $i,SY135: $i] :
( ~ ( aNaturalNumber0 @ SV26 )
| ~ ( aNaturalNumber0 @ SY134 )
| ~ ( aNaturalNumber0 @ SY135 )
| ( SV26 = sz00 )
| ( SY134 = SY135 )
| ~ ( sdtlseqdt0 @ SY134 @ SY135 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SY134 @ SV26 ) @ ( sdtasdt0 @ SY135 @ SV26 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[225]) ).
thf(272,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( sz10 != SX0 )
| ( SX0 = sz00 )
| ( SX0 = sz10 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[226]) ).
thf(273,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( sdtlseqdt0 @ sz10 @ SX0 )
| ( SX0 = sz00 )
| ( SX0 = sz10 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[226]) ).
thf(274,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 )
| ( ( sdtpldt0 @ SX0 @ SX1 )
!= sz00 )
| ( SX0 = sz00 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[227]) ).
thf(275,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 )
| ( ( sdtpldt0 @ SX0 @ SX1 )
!= sz00 )
| ( SX1 = sz00 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[227]) ).
thf(276,plain,
! [SV27: $i,SV2: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV2 )
| ~ ( aNaturalNumber0 @ SV27 ) )
= $true )
| ( ( aNaturalNumber0 @ ( sdtpldt0 @ SV2 @ SV27 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[228]) ).
thf(277,plain,
! [SV28: $i,SV3: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV3 )
| ~ ( aNaturalNumber0 @ SV28 ) )
= $true )
| ( ( aNaturalNumber0 @ ( sdtasdt0 @ SV3 @ SV28 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[229]) ).
thf(278,plain,
! [SV29: $i,SV4: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV4 )
| ~ ( aNaturalNumber0 @ SV29 ) )
= $true )
| ( ( ( sdtpldt0 @ SV4 @ SV29 )
= ( sdtpldt0 @ SV29 @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[230]) ).
thf(279,plain,
! [SV45: $i,SV30: $i,SV5: $i] :
( ( ~ ( aNaturalNumber0 @ SV5 )
| ~ ( aNaturalNumber0 @ SV30 )
| ~ ( aNaturalNumber0 @ SV45 )
| ( ( sdtpldt0 @ ( sdtpldt0 @ SV5 @ SV30 ) @ SV45 )
= ( sdtpldt0 @ SV5 @ ( sdtpldt0 @ SV30 @ SV45 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[231]) ).
thf(280,plain,
! [SV31: $i,SV6: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV6 )
| ~ ( aNaturalNumber0 @ SV31 ) )
= $true )
| ( ( ( sdtasdt0 @ SV6 @ SV31 )
= ( sdtasdt0 @ SV31 @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[232]) ).
thf(281,plain,
! [SV46: $i,SV32: $i,SV7: $i] :
( ( ~ ( aNaturalNumber0 @ SV7 )
| ~ ( aNaturalNumber0 @ SV32 )
| ~ ( aNaturalNumber0 @ SV46 )
| ( ( sdtasdt0 @ ( sdtasdt0 @ SV7 @ SV32 ) @ SV46 )
= ( sdtasdt0 @ SV7 @ ( sdtasdt0 @ SV32 @ SV46 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[233]) ).
thf(282,plain,
! [SV33: $i,SV8: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV8 )
| ~ ( aNaturalNumber0 @ SV33 ) )
= $true )
| ( ( ( ( sdtasdt0 @ SV8 @ SV33 )
!= sz00 )
| ( SV8 = sz00 )
| ( SV33 = sz00 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[234]) ).
thf(283,plain,
! [SV9: $i] :
( ( ( aNaturalNumber0 @ SV9 )
= $false )
| ( ( sdtlseqdt0 @ SV9 @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[235]) ).
thf(284,plain,
! [SV34: $i,SV10: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV10 )
| ~ ( aNaturalNumber0 @ SV34 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV10 @ SV34 )
| ~ ( sdtlseqdt0 @ SV34 @ SV10 )
| ( SV10 = SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[236]) ).
thf(285,plain,
! [SV47: $i,SV35: $i,SV11: $i] :
( ( ~ ( aNaturalNumber0 @ SV11 )
| ~ ( aNaturalNumber0 @ SV35 )
| ~ ( aNaturalNumber0 @ SV47 )
| ~ ( sdtlseqdt0 @ SV11 @ SV35 )
| ~ ( sdtlseqdt0 @ SV35 @ SV47 )
| ( sdtlseqdt0 @ SV11 @ SV47 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[237]) ).
thf(286,plain,
! [SV36: $i,SV12: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV12 )
| ~ ( aNaturalNumber0 @ SV36 ) )
= $true )
| ( ( ( SV12 = sz00 )
| ( sdtlseqdt0 @ SV36 @ ( sdtasdt0 @ SV36 @ SV12 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[238]) ).
thf(287,plain,
! [SV48: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV48 ) )
= $true )
| ( ( ! [W1: $i] :
~ ( aNaturalNumber0 @ W1 ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[239]) ).
thf(288,plain,
! [SV37: $i,SV13: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV13 )
| ~ ( aNaturalNumber0 @ SV37 ) )
= $true )
| ( ( ( SV13 = SV37 )
| ~ ( sdtlseqdt0 @ SV13 @ SV37 )
| ( iLess0 @ SV13 @ SV37 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[240]) ).
thf(289,plain,
! [SV49: $i,SV38: $i,SV14: $i] :
( ( ~ ( aNaturalNumber0 @ SV14 )
| ~ ( aNaturalNumber0 @ SV38 )
| ~ ( aNaturalNumber0 @ SV49 )
| ~ ( doDivides0 @ SV14 @ SV38 )
| ~ ( doDivides0 @ SV38 @ SV49 )
| ( doDivides0 @ SV14 @ SV49 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[241]) ).
thf(290,plain,
! [SV50: $i,SV39: $i,SV15: $i] :
( ( ~ ( aNaturalNumber0 @ SV15 )
| ~ ( aNaturalNumber0 @ SV39 )
| ~ ( aNaturalNumber0 @ SV50 )
| ~ ( doDivides0 @ SV15 @ SV39 )
| ~ ( doDivides0 @ SV15 @ SV50 )
| ( doDivides0 @ SV15 @ ( sdtpldt0 @ SV39 @ SV50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[242]) ).
thf(291,plain,
! [SV51: $i,SV40: $i,SV16: $i] :
( ( ~ ( aNaturalNumber0 @ SV16 )
| ~ ( aNaturalNumber0 @ SV40 )
| ~ ( aNaturalNumber0 @ SV51 )
| ~ ( doDivides0 @ SV16 @ SV40 )
| ~ ( doDivides0 @ SV16 @ ( sdtpldt0 @ SV40 @ SV51 ) )
| ( doDivides0 @ SV16 @ SV51 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[243]) ).
thf(292,plain,
! [SV41: $i,SV17: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV17 )
| ~ ( aNaturalNumber0 @ SV41 ) )
= $true )
| ( ( ( SV41 = sz00 )
| ~ ( doDivides0 @ SV17 @ SV41 )
| ( sdtlseqdt0 @ SV17 @ SV41 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[244]) ).
thf(293,plain,
! [SV42: $i,SV18: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV18 )
| ~ ( aNaturalNumber0 @ SV42 ) )
= $true )
| ( ( ( SV18 = sz00 )
| ~ ( doDivides0 @ SV18 @ SV42 )
| ! [SY142: $i] :
( ~ ( aNaturalNumber0 @ SY142 )
| ( ( sdtasdt0 @ SY142 @ ( sdtsldt0 @ SV42 @ SV18 ) )
= ( sdtsldt0 @ ( sdtasdt0 @ SY142 @ SV42 ) @ SV18 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[245]) ).
thf(294,plain,
! [SV52: $i,SV43: $i,SV19: $i] :
( ( ~ ( aNaturalNumber0 @ SV19 )
| ~ ( aNaturalNumber0 @ SV43 )
| ~ ( aNaturalNumber0 @ SV52 )
| ~ ( doDivides0 @ SV52 @ ( sdtasdt0 @ SV19 @ SV43 ) )
| ~ ( isPrime0 @ SV52 )
| ( doDivides0 @ SV52 @ SV19 )
| ( doDivides0 @ SV52 @ SV43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[246]) ).
thf(295,plain,
! [SV20: $i] :
( ( ~ ! [SY107: $i,SY108: $i] :
( ~ ( aNaturalNumber0 @ SV20 )
| ~ ( aNaturalNumber0 @ SY107 )
| ~ ( aNaturalNumber0 @ SY108 )
| ( ( sdtasdt0 @ SV20 @ ( sdtpldt0 @ SY107 @ SY108 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV20 @ SY107 ) @ ( sdtasdt0 @ SV20 @ SY108 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[247]) ).
thf(296,plain,
! [SV20: $i] :
( ( ~ ! [SY109: $i,SY110: $i] :
( ~ ( aNaturalNumber0 @ SV20 )
| ~ ( aNaturalNumber0 @ SY109 )
| ~ ( aNaturalNumber0 @ SY110 )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SY109 @ SY110 ) @ SV20 )
= ( sdtpldt0 @ ( sdtasdt0 @ SY109 @ SV20 ) @ ( sdtasdt0 @ SY110 @ SV20 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[247]) ).
thf(297,plain,
( ( ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( ( sdtasdt0 @ SX0 @ sz10 )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[248]) ).
thf(298,plain,
( ( ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( SX0
= ( sdtasdt0 @ sz10 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[249]) ).
thf(299,plain,
( ( sz10 != sz00 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[250]) ).
thf(300,plain,
( ( aNaturalNumber0 @ sz10 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[251]) ).
thf(301,plain,
! [SV44: $i,SV21: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV21 )
| ~ ( aNaturalNumber0 @ SV44 ) )
= $true )
| ( ( ( SV21 = SV44 )
| ~ ( sdtlseqdt0 @ SV21 @ SV44 )
| ~ ( ~ ~ ( ~ ! [SY144: $i] :
( ~ ( aNaturalNumber0 @ SY144 )
| ( ( sdtpldt0 @ SV21 @ SY144 )
!= ( sdtpldt0 @ SV44 @ SY144 ) ) )
| ~ ~ ( ~ ! [SY145: $i] :
( ~ ( aNaturalNumber0 @ SY145 )
| ( ( sdtpldt0 @ SY145 @ SV21 )
!= ( sdtpldt0 @ SY145 @ SV44 ) ) )
| ~ ! [SY146: $i] :
( ~ ( aNaturalNumber0 @ SY146 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SY146 @ SV21 ) @ ( sdtpldt0 @ SY146 @ SV44 ) ) ) ) )
| ~ ! [SY147: $i] :
( ~ ( aNaturalNumber0 @ SY147 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SV21 @ SY147 ) @ ( sdtpldt0 @ SV44 @ SY147 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[252]) ).
thf(302,plain,
! [SV22: $i] :
( ( ( aNaturalNumber0 @ SV22 )
= $false )
| ( ( ( SV22 = sz00 )
| ~ ( ~ ! [SY116: $i,SY117: $i] :
( ~ ( aNaturalNumber0 @ SY116 )
| ~ ( aNaturalNumber0 @ SY117 )
| ( ( sdtasdt0 @ SV22 @ SY116 )
!= ( sdtasdt0 @ SV22 @ SY117 ) )
| ( SY116 = SY117 ) )
| ~ ! [SY118: $i,SY119: $i] :
( ~ ( aNaturalNumber0 @ SY118 )
| ~ ( aNaturalNumber0 @ SY119 )
| ( ( sdtasdt0 @ SY118 @ SV22 )
!= ( sdtasdt0 @ SY119 @ SV22 ) )
| ( SY118 = SY119 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[253]) ).
thf(303,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xn @ xn )
!= ( sdtasdt0 @ xp @ sK3_W0 ) )
| ~ ( aNaturalNumber0 @ sK3_W0 ) )
| ~ ( doDivides0 @ xp @ ( sdtasdt0 @ xn @ xn ) ) )
| ~ ~ ( ( xn
!= ( sdtasdt0 @ xp @ sK2_W0 ) )
| ~ ( aNaturalNumber0 @ sK2_W0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[254]) ).
thf(304,plain,
( ( doDivides0 @ xp @ xn )
= $true ),
inference(extcnf_not_neg,[status(thm)],[255]) ).
thf(305,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ! [SX1: $i] :
( ( xp
!= ( sdtasdt0 @ SX0 @ SX1 ) )
| ~ ( aNaturalNumber0 @ SX1 ) )
| ( SX0 = sz10 )
| ( SX0 = xp ) )
| ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( doDivides0 @ SX0 @ xp )
| ( SX0 = sz10 )
| ( SX0 = xp ) ) )
| ~ ( ( xp != sz10 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[256]) ).
thf(306,plain,
( ( isPrime0 @ xp )
= $true ),
inference(extcnf_not_neg,[status(thm)],[257]) ).
thf(307,plain,
( ( xp != sz00 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[258]) ).
thf(308,plain,
( ( ~ ( ~ ( ( xm != sz00 ) )
| ~ ~ ( ~ ( ( xn != sz00 ) )
| ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ xn )
| ~ ( aNaturalNumber0 @ xm ) )
| ~ ( aNaturalNumber0 @ xp ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[259]) ).
thf(309,plain,
( ( ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( ( sdtasdt0 @ SX0 @ sz00 )
= sz00 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[260]) ).
thf(310,plain,
( ( ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( sz00
= ( sdtasdt0 @ sz00 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[261]) ).
thf(311,plain,
! [SV23: $i] :
( ( ( SV23 = sz10 )
= $true )
| ( ( ( SV23 = sz00 )
| ~ ( aNaturalNumber0 @ SV23 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ ( sK1_W1 @ SV23 ) )
| ~ ( doDivides0 @ ( sK1_W1 @ SV23 ) @ SV23 ) )
| ~ ( isPrime0 @ ( sK1_W1 @ SV23 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[262]) ).
thf(312,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 )
| ( SX1 != SX0 )
| ( sdtlseqdt0 @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[263]) ).
thf(313,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 )
| ( sdtlseqdt0 @ SX1 @ SX0 )
| ( sdtlseqdt0 @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[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,
! [SV24: $i] :
( ( ~ ! [SY120: $i,SY121: $i] :
( ~ ( aNaturalNumber0 @ SV24 )
| ~ ( aNaturalNumber0 @ SY120 )
| ~ ( aNaturalNumber0 @ SY121 )
| ( ( sdtpldt0 @ SV24 @ SY120 )
!= ( sdtpldt0 @ SV24 @ SY121 ) )
| ( SY120 = SY121 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[267]) ).
thf(317,plain,
! [SV24: $i] :
( ( ~ ! [SY122: $i,SY123: $i] :
( ~ ( aNaturalNumber0 @ SV24 )
| ~ ( aNaturalNumber0 @ SY122 )
| ~ ( aNaturalNumber0 @ SY123 )
| ( ( sdtpldt0 @ SY122 @ SV24 )
!= ( sdtpldt0 @ SY123 @ SV24 ) )
| ( SY122 = SY123 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[267]) ).
thf(318,plain,
( ( ~ ( ( xn
!= ( sdtasdt0 @ xp @ xq ) )
| ~ ( aNaturalNumber0 @ xq ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[268]) ).
thf(319,plain,
( ( xq
= ( sdtsldt0 @ xn @ xp ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[269]) ).
thf(320,plain,
! [SV25: $i] :
( ( ~ ! [SY124: $i,SY125: $i] :
( ( SY125 = sz00 )
| ( SY124 = sz00 )
| ( SV25 = sz00 )
| ~ ( aNaturalNumber0 @ SV25 )
| ~ ( aNaturalNumber0 @ SY124 )
| ~ ( aNaturalNumber0 @ SY125 )
| ( ( sdtasdt0 @ SY125 @ ( sdtasdt0 @ SY124 @ SY124 ) )
!= ( sdtasdt0 @ SV25 @ SV25 ) )
| ~ ( iLess0 @ SV25 @ xn )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( SY125
!= ( sdtasdt0 @ ( sK4_W3 @ SY125 @ SY124 @ SV25 ) @ ( sK5_SY81 @ SY125 @ SY124 @ SV25 ) ) )
| ~ ( aNaturalNumber0 @ ( sK5_SY81 @ SY125 @ SY124 @ SV25 ) ) )
| ~ ( aNaturalNumber0 @ ( sK4_W3 @ SY125 @ SY124 @ SV25 ) ) )
| ~ ( doDivides0 @ ( sK4_W3 @ SY125 @ SY124 @ SV25 ) @ SY125 ) )
| ~ ~ ( ~ ( ( ( sK4_W3 @ SY125 @ SY124 @ SV25 )
!= sz10 ) )
| ~ ( ( ( sK4_W3 @ SY125 @ SY124 @ SV25 )
!= SY125 ) ) ) )
| ( SY125 = sz10 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[270]) ).
thf(321,plain,
! [SV25: $i] :
( ( ~ ! [SY126: $i,SY127: $i] :
( ( SY127 = sz00 )
| ( SY126 = sz00 )
| ( SV25 = sz00 )
| ~ ( aNaturalNumber0 @ SV25 )
| ~ ( aNaturalNumber0 @ SY126 )
| ~ ( aNaturalNumber0 @ SY127 )
| ( ( sdtasdt0 @ SY127 @ ( sdtasdt0 @ SY126 @ SY126 ) )
!= ( sdtasdt0 @ SV25 @ SV25 ) )
| ~ ( iLess0 @ SV25 @ xn )
| ~ ( isPrime0 @ SY127 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[270]) ).
thf(322,plain,
! [SV26: $i] :
( ( ~ ~ ( ~ ! [SY128: $i,SY129: $i] :
( ~ ( aNaturalNumber0 @ SV26 )
| ~ ( aNaturalNumber0 @ SY128 )
| ~ ( aNaturalNumber0 @ SY129 )
| ( SV26 = sz00 )
| ( SY128 = SY129 )
| ~ ( sdtlseqdt0 @ SY128 @ SY129 )
| ( ( sdtasdt0 @ SY128 @ SV26 )
!= ( sdtasdt0 @ SY129 @ SV26 ) ) )
| ~ ~ ( ~ ! [SY130: $i,SY131: $i] :
( ~ ( aNaturalNumber0 @ SV26 )
| ~ ( aNaturalNumber0 @ SY130 )
| ~ ( aNaturalNumber0 @ SY131 )
| ( SV26 = sz00 )
| ( SY130 = SY131 )
| ~ ( sdtlseqdt0 @ SY130 @ SY131 )
| ( ( sdtasdt0 @ SV26 @ SY130 )
!= ( sdtasdt0 @ SV26 @ SY131 ) ) )
| ~ ! [SY132: $i,SY133: $i] :
( ~ ( aNaturalNumber0 @ SV26 )
| ~ ( aNaturalNumber0 @ SY132 )
| ~ ( aNaturalNumber0 @ SY133 )
| ( SV26 = sz00 )
| ( SY132 = SY133 )
| ~ ( sdtlseqdt0 @ SY132 @ SY133 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV26 @ SY132 ) @ ( sdtasdt0 @ SV26 @ SY133 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[271]) ).
thf(323,plain,
! [SV26: $i] :
( ( ~ ! [SY134: $i,SY135: $i] :
( ~ ( aNaturalNumber0 @ SV26 )
| ~ ( aNaturalNumber0 @ SY134 )
| ~ ( aNaturalNumber0 @ SY135 )
| ( SV26 = sz00 )
| ( SY134 = SY135 )
| ~ ( sdtlseqdt0 @ SY134 @ SY135 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SY134 @ SV26 ) @ ( sdtasdt0 @ SY135 @ SV26 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[271]) ).
thf(324,plain,
( ( ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( sz10 != SX0 )
| ( SX0 = sz00 )
| ( SX0 = sz10 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[272]) ).
thf(325,plain,
( ( ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( sdtlseqdt0 @ sz10 @ SX0 )
| ( SX0 = sz00 )
| ( SX0 = sz10 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[273]) ).
thf(326,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 )
| ( ( sdtpldt0 @ SX0 @ SX1 )
!= sz00 )
| ( SX0 = sz00 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[274]) ).
thf(327,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 )
| ( ( sdtpldt0 @ SX0 @ SX1 )
!= sz00 )
| ( SX1 = sz00 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[275]) ).
thf(328,plain,
! [SV27: $i,SV2: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV2 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV27 ) )
= $true )
| ( ( aNaturalNumber0 @ ( sdtpldt0 @ SV2 @ SV27 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[276]) ).
thf(329,plain,
! [SV28: $i,SV3: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV3 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV28 ) )
= $true )
| ( ( aNaturalNumber0 @ ( sdtasdt0 @ SV3 @ SV28 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[277]) ).
thf(330,plain,
! [SV29: $i,SV4: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV4 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV29 ) )
= $true )
| ( ( ( sdtpldt0 @ SV4 @ SV29 )
= ( sdtpldt0 @ SV29 @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[278]) ).
thf(331,plain,
! [SV45: $i,SV30: $i,SV5: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV5 )
| ~ ( aNaturalNumber0 @ SV30 )
| ~ ( aNaturalNumber0 @ SV45 ) )
= $true )
| ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV5 @ SV30 ) @ SV45 )
= ( sdtpldt0 @ SV5 @ ( sdtpldt0 @ SV30 @ SV45 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[279]) ).
thf(332,plain,
! [SV31: $i,SV6: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV6 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV31 ) )
= $true )
| ( ( ( sdtasdt0 @ SV6 @ SV31 )
= ( sdtasdt0 @ SV31 @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[280]) ).
thf(333,plain,
! [SV46: $i,SV32: $i,SV7: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV7 )
| ~ ( aNaturalNumber0 @ SV32 )
| ~ ( aNaturalNumber0 @ SV46 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV7 @ SV32 ) @ SV46 )
= ( sdtasdt0 @ SV7 @ ( sdtasdt0 @ SV32 @ SV46 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[281]) ).
thf(334,plain,
! [SV33: $i,SV8: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV8 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV33 ) )
= $true )
| ( ( ( ( sdtasdt0 @ SV8 @ SV33 )
!= sz00 )
| ( SV8 = sz00 )
| ( SV33 = sz00 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[282]) ).
thf(335,plain,
! [SV34: $i,SV10: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV10 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV34 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV10 @ SV34 )
| ~ ( sdtlseqdt0 @ SV34 @ SV10 )
| ( SV10 = SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[284]) ).
thf(336,plain,
! [SV47: $i,SV35: $i,SV11: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV11 )
| ~ ( aNaturalNumber0 @ SV35 )
| ~ ( aNaturalNumber0 @ SV47 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV11 @ SV35 )
| ~ ( sdtlseqdt0 @ SV35 @ SV47 )
| ( sdtlseqdt0 @ SV11 @ SV47 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[285]) ).
thf(337,plain,
! [SV36: $i,SV12: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV12 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV36 ) )
= $true )
| ( ( ( SV12 = sz00 )
| ( sdtlseqdt0 @ SV36 @ ( sdtasdt0 @ SV36 @ SV12 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[286]) ).
thf(338,plain,
! [SV48: $i] :
( ( ( aNaturalNumber0 @ SV48 )
= $false )
| ( ( ! [W1: $i] :
~ ( aNaturalNumber0 @ W1 ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[287]) ).
thf(339,plain,
! [SV37: $i,SV13: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV13 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV37 ) )
= $true )
| ( ( ( SV13 = SV37 )
| ~ ( sdtlseqdt0 @ SV13 @ SV37 )
| ( iLess0 @ SV13 @ SV37 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[288]) ).
thf(340,plain,
! [SV49: $i,SV38: $i,SV14: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV14 )
| ~ ( aNaturalNumber0 @ SV38 )
| ~ ( aNaturalNumber0 @ SV49 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV14 @ SV38 )
| ~ ( doDivides0 @ SV38 @ SV49 )
| ( doDivides0 @ SV14 @ SV49 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[289]) ).
thf(341,plain,
! [SV50: $i,SV39: $i,SV15: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV15 )
| ~ ( aNaturalNumber0 @ SV39 )
| ~ ( aNaturalNumber0 @ SV50 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV15 @ SV39 )
| ~ ( doDivides0 @ SV15 @ SV50 )
| ( doDivides0 @ SV15 @ ( sdtpldt0 @ SV39 @ SV50 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[290]) ).
thf(342,plain,
! [SV51: $i,SV40: $i,SV16: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV16 )
| ~ ( aNaturalNumber0 @ SV40 )
| ~ ( aNaturalNumber0 @ SV51 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV16 @ SV40 )
| ~ ( doDivides0 @ SV16 @ ( sdtpldt0 @ SV40 @ SV51 ) )
| ( doDivides0 @ SV16 @ SV51 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[291]) ).
thf(343,plain,
! [SV41: $i,SV17: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV17 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV41 ) )
= $true )
| ( ( ( SV41 = sz00 )
| ~ ( doDivides0 @ SV17 @ SV41 )
| ( sdtlseqdt0 @ SV17 @ SV41 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[292]) ).
thf(344,plain,
! [SV42: $i,SV18: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV18 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV42 ) )
= $true )
| ( ( ( SV18 = sz00 )
| ~ ( doDivides0 @ SV18 @ SV42 )
| ! [SY142: $i] :
( ~ ( aNaturalNumber0 @ SY142 )
| ( ( sdtasdt0 @ SY142 @ ( sdtsldt0 @ SV42 @ SV18 ) )
= ( sdtsldt0 @ ( sdtasdt0 @ SY142 @ SV42 ) @ SV18 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[293]) ).
thf(345,plain,
! [SV52: $i,SV43: $i,SV19: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV19 )
| ~ ( aNaturalNumber0 @ SV43 )
| ~ ( aNaturalNumber0 @ SV52 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV52 @ ( sdtasdt0 @ SV19 @ SV43 ) )
| ~ ( isPrime0 @ SV52 )
| ( doDivides0 @ SV52 @ SV19 )
| ( doDivides0 @ SV52 @ SV43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[294]) ).
thf(346,plain,
! [SV20: $i] :
( ( ! [SY107: $i,SY108: $i] :
( ~ ( aNaturalNumber0 @ SV20 )
| ~ ( aNaturalNumber0 @ SY107 )
| ~ ( aNaturalNumber0 @ SY108 )
| ( ( sdtasdt0 @ SV20 @ ( sdtpldt0 @ SY107 @ SY108 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV20 @ SY107 ) @ ( sdtasdt0 @ SV20 @ SY108 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[295]) ).
thf(347,plain,
! [SV20: $i] :
( ( ! [SY109: $i,SY110: $i] :
( ~ ( aNaturalNumber0 @ SV20 )
| ~ ( aNaturalNumber0 @ SY109 )
| ~ ( aNaturalNumber0 @ SY110 )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SY109 @ SY110 ) @ SV20 )
= ( sdtpldt0 @ ( sdtasdt0 @ SY109 @ SV20 ) @ ( sdtasdt0 @ SY110 @ SV20 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[296]) ).
thf(348,plain,
! [SV53: $i] :
( ( ~ ( aNaturalNumber0 @ SV53 )
| ( ( sdtasdt0 @ SV53 @ sz10 )
= SV53 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[297]) ).
thf(349,plain,
! [SV54: $i] :
( ( ~ ( aNaturalNumber0 @ SV54 )
| ( SV54
= ( sdtasdt0 @ sz10 @ SV54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[298]) ).
thf(350,plain,
( ( sz10 = sz00 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[299]) ).
thf(351,plain,
! [SV44: $i,SV21: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV21 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV44 ) )
= $true )
| ( ( ( SV21 = SV44 )
| ~ ( sdtlseqdt0 @ SV21 @ SV44 )
| ~ ( ~ ~ ( ~ ! [SY144: $i] :
( ~ ( aNaturalNumber0 @ SY144 )
| ( ( sdtpldt0 @ SV21 @ SY144 )
!= ( sdtpldt0 @ SV44 @ SY144 ) ) )
| ~ ~ ( ~ ! [SY145: $i] :
( ~ ( aNaturalNumber0 @ SY145 )
| ( ( sdtpldt0 @ SY145 @ SV21 )
!= ( sdtpldt0 @ SY145 @ SV44 ) ) )
| ~ ! [SY146: $i] :
( ~ ( aNaturalNumber0 @ SY146 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SY146 @ SV21 ) @ ( sdtpldt0 @ SY146 @ SV44 ) ) ) ) )
| ~ ! [SY147: $i] :
( ~ ( aNaturalNumber0 @ SY147 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SV21 @ SY147 ) @ ( sdtpldt0 @ SV44 @ SY147 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[301]) ).
thf(352,plain,
! [SV22: $i] :
( ( ( SV22 = sz00 )
= $true )
| ( ( ~ ( ~ ! [SY116: $i,SY117: $i] :
( ~ ( aNaturalNumber0 @ SY116 )
| ~ ( aNaturalNumber0 @ SY117 )
| ( ( sdtasdt0 @ SV22 @ SY116 )
!= ( sdtasdt0 @ SV22 @ SY117 ) )
| ( SY116 = SY117 ) )
| ~ ! [SY118: $i,SY119: $i] :
( ~ ( aNaturalNumber0 @ SY118 )
| ~ ( aNaturalNumber0 @ SY119 )
| ( ( sdtasdt0 @ SY118 @ SV22 )
!= ( sdtasdt0 @ SY119 @ SV22 ) )
| ( SY118 = SY119 ) ) ) )
= $true )
| ( ( aNaturalNumber0 @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[302]) ).
thf(353,plain,
( ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xn @ xn )
!= ( sdtasdt0 @ xp @ sK3_W0 ) )
| ~ ( aNaturalNumber0 @ sK3_W0 ) )
| ~ ( doDivides0 @ xp @ ( sdtasdt0 @ xn @ xn ) ) )
| ~ ~ ( ( xn
!= ( sdtasdt0 @ xp @ sK2_W0 ) )
| ~ ( aNaturalNumber0 @ sK2_W0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[303]) ).
thf(354,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ! [SX1: $i] :
( ( xp
!= ( sdtasdt0 @ SX0 @ SX1 ) )
| ~ ( aNaturalNumber0 @ SX1 ) )
| ( SX0 = sz10 )
| ( SX0 = xp ) )
| ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( doDivides0 @ SX0 @ xp )
| ( SX0 = sz10 )
| ( SX0 = xp ) ) )
| ~ ( ( xp != sz10 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[305]) ).
thf(355,plain,
( ( xp = sz00 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[307]) ).
thf(356,plain,
( ( ~ ( ( xm != sz00 ) )
| ~ ~ ( ~ ( ( xn != sz00 ) )
| ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ xn )
| ~ ( aNaturalNumber0 @ xm ) )
| ~ ( aNaturalNumber0 @ xp ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[308]) ).
thf(357,plain,
! [SV55: $i] :
( ( ~ ( aNaturalNumber0 @ SV55 )
| ( ( sdtasdt0 @ SV55 @ sz00 )
= sz00 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[309]) ).
thf(358,plain,
! [SV56: $i] :
( ( ~ ( aNaturalNumber0 @ SV56 )
| ( sz00
= ( sdtasdt0 @ sz00 @ SV56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[310]) ).
thf(359,plain,
! [SV23: $i] :
( ( ( SV23 = sz00 )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV23 ) )
= $true )
| ( ( SV23 = sz10 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ ( sK1_W1 @ SV23 ) )
| ~ ( doDivides0 @ ( sK1_W1 @ SV23 ) @ SV23 ) )
| ~ ( isPrime0 @ ( sK1_W1 @ SV23 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[311]) ).
thf(360,plain,
! [SV57: $i] :
( ( ! [SY148: $i] :
( ~ ( aNaturalNumber0 @ SV57 )
| ~ ( aNaturalNumber0 @ SY148 )
| ( SY148 != SV57 )
| ( sdtlseqdt0 @ SV57 @ SY148 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[312]) ).
thf(361,plain,
! [SV58: $i] :
( ( ! [SY149: $i] :
( ~ ( aNaturalNumber0 @ SV58 )
| ~ ( aNaturalNumber0 @ SY149 )
| ( sdtlseqdt0 @ SY149 @ SV58 )
| ( sdtlseqdt0 @ SV58 @ SY149 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[313]) ).
thf(362,plain,
! [SV59: $i] :
( ( ~ ( aNaturalNumber0 @ SV59 )
| ( ( sdtpldt0 @ SV59 @ sz00 )
= SV59 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[314]) ).
thf(363,plain,
! [SV60: $i] :
( ( ~ ( aNaturalNumber0 @ SV60 )
| ( SV60
= ( sdtpldt0 @ sz00 @ SV60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[315]) ).
thf(364,plain,
! [SV24: $i] :
( ( ! [SY120: $i,SY121: $i] :
( ~ ( aNaturalNumber0 @ SV24 )
| ~ ( aNaturalNumber0 @ SY120 )
| ~ ( aNaturalNumber0 @ SY121 )
| ( ( sdtpldt0 @ SV24 @ SY120 )
!= ( sdtpldt0 @ SV24 @ SY121 ) )
| ( SY120 = SY121 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[316]) ).
thf(365,plain,
! [SV24: $i] :
( ( ! [SY122: $i,SY123: $i] :
( ~ ( aNaturalNumber0 @ SV24 )
| ~ ( aNaturalNumber0 @ SY122 )
| ~ ( aNaturalNumber0 @ SY123 )
| ( ( sdtpldt0 @ SY122 @ SV24 )
!= ( sdtpldt0 @ SY123 @ SV24 ) )
| ( SY122 = SY123 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[317]) ).
thf(366,plain,
( ( ( xn
!= ( sdtasdt0 @ xp @ xq ) )
| ~ ( aNaturalNumber0 @ xq ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[318]) ).
thf(367,plain,
! [SV25: $i] :
( ( ! [SY124: $i,SY125: $i] :
( ( SY125 = sz00 )
| ( SY124 = sz00 )
| ( SV25 = sz00 )
| ~ ( aNaturalNumber0 @ SV25 )
| ~ ( aNaturalNumber0 @ SY124 )
| ~ ( aNaturalNumber0 @ SY125 )
| ( ( sdtasdt0 @ SY125 @ ( sdtasdt0 @ SY124 @ SY124 ) )
!= ( sdtasdt0 @ SV25 @ SV25 ) )
| ~ ( iLess0 @ SV25 @ xn )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( SY125
!= ( sdtasdt0 @ ( sK4_W3 @ SY125 @ SY124 @ SV25 ) @ ( sK5_SY81 @ SY125 @ SY124 @ SV25 ) ) )
| ~ ( aNaturalNumber0 @ ( sK5_SY81 @ SY125 @ SY124 @ SV25 ) ) )
| ~ ( aNaturalNumber0 @ ( sK4_W3 @ SY125 @ SY124 @ SV25 ) ) )
| ~ ( doDivides0 @ ( sK4_W3 @ SY125 @ SY124 @ SV25 ) @ SY125 ) )
| ~ ~ ( ~ ( ( ( sK4_W3 @ SY125 @ SY124 @ SV25 )
!= sz10 ) )
| ~ ( ( ( sK4_W3 @ SY125 @ SY124 @ SV25 )
!= SY125 ) ) ) )
| ( SY125 = sz10 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[320]) ).
thf(368,plain,
! [SV25: $i] :
( ( ! [SY126: $i,SY127: $i] :
( ( SY127 = sz00 )
| ( SY126 = sz00 )
| ( SV25 = sz00 )
| ~ ( aNaturalNumber0 @ SV25 )
| ~ ( aNaturalNumber0 @ SY126 )
| ~ ( aNaturalNumber0 @ SY127 )
| ( ( sdtasdt0 @ SY127 @ ( sdtasdt0 @ SY126 @ SY126 ) )
!= ( sdtasdt0 @ SV25 @ SV25 ) )
| ~ ( iLess0 @ SV25 @ xn )
| ~ ( isPrime0 @ SY127 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[321]) ).
thf(369,plain,
! [SV26: $i] :
( ( ~ ( ~ ! [SY128: $i,SY129: $i] :
( ~ ( aNaturalNumber0 @ SV26 )
| ~ ( aNaturalNumber0 @ SY128 )
| ~ ( aNaturalNumber0 @ SY129 )
| ( SV26 = sz00 )
| ( SY128 = SY129 )
| ~ ( sdtlseqdt0 @ SY128 @ SY129 )
| ( ( sdtasdt0 @ SY128 @ SV26 )
!= ( sdtasdt0 @ SY129 @ SV26 ) ) )
| ~ ~ ( ~ ! [SY130: $i,SY131: $i] :
( ~ ( aNaturalNumber0 @ SV26 )
| ~ ( aNaturalNumber0 @ SY130 )
| ~ ( aNaturalNumber0 @ SY131 )
| ( SV26 = sz00 )
| ( SY130 = SY131 )
| ~ ( sdtlseqdt0 @ SY130 @ SY131 )
| ( ( sdtasdt0 @ SV26 @ SY130 )
!= ( sdtasdt0 @ SV26 @ SY131 ) ) )
| ~ ! [SY132: $i,SY133: $i] :
( ~ ( aNaturalNumber0 @ SV26 )
| ~ ( aNaturalNumber0 @ SY132 )
| ~ ( aNaturalNumber0 @ SY133 )
| ( SV26 = sz00 )
| ( SY132 = SY133 )
| ~ ( sdtlseqdt0 @ SY132 @ SY133 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV26 @ SY132 ) @ ( sdtasdt0 @ SV26 @ SY133 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[322]) ).
thf(370,plain,
! [SV26: $i] :
( ( ! [SY134: $i,SY135: $i] :
( ~ ( aNaturalNumber0 @ SV26 )
| ~ ( aNaturalNumber0 @ SY134 )
| ~ ( aNaturalNumber0 @ SY135 )
| ( SV26 = sz00 )
| ( SY134 = SY135 )
| ~ ( sdtlseqdt0 @ SY134 @ SY135 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SY134 @ SV26 ) @ ( sdtasdt0 @ SY135 @ SV26 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[323]) ).
thf(371,plain,
! [SV61: $i] :
( ( ~ ( aNaturalNumber0 @ SV61 )
| ( sz10 != SV61 )
| ( SV61 = sz00 )
| ( SV61 = sz10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[324]) ).
thf(372,plain,
! [SV62: $i] :
( ( ~ ( aNaturalNumber0 @ SV62 )
| ( sdtlseqdt0 @ sz10 @ SV62 )
| ( SV62 = sz00 )
| ( SV62 = sz10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[325]) ).
thf(373,plain,
! [SV63: $i] :
( ( ! [SY150: $i] :
( ~ ( aNaturalNumber0 @ SV63 )
| ~ ( aNaturalNumber0 @ SY150 )
| ( ( sdtpldt0 @ SV63 @ SY150 )
!= sz00 )
| ( SV63 = sz00 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[326]) ).
thf(374,plain,
! [SV64: $i] :
( ( ! [SY151: $i] :
( ~ ( aNaturalNumber0 @ SV64 )
| ~ ( aNaturalNumber0 @ SY151 )
| ( ( sdtpldt0 @ SV64 @ SY151 )
!= sz00 )
| ( SY151 = sz00 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[327]) ).
thf(375,plain,
! [SV27: $i,SV2: $i] :
( ( ( aNaturalNumber0 @ SV2 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV27 ) )
= $true )
| ( ( aNaturalNumber0 @ ( sdtpldt0 @ SV2 @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[328]) ).
thf(376,plain,
! [SV28: $i,SV3: $i] :
( ( ( aNaturalNumber0 @ SV3 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV28 ) )
= $true )
| ( ( aNaturalNumber0 @ ( sdtasdt0 @ SV3 @ SV28 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[329]) ).
thf(377,plain,
! [SV29: $i,SV4: $i] :
( ( ( aNaturalNumber0 @ SV4 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV29 ) )
= $true )
| ( ( ( sdtpldt0 @ SV4 @ SV29 )
= ( sdtpldt0 @ SV29 @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[330]) ).
thf(378,plain,
! [SV45: $i,SV30: $i,SV5: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV5 )
| ~ ( aNaturalNumber0 @ SV30 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV45 ) )
= $true )
| ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV5 @ SV30 ) @ SV45 )
= ( sdtpldt0 @ SV5 @ ( sdtpldt0 @ SV30 @ SV45 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[331]) ).
thf(379,plain,
! [SV31: $i,SV6: $i] :
( ( ( aNaturalNumber0 @ SV6 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV31 ) )
= $true )
| ( ( ( sdtasdt0 @ SV6 @ SV31 )
= ( sdtasdt0 @ SV31 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[332]) ).
thf(380,plain,
! [SV46: $i,SV32: $i,SV7: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV7 )
| ~ ( aNaturalNumber0 @ SV32 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV46 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV7 @ SV32 ) @ SV46 )
= ( sdtasdt0 @ SV7 @ ( sdtasdt0 @ SV32 @ SV46 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[333]) ).
thf(381,plain,
! [SV33: $i,SV8: $i] :
( ( ( aNaturalNumber0 @ SV8 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV33 ) )
= $true )
| ( ( ( ( sdtasdt0 @ SV8 @ SV33 )
!= sz00 )
| ( SV8 = sz00 )
| ( SV33 = sz00 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[334]) ).
thf(382,plain,
! [SV34: $i,SV10: $i] :
( ( ( aNaturalNumber0 @ SV10 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV34 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV10 @ SV34 )
| ~ ( sdtlseqdt0 @ SV34 @ SV10 )
| ( SV10 = SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[335]) ).
thf(383,plain,
! [SV47: $i,SV35: $i,SV11: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV11 )
| ~ ( aNaturalNumber0 @ SV35 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV47 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV11 @ SV35 )
| ~ ( sdtlseqdt0 @ SV35 @ SV47 )
| ( sdtlseqdt0 @ SV11 @ SV47 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[336]) ).
thf(384,plain,
! [SV36: $i,SV12: $i] :
( ( ( aNaturalNumber0 @ SV12 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV36 ) )
= $true )
| ( ( ( SV12 = sz00 )
| ( sdtlseqdt0 @ SV36 @ ( sdtasdt0 @ SV36 @ SV12 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[337]) ).
thf(385,plain,
! [SV48: $i,SV65: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV65 ) )
= $true )
| ( ( aNaturalNumber0 @ SV48 )
= $false )
| ( $true = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[338]) ).
thf(386,plain,
! [SV37: $i,SV13: $i] :
( ( ( aNaturalNumber0 @ SV13 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV37 ) )
= $true )
| ( ( ( SV13 = SV37 )
| ~ ( sdtlseqdt0 @ SV13 @ SV37 )
| ( iLess0 @ SV13 @ SV37 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[339]) ).
thf(387,plain,
! [SV49: $i,SV38: $i,SV14: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV14 )
| ~ ( aNaturalNumber0 @ SV38 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV49 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV14 @ SV38 )
| ~ ( doDivides0 @ SV38 @ SV49 )
| ( doDivides0 @ SV14 @ SV49 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[340]) ).
thf(388,plain,
! [SV50: $i,SV39: $i,SV15: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV15 )
| ~ ( aNaturalNumber0 @ SV39 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV50 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV15 @ SV39 )
| ~ ( doDivides0 @ SV15 @ SV50 )
| ( doDivides0 @ SV15 @ ( sdtpldt0 @ SV39 @ SV50 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[341]) ).
thf(389,plain,
! [SV51: $i,SV40: $i,SV16: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV16 )
| ~ ( aNaturalNumber0 @ SV40 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV51 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV16 @ SV40 )
| ~ ( doDivides0 @ SV16 @ ( sdtpldt0 @ SV40 @ SV51 ) )
| ( doDivides0 @ SV16 @ SV51 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[342]) ).
thf(390,plain,
! [SV41: $i,SV17: $i] :
( ( ( aNaturalNumber0 @ SV17 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV41 ) )
= $true )
| ( ( ( SV41 = sz00 )
| ~ ( doDivides0 @ SV17 @ SV41 )
| ( sdtlseqdt0 @ SV17 @ SV41 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[343]) ).
thf(391,plain,
! [SV42: $i,SV18: $i] :
( ( ( aNaturalNumber0 @ SV18 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV42 ) )
= $true )
| ( ( ( SV18 = sz00 )
| ~ ( doDivides0 @ SV18 @ SV42 )
| ! [SY142: $i] :
( ~ ( aNaturalNumber0 @ SY142 )
| ( ( sdtasdt0 @ SY142 @ ( sdtsldt0 @ SV42 @ SV18 ) )
= ( sdtsldt0 @ ( sdtasdt0 @ SY142 @ SV42 ) @ SV18 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[344]) ).
thf(392,plain,
! [SV52: $i,SV43: $i,SV19: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV19 )
| ~ ( aNaturalNumber0 @ SV43 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV52 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV52 @ ( sdtasdt0 @ SV19 @ SV43 ) )
| ~ ( isPrime0 @ SV52 )
| ( doDivides0 @ SV52 @ SV19 )
| ( doDivides0 @ SV52 @ SV43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[345]) ).
thf(393,plain,
! [SV66: $i,SV20: $i] :
( ( ! [SY152: $i] :
( ~ ( aNaturalNumber0 @ SV20 )
| ~ ( aNaturalNumber0 @ SV66 )
| ~ ( aNaturalNumber0 @ SY152 )
| ( ( sdtasdt0 @ SV20 @ ( sdtpldt0 @ SV66 @ SY152 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV20 @ SV66 ) @ ( sdtasdt0 @ SV20 @ SY152 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[346]) ).
thf(394,plain,
! [SV67: $i,SV20: $i] :
( ( ! [SY153: $i] :
( ~ ( aNaturalNumber0 @ SV20 )
| ~ ( aNaturalNumber0 @ SV67 )
| ~ ( aNaturalNumber0 @ SY153 )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SV67 @ SY153 ) @ SV20 )
= ( sdtpldt0 @ ( sdtasdt0 @ SV67 @ SV20 ) @ ( sdtasdt0 @ SY153 @ SV20 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[347]) ).
thf(395,plain,
! [SV53: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV53 ) )
= $true )
| ( ( ( sdtasdt0 @ SV53 @ sz10 )
= SV53 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[348]) ).
thf(396,plain,
! [SV54: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV54 ) )
= $true )
| ( ( SV54
= ( sdtasdt0 @ sz10 @ SV54 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[349]) ).
thf(397,plain,
! [SV44: $i,SV21: $i] :
( ( ( aNaturalNumber0 @ SV21 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV44 ) )
= $true )
| ( ( ( SV21 = SV44 )
| ~ ( sdtlseqdt0 @ SV21 @ SV44 )
| ~ ( ~ ~ ( ~ ! [SY144: $i] :
( ~ ( aNaturalNumber0 @ SY144 )
| ( ( sdtpldt0 @ SV21 @ SY144 )
!= ( sdtpldt0 @ SV44 @ SY144 ) ) )
| ~ ~ ( ~ ! [SY145: $i] :
( ~ ( aNaturalNumber0 @ SY145 )
| ( ( sdtpldt0 @ SY145 @ SV21 )
!= ( sdtpldt0 @ SY145 @ SV44 ) ) )
| ~ ! [SY146: $i] :
( ~ ( aNaturalNumber0 @ SY146 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SY146 @ SV21 ) @ ( sdtpldt0 @ SY146 @ SV44 ) ) ) ) )
| ~ ! [SY147: $i] :
( ~ ( aNaturalNumber0 @ SY147 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SV21 @ SY147 ) @ ( sdtpldt0 @ SV44 @ SY147 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[351]) ).
thf(398,plain,
! [SV22: $i] :
( ( ( ~ ! [SY116: $i,SY117: $i] :
( ~ ( aNaturalNumber0 @ SY116 )
| ~ ( aNaturalNumber0 @ SY117 )
| ( ( sdtasdt0 @ SV22 @ SY116 )
!= ( sdtasdt0 @ SV22 @ SY117 ) )
| ( SY116 = SY117 ) )
| ~ ! [SY118: $i,SY119: $i] :
( ~ ( aNaturalNumber0 @ SY118 )
| ~ ( aNaturalNumber0 @ SY119 )
| ( ( sdtasdt0 @ SY118 @ SV22 )
!= ( sdtasdt0 @ SY119 @ SV22 ) )
| ( SY118 = SY119 ) ) )
= $false )
| ( ( SV22 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[352]) ).
thf(399,plain,
( ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xn @ xn )
!= ( sdtasdt0 @ xp @ sK3_W0 ) )
| ~ ( aNaturalNumber0 @ sK3_W0 ) )
| ~ ( doDivides0 @ xp @ ( sdtasdt0 @ xn @ xn ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[353]) ).
thf(400,plain,
( ( ~ ~ ( ( xn
!= ( sdtasdt0 @ xp @ sK2_W0 ) )
| ~ ( aNaturalNumber0 @ sK2_W0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[353]) ).
thf(401,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ! [SX1: $i] :
( ( xp
!= ( sdtasdt0 @ SX0 @ SX1 ) )
| ~ ( aNaturalNumber0 @ SX1 ) )
| ( SX0 = sz10 )
| ( SX0 = xp ) )
| ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( doDivides0 @ SX0 @ xp )
| ( SX0 = sz10 )
| ( SX0 = xp ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[354]) ).
thf(402,plain,
( ( ~ ( ( xp != sz10 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[354]) ).
thf(403,plain,
( ( ~ ( ( xm != sz00 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[356]) ).
thf(404,plain,
( ( ~ ~ ( ~ ( ( xn != sz00 ) )
| ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ xn )
| ~ ( aNaturalNumber0 @ xm ) )
| ~ ( aNaturalNumber0 @ xp ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[356]) ).
thf(405,plain,
! [SV55: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV55 ) )
= $true )
| ( ( ( sdtasdt0 @ SV55 @ sz00 )
= sz00 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[357]) ).
thf(406,plain,
! [SV56: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV56 ) )
= $true )
| ( ( sz00
= ( sdtasdt0 @ sz00 @ SV56 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[358]) ).
thf(407,plain,
! [SV23: $i] :
( ( ( aNaturalNumber0 @ SV23 )
= $false )
| ( ( SV23 = sz00 )
= $true )
| ( ( SV23 = sz10 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ ( sK1_W1 @ SV23 ) )
| ~ ( doDivides0 @ ( sK1_W1 @ SV23 ) @ SV23 ) )
| ~ ( isPrime0 @ ( sK1_W1 @ SV23 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[359]) ).
thf(408,plain,
! [SV68: $i,SV57: $i] :
( ( ~ ( aNaturalNumber0 @ SV57 )
| ~ ( aNaturalNumber0 @ SV68 )
| ( SV68 != SV57 )
| ( sdtlseqdt0 @ SV57 @ SV68 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[360]) ).
thf(409,plain,
! [SV69: $i,SV58: $i] :
( ( ~ ( aNaturalNumber0 @ SV58 )
| ~ ( aNaturalNumber0 @ SV69 )
| ( sdtlseqdt0 @ SV69 @ SV58 )
| ( sdtlseqdt0 @ SV58 @ SV69 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[361]) ).
thf(410,plain,
! [SV59: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV59 ) )
= $true )
| ( ( ( sdtpldt0 @ SV59 @ sz00 )
= SV59 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[362]) ).
thf(411,plain,
! [SV60: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV60 ) )
= $true )
| ( ( SV60
= ( sdtpldt0 @ sz00 @ SV60 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[363]) ).
thf(412,plain,
! [SV70: $i,SV24: $i] :
( ( ! [SY154: $i] :
( ~ ( aNaturalNumber0 @ SV24 )
| ~ ( aNaturalNumber0 @ SV70 )
| ~ ( aNaturalNumber0 @ SY154 )
| ( ( sdtpldt0 @ SV24 @ SV70 )
!= ( sdtpldt0 @ SV24 @ SY154 ) )
| ( SV70 = SY154 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[364]) ).
thf(413,plain,
! [SV71: $i,SV24: $i] :
( ( ! [SY155: $i] :
( ~ ( aNaturalNumber0 @ SV24 )
| ~ ( aNaturalNumber0 @ SV71 )
| ~ ( aNaturalNumber0 @ SY155 )
| ( ( sdtpldt0 @ SV71 @ SV24 )
!= ( sdtpldt0 @ SY155 @ SV24 ) )
| ( SV71 = SY155 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[365]) ).
thf(414,plain,
( ( xn
!= ( sdtasdt0 @ xp @ xq ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[366]) ).
thf(415,plain,
( ( ~ ( aNaturalNumber0 @ xq ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[366]) ).
thf(416,plain,
! [SV25: $i,SV72: $i] :
( ( ! [SY156: $i] :
( ( SY156 = sz00 )
| ( SV72 = sz00 )
| ( SV25 = sz00 )
| ~ ( aNaturalNumber0 @ SV25 )
| ~ ( aNaturalNumber0 @ SV72 )
| ~ ( aNaturalNumber0 @ SY156 )
| ( ( sdtasdt0 @ SY156 @ ( sdtasdt0 @ SV72 @ SV72 ) )
!= ( sdtasdt0 @ SV25 @ SV25 ) )
| ~ ( iLess0 @ SV25 @ xn )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( SY156
!= ( sdtasdt0 @ ( sK4_W3 @ SY156 @ SV72 @ SV25 ) @ ( sK5_SY81 @ SY156 @ SV72 @ SV25 ) ) )
| ~ ( aNaturalNumber0 @ ( sK5_SY81 @ SY156 @ SV72 @ SV25 ) ) )
| ~ ( aNaturalNumber0 @ ( sK4_W3 @ SY156 @ SV72 @ SV25 ) ) )
| ~ ( doDivides0 @ ( sK4_W3 @ SY156 @ SV72 @ SV25 ) @ SY156 ) )
| ~ ~ ( ~ ( ( ( sK4_W3 @ SY156 @ SV72 @ SV25 )
!= sz10 ) )
| ~ ( ( ( sK4_W3 @ SY156 @ SV72 @ SV25 )
!= SY156 ) ) ) )
| ( SY156 = sz10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[367]) ).
thf(417,plain,
! [SV25: $i,SV73: $i] :
( ( ! [SY157: $i] :
( ( SY157 = sz00 )
| ( SV73 = sz00 )
| ( SV25 = sz00 )
| ~ ( aNaturalNumber0 @ SV25 )
| ~ ( aNaturalNumber0 @ SV73 )
| ~ ( aNaturalNumber0 @ SY157 )
| ( ( sdtasdt0 @ SY157 @ ( sdtasdt0 @ SV73 @ SV73 ) )
!= ( sdtasdt0 @ SV25 @ SV25 ) )
| ~ ( iLess0 @ SV25 @ xn )
| ~ ( isPrime0 @ SY157 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[368]) ).
thf(418,plain,
! [SV26: $i] :
( ( ~ ! [SY128: $i,SY129: $i] :
( ~ ( aNaturalNumber0 @ SV26 )
| ~ ( aNaturalNumber0 @ SY128 )
| ~ ( aNaturalNumber0 @ SY129 )
| ( SV26 = sz00 )
| ( SY128 = SY129 )
| ~ ( sdtlseqdt0 @ SY128 @ SY129 )
| ( ( sdtasdt0 @ SY128 @ SV26 )
!= ( sdtasdt0 @ SY129 @ SV26 ) ) )
| ~ ~ ( ~ ! [SY130: $i,SY131: $i] :
( ~ ( aNaturalNumber0 @ SV26 )
| ~ ( aNaturalNumber0 @ SY130 )
| ~ ( aNaturalNumber0 @ SY131 )
| ( SV26 = sz00 )
| ( SY130 = SY131 )
| ~ ( sdtlseqdt0 @ SY130 @ SY131 )
| ( ( sdtasdt0 @ SV26 @ SY130 )
!= ( sdtasdt0 @ SV26 @ SY131 ) ) )
| ~ ! [SY132: $i,SY133: $i] :
( ~ ( aNaturalNumber0 @ SV26 )
| ~ ( aNaturalNumber0 @ SY132 )
| ~ ( aNaturalNumber0 @ SY133 )
| ( SV26 = sz00 )
| ( SY132 = SY133 )
| ~ ( sdtlseqdt0 @ SY132 @ SY133 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV26 @ SY132 ) @ ( sdtasdt0 @ SV26 @ SY133 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[369]) ).
thf(419,plain,
! [SV74: $i,SV26: $i] :
( ( ! [SY158: $i] :
( ~ ( aNaturalNumber0 @ SV26 )
| ~ ( aNaturalNumber0 @ SV74 )
| ~ ( aNaturalNumber0 @ SY158 )
| ( SV26 = sz00 )
| ( SV74 = SY158 )
| ~ ( sdtlseqdt0 @ SV74 @ SY158 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV74 @ SV26 ) @ ( sdtasdt0 @ SY158 @ SV26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[370]) ).
thf(420,plain,
! [SV61: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV61 ) )
= $true )
| ( ( ( sz10 != SV61 )
| ( SV61 = sz00 )
| ( SV61 = sz10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[371]) ).
thf(421,plain,
! [SV62: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV62 ) )
= $true )
| ( ( ( sdtlseqdt0 @ sz10 @ SV62 )
| ( SV62 = sz00 )
| ( SV62 = sz10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[372]) ).
thf(422,plain,
! [SV75: $i,SV63: $i] :
( ( ~ ( aNaturalNumber0 @ SV63 )
| ~ ( aNaturalNumber0 @ SV75 )
| ( ( sdtpldt0 @ SV63 @ SV75 )
!= sz00 )
| ( SV63 = sz00 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[373]) ).
thf(423,plain,
! [SV76: $i,SV64: $i] :
( ( ~ ( aNaturalNumber0 @ SV64 )
| ~ ( aNaturalNumber0 @ SV76 )
| ( ( sdtpldt0 @ SV64 @ SV76 )
!= sz00 )
| ( SV76 = sz00 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[374]) ).
thf(424,plain,
! [SV2: $i,SV27: $i] :
( ( ( aNaturalNumber0 @ SV27 )
= $false )
| ( ( aNaturalNumber0 @ SV2 )
= $false )
| ( ( aNaturalNumber0 @ ( sdtpldt0 @ SV2 @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[375]) ).
thf(425,plain,
! [SV3: $i,SV28: $i] :
( ( ( aNaturalNumber0 @ SV28 )
= $false )
| ( ( aNaturalNumber0 @ SV3 )
= $false )
| ( ( aNaturalNumber0 @ ( sdtasdt0 @ SV3 @ SV28 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[376]) ).
thf(426,plain,
! [SV4: $i,SV29: $i] :
( ( ( aNaturalNumber0 @ SV29 )
= $false )
| ( ( aNaturalNumber0 @ SV4 )
= $false )
| ( ( ( sdtpldt0 @ SV4 @ SV29 )
= ( sdtpldt0 @ SV29 @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[377]) ).
thf(427,plain,
! [SV45: $i,SV30: $i,SV5: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV5 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV30 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV45 ) )
= $true )
| ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV5 @ SV30 ) @ SV45 )
= ( sdtpldt0 @ SV5 @ ( sdtpldt0 @ SV30 @ SV45 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[378]) ).
thf(428,plain,
! [SV6: $i,SV31: $i] :
( ( ( aNaturalNumber0 @ SV31 )
= $false )
| ( ( aNaturalNumber0 @ SV6 )
= $false )
| ( ( ( sdtasdt0 @ SV6 @ SV31 )
= ( sdtasdt0 @ SV31 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[379]) ).
thf(429,plain,
! [SV46: $i,SV32: $i,SV7: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV7 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV32 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV46 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV7 @ SV32 ) @ SV46 )
= ( sdtasdt0 @ SV7 @ ( sdtasdt0 @ SV32 @ SV46 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[380]) ).
thf(430,plain,
! [SV8: $i,SV33: $i] :
( ( ( aNaturalNumber0 @ SV33 )
= $false )
| ( ( aNaturalNumber0 @ SV8 )
= $false )
| ( ( ( ( sdtasdt0 @ SV8 @ SV33 )
!= sz00 )
| ( SV8 = sz00 )
| ( SV33 = sz00 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[381]) ).
thf(431,plain,
! [SV10: $i,SV34: $i] :
( ( ( aNaturalNumber0 @ SV34 )
= $false )
| ( ( aNaturalNumber0 @ SV10 )
= $false )
| ( ( ~ ( sdtlseqdt0 @ SV10 @ SV34 )
| ~ ( sdtlseqdt0 @ SV34 @ SV10 )
| ( SV10 = SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[382]) ).
thf(432,plain,
! [SV47: $i,SV35: $i,SV11: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV11 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV35 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV47 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV11 @ SV35 )
| ~ ( sdtlseqdt0 @ SV35 @ SV47 )
| ( sdtlseqdt0 @ SV11 @ SV47 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[383]) ).
thf(433,plain,
! [SV12: $i,SV36: $i] :
( ( ( aNaturalNumber0 @ SV36 )
= $false )
| ( ( aNaturalNumber0 @ SV12 )
= $false )
| ( ( ( SV12 = sz00 )
| ( sdtlseqdt0 @ SV36 @ ( sdtasdt0 @ SV36 @ SV12 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[384]) ).
thf(434,plain,
! [SV48: $i,SV65: $i] :
( ( ( aNaturalNumber0 @ SV65 )
= $false )
| ( ( aNaturalNumber0 @ SV48 )
= $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[385]) ).
thf(435,plain,
! [SV13: $i,SV37: $i] :
( ( ( aNaturalNumber0 @ SV37 )
= $false )
| ( ( aNaturalNumber0 @ SV13 )
= $false )
| ( ( ( SV13 = SV37 )
| ~ ( sdtlseqdt0 @ SV13 @ SV37 )
| ( iLess0 @ SV13 @ SV37 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[386]) ).
thf(436,plain,
! [SV49: $i,SV38: $i,SV14: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV14 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV38 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV49 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV14 @ SV38 )
| ~ ( doDivides0 @ SV38 @ SV49 )
| ( doDivides0 @ SV14 @ SV49 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[387]) ).
thf(437,plain,
! [SV50: $i,SV39: $i,SV15: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV15 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV39 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV50 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV15 @ SV39 )
| ~ ( doDivides0 @ SV15 @ SV50 )
| ( doDivides0 @ SV15 @ ( sdtpldt0 @ SV39 @ SV50 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[388]) ).
thf(438,plain,
! [SV51: $i,SV40: $i,SV16: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV16 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV40 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV51 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV16 @ SV40 )
| ~ ( doDivides0 @ SV16 @ ( sdtpldt0 @ SV40 @ SV51 ) )
| ( doDivides0 @ SV16 @ SV51 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[389]) ).
thf(439,plain,
! [SV17: $i,SV41: $i] :
( ( ( aNaturalNumber0 @ SV41 )
= $false )
| ( ( aNaturalNumber0 @ SV17 )
= $false )
| ( ( ( SV41 = sz00 )
| ~ ( doDivides0 @ SV17 @ SV41 )
| ( sdtlseqdt0 @ SV17 @ SV41 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[390]) ).
thf(440,plain,
! [SV18: $i,SV42: $i] :
( ( ( aNaturalNumber0 @ SV42 )
= $false )
| ( ( aNaturalNumber0 @ SV18 )
= $false )
| ( ( ( SV18 = sz00 )
| ~ ( doDivides0 @ SV18 @ SV42 )
| ! [SY142: $i] :
( ~ ( aNaturalNumber0 @ SY142 )
| ( ( sdtasdt0 @ SY142 @ ( sdtsldt0 @ SV42 @ SV18 ) )
= ( sdtsldt0 @ ( sdtasdt0 @ SY142 @ SV42 ) @ SV18 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[391]) ).
thf(441,plain,
! [SV52: $i,SV43: $i,SV19: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV19 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV43 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV52 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV52 @ ( sdtasdt0 @ SV19 @ SV43 ) )
| ~ ( isPrime0 @ SV52 )
| ( doDivides0 @ SV52 @ SV19 )
| ( doDivides0 @ SV52 @ SV43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[392]) ).
thf(442,plain,
! [SV77: $i,SV66: $i,SV20: $i] :
( ( ~ ( aNaturalNumber0 @ SV20 )
| ~ ( aNaturalNumber0 @ SV66 )
| ~ ( aNaturalNumber0 @ SV77 )
| ( ( sdtasdt0 @ SV20 @ ( sdtpldt0 @ SV66 @ SV77 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV20 @ SV66 ) @ ( sdtasdt0 @ SV20 @ SV77 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[393]) ).
thf(443,plain,
! [SV78: $i,SV67: $i,SV20: $i] :
( ( ~ ( aNaturalNumber0 @ SV20 )
| ~ ( aNaturalNumber0 @ SV67 )
| ~ ( aNaturalNumber0 @ SV78 )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SV67 @ SV78 ) @ SV20 )
= ( sdtpldt0 @ ( sdtasdt0 @ SV67 @ SV20 ) @ ( sdtasdt0 @ SV78 @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[394]) ).
thf(444,plain,
! [SV53: $i] :
( ( ( aNaturalNumber0 @ SV53 )
= $false )
| ( ( ( sdtasdt0 @ SV53 @ sz10 )
= SV53 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[395]) ).
thf(445,plain,
! [SV54: $i] :
( ( ( aNaturalNumber0 @ SV54 )
= $false )
| ( ( SV54
= ( sdtasdt0 @ sz10 @ SV54 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[396]) ).
thf(446,plain,
! [SV21: $i,SV44: $i] :
( ( ( aNaturalNumber0 @ SV44 )
= $false )
| ( ( aNaturalNumber0 @ SV21 )
= $false )
| ( ( ( SV21 = SV44 )
| ~ ( sdtlseqdt0 @ SV21 @ SV44 )
| ~ ( ~ ~ ( ~ ! [SY144: $i] :
( ~ ( aNaturalNumber0 @ SY144 )
| ( ( sdtpldt0 @ SV21 @ SY144 )
!= ( sdtpldt0 @ SV44 @ SY144 ) ) )
| ~ ~ ( ~ ! [SY145: $i] :
( ~ ( aNaturalNumber0 @ SY145 )
| ( ( sdtpldt0 @ SY145 @ SV21 )
!= ( sdtpldt0 @ SY145 @ SV44 ) ) )
| ~ ! [SY146: $i] :
( ~ ( aNaturalNumber0 @ SY146 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SY146 @ SV21 ) @ ( sdtpldt0 @ SY146 @ SV44 ) ) ) ) )
| ~ ! [SY147: $i] :
( ~ ( aNaturalNumber0 @ SY147 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SV21 @ SY147 ) @ ( sdtpldt0 @ SV44 @ SY147 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[397]) ).
thf(447,plain,
! [SV22: $i] :
( ( ( ~ ! [SY116: $i,SY117: $i] :
( ~ ( aNaturalNumber0 @ SY116 )
| ~ ( aNaturalNumber0 @ SY117 )
| ( ( sdtasdt0 @ SV22 @ SY116 )
!= ( sdtasdt0 @ SV22 @ SY117 ) )
| ( SY116 = SY117 ) ) )
= $false )
| ( ( SV22 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV22 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[398]) ).
thf(448,plain,
! [SV22: $i] :
( ( ( ~ ! [SY118: $i,SY119: $i] :
( ~ ( aNaturalNumber0 @ SY118 )
| ~ ( aNaturalNumber0 @ SY119 )
| ( ( sdtasdt0 @ SY118 @ SV22 )
!= ( sdtasdt0 @ SY119 @ SV22 ) )
| ( SY118 = SY119 ) ) )
= $false )
| ( ( SV22 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV22 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[398]) ).
thf(449,plain,
( ( ~ ( ~ ~ ( ( ( sdtasdt0 @ xn @ xn )
!= ( sdtasdt0 @ xp @ sK3_W0 ) )
| ~ ( aNaturalNumber0 @ sK3_W0 ) )
| ~ ( doDivides0 @ xp @ ( sdtasdt0 @ xn @ xn ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[399]) ).
thf(450,plain,
( ( ~ ( ( xn
!= ( sdtasdt0 @ xp @ sK2_W0 ) )
| ~ ( aNaturalNumber0 @ sK2_W0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[400]) ).
thf(451,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ! [SX1: $i] :
( ( xp
!= ( sdtasdt0 @ SX0 @ SX1 ) )
| ~ ( aNaturalNumber0 @ SX1 ) )
| ( SX0 = sz10 )
| ( SX0 = xp ) )
| ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( doDivides0 @ SX0 @ xp )
| ( SX0 = sz10 )
| ( SX0 = xp ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[401]) ).
thf(452,plain,
( ( xp != sz10 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[402]) ).
thf(453,plain,
( ( xm != sz00 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[403]) ).
thf(454,plain,
( ( ~ ( ~ ( ( xn != sz00 ) )
| ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ xn )
| ~ ( aNaturalNumber0 @ xm ) )
| ~ ( aNaturalNumber0 @ xp ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[404]) ).
thf(455,plain,
! [SV55: $i] :
( ( ( aNaturalNumber0 @ SV55 )
= $false )
| ( ( ( sdtasdt0 @ SV55 @ sz00 )
= sz00 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[405]) ).
thf(456,plain,
! [SV56: $i] :
( ( ( aNaturalNumber0 @ SV56 )
= $false )
| ( ( sz00
= ( sdtasdt0 @ sz00 @ SV56 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[406]) ).
thf(457,plain,
! [SV23: $i] :
( ( ( ~ ~ ( ~ ( aNaturalNumber0 @ ( sK1_W1 @ SV23 ) )
| ~ ( doDivides0 @ ( sK1_W1 @ SV23 ) @ SV23 ) )
| ~ ( isPrime0 @ ( sK1_W1 @ SV23 ) ) )
= $false )
| ( ( SV23 = sz10 )
= $true )
| ( ( SV23 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[407]) ).
thf(458,plain,
! [SV68: $i,SV57: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV57 )
| ~ ( aNaturalNumber0 @ SV68 ) )
= $true )
| ( ( ( SV68 != SV57 )
| ( sdtlseqdt0 @ SV57 @ SV68 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[408]) ).
thf(459,plain,
! [SV69: $i,SV58: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV58 )
| ~ ( aNaturalNumber0 @ SV69 ) )
= $true )
| ( ( ( sdtlseqdt0 @ SV69 @ SV58 )
| ( sdtlseqdt0 @ SV58 @ SV69 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[409]) ).
thf(460,plain,
! [SV59: $i] :
( ( ( aNaturalNumber0 @ SV59 )
= $false )
| ( ( ( sdtpldt0 @ SV59 @ sz00 )
= SV59 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[410]) ).
thf(461,plain,
! [SV60: $i] :
( ( ( aNaturalNumber0 @ SV60 )
= $false )
| ( ( SV60
= ( sdtpldt0 @ sz00 @ SV60 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[411]) ).
thf(462,plain,
! [SV79: $i,SV70: $i,SV24: $i] :
( ( ~ ( aNaturalNumber0 @ SV24 )
| ~ ( aNaturalNumber0 @ SV70 )
| ~ ( aNaturalNumber0 @ SV79 )
| ( ( sdtpldt0 @ SV24 @ SV70 )
!= ( sdtpldt0 @ SV24 @ SV79 ) )
| ( SV70 = SV79 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[412]) ).
thf(463,plain,
! [SV80: $i,SV71: $i,SV24: $i] :
( ( ~ ( aNaturalNumber0 @ SV24 )
| ~ ( aNaturalNumber0 @ SV71 )
| ~ ( aNaturalNumber0 @ SV80 )
| ( ( sdtpldt0 @ SV71 @ SV24 )
!= ( sdtpldt0 @ SV80 @ SV24 ) )
| ( SV71 = SV80 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[413]) ).
thf(464,plain,
( ( xn
= ( sdtasdt0 @ xp @ xq ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[414]) ).
thf(465,plain,
( ( aNaturalNumber0 @ xq )
= $true ),
inference(extcnf_not_neg,[status(thm)],[415]) ).
thf(466,plain,
! [SV25: $i,SV72: $i,SV81: $i] :
( ( ( SV81 = sz00 )
| ( SV72 = sz00 )
| ( SV25 = sz00 )
| ~ ( aNaturalNumber0 @ SV25 )
| ~ ( aNaturalNumber0 @ SV72 )
| ~ ( aNaturalNumber0 @ SV81 )
| ( ( sdtasdt0 @ SV81 @ ( sdtasdt0 @ SV72 @ SV72 ) )
!= ( sdtasdt0 @ SV25 @ SV25 ) )
| ~ ( iLess0 @ SV25 @ xn )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( SV81
!= ( sdtasdt0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) @ ( sK5_SY81 @ SV81 @ SV72 @ SV25 ) ) )
| ~ ( aNaturalNumber0 @ ( sK5_SY81 @ SV81 @ SV72 @ SV25 ) ) )
| ~ ( aNaturalNumber0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) ) )
| ~ ( doDivides0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) @ SV81 ) )
| ~ ~ ( ~ ( ( ( sK4_W3 @ SV81 @ SV72 @ SV25 )
!= sz10 ) )
| ~ ( ( ( sK4_W3 @ SV81 @ SV72 @ SV25 )
!= SV81 ) ) ) )
| ( SV81 = sz10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[416]) ).
thf(467,plain,
! [SV25: $i,SV73: $i,SV82: $i] :
( ( ( SV82 = sz00 )
| ( SV73 = sz00 )
| ( SV25 = sz00 )
| ~ ( aNaturalNumber0 @ SV25 )
| ~ ( aNaturalNumber0 @ SV73 )
| ~ ( aNaturalNumber0 @ SV82 )
| ( ( sdtasdt0 @ SV82 @ ( sdtasdt0 @ SV73 @ SV73 ) )
!= ( sdtasdt0 @ SV25 @ SV25 ) )
| ~ ( iLess0 @ SV25 @ xn )
| ~ ( isPrime0 @ SV82 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[417]) ).
thf(468,plain,
! [SV26: $i] :
( ( ~ ! [SY128: $i,SY129: $i] :
( ~ ( aNaturalNumber0 @ SV26 )
| ~ ( aNaturalNumber0 @ SY128 )
| ~ ( aNaturalNumber0 @ SY129 )
| ( SV26 = sz00 )
| ( SY128 = SY129 )
| ~ ( sdtlseqdt0 @ SY128 @ SY129 )
| ( ( sdtasdt0 @ SY128 @ SV26 )
!= ( sdtasdt0 @ SY129 @ SV26 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[418]) ).
thf(469,plain,
! [SV26: $i] :
( ( ~ ~ ( ~ ! [SY130: $i,SY131: $i] :
( ~ ( aNaturalNumber0 @ SV26 )
| ~ ( aNaturalNumber0 @ SY130 )
| ~ ( aNaturalNumber0 @ SY131 )
| ( SV26 = sz00 )
| ( SY130 = SY131 )
| ~ ( sdtlseqdt0 @ SY130 @ SY131 )
| ( ( sdtasdt0 @ SV26 @ SY130 )
!= ( sdtasdt0 @ SV26 @ SY131 ) ) )
| ~ ! [SY132: $i,SY133: $i] :
( ~ ( aNaturalNumber0 @ SV26 )
| ~ ( aNaturalNumber0 @ SY132 )
| ~ ( aNaturalNumber0 @ SY133 )
| ( SV26 = sz00 )
| ( SY132 = SY133 )
| ~ ( sdtlseqdt0 @ SY132 @ SY133 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV26 @ SY132 ) @ ( sdtasdt0 @ SV26 @ SY133 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[418]) ).
thf(470,plain,
! [SV83: $i,SV74: $i,SV26: $i] :
( ( ~ ( aNaturalNumber0 @ SV26 )
| ~ ( aNaturalNumber0 @ SV74 )
| ~ ( aNaturalNumber0 @ SV83 )
| ( SV26 = sz00 )
| ( SV74 = SV83 )
| ~ ( sdtlseqdt0 @ SV74 @ SV83 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV74 @ SV26 ) @ ( sdtasdt0 @ SV83 @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[419]) ).
thf(471,plain,
! [SV61: $i] :
( ( ( aNaturalNumber0 @ SV61 )
= $false )
| ( ( ( sz10 != SV61 )
| ( SV61 = sz00 )
| ( SV61 = sz10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[420]) ).
thf(472,plain,
! [SV62: $i] :
( ( ( aNaturalNumber0 @ SV62 )
= $false )
| ( ( ( sdtlseqdt0 @ sz10 @ SV62 )
| ( SV62 = sz00 )
| ( SV62 = sz10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[421]) ).
thf(473,plain,
! [SV75: $i,SV63: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV63 )
| ~ ( aNaturalNumber0 @ SV75 ) )
= $true )
| ( ( ( ( sdtpldt0 @ SV63 @ SV75 )
!= sz00 )
| ( SV63 = sz00 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[422]) ).
thf(474,plain,
! [SV76: $i,SV64: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV64 )
| ~ ( aNaturalNumber0 @ SV76 ) )
= $true )
| ( ( ( ( sdtpldt0 @ SV64 @ SV76 )
!= sz00 )
| ( SV76 = sz00 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[423]) ).
thf(475,plain,
! [SV45: $i,SV30: $i,SV5: $i] :
( ( ( aNaturalNumber0 @ SV5 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV30 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV45 ) )
= $true )
| ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV5 @ SV30 ) @ SV45 )
= ( sdtpldt0 @ SV5 @ ( sdtpldt0 @ SV30 @ SV45 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[427]) ).
thf(476,plain,
! [SV46: $i,SV32: $i,SV7: $i] :
( ( ( aNaturalNumber0 @ SV7 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV32 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV46 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV7 @ SV32 ) @ SV46 )
= ( sdtasdt0 @ SV7 @ ( sdtasdt0 @ SV32 @ SV46 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[429]) ).
thf(477,plain,
! [SV33: $i,SV8: $i] :
( ( ( ( sdtasdt0 @ SV8 @ SV33 )
!= sz00 )
= $true )
| ( ( ( SV8 = sz00 )
| ( SV33 = sz00 ) )
= $true )
| ( ( aNaturalNumber0 @ SV8 )
= $false )
| ( ( aNaturalNumber0 @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[430]) ).
thf(478,plain,
! [SV34: $i,SV10: $i] :
( ( ( ~ ( sdtlseqdt0 @ SV10 @ SV34 )
| ~ ( sdtlseqdt0 @ SV34 @ SV10 ) )
= $true )
| ( ( SV10 = SV34 )
= $true )
| ( ( aNaturalNumber0 @ SV10 )
= $false )
| ( ( aNaturalNumber0 @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[431]) ).
thf(479,plain,
! [SV47: $i,SV35: $i,SV11: $i] :
( ( ( aNaturalNumber0 @ SV11 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV35 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV47 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV11 @ SV35 )
| ~ ( sdtlseqdt0 @ SV35 @ SV47 )
| ( sdtlseqdt0 @ SV11 @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[432]) ).
thf(480,plain,
! [SV36: $i,SV12: $i] :
( ( ( SV12 = sz00 )
= $true )
| ( ( sdtlseqdt0 @ SV36 @ ( sdtasdt0 @ SV36 @ SV12 ) )
= $true )
| ( ( aNaturalNumber0 @ SV12 )
= $false )
| ( ( aNaturalNumber0 @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[433]) ).
thf(481,plain,
! [SV37: $i,SV13: $i] :
( ( ( ( SV13 = SV37 )
| ~ ( sdtlseqdt0 @ SV13 @ SV37 ) )
= $true )
| ( ( iLess0 @ SV13 @ SV37 )
= $true )
| ( ( aNaturalNumber0 @ SV13 )
= $false )
| ( ( aNaturalNumber0 @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[435]) ).
thf(482,plain,
! [SV49: $i,SV38: $i,SV14: $i] :
( ( ( aNaturalNumber0 @ SV14 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV38 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV49 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV14 @ SV38 )
| ~ ( doDivides0 @ SV38 @ SV49 )
| ( doDivides0 @ SV14 @ SV49 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[436]) ).
thf(483,plain,
! [SV50: $i,SV39: $i,SV15: $i] :
( ( ( aNaturalNumber0 @ SV15 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV39 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV50 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV15 @ SV39 )
| ~ ( doDivides0 @ SV15 @ SV50 )
| ( doDivides0 @ SV15 @ ( sdtpldt0 @ SV39 @ SV50 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[437]) ).
thf(484,plain,
! [SV51: $i,SV40: $i,SV16: $i] :
( ( ( aNaturalNumber0 @ SV16 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV40 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV51 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV16 @ SV40 )
| ~ ( doDivides0 @ SV16 @ ( sdtpldt0 @ SV40 @ SV51 ) )
| ( doDivides0 @ SV16 @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[438]) ).
thf(485,plain,
! [SV17: $i,SV41: $i] :
( ( ( ( SV41 = sz00 )
| ~ ( doDivides0 @ SV17 @ SV41 ) )
= $true )
| ( ( sdtlseqdt0 @ SV17 @ SV41 )
= $true )
| ( ( aNaturalNumber0 @ SV17 )
= $false )
| ( ( aNaturalNumber0 @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[439]) ).
thf(486,plain,
! [SV42: $i,SV18: $i] :
( ( ( ( SV18 = sz00 )
| ~ ( doDivides0 @ SV18 @ SV42 ) )
= $true )
| ( ( ! [SY142: $i] :
( ~ ( aNaturalNumber0 @ SY142 )
| ( ( sdtasdt0 @ SY142 @ ( sdtsldt0 @ SV42 @ SV18 ) )
= ( sdtsldt0 @ ( sdtasdt0 @ SY142 @ SV42 ) @ SV18 ) ) ) )
= $true )
| ( ( aNaturalNumber0 @ SV18 )
= $false )
| ( ( aNaturalNumber0 @ SV42 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[440]) ).
thf(487,plain,
! [SV52: $i,SV43: $i,SV19: $i] :
( ( ( aNaturalNumber0 @ SV19 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV43 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV52 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV52 @ ( sdtasdt0 @ SV19 @ SV43 ) )
| ~ ( isPrime0 @ SV52 )
| ( doDivides0 @ SV52 @ SV19 )
| ( doDivides0 @ SV52 @ SV43 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[441]) ).
thf(488,plain,
! [SV77: $i,SV66: $i,SV20: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV20 )
| ~ ( aNaturalNumber0 @ SV66 )
| ~ ( aNaturalNumber0 @ SV77 ) )
= $true )
| ( ( ( sdtasdt0 @ SV20 @ ( sdtpldt0 @ SV66 @ SV77 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV20 @ SV66 ) @ ( sdtasdt0 @ SV20 @ SV77 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[442]) ).
thf(489,plain,
! [SV78: $i,SV67: $i,SV20: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV20 )
| ~ ( aNaturalNumber0 @ SV67 )
| ~ ( aNaturalNumber0 @ SV78 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV67 @ SV78 ) @ SV20 )
= ( sdtpldt0 @ ( sdtasdt0 @ SV67 @ SV20 ) @ ( sdtasdt0 @ SV78 @ SV20 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[443]) ).
thf(490,plain,
! [SV44: $i,SV21: $i] :
( ( ( ( SV21 = SV44 )
| ~ ( sdtlseqdt0 @ SV21 @ SV44 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY144: $i] :
( ~ ( aNaturalNumber0 @ SY144 )
| ( ( sdtpldt0 @ SV21 @ SY144 )
!= ( sdtpldt0 @ SV44 @ SY144 ) ) )
| ~ ~ ( ~ ! [SY145: $i] :
( ~ ( aNaturalNumber0 @ SY145 )
| ( ( sdtpldt0 @ SY145 @ SV21 )
!= ( sdtpldt0 @ SY145 @ SV44 ) ) )
| ~ ! [SY146: $i] :
( ~ ( aNaturalNumber0 @ SY146 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SY146 @ SV21 ) @ ( sdtpldt0 @ SY146 @ SV44 ) ) ) ) )
| ~ ! [SY147: $i] :
( ~ ( aNaturalNumber0 @ SY147 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SV21 @ SY147 ) @ ( sdtpldt0 @ SV44 @ SY147 ) ) ) ) )
= $true )
| ( ( aNaturalNumber0 @ SV21 )
= $false )
| ( ( aNaturalNumber0 @ SV44 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[446]) ).
thf(491,plain,
! [SV22: $i] :
( ( ( ! [SY116: $i,SY117: $i] :
( ~ ( aNaturalNumber0 @ SY116 )
| ~ ( aNaturalNumber0 @ SY117 )
| ( ( sdtasdt0 @ SV22 @ SY116 )
!= ( sdtasdt0 @ SV22 @ SY117 ) )
| ( SY116 = SY117 ) ) )
= $true )
| ( ( SV22 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV22 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[447]) ).
thf(492,plain,
! [SV22: $i] :
( ( ( ! [SY118: $i,SY119: $i] :
( ~ ( aNaturalNumber0 @ SY118 )
| ~ ( aNaturalNumber0 @ SY119 )
| ( ( sdtasdt0 @ SY118 @ SV22 )
!= ( sdtasdt0 @ SY119 @ SV22 ) )
| ( SY118 = SY119 ) ) )
= $true )
| ( ( SV22 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV22 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[448]) ).
thf(493,plain,
( ( ~ ~ ( ( ( sdtasdt0 @ xn @ xn )
!= ( sdtasdt0 @ xp @ sK3_W0 ) )
| ~ ( aNaturalNumber0 @ sK3_W0 ) )
| ~ ( doDivides0 @ xp @ ( sdtasdt0 @ xn @ xn ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[449]) ).
thf(494,plain,
( ( ( xn
!= ( sdtasdt0 @ xp @ sK2_W0 ) )
| ~ ( aNaturalNumber0 @ sK2_W0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[450]) ).
thf(495,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ! [SX1: $i] :
( ( xp
!= ( sdtasdt0 @ SX0 @ SX1 ) )
| ~ ( aNaturalNumber0 @ SX1 ) )
| ( SX0 = sz10 )
| ( SX0 = xp ) )
| ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( doDivides0 @ SX0 @ xp )
| ( SX0 = sz10 )
| ( SX0 = xp ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[451]) ).
thf(496,plain,
( ( xp = sz10 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[452]) ).
thf(497,plain,
( ( xm = sz00 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[453]) ).
thf(498,plain,
( ( ~ ( ( xn != sz00 ) )
| ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ xn )
| ~ ( aNaturalNumber0 @ xm ) )
| ~ ( aNaturalNumber0 @ xp ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[454]) ).
thf(499,plain,
! [SV23: $i] :
( ( ( ~ ~ ( ~ ( aNaturalNumber0 @ ( sK1_W1 @ SV23 ) )
| ~ ( doDivides0 @ ( sK1_W1 @ SV23 ) @ SV23 ) ) )
= $false )
| ( ( SV23 = sz10 )
= $true )
| ( ( SV23 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[457]) ).
thf(500,plain,
! [SV23: $i] :
( ( ( ~ ( isPrime0 @ ( sK1_W1 @ SV23 ) ) )
= $false )
| ( ( SV23 = sz10 )
= $true )
| ( ( SV23 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[457]) ).
thf(501,plain,
! [SV68: $i,SV57: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV57 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV68 ) )
= $true )
| ( ( ( SV68 != SV57 )
| ( sdtlseqdt0 @ SV57 @ SV68 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[458]) ).
thf(502,plain,
! [SV69: $i,SV58: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV58 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV69 ) )
= $true )
| ( ( ( sdtlseqdt0 @ SV69 @ SV58 )
| ( sdtlseqdt0 @ SV58 @ SV69 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[459]) ).
thf(503,plain,
! [SV79: $i,SV70: $i,SV24: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV24 )
| ~ ( aNaturalNumber0 @ SV70 )
| ~ ( aNaturalNumber0 @ SV79 ) )
= $true )
| ( ( ( ( sdtpldt0 @ SV24 @ SV70 )
!= ( sdtpldt0 @ SV24 @ SV79 ) )
| ( SV70 = SV79 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[462]) ).
thf(504,plain,
! [SV80: $i,SV71: $i,SV24: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV24 )
| ~ ( aNaturalNumber0 @ SV71 )
| ~ ( aNaturalNumber0 @ SV80 ) )
= $true )
| ( ( ( ( sdtpldt0 @ SV71 @ SV24 )
!= ( sdtpldt0 @ SV80 @ SV24 ) )
| ( SV71 = SV80 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[463]) ).
thf(505,plain,
! [SV25: $i,SV72: $i,SV81: $i] :
( ( ( ( SV81 = sz00 )
| ( SV72 = sz00 )
| ( SV25 = sz00 )
| ~ ( aNaturalNumber0 @ SV25 )
| ~ ( aNaturalNumber0 @ SV72 )
| ~ ( aNaturalNumber0 @ SV81 ) )
= $true )
| ( ( ( ( sdtasdt0 @ SV81 @ ( sdtasdt0 @ SV72 @ SV72 ) )
!= ( sdtasdt0 @ SV25 @ SV25 ) )
| ~ ( iLess0 @ SV25 @ xn )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( SV81
!= ( sdtasdt0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) @ ( sK5_SY81 @ SV81 @ SV72 @ SV25 ) ) )
| ~ ( aNaturalNumber0 @ ( sK5_SY81 @ SV81 @ SV72 @ SV25 ) ) )
| ~ ( aNaturalNumber0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) ) )
| ~ ( doDivides0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) @ SV81 ) )
| ~ ~ ( ~ ( ( ( sK4_W3 @ SV81 @ SV72 @ SV25 )
!= sz10 ) )
| ~ ( ( ( sK4_W3 @ SV81 @ SV72 @ SV25 )
!= SV81 ) ) ) )
| ( SV81 = sz10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[466]) ).
thf(506,plain,
! [SV25: $i,SV73: $i,SV82: $i] :
( ( ( ( SV82 = sz00 )
| ( SV73 = sz00 )
| ( SV25 = sz00 )
| ~ ( aNaturalNumber0 @ SV25 )
| ~ ( aNaturalNumber0 @ SV73 )
| ~ ( aNaturalNumber0 @ SV82 ) )
= $true )
| ( ( ( ( sdtasdt0 @ SV82 @ ( sdtasdt0 @ SV73 @ SV73 ) )
!= ( sdtasdt0 @ SV25 @ SV25 ) )
| ~ ( iLess0 @ SV25 @ xn )
| ~ ( isPrime0 @ SV82 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[467]) ).
thf(507,plain,
! [SV26: $i] :
( ( ! [SY128: $i,SY129: $i] :
( ~ ( aNaturalNumber0 @ SV26 )
| ~ ( aNaturalNumber0 @ SY128 )
| ~ ( aNaturalNumber0 @ SY129 )
| ( SV26 = sz00 )
| ( SY128 = SY129 )
| ~ ( sdtlseqdt0 @ SY128 @ SY129 )
| ( ( sdtasdt0 @ SY128 @ SV26 )
!= ( sdtasdt0 @ SY129 @ SV26 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[468]) ).
thf(508,plain,
! [SV26: $i] :
( ( ~ ( ~ ! [SY130: $i,SY131: $i] :
( ~ ( aNaturalNumber0 @ SV26 )
| ~ ( aNaturalNumber0 @ SY130 )
| ~ ( aNaturalNumber0 @ SY131 )
| ( SV26 = sz00 )
| ( SY130 = SY131 )
| ~ ( sdtlseqdt0 @ SY130 @ SY131 )
| ( ( sdtasdt0 @ SV26 @ SY130 )
!= ( sdtasdt0 @ SV26 @ SY131 ) ) )
| ~ ! [SY132: $i,SY133: $i] :
( ~ ( aNaturalNumber0 @ SV26 )
| ~ ( aNaturalNumber0 @ SY132 )
| ~ ( aNaturalNumber0 @ SY133 )
| ( SV26 = sz00 )
| ( SY132 = SY133 )
| ~ ( sdtlseqdt0 @ SY132 @ SY133 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV26 @ SY132 ) @ ( sdtasdt0 @ SV26 @ SY133 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[469]) ).
thf(509,plain,
! [SV83: $i,SV74: $i,SV26: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV26 )
| ~ ( aNaturalNumber0 @ SV74 )
| ~ ( aNaturalNumber0 @ SV83 ) )
= $true )
| ( ( ( SV26 = sz00 )
| ( SV74 = SV83 )
| ~ ( sdtlseqdt0 @ SV74 @ SV83 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV74 @ SV26 ) @ ( sdtasdt0 @ SV83 @ SV26 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[470]) ).
thf(510,plain,
! [SV61: $i] :
( ( ( sz10 != SV61 )
= $true )
| ( ( ( SV61 = sz00 )
| ( SV61 = sz10 ) )
= $true )
| ( ( aNaturalNumber0 @ SV61 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[471]) ).
thf(511,plain,
! [SV62: $i] :
( ( ( sdtlseqdt0 @ sz10 @ SV62 )
= $true )
| ( ( ( SV62 = sz00 )
| ( SV62 = sz10 ) )
= $true )
| ( ( aNaturalNumber0 @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[472]) ).
thf(512,plain,
! [SV75: $i,SV63: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV63 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV75 ) )
= $true )
| ( ( ( ( sdtpldt0 @ SV63 @ SV75 )
!= sz00 )
| ( SV63 = sz00 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[473]) ).
thf(513,plain,
! [SV76: $i,SV64: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV64 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV76 ) )
= $true )
| ( ( ( ( sdtpldt0 @ SV64 @ SV76 )
!= sz00 )
| ( SV76 = sz00 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[474]) ).
thf(514,plain,
! [SV45: $i,SV5: $i,SV30: $i] :
( ( ( aNaturalNumber0 @ SV30 )
= $false )
| ( ( aNaturalNumber0 @ SV5 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV45 ) )
= $true )
| ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV5 @ SV30 ) @ SV45 )
= ( sdtpldt0 @ SV5 @ ( sdtpldt0 @ SV30 @ SV45 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[475]) ).
thf(515,plain,
! [SV46: $i,SV7: $i,SV32: $i] :
( ( ( aNaturalNumber0 @ SV32 )
= $false )
| ( ( aNaturalNumber0 @ SV7 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV46 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV7 @ SV32 ) @ SV46 )
= ( sdtasdt0 @ SV7 @ ( sdtasdt0 @ SV32 @ SV46 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[476]) ).
thf(516,plain,
! [SV33: $i,SV8: $i] :
( ( ( ( sdtasdt0 @ SV8 @ SV33 )
= sz00 )
= $false )
| ( ( ( SV8 = sz00 )
| ( SV33 = sz00 ) )
= $true )
| ( ( aNaturalNumber0 @ SV8 )
= $false )
| ( ( aNaturalNumber0 @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[477]) ).
thf(517,plain,
! [SV34: $i,SV10: $i] :
( ( ( ~ ( sdtlseqdt0 @ SV10 @ SV34 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV34 @ SV10 ) )
= $true )
| ( ( SV10 = SV34 )
= $true )
| ( ( aNaturalNumber0 @ SV10 )
= $false )
| ( ( aNaturalNumber0 @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[478]) ).
thf(518,plain,
! [SV47: $i,SV11: $i,SV35: $i] :
( ( ( aNaturalNumber0 @ SV35 )
= $false )
| ( ( aNaturalNumber0 @ SV11 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV47 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV11 @ SV35 )
| ~ ( sdtlseqdt0 @ SV35 @ SV47 )
| ( sdtlseqdt0 @ SV11 @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[479]) ).
thf(519,plain,
! [SV37: $i,SV13: $i] :
( ( ( SV13 = SV37 )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV13 @ SV37 ) )
= $true )
| ( ( iLess0 @ SV13 @ SV37 )
= $true )
| ( ( aNaturalNumber0 @ SV13 )
= $false )
| ( ( aNaturalNumber0 @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[481]) ).
thf(520,plain,
! [SV49: $i,SV14: $i,SV38: $i] :
( ( ( aNaturalNumber0 @ SV38 )
= $false )
| ( ( aNaturalNumber0 @ SV14 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV49 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV14 @ SV38 )
| ~ ( doDivides0 @ SV38 @ SV49 )
| ( doDivides0 @ SV14 @ SV49 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[482]) ).
thf(521,plain,
! [SV50: $i,SV15: $i,SV39: $i] :
( ( ( aNaturalNumber0 @ SV39 )
= $false )
| ( ( aNaturalNumber0 @ SV15 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV50 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV15 @ SV39 )
| ~ ( doDivides0 @ SV15 @ SV50 )
| ( doDivides0 @ SV15 @ ( sdtpldt0 @ SV39 @ SV50 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[483]) ).
thf(522,plain,
! [SV51: $i,SV16: $i,SV40: $i] :
( ( ( aNaturalNumber0 @ SV40 )
= $false )
| ( ( aNaturalNumber0 @ SV16 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV51 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV16 @ SV40 )
| ~ ( doDivides0 @ SV16 @ ( sdtpldt0 @ SV40 @ SV51 ) )
| ( doDivides0 @ SV16 @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[484]) ).
thf(523,plain,
! [SV17: $i,SV41: $i] :
( ( ( SV41 = sz00 )
= $true )
| ( ( ~ ( doDivides0 @ SV17 @ SV41 ) )
= $true )
| ( ( sdtlseqdt0 @ SV17 @ SV41 )
= $true )
| ( ( aNaturalNumber0 @ SV17 )
= $false )
| ( ( aNaturalNumber0 @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[485]) ).
thf(524,plain,
! [SV42: $i,SV18: $i] :
( ( ( SV18 = sz00 )
= $true )
| ( ( ~ ( doDivides0 @ SV18 @ SV42 ) )
= $true )
| ( ( ! [SY142: $i] :
( ~ ( aNaturalNumber0 @ SY142 )
| ( ( sdtasdt0 @ SY142 @ ( sdtsldt0 @ SV42 @ SV18 ) )
= ( sdtsldt0 @ ( sdtasdt0 @ SY142 @ SV42 ) @ SV18 ) ) ) )
= $true )
| ( ( aNaturalNumber0 @ SV18 )
= $false )
| ( ( aNaturalNumber0 @ SV42 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[486]) ).
thf(525,plain,
! [SV52: $i,SV19: $i,SV43: $i] :
( ( ( aNaturalNumber0 @ SV43 )
= $false )
| ( ( aNaturalNumber0 @ SV19 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV52 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV52 @ ( sdtasdt0 @ SV19 @ SV43 ) )
| ~ ( isPrime0 @ SV52 )
| ( doDivides0 @ SV52 @ SV19 )
| ( doDivides0 @ SV52 @ SV43 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[487]) ).
thf(526,plain,
! [SV77: $i,SV66: $i,SV20: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV20 )
| ~ ( aNaturalNumber0 @ SV66 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV77 ) )
= $true )
| ( ( ( sdtasdt0 @ SV20 @ ( sdtpldt0 @ SV66 @ SV77 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV20 @ SV66 ) @ ( sdtasdt0 @ SV20 @ SV77 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[488]) ).
thf(527,plain,
! [SV78: $i,SV67: $i,SV20: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV20 )
| ~ ( aNaturalNumber0 @ SV67 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV78 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV67 @ SV78 ) @ SV20 )
= ( sdtpldt0 @ ( sdtasdt0 @ SV67 @ SV20 ) @ ( sdtasdt0 @ SV78 @ SV20 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[489]) ).
thf(528,plain,
! [SV44: $i,SV21: $i] :
( ( ( SV21 = SV44 )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV21 @ SV44 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY144: $i] :
( ~ ( aNaturalNumber0 @ SY144 )
| ( ( sdtpldt0 @ SV21 @ SY144 )
!= ( sdtpldt0 @ SV44 @ SY144 ) ) )
| ~ ~ ( ~ ! [SY145: $i] :
( ~ ( aNaturalNumber0 @ SY145 )
| ( ( sdtpldt0 @ SY145 @ SV21 )
!= ( sdtpldt0 @ SY145 @ SV44 ) ) )
| ~ ! [SY146: $i] :
( ~ ( aNaturalNumber0 @ SY146 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SY146 @ SV21 ) @ ( sdtpldt0 @ SY146 @ SV44 ) ) ) ) )
| ~ ! [SY147: $i] :
( ~ ( aNaturalNumber0 @ SY147 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SV21 @ SY147 ) @ ( sdtpldt0 @ SV44 @ SY147 ) ) ) ) )
= $true )
| ( ( aNaturalNumber0 @ SV21 )
= $false )
| ( ( aNaturalNumber0 @ SV44 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[490]) ).
thf(529,plain,
! [SV22: $i,SV84: $i] :
( ( ( ! [SY159: $i] :
( ~ ( aNaturalNumber0 @ SV84 )
| ~ ( aNaturalNumber0 @ SY159 )
| ( ( sdtasdt0 @ SV22 @ SV84 )
!= ( sdtasdt0 @ SV22 @ SY159 ) )
| ( SV84 = SY159 ) ) )
= $true )
| ( ( SV22 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV22 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[491]) ).
thf(530,plain,
! [SV22: $i,SV85: $i] :
( ( ( ! [SY160: $i] :
( ~ ( aNaturalNumber0 @ SV85 )
| ~ ( aNaturalNumber0 @ SY160 )
| ( ( sdtasdt0 @ SV85 @ SV22 )
!= ( sdtasdt0 @ SY160 @ SV22 ) )
| ( SV85 = SY160 ) ) )
= $true )
| ( ( SV22 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV22 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[492]) ).
thf(531,plain,
( ( ~ ~ ( ( ( sdtasdt0 @ xn @ xn )
!= ( sdtasdt0 @ xp @ sK3_W0 ) )
| ~ ( aNaturalNumber0 @ sK3_W0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[493]) ).
thf(532,plain,
( ( ~ ( doDivides0 @ xp @ ( sdtasdt0 @ xn @ xn ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[493]) ).
thf(533,plain,
( ( xn
!= ( sdtasdt0 @ xp @ sK2_W0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[494]) ).
thf(534,plain,
( ( ~ ( aNaturalNumber0 @ sK2_W0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[494]) ).
thf(535,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ! [SX1: $i] :
( ( xp
!= ( sdtasdt0 @ SX0 @ SX1 ) )
| ~ ( aNaturalNumber0 @ SX1 ) )
| ( SX0 = sz10 )
| ( SX0 = xp ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[495]) ).
thf(536,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( doDivides0 @ SX0 @ xp )
| ( SX0 = sz10 )
| ( SX0 = xp ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[495]) ).
thf(537,plain,
( ( ~ ( ( xn != sz00 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[498]) ).
thf(538,plain,
( ( ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ xn )
| ~ ( aNaturalNumber0 @ xm ) )
| ~ ( aNaturalNumber0 @ xp ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[498]) ).
thf(539,plain,
! [SV23: $i] :
( ( ( ~ ( ~ ( aNaturalNumber0 @ ( sK1_W1 @ SV23 ) )
| ~ ( doDivides0 @ ( sK1_W1 @ SV23 ) @ SV23 ) ) )
= $true )
| ( ( SV23 = sz10 )
= $true )
| ( ( SV23 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[499]) ).
thf(540,plain,
! [SV23: $i] :
( ( ( isPrime0 @ ( sK1_W1 @ SV23 ) )
= $true )
| ( ( SV23 = sz10 )
= $true )
| ( ( SV23 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[500]) ).
thf(541,plain,
! [SV68: $i,SV57: $i] :
( ( ( aNaturalNumber0 @ SV57 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV68 ) )
= $true )
| ( ( ( SV68 != SV57 )
| ( sdtlseqdt0 @ SV57 @ SV68 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[501]) ).
thf(542,plain,
! [SV69: $i,SV58: $i] :
( ( ( aNaturalNumber0 @ SV58 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV69 ) )
= $true )
| ( ( ( sdtlseqdt0 @ SV69 @ SV58 )
| ( sdtlseqdt0 @ SV58 @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[502]) ).
thf(543,plain,
! [SV79: $i,SV70: $i,SV24: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV24 )
| ~ ( aNaturalNumber0 @ SV70 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV79 ) )
= $true )
| ( ( ( ( sdtpldt0 @ SV24 @ SV70 )
!= ( sdtpldt0 @ SV24 @ SV79 ) )
| ( SV70 = SV79 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[503]) ).
thf(544,plain,
! [SV80: $i,SV71: $i,SV24: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV24 )
| ~ ( aNaturalNumber0 @ SV71 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV80 ) )
= $true )
| ( ( ( ( sdtpldt0 @ SV71 @ SV24 )
!= ( sdtpldt0 @ SV80 @ SV24 ) )
| ( SV71 = SV80 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[504]) ).
thf(545,plain,
! [SV25: $i,SV72: $i,SV81: $i] :
( ( ( SV81 = sz00 )
= $true )
| ( ( ( SV72 = sz00 )
| ( SV25 = sz00 )
| ~ ( aNaturalNumber0 @ SV25 )
| ~ ( aNaturalNumber0 @ SV72 )
| ~ ( aNaturalNumber0 @ SV81 ) )
= $true )
| ( ( ( ( sdtasdt0 @ SV81 @ ( sdtasdt0 @ SV72 @ SV72 ) )
!= ( sdtasdt0 @ SV25 @ SV25 ) )
| ~ ( iLess0 @ SV25 @ xn )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( SV81
!= ( sdtasdt0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) @ ( sK5_SY81 @ SV81 @ SV72 @ SV25 ) ) )
| ~ ( aNaturalNumber0 @ ( sK5_SY81 @ SV81 @ SV72 @ SV25 ) ) )
| ~ ( aNaturalNumber0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) ) )
| ~ ( doDivides0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) @ SV81 ) )
| ~ ~ ( ~ ( ( ( sK4_W3 @ SV81 @ SV72 @ SV25 )
!= sz10 ) )
| ~ ( ( ( sK4_W3 @ SV81 @ SV72 @ SV25 )
!= SV81 ) ) ) )
| ( SV81 = sz10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[505]) ).
thf(546,plain,
! [SV25: $i,SV73: $i,SV82: $i] :
( ( ( SV82 = sz00 )
= $true )
| ( ( ( SV73 = sz00 )
| ( SV25 = sz00 )
| ~ ( aNaturalNumber0 @ SV25 )
| ~ ( aNaturalNumber0 @ SV73 )
| ~ ( aNaturalNumber0 @ SV82 ) )
= $true )
| ( ( ( ( sdtasdt0 @ SV82 @ ( sdtasdt0 @ SV73 @ SV73 ) )
!= ( sdtasdt0 @ SV25 @ SV25 ) )
| ~ ( iLess0 @ SV25 @ xn )
| ~ ( isPrime0 @ SV82 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[506]) ).
thf(547,plain,
! [SV86: $i,SV26: $i] :
( ( ! [SY161: $i] :
( ~ ( aNaturalNumber0 @ SV26 )
| ~ ( aNaturalNumber0 @ SV86 )
| ~ ( aNaturalNumber0 @ SY161 )
| ( SV26 = sz00 )
| ( SV86 = SY161 )
| ~ ( sdtlseqdt0 @ SV86 @ SY161 )
| ( ( sdtasdt0 @ SV86 @ SV26 )
!= ( sdtasdt0 @ SY161 @ SV26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[507]) ).
thf(548,plain,
! [SV26: $i] :
( ( ~ ! [SY130: $i,SY131: $i] :
( ~ ( aNaturalNumber0 @ SV26 )
| ~ ( aNaturalNumber0 @ SY130 )
| ~ ( aNaturalNumber0 @ SY131 )
| ( SV26 = sz00 )
| ( SY130 = SY131 )
| ~ ( sdtlseqdt0 @ SY130 @ SY131 )
| ( ( sdtasdt0 @ SV26 @ SY130 )
!= ( sdtasdt0 @ SV26 @ SY131 ) ) )
| ~ ! [SY132: $i,SY133: $i] :
( ~ ( aNaturalNumber0 @ SV26 )
| ~ ( aNaturalNumber0 @ SY132 )
| ~ ( aNaturalNumber0 @ SY133 )
| ( SV26 = sz00 )
| ( SY132 = SY133 )
| ~ ( sdtlseqdt0 @ SY132 @ SY133 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV26 @ SY132 ) @ ( sdtasdt0 @ SV26 @ SY133 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[508]) ).
thf(549,plain,
! [SV83: $i,SV74: $i,SV26: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV26 )
| ~ ( aNaturalNumber0 @ SV74 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV83 ) )
= $true )
| ( ( ( SV26 = sz00 )
| ( SV74 = SV83 )
| ~ ( sdtlseqdt0 @ SV74 @ SV83 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV74 @ SV26 ) @ ( sdtasdt0 @ SV83 @ SV26 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[509]) ).
thf(550,plain,
! [SV61: $i] :
( ( ( sz10 = SV61 )
= $false )
| ( ( ( SV61 = sz00 )
| ( SV61 = sz10 ) )
= $true )
| ( ( aNaturalNumber0 @ SV61 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[510]) ).
thf(551,plain,
! [SV62: $i] :
( ( ( SV62 = sz00 )
= $true )
| ( ( SV62 = sz10 )
= $true )
| ( ( sdtlseqdt0 @ sz10 @ SV62 )
= $true )
| ( ( aNaturalNumber0 @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[511]) ).
thf(552,plain,
! [SV75: $i,SV63: $i] :
( ( ( aNaturalNumber0 @ SV63 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV75 ) )
= $true )
| ( ( ( ( sdtpldt0 @ SV63 @ SV75 )
!= sz00 )
| ( SV63 = sz00 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[512]) ).
thf(553,plain,
! [SV76: $i,SV64: $i] :
( ( ( aNaturalNumber0 @ SV64 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV76 ) )
= $true )
| ( ( ( ( sdtpldt0 @ SV64 @ SV76 )
!= sz00 )
| ( SV76 = sz00 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[513]) ).
thf(554,plain,
! [SV30: $i,SV5: $i,SV45: $i] :
( ( ( aNaturalNumber0 @ SV45 )
= $false )
| ( ( aNaturalNumber0 @ SV5 )
= $false )
| ( ( aNaturalNumber0 @ SV30 )
= $false )
| ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV5 @ SV30 ) @ SV45 )
= ( sdtpldt0 @ SV5 @ ( sdtpldt0 @ SV30 @ SV45 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[514]) ).
thf(555,plain,
! [SV32: $i,SV7: $i,SV46: $i] :
( ( ( aNaturalNumber0 @ SV46 )
= $false )
| ( ( aNaturalNumber0 @ SV7 )
= $false )
| ( ( aNaturalNumber0 @ SV32 )
= $false )
| ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV7 @ SV32 ) @ SV46 )
= ( sdtasdt0 @ SV7 @ ( sdtasdt0 @ SV32 @ SV46 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[515]) ).
thf(556,plain,
! [SV33: $i,SV8: $i] :
( ( ( SV8 = sz00 )
= $true )
| ( ( SV33 = sz00 )
= $true )
| ( ( ( sdtasdt0 @ SV8 @ SV33 )
= sz00 )
= $false )
| ( ( aNaturalNumber0 @ SV8 )
= $false )
| ( ( aNaturalNumber0 @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[516]) ).
thf(557,plain,
! [SV34: $i,SV10: $i] :
( ( ( sdtlseqdt0 @ SV10 @ SV34 )
= $false )
| ( ( ~ ( sdtlseqdt0 @ SV34 @ SV10 ) )
= $true )
| ( ( SV10 = SV34 )
= $true )
| ( ( aNaturalNumber0 @ SV10 )
= $false )
| ( ( aNaturalNumber0 @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[517]) ).
thf(558,plain,
! [SV35: $i,SV11: $i,SV47: $i] :
( ( ( aNaturalNumber0 @ SV47 )
= $false )
| ( ( aNaturalNumber0 @ SV11 )
= $false )
| ( ( aNaturalNumber0 @ SV35 )
= $false )
| ( ( ~ ( sdtlseqdt0 @ SV11 @ SV35 )
| ~ ( sdtlseqdt0 @ SV35 @ SV47 )
| ( sdtlseqdt0 @ SV11 @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[518]) ).
thf(559,plain,
! [SV37: $i,SV13: $i] :
( ( ( sdtlseqdt0 @ SV13 @ SV37 )
= $false )
| ( ( SV13 = SV37 )
= $true )
| ( ( iLess0 @ SV13 @ SV37 )
= $true )
| ( ( aNaturalNumber0 @ SV13 )
= $false )
| ( ( aNaturalNumber0 @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[519]) ).
thf(560,plain,
! [SV38: $i,SV14: $i,SV49: $i] :
( ( ( aNaturalNumber0 @ SV49 )
= $false )
| ( ( aNaturalNumber0 @ SV14 )
= $false )
| ( ( aNaturalNumber0 @ SV38 )
= $false )
| ( ( ~ ( doDivides0 @ SV14 @ SV38 )
| ~ ( doDivides0 @ SV38 @ SV49 )
| ( doDivides0 @ SV14 @ SV49 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[520]) ).
thf(561,plain,
! [SV39: $i,SV15: $i,SV50: $i] :
( ( ( aNaturalNumber0 @ SV50 )
= $false )
| ( ( aNaturalNumber0 @ SV15 )
= $false )
| ( ( aNaturalNumber0 @ SV39 )
= $false )
| ( ( ~ ( doDivides0 @ SV15 @ SV39 )
| ~ ( doDivides0 @ SV15 @ SV50 )
| ( doDivides0 @ SV15 @ ( sdtpldt0 @ SV39 @ SV50 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[521]) ).
thf(562,plain,
! [SV40: $i,SV16: $i,SV51: $i] :
( ( ( aNaturalNumber0 @ SV51 )
= $false )
| ( ( aNaturalNumber0 @ SV16 )
= $false )
| ( ( aNaturalNumber0 @ SV40 )
= $false )
| ( ( ~ ( doDivides0 @ SV16 @ SV40 )
| ~ ( doDivides0 @ SV16 @ ( sdtpldt0 @ SV40 @ SV51 ) )
| ( doDivides0 @ SV16 @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[522]) ).
thf(563,plain,
! [SV41: $i,SV17: $i] :
( ( ( doDivides0 @ SV17 @ SV41 )
= $false )
| ( ( SV41 = sz00 )
= $true )
| ( ( sdtlseqdt0 @ SV17 @ SV41 )
= $true )
| ( ( aNaturalNumber0 @ SV17 )
= $false )
| ( ( aNaturalNumber0 @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[523]) ).
thf(564,plain,
! [SV42: $i,SV18: $i] :
( ( ( doDivides0 @ SV18 @ SV42 )
= $false )
| ( ( SV18 = sz00 )
= $true )
| ( ( ! [SY142: $i] :
( ~ ( aNaturalNumber0 @ SY142 )
| ( ( sdtasdt0 @ SY142 @ ( sdtsldt0 @ SV42 @ SV18 ) )
= ( sdtsldt0 @ ( sdtasdt0 @ SY142 @ SV42 ) @ SV18 ) ) ) )
= $true )
| ( ( aNaturalNumber0 @ SV18 )
= $false )
| ( ( aNaturalNumber0 @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[524]) ).
thf(565,plain,
! [SV43: $i,SV19: $i,SV52: $i] :
( ( ( aNaturalNumber0 @ SV52 )
= $false )
| ( ( aNaturalNumber0 @ SV19 )
= $false )
| ( ( aNaturalNumber0 @ SV43 )
= $false )
| ( ( ~ ( doDivides0 @ SV52 @ ( sdtasdt0 @ SV19 @ SV43 ) )
| ~ ( isPrime0 @ SV52 )
| ( doDivides0 @ SV52 @ SV19 )
| ( doDivides0 @ SV52 @ SV43 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[525]) ).
thf(566,plain,
! [SV77: $i,SV66: $i,SV20: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV20 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV66 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV77 ) )
= $true )
| ( ( ( sdtasdt0 @ SV20 @ ( sdtpldt0 @ SV66 @ SV77 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV20 @ SV66 ) @ ( sdtasdt0 @ SV20 @ SV77 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[526]) ).
thf(567,plain,
! [SV78: $i,SV67: $i,SV20: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV20 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV67 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV78 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV67 @ SV78 ) @ SV20 )
= ( sdtpldt0 @ ( sdtasdt0 @ SV67 @ SV20 ) @ ( sdtasdt0 @ SV78 @ SV20 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[527]) ).
thf(568,plain,
! [SV44: $i,SV21: $i] :
( ( ( sdtlseqdt0 @ SV21 @ SV44 )
= $false )
| ( ( SV21 = SV44 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY144: $i] :
( ~ ( aNaturalNumber0 @ SY144 )
| ( ( sdtpldt0 @ SV21 @ SY144 )
!= ( sdtpldt0 @ SV44 @ SY144 ) ) )
| ~ ~ ( ~ ! [SY145: $i] :
( ~ ( aNaturalNumber0 @ SY145 )
| ( ( sdtpldt0 @ SY145 @ SV21 )
!= ( sdtpldt0 @ SY145 @ SV44 ) ) )
| ~ ! [SY146: $i] :
( ~ ( aNaturalNumber0 @ SY146 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SY146 @ SV21 ) @ ( sdtpldt0 @ SY146 @ SV44 ) ) ) ) )
| ~ ! [SY147: $i] :
( ~ ( aNaturalNumber0 @ SY147 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SV21 @ SY147 ) @ ( sdtpldt0 @ SV44 @ SY147 ) ) ) ) )
= $true )
| ( ( aNaturalNumber0 @ SV21 )
= $false )
| ( ( aNaturalNumber0 @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[528]) ).
thf(569,plain,
! [SV22: $i,SV87: $i,SV84: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV84 )
| ~ ( aNaturalNumber0 @ SV87 )
| ( ( sdtasdt0 @ SV22 @ SV84 )
!= ( sdtasdt0 @ SV22 @ SV87 ) )
| ( SV84 = SV87 ) )
= $true )
| ( ( SV22 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV22 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[529]) ).
thf(570,plain,
! [SV22: $i,SV88: $i,SV85: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV85 )
| ~ ( aNaturalNumber0 @ SV88 )
| ( ( sdtasdt0 @ SV85 @ SV22 )
!= ( sdtasdt0 @ SV88 @ SV22 ) )
| ( SV85 = SV88 ) )
= $true )
| ( ( SV22 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV22 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[530]) ).
thf(571,plain,
( ( ~ ( ( ( sdtasdt0 @ xn @ xn )
!= ( sdtasdt0 @ xp @ sK3_W0 ) )
| ~ ( aNaturalNumber0 @ sK3_W0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[531]) ).
thf(572,plain,
( ( doDivides0 @ xp @ ( sdtasdt0 @ xn @ xn ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[532]) ).
thf(573,plain,
( ( xn
= ( sdtasdt0 @ xp @ sK2_W0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[533]) ).
thf(574,plain,
( ( aNaturalNumber0 @ sK2_W0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[534]) ).
thf(575,plain,
( ( ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ! [SX1: $i] :
( ( xp
!= ( sdtasdt0 @ SX0 @ SX1 ) )
| ~ ( aNaturalNumber0 @ SX1 ) )
| ( SX0 = sz10 )
| ( SX0 = xp ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[535]) ).
thf(576,plain,
( ( ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( doDivides0 @ SX0 @ xp )
| ( SX0 = sz10 )
| ( SX0 = xp ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[536]) ).
thf(577,plain,
( ( xn != sz00 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[537]) ).
thf(578,plain,
( ( ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ xn )
| ~ ( aNaturalNumber0 @ xm ) )
| ~ ( aNaturalNumber0 @ xp ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[538]) ).
thf(579,plain,
! [SV23: $i] :
( ( ( ~ ( aNaturalNumber0 @ ( sK1_W1 @ SV23 ) )
| ~ ( doDivides0 @ ( sK1_W1 @ SV23 ) @ SV23 ) )
= $false )
| ( ( SV23 = sz10 )
= $true )
| ( ( SV23 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[539]) ).
thf(580,plain,
! [SV57: $i,SV68: $i] :
( ( ( aNaturalNumber0 @ SV68 )
= $false )
| ( ( aNaturalNumber0 @ SV57 )
= $false )
| ( ( ( SV68 != SV57 )
| ( sdtlseqdt0 @ SV57 @ SV68 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[541]) ).
thf(581,plain,
! [SV58: $i,SV69: $i] :
( ( ( aNaturalNumber0 @ SV69 )
= $false )
| ( ( aNaturalNumber0 @ SV58 )
= $false )
| ( ( ( sdtlseqdt0 @ SV69 @ SV58 )
| ( sdtlseqdt0 @ SV58 @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[542]) ).
thf(582,plain,
! [SV79: $i,SV70: $i,SV24: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV24 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV70 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV79 ) )
= $true )
| ( ( ( ( sdtpldt0 @ SV24 @ SV70 )
!= ( sdtpldt0 @ SV24 @ SV79 ) )
| ( SV70 = SV79 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[543]) ).
thf(583,plain,
! [SV80: $i,SV71: $i,SV24: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV24 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV71 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV80 ) )
= $true )
| ( ( ( ( sdtpldt0 @ SV71 @ SV24 )
!= ( sdtpldt0 @ SV80 @ SV24 ) )
| ( SV71 = SV80 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[544]) ).
thf(584,plain,
! [SV81: $i,SV25: $i,SV72: $i] :
( ( ( SV72 = sz00 )
= $true )
| ( ( ( SV25 = sz00 )
| ~ ( aNaturalNumber0 @ SV25 )
| ~ ( aNaturalNumber0 @ SV72 )
| ~ ( aNaturalNumber0 @ SV81 ) )
= $true )
| ( ( SV81 = sz00 )
= $true )
| ( ( ( ( sdtasdt0 @ SV81 @ ( sdtasdt0 @ SV72 @ SV72 ) )
!= ( sdtasdt0 @ SV25 @ SV25 ) )
| ~ ( iLess0 @ SV25 @ xn )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( SV81
!= ( sdtasdt0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) @ ( sK5_SY81 @ SV81 @ SV72 @ SV25 ) ) )
| ~ ( aNaturalNumber0 @ ( sK5_SY81 @ SV81 @ SV72 @ SV25 ) ) )
| ~ ( aNaturalNumber0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) ) )
| ~ ( doDivides0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) @ SV81 ) )
| ~ ~ ( ~ ( ( ( sK4_W3 @ SV81 @ SV72 @ SV25 )
!= sz10 ) )
| ~ ( ( ( sK4_W3 @ SV81 @ SV72 @ SV25 )
!= SV81 ) ) ) )
| ( SV81 = sz10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[545]) ).
thf(585,plain,
! [SV82: $i,SV25: $i,SV73: $i] :
( ( ( SV73 = sz00 )
= $true )
| ( ( ( SV25 = sz00 )
| ~ ( aNaturalNumber0 @ SV25 )
| ~ ( aNaturalNumber0 @ SV73 )
| ~ ( aNaturalNumber0 @ SV82 ) )
= $true )
| ( ( SV82 = sz00 )
= $true )
| ( ( ( ( sdtasdt0 @ SV82 @ ( sdtasdt0 @ SV73 @ SV73 ) )
!= ( sdtasdt0 @ SV25 @ SV25 ) )
| ~ ( iLess0 @ SV25 @ xn )
| ~ ( isPrime0 @ SV82 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[546]) ).
thf(586,plain,
! [SV89: $i,SV86: $i,SV26: $i] :
( ( ~ ( aNaturalNumber0 @ SV26 )
| ~ ( aNaturalNumber0 @ SV86 )
| ~ ( aNaturalNumber0 @ SV89 )
| ( SV26 = sz00 )
| ( SV86 = SV89 )
| ~ ( sdtlseqdt0 @ SV86 @ SV89 )
| ( ( sdtasdt0 @ SV86 @ SV26 )
!= ( sdtasdt0 @ SV89 @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[547]) ).
thf(587,plain,
! [SV26: $i] :
( ( ~ ! [SY130: $i,SY131: $i] :
( ~ ( aNaturalNumber0 @ SV26 )
| ~ ( aNaturalNumber0 @ SY130 )
| ~ ( aNaturalNumber0 @ SY131 )
| ( SV26 = sz00 )
| ( SY130 = SY131 )
| ~ ( sdtlseqdt0 @ SY130 @ SY131 )
| ( ( sdtasdt0 @ SV26 @ SY130 )
!= ( sdtasdt0 @ SV26 @ SY131 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[548]) ).
thf(588,plain,
! [SV26: $i] :
( ( ~ ! [SY132: $i,SY133: $i] :
( ~ ( aNaturalNumber0 @ SV26 )
| ~ ( aNaturalNumber0 @ SY132 )
| ~ ( aNaturalNumber0 @ SY133 )
| ( SV26 = sz00 )
| ( SY132 = SY133 )
| ~ ( sdtlseqdt0 @ SY132 @ SY133 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV26 @ SY132 ) @ ( sdtasdt0 @ SV26 @ SY133 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[548]) ).
thf(589,plain,
! [SV83: $i,SV74: $i,SV26: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV26 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV74 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV83 ) )
= $true )
| ( ( ( SV26 = sz00 )
| ( SV74 = SV83 )
| ~ ( sdtlseqdt0 @ SV74 @ SV83 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV74 @ SV26 ) @ ( sdtasdt0 @ SV83 @ SV26 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[549]) ).
thf(590,plain,
! [SV61: $i] :
( ( ( SV61 = sz00 )
= $true )
| ( ( SV61 = sz10 )
= $true )
| ( ( sz10 = SV61 )
= $false )
| ( ( aNaturalNumber0 @ SV61 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[550]) ).
thf(591,plain,
! [SV63: $i,SV75: $i] :
( ( ( aNaturalNumber0 @ SV75 )
= $false )
| ( ( aNaturalNumber0 @ SV63 )
= $false )
| ( ( ( ( sdtpldt0 @ SV63 @ SV75 )
!= sz00 )
| ( SV63 = sz00 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[552]) ).
thf(592,plain,
! [SV64: $i,SV76: $i] :
( ( ( aNaturalNumber0 @ SV76 )
= $false )
| ( ( aNaturalNumber0 @ SV64 )
= $false )
| ( ( ( ( sdtpldt0 @ SV64 @ SV76 )
!= sz00 )
| ( SV76 = sz00 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[553]) ).
thf(593,plain,
! [SV10: $i,SV34: $i] :
( ( ( sdtlseqdt0 @ SV34 @ SV10 )
= $false )
| ( ( sdtlseqdt0 @ SV10 @ SV34 )
= $false )
| ( ( SV10 = SV34 )
= $true )
| ( ( aNaturalNumber0 @ SV10 )
= $false )
| ( ( aNaturalNumber0 @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[557]) ).
thf(594,plain,
! [SV47: $i,SV35: $i,SV11: $i] :
( ( ( ~ ( sdtlseqdt0 @ SV11 @ SV35 )
| ~ ( sdtlseqdt0 @ SV35 @ SV47 ) )
= $true )
| ( ( sdtlseqdt0 @ SV11 @ SV47 )
= $true )
| ( ( aNaturalNumber0 @ SV35 )
= $false )
| ( ( aNaturalNumber0 @ SV11 )
= $false )
| ( ( aNaturalNumber0 @ SV47 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[558]) ).
thf(595,plain,
! [SV49: $i,SV38: $i,SV14: $i] :
( ( ( ~ ( doDivides0 @ SV14 @ SV38 )
| ~ ( doDivides0 @ SV38 @ SV49 ) )
= $true )
| ( ( doDivides0 @ SV14 @ SV49 )
= $true )
| ( ( aNaturalNumber0 @ SV38 )
= $false )
| ( ( aNaturalNumber0 @ SV14 )
= $false )
| ( ( aNaturalNumber0 @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[560]) ).
thf(596,plain,
! [SV50: $i,SV39: $i,SV15: $i] :
( ( ( ~ ( doDivides0 @ SV15 @ SV39 )
| ~ ( doDivides0 @ SV15 @ SV50 ) )
= $true )
| ( ( doDivides0 @ SV15 @ ( sdtpldt0 @ SV39 @ SV50 ) )
= $true )
| ( ( aNaturalNumber0 @ SV39 )
= $false )
| ( ( aNaturalNumber0 @ SV15 )
= $false )
| ( ( aNaturalNumber0 @ SV50 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[561]) ).
thf(597,plain,
! [SV51: $i,SV40: $i,SV16: $i] :
( ( ( ~ ( doDivides0 @ SV16 @ SV40 )
| ~ ( doDivides0 @ SV16 @ ( sdtpldt0 @ SV40 @ SV51 ) ) )
= $true )
| ( ( doDivides0 @ SV16 @ SV51 )
= $true )
| ( ( aNaturalNumber0 @ SV40 )
= $false )
| ( ( aNaturalNumber0 @ SV16 )
= $false )
| ( ( aNaturalNumber0 @ SV51 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[562]) ).
thf(598,plain,
! [SV18: $i,SV42: $i,SV90: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV90 )
| ( ( sdtasdt0 @ SV90 @ ( sdtsldt0 @ SV42 @ SV18 ) )
= ( sdtsldt0 @ ( sdtasdt0 @ SV90 @ SV42 ) @ SV18 ) ) )
= $true )
| ( ( SV18 = sz00 )
= $true )
| ( ( doDivides0 @ SV18 @ SV42 )
= $false )
| ( ( aNaturalNumber0 @ SV18 )
= $false )
| ( ( aNaturalNumber0 @ SV42 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[564]) ).
thf(599,plain,
! [SV43: $i,SV19: $i,SV52: $i] :
( ( ( ~ ( doDivides0 @ SV52 @ ( sdtasdt0 @ SV19 @ SV43 ) )
| ~ ( isPrime0 @ SV52 ) )
= $true )
| ( ( ( doDivides0 @ SV52 @ SV19 )
| ( doDivides0 @ SV52 @ SV43 ) )
= $true )
| ( ( aNaturalNumber0 @ SV43 )
= $false )
| ( ( aNaturalNumber0 @ SV19 )
= $false )
| ( ( aNaturalNumber0 @ SV52 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[565]) ).
thf(600,plain,
! [SV77: $i,SV66: $i,SV20: $i] :
( ( ( aNaturalNumber0 @ SV20 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV66 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV77 ) )
= $true )
| ( ( ( sdtasdt0 @ SV20 @ ( sdtpldt0 @ SV66 @ SV77 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV20 @ SV66 ) @ ( sdtasdt0 @ SV20 @ SV77 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[566]) ).
thf(601,plain,
! [SV78: $i,SV67: $i,SV20: $i] :
( ( ( aNaturalNumber0 @ SV20 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV67 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV78 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV67 @ SV78 ) @ SV20 )
= ( sdtpldt0 @ ( sdtasdt0 @ SV67 @ SV20 ) @ ( sdtasdt0 @ SV78 @ SV20 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[567]) ).
thf(602,plain,
! [SV44: $i,SV21: $i] :
( ( ( ~ ~ ( ~ ! [SY144: $i] :
( ~ ( aNaturalNumber0 @ SY144 )
| ( ( sdtpldt0 @ SV21 @ SY144 )
!= ( sdtpldt0 @ SV44 @ SY144 ) ) )
| ~ ~ ( ~ ! [SY145: $i] :
( ~ ( aNaturalNumber0 @ SY145 )
| ( ( sdtpldt0 @ SY145 @ SV21 )
!= ( sdtpldt0 @ SY145 @ SV44 ) ) )
| ~ ! [SY146: $i] :
( ~ ( aNaturalNumber0 @ SY146 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SY146 @ SV21 ) @ ( sdtpldt0 @ SY146 @ SV44 ) ) ) ) )
| ~ ! [SY147: $i] :
( ~ ( aNaturalNumber0 @ SY147 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SV21 @ SY147 ) @ ( sdtpldt0 @ SV44 @ SY147 ) ) ) )
= $false )
| ( ( SV21 = SV44 )
= $true )
| ( ( sdtlseqdt0 @ SV21 @ SV44 )
= $false )
| ( ( aNaturalNumber0 @ SV21 )
= $false )
| ( ( aNaturalNumber0 @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[568]) ).
thf(603,plain,
! [SV22: $i,SV87: $i,SV84: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV84 )
| ~ ( aNaturalNumber0 @ SV87 ) )
= $true )
| ( ( ( ( sdtasdt0 @ SV22 @ SV84 )
!= ( sdtasdt0 @ SV22 @ SV87 ) )
| ( SV84 = SV87 ) )
= $true )
| ( ( SV22 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[569]) ).
thf(604,plain,
! [SV22: $i,SV88: $i,SV85: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV85 )
| ~ ( aNaturalNumber0 @ SV88 ) )
= $true )
| ( ( ( ( sdtasdt0 @ SV85 @ SV22 )
!= ( sdtasdt0 @ SV88 @ SV22 ) )
| ( SV85 = SV88 ) )
= $true )
| ( ( SV22 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[570]) ).
thf(605,plain,
( ( ( ( sdtasdt0 @ xn @ xn )
!= ( sdtasdt0 @ xp @ sK3_W0 ) )
| ~ ( aNaturalNumber0 @ sK3_W0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[571]) ).
thf(606,plain,
! [SV91: $i] :
( ( ~ ( aNaturalNumber0 @ SV91 )
| ! [SY162: $i] :
( ( xp
!= ( sdtasdt0 @ SV91 @ SY162 ) )
| ~ ( aNaturalNumber0 @ SY162 ) )
| ( SV91 = sz10 )
| ( SV91 = xp ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[575]) ).
thf(607,plain,
! [SV92: $i] :
( ( ~ ( aNaturalNumber0 @ SV92 )
| ~ ( doDivides0 @ SV92 @ xp )
| ( SV92 = sz10 )
| ( SV92 = xp ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[576]) ).
thf(608,plain,
( ( xn = sz00 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[577]) ).
thf(609,plain,
( ( ~ ~ ( ~ ( aNaturalNumber0 @ xn )
| ~ ( aNaturalNumber0 @ xm ) )
| ~ ( aNaturalNumber0 @ xp ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[578]) ).
thf(610,plain,
! [SV23: $i] :
( ( ( ~ ( aNaturalNumber0 @ ( sK1_W1 @ SV23 ) ) )
= $false )
| ( ( SV23 = sz10 )
= $true )
| ( ( SV23 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[579]) ).
thf(611,plain,
! [SV23: $i] :
( ( ( ~ ( doDivides0 @ ( sK1_W1 @ SV23 ) @ SV23 ) )
= $false )
| ( ( SV23 = sz10 )
= $true )
| ( ( SV23 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[579]) ).
thf(612,plain,
! [SV57: $i,SV68: $i] :
( ( ( SV68 != SV57 )
= $true )
| ( ( sdtlseqdt0 @ SV57 @ SV68 )
= $true )
| ( ( aNaturalNumber0 @ SV57 )
= $false )
| ( ( aNaturalNumber0 @ SV68 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[580]) ).
thf(613,plain,
! [SV58: $i,SV69: $i] :
( ( ( sdtlseqdt0 @ SV69 @ SV58 )
= $true )
| ( ( sdtlseqdt0 @ SV58 @ SV69 )
= $true )
| ( ( aNaturalNumber0 @ SV58 )
= $false )
| ( ( aNaturalNumber0 @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[581]) ).
thf(614,plain,
! [SV79: $i,SV70: $i,SV24: $i] :
( ( ( aNaturalNumber0 @ SV24 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV70 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV79 ) )
= $true )
| ( ( ( ( sdtpldt0 @ SV24 @ SV70 )
!= ( sdtpldt0 @ SV24 @ SV79 ) )
| ( SV70 = SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[582]) ).
thf(615,plain,
! [SV80: $i,SV71: $i,SV24: $i] :
( ( ( aNaturalNumber0 @ SV24 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV71 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV80 ) )
= $true )
| ( ( ( ( sdtpldt0 @ SV71 @ SV24 )
!= ( sdtpldt0 @ SV80 @ SV24 ) )
| ( SV71 = SV80 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[583]) ).
thf(616,plain,
! [SV81: $i,SV72: $i,SV25: $i] :
( ( ( SV25 = sz00 )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV25 )
| ~ ( aNaturalNumber0 @ SV72 )
| ~ ( aNaturalNumber0 @ SV81 ) )
= $true )
| ( ( SV72 = sz00 )
= $true )
| ( ( SV81 = sz00 )
= $true )
| ( ( ( ( sdtasdt0 @ SV81 @ ( sdtasdt0 @ SV72 @ SV72 ) )
!= ( sdtasdt0 @ SV25 @ SV25 ) )
| ~ ( iLess0 @ SV25 @ xn )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( SV81
!= ( sdtasdt0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) @ ( sK5_SY81 @ SV81 @ SV72 @ SV25 ) ) )
| ~ ( aNaturalNumber0 @ ( sK5_SY81 @ SV81 @ SV72 @ SV25 ) ) )
| ~ ( aNaturalNumber0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) ) )
| ~ ( doDivides0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) @ SV81 ) )
| ~ ~ ( ~ ( ( ( sK4_W3 @ SV81 @ SV72 @ SV25 )
!= sz10 ) )
| ~ ( ( ( sK4_W3 @ SV81 @ SV72 @ SV25 )
!= SV81 ) ) ) )
| ( SV81 = sz10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[584]) ).
thf(617,plain,
! [SV82: $i,SV73: $i,SV25: $i] :
( ( ( SV25 = sz00 )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV25 )
| ~ ( aNaturalNumber0 @ SV73 )
| ~ ( aNaturalNumber0 @ SV82 ) )
= $true )
| ( ( SV73 = sz00 )
= $true )
| ( ( SV82 = sz00 )
= $true )
| ( ( ( ( sdtasdt0 @ SV82 @ ( sdtasdt0 @ SV73 @ SV73 ) )
!= ( sdtasdt0 @ SV25 @ SV25 ) )
| ~ ( iLess0 @ SV25 @ xn )
| ~ ( isPrime0 @ SV82 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[585]) ).
thf(618,plain,
! [SV89: $i,SV86: $i,SV26: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV26 )
| ~ ( aNaturalNumber0 @ SV86 )
| ~ ( aNaturalNumber0 @ SV89 ) )
= $true )
| ( ( ( SV26 = sz00 )
| ( SV86 = SV89 )
| ~ ( sdtlseqdt0 @ SV86 @ SV89 )
| ( ( sdtasdt0 @ SV86 @ SV26 )
!= ( sdtasdt0 @ SV89 @ SV26 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[586]) ).
thf(619,plain,
! [SV26: $i] :
( ( ! [SY130: $i,SY131: $i] :
( ~ ( aNaturalNumber0 @ SV26 )
| ~ ( aNaturalNumber0 @ SY130 )
| ~ ( aNaturalNumber0 @ SY131 )
| ( SV26 = sz00 )
| ( SY130 = SY131 )
| ~ ( sdtlseqdt0 @ SY130 @ SY131 )
| ( ( sdtasdt0 @ SV26 @ SY130 )
!= ( sdtasdt0 @ SV26 @ SY131 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[587]) ).
thf(620,plain,
! [SV26: $i] :
( ( ! [SY132: $i,SY133: $i] :
( ~ ( aNaturalNumber0 @ SV26 )
| ~ ( aNaturalNumber0 @ SY132 )
| ~ ( aNaturalNumber0 @ SY133 )
| ( SV26 = sz00 )
| ( SY132 = SY133 )
| ~ ( sdtlseqdt0 @ SY132 @ SY133 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV26 @ SY132 ) @ ( sdtasdt0 @ SV26 @ SY133 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[588]) ).
thf(621,plain,
! [SV83: $i,SV74: $i,SV26: $i] :
( ( ( aNaturalNumber0 @ SV26 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV74 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV83 ) )
= $true )
| ( ( ( SV26 = sz00 )
| ( SV74 = SV83 )
| ~ ( sdtlseqdt0 @ SV74 @ SV83 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV74 @ SV26 ) @ ( sdtasdt0 @ SV83 @ SV26 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[589]) ).
thf(622,plain,
! [SV75: $i,SV63: $i] :
( ( ( ( sdtpldt0 @ SV63 @ SV75 )
!= sz00 )
= $true )
| ( ( SV63 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV63 )
= $false )
| ( ( aNaturalNumber0 @ SV75 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[591]) ).
thf(623,plain,
! [SV76: $i,SV64: $i] :
( ( ( ( sdtpldt0 @ SV64 @ SV76 )
!= sz00 )
= $true )
| ( ( SV76 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV64 )
= $false )
| ( ( aNaturalNumber0 @ SV76 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[592]) ).
thf(624,plain,
! [SV47: $i,SV35: $i,SV11: $i] :
( ( ( ~ ( sdtlseqdt0 @ SV11 @ SV35 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV35 @ SV47 ) )
= $true )
| ( ( sdtlseqdt0 @ SV11 @ SV47 )
= $true )
| ( ( aNaturalNumber0 @ SV35 )
= $false )
| ( ( aNaturalNumber0 @ SV11 )
= $false )
| ( ( aNaturalNumber0 @ SV47 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[594]) ).
thf(625,plain,
! [SV49: $i,SV38: $i,SV14: $i] :
( ( ( ~ ( doDivides0 @ SV14 @ SV38 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV38 @ SV49 ) )
= $true )
| ( ( doDivides0 @ SV14 @ SV49 )
= $true )
| ( ( aNaturalNumber0 @ SV38 )
= $false )
| ( ( aNaturalNumber0 @ SV14 )
= $false )
| ( ( aNaturalNumber0 @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[595]) ).
thf(626,plain,
! [SV50: $i,SV39: $i,SV15: $i] :
( ( ( ~ ( doDivides0 @ SV15 @ SV39 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV15 @ SV50 ) )
= $true )
| ( ( doDivides0 @ SV15 @ ( sdtpldt0 @ SV39 @ SV50 ) )
= $true )
| ( ( aNaturalNumber0 @ SV39 )
= $false )
| ( ( aNaturalNumber0 @ SV15 )
= $false )
| ( ( aNaturalNumber0 @ SV50 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[596]) ).
thf(627,plain,
! [SV51: $i,SV40: $i,SV16: $i] :
( ( ( ~ ( doDivides0 @ SV16 @ SV40 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV16 @ ( sdtpldt0 @ SV40 @ SV51 ) ) )
= $true )
| ( ( doDivides0 @ SV16 @ SV51 )
= $true )
| ( ( aNaturalNumber0 @ SV40 )
= $false )
| ( ( aNaturalNumber0 @ SV16 )
= $false )
| ( ( aNaturalNumber0 @ SV51 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[597]) ).
thf(628,plain,
! [SV18: $i,SV42: $i,SV90: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV90 ) )
= $true )
| ( ( ( sdtasdt0 @ SV90 @ ( sdtsldt0 @ SV42 @ SV18 ) )
= ( sdtsldt0 @ ( sdtasdt0 @ SV90 @ SV42 ) @ SV18 ) )
= $true )
| ( ( SV18 = sz00 )
= $true )
| ( ( doDivides0 @ SV18 @ SV42 )
= $false )
| ( ( aNaturalNumber0 @ SV18 )
= $false )
| ( ( aNaturalNumber0 @ SV42 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[598]) ).
thf(629,plain,
! [SV43: $i,SV19: $i,SV52: $i] :
( ( ( ~ ( doDivides0 @ SV52 @ ( sdtasdt0 @ SV19 @ SV43 ) ) )
= $true )
| ( ( ~ ( isPrime0 @ SV52 ) )
= $true )
| ( ( ( doDivides0 @ SV52 @ SV19 )
| ( doDivides0 @ SV52 @ SV43 ) )
= $true )
| ( ( aNaturalNumber0 @ SV43 )
= $false )
| ( ( aNaturalNumber0 @ SV19 )
= $false )
| ( ( aNaturalNumber0 @ SV52 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[599]) ).
thf(630,plain,
! [SV77: $i,SV20: $i,SV66: $i] :
( ( ( aNaturalNumber0 @ SV66 )
= $false )
| ( ( aNaturalNumber0 @ SV20 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV77 ) )
= $true )
| ( ( ( sdtasdt0 @ SV20 @ ( sdtpldt0 @ SV66 @ SV77 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV20 @ SV66 ) @ ( sdtasdt0 @ SV20 @ SV77 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[600]) ).
thf(631,plain,
! [SV78: $i,SV20: $i,SV67: $i] :
( ( ( aNaturalNumber0 @ SV67 )
= $false )
| ( ( aNaturalNumber0 @ SV20 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV78 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV67 @ SV78 ) @ SV20 )
= ( sdtpldt0 @ ( sdtasdt0 @ SV67 @ SV20 ) @ ( sdtasdt0 @ SV78 @ SV20 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[601]) ).
thf(632,plain,
! [SV44: $i,SV21: $i] :
( ( ( ~ ~ ( ~ ! [SY144: $i] :
( ~ ( aNaturalNumber0 @ SY144 )
| ( ( sdtpldt0 @ SV21 @ SY144 )
!= ( sdtpldt0 @ SV44 @ SY144 ) ) )
| ~ ~ ( ~ ! [SY145: $i] :
( ~ ( aNaturalNumber0 @ SY145 )
| ( ( sdtpldt0 @ SY145 @ SV21 )
!= ( sdtpldt0 @ SY145 @ SV44 ) ) )
| ~ ! [SY146: $i] :
( ~ ( aNaturalNumber0 @ SY146 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SY146 @ SV21 ) @ ( sdtpldt0 @ SY146 @ SV44 ) ) ) ) ) )
= $false )
| ( ( SV21 = SV44 )
= $true )
| ( ( sdtlseqdt0 @ SV21 @ SV44 )
= $false )
| ( ( aNaturalNumber0 @ SV21 )
= $false )
| ( ( aNaturalNumber0 @ SV44 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[602]) ).
thf(633,plain,
! [SV44: $i,SV21: $i] :
( ( ( ~ ! [SY147: $i] :
( ~ ( aNaturalNumber0 @ SY147 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SV21 @ SY147 ) @ ( sdtpldt0 @ SV44 @ SY147 ) ) ) )
= $false )
| ( ( SV21 = SV44 )
= $true )
| ( ( sdtlseqdt0 @ SV21 @ SV44 )
= $false )
| ( ( aNaturalNumber0 @ SV21 )
= $false )
| ( ( aNaturalNumber0 @ SV44 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[602]) ).
thf(634,plain,
! [SV22: $i,SV87: $i,SV84: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV84 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV87 ) )
= $true )
| ( ( ( ( sdtasdt0 @ SV22 @ SV84 )
!= ( sdtasdt0 @ SV22 @ SV87 ) )
| ( SV84 = SV87 ) )
= $true )
| ( ( SV22 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[603]) ).
thf(635,plain,
! [SV22: $i,SV88: $i,SV85: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV85 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV88 ) )
= $true )
| ( ( ( ( sdtasdt0 @ SV85 @ SV22 )
!= ( sdtasdt0 @ SV88 @ SV22 ) )
| ( SV85 = SV88 ) )
= $true )
| ( ( SV22 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[604]) ).
thf(636,plain,
( ( ( sdtasdt0 @ xn @ xn )
!= ( sdtasdt0 @ xp @ sK3_W0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[605]) ).
thf(637,plain,
( ( ~ ( aNaturalNumber0 @ sK3_W0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[605]) ).
thf(638,plain,
! [SV91: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV91 )
| ! [SY162: $i] :
( ( xp
!= ( sdtasdt0 @ SV91 @ SY162 ) )
| ~ ( aNaturalNumber0 @ SY162 ) ) )
= $true )
| ( ( ( SV91 = sz10 )
| ( SV91 = xp ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[606]) ).
thf(639,plain,
! [SV92: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV92 )
| ~ ( doDivides0 @ SV92 @ xp ) )
= $true )
| ( ( ( SV92 = sz10 )
| ( SV92 = xp ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[607]) ).
thf(640,plain,
( ( ~ ~ ( ~ ( aNaturalNumber0 @ xn )
| ~ ( aNaturalNumber0 @ xm ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[609]) ).
thf(641,plain,
( ( ~ ( aNaturalNumber0 @ xp ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[609]) ).
thf(642,plain,
! [SV23: $i] :
( ( ( aNaturalNumber0 @ ( sK1_W1 @ SV23 ) )
= $true )
| ( ( SV23 = sz10 )
= $true )
| ( ( SV23 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[610]) ).
thf(643,plain,
! [SV23: $i] :
( ( ( doDivides0 @ ( sK1_W1 @ SV23 ) @ SV23 )
= $true )
| ( ( SV23 = sz10 )
= $true )
| ( ( SV23 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[611]) ).
thf(644,plain,
! [SV57: $i,SV68: $i] :
( ( ( SV68 = SV57 )
= $false )
| ( ( sdtlseqdt0 @ SV57 @ SV68 )
= $true )
| ( ( aNaturalNumber0 @ SV57 )
= $false )
| ( ( aNaturalNumber0 @ SV68 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[612]) ).
thf(645,plain,
! [SV79: $i,SV24: $i,SV70: $i] :
( ( ( aNaturalNumber0 @ SV70 )
= $false )
| ( ( aNaturalNumber0 @ SV24 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV79 ) )
= $true )
| ( ( ( ( sdtpldt0 @ SV24 @ SV70 )
!= ( sdtpldt0 @ SV24 @ SV79 ) )
| ( SV70 = SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[614]) ).
thf(646,plain,
! [SV80: $i,SV24: $i,SV71: $i] :
( ( ( aNaturalNumber0 @ SV71 )
= $false )
| ( ( aNaturalNumber0 @ SV24 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV80 ) )
= $true )
| ( ( ( ( sdtpldt0 @ SV71 @ SV24 )
!= ( sdtpldt0 @ SV80 @ SV24 ) )
| ( SV71 = SV80 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[615]) ).
thf(647,plain,
! [SV81: $i,SV72: $i,SV25: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV25 )
| ~ ( aNaturalNumber0 @ SV72 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV81 ) )
= $true )
| ( ( SV25 = sz00 )
= $true )
| ( ( SV72 = sz00 )
= $true )
| ( ( SV81 = sz00 )
= $true )
| ( ( ( ( sdtasdt0 @ SV81 @ ( sdtasdt0 @ SV72 @ SV72 ) )
!= ( sdtasdt0 @ SV25 @ SV25 ) )
| ~ ( iLess0 @ SV25 @ xn )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( SV81
!= ( sdtasdt0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) @ ( sK5_SY81 @ SV81 @ SV72 @ SV25 ) ) )
| ~ ( aNaturalNumber0 @ ( sK5_SY81 @ SV81 @ SV72 @ SV25 ) ) )
| ~ ( aNaturalNumber0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) ) )
| ~ ( doDivides0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) @ SV81 ) )
| ~ ~ ( ~ ( ( ( sK4_W3 @ SV81 @ SV72 @ SV25 )
!= sz10 ) )
| ~ ( ( ( sK4_W3 @ SV81 @ SV72 @ SV25 )
!= SV81 ) ) ) )
| ( SV81 = sz10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[616]) ).
thf(648,plain,
! [SV82: $i,SV73: $i,SV25: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV25 )
| ~ ( aNaturalNumber0 @ SV73 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV82 ) )
= $true )
| ( ( SV25 = sz00 )
= $true )
| ( ( SV73 = sz00 )
= $true )
| ( ( SV82 = sz00 )
= $true )
| ( ( ( ( sdtasdt0 @ SV82 @ ( sdtasdt0 @ SV73 @ SV73 ) )
!= ( sdtasdt0 @ SV25 @ SV25 ) )
| ~ ( iLess0 @ SV25 @ xn )
| ~ ( isPrime0 @ SV82 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[617]) ).
thf(649,plain,
! [SV89: $i,SV86: $i,SV26: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV26 )
| ~ ( aNaturalNumber0 @ SV86 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV89 ) )
= $true )
| ( ( ( SV26 = sz00 )
| ( SV86 = SV89 )
| ~ ( sdtlseqdt0 @ SV86 @ SV89 )
| ( ( sdtasdt0 @ SV86 @ SV26 )
!= ( sdtasdt0 @ SV89 @ SV26 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[618]) ).
thf(650,plain,
! [SV93: $i,SV26: $i] :
( ( ! [SY163: $i] :
( ~ ( aNaturalNumber0 @ SV26 )
| ~ ( aNaturalNumber0 @ SV93 )
| ~ ( aNaturalNumber0 @ SY163 )
| ( SV26 = sz00 )
| ( SV93 = SY163 )
| ~ ( sdtlseqdt0 @ SV93 @ SY163 )
| ( ( sdtasdt0 @ SV26 @ SV93 )
!= ( sdtasdt0 @ SV26 @ SY163 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[619]) ).
thf(651,plain,
! [SV94: $i,SV26: $i] :
( ( ! [SY164: $i] :
( ~ ( aNaturalNumber0 @ SV26 )
| ~ ( aNaturalNumber0 @ SV94 )
| ~ ( aNaturalNumber0 @ SY164 )
| ( SV26 = sz00 )
| ( SV94 = SY164 )
| ~ ( sdtlseqdt0 @ SV94 @ SY164 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV26 @ SV94 ) @ ( sdtasdt0 @ SV26 @ SY164 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[620]) ).
thf(652,plain,
! [SV83: $i,SV26: $i,SV74: $i] :
( ( ( aNaturalNumber0 @ SV74 )
= $false )
| ( ( aNaturalNumber0 @ SV26 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV83 ) )
= $true )
| ( ( ( SV26 = sz00 )
| ( SV74 = SV83 )
| ~ ( sdtlseqdt0 @ SV74 @ SV83 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV74 @ SV26 ) @ ( sdtasdt0 @ SV83 @ SV26 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[621]) ).
thf(653,plain,
! [SV75: $i,SV63: $i] :
( ( ( ( sdtpldt0 @ SV63 @ SV75 )
= sz00 )
= $false )
| ( ( SV63 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV63 )
= $false )
| ( ( aNaturalNumber0 @ SV75 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[622]) ).
thf(654,plain,
! [SV76: $i,SV64: $i] :
( ( ( ( sdtpldt0 @ SV64 @ SV76 )
= sz00 )
= $false )
| ( ( SV76 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV64 )
= $false )
| ( ( aNaturalNumber0 @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[623]) ).
thf(655,plain,
! [SV47: $i,SV35: $i,SV11: $i] :
( ( ( sdtlseqdt0 @ SV11 @ SV35 )
= $false )
| ( ( ~ ( sdtlseqdt0 @ SV35 @ SV47 ) )
= $true )
| ( ( sdtlseqdt0 @ SV11 @ SV47 )
= $true )
| ( ( aNaturalNumber0 @ SV35 )
= $false )
| ( ( aNaturalNumber0 @ SV11 )
= $false )
| ( ( aNaturalNumber0 @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[624]) ).
thf(656,plain,
! [SV49: $i,SV38: $i,SV14: $i] :
( ( ( doDivides0 @ SV14 @ SV38 )
= $false )
| ( ( ~ ( doDivides0 @ SV38 @ SV49 ) )
= $true )
| ( ( doDivides0 @ SV14 @ SV49 )
= $true )
| ( ( aNaturalNumber0 @ SV38 )
= $false )
| ( ( aNaturalNumber0 @ SV14 )
= $false )
| ( ( aNaturalNumber0 @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[625]) ).
thf(657,plain,
! [SV50: $i,SV39: $i,SV15: $i] :
( ( ( doDivides0 @ SV15 @ SV39 )
= $false )
| ( ( ~ ( doDivides0 @ SV15 @ SV50 ) )
= $true )
| ( ( doDivides0 @ SV15 @ ( sdtpldt0 @ SV39 @ SV50 ) )
= $true )
| ( ( aNaturalNumber0 @ SV39 )
= $false )
| ( ( aNaturalNumber0 @ SV15 )
= $false )
| ( ( aNaturalNumber0 @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[626]) ).
thf(658,plain,
! [SV51: $i,SV40: $i,SV16: $i] :
( ( ( doDivides0 @ SV16 @ SV40 )
= $false )
| ( ( ~ ( doDivides0 @ SV16 @ ( sdtpldt0 @ SV40 @ SV51 ) ) )
= $true )
| ( ( doDivides0 @ SV16 @ SV51 )
= $true )
| ( ( aNaturalNumber0 @ SV40 )
= $false )
| ( ( aNaturalNumber0 @ SV16 )
= $false )
| ( ( aNaturalNumber0 @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[627]) ).
thf(659,plain,
! [SV18: $i,SV42: $i,SV90: $i] :
( ( ( aNaturalNumber0 @ SV90 )
= $false )
| ( ( ( sdtasdt0 @ SV90 @ ( sdtsldt0 @ SV42 @ SV18 ) )
= ( sdtsldt0 @ ( sdtasdt0 @ SV90 @ SV42 ) @ SV18 ) )
= $true )
| ( ( SV18 = sz00 )
= $true )
| ( ( doDivides0 @ SV18 @ SV42 )
= $false )
| ( ( aNaturalNumber0 @ SV18 )
= $false )
| ( ( aNaturalNumber0 @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[628]) ).
thf(660,plain,
! [SV43: $i,SV19: $i,SV52: $i] :
( ( ( doDivides0 @ SV52 @ ( sdtasdt0 @ SV19 @ SV43 ) )
= $false )
| ( ( ~ ( isPrime0 @ SV52 ) )
= $true )
| ( ( ( doDivides0 @ SV52 @ SV19 )
| ( doDivides0 @ SV52 @ SV43 ) )
= $true )
| ( ( aNaturalNumber0 @ SV43 )
= $false )
| ( ( aNaturalNumber0 @ SV19 )
= $false )
| ( ( aNaturalNumber0 @ SV52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[629]) ).
thf(661,plain,
! [SV66: $i,SV20: $i,SV77: $i] :
( ( ( aNaturalNumber0 @ SV77 )
= $false )
| ( ( aNaturalNumber0 @ SV20 )
= $false )
| ( ( aNaturalNumber0 @ SV66 )
= $false )
| ( ( ( sdtasdt0 @ SV20 @ ( sdtpldt0 @ SV66 @ SV77 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV20 @ SV66 ) @ ( sdtasdt0 @ SV20 @ SV77 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[630]) ).
thf(662,plain,
! [SV67: $i,SV20: $i,SV78: $i] :
( ( ( aNaturalNumber0 @ SV78 )
= $false )
| ( ( aNaturalNumber0 @ SV20 )
= $false )
| ( ( aNaturalNumber0 @ SV67 )
= $false )
| ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV67 @ SV78 ) @ SV20 )
= ( sdtpldt0 @ ( sdtasdt0 @ SV67 @ SV20 ) @ ( sdtasdt0 @ SV78 @ SV20 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[631]) ).
thf(663,plain,
! [SV44: $i,SV21: $i] :
( ( ( ~ ( ~ ! [SY144: $i] :
( ~ ( aNaturalNumber0 @ SY144 )
| ( ( sdtpldt0 @ SV21 @ SY144 )
!= ( sdtpldt0 @ SV44 @ SY144 ) ) )
| ~ ~ ( ~ ! [SY145: $i] :
( ~ ( aNaturalNumber0 @ SY145 )
| ( ( sdtpldt0 @ SY145 @ SV21 )
!= ( sdtpldt0 @ SY145 @ SV44 ) ) )
| ~ ! [SY146: $i] :
( ~ ( aNaturalNumber0 @ SY146 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SY146 @ SV21 ) @ ( sdtpldt0 @ SY146 @ SV44 ) ) ) ) ) )
= $true )
| ( ( SV21 = SV44 )
= $true )
| ( ( sdtlseqdt0 @ SV21 @ SV44 )
= $false )
| ( ( aNaturalNumber0 @ SV21 )
= $false )
| ( ( aNaturalNumber0 @ SV44 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[632]) ).
thf(664,plain,
! [SV44: $i,SV21: $i] :
( ( ( ! [SY147: $i] :
( ~ ( aNaturalNumber0 @ SY147 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SV21 @ SY147 ) @ ( sdtpldt0 @ SV44 @ SY147 ) ) ) )
= $true )
| ( ( SV21 = SV44 )
= $true )
| ( ( sdtlseqdt0 @ SV21 @ SV44 )
= $false )
| ( ( aNaturalNumber0 @ SV21 )
= $false )
| ( ( aNaturalNumber0 @ SV44 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[633]) ).
thf(665,plain,
! [SV22: $i,SV87: $i,SV84: $i] :
( ( ( aNaturalNumber0 @ SV84 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV87 ) )
= $true )
| ( ( ( ( sdtasdt0 @ SV22 @ SV84 )
!= ( sdtasdt0 @ SV22 @ SV87 ) )
| ( SV84 = SV87 ) )
= $true )
| ( ( SV22 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[634]) ).
thf(666,plain,
! [SV22: $i,SV88: $i,SV85: $i] :
( ( ( aNaturalNumber0 @ SV85 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV88 ) )
= $true )
| ( ( ( ( sdtasdt0 @ SV85 @ SV22 )
!= ( sdtasdt0 @ SV88 @ SV22 ) )
| ( SV85 = SV88 ) )
= $true )
| ( ( SV22 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[635]) ).
thf(667,plain,
( ( ( sdtasdt0 @ xn @ xn )
= ( sdtasdt0 @ xp @ sK3_W0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[636]) ).
thf(668,plain,
( ( aNaturalNumber0 @ sK3_W0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[637]) ).
thf(669,plain,
! [SV91: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV91 ) )
= $true )
| ( ( ! [SY162: $i] :
( ( xp
!= ( sdtasdt0 @ SV91 @ SY162 ) )
| ~ ( aNaturalNumber0 @ SY162 ) ) )
= $true )
| ( ( ( SV91 = sz10 )
| ( SV91 = xp ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[638]) ).
thf(670,plain,
! [SV92: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV92 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV92 @ xp ) )
= $true )
| ( ( ( SV92 = sz10 )
| ( SV92 = xp ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[639]) ).
thf(671,plain,
( ( ~ ( ~ ( aNaturalNumber0 @ xn )
| ~ ( aNaturalNumber0 @ xm ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[640]) ).
thf(672,plain,
( ( aNaturalNumber0 @ xp )
= $true ),
inference(extcnf_not_neg,[status(thm)],[641]) ).
thf(673,plain,
! [SV70: $i,SV24: $i,SV79: $i] :
( ( ( aNaturalNumber0 @ SV79 )
= $false )
| ( ( aNaturalNumber0 @ SV24 )
= $false )
| ( ( aNaturalNumber0 @ SV70 )
= $false )
| ( ( ( ( sdtpldt0 @ SV24 @ SV70 )
!= ( sdtpldt0 @ SV24 @ SV79 ) )
| ( SV70 = SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[645]) ).
thf(674,plain,
! [SV71: $i,SV24: $i,SV80: $i] :
( ( ( aNaturalNumber0 @ SV80 )
= $false )
| ( ( aNaturalNumber0 @ SV24 )
= $false )
| ( ( aNaturalNumber0 @ SV71 )
= $false )
| ( ( ( ( sdtpldt0 @ SV71 @ SV24 )
!= ( sdtpldt0 @ SV80 @ SV24 ) )
| ( SV71 = SV80 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[646]) ).
thf(675,plain,
! [SV81: $i,SV72: $i,SV25: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV25 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV72 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV81 ) )
= $true )
| ( ( SV25 = sz00 )
= $true )
| ( ( SV72 = sz00 )
= $true )
| ( ( SV81 = sz00 )
= $true )
| ( ( ( ( sdtasdt0 @ SV81 @ ( sdtasdt0 @ SV72 @ SV72 ) )
!= ( sdtasdt0 @ SV25 @ SV25 ) )
| ~ ( iLess0 @ SV25 @ xn )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( SV81
!= ( sdtasdt0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) @ ( sK5_SY81 @ SV81 @ SV72 @ SV25 ) ) )
| ~ ( aNaturalNumber0 @ ( sK5_SY81 @ SV81 @ SV72 @ SV25 ) ) )
| ~ ( aNaturalNumber0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) ) )
| ~ ( doDivides0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) @ SV81 ) )
| ~ ~ ( ~ ( ( ( sK4_W3 @ SV81 @ SV72 @ SV25 )
!= sz10 ) )
| ~ ( ( ( sK4_W3 @ SV81 @ SV72 @ SV25 )
!= SV81 ) ) ) )
| ( SV81 = sz10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[647]) ).
thf(676,plain,
! [SV82: $i,SV73: $i,SV25: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV25 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV73 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV82 ) )
= $true )
| ( ( SV25 = sz00 )
= $true )
| ( ( SV73 = sz00 )
= $true )
| ( ( SV82 = sz00 )
= $true )
| ( ( ( ( sdtasdt0 @ SV82 @ ( sdtasdt0 @ SV73 @ SV73 ) )
!= ( sdtasdt0 @ SV25 @ SV25 ) )
| ~ ( iLess0 @ SV25 @ xn )
| ~ ( isPrime0 @ SV82 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[648]) ).
thf(677,plain,
! [SV89: $i,SV86: $i,SV26: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV26 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV86 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV89 ) )
= $true )
| ( ( ( SV26 = sz00 )
| ( SV86 = SV89 )
| ~ ( sdtlseqdt0 @ SV86 @ SV89 )
| ( ( sdtasdt0 @ SV86 @ SV26 )
!= ( sdtasdt0 @ SV89 @ SV26 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[649]) ).
thf(678,plain,
! [SV95: $i,SV93: $i,SV26: $i] :
( ( ~ ( aNaturalNumber0 @ SV26 )
| ~ ( aNaturalNumber0 @ SV93 )
| ~ ( aNaturalNumber0 @ SV95 )
| ( SV26 = sz00 )
| ( SV93 = SV95 )
| ~ ( sdtlseqdt0 @ SV93 @ SV95 )
| ( ( sdtasdt0 @ SV26 @ SV93 )
!= ( sdtasdt0 @ SV26 @ SV95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[650]) ).
thf(679,plain,
! [SV96: $i,SV94: $i,SV26: $i] :
( ( ~ ( aNaturalNumber0 @ SV26 )
| ~ ( aNaturalNumber0 @ SV94 )
| ~ ( aNaturalNumber0 @ SV96 )
| ( SV26 = sz00 )
| ( SV94 = SV96 )
| ~ ( sdtlseqdt0 @ SV94 @ SV96 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV26 @ SV94 ) @ ( sdtasdt0 @ SV26 @ SV96 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[651]) ).
thf(680,plain,
! [SV74: $i,SV26: $i,SV83: $i] :
( ( ( aNaturalNumber0 @ SV83 )
= $false )
| ( ( aNaturalNumber0 @ SV26 )
= $false )
| ( ( aNaturalNumber0 @ SV74 )
= $false )
| ( ( ( SV26 = sz00 )
| ( SV74 = SV83 )
| ~ ( sdtlseqdt0 @ SV74 @ SV83 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV74 @ SV26 ) @ ( sdtasdt0 @ SV83 @ SV26 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[652]) ).
thf(681,plain,
! [SV11: $i,SV47: $i,SV35: $i] :
( ( ( sdtlseqdt0 @ SV35 @ SV47 )
= $false )
| ( ( sdtlseqdt0 @ SV11 @ SV35 )
= $false )
| ( ( sdtlseqdt0 @ SV11 @ SV47 )
= $true )
| ( ( aNaturalNumber0 @ SV35 )
= $false )
| ( ( aNaturalNumber0 @ SV11 )
= $false )
| ( ( aNaturalNumber0 @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[655]) ).
thf(682,plain,
! [SV14: $i,SV49: $i,SV38: $i] :
( ( ( doDivides0 @ SV38 @ SV49 )
= $false )
| ( ( doDivides0 @ SV14 @ SV38 )
= $false )
| ( ( doDivides0 @ SV14 @ SV49 )
= $true )
| ( ( aNaturalNumber0 @ SV38 )
= $false )
| ( ( aNaturalNumber0 @ SV14 )
= $false )
| ( ( aNaturalNumber0 @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[656]) ).
thf(683,plain,
! [SV39: $i,SV50: $i,SV15: $i] :
( ( ( doDivides0 @ SV15 @ SV50 )
= $false )
| ( ( doDivides0 @ SV15 @ SV39 )
= $false )
| ( ( doDivides0 @ SV15 @ ( sdtpldt0 @ SV39 @ SV50 ) )
= $true )
| ( ( aNaturalNumber0 @ SV39 )
= $false )
| ( ( aNaturalNumber0 @ SV15 )
= $false )
| ( ( aNaturalNumber0 @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[657]) ).
thf(684,plain,
! [SV51: $i,SV40: $i,SV16: $i] :
( ( ( doDivides0 @ SV16 @ ( sdtpldt0 @ SV40 @ SV51 ) )
= $false )
| ( ( doDivides0 @ SV16 @ SV40 )
= $false )
| ( ( doDivides0 @ SV16 @ SV51 )
= $true )
| ( ( aNaturalNumber0 @ SV40 )
= $false )
| ( ( aNaturalNumber0 @ SV16 )
= $false )
| ( ( aNaturalNumber0 @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[658]) ).
thf(685,plain,
! [SV43: $i,SV19: $i,SV52: $i] :
( ( ( isPrime0 @ SV52 )
= $false )
| ( ( doDivides0 @ SV52 @ ( sdtasdt0 @ SV19 @ SV43 ) )
= $false )
| ( ( ( doDivides0 @ SV52 @ SV19 )
| ( doDivides0 @ SV52 @ SV43 ) )
= $true )
| ( ( aNaturalNumber0 @ SV43 )
= $false )
| ( ( aNaturalNumber0 @ SV19 )
= $false )
| ( ( aNaturalNumber0 @ SV52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[660]) ).
thf(686,plain,
! [SV44: $i,SV21: $i] :
( ( ( ~ ! [SY144: $i] :
( ~ ( aNaturalNumber0 @ SY144 )
| ( ( sdtpldt0 @ SV21 @ SY144 )
!= ( sdtpldt0 @ SV44 @ SY144 ) ) )
| ~ ~ ( ~ ! [SY145: $i] :
( ~ ( aNaturalNumber0 @ SY145 )
| ( ( sdtpldt0 @ SY145 @ SV21 )
!= ( sdtpldt0 @ SY145 @ SV44 ) ) )
| ~ ! [SY146: $i] :
( ~ ( aNaturalNumber0 @ SY146 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SY146 @ SV21 ) @ ( sdtpldt0 @ SY146 @ SV44 ) ) ) ) )
= $false )
| ( ( SV21 = SV44 )
= $true )
| ( ( sdtlseqdt0 @ SV21 @ SV44 )
= $false )
| ( ( aNaturalNumber0 @ SV21 )
= $false )
| ( ( aNaturalNumber0 @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[663]) ).
thf(687,plain,
! [SV44: $i,SV21: $i,SV97: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV97 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SV21 @ SV97 ) @ ( sdtpldt0 @ SV44 @ SV97 ) ) )
= $true )
| ( ( SV21 = SV44 )
= $true )
| ( ( sdtlseqdt0 @ SV21 @ SV44 )
= $false )
| ( ( aNaturalNumber0 @ SV21 )
= $false )
| ( ( aNaturalNumber0 @ SV44 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[664]) ).
thf(688,plain,
! [SV22: $i,SV84: $i,SV87: $i] :
( ( ( aNaturalNumber0 @ SV87 )
= $false )
| ( ( aNaturalNumber0 @ SV84 )
= $false )
| ( ( ( ( sdtasdt0 @ SV22 @ SV84 )
!= ( sdtasdt0 @ SV22 @ SV87 ) )
| ( SV84 = SV87 ) )
= $true )
| ( ( SV22 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[665]) ).
thf(689,plain,
! [SV22: $i,SV85: $i,SV88: $i] :
( ( ( aNaturalNumber0 @ SV88 )
= $false )
| ( ( aNaturalNumber0 @ SV85 )
= $false )
| ( ( ( ( sdtasdt0 @ SV85 @ SV22 )
!= ( sdtasdt0 @ SV88 @ SV22 ) )
| ( SV85 = SV88 ) )
= $true )
| ( ( SV22 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[666]) ).
thf(690,plain,
! [SV91: $i] :
( ( ( aNaturalNumber0 @ SV91 )
= $false )
| ( ( ! [SY162: $i] :
( ( xp
!= ( sdtasdt0 @ SV91 @ SY162 ) )
| ~ ( aNaturalNumber0 @ SY162 ) ) )
= $true )
| ( ( ( SV91 = sz10 )
| ( SV91 = xp ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[669]) ).
thf(691,plain,
! [SV92: $i] :
( ( ( aNaturalNumber0 @ SV92 )
= $false )
| ( ( ~ ( doDivides0 @ SV92 @ xp ) )
= $true )
| ( ( ( SV92 = sz10 )
| ( SV92 = xp ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[670]) ).
thf(692,plain,
( ( ~ ( aNaturalNumber0 @ xn )
| ~ ( aNaturalNumber0 @ xm ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[671]) ).
thf(693,plain,
! [SV79: $i,SV70: $i,SV24: $i] :
( ( ( ( sdtpldt0 @ SV24 @ SV70 )
!= ( sdtpldt0 @ SV24 @ SV79 ) )
= $true )
| ( ( SV70 = SV79 )
= $true )
| ( ( aNaturalNumber0 @ SV70 )
= $false )
| ( ( aNaturalNumber0 @ SV24 )
= $false )
| ( ( aNaturalNumber0 @ SV79 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[673]) ).
thf(694,plain,
! [SV80: $i,SV24: $i,SV71: $i] :
( ( ( ( sdtpldt0 @ SV71 @ SV24 )
!= ( sdtpldt0 @ SV80 @ SV24 ) )
= $true )
| ( ( SV71 = SV80 )
= $true )
| ( ( aNaturalNumber0 @ SV71 )
= $false )
| ( ( aNaturalNumber0 @ SV24 )
= $false )
| ( ( aNaturalNumber0 @ SV80 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[674]) ).
thf(695,plain,
! [SV81: $i,SV72: $i,SV25: $i] :
( ( ( aNaturalNumber0 @ SV25 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV72 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV81 ) )
= $true )
| ( ( SV25 = sz00 )
= $true )
| ( ( SV72 = sz00 )
= $true )
| ( ( SV81 = sz00 )
= $true )
| ( ( ( ( sdtasdt0 @ SV81 @ ( sdtasdt0 @ SV72 @ SV72 ) )
!= ( sdtasdt0 @ SV25 @ SV25 ) )
| ~ ( iLess0 @ SV25 @ xn )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( SV81
!= ( sdtasdt0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) @ ( sK5_SY81 @ SV81 @ SV72 @ SV25 ) ) )
| ~ ( aNaturalNumber0 @ ( sK5_SY81 @ SV81 @ SV72 @ SV25 ) ) )
| ~ ( aNaturalNumber0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) ) )
| ~ ( doDivides0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) @ SV81 ) )
| ~ ~ ( ~ ( ( ( sK4_W3 @ SV81 @ SV72 @ SV25 )
!= sz10 ) )
| ~ ( ( ( sK4_W3 @ SV81 @ SV72 @ SV25 )
!= SV81 ) ) ) )
| ( SV81 = sz10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[675]) ).
thf(696,plain,
! [SV82: $i,SV73: $i,SV25: $i] :
( ( ( aNaturalNumber0 @ SV25 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV73 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV82 ) )
= $true )
| ( ( SV25 = sz00 )
= $true )
| ( ( SV73 = sz00 )
= $true )
| ( ( SV82 = sz00 )
= $true )
| ( ( ( ( sdtasdt0 @ SV82 @ ( sdtasdt0 @ SV73 @ SV73 ) )
!= ( sdtasdt0 @ SV25 @ SV25 ) )
| ~ ( iLess0 @ SV25 @ xn )
| ~ ( isPrime0 @ SV82 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[676]) ).
thf(697,plain,
! [SV89: $i,SV86: $i,SV26: $i] :
( ( ( aNaturalNumber0 @ SV26 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV86 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV89 ) )
= $true )
| ( ( ( SV26 = sz00 )
| ( SV86 = SV89 )
| ~ ( sdtlseqdt0 @ SV86 @ SV89 )
| ( ( sdtasdt0 @ SV86 @ SV26 )
!= ( sdtasdt0 @ SV89 @ SV26 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[677]) ).
thf(698,plain,
! [SV95: $i,SV93: $i,SV26: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV26 )
| ~ ( aNaturalNumber0 @ SV93 )
| ~ ( aNaturalNumber0 @ SV95 ) )
= $true )
| ( ( ( SV26 = sz00 )
| ( SV93 = SV95 )
| ~ ( sdtlseqdt0 @ SV93 @ SV95 )
| ( ( sdtasdt0 @ SV26 @ SV93 )
!= ( sdtasdt0 @ SV26 @ SV95 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[678]) ).
thf(699,plain,
! [SV96: $i,SV94: $i,SV26: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV26 )
| ~ ( aNaturalNumber0 @ SV94 )
| ~ ( aNaturalNumber0 @ SV96 ) )
= $true )
| ( ( ( SV26 = sz00 )
| ( SV94 = SV96 )
| ~ ( sdtlseqdt0 @ SV94 @ SV96 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV26 @ SV94 ) @ ( sdtasdt0 @ SV26 @ SV96 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[679]) ).
thf(700,plain,
! [SV83: $i,SV74: $i,SV26: $i] :
( ( ( ( SV26 = sz00 )
| ( SV74 = SV83 )
| ~ ( sdtlseqdt0 @ SV74 @ SV83 ) )
= $true )
| ( ( sdtlseqdt0 @ ( sdtasdt0 @ SV74 @ SV26 ) @ ( sdtasdt0 @ SV83 @ SV26 ) )
= $true )
| ( ( aNaturalNumber0 @ SV74 )
= $false )
| ( ( aNaturalNumber0 @ SV26 )
= $false )
| ( ( aNaturalNumber0 @ SV83 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[680]) ).
thf(701,plain,
! [SV43: $i,SV19: $i,SV52: $i] :
( ( ( doDivides0 @ SV52 @ SV19 )
= $true )
| ( ( doDivides0 @ SV52 @ SV43 )
= $true )
| ( ( doDivides0 @ SV52 @ ( sdtasdt0 @ SV19 @ SV43 ) )
= $false )
| ( ( isPrime0 @ SV52 )
= $false )
| ( ( aNaturalNumber0 @ SV43 )
= $false )
| ( ( aNaturalNumber0 @ SV19 )
= $false )
| ( ( aNaturalNumber0 @ SV52 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[685]) ).
thf(702,plain,
! [SV44: $i,SV21: $i] :
( ( ( ~ ! [SY144: $i] :
( ~ ( aNaturalNumber0 @ SY144 )
| ( ( sdtpldt0 @ SV21 @ SY144 )
!= ( sdtpldt0 @ SV44 @ SY144 ) ) ) )
= $false )
| ( ( SV21 = SV44 )
= $true )
| ( ( sdtlseqdt0 @ SV21 @ SV44 )
= $false )
| ( ( aNaturalNumber0 @ SV21 )
= $false )
| ( ( aNaturalNumber0 @ SV44 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[686]) ).
thf(703,plain,
! [SV44: $i,SV21: $i] :
( ( ( ~ ~ ( ~ ! [SY145: $i] :
( ~ ( aNaturalNumber0 @ SY145 )
| ( ( sdtpldt0 @ SY145 @ SV21 )
!= ( sdtpldt0 @ SY145 @ SV44 ) ) )
| ~ ! [SY146: $i] :
( ~ ( aNaturalNumber0 @ SY146 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SY146 @ SV21 ) @ ( sdtpldt0 @ SY146 @ SV44 ) ) ) ) )
= $false )
| ( ( SV21 = SV44 )
= $true )
| ( ( sdtlseqdt0 @ SV21 @ SV44 )
= $false )
| ( ( aNaturalNumber0 @ SV21 )
= $false )
| ( ( aNaturalNumber0 @ SV44 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[686]) ).
thf(704,plain,
! [SV44: $i,SV21: $i,SV97: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV97 ) )
= $true )
| ( ( sdtlseqdt0 @ ( sdtpldt0 @ SV21 @ SV97 ) @ ( sdtpldt0 @ SV44 @ SV97 ) )
= $true )
| ( ( SV21 = SV44 )
= $true )
| ( ( sdtlseqdt0 @ SV21 @ SV44 )
= $false )
| ( ( aNaturalNumber0 @ SV21 )
= $false )
| ( ( aNaturalNumber0 @ SV44 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[687]) ).
thf(705,plain,
! [SV87: $i,SV84: $i,SV22: $i] :
( ( ( ( sdtasdt0 @ SV22 @ SV84 )
!= ( sdtasdt0 @ SV22 @ SV87 ) )
= $true )
| ( ( SV84 = SV87 )
= $true )
| ( ( aNaturalNumber0 @ SV84 )
= $false )
| ( ( aNaturalNumber0 @ SV87 )
= $false )
| ( ( SV22 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[688]) ).
thf(706,plain,
! [SV88: $i,SV22: $i,SV85: $i] :
( ( ( ( sdtasdt0 @ SV85 @ SV22 )
!= ( sdtasdt0 @ SV88 @ SV22 ) )
= $true )
| ( ( SV85 = SV88 )
= $true )
| ( ( aNaturalNumber0 @ SV85 )
= $false )
| ( ( aNaturalNumber0 @ SV88 )
= $false )
| ( ( SV22 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[689]) ).
thf(707,plain,
! [SV98: $i,SV91: $i] :
( ( ( ( xp
!= ( sdtasdt0 @ SV91 @ SV98 ) )
| ~ ( aNaturalNumber0 @ SV98 ) )
= $true )
| ( ( aNaturalNumber0 @ SV91 )
= $false )
| ( ( ( SV91 = sz10 )
| ( SV91 = xp ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[690]) ).
thf(708,plain,
! [SV92: $i] :
( ( ( doDivides0 @ SV92 @ xp )
= $false )
| ( ( aNaturalNumber0 @ SV92 )
= $false )
| ( ( ( SV92 = sz10 )
| ( SV92 = xp ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[691]) ).
thf(709,plain,
( ( ~ ( aNaturalNumber0 @ xn ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[692]) ).
thf(710,plain,
( ( ~ ( aNaturalNumber0 @ xm ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[692]) ).
thf(711,plain,
! [SV79: $i,SV70: $i,SV24: $i] :
( ( ( ( sdtpldt0 @ SV24 @ SV70 )
= ( sdtpldt0 @ SV24 @ SV79 ) )
= $false )
| ( ( SV70 = SV79 )
= $true )
| ( ( aNaturalNumber0 @ SV70 )
= $false )
| ( ( aNaturalNumber0 @ SV24 )
= $false )
| ( ( aNaturalNumber0 @ SV79 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[693]) ).
thf(712,plain,
! [SV80: $i,SV24: $i,SV71: $i] :
( ( ( ( sdtpldt0 @ SV71 @ SV24 )
= ( sdtpldt0 @ SV80 @ SV24 ) )
= $false )
| ( ( SV71 = SV80 )
= $true )
| ( ( aNaturalNumber0 @ SV71 )
= $false )
| ( ( aNaturalNumber0 @ SV24 )
= $false )
| ( ( aNaturalNumber0 @ SV80 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[694]) ).
thf(713,plain,
! [SV81: $i,SV25: $i,SV72: $i] :
( ( ( aNaturalNumber0 @ SV72 )
= $false )
| ( ( aNaturalNumber0 @ SV25 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV81 ) )
= $true )
| ( ( SV25 = sz00 )
= $true )
| ( ( SV72 = sz00 )
= $true )
| ( ( SV81 = sz00 )
= $true )
| ( ( ( ( sdtasdt0 @ SV81 @ ( sdtasdt0 @ SV72 @ SV72 ) )
!= ( sdtasdt0 @ SV25 @ SV25 ) )
| ~ ( iLess0 @ SV25 @ xn )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( SV81
!= ( sdtasdt0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) @ ( sK5_SY81 @ SV81 @ SV72 @ SV25 ) ) )
| ~ ( aNaturalNumber0 @ ( sK5_SY81 @ SV81 @ SV72 @ SV25 ) ) )
| ~ ( aNaturalNumber0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) ) )
| ~ ( doDivides0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) @ SV81 ) )
| ~ ~ ( ~ ( ( ( sK4_W3 @ SV81 @ SV72 @ SV25 )
!= sz10 ) )
| ~ ( ( ( sK4_W3 @ SV81 @ SV72 @ SV25 )
!= SV81 ) ) ) )
| ( SV81 = sz10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[695]) ).
thf(714,plain,
! [SV82: $i,SV25: $i,SV73: $i] :
( ( ( aNaturalNumber0 @ SV73 )
= $false )
| ( ( aNaturalNumber0 @ SV25 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV82 ) )
= $true )
| ( ( SV25 = sz00 )
= $true )
| ( ( SV73 = sz00 )
= $true )
| ( ( SV82 = sz00 )
= $true )
| ( ( ( ( sdtasdt0 @ SV82 @ ( sdtasdt0 @ SV73 @ SV73 ) )
!= ( sdtasdt0 @ SV25 @ SV25 ) )
| ~ ( iLess0 @ SV25 @ xn )
| ~ ( isPrime0 @ SV82 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[696]) ).
thf(715,plain,
! [SV89: $i,SV26: $i,SV86: $i] :
( ( ( aNaturalNumber0 @ SV86 )
= $false )
| ( ( aNaturalNumber0 @ SV26 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV89 ) )
= $true )
| ( ( ( SV26 = sz00 )
| ( SV86 = SV89 )
| ~ ( sdtlseqdt0 @ SV86 @ SV89 )
| ( ( sdtasdt0 @ SV86 @ SV26 )
!= ( sdtasdt0 @ SV89 @ SV26 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[697]) ).
thf(716,plain,
! [SV95: $i,SV93: $i,SV26: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV26 )
| ~ ( aNaturalNumber0 @ SV93 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV95 ) )
= $true )
| ( ( ( SV26 = sz00 )
| ( SV93 = SV95 )
| ~ ( sdtlseqdt0 @ SV93 @ SV95 )
| ( ( sdtasdt0 @ SV26 @ SV93 )
!= ( sdtasdt0 @ SV26 @ SV95 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[698]) ).
thf(717,plain,
! [SV96: $i,SV94: $i,SV26: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV26 )
| ~ ( aNaturalNumber0 @ SV94 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV96 ) )
= $true )
| ( ( ( SV26 = sz00 )
| ( SV94 = SV96 )
| ~ ( sdtlseqdt0 @ SV94 @ SV96 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV26 @ SV94 ) @ ( sdtasdt0 @ SV26 @ SV96 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[699]) ).
thf(718,plain,
! [SV83: $i,SV74: $i,SV26: $i] :
( ( ( ( SV26 = sz00 )
| ( SV74 = SV83 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV74 @ SV83 ) )
= $true )
| ( ( sdtlseqdt0 @ ( sdtasdt0 @ SV74 @ SV26 ) @ ( sdtasdt0 @ SV83 @ SV26 ) )
= $true )
| ( ( aNaturalNumber0 @ SV74 )
= $false )
| ( ( aNaturalNumber0 @ SV26 )
= $false )
| ( ( aNaturalNumber0 @ SV83 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[700]) ).
thf(719,plain,
! [SV44: $i,SV21: $i] :
( ( ( ! [SY144: $i] :
( ~ ( aNaturalNumber0 @ SY144 )
| ( ( sdtpldt0 @ SV21 @ SY144 )
!= ( sdtpldt0 @ SV44 @ SY144 ) ) ) )
= $true )
| ( ( SV21 = SV44 )
= $true )
| ( ( sdtlseqdt0 @ SV21 @ SV44 )
= $false )
| ( ( aNaturalNumber0 @ SV21 )
= $false )
| ( ( aNaturalNumber0 @ SV44 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[702]) ).
thf(720,plain,
! [SV44: $i,SV21: $i] :
( ( ( ~ ( ~ ! [SY145: $i] :
( ~ ( aNaturalNumber0 @ SY145 )
| ( ( sdtpldt0 @ SY145 @ SV21 )
!= ( sdtpldt0 @ SY145 @ SV44 ) ) )
| ~ ! [SY146: $i] :
( ~ ( aNaturalNumber0 @ SY146 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SY146 @ SV21 ) @ ( sdtpldt0 @ SY146 @ SV44 ) ) ) ) )
= $true )
| ( ( SV21 = SV44 )
= $true )
| ( ( sdtlseqdt0 @ SV21 @ SV44 )
= $false )
| ( ( aNaturalNumber0 @ SV21 )
= $false )
| ( ( aNaturalNumber0 @ SV44 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[703]) ).
thf(721,plain,
! [SV44: $i,SV21: $i,SV97: $i] :
( ( ( aNaturalNumber0 @ SV97 )
= $false )
| ( ( sdtlseqdt0 @ ( sdtpldt0 @ SV21 @ SV97 ) @ ( sdtpldt0 @ SV44 @ SV97 ) )
= $true )
| ( ( SV21 = SV44 )
= $true )
| ( ( sdtlseqdt0 @ SV21 @ SV44 )
= $false )
| ( ( aNaturalNumber0 @ SV21 )
= $false )
| ( ( aNaturalNumber0 @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[704]) ).
thf(722,plain,
! [SV87: $i,SV84: $i,SV22: $i] :
( ( ( ( sdtasdt0 @ SV22 @ SV84 )
= ( sdtasdt0 @ SV22 @ SV87 ) )
= $false )
| ( ( SV84 = SV87 )
= $true )
| ( ( aNaturalNumber0 @ SV84 )
= $false )
| ( ( aNaturalNumber0 @ SV87 )
= $false )
| ( ( SV22 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[705]) ).
thf(723,plain,
! [SV88: $i,SV22: $i,SV85: $i] :
( ( ( ( sdtasdt0 @ SV85 @ SV22 )
= ( sdtasdt0 @ SV88 @ SV22 ) )
= $false )
| ( ( SV85 = SV88 )
= $true )
| ( ( aNaturalNumber0 @ SV85 )
= $false )
| ( ( aNaturalNumber0 @ SV88 )
= $false )
| ( ( SV22 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[706]) ).
thf(724,plain,
! [SV98: $i,SV91: $i] :
( ( ( xp
!= ( sdtasdt0 @ SV91 @ SV98 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV98 ) )
= $true )
| ( ( aNaturalNumber0 @ SV91 )
= $false )
| ( ( ( SV91 = sz10 )
| ( SV91 = xp ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[707]) ).
thf(725,plain,
! [SV92: $i] :
( ( ( SV92 = sz10 )
= $true )
| ( ( SV92 = xp )
= $true )
| ( ( aNaturalNumber0 @ SV92 )
= $false )
| ( ( doDivides0 @ SV92 @ xp )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[708]) ).
thf(726,plain,
( ( aNaturalNumber0 @ xn )
= $true ),
inference(extcnf_not_neg,[status(thm)],[709]) ).
thf(727,plain,
( ( aNaturalNumber0 @ xm )
= $true ),
inference(extcnf_not_neg,[status(thm)],[710]) ).
thf(728,plain,
! [SV72: $i,SV25: $i,SV81: $i] :
( ( ( aNaturalNumber0 @ SV81 )
= $false )
| ( ( aNaturalNumber0 @ SV25 )
= $false )
| ( ( aNaturalNumber0 @ SV72 )
= $false )
| ( ( SV25 = sz00 )
= $true )
| ( ( SV72 = sz00 )
= $true )
| ( ( SV81 = sz00 )
= $true )
| ( ( ( ( sdtasdt0 @ SV81 @ ( sdtasdt0 @ SV72 @ SV72 ) )
!= ( sdtasdt0 @ SV25 @ SV25 ) )
| ~ ( iLess0 @ SV25 @ xn )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( SV81
!= ( sdtasdt0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) @ ( sK5_SY81 @ SV81 @ SV72 @ SV25 ) ) )
| ~ ( aNaturalNumber0 @ ( sK5_SY81 @ SV81 @ SV72 @ SV25 ) ) )
| ~ ( aNaturalNumber0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) ) )
| ~ ( doDivides0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) @ SV81 ) )
| ~ ~ ( ~ ( ( ( sK4_W3 @ SV81 @ SV72 @ SV25 )
!= sz10 ) )
| ~ ( ( ( sK4_W3 @ SV81 @ SV72 @ SV25 )
!= SV81 ) ) ) )
| ( SV81 = sz10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[713]) ).
thf(729,plain,
! [SV73: $i,SV25: $i,SV82: $i] :
( ( ( aNaturalNumber0 @ SV82 )
= $false )
| ( ( aNaturalNumber0 @ SV25 )
= $false )
| ( ( aNaturalNumber0 @ SV73 )
= $false )
| ( ( SV25 = sz00 )
= $true )
| ( ( SV73 = sz00 )
= $true )
| ( ( SV82 = sz00 )
= $true )
| ( ( ( ( sdtasdt0 @ SV82 @ ( sdtasdt0 @ SV73 @ SV73 ) )
!= ( sdtasdt0 @ SV25 @ SV25 ) )
| ~ ( iLess0 @ SV25 @ xn )
| ~ ( isPrime0 @ SV82 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[714]) ).
thf(730,plain,
! [SV86: $i,SV26: $i,SV89: $i] :
( ( ( aNaturalNumber0 @ SV89 )
= $false )
| ( ( aNaturalNumber0 @ SV26 )
= $false )
| ( ( aNaturalNumber0 @ SV86 )
= $false )
| ( ( ( SV26 = sz00 )
| ( SV86 = SV89 )
| ~ ( sdtlseqdt0 @ SV86 @ SV89 )
| ( ( sdtasdt0 @ SV86 @ SV26 )
!= ( sdtasdt0 @ SV89 @ SV26 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[715]) ).
thf(731,plain,
! [SV95: $i,SV93: $i,SV26: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV26 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV93 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV95 ) )
= $true )
| ( ( ( SV26 = sz00 )
| ( SV93 = SV95 )
| ~ ( sdtlseqdt0 @ SV93 @ SV95 )
| ( ( sdtasdt0 @ SV26 @ SV93 )
!= ( sdtasdt0 @ SV26 @ SV95 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[716]) ).
thf(732,plain,
! [SV96: $i,SV94: $i,SV26: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV26 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV94 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV96 ) )
= $true )
| ( ( ( SV26 = sz00 )
| ( SV94 = SV96 )
| ~ ( sdtlseqdt0 @ SV94 @ SV96 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV26 @ SV94 ) @ ( sdtasdt0 @ SV26 @ SV96 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[717]) ).
thf(733,plain,
! [SV83: $i,SV74: $i,SV26: $i] :
( ( ( SV26 = sz00 )
= $true )
| ( ( SV74 = SV83 )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV74 @ SV83 ) )
= $true )
| ( ( sdtlseqdt0 @ ( sdtasdt0 @ SV74 @ SV26 ) @ ( sdtasdt0 @ SV83 @ SV26 ) )
= $true )
| ( ( aNaturalNumber0 @ SV74 )
= $false )
| ( ( aNaturalNumber0 @ SV26 )
= $false )
| ( ( aNaturalNumber0 @ SV83 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[718]) ).
thf(734,plain,
! [SV44: $i,SV21: $i,SV99: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV99 )
| ( ( sdtpldt0 @ SV21 @ SV99 )
!= ( sdtpldt0 @ SV44 @ SV99 ) ) )
= $true )
| ( ( SV21 = SV44 )
= $true )
| ( ( sdtlseqdt0 @ SV21 @ SV44 )
= $false )
| ( ( aNaturalNumber0 @ SV21 )
= $false )
| ( ( aNaturalNumber0 @ SV44 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[719]) ).
thf(735,plain,
! [SV44: $i,SV21: $i] :
( ( ( ~ ! [SY145: $i] :
( ~ ( aNaturalNumber0 @ SY145 )
| ( ( sdtpldt0 @ SY145 @ SV21 )
!= ( sdtpldt0 @ SY145 @ SV44 ) ) )
| ~ ! [SY146: $i] :
( ~ ( aNaturalNumber0 @ SY146 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SY146 @ SV21 ) @ ( sdtpldt0 @ SY146 @ SV44 ) ) ) )
= $false )
| ( ( SV21 = SV44 )
= $true )
| ( ( sdtlseqdt0 @ SV21 @ SV44 )
= $false )
| ( ( aNaturalNumber0 @ SV21 )
= $false )
| ( ( aNaturalNumber0 @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[720]) ).
thf(736,plain,
! [SV98: $i,SV91: $i] :
( ( ( xp
= ( sdtasdt0 @ SV91 @ SV98 ) )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV98 ) )
= $true )
| ( ( aNaturalNumber0 @ SV91 )
= $false )
| ( ( ( SV91 = sz10 )
| ( SV91 = xp ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[724]) ).
thf(737,plain,
! [SV25: $i,SV72: $i,SV81: $i] :
( ( ( ( sdtasdt0 @ SV81 @ ( sdtasdt0 @ SV72 @ SV72 ) )
!= ( sdtasdt0 @ SV25 @ SV25 ) )
= $true )
| ( ( ~ ( iLess0 @ SV25 @ xn )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( SV81
!= ( sdtasdt0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) @ ( sK5_SY81 @ SV81 @ SV72 @ SV25 ) ) )
| ~ ( aNaturalNumber0 @ ( sK5_SY81 @ SV81 @ SV72 @ SV25 ) ) )
| ~ ( aNaturalNumber0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) ) )
| ~ ( doDivides0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) @ SV81 ) )
| ~ ~ ( ~ ( ( ( sK4_W3 @ SV81 @ SV72 @ SV25 )
!= sz10 ) )
| ~ ( ( ( sK4_W3 @ SV81 @ SV72 @ SV25 )
!= SV81 ) ) ) )
| ( SV81 = sz10 ) )
= $true )
| ( ( SV81 = sz00 )
= $true )
| ( ( SV72 = sz00 )
= $true )
| ( ( SV25 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV72 )
= $false )
| ( ( aNaturalNumber0 @ SV25 )
= $false )
| ( ( aNaturalNumber0 @ SV81 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[728]) ).
thf(738,plain,
! [SV25: $i,SV73: $i,SV82: $i] :
( ( ( ( sdtasdt0 @ SV82 @ ( sdtasdt0 @ SV73 @ SV73 ) )
!= ( sdtasdt0 @ SV25 @ SV25 ) )
= $true )
| ( ( ~ ( iLess0 @ SV25 @ xn )
| ~ ( isPrime0 @ SV82 ) )
= $true )
| ( ( SV82 = sz00 )
= $true )
| ( ( SV73 = sz00 )
= $true )
| ( ( SV25 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV73 )
= $false )
| ( ( aNaturalNumber0 @ SV25 )
= $false )
| ( ( aNaturalNumber0 @ SV82 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[729]) ).
thf(739,plain,
! [SV89: $i,SV86: $i,SV26: $i] :
( ( ( ( SV26 = sz00 )
| ( SV86 = SV89 )
| ~ ( sdtlseqdt0 @ SV86 @ SV89 ) )
= $true )
| ( ( ( sdtasdt0 @ SV86 @ SV26 )
!= ( sdtasdt0 @ SV89 @ SV26 ) )
= $true )
| ( ( aNaturalNumber0 @ SV86 )
= $false )
| ( ( aNaturalNumber0 @ SV26 )
= $false )
| ( ( aNaturalNumber0 @ SV89 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[730]) ).
thf(740,plain,
! [SV95: $i,SV93: $i,SV26: $i] :
( ( ( aNaturalNumber0 @ SV26 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV93 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV95 ) )
= $true )
| ( ( ( SV26 = sz00 )
| ( SV93 = SV95 )
| ~ ( sdtlseqdt0 @ SV93 @ SV95 )
| ( ( sdtasdt0 @ SV26 @ SV93 )
!= ( sdtasdt0 @ SV26 @ SV95 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[731]) ).
thf(741,plain,
! [SV96: $i,SV94: $i,SV26: $i] :
( ( ( aNaturalNumber0 @ SV26 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV94 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV96 ) )
= $true )
| ( ( ( SV26 = sz00 )
| ( SV94 = SV96 )
| ~ ( sdtlseqdt0 @ SV94 @ SV96 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV26 @ SV94 ) @ ( sdtasdt0 @ SV26 @ SV96 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[732]) ).
thf(742,plain,
! [SV26: $i,SV83: $i,SV74: $i] :
( ( ( sdtlseqdt0 @ SV74 @ SV83 )
= $false )
| ( ( SV74 = SV83 )
= $true )
| ( ( SV26 = sz00 )
= $true )
| ( ( sdtlseqdt0 @ ( sdtasdt0 @ SV74 @ SV26 ) @ ( sdtasdt0 @ SV83 @ SV26 ) )
= $true )
| ( ( aNaturalNumber0 @ SV74 )
= $false )
| ( ( aNaturalNumber0 @ SV26 )
= $false )
| ( ( aNaturalNumber0 @ SV83 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[733]) ).
thf(743,plain,
! [SV44: $i,SV21: $i,SV99: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV99 ) )
= $true )
| ( ( ( sdtpldt0 @ SV21 @ SV99 )
!= ( sdtpldt0 @ SV44 @ SV99 ) )
= $true )
| ( ( SV21 = SV44 )
= $true )
| ( ( sdtlseqdt0 @ SV21 @ SV44 )
= $false )
| ( ( aNaturalNumber0 @ SV21 )
= $false )
| ( ( aNaturalNumber0 @ SV44 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[734]) ).
thf(744,plain,
! [SV44: $i,SV21: $i] :
( ( ( ~ ! [SY145: $i] :
( ~ ( aNaturalNumber0 @ SY145 )
| ( ( sdtpldt0 @ SY145 @ SV21 )
!= ( sdtpldt0 @ SY145 @ SV44 ) ) ) )
= $false )
| ( ( SV21 = SV44 )
= $true )
| ( ( sdtlseqdt0 @ SV21 @ SV44 )
= $false )
| ( ( aNaturalNumber0 @ SV21 )
= $false )
| ( ( aNaturalNumber0 @ SV44 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[735]) ).
thf(745,plain,
! [SV44: $i,SV21: $i] :
( ( ( ~ ! [SY146: $i] :
( ~ ( aNaturalNumber0 @ SY146 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SY146 @ SV21 ) @ ( sdtpldt0 @ SY146 @ SV44 ) ) ) )
= $false )
| ( ( SV21 = SV44 )
= $true )
| ( ( sdtlseqdt0 @ SV21 @ SV44 )
= $false )
| ( ( aNaturalNumber0 @ SV21 )
= $false )
| ( ( aNaturalNumber0 @ SV44 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[735]) ).
thf(746,plain,
! [SV91: $i,SV98: $i] :
( ( ( aNaturalNumber0 @ SV98 )
= $false )
| ( ( xp
= ( sdtasdt0 @ SV91 @ SV98 ) )
= $false )
| ( ( aNaturalNumber0 @ SV91 )
= $false )
| ( ( ( SV91 = sz10 )
| ( SV91 = xp ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[736]) ).
thf(747,plain,
! [SV25: $i,SV72: $i,SV81: $i] :
( ( ( ( sdtasdt0 @ SV81 @ ( sdtasdt0 @ SV72 @ SV72 ) )
= ( sdtasdt0 @ SV25 @ SV25 ) )
= $false )
| ( ( ~ ( iLess0 @ SV25 @ xn )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( SV81
!= ( sdtasdt0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) @ ( sK5_SY81 @ SV81 @ SV72 @ SV25 ) ) )
| ~ ( aNaturalNumber0 @ ( sK5_SY81 @ SV81 @ SV72 @ SV25 ) ) )
| ~ ( aNaturalNumber0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) ) )
| ~ ( doDivides0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) @ SV81 ) )
| ~ ~ ( ~ ( ( ( sK4_W3 @ SV81 @ SV72 @ SV25 )
!= sz10 ) )
| ~ ( ( ( sK4_W3 @ SV81 @ SV72 @ SV25 )
!= SV81 ) ) ) )
| ( SV81 = sz10 ) )
= $true )
| ( ( SV81 = sz00 )
= $true )
| ( ( SV72 = sz00 )
= $true )
| ( ( SV25 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV72 )
= $false )
| ( ( aNaturalNumber0 @ SV25 )
= $false )
| ( ( aNaturalNumber0 @ SV81 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[737]) ).
thf(748,plain,
! [SV25: $i,SV73: $i,SV82: $i] :
( ( ( ( sdtasdt0 @ SV82 @ ( sdtasdt0 @ SV73 @ SV73 ) )
= ( sdtasdt0 @ SV25 @ SV25 ) )
= $false )
| ( ( ~ ( iLess0 @ SV25 @ xn )
| ~ ( isPrime0 @ SV82 ) )
= $true )
| ( ( SV82 = sz00 )
= $true )
| ( ( SV73 = sz00 )
= $true )
| ( ( SV25 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV73 )
= $false )
| ( ( aNaturalNumber0 @ SV25 )
= $false )
| ( ( aNaturalNumber0 @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[738]) ).
thf(749,plain,
! [SV89: $i,SV86: $i,SV26: $i] :
( ( ( ( SV26 = sz00 )
| ( SV86 = SV89 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV86 @ SV89 ) )
= $true )
| ( ( ( sdtasdt0 @ SV86 @ SV26 )
!= ( sdtasdt0 @ SV89 @ SV26 ) )
= $true )
| ( ( aNaturalNumber0 @ SV86 )
= $false )
| ( ( aNaturalNumber0 @ SV26 )
= $false )
| ( ( aNaturalNumber0 @ SV89 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[739]) ).
thf(750,plain,
! [SV95: $i,SV26: $i,SV93: $i] :
( ( ( aNaturalNumber0 @ SV93 )
= $false )
| ( ( aNaturalNumber0 @ SV26 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV95 ) )
= $true )
| ( ( ( SV26 = sz00 )
| ( SV93 = SV95 )
| ~ ( sdtlseqdt0 @ SV93 @ SV95 )
| ( ( sdtasdt0 @ SV26 @ SV93 )
!= ( sdtasdt0 @ SV26 @ SV95 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[740]) ).
thf(751,plain,
! [SV96: $i,SV26: $i,SV94: $i] :
( ( ( aNaturalNumber0 @ SV94 )
= $false )
| ( ( aNaturalNumber0 @ SV26 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV96 ) )
= $true )
| ( ( ( SV26 = sz00 )
| ( SV94 = SV96 )
| ~ ( sdtlseqdt0 @ SV94 @ SV96 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV26 @ SV94 ) @ ( sdtasdt0 @ SV26 @ SV96 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[741]) ).
thf(752,plain,
! [SV44: $i,SV21: $i,SV99: $i] :
( ( ( aNaturalNumber0 @ SV99 )
= $false )
| ( ( ( sdtpldt0 @ SV21 @ SV99 )
!= ( sdtpldt0 @ SV44 @ SV99 ) )
= $true )
| ( ( SV21 = SV44 )
= $true )
| ( ( sdtlseqdt0 @ SV21 @ SV44 )
= $false )
| ( ( aNaturalNumber0 @ SV21 )
= $false )
| ( ( aNaturalNumber0 @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[743]) ).
thf(753,plain,
! [SV44: $i,SV21: $i] :
( ( ( ! [SY145: $i] :
( ~ ( aNaturalNumber0 @ SY145 )
| ( ( sdtpldt0 @ SY145 @ SV21 )
!= ( sdtpldt0 @ SY145 @ SV44 ) ) ) )
= $true )
| ( ( SV21 = SV44 )
= $true )
| ( ( sdtlseqdt0 @ SV21 @ SV44 )
= $false )
| ( ( aNaturalNumber0 @ SV21 )
= $false )
| ( ( aNaturalNumber0 @ SV44 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[744]) ).
thf(754,plain,
! [SV44: $i,SV21: $i] :
( ( ( ! [SY146: $i] :
( ~ ( aNaturalNumber0 @ SY146 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SY146 @ SV21 ) @ ( sdtpldt0 @ SY146 @ SV44 ) ) ) )
= $true )
| ( ( SV21 = SV44 )
= $true )
| ( ( sdtlseqdt0 @ SV21 @ SV44 )
= $false )
| ( ( aNaturalNumber0 @ SV21 )
= $false )
| ( ( aNaturalNumber0 @ SV44 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[745]) ).
thf(755,plain,
! [SV98: $i,SV91: $i] :
( ( ( SV91 = sz10 )
= $true )
| ( ( SV91 = xp )
= $true )
| ( ( aNaturalNumber0 @ SV91 )
= $false )
| ( ( xp
= ( sdtasdt0 @ SV91 @ SV98 ) )
= $false )
| ( ( aNaturalNumber0 @ SV98 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[746]) ).
thf(756,plain,
! [SV72: $i,SV81: $i,SV25: $i] :
( ( ( ~ ( iLess0 @ SV25 @ xn ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( SV81
!= ( sdtasdt0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) @ ( sK5_SY81 @ SV81 @ SV72 @ SV25 ) ) )
| ~ ( aNaturalNumber0 @ ( sK5_SY81 @ SV81 @ SV72 @ SV25 ) ) )
| ~ ( aNaturalNumber0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) ) )
| ~ ( doDivides0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) @ SV81 ) )
| ~ ~ ( ~ ( ( ( sK4_W3 @ SV81 @ SV72 @ SV25 )
!= sz10 ) )
| ~ ( ( ( sK4_W3 @ SV81 @ SV72 @ SV25 )
!= SV81 ) ) ) )
| ( SV81 = sz10 ) )
= $true )
| ( ( ( sdtasdt0 @ SV81 @ ( sdtasdt0 @ SV72 @ SV72 ) )
= ( sdtasdt0 @ SV25 @ SV25 ) )
= $false )
| ( ( SV81 = sz00 )
= $true )
| ( ( SV72 = sz00 )
= $true )
| ( ( SV25 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV72 )
= $false )
| ( ( aNaturalNumber0 @ SV25 )
= $false )
| ( ( aNaturalNumber0 @ SV81 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[747]) ).
thf(757,plain,
! [SV73: $i,SV82: $i,SV25: $i] :
( ( ( ~ ( iLess0 @ SV25 @ xn ) )
= $true )
| ( ( ~ ( isPrime0 @ SV82 ) )
= $true )
| ( ( ( sdtasdt0 @ SV82 @ ( sdtasdt0 @ SV73 @ SV73 ) )
= ( sdtasdt0 @ SV25 @ SV25 ) )
= $false )
| ( ( SV82 = sz00 )
= $true )
| ( ( SV73 = sz00 )
= $true )
| ( ( SV25 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV73 )
= $false )
| ( ( aNaturalNumber0 @ SV25 )
= $false )
| ( ( aNaturalNumber0 @ SV82 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[748]) ).
thf(758,plain,
! [SV89: $i,SV86: $i,SV26: $i] :
( ( ( SV26 = sz00 )
= $true )
| ( ( SV86 = SV89 )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV86 @ SV89 ) )
= $true )
| ( ( ( sdtasdt0 @ SV86 @ SV26 )
!= ( sdtasdt0 @ SV89 @ SV26 ) )
= $true )
| ( ( aNaturalNumber0 @ SV86 )
= $false )
| ( ( aNaturalNumber0 @ SV26 )
= $false )
| ( ( aNaturalNumber0 @ SV89 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[749]) ).
thf(759,plain,
! [SV93: $i,SV26: $i,SV95: $i] :
( ( ( aNaturalNumber0 @ SV95 )
= $false )
| ( ( aNaturalNumber0 @ SV26 )
= $false )
| ( ( aNaturalNumber0 @ SV93 )
= $false )
| ( ( ( SV26 = sz00 )
| ( SV93 = SV95 )
| ~ ( sdtlseqdt0 @ SV93 @ SV95 )
| ( ( sdtasdt0 @ SV26 @ SV93 )
!= ( sdtasdt0 @ SV26 @ SV95 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[750]) ).
thf(760,plain,
! [SV94: $i,SV26: $i,SV96: $i] :
( ( ( aNaturalNumber0 @ SV96 )
= $false )
| ( ( aNaturalNumber0 @ SV26 )
= $false )
| ( ( aNaturalNumber0 @ SV94 )
= $false )
| ( ( ( SV26 = sz00 )
| ( SV94 = SV96 )
| ~ ( sdtlseqdt0 @ SV94 @ SV96 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV26 @ SV94 ) @ ( sdtasdt0 @ SV26 @ SV96 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[751]) ).
thf(761,plain,
! [SV44: $i,SV99: $i,SV21: $i] :
( ( ( ( sdtpldt0 @ SV21 @ SV99 )
= ( sdtpldt0 @ SV44 @ SV99 ) )
= $false )
| ( ( aNaturalNumber0 @ SV99 )
= $false )
| ( ( SV21 = SV44 )
= $true )
| ( ( sdtlseqdt0 @ SV21 @ SV44 )
= $false )
| ( ( aNaturalNumber0 @ SV21 )
= $false )
| ( ( aNaturalNumber0 @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[752]) ).
thf(762,plain,
! [SV44: $i,SV21: $i,SV100: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV100 )
| ( ( sdtpldt0 @ SV100 @ SV21 )
!= ( sdtpldt0 @ SV100 @ SV44 ) ) )
= $true )
| ( ( SV21 = SV44 )
= $true )
| ( ( sdtlseqdt0 @ SV21 @ SV44 )
= $false )
| ( ( aNaturalNumber0 @ SV21 )
= $false )
| ( ( aNaturalNumber0 @ SV44 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[753]) ).
thf(763,plain,
! [SV44: $i,SV21: $i,SV101: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV101 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SV101 @ SV21 ) @ ( sdtpldt0 @ SV101 @ SV44 ) ) )
= $true )
| ( ( SV21 = SV44 )
= $true )
| ( ( sdtlseqdt0 @ SV21 @ SV44 )
= $false )
| ( ( aNaturalNumber0 @ SV21 )
= $false )
| ( ( aNaturalNumber0 @ SV44 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[754]) ).
thf(764,plain,
! [SV72: $i,SV81: $i,SV25: $i] :
( ( ( iLess0 @ SV25 @ xn )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( SV81
!= ( sdtasdt0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) @ ( sK5_SY81 @ SV81 @ SV72 @ SV25 ) ) )
| ~ ( aNaturalNumber0 @ ( sK5_SY81 @ SV81 @ SV72 @ SV25 ) ) )
| ~ ( aNaturalNumber0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) ) )
| ~ ( doDivides0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) @ SV81 ) )
| ~ ~ ( ~ ( ( ( sK4_W3 @ SV81 @ SV72 @ SV25 )
!= sz10 ) )
| ~ ( ( ( sK4_W3 @ SV81 @ SV72 @ SV25 )
!= SV81 ) ) ) )
| ( SV81 = sz10 ) )
= $true )
| ( ( ( sdtasdt0 @ SV81 @ ( sdtasdt0 @ SV72 @ SV72 ) )
= ( sdtasdt0 @ SV25 @ SV25 ) )
= $false )
| ( ( SV81 = sz00 )
= $true )
| ( ( SV72 = sz00 )
= $true )
| ( ( SV25 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV72 )
= $false )
| ( ( aNaturalNumber0 @ SV25 )
= $false )
| ( ( aNaturalNumber0 @ SV81 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[756]) ).
thf(765,plain,
! [SV73: $i,SV82: $i,SV25: $i] :
( ( ( iLess0 @ SV25 @ xn )
= $false )
| ( ( ~ ( isPrime0 @ SV82 ) )
= $true )
| ( ( ( sdtasdt0 @ SV82 @ ( sdtasdt0 @ SV73 @ SV73 ) )
= ( sdtasdt0 @ SV25 @ SV25 ) )
= $false )
| ( ( SV82 = sz00 )
= $true )
| ( ( SV73 = sz00 )
= $true )
| ( ( SV25 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV73 )
= $false )
| ( ( aNaturalNumber0 @ SV25 )
= $false )
| ( ( aNaturalNumber0 @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[757]) ).
thf(766,plain,
! [SV26: $i,SV89: $i,SV86: $i] :
( ( ( sdtlseqdt0 @ SV86 @ SV89 )
= $false )
| ( ( SV86 = SV89 )
= $true )
| ( ( SV26 = sz00 )
= $true )
| ( ( ( sdtasdt0 @ SV86 @ SV26 )
!= ( sdtasdt0 @ SV89 @ SV26 ) )
= $true )
| ( ( aNaturalNumber0 @ SV86 )
= $false )
| ( ( aNaturalNumber0 @ SV26 )
= $false )
| ( ( aNaturalNumber0 @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[758]) ).
thf(767,plain,
! [SV95: $i,SV93: $i,SV26: $i] :
( ( ( ( SV26 = sz00 )
| ( SV93 = SV95 )
| ~ ( sdtlseqdt0 @ SV93 @ SV95 ) )
= $true )
| ( ( ( sdtasdt0 @ SV26 @ SV93 )
!= ( sdtasdt0 @ SV26 @ SV95 ) )
= $true )
| ( ( aNaturalNumber0 @ SV93 )
= $false )
| ( ( aNaturalNumber0 @ SV26 )
= $false )
| ( ( aNaturalNumber0 @ SV95 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[759]) ).
thf(768,plain,
! [SV96: $i,SV94: $i,SV26: $i] :
( ( ( ( SV26 = sz00 )
| ( SV94 = SV96 )
| ~ ( sdtlseqdt0 @ SV94 @ SV96 ) )
= $true )
| ( ( sdtlseqdt0 @ ( sdtasdt0 @ SV26 @ SV94 ) @ ( sdtasdt0 @ SV26 @ SV96 ) )
= $true )
| ( ( aNaturalNumber0 @ SV94 )
= $false )
| ( ( aNaturalNumber0 @ SV26 )
= $false )
| ( ( aNaturalNumber0 @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[760]) ).
thf(769,plain,
! [SV44: $i,SV21: $i,SV100: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV100 ) )
= $true )
| ( ( ( sdtpldt0 @ SV100 @ SV21 )
!= ( sdtpldt0 @ SV100 @ SV44 ) )
= $true )
| ( ( SV21 = SV44 )
= $true )
| ( ( sdtlseqdt0 @ SV21 @ SV44 )
= $false )
| ( ( aNaturalNumber0 @ SV21 )
= $false )
| ( ( aNaturalNumber0 @ SV44 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[762]) ).
thf(770,plain,
! [SV44: $i,SV21: $i,SV101: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV101 ) )
= $true )
| ( ( sdtlseqdt0 @ ( sdtpldt0 @ SV101 @ SV21 ) @ ( sdtpldt0 @ SV101 @ SV44 ) )
= $true )
| ( ( SV21 = SV44 )
= $true )
| ( ( sdtlseqdt0 @ SV21 @ SV44 )
= $false )
| ( ( aNaturalNumber0 @ SV21 )
= $false )
| ( ( aNaturalNumber0 @ SV44 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[763]) ).
thf(771,plain,
! [SV25: $i,SV72: $i,SV81: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( SV81
!= ( sdtasdt0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) @ ( sK5_SY81 @ SV81 @ SV72 @ SV25 ) ) )
| ~ ( aNaturalNumber0 @ ( sK5_SY81 @ SV81 @ SV72 @ SV25 ) ) )
| ~ ( aNaturalNumber0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) ) )
| ~ ( doDivides0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) @ SV81 ) )
| ~ ~ ( ~ ( ( ( sK4_W3 @ SV81 @ SV72 @ SV25 )
!= sz10 ) )
| ~ ( ( ( sK4_W3 @ SV81 @ SV72 @ SV25 )
!= SV81 ) ) ) ) )
= $true )
| ( ( SV81 = sz10 )
= $true )
| ( ( iLess0 @ SV25 @ xn )
= $false )
| ( ( ( sdtasdt0 @ SV81 @ ( sdtasdt0 @ SV72 @ SV72 ) )
= ( sdtasdt0 @ SV25 @ SV25 ) )
= $false )
| ( ( SV81 = sz00 )
= $true )
| ( ( SV72 = sz00 )
= $true )
| ( ( SV25 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV72 )
= $false )
| ( ( aNaturalNumber0 @ SV25 )
= $false )
| ( ( aNaturalNumber0 @ SV81 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[764]) ).
thf(772,plain,
! [SV73: $i,SV25: $i,SV82: $i] :
( ( ( isPrime0 @ SV82 )
= $false )
| ( ( iLess0 @ SV25 @ xn )
= $false )
| ( ( ( sdtasdt0 @ SV82 @ ( sdtasdt0 @ SV73 @ SV73 ) )
= ( sdtasdt0 @ SV25 @ SV25 ) )
= $false )
| ( ( SV82 = sz00 )
= $true )
| ( ( SV73 = sz00 )
= $true )
| ( ( SV25 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV73 )
= $false )
| ( ( aNaturalNumber0 @ SV25 )
= $false )
| ( ( aNaturalNumber0 @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[765]) ).
thf(773,plain,
! [SV89: $i,SV26: $i,SV86: $i] :
( ( ( ( sdtasdt0 @ SV86 @ SV26 )
= ( sdtasdt0 @ SV89 @ SV26 ) )
= $false )
| ( ( SV26 = sz00 )
= $true )
| ( ( SV86 = SV89 )
= $true )
| ( ( sdtlseqdt0 @ SV86 @ SV89 )
= $false )
| ( ( aNaturalNumber0 @ SV86 )
= $false )
| ( ( aNaturalNumber0 @ SV26 )
= $false )
| ( ( aNaturalNumber0 @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[766]) ).
thf(774,plain,
! [SV95: $i,SV93: $i,SV26: $i] :
( ( ( ( SV26 = sz00 )
| ( SV93 = SV95 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV93 @ SV95 ) )
= $true )
| ( ( ( sdtasdt0 @ SV26 @ SV93 )
!= ( sdtasdt0 @ SV26 @ SV95 ) )
= $true )
| ( ( aNaturalNumber0 @ SV93 )
= $false )
| ( ( aNaturalNumber0 @ SV26 )
= $false )
| ( ( aNaturalNumber0 @ SV95 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[767]) ).
thf(775,plain,
! [SV96: $i,SV94: $i,SV26: $i] :
( ( ( ( SV26 = sz00 )
| ( SV94 = SV96 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV94 @ SV96 ) )
= $true )
| ( ( sdtlseqdt0 @ ( sdtasdt0 @ SV26 @ SV94 ) @ ( sdtasdt0 @ SV26 @ SV96 ) )
= $true )
| ( ( aNaturalNumber0 @ SV94 )
= $false )
| ( ( aNaturalNumber0 @ SV26 )
= $false )
| ( ( aNaturalNumber0 @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[768]) ).
thf(776,plain,
! [SV44: $i,SV21: $i,SV100: $i] :
( ( ( aNaturalNumber0 @ SV100 )
= $false )
| ( ( ( sdtpldt0 @ SV100 @ SV21 )
!= ( sdtpldt0 @ SV100 @ SV44 ) )
= $true )
| ( ( SV21 = SV44 )
= $true )
| ( ( sdtlseqdt0 @ SV21 @ SV44 )
= $false )
| ( ( aNaturalNumber0 @ SV21 )
= $false )
| ( ( aNaturalNumber0 @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[769]) ).
thf(777,plain,
! [SV44: $i,SV21: $i,SV101: $i] :
( ( ( aNaturalNumber0 @ SV101 )
= $false )
| ( ( sdtlseqdt0 @ ( sdtpldt0 @ SV101 @ SV21 ) @ ( sdtpldt0 @ SV101 @ SV44 ) )
= $true )
| ( ( SV21 = SV44 )
= $true )
| ( ( sdtlseqdt0 @ SV21 @ SV44 )
= $false )
| ( ( aNaturalNumber0 @ SV21 )
= $false )
| ( ( aNaturalNumber0 @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[770]) ).
thf(778,plain,
! [SV25: $i,SV72: $i,SV81: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ( SV81
!= ( sdtasdt0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) @ ( sK5_SY81 @ SV81 @ SV72 @ SV25 ) ) )
| ~ ( aNaturalNumber0 @ ( sK5_SY81 @ SV81 @ SV72 @ SV25 ) ) )
| ~ ( aNaturalNumber0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) ) )
| ~ ( doDivides0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) @ SV81 ) )
| ~ ~ ( ~ ( ( ( sK4_W3 @ SV81 @ SV72 @ SV25 )
!= sz10 ) )
| ~ ( ( ( sK4_W3 @ SV81 @ SV72 @ SV25 )
!= SV81 ) ) ) )
= $false )
| ( ( SV81 = sz10 )
= $true )
| ( ( iLess0 @ SV25 @ xn )
= $false )
| ( ( ( sdtasdt0 @ SV81 @ ( sdtasdt0 @ SV72 @ SV72 ) )
= ( sdtasdt0 @ SV25 @ SV25 ) )
= $false )
| ( ( SV81 = sz00 )
= $true )
| ( ( SV72 = sz00 )
= $true )
| ( ( SV25 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV72 )
= $false )
| ( ( aNaturalNumber0 @ SV25 )
= $false )
| ( ( aNaturalNumber0 @ SV81 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[771]) ).
thf(779,plain,
! [SV95: $i,SV93: $i,SV26: $i] :
( ( ( SV26 = sz00 )
= $true )
| ( ( SV93 = SV95 )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV93 @ SV95 ) )
= $true )
| ( ( ( sdtasdt0 @ SV26 @ SV93 )
!= ( sdtasdt0 @ SV26 @ SV95 ) )
= $true )
| ( ( aNaturalNumber0 @ SV93 )
= $false )
| ( ( aNaturalNumber0 @ SV26 )
= $false )
| ( ( aNaturalNumber0 @ SV95 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[774]) ).
thf(780,plain,
! [SV96: $i,SV94: $i,SV26: $i] :
( ( ( SV26 = sz00 )
= $true )
| ( ( SV94 = SV96 )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV94 @ SV96 ) )
= $true )
| ( ( sdtlseqdt0 @ ( sdtasdt0 @ SV26 @ SV94 ) @ ( sdtasdt0 @ SV26 @ SV96 ) )
= $true )
| ( ( aNaturalNumber0 @ SV94 )
= $false )
| ( ( aNaturalNumber0 @ SV26 )
= $false )
| ( ( aNaturalNumber0 @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[775]) ).
thf(781,plain,
! [SV44: $i,SV21: $i,SV100: $i] :
( ( ( ( sdtpldt0 @ SV100 @ SV21 )
= ( sdtpldt0 @ SV100 @ SV44 ) )
= $false )
| ( ( aNaturalNumber0 @ SV100 )
= $false )
| ( ( SV21 = SV44 )
= $true )
| ( ( sdtlseqdt0 @ SV21 @ SV44 )
= $false )
| ( ( aNaturalNumber0 @ SV21 )
= $false )
| ( ( aNaturalNumber0 @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[776]) ).
thf(782,plain,
! [SV25: $i,SV72: $i,SV81: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ( SV81
!= ( sdtasdt0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) @ ( sK5_SY81 @ SV81 @ SV72 @ SV25 ) ) )
| ~ ( aNaturalNumber0 @ ( sK5_SY81 @ SV81 @ SV72 @ SV25 ) ) )
| ~ ( aNaturalNumber0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) ) )
| ~ ( doDivides0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) @ SV81 ) ) )
= $false )
| ( ( SV81 = sz10 )
= $true )
| ( ( iLess0 @ SV25 @ xn )
= $false )
| ( ( ( sdtasdt0 @ SV81 @ ( sdtasdt0 @ SV72 @ SV72 ) )
= ( sdtasdt0 @ SV25 @ SV25 ) )
= $false )
| ( ( SV81 = sz00 )
= $true )
| ( ( SV72 = sz00 )
= $true )
| ( ( SV25 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV72 )
= $false )
| ( ( aNaturalNumber0 @ SV25 )
= $false )
| ( ( aNaturalNumber0 @ SV81 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[778]) ).
thf(783,plain,
! [SV25: $i,SV72: $i,SV81: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK4_W3 @ SV81 @ SV72 @ SV25 )
!= sz10 ) )
| ~ ( ( ( sK4_W3 @ SV81 @ SV72 @ SV25 )
!= SV81 ) ) ) )
= $false )
| ( ( SV81 = sz10 )
= $true )
| ( ( iLess0 @ SV25 @ xn )
= $false )
| ( ( ( sdtasdt0 @ SV81 @ ( sdtasdt0 @ SV72 @ SV72 ) )
= ( sdtasdt0 @ SV25 @ SV25 ) )
= $false )
| ( ( SV81 = sz00 )
= $true )
| ( ( SV72 = sz00 )
= $true )
| ( ( SV25 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV72 )
= $false )
| ( ( aNaturalNumber0 @ SV25 )
= $false )
| ( ( aNaturalNumber0 @ SV81 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[778]) ).
thf(784,plain,
! [SV26: $i,SV95: $i,SV93: $i] :
( ( ( sdtlseqdt0 @ SV93 @ SV95 )
= $false )
| ( ( SV93 = SV95 )
= $true )
| ( ( SV26 = sz00 )
= $true )
| ( ( ( sdtasdt0 @ SV26 @ SV93 )
!= ( sdtasdt0 @ SV26 @ SV95 ) )
= $true )
| ( ( aNaturalNumber0 @ SV93 )
= $false )
| ( ( aNaturalNumber0 @ SV26 )
= $false )
| ( ( aNaturalNumber0 @ SV95 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[779]) ).
thf(785,plain,
! [SV26: $i,SV96: $i,SV94: $i] :
( ( ( sdtlseqdt0 @ SV94 @ SV96 )
= $false )
| ( ( SV94 = SV96 )
= $true )
| ( ( SV26 = sz00 )
= $true )
| ( ( sdtlseqdt0 @ ( sdtasdt0 @ SV26 @ SV94 ) @ ( sdtasdt0 @ SV26 @ SV96 ) )
= $true )
| ( ( aNaturalNumber0 @ SV94 )
= $false )
| ( ( aNaturalNumber0 @ SV26 )
= $false )
| ( ( aNaturalNumber0 @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[780]) ).
thf(786,plain,
! [SV25: $i,SV72: $i,SV81: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ( SV81
!= ( sdtasdt0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) @ ( sK5_SY81 @ SV81 @ SV72 @ SV25 ) ) )
| ~ ( aNaturalNumber0 @ ( sK5_SY81 @ SV81 @ SV72 @ SV25 ) ) )
| ~ ( aNaturalNumber0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) ) )
| ~ ( doDivides0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) @ SV81 ) ) )
= $true )
| ( ( SV81 = sz10 )
= $true )
| ( ( iLess0 @ SV25 @ xn )
= $false )
| ( ( ( sdtasdt0 @ SV81 @ ( sdtasdt0 @ SV72 @ SV72 ) )
= ( sdtasdt0 @ SV25 @ SV25 ) )
= $false )
| ( ( SV81 = sz00 )
= $true )
| ( ( SV72 = sz00 )
= $true )
| ( ( SV25 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV72 )
= $false )
| ( ( aNaturalNumber0 @ SV25 )
= $false )
| ( ( aNaturalNumber0 @ SV81 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[782]) ).
thf(787,plain,
! [SV25: $i,SV72: $i,SV81: $i] :
( ( ( ~ ( ~ ( ( ( sK4_W3 @ SV81 @ SV72 @ SV25 )
!= sz10 ) )
| ~ ( ( ( sK4_W3 @ SV81 @ SV72 @ SV25 )
!= SV81 ) ) ) )
= $true )
| ( ( SV81 = sz10 )
= $true )
| ( ( iLess0 @ SV25 @ xn )
= $false )
| ( ( ( sdtasdt0 @ SV81 @ ( sdtasdt0 @ SV72 @ SV72 ) )
= ( sdtasdt0 @ SV25 @ SV25 ) )
= $false )
| ( ( SV81 = sz00 )
= $true )
| ( ( SV72 = sz00 )
= $true )
| ( ( SV25 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV72 )
= $false )
| ( ( aNaturalNumber0 @ SV25 )
= $false )
| ( ( aNaturalNumber0 @ SV81 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[783]) ).
thf(788,plain,
! [SV95: $i,SV93: $i,SV26: $i] :
( ( ( ( sdtasdt0 @ SV26 @ SV93 )
= ( sdtasdt0 @ SV26 @ SV95 ) )
= $false )
| ( ( SV26 = sz00 )
= $true )
| ( ( SV93 = SV95 )
= $true )
| ( ( sdtlseqdt0 @ SV93 @ SV95 )
= $false )
| ( ( aNaturalNumber0 @ SV93 )
= $false )
| ( ( aNaturalNumber0 @ SV26 )
= $false )
| ( ( aNaturalNumber0 @ SV95 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[784]) ).
thf(789,plain,
! [SV25: $i,SV72: $i,SV81: $i] :
( ( ( ~ ~ ( ~ ~ ( ( SV81
!= ( sdtasdt0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) @ ( sK5_SY81 @ SV81 @ SV72 @ SV25 ) ) )
| ~ ( aNaturalNumber0 @ ( sK5_SY81 @ SV81 @ SV72 @ SV25 ) ) )
| ~ ( aNaturalNumber0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) ) )
| ~ ( doDivides0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) @ SV81 ) )
= $false )
| ( ( SV81 = sz10 )
= $true )
| ( ( iLess0 @ SV25 @ xn )
= $false )
| ( ( ( sdtasdt0 @ SV81 @ ( sdtasdt0 @ SV72 @ SV72 ) )
= ( sdtasdt0 @ SV25 @ SV25 ) )
= $false )
| ( ( SV81 = sz00 )
= $true )
| ( ( SV72 = sz00 )
= $true )
| ( ( SV25 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV72 )
= $false )
| ( ( aNaturalNumber0 @ SV25 )
= $false )
| ( ( aNaturalNumber0 @ SV81 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[786]) ).
thf(790,plain,
! [SV25: $i,SV72: $i,SV81: $i] :
( ( ( ~ ( ( ( sK4_W3 @ SV81 @ SV72 @ SV25 )
!= sz10 ) )
| ~ ( ( ( sK4_W3 @ SV81 @ SV72 @ SV25 )
!= SV81 ) ) )
= $false )
| ( ( SV81 = sz10 )
= $true )
| ( ( iLess0 @ SV25 @ xn )
= $false )
| ( ( ( sdtasdt0 @ SV81 @ ( sdtasdt0 @ SV72 @ SV72 ) )
= ( sdtasdt0 @ SV25 @ SV25 ) )
= $false )
| ( ( SV81 = sz00 )
= $true )
| ( ( SV72 = sz00 )
= $true )
| ( ( SV25 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV72 )
= $false )
| ( ( aNaturalNumber0 @ SV25 )
= $false )
| ( ( aNaturalNumber0 @ SV81 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[787]) ).
thf(791,plain,
! [SV25: $i,SV72: $i,SV81: $i] :
( ( ( ~ ~ ( ~ ~ ( ( SV81
!= ( sdtasdt0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) @ ( sK5_SY81 @ SV81 @ SV72 @ SV25 ) ) )
| ~ ( aNaturalNumber0 @ ( sK5_SY81 @ SV81 @ SV72 @ SV25 ) ) )
| ~ ( aNaturalNumber0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) ) ) )
= $false )
| ( ( SV81 = sz10 )
= $true )
| ( ( iLess0 @ SV25 @ xn )
= $false )
| ( ( ( sdtasdt0 @ SV81 @ ( sdtasdt0 @ SV72 @ SV72 ) )
= ( sdtasdt0 @ SV25 @ SV25 ) )
= $false )
| ( ( SV81 = sz00 )
= $true )
| ( ( SV72 = sz00 )
= $true )
| ( ( SV25 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV72 )
= $false )
| ( ( aNaturalNumber0 @ SV25 )
= $false )
| ( ( aNaturalNumber0 @ SV81 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[789]) ).
thf(792,plain,
! [SV25: $i,SV72: $i,SV81: $i] :
( ( ( ~ ( doDivides0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) @ SV81 ) )
= $false )
| ( ( SV81 = sz10 )
= $true )
| ( ( iLess0 @ SV25 @ xn )
= $false )
| ( ( ( sdtasdt0 @ SV81 @ ( sdtasdt0 @ SV72 @ SV72 ) )
= ( sdtasdt0 @ SV25 @ SV25 ) )
= $false )
| ( ( SV81 = sz00 )
= $true )
| ( ( SV72 = sz00 )
= $true )
| ( ( SV25 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV72 )
= $false )
| ( ( aNaturalNumber0 @ SV25 )
= $false )
| ( ( aNaturalNumber0 @ SV81 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[789]) ).
thf(793,plain,
! [SV25: $i,SV72: $i,SV81: $i] :
( ( ( ~ ( ( ( sK4_W3 @ SV81 @ SV72 @ SV25 )
!= sz10 ) ) )
= $false )
| ( ( SV81 = sz10 )
= $true )
| ( ( iLess0 @ SV25 @ xn )
= $false )
| ( ( ( sdtasdt0 @ SV81 @ ( sdtasdt0 @ SV72 @ SV72 ) )
= ( sdtasdt0 @ SV25 @ SV25 ) )
= $false )
| ( ( SV81 = sz00 )
= $true )
| ( ( SV72 = sz00 )
= $true )
| ( ( SV25 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV72 )
= $false )
| ( ( aNaturalNumber0 @ SV25 )
= $false )
| ( ( aNaturalNumber0 @ SV81 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[790]) ).
thf(794,plain,
! [SV25: $i,SV72: $i,SV81: $i] :
( ( ( ~ ( ( ( sK4_W3 @ SV81 @ SV72 @ SV25 )
!= SV81 ) ) )
= $false )
| ( ( SV81 = sz10 )
= $true )
| ( ( iLess0 @ SV25 @ xn )
= $false )
| ( ( ( sdtasdt0 @ SV81 @ ( sdtasdt0 @ SV72 @ SV72 ) )
= ( sdtasdt0 @ SV25 @ SV25 ) )
= $false )
| ( ( SV81 = sz00 )
= $true )
| ( ( SV72 = sz00 )
= $true )
| ( ( SV25 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV72 )
= $false )
| ( ( aNaturalNumber0 @ SV25 )
= $false )
| ( ( aNaturalNumber0 @ SV81 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[790]) ).
thf(795,plain,
! [SV25: $i,SV72: $i,SV81: $i] :
( ( ( ~ ( ~ ~ ( ( SV81
!= ( sdtasdt0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) @ ( sK5_SY81 @ SV81 @ SV72 @ SV25 ) ) )
| ~ ( aNaturalNumber0 @ ( sK5_SY81 @ SV81 @ SV72 @ SV25 ) ) )
| ~ ( aNaturalNumber0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) ) ) )
= $true )
| ( ( SV81 = sz10 )
= $true )
| ( ( iLess0 @ SV25 @ xn )
= $false )
| ( ( ( sdtasdt0 @ SV81 @ ( sdtasdt0 @ SV72 @ SV72 ) )
= ( sdtasdt0 @ SV25 @ SV25 ) )
= $false )
| ( ( SV81 = sz00 )
= $true )
| ( ( SV72 = sz00 )
= $true )
| ( ( SV25 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV72 )
= $false )
| ( ( aNaturalNumber0 @ SV25 )
= $false )
| ( ( aNaturalNumber0 @ SV81 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[791]) ).
thf(796,plain,
! [SV25: $i,SV72: $i,SV81: $i] :
( ( ( doDivides0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) @ SV81 )
= $true )
| ( ( SV81 = sz10 )
= $true )
| ( ( iLess0 @ SV25 @ xn )
= $false )
| ( ( ( sdtasdt0 @ SV81 @ ( sdtasdt0 @ SV72 @ SV72 ) )
= ( sdtasdt0 @ SV25 @ SV25 ) )
= $false )
| ( ( SV81 = sz00 )
= $true )
| ( ( SV72 = sz00 )
= $true )
| ( ( SV25 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV72 )
= $false )
| ( ( aNaturalNumber0 @ SV25 )
= $false )
| ( ( aNaturalNumber0 @ SV81 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[792]) ).
thf(797,plain,
! [SV25: $i,SV72: $i,SV81: $i] :
( ( ( ( sK4_W3 @ SV81 @ SV72 @ SV25 )
!= sz10 )
= $true )
| ( ( SV81 = sz10 )
= $true )
| ( ( iLess0 @ SV25 @ xn )
= $false )
| ( ( ( sdtasdt0 @ SV81 @ ( sdtasdt0 @ SV72 @ SV72 ) )
= ( sdtasdt0 @ SV25 @ SV25 ) )
= $false )
| ( ( SV81 = sz00 )
= $true )
| ( ( SV72 = sz00 )
= $true )
| ( ( SV25 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV72 )
= $false )
| ( ( aNaturalNumber0 @ SV25 )
= $false )
| ( ( aNaturalNumber0 @ SV81 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[793]) ).
thf(798,plain,
! [SV25: $i,SV72: $i,SV81: $i] :
( ( ( ( sK4_W3 @ SV81 @ SV72 @ SV25 )
!= SV81 )
= $true )
| ( ( SV81 = sz10 )
= $true )
| ( ( iLess0 @ SV25 @ xn )
= $false )
| ( ( ( sdtasdt0 @ SV81 @ ( sdtasdt0 @ SV72 @ SV72 ) )
= ( sdtasdt0 @ SV25 @ SV25 ) )
= $false )
| ( ( SV81 = sz00 )
= $true )
| ( ( SV72 = sz00 )
= $true )
| ( ( SV25 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV72 )
= $false )
| ( ( aNaturalNumber0 @ SV25 )
= $false )
| ( ( aNaturalNumber0 @ SV81 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[794]) ).
thf(799,plain,
! [SV25: $i,SV72: $i,SV81: $i] :
( ( ( ~ ~ ( ( SV81
!= ( sdtasdt0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) @ ( sK5_SY81 @ SV81 @ SV72 @ SV25 ) ) )
| ~ ( aNaturalNumber0 @ ( sK5_SY81 @ SV81 @ SV72 @ SV25 ) ) )
| ~ ( aNaturalNumber0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) ) )
= $false )
| ( ( SV81 = sz10 )
= $true )
| ( ( iLess0 @ SV25 @ xn )
= $false )
| ( ( ( sdtasdt0 @ SV81 @ ( sdtasdt0 @ SV72 @ SV72 ) )
= ( sdtasdt0 @ SV25 @ SV25 ) )
= $false )
| ( ( SV81 = sz00 )
= $true )
| ( ( SV72 = sz00 )
= $true )
| ( ( SV25 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV72 )
= $false )
| ( ( aNaturalNumber0 @ SV25 )
= $false )
| ( ( aNaturalNumber0 @ SV81 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[795]) ).
thf(800,plain,
! [SV25: $i,SV72: $i,SV81: $i] :
( ( ( ( sK4_W3 @ SV81 @ SV72 @ SV25 )
= sz10 )
= $false )
| ( ( SV81 = sz10 )
= $true )
| ( ( iLess0 @ SV25 @ xn )
= $false )
| ( ( ( sdtasdt0 @ SV81 @ ( sdtasdt0 @ SV72 @ SV72 ) )
= ( sdtasdt0 @ SV25 @ SV25 ) )
= $false )
| ( ( SV81 = sz00 )
= $true )
| ( ( SV72 = sz00 )
= $true )
| ( ( SV25 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV72 )
= $false )
| ( ( aNaturalNumber0 @ SV25 )
= $false )
| ( ( aNaturalNumber0 @ SV81 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[797]) ).
thf(801,plain,
! [SV25: $i,SV72: $i,SV81: $i] :
( ( ( ( sK4_W3 @ SV81 @ SV72 @ SV25 )
= SV81 )
= $false )
| ( ( SV81 = sz10 )
= $true )
| ( ( iLess0 @ SV25 @ xn )
= $false )
| ( ( ( sdtasdt0 @ SV81 @ ( sdtasdt0 @ SV72 @ SV72 ) )
= ( sdtasdt0 @ SV25 @ SV25 ) )
= $false )
| ( ( SV81 = sz00 )
= $true )
| ( ( SV72 = sz00 )
= $true )
| ( ( SV25 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV72 )
= $false )
| ( ( aNaturalNumber0 @ SV25 )
= $false )
| ( ( aNaturalNumber0 @ SV81 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[798]) ).
thf(802,plain,
! [SV25: $i,SV72: $i,SV81: $i] :
( ( ( ~ ~ ( ( SV81
!= ( sdtasdt0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) @ ( sK5_SY81 @ SV81 @ SV72 @ SV25 ) ) )
| ~ ( aNaturalNumber0 @ ( sK5_SY81 @ SV81 @ SV72 @ SV25 ) ) ) )
= $false )
| ( ( SV81 = sz10 )
= $true )
| ( ( iLess0 @ SV25 @ xn )
= $false )
| ( ( ( sdtasdt0 @ SV81 @ ( sdtasdt0 @ SV72 @ SV72 ) )
= ( sdtasdt0 @ SV25 @ SV25 ) )
= $false )
| ( ( SV81 = sz00 )
= $true )
| ( ( SV72 = sz00 )
= $true )
| ( ( SV25 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV72 )
= $false )
| ( ( aNaturalNumber0 @ SV25 )
= $false )
| ( ( aNaturalNumber0 @ SV81 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[799]) ).
thf(803,plain,
! [SV25: $i,SV72: $i,SV81: $i] :
( ( ( ~ ( aNaturalNumber0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) ) )
= $false )
| ( ( SV81 = sz10 )
= $true )
| ( ( iLess0 @ SV25 @ xn )
= $false )
| ( ( ( sdtasdt0 @ SV81 @ ( sdtasdt0 @ SV72 @ SV72 ) )
= ( sdtasdt0 @ SV25 @ SV25 ) )
= $false )
| ( ( SV81 = sz00 )
= $true )
| ( ( SV72 = sz00 )
= $true )
| ( ( SV25 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV72 )
= $false )
| ( ( aNaturalNumber0 @ SV25 )
= $false )
| ( ( aNaturalNumber0 @ SV81 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[799]) ).
thf(804,plain,
! [SV25: $i,SV72: $i,SV81: $i] :
( ( ( ~ ( ( SV81
!= ( sdtasdt0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) @ ( sK5_SY81 @ SV81 @ SV72 @ SV25 ) ) )
| ~ ( aNaturalNumber0 @ ( sK5_SY81 @ SV81 @ SV72 @ SV25 ) ) ) )
= $true )
| ( ( SV81 = sz10 )
= $true )
| ( ( iLess0 @ SV25 @ xn )
= $false )
| ( ( ( sdtasdt0 @ SV81 @ ( sdtasdt0 @ SV72 @ SV72 ) )
= ( sdtasdt0 @ SV25 @ SV25 ) )
= $false )
| ( ( SV81 = sz00 )
= $true )
| ( ( SV72 = sz00 )
= $true )
| ( ( SV25 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV72 )
= $false )
| ( ( aNaturalNumber0 @ SV25 )
= $false )
| ( ( aNaturalNumber0 @ SV81 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[802]) ).
thf(805,plain,
! [SV25: $i,SV72: $i,SV81: $i] :
( ( ( aNaturalNumber0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) )
= $true )
| ( ( SV81 = sz10 )
= $true )
| ( ( iLess0 @ SV25 @ xn )
= $false )
| ( ( ( sdtasdt0 @ SV81 @ ( sdtasdt0 @ SV72 @ SV72 ) )
= ( sdtasdt0 @ SV25 @ SV25 ) )
= $false )
| ( ( SV81 = sz00 )
= $true )
| ( ( SV72 = sz00 )
= $true )
| ( ( SV25 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV72 )
= $false )
| ( ( aNaturalNumber0 @ SV25 )
= $false )
| ( ( aNaturalNumber0 @ SV81 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[803]) ).
thf(806,plain,
! [SV25: $i,SV72: $i,SV81: $i] :
( ( ( ( SV81
!= ( sdtasdt0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) @ ( sK5_SY81 @ SV81 @ SV72 @ SV25 ) ) )
| ~ ( aNaturalNumber0 @ ( sK5_SY81 @ SV81 @ SV72 @ SV25 ) ) )
= $false )
| ( ( SV81 = sz10 )
= $true )
| ( ( iLess0 @ SV25 @ xn )
= $false )
| ( ( ( sdtasdt0 @ SV81 @ ( sdtasdt0 @ SV72 @ SV72 ) )
= ( sdtasdt0 @ SV25 @ SV25 ) )
= $false )
| ( ( SV81 = sz00 )
= $true )
| ( ( SV72 = sz00 )
= $true )
| ( ( SV25 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV72 )
= $false )
| ( ( aNaturalNumber0 @ SV25 )
= $false )
| ( ( aNaturalNumber0 @ SV81 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[804]) ).
thf(807,plain,
! [SV25: $i,SV72: $i,SV81: $i] :
( ( ( SV81
!= ( sdtasdt0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) @ ( sK5_SY81 @ SV81 @ SV72 @ SV25 ) ) )
= $false )
| ( ( SV81 = sz10 )
= $true )
| ( ( iLess0 @ SV25 @ xn )
= $false )
| ( ( ( sdtasdt0 @ SV81 @ ( sdtasdt0 @ SV72 @ SV72 ) )
= ( sdtasdt0 @ SV25 @ SV25 ) )
= $false )
| ( ( SV81 = sz00 )
= $true )
| ( ( SV72 = sz00 )
= $true )
| ( ( SV25 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV72 )
= $false )
| ( ( aNaturalNumber0 @ SV25 )
= $false )
| ( ( aNaturalNumber0 @ SV81 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[806]) ).
thf(808,plain,
! [SV25: $i,SV72: $i,SV81: $i] :
( ( ( ~ ( aNaturalNumber0 @ ( sK5_SY81 @ SV81 @ SV72 @ SV25 ) ) )
= $false )
| ( ( SV81 = sz10 )
= $true )
| ( ( iLess0 @ SV25 @ xn )
= $false )
| ( ( ( sdtasdt0 @ SV81 @ ( sdtasdt0 @ SV72 @ SV72 ) )
= ( sdtasdt0 @ SV25 @ SV25 ) )
= $false )
| ( ( SV81 = sz00 )
= $true )
| ( ( SV72 = sz00 )
= $true )
| ( ( SV25 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV72 )
= $false )
| ( ( aNaturalNumber0 @ SV25 )
= $false )
| ( ( aNaturalNumber0 @ SV81 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[806]) ).
thf(809,plain,
! [SV25: $i,SV72: $i,SV81: $i] :
( ( ( SV81
= ( sdtasdt0 @ ( sK4_W3 @ SV81 @ SV72 @ SV25 ) @ ( sK5_SY81 @ SV81 @ SV72 @ SV25 ) ) )
= $true )
| ( ( SV81 = sz10 )
= $true )
| ( ( iLess0 @ SV25 @ xn )
= $false )
| ( ( ( sdtasdt0 @ SV81 @ ( sdtasdt0 @ SV72 @ SV72 ) )
= ( sdtasdt0 @ SV25 @ SV25 ) )
= $false )
| ( ( SV81 = sz00 )
= $true )
| ( ( SV72 = sz00 )
= $true )
| ( ( SV25 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV72 )
= $false )
| ( ( aNaturalNumber0 @ SV25 )
= $false )
| ( ( aNaturalNumber0 @ SV81 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[807]) ).
thf(810,plain,
! [SV25: $i,SV72: $i,SV81: $i] :
( ( ( aNaturalNumber0 @ ( sK5_SY81 @ SV81 @ SV72 @ SV25 ) )
= $true )
| ( ( SV81 = sz10 )
= $true )
| ( ( iLess0 @ SV25 @ xn )
= $false )
| ( ( ( sdtasdt0 @ SV81 @ ( sdtasdt0 @ SV72 @ SV72 ) )
= ( sdtasdt0 @ SV25 @ SV25 ) )
= $false )
| ( ( SV81 = sz00 )
= $true )
| ( ( SV72 = sz00 )
= $true )
| ( ( SV25 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV72 )
= $false )
| ( ( aNaturalNumber0 @ SV25 )
= $false )
| ( ( aNaturalNumber0 @ SV81 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[808]) ).
thf(811,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[132,810,809,805,801,800,796,788,785,781,777,773,772,761,755,742,727,726,725,723,722,721,712,711,701,684,683,682,681,672,668,667,662,661,659,654,653,644,643,642,613,608,593,590,574,573,572,563,559,556,555,554,551,540,497,496,480,465,464,461,460,456,455,445,444,434,428,426,425,424,355,350,319,306,304,300,283,190,171,138,136]) ).
thf(812,plain,
( ( ( xp != sz00 )
& ( xm != sz00 )
& ( xn != sz00 )
& ( aNaturalNumber0 @ xn )
& ( aNaturalNumber0 @ xm )
& ( aNaturalNumber0 @ xp ) )
= $true ),
inference(copy,[status(thm)],[129]) ).
thf(813,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 )
| ( ( W2
= ( sdtasdt0 @ ( sK4_W3 @ W2 @ W1 @ W0 ) @ ( sK5_SY81 @ W2 @ W1 @ W0 ) ) )
& ( aNaturalNumber0 @ ( sK5_SY81 @ W2 @ W1 @ W0 ) )
& ( aNaturalNumber0 @ ( sK4_W3 @ W2 @ W1 @ W0 ) )
& ( doDivides0 @ ( sK4_W3 @ W2 @ W1 @ W0 ) @ W2 )
& ( ( sK4_W3 @ W2 @ W1 @ W0 )
!= sz10 )
& ( ( sK4_W3 @ W2 @ W1 @ W0 )
!= W2 ) )
| ( W2 = sz10 ) )
& ! [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)],[128]) ).
thf(814,plain,
( ( ( sdtasdt0 @ xp @ ( sdtasdt0 @ xm @ xm ) )
= ( sdtasdt0 @ xn @ xn ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(815,plain,
( ( ! [W0: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ! [W1: $i] :
( ( xp
!= ( sdtasdt0 @ W0 @ W1 ) )
| ~ ( aNaturalNumber0 @ W1 ) )
| ( W0 = sz10 )
| ( W0 = xp ) )
& ! [W0: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( doDivides0 @ W0 @ xp )
| ( W0 = sz10 )
| ( W0 = xp ) )
& ( xp != sz10 )
& ( isPrime0 @ xp ) )
= $true ),
inference(copy,[status(thm)],[127]) ).
thf(816,plain,
( ( ( ( sdtasdt0 @ xn @ xn )
= ( sdtasdt0 @ xp @ sK3_W0 ) )
& ( aNaturalNumber0 @ sK3_W0 )
& ( doDivides0 @ xp @ ( sdtasdt0 @ xn @ xn ) )
& ( xn
= ( sdtasdt0 @ xp @ sK2_W0 ) )
& ( aNaturalNumber0 @ sK2_W0 )
& ( doDivides0 @ xp @ xn ) )
= $true ),
inference(copy,[status(thm)],[126]) ).
thf(817,plain,
( ( ( xn
= ( sdtasdt0 @ xp @ xq ) )
& ( aNaturalNumber0 @ xq )
& ( xq
= ( sdtsldt0 @ xn @ xp ) ) )
= $true ),
inference(copy,[status(thm)],[125]) ).
thf(818,plain,
( ( ( sdtasdt0 @ xm @ xm )
= ( sdtasdt0 @ xp @ ( sdtasdt0 @ xq @ xq ) ) )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(819,plain,
( ( ! [W0: $i] : $true )
= $true ),
inference(copy,[status(thm)],[124]) ).
thf(820,plain,
( ( aNaturalNumber0 @ sz00 )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(821,plain,
( ( ( sz10 != sz00 )
& ( aNaturalNumber0 @ sz10 ) )
= $true ),
inference(copy,[status(thm)],[123]) ).
thf(822,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ( aNaturalNumber0 @ ( sdtpldt0 @ W0 @ W1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(823,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ( aNaturalNumber0 @ ( sdtasdt0 @ W0 @ W1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[121]) ).
thf(824,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ( ( sdtpldt0 @ W0 @ W1 )
= ( sdtpldt0 @ W1 @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[120]) ).
thf(825,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)],[119]) ).
thf(826,plain,
( ( ! [W0: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ( ( sdtpldt0 @ W0 @ sz00 )
= W0 ) )
& ! [W0: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ( W0
= ( sdtpldt0 @ sz00 @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(827,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ( ( sdtasdt0 @ W0 @ W1 )
= ( sdtasdt0 @ W1 @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(828,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)],[116]) ).
thf(829,plain,
( ( ! [W0: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ( ( sdtasdt0 @ W0 @ sz10 )
= W0 ) )
& ! [W0: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ( W0
= ( sdtasdt0 @ sz10 @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[115]) ).
thf(830,plain,
( ( ! [W0: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ( ( sdtasdt0 @ W0 @ sz00 )
= sz00 ) )
& ! [W0: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ( sz00
= ( sdtasdt0 @ sz00 @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(831,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)],[113]) ).
thf(832,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)],[112]) ).
thf(833,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)],[111]) ).
thf(834,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)],[110]) ).
thf(835,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ( ( sdtasdt0 @ W0 @ W1 )
!= sz00 )
| ( W0 = sz00 )
| ( W1 = sz00 ) ) )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(836,plain,
( ( ! [W0: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ( sdtlseqdt0 @ W0 @ W0 ) ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(837,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ~ ( sdtlseqdt0 @ W0 @ W1 )
| ~ ( sdtlseqdt0 @ W1 @ W0 )
| ( W0 = W1 ) ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(838,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)],[106]) ).
thf(839,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)],[105]) ).
thf(840,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)],[104]) ).
thf(841,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)],[103]) ).
thf(842,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)],[102]) ).
thf(843,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ( W0 = sz00 )
| ( sdtlseqdt0 @ W1 @ ( sdtasdt0 @ W1 @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(844,plain,
( ( ! [W0: $i] :
~ ( aNaturalNumber0 @ W0 )
| ! [W1: $i] :
~ ( aNaturalNumber0 @ W1 )
| $true )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(845,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ( W0 = W1 )
| ~ ( sdtlseqdt0 @ W0 @ W1 )
| ( iLess0 @ W0 @ W1 ) ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(846,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)],[98]) ).
thf(847,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)],[97]) ).
thf(848,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)],[96]) ).
thf(849,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ( W1 = sz00 )
| ~ ( doDivides0 @ W0 @ W1 )
| ( sdtlseqdt0 @ W0 @ W1 ) ) )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(850,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)],[94]) ).
thf(851,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)],[93]) ).
thf(852,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)],[92]) ).
thf(853,plain,
( ( ! [W0: $i] :
( ( ( sdtpldt0 @ xm @ W0 )
!= xn )
| ~ ( aNaturalNumber0 @ W0 ) )
& ~ ( sdtlseqdt0 @ xm @ xn ) )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(854,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ! [SX1: $i] :
( ( xp
!= ( sdtasdt0 @ SX0 @ SX1 ) )
| ~ ( aNaturalNumber0 @ SX1 ) )
| ( SX0 = sz10 )
| ( SX0 = xp ) )
| ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( doDivides0 @ SX0 @ xp )
| ( SX0 = sz10 )
| ( SX0 = xp ) ) )
| ~ ( ( xp != sz10 ) ) )
| ~ ( isPrime0 @ xp ) ) )
= $true ),
inference(unfold_def,[status(thm)],[815]) ).
thf(855,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)],[831]) ).
thf(856,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( ( sdtasdt0 @ SX0 @ sz00 )
= sz00 ) )
| ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( sz00
= ( sdtasdt0 @ sz00 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[830]) ).
thf(857,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)],[833]) ).
thf(858,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( ( sdtpldt0 @ xm @ SX0 )
!= xn )
| ~ ( aNaturalNumber0 @ SX0 ) )
| ~ ~ ( sdtlseqdt0 @ xm @ xn ) ) )
= $true ),
inference(unfold_def,[status(thm)],[853]) ).
thf(859,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)],[841]) ).
thf(860,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xn @ xn )
!= ( sdtasdt0 @ xp @ sK3_W0 ) )
| ~ ( aNaturalNumber0 @ sK3_W0 ) )
| ~ ( doDivides0 @ xp @ ( sdtasdt0 @ xn @ xn ) ) )
| ~ ~ ( ( xn
!= ( sdtasdt0 @ xp @ sK2_W0 ) )
| ~ ( aNaturalNumber0 @ sK2_W0 ) ) )
| ~ ( doDivides0 @ xp @ xn ) ) )
= $true ),
inference(unfold_def,[status(thm)],[816]) ).
thf(861,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ( SX2 = sz00 )
| ( SX1 = sz00 )
| ( SX0 = sz00 )
| ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 )
| ~ ( aNaturalNumber0 @ SX2 )
| ( ( sdtasdt0 @ SX2 @ ( sdtasdt0 @ SX1 @ SX1 ) )
!= ( sdtasdt0 @ SX0 @ SX0 ) )
| ~ ( iLess0 @ SX0 @ xn )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( SX2
!= ( sdtasdt0 @ ( sK4_W3 @ SX2 @ SX1 @ SX0 ) @ ( sK5_SY81 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( aNaturalNumber0 @ ( sK5_SY81 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( aNaturalNumber0 @ ( sK4_W3 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( doDivides0 @ ( sK4_W3 @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ~ ( ~ ( ( ( sK4_W3 @ SX2 @ SX1 @ SX0 )
!= sz10 ) )
| ~ ( ( ( sK4_W3 @ SX2 @ SX1 @ SX0 )
!= SX2 ) ) ) )
| ( SX2 = sz10 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2 = sz00 )
| ( SX1 = sz00 )
| ( SX0 = sz00 )
| ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 )
| ~ ( aNaturalNumber0 @ SX2 )
| ( ( sdtasdt0 @ SX2 @ ( sdtasdt0 @ SX1 @ SX1 ) )
!= ( sdtasdt0 @ SX0 @ SX0 ) )
| ~ ( iLess0 @ SX0 @ xn )
| ~ ( isPrime0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[813]) ).
thf(862,plain,
( ( ~ ( ~ ( ( xp != sz00 ) )
| ~ ~ ( ~ ( ( xm != sz00 ) )
| ~ ~ ( ~ ( ( xn != sz00 ) )
| ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ xn )
| ~ ( aNaturalNumber0 @ xm ) )
| ~ ( aNaturalNumber0 @ xp ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[812]) ).
thf(863,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)],[839]) ).
thf(864,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)],[840]) ).
thf(865,plain,
( ( ~ ( ~ ~ ( ( xn
!= ( sdtasdt0 @ xp @ xq ) )
| ~ ( aNaturalNumber0 @ xq ) )
| ( xq
!= ( sdtsldt0 @ xn @ xp ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[817]) ).
thf(866,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)],[832]) ).
thf(867,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)],[842]) ).
thf(868,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)],[851]) ).
thf(869,plain,
( ( ~ ( ~ ( ( sz10 != sz00 ) )
| ~ ( aNaturalNumber0 @ sz10 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[821]) ).
thf(870,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( ( sdtpldt0 @ SX0 @ sz00 )
= SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( SX0
= ( sdtpldt0 @ sz00 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[826]) ).
thf(871,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( ( sdtasdt0 @ SX0 @ sz10 )
= SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( SX0
= ( sdtasdt0 @ sz10 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[829]) ).
thf(872,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)],[834]) ).
thf(873,plain,
$true = $true,
inference(extcnf_forall_pos,[status(thm)],[819]) ).
thf(874,plain,
! [SV103: $i] :
( ( ! [SY165: $i] :
( ~ ( aNaturalNumber0 @ SV103 )
| ~ ( aNaturalNumber0 @ SY165 )
| ( aNaturalNumber0 @ ( sdtpldt0 @ SV103 @ SY165 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[822]) ).
thf(875,plain,
! [SV104: $i] :
( ( ! [SY166: $i] :
( ~ ( aNaturalNumber0 @ SV104 )
| ~ ( aNaturalNumber0 @ SY166 )
| ( aNaturalNumber0 @ ( sdtasdt0 @ SV104 @ SY166 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[823]) ).
thf(876,plain,
! [SV105: $i] :
( ( ! [SY167: $i] :
( ~ ( aNaturalNumber0 @ SV105 )
| ~ ( aNaturalNumber0 @ SY167 )
| ( ( sdtpldt0 @ SV105 @ SY167 )
= ( sdtpldt0 @ SY167 @ SV105 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[824]) ).
thf(877,plain,
! [SV106: $i] :
( ( ! [SY168: $i,SY169: $i] :
( ~ ( aNaturalNumber0 @ SV106 )
| ~ ( aNaturalNumber0 @ SY168 )
| ~ ( aNaturalNumber0 @ SY169 )
| ( ( sdtpldt0 @ ( sdtpldt0 @ SV106 @ SY168 ) @ SY169 )
= ( sdtpldt0 @ SV106 @ ( sdtpldt0 @ SY168 @ SY169 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[825]) ).
thf(878,plain,
! [SV107: $i] :
( ( ! [SY170: $i] :
( ~ ( aNaturalNumber0 @ SV107 )
| ~ ( aNaturalNumber0 @ SY170 )
| ( ( sdtasdt0 @ SV107 @ SY170 )
= ( sdtasdt0 @ SY170 @ SV107 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[827]) ).
thf(879,plain,
! [SV108: $i] :
( ( ! [SY171: $i,SY172: $i] :
( ~ ( aNaturalNumber0 @ SV108 )
| ~ ( aNaturalNumber0 @ SY171 )
| ~ ( aNaturalNumber0 @ SY172 )
| ( ( sdtasdt0 @ ( sdtasdt0 @ SV108 @ SY171 ) @ SY172 )
= ( sdtasdt0 @ SV108 @ ( sdtasdt0 @ SY171 @ SY172 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[828]) ).
thf(880,plain,
! [SV109: $i] :
( ( ! [SY173: $i] :
( ~ ( aNaturalNumber0 @ SV109 )
| ~ ( aNaturalNumber0 @ SY173 )
| ( ( sdtasdt0 @ SV109 @ SY173 )
!= sz00 )
| ( SV109 = sz00 )
| ( SY173 = sz00 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[835]) ).
thf(881,plain,
! [SV110: $i] :
( ( ~ ( aNaturalNumber0 @ SV110 )
| ( sdtlseqdt0 @ SV110 @ SV110 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[836]) ).
thf(882,plain,
! [SV111: $i] :
( ( ! [SY174: $i] :
( ~ ( aNaturalNumber0 @ SV111 )
| ~ ( aNaturalNumber0 @ SY174 )
| ~ ( sdtlseqdt0 @ SV111 @ SY174 )
| ~ ( sdtlseqdt0 @ SY174 @ SV111 )
| ( SV111 = SY174 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[837]) ).
thf(883,plain,
! [SV112: $i] :
( ( ! [SY175: $i,SY176: $i] :
( ~ ( aNaturalNumber0 @ SV112 )
| ~ ( aNaturalNumber0 @ SY175 )
| ~ ( aNaturalNumber0 @ SY176 )
| ~ ( sdtlseqdt0 @ SV112 @ SY175 )
| ~ ( sdtlseqdt0 @ SY175 @ SY176 )
| ( sdtlseqdt0 @ SV112 @ SY176 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[838]) ).
thf(884,plain,
! [SV113: $i] :
( ( ! [SY177: $i] :
( ~ ( aNaturalNumber0 @ SV113 )
| ~ ( aNaturalNumber0 @ SY177 )
| ( SV113 = sz00 )
| ( sdtlseqdt0 @ SY177 @ ( sdtasdt0 @ SY177 @ SV113 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[843]) ).
thf(885,plain,
( ( ( ! [W0: $i] :
~ ( aNaturalNumber0 @ W0 )
| ! [W1: $i] :
~ ( aNaturalNumber0 @ W1 ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[844]) ).
thf(886,plain,
! [SV114: $i] :
( ( ! [SY178: $i] :
( ~ ( aNaturalNumber0 @ SV114 )
| ~ ( aNaturalNumber0 @ SY178 )
| ( SV114 = SY178 )
| ~ ( sdtlseqdt0 @ SV114 @ SY178 )
| ( iLess0 @ SV114 @ SY178 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[845]) ).
thf(887,plain,
! [SV115: $i] :
( ( ! [SY179: $i,SY180: $i] :
( ~ ( aNaturalNumber0 @ SV115 )
| ~ ( aNaturalNumber0 @ SY179 )
| ~ ( aNaturalNumber0 @ SY180 )
| ~ ( doDivides0 @ SV115 @ SY179 )
| ~ ( doDivides0 @ SY179 @ SY180 )
| ( doDivides0 @ SV115 @ SY180 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[846]) ).
thf(888,plain,
! [SV116: $i] :
( ( ! [SY181: $i,SY182: $i] :
( ~ ( aNaturalNumber0 @ SV116 )
| ~ ( aNaturalNumber0 @ SY181 )
| ~ ( aNaturalNumber0 @ SY182 )
| ~ ( doDivides0 @ SV116 @ SY181 )
| ~ ( doDivides0 @ SV116 @ SY182 )
| ( doDivides0 @ SV116 @ ( sdtpldt0 @ SY181 @ SY182 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[847]) ).
thf(889,plain,
! [SV117: $i] :
( ( ! [SY183: $i,SY184: $i] :
( ~ ( aNaturalNumber0 @ SV117 )
| ~ ( aNaturalNumber0 @ SY183 )
| ~ ( aNaturalNumber0 @ SY184 )
| ~ ( doDivides0 @ SV117 @ SY183 )
| ~ ( doDivides0 @ SV117 @ ( sdtpldt0 @ SY183 @ SY184 ) )
| ( doDivides0 @ SV117 @ SY184 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[848]) ).
thf(890,plain,
! [SV118: $i] :
( ( ! [SY185: $i] :
( ~ ( aNaturalNumber0 @ SV118 )
| ~ ( aNaturalNumber0 @ SY185 )
| ( SY185 = sz00 )
| ~ ( doDivides0 @ SV118 @ SY185 )
| ( sdtlseqdt0 @ SV118 @ SY185 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[849]) ).
thf(891,plain,
! [SV119: $i] :
( ( ! [SY186: $i] :
( ~ ( aNaturalNumber0 @ SV119 )
| ~ ( aNaturalNumber0 @ SY186 )
| ( SV119 = sz00 )
| ~ ( doDivides0 @ SV119 @ SY186 )
| ! [SY187: $i] :
( ~ ( aNaturalNumber0 @ SY187 )
| ( ( sdtasdt0 @ SY187 @ ( sdtsldt0 @ SY186 @ SV119 ) )
= ( sdtsldt0 @ ( sdtasdt0 @ SY187 @ SY186 ) @ SV119 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[850]) ).
thf(892,plain,
! [SV120: $i] :
( ( ! [SY188: $i,SY189: $i] :
( ~ ( aNaturalNumber0 @ SV120 )
| ~ ( aNaturalNumber0 @ SY188 )
| ~ ( aNaturalNumber0 @ SY189 )
| ~ ( doDivides0 @ SY189 @ ( sdtasdt0 @ SV120 @ SY188 ) )
| ~ ( isPrime0 @ SY189 )
| ( doDivides0 @ SY189 @ SV120 )
| ( doDivides0 @ SY189 @ SY188 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[852]) ).
thf(893,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ! [SX1: $i] :
( ( xp
!= ( sdtasdt0 @ SX0 @ SX1 ) )
| ~ ( aNaturalNumber0 @ SX1 ) )
| ( SX0 = sz10 )
| ( SX0 = xp ) )
| ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( doDivides0 @ SX0 @ xp )
| ( SX0 = sz10 )
| ( SX0 = xp ) ) )
| ~ ( ( xp != sz10 ) ) )
| ~ ( isPrime0 @ xp ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[854]) ).
thf(894,plain,
! [SV121: $i] :
( ( ~ ( ~ ! [SY190: $i,SY191: $i] :
( ~ ( aNaturalNumber0 @ SV121 )
| ~ ( aNaturalNumber0 @ SY190 )
| ~ ( aNaturalNumber0 @ SY191 )
| ( ( sdtasdt0 @ SV121 @ ( sdtpldt0 @ SY190 @ SY191 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV121 @ SY190 ) @ ( sdtasdt0 @ SV121 @ SY191 ) ) ) )
| ~ ! [SY192: $i,SY193: $i] :
( ~ ( aNaturalNumber0 @ SV121 )
| ~ ( aNaturalNumber0 @ SY192 )
| ~ ( aNaturalNumber0 @ SY193 )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SY192 @ SY193 ) @ SV121 )
= ( sdtpldt0 @ ( sdtasdt0 @ SY192 @ SV121 ) @ ( sdtasdt0 @ SY193 @ SV121 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[855]) ).
thf(895,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( ( sdtasdt0 @ SX0 @ sz00 )
= sz00 ) )
| ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( sz00
= ( sdtasdt0 @ sz00 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[856]) ).
thf(896,plain,
! [SV122: $i] :
( ( ~ ( aNaturalNumber0 @ SV122 )
| ( SV122 = sz00 )
| ~ ( ~ ! [SY194: $i,SY195: $i] :
( ~ ( aNaturalNumber0 @ SY194 )
| ~ ( aNaturalNumber0 @ SY195 )
| ( ( sdtasdt0 @ SV122 @ SY194 )
!= ( sdtasdt0 @ SV122 @ SY195 ) )
| ( SY194 = SY195 ) )
| ~ ! [SY196: $i,SY197: $i] :
( ~ ( aNaturalNumber0 @ SY196 )
| ~ ( aNaturalNumber0 @ SY197 )
| ( ( sdtasdt0 @ SY196 @ SV122 )
!= ( sdtasdt0 @ SY197 @ SV122 ) )
| ( SY196 = SY197 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[857]) ).
thf(897,plain,
( ( ~ ! [SX0: $i] :
( ( ( sdtpldt0 @ xm @ SX0 )
!= xn )
| ~ ( aNaturalNumber0 @ SX0 ) )
| ~ ~ ( sdtlseqdt0 @ xm @ xn ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[858]) ).
thf(898,plain,
! [SV123: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY198: $i,SY199: $i] :
( ~ ( aNaturalNumber0 @ SV123 )
| ~ ( aNaturalNumber0 @ SY198 )
| ~ ( aNaturalNumber0 @ SY199 )
| ( SV123 = sz00 )
| ( SY198 = SY199 )
| ~ ( sdtlseqdt0 @ SY198 @ SY199 )
| ( ( sdtasdt0 @ SY198 @ SV123 )
!= ( sdtasdt0 @ SY199 @ SV123 ) ) )
| ~ ~ ( ~ ! [SY200: $i,SY201: $i] :
( ~ ( aNaturalNumber0 @ SV123 )
| ~ ( aNaturalNumber0 @ SY200 )
| ~ ( aNaturalNumber0 @ SY201 )
| ( SV123 = sz00 )
| ( SY200 = SY201 )
| ~ ( sdtlseqdt0 @ SY200 @ SY201 )
| ( ( sdtasdt0 @ SV123 @ SY200 )
!= ( sdtasdt0 @ SV123 @ SY201 ) ) )
| ~ ! [SY202: $i,SY203: $i] :
( ~ ( aNaturalNumber0 @ SV123 )
| ~ ( aNaturalNumber0 @ SY202 )
| ~ ( aNaturalNumber0 @ SY203 )
| ( SV123 = sz00 )
| ( SY202 = SY203 )
| ~ ( sdtlseqdt0 @ SY202 @ SY203 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV123 @ SY202 ) @ ( sdtasdt0 @ SV123 @ SY203 ) ) ) ) )
| ~ ! [SY204: $i,SY205: $i] :
( ~ ( aNaturalNumber0 @ SV123 )
| ~ ( aNaturalNumber0 @ SY204 )
| ~ ( aNaturalNumber0 @ SY205 )
| ( SV123 = sz00 )
| ( SY204 = SY205 )
| ~ ( sdtlseqdt0 @ SY204 @ SY205 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SY204 @ SV123 ) @ ( sdtasdt0 @ SY205 @ SV123 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[859]) ).
thf(899,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xn @ xn )
!= ( sdtasdt0 @ xp @ sK3_W0 ) )
| ~ ( aNaturalNumber0 @ sK3_W0 ) )
| ~ ( doDivides0 @ xp @ ( sdtasdt0 @ xn @ xn ) ) )
| ~ ~ ( ( xn
!= ( sdtasdt0 @ xp @ sK2_W0 ) )
| ~ ( aNaturalNumber0 @ sK2_W0 ) ) )
| ~ ( doDivides0 @ xp @ xn ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[860]) ).
thf(900,plain,
! [SV124: $i] :
( ( ~ ( ~ ! [SY206: $i,SY207: $i] :
( ( SY207 = sz00 )
| ( SY206 = sz00 )
| ( SV124 = sz00 )
| ~ ( aNaturalNumber0 @ SV124 )
| ~ ( aNaturalNumber0 @ SY206 )
| ~ ( aNaturalNumber0 @ SY207 )
| ( ( sdtasdt0 @ SY207 @ ( sdtasdt0 @ SY206 @ SY206 ) )
!= ( sdtasdt0 @ SV124 @ SV124 ) )
| ~ ( iLess0 @ SV124 @ xn )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( SY207
!= ( sdtasdt0 @ ( sK4_W3 @ SY207 @ SY206 @ SV124 ) @ ( sK5_SY81 @ SY207 @ SY206 @ SV124 ) ) )
| ~ ( aNaturalNumber0 @ ( sK5_SY81 @ SY207 @ SY206 @ SV124 ) ) )
| ~ ( aNaturalNumber0 @ ( sK4_W3 @ SY207 @ SY206 @ SV124 ) ) )
| ~ ( doDivides0 @ ( sK4_W3 @ SY207 @ SY206 @ SV124 ) @ SY207 ) )
| ~ ~ ( ~ ( ( ( sK4_W3 @ SY207 @ SY206 @ SV124 )
!= sz10 ) )
| ~ ( ( ( sK4_W3 @ SY207 @ SY206 @ SV124 )
!= SY207 ) ) ) )
| ( SY207 = sz10 ) )
| ~ ! [SY208: $i,SY209: $i] :
( ( SY209 = sz00 )
| ( SY208 = sz00 )
| ( SV124 = sz00 )
| ~ ( aNaturalNumber0 @ SV124 )
| ~ ( aNaturalNumber0 @ SY208 )
| ~ ( aNaturalNumber0 @ SY209 )
| ( ( sdtasdt0 @ SY209 @ ( sdtasdt0 @ SY208 @ SY208 ) )
!= ( sdtasdt0 @ SV124 @ SV124 ) )
| ~ ( iLess0 @ SV124 @ xn )
| ~ ( isPrime0 @ SY209 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[861]) ).
thf(901,plain,
( ( ~ ( ( xp != sz00 ) )
| ~ ~ ( ~ ( ( xm != sz00 ) )
| ~ ~ ( ~ ( ( xn != sz00 ) )
| ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ xn )
| ~ ( aNaturalNumber0 @ xm ) )
| ~ ( aNaturalNumber0 @ xp ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[862]) ).
thf(902,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)],[863]) ).
thf(903,plain,
! [SV125: $i] :
( ( ! [SY210: $i] :
( ~ ( aNaturalNumber0 @ SV125 )
| ~ ( aNaturalNumber0 @ SY210 )
| ( SV125 = SY210 )
| ~ ( sdtlseqdt0 @ SV125 @ SY210 )
| ~ ( ~ ~ ( ~ ! [SY211: $i] :
( ~ ( aNaturalNumber0 @ SY211 )
| ( ( sdtpldt0 @ SV125 @ SY211 )
!= ( sdtpldt0 @ SY210 @ SY211 ) ) )
| ~ ~ ( ~ ! [SY212: $i] :
( ~ ( aNaturalNumber0 @ SY212 )
| ( ( sdtpldt0 @ SY212 @ SV125 )
!= ( sdtpldt0 @ SY212 @ SY210 ) ) )
| ~ ! [SY213: $i] :
( ~ ( aNaturalNumber0 @ SY213 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SY213 @ SV125 ) @ ( sdtpldt0 @ SY213 @ SY210 ) ) ) ) )
| ~ ! [SY214: $i] :
( ~ ( aNaturalNumber0 @ SY214 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SV125 @ SY214 ) @ ( sdtpldt0 @ SY210 @ SY214 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[864]) ).
thf(904,plain,
( ( ~ ~ ( ( xn
!= ( sdtasdt0 @ xp @ xq ) )
| ~ ( aNaturalNumber0 @ xq ) )
| ( xq
!= ( sdtsldt0 @ xn @ xp ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[865]) ).
thf(905,plain,
! [SV126: $i] :
( ( ~ ( ~ ! [SY215: $i,SY216: $i] :
( ~ ( aNaturalNumber0 @ SV126 )
| ~ ( aNaturalNumber0 @ SY215 )
| ~ ( aNaturalNumber0 @ SY216 )
| ( ( sdtpldt0 @ SV126 @ SY215 )
!= ( sdtpldt0 @ SV126 @ SY216 ) )
| ( SY215 = SY216 ) )
| ~ ! [SY217: $i,SY218: $i] :
( ~ ( aNaturalNumber0 @ SV126 )
| ~ ( aNaturalNumber0 @ SY217 )
| ~ ( aNaturalNumber0 @ SY218 )
| ( ( sdtpldt0 @ SY217 @ SV126 )
!= ( sdtpldt0 @ SY218 @ SV126 ) )
| ( SY217 = SY218 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[866]) ).
thf(906,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)],[867]) ).
thf(907,plain,
! [SV127: $i] :
( ( ( SV127 = sz10 )
| ( SV127 = sz00 )
| ~ ( aNaturalNumber0 @ SV127 )
| ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ ( sK1_W1 @ SV127 ) )
| ~ ( doDivides0 @ ( sK1_W1 @ SV127 ) @ SV127 ) )
| ~ ( isPrime0 @ ( sK1_W1 @ SV127 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[868]) ).
thf(908,plain,
( ( ~ ( ( sz10 != sz00 ) )
| ~ ( aNaturalNumber0 @ sz10 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[869]) ).
thf(909,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( ( sdtpldt0 @ SX0 @ sz00 )
= SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( SX0
= ( sdtpldt0 @ sz00 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[870]) ).
thf(910,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( ( sdtasdt0 @ SX0 @ sz10 )
= SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( SX0
= ( sdtasdt0 @ sz10 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[871]) ).
thf(911,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)],[872]) ).
thf(912,plain,
! [SV128: $i,SV103: $i] :
( ( ~ ( aNaturalNumber0 @ SV103 )
| ~ ( aNaturalNumber0 @ SV128 )
| ( aNaturalNumber0 @ ( sdtpldt0 @ SV103 @ SV128 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[874]) ).
thf(913,plain,
! [SV129: $i,SV104: $i] :
( ( ~ ( aNaturalNumber0 @ SV104 )
| ~ ( aNaturalNumber0 @ SV129 )
| ( aNaturalNumber0 @ ( sdtasdt0 @ SV104 @ SV129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[875]) ).
thf(914,plain,
! [SV130: $i,SV105: $i] :
( ( ~ ( aNaturalNumber0 @ SV105 )
| ~ ( aNaturalNumber0 @ SV130 )
| ( ( sdtpldt0 @ SV105 @ SV130 )
= ( sdtpldt0 @ SV130 @ SV105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[876]) ).
thf(915,plain,
! [SV131: $i,SV106: $i] :
( ( ! [SY219: $i] :
( ~ ( aNaturalNumber0 @ SV106 )
| ~ ( aNaturalNumber0 @ SV131 )
| ~ ( aNaturalNumber0 @ SY219 )
| ( ( sdtpldt0 @ ( sdtpldt0 @ SV106 @ SV131 ) @ SY219 )
= ( sdtpldt0 @ SV106 @ ( sdtpldt0 @ SV131 @ SY219 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[877]) ).
thf(916,plain,
! [SV132: $i,SV107: $i] :
( ( ~ ( aNaturalNumber0 @ SV107 )
| ~ ( aNaturalNumber0 @ SV132 )
| ( ( sdtasdt0 @ SV107 @ SV132 )
= ( sdtasdt0 @ SV132 @ SV107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[878]) ).
thf(917,plain,
! [SV133: $i,SV108: $i] :
( ( ! [SY220: $i] :
( ~ ( aNaturalNumber0 @ SV108 )
| ~ ( aNaturalNumber0 @ SV133 )
| ~ ( aNaturalNumber0 @ SY220 )
| ( ( sdtasdt0 @ ( sdtasdt0 @ SV108 @ SV133 ) @ SY220 )
= ( sdtasdt0 @ SV108 @ ( sdtasdt0 @ SV133 @ SY220 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[879]) ).
thf(918,plain,
! [SV134: $i,SV109: $i] :
( ( ~ ( aNaturalNumber0 @ SV109 )
| ~ ( aNaturalNumber0 @ SV134 )
| ( ( sdtasdt0 @ SV109 @ SV134 )
!= sz00 )
| ( SV109 = sz00 )
| ( SV134 = sz00 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[880]) ).
thf(919,plain,
! [SV110: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV110 ) )
= $true )
| ( ( sdtlseqdt0 @ SV110 @ SV110 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[881]) ).
thf(920,plain,
! [SV135: $i,SV111: $i] :
( ( ~ ( aNaturalNumber0 @ SV111 )
| ~ ( aNaturalNumber0 @ SV135 )
| ~ ( sdtlseqdt0 @ SV111 @ SV135 )
| ~ ( sdtlseqdt0 @ SV135 @ SV111 )
| ( SV111 = SV135 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[882]) ).
thf(921,plain,
! [SV136: $i,SV112: $i] :
( ( ! [SY221: $i] :
( ~ ( aNaturalNumber0 @ SV112 )
| ~ ( aNaturalNumber0 @ SV136 )
| ~ ( aNaturalNumber0 @ SY221 )
| ~ ( sdtlseqdt0 @ SV112 @ SV136 )
| ~ ( sdtlseqdt0 @ SV136 @ SY221 )
| ( sdtlseqdt0 @ SV112 @ SY221 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[883]) ).
thf(922,plain,
! [SV137: $i,SV113: $i] :
( ( ~ ( aNaturalNumber0 @ SV113 )
| ~ ( aNaturalNumber0 @ SV137 )
| ( SV113 = sz00 )
| ( sdtlseqdt0 @ SV137 @ ( sdtasdt0 @ SV137 @ SV113 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[884]) ).
thf(923,plain,
( ( ( ! [W0: $i] :
~ ( aNaturalNumber0 @ W0 ) )
= $true )
| ( ( ! [W1: $i] :
~ ( aNaturalNumber0 @ W1 ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[885]) ).
thf(924,plain,
! [SV138: $i,SV114: $i] :
( ( ~ ( aNaturalNumber0 @ SV114 )
| ~ ( aNaturalNumber0 @ SV138 )
| ( SV114 = SV138 )
| ~ ( sdtlseqdt0 @ SV114 @ SV138 )
| ( iLess0 @ SV114 @ SV138 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[886]) ).
thf(925,plain,
! [SV139: $i,SV115: $i] :
( ( ! [SY222: $i] :
( ~ ( aNaturalNumber0 @ SV115 )
| ~ ( aNaturalNumber0 @ SV139 )
| ~ ( aNaturalNumber0 @ SY222 )
| ~ ( doDivides0 @ SV115 @ SV139 )
| ~ ( doDivides0 @ SV139 @ SY222 )
| ( doDivides0 @ SV115 @ SY222 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[887]) ).
thf(926,plain,
! [SV140: $i,SV116: $i] :
( ( ! [SY223: $i] :
( ~ ( aNaturalNumber0 @ SV116 )
| ~ ( aNaturalNumber0 @ SV140 )
| ~ ( aNaturalNumber0 @ SY223 )
| ~ ( doDivides0 @ SV116 @ SV140 )
| ~ ( doDivides0 @ SV116 @ SY223 )
| ( doDivides0 @ SV116 @ ( sdtpldt0 @ SV140 @ SY223 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[888]) ).
thf(927,plain,
! [SV141: $i,SV117: $i] :
( ( ! [SY224: $i] :
( ~ ( aNaturalNumber0 @ SV117 )
| ~ ( aNaturalNumber0 @ SV141 )
| ~ ( aNaturalNumber0 @ SY224 )
| ~ ( doDivides0 @ SV117 @ SV141 )
| ~ ( doDivides0 @ SV117 @ ( sdtpldt0 @ SV141 @ SY224 ) )
| ( doDivides0 @ SV117 @ SY224 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[889]) ).
thf(928,plain,
! [SV142: $i,SV118: $i] :
( ( ~ ( aNaturalNumber0 @ SV118 )
| ~ ( aNaturalNumber0 @ SV142 )
| ( SV142 = sz00 )
| ~ ( doDivides0 @ SV118 @ SV142 )
| ( sdtlseqdt0 @ SV118 @ SV142 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[890]) ).
thf(929,plain,
! [SV143: $i,SV119: $i] :
( ( ~ ( aNaturalNumber0 @ SV119 )
| ~ ( aNaturalNumber0 @ SV143 )
| ( SV119 = sz00 )
| ~ ( doDivides0 @ SV119 @ SV143 )
| ! [SY225: $i] :
( ~ ( aNaturalNumber0 @ SY225 )
| ( ( sdtasdt0 @ SY225 @ ( sdtsldt0 @ SV143 @ SV119 ) )
= ( sdtsldt0 @ ( sdtasdt0 @ SY225 @ SV143 ) @ SV119 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[891]) ).
thf(930,plain,
! [SV144: $i,SV120: $i] :
( ( ! [SY226: $i] :
( ~ ( aNaturalNumber0 @ SV120 )
| ~ ( aNaturalNumber0 @ SV144 )
| ~ ( aNaturalNumber0 @ SY226 )
| ~ ( doDivides0 @ SY226 @ ( sdtasdt0 @ SV120 @ SV144 ) )
| ~ ( isPrime0 @ SY226 )
| ( doDivides0 @ SY226 @ SV120 )
| ( doDivides0 @ SY226 @ SV144 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[892]) ).
thf(931,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ! [SX1: $i] :
( ( xp
!= ( sdtasdt0 @ SX0 @ SX1 ) )
| ~ ( aNaturalNumber0 @ SX1 ) )
| ( SX0 = sz10 )
| ( SX0 = xp ) )
| ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( doDivides0 @ SX0 @ xp )
| ( SX0 = sz10 )
| ( SX0 = xp ) ) )
| ~ ( ( xp != sz10 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[893]) ).
thf(932,plain,
( ( ~ ( isPrime0 @ xp ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[893]) ).
thf(933,plain,
! [SV121: $i] :
( ( ~ ! [SY190: $i,SY191: $i] :
( ~ ( aNaturalNumber0 @ SV121 )
| ~ ( aNaturalNumber0 @ SY190 )
| ~ ( aNaturalNumber0 @ SY191 )
| ( ( sdtasdt0 @ SV121 @ ( sdtpldt0 @ SY190 @ SY191 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV121 @ SY190 ) @ ( sdtasdt0 @ SV121 @ SY191 ) ) ) )
| ~ ! [SY192: $i,SY193: $i] :
( ~ ( aNaturalNumber0 @ SV121 )
| ~ ( aNaturalNumber0 @ SY192 )
| ~ ( aNaturalNumber0 @ SY193 )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SY192 @ SY193 ) @ SV121 )
= ( sdtpldt0 @ ( sdtasdt0 @ SY192 @ SV121 ) @ ( sdtasdt0 @ SY193 @ SV121 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[894]) ).
thf(934,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( ( sdtasdt0 @ SX0 @ sz00 )
= sz00 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[895]) ).
thf(935,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( sz00
= ( sdtasdt0 @ sz00 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[895]) ).
thf(936,plain,
! [SV122: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV122 ) )
= $true )
| ( ( ( SV122 = sz00 )
| ~ ( ~ ! [SY194: $i,SY195: $i] :
( ~ ( aNaturalNumber0 @ SY194 )
| ~ ( aNaturalNumber0 @ SY195 )
| ( ( sdtasdt0 @ SV122 @ SY194 )
!= ( sdtasdt0 @ SV122 @ SY195 ) )
| ( SY194 = SY195 ) )
| ~ ! [SY196: $i,SY197: $i] :
( ~ ( aNaturalNumber0 @ SY196 )
| ~ ( aNaturalNumber0 @ SY197 )
| ( ( sdtasdt0 @ SY196 @ SV122 )
!= ( sdtasdt0 @ SY197 @ SV122 ) )
| ( SY196 = SY197 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[896]) ).
thf(937,plain,
( ( ~ ! [SX0: $i] :
( ( ( sdtpldt0 @ xm @ SX0 )
!= xn )
| ~ ( aNaturalNumber0 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[897]) ).
thf(938,plain,
( ( ~ ~ ( sdtlseqdt0 @ xm @ xn ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[897]) ).
thf(939,plain,
! [SV123: $i] :
( ( ~ ~ ( ~ ! [SY198: $i,SY199: $i] :
( ~ ( aNaturalNumber0 @ SV123 )
| ~ ( aNaturalNumber0 @ SY198 )
| ~ ( aNaturalNumber0 @ SY199 )
| ( SV123 = sz00 )
| ( SY198 = SY199 )
| ~ ( sdtlseqdt0 @ SY198 @ SY199 )
| ( ( sdtasdt0 @ SY198 @ SV123 )
!= ( sdtasdt0 @ SY199 @ SV123 ) ) )
| ~ ~ ( ~ ! [SY200: $i,SY201: $i] :
( ~ ( aNaturalNumber0 @ SV123 )
| ~ ( aNaturalNumber0 @ SY200 )
| ~ ( aNaturalNumber0 @ SY201 )
| ( SV123 = sz00 )
| ( SY200 = SY201 )
| ~ ( sdtlseqdt0 @ SY200 @ SY201 )
| ( ( sdtasdt0 @ SV123 @ SY200 )
!= ( sdtasdt0 @ SV123 @ SY201 ) ) )
| ~ ! [SY202: $i,SY203: $i] :
( ~ ( aNaturalNumber0 @ SV123 )
| ~ ( aNaturalNumber0 @ SY202 )
| ~ ( aNaturalNumber0 @ SY203 )
| ( SV123 = sz00 )
| ( SY202 = SY203 )
| ~ ( sdtlseqdt0 @ SY202 @ SY203 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV123 @ SY202 ) @ ( sdtasdt0 @ SV123 @ SY203 ) ) ) ) )
| ~ ! [SY204: $i,SY205: $i] :
( ~ ( aNaturalNumber0 @ SV123 )
| ~ ( aNaturalNumber0 @ SY204 )
| ~ ( aNaturalNumber0 @ SY205 )
| ( SV123 = sz00 )
| ( SY204 = SY205 )
| ~ ( sdtlseqdt0 @ SY204 @ SY205 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SY204 @ SV123 ) @ ( sdtasdt0 @ SY205 @ SV123 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[898]) ).
thf(940,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xn @ xn )
!= ( sdtasdt0 @ xp @ sK3_W0 ) )
| ~ ( aNaturalNumber0 @ sK3_W0 ) )
| ~ ( doDivides0 @ xp @ ( sdtasdt0 @ xn @ xn ) ) )
| ~ ~ ( ( xn
!= ( sdtasdt0 @ xp @ sK2_W0 ) )
| ~ ( aNaturalNumber0 @ sK2_W0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[899]) ).
thf(941,plain,
( ( ~ ( doDivides0 @ xp @ xn ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[899]) ).
thf(942,plain,
! [SV124: $i] :
( ( ~ ! [SY206: $i,SY207: $i] :
( ( SY207 = sz00 )
| ( SY206 = sz00 )
| ( SV124 = sz00 )
| ~ ( aNaturalNumber0 @ SV124 )
| ~ ( aNaturalNumber0 @ SY206 )
| ~ ( aNaturalNumber0 @ SY207 )
| ( ( sdtasdt0 @ SY207 @ ( sdtasdt0 @ SY206 @ SY206 ) )
!= ( sdtasdt0 @ SV124 @ SV124 ) )
| ~ ( iLess0 @ SV124 @ xn )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( SY207
!= ( sdtasdt0 @ ( sK4_W3 @ SY207 @ SY206 @ SV124 ) @ ( sK5_SY81 @ SY207 @ SY206 @ SV124 ) ) )
| ~ ( aNaturalNumber0 @ ( sK5_SY81 @ SY207 @ SY206 @ SV124 ) ) )
| ~ ( aNaturalNumber0 @ ( sK4_W3 @ SY207 @ SY206 @ SV124 ) ) )
| ~ ( doDivides0 @ ( sK4_W3 @ SY207 @ SY206 @ SV124 ) @ SY207 ) )
| ~ ~ ( ~ ( ( ( sK4_W3 @ SY207 @ SY206 @ SV124 )
!= sz10 ) )
| ~ ( ( ( sK4_W3 @ SY207 @ SY206 @ SV124 )
!= SY207 ) ) ) )
| ( SY207 = sz10 ) )
| ~ ! [SY208: $i,SY209: $i] :
( ( SY209 = sz00 )
| ( SY208 = sz00 )
| ( SV124 = sz00 )
| ~ ( aNaturalNumber0 @ SV124 )
| ~ ( aNaturalNumber0 @ SY208 )
| ~ ( aNaturalNumber0 @ SY209 )
| ( ( sdtasdt0 @ SY209 @ ( sdtasdt0 @ SY208 @ SY208 ) )
!= ( sdtasdt0 @ SV124 @ SV124 ) )
| ~ ( iLess0 @ SV124 @ xn )
| ~ ( isPrime0 @ SY209 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[900]) ).
thf(943,plain,
( ( ~ ( ( xp != sz00 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[901]) ).
thf(944,plain,
( ( ~ ~ ( ~ ( ( xm != sz00 ) )
| ~ ~ ( ~ ( ( xn != sz00 ) )
| ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ xn )
| ~ ( aNaturalNumber0 @ xm ) )
| ~ ( aNaturalNumber0 @ xp ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[901]) ).
thf(945,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 )
| ( SX1 != SX0 )
| ( sdtlseqdt0 @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[902]) ).
thf(946,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 )
| ( sdtlseqdt0 @ SX1 @ SX0 )
| ( sdtlseqdt0 @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[902]) ).
thf(947,plain,
! [SV145: $i,SV125: $i] :
( ( ~ ( aNaturalNumber0 @ SV125 )
| ~ ( aNaturalNumber0 @ SV145 )
| ( SV125 = SV145 )
| ~ ( sdtlseqdt0 @ SV125 @ SV145 )
| ~ ( ~ ~ ( ~ ! [SY227: $i] :
( ~ ( aNaturalNumber0 @ SY227 )
| ( ( sdtpldt0 @ SV125 @ SY227 )
!= ( sdtpldt0 @ SV145 @ SY227 ) ) )
| ~ ~ ( ~ ! [SY228: $i] :
( ~ ( aNaturalNumber0 @ SY228 )
| ( ( sdtpldt0 @ SY228 @ SV125 )
!= ( sdtpldt0 @ SY228 @ SV145 ) ) )
| ~ ! [SY229: $i] :
( ~ ( aNaturalNumber0 @ SY229 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SY229 @ SV125 ) @ ( sdtpldt0 @ SY229 @ SV145 ) ) ) ) )
| ~ ! [SY230: $i] :
( ~ ( aNaturalNumber0 @ SY230 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SV125 @ SY230 ) @ ( sdtpldt0 @ SV145 @ SY230 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[903]) ).
thf(948,plain,
( ( ~ ~ ( ( xn
!= ( sdtasdt0 @ xp @ xq ) )
| ~ ( aNaturalNumber0 @ xq ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[904]) ).
thf(949,plain,
( ( xq
!= ( sdtsldt0 @ xn @ xp ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[904]) ).
thf(950,plain,
! [SV126: $i] :
( ( ~ ! [SY215: $i,SY216: $i] :
( ~ ( aNaturalNumber0 @ SV126 )
| ~ ( aNaturalNumber0 @ SY215 )
| ~ ( aNaturalNumber0 @ SY216 )
| ( ( sdtpldt0 @ SV126 @ SY215 )
!= ( sdtpldt0 @ SV126 @ SY216 ) )
| ( SY215 = SY216 ) )
| ~ ! [SY217: $i,SY218: $i] :
( ~ ( aNaturalNumber0 @ SV126 )
| ~ ( aNaturalNumber0 @ SY217 )
| ~ ( aNaturalNumber0 @ SY218 )
| ( ( sdtpldt0 @ SY217 @ SV126 )
!= ( sdtpldt0 @ SY218 @ SV126 ) )
| ( SY217 = SY218 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[905]) ).
thf(951,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( sz10 != SX0 )
| ( SX0 = sz00 )
| ( SX0 = sz10 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[906]) ).
thf(952,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( sdtlseqdt0 @ sz10 @ SX0 )
| ( SX0 = sz00 )
| ( SX0 = sz10 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[906]) ).
thf(953,plain,
! [SV127: $i] :
( ( ( ( SV127 = sz10 )
| ( SV127 = sz00 )
| ~ ( aNaturalNumber0 @ SV127 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ ( sK1_W1 @ SV127 ) )
| ~ ( doDivides0 @ ( sK1_W1 @ SV127 ) @ SV127 ) )
| ~ ( isPrime0 @ ( sK1_W1 @ SV127 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[907]) ).
thf(954,plain,
( ( ~ ( ( sz10 != sz00 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[908]) ).
thf(955,plain,
( ( ~ ( aNaturalNumber0 @ sz10 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[908]) ).
thf(956,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( ( sdtpldt0 @ SX0 @ sz00 )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[909]) ).
thf(957,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( SX0
= ( sdtpldt0 @ sz00 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[909]) ).
thf(958,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( ( sdtasdt0 @ SX0 @ sz10 )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[910]) ).
thf(959,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( SX0
= ( sdtasdt0 @ sz10 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[910]) ).
thf(960,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 )
| ( ( sdtpldt0 @ SX0 @ SX1 )
!= sz00 )
| ( SX0 = sz00 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[911]) ).
thf(961,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 )
| ( ( sdtpldt0 @ SX0 @ SX1 )
!= sz00 )
| ( SX1 = sz00 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[911]) ).
thf(962,plain,
! [SV128: $i,SV103: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV103 )
| ~ ( aNaturalNumber0 @ SV128 ) )
= $true )
| ( ( aNaturalNumber0 @ ( sdtpldt0 @ SV103 @ SV128 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[912]) ).
thf(963,plain,
! [SV129: $i,SV104: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV104 )
| ~ ( aNaturalNumber0 @ SV129 ) )
= $true )
| ( ( aNaturalNumber0 @ ( sdtasdt0 @ SV104 @ SV129 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[913]) ).
thf(964,plain,
! [SV130: $i,SV105: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV105 )
| ~ ( aNaturalNumber0 @ SV130 ) )
= $true )
| ( ( ( sdtpldt0 @ SV105 @ SV130 )
= ( sdtpldt0 @ SV130 @ SV105 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[914]) ).
thf(965,plain,
! [SV146: $i,SV131: $i,SV106: $i] :
( ( ~ ( aNaturalNumber0 @ SV106 )
| ~ ( aNaturalNumber0 @ SV131 )
| ~ ( aNaturalNumber0 @ SV146 )
| ( ( sdtpldt0 @ ( sdtpldt0 @ SV106 @ SV131 ) @ SV146 )
= ( sdtpldt0 @ SV106 @ ( sdtpldt0 @ SV131 @ SV146 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[915]) ).
thf(966,plain,
! [SV132: $i,SV107: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV107 )
| ~ ( aNaturalNumber0 @ SV132 ) )
= $true )
| ( ( ( sdtasdt0 @ SV107 @ SV132 )
= ( sdtasdt0 @ SV132 @ SV107 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[916]) ).
thf(967,plain,
! [SV147: $i,SV133: $i,SV108: $i] :
( ( ~ ( aNaturalNumber0 @ SV108 )
| ~ ( aNaturalNumber0 @ SV133 )
| ~ ( aNaturalNumber0 @ SV147 )
| ( ( sdtasdt0 @ ( sdtasdt0 @ SV108 @ SV133 ) @ SV147 )
= ( sdtasdt0 @ SV108 @ ( sdtasdt0 @ SV133 @ SV147 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[917]) ).
thf(968,plain,
! [SV134: $i,SV109: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV109 )
| ~ ( aNaturalNumber0 @ SV134 ) )
= $true )
| ( ( ( ( sdtasdt0 @ SV109 @ SV134 )
!= sz00 )
| ( SV109 = sz00 )
| ( SV134 = sz00 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[918]) ).
thf(969,plain,
! [SV110: $i] :
( ( ( aNaturalNumber0 @ SV110 )
= $false )
| ( ( sdtlseqdt0 @ SV110 @ SV110 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[919]) ).
thf(970,plain,
! [SV135: $i,SV111: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV111 )
| ~ ( aNaturalNumber0 @ SV135 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV111 @ SV135 )
| ~ ( sdtlseqdt0 @ SV135 @ SV111 )
| ( SV111 = SV135 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[920]) ).
thf(971,plain,
! [SV148: $i,SV136: $i,SV112: $i] :
( ( ~ ( aNaturalNumber0 @ SV112 )
| ~ ( aNaturalNumber0 @ SV136 )
| ~ ( aNaturalNumber0 @ SV148 )
| ~ ( sdtlseqdt0 @ SV112 @ SV136 )
| ~ ( sdtlseqdt0 @ SV136 @ SV148 )
| ( sdtlseqdt0 @ SV112 @ SV148 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[921]) ).
thf(972,plain,
! [SV137: $i,SV113: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV113 )
| ~ ( aNaturalNumber0 @ SV137 ) )
= $true )
| ( ( ( SV113 = sz00 )
| ( sdtlseqdt0 @ SV137 @ ( sdtasdt0 @ SV137 @ SV113 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[922]) ).
thf(973,plain,
! [SV149: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV149 ) )
= $true )
| ( ( ! [W1: $i] :
~ ( aNaturalNumber0 @ W1 ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[923]) ).
thf(974,plain,
! [SV138: $i,SV114: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV114 )
| ~ ( aNaturalNumber0 @ SV138 ) )
= $true )
| ( ( ( SV114 = SV138 )
| ~ ( sdtlseqdt0 @ SV114 @ SV138 )
| ( iLess0 @ SV114 @ SV138 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[924]) ).
thf(975,plain,
! [SV150: $i,SV139: $i,SV115: $i] :
( ( ~ ( aNaturalNumber0 @ SV115 )
| ~ ( aNaturalNumber0 @ SV139 )
| ~ ( aNaturalNumber0 @ SV150 )
| ~ ( doDivides0 @ SV115 @ SV139 )
| ~ ( doDivides0 @ SV139 @ SV150 )
| ( doDivides0 @ SV115 @ SV150 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[925]) ).
thf(976,plain,
! [SV151: $i,SV140: $i,SV116: $i] :
( ( ~ ( aNaturalNumber0 @ SV116 )
| ~ ( aNaturalNumber0 @ SV140 )
| ~ ( aNaturalNumber0 @ SV151 )
| ~ ( doDivides0 @ SV116 @ SV140 )
| ~ ( doDivides0 @ SV116 @ SV151 )
| ( doDivides0 @ SV116 @ ( sdtpldt0 @ SV140 @ SV151 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[926]) ).
thf(977,plain,
! [SV152: $i,SV141: $i,SV117: $i] :
( ( ~ ( aNaturalNumber0 @ SV117 )
| ~ ( aNaturalNumber0 @ SV141 )
| ~ ( aNaturalNumber0 @ SV152 )
| ~ ( doDivides0 @ SV117 @ SV141 )
| ~ ( doDivides0 @ SV117 @ ( sdtpldt0 @ SV141 @ SV152 ) )
| ( doDivides0 @ SV117 @ SV152 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[927]) ).
thf(978,plain,
! [SV142: $i,SV118: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV118 )
| ~ ( aNaturalNumber0 @ SV142 ) )
= $true )
| ( ( ( SV142 = sz00 )
| ~ ( doDivides0 @ SV118 @ SV142 )
| ( sdtlseqdt0 @ SV118 @ SV142 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[928]) ).
thf(979,plain,
! [SV143: $i,SV119: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV119 )
| ~ ( aNaturalNumber0 @ SV143 ) )
= $true )
| ( ( ( SV119 = sz00 )
| ~ ( doDivides0 @ SV119 @ SV143 )
| ! [SY225: $i] :
( ~ ( aNaturalNumber0 @ SY225 )
| ( ( sdtasdt0 @ SY225 @ ( sdtsldt0 @ SV143 @ SV119 ) )
= ( sdtsldt0 @ ( sdtasdt0 @ SY225 @ SV143 ) @ SV119 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[929]) ).
thf(980,plain,
! [SV153: $i,SV144: $i,SV120: $i] :
( ( ~ ( aNaturalNumber0 @ SV120 )
| ~ ( aNaturalNumber0 @ SV144 )
| ~ ( aNaturalNumber0 @ SV153 )
| ~ ( doDivides0 @ SV153 @ ( sdtasdt0 @ SV120 @ SV144 ) )
| ~ ( isPrime0 @ SV153 )
| ( doDivides0 @ SV153 @ SV120 )
| ( doDivides0 @ SV153 @ SV144 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[930]) ).
thf(981,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ! [SX1: $i] :
( ( xp
!= ( sdtasdt0 @ SX0 @ SX1 ) )
| ~ ( aNaturalNumber0 @ SX1 ) )
| ( SX0 = sz10 )
| ( SX0 = xp ) )
| ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( doDivides0 @ SX0 @ xp )
| ( SX0 = sz10 )
| ( SX0 = xp ) ) )
| ~ ( ( xp != sz10 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[931]) ).
thf(982,plain,
( ( isPrime0 @ xp )
= $true ),
inference(extcnf_not_neg,[status(thm)],[932]) ).
thf(983,plain,
! [SV121: $i] :
( ( ~ ! [SY190: $i,SY191: $i] :
( ~ ( aNaturalNumber0 @ SV121 )
| ~ ( aNaturalNumber0 @ SY190 )
| ~ ( aNaturalNumber0 @ SY191 )
| ( ( sdtasdt0 @ SV121 @ ( sdtpldt0 @ SY190 @ SY191 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV121 @ SY190 ) @ ( sdtasdt0 @ SV121 @ SY191 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[933]) ).
thf(984,plain,
! [SV121: $i] :
( ( ~ ! [SY192: $i,SY193: $i] :
( ~ ( aNaturalNumber0 @ SV121 )
| ~ ( aNaturalNumber0 @ SY192 )
| ~ ( aNaturalNumber0 @ SY193 )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SY192 @ SY193 ) @ SV121 )
= ( sdtpldt0 @ ( sdtasdt0 @ SY192 @ SV121 ) @ ( sdtasdt0 @ SY193 @ SV121 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[933]) ).
thf(985,plain,
( ( ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( ( sdtasdt0 @ SX0 @ sz00 )
= sz00 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[934]) ).
thf(986,plain,
( ( ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( sz00
= ( sdtasdt0 @ sz00 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[935]) ).
thf(987,plain,
! [SV122: $i] :
( ( ( aNaturalNumber0 @ SV122 )
= $false )
| ( ( ( SV122 = sz00 )
| ~ ( ~ ! [SY194: $i,SY195: $i] :
( ~ ( aNaturalNumber0 @ SY194 )
| ~ ( aNaturalNumber0 @ SY195 )
| ( ( sdtasdt0 @ SV122 @ SY194 )
!= ( sdtasdt0 @ SV122 @ SY195 ) )
| ( SY194 = SY195 ) )
| ~ ! [SY196: $i,SY197: $i] :
( ~ ( aNaturalNumber0 @ SY196 )
| ~ ( aNaturalNumber0 @ SY197 )
| ( ( sdtasdt0 @ SY196 @ SV122 )
!= ( sdtasdt0 @ SY197 @ SV122 ) )
| ( SY196 = SY197 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[936]) ).
thf(988,plain,
( ( ! [SX0: $i] :
( ( ( sdtpldt0 @ xm @ SX0 )
!= xn )
| ~ ( aNaturalNumber0 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[937]) ).
thf(989,plain,
( ( ~ ( sdtlseqdt0 @ xm @ xn ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[938]) ).
thf(990,plain,
! [SV123: $i] :
( ( ~ ~ ( ~ ! [SY198: $i,SY199: $i] :
( ~ ( aNaturalNumber0 @ SV123 )
| ~ ( aNaturalNumber0 @ SY198 )
| ~ ( aNaturalNumber0 @ SY199 )
| ( SV123 = sz00 )
| ( SY198 = SY199 )
| ~ ( sdtlseqdt0 @ SY198 @ SY199 )
| ( ( sdtasdt0 @ SY198 @ SV123 )
!= ( sdtasdt0 @ SY199 @ SV123 ) ) )
| ~ ~ ( ~ ! [SY200: $i,SY201: $i] :
( ~ ( aNaturalNumber0 @ SV123 )
| ~ ( aNaturalNumber0 @ SY200 )
| ~ ( aNaturalNumber0 @ SY201 )
| ( SV123 = sz00 )
| ( SY200 = SY201 )
| ~ ( sdtlseqdt0 @ SY200 @ SY201 )
| ( ( sdtasdt0 @ SV123 @ SY200 )
!= ( sdtasdt0 @ SV123 @ SY201 ) ) )
| ~ ! [SY202: $i,SY203: $i] :
( ~ ( aNaturalNumber0 @ SV123 )
| ~ ( aNaturalNumber0 @ SY202 )
| ~ ( aNaturalNumber0 @ SY203 )
| ( SV123 = sz00 )
| ( SY202 = SY203 )
| ~ ( sdtlseqdt0 @ SY202 @ SY203 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV123 @ SY202 ) @ ( sdtasdt0 @ SV123 @ SY203 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[939]) ).
thf(991,plain,
! [SV123: $i] :
( ( ~ ! [SY204: $i,SY205: $i] :
( ~ ( aNaturalNumber0 @ SV123 )
| ~ ( aNaturalNumber0 @ SY204 )
| ~ ( aNaturalNumber0 @ SY205 )
| ( SV123 = sz00 )
| ( SY204 = SY205 )
| ~ ( sdtlseqdt0 @ SY204 @ SY205 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SY204 @ SV123 ) @ ( sdtasdt0 @ SY205 @ SV123 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[939]) ).
thf(992,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xn @ xn )
!= ( sdtasdt0 @ xp @ sK3_W0 ) )
| ~ ( aNaturalNumber0 @ sK3_W0 ) )
| ~ ( doDivides0 @ xp @ ( sdtasdt0 @ xn @ xn ) ) )
| ~ ~ ( ( xn
!= ( sdtasdt0 @ xp @ sK2_W0 ) )
| ~ ( aNaturalNumber0 @ sK2_W0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[940]) ).
thf(993,plain,
( ( doDivides0 @ xp @ xn )
= $true ),
inference(extcnf_not_neg,[status(thm)],[941]) ).
thf(994,plain,
! [SV124: $i] :
( ( ~ ! [SY206: $i,SY207: $i] :
( ( SY207 = sz00 )
| ( SY206 = sz00 )
| ( SV124 = sz00 )
| ~ ( aNaturalNumber0 @ SV124 )
| ~ ( aNaturalNumber0 @ SY206 )
| ~ ( aNaturalNumber0 @ SY207 )
| ( ( sdtasdt0 @ SY207 @ ( sdtasdt0 @ SY206 @ SY206 ) )
!= ( sdtasdt0 @ SV124 @ SV124 ) )
| ~ ( iLess0 @ SV124 @ xn )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( SY207
!= ( sdtasdt0 @ ( sK4_W3 @ SY207 @ SY206 @ SV124 ) @ ( sK5_SY81 @ SY207 @ SY206 @ SV124 ) ) )
| ~ ( aNaturalNumber0 @ ( sK5_SY81 @ SY207 @ SY206 @ SV124 ) ) )
| ~ ( aNaturalNumber0 @ ( sK4_W3 @ SY207 @ SY206 @ SV124 ) ) )
| ~ ( doDivides0 @ ( sK4_W3 @ SY207 @ SY206 @ SV124 ) @ SY207 ) )
| ~ ~ ( ~ ( ( ( sK4_W3 @ SY207 @ SY206 @ SV124 )
!= sz10 ) )
| ~ ( ( ( sK4_W3 @ SY207 @ SY206 @ SV124 )
!= SY207 ) ) ) )
| ( SY207 = sz10 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[942]) ).
thf(995,plain,
! [SV124: $i] :
( ( ~ ! [SY208: $i,SY209: $i] :
( ( SY209 = sz00 )
| ( SY208 = sz00 )
| ( SV124 = sz00 )
| ~ ( aNaturalNumber0 @ SV124 )
| ~ ( aNaturalNumber0 @ SY208 )
| ~ ( aNaturalNumber0 @ SY209 )
| ( ( sdtasdt0 @ SY209 @ ( sdtasdt0 @ SY208 @ SY208 ) )
!= ( sdtasdt0 @ SV124 @ SV124 ) )
| ~ ( iLess0 @ SV124 @ xn )
| ~ ( isPrime0 @ SY209 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[942]) ).
thf(996,plain,
( ( xp != sz00 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[943]) ).
thf(997,plain,
( ( ~ ( ~ ( ( xm != sz00 ) )
| ~ ~ ( ~ ( ( xn != sz00 ) )
| ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ xn )
| ~ ( aNaturalNumber0 @ xm ) )
| ~ ( aNaturalNumber0 @ xp ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[944]) ).
thf(998,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 )
| ( SX1 != SX0 )
| ( sdtlseqdt0 @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[945]) ).
thf(999,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 )
| ( sdtlseqdt0 @ SX1 @ SX0 )
| ( sdtlseqdt0 @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[946]) ).
thf(1000,plain,
! [SV145: $i,SV125: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV125 )
| ~ ( aNaturalNumber0 @ SV145 ) )
= $true )
| ( ( ( SV125 = SV145 )
| ~ ( sdtlseqdt0 @ SV125 @ SV145 )
| ~ ( ~ ~ ( ~ ! [SY227: $i] :
( ~ ( aNaturalNumber0 @ SY227 )
| ( ( sdtpldt0 @ SV125 @ SY227 )
!= ( sdtpldt0 @ SV145 @ SY227 ) ) )
| ~ ~ ( ~ ! [SY228: $i] :
( ~ ( aNaturalNumber0 @ SY228 )
| ( ( sdtpldt0 @ SY228 @ SV125 )
!= ( sdtpldt0 @ SY228 @ SV145 ) ) )
| ~ ! [SY229: $i] :
( ~ ( aNaturalNumber0 @ SY229 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SY229 @ SV125 ) @ ( sdtpldt0 @ SY229 @ SV145 ) ) ) ) )
| ~ ! [SY230: $i] :
( ~ ( aNaturalNumber0 @ SY230 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SV125 @ SY230 ) @ ( sdtpldt0 @ SV145 @ SY230 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[947]) ).
thf(1001,plain,
( ( ~ ( ( xn
!= ( sdtasdt0 @ xp @ xq ) )
| ~ ( aNaturalNumber0 @ xq ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[948]) ).
thf(1002,plain,
( ( xq
= ( sdtsldt0 @ xn @ xp ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[949]) ).
thf(1003,plain,
! [SV126: $i] :
( ( ~ ! [SY215: $i,SY216: $i] :
( ~ ( aNaturalNumber0 @ SV126 )
| ~ ( aNaturalNumber0 @ SY215 )
| ~ ( aNaturalNumber0 @ SY216 )
| ( ( sdtpldt0 @ SV126 @ SY215 )
!= ( sdtpldt0 @ SV126 @ SY216 ) )
| ( SY215 = SY216 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[950]) ).
thf(1004,plain,
! [SV126: $i] :
( ( ~ ! [SY217: $i,SY218: $i] :
( ~ ( aNaturalNumber0 @ SV126 )
| ~ ( aNaturalNumber0 @ SY217 )
| ~ ( aNaturalNumber0 @ SY218 )
| ( ( sdtpldt0 @ SY217 @ SV126 )
!= ( sdtpldt0 @ SY218 @ SV126 ) )
| ( SY217 = SY218 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[950]) ).
thf(1005,plain,
( ( ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( sz10 != SX0 )
| ( SX0 = sz00 )
| ( SX0 = sz10 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[951]) ).
thf(1006,plain,
( ( ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( sdtlseqdt0 @ sz10 @ SX0 )
| ( SX0 = sz00 )
| ( SX0 = sz10 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[952]) ).
thf(1007,plain,
! [SV127: $i] :
( ( ( SV127 = sz10 )
= $true )
| ( ( ( SV127 = sz00 )
| ~ ( aNaturalNumber0 @ SV127 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ ( sK1_W1 @ SV127 ) )
| ~ ( doDivides0 @ ( sK1_W1 @ SV127 ) @ SV127 ) )
| ~ ( isPrime0 @ ( sK1_W1 @ SV127 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[953]) ).
thf(1008,plain,
( ( sz10 != sz00 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[954]) ).
thf(1009,plain,
( ( aNaturalNumber0 @ sz10 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[955]) ).
thf(1010,plain,
( ( ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( ( sdtpldt0 @ SX0 @ sz00 )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[956]) ).
thf(1011,plain,
( ( ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( SX0
= ( sdtpldt0 @ sz00 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[957]) ).
thf(1012,plain,
( ( ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( ( sdtasdt0 @ SX0 @ sz10 )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[958]) ).
thf(1013,plain,
( ( ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( SX0
= ( sdtasdt0 @ sz10 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[959]) ).
thf(1014,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 )
| ( ( sdtpldt0 @ SX0 @ SX1 )
!= sz00 )
| ( SX0 = sz00 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[960]) ).
thf(1015,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 )
| ( ( sdtpldt0 @ SX0 @ SX1 )
!= sz00 )
| ( SX1 = sz00 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[961]) ).
thf(1016,plain,
! [SV128: $i,SV103: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV103 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV128 ) )
= $true )
| ( ( aNaturalNumber0 @ ( sdtpldt0 @ SV103 @ SV128 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[962]) ).
thf(1017,plain,
! [SV129: $i,SV104: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV104 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV129 ) )
= $true )
| ( ( aNaturalNumber0 @ ( sdtasdt0 @ SV104 @ SV129 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[963]) ).
thf(1018,plain,
! [SV130: $i,SV105: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV105 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV130 ) )
= $true )
| ( ( ( sdtpldt0 @ SV105 @ SV130 )
= ( sdtpldt0 @ SV130 @ SV105 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[964]) ).
thf(1019,plain,
! [SV146: $i,SV131: $i,SV106: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV106 )
| ~ ( aNaturalNumber0 @ SV131 )
| ~ ( aNaturalNumber0 @ SV146 ) )
= $true )
| ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV106 @ SV131 ) @ SV146 )
= ( sdtpldt0 @ SV106 @ ( sdtpldt0 @ SV131 @ SV146 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[965]) ).
thf(1020,plain,
! [SV132: $i,SV107: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV107 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV132 ) )
= $true )
| ( ( ( sdtasdt0 @ SV107 @ SV132 )
= ( sdtasdt0 @ SV132 @ SV107 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[966]) ).
thf(1021,plain,
! [SV147: $i,SV133: $i,SV108: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV108 )
| ~ ( aNaturalNumber0 @ SV133 )
| ~ ( aNaturalNumber0 @ SV147 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV108 @ SV133 ) @ SV147 )
= ( sdtasdt0 @ SV108 @ ( sdtasdt0 @ SV133 @ SV147 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[967]) ).
thf(1022,plain,
! [SV134: $i,SV109: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV109 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV134 ) )
= $true )
| ( ( ( ( sdtasdt0 @ SV109 @ SV134 )
!= sz00 )
| ( SV109 = sz00 )
| ( SV134 = sz00 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[968]) ).
thf(1023,plain,
! [SV135: $i,SV111: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV111 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV135 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV111 @ SV135 )
| ~ ( sdtlseqdt0 @ SV135 @ SV111 )
| ( SV111 = SV135 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[970]) ).
thf(1024,plain,
! [SV148: $i,SV136: $i,SV112: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV112 )
| ~ ( aNaturalNumber0 @ SV136 )
| ~ ( aNaturalNumber0 @ SV148 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV112 @ SV136 )
| ~ ( sdtlseqdt0 @ SV136 @ SV148 )
| ( sdtlseqdt0 @ SV112 @ SV148 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[971]) ).
thf(1025,plain,
! [SV137: $i,SV113: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV113 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV137 ) )
= $true )
| ( ( ( SV113 = sz00 )
| ( sdtlseqdt0 @ SV137 @ ( sdtasdt0 @ SV137 @ SV113 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[972]) ).
thf(1026,plain,
! [SV149: $i] :
( ( ( aNaturalNumber0 @ SV149 )
= $false )
| ( ( ! [W1: $i] :
~ ( aNaturalNumber0 @ W1 ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[973]) ).
thf(1027,plain,
! [SV138: $i,SV114: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV114 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV138 ) )
= $true )
| ( ( ( SV114 = SV138 )
| ~ ( sdtlseqdt0 @ SV114 @ SV138 )
| ( iLess0 @ SV114 @ SV138 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[974]) ).
thf(1028,plain,
! [SV150: $i,SV139: $i,SV115: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV115 )
| ~ ( aNaturalNumber0 @ SV139 )
| ~ ( aNaturalNumber0 @ SV150 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV115 @ SV139 )
| ~ ( doDivides0 @ SV139 @ SV150 )
| ( doDivides0 @ SV115 @ SV150 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[975]) ).
thf(1029,plain,
! [SV151: $i,SV140: $i,SV116: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV116 )
| ~ ( aNaturalNumber0 @ SV140 )
| ~ ( aNaturalNumber0 @ SV151 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV116 @ SV140 )
| ~ ( doDivides0 @ SV116 @ SV151 )
| ( doDivides0 @ SV116 @ ( sdtpldt0 @ SV140 @ SV151 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[976]) ).
thf(1030,plain,
! [SV152: $i,SV141: $i,SV117: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV117 )
| ~ ( aNaturalNumber0 @ SV141 )
| ~ ( aNaturalNumber0 @ SV152 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV117 @ SV141 )
| ~ ( doDivides0 @ SV117 @ ( sdtpldt0 @ SV141 @ SV152 ) )
| ( doDivides0 @ SV117 @ SV152 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[977]) ).
thf(1031,plain,
! [SV142: $i,SV118: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV118 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV142 ) )
= $true )
| ( ( ( SV142 = sz00 )
| ~ ( doDivides0 @ SV118 @ SV142 )
| ( sdtlseqdt0 @ SV118 @ SV142 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[978]) ).
thf(1032,plain,
! [SV143: $i,SV119: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV119 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV143 ) )
= $true )
| ( ( ( SV119 = sz00 )
| ~ ( doDivides0 @ SV119 @ SV143 )
| ! [SY225: $i] :
( ~ ( aNaturalNumber0 @ SY225 )
| ( ( sdtasdt0 @ SY225 @ ( sdtsldt0 @ SV143 @ SV119 ) )
= ( sdtsldt0 @ ( sdtasdt0 @ SY225 @ SV143 ) @ SV119 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[979]) ).
thf(1033,plain,
! [SV153: $i,SV144: $i,SV120: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV120 )
| ~ ( aNaturalNumber0 @ SV144 )
| ~ ( aNaturalNumber0 @ SV153 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV153 @ ( sdtasdt0 @ SV120 @ SV144 ) )
| ~ ( isPrime0 @ SV153 )
| ( doDivides0 @ SV153 @ SV120 )
| ( doDivides0 @ SV153 @ SV144 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[980]) ).
thf(1034,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ! [SX1: $i] :
( ( xp
!= ( sdtasdt0 @ SX0 @ SX1 ) )
| ~ ( aNaturalNumber0 @ SX1 ) )
| ( SX0 = sz10 )
| ( SX0 = xp ) )
| ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( doDivides0 @ SX0 @ xp )
| ( SX0 = sz10 )
| ( SX0 = xp ) ) )
| ~ ( ( xp != sz10 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[981]) ).
thf(1035,plain,
! [SV121: $i] :
( ( ! [SY190: $i,SY191: $i] :
( ~ ( aNaturalNumber0 @ SV121 )
| ~ ( aNaturalNumber0 @ SY190 )
| ~ ( aNaturalNumber0 @ SY191 )
| ( ( sdtasdt0 @ SV121 @ ( sdtpldt0 @ SY190 @ SY191 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV121 @ SY190 ) @ ( sdtasdt0 @ SV121 @ SY191 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[983]) ).
thf(1036,plain,
! [SV121: $i] :
( ( ! [SY192: $i,SY193: $i] :
( ~ ( aNaturalNumber0 @ SV121 )
| ~ ( aNaturalNumber0 @ SY192 )
| ~ ( aNaturalNumber0 @ SY193 )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SY192 @ SY193 ) @ SV121 )
= ( sdtpldt0 @ ( sdtasdt0 @ SY192 @ SV121 ) @ ( sdtasdt0 @ SY193 @ SV121 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[984]) ).
thf(1037,plain,
! [SV154: $i] :
( ( ~ ( aNaturalNumber0 @ SV154 )
| ( ( sdtasdt0 @ SV154 @ sz00 )
= sz00 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[985]) ).
thf(1038,plain,
! [SV155: $i] :
( ( ~ ( aNaturalNumber0 @ SV155 )
| ( sz00
= ( sdtasdt0 @ sz00 @ SV155 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[986]) ).
thf(1039,plain,
! [SV122: $i] :
( ( ( SV122 = sz00 )
= $true )
| ( ( ~ ( ~ ! [SY194: $i,SY195: $i] :
( ~ ( aNaturalNumber0 @ SY194 )
| ~ ( aNaturalNumber0 @ SY195 )
| ( ( sdtasdt0 @ SV122 @ SY194 )
!= ( sdtasdt0 @ SV122 @ SY195 ) )
| ( SY194 = SY195 ) )
| ~ ! [SY196: $i,SY197: $i] :
( ~ ( aNaturalNumber0 @ SY196 )
| ~ ( aNaturalNumber0 @ SY197 )
| ( ( sdtasdt0 @ SY196 @ SV122 )
!= ( sdtasdt0 @ SY197 @ SV122 ) )
| ( SY196 = SY197 ) ) ) )
= $true )
| ( ( aNaturalNumber0 @ SV122 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[987]) ).
thf(1040,plain,
! [SV156: $i] :
( ( ( ( sdtpldt0 @ xm @ SV156 )
!= xn )
| ~ ( aNaturalNumber0 @ SV156 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[988]) ).
thf(1041,plain,
( ( sdtlseqdt0 @ xm @ xn )
= $false ),
inference(extcnf_not_pos,[status(thm)],[989]) ).
thf(1042,plain,
! [SV123: $i] :
( ( ~ ( ~ ! [SY198: $i,SY199: $i] :
( ~ ( aNaturalNumber0 @ SV123 )
| ~ ( aNaturalNumber0 @ SY198 )
| ~ ( aNaturalNumber0 @ SY199 )
| ( SV123 = sz00 )
| ( SY198 = SY199 )
| ~ ( sdtlseqdt0 @ SY198 @ SY199 )
| ( ( sdtasdt0 @ SY198 @ SV123 )
!= ( sdtasdt0 @ SY199 @ SV123 ) ) )
| ~ ~ ( ~ ! [SY200: $i,SY201: $i] :
( ~ ( aNaturalNumber0 @ SV123 )
| ~ ( aNaturalNumber0 @ SY200 )
| ~ ( aNaturalNumber0 @ SY201 )
| ( SV123 = sz00 )
| ( SY200 = SY201 )
| ~ ( sdtlseqdt0 @ SY200 @ SY201 )
| ( ( sdtasdt0 @ SV123 @ SY200 )
!= ( sdtasdt0 @ SV123 @ SY201 ) ) )
| ~ ! [SY202: $i,SY203: $i] :
( ~ ( aNaturalNumber0 @ SV123 )
| ~ ( aNaturalNumber0 @ SY202 )
| ~ ( aNaturalNumber0 @ SY203 )
| ( SV123 = sz00 )
| ( SY202 = SY203 )
| ~ ( sdtlseqdt0 @ SY202 @ SY203 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV123 @ SY202 ) @ ( sdtasdt0 @ SV123 @ SY203 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[990]) ).
thf(1043,plain,
! [SV123: $i] :
( ( ! [SY204: $i,SY205: $i] :
( ~ ( aNaturalNumber0 @ SV123 )
| ~ ( aNaturalNumber0 @ SY204 )
| ~ ( aNaturalNumber0 @ SY205 )
| ( SV123 = sz00 )
| ( SY204 = SY205 )
| ~ ( sdtlseqdt0 @ SY204 @ SY205 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SY204 @ SV123 ) @ ( sdtasdt0 @ SY205 @ SV123 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[991]) ).
thf(1044,plain,
( ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xn @ xn )
!= ( sdtasdt0 @ xp @ sK3_W0 ) )
| ~ ( aNaturalNumber0 @ sK3_W0 ) )
| ~ ( doDivides0 @ xp @ ( sdtasdt0 @ xn @ xn ) ) )
| ~ ~ ( ( xn
!= ( sdtasdt0 @ xp @ sK2_W0 ) )
| ~ ( aNaturalNumber0 @ sK2_W0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[992]) ).
thf(1045,plain,
! [SV124: $i] :
( ( ! [SY206: $i,SY207: $i] :
( ( SY207 = sz00 )
| ( SY206 = sz00 )
| ( SV124 = sz00 )
| ~ ( aNaturalNumber0 @ SV124 )
| ~ ( aNaturalNumber0 @ SY206 )
| ~ ( aNaturalNumber0 @ SY207 )
| ( ( sdtasdt0 @ SY207 @ ( sdtasdt0 @ SY206 @ SY206 ) )
!= ( sdtasdt0 @ SV124 @ SV124 ) )
| ~ ( iLess0 @ SV124 @ xn )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( SY207
!= ( sdtasdt0 @ ( sK4_W3 @ SY207 @ SY206 @ SV124 ) @ ( sK5_SY81 @ SY207 @ SY206 @ SV124 ) ) )
| ~ ( aNaturalNumber0 @ ( sK5_SY81 @ SY207 @ SY206 @ SV124 ) ) )
| ~ ( aNaturalNumber0 @ ( sK4_W3 @ SY207 @ SY206 @ SV124 ) ) )
| ~ ( doDivides0 @ ( sK4_W3 @ SY207 @ SY206 @ SV124 ) @ SY207 ) )
| ~ ~ ( ~ ( ( ( sK4_W3 @ SY207 @ SY206 @ SV124 )
!= sz10 ) )
| ~ ( ( ( sK4_W3 @ SY207 @ SY206 @ SV124 )
!= SY207 ) ) ) )
| ( SY207 = sz10 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[994]) ).
thf(1046,plain,
! [SV124: $i] :
( ( ! [SY208: $i,SY209: $i] :
( ( SY209 = sz00 )
| ( SY208 = sz00 )
| ( SV124 = sz00 )
| ~ ( aNaturalNumber0 @ SV124 )
| ~ ( aNaturalNumber0 @ SY208 )
| ~ ( aNaturalNumber0 @ SY209 )
| ( ( sdtasdt0 @ SY209 @ ( sdtasdt0 @ SY208 @ SY208 ) )
!= ( sdtasdt0 @ SV124 @ SV124 ) )
| ~ ( iLess0 @ SV124 @ xn )
| ~ ( isPrime0 @ SY209 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[995]) ).
thf(1047,plain,
( ( xp = sz00 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[996]) ).
thf(1048,plain,
( ( ~ ( ( xm != sz00 ) )
| ~ ~ ( ~ ( ( xn != sz00 ) )
| ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ xn )
| ~ ( aNaturalNumber0 @ xm ) )
| ~ ( aNaturalNumber0 @ xp ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[997]) ).
thf(1049,plain,
! [SV157: $i] :
( ( ! [SY231: $i] :
( ~ ( aNaturalNumber0 @ SV157 )
| ~ ( aNaturalNumber0 @ SY231 )
| ( SY231 != SV157 )
| ( sdtlseqdt0 @ SV157 @ SY231 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[998]) ).
thf(1050,plain,
! [SV158: $i] :
( ( ! [SY232: $i] :
( ~ ( aNaturalNumber0 @ SV158 )
| ~ ( aNaturalNumber0 @ SY232 )
| ( sdtlseqdt0 @ SY232 @ SV158 )
| ( sdtlseqdt0 @ SV158 @ SY232 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[999]) ).
thf(1051,plain,
! [SV145: $i,SV125: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV125 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV145 ) )
= $true )
| ( ( ( SV125 = SV145 )
| ~ ( sdtlseqdt0 @ SV125 @ SV145 )
| ~ ( ~ ~ ( ~ ! [SY227: $i] :
( ~ ( aNaturalNumber0 @ SY227 )
| ( ( sdtpldt0 @ SV125 @ SY227 )
!= ( sdtpldt0 @ SV145 @ SY227 ) ) )
| ~ ~ ( ~ ! [SY228: $i] :
( ~ ( aNaturalNumber0 @ SY228 )
| ( ( sdtpldt0 @ SY228 @ SV125 )
!= ( sdtpldt0 @ SY228 @ SV145 ) ) )
| ~ ! [SY229: $i] :
( ~ ( aNaturalNumber0 @ SY229 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SY229 @ SV125 ) @ ( sdtpldt0 @ SY229 @ SV145 ) ) ) ) )
| ~ ! [SY230: $i] :
( ~ ( aNaturalNumber0 @ SY230 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SV125 @ SY230 ) @ ( sdtpldt0 @ SV145 @ SY230 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1000]) ).
thf(1052,plain,
( ( ( xn
!= ( sdtasdt0 @ xp @ xq ) )
| ~ ( aNaturalNumber0 @ xq ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1001]) ).
thf(1053,plain,
! [SV126: $i] :
( ( ! [SY215: $i,SY216: $i] :
( ~ ( aNaturalNumber0 @ SV126 )
| ~ ( aNaturalNumber0 @ SY215 )
| ~ ( aNaturalNumber0 @ SY216 )
| ( ( sdtpldt0 @ SV126 @ SY215 )
!= ( sdtpldt0 @ SV126 @ SY216 ) )
| ( SY215 = SY216 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1003]) ).
thf(1054,plain,
! [SV126: $i] :
( ( ! [SY217: $i,SY218: $i] :
( ~ ( aNaturalNumber0 @ SV126 )
| ~ ( aNaturalNumber0 @ SY217 )
| ~ ( aNaturalNumber0 @ SY218 )
| ( ( sdtpldt0 @ SY217 @ SV126 )
!= ( sdtpldt0 @ SY218 @ SV126 ) )
| ( SY217 = SY218 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1004]) ).
thf(1055,plain,
! [SV159: $i] :
( ( ~ ( aNaturalNumber0 @ SV159 )
| ( sz10 != SV159 )
| ( SV159 = sz00 )
| ( SV159 = sz10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1005]) ).
thf(1056,plain,
! [SV160: $i] :
( ( ~ ( aNaturalNumber0 @ SV160 )
| ( sdtlseqdt0 @ sz10 @ SV160 )
| ( SV160 = sz00 )
| ( SV160 = sz10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1006]) ).
thf(1057,plain,
! [SV127: $i] :
( ( ( SV127 = sz00 )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV127 ) )
= $true )
| ( ( SV127 = sz10 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ ( sK1_W1 @ SV127 ) )
| ~ ( doDivides0 @ ( sK1_W1 @ SV127 ) @ SV127 ) )
| ~ ( isPrime0 @ ( sK1_W1 @ SV127 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1007]) ).
thf(1058,plain,
( ( sz10 = sz00 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1008]) ).
thf(1059,plain,
! [SV161: $i] :
( ( ~ ( aNaturalNumber0 @ SV161 )
| ( ( sdtpldt0 @ SV161 @ sz00 )
= SV161 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1010]) ).
thf(1060,plain,
! [SV162: $i] :
( ( ~ ( aNaturalNumber0 @ SV162 )
| ( SV162
= ( sdtpldt0 @ sz00 @ SV162 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1011]) ).
thf(1061,plain,
! [SV163: $i] :
( ( ~ ( aNaturalNumber0 @ SV163 )
| ( ( sdtasdt0 @ SV163 @ sz10 )
= SV163 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1012]) ).
thf(1062,plain,
! [SV164: $i] :
( ( ~ ( aNaturalNumber0 @ SV164 )
| ( SV164
= ( sdtasdt0 @ sz10 @ SV164 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1013]) ).
thf(1063,plain,
! [SV165: $i] :
( ( ! [SY233: $i] :
( ~ ( aNaturalNumber0 @ SV165 )
| ~ ( aNaturalNumber0 @ SY233 )
| ( ( sdtpldt0 @ SV165 @ SY233 )
!= sz00 )
| ( SV165 = sz00 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1014]) ).
thf(1064,plain,
! [SV166: $i] :
( ( ! [SY234: $i] :
( ~ ( aNaturalNumber0 @ SV166 )
| ~ ( aNaturalNumber0 @ SY234 )
| ( ( sdtpldt0 @ SV166 @ SY234 )
!= sz00 )
| ( SY234 = sz00 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1015]) ).
thf(1065,plain,
! [SV128: $i,SV103: $i] :
( ( ( aNaturalNumber0 @ SV103 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV128 ) )
= $true )
| ( ( aNaturalNumber0 @ ( sdtpldt0 @ SV103 @ SV128 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1016]) ).
thf(1066,plain,
! [SV129: $i,SV104: $i] :
( ( ( aNaturalNumber0 @ SV104 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV129 ) )
= $true )
| ( ( aNaturalNumber0 @ ( sdtasdt0 @ SV104 @ SV129 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1017]) ).
thf(1067,plain,
! [SV130: $i,SV105: $i] :
( ( ( aNaturalNumber0 @ SV105 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV130 ) )
= $true )
| ( ( ( sdtpldt0 @ SV105 @ SV130 )
= ( sdtpldt0 @ SV130 @ SV105 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1018]) ).
thf(1068,plain,
! [SV146: $i,SV131: $i,SV106: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV106 )
| ~ ( aNaturalNumber0 @ SV131 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV146 ) )
= $true )
| ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV106 @ SV131 ) @ SV146 )
= ( sdtpldt0 @ SV106 @ ( sdtpldt0 @ SV131 @ SV146 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1019]) ).
thf(1069,plain,
! [SV132: $i,SV107: $i] :
( ( ( aNaturalNumber0 @ SV107 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV132 ) )
= $true )
| ( ( ( sdtasdt0 @ SV107 @ SV132 )
= ( sdtasdt0 @ SV132 @ SV107 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1020]) ).
thf(1070,plain,
! [SV147: $i,SV133: $i,SV108: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV108 )
| ~ ( aNaturalNumber0 @ SV133 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV147 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV108 @ SV133 ) @ SV147 )
= ( sdtasdt0 @ SV108 @ ( sdtasdt0 @ SV133 @ SV147 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1021]) ).
thf(1071,plain,
! [SV134: $i,SV109: $i] :
( ( ( aNaturalNumber0 @ SV109 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV134 ) )
= $true )
| ( ( ( ( sdtasdt0 @ SV109 @ SV134 )
!= sz00 )
| ( SV109 = sz00 )
| ( SV134 = sz00 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1022]) ).
thf(1072,plain,
! [SV135: $i,SV111: $i] :
( ( ( aNaturalNumber0 @ SV111 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV135 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV111 @ SV135 )
| ~ ( sdtlseqdt0 @ SV135 @ SV111 )
| ( SV111 = SV135 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1023]) ).
thf(1073,plain,
! [SV148: $i,SV136: $i,SV112: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV112 )
| ~ ( aNaturalNumber0 @ SV136 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV148 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV112 @ SV136 )
| ~ ( sdtlseqdt0 @ SV136 @ SV148 )
| ( sdtlseqdt0 @ SV112 @ SV148 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1024]) ).
thf(1074,plain,
! [SV137: $i,SV113: $i] :
( ( ( aNaturalNumber0 @ SV113 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV137 ) )
= $true )
| ( ( ( SV113 = sz00 )
| ( sdtlseqdt0 @ SV137 @ ( sdtasdt0 @ SV137 @ SV113 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1025]) ).
thf(1075,plain,
! [SV149: $i,SV167: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV167 ) )
= $true )
| ( ( aNaturalNumber0 @ SV149 )
= $false )
| ( $true = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1026]) ).
thf(1076,plain,
! [SV138: $i,SV114: $i] :
( ( ( aNaturalNumber0 @ SV114 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV138 ) )
= $true )
| ( ( ( SV114 = SV138 )
| ~ ( sdtlseqdt0 @ SV114 @ SV138 )
| ( iLess0 @ SV114 @ SV138 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1027]) ).
thf(1077,plain,
! [SV150: $i,SV139: $i,SV115: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV115 )
| ~ ( aNaturalNumber0 @ SV139 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV150 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV115 @ SV139 )
| ~ ( doDivides0 @ SV139 @ SV150 )
| ( doDivides0 @ SV115 @ SV150 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1028]) ).
thf(1078,plain,
! [SV151: $i,SV140: $i,SV116: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV116 )
| ~ ( aNaturalNumber0 @ SV140 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV151 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV116 @ SV140 )
| ~ ( doDivides0 @ SV116 @ SV151 )
| ( doDivides0 @ SV116 @ ( sdtpldt0 @ SV140 @ SV151 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1029]) ).
thf(1079,plain,
! [SV152: $i,SV141: $i,SV117: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV117 )
| ~ ( aNaturalNumber0 @ SV141 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV152 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV117 @ SV141 )
| ~ ( doDivides0 @ SV117 @ ( sdtpldt0 @ SV141 @ SV152 ) )
| ( doDivides0 @ SV117 @ SV152 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1030]) ).
thf(1080,plain,
! [SV142: $i,SV118: $i] :
( ( ( aNaturalNumber0 @ SV118 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV142 ) )
= $true )
| ( ( ( SV142 = sz00 )
| ~ ( doDivides0 @ SV118 @ SV142 )
| ( sdtlseqdt0 @ SV118 @ SV142 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1031]) ).
thf(1081,plain,
! [SV143: $i,SV119: $i] :
( ( ( aNaturalNumber0 @ SV119 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV143 ) )
= $true )
| ( ( ( SV119 = sz00 )
| ~ ( doDivides0 @ SV119 @ SV143 )
| ! [SY225: $i] :
( ~ ( aNaturalNumber0 @ SY225 )
| ( ( sdtasdt0 @ SY225 @ ( sdtsldt0 @ SV143 @ SV119 ) )
= ( sdtsldt0 @ ( sdtasdt0 @ SY225 @ SV143 ) @ SV119 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1032]) ).
thf(1082,plain,
! [SV153: $i,SV144: $i,SV120: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV120 )
| ~ ( aNaturalNumber0 @ SV144 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV153 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV153 @ ( sdtasdt0 @ SV120 @ SV144 ) )
| ~ ( isPrime0 @ SV153 )
| ( doDivides0 @ SV153 @ SV120 )
| ( doDivides0 @ SV153 @ SV144 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1033]) ).
thf(1083,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ! [SX1: $i] :
( ( xp
!= ( sdtasdt0 @ SX0 @ SX1 ) )
| ~ ( aNaturalNumber0 @ SX1 ) )
| ( SX0 = sz10 )
| ( SX0 = xp ) )
| ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( doDivides0 @ SX0 @ xp )
| ( SX0 = sz10 )
| ( SX0 = xp ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1034]) ).
thf(1084,plain,
( ( ~ ( ( xp != sz10 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1034]) ).
thf(1085,plain,
! [SV168: $i,SV121: $i] :
( ( ! [SY235: $i] :
( ~ ( aNaturalNumber0 @ SV121 )
| ~ ( aNaturalNumber0 @ SV168 )
| ~ ( aNaturalNumber0 @ SY235 )
| ( ( sdtasdt0 @ SV121 @ ( sdtpldt0 @ SV168 @ SY235 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV121 @ SV168 ) @ ( sdtasdt0 @ SV121 @ SY235 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1035]) ).
thf(1086,plain,
! [SV169: $i,SV121: $i] :
( ( ! [SY236: $i] :
( ~ ( aNaturalNumber0 @ SV121 )
| ~ ( aNaturalNumber0 @ SV169 )
| ~ ( aNaturalNumber0 @ SY236 )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SV169 @ SY236 ) @ SV121 )
= ( sdtpldt0 @ ( sdtasdt0 @ SV169 @ SV121 ) @ ( sdtasdt0 @ SY236 @ SV121 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1036]) ).
thf(1087,plain,
! [SV154: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV154 ) )
= $true )
| ( ( ( sdtasdt0 @ SV154 @ sz00 )
= sz00 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1037]) ).
thf(1088,plain,
! [SV155: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV155 ) )
= $true )
| ( ( sz00
= ( sdtasdt0 @ sz00 @ SV155 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1038]) ).
thf(1089,plain,
! [SV122: $i] :
( ( ( ~ ! [SY194: $i,SY195: $i] :
( ~ ( aNaturalNumber0 @ SY194 )
| ~ ( aNaturalNumber0 @ SY195 )
| ( ( sdtasdt0 @ SV122 @ SY194 )
!= ( sdtasdt0 @ SV122 @ SY195 ) )
| ( SY194 = SY195 ) )
| ~ ! [SY196: $i,SY197: $i] :
( ~ ( aNaturalNumber0 @ SY196 )
| ~ ( aNaturalNumber0 @ SY197 )
| ( ( sdtasdt0 @ SY196 @ SV122 )
!= ( sdtasdt0 @ SY197 @ SV122 ) )
| ( SY196 = SY197 ) ) )
= $false )
| ( ( SV122 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV122 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1039]) ).
thf(1090,plain,
! [SV156: $i] :
( ( ( ( sdtpldt0 @ xm @ SV156 )
!= xn )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV156 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1040]) ).
thf(1091,plain,
! [SV123: $i] :
( ( ~ ! [SY198: $i,SY199: $i] :
( ~ ( aNaturalNumber0 @ SV123 )
| ~ ( aNaturalNumber0 @ SY198 )
| ~ ( aNaturalNumber0 @ SY199 )
| ( SV123 = sz00 )
| ( SY198 = SY199 )
| ~ ( sdtlseqdt0 @ SY198 @ SY199 )
| ( ( sdtasdt0 @ SY198 @ SV123 )
!= ( sdtasdt0 @ SY199 @ SV123 ) ) )
| ~ ~ ( ~ ! [SY200: $i,SY201: $i] :
( ~ ( aNaturalNumber0 @ SV123 )
| ~ ( aNaturalNumber0 @ SY200 )
| ~ ( aNaturalNumber0 @ SY201 )
| ( SV123 = sz00 )
| ( SY200 = SY201 )
| ~ ( sdtlseqdt0 @ SY200 @ SY201 )
| ( ( sdtasdt0 @ SV123 @ SY200 )
!= ( sdtasdt0 @ SV123 @ SY201 ) ) )
| ~ ! [SY202: $i,SY203: $i] :
( ~ ( aNaturalNumber0 @ SV123 )
| ~ ( aNaturalNumber0 @ SY202 )
| ~ ( aNaturalNumber0 @ SY203 )
| ( SV123 = sz00 )
| ( SY202 = SY203 )
| ~ ( sdtlseqdt0 @ SY202 @ SY203 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV123 @ SY202 ) @ ( sdtasdt0 @ SV123 @ SY203 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1042]) ).
thf(1092,plain,
! [SV170: $i,SV123: $i] :
( ( ! [SY237: $i] :
( ~ ( aNaturalNumber0 @ SV123 )
| ~ ( aNaturalNumber0 @ SV170 )
| ~ ( aNaturalNumber0 @ SY237 )
| ( SV123 = sz00 )
| ( SV170 = SY237 )
| ~ ( sdtlseqdt0 @ SV170 @ SY237 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV170 @ SV123 ) @ ( sdtasdt0 @ SY237 @ SV123 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1043]) ).
thf(1093,plain,
( ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xn @ xn )
!= ( sdtasdt0 @ xp @ sK3_W0 ) )
| ~ ( aNaturalNumber0 @ sK3_W0 ) )
| ~ ( doDivides0 @ xp @ ( sdtasdt0 @ xn @ xn ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1044]) ).
thf(1094,plain,
( ( ~ ~ ( ( xn
!= ( sdtasdt0 @ xp @ sK2_W0 ) )
| ~ ( aNaturalNumber0 @ sK2_W0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1044]) ).
thf(1095,plain,
! [SV124: $i,SV171: $i] :
( ( ! [SY238: $i] :
( ( SY238 = sz00 )
| ( SV171 = sz00 )
| ( SV124 = sz00 )
| ~ ( aNaturalNumber0 @ SV124 )
| ~ ( aNaturalNumber0 @ SV171 )
| ~ ( aNaturalNumber0 @ SY238 )
| ( ( sdtasdt0 @ SY238 @ ( sdtasdt0 @ SV171 @ SV171 ) )
!= ( sdtasdt0 @ SV124 @ SV124 ) )
| ~ ( iLess0 @ SV124 @ xn )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( SY238
!= ( sdtasdt0 @ ( sK4_W3 @ SY238 @ SV171 @ SV124 ) @ ( sK5_SY81 @ SY238 @ SV171 @ SV124 ) ) )
| ~ ( aNaturalNumber0 @ ( sK5_SY81 @ SY238 @ SV171 @ SV124 ) ) )
| ~ ( aNaturalNumber0 @ ( sK4_W3 @ SY238 @ SV171 @ SV124 ) ) )
| ~ ( doDivides0 @ ( sK4_W3 @ SY238 @ SV171 @ SV124 ) @ SY238 ) )
| ~ ~ ( ~ ( ( ( sK4_W3 @ SY238 @ SV171 @ SV124 )
!= sz10 ) )
| ~ ( ( ( sK4_W3 @ SY238 @ SV171 @ SV124 )
!= SY238 ) ) ) )
| ( SY238 = sz10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1045]) ).
thf(1096,plain,
! [SV124: $i,SV172: $i] :
( ( ! [SY239: $i] :
( ( SY239 = sz00 )
| ( SV172 = sz00 )
| ( SV124 = sz00 )
| ~ ( aNaturalNumber0 @ SV124 )
| ~ ( aNaturalNumber0 @ SV172 )
| ~ ( aNaturalNumber0 @ SY239 )
| ( ( sdtasdt0 @ SY239 @ ( sdtasdt0 @ SV172 @ SV172 ) )
!= ( sdtasdt0 @ SV124 @ SV124 ) )
| ~ ( iLess0 @ SV124 @ xn )
| ~ ( isPrime0 @ SY239 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1046]) ).
thf(1097,plain,
( ( ~ ( ( xm != sz00 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1048]) ).
thf(1098,plain,
( ( ~ ~ ( ~ ( ( xn != sz00 ) )
| ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ xn )
| ~ ( aNaturalNumber0 @ xm ) )
| ~ ( aNaturalNumber0 @ xp ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1048]) ).
thf(1099,plain,
! [SV173: $i,SV157: $i] :
( ( ~ ( aNaturalNumber0 @ SV157 )
| ~ ( aNaturalNumber0 @ SV173 )
| ( SV173 != SV157 )
| ( sdtlseqdt0 @ SV157 @ SV173 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1049]) ).
thf(1100,plain,
! [SV174: $i,SV158: $i] :
( ( ~ ( aNaturalNumber0 @ SV158 )
| ~ ( aNaturalNumber0 @ SV174 )
| ( sdtlseqdt0 @ SV174 @ SV158 )
| ( sdtlseqdt0 @ SV158 @ SV174 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1050]) ).
thf(1101,plain,
! [SV145: $i,SV125: $i] :
( ( ( aNaturalNumber0 @ SV125 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV145 ) )
= $true )
| ( ( ( SV125 = SV145 )
| ~ ( sdtlseqdt0 @ SV125 @ SV145 )
| ~ ( ~ ~ ( ~ ! [SY227: $i] :
( ~ ( aNaturalNumber0 @ SY227 )
| ( ( sdtpldt0 @ SV125 @ SY227 )
!= ( sdtpldt0 @ SV145 @ SY227 ) ) )
| ~ ~ ( ~ ! [SY228: $i] :
( ~ ( aNaturalNumber0 @ SY228 )
| ( ( sdtpldt0 @ SY228 @ SV125 )
!= ( sdtpldt0 @ SY228 @ SV145 ) ) )
| ~ ! [SY229: $i] :
( ~ ( aNaturalNumber0 @ SY229 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SY229 @ SV125 ) @ ( sdtpldt0 @ SY229 @ SV145 ) ) ) ) )
| ~ ! [SY230: $i] :
( ~ ( aNaturalNumber0 @ SY230 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SV125 @ SY230 ) @ ( sdtpldt0 @ SV145 @ SY230 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1051]) ).
thf(1102,plain,
( ( xn
!= ( sdtasdt0 @ xp @ xq ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1052]) ).
thf(1103,plain,
( ( ~ ( aNaturalNumber0 @ xq ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1052]) ).
thf(1104,plain,
! [SV175: $i,SV126: $i] :
( ( ! [SY240: $i] :
( ~ ( aNaturalNumber0 @ SV126 )
| ~ ( aNaturalNumber0 @ SV175 )
| ~ ( aNaturalNumber0 @ SY240 )
| ( ( sdtpldt0 @ SV126 @ SV175 )
!= ( sdtpldt0 @ SV126 @ SY240 ) )
| ( SV175 = SY240 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1053]) ).
thf(1105,plain,
! [SV176: $i,SV126: $i] :
( ( ! [SY241: $i] :
( ~ ( aNaturalNumber0 @ SV126 )
| ~ ( aNaturalNumber0 @ SV176 )
| ~ ( aNaturalNumber0 @ SY241 )
| ( ( sdtpldt0 @ SV176 @ SV126 )
!= ( sdtpldt0 @ SY241 @ SV126 ) )
| ( SV176 = SY241 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1054]) ).
thf(1106,plain,
! [SV159: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV159 ) )
= $true )
| ( ( ( sz10 != SV159 )
| ( SV159 = sz00 )
| ( SV159 = sz10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1055]) ).
thf(1107,plain,
! [SV160: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV160 ) )
= $true )
| ( ( ( sdtlseqdt0 @ sz10 @ SV160 )
| ( SV160 = sz00 )
| ( SV160 = sz10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1056]) ).
thf(1108,plain,
! [SV127: $i] :
( ( ( aNaturalNumber0 @ SV127 )
= $false )
| ( ( SV127 = sz00 )
= $true )
| ( ( SV127 = sz10 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ ( sK1_W1 @ SV127 ) )
| ~ ( doDivides0 @ ( sK1_W1 @ SV127 ) @ SV127 ) )
| ~ ( isPrime0 @ ( sK1_W1 @ SV127 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1057]) ).
thf(1109,plain,
! [SV161: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV161 ) )
= $true )
| ( ( ( sdtpldt0 @ SV161 @ sz00 )
= SV161 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1059]) ).
thf(1110,plain,
! [SV162: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV162 ) )
= $true )
| ( ( SV162
= ( sdtpldt0 @ sz00 @ SV162 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1060]) ).
thf(1111,plain,
! [SV163: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV163 ) )
= $true )
| ( ( ( sdtasdt0 @ SV163 @ sz10 )
= SV163 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1061]) ).
thf(1112,plain,
! [SV164: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV164 ) )
= $true )
| ( ( SV164
= ( sdtasdt0 @ sz10 @ SV164 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1062]) ).
thf(1113,plain,
! [SV177: $i,SV165: $i] :
( ( ~ ( aNaturalNumber0 @ SV165 )
| ~ ( aNaturalNumber0 @ SV177 )
| ( ( sdtpldt0 @ SV165 @ SV177 )
!= sz00 )
| ( SV165 = sz00 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1063]) ).
thf(1114,plain,
! [SV178: $i,SV166: $i] :
( ( ~ ( aNaturalNumber0 @ SV166 )
| ~ ( aNaturalNumber0 @ SV178 )
| ( ( sdtpldt0 @ SV166 @ SV178 )
!= sz00 )
| ( SV178 = sz00 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1064]) ).
thf(1115,plain,
! [SV103: $i,SV128: $i] :
( ( ( aNaturalNumber0 @ SV128 )
= $false )
| ( ( aNaturalNumber0 @ SV103 )
= $false )
| ( ( aNaturalNumber0 @ ( sdtpldt0 @ SV103 @ SV128 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1065]) ).
thf(1116,plain,
! [SV104: $i,SV129: $i] :
( ( ( aNaturalNumber0 @ SV129 )
= $false )
| ( ( aNaturalNumber0 @ SV104 )
= $false )
| ( ( aNaturalNumber0 @ ( sdtasdt0 @ SV104 @ SV129 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1066]) ).
thf(1117,plain,
! [SV105: $i,SV130: $i] :
( ( ( aNaturalNumber0 @ SV130 )
= $false )
| ( ( aNaturalNumber0 @ SV105 )
= $false )
| ( ( ( sdtpldt0 @ SV105 @ SV130 )
= ( sdtpldt0 @ SV130 @ SV105 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1067]) ).
thf(1118,plain,
! [SV146: $i,SV131: $i,SV106: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV106 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV131 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV146 ) )
= $true )
| ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV106 @ SV131 ) @ SV146 )
= ( sdtpldt0 @ SV106 @ ( sdtpldt0 @ SV131 @ SV146 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1068]) ).
thf(1119,plain,
! [SV107: $i,SV132: $i] :
( ( ( aNaturalNumber0 @ SV132 )
= $false )
| ( ( aNaturalNumber0 @ SV107 )
= $false )
| ( ( ( sdtasdt0 @ SV107 @ SV132 )
= ( sdtasdt0 @ SV132 @ SV107 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1069]) ).
thf(1120,plain,
! [SV147: $i,SV133: $i,SV108: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV108 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV133 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV147 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV108 @ SV133 ) @ SV147 )
= ( sdtasdt0 @ SV108 @ ( sdtasdt0 @ SV133 @ SV147 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1070]) ).
thf(1121,plain,
! [SV109: $i,SV134: $i] :
( ( ( aNaturalNumber0 @ SV134 )
= $false )
| ( ( aNaturalNumber0 @ SV109 )
= $false )
| ( ( ( ( sdtasdt0 @ SV109 @ SV134 )
!= sz00 )
| ( SV109 = sz00 )
| ( SV134 = sz00 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1071]) ).
thf(1122,plain,
! [SV111: $i,SV135: $i] :
( ( ( aNaturalNumber0 @ SV135 )
= $false )
| ( ( aNaturalNumber0 @ SV111 )
= $false )
| ( ( ~ ( sdtlseqdt0 @ SV111 @ SV135 )
| ~ ( sdtlseqdt0 @ SV135 @ SV111 )
| ( SV111 = SV135 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1072]) ).
thf(1123,plain,
! [SV148: $i,SV136: $i,SV112: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV112 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV136 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV148 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV112 @ SV136 )
| ~ ( sdtlseqdt0 @ SV136 @ SV148 )
| ( sdtlseqdt0 @ SV112 @ SV148 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1073]) ).
thf(1124,plain,
! [SV113: $i,SV137: $i] :
( ( ( aNaturalNumber0 @ SV137 )
= $false )
| ( ( aNaturalNumber0 @ SV113 )
= $false )
| ( ( ( SV113 = sz00 )
| ( sdtlseqdt0 @ SV137 @ ( sdtasdt0 @ SV137 @ SV113 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1074]) ).
thf(1125,plain,
! [SV149: $i,SV167: $i] :
( ( ( aNaturalNumber0 @ SV167 )
= $false )
| ( ( aNaturalNumber0 @ SV149 )
= $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1075]) ).
thf(1126,plain,
! [SV114: $i,SV138: $i] :
( ( ( aNaturalNumber0 @ SV138 )
= $false )
| ( ( aNaturalNumber0 @ SV114 )
= $false )
| ( ( ( SV114 = SV138 )
| ~ ( sdtlseqdt0 @ SV114 @ SV138 )
| ( iLess0 @ SV114 @ SV138 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1076]) ).
thf(1127,plain,
! [SV150: $i,SV139: $i,SV115: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV115 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV139 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV150 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV115 @ SV139 )
| ~ ( doDivides0 @ SV139 @ SV150 )
| ( doDivides0 @ SV115 @ SV150 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1077]) ).
thf(1128,plain,
! [SV151: $i,SV140: $i,SV116: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV116 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV140 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV151 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV116 @ SV140 )
| ~ ( doDivides0 @ SV116 @ SV151 )
| ( doDivides0 @ SV116 @ ( sdtpldt0 @ SV140 @ SV151 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1078]) ).
thf(1129,plain,
! [SV152: $i,SV141: $i,SV117: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV117 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV141 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV152 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV117 @ SV141 )
| ~ ( doDivides0 @ SV117 @ ( sdtpldt0 @ SV141 @ SV152 ) )
| ( doDivides0 @ SV117 @ SV152 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1079]) ).
thf(1130,plain,
! [SV118: $i,SV142: $i] :
( ( ( aNaturalNumber0 @ SV142 )
= $false )
| ( ( aNaturalNumber0 @ SV118 )
= $false )
| ( ( ( SV142 = sz00 )
| ~ ( doDivides0 @ SV118 @ SV142 )
| ( sdtlseqdt0 @ SV118 @ SV142 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1080]) ).
thf(1131,plain,
! [SV119: $i,SV143: $i] :
( ( ( aNaturalNumber0 @ SV143 )
= $false )
| ( ( aNaturalNumber0 @ SV119 )
= $false )
| ( ( ( SV119 = sz00 )
| ~ ( doDivides0 @ SV119 @ SV143 )
| ! [SY225: $i] :
( ~ ( aNaturalNumber0 @ SY225 )
| ( ( sdtasdt0 @ SY225 @ ( sdtsldt0 @ SV143 @ SV119 ) )
= ( sdtsldt0 @ ( sdtasdt0 @ SY225 @ SV143 ) @ SV119 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1081]) ).
thf(1132,plain,
! [SV153: $i,SV144: $i,SV120: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV120 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV144 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV153 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV153 @ ( sdtasdt0 @ SV120 @ SV144 ) )
| ~ ( isPrime0 @ SV153 )
| ( doDivides0 @ SV153 @ SV120 )
| ( doDivides0 @ SV153 @ SV144 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1082]) ).
thf(1133,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ! [SX1: $i] :
( ( xp
!= ( sdtasdt0 @ SX0 @ SX1 ) )
| ~ ( aNaturalNumber0 @ SX1 ) )
| ( SX0 = sz10 )
| ( SX0 = xp ) )
| ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( doDivides0 @ SX0 @ xp )
| ( SX0 = sz10 )
| ( SX0 = xp ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1083]) ).
thf(1134,plain,
( ( xp != sz10 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1084]) ).
thf(1135,plain,
! [SV179: $i,SV168: $i,SV121: $i] :
( ( ~ ( aNaturalNumber0 @ SV121 )
| ~ ( aNaturalNumber0 @ SV168 )
| ~ ( aNaturalNumber0 @ SV179 )
| ( ( sdtasdt0 @ SV121 @ ( sdtpldt0 @ SV168 @ SV179 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV121 @ SV168 ) @ ( sdtasdt0 @ SV121 @ SV179 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1085]) ).
thf(1136,plain,
! [SV180: $i,SV169: $i,SV121: $i] :
( ( ~ ( aNaturalNumber0 @ SV121 )
| ~ ( aNaturalNumber0 @ SV169 )
| ~ ( aNaturalNumber0 @ SV180 )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SV169 @ SV180 ) @ SV121 )
= ( sdtpldt0 @ ( sdtasdt0 @ SV169 @ SV121 ) @ ( sdtasdt0 @ SV180 @ SV121 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1086]) ).
thf(1137,plain,
! [SV154: $i] :
( ( ( aNaturalNumber0 @ SV154 )
= $false )
| ( ( ( sdtasdt0 @ SV154 @ sz00 )
= sz00 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1087]) ).
thf(1138,plain,
! [SV155: $i] :
( ( ( aNaturalNumber0 @ SV155 )
= $false )
| ( ( sz00
= ( sdtasdt0 @ sz00 @ SV155 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1088]) ).
thf(1139,plain,
! [SV122: $i] :
( ( ( ~ ! [SY194: $i,SY195: $i] :
( ~ ( aNaturalNumber0 @ SY194 )
| ~ ( aNaturalNumber0 @ SY195 )
| ( ( sdtasdt0 @ SV122 @ SY194 )
!= ( sdtasdt0 @ SV122 @ SY195 ) )
| ( SY194 = SY195 ) ) )
= $false )
| ( ( SV122 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV122 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1089]) ).
thf(1140,plain,
! [SV122: $i] :
( ( ( ~ ! [SY196: $i,SY197: $i] :
( ~ ( aNaturalNumber0 @ SY196 )
| ~ ( aNaturalNumber0 @ SY197 )
| ( ( sdtasdt0 @ SY196 @ SV122 )
!= ( sdtasdt0 @ SY197 @ SV122 ) )
| ( SY196 = SY197 ) ) )
= $false )
| ( ( SV122 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV122 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1089]) ).
thf(1141,plain,
! [SV156: $i] :
( ( ( ( sdtpldt0 @ xm @ SV156 )
= xn )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV156 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1090]) ).
thf(1142,plain,
! [SV123: $i] :
( ( ~ ! [SY198: $i,SY199: $i] :
( ~ ( aNaturalNumber0 @ SV123 )
| ~ ( aNaturalNumber0 @ SY198 )
| ~ ( aNaturalNumber0 @ SY199 )
| ( SV123 = sz00 )
| ( SY198 = SY199 )
| ~ ( sdtlseqdt0 @ SY198 @ SY199 )
| ( ( sdtasdt0 @ SY198 @ SV123 )
!= ( sdtasdt0 @ SY199 @ SV123 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1091]) ).
thf(1143,plain,
! [SV123: $i] :
( ( ~ ~ ( ~ ! [SY200: $i,SY201: $i] :
( ~ ( aNaturalNumber0 @ SV123 )
| ~ ( aNaturalNumber0 @ SY200 )
| ~ ( aNaturalNumber0 @ SY201 )
| ( SV123 = sz00 )
| ( SY200 = SY201 )
| ~ ( sdtlseqdt0 @ SY200 @ SY201 )
| ( ( sdtasdt0 @ SV123 @ SY200 )
!= ( sdtasdt0 @ SV123 @ SY201 ) ) )
| ~ ! [SY202: $i,SY203: $i] :
( ~ ( aNaturalNumber0 @ SV123 )
| ~ ( aNaturalNumber0 @ SY202 )
| ~ ( aNaturalNumber0 @ SY203 )
| ( SV123 = sz00 )
| ( SY202 = SY203 )
| ~ ( sdtlseqdt0 @ SY202 @ SY203 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV123 @ SY202 ) @ ( sdtasdt0 @ SV123 @ SY203 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1091]) ).
thf(1144,plain,
! [SV181: $i,SV170: $i,SV123: $i] :
( ( ~ ( aNaturalNumber0 @ SV123 )
| ~ ( aNaturalNumber0 @ SV170 )
| ~ ( aNaturalNumber0 @ SV181 )
| ( SV123 = sz00 )
| ( SV170 = SV181 )
| ~ ( sdtlseqdt0 @ SV170 @ SV181 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV170 @ SV123 ) @ ( sdtasdt0 @ SV181 @ SV123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1092]) ).
thf(1145,plain,
( ( ~ ( ~ ~ ( ( ( sdtasdt0 @ xn @ xn )
!= ( sdtasdt0 @ xp @ sK3_W0 ) )
| ~ ( aNaturalNumber0 @ sK3_W0 ) )
| ~ ( doDivides0 @ xp @ ( sdtasdt0 @ xn @ xn ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1093]) ).
thf(1146,plain,
( ( ~ ( ( xn
!= ( sdtasdt0 @ xp @ sK2_W0 ) )
| ~ ( aNaturalNumber0 @ sK2_W0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1094]) ).
thf(1147,plain,
! [SV124: $i,SV171: $i,SV182: $i] :
( ( ( SV182 = sz00 )
| ( SV171 = sz00 )
| ( SV124 = sz00 )
| ~ ( aNaturalNumber0 @ SV124 )
| ~ ( aNaturalNumber0 @ SV171 )
| ~ ( aNaturalNumber0 @ SV182 )
| ( ( sdtasdt0 @ SV182 @ ( sdtasdt0 @ SV171 @ SV171 ) )
!= ( sdtasdt0 @ SV124 @ SV124 ) )
| ~ ( iLess0 @ SV124 @ xn )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( SV182
!= ( sdtasdt0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) @ ( sK5_SY81 @ SV182 @ SV171 @ SV124 ) ) )
| ~ ( aNaturalNumber0 @ ( sK5_SY81 @ SV182 @ SV171 @ SV124 ) ) )
| ~ ( aNaturalNumber0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) ) )
| ~ ( doDivides0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) @ SV182 ) )
| ~ ~ ( ~ ( ( ( sK4_W3 @ SV182 @ SV171 @ SV124 )
!= sz10 ) )
| ~ ( ( ( sK4_W3 @ SV182 @ SV171 @ SV124 )
!= SV182 ) ) ) )
| ( SV182 = sz10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1095]) ).
thf(1148,plain,
! [SV124: $i,SV172: $i,SV183: $i] :
( ( ( SV183 = sz00 )
| ( SV172 = sz00 )
| ( SV124 = sz00 )
| ~ ( aNaturalNumber0 @ SV124 )
| ~ ( aNaturalNumber0 @ SV172 )
| ~ ( aNaturalNumber0 @ SV183 )
| ( ( sdtasdt0 @ SV183 @ ( sdtasdt0 @ SV172 @ SV172 ) )
!= ( sdtasdt0 @ SV124 @ SV124 ) )
| ~ ( iLess0 @ SV124 @ xn )
| ~ ( isPrime0 @ SV183 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1096]) ).
thf(1149,plain,
( ( xm != sz00 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1097]) ).
thf(1150,plain,
( ( ~ ( ~ ( ( xn != sz00 ) )
| ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ xn )
| ~ ( aNaturalNumber0 @ xm ) )
| ~ ( aNaturalNumber0 @ xp ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1098]) ).
thf(1151,plain,
! [SV173: $i,SV157: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV157 )
| ~ ( aNaturalNumber0 @ SV173 ) )
= $true )
| ( ( ( SV173 != SV157 )
| ( sdtlseqdt0 @ SV157 @ SV173 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1099]) ).
thf(1152,plain,
! [SV174: $i,SV158: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV158 )
| ~ ( aNaturalNumber0 @ SV174 ) )
= $true )
| ( ( ( sdtlseqdt0 @ SV174 @ SV158 )
| ( sdtlseqdt0 @ SV158 @ SV174 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1100]) ).
thf(1153,plain,
! [SV125: $i,SV145: $i] :
( ( ( aNaturalNumber0 @ SV145 )
= $false )
| ( ( aNaturalNumber0 @ SV125 )
= $false )
| ( ( ( SV125 = SV145 )
| ~ ( sdtlseqdt0 @ SV125 @ SV145 )
| ~ ( ~ ~ ( ~ ! [SY227: $i] :
( ~ ( aNaturalNumber0 @ SY227 )
| ( ( sdtpldt0 @ SV125 @ SY227 )
!= ( sdtpldt0 @ SV145 @ SY227 ) ) )
| ~ ~ ( ~ ! [SY228: $i] :
( ~ ( aNaturalNumber0 @ SY228 )
| ( ( sdtpldt0 @ SY228 @ SV125 )
!= ( sdtpldt0 @ SY228 @ SV145 ) ) )
| ~ ! [SY229: $i] :
( ~ ( aNaturalNumber0 @ SY229 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SY229 @ SV125 ) @ ( sdtpldt0 @ SY229 @ SV145 ) ) ) ) )
| ~ ! [SY230: $i] :
( ~ ( aNaturalNumber0 @ SY230 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SV125 @ SY230 ) @ ( sdtpldt0 @ SV145 @ SY230 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1101]) ).
thf(1154,plain,
( ( xn
= ( sdtasdt0 @ xp @ xq ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1102]) ).
thf(1155,plain,
( ( aNaturalNumber0 @ xq )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1103]) ).
thf(1156,plain,
! [SV184: $i,SV175: $i,SV126: $i] :
( ( ~ ( aNaturalNumber0 @ SV126 )
| ~ ( aNaturalNumber0 @ SV175 )
| ~ ( aNaturalNumber0 @ SV184 )
| ( ( sdtpldt0 @ SV126 @ SV175 )
!= ( sdtpldt0 @ SV126 @ SV184 ) )
| ( SV175 = SV184 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1104]) ).
thf(1157,plain,
! [SV185: $i,SV176: $i,SV126: $i] :
( ( ~ ( aNaturalNumber0 @ SV126 )
| ~ ( aNaturalNumber0 @ SV176 )
| ~ ( aNaturalNumber0 @ SV185 )
| ( ( sdtpldt0 @ SV176 @ SV126 )
!= ( sdtpldt0 @ SV185 @ SV126 ) )
| ( SV176 = SV185 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1105]) ).
thf(1158,plain,
! [SV159: $i] :
( ( ( aNaturalNumber0 @ SV159 )
= $false )
| ( ( ( sz10 != SV159 )
| ( SV159 = sz00 )
| ( SV159 = sz10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1106]) ).
thf(1159,plain,
! [SV160: $i] :
( ( ( aNaturalNumber0 @ SV160 )
= $false )
| ( ( ( sdtlseqdt0 @ sz10 @ SV160 )
| ( SV160 = sz00 )
| ( SV160 = sz10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1107]) ).
thf(1160,plain,
! [SV127: $i] :
( ( ( ~ ~ ( ~ ( aNaturalNumber0 @ ( sK1_W1 @ SV127 ) )
| ~ ( doDivides0 @ ( sK1_W1 @ SV127 ) @ SV127 ) )
| ~ ( isPrime0 @ ( sK1_W1 @ SV127 ) ) )
= $false )
| ( ( SV127 = sz10 )
= $true )
| ( ( SV127 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV127 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1108]) ).
thf(1161,plain,
! [SV161: $i] :
( ( ( aNaturalNumber0 @ SV161 )
= $false )
| ( ( ( sdtpldt0 @ SV161 @ sz00 )
= SV161 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1109]) ).
thf(1162,plain,
! [SV162: $i] :
( ( ( aNaturalNumber0 @ SV162 )
= $false )
| ( ( SV162
= ( sdtpldt0 @ sz00 @ SV162 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1110]) ).
thf(1163,plain,
! [SV163: $i] :
( ( ( aNaturalNumber0 @ SV163 )
= $false )
| ( ( ( sdtasdt0 @ SV163 @ sz10 )
= SV163 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1111]) ).
thf(1164,plain,
! [SV164: $i] :
( ( ( aNaturalNumber0 @ SV164 )
= $false )
| ( ( SV164
= ( sdtasdt0 @ sz10 @ SV164 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1112]) ).
thf(1165,plain,
! [SV177: $i,SV165: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV165 )
| ~ ( aNaturalNumber0 @ SV177 ) )
= $true )
| ( ( ( ( sdtpldt0 @ SV165 @ SV177 )
!= sz00 )
| ( SV165 = sz00 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1113]) ).
thf(1166,plain,
! [SV178: $i,SV166: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV166 )
| ~ ( aNaturalNumber0 @ SV178 ) )
= $true )
| ( ( ( ( sdtpldt0 @ SV166 @ SV178 )
!= sz00 )
| ( SV178 = sz00 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1114]) ).
thf(1167,plain,
! [SV146: $i,SV131: $i,SV106: $i] :
( ( ( aNaturalNumber0 @ SV106 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV131 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV146 ) )
= $true )
| ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV106 @ SV131 ) @ SV146 )
= ( sdtpldt0 @ SV106 @ ( sdtpldt0 @ SV131 @ SV146 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1118]) ).
thf(1168,plain,
! [SV147: $i,SV133: $i,SV108: $i] :
( ( ( aNaturalNumber0 @ SV108 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV133 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV147 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV108 @ SV133 ) @ SV147 )
= ( sdtasdt0 @ SV108 @ ( sdtasdt0 @ SV133 @ SV147 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1120]) ).
thf(1169,plain,
! [SV134: $i,SV109: $i] :
( ( ( ( sdtasdt0 @ SV109 @ SV134 )
!= sz00 )
= $true )
| ( ( ( SV109 = sz00 )
| ( SV134 = sz00 ) )
= $true )
| ( ( aNaturalNumber0 @ SV109 )
= $false )
| ( ( aNaturalNumber0 @ SV134 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1121]) ).
thf(1170,plain,
! [SV135: $i,SV111: $i] :
( ( ( ~ ( sdtlseqdt0 @ SV111 @ SV135 )
| ~ ( sdtlseqdt0 @ SV135 @ SV111 ) )
= $true )
| ( ( SV111 = SV135 )
= $true )
| ( ( aNaturalNumber0 @ SV111 )
= $false )
| ( ( aNaturalNumber0 @ SV135 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1122]) ).
thf(1171,plain,
! [SV148: $i,SV136: $i,SV112: $i] :
( ( ( aNaturalNumber0 @ SV112 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV136 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV148 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV112 @ SV136 )
| ~ ( sdtlseqdt0 @ SV136 @ SV148 )
| ( sdtlseqdt0 @ SV112 @ SV148 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1123]) ).
thf(1172,plain,
! [SV137: $i,SV113: $i] :
( ( ( SV113 = sz00 )
= $true )
| ( ( sdtlseqdt0 @ SV137 @ ( sdtasdt0 @ SV137 @ SV113 ) )
= $true )
| ( ( aNaturalNumber0 @ SV113 )
= $false )
| ( ( aNaturalNumber0 @ SV137 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1124]) ).
thf(1173,plain,
! [SV138: $i,SV114: $i] :
( ( ( ( SV114 = SV138 )
| ~ ( sdtlseqdt0 @ SV114 @ SV138 ) )
= $true )
| ( ( iLess0 @ SV114 @ SV138 )
= $true )
| ( ( aNaturalNumber0 @ SV114 )
= $false )
| ( ( aNaturalNumber0 @ SV138 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1126]) ).
thf(1174,plain,
! [SV150: $i,SV139: $i,SV115: $i] :
( ( ( aNaturalNumber0 @ SV115 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV139 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV150 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV115 @ SV139 )
| ~ ( doDivides0 @ SV139 @ SV150 )
| ( doDivides0 @ SV115 @ SV150 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1127]) ).
thf(1175,plain,
! [SV151: $i,SV140: $i,SV116: $i] :
( ( ( aNaturalNumber0 @ SV116 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV140 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV151 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV116 @ SV140 )
| ~ ( doDivides0 @ SV116 @ SV151 )
| ( doDivides0 @ SV116 @ ( sdtpldt0 @ SV140 @ SV151 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1128]) ).
thf(1176,plain,
! [SV152: $i,SV141: $i,SV117: $i] :
( ( ( aNaturalNumber0 @ SV117 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV141 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV152 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV117 @ SV141 )
| ~ ( doDivides0 @ SV117 @ ( sdtpldt0 @ SV141 @ SV152 ) )
| ( doDivides0 @ SV117 @ SV152 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1129]) ).
thf(1177,plain,
! [SV118: $i,SV142: $i] :
( ( ( ( SV142 = sz00 )
| ~ ( doDivides0 @ SV118 @ SV142 ) )
= $true )
| ( ( sdtlseqdt0 @ SV118 @ SV142 )
= $true )
| ( ( aNaturalNumber0 @ SV118 )
= $false )
| ( ( aNaturalNumber0 @ SV142 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1130]) ).
thf(1178,plain,
! [SV143: $i,SV119: $i] :
( ( ( ( SV119 = sz00 )
| ~ ( doDivides0 @ SV119 @ SV143 ) )
= $true )
| ( ( ! [SY225: $i] :
( ~ ( aNaturalNumber0 @ SY225 )
| ( ( sdtasdt0 @ SY225 @ ( sdtsldt0 @ SV143 @ SV119 ) )
= ( sdtsldt0 @ ( sdtasdt0 @ SY225 @ SV143 ) @ SV119 ) ) ) )
= $true )
| ( ( aNaturalNumber0 @ SV119 )
= $false )
| ( ( aNaturalNumber0 @ SV143 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1131]) ).
thf(1179,plain,
! [SV153: $i,SV144: $i,SV120: $i] :
( ( ( aNaturalNumber0 @ SV120 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV144 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV153 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV153 @ ( sdtasdt0 @ SV120 @ SV144 ) )
| ~ ( isPrime0 @ SV153 )
| ( doDivides0 @ SV153 @ SV120 )
| ( doDivides0 @ SV153 @ SV144 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1132]) ).
thf(1180,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ! [SX1: $i] :
( ( xp
!= ( sdtasdt0 @ SX0 @ SX1 ) )
| ~ ( aNaturalNumber0 @ SX1 ) )
| ( SX0 = sz10 )
| ( SX0 = xp ) )
| ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( doDivides0 @ SX0 @ xp )
| ( SX0 = sz10 )
| ( SX0 = xp ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1133]) ).
thf(1181,plain,
( ( xp = sz10 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1134]) ).
thf(1182,plain,
! [SV179: $i,SV168: $i,SV121: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV121 )
| ~ ( aNaturalNumber0 @ SV168 )
| ~ ( aNaturalNumber0 @ SV179 ) )
= $true )
| ( ( ( sdtasdt0 @ SV121 @ ( sdtpldt0 @ SV168 @ SV179 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV121 @ SV168 ) @ ( sdtasdt0 @ SV121 @ SV179 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1135]) ).
thf(1183,plain,
! [SV180: $i,SV169: $i,SV121: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV121 )
| ~ ( aNaturalNumber0 @ SV169 )
| ~ ( aNaturalNumber0 @ SV180 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV169 @ SV180 ) @ SV121 )
= ( sdtpldt0 @ ( sdtasdt0 @ SV169 @ SV121 ) @ ( sdtasdt0 @ SV180 @ SV121 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1136]) ).
thf(1184,plain,
! [SV122: $i] :
( ( ( ! [SY194: $i,SY195: $i] :
( ~ ( aNaturalNumber0 @ SY194 )
| ~ ( aNaturalNumber0 @ SY195 )
| ( ( sdtasdt0 @ SV122 @ SY194 )
!= ( sdtasdt0 @ SV122 @ SY195 ) )
| ( SY194 = SY195 ) ) )
= $true )
| ( ( SV122 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV122 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1139]) ).
thf(1185,plain,
! [SV122: $i] :
( ( ( ! [SY196: $i,SY197: $i] :
( ~ ( aNaturalNumber0 @ SY196 )
| ~ ( aNaturalNumber0 @ SY197 )
| ( ( sdtasdt0 @ SY196 @ SV122 )
!= ( sdtasdt0 @ SY197 @ SV122 ) )
| ( SY196 = SY197 ) ) )
= $true )
| ( ( SV122 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV122 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1140]) ).
thf(1186,plain,
! [SV156: $i] :
( ( ( aNaturalNumber0 @ SV156 )
= $false )
| ( ( ( sdtpldt0 @ xm @ SV156 )
= xn )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1141]) ).
thf(1187,plain,
! [SV123: $i] :
( ( ! [SY198: $i,SY199: $i] :
( ~ ( aNaturalNumber0 @ SV123 )
| ~ ( aNaturalNumber0 @ SY198 )
| ~ ( aNaturalNumber0 @ SY199 )
| ( SV123 = sz00 )
| ( SY198 = SY199 )
| ~ ( sdtlseqdt0 @ SY198 @ SY199 )
| ( ( sdtasdt0 @ SY198 @ SV123 )
!= ( sdtasdt0 @ SY199 @ SV123 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1142]) ).
thf(1188,plain,
! [SV123: $i] :
( ( ~ ( ~ ! [SY200: $i,SY201: $i] :
( ~ ( aNaturalNumber0 @ SV123 )
| ~ ( aNaturalNumber0 @ SY200 )
| ~ ( aNaturalNumber0 @ SY201 )
| ( SV123 = sz00 )
| ( SY200 = SY201 )
| ~ ( sdtlseqdt0 @ SY200 @ SY201 )
| ( ( sdtasdt0 @ SV123 @ SY200 )
!= ( sdtasdt0 @ SV123 @ SY201 ) ) )
| ~ ! [SY202: $i,SY203: $i] :
( ~ ( aNaturalNumber0 @ SV123 )
| ~ ( aNaturalNumber0 @ SY202 )
| ~ ( aNaturalNumber0 @ SY203 )
| ( SV123 = sz00 )
| ( SY202 = SY203 )
| ~ ( sdtlseqdt0 @ SY202 @ SY203 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV123 @ SY202 ) @ ( sdtasdt0 @ SV123 @ SY203 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1143]) ).
thf(1189,plain,
! [SV181: $i,SV170: $i,SV123: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV123 )
| ~ ( aNaturalNumber0 @ SV170 )
| ~ ( aNaturalNumber0 @ SV181 ) )
= $true )
| ( ( ( SV123 = sz00 )
| ( SV170 = SV181 )
| ~ ( sdtlseqdt0 @ SV170 @ SV181 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV170 @ SV123 ) @ ( sdtasdt0 @ SV181 @ SV123 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1144]) ).
thf(1190,plain,
( ( ~ ~ ( ( ( sdtasdt0 @ xn @ xn )
!= ( sdtasdt0 @ xp @ sK3_W0 ) )
| ~ ( aNaturalNumber0 @ sK3_W0 ) )
| ~ ( doDivides0 @ xp @ ( sdtasdt0 @ xn @ xn ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1145]) ).
thf(1191,plain,
( ( ( xn
!= ( sdtasdt0 @ xp @ sK2_W0 ) )
| ~ ( aNaturalNumber0 @ sK2_W0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1146]) ).
thf(1192,plain,
! [SV124: $i,SV171: $i,SV182: $i] :
( ( ( ( SV182 = sz00 )
| ( SV171 = sz00 )
| ( SV124 = sz00 )
| ~ ( aNaturalNumber0 @ SV124 )
| ~ ( aNaturalNumber0 @ SV171 )
| ~ ( aNaturalNumber0 @ SV182 ) )
= $true )
| ( ( ( ( sdtasdt0 @ SV182 @ ( sdtasdt0 @ SV171 @ SV171 ) )
!= ( sdtasdt0 @ SV124 @ SV124 ) )
| ~ ( iLess0 @ SV124 @ xn )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( SV182
!= ( sdtasdt0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) @ ( sK5_SY81 @ SV182 @ SV171 @ SV124 ) ) )
| ~ ( aNaturalNumber0 @ ( sK5_SY81 @ SV182 @ SV171 @ SV124 ) ) )
| ~ ( aNaturalNumber0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) ) )
| ~ ( doDivides0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) @ SV182 ) )
| ~ ~ ( ~ ( ( ( sK4_W3 @ SV182 @ SV171 @ SV124 )
!= sz10 ) )
| ~ ( ( ( sK4_W3 @ SV182 @ SV171 @ SV124 )
!= SV182 ) ) ) )
| ( SV182 = sz10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1147]) ).
thf(1193,plain,
! [SV124: $i,SV172: $i,SV183: $i] :
( ( ( ( SV183 = sz00 )
| ( SV172 = sz00 )
| ( SV124 = sz00 )
| ~ ( aNaturalNumber0 @ SV124 )
| ~ ( aNaturalNumber0 @ SV172 )
| ~ ( aNaturalNumber0 @ SV183 ) )
= $true )
| ( ( ( ( sdtasdt0 @ SV183 @ ( sdtasdt0 @ SV172 @ SV172 ) )
!= ( sdtasdt0 @ SV124 @ SV124 ) )
| ~ ( iLess0 @ SV124 @ xn )
| ~ ( isPrime0 @ SV183 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1148]) ).
thf(1194,plain,
( ( xm = sz00 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1149]) ).
thf(1195,plain,
( ( ~ ( ( xn != sz00 ) )
| ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ xn )
| ~ ( aNaturalNumber0 @ xm ) )
| ~ ( aNaturalNumber0 @ xp ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1150]) ).
thf(1196,plain,
! [SV173: $i,SV157: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV157 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV173 ) )
= $true )
| ( ( ( SV173 != SV157 )
| ( sdtlseqdt0 @ SV157 @ SV173 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1151]) ).
thf(1197,plain,
! [SV174: $i,SV158: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV158 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV174 ) )
= $true )
| ( ( ( sdtlseqdt0 @ SV174 @ SV158 )
| ( sdtlseqdt0 @ SV158 @ SV174 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1152]) ).
thf(1198,plain,
! [SV145: $i,SV125: $i] :
( ( ( ( SV125 = SV145 )
| ~ ( sdtlseqdt0 @ SV125 @ SV145 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY227: $i] :
( ~ ( aNaturalNumber0 @ SY227 )
| ( ( sdtpldt0 @ SV125 @ SY227 )
!= ( sdtpldt0 @ SV145 @ SY227 ) ) )
| ~ ~ ( ~ ! [SY228: $i] :
( ~ ( aNaturalNumber0 @ SY228 )
| ( ( sdtpldt0 @ SY228 @ SV125 )
!= ( sdtpldt0 @ SY228 @ SV145 ) ) )
| ~ ! [SY229: $i] :
( ~ ( aNaturalNumber0 @ SY229 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SY229 @ SV125 ) @ ( sdtpldt0 @ SY229 @ SV145 ) ) ) ) )
| ~ ! [SY230: $i] :
( ~ ( aNaturalNumber0 @ SY230 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SV125 @ SY230 ) @ ( sdtpldt0 @ SV145 @ SY230 ) ) ) ) )
= $true )
| ( ( aNaturalNumber0 @ SV125 )
= $false )
| ( ( aNaturalNumber0 @ SV145 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1153]) ).
thf(1199,plain,
! [SV184: $i,SV175: $i,SV126: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV126 )
| ~ ( aNaturalNumber0 @ SV175 )
| ~ ( aNaturalNumber0 @ SV184 ) )
= $true )
| ( ( ( ( sdtpldt0 @ SV126 @ SV175 )
!= ( sdtpldt0 @ SV126 @ SV184 ) )
| ( SV175 = SV184 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1156]) ).
thf(1200,plain,
! [SV185: $i,SV176: $i,SV126: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV126 )
| ~ ( aNaturalNumber0 @ SV176 )
| ~ ( aNaturalNumber0 @ SV185 ) )
= $true )
| ( ( ( ( sdtpldt0 @ SV176 @ SV126 )
!= ( sdtpldt0 @ SV185 @ SV126 ) )
| ( SV176 = SV185 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1157]) ).
thf(1201,plain,
! [SV159: $i] :
( ( ( sz10 != SV159 )
= $true )
| ( ( ( SV159 = sz00 )
| ( SV159 = sz10 ) )
= $true )
| ( ( aNaturalNumber0 @ SV159 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1158]) ).
thf(1202,plain,
! [SV160: $i] :
( ( ( sdtlseqdt0 @ sz10 @ SV160 )
= $true )
| ( ( ( SV160 = sz00 )
| ( SV160 = sz10 ) )
= $true )
| ( ( aNaturalNumber0 @ SV160 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1159]) ).
thf(1203,plain,
! [SV127: $i] :
( ( ( ~ ~ ( ~ ( aNaturalNumber0 @ ( sK1_W1 @ SV127 ) )
| ~ ( doDivides0 @ ( sK1_W1 @ SV127 ) @ SV127 ) ) )
= $false )
| ( ( SV127 = sz10 )
= $true )
| ( ( SV127 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV127 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1160]) ).
thf(1204,plain,
! [SV127: $i] :
( ( ( ~ ( isPrime0 @ ( sK1_W1 @ SV127 ) ) )
= $false )
| ( ( SV127 = sz10 )
= $true )
| ( ( SV127 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV127 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1160]) ).
thf(1205,plain,
! [SV177: $i,SV165: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV165 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV177 ) )
= $true )
| ( ( ( ( sdtpldt0 @ SV165 @ SV177 )
!= sz00 )
| ( SV165 = sz00 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1165]) ).
thf(1206,plain,
! [SV178: $i,SV166: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV166 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV178 ) )
= $true )
| ( ( ( ( sdtpldt0 @ SV166 @ SV178 )
!= sz00 )
| ( SV178 = sz00 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1166]) ).
thf(1207,plain,
! [SV146: $i,SV106: $i,SV131: $i] :
( ( ( aNaturalNumber0 @ SV131 )
= $false )
| ( ( aNaturalNumber0 @ SV106 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV146 ) )
= $true )
| ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV106 @ SV131 ) @ SV146 )
= ( sdtpldt0 @ SV106 @ ( sdtpldt0 @ SV131 @ SV146 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1167]) ).
thf(1208,plain,
! [SV147: $i,SV108: $i,SV133: $i] :
( ( ( aNaturalNumber0 @ SV133 )
= $false )
| ( ( aNaturalNumber0 @ SV108 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV147 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV108 @ SV133 ) @ SV147 )
= ( sdtasdt0 @ SV108 @ ( sdtasdt0 @ SV133 @ SV147 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1168]) ).
thf(1209,plain,
! [SV134: $i,SV109: $i] :
( ( ( ( sdtasdt0 @ SV109 @ SV134 )
= sz00 )
= $false )
| ( ( ( SV109 = sz00 )
| ( SV134 = sz00 ) )
= $true )
| ( ( aNaturalNumber0 @ SV109 )
= $false )
| ( ( aNaturalNumber0 @ SV134 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1169]) ).
thf(1210,plain,
! [SV135: $i,SV111: $i] :
( ( ( ~ ( sdtlseqdt0 @ SV111 @ SV135 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV135 @ SV111 ) )
= $true )
| ( ( SV111 = SV135 )
= $true )
| ( ( aNaturalNumber0 @ SV111 )
= $false )
| ( ( aNaturalNumber0 @ SV135 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1170]) ).
thf(1211,plain,
! [SV148: $i,SV112: $i,SV136: $i] :
( ( ( aNaturalNumber0 @ SV136 )
= $false )
| ( ( aNaturalNumber0 @ SV112 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV148 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV112 @ SV136 )
| ~ ( sdtlseqdt0 @ SV136 @ SV148 )
| ( sdtlseqdt0 @ SV112 @ SV148 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1171]) ).
thf(1212,plain,
! [SV138: $i,SV114: $i] :
( ( ( SV114 = SV138 )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV114 @ SV138 ) )
= $true )
| ( ( iLess0 @ SV114 @ SV138 )
= $true )
| ( ( aNaturalNumber0 @ SV114 )
= $false )
| ( ( aNaturalNumber0 @ SV138 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1173]) ).
thf(1213,plain,
! [SV150: $i,SV115: $i,SV139: $i] :
( ( ( aNaturalNumber0 @ SV139 )
= $false )
| ( ( aNaturalNumber0 @ SV115 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV150 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV115 @ SV139 )
| ~ ( doDivides0 @ SV139 @ SV150 )
| ( doDivides0 @ SV115 @ SV150 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1174]) ).
thf(1214,plain,
! [SV151: $i,SV116: $i,SV140: $i] :
( ( ( aNaturalNumber0 @ SV140 )
= $false )
| ( ( aNaturalNumber0 @ SV116 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV151 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV116 @ SV140 )
| ~ ( doDivides0 @ SV116 @ SV151 )
| ( doDivides0 @ SV116 @ ( sdtpldt0 @ SV140 @ SV151 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1175]) ).
thf(1215,plain,
! [SV152: $i,SV117: $i,SV141: $i] :
( ( ( aNaturalNumber0 @ SV141 )
= $false )
| ( ( aNaturalNumber0 @ SV117 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV152 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV117 @ SV141 )
| ~ ( doDivides0 @ SV117 @ ( sdtpldt0 @ SV141 @ SV152 ) )
| ( doDivides0 @ SV117 @ SV152 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1176]) ).
thf(1216,plain,
! [SV118: $i,SV142: $i] :
( ( ( SV142 = sz00 )
= $true )
| ( ( ~ ( doDivides0 @ SV118 @ SV142 ) )
= $true )
| ( ( sdtlseqdt0 @ SV118 @ SV142 )
= $true )
| ( ( aNaturalNumber0 @ SV118 )
= $false )
| ( ( aNaturalNumber0 @ SV142 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1177]) ).
thf(1217,plain,
! [SV143: $i,SV119: $i] :
( ( ( SV119 = sz00 )
= $true )
| ( ( ~ ( doDivides0 @ SV119 @ SV143 ) )
= $true )
| ( ( ! [SY225: $i] :
( ~ ( aNaturalNumber0 @ SY225 )
| ( ( sdtasdt0 @ SY225 @ ( sdtsldt0 @ SV143 @ SV119 ) )
= ( sdtsldt0 @ ( sdtasdt0 @ SY225 @ SV143 ) @ SV119 ) ) ) )
= $true )
| ( ( aNaturalNumber0 @ SV119 )
= $false )
| ( ( aNaturalNumber0 @ SV143 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1178]) ).
thf(1218,plain,
! [SV153: $i,SV120: $i,SV144: $i] :
( ( ( aNaturalNumber0 @ SV144 )
= $false )
| ( ( aNaturalNumber0 @ SV120 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV153 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV153 @ ( sdtasdt0 @ SV120 @ SV144 ) )
| ~ ( isPrime0 @ SV153 )
| ( doDivides0 @ SV153 @ SV120 )
| ( doDivides0 @ SV153 @ SV144 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1179]) ).
thf(1219,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ! [SX1: $i] :
( ( xp
!= ( sdtasdt0 @ SX0 @ SX1 ) )
| ~ ( aNaturalNumber0 @ SX1 ) )
| ( SX0 = sz10 )
| ( SX0 = xp ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1180]) ).
thf(1220,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( doDivides0 @ SX0 @ xp )
| ( SX0 = sz10 )
| ( SX0 = xp ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1180]) ).
thf(1221,plain,
! [SV179: $i,SV168: $i,SV121: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV121 )
| ~ ( aNaturalNumber0 @ SV168 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV179 ) )
= $true )
| ( ( ( sdtasdt0 @ SV121 @ ( sdtpldt0 @ SV168 @ SV179 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV121 @ SV168 ) @ ( sdtasdt0 @ SV121 @ SV179 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1182]) ).
thf(1222,plain,
! [SV180: $i,SV169: $i,SV121: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV121 )
| ~ ( aNaturalNumber0 @ SV169 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV180 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV169 @ SV180 ) @ SV121 )
= ( sdtpldt0 @ ( sdtasdt0 @ SV169 @ SV121 ) @ ( sdtasdt0 @ SV180 @ SV121 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1183]) ).
thf(1223,plain,
! [SV122: $i,SV186: $i] :
( ( ( ! [SY242: $i] :
( ~ ( aNaturalNumber0 @ SV186 )
| ~ ( aNaturalNumber0 @ SY242 )
| ( ( sdtasdt0 @ SV122 @ SV186 )
!= ( sdtasdt0 @ SV122 @ SY242 ) )
| ( SV186 = SY242 ) ) )
= $true )
| ( ( SV122 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV122 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1184]) ).
thf(1224,plain,
! [SV122: $i,SV187: $i] :
( ( ( ! [SY243: $i] :
( ~ ( aNaturalNumber0 @ SV187 )
| ~ ( aNaturalNumber0 @ SY243 )
| ( ( sdtasdt0 @ SV187 @ SV122 )
!= ( sdtasdt0 @ SY243 @ SV122 ) )
| ( SV187 = SY243 ) ) )
= $true )
| ( ( SV122 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV122 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1185]) ).
thf(1225,plain,
! [SV188: $i,SV123: $i] :
( ( ! [SY244: $i] :
( ~ ( aNaturalNumber0 @ SV123 )
| ~ ( aNaturalNumber0 @ SV188 )
| ~ ( aNaturalNumber0 @ SY244 )
| ( SV123 = sz00 )
| ( SV188 = SY244 )
| ~ ( sdtlseqdt0 @ SV188 @ SY244 )
| ( ( sdtasdt0 @ SV188 @ SV123 )
!= ( sdtasdt0 @ SY244 @ SV123 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1187]) ).
thf(1226,plain,
! [SV123: $i] :
( ( ~ ! [SY200: $i,SY201: $i] :
( ~ ( aNaturalNumber0 @ SV123 )
| ~ ( aNaturalNumber0 @ SY200 )
| ~ ( aNaturalNumber0 @ SY201 )
| ( SV123 = sz00 )
| ( SY200 = SY201 )
| ~ ( sdtlseqdt0 @ SY200 @ SY201 )
| ( ( sdtasdt0 @ SV123 @ SY200 )
!= ( sdtasdt0 @ SV123 @ SY201 ) ) )
| ~ ! [SY202: $i,SY203: $i] :
( ~ ( aNaturalNumber0 @ SV123 )
| ~ ( aNaturalNumber0 @ SY202 )
| ~ ( aNaturalNumber0 @ SY203 )
| ( SV123 = sz00 )
| ( SY202 = SY203 )
| ~ ( sdtlseqdt0 @ SY202 @ SY203 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV123 @ SY202 ) @ ( sdtasdt0 @ SV123 @ SY203 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1188]) ).
thf(1227,plain,
! [SV181: $i,SV170: $i,SV123: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV123 )
| ~ ( aNaturalNumber0 @ SV170 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV181 ) )
= $true )
| ( ( ( SV123 = sz00 )
| ( SV170 = SV181 )
| ~ ( sdtlseqdt0 @ SV170 @ SV181 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV170 @ SV123 ) @ ( sdtasdt0 @ SV181 @ SV123 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1189]) ).
thf(1228,plain,
( ( ~ ~ ( ( ( sdtasdt0 @ xn @ xn )
!= ( sdtasdt0 @ xp @ sK3_W0 ) )
| ~ ( aNaturalNumber0 @ sK3_W0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1190]) ).
thf(1229,plain,
( ( ~ ( doDivides0 @ xp @ ( sdtasdt0 @ xn @ xn ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1190]) ).
thf(1230,plain,
( ( xn
!= ( sdtasdt0 @ xp @ sK2_W0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1191]) ).
thf(1231,plain,
( ( ~ ( aNaturalNumber0 @ sK2_W0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1191]) ).
thf(1232,plain,
! [SV124: $i,SV171: $i,SV182: $i] :
( ( ( SV182 = sz00 )
= $true )
| ( ( ( SV171 = sz00 )
| ( SV124 = sz00 )
| ~ ( aNaturalNumber0 @ SV124 )
| ~ ( aNaturalNumber0 @ SV171 )
| ~ ( aNaturalNumber0 @ SV182 ) )
= $true )
| ( ( ( ( sdtasdt0 @ SV182 @ ( sdtasdt0 @ SV171 @ SV171 ) )
!= ( sdtasdt0 @ SV124 @ SV124 ) )
| ~ ( iLess0 @ SV124 @ xn )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( SV182
!= ( sdtasdt0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) @ ( sK5_SY81 @ SV182 @ SV171 @ SV124 ) ) )
| ~ ( aNaturalNumber0 @ ( sK5_SY81 @ SV182 @ SV171 @ SV124 ) ) )
| ~ ( aNaturalNumber0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) ) )
| ~ ( doDivides0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) @ SV182 ) )
| ~ ~ ( ~ ( ( ( sK4_W3 @ SV182 @ SV171 @ SV124 )
!= sz10 ) )
| ~ ( ( ( sK4_W3 @ SV182 @ SV171 @ SV124 )
!= SV182 ) ) ) )
| ( SV182 = sz10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1192]) ).
thf(1233,plain,
! [SV124: $i,SV172: $i,SV183: $i] :
( ( ( SV183 = sz00 )
= $true )
| ( ( ( SV172 = sz00 )
| ( SV124 = sz00 )
| ~ ( aNaturalNumber0 @ SV124 )
| ~ ( aNaturalNumber0 @ SV172 )
| ~ ( aNaturalNumber0 @ SV183 ) )
= $true )
| ( ( ( ( sdtasdt0 @ SV183 @ ( sdtasdt0 @ SV172 @ SV172 ) )
!= ( sdtasdt0 @ SV124 @ SV124 ) )
| ~ ( iLess0 @ SV124 @ xn )
| ~ ( isPrime0 @ SV183 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1193]) ).
thf(1234,plain,
( ( ~ ( ( xn != sz00 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1195]) ).
thf(1235,plain,
( ( ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ xn )
| ~ ( aNaturalNumber0 @ xm ) )
| ~ ( aNaturalNumber0 @ xp ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1195]) ).
thf(1236,plain,
! [SV173: $i,SV157: $i] :
( ( ( aNaturalNumber0 @ SV157 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV173 ) )
= $true )
| ( ( ( SV173 != SV157 )
| ( sdtlseqdt0 @ SV157 @ SV173 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1196]) ).
thf(1237,plain,
! [SV174: $i,SV158: $i] :
( ( ( aNaturalNumber0 @ SV158 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV174 ) )
= $true )
| ( ( ( sdtlseqdt0 @ SV174 @ SV158 )
| ( sdtlseqdt0 @ SV158 @ SV174 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1197]) ).
thf(1238,plain,
! [SV145: $i,SV125: $i] :
( ( ( SV125 = SV145 )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV125 @ SV145 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY227: $i] :
( ~ ( aNaturalNumber0 @ SY227 )
| ( ( sdtpldt0 @ SV125 @ SY227 )
!= ( sdtpldt0 @ SV145 @ SY227 ) ) )
| ~ ~ ( ~ ! [SY228: $i] :
( ~ ( aNaturalNumber0 @ SY228 )
| ( ( sdtpldt0 @ SY228 @ SV125 )
!= ( sdtpldt0 @ SY228 @ SV145 ) ) )
| ~ ! [SY229: $i] :
( ~ ( aNaturalNumber0 @ SY229 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SY229 @ SV125 ) @ ( sdtpldt0 @ SY229 @ SV145 ) ) ) ) )
| ~ ! [SY230: $i] :
( ~ ( aNaturalNumber0 @ SY230 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SV125 @ SY230 ) @ ( sdtpldt0 @ SV145 @ SY230 ) ) ) ) )
= $true )
| ( ( aNaturalNumber0 @ SV125 )
= $false )
| ( ( aNaturalNumber0 @ SV145 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1198]) ).
thf(1239,plain,
! [SV184: $i,SV175: $i,SV126: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV126 )
| ~ ( aNaturalNumber0 @ SV175 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV184 ) )
= $true )
| ( ( ( ( sdtpldt0 @ SV126 @ SV175 )
!= ( sdtpldt0 @ SV126 @ SV184 ) )
| ( SV175 = SV184 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1199]) ).
thf(1240,plain,
! [SV185: $i,SV176: $i,SV126: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV126 )
| ~ ( aNaturalNumber0 @ SV176 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV185 ) )
= $true )
| ( ( ( ( sdtpldt0 @ SV176 @ SV126 )
!= ( sdtpldt0 @ SV185 @ SV126 ) )
| ( SV176 = SV185 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1200]) ).
thf(1241,plain,
! [SV159: $i] :
( ( ( sz10 = SV159 )
= $false )
| ( ( ( SV159 = sz00 )
| ( SV159 = sz10 ) )
= $true )
| ( ( aNaturalNumber0 @ SV159 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1201]) ).
thf(1242,plain,
! [SV160: $i] :
( ( ( SV160 = sz00 )
= $true )
| ( ( SV160 = sz10 )
= $true )
| ( ( sdtlseqdt0 @ sz10 @ SV160 )
= $true )
| ( ( aNaturalNumber0 @ SV160 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1202]) ).
thf(1243,plain,
! [SV127: $i] :
( ( ( ~ ( ~ ( aNaturalNumber0 @ ( sK1_W1 @ SV127 ) )
| ~ ( doDivides0 @ ( sK1_W1 @ SV127 ) @ SV127 ) ) )
= $true )
| ( ( SV127 = sz10 )
= $true )
| ( ( SV127 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV127 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1203]) ).
thf(1244,plain,
! [SV127: $i] :
( ( ( isPrime0 @ ( sK1_W1 @ SV127 ) )
= $true )
| ( ( SV127 = sz10 )
= $true )
| ( ( SV127 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV127 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1204]) ).
thf(1245,plain,
! [SV177: $i,SV165: $i] :
( ( ( aNaturalNumber0 @ SV165 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV177 ) )
= $true )
| ( ( ( ( sdtpldt0 @ SV165 @ SV177 )
!= sz00 )
| ( SV165 = sz00 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1205]) ).
thf(1246,plain,
! [SV178: $i,SV166: $i] :
( ( ( aNaturalNumber0 @ SV166 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV178 ) )
= $true )
| ( ( ( ( sdtpldt0 @ SV166 @ SV178 )
!= sz00 )
| ( SV178 = sz00 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1206]) ).
thf(1247,plain,
! [SV131: $i,SV106: $i,SV146: $i] :
( ( ( aNaturalNumber0 @ SV146 )
= $false )
| ( ( aNaturalNumber0 @ SV106 )
= $false )
| ( ( aNaturalNumber0 @ SV131 )
= $false )
| ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV106 @ SV131 ) @ SV146 )
= ( sdtpldt0 @ SV106 @ ( sdtpldt0 @ SV131 @ SV146 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1207]) ).
thf(1248,plain,
! [SV133: $i,SV108: $i,SV147: $i] :
( ( ( aNaturalNumber0 @ SV147 )
= $false )
| ( ( aNaturalNumber0 @ SV108 )
= $false )
| ( ( aNaturalNumber0 @ SV133 )
= $false )
| ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV108 @ SV133 ) @ SV147 )
= ( sdtasdt0 @ SV108 @ ( sdtasdt0 @ SV133 @ SV147 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1208]) ).
thf(1249,plain,
! [SV134: $i,SV109: $i] :
( ( ( SV109 = sz00 )
= $true )
| ( ( SV134 = sz00 )
= $true )
| ( ( ( sdtasdt0 @ SV109 @ SV134 )
= sz00 )
= $false )
| ( ( aNaturalNumber0 @ SV109 )
= $false )
| ( ( aNaturalNumber0 @ SV134 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1209]) ).
thf(1250,plain,
! [SV135: $i,SV111: $i] :
( ( ( sdtlseqdt0 @ SV111 @ SV135 )
= $false )
| ( ( ~ ( sdtlseqdt0 @ SV135 @ SV111 ) )
= $true )
| ( ( SV111 = SV135 )
= $true )
| ( ( aNaturalNumber0 @ SV111 )
= $false )
| ( ( aNaturalNumber0 @ SV135 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1210]) ).
thf(1251,plain,
! [SV136: $i,SV112: $i,SV148: $i] :
( ( ( aNaturalNumber0 @ SV148 )
= $false )
| ( ( aNaturalNumber0 @ SV112 )
= $false )
| ( ( aNaturalNumber0 @ SV136 )
= $false )
| ( ( ~ ( sdtlseqdt0 @ SV112 @ SV136 )
| ~ ( sdtlseqdt0 @ SV136 @ SV148 )
| ( sdtlseqdt0 @ SV112 @ SV148 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1211]) ).
thf(1252,plain,
! [SV138: $i,SV114: $i] :
( ( ( sdtlseqdt0 @ SV114 @ SV138 )
= $false )
| ( ( SV114 = SV138 )
= $true )
| ( ( iLess0 @ SV114 @ SV138 )
= $true )
| ( ( aNaturalNumber0 @ SV114 )
= $false )
| ( ( aNaturalNumber0 @ SV138 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1212]) ).
thf(1253,plain,
! [SV139: $i,SV115: $i,SV150: $i] :
( ( ( aNaturalNumber0 @ SV150 )
= $false )
| ( ( aNaturalNumber0 @ SV115 )
= $false )
| ( ( aNaturalNumber0 @ SV139 )
= $false )
| ( ( ~ ( doDivides0 @ SV115 @ SV139 )
| ~ ( doDivides0 @ SV139 @ SV150 )
| ( doDivides0 @ SV115 @ SV150 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1213]) ).
thf(1254,plain,
! [SV140: $i,SV116: $i,SV151: $i] :
( ( ( aNaturalNumber0 @ SV151 )
= $false )
| ( ( aNaturalNumber0 @ SV116 )
= $false )
| ( ( aNaturalNumber0 @ SV140 )
= $false )
| ( ( ~ ( doDivides0 @ SV116 @ SV140 )
| ~ ( doDivides0 @ SV116 @ SV151 )
| ( doDivides0 @ SV116 @ ( sdtpldt0 @ SV140 @ SV151 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1214]) ).
thf(1255,plain,
! [SV141: $i,SV117: $i,SV152: $i] :
( ( ( aNaturalNumber0 @ SV152 )
= $false )
| ( ( aNaturalNumber0 @ SV117 )
= $false )
| ( ( aNaturalNumber0 @ SV141 )
= $false )
| ( ( ~ ( doDivides0 @ SV117 @ SV141 )
| ~ ( doDivides0 @ SV117 @ ( sdtpldt0 @ SV141 @ SV152 ) )
| ( doDivides0 @ SV117 @ SV152 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1215]) ).
thf(1256,plain,
! [SV142: $i,SV118: $i] :
( ( ( doDivides0 @ SV118 @ SV142 )
= $false )
| ( ( SV142 = sz00 )
= $true )
| ( ( sdtlseqdt0 @ SV118 @ SV142 )
= $true )
| ( ( aNaturalNumber0 @ SV118 )
= $false )
| ( ( aNaturalNumber0 @ SV142 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1216]) ).
thf(1257,plain,
! [SV143: $i,SV119: $i] :
( ( ( doDivides0 @ SV119 @ SV143 )
= $false )
| ( ( SV119 = sz00 )
= $true )
| ( ( ! [SY225: $i] :
( ~ ( aNaturalNumber0 @ SY225 )
| ( ( sdtasdt0 @ SY225 @ ( sdtsldt0 @ SV143 @ SV119 ) )
= ( sdtsldt0 @ ( sdtasdt0 @ SY225 @ SV143 ) @ SV119 ) ) ) )
= $true )
| ( ( aNaturalNumber0 @ SV119 )
= $false )
| ( ( aNaturalNumber0 @ SV143 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1217]) ).
thf(1258,plain,
! [SV144: $i,SV120: $i,SV153: $i] :
( ( ( aNaturalNumber0 @ SV153 )
= $false )
| ( ( aNaturalNumber0 @ SV120 )
= $false )
| ( ( aNaturalNumber0 @ SV144 )
= $false )
| ( ( ~ ( doDivides0 @ SV153 @ ( sdtasdt0 @ SV120 @ SV144 ) )
| ~ ( isPrime0 @ SV153 )
| ( doDivides0 @ SV153 @ SV120 )
| ( doDivides0 @ SV153 @ SV144 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1218]) ).
thf(1259,plain,
( ( ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ! [SX1: $i] :
( ( xp
!= ( sdtasdt0 @ SX0 @ SX1 ) )
| ~ ( aNaturalNumber0 @ SX1 ) )
| ( SX0 = sz10 )
| ( SX0 = xp ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1219]) ).
thf(1260,plain,
( ( ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( doDivides0 @ SX0 @ xp )
| ( SX0 = sz10 )
| ( SX0 = xp ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1220]) ).
thf(1261,plain,
! [SV179: $i,SV168: $i,SV121: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV121 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV168 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV179 ) )
= $true )
| ( ( ( sdtasdt0 @ SV121 @ ( sdtpldt0 @ SV168 @ SV179 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV121 @ SV168 ) @ ( sdtasdt0 @ SV121 @ SV179 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1221]) ).
thf(1262,plain,
! [SV180: $i,SV169: $i,SV121: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV121 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV169 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV180 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV169 @ SV180 ) @ SV121 )
= ( sdtpldt0 @ ( sdtasdt0 @ SV169 @ SV121 ) @ ( sdtasdt0 @ SV180 @ SV121 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1222]) ).
thf(1263,plain,
! [SV122: $i,SV189: $i,SV186: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV186 )
| ~ ( aNaturalNumber0 @ SV189 )
| ( ( sdtasdt0 @ SV122 @ SV186 )
!= ( sdtasdt0 @ SV122 @ SV189 ) )
| ( SV186 = SV189 ) )
= $true )
| ( ( SV122 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV122 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1223]) ).
thf(1264,plain,
! [SV122: $i,SV190: $i,SV187: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV187 )
| ~ ( aNaturalNumber0 @ SV190 )
| ( ( sdtasdt0 @ SV187 @ SV122 )
!= ( sdtasdt0 @ SV190 @ SV122 ) )
| ( SV187 = SV190 ) )
= $true )
| ( ( SV122 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV122 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1224]) ).
thf(1265,plain,
! [SV191: $i,SV188: $i,SV123: $i] :
( ( ~ ( aNaturalNumber0 @ SV123 )
| ~ ( aNaturalNumber0 @ SV188 )
| ~ ( aNaturalNumber0 @ SV191 )
| ( SV123 = sz00 )
| ( SV188 = SV191 )
| ~ ( sdtlseqdt0 @ SV188 @ SV191 )
| ( ( sdtasdt0 @ SV188 @ SV123 )
!= ( sdtasdt0 @ SV191 @ SV123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1225]) ).
thf(1266,plain,
! [SV123: $i] :
( ( ~ ! [SY200: $i,SY201: $i] :
( ~ ( aNaturalNumber0 @ SV123 )
| ~ ( aNaturalNumber0 @ SY200 )
| ~ ( aNaturalNumber0 @ SY201 )
| ( SV123 = sz00 )
| ( SY200 = SY201 )
| ~ ( sdtlseqdt0 @ SY200 @ SY201 )
| ( ( sdtasdt0 @ SV123 @ SY200 )
!= ( sdtasdt0 @ SV123 @ SY201 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1226]) ).
thf(1267,plain,
! [SV123: $i] :
( ( ~ ! [SY202: $i,SY203: $i] :
( ~ ( aNaturalNumber0 @ SV123 )
| ~ ( aNaturalNumber0 @ SY202 )
| ~ ( aNaturalNumber0 @ SY203 )
| ( SV123 = sz00 )
| ( SY202 = SY203 )
| ~ ( sdtlseqdt0 @ SY202 @ SY203 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV123 @ SY202 ) @ ( sdtasdt0 @ SV123 @ SY203 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1226]) ).
thf(1268,plain,
! [SV181: $i,SV170: $i,SV123: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV123 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV170 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV181 ) )
= $true )
| ( ( ( SV123 = sz00 )
| ( SV170 = SV181 )
| ~ ( sdtlseqdt0 @ SV170 @ SV181 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV170 @ SV123 ) @ ( sdtasdt0 @ SV181 @ SV123 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1227]) ).
thf(1269,plain,
( ( ~ ( ( ( sdtasdt0 @ xn @ xn )
!= ( sdtasdt0 @ xp @ sK3_W0 ) )
| ~ ( aNaturalNumber0 @ sK3_W0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1228]) ).
thf(1270,plain,
( ( doDivides0 @ xp @ ( sdtasdt0 @ xn @ xn ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1229]) ).
thf(1271,plain,
( ( xn
= ( sdtasdt0 @ xp @ sK2_W0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1230]) ).
thf(1272,plain,
( ( aNaturalNumber0 @ sK2_W0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1231]) ).
thf(1273,plain,
! [SV182: $i,SV124: $i,SV171: $i] :
( ( ( SV171 = sz00 )
= $true )
| ( ( ( SV124 = sz00 )
| ~ ( aNaturalNumber0 @ SV124 )
| ~ ( aNaturalNumber0 @ SV171 )
| ~ ( aNaturalNumber0 @ SV182 ) )
= $true )
| ( ( SV182 = sz00 )
= $true )
| ( ( ( ( sdtasdt0 @ SV182 @ ( sdtasdt0 @ SV171 @ SV171 ) )
!= ( sdtasdt0 @ SV124 @ SV124 ) )
| ~ ( iLess0 @ SV124 @ xn )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( SV182
!= ( sdtasdt0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) @ ( sK5_SY81 @ SV182 @ SV171 @ SV124 ) ) )
| ~ ( aNaturalNumber0 @ ( sK5_SY81 @ SV182 @ SV171 @ SV124 ) ) )
| ~ ( aNaturalNumber0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) ) )
| ~ ( doDivides0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) @ SV182 ) )
| ~ ~ ( ~ ( ( ( sK4_W3 @ SV182 @ SV171 @ SV124 )
!= sz10 ) )
| ~ ( ( ( sK4_W3 @ SV182 @ SV171 @ SV124 )
!= SV182 ) ) ) )
| ( SV182 = sz10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1232]) ).
thf(1274,plain,
! [SV183: $i,SV124: $i,SV172: $i] :
( ( ( SV172 = sz00 )
= $true )
| ( ( ( SV124 = sz00 )
| ~ ( aNaturalNumber0 @ SV124 )
| ~ ( aNaturalNumber0 @ SV172 )
| ~ ( aNaturalNumber0 @ SV183 ) )
= $true )
| ( ( SV183 = sz00 )
= $true )
| ( ( ( ( sdtasdt0 @ SV183 @ ( sdtasdt0 @ SV172 @ SV172 ) )
!= ( sdtasdt0 @ SV124 @ SV124 ) )
| ~ ( iLess0 @ SV124 @ xn )
| ~ ( isPrime0 @ SV183 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1233]) ).
thf(1275,plain,
( ( xn != sz00 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1234]) ).
thf(1276,plain,
( ( ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ xn )
| ~ ( aNaturalNumber0 @ xm ) )
| ~ ( aNaturalNumber0 @ xp ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1235]) ).
thf(1277,plain,
! [SV157: $i,SV173: $i] :
( ( ( aNaturalNumber0 @ SV173 )
= $false )
| ( ( aNaturalNumber0 @ SV157 )
= $false )
| ( ( ( SV173 != SV157 )
| ( sdtlseqdt0 @ SV157 @ SV173 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1236]) ).
thf(1278,plain,
! [SV158: $i,SV174: $i] :
( ( ( aNaturalNumber0 @ SV174 )
= $false )
| ( ( aNaturalNumber0 @ SV158 )
= $false )
| ( ( ( sdtlseqdt0 @ SV174 @ SV158 )
| ( sdtlseqdt0 @ SV158 @ SV174 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1237]) ).
thf(1279,plain,
! [SV145: $i,SV125: $i] :
( ( ( sdtlseqdt0 @ SV125 @ SV145 )
= $false )
| ( ( SV125 = SV145 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY227: $i] :
( ~ ( aNaturalNumber0 @ SY227 )
| ( ( sdtpldt0 @ SV125 @ SY227 )
!= ( sdtpldt0 @ SV145 @ SY227 ) ) )
| ~ ~ ( ~ ! [SY228: $i] :
( ~ ( aNaturalNumber0 @ SY228 )
| ( ( sdtpldt0 @ SY228 @ SV125 )
!= ( sdtpldt0 @ SY228 @ SV145 ) ) )
| ~ ! [SY229: $i] :
( ~ ( aNaturalNumber0 @ SY229 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SY229 @ SV125 ) @ ( sdtpldt0 @ SY229 @ SV145 ) ) ) ) )
| ~ ! [SY230: $i] :
( ~ ( aNaturalNumber0 @ SY230 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SV125 @ SY230 ) @ ( sdtpldt0 @ SV145 @ SY230 ) ) ) ) )
= $true )
| ( ( aNaturalNumber0 @ SV125 )
= $false )
| ( ( aNaturalNumber0 @ SV145 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1238]) ).
thf(1280,plain,
! [SV184: $i,SV175: $i,SV126: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV126 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV175 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV184 ) )
= $true )
| ( ( ( ( sdtpldt0 @ SV126 @ SV175 )
!= ( sdtpldt0 @ SV126 @ SV184 ) )
| ( SV175 = SV184 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1239]) ).
thf(1281,plain,
! [SV185: $i,SV176: $i,SV126: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV126 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV176 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV185 ) )
= $true )
| ( ( ( ( sdtpldt0 @ SV176 @ SV126 )
!= ( sdtpldt0 @ SV185 @ SV126 ) )
| ( SV176 = SV185 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1240]) ).
thf(1282,plain,
! [SV159: $i] :
( ( ( SV159 = sz00 )
= $true )
| ( ( SV159 = sz10 )
= $true )
| ( ( sz10 = SV159 )
= $false )
| ( ( aNaturalNumber0 @ SV159 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1241]) ).
thf(1283,plain,
! [SV127: $i] :
( ( ( ~ ( aNaturalNumber0 @ ( sK1_W1 @ SV127 ) )
| ~ ( doDivides0 @ ( sK1_W1 @ SV127 ) @ SV127 ) )
= $false )
| ( ( SV127 = sz10 )
= $true )
| ( ( SV127 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV127 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1243]) ).
thf(1284,plain,
! [SV165: $i,SV177: $i] :
( ( ( aNaturalNumber0 @ SV177 )
= $false )
| ( ( aNaturalNumber0 @ SV165 )
= $false )
| ( ( ( ( sdtpldt0 @ SV165 @ SV177 )
!= sz00 )
| ( SV165 = sz00 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1245]) ).
thf(1285,plain,
! [SV166: $i,SV178: $i] :
( ( ( aNaturalNumber0 @ SV178 )
= $false )
| ( ( aNaturalNumber0 @ SV166 )
= $false )
| ( ( ( ( sdtpldt0 @ SV166 @ SV178 )
!= sz00 )
| ( SV178 = sz00 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1246]) ).
thf(1286,plain,
! [SV111: $i,SV135: $i] :
( ( ( sdtlseqdt0 @ SV135 @ SV111 )
= $false )
| ( ( sdtlseqdt0 @ SV111 @ SV135 )
= $false )
| ( ( SV111 = SV135 )
= $true )
| ( ( aNaturalNumber0 @ SV111 )
= $false )
| ( ( aNaturalNumber0 @ SV135 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1250]) ).
thf(1287,plain,
! [SV148: $i,SV136: $i,SV112: $i] :
( ( ( ~ ( sdtlseqdt0 @ SV112 @ SV136 )
| ~ ( sdtlseqdt0 @ SV136 @ SV148 ) )
= $true )
| ( ( sdtlseqdt0 @ SV112 @ SV148 )
= $true )
| ( ( aNaturalNumber0 @ SV136 )
= $false )
| ( ( aNaturalNumber0 @ SV112 )
= $false )
| ( ( aNaturalNumber0 @ SV148 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1251]) ).
thf(1288,plain,
! [SV150: $i,SV139: $i,SV115: $i] :
( ( ( ~ ( doDivides0 @ SV115 @ SV139 )
| ~ ( doDivides0 @ SV139 @ SV150 ) )
= $true )
| ( ( doDivides0 @ SV115 @ SV150 )
= $true )
| ( ( aNaturalNumber0 @ SV139 )
= $false )
| ( ( aNaturalNumber0 @ SV115 )
= $false )
| ( ( aNaturalNumber0 @ SV150 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1253]) ).
thf(1289,plain,
! [SV151: $i,SV140: $i,SV116: $i] :
( ( ( ~ ( doDivides0 @ SV116 @ SV140 )
| ~ ( doDivides0 @ SV116 @ SV151 ) )
= $true )
| ( ( doDivides0 @ SV116 @ ( sdtpldt0 @ SV140 @ SV151 ) )
= $true )
| ( ( aNaturalNumber0 @ SV140 )
= $false )
| ( ( aNaturalNumber0 @ SV116 )
= $false )
| ( ( aNaturalNumber0 @ SV151 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1254]) ).
thf(1290,plain,
! [SV152: $i,SV141: $i,SV117: $i] :
( ( ( ~ ( doDivides0 @ SV117 @ SV141 )
| ~ ( doDivides0 @ SV117 @ ( sdtpldt0 @ SV141 @ SV152 ) ) )
= $true )
| ( ( doDivides0 @ SV117 @ SV152 )
= $true )
| ( ( aNaturalNumber0 @ SV141 )
= $false )
| ( ( aNaturalNumber0 @ SV117 )
= $false )
| ( ( aNaturalNumber0 @ SV152 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1255]) ).
thf(1291,plain,
! [SV119: $i,SV143: $i,SV192: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV192 )
| ( ( sdtasdt0 @ SV192 @ ( sdtsldt0 @ SV143 @ SV119 ) )
= ( sdtsldt0 @ ( sdtasdt0 @ SV192 @ SV143 ) @ SV119 ) ) )
= $true )
| ( ( SV119 = sz00 )
= $true )
| ( ( doDivides0 @ SV119 @ SV143 )
= $false )
| ( ( aNaturalNumber0 @ SV119 )
= $false )
| ( ( aNaturalNumber0 @ SV143 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1257]) ).
thf(1292,plain,
! [SV144: $i,SV120: $i,SV153: $i] :
( ( ( ~ ( doDivides0 @ SV153 @ ( sdtasdt0 @ SV120 @ SV144 ) )
| ~ ( isPrime0 @ SV153 ) )
= $true )
| ( ( ( doDivides0 @ SV153 @ SV120 )
| ( doDivides0 @ SV153 @ SV144 ) )
= $true )
| ( ( aNaturalNumber0 @ SV144 )
= $false )
| ( ( aNaturalNumber0 @ SV120 )
= $false )
| ( ( aNaturalNumber0 @ SV153 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1258]) ).
thf(1293,plain,
! [SV193: $i] :
( ( ~ ( aNaturalNumber0 @ SV193 )
| ! [SY245: $i] :
( ( xp
!= ( sdtasdt0 @ SV193 @ SY245 ) )
| ~ ( aNaturalNumber0 @ SY245 ) )
| ( SV193 = sz10 )
| ( SV193 = xp ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1259]) ).
thf(1294,plain,
! [SV194: $i] :
( ( ~ ( aNaturalNumber0 @ SV194 )
| ~ ( doDivides0 @ SV194 @ xp )
| ( SV194 = sz10 )
| ( SV194 = xp ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1260]) ).
thf(1295,plain,
! [SV179: $i,SV168: $i,SV121: $i] :
( ( ( aNaturalNumber0 @ SV121 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV168 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV179 ) )
= $true )
| ( ( ( sdtasdt0 @ SV121 @ ( sdtpldt0 @ SV168 @ SV179 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV121 @ SV168 ) @ ( sdtasdt0 @ SV121 @ SV179 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1261]) ).
thf(1296,plain,
! [SV180: $i,SV169: $i,SV121: $i] :
( ( ( aNaturalNumber0 @ SV121 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV169 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV180 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV169 @ SV180 ) @ SV121 )
= ( sdtpldt0 @ ( sdtasdt0 @ SV169 @ SV121 ) @ ( sdtasdt0 @ SV180 @ SV121 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1262]) ).
thf(1297,plain,
! [SV122: $i,SV189: $i,SV186: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV186 )
| ~ ( aNaturalNumber0 @ SV189 ) )
= $true )
| ( ( ( ( sdtasdt0 @ SV122 @ SV186 )
!= ( sdtasdt0 @ SV122 @ SV189 ) )
| ( SV186 = SV189 ) )
= $true )
| ( ( SV122 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV122 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1263]) ).
thf(1298,plain,
! [SV122: $i,SV190: $i,SV187: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV187 )
| ~ ( aNaturalNumber0 @ SV190 ) )
= $true )
| ( ( ( ( sdtasdt0 @ SV187 @ SV122 )
!= ( sdtasdt0 @ SV190 @ SV122 ) )
| ( SV187 = SV190 ) )
= $true )
| ( ( SV122 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV122 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1264]) ).
thf(1299,plain,
! [SV191: $i,SV188: $i,SV123: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV123 )
| ~ ( aNaturalNumber0 @ SV188 )
| ~ ( aNaturalNumber0 @ SV191 ) )
= $true )
| ( ( ( SV123 = sz00 )
| ( SV188 = SV191 )
| ~ ( sdtlseqdt0 @ SV188 @ SV191 )
| ( ( sdtasdt0 @ SV188 @ SV123 )
!= ( sdtasdt0 @ SV191 @ SV123 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1265]) ).
thf(1300,plain,
! [SV123: $i] :
( ( ! [SY200: $i,SY201: $i] :
( ~ ( aNaturalNumber0 @ SV123 )
| ~ ( aNaturalNumber0 @ SY200 )
| ~ ( aNaturalNumber0 @ SY201 )
| ( SV123 = sz00 )
| ( SY200 = SY201 )
| ~ ( sdtlseqdt0 @ SY200 @ SY201 )
| ( ( sdtasdt0 @ SV123 @ SY200 )
!= ( sdtasdt0 @ SV123 @ SY201 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1266]) ).
thf(1301,plain,
! [SV123: $i] :
( ( ! [SY202: $i,SY203: $i] :
( ~ ( aNaturalNumber0 @ SV123 )
| ~ ( aNaturalNumber0 @ SY202 )
| ~ ( aNaturalNumber0 @ SY203 )
| ( SV123 = sz00 )
| ( SY202 = SY203 )
| ~ ( sdtlseqdt0 @ SY202 @ SY203 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV123 @ SY202 ) @ ( sdtasdt0 @ SV123 @ SY203 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1267]) ).
thf(1302,plain,
! [SV181: $i,SV170: $i,SV123: $i] :
( ( ( aNaturalNumber0 @ SV123 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV170 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV181 ) )
= $true )
| ( ( ( SV123 = sz00 )
| ( SV170 = SV181 )
| ~ ( sdtlseqdt0 @ SV170 @ SV181 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV170 @ SV123 ) @ ( sdtasdt0 @ SV181 @ SV123 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1268]) ).
thf(1303,plain,
( ( ( ( sdtasdt0 @ xn @ xn )
!= ( sdtasdt0 @ xp @ sK3_W0 ) )
| ~ ( aNaturalNumber0 @ sK3_W0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1269]) ).
thf(1304,plain,
! [SV182: $i,SV171: $i,SV124: $i] :
( ( ( SV124 = sz00 )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV124 )
| ~ ( aNaturalNumber0 @ SV171 )
| ~ ( aNaturalNumber0 @ SV182 ) )
= $true )
| ( ( SV171 = sz00 )
= $true )
| ( ( SV182 = sz00 )
= $true )
| ( ( ( ( sdtasdt0 @ SV182 @ ( sdtasdt0 @ SV171 @ SV171 ) )
!= ( sdtasdt0 @ SV124 @ SV124 ) )
| ~ ( iLess0 @ SV124 @ xn )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( SV182
!= ( sdtasdt0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) @ ( sK5_SY81 @ SV182 @ SV171 @ SV124 ) ) )
| ~ ( aNaturalNumber0 @ ( sK5_SY81 @ SV182 @ SV171 @ SV124 ) ) )
| ~ ( aNaturalNumber0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) ) )
| ~ ( doDivides0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) @ SV182 ) )
| ~ ~ ( ~ ( ( ( sK4_W3 @ SV182 @ SV171 @ SV124 )
!= sz10 ) )
| ~ ( ( ( sK4_W3 @ SV182 @ SV171 @ SV124 )
!= SV182 ) ) ) )
| ( SV182 = sz10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1273]) ).
thf(1305,plain,
! [SV183: $i,SV172: $i,SV124: $i] :
( ( ( SV124 = sz00 )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV124 )
| ~ ( aNaturalNumber0 @ SV172 )
| ~ ( aNaturalNumber0 @ SV183 ) )
= $true )
| ( ( SV172 = sz00 )
= $true )
| ( ( SV183 = sz00 )
= $true )
| ( ( ( ( sdtasdt0 @ SV183 @ ( sdtasdt0 @ SV172 @ SV172 ) )
!= ( sdtasdt0 @ SV124 @ SV124 ) )
| ~ ( iLess0 @ SV124 @ xn )
| ~ ( isPrime0 @ SV183 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1274]) ).
thf(1306,plain,
( ( xn = sz00 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1275]) ).
thf(1307,plain,
( ( ~ ~ ( ~ ( aNaturalNumber0 @ xn )
| ~ ( aNaturalNumber0 @ xm ) )
| ~ ( aNaturalNumber0 @ xp ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1276]) ).
thf(1308,plain,
! [SV157: $i,SV173: $i] :
( ( ( SV173 != SV157 )
= $true )
| ( ( sdtlseqdt0 @ SV157 @ SV173 )
= $true )
| ( ( aNaturalNumber0 @ SV157 )
= $false )
| ( ( aNaturalNumber0 @ SV173 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1277]) ).
thf(1309,plain,
! [SV158: $i,SV174: $i] :
( ( ( sdtlseqdt0 @ SV174 @ SV158 )
= $true )
| ( ( sdtlseqdt0 @ SV158 @ SV174 )
= $true )
| ( ( aNaturalNumber0 @ SV158 )
= $false )
| ( ( aNaturalNumber0 @ SV174 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1278]) ).
thf(1310,plain,
! [SV145: $i,SV125: $i] :
( ( ( ~ ~ ( ~ ! [SY227: $i] :
( ~ ( aNaturalNumber0 @ SY227 )
| ( ( sdtpldt0 @ SV125 @ SY227 )
!= ( sdtpldt0 @ SV145 @ SY227 ) ) )
| ~ ~ ( ~ ! [SY228: $i] :
( ~ ( aNaturalNumber0 @ SY228 )
| ( ( sdtpldt0 @ SY228 @ SV125 )
!= ( sdtpldt0 @ SY228 @ SV145 ) ) )
| ~ ! [SY229: $i] :
( ~ ( aNaturalNumber0 @ SY229 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SY229 @ SV125 ) @ ( sdtpldt0 @ SY229 @ SV145 ) ) ) ) )
| ~ ! [SY230: $i] :
( ~ ( aNaturalNumber0 @ SY230 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SV125 @ SY230 ) @ ( sdtpldt0 @ SV145 @ SY230 ) ) ) )
= $false )
| ( ( SV125 = SV145 )
= $true )
| ( ( sdtlseqdt0 @ SV125 @ SV145 )
= $false )
| ( ( aNaturalNumber0 @ SV125 )
= $false )
| ( ( aNaturalNumber0 @ SV145 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1279]) ).
thf(1311,plain,
! [SV184: $i,SV175: $i,SV126: $i] :
( ( ( aNaturalNumber0 @ SV126 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV175 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV184 ) )
= $true )
| ( ( ( ( sdtpldt0 @ SV126 @ SV175 )
!= ( sdtpldt0 @ SV126 @ SV184 ) )
| ( SV175 = SV184 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1280]) ).
thf(1312,plain,
! [SV185: $i,SV176: $i,SV126: $i] :
( ( ( aNaturalNumber0 @ SV126 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV176 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV185 ) )
= $true )
| ( ( ( ( sdtpldt0 @ SV176 @ SV126 )
!= ( sdtpldt0 @ SV185 @ SV126 ) )
| ( SV176 = SV185 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1281]) ).
thf(1313,plain,
! [SV127: $i] :
( ( ( ~ ( aNaturalNumber0 @ ( sK1_W1 @ SV127 ) ) )
= $false )
| ( ( SV127 = sz10 )
= $true )
| ( ( SV127 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV127 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1283]) ).
thf(1314,plain,
! [SV127: $i] :
( ( ( ~ ( doDivides0 @ ( sK1_W1 @ SV127 ) @ SV127 ) )
= $false )
| ( ( SV127 = sz10 )
= $true )
| ( ( SV127 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV127 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1283]) ).
thf(1315,plain,
! [SV177: $i,SV165: $i] :
( ( ( ( sdtpldt0 @ SV165 @ SV177 )
!= sz00 )
= $true )
| ( ( SV165 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV165 )
= $false )
| ( ( aNaturalNumber0 @ SV177 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1284]) ).
thf(1316,plain,
! [SV178: $i,SV166: $i] :
( ( ( ( sdtpldt0 @ SV166 @ SV178 )
!= sz00 )
= $true )
| ( ( SV178 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV166 )
= $false )
| ( ( aNaturalNumber0 @ SV178 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1285]) ).
thf(1317,plain,
! [SV148: $i,SV136: $i,SV112: $i] :
( ( ( ~ ( sdtlseqdt0 @ SV112 @ SV136 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV136 @ SV148 ) )
= $true )
| ( ( sdtlseqdt0 @ SV112 @ SV148 )
= $true )
| ( ( aNaturalNumber0 @ SV136 )
= $false )
| ( ( aNaturalNumber0 @ SV112 )
= $false )
| ( ( aNaturalNumber0 @ SV148 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1287]) ).
thf(1318,plain,
! [SV150: $i,SV139: $i,SV115: $i] :
( ( ( ~ ( doDivides0 @ SV115 @ SV139 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV139 @ SV150 ) )
= $true )
| ( ( doDivides0 @ SV115 @ SV150 )
= $true )
| ( ( aNaturalNumber0 @ SV139 )
= $false )
| ( ( aNaturalNumber0 @ SV115 )
= $false )
| ( ( aNaturalNumber0 @ SV150 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1288]) ).
thf(1319,plain,
! [SV151: $i,SV140: $i,SV116: $i] :
( ( ( ~ ( doDivides0 @ SV116 @ SV140 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV116 @ SV151 ) )
= $true )
| ( ( doDivides0 @ SV116 @ ( sdtpldt0 @ SV140 @ SV151 ) )
= $true )
| ( ( aNaturalNumber0 @ SV140 )
= $false )
| ( ( aNaturalNumber0 @ SV116 )
= $false )
| ( ( aNaturalNumber0 @ SV151 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1289]) ).
thf(1320,plain,
! [SV152: $i,SV141: $i,SV117: $i] :
( ( ( ~ ( doDivides0 @ SV117 @ SV141 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV117 @ ( sdtpldt0 @ SV141 @ SV152 ) ) )
= $true )
| ( ( doDivides0 @ SV117 @ SV152 )
= $true )
| ( ( aNaturalNumber0 @ SV141 )
= $false )
| ( ( aNaturalNumber0 @ SV117 )
= $false )
| ( ( aNaturalNumber0 @ SV152 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1290]) ).
thf(1321,plain,
! [SV119: $i,SV143: $i,SV192: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV192 ) )
= $true )
| ( ( ( sdtasdt0 @ SV192 @ ( sdtsldt0 @ SV143 @ SV119 ) )
= ( sdtsldt0 @ ( sdtasdt0 @ SV192 @ SV143 ) @ SV119 ) )
= $true )
| ( ( SV119 = sz00 )
= $true )
| ( ( doDivides0 @ SV119 @ SV143 )
= $false )
| ( ( aNaturalNumber0 @ SV119 )
= $false )
| ( ( aNaturalNumber0 @ SV143 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1291]) ).
thf(1322,plain,
! [SV144: $i,SV120: $i,SV153: $i] :
( ( ( ~ ( doDivides0 @ SV153 @ ( sdtasdt0 @ SV120 @ SV144 ) ) )
= $true )
| ( ( ~ ( isPrime0 @ SV153 ) )
= $true )
| ( ( ( doDivides0 @ SV153 @ SV120 )
| ( doDivides0 @ SV153 @ SV144 ) )
= $true )
| ( ( aNaturalNumber0 @ SV144 )
= $false )
| ( ( aNaturalNumber0 @ SV120 )
= $false )
| ( ( aNaturalNumber0 @ SV153 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1292]) ).
thf(1323,plain,
! [SV193: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV193 )
| ! [SY245: $i] :
( ( xp
!= ( sdtasdt0 @ SV193 @ SY245 ) )
| ~ ( aNaturalNumber0 @ SY245 ) ) )
= $true )
| ( ( ( SV193 = sz10 )
| ( SV193 = xp ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1293]) ).
thf(1324,plain,
! [SV194: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV194 )
| ~ ( doDivides0 @ SV194 @ xp ) )
= $true )
| ( ( ( SV194 = sz10 )
| ( SV194 = xp ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1294]) ).
thf(1325,plain,
! [SV179: $i,SV121: $i,SV168: $i] :
( ( ( aNaturalNumber0 @ SV168 )
= $false )
| ( ( aNaturalNumber0 @ SV121 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV179 ) )
= $true )
| ( ( ( sdtasdt0 @ SV121 @ ( sdtpldt0 @ SV168 @ SV179 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV121 @ SV168 ) @ ( sdtasdt0 @ SV121 @ SV179 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1295]) ).
thf(1326,plain,
! [SV180: $i,SV121: $i,SV169: $i] :
( ( ( aNaturalNumber0 @ SV169 )
= $false )
| ( ( aNaturalNumber0 @ SV121 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV180 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV169 @ SV180 ) @ SV121 )
= ( sdtpldt0 @ ( sdtasdt0 @ SV169 @ SV121 ) @ ( sdtasdt0 @ SV180 @ SV121 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1296]) ).
thf(1327,plain,
! [SV122: $i,SV189: $i,SV186: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV186 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV189 ) )
= $true )
| ( ( ( ( sdtasdt0 @ SV122 @ SV186 )
!= ( sdtasdt0 @ SV122 @ SV189 ) )
| ( SV186 = SV189 ) )
= $true )
| ( ( SV122 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV122 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1297]) ).
thf(1328,plain,
! [SV122: $i,SV190: $i,SV187: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV187 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV190 ) )
= $true )
| ( ( ( ( sdtasdt0 @ SV187 @ SV122 )
!= ( sdtasdt0 @ SV190 @ SV122 ) )
| ( SV187 = SV190 ) )
= $true )
| ( ( SV122 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV122 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1298]) ).
thf(1329,plain,
! [SV191: $i,SV188: $i,SV123: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV123 )
| ~ ( aNaturalNumber0 @ SV188 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV191 ) )
= $true )
| ( ( ( SV123 = sz00 )
| ( SV188 = SV191 )
| ~ ( sdtlseqdt0 @ SV188 @ SV191 )
| ( ( sdtasdt0 @ SV188 @ SV123 )
!= ( sdtasdt0 @ SV191 @ SV123 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1299]) ).
thf(1330,plain,
! [SV195: $i,SV123: $i] :
( ( ! [SY246: $i] :
( ~ ( aNaturalNumber0 @ SV123 )
| ~ ( aNaturalNumber0 @ SV195 )
| ~ ( aNaturalNumber0 @ SY246 )
| ( SV123 = sz00 )
| ( SV195 = SY246 )
| ~ ( sdtlseqdt0 @ SV195 @ SY246 )
| ( ( sdtasdt0 @ SV123 @ SV195 )
!= ( sdtasdt0 @ SV123 @ SY246 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1300]) ).
thf(1331,plain,
! [SV196: $i,SV123: $i] :
( ( ! [SY247: $i] :
( ~ ( aNaturalNumber0 @ SV123 )
| ~ ( aNaturalNumber0 @ SV196 )
| ~ ( aNaturalNumber0 @ SY247 )
| ( SV123 = sz00 )
| ( SV196 = SY247 )
| ~ ( sdtlseqdt0 @ SV196 @ SY247 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV123 @ SV196 ) @ ( sdtasdt0 @ SV123 @ SY247 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1301]) ).
thf(1332,plain,
! [SV181: $i,SV123: $i,SV170: $i] :
( ( ( aNaturalNumber0 @ SV170 )
= $false )
| ( ( aNaturalNumber0 @ SV123 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV181 ) )
= $true )
| ( ( ( SV123 = sz00 )
| ( SV170 = SV181 )
| ~ ( sdtlseqdt0 @ SV170 @ SV181 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV170 @ SV123 ) @ ( sdtasdt0 @ SV181 @ SV123 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1302]) ).
thf(1333,plain,
( ( ( sdtasdt0 @ xn @ xn )
!= ( sdtasdt0 @ xp @ sK3_W0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1303]) ).
thf(1334,plain,
( ( ~ ( aNaturalNumber0 @ sK3_W0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1303]) ).
thf(1335,plain,
! [SV182: $i,SV171: $i,SV124: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV124 )
| ~ ( aNaturalNumber0 @ SV171 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV182 ) )
= $true )
| ( ( SV124 = sz00 )
= $true )
| ( ( SV171 = sz00 )
= $true )
| ( ( SV182 = sz00 )
= $true )
| ( ( ( ( sdtasdt0 @ SV182 @ ( sdtasdt0 @ SV171 @ SV171 ) )
!= ( sdtasdt0 @ SV124 @ SV124 ) )
| ~ ( iLess0 @ SV124 @ xn )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( SV182
!= ( sdtasdt0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) @ ( sK5_SY81 @ SV182 @ SV171 @ SV124 ) ) )
| ~ ( aNaturalNumber0 @ ( sK5_SY81 @ SV182 @ SV171 @ SV124 ) ) )
| ~ ( aNaturalNumber0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) ) )
| ~ ( doDivides0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) @ SV182 ) )
| ~ ~ ( ~ ( ( ( sK4_W3 @ SV182 @ SV171 @ SV124 )
!= sz10 ) )
| ~ ( ( ( sK4_W3 @ SV182 @ SV171 @ SV124 )
!= SV182 ) ) ) )
| ( SV182 = sz10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1304]) ).
thf(1336,plain,
! [SV183: $i,SV172: $i,SV124: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV124 )
| ~ ( aNaturalNumber0 @ SV172 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV183 ) )
= $true )
| ( ( SV124 = sz00 )
= $true )
| ( ( SV172 = sz00 )
= $true )
| ( ( SV183 = sz00 )
= $true )
| ( ( ( ( sdtasdt0 @ SV183 @ ( sdtasdt0 @ SV172 @ SV172 ) )
!= ( sdtasdt0 @ SV124 @ SV124 ) )
| ~ ( iLess0 @ SV124 @ xn )
| ~ ( isPrime0 @ SV183 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1305]) ).
thf(1337,plain,
( ( ~ ~ ( ~ ( aNaturalNumber0 @ xn )
| ~ ( aNaturalNumber0 @ xm ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1307]) ).
thf(1338,plain,
( ( ~ ( aNaturalNumber0 @ xp ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1307]) ).
thf(1339,plain,
! [SV157: $i,SV173: $i] :
( ( ( SV173 = SV157 )
= $false )
| ( ( sdtlseqdt0 @ SV157 @ SV173 )
= $true )
| ( ( aNaturalNumber0 @ SV157 )
= $false )
| ( ( aNaturalNumber0 @ SV173 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1308]) ).
thf(1340,plain,
! [SV145: $i,SV125: $i] :
( ( ( ~ ~ ( ~ ! [SY227: $i] :
( ~ ( aNaturalNumber0 @ SY227 )
| ( ( sdtpldt0 @ SV125 @ SY227 )
!= ( sdtpldt0 @ SV145 @ SY227 ) ) )
| ~ ~ ( ~ ! [SY228: $i] :
( ~ ( aNaturalNumber0 @ SY228 )
| ( ( sdtpldt0 @ SY228 @ SV125 )
!= ( sdtpldt0 @ SY228 @ SV145 ) ) )
| ~ ! [SY229: $i] :
( ~ ( aNaturalNumber0 @ SY229 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SY229 @ SV125 ) @ ( sdtpldt0 @ SY229 @ SV145 ) ) ) ) ) )
= $false )
| ( ( SV125 = SV145 )
= $true )
| ( ( sdtlseqdt0 @ SV125 @ SV145 )
= $false )
| ( ( aNaturalNumber0 @ SV125 )
= $false )
| ( ( aNaturalNumber0 @ SV145 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1310]) ).
thf(1341,plain,
! [SV145: $i,SV125: $i] :
( ( ( ~ ! [SY230: $i] :
( ~ ( aNaturalNumber0 @ SY230 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SV125 @ SY230 ) @ ( sdtpldt0 @ SV145 @ SY230 ) ) ) )
= $false )
| ( ( SV125 = SV145 )
= $true )
| ( ( sdtlseqdt0 @ SV125 @ SV145 )
= $false )
| ( ( aNaturalNumber0 @ SV125 )
= $false )
| ( ( aNaturalNumber0 @ SV145 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1310]) ).
thf(1342,plain,
! [SV184: $i,SV126: $i,SV175: $i] :
( ( ( aNaturalNumber0 @ SV175 )
= $false )
| ( ( aNaturalNumber0 @ SV126 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV184 ) )
= $true )
| ( ( ( ( sdtpldt0 @ SV126 @ SV175 )
!= ( sdtpldt0 @ SV126 @ SV184 ) )
| ( SV175 = SV184 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1311]) ).
thf(1343,plain,
! [SV185: $i,SV126: $i,SV176: $i] :
( ( ( aNaturalNumber0 @ SV176 )
= $false )
| ( ( aNaturalNumber0 @ SV126 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV185 ) )
= $true )
| ( ( ( ( sdtpldt0 @ SV176 @ SV126 )
!= ( sdtpldt0 @ SV185 @ SV126 ) )
| ( SV176 = SV185 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1312]) ).
thf(1344,plain,
! [SV127: $i] :
( ( ( aNaturalNumber0 @ ( sK1_W1 @ SV127 ) )
= $true )
| ( ( SV127 = sz10 )
= $true )
| ( ( SV127 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV127 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1313]) ).
thf(1345,plain,
! [SV127: $i] :
( ( ( doDivides0 @ ( sK1_W1 @ SV127 ) @ SV127 )
= $true )
| ( ( SV127 = sz10 )
= $true )
| ( ( SV127 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV127 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1314]) ).
thf(1346,plain,
! [SV177: $i,SV165: $i] :
( ( ( ( sdtpldt0 @ SV165 @ SV177 )
= sz00 )
= $false )
| ( ( SV165 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV165 )
= $false )
| ( ( aNaturalNumber0 @ SV177 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1315]) ).
thf(1347,plain,
! [SV178: $i,SV166: $i] :
( ( ( ( sdtpldt0 @ SV166 @ SV178 )
= sz00 )
= $false )
| ( ( SV178 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV166 )
= $false )
| ( ( aNaturalNumber0 @ SV178 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1316]) ).
thf(1348,plain,
! [SV148: $i,SV136: $i,SV112: $i] :
( ( ( sdtlseqdt0 @ SV112 @ SV136 )
= $false )
| ( ( ~ ( sdtlseqdt0 @ SV136 @ SV148 ) )
= $true )
| ( ( sdtlseqdt0 @ SV112 @ SV148 )
= $true )
| ( ( aNaturalNumber0 @ SV136 )
= $false )
| ( ( aNaturalNumber0 @ SV112 )
= $false )
| ( ( aNaturalNumber0 @ SV148 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1317]) ).
thf(1349,plain,
! [SV150: $i,SV139: $i,SV115: $i] :
( ( ( doDivides0 @ SV115 @ SV139 )
= $false )
| ( ( ~ ( doDivides0 @ SV139 @ SV150 ) )
= $true )
| ( ( doDivides0 @ SV115 @ SV150 )
= $true )
| ( ( aNaturalNumber0 @ SV139 )
= $false )
| ( ( aNaturalNumber0 @ SV115 )
= $false )
| ( ( aNaturalNumber0 @ SV150 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1318]) ).
thf(1350,plain,
! [SV151: $i,SV140: $i,SV116: $i] :
( ( ( doDivides0 @ SV116 @ SV140 )
= $false )
| ( ( ~ ( doDivides0 @ SV116 @ SV151 ) )
= $true )
| ( ( doDivides0 @ SV116 @ ( sdtpldt0 @ SV140 @ SV151 ) )
= $true )
| ( ( aNaturalNumber0 @ SV140 )
= $false )
| ( ( aNaturalNumber0 @ SV116 )
= $false )
| ( ( aNaturalNumber0 @ SV151 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1319]) ).
thf(1351,plain,
! [SV152: $i,SV141: $i,SV117: $i] :
( ( ( doDivides0 @ SV117 @ SV141 )
= $false )
| ( ( ~ ( doDivides0 @ SV117 @ ( sdtpldt0 @ SV141 @ SV152 ) ) )
= $true )
| ( ( doDivides0 @ SV117 @ SV152 )
= $true )
| ( ( aNaturalNumber0 @ SV141 )
= $false )
| ( ( aNaturalNumber0 @ SV117 )
= $false )
| ( ( aNaturalNumber0 @ SV152 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1320]) ).
thf(1352,plain,
! [SV119: $i,SV143: $i,SV192: $i] :
( ( ( aNaturalNumber0 @ SV192 )
= $false )
| ( ( ( sdtasdt0 @ SV192 @ ( sdtsldt0 @ SV143 @ SV119 ) )
= ( sdtsldt0 @ ( sdtasdt0 @ SV192 @ SV143 ) @ SV119 ) )
= $true )
| ( ( SV119 = sz00 )
= $true )
| ( ( doDivides0 @ SV119 @ SV143 )
= $false )
| ( ( aNaturalNumber0 @ SV119 )
= $false )
| ( ( aNaturalNumber0 @ SV143 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1321]) ).
thf(1353,plain,
! [SV144: $i,SV120: $i,SV153: $i] :
( ( ( doDivides0 @ SV153 @ ( sdtasdt0 @ SV120 @ SV144 ) )
= $false )
| ( ( ~ ( isPrime0 @ SV153 ) )
= $true )
| ( ( ( doDivides0 @ SV153 @ SV120 )
| ( doDivides0 @ SV153 @ SV144 ) )
= $true )
| ( ( aNaturalNumber0 @ SV144 )
= $false )
| ( ( aNaturalNumber0 @ SV120 )
= $false )
| ( ( aNaturalNumber0 @ SV153 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1322]) ).
thf(1354,plain,
! [SV193: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV193 ) )
= $true )
| ( ( ! [SY245: $i] :
( ( xp
!= ( sdtasdt0 @ SV193 @ SY245 ) )
| ~ ( aNaturalNumber0 @ SY245 ) ) )
= $true )
| ( ( ( SV193 = sz10 )
| ( SV193 = xp ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1323]) ).
thf(1355,plain,
! [SV194: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV194 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV194 @ xp ) )
= $true )
| ( ( ( SV194 = sz10 )
| ( SV194 = xp ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1324]) ).
thf(1356,plain,
! [SV168: $i,SV121: $i,SV179: $i] :
( ( ( aNaturalNumber0 @ SV179 )
= $false )
| ( ( aNaturalNumber0 @ SV121 )
= $false )
| ( ( aNaturalNumber0 @ SV168 )
= $false )
| ( ( ( sdtasdt0 @ SV121 @ ( sdtpldt0 @ SV168 @ SV179 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV121 @ SV168 ) @ ( sdtasdt0 @ SV121 @ SV179 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1325]) ).
thf(1357,plain,
! [SV169: $i,SV121: $i,SV180: $i] :
( ( ( aNaturalNumber0 @ SV180 )
= $false )
| ( ( aNaturalNumber0 @ SV121 )
= $false )
| ( ( aNaturalNumber0 @ SV169 )
= $false )
| ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV169 @ SV180 ) @ SV121 )
= ( sdtpldt0 @ ( sdtasdt0 @ SV169 @ SV121 ) @ ( sdtasdt0 @ SV180 @ SV121 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1326]) ).
thf(1358,plain,
! [SV122: $i,SV189: $i,SV186: $i] :
( ( ( aNaturalNumber0 @ SV186 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV189 ) )
= $true )
| ( ( ( ( sdtasdt0 @ SV122 @ SV186 )
!= ( sdtasdt0 @ SV122 @ SV189 ) )
| ( SV186 = SV189 ) )
= $true )
| ( ( SV122 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV122 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1327]) ).
thf(1359,plain,
! [SV122: $i,SV190: $i,SV187: $i] :
( ( ( aNaturalNumber0 @ SV187 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV190 ) )
= $true )
| ( ( ( ( sdtasdt0 @ SV187 @ SV122 )
!= ( sdtasdt0 @ SV190 @ SV122 ) )
| ( SV187 = SV190 ) )
= $true )
| ( ( SV122 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV122 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1328]) ).
thf(1360,plain,
! [SV191: $i,SV188: $i,SV123: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV123 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV188 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV191 ) )
= $true )
| ( ( ( SV123 = sz00 )
| ( SV188 = SV191 )
| ~ ( sdtlseqdt0 @ SV188 @ SV191 )
| ( ( sdtasdt0 @ SV188 @ SV123 )
!= ( sdtasdt0 @ SV191 @ SV123 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1329]) ).
thf(1361,plain,
! [SV197: $i,SV195: $i,SV123: $i] :
( ( ~ ( aNaturalNumber0 @ SV123 )
| ~ ( aNaturalNumber0 @ SV195 )
| ~ ( aNaturalNumber0 @ SV197 )
| ( SV123 = sz00 )
| ( SV195 = SV197 )
| ~ ( sdtlseqdt0 @ SV195 @ SV197 )
| ( ( sdtasdt0 @ SV123 @ SV195 )
!= ( sdtasdt0 @ SV123 @ SV197 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1330]) ).
thf(1362,plain,
! [SV198: $i,SV196: $i,SV123: $i] :
( ( ~ ( aNaturalNumber0 @ SV123 )
| ~ ( aNaturalNumber0 @ SV196 )
| ~ ( aNaturalNumber0 @ SV198 )
| ( SV123 = sz00 )
| ( SV196 = SV198 )
| ~ ( sdtlseqdt0 @ SV196 @ SV198 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV123 @ SV196 ) @ ( sdtasdt0 @ SV123 @ SV198 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1331]) ).
thf(1363,plain,
! [SV170: $i,SV123: $i,SV181: $i] :
( ( ( aNaturalNumber0 @ SV181 )
= $false )
| ( ( aNaturalNumber0 @ SV123 )
= $false )
| ( ( aNaturalNumber0 @ SV170 )
= $false )
| ( ( ( SV123 = sz00 )
| ( SV170 = SV181 )
| ~ ( sdtlseqdt0 @ SV170 @ SV181 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV170 @ SV123 ) @ ( sdtasdt0 @ SV181 @ SV123 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1332]) ).
thf(1364,plain,
( ( ( sdtasdt0 @ xn @ xn )
= ( sdtasdt0 @ xp @ sK3_W0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1333]) ).
thf(1365,plain,
( ( aNaturalNumber0 @ sK3_W0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1334]) ).
thf(1366,plain,
! [SV182: $i,SV171: $i,SV124: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV124 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV171 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV182 ) )
= $true )
| ( ( SV124 = sz00 )
= $true )
| ( ( SV171 = sz00 )
= $true )
| ( ( SV182 = sz00 )
= $true )
| ( ( ( ( sdtasdt0 @ SV182 @ ( sdtasdt0 @ SV171 @ SV171 ) )
!= ( sdtasdt0 @ SV124 @ SV124 ) )
| ~ ( iLess0 @ SV124 @ xn )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( SV182
!= ( sdtasdt0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) @ ( sK5_SY81 @ SV182 @ SV171 @ SV124 ) ) )
| ~ ( aNaturalNumber0 @ ( sK5_SY81 @ SV182 @ SV171 @ SV124 ) ) )
| ~ ( aNaturalNumber0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) ) )
| ~ ( doDivides0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) @ SV182 ) )
| ~ ~ ( ~ ( ( ( sK4_W3 @ SV182 @ SV171 @ SV124 )
!= sz10 ) )
| ~ ( ( ( sK4_W3 @ SV182 @ SV171 @ SV124 )
!= SV182 ) ) ) )
| ( SV182 = sz10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1335]) ).
thf(1367,plain,
! [SV183: $i,SV172: $i,SV124: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV124 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV172 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV183 ) )
= $true )
| ( ( SV124 = sz00 )
= $true )
| ( ( SV172 = sz00 )
= $true )
| ( ( SV183 = sz00 )
= $true )
| ( ( ( ( sdtasdt0 @ SV183 @ ( sdtasdt0 @ SV172 @ SV172 ) )
!= ( sdtasdt0 @ SV124 @ SV124 ) )
| ~ ( iLess0 @ SV124 @ xn )
| ~ ( isPrime0 @ SV183 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1336]) ).
thf(1368,plain,
( ( ~ ( ~ ( aNaturalNumber0 @ xn )
| ~ ( aNaturalNumber0 @ xm ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1337]) ).
thf(1369,plain,
( ( aNaturalNumber0 @ xp )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1338]) ).
thf(1370,plain,
! [SV145: $i,SV125: $i] :
( ( ( ~ ( ~ ! [SY227: $i] :
( ~ ( aNaturalNumber0 @ SY227 )
| ( ( sdtpldt0 @ SV125 @ SY227 )
!= ( sdtpldt0 @ SV145 @ SY227 ) ) )
| ~ ~ ( ~ ! [SY228: $i] :
( ~ ( aNaturalNumber0 @ SY228 )
| ( ( sdtpldt0 @ SY228 @ SV125 )
!= ( sdtpldt0 @ SY228 @ SV145 ) ) )
| ~ ! [SY229: $i] :
( ~ ( aNaturalNumber0 @ SY229 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SY229 @ SV125 ) @ ( sdtpldt0 @ SY229 @ SV145 ) ) ) ) ) )
= $true )
| ( ( SV125 = SV145 )
= $true )
| ( ( sdtlseqdt0 @ SV125 @ SV145 )
= $false )
| ( ( aNaturalNumber0 @ SV125 )
= $false )
| ( ( aNaturalNumber0 @ SV145 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1340]) ).
thf(1371,plain,
! [SV145: $i,SV125: $i] :
( ( ( ! [SY230: $i] :
( ~ ( aNaturalNumber0 @ SY230 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SV125 @ SY230 ) @ ( sdtpldt0 @ SV145 @ SY230 ) ) ) )
= $true )
| ( ( SV125 = SV145 )
= $true )
| ( ( sdtlseqdt0 @ SV125 @ SV145 )
= $false )
| ( ( aNaturalNumber0 @ SV125 )
= $false )
| ( ( aNaturalNumber0 @ SV145 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1341]) ).
thf(1372,plain,
! [SV175: $i,SV126: $i,SV184: $i] :
( ( ( aNaturalNumber0 @ SV184 )
= $false )
| ( ( aNaturalNumber0 @ SV126 )
= $false )
| ( ( aNaturalNumber0 @ SV175 )
= $false )
| ( ( ( ( sdtpldt0 @ SV126 @ SV175 )
!= ( sdtpldt0 @ SV126 @ SV184 ) )
| ( SV175 = SV184 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1342]) ).
thf(1373,plain,
! [SV176: $i,SV126: $i,SV185: $i] :
( ( ( aNaturalNumber0 @ SV185 )
= $false )
| ( ( aNaturalNumber0 @ SV126 )
= $false )
| ( ( aNaturalNumber0 @ SV176 )
= $false )
| ( ( ( ( sdtpldt0 @ SV176 @ SV126 )
!= ( sdtpldt0 @ SV185 @ SV126 ) )
| ( SV176 = SV185 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1343]) ).
thf(1374,plain,
! [SV112: $i,SV148: $i,SV136: $i] :
( ( ( sdtlseqdt0 @ SV136 @ SV148 )
= $false )
| ( ( sdtlseqdt0 @ SV112 @ SV136 )
= $false )
| ( ( sdtlseqdt0 @ SV112 @ SV148 )
= $true )
| ( ( aNaturalNumber0 @ SV136 )
= $false )
| ( ( aNaturalNumber0 @ SV112 )
= $false )
| ( ( aNaturalNumber0 @ SV148 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1348]) ).
thf(1375,plain,
! [SV115: $i,SV150: $i,SV139: $i] :
( ( ( doDivides0 @ SV139 @ SV150 )
= $false )
| ( ( doDivides0 @ SV115 @ SV139 )
= $false )
| ( ( doDivides0 @ SV115 @ SV150 )
= $true )
| ( ( aNaturalNumber0 @ SV139 )
= $false )
| ( ( aNaturalNumber0 @ SV115 )
= $false )
| ( ( aNaturalNumber0 @ SV150 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1349]) ).
thf(1376,plain,
! [SV140: $i,SV151: $i,SV116: $i] :
( ( ( doDivides0 @ SV116 @ SV151 )
= $false )
| ( ( doDivides0 @ SV116 @ SV140 )
= $false )
| ( ( doDivides0 @ SV116 @ ( sdtpldt0 @ SV140 @ SV151 ) )
= $true )
| ( ( aNaturalNumber0 @ SV140 )
= $false )
| ( ( aNaturalNumber0 @ SV116 )
= $false )
| ( ( aNaturalNumber0 @ SV151 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1350]) ).
thf(1377,plain,
! [SV152: $i,SV141: $i,SV117: $i] :
( ( ( doDivides0 @ SV117 @ ( sdtpldt0 @ SV141 @ SV152 ) )
= $false )
| ( ( doDivides0 @ SV117 @ SV141 )
= $false )
| ( ( doDivides0 @ SV117 @ SV152 )
= $true )
| ( ( aNaturalNumber0 @ SV141 )
= $false )
| ( ( aNaturalNumber0 @ SV117 )
= $false )
| ( ( aNaturalNumber0 @ SV152 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1351]) ).
thf(1378,plain,
! [SV144: $i,SV120: $i,SV153: $i] :
( ( ( isPrime0 @ SV153 )
= $false )
| ( ( doDivides0 @ SV153 @ ( sdtasdt0 @ SV120 @ SV144 ) )
= $false )
| ( ( ( doDivides0 @ SV153 @ SV120 )
| ( doDivides0 @ SV153 @ SV144 ) )
= $true )
| ( ( aNaturalNumber0 @ SV144 )
= $false )
| ( ( aNaturalNumber0 @ SV120 )
= $false )
| ( ( aNaturalNumber0 @ SV153 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1353]) ).
thf(1379,plain,
! [SV193: $i] :
( ( ( aNaturalNumber0 @ SV193 )
= $false )
| ( ( ! [SY245: $i] :
( ( xp
!= ( sdtasdt0 @ SV193 @ SY245 ) )
| ~ ( aNaturalNumber0 @ SY245 ) ) )
= $true )
| ( ( ( SV193 = sz10 )
| ( SV193 = xp ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1354]) ).
thf(1380,plain,
! [SV194: $i] :
( ( ( aNaturalNumber0 @ SV194 )
= $false )
| ( ( ~ ( doDivides0 @ SV194 @ xp ) )
= $true )
| ( ( ( SV194 = sz10 )
| ( SV194 = xp ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1355]) ).
thf(1381,plain,
! [SV122: $i,SV186: $i,SV189: $i] :
( ( ( aNaturalNumber0 @ SV189 )
= $false )
| ( ( aNaturalNumber0 @ SV186 )
= $false )
| ( ( ( ( sdtasdt0 @ SV122 @ SV186 )
!= ( sdtasdt0 @ SV122 @ SV189 ) )
| ( SV186 = SV189 ) )
= $true )
| ( ( SV122 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV122 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1358]) ).
thf(1382,plain,
! [SV122: $i,SV187: $i,SV190: $i] :
( ( ( aNaturalNumber0 @ SV190 )
= $false )
| ( ( aNaturalNumber0 @ SV187 )
= $false )
| ( ( ( ( sdtasdt0 @ SV187 @ SV122 )
!= ( sdtasdt0 @ SV190 @ SV122 ) )
| ( SV187 = SV190 ) )
= $true )
| ( ( SV122 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV122 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1359]) ).
thf(1383,plain,
! [SV191: $i,SV188: $i,SV123: $i] :
( ( ( aNaturalNumber0 @ SV123 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV188 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV191 ) )
= $true )
| ( ( ( SV123 = sz00 )
| ( SV188 = SV191 )
| ~ ( sdtlseqdt0 @ SV188 @ SV191 )
| ( ( sdtasdt0 @ SV188 @ SV123 )
!= ( sdtasdt0 @ SV191 @ SV123 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1360]) ).
thf(1384,plain,
! [SV197: $i,SV195: $i,SV123: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV123 )
| ~ ( aNaturalNumber0 @ SV195 )
| ~ ( aNaturalNumber0 @ SV197 ) )
= $true )
| ( ( ( SV123 = sz00 )
| ( SV195 = SV197 )
| ~ ( sdtlseqdt0 @ SV195 @ SV197 )
| ( ( sdtasdt0 @ SV123 @ SV195 )
!= ( sdtasdt0 @ SV123 @ SV197 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1361]) ).
thf(1385,plain,
! [SV198: $i,SV196: $i,SV123: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV123 )
| ~ ( aNaturalNumber0 @ SV196 )
| ~ ( aNaturalNumber0 @ SV198 ) )
= $true )
| ( ( ( SV123 = sz00 )
| ( SV196 = SV198 )
| ~ ( sdtlseqdt0 @ SV196 @ SV198 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV123 @ SV196 ) @ ( sdtasdt0 @ SV123 @ SV198 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1362]) ).
thf(1386,plain,
! [SV181: $i,SV170: $i,SV123: $i] :
( ( ( ( SV123 = sz00 )
| ( SV170 = SV181 )
| ~ ( sdtlseqdt0 @ SV170 @ SV181 ) )
= $true )
| ( ( sdtlseqdt0 @ ( sdtasdt0 @ SV170 @ SV123 ) @ ( sdtasdt0 @ SV181 @ SV123 ) )
= $true )
| ( ( aNaturalNumber0 @ SV170 )
= $false )
| ( ( aNaturalNumber0 @ SV123 )
= $false )
| ( ( aNaturalNumber0 @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1363]) ).
thf(1387,plain,
! [SV182: $i,SV171: $i,SV124: $i] :
( ( ( aNaturalNumber0 @ SV124 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV171 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV182 ) )
= $true )
| ( ( SV124 = sz00 )
= $true )
| ( ( SV171 = sz00 )
= $true )
| ( ( SV182 = sz00 )
= $true )
| ( ( ( ( sdtasdt0 @ SV182 @ ( sdtasdt0 @ SV171 @ SV171 ) )
!= ( sdtasdt0 @ SV124 @ SV124 ) )
| ~ ( iLess0 @ SV124 @ xn )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( SV182
!= ( sdtasdt0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) @ ( sK5_SY81 @ SV182 @ SV171 @ SV124 ) ) )
| ~ ( aNaturalNumber0 @ ( sK5_SY81 @ SV182 @ SV171 @ SV124 ) ) )
| ~ ( aNaturalNumber0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) ) )
| ~ ( doDivides0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) @ SV182 ) )
| ~ ~ ( ~ ( ( ( sK4_W3 @ SV182 @ SV171 @ SV124 )
!= sz10 ) )
| ~ ( ( ( sK4_W3 @ SV182 @ SV171 @ SV124 )
!= SV182 ) ) ) )
| ( SV182 = sz10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1366]) ).
thf(1388,plain,
! [SV183: $i,SV172: $i,SV124: $i] :
( ( ( aNaturalNumber0 @ SV124 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV172 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV183 ) )
= $true )
| ( ( SV124 = sz00 )
= $true )
| ( ( SV172 = sz00 )
= $true )
| ( ( SV183 = sz00 )
= $true )
| ( ( ( ( sdtasdt0 @ SV183 @ ( sdtasdt0 @ SV172 @ SV172 ) )
!= ( sdtasdt0 @ SV124 @ SV124 ) )
| ~ ( iLess0 @ SV124 @ xn )
| ~ ( isPrime0 @ SV183 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1367]) ).
thf(1389,plain,
( ( ~ ( aNaturalNumber0 @ xn )
| ~ ( aNaturalNumber0 @ xm ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1368]) ).
thf(1390,plain,
! [SV145: $i,SV125: $i] :
( ( ( ~ ! [SY227: $i] :
( ~ ( aNaturalNumber0 @ SY227 )
| ( ( sdtpldt0 @ SV125 @ SY227 )
!= ( sdtpldt0 @ SV145 @ SY227 ) ) )
| ~ ~ ( ~ ! [SY228: $i] :
( ~ ( aNaturalNumber0 @ SY228 )
| ( ( sdtpldt0 @ SY228 @ SV125 )
!= ( sdtpldt0 @ SY228 @ SV145 ) ) )
| ~ ! [SY229: $i] :
( ~ ( aNaturalNumber0 @ SY229 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SY229 @ SV125 ) @ ( sdtpldt0 @ SY229 @ SV145 ) ) ) ) )
= $false )
| ( ( SV125 = SV145 )
= $true )
| ( ( sdtlseqdt0 @ SV125 @ SV145 )
= $false )
| ( ( aNaturalNumber0 @ SV125 )
= $false )
| ( ( aNaturalNumber0 @ SV145 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1370]) ).
thf(1391,plain,
! [SV145: $i,SV125: $i,SV199: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV199 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SV125 @ SV199 ) @ ( sdtpldt0 @ SV145 @ SV199 ) ) )
= $true )
| ( ( SV125 = SV145 )
= $true )
| ( ( sdtlseqdt0 @ SV125 @ SV145 )
= $false )
| ( ( aNaturalNumber0 @ SV125 )
= $false )
| ( ( aNaturalNumber0 @ SV145 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1371]) ).
thf(1392,plain,
! [SV184: $i,SV175: $i,SV126: $i] :
( ( ( ( sdtpldt0 @ SV126 @ SV175 )
!= ( sdtpldt0 @ SV126 @ SV184 ) )
= $true )
| ( ( SV175 = SV184 )
= $true )
| ( ( aNaturalNumber0 @ SV175 )
= $false )
| ( ( aNaturalNumber0 @ SV126 )
= $false )
| ( ( aNaturalNumber0 @ SV184 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1372]) ).
thf(1393,plain,
! [SV185: $i,SV126: $i,SV176: $i] :
( ( ( ( sdtpldt0 @ SV176 @ SV126 )
!= ( sdtpldt0 @ SV185 @ SV126 ) )
= $true )
| ( ( SV176 = SV185 )
= $true )
| ( ( aNaturalNumber0 @ SV176 )
= $false )
| ( ( aNaturalNumber0 @ SV126 )
= $false )
| ( ( aNaturalNumber0 @ SV185 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1373]) ).
thf(1394,plain,
! [SV144: $i,SV120: $i,SV153: $i] :
( ( ( doDivides0 @ SV153 @ SV120 )
= $true )
| ( ( doDivides0 @ SV153 @ SV144 )
= $true )
| ( ( doDivides0 @ SV153 @ ( sdtasdt0 @ SV120 @ SV144 ) )
= $false )
| ( ( isPrime0 @ SV153 )
= $false )
| ( ( aNaturalNumber0 @ SV144 )
= $false )
| ( ( aNaturalNumber0 @ SV120 )
= $false )
| ( ( aNaturalNumber0 @ SV153 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1378]) ).
thf(1395,plain,
! [SV200: $i,SV193: $i] :
( ( ( ( xp
!= ( sdtasdt0 @ SV193 @ SV200 ) )
| ~ ( aNaturalNumber0 @ SV200 ) )
= $true )
| ( ( aNaturalNumber0 @ SV193 )
= $false )
| ( ( ( SV193 = sz10 )
| ( SV193 = xp ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1379]) ).
thf(1396,plain,
! [SV194: $i] :
( ( ( doDivides0 @ SV194 @ xp )
= $false )
| ( ( aNaturalNumber0 @ SV194 )
= $false )
| ( ( ( SV194 = sz10 )
| ( SV194 = xp ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1380]) ).
thf(1397,plain,
! [SV189: $i,SV186: $i,SV122: $i] :
( ( ( ( sdtasdt0 @ SV122 @ SV186 )
!= ( sdtasdt0 @ SV122 @ SV189 ) )
= $true )
| ( ( SV186 = SV189 )
= $true )
| ( ( aNaturalNumber0 @ SV186 )
= $false )
| ( ( aNaturalNumber0 @ SV189 )
= $false )
| ( ( SV122 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV122 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1381]) ).
thf(1398,plain,
! [SV190: $i,SV122: $i,SV187: $i] :
( ( ( ( sdtasdt0 @ SV187 @ SV122 )
!= ( sdtasdt0 @ SV190 @ SV122 ) )
= $true )
| ( ( SV187 = SV190 )
= $true )
| ( ( aNaturalNumber0 @ SV187 )
= $false )
| ( ( aNaturalNumber0 @ SV190 )
= $false )
| ( ( SV122 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV122 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1382]) ).
thf(1399,plain,
! [SV191: $i,SV123: $i,SV188: $i] :
( ( ( aNaturalNumber0 @ SV188 )
= $false )
| ( ( aNaturalNumber0 @ SV123 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV191 ) )
= $true )
| ( ( ( SV123 = sz00 )
| ( SV188 = SV191 )
| ~ ( sdtlseqdt0 @ SV188 @ SV191 )
| ( ( sdtasdt0 @ SV188 @ SV123 )
!= ( sdtasdt0 @ SV191 @ SV123 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1383]) ).
thf(1400,plain,
! [SV197: $i,SV195: $i,SV123: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV123 )
| ~ ( aNaturalNumber0 @ SV195 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV197 ) )
= $true )
| ( ( ( SV123 = sz00 )
| ( SV195 = SV197 )
| ~ ( sdtlseqdt0 @ SV195 @ SV197 )
| ( ( sdtasdt0 @ SV123 @ SV195 )
!= ( sdtasdt0 @ SV123 @ SV197 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1384]) ).
thf(1401,plain,
! [SV198: $i,SV196: $i,SV123: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV123 )
| ~ ( aNaturalNumber0 @ SV196 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV198 ) )
= $true )
| ( ( ( SV123 = sz00 )
| ( SV196 = SV198 )
| ~ ( sdtlseqdt0 @ SV196 @ SV198 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV123 @ SV196 ) @ ( sdtasdt0 @ SV123 @ SV198 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1385]) ).
thf(1402,plain,
! [SV181: $i,SV170: $i,SV123: $i] :
( ( ( ( SV123 = sz00 )
| ( SV170 = SV181 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV170 @ SV181 ) )
= $true )
| ( ( sdtlseqdt0 @ ( sdtasdt0 @ SV170 @ SV123 ) @ ( sdtasdt0 @ SV181 @ SV123 ) )
= $true )
| ( ( aNaturalNumber0 @ SV170 )
= $false )
| ( ( aNaturalNumber0 @ SV123 )
= $false )
| ( ( aNaturalNumber0 @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1386]) ).
thf(1403,plain,
! [SV182: $i,SV124: $i,SV171: $i] :
( ( ( aNaturalNumber0 @ SV171 )
= $false )
| ( ( aNaturalNumber0 @ SV124 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV182 ) )
= $true )
| ( ( SV124 = sz00 )
= $true )
| ( ( SV171 = sz00 )
= $true )
| ( ( SV182 = sz00 )
= $true )
| ( ( ( ( sdtasdt0 @ SV182 @ ( sdtasdt0 @ SV171 @ SV171 ) )
!= ( sdtasdt0 @ SV124 @ SV124 ) )
| ~ ( iLess0 @ SV124 @ xn )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( SV182
!= ( sdtasdt0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) @ ( sK5_SY81 @ SV182 @ SV171 @ SV124 ) ) )
| ~ ( aNaturalNumber0 @ ( sK5_SY81 @ SV182 @ SV171 @ SV124 ) ) )
| ~ ( aNaturalNumber0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) ) )
| ~ ( doDivides0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) @ SV182 ) )
| ~ ~ ( ~ ( ( ( sK4_W3 @ SV182 @ SV171 @ SV124 )
!= sz10 ) )
| ~ ( ( ( sK4_W3 @ SV182 @ SV171 @ SV124 )
!= SV182 ) ) ) )
| ( SV182 = sz10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1387]) ).
thf(1404,plain,
! [SV183: $i,SV124: $i,SV172: $i] :
( ( ( aNaturalNumber0 @ SV172 )
= $false )
| ( ( aNaturalNumber0 @ SV124 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV183 ) )
= $true )
| ( ( SV124 = sz00 )
= $true )
| ( ( SV172 = sz00 )
= $true )
| ( ( SV183 = sz00 )
= $true )
| ( ( ( ( sdtasdt0 @ SV183 @ ( sdtasdt0 @ SV172 @ SV172 ) )
!= ( sdtasdt0 @ SV124 @ SV124 ) )
| ~ ( iLess0 @ SV124 @ xn )
| ~ ( isPrime0 @ SV183 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1388]) ).
thf(1405,plain,
( ( ~ ( aNaturalNumber0 @ xn ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1389]) ).
thf(1406,plain,
( ( ~ ( aNaturalNumber0 @ xm ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1389]) ).
thf(1407,plain,
! [SV145: $i,SV125: $i] :
( ( ( ~ ! [SY227: $i] :
( ~ ( aNaturalNumber0 @ SY227 )
| ( ( sdtpldt0 @ SV125 @ SY227 )
!= ( sdtpldt0 @ SV145 @ SY227 ) ) ) )
= $false )
| ( ( SV125 = SV145 )
= $true )
| ( ( sdtlseqdt0 @ SV125 @ SV145 )
= $false )
| ( ( aNaturalNumber0 @ SV125 )
= $false )
| ( ( aNaturalNumber0 @ SV145 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1390]) ).
thf(1408,plain,
! [SV145: $i,SV125: $i] :
( ( ( ~ ~ ( ~ ! [SY228: $i] :
( ~ ( aNaturalNumber0 @ SY228 )
| ( ( sdtpldt0 @ SY228 @ SV125 )
!= ( sdtpldt0 @ SY228 @ SV145 ) ) )
| ~ ! [SY229: $i] :
( ~ ( aNaturalNumber0 @ SY229 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SY229 @ SV125 ) @ ( sdtpldt0 @ SY229 @ SV145 ) ) ) ) )
= $false )
| ( ( SV125 = SV145 )
= $true )
| ( ( sdtlseqdt0 @ SV125 @ SV145 )
= $false )
| ( ( aNaturalNumber0 @ SV125 )
= $false )
| ( ( aNaturalNumber0 @ SV145 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1390]) ).
thf(1409,plain,
! [SV145: $i,SV125: $i,SV199: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV199 ) )
= $true )
| ( ( sdtlseqdt0 @ ( sdtpldt0 @ SV125 @ SV199 ) @ ( sdtpldt0 @ SV145 @ SV199 ) )
= $true )
| ( ( SV125 = SV145 )
= $true )
| ( ( sdtlseqdt0 @ SV125 @ SV145 )
= $false )
| ( ( aNaturalNumber0 @ SV125 )
= $false )
| ( ( aNaturalNumber0 @ SV145 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1391]) ).
thf(1410,plain,
! [SV184: $i,SV175: $i,SV126: $i] :
( ( ( ( sdtpldt0 @ SV126 @ SV175 )
= ( sdtpldt0 @ SV126 @ SV184 ) )
= $false )
| ( ( SV175 = SV184 )
= $true )
| ( ( aNaturalNumber0 @ SV175 )
= $false )
| ( ( aNaturalNumber0 @ SV126 )
= $false )
| ( ( aNaturalNumber0 @ SV184 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1392]) ).
thf(1411,plain,
! [SV185: $i,SV126: $i,SV176: $i] :
( ( ( ( sdtpldt0 @ SV176 @ SV126 )
= ( sdtpldt0 @ SV185 @ SV126 ) )
= $false )
| ( ( SV176 = SV185 )
= $true )
| ( ( aNaturalNumber0 @ SV176 )
= $false )
| ( ( aNaturalNumber0 @ SV126 )
= $false )
| ( ( aNaturalNumber0 @ SV185 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1393]) ).
thf(1412,plain,
! [SV200: $i,SV193: $i] :
( ( ( xp
!= ( sdtasdt0 @ SV193 @ SV200 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV200 ) )
= $true )
| ( ( aNaturalNumber0 @ SV193 )
= $false )
| ( ( ( SV193 = sz10 )
| ( SV193 = xp ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1395]) ).
thf(1413,plain,
! [SV194: $i] :
( ( ( SV194 = sz10 )
= $true )
| ( ( SV194 = xp )
= $true )
| ( ( aNaturalNumber0 @ SV194 )
= $false )
| ( ( doDivides0 @ SV194 @ xp )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1396]) ).
thf(1414,plain,
! [SV189: $i,SV186: $i,SV122: $i] :
( ( ( ( sdtasdt0 @ SV122 @ SV186 )
= ( sdtasdt0 @ SV122 @ SV189 ) )
= $false )
| ( ( SV186 = SV189 )
= $true )
| ( ( aNaturalNumber0 @ SV186 )
= $false )
| ( ( aNaturalNumber0 @ SV189 )
= $false )
| ( ( SV122 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV122 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1397]) ).
thf(1415,plain,
! [SV190: $i,SV122: $i,SV187: $i] :
( ( ( ( sdtasdt0 @ SV187 @ SV122 )
= ( sdtasdt0 @ SV190 @ SV122 ) )
= $false )
| ( ( SV187 = SV190 )
= $true )
| ( ( aNaturalNumber0 @ SV187 )
= $false )
| ( ( aNaturalNumber0 @ SV190 )
= $false )
| ( ( SV122 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV122 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1398]) ).
thf(1416,plain,
! [SV188: $i,SV123: $i,SV191: $i] :
( ( ( aNaturalNumber0 @ SV191 )
= $false )
| ( ( aNaturalNumber0 @ SV123 )
= $false )
| ( ( aNaturalNumber0 @ SV188 )
= $false )
| ( ( ( SV123 = sz00 )
| ( SV188 = SV191 )
| ~ ( sdtlseqdt0 @ SV188 @ SV191 )
| ( ( sdtasdt0 @ SV188 @ SV123 )
!= ( sdtasdt0 @ SV191 @ SV123 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1399]) ).
thf(1417,plain,
! [SV197: $i,SV195: $i,SV123: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV123 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV195 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV197 ) )
= $true )
| ( ( ( SV123 = sz00 )
| ( SV195 = SV197 )
| ~ ( sdtlseqdt0 @ SV195 @ SV197 )
| ( ( sdtasdt0 @ SV123 @ SV195 )
!= ( sdtasdt0 @ SV123 @ SV197 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1400]) ).
thf(1418,plain,
! [SV198: $i,SV196: $i,SV123: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV123 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV196 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV198 ) )
= $true )
| ( ( ( SV123 = sz00 )
| ( SV196 = SV198 )
| ~ ( sdtlseqdt0 @ SV196 @ SV198 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV123 @ SV196 ) @ ( sdtasdt0 @ SV123 @ SV198 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1401]) ).
thf(1419,plain,
! [SV181: $i,SV170: $i,SV123: $i] :
( ( ( SV123 = sz00 )
= $true )
| ( ( SV170 = SV181 )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV170 @ SV181 ) )
= $true )
| ( ( sdtlseqdt0 @ ( sdtasdt0 @ SV170 @ SV123 ) @ ( sdtasdt0 @ SV181 @ SV123 ) )
= $true )
| ( ( aNaturalNumber0 @ SV170 )
= $false )
| ( ( aNaturalNumber0 @ SV123 )
= $false )
| ( ( aNaturalNumber0 @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1402]) ).
thf(1420,plain,
! [SV171: $i,SV124: $i,SV182: $i] :
( ( ( aNaturalNumber0 @ SV182 )
= $false )
| ( ( aNaturalNumber0 @ SV124 )
= $false )
| ( ( aNaturalNumber0 @ SV171 )
= $false )
| ( ( SV124 = sz00 )
= $true )
| ( ( SV171 = sz00 )
= $true )
| ( ( SV182 = sz00 )
= $true )
| ( ( ( ( sdtasdt0 @ SV182 @ ( sdtasdt0 @ SV171 @ SV171 ) )
!= ( sdtasdt0 @ SV124 @ SV124 ) )
| ~ ( iLess0 @ SV124 @ xn )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( SV182
!= ( sdtasdt0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) @ ( sK5_SY81 @ SV182 @ SV171 @ SV124 ) ) )
| ~ ( aNaturalNumber0 @ ( sK5_SY81 @ SV182 @ SV171 @ SV124 ) ) )
| ~ ( aNaturalNumber0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) ) )
| ~ ( doDivides0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) @ SV182 ) )
| ~ ~ ( ~ ( ( ( sK4_W3 @ SV182 @ SV171 @ SV124 )
!= sz10 ) )
| ~ ( ( ( sK4_W3 @ SV182 @ SV171 @ SV124 )
!= SV182 ) ) ) )
| ( SV182 = sz10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1403]) ).
thf(1421,plain,
! [SV172: $i,SV124: $i,SV183: $i] :
( ( ( aNaturalNumber0 @ SV183 )
= $false )
| ( ( aNaturalNumber0 @ SV124 )
= $false )
| ( ( aNaturalNumber0 @ SV172 )
= $false )
| ( ( SV124 = sz00 )
= $true )
| ( ( SV172 = sz00 )
= $true )
| ( ( SV183 = sz00 )
= $true )
| ( ( ( ( sdtasdt0 @ SV183 @ ( sdtasdt0 @ SV172 @ SV172 ) )
!= ( sdtasdt0 @ SV124 @ SV124 ) )
| ~ ( iLess0 @ SV124 @ xn )
| ~ ( isPrime0 @ SV183 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1404]) ).
thf(1422,plain,
( ( aNaturalNumber0 @ xn )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1405]) ).
thf(1423,plain,
( ( aNaturalNumber0 @ xm )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1406]) ).
thf(1424,plain,
! [SV145: $i,SV125: $i] :
( ( ( ! [SY227: $i] :
( ~ ( aNaturalNumber0 @ SY227 )
| ( ( sdtpldt0 @ SV125 @ SY227 )
!= ( sdtpldt0 @ SV145 @ SY227 ) ) ) )
= $true )
| ( ( SV125 = SV145 )
= $true )
| ( ( sdtlseqdt0 @ SV125 @ SV145 )
= $false )
| ( ( aNaturalNumber0 @ SV125 )
= $false )
| ( ( aNaturalNumber0 @ SV145 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1407]) ).
thf(1425,plain,
! [SV145: $i,SV125: $i] :
( ( ( ~ ( ~ ! [SY228: $i] :
( ~ ( aNaturalNumber0 @ SY228 )
| ( ( sdtpldt0 @ SY228 @ SV125 )
!= ( sdtpldt0 @ SY228 @ SV145 ) ) )
| ~ ! [SY229: $i] :
( ~ ( aNaturalNumber0 @ SY229 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SY229 @ SV125 ) @ ( sdtpldt0 @ SY229 @ SV145 ) ) ) ) )
= $true )
| ( ( SV125 = SV145 )
= $true )
| ( ( sdtlseqdt0 @ SV125 @ SV145 )
= $false )
| ( ( aNaturalNumber0 @ SV125 )
= $false )
| ( ( aNaturalNumber0 @ SV145 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1408]) ).
thf(1426,plain,
! [SV145: $i,SV125: $i,SV199: $i] :
( ( ( aNaturalNumber0 @ SV199 )
= $false )
| ( ( sdtlseqdt0 @ ( sdtpldt0 @ SV125 @ SV199 ) @ ( sdtpldt0 @ SV145 @ SV199 ) )
= $true )
| ( ( SV125 = SV145 )
= $true )
| ( ( sdtlseqdt0 @ SV125 @ SV145 )
= $false )
| ( ( aNaturalNumber0 @ SV125 )
= $false )
| ( ( aNaturalNumber0 @ SV145 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1409]) ).
thf(1427,plain,
! [SV200: $i,SV193: $i] :
( ( ( xp
= ( sdtasdt0 @ SV193 @ SV200 ) )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV200 ) )
= $true )
| ( ( aNaturalNumber0 @ SV193 )
= $false )
| ( ( ( SV193 = sz10 )
| ( SV193 = xp ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1412]) ).
thf(1428,plain,
! [SV191: $i,SV188: $i,SV123: $i] :
( ( ( ( SV123 = sz00 )
| ( SV188 = SV191 )
| ~ ( sdtlseqdt0 @ SV188 @ SV191 ) )
= $true )
| ( ( ( sdtasdt0 @ SV188 @ SV123 )
!= ( sdtasdt0 @ SV191 @ SV123 ) )
= $true )
| ( ( aNaturalNumber0 @ SV188 )
= $false )
| ( ( aNaturalNumber0 @ SV123 )
= $false )
| ( ( aNaturalNumber0 @ SV191 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1416]) ).
thf(1429,plain,
! [SV197: $i,SV195: $i,SV123: $i] :
( ( ( aNaturalNumber0 @ SV123 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV195 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV197 ) )
= $true )
| ( ( ( SV123 = sz00 )
| ( SV195 = SV197 )
| ~ ( sdtlseqdt0 @ SV195 @ SV197 )
| ( ( sdtasdt0 @ SV123 @ SV195 )
!= ( sdtasdt0 @ SV123 @ SV197 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1417]) ).
thf(1430,plain,
! [SV198: $i,SV196: $i,SV123: $i] :
( ( ( aNaturalNumber0 @ SV123 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV196 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV198 ) )
= $true )
| ( ( ( SV123 = sz00 )
| ( SV196 = SV198 )
| ~ ( sdtlseqdt0 @ SV196 @ SV198 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV123 @ SV196 ) @ ( sdtasdt0 @ SV123 @ SV198 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1418]) ).
thf(1431,plain,
! [SV123: $i,SV181: $i,SV170: $i] :
( ( ( sdtlseqdt0 @ SV170 @ SV181 )
= $false )
| ( ( SV170 = SV181 )
= $true )
| ( ( SV123 = sz00 )
= $true )
| ( ( sdtlseqdt0 @ ( sdtasdt0 @ SV170 @ SV123 ) @ ( sdtasdt0 @ SV181 @ SV123 ) )
= $true )
| ( ( aNaturalNumber0 @ SV170 )
= $false )
| ( ( aNaturalNumber0 @ SV123 )
= $false )
| ( ( aNaturalNumber0 @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1419]) ).
thf(1432,plain,
! [SV124: $i,SV171: $i,SV182: $i] :
( ( ( ( sdtasdt0 @ SV182 @ ( sdtasdt0 @ SV171 @ SV171 ) )
!= ( sdtasdt0 @ SV124 @ SV124 ) )
= $true )
| ( ( ~ ( iLess0 @ SV124 @ xn )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( SV182
!= ( sdtasdt0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) @ ( sK5_SY81 @ SV182 @ SV171 @ SV124 ) ) )
| ~ ( aNaturalNumber0 @ ( sK5_SY81 @ SV182 @ SV171 @ SV124 ) ) )
| ~ ( aNaturalNumber0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) ) )
| ~ ( doDivides0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) @ SV182 ) )
| ~ ~ ( ~ ( ( ( sK4_W3 @ SV182 @ SV171 @ SV124 )
!= sz10 ) )
| ~ ( ( ( sK4_W3 @ SV182 @ SV171 @ SV124 )
!= SV182 ) ) ) )
| ( SV182 = sz10 ) )
= $true )
| ( ( SV182 = sz00 )
= $true )
| ( ( SV171 = sz00 )
= $true )
| ( ( SV124 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV171 )
= $false )
| ( ( aNaturalNumber0 @ SV124 )
= $false )
| ( ( aNaturalNumber0 @ SV182 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1420]) ).
thf(1433,plain,
! [SV124: $i,SV172: $i,SV183: $i] :
( ( ( ( sdtasdt0 @ SV183 @ ( sdtasdt0 @ SV172 @ SV172 ) )
!= ( sdtasdt0 @ SV124 @ SV124 ) )
= $true )
| ( ( ~ ( iLess0 @ SV124 @ xn )
| ~ ( isPrime0 @ SV183 ) )
= $true )
| ( ( SV183 = sz00 )
= $true )
| ( ( SV172 = sz00 )
= $true )
| ( ( SV124 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV172 )
= $false )
| ( ( aNaturalNumber0 @ SV124 )
= $false )
| ( ( aNaturalNumber0 @ SV183 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1421]) ).
thf(1434,plain,
! [SV145: $i,SV125: $i,SV201: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV201 )
| ( ( sdtpldt0 @ SV125 @ SV201 )
!= ( sdtpldt0 @ SV145 @ SV201 ) ) )
= $true )
| ( ( SV125 = SV145 )
= $true )
| ( ( sdtlseqdt0 @ SV125 @ SV145 )
= $false )
| ( ( aNaturalNumber0 @ SV125 )
= $false )
| ( ( aNaturalNumber0 @ SV145 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1424]) ).
thf(1435,plain,
! [SV145: $i,SV125: $i] :
( ( ( ~ ! [SY228: $i] :
( ~ ( aNaturalNumber0 @ SY228 )
| ( ( sdtpldt0 @ SY228 @ SV125 )
!= ( sdtpldt0 @ SY228 @ SV145 ) ) )
| ~ ! [SY229: $i] :
( ~ ( aNaturalNumber0 @ SY229 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SY229 @ SV125 ) @ ( sdtpldt0 @ SY229 @ SV145 ) ) ) )
= $false )
| ( ( SV125 = SV145 )
= $true )
| ( ( sdtlseqdt0 @ SV125 @ SV145 )
= $false )
| ( ( aNaturalNumber0 @ SV125 )
= $false )
| ( ( aNaturalNumber0 @ SV145 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1425]) ).
thf(1436,plain,
! [SV193: $i,SV200: $i] :
( ( ( aNaturalNumber0 @ SV200 )
= $false )
| ( ( xp
= ( sdtasdt0 @ SV193 @ SV200 ) )
= $false )
| ( ( aNaturalNumber0 @ SV193 )
= $false )
| ( ( ( SV193 = sz10 )
| ( SV193 = xp ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1427]) ).
thf(1437,plain,
! [SV191: $i,SV188: $i,SV123: $i] :
( ( ( ( SV123 = sz00 )
| ( SV188 = SV191 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV188 @ SV191 ) )
= $true )
| ( ( ( sdtasdt0 @ SV188 @ SV123 )
!= ( sdtasdt0 @ SV191 @ SV123 ) )
= $true )
| ( ( aNaturalNumber0 @ SV188 )
= $false )
| ( ( aNaturalNumber0 @ SV123 )
= $false )
| ( ( aNaturalNumber0 @ SV191 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1428]) ).
thf(1438,plain,
! [SV197: $i,SV123: $i,SV195: $i] :
( ( ( aNaturalNumber0 @ SV195 )
= $false )
| ( ( aNaturalNumber0 @ SV123 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV197 ) )
= $true )
| ( ( ( SV123 = sz00 )
| ( SV195 = SV197 )
| ~ ( sdtlseqdt0 @ SV195 @ SV197 )
| ( ( sdtasdt0 @ SV123 @ SV195 )
!= ( sdtasdt0 @ SV123 @ SV197 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1429]) ).
thf(1439,plain,
! [SV198: $i,SV123: $i,SV196: $i] :
( ( ( aNaturalNumber0 @ SV196 )
= $false )
| ( ( aNaturalNumber0 @ SV123 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV198 ) )
= $true )
| ( ( ( SV123 = sz00 )
| ( SV196 = SV198 )
| ~ ( sdtlseqdt0 @ SV196 @ SV198 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV123 @ SV196 ) @ ( sdtasdt0 @ SV123 @ SV198 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1430]) ).
thf(1440,plain,
! [SV124: $i,SV171: $i,SV182: $i] :
( ( ( ( sdtasdt0 @ SV182 @ ( sdtasdt0 @ SV171 @ SV171 ) )
= ( sdtasdt0 @ SV124 @ SV124 ) )
= $false )
| ( ( ~ ( iLess0 @ SV124 @ xn )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( SV182
!= ( sdtasdt0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) @ ( sK5_SY81 @ SV182 @ SV171 @ SV124 ) ) )
| ~ ( aNaturalNumber0 @ ( sK5_SY81 @ SV182 @ SV171 @ SV124 ) ) )
| ~ ( aNaturalNumber0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) ) )
| ~ ( doDivides0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) @ SV182 ) )
| ~ ~ ( ~ ( ( ( sK4_W3 @ SV182 @ SV171 @ SV124 )
!= sz10 ) )
| ~ ( ( ( sK4_W3 @ SV182 @ SV171 @ SV124 )
!= SV182 ) ) ) )
| ( SV182 = sz10 ) )
= $true )
| ( ( SV182 = sz00 )
= $true )
| ( ( SV171 = sz00 )
= $true )
| ( ( SV124 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV171 )
= $false )
| ( ( aNaturalNumber0 @ SV124 )
= $false )
| ( ( aNaturalNumber0 @ SV182 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1432]) ).
thf(1441,plain,
! [SV124: $i,SV172: $i,SV183: $i] :
( ( ( ( sdtasdt0 @ SV183 @ ( sdtasdt0 @ SV172 @ SV172 ) )
= ( sdtasdt0 @ SV124 @ SV124 ) )
= $false )
| ( ( ~ ( iLess0 @ SV124 @ xn )
| ~ ( isPrime0 @ SV183 ) )
= $true )
| ( ( SV183 = sz00 )
= $true )
| ( ( SV172 = sz00 )
= $true )
| ( ( SV124 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV172 )
= $false )
| ( ( aNaturalNumber0 @ SV124 )
= $false )
| ( ( aNaturalNumber0 @ SV183 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1433]) ).
thf(1442,plain,
! [SV145: $i,SV125: $i,SV201: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV201 ) )
= $true )
| ( ( ( sdtpldt0 @ SV125 @ SV201 )
!= ( sdtpldt0 @ SV145 @ SV201 ) )
= $true )
| ( ( SV125 = SV145 )
= $true )
| ( ( sdtlseqdt0 @ SV125 @ SV145 )
= $false )
| ( ( aNaturalNumber0 @ SV125 )
= $false )
| ( ( aNaturalNumber0 @ SV145 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1434]) ).
thf(1443,plain,
! [SV145: $i,SV125: $i] :
( ( ( ~ ! [SY228: $i] :
( ~ ( aNaturalNumber0 @ SY228 )
| ( ( sdtpldt0 @ SY228 @ SV125 )
!= ( sdtpldt0 @ SY228 @ SV145 ) ) ) )
= $false )
| ( ( SV125 = SV145 )
= $true )
| ( ( sdtlseqdt0 @ SV125 @ SV145 )
= $false )
| ( ( aNaturalNumber0 @ SV125 )
= $false )
| ( ( aNaturalNumber0 @ SV145 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1435]) ).
thf(1444,plain,
! [SV145: $i,SV125: $i] :
( ( ( ~ ! [SY229: $i] :
( ~ ( aNaturalNumber0 @ SY229 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SY229 @ SV125 ) @ ( sdtpldt0 @ SY229 @ SV145 ) ) ) )
= $false )
| ( ( SV125 = SV145 )
= $true )
| ( ( sdtlseqdt0 @ SV125 @ SV145 )
= $false )
| ( ( aNaturalNumber0 @ SV125 )
= $false )
| ( ( aNaturalNumber0 @ SV145 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1435]) ).
thf(1445,plain,
! [SV200: $i,SV193: $i] :
( ( ( SV193 = sz10 )
= $true )
| ( ( SV193 = xp )
= $true )
| ( ( aNaturalNumber0 @ SV193 )
= $false )
| ( ( xp
= ( sdtasdt0 @ SV193 @ SV200 ) )
= $false )
| ( ( aNaturalNumber0 @ SV200 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1436]) ).
thf(1446,plain,
! [SV191: $i,SV188: $i,SV123: $i] :
( ( ( SV123 = sz00 )
= $true )
| ( ( SV188 = SV191 )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV188 @ SV191 ) )
= $true )
| ( ( ( sdtasdt0 @ SV188 @ SV123 )
!= ( sdtasdt0 @ SV191 @ SV123 ) )
= $true )
| ( ( aNaturalNumber0 @ SV188 )
= $false )
| ( ( aNaturalNumber0 @ SV123 )
= $false )
| ( ( aNaturalNumber0 @ SV191 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1437]) ).
thf(1447,plain,
! [SV195: $i,SV123: $i,SV197: $i] :
( ( ( aNaturalNumber0 @ SV197 )
= $false )
| ( ( aNaturalNumber0 @ SV123 )
= $false )
| ( ( aNaturalNumber0 @ SV195 )
= $false )
| ( ( ( SV123 = sz00 )
| ( SV195 = SV197 )
| ~ ( sdtlseqdt0 @ SV195 @ SV197 )
| ( ( sdtasdt0 @ SV123 @ SV195 )
!= ( sdtasdt0 @ SV123 @ SV197 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1438]) ).
thf(1448,plain,
! [SV196: $i,SV123: $i,SV198: $i] :
( ( ( aNaturalNumber0 @ SV198 )
= $false )
| ( ( aNaturalNumber0 @ SV123 )
= $false )
| ( ( aNaturalNumber0 @ SV196 )
= $false )
| ( ( ( SV123 = sz00 )
| ( SV196 = SV198 )
| ~ ( sdtlseqdt0 @ SV196 @ SV198 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV123 @ SV196 ) @ ( sdtasdt0 @ SV123 @ SV198 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1439]) ).
thf(1449,plain,
! [SV171: $i,SV182: $i,SV124: $i] :
( ( ( ~ ( iLess0 @ SV124 @ xn ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( SV182
!= ( sdtasdt0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) @ ( sK5_SY81 @ SV182 @ SV171 @ SV124 ) ) )
| ~ ( aNaturalNumber0 @ ( sK5_SY81 @ SV182 @ SV171 @ SV124 ) ) )
| ~ ( aNaturalNumber0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) ) )
| ~ ( doDivides0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) @ SV182 ) )
| ~ ~ ( ~ ( ( ( sK4_W3 @ SV182 @ SV171 @ SV124 )
!= sz10 ) )
| ~ ( ( ( sK4_W3 @ SV182 @ SV171 @ SV124 )
!= SV182 ) ) ) )
| ( SV182 = sz10 ) )
= $true )
| ( ( ( sdtasdt0 @ SV182 @ ( sdtasdt0 @ SV171 @ SV171 ) )
= ( sdtasdt0 @ SV124 @ SV124 ) )
= $false )
| ( ( SV182 = sz00 )
= $true )
| ( ( SV171 = sz00 )
= $true )
| ( ( SV124 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV171 )
= $false )
| ( ( aNaturalNumber0 @ SV124 )
= $false )
| ( ( aNaturalNumber0 @ SV182 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1440]) ).
thf(1450,plain,
! [SV172: $i,SV183: $i,SV124: $i] :
( ( ( ~ ( iLess0 @ SV124 @ xn ) )
= $true )
| ( ( ~ ( isPrime0 @ SV183 ) )
= $true )
| ( ( ( sdtasdt0 @ SV183 @ ( sdtasdt0 @ SV172 @ SV172 ) )
= ( sdtasdt0 @ SV124 @ SV124 ) )
= $false )
| ( ( SV183 = sz00 )
= $true )
| ( ( SV172 = sz00 )
= $true )
| ( ( SV124 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV172 )
= $false )
| ( ( aNaturalNumber0 @ SV124 )
= $false )
| ( ( aNaturalNumber0 @ SV183 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1441]) ).
thf(1451,plain,
! [SV145: $i,SV125: $i,SV201: $i] :
( ( ( aNaturalNumber0 @ SV201 )
= $false )
| ( ( ( sdtpldt0 @ SV125 @ SV201 )
!= ( sdtpldt0 @ SV145 @ SV201 ) )
= $true )
| ( ( SV125 = SV145 )
= $true )
| ( ( sdtlseqdt0 @ SV125 @ SV145 )
= $false )
| ( ( aNaturalNumber0 @ SV125 )
= $false )
| ( ( aNaturalNumber0 @ SV145 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1442]) ).
thf(1452,plain,
! [SV145: $i,SV125: $i] :
( ( ( ! [SY228: $i] :
( ~ ( aNaturalNumber0 @ SY228 )
| ( ( sdtpldt0 @ SY228 @ SV125 )
!= ( sdtpldt0 @ SY228 @ SV145 ) ) ) )
= $true )
| ( ( SV125 = SV145 )
= $true )
| ( ( sdtlseqdt0 @ SV125 @ SV145 )
= $false )
| ( ( aNaturalNumber0 @ SV125 )
= $false )
| ( ( aNaturalNumber0 @ SV145 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1443]) ).
thf(1453,plain,
! [SV145: $i,SV125: $i] :
( ( ( ! [SY229: $i] :
( ~ ( aNaturalNumber0 @ SY229 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SY229 @ SV125 ) @ ( sdtpldt0 @ SY229 @ SV145 ) ) ) )
= $true )
| ( ( SV125 = SV145 )
= $true )
| ( ( sdtlseqdt0 @ SV125 @ SV145 )
= $false )
| ( ( aNaturalNumber0 @ SV125 )
= $false )
| ( ( aNaturalNumber0 @ SV145 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1444]) ).
thf(1454,plain,
! [SV123: $i,SV191: $i,SV188: $i] :
( ( ( sdtlseqdt0 @ SV188 @ SV191 )
= $false )
| ( ( SV188 = SV191 )
= $true )
| ( ( SV123 = sz00 )
= $true )
| ( ( ( sdtasdt0 @ SV188 @ SV123 )
!= ( sdtasdt0 @ SV191 @ SV123 ) )
= $true )
| ( ( aNaturalNumber0 @ SV188 )
= $false )
| ( ( aNaturalNumber0 @ SV123 )
= $false )
| ( ( aNaturalNumber0 @ SV191 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1446]) ).
thf(1455,plain,
! [SV197: $i,SV195: $i,SV123: $i] :
( ( ( ( SV123 = sz00 )
| ( SV195 = SV197 )
| ~ ( sdtlseqdt0 @ SV195 @ SV197 ) )
= $true )
| ( ( ( sdtasdt0 @ SV123 @ SV195 )
!= ( sdtasdt0 @ SV123 @ SV197 ) )
= $true )
| ( ( aNaturalNumber0 @ SV195 )
= $false )
| ( ( aNaturalNumber0 @ SV123 )
= $false )
| ( ( aNaturalNumber0 @ SV197 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1447]) ).
thf(1456,plain,
! [SV198: $i,SV196: $i,SV123: $i] :
( ( ( ( SV123 = sz00 )
| ( SV196 = SV198 )
| ~ ( sdtlseqdt0 @ SV196 @ SV198 ) )
= $true )
| ( ( sdtlseqdt0 @ ( sdtasdt0 @ SV123 @ SV196 ) @ ( sdtasdt0 @ SV123 @ SV198 ) )
= $true )
| ( ( aNaturalNumber0 @ SV196 )
= $false )
| ( ( aNaturalNumber0 @ SV123 )
= $false )
| ( ( aNaturalNumber0 @ SV198 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1448]) ).
thf(1457,plain,
! [SV171: $i,SV182: $i,SV124: $i] :
( ( ( iLess0 @ SV124 @ xn )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( SV182
!= ( sdtasdt0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) @ ( sK5_SY81 @ SV182 @ SV171 @ SV124 ) ) )
| ~ ( aNaturalNumber0 @ ( sK5_SY81 @ SV182 @ SV171 @ SV124 ) ) )
| ~ ( aNaturalNumber0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) ) )
| ~ ( doDivides0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) @ SV182 ) )
| ~ ~ ( ~ ( ( ( sK4_W3 @ SV182 @ SV171 @ SV124 )
!= sz10 ) )
| ~ ( ( ( sK4_W3 @ SV182 @ SV171 @ SV124 )
!= SV182 ) ) ) )
| ( SV182 = sz10 ) )
= $true )
| ( ( ( sdtasdt0 @ SV182 @ ( sdtasdt0 @ SV171 @ SV171 ) )
= ( sdtasdt0 @ SV124 @ SV124 ) )
= $false )
| ( ( SV182 = sz00 )
= $true )
| ( ( SV171 = sz00 )
= $true )
| ( ( SV124 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV171 )
= $false )
| ( ( aNaturalNumber0 @ SV124 )
= $false )
| ( ( aNaturalNumber0 @ SV182 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1449]) ).
thf(1458,plain,
! [SV172: $i,SV183: $i,SV124: $i] :
( ( ( iLess0 @ SV124 @ xn )
= $false )
| ( ( ~ ( isPrime0 @ SV183 ) )
= $true )
| ( ( ( sdtasdt0 @ SV183 @ ( sdtasdt0 @ SV172 @ SV172 ) )
= ( sdtasdt0 @ SV124 @ SV124 ) )
= $false )
| ( ( SV183 = sz00 )
= $true )
| ( ( SV172 = sz00 )
= $true )
| ( ( SV124 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV172 )
= $false )
| ( ( aNaturalNumber0 @ SV124 )
= $false )
| ( ( aNaturalNumber0 @ SV183 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1450]) ).
thf(1459,plain,
! [SV145: $i,SV201: $i,SV125: $i] :
( ( ( ( sdtpldt0 @ SV125 @ SV201 )
= ( sdtpldt0 @ SV145 @ SV201 ) )
= $false )
| ( ( aNaturalNumber0 @ SV201 )
= $false )
| ( ( SV125 = SV145 )
= $true )
| ( ( sdtlseqdt0 @ SV125 @ SV145 )
= $false )
| ( ( aNaturalNumber0 @ SV125 )
= $false )
| ( ( aNaturalNumber0 @ SV145 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1451]) ).
thf(1460,plain,
! [SV145: $i,SV125: $i,SV202: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV202 )
| ( ( sdtpldt0 @ SV202 @ SV125 )
!= ( sdtpldt0 @ SV202 @ SV145 ) ) )
= $true )
| ( ( SV125 = SV145 )
= $true )
| ( ( sdtlseqdt0 @ SV125 @ SV145 )
= $false )
| ( ( aNaturalNumber0 @ SV125 )
= $false )
| ( ( aNaturalNumber0 @ SV145 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1452]) ).
thf(1461,plain,
! [SV145: $i,SV125: $i,SV203: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV203 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SV203 @ SV125 ) @ ( sdtpldt0 @ SV203 @ SV145 ) ) )
= $true )
| ( ( SV125 = SV145 )
= $true )
| ( ( sdtlseqdt0 @ SV125 @ SV145 )
= $false )
| ( ( aNaturalNumber0 @ SV125 )
= $false )
| ( ( aNaturalNumber0 @ SV145 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1453]) ).
thf(1462,plain,
! [SV191: $i,SV123: $i,SV188: $i] :
( ( ( ( sdtasdt0 @ SV188 @ SV123 )
= ( sdtasdt0 @ SV191 @ SV123 ) )
= $false )
| ( ( SV123 = sz00 )
= $true )
| ( ( SV188 = SV191 )
= $true )
| ( ( sdtlseqdt0 @ SV188 @ SV191 )
= $false )
| ( ( aNaturalNumber0 @ SV188 )
= $false )
| ( ( aNaturalNumber0 @ SV123 )
= $false )
| ( ( aNaturalNumber0 @ SV191 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1454]) ).
thf(1463,plain,
! [SV197: $i,SV195: $i,SV123: $i] :
( ( ( ( SV123 = sz00 )
| ( SV195 = SV197 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV195 @ SV197 ) )
= $true )
| ( ( ( sdtasdt0 @ SV123 @ SV195 )
!= ( sdtasdt0 @ SV123 @ SV197 ) )
= $true )
| ( ( aNaturalNumber0 @ SV195 )
= $false )
| ( ( aNaturalNumber0 @ SV123 )
= $false )
| ( ( aNaturalNumber0 @ SV197 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1455]) ).
thf(1464,plain,
! [SV198: $i,SV196: $i,SV123: $i] :
( ( ( ( SV123 = sz00 )
| ( SV196 = SV198 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV196 @ SV198 ) )
= $true )
| ( ( sdtlseqdt0 @ ( sdtasdt0 @ SV123 @ SV196 ) @ ( sdtasdt0 @ SV123 @ SV198 ) )
= $true )
| ( ( aNaturalNumber0 @ SV196 )
= $false )
| ( ( aNaturalNumber0 @ SV123 )
= $false )
| ( ( aNaturalNumber0 @ SV198 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1456]) ).
thf(1465,plain,
! [SV124: $i,SV171: $i,SV182: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( SV182
!= ( sdtasdt0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) @ ( sK5_SY81 @ SV182 @ SV171 @ SV124 ) ) )
| ~ ( aNaturalNumber0 @ ( sK5_SY81 @ SV182 @ SV171 @ SV124 ) ) )
| ~ ( aNaturalNumber0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) ) )
| ~ ( doDivides0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) @ SV182 ) )
| ~ ~ ( ~ ( ( ( sK4_W3 @ SV182 @ SV171 @ SV124 )
!= sz10 ) )
| ~ ( ( ( sK4_W3 @ SV182 @ SV171 @ SV124 )
!= SV182 ) ) ) ) )
= $true )
| ( ( SV182 = sz10 )
= $true )
| ( ( iLess0 @ SV124 @ xn )
= $false )
| ( ( ( sdtasdt0 @ SV182 @ ( sdtasdt0 @ SV171 @ SV171 ) )
= ( sdtasdt0 @ SV124 @ SV124 ) )
= $false )
| ( ( SV182 = sz00 )
= $true )
| ( ( SV171 = sz00 )
= $true )
| ( ( SV124 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV171 )
= $false )
| ( ( aNaturalNumber0 @ SV124 )
= $false )
| ( ( aNaturalNumber0 @ SV182 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1457]) ).
thf(1466,plain,
! [SV172: $i,SV124: $i,SV183: $i] :
( ( ( isPrime0 @ SV183 )
= $false )
| ( ( iLess0 @ SV124 @ xn )
= $false )
| ( ( ( sdtasdt0 @ SV183 @ ( sdtasdt0 @ SV172 @ SV172 ) )
= ( sdtasdt0 @ SV124 @ SV124 ) )
= $false )
| ( ( SV183 = sz00 )
= $true )
| ( ( SV172 = sz00 )
= $true )
| ( ( SV124 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV172 )
= $false )
| ( ( aNaturalNumber0 @ SV124 )
= $false )
| ( ( aNaturalNumber0 @ SV183 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1458]) ).
thf(1467,plain,
! [SV145: $i,SV125: $i,SV202: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV202 ) )
= $true )
| ( ( ( sdtpldt0 @ SV202 @ SV125 )
!= ( sdtpldt0 @ SV202 @ SV145 ) )
= $true )
| ( ( SV125 = SV145 )
= $true )
| ( ( sdtlseqdt0 @ SV125 @ SV145 )
= $false )
| ( ( aNaturalNumber0 @ SV125 )
= $false )
| ( ( aNaturalNumber0 @ SV145 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1460]) ).
thf(1468,plain,
! [SV145: $i,SV125: $i,SV203: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV203 ) )
= $true )
| ( ( sdtlseqdt0 @ ( sdtpldt0 @ SV203 @ SV125 ) @ ( sdtpldt0 @ SV203 @ SV145 ) )
= $true )
| ( ( SV125 = SV145 )
= $true )
| ( ( sdtlseqdt0 @ SV125 @ SV145 )
= $false )
| ( ( aNaturalNumber0 @ SV125 )
= $false )
| ( ( aNaturalNumber0 @ SV145 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1461]) ).
thf(1469,plain,
! [SV197: $i,SV195: $i,SV123: $i] :
( ( ( SV123 = sz00 )
= $true )
| ( ( SV195 = SV197 )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV195 @ SV197 ) )
= $true )
| ( ( ( sdtasdt0 @ SV123 @ SV195 )
!= ( sdtasdt0 @ SV123 @ SV197 ) )
= $true )
| ( ( aNaturalNumber0 @ SV195 )
= $false )
| ( ( aNaturalNumber0 @ SV123 )
= $false )
| ( ( aNaturalNumber0 @ SV197 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1463]) ).
thf(1470,plain,
! [SV198: $i,SV196: $i,SV123: $i] :
( ( ( SV123 = sz00 )
= $true )
| ( ( SV196 = SV198 )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV196 @ SV198 ) )
= $true )
| ( ( sdtlseqdt0 @ ( sdtasdt0 @ SV123 @ SV196 ) @ ( sdtasdt0 @ SV123 @ SV198 ) )
= $true )
| ( ( aNaturalNumber0 @ SV196 )
= $false )
| ( ( aNaturalNumber0 @ SV123 )
= $false )
| ( ( aNaturalNumber0 @ SV198 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1464]) ).
thf(1471,plain,
! [SV124: $i,SV171: $i,SV182: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ( SV182
!= ( sdtasdt0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) @ ( sK5_SY81 @ SV182 @ SV171 @ SV124 ) ) )
| ~ ( aNaturalNumber0 @ ( sK5_SY81 @ SV182 @ SV171 @ SV124 ) ) )
| ~ ( aNaturalNumber0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) ) )
| ~ ( doDivides0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) @ SV182 ) )
| ~ ~ ( ~ ( ( ( sK4_W3 @ SV182 @ SV171 @ SV124 )
!= sz10 ) )
| ~ ( ( ( sK4_W3 @ SV182 @ SV171 @ SV124 )
!= SV182 ) ) ) )
= $false )
| ( ( SV182 = sz10 )
= $true )
| ( ( iLess0 @ SV124 @ xn )
= $false )
| ( ( ( sdtasdt0 @ SV182 @ ( sdtasdt0 @ SV171 @ SV171 ) )
= ( sdtasdt0 @ SV124 @ SV124 ) )
= $false )
| ( ( SV182 = sz00 )
= $true )
| ( ( SV171 = sz00 )
= $true )
| ( ( SV124 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV171 )
= $false )
| ( ( aNaturalNumber0 @ SV124 )
= $false )
| ( ( aNaturalNumber0 @ SV182 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1465]) ).
thf(1472,plain,
! [SV145: $i,SV125: $i,SV202: $i] :
( ( ( aNaturalNumber0 @ SV202 )
= $false )
| ( ( ( sdtpldt0 @ SV202 @ SV125 )
!= ( sdtpldt0 @ SV202 @ SV145 ) )
= $true )
| ( ( SV125 = SV145 )
= $true )
| ( ( sdtlseqdt0 @ SV125 @ SV145 )
= $false )
| ( ( aNaturalNumber0 @ SV125 )
= $false )
| ( ( aNaturalNumber0 @ SV145 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1467]) ).
thf(1473,plain,
! [SV145: $i,SV125: $i,SV203: $i] :
( ( ( aNaturalNumber0 @ SV203 )
= $false )
| ( ( sdtlseqdt0 @ ( sdtpldt0 @ SV203 @ SV125 ) @ ( sdtpldt0 @ SV203 @ SV145 ) )
= $true )
| ( ( SV125 = SV145 )
= $true )
| ( ( sdtlseqdt0 @ SV125 @ SV145 )
= $false )
| ( ( aNaturalNumber0 @ SV125 )
= $false )
| ( ( aNaturalNumber0 @ SV145 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1468]) ).
thf(1474,plain,
! [SV123: $i,SV197: $i,SV195: $i] :
( ( ( sdtlseqdt0 @ SV195 @ SV197 )
= $false )
| ( ( SV195 = SV197 )
= $true )
| ( ( SV123 = sz00 )
= $true )
| ( ( ( sdtasdt0 @ SV123 @ SV195 )
!= ( sdtasdt0 @ SV123 @ SV197 ) )
= $true )
| ( ( aNaturalNumber0 @ SV195 )
= $false )
| ( ( aNaturalNumber0 @ SV123 )
= $false )
| ( ( aNaturalNumber0 @ SV197 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1469]) ).
thf(1475,plain,
! [SV123: $i,SV198: $i,SV196: $i] :
( ( ( sdtlseqdt0 @ SV196 @ SV198 )
= $false )
| ( ( SV196 = SV198 )
= $true )
| ( ( SV123 = sz00 )
= $true )
| ( ( sdtlseqdt0 @ ( sdtasdt0 @ SV123 @ SV196 ) @ ( sdtasdt0 @ SV123 @ SV198 ) )
= $true )
| ( ( aNaturalNumber0 @ SV196 )
= $false )
| ( ( aNaturalNumber0 @ SV123 )
= $false )
| ( ( aNaturalNumber0 @ SV198 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1470]) ).
thf(1476,plain,
! [SV124: $i,SV171: $i,SV182: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ( SV182
!= ( sdtasdt0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) @ ( sK5_SY81 @ SV182 @ SV171 @ SV124 ) ) )
| ~ ( aNaturalNumber0 @ ( sK5_SY81 @ SV182 @ SV171 @ SV124 ) ) )
| ~ ( aNaturalNumber0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) ) )
| ~ ( doDivides0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) @ SV182 ) ) )
= $false )
| ( ( SV182 = sz10 )
= $true )
| ( ( iLess0 @ SV124 @ xn )
= $false )
| ( ( ( sdtasdt0 @ SV182 @ ( sdtasdt0 @ SV171 @ SV171 ) )
= ( sdtasdt0 @ SV124 @ SV124 ) )
= $false )
| ( ( SV182 = sz00 )
= $true )
| ( ( SV171 = sz00 )
= $true )
| ( ( SV124 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV171 )
= $false )
| ( ( aNaturalNumber0 @ SV124 )
= $false )
| ( ( aNaturalNumber0 @ SV182 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1471]) ).
thf(1477,plain,
! [SV124: $i,SV171: $i,SV182: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK4_W3 @ SV182 @ SV171 @ SV124 )
!= sz10 ) )
| ~ ( ( ( sK4_W3 @ SV182 @ SV171 @ SV124 )
!= SV182 ) ) ) )
= $false )
| ( ( SV182 = sz10 )
= $true )
| ( ( iLess0 @ SV124 @ xn )
= $false )
| ( ( ( sdtasdt0 @ SV182 @ ( sdtasdt0 @ SV171 @ SV171 ) )
= ( sdtasdt0 @ SV124 @ SV124 ) )
= $false )
| ( ( SV182 = sz00 )
= $true )
| ( ( SV171 = sz00 )
= $true )
| ( ( SV124 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV171 )
= $false )
| ( ( aNaturalNumber0 @ SV124 )
= $false )
| ( ( aNaturalNumber0 @ SV182 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1471]) ).
thf(1478,plain,
! [SV145: $i,SV125: $i,SV202: $i] :
( ( ( ( sdtpldt0 @ SV202 @ SV125 )
= ( sdtpldt0 @ SV202 @ SV145 ) )
= $false )
| ( ( aNaturalNumber0 @ SV202 )
= $false )
| ( ( SV125 = SV145 )
= $true )
| ( ( sdtlseqdt0 @ SV125 @ SV145 )
= $false )
| ( ( aNaturalNumber0 @ SV125 )
= $false )
| ( ( aNaturalNumber0 @ SV145 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1472]) ).
thf(1479,plain,
! [SV197: $i,SV195: $i,SV123: $i] :
( ( ( ( sdtasdt0 @ SV123 @ SV195 )
= ( sdtasdt0 @ SV123 @ SV197 ) )
= $false )
| ( ( SV123 = sz00 )
= $true )
| ( ( SV195 = SV197 )
= $true )
| ( ( sdtlseqdt0 @ SV195 @ SV197 )
= $false )
| ( ( aNaturalNumber0 @ SV195 )
= $false )
| ( ( aNaturalNumber0 @ SV123 )
= $false )
| ( ( aNaturalNumber0 @ SV197 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1474]) ).
thf(1480,plain,
! [SV124: $i,SV171: $i,SV182: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ( SV182
!= ( sdtasdt0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) @ ( sK5_SY81 @ SV182 @ SV171 @ SV124 ) ) )
| ~ ( aNaturalNumber0 @ ( sK5_SY81 @ SV182 @ SV171 @ SV124 ) ) )
| ~ ( aNaturalNumber0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) ) )
| ~ ( doDivides0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) @ SV182 ) ) )
= $true )
| ( ( SV182 = sz10 )
= $true )
| ( ( iLess0 @ SV124 @ xn )
= $false )
| ( ( ( sdtasdt0 @ SV182 @ ( sdtasdt0 @ SV171 @ SV171 ) )
= ( sdtasdt0 @ SV124 @ SV124 ) )
= $false )
| ( ( SV182 = sz00 )
= $true )
| ( ( SV171 = sz00 )
= $true )
| ( ( SV124 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV171 )
= $false )
| ( ( aNaturalNumber0 @ SV124 )
= $false )
| ( ( aNaturalNumber0 @ SV182 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1476]) ).
thf(1481,plain,
! [SV124: $i,SV171: $i,SV182: $i] :
( ( ( ~ ( ~ ( ( ( sK4_W3 @ SV182 @ SV171 @ SV124 )
!= sz10 ) )
| ~ ( ( ( sK4_W3 @ SV182 @ SV171 @ SV124 )
!= SV182 ) ) ) )
= $true )
| ( ( SV182 = sz10 )
= $true )
| ( ( iLess0 @ SV124 @ xn )
= $false )
| ( ( ( sdtasdt0 @ SV182 @ ( sdtasdt0 @ SV171 @ SV171 ) )
= ( sdtasdt0 @ SV124 @ SV124 ) )
= $false )
| ( ( SV182 = sz00 )
= $true )
| ( ( SV171 = sz00 )
= $true )
| ( ( SV124 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV171 )
= $false )
| ( ( aNaturalNumber0 @ SV124 )
= $false )
| ( ( aNaturalNumber0 @ SV182 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1477]) ).
thf(1482,plain,
! [SV124: $i,SV171: $i,SV182: $i] :
( ( ( ~ ~ ( ~ ~ ( ( SV182
!= ( sdtasdt0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) @ ( sK5_SY81 @ SV182 @ SV171 @ SV124 ) ) )
| ~ ( aNaturalNumber0 @ ( sK5_SY81 @ SV182 @ SV171 @ SV124 ) ) )
| ~ ( aNaturalNumber0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) ) )
| ~ ( doDivides0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) @ SV182 ) )
= $false )
| ( ( SV182 = sz10 )
= $true )
| ( ( iLess0 @ SV124 @ xn )
= $false )
| ( ( ( sdtasdt0 @ SV182 @ ( sdtasdt0 @ SV171 @ SV171 ) )
= ( sdtasdt0 @ SV124 @ SV124 ) )
= $false )
| ( ( SV182 = sz00 )
= $true )
| ( ( SV171 = sz00 )
= $true )
| ( ( SV124 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV171 )
= $false )
| ( ( aNaturalNumber0 @ SV124 )
= $false )
| ( ( aNaturalNumber0 @ SV182 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1480]) ).
thf(1483,plain,
! [SV124: $i,SV171: $i,SV182: $i] :
( ( ( ~ ( ( ( sK4_W3 @ SV182 @ SV171 @ SV124 )
!= sz10 ) )
| ~ ( ( ( sK4_W3 @ SV182 @ SV171 @ SV124 )
!= SV182 ) ) )
= $false )
| ( ( SV182 = sz10 )
= $true )
| ( ( iLess0 @ SV124 @ xn )
= $false )
| ( ( ( sdtasdt0 @ SV182 @ ( sdtasdt0 @ SV171 @ SV171 ) )
= ( sdtasdt0 @ SV124 @ SV124 ) )
= $false )
| ( ( SV182 = sz00 )
= $true )
| ( ( SV171 = sz00 )
= $true )
| ( ( SV124 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV171 )
= $false )
| ( ( aNaturalNumber0 @ SV124 )
= $false )
| ( ( aNaturalNumber0 @ SV182 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1481]) ).
thf(1484,plain,
! [SV124: $i,SV171: $i,SV182: $i] :
( ( ( ~ ~ ( ~ ~ ( ( SV182
!= ( sdtasdt0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) @ ( sK5_SY81 @ SV182 @ SV171 @ SV124 ) ) )
| ~ ( aNaturalNumber0 @ ( sK5_SY81 @ SV182 @ SV171 @ SV124 ) ) )
| ~ ( aNaturalNumber0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) ) ) )
= $false )
| ( ( SV182 = sz10 )
= $true )
| ( ( iLess0 @ SV124 @ xn )
= $false )
| ( ( ( sdtasdt0 @ SV182 @ ( sdtasdt0 @ SV171 @ SV171 ) )
= ( sdtasdt0 @ SV124 @ SV124 ) )
= $false )
| ( ( SV182 = sz00 )
= $true )
| ( ( SV171 = sz00 )
= $true )
| ( ( SV124 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV171 )
= $false )
| ( ( aNaturalNumber0 @ SV124 )
= $false )
| ( ( aNaturalNumber0 @ SV182 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1482]) ).
thf(1485,plain,
! [SV124: $i,SV171: $i,SV182: $i] :
( ( ( ~ ( doDivides0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) @ SV182 ) )
= $false )
| ( ( SV182 = sz10 )
= $true )
| ( ( iLess0 @ SV124 @ xn )
= $false )
| ( ( ( sdtasdt0 @ SV182 @ ( sdtasdt0 @ SV171 @ SV171 ) )
= ( sdtasdt0 @ SV124 @ SV124 ) )
= $false )
| ( ( SV182 = sz00 )
= $true )
| ( ( SV171 = sz00 )
= $true )
| ( ( SV124 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV171 )
= $false )
| ( ( aNaturalNumber0 @ SV124 )
= $false )
| ( ( aNaturalNumber0 @ SV182 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1482]) ).
thf(1486,plain,
! [SV124: $i,SV171: $i,SV182: $i] :
( ( ( ~ ( ( ( sK4_W3 @ SV182 @ SV171 @ SV124 )
!= sz10 ) ) )
= $false )
| ( ( SV182 = sz10 )
= $true )
| ( ( iLess0 @ SV124 @ xn )
= $false )
| ( ( ( sdtasdt0 @ SV182 @ ( sdtasdt0 @ SV171 @ SV171 ) )
= ( sdtasdt0 @ SV124 @ SV124 ) )
= $false )
| ( ( SV182 = sz00 )
= $true )
| ( ( SV171 = sz00 )
= $true )
| ( ( SV124 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV171 )
= $false )
| ( ( aNaturalNumber0 @ SV124 )
= $false )
| ( ( aNaturalNumber0 @ SV182 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1483]) ).
thf(1487,plain,
! [SV124: $i,SV171: $i,SV182: $i] :
( ( ( ~ ( ( ( sK4_W3 @ SV182 @ SV171 @ SV124 )
!= SV182 ) ) )
= $false )
| ( ( SV182 = sz10 )
= $true )
| ( ( iLess0 @ SV124 @ xn )
= $false )
| ( ( ( sdtasdt0 @ SV182 @ ( sdtasdt0 @ SV171 @ SV171 ) )
= ( sdtasdt0 @ SV124 @ SV124 ) )
= $false )
| ( ( SV182 = sz00 )
= $true )
| ( ( SV171 = sz00 )
= $true )
| ( ( SV124 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV171 )
= $false )
| ( ( aNaturalNumber0 @ SV124 )
= $false )
| ( ( aNaturalNumber0 @ SV182 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1483]) ).
thf(1488,plain,
! [SV124: $i,SV171: $i,SV182: $i] :
( ( ( ~ ( ~ ~ ( ( SV182
!= ( sdtasdt0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) @ ( sK5_SY81 @ SV182 @ SV171 @ SV124 ) ) )
| ~ ( aNaturalNumber0 @ ( sK5_SY81 @ SV182 @ SV171 @ SV124 ) ) )
| ~ ( aNaturalNumber0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) ) ) )
= $true )
| ( ( SV182 = sz10 )
= $true )
| ( ( iLess0 @ SV124 @ xn )
= $false )
| ( ( ( sdtasdt0 @ SV182 @ ( sdtasdt0 @ SV171 @ SV171 ) )
= ( sdtasdt0 @ SV124 @ SV124 ) )
= $false )
| ( ( SV182 = sz00 )
= $true )
| ( ( SV171 = sz00 )
= $true )
| ( ( SV124 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV171 )
= $false )
| ( ( aNaturalNumber0 @ SV124 )
= $false )
| ( ( aNaturalNumber0 @ SV182 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1484]) ).
thf(1489,plain,
! [SV124: $i,SV171: $i,SV182: $i] :
( ( ( doDivides0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) @ SV182 )
= $true )
| ( ( SV182 = sz10 )
= $true )
| ( ( iLess0 @ SV124 @ xn )
= $false )
| ( ( ( sdtasdt0 @ SV182 @ ( sdtasdt0 @ SV171 @ SV171 ) )
= ( sdtasdt0 @ SV124 @ SV124 ) )
= $false )
| ( ( SV182 = sz00 )
= $true )
| ( ( SV171 = sz00 )
= $true )
| ( ( SV124 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV171 )
= $false )
| ( ( aNaturalNumber0 @ SV124 )
= $false )
| ( ( aNaturalNumber0 @ SV182 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1485]) ).
thf(1490,plain,
! [SV124: $i,SV171: $i,SV182: $i] :
( ( ( ( sK4_W3 @ SV182 @ SV171 @ SV124 )
!= sz10 )
= $true )
| ( ( SV182 = sz10 )
= $true )
| ( ( iLess0 @ SV124 @ xn )
= $false )
| ( ( ( sdtasdt0 @ SV182 @ ( sdtasdt0 @ SV171 @ SV171 ) )
= ( sdtasdt0 @ SV124 @ SV124 ) )
= $false )
| ( ( SV182 = sz00 )
= $true )
| ( ( SV171 = sz00 )
= $true )
| ( ( SV124 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV171 )
= $false )
| ( ( aNaturalNumber0 @ SV124 )
= $false )
| ( ( aNaturalNumber0 @ SV182 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1486]) ).
thf(1491,plain,
! [SV124: $i,SV171: $i,SV182: $i] :
( ( ( ( sK4_W3 @ SV182 @ SV171 @ SV124 )
!= SV182 )
= $true )
| ( ( SV182 = sz10 )
= $true )
| ( ( iLess0 @ SV124 @ xn )
= $false )
| ( ( ( sdtasdt0 @ SV182 @ ( sdtasdt0 @ SV171 @ SV171 ) )
= ( sdtasdt0 @ SV124 @ SV124 ) )
= $false )
| ( ( SV182 = sz00 )
= $true )
| ( ( SV171 = sz00 )
= $true )
| ( ( SV124 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV171 )
= $false )
| ( ( aNaturalNumber0 @ SV124 )
= $false )
| ( ( aNaturalNumber0 @ SV182 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1487]) ).
thf(1492,plain,
! [SV124: $i,SV171: $i,SV182: $i] :
( ( ( ~ ~ ( ( SV182
!= ( sdtasdt0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) @ ( sK5_SY81 @ SV182 @ SV171 @ SV124 ) ) )
| ~ ( aNaturalNumber0 @ ( sK5_SY81 @ SV182 @ SV171 @ SV124 ) ) )
| ~ ( aNaturalNumber0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) ) )
= $false )
| ( ( SV182 = sz10 )
= $true )
| ( ( iLess0 @ SV124 @ xn )
= $false )
| ( ( ( sdtasdt0 @ SV182 @ ( sdtasdt0 @ SV171 @ SV171 ) )
= ( sdtasdt0 @ SV124 @ SV124 ) )
= $false )
| ( ( SV182 = sz00 )
= $true )
| ( ( SV171 = sz00 )
= $true )
| ( ( SV124 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV171 )
= $false )
| ( ( aNaturalNumber0 @ SV124 )
= $false )
| ( ( aNaturalNumber0 @ SV182 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1488]) ).
thf(1493,plain,
! [SV124: $i,SV171: $i,SV182: $i] :
( ( ( ( sK4_W3 @ SV182 @ SV171 @ SV124 )
= sz10 )
= $false )
| ( ( SV182 = sz10 )
= $true )
| ( ( iLess0 @ SV124 @ xn )
= $false )
| ( ( ( sdtasdt0 @ SV182 @ ( sdtasdt0 @ SV171 @ SV171 ) )
= ( sdtasdt0 @ SV124 @ SV124 ) )
= $false )
| ( ( SV182 = sz00 )
= $true )
| ( ( SV171 = sz00 )
= $true )
| ( ( SV124 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV171 )
= $false )
| ( ( aNaturalNumber0 @ SV124 )
= $false )
| ( ( aNaturalNumber0 @ SV182 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1490]) ).
thf(1494,plain,
! [SV124: $i,SV171: $i,SV182: $i] :
( ( ( ( sK4_W3 @ SV182 @ SV171 @ SV124 )
= SV182 )
= $false )
| ( ( SV182 = sz10 )
= $true )
| ( ( iLess0 @ SV124 @ xn )
= $false )
| ( ( ( sdtasdt0 @ SV182 @ ( sdtasdt0 @ SV171 @ SV171 ) )
= ( sdtasdt0 @ SV124 @ SV124 ) )
= $false )
| ( ( SV182 = sz00 )
= $true )
| ( ( SV171 = sz00 )
= $true )
| ( ( SV124 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV171 )
= $false )
| ( ( aNaturalNumber0 @ SV124 )
= $false )
| ( ( aNaturalNumber0 @ SV182 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1491]) ).
thf(1495,plain,
! [SV124: $i,SV171: $i,SV182: $i] :
( ( ( ~ ~ ( ( SV182
!= ( sdtasdt0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) @ ( sK5_SY81 @ SV182 @ SV171 @ SV124 ) ) )
| ~ ( aNaturalNumber0 @ ( sK5_SY81 @ SV182 @ SV171 @ SV124 ) ) ) )
= $false )
| ( ( SV182 = sz10 )
= $true )
| ( ( iLess0 @ SV124 @ xn )
= $false )
| ( ( ( sdtasdt0 @ SV182 @ ( sdtasdt0 @ SV171 @ SV171 ) )
= ( sdtasdt0 @ SV124 @ SV124 ) )
= $false )
| ( ( SV182 = sz00 )
= $true )
| ( ( SV171 = sz00 )
= $true )
| ( ( SV124 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV171 )
= $false )
| ( ( aNaturalNumber0 @ SV124 )
= $false )
| ( ( aNaturalNumber0 @ SV182 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1492]) ).
thf(1496,plain,
! [SV124: $i,SV171: $i,SV182: $i] :
( ( ( ~ ( aNaturalNumber0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) ) )
= $false )
| ( ( SV182 = sz10 )
= $true )
| ( ( iLess0 @ SV124 @ xn )
= $false )
| ( ( ( sdtasdt0 @ SV182 @ ( sdtasdt0 @ SV171 @ SV171 ) )
= ( sdtasdt0 @ SV124 @ SV124 ) )
= $false )
| ( ( SV182 = sz00 )
= $true )
| ( ( SV171 = sz00 )
= $true )
| ( ( SV124 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV171 )
= $false )
| ( ( aNaturalNumber0 @ SV124 )
= $false )
| ( ( aNaturalNumber0 @ SV182 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1492]) ).
thf(1497,plain,
! [SV124: $i,SV171: $i,SV182: $i] :
( ( ( ~ ( ( SV182
!= ( sdtasdt0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) @ ( sK5_SY81 @ SV182 @ SV171 @ SV124 ) ) )
| ~ ( aNaturalNumber0 @ ( sK5_SY81 @ SV182 @ SV171 @ SV124 ) ) ) )
= $true )
| ( ( SV182 = sz10 )
= $true )
| ( ( iLess0 @ SV124 @ xn )
= $false )
| ( ( ( sdtasdt0 @ SV182 @ ( sdtasdt0 @ SV171 @ SV171 ) )
= ( sdtasdt0 @ SV124 @ SV124 ) )
= $false )
| ( ( SV182 = sz00 )
= $true )
| ( ( SV171 = sz00 )
= $true )
| ( ( SV124 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV171 )
= $false )
| ( ( aNaturalNumber0 @ SV124 )
= $false )
| ( ( aNaturalNumber0 @ SV182 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1495]) ).
thf(1498,plain,
! [SV124: $i,SV171: $i,SV182: $i] :
( ( ( aNaturalNumber0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) )
= $true )
| ( ( SV182 = sz10 )
= $true )
| ( ( iLess0 @ SV124 @ xn )
= $false )
| ( ( ( sdtasdt0 @ SV182 @ ( sdtasdt0 @ SV171 @ SV171 ) )
= ( sdtasdt0 @ SV124 @ SV124 ) )
= $false )
| ( ( SV182 = sz00 )
= $true )
| ( ( SV171 = sz00 )
= $true )
| ( ( SV124 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV171 )
= $false )
| ( ( aNaturalNumber0 @ SV124 )
= $false )
| ( ( aNaturalNumber0 @ SV182 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1496]) ).
thf(1499,plain,
! [SV124: $i,SV171: $i,SV182: $i] :
( ( ( ( SV182
!= ( sdtasdt0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) @ ( sK5_SY81 @ SV182 @ SV171 @ SV124 ) ) )
| ~ ( aNaturalNumber0 @ ( sK5_SY81 @ SV182 @ SV171 @ SV124 ) ) )
= $false )
| ( ( SV182 = sz10 )
= $true )
| ( ( iLess0 @ SV124 @ xn )
= $false )
| ( ( ( sdtasdt0 @ SV182 @ ( sdtasdt0 @ SV171 @ SV171 ) )
= ( sdtasdt0 @ SV124 @ SV124 ) )
= $false )
| ( ( SV182 = sz00 )
= $true )
| ( ( SV171 = sz00 )
= $true )
| ( ( SV124 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV171 )
= $false )
| ( ( aNaturalNumber0 @ SV124 )
= $false )
| ( ( aNaturalNumber0 @ SV182 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1497]) ).
thf(1500,plain,
! [SV124: $i,SV171: $i,SV182: $i] :
( ( ( SV182
!= ( sdtasdt0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) @ ( sK5_SY81 @ SV182 @ SV171 @ SV124 ) ) )
= $false )
| ( ( SV182 = sz10 )
= $true )
| ( ( iLess0 @ SV124 @ xn )
= $false )
| ( ( ( sdtasdt0 @ SV182 @ ( sdtasdt0 @ SV171 @ SV171 ) )
= ( sdtasdt0 @ SV124 @ SV124 ) )
= $false )
| ( ( SV182 = sz00 )
= $true )
| ( ( SV171 = sz00 )
= $true )
| ( ( SV124 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV171 )
= $false )
| ( ( aNaturalNumber0 @ SV124 )
= $false )
| ( ( aNaturalNumber0 @ SV182 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1499]) ).
thf(1501,plain,
! [SV124: $i,SV171: $i,SV182: $i] :
( ( ( ~ ( aNaturalNumber0 @ ( sK5_SY81 @ SV182 @ SV171 @ SV124 ) ) )
= $false )
| ( ( SV182 = sz10 )
= $true )
| ( ( iLess0 @ SV124 @ xn )
= $false )
| ( ( ( sdtasdt0 @ SV182 @ ( sdtasdt0 @ SV171 @ SV171 ) )
= ( sdtasdt0 @ SV124 @ SV124 ) )
= $false )
| ( ( SV182 = sz00 )
= $true )
| ( ( SV171 = sz00 )
= $true )
| ( ( SV124 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV171 )
= $false )
| ( ( aNaturalNumber0 @ SV124 )
= $false )
| ( ( aNaturalNumber0 @ SV182 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1499]) ).
thf(1502,plain,
! [SV124: $i,SV171: $i,SV182: $i] :
( ( ( SV182
= ( sdtasdt0 @ ( sK4_W3 @ SV182 @ SV171 @ SV124 ) @ ( sK5_SY81 @ SV182 @ SV171 @ SV124 ) ) )
= $true )
| ( ( SV182 = sz10 )
= $true )
| ( ( iLess0 @ SV124 @ xn )
= $false )
| ( ( ( sdtasdt0 @ SV182 @ ( sdtasdt0 @ SV171 @ SV171 ) )
= ( sdtasdt0 @ SV124 @ SV124 ) )
= $false )
| ( ( SV182 = sz00 )
= $true )
| ( ( SV171 = sz00 )
= $true )
| ( ( SV124 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV171 )
= $false )
| ( ( aNaturalNumber0 @ SV124 )
= $false )
| ( ( aNaturalNumber0 @ SV182 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1500]) ).
thf(1503,plain,
! [SV124: $i,SV171: $i,SV182: $i] :
( ( ( aNaturalNumber0 @ ( sK5_SY81 @ SV182 @ SV171 @ SV124 ) )
= $true )
| ( ( SV182 = sz10 )
= $true )
| ( ( iLess0 @ SV124 @ xn )
= $false )
| ( ( ( sdtasdt0 @ SV182 @ ( sdtasdt0 @ SV171 @ SV171 ) )
= ( sdtasdt0 @ SV124 @ SV124 ) )
= $false )
| ( ( SV182 = sz00 )
= $true )
| ( ( SV171 = sz00 )
= $true )
| ( ( SV124 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV171 )
= $false )
| ( ( aNaturalNumber0 @ SV124 )
= $false )
| ( ( aNaturalNumber0 @ SV182 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1501]) ).
thf(1504,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[814,1503,1502,1498,1494,1493,1489,1479,1478,1475,1473,1466,1462,1459,1445,1431,1426,1423,1422,1415,1414,1413,1411,1410,1394,1377,1376,1375,1374,1369,1365,1364,1357,1356,1352,1347,1346,1345,1344,1339,1309,1306,1286,1282,1272,1271,1270,1256,1252,1249,1248,1247,1244,1242,1194,1186,1181,1172,1164,1163,1162,1161,1155,1154,1138,1137,1125,1119,1117,1116,1115,1058,1047,1041,1009,1002,993,982,969,873,820,818]) ).
thf(1505,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[1504,811]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM526+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.18 % Computer : n001.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Oct 6 13:30:36 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 192.43/32.34
% 192.43/32.34 No.of.Axioms: 41
% 192.43/32.34
% 192.43/32.34 Length.of.Defs: 0
% 192.43/32.34
% 192.43/32.34 Contains.Choice.Funs: false
% 192.43/32.34 ...................................................
% 192.43/32.34
% 192.43/32.34 ********************************
% 192.43/32.34 * All subproblems solved! *
% 192.43/32.34 ********************************
% 192.43/32.34 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:41,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:298,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:1504,loop_count:0,foatp_calls:1,translation:fof_full)
% 192.43/32.34
% 192.43/32.34 %**** Beginning of derivation protocol ****
% 192.43/32.34 % SZS output start CNFRefutation
% See solution above
% 192.43/32.35
% 192.43/32.35 %**** End of derivation protocol ****
% 192.43/32.35 %**** no. of clauses in derivation: 1505 ****
% 192.43/32.35 %**** clause counter: 1504 ****
% 192.43/32.35
% 192.43/32.35 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:41,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:298,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:1504,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------