%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : RNG119+4 : 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 10:37:51 AM UTC 2026
% Result : Theorem 225.26s 38.02s
% Output : CNFRefutation 225.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 49
% Number of leaves : 42
% Syntax : Number of formulae : 1177 ( 501 unt; 0 typ; 0 def)
% Number of atoms : 10725 (4076 equ; 0 cnn)
% Maximal formula atoms : 23 ( 9 avg)
% Number of connectives : 22542 (7468 ~;3865 |; 297 &;10774 @)
% ( 15 <=>; 123 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 67 ( 64 usr; 25 con; 0-4 aty)
% Number of variables : 2498 ( 0 ^;2405 !; 93 ?;2498 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_aDivisorOf0,type,
aDivisorOf0: $i > $i > $o ).
thf(tp_aElement0,type,
aElement0: $i > $o ).
thf(tp_aElementOf0,type,
aElementOf0: $i > $i > $o ).
thf(tp_aGcdOfAnd0,type,
aGcdOfAnd0: $i > $i > $i > $o ).
thf(tp_aIdeal0,type,
aIdeal0: $i > $o ).
thf(tp_aNaturalNumber0,type,
aNaturalNumber0: $i > $o ).
thf(tp_aSet0,type,
aSet0: $i > $o ).
thf(tp_doDivides0,type,
doDivides0: $i > $i > $o ).
thf(tp_iLess0,type,
iLess0: $i > $i > $o ).
thf(tp_misRelativelyPrime0,type,
misRelativelyPrime0: $i > $i > $o ).
thf(tp_sK10_SY147,type,
sK10_SY147: $i ).
thf(tp_sK11_SX0,type,
sK11_SX0: $i ).
thf(tp_sK12_SY138,type,
sK12_SY138: $i > $i ).
thf(tp_sK13_SY116,type,
sK13_SY116: $i > $i > $i ).
thf(tp_sK14_SY153,type,
sK14_SY153: $i ).
thf(tp_sK15_SY128,type,
sK15_SY128: $i > $i > $i ).
thf(tp_sK16_SY145,type,
sK16_SY145: $i > $i ).
thf(tp_sK17_SY154,type,
sK17_SY154: $i > $i ).
thf(tp_sK18_SX0,type,
sK18_SX0: $i ).
thf(tp_sK19_SY159,type,
sK19_SY159: $i > $i > $i ).
thf(tp_sK1_SX0,type,
sK1_SX0: $i ).
thf(tp_sK20_SY128,type,
sK20_SY128: $i > $i > $i ).
thf(tp_sK21_SX0,type,
sK21_SX0: $i ).
thf(tp_sK22_SY149,type,
sK22_SY149: $i > $i ).
thf(tp_sK23_SY144,type,
sK23_SY144: $i > $i ).
thf(tp_sK24_SY144,type,
sK24_SY144: $i > $i ).
thf(tp_sK25_SY158,type,
sK25_SY158: $i > $i > $i > $i > $i ).
thf(tp_sK26_SY161,type,
sK26_SY161: $i > $i ).
thf(tp_sK27_SY163,type,
sK27_SY163: $i > $i ).
thf(tp_sK28_SX0,type,
sK28_SX0: $i ).
thf(tp_sK29_SY160,type,
sK29_SY160: $i > $i > $i > $i > $i ).
thf(tp_sK2_SX0,type,
sK2_SX0: $i ).
thf(tp_sK30_SY144,type,
sK30_SY144: $i > $i ).
thf(tp_sK31_SY144,type,
sK31_SY144: $i > $i ).
thf(tp_sK32_SY144,type,
sK32_SY144: $i > $i > $i ).
thf(tp_sK33_SX0,type,
sK33_SX0: $i ).
thf(tp_sK34_SY144,type,
sK34_SY144: $i > $i > $i ).
thf(tp_sK35_SY144,type,
sK35_SY144: $i > $i > $i ).
thf(tp_sK36_SY144,type,
sK36_SY144: $i > $i > $i ).
thf(tp_sK37_SY144,type,
sK37_SY144: $i > $i > $i > $i ).
thf(tp_sK3_SY126,type,
sK3_SY126: $i ).
thf(tp_sK4_SX0,type,
sK4_SX0: $i ).
thf(tp_sK5_SX0,type,
sK5_SX0: $i ).
thf(tp_sK6_SX0,type,
sK6_SX0: $i ).
thf(tp_sK7_SY131,type,
sK7_SY131: $i > $i > $i ).
thf(tp_sK8_SY124,type,
sK8_SY124: $i ).
thf(tp_sK9_SY127,type,
sK9_SY127: $i > $i > $i ).
thf(tp_sbrdtbr0,type,
sbrdtbr0: $i > $i ).
thf(tp_sdtasasdt0,type,
sdtasasdt0: $i > $i > $i ).
thf(tp_sdtasdt0,type,
sdtasdt0: $i > $i > $i ).
thf(tp_sdteqdtlpzmzozddtrp0,type,
sdteqdtlpzmzozddtrp0: $i > $i > $i > $o ).
thf(tp_sdtpldt0,type,
sdtpldt0: $i > $i > $i ).
thf(tp_sdtpldt1,type,
sdtpldt1: $i > $i > $i ).
thf(tp_slsdtgt0,type,
slsdtgt0: $i > $i ).
thf(tp_smndt0,type,
smndt0: $i > $i ).
thf(tp_sz00,type,
sz00: $i ).
thf(tp_sz10,type,
sz10: $i ).
thf(tp_xI,type,
xI: $i ).
thf(tp_xa,type,
xa: $i ).
thf(tp_xb,type,
xb: $i ).
thf(tp_xc,type,
xc: $i ).
thf(tp_xq,type,
xq: $i ).
thf(tp_xr,type,
xr: $i ).
thf(tp_xu,type,
xu: $i ).
thf(1,axiom,
! [W0: $i] :
( ( aElement0 @ W0 )
=> ( aIdeal0 @ ( slsdtgt0 @ W0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mPrIdeal) ).
thf(2,axiom,
! [W0: $i,W1: $i] :
( ( ( aElement0 @ W0 )
& ( aElement0 @ W1 )
& ( W1 != sz00 ) )
=> ? [W2: $i,W3: $i] :
( ( aElement0 @ W2 )
& ( aElement0 @ W3 )
& ( W0
= ( sdtpldt0 @ ( sdtasdt0 @ W2 @ W1 ) @ W3 ) )
& ( ( W3 != sz00 )
=> ( iLess0 @ ( sbrdtbr0 @ W3 ) @ ( sbrdtbr0 @ W1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivision) ).
thf(3,axiom,
! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( iLess0 @ W0 @ W1 )
=> $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNatLess) ).
thf(4,axiom,
! [W0: $i] :
( ( ( aElement0 @ W0 )
& ( W0 != sz00 ) )
=> ( aNaturalNumber0 @ ( sbrdtbr0 @ W0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEucSort) ).
thf(5,axiom,
! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNatSort) ).
thf(6,axiom,
! [W0: $i,W1: $i] :
( ( ( aIdeal0 @ W0 )
& ( aIdeal0 @ W1 ) )
=> ( ! [W2: $i] :
( ( aElement0 @ W2 )
=> ( aElementOf0 @ W2 @ ( sdtpldt1 @ W0 @ W1 ) ) )
=> ! [W2: $i,W3: $i] :
( ( ( aElement0 @ W2 )
& ( aElement0 @ W3 ) )
=> ? [W4: $i] :
( ( aElement0 @ W4 )
& ( sdteqdtlpzmzozddtrp0 @ W4 @ W2 @ W0 )
& ( sdteqdtlpzmzozddtrp0 @ W4 @ W3 @ W1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mChineseRemainder) ).
thf(7,axiom,
! [W0: $i,W1: $i] :
( ( ( aIdeal0 @ W0 )
& ( aIdeal0 @ W1 ) )
=> ( aIdeal0 @ ( sdtasasdt0 @ W0 @ W1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIdeInt) ).
thf(8,axiom,
! [W0: $i,W1: $i] :
( ( ( aIdeal0 @ W0 )
& ( aIdeal0 @ W1 ) )
=> ( aIdeal0 @ ( sdtpldt1 @ W0 @ W1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIdeSum) ).
thf(9,axiom,
! [W0: $i,W1: $i] :
( ( ( aSet0 @ W0 )
& ( aSet0 @ W1 ) )
=> ( ( ! [W2: $i] :
( ( aElementOf0 @ W2 @ W0 )
=> ( aElementOf0 @ W2 @ W1 ) )
& ! [W2: $i] :
( ( aElementOf0 @ W2 @ W1 )
=> ( aElementOf0 @ W2 @ W0 ) ) )
=> ( W0 = W1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSetEq) ).
thf(10,axiom,
! [W0: $i] :
( ( aSet0 @ W0 )
=> ! [W1: $i] :
( ( aElementOf0 @ W1 @ W0 )
=> ( aElement0 @ W1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
thf(11,axiom,
! [W0: $i] :
( ( aSet0 @ W0 )
=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSetSort) ).
thf(12,axiom,
sz10 != sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mUnNeZr) ).
thf(13,axiom,
! [W0: $i,W1: $i] :
( ( ( aElement0 @ W0 )
& ( aElement0 @ W1 ) )
=> ( ( ( sdtasdt0 @ W0 @ W1 )
= sz00 )
=> ( ( W0 = sz00 )
| ( W1 = sz00 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCancel) ).
thf(14,axiom,
! [W0: $i] :
( ( aElement0 @ W0 )
=> ( ( ( sdtasdt0 @ W0 @ sz00 )
= sz00 )
& ( sz00
= ( sdtasdt0 @ sz00 @ W0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulZero) ).
thf(15,axiom,
! [W0: $i] :
( ( aElement0 @ W0 )
=> ( ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ W0 )
= ( smndt0 @ W0 ) )
& ( ( smndt0 @ W0 )
= ( sdtasdt0 @ W0 @ ( smndt0 @ sz10 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulMnOne) ).
thf(16,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( ( aElement0 @ W0 )
& ( aElement0 @ W1 )
& ( aElement0 @ 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(17,axiom,
! [W0: $i] :
( ( aElement0 @ W0 )
=> ( ( ( sdtasdt0 @ W0 @ sz10 )
= W0 )
& ( W0
= ( sdtasdt0 @ sz10 @ W0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulUnit) ).
thf(18,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( ( aElement0 @ W0 )
& ( aElement0 @ W1 )
& ( aElement0 @ W2 ) )
=> ( ( sdtasdt0 @ ( sdtasdt0 @ W0 @ W1 ) @ W2 )
= ( sdtasdt0 @ W0 @ ( sdtasdt0 @ W1 @ W2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulAsso) ).
thf(19,axiom,
! [W0: $i,W1: $i] :
( ( ( aElement0 @ W0 )
& ( aElement0 @ W1 ) )
=> ( ( sdtasdt0 @ W0 @ W1 )
= ( sdtasdt0 @ W1 @ W0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
thf(20,axiom,
! [W0: $i] :
( ( aElement0 @ W0 )
=> ( ( ( sdtpldt0 @ W0 @ ( smndt0 @ W0 ) )
= sz00 )
& ( sz00
= ( sdtpldt0 @ ( smndt0 @ W0 ) @ W0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddInvr) ).
thf(21,axiom,
! [W0: $i] :
( ( aElement0 @ W0 )
=> ( ( ( sdtpldt0 @ W0 @ sz00 )
= W0 )
& ( W0
= ( sdtpldt0 @ sz00 @ W0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddZero) ).
thf(22,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( ( aElement0 @ W0 )
& ( aElement0 @ W1 )
& ( aElement0 @ W2 ) )
=> ( ( sdtpldt0 @ ( sdtpldt0 @ W0 @ W1 ) @ W2 )
= ( sdtpldt0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddAsso) ).
thf(23,axiom,
! [W0: $i,W1: $i] :
( ( ( aElement0 @ W0 )
& ( aElement0 @ W1 ) )
=> ( ( sdtpldt0 @ W0 @ W1 )
= ( sdtpldt0 @ W1 @ W0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
thf(24,axiom,
! [W0: $i,W1: $i] :
( ( ( aElement0 @ W0 )
& ( aElement0 @ W1 ) )
=> ( aElement0 @ ( sdtasdt0 @ W0 @ W1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
thf(25,axiom,
! [W0: $i,W1: $i] :
( ( ( aElement0 @ W0 )
& ( aElement0 @ W1 ) )
=> ( aElement0 @ ( sdtpldt0 @ W0 @ W1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
thf(26,axiom,
! [W0: $i] :
( ( aElement0 @ W0 )
=> ( aElement0 @ ( smndt0 @ W0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsU) ).
thf(27,axiom,
aElement0 @ sz10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
thf(28,axiom,
aElement0 @ sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
thf(29,axiom,
! [W0: $i] :
( ( aElement0 @ W0 )
=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mElmSort) ).
thf(30,axiom,
( ( aElement0 @ xq )
& ( aElement0 @ xr )
& ( xb
= ( sdtpldt0 @ ( sdtasdt0 @ xq @ xu ) @ xr ) )
& ( ( xr = sz00 )
| ( iLess0 @ ( sbrdtbr0 @ xr ) @ ( sbrdtbr0 @ xu ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2666) ).
thf(31,axiom,
~ ( ? [W0: $i] :
( ( aElement0 @ W0 )
& ( ( sdtasdt0 @ xu @ W0 )
= xb ) )
| ( doDivides0 @ xu @ xb ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2612) ).
thf(32,axiom,
~ ~ ( ? [W0: $i] :
( ( aElement0 @ W0 )
& ( ( sdtasdt0 @ xu @ W0 )
= xa ) )
& ( doDivides0 @ xu @ xa ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2479) ).
thf(33,axiom,
? [W0: $i,W1: $i] :
( ( aElement0 @ W0 )
& ( aElement0 @ W1 )
& ( xu
= ( sdtpldt0 @ ( sdtasdt0 @ xa @ W0 ) @ ( sdtasdt0 @ xb @ W1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2416) ).
thf(34,axiom,
~ ( ( ? [W0: $i] :
( ( aElement0 @ W0 )
& ( ( sdtasdt0 @ xu @ W0 )
= xa ) )
| ( doDivides0 @ xu @ xa )
| ( aDivisorOf0 @ xu @ xa ) )
& ( ? [W0: $i] :
( ( aElement0 @ W0 )
& ( ( sdtasdt0 @ xu @ W0 )
= xb ) )
| ( doDivides0 @ xu @ xb )
| ( aDivisorOf0 @ xu @ xb ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2383) ).
thf(35,axiom,
( ? [W0: $i,W1: $i] :
( ( aElementOf0 @ W0 @ ( slsdtgt0 @ xa ) )
& ( aElementOf0 @ W1 @ ( slsdtgt0 @ xb ) )
& ( ( sdtpldt0 @ W0 @ W1 )
= xu ) )
& ( aElementOf0 @ xu @ xI )
& ( xu != sz00 )
& ! [W0: $i] :
( ( ( ? [W1: $i,W2: $i] :
( ( aElementOf0 @ W1 @ ( slsdtgt0 @ xa ) )
& ( aElementOf0 @ W2 @ ( slsdtgt0 @ xb ) )
& ( ( sdtpldt0 @ W1 @ W2 )
= W0 ) )
| ( aElementOf0 @ W0 @ xI ) )
& ( W0 != sz00 ) )
=> ~ ( iLess0 @ ( sbrdtbr0 @ W0 ) @ ( sbrdtbr0 @ xu ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2273) ).
thf(36,axiom,
? [W0: $i] :
( ! [W1: $i] :
( ( aElementOf0 @ W1 @ ( slsdtgt0 @ xa ) )
<=> ? [W2: $i] :
( ( aElement0 @ W2 )
& ( ( sdtasdt0 @ xa @ W2 )
= W1 ) ) )
& ! [W1: $i] :
( ( aElementOf0 @ W1 @ ( slsdtgt0 @ xb ) )
<=> ? [W2: $i] :
( ( aElement0 @ W2 )
& ( ( sdtasdt0 @ xb @ W2 )
= W1 ) ) )
& ? [W1: $i,W2: $i] :
( ( aElementOf0 @ W1 @ ( slsdtgt0 @ xa ) )
& ( aElementOf0 @ W2 @ ( slsdtgt0 @ xb ) )
& ( ( sdtpldt0 @ W1 @ W2 )
= W0 ) )
& ( aElementOf0 @ W0 @ ( sdtpldt1 @ ( slsdtgt0 @ xa ) @ ( slsdtgt0 @ xb ) ) )
& ( W0 != sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2228) ).
thf(37,axiom,
( ? [W0: $i] :
( ( aElement0 @ W0 )
& ( ( sdtasdt0 @ xa @ W0 )
= sz00 ) )
& ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xa ) )
& ? [W0: $i] :
( ( aElement0 @ W0 )
& ( ( sdtasdt0 @ xa @ W0 )
= xa ) )
& ( aElementOf0 @ xa @ ( slsdtgt0 @ xa ) )
& ? [W0: $i] :
( ( aElement0 @ W0 )
& ( ( sdtasdt0 @ xb @ W0 )
= sz00 ) )
& ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xb ) )
& ? [W0: $i] :
( ( aElement0 @ W0 )
& ( ( sdtasdt0 @ xb @ W0 )
= xb ) )
& ( aElementOf0 @ xb @ ( slsdtgt0 @ xb ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2203) ).
thf(38,axiom,
( ( aSet0 @ xI )
& ! [W0: $i] :
( ( aElementOf0 @ W0 @ xI )
=> ( ! [W1: $i] :
( ( aElementOf0 @ W1 @ xI )
=> ( aElementOf0 @ ( sdtpldt0 @ W0 @ W1 ) @ xI ) )
& ! [W1: $i] :
( ( aElement0 @ W1 )
=> ( aElementOf0 @ ( sdtasdt0 @ W1 @ W0 ) @ xI ) ) ) )
& ( aIdeal0 @ xI )
& ! [W0: $i] :
( ( aElementOf0 @ W0 @ ( slsdtgt0 @ xa ) )
<=> ? [W1: $i] :
( ( aElement0 @ W1 )
& ( ( sdtasdt0 @ xa @ W1 )
= W0 ) ) )
& ! [W0: $i] :
( ( aElementOf0 @ W0 @ ( slsdtgt0 @ xb ) )
<=> ? [W1: $i] :
( ( aElement0 @ W1 )
& ( ( sdtasdt0 @ xb @ W1 )
= W0 ) ) )
& ! [W0: $i] :
( ( aElementOf0 @ W0 @ xI )
<=> ? [W1: $i,W2: $i] :
( ( aElementOf0 @ W1 @ ( slsdtgt0 @ xa ) )
& ( aElementOf0 @ W2 @ ( slsdtgt0 @ xb ) )
& ( ( sdtpldt0 @ W1 @ W2 )
= W0 ) ) )
& ( xI
= ( sdtpldt1 @ ( slsdtgt0 @ xa ) @ ( slsdtgt0 @ xb ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2174) ).
thf(39,axiom,
( ( aElement0 @ xc )
& ? [W0: $i] :
( ( aElement0 @ W0 )
& ( ( sdtasdt0 @ xc @ W0 )
= xa ) )
& ( doDivides0 @ xc @ xa )
& ( aDivisorOf0 @ xc @ xa )
& ( aElement0 @ xc )
& ? [W0: $i] :
( ( aElement0 @ W0 )
& ( ( sdtasdt0 @ xc @ W0 )
= xb ) )
& ( doDivides0 @ xc @ xb )
& ( aDivisorOf0 @ xc @ xb )
& ! [W0: $i] :
( ( ( ( ( aElement0 @ W0 )
& ( ? [W1: $i] :
( ( aElement0 @ W1 )
& ( ( sdtasdt0 @ W0 @ W1 )
= xa ) )
| ( doDivides0 @ W0 @ xa ) ) )
| ( aDivisorOf0 @ W0 @ xa ) )
& ( ? [W1: $i] :
( ( aElement0 @ W1 )
& ( ( sdtasdt0 @ W0 @ W1 )
= xb ) )
| ( doDivides0 @ W0 @ xb )
| ( aDivisorOf0 @ W0 @ xb ) ) )
=> ( ? [W1: $i] :
( ( aElement0 @ W1 )
& ( ( sdtasdt0 @ W0 @ W1 )
= xc ) )
& ( doDivides0 @ W0 @ xc ) ) )
& ( aGcdOfAnd0 @ xc @ xa @ xb ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2129) ).
thf(40,axiom,
( ( xa != sz00 )
| ( xb != sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2110) ).
thf(41,axiom,
( ( aElement0 @ xa )
& ( aElement0 @ xb ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2091) ).
thf(42,conjecture,
xr != sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(43,negated_conjecture,
( ( xr != sz00 )
= $false ),
inference(negate_conjecture,[status(cth)],[42]) ).
thf(44,plain,
( ( xr != sz00 )
= $false ),
inference(unfold_def,[status(thm)],[43]) ).
thf(45,plain,
( ( ! [W0: $i] :
( ( aElement0 @ W0 )
=> ( aIdeal0 @ ( slsdtgt0 @ W0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(46,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aElement0 @ W0 )
& ( aElement0 @ W1 )
& ( W1 != sz00 ) )
=> ? [W2: $i,W3: $i] :
( ( aElement0 @ W2 )
& ( aElement0 @ W3 )
& ( W0
= ( sdtpldt0 @ ( sdtasdt0 @ W2 @ W1 ) @ W3 ) )
& ( ( W3 != sz00 )
=> ( iLess0 @ ( sbrdtbr0 @ W3 ) @ ( sbrdtbr0 @ W1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(47,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( iLess0 @ W0 @ W1 )
=> $true ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(48,plain,
( ( ! [W0: $i] :
( ( ( aElement0 @ W0 )
& ( W0 != sz00 ) )
=> ( aNaturalNumber0 @ ( sbrdtbr0 @ W0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(49,plain,
( ( ! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> $true ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(50,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aIdeal0 @ W0 )
& ( aIdeal0 @ W1 ) )
=> ( ! [W2: $i] :
( ( aElement0 @ W2 )
=> ( aElementOf0 @ W2 @ ( sdtpldt1 @ W0 @ W1 ) ) )
=> ! [W2: $i,W3: $i] :
( ( ( aElement0 @ W2 )
& ( aElement0 @ W3 ) )
=> ? [W4: $i] :
( ( aElement0 @ W4 )
& ( sdteqdtlpzmzozddtrp0 @ W4 @ W2 @ W0 )
& ( sdteqdtlpzmzozddtrp0 @ W4 @ W3 @ W1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(51,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aIdeal0 @ W0 )
& ( aIdeal0 @ W1 ) )
=> ( aIdeal0 @ ( sdtasasdt0 @ W0 @ W1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(52,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aIdeal0 @ W0 )
& ( aIdeal0 @ W1 ) )
=> ( aIdeal0 @ ( sdtpldt1 @ W0 @ W1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(53,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aSet0 @ W0 )
& ( aSet0 @ W1 ) )
=> ( ( ! [W2: $i] :
( ( aElementOf0 @ W2 @ W0 )
=> ( aElementOf0 @ W2 @ W1 ) )
& ! [W2: $i] :
( ( aElementOf0 @ W2 @ W1 )
=> ( aElementOf0 @ W2 @ W0 ) ) )
=> ( W0 = W1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(54,plain,
( ( ! [W0: $i] :
( ( aSet0 @ W0 )
=> ! [W1: $i] :
( ( aElementOf0 @ W1 @ W0 )
=> ( aElement0 @ W1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(55,plain,
( ( ! [W0: $i] :
( ( aSet0 @ W0 )
=> $true ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(56,plain,
( ( sz10 != sz00 )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(57,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aElement0 @ W0 )
& ( aElement0 @ W1 ) )
=> ( ( ( sdtasdt0 @ W0 @ W1 )
= sz00 )
=> ( ( W0 = sz00 )
| ( W1 = sz00 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(58,plain,
( ( ! [W0: $i] :
( ( aElement0 @ W0 )
=> ( ( ( sdtasdt0 @ W0 @ sz00 )
= sz00 )
& ( sz00
= ( sdtasdt0 @ sz00 @ W0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(59,plain,
( ( ! [W0: $i] :
( ( aElement0 @ W0 )
=> ( ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ W0 )
= ( smndt0 @ W0 ) )
& ( ( smndt0 @ W0 )
= ( sdtasdt0 @ W0 @ ( smndt0 @ sz10 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(60,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ( ( aElement0 @ W0 )
& ( aElement0 @ W1 )
& ( aElement0 @ 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)],[16]) ).
thf(61,plain,
( ( ! [W0: $i] :
( ( aElement0 @ W0 )
=> ( ( ( sdtasdt0 @ W0 @ sz10 )
= W0 )
& ( W0
= ( sdtasdt0 @ sz10 @ W0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(62,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ( ( aElement0 @ W0 )
& ( aElement0 @ W1 )
& ( aElement0 @ W2 ) )
=> ( ( sdtasdt0 @ ( sdtasdt0 @ W0 @ W1 ) @ W2 )
= ( sdtasdt0 @ W0 @ ( sdtasdt0 @ W1 @ W2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(63,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aElement0 @ W0 )
& ( aElement0 @ W1 ) )
=> ( ( sdtasdt0 @ W0 @ W1 )
= ( sdtasdt0 @ W1 @ W0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(64,plain,
( ( ! [W0: $i] :
( ( aElement0 @ W0 )
=> ( ( ( sdtpldt0 @ W0 @ ( smndt0 @ W0 ) )
= sz00 )
& ( sz00
= ( sdtpldt0 @ ( smndt0 @ W0 ) @ W0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(65,plain,
( ( ! [W0: $i] :
( ( aElement0 @ W0 )
=> ( ( ( sdtpldt0 @ W0 @ sz00 )
= W0 )
& ( W0
= ( sdtpldt0 @ sz00 @ W0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(66,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ( ( aElement0 @ W0 )
& ( aElement0 @ W1 )
& ( aElement0 @ W2 ) )
=> ( ( sdtpldt0 @ ( sdtpldt0 @ W0 @ W1 ) @ W2 )
= ( sdtpldt0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(67,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aElement0 @ W0 )
& ( aElement0 @ W1 ) )
=> ( ( sdtpldt0 @ W0 @ W1 )
= ( sdtpldt0 @ W1 @ W0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(68,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aElement0 @ W0 )
& ( aElement0 @ W1 ) )
=> ( aElement0 @ ( sdtasdt0 @ W0 @ W1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(69,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aElement0 @ W0 )
& ( aElement0 @ W1 ) )
=> ( aElement0 @ ( sdtpldt0 @ W0 @ W1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(70,plain,
( ( ! [W0: $i] :
( ( aElement0 @ W0 )
=> ( aElement0 @ ( smndt0 @ W0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(71,plain,
( ( aElement0 @ sz10 )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(72,plain,
( ( aElement0 @ sz00 )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(73,plain,
( ( ! [W0: $i] :
( ( aElement0 @ W0 )
=> $true ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(74,plain,
( ( ( aElement0 @ xq )
& ( aElement0 @ xr )
& ( xb
= ( sdtpldt0 @ ( sdtasdt0 @ xq @ xu ) @ xr ) )
& ( ( xr = sz00 )
| ( iLess0 @ ( sbrdtbr0 @ xr ) @ ( sbrdtbr0 @ xu ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(75,plain,
( ( ~ ( ? [W0: $i] :
( ( aElement0 @ W0 )
& ( ( sdtasdt0 @ xu @ W0 )
= xb ) )
| ( doDivides0 @ xu @ xb ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(76,plain,
( ( ~ ~ ( ? [W0: $i] :
( ( aElement0 @ W0 )
& ( ( sdtasdt0 @ xu @ W0 )
= xa ) )
& ( doDivides0 @ xu @ xa ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(77,plain,
( ( ? [W0: $i,W1: $i] :
( ( aElement0 @ W0 )
& ( aElement0 @ W1 )
& ( xu
= ( sdtpldt0 @ ( sdtasdt0 @ xa @ W0 ) @ ( sdtasdt0 @ xb @ W1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(78,plain,
( ( ~ ( ( ? [W0: $i] :
( ( aElement0 @ W0 )
& ( ( sdtasdt0 @ xu @ W0 )
= xa ) )
| ( doDivides0 @ xu @ xa )
| ( aDivisorOf0 @ xu @ xa ) )
& ( ? [W0: $i] :
( ( aElement0 @ W0 )
& ( ( sdtasdt0 @ xu @ W0 )
= xb ) )
| ( doDivides0 @ xu @ xb )
| ( aDivisorOf0 @ xu @ xb ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(79,plain,
( ( ? [W0: $i,W1: $i] :
( ( aElementOf0 @ W0 @ ( slsdtgt0 @ xa ) )
& ( aElementOf0 @ W1 @ ( slsdtgt0 @ xb ) )
& ( ( sdtpldt0 @ W0 @ W1 )
= xu ) )
& ( aElementOf0 @ xu @ xI )
& ( xu != sz00 )
& ! [W0: $i] :
( ( ( ? [W1: $i,W2: $i] :
( ( aElementOf0 @ W1 @ ( slsdtgt0 @ xa ) )
& ( aElementOf0 @ W2 @ ( slsdtgt0 @ xb ) )
& ( ( sdtpldt0 @ W1 @ W2 )
= W0 ) )
| ( aElementOf0 @ W0 @ xI ) )
& ( W0 != sz00 ) )
=> ~ ( iLess0 @ ( sbrdtbr0 @ W0 ) @ ( sbrdtbr0 @ xu ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(80,plain,
( ( ? [W0: $i] :
( ! [W1: $i] :
( ( aElementOf0 @ W1 @ ( slsdtgt0 @ xa ) )
<=> ? [W2: $i] :
( ( aElement0 @ W2 )
& ( ( sdtasdt0 @ xa @ W2 )
= W1 ) ) )
& ! [W1: $i] :
( ( aElementOf0 @ W1 @ ( slsdtgt0 @ xb ) )
<=> ? [W2: $i] :
( ( aElement0 @ W2 )
& ( ( sdtasdt0 @ xb @ W2 )
= W1 ) ) )
& ? [W1: $i,W2: $i] :
( ( aElementOf0 @ W1 @ ( slsdtgt0 @ xa ) )
& ( aElementOf0 @ W2 @ ( slsdtgt0 @ xb ) )
& ( ( sdtpldt0 @ W1 @ W2 )
= W0 ) )
& ( aElementOf0 @ W0 @ ( sdtpldt1 @ ( slsdtgt0 @ xa ) @ ( slsdtgt0 @ xb ) ) )
& ( W0 != sz00 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(81,plain,
( ( ? [W0: $i] :
( ( aElement0 @ W0 )
& ( ( sdtasdt0 @ xa @ W0 )
= sz00 ) )
& ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xa ) )
& ? [W0: $i] :
( ( aElement0 @ W0 )
& ( ( sdtasdt0 @ xa @ W0 )
= xa ) )
& ( aElementOf0 @ xa @ ( slsdtgt0 @ xa ) )
& ? [W0: $i] :
( ( aElement0 @ W0 )
& ( ( sdtasdt0 @ xb @ W0 )
= sz00 ) )
& ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xb ) )
& ? [W0: $i] :
( ( aElement0 @ W0 )
& ( ( sdtasdt0 @ xb @ W0 )
= xb ) )
& ( aElementOf0 @ xb @ ( slsdtgt0 @ xb ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(82,plain,
( ( ( aSet0 @ xI )
& ! [W0: $i] :
( ( aElementOf0 @ W0 @ xI )
=> ( ! [W1: $i] :
( ( aElementOf0 @ W1 @ xI )
=> ( aElementOf0 @ ( sdtpldt0 @ W0 @ W1 ) @ xI ) )
& ! [W1: $i] :
( ( aElement0 @ W1 )
=> ( aElementOf0 @ ( sdtasdt0 @ W1 @ W0 ) @ xI ) ) ) )
& ( aIdeal0 @ xI )
& ! [W0: $i] :
( ( aElementOf0 @ W0 @ ( slsdtgt0 @ xa ) )
<=> ? [W1: $i] :
( ( aElement0 @ W1 )
& ( ( sdtasdt0 @ xa @ W1 )
= W0 ) ) )
& ! [W0: $i] :
( ( aElementOf0 @ W0 @ ( slsdtgt0 @ xb ) )
<=> ? [W1: $i] :
( ( aElement0 @ W1 )
& ( ( sdtasdt0 @ xb @ W1 )
= W0 ) ) )
& ! [W0: $i] :
( ( aElementOf0 @ W0 @ xI )
<=> ? [W1: $i,W2: $i] :
( ( aElementOf0 @ W1 @ ( slsdtgt0 @ xa ) )
& ( aElementOf0 @ W2 @ ( slsdtgt0 @ xb ) )
& ( ( sdtpldt0 @ W1 @ W2 )
= W0 ) ) )
& ( xI
= ( sdtpldt1 @ ( slsdtgt0 @ xa ) @ ( slsdtgt0 @ xb ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(83,plain,
( ( ( aElement0 @ xc )
& ? [W0: $i] :
( ( aElement0 @ W0 )
& ( ( sdtasdt0 @ xc @ W0 )
= xa ) )
& ( doDivides0 @ xc @ xa )
& ( aDivisorOf0 @ xc @ xa )
& ( aElement0 @ xc )
& ? [W0: $i] :
( ( aElement0 @ W0 )
& ( ( sdtasdt0 @ xc @ W0 )
= xb ) )
& ( doDivides0 @ xc @ xb )
& ( aDivisorOf0 @ xc @ xb )
& ! [W0: $i] :
( ( ( ( ( aElement0 @ W0 )
& ( ? [W1: $i] :
( ( aElement0 @ W1 )
& ( ( sdtasdt0 @ W0 @ W1 )
= xa ) )
| ( doDivides0 @ W0 @ xa ) ) )
| ( aDivisorOf0 @ W0 @ xa ) )
& ( ? [W1: $i] :
( ( aElement0 @ W1 )
& ( ( sdtasdt0 @ W0 @ W1 )
= xb ) )
| ( doDivides0 @ W0 @ xb )
| ( aDivisorOf0 @ W0 @ xb ) ) )
=> ( ? [W1: $i] :
( ( aElement0 @ W1 )
& ( ( sdtasdt0 @ W0 @ W1 )
= xc ) )
& ( doDivides0 @ W0 @ xc ) ) )
& ( aGcdOfAnd0 @ xc @ xa @ xb ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(84,plain,
( ( ( xa != sz00 )
| ( xb != sz00 ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(85,plain,
( ( ( aElement0 @ xa )
& ( aElement0 @ xb ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(86,plain,
( ( ~ ( ( xr != sz00 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[44]) ).
thf(87,plain,
( ( ( aElement0 @ xa )
& ( aElement0 @ xb ) )
= $true ),
inference(copy,[status(thm)],[85]) ).
thf(88,plain,
( ( ( xa != sz00 )
| ( xb != sz00 ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(89,plain,
( ( ( aElement0 @ xc )
& ? [W0: $i] :
( ( aElement0 @ W0 )
& ( ( sdtasdt0 @ xc @ W0 )
= xa ) )
& ( doDivides0 @ xc @ xa )
& ( aDivisorOf0 @ xc @ xa )
& ( aElement0 @ xc )
& ? [W0: $i] :
( ( aElement0 @ W0 )
& ( ( sdtasdt0 @ xc @ W0 )
= xb ) )
& ( doDivides0 @ xc @ xb )
& ( aDivisorOf0 @ xc @ xb )
& ! [W0: $i] :
( ( ( ( ( aElement0 @ W0 )
& ( ? [W1: $i] :
( ( aElement0 @ W1 )
& ( ( sdtasdt0 @ W0 @ W1 )
= xa ) )
| ( doDivides0 @ W0 @ xa ) ) )
| ( aDivisorOf0 @ W0 @ xa ) )
& ( ? [W1: $i] :
( ( aElement0 @ W1 )
& ( ( sdtasdt0 @ W0 @ W1 )
= xb ) )
| ( doDivides0 @ W0 @ xb )
| ( aDivisorOf0 @ W0 @ xb ) ) )
=> ( ? [W1: $i] :
( ( aElement0 @ W1 )
& ( ( sdtasdt0 @ W0 @ W1 )
= xc ) )
& ( doDivides0 @ W0 @ xc ) ) )
& ( aGcdOfAnd0 @ xc @ xa @ xb ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(90,plain,
( ( ( aSet0 @ xI )
& ! [W0: $i] :
( ( aElementOf0 @ W0 @ xI )
=> ( ! [W1: $i] :
( ( aElementOf0 @ W1 @ xI )
=> ( aElementOf0 @ ( sdtpldt0 @ W0 @ W1 ) @ xI ) )
& ! [W1: $i] :
( ( aElement0 @ W1 )
=> ( aElementOf0 @ ( sdtasdt0 @ W1 @ W0 ) @ xI ) ) ) )
& ( aIdeal0 @ xI )
& ! [W0: $i] :
( ( aElementOf0 @ W0 @ ( slsdtgt0 @ xa ) )
<=> ? [W1: $i] :
( ( aElement0 @ W1 )
& ( ( sdtasdt0 @ xa @ W1 )
= W0 ) ) )
& ! [W0: $i] :
( ( aElementOf0 @ W0 @ ( slsdtgt0 @ xb ) )
<=> ? [W1: $i] :
( ( aElement0 @ W1 )
& ( ( sdtasdt0 @ xb @ W1 )
= W0 ) ) )
& ! [W0: $i] :
( ( aElementOf0 @ W0 @ xI )
<=> ? [W1: $i,W2: $i] :
( ( aElementOf0 @ W1 @ ( slsdtgt0 @ xa ) )
& ( aElementOf0 @ W2 @ ( slsdtgt0 @ xb ) )
& ( ( sdtpldt0 @ W1 @ W2 )
= W0 ) ) )
& ( xI
= ( sdtpldt1 @ ( slsdtgt0 @ xa ) @ ( slsdtgt0 @ xb ) ) ) )
= $true ),
inference(copy,[status(thm)],[82]) ).
thf(91,plain,
( ( ? [W0: $i] :
( ( aElement0 @ W0 )
& ( ( sdtasdt0 @ xa @ W0 )
= sz00 ) )
& ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xa ) )
& ? [W0: $i] :
( ( aElement0 @ W0 )
& ( ( sdtasdt0 @ xa @ W0 )
= xa ) )
& ( aElementOf0 @ xa @ ( slsdtgt0 @ xa ) )
& ? [W0: $i] :
( ( aElement0 @ W0 )
& ( ( sdtasdt0 @ xb @ W0 )
= sz00 ) )
& ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xb ) )
& ? [W0: $i] :
( ( aElement0 @ W0 )
& ( ( sdtasdt0 @ xb @ W0 )
= xb ) )
& ( aElementOf0 @ xb @ ( slsdtgt0 @ xb ) ) )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(92,plain,
( ( ? [W0: $i] :
( ! [W1: $i] :
( ( aElementOf0 @ W1 @ ( slsdtgt0 @ xa ) )
<=> ? [W2: $i] :
( ( aElement0 @ W2 )
& ( ( sdtasdt0 @ xa @ W2 )
= W1 ) ) )
& ! [W1: $i] :
( ( aElementOf0 @ W1 @ ( slsdtgt0 @ xb ) )
<=> ? [W2: $i] :
( ( aElement0 @ W2 )
& ( ( sdtasdt0 @ xb @ W2 )
= W1 ) ) )
& ? [W1: $i,W2: $i] :
( ( aElementOf0 @ W1 @ ( slsdtgt0 @ xa ) )
& ( aElementOf0 @ W2 @ ( slsdtgt0 @ xb ) )
& ( ( sdtpldt0 @ W1 @ W2 )
= W0 ) )
& ( aElementOf0 @ W0 @ ( sdtpldt1 @ ( slsdtgt0 @ xa ) @ ( slsdtgt0 @ xb ) ) )
& ( W0 != sz00 ) ) )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(93,plain,
( ( ? [W0: $i,W1: $i] :
( ( aElementOf0 @ W0 @ ( slsdtgt0 @ xa ) )
& ( aElementOf0 @ W1 @ ( slsdtgt0 @ xb ) )
& ( ( sdtpldt0 @ W0 @ W1 )
= xu ) )
& ( aElementOf0 @ xu @ xI )
& ( xu != sz00 )
& ! [W0: $i] :
( ( ( ? [W1: $i,W2: $i] :
( ( aElementOf0 @ W1 @ ( slsdtgt0 @ xa ) )
& ( aElementOf0 @ W2 @ ( slsdtgt0 @ xb ) )
& ( ( sdtpldt0 @ W1 @ W2 )
= W0 ) )
| ( aElementOf0 @ W0 @ xI ) )
& ( W0 != sz00 ) )
=> ~ ( iLess0 @ ( sbrdtbr0 @ W0 ) @ ( sbrdtbr0 @ xu ) ) ) )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(94,plain,
( ( ~ ( ( ? [W0: $i] :
( ( aElement0 @ W0 )
& ( ( sdtasdt0 @ xu @ W0 )
= xa ) )
| ( doDivides0 @ xu @ xa )
| ( aDivisorOf0 @ xu @ xa ) )
& ( ? [W0: $i] :
( ( aElement0 @ W0 )
& ( ( sdtasdt0 @ xu @ W0 )
= xb ) )
| ( doDivides0 @ xu @ xb )
| ( aDivisorOf0 @ xu @ xb ) ) ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(95,plain,
( ( ? [W0: $i,W1: $i] :
( ( aElement0 @ W0 )
& ( aElement0 @ W1 )
& ( xu
= ( sdtpldt0 @ ( sdtasdt0 @ xa @ W0 ) @ ( sdtasdt0 @ xb @ W1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(96,plain,
( ( ~ ~ ( ? [W0: $i] :
( ( aElement0 @ W0 )
& ( ( sdtasdt0 @ xu @ W0 )
= xa ) )
& ( doDivides0 @ xu @ xa ) ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(97,plain,
( ( ~ ( ? [W0: $i] :
( ( aElement0 @ W0 )
& ( ( sdtasdt0 @ xu @ W0 )
= xb ) )
| ( doDivides0 @ xu @ xb ) ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(98,plain,
( ( ( aElement0 @ xq )
& ( aElement0 @ xr )
& ( xb
= ( sdtpldt0 @ ( sdtasdt0 @ xq @ xu ) @ xr ) )
& ( ( xr = sz00 )
| ( iLess0 @ ( sbrdtbr0 @ xr ) @ ( sbrdtbr0 @ xu ) ) ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(99,plain,
( ( ! [W0: $i] :
( ( aElement0 @ W0 )
=> $true ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(100,plain,
( ( aElement0 @ sz00 )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(101,plain,
( ( aElement0 @ sz10 )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(102,plain,
( ( ! [W0: $i] :
( ( aElement0 @ W0 )
=> ( aElement0 @ ( smndt0 @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(103,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aElement0 @ W0 )
& ( aElement0 @ W1 ) )
=> ( aElement0 @ ( sdtpldt0 @ W0 @ W1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(104,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aElement0 @ W0 )
& ( aElement0 @ W1 ) )
=> ( aElement0 @ ( sdtasdt0 @ W0 @ W1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(105,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aElement0 @ W0 )
& ( aElement0 @ W1 ) )
=> ( ( sdtpldt0 @ W0 @ W1 )
= ( sdtpldt0 @ W1 @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(106,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ( ( aElement0 @ W0 )
& ( aElement0 @ W1 )
& ( aElement0 @ W2 ) )
=> ( ( sdtpldt0 @ ( sdtpldt0 @ W0 @ W1 ) @ W2 )
= ( sdtpldt0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(107,plain,
( ( ! [W0: $i] :
( ( aElement0 @ W0 )
=> ( ( ( sdtpldt0 @ W0 @ sz00 )
= W0 )
& ( W0
= ( sdtpldt0 @ sz00 @ W0 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(108,plain,
( ( ! [W0: $i] :
( ( aElement0 @ W0 )
=> ( ( ( sdtpldt0 @ W0 @ ( smndt0 @ W0 ) )
= sz00 )
& ( sz00
= ( sdtpldt0 @ ( smndt0 @ W0 ) @ W0 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(109,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aElement0 @ W0 )
& ( aElement0 @ W1 ) )
=> ( ( sdtasdt0 @ W0 @ W1 )
= ( sdtasdt0 @ W1 @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(110,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ( ( aElement0 @ W0 )
& ( aElement0 @ W1 )
& ( aElement0 @ W2 ) )
=> ( ( sdtasdt0 @ ( sdtasdt0 @ W0 @ W1 ) @ W2 )
= ( sdtasdt0 @ W0 @ ( sdtasdt0 @ W1 @ W2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(111,plain,
( ( ! [W0: $i] :
( ( aElement0 @ W0 )
=> ( ( ( sdtasdt0 @ W0 @ sz10 )
= W0 )
& ( W0
= ( sdtasdt0 @ sz10 @ W0 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(112,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ( ( aElement0 @ W0 )
& ( aElement0 @ W1 )
& ( aElement0 @ 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)],[60]) ).
thf(113,plain,
( ( ! [W0: $i] :
( ( aElement0 @ W0 )
=> ( ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ W0 )
= ( smndt0 @ W0 ) )
& ( ( smndt0 @ W0 )
= ( sdtasdt0 @ W0 @ ( smndt0 @ sz10 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(114,plain,
( ( ! [W0: $i] :
( ( aElement0 @ W0 )
=> ( ( ( sdtasdt0 @ W0 @ sz00 )
= sz00 )
& ( sz00
= ( sdtasdt0 @ sz00 @ W0 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(115,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aElement0 @ W0 )
& ( aElement0 @ W1 ) )
=> ( ( ( sdtasdt0 @ W0 @ W1 )
= sz00 )
=> ( ( W0 = sz00 )
| ( W1 = sz00 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(116,plain,
( ( sz10 != sz00 )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(117,plain,
( ( ! [W0: $i] :
( ( aSet0 @ W0 )
=> $true ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(118,plain,
( ( ! [W0: $i] :
( ( aSet0 @ W0 )
=> ! [W1: $i] :
( ( aElementOf0 @ W1 @ W0 )
=> ( aElement0 @ W1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(119,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aSet0 @ W0 )
& ( aSet0 @ W1 ) )
=> ( ( ! [W2: $i] :
( ( aElementOf0 @ W2 @ W0 )
=> ( aElementOf0 @ W2 @ W1 ) )
& ! [W2: $i] :
( ( aElementOf0 @ W2 @ W1 )
=> ( aElementOf0 @ W2 @ W0 ) ) )
=> ( W0 = W1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(120,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aIdeal0 @ W0 )
& ( aIdeal0 @ W1 ) )
=> ( aIdeal0 @ ( sdtpldt1 @ W0 @ W1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(121,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aIdeal0 @ W0 )
& ( aIdeal0 @ W1 ) )
=> ( aIdeal0 @ ( sdtasasdt0 @ W0 @ W1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(122,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aIdeal0 @ W0 )
& ( aIdeal0 @ W1 ) )
=> ( ! [W2: $i] :
( ( aElement0 @ W2 )
=> ( aElementOf0 @ W2 @ ( sdtpldt1 @ W0 @ W1 ) ) )
=> ! [W2: $i,W3: $i] :
( ( ( aElement0 @ W2 )
& ( aElement0 @ W3 ) )
=> ? [W4: $i] :
( ( aElement0 @ W4 )
& ( sdteqdtlpzmzozddtrp0 @ W4 @ W2 @ W0 )
& ( sdteqdtlpzmzozddtrp0 @ W4 @ W3 @ W1 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(123,plain,
( ( ! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> $true ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(124,plain,
( ( ! [W0: $i] :
( ( ( aElement0 @ W0 )
& ( W0 != sz00 ) )
=> ( aNaturalNumber0 @ ( sbrdtbr0 @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(125,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( iLess0 @ W0 @ W1 )
=> $true ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(126,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aElement0 @ W0 )
& ( aElement0 @ W1 )
& ( W1 != sz00 ) )
=> ? [W2: $i,W3: $i] :
( ( aElement0 @ W2 )
& ( aElement0 @ W3 )
& ( W0
= ( sdtpldt0 @ ( sdtasdt0 @ W2 @ W1 ) @ W3 ) )
& ( ( W3 != sz00 )
=> ( iLess0 @ ( sbrdtbr0 @ W3 ) @ ( sbrdtbr0 @ W1 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(127,plain,
( ( ! [W0: $i] :
( ( aElement0 @ W0 )
=> ( aIdeal0 @ ( slsdtgt0 @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(128,plain,
( ( ~ ( ( xr != sz00 ) ) )
= $true ),
inference(copy,[status(thm)],[86]) ).
thf(129,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ~ ( ~ ( aElement0 @ SX0 )
| ~ ( aElement0 @ SX1 ) )
| ~ ( ( SX1 != sz00 ) ) )
| ~ ! [SX2: $i] :
~ ~ ! [SX3: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ SX2 )
| ~ ( aElement0 @ SX3 ) )
| ( SX0
!= ( sdtpldt0 @ ( sdtasdt0 @ SX2 @ SX1 ) @ SX3 ) ) )
| ~ ( ~ ( ( SX3 != sz00 ) )
| ( iLess0 @ ( sbrdtbr0 @ SX3 ) @ ( sbrdtbr0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[126]) ).
thf(130,plain,
( ( ( xa != sz00 )
| ( xb != sz00 ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(131,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aElement0 @ SX0 )
| ~ ( aElement0 @ SX1 ) )
| ( ( sdtasdt0 @ SX0 @ SX1 )
!= sz00 )
| ( SX0 = sz00 )
| ( SX1 = sz00 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[115]) ).
thf(132,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX1: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( aElement0 @ SX2 )
| ( ( sdtasdt0 @ xa @ SX2 )
!= SX1 ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( aElement0 @ SX2 )
| ( ( sdtasdt0 @ xa @ SX2 )
!= SX1 ) )
| ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) ) ) )
| ~ ! [SX1: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xb ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( aElement0 @ SX2 )
| ( ( sdtasdt0 @ xb @ SX2 )
!= SX1 ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( aElement0 @ SX2 )
| ( ( sdtasdt0 @ xb @ SX2 )
!= SX1 ) )
| ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xb ) ) ) ) )
| ~ ~ ! [SX1: $i] :
~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SX2 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SX1 @ SX2 )
!= SX0 ) ) )
| ~ ( aElementOf0 @ SX0 @ ( sdtpldt1 @ ( slsdtgt0 @ xa ) @ ( slsdtgt0 @ xb ) ) ) )
| ~ ( ( SX0 != sz00 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(133,plain,
( ( ~ ! [SX0: $i] :
~ ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ( aElement0 @ SX0 )
| ~ ( aElement0 @ SX1 ) )
| ( xu
!= ( sdtpldt0 @ ( sdtasdt0 @ xa @ SX0 ) @ ( sdtasdt0 @ xb @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(134,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aSet0 @ SX0 )
| ~ ( aSet0 @ SX1 ) )
| ~ ~ ( ~ ! [SX2: $i] :
( ~ ( aElementOf0 @ SX2 @ SX0 )
| ( aElementOf0 @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( aElementOf0 @ SX2 @ SX1 )
| ( aElementOf0 @ SX2 @ SX0 ) ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[119]) ).
thf(135,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ! [SX0: $i] :
~ ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SX0 @ SX1 )
!= xu ) )
| ~ ( aElementOf0 @ xu @ xI ) )
| ~ ( ( xu != sz00 ) ) )
| ~ ! [SX0: $i] :
( ~ ~ ( ~ ( ~ ! [SX1: $i] :
~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SX2 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SX1 @ SX2 )
!= SX0 ) )
| ( aElementOf0 @ SX0 @ xI ) )
| ~ ( ( SX0 != sz00 ) ) )
| ~ ( iLess0 @ ( sbrdtbr0 @ SX0 ) @ ( sbrdtbr0 @ xu ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(136,plain,
( ( ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ~ ( ( ( sdtasdt0 @ SX0 @ sz00 )
!= sz00 )
| ( sz00
!= ( sdtasdt0 @ sz00 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[114]) ).
thf(137,plain,
( ( ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| $true ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(138,plain,
( ( ~ ( ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xu @ SX0 )
!= xb ) )
| ( doDivides0 @ xu @ xb ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(139,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aIdeal0 @ SX0 )
| ~ ( aIdeal0 @ SX1 ) )
| ( aIdeal0 @ ( sdtpldt1 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[120]) ).
thf(140,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xa @ SX0 )
!= sz00 ) )
| ~ ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xa ) ) )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xa @ SX0 )
!= xa ) ) )
| ~ ( aElementOf0 @ xa @ ( slsdtgt0 @ xa ) ) )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xb @ SX0 )
!= sz00 ) ) )
| ~ ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xb ) ) )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xb @ SX0 )
!= xb ) ) )
| ~ ( aElementOf0 @ xb @ ( slsdtgt0 @ xb ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(141,plain,
( ( ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( aIdeal0 @ ( slsdtgt0 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[127]) ).
thf(142,plain,
( ( ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| $true ) )
= $true ),
inference(unfold_def,[status(thm)],[123]) ).
thf(143,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ~ ( ~ ( aElement0 @ SX0 )
| ~ ( aElement0 @ SX1 ) )
| ~ ( aElement0 @ 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)],[112]) ).
thf(144,plain,
( ( ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ~ ( ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ SX0 )
!= ( smndt0 @ SX0 ) )
| ( ( smndt0 @ SX0 )
!= ( sdtasdt0 @ SX0 @ ( smndt0 @ sz10 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[113]) ).
thf(145,plain,
( ( ~ ( ~ ( aElement0 @ xa )
| ~ ( aElement0 @ xb ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(146,plain,
( ( sz10 != sz00 )
= $true ),
inference(unfold_def,[status(thm)],[116]) ).
thf(147,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ~ ( ~ ( aElement0 @ SX0 )
| ~ ( aElement0 @ SX1 ) )
| ~ ( aElement0 @ SX2 ) )
| ( ( sdtasdt0 @ ( sdtasdt0 @ SX0 @ SX1 ) @ SX2 )
= ( sdtasdt0 @ SX0 @ ( sdtasdt0 @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[110]) ).
thf(148,plain,
( ( ! [SX0: $i] :
( ~ ( aSet0 @ SX0 )
| $true ) )
= $true ),
inference(unfold_def,[status(thm)],[117]) ).
thf(149,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aSet0 @ xI )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ~ ( ~ ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) )
| ~ ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) ) )
| ~ ( aIdeal0 @ xI ) )
| ~ ! [SX0: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( aElement0 @ SX1 )
| ( ( sdtasdt0 @ xa @ SX1 )
!= SX0 ) ) )
| ~ ( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( aElement0 @ SX1 )
| ( ( sdtasdt0 @ xa @ SX1 )
!= SX0 ) )
| ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) ) ) )
| ~ ! [SX0: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( aElement0 @ SX1 )
| ( ( sdtasdt0 @ xb @ SX1 )
!= SX0 ) ) )
| ~ ( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( aElement0 @ SX1 )
| ( ( sdtasdt0 @ xb @ SX1 )
!= SX0 ) )
| ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) ) ) ) )
| ~ ! [SX0: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX0 @ xI )
| ~ ! [SX1: $i] :
~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SX2 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SX1 @ SX2 )
!= SX0 ) ) )
| ~ ( ~ ~ ! [SX1: $i] :
~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SX2 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SX1 @ SX2 )
!= SX0 ) )
| ( aElementOf0 @ SX0 @ xI ) ) ) )
| ( xI
!= ( sdtpldt1 @ ( slsdtgt0 @ xa ) @ ( slsdtgt0 @ xb ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(150,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 ) )
| ~ ( iLess0 @ SX0 @ SX1 )
| $true ) )
= $true ),
inference(unfold_def,[status(thm)],[125]) ).
thf(151,plain,
( ( ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ~ ( ( ( sdtpldt0 @ SX0 @ sz00 )
!= SX0 )
| ( SX0
!= ( sdtpldt0 @ sz00 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(152,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aElement0 @ SX0 )
| ~ ( aElement0 @ SX1 ) )
| ( ( sdtpldt0 @ SX0 @ SX1 )
= ( sdtpldt0 @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[105]) ).
thf(153,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ xq )
| ~ ( aElement0 @ xr ) )
| ( xb
!= ( sdtpldt0 @ ( sdtasdt0 @ xq @ xu ) @ xr ) ) )
| ~ ( ( xr = sz00 )
| ( iLess0 @ ( sbrdtbr0 @ xr ) @ ( sbrdtbr0 @ xu ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(154,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aIdeal0 @ SX0 )
| ~ ( aIdeal0 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( aElement0 @ SX2 )
| ( aElementOf0 @ SX2 @ ( sdtpldt1 @ SX0 @ SX1 ) ) )
| ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( aElement0 @ SX2 )
| ~ ( aElement0 @ SX3 ) )
| ~ ! [SX4: $i] :
~ ~ ( ~ ~ ( ~ ( aElement0 @ SX4 )
| ~ ( sdteqdtlpzmzozddtrp0 @ SX4 @ SX2 @ SX0 ) )
| ~ ( sdteqdtlpzmzozddtrp0 @ SX4 @ SX3 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[122]) ).
thf(155,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aElement0 @ SX0 )
| ~ ( aElement0 @ SX1 ) )
| ( ( sdtasdt0 @ SX0 @ SX1 )
= ( sdtasdt0 @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(156,plain,
( ( ~ ~ ( ~ ( ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xu @ SX0 )
!= xa ) )
| ( doDivides0 @ xu @ xa )
| ( aDivisorOf0 @ xu @ xa ) )
| ~ ( ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xu @ SX0 )
!= xb ) )
| ( doDivides0 @ xu @ xb )
| ( aDivisorOf0 @ xu @ xb ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(157,plain,
( ( ~ ( ( xr != sz00 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[128]) ).
thf(158,plain,
( ( ! [SX0: $i] :
( ~ ( aSet0 @ SX0 )
| ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ SX0 )
| ( aElement0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[118]) ).
thf(159,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( aElement0 @ SX0 )
| ~ ( ( SX0 != sz00 ) ) )
| ( aNaturalNumber0 @ ( sbrdtbr0 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[124]) ).
thf(160,plain,
( ( ~ ~ ~ ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xu @ SX0 )
!= xa ) )
| ~ ( doDivides0 @ xu @ xa ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(161,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aIdeal0 @ SX0 )
| ~ ( aIdeal0 @ SX1 ) )
| ( aIdeal0 @ ( sdtasasdt0 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[121]) ).
thf(162,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ xc )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xc @ SX0 )
!= xa ) ) )
| ~ ( doDivides0 @ xc @ xa ) )
| ~ ( aDivisorOf0 @ xc @ xa ) )
| ~ ( aElement0 @ xc ) )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xc @ SX0 )
!= xb ) ) )
| ~ ( doDivides0 @ xc @ xb ) )
| ~ ( aDivisorOf0 @ xc @ xb ) )
| ~ ! [SX0: $i] :
( ~ ~ ( ~ ( ~ ( ~ ( aElement0 @ SX0 )
| ~ ( ~ ! [SX1: $i] :
~ ~ ( ~ ( aElement0 @ SX1 )
| ( ( sdtasdt0 @ SX0 @ SX1 )
!= xa ) )
| ( doDivides0 @ SX0 @ xa ) ) )
| ( aDivisorOf0 @ SX0 @ xa ) )
| ~ ( ~ ! [SX1: $i] :
~ ~ ( ~ ( aElement0 @ SX1 )
| ( ( sdtasdt0 @ SX0 @ SX1 )
!= xb ) )
| ( doDivides0 @ SX0 @ xb )
| ( aDivisorOf0 @ SX0 @ xb ) ) )
| ~ ( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( aElement0 @ SX1 )
| ( ( sdtasdt0 @ SX0 @ SX1 )
!= xc ) )
| ~ ( doDivides0 @ SX0 @ xc ) ) ) )
| ~ ( aGcdOfAnd0 @ xc @ xa @ xb ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(163,plain,
( ( ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ~ ( ( ( sdtasdt0 @ SX0 @ sz10 )
!= SX0 )
| ( SX0
!= ( sdtasdt0 @ sz10 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[111]) ).
thf(164,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ~ ( ~ ( aElement0 @ SX0 )
| ~ ( aElement0 @ SX1 ) )
| ~ ( aElement0 @ SX2 ) )
| ( ( sdtpldt0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ SX2 )
= ( sdtpldt0 @ SX0 @ ( sdtpldt0 @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(165,plain,
( ( ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( aElement0 @ ( smndt0 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(166,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aElement0 @ SX0 )
| ~ ( aElement0 @ SX1 ) )
| ( aElement0 @ ( sdtpldt0 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(167,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aElement0 @ SX0 )
| ~ ( aElement0 @ SX1 ) )
| ( aElement0 @ ( sdtasdt0 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(168,plain,
( ( ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ~ ( ( ( sdtpldt0 @ SX0 @ ( smndt0 @ SX0 ) )
!= sz00 )
| ( sz00
!= ( sdtpldt0 @ ( smndt0 @ SX0 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[108]) ).
thf(169,plain,
! [SV1: $i] :
( ( ! [SY90: $i] :
( ~ ~ ( ~ ~ ( ~ ( aElement0 @ SV1 )
| ~ ( aElement0 @ SY90 ) )
| ~ ( ( SY90 != sz00 ) ) )
| ~ ! [SY91: $i] :
~ ~ ! [SY92: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ SY91 )
| ~ ( aElement0 @ SY92 ) )
| ( SV1
!= ( sdtpldt0 @ ( sdtasdt0 @ SY91 @ SY90 ) @ SY92 ) ) )
| ~ ( ~ ( ( SY92 != sz00 ) )
| ( iLess0 @ ( sbrdtbr0 @ SY92 ) @ ( sbrdtbr0 @ SY90 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(170,plain,
( ( ( xa != sz00 )
= $true )
| ( ( xb != sz00 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[130]) ).
thf(171,plain,
! [SV2: $i] :
( ( ! [SY93: $i] :
( ~ ~ ( ~ ( aElement0 @ SV2 )
| ~ ( aElement0 @ SY93 ) )
| ( ( sdtasdt0 @ SV2 @ SY93 )
!= sz00 )
| ( SV2 = sz00 )
| ( SY93 = sz00 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(172,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX1: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( aElement0 @ SX2 )
| ( ( sdtasdt0 @ xa @ SX2 )
!= SX1 ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( aElement0 @ SX2 )
| ( ( sdtasdt0 @ xa @ SX2 )
!= SX1 ) )
| ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) ) ) )
| ~ ! [SX1: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xb ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( aElement0 @ SX2 )
| ( ( sdtasdt0 @ xb @ SX2 )
!= SX1 ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( aElement0 @ SX2 )
| ( ( sdtasdt0 @ xb @ SX2 )
!= SX1 ) )
| ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xb ) ) ) ) )
| ~ ~ ! [SX1: $i] :
~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SX2 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SX1 @ SX2 )
!= SX0 ) ) )
| ~ ( aElementOf0 @ SX0 @ ( sdtpldt1 @ ( slsdtgt0 @ xa ) @ ( slsdtgt0 @ xb ) ) ) )
| ~ ( ( SX0 != sz00 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(173,plain,
( ( ! [SX0: $i] :
~ ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ( aElement0 @ SX0 )
| ~ ( aElement0 @ SX1 ) )
| ( xu
!= ( sdtpldt0 @ ( sdtasdt0 @ xa @ SX0 ) @ ( sdtasdt0 @ xb @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(174,plain,
! [SV3: $i] :
( ( ! [SY94: $i] :
( ~ ~ ( ~ ( aSet0 @ SV3 )
| ~ ( aSet0 @ SY94 ) )
| ~ ~ ( ~ ! [SY95: $i] :
( ~ ( aElementOf0 @ SY95 @ SV3 )
| ( aElementOf0 @ SY95 @ SY94 ) )
| ~ ! [SY96: $i] :
( ~ ( aElementOf0 @ SY96 @ SY94 )
| ( aElementOf0 @ SY96 @ SV3 ) ) )
| ( SV3 = SY94 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(175,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ! [SX0: $i] :
~ ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SX0 @ SX1 )
!= xu ) )
| ~ ( aElementOf0 @ xu @ xI ) )
| ~ ( ( xu != sz00 ) ) )
| ~ ! [SX0: $i] :
( ~ ~ ( ~ ( ~ ! [SX1: $i] :
~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SX2 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SX1 @ SX2 )
!= SX0 ) )
| ( aElementOf0 @ SX0 @ xI ) )
| ~ ( ( SX0 != sz00 ) ) )
| ~ ( iLess0 @ ( sbrdtbr0 @ SX0 ) @ ( sbrdtbr0 @ xu ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(176,plain,
! [SV4: $i] :
( ( ~ ( aElement0 @ SV4 )
| ~ ( ( ( sdtasdt0 @ SV4 @ sz00 )
!= sz00 )
| ( sz00
!= ( sdtasdt0 @ sz00 @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(177,plain,
! [SV5: $i] :
( ( ~ ( aElement0 @ SV5 )
| $true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(178,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xu @ SX0 )
!= xb ) )
| ( doDivides0 @ xu @ xb ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(179,plain,
! [SV6: $i] :
( ( ! [SY97: $i] :
( ~ ~ ( ~ ( aIdeal0 @ SV6 )
| ~ ( aIdeal0 @ SY97 ) )
| ( aIdeal0 @ ( sdtpldt1 @ SV6 @ SY97 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(180,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xa @ SX0 )
!= sz00 ) )
| ~ ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xa ) ) )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xa @ SX0 )
!= xa ) ) )
| ~ ( aElementOf0 @ xa @ ( slsdtgt0 @ xa ) ) )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xb @ SX0 )
!= sz00 ) ) )
| ~ ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xb ) ) )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xb @ SX0 )
!= xb ) ) )
| ~ ( aElementOf0 @ xb @ ( slsdtgt0 @ xb ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(181,plain,
! [SV7: $i] :
( ( ~ ( aElement0 @ SV7 )
| ( aIdeal0 @ ( slsdtgt0 @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(182,plain,
! [SV8: $i] :
( ( ~ ( aNaturalNumber0 @ SV8 )
| $true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(183,plain,
! [SV9: $i] :
( ( ! [SY98: $i,SY99: $i] :
( ~ ~ ( ~ ~ ( ~ ( aElement0 @ SV9 )
| ~ ( aElement0 @ SY98 ) )
| ~ ( aElement0 @ SY99 ) )
| ~ ( ( ( sdtasdt0 @ SV9 @ ( sdtpldt0 @ SY98 @ SY99 ) )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV9 @ SY98 ) @ ( sdtasdt0 @ SV9 @ SY99 ) ) )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SY98 @ SY99 ) @ SV9 )
!= ( sdtpldt0 @ ( sdtasdt0 @ SY98 @ SV9 ) @ ( sdtasdt0 @ SY99 @ SV9 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(184,plain,
! [SV10: $i] :
( ( ~ ( aElement0 @ SV10 )
| ~ ( ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ SV10 )
!= ( smndt0 @ SV10 ) )
| ( ( smndt0 @ SV10 )
!= ( sdtasdt0 @ SV10 @ ( smndt0 @ sz10 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(185,plain,
( ( ~ ( aElement0 @ xa )
| ~ ( aElement0 @ xb ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(186,plain,
( ( sz10 = sz00 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(187,plain,
! [SV11: $i] :
( ( ! [SY100: $i,SY101: $i] :
( ~ ~ ( ~ ~ ( ~ ( aElement0 @ SV11 )
| ~ ( aElement0 @ SY100 ) )
| ~ ( aElement0 @ SY101 ) )
| ( ( sdtasdt0 @ ( sdtasdt0 @ SV11 @ SY100 ) @ SY101 )
= ( sdtasdt0 @ SV11 @ ( sdtasdt0 @ SY100 @ SY101 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(188,plain,
! [SV12: $i] :
( ( ~ ( aSet0 @ SV12 )
| $true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(189,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aSet0 @ xI )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ~ ( ~ ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) )
| ~ ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) ) )
| ~ ( aIdeal0 @ xI ) )
| ~ ! [SX0: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( aElement0 @ SX1 )
| ( ( sdtasdt0 @ xa @ SX1 )
!= SX0 ) ) )
| ~ ( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( aElement0 @ SX1 )
| ( ( sdtasdt0 @ xa @ SX1 )
!= SX0 ) )
| ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) ) ) )
| ~ ! [SX0: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( aElement0 @ SX1 )
| ( ( sdtasdt0 @ xb @ SX1 )
!= SX0 ) ) )
| ~ ( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( aElement0 @ SX1 )
| ( ( sdtasdt0 @ xb @ SX1 )
!= SX0 ) )
| ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) ) ) ) )
| ~ ! [SX0: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX0 @ xI )
| ~ ! [SX1: $i] :
~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SX2 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SX1 @ SX2 )
!= SX0 ) ) )
| ~ ( ~ ~ ! [SX1: $i] :
~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SX2 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SX1 @ SX2 )
!= SX0 ) )
| ( aElementOf0 @ SX0 @ xI ) ) ) )
| ( xI
!= ( sdtpldt1 @ ( slsdtgt0 @ xa ) @ ( slsdtgt0 @ xb ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(190,plain,
! [SV13: $i] :
( ( ! [SY102: $i] :
( ~ ~ ( ~ ( aNaturalNumber0 @ SV13 )
| ~ ( aNaturalNumber0 @ SY102 ) )
| ~ ( iLess0 @ SV13 @ SY102 )
| $true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(191,plain,
! [SV14: $i] :
( ( ~ ( aElement0 @ SV14 )
| ~ ( ( ( sdtpldt0 @ SV14 @ sz00 )
!= SV14 )
| ( SV14
!= ( sdtpldt0 @ sz00 @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(192,plain,
! [SV15: $i] :
( ( ! [SY103: $i] :
( ~ ~ ( ~ ( aElement0 @ SV15 )
| ~ ( aElement0 @ SY103 ) )
| ( ( sdtpldt0 @ SV15 @ SY103 )
= ( sdtpldt0 @ SY103 @ SV15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(193,plain,
( ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ xq )
| ~ ( aElement0 @ xr ) )
| ( xb
!= ( sdtpldt0 @ ( sdtasdt0 @ xq @ xu ) @ xr ) ) )
| ~ ( ( xr = sz00 )
| ( iLess0 @ ( sbrdtbr0 @ xr ) @ ( sbrdtbr0 @ xu ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(194,plain,
! [SV16: $i] :
( ( ! [SY104: $i] :
( ~ ~ ( ~ ( aIdeal0 @ SV16 )
| ~ ( aIdeal0 @ SY104 ) )
| ~ ! [SY105: $i] :
( ~ ( aElement0 @ SY105 )
| ( aElementOf0 @ SY105 @ ( sdtpldt1 @ SV16 @ SY104 ) ) )
| ! [SY106: $i,SY107: $i] :
( ~ ~ ( ~ ( aElement0 @ SY106 )
| ~ ( aElement0 @ SY107 ) )
| ~ ! [SY108: $i] :
~ ~ ( ~ ~ ( ~ ( aElement0 @ SY108 )
| ~ ( sdteqdtlpzmzozddtrp0 @ SY108 @ SY106 @ SV16 ) )
| ~ ( sdteqdtlpzmzozddtrp0 @ SY108 @ SY107 @ SY104 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(195,plain,
! [SV17: $i] :
( ( ! [SY109: $i] :
( ~ ~ ( ~ ( aElement0 @ SV17 )
| ~ ( aElement0 @ SY109 ) )
| ( ( sdtasdt0 @ SV17 @ SY109 )
= ( sdtasdt0 @ SY109 @ SV17 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(196,plain,
( ( ~ ( ~ ( ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xu @ SX0 )
!= xa ) )
| ( doDivides0 @ xu @ xa )
| ( aDivisorOf0 @ xu @ xa ) )
| ~ ( ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xu @ SX0 )
!= xb ) )
| ( doDivides0 @ xu @ xb )
| ( aDivisorOf0 @ xu @ xb ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(197,plain,
( ( xr != sz00 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(198,plain,
! [SV18: $i] :
( ( ~ ( aSet0 @ SV18 )
| ! [SY110: $i] :
( ~ ( aElementOf0 @ SY110 @ SV18 )
| ( aElement0 @ SY110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(199,plain,
! [SV19: $i] :
( ( ~ ~ ( ~ ( aElement0 @ SV19 )
| ~ ( ( SV19 != sz00 ) ) )
| ( aNaturalNumber0 @ ( sbrdtbr0 @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(200,plain,
( ( ~ ~ ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xu @ SX0 )
!= xa ) )
| ~ ( doDivides0 @ xu @ xa ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(201,plain,
! [SV20: $i] :
( ( ! [SY111: $i] :
( ~ ~ ( ~ ( aIdeal0 @ SV20 )
| ~ ( aIdeal0 @ SY111 ) )
| ( aIdeal0 @ ( sdtasasdt0 @ SV20 @ SY111 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(202,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ xc )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xc @ SX0 )
!= xa ) ) )
| ~ ( doDivides0 @ xc @ xa ) )
| ~ ( aDivisorOf0 @ xc @ xa ) )
| ~ ( aElement0 @ xc ) )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xc @ SX0 )
!= xb ) ) )
| ~ ( doDivides0 @ xc @ xb ) )
| ~ ( aDivisorOf0 @ xc @ xb ) )
| ~ ! [SX0: $i] :
( ~ ~ ( ~ ( ~ ( ~ ( aElement0 @ SX0 )
| ~ ( ~ ! [SX1: $i] :
~ ~ ( ~ ( aElement0 @ SX1 )
| ( ( sdtasdt0 @ SX0 @ SX1 )
!= xa ) )
| ( doDivides0 @ SX0 @ xa ) ) )
| ( aDivisorOf0 @ SX0 @ xa ) )
| ~ ( ~ ! [SX1: $i] :
~ ~ ( ~ ( aElement0 @ SX1 )
| ( ( sdtasdt0 @ SX0 @ SX1 )
!= xb ) )
| ( doDivides0 @ SX0 @ xb )
| ( aDivisorOf0 @ SX0 @ xb ) ) )
| ~ ( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( aElement0 @ SX1 )
| ( ( sdtasdt0 @ SX0 @ SX1 )
!= xc ) )
| ~ ( doDivides0 @ SX0 @ xc ) ) ) )
| ~ ( aGcdOfAnd0 @ xc @ xa @ xb ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(203,plain,
! [SV21: $i] :
( ( ~ ( aElement0 @ SV21 )
| ~ ( ( ( sdtasdt0 @ SV21 @ sz10 )
!= SV21 )
| ( SV21
!= ( sdtasdt0 @ sz10 @ SV21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(204,plain,
! [SV22: $i] :
( ( ! [SY112: $i,SY113: $i] :
( ~ ~ ( ~ ~ ( ~ ( aElement0 @ SV22 )
| ~ ( aElement0 @ SY112 ) )
| ~ ( aElement0 @ SY113 ) )
| ( ( sdtpldt0 @ ( sdtpldt0 @ SV22 @ SY112 ) @ SY113 )
= ( sdtpldt0 @ SV22 @ ( sdtpldt0 @ SY112 @ SY113 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(205,plain,
! [SV23: $i] :
( ( ~ ( aElement0 @ SV23 )
| ( aElement0 @ ( smndt0 @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(206,plain,
! [SV24: $i] :
( ( ! [SY114: $i] :
( ~ ~ ( ~ ( aElement0 @ SV24 )
| ~ ( aElement0 @ SY114 ) )
| ( aElement0 @ ( sdtpldt0 @ SV24 @ SY114 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(207,plain,
! [SV25: $i] :
( ( ! [SY115: $i] :
( ~ ~ ( ~ ( aElement0 @ SV25 )
| ~ ( aElement0 @ SY115 ) )
| ( aElement0 @ ( sdtasdt0 @ SV25 @ SY115 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(208,plain,
! [SV26: $i] :
( ( ~ ( aElement0 @ SV26 )
| ~ ( ( ( sdtpldt0 @ SV26 @ ( smndt0 @ SV26 ) )
!= sz00 )
| ( sz00
!= ( sdtpldt0 @ ( smndt0 @ SV26 ) @ SV26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(209,plain,
! [SV27: $i,SV1: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ SV1 )
| ~ ( aElement0 @ SV27 ) )
| ~ ( ( SV27 != sz00 ) ) )
| ~ ! [SY116: $i] :
~ ~ ! [SY117: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ SY116 )
| ~ ( aElement0 @ SY117 ) )
| ( SV1
!= ( sdtpldt0 @ ( sdtasdt0 @ SY116 @ SV27 ) @ SY117 ) ) )
| ~ ( ~ ( ( SY117 != sz00 ) )
| ( iLess0 @ ( sbrdtbr0 @ SY117 ) @ ( sbrdtbr0 @ SV27 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(210,plain,
( ( ( xa = sz00 )
= $false )
| ( ( xb != sz00 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(211,plain,
! [SV28: $i,SV2: $i] :
( ( ~ ~ ( ~ ( aElement0 @ SV2 )
| ~ ( aElement0 @ SV28 ) )
| ( ( sdtasdt0 @ SV2 @ SV28 )
!= sz00 )
| ( SV2 = sz00 )
| ( SV28 = sz00 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(212,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX1: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( aElement0 @ SX2 )
| ( ( sdtasdt0 @ xa @ SX2 )
!= SX1 ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( aElement0 @ SX2 )
| ( ( sdtasdt0 @ xa @ SX2 )
!= SX1 ) )
| ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) ) ) )
| ~ ! [SX1: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xb ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( aElement0 @ SX2 )
| ( ( sdtasdt0 @ xb @ SX2 )
!= SX1 ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( aElement0 @ SX2 )
| ( ( sdtasdt0 @ xb @ SX2 )
!= SX1 ) )
| ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xb ) ) ) ) )
| ~ ~ ! [SY124: $i] :
~ ~ ! [SY125: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY124 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SY125 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SY124 @ SY125 )
!= sK1_SX0 ) ) )
| ~ ( aElementOf0 @ sK1_SX0 @ ( sdtpldt1 @ ( slsdtgt0 @ xa ) @ ( slsdtgt0 @ xb ) ) ) )
| ~ ( ( sK1_SX0 != sz00 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[172]) ).
thf(213,plain,
( ( ~ ~ ! [SY126: $i] :
~ ~ ( ~ ~ ( ~ ( aElement0 @ sK2_SX0 )
| ~ ( aElement0 @ SY126 ) )
| ( xu
!= ( sdtpldt0 @ ( sdtasdt0 @ xa @ sK2_SX0 ) @ ( sdtasdt0 @ xb @ SY126 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[173]) ).
thf(214,plain,
! [SV29: $i,SV3: $i] :
( ( ~ ~ ( ~ ( aSet0 @ SV3 )
| ~ ( aSet0 @ SV29 ) )
| ~ ~ ( ~ ! [SY127: $i] :
( ~ ( aElementOf0 @ SY127 @ SV3 )
| ( aElementOf0 @ SY127 @ SV29 ) )
| ~ ! [SY128: $i] :
( ~ ( aElementOf0 @ SY128 @ SV29 )
| ( aElementOf0 @ SY128 @ SV3 ) ) )
| ( SV3 = SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(215,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ! [SX0: $i] :
~ ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SX0 @ SX1 )
!= xu ) )
| ~ ( aElementOf0 @ xu @ xI ) )
| ~ ( ( xu != sz00 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[175]) ).
thf(216,plain,
( ( ~ ! [SX0: $i] :
( ~ ~ ( ~ ( ~ ! [SX1: $i] :
~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SX2 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SX1 @ SX2 )
!= SX0 ) )
| ( aElementOf0 @ SX0 @ xI ) )
| ~ ( ( SX0 != sz00 ) ) )
| ~ ( iLess0 @ ( sbrdtbr0 @ SX0 ) @ ( sbrdtbr0 @ xu ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[175]) ).
thf(217,plain,
! [SV4: $i] :
( ( ( ~ ( aElement0 @ SV4 ) )
= $true )
| ( ( ~ ( ( ( sdtasdt0 @ SV4 @ sz00 )
!= sz00 )
| ( sz00
!= ( sdtasdt0 @ sz00 @ SV4 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[176]) ).
thf(218,plain,
! [SV5: $i] :
( ( ( ~ ( aElement0 @ SV5 ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[177]) ).
thf(219,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xu @ SX0 )
!= xb ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[178]) ).
thf(220,plain,
( ( doDivides0 @ xu @ xb )
= $false ),
inference(extcnf_or_neg,[status(thm)],[178]) ).
thf(221,plain,
! [SV30: $i,SV6: $i] :
( ( ~ ~ ( ~ ( aIdeal0 @ SV6 )
| ~ ( aIdeal0 @ SV30 ) )
| ( aIdeal0 @ ( sdtpldt1 @ SV6 @ SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(222,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xa @ SX0 )
!= sz00 ) )
| ~ ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xa ) ) )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xa @ SX0 )
!= xa ) ) )
| ~ ( aElementOf0 @ xa @ ( slsdtgt0 @ xa ) ) )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xb @ SX0 )
!= sz00 ) ) )
| ~ ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xb ) ) )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xb @ SX0 )
!= xb ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[180]) ).
thf(223,plain,
( ( ~ ( aElementOf0 @ xb @ ( slsdtgt0 @ xb ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[180]) ).
thf(224,plain,
! [SV7: $i] :
( ( ( ~ ( aElement0 @ SV7 ) )
= $true )
| ( ( aIdeal0 @ ( slsdtgt0 @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[181]) ).
thf(225,plain,
! [SV8: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV8 ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[182]) ).
thf(226,plain,
! [SV31: $i,SV9: $i] :
( ( ! [SY129: $i] :
( ~ ~ ( ~ ~ ( ~ ( aElement0 @ SV9 )
| ~ ( aElement0 @ SV31 ) )
| ~ ( aElement0 @ SY129 ) )
| ~ ( ( ( sdtasdt0 @ SV9 @ ( sdtpldt0 @ SV31 @ SY129 ) )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV9 @ SV31 ) @ ( sdtasdt0 @ SV9 @ SY129 ) ) )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SV31 @ SY129 ) @ SV9 )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV31 @ SV9 ) @ ( sdtasdt0 @ SY129 @ SV9 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(227,plain,
! [SV10: $i] :
( ( ( ~ ( aElement0 @ SV10 ) )
= $true )
| ( ( ~ ( ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ SV10 )
!= ( smndt0 @ SV10 ) )
| ( ( smndt0 @ SV10 )
!= ( sdtasdt0 @ SV10 @ ( smndt0 @ sz10 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[184]) ).
thf(228,plain,
( ( ~ ( aElement0 @ xa ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[185]) ).
thf(229,plain,
( ( ~ ( aElement0 @ xb ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[185]) ).
thf(230,plain,
! [SV32: $i,SV11: $i] :
( ( ! [SY130: $i] :
( ~ ~ ( ~ ~ ( ~ ( aElement0 @ SV11 )
| ~ ( aElement0 @ SV32 ) )
| ~ ( aElement0 @ SY130 ) )
| ( ( sdtasdt0 @ ( sdtasdt0 @ SV11 @ SV32 ) @ SY130 )
= ( sdtasdt0 @ SV11 @ ( sdtasdt0 @ SV32 @ SY130 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(231,plain,
! [SV12: $i] :
( ( ( ~ ( aSet0 @ SV12 ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[188]) ).
thf(232,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aSet0 @ xI )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ~ ( ~ ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) )
| ~ ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) ) )
| ~ ( aIdeal0 @ xI ) )
| ~ ! [SX0: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( aElement0 @ SX1 )
| ( ( sdtasdt0 @ xa @ SX1 )
!= SX0 ) ) )
| ~ ( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( aElement0 @ SX1 )
| ( ( sdtasdt0 @ xa @ SX1 )
!= SX0 ) )
| ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) ) ) )
| ~ ! [SX0: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( aElement0 @ SX1 )
| ( ( sdtasdt0 @ xb @ SX1 )
!= SX0 ) ) )
| ~ ( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( aElement0 @ SX1 )
| ( ( sdtasdt0 @ xb @ SX1 )
!= SX0 ) )
| ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) ) ) ) )
| ~ ! [SX0: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX0 @ xI )
| ~ ! [SX1: $i] :
~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SX2 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SX1 @ SX2 )
!= SX0 ) ) )
| ~ ( ~ ~ ! [SX1: $i] :
~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SX2 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SX1 @ SX2 )
!= SX0 ) )
| ( aElementOf0 @ SX0 @ xI ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[189]) ).
thf(233,plain,
( ( xI
!= ( sdtpldt1 @ ( slsdtgt0 @ xa ) @ ( slsdtgt0 @ xb ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[189]) ).
thf(234,plain,
! [SV33: $i,SV13: $i] :
( ( ~ ~ ( ~ ( aNaturalNumber0 @ SV13 )
| ~ ( aNaturalNumber0 @ SV33 ) )
| ~ ( iLess0 @ SV13 @ SV33 )
| $true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(235,plain,
! [SV14: $i] :
( ( ( ~ ( aElement0 @ SV14 ) )
= $true )
| ( ( ~ ( ( ( sdtpldt0 @ SV14 @ sz00 )
!= SV14 )
| ( SV14
!= ( sdtpldt0 @ sz00 @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[191]) ).
thf(236,plain,
! [SV34: $i,SV15: $i] :
( ( ~ ~ ( ~ ( aElement0 @ SV15 )
| ~ ( aElement0 @ SV34 ) )
| ( ( sdtpldt0 @ SV15 @ SV34 )
= ( sdtpldt0 @ SV34 @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[192]) ).
thf(237,plain,
( ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ xq )
| ~ ( aElement0 @ xr ) )
| ( xb
!= ( sdtpldt0 @ ( sdtasdt0 @ xq @ xu ) @ xr ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[193]) ).
thf(238,plain,
( ( ~ ( ( xr = sz00 )
| ( iLess0 @ ( sbrdtbr0 @ xr ) @ ( sbrdtbr0 @ xu ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[193]) ).
thf(239,plain,
! [SV35: $i,SV16: $i] :
( ( ~ ~ ( ~ ( aIdeal0 @ SV16 )
| ~ ( aIdeal0 @ SV35 ) )
| ~ ! [SY131: $i] :
( ~ ( aElement0 @ SY131 )
| ( aElementOf0 @ SY131 @ ( sdtpldt1 @ SV16 @ SV35 ) ) )
| ! [SY132: $i,SY133: $i] :
( ~ ~ ( ~ ( aElement0 @ SY132 )
| ~ ( aElement0 @ SY133 ) )
| ~ ! [SY134: $i] :
~ ~ ( ~ ~ ( ~ ( aElement0 @ SY134 )
| ~ ( sdteqdtlpzmzozddtrp0 @ SY134 @ SY132 @ SV16 ) )
| ~ ( sdteqdtlpzmzozddtrp0 @ SY134 @ SY133 @ SV35 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(240,plain,
! [SV36: $i,SV17: $i] :
( ( ~ ~ ( ~ ( aElement0 @ SV17 )
| ~ ( aElement0 @ SV36 ) )
| ( ( sdtasdt0 @ SV17 @ SV36 )
= ( sdtasdt0 @ SV36 @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[195]) ).
thf(241,plain,
( ( ~ ( ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xu @ SX0 )
!= xa ) )
| ( doDivides0 @ xu @ xa )
| ( aDivisorOf0 @ xu @ xa ) )
| ~ ( ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xu @ SX0 )
!= xb ) )
| ( doDivides0 @ xu @ xb )
| ( aDivisorOf0 @ xu @ xb ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[196]) ).
thf(242,plain,
( ( xr = sz00 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[197]) ).
thf(243,plain,
! [SV18: $i] :
( ( ( ~ ( aSet0 @ SV18 ) )
= $true )
| ( ( ! [SY110: $i] :
( ~ ( aElementOf0 @ SY110 @ SV18 )
| ( aElement0 @ SY110 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[198]) ).
thf(244,plain,
! [SV19: $i] :
( ( ( ~ ~ ( ~ ( aElement0 @ SV19 )
| ~ ( ( SV19 != sz00 ) ) ) )
= $true )
| ( ( aNaturalNumber0 @ ( sbrdtbr0 @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[199]) ).
thf(245,plain,
( ( ~ ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xu @ SX0 )
!= xa ) )
| ~ ( doDivides0 @ xu @ xa ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[200]) ).
thf(246,plain,
! [SV37: $i,SV20: $i] :
( ( ~ ~ ( ~ ( aIdeal0 @ SV20 )
| ~ ( aIdeal0 @ SV37 ) )
| ( aIdeal0 @ ( sdtasasdt0 @ SV20 @ SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[201]) ).
thf(247,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ xc )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xc @ SX0 )
!= xa ) ) )
| ~ ( doDivides0 @ xc @ xa ) )
| ~ ( aDivisorOf0 @ xc @ xa ) )
| ~ ( aElement0 @ xc ) )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xc @ SX0 )
!= xb ) ) )
| ~ ( doDivides0 @ xc @ xb ) )
| ~ ( aDivisorOf0 @ xc @ xb ) )
| ~ ! [SX0: $i] :
( ~ ~ ( ~ ( ~ ( ~ ( aElement0 @ SX0 )
| ~ ( ~ ! [SX1: $i] :
~ ~ ( ~ ( aElement0 @ SX1 )
| ( ( sdtasdt0 @ SX0 @ SX1 )
!= xa ) )
| ( doDivides0 @ SX0 @ xa ) ) )
| ( aDivisorOf0 @ SX0 @ xa ) )
| ~ ( ~ ! [SX1: $i] :
~ ~ ( ~ ( aElement0 @ SX1 )
| ( ( sdtasdt0 @ SX0 @ SX1 )
!= xb ) )
| ( doDivides0 @ SX0 @ xb )
| ( aDivisorOf0 @ SX0 @ xb ) ) )
| ~ ( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( aElement0 @ SX1 )
| ( ( sdtasdt0 @ SX0 @ SX1 )
!= xc ) )
| ~ ( doDivides0 @ SX0 @ xc ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[202]) ).
thf(248,plain,
( ( ~ ( aGcdOfAnd0 @ xc @ xa @ xb ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[202]) ).
thf(249,plain,
! [SV21: $i] :
( ( ( ~ ( aElement0 @ SV21 ) )
= $true )
| ( ( ~ ( ( ( sdtasdt0 @ SV21 @ sz10 )
!= SV21 )
| ( SV21
!= ( sdtasdt0 @ sz10 @ SV21 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[203]) ).
thf(250,plain,
! [SV38: $i,SV22: $i] :
( ( ! [SY135: $i] :
( ~ ~ ( ~ ~ ( ~ ( aElement0 @ SV22 )
| ~ ( aElement0 @ SV38 ) )
| ~ ( aElement0 @ SY135 ) )
| ( ( sdtpldt0 @ ( sdtpldt0 @ SV22 @ SV38 ) @ SY135 )
= ( sdtpldt0 @ SV22 @ ( sdtpldt0 @ SV38 @ SY135 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(251,plain,
! [SV23: $i] :
( ( ( ~ ( aElement0 @ SV23 ) )
= $true )
| ( ( aElement0 @ ( smndt0 @ SV23 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[205]) ).
thf(252,plain,
! [SV39: $i,SV24: $i] :
( ( ~ ~ ( ~ ( aElement0 @ SV24 )
| ~ ( aElement0 @ SV39 ) )
| ( aElement0 @ ( sdtpldt0 @ SV24 @ SV39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(253,plain,
! [SV40: $i,SV25: $i] :
( ( ~ ~ ( ~ ( aElement0 @ SV25 )
| ~ ( aElement0 @ SV40 ) )
| ( aElement0 @ ( sdtasdt0 @ SV25 @ SV40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(254,plain,
! [SV26: $i] :
( ( ( ~ ( aElement0 @ SV26 ) )
= $true )
| ( ( ~ ( ( ( sdtpldt0 @ SV26 @ ( smndt0 @ SV26 ) )
!= sz00 )
| ( sz00
!= ( sdtpldt0 @ ( smndt0 @ SV26 ) @ SV26 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[208]) ).
thf(255,plain,
! [SV27: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ SV1 )
| ~ ( aElement0 @ SV27 ) )
| ~ ( ( SV27 != sz00 ) ) ) )
= $true )
| ( ( ~ ! [SY116: $i] :
~ ~ ! [SY117: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ SY116 )
| ~ ( aElement0 @ SY117 ) )
| ( SV1
!= ( sdtpldt0 @ ( sdtasdt0 @ SY116 @ SV27 ) @ SY117 ) ) )
| ~ ( ~ ( ( SY117 != sz00 ) )
| ( iLess0 @ ( sbrdtbr0 @ SY117 ) @ ( sbrdtbr0 @ SV27 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[209]) ).
thf(256,plain,
( ( ( xb = sz00 )
= $false )
| ( ( xa = sz00 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(257,plain,
! [SV28: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ( aElement0 @ SV2 )
| ~ ( aElement0 @ SV28 ) ) )
= $true )
| ( ( ( ( sdtasdt0 @ SV2 @ SV28 )
!= sz00 )
| ( SV2 = sz00 )
| ( SV28 = sz00 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[211]) ).
thf(258,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX1: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( aElement0 @ SX2 )
| ( ( sdtasdt0 @ xa @ SX2 )
!= SX1 ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( aElement0 @ SX2 )
| ( ( sdtasdt0 @ xa @ SX2 )
!= SX1 ) )
| ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) ) ) )
| ~ ! [SX1: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xb ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( aElement0 @ SX2 )
| ( ( sdtasdt0 @ xb @ SX2 )
!= SX1 ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( aElement0 @ SX2 )
| ( ( sdtasdt0 @ xb @ SX2 )
!= SX1 ) )
| ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xb ) ) ) ) )
| ~ ~ ! [SY124: $i] :
~ ~ ! [SY125: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY124 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SY125 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SY124 @ SY125 )
!= sK1_SX0 ) ) )
| ~ ( aElementOf0 @ sK1_SX0 @ ( sdtpldt1 @ ( slsdtgt0 @ xa ) @ ( slsdtgt0 @ xb ) ) ) )
| ~ ( ( sK1_SX0 != sz00 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[212]) ).
thf(259,plain,
( ( ~ ! [SY126: $i] :
~ ~ ( ~ ~ ( ~ ( aElement0 @ sK2_SX0 )
| ~ ( aElement0 @ SY126 ) )
| ( xu
!= ( sdtpldt0 @ ( sdtasdt0 @ xa @ sK2_SX0 ) @ ( sdtasdt0 @ xb @ SY126 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[213]) ).
thf(260,plain,
! [SV29: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( aSet0 @ SV3 )
| ~ ( aSet0 @ SV29 ) ) )
= $true )
| ( ( ~ ~ ( ~ ! [SY127: $i] :
( ~ ( aElementOf0 @ SY127 @ SV3 )
| ( aElementOf0 @ SY127 @ SV29 ) )
| ~ ! [SY128: $i] :
( ~ ( aElementOf0 @ SY128 @ SV29 )
| ( aElementOf0 @ SY128 @ SV3 ) ) )
| ( SV3 = SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[214]) ).
thf(261,plain,
( ( ~ ( ~ ~ ( ~ ~ ! [SX0: $i] :
~ ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SX0 @ SX1 )
!= xu ) )
| ~ ( aElementOf0 @ xu @ xI ) )
| ~ ( ( xu != sz00 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[215]) ).
thf(262,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( ~ ! [SX1: $i] :
~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SX2 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SX1 @ SX2 )
!= SX0 ) )
| ( aElementOf0 @ SX0 @ xI ) )
| ~ ( ( SX0 != sz00 ) ) )
| ~ ( iLess0 @ ( sbrdtbr0 @ SX0 ) @ ( sbrdtbr0 @ xu ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[216]) ).
thf(263,plain,
! [SV4: $i] :
( ( ( aElement0 @ SV4 )
= $false )
| ( ( ~ ( ( ( sdtasdt0 @ SV4 @ sz00 )
!= sz00 )
| ( sz00
!= ( sdtasdt0 @ sz00 @ SV4 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[217]) ).
thf(264,plain,
! [SV5: $i] :
( ( ( aElement0 @ SV5 )
= $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[218]) ).
thf(265,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xu @ SX0 )
!= xb ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[219]) ).
thf(266,plain,
! [SV30: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ( aIdeal0 @ SV6 )
| ~ ( aIdeal0 @ SV30 ) ) )
= $true )
| ( ( aIdeal0 @ ( sdtpldt1 @ SV6 @ SV30 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[221]) ).
thf(267,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xa @ SX0 )
!= sz00 ) )
| ~ ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xa ) ) )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xa @ SX0 )
!= xa ) ) )
| ~ ( aElementOf0 @ xa @ ( slsdtgt0 @ xa ) ) )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xb @ SX0 )
!= sz00 ) ) )
| ~ ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xb ) ) )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xb @ SX0 )
!= xb ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[222]) ).
thf(268,plain,
( ( aElementOf0 @ xb @ ( slsdtgt0 @ xb ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[223]) ).
thf(269,plain,
! [SV7: $i] :
( ( ( aElement0 @ SV7 )
= $false )
| ( ( aIdeal0 @ ( slsdtgt0 @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[224]) ).
thf(270,plain,
! [SV8: $i] :
( ( ( aNaturalNumber0 @ SV8 )
= $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[225]) ).
thf(271,plain,
! [SV41: $i,SV31: $i,SV9: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ SV9 )
| ~ ( aElement0 @ SV31 ) )
| ~ ( aElement0 @ SV41 ) )
| ~ ( ( ( sdtasdt0 @ SV9 @ ( sdtpldt0 @ SV31 @ SV41 ) )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV9 @ SV31 ) @ ( sdtasdt0 @ SV9 @ SV41 ) ) )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SV31 @ SV41 ) @ SV9 )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV31 @ SV9 ) @ ( sdtasdt0 @ SV41 @ SV9 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[226]) ).
thf(272,plain,
! [SV10: $i] :
( ( ( aElement0 @ SV10 )
= $false )
| ( ( ~ ( ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ SV10 )
!= ( smndt0 @ SV10 ) )
| ( ( smndt0 @ SV10 )
!= ( sdtasdt0 @ SV10 @ ( smndt0 @ sz10 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[227]) ).
thf(273,plain,
( ( aElement0 @ xa )
= $true ),
inference(extcnf_not_neg,[status(thm)],[228]) ).
thf(274,plain,
( ( aElement0 @ xb )
= $true ),
inference(extcnf_not_neg,[status(thm)],[229]) ).
thf(275,plain,
! [SV42: $i,SV32: $i,SV11: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ SV11 )
| ~ ( aElement0 @ SV32 ) )
| ~ ( aElement0 @ SV42 ) )
| ( ( sdtasdt0 @ ( sdtasdt0 @ SV11 @ SV32 ) @ SV42 )
= ( sdtasdt0 @ SV11 @ ( sdtasdt0 @ SV32 @ SV42 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[230]) ).
thf(276,plain,
! [SV12: $i] :
( ( ( aSet0 @ SV12 )
= $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[231]) ).
thf(277,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aSet0 @ xI )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ~ ( ~ ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) )
| ~ ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) ) )
| ~ ( aIdeal0 @ xI ) )
| ~ ! [SX0: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( aElement0 @ SX1 )
| ( ( sdtasdt0 @ xa @ SX1 )
!= SX0 ) ) )
| ~ ( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( aElement0 @ SX1 )
| ( ( sdtasdt0 @ xa @ SX1 )
!= SX0 ) )
| ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) ) ) )
| ~ ! [SX0: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( aElement0 @ SX1 )
| ( ( sdtasdt0 @ xb @ SX1 )
!= SX0 ) ) )
| ~ ( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( aElement0 @ SX1 )
| ( ( sdtasdt0 @ xb @ SX1 )
!= SX0 ) )
| ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) ) ) ) )
| ~ ! [SX0: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX0 @ xI )
| ~ ! [SX1: $i] :
~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SX2 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SX1 @ SX2 )
!= SX0 ) ) )
| ~ ( ~ ~ ! [SX1: $i] :
~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SX2 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SX1 @ SX2 )
!= SX0 ) )
| ( aElementOf0 @ SX0 @ xI ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[232]) ).
thf(278,plain,
( ( xI
= ( sdtpldt1 @ ( slsdtgt0 @ xa ) @ ( slsdtgt0 @ xb ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[233]) ).
thf(279,plain,
! [SV33: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ( aNaturalNumber0 @ SV13 )
| ~ ( aNaturalNumber0 @ SV33 ) ) )
= $true )
| ( ( ~ ( iLess0 @ SV13 @ SV33 )
| $true )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[234]) ).
thf(280,plain,
! [SV14: $i] :
( ( ( aElement0 @ SV14 )
= $false )
| ( ( ~ ( ( ( sdtpldt0 @ SV14 @ sz00 )
!= SV14 )
| ( SV14
!= ( sdtpldt0 @ sz00 @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[235]) ).
thf(281,plain,
! [SV34: $i,SV15: $i] :
( ( ( ~ ~ ( ~ ( aElement0 @ SV15 )
| ~ ( aElement0 @ SV34 ) ) )
= $true )
| ( ( ( sdtpldt0 @ SV15 @ SV34 )
= ( sdtpldt0 @ SV34 @ SV15 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[236]) ).
thf(282,plain,
( ( ~ ( ~ ~ ( ~ ( aElement0 @ xq )
| ~ ( aElement0 @ xr ) )
| ( xb
!= ( sdtpldt0 @ ( sdtasdt0 @ xq @ xu ) @ xr ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[237]) ).
thf(283,plain,
( ( ( xr = sz00 )
| ( iLess0 @ ( sbrdtbr0 @ xr ) @ ( sbrdtbr0 @ xu ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[238]) ).
thf(284,plain,
! [SV35: $i,SV16: $i] :
( ( ( ~ ~ ( ~ ( aIdeal0 @ SV16 )
| ~ ( aIdeal0 @ SV35 ) ) )
= $true )
| ( ( ~ ! [SY131: $i] :
( ~ ( aElement0 @ SY131 )
| ( aElementOf0 @ SY131 @ ( sdtpldt1 @ SV16 @ SV35 ) ) )
| ! [SY132: $i,SY133: $i] :
( ~ ~ ( ~ ( aElement0 @ SY132 )
| ~ ( aElement0 @ SY133 ) )
| ~ ! [SY134: $i] :
~ ~ ( ~ ~ ( ~ ( aElement0 @ SY134 )
| ~ ( sdteqdtlpzmzozddtrp0 @ SY134 @ SY132 @ SV16 ) )
| ~ ( sdteqdtlpzmzozddtrp0 @ SY134 @ SY133 @ SV35 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[239]) ).
thf(285,plain,
! [SV36: $i,SV17: $i] :
( ( ( ~ ~ ( ~ ( aElement0 @ SV17 )
| ~ ( aElement0 @ SV36 ) ) )
= $true )
| ( ( ( sdtasdt0 @ SV17 @ SV36 )
= ( sdtasdt0 @ SV36 @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[240]) ).
thf(286,plain,
( ( ( ~ ( ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xu @ SX0 )
!= xa ) )
| ( doDivides0 @ xu @ xa )
| ( aDivisorOf0 @ xu @ xa ) ) )
= $true )
| ( ( ~ ( ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xu @ SX0 )
!= xb ) )
| ( doDivides0 @ xu @ xb )
| ( aDivisorOf0 @ xu @ xb ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[241]) ).
thf(287,plain,
! [SV18: $i] :
( ( ( aSet0 @ SV18 )
= $false )
| ( ( ! [SY110: $i] :
( ~ ( aElementOf0 @ SY110 @ SV18 )
| ( aElement0 @ SY110 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[243]) ).
thf(288,plain,
! [SV19: $i] :
( ( ( ~ ( ~ ( aElement0 @ SV19 )
| ~ ( ( SV19 != sz00 ) ) ) )
= $false )
| ( ( aNaturalNumber0 @ ( sbrdtbr0 @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[244]) ).
thf(289,plain,
( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xu @ SX0 )
!= xa ) )
| ~ ( doDivides0 @ xu @ xa ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[245]) ).
thf(290,plain,
! [SV37: $i,SV20: $i] :
( ( ( ~ ~ ( ~ ( aIdeal0 @ SV20 )
| ~ ( aIdeal0 @ SV37 ) ) )
= $true )
| ( ( aIdeal0 @ ( sdtasasdt0 @ SV20 @ SV37 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[246]) ).
thf(291,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ xc )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xc @ SX0 )
!= xa ) ) )
| ~ ( doDivides0 @ xc @ xa ) )
| ~ ( aDivisorOf0 @ xc @ xa ) )
| ~ ( aElement0 @ xc ) )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xc @ SX0 )
!= xb ) ) )
| ~ ( doDivides0 @ xc @ xb ) )
| ~ ( aDivisorOf0 @ xc @ xb ) )
| ~ ! [SX0: $i] :
( ~ ~ ( ~ ( ~ ( ~ ( aElement0 @ SX0 )
| ~ ( ~ ! [SX1: $i] :
~ ~ ( ~ ( aElement0 @ SX1 )
| ( ( sdtasdt0 @ SX0 @ SX1 )
!= xa ) )
| ( doDivides0 @ SX0 @ xa ) ) )
| ( aDivisorOf0 @ SX0 @ xa ) )
| ~ ( ~ ! [SX1: $i] :
~ ~ ( ~ ( aElement0 @ SX1 )
| ( ( sdtasdt0 @ SX0 @ SX1 )
!= xb ) )
| ( doDivides0 @ SX0 @ xb )
| ( aDivisorOf0 @ SX0 @ xb ) ) )
| ~ ( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( aElement0 @ SX1 )
| ( ( sdtasdt0 @ SX0 @ SX1 )
!= xc ) )
| ~ ( doDivides0 @ SX0 @ xc ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[247]) ).
thf(292,plain,
( ( aGcdOfAnd0 @ xc @ xa @ xb )
= $true ),
inference(extcnf_not_neg,[status(thm)],[248]) ).
thf(293,plain,
! [SV21: $i] :
( ( ( aElement0 @ SV21 )
= $false )
| ( ( ~ ( ( ( sdtasdt0 @ SV21 @ sz10 )
!= SV21 )
| ( SV21
!= ( sdtasdt0 @ sz10 @ SV21 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[249]) ).
thf(294,plain,
! [SV43: $i,SV38: $i,SV22: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ SV22 )
| ~ ( aElement0 @ SV38 ) )
| ~ ( aElement0 @ SV43 ) )
| ( ( sdtpldt0 @ ( sdtpldt0 @ SV22 @ SV38 ) @ SV43 )
= ( sdtpldt0 @ SV22 @ ( sdtpldt0 @ SV38 @ SV43 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[250]) ).
thf(295,plain,
! [SV23: $i] :
( ( ( aElement0 @ SV23 )
= $false )
| ( ( aElement0 @ ( smndt0 @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[251]) ).
thf(296,plain,
! [SV39: $i,SV24: $i] :
( ( ( ~ ~ ( ~ ( aElement0 @ SV24 )
| ~ ( aElement0 @ SV39 ) ) )
= $true )
| ( ( aElement0 @ ( sdtpldt0 @ SV24 @ SV39 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[252]) ).
thf(297,plain,
! [SV40: $i,SV25: $i] :
( ( ( ~ ~ ( ~ ( aElement0 @ SV25 )
| ~ ( aElement0 @ SV40 ) ) )
= $true )
| ( ( aElement0 @ ( sdtasdt0 @ SV25 @ SV40 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[253]) ).
thf(298,plain,
! [SV26: $i] :
( ( ( aElement0 @ SV26 )
= $false )
| ( ( ~ ( ( ( sdtpldt0 @ SV26 @ ( smndt0 @ SV26 ) )
!= sz00 )
| ( sz00
!= ( sdtpldt0 @ ( smndt0 @ SV26 ) @ SV26 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[254]) ).
thf(299,plain,
! [SV27: $i,SV1: $i] :
( ( ( ~ ( ~ ~ ( ~ ( aElement0 @ SV1 )
| ~ ( aElement0 @ SV27 ) )
| ~ ( ( SV27 != sz00 ) ) ) )
= $false )
| ( ( ~ ! [SY116: $i] :
~ ~ ! [SY117: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ SY116 )
| ~ ( aElement0 @ SY117 ) )
| ( SV1
!= ( sdtpldt0 @ ( sdtasdt0 @ SY116 @ SV27 ) @ SY117 ) ) )
| ~ ( ~ ( ( SY117 != sz00 ) )
| ( iLess0 @ ( sbrdtbr0 @ SY117 ) @ ( sbrdtbr0 @ SV27 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[255]) ).
thf(300,plain,
! [SV28: $i,SV2: $i] :
( ( ( ~ ( ~ ( aElement0 @ SV2 )
| ~ ( aElement0 @ SV28 ) ) )
= $false )
| ( ( ( ( sdtasdt0 @ SV2 @ SV28 )
!= sz00 )
| ( SV2 = sz00 )
| ( SV28 = sz00 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[257]) ).
thf(301,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX1: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( aElement0 @ SX2 )
| ( ( sdtasdt0 @ xa @ SX2 )
!= SX1 ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( aElement0 @ SX2 )
| ( ( sdtasdt0 @ xa @ SX2 )
!= SX1 ) )
| ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) ) ) )
| ~ ! [SX1: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xb ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( aElement0 @ SX2 )
| ( ( sdtasdt0 @ xb @ SX2 )
!= SX1 ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( aElement0 @ SX2 )
| ( ( sdtasdt0 @ xb @ SX2 )
!= SX1 ) )
| ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xb ) ) ) ) )
| ~ ~ ! [SY124: $i] :
~ ~ ! [SY125: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY124 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SY125 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SY124 @ SY125 )
!= sK1_SX0 ) ) )
| ~ ( aElementOf0 @ sK1_SX0 @ ( sdtpldt1 @ ( slsdtgt0 @ xa ) @ ( slsdtgt0 @ xb ) ) ) )
| ~ ( ( sK1_SX0 != sz00 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[258]) ).
thf(302,plain,
( ( ! [SY126: $i] :
~ ~ ( ~ ~ ( ~ ( aElement0 @ sK2_SX0 )
| ~ ( aElement0 @ SY126 ) )
| ( xu
!= ( sdtpldt0 @ ( sdtasdt0 @ xa @ sK2_SX0 ) @ ( sdtasdt0 @ xb @ SY126 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[259]) ).
thf(303,plain,
! [SV29: $i,SV3: $i] :
( ( ( ~ ( ~ ( aSet0 @ SV3 )
| ~ ( aSet0 @ SV29 ) ) )
= $false )
| ( ( ~ ~ ( ~ ! [SY127: $i] :
( ~ ( aElementOf0 @ SY127 @ SV3 )
| ( aElementOf0 @ SY127 @ SV29 ) )
| ~ ! [SY128: $i] :
( ~ ( aElementOf0 @ SY128 @ SV29 )
| ( aElementOf0 @ SY128 @ SV3 ) ) )
| ( SV3 = SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[260]) ).
thf(304,plain,
( ( ~ ~ ( ~ ~ ! [SX0: $i] :
~ ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SX0 @ SX1 )
!= xu ) )
| ~ ( aElementOf0 @ xu @ xI ) )
| ~ ( ( xu != sz00 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[261]) ).
thf(305,plain,
! [SV44: $i] :
( ( ~ ~ ( ~ ( ~ ! [SY136: $i] :
~ ~ ! [SY137: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY136 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SY137 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SY136 @ SY137 )
!= SV44 ) )
| ( aElementOf0 @ SV44 @ xI ) )
| ~ ( ( SV44 != sz00 ) ) )
| ~ ( iLess0 @ ( sbrdtbr0 @ SV44 ) @ ( sbrdtbr0 @ xu ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[262]) ).
thf(306,plain,
! [SV4: $i] :
( ( ( ( ( sdtasdt0 @ SV4 @ sz00 )
!= sz00 )
| ( sz00
!= ( sdtasdt0 @ sz00 @ SV4 ) ) )
= $false )
| ( ( aElement0 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[263]) ).
thf(307,plain,
! [SV45: $i] :
( ( ~ ~ ( ~ ( aElement0 @ SV45 )
| ( ( sdtasdt0 @ xu @ SV45 )
!= xb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[265]) ).
thf(308,plain,
! [SV30: $i,SV6: $i] :
( ( ( ~ ( ~ ( aIdeal0 @ SV6 )
| ~ ( aIdeal0 @ SV30 ) ) )
= $false )
| ( ( aIdeal0 @ ( sdtpldt1 @ SV6 @ SV30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[266]) ).
thf(309,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xa @ SX0 )
!= sz00 ) )
| ~ ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xa ) ) )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xa @ SX0 )
!= xa ) ) )
| ~ ( aElementOf0 @ xa @ ( slsdtgt0 @ xa ) ) )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xb @ SX0 )
!= sz00 ) ) )
| ~ ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xb ) ) )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xb @ SX0 )
!= xb ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[267]) ).
thf(310,plain,
! [SV41: $i,SV31: $i,SV9: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ SV9 )
| ~ ( aElement0 @ SV31 ) )
| ~ ( aElement0 @ SV41 ) ) )
= $true )
| ( ( ~ ( ( ( sdtasdt0 @ SV9 @ ( sdtpldt0 @ SV31 @ SV41 ) )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV9 @ SV31 ) @ ( sdtasdt0 @ SV9 @ SV41 ) ) )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SV31 @ SV41 ) @ SV9 )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV31 @ SV9 ) @ ( sdtasdt0 @ SV41 @ SV9 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[271]) ).
thf(311,plain,
! [SV10: $i] :
( ( ( ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ SV10 )
!= ( smndt0 @ SV10 ) )
| ( ( smndt0 @ SV10 )
!= ( sdtasdt0 @ SV10 @ ( smndt0 @ sz10 ) ) ) )
= $false )
| ( ( aElement0 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[272]) ).
thf(312,plain,
! [SV42: $i,SV32: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ SV11 )
| ~ ( aElement0 @ SV32 ) )
| ~ ( aElement0 @ SV42 ) ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV11 @ SV32 ) @ SV42 )
= ( sdtasdt0 @ SV11 @ ( sdtasdt0 @ SV32 @ SV42 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[275]) ).
thf(313,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aSet0 @ xI )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ~ ( ~ ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) )
| ~ ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) ) )
| ~ ( aIdeal0 @ xI ) )
| ~ ! [SX0: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( aElement0 @ SX1 )
| ( ( sdtasdt0 @ xa @ SX1 )
!= SX0 ) ) )
| ~ ( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( aElement0 @ SX1 )
| ( ( sdtasdt0 @ xa @ SX1 )
!= SX0 ) )
| ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) ) ) )
| ~ ! [SX0: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( aElement0 @ SX1 )
| ( ( sdtasdt0 @ xb @ SX1 )
!= SX0 ) ) )
| ~ ( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( aElement0 @ SX1 )
| ( ( sdtasdt0 @ xb @ SX1 )
!= SX0 ) )
| ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) ) ) ) )
| ~ ! [SX0: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX0 @ xI )
| ~ ! [SX1: $i] :
~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SX2 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SX1 @ SX2 )
!= SX0 ) ) )
| ~ ( ~ ~ ! [SX1: $i] :
~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SX2 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SX1 @ SX2 )
!= SX0 ) )
| ( aElementOf0 @ SX0 @ xI ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[277]) ).
thf(314,plain,
! [SV33: $i,SV13: $i] :
( ( ( ~ ( ~ ( aNaturalNumber0 @ SV13 )
| ~ ( aNaturalNumber0 @ SV33 ) ) )
= $false )
| ( ( ~ ( iLess0 @ SV13 @ SV33 )
| $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[279]) ).
thf(315,plain,
! [SV14: $i] :
( ( ( ( ( sdtpldt0 @ SV14 @ sz00 )
!= SV14 )
| ( SV14
!= ( sdtpldt0 @ sz00 @ SV14 ) ) )
= $false )
| ( ( aElement0 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[280]) ).
thf(316,plain,
! [SV34: $i,SV15: $i] :
( ( ( ~ ( ~ ( aElement0 @ SV15 )
| ~ ( aElement0 @ SV34 ) ) )
= $false )
| ( ( ( sdtpldt0 @ SV15 @ SV34 )
= ( sdtpldt0 @ SV34 @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[281]) ).
thf(317,plain,
( ( ~ ~ ( ~ ( aElement0 @ xq )
| ~ ( aElement0 @ xr ) )
| ( xb
!= ( sdtpldt0 @ ( sdtasdt0 @ xq @ xu ) @ xr ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[282]) ).
thf(318,plain,
( ( ( xr = sz00 )
= $true )
| ( ( iLess0 @ ( sbrdtbr0 @ xr ) @ ( sbrdtbr0 @ xu ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[283]) ).
thf(319,plain,
! [SV35: $i,SV16: $i] :
( ( ( ~ ( ~ ( aIdeal0 @ SV16 )
| ~ ( aIdeal0 @ SV35 ) ) )
= $false )
| ( ( ~ ! [SY131: $i] :
( ~ ( aElement0 @ SY131 )
| ( aElementOf0 @ SY131 @ ( sdtpldt1 @ SV16 @ SV35 ) ) )
| ! [SY132: $i,SY133: $i] :
( ~ ~ ( ~ ( aElement0 @ SY132 )
| ~ ( aElement0 @ SY133 ) )
| ~ ! [SY134: $i] :
~ ~ ( ~ ~ ( ~ ( aElement0 @ SY134 )
| ~ ( sdteqdtlpzmzozddtrp0 @ SY134 @ SY132 @ SV16 ) )
| ~ ( sdteqdtlpzmzozddtrp0 @ SY134 @ SY133 @ SV35 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[284]) ).
thf(320,plain,
! [SV36: $i,SV17: $i] :
( ( ( ~ ( ~ ( aElement0 @ SV17 )
| ~ ( aElement0 @ SV36 ) ) )
= $false )
| ( ( ( sdtasdt0 @ SV17 @ SV36 )
= ( sdtasdt0 @ SV36 @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[285]) ).
thf(321,plain,
( ( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xu @ SX0 )
!= xa ) )
| ( doDivides0 @ xu @ xa )
| ( aDivisorOf0 @ xu @ xa ) )
= $false )
| ( ( ~ ( ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xu @ SX0 )
!= xb ) )
| ( doDivides0 @ xu @ xb )
| ( aDivisorOf0 @ xu @ xb ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[286]) ).
thf(322,plain,
! [SV18: $i,SV46: $i] :
( ( ( ~ ( aElementOf0 @ SV46 @ SV18 )
| ( aElement0 @ SV46 ) )
= $true )
| ( ( aSet0 @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[287]) ).
thf(323,plain,
! [SV19: $i] :
( ( ( ~ ( aElement0 @ SV19 )
| ~ ( ( SV19 != sz00 ) ) )
= $true )
| ( ( aNaturalNumber0 @ ( sbrdtbr0 @ SV19 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[288]) ).
thf(324,plain,
( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xu @ SX0 )
!= xa ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[289]) ).
thf(325,plain,
( ( ~ ( doDivides0 @ xu @ xa ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[289]) ).
thf(326,plain,
! [SV37: $i,SV20: $i] :
( ( ( ~ ( ~ ( aIdeal0 @ SV20 )
| ~ ( aIdeal0 @ SV37 ) ) )
= $false )
| ( ( aIdeal0 @ ( sdtasasdt0 @ SV20 @ SV37 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[290]) ).
thf(327,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ xc )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xc @ SX0 )
!= xa ) ) )
| ~ ( doDivides0 @ xc @ xa ) )
| ~ ( aDivisorOf0 @ xc @ xa ) )
| ~ ( aElement0 @ xc ) )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xc @ SX0 )
!= xb ) ) )
| ~ ( doDivides0 @ xc @ xb ) )
| ~ ( aDivisorOf0 @ xc @ xb ) )
| ~ ! [SX0: $i] :
( ~ ~ ( ~ ( ~ ( ~ ( aElement0 @ SX0 )
| ~ ( ~ ! [SX1: $i] :
~ ~ ( ~ ( aElement0 @ SX1 )
| ( ( sdtasdt0 @ SX0 @ SX1 )
!= xa ) )
| ( doDivides0 @ SX0 @ xa ) ) )
| ( aDivisorOf0 @ SX0 @ xa ) )
| ~ ( ~ ! [SX1: $i] :
~ ~ ( ~ ( aElement0 @ SX1 )
| ( ( sdtasdt0 @ SX0 @ SX1 )
!= xb ) )
| ( doDivides0 @ SX0 @ xb )
| ( aDivisorOf0 @ SX0 @ xb ) ) )
| ~ ( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( aElement0 @ SX1 )
| ( ( sdtasdt0 @ SX0 @ SX1 )
!= xc ) )
| ~ ( doDivides0 @ SX0 @ xc ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[291]) ).
thf(328,plain,
! [SV21: $i] :
( ( ( ( ( sdtasdt0 @ SV21 @ sz10 )
!= SV21 )
| ( SV21
!= ( sdtasdt0 @ sz10 @ SV21 ) ) )
= $false )
| ( ( aElement0 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[293]) ).
thf(329,plain,
! [SV43: $i,SV38: $i,SV22: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ SV22 )
| ~ ( aElement0 @ SV38 ) )
| ~ ( aElement0 @ SV43 ) ) )
= $true )
| ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV22 @ SV38 ) @ SV43 )
= ( sdtpldt0 @ SV22 @ ( sdtpldt0 @ SV38 @ SV43 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[294]) ).
thf(330,plain,
! [SV39: $i,SV24: $i] :
( ( ( ~ ( ~ ( aElement0 @ SV24 )
| ~ ( aElement0 @ SV39 ) ) )
= $false )
| ( ( aElement0 @ ( sdtpldt0 @ SV24 @ SV39 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[296]) ).
thf(331,plain,
! [SV40: $i,SV25: $i] :
( ( ( ~ ( ~ ( aElement0 @ SV25 )
| ~ ( aElement0 @ SV40 ) ) )
= $false )
| ( ( aElement0 @ ( sdtasdt0 @ SV25 @ SV40 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[297]) ).
thf(332,plain,
! [SV26: $i] :
( ( ( ( ( sdtpldt0 @ SV26 @ ( smndt0 @ SV26 ) )
!= sz00 )
| ( sz00
!= ( sdtpldt0 @ ( smndt0 @ SV26 ) @ SV26 ) ) )
= $false )
| ( ( aElement0 @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[298]) ).
thf(333,plain,
! [SV27: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ( aElement0 @ SV1 )
| ~ ( aElement0 @ SV27 ) )
| ~ ( ( SV27 != sz00 ) ) )
= $true )
| ( ( ~ ! [SY116: $i] :
~ ~ ! [SY117: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ SY116 )
| ~ ( aElement0 @ SY117 ) )
| ( SV1
!= ( sdtpldt0 @ ( sdtasdt0 @ SY116 @ SV27 ) @ SY117 ) ) )
| ~ ( ~ ( ( SY117 != sz00 ) )
| ( iLess0 @ ( sbrdtbr0 @ SY117 ) @ ( sbrdtbr0 @ SV27 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[299]) ).
thf(334,plain,
! [SV28: $i,SV2: $i] :
( ( ( ~ ( aElement0 @ SV2 )
| ~ ( aElement0 @ SV28 ) )
= $true )
| ( ( ( ( sdtasdt0 @ SV2 @ SV28 )
!= sz00 )
| ( SV2 = sz00 )
| ( SV28 = sz00 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[300]) ).
thf(335,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX1: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( aElement0 @ SX2 )
| ( ( sdtasdt0 @ xa @ SX2 )
!= SX1 ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( aElement0 @ SX2 )
| ( ( sdtasdt0 @ xa @ SX2 )
!= SX1 ) )
| ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) ) ) )
| ~ ! [SX1: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xb ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( aElement0 @ SX2 )
| ( ( sdtasdt0 @ xb @ SX2 )
!= SX1 ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( aElement0 @ SX2 )
| ( ( sdtasdt0 @ xb @ SX2 )
!= SX1 ) )
| ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xb ) ) ) ) )
| ~ ~ ! [SY124: $i] :
~ ~ ! [SY125: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY124 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SY125 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SY124 @ SY125 )
!= sK1_SX0 ) ) )
| ~ ( aElementOf0 @ sK1_SX0 @ ( sdtpldt1 @ ( slsdtgt0 @ xa ) @ ( slsdtgt0 @ xb ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[301]) ).
thf(336,plain,
( ( ~ ( ( sK1_SX0 != sz00 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[301]) ).
thf(337,plain,
( ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ sK2_SX0 )
| ~ ( aElement0 @ sK3_SY126 ) )
| ( xu
!= ( sdtpldt0 @ ( sdtasdt0 @ xa @ sK2_SX0 ) @ ( sdtasdt0 @ xb @ sK3_SY126 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[302]) ).
thf(338,plain,
! [SV29: $i,SV3: $i] :
( ( ( ~ ( aSet0 @ SV3 )
| ~ ( aSet0 @ SV29 ) )
= $true )
| ( ( ~ ~ ( ~ ! [SY127: $i] :
( ~ ( aElementOf0 @ SY127 @ SV3 )
| ( aElementOf0 @ SY127 @ SV29 ) )
| ~ ! [SY128: $i] :
( ~ ( aElementOf0 @ SY128 @ SV29 )
| ( aElementOf0 @ SY128 @ SV3 ) ) )
| ( SV3 = SV29 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[303]) ).
thf(339,plain,
( ( ~ ~ ( ~ ~ ! [SX0: $i] :
~ ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SX0 @ SX1 )
!= xu ) )
| ~ ( aElementOf0 @ xu @ xI ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[304]) ).
thf(340,plain,
( ( ~ ( ( xu != sz00 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[304]) ).
thf(341,plain,
! [SV44: $i] :
( ( ( ~ ~ ( ~ ( ~ ! [SY136: $i] :
~ ~ ! [SY137: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY136 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SY137 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SY136 @ SY137 )
!= SV44 ) )
| ( aElementOf0 @ SV44 @ xI ) )
| ~ ( ( SV44 != sz00 ) ) ) )
= $true )
| ( ( ~ ( iLess0 @ ( sbrdtbr0 @ SV44 ) @ ( sbrdtbr0 @ xu ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[305]) ).
thf(342,plain,
! [SV4: $i] :
( ( ( ( sdtasdt0 @ SV4 @ sz00 )
!= sz00 )
= $false )
| ( ( aElement0 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[306]) ).
thf(343,plain,
! [SV4: $i] :
( ( ( sz00
!= ( sdtasdt0 @ sz00 @ SV4 ) )
= $false )
| ( ( aElement0 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[306]) ).
thf(344,plain,
! [SV45: $i] :
( ( ~ ( ~ ( aElement0 @ SV45 )
| ( ( sdtasdt0 @ xu @ SV45 )
!= xb ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[307]) ).
thf(345,plain,
! [SV30: $i,SV6: $i] :
( ( ( ~ ( aIdeal0 @ SV6 )
| ~ ( aIdeal0 @ SV30 ) )
= $true )
| ( ( aIdeal0 @ ( sdtpldt1 @ SV6 @ SV30 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[308]) ).
thf(346,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xa @ SX0 )
!= sz00 ) )
| ~ ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xa ) ) )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xa @ SX0 )
!= xa ) ) )
| ~ ( aElementOf0 @ xa @ ( slsdtgt0 @ xa ) ) )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xb @ SX0 )
!= sz00 ) ) )
| ~ ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xb ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[309]) ).
thf(347,plain,
( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xb @ SX0 )
!= xb ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[309]) ).
thf(348,plain,
! [SV41: $i,SV31: $i,SV9: $i] :
( ( ( ~ ( ~ ~ ( ~ ( aElement0 @ SV9 )
| ~ ( aElement0 @ SV31 ) )
| ~ ( aElement0 @ SV41 ) ) )
= $false )
| ( ( ~ ( ( ( sdtasdt0 @ SV9 @ ( sdtpldt0 @ SV31 @ SV41 ) )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV9 @ SV31 ) @ ( sdtasdt0 @ SV9 @ SV41 ) ) )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SV31 @ SV41 ) @ SV9 )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV31 @ SV9 ) @ ( sdtasdt0 @ SV41 @ SV9 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[310]) ).
thf(349,plain,
! [SV10: $i] :
( ( ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ SV10 )
!= ( smndt0 @ SV10 ) )
= $false )
| ( ( aElement0 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[311]) ).
thf(350,plain,
! [SV10: $i] :
( ( ( ( smndt0 @ SV10 )
!= ( sdtasdt0 @ SV10 @ ( smndt0 @ sz10 ) ) )
= $false )
| ( ( aElement0 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[311]) ).
thf(351,plain,
! [SV42: $i,SV32: $i,SV11: $i] :
( ( ( ~ ( ~ ~ ( ~ ( aElement0 @ SV11 )
| ~ ( aElement0 @ SV32 ) )
| ~ ( aElement0 @ SV42 ) ) )
= $false )
| ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV11 @ SV32 ) @ SV42 )
= ( sdtasdt0 @ SV11 @ ( sdtasdt0 @ SV32 @ SV42 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[312]) ).
thf(352,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aSet0 @ xI )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ~ ( ~ ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) )
| ~ ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) ) )
| ~ ( aIdeal0 @ xI ) )
| ~ ! [SX0: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( aElement0 @ SX1 )
| ( ( sdtasdt0 @ xa @ SX1 )
!= SX0 ) ) )
| ~ ( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( aElement0 @ SX1 )
| ( ( sdtasdt0 @ xa @ SX1 )
!= SX0 ) )
| ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) ) ) )
| ~ ! [SX0: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( aElement0 @ SX1 )
| ( ( sdtasdt0 @ xb @ SX1 )
!= SX0 ) ) )
| ~ ( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( aElement0 @ SX1 )
| ( ( sdtasdt0 @ xb @ SX1 )
!= SX0 ) )
| ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[313]) ).
thf(353,plain,
( ( ~ ! [SX0: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX0 @ xI )
| ~ ! [SX1: $i] :
~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SX2 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SX1 @ SX2 )
!= SX0 ) ) )
| ~ ( ~ ~ ! [SX1: $i] :
~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SX2 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SX1 @ SX2 )
!= SX0 ) )
| ( aElementOf0 @ SX0 @ xI ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[313]) ).
thf(354,plain,
! [SV33: $i,SV13: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV13 )
| ~ ( aNaturalNumber0 @ SV33 ) )
= $true )
| ( ( ~ ( iLess0 @ SV13 @ SV33 )
| $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[314]) ).
thf(355,plain,
! [SV14: $i] :
( ( ( ( sdtpldt0 @ SV14 @ sz00 )
!= SV14 )
= $false )
| ( ( aElement0 @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[315]) ).
thf(356,plain,
! [SV14: $i] :
( ( ( SV14
!= ( sdtpldt0 @ sz00 @ SV14 ) )
= $false )
| ( ( aElement0 @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[315]) ).
thf(357,plain,
! [SV34: $i,SV15: $i] :
( ( ( ~ ( aElement0 @ SV15 )
| ~ ( aElement0 @ SV34 ) )
= $true )
| ( ( ( sdtpldt0 @ SV15 @ SV34 )
= ( sdtpldt0 @ SV34 @ SV15 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[316]) ).
thf(358,plain,
( ( ~ ~ ( ~ ( aElement0 @ xq )
| ~ ( aElement0 @ xr ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[317]) ).
thf(359,plain,
( ( xb
!= ( sdtpldt0 @ ( sdtasdt0 @ xq @ xu ) @ xr ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[317]) ).
thf(360,plain,
! [SV35: $i,SV16: $i] :
( ( ( ~ ( aIdeal0 @ SV16 )
| ~ ( aIdeal0 @ SV35 ) )
= $true )
| ( ( ~ ! [SY131: $i] :
( ~ ( aElement0 @ SY131 )
| ( aElementOf0 @ SY131 @ ( sdtpldt1 @ SV16 @ SV35 ) ) )
| ! [SY132: $i,SY133: $i] :
( ~ ~ ( ~ ( aElement0 @ SY132 )
| ~ ( aElement0 @ SY133 ) )
| ~ ! [SY134: $i] :
~ ~ ( ~ ~ ( ~ ( aElement0 @ SY134 )
| ~ ( sdteqdtlpzmzozddtrp0 @ SY134 @ SY132 @ SV16 ) )
| ~ ( sdteqdtlpzmzozddtrp0 @ SY134 @ SY133 @ SV35 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[319]) ).
thf(361,plain,
! [SV36: $i,SV17: $i] :
( ( ( ~ ( aElement0 @ SV17 )
| ~ ( aElement0 @ SV36 ) )
= $true )
| ( ( ( sdtasdt0 @ SV17 @ SV36 )
= ( sdtasdt0 @ SV36 @ SV17 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[320]) ).
thf(362,plain,
( ( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xu @ SX0 )
!= xa ) )
| ( doDivides0 @ xu @ xa ) )
= $false )
| ( ( ~ ( ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xu @ SX0 )
!= xb ) )
| ( doDivides0 @ xu @ xb )
| ( aDivisorOf0 @ xu @ xb ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[321]) ).
thf(363,plain,
( ( ( aDivisorOf0 @ xu @ xa )
= $false )
| ( ( ~ ( ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xu @ SX0 )
!= xb ) )
| ( doDivides0 @ xu @ xb )
| ( aDivisorOf0 @ xu @ xb ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[321]) ).
thf(364,plain,
! [SV18: $i,SV46: $i] :
( ( ( ~ ( aElementOf0 @ SV46 @ SV18 ) )
= $true )
| ( ( aElement0 @ SV46 )
= $true )
| ( ( aSet0 @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[322]) ).
thf(365,plain,
! [SV19: $i] :
( ( ( ~ ( aElement0 @ SV19 ) )
= $true )
| ( ( ~ ( ( SV19 != sz00 ) ) )
= $true )
| ( ( aNaturalNumber0 @ ( sbrdtbr0 @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[323]) ).
thf(366,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xu @ SX0 )
!= xa ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[324]) ).
thf(367,plain,
( ( doDivides0 @ xu @ xa )
= $true ),
inference(extcnf_not_neg,[status(thm)],[325]) ).
thf(368,plain,
! [SV37: $i,SV20: $i] :
( ( ( ~ ( aIdeal0 @ SV20 )
| ~ ( aIdeal0 @ SV37 ) )
= $true )
| ( ( aIdeal0 @ ( sdtasasdt0 @ SV20 @ SV37 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[326]) ).
thf(369,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ xc )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xc @ SX0 )
!= xa ) ) )
| ~ ( doDivides0 @ xc @ xa ) )
| ~ ( aDivisorOf0 @ xc @ xa ) )
| ~ ( aElement0 @ xc ) )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xc @ SX0 )
!= xb ) ) )
| ~ ( doDivides0 @ xc @ xb ) )
| ~ ( aDivisorOf0 @ xc @ xb ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[327]) ).
thf(370,plain,
( ( ~ ! [SX0: $i] :
( ~ ~ ( ~ ( ~ ( ~ ( aElement0 @ SX0 )
| ~ ( ~ ! [SX1: $i] :
~ ~ ( ~ ( aElement0 @ SX1 )
| ( ( sdtasdt0 @ SX0 @ SX1 )
!= xa ) )
| ( doDivides0 @ SX0 @ xa ) ) )
| ( aDivisorOf0 @ SX0 @ xa ) )
| ~ ( ~ ! [SX1: $i] :
~ ~ ( ~ ( aElement0 @ SX1 )
| ( ( sdtasdt0 @ SX0 @ SX1 )
!= xb ) )
| ( doDivides0 @ SX0 @ xb )
| ( aDivisorOf0 @ SX0 @ xb ) ) )
| ~ ( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( aElement0 @ SX1 )
| ( ( sdtasdt0 @ SX0 @ SX1 )
!= xc ) )
| ~ ( doDivides0 @ SX0 @ xc ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[327]) ).
thf(371,plain,
! [SV21: $i] :
( ( ( ( sdtasdt0 @ SV21 @ sz10 )
!= SV21 )
= $false )
| ( ( aElement0 @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[328]) ).
thf(372,plain,
! [SV21: $i] :
( ( ( SV21
!= ( sdtasdt0 @ sz10 @ SV21 ) )
= $false )
| ( ( aElement0 @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[328]) ).
thf(373,plain,
! [SV43: $i,SV38: $i,SV22: $i] :
( ( ( ~ ( ~ ~ ( ~ ( aElement0 @ SV22 )
| ~ ( aElement0 @ SV38 ) )
| ~ ( aElement0 @ SV43 ) ) )
= $false )
| ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV22 @ SV38 ) @ SV43 )
= ( sdtpldt0 @ SV22 @ ( sdtpldt0 @ SV38 @ SV43 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[329]) ).
thf(374,plain,
! [SV39: $i,SV24: $i] :
( ( ( ~ ( aElement0 @ SV24 )
| ~ ( aElement0 @ SV39 ) )
= $true )
| ( ( aElement0 @ ( sdtpldt0 @ SV24 @ SV39 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[330]) ).
thf(375,plain,
! [SV40: $i,SV25: $i] :
( ( ( ~ ( aElement0 @ SV25 )
| ~ ( aElement0 @ SV40 ) )
= $true )
| ( ( aElement0 @ ( sdtasdt0 @ SV25 @ SV40 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[331]) ).
thf(376,plain,
! [SV26: $i] :
( ( ( ( sdtpldt0 @ SV26 @ ( smndt0 @ SV26 ) )
!= sz00 )
= $false )
| ( ( aElement0 @ SV26 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[332]) ).
thf(377,plain,
! [SV26: $i] :
( ( ( sz00
!= ( sdtpldt0 @ ( smndt0 @ SV26 ) @ SV26 ) )
= $false )
| ( ( aElement0 @ SV26 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[332]) ).
thf(378,plain,
! [SV27: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ( aElement0 @ SV1 )
| ~ ( aElement0 @ SV27 ) ) )
= $true )
| ( ( ~ ( ( SV27 != sz00 ) ) )
= $true )
| ( ( ~ ! [SY116: $i] :
~ ~ ! [SY117: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ SY116 )
| ~ ( aElement0 @ SY117 ) )
| ( SV1
!= ( sdtpldt0 @ ( sdtasdt0 @ SY116 @ SV27 ) @ SY117 ) ) )
| ~ ( ~ ( ( SY117 != sz00 ) )
| ( iLess0 @ ( sbrdtbr0 @ SY117 ) @ ( sbrdtbr0 @ SV27 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[333]) ).
thf(379,plain,
! [SV28: $i,SV2: $i] :
( ( ( ~ ( aElement0 @ SV2 ) )
= $true )
| ( ( ~ ( aElement0 @ SV28 ) )
= $true )
| ( ( ( ( sdtasdt0 @ SV2 @ SV28 )
!= sz00 )
| ( SV2 = sz00 )
| ( SV28 = sz00 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[334]) ).
thf(380,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SX1: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( aElement0 @ SX2 )
| ( ( sdtasdt0 @ xa @ SX2 )
!= SX1 ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( aElement0 @ SX2 )
| ( ( sdtasdt0 @ xa @ SX2 )
!= SX1 ) )
| ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) ) ) )
| ~ ! [SX1: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xb ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( aElement0 @ SX2 )
| ( ( sdtasdt0 @ xb @ SX2 )
!= SX1 ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( aElement0 @ SX2 )
| ( ( sdtasdt0 @ xb @ SX2 )
!= SX1 ) )
| ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xb ) ) ) ) )
| ~ ~ ! [SY124: $i] :
~ ~ ! [SY125: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY124 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SY125 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SY124 @ SY125 )
!= sK1_SX0 ) ) )
| ~ ( aElementOf0 @ sK1_SX0 @ ( sdtpldt1 @ ( slsdtgt0 @ xa ) @ ( slsdtgt0 @ xb ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[335]) ).
thf(381,plain,
( ( sK1_SX0 != sz00 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[336]) ).
thf(382,plain,
( ( ~ ( ~ ~ ( ~ ( aElement0 @ sK2_SX0 )
| ~ ( aElement0 @ sK3_SY126 ) )
| ( xu
!= ( sdtpldt0 @ ( sdtasdt0 @ xa @ sK2_SX0 ) @ ( sdtasdt0 @ xb @ sK3_SY126 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[337]) ).
thf(383,plain,
! [SV29: $i,SV3: $i] :
( ( ( ~ ( aSet0 @ SV3 ) )
= $true )
| ( ( ~ ( aSet0 @ SV29 ) )
= $true )
| ( ( ~ ~ ( ~ ! [SY127: $i] :
( ~ ( aElementOf0 @ SY127 @ SV3 )
| ( aElementOf0 @ SY127 @ SV29 ) )
| ~ ! [SY128: $i] :
( ~ ( aElementOf0 @ SY128 @ SV29 )
| ( aElementOf0 @ SY128 @ SV3 ) ) )
| ( SV3 = SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[338]) ).
thf(384,plain,
( ( ~ ( ~ ~ ! [SX0: $i] :
~ ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SX0 @ SX1 )
!= xu ) )
| ~ ( aElementOf0 @ xu @ xI ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[339]) ).
thf(385,plain,
( ( xu != sz00 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[340]) ).
thf(386,plain,
! [SV44: $i] :
( ( ( ~ ( ~ ( ~ ! [SY136: $i] :
~ ~ ! [SY137: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY136 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SY137 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SY136 @ SY137 )
!= SV44 ) )
| ( aElementOf0 @ SV44 @ xI ) )
| ~ ( ( SV44 != sz00 ) ) ) )
= $false )
| ( ( ~ ( iLess0 @ ( sbrdtbr0 @ SV44 ) @ ( sbrdtbr0 @ xu ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[341]) ).
thf(387,plain,
! [SV4: $i] :
( ( ( ( sdtasdt0 @ SV4 @ sz00 )
= sz00 )
= $true )
| ( ( aElement0 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[342]) ).
thf(388,plain,
! [SV4: $i] :
( ( ( sz00
= ( sdtasdt0 @ sz00 @ SV4 ) )
= $true )
| ( ( aElement0 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[343]) ).
thf(389,plain,
! [SV45: $i] :
( ( ~ ( aElement0 @ SV45 )
| ( ( sdtasdt0 @ xu @ SV45 )
!= xb ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[344]) ).
thf(390,plain,
! [SV30: $i,SV6: $i] :
( ( ( ~ ( aIdeal0 @ SV6 ) )
= $true )
| ( ( ~ ( aIdeal0 @ SV30 ) )
= $true )
| ( ( aIdeal0 @ ( sdtpldt1 @ SV6 @ SV30 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[345]) ).
thf(391,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xa @ SX0 )
!= sz00 ) )
| ~ ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xa ) ) )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xa @ SX0 )
!= xa ) ) )
| ~ ( aElementOf0 @ xa @ ( slsdtgt0 @ xa ) ) )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xb @ SX0 )
!= sz00 ) ) )
| ~ ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xb ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[346]) ).
thf(392,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xb @ SX0 )
!= xb ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[347]) ).
thf(393,plain,
! [SV41: $i,SV31: $i,SV9: $i] :
( ( ( ~ ~ ( ~ ( aElement0 @ SV9 )
| ~ ( aElement0 @ SV31 ) )
| ~ ( aElement0 @ SV41 ) )
= $true )
| ( ( ~ ( ( ( sdtasdt0 @ SV9 @ ( sdtpldt0 @ SV31 @ SV41 ) )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV9 @ SV31 ) @ ( sdtasdt0 @ SV9 @ SV41 ) ) )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SV31 @ SV41 ) @ SV9 )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV31 @ SV9 ) @ ( sdtasdt0 @ SV41 @ SV9 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[348]) ).
thf(394,plain,
! [SV10: $i] :
( ( ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ SV10 )
= ( smndt0 @ SV10 ) )
= $true )
| ( ( aElement0 @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[349]) ).
thf(395,plain,
! [SV10: $i] :
( ( ( ( smndt0 @ SV10 )
= ( sdtasdt0 @ SV10 @ ( smndt0 @ sz10 ) ) )
= $true )
| ( ( aElement0 @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[350]) ).
thf(396,plain,
! [SV42: $i,SV32: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ( aElement0 @ SV11 )
| ~ ( aElement0 @ SV32 ) )
| ~ ( aElement0 @ SV42 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV11 @ SV32 ) @ SV42 )
= ( sdtasdt0 @ SV11 @ ( sdtasdt0 @ SV32 @ SV42 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[351]) ).
thf(397,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aSet0 @ xI )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ~ ( ~ ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) )
| ~ ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) ) )
| ~ ( aIdeal0 @ xI ) )
| ~ ! [SX0: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( aElement0 @ SX1 )
| ( ( sdtasdt0 @ xa @ SX1 )
!= SX0 ) ) )
| ~ ( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( aElement0 @ SX1 )
| ( ( sdtasdt0 @ xa @ SX1 )
!= SX0 ) )
| ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) ) ) )
| ~ ! [SX0: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( aElement0 @ SX1 )
| ( ( sdtasdt0 @ xb @ SX1 )
!= SX0 ) ) )
| ~ ( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( aElement0 @ SX1 )
| ( ( sdtasdt0 @ xb @ SX1 )
!= SX0 ) )
| ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[352]) ).
thf(398,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX0 @ xI )
| ~ ! [SX1: $i] :
~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SX2 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SX1 @ SX2 )
!= SX0 ) ) )
| ~ ( ~ ~ ! [SX1: $i] :
~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SX2 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SX1 @ SX2 )
!= SX0 ) )
| ( aElementOf0 @ SX0 @ xI ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[353]) ).
thf(399,plain,
! [SV33: $i,SV13: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV13 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV33 ) )
= $true )
| ( ( ~ ( iLess0 @ SV13 @ SV33 )
| $true )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[354]) ).
thf(400,plain,
! [SV14: $i] :
( ( ( ( sdtpldt0 @ SV14 @ sz00 )
= SV14 )
= $true )
| ( ( aElement0 @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[355]) ).
thf(401,plain,
! [SV14: $i] :
( ( ( SV14
= ( sdtpldt0 @ sz00 @ SV14 ) )
= $true )
| ( ( aElement0 @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[356]) ).
thf(402,plain,
! [SV34: $i,SV15: $i] :
( ( ( ~ ( aElement0 @ SV15 ) )
= $true )
| ( ( ~ ( aElement0 @ SV34 ) )
= $true )
| ( ( ( sdtpldt0 @ SV15 @ SV34 )
= ( sdtpldt0 @ SV34 @ SV15 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[357]) ).
thf(403,plain,
( ( ~ ( ~ ( aElement0 @ xq )
| ~ ( aElement0 @ xr ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[358]) ).
thf(404,plain,
( ( xb
= ( sdtpldt0 @ ( sdtasdt0 @ xq @ xu ) @ xr ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[359]) ).
thf(405,plain,
! [SV35: $i,SV16: $i] :
( ( ( ~ ( aIdeal0 @ SV16 ) )
= $true )
| ( ( ~ ( aIdeal0 @ SV35 ) )
= $true )
| ( ( ~ ! [SY131: $i] :
( ~ ( aElement0 @ SY131 )
| ( aElementOf0 @ SY131 @ ( sdtpldt1 @ SV16 @ SV35 ) ) )
| ! [SY132: $i,SY133: $i] :
( ~ ~ ( ~ ( aElement0 @ SY132 )
| ~ ( aElement0 @ SY133 ) )
| ~ ! [SY134: $i] :
~ ~ ( ~ ~ ( ~ ( aElement0 @ SY134 )
| ~ ( sdteqdtlpzmzozddtrp0 @ SY134 @ SY132 @ SV16 ) )
| ~ ( sdteqdtlpzmzozddtrp0 @ SY134 @ SY133 @ SV35 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[360]) ).
thf(406,plain,
! [SV36: $i,SV17: $i] :
( ( ( ~ ( aElement0 @ SV17 ) )
= $true )
| ( ( ~ ( aElement0 @ SV36 ) )
= $true )
| ( ( ( sdtasdt0 @ SV17 @ SV36 )
= ( sdtasdt0 @ SV36 @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[361]) ).
thf(407,plain,
( ( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xu @ SX0 )
!= xa ) ) )
= $false )
| ( ( ~ ( ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xu @ SX0 )
!= xb ) )
| ( doDivides0 @ xu @ xb )
| ( aDivisorOf0 @ xu @ xb ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[362]) ).
thf(408,plain,
( ( ( doDivides0 @ xu @ xa )
= $false )
| ( ( ~ ( ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xu @ SX0 )
!= xb ) )
| ( doDivides0 @ xu @ xb )
| ( aDivisorOf0 @ xu @ xb ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[362]) ).
thf(409,plain,
( ( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xu @ SX0 )
!= xb ) )
| ( doDivides0 @ xu @ xb )
| ( aDivisorOf0 @ xu @ xb ) )
= $false )
| ( ( aDivisorOf0 @ xu @ xa )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[363]) ).
thf(410,plain,
! [SV18: $i,SV46: $i] :
( ( ( aElementOf0 @ SV46 @ SV18 )
= $false )
| ( ( aElement0 @ SV46 )
= $true )
| ( ( aSet0 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[364]) ).
thf(411,plain,
! [SV19: $i] :
( ( ( aElement0 @ SV19 )
= $false )
| ( ( ~ ( ( SV19 != sz00 ) ) )
= $true )
| ( ( aNaturalNumber0 @ ( sbrdtbr0 @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[365]) ).
thf(412,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xu @ SX0 )
!= xa ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[366]) ).
thf(413,plain,
! [SV37: $i,SV20: $i] :
( ( ( ~ ( aIdeal0 @ SV20 ) )
= $true )
| ( ( ~ ( aIdeal0 @ SV37 ) )
= $true )
| ( ( aIdeal0 @ ( sdtasasdt0 @ SV20 @ SV37 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[368]) ).
thf(414,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ xc )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xc @ SX0 )
!= xa ) ) )
| ~ ( doDivides0 @ xc @ xa ) )
| ~ ( aDivisorOf0 @ xc @ xa ) )
| ~ ( aElement0 @ xc ) )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xc @ SX0 )
!= xb ) ) )
| ~ ( doDivides0 @ xc @ xb ) )
| ~ ( aDivisorOf0 @ xc @ xb ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[369]) ).
thf(415,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( ~ ( ~ ( aElement0 @ SX0 )
| ~ ( ~ ! [SX1: $i] :
~ ~ ( ~ ( aElement0 @ SX1 )
| ( ( sdtasdt0 @ SX0 @ SX1 )
!= xa ) )
| ( doDivides0 @ SX0 @ xa ) ) )
| ( aDivisorOf0 @ SX0 @ xa ) )
| ~ ( ~ ! [SX1: $i] :
~ ~ ( ~ ( aElement0 @ SX1 )
| ( ( sdtasdt0 @ SX0 @ SX1 )
!= xb ) )
| ( doDivides0 @ SX0 @ xb )
| ( aDivisorOf0 @ SX0 @ xb ) ) )
| ~ ( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( aElement0 @ SX1 )
| ( ( sdtasdt0 @ SX0 @ SX1 )
!= xc ) )
| ~ ( doDivides0 @ SX0 @ xc ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[370]) ).
thf(416,plain,
! [SV21: $i] :
( ( ( ( sdtasdt0 @ SV21 @ sz10 )
= SV21 )
= $true )
| ( ( aElement0 @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[371]) ).
thf(417,plain,
! [SV21: $i] :
( ( ( SV21
= ( sdtasdt0 @ sz10 @ SV21 ) )
= $true )
| ( ( aElement0 @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[372]) ).
thf(418,plain,
! [SV43: $i,SV38: $i,SV22: $i] :
( ( ( ~ ~ ( ~ ( aElement0 @ SV22 )
| ~ ( aElement0 @ SV38 ) )
| ~ ( aElement0 @ SV43 ) )
= $true )
| ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV22 @ SV38 ) @ SV43 )
= ( sdtpldt0 @ SV22 @ ( sdtpldt0 @ SV38 @ SV43 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[373]) ).
thf(419,plain,
! [SV39: $i,SV24: $i] :
( ( ( ~ ( aElement0 @ SV24 ) )
= $true )
| ( ( ~ ( aElement0 @ SV39 ) )
= $true )
| ( ( aElement0 @ ( sdtpldt0 @ SV24 @ SV39 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[374]) ).
thf(420,plain,
! [SV40: $i,SV25: $i] :
( ( ( ~ ( aElement0 @ SV25 ) )
= $true )
| ( ( ~ ( aElement0 @ SV40 ) )
= $true )
| ( ( aElement0 @ ( sdtasdt0 @ SV25 @ SV40 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[375]) ).
thf(421,plain,
! [SV26: $i] :
( ( ( ( sdtpldt0 @ SV26 @ ( smndt0 @ SV26 ) )
= sz00 )
= $true )
| ( ( aElement0 @ SV26 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[376]) ).
thf(422,plain,
! [SV26: $i] :
( ( ( sz00
= ( sdtpldt0 @ ( smndt0 @ SV26 ) @ SV26 ) )
= $true )
| ( ( aElement0 @ SV26 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[377]) ).
thf(423,plain,
! [SV27: $i,SV1: $i] :
( ( ( ~ ( ~ ( aElement0 @ SV1 )
| ~ ( aElement0 @ SV27 ) ) )
= $false )
| ( ( ~ ( ( SV27 != sz00 ) ) )
= $true )
| ( ( ~ ! [SY116: $i] :
~ ~ ! [SY117: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ SY116 )
| ~ ( aElement0 @ SY117 ) )
| ( SV1
!= ( sdtpldt0 @ ( sdtasdt0 @ SY116 @ SV27 ) @ SY117 ) ) )
| ~ ( ~ ( ( SY117 != sz00 ) )
| ( iLess0 @ ( sbrdtbr0 @ SY117 ) @ ( sbrdtbr0 @ SV27 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[378]) ).
thf(424,plain,
! [SV28: $i,SV2: $i] :
( ( ( aElement0 @ SV2 )
= $false )
| ( ( ~ ( aElement0 @ SV28 ) )
= $true )
| ( ( ( ( sdtasdt0 @ SV2 @ SV28 )
!= sz00 )
| ( SV2 = sz00 )
| ( SV28 = sz00 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[379]) ).
thf(425,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX1: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( aElement0 @ SX2 )
| ( ( sdtasdt0 @ xa @ SX2 )
!= SX1 ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( aElement0 @ SX2 )
| ( ( sdtasdt0 @ xa @ SX2 )
!= SX1 ) )
| ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) ) ) )
| ~ ! [SX1: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xb ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( aElement0 @ SX2 )
| ( ( sdtasdt0 @ xb @ SX2 )
!= SX1 ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( aElement0 @ SX2 )
| ( ( sdtasdt0 @ xb @ SX2 )
!= SX1 ) )
| ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xb ) ) ) ) )
| ~ ~ ! [SY124: $i] :
~ ~ ! [SY125: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY124 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SY125 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SY124 @ SY125 )
!= sK1_SX0 ) ) )
| ~ ( aElementOf0 @ sK1_SX0 @ ( sdtpldt1 @ ( slsdtgt0 @ xa ) @ ( slsdtgt0 @ xb ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[380]) ).
thf(426,plain,
( ( sK1_SX0 = sz00 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[381]) ).
thf(427,plain,
( ( ~ ~ ( ~ ( aElement0 @ sK2_SX0 )
| ~ ( aElement0 @ sK3_SY126 ) )
| ( xu
!= ( sdtpldt0 @ ( sdtasdt0 @ xa @ sK2_SX0 ) @ ( sdtasdt0 @ xb @ sK3_SY126 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[382]) ).
thf(428,plain,
! [SV29: $i,SV3: $i] :
( ( ( aSet0 @ SV3 )
= $false )
| ( ( ~ ( aSet0 @ SV29 ) )
= $true )
| ( ( ~ ~ ( ~ ! [SY127: $i] :
( ~ ( aElementOf0 @ SY127 @ SV3 )
| ( aElementOf0 @ SY127 @ SV29 ) )
| ~ ! [SY128: $i] :
( ~ ( aElementOf0 @ SY128 @ SV29 )
| ( aElementOf0 @ SY128 @ SV3 ) ) )
| ( SV3 = SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[383]) ).
thf(429,plain,
( ( ~ ~ ! [SX0: $i] :
~ ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SX0 @ SX1 )
!= xu ) )
| ~ ( aElementOf0 @ xu @ xI ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[384]) ).
thf(430,plain,
( ( xu = sz00 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[385]) ).
thf(431,plain,
! [SV44: $i] :
( ( ( ~ ( ~ ! [SY136: $i] :
~ ~ ! [SY137: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY136 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SY137 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SY136 @ SY137 )
!= SV44 ) )
| ( aElementOf0 @ SV44 @ xI ) )
| ~ ( ( SV44 != sz00 ) ) )
= $true )
| ( ( ~ ( iLess0 @ ( sbrdtbr0 @ SV44 ) @ ( sbrdtbr0 @ xu ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[386]) ).
thf(432,plain,
! [SV45: $i] :
( ( ( ~ ( aElement0 @ SV45 ) )
= $true )
| ( ( ( sdtasdt0 @ xu @ SV45 )
!= xb )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[389]) ).
thf(433,plain,
! [SV30: $i,SV6: $i] :
( ( ( aIdeal0 @ SV6 )
= $false )
| ( ( ~ ( aIdeal0 @ SV30 ) )
= $true )
| ( ( aIdeal0 @ ( sdtpldt1 @ SV6 @ SV30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[390]) ).
thf(434,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xa @ SX0 )
!= sz00 ) )
| ~ ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xa ) ) )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xa @ SX0 )
!= xa ) ) )
| ~ ( aElementOf0 @ xa @ ( slsdtgt0 @ xa ) ) )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xb @ SX0 )
!= sz00 ) ) )
| ~ ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xb ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[391]) ).
thf(435,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xb @ SX0 )
!= xb ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[392]) ).
thf(436,plain,
! [SV41: $i,SV31: $i,SV9: $i] :
( ( ( ~ ~ ( ~ ( aElement0 @ SV9 )
| ~ ( aElement0 @ SV31 ) ) )
= $true )
| ( ( ~ ( aElement0 @ SV41 ) )
= $true )
| ( ( ~ ( ( ( sdtasdt0 @ SV9 @ ( sdtpldt0 @ SV31 @ SV41 ) )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV9 @ SV31 ) @ ( sdtasdt0 @ SV9 @ SV41 ) ) )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SV31 @ SV41 ) @ SV9 )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV31 @ SV9 ) @ ( sdtasdt0 @ SV41 @ SV9 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[393]) ).
thf(437,plain,
! [SV42: $i,SV32: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ( aElement0 @ SV11 )
| ~ ( aElement0 @ SV32 ) ) )
= $true )
| ( ( ~ ( aElement0 @ SV42 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV11 @ SV32 ) @ SV42 )
= ( sdtasdt0 @ SV11 @ ( sdtasdt0 @ SV32 @ SV42 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[396]) ).
thf(438,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aSet0 @ xI )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ~ ( ~ ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) )
| ~ ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) ) )
| ~ ( aIdeal0 @ xI ) )
| ~ ! [SX0: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( aElement0 @ SX1 )
| ( ( sdtasdt0 @ xa @ SX1 )
!= SX0 ) ) )
| ~ ( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( aElement0 @ SX1 )
| ( ( sdtasdt0 @ xa @ SX1 )
!= SX0 ) )
| ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) ) ) )
| ~ ! [SX0: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( aElement0 @ SX1 )
| ( ( sdtasdt0 @ xb @ SX1 )
!= SX0 ) ) )
| ~ ( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( aElement0 @ SX1 )
| ( ( sdtasdt0 @ xb @ SX1 )
!= SX0 ) )
| ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[397]) ).
thf(439,plain,
! [SV47: $i] :
( ( ~ ( ~ ( ~ ( aElementOf0 @ SV47 @ xI )
| ~ ! [SY138: $i] :
~ ~ ! [SY139: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY138 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SY139 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SY138 @ SY139 )
!= SV47 ) ) )
| ~ ( ~ ~ ! [SY140: $i] :
~ ~ ! [SY141: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY140 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SY141 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SY140 @ SY141 )
!= SV47 ) )
| ( aElementOf0 @ SV47 @ xI ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[398]) ).
thf(440,plain,
! [SV33: $i,SV13: $i] :
( ( ( aNaturalNumber0 @ SV13 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV33 ) )
= $true )
| ( ( ~ ( iLess0 @ SV13 @ SV33 )
| $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[399]) ).
thf(441,plain,
! [SV34: $i,SV15: $i] :
( ( ( aElement0 @ SV15 )
= $false )
| ( ( ~ ( aElement0 @ SV34 ) )
= $true )
| ( ( ( sdtpldt0 @ SV15 @ SV34 )
= ( sdtpldt0 @ SV34 @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[402]) ).
thf(442,plain,
( ( ~ ( aElement0 @ xq )
| ~ ( aElement0 @ xr ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[403]) ).
thf(443,plain,
! [SV35: $i,SV16: $i] :
( ( ( aIdeal0 @ SV16 )
= $false )
| ( ( ~ ( aIdeal0 @ SV35 ) )
= $true )
| ( ( ~ ! [SY131: $i] :
( ~ ( aElement0 @ SY131 )
| ( aElementOf0 @ SY131 @ ( sdtpldt1 @ SV16 @ SV35 ) ) )
| ! [SY132: $i,SY133: $i] :
( ~ ~ ( ~ ( aElement0 @ SY132 )
| ~ ( aElement0 @ SY133 ) )
| ~ ! [SY134: $i] :
~ ~ ( ~ ~ ( ~ ( aElement0 @ SY134 )
| ~ ( sdteqdtlpzmzozddtrp0 @ SY134 @ SY132 @ SV16 ) )
| ~ ( sdteqdtlpzmzozddtrp0 @ SY134 @ SY133 @ SV35 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[405]) ).
thf(444,plain,
! [SV36: $i,SV17: $i] :
( ( ( aElement0 @ SV17 )
= $false )
| ( ( ~ ( aElement0 @ SV36 ) )
= $true )
| ( ( ( sdtasdt0 @ SV17 @ SV36 )
= ( sdtasdt0 @ SV36 @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[406]) ).
thf(445,plain,
( ( ( ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xu @ SX0 )
!= xa ) ) )
= $true )
| ( ( ~ ( ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xu @ SX0 )
!= xb ) )
| ( doDivides0 @ xu @ xb )
| ( aDivisorOf0 @ xu @ xb ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[407]) ).
thf(446,plain,
( ( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xu @ SX0 )
!= xb ) )
| ( doDivides0 @ xu @ xb )
| ( aDivisorOf0 @ xu @ xb ) )
= $false )
| ( ( doDivides0 @ xu @ xa )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[408]) ).
thf(447,plain,
( ( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xu @ SX0 )
!= xb ) )
| ( doDivides0 @ xu @ xb ) )
= $false )
| ( ( aDivisorOf0 @ xu @ xa )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[409]) ).
thf(448,plain,
( ( ( aDivisorOf0 @ xu @ xb )
= $false )
| ( ( aDivisorOf0 @ xu @ xa )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[409]) ).
thf(449,plain,
! [SV19: $i] :
( ( ( SV19 != sz00 )
= $false )
| ( ( aElement0 @ SV19 )
= $false )
| ( ( aNaturalNumber0 @ ( sbrdtbr0 @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[411]) ).
thf(450,plain,
( ( ~ ~ ( ~ ( aElement0 @ sK4_SX0 )
| ( ( sdtasdt0 @ xu @ sK4_SX0 )
!= xa ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[412]) ).
thf(451,plain,
! [SV37: $i,SV20: $i] :
( ( ( aIdeal0 @ SV20 )
= $false )
| ( ( ~ ( aIdeal0 @ SV37 ) )
= $true )
| ( ( aIdeal0 @ ( sdtasasdt0 @ SV20 @ SV37 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[413]) ).
thf(452,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ xc )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xc @ SX0 )
!= xa ) ) )
| ~ ( doDivides0 @ xc @ xa ) )
| ~ ( aDivisorOf0 @ xc @ xa ) )
| ~ ( aElement0 @ xc ) )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xc @ SX0 )
!= xb ) ) )
| ~ ( doDivides0 @ xc @ xb ) )
| ~ ( aDivisorOf0 @ xc @ xb ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[414]) ).
thf(453,plain,
! [SV48: $i] :
( ( ~ ~ ( ~ ( ~ ( ~ ( aElement0 @ SV48 )
| ~ ( ~ ! [SY142: $i] :
~ ~ ( ~ ( aElement0 @ SY142 )
| ( ( sdtasdt0 @ SV48 @ SY142 )
!= xa ) )
| ( doDivides0 @ SV48 @ xa ) ) )
| ( aDivisorOf0 @ SV48 @ xa ) )
| ~ ( ~ ! [SY143: $i] :
~ ~ ( ~ ( aElement0 @ SY143 )
| ( ( sdtasdt0 @ SV48 @ SY143 )
!= xb ) )
| ( doDivides0 @ SV48 @ xb )
| ( aDivisorOf0 @ SV48 @ xb ) ) )
| ~ ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) )
| ~ ( doDivides0 @ SV48 @ xc ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[415]) ).
thf(454,plain,
! [SV43: $i,SV38: $i,SV22: $i] :
( ( ( ~ ~ ( ~ ( aElement0 @ SV22 )
| ~ ( aElement0 @ SV38 ) ) )
= $true )
| ( ( ~ ( aElement0 @ SV43 ) )
= $true )
| ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV22 @ SV38 ) @ SV43 )
= ( sdtpldt0 @ SV22 @ ( sdtpldt0 @ SV38 @ SV43 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[418]) ).
thf(455,plain,
! [SV39: $i,SV24: $i] :
( ( ( aElement0 @ SV24 )
= $false )
| ( ( ~ ( aElement0 @ SV39 ) )
= $true )
| ( ( aElement0 @ ( sdtpldt0 @ SV24 @ SV39 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[419]) ).
thf(456,plain,
! [SV40: $i,SV25: $i] :
( ( ( aElement0 @ SV25 )
= $false )
| ( ( ~ ( aElement0 @ SV40 ) )
= $true )
| ( ( aElement0 @ ( sdtasdt0 @ SV25 @ SV40 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[420]) ).
thf(457,plain,
! [SV27: $i,SV1: $i] :
( ( ( ~ ( aElement0 @ SV1 )
| ~ ( aElement0 @ SV27 ) )
= $true )
| ( ( ~ ( ( SV27 != sz00 ) ) )
= $true )
| ( ( ~ ! [SY116: $i] :
~ ~ ! [SY117: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ SY116 )
| ~ ( aElement0 @ SY117 ) )
| ( SV1
!= ( sdtpldt0 @ ( sdtasdt0 @ SY116 @ SV27 ) @ SY117 ) ) )
| ~ ( ~ ( ( SY117 != sz00 ) )
| ( iLess0 @ ( sbrdtbr0 @ SY117 ) @ ( sbrdtbr0 @ SV27 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[423]) ).
thf(458,plain,
! [SV2: $i,SV28: $i] :
( ( ( aElement0 @ SV28 )
= $false )
| ( ( aElement0 @ SV2 )
= $false )
| ( ( ( ( sdtasdt0 @ SV2 @ SV28 )
!= sz00 )
| ( SV2 = sz00 )
| ( SV28 = sz00 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[424]) ).
thf(459,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX1: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( aElement0 @ SX2 )
| ( ( sdtasdt0 @ xa @ SX2 )
!= SX1 ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( aElement0 @ SX2 )
| ( ( sdtasdt0 @ xa @ SX2 )
!= SX1 ) )
| ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) ) ) )
| ~ ! [SX1: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xb ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( aElement0 @ SX2 )
| ( ( sdtasdt0 @ xb @ SX2 )
!= SX1 ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( aElement0 @ SX2 )
| ( ( sdtasdt0 @ xb @ SX2 )
!= SX1 ) )
| ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xb ) ) ) ) )
| ~ ~ ! [SY124: $i] :
~ ~ ! [SY125: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY124 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SY125 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SY124 @ SY125 )
!= sK1_SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[425]) ).
thf(460,plain,
( ( ~ ( aElementOf0 @ sK1_SX0 @ ( sdtpldt1 @ ( slsdtgt0 @ xa ) @ ( slsdtgt0 @ xb ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[425]) ).
thf(461,plain,
( ( ~ ~ ( ~ ( aElement0 @ sK2_SX0 )
| ~ ( aElement0 @ sK3_SY126 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[427]) ).
thf(462,plain,
( ( xu
!= ( sdtpldt0 @ ( sdtasdt0 @ xa @ sK2_SX0 ) @ ( sdtasdt0 @ xb @ sK3_SY126 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[427]) ).
thf(463,plain,
! [SV3: $i,SV29: $i] :
( ( ( aSet0 @ SV29 )
= $false )
| ( ( aSet0 @ SV3 )
= $false )
| ( ( ~ ~ ( ~ ! [SY127: $i] :
( ~ ( aElementOf0 @ SY127 @ SV3 )
| ( aElementOf0 @ SY127 @ SV29 ) )
| ~ ! [SY128: $i] :
( ~ ( aElementOf0 @ SY128 @ SV29 )
| ( aElementOf0 @ SY128 @ SV3 ) ) )
| ( SV3 = SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[428]) ).
thf(464,plain,
( ( ~ ~ ! [SX0: $i] :
~ ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SX0 @ SX1 )
!= xu ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[429]) ).
thf(465,plain,
( ( ~ ( aElementOf0 @ xu @ xI ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[429]) ).
thf(466,plain,
! [SV44: $i] :
( ( ( ~ ( ~ ! [SY136: $i] :
~ ~ ! [SY137: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY136 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SY137 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SY136 @ SY137 )
!= SV44 ) )
| ( aElementOf0 @ SV44 @ xI ) ) )
= $true )
| ( ( ~ ( ( SV44 != sz00 ) ) )
= $true )
| ( ( ~ ( iLess0 @ ( sbrdtbr0 @ SV44 ) @ ( sbrdtbr0 @ xu ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[431]) ).
thf(467,plain,
! [SV45: $i] :
( ( ( aElement0 @ SV45 )
= $false )
| ( ( ( sdtasdt0 @ xu @ SV45 )
!= xb )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[432]) ).
thf(468,plain,
! [SV6: $i,SV30: $i] :
( ( ( aIdeal0 @ SV30 )
= $false )
| ( ( aIdeal0 @ SV6 )
= $false )
| ( ( aIdeal0 @ ( sdtpldt1 @ SV6 @ SV30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[433]) ).
thf(469,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xa @ SX0 )
!= sz00 ) )
| ~ ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xa ) ) )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xa @ SX0 )
!= xa ) ) )
| ~ ( aElementOf0 @ xa @ ( slsdtgt0 @ xa ) ) )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xb @ SX0 )
!= sz00 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[434]) ).
thf(470,plain,
( ( ~ ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xb ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[434]) ).
thf(471,plain,
( ( ~ ~ ( ~ ( aElement0 @ sK5_SX0 )
| ( ( sdtasdt0 @ xb @ sK5_SX0 )
!= xb ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[435]) ).
thf(472,plain,
! [SV41: $i,SV31: $i,SV9: $i] :
( ( ( ~ ( ~ ( aElement0 @ SV9 )
| ~ ( aElement0 @ SV31 ) ) )
= $false )
| ( ( ~ ( aElement0 @ SV41 ) )
= $true )
| ( ( ~ ( ( ( sdtasdt0 @ SV9 @ ( sdtpldt0 @ SV31 @ SV41 ) )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV9 @ SV31 ) @ ( sdtasdt0 @ SV9 @ SV41 ) ) )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SV31 @ SV41 ) @ SV9 )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV31 @ SV9 ) @ ( sdtasdt0 @ SV41 @ SV9 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[436]) ).
thf(473,plain,
! [SV42: $i,SV32: $i,SV11: $i] :
( ( ( ~ ( ~ ( aElement0 @ SV11 )
| ~ ( aElement0 @ SV32 ) ) )
= $false )
| ( ( ~ ( aElement0 @ SV42 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV11 @ SV32 ) @ SV42 )
= ( sdtasdt0 @ SV11 @ ( sdtasdt0 @ SV32 @ SV42 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[437]) ).
thf(474,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aSet0 @ xI )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ~ ( ~ ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) )
| ~ ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) ) )
| ~ ( aIdeal0 @ xI ) )
| ~ ! [SX0: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( aElement0 @ SX1 )
| ( ( sdtasdt0 @ xa @ SX1 )
!= SX0 ) ) )
| ~ ( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( aElement0 @ SX1 )
| ( ( sdtasdt0 @ xa @ SX1 )
!= SX0 ) )
| ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[438]) ).
thf(475,plain,
( ( ~ ! [SX0: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( aElement0 @ SX1 )
| ( ( sdtasdt0 @ xb @ SX1 )
!= SX0 ) ) )
| ~ ( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( aElement0 @ SX1 )
| ( ( sdtasdt0 @ xb @ SX1 )
!= SX0 ) )
| ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[438]) ).
thf(476,plain,
! [SV47: $i] :
( ( ~ ( ~ ( aElementOf0 @ SV47 @ xI )
| ~ ! [SY138: $i] :
~ ~ ! [SY139: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY138 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SY139 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SY138 @ SY139 )
!= SV47 ) ) )
| ~ ( ~ ~ ! [SY140: $i] :
~ ~ ! [SY141: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY140 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SY141 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SY140 @ SY141 )
!= SV47 ) )
| ( aElementOf0 @ SV47 @ xI ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[439]) ).
thf(477,plain,
! [SV13: $i,SV33: $i] :
( ( ( aNaturalNumber0 @ SV33 )
= $false )
| ( ( aNaturalNumber0 @ SV13 )
= $false )
| ( ( ~ ( iLess0 @ SV13 @ SV33 )
| $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[440]) ).
thf(478,plain,
! [SV15: $i,SV34: $i] :
( ( ( aElement0 @ SV34 )
= $false )
| ( ( aElement0 @ SV15 )
= $false )
| ( ( ( sdtpldt0 @ SV15 @ SV34 )
= ( sdtpldt0 @ SV34 @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[441]) ).
thf(479,plain,
( ( ~ ( aElement0 @ xq ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[442]) ).
thf(480,plain,
( ( ~ ( aElement0 @ xr ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[442]) ).
thf(481,plain,
! [SV16: $i,SV35: $i] :
( ( ( aIdeal0 @ SV35 )
= $false )
| ( ( aIdeal0 @ SV16 )
= $false )
| ( ( ~ ! [SY131: $i] :
( ~ ( aElement0 @ SY131 )
| ( aElementOf0 @ SY131 @ ( sdtpldt1 @ SV16 @ SV35 ) ) )
| ! [SY132: $i,SY133: $i] :
( ~ ~ ( ~ ( aElement0 @ SY132 )
| ~ ( aElement0 @ SY133 ) )
| ~ ! [SY134: $i] :
~ ~ ( ~ ~ ( ~ ( aElement0 @ SY134 )
| ~ ( sdteqdtlpzmzozddtrp0 @ SY134 @ SY132 @ SV16 ) )
| ~ ( sdteqdtlpzmzozddtrp0 @ SY134 @ SY133 @ SV35 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[443]) ).
thf(482,plain,
! [SV17: $i,SV36: $i] :
( ( ( aElement0 @ SV36 )
= $false )
| ( ( aElement0 @ SV17 )
= $false )
| ( ( ( sdtasdt0 @ SV17 @ SV36 )
= ( sdtasdt0 @ SV36 @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[444]) ).
thf(483,plain,
! [SV49: $i] :
( ( ( ~ ~ ( ~ ( aElement0 @ SV49 )
| ( ( sdtasdt0 @ xu @ SV49 )
!= xa ) ) )
= $true )
| ( ( ~ ( ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xu @ SX0 )
!= xb ) )
| ( doDivides0 @ xu @ xb )
| ( aDivisorOf0 @ xu @ xb ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[445]) ).
thf(484,plain,
( ( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xu @ SX0 )
!= xb ) )
| ( doDivides0 @ xu @ xb ) )
= $false )
| ( ( doDivides0 @ xu @ xa )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[446]) ).
thf(485,plain,
( ( ( aDivisorOf0 @ xu @ xb )
= $false )
| ( ( doDivides0 @ xu @ xa )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[446]) ).
thf(486,plain,
( ( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xu @ SX0 )
!= xb ) ) )
= $false )
| ( ( aDivisorOf0 @ xu @ xa )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[447]) ).
thf(487,plain,
( ( ( doDivides0 @ xu @ xb )
= $false )
| ( ( aDivisorOf0 @ xu @ xa )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[447]) ).
thf(488,plain,
! [SV19: $i] :
( ( ( SV19 = sz00 )
= $true )
| ( ( aElement0 @ SV19 )
= $false )
| ( ( aNaturalNumber0 @ ( sbrdtbr0 @ SV19 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[449]) ).
thf(489,plain,
( ( ~ ( ~ ( aElement0 @ sK4_SX0 )
| ( ( sdtasdt0 @ xu @ sK4_SX0 )
!= xa ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[450]) ).
thf(490,plain,
! [SV20: $i,SV37: $i] :
( ( ( aIdeal0 @ SV37 )
= $false )
| ( ( aIdeal0 @ SV20 )
= $false )
| ( ( aIdeal0 @ ( sdtasasdt0 @ SV20 @ SV37 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[451]) ).
thf(491,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ xc )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xc @ SX0 )
!= xa ) ) )
| ~ ( doDivides0 @ xc @ xa ) )
| ~ ( aDivisorOf0 @ xc @ xa ) )
| ~ ( aElement0 @ xc ) )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xc @ SX0 )
!= xb ) ) )
| ~ ( doDivides0 @ xc @ xb ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[452]) ).
thf(492,plain,
( ( ~ ( aDivisorOf0 @ xc @ xb ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[452]) ).
thf(493,plain,
! [SV48: $i] :
( ( ( ~ ~ ( ~ ( ~ ( ~ ( aElement0 @ SV48 )
| ~ ( ~ ! [SY142: $i] :
~ ~ ( ~ ( aElement0 @ SY142 )
| ( ( sdtasdt0 @ SV48 @ SY142 )
!= xa ) )
| ( doDivides0 @ SV48 @ xa ) ) )
| ( aDivisorOf0 @ SV48 @ xa ) )
| ~ ( ~ ! [SY143: $i] :
~ ~ ( ~ ( aElement0 @ SY143 )
| ( ( sdtasdt0 @ SV48 @ SY143 )
!= xb ) )
| ( doDivides0 @ SV48 @ xb )
| ( aDivisorOf0 @ SV48 @ xb ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) )
| ~ ( doDivides0 @ SV48 @ xc ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[453]) ).
thf(494,plain,
! [SV43: $i,SV38: $i,SV22: $i] :
( ( ( ~ ( ~ ( aElement0 @ SV22 )
| ~ ( aElement0 @ SV38 ) ) )
= $false )
| ( ( ~ ( aElement0 @ SV43 ) )
= $true )
| ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV22 @ SV38 ) @ SV43 )
= ( sdtpldt0 @ SV22 @ ( sdtpldt0 @ SV38 @ SV43 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[454]) ).
thf(495,plain,
! [SV24: $i,SV39: $i] :
( ( ( aElement0 @ SV39 )
= $false )
| ( ( aElement0 @ SV24 )
= $false )
| ( ( aElement0 @ ( sdtpldt0 @ SV24 @ SV39 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[455]) ).
thf(496,plain,
! [SV25: $i,SV40: $i] :
( ( ( aElement0 @ SV40 )
= $false )
| ( ( aElement0 @ SV25 )
= $false )
| ( ( aElement0 @ ( sdtasdt0 @ SV25 @ SV40 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[456]) ).
thf(497,plain,
! [SV27: $i,SV1: $i] :
( ( ( ~ ( aElement0 @ SV1 ) )
= $true )
| ( ( ~ ( aElement0 @ SV27 ) )
= $true )
| ( ( ~ ( ( SV27 != sz00 ) ) )
= $true )
| ( ( ~ ! [SY116: $i] :
~ ~ ! [SY117: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ SY116 )
| ~ ( aElement0 @ SY117 ) )
| ( SV1
!= ( sdtpldt0 @ ( sdtasdt0 @ SY116 @ SV27 ) @ SY117 ) ) )
| ~ ( ~ ( ( SY117 != sz00 ) )
| ( iLess0 @ ( sbrdtbr0 @ SY117 ) @ ( sbrdtbr0 @ SV27 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[457]) ).
thf(498,plain,
! [SV28: $i,SV2: $i] :
( ( ( ( sdtasdt0 @ SV2 @ SV28 )
!= sz00 )
= $true )
| ( ( ( SV2 = sz00 )
| ( SV28 = sz00 ) )
= $true )
| ( ( aElement0 @ SV2 )
= $false )
| ( ( aElement0 @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[458]) ).
thf(499,plain,
( ( ~ ( ~ ~ ( ~ ! [SX1: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( aElement0 @ SX2 )
| ( ( sdtasdt0 @ xa @ SX2 )
!= SX1 ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( aElement0 @ SX2 )
| ( ( sdtasdt0 @ xa @ SX2 )
!= SX1 ) )
| ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) ) ) )
| ~ ! [SX1: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xb ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( aElement0 @ SX2 )
| ( ( sdtasdt0 @ xb @ SX2 )
!= SX1 ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( aElement0 @ SX2 )
| ( ( sdtasdt0 @ xb @ SX2 )
!= SX1 ) )
| ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xb ) ) ) ) )
| ~ ~ ! [SY124: $i] :
~ ~ ! [SY125: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY124 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SY125 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SY124 @ SY125 )
!= sK1_SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[459]) ).
thf(500,plain,
( ( aElementOf0 @ sK1_SX0 @ ( sdtpldt1 @ ( slsdtgt0 @ xa ) @ ( slsdtgt0 @ xb ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[460]) ).
thf(501,plain,
( ( ~ ( ~ ( aElement0 @ sK2_SX0 )
| ~ ( aElement0 @ sK3_SY126 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[461]) ).
thf(502,plain,
( ( xu
= ( sdtpldt0 @ ( sdtasdt0 @ xa @ sK2_SX0 ) @ ( sdtasdt0 @ xb @ sK3_SY126 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[462]) ).
thf(503,plain,
! [SV29: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ! [SY127: $i] :
( ~ ( aElementOf0 @ SY127 @ SV3 )
| ( aElementOf0 @ SY127 @ SV29 ) )
| ~ ! [SY128: $i] :
( ~ ( aElementOf0 @ SY128 @ SV29 )
| ( aElementOf0 @ SY128 @ SV3 ) ) ) )
= $true )
| ( ( SV3 = SV29 )
= $true )
| ( ( aSet0 @ SV3 )
= $false )
| ( ( aSet0 @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[463]) ).
thf(504,plain,
( ( ~ ! [SX0: $i] :
~ ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SX0 @ SX1 )
!= xu ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[464]) ).
thf(505,plain,
( ( aElementOf0 @ xu @ xI )
= $true ),
inference(extcnf_not_neg,[status(thm)],[465]) ).
thf(506,plain,
! [SV44: $i] :
( ( ( ~ ! [SY136: $i] :
~ ~ ! [SY137: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY136 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SY137 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SY136 @ SY137 )
!= SV44 ) )
| ( aElementOf0 @ SV44 @ xI ) )
= $false )
| ( ( ~ ( ( SV44 != sz00 ) ) )
= $true )
| ( ( ~ ( iLess0 @ ( sbrdtbr0 @ SV44 ) @ ( sbrdtbr0 @ xu ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[466]) ).
thf(507,plain,
! [SV45: $i] :
( ( ( ( sdtasdt0 @ xu @ SV45 )
= xb )
= $false )
| ( ( aElement0 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[467]) ).
thf(508,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xa @ SX0 )
!= sz00 ) )
| ~ ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xa ) ) )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xa @ SX0 )
!= xa ) ) )
| ~ ( aElementOf0 @ xa @ ( slsdtgt0 @ xa ) ) )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xb @ SX0 )
!= sz00 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[469]) ).
thf(509,plain,
( ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xb ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[470]) ).
thf(510,plain,
( ( ~ ( ~ ( aElement0 @ sK5_SX0 )
| ( ( sdtasdt0 @ xb @ sK5_SX0 )
!= xb ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[471]) ).
thf(511,plain,
! [SV41: $i,SV31: $i,SV9: $i] :
( ( ( ~ ( aElement0 @ SV9 )
| ~ ( aElement0 @ SV31 ) )
= $true )
| ( ( ~ ( aElement0 @ SV41 ) )
= $true )
| ( ( ~ ( ( ( sdtasdt0 @ SV9 @ ( sdtpldt0 @ SV31 @ SV41 ) )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV9 @ SV31 ) @ ( sdtasdt0 @ SV9 @ SV41 ) ) )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SV31 @ SV41 ) @ SV9 )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV31 @ SV9 ) @ ( sdtasdt0 @ SV41 @ SV9 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[472]) ).
thf(512,plain,
! [SV42: $i,SV32: $i,SV11: $i] :
( ( ( ~ ( aElement0 @ SV11 )
| ~ ( aElement0 @ SV32 ) )
= $true )
| ( ( ~ ( aElement0 @ SV42 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV11 @ SV32 ) @ SV42 )
= ( sdtasdt0 @ SV11 @ ( sdtasdt0 @ SV32 @ SV42 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[473]) ).
thf(513,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( aSet0 @ xI )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ~ ( ~ ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) )
| ~ ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) ) )
| ~ ( aIdeal0 @ xI ) )
| ~ ! [SX0: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( aElement0 @ SX1 )
| ( ( sdtasdt0 @ xa @ SX1 )
!= SX0 ) ) )
| ~ ( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( aElement0 @ SX1 )
| ( ( sdtasdt0 @ xa @ SX1 )
!= SX0 ) )
| ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[474]) ).
thf(514,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( aElement0 @ SX1 )
| ( ( sdtasdt0 @ xb @ SX1 )
!= SX0 ) ) )
| ~ ( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( aElement0 @ SX1 )
| ( ( sdtasdt0 @ xb @ SX1 )
!= SX0 ) )
| ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[475]) ).
thf(515,plain,
! [SV47: $i] :
( ( ~ ( ~ ( aElementOf0 @ SV47 @ xI )
| ~ ! [SY138: $i] :
~ ~ ! [SY139: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY138 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SY139 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SY138 @ SY139 )
!= SV47 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[476]) ).
thf(516,plain,
! [SV47: $i] :
( ( ~ ( ~ ~ ! [SY140: $i] :
~ ~ ! [SY141: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY140 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SY141 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SY140 @ SY141 )
!= SV47 ) )
| ( aElementOf0 @ SV47 @ xI ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[476]) ).
thf(517,plain,
! [SV33: $i,SV13: $i] :
( ( ( ~ ( iLess0 @ SV13 @ SV33 ) )
= $true )
| ( $true = $true )
| ( ( aNaturalNumber0 @ SV13 )
= $false )
| ( ( aNaturalNumber0 @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[477]) ).
thf(518,plain,
( ( aElement0 @ xq )
= $true ),
inference(extcnf_not_neg,[status(thm)],[479]) ).
thf(519,plain,
( ( aElement0 @ xr )
= $true ),
inference(extcnf_not_neg,[status(thm)],[480]) ).
thf(520,plain,
! [SV35: $i,SV16: $i] :
( ( ( ~ ! [SY131: $i] :
( ~ ( aElement0 @ SY131 )
| ( aElementOf0 @ SY131 @ ( sdtpldt1 @ SV16 @ SV35 ) ) ) )
= $true )
| ( ( ! [SY132: $i,SY133: $i] :
( ~ ~ ( ~ ( aElement0 @ SY132 )
| ~ ( aElement0 @ SY133 ) )
| ~ ! [SY134: $i] :
~ ~ ( ~ ~ ( ~ ( aElement0 @ SY134 )
| ~ ( sdteqdtlpzmzozddtrp0 @ SY134 @ SY132 @ SV16 ) )
| ~ ( sdteqdtlpzmzozddtrp0 @ SY134 @ SY133 @ SV35 ) ) ) )
= $true )
| ( ( aIdeal0 @ SV16 )
= $false )
| ( ( aIdeal0 @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[481]) ).
thf(521,plain,
! [SV49: $i] :
( ( ( ~ ( ~ ( aElement0 @ SV49 )
| ( ( sdtasdt0 @ xu @ SV49 )
!= xa ) ) )
= $false )
| ( ( ~ ( ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xu @ SX0 )
!= xb ) )
| ( doDivides0 @ xu @ xb )
| ( aDivisorOf0 @ xu @ xb ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[483]) ).
thf(522,plain,
( ( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xu @ SX0 )
!= xb ) ) )
= $false )
| ( ( doDivides0 @ xu @ xa )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[484]) ).
thf(523,plain,
( ( ( doDivides0 @ xu @ xb )
= $false )
| ( ( doDivides0 @ xu @ xa )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[484]) ).
thf(524,plain,
( ( ( ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xu @ SX0 )
!= xb ) ) )
= $true )
| ( ( aDivisorOf0 @ xu @ xa )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[486]) ).
thf(525,plain,
( ( ~ ( aElement0 @ sK4_SX0 )
| ( ( sdtasdt0 @ xu @ sK4_SX0 )
!= xa ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[489]) ).
thf(526,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ xc )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xc @ SX0 )
!= xa ) ) )
| ~ ( doDivides0 @ xc @ xa ) )
| ~ ( aDivisorOf0 @ xc @ xa ) )
| ~ ( aElement0 @ xc ) )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xc @ SX0 )
!= xb ) ) )
| ~ ( doDivides0 @ xc @ xb ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[491]) ).
thf(527,plain,
( ( aDivisorOf0 @ xc @ xb )
= $true ),
inference(extcnf_not_neg,[status(thm)],[492]) ).
thf(528,plain,
! [SV48: $i] :
( ( ( ~ ( ~ ( ~ ( ~ ( aElement0 @ SV48 )
| ~ ( ~ ! [SY142: $i] :
~ ~ ( ~ ( aElement0 @ SY142 )
| ( ( sdtasdt0 @ SV48 @ SY142 )
!= xa ) )
| ( doDivides0 @ SV48 @ xa ) ) )
| ( aDivisorOf0 @ SV48 @ xa ) )
| ~ ( ~ ! [SY143: $i] :
~ ~ ( ~ ( aElement0 @ SY143 )
| ( ( sdtasdt0 @ SV48 @ SY143 )
!= xb ) )
| ( doDivides0 @ SV48 @ xb )
| ( aDivisorOf0 @ SV48 @ xb ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) )
| ~ ( doDivides0 @ SV48 @ xc ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[493]) ).
thf(529,plain,
! [SV43: $i,SV38: $i,SV22: $i] :
( ( ( ~ ( aElement0 @ SV22 )
| ~ ( aElement0 @ SV38 ) )
= $true )
| ( ( ~ ( aElement0 @ SV43 ) )
= $true )
| ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV22 @ SV38 ) @ SV43 )
= ( sdtpldt0 @ SV22 @ ( sdtpldt0 @ SV38 @ SV43 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[494]) ).
thf(530,plain,
! [SV27: $i,SV1: $i] :
( ( ( aElement0 @ SV1 )
= $false )
| ( ( ~ ( aElement0 @ SV27 ) )
= $true )
| ( ( ~ ( ( SV27 != sz00 ) ) )
= $true )
| ( ( ~ ! [SY116: $i] :
~ ~ ! [SY117: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ SY116 )
| ~ ( aElement0 @ SY117 ) )
| ( SV1
!= ( sdtpldt0 @ ( sdtasdt0 @ SY116 @ SV27 ) @ SY117 ) ) )
| ~ ( ~ ( ( SY117 != sz00 ) )
| ( iLess0 @ ( sbrdtbr0 @ SY117 ) @ ( sbrdtbr0 @ SV27 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[497]) ).
thf(531,plain,
! [SV28: $i,SV2: $i] :
( ( ( ( sdtasdt0 @ SV2 @ SV28 )
= sz00 )
= $false )
| ( ( ( SV2 = sz00 )
| ( SV28 = sz00 ) )
= $true )
| ( ( aElement0 @ SV2 )
= $false )
| ( ( aElement0 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[498]) ).
thf(532,plain,
( ( ~ ~ ( ~ ! [SX1: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( aElement0 @ SX2 )
| ( ( sdtasdt0 @ xa @ SX2 )
!= SX1 ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( aElement0 @ SX2 )
| ( ( sdtasdt0 @ xa @ SX2 )
!= SX1 ) )
| ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) ) ) )
| ~ ! [SX1: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xb ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( aElement0 @ SX2 )
| ( ( sdtasdt0 @ xb @ SX2 )
!= SX1 ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( aElement0 @ SX2 )
| ( ( sdtasdt0 @ xb @ SX2 )
!= SX1 ) )
| ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xb ) ) ) ) )
| ~ ~ ! [SY124: $i] :
~ ~ ! [SY125: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY124 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SY125 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SY124 @ SY125 )
!= sK1_SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[499]) ).
thf(533,plain,
( ( ~ ( aElement0 @ sK2_SX0 )
| ~ ( aElement0 @ sK3_SY126 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[501]) ).
thf(534,plain,
! [SV29: $i,SV3: $i] :
( ( ( ~ ( ~ ! [SY127: $i] :
( ~ ( aElementOf0 @ SY127 @ SV3 )
| ( aElementOf0 @ SY127 @ SV29 ) )
| ~ ! [SY128: $i] :
( ~ ( aElementOf0 @ SY128 @ SV29 )
| ( aElementOf0 @ SY128 @ SV3 ) ) ) )
= $false )
| ( ( SV3 = SV29 )
= $true )
| ( ( aSet0 @ SV3 )
= $false )
| ( ( aSet0 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[503]) ).
thf(535,plain,
( ( ! [SX0: $i] :
~ ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SX0 @ SX1 )
!= xu ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[504]) ).
thf(536,plain,
! [SV44: $i] :
( ( ( ~ ! [SY136: $i] :
~ ~ ! [SY137: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY136 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SY137 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SY136 @ SY137 )
!= SV44 ) ) )
= $false )
| ( ( ~ ( ( SV44 != sz00 ) ) )
= $true )
| ( ( ~ ( iLess0 @ ( sbrdtbr0 @ SV44 ) @ ( sbrdtbr0 @ xu ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[506]) ).
thf(537,plain,
! [SV44: $i] :
( ( ( aElementOf0 @ SV44 @ xI )
= $false )
| ( ( ~ ( ( SV44 != sz00 ) ) )
= $true )
| ( ( ~ ( iLess0 @ ( sbrdtbr0 @ SV44 ) @ ( sbrdtbr0 @ xu ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[506]) ).
thf(538,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xa @ SX0 )
!= sz00 ) )
| ~ ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xa ) ) )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xa @ SX0 )
!= xa ) ) )
| ~ ( aElementOf0 @ xa @ ( slsdtgt0 @ xa ) ) )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xb @ SX0 )
!= sz00 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[508]) ).
thf(539,plain,
( ( ~ ( aElement0 @ sK5_SX0 )
| ( ( sdtasdt0 @ xb @ sK5_SX0 )
!= xb ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[510]) ).
thf(540,plain,
! [SV41: $i,SV31: $i,SV9: $i] :
( ( ( ~ ( aElement0 @ SV9 ) )
= $true )
| ( ( ~ ( aElement0 @ SV31 ) )
= $true )
| ( ( ~ ( aElement0 @ SV41 ) )
= $true )
| ( ( ~ ( ( ( sdtasdt0 @ SV9 @ ( sdtpldt0 @ SV31 @ SV41 ) )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV9 @ SV31 ) @ ( sdtasdt0 @ SV9 @ SV41 ) ) )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SV31 @ SV41 ) @ SV9 )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV31 @ SV9 ) @ ( sdtasdt0 @ SV41 @ SV9 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[511]) ).
thf(541,plain,
! [SV42: $i,SV32: $i,SV11: $i] :
( ( ( ~ ( aElement0 @ SV11 ) )
= $true )
| ( ( ~ ( aElement0 @ SV32 ) )
= $true )
| ( ( ~ ( aElement0 @ SV42 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV11 @ SV32 ) @ SV42 )
= ( sdtasdt0 @ SV11 @ ( sdtasdt0 @ SV32 @ SV42 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[512]) ).
thf(542,plain,
( ( ~ ~ ( ~ ~ ( ~ ( aSet0 @ xI )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ~ ( ~ ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) )
| ~ ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) ) )
| ~ ( aIdeal0 @ xI ) )
| ~ ! [SX0: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( aElement0 @ SX1 )
| ( ( sdtasdt0 @ xa @ SX1 )
!= SX0 ) ) )
| ~ ( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( aElement0 @ SX1 )
| ( ( sdtasdt0 @ xa @ SX1 )
!= SX0 ) )
| ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[513]) ).
thf(543,plain,
! [SV50: $i] :
( ( ~ ( ~ ( ~ ( aElementOf0 @ SV50 @ ( slsdtgt0 @ xb ) )
| ~ ! [SY145: $i] :
~ ~ ( ~ ( aElement0 @ SY145 )
| ( ( sdtasdt0 @ xb @ SY145 )
!= SV50 ) ) )
| ~ ( ~ ~ ! [SY146: $i] :
~ ~ ( ~ ( aElement0 @ SY146 )
| ( ( sdtasdt0 @ xb @ SY146 )
!= SV50 ) )
| ( aElementOf0 @ SV50 @ ( slsdtgt0 @ xb ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[514]) ).
thf(544,plain,
! [SV47: $i] :
( ( ~ ( aElementOf0 @ SV47 @ xI )
| ~ ! [SY138: $i] :
~ ~ ! [SY139: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY138 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SY139 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SY138 @ SY139 )
!= SV47 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[515]) ).
thf(545,plain,
! [SV47: $i] :
( ( ~ ~ ! [SY140: $i] :
~ ~ ! [SY141: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY140 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SY141 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SY140 @ SY141 )
!= SV47 ) )
| ( aElementOf0 @ SV47 @ xI ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[516]) ).
thf(546,plain,
! [SV33: $i,SV13: $i] :
( ( ( iLess0 @ SV13 @ SV33 )
= $false )
| ( $true = $true )
| ( ( aNaturalNumber0 @ SV13 )
= $false )
| ( ( aNaturalNumber0 @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[517]) ).
thf(547,plain,
! [SV35: $i,SV16: $i] :
( ( ( ! [SY131: $i] :
( ~ ( aElement0 @ SY131 )
| ( aElementOf0 @ SY131 @ ( sdtpldt1 @ SV16 @ SV35 ) ) ) )
= $false )
| ( ( ! [SY132: $i,SY133: $i] :
( ~ ~ ( ~ ( aElement0 @ SY132 )
| ~ ( aElement0 @ SY133 ) )
| ~ ! [SY134: $i] :
~ ~ ( ~ ~ ( ~ ( aElement0 @ SY134 )
| ~ ( sdteqdtlpzmzozddtrp0 @ SY134 @ SY132 @ SV16 ) )
| ~ ( sdteqdtlpzmzozddtrp0 @ SY134 @ SY133 @ SV35 ) ) ) )
= $true )
| ( ( aIdeal0 @ SV16 )
= $false )
| ( ( aIdeal0 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[520]) ).
thf(548,plain,
! [SV49: $i] :
( ( ( ~ ( aElement0 @ SV49 )
| ( ( sdtasdt0 @ xu @ SV49 )
!= xa ) )
= $true )
| ( ( ~ ( ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xu @ SX0 )
!= xb ) )
| ( doDivides0 @ xu @ xb )
| ( aDivisorOf0 @ xu @ xb ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[521]) ).
thf(549,plain,
( ( ( ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xu @ SX0 )
!= xb ) ) )
= $true )
| ( ( doDivides0 @ xu @ xa )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[522]) ).
thf(550,plain,
! [SV51: $i] :
( ( ( ~ ~ ( ~ ( aElement0 @ SV51 )
| ( ( sdtasdt0 @ xu @ SV51 )
!= xb ) ) )
= $true )
| ( ( aDivisorOf0 @ xu @ xa )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[524]) ).
thf(551,plain,
( ( ~ ( aElement0 @ sK4_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[525]) ).
thf(552,plain,
( ( ( sdtasdt0 @ xu @ sK4_SX0 )
!= xa )
= $false ),
inference(extcnf_or_neg,[status(thm)],[525]) ).
thf(553,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ xc )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xc @ SX0 )
!= xa ) ) )
| ~ ( doDivides0 @ xc @ xa ) )
| ~ ( aDivisorOf0 @ xc @ xa ) )
| ~ ( aElement0 @ xc ) )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xc @ SX0 )
!= xb ) ) )
| ~ ( doDivides0 @ xc @ xb ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[526]) ).
thf(554,plain,
! [SV48: $i] :
( ( ( ~ ( ~ ( ~ ( aElement0 @ SV48 )
| ~ ( ~ ! [SY142: $i] :
~ ~ ( ~ ( aElement0 @ SY142 )
| ( ( sdtasdt0 @ SV48 @ SY142 )
!= xa ) )
| ( doDivides0 @ SV48 @ xa ) ) )
| ( aDivisorOf0 @ SV48 @ xa ) )
| ~ ( ~ ! [SY143: $i] :
~ ~ ( ~ ( aElement0 @ SY143 )
| ( ( sdtasdt0 @ SV48 @ SY143 )
!= xb ) )
| ( doDivides0 @ SV48 @ xb )
| ( aDivisorOf0 @ SV48 @ xb ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) )
| ~ ( doDivides0 @ SV48 @ xc ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[528]) ).
thf(555,plain,
! [SV43: $i,SV38: $i,SV22: $i] :
( ( ( ~ ( aElement0 @ SV22 ) )
= $true )
| ( ( ~ ( aElement0 @ SV38 ) )
= $true )
| ( ( ~ ( aElement0 @ SV43 ) )
= $true )
| ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV22 @ SV38 ) @ SV43 )
= ( sdtpldt0 @ SV22 @ ( sdtpldt0 @ SV38 @ SV43 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[529]) ).
thf(556,plain,
! [SV1: $i,SV27: $i] :
( ( ( aElement0 @ SV27 )
= $false )
| ( ( aElement0 @ SV1 )
= $false )
| ( ( ~ ( ( SV27 != sz00 ) ) )
= $true )
| ( ( ~ ! [SY116: $i] :
~ ~ ! [SY117: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ SY116 )
| ~ ( aElement0 @ SY117 ) )
| ( SV1
!= ( sdtpldt0 @ ( sdtasdt0 @ SY116 @ SV27 ) @ SY117 ) ) )
| ~ ( ~ ( ( SY117 != sz00 ) )
| ( iLess0 @ ( sbrdtbr0 @ SY117 ) @ ( sbrdtbr0 @ SV27 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[530]) ).
thf(557,plain,
! [SV28: $i,SV2: $i] :
( ( ( SV2 = sz00 )
= $true )
| ( ( SV28 = sz00 )
= $true )
| ( ( ( sdtasdt0 @ SV2 @ SV28 )
= sz00 )
= $false )
| ( ( aElement0 @ SV2 )
= $false )
| ( ( aElement0 @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[531]) ).
thf(558,plain,
( ( ~ ~ ( ~ ! [SX1: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( aElement0 @ SX2 )
| ( ( sdtasdt0 @ xa @ SX2 )
!= SX1 ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( aElement0 @ SX2 )
| ( ( sdtasdt0 @ xa @ SX2 )
!= SX1 ) )
| ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) ) ) )
| ~ ! [SX1: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xb ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( aElement0 @ SX2 )
| ( ( sdtasdt0 @ xb @ SX2 )
!= SX1 ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( aElement0 @ SX2 )
| ( ( sdtasdt0 @ xb @ SX2 )
!= SX1 ) )
| ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xb ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[532]) ).
thf(559,plain,
( ( ~ ~ ! [SY124: $i] :
~ ~ ! [SY125: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY124 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SY125 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SY124 @ SY125 )
!= sK1_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[532]) ).
thf(560,plain,
( ( ~ ( aElement0 @ sK2_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[533]) ).
thf(561,plain,
( ( ~ ( aElement0 @ sK3_SY126 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[533]) ).
thf(562,plain,
! [SV29: $i,SV3: $i] :
( ( ( ~ ! [SY127: $i] :
( ~ ( aElementOf0 @ SY127 @ SV3 )
| ( aElementOf0 @ SY127 @ SV29 ) )
| ~ ! [SY128: $i] :
( ~ ( aElementOf0 @ SY128 @ SV29 )
| ( aElementOf0 @ SY128 @ SV3 ) ) )
= $true )
| ( ( SV3 = SV29 )
= $true )
| ( ( aSet0 @ SV3 )
= $false )
| ( ( aSet0 @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[534]) ).
thf(563,plain,
( ( ~ ~ ! [SY147: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ sK6_SX0 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SY147 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ sK6_SX0 @ SY147 )
!= xu ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[535]) ).
thf(564,plain,
! [SV44: $i] :
( ( ( ! [SY136: $i] :
~ ~ ! [SY137: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY136 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SY137 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SY136 @ SY137 )
!= SV44 ) ) )
= $true )
| ( ( ~ ( ( SV44 != sz00 ) ) )
= $true )
| ( ( ~ ( iLess0 @ ( sbrdtbr0 @ SV44 ) @ ( sbrdtbr0 @ xu ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[536]) ).
thf(565,plain,
! [SV44: $i] :
( ( ( SV44 != sz00 )
= $false )
| ( ( aElementOf0 @ SV44 @ xI )
= $false )
| ( ( ~ ( iLess0 @ ( sbrdtbr0 @ SV44 ) @ ( sbrdtbr0 @ xu ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[537]) ).
thf(566,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xa @ SX0 )
!= sz00 ) )
| ~ ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xa ) ) )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xa @ SX0 )
!= xa ) ) )
| ~ ( aElementOf0 @ xa @ ( slsdtgt0 @ xa ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[538]) ).
thf(567,plain,
( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xb @ SX0 )
!= sz00 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[538]) ).
thf(568,plain,
( ( ~ ( aElement0 @ sK5_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[539]) ).
thf(569,plain,
( ( ( sdtasdt0 @ xb @ sK5_SX0 )
!= xb )
= $false ),
inference(extcnf_or_neg,[status(thm)],[539]) ).
thf(570,plain,
! [SV41: $i,SV31: $i,SV9: $i] :
( ( ( aElement0 @ SV9 )
= $false )
| ( ( ~ ( aElement0 @ SV31 ) )
= $true )
| ( ( ~ ( aElement0 @ SV41 ) )
= $true )
| ( ( ~ ( ( ( sdtasdt0 @ SV9 @ ( sdtpldt0 @ SV31 @ SV41 ) )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV9 @ SV31 ) @ ( sdtasdt0 @ SV9 @ SV41 ) ) )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SV31 @ SV41 ) @ SV9 )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV31 @ SV9 ) @ ( sdtasdt0 @ SV41 @ SV9 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[540]) ).
thf(571,plain,
! [SV42: $i,SV32: $i,SV11: $i] :
( ( ( aElement0 @ SV11 )
= $false )
| ( ( ~ ( aElement0 @ SV32 ) )
= $true )
| ( ( ~ ( aElement0 @ SV42 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV11 @ SV32 ) @ SV42 )
= ( sdtasdt0 @ SV11 @ ( sdtasdt0 @ SV32 @ SV42 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[541]) ).
thf(572,plain,
( ( ~ ~ ( ~ ~ ( ~ ( aSet0 @ xI )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ~ ( ~ ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) )
| ~ ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) ) )
| ~ ( aIdeal0 @ xI ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[542]) ).
thf(573,plain,
( ( ~ ! [SX0: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( aElement0 @ SX1 )
| ( ( sdtasdt0 @ xa @ SX1 )
!= SX0 ) ) )
| ~ ( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( aElement0 @ SX1 )
| ( ( sdtasdt0 @ xa @ SX1 )
!= SX0 ) )
| ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[542]) ).
thf(574,plain,
! [SV50: $i] :
( ( ~ ( ~ ( aElementOf0 @ SV50 @ ( slsdtgt0 @ xb ) )
| ~ ! [SY145: $i] :
~ ~ ( ~ ( aElement0 @ SY145 )
| ( ( sdtasdt0 @ xb @ SY145 )
!= SV50 ) ) )
| ~ ( ~ ~ ! [SY146: $i] :
~ ~ ( ~ ( aElement0 @ SY146 )
| ( ( sdtasdt0 @ xb @ SY146 )
!= SV50 ) )
| ( aElementOf0 @ SV50 @ ( slsdtgt0 @ xb ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[543]) ).
thf(575,plain,
! [SV47: $i] :
( ( ( ~ ( aElementOf0 @ SV47 @ xI ) )
= $true )
| ( ( ~ ! [SY138: $i] :
~ ~ ! [SY139: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY138 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SY139 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SY138 @ SY139 )
!= SV47 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[544]) ).
thf(576,plain,
! [SV47: $i] :
( ( ( ~ ~ ! [SY140: $i] :
~ ~ ! [SY141: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY140 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SY141 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SY140 @ SY141 )
!= SV47 ) ) )
= $true )
| ( ( aElementOf0 @ SV47 @ xI )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[545]) ).
thf(577,plain,
! [SV16: $i,SV35: $i] :
( ( ( ~ ( aElement0 @ ( sK7_SY131 @ SV35 @ SV16 ) )
| ( aElementOf0 @ ( sK7_SY131 @ SV35 @ SV16 ) @ ( sdtpldt1 @ SV16 @ SV35 ) ) )
= $false )
| ( ( ! [SY132: $i,SY133: $i] :
( ~ ~ ( ~ ( aElement0 @ SY132 )
| ~ ( aElement0 @ SY133 ) )
| ~ ! [SY134: $i] :
~ ~ ( ~ ~ ( ~ ( aElement0 @ SY134 )
| ~ ( sdteqdtlpzmzozddtrp0 @ SY134 @ SY132 @ SV16 ) )
| ~ ( sdteqdtlpzmzozddtrp0 @ SY134 @ SY133 @ SV35 ) ) ) )
= $true )
| ( ( aIdeal0 @ SV16 )
= $false )
| ( ( aIdeal0 @ SV35 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[547]) ).
thf(578,plain,
! [SV49: $i] :
( ( ( ~ ( aElement0 @ SV49 ) )
= $true )
| ( ( ( sdtasdt0 @ xu @ SV49 )
!= xa )
= $true )
| ( ( ~ ( ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xu @ SX0 )
!= xb ) )
| ( doDivides0 @ xu @ xb )
| ( aDivisorOf0 @ xu @ xb ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[548]) ).
thf(579,plain,
! [SV52: $i] :
( ( ( ~ ~ ( ~ ( aElement0 @ SV52 )
| ( ( sdtasdt0 @ xu @ SV52 )
!= xb ) ) )
= $true )
| ( ( doDivides0 @ xu @ xa )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[549]) ).
thf(580,plain,
! [SV51: $i] :
( ( ( ~ ( ~ ( aElement0 @ SV51 )
| ( ( sdtasdt0 @ xu @ SV51 )
!= xb ) ) )
= $false )
| ( ( aDivisorOf0 @ xu @ xa )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[550]) ).
thf(581,plain,
( ( aElement0 @ sK4_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[551]) ).
thf(582,plain,
( ( ( sdtasdt0 @ xu @ sK4_SX0 )
= xa )
= $true ),
inference(extcnf_not_neg,[status(thm)],[552]) ).
thf(583,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ xc )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xc @ SX0 )
!= xa ) ) )
| ~ ( doDivides0 @ xc @ xa ) )
| ~ ( aDivisorOf0 @ xc @ xa ) )
| ~ ( aElement0 @ xc ) )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xc @ SX0 )
!= xb ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[553]) ).
thf(584,plain,
( ( ~ ( doDivides0 @ xc @ xb ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[553]) ).
thf(585,plain,
! [SV48: $i] :
( ( ( ~ ( ~ ( ~ ( aElement0 @ SV48 )
| ~ ( ~ ! [SY142: $i] :
~ ~ ( ~ ( aElement0 @ SY142 )
| ( ( sdtasdt0 @ SV48 @ SY142 )
!= xa ) )
| ( doDivides0 @ SV48 @ xa ) ) )
| ( aDivisorOf0 @ SV48 @ xa ) ) )
= $true )
| ( ( ~ ( ~ ! [SY143: $i] :
~ ~ ( ~ ( aElement0 @ SY143 )
| ( ( sdtasdt0 @ SV48 @ SY143 )
!= xb ) )
| ( doDivides0 @ SV48 @ xb )
| ( aDivisorOf0 @ SV48 @ xb ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) )
| ~ ( doDivides0 @ SV48 @ xc ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[554]) ).
thf(586,plain,
! [SV43: $i,SV38: $i,SV22: $i] :
( ( ( aElement0 @ SV22 )
= $false )
| ( ( ~ ( aElement0 @ SV38 ) )
= $true )
| ( ( ~ ( aElement0 @ SV43 ) )
= $true )
| ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV22 @ SV38 ) @ SV43 )
= ( sdtpldt0 @ SV22 @ ( sdtpldt0 @ SV38 @ SV43 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[555]) ).
thf(587,plain,
! [SV1: $i,SV27: $i] :
( ( ( SV27 != sz00 )
= $false )
| ( ( aElement0 @ SV1 )
= $false )
| ( ( aElement0 @ SV27 )
= $false )
| ( ( ~ ! [SY116: $i] :
~ ~ ! [SY117: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ SY116 )
| ~ ( aElement0 @ SY117 ) )
| ( SV1
!= ( sdtpldt0 @ ( sdtasdt0 @ SY116 @ SV27 ) @ SY117 ) ) )
| ~ ( ~ ( ( SY117 != sz00 ) )
| ( iLess0 @ ( sbrdtbr0 @ SY117 ) @ ( sbrdtbr0 @ SV27 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[556]) ).
thf(588,plain,
( ( ~ ( ~ ! [SX1: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( aElement0 @ SX2 )
| ( ( sdtasdt0 @ xa @ SX2 )
!= SX1 ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( aElement0 @ SX2 )
| ( ( sdtasdt0 @ xa @ SX2 )
!= SX1 ) )
| ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) ) ) )
| ~ ! [SX1: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xb ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( aElement0 @ SX2 )
| ( ( sdtasdt0 @ xb @ SX2 )
!= SX1 ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( aElement0 @ SX2 )
| ( ( sdtasdt0 @ xb @ SX2 )
!= SX1 ) )
| ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xb ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[558]) ).
thf(589,plain,
( ( ~ ! [SY124: $i] :
~ ~ ! [SY125: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY124 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SY125 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SY124 @ SY125 )
!= sK1_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[559]) ).
thf(590,plain,
( ( aElement0 @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[560]) ).
thf(591,plain,
( ( aElement0 @ sK3_SY126 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[561]) ).
thf(592,plain,
! [SV29: $i,SV3: $i] :
( ( ( ~ ! [SY127: $i] :
( ~ ( aElementOf0 @ SY127 @ SV3 )
| ( aElementOf0 @ SY127 @ SV29 ) ) )
= $true )
| ( ( ~ ! [SY128: $i] :
( ~ ( aElementOf0 @ SY128 @ SV29 )
| ( aElementOf0 @ SY128 @ SV3 ) ) )
= $true )
| ( ( SV3 = SV29 )
= $true )
| ( ( aSet0 @ SV3 )
= $false )
| ( ( aSet0 @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[562]) ).
thf(593,plain,
( ( ~ ! [SY147: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ sK6_SX0 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SY147 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ sK6_SX0 @ SY147 )
!= xu ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[563]) ).
thf(594,plain,
! [SV44: $i,SV53: $i] :
( ( ( ~ ~ ! [SY148: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SV53 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SY148 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SV53 @ SY148 )
!= SV44 ) ) )
= $true )
| ( ( ~ ( ( SV44 != sz00 ) ) )
= $true )
| ( ( ~ ( iLess0 @ ( sbrdtbr0 @ SV44 ) @ ( sbrdtbr0 @ xu ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[564]) ).
thf(595,plain,
! [SV44: $i] :
( ( ( SV44 = sz00 )
= $true )
| ( ( aElementOf0 @ SV44 @ xI )
= $false )
| ( ( ~ ( iLess0 @ ( sbrdtbr0 @ SV44 ) @ ( sbrdtbr0 @ xu ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[565]) ).
thf(596,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xa @ SX0 )
!= sz00 ) )
| ~ ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xa ) ) )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xa @ SX0 )
!= xa ) ) )
| ~ ( aElementOf0 @ xa @ ( slsdtgt0 @ xa ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[566]) ).
thf(597,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xb @ SX0 )
!= sz00 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[567]) ).
thf(598,plain,
( ( aElement0 @ sK5_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[568]) ).
thf(599,plain,
( ( ( sdtasdt0 @ xb @ sK5_SX0 )
= xb )
= $true ),
inference(extcnf_not_neg,[status(thm)],[569]) ).
thf(600,plain,
! [SV41: $i,SV9: $i,SV31: $i] :
( ( ( aElement0 @ SV31 )
= $false )
| ( ( aElement0 @ SV9 )
= $false )
| ( ( ~ ( aElement0 @ SV41 ) )
= $true )
| ( ( ~ ( ( ( sdtasdt0 @ SV9 @ ( sdtpldt0 @ SV31 @ SV41 ) )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV9 @ SV31 ) @ ( sdtasdt0 @ SV9 @ SV41 ) ) )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SV31 @ SV41 ) @ SV9 )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV31 @ SV9 ) @ ( sdtasdt0 @ SV41 @ SV9 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[570]) ).
thf(601,plain,
! [SV42: $i,SV11: $i,SV32: $i] :
( ( ( aElement0 @ SV32 )
= $false )
| ( ( aElement0 @ SV11 )
= $false )
| ( ( ~ ( aElement0 @ SV42 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV11 @ SV32 ) @ SV42 )
= ( sdtasdt0 @ SV11 @ ( sdtasdt0 @ SV32 @ SV42 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[571]) ).
thf(602,plain,
( ( ~ ( ~ ~ ( ~ ( aSet0 @ xI )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ~ ( ~ ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) )
| ~ ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) ) )
| ~ ( aIdeal0 @ xI ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[572]) ).
thf(603,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( aElement0 @ SX1 )
| ( ( sdtasdt0 @ xa @ SX1 )
!= SX0 ) ) )
| ~ ( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( aElement0 @ SX1 )
| ( ( sdtasdt0 @ xa @ SX1 )
!= SX0 ) )
| ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[573]) ).
thf(604,plain,
! [SV50: $i] :
( ( ~ ( ~ ( aElementOf0 @ SV50 @ ( slsdtgt0 @ xb ) )
| ~ ! [SY145: $i] :
~ ~ ( ~ ( aElement0 @ SY145 )
| ( ( sdtasdt0 @ xb @ SY145 )
!= SV50 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[574]) ).
thf(605,plain,
! [SV50: $i] :
( ( ~ ( ~ ~ ! [SY146: $i] :
~ ~ ( ~ ( aElement0 @ SY146 )
| ( ( sdtasdt0 @ xb @ SY146 )
!= SV50 ) )
| ( aElementOf0 @ SV50 @ ( slsdtgt0 @ xb ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[574]) ).
thf(606,plain,
! [SV47: $i] :
( ( ( aElementOf0 @ SV47 @ xI )
= $false )
| ( ( ~ ! [SY138: $i] :
~ ~ ! [SY139: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY138 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SY139 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SY138 @ SY139 )
!= SV47 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[575]) ).
thf(607,plain,
! [SV47: $i] :
( ( ( ~ ! [SY140: $i] :
~ ~ ! [SY141: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY140 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SY141 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SY140 @ SY141 )
!= SV47 ) ) )
= $false )
| ( ( aElementOf0 @ SV47 @ xI )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[576]) ).
thf(608,plain,
! [SV16: $i,SV35: $i] :
( ( ( ~ ( aElement0 @ ( sK7_SY131 @ SV35 @ SV16 ) ) )
= $false )
| ( ( ! [SY132: $i,SY133: $i] :
( ~ ~ ( ~ ( aElement0 @ SY132 )
| ~ ( aElement0 @ SY133 ) )
| ~ ! [SY134: $i] :
~ ~ ( ~ ~ ( ~ ( aElement0 @ SY134 )
| ~ ( sdteqdtlpzmzozddtrp0 @ SY134 @ SY132 @ SV16 ) )
| ~ ( sdteqdtlpzmzozddtrp0 @ SY134 @ SY133 @ SV35 ) ) ) )
= $true )
| ( ( aIdeal0 @ SV16 )
= $false )
| ( ( aIdeal0 @ SV35 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[577]) ).
thf(609,plain,
! [SV16: $i,SV35: $i] :
( ( ( aElementOf0 @ ( sK7_SY131 @ SV35 @ SV16 ) @ ( sdtpldt1 @ SV16 @ SV35 ) )
= $false )
| ( ( ! [SY132: $i,SY133: $i] :
( ~ ~ ( ~ ( aElement0 @ SY132 )
| ~ ( aElement0 @ SY133 ) )
| ~ ! [SY134: $i] :
~ ~ ( ~ ~ ( ~ ( aElement0 @ SY134 )
| ~ ( sdteqdtlpzmzozddtrp0 @ SY134 @ SY132 @ SV16 ) )
| ~ ( sdteqdtlpzmzozddtrp0 @ SY134 @ SY133 @ SV35 ) ) ) )
= $true )
| ( ( aIdeal0 @ SV16 )
= $false )
| ( ( aIdeal0 @ SV35 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[577]) ).
thf(610,plain,
! [SV49: $i] :
( ( ( aElement0 @ SV49 )
= $false )
| ( ( ( sdtasdt0 @ xu @ SV49 )
!= xa )
= $true )
| ( ( ~ ( ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xu @ SX0 )
!= xb ) )
| ( doDivides0 @ xu @ xb )
| ( aDivisorOf0 @ xu @ xb ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[578]) ).
thf(611,plain,
! [SV52: $i] :
( ( ( ~ ( ~ ( aElement0 @ SV52 )
| ( ( sdtasdt0 @ xu @ SV52 )
!= xb ) ) )
= $false )
| ( ( doDivides0 @ xu @ xa )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[579]) ).
thf(612,plain,
! [SV51: $i] :
( ( ( ~ ( aElement0 @ SV51 )
| ( ( sdtasdt0 @ xu @ SV51 )
!= xb ) )
= $true )
| ( ( aDivisorOf0 @ xu @ xa )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[580]) ).
thf(613,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ xc )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xc @ SX0 )
!= xa ) ) )
| ~ ( doDivides0 @ xc @ xa ) )
| ~ ( aDivisorOf0 @ xc @ xa ) )
| ~ ( aElement0 @ xc ) )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xc @ SX0 )
!= xb ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[583]) ).
thf(614,plain,
( ( doDivides0 @ xc @ xb )
= $true ),
inference(extcnf_not_neg,[status(thm)],[584]) ).
thf(615,plain,
! [SV48: $i] :
( ( ( ~ ( ~ ( aElement0 @ SV48 )
| ~ ( ~ ! [SY142: $i] :
~ ~ ( ~ ( aElement0 @ SY142 )
| ( ( sdtasdt0 @ SV48 @ SY142 )
!= xa ) )
| ( doDivides0 @ SV48 @ xa ) ) )
| ( aDivisorOf0 @ SV48 @ xa ) )
= $false )
| ( ( ~ ( ~ ! [SY143: $i] :
~ ~ ( ~ ( aElement0 @ SY143 )
| ( ( sdtasdt0 @ SV48 @ SY143 )
!= xb ) )
| ( doDivides0 @ SV48 @ xb )
| ( aDivisorOf0 @ SV48 @ xb ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) )
| ~ ( doDivides0 @ SV48 @ xc ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[585]) ).
thf(616,plain,
! [SV43: $i,SV22: $i,SV38: $i] :
( ( ( aElement0 @ SV38 )
= $false )
| ( ( aElement0 @ SV22 )
= $false )
| ( ( ~ ( aElement0 @ SV43 ) )
= $true )
| ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV22 @ SV38 ) @ SV43 )
= ( sdtpldt0 @ SV22 @ ( sdtpldt0 @ SV38 @ SV43 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[586]) ).
thf(617,plain,
! [SV1: $i,SV27: $i] :
( ( ( SV27 = sz00 )
= $true )
| ( ( aElement0 @ SV1 )
= $false )
| ( ( aElement0 @ SV27 )
= $false )
| ( ( ~ ! [SY116: $i] :
~ ~ ! [SY117: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ SY116 )
| ~ ( aElement0 @ SY117 ) )
| ( SV1
!= ( sdtpldt0 @ ( sdtasdt0 @ SY116 @ SV27 ) @ SY117 ) ) )
| ~ ( ~ ( ( SY117 != sz00 ) )
| ( iLess0 @ ( sbrdtbr0 @ SY117 ) @ ( sbrdtbr0 @ SV27 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[587]) ).
thf(618,plain,
( ( ~ ! [SX1: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( aElement0 @ SX2 )
| ( ( sdtasdt0 @ xa @ SX2 )
!= SX1 ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( aElement0 @ SX2 )
| ( ( sdtasdt0 @ xa @ SX2 )
!= SX1 ) )
| ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) ) ) )
| ~ ! [SX1: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xb ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( aElement0 @ SX2 )
| ( ( sdtasdt0 @ xb @ SX2 )
!= SX1 ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( aElement0 @ SX2 )
| ( ( sdtasdt0 @ xb @ SX2 )
!= SX1 ) )
| ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xb ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[588]) ).
thf(619,plain,
( ( ! [SY124: $i] :
~ ~ ! [SY125: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY124 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SY125 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SY124 @ SY125 )
!= sK1_SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[589]) ).
thf(620,plain,
! [SV29: $i,SV3: $i] :
( ( ( ! [SY127: $i] :
( ~ ( aElementOf0 @ SY127 @ SV3 )
| ( aElementOf0 @ SY127 @ SV29 ) ) )
= $false )
| ( ( ~ ! [SY128: $i] :
( ~ ( aElementOf0 @ SY128 @ SV29 )
| ( aElementOf0 @ SY128 @ SV3 ) ) )
= $true )
| ( ( SV3 = SV29 )
= $true )
| ( ( aSet0 @ SV3 )
= $false )
| ( ( aSet0 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[592]) ).
thf(621,plain,
( ( ! [SY147: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ sK6_SX0 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SY147 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ sK6_SX0 @ SY147 )
!= xu ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[593]) ).
thf(622,plain,
! [SV44: $i,SV53: $i] :
( ( ( ~ ! [SY148: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SV53 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SY148 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SV53 @ SY148 )
!= SV44 ) ) )
= $false )
| ( ( ~ ( ( SV44 != sz00 ) ) )
= $true )
| ( ( ~ ( iLess0 @ ( sbrdtbr0 @ SV44 ) @ ( sbrdtbr0 @ xu ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[594]) ).
thf(623,plain,
! [SV44: $i] :
( ( ( iLess0 @ ( sbrdtbr0 @ SV44 ) @ ( sbrdtbr0 @ xu ) )
= $false )
| ( ( aElementOf0 @ SV44 @ xI )
= $false )
| ( ( SV44 = sz00 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[595]) ).
thf(624,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xa @ SX0 )
!= sz00 ) )
| ~ ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xa ) ) )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xa @ SX0 )
!= xa ) ) )
| ~ ( aElementOf0 @ xa @ ( slsdtgt0 @ xa ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[596]) ).
thf(625,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xb @ SX0 )
!= sz00 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[597]) ).
thf(626,plain,
! [SV31: $i,SV9: $i,SV41: $i] :
( ( ( aElement0 @ SV41 )
= $false )
| ( ( aElement0 @ SV9 )
= $false )
| ( ( aElement0 @ SV31 )
= $false )
| ( ( ~ ( ( ( sdtasdt0 @ SV9 @ ( sdtpldt0 @ SV31 @ SV41 ) )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV9 @ SV31 ) @ ( sdtasdt0 @ SV9 @ SV41 ) ) )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SV31 @ SV41 ) @ SV9 )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV31 @ SV9 ) @ ( sdtasdt0 @ SV41 @ SV9 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[600]) ).
thf(627,plain,
! [SV32: $i,SV11: $i,SV42: $i] :
( ( ( aElement0 @ SV42 )
= $false )
| ( ( aElement0 @ SV11 )
= $false )
| ( ( aElement0 @ SV32 )
= $false )
| ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV11 @ SV32 ) @ SV42 )
= ( sdtasdt0 @ SV11 @ ( sdtasdt0 @ SV32 @ SV42 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[601]) ).
thf(628,plain,
( ( ~ ~ ( ~ ( aSet0 @ xI )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ~ ( ~ ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) )
| ~ ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) ) )
| ~ ( aIdeal0 @ xI ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[602]) ).
thf(629,plain,
! [SV54: $i] :
( ( ~ ( ~ ( ~ ( aElementOf0 @ SV54 @ ( slsdtgt0 @ xa ) )
| ~ ! [SY149: $i] :
~ ~ ( ~ ( aElement0 @ SY149 )
| ( ( sdtasdt0 @ xa @ SY149 )
!= SV54 ) ) )
| ~ ( ~ ~ ! [SY150: $i] :
~ ~ ( ~ ( aElement0 @ SY150 )
| ( ( sdtasdt0 @ xa @ SY150 )
!= SV54 ) )
| ( aElementOf0 @ SV54 @ ( slsdtgt0 @ xa ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[603]) ).
thf(630,plain,
! [SV50: $i] :
( ( ~ ( aElementOf0 @ SV50 @ ( slsdtgt0 @ xb ) )
| ~ ! [SY145: $i] :
~ ~ ( ~ ( aElement0 @ SY145 )
| ( ( sdtasdt0 @ xb @ SY145 )
!= SV50 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[604]) ).
thf(631,plain,
! [SV50: $i] :
( ( ~ ~ ! [SY146: $i] :
~ ~ ( ~ ( aElement0 @ SY146 )
| ( ( sdtasdt0 @ xb @ SY146 )
!= SV50 ) )
| ( aElementOf0 @ SV50 @ ( slsdtgt0 @ xb ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[605]) ).
thf(632,plain,
! [SV47: $i] :
( ( ( ! [SY138: $i] :
~ ~ ! [SY139: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY138 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SY139 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SY138 @ SY139 )
!= SV47 ) ) )
= $false )
| ( ( aElementOf0 @ SV47 @ xI )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[606]) ).
thf(633,plain,
! [SV47: $i] :
( ( ( ! [SY140: $i] :
~ ~ ! [SY141: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY140 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SY141 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SY140 @ SY141 )
!= SV47 ) ) )
= $true )
| ( ( aElementOf0 @ SV47 @ xI )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[607]) ).
thf(634,plain,
! [SV16: $i,SV35: $i] :
( ( ( aElement0 @ ( sK7_SY131 @ SV35 @ SV16 ) )
= $true )
| ( ( ! [SY132: $i,SY133: $i] :
( ~ ~ ( ~ ( aElement0 @ SY132 )
| ~ ( aElement0 @ SY133 ) )
| ~ ! [SY134: $i] :
~ ~ ( ~ ~ ( ~ ( aElement0 @ SY134 )
| ~ ( sdteqdtlpzmzozddtrp0 @ SY134 @ SY132 @ SV16 ) )
| ~ ( sdteqdtlpzmzozddtrp0 @ SY134 @ SY133 @ SV35 ) ) ) )
= $true )
| ( ( aIdeal0 @ SV16 )
= $false )
| ( ( aIdeal0 @ SV35 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[608]) ).
thf(635,plain,
! [SV35: $i,SV16: $i,SV55: $i] :
( ( ( ! [SY151: $i] :
( ~ ~ ( ~ ( aElement0 @ SV55 )
| ~ ( aElement0 @ SY151 ) )
| ~ ! [SY152: $i] :
~ ~ ( ~ ~ ( ~ ( aElement0 @ SY152 )
| ~ ( sdteqdtlpzmzozddtrp0 @ SY152 @ SV55 @ SV16 ) )
| ~ ( sdteqdtlpzmzozddtrp0 @ SY152 @ SY151 @ SV35 ) ) ) )
= $true )
| ( ( aElementOf0 @ ( sK7_SY131 @ SV35 @ SV16 ) @ ( sdtpldt1 @ SV16 @ SV35 ) )
= $false )
| ( ( aIdeal0 @ SV16 )
= $false )
| ( ( aIdeal0 @ SV35 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[609]) ).
thf(636,plain,
! [SV49: $i] :
( ( ( ( sdtasdt0 @ xu @ SV49 )
= xa )
= $false )
| ( ( aElement0 @ SV49 )
= $false )
| ( ( ~ ( ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xu @ SX0 )
!= xb ) )
| ( doDivides0 @ xu @ xb )
| ( aDivisorOf0 @ xu @ xb ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[610]) ).
thf(637,plain,
! [SV52: $i] :
( ( ( ~ ( aElement0 @ SV52 )
| ( ( sdtasdt0 @ xu @ SV52 )
!= xb ) )
= $true )
| ( ( doDivides0 @ xu @ xa )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[611]) ).
thf(638,plain,
! [SV51: $i] :
( ( ( ~ ( aElement0 @ SV51 ) )
= $true )
| ( ( ( sdtasdt0 @ xu @ SV51 )
!= xb )
= $true )
| ( ( aDivisorOf0 @ xu @ xa )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[612]) ).
thf(639,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ xc )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xc @ SX0 )
!= xa ) ) )
| ~ ( doDivides0 @ xc @ xa ) )
| ~ ( aDivisorOf0 @ xc @ xa ) )
| ~ ( aElement0 @ xc ) )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xc @ SX0 )
!= xb ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[613]) ).
thf(640,plain,
! [SV48: $i] :
( ( ( ~ ( ~ ( aElement0 @ SV48 )
| ~ ( ~ ! [SY142: $i] :
~ ~ ( ~ ( aElement0 @ SY142 )
| ( ( sdtasdt0 @ SV48 @ SY142 )
!= xa ) )
| ( doDivides0 @ SV48 @ xa ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY143: $i] :
~ ~ ( ~ ( aElement0 @ SY143 )
| ( ( sdtasdt0 @ SV48 @ SY143 )
!= xb ) )
| ( doDivides0 @ SV48 @ xb )
| ( aDivisorOf0 @ SV48 @ xb ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) )
| ~ ( doDivides0 @ SV48 @ xc ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[615]) ).
thf(641,plain,
! [SV48: $i] :
( ( ( aDivisorOf0 @ SV48 @ xa )
= $false )
| ( ( ~ ( ~ ! [SY143: $i] :
~ ~ ( ~ ( aElement0 @ SY143 )
| ( ( sdtasdt0 @ SV48 @ SY143 )
!= xb ) )
| ( doDivides0 @ SV48 @ xb )
| ( aDivisorOf0 @ SV48 @ xb ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) )
| ~ ( doDivides0 @ SV48 @ xc ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[615]) ).
thf(642,plain,
! [SV38: $i,SV22: $i,SV43: $i] :
( ( ( aElement0 @ SV43 )
= $false )
| ( ( aElement0 @ SV22 )
= $false )
| ( ( aElement0 @ SV38 )
= $false )
| ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV22 @ SV38 ) @ SV43 )
= ( sdtpldt0 @ SV22 @ ( sdtpldt0 @ SV38 @ SV43 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[616]) ).
thf(643,plain,
! [SV27: $i,SV1: $i] :
( ( ( ! [SY116: $i] :
~ ~ ! [SY117: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ SY116 )
| ~ ( aElement0 @ SY117 ) )
| ( SV1
!= ( sdtpldt0 @ ( sdtasdt0 @ SY116 @ SV27 ) @ SY117 ) ) )
| ~ ( ~ ( ( SY117 != sz00 ) )
| ( iLess0 @ ( sbrdtbr0 @ SY117 ) @ ( sbrdtbr0 @ SV27 ) ) ) ) )
= $false )
| ( ( aElement0 @ SV27 )
= $false )
| ( ( aElement0 @ SV1 )
= $false )
| ( ( SV27 = sz00 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[617]) ).
thf(644,plain,
( ( ~ ! [SX1: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( aElement0 @ SX2 )
| ( ( sdtasdt0 @ xa @ SX2 )
!= SX1 ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( aElement0 @ SX2 )
| ( ( sdtasdt0 @ xa @ SX2 )
!= SX1 ) )
| ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[618]) ).
thf(645,plain,
( ( ~ ! [SX1: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xb ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( aElement0 @ SX2 )
| ( ( sdtasdt0 @ xb @ SX2 )
!= SX1 ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( aElement0 @ SX2 )
| ( ( sdtasdt0 @ xb @ SX2 )
!= SX1 ) )
| ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xb ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[618]) ).
thf(646,plain,
( ( ~ ~ ! [SY153: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ sK8_SY124 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SY153 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ sK8_SY124 @ SY153 )
!= sK1_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[619]) ).
thf(647,plain,
! [SV3: $i,SV29: $i] :
( ( ( ~ ( aElementOf0 @ ( sK9_SY127 @ SV29 @ SV3 ) @ SV3 )
| ( aElementOf0 @ ( sK9_SY127 @ SV29 @ SV3 ) @ SV29 ) )
= $false )
| ( ( ~ ! [SY128: $i] :
( ~ ( aElementOf0 @ SY128 @ SV29 )
| ( aElementOf0 @ SY128 @ SV3 ) ) )
= $true )
| ( ( SV3 = SV29 )
= $true )
| ( ( aSet0 @ SV3 )
= $false )
| ( ( aSet0 @ SV29 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[620]) ).
thf(648,plain,
( ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ sK6_SX0 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ sK10_SY147 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ sK6_SX0 @ sK10_SY147 )
!= xu ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[621]) ).
thf(649,plain,
! [SV44: $i,SV53: $i] :
( ( ( ! [SY148: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SV53 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SY148 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SV53 @ SY148 )
!= SV44 ) ) )
= $true )
| ( ( ~ ( ( SV44 != sz00 ) ) )
= $true )
| ( ( ~ ( iLess0 @ ( sbrdtbr0 @ SV44 ) @ ( sbrdtbr0 @ xu ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[622]) ).
thf(650,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xa @ SX0 )
!= sz00 ) )
| ~ ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xa ) ) )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xa @ SX0 )
!= xa ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[624]) ).
thf(651,plain,
( ( ~ ( aElementOf0 @ xa @ ( slsdtgt0 @ xa ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[624]) ).
thf(652,plain,
( ( ~ ~ ( ~ ( aElement0 @ sK11_SX0 )
| ( ( sdtasdt0 @ xb @ sK11_SX0 )
!= sz00 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[625]) ).
thf(653,plain,
! [SV41: $i,SV31: $i,SV9: $i] :
( ( ( ( ( sdtasdt0 @ SV9 @ ( sdtpldt0 @ SV31 @ SV41 ) )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV9 @ SV31 ) @ ( sdtasdt0 @ SV9 @ SV41 ) ) )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SV31 @ SV41 ) @ SV9 )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV31 @ SV9 ) @ ( sdtasdt0 @ SV41 @ SV9 ) ) ) )
= $false )
| ( ( aElement0 @ SV31 )
= $false )
| ( ( aElement0 @ SV9 )
= $false )
| ( ( aElement0 @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[626]) ).
thf(654,plain,
( ( ~ ~ ( ~ ( aSet0 @ xI )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ~ ( ~ ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) )
| ~ ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[628]) ).
thf(655,plain,
( ( ~ ( aIdeal0 @ xI ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[628]) ).
thf(656,plain,
! [SV54: $i] :
( ( ~ ( ~ ( aElementOf0 @ SV54 @ ( slsdtgt0 @ xa ) )
| ~ ! [SY149: $i] :
~ ~ ( ~ ( aElement0 @ SY149 )
| ( ( sdtasdt0 @ xa @ SY149 )
!= SV54 ) ) )
| ~ ( ~ ~ ! [SY150: $i] :
~ ~ ( ~ ( aElement0 @ SY150 )
| ( ( sdtasdt0 @ xa @ SY150 )
!= SV54 ) )
| ( aElementOf0 @ SV54 @ ( slsdtgt0 @ xa ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[629]) ).
thf(657,plain,
! [SV50: $i] :
( ( ( ~ ( aElementOf0 @ SV50 @ ( slsdtgt0 @ xb ) ) )
= $true )
| ( ( ~ ! [SY145: $i] :
~ ~ ( ~ ( aElement0 @ SY145 )
| ( ( sdtasdt0 @ xb @ SY145 )
!= SV50 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[630]) ).
thf(658,plain,
! [SV50: $i] :
( ( ( ~ ~ ! [SY146: $i] :
~ ~ ( ~ ( aElement0 @ SY146 )
| ( ( sdtasdt0 @ xb @ SY146 )
!= SV50 ) ) )
= $true )
| ( ( aElementOf0 @ SV50 @ ( slsdtgt0 @ xb ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[631]) ).
thf(659,plain,
! [SV47: $i] :
( ( ( ~ ~ ! [SY154: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK12_SY138 @ SV47 ) @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SY154 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ ( sK12_SY138 @ SV47 ) @ SY154 )
!= SV47 ) ) )
= $false )
| ( ( aElementOf0 @ SV47 @ xI )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[632]) ).
thf(660,plain,
! [SV47: $i,SV56: $i] :
( ( ( ~ ~ ! [SY155: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SV56 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SY155 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SV56 @ SY155 )
!= SV47 ) ) )
= $true )
| ( ( aElementOf0 @ SV47 @ xI )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[633]) ).
thf(661,plain,
! [SV35: $i,SV16: $i,SV57: $i] :
( ( ( ! [SY156: $i] :
( ~ ~ ( ~ ( aElement0 @ SV57 )
| ~ ( aElement0 @ SY156 ) )
| ~ ! [SY157: $i] :
~ ~ ( ~ ~ ( ~ ( aElement0 @ SY157 )
| ~ ( sdteqdtlpzmzozddtrp0 @ SY157 @ SV57 @ SV16 ) )
| ~ ( sdteqdtlpzmzozddtrp0 @ SY157 @ SY156 @ SV35 ) ) ) )
= $true )
| ( ( aElement0 @ ( sK7_SY131 @ SV35 @ SV16 ) )
= $true )
| ( ( aIdeal0 @ SV16 )
= $false )
| ( ( aIdeal0 @ SV35 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[634]) ).
thf(662,plain,
! [SV35: $i,SV16: $i,SV58: $i,SV55: $i] :
( ( ( ~ ~ ( ~ ( aElement0 @ SV55 )
| ~ ( aElement0 @ SV58 ) )
| ~ ! [SY158: $i] :
~ ~ ( ~ ~ ( ~ ( aElement0 @ SY158 )
| ~ ( sdteqdtlpzmzozddtrp0 @ SY158 @ SV55 @ SV16 ) )
| ~ ( sdteqdtlpzmzozddtrp0 @ SY158 @ SV58 @ SV35 ) ) )
= $true )
| ( ( aElementOf0 @ ( sK7_SY131 @ SV35 @ SV16 ) @ ( sdtpldt1 @ SV16 @ SV35 ) )
= $false )
| ( ( aIdeal0 @ SV16 )
= $false )
| ( ( aIdeal0 @ SV35 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[635]) ).
thf(663,plain,
! [SV49: $i] :
( ( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xu @ SX0 )
!= xb ) )
| ( doDivides0 @ xu @ xb )
| ( aDivisorOf0 @ xu @ xb ) )
= $false )
| ( ( aElement0 @ SV49 )
= $false )
| ( ( ( sdtasdt0 @ xu @ SV49 )
= xa )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[636]) ).
thf(664,plain,
! [SV52: $i] :
( ( ( ~ ( aElement0 @ SV52 ) )
= $true )
| ( ( ( sdtasdt0 @ xu @ SV52 )
!= xb )
= $true )
| ( ( doDivides0 @ xu @ xa )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[637]) ).
thf(665,plain,
! [SV51: $i] :
( ( ( aElement0 @ SV51 )
= $false )
| ( ( ( sdtasdt0 @ xu @ SV51 )
!= xb )
= $true )
| ( ( aDivisorOf0 @ xu @ xa )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[638]) ).
thf(666,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ xc )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xc @ SX0 )
!= xa ) ) )
| ~ ( doDivides0 @ xc @ xa ) )
| ~ ( aDivisorOf0 @ xc @ xa ) )
| ~ ( aElement0 @ xc ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[639]) ).
thf(667,plain,
( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xc @ SX0 )
!= xb ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[639]) ).
thf(668,plain,
! [SV48: $i] :
( ( ( ~ ( aElement0 @ SV48 )
| ~ ( ~ ! [SY142: $i] :
~ ~ ( ~ ( aElement0 @ SY142 )
| ( ( sdtasdt0 @ SV48 @ SY142 )
!= xa ) )
| ( doDivides0 @ SV48 @ xa ) ) )
= $true )
| ( ( ~ ( ~ ! [SY143: $i] :
~ ~ ( ~ ( aElement0 @ SY143 )
| ( ( sdtasdt0 @ SV48 @ SY143 )
!= xb ) )
| ( doDivides0 @ SV48 @ xb )
| ( aDivisorOf0 @ SV48 @ xb ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) )
| ~ ( doDivides0 @ SV48 @ xc ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[640]) ).
thf(669,plain,
! [SV48: $i] :
( ( ( ~ ! [SY143: $i] :
~ ~ ( ~ ( aElement0 @ SY143 )
| ( ( sdtasdt0 @ SV48 @ SY143 )
!= xb ) )
| ( doDivides0 @ SV48 @ xb )
| ( aDivisorOf0 @ SV48 @ xb ) )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xa )
= $false )
| ( ( ~ ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) )
| ~ ( doDivides0 @ SV48 @ xc ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[641]) ).
thf(670,plain,
! [SV1: $i,SV27: $i] :
( ( ( ~ ~ ! [SY159: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ ( sK13_SY116 @ SV27 @ SV1 ) )
| ~ ( aElement0 @ SY159 ) )
| ( SV1
!= ( sdtpldt0 @ ( sdtasdt0 @ ( sK13_SY116 @ SV27 @ SV1 ) @ SV27 ) @ SY159 ) ) )
| ~ ( ~ ( ( SY159 != sz00 ) )
| ( iLess0 @ ( sbrdtbr0 @ SY159 ) @ ( sbrdtbr0 @ SV27 ) ) ) ) )
= $false )
| ( ( aElement0 @ SV27 )
= $false )
| ( ( aElement0 @ SV1 )
= $false )
| ( ( SV27 = sz00 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[643]) ).
thf(671,plain,
( ( ! [SX1: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( aElement0 @ SX2 )
| ( ( sdtasdt0 @ xa @ SX2 )
!= SX1 ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( aElement0 @ SX2 )
| ( ( sdtasdt0 @ xa @ SX2 )
!= SX1 ) )
| ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[644]) ).
thf(672,plain,
( ( ! [SX1: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xb ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( aElement0 @ SX2 )
| ( ( sdtasdt0 @ xb @ SX2 )
!= SX1 ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( aElement0 @ SX2 )
| ( ( sdtasdt0 @ xb @ SX2 )
!= SX1 ) )
| ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xb ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[645]) ).
thf(673,plain,
( ( ~ ! [SY153: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ sK8_SY124 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SY153 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ sK8_SY124 @ SY153 )
!= sK1_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[646]) ).
thf(674,plain,
! [SV3: $i,SV29: $i] :
( ( ( ~ ( aElementOf0 @ ( sK9_SY127 @ SV29 @ SV3 ) @ SV3 ) )
= $false )
| ( ( ~ ! [SY128: $i] :
( ~ ( aElementOf0 @ SY128 @ SV29 )
| ( aElementOf0 @ SY128 @ SV3 ) ) )
= $true )
| ( ( SV3 = SV29 )
= $true )
| ( ( aSet0 @ SV3 )
= $false )
| ( ( aSet0 @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[647]) ).
thf(675,plain,
! [SV3: $i,SV29: $i] :
( ( ( aElementOf0 @ ( sK9_SY127 @ SV29 @ SV3 ) @ SV29 )
= $false )
| ( ( ~ ! [SY128: $i] :
( ~ ( aElementOf0 @ SY128 @ SV29 )
| ( aElementOf0 @ SY128 @ SV3 ) ) )
= $true )
| ( ( SV3 = SV29 )
= $true )
| ( ( aSet0 @ SV3 )
= $false )
| ( ( aSet0 @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[647]) ).
thf(676,plain,
( ( ~ ( ~ ~ ( ~ ( aElementOf0 @ sK6_SX0 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ sK10_SY147 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ sK6_SX0 @ sK10_SY147 )
!= xu ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[648]) ).
thf(677,plain,
! [SV44: $i,SV59: $i,SV53: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SV53 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SV59 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SV53 @ SV59 )
!= SV44 ) ) )
= $true )
| ( ( ~ ( ( SV44 != sz00 ) ) )
= $true )
| ( ( ~ ( iLess0 @ ( sbrdtbr0 @ SV44 ) @ ( sbrdtbr0 @ xu ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[649]) ).
thf(678,plain,
( ( ~ ( ~ ~ ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xa @ SX0 )
!= sz00 ) )
| ~ ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xa ) ) )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xa @ SX0 )
!= xa ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[650]) ).
thf(679,plain,
( ( aElementOf0 @ xa @ ( slsdtgt0 @ xa ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[651]) ).
thf(680,plain,
( ( ~ ( ~ ( aElement0 @ sK11_SX0 )
| ( ( sdtasdt0 @ xb @ sK11_SX0 )
!= sz00 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[652]) ).
thf(681,plain,
! [SV41: $i,SV31: $i,SV9: $i] :
( ( ( ( sdtasdt0 @ SV9 @ ( sdtpldt0 @ SV31 @ SV41 ) )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV9 @ SV31 ) @ ( sdtasdt0 @ SV9 @ SV41 ) ) )
= $false )
| ( ( aElement0 @ SV31 )
= $false )
| ( ( aElement0 @ SV9 )
= $false )
| ( ( aElement0 @ SV41 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[653]) ).
thf(682,plain,
! [SV9: $i,SV41: $i,SV31: $i] :
( ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV31 @ SV41 ) @ SV9 )
!= ( sdtpldt0 @ ( sdtasdt0 @ SV31 @ SV9 ) @ ( sdtasdt0 @ SV41 @ SV9 ) ) )
= $false )
| ( ( aElement0 @ SV31 )
= $false )
| ( ( aElement0 @ SV9 )
= $false )
| ( ( aElement0 @ SV41 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[653]) ).
thf(683,plain,
( ( ~ ( ~ ( aSet0 @ xI )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ~ ( ~ ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) )
| ~ ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[654]) ).
thf(684,plain,
( ( aIdeal0 @ xI )
= $true ),
inference(extcnf_not_neg,[status(thm)],[655]) ).
thf(685,plain,
! [SV54: $i] :
( ( ~ ( ~ ( aElementOf0 @ SV54 @ ( slsdtgt0 @ xa ) )
| ~ ! [SY149: $i] :
~ ~ ( ~ ( aElement0 @ SY149 )
| ( ( sdtasdt0 @ xa @ SY149 )
!= SV54 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[656]) ).
thf(686,plain,
! [SV54: $i] :
( ( ~ ( ~ ~ ! [SY150: $i] :
~ ~ ( ~ ( aElement0 @ SY150 )
| ( ( sdtasdt0 @ xa @ SY150 )
!= SV54 ) )
| ( aElementOf0 @ SV54 @ ( slsdtgt0 @ xa ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[656]) ).
thf(687,plain,
! [SV50: $i] :
( ( ( aElementOf0 @ SV50 @ ( slsdtgt0 @ xb ) )
= $false )
| ( ( ~ ! [SY145: $i] :
~ ~ ( ~ ( aElement0 @ SY145 )
| ( ( sdtasdt0 @ xb @ SY145 )
!= SV50 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[657]) ).
thf(688,plain,
! [SV50: $i] :
( ( ( ~ ! [SY146: $i] :
~ ~ ( ~ ( aElement0 @ SY146 )
| ( ( sdtasdt0 @ xb @ SY146 )
!= SV50 ) ) )
= $false )
| ( ( aElementOf0 @ SV50 @ ( slsdtgt0 @ xb ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[658]) ).
thf(689,plain,
! [SV47: $i] :
( ( ( ~ ! [SY154: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK12_SY138 @ SV47 ) @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SY154 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ ( sK12_SY138 @ SV47 ) @ SY154 )
!= SV47 ) ) )
= $true )
| ( ( aElementOf0 @ SV47 @ xI )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[659]) ).
thf(690,plain,
! [SV47: $i,SV56: $i] :
( ( ( ~ ! [SY155: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SV56 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SY155 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SV56 @ SY155 )
!= SV47 ) ) )
= $false )
| ( ( aElementOf0 @ SV47 @ xI )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[660]) ).
thf(691,plain,
! [SV35: $i,SV16: $i,SV60: $i,SV57: $i] :
( ( ( ~ ~ ( ~ ( aElement0 @ SV57 )
| ~ ( aElement0 @ SV60 ) )
| ~ ! [SY160: $i] :
~ ~ ( ~ ~ ( ~ ( aElement0 @ SY160 )
| ~ ( sdteqdtlpzmzozddtrp0 @ SY160 @ SV57 @ SV16 ) )
| ~ ( sdteqdtlpzmzozddtrp0 @ SY160 @ SV60 @ SV35 ) ) )
= $true )
| ( ( aElement0 @ ( sK7_SY131 @ SV35 @ SV16 ) )
= $true )
| ( ( aIdeal0 @ SV16 )
= $false )
| ( ( aIdeal0 @ SV35 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[661]) ).
thf(692,plain,
! [SV35: $i,SV16: $i,SV58: $i,SV55: $i] :
( ( ( ~ ~ ( ~ ( aElement0 @ SV55 )
| ~ ( aElement0 @ SV58 ) ) )
= $true )
| ( ( ~ ! [SY158: $i] :
~ ~ ( ~ ~ ( ~ ( aElement0 @ SY158 )
| ~ ( sdteqdtlpzmzozddtrp0 @ SY158 @ SV55 @ SV16 ) )
| ~ ( sdteqdtlpzmzozddtrp0 @ SY158 @ SV58 @ SV35 ) ) )
= $true )
| ( ( aElementOf0 @ ( sK7_SY131 @ SV35 @ SV16 ) @ ( sdtpldt1 @ SV16 @ SV35 ) )
= $false )
| ( ( aIdeal0 @ SV16 )
= $false )
| ( ( aIdeal0 @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[662]) ).
thf(693,plain,
! [SV49: $i] :
( ( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xu @ SX0 )
!= xb ) )
| ( doDivides0 @ xu @ xb ) )
= $false )
| ( ( aElement0 @ SV49 )
= $false )
| ( ( ( sdtasdt0 @ xu @ SV49 )
= xa )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[663]) ).
thf(694,plain,
! [SV49: $i] :
( ( ( aDivisorOf0 @ xu @ xb )
= $false )
| ( ( aElement0 @ SV49 )
= $false )
| ( ( ( sdtasdt0 @ xu @ SV49 )
= xa )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[663]) ).
thf(695,plain,
! [SV52: $i] :
( ( ( aElement0 @ SV52 )
= $false )
| ( ( ( sdtasdt0 @ xu @ SV52 )
!= xb )
= $true )
| ( ( doDivides0 @ xu @ xa )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[664]) ).
thf(696,plain,
! [SV51: $i] :
( ( ( ( sdtasdt0 @ xu @ SV51 )
= xb )
= $false )
| ( ( aElement0 @ SV51 )
= $false )
| ( ( aDivisorOf0 @ xu @ xa )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[665]) ).
thf(697,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ xc )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xc @ SX0 )
!= xa ) ) )
| ~ ( doDivides0 @ xc @ xa ) )
| ~ ( aDivisorOf0 @ xc @ xa ) )
| ~ ( aElement0 @ xc ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[666]) ).
thf(698,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xc @ SX0 )
!= xb ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[667]) ).
thf(699,plain,
! [SV48: $i] :
( ( ( ~ ( aElement0 @ SV48 ) )
= $true )
| ( ( ~ ( ~ ! [SY142: $i] :
~ ~ ( ~ ( aElement0 @ SY142 )
| ( ( sdtasdt0 @ SV48 @ SY142 )
!= xa ) )
| ( doDivides0 @ SV48 @ xa ) ) )
= $true )
| ( ( ~ ( ~ ! [SY143: $i] :
~ ~ ( ~ ( aElement0 @ SY143 )
| ( ( sdtasdt0 @ SV48 @ SY143 )
!= xb ) )
| ( doDivides0 @ SV48 @ xb )
| ( aDivisorOf0 @ SV48 @ xb ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) )
| ~ ( doDivides0 @ SV48 @ xc ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[668]) ).
thf(700,plain,
! [SV48: $i] :
( ( ( ~ ! [SY143: $i] :
~ ~ ( ~ ( aElement0 @ SY143 )
| ( ( sdtasdt0 @ SV48 @ SY143 )
!= xb ) )
| ( doDivides0 @ SV48 @ xb ) )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xa )
= $false )
| ( ( ~ ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) )
| ~ ( doDivides0 @ SV48 @ xc ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[669]) ).
thf(701,plain,
! [SV48: $i] :
( ( ( aDivisorOf0 @ SV48 @ xb )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xa )
= $false )
| ( ( ~ ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) )
| ~ ( doDivides0 @ SV48 @ xc ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[669]) ).
thf(702,plain,
! [SV1: $i,SV27: $i] :
( ( ( ~ ! [SY159: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ ( sK13_SY116 @ SV27 @ SV1 ) )
| ~ ( aElement0 @ SY159 ) )
| ( SV1
!= ( sdtpldt0 @ ( sdtasdt0 @ ( sK13_SY116 @ SV27 @ SV1 ) @ SV27 ) @ SY159 ) ) )
| ~ ( ~ ( ( SY159 != sz00 ) )
| ( iLess0 @ ( sbrdtbr0 @ SY159 ) @ ( sbrdtbr0 @ SV27 ) ) ) ) )
= $true )
| ( ( aElement0 @ SV27 )
= $false )
| ( ( aElement0 @ SV1 )
= $false )
| ( ( SV27 = sz00 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[670]) ).
thf(703,plain,
! [SV61: $i] :
( ( ~ ( ~ ( ~ ( aElementOf0 @ SV61 @ ( slsdtgt0 @ xa ) )
| ~ ! [SY161: $i] :
~ ~ ( ~ ( aElement0 @ SY161 )
| ( ( sdtasdt0 @ xa @ SY161 )
!= SV61 ) ) )
| ~ ( ~ ~ ! [SY162: $i] :
~ ~ ( ~ ( aElement0 @ SY162 )
| ( ( sdtasdt0 @ xa @ SY162 )
!= SV61 ) )
| ( aElementOf0 @ SV61 @ ( slsdtgt0 @ xa ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[671]) ).
thf(704,plain,
! [SV62: $i] :
( ( ~ ( ~ ( ~ ( aElementOf0 @ SV62 @ ( slsdtgt0 @ xb ) )
| ~ ! [SY163: $i] :
~ ~ ( ~ ( aElement0 @ SY163 )
| ( ( sdtasdt0 @ xb @ SY163 )
!= SV62 ) ) )
| ~ ( ~ ~ ! [SY164: $i] :
~ ~ ( ~ ( aElement0 @ SY164 )
| ( ( sdtasdt0 @ xb @ SY164 )
!= SV62 ) )
| ( aElementOf0 @ SV62 @ ( slsdtgt0 @ xb ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[672]) ).
thf(705,plain,
( ( ! [SY153: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ sK8_SY124 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SY153 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ sK8_SY124 @ SY153 )
!= sK1_SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[673]) ).
thf(706,plain,
! [SV3: $i,SV29: $i] :
( ( ( aElementOf0 @ ( sK9_SY127 @ SV29 @ SV3 ) @ SV3 )
= $true )
| ( ( ~ ! [SY128: $i] :
( ~ ( aElementOf0 @ SY128 @ SV29 )
| ( aElementOf0 @ SY128 @ SV3 ) ) )
= $true )
| ( ( SV3 = SV29 )
= $true )
| ( ( aSet0 @ SV3 )
= $false )
| ( ( aSet0 @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[674]) ).
thf(707,plain,
! [SV3: $i,SV29: $i] :
( ( ( ! [SY128: $i] :
( ~ ( aElementOf0 @ SY128 @ SV29 )
| ( aElementOf0 @ SY128 @ SV3 ) ) )
= $false )
| ( ( aElementOf0 @ ( sK9_SY127 @ SV29 @ SV3 ) @ SV29 )
= $false )
| ( ( SV3 = SV29 )
= $true )
| ( ( aSet0 @ SV3 )
= $false )
| ( ( aSet0 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[675]) ).
thf(708,plain,
( ( ~ ~ ( ~ ( aElementOf0 @ sK6_SX0 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ sK10_SY147 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ sK6_SX0 @ sK10_SY147 )
!= xu ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[676]) ).
thf(709,plain,
! [SV44: $i,SV59: $i,SV53: $i] :
( ( ( ~ ( ~ ~ ( ~ ( aElementOf0 @ SV53 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SV59 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SV53 @ SV59 )
!= SV44 ) ) )
= $false )
| ( ( ~ ( ( SV44 != sz00 ) ) )
= $true )
| ( ( ~ ( iLess0 @ ( sbrdtbr0 @ SV44 ) @ ( sbrdtbr0 @ xu ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[677]) ).
thf(710,plain,
( ( ~ ~ ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xa @ SX0 )
!= sz00 ) )
| ~ ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xa ) ) )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xa @ SX0 )
!= xa ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[678]) ).
thf(711,plain,
( ( ~ ( aElement0 @ sK11_SX0 )
| ( ( sdtasdt0 @ xb @ sK11_SX0 )
!= sz00 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[680]) ).
thf(712,plain,
! [SV41: $i,SV31: $i,SV9: $i] :
( ( ( ( sdtasdt0 @ SV9 @ ( sdtpldt0 @ SV31 @ SV41 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV9 @ SV31 ) @ ( sdtasdt0 @ SV9 @ SV41 ) ) )
= $true )
| ( ( aElement0 @ SV31 )
= $false )
| ( ( aElement0 @ SV9 )
= $false )
| ( ( aElement0 @ SV41 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[681]) ).
thf(713,plain,
! [SV9: $i,SV41: $i,SV31: $i] :
( ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV31 @ SV41 ) @ SV9 )
= ( sdtpldt0 @ ( sdtasdt0 @ SV31 @ SV9 ) @ ( sdtasdt0 @ SV41 @ SV9 ) ) )
= $true )
| ( ( aElement0 @ SV31 )
= $false )
| ( ( aElement0 @ SV9 )
= $false )
| ( ( aElement0 @ SV41 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[682]) ).
thf(714,plain,
( ( ~ ( aSet0 @ xI )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ~ ( ~ ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) )
| ~ ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[683]) ).
thf(715,plain,
! [SV54: $i] :
( ( ~ ( aElementOf0 @ SV54 @ ( slsdtgt0 @ xa ) )
| ~ ! [SY149: $i] :
~ ~ ( ~ ( aElement0 @ SY149 )
| ( ( sdtasdt0 @ xa @ SY149 )
!= SV54 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[685]) ).
thf(716,plain,
! [SV54: $i] :
( ( ~ ~ ! [SY150: $i] :
~ ~ ( ~ ( aElement0 @ SY150 )
| ( ( sdtasdt0 @ xa @ SY150 )
!= SV54 ) )
| ( aElementOf0 @ SV54 @ ( slsdtgt0 @ xa ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[686]) ).
thf(717,plain,
! [SV50: $i] :
( ( ( ! [SY145: $i] :
~ ~ ( ~ ( aElement0 @ SY145 )
| ( ( sdtasdt0 @ xb @ SY145 )
!= SV50 ) ) )
= $false )
| ( ( aElementOf0 @ SV50 @ ( slsdtgt0 @ xb ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[687]) ).
thf(718,plain,
! [SV50: $i] :
( ( ( ! [SY146: $i] :
~ ~ ( ~ ( aElement0 @ SY146 )
| ( ( sdtasdt0 @ xb @ SY146 )
!= SV50 ) ) )
= $true )
| ( ( aElementOf0 @ SV50 @ ( slsdtgt0 @ xb ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[688]) ).
thf(719,plain,
! [SV47: $i] :
( ( ( ! [SY154: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK12_SY138 @ SV47 ) @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SY154 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ ( sK12_SY138 @ SV47 ) @ SY154 )
!= SV47 ) ) )
= $false )
| ( ( aElementOf0 @ SV47 @ xI )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[689]) ).
thf(720,plain,
! [SV47: $i,SV56: $i] :
( ( ( ! [SY155: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SV56 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SY155 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SV56 @ SY155 )
!= SV47 ) ) )
= $true )
| ( ( aElementOf0 @ SV47 @ xI )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[690]) ).
thf(721,plain,
! [SV35: $i,SV16: $i,SV60: $i,SV57: $i] :
( ( ( ~ ~ ( ~ ( aElement0 @ SV57 )
| ~ ( aElement0 @ SV60 ) ) )
= $true )
| ( ( ~ ! [SY160: $i] :
~ ~ ( ~ ~ ( ~ ( aElement0 @ SY160 )
| ~ ( sdteqdtlpzmzozddtrp0 @ SY160 @ SV57 @ SV16 ) )
| ~ ( sdteqdtlpzmzozddtrp0 @ SY160 @ SV60 @ SV35 ) ) )
= $true )
| ( ( aElement0 @ ( sK7_SY131 @ SV35 @ SV16 ) )
= $true )
| ( ( aIdeal0 @ SV16 )
= $false )
| ( ( aIdeal0 @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[691]) ).
thf(722,plain,
! [SV35: $i,SV16: $i,SV58: $i,SV55: $i] :
( ( ( ~ ( ~ ( aElement0 @ SV55 )
| ~ ( aElement0 @ SV58 ) ) )
= $false )
| ( ( ~ ! [SY158: $i] :
~ ~ ( ~ ~ ( ~ ( aElement0 @ SY158 )
| ~ ( sdteqdtlpzmzozddtrp0 @ SY158 @ SV55 @ SV16 ) )
| ~ ( sdteqdtlpzmzozddtrp0 @ SY158 @ SV58 @ SV35 ) ) )
= $true )
| ( ( aElementOf0 @ ( sK7_SY131 @ SV35 @ SV16 ) @ ( sdtpldt1 @ SV16 @ SV35 ) )
= $false )
| ( ( aIdeal0 @ SV16 )
= $false )
| ( ( aIdeal0 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[692]) ).
thf(723,plain,
! [SV49: $i] :
( ( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xu @ SX0 )
!= xb ) ) )
= $false )
| ( ( aElement0 @ SV49 )
= $false )
| ( ( ( sdtasdt0 @ xu @ SV49 )
= xa )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[693]) ).
thf(724,plain,
! [SV49: $i] :
( ( ( doDivides0 @ xu @ xb )
= $false )
| ( ( aElement0 @ SV49 )
= $false )
| ( ( ( sdtasdt0 @ xu @ SV49 )
= xa )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[693]) ).
thf(725,plain,
! [SV52: $i] :
( ( ( ( sdtasdt0 @ xu @ SV52 )
= xb )
= $false )
| ( ( aElement0 @ SV52 )
= $false )
| ( ( doDivides0 @ xu @ xa )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[695]) ).
thf(726,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ xc )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xc @ SX0 )
!= xa ) ) )
| ~ ( doDivides0 @ xc @ xa ) )
| ~ ( aDivisorOf0 @ xc @ xa ) )
| ~ ( aElement0 @ xc ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[697]) ).
thf(727,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xc @ SX0 )
!= xb ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[698]) ).
thf(728,plain,
! [SV48: $i] :
( ( ( aElement0 @ SV48 )
= $false )
| ( ( ~ ( ~ ! [SY142: $i] :
~ ~ ( ~ ( aElement0 @ SY142 )
| ( ( sdtasdt0 @ SV48 @ SY142 )
!= xa ) )
| ( doDivides0 @ SV48 @ xa ) ) )
= $true )
| ( ( ~ ( ~ ! [SY143: $i] :
~ ~ ( ~ ( aElement0 @ SY143 )
| ( ( sdtasdt0 @ SV48 @ SY143 )
!= xb ) )
| ( doDivides0 @ SV48 @ xb )
| ( aDivisorOf0 @ SV48 @ xb ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) )
| ~ ( doDivides0 @ SV48 @ xc ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[699]) ).
thf(729,plain,
! [SV48: $i] :
( ( ( ~ ! [SY143: $i] :
~ ~ ( ~ ( aElement0 @ SY143 )
| ( ( sdtasdt0 @ SV48 @ SY143 )
!= xb ) ) )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xa )
= $false )
| ( ( ~ ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) )
| ~ ( doDivides0 @ SV48 @ xc ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[700]) ).
thf(730,plain,
! [SV48: $i] :
( ( ( doDivides0 @ SV48 @ xb )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xa )
= $false )
| ( ( ~ ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) )
| ~ ( doDivides0 @ SV48 @ xc ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[700]) ).
thf(731,plain,
! [SV48: $i] :
( ( ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) )
| ~ ( doDivides0 @ SV48 @ xc ) )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xa )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[701]) ).
thf(732,plain,
! [SV1: $i,SV27: $i] :
( ( ( ! [SY159: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ ( sK13_SY116 @ SV27 @ SV1 ) )
| ~ ( aElement0 @ SY159 ) )
| ( SV1
!= ( sdtpldt0 @ ( sdtasdt0 @ ( sK13_SY116 @ SV27 @ SV1 ) @ SV27 ) @ SY159 ) ) )
| ~ ( ~ ( ( SY159 != sz00 ) )
| ( iLess0 @ ( sbrdtbr0 @ SY159 ) @ ( sbrdtbr0 @ SV27 ) ) ) ) )
= $false )
| ( ( aElement0 @ SV27 )
= $false )
| ( ( aElement0 @ SV1 )
= $false )
| ( ( SV27 = sz00 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[702]) ).
thf(733,plain,
! [SV61: $i] :
( ( ~ ( ~ ( aElementOf0 @ SV61 @ ( slsdtgt0 @ xa ) )
| ~ ! [SY161: $i] :
~ ~ ( ~ ( aElement0 @ SY161 )
| ( ( sdtasdt0 @ xa @ SY161 )
!= SV61 ) ) )
| ~ ( ~ ~ ! [SY162: $i] :
~ ~ ( ~ ( aElement0 @ SY162 )
| ( ( sdtasdt0 @ xa @ SY162 )
!= SV61 ) )
| ( aElementOf0 @ SV61 @ ( slsdtgt0 @ xa ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[703]) ).
thf(734,plain,
! [SV62: $i] :
( ( ~ ( ~ ( aElementOf0 @ SV62 @ ( slsdtgt0 @ xb ) )
| ~ ! [SY163: $i] :
~ ~ ( ~ ( aElement0 @ SY163 )
| ( ( sdtasdt0 @ xb @ SY163 )
!= SV62 ) ) )
| ~ ( ~ ~ ! [SY164: $i] :
~ ~ ( ~ ( aElement0 @ SY164 )
| ( ( sdtasdt0 @ xb @ SY164 )
!= SV62 ) )
| ( aElementOf0 @ SV62 @ ( slsdtgt0 @ xb ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[704]) ).
thf(735,plain,
( ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ sK8_SY124 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ sK14_SY153 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ sK8_SY124 @ sK14_SY153 )
!= sK1_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[705]) ).
thf(736,plain,
! [SV3: $i,SV29: $i] :
( ( ( ! [SY128: $i] :
( ~ ( aElementOf0 @ SY128 @ SV29 )
| ( aElementOf0 @ SY128 @ SV3 ) ) )
= $false )
| ( ( aElementOf0 @ ( sK9_SY127 @ SV29 @ SV3 ) @ SV3 )
= $true )
| ( ( SV3 = SV29 )
= $true )
| ( ( aSet0 @ SV3 )
= $false )
| ( ( aSet0 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[706]) ).
thf(737,plain,
! [SV29: $i,SV3: $i] :
( ( ( ~ ( aElementOf0 @ ( sK15_SY128 @ SV3 @ SV29 ) @ SV29 )
| ( aElementOf0 @ ( sK15_SY128 @ SV3 @ SV29 ) @ SV3 ) )
= $false )
| ( ( aElementOf0 @ ( sK9_SY127 @ SV29 @ SV3 ) @ SV29 )
= $false )
| ( ( SV3 = SV29 )
= $true )
| ( ( aSet0 @ SV3 )
= $false )
| ( ( aSet0 @ SV29 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[707]) ).
thf(738,plain,
( ( ~ ~ ( ~ ( aElementOf0 @ sK6_SX0 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ sK10_SY147 @ ( slsdtgt0 @ xb ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[708]) ).
thf(739,plain,
( ( ( sdtpldt0 @ sK6_SX0 @ sK10_SY147 )
!= xu )
= $false ),
inference(extcnf_or_neg,[status(thm)],[708]) ).
thf(740,plain,
! [SV44: $i,SV59: $i,SV53: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ SV53 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SV59 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SV53 @ SV59 )
!= SV44 ) )
= $true )
| ( ( ~ ( ( SV44 != sz00 ) ) )
= $true )
| ( ( ~ ( iLess0 @ ( sbrdtbr0 @ SV44 ) @ ( sbrdtbr0 @ xu ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[709]) ).
thf(741,plain,
( ( ~ ~ ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xa @ SX0 )
!= sz00 ) )
| ~ ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xa ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[710]) ).
thf(742,plain,
( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xa @ SX0 )
!= xa ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[710]) ).
thf(743,plain,
( ( ~ ( aElement0 @ sK11_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[711]) ).
thf(744,plain,
( ( ( sdtasdt0 @ xb @ sK11_SX0 )
!= sz00 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[711]) ).
thf(745,plain,
( ( ~ ( aSet0 @ xI ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[714]) ).
thf(746,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ~ ( ~ ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) )
| ~ ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[714]) ).
thf(747,plain,
! [SV54: $i] :
( ( ( ~ ( aElementOf0 @ SV54 @ ( slsdtgt0 @ xa ) ) )
= $true )
| ( ( ~ ! [SY149: $i] :
~ ~ ( ~ ( aElement0 @ SY149 )
| ( ( sdtasdt0 @ xa @ SY149 )
!= SV54 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[715]) ).
thf(748,plain,
! [SV54: $i] :
( ( ( ~ ~ ! [SY150: $i] :
~ ~ ( ~ ( aElement0 @ SY150 )
| ( ( sdtasdt0 @ xa @ SY150 )
!= SV54 ) ) )
= $true )
| ( ( aElementOf0 @ SV54 @ ( slsdtgt0 @ xa ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[716]) ).
thf(749,plain,
! [SV50: $i] :
( ( ( ~ ~ ( ~ ( aElement0 @ ( sK16_SY145 @ SV50 ) )
| ( ( sdtasdt0 @ xb @ ( sK16_SY145 @ SV50 ) )
!= SV50 ) ) )
= $false )
| ( ( aElementOf0 @ SV50 @ ( slsdtgt0 @ xb ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[717]) ).
thf(750,plain,
! [SV50: $i,SV63: $i] :
( ( ( ~ ~ ( ~ ( aElement0 @ SV63 )
| ( ( sdtasdt0 @ xb @ SV63 )
!= SV50 ) ) )
= $true )
| ( ( aElementOf0 @ SV50 @ ( slsdtgt0 @ xb ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[718]) ).
thf(751,plain,
! [SV47: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK12_SY138 @ SV47 ) @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ ( sK17_SY154 @ SV47 ) @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ ( sK12_SY138 @ SV47 ) @ ( sK17_SY154 @ SV47 ) )
!= SV47 ) ) )
= $false )
| ( ( aElementOf0 @ SV47 @ xI )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[719]) ).
thf(752,plain,
! [SV47: $i,SV64: $i,SV56: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SV56 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SV64 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SV56 @ SV64 )
!= SV47 ) ) )
= $true )
| ( ( aElementOf0 @ SV47 @ xI )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[720]) ).
thf(753,plain,
! [SV35: $i,SV16: $i,SV60: $i,SV57: $i] :
( ( ( ~ ( ~ ( aElement0 @ SV57 )
| ~ ( aElement0 @ SV60 ) ) )
= $false )
| ( ( ~ ! [SY160: $i] :
~ ~ ( ~ ~ ( ~ ( aElement0 @ SY160 )
| ~ ( sdteqdtlpzmzozddtrp0 @ SY160 @ SV57 @ SV16 ) )
| ~ ( sdteqdtlpzmzozddtrp0 @ SY160 @ SV60 @ SV35 ) ) )
= $true )
| ( ( aElement0 @ ( sK7_SY131 @ SV35 @ SV16 ) )
= $true )
| ( ( aIdeal0 @ SV16 )
= $false )
| ( ( aIdeal0 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[721]) ).
thf(754,plain,
! [SV35: $i,SV16: $i,SV58: $i,SV55: $i] :
( ( ( ~ ( aElement0 @ SV55 )
| ~ ( aElement0 @ SV58 ) )
= $true )
| ( ( ~ ! [SY158: $i] :
~ ~ ( ~ ~ ( ~ ( aElement0 @ SY158 )
| ~ ( sdteqdtlpzmzozddtrp0 @ SY158 @ SV55 @ SV16 ) )
| ~ ( sdteqdtlpzmzozddtrp0 @ SY158 @ SV58 @ SV35 ) ) )
= $true )
| ( ( aElementOf0 @ ( sK7_SY131 @ SV35 @ SV16 ) @ ( sdtpldt1 @ SV16 @ SV35 ) )
= $false )
| ( ( aIdeal0 @ SV16 )
= $false )
| ( ( aIdeal0 @ SV35 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[722]) ).
thf(755,plain,
! [SV49: $i] :
( ( ( ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xu @ SX0 )
!= xb ) ) )
= $true )
| ( ( aElement0 @ SV49 )
= $false )
| ( ( ( sdtasdt0 @ xu @ SV49 )
= xa )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[723]) ).
thf(756,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ xc )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xc @ SX0 )
!= xa ) ) )
| ~ ( doDivides0 @ xc @ xa ) )
| ~ ( aDivisorOf0 @ xc @ xa ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[726]) ).
thf(757,plain,
( ( ~ ( aElement0 @ xc ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[726]) ).
thf(758,plain,
( ( ~ ~ ( ~ ( aElement0 @ sK18_SX0 )
| ( ( sdtasdt0 @ xc @ sK18_SX0 )
!= xb ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[727]) ).
thf(759,plain,
! [SV48: $i] :
( ( ( ~ ! [SY142: $i] :
~ ~ ( ~ ( aElement0 @ SY142 )
| ( ( sdtasdt0 @ SV48 @ SY142 )
!= xa ) )
| ( doDivides0 @ SV48 @ xa ) )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( ~ ( ~ ! [SY143: $i] :
~ ~ ( ~ ( aElement0 @ SY143 )
| ( ( sdtasdt0 @ SV48 @ SY143 )
!= xb ) )
| ( doDivides0 @ SV48 @ xb )
| ( aDivisorOf0 @ SV48 @ xb ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) )
| ~ ( doDivides0 @ SV48 @ xc ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[728]) ).
thf(760,plain,
! [SV48: $i] :
( ( ( ! [SY143: $i] :
~ ~ ( ~ ( aElement0 @ SY143 )
| ( ( sdtasdt0 @ SV48 @ SY143 )
!= xb ) ) )
= $true )
| ( ( aDivisorOf0 @ SV48 @ xa )
= $false )
| ( ( ~ ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) )
| ~ ( doDivides0 @ SV48 @ xc ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[729]) ).
thf(761,plain,
! [SV48: $i] :
( ( ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) )
| ~ ( doDivides0 @ SV48 @ xc ) )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xa )
= $false )
| ( ( doDivides0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[730]) ).
thf(762,plain,
! [SV48: $i] :
( ( ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) ) )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xa )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[731]) ).
thf(763,plain,
! [SV48: $i] :
( ( ( ~ ( doDivides0 @ SV48 @ xc ) )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xa )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[731]) ).
thf(764,plain,
! [SV1: $i,SV27: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ ( sK13_SY116 @ SV27 @ SV1 ) )
| ~ ( aElement0 @ ( sK19_SY159 @ SV1 @ SV27 ) ) )
| ( SV1
!= ( sdtpldt0 @ ( sdtasdt0 @ ( sK13_SY116 @ SV27 @ SV1 ) @ SV27 ) @ ( sK19_SY159 @ SV1 @ SV27 ) ) ) )
| ~ ( ~ ( ( ( sK19_SY159 @ SV1 @ SV27 )
!= sz00 ) )
| ( iLess0 @ ( sbrdtbr0 @ ( sK19_SY159 @ SV1 @ SV27 ) ) @ ( sbrdtbr0 @ SV27 ) ) ) ) )
= $false )
| ( ( aElement0 @ SV27 )
= $false )
| ( ( aElement0 @ SV1 )
= $false )
| ( ( SV27 = sz00 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[732]) ).
thf(765,plain,
! [SV61: $i] :
( ( ~ ( ~ ( aElementOf0 @ SV61 @ ( slsdtgt0 @ xa ) )
| ~ ! [SY161: $i] :
~ ~ ( ~ ( aElement0 @ SY161 )
| ( ( sdtasdt0 @ xa @ SY161 )
!= SV61 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[733]) ).
thf(766,plain,
! [SV61: $i] :
( ( ~ ( ~ ~ ! [SY162: $i] :
~ ~ ( ~ ( aElement0 @ SY162 )
| ( ( sdtasdt0 @ xa @ SY162 )
!= SV61 ) )
| ( aElementOf0 @ SV61 @ ( slsdtgt0 @ xa ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[733]) ).
thf(767,plain,
! [SV62: $i] :
( ( ~ ( ~ ( aElementOf0 @ SV62 @ ( slsdtgt0 @ xb ) )
| ~ ! [SY163: $i] :
~ ~ ( ~ ( aElement0 @ SY163 )
| ( ( sdtasdt0 @ xb @ SY163 )
!= SV62 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[734]) ).
thf(768,plain,
! [SV62: $i] :
( ( ~ ( ~ ~ ! [SY164: $i] :
~ ~ ( ~ ( aElement0 @ SY164 )
| ( ( sdtasdt0 @ xb @ SY164 )
!= SV62 ) )
| ( aElementOf0 @ SV62 @ ( slsdtgt0 @ xb ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[734]) ).
thf(769,plain,
( ( ~ ( ~ ~ ( ~ ( aElementOf0 @ sK8_SY124 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ sK14_SY153 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ sK8_SY124 @ sK14_SY153 )
!= sK1_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[735]) ).
thf(770,plain,
! [SV29: $i,SV3: $i] :
( ( ( ~ ( aElementOf0 @ ( sK20_SY128 @ SV3 @ SV29 ) @ SV29 )
| ( aElementOf0 @ ( sK20_SY128 @ SV3 @ SV29 ) @ SV3 ) )
= $false )
| ( ( aElementOf0 @ ( sK9_SY127 @ SV29 @ SV3 ) @ SV3 )
= $true )
| ( ( SV3 = SV29 )
= $true )
| ( ( aSet0 @ SV3 )
= $false )
| ( ( aSet0 @ SV29 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[736]) ).
thf(771,plain,
! [SV29: $i,SV3: $i] :
( ( ( ~ ( aElementOf0 @ ( sK15_SY128 @ SV3 @ SV29 ) @ SV29 ) )
= $false )
| ( ( aElementOf0 @ ( sK9_SY127 @ SV29 @ SV3 ) @ SV29 )
= $false )
| ( ( SV3 = SV29 )
= $true )
| ( ( aSet0 @ SV3 )
= $false )
| ( ( aSet0 @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[737]) ).
thf(772,plain,
! [SV29: $i,SV3: $i] :
( ( ( aElementOf0 @ ( sK15_SY128 @ SV3 @ SV29 ) @ SV3 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY127 @ SV29 @ SV3 ) @ SV29 )
= $false )
| ( ( SV3 = SV29 )
= $true )
| ( ( aSet0 @ SV3 )
= $false )
| ( ( aSet0 @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[737]) ).
thf(773,plain,
( ( ~ ( ~ ( aElementOf0 @ sK6_SX0 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ sK10_SY147 @ ( slsdtgt0 @ xb ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[738]) ).
thf(774,plain,
( ( ( sdtpldt0 @ sK6_SX0 @ sK10_SY147 )
= xu )
= $true ),
inference(extcnf_not_neg,[status(thm)],[739]) ).
thf(775,plain,
! [SV44: $i,SV59: $i,SV53: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ SV53 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SV59 @ ( slsdtgt0 @ xb ) ) ) )
= $true )
| ( ( ( sdtpldt0 @ SV53 @ SV59 )
!= SV44 )
= $true )
| ( ( ~ ( ( SV44 != sz00 ) ) )
= $true )
| ( ( ~ ( iLess0 @ ( sbrdtbr0 @ SV44 ) @ ( sbrdtbr0 @ xu ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[740]) ).
thf(776,plain,
( ( ~ ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xa @ SX0 )
!= sz00 ) )
| ~ ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xa ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[741]) ).
thf(777,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xa @ SX0 )
!= xa ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[742]) ).
thf(778,plain,
( ( aElement0 @ sK11_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[743]) ).
thf(779,plain,
( ( ( sdtasdt0 @ xb @ sK11_SX0 )
= sz00 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[744]) ).
thf(780,plain,
( ( aSet0 @ xI )
= $true ),
inference(extcnf_not_neg,[status(thm)],[745]) ).
thf(781,plain,
( ( ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xI )
| ~ ( ~ ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) )
| ~ ! [SX1: $i] :
( ~ ( aElement0 @ SX1 )
| ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[746]) ).
thf(782,plain,
! [SV54: $i] :
( ( ( aElementOf0 @ SV54 @ ( slsdtgt0 @ xa ) )
= $false )
| ( ( ~ ! [SY149: $i] :
~ ~ ( ~ ( aElement0 @ SY149 )
| ( ( sdtasdt0 @ xa @ SY149 )
!= SV54 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[747]) ).
thf(783,plain,
! [SV54: $i] :
( ( ( ~ ! [SY150: $i] :
~ ~ ( ~ ( aElement0 @ SY150 )
| ( ( sdtasdt0 @ xa @ SY150 )
!= SV54 ) ) )
= $false )
| ( ( aElementOf0 @ SV54 @ ( slsdtgt0 @ xa ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[748]) ).
thf(784,plain,
! [SV50: $i] :
( ( ( ~ ( ~ ( aElement0 @ ( sK16_SY145 @ SV50 ) )
| ( ( sdtasdt0 @ xb @ ( sK16_SY145 @ SV50 ) )
!= SV50 ) ) )
= $true )
| ( ( aElementOf0 @ SV50 @ ( slsdtgt0 @ xb ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[749]) ).
thf(785,plain,
! [SV50: $i,SV63: $i] :
( ( ( ~ ( ~ ( aElement0 @ SV63 )
| ( ( sdtasdt0 @ xb @ SV63 )
!= SV50 ) ) )
= $false )
| ( ( aElementOf0 @ SV50 @ ( slsdtgt0 @ xb ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[750]) ).
thf(786,plain,
! [SV47: $i] :
( ( ( ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK12_SY138 @ SV47 ) @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ ( sK17_SY154 @ SV47 ) @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ ( sK12_SY138 @ SV47 ) @ ( sK17_SY154 @ SV47 ) )
!= SV47 ) ) )
= $true )
| ( ( aElementOf0 @ SV47 @ xI )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[751]) ).
thf(787,plain,
! [SV47: $i,SV64: $i,SV56: $i] :
( ( ( ~ ( ~ ~ ( ~ ( aElementOf0 @ SV56 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SV64 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SV56 @ SV64 )
!= SV47 ) ) )
= $false )
| ( ( aElementOf0 @ SV47 @ xI )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[752]) ).
thf(788,plain,
! [SV35: $i,SV16: $i,SV60: $i,SV57: $i] :
( ( ( ~ ( aElement0 @ SV57 )
| ~ ( aElement0 @ SV60 ) )
= $true )
| ( ( ~ ! [SY160: $i] :
~ ~ ( ~ ~ ( ~ ( aElement0 @ SY160 )
| ~ ( sdteqdtlpzmzozddtrp0 @ SY160 @ SV57 @ SV16 ) )
| ~ ( sdteqdtlpzmzozddtrp0 @ SY160 @ SV60 @ SV35 ) ) )
= $true )
| ( ( aElement0 @ ( sK7_SY131 @ SV35 @ SV16 ) )
= $true )
| ( ( aIdeal0 @ SV16 )
= $false )
| ( ( aIdeal0 @ SV35 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[753]) ).
thf(789,plain,
! [SV35: $i,SV16: $i,SV58: $i,SV55: $i] :
( ( ( ~ ( aElement0 @ SV55 ) )
= $true )
| ( ( ~ ( aElement0 @ SV58 ) )
= $true )
| ( ( ~ ! [SY158: $i] :
~ ~ ( ~ ~ ( ~ ( aElement0 @ SY158 )
| ~ ( sdteqdtlpzmzozddtrp0 @ SY158 @ SV55 @ SV16 ) )
| ~ ( sdteqdtlpzmzozddtrp0 @ SY158 @ SV58 @ SV35 ) ) )
= $true )
| ( ( aElementOf0 @ ( sK7_SY131 @ SV35 @ SV16 ) @ ( sdtpldt1 @ SV16 @ SV35 ) )
= $false )
| ( ( aIdeal0 @ SV16 )
= $false )
| ( ( aIdeal0 @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[754]) ).
thf(790,plain,
! [SV49: $i,SV65: $i] :
( ( ( ~ ~ ( ~ ( aElement0 @ SV65 )
| ( ( sdtasdt0 @ xu @ SV65 )
!= xb ) ) )
= $true )
| ( ( aElement0 @ SV49 )
= $false )
| ( ( ( sdtasdt0 @ xu @ SV49 )
= xa )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[755]) ).
thf(791,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ xc )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xc @ SX0 )
!= xa ) ) )
| ~ ( doDivides0 @ xc @ xa ) )
| ~ ( aDivisorOf0 @ xc @ xa ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[756]) ).
thf(792,plain,
( ( aElement0 @ xc )
= $true ),
inference(extcnf_not_neg,[status(thm)],[757]) ).
thf(793,plain,
( ( ~ ( ~ ( aElement0 @ sK18_SX0 )
| ( ( sdtasdt0 @ xc @ sK18_SX0 )
!= xb ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[758]) ).
thf(794,plain,
! [SV48: $i] :
( ( ( ~ ! [SY142: $i] :
~ ~ ( ~ ( aElement0 @ SY142 )
| ( ( sdtasdt0 @ SV48 @ SY142 )
!= xa ) ) )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( ~ ( ~ ! [SY143: $i] :
~ ~ ( ~ ( aElement0 @ SY143 )
| ( ( sdtasdt0 @ SV48 @ SY143 )
!= xb ) )
| ( doDivides0 @ SV48 @ xb )
| ( aDivisorOf0 @ SV48 @ xb ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) )
| ~ ( doDivides0 @ SV48 @ xc ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[759]) ).
thf(795,plain,
! [SV48: $i] :
( ( ( doDivides0 @ SV48 @ xa )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( ~ ( ~ ! [SY143: $i] :
~ ~ ( ~ ( aElement0 @ SY143 )
| ( ( sdtasdt0 @ SV48 @ SY143 )
!= xb ) )
| ( doDivides0 @ SV48 @ xb )
| ( aDivisorOf0 @ SV48 @ xb ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) )
| ~ ( doDivides0 @ SV48 @ xc ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[759]) ).
thf(796,plain,
! [SV48: $i,SV66: $i] :
( ( ( ~ ~ ( ~ ( aElement0 @ SV66 )
| ( ( sdtasdt0 @ SV48 @ SV66 )
!= xb ) ) )
= $true )
| ( ( aDivisorOf0 @ SV48 @ xa )
= $false )
| ( ( ~ ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) )
| ~ ( doDivides0 @ SV48 @ xc ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[760]) ).
thf(797,plain,
! [SV48: $i] :
( ( ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) ) )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xa )
= $false )
| ( ( doDivides0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[761]) ).
thf(798,plain,
! [SV48: $i] :
( ( ( ~ ( doDivides0 @ SV48 @ xc ) )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xa )
= $false )
| ( ( doDivides0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[761]) ).
thf(799,plain,
! [SV48: $i] :
( ( ( ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) ) )
= $true )
| ( ( aDivisorOf0 @ SV48 @ xa )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[762]) ).
thf(800,plain,
! [SV48: $i] :
( ( ( doDivides0 @ SV48 @ xc )
= $true )
| ( ( aDivisorOf0 @ SV48 @ xa )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[763]) ).
thf(801,plain,
! [SV1: $i,SV27: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ ( sK13_SY116 @ SV27 @ SV1 ) )
| ~ ( aElement0 @ ( sK19_SY159 @ SV1 @ SV27 ) ) )
| ( SV1
!= ( sdtpldt0 @ ( sdtasdt0 @ ( sK13_SY116 @ SV27 @ SV1 ) @ SV27 ) @ ( sK19_SY159 @ SV1 @ SV27 ) ) ) )
| ~ ( ~ ( ( ( sK19_SY159 @ SV1 @ SV27 )
!= sz00 ) )
| ( iLess0 @ ( sbrdtbr0 @ ( sK19_SY159 @ SV1 @ SV27 ) ) @ ( sbrdtbr0 @ SV27 ) ) ) ) )
= $true )
| ( ( aElement0 @ SV27 )
= $false )
| ( ( aElement0 @ SV1 )
= $false )
| ( ( SV27 = sz00 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[764]) ).
thf(802,plain,
! [SV61: $i] :
( ( ~ ( aElementOf0 @ SV61 @ ( slsdtgt0 @ xa ) )
| ~ ! [SY161: $i] :
~ ~ ( ~ ( aElement0 @ SY161 )
| ( ( sdtasdt0 @ xa @ SY161 )
!= SV61 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[765]) ).
thf(803,plain,
! [SV61: $i] :
( ( ~ ~ ! [SY162: $i] :
~ ~ ( ~ ( aElement0 @ SY162 )
| ( ( sdtasdt0 @ xa @ SY162 )
!= SV61 ) )
| ( aElementOf0 @ SV61 @ ( slsdtgt0 @ xa ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[766]) ).
thf(804,plain,
! [SV62: $i] :
( ( ~ ( aElementOf0 @ SV62 @ ( slsdtgt0 @ xb ) )
| ~ ! [SY163: $i] :
~ ~ ( ~ ( aElement0 @ SY163 )
| ( ( sdtasdt0 @ xb @ SY163 )
!= SV62 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[767]) ).
thf(805,plain,
! [SV62: $i] :
( ( ~ ~ ! [SY164: $i] :
~ ~ ( ~ ( aElement0 @ SY164 )
| ( ( sdtasdt0 @ xb @ SY164 )
!= SV62 ) )
| ( aElementOf0 @ SV62 @ ( slsdtgt0 @ xb ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[768]) ).
thf(806,plain,
( ( ~ ~ ( ~ ( aElementOf0 @ sK8_SY124 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ sK14_SY153 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ sK8_SY124 @ sK14_SY153 )
!= sK1_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[769]) ).
thf(807,plain,
! [SV29: $i,SV3: $i] :
( ( ( ~ ( aElementOf0 @ ( sK20_SY128 @ SV3 @ SV29 ) @ SV29 ) )
= $false )
| ( ( aElementOf0 @ ( sK9_SY127 @ SV29 @ SV3 ) @ SV3 )
= $true )
| ( ( SV3 = SV29 )
= $true )
| ( ( aSet0 @ SV3 )
= $false )
| ( ( aSet0 @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[770]) ).
thf(808,plain,
! [SV29: $i,SV3: $i] :
( ( ( aElementOf0 @ ( sK20_SY128 @ SV3 @ SV29 ) @ SV3 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY127 @ SV29 @ SV3 ) @ SV3 )
= $true )
| ( ( SV3 = SV29 )
= $true )
| ( ( aSet0 @ SV3 )
= $false )
| ( ( aSet0 @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[770]) ).
thf(809,plain,
! [SV29: $i,SV3: $i] :
( ( ( aElementOf0 @ ( sK15_SY128 @ SV3 @ SV29 ) @ SV29 )
= $true )
| ( ( aElementOf0 @ ( sK9_SY127 @ SV29 @ SV3 ) @ SV29 )
= $false )
| ( ( SV3 = SV29 )
= $true )
| ( ( aSet0 @ SV3 )
= $false )
| ( ( aSet0 @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[771]) ).
thf(810,plain,
( ( ~ ( aElementOf0 @ sK6_SX0 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ sK10_SY147 @ ( slsdtgt0 @ xb ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[773]) ).
thf(811,plain,
! [SV44: $i,SV59: $i,SV53: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ SV53 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SV59 @ ( slsdtgt0 @ xb ) ) ) )
= $false )
| ( ( ( sdtpldt0 @ SV53 @ SV59 )
!= SV44 )
= $true )
| ( ( ~ ( ( SV44 != sz00 ) ) )
= $true )
| ( ( ~ ( iLess0 @ ( sbrdtbr0 @ SV44 ) @ ( sbrdtbr0 @ xu ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[775]) ).
thf(812,plain,
( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xa @ SX0 )
!= sz00 ) )
| ~ ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xa ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[776]) ).
thf(813,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xa @ SX0 )
!= xa ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[777]) ).
thf(814,plain,
! [SV67: $i] :
( ( ~ ( aElementOf0 @ SV67 @ xI )
| ~ ( ~ ! [SY165: $i] :
( ~ ( aElementOf0 @ SY165 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SV67 @ SY165 ) @ xI ) )
| ~ ! [SY166: $i] :
( ~ ( aElement0 @ SY166 )
| ( aElementOf0 @ ( sdtasdt0 @ SY166 @ SV67 ) @ xI ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[781]) ).
thf(815,plain,
! [SV54: $i] :
( ( ( ! [SY149: $i] :
~ ~ ( ~ ( aElement0 @ SY149 )
| ( ( sdtasdt0 @ xa @ SY149 )
!= SV54 ) ) )
= $false )
| ( ( aElementOf0 @ SV54 @ ( slsdtgt0 @ xa ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[782]) ).
thf(816,plain,
! [SV54: $i] :
( ( ( ! [SY150: $i] :
~ ~ ( ~ ( aElement0 @ SY150 )
| ( ( sdtasdt0 @ xa @ SY150 )
!= SV54 ) ) )
= $true )
| ( ( aElementOf0 @ SV54 @ ( slsdtgt0 @ xa ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[783]) ).
thf(817,plain,
! [SV50: $i] :
( ( ( ~ ( aElement0 @ ( sK16_SY145 @ SV50 ) )
| ( ( sdtasdt0 @ xb @ ( sK16_SY145 @ SV50 ) )
!= SV50 ) )
= $false )
| ( ( aElementOf0 @ SV50 @ ( slsdtgt0 @ xb ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[784]) ).
thf(818,plain,
! [SV50: $i,SV63: $i] :
( ( ( ~ ( aElement0 @ SV63 )
| ( ( sdtasdt0 @ xb @ SV63 )
!= SV50 ) )
= $true )
| ( ( aElementOf0 @ SV50 @ ( slsdtgt0 @ xb ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[785]) ).
thf(819,plain,
! [SV47: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ ( sK12_SY138 @ SV47 ) @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ ( sK17_SY154 @ SV47 ) @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ ( sK12_SY138 @ SV47 ) @ ( sK17_SY154 @ SV47 ) )
!= SV47 ) )
= $false )
| ( ( aElementOf0 @ SV47 @ xI )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[786]) ).
thf(820,plain,
! [SV47: $i,SV64: $i,SV56: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ SV56 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SV64 @ ( slsdtgt0 @ xb ) ) )
| ( ( sdtpldt0 @ SV56 @ SV64 )
!= SV47 ) )
= $true )
| ( ( aElementOf0 @ SV47 @ xI )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[787]) ).
thf(821,plain,
! [SV35: $i,SV16: $i,SV60: $i,SV57: $i] :
( ( ( ~ ( aElement0 @ SV57 ) )
= $true )
| ( ( ~ ( aElement0 @ SV60 ) )
= $true )
| ( ( ~ ! [SY160: $i] :
~ ~ ( ~ ~ ( ~ ( aElement0 @ SY160 )
| ~ ( sdteqdtlpzmzozddtrp0 @ SY160 @ SV57 @ SV16 ) )
| ~ ( sdteqdtlpzmzozddtrp0 @ SY160 @ SV60 @ SV35 ) ) )
= $true )
| ( ( aElement0 @ ( sK7_SY131 @ SV35 @ SV16 ) )
= $true )
| ( ( aIdeal0 @ SV16 )
= $false )
| ( ( aIdeal0 @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[788]) ).
thf(822,plain,
! [SV35: $i,SV16: $i,SV58: $i,SV55: $i] :
( ( ( aElement0 @ SV55 )
= $false )
| ( ( ~ ( aElement0 @ SV58 ) )
= $true )
| ( ( ~ ! [SY158: $i] :
~ ~ ( ~ ~ ( ~ ( aElement0 @ SY158 )
| ~ ( sdteqdtlpzmzozddtrp0 @ SY158 @ SV55 @ SV16 ) )
| ~ ( sdteqdtlpzmzozddtrp0 @ SY158 @ SV58 @ SV35 ) ) )
= $true )
| ( ( aElementOf0 @ ( sK7_SY131 @ SV35 @ SV16 ) @ ( sdtpldt1 @ SV16 @ SV35 ) )
= $false )
| ( ( aIdeal0 @ SV16 )
= $false )
| ( ( aIdeal0 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[789]) ).
thf(823,plain,
! [SV49: $i,SV65: $i] :
( ( ( ~ ( ~ ( aElement0 @ SV65 )
| ( ( sdtasdt0 @ xu @ SV65 )
!= xb ) ) )
= $false )
| ( ( aElement0 @ SV49 )
= $false )
| ( ( ( sdtasdt0 @ xu @ SV49 )
= xa )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[790]) ).
thf(824,plain,
( ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ xc )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xc @ SX0 )
!= xa ) ) )
| ~ ( doDivides0 @ xc @ xa ) )
| ~ ( aDivisorOf0 @ xc @ xa ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[791]) ).
thf(825,plain,
( ( ~ ( aElement0 @ sK18_SX0 )
| ( ( sdtasdt0 @ xc @ sK18_SX0 )
!= xb ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[793]) ).
thf(826,plain,
! [SV48: $i] :
( ( ( ! [SY142: $i] :
~ ~ ( ~ ( aElement0 @ SY142 )
| ( ( sdtasdt0 @ SV48 @ SY142 )
!= xa ) ) )
= $true )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( ~ ( ~ ! [SY143: $i] :
~ ~ ( ~ ( aElement0 @ SY143 )
| ( ( sdtasdt0 @ SV48 @ SY143 )
!= xb ) )
| ( doDivides0 @ SV48 @ xb )
| ( aDivisorOf0 @ SV48 @ xb ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) )
| ~ ( doDivides0 @ SV48 @ xc ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[794]) ).
thf(827,plain,
! [SV48: $i] :
( ( ( ~ ! [SY143: $i] :
~ ~ ( ~ ( aElement0 @ SY143 )
| ( ( sdtasdt0 @ SV48 @ SY143 )
!= xb ) )
| ( doDivides0 @ SV48 @ xb )
| ( aDivisorOf0 @ SV48 @ xb ) )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( doDivides0 @ SV48 @ xa )
= $false )
| ( ( ~ ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) )
| ~ ( doDivides0 @ SV48 @ xc ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[795]) ).
thf(828,plain,
! [SV48: $i,SV66: $i] :
( ( ( ~ ( ~ ( aElement0 @ SV66 )
| ( ( sdtasdt0 @ SV48 @ SV66 )
!= xb ) ) )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xa )
= $false )
| ( ( ~ ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) )
| ~ ( doDivides0 @ SV48 @ xc ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[796]) ).
thf(829,plain,
! [SV48: $i] :
( ( ( ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) ) )
= $true )
| ( ( aDivisorOf0 @ SV48 @ xa )
= $false )
| ( ( doDivides0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[797]) ).
thf(830,plain,
! [SV48: $i] :
( ( ( doDivides0 @ SV48 @ xc )
= $true )
| ( ( aDivisorOf0 @ SV48 @ xa )
= $false )
| ( ( doDivides0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[798]) ).
thf(831,plain,
! [SV48: $i] :
( ( ( ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) ) )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xa )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[799]) ).
thf(832,plain,
! [SV1: $i,SV27: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ ( sK13_SY116 @ SV27 @ SV1 ) )
| ~ ( aElement0 @ ( sK19_SY159 @ SV1 @ SV27 ) ) )
| ( SV1
!= ( sdtpldt0 @ ( sdtasdt0 @ ( sK13_SY116 @ SV27 @ SV1 ) @ SV27 ) @ ( sK19_SY159 @ SV1 @ SV27 ) ) ) )
| ~ ( ~ ( ( ( sK19_SY159 @ SV1 @ SV27 )
!= sz00 ) )
| ( iLess0 @ ( sbrdtbr0 @ ( sK19_SY159 @ SV1 @ SV27 ) ) @ ( sbrdtbr0 @ SV27 ) ) ) )
= $false )
| ( ( aElement0 @ SV27 )
= $false )
| ( ( aElement0 @ SV1 )
= $false )
| ( ( SV27 = sz00 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[801]) ).
thf(833,plain,
! [SV61: $i] :
( ( ( ~ ( aElementOf0 @ SV61 @ ( slsdtgt0 @ xa ) ) )
= $true )
| ( ( ~ ! [SY161: $i] :
~ ~ ( ~ ( aElement0 @ SY161 )
| ( ( sdtasdt0 @ xa @ SY161 )
!= SV61 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[802]) ).
thf(834,plain,
! [SV61: $i] :
( ( ( ~ ~ ! [SY162: $i] :
~ ~ ( ~ ( aElement0 @ SY162 )
| ( ( sdtasdt0 @ xa @ SY162 )
!= SV61 ) ) )
= $true )
| ( ( aElementOf0 @ SV61 @ ( slsdtgt0 @ xa ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[803]) ).
thf(835,plain,
! [SV62: $i] :
( ( ( ~ ( aElementOf0 @ SV62 @ ( slsdtgt0 @ xb ) ) )
= $true )
| ( ( ~ ! [SY163: $i] :
~ ~ ( ~ ( aElement0 @ SY163 )
| ( ( sdtasdt0 @ xb @ SY163 )
!= SV62 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[804]) ).
thf(836,plain,
! [SV62: $i] :
( ( ( ~ ~ ! [SY164: $i] :
~ ~ ( ~ ( aElement0 @ SY164 )
| ( ( sdtasdt0 @ xb @ SY164 )
!= SV62 ) ) )
= $true )
| ( ( aElementOf0 @ SV62 @ ( slsdtgt0 @ xb ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[805]) ).
thf(837,plain,
( ( ~ ~ ( ~ ( aElementOf0 @ sK8_SY124 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ sK14_SY153 @ ( slsdtgt0 @ xb ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[806]) ).
thf(838,plain,
( ( ( sdtpldt0 @ sK8_SY124 @ sK14_SY153 )
!= sK1_SX0 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[806]) ).
thf(839,plain,
! [SV29: $i,SV3: $i] :
( ( ( aElementOf0 @ ( sK20_SY128 @ SV3 @ SV29 ) @ SV29 )
= $true )
| ( ( aElementOf0 @ ( sK9_SY127 @ SV29 @ SV3 ) @ SV3 )
= $true )
| ( ( SV3 = SV29 )
= $true )
| ( ( aSet0 @ SV3 )
= $false )
| ( ( aSet0 @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[807]) ).
thf(840,plain,
( ( ~ ( aElementOf0 @ sK6_SX0 @ ( slsdtgt0 @ xa ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[810]) ).
thf(841,plain,
( ( ~ ( aElementOf0 @ sK10_SY147 @ ( slsdtgt0 @ xb ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[810]) ).
thf(842,plain,
! [SV44: $i,SV59: $i,SV53: $i] :
( ( ( ~ ( aElementOf0 @ SV53 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SV59 @ ( slsdtgt0 @ xb ) ) )
= $true )
| ( ( ( sdtpldt0 @ SV53 @ SV59 )
!= SV44 )
= $true )
| ( ( ~ ( ( SV44 != sz00 ) ) )
= $true )
| ( ( ~ ( iLess0 @ ( sbrdtbr0 @ SV44 ) @ ( sbrdtbr0 @ xu ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[811]) ).
thf(843,plain,
( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xa @ SX0 )
!= sz00 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[812]) ).
thf(844,plain,
( ( ~ ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xa ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[812]) ).
thf(845,plain,
( ( ~ ~ ( ~ ( aElement0 @ sK21_SX0 )
| ( ( sdtasdt0 @ xa @ sK21_SX0 )
!= xa ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[813]) ).
thf(846,plain,
! [SV67: $i] :
( ( ( ~ ( aElementOf0 @ SV67 @ xI ) )
= $true )
| ( ( ~ ( ~ ! [SY165: $i] :
( ~ ( aElementOf0 @ SY165 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SV67 @ SY165 ) @ xI ) )
| ~ ! [SY166: $i] :
( ~ ( aElement0 @ SY166 )
| ( aElementOf0 @ ( sdtasdt0 @ SY166 @ SV67 ) @ xI ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[814]) ).
thf(847,plain,
! [SV54: $i] :
( ( ( ~ ~ ( ~ ( aElement0 @ ( sK22_SY149 @ SV54 ) )
| ( ( sdtasdt0 @ xa @ ( sK22_SY149 @ SV54 ) )
!= SV54 ) ) )
= $false )
| ( ( aElementOf0 @ SV54 @ ( slsdtgt0 @ xa ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[815]) ).
thf(848,plain,
! [SV54: $i,SV68: $i] :
( ( ( ~ ~ ( ~ ( aElement0 @ SV68 )
| ( ( sdtasdt0 @ xa @ SV68 )
!= SV54 ) ) )
= $true )
| ( ( aElementOf0 @ SV54 @ ( slsdtgt0 @ xa ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[816]) ).
thf(849,plain,
! [SV50: $i] :
( ( ( ~ ( aElement0 @ ( sK16_SY145 @ SV50 ) ) )
= $false )
| ( ( aElementOf0 @ SV50 @ ( slsdtgt0 @ xb ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[817]) ).
thf(850,plain,
! [SV50: $i] :
( ( ( ( sdtasdt0 @ xb @ ( sK16_SY145 @ SV50 ) )
!= SV50 )
= $false )
| ( ( aElementOf0 @ SV50 @ ( slsdtgt0 @ xb ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[817]) ).
thf(851,plain,
! [SV50: $i,SV63: $i] :
( ( ( ~ ( aElement0 @ SV63 ) )
= $true )
| ( ( ( sdtasdt0 @ xb @ SV63 )
!= SV50 )
= $true )
| ( ( aElementOf0 @ SV50 @ ( slsdtgt0 @ xb ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[818]) ).
thf(852,plain,
! [SV47: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ ( sK12_SY138 @ SV47 ) @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ ( sK17_SY154 @ SV47 ) @ ( slsdtgt0 @ xb ) ) ) )
= $false )
| ( ( aElementOf0 @ SV47 @ xI )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[819]) ).
thf(853,plain,
! [SV47: $i] :
( ( ( ( sdtpldt0 @ ( sK12_SY138 @ SV47 ) @ ( sK17_SY154 @ SV47 ) )
!= SV47 )
= $false )
| ( ( aElementOf0 @ SV47 @ xI )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[819]) ).
thf(854,plain,
! [SV47: $i,SV64: $i,SV56: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ SV56 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SV64 @ ( slsdtgt0 @ xb ) ) ) )
= $true )
| ( ( ( sdtpldt0 @ SV56 @ SV64 )
!= SV47 )
= $true )
| ( ( aElementOf0 @ SV47 @ xI )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[820]) ).
thf(855,plain,
! [SV35: $i,SV16: $i,SV60: $i,SV57: $i] :
( ( ( aElement0 @ SV57 )
= $false )
| ( ( ~ ( aElement0 @ SV60 ) )
= $true )
| ( ( ~ ! [SY160: $i] :
~ ~ ( ~ ~ ( ~ ( aElement0 @ SY160 )
| ~ ( sdteqdtlpzmzozddtrp0 @ SY160 @ SV57 @ SV16 ) )
| ~ ( sdteqdtlpzmzozddtrp0 @ SY160 @ SV60 @ SV35 ) ) )
= $true )
| ( ( aElement0 @ ( sK7_SY131 @ SV35 @ SV16 ) )
= $true )
| ( ( aIdeal0 @ SV16 )
= $false )
| ( ( aIdeal0 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[821]) ).
thf(856,plain,
! [SV35: $i,SV16: $i,SV55: $i,SV58: $i] :
( ( ( aElement0 @ SV58 )
= $false )
| ( ( aElement0 @ SV55 )
= $false )
| ( ( ~ ! [SY158: $i] :
~ ~ ( ~ ~ ( ~ ( aElement0 @ SY158 )
| ~ ( sdteqdtlpzmzozddtrp0 @ SY158 @ SV55 @ SV16 ) )
| ~ ( sdteqdtlpzmzozddtrp0 @ SY158 @ SV58 @ SV35 ) ) )
= $true )
| ( ( aElementOf0 @ ( sK7_SY131 @ SV35 @ SV16 ) @ ( sdtpldt1 @ SV16 @ SV35 ) )
= $false )
| ( ( aIdeal0 @ SV16 )
= $false )
| ( ( aIdeal0 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[822]) ).
thf(857,plain,
! [SV49: $i,SV65: $i] :
( ( ( ~ ( aElement0 @ SV65 )
| ( ( sdtasdt0 @ xu @ SV65 )
!= xb ) )
= $true )
| ( ( aElement0 @ SV49 )
= $false )
| ( ( ( sdtasdt0 @ xu @ SV49 )
= xa )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[823]) ).
thf(858,plain,
( ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ xc )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xc @ SX0 )
!= xa ) ) )
| ~ ( doDivides0 @ xc @ xa ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[824]) ).
thf(859,plain,
( ( ~ ( aDivisorOf0 @ xc @ xa ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[824]) ).
thf(860,plain,
( ( ~ ( aElement0 @ sK18_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[825]) ).
thf(861,plain,
( ( ( sdtasdt0 @ xc @ sK18_SX0 )
!= xb )
= $false ),
inference(extcnf_or_neg,[status(thm)],[825]) ).
thf(862,plain,
! [SV48: $i,SV69: $i] :
( ( ( ~ ~ ( ~ ( aElement0 @ SV69 )
| ( ( sdtasdt0 @ SV48 @ SV69 )
!= xa ) ) )
= $true )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( ~ ( ~ ! [SY143: $i] :
~ ~ ( ~ ( aElement0 @ SY143 )
| ( ( sdtasdt0 @ SV48 @ SY143 )
!= xb ) )
| ( doDivides0 @ SV48 @ xb )
| ( aDivisorOf0 @ SV48 @ xb ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) )
| ~ ( doDivides0 @ SV48 @ xc ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[826]) ).
thf(863,plain,
! [SV48: $i] :
( ( ( ~ ! [SY143: $i] :
~ ~ ( ~ ( aElement0 @ SY143 )
| ( ( sdtasdt0 @ SV48 @ SY143 )
!= xb ) )
| ( doDivides0 @ SV48 @ xb ) )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( doDivides0 @ SV48 @ xa )
= $false )
| ( ( ~ ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) )
| ~ ( doDivides0 @ SV48 @ xc ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[827]) ).
thf(864,plain,
! [SV48: $i] :
( ( ( aDivisorOf0 @ SV48 @ xb )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( doDivides0 @ SV48 @ xa )
= $false )
| ( ( ~ ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) )
| ~ ( doDivides0 @ SV48 @ xc ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[827]) ).
thf(865,plain,
! [SV48: $i,SV66: $i] :
( ( ( ~ ( aElement0 @ SV66 )
| ( ( sdtasdt0 @ SV48 @ SV66 )
!= xb ) )
= $true )
| ( ( aDivisorOf0 @ SV48 @ xa )
= $false )
| ( ( ~ ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) )
| ~ ( doDivides0 @ SV48 @ xc ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[828]) ).
thf(866,plain,
! [SV48: $i] :
( ( ( ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) ) )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xa )
= $false )
| ( ( doDivides0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[829]) ).
thf(867,plain,
! [SV48: $i] :
( ( ( ~ ~ ( ~ ( aElement0 @ ( sK23_SY144 @ SV48 ) )
| ( ( sdtasdt0 @ SV48 @ ( sK23_SY144 @ SV48 ) )
!= xc ) ) )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xa )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[831]) ).
thf(868,plain,
! [SV1: $i,SV27: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ ( sK13_SY116 @ SV27 @ SV1 ) )
| ~ ( aElement0 @ ( sK19_SY159 @ SV1 @ SV27 ) ) )
| ( SV1
!= ( sdtpldt0 @ ( sdtasdt0 @ ( sK13_SY116 @ SV27 @ SV1 ) @ SV27 ) @ ( sK19_SY159 @ SV1 @ SV27 ) ) ) ) )
= $false )
| ( ( aElement0 @ SV27 )
= $false )
| ( ( aElement0 @ SV1 )
= $false )
| ( ( SV27 = sz00 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[832]) ).
thf(869,plain,
! [SV27: $i,SV1: $i] :
( ( ( ~ ( ~ ( ( ( sK19_SY159 @ SV1 @ SV27 )
!= sz00 ) )
| ( iLess0 @ ( sbrdtbr0 @ ( sK19_SY159 @ SV1 @ SV27 ) ) @ ( sbrdtbr0 @ SV27 ) ) ) )
= $false )
| ( ( aElement0 @ SV27 )
= $false )
| ( ( aElement0 @ SV1 )
= $false )
| ( ( SV27 = sz00 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[832]) ).
thf(870,plain,
! [SV61: $i] :
( ( ( aElementOf0 @ SV61 @ ( slsdtgt0 @ xa ) )
= $false )
| ( ( ~ ! [SY161: $i] :
~ ~ ( ~ ( aElement0 @ SY161 )
| ( ( sdtasdt0 @ xa @ SY161 )
!= SV61 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[833]) ).
thf(871,plain,
! [SV61: $i] :
( ( ( ~ ! [SY162: $i] :
~ ~ ( ~ ( aElement0 @ SY162 )
| ( ( sdtasdt0 @ xa @ SY162 )
!= SV61 ) ) )
= $false )
| ( ( aElementOf0 @ SV61 @ ( slsdtgt0 @ xa ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[834]) ).
thf(872,plain,
! [SV62: $i] :
( ( ( aElementOf0 @ SV62 @ ( slsdtgt0 @ xb ) )
= $false )
| ( ( ~ ! [SY163: $i] :
~ ~ ( ~ ( aElement0 @ SY163 )
| ( ( sdtasdt0 @ xb @ SY163 )
!= SV62 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[835]) ).
thf(873,plain,
! [SV62: $i] :
( ( ( ~ ! [SY164: $i] :
~ ~ ( ~ ( aElement0 @ SY164 )
| ( ( sdtasdt0 @ xb @ SY164 )
!= SV62 ) ) )
= $false )
| ( ( aElementOf0 @ SV62 @ ( slsdtgt0 @ xb ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[836]) ).
thf(874,plain,
( ( ~ ( ~ ( aElementOf0 @ sK8_SY124 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ sK14_SY153 @ ( slsdtgt0 @ xb ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[837]) ).
thf(875,plain,
( ( ( sdtpldt0 @ sK8_SY124 @ sK14_SY153 )
= sK1_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[838]) ).
thf(876,plain,
( ( aElementOf0 @ sK6_SX0 @ ( slsdtgt0 @ xa ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[840]) ).
thf(877,plain,
( ( aElementOf0 @ sK10_SY147 @ ( slsdtgt0 @ xb ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[841]) ).
thf(878,plain,
! [SV44: $i,SV59: $i,SV53: $i] :
( ( ( ~ ( aElementOf0 @ SV53 @ ( slsdtgt0 @ xa ) ) )
= $true )
| ( ( ~ ( aElementOf0 @ SV59 @ ( slsdtgt0 @ xb ) ) )
= $true )
| ( ( ( sdtpldt0 @ SV53 @ SV59 )
!= SV44 )
= $true )
| ( ( ~ ( ( SV44 != sz00 ) ) )
= $true )
| ( ( ~ ( iLess0 @ ( sbrdtbr0 @ SV44 ) @ ( sbrdtbr0 @ xu ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[842]) ).
thf(879,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xa @ SX0 )
!= sz00 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[843]) ).
thf(880,plain,
( ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xa ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[844]) ).
thf(881,plain,
( ( ~ ( ~ ( aElement0 @ sK21_SX0 )
| ( ( sdtasdt0 @ xa @ sK21_SX0 )
!= xa ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[845]) ).
thf(882,plain,
! [SV67: $i] :
( ( ( aElementOf0 @ SV67 @ xI )
= $false )
| ( ( ~ ( ~ ! [SY165: $i] :
( ~ ( aElementOf0 @ SY165 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SV67 @ SY165 ) @ xI ) )
| ~ ! [SY166: $i] :
( ~ ( aElement0 @ SY166 )
| ( aElementOf0 @ ( sdtasdt0 @ SY166 @ SV67 ) @ xI ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[846]) ).
thf(883,plain,
! [SV54: $i] :
( ( ( ~ ( ~ ( aElement0 @ ( sK22_SY149 @ SV54 ) )
| ( ( sdtasdt0 @ xa @ ( sK22_SY149 @ SV54 ) )
!= SV54 ) ) )
= $true )
| ( ( aElementOf0 @ SV54 @ ( slsdtgt0 @ xa ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[847]) ).
thf(884,plain,
! [SV54: $i,SV68: $i] :
( ( ( ~ ( ~ ( aElement0 @ SV68 )
| ( ( sdtasdt0 @ xa @ SV68 )
!= SV54 ) ) )
= $false )
| ( ( aElementOf0 @ SV54 @ ( slsdtgt0 @ xa ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[848]) ).
thf(885,plain,
! [SV50: $i] :
( ( ( aElement0 @ ( sK16_SY145 @ SV50 ) )
= $true )
| ( ( aElementOf0 @ SV50 @ ( slsdtgt0 @ xb ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[849]) ).
thf(886,plain,
! [SV50: $i] :
( ( ( ( sdtasdt0 @ xb @ ( sK16_SY145 @ SV50 ) )
= SV50 )
= $true )
| ( ( aElementOf0 @ SV50 @ ( slsdtgt0 @ xb ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[850]) ).
thf(887,plain,
! [SV50: $i,SV63: $i] :
( ( ( aElement0 @ SV63 )
= $false )
| ( ( ( sdtasdt0 @ xb @ SV63 )
!= SV50 )
= $true )
| ( ( aElementOf0 @ SV50 @ ( slsdtgt0 @ xb ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[851]) ).
thf(888,plain,
! [SV47: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ ( sK12_SY138 @ SV47 ) @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ ( sK17_SY154 @ SV47 ) @ ( slsdtgt0 @ xb ) ) ) )
= $true )
| ( ( aElementOf0 @ SV47 @ xI )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[852]) ).
thf(889,plain,
! [SV47: $i] :
( ( ( ( sdtpldt0 @ ( sK12_SY138 @ SV47 ) @ ( sK17_SY154 @ SV47 ) )
= SV47 )
= $true )
| ( ( aElementOf0 @ SV47 @ xI )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[853]) ).
thf(890,plain,
! [SV47: $i,SV64: $i,SV56: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ SV56 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SV64 @ ( slsdtgt0 @ xb ) ) ) )
= $false )
| ( ( ( sdtpldt0 @ SV56 @ SV64 )
!= SV47 )
= $true )
| ( ( aElementOf0 @ SV47 @ xI )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[854]) ).
thf(891,plain,
! [SV35: $i,SV16: $i,SV57: $i,SV60: $i] :
( ( ( aElement0 @ SV60 )
= $false )
| ( ( aElement0 @ SV57 )
= $false )
| ( ( ~ ! [SY160: $i] :
~ ~ ( ~ ~ ( ~ ( aElement0 @ SY160 )
| ~ ( sdteqdtlpzmzozddtrp0 @ SY160 @ SV57 @ SV16 ) )
| ~ ( sdteqdtlpzmzozddtrp0 @ SY160 @ SV60 @ SV35 ) ) )
= $true )
| ( ( aElement0 @ ( sK7_SY131 @ SV35 @ SV16 ) )
= $true )
| ( ( aIdeal0 @ SV16 )
= $false )
| ( ( aIdeal0 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[855]) ).
thf(892,plain,
! [SV35: $i,SV58: $i,SV16: $i,SV55: $i] :
( ( ( ! [SY158: $i] :
~ ~ ( ~ ~ ( ~ ( aElement0 @ SY158 )
| ~ ( sdteqdtlpzmzozddtrp0 @ SY158 @ SV55 @ SV16 ) )
| ~ ( sdteqdtlpzmzozddtrp0 @ SY158 @ SV58 @ SV35 ) ) )
= $false )
| ( ( aElement0 @ SV55 )
= $false )
| ( ( aElement0 @ SV58 )
= $false )
| ( ( aElementOf0 @ ( sK7_SY131 @ SV35 @ SV16 ) @ ( sdtpldt1 @ SV16 @ SV35 ) )
= $false )
| ( ( aIdeal0 @ SV16 )
= $false )
| ( ( aIdeal0 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[856]) ).
thf(893,plain,
! [SV49: $i,SV65: $i] :
( ( ( ~ ( aElement0 @ SV65 ) )
= $true )
| ( ( ( sdtasdt0 @ xu @ SV65 )
!= xb )
= $true )
| ( ( aElement0 @ SV49 )
= $false )
| ( ( ( sdtasdt0 @ xu @ SV49 )
= xa )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[857]) ).
thf(894,plain,
( ( ~ ( ~ ~ ( ~ ( aElement0 @ xc )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xc @ SX0 )
!= xa ) ) )
| ~ ( doDivides0 @ xc @ xa ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[858]) ).
thf(895,plain,
( ( aDivisorOf0 @ xc @ xa )
= $true ),
inference(extcnf_not_neg,[status(thm)],[859]) ).
thf(896,plain,
( ( aElement0 @ sK18_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[860]) ).
thf(897,plain,
( ( ( sdtasdt0 @ xc @ sK18_SX0 )
= xb )
= $true ),
inference(extcnf_not_neg,[status(thm)],[861]) ).
thf(898,plain,
! [SV48: $i,SV69: $i] :
( ( ( ~ ( ~ ( aElement0 @ SV69 )
| ( ( sdtasdt0 @ SV48 @ SV69 )
!= xa ) ) )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( ~ ( ~ ! [SY143: $i] :
~ ~ ( ~ ( aElement0 @ SY143 )
| ( ( sdtasdt0 @ SV48 @ SY143 )
!= xb ) )
| ( doDivides0 @ SV48 @ xb )
| ( aDivisorOf0 @ SV48 @ xb ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) )
| ~ ( doDivides0 @ SV48 @ xc ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[862]) ).
thf(899,plain,
! [SV48: $i] :
( ( ( ~ ! [SY143: $i] :
~ ~ ( ~ ( aElement0 @ SY143 )
| ( ( sdtasdt0 @ SV48 @ SY143 )
!= xb ) ) )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( doDivides0 @ SV48 @ xa )
= $false )
| ( ( ~ ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) )
| ~ ( doDivides0 @ SV48 @ xc ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[863]) ).
thf(900,plain,
! [SV48: $i] :
( ( ( doDivides0 @ SV48 @ xb )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( doDivides0 @ SV48 @ xa )
= $false )
| ( ( ~ ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) )
| ~ ( doDivides0 @ SV48 @ xc ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[863]) ).
thf(901,plain,
! [SV48: $i] :
( ( ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) )
| ~ ( doDivides0 @ SV48 @ xc ) )
= $false )
| ( ( doDivides0 @ SV48 @ xa )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[864]) ).
thf(902,plain,
! [SV48: $i,SV66: $i] :
( ( ( ~ ( aElement0 @ SV66 ) )
= $true )
| ( ( ( sdtasdt0 @ SV48 @ SV66 )
!= xb )
= $true )
| ( ( aDivisorOf0 @ SV48 @ xa )
= $false )
| ( ( ~ ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) )
| ~ ( doDivides0 @ SV48 @ xc ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[865]) ).
thf(903,plain,
! [SV48: $i] :
( ( ( ~ ~ ( ~ ( aElement0 @ ( sK24_SY144 @ SV48 ) )
| ( ( sdtasdt0 @ SV48 @ ( sK24_SY144 @ SV48 ) )
!= xc ) ) )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xa )
= $false )
| ( ( doDivides0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[866]) ).
thf(904,plain,
! [SV48: $i] :
( ( ( ~ ( ~ ( aElement0 @ ( sK23_SY144 @ SV48 ) )
| ( ( sdtasdt0 @ SV48 @ ( sK23_SY144 @ SV48 ) )
!= xc ) ) )
= $true )
| ( ( aDivisorOf0 @ SV48 @ xa )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[867]) ).
thf(905,plain,
! [SV1: $i,SV27: $i] :
( ( ( ~ ( ~ ~ ( ~ ( aElement0 @ ( sK13_SY116 @ SV27 @ SV1 ) )
| ~ ( aElement0 @ ( sK19_SY159 @ SV1 @ SV27 ) ) )
| ( SV1
!= ( sdtpldt0 @ ( sdtasdt0 @ ( sK13_SY116 @ SV27 @ SV1 ) @ SV27 ) @ ( sK19_SY159 @ SV1 @ SV27 ) ) ) ) )
= $true )
| ( ( aElement0 @ SV27 )
= $false )
| ( ( aElement0 @ SV1 )
= $false )
| ( ( SV27 = sz00 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[868]) ).
thf(906,plain,
! [SV27: $i,SV1: $i] :
( ( ( ~ ( ( ( sK19_SY159 @ SV1 @ SV27 )
!= sz00 ) )
| ( iLess0 @ ( sbrdtbr0 @ ( sK19_SY159 @ SV1 @ SV27 ) ) @ ( sbrdtbr0 @ SV27 ) ) )
= $true )
| ( ( aElement0 @ SV27 )
= $false )
| ( ( aElement0 @ SV1 )
= $false )
| ( ( SV27 = sz00 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[869]) ).
thf(907,plain,
! [SV61: $i] :
( ( ( ! [SY161: $i] :
~ ~ ( ~ ( aElement0 @ SY161 )
| ( ( sdtasdt0 @ xa @ SY161 )
!= SV61 ) ) )
= $false )
| ( ( aElementOf0 @ SV61 @ ( slsdtgt0 @ xa ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[870]) ).
thf(908,plain,
! [SV61: $i] :
( ( ( ! [SY162: $i] :
~ ~ ( ~ ( aElement0 @ SY162 )
| ( ( sdtasdt0 @ xa @ SY162 )
!= SV61 ) ) )
= $true )
| ( ( aElementOf0 @ SV61 @ ( slsdtgt0 @ xa ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[871]) ).
thf(909,plain,
! [SV62: $i] :
( ( ( ! [SY163: $i] :
~ ~ ( ~ ( aElement0 @ SY163 )
| ( ( sdtasdt0 @ xb @ SY163 )
!= SV62 ) ) )
= $false )
| ( ( aElementOf0 @ SV62 @ ( slsdtgt0 @ xb ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[872]) ).
thf(910,plain,
! [SV62: $i] :
( ( ( ! [SY164: $i] :
~ ~ ( ~ ( aElement0 @ SY164 )
| ( ( sdtasdt0 @ xb @ SY164 )
!= SV62 ) ) )
= $true )
| ( ( aElementOf0 @ SV62 @ ( slsdtgt0 @ xb ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[873]) ).
thf(911,plain,
( ( ~ ( aElementOf0 @ sK8_SY124 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ sK14_SY153 @ ( slsdtgt0 @ xb ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[874]) ).
thf(912,plain,
! [SV44: $i,SV59: $i,SV53: $i] :
( ( ( aElementOf0 @ SV53 @ ( slsdtgt0 @ xa ) )
= $false )
| ( ( ~ ( aElementOf0 @ SV59 @ ( slsdtgt0 @ xb ) ) )
= $true )
| ( ( ( sdtpldt0 @ SV53 @ SV59 )
!= SV44 )
= $true )
| ( ( ~ ( ( SV44 != sz00 ) ) )
= $true )
| ( ( ~ ( iLess0 @ ( sbrdtbr0 @ SV44 ) @ ( sbrdtbr0 @ xu ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[878]) ).
thf(913,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xa @ SX0 )
!= sz00 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[879]) ).
thf(914,plain,
( ( ~ ( aElement0 @ sK21_SX0 )
| ( ( sdtasdt0 @ xa @ sK21_SX0 )
!= xa ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[881]) ).
thf(915,plain,
! [SV67: $i] :
( ( ( ~ ! [SY165: $i] :
( ~ ( aElementOf0 @ SY165 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SV67 @ SY165 ) @ xI ) )
| ~ ! [SY166: $i] :
( ~ ( aElement0 @ SY166 )
| ( aElementOf0 @ ( sdtasdt0 @ SY166 @ SV67 ) @ xI ) ) )
= $false )
| ( ( aElementOf0 @ SV67 @ xI )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[882]) ).
thf(916,plain,
! [SV54: $i] :
( ( ( ~ ( aElement0 @ ( sK22_SY149 @ SV54 ) )
| ( ( sdtasdt0 @ xa @ ( sK22_SY149 @ SV54 ) )
!= SV54 ) )
= $false )
| ( ( aElementOf0 @ SV54 @ ( slsdtgt0 @ xa ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[883]) ).
thf(917,plain,
! [SV54: $i,SV68: $i] :
( ( ( ~ ( aElement0 @ SV68 )
| ( ( sdtasdt0 @ xa @ SV68 )
!= SV54 ) )
= $true )
| ( ( aElementOf0 @ SV54 @ ( slsdtgt0 @ xa ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[884]) ).
thf(918,plain,
! [SV50: $i,SV63: $i] :
( ( ( ( sdtasdt0 @ xb @ SV63 )
= SV50 )
= $false )
| ( ( aElement0 @ SV63 )
= $false )
| ( ( aElementOf0 @ SV50 @ ( slsdtgt0 @ xb ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[887]) ).
thf(919,plain,
! [SV47: $i] :
( ( ( ~ ( aElementOf0 @ ( sK12_SY138 @ SV47 ) @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ ( sK17_SY154 @ SV47 ) @ ( slsdtgt0 @ xb ) ) )
= $false )
| ( ( aElementOf0 @ SV47 @ xI )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[888]) ).
thf(920,plain,
! [SV47: $i,SV64: $i,SV56: $i] :
( ( ( ~ ( aElementOf0 @ SV56 @ ( slsdtgt0 @ xa ) )
| ~ ( aElementOf0 @ SV64 @ ( slsdtgt0 @ xb ) ) )
= $true )
| ( ( ( sdtpldt0 @ SV56 @ SV64 )
!= SV47 )
= $true )
| ( ( aElementOf0 @ SV47 @ xI )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[890]) ).
thf(921,plain,
! [SV35: $i,SV60: $i,SV16: $i,SV57: $i] :
( ( ( ! [SY160: $i] :
~ ~ ( ~ ~ ( ~ ( aElement0 @ SY160 )
| ~ ( sdteqdtlpzmzozddtrp0 @ SY160 @ SV57 @ SV16 ) )
| ~ ( sdteqdtlpzmzozddtrp0 @ SY160 @ SV60 @ SV35 ) ) )
= $false )
| ( ( aElement0 @ SV57 )
= $false )
| ( ( aElement0 @ SV60 )
= $false )
| ( ( aElement0 @ ( sK7_SY131 @ SV35 @ SV16 ) )
= $true )
| ( ( aIdeal0 @ SV16 )
= $false )
| ( ( aIdeal0 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[891]) ).
thf(922,plain,
! [SV55: $i,SV16: $i,SV58: $i,SV35: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ ( sK25_SY158 @ SV35 @ SV58 @ SV16 @ SV55 ) )
| ~ ( sdteqdtlpzmzozddtrp0 @ ( sK25_SY158 @ SV35 @ SV58 @ SV16 @ SV55 ) @ SV55 @ SV16 ) )
| ~ ( sdteqdtlpzmzozddtrp0 @ ( sK25_SY158 @ SV35 @ SV58 @ SV16 @ SV55 ) @ SV58 @ SV35 ) ) )
= $false )
| ( ( aElement0 @ SV55 )
= $false )
| ( ( aElement0 @ SV58 )
= $false )
| ( ( aElementOf0 @ ( sK7_SY131 @ SV35 @ SV16 ) @ ( sdtpldt1 @ SV16 @ SV35 ) )
= $false )
| ( ( aIdeal0 @ SV16 )
= $false )
| ( ( aIdeal0 @ SV35 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[892]) ).
thf(923,plain,
! [SV49: $i,SV65: $i] :
( ( ( aElement0 @ SV65 )
= $false )
| ( ( ( sdtasdt0 @ xu @ SV65 )
!= xb )
= $true )
| ( ( aElement0 @ SV49 )
= $false )
| ( ( ( sdtasdt0 @ xu @ SV49 )
= xa )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[893]) ).
thf(924,plain,
( ( ~ ~ ( ~ ( aElement0 @ xc )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xc @ SX0 )
!= xa ) ) )
| ~ ( doDivides0 @ xc @ xa ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[894]) ).
thf(925,plain,
! [SV48: $i,SV69: $i] :
( ( ( ~ ( aElement0 @ SV69 )
| ( ( sdtasdt0 @ SV48 @ SV69 )
!= xa ) )
= $true )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( ~ ( ~ ! [SY143: $i] :
~ ~ ( ~ ( aElement0 @ SY143 )
| ( ( sdtasdt0 @ SV48 @ SY143 )
!= xb ) )
| ( doDivides0 @ SV48 @ xb )
| ( aDivisorOf0 @ SV48 @ xb ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) )
| ~ ( doDivides0 @ SV48 @ xc ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[898]) ).
thf(926,plain,
! [SV48: $i] :
( ( ( ! [SY143: $i] :
~ ~ ( ~ ( aElement0 @ SY143 )
| ( ( sdtasdt0 @ SV48 @ SY143 )
!= xb ) ) )
= $true )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( doDivides0 @ SV48 @ xa )
= $false )
| ( ( ~ ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) )
| ~ ( doDivides0 @ SV48 @ xc ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[899]) ).
thf(927,plain,
! [SV48: $i] :
( ( ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) )
| ~ ( doDivides0 @ SV48 @ xc ) )
= $false )
| ( ( doDivides0 @ SV48 @ xa )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( doDivides0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[900]) ).
thf(928,plain,
! [SV48: $i] :
( ( ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) ) )
= $false )
| ( ( doDivides0 @ SV48 @ xa )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[901]) ).
thf(929,plain,
! [SV48: $i] :
( ( ( ~ ( doDivides0 @ SV48 @ xc ) )
= $false )
| ( ( doDivides0 @ SV48 @ xa )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[901]) ).
thf(930,plain,
! [SV48: $i,SV66: $i] :
( ( ( aElement0 @ SV66 )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV66 )
!= xb )
= $true )
| ( ( aDivisorOf0 @ SV48 @ xa )
= $false )
| ( ( ~ ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) )
| ~ ( doDivides0 @ SV48 @ xc ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[902]) ).
thf(931,plain,
! [SV48: $i] :
( ( ( ~ ( ~ ( aElement0 @ ( sK24_SY144 @ SV48 ) )
| ( ( sdtasdt0 @ SV48 @ ( sK24_SY144 @ SV48 ) )
!= xc ) ) )
= $true )
| ( ( aDivisorOf0 @ SV48 @ xa )
= $false )
| ( ( doDivides0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[903]) ).
thf(932,plain,
! [SV48: $i] :
( ( ( ~ ( aElement0 @ ( sK23_SY144 @ SV48 ) )
| ( ( sdtasdt0 @ SV48 @ ( sK23_SY144 @ SV48 ) )
!= xc ) )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xa )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[904]) ).
thf(933,plain,
! [SV1: $i,SV27: $i] :
( ( ( ~ ~ ( ~ ( aElement0 @ ( sK13_SY116 @ SV27 @ SV1 ) )
| ~ ( aElement0 @ ( sK19_SY159 @ SV1 @ SV27 ) ) )
| ( SV1
!= ( sdtpldt0 @ ( sdtasdt0 @ ( sK13_SY116 @ SV27 @ SV1 ) @ SV27 ) @ ( sK19_SY159 @ SV1 @ SV27 ) ) ) )
= $false )
| ( ( aElement0 @ SV27 )
= $false )
| ( ( aElement0 @ SV1 )
= $false )
| ( ( SV27 = sz00 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[905]) ).
thf(934,plain,
! [SV27: $i,SV1: $i] :
( ( ( ~ ( ( ( sK19_SY159 @ SV1 @ SV27 )
!= sz00 ) ) )
= $true )
| ( ( iLess0 @ ( sbrdtbr0 @ ( sK19_SY159 @ SV1 @ SV27 ) ) @ ( sbrdtbr0 @ SV27 ) )
= $true )
| ( ( aElement0 @ SV27 )
= $false )
| ( ( aElement0 @ SV1 )
= $false )
| ( ( SV27 = sz00 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[906]) ).
thf(935,plain,
! [SV61: $i] :
( ( ( ~ ~ ( ~ ( aElement0 @ ( sK26_SY161 @ SV61 ) )
| ( ( sdtasdt0 @ xa @ ( sK26_SY161 @ SV61 ) )
!= SV61 ) ) )
= $false )
| ( ( aElementOf0 @ SV61 @ ( slsdtgt0 @ xa ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[907]) ).
thf(936,plain,
! [SV61: $i,SV70: $i] :
( ( ( ~ ~ ( ~ ( aElement0 @ SV70 )
| ( ( sdtasdt0 @ xa @ SV70 )
!= SV61 ) ) )
= $true )
| ( ( aElementOf0 @ SV61 @ ( slsdtgt0 @ xa ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[908]) ).
thf(937,plain,
! [SV62: $i] :
( ( ( ~ ~ ( ~ ( aElement0 @ ( sK27_SY163 @ SV62 ) )
| ( ( sdtasdt0 @ xb @ ( sK27_SY163 @ SV62 ) )
!= SV62 ) ) )
= $false )
| ( ( aElementOf0 @ SV62 @ ( slsdtgt0 @ xb ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[909]) ).
thf(938,plain,
! [SV62: $i,SV71: $i] :
( ( ( ~ ~ ( ~ ( aElement0 @ SV71 )
| ( ( sdtasdt0 @ xb @ SV71 )
!= SV62 ) ) )
= $true )
| ( ( aElementOf0 @ SV62 @ ( slsdtgt0 @ xb ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[910]) ).
thf(939,plain,
( ( ~ ( aElementOf0 @ sK8_SY124 @ ( slsdtgt0 @ xa ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[911]) ).
thf(940,plain,
( ( ~ ( aElementOf0 @ sK14_SY153 @ ( slsdtgt0 @ xb ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[911]) ).
thf(941,plain,
! [SV44: $i,SV53: $i,SV59: $i] :
( ( ( aElementOf0 @ SV59 @ ( slsdtgt0 @ xb ) )
= $false )
| ( ( aElementOf0 @ SV53 @ ( slsdtgt0 @ xa ) )
= $false )
| ( ( ( sdtpldt0 @ SV53 @ SV59 )
!= SV44 )
= $true )
| ( ( ~ ( ( SV44 != sz00 ) ) )
= $true )
| ( ( ~ ( iLess0 @ ( sbrdtbr0 @ SV44 ) @ ( sbrdtbr0 @ xu ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[912]) ).
thf(942,plain,
( ( ~ ~ ( ~ ( aElement0 @ sK28_SX0 )
| ( ( sdtasdt0 @ xa @ sK28_SX0 )
!= sz00 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[913]) ).
thf(943,plain,
( ( ~ ( aElement0 @ sK21_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[914]) ).
thf(944,plain,
( ( ( sdtasdt0 @ xa @ sK21_SX0 )
!= xa )
= $false ),
inference(extcnf_or_neg,[status(thm)],[914]) ).
thf(945,plain,
! [SV67: $i] :
( ( ( ~ ! [SY165: $i] :
( ~ ( aElementOf0 @ SY165 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SV67 @ SY165 ) @ xI ) ) )
= $false )
| ( ( aElementOf0 @ SV67 @ xI )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[915]) ).
thf(946,plain,
! [SV67: $i] :
( ( ( ~ ! [SY166: $i] :
( ~ ( aElement0 @ SY166 )
| ( aElementOf0 @ ( sdtasdt0 @ SY166 @ SV67 ) @ xI ) ) )
= $false )
| ( ( aElementOf0 @ SV67 @ xI )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[915]) ).
thf(947,plain,
! [SV54: $i] :
( ( ( ~ ( aElement0 @ ( sK22_SY149 @ SV54 ) ) )
= $false )
| ( ( aElementOf0 @ SV54 @ ( slsdtgt0 @ xa ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[916]) ).
thf(948,plain,
! [SV54: $i] :
( ( ( ( sdtasdt0 @ xa @ ( sK22_SY149 @ SV54 ) )
!= SV54 )
= $false )
| ( ( aElementOf0 @ SV54 @ ( slsdtgt0 @ xa ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[916]) ).
thf(949,plain,
! [SV54: $i,SV68: $i] :
( ( ( ~ ( aElement0 @ SV68 ) )
= $true )
| ( ( ( sdtasdt0 @ xa @ SV68 )
!= SV54 )
= $true )
| ( ( aElementOf0 @ SV54 @ ( slsdtgt0 @ xa ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[917]) ).
thf(950,plain,
! [SV47: $i] :
( ( ( ~ ( aElementOf0 @ ( sK12_SY138 @ SV47 ) @ ( slsdtgt0 @ xa ) ) )
= $false )
| ( ( aElementOf0 @ SV47 @ xI )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[919]) ).
thf(951,plain,
! [SV47: $i] :
( ( ( ~ ( aElementOf0 @ ( sK17_SY154 @ SV47 ) @ ( slsdtgt0 @ xb ) ) )
= $false )
| ( ( aElementOf0 @ SV47 @ xI )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[919]) ).
thf(952,plain,
! [SV47: $i,SV64: $i,SV56: $i] :
( ( ( ~ ( aElementOf0 @ SV56 @ ( slsdtgt0 @ xa ) ) )
= $true )
| ( ( ~ ( aElementOf0 @ SV64 @ ( slsdtgt0 @ xb ) ) )
= $true )
| ( ( ( sdtpldt0 @ SV56 @ SV64 )
!= SV47 )
= $true )
| ( ( aElementOf0 @ SV47 @ xI )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[920]) ).
thf(953,plain,
! [SV57: $i,SV16: $i,SV60: $i,SV35: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ ( sK29_SY160 @ SV35 @ SV60 @ SV16 @ SV57 ) )
| ~ ( sdteqdtlpzmzozddtrp0 @ ( sK29_SY160 @ SV35 @ SV60 @ SV16 @ SV57 ) @ SV57 @ SV16 ) )
| ~ ( sdteqdtlpzmzozddtrp0 @ ( sK29_SY160 @ SV35 @ SV60 @ SV16 @ SV57 ) @ SV60 @ SV35 ) ) )
= $false )
| ( ( aElement0 @ SV57 )
= $false )
| ( ( aElement0 @ SV60 )
= $false )
| ( ( aElement0 @ ( sK7_SY131 @ SV35 @ SV16 ) )
= $true )
| ( ( aIdeal0 @ SV16 )
= $false )
| ( ( aIdeal0 @ SV35 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[921]) ).
thf(954,plain,
! [SV55: $i,SV16: $i,SV58: $i,SV35: $i] :
( ( ( ~ ( ~ ~ ( ~ ( aElement0 @ ( sK25_SY158 @ SV35 @ SV58 @ SV16 @ SV55 ) )
| ~ ( sdteqdtlpzmzozddtrp0 @ ( sK25_SY158 @ SV35 @ SV58 @ SV16 @ SV55 ) @ SV55 @ SV16 ) )
| ~ ( sdteqdtlpzmzozddtrp0 @ ( sK25_SY158 @ SV35 @ SV58 @ SV16 @ SV55 ) @ SV58 @ SV35 ) ) )
= $true )
| ( ( aElement0 @ SV55 )
= $false )
| ( ( aElement0 @ SV58 )
= $false )
| ( ( aElementOf0 @ ( sK7_SY131 @ SV35 @ SV16 ) @ ( sdtpldt1 @ SV16 @ SV35 ) )
= $false )
| ( ( aIdeal0 @ SV16 )
= $false )
| ( ( aIdeal0 @ SV35 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[922]) ).
thf(955,plain,
! [SV49: $i,SV65: $i] :
( ( ( ( sdtasdt0 @ xu @ SV65 )
= xb )
= $false )
| ( ( aElement0 @ SV65 )
= $false )
| ( ( aElement0 @ SV49 )
= $false )
| ( ( ( sdtasdt0 @ xu @ SV49 )
= xa )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[923]) ).
thf(956,plain,
( ( ~ ~ ( ~ ( aElement0 @ xc )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xc @ SX0 )
!= xa ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[924]) ).
thf(957,plain,
( ( ~ ( doDivides0 @ xc @ xa ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[924]) ).
thf(958,plain,
! [SV48: $i,SV69: $i] :
( ( ( ~ ( aElement0 @ SV69 ) )
= $true )
| ( ( ( sdtasdt0 @ SV48 @ SV69 )
!= xa )
= $true )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( ~ ( ~ ! [SY143: $i] :
~ ~ ( ~ ( aElement0 @ SY143 )
| ( ( sdtasdt0 @ SV48 @ SY143 )
!= xb ) )
| ( doDivides0 @ SV48 @ xb )
| ( aDivisorOf0 @ SV48 @ xb ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) )
| ~ ( doDivides0 @ SV48 @ xc ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[925]) ).
thf(959,plain,
! [SV48: $i,SV72: $i] :
( ( ( ~ ~ ( ~ ( aElement0 @ SV72 )
| ( ( sdtasdt0 @ SV48 @ SV72 )
!= xb ) ) )
= $true )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( doDivides0 @ SV48 @ xa )
= $false )
| ( ( ~ ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) )
| ~ ( doDivides0 @ SV48 @ xc ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[926]) ).
thf(960,plain,
! [SV48: $i] :
( ( ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) ) )
= $false )
| ( ( doDivides0 @ SV48 @ xa )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( doDivides0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[927]) ).
thf(961,plain,
! [SV48: $i] :
( ( ( ~ ( doDivides0 @ SV48 @ xc ) )
= $false )
| ( ( doDivides0 @ SV48 @ xa )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( doDivides0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[927]) ).
thf(962,plain,
! [SV48: $i] :
( ( ( ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) ) )
= $true )
| ( ( doDivides0 @ SV48 @ xa )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[928]) ).
thf(963,plain,
! [SV48: $i] :
( ( ( doDivides0 @ SV48 @ xc )
= $true )
| ( ( doDivides0 @ SV48 @ xa )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[929]) ).
thf(964,plain,
! [SV66: $i,SV48: $i] :
( ( ( ( sdtasdt0 @ SV48 @ SV66 )
= xb )
= $false )
| ( ( aElement0 @ SV66 )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xa )
= $false )
| ( ( ~ ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) )
| ~ ( doDivides0 @ SV48 @ xc ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[930]) ).
thf(965,plain,
! [SV48: $i] :
( ( ( ~ ( aElement0 @ ( sK24_SY144 @ SV48 ) )
| ( ( sdtasdt0 @ SV48 @ ( sK24_SY144 @ SV48 ) )
!= xc ) )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xa )
= $false )
| ( ( doDivides0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[931]) ).
thf(966,plain,
! [SV48: $i] :
( ( ( ~ ( aElement0 @ ( sK23_SY144 @ SV48 ) ) )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xa )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[932]) ).
thf(967,plain,
! [SV48: $i] :
( ( ( ( sdtasdt0 @ SV48 @ ( sK23_SY144 @ SV48 ) )
!= xc )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xa )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[932]) ).
thf(968,plain,
! [SV1: $i,SV27: $i] :
( ( ( ~ ~ ( ~ ( aElement0 @ ( sK13_SY116 @ SV27 @ SV1 ) )
| ~ ( aElement0 @ ( sK19_SY159 @ SV1 @ SV27 ) ) ) )
= $false )
| ( ( aElement0 @ SV27 )
= $false )
| ( ( aElement0 @ SV1 )
= $false )
| ( ( SV27 = sz00 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[933]) ).
thf(969,plain,
! [SV27: $i,SV1: $i] :
( ( ( SV1
!= ( sdtpldt0 @ ( sdtasdt0 @ ( sK13_SY116 @ SV27 @ SV1 ) @ SV27 ) @ ( sK19_SY159 @ SV1 @ SV27 ) ) )
= $false )
| ( ( aElement0 @ SV27 )
= $false )
| ( ( aElement0 @ SV1 )
= $false )
| ( ( SV27 = sz00 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[933]) ).
thf(970,plain,
! [SV27: $i,SV1: $i] :
( ( ( ( sK19_SY159 @ SV1 @ SV27 )
!= sz00 )
= $false )
| ( ( iLess0 @ ( sbrdtbr0 @ ( sK19_SY159 @ SV1 @ SV27 ) ) @ ( sbrdtbr0 @ SV27 ) )
= $true )
| ( ( aElement0 @ SV27 )
= $false )
| ( ( aElement0 @ SV1 )
= $false )
| ( ( SV27 = sz00 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[934]) ).
thf(971,plain,
! [SV61: $i] :
( ( ( ~ ( ~ ( aElement0 @ ( sK26_SY161 @ SV61 ) )
| ( ( sdtasdt0 @ xa @ ( sK26_SY161 @ SV61 ) )
!= SV61 ) ) )
= $true )
| ( ( aElementOf0 @ SV61 @ ( slsdtgt0 @ xa ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[935]) ).
thf(972,plain,
! [SV61: $i,SV70: $i] :
( ( ( ~ ( ~ ( aElement0 @ SV70 )
| ( ( sdtasdt0 @ xa @ SV70 )
!= SV61 ) ) )
= $false )
| ( ( aElementOf0 @ SV61 @ ( slsdtgt0 @ xa ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[936]) ).
thf(973,plain,
! [SV62: $i] :
( ( ( ~ ( ~ ( aElement0 @ ( sK27_SY163 @ SV62 ) )
| ( ( sdtasdt0 @ xb @ ( sK27_SY163 @ SV62 ) )
!= SV62 ) ) )
= $true )
| ( ( aElementOf0 @ SV62 @ ( slsdtgt0 @ xb ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[937]) ).
thf(974,plain,
! [SV62: $i,SV71: $i] :
( ( ( ~ ( ~ ( aElement0 @ SV71 )
| ( ( sdtasdt0 @ xb @ SV71 )
!= SV62 ) ) )
= $false )
| ( ( aElementOf0 @ SV62 @ ( slsdtgt0 @ xb ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[938]) ).
thf(975,plain,
( ( aElementOf0 @ sK8_SY124 @ ( slsdtgt0 @ xa ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[939]) ).
thf(976,plain,
( ( aElementOf0 @ sK14_SY153 @ ( slsdtgt0 @ xb ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[940]) ).
thf(977,plain,
! [SV44: $i,SV59: $i,SV53: $i] :
( ( ( ( sdtpldt0 @ SV53 @ SV59 )
= SV44 )
= $false )
| ( ( aElementOf0 @ SV53 @ ( slsdtgt0 @ xa ) )
= $false )
| ( ( aElementOf0 @ SV59 @ ( slsdtgt0 @ xb ) )
= $false )
| ( ( ~ ( ( SV44 != sz00 ) ) )
= $true )
| ( ( ~ ( iLess0 @ ( sbrdtbr0 @ SV44 ) @ ( sbrdtbr0 @ xu ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[941]) ).
thf(978,plain,
( ( ~ ( ~ ( aElement0 @ sK28_SX0 )
| ( ( sdtasdt0 @ xa @ sK28_SX0 )
!= sz00 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[942]) ).
thf(979,plain,
( ( aElement0 @ sK21_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[943]) ).
thf(980,plain,
( ( ( sdtasdt0 @ xa @ sK21_SX0 )
= xa )
= $true ),
inference(extcnf_not_neg,[status(thm)],[944]) ).
thf(981,plain,
! [SV67: $i] :
( ( ( ! [SY165: $i] :
( ~ ( aElementOf0 @ SY165 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SV67 @ SY165 ) @ xI ) ) )
= $true )
| ( ( aElementOf0 @ SV67 @ xI )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[945]) ).
thf(982,plain,
! [SV67: $i] :
( ( ( ! [SY166: $i] :
( ~ ( aElement0 @ SY166 )
| ( aElementOf0 @ ( sdtasdt0 @ SY166 @ SV67 ) @ xI ) ) )
= $true )
| ( ( aElementOf0 @ SV67 @ xI )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[946]) ).
thf(983,plain,
! [SV54: $i] :
( ( ( aElement0 @ ( sK22_SY149 @ SV54 ) )
= $true )
| ( ( aElementOf0 @ SV54 @ ( slsdtgt0 @ xa ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[947]) ).
thf(984,plain,
! [SV54: $i] :
( ( ( ( sdtasdt0 @ xa @ ( sK22_SY149 @ SV54 ) )
= SV54 )
= $true )
| ( ( aElementOf0 @ SV54 @ ( slsdtgt0 @ xa ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[948]) ).
thf(985,plain,
! [SV54: $i,SV68: $i] :
( ( ( aElement0 @ SV68 )
= $false )
| ( ( ( sdtasdt0 @ xa @ SV68 )
!= SV54 )
= $true )
| ( ( aElementOf0 @ SV54 @ ( slsdtgt0 @ xa ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[949]) ).
thf(986,plain,
! [SV47: $i] :
( ( ( aElementOf0 @ ( sK12_SY138 @ SV47 ) @ ( slsdtgt0 @ xa ) )
= $true )
| ( ( aElementOf0 @ SV47 @ xI )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[950]) ).
thf(987,plain,
! [SV47: $i] :
( ( ( aElementOf0 @ ( sK17_SY154 @ SV47 ) @ ( slsdtgt0 @ xb ) )
= $true )
| ( ( aElementOf0 @ SV47 @ xI )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[951]) ).
thf(988,plain,
! [SV47: $i,SV64: $i,SV56: $i] :
( ( ( aElementOf0 @ SV56 @ ( slsdtgt0 @ xa ) )
= $false )
| ( ( ~ ( aElementOf0 @ SV64 @ ( slsdtgt0 @ xb ) ) )
= $true )
| ( ( ( sdtpldt0 @ SV56 @ SV64 )
!= SV47 )
= $true )
| ( ( aElementOf0 @ SV47 @ xI )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[952]) ).
thf(989,plain,
! [SV57: $i,SV16: $i,SV60: $i,SV35: $i] :
( ( ( ~ ( ~ ~ ( ~ ( aElement0 @ ( sK29_SY160 @ SV35 @ SV60 @ SV16 @ SV57 ) )
| ~ ( sdteqdtlpzmzozddtrp0 @ ( sK29_SY160 @ SV35 @ SV60 @ SV16 @ SV57 ) @ SV57 @ SV16 ) )
| ~ ( sdteqdtlpzmzozddtrp0 @ ( sK29_SY160 @ SV35 @ SV60 @ SV16 @ SV57 ) @ SV60 @ SV35 ) ) )
= $true )
| ( ( aElement0 @ SV57 )
= $false )
| ( ( aElement0 @ SV60 )
= $false )
| ( ( aElement0 @ ( sK7_SY131 @ SV35 @ SV16 ) )
= $true )
| ( ( aIdeal0 @ SV16 )
= $false )
| ( ( aIdeal0 @ SV35 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[953]) ).
thf(990,plain,
! [SV55: $i,SV16: $i,SV58: $i,SV35: $i] :
( ( ( ~ ~ ( ~ ( aElement0 @ ( sK25_SY158 @ SV35 @ SV58 @ SV16 @ SV55 ) )
| ~ ( sdteqdtlpzmzozddtrp0 @ ( sK25_SY158 @ SV35 @ SV58 @ SV16 @ SV55 ) @ SV55 @ SV16 ) )
| ~ ( sdteqdtlpzmzozddtrp0 @ ( sK25_SY158 @ SV35 @ SV58 @ SV16 @ SV55 ) @ SV58 @ SV35 ) )
= $false )
| ( ( aElement0 @ SV55 )
= $false )
| ( ( aElement0 @ SV58 )
= $false )
| ( ( aElementOf0 @ ( sK7_SY131 @ SV35 @ SV16 ) @ ( sdtpldt1 @ SV16 @ SV35 ) )
= $false )
| ( ( aIdeal0 @ SV16 )
= $false )
| ( ( aIdeal0 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[954]) ).
thf(991,plain,
( ( ~ ( ~ ( aElement0 @ xc )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xc @ SX0 )
!= xa ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[956]) ).
thf(992,plain,
( ( doDivides0 @ xc @ xa )
= $true ),
inference(extcnf_not_neg,[status(thm)],[957]) ).
thf(993,plain,
! [SV48: $i,SV69: $i] :
( ( ( aElement0 @ SV69 )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV69 )
!= xa )
= $true )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( ~ ( ~ ! [SY143: $i] :
~ ~ ( ~ ( aElement0 @ SY143 )
| ( ( sdtasdt0 @ SV48 @ SY143 )
!= xb ) )
| ( doDivides0 @ SV48 @ xb )
| ( aDivisorOf0 @ SV48 @ xb ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) )
| ~ ( doDivides0 @ SV48 @ xc ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[958]) ).
thf(994,plain,
! [SV48: $i,SV72: $i] :
( ( ( ~ ( ~ ( aElement0 @ SV72 )
| ( ( sdtasdt0 @ SV48 @ SV72 )
!= xb ) ) )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( doDivides0 @ SV48 @ xa )
= $false )
| ( ( ~ ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) )
| ~ ( doDivides0 @ SV48 @ xc ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[959]) ).
thf(995,plain,
! [SV48: $i] :
( ( ( ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) ) )
= $true )
| ( ( doDivides0 @ SV48 @ xa )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( doDivides0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[960]) ).
thf(996,plain,
! [SV48: $i] :
( ( ( doDivides0 @ SV48 @ xc )
= $true )
| ( ( doDivides0 @ SV48 @ xa )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( doDivides0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[961]) ).
thf(997,plain,
! [SV48: $i] :
( ( ( ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) ) )
= $false )
| ( ( doDivides0 @ SV48 @ xa )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[962]) ).
thf(998,plain,
! [SV66: $i,SV48: $i] :
( ( ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) )
| ~ ( doDivides0 @ SV48 @ xc ) )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xa )
= $false )
| ( ( aElement0 @ SV66 )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV66 )
= xb )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[964]) ).
thf(999,plain,
! [SV48: $i] :
( ( ( ~ ( aElement0 @ ( sK24_SY144 @ SV48 ) ) )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xa )
= $false )
| ( ( doDivides0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[965]) ).
thf(1000,plain,
! [SV48: $i] :
( ( ( ( sdtasdt0 @ SV48 @ ( sK24_SY144 @ SV48 ) )
!= xc )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xa )
= $false )
| ( ( doDivides0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[965]) ).
thf(1001,plain,
! [SV48: $i] :
( ( ( aElement0 @ ( sK23_SY144 @ SV48 ) )
= $true )
| ( ( aDivisorOf0 @ SV48 @ xa )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[966]) ).
thf(1002,plain,
! [SV48: $i] :
( ( ( ( sdtasdt0 @ SV48 @ ( sK23_SY144 @ SV48 ) )
= xc )
= $true )
| ( ( aDivisorOf0 @ SV48 @ xa )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[967]) ).
thf(1003,plain,
! [SV1: $i,SV27: $i] :
( ( ( ~ ( ~ ( aElement0 @ ( sK13_SY116 @ SV27 @ SV1 ) )
| ~ ( aElement0 @ ( sK19_SY159 @ SV1 @ SV27 ) ) ) )
= $true )
| ( ( aElement0 @ SV27 )
= $false )
| ( ( aElement0 @ SV1 )
= $false )
| ( ( SV27 = sz00 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[968]) ).
thf(1004,plain,
! [SV27: $i,SV1: $i] :
( ( ( SV1
= ( sdtpldt0 @ ( sdtasdt0 @ ( sK13_SY116 @ SV27 @ SV1 ) @ SV27 ) @ ( sK19_SY159 @ SV1 @ SV27 ) ) )
= $true )
| ( ( aElement0 @ SV27 )
= $false )
| ( ( aElement0 @ SV1 )
= $false )
| ( ( SV27 = sz00 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[969]) ).
thf(1005,plain,
! [SV27: $i,SV1: $i] :
( ( ( ( sK19_SY159 @ SV1 @ SV27 )
= sz00 )
= $true )
| ( ( iLess0 @ ( sbrdtbr0 @ ( sK19_SY159 @ SV1 @ SV27 ) ) @ ( sbrdtbr0 @ SV27 ) )
= $true )
| ( ( aElement0 @ SV27 )
= $false )
| ( ( aElement0 @ SV1 )
= $false )
| ( ( SV27 = sz00 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[970]) ).
thf(1006,plain,
! [SV61: $i] :
( ( ( ~ ( aElement0 @ ( sK26_SY161 @ SV61 ) )
| ( ( sdtasdt0 @ xa @ ( sK26_SY161 @ SV61 ) )
!= SV61 ) )
= $false )
| ( ( aElementOf0 @ SV61 @ ( slsdtgt0 @ xa ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[971]) ).
thf(1007,plain,
! [SV61: $i,SV70: $i] :
( ( ( ~ ( aElement0 @ SV70 )
| ( ( sdtasdt0 @ xa @ SV70 )
!= SV61 ) )
= $true )
| ( ( aElementOf0 @ SV61 @ ( slsdtgt0 @ xa ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[972]) ).
thf(1008,plain,
! [SV62: $i] :
( ( ( ~ ( aElement0 @ ( sK27_SY163 @ SV62 ) )
| ( ( sdtasdt0 @ xb @ ( sK27_SY163 @ SV62 ) )
!= SV62 ) )
= $false )
| ( ( aElementOf0 @ SV62 @ ( slsdtgt0 @ xb ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[973]) ).
thf(1009,plain,
! [SV62: $i,SV71: $i] :
( ( ( ~ ( aElement0 @ SV71 )
| ( ( sdtasdt0 @ xb @ SV71 )
!= SV62 ) )
= $true )
| ( ( aElementOf0 @ SV62 @ ( slsdtgt0 @ xb ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[974]) ).
thf(1010,plain,
! [SV53: $i,SV59: $i,SV44: $i] :
( ( ( SV44 != sz00 )
= $false )
| ( ( aElementOf0 @ SV59 @ ( slsdtgt0 @ xb ) )
= $false )
| ( ( aElementOf0 @ SV53 @ ( slsdtgt0 @ xa ) )
= $false )
| ( ( ( sdtpldt0 @ SV53 @ SV59 )
= SV44 )
= $false )
| ( ( ~ ( iLess0 @ ( sbrdtbr0 @ SV44 ) @ ( sbrdtbr0 @ xu ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[977]) ).
thf(1011,plain,
( ( ~ ( aElement0 @ sK28_SX0 )
| ( ( sdtasdt0 @ xa @ sK28_SX0 )
!= sz00 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[978]) ).
thf(1012,plain,
! [SV67: $i,SV73: $i] :
( ( ( ~ ( aElementOf0 @ SV73 @ xI )
| ( aElementOf0 @ ( sdtpldt0 @ SV67 @ SV73 ) @ xI ) )
= $true )
| ( ( aElementOf0 @ SV67 @ xI )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[981]) ).
thf(1013,plain,
! [SV67: $i,SV74: $i] :
( ( ( ~ ( aElement0 @ SV74 )
| ( aElementOf0 @ ( sdtasdt0 @ SV74 @ SV67 ) @ xI ) )
= $true )
| ( ( aElementOf0 @ SV67 @ xI )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[982]) ).
thf(1014,plain,
! [SV54: $i,SV68: $i] :
( ( ( ( sdtasdt0 @ xa @ SV68 )
= SV54 )
= $false )
| ( ( aElement0 @ SV68 )
= $false )
| ( ( aElementOf0 @ SV54 @ ( slsdtgt0 @ xa ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[985]) ).
thf(1015,plain,
! [SV47: $i,SV56: $i,SV64: $i] :
( ( ( aElementOf0 @ SV64 @ ( slsdtgt0 @ xb ) )
= $false )
| ( ( aElementOf0 @ SV56 @ ( slsdtgt0 @ xa ) )
= $false )
| ( ( ( sdtpldt0 @ SV56 @ SV64 )
!= SV47 )
= $true )
| ( ( aElementOf0 @ SV47 @ xI )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[988]) ).
thf(1016,plain,
! [SV57: $i,SV16: $i,SV60: $i,SV35: $i] :
( ( ( ~ ~ ( ~ ( aElement0 @ ( sK29_SY160 @ SV35 @ SV60 @ SV16 @ SV57 ) )
| ~ ( sdteqdtlpzmzozddtrp0 @ ( sK29_SY160 @ SV35 @ SV60 @ SV16 @ SV57 ) @ SV57 @ SV16 ) )
| ~ ( sdteqdtlpzmzozddtrp0 @ ( sK29_SY160 @ SV35 @ SV60 @ SV16 @ SV57 ) @ SV60 @ SV35 ) )
= $false )
| ( ( aElement0 @ SV57 )
= $false )
| ( ( aElement0 @ SV60 )
= $false )
| ( ( aElement0 @ ( sK7_SY131 @ SV35 @ SV16 ) )
= $true )
| ( ( aIdeal0 @ SV16 )
= $false )
| ( ( aIdeal0 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[989]) ).
thf(1017,plain,
! [SV55: $i,SV16: $i,SV58: $i,SV35: $i] :
( ( ( ~ ~ ( ~ ( aElement0 @ ( sK25_SY158 @ SV35 @ SV58 @ SV16 @ SV55 ) )
| ~ ( sdteqdtlpzmzozddtrp0 @ ( sK25_SY158 @ SV35 @ SV58 @ SV16 @ SV55 ) @ SV55 @ SV16 ) ) )
= $false )
| ( ( aElement0 @ SV55 )
= $false )
| ( ( aElement0 @ SV58 )
= $false )
| ( ( aElementOf0 @ ( sK7_SY131 @ SV35 @ SV16 ) @ ( sdtpldt1 @ SV16 @ SV35 ) )
= $false )
| ( ( aIdeal0 @ SV16 )
= $false )
| ( ( aIdeal0 @ SV35 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[990]) ).
thf(1018,plain,
! [SV55: $i,SV16: $i,SV58: $i,SV35: $i] :
( ( ( ~ ( sdteqdtlpzmzozddtrp0 @ ( sK25_SY158 @ SV35 @ SV58 @ SV16 @ SV55 ) @ SV58 @ SV35 ) )
= $false )
| ( ( aElement0 @ SV55 )
= $false )
| ( ( aElement0 @ SV58 )
= $false )
| ( ( aElementOf0 @ ( sK7_SY131 @ SV35 @ SV16 ) @ ( sdtpldt1 @ SV16 @ SV35 ) )
= $false )
| ( ( aIdeal0 @ SV16 )
= $false )
| ( ( aIdeal0 @ SV35 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[990]) ).
thf(1019,plain,
( ( ~ ( aElement0 @ xc )
| ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xc @ SX0 )
!= xa ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[991]) ).
thf(1020,plain,
! [SV69: $i,SV48: $i] :
( ( ( ( sdtasdt0 @ SV48 @ SV69 )
= xa )
= $false )
| ( ( aElement0 @ SV69 )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( ~ ( ~ ! [SY143: $i] :
~ ~ ( ~ ( aElement0 @ SY143 )
| ( ( sdtasdt0 @ SV48 @ SY143 )
!= xb ) )
| ( doDivides0 @ SV48 @ xb )
| ( aDivisorOf0 @ SV48 @ xb ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) )
| ~ ( doDivides0 @ SV48 @ xc ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[993]) ).
thf(1021,plain,
! [SV48: $i,SV72: $i] :
( ( ( ~ ( aElement0 @ SV72 )
| ( ( sdtasdt0 @ SV48 @ SV72 )
!= xb ) )
= $true )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( doDivides0 @ SV48 @ xa )
= $false )
| ( ( ~ ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) )
| ~ ( doDivides0 @ SV48 @ xc ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[994]) ).
thf(1022,plain,
! [SV48: $i] :
( ( ( ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) ) )
= $false )
| ( ( doDivides0 @ SV48 @ xa )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( doDivides0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[995]) ).
thf(1023,plain,
! [SV48: $i] :
( ( ( ~ ~ ( ~ ( aElement0 @ ( sK30_SY144 @ SV48 ) )
| ( ( sdtasdt0 @ SV48 @ ( sK30_SY144 @ SV48 ) )
!= xc ) ) )
= $false )
| ( ( doDivides0 @ SV48 @ xa )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[997]) ).
thf(1024,plain,
! [SV66: $i,SV48: $i] :
( ( ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) ) )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xa )
= $false )
| ( ( aElement0 @ SV66 )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV66 )
= xb )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[998]) ).
thf(1025,plain,
! [SV66: $i,SV48: $i] :
( ( ( ~ ( doDivides0 @ SV48 @ xc ) )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xa )
= $false )
| ( ( aElement0 @ SV66 )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV66 )
= xb )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[998]) ).
thf(1026,plain,
! [SV48: $i] :
( ( ( aElement0 @ ( sK24_SY144 @ SV48 ) )
= $true )
| ( ( aDivisorOf0 @ SV48 @ xa )
= $false )
| ( ( doDivides0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[999]) ).
thf(1027,plain,
! [SV48: $i] :
( ( ( ( sdtasdt0 @ SV48 @ ( sK24_SY144 @ SV48 ) )
= xc )
= $true )
| ( ( aDivisorOf0 @ SV48 @ xa )
= $false )
| ( ( doDivides0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1000]) ).
thf(1028,plain,
! [SV1: $i,SV27: $i] :
( ( ( ~ ( aElement0 @ ( sK13_SY116 @ SV27 @ SV1 ) )
| ~ ( aElement0 @ ( sK19_SY159 @ SV1 @ SV27 ) ) )
= $false )
| ( ( aElement0 @ SV27 )
= $false )
| ( ( aElement0 @ SV1 )
= $false )
| ( ( SV27 = sz00 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1003]) ).
thf(1029,plain,
! [SV61: $i] :
( ( ( ~ ( aElement0 @ ( sK26_SY161 @ SV61 ) ) )
= $false )
| ( ( aElementOf0 @ SV61 @ ( slsdtgt0 @ xa ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1006]) ).
thf(1030,plain,
! [SV61: $i] :
( ( ( ( sdtasdt0 @ xa @ ( sK26_SY161 @ SV61 ) )
!= SV61 )
= $false )
| ( ( aElementOf0 @ SV61 @ ( slsdtgt0 @ xa ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1006]) ).
thf(1031,plain,
! [SV61: $i,SV70: $i] :
( ( ( ~ ( aElement0 @ SV70 ) )
= $true )
| ( ( ( sdtasdt0 @ xa @ SV70 )
!= SV61 )
= $true )
| ( ( aElementOf0 @ SV61 @ ( slsdtgt0 @ xa ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1007]) ).
thf(1032,plain,
! [SV62: $i] :
( ( ( ~ ( aElement0 @ ( sK27_SY163 @ SV62 ) ) )
= $false )
| ( ( aElementOf0 @ SV62 @ ( slsdtgt0 @ xb ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1008]) ).
thf(1033,plain,
! [SV62: $i] :
( ( ( ( sdtasdt0 @ xb @ ( sK27_SY163 @ SV62 ) )
!= SV62 )
= $false )
| ( ( aElementOf0 @ SV62 @ ( slsdtgt0 @ xb ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1008]) ).
thf(1034,plain,
! [SV62: $i,SV71: $i] :
( ( ( ~ ( aElement0 @ SV71 ) )
= $true )
| ( ( ( sdtasdt0 @ xb @ SV71 )
!= SV62 )
= $true )
| ( ( aElementOf0 @ SV62 @ ( slsdtgt0 @ xb ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1009]) ).
thf(1035,plain,
! [SV53: $i,SV59: $i,SV44: $i] :
( ( ( SV44 = sz00 )
= $true )
| ( ( aElementOf0 @ SV59 @ ( slsdtgt0 @ xb ) )
= $false )
| ( ( aElementOf0 @ SV53 @ ( slsdtgt0 @ xa ) )
= $false )
| ( ( ( sdtpldt0 @ SV53 @ SV59 )
= SV44 )
= $false )
| ( ( ~ ( iLess0 @ ( sbrdtbr0 @ SV44 ) @ ( sbrdtbr0 @ xu ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1010]) ).
thf(1036,plain,
( ( ~ ( aElement0 @ sK28_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1011]) ).
thf(1037,plain,
( ( ( sdtasdt0 @ xa @ sK28_SX0 )
!= sz00 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1011]) ).
thf(1038,plain,
! [SV67: $i,SV73: $i] :
( ( ( ~ ( aElementOf0 @ SV73 @ xI ) )
= $true )
| ( ( aElementOf0 @ ( sdtpldt0 @ SV67 @ SV73 ) @ xI )
= $true )
| ( ( aElementOf0 @ SV67 @ xI )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1012]) ).
thf(1039,plain,
! [SV67: $i,SV74: $i] :
( ( ( ~ ( aElement0 @ SV74 ) )
= $true )
| ( ( aElementOf0 @ ( sdtasdt0 @ SV74 @ SV67 ) @ xI )
= $true )
| ( ( aElementOf0 @ SV67 @ xI )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1013]) ).
thf(1040,plain,
! [SV47: $i,SV64: $i,SV56: $i] :
( ( ( ( sdtpldt0 @ SV56 @ SV64 )
= SV47 )
= $false )
| ( ( aElementOf0 @ SV56 @ ( slsdtgt0 @ xa ) )
= $false )
| ( ( aElementOf0 @ SV64 @ ( slsdtgt0 @ xb ) )
= $false )
| ( ( aElementOf0 @ SV47 @ xI )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1015]) ).
thf(1041,plain,
! [SV57: $i,SV16: $i,SV60: $i,SV35: $i] :
( ( ( ~ ~ ( ~ ( aElement0 @ ( sK29_SY160 @ SV35 @ SV60 @ SV16 @ SV57 ) )
| ~ ( sdteqdtlpzmzozddtrp0 @ ( sK29_SY160 @ SV35 @ SV60 @ SV16 @ SV57 ) @ SV57 @ SV16 ) ) )
= $false )
| ( ( aElement0 @ SV57 )
= $false )
| ( ( aElement0 @ SV60 )
= $false )
| ( ( aElement0 @ ( sK7_SY131 @ SV35 @ SV16 ) )
= $true )
| ( ( aIdeal0 @ SV16 )
= $false )
| ( ( aIdeal0 @ SV35 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1016]) ).
thf(1042,plain,
! [SV57: $i,SV16: $i,SV60: $i,SV35: $i] :
( ( ( ~ ( sdteqdtlpzmzozddtrp0 @ ( sK29_SY160 @ SV35 @ SV60 @ SV16 @ SV57 ) @ SV60 @ SV35 ) )
= $false )
| ( ( aElement0 @ SV57 )
= $false )
| ( ( aElement0 @ SV60 )
= $false )
| ( ( aElement0 @ ( sK7_SY131 @ SV35 @ SV16 ) )
= $true )
| ( ( aIdeal0 @ SV16 )
= $false )
| ( ( aIdeal0 @ SV35 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1016]) ).
thf(1043,plain,
! [SV55: $i,SV16: $i,SV58: $i,SV35: $i] :
( ( ( ~ ( ~ ( aElement0 @ ( sK25_SY158 @ SV35 @ SV58 @ SV16 @ SV55 ) )
| ~ ( sdteqdtlpzmzozddtrp0 @ ( sK25_SY158 @ SV35 @ SV58 @ SV16 @ SV55 ) @ SV55 @ SV16 ) ) )
= $true )
| ( ( aElement0 @ SV55 )
= $false )
| ( ( aElement0 @ SV58 )
= $false )
| ( ( aElementOf0 @ ( sK7_SY131 @ SV35 @ SV16 ) @ ( sdtpldt1 @ SV16 @ SV35 ) )
= $false )
| ( ( aIdeal0 @ SV16 )
= $false )
| ( ( aIdeal0 @ SV35 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1017]) ).
thf(1044,plain,
! [SV55: $i,SV16: $i,SV58: $i,SV35: $i] :
( ( ( sdteqdtlpzmzozddtrp0 @ ( sK25_SY158 @ SV35 @ SV58 @ SV16 @ SV55 ) @ SV58 @ SV35 )
= $true )
| ( ( aElement0 @ SV55 )
= $false )
| ( ( aElement0 @ SV58 )
= $false )
| ( ( aElementOf0 @ ( sK7_SY131 @ SV35 @ SV16 ) @ ( sdtpldt1 @ SV16 @ SV35 ) )
= $false )
| ( ( aIdeal0 @ SV16 )
= $false )
| ( ( aIdeal0 @ SV35 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1018]) ).
thf(1045,plain,
( ( ~ ( aElement0 @ xc ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1019]) ).
thf(1046,plain,
( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xc @ SX0 )
!= xa ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1019]) ).
thf(1047,plain,
! [SV69: $i,SV48: $i] :
( ( ( ~ ! [SY143: $i] :
~ ~ ( ~ ( aElement0 @ SY143 )
| ( ( sdtasdt0 @ SV48 @ SY143 )
!= xb ) )
| ( doDivides0 @ SV48 @ xb )
| ( aDivisorOf0 @ SV48 @ xb ) )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( aElement0 @ SV69 )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV69 )
= xa )
= $false )
| ( ( ~ ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) )
| ~ ( doDivides0 @ SV48 @ xc ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1020]) ).
thf(1048,plain,
! [SV48: $i,SV72: $i] :
( ( ( ~ ( aElement0 @ SV72 ) )
= $true )
| ( ( ( sdtasdt0 @ SV48 @ SV72 )
!= xb )
= $true )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( doDivides0 @ SV48 @ xa )
= $false )
| ( ( ~ ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) )
| ~ ( doDivides0 @ SV48 @ xc ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1021]) ).
thf(1049,plain,
! [SV48: $i] :
( ( ( ~ ~ ( ~ ( aElement0 @ ( sK31_SY144 @ SV48 ) )
| ( ( sdtasdt0 @ SV48 @ ( sK31_SY144 @ SV48 ) )
!= xc ) ) )
= $false )
| ( ( doDivides0 @ SV48 @ xa )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( doDivides0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1022]) ).
thf(1050,plain,
! [SV48: $i] :
( ( ( ~ ( ~ ( aElement0 @ ( sK30_SY144 @ SV48 ) )
| ( ( sdtasdt0 @ SV48 @ ( sK30_SY144 @ SV48 ) )
!= xc ) ) )
= $true )
| ( ( doDivides0 @ SV48 @ xa )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1023]) ).
thf(1051,plain,
! [SV66: $i,SV48: $i] :
( ( ( ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) ) )
= $true )
| ( ( aDivisorOf0 @ SV48 @ xa )
= $false )
| ( ( aElement0 @ SV66 )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV66 )
= xb )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1024]) ).
thf(1052,plain,
! [SV66: $i,SV48: $i] :
( ( ( doDivides0 @ SV48 @ xc )
= $true )
| ( ( aDivisorOf0 @ SV48 @ xa )
= $false )
| ( ( aElement0 @ SV66 )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV66 )
= xb )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1025]) ).
thf(1053,plain,
! [SV1: $i,SV27: $i] :
( ( ( ~ ( aElement0 @ ( sK13_SY116 @ SV27 @ SV1 ) ) )
= $false )
| ( ( aElement0 @ SV27 )
= $false )
| ( ( aElement0 @ SV1 )
= $false )
| ( ( SV27 = sz00 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1028]) ).
thf(1054,plain,
! [SV27: $i,SV1: $i] :
( ( ( ~ ( aElement0 @ ( sK19_SY159 @ SV1 @ SV27 ) ) )
= $false )
| ( ( aElement0 @ SV27 )
= $false )
| ( ( aElement0 @ SV1 )
= $false )
| ( ( SV27 = sz00 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1028]) ).
thf(1055,plain,
! [SV61: $i] :
( ( ( aElement0 @ ( sK26_SY161 @ SV61 ) )
= $true )
| ( ( aElementOf0 @ SV61 @ ( slsdtgt0 @ xa ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1029]) ).
thf(1056,plain,
! [SV61: $i] :
( ( ( ( sdtasdt0 @ xa @ ( sK26_SY161 @ SV61 ) )
= SV61 )
= $true )
| ( ( aElementOf0 @ SV61 @ ( slsdtgt0 @ xa ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1030]) ).
thf(1057,plain,
! [SV61: $i,SV70: $i] :
( ( ( aElement0 @ SV70 )
= $false )
| ( ( ( sdtasdt0 @ xa @ SV70 )
!= SV61 )
= $true )
| ( ( aElementOf0 @ SV61 @ ( slsdtgt0 @ xa ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1031]) ).
thf(1058,plain,
! [SV62: $i] :
( ( ( aElement0 @ ( sK27_SY163 @ SV62 ) )
= $true )
| ( ( aElementOf0 @ SV62 @ ( slsdtgt0 @ xb ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1032]) ).
thf(1059,plain,
! [SV62: $i] :
( ( ( ( sdtasdt0 @ xb @ ( sK27_SY163 @ SV62 ) )
= SV62 )
= $true )
| ( ( aElementOf0 @ SV62 @ ( slsdtgt0 @ xb ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1033]) ).
thf(1060,plain,
! [SV62: $i,SV71: $i] :
( ( ( aElement0 @ SV71 )
= $false )
| ( ( ( sdtasdt0 @ xb @ SV71 )
!= SV62 )
= $true )
| ( ( aElementOf0 @ SV62 @ ( slsdtgt0 @ xb ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1034]) ).
thf(1061,plain,
! [SV59: $i,SV53: $i,SV44: $i] :
( ( ( iLess0 @ ( sbrdtbr0 @ SV44 ) @ ( sbrdtbr0 @ xu ) )
= $false )
| ( ( ( sdtpldt0 @ SV53 @ SV59 )
= SV44 )
= $false )
| ( ( aElementOf0 @ SV53 @ ( slsdtgt0 @ xa ) )
= $false )
| ( ( aElementOf0 @ SV59 @ ( slsdtgt0 @ xb ) )
= $false )
| ( ( SV44 = sz00 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1035]) ).
thf(1062,plain,
( ( aElement0 @ sK28_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1036]) ).
thf(1063,plain,
( ( ( sdtasdt0 @ xa @ sK28_SX0 )
= sz00 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1037]) ).
thf(1064,plain,
! [SV67: $i,SV73: $i] :
( ( ( aElementOf0 @ SV73 @ xI )
= $false )
| ( ( aElementOf0 @ ( sdtpldt0 @ SV67 @ SV73 ) @ xI )
= $true )
| ( ( aElementOf0 @ SV67 @ xI )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1038]) ).
thf(1065,plain,
! [SV67: $i,SV74: $i] :
( ( ( aElement0 @ SV74 )
= $false )
| ( ( aElementOf0 @ ( sdtasdt0 @ SV74 @ SV67 ) @ xI )
= $true )
| ( ( aElementOf0 @ SV67 @ xI )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1039]) ).
thf(1066,plain,
! [SV57: $i,SV16: $i,SV60: $i,SV35: $i] :
( ( ( ~ ( ~ ( aElement0 @ ( sK29_SY160 @ SV35 @ SV60 @ SV16 @ SV57 ) )
| ~ ( sdteqdtlpzmzozddtrp0 @ ( sK29_SY160 @ SV35 @ SV60 @ SV16 @ SV57 ) @ SV57 @ SV16 ) ) )
= $true )
| ( ( aElement0 @ SV57 )
= $false )
| ( ( aElement0 @ SV60 )
= $false )
| ( ( aElement0 @ ( sK7_SY131 @ SV35 @ SV16 ) )
= $true )
| ( ( aIdeal0 @ SV16 )
= $false )
| ( ( aIdeal0 @ SV35 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1041]) ).
thf(1067,plain,
! [SV57: $i,SV16: $i,SV60: $i,SV35: $i] :
( ( ( sdteqdtlpzmzozddtrp0 @ ( sK29_SY160 @ SV35 @ SV60 @ SV16 @ SV57 ) @ SV60 @ SV35 )
= $true )
| ( ( aElement0 @ SV57 )
= $false )
| ( ( aElement0 @ SV60 )
= $false )
| ( ( aElement0 @ ( sK7_SY131 @ SV35 @ SV16 ) )
= $true )
| ( ( aIdeal0 @ SV16 )
= $false )
| ( ( aIdeal0 @ SV35 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1042]) ).
thf(1068,plain,
! [SV55: $i,SV16: $i,SV58: $i,SV35: $i] :
( ( ( ~ ( aElement0 @ ( sK25_SY158 @ SV35 @ SV58 @ SV16 @ SV55 ) )
| ~ ( sdteqdtlpzmzozddtrp0 @ ( sK25_SY158 @ SV35 @ SV58 @ SV16 @ SV55 ) @ SV55 @ SV16 ) )
= $false )
| ( ( aElement0 @ SV55 )
= $false )
| ( ( aElement0 @ SV58 )
= $false )
| ( ( aElementOf0 @ ( sK7_SY131 @ SV35 @ SV16 ) @ ( sdtpldt1 @ SV16 @ SV35 ) )
= $false )
| ( ( aIdeal0 @ SV16 )
= $false )
| ( ( aIdeal0 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1043]) ).
thf(1069,plain,
( ( aElement0 @ xc )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1045]) ).
thf(1070,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xc @ SX0 )
!= xa ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1046]) ).
thf(1071,plain,
! [SV69: $i,SV48: $i] :
( ( ( ~ ! [SY143: $i] :
~ ~ ( ~ ( aElement0 @ SY143 )
| ( ( sdtasdt0 @ SV48 @ SY143 )
!= xb ) )
| ( doDivides0 @ SV48 @ xb ) )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( aElement0 @ SV69 )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV69 )
= xa )
= $false )
| ( ( ~ ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) )
| ~ ( doDivides0 @ SV48 @ xc ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1047]) ).
thf(1072,plain,
! [SV69: $i,SV48: $i] :
( ( ( aDivisorOf0 @ SV48 @ xb )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( aElement0 @ SV69 )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV69 )
= xa )
= $false )
| ( ( ~ ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) )
| ~ ( doDivides0 @ SV48 @ xc ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1047]) ).
thf(1073,plain,
! [SV48: $i,SV72: $i] :
( ( ( aElement0 @ SV72 )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV72 )
!= xb )
= $true )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( doDivides0 @ SV48 @ xa )
= $false )
| ( ( ~ ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) )
| ~ ( doDivides0 @ SV48 @ xc ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1048]) ).
thf(1074,plain,
! [SV48: $i] :
( ( ( ~ ( ~ ( aElement0 @ ( sK31_SY144 @ SV48 ) )
| ( ( sdtasdt0 @ SV48 @ ( sK31_SY144 @ SV48 ) )
!= xc ) ) )
= $true )
| ( ( doDivides0 @ SV48 @ xa )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( doDivides0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1049]) ).
thf(1075,plain,
! [SV48: $i] :
( ( ( ~ ( aElement0 @ ( sK30_SY144 @ SV48 ) )
| ( ( sdtasdt0 @ SV48 @ ( sK30_SY144 @ SV48 ) )
!= xc ) )
= $false )
| ( ( doDivides0 @ SV48 @ xa )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1050]) ).
thf(1076,plain,
! [SV66: $i,SV48: $i] :
( ( ( ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) ) )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xa )
= $false )
| ( ( aElement0 @ SV66 )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV66 )
= xb )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1051]) ).
thf(1077,plain,
! [SV1: $i,SV27: $i] :
( ( ( aElement0 @ ( sK13_SY116 @ SV27 @ SV1 ) )
= $true )
| ( ( aElement0 @ SV27 )
= $false )
| ( ( aElement0 @ SV1 )
= $false )
| ( ( SV27 = sz00 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1053]) ).
thf(1078,plain,
! [SV27: $i,SV1: $i] :
( ( ( aElement0 @ ( sK19_SY159 @ SV1 @ SV27 ) )
= $true )
| ( ( aElement0 @ SV27 )
= $false )
| ( ( aElement0 @ SV1 )
= $false )
| ( ( SV27 = sz00 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1054]) ).
thf(1079,plain,
! [SV61: $i,SV70: $i] :
( ( ( ( sdtasdt0 @ xa @ SV70 )
= SV61 )
= $false )
| ( ( aElement0 @ SV70 )
= $false )
| ( ( aElementOf0 @ SV61 @ ( slsdtgt0 @ xa ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1057]) ).
thf(1080,plain,
! [SV62: $i,SV71: $i] :
( ( ( ( sdtasdt0 @ xb @ SV71 )
= SV62 )
= $false )
| ( ( aElement0 @ SV71 )
= $false )
| ( ( aElementOf0 @ SV62 @ ( slsdtgt0 @ xb ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1060]) ).
thf(1081,plain,
! [SV57: $i,SV16: $i,SV60: $i,SV35: $i] :
( ( ( ~ ( aElement0 @ ( sK29_SY160 @ SV35 @ SV60 @ SV16 @ SV57 ) )
| ~ ( sdteqdtlpzmzozddtrp0 @ ( sK29_SY160 @ SV35 @ SV60 @ SV16 @ SV57 ) @ SV57 @ SV16 ) )
= $false )
| ( ( aElement0 @ SV57 )
= $false )
| ( ( aElement0 @ SV60 )
= $false )
| ( ( aElement0 @ ( sK7_SY131 @ SV35 @ SV16 ) )
= $true )
| ( ( aIdeal0 @ SV16 )
= $false )
| ( ( aIdeal0 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1066]) ).
thf(1082,plain,
! [SV55: $i,SV16: $i,SV58: $i,SV35: $i] :
( ( ( ~ ( aElement0 @ ( sK25_SY158 @ SV35 @ SV58 @ SV16 @ SV55 ) ) )
= $false )
| ( ( aElement0 @ SV55 )
= $false )
| ( ( aElement0 @ SV58 )
= $false )
| ( ( aElementOf0 @ ( sK7_SY131 @ SV35 @ SV16 ) @ ( sdtpldt1 @ SV16 @ SV35 ) )
= $false )
| ( ( aIdeal0 @ SV16 )
= $false )
| ( ( aIdeal0 @ SV35 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1068]) ).
thf(1083,plain,
! [SV55: $i,SV16: $i,SV58: $i,SV35: $i] :
( ( ( ~ ( sdteqdtlpzmzozddtrp0 @ ( sK25_SY158 @ SV35 @ SV58 @ SV16 @ SV55 ) @ SV55 @ SV16 ) )
= $false )
| ( ( aElement0 @ SV55 )
= $false )
| ( ( aElement0 @ SV58 )
= $false )
| ( ( aElementOf0 @ ( sK7_SY131 @ SV35 @ SV16 ) @ ( sdtpldt1 @ SV16 @ SV35 ) )
= $false )
| ( ( aIdeal0 @ SV16 )
= $false )
| ( ( aIdeal0 @ SV35 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1068]) ).
thf(1084,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( aElement0 @ SX0 )
| ( ( sdtasdt0 @ xc @ SX0 )
!= xa ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1070]) ).
thf(1085,plain,
! [SV69: $i,SV48: $i] :
( ( ( ~ ! [SY143: $i] :
~ ~ ( ~ ( aElement0 @ SY143 )
| ( ( sdtasdt0 @ SV48 @ SY143 )
!= xb ) ) )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( aElement0 @ SV69 )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV69 )
= xa )
= $false )
| ( ( ~ ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) )
| ~ ( doDivides0 @ SV48 @ xc ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1071]) ).
thf(1086,plain,
! [SV69: $i,SV48: $i] :
( ( ( doDivides0 @ SV48 @ xb )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( aElement0 @ SV69 )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV69 )
= xa )
= $false )
| ( ( ~ ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) )
| ~ ( doDivides0 @ SV48 @ xc ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1071]) ).
thf(1087,plain,
! [SV69: $i,SV48: $i] :
( ( ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) )
| ~ ( doDivides0 @ SV48 @ xc ) )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV69 )
= xa )
= $false )
| ( ( aElement0 @ SV69 )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1072]) ).
thf(1088,plain,
! [SV72: $i,SV48: $i] :
( ( ( ( sdtasdt0 @ SV48 @ SV72 )
= xb )
= $false )
| ( ( aElement0 @ SV72 )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( doDivides0 @ SV48 @ xa )
= $false )
| ( ( ~ ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) )
| ~ ( doDivides0 @ SV48 @ xc ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1073]) ).
thf(1089,plain,
! [SV48: $i] :
( ( ( ~ ( aElement0 @ ( sK31_SY144 @ SV48 ) )
| ( ( sdtasdt0 @ SV48 @ ( sK31_SY144 @ SV48 ) )
!= xc ) )
= $false )
| ( ( doDivides0 @ SV48 @ xa )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( doDivides0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1074]) ).
thf(1090,plain,
! [SV48: $i] :
( ( ( ~ ( aElement0 @ ( sK30_SY144 @ SV48 ) ) )
= $false )
| ( ( doDivides0 @ SV48 @ xa )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1075]) ).
thf(1091,plain,
! [SV48: $i] :
( ( ( ( sdtasdt0 @ SV48 @ ( sK30_SY144 @ SV48 ) )
!= xc )
= $false )
| ( ( doDivides0 @ SV48 @ xa )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1075]) ).
thf(1092,plain,
! [SV48: $i,SV66: $i] :
( ( ( ~ ~ ( ~ ( aElement0 @ ( sK32_SY144 @ SV66 @ SV48 ) )
| ( ( sdtasdt0 @ SV48 @ ( sK32_SY144 @ SV66 @ SV48 ) )
!= xc ) ) )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xa )
= $false )
| ( ( aElement0 @ SV66 )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV66 )
= xb )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1076]) ).
thf(1093,plain,
! [SV57: $i,SV16: $i,SV60: $i,SV35: $i] :
( ( ( ~ ( aElement0 @ ( sK29_SY160 @ SV35 @ SV60 @ SV16 @ SV57 ) ) )
= $false )
| ( ( aElement0 @ SV57 )
= $false )
| ( ( aElement0 @ SV60 )
= $false )
| ( ( aElement0 @ ( sK7_SY131 @ SV35 @ SV16 ) )
= $true )
| ( ( aIdeal0 @ SV16 )
= $false )
| ( ( aIdeal0 @ SV35 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1081]) ).
thf(1094,plain,
! [SV57: $i,SV16: $i,SV60: $i,SV35: $i] :
( ( ( ~ ( sdteqdtlpzmzozddtrp0 @ ( sK29_SY160 @ SV35 @ SV60 @ SV16 @ SV57 ) @ SV57 @ SV16 ) )
= $false )
| ( ( aElement0 @ SV57 )
= $false )
| ( ( aElement0 @ SV60 )
= $false )
| ( ( aElement0 @ ( sK7_SY131 @ SV35 @ SV16 ) )
= $true )
| ( ( aIdeal0 @ SV16 )
= $false )
| ( ( aIdeal0 @ SV35 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1081]) ).
thf(1095,plain,
! [SV55: $i,SV16: $i,SV58: $i,SV35: $i] :
( ( ( aElement0 @ ( sK25_SY158 @ SV35 @ SV58 @ SV16 @ SV55 ) )
= $true )
| ( ( aElement0 @ SV55 )
= $false )
| ( ( aElement0 @ SV58 )
= $false )
| ( ( aElementOf0 @ ( sK7_SY131 @ SV35 @ SV16 ) @ ( sdtpldt1 @ SV16 @ SV35 ) )
= $false )
| ( ( aIdeal0 @ SV16 )
= $false )
| ( ( aIdeal0 @ SV35 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1082]) ).
thf(1096,plain,
! [SV55: $i,SV16: $i,SV58: $i,SV35: $i] :
( ( ( sdteqdtlpzmzozddtrp0 @ ( sK25_SY158 @ SV35 @ SV58 @ SV16 @ SV55 ) @ SV55 @ SV16 )
= $true )
| ( ( aElement0 @ SV55 )
= $false )
| ( ( aElement0 @ SV58 )
= $false )
| ( ( aElementOf0 @ ( sK7_SY131 @ SV35 @ SV16 ) @ ( sdtpldt1 @ SV16 @ SV35 ) )
= $false )
| ( ( aIdeal0 @ SV16 )
= $false )
| ( ( aIdeal0 @ SV35 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1083]) ).
thf(1097,plain,
( ( ~ ~ ( ~ ( aElement0 @ sK33_SX0 )
| ( ( sdtasdt0 @ xc @ sK33_SX0 )
!= xa ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[1084]) ).
thf(1098,plain,
! [SV69: $i,SV48: $i] :
( ( ( ! [SY143: $i] :
~ ~ ( ~ ( aElement0 @ SY143 )
| ( ( sdtasdt0 @ SV48 @ SY143 )
!= xb ) ) )
= $true )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( aElement0 @ SV69 )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV69 )
= xa )
= $false )
| ( ( ~ ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) )
| ~ ( doDivides0 @ SV48 @ xc ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1085]) ).
thf(1099,plain,
! [SV69: $i,SV48: $i] :
( ( ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) )
| ~ ( doDivides0 @ SV48 @ xc ) )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV69 )
= xa )
= $false )
| ( ( aElement0 @ SV69 )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( doDivides0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1086]) ).
thf(1100,plain,
! [SV69: $i,SV48: $i] :
( ( ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) ) )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV69 )
= xa )
= $false )
| ( ( aElement0 @ SV69 )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1087]) ).
thf(1101,plain,
! [SV69: $i,SV48: $i] :
( ( ( ~ ( doDivides0 @ SV48 @ xc ) )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV69 )
= xa )
= $false )
| ( ( aElement0 @ SV69 )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1087]) ).
thf(1102,plain,
! [SV72: $i,SV48: $i] :
( ( ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) )
| ~ ( doDivides0 @ SV48 @ xc ) )
= $false )
| ( ( doDivides0 @ SV48 @ xa )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( aElement0 @ SV72 )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV72 )
= xb )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1088]) ).
thf(1103,plain,
! [SV48: $i] :
( ( ( ~ ( aElement0 @ ( sK31_SY144 @ SV48 ) ) )
= $false )
| ( ( doDivides0 @ SV48 @ xa )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( doDivides0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1089]) ).
thf(1104,plain,
! [SV48: $i] :
( ( ( ( sdtasdt0 @ SV48 @ ( sK31_SY144 @ SV48 ) )
!= xc )
= $false )
| ( ( doDivides0 @ SV48 @ xa )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( doDivides0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1089]) ).
thf(1105,plain,
! [SV48: $i] :
( ( ( aElement0 @ ( sK30_SY144 @ SV48 ) )
= $true )
| ( ( doDivides0 @ SV48 @ xa )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1090]) ).
thf(1106,plain,
! [SV48: $i] :
( ( ( ( sdtasdt0 @ SV48 @ ( sK30_SY144 @ SV48 ) )
= xc )
= $true )
| ( ( doDivides0 @ SV48 @ xa )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1091]) ).
thf(1107,plain,
! [SV48: $i,SV66: $i] :
( ( ( ~ ( ~ ( aElement0 @ ( sK32_SY144 @ SV66 @ SV48 ) )
| ( ( sdtasdt0 @ SV48 @ ( sK32_SY144 @ SV66 @ SV48 ) )
!= xc ) ) )
= $true )
| ( ( aDivisorOf0 @ SV48 @ xa )
= $false )
| ( ( aElement0 @ SV66 )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV66 )
= xb )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1092]) ).
thf(1108,plain,
! [SV57: $i,SV16: $i,SV60: $i,SV35: $i] :
( ( ( aElement0 @ ( sK29_SY160 @ SV35 @ SV60 @ SV16 @ SV57 ) )
= $true )
| ( ( aElement0 @ SV57 )
= $false )
| ( ( aElement0 @ SV60 )
= $false )
| ( ( aElement0 @ ( sK7_SY131 @ SV35 @ SV16 ) )
= $true )
| ( ( aIdeal0 @ SV16 )
= $false )
| ( ( aIdeal0 @ SV35 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1093]) ).
thf(1109,plain,
! [SV57: $i,SV16: $i,SV60: $i,SV35: $i] :
( ( ( sdteqdtlpzmzozddtrp0 @ ( sK29_SY160 @ SV35 @ SV60 @ SV16 @ SV57 ) @ SV57 @ SV16 )
= $true )
| ( ( aElement0 @ SV57 )
= $false )
| ( ( aElement0 @ SV60 )
= $false )
| ( ( aElement0 @ ( sK7_SY131 @ SV35 @ SV16 ) )
= $true )
| ( ( aIdeal0 @ SV16 )
= $false )
| ( ( aIdeal0 @ SV35 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1094]) ).
thf(1110,plain,
( ( ~ ( ~ ( aElement0 @ sK33_SX0 )
| ( ( sdtasdt0 @ xc @ sK33_SX0 )
!= xa ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1097]) ).
thf(1111,plain,
! [SV69: $i,SV48: $i,SV75: $i] :
( ( ( ~ ~ ( ~ ( aElement0 @ SV75 )
| ( ( sdtasdt0 @ SV48 @ SV75 )
!= xb ) ) )
= $true )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( aElement0 @ SV69 )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV69 )
= xa )
= $false )
| ( ( ~ ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) )
| ~ ( doDivides0 @ SV48 @ xc ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1098]) ).
thf(1112,plain,
! [SV69: $i,SV48: $i] :
( ( ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) ) )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV69 )
= xa )
= $false )
| ( ( aElement0 @ SV69 )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( doDivides0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1099]) ).
thf(1113,plain,
! [SV69: $i,SV48: $i] :
( ( ( ~ ( doDivides0 @ SV48 @ xc ) )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV69 )
= xa )
= $false )
| ( ( aElement0 @ SV69 )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( doDivides0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1099]) ).
thf(1114,plain,
! [SV69: $i,SV48: $i] :
( ( ( ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) ) )
= $true )
| ( ( ( sdtasdt0 @ SV48 @ SV69 )
= xa )
= $false )
| ( ( aElement0 @ SV69 )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1100]) ).
thf(1115,plain,
! [SV69: $i,SV48: $i] :
( ( ( doDivides0 @ SV48 @ xc )
= $true )
| ( ( ( sdtasdt0 @ SV48 @ SV69 )
= xa )
= $false )
| ( ( aElement0 @ SV69 )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1101]) ).
thf(1116,plain,
! [SV72: $i,SV48: $i] :
( ( ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) ) )
= $false )
| ( ( doDivides0 @ SV48 @ xa )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( aElement0 @ SV72 )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV72 )
= xb )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1102]) ).
thf(1117,plain,
! [SV72: $i,SV48: $i] :
( ( ( ~ ( doDivides0 @ SV48 @ xc ) )
= $false )
| ( ( doDivides0 @ SV48 @ xa )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( aElement0 @ SV72 )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV72 )
= xb )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1102]) ).
thf(1118,plain,
! [SV48: $i] :
( ( ( aElement0 @ ( sK31_SY144 @ SV48 ) )
= $true )
| ( ( doDivides0 @ SV48 @ xa )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( doDivides0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1103]) ).
thf(1119,plain,
! [SV48: $i] :
( ( ( ( sdtasdt0 @ SV48 @ ( sK31_SY144 @ SV48 ) )
= xc )
= $true )
| ( ( doDivides0 @ SV48 @ xa )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( doDivides0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1104]) ).
thf(1120,plain,
! [SV48: $i,SV66: $i] :
( ( ( ~ ( aElement0 @ ( sK32_SY144 @ SV66 @ SV48 ) )
| ( ( sdtasdt0 @ SV48 @ ( sK32_SY144 @ SV66 @ SV48 ) )
!= xc ) )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xa )
= $false )
| ( ( aElement0 @ SV66 )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV66 )
= xb )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1107]) ).
thf(1121,plain,
( ( ~ ( aElement0 @ sK33_SX0 )
| ( ( sdtasdt0 @ xc @ sK33_SX0 )
!= xa ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1110]) ).
thf(1122,plain,
! [SV69: $i,SV48: $i,SV75: $i] :
( ( ( ~ ( ~ ( aElement0 @ SV75 )
| ( ( sdtasdt0 @ SV48 @ SV75 )
!= xb ) ) )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( aElement0 @ SV69 )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV69 )
= xa )
= $false )
| ( ( ~ ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) )
| ~ ( doDivides0 @ SV48 @ xc ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1111]) ).
thf(1123,plain,
! [SV69: $i,SV48: $i] :
( ( ( ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) ) )
= $true )
| ( ( ( sdtasdt0 @ SV48 @ SV69 )
= xa )
= $false )
| ( ( aElement0 @ SV69 )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( doDivides0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1112]) ).
thf(1124,plain,
! [SV69: $i,SV48: $i] :
( ( ( doDivides0 @ SV48 @ xc )
= $true )
| ( ( ( sdtasdt0 @ SV48 @ SV69 )
= xa )
= $false )
| ( ( aElement0 @ SV69 )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( doDivides0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1113]) ).
thf(1125,plain,
! [SV69: $i,SV48: $i] :
( ( ( ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) ) )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV69 )
= xa )
= $false )
| ( ( aElement0 @ SV69 )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1114]) ).
thf(1126,plain,
! [SV72: $i,SV48: $i] :
( ( ( ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) ) )
= $true )
| ( ( doDivides0 @ SV48 @ xa )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( aElement0 @ SV72 )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV72 )
= xb )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1116]) ).
thf(1127,plain,
! [SV72: $i,SV48: $i] :
( ( ( doDivides0 @ SV48 @ xc )
= $true )
| ( ( doDivides0 @ SV48 @ xa )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( aElement0 @ SV72 )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV72 )
= xb )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1117]) ).
thf(1128,plain,
! [SV48: $i,SV66: $i] :
( ( ( ~ ( aElement0 @ ( sK32_SY144 @ SV66 @ SV48 ) ) )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xa )
= $false )
| ( ( aElement0 @ SV66 )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV66 )
= xb )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1120]) ).
thf(1129,plain,
! [SV66: $i,SV48: $i] :
( ( ( ( sdtasdt0 @ SV48 @ ( sK32_SY144 @ SV66 @ SV48 ) )
!= xc )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xa )
= $false )
| ( ( aElement0 @ SV66 )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV66 )
= xb )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1120]) ).
thf(1130,plain,
( ( ~ ( aElement0 @ sK33_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1121]) ).
thf(1131,plain,
( ( ( sdtasdt0 @ xc @ sK33_SX0 )
!= xa )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1121]) ).
thf(1132,plain,
! [SV69: $i,SV48: $i,SV75: $i] :
( ( ( ~ ( aElement0 @ SV75 )
| ( ( sdtasdt0 @ SV48 @ SV75 )
!= xb ) )
= $true )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( aElement0 @ SV69 )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV69 )
= xa )
= $false )
| ( ( ~ ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) )
| ~ ( doDivides0 @ SV48 @ xc ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1122]) ).
thf(1133,plain,
! [SV69: $i,SV48: $i] :
( ( ( ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) ) )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV69 )
= xa )
= $false )
| ( ( aElement0 @ SV69 )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( doDivides0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1123]) ).
thf(1134,plain,
! [SV48: $i,SV69: $i] :
( ( ( ~ ~ ( ~ ( aElement0 @ ( sK34_SY144 @ SV69 @ SV48 ) )
| ( ( sdtasdt0 @ SV48 @ ( sK34_SY144 @ SV69 @ SV48 ) )
!= xc ) ) )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV69 )
= xa )
= $false )
| ( ( aElement0 @ SV69 )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1125]) ).
thf(1135,plain,
! [SV72: $i,SV48: $i] :
( ( ( ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) ) )
= $false )
| ( ( doDivides0 @ SV48 @ xa )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( aElement0 @ SV72 )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV72 )
= xb )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1126]) ).
thf(1136,plain,
! [SV48: $i,SV66: $i] :
( ( ( aElement0 @ ( sK32_SY144 @ SV66 @ SV48 ) )
= $true )
| ( ( aDivisorOf0 @ SV48 @ xa )
= $false )
| ( ( aElement0 @ SV66 )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV66 )
= xb )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1128]) ).
thf(1137,plain,
! [SV66: $i,SV48: $i] :
( ( ( ( sdtasdt0 @ SV48 @ ( sK32_SY144 @ SV66 @ SV48 ) )
= xc )
= $true )
| ( ( aDivisorOf0 @ SV48 @ xa )
= $false )
| ( ( aElement0 @ SV66 )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV66 )
= xb )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1129]) ).
thf(1138,plain,
( ( aElement0 @ sK33_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1130]) ).
thf(1139,plain,
( ( ( sdtasdt0 @ xc @ sK33_SX0 )
= xa )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1131]) ).
thf(1140,plain,
! [SV69: $i,SV48: $i,SV75: $i] :
( ( ( ~ ( aElement0 @ SV75 ) )
= $true )
| ( ( ( sdtasdt0 @ SV48 @ SV75 )
!= xb )
= $true )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( aElement0 @ SV69 )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV69 )
= xa )
= $false )
| ( ( ~ ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) )
| ~ ( doDivides0 @ SV48 @ xc ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1132]) ).
thf(1141,plain,
! [SV48: $i,SV69: $i] :
( ( ( ~ ~ ( ~ ( aElement0 @ ( sK35_SY144 @ SV69 @ SV48 ) )
| ( ( sdtasdt0 @ SV48 @ ( sK35_SY144 @ SV69 @ SV48 ) )
!= xc ) ) )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV69 )
= xa )
= $false )
| ( ( aElement0 @ SV69 )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( doDivides0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1133]) ).
thf(1142,plain,
! [SV48: $i,SV69: $i] :
( ( ( ~ ( ~ ( aElement0 @ ( sK34_SY144 @ SV69 @ SV48 ) )
| ( ( sdtasdt0 @ SV48 @ ( sK34_SY144 @ SV69 @ SV48 ) )
!= xc ) ) )
= $true )
| ( ( ( sdtasdt0 @ SV48 @ SV69 )
= xa )
= $false )
| ( ( aElement0 @ SV69 )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1134]) ).
thf(1143,plain,
! [SV48: $i,SV72: $i] :
( ( ( ~ ~ ( ~ ( aElement0 @ ( sK36_SY144 @ SV72 @ SV48 ) )
| ( ( sdtasdt0 @ SV48 @ ( sK36_SY144 @ SV72 @ SV48 ) )
!= xc ) ) )
= $false )
| ( ( doDivides0 @ SV48 @ xa )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( aElement0 @ SV72 )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV72 )
= xb )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1135]) ).
thf(1144,plain,
! [SV69: $i,SV48: $i,SV75: $i] :
( ( ( aElement0 @ SV75 )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV75 )
!= xb )
= $true )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( aElement0 @ SV69 )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV69 )
= xa )
= $false )
| ( ( ~ ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) )
| ~ ( doDivides0 @ SV48 @ xc ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1140]) ).
thf(1145,plain,
! [SV48: $i,SV69: $i] :
( ( ( ~ ( ~ ( aElement0 @ ( sK35_SY144 @ SV69 @ SV48 ) )
| ( ( sdtasdt0 @ SV48 @ ( sK35_SY144 @ SV69 @ SV48 ) )
!= xc ) ) )
= $true )
| ( ( ( sdtasdt0 @ SV48 @ SV69 )
= xa )
= $false )
| ( ( aElement0 @ SV69 )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( doDivides0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1141]) ).
thf(1146,plain,
! [SV48: $i,SV69: $i] :
( ( ( ~ ( aElement0 @ ( sK34_SY144 @ SV69 @ SV48 ) )
| ( ( sdtasdt0 @ SV48 @ ( sK34_SY144 @ SV69 @ SV48 ) )
!= xc ) )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV69 )
= xa )
= $false )
| ( ( aElement0 @ SV69 )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1142]) ).
thf(1147,plain,
! [SV48: $i,SV72: $i] :
( ( ( ~ ( ~ ( aElement0 @ ( sK36_SY144 @ SV72 @ SV48 ) )
| ( ( sdtasdt0 @ SV48 @ ( sK36_SY144 @ SV72 @ SV48 ) )
!= xc ) ) )
= $true )
| ( ( doDivides0 @ SV48 @ xa )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( aElement0 @ SV72 )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV72 )
= xb )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1143]) ).
thf(1148,plain,
! [SV69: $i,SV75: $i,SV48: $i] :
( ( ( ( sdtasdt0 @ SV48 @ SV75 )
= xb )
= $false )
| ( ( aElement0 @ SV75 )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( aElement0 @ SV69 )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV69 )
= xa )
= $false )
| ( ( ~ ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) )
| ~ ( doDivides0 @ SV48 @ xc ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1144]) ).
thf(1149,plain,
! [SV48: $i,SV69: $i] :
( ( ( ~ ( aElement0 @ ( sK35_SY144 @ SV69 @ SV48 ) )
| ( ( sdtasdt0 @ SV48 @ ( sK35_SY144 @ SV69 @ SV48 ) )
!= xc ) )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV69 )
= xa )
= $false )
| ( ( aElement0 @ SV69 )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( doDivides0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1145]) ).
thf(1150,plain,
! [SV48: $i,SV69: $i] :
( ( ( ~ ( aElement0 @ ( sK34_SY144 @ SV69 @ SV48 ) ) )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV69 )
= xa )
= $false )
| ( ( aElement0 @ SV69 )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1146]) ).
thf(1151,plain,
! [SV69: $i,SV48: $i] :
( ( ( ( sdtasdt0 @ SV48 @ ( sK34_SY144 @ SV69 @ SV48 ) )
!= xc )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV69 )
= xa )
= $false )
| ( ( aElement0 @ SV69 )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1146]) ).
thf(1152,plain,
! [SV48: $i,SV72: $i] :
( ( ( ~ ( aElement0 @ ( sK36_SY144 @ SV72 @ SV48 ) )
| ( ( sdtasdt0 @ SV48 @ ( sK36_SY144 @ SV72 @ SV48 ) )
!= xc ) )
= $false )
| ( ( doDivides0 @ SV48 @ xa )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( aElement0 @ SV72 )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV72 )
= xb )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1147]) ).
thf(1153,plain,
! [SV75: $i,SV69: $i,SV48: $i] :
( ( ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) )
| ~ ( doDivides0 @ SV48 @ xc ) )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV69 )
= xa )
= $false )
| ( ( aElement0 @ SV69 )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( aElement0 @ SV75 )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV75 )
= xb )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1148]) ).
thf(1154,plain,
! [SV48: $i,SV69: $i] :
( ( ( ~ ( aElement0 @ ( sK35_SY144 @ SV69 @ SV48 ) ) )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV69 )
= xa )
= $false )
| ( ( aElement0 @ SV69 )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( doDivides0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1149]) ).
thf(1155,plain,
! [SV69: $i,SV48: $i] :
( ( ( ( sdtasdt0 @ SV48 @ ( sK35_SY144 @ SV69 @ SV48 ) )
!= xc )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV69 )
= xa )
= $false )
| ( ( aElement0 @ SV69 )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( doDivides0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1149]) ).
thf(1156,plain,
! [SV48: $i,SV69: $i] :
( ( ( aElement0 @ ( sK34_SY144 @ SV69 @ SV48 ) )
= $true )
| ( ( ( sdtasdt0 @ SV48 @ SV69 )
= xa )
= $false )
| ( ( aElement0 @ SV69 )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1150]) ).
thf(1157,plain,
! [SV69: $i,SV48: $i] :
( ( ( ( sdtasdt0 @ SV48 @ ( sK34_SY144 @ SV69 @ SV48 ) )
= xc )
= $true )
| ( ( ( sdtasdt0 @ SV48 @ SV69 )
= xa )
= $false )
| ( ( aElement0 @ SV69 )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( aDivisorOf0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1151]) ).
thf(1158,plain,
! [SV48: $i,SV72: $i] :
( ( ( ~ ( aElement0 @ ( sK36_SY144 @ SV72 @ SV48 ) ) )
= $false )
| ( ( doDivides0 @ SV48 @ xa )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( aElement0 @ SV72 )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV72 )
= xb )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1152]) ).
thf(1159,plain,
! [SV72: $i,SV48: $i] :
( ( ( ( sdtasdt0 @ SV48 @ ( sK36_SY144 @ SV72 @ SV48 ) )
!= xc )
= $false )
| ( ( doDivides0 @ SV48 @ xa )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( aElement0 @ SV72 )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV72 )
= xb )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1152]) ).
thf(1160,plain,
! [SV75: $i,SV69: $i,SV48: $i] :
( ( ( ~ ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) ) )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV69 )
= xa )
= $false )
| ( ( aElement0 @ SV69 )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( aElement0 @ SV75 )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV75 )
= xb )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1153]) ).
thf(1161,plain,
! [SV75: $i,SV69: $i,SV48: $i] :
( ( ( ~ ( doDivides0 @ SV48 @ xc ) )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV69 )
= xa )
= $false )
| ( ( aElement0 @ SV69 )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( aElement0 @ SV75 )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV75 )
= xb )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1153]) ).
thf(1162,plain,
! [SV48: $i,SV69: $i] :
( ( ( aElement0 @ ( sK35_SY144 @ SV69 @ SV48 ) )
= $true )
| ( ( ( sdtasdt0 @ SV48 @ SV69 )
= xa )
= $false )
| ( ( aElement0 @ SV69 )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( doDivides0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1154]) ).
thf(1163,plain,
! [SV69: $i,SV48: $i] :
( ( ( ( sdtasdt0 @ SV48 @ ( sK35_SY144 @ SV69 @ SV48 ) )
= xc )
= $true )
| ( ( ( sdtasdt0 @ SV48 @ SV69 )
= xa )
= $false )
| ( ( aElement0 @ SV69 )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( doDivides0 @ SV48 @ xb )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1155]) ).
thf(1164,plain,
! [SV48: $i,SV72: $i] :
( ( ( aElement0 @ ( sK36_SY144 @ SV72 @ SV48 ) )
= $true )
| ( ( doDivides0 @ SV48 @ xa )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( aElement0 @ SV72 )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV72 )
= xb )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1158]) ).
thf(1165,plain,
! [SV72: $i,SV48: $i] :
( ( ( ( sdtasdt0 @ SV48 @ ( sK36_SY144 @ SV72 @ SV48 ) )
= xc )
= $true )
| ( ( doDivides0 @ SV48 @ xa )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( aElement0 @ SV72 )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV72 )
= xb )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1159]) ).
thf(1166,plain,
! [SV75: $i,SV69: $i,SV48: $i] :
( ( ( ~ ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) ) )
= $true )
| ( ( ( sdtasdt0 @ SV48 @ SV69 )
= xa )
= $false )
| ( ( aElement0 @ SV69 )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( aElement0 @ SV75 )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV75 )
= xb )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1160]) ).
thf(1167,plain,
! [SV75: $i,SV69: $i,SV48: $i] :
( ( ( doDivides0 @ SV48 @ xc )
= $true )
| ( ( ( sdtasdt0 @ SV48 @ SV69 )
= xa )
= $false )
| ( ( aElement0 @ SV69 )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( aElement0 @ SV75 )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV75 )
= xb )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1161]) ).
thf(1168,plain,
! [SV75: $i,SV69: $i,SV48: $i] :
( ( ( ! [SY144: $i] :
~ ~ ( ~ ( aElement0 @ SY144 )
| ( ( sdtasdt0 @ SV48 @ SY144 )
!= xc ) ) )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV69 )
= xa )
= $false )
| ( ( aElement0 @ SV69 )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( aElement0 @ SV75 )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV75 )
= xb )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1166]) ).
thf(1169,plain,
! [SV48: $i,SV69: $i,SV75: $i] :
( ( ( ~ ~ ( ~ ( aElement0 @ ( sK37_SY144 @ SV75 @ SV69 @ SV48 ) )
| ( ( sdtasdt0 @ SV48 @ ( sK37_SY144 @ SV75 @ SV69 @ SV48 ) )
!= xc ) ) )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV69 )
= xa )
= $false )
| ( ( aElement0 @ SV69 )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( aElement0 @ SV75 )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV75 )
= xb )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1168]) ).
thf(1170,plain,
! [SV48: $i,SV69: $i,SV75: $i] :
( ( ( ~ ( ~ ( aElement0 @ ( sK37_SY144 @ SV75 @ SV69 @ SV48 ) )
| ( ( sdtasdt0 @ SV48 @ ( sK37_SY144 @ SV75 @ SV69 @ SV48 ) )
!= xc ) ) )
= $true )
| ( ( ( sdtasdt0 @ SV48 @ SV69 )
= xa )
= $false )
| ( ( aElement0 @ SV69 )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( aElement0 @ SV75 )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV75 )
= xb )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1169]) ).
thf(1171,plain,
! [SV48: $i,SV69: $i,SV75: $i] :
( ( ( ~ ( aElement0 @ ( sK37_SY144 @ SV75 @ SV69 @ SV48 ) )
| ( ( sdtasdt0 @ SV48 @ ( sK37_SY144 @ SV75 @ SV69 @ SV48 ) )
!= xc ) )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV69 )
= xa )
= $false )
| ( ( aElement0 @ SV69 )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( aElement0 @ SV75 )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV75 )
= xb )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1170]) ).
thf(1172,plain,
! [SV48: $i,SV69: $i,SV75: $i] :
( ( ( ~ ( aElement0 @ ( sK37_SY144 @ SV75 @ SV69 @ SV48 ) ) )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV69 )
= xa )
= $false )
| ( ( aElement0 @ SV69 )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( aElement0 @ SV75 )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV75 )
= xb )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1171]) ).
thf(1173,plain,
! [SV69: $i,SV75: $i,SV48: $i] :
( ( ( ( sdtasdt0 @ SV48 @ ( sK37_SY144 @ SV75 @ SV69 @ SV48 ) )
!= xc )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV69 )
= xa )
= $false )
| ( ( aElement0 @ SV69 )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( aElement0 @ SV75 )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV75 )
= xb )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1171]) ).
thf(1174,plain,
! [SV48: $i,SV69: $i,SV75: $i] :
( ( ( aElement0 @ ( sK37_SY144 @ SV75 @ SV69 @ SV48 ) )
= $true )
| ( ( ( sdtasdt0 @ SV48 @ SV69 )
= xa )
= $false )
| ( ( aElement0 @ SV69 )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( aElement0 @ SV75 )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV75 )
= xb )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1172]) ).
thf(1175,plain,
! [SV69: $i,SV75: $i,SV48: $i] :
( ( ( ( sdtasdt0 @ SV48 @ ( sK37_SY144 @ SV75 @ SV69 @ SV48 ) )
= xc )
= $true )
| ( ( ( sdtasdt0 @ SV48 @ SV69 )
= xa )
= $false )
| ( ( aElement0 @ SV69 )
= $false )
| ( ( aElement0 @ SV48 )
= $false )
| ( ( aElement0 @ SV75 )
= $false )
| ( ( ( sdtasdt0 @ SV48 @ SV75 )
= xb )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1173]) ).
thf(1176,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[100,1175,1174,1167,1165,1164,1163,1162,1157,1156,1139,1138,1137,1136,1127,1124,1119,1118,1115,1109,1108,1106,1105,1096,1095,1080,1079,1078,1077,1069,1067,1065,1064,1063,1062,1061,1059,1058,1056,1055,1052,1044,1040,1027,1026,1014,1005,1004,1002,1001,996,992,987,986,984,983,980,979,976,975,963,955,918,897,896,895,889,886,885,880,877,876,875,839,830,809,808,800,792,780,779,778,774,772,725,724,713,712,696,694,684,679,642,627,623,614,599,598,591,590,582,581,557,546,527,523,519,518,509,507,505,502,500,496,495,490,488,487,485,482,478,468,448,430,426,422,421,417,416,410,404,401,400,395,394,388,387,367,318,295,292,278,276,274,273,270,269,268,264,256,242,220,186,101]) ).
thf(1177,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[1176]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG119+4 : 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
% 0.09/0.16 % Computer : n001.cluster.edu
% 0.09/0.16 % Model : x86_64 x86_64
% 0.09/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.16 % Memory : 8046.5625MB
% 0.09/0.16 % OS : Linux 6.8.0-71-generic
% 0.09/0.16 % CPULimit : 300
% 0.09/0.16 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Oct 6 14:21:54 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 225.26/38.02
% 225.26/38.02 No.of.Axioms: 41
% 225.26/38.02
% 225.26/38.02 Length.of.Defs: 0
% 225.26/38.02
% 225.26/38.02 Contains.Choice.Funs: false
% 225.26/38.02 ..................................
% 225.26/38.02
% 225.26/38.02 ********************************
% 225.26/38.02 * All subproblems solved! *
% 225.26/38.02 ********************************
% 225.26/38.02 % 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:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:1176,loop_count:0,foatp_calls:1,translation:fof_full)
% 225.26/38.02
% 225.26/38.02 %**** Beginning of derivation protocol ****
% 225.26/38.02 % SZS output start CNFRefutation
% See solution above
% 225.26/38.03
% 225.26/38.03 %**** End of derivation protocol ****
% 225.26/38.03 %**** no. of clauses in derivation: 1177 ****
% 225.26/38.03 %**** clause counter: 1176 ****
% 225.26/38.03
% 225.26/38.03 % 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:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:1176,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------