%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM484+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:33:57 AM UTC 2026
% Result : Theorem 0.71s 0.31s
% Output : CNFRefutation 0.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 21
% Syntax : Number of formulae : 295 ( 112 unt; 0 typ; 0 def)
% Number of atoms : 2631 ( 824 equ; 0 cnn)
% Maximal formula atoms : 6 ( 8 avg)
% Number of connectives : 4253 (1089 ~; 836 |; 91 &;2168 @)
% ( 0 <=>; 69 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 5 con; 0-2 aty)
% Number of variables : 671 ( 0 ^; 666 !; 5 ?; 671 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_aNaturalNumber0,type,
aNaturalNumber0: $i > $o ).
thf(tp_doDivides0,type,
doDivides0: $i > $i > $o ).
thf(tp_iLess0,type,
iLess0: $i > $i > $o ).
thf(tp_isPrime0,type,
isPrime0: $i > $o ).
thf(tp_sdtasdt0,type,
sdtasdt0: $i > $i > $i ).
thf(tp_sdtlseqdt0,type,
sdtlseqdt0: $i > $i > $o ).
thf(tp_sdtmndt0,type,
sdtmndt0: $i > $i > $i ).
thf(tp_sdtpldt0,type,
sdtpldt0: $i > $i > $i ).
thf(tp_sdtsldt0,type,
sdtsldt0: $i > $i > $i ).
thf(tp_sz00,type,
sz00: $i ).
thf(tp_sz10,type,
sz10: $i ).
thf(tp_xk,type,
xk: $i ).
thf(3,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 )
& ( aNaturalNumber0 @ W2 ) )
=> ( ( ( doDivides0 @ W0 @ W1 )
& ( doDivides0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) ) )
=> ( doDivides0 @ W0 @ W2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivMin) ).
thf(4,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 )
& ( aNaturalNumber0 @ W2 ) )
=> ( ( ( doDivides0 @ W0 @ W1 )
& ( doDivides0 @ W0 @ W2 ) )
=> ( doDivides0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivSum) ).
thf(5,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 )
& ( aNaturalNumber0 @ W2 ) )
=> ( ( ( doDivides0 @ W0 @ W1 )
& ( doDivides0 @ W1 @ W2 ) )
=> ( doDivides0 @ W0 @ W2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivTrans) ).
thf(7,axiom,
! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( iLess0 @ W0 @ W1 )
=> $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIH) ).
thf(12,axiom,
! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( sdtlseqdt0 @ W0 @ W1 )
| ( ( W1 != W0 )
& ( sdtlseqdt0 @ W1 @ W0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETotal) ).
thf(13,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 )
& ( aNaturalNumber0 @ W2 ) )
=> ( ( ( sdtlseqdt0 @ W0 @ W1 )
& ( sdtlseqdt0 @ W1 @ W2 ) )
=> ( sdtlseqdt0 @ W0 @ W2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETran) ).
thf(14,axiom,
! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( ( sdtlseqdt0 @ W0 @ W1 )
& ( sdtlseqdt0 @ W1 @ W0 ) )
=> ( W0 = W1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLEAsym) ).
thf(15,axiom,
! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> ( sdtlseqdt0 @ W0 @ W0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLERefl) ).
thf(19,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 )
& ( aNaturalNumber0 @ W2 ) )
=> ( ( ( ( sdtpldt0 @ W0 @ W1 )
= ( sdtpldt0 @ W0 @ W2 ) )
| ( ( sdtpldt0 @ W1 @ W0 )
= ( sdtpldt0 @ W2 @ W0 ) ) )
=> ( W1 = W2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddCanc) ).
thf(23,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 )
& ( aNaturalNumber0 @ W2 ) )
=> ( ( sdtasdt0 @ ( sdtasdt0 @ W0 @ W1 ) @ W2 )
= ( sdtasdt0 @ W0 @ ( sdtasdt0 @ W1 @ W2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulAsso) ).
thf(24,axiom,
! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( sdtasdt0 @ W0 @ W1 )
= ( sdtasdt0 @ W1 @ W0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
thf(26,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 )
& ( aNaturalNumber0 @ W2 ) )
=> ( ( sdtpldt0 @ ( sdtpldt0 @ W0 @ W1 ) @ W2 )
= ( sdtpldt0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddAsso) ).
thf(27,axiom,
! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( sdtpldt0 @ W0 @ W1 )
= ( sdtpldt0 @ W1 @ W0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
thf(28,axiom,
! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( aNaturalNumber0 @ ( sdtasdt0 @ W0 @ W1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
thf(29,axiom,
! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( aNaturalNumber0 @ ( sdtpldt0 @ W0 @ W1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
thf(31,axiom,
aNaturalNumber0 @ sz00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
thf(32,axiom,
! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNatSort) ).
thf(33,axiom,
~ ~ ( isPrime0 @ xk ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1737) ).
thf(34,axiom,
~ ( isPrime0 @ xk ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1725) ).
thf(37,axiom,
aNaturalNumber0 @ xk,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1716) ).
thf(38,conjecture,
? [W0: $i] :
( ( aNaturalNumber0 @ W0 )
& ( doDivides0 @ W0 @ xk )
& ( isPrime0 @ W0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
thf(39,negated_conjecture,
( ( ? [W0: $i] :
( ( aNaturalNumber0 @ W0 )
& ( doDivides0 @ W0 @ xk )
& ( isPrime0 @ W0 ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[38]) ).
thf(40,plain,
( ( ? [W0: $i] :
( ( aNaturalNumber0 @ W0 )
& ( doDivides0 @ W0 @ xk )
& ( isPrime0 @ W0 ) ) )
= $false ),
inference(unfold_def,[status(thm)],[39]) ).
thf(41,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 )
& ( aNaturalNumber0 @ W2 ) )
=> ( ( ( doDivides0 @ W0 @ W1 )
& ( doDivides0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) ) )
=> ( doDivides0 @ W0 @ W2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(42,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 )
& ( aNaturalNumber0 @ W2 ) )
=> ( ( ( doDivides0 @ W0 @ W1 )
& ( doDivides0 @ W0 @ W2 ) )
=> ( doDivides0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(43,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 )
& ( aNaturalNumber0 @ W2 ) )
=> ( ( ( doDivides0 @ W0 @ W1 )
& ( doDivides0 @ W1 @ W2 ) )
=> ( doDivides0 @ W0 @ W2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(44,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( iLess0 @ W0 @ W1 )
=> $true ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(45,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( sdtlseqdt0 @ W0 @ W1 )
| ( ( W1 != W0 )
& ( sdtlseqdt0 @ W1 @ W0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(46,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 )
& ( aNaturalNumber0 @ W2 ) )
=> ( ( ( sdtlseqdt0 @ W0 @ W1 )
& ( sdtlseqdt0 @ W1 @ W2 ) )
=> ( sdtlseqdt0 @ W0 @ W2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(47,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( ( sdtlseqdt0 @ W0 @ W1 )
& ( sdtlseqdt0 @ W1 @ W0 ) )
=> ( W0 = W1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(48,plain,
( ( ! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> ( sdtlseqdt0 @ W0 @ W0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(49,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 )
& ( aNaturalNumber0 @ W2 ) )
=> ( ( ( ( sdtpldt0 @ W0 @ W1 )
= ( sdtpldt0 @ W0 @ W2 ) )
| ( ( sdtpldt0 @ W1 @ W0 )
= ( sdtpldt0 @ W2 @ W0 ) ) )
=> ( W1 = W2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(50,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 )
& ( aNaturalNumber0 @ W2 ) )
=> ( ( sdtasdt0 @ ( sdtasdt0 @ W0 @ W1 ) @ W2 )
= ( sdtasdt0 @ W0 @ ( sdtasdt0 @ W1 @ W2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(51,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( sdtasdt0 @ W0 @ W1 )
= ( sdtasdt0 @ W1 @ W0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(52,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 )
& ( aNaturalNumber0 @ W2 ) )
=> ( ( sdtpldt0 @ ( sdtpldt0 @ W0 @ W1 ) @ W2 )
= ( sdtpldt0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(53,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( sdtpldt0 @ W0 @ W1 )
= ( sdtpldt0 @ W1 @ W0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(54,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( aNaturalNumber0 @ ( sdtasdt0 @ W0 @ W1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(55,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( aNaturalNumber0 @ ( sdtpldt0 @ W0 @ W1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(56,plain,
( ( aNaturalNumber0 @ sz00 )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(57,plain,
( ( ! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> $true ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(58,plain,
( ( ~ ~ ( isPrime0 @ xk ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(59,plain,
( ( ~ ( isPrime0 @ xk ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(60,plain,
( ( aNaturalNumber0 @ xk )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(61,plain,
( ( ~ ? [W0: $i] :
( ( aNaturalNumber0 @ W0 )
& ( doDivides0 @ W0 @ xk )
& ( isPrime0 @ W0 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[40]) ).
thf(62,plain,
( ( aNaturalNumber0 @ xk )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(63,plain,
( ( ~ ( isPrime0 @ xk ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(64,plain,
( ( ~ ~ ( isPrime0 @ xk ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(65,plain,
( ( ! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> $true ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(66,plain,
( ( aNaturalNumber0 @ sz00 )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(67,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( aNaturalNumber0 @ ( sdtpldt0 @ W0 @ W1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(68,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( aNaturalNumber0 @ ( sdtasdt0 @ W0 @ W1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(69,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( sdtpldt0 @ W0 @ W1 )
= ( sdtpldt0 @ W1 @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(70,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 )
& ( aNaturalNumber0 @ W2 ) )
=> ( ( sdtpldt0 @ ( sdtpldt0 @ W0 @ W1 ) @ W2 )
= ( sdtpldt0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(71,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( sdtasdt0 @ W0 @ W1 )
= ( sdtasdt0 @ W1 @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(72,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 )
& ( aNaturalNumber0 @ W2 ) )
=> ( ( sdtasdt0 @ ( sdtasdt0 @ W0 @ W1 ) @ W2 )
= ( sdtasdt0 @ W0 @ ( sdtasdt0 @ W1 @ W2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(73,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 )
& ( aNaturalNumber0 @ W2 ) )
=> ( ( ( ( sdtpldt0 @ W0 @ W1 )
= ( sdtpldt0 @ W0 @ W2 ) )
| ( ( sdtpldt0 @ W1 @ W0 )
= ( sdtpldt0 @ W2 @ W0 ) ) )
=> ( W1 = W2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(74,plain,
( ( ! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> ( sdtlseqdt0 @ W0 @ W0 ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(75,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( ( sdtlseqdt0 @ W0 @ W1 )
& ( sdtlseqdt0 @ W1 @ W0 ) )
=> ( W0 = W1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(76,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 )
& ( aNaturalNumber0 @ W2 ) )
=> ( ( ( sdtlseqdt0 @ W0 @ W1 )
& ( sdtlseqdt0 @ W1 @ W2 ) )
=> ( sdtlseqdt0 @ W0 @ W2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(77,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( sdtlseqdt0 @ W0 @ W1 )
| ( ( W1 != W0 )
& ( sdtlseqdt0 @ W1 @ W0 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(78,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( iLess0 @ W0 @ W1 )
=> $true ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(79,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 )
& ( aNaturalNumber0 @ W2 ) )
=> ( ( ( doDivides0 @ W0 @ W1 )
& ( doDivides0 @ W1 @ W2 ) )
=> ( doDivides0 @ W0 @ W2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(80,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 )
& ( aNaturalNumber0 @ W2 ) )
=> ( ( ( doDivides0 @ W0 @ W1 )
& ( doDivides0 @ W0 @ W2 ) )
=> ( doDivides0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(81,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 )
& ( aNaturalNumber0 @ W2 ) )
=> ( ( ( doDivides0 @ W0 @ W1 )
& ( doDivides0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) ) )
=> ( doDivides0 @ W0 @ W2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(82,plain,
( ( ~ ? [W0: $i] :
( ( aNaturalNumber0 @ W0 )
& ( doDivides0 @ W0 @ xk )
& ( isPrime0 @ W0 ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(83,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 ) )
| ~ ( aNaturalNumber0 @ SX2 ) )
| ( ( sdtasdt0 @ ( sdtasdt0 @ SX0 @ SX1 ) @ SX2 )
= ( sdtasdt0 @ SX0 @ ( sdtasdt0 @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(84,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 ) )
| ~ ( aNaturalNumber0 @ SX2 ) )
| ~ ( ( ( sdtpldt0 @ SX0 @ SX1 )
= ( sdtpldt0 @ SX0 @ SX2 ) )
| ( ( sdtpldt0 @ SX1 @ SX0 )
= ( sdtpldt0 @ SX2 @ SX0 ) ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(85,plain,
( ( ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| $true ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(86,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 ) )
| ( ( sdtasdt0 @ SX0 @ SX1 )
= ( sdtasdt0 @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(87,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 ) )
| ~ ~ ( ~ ( sdtlseqdt0 @ SX0 @ SX1 )
| ~ ( sdtlseqdt0 @ SX1 @ SX0 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(88,plain,
( ( ! [SX0: $i] :
( ~ ( aNaturalNumber0 @ SX0 )
| ( sdtlseqdt0 @ SX0 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(89,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 ) )
| ( aNaturalNumber0 @ ( sdtpldt0 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(90,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 ) )
| ( aNaturalNumber0 @ ( sdtasdt0 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(91,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 ) )
| ~ ( aNaturalNumber0 @ SX2 ) )
| ~ ~ ( ~ ( sdtlseqdt0 @ SX0 @ SX1 )
| ~ ( sdtlseqdt0 @ SX1 @ SX2 ) )
| ( sdtlseqdt0 @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(92,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 ) )
| ~ ( aNaturalNumber0 @ SX2 ) )
| ( ( sdtpldt0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ SX2 )
= ( sdtpldt0 @ SX0 @ ( sdtpldt0 @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(93,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 ) )
| ( sdtlseqdt0 @ SX0 @ SX1 )
| ~ ( ~ ( ( SX1 != SX0 ) )
| ~ ( sdtlseqdt0 @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(94,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 ) )
| ~ ( aNaturalNumber0 @ SX2 ) )
| ~ ~ ( ~ ( doDivides0 @ SX0 @ SX1 )
| ~ ( doDivides0 @ SX0 @ ( sdtpldt0 @ SX1 @ SX2 ) ) )
| ( doDivides0 @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(95,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 ) )
| ~ ( iLess0 @ SX0 @ SX1 )
| $true ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(96,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 ) )
| ( ( sdtpldt0 @ SX0 @ SX1 )
= ( sdtpldt0 @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(97,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 ) )
| ~ ( aNaturalNumber0 @ SX2 ) )
| ~ ~ ( ~ ( doDivides0 @ SX0 @ SX1 )
| ~ ( doDivides0 @ SX1 @ SX2 ) )
| ( doDivides0 @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(98,plain,
( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( doDivides0 @ SX0 @ xk ) )
| ~ ( isPrime0 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(99,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( aNaturalNumber0 @ SX1 ) )
| ~ ( aNaturalNumber0 @ SX2 ) )
| ~ ~ ( ~ ( doDivides0 @ SX0 @ SX1 )
| ~ ( doDivides0 @ SX0 @ SX2 ) )
| ( doDivides0 @ SX0 @ ( sdtpldt0 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(100,plain,
( ( isPrime0 @ xk )
= $false ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(101,plain,
( ( ~ ( isPrime0 @ xk ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(102,plain,
! [SV1: $i] :
( ( ! [SY38: $i,SY39: $i] :
( ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SV1 )
| ~ ( aNaturalNumber0 @ SY38 ) )
| ~ ( aNaturalNumber0 @ SY39 ) )
| ( ( sdtasdt0 @ ( sdtasdt0 @ SV1 @ SY38 ) @ SY39 )
= ( sdtasdt0 @ SV1 @ ( sdtasdt0 @ SY38 @ SY39 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(103,plain,
! [SV2: $i] :
( ( ! [SY40: $i,SY41: $i] :
( ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SV2 )
| ~ ( aNaturalNumber0 @ SY40 ) )
| ~ ( aNaturalNumber0 @ SY41 ) )
| ~ ( ( ( sdtpldt0 @ SV2 @ SY40 )
= ( sdtpldt0 @ SV2 @ SY41 ) )
| ( ( sdtpldt0 @ SY40 @ SV2 )
= ( sdtpldt0 @ SY41 @ SV2 ) ) )
| ( SY40 = SY41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(104,plain,
! [SV3: $i] :
( ( ~ ( aNaturalNumber0 @ SV3 )
| $true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(105,plain,
! [SV4: $i] :
( ( ! [SY42: $i] :
( ~ ~ ( ~ ( aNaturalNumber0 @ SV4 )
| ~ ( aNaturalNumber0 @ SY42 ) )
| ( ( sdtasdt0 @ SV4 @ SY42 )
= ( sdtasdt0 @ SY42 @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(106,plain,
! [SV5: $i] :
( ( ! [SY43: $i] :
( ~ ~ ( ~ ( aNaturalNumber0 @ SV5 )
| ~ ( aNaturalNumber0 @ SY43 ) )
| ~ ~ ( ~ ( sdtlseqdt0 @ SV5 @ SY43 )
| ~ ( sdtlseqdt0 @ SY43 @ SV5 ) )
| ( SV5 = SY43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(107,plain,
! [SV6: $i] :
( ( ~ ( aNaturalNumber0 @ SV6 )
| ( sdtlseqdt0 @ SV6 @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(108,plain,
! [SV7: $i] :
( ( ! [SY44: $i] :
( ~ ~ ( ~ ( aNaturalNumber0 @ SV7 )
| ~ ( aNaturalNumber0 @ SY44 ) )
| ( aNaturalNumber0 @ ( sdtpldt0 @ SV7 @ SY44 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(109,plain,
! [SV8: $i] :
( ( ! [SY45: $i] :
( ~ ~ ( ~ ( aNaturalNumber0 @ SV8 )
| ~ ( aNaturalNumber0 @ SY45 ) )
| ( aNaturalNumber0 @ ( sdtasdt0 @ SV8 @ SY45 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(110,plain,
! [SV9: $i] :
( ( ! [SY46: $i,SY47: $i] :
( ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SV9 )
| ~ ( aNaturalNumber0 @ SY46 ) )
| ~ ( aNaturalNumber0 @ SY47 ) )
| ~ ~ ( ~ ( sdtlseqdt0 @ SV9 @ SY46 )
| ~ ( sdtlseqdt0 @ SY46 @ SY47 ) )
| ( sdtlseqdt0 @ SV9 @ SY47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(111,plain,
! [SV10: $i] :
( ( ! [SY48: $i,SY49: $i] :
( ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SV10 )
| ~ ( aNaturalNumber0 @ SY48 ) )
| ~ ( aNaturalNumber0 @ SY49 ) )
| ( ( sdtpldt0 @ ( sdtpldt0 @ SV10 @ SY48 ) @ SY49 )
= ( sdtpldt0 @ SV10 @ ( sdtpldt0 @ SY48 @ SY49 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(112,plain,
! [SV11: $i] :
( ( ! [SY50: $i] :
( ~ ~ ( ~ ( aNaturalNumber0 @ SV11 )
| ~ ( aNaturalNumber0 @ SY50 ) )
| ( sdtlseqdt0 @ SV11 @ SY50 )
| ~ ( ~ ( ( SY50 != SV11 ) )
| ~ ( sdtlseqdt0 @ SY50 @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(113,plain,
! [SV12: $i] :
( ( ! [SY51: $i,SY52: $i] :
( ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SV12 )
| ~ ( aNaturalNumber0 @ SY51 ) )
| ~ ( aNaturalNumber0 @ SY52 ) )
| ~ ~ ( ~ ( doDivides0 @ SV12 @ SY51 )
| ~ ( doDivides0 @ SV12 @ ( sdtpldt0 @ SY51 @ SY52 ) ) )
| ( doDivides0 @ SV12 @ SY52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(114,plain,
! [SV13: $i] :
( ( ! [SY53: $i] :
( ~ ~ ( ~ ( aNaturalNumber0 @ SV13 )
| ~ ( aNaturalNumber0 @ SY53 ) )
| ~ ( iLess0 @ SV13 @ SY53 )
| $true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(115,plain,
! [SV14: $i] :
( ( ! [SY54: $i] :
( ~ ~ ( ~ ( aNaturalNumber0 @ SV14 )
| ~ ( aNaturalNumber0 @ SY54 ) )
| ( ( sdtpldt0 @ SV14 @ SY54 )
= ( sdtpldt0 @ SY54 @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(116,plain,
! [SV15: $i] :
( ( ! [SY55: $i,SY56: $i] :
( ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SV15 )
| ~ ( aNaturalNumber0 @ SY55 ) )
| ~ ( aNaturalNumber0 @ SY56 ) )
| ~ ~ ( ~ ( doDivides0 @ SV15 @ SY55 )
| ~ ( doDivides0 @ SY55 @ SY56 ) )
| ( doDivides0 @ SV15 @ SY56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(117,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( doDivides0 @ SX0 @ xk ) )
| ~ ( isPrime0 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(118,plain,
! [SV16: $i] :
( ( ! [SY57: $i,SY58: $i] :
( ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SV16 )
| ~ ( aNaturalNumber0 @ SY57 ) )
| ~ ( aNaturalNumber0 @ SY58 ) )
| ~ ~ ( ~ ( doDivides0 @ SV16 @ SY57 )
| ~ ( doDivides0 @ SV16 @ SY58 ) )
| ( doDivides0 @ SV16 @ ( sdtpldt0 @ SY57 @ SY58 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(119,plain,
( ( isPrime0 @ xk )
= $true ),
inference(extcnf_not_neg,[status(thm)],[101]) ).
thf(120,plain,
! [SV17: $i,SV1: $i] :
( ( ! [SY59: $i] :
( ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SV1 )
| ~ ( aNaturalNumber0 @ SV17 ) )
| ~ ( aNaturalNumber0 @ SY59 ) )
| ( ( sdtasdt0 @ ( sdtasdt0 @ SV1 @ SV17 ) @ SY59 )
= ( sdtasdt0 @ SV1 @ ( sdtasdt0 @ SV17 @ SY59 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(121,plain,
! [SV18: $i,SV2: $i] :
( ( ! [SY60: $i] :
( ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SV2 )
| ~ ( aNaturalNumber0 @ SV18 ) )
| ~ ( aNaturalNumber0 @ SY60 ) )
| ~ ( ( ( sdtpldt0 @ SV2 @ SV18 )
= ( sdtpldt0 @ SV2 @ SY60 ) )
| ( ( sdtpldt0 @ SV18 @ SV2 )
= ( sdtpldt0 @ SY60 @ SV2 ) ) )
| ( SV18 = SY60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(122,plain,
! [SV3: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV3 ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(123,plain,
! [SV19: $i,SV4: $i] :
( ( ~ ~ ( ~ ( aNaturalNumber0 @ SV4 )
| ~ ( aNaturalNumber0 @ SV19 ) )
| ( ( sdtasdt0 @ SV4 @ SV19 )
= ( sdtasdt0 @ SV19 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(124,plain,
! [SV20: $i,SV5: $i] :
( ( ~ ~ ( ~ ( aNaturalNumber0 @ SV5 )
| ~ ( aNaturalNumber0 @ SV20 ) )
| ~ ~ ( ~ ( sdtlseqdt0 @ SV5 @ SV20 )
| ~ ( sdtlseqdt0 @ SV20 @ SV5 ) )
| ( SV5 = SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(125,plain,
! [SV6: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV6 ) )
= $true )
| ( ( sdtlseqdt0 @ SV6 @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[107]) ).
thf(126,plain,
! [SV21: $i,SV7: $i] :
( ( ~ ~ ( ~ ( aNaturalNumber0 @ SV7 )
| ~ ( aNaturalNumber0 @ SV21 ) )
| ( aNaturalNumber0 @ ( sdtpldt0 @ SV7 @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(127,plain,
! [SV22: $i,SV8: $i] :
( ( ~ ~ ( ~ ( aNaturalNumber0 @ SV8 )
| ~ ( aNaturalNumber0 @ SV22 ) )
| ( aNaturalNumber0 @ ( sdtasdt0 @ SV8 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(128,plain,
! [SV23: $i,SV9: $i] :
( ( ! [SY61: $i] :
( ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SV9 )
| ~ ( aNaturalNumber0 @ SV23 ) )
| ~ ( aNaturalNumber0 @ SY61 ) )
| ~ ~ ( ~ ( sdtlseqdt0 @ SV9 @ SV23 )
| ~ ( sdtlseqdt0 @ SV23 @ SY61 ) )
| ( sdtlseqdt0 @ SV9 @ SY61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(129,plain,
! [SV24: $i,SV10: $i] :
( ( ! [SY62: $i] :
( ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SV10 )
| ~ ( aNaturalNumber0 @ SV24 ) )
| ~ ( aNaturalNumber0 @ SY62 ) )
| ( ( sdtpldt0 @ ( sdtpldt0 @ SV10 @ SV24 ) @ SY62 )
= ( sdtpldt0 @ SV10 @ ( sdtpldt0 @ SV24 @ SY62 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(130,plain,
! [SV25: $i,SV11: $i] :
( ( ~ ~ ( ~ ( aNaturalNumber0 @ SV11 )
| ~ ( aNaturalNumber0 @ SV25 ) )
| ( sdtlseqdt0 @ SV11 @ SV25 )
| ~ ( ~ ( ( SV25 != SV11 ) )
| ~ ( sdtlseqdt0 @ SV25 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(131,plain,
! [SV26: $i,SV12: $i] :
( ( ! [SY63: $i] :
( ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SV12 )
| ~ ( aNaturalNumber0 @ SV26 ) )
| ~ ( aNaturalNumber0 @ SY63 ) )
| ~ ~ ( ~ ( doDivides0 @ SV12 @ SV26 )
| ~ ( doDivides0 @ SV12 @ ( sdtpldt0 @ SV26 @ SY63 ) ) )
| ( doDivides0 @ SV12 @ SY63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(132,plain,
! [SV27: $i,SV13: $i] :
( ( ~ ~ ( ~ ( aNaturalNumber0 @ SV13 )
| ~ ( aNaturalNumber0 @ SV27 ) )
| ~ ( iLess0 @ SV13 @ SV27 )
| $true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(133,plain,
! [SV28: $i,SV14: $i] :
( ( ~ ~ ( ~ ( aNaturalNumber0 @ SV14 )
| ~ ( aNaturalNumber0 @ SV28 ) )
| ( ( sdtpldt0 @ SV14 @ SV28 )
= ( sdtpldt0 @ SV28 @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(134,plain,
! [SV29: $i,SV15: $i] :
( ( ! [SY64: $i] :
( ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SV15 )
| ~ ( aNaturalNumber0 @ SV29 ) )
| ~ ( aNaturalNumber0 @ SY64 ) )
| ~ ~ ( ~ ( doDivides0 @ SV15 @ SV29 )
| ~ ( doDivides0 @ SV29 @ SY64 ) )
| ( doDivides0 @ SV15 @ SY64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(135,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SX0 )
| ~ ( doDivides0 @ SX0 @ xk ) )
| ~ ( isPrime0 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[117]) ).
thf(136,plain,
! [SV30: $i,SV16: $i] :
( ( ! [SY65: $i] :
( ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SV16 )
| ~ ( aNaturalNumber0 @ SV30 ) )
| ~ ( aNaturalNumber0 @ SY65 ) )
| ~ ~ ( ~ ( doDivides0 @ SV16 @ SV30 )
| ~ ( doDivides0 @ SV16 @ SY65 ) )
| ( doDivides0 @ SV16 @ ( sdtpldt0 @ SV30 @ SY65 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(137,plain,
! [SV31: $i,SV17: $i,SV1: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SV1 )
| ~ ( aNaturalNumber0 @ SV17 ) )
| ~ ( aNaturalNumber0 @ SV31 ) )
| ( ( sdtasdt0 @ ( sdtasdt0 @ SV1 @ SV17 ) @ SV31 )
= ( sdtasdt0 @ SV1 @ ( sdtasdt0 @ SV17 @ SV31 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(138,plain,
! [SV32: $i,SV18: $i,SV2: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SV2 )
| ~ ( aNaturalNumber0 @ SV18 ) )
| ~ ( aNaturalNumber0 @ SV32 ) )
| ~ ( ( ( sdtpldt0 @ SV2 @ SV18 )
= ( sdtpldt0 @ SV2 @ SV32 ) )
| ( ( sdtpldt0 @ SV18 @ SV2 )
= ( sdtpldt0 @ SV32 @ SV2 ) ) )
| ( SV18 = SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(139,plain,
! [SV3: $i] :
( ( ( aNaturalNumber0 @ SV3 )
= $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(140,plain,
! [SV19: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( aNaturalNumber0 @ SV4 )
| ~ ( aNaturalNumber0 @ SV19 ) ) )
= $true )
| ( ( ( sdtasdt0 @ SV4 @ SV19 )
= ( sdtasdt0 @ SV19 @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[123]) ).
thf(141,plain,
! [SV20: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ( aNaturalNumber0 @ SV5 )
| ~ ( aNaturalNumber0 @ SV20 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV5 @ SV20 )
| ~ ( sdtlseqdt0 @ SV20 @ SV5 ) )
| ( SV5 = SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[124]) ).
thf(142,plain,
! [SV6: $i] :
( ( ( aNaturalNumber0 @ SV6 )
= $false )
| ( ( sdtlseqdt0 @ SV6 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(143,plain,
! [SV21: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ( aNaturalNumber0 @ SV7 )
| ~ ( aNaturalNumber0 @ SV21 ) ) )
= $true )
| ( ( aNaturalNumber0 @ ( sdtpldt0 @ SV7 @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(144,plain,
! [SV22: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ( aNaturalNumber0 @ SV8 )
| ~ ( aNaturalNumber0 @ SV22 ) ) )
= $true )
| ( ( aNaturalNumber0 @ ( sdtasdt0 @ SV8 @ SV22 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[127]) ).
thf(145,plain,
! [SV33: $i,SV23: $i,SV9: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SV9 )
| ~ ( aNaturalNumber0 @ SV23 ) )
| ~ ( aNaturalNumber0 @ SV33 ) )
| ~ ~ ( ~ ( sdtlseqdt0 @ SV9 @ SV23 )
| ~ ( sdtlseqdt0 @ SV23 @ SV33 ) )
| ( sdtlseqdt0 @ SV9 @ SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(146,plain,
! [SV34: $i,SV24: $i,SV10: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SV10 )
| ~ ( aNaturalNumber0 @ SV24 ) )
| ~ ( aNaturalNumber0 @ SV34 ) )
| ( ( sdtpldt0 @ ( sdtpldt0 @ SV10 @ SV24 ) @ SV34 )
= ( sdtpldt0 @ SV10 @ ( sdtpldt0 @ SV24 @ SV34 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(147,plain,
! [SV25: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ( aNaturalNumber0 @ SV11 )
| ~ ( aNaturalNumber0 @ SV25 ) ) )
= $true )
| ( ( ( sdtlseqdt0 @ SV11 @ SV25 )
| ~ ( ~ ( ( SV25 != SV11 ) )
| ~ ( sdtlseqdt0 @ SV25 @ SV11 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[130]) ).
thf(148,plain,
! [SV35: $i,SV26: $i,SV12: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SV12 )
| ~ ( aNaturalNumber0 @ SV26 ) )
| ~ ( aNaturalNumber0 @ SV35 ) )
| ~ ~ ( ~ ( doDivides0 @ SV12 @ SV26 )
| ~ ( doDivides0 @ SV12 @ ( sdtpldt0 @ SV26 @ SV35 ) ) )
| ( doDivides0 @ SV12 @ SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(149,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ( aNaturalNumber0 @ SV13 )
| ~ ( aNaturalNumber0 @ SV27 ) ) )
= $true )
| ( ( ~ ( iLess0 @ SV13 @ SV27 )
| $true )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[132]) ).
thf(150,plain,
! [SV28: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ( aNaturalNumber0 @ SV14 )
| ~ ( aNaturalNumber0 @ SV28 ) ) )
= $true )
| ( ( ( sdtpldt0 @ SV14 @ SV28 )
= ( sdtpldt0 @ SV28 @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[133]) ).
thf(151,plain,
! [SV36: $i,SV29: $i,SV15: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SV15 )
| ~ ( aNaturalNumber0 @ SV29 ) )
| ~ ( aNaturalNumber0 @ SV36 ) )
| ~ ~ ( ~ ( doDivides0 @ SV15 @ SV29 )
| ~ ( doDivides0 @ SV29 @ SV36 ) )
| ( doDivides0 @ SV15 @ SV36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(152,plain,
! [SV37: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SV37 )
| ~ ( doDivides0 @ SV37 @ xk ) )
| ~ ( isPrime0 @ SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(153,plain,
! [SV38: $i,SV30: $i,SV16: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SV16 )
| ~ ( aNaturalNumber0 @ SV30 ) )
| ~ ( aNaturalNumber0 @ SV38 ) )
| ~ ~ ( ~ ( doDivides0 @ SV16 @ SV30 )
| ~ ( doDivides0 @ SV16 @ SV38 ) )
| ( doDivides0 @ SV16 @ ( sdtpldt0 @ SV30 @ SV38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(154,plain,
! [SV31: $i,SV17: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SV1 )
| ~ ( aNaturalNumber0 @ SV17 ) )
| ~ ( aNaturalNumber0 @ SV31 ) ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV1 @ SV17 ) @ SV31 )
= ( sdtasdt0 @ SV1 @ ( sdtasdt0 @ SV17 @ SV31 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[137]) ).
thf(155,plain,
! [SV32: $i,SV18: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SV2 )
| ~ ( aNaturalNumber0 @ SV18 ) )
| ~ ( aNaturalNumber0 @ SV32 ) ) )
= $true )
| ( ( ~ ( ( ( sdtpldt0 @ SV2 @ SV18 )
= ( sdtpldt0 @ SV2 @ SV32 ) )
| ( ( sdtpldt0 @ SV18 @ SV2 )
= ( sdtpldt0 @ SV32 @ SV2 ) ) )
| ( SV18 = SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[138]) ).
thf(156,plain,
! [SV19: $i,SV4: $i] :
( ( ( ~ ( ~ ( aNaturalNumber0 @ SV4 )
| ~ ( aNaturalNumber0 @ SV19 ) ) )
= $false )
| ( ( ( sdtasdt0 @ SV4 @ SV19 )
= ( sdtasdt0 @ SV19 @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(157,plain,
! [SV20: $i,SV5: $i] :
( ( ( ~ ( ~ ( aNaturalNumber0 @ SV5 )
| ~ ( aNaturalNumber0 @ SV20 ) ) )
= $false )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV5 @ SV20 )
| ~ ( sdtlseqdt0 @ SV20 @ SV5 ) )
| ( SV5 = SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(158,plain,
! [SV21: $i,SV7: $i] :
( ( ( ~ ( ~ ( aNaturalNumber0 @ SV7 )
| ~ ( aNaturalNumber0 @ SV21 ) ) )
= $false )
| ( ( aNaturalNumber0 @ ( sdtpldt0 @ SV7 @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[143]) ).
thf(159,plain,
! [SV22: $i,SV8: $i] :
( ( ( ~ ( ~ ( aNaturalNumber0 @ SV8 )
| ~ ( aNaturalNumber0 @ SV22 ) ) )
= $false )
| ( ( aNaturalNumber0 @ ( sdtasdt0 @ SV8 @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(160,plain,
! [SV33: $i,SV23: $i,SV9: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SV9 )
| ~ ( aNaturalNumber0 @ SV23 ) )
| ~ ( aNaturalNumber0 @ SV33 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV9 @ SV23 )
| ~ ( sdtlseqdt0 @ SV23 @ SV33 ) )
| ( sdtlseqdt0 @ SV9 @ SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[145]) ).
thf(161,plain,
! [SV34: $i,SV24: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SV10 )
| ~ ( aNaturalNumber0 @ SV24 ) )
| ~ ( aNaturalNumber0 @ SV34 ) ) )
= $true )
| ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV10 @ SV24 ) @ SV34 )
= ( sdtpldt0 @ SV10 @ ( sdtpldt0 @ SV24 @ SV34 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[146]) ).
thf(162,plain,
! [SV25: $i,SV11: $i] :
( ( ( ~ ( ~ ( aNaturalNumber0 @ SV11 )
| ~ ( aNaturalNumber0 @ SV25 ) ) )
= $false )
| ( ( ( sdtlseqdt0 @ SV11 @ SV25 )
| ~ ( ~ ( ( SV25 != SV11 ) )
| ~ ( sdtlseqdt0 @ SV25 @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(163,plain,
! [SV35: $i,SV26: $i,SV12: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SV12 )
| ~ ( aNaturalNumber0 @ SV26 ) )
| ~ ( aNaturalNumber0 @ SV35 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( doDivides0 @ SV12 @ SV26 )
| ~ ( doDivides0 @ SV12 @ ( sdtpldt0 @ SV26 @ SV35 ) ) )
| ( doDivides0 @ SV12 @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[148]) ).
thf(164,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ( ~ ( aNaturalNumber0 @ SV13 )
| ~ ( aNaturalNumber0 @ SV27 ) ) )
= $false )
| ( ( ~ ( iLess0 @ SV13 @ SV27 )
| $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(165,plain,
! [SV28: $i,SV14: $i] :
( ( ( ~ ( ~ ( aNaturalNumber0 @ SV14 )
| ~ ( aNaturalNumber0 @ SV28 ) ) )
= $false )
| ( ( ( sdtpldt0 @ SV14 @ SV28 )
= ( sdtpldt0 @ SV28 @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[150]) ).
thf(166,plain,
! [SV36: $i,SV29: $i,SV15: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SV15 )
| ~ ( aNaturalNumber0 @ SV29 ) )
| ~ ( aNaturalNumber0 @ SV36 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( doDivides0 @ SV15 @ SV29 )
| ~ ( doDivides0 @ SV29 @ SV36 ) )
| ( doDivides0 @ SV15 @ SV36 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[151]) ).
thf(167,plain,
! [SV37: $i] :
( ( ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SV37 )
| ~ ( doDivides0 @ SV37 @ xk ) )
| ~ ( isPrime0 @ SV37 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(168,plain,
! [SV38: $i,SV30: $i,SV16: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SV16 )
| ~ ( aNaturalNumber0 @ SV30 ) )
| ~ ( aNaturalNumber0 @ SV38 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( doDivides0 @ SV16 @ SV30 )
| ~ ( doDivides0 @ SV16 @ SV38 ) )
| ( doDivides0 @ SV16 @ ( sdtpldt0 @ SV30 @ SV38 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[153]) ).
thf(169,plain,
! [SV31: $i,SV17: $i,SV1: $i] :
( ( ( ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SV1 )
| ~ ( aNaturalNumber0 @ SV17 ) )
| ~ ( aNaturalNumber0 @ SV31 ) ) )
= $false )
| ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV1 @ SV17 ) @ SV31 )
= ( sdtasdt0 @ SV1 @ ( sdtasdt0 @ SV17 @ SV31 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(170,plain,
! [SV32: $i,SV18: $i,SV2: $i] :
( ( ( ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SV2 )
| ~ ( aNaturalNumber0 @ SV18 ) )
| ~ ( aNaturalNumber0 @ SV32 ) ) )
= $false )
| ( ( ~ ( ( ( sdtpldt0 @ SV2 @ SV18 )
= ( sdtpldt0 @ SV2 @ SV32 ) )
| ( ( sdtpldt0 @ SV18 @ SV2 )
= ( sdtpldt0 @ SV32 @ SV2 ) ) )
| ( SV18 = SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(171,plain,
! [SV19: $i,SV4: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV4 )
| ~ ( aNaturalNumber0 @ SV19 ) )
= $true )
| ( ( ( sdtasdt0 @ SV4 @ SV19 )
= ( sdtasdt0 @ SV19 @ SV4 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[156]) ).
thf(172,plain,
! [SV20: $i,SV5: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV5 )
| ~ ( aNaturalNumber0 @ SV20 ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV5 @ SV20 )
| ~ ( sdtlseqdt0 @ SV20 @ SV5 ) )
| ( SV5 = SV20 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[157]) ).
thf(173,plain,
! [SV21: $i,SV7: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV7 )
| ~ ( aNaturalNumber0 @ SV21 ) )
= $true )
| ( ( aNaturalNumber0 @ ( sdtpldt0 @ SV7 @ SV21 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[158]) ).
thf(174,plain,
! [SV22: $i,SV8: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV8 )
| ~ ( aNaturalNumber0 @ SV22 ) )
= $true )
| ( ( aNaturalNumber0 @ ( sdtasdt0 @ SV8 @ SV22 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[159]) ).
thf(175,plain,
! [SV33: $i,SV23: $i,SV9: $i] :
( ( ( ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SV9 )
| ~ ( aNaturalNumber0 @ SV23 ) )
| ~ ( aNaturalNumber0 @ SV33 ) ) )
= $false )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV9 @ SV23 )
| ~ ( sdtlseqdt0 @ SV23 @ SV33 ) )
| ( sdtlseqdt0 @ SV9 @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(176,plain,
! [SV34: $i,SV24: $i,SV10: $i] :
( ( ( ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SV10 )
| ~ ( aNaturalNumber0 @ SV24 ) )
| ~ ( aNaturalNumber0 @ SV34 ) ) )
= $false )
| ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV10 @ SV24 ) @ SV34 )
= ( sdtpldt0 @ SV10 @ ( sdtpldt0 @ SV24 @ SV34 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[161]) ).
thf(177,plain,
! [SV25: $i,SV11: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV11 )
| ~ ( aNaturalNumber0 @ SV25 ) )
= $true )
| ( ( ( sdtlseqdt0 @ SV11 @ SV25 )
| ~ ( ~ ( ( SV25 != SV11 ) )
| ~ ( sdtlseqdt0 @ SV25 @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[162]) ).
thf(178,plain,
! [SV35: $i,SV26: $i,SV12: $i] :
( ( ( ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SV12 )
| ~ ( aNaturalNumber0 @ SV26 ) )
| ~ ( aNaturalNumber0 @ SV35 ) ) )
= $false )
| ( ( ~ ~ ( ~ ( doDivides0 @ SV12 @ SV26 )
| ~ ( doDivides0 @ SV12 @ ( sdtpldt0 @ SV26 @ SV35 ) ) )
| ( doDivides0 @ SV12 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(179,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV13 )
| ~ ( aNaturalNumber0 @ SV27 ) )
= $true )
| ( ( ~ ( iLess0 @ SV13 @ SV27 )
| $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[164]) ).
thf(180,plain,
! [SV28: $i,SV14: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV14 )
| ~ ( aNaturalNumber0 @ SV28 ) )
= $true )
| ( ( ( sdtpldt0 @ SV14 @ SV28 )
= ( sdtpldt0 @ SV28 @ SV14 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[165]) ).
thf(181,plain,
! [SV36: $i,SV29: $i,SV15: $i] :
( ( ( ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SV15 )
| ~ ( aNaturalNumber0 @ SV29 ) )
| ~ ( aNaturalNumber0 @ SV36 ) ) )
= $false )
| ( ( ~ ~ ( ~ ( doDivides0 @ SV15 @ SV29 )
| ~ ( doDivides0 @ SV29 @ SV36 ) )
| ( doDivides0 @ SV15 @ SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(182,plain,
! [SV37: $i] :
( ( ~ ~ ( ~ ( aNaturalNumber0 @ SV37 )
| ~ ( doDivides0 @ SV37 @ xk ) )
| ~ ( isPrime0 @ SV37 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[167]) ).
thf(183,plain,
! [SV38: $i,SV30: $i,SV16: $i] :
( ( ( ~ ( ~ ~ ( ~ ( aNaturalNumber0 @ SV16 )
| ~ ( aNaturalNumber0 @ SV30 ) )
| ~ ( aNaturalNumber0 @ SV38 ) ) )
= $false )
| ( ( ~ ~ ( ~ ( doDivides0 @ SV16 @ SV30 )
| ~ ( doDivides0 @ SV16 @ SV38 ) )
| ( doDivides0 @ SV16 @ ( sdtpldt0 @ SV30 @ SV38 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[168]) ).
thf(184,plain,
! [SV31: $i,SV17: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ( aNaturalNumber0 @ SV1 )
| ~ ( aNaturalNumber0 @ SV17 ) )
| ~ ( aNaturalNumber0 @ SV31 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV1 @ SV17 ) @ SV31 )
= ( sdtasdt0 @ SV1 @ ( sdtasdt0 @ SV17 @ SV31 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[169]) ).
thf(185,plain,
! [SV32: $i,SV18: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ( aNaturalNumber0 @ SV2 )
| ~ ( aNaturalNumber0 @ SV18 ) )
| ~ ( aNaturalNumber0 @ SV32 ) )
= $true )
| ( ( ~ ( ( ( sdtpldt0 @ SV2 @ SV18 )
= ( sdtpldt0 @ SV2 @ SV32 ) )
| ( ( sdtpldt0 @ SV18 @ SV2 )
= ( sdtpldt0 @ SV32 @ SV2 ) ) )
| ( SV18 = SV32 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[170]) ).
thf(186,plain,
! [SV19: $i,SV4: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV4 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV19 ) )
= $true )
| ( ( ( sdtasdt0 @ SV4 @ SV19 )
= ( sdtasdt0 @ SV19 @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[171]) ).
thf(187,plain,
! [SV20: $i,SV5: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV5 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV20 ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV5 @ SV20 )
| ~ ( sdtlseqdt0 @ SV20 @ SV5 ) )
| ( SV5 = SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[172]) ).
thf(188,plain,
! [SV21: $i,SV7: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV7 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV21 ) )
= $true )
| ( ( aNaturalNumber0 @ ( sdtpldt0 @ SV7 @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[173]) ).
thf(189,plain,
! [SV22: $i,SV8: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV8 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV22 ) )
= $true )
| ( ( aNaturalNumber0 @ ( sdtasdt0 @ SV8 @ SV22 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[174]) ).
thf(190,plain,
! [SV33: $i,SV23: $i,SV9: $i] :
( ( ( ~ ~ ( ~ ( aNaturalNumber0 @ SV9 )
| ~ ( aNaturalNumber0 @ SV23 ) )
| ~ ( aNaturalNumber0 @ SV33 ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV9 @ SV23 )
| ~ ( sdtlseqdt0 @ SV23 @ SV33 ) )
| ( sdtlseqdt0 @ SV9 @ SV33 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[175]) ).
thf(191,plain,
! [SV34: $i,SV24: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ( aNaturalNumber0 @ SV10 )
| ~ ( aNaturalNumber0 @ SV24 ) )
| ~ ( aNaturalNumber0 @ SV34 ) )
= $true )
| ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV10 @ SV24 ) @ SV34 )
= ( sdtpldt0 @ SV10 @ ( sdtpldt0 @ SV24 @ SV34 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[176]) ).
thf(192,plain,
! [SV25: $i,SV11: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV11 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV25 ) )
= $true )
| ( ( ( sdtlseqdt0 @ SV11 @ SV25 )
| ~ ( ~ ( ( SV25 != SV11 ) )
| ~ ( sdtlseqdt0 @ SV25 @ SV11 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[177]) ).
thf(193,plain,
! [SV35: $i,SV26: $i,SV12: $i] :
( ( ( ~ ~ ( ~ ( aNaturalNumber0 @ SV12 )
| ~ ( aNaturalNumber0 @ SV26 ) )
| ~ ( aNaturalNumber0 @ SV35 ) )
= $true )
| ( ( ~ ~ ( ~ ( doDivides0 @ SV12 @ SV26 )
| ~ ( doDivides0 @ SV12 @ ( sdtpldt0 @ SV26 @ SV35 ) ) )
| ( doDivides0 @ SV12 @ SV35 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[178]) ).
thf(194,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV13 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV27 ) )
= $true )
| ( ( ~ ( iLess0 @ SV13 @ SV27 )
| $true )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[179]) ).
thf(195,plain,
! [SV28: $i,SV14: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV14 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV28 ) )
= $true )
| ( ( ( sdtpldt0 @ SV14 @ SV28 )
= ( sdtpldt0 @ SV28 @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[180]) ).
thf(196,plain,
! [SV36: $i,SV29: $i,SV15: $i] :
( ( ( ~ ~ ( ~ ( aNaturalNumber0 @ SV15 )
| ~ ( aNaturalNumber0 @ SV29 ) )
| ~ ( aNaturalNumber0 @ SV36 ) )
= $true )
| ( ( ~ ~ ( ~ ( doDivides0 @ SV15 @ SV29 )
| ~ ( doDivides0 @ SV29 @ SV36 ) )
| ( doDivides0 @ SV15 @ SV36 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[181]) ).
thf(197,plain,
! [SV37: $i] :
( ( ( ~ ~ ( ~ ( aNaturalNumber0 @ SV37 )
| ~ ( doDivides0 @ SV37 @ xk ) ) )
= $true )
| ( ( ~ ( isPrime0 @ SV37 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[182]) ).
thf(198,plain,
! [SV38: $i,SV30: $i,SV16: $i] :
( ( ( ~ ~ ( ~ ( aNaturalNumber0 @ SV16 )
| ~ ( aNaturalNumber0 @ SV30 ) )
| ~ ( aNaturalNumber0 @ SV38 ) )
= $true )
| ( ( ~ ~ ( ~ ( doDivides0 @ SV16 @ SV30 )
| ~ ( doDivides0 @ SV16 @ SV38 ) )
| ( doDivides0 @ SV16 @ ( sdtpldt0 @ SV30 @ SV38 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[183]) ).
thf(199,plain,
! [SV31: $i,SV17: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ( aNaturalNumber0 @ SV1 )
| ~ ( aNaturalNumber0 @ SV17 ) ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV31 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV1 @ SV17 ) @ SV31 )
= ( sdtasdt0 @ SV1 @ ( sdtasdt0 @ SV17 @ SV31 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[184]) ).
thf(200,plain,
! [SV32: $i,SV18: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ( aNaturalNumber0 @ SV2 )
| ~ ( aNaturalNumber0 @ SV18 ) ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV32 ) )
= $true )
| ( ( ~ ( ( ( sdtpldt0 @ SV2 @ SV18 )
= ( sdtpldt0 @ SV2 @ SV32 ) )
| ( ( sdtpldt0 @ SV18 @ SV2 )
= ( sdtpldt0 @ SV32 @ SV2 ) ) )
| ( SV18 = SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[185]) ).
thf(201,plain,
! [SV19: $i,SV4: $i] :
( ( ( aNaturalNumber0 @ SV4 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV19 ) )
= $true )
| ( ( ( sdtasdt0 @ SV4 @ SV19 )
= ( sdtasdt0 @ SV19 @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[186]) ).
thf(202,plain,
! [SV20: $i,SV5: $i] :
( ( ( aNaturalNumber0 @ SV5 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV20 ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV5 @ SV20 )
| ~ ( sdtlseqdt0 @ SV20 @ SV5 ) )
| ( SV5 = SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[187]) ).
thf(203,plain,
! [SV21: $i,SV7: $i] :
( ( ( aNaturalNumber0 @ SV7 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV21 ) )
= $true )
| ( ( aNaturalNumber0 @ ( sdtpldt0 @ SV7 @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[188]) ).
thf(204,plain,
! [SV22: $i,SV8: $i] :
( ( ( aNaturalNumber0 @ SV8 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV22 ) )
= $true )
| ( ( aNaturalNumber0 @ ( sdtasdt0 @ SV8 @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(205,plain,
! [SV33: $i,SV23: $i,SV9: $i] :
( ( ( ~ ~ ( ~ ( aNaturalNumber0 @ SV9 )
| ~ ( aNaturalNumber0 @ SV23 ) ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV33 ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV9 @ SV23 )
| ~ ( sdtlseqdt0 @ SV23 @ SV33 ) )
| ( sdtlseqdt0 @ SV9 @ SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[190]) ).
thf(206,plain,
! [SV34: $i,SV24: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ( aNaturalNumber0 @ SV10 )
| ~ ( aNaturalNumber0 @ SV24 ) ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV34 ) )
= $true )
| ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV10 @ SV24 ) @ SV34 )
= ( sdtpldt0 @ SV10 @ ( sdtpldt0 @ SV24 @ SV34 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[191]) ).
thf(207,plain,
! [SV25: $i,SV11: $i] :
( ( ( aNaturalNumber0 @ SV11 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV25 ) )
= $true )
| ( ( ( sdtlseqdt0 @ SV11 @ SV25 )
| ~ ( ~ ( ( SV25 != SV11 ) )
| ~ ( sdtlseqdt0 @ SV25 @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(208,plain,
! [SV35: $i,SV26: $i,SV12: $i] :
( ( ( ~ ~ ( ~ ( aNaturalNumber0 @ SV12 )
| ~ ( aNaturalNumber0 @ SV26 ) ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV35 ) )
= $true )
| ( ( ~ ~ ( ~ ( doDivides0 @ SV12 @ SV26 )
| ~ ( doDivides0 @ SV12 @ ( sdtpldt0 @ SV26 @ SV35 ) ) )
| ( doDivides0 @ SV12 @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[193]) ).
thf(209,plain,
! [SV27: $i,SV13: $i] :
( ( ( aNaturalNumber0 @ SV13 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV27 ) )
= $true )
| ( ( ~ ( iLess0 @ SV13 @ SV27 )
| $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(210,plain,
! [SV28: $i,SV14: $i] :
( ( ( aNaturalNumber0 @ SV14 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV28 ) )
= $true )
| ( ( ( sdtpldt0 @ SV14 @ SV28 )
= ( sdtpldt0 @ SV28 @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(211,plain,
! [SV36: $i,SV29: $i,SV15: $i] :
( ( ( ~ ~ ( ~ ( aNaturalNumber0 @ SV15 )
| ~ ( aNaturalNumber0 @ SV29 ) ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV36 ) )
= $true )
| ( ( ~ ~ ( ~ ( doDivides0 @ SV15 @ SV29 )
| ~ ( doDivides0 @ SV29 @ SV36 ) )
| ( doDivides0 @ SV15 @ SV36 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[196]) ).
thf(212,plain,
! [SV37: $i] :
( ( ( ~ ( ~ ( aNaturalNumber0 @ SV37 )
| ~ ( doDivides0 @ SV37 @ xk ) ) )
= $false )
| ( ( ~ ( isPrime0 @ SV37 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(213,plain,
! [SV38: $i,SV30: $i,SV16: $i] :
( ( ( ~ ~ ( ~ ( aNaturalNumber0 @ SV16 )
| ~ ( aNaturalNumber0 @ SV30 ) ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV38 ) )
= $true )
| ( ( ~ ~ ( ~ ( doDivides0 @ SV16 @ SV30 )
| ~ ( doDivides0 @ SV16 @ SV38 ) )
| ( doDivides0 @ SV16 @ ( sdtpldt0 @ SV30 @ SV38 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[198]) ).
thf(214,plain,
! [SV31: $i,SV17: $i,SV1: $i] :
( ( ( ~ ( ~ ( aNaturalNumber0 @ SV1 )
| ~ ( aNaturalNumber0 @ SV17 ) ) )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV31 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV1 @ SV17 ) @ SV31 )
= ( sdtasdt0 @ SV1 @ ( sdtasdt0 @ SV17 @ SV31 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[199]) ).
thf(215,plain,
! [SV32: $i,SV18: $i,SV2: $i] :
( ( ( ~ ( ~ ( aNaturalNumber0 @ SV2 )
| ~ ( aNaturalNumber0 @ SV18 ) ) )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV32 ) )
= $true )
| ( ( ~ ( ( ( sdtpldt0 @ SV2 @ SV18 )
= ( sdtpldt0 @ SV2 @ SV32 ) )
| ( ( sdtpldt0 @ SV18 @ SV2 )
= ( sdtpldt0 @ SV32 @ SV2 ) ) )
| ( SV18 = SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(216,plain,
! [SV4: $i,SV19: $i] :
( ( ( aNaturalNumber0 @ SV19 )
= $false )
| ( ( aNaturalNumber0 @ SV4 )
= $false )
| ( ( ( sdtasdt0 @ SV4 @ SV19 )
= ( sdtasdt0 @ SV19 @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(217,plain,
! [SV5: $i,SV20: $i] :
( ( ( aNaturalNumber0 @ SV20 )
= $false )
| ( ( aNaturalNumber0 @ SV5 )
= $false )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV5 @ SV20 )
| ~ ( sdtlseqdt0 @ SV20 @ SV5 ) )
| ( SV5 = SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[202]) ).
thf(218,plain,
! [SV7: $i,SV21: $i] :
( ( ( aNaturalNumber0 @ SV21 )
= $false )
| ( ( aNaturalNumber0 @ SV7 )
= $false )
| ( ( aNaturalNumber0 @ ( sdtpldt0 @ SV7 @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(219,plain,
! [SV8: $i,SV22: $i] :
( ( ( aNaturalNumber0 @ SV22 )
= $false )
| ( ( aNaturalNumber0 @ SV8 )
= $false )
| ( ( aNaturalNumber0 @ ( sdtasdt0 @ SV8 @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(220,plain,
! [SV33: $i,SV23: $i,SV9: $i] :
( ( ( ~ ( ~ ( aNaturalNumber0 @ SV9 )
| ~ ( aNaturalNumber0 @ SV23 ) ) )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV33 ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV9 @ SV23 )
| ~ ( sdtlseqdt0 @ SV23 @ SV33 ) )
| ( sdtlseqdt0 @ SV9 @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(221,plain,
! [SV34: $i,SV24: $i,SV10: $i] :
( ( ( ~ ( ~ ( aNaturalNumber0 @ SV10 )
| ~ ( aNaturalNumber0 @ SV24 ) ) )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV34 ) )
= $true )
| ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV10 @ SV24 ) @ SV34 )
= ( sdtpldt0 @ SV10 @ ( sdtpldt0 @ SV24 @ SV34 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[206]) ).
thf(222,plain,
! [SV11: $i,SV25: $i] :
( ( ( aNaturalNumber0 @ SV25 )
= $false )
| ( ( aNaturalNumber0 @ SV11 )
= $false )
| ( ( ( sdtlseqdt0 @ SV11 @ SV25 )
| ~ ( ~ ( ( SV25 != SV11 ) )
| ~ ( sdtlseqdt0 @ SV25 @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[207]) ).
thf(223,plain,
! [SV35: $i,SV26: $i,SV12: $i] :
( ( ( ~ ( ~ ( aNaturalNumber0 @ SV12 )
| ~ ( aNaturalNumber0 @ SV26 ) ) )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV35 ) )
= $true )
| ( ( ~ ~ ( ~ ( doDivides0 @ SV12 @ SV26 )
| ~ ( doDivides0 @ SV12 @ ( sdtpldt0 @ SV26 @ SV35 ) ) )
| ( doDivides0 @ SV12 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[208]) ).
thf(224,plain,
! [SV13: $i,SV27: $i] :
( ( ( aNaturalNumber0 @ SV27 )
= $false )
| ( ( aNaturalNumber0 @ SV13 )
= $false )
| ( ( ~ ( iLess0 @ SV13 @ SV27 )
| $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[209]) ).
thf(225,plain,
! [SV14: $i,SV28: $i] :
( ( ( aNaturalNumber0 @ SV28 )
= $false )
| ( ( aNaturalNumber0 @ SV14 )
= $false )
| ( ( ( sdtpldt0 @ SV14 @ SV28 )
= ( sdtpldt0 @ SV28 @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(226,plain,
! [SV36: $i,SV29: $i,SV15: $i] :
( ( ( ~ ( ~ ( aNaturalNumber0 @ SV15 )
| ~ ( aNaturalNumber0 @ SV29 ) ) )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV36 ) )
= $true )
| ( ( ~ ~ ( ~ ( doDivides0 @ SV15 @ SV29 )
| ~ ( doDivides0 @ SV29 @ SV36 ) )
| ( doDivides0 @ SV15 @ SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[211]) ).
thf(227,plain,
! [SV37: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV37 )
| ~ ( doDivides0 @ SV37 @ xk ) )
= $true )
| ( ( ~ ( isPrime0 @ SV37 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[212]) ).
thf(228,plain,
! [SV38: $i,SV30: $i,SV16: $i] :
( ( ( ~ ( ~ ( aNaturalNumber0 @ SV16 )
| ~ ( aNaturalNumber0 @ SV30 ) ) )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV38 ) )
= $true )
| ( ( ~ ~ ( ~ ( doDivides0 @ SV16 @ SV30 )
| ~ ( doDivides0 @ SV16 @ SV38 ) )
| ( doDivides0 @ SV16 @ ( sdtpldt0 @ SV30 @ SV38 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[213]) ).
thf(229,plain,
! [SV31: $i,SV17: $i,SV1: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV1 )
| ~ ( aNaturalNumber0 @ SV17 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV31 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV1 @ SV17 ) @ SV31 )
= ( sdtasdt0 @ SV1 @ ( sdtasdt0 @ SV17 @ SV31 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[214]) ).
thf(230,plain,
! [SV32: $i,SV18: $i,SV2: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV2 )
| ~ ( aNaturalNumber0 @ SV18 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV32 ) )
= $true )
| ( ( ~ ( ( ( sdtpldt0 @ SV2 @ SV18 )
= ( sdtpldt0 @ SV2 @ SV32 ) )
| ( ( sdtpldt0 @ SV18 @ SV2 )
= ( sdtpldt0 @ SV32 @ SV2 ) ) )
| ( SV18 = SV32 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[215]) ).
thf(231,plain,
! [SV20: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV5 @ SV20 )
| ~ ( sdtlseqdt0 @ SV20 @ SV5 ) ) )
= $true )
| ( ( SV5 = SV20 )
= $true )
| ( ( aNaturalNumber0 @ SV5 )
= $false )
| ( ( aNaturalNumber0 @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[217]) ).
thf(232,plain,
! [SV33: $i,SV23: $i,SV9: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV9 )
| ~ ( aNaturalNumber0 @ SV23 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV33 ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV9 @ SV23 )
| ~ ( sdtlseqdt0 @ SV23 @ SV33 ) )
| ( sdtlseqdt0 @ SV9 @ SV33 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[220]) ).
thf(233,plain,
! [SV34: $i,SV24: $i,SV10: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV10 )
| ~ ( aNaturalNumber0 @ SV24 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV34 ) )
= $true )
| ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV10 @ SV24 ) @ SV34 )
= ( sdtpldt0 @ SV10 @ ( sdtpldt0 @ SV24 @ SV34 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[221]) ).
thf(234,plain,
! [SV25: $i,SV11: $i] :
( ( ( sdtlseqdt0 @ SV11 @ SV25 )
= $true )
| ( ( ~ ( ~ ( ( SV25 != SV11 ) )
| ~ ( sdtlseqdt0 @ SV25 @ SV11 ) ) )
= $true )
| ( ( aNaturalNumber0 @ SV11 )
= $false )
| ( ( aNaturalNumber0 @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[222]) ).
thf(235,plain,
! [SV35: $i,SV26: $i,SV12: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV12 )
| ~ ( aNaturalNumber0 @ SV26 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV35 ) )
= $true )
| ( ( ~ ~ ( ~ ( doDivides0 @ SV12 @ SV26 )
| ~ ( doDivides0 @ SV12 @ ( sdtpldt0 @ SV26 @ SV35 ) ) )
| ( doDivides0 @ SV12 @ SV35 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[223]) ).
thf(236,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ( iLess0 @ SV13 @ SV27 ) )
= $true )
| ( $true = $true )
| ( ( aNaturalNumber0 @ SV13 )
= $false )
| ( ( aNaturalNumber0 @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[224]) ).
thf(237,plain,
! [SV36: $i,SV29: $i,SV15: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV15 )
| ~ ( aNaturalNumber0 @ SV29 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV36 ) )
= $true )
| ( ( ~ ~ ( ~ ( doDivides0 @ SV15 @ SV29 )
| ~ ( doDivides0 @ SV29 @ SV36 ) )
| ( doDivides0 @ SV15 @ SV36 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[226]) ).
thf(238,plain,
! [SV37: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV37 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV37 @ xk ) )
= $true )
| ( ( ~ ( isPrime0 @ SV37 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[227]) ).
thf(239,plain,
! [SV38: $i,SV30: $i,SV16: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV16 )
| ~ ( aNaturalNumber0 @ SV30 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV38 ) )
= $true )
| ( ( ~ ~ ( ~ ( doDivides0 @ SV16 @ SV30 )
| ~ ( doDivides0 @ SV16 @ SV38 ) )
| ( doDivides0 @ SV16 @ ( sdtpldt0 @ SV30 @ SV38 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[228]) ).
thf(240,plain,
! [SV31: $i,SV17: $i,SV1: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV1 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV17 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV31 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV1 @ SV17 ) @ SV31 )
= ( sdtasdt0 @ SV1 @ ( sdtasdt0 @ SV17 @ SV31 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[229]) ).
thf(241,plain,
! [SV32: $i,SV18: $i,SV2: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV2 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV18 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV32 ) )
= $true )
| ( ( ~ ( ( ( sdtpldt0 @ SV2 @ SV18 )
= ( sdtpldt0 @ SV2 @ SV32 ) )
| ( ( sdtpldt0 @ SV18 @ SV2 )
= ( sdtpldt0 @ SV32 @ SV2 ) ) )
| ( SV18 = SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[230]) ).
thf(242,plain,
! [SV20: $i,SV5: $i] :
( ( ( ~ ( ~ ( sdtlseqdt0 @ SV5 @ SV20 )
| ~ ( sdtlseqdt0 @ SV20 @ SV5 ) ) )
= $false )
| ( ( SV5 = SV20 )
= $true )
| ( ( aNaturalNumber0 @ SV5 )
= $false )
| ( ( aNaturalNumber0 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[231]) ).
thf(243,plain,
! [SV33: $i,SV23: $i,SV9: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV9 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV23 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV33 ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV9 @ SV23 )
| ~ ( sdtlseqdt0 @ SV23 @ SV33 ) )
| ( sdtlseqdt0 @ SV9 @ SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[232]) ).
thf(244,plain,
! [SV34: $i,SV24: $i,SV10: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV10 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV24 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV34 ) )
= $true )
| ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV10 @ SV24 ) @ SV34 )
= ( sdtpldt0 @ SV10 @ ( sdtpldt0 @ SV24 @ SV34 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[233]) ).
thf(245,plain,
! [SV11: $i,SV25: $i] :
( ( ( ~ ( ( SV25 != SV11 ) )
| ~ ( sdtlseqdt0 @ SV25 @ SV11 ) )
= $false )
| ( ( sdtlseqdt0 @ SV11 @ SV25 )
= $true )
| ( ( aNaturalNumber0 @ SV11 )
= $false )
| ( ( aNaturalNumber0 @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[234]) ).
thf(246,plain,
! [SV35: $i,SV26: $i,SV12: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV12 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV26 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV35 ) )
= $true )
| ( ( ~ ~ ( ~ ( doDivides0 @ SV12 @ SV26 )
| ~ ( doDivides0 @ SV12 @ ( sdtpldt0 @ SV26 @ SV35 ) ) )
| ( doDivides0 @ SV12 @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[235]) ).
thf(247,plain,
! [SV27: $i,SV13: $i] :
( ( ( iLess0 @ SV13 @ SV27 )
= $false )
| ( $true = $true )
| ( ( aNaturalNumber0 @ SV13 )
= $false )
| ( ( aNaturalNumber0 @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[236]) ).
thf(248,plain,
! [SV36: $i,SV29: $i,SV15: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV15 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV29 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV36 ) )
= $true )
| ( ( ~ ~ ( ~ ( doDivides0 @ SV15 @ SV29 )
| ~ ( doDivides0 @ SV29 @ SV36 ) )
| ( doDivides0 @ SV15 @ SV36 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[237]) ).
thf(249,plain,
! [SV37: $i] :
( ( ( aNaturalNumber0 @ SV37 )
= $false )
| ( ( ~ ( doDivides0 @ SV37 @ xk ) )
= $true )
| ( ( ~ ( isPrime0 @ SV37 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[238]) ).
thf(250,plain,
! [SV38: $i,SV30: $i,SV16: $i] :
( ( ( ~ ( aNaturalNumber0 @ SV16 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV30 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV38 ) )
= $true )
| ( ( ~ ~ ( ~ ( doDivides0 @ SV16 @ SV30 )
| ~ ( doDivides0 @ SV16 @ SV38 ) )
| ( doDivides0 @ SV16 @ ( sdtpldt0 @ SV30 @ SV38 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[239]) ).
thf(251,plain,
! [SV31: $i,SV17: $i,SV1: $i] :
( ( ( aNaturalNumber0 @ SV1 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV17 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV31 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV1 @ SV17 ) @ SV31 )
= ( sdtasdt0 @ SV1 @ ( sdtasdt0 @ SV17 @ SV31 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[240]) ).
thf(252,plain,
! [SV32: $i,SV18: $i,SV2: $i] :
( ( ( aNaturalNumber0 @ SV2 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV18 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV32 ) )
= $true )
| ( ( ~ ( ( ( sdtpldt0 @ SV2 @ SV18 )
= ( sdtpldt0 @ SV2 @ SV32 ) )
| ( ( sdtpldt0 @ SV18 @ SV2 )
= ( sdtpldt0 @ SV32 @ SV2 ) ) )
| ( SV18 = SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[241]) ).
thf(253,plain,
! [SV20: $i,SV5: $i] :
( ( ( ~ ( sdtlseqdt0 @ SV5 @ SV20 )
| ~ ( sdtlseqdt0 @ SV20 @ SV5 ) )
= $true )
| ( ( SV5 = SV20 )
= $true )
| ( ( aNaturalNumber0 @ SV5 )
= $false )
| ( ( aNaturalNumber0 @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[242]) ).
thf(254,plain,
! [SV33: $i,SV23: $i,SV9: $i] :
( ( ( aNaturalNumber0 @ SV9 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV23 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV33 ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV9 @ SV23 )
| ~ ( sdtlseqdt0 @ SV23 @ SV33 ) )
| ( sdtlseqdt0 @ SV9 @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[243]) ).
thf(255,plain,
! [SV34: $i,SV24: $i,SV10: $i] :
( ( ( aNaturalNumber0 @ SV10 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV24 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV34 ) )
= $true )
| ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV10 @ SV24 ) @ SV34 )
= ( sdtpldt0 @ SV10 @ ( sdtpldt0 @ SV24 @ SV34 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[244]) ).
thf(256,plain,
! [SV11: $i,SV25: $i] :
( ( ( ~ ( ( SV25 != SV11 ) ) )
= $false )
| ( ( sdtlseqdt0 @ SV11 @ SV25 )
= $true )
| ( ( aNaturalNumber0 @ SV11 )
= $false )
| ( ( aNaturalNumber0 @ SV25 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[245]) ).
thf(257,plain,
! [SV11: $i,SV25: $i] :
( ( ( ~ ( sdtlseqdt0 @ SV25 @ SV11 ) )
= $false )
| ( ( sdtlseqdt0 @ SV11 @ SV25 )
= $true )
| ( ( aNaturalNumber0 @ SV11 )
= $false )
| ( ( aNaturalNumber0 @ SV25 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[245]) ).
thf(258,plain,
! [SV35: $i,SV26: $i,SV12: $i] :
( ( ( aNaturalNumber0 @ SV12 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV26 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV35 ) )
= $true )
| ( ( ~ ~ ( ~ ( doDivides0 @ SV12 @ SV26 )
| ~ ( doDivides0 @ SV12 @ ( sdtpldt0 @ SV26 @ SV35 ) ) )
| ( doDivides0 @ SV12 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[246]) ).
thf(259,plain,
! [SV36: $i,SV29: $i,SV15: $i] :
( ( ( aNaturalNumber0 @ SV15 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV29 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV36 ) )
= $true )
| ( ( ~ ~ ( ~ ( doDivides0 @ SV15 @ SV29 )
| ~ ( doDivides0 @ SV29 @ SV36 ) )
| ( doDivides0 @ SV15 @ SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[248]) ).
thf(260,plain,
! [SV37: $i] :
( ( ( doDivides0 @ SV37 @ xk )
= $false )
| ( ( aNaturalNumber0 @ SV37 )
= $false )
| ( ( ~ ( isPrime0 @ SV37 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[249]) ).
thf(261,plain,
! [SV38: $i,SV30: $i,SV16: $i] :
( ( ( aNaturalNumber0 @ SV16 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV30 ) )
= $true )
| ( ( ~ ( aNaturalNumber0 @ SV38 ) )
= $true )
| ( ( ~ ~ ( ~ ( doDivides0 @ SV16 @ SV30 )
| ~ ( doDivides0 @ SV16 @ SV38 ) )
| ( doDivides0 @ SV16 @ ( sdtpldt0 @ SV30 @ SV38 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[250]) ).
thf(262,plain,
! [SV31: $i,SV1: $i,SV17: $i] :
( ( ( aNaturalNumber0 @ SV17 )
= $false )
| ( ( aNaturalNumber0 @ SV1 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV31 ) )
= $true )
| ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV1 @ SV17 ) @ SV31 )
= ( sdtasdt0 @ SV1 @ ( sdtasdt0 @ SV17 @ SV31 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[251]) ).
thf(263,plain,
! [SV32: $i,SV2: $i,SV18: $i] :
( ( ( aNaturalNumber0 @ SV18 )
= $false )
| ( ( aNaturalNumber0 @ SV2 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV32 ) )
= $true )
| ( ( ~ ( ( ( sdtpldt0 @ SV2 @ SV18 )
= ( sdtpldt0 @ SV2 @ SV32 ) )
| ( ( sdtpldt0 @ SV18 @ SV2 )
= ( sdtpldt0 @ SV32 @ SV2 ) ) )
| ( SV18 = SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[252]) ).
thf(264,plain,
! [SV20: $i,SV5: $i] :
( ( ( ~ ( sdtlseqdt0 @ SV5 @ SV20 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV20 @ SV5 ) )
= $true )
| ( ( SV5 = SV20 )
= $true )
| ( ( aNaturalNumber0 @ SV5 )
= $false )
| ( ( aNaturalNumber0 @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[253]) ).
thf(265,plain,
! [SV33: $i,SV9: $i,SV23: $i] :
( ( ( aNaturalNumber0 @ SV23 )
= $false )
| ( ( aNaturalNumber0 @ SV9 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV33 ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV9 @ SV23 )
| ~ ( sdtlseqdt0 @ SV23 @ SV33 ) )
| ( sdtlseqdt0 @ SV9 @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[254]) ).
thf(266,plain,
! [SV34: $i,SV10: $i,SV24: $i] :
( ( ( aNaturalNumber0 @ SV24 )
= $false )
| ( ( aNaturalNumber0 @ SV10 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV34 ) )
= $true )
| ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV10 @ SV24 ) @ SV34 )
= ( sdtpldt0 @ SV10 @ ( sdtpldt0 @ SV24 @ SV34 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[255]) ).
thf(267,plain,
! [SV11: $i,SV25: $i] :
( ( ( SV25 != SV11 )
= $true )
| ( ( sdtlseqdt0 @ SV11 @ SV25 )
= $true )
| ( ( aNaturalNumber0 @ SV11 )
= $false )
| ( ( aNaturalNumber0 @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[256]) ).
thf(268,plain,
! [SV11: $i,SV25: $i] :
( ( ( sdtlseqdt0 @ SV25 @ SV11 )
= $true )
| ( ( sdtlseqdt0 @ SV11 @ SV25 )
= $true )
| ( ( aNaturalNumber0 @ SV11 )
= $false )
| ( ( aNaturalNumber0 @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[257]) ).
thf(269,plain,
! [SV35: $i,SV12: $i,SV26: $i] :
( ( ( aNaturalNumber0 @ SV26 )
= $false )
| ( ( aNaturalNumber0 @ SV12 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV35 ) )
= $true )
| ( ( ~ ~ ( ~ ( doDivides0 @ SV12 @ SV26 )
| ~ ( doDivides0 @ SV12 @ ( sdtpldt0 @ SV26 @ SV35 ) ) )
| ( doDivides0 @ SV12 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[258]) ).
thf(270,plain,
! [SV36: $i,SV15: $i,SV29: $i] :
( ( ( aNaturalNumber0 @ SV29 )
= $false )
| ( ( aNaturalNumber0 @ SV15 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV36 ) )
= $true )
| ( ( ~ ~ ( ~ ( doDivides0 @ SV15 @ SV29 )
| ~ ( doDivides0 @ SV29 @ SV36 ) )
| ( doDivides0 @ SV15 @ SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[259]) ).
thf(271,plain,
! [SV37: $i] :
( ( ( isPrime0 @ SV37 )
= $false )
| ( ( aNaturalNumber0 @ SV37 )
= $false )
| ( ( doDivides0 @ SV37 @ xk )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[260]) ).
thf(272,plain,
! [SV38: $i,SV16: $i,SV30: $i] :
( ( ( aNaturalNumber0 @ SV30 )
= $false )
| ( ( aNaturalNumber0 @ SV16 )
= $false )
| ( ( ~ ( aNaturalNumber0 @ SV38 ) )
= $true )
| ( ( ~ ~ ( ~ ( doDivides0 @ SV16 @ SV30 )
| ~ ( doDivides0 @ SV16 @ SV38 ) )
| ( doDivides0 @ SV16 @ ( sdtpldt0 @ SV30 @ SV38 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[261]) ).
thf(273,plain,
! [SV17: $i,SV1: $i,SV31: $i] :
( ( ( aNaturalNumber0 @ SV31 )
= $false )
| ( ( aNaturalNumber0 @ SV1 )
= $false )
| ( ( aNaturalNumber0 @ SV17 )
= $false )
| ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV1 @ SV17 ) @ SV31 )
= ( sdtasdt0 @ SV1 @ ( sdtasdt0 @ SV17 @ SV31 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[262]) ).
thf(274,plain,
! [SV18: $i,SV2: $i,SV32: $i] :
( ( ( aNaturalNumber0 @ SV32 )
= $false )
| ( ( aNaturalNumber0 @ SV2 )
= $false )
| ( ( aNaturalNumber0 @ SV18 )
= $false )
| ( ( ~ ( ( ( sdtpldt0 @ SV2 @ SV18 )
= ( sdtpldt0 @ SV2 @ SV32 ) )
| ( ( sdtpldt0 @ SV18 @ SV2 )
= ( sdtpldt0 @ SV32 @ SV2 ) ) )
| ( SV18 = SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[263]) ).
thf(275,plain,
! [SV20: $i,SV5: $i] :
( ( ( sdtlseqdt0 @ SV5 @ SV20 )
= $false )
| ( ( ~ ( sdtlseqdt0 @ SV20 @ SV5 ) )
= $true )
| ( ( SV5 = SV20 )
= $true )
| ( ( aNaturalNumber0 @ SV5 )
= $false )
| ( ( aNaturalNumber0 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[264]) ).
thf(276,plain,
! [SV23: $i,SV9: $i,SV33: $i] :
( ( ( aNaturalNumber0 @ SV33 )
= $false )
| ( ( aNaturalNumber0 @ SV9 )
= $false )
| ( ( aNaturalNumber0 @ SV23 )
= $false )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV9 @ SV23 )
| ~ ( sdtlseqdt0 @ SV23 @ SV33 ) )
| ( sdtlseqdt0 @ SV9 @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[265]) ).
thf(277,plain,
! [SV24: $i,SV10: $i,SV34: $i] :
( ( ( aNaturalNumber0 @ SV34 )
= $false )
| ( ( aNaturalNumber0 @ SV10 )
= $false )
| ( ( aNaturalNumber0 @ SV24 )
= $false )
| ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV10 @ SV24 ) @ SV34 )
= ( sdtpldt0 @ SV10 @ ( sdtpldt0 @ SV24 @ SV34 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[266]) ).
thf(278,plain,
! [SV11: $i,SV25: $i] :
( ( ( SV25 = SV11 )
= $false )
| ( ( sdtlseqdt0 @ SV11 @ SV25 )
= $true )
| ( ( aNaturalNumber0 @ SV11 )
= $false )
| ( ( aNaturalNumber0 @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[267]) ).
thf(279,plain,
! [SV26: $i,SV12: $i,SV35: $i] :
( ( ( aNaturalNumber0 @ SV35 )
= $false )
| ( ( aNaturalNumber0 @ SV12 )
= $false )
| ( ( aNaturalNumber0 @ SV26 )
= $false )
| ( ( ~ ~ ( ~ ( doDivides0 @ SV12 @ SV26 )
| ~ ( doDivides0 @ SV12 @ ( sdtpldt0 @ SV26 @ SV35 ) ) )
| ( doDivides0 @ SV12 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[269]) ).
thf(280,plain,
! [SV29: $i,SV15: $i,SV36: $i] :
( ( ( aNaturalNumber0 @ SV36 )
= $false )
| ( ( aNaturalNumber0 @ SV15 )
= $false )
| ( ( aNaturalNumber0 @ SV29 )
= $false )
| ( ( ~ ~ ( ~ ( doDivides0 @ SV15 @ SV29 )
| ~ ( doDivides0 @ SV29 @ SV36 ) )
| ( doDivides0 @ SV15 @ SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[270]) ).
thf(281,plain,
! [SV30: $i,SV16: $i,SV38: $i] :
( ( ( aNaturalNumber0 @ SV38 )
= $false )
| ( ( aNaturalNumber0 @ SV16 )
= $false )
| ( ( aNaturalNumber0 @ SV30 )
= $false )
| ( ( ~ ~ ( ~ ( doDivides0 @ SV16 @ SV30 )
| ~ ( doDivides0 @ SV16 @ SV38 ) )
| ( doDivides0 @ SV16 @ ( sdtpldt0 @ SV30 @ SV38 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[272]) ).
thf(282,plain,
! [SV32: $i,SV18: $i,SV2: $i] :
( ( ( ~ ( ( ( sdtpldt0 @ SV2 @ SV18 )
= ( sdtpldt0 @ SV2 @ SV32 ) )
| ( ( sdtpldt0 @ SV18 @ SV2 )
= ( sdtpldt0 @ SV32 @ SV2 ) ) ) )
= $true )
| ( ( SV18 = SV32 )
= $true )
| ( ( aNaturalNumber0 @ SV18 )
= $false )
| ( ( aNaturalNumber0 @ SV2 )
= $false )
| ( ( aNaturalNumber0 @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[274]) ).
thf(283,plain,
! [SV5: $i,SV20: $i] :
( ( ( sdtlseqdt0 @ SV20 @ SV5 )
= $false )
| ( ( sdtlseqdt0 @ SV5 @ SV20 )
= $false )
| ( ( SV5 = SV20 )
= $true )
| ( ( aNaturalNumber0 @ SV5 )
= $false )
| ( ( aNaturalNumber0 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[275]) ).
thf(284,plain,
! [SV33: $i,SV23: $i,SV9: $i] :
( ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV9 @ SV23 )
| ~ ( sdtlseqdt0 @ SV23 @ SV33 ) ) )
= $true )
| ( ( sdtlseqdt0 @ SV9 @ SV33 )
= $true )
| ( ( aNaturalNumber0 @ SV23 )
= $false )
| ( ( aNaturalNumber0 @ SV9 )
= $false )
| ( ( aNaturalNumber0 @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[276]) ).
thf(285,plain,
! [SV35: $i,SV26: $i,SV12: $i] :
( ( ( ~ ~ ( ~ ( doDivides0 @ SV12 @ SV26 )
| ~ ( doDivides0 @ SV12 @ ( sdtpldt0 @ SV26 @ SV35 ) ) ) )
= $true )
| ( ( doDivides0 @ SV12 @ SV35 )
= $true )
| ( ( aNaturalNumber0 @ SV26 )
= $false )
| ( ( aNaturalNumber0 @ SV12 )
= $false )
| ( ( aNaturalNumber0 @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[279]) ).
thf(286,plain,
! [SV36: $i,SV29: $i,SV15: $i] :
( ( ( ~ ~ ( ~ ( doDivides0 @ SV15 @ SV29 )
| ~ ( doDivides0 @ SV29 @ SV36 ) ) )
= $true )
| ( ( doDivides0 @ SV15 @ SV36 )
= $true )
| ( ( aNaturalNumber0 @ SV29 )
= $false )
| ( ( aNaturalNumber0 @ SV15 )
= $false )
| ( ( aNaturalNumber0 @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[280]) ).
thf(287,plain,
! [SV38: $i,SV30: $i,SV16: $i] :
( ( ( ~ ~ ( ~ ( doDivides0 @ SV16 @ SV30 )
| ~ ( doDivides0 @ SV16 @ SV38 ) ) )
= $true )
| ( ( doDivides0 @ SV16 @ ( sdtpldt0 @ SV30 @ SV38 ) )
= $true )
| ( ( aNaturalNumber0 @ SV30 )
= $false )
| ( ( aNaturalNumber0 @ SV16 )
= $false )
| ( ( aNaturalNumber0 @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[281]) ).
thf(288,plain,
! [SV32: $i,SV18: $i,SV2: $i] :
( ( ( ( ( sdtpldt0 @ SV2 @ SV18 )
= ( sdtpldt0 @ SV2 @ SV32 ) )
| ( ( sdtpldt0 @ SV18 @ SV2 )
= ( sdtpldt0 @ SV32 @ SV2 ) ) )
= $false )
| ( ( SV18 = SV32 )
= $true )
| ( ( aNaturalNumber0 @ SV18 )
= $false )
| ( ( aNaturalNumber0 @ SV2 )
= $false )
| ( ( aNaturalNumber0 @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[282]) ).
thf(289,plain,
! [SV33: $i,SV23: $i,SV9: $i] :
( ( ( ~ ( ~ ( sdtlseqdt0 @ SV9 @ SV23 )
| ~ ( sdtlseqdt0 @ SV23 @ SV33 ) ) )
= $false )
| ( ( sdtlseqdt0 @ SV9 @ SV33 )
= $true )
| ( ( aNaturalNumber0 @ SV23 )
= $false )
| ( ( aNaturalNumber0 @ SV9 )
= $false )
| ( ( aNaturalNumber0 @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[284]) ).
thf(290,plain,
! [SV35: $i,SV26: $i,SV12: $i] :
( ( ( ~ ( ~ ( doDivides0 @ SV12 @ SV26 )
| ~ ( doDivides0 @ SV12 @ ( sdtpldt0 @ SV26 @ SV35 ) ) ) )
= $false )
| ( ( doDivides0 @ SV12 @ SV35 )
= $true )
| ( ( aNaturalNumber0 @ SV26 )
= $false )
| ( ( aNaturalNumber0 @ SV12 )
= $false )
| ( ( aNaturalNumber0 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[285]) ).
thf(291,plain,
! [SV36: $i,SV29: $i,SV15: $i] :
( ( ( ~ ( ~ ( doDivides0 @ SV15 @ SV29 )
| ~ ( doDivides0 @ SV29 @ SV36 ) ) )
= $false )
| ( ( doDivides0 @ SV15 @ SV36 )
= $true )
| ( ( aNaturalNumber0 @ SV29 )
= $false )
| ( ( aNaturalNumber0 @ SV15 )
= $false )
| ( ( aNaturalNumber0 @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[286]) ).
thf(292,plain,
! [SV38: $i,SV30: $i,SV16: $i] :
( ( ( ~ ( ~ ( doDivides0 @ SV16 @ SV30 )
| ~ ( doDivides0 @ SV16 @ SV38 ) ) )
= $false )
| ( ( doDivides0 @ SV16 @ ( sdtpldt0 @ SV30 @ SV38 ) )
= $true )
| ( ( aNaturalNumber0 @ SV30 )
= $false )
| ( ( aNaturalNumber0 @ SV16 )
= $false )
| ( ( aNaturalNumber0 @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[287]) ).
thf(293,plain,
! [SV32: $i,SV18: $i,SV2: $i] :
( ( ( ( sdtpldt0 @ SV2 @ SV18 )
= ( sdtpldt0 @ SV2 @ SV32 ) )
= $false )
| ( ( SV18 = SV32 )
= $true )
| ( ( aNaturalNumber0 @ SV18 )
= $false )
| ( ( aNaturalNumber0 @ SV2 )
= $false )
| ( ( aNaturalNumber0 @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[288]) ).
thf(294,plain,
! [SV32: $i,SV2: $i,SV18: $i] :
( ( ( ( sdtpldt0 @ SV18 @ SV2 )
= ( sdtpldt0 @ SV32 @ SV2 ) )
= $false )
| ( ( SV18 = SV32 )
= $true )
| ( ( aNaturalNumber0 @ SV18 )
= $false )
| ( ( aNaturalNumber0 @ SV2 )
= $false )
| ( ( aNaturalNumber0 @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[288]) ).
thf(295,plain,
! [SV33: $i,SV23: $i,SV9: $i] :
( ( ( ~ ( sdtlseqdt0 @ SV9 @ SV23 )
| ~ ( sdtlseqdt0 @ SV23 @ SV33 ) )
= $true )
| ( ( sdtlseqdt0 @ SV9 @ SV33 )
= $true )
| ( ( aNaturalNumber0 @ SV23 )
= $false )
| ( ( aNaturalNumber0 @ SV9 )
= $false )
| ( ( aNaturalNumber0 @ SV33 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[289]) ).
thf(296,plain,
! [SV35: $i,SV26: $i,SV12: $i] :
( ( ( ~ ( doDivides0 @ SV12 @ SV26 )
| ~ ( doDivides0 @ SV12 @ ( sdtpldt0 @ SV26 @ SV35 ) ) )
= $true )
| ( ( doDivides0 @ SV12 @ SV35 )
= $true )
| ( ( aNaturalNumber0 @ SV26 )
= $false )
| ( ( aNaturalNumber0 @ SV12 )
= $false )
| ( ( aNaturalNumber0 @ SV35 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[290]) ).
thf(297,plain,
! [SV36: $i,SV29: $i,SV15: $i] :
( ( ( ~ ( doDivides0 @ SV15 @ SV29 )
| ~ ( doDivides0 @ SV29 @ SV36 ) )
= $true )
| ( ( doDivides0 @ SV15 @ SV36 )
= $true )
| ( ( aNaturalNumber0 @ SV29 )
= $false )
| ( ( aNaturalNumber0 @ SV15 )
= $false )
| ( ( aNaturalNumber0 @ SV36 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[291]) ).
thf(298,plain,
! [SV38: $i,SV30: $i,SV16: $i] :
( ( ( ~ ( doDivides0 @ SV16 @ SV30 )
| ~ ( doDivides0 @ SV16 @ SV38 ) )
= $true )
| ( ( doDivides0 @ SV16 @ ( sdtpldt0 @ SV30 @ SV38 ) )
= $true )
| ( ( aNaturalNumber0 @ SV30 )
= $false )
| ( ( aNaturalNumber0 @ SV16 )
= $false )
| ( ( aNaturalNumber0 @ SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[292]) ).
thf(299,plain,
! [SV33: $i,SV23: $i,SV9: $i] :
( ( ( ~ ( sdtlseqdt0 @ SV9 @ SV23 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV23 @ SV33 ) )
= $true )
| ( ( sdtlseqdt0 @ SV9 @ SV33 )
= $true )
| ( ( aNaturalNumber0 @ SV23 )
= $false )
| ( ( aNaturalNumber0 @ SV9 )
= $false )
| ( ( aNaturalNumber0 @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[295]) ).
thf(300,plain,
! [SV35: $i,SV26: $i,SV12: $i] :
( ( ( ~ ( doDivides0 @ SV12 @ SV26 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV12 @ ( sdtpldt0 @ SV26 @ SV35 ) ) )
= $true )
| ( ( doDivides0 @ SV12 @ SV35 )
= $true )
| ( ( aNaturalNumber0 @ SV26 )
= $false )
| ( ( aNaturalNumber0 @ SV12 )
= $false )
| ( ( aNaturalNumber0 @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[296]) ).
thf(301,plain,
! [SV36: $i,SV29: $i,SV15: $i] :
( ( ( ~ ( doDivides0 @ SV15 @ SV29 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV29 @ SV36 ) )
= $true )
| ( ( doDivides0 @ SV15 @ SV36 )
= $true )
| ( ( aNaturalNumber0 @ SV29 )
= $false )
| ( ( aNaturalNumber0 @ SV15 )
= $false )
| ( ( aNaturalNumber0 @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[297]) ).
thf(302,plain,
! [SV38: $i,SV30: $i,SV16: $i] :
( ( ( ~ ( doDivides0 @ SV16 @ SV30 ) )
= $true )
| ( ( ~ ( doDivides0 @ SV16 @ SV38 ) )
= $true )
| ( ( doDivides0 @ SV16 @ ( sdtpldt0 @ SV30 @ SV38 ) )
= $true )
| ( ( aNaturalNumber0 @ SV30 )
= $false )
| ( ( aNaturalNumber0 @ SV16 )
= $false )
| ( ( aNaturalNumber0 @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[298]) ).
thf(303,plain,
! [SV33: $i,SV23: $i,SV9: $i] :
( ( ( sdtlseqdt0 @ SV9 @ SV23 )
= $false )
| ( ( ~ ( sdtlseqdt0 @ SV23 @ SV33 ) )
= $true )
| ( ( sdtlseqdt0 @ SV9 @ SV33 )
= $true )
| ( ( aNaturalNumber0 @ SV23 )
= $false )
| ( ( aNaturalNumber0 @ SV9 )
= $false )
| ( ( aNaturalNumber0 @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[299]) ).
thf(304,plain,
! [SV35: $i,SV26: $i,SV12: $i] :
( ( ( doDivides0 @ SV12 @ SV26 )
= $false )
| ( ( ~ ( doDivides0 @ SV12 @ ( sdtpldt0 @ SV26 @ SV35 ) ) )
= $true )
| ( ( doDivides0 @ SV12 @ SV35 )
= $true )
| ( ( aNaturalNumber0 @ SV26 )
= $false )
| ( ( aNaturalNumber0 @ SV12 )
= $false )
| ( ( aNaturalNumber0 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[300]) ).
thf(305,plain,
! [SV36: $i,SV29: $i,SV15: $i] :
( ( ( doDivides0 @ SV15 @ SV29 )
= $false )
| ( ( ~ ( doDivides0 @ SV29 @ SV36 ) )
= $true )
| ( ( doDivides0 @ SV15 @ SV36 )
= $true )
| ( ( aNaturalNumber0 @ SV29 )
= $false )
| ( ( aNaturalNumber0 @ SV15 )
= $false )
| ( ( aNaturalNumber0 @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[301]) ).
thf(306,plain,
! [SV38: $i,SV30: $i,SV16: $i] :
( ( ( doDivides0 @ SV16 @ SV30 )
= $false )
| ( ( ~ ( doDivides0 @ SV16 @ SV38 ) )
= $true )
| ( ( doDivides0 @ SV16 @ ( sdtpldt0 @ SV30 @ SV38 ) )
= $true )
| ( ( aNaturalNumber0 @ SV30 )
= $false )
| ( ( aNaturalNumber0 @ SV16 )
= $false )
| ( ( aNaturalNumber0 @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[302]) ).
thf(307,plain,
! [SV9: $i,SV33: $i,SV23: $i] :
( ( ( sdtlseqdt0 @ SV23 @ SV33 )
= $false )
| ( ( sdtlseqdt0 @ SV9 @ SV23 )
= $false )
| ( ( sdtlseqdt0 @ SV9 @ SV33 )
= $true )
| ( ( aNaturalNumber0 @ SV23 )
= $false )
| ( ( aNaturalNumber0 @ SV9 )
= $false )
| ( ( aNaturalNumber0 @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[303]) ).
thf(308,plain,
! [SV35: $i,SV26: $i,SV12: $i] :
( ( ( doDivides0 @ SV12 @ ( sdtpldt0 @ SV26 @ SV35 ) )
= $false )
| ( ( doDivides0 @ SV12 @ SV26 )
= $false )
| ( ( doDivides0 @ SV12 @ SV35 )
= $true )
| ( ( aNaturalNumber0 @ SV26 )
= $false )
| ( ( aNaturalNumber0 @ SV12 )
= $false )
| ( ( aNaturalNumber0 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[304]) ).
thf(309,plain,
! [SV15: $i,SV36: $i,SV29: $i] :
( ( ( doDivides0 @ SV29 @ SV36 )
= $false )
| ( ( doDivides0 @ SV15 @ SV29 )
= $false )
| ( ( doDivides0 @ SV15 @ SV36 )
= $true )
| ( ( aNaturalNumber0 @ SV29 )
= $false )
| ( ( aNaturalNumber0 @ SV15 )
= $false )
| ( ( aNaturalNumber0 @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[305]) ).
thf(310,plain,
! [SV30: $i,SV38: $i,SV16: $i] :
( ( ( doDivides0 @ SV16 @ SV38 )
= $false )
| ( ( doDivides0 @ SV16 @ SV30 )
= $false )
| ( ( doDivides0 @ SV16 @ ( sdtpldt0 @ SV30 @ SV38 ) )
= $true )
| ( ( aNaturalNumber0 @ SV30 )
= $false )
| ( ( aNaturalNumber0 @ SV16 )
= $false )
| ( ( aNaturalNumber0 @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[306]) ).
thf(311,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[62,310,309,308,307,294,293,283,278,277,273,271,268,247,225,219,218,216,142,139,119,100,66]) ).
thf(312,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[311]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM484+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.16 % Computer : n020.cluster.edu
% 0.08/0.16 % Model : x86_64 x86_64
% 0.08/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.16 % Memory : 8046.5625MB
% 0.08/0.16 % OS : Linux 6.8.0-71-generic
% 0.08/0.16 % CPULimit : 300
% 0.08/0.16 % WCLimit : 300
% 0.08/0.16 % DateTime : Tue Oct 6 13:22:06 UTC 2026
% 0.08/0.16 % CPUTime :
% 0.08/0.16 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.71/0.31
% 0.71/0.31 No.of.Axioms: 20
% 0.71/0.31
% 0.71/0.31 Length.of.Defs: 0
% 0.71/0.31
% 0.71/0.31 Contains.Choice.Funs: false
% 0.71/0.31 .......
% 0.71/0.31
% 0.71/0.31 ********************************
% 0.71/0.31 * All subproblems solved! *
% 0.71/0.31 ********************************
% 0.71/0.31 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:20,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:311,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.71/0.31
% 0.71/0.31 %**** Beginning of derivation protocol ****
% 0.71/0.31 % SZS output start CNFRefutation
% See solution above
% 0.71/0.31
% 0.71/0.31 %**** End of derivation protocol ****
% 0.71/0.31 %**** no. of clauses in derivation: 295 ****
% 0.71/0.31 %**** clause counter: 311 ****
% 0.71/0.31
% 0.71/0.31 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:20,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:311,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------