TSTP Solution File: RNG059+2 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : RNG059+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 20:34:08 EDT 2022
% Result : Theorem 2.42s 2.68s
% Output : CNFRefutation 2.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 89
% Syntax : Number of formulae : 773 ( 446 unt; 32 typ; 0 def)
% Number of atoms : 5411 (2061 equ; 0 cnn)
% Maximal formula atoms : 9 ( 7 avg)
% Number of connectives : 9773 (1793 ~;1773 |; 223 &;5880 @)
% ( 0 <=>; 104 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 35 ( 32 usr; 20 con; 0-2 aty)
% Number of variables : 1333 ( 0 ^1331 !; 2 ?;1333 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_aDimensionOf0,type,
aDimensionOf0: $i > $i ).
thf(tp_aNaturalNumber0,type,
aNaturalNumber0: $i > $o ).
thf(tp_aScalar0,type,
aScalar0: $i > $o ).
thf(tp_aVector0,type,
aVector0: $i > $o ).
thf(tp_iLess0,type,
iLess0: $i > $i > $o ).
thf(tp_sK1_W1,type,
sK1_W1: $i > $i ).
thf(tp_sdtasasdt0,type,
sdtasasdt0: $i > $i > $i ).
thf(tp_sdtasdt0,type,
sdtasdt0: $i > $i > $i ).
thf(tp_sdtlbdtrb0,type,
sdtlbdtrb0: $i > $i > $i ).
thf(tp_sdtlseqdt0,type,
sdtlseqdt0: $i > $i > $o ).
thf(tp_sdtpldt0,type,
sdtpldt0: $i > $i > $i ).
thf(tp_smndt0,type,
smndt0: $i > $i ).
thf(tp_sz00,type,
sz00: $i ).
thf(tp_sz0z00,type,
sz0z00: $i ).
thf(tp_sziznziztdt0,type,
sziznziztdt0: $i > $i ).
thf(tp_szszuzczcdt0,type,
szszuzczcdt0: $i > $i ).
thf(tp_xA,type,
xA: $i ).
thf(tp_xB,type,
xB: $i ).
thf(tp_xC,type,
xC: $i ).
thf(tp_xD,type,
xD: $i ).
thf(tp_xE,type,
xE: $i ).
thf(tp_xF,type,
xF: $i ).
thf(tp_xG,type,
xG: $i ).
thf(tp_xH,type,
xH: $i ).
thf(tp_xN,type,
xN: $i ).
thf(tp_xP,type,
xP: $i ).
thf(tp_xR,type,
xR: $i ).
thf(tp_xS,type,
xS: $i ).
thf(tp_xp,type,
xp: $i ).
thf(tp_xq,type,
xq: $i ).
thf(tp_xs,type,
xs: $i ).
thf(tp_xt,type,
xt: $i ).
thf(1,axiom,
! [W0: $i] :
( ( aVector0 @ W0 )
=> ( sdtlseqdt0 @ sz0z00 @ ( sdtasasdt0 @ W0 @ W0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mScSqPos) ).
thf(2,axiom,
! [W0: $i,W1: $i] :
( ( ( aVector0 @ W0 )
& ( aVector0 @ W1 ) )
=> ( ( ( ( aDimensionOf0 @ W0 )
= ( aDimensionOf0 @ W1 ) )
& ( ( aDimensionOf0 @ W1 )
!= sz00 ) )
=> ( ( sdtasasdt0 @ W0 @ W1 )
= ( sdtpldt0 @ ( sdtasasdt0 @ ( sziznziztdt0 @ W0 ) @ ( sziznziztdt0 @ W1 ) ) @ ( sdtasdt0 @ ( sdtlbdtrb0 @ W0 @ ( aDimensionOf0 @ W0 ) ) @ ( sdtlbdtrb0 @ W1 @ ( aDimensionOf0 @ W1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSPN) ).
thf(3,axiom,
! [W0: $i,W1: $i] :
( ( ( aVector0 @ W0 )
& ( aVector0 @ W1 ) )
=> ( ( ( ( aDimensionOf0 @ W0 )
= ( aDimensionOf0 @ W1 ) )
& ( ( aDimensionOf0 @ W1 )
= sz00 ) )
=> ( ( sdtasasdt0 @ W0 @ W1 )
= sz0z00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSPZ) ).
thf(4,axiom,
! [W0: $i,W1: $i] :
( ( ( aVector0 @ W0 )
& ( aVector0 @ W1 ) )
=> ( ( ( aDimensionOf0 @ W0 )
= ( aDimensionOf0 @ W1 ) )
=> ( aScalar0 @ ( sdtasasdt0 @ W0 @ W1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mScPr) ).
thf(5,axiom,
! [W0: $i,W1: $i] :
( ( ( aVector0 @ W0 )
& ( aVector0 @ W1 ) )
=> ( ( ( ( aDimensionOf0 @ W0 )
= ( aDimensionOf0 @ W1 ) )
& ( ( aDimensionOf0 @ W1 )
!= sz00 ) )
=> ( ( aDimensionOf0 @ ( sziznziztdt0 @ W0 ) )
= ( aDimensionOf0 @ ( sziznziztdt0 @ W1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEqInit) ).
thf(6,axiom,
! [W0: $i,W1: $i] :
( ( ( aVector0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( aScalar0 @ ( sdtlbdtrb0 @ W0 @ W1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mElmSc) ).
thf(7,axiom,
! [W0: $i] :
( ( aVector0 @ W0 )
=> ( aNaturalNumber0 @ ( aDimensionOf0 @ W0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDimNat) ).
thf(8,axiom,
! [W0: $i] :
( ( aVector0 @ W0 )
=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mVcSort) ).
thf(9,axiom,
! [W0: $i,W1: $i] :
( ( ( aScalar0 @ W0 )
& ( aScalar0 @ W1 ) )
=> ( ( ( sdtlseqdt0 @ sz0z00 @ W0 )
& ( sdtlseqdt0 @ sz0z00 @ W1 )
& ( ( sdtasdt0 @ W0 @ W0 )
= ( sdtasdt0 @ W1 @ W1 ) ) )
=> ( W0 = W1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSqrt) ).
thf(10,axiom,
! [W0: $i] :
( ( aScalar0 @ W0 )
=> ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ W0 @ W0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSqPos) ).
thf(11,axiom,
! [W0: $i,W1: $i] :
( ( ( aScalar0 @ W0 )
& ( aScalar0 @ W1 ) )
=> ( ( ( sdtlseqdt0 @ sz0z00 @ W0 )
& ( sdtlseqdt0 @ sz0z00 @ W1 ) )
=> ( ( sdtlseqdt0 @ sz0z00 @ ( sdtpldt0 @ W0 @ W1 ) )
& ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ W0 @ W1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mPosMon) ).
thf(12,axiom,
! [W0: $i,W1: $i] :
( ( ( aScalar0 @ W0 )
& ( aScalar0 @ W1 ) )
=> ( ( sdtlseqdt0 @ W0 @ W1 )
| ( sdtlseqdt0 @ W1 @ W0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETot) ).
thf(13,axiom,
! [W0: $i,W1: $i,W2: $i,W3: $i] :
( ( ( aScalar0 @ W0 )
& ( aScalar0 @ W1 )
& ( aScalar0 @ W2 )
& ( aScalar0 @ W3 ) )
=> ( ( ( sdtlseqdt0 @ W0 @ W1 )
& ( sdtlseqdt0 @ sz0z00 @ W2 )
& ( sdtlseqdt0 @ W2 @ W3 ) )
=> ( sdtlseqdt0 @ ( sdtasdt0 @ W0 @ W2 ) @ ( sdtasdt0 @ W1 @ W3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLEMonM) ).
thf(14,axiom,
! [W0: $i,W1: $i,W2: $i,W3: $i] :
( ( ( aScalar0 @ W0 )
& ( aScalar0 @ W1 )
& ( aScalar0 @ W2 )
& ( aScalar0 @ W3 ) )
=> ( ( ( sdtlseqdt0 @ W0 @ W1 )
& ( sdtlseqdt0 @ W2 @ W3 ) )
=> ( sdtlseqdt0 @ ( sdtpldt0 @ W0 @ W2 ) @ ( sdtpldt0 @ W1 @ W3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLEMon) ).
thf(15,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( ( aScalar0 @ W0 )
& ( aScalar0 @ W1 )
& ( aScalar0 @ W2 ) )
=> ( ( ( sdtlseqdt0 @ W0 @ W1 )
& ( sdtlseqdt0 @ W1 @ W2 ) )
=> ( sdtlseqdt0 @ W0 @ W2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETrn) ).
thf(16,axiom,
! [W0: $i,W1: $i] :
( ( ( aScalar0 @ W0 )
& ( aScalar0 @ W1 ) )
=> ( ( ( sdtlseqdt0 @ W0 @ W1 )
& ( sdtlseqdt0 @ W1 @ W0 ) )
=> ( W0 = W1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLEASm) ).
thf(17,axiom,
! [W0: $i] :
( ( aScalar0 @ W0 )
=> ( sdtlseqdt0 @ W0 @ W0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLERef) ).
thf(18,axiom,
! [W0: $i,W1: $i] :
( ( ( aScalar0 @ W0 )
& ( aScalar0 @ W1 ) )
=> ( ( sdtlseqdt0 @ W0 @ W1 )
=> $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLess) ).
thf(19,axiom,
! [W0: $i,W1: $i] :
( ( ( aScalar0 @ W0 )
& ( aScalar0 @ W1 ) )
=> ( ( sdtasdt0 @ ( smndt0 @ W0 ) @ ( smndt0 @ W1 ) )
= ( sdtasdt0 @ W0 @ W1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMDNeg) ).
thf(20,axiom,
! [W0: $i,W1: $i] :
( ( ( aScalar0 @ W0 )
& ( aScalar0 @ W1 ) )
=> ( ( ( sdtasdt0 @ W0 @ ( smndt0 @ W1 ) )
= ( smndt0 @ ( sdtasdt0 @ W0 @ W1 ) ) )
& ( ( sdtasdt0 @ ( smndt0 @ W0 ) @ W1 )
= ( smndt0 @ ( sdtasdt0 @ W0 @ W1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMNeg) ).
thf(21,axiom,
! [W0: $i,W1: $i,W2: $i,W3: $i] :
( ( ( aScalar0 @ W0 )
& ( aScalar0 @ W1 )
& ( aScalar0 @ W2 )
& ( aScalar0 @ W3 ) )
=> ( ( sdtasdt0 @ ( sdtpldt0 @ W0 @ W1 ) @ ( sdtpldt0 @ W2 @ W3 ) )
= ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ W0 @ W2 ) @ ( sdtasdt0 @ W0 @ W3 ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ W1 @ W2 ) @ ( sdtasdt0 @ W1 @ W3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDistr2) ).
thf(22,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( ( aScalar0 @ W0 )
& ( aScalar0 @ W1 )
& ( aScalar0 @ W2 ) )
=> ( ( ( sdtasdt0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ W0 @ W1 ) @ ( sdtasdt0 @ W0 @ W2 ) ) )
& ( ( sdtasdt0 @ ( sdtpldt0 @ W0 @ W1 ) @ W2 )
= ( sdtpldt0 @ ( sdtasdt0 @ W0 @ W2 ) @ ( sdtasdt0 @ W1 @ W2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDistr) ).
thf(23,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( ( aScalar0 @ W0 )
& ( aScalar0 @ W1 )
& ( aScalar0 @ W2 ) )
=> ( ( ( sdtpldt0 @ ( sdtpldt0 @ W0 @ W1 ) @ W2 )
= ( sdtpldt0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) ) )
& ( ( sdtpldt0 @ W0 @ W1 )
= ( sdtpldt0 @ W1 @ W0 ) )
& ( ( sdtasdt0 @ ( sdtasdt0 @ W0 @ W1 ) @ W2 )
= ( sdtasdt0 @ W0 @ ( sdtasdt0 @ W1 @ W2 ) ) )
& ( ( sdtasdt0 @ W0 @ W1 )
= ( sdtasdt0 @ W1 @ W0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mArith) ).
thf(24,axiom,
! [W0: $i] :
( ( aScalar0 @ W0 )
=> ( ( ( sdtpldt0 @ W0 @ sz0z00 )
= W0 )
& ( ( sdtpldt0 @ sz0z00 @ W0 )
= W0 )
& ( ( sdtasdt0 @ W0 @ sz0z00 )
= sz0z00 )
& ( ( sdtasdt0 @ sz0z00 @ W0 )
= sz0z00 )
& ( ( sdtpldt0 @ W0 @ ( smndt0 @ W0 ) )
= sz0z00 )
& ( ( sdtpldt0 @ ( smndt0 @ W0 ) @ W0 )
= sz0z00 )
& ( ( smndt0 @ ( smndt0 @ W0 ) )
= W0 )
& ( ( smndt0 @ sz0z00 )
= sz0z00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mScZero) ).
thf(25,axiom,
! [W0: $i] :
( ( aScalar0 @ W0 )
=> ( aScalar0 @ ( smndt0 @ W0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNegSc) ).
thf(26,axiom,
! [W0: $i,W1: $i] :
( ( ( aScalar0 @ W0 )
& ( aScalar0 @ W1 ) )
=> ( aScalar0 @ ( sdtasdt0 @ W0 @ W1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulSc) ).
thf(27,axiom,
! [W0: $i,W1: $i] :
( ( ( aScalar0 @ W0 )
& ( aScalar0 @ W1 ) )
=> ( aScalar0 @ ( sdtpldt0 @ W0 @ W1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSumSc) ).
thf(28,axiom,
aScalar0 @ sz0z00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSZeroSc) ).
thf(29,axiom,
! [W0: $i] :
( ( aScalar0 @ W0 )
=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mScSort) ).
thf(30,axiom,
! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> ( iLess0 @ W0 @ ( szszuzczcdt0 @ W0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIH) ).
thf(31,axiom,
! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( iLess0 @ W0 @ W1 )
=> $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIHOrd) ).
thf(32,axiom,
! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( ( szszuzczcdt0 @ W0 )
= ( szszuzczcdt0 @ W1 ) )
=> ( W0 = W1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccEqu) ).
thf(33,axiom,
! [W0: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( W0 != sz00 ) )
=> ? [W1: $i] :
( ( aNaturalNumber0 @ W1 )
& ( W0
= ( szszuzczcdt0 @ W1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNatExtr) ).
thf(34,axiom,
! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ W0 ) )
& ( ( szszuzczcdt0 @ W0 )
!= sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccNat) ).
thf(35,axiom,
aNaturalNumber0 @ sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroNat) ).
thf(36,axiom,
! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNatSort) ).
thf(37,axiom,
sdtlseqdt0 @ ( sdtasdt0 @ xP @ xP ) @ xN,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2004) ).
thf(38,axiom,
sdtlseqdt0 @ ( sdtasdt0 @ xE @ xE ) @ ( sdtasdt0 @ xC @ xD ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1967) ).
thf(39,axiom,
( ( aScalar0 @ xN )
& ( xN
= ( sdtasdt0 @ xR @ xS ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1949) ).
thf(40,axiom,
( ( aScalar0 @ xS )
& ( xS
= ( sdtasdt0 @ xF @ xD ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1930) ).
thf(41,axiom,
( ( aScalar0 @ xP )
& ( xP
= ( sdtasdt0 @ xE @ xH ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1911) ).
thf(42,axiom,
( ( aScalar0 @ xR )
& ( xR
= ( sdtasdt0 @ xC @ xG ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1892) ).
thf(43,axiom,
( ( aScalar0 @ xH )
& ( xH
= ( sdtasdt0 @ xA @ xB ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1873) ).
thf(44,axiom,
( ( aScalar0 @ xG )
& ( xG
= ( sdtasdt0 @ xB @ xB ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1854) ).
thf(45,axiom,
( ( aScalar0 @ xF )
& ( xF
= ( sdtasdt0 @ xA @ xA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
thf(46,axiom,
( ( aScalar0 @ xE )
& ( xE
= ( sdtasasdt0 @ xp @ xq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1820) ).
thf(47,axiom,
( ( aScalar0 @ xD )
& ( xD
= ( sdtasasdt0 @ xq @ xq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1800) ).
thf(48,axiom,
( ( aScalar0 @ xC )
& ( xC
= ( sdtasasdt0 @ xp @ xp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1783) ).
thf(49,axiom,
( ( aScalar0 @ xB )
& ( xB
= ( sdtlbdtrb0 @ xt @ ( aDimensionOf0 @ xt ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1766) ).
thf(50,axiom,
( ( aScalar0 @ xA )
& ( xA
= ( sdtlbdtrb0 @ xs @ ( aDimensionOf0 @ xs ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1746) ).
thf(51,axiom,
( ( aVector0 @ xq )
& ( ( szszuzczcdt0 @ ( aDimensionOf0 @ xq ) )
= ( aDimensionOf0 @ xt ) )
& ! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> ( ( sdtlbdtrb0 @ xq @ W0 )
= ( sdtlbdtrb0 @ xt @ W0 ) ) )
& ( xq
= ( sziznziztdt0 @ xt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1726) ).
thf(52,axiom,
( ( aVector0 @ xp )
& ( ( szszuzczcdt0 @ ( aDimensionOf0 @ xp ) )
= ( aDimensionOf0 @ xs ) )
& ! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> ( ( sdtlbdtrb0 @ xp @ W0 )
= ( sdtlbdtrb0 @ xs @ W0 ) ) )
& ( xp
= ( sziznziztdt0 @ xs ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1709) ).
thf(53,axiom,
( aDimensionOf0 @ xs )
!= sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1692) ).
thf(54,axiom,
( ( aDimensionOf0 @ xs )
= ( aDimensionOf0 @ xt ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1678_01) ).
thf(55,axiom,
! [W0: $i,W1: $i] :
( ( ( aVector0 @ W0 )
& ( aVector0 @ W1 ) )
=> ( ( ( aDimensionOf0 @ W0 )
= ( aDimensionOf0 @ W1 ) )
=> ( ( iLess0 @ ( aDimensionOf0 @ W0 ) @ ( aDimensionOf0 @ xs ) )
=> ( sdtlseqdt0 @ ( sdtasdt0 @ ( sdtasasdt0 @ W0 @ W1 ) @ ( sdtasasdt0 @ W0 @ W1 ) ) @ ( sdtasdt0 @ ( sdtasasdt0 @ W0 @ W0 ) @ ( sdtasasdt0 @ W1 @ W1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1652) ).
thf(56,axiom,
( ( aVector0 @ xs )
& ( aVector0 @ xt ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1678) ).
thf(57,conjecture,
( ( sdtasdt0 @ ( smndt0 @ xS ) @ xR )
= ( smndt0 @ xN ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(58,negated_conjecture,
( ( ( sdtasdt0 @ ( smndt0 @ xS ) @ xR )
= ( smndt0 @ xN ) )
= $false ),
inference(negate_conjecture,[status(cth)],[57]) ).
thf(59,plain,
( ( ( sdtasdt0 @ ( smndt0 @ xS ) @ xR )
= ( smndt0 @ xN ) )
= $false ),
inference(unfold_def,[status(thm)],[58]) ).
thf(60,plain,
( ( ! [W0: $i] :
( ( aVector0 @ W0 )
=> ( sdtlseqdt0 @ sz0z00 @ ( sdtasasdt0 @ W0 @ W0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(61,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aVector0 @ W0 )
& ( aVector0 @ W1 ) )
=> ( ( ( ( aDimensionOf0 @ W0 )
= ( aDimensionOf0 @ W1 ) )
& ( ( aDimensionOf0 @ W1 )
!= sz00 ) )
=> ( ( sdtasasdt0 @ W0 @ W1 )
= ( sdtpldt0 @ ( sdtasasdt0 @ ( sziznziztdt0 @ W0 ) @ ( sziznziztdt0 @ W1 ) ) @ ( sdtasdt0 @ ( sdtlbdtrb0 @ W0 @ ( aDimensionOf0 @ W0 ) ) @ ( sdtlbdtrb0 @ W1 @ ( aDimensionOf0 @ W1 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(62,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aVector0 @ W0 )
& ( aVector0 @ W1 ) )
=> ( ( ( ( aDimensionOf0 @ W0 )
= ( aDimensionOf0 @ W1 ) )
& ( ( aDimensionOf0 @ W1 )
= sz00 ) )
=> ( ( sdtasasdt0 @ W0 @ W1 )
= sz0z00 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(63,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aVector0 @ W0 )
& ( aVector0 @ W1 ) )
=> ( ( ( aDimensionOf0 @ W0 )
= ( aDimensionOf0 @ W1 ) )
=> ( aScalar0 @ ( sdtasasdt0 @ W0 @ W1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(64,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aVector0 @ W0 )
& ( aVector0 @ W1 ) )
=> ( ( ( ( aDimensionOf0 @ W0 )
= ( aDimensionOf0 @ W1 ) )
& ( ( aDimensionOf0 @ W1 )
!= sz00 ) )
=> ( ( aDimensionOf0 @ ( sziznziztdt0 @ W0 ) )
= ( aDimensionOf0 @ ( sziznziztdt0 @ W1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(65,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aVector0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( aScalar0 @ ( sdtlbdtrb0 @ W0 @ W1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(66,plain,
( ( ! [W0: $i] :
( ( aVector0 @ W0 )
=> ( aNaturalNumber0 @ ( aDimensionOf0 @ W0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(67,plain,
( ( ! [W0: $i] :
( ( aVector0 @ W0 )
=> $true ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(68,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aScalar0 @ W0 )
& ( aScalar0 @ W1 ) )
=> ( ( ( sdtlseqdt0 @ sz0z00 @ W0 )
& ( sdtlseqdt0 @ sz0z00 @ W1 )
& ( ( sdtasdt0 @ W0 @ W0 )
= ( sdtasdt0 @ W1 @ W1 ) ) )
=> ( W0 = W1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(69,plain,
( ( ! [W0: $i] :
( ( aScalar0 @ W0 )
=> ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ W0 @ W0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(70,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aScalar0 @ W0 )
& ( aScalar0 @ W1 ) )
=> ( ( ( sdtlseqdt0 @ sz0z00 @ W0 )
& ( sdtlseqdt0 @ sz0z00 @ W1 ) )
=> ( ( sdtlseqdt0 @ sz0z00 @ ( sdtpldt0 @ W0 @ W1 ) )
& ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ W0 @ W1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(71,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aScalar0 @ W0 )
& ( aScalar0 @ W1 ) )
=> ( ( sdtlseqdt0 @ W0 @ W1 )
| ( sdtlseqdt0 @ W1 @ W0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(72,plain,
( ( ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( ( ( aScalar0 @ W0 )
& ( aScalar0 @ W1 )
& ( aScalar0 @ W2 )
& ( aScalar0 @ W3 ) )
=> ( ( ( sdtlseqdt0 @ W0 @ W1 )
& ( sdtlseqdt0 @ sz0z00 @ W2 )
& ( sdtlseqdt0 @ W2 @ W3 ) )
=> ( sdtlseqdt0 @ ( sdtasdt0 @ W0 @ W2 ) @ ( sdtasdt0 @ W1 @ W3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(73,plain,
( ( ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( ( ( aScalar0 @ W0 )
& ( aScalar0 @ W1 )
& ( aScalar0 @ W2 )
& ( aScalar0 @ W3 ) )
=> ( ( ( sdtlseqdt0 @ W0 @ W1 )
& ( sdtlseqdt0 @ W2 @ W3 ) )
=> ( sdtlseqdt0 @ ( sdtpldt0 @ W0 @ W2 ) @ ( sdtpldt0 @ W1 @ W3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(74,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ( ( aScalar0 @ W0 )
& ( aScalar0 @ W1 )
& ( aScalar0 @ W2 ) )
=> ( ( ( sdtlseqdt0 @ W0 @ W1 )
& ( sdtlseqdt0 @ W1 @ W2 ) )
=> ( sdtlseqdt0 @ W0 @ W2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(75,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aScalar0 @ W0 )
& ( aScalar0 @ W1 ) )
=> ( ( ( sdtlseqdt0 @ W0 @ W1 )
& ( sdtlseqdt0 @ W1 @ W0 ) )
=> ( W0 = W1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(76,plain,
( ( ! [W0: $i] :
( ( aScalar0 @ W0 )
=> ( sdtlseqdt0 @ W0 @ W0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(77,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aScalar0 @ W0 )
& ( aScalar0 @ W1 ) )
=> ( ( sdtlseqdt0 @ W0 @ W1 )
=> $true ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(78,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aScalar0 @ W0 )
& ( aScalar0 @ W1 ) )
=> ( ( sdtasdt0 @ ( smndt0 @ W0 ) @ ( smndt0 @ W1 ) )
= ( sdtasdt0 @ W0 @ W1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(79,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aScalar0 @ W0 )
& ( aScalar0 @ W1 ) )
=> ( ( ( sdtasdt0 @ W0 @ ( smndt0 @ W1 ) )
= ( smndt0 @ ( sdtasdt0 @ W0 @ W1 ) ) )
& ( ( sdtasdt0 @ ( smndt0 @ W0 ) @ W1 )
= ( smndt0 @ ( sdtasdt0 @ W0 @ W1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(80,plain,
( ( ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( ( ( aScalar0 @ W0 )
& ( aScalar0 @ W1 )
& ( aScalar0 @ W2 )
& ( aScalar0 @ W3 ) )
=> ( ( sdtasdt0 @ ( sdtpldt0 @ W0 @ W1 ) @ ( sdtpldt0 @ W2 @ W3 ) )
= ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ W0 @ W2 ) @ ( sdtasdt0 @ W0 @ W3 ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ W1 @ W2 ) @ ( sdtasdt0 @ W1 @ W3 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(81,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ( ( aScalar0 @ W0 )
& ( aScalar0 @ W1 )
& ( aScalar0 @ W2 ) )
=> ( ( ( sdtasdt0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ W0 @ W1 ) @ ( sdtasdt0 @ W0 @ W2 ) ) )
& ( ( sdtasdt0 @ ( sdtpldt0 @ W0 @ W1 ) @ W2 )
= ( sdtpldt0 @ ( sdtasdt0 @ W0 @ W2 ) @ ( sdtasdt0 @ W1 @ W2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(82,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ( ( aScalar0 @ W0 )
& ( aScalar0 @ W1 )
& ( aScalar0 @ W2 ) )
=> ( ( ( sdtpldt0 @ ( sdtpldt0 @ W0 @ W1 ) @ W2 )
= ( sdtpldt0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) ) )
& ( ( sdtpldt0 @ W0 @ W1 )
= ( sdtpldt0 @ W1 @ W0 ) )
& ( ( sdtasdt0 @ ( sdtasdt0 @ W0 @ W1 ) @ W2 )
= ( sdtasdt0 @ W0 @ ( sdtasdt0 @ W1 @ W2 ) ) )
& ( ( sdtasdt0 @ W0 @ W1 )
= ( sdtasdt0 @ W1 @ W0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(83,plain,
( ( ! [W0: $i] :
( ( aScalar0 @ W0 )
=> ( ( ( sdtpldt0 @ W0 @ sz0z00 )
= W0 )
& ( ( sdtpldt0 @ sz0z00 @ W0 )
= W0 )
& ( ( sdtasdt0 @ W0 @ sz0z00 )
= sz0z00 )
& ( ( sdtasdt0 @ sz0z00 @ W0 )
= sz0z00 )
& ( ( sdtpldt0 @ W0 @ ( smndt0 @ W0 ) )
= sz0z00 )
& ( ( sdtpldt0 @ ( smndt0 @ W0 ) @ W0 )
= sz0z00 )
& ( ( smndt0 @ ( smndt0 @ W0 ) )
= W0 )
& ( ( smndt0 @ sz0z00 )
= sz0z00 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(84,plain,
( ( ! [W0: $i] :
( ( aScalar0 @ W0 )
=> ( aScalar0 @ ( smndt0 @ W0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(85,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aScalar0 @ W0 )
& ( aScalar0 @ W1 ) )
=> ( aScalar0 @ ( sdtasdt0 @ W0 @ W1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(86,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aScalar0 @ W0 )
& ( aScalar0 @ W1 ) )
=> ( aScalar0 @ ( sdtpldt0 @ W0 @ W1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(87,plain,
( ( aScalar0 @ sz0z00 )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(88,plain,
( ( ! [W0: $i] :
( ( aScalar0 @ W0 )
=> $true ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(89,plain,
( ( ! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> ( iLess0 @ W0 @ ( szszuzczcdt0 @ W0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(90,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( iLess0 @ W0 @ W1 )
=> $true ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(91,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( ( szszuzczcdt0 @ W0 )
= ( szszuzczcdt0 @ W1 ) )
=> ( W0 = W1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(92,plain,
( ( ! [W0: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( W0 != sz00 ) )
=> ? [W1: $i] :
( ( aNaturalNumber0 @ W1 )
& ( W0
= ( szszuzczcdt0 @ W1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(93,plain,
( ( ! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ W0 ) )
& ( ( szszuzczcdt0 @ W0 )
!= sz00 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(94,plain,
( ( aNaturalNumber0 @ sz00 )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(95,plain,
( ( ! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> $true ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(96,plain,
( ( sdtlseqdt0 @ ( sdtasdt0 @ xP @ xP ) @ xN )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(97,plain,
( ( sdtlseqdt0 @ ( sdtasdt0 @ xE @ xE ) @ ( sdtasdt0 @ xC @ xD ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(98,plain,
( ( ( aScalar0 @ xN )
& ( xN
= ( sdtasdt0 @ xR @ xS ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(99,plain,
( ( ( aScalar0 @ xS )
& ( xS
= ( sdtasdt0 @ xF @ xD ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(100,plain,
( ( ( aScalar0 @ xP )
& ( xP
= ( sdtasdt0 @ xE @ xH ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(101,plain,
( ( ( aScalar0 @ xR )
& ( xR
= ( sdtasdt0 @ xC @ xG ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(102,plain,
( ( ( aScalar0 @ xH )
& ( xH
= ( sdtasdt0 @ xA @ xB ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(103,plain,
( ( ( aScalar0 @ xG )
& ( xG
= ( sdtasdt0 @ xB @ xB ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(104,plain,
( ( ( aScalar0 @ xF )
& ( xF
= ( sdtasdt0 @ xA @ xA ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(105,plain,
( ( ( aScalar0 @ xE )
& ( xE
= ( sdtasasdt0 @ xp @ xq ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(106,plain,
( ( ( aScalar0 @ xD )
& ( xD
= ( sdtasasdt0 @ xq @ xq ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(107,plain,
( ( ( aScalar0 @ xC )
& ( xC
= ( sdtasasdt0 @ xp @ xp ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(108,plain,
( ( ( aScalar0 @ xB )
& ( xB
= ( sdtlbdtrb0 @ xt @ ( aDimensionOf0 @ xt ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(109,plain,
( ( ( aScalar0 @ xA )
& ( xA
= ( sdtlbdtrb0 @ xs @ ( aDimensionOf0 @ xs ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(110,plain,
( ( ( aVector0 @ xq )
& ( ( szszuzczcdt0 @ ( aDimensionOf0 @ xq ) )
= ( aDimensionOf0 @ xt ) )
& ! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> ( ( sdtlbdtrb0 @ xq @ W0 )
= ( sdtlbdtrb0 @ xt @ W0 ) ) )
& ( xq
= ( sziznziztdt0 @ xt ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(111,plain,
( ( ( aVector0 @ xp )
& ( ( szszuzczcdt0 @ ( aDimensionOf0 @ xp ) )
= ( aDimensionOf0 @ xs ) )
& ! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> ( ( sdtlbdtrb0 @ xp @ W0 )
= ( sdtlbdtrb0 @ xs @ W0 ) ) )
& ( xp
= ( sziznziztdt0 @ xs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(112,plain,
( ( ( ( aDimensionOf0 @ xs )
!= sz00 ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(113,plain,
( ( ( aDimensionOf0 @ xs )
= ( aDimensionOf0 @ xt ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(114,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aVector0 @ W0 )
& ( aVector0 @ W1 ) )
=> ( ( ( aDimensionOf0 @ W0 )
= ( aDimensionOf0 @ W1 ) )
=> ( ( iLess0 @ ( aDimensionOf0 @ W0 ) @ ( aDimensionOf0 @ xs ) )
=> ( sdtlseqdt0 @ ( sdtasdt0 @ ( sdtasasdt0 @ W0 @ W1 ) @ ( sdtasasdt0 @ W0 @ W1 ) ) @ ( sdtasdt0 @ ( sdtasasdt0 @ W0 @ W0 ) @ ( sdtasasdt0 @ W1 @ W1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(115,plain,
( ( ( aVector0 @ xs )
& ( aVector0 @ xt ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(116,plain,
( ( ( ( sdtasdt0 @ ( smndt0 @ xS ) @ xR )
!= ( smndt0 @ xN ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[59]) ).
thf(117,plain,
( ( ! [W0: $i] :
( ~ ( aVector0 @ W0 )
| ( sdtlseqdt0 @ sz0z00 @ ( sdtasasdt0 @ W0 @ W0 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[60]) ).
thf(118,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aVector0 @ W0 )
| ~ ( aVector0 @ W1 )
| ( ( aDimensionOf0 @ W1 )
= sz00 )
| ( ( aDimensionOf0 @ W0 )
!= ( aDimensionOf0 @ W1 ) )
| ( ( sdtasasdt0 @ W0 @ W1 )
= ( sdtpldt0 @ ( sdtasasdt0 @ ( sziznziztdt0 @ W0 ) @ ( sziznziztdt0 @ W1 ) ) @ ( sdtasdt0 @ ( sdtlbdtrb0 @ W0 @ ( aDimensionOf0 @ W0 ) ) @ ( sdtlbdtrb0 @ W1 @ ( aDimensionOf0 @ W1 ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[61]) ).
thf(119,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aVector0 @ W0 )
| ~ ( aVector0 @ W1 )
| ( ( aDimensionOf0 @ W0 )
!= ( aDimensionOf0 @ W1 ) )
| ( ( aDimensionOf0 @ W1 )
!= sz00 )
| ( ( sdtasasdt0 @ W0 @ W1 )
= sz0z00 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[62]) ).
thf(120,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aVector0 @ W0 )
| ~ ( aVector0 @ W1 )
| ( ( aDimensionOf0 @ W0 )
!= ( aDimensionOf0 @ W1 ) )
| ( aScalar0 @ ( sdtasasdt0 @ W0 @ W1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[63]) ).
thf(121,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aVector0 @ W0 )
| ~ ( aVector0 @ W1 )
| ( ( aDimensionOf0 @ W1 )
= sz00 )
| ( ( aDimensionOf0 @ W0 )
!= ( aDimensionOf0 @ W1 ) )
| ( ( aDimensionOf0 @ ( sziznziztdt0 @ W0 ) )
= ( aDimensionOf0 @ ( sziznziztdt0 @ W1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[64]) ).
thf(122,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0 @ W1 )
| ~ ( aVector0 @ W0 )
| ( aScalar0 @ ( sdtlbdtrb0 @ W0 @ W1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[65]) ).
thf(123,plain,
( ( ! [W0: $i] :
( ~ ( aVector0 @ W0 )
| ( aNaturalNumber0 @ ( aDimensionOf0 @ W0 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[66]) ).
thf(124,plain,
( ( ! [W0: $i] : $true )
= $true ),
inference(extcnf_combined,[status(esa)],[67]) ).
thf(125,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aScalar0 @ W0 )
| ~ ( aScalar0 @ W1 )
| ~ ( sdtlseqdt0 @ sz0z00 @ W0 )
| ~ ( sdtlseqdt0 @ sz0z00 @ W1 )
| ( ( sdtasdt0 @ W0 @ W0 )
!= ( sdtasdt0 @ W1 @ W1 ) )
| ( W0 = W1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[68]) ).
thf(126,plain,
( ( ! [W0: $i] :
( ~ ( aScalar0 @ W0 )
| ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ W0 @ W0 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[69]) ).
thf(127,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aScalar0 @ W0 )
| ~ ( aScalar0 @ W1 )
| ~ ( sdtlseqdt0 @ sz0z00 @ W0 )
| ~ ( sdtlseqdt0 @ sz0z00 @ W1 )
| ( sdtlseqdt0 @ sz0z00 @ ( sdtpldt0 @ W0 @ W1 ) ) )
& ! [W0: $i,W1: $i] :
( ~ ( aScalar0 @ W0 )
| ~ ( aScalar0 @ W1 )
| ~ ( sdtlseqdt0 @ sz0z00 @ W0 )
| ~ ( sdtlseqdt0 @ sz0z00 @ W1 )
| ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ W0 @ W1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[70]) ).
thf(128,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aScalar0 @ W0 )
| ~ ( aScalar0 @ W1 )
| ( sdtlseqdt0 @ W0 @ W1 )
| ( sdtlseqdt0 @ W1 @ W0 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[71]) ).
thf(129,plain,
( ( ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( ~ ( aScalar0 @ W0 )
| ~ ( aScalar0 @ W1 )
| ~ ( aScalar0 @ W2 )
| ~ ( aScalar0 @ W3 )
| ~ ( sdtlseqdt0 @ W0 @ W1 )
| ~ ( sdtlseqdt0 @ sz0z00 @ W2 )
| ~ ( sdtlseqdt0 @ W2 @ W3 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ W0 @ W2 ) @ ( sdtasdt0 @ W1 @ W3 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[72]) ).
thf(130,plain,
( ( ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( ~ ( aScalar0 @ W0 )
| ~ ( aScalar0 @ W1 )
| ~ ( aScalar0 @ W2 )
| ~ ( aScalar0 @ W3 )
| ~ ( sdtlseqdt0 @ W0 @ W1 )
| ~ ( sdtlseqdt0 @ W2 @ W3 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ W0 @ W2 ) @ ( sdtpldt0 @ W1 @ W3 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[73]) ).
thf(131,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aScalar0 @ W0 )
| ~ ( aScalar0 @ W1 )
| ~ ( aScalar0 @ W2 )
| ~ ( sdtlseqdt0 @ W0 @ W1 )
| ~ ( sdtlseqdt0 @ W1 @ W2 )
| ( sdtlseqdt0 @ W0 @ W2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[74]) ).
thf(132,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aScalar0 @ W0 )
| ~ ( aScalar0 @ W1 )
| ~ ( sdtlseqdt0 @ W0 @ W1 )
| ~ ( sdtlseqdt0 @ W1 @ W0 )
| ( W0 = W1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[75]) ).
thf(133,plain,
( ( ! [W0: $i] :
( ~ ( aScalar0 @ W0 )
| ( sdtlseqdt0 @ W0 @ W0 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[76]) ).
thf(134,plain,
( ( ! [W0: $i] :
~ ( aScalar0 @ W0 )
| ! [W1: $i] :
~ ( aScalar0 @ W1 )
| $true )
= $true ),
inference(extcnf_combined,[status(esa)],[77]) ).
thf(135,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aScalar0 @ W0 )
| ~ ( aScalar0 @ W1 )
| ( ( sdtasdt0 @ ( smndt0 @ W0 ) @ ( smndt0 @ W1 ) )
= ( sdtasdt0 @ W0 @ W1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[78]) ).
thf(136,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aScalar0 @ W0 )
| ~ ( aScalar0 @ W1 )
| ( ( sdtasdt0 @ W0 @ ( smndt0 @ W1 ) )
= ( smndt0 @ ( sdtasdt0 @ W0 @ W1 ) ) ) )
& ! [W0: $i,W1: $i] :
( ~ ( aScalar0 @ W0 )
| ~ ( aScalar0 @ W1 )
| ( ( sdtasdt0 @ ( smndt0 @ W0 ) @ W1 )
= ( smndt0 @ ( sdtasdt0 @ W0 @ W1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[79]) ).
thf(137,plain,
( ( ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( ~ ( aScalar0 @ W0 )
| ~ ( aScalar0 @ W1 )
| ~ ( aScalar0 @ W2 )
| ~ ( aScalar0 @ W3 )
| ( ( sdtasdt0 @ ( sdtpldt0 @ W0 @ W1 ) @ ( sdtpldt0 @ W2 @ W3 ) )
= ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ W0 @ W2 ) @ ( sdtasdt0 @ W0 @ W3 ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ W1 @ W2 ) @ ( sdtasdt0 @ W1 @ W3 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[80]) ).
thf(138,plain,
( ( ! [W0: $i] :
( ! [W1: $i,W2: $i] :
( ~ ( aScalar0 @ W0 )
| ~ ( aScalar0 @ W1 )
| ~ ( aScalar0 @ W2 )
| ( ( sdtasdt0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ W0 @ W1 ) @ ( sdtasdt0 @ W0 @ W2 ) ) ) )
& ! [W1: $i,W2: $i] :
( ~ ( aScalar0 @ W0 )
| ~ ( aScalar0 @ W1 )
| ~ ( aScalar0 @ W2 )
| ( ( sdtasdt0 @ ( sdtpldt0 @ W0 @ W1 ) @ W2 )
= ( sdtpldt0 @ ( sdtasdt0 @ W0 @ W2 ) @ ( sdtasdt0 @ W1 @ W2 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[81]) ).
thf(139,plain,
( ( ! [W0: $i] :
( ! [W1: $i,W2: $i] :
( ~ ( aScalar0 @ W0 )
| ~ ( aScalar0 @ W1 )
| ~ ( aScalar0 @ W2 )
| ( ( sdtpldt0 @ ( sdtpldt0 @ W0 @ W1 ) @ W2 )
= ( sdtpldt0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) ) ) )
& ! [W1: $i] :
( ~ ( aScalar0 @ W0 )
| ~ ( aScalar0 @ W1 )
| ! [W2: $i] :
~ ( aScalar0 @ W2 )
| ( ( sdtpldt0 @ W0 @ W1 )
= ( sdtpldt0 @ W1 @ W0 ) ) )
& ! [W1: $i,W2: $i] :
( ~ ( aScalar0 @ W0 )
| ~ ( aScalar0 @ W1 )
| ~ ( aScalar0 @ W2 )
| ( ( sdtasdt0 @ ( sdtasdt0 @ W0 @ W1 ) @ W2 )
= ( sdtasdt0 @ W0 @ ( sdtasdt0 @ W1 @ W2 ) ) ) )
& ! [W1: $i] :
( ~ ( aScalar0 @ W0 )
| ~ ( aScalar0 @ W1 )
| ! [W2: $i] :
~ ( aScalar0 @ W2 )
| ( ( sdtasdt0 @ W0 @ W1 )
= ( sdtasdt0 @ W1 @ W0 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[82]) ).
thf(140,plain,
( ( ! [W0: $i] :
( ~ ( aScalar0 @ W0 )
| ( ( sdtpldt0 @ W0 @ sz0z00 )
= W0 ) )
& ! [W0: $i] :
( ~ ( aScalar0 @ W0 )
| ( ( sdtpldt0 @ sz0z00 @ W0 )
= W0 ) )
& ! [W0: $i] :
( ~ ( aScalar0 @ W0 )
| ( ( sdtasdt0 @ W0 @ sz0z00 )
= sz0z00 ) )
& ! [W0: $i] :
( ~ ( aScalar0 @ W0 )
| ( ( sdtasdt0 @ sz0z00 @ W0 )
= sz0z00 ) )
& ! [W0: $i] :
( ~ ( aScalar0 @ W0 )
| ( ( sdtpldt0 @ W0 @ ( smndt0 @ W0 ) )
= sz0z00 ) )
& ! [W0: $i] :
( ~ ( aScalar0 @ W0 )
| ( ( sdtpldt0 @ ( smndt0 @ W0 ) @ W0 )
= sz0z00 ) )
& ! [W0: $i] :
( ~ ( aScalar0 @ W0 )
| ( ( smndt0 @ ( smndt0 @ W0 ) )
= W0 ) )
& ( ! [W0: $i] :
~ ( aScalar0 @ W0 )
| ( ( smndt0 @ sz0z00 )
= sz0z00 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[83]) ).
thf(141,plain,
( ( ! [W0: $i] :
( ~ ( aScalar0 @ W0 )
| ( aScalar0 @ ( smndt0 @ W0 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[84]) ).
thf(142,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aScalar0 @ W0 )
| ~ ( aScalar0 @ W1 )
| ( aScalar0 @ ( sdtasdt0 @ W0 @ W1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[85]) ).
thf(143,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aScalar0 @ W0 )
| ~ ( aScalar0 @ W1 )
| ( aScalar0 @ ( sdtpldt0 @ W0 @ W1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[86]) ).
thf(144,plain,
( ( ! [W0: $i] : $true )
= $true ),
inference(extcnf_combined,[status(esa)],[88]) ).
thf(145,plain,
( ( ! [W0: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ( iLess0 @ W0 @ ( szszuzczcdt0 @ W0 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[89]) ).
thf(146,plain,
( ( ! [W0: $i] :
~ ( aNaturalNumber0 @ W0 )
| ! [W1: $i] :
~ ( aNaturalNumber0 @ W1 )
| $true )
= $true ),
inference(extcnf_combined,[status(esa)],[90]) ).
thf(147,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ( ( szszuzczcdt0 @ W0 )
!= ( szszuzczcdt0 @ W1 ) )
| ( W0 = W1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[91]) ).
thf(148,plain,
( ( ! [W0: $i] :
( ( W0 = sz00 )
| ~ ( aNaturalNumber0 @ W0 )
| ( ( W0
= ( szszuzczcdt0 @ ( sK1_W1 @ W0 ) ) )
& ( aNaturalNumber0 @ ( sK1_W1 @ W0 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[92]) ).
thf(149,plain,
( ( ! [W0: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ( ( szszuzczcdt0 @ W0 )
!= sz00 ) )
& ! [W0: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ( aNaturalNumber0 @ ( szszuzczcdt0 @ W0 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[93]) ).
thf(150,plain,
( ( ! [W0: $i] : $true )
= $true ),
inference(extcnf_combined,[status(esa)],[95]) ).
thf(151,plain,
( ( ( xN
= ( sdtasdt0 @ xR @ xS ) )
& ( aScalar0 @ xN ) )
= $true ),
inference(extcnf_combined,[status(esa)],[98]) ).
thf(152,plain,
( ( ( xS
= ( sdtasdt0 @ xF @ xD ) )
& ( aScalar0 @ xS ) )
= $true ),
inference(extcnf_combined,[status(esa)],[99]) ).
thf(153,plain,
( ( ( xP
= ( sdtasdt0 @ xE @ xH ) )
& ( aScalar0 @ xP ) )
= $true ),
inference(extcnf_combined,[status(esa)],[100]) ).
thf(154,plain,
( ( ( xR
= ( sdtasdt0 @ xC @ xG ) )
& ( aScalar0 @ xR ) )
= $true ),
inference(extcnf_combined,[status(esa)],[101]) ).
thf(155,plain,
( ( ( xH
= ( sdtasdt0 @ xA @ xB ) )
& ( aScalar0 @ xH ) )
= $true ),
inference(extcnf_combined,[status(esa)],[102]) ).
thf(156,plain,
( ( ( xG
= ( sdtasdt0 @ xB @ xB ) )
& ( aScalar0 @ xG ) )
= $true ),
inference(extcnf_combined,[status(esa)],[103]) ).
thf(157,plain,
( ( ( xF
= ( sdtasdt0 @ xA @ xA ) )
& ( aScalar0 @ xF ) )
= $true ),
inference(extcnf_combined,[status(esa)],[104]) ).
thf(158,plain,
( ( ( xE
= ( sdtasasdt0 @ xp @ xq ) )
& ( aScalar0 @ xE ) )
= $true ),
inference(extcnf_combined,[status(esa)],[105]) ).
thf(159,plain,
( ( ( xD
= ( sdtasasdt0 @ xq @ xq ) )
& ( aScalar0 @ xD ) )
= $true ),
inference(extcnf_combined,[status(esa)],[106]) ).
thf(160,plain,
( ( ( xC
= ( sdtasasdt0 @ xp @ xp ) )
& ( aScalar0 @ xC ) )
= $true ),
inference(extcnf_combined,[status(esa)],[107]) ).
thf(161,plain,
( ( ( xB
= ( sdtlbdtrb0 @ xt @ ( aDimensionOf0 @ xt ) ) )
& ( aScalar0 @ xB ) )
= $true ),
inference(extcnf_combined,[status(esa)],[108]) ).
thf(162,plain,
( ( ( xA
= ( sdtlbdtrb0 @ xs @ ( aDimensionOf0 @ xs ) ) )
& ( aScalar0 @ xA ) )
= $true ),
inference(extcnf_combined,[status(esa)],[109]) ).
thf(163,plain,
( ( ! [W0: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ( ( sdtlbdtrb0 @ xq @ W0 )
= ( sdtlbdtrb0 @ xt @ W0 ) ) )
& ( ( szszuzczcdt0 @ ( aDimensionOf0 @ xq ) )
= ( aDimensionOf0 @ xt ) )
& ( aVector0 @ xq )
& ( xq
= ( sziznziztdt0 @ xt ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[110]) ).
thf(164,plain,
( ( ! [W0: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ( ( sdtlbdtrb0 @ xp @ W0 )
= ( sdtlbdtrb0 @ xs @ W0 ) ) )
& ( ( szszuzczcdt0 @ ( aDimensionOf0 @ xp ) )
= ( aDimensionOf0 @ xs ) )
& ( aVector0 @ xp )
& ( xp
= ( sziznziztdt0 @ xs ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[111]) ).
thf(165,plain,
( ( ( ( aDimensionOf0 @ xs )
!= sz00 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[112]) ).
thf(166,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aVector0 @ W0 )
| ~ ( aVector0 @ W1 )
| ( ( aDimensionOf0 @ W0 )
!= ( aDimensionOf0 @ W1 ) )
| ~ ( iLess0 @ ( aDimensionOf0 @ W0 ) @ ( aDimensionOf0 @ xs ) )
| ( sdtlseqdt0 @ ( sdtasdt0 @ ( sdtasasdt0 @ W0 @ W1 ) @ ( sdtasasdt0 @ W0 @ W1 ) ) @ ( sdtasdt0 @ ( sdtasasdt0 @ W0 @ W0 ) @ ( sdtasasdt0 @ W1 @ W1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[114]) ).
thf(167,plain,
( ( ( aVector0 @ xs )
& ( aVector0 @ xt ) )
= $true ),
inference(copy,[status(thm)],[115]) ).
thf(168,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aVector0 @ W0 )
| ~ ( aVector0 @ W1 )
| ( ( aDimensionOf0 @ W0 )
!= ( aDimensionOf0 @ W1 ) )
| ~ ( iLess0 @ ( aDimensionOf0 @ W0 ) @ ( aDimensionOf0 @ xs ) )
| ( sdtlseqdt0 @ ( sdtasdt0 @ ( sdtasasdt0 @ W0 @ W1 ) @ ( sdtasasdt0 @ W0 @ W1 ) ) @ ( sdtasdt0 @ ( sdtasasdt0 @ W0 @ W0 ) @ ( sdtasasdt0 @ W1 @ W1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[166]) ).
thf(169,plain,
( ( ( aDimensionOf0 @ xs )
= ( aDimensionOf0 @ xt ) )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(170,plain,
( ( ( ( aDimensionOf0 @ xs )
!= sz00 ) )
= $true ),
inference(copy,[status(thm)],[165]) ).
thf(171,plain,
( ( ! [W0: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ( ( sdtlbdtrb0 @ xp @ W0 )
= ( sdtlbdtrb0 @ xs @ W0 ) ) )
& ( ( szszuzczcdt0 @ ( aDimensionOf0 @ xp ) )
= ( aDimensionOf0 @ xs ) )
& ( aVector0 @ xp )
& ( xp
= ( sziznziztdt0 @ xs ) ) )
= $true ),
inference(copy,[status(thm)],[164]) ).
thf(172,plain,
( ( ! [W0: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ( ( sdtlbdtrb0 @ xq @ W0 )
= ( sdtlbdtrb0 @ xt @ W0 ) ) )
& ( ( szszuzczcdt0 @ ( aDimensionOf0 @ xq ) )
= ( aDimensionOf0 @ xt ) )
& ( aVector0 @ xq )
& ( xq
= ( sziznziztdt0 @ xt ) ) )
= $true ),
inference(copy,[status(thm)],[163]) ).
thf(173,plain,
( ( ( xA
= ( sdtlbdtrb0 @ xs @ ( aDimensionOf0 @ xs ) ) )
& ( aScalar0 @ xA ) )
= $true ),
inference(copy,[status(thm)],[162]) ).
thf(174,plain,
( ( ( xB
= ( sdtlbdtrb0 @ xt @ ( aDimensionOf0 @ xt ) ) )
& ( aScalar0 @ xB ) )
= $true ),
inference(copy,[status(thm)],[161]) ).
thf(175,plain,
( ( ( xC
= ( sdtasasdt0 @ xp @ xp ) )
& ( aScalar0 @ xC ) )
= $true ),
inference(copy,[status(thm)],[160]) ).
thf(176,plain,
( ( ( xD
= ( sdtasasdt0 @ xq @ xq ) )
& ( aScalar0 @ xD ) )
= $true ),
inference(copy,[status(thm)],[159]) ).
thf(177,plain,
( ( ( xE
= ( sdtasasdt0 @ xp @ xq ) )
& ( aScalar0 @ xE ) )
= $true ),
inference(copy,[status(thm)],[158]) ).
thf(178,plain,
( ( ( xF
= ( sdtasdt0 @ xA @ xA ) )
& ( aScalar0 @ xF ) )
= $true ),
inference(copy,[status(thm)],[157]) ).
thf(179,plain,
( ( ( xG
= ( sdtasdt0 @ xB @ xB ) )
& ( aScalar0 @ xG ) )
= $true ),
inference(copy,[status(thm)],[156]) ).
thf(180,plain,
( ( ( xH
= ( sdtasdt0 @ xA @ xB ) )
& ( aScalar0 @ xH ) )
= $true ),
inference(copy,[status(thm)],[155]) ).
thf(181,plain,
( ( ( xR
= ( sdtasdt0 @ xC @ xG ) )
& ( aScalar0 @ xR ) )
= $true ),
inference(copy,[status(thm)],[154]) ).
thf(182,plain,
( ( ( xP
= ( sdtasdt0 @ xE @ xH ) )
& ( aScalar0 @ xP ) )
= $true ),
inference(copy,[status(thm)],[153]) ).
thf(183,plain,
( ( ( xS
= ( sdtasdt0 @ xF @ xD ) )
& ( aScalar0 @ xS ) )
= $true ),
inference(copy,[status(thm)],[152]) ).
thf(184,plain,
( ( ( xN
= ( sdtasdt0 @ xR @ xS ) )
& ( aScalar0 @ xN ) )
= $true ),
inference(copy,[status(thm)],[151]) ).
thf(185,plain,
( ( sdtlseqdt0 @ ( sdtasdt0 @ xE @ xE ) @ ( sdtasdt0 @ xC @ xD ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(186,plain,
( ( sdtlseqdt0 @ ( sdtasdt0 @ xP @ xP ) @ xN )
= $true ),
inference(copy,[status(thm)],[96]) ).
thf(187,plain,
( ( ! [W0: $i] : $true )
= $true ),
inference(copy,[status(thm)],[150]) ).
thf(188,plain,
( ( aNaturalNumber0 @ sz00 )
= $true ),
inference(copy,[status(thm)],[94]) ).
thf(189,plain,
( ( ! [W0: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ( ( szszuzczcdt0 @ W0 )
!= sz00 ) )
& ! [W0: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ( aNaturalNumber0 @ ( szszuzczcdt0 @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[149]) ).
thf(190,plain,
( ( ! [W0: $i] :
( ( W0 = sz00 )
| ~ ( aNaturalNumber0 @ W0 )
| ( ( W0
= ( szszuzczcdt0 @ ( sK1_W1 @ W0 ) ) )
& ( aNaturalNumber0 @ ( sK1_W1 @ W0 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[148]) ).
thf(191,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ~ ( aNaturalNumber0 @ W1 )
| ( ( szszuzczcdt0 @ W0 )
!= ( szszuzczcdt0 @ W1 ) )
| ( W0 = W1 ) ) )
= $true ),
inference(copy,[status(thm)],[147]) ).
thf(192,plain,
( ( ! [W0: $i] :
~ ( aNaturalNumber0 @ W0 )
| ! [W1: $i] :
~ ( aNaturalNumber0 @ W1 )
| $true )
= $true ),
inference(copy,[status(thm)],[146]) ).
thf(193,plain,
( ( ! [W0: $i] :
( ~ ( aNaturalNumber0 @ W0 )
| ( iLess0 @ W0 @ ( szszuzczcdt0 @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[145]) ).
thf(194,plain,
( ( ! [W0: $i] : $true )
= $true ),
inference(copy,[status(thm)],[144]) ).
thf(195,plain,
( ( aScalar0 @ sz0z00 )
= $true ),
inference(copy,[status(thm)],[87]) ).
thf(196,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aScalar0 @ W0 )
| ~ ( aScalar0 @ W1 )
| ( aScalar0 @ ( sdtpldt0 @ W0 @ W1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[143]) ).
thf(197,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aScalar0 @ W0 )
| ~ ( aScalar0 @ W1 )
| ( aScalar0 @ ( sdtasdt0 @ W0 @ W1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[142]) ).
thf(198,plain,
( ( ! [W0: $i] :
( ~ ( aScalar0 @ W0 )
| ( aScalar0 @ ( smndt0 @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[141]) ).
thf(199,plain,
( ( ! [W0: $i] :
( ~ ( aScalar0 @ W0 )
| ( ( sdtpldt0 @ W0 @ sz0z00 )
= W0 ) )
& ! [W0: $i] :
( ~ ( aScalar0 @ W0 )
| ( ( sdtpldt0 @ sz0z00 @ W0 )
= W0 ) )
& ! [W0: $i] :
( ~ ( aScalar0 @ W0 )
| ( ( sdtasdt0 @ W0 @ sz0z00 )
= sz0z00 ) )
& ! [W0: $i] :
( ~ ( aScalar0 @ W0 )
| ( ( sdtasdt0 @ sz0z00 @ W0 )
= sz0z00 ) )
& ! [W0: $i] :
( ~ ( aScalar0 @ W0 )
| ( ( sdtpldt0 @ W0 @ ( smndt0 @ W0 ) )
= sz0z00 ) )
& ! [W0: $i] :
( ~ ( aScalar0 @ W0 )
| ( ( sdtpldt0 @ ( smndt0 @ W0 ) @ W0 )
= sz0z00 ) )
& ! [W0: $i] :
( ~ ( aScalar0 @ W0 )
| ( ( smndt0 @ ( smndt0 @ W0 ) )
= W0 ) )
& ( ! [W0: $i] :
~ ( aScalar0 @ W0 )
| ( ( smndt0 @ sz0z00 )
= sz0z00 ) ) )
= $true ),
inference(copy,[status(thm)],[140]) ).
thf(200,plain,
( ( ! [W0: $i] :
( ! [W1: $i,W2: $i] :
( ~ ( aScalar0 @ W0 )
| ~ ( aScalar0 @ W1 )
| ~ ( aScalar0 @ W2 )
| ( ( sdtpldt0 @ ( sdtpldt0 @ W0 @ W1 ) @ W2 )
= ( sdtpldt0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) ) ) )
& ! [W1: $i] :
( ~ ( aScalar0 @ W0 )
| ~ ( aScalar0 @ W1 )
| ! [W2: $i] :
~ ( aScalar0 @ W2 )
| ( ( sdtpldt0 @ W0 @ W1 )
= ( sdtpldt0 @ W1 @ W0 ) ) )
& ! [W1: $i,W2: $i] :
( ~ ( aScalar0 @ W0 )
| ~ ( aScalar0 @ W1 )
| ~ ( aScalar0 @ W2 )
| ( ( sdtasdt0 @ ( sdtasdt0 @ W0 @ W1 ) @ W2 )
= ( sdtasdt0 @ W0 @ ( sdtasdt0 @ W1 @ W2 ) ) ) )
& ! [W1: $i] :
( ~ ( aScalar0 @ W0 )
| ~ ( aScalar0 @ W1 )
| ! [W2: $i] :
~ ( aScalar0 @ W2 )
| ( ( sdtasdt0 @ W0 @ W1 )
= ( sdtasdt0 @ W1 @ W0 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[139]) ).
thf(201,plain,
( ( ! [W0: $i] :
( ! [W1: $i,W2: $i] :
( ~ ( aScalar0 @ W0 )
| ~ ( aScalar0 @ W1 )
| ~ ( aScalar0 @ W2 )
| ( ( sdtasdt0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ W0 @ W1 ) @ ( sdtasdt0 @ W0 @ W2 ) ) ) )
& ! [W1: $i,W2: $i] :
( ~ ( aScalar0 @ W0 )
| ~ ( aScalar0 @ W1 )
| ~ ( aScalar0 @ W2 )
| ( ( sdtasdt0 @ ( sdtpldt0 @ W0 @ W1 ) @ W2 )
= ( sdtpldt0 @ ( sdtasdt0 @ W0 @ W2 ) @ ( sdtasdt0 @ W1 @ W2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[138]) ).
thf(202,plain,
( ( ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( ~ ( aScalar0 @ W0 )
| ~ ( aScalar0 @ W1 )
| ~ ( aScalar0 @ W2 )
| ~ ( aScalar0 @ W3 )
| ( ( sdtasdt0 @ ( sdtpldt0 @ W0 @ W1 ) @ ( sdtpldt0 @ W2 @ W3 ) )
= ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ W0 @ W2 ) @ ( sdtasdt0 @ W0 @ W3 ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ W1 @ W2 ) @ ( sdtasdt0 @ W1 @ W3 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[137]) ).
thf(203,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aScalar0 @ W0 )
| ~ ( aScalar0 @ W1 )
| ( ( sdtasdt0 @ W0 @ ( smndt0 @ W1 ) )
= ( smndt0 @ ( sdtasdt0 @ W0 @ W1 ) ) ) )
& ! [W0: $i,W1: $i] :
( ~ ( aScalar0 @ W0 )
| ~ ( aScalar0 @ W1 )
| ( ( sdtasdt0 @ ( smndt0 @ W0 ) @ W1 )
= ( smndt0 @ ( sdtasdt0 @ W0 @ W1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[136]) ).
thf(204,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aScalar0 @ W0 )
| ~ ( aScalar0 @ W1 )
| ( ( sdtasdt0 @ ( smndt0 @ W0 ) @ ( smndt0 @ W1 ) )
= ( sdtasdt0 @ W0 @ W1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[135]) ).
thf(205,plain,
( ( ! [W0: $i] :
~ ( aScalar0 @ W0 )
| ! [W1: $i] :
~ ( aScalar0 @ W1 )
| $true )
= $true ),
inference(copy,[status(thm)],[134]) ).
thf(206,plain,
( ( ! [W0: $i] :
( ~ ( aScalar0 @ W0 )
| ( sdtlseqdt0 @ W0 @ W0 ) ) )
= $true ),
inference(copy,[status(thm)],[133]) ).
thf(207,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aScalar0 @ W0 )
| ~ ( aScalar0 @ W1 )
| ~ ( sdtlseqdt0 @ W0 @ W1 )
| ~ ( sdtlseqdt0 @ W1 @ W0 )
| ( W0 = W1 ) ) )
= $true ),
inference(copy,[status(thm)],[132]) ).
thf(208,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aScalar0 @ W0 )
| ~ ( aScalar0 @ W1 )
| ~ ( aScalar0 @ W2 )
| ~ ( sdtlseqdt0 @ W0 @ W1 )
| ~ ( sdtlseqdt0 @ W1 @ W2 )
| ( sdtlseqdt0 @ W0 @ W2 ) ) )
= $true ),
inference(copy,[status(thm)],[131]) ).
thf(209,plain,
( ( ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( ~ ( aScalar0 @ W0 )
| ~ ( aScalar0 @ W1 )
| ~ ( aScalar0 @ W2 )
| ~ ( aScalar0 @ W3 )
| ~ ( sdtlseqdt0 @ W0 @ W1 )
| ~ ( sdtlseqdt0 @ W2 @ W3 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ W0 @ W2 ) @ ( sdtpldt0 @ W1 @ W3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[130]) ).
thf(210,plain,
( ( ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( ~ ( aScalar0 @ W0 )
| ~ ( aScalar0 @ W1 )
| ~ ( aScalar0 @ W2 )
| ~ ( aScalar0 @ W3 )
| ~ ( sdtlseqdt0 @ W0 @ W1 )
| ~ ( sdtlseqdt0 @ sz0z00 @ W2 )
| ~ ( sdtlseqdt0 @ W2 @ W3 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ W0 @ W2 ) @ ( sdtasdt0 @ W1 @ W3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[129]) ).
thf(211,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aScalar0 @ W0 )
| ~ ( aScalar0 @ W1 )
| ( sdtlseqdt0 @ W0 @ W1 )
| ( sdtlseqdt0 @ W1 @ W0 ) ) )
= $true ),
inference(copy,[status(thm)],[128]) ).
thf(212,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aScalar0 @ W0 )
| ~ ( aScalar0 @ W1 )
| ~ ( sdtlseqdt0 @ sz0z00 @ W0 )
| ~ ( sdtlseqdt0 @ sz0z00 @ W1 )
| ( sdtlseqdt0 @ sz0z00 @ ( sdtpldt0 @ W0 @ W1 ) ) )
& ! [W0: $i,W1: $i] :
( ~ ( aScalar0 @ W0 )
| ~ ( aScalar0 @ W1 )
| ~ ( sdtlseqdt0 @ sz0z00 @ W0 )
| ~ ( sdtlseqdt0 @ sz0z00 @ W1 )
| ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ W0 @ W1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[127]) ).
thf(213,plain,
( ( ! [W0: $i] :
( ~ ( aScalar0 @ W0 )
| ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ W0 @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[126]) ).
thf(214,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aScalar0 @ W0 )
| ~ ( aScalar0 @ W1 )
| ~ ( sdtlseqdt0 @ sz0z00 @ W0 )
| ~ ( sdtlseqdt0 @ sz0z00 @ W1 )
| ( ( sdtasdt0 @ W0 @ W0 )
!= ( sdtasdt0 @ W1 @ W1 ) )
| ( W0 = W1 ) ) )
= $true ),
inference(copy,[status(thm)],[125]) ).
thf(215,plain,
( ( ! [W0: $i] : $true )
= $true ),
inference(copy,[status(thm)],[124]) ).
thf(216,plain,
( ( ! [W0: $i] :
( ~ ( aVector0 @ W0 )
| ( aNaturalNumber0 @ ( aDimensionOf0 @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[123]) ).
thf(217,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0 @ W1 )
| ~ ( aVector0 @ W0 )
| ( aScalar0 @ ( sdtlbdtrb0 @ W0 @ W1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(218,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aVector0 @ W0 )
| ~ ( aVector0 @ W1 )
| ( ( aDimensionOf0 @ W1 )
= sz00 )
| ( ( aDimensionOf0 @ W0 )
!= ( aDimensionOf0 @ W1 ) )
| ( ( aDimensionOf0 @ ( sziznziztdt0 @ W0 ) )
= ( aDimensionOf0 @ ( sziznziztdt0 @ W1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[121]) ).
thf(219,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aVector0 @ W0 )
| ~ ( aVector0 @ W1 )
| ( ( aDimensionOf0 @ W0 )
!= ( aDimensionOf0 @ W1 ) )
| ( aScalar0 @ ( sdtasasdt0 @ W0 @ W1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[120]) ).
thf(220,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aVector0 @ W0 )
| ~ ( aVector0 @ W1 )
| ( ( aDimensionOf0 @ W0 )
!= ( aDimensionOf0 @ W1 ) )
| ( ( aDimensionOf0 @ W1 )
!= sz00 )
| ( ( sdtasasdt0 @ W0 @ W1 )
= sz0z00 ) ) )
= $true ),
inference(copy,[status(thm)],[119]) ).
thf(221,plain,
( ( ! [W0: $i,W1: $i] :
( ~ ( aVector0 @ W0 )
| ~ ( aVector0 @ W1 )
| ( ( aDimensionOf0 @ W1 )
= sz00 )
| ( ( aDimensionOf0 @ W0 )
!= ( aDimensionOf0 @ W1 ) )
| ( ( sdtasasdt0 @ W0 @ W1 )
= ( sdtpldt0 @ ( sdtasasdt0 @ ( sziznziztdt0 @ W0 ) @ ( sziznziztdt0 @ W1 ) ) @ ( sdtasdt0 @ ( sdtlbdtrb0 @ W0 @ ( aDimensionOf0 @ W0 ) ) @ ( sdtlbdtrb0 @ W1 @ ( aDimensionOf0 @ W1 ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(222,plain,
( ( ! [W0: $i] :
( ~ ( aVector0 @ W0 )
| ( sdtlseqdt0 @ sz0z00 @ ( sdtasasdt0 @ W0 @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(223,plain,
( ( ( ( sdtasdt0 @ ( smndt0 @ xS ) @ xR )
!= ( smndt0 @ xN ) ) )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(224,plain,
( ( ~ ( ( xE
!= ( sdtasasdt0 @ xp @ xq ) )
| ~ ( aScalar0 @ xE ) ) )
= $true ),
inference(unfold_def,[status(thm)],[177]) ).
thf(225,plain,
( ( ~ ( ( xA
!= ( sdtlbdtrb0 @ xs @ ( aDimensionOf0 @ xs ) ) )
| ~ ( aScalar0 @ xA ) ) )
= $true ),
inference(unfold_def,[status(thm)],[173]) ).
thf(226,plain,
( ( ~ ( ( xF
!= ( sdtasdt0 @ xA @ xA ) )
| ~ ( aScalar0 @ xF ) ) )
= $true ),
inference(unfold_def,[status(thm)],[178]) ).
thf(227,plain,
( ( ~ ( ~ ( aVector0 @ xs )
| ~ ( aVector0 @ xt ) ) )
= $true ),
inference(unfold_def,[status(thm)],[167]) ).
thf(228,plain,
( ( ! [SX0: $i] :
( ( SX0 = sz00 )
| ~ ( aNaturalNumber0 @ SX0 )
| ~ ( ( SX0
!= ( szszuzczcdt0 @ ( sK1_W1 @ SX0 ) ) )
| ~ ( aNaturalNumber0 @ ( sK1_W1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[190]) ).
thf(229,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( aScalar0 @ SX0 )
| ~ ( aScalar0 @ SX1 )
| ( ( sdtasdt0 @ SX0 @ ( smndt0 @ SX1 ) )
= ( smndt0 @ ( sdtasdt0 @ SX0 @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( aScalar0 @ SX0 )
| ~ ( aScalar0 @ SX1 )
| ( ( sdtasdt0 @ ( smndt0 @ SX0 ) @ SX1 )
= ( smndt0 @ ( sdtasdt0 @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[203]) ).
thf(230,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( aScalar0 @ SX0 )
| ~ ( aScalar0 @ SX1 )
| ~ ( aScalar0 @ SX2 )
| ( ( sdtasdt0 @ SX0 @ ( sdtpldt0 @ SX1 @ SX2 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SX0 @ SX1 ) @ ( sdtasdt0 @ SX0 @ SX2 ) ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( aScalar0 @ SX0 )
| ~ ( aScalar0 @ SX1 )
| ~ ( aScalar0 @ SX2 )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ SX2 )
= ( sdtpldt0 @ ( sdtasdt0 @ SX0 @ SX2 ) @ ( sdtasdt0 @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[201]) ).
thf(231,plain,
( ( ! [SX0: $i] :
~ ( ~ ~ ( ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( aScalar0 @ SX0 )
| ~ ( aScalar0 @ SX1 )
| ~ ( aScalar0 @ SX2 )
| ( ( sdtpldt0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ SX2 )
= ( sdtpldt0 @ SX0 @ ( sdtpldt0 @ SX1 @ SX2 ) ) ) )
| ~ ! [SX1: $i] :
( ~ ( aScalar0 @ SX0 )
| ~ ( aScalar0 @ SX1 )
| ! [SX2: $i] :
~ ( aScalar0 @ SX2 )
| ( ( sdtpldt0 @ SX0 @ SX1 )
= ( sdtpldt0 @ SX1 @ SX0 ) ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( aScalar0 @ SX0 )
| ~ ( aScalar0 @ SX1 )
| ~ ( aScalar0 @ SX2 )
| ( ( sdtasdt0 @ ( sdtasdt0 @ SX0 @ SX1 ) @ SX2 )
= ( sdtasdt0 @ SX0 @ ( sdtasdt0 @ SX1 @ SX2 ) ) ) ) )
| ~ ! [SX1: $i] :
( ~ ( aScalar0 @ SX0 )
| ~ ( aScalar0 @ SX1 )
| ! [SX2: $i] :
~ ( aScalar0 @ SX2 )
| ( ( sdtasdt0 @ SX0 @ SX1 )
= ( sdtasdt0 @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[200]) ).
thf(232,plain,
( ( ~ ( ( xG
!= ( sdtasdt0 @ xB @ xB ) )
| ~ ( aScalar0 @ xG ) ) )
= $true ),
inference(unfold_def,[status(thm)],[179]) ).
thf(233,plain,
( ( ~ ( ( xB
!= ( sdtlbdtrb0 @ xt @ ( aDimensionOf0 @ xt ) ) )
| ~ ( aScalar0 @ xB ) ) )
= $true ),
inference(unfold_def,[status(thm)],[174]) ).
thf(234,plain,
( ( ~ ( ( xC
!= ( sdtasasdt0 @ xp @ xp ) )
| ~ ( aScalar0 @ xC ) ) )
= $true ),
inference(unfold_def,[status(thm)],[175]) ).
thf(235,plain,
( ( ~ ( ( xN
!= ( sdtasdt0 @ xR @ xS ) )
| ~ ( aScalar0 @ xN ) ) )
= $true ),
inference(unfold_def,[status(thm)],[184]) ).
thf(236,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( ( sdtlbdtrb0 @ xp @ SX0 )
= ( sdtlbdtrb0 @ xs @ SX0 ) ) )
| ~ ~ ( ( ( szszuzczcdt0 @ ( aDimensionOf0 @ xp ) )
!= ( aDimensionOf0 @ xs ) )
| ~ ( aVector0 @ xp ) ) )
| ( xp
!= ( sziznziztdt0 @ xs ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[171]) ).
thf(237,plain,
( ( ~ ( ( xS
!= ( sdtasdt0 @ xF @ xD ) )
| ~ ( aScalar0 @ xS ) ) )
= $true ),
inference(unfold_def,[status(thm)],[183]) ).
thf(238,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( aScalar0 @ SX0 )
| ~ ( aScalar0 @ SX1 )
| ~ ( sdtlseqdt0 @ sz0z00 @ SX0 )
| ~ ( sdtlseqdt0 @ sz0z00 @ SX1 )
| ( sdtlseqdt0 @ sz0z00 @ ( sdtpldt0 @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( aScalar0 @ SX0 )
| ~ ( aScalar0 @ SX1 )
| ~ ( sdtlseqdt0 @ sz0z00 @ SX0 )
| ~ ( sdtlseqdt0 @ sz0z00 @ SX1 )
| ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[212]) ).
thf(239,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtpldt0 @ SX0 @ sz0z00 )
= SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtpldt0 @ sz0z00 @ SX0 )
= SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtasdt0 @ SX0 @ sz0z00 )
= sz0z00 ) ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtasdt0 @ sz0z00 @ SX0 )
= sz0z00 ) ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtpldt0 @ SX0 @ ( smndt0 @ SX0 ) )
= sz0z00 ) ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtpldt0 @ ( smndt0 @ SX0 ) @ SX0 )
= sz0z00 ) ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( smndt0 @ ( smndt0 @ SX0 ) )
= SX0 ) ) )
| ~ ( ! [SX0: $i] :
~ ( aScalar0 @ SX0 )
| ( ( smndt0 @ sz0z00 )
= sz0z00 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[199]) ).
thf(240,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( ( sdtlbdtrb0 @ xq @ SX0 )
= ( sdtlbdtrb0 @ xt @ SX0 ) ) )
| ~ ~ ( ( ( szszuzczcdt0 @ ( aDimensionOf0 @ xq ) )
!= ( aDimensionOf0 @ xt ) )
| ~ ( aVector0 @ xq ) ) )
| ( xq
!= ( sziznziztdt0 @ xt ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[172]) ).
thf(241,plain,
( ( ~ ( ( xD
!= ( sdtasasdt0 @ xq @ xq ) )
| ~ ( aScalar0 @ xD ) ) )
= $true ),
inference(unfold_def,[status(thm)],[176]) ).
thf(242,plain,
( ( ~ ( ( xR
!= ( sdtasdt0 @ xC @ xG ) )
| ~ ( aScalar0 @ xR ) ) )
= $true ),
inference(unfold_def,[status(thm)],[181]) ).
thf(243,plain,
( ( ~ ( ( xH
!= ( sdtasdt0 @ xA @ xB ) )
| ~ ( aScalar0 @ xH ) ) )
= $true ),
inference(unfold_def,[status(thm)],[180]) ).
thf(244,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( ( szszuzczcdt0 @ SX0 )
!= sz00 ) )
| ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( aNaturalNumber0 @ ( szszuzczcdt0 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[189]) ).
thf(245,plain,
( ( ~ ( ( xP
!= ( sdtasdt0 @ xE @ xH ) )
| ~ ( aScalar0 @ xP ) ) )
= $true ),
inference(unfold_def,[status(thm)],[182]) ).
thf(246,plain,
! [SV1: $i] :
( ( ! [SY70: $i] :
( ~ ( aVector0 @ SV1 )
| ~ ( aVector0 @ SY70 )
| ( ( aDimensionOf0 @ SV1 )
!= ( aDimensionOf0 @ SY70 ) )
| ~ ( iLess0 @ ( aDimensionOf0 @ SV1 ) @ ( aDimensionOf0 @ xs ) )
| ( sdtlseqdt0 @ ( sdtasdt0 @ ( sdtasasdt0 @ SV1 @ SY70 ) @ ( sdtasasdt0 @ SV1 @ SY70 ) ) @ ( sdtasdt0 @ ( sdtasasdt0 @ SV1 @ SV1 ) @ ( sdtasasdt0 @ SY70 @ SY70 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(247,plain,
( ( ( aDimensionOf0 @ xs )
= sz00 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(248,plain,
$true = $true,
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(249,plain,
! [SV3: $i] :
( ( ! [SY71: $i] :
( ~ ( aNaturalNumber0 @ SV3 )
| ~ ( aNaturalNumber0 @ SY71 )
| ( ( szszuzczcdt0 @ SV3 )
!= ( szszuzczcdt0 @ SY71 ) )
| ( SV3 = SY71 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[191]) ).
thf(250,plain,
( ( ( ! [W0: $i] :
~ ( aNaturalNumber0 @ W0 )
| ! [W1: $i] :
~ ( aNaturalNumber0 @ W1 ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[192]) ).
thf(251,plain,
! [SV4: $i] :
( ( ~ ( aNaturalNumber0 @ SV4 )
| ( iLess0 @ SV4 @ ( szszuzczcdt0 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[193]) ).
thf(252,plain,
$true = $true,
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(253,plain,
! [SV6: $i] :
( ( ! [SY72: $i] :
( ~ ( aScalar0 @ SV6 )
| ~ ( aScalar0 @ SY72 )
| ( aScalar0 @ ( sdtpldt0 @ SV6 @ SY72 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(254,plain,
! [SV7: $i] :
( ( ! [SY73: $i] :
( ~ ( aScalar0 @ SV7 )
| ~ ( aScalar0 @ SY73 )
| ( aScalar0 @ ( sdtasdt0 @ SV7 @ SY73 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(255,plain,
! [SV8: $i] :
( ( ~ ( aScalar0 @ SV8 )
| ( aScalar0 @ ( smndt0 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(256,plain,
! [SV9: $i] :
( ( ! [SY74: $i,SY75: $i,SY76: $i] :
( ~ ( aScalar0 @ SV9 )
| ~ ( aScalar0 @ SY74 )
| ~ ( aScalar0 @ SY75 )
| ~ ( aScalar0 @ SY76 )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SV9 @ SY74 ) @ ( sdtpldt0 @ SY75 @ SY76 ) )
= ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ SV9 @ SY75 ) @ ( sdtasdt0 @ SV9 @ SY76 ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ SY74 @ SY75 ) @ ( sdtasdt0 @ SY74 @ SY76 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[202]) ).
thf(257,plain,
! [SV10: $i] :
( ( ! [SY77: $i] :
( ~ ( aScalar0 @ SV10 )
| ~ ( aScalar0 @ SY77 )
| ( ( sdtasdt0 @ ( smndt0 @ SV10 ) @ ( smndt0 @ SY77 ) )
= ( sdtasdt0 @ SV10 @ SY77 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(258,plain,
( ( ( ! [W0: $i] :
~ ( aScalar0 @ W0 )
| ! [W1: $i] :
~ ( aScalar0 @ W1 ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[205]) ).
thf(259,plain,
! [SV11: $i] :
( ( ~ ( aScalar0 @ SV11 )
| ( sdtlseqdt0 @ SV11 @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(260,plain,
! [SV12: $i] :
( ( ! [SY78: $i] :
( ~ ( aScalar0 @ SV12 )
| ~ ( aScalar0 @ SY78 )
| ~ ( sdtlseqdt0 @ SV12 @ SY78 )
| ~ ( sdtlseqdt0 @ SY78 @ SV12 )
| ( SV12 = SY78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(261,plain,
! [SV13: $i] :
( ( ! [SY79: $i,SY80: $i] :
( ~ ( aScalar0 @ SV13 )
| ~ ( aScalar0 @ SY79 )
| ~ ( aScalar0 @ SY80 )
| ~ ( sdtlseqdt0 @ SV13 @ SY79 )
| ~ ( sdtlseqdt0 @ SY79 @ SY80 )
| ( sdtlseqdt0 @ SV13 @ SY80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(262,plain,
! [SV14: $i] :
( ( ! [SY81: $i,SY82: $i,SY83: $i] :
( ~ ( aScalar0 @ SV14 )
| ~ ( aScalar0 @ SY81 )
| ~ ( aScalar0 @ SY82 )
| ~ ( aScalar0 @ SY83 )
| ~ ( sdtlseqdt0 @ SV14 @ SY81 )
| ~ ( sdtlseqdt0 @ SY82 @ SY83 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SV14 @ SY82 ) @ ( sdtpldt0 @ SY81 @ SY83 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[209]) ).
thf(263,plain,
! [SV15: $i] :
( ( ! [SY84: $i,SY85: $i,SY86: $i] :
( ~ ( aScalar0 @ SV15 )
| ~ ( aScalar0 @ SY84 )
| ~ ( aScalar0 @ SY85 )
| ~ ( aScalar0 @ SY86 )
| ~ ( sdtlseqdt0 @ SV15 @ SY84 )
| ~ ( sdtlseqdt0 @ sz0z00 @ SY85 )
| ~ ( sdtlseqdt0 @ SY85 @ SY86 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV15 @ SY85 ) @ ( sdtasdt0 @ SY84 @ SY86 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[210]) ).
thf(264,plain,
! [SV16: $i] :
( ( ! [SY87: $i] :
( ~ ( aScalar0 @ SV16 )
| ~ ( aScalar0 @ SY87 )
| ( sdtlseqdt0 @ SV16 @ SY87 )
| ( sdtlseqdt0 @ SY87 @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[211]) ).
thf(265,plain,
! [SV17: $i] :
( ( ~ ( aScalar0 @ SV17 )
| ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ SV17 @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[213]) ).
thf(266,plain,
! [SV18: $i] :
( ( ! [SY88: $i] :
( ~ ( aScalar0 @ SV18 )
| ~ ( aScalar0 @ SY88 )
| ~ ( sdtlseqdt0 @ sz0z00 @ SV18 )
| ~ ( sdtlseqdt0 @ sz0z00 @ SY88 )
| ( ( sdtasdt0 @ SV18 @ SV18 )
!= ( sdtasdt0 @ SY88 @ SY88 ) )
| ( SV18 = SY88 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[214]) ).
thf(267,plain,
$true = $true,
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(268,plain,
! [SV20: $i] :
( ( ~ ( aVector0 @ SV20 )
| ( aNaturalNumber0 @ ( aDimensionOf0 @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[216]) ).
thf(269,plain,
! [SV21: $i] :
( ( ! [SY89: $i] :
( ~ ( aNaturalNumber0 @ SY89 )
| ~ ( aVector0 @ SV21 )
| ( aScalar0 @ ( sdtlbdtrb0 @ SV21 @ SY89 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[217]) ).
thf(270,plain,
! [SV22: $i] :
( ( ! [SY90: $i] :
( ~ ( aVector0 @ SV22 )
| ~ ( aVector0 @ SY90 )
| ( ( aDimensionOf0 @ SY90 )
= sz00 )
| ( ( aDimensionOf0 @ SV22 )
!= ( aDimensionOf0 @ SY90 ) )
| ( ( aDimensionOf0 @ ( sziznziztdt0 @ SV22 ) )
= ( aDimensionOf0 @ ( sziznziztdt0 @ SY90 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[218]) ).
thf(271,plain,
! [SV23: $i] :
( ( ! [SY91: $i] :
( ~ ( aVector0 @ SV23 )
| ~ ( aVector0 @ SY91 )
| ( ( aDimensionOf0 @ SV23 )
!= ( aDimensionOf0 @ SY91 ) )
| ( aScalar0 @ ( sdtasasdt0 @ SV23 @ SY91 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[219]) ).
thf(272,plain,
! [SV24: $i] :
( ( ! [SY92: $i] :
( ~ ( aVector0 @ SV24 )
| ~ ( aVector0 @ SY92 )
| ( ( aDimensionOf0 @ SV24 )
!= ( aDimensionOf0 @ SY92 ) )
| ( ( aDimensionOf0 @ SY92 )
!= sz00 )
| ( ( sdtasasdt0 @ SV24 @ SY92 )
= sz0z00 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[220]) ).
thf(273,plain,
! [SV25: $i] :
( ( ! [SY93: $i] :
( ~ ( aVector0 @ SV25 )
| ~ ( aVector0 @ SY93 )
| ( ( aDimensionOf0 @ SY93 )
= sz00 )
| ( ( aDimensionOf0 @ SV25 )
!= ( aDimensionOf0 @ SY93 ) )
| ( ( sdtasasdt0 @ SV25 @ SY93 )
= ( sdtpldt0 @ ( sdtasasdt0 @ ( sziznziztdt0 @ SV25 ) @ ( sziznziztdt0 @ SY93 ) ) @ ( sdtasdt0 @ ( sdtlbdtrb0 @ SV25 @ ( aDimensionOf0 @ SV25 ) ) @ ( sdtlbdtrb0 @ SY93 @ ( aDimensionOf0 @ SY93 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[221]) ).
thf(274,plain,
! [SV26: $i] :
( ( ~ ( aVector0 @ SV26 )
| ( sdtlseqdt0 @ sz0z00 @ ( sdtasasdt0 @ SV26 @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[222]) ).
thf(275,plain,
( ( ( sdtasdt0 @ ( smndt0 @ xS ) @ xR )
= ( smndt0 @ xN ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[223]) ).
thf(276,plain,
( ( ( xE
!= ( sdtasasdt0 @ xp @ xq ) )
| ~ ( aScalar0 @ xE ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[224]) ).
thf(277,plain,
( ( ( xA
!= ( sdtlbdtrb0 @ xs @ ( aDimensionOf0 @ xs ) ) )
| ~ ( aScalar0 @ xA ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[225]) ).
thf(278,plain,
( ( ( xF
!= ( sdtasdt0 @ xA @ xA ) )
| ~ ( aScalar0 @ xF ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[226]) ).
thf(279,plain,
( ( ~ ( aVector0 @ xs )
| ~ ( aVector0 @ xt ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[227]) ).
thf(280,plain,
! [SV27: $i] :
( ( ( SV27 = sz00 )
| ~ ( aNaturalNumber0 @ SV27 )
| ~ ( ( SV27
!= ( szszuzczcdt0 @ ( sK1_W1 @ SV27 ) ) )
| ~ ( aNaturalNumber0 @ ( sK1_W1 @ SV27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[228]) ).
thf(281,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( aScalar0 @ SX0 )
| ~ ( aScalar0 @ SX1 )
| ( ( sdtasdt0 @ SX0 @ ( smndt0 @ SX1 ) )
= ( smndt0 @ ( sdtasdt0 @ SX0 @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( aScalar0 @ SX0 )
| ~ ( aScalar0 @ SX1 )
| ( ( sdtasdt0 @ ( smndt0 @ SX0 ) @ SX1 )
= ( smndt0 @ ( sdtasdt0 @ SX0 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[229]) ).
thf(282,plain,
! [SV28: $i] :
( ( ~ ( ~ ! [SY94: $i,SY95: $i] :
( ~ ( aScalar0 @ SV28 )
| ~ ( aScalar0 @ SY94 )
| ~ ( aScalar0 @ SY95 )
| ( ( sdtasdt0 @ SV28 @ ( sdtpldt0 @ SY94 @ SY95 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV28 @ SY94 ) @ ( sdtasdt0 @ SV28 @ SY95 ) ) ) )
| ~ ! [SY96: $i,SY97: $i] :
( ~ ( aScalar0 @ SV28 )
| ~ ( aScalar0 @ SY96 )
| ~ ( aScalar0 @ SY97 )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SV28 @ SY96 ) @ SY97 )
= ( sdtpldt0 @ ( sdtasdt0 @ SV28 @ SY97 ) @ ( sdtasdt0 @ SY96 @ SY97 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[230]) ).
thf(283,plain,
! [SV29: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SY98: $i,SY99: $i] :
( ~ ( aScalar0 @ SV29 )
| ~ ( aScalar0 @ SY98 )
| ~ ( aScalar0 @ SY99 )
| ( ( sdtpldt0 @ ( sdtpldt0 @ SV29 @ SY98 ) @ SY99 )
= ( sdtpldt0 @ SV29 @ ( sdtpldt0 @ SY98 @ SY99 ) ) ) )
| ~ ! [SY100: $i] :
( ~ ( aScalar0 @ SV29 )
| ~ ( aScalar0 @ SY100 )
| ! [SX2: $i] :
~ ( aScalar0 @ SX2 )
| ( ( sdtpldt0 @ SV29 @ SY100 )
= ( sdtpldt0 @ SY100 @ SV29 ) ) ) )
| ~ ! [SY102: $i,SY103: $i] :
( ~ ( aScalar0 @ SV29 )
| ~ ( aScalar0 @ SY102 )
| ~ ( aScalar0 @ SY103 )
| ( ( sdtasdt0 @ ( sdtasdt0 @ SV29 @ SY102 ) @ SY103 )
= ( sdtasdt0 @ SV29 @ ( sdtasdt0 @ SY102 @ SY103 ) ) ) ) )
| ~ ! [SY104: $i] :
( ~ ( aScalar0 @ SV29 )
| ~ ( aScalar0 @ SY104 )
| ! [SX2: $i] :
~ ( aScalar0 @ SX2 )
| ( ( sdtasdt0 @ SV29 @ SY104 )
= ( sdtasdt0 @ SY104 @ SV29 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[231]) ).
thf(284,plain,
( ( ( xG
!= ( sdtasdt0 @ xB @ xB ) )
| ~ ( aScalar0 @ xG ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[232]) ).
thf(285,plain,
( ( ( xB
!= ( sdtlbdtrb0 @ xt @ ( aDimensionOf0 @ xt ) ) )
| ~ ( aScalar0 @ xB ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[233]) ).
thf(286,plain,
( ( ( xC
!= ( sdtasasdt0 @ xp @ xp ) )
| ~ ( aScalar0 @ xC ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[234]) ).
thf(287,plain,
( ( ( xN
!= ( sdtasdt0 @ xR @ xS ) )
| ~ ( aScalar0 @ xN ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[235]) ).
thf(288,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( ( sdtlbdtrb0 @ xp @ SX0 )
= ( sdtlbdtrb0 @ xs @ SX0 ) ) )
| ~ ~ ( ( ( szszuzczcdt0 @ ( aDimensionOf0 @ xp ) )
!= ( aDimensionOf0 @ xs ) )
| ~ ( aVector0 @ xp ) ) )
| ( xp
!= ( sziznziztdt0 @ xs ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[236]) ).
thf(289,plain,
( ( ( xS
!= ( sdtasdt0 @ xF @ xD ) )
| ~ ( aScalar0 @ xS ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[237]) ).
thf(290,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( aScalar0 @ SX0 )
| ~ ( aScalar0 @ SX1 )
| ~ ( sdtlseqdt0 @ sz0z00 @ SX0 )
| ~ ( sdtlseqdt0 @ sz0z00 @ SX1 )
| ( sdtlseqdt0 @ sz0z00 @ ( sdtpldt0 @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( aScalar0 @ SX0 )
| ~ ( aScalar0 @ SX1 )
| ~ ( sdtlseqdt0 @ sz0z00 @ SX0 )
| ~ ( sdtlseqdt0 @ sz0z00 @ SX1 )
| ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[238]) ).
thf(291,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtpldt0 @ SX0 @ sz0z00 )
= SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtpldt0 @ sz0z00 @ SX0 )
= SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtasdt0 @ SX0 @ sz0z00 )
= sz0z00 ) ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtasdt0 @ sz0z00 @ SX0 )
= sz0z00 ) ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtpldt0 @ SX0 @ ( smndt0 @ SX0 ) )
= sz0z00 ) ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtpldt0 @ ( smndt0 @ SX0 ) @ SX0 )
= sz0z00 ) ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( smndt0 @ ( smndt0 @ SX0 ) )
= SX0 ) ) )
| ~ ( ! [SX0: $i] :
~ ( aScalar0 @ SX0 )
| ( ( smndt0 @ sz0z00 )
= sz0z00 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[239]) ).
thf(292,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( ( sdtlbdtrb0 @ xq @ SX0 )
= ( sdtlbdtrb0 @ xt @ SX0 ) ) )
| ~ ~ ( ( ( szszuzczcdt0 @ ( aDimensionOf0 @ xq ) )
!= ( aDimensionOf0 @ xt ) )
| ~ ( aVector0 @ xq ) ) )
| ( xq
!= ( sziznziztdt0 @ xt ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[240]) ).
thf(293,plain,
( ( ( xD
!= ( sdtasasdt0 @ xq @ xq ) )
| ~ ( aScalar0 @ xD ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[241]) ).
thf(294,plain,
( ( ( xR
!= ( sdtasdt0 @ xC @ xG ) )
| ~ ( aScalar0 @ xR ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[242]) ).
thf(295,plain,
( ( ( xH
!= ( sdtasdt0 @ xA @ xB ) )
| ~ ( aScalar0 @ xH ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[243]) ).
thf(296,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( ( szszuzczcdt0 @ SX0 )
!= sz00 ) )
| ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( aNaturalNumber0 @ ( szszuzczcdt0 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[244]) ).
thf(297,plain,
( ( ( xP
!= ( sdtasdt0 @ xE @ xH ) )
| ~ ( aScalar0 @ xP ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[245]) ).
thf(298,plain,
! [SV30: $i,SV1: $i] :
( ( ~ ( aVector0 @ SV1 )
| ~ ( aVector0 @ SV30 )
| ( ( aDimensionOf0 @ SV1 )
!= ( aDimensionOf0 @ SV30 ) )
| ~ ( iLess0 @ ( aDimensionOf0 @ SV1 ) @ ( aDimensionOf0 @ xs ) )
| ( sdtlseqdt0 @ ( sdtasdt0 @ ( sdtasasdt0 @ SV1 @ SV30 ) @ ( sdtasasdt0 @ SV1 @ SV30 ) ) @ ( sdtasdt0 @ ( sdtasasdt0 @ SV1 @ SV1 ) @ ( sdtasasdt0 @ SV30 @ SV30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[246]) ).
thf(299,plain,
! [SV31: $i,SV3: $i] :
( ( ~ ( aNaturalNumber0 @ SV3 )
| ~ ( aNaturalNumber0 @ SV31 )
| ( ( szszuzczcdt0 @ SV3 )
!= ( szszuzczcdt0 @ SV31 ) )
| ( SV3 = SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[249]) ).
thf(300,plain,
( ( ( ! [W0: $i] :
~ ( aNaturalNumber0 @ W0 ) )
= $true )
| ( ( ! [W1: $i] :
~ ( aNaturalNumber0 @ W1 ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[250]) ).
thf(301,plain,
! [SV4: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV4 ) )
= $true )
| ( ( iLess0 @ SV4 @ ( szszuzczcdt0 @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[251]) ).
thf(302,plain,
! [SV32: $i,SV6: $i] :
( ( ~ ( aScalar0 @ SV6 )
| ~ ( aScalar0 @ SV32 )
| ( aScalar0 @ ( sdtpldt0 @ SV6 @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[253]) ).
thf(303,plain,
! [SV33: $i,SV7: $i] :
( ( ~ ( aScalar0 @ SV7 )
| ~ ( aScalar0 @ SV33 )
| ( aScalar0 @ ( sdtasdt0 @ SV7 @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[254]) ).
thf(304,plain,
! [SV8: $i] :
( ( ( ~ ( aScalar0 @ SV8 ) )
= $true )
| ( ( aScalar0 @ ( smndt0 @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[255]) ).
thf(305,plain,
! [SV34: $i,SV9: $i] :
( ( ! [SY106: $i,SY107: $i] :
( ~ ( aScalar0 @ SV9 )
| ~ ( aScalar0 @ SV34 )
| ~ ( aScalar0 @ SY106 )
| ~ ( aScalar0 @ SY107 )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SV9 @ SV34 ) @ ( sdtpldt0 @ SY106 @ SY107 ) )
= ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ SV9 @ SY106 ) @ ( sdtasdt0 @ SV9 @ SY107 ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ SV34 @ SY106 ) @ ( sdtasdt0 @ SV34 @ SY107 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[256]) ).
thf(306,plain,
! [SV35: $i,SV10: $i] :
( ( ~ ( aScalar0 @ SV10 )
| ~ ( aScalar0 @ SV35 )
| ( ( sdtasdt0 @ ( smndt0 @ SV10 ) @ ( smndt0 @ SV35 ) )
= ( sdtasdt0 @ SV10 @ SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[257]) ).
thf(307,plain,
( ( ( ! [W0: $i] :
~ ( aScalar0 @ W0 ) )
= $true )
| ( ( ! [W1: $i] :
~ ( aScalar0 @ W1 ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[258]) ).
thf(308,plain,
! [SV11: $i] :
( ( ( ~ ( aScalar0 @ SV11 ) )
= $true )
| ( ( sdtlseqdt0 @ SV11 @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[259]) ).
thf(309,plain,
! [SV36: $i,SV12: $i] :
( ( ~ ( aScalar0 @ SV12 )
| ~ ( aScalar0 @ SV36 )
| ~ ( sdtlseqdt0 @ SV12 @ SV36 )
| ~ ( sdtlseqdt0 @ SV36 @ SV12 )
| ( SV12 = SV36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[260]) ).
thf(310,plain,
! [SV37: $i,SV13: $i] :
( ( ! [SY108: $i] :
( ~ ( aScalar0 @ SV13 )
| ~ ( aScalar0 @ SV37 )
| ~ ( aScalar0 @ SY108 )
| ~ ( sdtlseqdt0 @ SV13 @ SV37 )
| ~ ( sdtlseqdt0 @ SV37 @ SY108 )
| ( sdtlseqdt0 @ SV13 @ SY108 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[261]) ).
thf(311,plain,
! [SV38: $i,SV14: $i] :
( ( ! [SY109: $i,SY110: $i] :
( ~ ( aScalar0 @ SV14 )
| ~ ( aScalar0 @ SV38 )
| ~ ( aScalar0 @ SY109 )
| ~ ( aScalar0 @ SY110 )
| ~ ( sdtlseqdt0 @ SV14 @ SV38 )
| ~ ( sdtlseqdt0 @ SY109 @ SY110 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SV14 @ SY109 ) @ ( sdtpldt0 @ SV38 @ SY110 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[262]) ).
thf(312,plain,
! [SV39: $i,SV15: $i] :
( ( ! [SY111: $i,SY112: $i] :
( ~ ( aScalar0 @ SV15 )
| ~ ( aScalar0 @ SV39 )
| ~ ( aScalar0 @ SY111 )
| ~ ( aScalar0 @ SY112 )
| ~ ( sdtlseqdt0 @ SV15 @ SV39 )
| ~ ( sdtlseqdt0 @ sz0z00 @ SY111 )
| ~ ( sdtlseqdt0 @ SY111 @ SY112 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV15 @ SY111 ) @ ( sdtasdt0 @ SV39 @ SY112 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[263]) ).
thf(313,plain,
! [SV40: $i,SV16: $i] :
( ( ~ ( aScalar0 @ SV16 )
| ~ ( aScalar0 @ SV40 )
| ( sdtlseqdt0 @ SV16 @ SV40 )
| ( sdtlseqdt0 @ SV40 @ SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[264]) ).
thf(314,plain,
! [SV17: $i] :
( ( ( ~ ( aScalar0 @ SV17 ) )
= $true )
| ( ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ SV17 @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[265]) ).
thf(315,plain,
! [SV41: $i,SV18: $i] :
( ( ~ ( aScalar0 @ SV18 )
| ~ ( aScalar0 @ SV41 )
| ~ ( sdtlseqdt0 @ sz0z00 @ SV18 )
| ~ ( sdtlseqdt0 @ sz0z00 @ SV41 )
| ( ( sdtasdt0 @ SV18 @ SV18 )
!= ( sdtasdt0 @ SV41 @ SV41 ) )
| ( SV18 = SV41 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[266]) ).
thf(316,plain,
! [SV20: $i] :
( ( ( ~ ( aVector0 @ SV20 ) )
= $true )
| ( ( aNaturalNumber0 @ ( aDimensionOf0 @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[268]) ).
thf(317,plain,
! [SV21: $i,SV42: $i] :
( ( ~ ( aNaturalNumber0 @ SV42 )
| ~ ( aVector0 @ SV21 )
| ( aScalar0 @ ( sdtlbdtrb0 @ SV21 @ SV42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[269]) ).
thf(318,plain,
! [SV43: $i,SV22: $i] :
( ( ~ ( aVector0 @ SV22 )
| ~ ( aVector0 @ SV43 )
| ( ( aDimensionOf0 @ SV43 )
= sz00 )
| ( ( aDimensionOf0 @ SV22 )
!= ( aDimensionOf0 @ SV43 ) )
| ( ( aDimensionOf0 @ ( sziznziztdt0 @ SV22 ) )
= ( aDimensionOf0 @ ( sziznziztdt0 @ SV43 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[270]) ).
thf(319,plain,
! [SV44: $i,SV23: $i] :
( ( ~ ( aVector0 @ SV23 )
| ~ ( aVector0 @ SV44 )
| ( ( aDimensionOf0 @ SV23 )
!= ( aDimensionOf0 @ SV44 ) )
| ( aScalar0 @ ( sdtasasdt0 @ SV23 @ SV44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[271]) ).
thf(320,plain,
! [SV45: $i,SV24: $i] :
( ( ~ ( aVector0 @ SV24 )
| ~ ( aVector0 @ SV45 )
| ( ( aDimensionOf0 @ SV24 )
!= ( aDimensionOf0 @ SV45 ) )
| ( ( aDimensionOf0 @ SV45 )
!= sz00 )
| ( ( sdtasasdt0 @ SV24 @ SV45 )
= sz0z00 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[272]) ).
thf(321,plain,
! [SV46: $i,SV25: $i] :
( ( ~ ( aVector0 @ SV25 )
| ~ ( aVector0 @ SV46 )
| ( ( aDimensionOf0 @ SV46 )
= sz00 )
| ( ( aDimensionOf0 @ SV25 )
!= ( aDimensionOf0 @ SV46 ) )
| ( ( sdtasasdt0 @ SV25 @ SV46 )
= ( sdtpldt0 @ ( sdtasasdt0 @ ( sziznziztdt0 @ SV25 ) @ ( sziznziztdt0 @ SV46 ) ) @ ( sdtasdt0 @ ( sdtlbdtrb0 @ SV25 @ ( aDimensionOf0 @ SV25 ) ) @ ( sdtlbdtrb0 @ SV46 @ ( aDimensionOf0 @ SV46 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[273]) ).
thf(322,plain,
! [SV26: $i] :
( ( ( ~ ( aVector0 @ SV26 ) )
= $true )
| ( ( sdtlseqdt0 @ sz0z00 @ ( sdtasasdt0 @ SV26 @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[274]) ).
thf(323,plain,
( ( ( xE
!= ( sdtasasdt0 @ xp @ xq ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[276]) ).
thf(324,plain,
( ( ~ ( aScalar0 @ xE ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[276]) ).
thf(325,plain,
( ( ( xA
!= ( sdtlbdtrb0 @ xs @ ( aDimensionOf0 @ xs ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[277]) ).
thf(326,plain,
( ( ~ ( aScalar0 @ xA ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[277]) ).
thf(327,plain,
( ( ( xF
!= ( sdtasdt0 @ xA @ xA ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[278]) ).
thf(328,plain,
( ( ~ ( aScalar0 @ xF ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[278]) ).
thf(329,plain,
( ( ~ ( aVector0 @ xs ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[279]) ).
thf(330,plain,
( ( ~ ( aVector0 @ xt ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[279]) ).
thf(331,plain,
! [SV27: $i] :
( ( ( ( SV27 = sz00 )
| ~ ( aNaturalNumber0 @ SV27 ) )
= $true )
| ( ( ~ ( ( SV27
!= ( szszuzczcdt0 @ ( sK1_W1 @ SV27 ) ) )
| ~ ( aNaturalNumber0 @ ( sK1_W1 @ SV27 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[280]) ).
thf(332,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( aScalar0 @ SX0 )
| ~ ( aScalar0 @ SX1 )
| ( ( sdtasdt0 @ SX0 @ ( smndt0 @ SX1 ) )
= ( smndt0 @ ( sdtasdt0 @ SX0 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[281]) ).
thf(333,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( aScalar0 @ SX0 )
| ~ ( aScalar0 @ SX1 )
| ( ( sdtasdt0 @ ( smndt0 @ SX0 ) @ SX1 )
= ( smndt0 @ ( sdtasdt0 @ SX0 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[281]) ).
thf(334,plain,
! [SV28: $i] :
( ( ~ ! [SY94: $i,SY95: $i] :
( ~ ( aScalar0 @ SV28 )
| ~ ( aScalar0 @ SY94 )
| ~ ( aScalar0 @ SY95 )
| ( ( sdtasdt0 @ SV28 @ ( sdtpldt0 @ SY94 @ SY95 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV28 @ SY94 ) @ ( sdtasdt0 @ SV28 @ SY95 ) ) ) )
| ~ ! [SY96: $i,SY97: $i] :
( ~ ( aScalar0 @ SV28 )
| ~ ( aScalar0 @ SY96 )
| ~ ( aScalar0 @ SY97 )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SV28 @ SY96 ) @ SY97 )
= ( sdtpldt0 @ ( sdtasdt0 @ SV28 @ SY97 ) @ ( sdtasdt0 @ SY96 @ SY97 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[282]) ).
thf(335,plain,
! [SV29: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY98: $i,SY99: $i] :
( ~ ( aScalar0 @ SV29 )
| ~ ( aScalar0 @ SY98 )
| ~ ( aScalar0 @ SY99 )
| ( ( sdtpldt0 @ ( sdtpldt0 @ SV29 @ SY98 ) @ SY99 )
= ( sdtpldt0 @ SV29 @ ( sdtpldt0 @ SY98 @ SY99 ) ) ) )
| ~ ! [SY100: $i] :
( ~ ( aScalar0 @ SV29 )
| ~ ( aScalar0 @ SY100 )
| ! [SX2: $i] :
~ ( aScalar0 @ SX2 )
| ( ( sdtpldt0 @ SV29 @ SY100 )
= ( sdtpldt0 @ SY100 @ SV29 ) ) ) )
| ~ ! [SY102: $i,SY103: $i] :
( ~ ( aScalar0 @ SV29 )
| ~ ( aScalar0 @ SY102 )
| ~ ( aScalar0 @ SY103 )
| ( ( sdtasdt0 @ ( sdtasdt0 @ SV29 @ SY102 ) @ SY103 )
= ( sdtasdt0 @ SV29 @ ( sdtasdt0 @ SY102 @ SY103 ) ) ) ) )
| ~ ! [SY104: $i] :
( ~ ( aScalar0 @ SV29 )
| ~ ( aScalar0 @ SY104 )
| ! [SX2: $i] :
~ ( aScalar0 @ SX2 )
| ( ( sdtasdt0 @ SV29 @ SY104 )
= ( sdtasdt0 @ SY104 @ SV29 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[283]) ).
thf(336,plain,
( ( ( xG
!= ( sdtasdt0 @ xB @ xB ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[284]) ).
thf(337,plain,
( ( ~ ( aScalar0 @ xG ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[284]) ).
thf(338,plain,
( ( ( xB
!= ( sdtlbdtrb0 @ xt @ ( aDimensionOf0 @ xt ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[285]) ).
thf(339,plain,
( ( ~ ( aScalar0 @ xB ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[285]) ).
thf(340,plain,
( ( ( xC
!= ( sdtasasdt0 @ xp @ xp ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[286]) ).
thf(341,plain,
( ( ~ ( aScalar0 @ xC ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[286]) ).
thf(342,plain,
( ( ( xN
!= ( sdtasdt0 @ xR @ xS ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[287]) ).
thf(343,plain,
( ( ~ ( aScalar0 @ xN ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[287]) ).
thf(344,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( ( sdtlbdtrb0 @ xp @ SX0 )
= ( sdtlbdtrb0 @ xs @ SX0 ) ) )
| ~ ~ ( ( ( szszuzczcdt0 @ ( aDimensionOf0 @ xp ) )
!= ( aDimensionOf0 @ xs ) )
| ~ ( aVector0 @ xp ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[288]) ).
thf(345,plain,
( ( ( xp
!= ( sziznziztdt0 @ xs ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[288]) ).
thf(346,plain,
( ( ( xS
!= ( sdtasdt0 @ xF @ xD ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[289]) ).
thf(347,plain,
( ( ~ ( aScalar0 @ xS ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[289]) ).
thf(348,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( aScalar0 @ SX0 )
| ~ ( aScalar0 @ SX1 )
| ~ ( sdtlseqdt0 @ sz0z00 @ SX0 )
| ~ ( sdtlseqdt0 @ sz0z00 @ SX1 )
| ( sdtlseqdt0 @ sz0z00 @ ( sdtpldt0 @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[290]) ).
thf(349,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( aScalar0 @ SX0 )
| ~ ( aScalar0 @ SX1 )
| ~ ( sdtlseqdt0 @ sz0z00 @ SX0 )
| ~ ( sdtlseqdt0 @ sz0z00 @ SX1 )
| ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[290]) ).
thf(350,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtpldt0 @ SX0 @ sz0z00 )
= SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtpldt0 @ sz0z00 @ SX0 )
= SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtasdt0 @ SX0 @ sz0z00 )
= sz0z00 ) ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtasdt0 @ sz0z00 @ SX0 )
= sz0z00 ) ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtpldt0 @ SX0 @ ( smndt0 @ SX0 ) )
= sz0z00 ) ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtpldt0 @ ( smndt0 @ SX0 ) @ SX0 )
= sz0z00 ) ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( smndt0 @ ( smndt0 @ SX0 ) )
= SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[291]) ).
thf(351,plain,
( ( ~ ( ! [SX0: $i] :
~ ( aScalar0 @ SX0 )
| ( ( smndt0 @ sz0z00 )
= sz0z00 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[291]) ).
thf(352,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( ( sdtlbdtrb0 @ xq @ SX0 )
= ( sdtlbdtrb0 @ xt @ SX0 ) ) )
| ~ ~ ( ( ( szszuzczcdt0 @ ( aDimensionOf0 @ xq ) )
!= ( aDimensionOf0 @ xt ) )
| ~ ( aVector0 @ xq ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[292]) ).
thf(353,plain,
( ( ( xq
!= ( sziznziztdt0 @ xt ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[292]) ).
thf(354,plain,
( ( ( xD
!= ( sdtasasdt0 @ xq @ xq ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[293]) ).
thf(355,plain,
( ( ~ ( aScalar0 @ xD ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[293]) ).
thf(356,plain,
( ( ( xR
!= ( sdtasdt0 @ xC @ xG ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[294]) ).
thf(357,plain,
( ( ~ ( aScalar0 @ xR ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[294]) ).
thf(358,plain,
( ( ( xH
!= ( sdtasdt0 @ xA @ xB ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[295]) ).
thf(359,plain,
( ( ~ ( aScalar0 @ xH ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[295]) ).
thf(360,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( ( szszuzczcdt0 @ SX0 )
!= sz00 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[296]) ).
thf(361,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( aNaturalNumber0 @ ( szszuzczcdt0 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[296]) ).
thf(362,plain,
( ( ( xP
!= ( sdtasdt0 @ xE @ xH ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[297]) ).
thf(363,plain,
( ( ~ ( aScalar0 @ xP ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[297]) ).
thf(364,plain,
! [SV30: $i,SV1: $i] :
( ( ( ~ ( aVector0 @ SV1 )
| ~ ( aVector0 @ SV30 ) )
= $true )
| ( ( ( ( aDimensionOf0 @ SV1 )
!= ( aDimensionOf0 @ SV30 ) )
| ~ ( iLess0 @ ( aDimensionOf0 @ SV1 ) @ ( aDimensionOf0 @ xs ) )
| ( sdtlseqdt0 @ ( sdtasdt0 @ ( sdtasasdt0 @ SV1 @ SV30 ) @ ( sdtasasdt0 @ SV1 @ SV30 ) ) @ ( sdtasdt0 @ ( sdtasasdt0 @ SV1 @ SV1 ) @ ( sdtasasdt0 @ SV30 @ SV30 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[298]) ).
thf(365,plain,
! [SV31: $i,SV3: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV3 )
| ~ ( aNaturalNumber0 @ SV31 ) )
= $true )
| ( ( ( ( szszuzczcdt0 @ SV3 )
!= ( szszuzczcdt0 @ SV31 ) )
| ( SV3 = SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[299]) ).
thf(366,plain,
! [SV47: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV47 ) )
= $true )
| ( ( ! [W1: $i] :
~ ( aNaturalNumber0 @ W1 ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[300]) ).
thf(367,plain,
! [SV4: $i] :
( ( ( aNaturalNumber0 @ SV4 )
= $false )
| ( ( iLess0 @ SV4 @ ( szszuzczcdt0 @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[301]) ).
thf(368,plain,
! [SV32: $i,SV6: $i] :
( ( ( ~ ( aScalar0 @ SV6 )
| ~ ( aScalar0 @ SV32 ) )
= $true )
| ( ( aScalar0 @ ( sdtpldt0 @ SV6 @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[302]) ).
thf(369,plain,
! [SV33: $i,SV7: $i] :
( ( ( ~ ( aScalar0 @ SV7 )
| ~ ( aScalar0 @ SV33 ) )
= $true )
| ( ( aScalar0 @ ( sdtasdt0 @ SV7 @ SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[303]) ).
thf(370,plain,
! [SV8: $i] :
( ( ( aScalar0 @ SV8 )
= $false )
| ( ( aScalar0 @ ( smndt0 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[304]) ).
thf(371,plain,
! [SV48: $i,SV34: $i,SV9: $i] :
( ( ! [SY113: $i] :
( ~ ( aScalar0 @ SV9 )
| ~ ( aScalar0 @ SV34 )
| ~ ( aScalar0 @ SV48 )
| ~ ( aScalar0 @ SY113 )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SV9 @ SV34 ) @ ( sdtpldt0 @ SV48 @ SY113 ) )
= ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ SV9 @ SV48 ) @ ( sdtasdt0 @ SV9 @ SY113 ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ SV34 @ SV48 ) @ ( sdtasdt0 @ SV34 @ SY113 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[305]) ).
thf(372,plain,
! [SV35: $i,SV10: $i] :
( ( ( ~ ( aScalar0 @ SV10 )
| ~ ( aScalar0 @ SV35 ) )
= $true )
| ( ( ( sdtasdt0 @ ( smndt0 @ SV10 ) @ ( smndt0 @ SV35 ) )
= ( sdtasdt0 @ SV10 @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[306]) ).
thf(373,plain,
! [SV49: $i] :
( ( ( ~ ( aScalar0 @ SV49 ) )
= $true )
| ( ( ! [W1: $i] :
~ ( aScalar0 @ W1 ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[307]) ).
thf(374,plain,
! [SV11: $i] :
( ( ( aScalar0 @ SV11 )
= $false )
| ( ( sdtlseqdt0 @ SV11 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[308]) ).
thf(375,plain,
! [SV36: $i,SV12: $i] :
( ( ( ~ ( aScalar0 @ SV12 )
| ~ ( aScalar0 @ SV36 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV12 @ SV36 )
| ~ ( sdtlseqdt0 @ SV36 @ SV12 )
| ( SV12 = SV36 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[309]) ).
thf(376,plain,
! [SV50: $i,SV37: $i,SV13: $i] :
( ( ~ ( aScalar0 @ SV13 )
| ~ ( aScalar0 @ SV37 )
| ~ ( aScalar0 @ SV50 )
| ~ ( sdtlseqdt0 @ SV13 @ SV37 )
| ~ ( sdtlseqdt0 @ SV37 @ SV50 )
| ( sdtlseqdt0 @ SV13 @ SV50 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[310]) ).
thf(377,plain,
! [SV51: $i,SV38: $i,SV14: $i] :
( ( ! [SY114: $i] :
( ~ ( aScalar0 @ SV14 )
| ~ ( aScalar0 @ SV38 )
| ~ ( aScalar0 @ SV51 )
| ~ ( aScalar0 @ SY114 )
| ~ ( sdtlseqdt0 @ SV14 @ SV38 )
| ~ ( sdtlseqdt0 @ SV51 @ SY114 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SV14 @ SV51 ) @ ( sdtpldt0 @ SV38 @ SY114 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[311]) ).
thf(378,plain,
! [SV52: $i,SV39: $i,SV15: $i] :
( ( ! [SY115: $i] :
( ~ ( aScalar0 @ SV15 )
| ~ ( aScalar0 @ SV39 )
| ~ ( aScalar0 @ SV52 )
| ~ ( aScalar0 @ SY115 )
| ~ ( sdtlseqdt0 @ SV15 @ SV39 )
| ~ ( sdtlseqdt0 @ sz0z00 @ SV52 )
| ~ ( sdtlseqdt0 @ SV52 @ SY115 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV15 @ SV52 ) @ ( sdtasdt0 @ SV39 @ SY115 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[312]) ).
thf(379,plain,
! [SV40: $i,SV16: $i] :
( ( ( ~ ( aScalar0 @ SV16 )
| ~ ( aScalar0 @ SV40 ) )
= $true )
| ( ( ( sdtlseqdt0 @ SV16 @ SV40 )
| ( sdtlseqdt0 @ SV40 @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[313]) ).
thf(380,plain,
! [SV17: $i] :
( ( ( aScalar0 @ SV17 )
= $false )
| ( ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ SV17 @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[314]) ).
thf(381,plain,
! [SV41: $i,SV18: $i] :
( ( ( ~ ( aScalar0 @ SV18 )
| ~ ( aScalar0 @ SV41 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ sz0z00 @ SV18 )
| ~ ( sdtlseqdt0 @ sz0z00 @ SV41 )
| ( ( sdtasdt0 @ SV18 @ SV18 )
!= ( sdtasdt0 @ SV41 @ SV41 ) )
| ( SV18 = SV41 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[315]) ).
thf(382,plain,
! [SV20: $i] :
( ( ( aVector0 @ SV20 )
= $false )
| ( ( aNaturalNumber0 @ ( aDimensionOf0 @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[316]) ).
thf(383,plain,
! [SV21: $i,SV42: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV42 )
| ~ ( aVector0 @ SV21 ) )
= $true )
| ( ( aScalar0 @ ( sdtlbdtrb0 @ SV21 @ SV42 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[317]) ).
thf(384,plain,
! [SV43: $i,SV22: $i] :
( ( ( ~ ( aVector0 @ SV22 )
| ~ ( aVector0 @ SV43 ) )
= $true )
| ( ( ( ( aDimensionOf0 @ SV43 )
= sz00 )
| ( ( aDimensionOf0 @ SV22 )
!= ( aDimensionOf0 @ SV43 ) )
| ( ( aDimensionOf0 @ ( sziznziztdt0 @ SV22 ) )
= ( aDimensionOf0 @ ( sziznziztdt0 @ SV43 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[318]) ).
thf(385,plain,
! [SV44: $i,SV23: $i] :
( ( ( ~ ( aVector0 @ SV23 )
| ~ ( aVector0 @ SV44 ) )
= $true )
| ( ( ( ( aDimensionOf0 @ SV23 )
!= ( aDimensionOf0 @ SV44 ) )
| ( aScalar0 @ ( sdtasasdt0 @ SV23 @ SV44 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[319]) ).
thf(386,plain,
! [SV45: $i,SV24: $i] :
( ( ( ~ ( aVector0 @ SV24 )
| ~ ( aVector0 @ SV45 ) )
= $true )
| ( ( ( ( aDimensionOf0 @ SV24 )
!= ( aDimensionOf0 @ SV45 ) )
| ( ( aDimensionOf0 @ SV45 )
!= sz00 )
| ( ( sdtasasdt0 @ SV24 @ SV45 )
= sz0z00 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[320]) ).
thf(387,plain,
! [SV46: $i,SV25: $i] :
( ( ( ~ ( aVector0 @ SV25 )
| ~ ( aVector0 @ SV46 ) )
= $true )
| ( ( ( ( aDimensionOf0 @ SV46 )
= sz00 )
| ( ( aDimensionOf0 @ SV25 )
!= ( aDimensionOf0 @ SV46 ) )
| ( ( sdtasasdt0 @ SV25 @ SV46 )
= ( sdtpldt0 @ ( sdtasasdt0 @ ( sziznziztdt0 @ SV25 ) @ ( sziznziztdt0 @ SV46 ) ) @ ( sdtasdt0 @ ( sdtlbdtrb0 @ SV25 @ ( aDimensionOf0 @ SV25 ) ) @ ( sdtlbdtrb0 @ SV46 @ ( aDimensionOf0 @ SV46 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[321]) ).
thf(388,plain,
! [SV26: $i] :
( ( ( aVector0 @ SV26 )
= $false )
| ( ( sdtlseqdt0 @ sz0z00 @ ( sdtasasdt0 @ SV26 @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[322]) ).
thf(389,plain,
( ( xE
= ( sdtasasdt0 @ xp @ xq ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[323]) ).
thf(390,plain,
( ( aScalar0 @ xE )
= $true ),
inference(extcnf_not_neg,[status(thm)],[324]) ).
thf(391,plain,
( ( xA
= ( sdtlbdtrb0 @ xs @ ( aDimensionOf0 @ xs ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[325]) ).
thf(392,plain,
( ( aScalar0 @ xA )
= $true ),
inference(extcnf_not_neg,[status(thm)],[326]) ).
thf(393,plain,
( ( xF
= ( sdtasdt0 @ xA @ xA ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[327]) ).
thf(394,plain,
( ( aScalar0 @ xF )
= $true ),
inference(extcnf_not_neg,[status(thm)],[328]) ).
thf(395,plain,
( ( aVector0 @ xs )
= $true ),
inference(extcnf_not_neg,[status(thm)],[329]) ).
thf(396,plain,
( ( aVector0 @ xt )
= $true ),
inference(extcnf_not_neg,[status(thm)],[330]) ).
thf(397,plain,
! [SV27: $i] :
( ( ( SV27 = sz00 )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV27 ) )
= $true )
| ( ( ~ ( ( SV27
!= ( szszuzczcdt0 @ ( sK1_W1 @ SV27 ) ) )
| ~ ( aNaturalNumber0 @ ( sK1_W1 @ SV27 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[331]) ).
thf(398,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( aScalar0 @ SX0 )
| ~ ( aScalar0 @ SX1 )
| ( ( sdtasdt0 @ SX0 @ ( smndt0 @ SX1 ) )
= ( smndt0 @ ( sdtasdt0 @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[332]) ).
thf(399,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( aScalar0 @ SX0 )
| ~ ( aScalar0 @ SX1 )
| ( ( sdtasdt0 @ ( smndt0 @ SX0 ) @ SX1 )
= ( smndt0 @ ( sdtasdt0 @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[333]) ).
thf(400,plain,
! [SV28: $i] :
( ( ~ ! [SY94: $i,SY95: $i] :
( ~ ( aScalar0 @ SV28 )
| ~ ( aScalar0 @ SY94 )
| ~ ( aScalar0 @ SY95 )
| ( ( sdtasdt0 @ SV28 @ ( sdtpldt0 @ SY94 @ SY95 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV28 @ SY94 ) @ ( sdtasdt0 @ SV28 @ SY95 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[334]) ).
thf(401,plain,
! [SV28: $i] :
( ( ~ ! [SY96: $i,SY97: $i] :
( ~ ( aScalar0 @ SV28 )
| ~ ( aScalar0 @ SY96 )
| ~ ( aScalar0 @ SY97 )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SV28 @ SY96 ) @ SY97 )
= ( sdtpldt0 @ ( sdtasdt0 @ SV28 @ SY97 ) @ ( sdtasdt0 @ SY96 @ SY97 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[334]) ).
thf(402,plain,
! [SV29: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY98: $i,SY99: $i] :
( ~ ( aScalar0 @ SV29 )
| ~ ( aScalar0 @ SY98 )
| ~ ( aScalar0 @ SY99 )
| ( ( sdtpldt0 @ ( sdtpldt0 @ SV29 @ SY98 ) @ SY99 )
= ( sdtpldt0 @ SV29 @ ( sdtpldt0 @ SY98 @ SY99 ) ) ) )
| ~ ! [SY100: $i] :
( ~ ( aScalar0 @ SV29 )
| ~ ( aScalar0 @ SY100 )
| ! [SX2: $i] :
~ ( aScalar0 @ SX2 )
| ( ( sdtpldt0 @ SV29 @ SY100 )
= ( sdtpldt0 @ SY100 @ SV29 ) ) ) )
| ~ ! [SY102: $i,SY103: $i] :
( ~ ( aScalar0 @ SV29 )
| ~ ( aScalar0 @ SY102 )
| ~ ( aScalar0 @ SY103 )
| ( ( sdtasdt0 @ ( sdtasdt0 @ SV29 @ SY102 ) @ SY103 )
= ( sdtasdt0 @ SV29 @ ( sdtasdt0 @ SY102 @ SY103 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[335]) ).
thf(403,plain,
! [SV29: $i] :
( ( ~ ! [SY104: $i] :
( ~ ( aScalar0 @ SV29 )
| ~ ( aScalar0 @ SY104 )
| ! [SX2: $i] :
~ ( aScalar0 @ SX2 )
| ( ( sdtasdt0 @ SV29 @ SY104 )
= ( sdtasdt0 @ SY104 @ SV29 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[335]) ).
thf(404,plain,
( ( xG
= ( sdtasdt0 @ xB @ xB ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[336]) ).
thf(405,plain,
( ( aScalar0 @ xG )
= $true ),
inference(extcnf_not_neg,[status(thm)],[337]) ).
thf(406,plain,
( ( xB
= ( sdtlbdtrb0 @ xt @ ( aDimensionOf0 @ xt ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[338]) ).
thf(407,plain,
( ( aScalar0 @ xB )
= $true ),
inference(extcnf_not_neg,[status(thm)],[339]) ).
thf(408,plain,
( ( xC
= ( sdtasasdt0 @ xp @ xp ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[340]) ).
thf(409,plain,
( ( aScalar0 @ xC )
= $true ),
inference(extcnf_not_neg,[status(thm)],[341]) ).
thf(410,plain,
( ( xN
= ( sdtasdt0 @ xR @ xS ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[342]) ).
thf(411,plain,
( ( aScalar0 @ xN )
= $true ),
inference(extcnf_not_neg,[status(thm)],[343]) ).
thf(412,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( ( sdtlbdtrb0 @ xp @ SX0 )
= ( sdtlbdtrb0 @ xs @ SX0 ) ) )
| ~ ~ ( ( ( szszuzczcdt0 @ ( aDimensionOf0 @ xp ) )
!= ( aDimensionOf0 @ xs ) )
| ~ ( aVector0 @ xp ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[344]) ).
thf(413,plain,
( ( xp
= ( sziznziztdt0 @ xs ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[345]) ).
thf(414,plain,
( ( xS
= ( sdtasdt0 @ xF @ xD ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[346]) ).
thf(415,plain,
( ( aScalar0 @ xS )
= $true ),
inference(extcnf_not_neg,[status(thm)],[347]) ).
thf(416,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( aScalar0 @ SX0 )
| ~ ( aScalar0 @ SX1 )
| ~ ( sdtlseqdt0 @ sz0z00 @ SX0 )
| ~ ( sdtlseqdt0 @ sz0z00 @ SX1 )
| ( sdtlseqdt0 @ sz0z00 @ ( sdtpldt0 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[348]) ).
thf(417,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( aScalar0 @ SX0 )
| ~ ( aScalar0 @ SX1 )
| ~ ( sdtlseqdt0 @ sz0z00 @ SX0 )
| ~ ( sdtlseqdt0 @ sz0z00 @ SX1 )
| ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[349]) ).
thf(418,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtpldt0 @ SX0 @ sz0z00 )
= SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtpldt0 @ sz0z00 @ SX0 )
= SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtasdt0 @ SX0 @ sz0z00 )
= sz0z00 ) ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtasdt0 @ sz0z00 @ SX0 )
= sz0z00 ) ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtpldt0 @ SX0 @ ( smndt0 @ SX0 ) )
= sz0z00 ) ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtpldt0 @ ( smndt0 @ SX0 ) @ SX0 )
= sz0z00 ) ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( smndt0 @ ( smndt0 @ SX0 ) )
= SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[350]) ).
thf(419,plain,
( ( ! [SX0: $i] :
~ ( aScalar0 @ SX0 )
| ( ( smndt0 @ sz0z00 )
= sz0z00 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[351]) ).
thf(420,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( ( sdtlbdtrb0 @ xq @ SX0 )
= ( sdtlbdtrb0 @ xt @ SX0 ) ) )
| ~ ~ ( ( ( szszuzczcdt0 @ ( aDimensionOf0 @ xq ) )
!= ( aDimensionOf0 @ xt ) )
| ~ ( aVector0 @ xq ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[352]) ).
thf(421,plain,
( ( xq
= ( sziznziztdt0 @ xt ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[353]) ).
thf(422,plain,
( ( xD
= ( sdtasasdt0 @ xq @ xq ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[354]) ).
thf(423,plain,
( ( aScalar0 @ xD )
= $true ),
inference(extcnf_not_neg,[status(thm)],[355]) ).
thf(424,plain,
( ( xR
= ( sdtasdt0 @ xC @ xG ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[356]) ).
thf(425,plain,
( ( aScalar0 @ xR )
= $true ),
inference(extcnf_not_neg,[status(thm)],[357]) ).
thf(426,plain,
( ( xH
= ( sdtasdt0 @ xA @ xB ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[358]) ).
thf(427,plain,
( ( aScalar0 @ xH )
= $true ),
inference(extcnf_not_neg,[status(thm)],[359]) ).
thf(428,plain,
( ( ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( ( szszuzczcdt0 @ SX0 )
!= sz00 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[360]) ).
thf(429,plain,
( ( ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( aNaturalNumber0 @ ( szszuzczcdt0 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[361]) ).
thf(430,plain,
( ( xP
= ( sdtasdt0 @ xE @ xH ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[362]) ).
thf(431,plain,
( ( aScalar0 @ xP )
= $true ),
inference(extcnf_not_neg,[status(thm)],[363]) ).
thf(432,plain,
! [SV30: $i,SV1: $i] :
( ( ( ~ ( aVector0 @ SV1 ) )
= $true )
| ( ( ~ ( aVector0 @ SV30 ) )
= $true )
| ( ( ( ( aDimensionOf0 @ SV1 )
!= ( aDimensionOf0 @ SV30 ) )
| ~ ( iLess0 @ ( aDimensionOf0 @ SV1 ) @ ( aDimensionOf0 @ xs ) )
| ( sdtlseqdt0 @ ( sdtasdt0 @ ( sdtasasdt0 @ SV1 @ SV30 ) @ ( sdtasasdt0 @ SV1 @ SV30 ) ) @ ( sdtasdt0 @ ( sdtasasdt0 @ SV1 @ SV1 ) @ ( sdtasasdt0 @ SV30 @ SV30 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[364]) ).
thf(433,plain,
! [SV31: $i,SV3: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV3 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV31 ) )
= $true )
| ( ( ( ( szszuzczcdt0 @ SV3 )
!= ( szszuzczcdt0 @ SV31 ) )
| ( SV3 = SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[365]) ).
thf(434,plain,
! [SV47: $i] :
( ( ( aNaturalNumber0 @ SV47 )
= $false )
| ( ( ! [W1: $i] :
~ ( aNaturalNumber0 @ W1 ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[366]) ).
thf(435,plain,
! [SV32: $i,SV6: $i] :
( ( ( ~ ( aScalar0 @ SV6 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV32 ) )
= $true )
| ( ( aScalar0 @ ( sdtpldt0 @ SV6 @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[368]) ).
thf(436,plain,
! [SV33: $i,SV7: $i] :
( ( ( ~ ( aScalar0 @ SV7 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV33 ) )
= $true )
| ( ( aScalar0 @ ( sdtasdt0 @ SV7 @ SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[369]) ).
thf(437,plain,
! [SV53: $i,SV48: $i,SV34: $i,SV9: $i] :
( ( ~ ( aScalar0 @ SV9 )
| ~ ( aScalar0 @ SV34 )
| ~ ( aScalar0 @ SV48 )
| ~ ( aScalar0 @ SV53 )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SV9 @ SV34 ) @ ( sdtpldt0 @ SV48 @ SV53 ) )
= ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ SV9 @ SV48 ) @ ( sdtasdt0 @ SV9 @ SV53 ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ SV34 @ SV48 ) @ ( sdtasdt0 @ SV34 @ SV53 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[371]) ).
thf(438,plain,
! [SV35: $i,SV10: $i] :
( ( ( ~ ( aScalar0 @ SV10 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV35 ) )
= $true )
| ( ( ( sdtasdt0 @ ( smndt0 @ SV10 ) @ ( smndt0 @ SV35 ) )
= ( sdtasdt0 @ SV10 @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[372]) ).
thf(439,plain,
! [SV49: $i] :
( ( ( aScalar0 @ SV49 )
= $false )
| ( ( ! [W1: $i] :
~ ( aScalar0 @ W1 ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[373]) ).
thf(440,plain,
! [SV36: $i,SV12: $i] :
( ( ( ~ ( aScalar0 @ SV12 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV36 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV12 @ SV36 )
| ~ ( sdtlseqdt0 @ SV36 @ SV12 )
| ( SV12 = SV36 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[375]) ).
thf(441,plain,
! [SV50: $i,SV37: $i,SV13: $i] :
( ( ( ~ ( aScalar0 @ SV13 )
| ~ ( aScalar0 @ SV37 )
| ~ ( aScalar0 @ SV50 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV13 @ SV37 )
| ~ ( sdtlseqdt0 @ SV37 @ SV50 )
| ( sdtlseqdt0 @ SV13 @ SV50 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[376]) ).
thf(442,plain,
! [SV54: $i,SV51: $i,SV38: $i,SV14: $i] :
( ( ~ ( aScalar0 @ SV14 )
| ~ ( aScalar0 @ SV38 )
| ~ ( aScalar0 @ SV51 )
| ~ ( aScalar0 @ SV54 )
| ~ ( sdtlseqdt0 @ SV14 @ SV38 )
| ~ ( sdtlseqdt0 @ SV51 @ SV54 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SV14 @ SV51 ) @ ( sdtpldt0 @ SV38 @ SV54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[377]) ).
thf(443,plain,
! [SV55: $i,SV52: $i,SV39: $i,SV15: $i] :
( ( ~ ( aScalar0 @ SV15 )
| ~ ( aScalar0 @ SV39 )
| ~ ( aScalar0 @ SV52 )
| ~ ( aScalar0 @ SV55 )
| ~ ( sdtlseqdt0 @ SV15 @ SV39 )
| ~ ( sdtlseqdt0 @ sz0z00 @ SV52 )
| ~ ( sdtlseqdt0 @ SV52 @ SV55 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV15 @ SV52 ) @ ( sdtasdt0 @ SV39 @ SV55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[378]) ).
thf(444,plain,
! [SV40: $i,SV16: $i] :
( ( ( ~ ( aScalar0 @ SV16 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV40 ) )
= $true )
| ( ( ( sdtlseqdt0 @ SV16 @ SV40 )
| ( sdtlseqdt0 @ SV40 @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[379]) ).
thf(445,plain,
! [SV41: $i,SV18: $i] :
( ( ( ~ ( aScalar0 @ SV18 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV41 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ sz0z00 @ SV18 )
| ~ ( sdtlseqdt0 @ sz0z00 @ SV41 )
| ( ( sdtasdt0 @ SV18 @ SV18 )
!= ( sdtasdt0 @ SV41 @ SV41 ) )
| ( SV18 = SV41 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[381]) ).
thf(446,plain,
! [SV21: $i,SV42: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV42 ) )
= $true )
| ( ( ~ ( aVector0 @ SV21 ) )
= $true )
| ( ( aScalar0 @ ( sdtlbdtrb0 @ SV21 @ SV42 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[383]) ).
thf(447,plain,
! [SV43: $i,SV22: $i] :
( ( ( ~ ( aVector0 @ SV22 ) )
= $true )
| ( ( ~ ( aVector0 @ SV43 ) )
= $true )
| ( ( ( ( aDimensionOf0 @ SV43 )
= sz00 )
| ( ( aDimensionOf0 @ SV22 )
!= ( aDimensionOf0 @ SV43 ) )
| ( ( aDimensionOf0 @ ( sziznziztdt0 @ SV22 ) )
= ( aDimensionOf0 @ ( sziznziztdt0 @ SV43 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[384]) ).
thf(448,plain,
! [SV44: $i,SV23: $i] :
( ( ( ~ ( aVector0 @ SV23 ) )
= $true )
| ( ( ~ ( aVector0 @ SV44 ) )
= $true )
| ( ( ( ( aDimensionOf0 @ SV23 )
!= ( aDimensionOf0 @ SV44 ) )
| ( aScalar0 @ ( sdtasasdt0 @ SV23 @ SV44 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[385]) ).
thf(449,plain,
! [SV45: $i,SV24: $i] :
( ( ( ~ ( aVector0 @ SV24 ) )
= $true )
| ( ( ~ ( aVector0 @ SV45 ) )
= $true )
| ( ( ( ( aDimensionOf0 @ SV24 )
!= ( aDimensionOf0 @ SV45 ) )
| ( ( aDimensionOf0 @ SV45 )
!= sz00 )
| ( ( sdtasasdt0 @ SV24 @ SV45 )
= sz0z00 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[386]) ).
thf(450,plain,
! [SV46: $i,SV25: $i] :
( ( ( ~ ( aVector0 @ SV25 ) )
= $true )
| ( ( ~ ( aVector0 @ SV46 ) )
= $true )
| ( ( ( ( aDimensionOf0 @ SV46 )
= sz00 )
| ( ( aDimensionOf0 @ SV25 )
!= ( aDimensionOf0 @ SV46 ) )
| ( ( sdtasasdt0 @ SV25 @ SV46 )
= ( sdtpldt0 @ ( sdtasasdt0 @ ( sziznziztdt0 @ SV25 ) @ ( sziznziztdt0 @ SV46 ) ) @ ( sdtasdt0 @ ( sdtlbdtrb0 @ SV25 @ ( aDimensionOf0 @ SV25 ) ) @ ( sdtlbdtrb0 @ SV46 @ ( aDimensionOf0 @ SV46 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[387]) ).
thf(451,plain,
! [SV27: $i] :
( ( ( aNaturalNumber0 @ SV27 )
= $false )
| ( ( SV27 = sz00 )
= $true )
| ( ( ~ ( ( SV27
!= ( szszuzczcdt0 @ ( sK1_W1 @ SV27 ) ) )
| ~ ( aNaturalNumber0 @ ( sK1_W1 @ SV27 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[397]) ).
thf(452,plain,
! [SV56: $i] :
( ( ! [SY116: $i] :
( ~ ( aScalar0 @ SV56 )
| ~ ( aScalar0 @ SY116 )
| ( ( sdtasdt0 @ SV56 @ ( smndt0 @ SY116 ) )
= ( smndt0 @ ( sdtasdt0 @ SV56 @ SY116 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[398]) ).
thf(453,plain,
! [SV57: $i] :
( ( ! [SY117: $i] :
( ~ ( aScalar0 @ SV57 )
| ~ ( aScalar0 @ SY117 )
| ( ( sdtasdt0 @ ( smndt0 @ SV57 ) @ SY117 )
= ( smndt0 @ ( sdtasdt0 @ SV57 @ SY117 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[399]) ).
thf(454,plain,
! [SV28: $i] :
( ( ! [SY94: $i,SY95: $i] :
( ~ ( aScalar0 @ SV28 )
| ~ ( aScalar0 @ SY94 )
| ~ ( aScalar0 @ SY95 )
| ( ( sdtasdt0 @ SV28 @ ( sdtpldt0 @ SY94 @ SY95 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV28 @ SY94 ) @ ( sdtasdt0 @ SV28 @ SY95 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[400]) ).
thf(455,plain,
! [SV28: $i] :
( ( ! [SY96: $i,SY97: $i] :
( ~ ( aScalar0 @ SV28 )
| ~ ( aScalar0 @ SY96 )
| ~ ( aScalar0 @ SY97 )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SV28 @ SY96 ) @ SY97 )
= ( sdtpldt0 @ ( sdtasdt0 @ SV28 @ SY97 ) @ ( sdtasdt0 @ SY96 @ SY97 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[401]) ).
thf(456,plain,
! [SV29: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY98: $i,SY99: $i] :
( ~ ( aScalar0 @ SV29 )
| ~ ( aScalar0 @ SY98 )
| ~ ( aScalar0 @ SY99 )
| ( ( sdtpldt0 @ ( sdtpldt0 @ SV29 @ SY98 ) @ SY99 )
= ( sdtpldt0 @ SV29 @ ( sdtpldt0 @ SY98 @ SY99 ) ) ) )
| ~ ! [SY100: $i] :
( ~ ( aScalar0 @ SV29 )
| ~ ( aScalar0 @ SY100 )
| ! [SX2: $i] :
~ ( aScalar0 @ SX2 )
| ( ( sdtpldt0 @ SV29 @ SY100 )
= ( sdtpldt0 @ SY100 @ SV29 ) ) ) )
| ~ ! [SY102: $i,SY103: $i] :
( ~ ( aScalar0 @ SV29 )
| ~ ( aScalar0 @ SY102 )
| ~ ( aScalar0 @ SY103 )
| ( ( sdtasdt0 @ ( sdtasdt0 @ SV29 @ SY102 ) @ SY103 )
= ( sdtasdt0 @ SV29 @ ( sdtasdt0 @ SY102 @ SY103 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[402]) ).
thf(457,plain,
! [SV29: $i] :
( ( ! [SY104: $i] :
( ~ ( aScalar0 @ SV29 )
| ~ ( aScalar0 @ SY104 )
| ! [SX2: $i] :
~ ( aScalar0 @ SX2 )
| ( ( sdtasdt0 @ SV29 @ SY104 )
= ( sdtasdt0 @ SY104 @ SV29 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[403]) ).
thf(458,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( ( sdtlbdtrb0 @ xp @ SX0 )
= ( sdtlbdtrb0 @ xs @ SX0 ) ) )
| ~ ~ ( ( ( szszuzczcdt0 @ ( aDimensionOf0 @ xp ) )
!= ( aDimensionOf0 @ xs ) )
| ~ ( aVector0 @ xp ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[412]) ).
thf(459,plain,
! [SV58: $i] :
( ( ! [SY118: $i] :
( ~ ( aScalar0 @ SV58 )
| ~ ( aScalar0 @ SY118 )
| ~ ( sdtlseqdt0 @ sz0z00 @ SV58 )
| ~ ( sdtlseqdt0 @ sz0z00 @ SY118 )
| ( sdtlseqdt0 @ sz0z00 @ ( sdtpldt0 @ SV58 @ SY118 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[416]) ).
thf(460,plain,
! [SV59: $i] :
( ( ! [SY119: $i] :
( ~ ( aScalar0 @ SV59 )
| ~ ( aScalar0 @ SY119 )
| ~ ( sdtlseqdt0 @ sz0z00 @ SV59 )
| ~ ( sdtlseqdt0 @ sz0z00 @ SY119 )
| ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ SV59 @ SY119 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[417]) ).
thf(461,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtpldt0 @ SX0 @ sz0z00 )
= SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtpldt0 @ sz0z00 @ SX0 )
= SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtasdt0 @ SX0 @ sz0z00 )
= sz0z00 ) ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtasdt0 @ sz0z00 @ SX0 )
= sz0z00 ) ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtpldt0 @ SX0 @ ( smndt0 @ SX0 ) )
= sz0z00 ) ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtpldt0 @ ( smndt0 @ SX0 ) @ SX0 )
= sz0z00 ) ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( smndt0 @ ( smndt0 @ SX0 ) )
= SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[418]) ).
thf(462,plain,
( ( ( ! [SX0: $i] :
~ ( aScalar0 @ SX0 ) )
= $true )
| ( ( ( smndt0 @ sz0z00 )
= sz0z00 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[419]) ).
thf(463,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( ( sdtlbdtrb0 @ xq @ SX0 )
= ( sdtlbdtrb0 @ xt @ SX0 ) ) )
| ~ ~ ( ( ( szszuzczcdt0 @ ( aDimensionOf0 @ xq ) )
!= ( aDimensionOf0 @ xt ) )
| ~ ( aVector0 @ xq ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[420]) ).
thf(464,plain,
! [SV60: $i] :
( ( ~ ( aNaturalNumber0 @ SV60 )
| ( ( szszuzczcdt0 @ SV60 )
!= sz00 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[428]) ).
thf(465,plain,
! [SV61: $i] :
( ( ~ ( aNaturalNumber0 @ SV61 )
| ( aNaturalNumber0 @ ( szszuzczcdt0 @ SV61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[429]) ).
thf(466,plain,
! [SV30: $i,SV1: $i] :
( ( ( aVector0 @ SV1 )
= $false )
| ( ( ~ ( aVector0 @ SV30 ) )
= $true )
| ( ( ( ( aDimensionOf0 @ SV1 )
!= ( aDimensionOf0 @ SV30 ) )
| ~ ( iLess0 @ ( aDimensionOf0 @ SV1 ) @ ( aDimensionOf0 @ xs ) )
| ( sdtlseqdt0 @ ( sdtasdt0 @ ( sdtasasdt0 @ SV1 @ SV30 ) @ ( sdtasasdt0 @ SV1 @ SV30 ) ) @ ( sdtasdt0 @ ( sdtasasdt0 @ SV1 @ SV1 ) @ ( sdtasasdt0 @ SV30 @ SV30 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[432]) ).
thf(467,plain,
! [SV31: $i,SV3: $i] :
( ( ( aNaturalNumber0 @ SV3 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV31 ) )
= $true )
| ( ( ( ( szszuzczcdt0 @ SV3 )
!= ( szszuzczcdt0 @ SV31 ) )
| ( SV3 = SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[433]) ).
thf(468,plain,
! [SV47: $i,SV62: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV62 ) )
= $true )
| ( ( aNaturalNumber0 @ SV47 )
= $false )
| ( $true = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[434]) ).
thf(469,plain,
! [SV32: $i,SV6: $i] :
( ( ( aScalar0 @ SV6 )
= $false )
| ( ( ~ ( aScalar0 @ SV32 ) )
= $true )
| ( ( aScalar0 @ ( sdtpldt0 @ SV6 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[435]) ).
thf(470,plain,
! [SV33: $i,SV7: $i] :
( ( ( aScalar0 @ SV7 )
= $false )
| ( ( ~ ( aScalar0 @ SV33 ) )
= $true )
| ( ( aScalar0 @ ( sdtasdt0 @ SV7 @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[436]) ).
thf(471,plain,
! [SV53: $i,SV48: $i,SV34: $i,SV9: $i] :
( ( ( ~ ( aScalar0 @ SV9 )
| ~ ( aScalar0 @ SV34 )
| ~ ( aScalar0 @ SV48 )
| ~ ( aScalar0 @ SV53 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV9 @ SV34 ) @ ( sdtpldt0 @ SV48 @ SV53 ) )
= ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ SV9 @ SV48 ) @ ( sdtasdt0 @ SV9 @ SV53 ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ SV34 @ SV48 ) @ ( sdtasdt0 @ SV34 @ SV53 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[437]) ).
thf(472,plain,
! [SV35: $i,SV10: $i] :
( ( ( aScalar0 @ SV10 )
= $false )
| ( ( ~ ( aScalar0 @ SV35 ) )
= $true )
| ( ( ( sdtasdt0 @ ( smndt0 @ SV10 ) @ ( smndt0 @ SV35 ) )
= ( sdtasdt0 @ SV10 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[438]) ).
thf(473,plain,
! [SV49: $i,SV63: $i] :
( ( ( ~ ( aScalar0 @ SV63 ) )
= $true )
| ( ( aScalar0 @ SV49 )
= $false )
| ( $true = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[439]) ).
thf(474,plain,
! [SV36: $i,SV12: $i] :
( ( ( aScalar0 @ SV12 )
= $false )
| ( ( ~ ( aScalar0 @ SV36 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV12 @ SV36 )
| ~ ( sdtlseqdt0 @ SV36 @ SV12 )
| ( SV12 = SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[440]) ).
thf(475,plain,
! [SV50: $i,SV37: $i,SV13: $i] :
( ( ( ~ ( aScalar0 @ SV13 )
| ~ ( aScalar0 @ SV37 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV50 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV13 @ SV37 )
| ~ ( sdtlseqdt0 @ SV37 @ SV50 )
| ( sdtlseqdt0 @ SV13 @ SV50 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[441]) ).
thf(476,plain,
! [SV54: $i,SV51: $i,SV38: $i,SV14: $i] :
( ( ( ~ ( aScalar0 @ SV14 )
| ~ ( aScalar0 @ SV38 )
| ~ ( aScalar0 @ SV51 )
| ~ ( aScalar0 @ SV54 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV14 @ SV38 )
| ~ ( sdtlseqdt0 @ SV51 @ SV54 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SV14 @ SV51 ) @ ( sdtpldt0 @ SV38 @ SV54 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[442]) ).
thf(477,plain,
! [SV55: $i,SV52: $i,SV39: $i,SV15: $i] :
( ( ( ~ ( aScalar0 @ SV15 )
| ~ ( aScalar0 @ SV39 )
| ~ ( aScalar0 @ SV52 )
| ~ ( aScalar0 @ SV55 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV15 @ SV39 )
| ~ ( sdtlseqdt0 @ sz0z00 @ SV52 )
| ~ ( sdtlseqdt0 @ SV52 @ SV55 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV15 @ SV52 ) @ ( sdtasdt0 @ SV39 @ SV55 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[443]) ).
thf(478,plain,
! [SV40: $i,SV16: $i] :
( ( ( aScalar0 @ SV16 )
= $false )
| ( ( ~ ( aScalar0 @ SV40 ) )
= $true )
| ( ( ( sdtlseqdt0 @ SV16 @ SV40 )
| ( sdtlseqdt0 @ SV40 @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[444]) ).
thf(479,plain,
! [SV41: $i,SV18: $i] :
( ( ( aScalar0 @ SV18 )
= $false )
| ( ( ~ ( aScalar0 @ SV41 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ sz0z00 @ SV18 )
| ~ ( sdtlseqdt0 @ sz0z00 @ SV41 )
| ( ( sdtasdt0 @ SV18 @ SV18 )
!= ( sdtasdt0 @ SV41 @ SV41 ) )
| ( SV18 = SV41 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[445]) ).
thf(480,plain,
! [SV21: $i,SV42: $i] :
( ( ( aNaturalNumber0 @ SV42 )
= $false )
| ( ( ~ ( aVector0 @ SV21 ) )
= $true )
| ( ( aScalar0 @ ( sdtlbdtrb0 @ SV21 @ SV42 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[446]) ).
thf(481,plain,
! [SV43: $i,SV22: $i] :
( ( ( aVector0 @ SV22 )
= $false )
| ( ( ~ ( aVector0 @ SV43 ) )
= $true )
| ( ( ( ( aDimensionOf0 @ SV43 )
= sz00 )
| ( ( aDimensionOf0 @ SV22 )
!= ( aDimensionOf0 @ SV43 ) )
| ( ( aDimensionOf0 @ ( sziznziztdt0 @ SV22 ) )
= ( aDimensionOf0 @ ( sziznziztdt0 @ SV43 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[447]) ).
thf(482,plain,
! [SV44: $i,SV23: $i] :
( ( ( aVector0 @ SV23 )
= $false )
| ( ( ~ ( aVector0 @ SV44 ) )
= $true )
| ( ( ( ( aDimensionOf0 @ SV23 )
!= ( aDimensionOf0 @ SV44 ) )
| ( aScalar0 @ ( sdtasasdt0 @ SV23 @ SV44 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[448]) ).
thf(483,plain,
! [SV45: $i,SV24: $i] :
( ( ( aVector0 @ SV24 )
= $false )
| ( ( ~ ( aVector0 @ SV45 ) )
= $true )
| ( ( ( ( aDimensionOf0 @ SV24 )
!= ( aDimensionOf0 @ SV45 ) )
| ( ( aDimensionOf0 @ SV45 )
!= sz00 )
| ( ( sdtasasdt0 @ SV24 @ SV45 )
= sz0z00 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[449]) ).
thf(484,plain,
! [SV46: $i,SV25: $i] :
( ( ( aVector0 @ SV25 )
= $false )
| ( ( ~ ( aVector0 @ SV46 ) )
= $true )
| ( ( ( ( aDimensionOf0 @ SV46 )
= sz00 )
| ( ( aDimensionOf0 @ SV25 )
!= ( aDimensionOf0 @ SV46 ) )
| ( ( sdtasasdt0 @ SV25 @ SV46 )
= ( sdtpldt0 @ ( sdtasasdt0 @ ( sziznziztdt0 @ SV25 ) @ ( sziznziztdt0 @ SV46 ) ) @ ( sdtasdt0 @ ( sdtlbdtrb0 @ SV25 @ ( aDimensionOf0 @ SV25 ) ) @ ( sdtlbdtrb0 @ SV46 @ ( aDimensionOf0 @ SV46 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[450]) ).
thf(485,plain,
! [SV27: $i] :
( ( ( ( SV27
!= ( szszuzczcdt0 @ ( sK1_W1 @ SV27 ) ) )
| ~ ( aNaturalNumber0 @ ( sK1_W1 @ SV27 ) ) )
= $false )
| ( ( SV27 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[451]) ).
thf(486,plain,
! [SV64: $i,SV56: $i] :
( ( ~ ( aScalar0 @ SV56 )
| ~ ( aScalar0 @ SV64 )
| ( ( sdtasdt0 @ SV56 @ ( smndt0 @ SV64 ) )
= ( smndt0 @ ( sdtasdt0 @ SV56 @ SV64 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[452]) ).
thf(487,plain,
! [SV65: $i,SV57: $i] :
( ( ~ ( aScalar0 @ SV57 )
| ~ ( aScalar0 @ SV65 )
| ( ( sdtasdt0 @ ( smndt0 @ SV57 ) @ SV65 )
= ( smndt0 @ ( sdtasdt0 @ SV57 @ SV65 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[453]) ).
thf(488,plain,
! [SV66: $i,SV28: $i] :
( ( ! [SY120: $i] :
( ~ ( aScalar0 @ SV28 )
| ~ ( aScalar0 @ SV66 )
| ~ ( aScalar0 @ SY120 )
| ( ( sdtasdt0 @ SV28 @ ( sdtpldt0 @ SV66 @ SY120 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV28 @ SV66 ) @ ( sdtasdt0 @ SV28 @ SY120 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[454]) ).
thf(489,plain,
! [SV67: $i,SV28: $i] :
( ( ! [SY121: $i] :
( ~ ( aScalar0 @ SV28 )
| ~ ( aScalar0 @ SV67 )
| ~ ( aScalar0 @ SY121 )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SV28 @ SV67 ) @ SY121 )
= ( sdtpldt0 @ ( sdtasdt0 @ SV28 @ SY121 ) @ ( sdtasdt0 @ SV67 @ SY121 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[455]) ).
thf(490,plain,
! [SV29: $i] :
( ( ~ ~ ( ~ ! [SY98: $i,SY99: $i] :
( ~ ( aScalar0 @ SV29 )
| ~ ( aScalar0 @ SY98 )
| ~ ( aScalar0 @ SY99 )
| ( ( sdtpldt0 @ ( sdtpldt0 @ SV29 @ SY98 ) @ SY99 )
= ( sdtpldt0 @ SV29 @ ( sdtpldt0 @ SY98 @ SY99 ) ) ) )
| ~ ! [SY100: $i] :
( ~ ( aScalar0 @ SV29 )
| ~ ( aScalar0 @ SY100 )
| ! [SX2: $i] :
~ ( aScalar0 @ SX2 )
| ( ( sdtpldt0 @ SV29 @ SY100 )
= ( sdtpldt0 @ SY100 @ SV29 ) ) ) )
| ~ ! [SY102: $i,SY103: $i] :
( ~ ( aScalar0 @ SV29 )
| ~ ( aScalar0 @ SY102 )
| ~ ( aScalar0 @ SY103 )
| ( ( sdtasdt0 @ ( sdtasdt0 @ SV29 @ SY102 ) @ SY103 )
= ( sdtasdt0 @ SV29 @ ( sdtasdt0 @ SY102 @ SY103 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[456]) ).
thf(491,plain,
! [SV68: $i,SV29: $i] :
( ( ~ ( aScalar0 @ SV29 )
| ~ ( aScalar0 @ SV68 )
| ! [SX2: $i] :
~ ( aScalar0 @ SX2 )
| ( ( sdtasdt0 @ SV29 @ SV68 )
= ( sdtasdt0 @ SV68 @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[457]) ).
thf(492,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( ( sdtlbdtrb0 @ xp @ SX0 )
= ( sdtlbdtrb0 @ xs @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[458]) ).
thf(493,plain,
( ( ~ ~ ( ( ( szszuzczcdt0 @ ( aDimensionOf0 @ xp ) )
!= ( aDimensionOf0 @ xs ) )
| ~ ( aVector0 @ xp ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[458]) ).
thf(494,plain,
! [SV69: $i,SV58: $i] :
( ( ~ ( aScalar0 @ SV58 )
| ~ ( aScalar0 @ SV69 )
| ~ ( sdtlseqdt0 @ sz0z00 @ SV58 )
| ~ ( sdtlseqdt0 @ sz0z00 @ SV69 )
| ( sdtlseqdt0 @ sz0z00 @ ( sdtpldt0 @ SV58 @ SV69 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[459]) ).
thf(495,plain,
! [SV70: $i,SV59: $i] :
( ( ~ ( aScalar0 @ SV59 )
| ~ ( aScalar0 @ SV70 )
| ~ ( sdtlseqdt0 @ sz0z00 @ SV59 )
| ~ ( sdtlseqdt0 @ sz0z00 @ SV70 )
| ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ SV59 @ SV70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[460]) ).
thf(496,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtpldt0 @ SX0 @ sz0z00 )
= SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtpldt0 @ sz0z00 @ SX0 )
= SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtasdt0 @ SX0 @ sz0z00 )
= sz0z00 ) ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtasdt0 @ sz0z00 @ SX0 )
= sz0z00 ) ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtpldt0 @ SX0 @ ( smndt0 @ SX0 ) )
= sz0z00 ) ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtpldt0 @ ( smndt0 @ SX0 ) @ SX0 )
= sz0z00 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[461]) ).
thf(497,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( smndt0 @ ( smndt0 @ SX0 ) )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[461]) ).
thf(498,plain,
! [SV71: $i] :
( ( ( ~ ( aScalar0 @ SV71 ) )
= $true )
| ( ( ( smndt0 @ sz0z00 )
= sz0z00 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[462]) ).
thf(499,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( ( sdtlbdtrb0 @ xq @ SX0 )
= ( sdtlbdtrb0 @ xt @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[463]) ).
thf(500,plain,
( ( ~ ~ ( ( ( szszuzczcdt0 @ ( aDimensionOf0 @ xq ) )
!= ( aDimensionOf0 @ xt ) )
| ~ ( aVector0 @ xq ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[463]) ).
thf(501,plain,
! [SV60: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV60 ) )
= $true )
| ( ( ( ( szszuzczcdt0 @ SV60 )
!= sz00 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[464]) ).
thf(502,plain,
! [SV61: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV61 ) )
= $true )
| ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ SV61 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[465]) ).
thf(503,plain,
! [SV1: $i,SV30: $i] :
( ( ( aVector0 @ SV30 )
= $false )
| ( ( aVector0 @ SV1 )
= $false )
| ( ( ( ( aDimensionOf0 @ SV1 )
!= ( aDimensionOf0 @ SV30 ) )
| ~ ( iLess0 @ ( aDimensionOf0 @ SV1 ) @ ( aDimensionOf0 @ xs ) )
| ( sdtlseqdt0 @ ( sdtasdt0 @ ( sdtasasdt0 @ SV1 @ SV30 ) @ ( sdtasasdt0 @ SV1 @ SV30 ) ) @ ( sdtasdt0 @ ( sdtasasdt0 @ SV1 @ SV1 ) @ ( sdtasasdt0 @ SV30 @ SV30 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[466]) ).
thf(504,plain,
! [SV3: $i,SV31: $i] :
( ( ( aNaturalNumber0 @ SV31 )
= $false )
| ( ( aNaturalNumber0 @ SV3 )
= $false )
| ( ( ( ( szszuzczcdt0 @ SV3 )
!= ( szszuzczcdt0 @ SV31 ) )
| ( SV3 = SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[467]) ).
thf(505,plain,
! [SV47: $i,SV62: $i] :
( ( ( aNaturalNumber0 @ SV62 )
= $false )
| ( ( aNaturalNumber0 @ SV47 )
= $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[468]) ).
thf(506,plain,
! [SV6: $i,SV32: $i] :
( ( ( aScalar0 @ SV32 )
= $false )
| ( ( aScalar0 @ SV6 )
= $false )
| ( ( aScalar0 @ ( sdtpldt0 @ SV6 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[469]) ).
thf(507,plain,
! [SV7: $i,SV33: $i] :
( ( ( aScalar0 @ SV33 )
= $false )
| ( ( aScalar0 @ SV7 )
= $false )
| ( ( aScalar0 @ ( sdtasdt0 @ SV7 @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[470]) ).
thf(508,plain,
! [SV53: $i,SV48: $i,SV34: $i,SV9: $i] :
( ( ( ~ ( aScalar0 @ SV9 )
| ~ ( aScalar0 @ SV34 )
| ~ ( aScalar0 @ SV48 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV53 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV9 @ SV34 ) @ ( sdtpldt0 @ SV48 @ SV53 ) )
= ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ SV9 @ SV48 ) @ ( sdtasdt0 @ SV9 @ SV53 ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ SV34 @ SV48 ) @ ( sdtasdt0 @ SV34 @ SV53 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[471]) ).
thf(509,plain,
! [SV10: $i,SV35: $i] :
( ( ( aScalar0 @ SV35 )
= $false )
| ( ( aScalar0 @ SV10 )
= $false )
| ( ( ( sdtasdt0 @ ( smndt0 @ SV10 ) @ ( smndt0 @ SV35 ) )
= ( sdtasdt0 @ SV10 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[472]) ).
thf(510,plain,
! [SV49: $i,SV63: $i] :
( ( ( aScalar0 @ SV63 )
= $false )
| ( ( aScalar0 @ SV49 )
= $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[473]) ).
thf(511,plain,
! [SV12: $i,SV36: $i] :
( ( ( aScalar0 @ SV36 )
= $false )
| ( ( aScalar0 @ SV12 )
= $false )
| ( ( ~ ( sdtlseqdt0 @ SV12 @ SV36 )
| ~ ( sdtlseqdt0 @ SV36 @ SV12 )
| ( SV12 = SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[474]) ).
thf(512,plain,
! [SV50: $i,SV37: $i,SV13: $i] :
( ( ( ~ ( aScalar0 @ SV13 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV37 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV50 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV13 @ SV37 )
| ~ ( sdtlseqdt0 @ SV37 @ SV50 )
| ( sdtlseqdt0 @ SV13 @ SV50 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[475]) ).
thf(513,plain,
! [SV54: $i,SV51: $i,SV38: $i,SV14: $i] :
( ( ( ~ ( aScalar0 @ SV14 )
| ~ ( aScalar0 @ SV38 )
| ~ ( aScalar0 @ SV51 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV54 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV14 @ SV38 )
| ~ ( sdtlseqdt0 @ SV51 @ SV54 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SV14 @ SV51 ) @ ( sdtpldt0 @ SV38 @ SV54 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[476]) ).
thf(514,plain,
! [SV55: $i,SV52: $i,SV39: $i,SV15: $i] :
( ( ( ~ ( aScalar0 @ SV15 )
| ~ ( aScalar0 @ SV39 )
| ~ ( aScalar0 @ SV52 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV55 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV15 @ SV39 )
| ~ ( sdtlseqdt0 @ sz0z00 @ SV52 )
| ~ ( sdtlseqdt0 @ SV52 @ SV55 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV15 @ SV52 ) @ ( sdtasdt0 @ SV39 @ SV55 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[477]) ).
thf(515,plain,
! [SV16: $i,SV40: $i] :
( ( ( aScalar0 @ SV40 )
= $false )
| ( ( aScalar0 @ SV16 )
= $false )
| ( ( ( sdtlseqdt0 @ SV16 @ SV40 )
| ( sdtlseqdt0 @ SV40 @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[478]) ).
thf(516,plain,
! [SV18: $i,SV41: $i] :
( ( ( aScalar0 @ SV41 )
= $false )
| ( ( aScalar0 @ SV18 )
= $false )
| ( ( ~ ( sdtlseqdt0 @ sz0z00 @ SV18 )
| ~ ( sdtlseqdt0 @ sz0z00 @ SV41 )
| ( ( sdtasdt0 @ SV18 @ SV18 )
!= ( sdtasdt0 @ SV41 @ SV41 ) )
| ( SV18 = SV41 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[479]) ).
thf(517,plain,
! [SV42: $i,SV21: $i] :
( ( ( aVector0 @ SV21 )
= $false )
| ( ( aNaturalNumber0 @ SV42 )
= $false )
| ( ( aScalar0 @ ( sdtlbdtrb0 @ SV21 @ SV42 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[480]) ).
thf(518,plain,
! [SV22: $i,SV43: $i] :
( ( ( aVector0 @ SV43 )
= $false )
| ( ( aVector0 @ SV22 )
= $false )
| ( ( ( ( aDimensionOf0 @ SV43 )
= sz00 )
| ( ( aDimensionOf0 @ SV22 )
!= ( aDimensionOf0 @ SV43 ) )
| ( ( aDimensionOf0 @ ( sziznziztdt0 @ SV22 ) )
= ( aDimensionOf0 @ ( sziznziztdt0 @ SV43 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[481]) ).
thf(519,plain,
! [SV23: $i,SV44: $i] :
( ( ( aVector0 @ SV44 )
= $false )
| ( ( aVector0 @ SV23 )
= $false )
| ( ( ( ( aDimensionOf0 @ SV23 )
!= ( aDimensionOf0 @ SV44 ) )
| ( aScalar0 @ ( sdtasasdt0 @ SV23 @ SV44 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[482]) ).
thf(520,plain,
! [SV24: $i,SV45: $i] :
( ( ( aVector0 @ SV45 )
= $false )
| ( ( aVector0 @ SV24 )
= $false )
| ( ( ( ( aDimensionOf0 @ SV24 )
!= ( aDimensionOf0 @ SV45 ) )
| ( ( aDimensionOf0 @ SV45 )
!= sz00 )
| ( ( sdtasasdt0 @ SV24 @ SV45 )
= sz0z00 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[483]) ).
thf(521,plain,
! [SV25: $i,SV46: $i] :
( ( ( aVector0 @ SV46 )
= $false )
| ( ( aVector0 @ SV25 )
= $false )
| ( ( ( ( aDimensionOf0 @ SV46 )
= sz00 )
| ( ( aDimensionOf0 @ SV25 )
!= ( aDimensionOf0 @ SV46 ) )
| ( ( sdtasasdt0 @ SV25 @ SV46 )
= ( sdtpldt0 @ ( sdtasasdt0 @ ( sziznziztdt0 @ SV25 ) @ ( sziznziztdt0 @ SV46 ) ) @ ( sdtasdt0 @ ( sdtlbdtrb0 @ SV25 @ ( aDimensionOf0 @ SV25 ) ) @ ( sdtlbdtrb0 @ SV46 @ ( aDimensionOf0 @ SV46 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[484]) ).
thf(522,plain,
! [SV27: $i] :
( ( ( ( SV27
!= ( szszuzczcdt0 @ ( sK1_W1 @ SV27 ) ) ) )
= $false )
| ( ( SV27 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV27 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[485]) ).
thf(523,plain,
! [SV27: $i] :
( ( ( ~ ( aNaturalNumber0 @ ( sK1_W1 @ SV27 ) ) )
= $false )
| ( ( SV27 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV27 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[485]) ).
thf(524,plain,
! [SV64: $i,SV56: $i] :
( ( ( ~ ( aScalar0 @ SV56 )
| ~ ( aScalar0 @ SV64 ) )
= $true )
| ( ( ( sdtasdt0 @ SV56 @ ( smndt0 @ SV64 ) )
= ( smndt0 @ ( sdtasdt0 @ SV56 @ SV64 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[486]) ).
thf(525,plain,
! [SV65: $i,SV57: $i] :
( ( ( ~ ( aScalar0 @ SV57 )
| ~ ( aScalar0 @ SV65 ) )
= $true )
| ( ( ( sdtasdt0 @ ( smndt0 @ SV57 ) @ SV65 )
= ( smndt0 @ ( sdtasdt0 @ SV57 @ SV65 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[487]) ).
thf(526,plain,
! [SV72: $i,SV66: $i,SV28: $i] :
( ( ~ ( aScalar0 @ SV28 )
| ~ ( aScalar0 @ SV66 )
| ~ ( aScalar0 @ SV72 )
| ( ( sdtasdt0 @ SV28 @ ( sdtpldt0 @ SV66 @ SV72 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV28 @ SV66 ) @ ( sdtasdt0 @ SV28 @ SV72 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[488]) ).
thf(527,plain,
! [SV73: $i,SV67: $i,SV28: $i] :
( ( ~ ( aScalar0 @ SV28 )
| ~ ( aScalar0 @ SV67 )
| ~ ( aScalar0 @ SV73 )
| ( ( sdtasdt0 @ ( sdtpldt0 @ SV28 @ SV67 ) @ SV73 )
= ( sdtpldt0 @ ( sdtasdt0 @ SV28 @ SV73 ) @ ( sdtasdt0 @ SV67 @ SV73 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[489]) ).
thf(528,plain,
! [SV29: $i] :
( ( ~ ~ ( ~ ! [SY98: $i,SY99: $i] :
( ~ ( aScalar0 @ SV29 )
| ~ ( aScalar0 @ SY98 )
| ~ ( aScalar0 @ SY99 )
| ( ( sdtpldt0 @ ( sdtpldt0 @ SV29 @ SY98 ) @ SY99 )
= ( sdtpldt0 @ SV29 @ ( sdtpldt0 @ SY98 @ SY99 ) ) ) )
| ~ ! [SY100: $i] :
( ~ ( aScalar0 @ SV29 )
| ~ ( aScalar0 @ SY100 )
| ! [SX2: $i] :
~ ( aScalar0 @ SX2 )
| ( ( sdtpldt0 @ SV29 @ SY100 )
= ( sdtpldt0 @ SY100 @ SV29 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[490]) ).
thf(529,plain,
! [SV29: $i] :
( ( ~ ! [SY102: $i,SY103: $i] :
( ~ ( aScalar0 @ SV29 )
| ~ ( aScalar0 @ SY102 )
| ~ ( aScalar0 @ SY103 )
| ( ( sdtasdt0 @ ( sdtasdt0 @ SV29 @ SY102 ) @ SY103 )
= ( sdtasdt0 @ SV29 @ ( sdtasdt0 @ SY102 @ SY103 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[490]) ).
thf(530,plain,
! [SV68: $i,SV29: $i] :
( ( ( ~ ( aScalar0 @ SV29 )
| ~ ( aScalar0 @ SV68 )
| ! [SX2: $i] :
~ ( aScalar0 @ SX2 ) )
= $true )
| ( ( ( sdtasdt0 @ SV29 @ SV68 )
= ( sdtasdt0 @ SV68 @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[491]) ).
thf(531,plain,
( ( ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( ( sdtlbdtrb0 @ xp @ SX0 )
= ( sdtlbdtrb0 @ xs @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[492]) ).
thf(532,plain,
( ( ~ ( ( ( szszuzczcdt0 @ ( aDimensionOf0 @ xp ) )
!= ( aDimensionOf0 @ xs ) )
| ~ ( aVector0 @ xp ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[493]) ).
thf(533,plain,
! [SV69: $i,SV58: $i] :
( ( ( ~ ( aScalar0 @ SV58 )
| ~ ( aScalar0 @ SV69 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ sz0z00 @ SV58 )
| ~ ( sdtlseqdt0 @ sz0z00 @ SV69 )
| ( sdtlseqdt0 @ sz0z00 @ ( sdtpldt0 @ SV58 @ SV69 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[494]) ).
thf(534,plain,
! [SV70: $i,SV59: $i] :
( ( ( ~ ( aScalar0 @ SV59 )
| ~ ( aScalar0 @ SV70 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ sz0z00 @ SV59 )
| ~ ( sdtlseqdt0 @ sz0z00 @ SV70 )
| ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ SV59 @ SV70 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[495]) ).
thf(535,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtpldt0 @ SX0 @ sz0z00 )
= SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtpldt0 @ sz0z00 @ SX0 )
= SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtasdt0 @ SX0 @ sz0z00 )
= sz0z00 ) ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtasdt0 @ sz0z00 @ SX0 )
= sz0z00 ) ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtpldt0 @ SX0 @ ( smndt0 @ SX0 ) )
= sz0z00 ) ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtpldt0 @ ( smndt0 @ SX0 ) @ SX0 )
= sz0z00 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[496]) ).
thf(536,plain,
( ( ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( smndt0 @ ( smndt0 @ SX0 ) )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[497]) ).
thf(537,plain,
! [SV71: $i] :
( ( ( aScalar0 @ SV71 )
= $false )
| ( ( ( smndt0 @ sz0z00 )
= sz0z00 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[498]) ).
thf(538,plain,
( ( ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( ( sdtlbdtrb0 @ xq @ SX0 )
= ( sdtlbdtrb0 @ xt @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[499]) ).
thf(539,plain,
( ( ~ ( ( ( szszuzczcdt0 @ ( aDimensionOf0 @ xq ) )
!= ( aDimensionOf0 @ xt ) )
| ~ ( aVector0 @ xq ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[500]) ).
thf(540,plain,
! [SV60: $i] :
( ( ( aNaturalNumber0 @ SV60 )
= $false )
| ( ( ( ( szszuzczcdt0 @ SV60 )
!= sz00 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[501]) ).
thf(541,plain,
! [SV61: $i] :
( ( ( aNaturalNumber0 @ SV61 )
= $false )
| ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ SV61 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[502]) ).
thf(542,plain,
! [SV30: $i,SV1: $i] :
( ( ( ( ( aDimensionOf0 @ SV1 )
!= ( aDimensionOf0 @ SV30 ) ) )
= $true )
| ( ( ~ ( iLess0 @ ( aDimensionOf0 @ SV1 ) @ ( aDimensionOf0 @ xs ) )
| ( sdtlseqdt0 @ ( sdtasdt0 @ ( sdtasasdt0 @ SV1 @ SV30 ) @ ( sdtasasdt0 @ SV1 @ SV30 ) ) @ ( sdtasdt0 @ ( sdtasasdt0 @ SV1 @ SV1 ) @ ( sdtasasdt0 @ SV30 @ SV30 ) ) ) )
= $true )
| ( ( aVector0 @ SV1 )
= $false )
| ( ( aVector0 @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[503]) ).
thf(543,plain,
! [SV31: $i,SV3: $i] :
( ( ( ( ( szszuzczcdt0 @ SV3 )
!= ( szszuzczcdt0 @ SV31 ) ) )
= $true )
| ( ( SV3 = SV31 )
= $true )
| ( ( aNaturalNumber0 @ SV3 )
= $false )
| ( ( aNaturalNumber0 @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[504]) ).
thf(544,plain,
! [SV53: $i,SV48: $i,SV34: $i,SV9: $i] :
( ( ( ~ ( aScalar0 @ SV9 )
| ~ ( aScalar0 @ SV34 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV48 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV53 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV9 @ SV34 ) @ ( sdtpldt0 @ SV48 @ SV53 ) )
= ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ SV9 @ SV48 ) @ ( sdtasdt0 @ SV9 @ SV53 ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ SV34 @ SV48 ) @ ( sdtasdt0 @ SV34 @ SV53 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[508]) ).
thf(545,plain,
! [SV36: $i,SV12: $i] :
( ( ( ~ ( sdtlseqdt0 @ SV12 @ SV36 )
| ~ ( sdtlseqdt0 @ SV36 @ SV12 ) )
= $true )
| ( ( SV12 = SV36 )
= $true )
| ( ( aScalar0 @ SV12 )
= $false )
| ( ( aScalar0 @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[511]) ).
thf(546,plain,
! [SV50: $i,SV37: $i,SV13: $i] :
( ( ( aScalar0 @ SV13 )
= $false )
| ( ( ~ ( aScalar0 @ SV37 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV50 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV13 @ SV37 )
| ~ ( sdtlseqdt0 @ SV37 @ SV50 )
| ( sdtlseqdt0 @ SV13 @ SV50 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[512]) ).
thf(547,plain,
! [SV54: $i,SV51: $i,SV38: $i,SV14: $i] :
( ( ( ~ ( aScalar0 @ SV14 )
| ~ ( aScalar0 @ SV38 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV51 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV54 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV14 @ SV38 )
| ~ ( sdtlseqdt0 @ SV51 @ SV54 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SV14 @ SV51 ) @ ( sdtpldt0 @ SV38 @ SV54 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[513]) ).
thf(548,plain,
! [SV55: $i,SV52: $i,SV39: $i,SV15: $i] :
( ( ( ~ ( aScalar0 @ SV15 )
| ~ ( aScalar0 @ SV39 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV52 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV55 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV15 @ SV39 )
| ~ ( sdtlseqdt0 @ sz0z00 @ SV52 )
| ~ ( sdtlseqdt0 @ SV52 @ SV55 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV15 @ SV52 ) @ ( sdtasdt0 @ SV39 @ SV55 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[514]) ).
thf(549,plain,
! [SV40: $i,SV16: $i] :
( ( ( sdtlseqdt0 @ SV16 @ SV40 )
= $true )
| ( ( sdtlseqdt0 @ SV40 @ SV16 )
= $true )
| ( ( aScalar0 @ SV16 )
= $false )
| ( ( aScalar0 @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[515]) ).
thf(550,plain,
! [SV41: $i,SV18: $i] :
( ( ( ~ ( sdtlseqdt0 @ sz0z00 @ SV18 )
| ~ ( sdtlseqdt0 @ sz0z00 @ SV41 )
| ( ( sdtasdt0 @ SV18 @ SV18 )
!= ( sdtasdt0 @ SV41 @ SV41 ) ) )
= $true )
| ( ( SV18 = SV41 )
= $true )
| ( ( aScalar0 @ SV18 )
= $false )
| ( ( aScalar0 @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[516]) ).
thf(551,plain,
! [SV22: $i,SV43: $i] :
( ( ( ( ( aDimensionOf0 @ SV43 )
= sz00 )
| ( ( aDimensionOf0 @ SV22 )
!= ( aDimensionOf0 @ SV43 ) ) )
= $true )
| ( ( ( aDimensionOf0 @ ( sziznziztdt0 @ SV22 ) )
= ( aDimensionOf0 @ ( sziznziztdt0 @ SV43 ) ) )
= $true )
| ( ( aVector0 @ SV22 )
= $false )
| ( ( aVector0 @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[518]) ).
thf(552,plain,
! [SV44: $i,SV23: $i] :
( ( ( ( ( aDimensionOf0 @ SV23 )
!= ( aDimensionOf0 @ SV44 ) ) )
= $true )
| ( ( aScalar0 @ ( sdtasasdt0 @ SV23 @ SV44 ) )
= $true )
| ( ( aVector0 @ SV23 )
= $false )
| ( ( aVector0 @ SV44 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[519]) ).
thf(553,plain,
! [SV45: $i,SV24: $i] :
( ( ( ( ( aDimensionOf0 @ SV24 )
!= ( aDimensionOf0 @ SV45 ) )
| ( ( aDimensionOf0 @ SV45 )
!= sz00 ) )
= $true )
| ( ( ( sdtasasdt0 @ SV24 @ SV45 )
= sz0z00 )
= $true )
| ( ( aVector0 @ SV24 )
= $false )
| ( ( aVector0 @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[520]) ).
thf(554,plain,
! [SV25: $i,SV46: $i] :
( ( ( ( ( aDimensionOf0 @ SV46 )
= sz00 )
| ( ( aDimensionOf0 @ SV25 )
!= ( aDimensionOf0 @ SV46 ) ) )
= $true )
| ( ( ( sdtasasdt0 @ SV25 @ SV46 )
= ( sdtpldt0 @ ( sdtasasdt0 @ ( sziznziztdt0 @ SV25 ) @ ( sziznziztdt0 @ SV46 ) ) @ ( sdtasdt0 @ ( sdtlbdtrb0 @ SV25 @ ( aDimensionOf0 @ SV25 ) ) @ ( sdtlbdtrb0 @ SV46 @ ( aDimensionOf0 @ SV46 ) ) ) ) )
= $true )
| ( ( aVector0 @ SV25 )
= $false )
| ( ( aVector0 @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[521]) ).
thf(555,plain,
! [SV27: $i] :
( ( ( SV27
= ( szszuzczcdt0 @ ( sK1_W1 @ SV27 ) ) )
= $true )
| ( ( SV27 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV27 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[522]) ).
thf(556,plain,
! [SV27: $i] :
( ( ( aNaturalNumber0 @ ( sK1_W1 @ SV27 ) )
= $true )
| ( ( SV27 = sz00 )
= $true )
| ( ( aNaturalNumber0 @ SV27 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[523]) ).
thf(557,plain,
! [SV64: $i,SV56: $i] :
( ( ( ~ ( aScalar0 @ SV56 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV64 ) )
= $true )
| ( ( ( sdtasdt0 @ SV56 @ ( smndt0 @ SV64 ) )
= ( smndt0 @ ( sdtasdt0 @ SV56 @ SV64 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[524]) ).
thf(558,plain,
! [SV65: $i,SV57: $i] :
( ( ( ~ ( aScalar0 @ SV57 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV65 ) )
= $true )
| ( ( ( sdtasdt0 @ ( smndt0 @ SV57 ) @ SV65 )
= ( smndt0 @ ( sdtasdt0 @ SV57 @ SV65 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[525]) ).
thf(559,plain,
! [SV72: $i,SV66: $i,SV28: $i] :
( ( ( ~ ( aScalar0 @ SV28 )
| ~ ( aScalar0 @ SV66 )
| ~ ( aScalar0 @ SV72 ) )
= $true )
| ( ( ( sdtasdt0 @ SV28 @ ( sdtpldt0 @ SV66 @ SV72 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV28 @ SV66 ) @ ( sdtasdt0 @ SV28 @ SV72 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[526]) ).
thf(560,plain,
! [SV73: $i,SV67: $i,SV28: $i] :
( ( ( ~ ( aScalar0 @ SV28 )
| ~ ( aScalar0 @ SV67 )
| ~ ( aScalar0 @ SV73 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV28 @ SV67 ) @ SV73 )
= ( sdtpldt0 @ ( sdtasdt0 @ SV28 @ SV73 ) @ ( sdtasdt0 @ SV67 @ SV73 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[527]) ).
thf(561,plain,
! [SV29: $i] :
( ( ~ ( ~ ! [SY98: $i,SY99: $i] :
( ~ ( aScalar0 @ SV29 )
| ~ ( aScalar0 @ SY98 )
| ~ ( aScalar0 @ SY99 )
| ( ( sdtpldt0 @ ( sdtpldt0 @ SV29 @ SY98 ) @ SY99 )
= ( sdtpldt0 @ SV29 @ ( sdtpldt0 @ SY98 @ SY99 ) ) ) )
| ~ ! [SY100: $i] :
( ~ ( aScalar0 @ SV29 )
| ~ ( aScalar0 @ SY100 )
| ! [SX2: $i] :
~ ( aScalar0 @ SX2 )
| ( ( sdtpldt0 @ SV29 @ SY100 )
= ( sdtpldt0 @ SY100 @ SV29 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[528]) ).
thf(562,plain,
! [SV29: $i] :
( ( ! [SY102: $i,SY103: $i] :
( ~ ( aScalar0 @ SV29 )
| ~ ( aScalar0 @ SY102 )
| ~ ( aScalar0 @ SY103 )
| ( ( sdtasdt0 @ ( sdtasdt0 @ SV29 @ SY102 ) @ SY103 )
= ( sdtasdt0 @ SV29 @ ( sdtasdt0 @ SY102 @ SY103 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[529]) ).
thf(563,plain,
! [SV68: $i,SV29: $i] :
( ( ( ~ ( aScalar0 @ SV29 )
| ~ ( aScalar0 @ SV68 ) )
= $true )
| ( ( ! [SX2: $i] :
~ ( aScalar0 @ SX2 ) )
= $true )
| ( ( ( sdtasdt0 @ SV29 @ SV68 )
= ( sdtasdt0 @ SV68 @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[530]) ).
thf(564,plain,
! [SV74: $i] :
( ( ~ ( aNaturalNumber0 @ SV74 )
| ( ( sdtlbdtrb0 @ xp @ SV74 )
= ( sdtlbdtrb0 @ xs @ SV74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[531]) ).
thf(565,plain,
( ( ( ( szszuzczcdt0 @ ( aDimensionOf0 @ xp ) )
!= ( aDimensionOf0 @ xs ) )
| ~ ( aVector0 @ xp ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[532]) ).
thf(566,plain,
! [SV69: $i,SV58: $i] :
( ( ( ~ ( aScalar0 @ SV58 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV69 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ sz0z00 @ SV58 )
| ~ ( sdtlseqdt0 @ sz0z00 @ SV69 )
| ( sdtlseqdt0 @ sz0z00 @ ( sdtpldt0 @ SV58 @ SV69 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[533]) ).
thf(567,plain,
! [SV70: $i,SV59: $i] :
( ( ( ~ ( aScalar0 @ SV59 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV70 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ sz0z00 @ SV59 )
| ~ ( sdtlseqdt0 @ sz0z00 @ SV70 )
| ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ SV59 @ SV70 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[534]) ).
thf(568,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtpldt0 @ SX0 @ sz0z00 )
= SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtpldt0 @ sz0z00 @ SX0 )
= SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtasdt0 @ SX0 @ sz0z00 )
= sz0z00 ) ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtasdt0 @ sz0z00 @ SX0 )
= sz0z00 ) ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtpldt0 @ SX0 @ ( smndt0 @ SX0 ) )
= sz0z00 ) ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtpldt0 @ ( smndt0 @ SX0 ) @ SX0 )
= sz0z00 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[535]) ).
thf(569,plain,
! [SV75: $i] :
( ( ~ ( aScalar0 @ SV75 )
| ( ( smndt0 @ ( smndt0 @ SV75 ) )
= SV75 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[536]) ).
thf(570,plain,
! [SV76: $i] :
( ( ~ ( aNaturalNumber0 @ SV76 )
| ( ( sdtlbdtrb0 @ xq @ SV76 )
= ( sdtlbdtrb0 @ xt @ SV76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[538]) ).
thf(571,plain,
( ( ( ( szszuzczcdt0 @ ( aDimensionOf0 @ xq ) )
!= ( aDimensionOf0 @ xt ) )
| ~ ( aVector0 @ xq ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[539]) ).
thf(572,plain,
! [SV60: $i] :
( ( ( ( szszuzczcdt0 @ SV60 )
= sz00 )
= $false )
| ( ( aNaturalNumber0 @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[540]) ).
thf(573,plain,
! [SV30: $i,SV1: $i] :
( ( ( ( aDimensionOf0 @ SV1 )
= ( aDimensionOf0 @ SV30 ) )
= $false )
| ( ( ~ ( iLess0 @ ( aDimensionOf0 @ SV1 ) @ ( aDimensionOf0 @ xs ) )
| ( sdtlseqdt0 @ ( sdtasdt0 @ ( sdtasasdt0 @ SV1 @ SV30 ) @ ( sdtasasdt0 @ SV1 @ SV30 ) ) @ ( sdtasdt0 @ ( sdtasasdt0 @ SV1 @ SV1 ) @ ( sdtasasdt0 @ SV30 @ SV30 ) ) ) )
= $true )
| ( ( aVector0 @ SV1 )
= $false )
| ( ( aVector0 @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[542]) ).
thf(574,plain,
! [SV31: $i,SV3: $i] :
( ( ( ( szszuzczcdt0 @ SV3 )
= ( szszuzczcdt0 @ SV31 ) )
= $false )
| ( ( SV3 = SV31 )
= $true )
| ( ( aNaturalNumber0 @ SV3 )
= $false )
| ( ( aNaturalNumber0 @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[543]) ).
thf(575,plain,
! [SV53: $i,SV48: $i,SV34: $i,SV9: $i] :
( ( ( ~ ( aScalar0 @ SV9 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV34 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV48 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV53 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV9 @ SV34 ) @ ( sdtpldt0 @ SV48 @ SV53 ) )
= ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ SV9 @ SV48 ) @ ( sdtasdt0 @ SV9 @ SV53 ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ SV34 @ SV48 ) @ ( sdtasdt0 @ SV34 @ SV53 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[544]) ).
thf(576,plain,
! [SV36: $i,SV12: $i] :
( ( ( ~ ( sdtlseqdt0 @ SV12 @ SV36 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV36 @ SV12 ) )
= $true )
| ( ( SV12 = SV36 )
= $true )
| ( ( aScalar0 @ SV12 )
= $false )
| ( ( aScalar0 @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[545]) ).
thf(577,plain,
! [SV50: $i,SV13: $i,SV37: $i] :
( ( ( aScalar0 @ SV37 )
= $false )
| ( ( aScalar0 @ SV13 )
= $false )
| ( ( ~ ( aScalar0 @ SV50 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV13 @ SV37 )
| ~ ( sdtlseqdt0 @ SV37 @ SV50 )
| ( sdtlseqdt0 @ SV13 @ SV50 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[546]) ).
thf(578,plain,
! [SV54: $i,SV51: $i,SV38: $i,SV14: $i] :
( ( ( ~ ( aScalar0 @ SV14 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV38 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV51 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV54 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV14 @ SV38 )
| ~ ( sdtlseqdt0 @ SV51 @ SV54 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SV14 @ SV51 ) @ ( sdtpldt0 @ SV38 @ SV54 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[547]) ).
thf(579,plain,
! [SV55: $i,SV52: $i,SV39: $i,SV15: $i] :
( ( ( ~ ( aScalar0 @ SV15 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV39 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV52 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV55 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV15 @ SV39 )
| ~ ( sdtlseqdt0 @ sz0z00 @ SV52 )
| ~ ( sdtlseqdt0 @ SV52 @ SV55 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV15 @ SV52 ) @ ( sdtasdt0 @ SV39 @ SV55 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[548]) ).
thf(580,plain,
! [SV41: $i,SV18: $i] :
( ( ( ~ ( sdtlseqdt0 @ sz0z00 @ SV18 )
| ~ ( sdtlseqdt0 @ sz0z00 @ SV41 ) )
= $true )
| ( ( ( ( sdtasdt0 @ SV18 @ SV18 )
!= ( sdtasdt0 @ SV41 @ SV41 ) ) )
= $true )
| ( ( SV18 = SV41 )
= $true )
| ( ( aScalar0 @ SV18 )
= $false )
| ( ( aScalar0 @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[550]) ).
thf(581,plain,
! [SV22: $i,SV43: $i] :
( ( ( ( aDimensionOf0 @ SV43 )
= sz00 )
= $true )
| ( ( ( ( aDimensionOf0 @ SV22 )
!= ( aDimensionOf0 @ SV43 ) ) )
= $true )
| ( ( ( aDimensionOf0 @ ( sziznziztdt0 @ SV22 ) )
= ( aDimensionOf0 @ ( sziznziztdt0 @ SV43 ) ) )
= $true )
| ( ( aVector0 @ SV22 )
= $false )
| ( ( aVector0 @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[551]) ).
thf(582,plain,
! [SV44: $i,SV23: $i] :
( ( ( ( aDimensionOf0 @ SV23 )
= ( aDimensionOf0 @ SV44 ) )
= $false )
| ( ( aScalar0 @ ( sdtasasdt0 @ SV23 @ SV44 ) )
= $true )
| ( ( aVector0 @ SV23 )
= $false )
| ( ( aVector0 @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[552]) ).
thf(583,plain,
! [SV45: $i,SV24: $i] :
( ( ( ( ( aDimensionOf0 @ SV24 )
!= ( aDimensionOf0 @ SV45 ) ) )
= $true )
| ( ( ( ( aDimensionOf0 @ SV45 )
!= sz00 ) )
= $true )
| ( ( ( sdtasasdt0 @ SV24 @ SV45 )
= sz0z00 )
= $true )
| ( ( aVector0 @ SV24 )
= $false )
| ( ( aVector0 @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[553]) ).
thf(584,plain,
! [SV25: $i,SV46: $i] :
( ( ( ( aDimensionOf0 @ SV46 )
= sz00 )
= $true )
| ( ( ( ( aDimensionOf0 @ SV25 )
!= ( aDimensionOf0 @ SV46 ) ) )
= $true )
| ( ( ( sdtasasdt0 @ SV25 @ SV46 )
= ( sdtpldt0 @ ( sdtasasdt0 @ ( sziznziztdt0 @ SV25 ) @ ( sziznziztdt0 @ SV46 ) ) @ ( sdtasdt0 @ ( sdtlbdtrb0 @ SV25 @ ( aDimensionOf0 @ SV25 ) ) @ ( sdtlbdtrb0 @ SV46 @ ( aDimensionOf0 @ SV46 ) ) ) ) )
= $true )
| ( ( aVector0 @ SV25 )
= $false )
| ( ( aVector0 @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[554]) ).
thf(585,plain,
! [SV64: $i,SV56: $i] :
( ( ( aScalar0 @ SV56 )
= $false )
| ( ( ~ ( aScalar0 @ SV64 ) )
= $true )
| ( ( ( sdtasdt0 @ SV56 @ ( smndt0 @ SV64 ) )
= ( smndt0 @ ( sdtasdt0 @ SV56 @ SV64 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[557]) ).
thf(586,plain,
! [SV65: $i,SV57: $i] :
( ( ( aScalar0 @ SV57 )
= $false )
| ( ( ~ ( aScalar0 @ SV65 ) )
= $true )
| ( ( ( sdtasdt0 @ ( smndt0 @ SV57 ) @ SV65 )
= ( smndt0 @ ( sdtasdt0 @ SV57 @ SV65 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[558]) ).
thf(587,plain,
! [SV72: $i,SV66: $i,SV28: $i] :
( ( ( ~ ( aScalar0 @ SV28 )
| ~ ( aScalar0 @ SV66 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV72 ) )
= $true )
| ( ( ( sdtasdt0 @ SV28 @ ( sdtpldt0 @ SV66 @ SV72 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV28 @ SV66 ) @ ( sdtasdt0 @ SV28 @ SV72 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[559]) ).
thf(588,plain,
! [SV73: $i,SV67: $i,SV28: $i] :
( ( ( ~ ( aScalar0 @ SV28 )
| ~ ( aScalar0 @ SV67 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV73 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV28 @ SV67 ) @ SV73 )
= ( sdtpldt0 @ ( sdtasdt0 @ SV28 @ SV73 ) @ ( sdtasdt0 @ SV67 @ SV73 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[560]) ).
thf(589,plain,
! [SV29: $i] :
( ( ~ ! [SY98: $i,SY99: $i] :
( ~ ( aScalar0 @ SV29 )
| ~ ( aScalar0 @ SY98 )
| ~ ( aScalar0 @ SY99 )
| ( ( sdtpldt0 @ ( sdtpldt0 @ SV29 @ SY98 ) @ SY99 )
= ( sdtpldt0 @ SV29 @ ( sdtpldt0 @ SY98 @ SY99 ) ) ) )
| ~ ! [SY100: $i] :
( ~ ( aScalar0 @ SV29 )
| ~ ( aScalar0 @ SY100 )
| ! [SX2: $i] :
~ ( aScalar0 @ SX2 )
| ( ( sdtpldt0 @ SV29 @ SY100 )
= ( sdtpldt0 @ SY100 @ SV29 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[561]) ).
thf(590,plain,
! [SV77: $i,SV29: $i] :
( ( ! [SY123: $i] :
( ~ ( aScalar0 @ SV29 )
| ~ ( aScalar0 @ SV77 )
| ~ ( aScalar0 @ SY123 )
| ( ( sdtasdt0 @ ( sdtasdt0 @ SV29 @ SV77 ) @ SY123 )
= ( sdtasdt0 @ SV29 @ ( sdtasdt0 @ SV77 @ SY123 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[562]) ).
thf(591,plain,
! [SV68: $i,SV29: $i] :
( ( ( ~ ( aScalar0 @ SV29 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV68 ) )
= $true )
| ( ( ! [SX2: $i] :
~ ( aScalar0 @ SX2 ) )
= $true )
| ( ( ( sdtasdt0 @ SV29 @ SV68 )
= ( sdtasdt0 @ SV68 @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[563]) ).
thf(592,plain,
! [SV74: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV74 ) )
= $true )
| ( ( ( sdtlbdtrb0 @ xp @ SV74 )
= ( sdtlbdtrb0 @ xs @ SV74 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[564]) ).
thf(593,plain,
( ( ( ( szszuzczcdt0 @ ( aDimensionOf0 @ xp ) )
!= ( aDimensionOf0 @ xs ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[565]) ).
thf(594,plain,
( ( ~ ( aVector0 @ xp ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[565]) ).
thf(595,plain,
! [SV69: $i,SV58: $i] :
( ( ( aScalar0 @ SV58 )
= $false )
| ( ( ~ ( aScalar0 @ SV69 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ sz0z00 @ SV58 )
| ~ ( sdtlseqdt0 @ sz0z00 @ SV69 )
| ( sdtlseqdt0 @ sz0z00 @ ( sdtpldt0 @ SV58 @ SV69 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[566]) ).
thf(596,plain,
! [SV70: $i,SV59: $i] :
( ( ( aScalar0 @ SV59 )
= $false )
| ( ( ~ ( aScalar0 @ SV70 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ sz0z00 @ SV59 )
| ~ ( sdtlseqdt0 @ sz0z00 @ SV70 )
| ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ SV59 @ SV70 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[567]) ).
thf(597,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtpldt0 @ SX0 @ sz0z00 )
= SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtpldt0 @ sz0z00 @ SX0 )
= SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtasdt0 @ SX0 @ sz0z00 )
= sz0z00 ) ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtasdt0 @ sz0z00 @ SX0 )
= sz0z00 ) ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtpldt0 @ SX0 @ ( smndt0 @ SX0 ) )
= sz0z00 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[568]) ).
thf(598,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtpldt0 @ ( smndt0 @ SX0 ) @ SX0 )
= sz0z00 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[568]) ).
thf(599,plain,
! [SV75: $i] :
( ( ( ~ ( aScalar0 @ SV75 ) )
= $true )
| ( ( ( smndt0 @ ( smndt0 @ SV75 ) )
= SV75 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[569]) ).
thf(600,plain,
! [SV76: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV76 ) )
= $true )
| ( ( ( sdtlbdtrb0 @ xq @ SV76 )
= ( sdtlbdtrb0 @ xt @ SV76 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[570]) ).
thf(601,plain,
( ( ( ( szszuzczcdt0 @ ( aDimensionOf0 @ xq ) )
!= ( aDimensionOf0 @ xt ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[571]) ).
thf(602,plain,
( ( ~ ( aVector0 @ xq ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[571]) ).
thf(603,plain,
! [SV30: $i,SV1: $i] :
( ( ( ~ ( iLess0 @ ( aDimensionOf0 @ SV1 ) @ ( aDimensionOf0 @ xs ) ) )
= $true )
| ( ( sdtlseqdt0 @ ( sdtasdt0 @ ( sdtasasdt0 @ SV1 @ SV30 ) @ ( sdtasasdt0 @ SV1 @ SV30 ) ) @ ( sdtasdt0 @ ( sdtasasdt0 @ SV1 @ SV1 ) @ ( sdtasasdt0 @ SV30 @ SV30 ) ) )
= $true )
| ( ( ( aDimensionOf0 @ SV1 )
= ( aDimensionOf0 @ SV30 ) )
= $false )
| ( ( aVector0 @ SV1 )
= $false )
| ( ( aVector0 @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[573]) ).
thf(604,plain,
! [SV53: $i,SV48: $i,SV34: $i,SV9: $i] :
( ( ( aScalar0 @ SV9 )
= $false )
| ( ( ~ ( aScalar0 @ SV34 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV48 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV53 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV9 @ SV34 ) @ ( sdtpldt0 @ SV48 @ SV53 ) )
= ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ SV9 @ SV48 ) @ ( sdtasdt0 @ SV9 @ SV53 ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ SV34 @ SV48 ) @ ( sdtasdt0 @ SV34 @ SV53 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[575]) ).
thf(605,plain,
! [SV36: $i,SV12: $i] :
( ( ( sdtlseqdt0 @ SV12 @ SV36 )
= $false )
| ( ( ~ ( sdtlseqdt0 @ SV36 @ SV12 ) )
= $true )
| ( ( SV12 = SV36 )
= $true )
| ( ( aScalar0 @ SV12 )
= $false )
| ( ( aScalar0 @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[576]) ).
thf(606,plain,
! [SV37: $i,SV13: $i,SV50: $i] :
( ( ( aScalar0 @ SV50 )
= $false )
| ( ( aScalar0 @ SV13 )
= $false )
| ( ( aScalar0 @ SV37 )
= $false )
| ( ( ~ ( sdtlseqdt0 @ SV13 @ SV37 )
| ~ ( sdtlseqdt0 @ SV37 @ SV50 )
| ( sdtlseqdt0 @ SV13 @ SV50 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[577]) ).
thf(607,plain,
! [SV54: $i,SV51: $i,SV38: $i,SV14: $i] :
( ( ( aScalar0 @ SV14 )
= $false )
| ( ( ~ ( aScalar0 @ SV38 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV51 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV54 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV14 @ SV38 )
| ~ ( sdtlseqdt0 @ SV51 @ SV54 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SV14 @ SV51 ) @ ( sdtpldt0 @ SV38 @ SV54 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[578]) ).
thf(608,plain,
! [SV55: $i,SV52: $i,SV39: $i,SV15: $i] :
( ( ( aScalar0 @ SV15 )
= $false )
| ( ( ~ ( aScalar0 @ SV39 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV52 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV55 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV15 @ SV39 )
| ~ ( sdtlseqdt0 @ sz0z00 @ SV52 )
| ~ ( sdtlseqdt0 @ SV52 @ SV55 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV15 @ SV52 ) @ ( sdtasdt0 @ SV39 @ SV55 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[579]) ).
thf(609,plain,
! [SV41: $i,SV18: $i] :
( ( ( ~ ( sdtlseqdt0 @ sz0z00 @ SV18 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ sz0z00 @ SV41 ) )
= $true )
| ( ( ( ( sdtasdt0 @ SV18 @ SV18 )
!= ( sdtasdt0 @ SV41 @ SV41 ) ) )
= $true )
| ( ( SV18 = SV41 )
= $true )
| ( ( aScalar0 @ SV18 )
= $false )
| ( ( aScalar0 @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[580]) ).
thf(610,plain,
! [SV43: $i,SV22: $i] :
( ( ( ( aDimensionOf0 @ SV22 )
= ( aDimensionOf0 @ SV43 ) )
= $false )
| ( ( ( aDimensionOf0 @ SV43 )
= sz00 )
= $true )
| ( ( ( aDimensionOf0 @ ( sziznziztdt0 @ SV22 ) )
= ( aDimensionOf0 @ ( sziznziztdt0 @ SV43 ) ) )
= $true )
| ( ( aVector0 @ SV22 )
= $false )
| ( ( aVector0 @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[581]) ).
thf(611,plain,
! [SV45: $i,SV24: $i] :
( ( ( ( aDimensionOf0 @ SV24 )
= ( aDimensionOf0 @ SV45 ) )
= $false )
| ( ( ( ( aDimensionOf0 @ SV45 )
!= sz00 ) )
= $true )
| ( ( ( sdtasasdt0 @ SV24 @ SV45 )
= sz0z00 )
= $true )
| ( ( aVector0 @ SV24 )
= $false )
| ( ( aVector0 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[583]) ).
thf(612,plain,
! [SV46: $i,SV25: $i] :
( ( ( ( aDimensionOf0 @ SV25 )
= ( aDimensionOf0 @ SV46 ) )
= $false )
| ( ( ( aDimensionOf0 @ SV46 )
= sz00 )
= $true )
| ( ( ( sdtasasdt0 @ SV25 @ SV46 )
= ( sdtpldt0 @ ( sdtasasdt0 @ ( sziznziztdt0 @ SV25 ) @ ( sziznziztdt0 @ SV46 ) ) @ ( sdtasdt0 @ ( sdtlbdtrb0 @ SV25 @ ( aDimensionOf0 @ SV25 ) ) @ ( sdtlbdtrb0 @ SV46 @ ( aDimensionOf0 @ SV46 ) ) ) ) )
= $true )
| ( ( aVector0 @ SV25 )
= $false )
| ( ( aVector0 @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[584]) ).
thf(613,plain,
! [SV56: $i,SV64: $i] :
( ( ( aScalar0 @ SV64 )
= $false )
| ( ( aScalar0 @ SV56 )
= $false )
| ( ( ( sdtasdt0 @ SV56 @ ( smndt0 @ SV64 ) )
= ( smndt0 @ ( sdtasdt0 @ SV56 @ SV64 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[585]) ).
thf(614,plain,
! [SV57: $i,SV65: $i] :
( ( ( aScalar0 @ SV65 )
= $false )
| ( ( aScalar0 @ SV57 )
= $false )
| ( ( ( sdtasdt0 @ ( smndt0 @ SV57 ) @ SV65 )
= ( smndt0 @ ( sdtasdt0 @ SV57 @ SV65 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[586]) ).
thf(615,plain,
! [SV72: $i,SV66: $i,SV28: $i] :
( ( ( ~ ( aScalar0 @ SV28 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV66 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV72 ) )
= $true )
| ( ( ( sdtasdt0 @ SV28 @ ( sdtpldt0 @ SV66 @ SV72 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV28 @ SV66 ) @ ( sdtasdt0 @ SV28 @ SV72 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[587]) ).
thf(616,plain,
! [SV73: $i,SV67: $i,SV28: $i] :
( ( ( ~ ( aScalar0 @ SV28 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV67 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV73 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV28 @ SV67 ) @ SV73 )
= ( sdtpldt0 @ ( sdtasdt0 @ SV28 @ SV73 ) @ ( sdtasdt0 @ SV67 @ SV73 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[588]) ).
thf(617,plain,
! [SV29: $i] :
( ( ~ ! [SY98: $i,SY99: $i] :
( ~ ( aScalar0 @ SV29 )
| ~ ( aScalar0 @ SY98 )
| ~ ( aScalar0 @ SY99 )
| ( ( sdtpldt0 @ ( sdtpldt0 @ SV29 @ SY98 ) @ SY99 )
= ( sdtpldt0 @ SV29 @ ( sdtpldt0 @ SY98 @ SY99 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[589]) ).
thf(618,plain,
! [SV29: $i] :
( ( ~ ! [SY100: $i] :
( ~ ( aScalar0 @ SV29 )
| ~ ( aScalar0 @ SY100 )
| ! [SX2: $i] :
~ ( aScalar0 @ SX2 )
| ( ( sdtpldt0 @ SV29 @ SY100 )
= ( sdtpldt0 @ SY100 @ SV29 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[589]) ).
thf(619,plain,
! [SV78: $i,SV77: $i,SV29: $i] :
( ( ~ ( aScalar0 @ SV29 )
| ~ ( aScalar0 @ SV77 )
| ~ ( aScalar0 @ SV78 )
| ( ( sdtasdt0 @ ( sdtasdt0 @ SV29 @ SV77 ) @ SV78 )
= ( sdtasdt0 @ SV29 @ ( sdtasdt0 @ SV77 @ SV78 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[590]) ).
thf(620,plain,
! [SV68: $i,SV29: $i] :
( ( ( aScalar0 @ SV29 )
= $false )
| ( ( ~ ( aScalar0 @ SV68 ) )
= $true )
| ( ( ! [SX2: $i] :
~ ( aScalar0 @ SX2 ) )
= $true )
| ( ( ( sdtasdt0 @ SV29 @ SV68 )
= ( sdtasdt0 @ SV68 @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[591]) ).
thf(621,plain,
! [SV74: $i] :
( ( ( aNaturalNumber0 @ SV74 )
= $false )
| ( ( ( sdtlbdtrb0 @ xp @ SV74 )
= ( sdtlbdtrb0 @ xs @ SV74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[592]) ).
thf(622,plain,
( ( ( szszuzczcdt0 @ ( aDimensionOf0 @ xp ) )
= ( aDimensionOf0 @ xs ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[593]) ).
thf(623,plain,
( ( aVector0 @ xp )
= $true ),
inference(extcnf_not_neg,[status(thm)],[594]) ).
thf(624,plain,
! [SV58: $i,SV69: $i] :
( ( ( aScalar0 @ SV69 )
= $false )
| ( ( aScalar0 @ SV58 )
= $false )
| ( ( ~ ( sdtlseqdt0 @ sz0z00 @ SV58 )
| ~ ( sdtlseqdt0 @ sz0z00 @ SV69 )
| ( sdtlseqdt0 @ sz0z00 @ ( sdtpldt0 @ SV58 @ SV69 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[595]) ).
thf(625,plain,
! [SV59: $i,SV70: $i] :
( ( ( aScalar0 @ SV70 )
= $false )
| ( ( aScalar0 @ SV59 )
= $false )
| ( ( ~ ( sdtlseqdt0 @ sz0z00 @ SV59 )
| ~ ( sdtlseqdt0 @ sz0z00 @ SV70 )
| ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ SV59 @ SV70 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[596]) ).
thf(626,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtpldt0 @ SX0 @ sz0z00 )
= SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtpldt0 @ sz0z00 @ SX0 )
= SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtasdt0 @ SX0 @ sz0z00 )
= sz0z00 ) ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtasdt0 @ sz0z00 @ SX0 )
= sz0z00 ) ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtpldt0 @ SX0 @ ( smndt0 @ SX0 ) )
= sz0z00 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[597]) ).
thf(627,plain,
( ( ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtpldt0 @ ( smndt0 @ SX0 ) @ SX0 )
= sz0z00 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[598]) ).
thf(628,plain,
! [SV75: $i] :
( ( ( aScalar0 @ SV75 )
= $false )
| ( ( ( smndt0 @ ( smndt0 @ SV75 ) )
= SV75 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[599]) ).
thf(629,plain,
! [SV76: $i] :
( ( ( aNaturalNumber0 @ SV76 )
= $false )
| ( ( ( sdtlbdtrb0 @ xq @ SV76 )
= ( sdtlbdtrb0 @ xt @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[600]) ).
thf(630,plain,
( ( ( szszuzczcdt0 @ ( aDimensionOf0 @ xq ) )
= ( aDimensionOf0 @ xt ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[601]) ).
thf(631,plain,
( ( aVector0 @ xq )
= $true ),
inference(extcnf_not_neg,[status(thm)],[602]) ).
thf(632,plain,
! [SV30: $i,SV1: $i] :
( ( ( iLess0 @ ( aDimensionOf0 @ SV1 ) @ ( aDimensionOf0 @ xs ) )
= $false )
| ( ( sdtlseqdt0 @ ( sdtasdt0 @ ( sdtasasdt0 @ SV1 @ SV30 ) @ ( sdtasasdt0 @ SV1 @ SV30 ) ) @ ( sdtasdt0 @ ( sdtasasdt0 @ SV1 @ SV1 ) @ ( sdtasasdt0 @ SV30 @ SV30 ) ) )
= $true )
| ( ( ( aDimensionOf0 @ SV1 )
= ( aDimensionOf0 @ SV30 ) )
= $false )
| ( ( aVector0 @ SV1 )
= $false )
| ( ( aVector0 @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[603]) ).
thf(633,plain,
! [SV53: $i,SV48: $i,SV9: $i,SV34: $i] :
( ( ( aScalar0 @ SV34 )
= $false )
| ( ( aScalar0 @ SV9 )
= $false )
| ( ( ~ ( aScalar0 @ SV48 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV53 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV9 @ SV34 ) @ ( sdtpldt0 @ SV48 @ SV53 ) )
= ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ SV9 @ SV48 ) @ ( sdtasdt0 @ SV9 @ SV53 ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ SV34 @ SV48 ) @ ( sdtasdt0 @ SV34 @ SV53 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[604]) ).
thf(634,plain,
! [SV12: $i,SV36: $i] :
( ( ( sdtlseqdt0 @ SV36 @ SV12 )
= $false )
| ( ( sdtlseqdt0 @ SV12 @ SV36 )
= $false )
| ( ( SV12 = SV36 )
= $true )
| ( ( aScalar0 @ SV12 )
= $false )
| ( ( aScalar0 @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[605]) ).
thf(635,plain,
! [SV50: $i,SV37: $i,SV13: $i] :
( ( ( ~ ( sdtlseqdt0 @ SV13 @ SV37 )
| ~ ( sdtlseqdt0 @ SV37 @ SV50 ) )
= $true )
| ( ( sdtlseqdt0 @ SV13 @ SV50 )
= $true )
| ( ( aScalar0 @ SV37 )
= $false )
| ( ( aScalar0 @ SV13 )
= $false )
| ( ( aScalar0 @ SV50 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[606]) ).
thf(636,plain,
! [SV54: $i,SV51: $i,SV14: $i,SV38: $i] :
( ( ( aScalar0 @ SV38 )
= $false )
| ( ( aScalar0 @ SV14 )
= $false )
| ( ( ~ ( aScalar0 @ SV51 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV54 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV14 @ SV38 )
| ~ ( sdtlseqdt0 @ SV51 @ SV54 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SV14 @ SV51 ) @ ( sdtpldt0 @ SV38 @ SV54 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[607]) ).
thf(637,plain,
! [SV55: $i,SV52: $i,SV15: $i,SV39: $i] :
( ( ( aScalar0 @ SV39 )
= $false )
| ( ( aScalar0 @ SV15 )
= $false )
| ( ( ~ ( aScalar0 @ SV52 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV55 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV15 @ SV39 )
| ~ ( sdtlseqdt0 @ sz0z00 @ SV52 )
| ~ ( sdtlseqdt0 @ SV52 @ SV55 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV15 @ SV52 ) @ ( sdtasdt0 @ SV39 @ SV55 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[608]) ).
thf(638,plain,
! [SV41: $i,SV18: $i] :
( ( ( sdtlseqdt0 @ sz0z00 @ SV18 )
= $false )
| ( ( ~ ( sdtlseqdt0 @ sz0z00 @ SV41 ) )
= $true )
| ( ( ( ( sdtasdt0 @ SV18 @ SV18 )
!= ( sdtasdt0 @ SV41 @ SV41 ) ) )
= $true )
| ( ( SV18 = SV41 )
= $true )
| ( ( aScalar0 @ SV18 )
= $false )
| ( ( aScalar0 @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[609]) ).
thf(639,plain,
! [SV24: $i,SV45: $i] :
( ( ( ( aDimensionOf0 @ SV45 )
= sz00 )
= $false )
| ( ( ( aDimensionOf0 @ SV24 )
= ( aDimensionOf0 @ SV45 ) )
= $false )
| ( ( ( sdtasasdt0 @ SV24 @ SV45 )
= sz0z00 )
= $true )
| ( ( aVector0 @ SV24 )
= $false )
| ( ( aVector0 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[611]) ).
thf(640,plain,
! [SV72: $i,SV66: $i,SV28: $i] :
( ( ( aScalar0 @ SV28 )
= $false )
| ( ( ~ ( aScalar0 @ SV66 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV72 ) )
= $true )
| ( ( ( sdtasdt0 @ SV28 @ ( sdtpldt0 @ SV66 @ SV72 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV28 @ SV66 ) @ ( sdtasdt0 @ SV28 @ SV72 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[615]) ).
thf(641,plain,
! [SV73: $i,SV67: $i,SV28: $i] :
( ( ( aScalar0 @ SV28 )
= $false )
| ( ( ~ ( aScalar0 @ SV67 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV73 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV28 @ SV67 ) @ SV73 )
= ( sdtpldt0 @ ( sdtasdt0 @ SV28 @ SV73 ) @ ( sdtasdt0 @ SV67 @ SV73 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[616]) ).
thf(642,plain,
! [SV29: $i] :
( ( ! [SY98: $i,SY99: $i] :
( ~ ( aScalar0 @ SV29 )
| ~ ( aScalar0 @ SY98 )
| ~ ( aScalar0 @ SY99 )
| ( ( sdtpldt0 @ ( sdtpldt0 @ SV29 @ SY98 ) @ SY99 )
= ( sdtpldt0 @ SV29 @ ( sdtpldt0 @ SY98 @ SY99 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[617]) ).
thf(643,plain,
! [SV29: $i] :
( ( ! [SY100: $i] :
( ~ ( aScalar0 @ SV29 )
| ~ ( aScalar0 @ SY100 )
| ! [SX2: $i] :
~ ( aScalar0 @ SX2 )
| ( ( sdtpldt0 @ SV29 @ SY100 )
= ( sdtpldt0 @ SY100 @ SV29 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[618]) ).
thf(644,plain,
! [SV78: $i,SV77: $i,SV29: $i] :
( ( ( ~ ( aScalar0 @ SV29 )
| ~ ( aScalar0 @ SV77 )
| ~ ( aScalar0 @ SV78 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV29 @ SV77 ) @ SV78 )
= ( sdtasdt0 @ SV29 @ ( sdtasdt0 @ SV77 @ SV78 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[619]) ).
thf(645,plain,
! [SV29: $i,SV68: $i] :
( ( ( aScalar0 @ SV68 )
= $false )
| ( ( aScalar0 @ SV29 )
= $false )
| ( ( ! [SX2: $i] :
~ ( aScalar0 @ SX2 ) )
= $true )
| ( ( ( sdtasdt0 @ SV29 @ SV68 )
= ( sdtasdt0 @ SV68 @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[620]) ).
thf(646,plain,
! [SV69: $i,SV58: $i] :
( ( ( ~ ( sdtlseqdt0 @ sz0z00 @ SV58 )
| ~ ( sdtlseqdt0 @ sz0z00 @ SV69 ) )
= $true )
| ( ( sdtlseqdt0 @ sz0z00 @ ( sdtpldt0 @ SV58 @ SV69 ) )
= $true )
| ( ( aScalar0 @ SV58 )
= $false )
| ( ( aScalar0 @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[624]) ).
thf(647,plain,
! [SV70: $i,SV59: $i] :
( ( ( ~ ( sdtlseqdt0 @ sz0z00 @ SV59 )
| ~ ( sdtlseqdt0 @ sz0z00 @ SV70 ) )
= $true )
| ( ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ SV59 @ SV70 ) )
= $true )
| ( ( aScalar0 @ SV59 )
= $false )
| ( ( aScalar0 @ SV70 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[625]) ).
thf(648,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtpldt0 @ SX0 @ sz0z00 )
= SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtpldt0 @ sz0z00 @ SX0 )
= SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtasdt0 @ SX0 @ sz0z00 )
= sz0z00 ) ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtasdt0 @ sz0z00 @ SX0 )
= sz0z00 ) ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtpldt0 @ SX0 @ ( smndt0 @ SX0 ) )
= sz0z00 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[626]) ).
thf(649,plain,
! [SV79: $i] :
( ( ~ ( aScalar0 @ SV79 )
| ( ( sdtpldt0 @ ( smndt0 @ SV79 ) @ SV79 )
= sz0z00 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[627]) ).
thf(650,plain,
! [SV53: $i,SV34: $i,SV9: $i,SV48: $i] :
( ( ( aScalar0 @ SV48 )
= $false )
| ( ( aScalar0 @ SV9 )
= $false )
| ( ( aScalar0 @ SV34 )
= $false )
| ( ( ~ ( aScalar0 @ SV53 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV9 @ SV34 ) @ ( sdtpldt0 @ SV48 @ SV53 ) )
= ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ SV9 @ SV48 ) @ ( sdtasdt0 @ SV9 @ SV53 ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ SV34 @ SV48 ) @ ( sdtasdt0 @ SV34 @ SV53 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[633]) ).
thf(651,plain,
! [SV50: $i,SV37: $i,SV13: $i] :
( ( ( ~ ( sdtlseqdt0 @ SV13 @ SV37 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV37 @ SV50 ) )
= $true )
| ( ( sdtlseqdt0 @ SV13 @ SV50 )
= $true )
| ( ( aScalar0 @ SV37 )
= $false )
| ( ( aScalar0 @ SV13 )
= $false )
| ( ( aScalar0 @ SV50 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[635]) ).
thf(652,plain,
! [SV54: $i,SV38: $i,SV14: $i,SV51: $i] :
( ( ( aScalar0 @ SV51 )
= $false )
| ( ( aScalar0 @ SV14 )
= $false )
| ( ( aScalar0 @ SV38 )
= $false )
| ( ( ~ ( aScalar0 @ SV54 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV14 @ SV38 )
| ~ ( sdtlseqdt0 @ SV51 @ SV54 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SV14 @ SV51 ) @ ( sdtpldt0 @ SV38 @ SV54 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[636]) ).
thf(653,plain,
! [SV55: $i,SV39: $i,SV15: $i,SV52: $i] :
( ( ( aScalar0 @ SV52 )
= $false )
| ( ( aScalar0 @ SV15 )
= $false )
| ( ( aScalar0 @ SV39 )
= $false )
| ( ( ~ ( aScalar0 @ SV55 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV15 @ SV39 )
| ~ ( sdtlseqdt0 @ sz0z00 @ SV52 )
| ~ ( sdtlseqdt0 @ SV52 @ SV55 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV15 @ SV52 ) @ ( sdtasdt0 @ SV39 @ SV55 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[637]) ).
thf(654,plain,
! [SV18: $i,SV41: $i] :
( ( ( sdtlseqdt0 @ sz0z00 @ SV41 )
= $false )
| ( ( sdtlseqdt0 @ sz0z00 @ SV18 )
= $false )
| ( ( ( ( sdtasdt0 @ SV18 @ SV18 )
!= ( sdtasdt0 @ SV41 @ SV41 ) ) )
= $true )
| ( ( SV18 = SV41 )
= $true )
| ( ( aScalar0 @ SV18 )
= $false )
| ( ( aScalar0 @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[638]) ).
thf(655,plain,
! [SV72: $i,SV28: $i,SV66: $i] :
( ( ( aScalar0 @ SV66 )
= $false )
| ( ( aScalar0 @ SV28 )
= $false )
| ( ( ~ ( aScalar0 @ SV72 ) )
= $true )
| ( ( ( sdtasdt0 @ SV28 @ ( sdtpldt0 @ SV66 @ SV72 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV28 @ SV66 ) @ ( sdtasdt0 @ SV28 @ SV72 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[640]) ).
thf(656,plain,
! [SV73: $i,SV28: $i,SV67: $i] :
( ( ( aScalar0 @ SV67 )
= $false )
| ( ( aScalar0 @ SV28 )
= $false )
| ( ( ~ ( aScalar0 @ SV73 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV28 @ SV67 ) @ SV73 )
= ( sdtpldt0 @ ( sdtasdt0 @ SV28 @ SV73 ) @ ( sdtasdt0 @ SV67 @ SV73 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[641]) ).
thf(657,plain,
! [SV80: $i,SV29: $i] :
( ( ! [SY124: $i] :
( ~ ( aScalar0 @ SV29 )
| ~ ( aScalar0 @ SV80 )
| ~ ( aScalar0 @ SY124 )
| ( ( sdtpldt0 @ ( sdtpldt0 @ SV29 @ SV80 ) @ SY124 )
= ( sdtpldt0 @ SV29 @ ( sdtpldt0 @ SV80 @ SY124 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[642]) ).
thf(658,plain,
! [SV81: $i,SV29: $i] :
( ( ~ ( aScalar0 @ SV29 )
| ~ ( aScalar0 @ SV81 )
| ! [SX2: $i] :
~ ( aScalar0 @ SX2 )
| ( ( sdtpldt0 @ SV29 @ SV81 )
= ( sdtpldt0 @ SV81 @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[643]) ).
thf(659,plain,
! [SV78: $i,SV77: $i,SV29: $i] :
( ( ( ~ ( aScalar0 @ SV29 )
| ~ ( aScalar0 @ SV77 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV78 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV29 @ SV77 ) @ SV78 )
= ( sdtasdt0 @ SV29 @ ( sdtasdt0 @ SV77 @ SV78 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[644]) ).
thf(660,plain,
! [SV68: $i,SV29: $i,SV82: $i] :
( ( ( ~ ( aScalar0 @ SV82 ) )
= $true )
| ( ( aScalar0 @ SV29 )
= $false )
| ( ( aScalar0 @ SV68 )
= $false )
| ( ( ( sdtasdt0 @ SV29 @ SV68 )
= ( sdtasdt0 @ SV68 @ SV29 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[645]) ).
thf(661,plain,
! [SV69: $i,SV58: $i] :
( ( ( ~ ( sdtlseqdt0 @ sz0z00 @ SV58 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ sz0z00 @ SV69 ) )
= $true )
| ( ( sdtlseqdt0 @ sz0z00 @ ( sdtpldt0 @ SV58 @ SV69 ) )
= $true )
| ( ( aScalar0 @ SV58 )
= $false )
| ( ( aScalar0 @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[646]) ).
thf(662,plain,
! [SV70: $i,SV59: $i] :
( ( ( ~ ( sdtlseqdt0 @ sz0z00 @ SV59 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ sz0z00 @ SV70 ) )
= $true )
| ( ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ SV59 @ SV70 ) )
= $true )
| ( ( aScalar0 @ SV59 )
= $false )
| ( ( aScalar0 @ SV70 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[647]) ).
thf(663,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtpldt0 @ SX0 @ sz0z00 )
= SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtpldt0 @ sz0z00 @ SX0 )
= SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtasdt0 @ SX0 @ sz0z00 )
= sz0z00 ) ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtasdt0 @ sz0z00 @ SX0 )
= sz0z00 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[648]) ).
thf(664,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtpldt0 @ SX0 @ ( smndt0 @ SX0 ) )
= sz0z00 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[648]) ).
thf(665,plain,
! [SV79: $i] :
( ( ( ~ ( aScalar0 @ SV79 ) )
= $true )
| ( ( ( sdtpldt0 @ ( smndt0 @ SV79 ) @ SV79 )
= sz0z00 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[649]) ).
thf(666,plain,
! [SV48: $i,SV9: $i,SV34: $i,SV53: $i] :
( ( ( aScalar0 @ SV53 )
= $false )
| ( ( aScalar0 @ SV34 )
= $false )
| ( ( aScalar0 @ SV9 )
= $false )
| ( ( aScalar0 @ SV48 )
= $false )
| ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV9 @ SV34 ) @ ( sdtpldt0 @ SV48 @ SV53 ) )
= ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ SV9 @ SV48 ) @ ( sdtasdt0 @ SV9 @ SV53 ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ SV34 @ SV48 ) @ ( sdtasdt0 @ SV34 @ SV53 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[650]) ).
thf(667,plain,
! [SV50: $i,SV37: $i,SV13: $i] :
( ( ( sdtlseqdt0 @ SV13 @ SV37 )
= $false )
| ( ( ~ ( sdtlseqdt0 @ SV37 @ SV50 ) )
= $true )
| ( ( sdtlseqdt0 @ SV13 @ SV50 )
= $true )
| ( ( aScalar0 @ SV37 )
= $false )
| ( ( aScalar0 @ SV13 )
= $false )
| ( ( aScalar0 @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[651]) ).
thf(668,plain,
! [SV51: $i,SV14: $i,SV38: $i,SV54: $i] :
( ( ( aScalar0 @ SV54 )
= $false )
| ( ( aScalar0 @ SV38 )
= $false )
| ( ( aScalar0 @ SV14 )
= $false )
| ( ( aScalar0 @ SV51 )
= $false )
| ( ( ~ ( sdtlseqdt0 @ SV14 @ SV38 )
| ~ ( sdtlseqdt0 @ SV51 @ SV54 )
| ( sdtlseqdt0 @ ( sdtpldt0 @ SV14 @ SV51 ) @ ( sdtpldt0 @ SV38 @ SV54 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[652]) ).
thf(669,plain,
! [SV52: $i,SV15: $i,SV39: $i,SV55: $i] :
( ( ( aScalar0 @ SV55 )
= $false )
| ( ( aScalar0 @ SV39 )
= $false )
| ( ( aScalar0 @ SV15 )
= $false )
| ( ( aScalar0 @ SV52 )
= $false )
| ( ( ~ ( sdtlseqdt0 @ SV15 @ SV39 )
| ~ ( sdtlseqdt0 @ sz0z00 @ SV52 )
| ~ ( sdtlseqdt0 @ SV52 @ SV55 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ SV15 @ SV52 ) @ ( sdtasdt0 @ SV39 @ SV55 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[653]) ).
thf(670,plain,
! [SV41: $i,SV18: $i] :
( ( ( ( sdtasdt0 @ SV18 @ SV18 )
= ( sdtasdt0 @ SV41 @ SV41 ) )
= $false )
| ( ( sdtlseqdt0 @ sz0z00 @ SV18 )
= $false )
| ( ( sdtlseqdt0 @ sz0z00 @ SV41 )
= $false )
| ( ( SV18 = SV41 )
= $true )
| ( ( aScalar0 @ SV18 )
= $false )
| ( ( aScalar0 @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[654]) ).
thf(671,plain,
! [SV66: $i,SV28: $i,SV72: $i] :
( ( ( aScalar0 @ SV72 )
= $false )
| ( ( aScalar0 @ SV28 )
= $false )
| ( ( aScalar0 @ SV66 )
= $false )
| ( ( ( sdtasdt0 @ SV28 @ ( sdtpldt0 @ SV66 @ SV72 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ SV28 @ SV66 ) @ ( sdtasdt0 @ SV28 @ SV72 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[655]) ).
thf(672,plain,
! [SV67: $i,SV28: $i,SV73: $i] :
( ( ( aScalar0 @ SV73 )
= $false )
| ( ( aScalar0 @ SV28 )
= $false )
| ( ( aScalar0 @ SV67 )
= $false )
| ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV28 @ SV67 ) @ SV73 )
= ( sdtpldt0 @ ( sdtasdt0 @ SV28 @ SV73 ) @ ( sdtasdt0 @ SV67 @ SV73 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[656]) ).
thf(673,plain,
! [SV83: $i,SV80: $i,SV29: $i] :
( ( ~ ( aScalar0 @ SV29 )
| ~ ( aScalar0 @ SV80 )
| ~ ( aScalar0 @ SV83 )
| ( ( sdtpldt0 @ ( sdtpldt0 @ SV29 @ SV80 ) @ SV83 )
= ( sdtpldt0 @ SV29 @ ( sdtpldt0 @ SV80 @ SV83 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[657]) ).
thf(674,plain,
! [SV81: $i,SV29: $i] :
( ( ( ~ ( aScalar0 @ SV29 )
| ~ ( aScalar0 @ SV81 )
| ! [SX2: $i] :
~ ( aScalar0 @ SX2 ) )
= $true )
| ( ( ( sdtpldt0 @ SV29 @ SV81 )
= ( sdtpldt0 @ SV81 @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[658]) ).
thf(675,plain,
! [SV78: $i,SV77: $i,SV29: $i] :
( ( ( ~ ( aScalar0 @ SV29 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV77 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV78 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV29 @ SV77 ) @ SV78 )
= ( sdtasdt0 @ SV29 @ ( sdtasdt0 @ SV77 @ SV78 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[659]) ).
thf(676,plain,
! [SV68: $i,SV29: $i,SV82: $i] :
( ( ( aScalar0 @ SV82 )
= $false )
| ( ( aScalar0 @ SV29 )
= $false )
| ( ( aScalar0 @ SV68 )
= $false )
| ( ( ( sdtasdt0 @ SV29 @ SV68 )
= ( sdtasdt0 @ SV68 @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[660]) ).
thf(677,plain,
! [SV69: $i,SV58: $i] :
( ( ( sdtlseqdt0 @ sz0z00 @ SV58 )
= $false )
| ( ( ~ ( sdtlseqdt0 @ sz0z00 @ SV69 ) )
= $true )
| ( ( sdtlseqdt0 @ sz0z00 @ ( sdtpldt0 @ SV58 @ SV69 ) )
= $true )
| ( ( aScalar0 @ SV58 )
= $false )
| ( ( aScalar0 @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[661]) ).
thf(678,plain,
! [SV70: $i,SV59: $i] :
( ( ( sdtlseqdt0 @ sz0z00 @ SV59 )
= $false )
| ( ( ~ ( sdtlseqdt0 @ sz0z00 @ SV70 ) )
= $true )
| ( ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ SV59 @ SV70 ) )
= $true )
| ( ( aScalar0 @ SV59 )
= $false )
| ( ( aScalar0 @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[662]) ).
thf(679,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtpldt0 @ SX0 @ sz0z00 )
= SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtpldt0 @ sz0z00 @ SX0 )
= SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtasdt0 @ SX0 @ sz0z00 )
= sz0z00 ) ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtasdt0 @ sz0z00 @ SX0 )
= sz0z00 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[663]) ).
thf(680,plain,
( ( ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtpldt0 @ SX0 @ ( smndt0 @ SX0 ) )
= sz0z00 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[664]) ).
thf(681,plain,
! [SV79: $i] :
( ( ( aScalar0 @ SV79 )
= $false )
| ( ( ( sdtpldt0 @ ( smndt0 @ SV79 ) @ SV79 )
= sz0z00 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[665]) ).
thf(682,plain,
! [SV13: $i,SV50: $i,SV37: $i] :
( ( ( sdtlseqdt0 @ SV37 @ SV50 )
= $false )
| ( ( sdtlseqdt0 @ SV13 @ SV37 )
= $false )
| ( ( sdtlseqdt0 @ SV13 @ SV50 )
= $true )
| ( ( aScalar0 @ SV37 )
= $false )
| ( ( aScalar0 @ SV13 )
= $false )
| ( ( aScalar0 @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[667]) ).
thf(683,plain,
! [SV54: $i,SV51: $i,SV38: $i,SV14: $i] :
( ( ( ~ ( sdtlseqdt0 @ SV14 @ SV38 )
| ~ ( sdtlseqdt0 @ SV51 @ SV54 ) )
= $true )
| ( ( sdtlseqdt0 @ ( sdtpldt0 @ SV14 @ SV51 ) @ ( sdtpldt0 @ SV38 @ SV54 ) )
= $true )
| ( ( aScalar0 @ SV51 )
= $false )
| ( ( aScalar0 @ SV14 )
= $false )
| ( ( aScalar0 @ SV38 )
= $false )
| ( ( aScalar0 @ SV54 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[668]) ).
thf(684,plain,
! [SV55: $i,SV52: $i,SV39: $i,SV15: $i] :
( ( ( ~ ( sdtlseqdt0 @ SV15 @ SV39 )
| ~ ( sdtlseqdt0 @ sz0z00 @ SV52 )
| ~ ( sdtlseqdt0 @ SV52 @ SV55 ) )
= $true )
| ( ( sdtlseqdt0 @ ( sdtasdt0 @ SV15 @ SV52 ) @ ( sdtasdt0 @ SV39 @ SV55 ) )
= $true )
| ( ( aScalar0 @ SV52 )
= $false )
| ( ( aScalar0 @ SV15 )
= $false )
| ( ( aScalar0 @ SV39 )
= $false )
| ( ( aScalar0 @ SV55 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[669]) ).
thf(685,plain,
! [SV83: $i,SV80: $i,SV29: $i] :
( ( ( ~ ( aScalar0 @ SV29 )
| ~ ( aScalar0 @ SV80 )
| ~ ( aScalar0 @ SV83 ) )
= $true )
| ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV29 @ SV80 ) @ SV83 )
= ( sdtpldt0 @ SV29 @ ( sdtpldt0 @ SV80 @ SV83 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[673]) ).
thf(686,plain,
! [SV81: $i,SV29: $i] :
( ( ( ~ ( aScalar0 @ SV29 )
| ~ ( aScalar0 @ SV81 ) )
= $true )
| ( ( ! [SX2: $i] :
~ ( aScalar0 @ SX2 ) )
= $true )
| ( ( ( sdtpldt0 @ SV29 @ SV81 )
= ( sdtpldt0 @ SV81 @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[674]) ).
thf(687,plain,
! [SV78: $i,SV77: $i,SV29: $i] :
( ( ( aScalar0 @ SV29 )
= $false )
| ( ( ~ ( aScalar0 @ SV77 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV78 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV29 @ SV77 ) @ SV78 )
= ( sdtasdt0 @ SV29 @ ( sdtasdt0 @ SV77 @ SV78 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[675]) ).
thf(688,plain,
! [SV58: $i,SV69: $i] :
( ( ( sdtlseqdt0 @ sz0z00 @ SV69 )
= $false )
| ( ( sdtlseqdt0 @ sz0z00 @ SV58 )
= $false )
| ( ( sdtlseqdt0 @ sz0z00 @ ( sdtpldt0 @ SV58 @ SV69 ) )
= $true )
| ( ( aScalar0 @ SV58 )
= $false )
| ( ( aScalar0 @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[677]) ).
thf(689,plain,
! [SV59: $i,SV70: $i] :
( ( ( sdtlseqdt0 @ sz0z00 @ SV70 )
= $false )
| ( ( sdtlseqdt0 @ sz0z00 @ SV59 )
= $false )
| ( ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ SV59 @ SV70 ) )
= $true )
| ( ( aScalar0 @ SV59 )
= $false )
| ( ( aScalar0 @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[678]) ).
thf(690,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtpldt0 @ SX0 @ sz0z00 )
= SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtpldt0 @ sz0z00 @ SX0 )
= SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtasdt0 @ SX0 @ sz0z00 )
= sz0z00 ) ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtasdt0 @ sz0z00 @ SX0 )
= sz0z00 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[679]) ).
thf(691,plain,
! [SV84: $i] :
( ( ~ ( aScalar0 @ SV84 )
| ( ( sdtpldt0 @ SV84 @ ( smndt0 @ SV84 ) )
= sz0z00 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[680]) ).
thf(692,plain,
! [SV54: $i,SV51: $i,SV38: $i,SV14: $i] :
( ( ( ~ ( sdtlseqdt0 @ SV14 @ SV38 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV51 @ SV54 ) )
= $true )
| ( ( sdtlseqdt0 @ ( sdtpldt0 @ SV14 @ SV51 ) @ ( sdtpldt0 @ SV38 @ SV54 ) )
= $true )
| ( ( aScalar0 @ SV51 )
= $false )
| ( ( aScalar0 @ SV14 )
= $false )
| ( ( aScalar0 @ SV38 )
= $false )
| ( ( aScalar0 @ SV54 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[683]) ).
thf(693,plain,
! [SV55: $i,SV52: $i,SV39: $i,SV15: $i] :
( ( ( ~ ( sdtlseqdt0 @ SV15 @ SV39 )
| ~ ( sdtlseqdt0 @ sz0z00 @ SV52 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV52 @ SV55 ) )
= $true )
| ( ( sdtlseqdt0 @ ( sdtasdt0 @ SV15 @ SV52 ) @ ( sdtasdt0 @ SV39 @ SV55 ) )
= $true )
| ( ( aScalar0 @ SV52 )
= $false )
| ( ( aScalar0 @ SV15 )
= $false )
| ( ( aScalar0 @ SV39 )
= $false )
| ( ( aScalar0 @ SV55 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[684]) ).
thf(694,plain,
! [SV83: $i,SV80: $i,SV29: $i] :
( ( ( ~ ( aScalar0 @ SV29 )
| ~ ( aScalar0 @ SV80 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV83 ) )
= $true )
| ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV29 @ SV80 ) @ SV83 )
= ( sdtpldt0 @ SV29 @ ( sdtpldt0 @ SV80 @ SV83 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[685]) ).
thf(695,plain,
! [SV81: $i,SV29: $i] :
( ( ( ~ ( aScalar0 @ SV29 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV81 ) )
= $true )
| ( ( ! [SX2: $i] :
~ ( aScalar0 @ SX2 ) )
= $true )
| ( ( ( sdtpldt0 @ SV29 @ SV81 )
= ( sdtpldt0 @ SV81 @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[686]) ).
thf(696,plain,
! [SV78: $i,SV29: $i,SV77: $i] :
( ( ( aScalar0 @ SV77 )
= $false )
| ( ( aScalar0 @ SV29 )
= $false )
| ( ( ~ ( aScalar0 @ SV78 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV29 @ SV77 ) @ SV78 )
= ( sdtasdt0 @ SV29 @ ( sdtasdt0 @ SV77 @ SV78 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[687]) ).
thf(697,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtpldt0 @ SX0 @ sz0z00 )
= SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtpldt0 @ sz0z00 @ SX0 )
= SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtasdt0 @ SX0 @ sz0z00 )
= sz0z00 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[690]) ).
thf(698,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtasdt0 @ sz0z00 @ SX0 )
= sz0z00 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[690]) ).
thf(699,plain,
! [SV84: $i] :
( ( ( ~ ( aScalar0 @ SV84 ) )
= $true )
| ( ( ( sdtpldt0 @ SV84 @ ( smndt0 @ SV84 ) )
= sz0z00 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[691]) ).
thf(700,plain,
! [SV54: $i,SV51: $i,SV38: $i,SV14: $i] :
( ( ( sdtlseqdt0 @ SV14 @ SV38 )
= $false )
| ( ( ~ ( sdtlseqdt0 @ SV51 @ SV54 ) )
= $true )
| ( ( sdtlseqdt0 @ ( sdtpldt0 @ SV14 @ SV51 ) @ ( sdtpldt0 @ SV38 @ SV54 ) )
= $true )
| ( ( aScalar0 @ SV51 )
= $false )
| ( ( aScalar0 @ SV14 )
= $false )
| ( ( aScalar0 @ SV38 )
= $false )
| ( ( aScalar0 @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[692]) ).
thf(701,plain,
! [SV55: $i,SV52: $i,SV39: $i,SV15: $i] :
( ( ( ~ ( sdtlseqdt0 @ SV15 @ SV39 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ sz0z00 @ SV52 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV52 @ SV55 ) )
= $true )
| ( ( sdtlseqdt0 @ ( sdtasdt0 @ SV15 @ SV52 ) @ ( sdtasdt0 @ SV39 @ SV55 ) )
= $true )
| ( ( aScalar0 @ SV52 )
= $false )
| ( ( aScalar0 @ SV15 )
= $false )
| ( ( aScalar0 @ SV39 )
= $false )
| ( ( aScalar0 @ SV55 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[693]) ).
thf(702,plain,
! [SV83: $i,SV80: $i,SV29: $i] :
( ( ( ~ ( aScalar0 @ SV29 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV80 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV83 ) )
= $true )
| ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV29 @ SV80 ) @ SV83 )
= ( sdtpldt0 @ SV29 @ ( sdtpldt0 @ SV80 @ SV83 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[694]) ).
thf(703,plain,
! [SV81: $i,SV29: $i] :
( ( ( aScalar0 @ SV29 )
= $false )
| ( ( ~ ( aScalar0 @ SV81 ) )
= $true )
| ( ( ! [SX2: $i] :
~ ( aScalar0 @ SX2 ) )
= $true )
| ( ( ( sdtpldt0 @ SV29 @ SV81 )
= ( sdtpldt0 @ SV81 @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[695]) ).
thf(704,plain,
! [SV77: $i,SV29: $i,SV78: $i] :
( ( ( aScalar0 @ SV78 )
= $false )
| ( ( aScalar0 @ SV29 )
= $false )
| ( ( aScalar0 @ SV77 )
= $false )
| ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV29 @ SV77 ) @ SV78 )
= ( sdtasdt0 @ SV29 @ ( sdtasdt0 @ SV77 @ SV78 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[696]) ).
thf(705,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtpldt0 @ SX0 @ sz0z00 )
= SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtpldt0 @ sz0z00 @ SX0 )
= SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtasdt0 @ SX0 @ sz0z00 )
= sz0z00 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[697]) ).
thf(706,plain,
( ( ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtasdt0 @ sz0z00 @ SX0 )
= sz0z00 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[698]) ).
thf(707,plain,
! [SV84: $i] :
( ( ( aScalar0 @ SV84 )
= $false )
| ( ( ( sdtpldt0 @ SV84 @ ( smndt0 @ SV84 ) )
= sz0z00 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[699]) ).
thf(708,plain,
! [SV38: $i,SV14: $i,SV54: $i,SV51: $i] :
( ( ( sdtlseqdt0 @ SV51 @ SV54 )
= $false )
| ( ( sdtlseqdt0 @ SV14 @ SV38 )
= $false )
| ( ( sdtlseqdt0 @ ( sdtpldt0 @ SV14 @ SV51 ) @ ( sdtpldt0 @ SV38 @ SV54 ) )
= $true )
| ( ( aScalar0 @ SV51 )
= $false )
| ( ( aScalar0 @ SV14 )
= $false )
| ( ( aScalar0 @ SV38 )
= $false )
| ( ( aScalar0 @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[700]) ).
thf(709,plain,
! [SV55: $i,SV52: $i,SV39: $i,SV15: $i] :
( ( ( sdtlseqdt0 @ SV15 @ SV39 )
= $false )
| ( ( ~ ( sdtlseqdt0 @ sz0z00 @ SV52 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV52 @ SV55 ) )
= $true )
| ( ( sdtlseqdt0 @ ( sdtasdt0 @ SV15 @ SV52 ) @ ( sdtasdt0 @ SV39 @ SV55 ) )
= $true )
| ( ( aScalar0 @ SV52 )
= $false )
| ( ( aScalar0 @ SV15 )
= $false )
| ( ( aScalar0 @ SV39 )
= $false )
| ( ( aScalar0 @ SV55 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[701]) ).
thf(710,plain,
! [SV83: $i,SV80: $i,SV29: $i] :
( ( ( aScalar0 @ SV29 )
= $false )
| ( ( ~ ( aScalar0 @ SV80 ) )
= $true )
| ( ( ~ ( aScalar0 @ SV83 ) )
= $true )
| ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV29 @ SV80 ) @ SV83 )
= ( sdtpldt0 @ SV29 @ ( sdtpldt0 @ SV80 @ SV83 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[702]) ).
thf(711,plain,
! [SV29: $i,SV81: $i] :
( ( ( aScalar0 @ SV81 )
= $false )
| ( ( aScalar0 @ SV29 )
= $false )
| ( ( ! [SX2: $i] :
~ ( aScalar0 @ SX2 ) )
= $true )
| ( ( ( sdtpldt0 @ SV29 @ SV81 )
= ( sdtpldt0 @ SV81 @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[703]) ).
thf(712,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtpldt0 @ SX0 @ sz0z00 )
= SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtpldt0 @ sz0z00 @ SX0 )
= SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtasdt0 @ SX0 @ sz0z00 )
= sz0z00 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[705]) ).
thf(713,plain,
! [SV85: $i] :
( ( ~ ( aScalar0 @ SV85 )
| ( ( sdtasdt0 @ sz0z00 @ SV85 )
= sz0z00 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[706]) ).
thf(714,plain,
! [SV55: $i,SV39: $i,SV15: $i,SV52: $i] :
( ( ( sdtlseqdt0 @ sz0z00 @ SV52 )
= $false )
| ( ( sdtlseqdt0 @ SV15 @ SV39 )
= $false )
| ( ( ~ ( sdtlseqdt0 @ SV52 @ SV55 ) )
= $true )
| ( ( sdtlseqdt0 @ ( sdtasdt0 @ SV15 @ SV52 ) @ ( sdtasdt0 @ SV39 @ SV55 ) )
= $true )
| ( ( aScalar0 @ SV52 )
= $false )
| ( ( aScalar0 @ SV15 )
= $false )
| ( ( aScalar0 @ SV39 )
= $false )
| ( ( aScalar0 @ SV55 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[709]) ).
thf(715,plain,
! [SV83: $i,SV29: $i,SV80: $i] :
( ( ( aScalar0 @ SV80 )
= $false )
| ( ( aScalar0 @ SV29 )
= $false )
| ( ( ~ ( aScalar0 @ SV83 ) )
= $true )
| ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV29 @ SV80 ) @ SV83 )
= ( sdtpldt0 @ SV29 @ ( sdtpldt0 @ SV80 @ SV83 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[710]) ).
thf(716,plain,
! [SV81: $i,SV29: $i,SV86: $i] :
( ( ( ~ ( aScalar0 @ SV86 ) )
= $true )
| ( ( aScalar0 @ SV29 )
= $false )
| ( ( aScalar0 @ SV81 )
= $false )
| ( ( ( sdtpldt0 @ SV29 @ SV81 )
= ( sdtpldt0 @ SV81 @ SV29 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[711]) ).
thf(717,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtpldt0 @ SX0 @ sz0z00 )
= SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtpldt0 @ sz0z00 @ SX0 )
= SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[712]) ).
thf(718,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtasdt0 @ SX0 @ sz0z00 )
= sz0z00 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[712]) ).
thf(719,plain,
! [SV85: $i] :
( ( ( ~ ( aScalar0 @ SV85 ) )
= $true )
| ( ( ( sdtasdt0 @ sz0z00 @ SV85 )
= sz0z00 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[713]) ).
thf(720,plain,
! [SV39: $i,SV15: $i,SV55: $i,SV52: $i] :
( ( ( sdtlseqdt0 @ SV52 @ SV55 )
= $false )
| ( ( sdtlseqdt0 @ SV15 @ SV39 )
= $false )
| ( ( sdtlseqdt0 @ sz0z00 @ SV52 )
= $false )
| ( ( sdtlseqdt0 @ ( sdtasdt0 @ SV15 @ SV52 ) @ ( sdtasdt0 @ SV39 @ SV55 ) )
= $true )
| ( ( aScalar0 @ SV52 )
= $false )
| ( ( aScalar0 @ SV15 )
= $false )
| ( ( aScalar0 @ SV39 )
= $false )
| ( ( aScalar0 @ SV55 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[714]) ).
thf(721,plain,
! [SV80: $i,SV29: $i,SV83: $i] :
( ( ( aScalar0 @ SV83 )
= $false )
| ( ( aScalar0 @ SV29 )
= $false )
| ( ( aScalar0 @ SV80 )
= $false )
| ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV29 @ SV80 ) @ SV83 )
= ( sdtpldt0 @ SV29 @ ( sdtpldt0 @ SV80 @ SV83 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[715]) ).
thf(722,plain,
! [SV81: $i,SV29: $i,SV86: $i] :
( ( ( aScalar0 @ SV86 )
= $false )
| ( ( aScalar0 @ SV29 )
= $false )
| ( ( aScalar0 @ SV81 )
= $false )
| ( ( ( sdtpldt0 @ SV29 @ SV81 )
= ( sdtpldt0 @ SV81 @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[716]) ).
thf(723,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtpldt0 @ SX0 @ sz0z00 )
= SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtpldt0 @ sz0z00 @ SX0 )
= SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[717]) ).
thf(724,plain,
( ( ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtasdt0 @ SX0 @ sz0z00 )
= sz0z00 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[718]) ).
thf(725,plain,
! [SV85: $i] :
( ( ( aScalar0 @ SV85 )
= $false )
| ( ( ( sdtasdt0 @ sz0z00 @ SV85 )
= sz0z00 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[719]) ).
thf(726,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtpldt0 @ SX0 @ sz0z00 )
= SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtpldt0 @ sz0z00 @ SX0 )
= SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[723]) ).
thf(727,plain,
! [SV87: $i] :
( ( ~ ( aScalar0 @ SV87 )
| ( ( sdtasdt0 @ SV87 @ sz0z00 )
= sz0z00 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[724]) ).
thf(728,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtpldt0 @ SX0 @ sz0z00 )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[726]) ).
thf(729,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtpldt0 @ sz0z00 @ SX0 )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[726]) ).
thf(730,plain,
! [SV87: $i] :
( ( ( ~ ( aScalar0 @ SV87 ) )
= $true )
| ( ( ( sdtasdt0 @ SV87 @ sz0z00 )
= sz0z00 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[727]) ).
thf(731,plain,
( ( ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtpldt0 @ SX0 @ sz0z00 )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[728]) ).
thf(732,plain,
( ( ! [SX0: $i] :
( ~ ( aScalar0 @ SX0 )
| ( ( sdtpldt0 @ sz0z00 @ SX0 )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[729]) ).
thf(733,plain,
! [SV87: $i] :
( ( ( aScalar0 @ SV87 )
= $false )
| ( ( ( sdtasdt0 @ SV87 @ sz0z00 )
= sz0z00 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[730]) ).
thf(734,plain,
! [SV88: $i] :
( ( ~ ( aScalar0 @ SV88 )
| ( ( sdtpldt0 @ SV88 @ sz0z00 )
= SV88 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[731]) ).
thf(735,plain,
! [SV89: $i] :
( ( ~ ( aScalar0 @ SV89 )
| ( ( sdtpldt0 @ sz0z00 @ SV89 )
= SV89 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[732]) ).
thf(736,plain,
! [SV88: $i] :
( ( ( ~ ( aScalar0 @ SV88 ) )
= $true )
| ( ( ( sdtpldt0 @ SV88 @ sz0z00 )
= SV88 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[734]) ).
thf(737,plain,
! [SV89: $i] :
( ( ( ~ ( aScalar0 @ SV89 ) )
= $true )
| ( ( ( sdtpldt0 @ sz0z00 @ SV89 )
= SV89 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[735]) ).
thf(738,plain,
! [SV88: $i] :
( ( ( aScalar0 @ SV88 )
= $false )
| ( ( ( sdtpldt0 @ SV88 @ sz0z00 )
= SV88 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[736]) ).
thf(739,plain,
! [SV89: $i] :
( ( ( aScalar0 @ SV89 )
= $false )
| ( ( ( sdtpldt0 @ sz0z00 @ SV89 )
= SV89 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[737]) ).
thf(740,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[169,739,738,733,725,722,721,720,708,707,704,689,688,682,681,676,672,671,670,666,639,634,632,631,630,629,628,623,622,621,614,613,612,610,582,574,572,556,555,549,541,537,517,510,509,507,506,505,431,430,427,426,425,424,423,422,421,415,414,413,411,410,409,408,407,406,405,404,396,395,394,393,392,391,390,389,388,382,380,374,370,367,275,267,252,248,247,195,188,186,185]) ).
thf(741,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[740]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : RNG059+2 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33 % Computer : n028.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon May 30 12:58:04 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.38
% 0.19/0.38 No.of.Axioms: 56
% 0.19/0.38
% 0.19/0.38 Length.of.Defs: 0
% 0.19/0.38
% 0.19/0.38 Contains.Choice.Funs: false
% 0.19/0.41 .
% 0.19/0.42 (rf:0,axioms:56,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:58,loop_count:0,foatp_calls:0,translation:fof_full).....................................
% 2.42/2.68
% 2.42/2.68 ********************************
% 2.42/2.68 * All subproblems solved! *
% 2.42/2.68 ********************************
% 2.42/2.68 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:56,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:740,loop_count:0,foatp_calls:1,translation:fof_full)
% 2.73/2.89
% 2.73/2.89 %**** Beginning of derivation protocol ****
% 2.73/2.89 % SZS output start CNFRefutation
% See solution above
% 2.73/2.90
% 2.73/2.90 %**** End of derivation protocol ****
% 2.73/2.90 %**** no. of clauses in derivation: 741 ****
% 2.73/2.90 %**** clause counter: 740 ****
% 2.73/2.90
% 2.73/2.90 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:56,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:740,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------