%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM489+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 : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:34:00 AM UTC 2026
% Result : Theorem 1.29s 0.41s
% Output : CNFRefutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 15
% Syntax : Number of formulae : 276 ( 126 unt; 0 typ; 0 def)
% Number of atoms : 2502 (1004 equ; 0 cnn)
% Maximal formula atoms : 9 ( 9 avg)
% Number of connectives : 4770 (1205 ~; 806 |; 96 &;2615 @)
% ( 0 <=>; 48 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 17 usr; 10 con; 0-2 aty)
% Number of variables : 552 ( 0 ^; 546 !; 6 ?; 552 :)
% 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_SX0,type,
sK1_SX0: $i ).
thf(tp_sK2_SX0,type,
sK2_SX0: $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_xr,type,
xr: $i ).
thf(4,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(5,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(12,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(18,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,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(21,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(26,axiom,
! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> ( ( ( sdtpldt0 @ W0 @ sz00 )
= W0 )
& ( W0
= ( sdtpldt0 @ sz00 @ W0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_AddZero) ).
thf(27,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(28,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 @ ( sdtpldt0 @ W0 @ W1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
thf(34,axiom,
( ( xr != xn )
& ? [W0: $i] :
( ( aNaturalNumber0 @ W0 )
& ( ( sdtpldt0 @ xr @ W0 )
= xn ) )
& ( sdtlseqdt0 @ xr @ xn ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1894) ).
thf(35,axiom,
( ( aNaturalNumber0 @ xr )
& ( ( sdtpldt0 @ xp @ xr )
= xn )
& ( xr
= ( sdtmndt0 @ xn @ xp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1883) ).
thf(36,axiom,
( ? [W0: $i] :
( ( aNaturalNumber0 @ W0 )
& ( ( sdtpldt0 @ xp @ W0 )
= xn ) )
& ( sdtlseqdt0 @ xp @ xn ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1870) ).
thf(39,axiom,
( ( aNaturalNumber0 @ xn )
& ( aNaturalNumber0 @ xm )
& ( aNaturalNumber0 @ xp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
thf(40,conjecture,
( xn
= ( sdtpldt0 @ xp @ xr ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(41,negated_conjecture,
( ( xn
= ( sdtpldt0 @ xp @ xr ) )
= $false ),
inference(negate_conjecture,[status(cth)],[40]) ).
thf(42,plain,
( ( xn
= ( sdtpldt0 @ xp @ xr ) )
= $false ),
inference(unfold_def,[status(thm)],[41]) ).
thf(43,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)],[4]) ).
thf(44,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)],[5]) ).
thf(45,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)],[12]) ).
thf(46,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( ( sdtpldt0 @ W0 @ W1 )
= sz00 )
=> ( ( W0 = sz00 )
& ( W1 = sz00 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(47,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)],[20]) ).
thf(48,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)],[21]) ).
thf(49,plain,
( ( ! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> ( ( ( sdtpldt0 @ W0 @ sz00 )
= W0 )
& ( W0
= ( sdtpldt0 @ sz00 @ W0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(50,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)],[27]) ).
thf(51,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( sdtpldt0 @ W0 @ W1 )
= ( sdtpldt0 @ W1 @ W0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(52,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( aNaturalNumber0 @ ( sdtpldt0 @ W0 @ W1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(53,plain,
( ( ( xr != xn )
& ? [W0: $i] :
( ( aNaturalNumber0 @ W0 )
& ( ( sdtpldt0 @ xr @ W0 )
= xn ) )
& ( sdtlseqdt0 @ xr @ xn ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(54,plain,
( ( ( aNaturalNumber0 @ xr )
& ( ( sdtpldt0 @ xp @ xr )
= xn )
& ( xr
= ( sdtmndt0 @ xn @ xp ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(55,plain,
( ( ? [W0: $i] :
( ( aNaturalNumber0 @ W0 )
& ( ( sdtpldt0 @ xp @ W0 )
= xn ) )
& ( sdtlseqdt0 @ xp @ xn ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(56,plain,
( ( ( aNaturalNumber0 @ xn )
& ( aNaturalNumber0 @ xm )
& ( aNaturalNumber0 @ xp ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(57,plain,
( ( xn
!= ( sdtpldt0 @ xp @ xr ) )
= $true ),
inference(polarity_switch,[status(thm)],[42]) ).
thf(58,plain,
( ( ( aNaturalNumber0 @ xn )
& ( aNaturalNumber0 @ xm )
& ( aNaturalNumber0 @ xp ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(59,plain,
( ( ? [W0: $i] :
( ( aNaturalNumber0 @ W0 )
& ( ( sdtpldt0 @ xp @ W0 )
= xn ) )
& ( sdtlseqdt0 @ xp @ xn ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(60,plain,
( ( ( aNaturalNumber0 @ xr )
& ( ( sdtpldt0 @ xp @ xr )
= xn )
& ( xr
= ( sdtmndt0 @ xn @ xp ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(61,plain,
( ( ( xr != xn )
& ? [W0: $i] :
( ( aNaturalNumber0 @ W0 )
& ( ( sdtpldt0 @ xr @ W0 )
= xn ) )
& ( sdtlseqdt0 @ xr @ xn ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(62,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( aNaturalNumber0 @ ( sdtpldt0 @ W0 @ W1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(63,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( sdtpldt0 @ W0 @ W1 )
= ( sdtpldt0 @ W1 @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(64,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)],[50]) ).
thf(65,plain,
( ( ! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> ( ( ( sdtpldt0 @ W0 @ sz00 )
= W0 )
& ( W0
= ( sdtpldt0 @ sz00 @ W0 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
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(copy,[status(thm)],[48]) ).
thf(67,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 )
& ( aNaturalNumber0 @ W2 ) )
=> ( ( ( ( sdtpldt0 @ W0 @ W1 )
= ( sdtpldt0 @ W0 @ W2 ) )
| ( ( sdtpldt0 @ W1 @ W0 )
= ( sdtpldt0 @ W2 @ W0 ) ) )
=> ( W1 = W2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(68,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( ( sdtpldt0 @ W0 @ W1 )
= sz00 )
=> ( ( W0 = sz00 )
& ( W1 = sz00 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(69,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(copy,[status(thm)],[45]) ).
thf(70,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)],[44]) ).
thf(71,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)],[43]) ).
thf(72,plain,
( ( xn
!= ( sdtpldt0 @ xp @ xr ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(73,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 ) ) )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SX1 @ SX2 ) @ SX0 )
!= ( sdtpldt0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ ( sdtasdt0 @ SX2 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(74,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 ) )
| ~ ( aNaturalNumber0 @ SX2 ) )
| ( ( sdtpldt0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ SX2 )
= ( sdtpldt0 @ SX0 @ ( sdtpldt0 @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(75,plain,
( ( ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( ( ( sdtpldt0 @ SX0 @ sz00 )
!= SX0 )
| ( SX0
!= ( sdtpldt0 @ sz00 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(76,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 ) )
| ~ ( aNaturalNumber0 @ SX2 ) )
| ~ ~ ( ~ ( doDivides0 @ SX0 @ SX1 )
| ~ ( doDivides0 @ SX0 @ ( sdtpldt0 @ SX1 @ SX2 ) ) )
| ( doDivides0 @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(77,plain,
( ( ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ xn )
| ~ ( aNaturalNumber0 @ xm ) )
| ~ ( aNaturalNumber0 @ xp ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(78,plain,
( ( ~ ( ~ ~ ( ~ ( ( xr != xn ) )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aNaturalNumber0 @ SX0 )
| ( ( sdtpldt0 @ xr @ SX0 )
!= xn ) ) )
| ~ ( sdtlseqdt0 @ xr @ xn ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(79,plain,
( ( ~ ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aNaturalNumber0 @ SX0 )
| ( ( sdtpldt0 @ xp @ SX0 )
!= xn ) )
| ~ ( sdtlseqdt0 @ xp @ xn ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(80,plain,
( ( ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ xr )
| ( ( sdtpldt0 @ xp @ xr )
!= xn ) )
| ( xr
!= ( sdtmndt0 @ xn @ xp ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(81,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 ) )
| ~ ( aNaturalNumber0 @ SX2 ) )
| ~ ( ( ( sdtpldt0 @ SX0 @ SX1 )
= ( sdtpldt0 @ SX0 @ SX2 ) )
| ( ( sdtpldt0 @ SX1 @ SX0 )
= ( sdtpldt0 @ SX2 @ SX0 ) ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(82,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 ) )
| ( ( sdtpldt0 @ SX0 @ SX1 )
= ( sdtpldt0 @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(83,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 ) )
| ( ( sdtpldt0 @ SX0 @ SX1 )
!= sz00 )
| ~ ( ( SX0 != sz00 )
| ( SX1 != sz00 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(84,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 ) )
| ~ ( aNaturalNumber0 @ SX2 ) )
| ~ ~ ( ~ ( doDivides0 @ SX0 @ SX1 )
| ~ ( doDivides0 @ SX0 @ SX2 ) )
| ( doDivides0 @ SX0 @ ( sdtpldt0 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(85,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 ) )
| ~ ~ ( ~ ( ( SX0 != SX1 ) )
| ~ ( sdtlseqdt0 @ SX0 @ SX1 ) )
| ! [SX2: $i] :
( ~ ( aNaturalNumber0 @ SX2 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sdtpldt0 @ SX2 @ SX0 )
!= ( sdtpldt0 @ SX2 @ SX1 ) ) )
| ~ ( sdtlseqdt0 @ ( sdtpldt0 @ SX2 @ SX0 ) @ ( sdtpldt0 @ SX2 @ SX1 ) ) )
| ~ ( ( ( sdtpldt0 @ SX0 @ SX2 )
!= ( sdtpldt0 @ SX1 @ SX2 ) ) ) )
| ~ ( sdtlseqdt0 @ ( sdtpldt0 @ SX0 @ SX2 ) @ ( sdtpldt0 @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(86,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 ) )
| ( aNaturalNumber0 @ ( sdtpldt0 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(87,plain,
( ( xn
= ( sdtpldt0 @ xp @ xr ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(88,plain,
! [SV1: $i] :
( ( ! [SY27: $i,SY28: $i] :
( ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SV1 )
| ~ ( aNaturalNumber0 @ SY27 ) )
| ~ ( aNaturalNumber0 @ SY28 ) )
| ~ ( ( ( sdtasdt0 @ SV1 @ ( sdtpldt0 @ SY27 @ SY28 ) )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV1 @ SY27 ) @ ( sdtasdt0 @ SV1 @ SY28 ) ) )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SY27 @ SY28 ) @ SV1 )
!= ( sdtpldt0 @ ( sdtasdt0 @ SY27 @ SV1 ) @ ( sdtasdt0 @ SY28 @ SV1 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(89,plain,
! [SV2: $i] :
( ( ! [SY29: $i,SY30: $i] :
( ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SV2 )
| ~ ( aNaturalNumber0 @ SY29 ) )
| ~ ( aNaturalNumber0 @ SY30 ) )
| ( ( sdtpldt0 @ ( sdtpldt0 @ SV2 @ SY29 ) @ SY30 )
= ( sdtpldt0 @ SV2 @ ( sdtpldt0 @ SY29 @ SY30 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(90,plain,
! [SV3: $i] :
( ( ~ ( aNaturalNumber0 @ SV3 )
| ~ ( ( ( sdtpldt0 @ SV3 @ sz00 )
!= SV3 )
| ( SV3
!= ( sdtpldt0 @ sz00 @ SV3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(91,plain,
! [SV4: $i] :
( ( ! [SY31: $i,SY32: $i] :
( ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SV4 )
| ~ ( aNaturalNumber0 @ SY31 ) )
| ~ ( aNaturalNumber0 @ SY32 ) )
| ~ ~ ( ~ ( doDivides0 @ SV4 @ SY31 )
| ~ ( doDivides0 @ SV4 @ ( sdtpldt0 @ SY31 @ SY32 ) ) )
| ( doDivides0 @ SV4 @ SY32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(92,plain,
( ( ~ ~ ( ~ ( aNaturalNumber0 @ xn )
| ~ ( aNaturalNumber0 @ xm ) )
| ~ ( aNaturalNumber0 @ xp ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(93,plain,
( ( ~ ~ ( ~ ( ( xr != xn ) )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aNaturalNumber0 @ SX0 )
| ( ( sdtpldt0 @ xr @ SX0 )
!= xn ) ) )
| ~ ( sdtlseqdt0 @ xr @ xn ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(94,plain,
( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aNaturalNumber0 @ SX0 )
| ( ( sdtpldt0 @ xp @ SX0 )
!= xn ) )
| ~ ( sdtlseqdt0 @ xp @ xn ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(95,plain,
( ( ~ ~ ( ~ ( aNaturalNumber0 @ xr )
| ( ( sdtpldt0 @ xp @ xr )
!= xn ) )
| ( xr
!= ( sdtmndt0 @ xn @ xp ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(96,plain,
! [SV5: $i] :
( ( ! [SY33: $i,SY34: $i] :
( ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SV5 )
| ~ ( aNaturalNumber0 @ SY33 ) )
| ~ ( aNaturalNumber0 @ SY34 ) )
| ~ ( ( ( sdtpldt0 @ SV5 @ SY33 )
= ( sdtpldt0 @ SV5 @ SY34 ) )
| ( ( sdtpldt0 @ SY33 @ SV5 )
= ( sdtpldt0 @ SY34 @ SV5 ) ) )
| ( SY33 = SY34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(97,plain,
! [SV6: $i] :
( ( ! [SY35: $i] :
( ~ ~ ( ~ ( aNaturalNumber0 @ SV6 )
| ~ ( aNaturalNumber0 @ SY35 ) )
| ( ( sdtpldt0 @ SV6 @ SY35 )
= ( sdtpldt0 @ SY35 @ SV6 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(98,plain,
! [SV7: $i] :
( ( ! [SY36: $i] :
( ~ ~ ( ~ ( aNaturalNumber0 @ SV7 )
| ~ ( aNaturalNumber0 @ SY36 ) )
| ( ( sdtpldt0 @ SV7 @ SY36 )
!= sz00 )
| ~ ( ( SV7 != sz00 )
| ( SY36 != sz00 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(99,plain,
! [SV8: $i] :
( ( ! [SY37: $i,SY38: $i] :
( ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SV8 )
| ~ ( aNaturalNumber0 @ SY37 ) )
| ~ ( aNaturalNumber0 @ SY38 ) )
| ~ ~ ( ~ ( doDivides0 @ SV8 @ SY37 )
| ~ ( doDivides0 @ SV8 @ SY38 ) )
| ( doDivides0 @ SV8 @ ( sdtpldt0 @ SY37 @ SY38 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(100,plain,
! [SV9: $i] :
( ( ! [SY39: $i] :
( ~ ~ ( ~ ( aNaturalNumber0 @ SV9 )
| ~ ( aNaturalNumber0 @ SY39 ) )
| ~ ~ ( ~ ( ( SV9 != SY39 ) )
| ~ ( sdtlseqdt0 @ SV9 @ SY39 ) )
| ! [SY40: $i] :
( ~ ( aNaturalNumber0 @ SY40 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sdtpldt0 @ SY40 @ SV9 )
!= ( sdtpldt0 @ SY40 @ SY39 ) ) )
| ~ ( sdtlseqdt0 @ ( sdtpldt0 @ SY40 @ SV9 ) @ ( sdtpldt0 @ SY40 @ SY39 ) ) )
| ~ ( ( ( sdtpldt0 @ SV9 @ SY40 )
!= ( sdtpldt0 @ SY39 @ SY40 ) ) ) )
| ~ ( sdtlseqdt0 @ ( sdtpldt0 @ SV9 @ SY40 ) @ ( sdtpldt0 @ SY39 @ SY40 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(101,plain,
! [SV10: $i] :
( ( ! [SY41: $i] :
( ~ ~ ( ~ ( aNaturalNumber0 @ SV10 )
| ~ ( aNaturalNumber0 @ SY41 ) )
| ( aNaturalNumber0 @ ( sdtpldt0 @ SV10 @ SY41 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(102,plain,
! [SV11: $i,SV1: $i] :
( ( ! [SY42: $i] :
( ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SV1 )
| ~ ( aNaturalNumber0 @ SV11 ) )
| ~ ( aNaturalNumber0 @ SY42 ) )
| ~ ( ( ( sdtasdt0 @ SV1 @ ( sdtpldt0 @ SV11 @ SY42 ) )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV1 @ SV11 ) @ ( sdtasdt0 @ SV1 @ SY42 ) ) )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SV11 @ SY42 ) @ SV1 )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV11 @ SV1 ) @ ( sdtasdt0 @ SY42 @ SV1 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(103,plain,
! [SV12: $i,SV2: $i] :
( ( ! [SY43: $i] :
( ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SV2 )
| ~ ( aNaturalNumber0 @ SV12 ) )
| ~ ( aNaturalNumber0 @ SY43 ) )
| ( ( sdtpldt0 @ ( sdtpldt0 @ SV2 @ SV12 ) @ SY43 )
= ( sdtpldt0 @ SV2 @ ( sdtpldt0 @ SV12 @ SY43 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(104,plain,
! [SV3: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV3 ) )
= $true )
| ( ( ~ ( ( ( sdtpldt0 @ SV3 @ sz00 )
!= SV3 )
| ( SV3
!= ( sdtpldt0 @ sz00 @ SV3 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[90]) ).
thf(105,plain,
! [SV13: $i,SV4: $i] :
( ( ! [SY44: $i] :
( ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SV4 )
| ~ ( aNaturalNumber0 @ SV13 ) )
| ~ ( aNaturalNumber0 @ SY44 ) )
| ~ ~ ( ~ ( doDivides0 @ SV4 @ SV13 )
| ~ ( doDivides0 @ SV4 @ ( sdtpldt0 @ SV13 @ SY44 ) ) )
| ( doDivides0 @ SV4 @ SY44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(106,plain,
( ( ~ ~ ( ~ ( aNaturalNumber0 @ xn )
| ~ ( aNaturalNumber0 @ xm ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[92]) ).
thf(107,plain,
( ( ~ ( aNaturalNumber0 @ xp ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[92]) ).
thf(108,plain,
( ( ~ ~ ( ~ ( ( xr != xn ) )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aNaturalNumber0 @ SX0 )
| ( ( sdtpldt0 @ xr @ SX0 )
!= xn ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[93]) ).
thf(109,plain,
( ( ~ ( sdtlseqdt0 @ xr @ xn ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[93]) ).
thf(110,plain,
( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aNaturalNumber0 @ SX0 )
| ( ( sdtpldt0 @ xp @ SX0 )
!= xn ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[94]) ).
thf(111,plain,
( ( ~ ( sdtlseqdt0 @ xp @ xn ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[94]) ).
thf(112,plain,
( ( ~ ~ ( ~ ( aNaturalNumber0 @ xr )
| ( ( sdtpldt0 @ xp @ xr )
!= xn ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[95]) ).
thf(113,plain,
( ( xr
!= ( sdtmndt0 @ xn @ xp ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[95]) ).
thf(114,plain,
! [SV14: $i,SV5: $i] :
( ( ! [SY45: $i] :
( ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SV5 )
| ~ ( aNaturalNumber0 @ SV14 ) )
| ~ ( aNaturalNumber0 @ SY45 ) )
| ~ ( ( ( sdtpldt0 @ SV5 @ SV14 )
= ( sdtpldt0 @ SV5 @ SY45 ) )
| ( ( sdtpldt0 @ SV14 @ SV5 )
= ( sdtpldt0 @ SY45 @ SV5 ) ) )
| ( SV14 = SY45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(115,plain,
! [SV15: $i,SV6: $i] :
( ( ~ ~ ( ~ ( aNaturalNumber0 @ SV6 )
| ~ ( aNaturalNumber0 @ SV15 ) )
| ( ( sdtpldt0 @ SV6 @ SV15 )
= ( sdtpldt0 @ SV15 @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(116,plain,
! [SV16: $i,SV7: $i] :
( ( ~ ~ ( ~ ( aNaturalNumber0 @ SV7 )
| ~ ( aNaturalNumber0 @ SV16 ) )
| ( ( sdtpldt0 @ SV7 @ SV16 )
!= sz00 )
| ~ ( ( SV7 != sz00 )
| ( SV16 != sz00 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(117,plain,
! [SV17: $i,SV8: $i] :
( ( ! [SY46: $i] :
( ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SV8 )
| ~ ( aNaturalNumber0 @ SV17 ) )
| ~ ( aNaturalNumber0 @ SY46 ) )
| ~ ~ ( ~ ( doDivides0 @ SV8 @ SV17 )
| ~ ( doDivides0 @ SV8 @ SY46 ) )
| ( doDivides0 @ SV8 @ ( sdtpldt0 @ SV17 @ SY46 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(118,plain,
! [SV18: $i,SV9: $i] :
( ( ~ ~ ( ~ ( aNaturalNumber0 @ SV9 )
| ~ ( aNaturalNumber0 @ SV18 ) )
| ~ ~ ( ~ ( ( SV9 != SV18 ) )
| ~ ( sdtlseqdt0 @ SV9 @ SV18 ) )
| ! [SY47: $i] :
( ~ ( aNaturalNumber0 @ SY47 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sdtpldt0 @ SY47 @ SV9 )
!= ( sdtpldt0 @ SY47 @ SV18 ) ) )
| ~ ( sdtlseqdt0 @ ( sdtpldt0 @ SY47 @ SV9 ) @ ( sdtpldt0 @ SY47 @ SV18 ) ) )
| ~ ( ( ( sdtpldt0 @ SV9 @ SY47 )
!= ( sdtpldt0 @ SV18 @ SY47 ) ) ) )
| ~ ( sdtlseqdt0 @ ( sdtpldt0 @ SV9 @ SY47 ) @ ( sdtpldt0 @ SV18 @ SY47 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(119,plain,
! [SV19: $i,SV10: $i] :
( ( ~ ~ ( ~ ( aNaturalNumber0 @ SV10 )
| ~ ( aNaturalNumber0 @ SV19 ) )
| ( aNaturalNumber0 @ ( sdtpldt0 @ SV10 @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(120,plain,
! [SV20: $i,SV11: $i,SV1: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SV1 )
| ~ ( aNaturalNumber0 @ SV11 ) )
| ~ ( aNaturalNumber0 @ SV20 ) )
| ~ ( ( ( sdtasdt0 @ SV1 @ ( sdtpldt0 @ SV11 @ SV20 ) )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV1 @ SV11 ) @ ( sdtasdt0 @ SV1 @ SV20 ) ) )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SV11 @ SV20 ) @ SV1 )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV11 @ SV1 ) @ ( sdtasdt0 @ SV20 @ SV1 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(121,plain,
! [SV21: $i,SV12: $i,SV2: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SV2 )
| ~ ( aNaturalNumber0 @ SV12 ) )
| ~ ( aNaturalNumber0 @ SV21 ) )
| ( ( sdtpldt0 @ ( sdtpldt0 @ SV2 @ SV12 ) @ SV21 )
= ( sdtpldt0 @ SV2 @ ( sdtpldt0 @ SV12 @ SV21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(122,plain,
! [SV3: $i] :
( ( ( aNaturalNumber0 @ SV3 )
= $false )
| ( ( ~ ( ( ( sdtpldt0 @ SV3 @ sz00 )
!= SV3 )
| ( SV3
!= ( sdtpldt0 @ sz00 @ SV3 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(123,plain,
! [SV22: $i,SV13: $i,SV4: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SV4 )
| ~ ( aNaturalNumber0 @ SV13 ) )
| ~ ( aNaturalNumber0 @ SV22 ) )
| ~ ~ ( ~ ( doDivides0 @ SV4 @ SV13 )
| ~ ( doDivides0 @ SV4 @ ( sdtpldt0 @ SV13 @ SV22 ) ) )
| ( doDivides0 @ SV4 @ SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(124,plain,
( ( ~ ( ~ ( aNaturalNumber0 @ xn )
| ~ ( aNaturalNumber0 @ xm ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[106]) ).
thf(125,plain,
( ( aNaturalNumber0 @ xp )
= $true ),
inference(extcnf_not_neg,[status(thm)],[107]) ).
thf(126,plain,
( ( ~ ( ~ ( ( xr != xn ) )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aNaturalNumber0 @ SX0 )
| ( ( sdtpldt0 @ xr @ SX0 )
!= xn ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[108]) ).
thf(127,plain,
( ( sdtlseqdt0 @ xr @ xn )
= $true ),
inference(extcnf_not_neg,[status(thm)],[109]) ).
thf(128,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( aNaturalNumber0 @ SX0 )
| ( ( sdtpldt0 @ xp @ SX0 )
!= xn ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[110]) ).
thf(129,plain,
( ( sdtlseqdt0 @ xp @ xn )
= $true ),
inference(extcnf_not_neg,[status(thm)],[111]) ).
thf(130,plain,
( ( ~ ( ~ ( aNaturalNumber0 @ xr )
| ( ( sdtpldt0 @ xp @ xr )
!= xn ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[112]) ).
thf(131,plain,
( ( xr
= ( sdtmndt0 @ xn @ xp ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[113]) ).
thf(132,plain,
! [SV23: $i,SV14: $i,SV5: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SV5 )
| ~ ( aNaturalNumber0 @ SV14 ) )
| ~ ( aNaturalNumber0 @ SV23 ) )
| ~ ( ( ( sdtpldt0 @ SV5 @ SV14 )
= ( sdtpldt0 @ SV5 @ SV23 ) )
| ( ( sdtpldt0 @ SV14 @ SV5 )
= ( sdtpldt0 @ SV23 @ SV5 ) ) )
| ( SV14 = SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(133,plain,
! [SV15: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ( aNaturalNumber0 @ SV6 )
| ~ ( aNaturalNumber0 @ SV15 ) ) )
= $true )
| ( ( ( sdtpldt0 @ SV6 @ SV15 )
= ( sdtpldt0 @ SV15 @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[115]) ).
thf(134,plain,
! [SV16: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ( aNaturalNumber0 @ SV7 )
| ~ ( aNaturalNumber0 @ SV16 ) ) )
= $true )
| ( ( ( ( sdtpldt0 @ SV7 @ SV16 )
!= sz00 )
| ~ ( ( SV7 != sz00 )
| ( SV16 != sz00 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[116]) ).
thf(135,plain,
! [SV24: $i,SV17: $i,SV8: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SV8 )
| ~ ( aNaturalNumber0 @ SV17 ) )
| ~ ( aNaturalNumber0 @ SV24 ) )
| ~ ~ ( ~ ( doDivides0 @ SV8 @ SV17 )
| ~ ( doDivides0 @ SV8 @ SV24 ) )
| ( doDivides0 @ SV8 @ ( sdtpldt0 @ SV17 @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(136,plain,
! [SV18: $i,SV9: $i] :
( ( ( ~ ~ ( ~ ( aNaturalNumber0 @ SV9 )
| ~ ( aNaturalNumber0 @ SV18 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( ( SV9 != SV18 ) )
| ~ ( sdtlseqdt0 @ SV9 @ SV18 ) )
| ! [SY47: $i] :
( ~ ( aNaturalNumber0 @ SY47 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sdtpldt0 @ SY47 @ SV9 )
!= ( sdtpldt0 @ SY47 @ SV18 ) ) )
| ~ ( sdtlseqdt0 @ ( sdtpldt0 @ SY47 @ SV9 ) @ ( sdtpldt0 @ SY47 @ SV18 ) ) )
| ~ ( ( ( sdtpldt0 @ SV9 @ SY47 )
!= ( sdtpldt0 @ SV18 @ SY47 ) ) ) )
| ~ ( sdtlseqdt0 @ ( sdtpldt0 @ SV9 @ SY47 ) @ ( sdtpldt0 @ SV18 @ SY47 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[118]) ).
thf(137,plain,
! [SV19: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ( aNaturalNumber0 @ SV10 )
| ~ ( aNaturalNumber0 @ SV19 ) ) )
= $true )
| ( ( aNaturalNumber0 @ ( sdtpldt0 @ SV10 @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[119]) ).
thf(138,plain,
! [SV20: $i,SV11: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SV1 )
| ~ ( aNaturalNumber0 @ SV11 ) )
| ~ ( aNaturalNumber0 @ SV20 ) ) )
= $true )
| ( ( ~ ( ( ( sdtasdt0 @ SV1 @ ( sdtpldt0 @ SV11 @ SV20 ) )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV1 @ SV11 ) @ ( sdtasdt0 @ SV1 @ SV20 ) ) )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SV11 @ SV20 ) @ SV1 )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV11 @ SV1 ) @ ( sdtasdt0 @ SV20 @ SV1 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[120]) ).
thf(139,plain,
! [SV21: $i,SV12: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SV2 )
| ~ ( aNaturalNumber0 @ SV12 ) )
| ~ ( aNaturalNumber0 @ SV21 ) ) )
= $true )
| ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV2 @ SV12 ) @ SV21 )
= ( sdtpldt0 @ SV2 @ ( sdtpldt0 @ SV12 @ SV21 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[121]) ).
thf(140,plain,
! [SV3: $i] :
( ( ( ( ( sdtpldt0 @ SV3 @ sz00 )
!= SV3 )
| ( SV3
!= ( sdtpldt0 @ sz00 @ SV3 ) ) )
= $false )
| ( ( aNaturalNumber0 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(141,plain,
! [SV22: $i,SV13: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SV4 )
| ~ ( aNaturalNumber0 @ SV13 ) )
| ~ ( aNaturalNumber0 @ SV22 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( doDivides0 @ SV4 @ SV13 )
| ~ ( doDivides0 @ SV4 @ ( sdtpldt0 @ SV13 @ SV22 ) ) )
| ( doDivides0 @ SV4 @ SV22 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[123]) ).
thf(142,plain,
( ( ~ ( aNaturalNumber0 @ xn )
| ~ ( aNaturalNumber0 @ xm ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(143,plain,
( ( ~ ( ( xr != xn ) )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aNaturalNumber0 @ SX0 )
| ( ( sdtpldt0 @ xr @ SX0 )
!= xn ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(144,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( aNaturalNumber0 @ SX0 )
| ( ( sdtpldt0 @ xp @ SX0 )
!= xn ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(145,plain,
( ( ~ ( aNaturalNumber0 @ xr )
| ( ( sdtpldt0 @ xp @ xr )
!= xn ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(146,plain,
! [SV23: $i,SV14: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SV5 )
| ~ ( aNaturalNumber0 @ SV14 ) )
| ~ ( aNaturalNumber0 @ SV23 ) ) )
= $true )
| ( ( ~ ( ( ( sdtpldt0 @ SV5 @ SV14 )
= ( sdtpldt0 @ SV5 @ SV23 ) )
| ( ( sdtpldt0 @ SV14 @ SV5 )
= ( sdtpldt0 @ SV23 @ SV5 ) ) )
| ( SV14 = SV23 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[132]) ).
thf(147,plain,
! [SV15: $i,SV6: $i] :
( ( ( ~ ( ~ ( aNaturalNumber0 @ SV6 )
| ~ ( aNaturalNumber0 @ SV15 ) ) )
= $false )
| ( ( ( sdtpldt0 @ SV6 @ SV15 )
= ( sdtpldt0 @ SV15 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(148,plain,
! [SV16: $i,SV7: $i] :
( ( ( ~ ( ~ ( aNaturalNumber0 @ SV7 )
| ~ ( aNaturalNumber0 @ SV16 ) ) )
= $false )
| ( ( ( ( sdtpldt0 @ SV7 @ SV16 )
!= sz00 )
| ~ ( ( SV7 != sz00 )
| ( SV16 != sz00 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(149,plain,
! [SV24: $i,SV17: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SV8 )
| ~ ( aNaturalNumber0 @ SV17 ) )
| ~ ( aNaturalNumber0 @ SV24 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( doDivides0 @ SV8 @ SV17 )
| ~ ( doDivides0 @ SV8 @ SV24 ) )
| ( doDivides0 @ SV8 @ ( sdtpldt0 @ SV17 @ SV24 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[135]) ).
thf(150,plain,
! [SV18: $i,SV9: $i] :
( ( ( ~ ( ~ ( aNaturalNumber0 @ SV9 )
| ~ ( aNaturalNumber0 @ SV18 ) ) )
= $false )
| ( ( ~ ~ ( ~ ( ( SV9 != SV18 ) )
| ~ ( sdtlseqdt0 @ SV9 @ SV18 ) )
| ! [SY47: $i] :
( ~ ( aNaturalNumber0 @ SY47 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sdtpldt0 @ SY47 @ SV9 )
!= ( sdtpldt0 @ SY47 @ SV18 ) ) )
| ~ ( sdtlseqdt0 @ ( sdtpldt0 @ SY47 @ SV9 ) @ ( sdtpldt0 @ SY47 @ SV18 ) ) )
| ~ ( ( ( sdtpldt0 @ SV9 @ SY47 )
!= ( sdtpldt0 @ SV18 @ SY47 ) ) ) )
| ~ ( sdtlseqdt0 @ ( sdtpldt0 @ SV9 @ SY47 ) @ ( sdtpldt0 @ SV18 @ SY47 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(151,plain,
! [SV19: $i,SV10: $i] :
( ( ( ~ ( ~ ( aNaturalNumber0 @ SV10 )
| ~ ( aNaturalNumber0 @ SV19 ) ) )
= $false )
| ( ( aNaturalNumber0 @ ( sdtpldt0 @ SV10 @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(152,plain,
! [SV20: $i,SV11: $i,SV1: $i] :
( ( ( ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SV1 )
| ~ ( aNaturalNumber0 @ SV11 ) )
| ~ ( aNaturalNumber0 @ SV20 ) ) )
= $false )
| ( ( ~ ( ( ( sdtasdt0 @ SV1 @ ( sdtpldt0 @ SV11 @ SV20 ) )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV1 @ SV11 ) @ ( sdtasdt0 @ SV1 @ SV20 ) ) )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SV11 @ SV20 ) @ SV1 )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV11 @ SV1 ) @ ( sdtasdt0 @ SV20 @ SV1 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(153,plain,
! [SV21: $i,SV12: $i,SV2: $i] :
( ( ( ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SV2 )
| ~ ( aNaturalNumber0 @ SV12 ) )
| ~ ( aNaturalNumber0 @ SV21 ) ) )
= $false )
| ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV2 @ SV12 ) @ SV21 )
= ( sdtpldt0 @ SV2 @ ( sdtpldt0 @ SV12 @ SV21 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(154,plain,
! [SV3: $i] :
( ( ( ( sdtpldt0 @ SV3 @ sz00 )
!= SV3 )
= $false )
| ( ( aNaturalNumber0 @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[140]) ).
thf(155,plain,
! [SV3: $i] :
( ( ( SV3
!= ( sdtpldt0 @ sz00 @ SV3 ) )
= $false )
| ( ( aNaturalNumber0 @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[140]) ).
thf(156,plain,
! [SV22: $i,SV13: $i,SV4: $i] :
( ( ( ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SV4 )
| ~ ( aNaturalNumber0 @ SV13 ) )
| ~ ( aNaturalNumber0 @ SV22 ) ) )
= $false )
| ( ( ~ ~ ( ~ ( doDivides0 @ SV4 @ SV13 )
| ~ ( doDivides0 @ SV4 @ ( sdtpldt0 @ SV13 @ SV22 ) ) )
| ( doDivides0 @ SV4 @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(157,plain,
( ( ~ ( aNaturalNumber0 @ xn ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[142]) ).
thf(158,plain,
( ( ~ ( aNaturalNumber0 @ xm ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[142]) ).
thf(159,plain,
( ( ~ ( ( xr != xn ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[143]) ).
thf(160,plain,
( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aNaturalNumber0 @ SX0 )
| ( ( sdtpldt0 @ xr @ SX0 )
!= xn ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[143]) ).
thf(161,plain,
( ( ~ ~ ( ~ ( aNaturalNumber0 @ sK1_SX0 )
| ( ( sdtpldt0 @ xp @ sK1_SX0 )
!= xn ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[144]) ).
thf(162,plain,
( ( ~ ( aNaturalNumber0 @ xr ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[145]) ).
thf(163,plain,
( ( ( sdtpldt0 @ xp @ xr )
!= xn )
= $false ),
inference(extcnf_or_neg,[status(thm)],[145]) ).
thf(164,plain,
! [SV23: $i,SV14: $i,SV5: $i] :
( ( ( ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SV5 )
| ~ ( aNaturalNumber0 @ SV14 ) )
| ~ ( aNaturalNumber0 @ SV23 ) ) )
= $false )
| ( ( ~ ( ( ( sdtpldt0 @ SV5 @ SV14 )
= ( sdtpldt0 @ SV5 @ SV23 ) )
| ( ( sdtpldt0 @ SV14 @ SV5 )
= ( sdtpldt0 @ SV23 @ SV5 ) ) )
| ( SV14 = SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(165,plain,
! [SV15: $i,SV6: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV6 )
| ~ ( aNaturalNumber0 @ SV15 ) )
= $true )
| ( ( ( sdtpldt0 @ SV6 @ SV15 )
= ( sdtpldt0 @ SV15 @ SV6 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[147]) ).
thf(166,plain,
! [SV16: $i,SV7: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV7 )
| ~ ( aNaturalNumber0 @ SV16 ) )
= $true )
| ( ( ( ( sdtpldt0 @ SV7 @ SV16 )
!= sz00 )
| ~ ( ( SV7 != sz00 )
| ( SV16 != sz00 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[148]) ).
thf(167,plain,
! [SV24: $i,SV17: $i,SV8: $i] :
( ( ( ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SV8 )
| ~ ( aNaturalNumber0 @ SV17 ) )
| ~ ( aNaturalNumber0 @ SV24 ) ) )
= $false )
| ( ( ~ ~ ( ~ ( doDivides0 @ SV8 @ SV17 )
| ~ ( doDivides0 @ SV8 @ SV24 ) )
| ( doDivides0 @ SV8 @ ( sdtpldt0 @ SV17 @ SV24 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(168,plain,
! [SV18: $i,SV9: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV9 )
| ~ ( aNaturalNumber0 @ SV18 ) )
= $true )
| ( ( ~ ~ ( ~ ( ( SV9 != SV18 ) )
| ~ ( sdtlseqdt0 @ SV9 @ SV18 ) )
| ! [SY47: $i] :
( ~ ( aNaturalNumber0 @ SY47 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sdtpldt0 @ SY47 @ SV9 )
!= ( sdtpldt0 @ SY47 @ SV18 ) ) )
| ~ ( sdtlseqdt0 @ ( sdtpldt0 @ SY47 @ SV9 ) @ ( sdtpldt0 @ SY47 @ SV18 ) ) )
| ~ ( ( ( sdtpldt0 @ SV9 @ SY47 )
!= ( sdtpldt0 @ SV18 @ SY47 ) ) ) )
| ~ ( sdtlseqdt0 @ ( sdtpldt0 @ SV9 @ SY47 ) @ ( sdtpldt0 @ SV18 @ SY47 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[150]) ).
thf(169,plain,
! [SV19: $i,SV10: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV10 )
| ~ ( aNaturalNumber0 @ SV19 ) )
= $true )
| ( ( aNaturalNumber0 @ ( sdtpldt0 @ SV10 @ SV19 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[151]) ).
thf(170,plain,
! [SV20: $i,SV11: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ( aNaturalNumber0 @ SV1 )
| ~ ( aNaturalNumber0 @ SV11 ) )
| ~ ( aNaturalNumber0 @ SV20 ) )
= $true )
| ( ( ~ ( ( ( sdtasdt0 @ SV1 @ ( sdtpldt0 @ SV11 @ SV20 ) )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV1 @ SV11 ) @ ( sdtasdt0 @ SV1 @ SV20 ) ) )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SV11 @ SV20 ) @ SV1 )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV11 @ SV1 ) @ ( sdtasdt0 @ SV20 @ SV1 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[152]) ).
thf(171,plain,
! [SV21: $i,SV12: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ( aNaturalNumber0 @ SV2 )
| ~ ( aNaturalNumber0 @ SV12 ) )
| ~ ( aNaturalNumber0 @ SV21 ) )
= $true )
| ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV2 @ SV12 ) @ SV21 )
= ( sdtpldt0 @ SV2 @ ( sdtpldt0 @ SV12 @ SV21 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[153]) ).
thf(172,plain,
! [SV3: $i] :
( ( ( ( sdtpldt0 @ SV3 @ sz00 )
= SV3 )
= $true )
| ( ( aNaturalNumber0 @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[154]) ).
thf(173,plain,
! [SV3: $i] :
( ( ( SV3
= ( sdtpldt0 @ sz00 @ SV3 ) )
= $true )
| ( ( aNaturalNumber0 @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[155]) ).
thf(174,plain,
! [SV22: $i,SV13: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( aNaturalNumber0 @ SV4 )
| ~ ( aNaturalNumber0 @ SV13 ) )
| ~ ( aNaturalNumber0 @ SV22 ) )
= $true )
| ( ( ~ ~ ( ~ ( doDivides0 @ SV4 @ SV13 )
| ~ ( doDivides0 @ SV4 @ ( sdtpldt0 @ SV13 @ SV22 ) ) )
| ( doDivides0 @ SV4 @ SV22 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[156]) ).
thf(175,plain,
( ( aNaturalNumber0 @ xn )
= $true ),
inference(extcnf_not_neg,[status(thm)],[157]) ).
thf(176,plain,
( ( aNaturalNumber0 @ xm )
= $true ),
inference(extcnf_not_neg,[status(thm)],[158]) ).
thf(177,plain,
( ( xr != xn )
= $true ),
inference(extcnf_not_neg,[status(thm)],[159]) ).
thf(178,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( aNaturalNumber0 @ SX0 )
| ( ( sdtpldt0 @ xr @ SX0 )
!= xn ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[160]) ).
thf(179,plain,
( ( ~ ( ~ ( aNaturalNumber0 @ sK1_SX0 )
| ( ( sdtpldt0 @ xp @ sK1_SX0 )
!= xn ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[161]) ).
thf(180,plain,
( ( aNaturalNumber0 @ xr )
= $true ),
inference(extcnf_not_neg,[status(thm)],[162]) ).
thf(181,plain,
( ( ( sdtpldt0 @ xp @ xr )
= xn )
= $true ),
inference(extcnf_not_neg,[status(thm)],[163]) ).
thf(182,plain,
! [SV23: $i,SV14: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ( aNaturalNumber0 @ SV5 )
| ~ ( aNaturalNumber0 @ SV14 ) )
| ~ ( aNaturalNumber0 @ SV23 ) )
= $true )
| ( ( ~ ( ( ( sdtpldt0 @ SV5 @ SV14 )
= ( sdtpldt0 @ SV5 @ SV23 ) )
| ( ( sdtpldt0 @ SV14 @ SV5 )
= ( sdtpldt0 @ SV23 @ SV5 ) ) )
| ( SV14 = SV23 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[164]) ).
thf(183,plain,
! [SV15: $i,SV6: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV6 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV15 ) )
= $true )
| ( ( ( sdtpldt0 @ SV6 @ SV15 )
= ( sdtpldt0 @ SV15 @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[165]) ).
thf(184,plain,
! [SV16: $i,SV7: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV7 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV16 ) )
= $true )
| ( ( ( ( sdtpldt0 @ SV7 @ SV16 )
!= sz00 )
| ~ ( ( SV7 != sz00 )
| ( SV16 != sz00 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(185,plain,
! [SV24: $i,SV17: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ( aNaturalNumber0 @ SV8 )
| ~ ( aNaturalNumber0 @ SV17 ) )
| ~ ( aNaturalNumber0 @ SV24 ) )
= $true )
| ( ( ~ ~ ( ~ ( doDivides0 @ SV8 @ SV17 )
| ~ ( doDivides0 @ SV8 @ SV24 ) )
| ( doDivides0 @ SV8 @ ( sdtpldt0 @ SV17 @ SV24 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[167]) ).
thf(186,plain,
! [SV18: $i,SV9: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV9 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV18 ) )
= $true )
| ( ( ~ ~ ( ~ ( ( SV9 != SV18 ) )
| ~ ( sdtlseqdt0 @ SV9 @ SV18 ) )
| ! [SY47: $i] :
( ~ ( aNaturalNumber0 @ SY47 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sdtpldt0 @ SY47 @ SV9 )
!= ( sdtpldt0 @ SY47 @ SV18 ) ) )
| ~ ( sdtlseqdt0 @ ( sdtpldt0 @ SY47 @ SV9 ) @ ( sdtpldt0 @ SY47 @ SV18 ) ) )
| ~ ( ( ( sdtpldt0 @ SV9 @ SY47 )
!= ( sdtpldt0 @ SV18 @ SY47 ) ) ) )
| ~ ( sdtlseqdt0 @ ( sdtpldt0 @ SV9 @ SY47 ) @ ( sdtpldt0 @ SV18 @ SY47 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[168]) ).
thf(187,plain,
! [SV19: $i,SV10: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV10 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV19 ) )
= $true )
| ( ( aNaturalNumber0 @ ( sdtpldt0 @ SV10 @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[169]) ).
thf(188,plain,
! [SV20: $i,SV11: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ( aNaturalNumber0 @ SV1 )
| ~ ( aNaturalNumber0 @ SV11 ) ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV20 ) )
= $true )
| ( ( ~ ( ( ( sdtasdt0 @ SV1 @ ( sdtpldt0 @ SV11 @ SV20 ) )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV1 @ SV11 ) @ ( sdtasdt0 @ SV1 @ SV20 ) ) )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SV11 @ SV20 ) @ SV1 )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV11 @ SV1 ) @ ( sdtasdt0 @ SV20 @ SV1 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[170]) ).
thf(189,plain,
! [SV21: $i,SV12: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ( aNaturalNumber0 @ SV2 )
| ~ ( aNaturalNumber0 @ SV12 ) ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV21 ) )
= $true )
| ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV2 @ SV12 ) @ SV21 )
= ( sdtpldt0 @ SV2 @ ( sdtpldt0 @ SV12 @ SV21 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[171]) ).
thf(190,plain,
! [SV22: $i,SV13: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( aNaturalNumber0 @ SV4 )
| ~ ( aNaturalNumber0 @ SV13 ) ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV22 ) )
= $true )
| ( ( ~ ~ ( ~ ( doDivides0 @ SV4 @ SV13 )
| ~ ( doDivides0 @ SV4 @ ( sdtpldt0 @ SV13 @ SV22 ) ) )
| ( doDivides0 @ SV4 @ SV22 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[174]) ).
thf(191,plain,
( ( xr = xn )
= $false ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(192,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( aNaturalNumber0 @ SX0 )
| ( ( sdtpldt0 @ xr @ SX0 )
!= xn ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(193,plain,
( ( ~ ( aNaturalNumber0 @ sK1_SX0 )
| ( ( sdtpldt0 @ xp @ sK1_SX0 )
!= xn ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(194,plain,
! [SV23: $i,SV14: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ( aNaturalNumber0 @ SV5 )
| ~ ( aNaturalNumber0 @ SV14 ) ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV23 ) )
= $true )
| ( ( ~ ( ( ( sdtpldt0 @ SV5 @ SV14 )
= ( sdtpldt0 @ SV5 @ SV23 ) )
| ( ( sdtpldt0 @ SV14 @ SV5 )
= ( sdtpldt0 @ SV23 @ SV5 ) ) )
| ( SV14 = SV23 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[182]) ).
thf(195,plain,
! [SV15: $i,SV6: $i] :
( ( ( aNaturalNumber0 @ SV6 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV15 ) )
= $true )
| ( ( ( sdtpldt0 @ SV6 @ SV15 )
= ( sdtpldt0 @ SV15 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[183]) ).
thf(196,plain,
! [SV16: $i,SV7: $i] :
( ( ( aNaturalNumber0 @ SV7 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV16 ) )
= $true )
| ( ( ( ( sdtpldt0 @ SV7 @ SV16 )
!= sz00 )
| ~ ( ( SV7 != sz00 )
| ( SV16 != sz00 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[184]) ).
thf(197,plain,
! [SV24: $i,SV17: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ( aNaturalNumber0 @ SV8 )
| ~ ( aNaturalNumber0 @ SV17 ) ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV24 ) )
= $true )
| ( ( ~ ~ ( ~ ( doDivides0 @ SV8 @ SV17 )
| ~ ( doDivides0 @ SV8 @ SV24 ) )
| ( doDivides0 @ SV8 @ ( sdtpldt0 @ SV17 @ SV24 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[185]) ).
thf(198,plain,
! [SV18: $i,SV9: $i] :
( ( ( aNaturalNumber0 @ SV9 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV18 ) )
= $true )
| ( ( ~ ~ ( ~ ( ( SV9 != SV18 ) )
| ~ ( sdtlseqdt0 @ SV9 @ SV18 ) )
| ! [SY47: $i] :
( ~ ( aNaturalNumber0 @ SY47 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sdtpldt0 @ SY47 @ SV9 )
!= ( sdtpldt0 @ SY47 @ SV18 ) ) )
| ~ ( sdtlseqdt0 @ ( sdtpldt0 @ SY47 @ SV9 ) @ ( sdtpldt0 @ SY47 @ SV18 ) ) )
| ~ ( ( ( sdtpldt0 @ SV9 @ SY47 )
!= ( sdtpldt0 @ SV18 @ SY47 ) ) ) )
| ~ ( sdtlseqdt0 @ ( sdtpldt0 @ SV9 @ SY47 ) @ ( sdtpldt0 @ SV18 @ SY47 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[186]) ).
thf(199,plain,
! [SV19: $i,SV10: $i] :
( ( ( aNaturalNumber0 @ SV10 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV19 ) )
= $true )
| ( ( aNaturalNumber0 @ ( sdtpldt0 @ SV10 @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[187]) ).
thf(200,plain,
! [SV20: $i,SV11: $i,SV1: $i] :
( ( ( ~ ( ~ ( aNaturalNumber0 @ SV1 )
| ~ ( aNaturalNumber0 @ SV11 ) ) )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV20 ) )
= $true )
| ( ( ~ ( ( ( sdtasdt0 @ SV1 @ ( sdtpldt0 @ SV11 @ SV20 ) )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV1 @ SV11 ) @ ( sdtasdt0 @ SV1 @ SV20 ) ) )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SV11 @ SV20 ) @ SV1 )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV11 @ SV1 ) @ ( sdtasdt0 @ SV20 @ SV1 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[188]) ).
thf(201,plain,
! [SV21: $i,SV12: $i,SV2: $i] :
( ( ( ~ ( ~ ( aNaturalNumber0 @ SV2 )
| ~ ( aNaturalNumber0 @ SV12 ) ) )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV21 ) )
= $true )
| ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV2 @ SV12 ) @ SV21 )
= ( sdtpldt0 @ SV2 @ ( sdtpldt0 @ SV12 @ SV21 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(202,plain,
! [SV22: $i,SV13: $i,SV4: $i] :
( ( ( ~ ( ~ ( aNaturalNumber0 @ SV4 )
| ~ ( aNaturalNumber0 @ SV13 ) ) )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV22 ) )
= $true )
| ( ( ~ ~ ( ~ ( doDivides0 @ SV4 @ SV13 )
| ~ ( doDivides0 @ SV4 @ ( sdtpldt0 @ SV13 @ SV22 ) ) )
| ( doDivides0 @ SV4 @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(203,plain,
( ( ~ ~ ( ~ ( aNaturalNumber0 @ sK2_SX0 )
| ( ( sdtpldt0 @ xr @ sK2_SX0 )
!= xn ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[192]) ).
thf(204,plain,
( ( ~ ( aNaturalNumber0 @ sK1_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[193]) ).
thf(205,plain,
( ( ( sdtpldt0 @ xp @ sK1_SX0 )
!= xn )
= $false ),
inference(extcnf_or_neg,[status(thm)],[193]) ).
thf(206,plain,
! [SV23: $i,SV14: $i,SV5: $i] :
( ( ( ~ ( ~ ( aNaturalNumber0 @ SV5 )
| ~ ( aNaturalNumber0 @ SV14 ) ) )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV23 ) )
= $true )
| ( ( ~ ( ( ( sdtpldt0 @ SV5 @ SV14 )
= ( sdtpldt0 @ SV5 @ SV23 ) )
| ( ( sdtpldt0 @ SV14 @ SV5 )
= ( sdtpldt0 @ SV23 @ SV5 ) ) )
| ( SV14 = SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(207,plain,
! [SV6: $i,SV15: $i] :
( ( ( aNaturalNumber0 @ SV15 )
= $false )
| ( ( aNaturalNumber0 @ SV6 )
= $false )
| ( ( ( sdtpldt0 @ SV6 @ SV15 )
= ( sdtpldt0 @ SV15 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(208,plain,
! [SV7: $i,SV16: $i] :
( ( ( aNaturalNumber0 @ SV16 )
= $false )
| ( ( aNaturalNumber0 @ SV7 )
= $false )
| ( ( ( ( sdtpldt0 @ SV7 @ SV16 )
!= sz00 )
| ~ ( ( SV7 != sz00 )
| ( SV16 != sz00 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(209,plain,
! [SV24: $i,SV17: $i,SV8: $i] :
( ( ( ~ ( ~ ( aNaturalNumber0 @ SV8 )
| ~ ( aNaturalNumber0 @ SV17 ) ) )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV24 ) )
= $true )
| ( ( ~ ~ ( ~ ( doDivides0 @ SV8 @ SV17 )
| ~ ( doDivides0 @ SV8 @ SV24 ) )
| ( doDivides0 @ SV8 @ ( sdtpldt0 @ SV17 @ SV24 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(210,plain,
! [SV9: $i,SV18: $i] :
( ( ( aNaturalNumber0 @ SV18 )
= $false )
| ( ( aNaturalNumber0 @ SV9 )
= $false )
| ( ( ~ ~ ( ~ ( ( SV9 != SV18 ) )
| ~ ( sdtlseqdt0 @ SV9 @ SV18 ) )
| ! [SY47: $i] :
( ~ ( aNaturalNumber0 @ SY47 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sdtpldt0 @ SY47 @ SV9 )
!= ( sdtpldt0 @ SY47 @ SV18 ) ) )
| ~ ( sdtlseqdt0 @ ( sdtpldt0 @ SY47 @ SV9 ) @ ( sdtpldt0 @ SY47 @ SV18 ) ) )
| ~ ( ( ( sdtpldt0 @ SV9 @ SY47 )
!= ( sdtpldt0 @ SV18 @ SY47 ) ) ) )
| ~ ( sdtlseqdt0 @ ( sdtpldt0 @ SV9 @ SY47 ) @ ( sdtpldt0 @ SV18 @ SY47 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[198]) ).
thf(211,plain,
! [SV10: $i,SV19: $i] :
( ( ( aNaturalNumber0 @ SV19 )
= $false )
| ( ( aNaturalNumber0 @ SV10 )
= $false )
| ( ( aNaturalNumber0 @ ( sdtpldt0 @ SV10 @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[199]) ).
thf(212,plain,
! [SV20: $i,SV11: $i,SV1: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV1 )
| ~ ( aNaturalNumber0 @ SV11 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV20 ) )
= $true )
| ( ( ~ ( ( ( sdtasdt0 @ SV1 @ ( sdtpldt0 @ SV11 @ SV20 ) )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV1 @ SV11 ) @ ( sdtasdt0 @ SV1 @ SV20 ) ) )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SV11 @ SV20 ) @ SV1 )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV11 @ SV1 ) @ ( sdtasdt0 @ SV20 @ SV1 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[200]) ).
thf(213,plain,
! [SV21: $i,SV12: $i,SV2: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV2 )
| ~ ( aNaturalNumber0 @ SV12 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV21 ) )
= $true )
| ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV2 @ SV12 ) @ SV21 )
= ( sdtpldt0 @ SV2 @ ( sdtpldt0 @ SV12 @ SV21 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[201]) ).
thf(214,plain,
! [SV22: $i,SV13: $i,SV4: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV4 )
| ~ ( aNaturalNumber0 @ SV13 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV22 ) )
= $true )
| ( ( ~ ~ ( ~ ( doDivides0 @ SV4 @ SV13 )
| ~ ( doDivides0 @ SV4 @ ( sdtpldt0 @ SV13 @ SV22 ) ) )
| ( doDivides0 @ SV4 @ SV22 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[202]) ).
thf(215,plain,
( ( ~ ( ~ ( aNaturalNumber0 @ sK2_SX0 )
| ( ( sdtpldt0 @ xr @ sK2_SX0 )
!= xn ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[203]) ).
thf(216,plain,
( ( aNaturalNumber0 @ sK1_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[204]) ).
thf(217,plain,
( ( ( sdtpldt0 @ xp @ sK1_SX0 )
= xn )
= $true ),
inference(extcnf_not_neg,[status(thm)],[205]) ).
thf(218,plain,
! [SV23: $i,SV14: $i,SV5: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV5 )
| ~ ( aNaturalNumber0 @ SV14 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV23 ) )
= $true )
| ( ( ~ ( ( ( sdtpldt0 @ SV5 @ SV14 )
= ( sdtpldt0 @ SV5 @ SV23 ) )
| ( ( sdtpldt0 @ SV14 @ SV5 )
= ( sdtpldt0 @ SV23 @ SV5 ) ) )
| ( SV14 = SV23 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[206]) ).
thf(219,plain,
! [SV16: $i,SV7: $i] :
( ( ( ( sdtpldt0 @ SV7 @ SV16 )
!= sz00 )
= $true )
| ( ( ~ ( ( SV7 != sz00 )
| ( SV16 != sz00 ) ) )
= $true )
| ( ( aNaturalNumber0 @ SV7 )
= $false )
| ( ( aNaturalNumber0 @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[208]) ).
thf(220,plain,
! [SV24: $i,SV17: $i,SV8: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV8 )
| ~ ( aNaturalNumber0 @ SV17 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV24 ) )
= $true )
| ( ( ~ ~ ( ~ ( doDivides0 @ SV8 @ SV17 )
| ~ ( doDivides0 @ SV8 @ SV24 ) )
| ( doDivides0 @ SV8 @ ( sdtpldt0 @ SV17 @ SV24 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[209]) ).
thf(221,plain,
! [SV18: $i,SV9: $i] :
( ( ( ~ ~ ( ~ ( ( SV9 != SV18 ) )
| ~ ( sdtlseqdt0 @ SV9 @ SV18 ) ) )
= $true )
| ( ( ! [SY47: $i] :
( ~ ( aNaturalNumber0 @ SY47 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sdtpldt0 @ SY47 @ SV9 )
!= ( sdtpldt0 @ SY47 @ SV18 ) ) )
| ~ ( sdtlseqdt0 @ ( sdtpldt0 @ SY47 @ SV9 ) @ ( sdtpldt0 @ SY47 @ SV18 ) ) )
| ~ ( ( ( sdtpldt0 @ SV9 @ SY47 )
!= ( sdtpldt0 @ SV18 @ SY47 ) ) ) )
| ~ ( sdtlseqdt0 @ ( sdtpldt0 @ SV9 @ SY47 ) @ ( sdtpldt0 @ SV18 @ SY47 ) ) ) ) )
= $true )
| ( ( aNaturalNumber0 @ SV9 )
= $false )
| ( ( aNaturalNumber0 @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[210]) ).
thf(222,plain,
! [SV20: $i,SV11: $i,SV1: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV1 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV11 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV20 ) )
= $true )
| ( ( ~ ( ( ( sdtasdt0 @ SV1 @ ( sdtpldt0 @ SV11 @ SV20 ) )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV1 @ SV11 ) @ ( sdtasdt0 @ SV1 @ SV20 ) ) )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SV11 @ SV20 ) @ SV1 )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV11 @ SV1 ) @ ( sdtasdt0 @ SV20 @ SV1 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[212]) ).
thf(223,plain,
! [SV21: $i,SV12: $i,SV2: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV2 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV12 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV21 ) )
= $true )
| ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV2 @ SV12 ) @ SV21 )
= ( sdtpldt0 @ SV2 @ ( sdtpldt0 @ SV12 @ SV21 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[213]) ).
thf(224,plain,
! [SV22: $i,SV13: $i,SV4: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV4 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV13 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV22 ) )
= $true )
| ( ( ~ ~ ( ~ ( doDivides0 @ SV4 @ SV13 )
| ~ ( doDivides0 @ SV4 @ ( sdtpldt0 @ SV13 @ SV22 ) ) )
| ( doDivides0 @ SV4 @ SV22 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[214]) ).
thf(225,plain,
( ( ~ ( aNaturalNumber0 @ sK2_SX0 )
| ( ( sdtpldt0 @ xr @ sK2_SX0 )
!= xn ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[215]) ).
thf(226,plain,
! [SV23: $i,SV14: $i,SV5: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV5 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV14 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV23 ) )
= $true )
| ( ( ~ ( ( ( sdtpldt0 @ SV5 @ SV14 )
= ( sdtpldt0 @ SV5 @ SV23 ) )
| ( ( sdtpldt0 @ SV14 @ SV5 )
= ( sdtpldt0 @ SV23 @ SV5 ) ) )
| ( SV14 = SV23 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[218]) ).
thf(227,plain,
! [SV16: $i,SV7: $i] :
( ( ( ( sdtpldt0 @ SV7 @ SV16 )
= sz00 )
= $false )
| ( ( ~ ( ( SV7 != sz00 )
| ( SV16 != sz00 ) ) )
= $true )
| ( ( aNaturalNumber0 @ SV7 )
= $false )
| ( ( aNaturalNumber0 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[219]) ).
thf(228,plain,
! [SV24: $i,SV17: $i,SV8: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV8 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV17 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV24 ) )
= $true )
| ( ( ~ ~ ( ~ ( doDivides0 @ SV8 @ SV17 )
| ~ ( doDivides0 @ SV8 @ SV24 ) )
| ( doDivides0 @ SV8 @ ( sdtpldt0 @ SV17 @ SV24 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[220]) ).
thf(229,plain,
! [SV18: $i,SV9: $i] :
( ( ( ~ ( ~ ( ( SV9 != SV18 ) )
| ~ ( sdtlseqdt0 @ SV9 @ SV18 ) ) )
= $false )
| ( ( ! [SY47: $i] :
( ~ ( aNaturalNumber0 @ SY47 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sdtpldt0 @ SY47 @ SV9 )
!= ( sdtpldt0 @ SY47 @ SV18 ) ) )
| ~ ( sdtlseqdt0 @ ( sdtpldt0 @ SY47 @ SV9 ) @ ( sdtpldt0 @ SY47 @ SV18 ) ) )
| ~ ( ( ( sdtpldt0 @ SV9 @ SY47 )
!= ( sdtpldt0 @ SV18 @ SY47 ) ) ) )
| ~ ( sdtlseqdt0 @ ( sdtpldt0 @ SV9 @ SY47 ) @ ( sdtpldt0 @ SV18 @ SY47 ) ) ) ) )
= $true )
| ( ( aNaturalNumber0 @ SV9 )
= $false )
| ( ( aNaturalNumber0 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[221]) ).
thf(230,plain,
! [SV20: $i,SV11: $i,SV1: $i] :
( ( ( aNaturalNumber0 @ SV1 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV11 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV20 ) )
= $true )
| ( ( ~ ( ( ( sdtasdt0 @ SV1 @ ( sdtpldt0 @ SV11 @ SV20 ) )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV1 @ SV11 ) @ ( sdtasdt0 @ SV1 @ SV20 ) ) )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SV11 @ SV20 ) @ SV1 )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV11 @ SV1 ) @ ( sdtasdt0 @ SV20 @ SV1 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[222]) ).
thf(231,plain,
! [SV21: $i,SV12: $i,SV2: $i] :
( ( ( aNaturalNumber0 @ SV2 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV12 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV21 ) )
= $true )
| ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV2 @ SV12 ) @ SV21 )
= ( sdtpldt0 @ SV2 @ ( sdtpldt0 @ SV12 @ SV21 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[223]) ).
thf(232,plain,
! [SV22: $i,SV13: $i,SV4: $i] :
( ( ( aNaturalNumber0 @ SV4 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV13 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV22 ) )
= $true )
| ( ( ~ ~ ( ~ ( doDivides0 @ SV4 @ SV13 )
| ~ ( doDivides0 @ SV4 @ ( sdtpldt0 @ SV13 @ SV22 ) ) )
| ( doDivides0 @ SV4 @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[224]) ).
thf(233,plain,
( ( ~ ( aNaturalNumber0 @ sK2_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[225]) ).
thf(234,plain,
( ( ( sdtpldt0 @ xr @ sK2_SX0 )
!= xn )
= $false ),
inference(extcnf_or_neg,[status(thm)],[225]) ).
thf(235,plain,
! [SV23: $i,SV14: $i,SV5: $i] :
( ( ( aNaturalNumber0 @ SV5 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV14 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV23 ) )
= $true )
| ( ( ~ ( ( ( sdtpldt0 @ SV5 @ SV14 )
= ( sdtpldt0 @ SV5 @ SV23 ) )
| ( ( sdtpldt0 @ SV14 @ SV5 )
= ( sdtpldt0 @ SV23 @ SV5 ) ) )
| ( SV14 = SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[226]) ).
thf(236,plain,
! [SV16: $i,SV7: $i] :
( ( ( ( SV7 != sz00 )
| ( SV16 != sz00 ) )
= $false )
| ( ( ( sdtpldt0 @ SV7 @ SV16 )
= sz00 )
= $false )
| ( ( aNaturalNumber0 @ SV7 )
= $false )
| ( ( aNaturalNumber0 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[227]) ).
thf(237,plain,
! [SV24: $i,SV17: $i,SV8: $i] :
( ( ( aNaturalNumber0 @ SV8 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV17 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV24 ) )
= $true )
| ( ( ~ ~ ( ~ ( doDivides0 @ SV8 @ SV17 )
| ~ ( doDivides0 @ SV8 @ SV24 ) )
| ( doDivides0 @ SV8 @ ( sdtpldt0 @ SV17 @ SV24 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[228]) ).
thf(238,plain,
! [SV18: $i,SV9: $i] :
( ( ( ~ ( ( SV9 != SV18 ) )
| ~ ( sdtlseqdt0 @ SV9 @ SV18 ) )
= $true )
| ( ( ! [SY47: $i] :
( ~ ( aNaturalNumber0 @ SY47 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sdtpldt0 @ SY47 @ SV9 )
!= ( sdtpldt0 @ SY47 @ SV18 ) ) )
| ~ ( sdtlseqdt0 @ ( sdtpldt0 @ SY47 @ SV9 ) @ ( sdtpldt0 @ SY47 @ SV18 ) ) )
| ~ ( ( ( sdtpldt0 @ SV9 @ SY47 )
!= ( sdtpldt0 @ SV18 @ SY47 ) ) ) )
| ~ ( sdtlseqdt0 @ ( sdtpldt0 @ SV9 @ SY47 ) @ ( sdtpldt0 @ SV18 @ SY47 ) ) ) ) )
= $true )
| ( ( aNaturalNumber0 @ SV9 )
= $false )
| ( ( aNaturalNumber0 @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[229]) ).
thf(239,plain,
! [SV20: $i,SV1: $i,SV11: $i] :
( ( ( aNaturalNumber0 @ SV11 )
= $false )
| ( ( aNaturalNumber0 @ SV1 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV20 ) )
= $true )
| ( ( ~ ( ( ( sdtasdt0 @ SV1 @ ( sdtpldt0 @ SV11 @ SV20 ) )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV1 @ SV11 ) @ ( sdtasdt0 @ SV1 @ SV20 ) ) )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SV11 @ SV20 ) @ SV1 )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV11 @ SV1 ) @ ( sdtasdt0 @ SV20 @ SV1 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[230]) ).
thf(240,plain,
! [SV21: $i,SV2: $i,SV12: $i] :
( ( ( aNaturalNumber0 @ SV12 )
= $false )
| ( ( aNaturalNumber0 @ SV2 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV21 ) )
= $true )
| ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV2 @ SV12 ) @ SV21 )
= ( sdtpldt0 @ SV2 @ ( sdtpldt0 @ SV12 @ SV21 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[231]) ).
thf(241,plain,
! [SV22: $i,SV4: $i,SV13: $i] :
( ( ( aNaturalNumber0 @ SV13 )
= $false )
| ( ( aNaturalNumber0 @ SV4 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV22 ) )
= $true )
| ( ( ~ ~ ( ~ ( doDivides0 @ SV4 @ SV13 )
| ~ ( doDivides0 @ SV4 @ ( sdtpldt0 @ SV13 @ SV22 ) ) )
| ( doDivides0 @ SV4 @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[232]) ).
thf(242,plain,
( ( aNaturalNumber0 @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[233]) ).
thf(243,plain,
( ( ( sdtpldt0 @ xr @ sK2_SX0 )
= xn )
= $true ),
inference(extcnf_not_neg,[status(thm)],[234]) ).
thf(244,plain,
! [SV23: $i,SV5: $i,SV14: $i] :
( ( ( aNaturalNumber0 @ SV14 )
= $false )
| ( ( aNaturalNumber0 @ SV5 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV23 ) )
= $true )
| ( ( ~ ( ( ( sdtpldt0 @ SV5 @ SV14 )
= ( sdtpldt0 @ SV5 @ SV23 ) )
| ( ( sdtpldt0 @ SV14 @ SV5 )
= ( sdtpldt0 @ SV23 @ SV5 ) ) )
| ( SV14 = SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[235]) ).
thf(245,plain,
! [SV16: $i,SV7: $i] :
( ( ( SV7 != sz00 )
= $false )
| ( ( ( sdtpldt0 @ SV7 @ SV16 )
= sz00 )
= $false )
| ( ( aNaturalNumber0 @ SV7 )
= $false )
| ( ( aNaturalNumber0 @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[236]) ).
thf(246,plain,
! [SV7: $i,SV16: $i] :
( ( ( SV16 != sz00 )
= $false )
| ( ( ( sdtpldt0 @ SV7 @ SV16 )
= sz00 )
= $false )
| ( ( aNaturalNumber0 @ SV7 )
= $false )
| ( ( aNaturalNumber0 @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[236]) ).
thf(247,plain,
! [SV24: $i,SV8: $i,SV17: $i] :
( ( ( aNaturalNumber0 @ SV17 )
= $false )
| ( ( aNaturalNumber0 @ SV8 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV24 ) )
= $true )
| ( ( ~ ~ ( ~ ( doDivides0 @ SV8 @ SV17 )
| ~ ( doDivides0 @ SV8 @ SV24 ) )
| ( doDivides0 @ SV8 @ ( sdtpldt0 @ SV17 @ SV24 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[237]) ).
thf(248,plain,
! [SV18: $i,SV9: $i] :
( ( ( ~ ( ( SV9 != SV18 ) ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV9 @ SV18 ) )
= $true )
| ( ( ! [SY47: $i] :
( ~ ( aNaturalNumber0 @ SY47 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sdtpldt0 @ SY47 @ SV9 )
!= ( sdtpldt0 @ SY47 @ SV18 ) ) )
| ~ ( sdtlseqdt0 @ ( sdtpldt0 @ SY47 @ SV9 ) @ ( sdtpldt0 @ SY47 @ SV18 ) ) )
| ~ ( ( ( sdtpldt0 @ SV9 @ SY47 )
!= ( sdtpldt0 @ SV18 @ SY47 ) ) ) )
| ~ ( sdtlseqdt0 @ ( sdtpldt0 @ SV9 @ SY47 ) @ ( sdtpldt0 @ SV18 @ SY47 ) ) ) ) )
= $true )
| ( ( aNaturalNumber0 @ SV9 )
= $false )
| ( ( aNaturalNumber0 @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[238]) ).
thf(249,plain,
! [SV11: $i,SV1: $i,SV20: $i] :
( ( ( aNaturalNumber0 @ SV20 )
= $false )
| ( ( aNaturalNumber0 @ SV1 )
= $false )
| ( ( aNaturalNumber0 @ SV11 )
= $false )
| ( ( ~ ( ( ( sdtasdt0 @ SV1 @ ( sdtpldt0 @ SV11 @ SV20 ) )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV1 @ SV11 ) @ ( sdtasdt0 @ SV1 @ SV20 ) ) )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SV11 @ SV20 ) @ SV1 )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV11 @ SV1 ) @ ( sdtasdt0 @ SV20 @ SV1 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[239]) ).
thf(250,plain,
! [SV12: $i,SV2: $i,SV21: $i] :
( ( ( aNaturalNumber0 @ SV21 )
= $false )
| ( ( aNaturalNumber0 @ SV2 )
= $false )
| ( ( aNaturalNumber0 @ SV12 )
= $false )
| ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV2 @ SV12 ) @ SV21 )
= ( sdtpldt0 @ SV2 @ ( sdtpldt0 @ SV12 @ SV21 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[240]) ).
thf(251,plain,
! [SV13: $i,SV4: $i,SV22: $i] :
( ( ( aNaturalNumber0 @ SV22 )
= $false )
| ( ( aNaturalNumber0 @ SV4 )
= $false )
| ( ( aNaturalNumber0 @ SV13 )
= $false )
| ( ( ~ ~ ( ~ ( doDivides0 @ SV4 @ SV13 )
| ~ ( doDivides0 @ SV4 @ ( sdtpldt0 @ SV13 @ SV22 ) ) )
| ( doDivides0 @ SV4 @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[241]) ).
thf(252,plain,
! [SV14: $i,SV5: $i,SV23: $i] :
( ( ( aNaturalNumber0 @ SV23 )
= $false )
| ( ( aNaturalNumber0 @ SV5 )
= $false )
| ( ( aNaturalNumber0 @ SV14 )
= $false )
| ( ( ~ ( ( ( sdtpldt0 @ SV5 @ SV14 )
= ( sdtpldt0 @ SV5 @ SV23 ) )
| ( ( sdtpldt0 @ SV14 @ SV5 )
= ( sdtpldt0 @ SV23 @ SV5 ) ) )
| ( SV14 = SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[244]) ).
thf(253,plain,
! [SV16: $i,SV7: $i] :
( ( ( SV7 = sz00 )
= $true )
| ( ( ( sdtpldt0 @ SV7 @ SV16 )
= sz00 )
= $false )
| ( ( aNaturalNumber0 @ SV7 )
= $false )
| ( ( aNaturalNumber0 @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[245]) ).
thf(254,plain,
! [SV7: $i,SV16: $i] :
( ( ( SV16 = sz00 )
= $true )
| ( ( ( sdtpldt0 @ SV7 @ SV16 )
= sz00 )
= $false )
| ( ( aNaturalNumber0 @ SV7 )
= $false )
| ( ( aNaturalNumber0 @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[246]) ).
thf(255,plain,
! [SV17: $i,SV8: $i,SV24: $i] :
( ( ( aNaturalNumber0 @ SV24 )
= $false )
| ( ( aNaturalNumber0 @ SV8 )
= $false )
| ( ( aNaturalNumber0 @ SV17 )
= $false )
| ( ( ~ ~ ( ~ ( doDivides0 @ SV8 @ SV17 )
| ~ ( doDivides0 @ SV8 @ SV24 ) )
| ( doDivides0 @ SV8 @ ( sdtpldt0 @ SV17 @ SV24 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[247]) ).
thf(256,plain,
! [SV18: $i,SV9: $i] :
( ( ( SV9 != SV18 )
= $false )
| ( ( ~ ( sdtlseqdt0 @ SV9 @ SV18 ) )
= $true )
| ( ( ! [SY47: $i] :
( ~ ( aNaturalNumber0 @ SY47 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sdtpldt0 @ SY47 @ SV9 )
!= ( sdtpldt0 @ SY47 @ SV18 ) ) )
| ~ ( sdtlseqdt0 @ ( sdtpldt0 @ SY47 @ SV9 ) @ ( sdtpldt0 @ SY47 @ SV18 ) ) )
| ~ ( ( ( sdtpldt0 @ SV9 @ SY47 )
!= ( sdtpldt0 @ SV18 @ SY47 ) ) ) )
| ~ ( sdtlseqdt0 @ ( sdtpldt0 @ SV9 @ SY47 ) @ ( sdtpldt0 @ SV18 @ SY47 ) ) ) ) )
= $true )
| ( ( aNaturalNumber0 @ SV9 )
= $false )
| ( ( aNaturalNumber0 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[248]) ).
thf(257,plain,
! [SV20: $i,SV11: $i,SV1: $i] :
( ( ( ( ( sdtasdt0 @ SV1 @ ( sdtpldt0 @ SV11 @ SV20 ) )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV1 @ SV11 ) @ ( sdtasdt0 @ SV1 @ SV20 ) ) )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SV11 @ SV20 ) @ SV1 )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV11 @ SV1 ) @ ( sdtasdt0 @ SV20 @ SV1 ) ) ) )
= $false )
| ( ( aNaturalNumber0 @ SV11 )
= $false )
| ( ( aNaturalNumber0 @ SV1 )
= $false )
| ( ( aNaturalNumber0 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[249]) ).
thf(258,plain,
! [SV22: $i,SV13: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( doDivides0 @ SV4 @ SV13 )
| ~ ( doDivides0 @ SV4 @ ( sdtpldt0 @ SV13 @ SV22 ) ) ) )
= $true )
| ( ( doDivides0 @ SV4 @ SV22 )
= $true )
| ( ( aNaturalNumber0 @ SV13 )
= $false )
| ( ( aNaturalNumber0 @ SV4 )
= $false )
| ( ( aNaturalNumber0 @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[251]) ).
thf(259,plain,
! [SV23: $i,SV14: $i,SV5: $i] :
( ( ( ~ ( ( ( sdtpldt0 @ SV5 @ SV14 )
= ( sdtpldt0 @ SV5 @ SV23 ) )
| ( ( sdtpldt0 @ SV14 @ SV5 )
= ( sdtpldt0 @ SV23 @ SV5 ) ) ) )
= $true )
| ( ( SV14 = SV23 )
= $true )
| ( ( aNaturalNumber0 @ SV14 )
= $false )
| ( ( aNaturalNumber0 @ SV5 )
= $false )
| ( ( aNaturalNumber0 @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[252]) ).
thf(260,plain,
! [SV24: $i,SV17: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ( doDivides0 @ SV8 @ SV17 )
| ~ ( doDivides0 @ SV8 @ SV24 ) ) )
= $true )
| ( ( doDivides0 @ SV8 @ ( sdtpldt0 @ SV17 @ SV24 ) )
= $true )
| ( ( aNaturalNumber0 @ SV17 )
= $false )
| ( ( aNaturalNumber0 @ SV8 )
= $false )
| ( ( aNaturalNumber0 @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[255]) ).
thf(261,plain,
! [SV18: $i,SV9: $i] :
( ( ( SV9 = SV18 )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV9 @ SV18 ) )
= $true )
| ( ( ! [SY47: $i] :
( ~ ( aNaturalNumber0 @ SY47 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sdtpldt0 @ SY47 @ SV9 )
!= ( sdtpldt0 @ SY47 @ SV18 ) ) )
| ~ ( sdtlseqdt0 @ ( sdtpldt0 @ SY47 @ SV9 ) @ ( sdtpldt0 @ SY47 @ SV18 ) ) )
| ~ ( ( ( sdtpldt0 @ SV9 @ SY47 )
!= ( sdtpldt0 @ SV18 @ SY47 ) ) ) )
| ~ ( sdtlseqdt0 @ ( sdtpldt0 @ SV9 @ SY47 ) @ ( sdtpldt0 @ SV18 @ SY47 ) ) ) ) )
= $true )
| ( ( aNaturalNumber0 @ SV9 )
= $false )
| ( ( aNaturalNumber0 @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[256]) ).
thf(262,plain,
! [SV20: $i,SV11: $i,SV1: $i] :
( ( ( ( sdtasdt0 @ SV1 @ ( sdtpldt0 @ SV11 @ SV20 ) )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV1 @ SV11 ) @ ( sdtasdt0 @ SV1 @ SV20 ) ) )
= $false )
| ( ( aNaturalNumber0 @ SV11 )
= $false )
| ( ( aNaturalNumber0 @ SV1 )
= $false )
| ( ( aNaturalNumber0 @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[257]) ).
thf(263,plain,
! [SV1: $i,SV20: $i,SV11: $i] :
( ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV11 @ SV20 ) @ SV1 )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV11 @ SV1 ) @ ( sdtasdt0 @ SV20 @ SV1 ) ) )
= $false )
| ( ( aNaturalNumber0 @ SV11 )
= $false )
| ( ( aNaturalNumber0 @ SV1 )
= $false )
| ( ( aNaturalNumber0 @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[257]) ).
thf(264,plain,
! [SV22: $i,SV13: $i,SV4: $i] :
( ( ( ~ ( ~ ( doDivides0 @ SV4 @ SV13 )
| ~ ( doDivides0 @ SV4 @ ( sdtpldt0 @ SV13 @ SV22 ) ) ) )
= $false )
| ( ( doDivides0 @ SV4 @ SV22 )
= $true )
| ( ( aNaturalNumber0 @ SV13 )
= $false )
| ( ( aNaturalNumber0 @ SV4 )
= $false )
| ( ( aNaturalNumber0 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[258]) ).
thf(265,plain,
! [SV23: $i,SV14: $i,SV5: $i] :
( ( ( ( ( sdtpldt0 @ SV5 @ SV14 )
= ( sdtpldt0 @ SV5 @ SV23 ) )
| ( ( sdtpldt0 @ SV14 @ SV5 )
= ( sdtpldt0 @ SV23 @ SV5 ) ) )
= $false )
| ( ( SV14 = SV23 )
= $true )
| ( ( aNaturalNumber0 @ SV14 )
= $false )
| ( ( aNaturalNumber0 @ SV5 )
= $false )
| ( ( aNaturalNumber0 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[259]) ).
thf(266,plain,
! [SV24: $i,SV17: $i,SV8: $i] :
( ( ( ~ ( ~ ( doDivides0 @ SV8 @ SV17 )
| ~ ( doDivides0 @ SV8 @ SV24 ) ) )
= $false )
| ( ( doDivides0 @ SV8 @ ( sdtpldt0 @ SV17 @ SV24 ) )
= $true )
| ( ( aNaturalNumber0 @ SV17 )
= $false )
| ( ( aNaturalNumber0 @ SV8 )
= $false )
| ( ( aNaturalNumber0 @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[260]) ).
thf(267,plain,
! [SV18: $i,SV9: $i] :
( ( ( sdtlseqdt0 @ SV9 @ SV18 )
= $false )
| ( ( SV9 = SV18 )
= $true )
| ( ( ! [SY47: $i] :
( ~ ( aNaturalNumber0 @ SY47 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sdtpldt0 @ SY47 @ SV9 )
!= ( sdtpldt0 @ SY47 @ SV18 ) ) )
| ~ ( sdtlseqdt0 @ ( sdtpldt0 @ SY47 @ SV9 ) @ ( sdtpldt0 @ SY47 @ SV18 ) ) )
| ~ ( ( ( sdtpldt0 @ SV9 @ SY47 )
!= ( sdtpldt0 @ SV18 @ SY47 ) ) ) )
| ~ ( sdtlseqdt0 @ ( sdtpldt0 @ SV9 @ SY47 ) @ ( sdtpldt0 @ SV18 @ SY47 ) ) ) ) )
= $true )
| ( ( aNaturalNumber0 @ SV9 )
= $false )
| ( ( aNaturalNumber0 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[261]) ).
thf(268,plain,
! [SV20: $i,SV11: $i,SV1: $i] :
( ( ( ( sdtasdt0 @ SV1 @ ( sdtpldt0 @ SV11 @ SV20 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV1 @ SV11 ) @ ( sdtasdt0 @ SV1 @ SV20 ) ) )
= $true )
| ( ( aNaturalNumber0 @ SV11 )
= $false )
| ( ( aNaturalNumber0 @ SV1 )
= $false )
| ( ( aNaturalNumber0 @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[262]) ).
thf(269,plain,
! [SV1: $i,SV20: $i,SV11: $i] :
( ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV11 @ SV20 ) @ SV1 )
= ( sdtpldt0 @ ( sdtasdt0 @ SV11 @ SV1 ) @ ( sdtasdt0 @ SV20 @ SV1 ) ) )
= $true )
| ( ( aNaturalNumber0 @ SV11 )
= $false )
| ( ( aNaturalNumber0 @ SV1 )
= $false )
| ( ( aNaturalNumber0 @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[263]) ).
thf(270,plain,
! [SV22: $i,SV13: $i,SV4: $i] :
( ( ( ~ ( doDivides0 @ SV4 @ SV13 )
| ~ ( doDivides0 @ SV4 @ ( sdtpldt0 @ SV13 @ SV22 ) ) )
= $true )
| ( ( doDivides0 @ SV4 @ SV22 )
= $true )
| ( ( aNaturalNumber0 @ SV13 )
= $false )
| ( ( aNaturalNumber0 @ SV4 )
= $false )
| ( ( aNaturalNumber0 @ SV22 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[264]) ).
thf(271,plain,
! [SV23: $i,SV14: $i,SV5: $i] :
( ( ( ( sdtpldt0 @ SV5 @ SV14 )
= ( sdtpldt0 @ SV5 @ SV23 ) )
= $false )
| ( ( SV14 = SV23 )
= $true )
| ( ( aNaturalNumber0 @ SV14 )
= $false )
| ( ( aNaturalNumber0 @ SV5 )
= $false )
| ( ( aNaturalNumber0 @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[265]) ).
thf(272,plain,
! [SV23: $i,SV5: $i,SV14: $i] :
( ( ( ( sdtpldt0 @ SV14 @ SV5 )
= ( sdtpldt0 @ SV23 @ SV5 ) )
= $false )
| ( ( SV14 = SV23 )
= $true )
| ( ( aNaturalNumber0 @ SV14 )
= $false )
| ( ( aNaturalNumber0 @ SV5 )
= $false )
| ( ( aNaturalNumber0 @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[265]) ).
thf(273,plain,
! [SV24: $i,SV17: $i,SV8: $i] :
( ( ( ~ ( doDivides0 @ SV8 @ SV17 )
| ~ ( doDivides0 @ SV8 @ SV24 ) )
= $true )
| ( ( doDivides0 @ SV8 @ ( sdtpldt0 @ SV17 @ SV24 ) )
= $true )
| ( ( aNaturalNumber0 @ SV17 )
= $false )
| ( ( aNaturalNumber0 @ SV8 )
= $false )
| ( ( aNaturalNumber0 @ SV24 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[266]) ).
thf(274,plain,
! [SV18: $i,SV9: $i,SV25: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV25 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sdtpldt0 @ SV25 @ SV9 )
!= ( sdtpldt0 @ SV25 @ SV18 ) ) )
| ~ ( sdtlseqdt0 @ ( sdtpldt0 @ SV25 @ SV9 ) @ ( sdtpldt0 @ SV25 @ SV18 ) ) )
| ~ ( ( ( sdtpldt0 @ SV9 @ SV25 )
!= ( sdtpldt0 @ SV18 @ SV25 ) ) ) )
| ~ ( sdtlseqdt0 @ ( sdtpldt0 @ SV9 @ SV25 ) @ ( sdtpldt0 @ SV18 @ SV25 ) ) ) )
= $true )
| ( ( SV9 = SV18 )
= $true )
| ( ( sdtlseqdt0 @ SV9 @ SV18 )
= $false )
| ( ( aNaturalNumber0 @ SV9 )
= $false )
| ( ( aNaturalNumber0 @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[267]) ).
thf(275,plain,
! [SV22: $i,SV13: $i,SV4: $i] :
( ( ( ~ ( doDivides0 @ SV4 @ SV13 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV4 @ ( sdtpldt0 @ SV13 @ SV22 ) ) )
= $true )
| ( ( doDivides0 @ SV4 @ SV22 )
= $true )
| ( ( aNaturalNumber0 @ SV13 )
= $false )
| ( ( aNaturalNumber0 @ SV4 )
= $false )
| ( ( aNaturalNumber0 @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[270]) ).
thf(276,plain,
! [SV24: $i,SV17: $i,SV8: $i] :
( ( ( ~ ( doDivides0 @ SV8 @ SV17 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV8 @ SV24 ) )
= $true )
| ( ( doDivides0 @ SV8 @ ( sdtpldt0 @ SV17 @ SV24 ) )
= $true )
| ( ( aNaturalNumber0 @ SV17 )
= $false )
| ( ( aNaturalNumber0 @ SV8 )
= $false )
| ( ( aNaturalNumber0 @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[273]) ).
thf(277,plain,
! [SV18: $i,SV9: $i,SV25: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV25 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sdtpldt0 @ SV25 @ SV9 )
!= ( sdtpldt0 @ SV25 @ SV18 ) ) )
| ~ ( sdtlseqdt0 @ ( sdtpldt0 @ SV25 @ SV9 ) @ ( sdtpldt0 @ SV25 @ SV18 ) ) )
| ~ ( ( ( sdtpldt0 @ SV9 @ SV25 )
!= ( sdtpldt0 @ SV18 @ SV25 ) ) ) )
| ~ ( sdtlseqdt0 @ ( sdtpldt0 @ SV9 @ SV25 ) @ ( sdtpldt0 @ SV18 @ SV25 ) ) ) )
= $true )
| ( ( SV9 = SV18 )
= $true )
| ( ( sdtlseqdt0 @ SV9 @ SV18 )
= $false )
| ( ( aNaturalNumber0 @ SV9 )
= $false )
| ( ( aNaturalNumber0 @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[274]) ).
thf(278,plain,
! [SV22: $i,SV13: $i,SV4: $i] :
( ( ( doDivides0 @ SV4 @ SV13 )
= $false )
| ( ( ~ ( doDivides0 @ SV4 @ ( sdtpldt0 @ SV13 @ SV22 ) ) )
= $true )
| ( ( doDivides0 @ SV4 @ SV22 )
= $true )
| ( ( aNaturalNumber0 @ SV13 )
= $false )
| ( ( aNaturalNumber0 @ SV4 )
= $false )
| ( ( aNaturalNumber0 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[275]) ).
thf(279,plain,
! [SV24: $i,SV17: $i,SV8: $i] :
( ( ( doDivides0 @ SV8 @ SV17 )
= $false )
| ( ( ~ ( doDivides0 @ SV8 @ SV24 ) )
= $true )
| ( ( doDivides0 @ SV8 @ ( sdtpldt0 @ SV17 @ SV24 ) )
= $true )
| ( ( aNaturalNumber0 @ SV17 )
= $false )
| ( ( aNaturalNumber0 @ SV8 )
= $false )
| ( ( aNaturalNumber0 @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(280,plain,
! [SV18: $i,SV9: $i,SV25: $i] :
( ( ( aNaturalNumber0 @ SV25 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sdtpldt0 @ SV25 @ SV9 )
!= ( sdtpldt0 @ SV25 @ SV18 ) ) )
| ~ ( sdtlseqdt0 @ ( sdtpldt0 @ SV25 @ SV9 ) @ ( sdtpldt0 @ SV25 @ SV18 ) ) )
| ~ ( ( ( sdtpldt0 @ SV9 @ SV25 )
!= ( sdtpldt0 @ SV18 @ SV25 ) ) ) )
| ~ ( sdtlseqdt0 @ ( sdtpldt0 @ SV9 @ SV25 ) @ ( sdtpldt0 @ SV18 @ SV25 ) ) ) )
= $true )
| ( ( SV9 = SV18 )
= $true )
| ( ( sdtlseqdt0 @ SV9 @ SV18 )
= $false )
| ( ( aNaturalNumber0 @ SV9 )
= $false )
| ( ( aNaturalNumber0 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[277]) ).
thf(281,plain,
! [SV22: $i,SV13: $i,SV4: $i] :
( ( ( doDivides0 @ SV4 @ ( sdtpldt0 @ SV13 @ SV22 ) )
= $false )
| ( ( doDivides0 @ SV4 @ SV13 )
= $false )
| ( ( doDivides0 @ SV4 @ SV22 )
= $true )
| ( ( aNaturalNumber0 @ SV13 )
= $false )
| ( ( aNaturalNumber0 @ SV4 )
= $false )
| ( ( aNaturalNumber0 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[278]) ).
thf(282,plain,
! [SV17: $i,SV24: $i,SV8: $i] :
( ( ( doDivides0 @ SV8 @ SV24 )
= $false )
| ( ( doDivides0 @ SV8 @ SV17 )
= $false )
| ( ( doDivides0 @ SV8 @ ( sdtpldt0 @ SV17 @ SV24 ) )
= $true )
| ( ( aNaturalNumber0 @ SV17 )
= $false )
| ( ( aNaturalNumber0 @ SV8 )
= $false )
| ( ( aNaturalNumber0 @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[279]) ).
thf(283,plain,
! [SV18: $i,SV9: $i,SV25: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( ( sdtpldt0 @ SV25 @ SV9 )
!= ( sdtpldt0 @ SV25 @ SV18 ) ) )
| ~ ( sdtlseqdt0 @ ( sdtpldt0 @ SV25 @ SV9 ) @ ( sdtpldt0 @ SV25 @ SV18 ) ) )
| ~ ( ( ( sdtpldt0 @ SV9 @ SV25 )
!= ( sdtpldt0 @ SV18 @ SV25 ) ) ) )
| ~ ( sdtlseqdt0 @ ( sdtpldt0 @ SV9 @ SV25 ) @ ( sdtpldt0 @ SV18 @ SV25 ) ) )
= $false )
| ( ( aNaturalNumber0 @ SV25 )
= $false )
| ( ( SV9 = SV18 )
= $true )
| ( ( sdtlseqdt0 @ SV9 @ SV18 )
= $false )
| ( ( aNaturalNumber0 @ SV9 )
= $false )
| ( ( aNaturalNumber0 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[280]) ).
thf(284,plain,
! [SV18: $i,SV9: $i,SV25: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( ( sdtpldt0 @ SV25 @ SV9 )
!= ( sdtpldt0 @ SV25 @ SV18 ) ) )
| ~ ( sdtlseqdt0 @ ( sdtpldt0 @ SV25 @ SV9 ) @ ( sdtpldt0 @ SV25 @ SV18 ) ) )
| ~ ( ( ( sdtpldt0 @ SV9 @ SV25 )
!= ( sdtpldt0 @ SV18 @ SV25 ) ) ) ) )
= $false )
| ( ( aNaturalNumber0 @ SV25 )
= $false )
| ( ( SV9 = SV18 )
= $true )
| ( ( sdtlseqdt0 @ SV9 @ SV18 )
= $false )
| ( ( aNaturalNumber0 @ SV9 )
= $false )
| ( ( aNaturalNumber0 @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[283]) ).
thf(285,plain,
! [SV18: $i,SV25: $i,SV9: $i] :
( ( ( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ SV9 @ SV25 ) @ ( sdtpldt0 @ SV18 @ SV25 ) ) )
= $false )
| ( ( aNaturalNumber0 @ SV25 )
= $false )
| ( ( SV9 = SV18 )
= $true )
| ( ( sdtlseqdt0 @ SV9 @ SV18 )
= $false )
| ( ( aNaturalNumber0 @ SV9 )
= $false )
| ( ( aNaturalNumber0 @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[283]) ).
thf(286,plain,
! [SV18: $i,SV9: $i,SV25: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( ( sdtpldt0 @ SV25 @ SV9 )
!= ( sdtpldt0 @ SV25 @ SV18 ) ) )
| ~ ( sdtlseqdt0 @ ( sdtpldt0 @ SV25 @ SV9 ) @ ( sdtpldt0 @ SV25 @ SV18 ) ) )
| ~ ( ( ( sdtpldt0 @ SV9 @ SV25 )
!= ( sdtpldt0 @ SV18 @ SV25 ) ) ) ) )
= $true )
| ( ( aNaturalNumber0 @ SV25 )
= $false )
| ( ( SV9 = SV18 )
= $true )
| ( ( sdtlseqdt0 @ SV9 @ SV18 )
= $false )
| ( ( aNaturalNumber0 @ SV9 )
= $false )
| ( ( aNaturalNumber0 @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[284]) ).
thf(287,plain,
! [SV18: $i,SV25: $i,SV9: $i] :
( ( ( sdtlseqdt0 @ ( sdtpldt0 @ SV9 @ SV25 ) @ ( sdtpldt0 @ SV18 @ SV25 ) )
= $true )
| ( ( aNaturalNumber0 @ SV25 )
= $false )
| ( ( SV9 = SV18 )
= $true )
| ( ( sdtlseqdt0 @ SV9 @ SV18 )
= $false )
| ( ( aNaturalNumber0 @ SV9 )
= $false )
| ( ( aNaturalNumber0 @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[285]) ).
thf(288,plain,
! [SV18: $i,SV9: $i,SV25: $i] :
( ( ( ~ ~ ( ~ ( ( ( sdtpldt0 @ SV25 @ SV9 )
!= ( sdtpldt0 @ SV25 @ SV18 ) ) )
| ~ ( sdtlseqdt0 @ ( sdtpldt0 @ SV25 @ SV9 ) @ ( sdtpldt0 @ SV25 @ SV18 ) ) )
| ~ ( ( ( sdtpldt0 @ SV9 @ SV25 )
!= ( sdtpldt0 @ SV18 @ SV25 ) ) ) )
= $false )
| ( ( aNaturalNumber0 @ SV25 )
= $false )
| ( ( SV9 = SV18 )
= $true )
| ( ( sdtlseqdt0 @ SV9 @ SV18 )
= $false )
| ( ( aNaturalNumber0 @ SV9 )
= $false )
| ( ( aNaturalNumber0 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[286]) ).
thf(289,plain,
! [SV18: $i,SV9: $i,SV25: $i] :
( ( ( ~ ~ ( ~ ( ( ( sdtpldt0 @ SV25 @ SV9 )
!= ( sdtpldt0 @ SV25 @ SV18 ) ) )
| ~ ( sdtlseqdt0 @ ( sdtpldt0 @ SV25 @ SV9 ) @ ( sdtpldt0 @ SV25 @ SV18 ) ) ) )
= $false )
| ( ( aNaturalNumber0 @ SV25 )
= $false )
| ( ( SV9 = SV18 )
= $true )
| ( ( sdtlseqdt0 @ SV9 @ SV18 )
= $false )
| ( ( aNaturalNumber0 @ SV9 )
= $false )
| ( ( aNaturalNumber0 @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[288]) ).
thf(290,plain,
! [SV18: $i,SV25: $i,SV9: $i] :
( ( ( ~ ( ( ( sdtpldt0 @ SV9 @ SV25 )
!= ( sdtpldt0 @ SV18 @ SV25 ) ) ) )
= $false )
| ( ( aNaturalNumber0 @ SV25 )
= $false )
| ( ( SV9 = SV18 )
= $true )
| ( ( sdtlseqdt0 @ SV9 @ SV18 )
= $false )
| ( ( aNaturalNumber0 @ SV9 )
= $false )
| ( ( aNaturalNumber0 @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[288]) ).
thf(291,plain,
! [SV18: $i,SV9: $i,SV25: $i] :
( ( ( ~ ( ~ ( ( ( sdtpldt0 @ SV25 @ SV9 )
!= ( sdtpldt0 @ SV25 @ SV18 ) ) )
| ~ ( sdtlseqdt0 @ ( sdtpldt0 @ SV25 @ SV9 ) @ ( sdtpldt0 @ SV25 @ SV18 ) ) ) )
= $true )
| ( ( aNaturalNumber0 @ SV25 )
= $false )
| ( ( SV9 = SV18 )
= $true )
| ( ( sdtlseqdt0 @ SV9 @ SV18 )
= $false )
| ( ( aNaturalNumber0 @ SV9 )
= $false )
| ( ( aNaturalNumber0 @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[289]) ).
thf(292,plain,
! [SV18: $i,SV25: $i,SV9: $i] :
( ( ( ( sdtpldt0 @ SV9 @ SV25 )
!= ( sdtpldt0 @ SV18 @ SV25 ) )
= $true )
| ( ( aNaturalNumber0 @ SV25 )
= $false )
| ( ( SV9 = SV18 )
= $true )
| ( ( sdtlseqdt0 @ SV9 @ SV18 )
= $false )
| ( ( aNaturalNumber0 @ SV9 )
= $false )
| ( ( aNaturalNumber0 @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[290]) ).
thf(293,plain,
! [SV18: $i,SV9: $i,SV25: $i] :
( ( ( ~ ( ( ( sdtpldt0 @ SV25 @ SV9 )
!= ( sdtpldt0 @ SV25 @ SV18 ) ) )
| ~ ( sdtlseqdt0 @ ( sdtpldt0 @ SV25 @ SV9 ) @ ( sdtpldt0 @ SV25 @ SV18 ) ) )
= $false )
| ( ( aNaturalNumber0 @ SV25 )
= $false )
| ( ( SV9 = SV18 )
= $true )
| ( ( sdtlseqdt0 @ SV9 @ SV18 )
= $false )
| ( ( aNaturalNumber0 @ SV9 )
= $false )
| ( ( aNaturalNumber0 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[291]) ).
thf(294,plain,
! [SV18: $i,SV25: $i,SV9: $i] :
( ( ( ( sdtpldt0 @ SV9 @ SV25 )
= ( sdtpldt0 @ SV18 @ SV25 ) )
= $false )
| ( ( aNaturalNumber0 @ SV25 )
= $false )
| ( ( SV9 = SV18 )
= $true )
| ( ( sdtlseqdt0 @ SV9 @ SV18 )
= $false )
| ( ( aNaturalNumber0 @ SV9 )
= $false )
| ( ( aNaturalNumber0 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[292]) ).
thf(295,plain,
! [SV18: $i,SV9: $i,SV25: $i] :
( ( ( ~ ( ( ( sdtpldt0 @ SV25 @ SV9 )
!= ( sdtpldt0 @ SV25 @ SV18 ) ) ) )
= $false )
| ( ( aNaturalNumber0 @ SV25 )
= $false )
| ( ( SV9 = SV18 )
= $true )
| ( ( sdtlseqdt0 @ SV9 @ SV18 )
= $false )
| ( ( aNaturalNumber0 @ SV9 )
= $false )
| ( ( aNaturalNumber0 @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[293]) ).
thf(296,plain,
! [SV18: $i,SV9: $i,SV25: $i] :
( ( ( ~ ( sdtlseqdt0 @ ( sdtpldt0 @ SV25 @ SV9 ) @ ( sdtpldt0 @ SV25 @ SV18 ) ) )
= $false )
| ( ( aNaturalNumber0 @ SV25 )
= $false )
| ( ( SV9 = SV18 )
= $true )
| ( ( sdtlseqdt0 @ SV9 @ SV18 )
= $false )
| ( ( aNaturalNumber0 @ SV9 )
= $false )
| ( ( aNaturalNumber0 @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[293]) ).
thf(297,plain,
! [SV18: $i,SV9: $i,SV25: $i] :
( ( ( ( sdtpldt0 @ SV25 @ SV9 )
!= ( sdtpldt0 @ SV25 @ SV18 ) )
= $true )
| ( ( aNaturalNumber0 @ SV25 )
= $false )
| ( ( SV9 = SV18 )
= $true )
| ( ( sdtlseqdt0 @ SV9 @ SV18 )
= $false )
| ( ( aNaturalNumber0 @ SV9 )
= $false )
| ( ( aNaturalNumber0 @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[295]) ).
thf(298,plain,
! [SV18: $i,SV9: $i,SV25: $i] :
( ( ( sdtlseqdt0 @ ( sdtpldt0 @ SV25 @ SV9 ) @ ( sdtpldt0 @ SV25 @ SV18 ) )
= $true )
| ( ( aNaturalNumber0 @ SV25 )
= $false )
| ( ( SV9 = SV18 )
= $true )
| ( ( sdtlseqdt0 @ SV9 @ SV18 )
= $false )
| ( ( aNaturalNumber0 @ SV9 )
= $false )
| ( ( aNaturalNumber0 @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[296]) ).
thf(299,plain,
! [SV18: $i,SV9: $i,SV25: $i] :
( ( ( ( sdtpldt0 @ SV25 @ SV9 )
= ( sdtpldt0 @ SV25 @ SV18 ) )
= $false )
| ( ( aNaturalNumber0 @ SV25 )
= $false )
| ( ( SV9 = SV18 )
= $true )
| ( ( sdtlseqdt0 @ SV9 @ SV18 )
= $false )
| ( ( aNaturalNumber0 @ SV9 )
= $false )
| ( ( aNaturalNumber0 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[297]) ).
thf(300,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[87,299,298,294,287,282,281,272,271,269,268,254,253,250,243,242,217,216,211,207,191,181,180,176,175,173,172,131,129,127,125]) ).
thf(301,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[300]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM489+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
% 0.07/0.17 % Computer : n003.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Oct 6 13:23:24 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.29/0.41
% 1.29/0.41 No.of.Axioms: 14
% 1.29/0.41
% 1.29/0.41 Length.of.Defs: 0
% 1.29/0.41
% 1.29/0.41 Contains.Choice.Funs: false
% 1.29/0.41 ........
% 1.29/0.41
% 1.29/0.41 ********************************
% 1.29/0.41 * All subproblems solved! *
% 1.29/0.41 ********************************
% 1.29/0.41 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:14,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:300,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.29/0.41
% 1.29/0.41 %**** Beginning of derivation protocol ****
% 1.29/0.41 % SZS output start CNFRefutation
% See solution above
% 1.29/0.42
% 1.29/0.42 %**** End of derivation protocol ****
% 1.29/0.42 %**** no. of clauses in derivation: 276 ****
% 1.29/0.42 %**** clause counter: 300 ****
% 1.29/0.42
% 1.29/0.42 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:14,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:300,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------