%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWV077+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 10:54:46 AM UTC 2026
% Result : Theorem 1.53s 0.55s
% Output : CNFRefutation 1.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 21
% Syntax : Number of formulae : 560 ( 336 unt; 0 typ; 0 def)
% Number of atoms : 3164 (1192 equ; 0 cnn)
% Maximal formula atoms : 9 ( 5 avg)
% Number of connectives : 4417 ( 827 ~; 781 |; 52 &;2668 @)
% ( 12 <=>; 77 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 38 ( 35 usr; 15 con; 0-4 aty)
% Number of variables : 852 ( 0 ^; 852 !; 0 ?; 852 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a_select2,type,
a_select2: $i > $i > $i ).
thf(tp_a_select3,type,
a_select3: $i > $i > $i > $i ).
thf(tp_def,type,
def: $i ).
thf(tp_dim,type,
dim: $i > $i > $i ).
thf(tp_geq,type,
geq: $i > $i > $o ).
thf(tp_gt,type,
gt: $i > $i > $o ).
thf(tp_inv,type,
inv: $i > $i ).
thf(tp_leq,type,
leq: $i > $i > $o ).
thf(tp_lt,type,
lt: $i > $i > $o ).
thf(tp_minus,type,
minus: $i > $i > $i ).
thf(tp_n0,type,
n0: $i ).
thf(tp_n1,type,
n1: $i ).
thf(tp_n2,type,
n2: $i ).
thf(tp_n3,type,
n3: $i ).
thf(tp_n4,type,
n4: $i ).
thf(tp_n5,type,
n5: $i ).
thf(tp_plus,type,
plus: $i > $i > $i ).
thf(tp_pred,type,
pred: $i > $i ).
thf(tp_pv31,type,
pv31: $i ).
thf(tp_pv40,type,
pv40: $i ).
thf(tp_succ,type,
succ: $i > $i ).
thf(tp_sum,type,
sum: $i > $i > $i > $i ).
thf(tp_tptp_const_array1,type,
tptp_const_array1: $i > $i > $i ).
thf(tp_tptp_const_array2,type,
tptp_const_array2: $i > $i > $i > $i ).
thf(tp_tptp_float_0_0,type,
tptp_float_0_0: $i ).
thf(tp_tptp_madd,type,
tptp_madd: $i > $i > $i ).
thf(tp_tptp_minus_1,type,
tptp_minus_1: $i ).
thf(tp_tptp_mmul,type,
tptp_mmul: $i > $i > $i ).
thf(tp_tptp_msub,type,
tptp_msub: $i > $i > $i ).
thf(tp_tptp_update2,type,
tptp_update2: $i > $i > $i > $i ).
thf(tp_tptp_update3,type,
tptp_update3: $i > $i > $i > $i > $i ).
thf(tp_trans,type,
trans: $i > $i ).
thf(tp_true,type,
true: $o ).
thf(tp_uniform_int_rnd,type,
uniform_int_rnd: $i > $i > $i ).
thf(tp_use,type,
use: $i ).
thf(3,axiom,
( ( succ @ n0 )
= n1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_1) ).
thf(4,axiom,
( ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ n0 ) ) ) ) )
= n5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_5) ).
thf(7,axiom,
! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n2 ) )
=> ( ( X = n0 )
| ( X = n1 )
| ( X = n2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',finite_domain_2) ).
thf(8,axiom,
! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n1 ) )
=> ( ( X = n0 )
| ( X = n1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',finite_domain_1) ).
thf(9,axiom,
! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n0 ) )
=> ( X = n0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',finite_domain_0) ).
thf(19,axiom,
gt @ n5 @ n1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_5_1) ).
thf(23,axiom,
gt @ n1 @ n0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_1_0) ).
thf(24,axiom,
gt @ n5 @ n0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_5_0) ).
thf(34,axiom,
true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ttrue) ).
thf(41,axiom,
! [X: $i,Y: $i] :
( ( leq @ ( minus @ X @ Y ) @ X )
=> ( leq @ n0 @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_minus) ).
thf(43,axiom,
! [X: $i,Y: $i] :
( ( leq @ ( succ @ X ) @ ( succ @ Y ) )
<=> ( leq @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_succ_succ) ).
thf(46,axiom,
! [X: $i] :
( ( minus @ X @ n1 )
= ( pred @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pred_minus_1) ).
thf(70,axiom,
! [X: $i,C: $i] :
( ( leq @ n0 @ X )
=> ( leq @ n0 @ ( uniform_int_rnd @ C @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniform_int_rand_ranges_lo) ).
thf(71,axiom,
! [X: $i,C: $i] :
( ( leq @ n0 @ X )
=> ( leq @ ( uniform_int_rnd @ C @ X ) @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniform_int_rand_ranges_hi) ).
thf(73,axiom,
! [X: $i,Y: $i] :
( ( leq @ X @ Y )
=> ( leq @ X @ ( succ @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_succ) ).
thf(76,axiom,
! [X: $i,Y: $i] :
( ( ( leq @ X @ Y )
& ( X != Y ) )
=> ( gt @ Y @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_gt2) ).
thf(77,axiom,
! [X: $i,Y: $i] :
( ( gt @ Y @ X )
=> ( leq @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_gt1) ).
thf(78,axiom,
! [X: $i,Y: $i] :
( ( geq @ X @ Y )
<=> ( leq @ Y @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_geq) ).
thf(80,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( ( leq @ X @ Y )
& ( leq @ Y @ Z ) )
=> ( leq @ X @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_leq) ).
thf(81,axiom,
! [X: $i] : ( leq @ X @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_leq) ).
thf(85,conjecture,
( ( ( leq @ n0 @ pv31 )
& ( leq @ pv31 @ ( minus @ n5 @ n1 ) ) )
=> ( ( leq @ n0 @ pv31 )
& ( leq @ pv31 @ ( minus @ n5 @ n1 ) )
& ( ( n0 != pv40 )
=> ( ( leq @ n0 @ pv31 )
& ( leq @ pv31 @ ( minus @ n5 @ n1 ) ) ) )
& ( ( n0 = pv40 )
=> true ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cl5_nebula_array_0018) ).
thf(86,negated_conjecture,
( ( ( ( leq @ n0 @ pv31 )
& ( leq @ pv31 @ ( minus @ n5 @ n1 ) ) )
=> ( ( leq @ n0 @ pv31 )
& ( leq @ pv31 @ ( minus @ n5 @ n1 ) )
& ( ( n0 != pv40 )
=> ( ( leq @ n0 @ pv31 )
& ( leq @ pv31 @ ( minus @ n5 @ n1 ) ) ) )
& ( ( n0 = pv40 )
=> true ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[85]) ).
thf(87,plain,
( ( ( ( leq @ n0 @ pv31 )
& ( leq @ pv31 @ ( minus @ n5 @ n1 ) ) )
=> ( ( leq @ n0 @ pv31 )
& ( leq @ pv31 @ ( minus @ n5 @ n1 ) )
& ( ( n0 != pv40 )
=> ( ( leq @ n0 @ pv31 )
& ( leq @ pv31 @ ( minus @ n5 @ n1 ) ) ) )
& ( ( n0 = pv40 )
=> true ) ) )
= $false ),
inference(unfold_def,[status(thm)],[86]) ).
thf(88,plain,
( ( ( succ @ n0 )
= n1 )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(89,plain,
( ( ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ n0 ) ) ) ) )
= n5 )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(90,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n2 ) )
=> ( ( X = n0 )
| ( X = n1 )
| ( X = n2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(91,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n1 ) )
=> ( ( X = n0 )
| ( X = n1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(92,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n0 ) )
=> ( X = n0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(93,plain,
( ( gt @ n5 @ n1 )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(94,plain,
( ( gt @ n1 @ n0 )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(95,plain,
( ( gt @ n5 @ n0 )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(96,plain,
true = $true,
inference(unfold_def,[status(thm)],[34]) ).
thf(97,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ ( minus @ X @ Y ) @ X )
=> ( leq @ n0 @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(98,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ ( succ @ X ) @ ( succ @ Y ) )
<=> ( leq @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(99,plain,
( ( ! [X: $i] :
( ( minus @ X @ n1 )
= ( pred @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(100,plain,
( ( ! [X: $i,C: $i] :
( ( leq @ n0 @ X )
=> ( leq @ n0 @ ( uniform_int_rnd @ C @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(101,plain,
( ( ! [X: $i,C: $i] :
( ( leq @ n0 @ X )
=> ( leq @ ( uniform_int_rnd @ C @ X ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(102,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ X @ Y )
=> ( leq @ X @ ( succ @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(103,plain,
( ( ! [X: $i,Y: $i] :
( ( ( leq @ X @ Y )
& ( X != Y ) )
=> ( gt @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(104,plain,
( ( ! [X: $i,Y: $i] :
( ( gt @ Y @ X )
=> ( leq @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(105,plain,
( ( ! [X: $i,Y: $i] :
( ( geq @ X @ Y )
<=> ( leq @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(106,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( leq @ X @ Y )
& ( leq @ Y @ Z ) )
=> ( leq @ X @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(107,plain,
( ( ! [X: $i] : ( leq @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(108,plain,
( ( leq @ n0 @ pv31 )
= $true ),
inference(standard_cnf,[status(thm)],[87]) ).
thf(109,plain,
( ( leq @ pv31 @ ( minus @ n5 @ n1 ) )
= $true ),
inference(standard_cnf,[status(thm)],[87]) ).
thf(110,plain,
( ( ( leq @ n0 @ pv31 )
& ( leq @ pv31 @ ( minus @ n5 @ n1 ) )
& ( ( n0 != pv40 )
=> ( ( leq @ n0 @ pv31 )
& ( leq @ pv31 @ ( minus @ n5 @ n1 ) ) ) )
& ( ( n0 = pv40 )
=> true ) )
= $false ),
inference(standard_cnf,[status(thm)],[87]) ).
thf(111,plain,
( ( leq @ n0 @ pv31 )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[110]) ).
thf(112,plain,
( ( leq @ pv31 @ ( minus @ n5 @ n1 ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[110]) ).
thf(113,plain,
( ( ( n0 != pv40 )
=> ( ( leq @ n0 @ pv31 )
& ( leq @ pv31 @ ( minus @ n5 @ n1 ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[110]) ).
thf(114,plain,
( ( ( n0 = pv40 )
=> true )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[110]) ).
thf(115,plain,
( ( ~ ( leq @ n0 @ pv31 ) )
= $true ),
inference(polarity_switch,[status(thm)],[111]) ).
thf(116,plain,
( ( ~ ( leq @ pv31 @ ( minus @ n5 @ n1 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[112]) ).
thf(117,plain,
( ( ~ ( ( n0 != pv40 )
=> ( ( leq @ n0 @ pv31 )
& ( leq @ pv31 @ ( minus @ n5 @ n1 ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[113]) ).
thf(118,plain,
( ( ~ ( ( n0 = pv40 )
=> true ) )
= $true ),
inference(polarity_switch,[status(thm)],[114]) ).
thf(119,plain,
( ( ! [X: $i] : ( leq @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(120,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( leq @ X @ Y )
& ( leq @ Y @ Z ) )
=> ( leq @ X @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(121,plain,
( ( ! [X: $i,Y: $i] :
( ( geq @ X @ Y )
<=> ( leq @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(122,plain,
( ( ! [X: $i,Y: $i] :
( ( gt @ Y @ X )
=> ( leq @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(123,plain,
( ( ! [X: $i,Y: $i] :
( ( ( leq @ X @ Y )
& ( X != Y ) )
=> ( gt @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(124,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ X @ Y )
=> ( leq @ X @ ( succ @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(125,plain,
( ( ! [X: $i,C: $i] :
( ( leq @ n0 @ X )
=> ( leq @ ( uniform_int_rnd @ C @ X ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(126,plain,
( ( ! [X: $i,C: $i] :
( ( leq @ n0 @ X )
=> ( leq @ n0 @ ( uniform_int_rnd @ C @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(127,plain,
( ( ! [X: $i] :
( ( minus @ X @ n1 )
= ( pred @ X ) ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(128,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ ( succ @ X ) @ ( succ @ Y ) )
<=> ( leq @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(129,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ ( minus @ X @ Y ) @ X )
=> ( leq @ n0 @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(130,plain,
true = $true,
inference(copy,[status(thm)],[96]) ).
thf(131,plain,
( ( gt @ n5 @ n0 )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(132,plain,
( ( gt @ n1 @ n0 )
= $true ),
inference(copy,[status(thm)],[94]) ).
thf(133,plain,
( ( gt @ n5 @ n1 )
= $true ),
inference(copy,[status(thm)],[93]) ).
thf(134,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n0 ) )
=> ( X = n0 ) ) )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(135,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n1 ) )
=> ( ( X = n0 )
| ( X = n1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(136,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n2 ) )
=> ( ( X = n0 )
| ( X = n1 )
| ( X = n2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(137,plain,
( ( ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ n0 ) ) ) ) )
= n5 )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(138,plain,
( ( ( succ @ n0 )
= n1 )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(139,plain,
( ( leq @ pv31 @ ( minus @ n5 @ n1 ) )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(140,plain,
( ( leq @ n0 @ pv31 )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(141,plain,
( ( ~ ( leq @ n0 @ pv31 ) )
= $true ),
inference(copy,[status(thm)],[115]) ).
thf(142,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( leq @ SX0 @ SX1 )
| ~ ( ( SX0 != SX1 ) ) )
| ( gt @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[123]) ).
thf(143,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( leq @ n0 @ SX0 )
| ~ ( leq @ SX0 @ n0 ) )
| ( SX0 = n0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[134]) ).
thf(144,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( leq @ ( succ @ SX0 ) @ ( succ @ SX1 ) )
| ( leq @ SX0 @ SX1 ) )
| ~ ( ~ ( leq @ SX0 @ SX1 )
| ( leq @ ( succ @ SX0 ) @ ( succ @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[128]) ).
thf(145,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ ( minus @ SX0 @ SX1 ) @ SX0 )
| ( leq @ n0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[129]) ).
thf(146,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ n0 @ SX0 )
| ( leq @ n0 @ ( uniform_int_rnd @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[126]) ).
thf(147,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( leq @ n0 @ SX0 )
| ~ ( leq @ SX0 @ n2 ) )
| ( SX0 = n0 )
| ( SX0 = n1 )
| ( SX0 = n2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[136]) ).
thf(148,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( leq @ SX0 @ SX1 )
| ~ ( leq @ SX1 @ SX2 ) )
| ( leq @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[120]) ).
thf(149,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ n0 @ SX0 )
| ( leq @ ( uniform_int_rnd @ SX1 @ SX0 ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[125]) ).
thf(150,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( leq @ n0 @ SX0 )
| ~ ( leq @ SX0 @ n1 ) )
| ( SX0 = n0 )
| ( SX0 = n1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[135]) ).
thf(151,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( gt @ SX1 @ SX0 )
| ( leq @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[122]) ).
thf(152,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX0 @ SX1 )
| ( leq @ SX0 @ ( succ @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[124]) ).
thf(153,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( geq @ SX0 @ SX1 )
| ( leq @ SX1 @ SX0 ) )
| ~ ( ~ ( leq @ SX1 @ SX0 )
| ( geq @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[121]) ).
thf(154,plain,
! [SV1: $i] :
( ( leq @ SV1 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(155,plain,
! [SV2: $i] :
( ( ( minus @ SV2 @ n1 )
= ( pred @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(156,plain,
( ( leq @ n0 @ pv31 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(157,plain,
! [SV3: $i] :
( ( ! [SY24: $i] :
( ~ ~ ( ~ ( leq @ SV3 @ SY24 )
| ~ ( ( SV3 != SY24 ) ) )
| ( gt @ SY24 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(158,plain,
! [SV4: $i] :
( ( ~ ~ ( ~ ( leq @ n0 @ SV4 )
| ~ ( leq @ SV4 @ n0 ) )
| ( SV4 = n0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(159,plain,
! [SV5: $i] :
( ( ! [SY25: $i] :
~ ( ~ ( ~ ( leq @ ( succ @ SV5 ) @ ( succ @ SY25 ) )
| ( leq @ SV5 @ SY25 ) )
| ~ ( ~ ( leq @ SV5 @ SY25 )
| ( leq @ ( succ @ SV5 ) @ ( succ @ SY25 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(160,plain,
! [SV6: $i] :
( ( ! [SY26: $i] :
( ~ ( leq @ ( minus @ SV6 @ SY26 ) @ SV6 )
| ( leq @ n0 @ SY26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(161,plain,
! [SV7: $i] :
( ( ! [SY27: $i] :
( ~ ( leq @ n0 @ SV7 )
| ( leq @ n0 @ ( uniform_int_rnd @ SY27 @ SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(162,plain,
! [SV8: $i] :
( ( ~ ~ ( ~ ( leq @ n0 @ SV8 )
| ~ ( leq @ SV8 @ n2 ) )
| ( SV8 = n0 )
| ( SV8 = n1 )
| ( SV8 = n2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(163,plain,
! [SV9: $i] :
( ( ! [SY28: $i,SY29: $i] :
( ~ ~ ( ~ ( leq @ SV9 @ SY28 )
| ~ ( leq @ SY28 @ SY29 ) )
| ( leq @ SV9 @ SY29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(164,plain,
! [SV10: $i] :
( ( ! [SY30: $i] :
( ~ ( leq @ n0 @ SV10 )
| ( leq @ ( uniform_int_rnd @ SY30 @ SV10 ) @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(165,plain,
! [SV11: $i] :
( ( ~ ~ ( ~ ( leq @ n0 @ SV11 )
| ~ ( leq @ SV11 @ n1 ) )
| ( SV11 = n0 )
| ( SV11 = n1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(166,plain,
! [SV12: $i] :
( ( ! [SY31: $i] :
( ~ ( gt @ SY31 @ SV12 )
| ( leq @ SV12 @ SY31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(167,plain,
! [SV13: $i] :
( ( ! [SY32: $i] :
( ~ ( leq @ SV13 @ SY32 )
| ( leq @ SV13 @ ( succ @ SY32 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(168,plain,
! [SV14: $i] :
( ( ! [SY33: $i] :
~ ( ~ ( ~ ( geq @ SV14 @ SY33 )
| ( leq @ SY33 @ SV14 ) )
| ~ ( ~ ( leq @ SY33 @ SV14 )
| ( geq @ SV14 @ SY33 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(169,plain,
! [SV15: $i,SV3: $i] :
( ( ~ ~ ( ~ ( leq @ SV3 @ SV15 )
| ~ ( ( SV3 != SV15 ) ) )
| ( gt @ SV15 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(170,plain,
! [SV4: $i] :
( ( ( ~ ~ ( ~ ( leq @ n0 @ SV4 )
| ~ ( leq @ SV4 @ n0 ) ) )
= $true )
| ( ( SV4 = n0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[158]) ).
thf(171,plain,
! [SV16: $i,SV5: $i] :
( ( ~ ( ~ ( ~ ( leq @ ( succ @ SV5 ) @ ( succ @ SV16 ) )
| ( leq @ SV5 @ SV16 ) )
| ~ ( ~ ( leq @ SV5 @ SV16 )
| ( leq @ ( succ @ SV5 ) @ ( succ @ SV16 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(172,plain,
! [SV17: $i,SV6: $i] :
( ( ~ ( leq @ ( minus @ SV6 @ SV17 ) @ SV6 )
| ( leq @ n0 @ SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(173,plain,
! [SV18: $i,SV7: $i] :
( ( ~ ( leq @ n0 @ SV7 )
| ( leq @ n0 @ ( uniform_int_rnd @ SV18 @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(174,plain,
! [SV8: $i] :
( ( ( ~ ~ ( ~ ( leq @ n0 @ SV8 )
| ~ ( leq @ SV8 @ n2 ) ) )
= $true )
| ( ( ( SV8 = n0 )
| ( SV8 = n1 )
| ( SV8 = n2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[162]) ).
thf(175,plain,
! [SV19: $i,SV9: $i] :
( ( ! [SY34: $i] :
( ~ ~ ( ~ ( leq @ SV9 @ SV19 )
| ~ ( leq @ SV19 @ SY34 ) )
| ( leq @ SV9 @ SY34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(176,plain,
! [SV20: $i,SV10: $i] :
( ( ~ ( leq @ n0 @ SV10 )
| ( leq @ ( uniform_int_rnd @ SV20 @ SV10 ) @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(177,plain,
! [SV11: $i] :
( ( ( ~ ~ ( ~ ( leq @ n0 @ SV11 )
| ~ ( leq @ SV11 @ n1 ) ) )
= $true )
| ( ( ( SV11 = n0 )
| ( SV11 = n1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[165]) ).
thf(178,plain,
! [SV12: $i,SV21: $i] :
( ( ~ ( gt @ SV21 @ SV12 )
| ( leq @ SV12 @ SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(179,plain,
! [SV22: $i,SV13: $i] :
( ( ~ ( leq @ SV13 @ SV22 )
| ( leq @ SV13 @ ( succ @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(180,plain,
! [SV23: $i,SV14: $i] :
( ( ~ ( ~ ( ~ ( geq @ SV14 @ SV23 )
| ( leq @ SV23 @ SV14 ) )
| ~ ( ~ ( leq @ SV23 @ SV14 )
| ( geq @ SV14 @ SV23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(181,plain,
! [SV15: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( leq @ SV3 @ SV15 )
| ~ ( ( SV3 != SV15 ) ) ) )
= $true )
| ( ( gt @ SV15 @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[169]) ).
thf(182,plain,
! [SV4: $i] :
( ( ( ~ ( ~ ( leq @ n0 @ SV4 )
| ~ ( leq @ SV4 @ n0 ) ) )
= $false )
| ( ( SV4 = n0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(183,plain,
! [SV16: $i,SV5: $i] :
( ( ~ ( ~ ( leq @ ( succ @ SV5 ) @ ( succ @ SV16 ) )
| ( leq @ SV5 @ SV16 ) )
| ~ ( ~ ( leq @ SV5 @ SV16 )
| ( leq @ ( succ @ SV5 ) @ ( succ @ SV16 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(184,plain,
! [SV17: $i,SV6: $i] :
( ( ( ~ ( leq @ ( minus @ SV6 @ SV17 ) @ SV6 ) )
= $true )
| ( ( leq @ n0 @ SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[172]) ).
thf(185,plain,
! [SV18: $i,SV7: $i] :
( ( ( ~ ( leq @ n0 @ SV7 ) )
= $true )
| ( ( leq @ n0 @ ( uniform_int_rnd @ SV18 @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[173]) ).
thf(186,plain,
! [SV8: $i] :
( ( ( ~ ( ~ ( leq @ n0 @ SV8 )
| ~ ( leq @ SV8 @ n2 ) ) )
= $false )
| ( ( ( SV8 = n0 )
| ( SV8 = n1 )
| ( SV8 = n2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(187,plain,
! [SV24: $i,SV19: $i,SV9: $i] :
( ( ~ ~ ( ~ ( leq @ SV9 @ SV19 )
| ~ ( leq @ SV19 @ SV24 ) )
| ( leq @ SV9 @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(188,plain,
! [SV20: $i,SV10: $i] :
( ( ( ~ ( leq @ n0 @ SV10 ) )
= $true )
| ( ( leq @ ( uniform_int_rnd @ SV20 @ SV10 ) @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[176]) ).
thf(189,plain,
! [SV11: $i] :
( ( ( ~ ( ~ ( leq @ n0 @ SV11 )
| ~ ( leq @ SV11 @ n1 ) ) )
= $false )
| ( ( ( SV11 = n0 )
| ( SV11 = n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(190,plain,
! [SV12: $i,SV21: $i] :
( ( ( ~ ( gt @ SV21 @ SV12 ) )
= $true )
| ( ( leq @ SV12 @ SV21 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[178]) ).
thf(191,plain,
! [SV22: $i,SV13: $i] :
( ( ( ~ ( leq @ SV13 @ SV22 ) )
= $true )
| ( ( leq @ SV13 @ ( succ @ SV22 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[179]) ).
thf(192,plain,
! [SV23: $i,SV14: $i] :
( ( ~ ( ~ ( geq @ SV14 @ SV23 )
| ( leq @ SV23 @ SV14 ) )
| ~ ( ~ ( leq @ SV23 @ SV14 )
| ( geq @ SV14 @ SV23 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(193,plain,
! [SV15: $i,SV3: $i] :
( ( ( ~ ( ~ ( leq @ SV3 @ SV15 )
| ~ ( ( SV3 != SV15 ) ) ) )
= $false )
| ( ( gt @ SV15 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(194,plain,
! [SV4: $i] :
( ( ( ~ ( leq @ n0 @ SV4 )
| ~ ( leq @ SV4 @ n0 ) )
= $true )
| ( ( SV4 = n0 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[182]) ).
thf(195,plain,
! [SV16: $i,SV5: $i] :
( ( ~ ( ~ ( leq @ ( succ @ SV5 ) @ ( succ @ SV16 ) )
| ( leq @ SV5 @ SV16 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[183]) ).
thf(196,plain,
! [SV16: $i,SV5: $i] :
( ( ~ ( ~ ( leq @ SV5 @ SV16 )
| ( leq @ ( succ @ SV5 ) @ ( succ @ SV16 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[183]) ).
thf(197,plain,
! [SV17: $i,SV6: $i] :
( ( ( leq @ ( minus @ SV6 @ SV17 ) @ SV6 )
= $false )
| ( ( leq @ n0 @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[184]) ).
thf(198,plain,
! [SV18: $i,SV7: $i] :
( ( ( leq @ n0 @ SV7 )
= $false )
| ( ( leq @ n0 @ ( uniform_int_rnd @ SV18 @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(199,plain,
! [SV8: $i] :
( ( ( ~ ( leq @ n0 @ SV8 )
| ~ ( leq @ SV8 @ n2 ) )
= $true )
| ( ( ( SV8 = n0 )
| ( SV8 = n1 )
| ( SV8 = n2 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[186]) ).
thf(200,plain,
! [SV24: $i,SV19: $i,SV9: $i] :
( ( ( ~ ~ ( ~ ( leq @ SV9 @ SV19 )
| ~ ( leq @ SV19 @ SV24 ) ) )
= $true )
| ( ( leq @ SV9 @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[187]) ).
thf(201,plain,
! [SV20: $i,SV10: $i] :
( ( ( leq @ n0 @ SV10 )
= $false )
| ( ( leq @ ( uniform_int_rnd @ SV20 @ SV10 ) @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[188]) ).
thf(202,plain,
! [SV11: $i] :
( ( ( ~ ( leq @ n0 @ SV11 )
| ~ ( leq @ SV11 @ n1 ) )
= $true )
| ( ( ( SV11 = n0 )
| ( SV11 = n1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[189]) ).
thf(203,plain,
! [SV12: $i,SV21: $i] :
( ( ( gt @ SV21 @ SV12 )
= $false )
| ( ( leq @ SV12 @ SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(204,plain,
! [SV22: $i,SV13: $i] :
( ( ( leq @ SV13 @ SV22 )
= $false )
| ( ( leq @ SV13 @ ( succ @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(205,plain,
! [SV23: $i,SV14: $i] :
( ( ~ ( ~ ( geq @ SV14 @ SV23 )
| ( leq @ SV23 @ SV14 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[192]) ).
thf(206,plain,
! [SV14: $i,SV23: $i] :
( ( ~ ( ~ ( leq @ SV23 @ SV14 )
| ( geq @ SV14 @ SV23 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[192]) ).
thf(207,plain,
! [SV15: $i,SV3: $i] :
( ( ( ~ ( leq @ SV3 @ SV15 )
| ~ ( ( SV3 != SV15 ) ) )
= $true )
| ( ( gt @ SV15 @ SV3 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[193]) ).
thf(208,plain,
! [SV4: $i] :
( ( ( ~ ( leq @ n0 @ SV4 ) )
= $true )
| ( ( ~ ( leq @ SV4 @ n0 ) )
= $true )
| ( ( SV4 = n0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[194]) ).
thf(209,plain,
! [SV16: $i,SV5: $i] :
( ( ~ ( leq @ ( succ @ SV5 ) @ ( succ @ SV16 ) )
| ( leq @ SV5 @ SV16 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[195]) ).
thf(210,plain,
! [SV16: $i,SV5: $i] :
( ( ~ ( leq @ SV5 @ SV16 )
| ( leq @ ( succ @ SV5 ) @ ( succ @ SV16 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[196]) ).
thf(211,plain,
! [SV8: $i] :
( ( ( ~ ( leq @ n0 @ SV8 ) )
= $true )
| ( ( ~ ( leq @ SV8 @ n2 ) )
= $true )
| ( ( ( SV8 = n0 )
| ( SV8 = n1 )
| ( SV8 = n2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[199]) ).
thf(212,plain,
! [SV24: $i,SV19: $i,SV9: $i] :
( ( ( ~ ( ~ ( leq @ SV9 @ SV19 )
| ~ ( leq @ SV19 @ SV24 ) ) )
= $false )
| ( ( leq @ SV9 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(213,plain,
! [SV11: $i] :
( ( ( ~ ( leq @ n0 @ SV11 ) )
= $true )
| ( ( ~ ( leq @ SV11 @ n1 ) )
= $true )
| ( ( ( SV11 = n0 )
| ( SV11 = n1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[202]) ).
thf(214,plain,
! [SV23: $i,SV14: $i] :
( ( ~ ( geq @ SV14 @ SV23 )
| ( leq @ SV23 @ SV14 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[205]) ).
thf(215,plain,
! [SV14: $i,SV23: $i] :
( ( ~ ( leq @ SV23 @ SV14 )
| ( geq @ SV14 @ SV23 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[206]) ).
thf(216,plain,
! [SV15: $i,SV3: $i] :
( ( ( ~ ( leq @ SV3 @ SV15 ) )
= $true )
| ( ( ~ ( ( SV3 != SV15 ) ) )
= $true )
| ( ( gt @ SV15 @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[207]) ).
thf(217,plain,
! [SV4: $i] :
( ( ( leq @ n0 @ SV4 )
= $false )
| ( ( ~ ( leq @ SV4 @ n0 ) )
= $true )
| ( ( SV4 = n0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[208]) ).
thf(218,plain,
! [SV16: $i,SV5: $i] :
( ( ( ~ ( leq @ ( succ @ SV5 ) @ ( succ @ SV16 ) ) )
= $true )
| ( ( leq @ SV5 @ SV16 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[209]) ).
thf(219,plain,
! [SV16: $i,SV5: $i] :
( ( ( ~ ( leq @ SV5 @ SV16 ) )
= $true )
| ( ( leq @ ( succ @ SV5 ) @ ( succ @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[210]) ).
thf(220,plain,
! [SV8: $i] :
( ( ( leq @ n0 @ SV8 )
= $false )
| ( ( ~ ( leq @ SV8 @ n2 ) )
= $true )
| ( ( ( SV8 = n0 )
| ( SV8 = n1 )
| ( SV8 = n2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[211]) ).
thf(221,plain,
! [SV24: $i,SV19: $i,SV9: $i] :
( ( ( ~ ( leq @ SV9 @ SV19 )
| ~ ( leq @ SV19 @ SV24 ) )
= $true )
| ( ( leq @ SV9 @ SV24 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[212]) ).
thf(222,plain,
! [SV11: $i] :
( ( ( leq @ n0 @ SV11 )
= $false )
| ( ( ~ ( leq @ SV11 @ n1 ) )
= $true )
| ( ( ( SV11 = n0 )
| ( SV11 = n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[213]) ).
thf(223,plain,
! [SV23: $i,SV14: $i] :
( ( ( ~ ( geq @ SV14 @ SV23 ) )
= $true )
| ( ( leq @ SV23 @ SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[214]) ).
thf(224,plain,
! [SV14: $i,SV23: $i] :
( ( ( ~ ( leq @ SV23 @ SV14 ) )
= $true )
| ( ( geq @ SV14 @ SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[215]) ).
thf(225,plain,
! [SV15: $i,SV3: $i] :
( ( ( leq @ SV3 @ SV15 )
= $false )
| ( ( ~ ( ( SV3 != SV15 ) ) )
= $true )
| ( ( gt @ SV15 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[216]) ).
thf(226,plain,
! [SV4: $i] :
( ( ( leq @ SV4 @ n0 )
= $false )
| ( ( leq @ n0 @ SV4 )
= $false )
| ( ( SV4 = n0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[217]) ).
thf(227,plain,
! [SV16: $i,SV5: $i] :
( ( ( leq @ ( succ @ SV5 ) @ ( succ @ SV16 ) )
= $false )
| ( ( leq @ SV5 @ SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[218]) ).
thf(228,plain,
! [SV16: $i,SV5: $i] :
( ( ( leq @ SV5 @ SV16 )
= $false )
| ( ( leq @ ( succ @ SV5 ) @ ( succ @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[219]) ).
thf(229,plain,
! [SV8: $i] :
( ( ( leq @ SV8 @ n2 )
= $false )
| ( ( leq @ n0 @ SV8 )
= $false )
| ( ( ( SV8 = n0 )
| ( SV8 = n1 )
| ( SV8 = n2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[220]) ).
thf(230,plain,
! [SV24: $i,SV19: $i,SV9: $i] :
( ( ( ~ ( leq @ SV9 @ SV19 ) )
= $true )
| ( ( ~ ( leq @ SV19 @ SV24 ) )
= $true )
| ( ( leq @ SV9 @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[221]) ).
thf(231,plain,
! [SV11: $i] :
( ( ( leq @ SV11 @ n1 )
= $false )
| ( ( leq @ n0 @ SV11 )
= $false )
| ( ( ( SV11 = n0 )
| ( SV11 = n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[222]) ).
thf(232,plain,
! [SV23: $i,SV14: $i] :
( ( ( geq @ SV14 @ SV23 )
= $false )
| ( ( leq @ SV23 @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[223]) ).
thf(233,plain,
! [SV14: $i,SV23: $i] :
( ( ( leq @ SV23 @ SV14 )
= $false )
| ( ( geq @ SV14 @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[224]) ).
thf(234,plain,
! [SV15: $i,SV3: $i] :
( ( ( SV3 != SV15 )
= $false )
| ( ( leq @ SV3 @ SV15 )
= $false )
| ( ( gt @ SV15 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[225]) ).
thf(235,plain,
! [SV8: $i] :
( ( ( ( SV8 = n0 )
| ( SV8 = n1 ) )
= $true )
| ( ( SV8 = n2 )
= $true )
| ( ( leq @ n0 @ SV8 )
= $false )
| ( ( leq @ SV8 @ n2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[229]) ).
thf(236,plain,
! [SV24: $i,SV19: $i,SV9: $i] :
( ( ( leq @ SV9 @ SV19 )
= $false )
| ( ( ~ ( leq @ SV19 @ SV24 ) )
= $true )
| ( ( leq @ SV9 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[230]) ).
thf(237,plain,
! [SV11: $i] :
( ( ( SV11 = n0 )
= $true )
| ( ( SV11 = n1 )
= $true )
| ( ( leq @ n0 @ SV11 )
= $false )
| ( ( leq @ SV11 @ n1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[231]) ).
thf(238,plain,
! [SV15: $i,SV3: $i] :
( ( ( SV3 = SV15 )
= $true )
| ( ( leq @ SV3 @ SV15 )
= $false )
| ( ( gt @ SV15 @ SV3 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[234]) ).
thf(239,plain,
! [SV8: $i] :
( ( ( SV8 = n0 )
= $true )
| ( ( SV8 = n1 )
= $true )
| ( ( SV8 = n2 )
= $true )
| ( ( leq @ n0 @ SV8 )
= $false )
| ( ( leq @ SV8 @ n2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[235]) ).
thf(240,plain,
! [SV9: $i,SV24: $i,SV19: $i] :
( ( ( leq @ SV19 @ SV24 )
= $false )
| ( ( leq @ SV9 @ SV19 )
= $false )
| ( ( leq @ SV9 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[236]) ).
thf(241,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[130,240,239,238,237,233,232,228,227,226,204,203,201,198,197,156,155,154,140,139,138,137,133,132,131]) ).
thf(242,plain,
( ( ! [X: $i] : ( leq @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(243,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( leq @ X @ Y )
& ( leq @ Y @ Z ) )
=> ( leq @ X @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(244,plain,
( ( ! [X: $i,Y: $i] :
( ( geq @ X @ Y )
<=> ( leq @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(245,plain,
( ( ! [X: $i,Y: $i] :
( ( gt @ Y @ X )
=> ( leq @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(246,plain,
( ( ! [X: $i,Y: $i] :
( ( ( leq @ X @ Y )
& ( X != Y ) )
=> ( gt @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(247,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ X @ Y )
=> ( leq @ X @ ( succ @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(248,plain,
( ( ! [X: $i,C: $i] :
( ( leq @ n0 @ X )
=> ( leq @ ( uniform_int_rnd @ C @ X ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(249,plain,
( ( ! [X: $i,C: $i] :
( ( leq @ n0 @ X )
=> ( leq @ n0 @ ( uniform_int_rnd @ C @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(250,plain,
( ( ! [X: $i] :
( ( minus @ X @ n1 )
= ( pred @ X ) ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(251,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ ( succ @ X ) @ ( succ @ Y ) )
<=> ( leq @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(252,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ ( minus @ X @ Y ) @ X )
=> ( leq @ n0 @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(253,plain,
true = $true,
inference(copy,[status(thm)],[96]) ).
thf(254,plain,
( ( gt @ n5 @ n0 )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(255,plain,
( ( gt @ n1 @ n0 )
= $true ),
inference(copy,[status(thm)],[94]) ).
thf(256,plain,
( ( gt @ n5 @ n1 )
= $true ),
inference(copy,[status(thm)],[93]) ).
thf(257,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n0 ) )
=> ( X = n0 ) ) )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(258,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n1 ) )
=> ( ( X = n0 )
| ( X = n1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(259,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n2 ) )
=> ( ( X = n0 )
| ( X = n1 )
| ( X = n2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(260,plain,
( ( ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ n0 ) ) ) ) )
= n5 )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(261,plain,
( ( ( succ @ n0 )
= n1 )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(262,plain,
( ( leq @ pv31 @ ( minus @ n5 @ n1 ) )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(263,plain,
( ( leq @ n0 @ pv31 )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(264,plain,
( ( ~ ( leq @ pv31 @ ( minus @ n5 @ n1 ) ) )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(265,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ n0 @ SX0 )
| ( leq @ ( uniform_int_rnd @ SX1 @ SX0 ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[248]) ).
thf(266,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( leq @ SX0 @ SX1 )
| ~ ( leq @ SX1 @ SX2 ) )
| ( leq @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[243]) ).
thf(267,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( geq @ SX0 @ SX1 )
| ( leq @ SX1 @ SX0 ) )
| ~ ( ~ ( leq @ SX1 @ SX0 )
| ( geq @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[244]) ).
thf(268,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( leq @ n0 @ SX0 )
| ~ ( leq @ SX0 @ n2 ) )
| ( SX0 = n0 )
| ( SX0 = n1 )
| ( SX0 = n2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[259]) ).
thf(269,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( leq @ n0 @ SX0 )
| ~ ( leq @ SX0 @ n1 ) )
| ( SX0 = n0 )
| ( SX0 = n1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[258]) ).
thf(270,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ ( minus @ SX0 @ SX1 ) @ SX0 )
| ( leq @ n0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[252]) ).
thf(271,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ n0 @ SX0 )
| ( leq @ n0 @ ( uniform_int_rnd @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[249]) ).
thf(272,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( leq @ n0 @ SX0 )
| ~ ( leq @ SX0 @ n0 ) )
| ( SX0 = n0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[257]) ).
thf(273,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( gt @ SX1 @ SX0 )
| ( leq @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[245]) ).
thf(274,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( leq @ ( succ @ SX0 ) @ ( succ @ SX1 ) )
| ( leq @ SX0 @ SX1 ) )
| ~ ( ~ ( leq @ SX0 @ SX1 )
| ( leq @ ( succ @ SX0 ) @ ( succ @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[251]) ).
thf(275,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX0 @ SX1 )
| ( leq @ SX0 @ ( succ @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[247]) ).
thf(276,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( leq @ SX0 @ SX1 )
| ~ ( ( SX0 != SX1 ) ) )
| ( gt @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[246]) ).
thf(277,plain,
! [SV25: $i] :
( ( leq @ SV25 @ SV25 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[242]) ).
thf(278,plain,
! [SV26: $i] :
( ( ( minus @ SV26 @ n1 )
= ( pred @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[250]) ).
thf(279,plain,
( ( leq @ pv31 @ ( minus @ n5 @ n1 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[264]) ).
thf(280,plain,
! [SV27: $i] :
( ( ! [SY35: $i] :
( ~ ( leq @ n0 @ SV27 )
| ( leq @ ( uniform_int_rnd @ SY35 @ SV27 ) @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[265]) ).
thf(281,plain,
! [SV28: $i] :
( ( ! [SY36: $i,SY37: $i] :
( ~ ~ ( ~ ( leq @ SV28 @ SY36 )
| ~ ( leq @ SY36 @ SY37 ) )
| ( leq @ SV28 @ SY37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[266]) ).
thf(282,plain,
! [SV29: $i] :
( ( ! [SY38: $i] :
~ ( ~ ( ~ ( geq @ SV29 @ SY38 )
| ( leq @ SY38 @ SV29 ) )
| ~ ( ~ ( leq @ SY38 @ SV29 )
| ( geq @ SV29 @ SY38 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[267]) ).
thf(283,plain,
! [SV30: $i] :
( ( ~ ~ ( ~ ( leq @ n0 @ SV30 )
| ~ ( leq @ SV30 @ n2 ) )
| ( SV30 = n0 )
| ( SV30 = n1 )
| ( SV30 = n2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[268]) ).
thf(284,plain,
! [SV31: $i] :
( ( ~ ~ ( ~ ( leq @ n0 @ SV31 )
| ~ ( leq @ SV31 @ n1 ) )
| ( SV31 = n0 )
| ( SV31 = n1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[269]) ).
thf(285,plain,
! [SV32: $i] :
( ( ! [SY39: $i] :
( ~ ( leq @ ( minus @ SV32 @ SY39 ) @ SV32 )
| ( leq @ n0 @ SY39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[270]) ).
thf(286,plain,
! [SV33: $i] :
( ( ! [SY40: $i] :
( ~ ( leq @ n0 @ SV33 )
| ( leq @ n0 @ ( uniform_int_rnd @ SY40 @ SV33 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[271]) ).
thf(287,plain,
! [SV34: $i] :
( ( ~ ~ ( ~ ( leq @ n0 @ SV34 )
| ~ ( leq @ SV34 @ n0 ) )
| ( SV34 = n0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[272]) ).
thf(288,plain,
! [SV35: $i] :
( ( ! [SY41: $i] :
( ~ ( gt @ SY41 @ SV35 )
| ( leq @ SV35 @ SY41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[273]) ).
thf(289,plain,
! [SV36: $i] :
( ( ! [SY42: $i] :
~ ( ~ ( ~ ( leq @ ( succ @ SV36 ) @ ( succ @ SY42 ) )
| ( leq @ SV36 @ SY42 ) )
| ~ ( ~ ( leq @ SV36 @ SY42 )
| ( leq @ ( succ @ SV36 ) @ ( succ @ SY42 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[274]) ).
thf(290,plain,
! [SV37: $i] :
( ( ! [SY43: $i] :
( ~ ( leq @ SV37 @ SY43 )
| ( leq @ SV37 @ ( succ @ SY43 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[275]) ).
thf(291,plain,
! [SV38: $i] :
( ( ! [SY44: $i] :
( ~ ~ ( ~ ( leq @ SV38 @ SY44 )
| ~ ( ( SV38 != SY44 ) ) )
| ( gt @ SY44 @ SV38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[276]) ).
thf(292,plain,
! [SV39: $i,SV27: $i] :
( ( ~ ( leq @ n0 @ SV27 )
| ( leq @ ( uniform_int_rnd @ SV39 @ SV27 ) @ SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[280]) ).
thf(293,plain,
! [SV40: $i,SV28: $i] :
( ( ! [SY45: $i] :
( ~ ~ ( ~ ( leq @ SV28 @ SV40 )
| ~ ( leq @ SV40 @ SY45 ) )
| ( leq @ SV28 @ SY45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[281]) ).
thf(294,plain,
! [SV41: $i,SV29: $i] :
( ( ~ ( ~ ( ~ ( geq @ SV29 @ SV41 )
| ( leq @ SV41 @ SV29 ) )
| ~ ( ~ ( leq @ SV41 @ SV29 )
| ( geq @ SV29 @ SV41 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[282]) ).
thf(295,plain,
! [SV30: $i] :
( ( ( ~ ~ ( ~ ( leq @ n0 @ SV30 )
| ~ ( leq @ SV30 @ n2 ) ) )
= $true )
| ( ( ( SV30 = n0 )
| ( SV30 = n1 )
| ( SV30 = n2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[283]) ).
thf(296,plain,
! [SV31: $i] :
( ( ( ~ ~ ( ~ ( leq @ n0 @ SV31 )
| ~ ( leq @ SV31 @ n1 ) ) )
= $true )
| ( ( ( SV31 = n0 )
| ( SV31 = n1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[284]) ).
thf(297,plain,
! [SV42: $i,SV32: $i] :
( ( ~ ( leq @ ( minus @ SV32 @ SV42 ) @ SV32 )
| ( leq @ n0 @ SV42 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[285]) ).
thf(298,plain,
! [SV43: $i,SV33: $i] :
( ( ~ ( leq @ n0 @ SV33 )
| ( leq @ n0 @ ( uniform_int_rnd @ SV43 @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[286]) ).
thf(299,plain,
! [SV34: $i] :
( ( ( ~ ~ ( ~ ( leq @ n0 @ SV34 )
| ~ ( leq @ SV34 @ n0 ) ) )
= $true )
| ( ( SV34 = n0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[287]) ).
thf(300,plain,
! [SV35: $i,SV44: $i] :
( ( ~ ( gt @ SV44 @ SV35 )
| ( leq @ SV35 @ SV44 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[288]) ).
thf(301,plain,
! [SV45: $i,SV36: $i] :
( ( ~ ( ~ ( ~ ( leq @ ( succ @ SV36 ) @ ( succ @ SV45 ) )
| ( leq @ SV36 @ SV45 ) )
| ~ ( ~ ( leq @ SV36 @ SV45 )
| ( leq @ ( succ @ SV36 ) @ ( succ @ SV45 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[289]) ).
thf(302,plain,
! [SV46: $i,SV37: $i] :
( ( ~ ( leq @ SV37 @ SV46 )
| ( leq @ SV37 @ ( succ @ SV46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[290]) ).
thf(303,plain,
! [SV47: $i,SV38: $i] :
( ( ~ ~ ( ~ ( leq @ SV38 @ SV47 )
| ~ ( ( SV38 != SV47 ) ) )
| ( gt @ SV47 @ SV38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[291]) ).
thf(304,plain,
! [SV39: $i,SV27: $i] :
( ( ( ~ ( leq @ n0 @ SV27 ) )
= $true )
| ( ( leq @ ( uniform_int_rnd @ SV39 @ SV27 ) @ SV27 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[292]) ).
thf(305,plain,
! [SV48: $i,SV40: $i,SV28: $i] :
( ( ~ ~ ( ~ ( leq @ SV28 @ SV40 )
| ~ ( leq @ SV40 @ SV48 ) )
| ( leq @ SV28 @ SV48 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[293]) ).
thf(306,plain,
! [SV41: $i,SV29: $i] :
( ( ~ ( ~ ( geq @ SV29 @ SV41 )
| ( leq @ SV41 @ SV29 ) )
| ~ ( ~ ( leq @ SV41 @ SV29 )
| ( geq @ SV29 @ SV41 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[294]) ).
thf(307,plain,
! [SV30: $i] :
( ( ( ~ ( ~ ( leq @ n0 @ SV30 )
| ~ ( leq @ SV30 @ n2 ) ) )
= $false )
| ( ( ( SV30 = n0 )
| ( SV30 = n1 )
| ( SV30 = n2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[295]) ).
thf(308,plain,
! [SV31: $i] :
( ( ( ~ ( ~ ( leq @ n0 @ SV31 )
| ~ ( leq @ SV31 @ n1 ) ) )
= $false )
| ( ( ( SV31 = n0 )
| ( SV31 = n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[296]) ).
thf(309,plain,
! [SV42: $i,SV32: $i] :
( ( ( ~ ( leq @ ( minus @ SV32 @ SV42 ) @ SV32 ) )
= $true )
| ( ( leq @ n0 @ SV42 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[297]) ).
thf(310,plain,
! [SV43: $i,SV33: $i] :
( ( ( ~ ( leq @ n0 @ SV33 ) )
= $true )
| ( ( leq @ n0 @ ( uniform_int_rnd @ SV43 @ SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[298]) ).
thf(311,plain,
! [SV34: $i] :
( ( ( ~ ( ~ ( leq @ n0 @ SV34 )
| ~ ( leq @ SV34 @ n0 ) ) )
= $false )
| ( ( SV34 = n0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[299]) ).
thf(312,plain,
! [SV35: $i,SV44: $i] :
( ( ( ~ ( gt @ SV44 @ SV35 ) )
= $true )
| ( ( leq @ SV35 @ SV44 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[300]) ).
thf(313,plain,
! [SV45: $i,SV36: $i] :
( ( ~ ( ~ ( leq @ ( succ @ SV36 ) @ ( succ @ SV45 ) )
| ( leq @ SV36 @ SV45 ) )
| ~ ( ~ ( leq @ SV36 @ SV45 )
| ( leq @ ( succ @ SV36 ) @ ( succ @ SV45 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[301]) ).
thf(314,plain,
! [SV46: $i,SV37: $i] :
( ( ( ~ ( leq @ SV37 @ SV46 ) )
= $true )
| ( ( leq @ SV37 @ ( succ @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[302]) ).
thf(315,plain,
! [SV47: $i,SV38: $i] :
( ( ( ~ ~ ( ~ ( leq @ SV38 @ SV47 )
| ~ ( ( SV38 != SV47 ) ) ) )
= $true )
| ( ( gt @ SV47 @ SV38 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[303]) ).
thf(316,plain,
! [SV39: $i,SV27: $i] :
( ( ( leq @ n0 @ SV27 )
= $false )
| ( ( leq @ ( uniform_int_rnd @ SV39 @ SV27 ) @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[304]) ).
thf(317,plain,
! [SV48: $i,SV40: $i,SV28: $i] :
( ( ( ~ ~ ( ~ ( leq @ SV28 @ SV40 )
| ~ ( leq @ SV40 @ SV48 ) ) )
= $true )
| ( ( leq @ SV28 @ SV48 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[305]) ).
thf(318,plain,
! [SV41: $i,SV29: $i] :
( ( ~ ( ~ ( geq @ SV29 @ SV41 )
| ( leq @ SV41 @ SV29 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[306]) ).
thf(319,plain,
! [SV29: $i,SV41: $i] :
( ( ~ ( ~ ( leq @ SV41 @ SV29 )
| ( geq @ SV29 @ SV41 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[306]) ).
thf(320,plain,
! [SV30: $i] :
( ( ( ~ ( leq @ n0 @ SV30 )
| ~ ( leq @ SV30 @ n2 ) )
= $true )
| ( ( ( SV30 = n0 )
| ( SV30 = n1 )
| ( SV30 = n2 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[307]) ).
thf(321,plain,
! [SV31: $i] :
( ( ( ~ ( leq @ n0 @ SV31 )
| ~ ( leq @ SV31 @ n1 ) )
= $true )
| ( ( ( SV31 = n0 )
| ( SV31 = n1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[308]) ).
thf(322,plain,
! [SV42: $i,SV32: $i] :
( ( ( leq @ ( minus @ SV32 @ SV42 ) @ SV32 )
= $false )
| ( ( leq @ n0 @ SV42 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[309]) ).
thf(323,plain,
! [SV43: $i,SV33: $i] :
( ( ( leq @ n0 @ SV33 )
= $false )
| ( ( leq @ n0 @ ( uniform_int_rnd @ SV43 @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[310]) ).
thf(324,plain,
! [SV34: $i] :
( ( ( ~ ( leq @ n0 @ SV34 )
| ~ ( leq @ SV34 @ n0 ) )
= $true )
| ( ( SV34 = n0 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[311]) ).
thf(325,plain,
! [SV35: $i,SV44: $i] :
( ( ( gt @ SV44 @ SV35 )
= $false )
| ( ( leq @ SV35 @ SV44 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[312]) ).
thf(326,plain,
! [SV45: $i,SV36: $i] :
( ( ~ ( ~ ( leq @ ( succ @ SV36 ) @ ( succ @ SV45 ) )
| ( leq @ SV36 @ SV45 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[313]) ).
thf(327,plain,
! [SV45: $i,SV36: $i] :
( ( ~ ( ~ ( leq @ SV36 @ SV45 )
| ( leq @ ( succ @ SV36 ) @ ( succ @ SV45 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[313]) ).
thf(328,plain,
! [SV46: $i,SV37: $i] :
( ( ( leq @ SV37 @ SV46 )
= $false )
| ( ( leq @ SV37 @ ( succ @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[314]) ).
thf(329,plain,
! [SV47: $i,SV38: $i] :
( ( ( ~ ( ~ ( leq @ SV38 @ SV47 )
| ~ ( ( SV38 != SV47 ) ) ) )
= $false )
| ( ( gt @ SV47 @ SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[315]) ).
thf(330,plain,
! [SV48: $i,SV40: $i,SV28: $i] :
( ( ( ~ ( ~ ( leq @ SV28 @ SV40 )
| ~ ( leq @ SV40 @ SV48 ) ) )
= $false )
| ( ( leq @ SV28 @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[317]) ).
thf(331,plain,
! [SV41: $i,SV29: $i] :
( ( ~ ( geq @ SV29 @ SV41 )
| ( leq @ SV41 @ SV29 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[318]) ).
thf(332,plain,
! [SV29: $i,SV41: $i] :
( ( ~ ( leq @ SV41 @ SV29 )
| ( geq @ SV29 @ SV41 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[319]) ).
thf(333,plain,
! [SV30: $i] :
( ( ( ~ ( leq @ n0 @ SV30 ) )
= $true )
| ( ( ~ ( leq @ SV30 @ n2 ) )
= $true )
| ( ( ( SV30 = n0 )
| ( SV30 = n1 )
| ( SV30 = n2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[320]) ).
thf(334,plain,
! [SV31: $i] :
( ( ( ~ ( leq @ n0 @ SV31 ) )
= $true )
| ( ( ~ ( leq @ SV31 @ n1 ) )
= $true )
| ( ( ( SV31 = n0 )
| ( SV31 = n1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[321]) ).
thf(335,plain,
! [SV34: $i] :
( ( ( ~ ( leq @ n0 @ SV34 ) )
= $true )
| ( ( ~ ( leq @ SV34 @ n0 ) )
= $true )
| ( ( SV34 = n0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[324]) ).
thf(336,plain,
! [SV45: $i,SV36: $i] :
( ( ~ ( leq @ ( succ @ SV36 ) @ ( succ @ SV45 ) )
| ( leq @ SV36 @ SV45 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[326]) ).
thf(337,plain,
! [SV45: $i,SV36: $i] :
( ( ~ ( leq @ SV36 @ SV45 )
| ( leq @ ( succ @ SV36 ) @ ( succ @ SV45 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[327]) ).
thf(338,plain,
! [SV47: $i,SV38: $i] :
( ( ( ~ ( leq @ SV38 @ SV47 )
| ~ ( ( SV38 != SV47 ) ) )
= $true )
| ( ( gt @ SV47 @ SV38 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[329]) ).
thf(339,plain,
! [SV48: $i,SV40: $i,SV28: $i] :
( ( ( ~ ( leq @ SV28 @ SV40 )
| ~ ( leq @ SV40 @ SV48 ) )
= $true )
| ( ( leq @ SV28 @ SV48 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[330]) ).
thf(340,plain,
! [SV41: $i,SV29: $i] :
( ( ( ~ ( geq @ SV29 @ SV41 ) )
= $true )
| ( ( leq @ SV41 @ SV29 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[331]) ).
thf(341,plain,
! [SV29: $i,SV41: $i] :
( ( ( ~ ( leq @ SV41 @ SV29 ) )
= $true )
| ( ( geq @ SV29 @ SV41 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[332]) ).
thf(342,plain,
! [SV30: $i] :
( ( ( leq @ n0 @ SV30 )
= $false )
| ( ( ~ ( leq @ SV30 @ n2 ) )
= $true )
| ( ( ( SV30 = n0 )
| ( SV30 = n1 )
| ( SV30 = n2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[333]) ).
thf(343,plain,
! [SV31: $i] :
( ( ( leq @ n0 @ SV31 )
= $false )
| ( ( ~ ( leq @ SV31 @ n1 ) )
= $true )
| ( ( ( SV31 = n0 )
| ( SV31 = n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[334]) ).
thf(344,plain,
! [SV34: $i] :
( ( ( leq @ n0 @ SV34 )
= $false )
| ( ( ~ ( leq @ SV34 @ n0 ) )
= $true )
| ( ( SV34 = n0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[335]) ).
thf(345,plain,
! [SV45: $i,SV36: $i] :
( ( ( ~ ( leq @ ( succ @ SV36 ) @ ( succ @ SV45 ) ) )
= $true )
| ( ( leq @ SV36 @ SV45 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[336]) ).
thf(346,plain,
! [SV45: $i,SV36: $i] :
( ( ( ~ ( leq @ SV36 @ SV45 ) )
= $true )
| ( ( leq @ ( succ @ SV36 ) @ ( succ @ SV45 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[337]) ).
thf(347,plain,
! [SV47: $i,SV38: $i] :
( ( ( ~ ( leq @ SV38 @ SV47 ) )
= $true )
| ( ( ~ ( ( SV38 != SV47 ) ) )
= $true )
| ( ( gt @ SV47 @ SV38 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[338]) ).
thf(348,plain,
! [SV48: $i,SV40: $i,SV28: $i] :
( ( ( ~ ( leq @ SV28 @ SV40 ) )
= $true )
| ( ( ~ ( leq @ SV40 @ SV48 ) )
= $true )
| ( ( leq @ SV28 @ SV48 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[339]) ).
thf(349,plain,
! [SV41: $i,SV29: $i] :
( ( ( geq @ SV29 @ SV41 )
= $false )
| ( ( leq @ SV41 @ SV29 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[340]) ).
thf(350,plain,
! [SV29: $i,SV41: $i] :
( ( ( leq @ SV41 @ SV29 )
= $false )
| ( ( geq @ SV29 @ SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[341]) ).
thf(351,plain,
! [SV30: $i] :
( ( ( leq @ SV30 @ n2 )
= $false )
| ( ( leq @ n0 @ SV30 )
= $false )
| ( ( ( SV30 = n0 )
| ( SV30 = n1 )
| ( SV30 = n2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[342]) ).
thf(352,plain,
! [SV31: $i] :
( ( ( leq @ SV31 @ n1 )
= $false )
| ( ( leq @ n0 @ SV31 )
= $false )
| ( ( ( SV31 = n0 )
| ( SV31 = n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[343]) ).
thf(353,plain,
! [SV34: $i] :
( ( ( leq @ SV34 @ n0 )
= $false )
| ( ( leq @ n0 @ SV34 )
= $false )
| ( ( SV34 = n0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[344]) ).
thf(354,plain,
! [SV45: $i,SV36: $i] :
( ( ( leq @ ( succ @ SV36 ) @ ( succ @ SV45 ) )
= $false )
| ( ( leq @ SV36 @ SV45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[345]) ).
thf(355,plain,
! [SV45: $i,SV36: $i] :
( ( ( leq @ SV36 @ SV45 )
= $false )
| ( ( leq @ ( succ @ SV36 ) @ ( succ @ SV45 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[346]) ).
thf(356,plain,
! [SV47: $i,SV38: $i] :
( ( ( leq @ SV38 @ SV47 )
= $false )
| ( ( ~ ( ( SV38 != SV47 ) ) )
= $true )
| ( ( gt @ SV47 @ SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[347]) ).
thf(357,plain,
! [SV48: $i,SV40: $i,SV28: $i] :
( ( ( leq @ SV28 @ SV40 )
= $false )
| ( ( ~ ( leq @ SV40 @ SV48 ) )
= $true )
| ( ( leq @ SV28 @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[348]) ).
thf(358,plain,
! [SV30: $i] :
( ( ( ( SV30 = n0 )
| ( SV30 = n1 ) )
= $true )
| ( ( SV30 = n2 )
= $true )
| ( ( leq @ n0 @ SV30 )
= $false )
| ( ( leq @ SV30 @ n2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[351]) ).
thf(359,plain,
! [SV31: $i] :
( ( ( SV31 = n0 )
= $true )
| ( ( SV31 = n1 )
= $true )
| ( ( leq @ n0 @ SV31 )
= $false )
| ( ( leq @ SV31 @ n1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[352]) ).
thf(360,plain,
! [SV47: $i,SV38: $i] :
( ( ( SV38 != SV47 )
= $false )
| ( ( leq @ SV38 @ SV47 )
= $false )
| ( ( gt @ SV47 @ SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[356]) ).
thf(361,plain,
! [SV28: $i,SV48: $i,SV40: $i] :
( ( ( leq @ SV40 @ SV48 )
= $false )
| ( ( leq @ SV28 @ SV40 )
= $false )
| ( ( leq @ SV28 @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[357]) ).
thf(362,plain,
! [SV30: $i] :
( ( ( SV30 = n0 )
= $true )
| ( ( SV30 = n1 )
= $true )
| ( ( SV30 = n2 )
= $true )
| ( ( leq @ n0 @ SV30 )
= $false )
| ( ( leq @ SV30 @ n2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[358]) ).
thf(363,plain,
! [SV47: $i,SV38: $i] :
( ( ( SV38 = SV47 )
= $true )
| ( ( leq @ SV38 @ SV47 )
= $false )
| ( ( gt @ SV47 @ SV38 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[360]) ).
thf(364,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[253,363,362,361,359,355,354,353,350,349,328,325,323,322,316,279,278,277,263,262,261,260,256,255,254]) ).
thf(365,plain,
( ( ! [X: $i] : ( leq @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(366,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( leq @ X @ Y )
& ( leq @ Y @ Z ) )
=> ( leq @ X @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(367,plain,
( ( ! [X: $i,Y: $i] :
( ( geq @ X @ Y )
<=> ( leq @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(368,plain,
( ( ! [X: $i,Y: $i] :
( ( gt @ Y @ X )
=> ( leq @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(369,plain,
( ( ! [X: $i,Y: $i] :
( ( ( leq @ X @ Y )
& ( X != Y ) )
=> ( gt @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(370,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ X @ Y )
=> ( leq @ X @ ( succ @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(371,plain,
( ( ! [X: $i,C: $i] :
( ( leq @ n0 @ X )
=> ( leq @ ( uniform_int_rnd @ C @ X ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(372,plain,
( ( ! [X: $i,C: $i] :
( ( leq @ n0 @ X )
=> ( leq @ n0 @ ( uniform_int_rnd @ C @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(373,plain,
( ( ! [X: $i] :
( ( minus @ X @ n1 )
= ( pred @ X ) ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(374,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ ( succ @ X ) @ ( succ @ Y ) )
<=> ( leq @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(375,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ ( minus @ X @ Y ) @ X )
=> ( leq @ n0 @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(376,plain,
true = $true,
inference(copy,[status(thm)],[96]) ).
thf(377,plain,
( ( gt @ n5 @ n0 )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(378,plain,
( ( gt @ n1 @ n0 )
= $true ),
inference(copy,[status(thm)],[94]) ).
thf(379,plain,
( ( gt @ n5 @ n1 )
= $true ),
inference(copy,[status(thm)],[93]) ).
thf(380,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n0 ) )
=> ( X = n0 ) ) )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(381,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n1 ) )
=> ( ( X = n0 )
| ( X = n1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(382,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n2 ) )
=> ( ( X = n0 )
| ( X = n1 )
| ( X = n2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(383,plain,
( ( ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ n0 ) ) ) ) )
= n5 )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(384,plain,
( ( ( succ @ n0 )
= n1 )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(385,plain,
( ( leq @ pv31 @ ( minus @ n5 @ n1 ) )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(386,plain,
( ( leq @ n0 @ pv31 )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(387,plain,
( ( ~ ( ( n0 != pv40 )
=> ( ( leq @ n0 @ pv31 )
& ( leq @ pv31 @ ( minus @ n5 @ n1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(388,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( leq @ SX0 @ SX1 )
| ~ ( ( SX0 != SX1 ) ) )
| ( gt @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[369]) ).
thf(389,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( geq @ SX0 @ SX1 )
| ( leq @ SX1 @ SX0 ) )
| ~ ( ~ ( leq @ SX1 @ SX0 )
| ( geq @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[367]) ).
thf(390,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( leq @ n0 @ SX0 )
| ~ ( leq @ SX0 @ n2 ) )
| ( SX0 = n0 )
| ( SX0 = n1 )
| ( SX0 = n2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[382]) ).
thf(391,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX0 @ SX1 )
| ( leq @ SX0 @ ( succ @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[370]) ).
thf(392,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( gt @ SX1 @ SX0 )
| ( leq @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[368]) ).
thf(393,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( leq @ n0 @ SX0 )
| ~ ( leq @ SX0 @ n0 ) )
| ( SX0 = n0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[380]) ).
thf(394,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ n0 @ SX0 )
| ( leq @ n0 @ ( uniform_int_rnd @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[372]) ).
thf(395,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( leq @ ( succ @ SX0 ) @ ( succ @ SX1 ) )
| ( leq @ SX0 @ SX1 ) )
| ~ ( ~ ( leq @ SX0 @ SX1 )
| ( leq @ ( succ @ SX0 ) @ ( succ @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[374]) ).
thf(396,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ ( minus @ SX0 @ SX1 ) @ SX0 )
| ( leq @ n0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[375]) ).
thf(397,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( leq @ SX0 @ SX1 )
| ~ ( leq @ SX1 @ SX2 ) )
| ( leq @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[366]) ).
thf(398,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ n0 @ SX0 )
| ( leq @ ( uniform_int_rnd @ SX1 @ SX0 ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[371]) ).
thf(399,plain,
( ( ~ ( ~ ( ( n0 != pv40 ) )
| ~ ( ~ ( leq @ n0 @ pv31 )
| ~ ( leq @ pv31 @ ( minus @ n5 @ n1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[387]) ).
thf(400,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( leq @ n0 @ SX0 )
| ~ ( leq @ SX0 @ n1 ) )
| ( SX0 = n0 )
| ( SX0 = n1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[381]) ).
thf(401,plain,
! [SV49: $i] :
( ( leq @ SV49 @ SV49 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[365]) ).
thf(402,plain,
! [SV50: $i] :
( ( ( minus @ SV50 @ n1 )
= ( pred @ SV50 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[373]) ).
thf(403,plain,
! [SV51: $i] :
( ( ! [SY46: $i] :
( ~ ~ ( ~ ( leq @ SV51 @ SY46 )
| ~ ( ( SV51 != SY46 ) ) )
| ( gt @ SY46 @ SV51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[388]) ).
thf(404,plain,
! [SV52: $i] :
( ( ! [SY47: $i] :
~ ( ~ ( ~ ( geq @ SV52 @ SY47 )
| ( leq @ SY47 @ SV52 ) )
| ~ ( ~ ( leq @ SY47 @ SV52 )
| ( geq @ SV52 @ SY47 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[389]) ).
thf(405,plain,
! [SV53: $i] :
( ( ~ ~ ( ~ ( leq @ n0 @ SV53 )
| ~ ( leq @ SV53 @ n2 ) )
| ( SV53 = n0 )
| ( SV53 = n1 )
| ( SV53 = n2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[390]) ).
thf(406,plain,
! [SV54: $i] :
( ( ! [SY48: $i] :
( ~ ( leq @ SV54 @ SY48 )
| ( leq @ SV54 @ ( succ @ SY48 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[391]) ).
thf(407,plain,
! [SV55: $i] :
( ( ! [SY49: $i] :
( ~ ( gt @ SY49 @ SV55 )
| ( leq @ SV55 @ SY49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[392]) ).
thf(408,plain,
! [SV56: $i] :
( ( ~ ~ ( ~ ( leq @ n0 @ SV56 )
| ~ ( leq @ SV56 @ n0 ) )
| ( SV56 = n0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[393]) ).
thf(409,plain,
! [SV57: $i] :
( ( ! [SY50: $i] :
( ~ ( leq @ n0 @ SV57 )
| ( leq @ n0 @ ( uniform_int_rnd @ SY50 @ SV57 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[394]) ).
thf(410,plain,
! [SV58: $i] :
( ( ! [SY51: $i] :
~ ( ~ ( ~ ( leq @ ( succ @ SV58 ) @ ( succ @ SY51 ) )
| ( leq @ SV58 @ SY51 ) )
| ~ ( ~ ( leq @ SV58 @ SY51 )
| ( leq @ ( succ @ SV58 ) @ ( succ @ SY51 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[395]) ).
thf(411,plain,
! [SV59: $i] :
( ( ! [SY52: $i] :
( ~ ( leq @ ( minus @ SV59 @ SY52 ) @ SV59 )
| ( leq @ n0 @ SY52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[396]) ).
thf(412,plain,
! [SV60: $i] :
( ( ! [SY53: $i,SY54: $i] :
( ~ ~ ( ~ ( leq @ SV60 @ SY53 )
| ~ ( leq @ SY53 @ SY54 ) )
| ( leq @ SV60 @ SY54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[397]) ).
thf(413,plain,
! [SV61: $i] :
( ( ! [SY55: $i] :
( ~ ( leq @ n0 @ SV61 )
| ( leq @ ( uniform_int_rnd @ SY55 @ SV61 ) @ SV61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[398]) ).
thf(414,plain,
( ( ~ ( ( n0 != pv40 ) )
| ~ ( ~ ( leq @ n0 @ pv31 )
| ~ ( leq @ pv31 @ ( minus @ n5 @ n1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[399]) ).
thf(415,plain,
! [SV62: $i] :
( ( ~ ~ ( ~ ( leq @ n0 @ SV62 )
| ~ ( leq @ SV62 @ n1 ) )
| ( SV62 = n0 )
| ( SV62 = n1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[400]) ).
thf(416,plain,
! [SV63: $i,SV51: $i] :
( ( ~ ~ ( ~ ( leq @ SV51 @ SV63 )
| ~ ( ( SV51 != SV63 ) ) )
| ( gt @ SV63 @ SV51 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[403]) ).
thf(417,plain,
! [SV64: $i,SV52: $i] :
( ( ~ ( ~ ( ~ ( geq @ SV52 @ SV64 )
| ( leq @ SV64 @ SV52 ) )
| ~ ( ~ ( leq @ SV64 @ SV52 )
| ( geq @ SV52 @ SV64 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[404]) ).
thf(418,plain,
! [SV53: $i] :
( ( ( ~ ~ ( ~ ( leq @ n0 @ SV53 )
| ~ ( leq @ SV53 @ n2 ) ) )
= $true )
| ( ( ( SV53 = n0 )
| ( SV53 = n1 )
| ( SV53 = n2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[405]) ).
thf(419,plain,
! [SV65: $i,SV54: $i] :
( ( ~ ( leq @ SV54 @ SV65 )
| ( leq @ SV54 @ ( succ @ SV65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[406]) ).
thf(420,plain,
! [SV55: $i,SV66: $i] :
( ( ~ ( gt @ SV66 @ SV55 )
| ( leq @ SV55 @ SV66 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[407]) ).
thf(421,plain,
! [SV56: $i] :
( ( ( ~ ~ ( ~ ( leq @ n0 @ SV56 )
| ~ ( leq @ SV56 @ n0 ) ) )
= $true )
| ( ( SV56 = n0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[408]) ).
thf(422,plain,
! [SV67: $i,SV57: $i] :
( ( ~ ( leq @ n0 @ SV57 )
| ( leq @ n0 @ ( uniform_int_rnd @ SV67 @ SV57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[409]) ).
thf(423,plain,
! [SV68: $i,SV58: $i] :
( ( ~ ( ~ ( ~ ( leq @ ( succ @ SV58 ) @ ( succ @ SV68 ) )
| ( leq @ SV58 @ SV68 ) )
| ~ ( ~ ( leq @ SV58 @ SV68 )
| ( leq @ ( succ @ SV58 ) @ ( succ @ SV68 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[410]) ).
thf(424,plain,
! [SV69: $i,SV59: $i] :
( ( ~ ( leq @ ( minus @ SV59 @ SV69 ) @ SV59 )
| ( leq @ n0 @ SV69 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[411]) ).
thf(425,plain,
! [SV70: $i,SV60: $i] :
( ( ! [SY56: $i] :
( ~ ~ ( ~ ( leq @ SV60 @ SV70 )
| ~ ( leq @ SV70 @ SY56 ) )
| ( leq @ SV60 @ SY56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[412]) ).
thf(426,plain,
! [SV71: $i,SV61: $i] :
( ( ~ ( leq @ n0 @ SV61 )
| ( leq @ ( uniform_int_rnd @ SV71 @ SV61 ) @ SV61 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[413]) ).
thf(427,plain,
( ( ~ ( ( n0 != pv40 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[414]) ).
thf(428,plain,
( ( ~ ( ~ ( leq @ n0 @ pv31 )
| ~ ( leq @ pv31 @ ( minus @ n5 @ n1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[414]) ).
thf(429,plain,
! [SV62: $i] :
( ( ( ~ ~ ( ~ ( leq @ n0 @ SV62 )
| ~ ( leq @ SV62 @ n1 ) ) )
= $true )
| ( ( ( SV62 = n0 )
| ( SV62 = n1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[415]) ).
thf(430,plain,
! [SV63: $i,SV51: $i] :
( ( ( ~ ~ ( ~ ( leq @ SV51 @ SV63 )
| ~ ( ( SV51 != SV63 ) ) ) )
= $true )
| ( ( gt @ SV63 @ SV51 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[416]) ).
thf(431,plain,
! [SV64: $i,SV52: $i] :
( ( ~ ( ~ ( geq @ SV52 @ SV64 )
| ( leq @ SV64 @ SV52 ) )
| ~ ( ~ ( leq @ SV64 @ SV52 )
| ( geq @ SV52 @ SV64 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[417]) ).
thf(432,plain,
! [SV53: $i] :
( ( ( ~ ( ~ ( leq @ n0 @ SV53 )
| ~ ( leq @ SV53 @ n2 ) ) )
= $false )
| ( ( ( SV53 = n0 )
| ( SV53 = n1 )
| ( SV53 = n2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[418]) ).
thf(433,plain,
! [SV65: $i,SV54: $i] :
( ( ( ~ ( leq @ SV54 @ SV65 ) )
= $true )
| ( ( leq @ SV54 @ ( succ @ SV65 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[419]) ).
thf(434,plain,
! [SV55: $i,SV66: $i] :
( ( ( ~ ( gt @ SV66 @ SV55 ) )
= $true )
| ( ( leq @ SV55 @ SV66 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[420]) ).
thf(435,plain,
! [SV56: $i] :
( ( ( ~ ( ~ ( leq @ n0 @ SV56 )
| ~ ( leq @ SV56 @ n0 ) ) )
= $false )
| ( ( SV56 = n0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[421]) ).
thf(436,plain,
! [SV67: $i,SV57: $i] :
( ( ( ~ ( leq @ n0 @ SV57 ) )
= $true )
| ( ( leq @ n0 @ ( uniform_int_rnd @ SV67 @ SV57 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[422]) ).
thf(437,plain,
! [SV68: $i,SV58: $i] :
( ( ~ ( ~ ( leq @ ( succ @ SV58 ) @ ( succ @ SV68 ) )
| ( leq @ SV58 @ SV68 ) )
| ~ ( ~ ( leq @ SV58 @ SV68 )
| ( leq @ ( succ @ SV58 ) @ ( succ @ SV68 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[423]) ).
thf(438,plain,
! [SV69: $i,SV59: $i] :
( ( ( ~ ( leq @ ( minus @ SV59 @ SV69 ) @ SV59 ) )
= $true )
| ( ( leq @ n0 @ SV69 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[424]) ).
thf(439,plain,
! [SV72: $i,SV70: $i,SV60: $i] :
( ( ~ ~ ( ~ ( leq @ SV60 @ SV70 )
| ~ ( leq @ SV70 @ SV72 ) )
| ( leq @ SV60 @ SV72 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[425]) ).
thf(440,plain,
! [SV71: $i,SV61: $i] :
( ( ( ~ ( leq @ n0 @ SV61 ) )
= $true )
| ( ( leq @ ( uniform_int_rnd @ SV71 @ SV61 ) @ SV61 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[426]) ).
thf(441,plain,
( ( n0 != pv40 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[427]) ).
thf(442,plain,
( ( ~ ( leq @ n0 @ pv31 )
| ~ ( leq @ pv31 @ ( minus @ n5 @ n1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[428]) ).
thf(443,plain,
! [SV62: $i] :
( ( ( ~ ( ~ ( leq @ n0 @ SV62 )
| ~ ( leq @ SV62 @ n1 ) ) )
= $false )
| ( ( ( SV62 = n0 )
| ( SV62 = n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[429]) ).
thf(444,plain,
! [SV63: $i,SV51: $i] :
( ( ( ~ ( ~ ( leq @ SV51 @ SV63 )
| ~ ( ( SV51 != SV63 ) ) ) )
= $false )
| ( ( gt @ SV63 @ SV51 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[430]) ).
thf(445,plain,
! [SV64: $i,SV52: $i] :
( ( ~ ( ~ ( geq @ SV52 @ SV64 )
| ( leq @ SV64 @ SV52 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[431]) ).
thf(446,plain,
! [SV52: $i,SV64: $i] :
( ( ~ ( ~ ( leq @ SV64 @ SV52 )
| ( geq @ SV52 @ SV64 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[431]) ).
thf(447,plain,
! [SV53: $i] :
( ( ( ~ ( leq @ n0 @ SV53 )
| ~ ( leq @ SV53 @ n2 ) )
= $true )
| ( ( ( SV53 = n0 )
| ( SV53 = n1 )
| ( SV53 = n2 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[432]) ).
thf(448,plain,
! [SV65: $i,SV54: $i] :
( ( ( leq @ SV54 @ SV65 )
= $false )
| ( ( leq @ SV54 @ ( succ @ SV65 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[433]) ).
thf(449,plain,
! [SV55: $i,SV66: $i] :
( ( ( gt @ SV66 @ SV55 )
= $false )
| ( ( leq @ SV55 @ SV66 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[434]) ).
thf(450,plain,
! [SV56: $i] :
( ( ( ~ ( leq @ n0 @ SV56 )
| ~ ( leq @ SV56 @ n0 ) )
= $true )
| ( ( SV56 = n0 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[435]) ).
thf(451,plain,
! [SV67: $i,SV57: $i] :
( ( ( leq @ n0 @ SV57 )
= $false )
| ( ( leq @ n0 @ ( uniform_int_rnd @ SV67 @ SV57 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[436]) ).
thf(452,plain,
! [SV68: $i,SV58: $i] :
( ( ~ ( ~ ( leq @ ( succ @ SV58 ) @ ( succ @ SV68 ) )
| ( leq @ SV58 @ SV68 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[437]) ).
thf(453,plain,
! [SV68: $i,SV58: $i] :
( ( ~ ( ~ ( leq @ SV58 @ SV68 )
| ( leq @ ( succ @ SV58 ) @ ( succ @ SV68 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[437]) ).
thf(454,plain,
! [SV69: $i,SV59: $i] :
( ( ( leq @ ( minus @ SV59 @ SV69 ) @ SV59 )
= $false )
| ( ( leq @ n0 @ SV69 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[438]) ).
thf(455,plain,
! [SV72: $i,SV70: $i,SV60: $i] :
( ( ( ~ ~ ( ~ ( leq @ SV60 @ SV70 )
| ~ ( leq @ SV70 @ SV72 ) ) )
= $true )
| ( ( leq @ SV60 @ SV72 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[439]) ).
thf(456,plain,
! [SV71: $i,SV61: $i] :
( ( ( leq @ n0 @ SV61 )
= $false )
| ( ( leq @ ( uniform_int_rnd @ SV71 @ SV61 ) @ SV61 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[440]) ).
thf(457,plain,
( ( n0 = pv40 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[441]) ).
thf(458,plain,
( ( ( ~ ( leq @ n0 @ pv31 ) )
= $true )
| ( ( ~ ( leq @ pv31 @ ( minus @ n5 @ n1 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[442]) ).
thf(459,plain,
! [SV62: $i] :
( ( ( ~ ( leq @ n0 @ SV62 )
| ~ ( leq @ SV62 @ n1 ) )
= $true )
| ( ( ( SV62 = n0 )
| ( SV62 = n1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[443]) ).
thf(460,plain,
! [SV63: $i,SV51: $i] :
( ( ( ~ ( leq @ SV51 @ SV63 )
| ~ ( ( SV51 != SV63 ) ) )
= $true )
| ( ( gt @ SV63 @ SV51 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[444]) ).
thf(461,plain,
! [SV64: $i,SV52: $i] :
( ( ~ ( geq @ SV52 @ SV64 )
| ( leq @ SV64 @ SV52 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[445]) ).
thf(462,plain,
! [SV52: $i,SV64: $i] :
( ( ~ ( leq @ SV64 @ SV52 )
| ( geq @ SV52 @ SV64 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[446]) ).
thf(463,plain,
! [SV53: $i] :
( ( ( ~ ( leq @ n0 @ SV53 ) )
= $true )
| ( ( ~ ( leq @ SV53 @ n2 ) )
= $true )
| ( ( ( SV53 = n0 )
| ( SV53 = n1 )
| ( SV53 = n2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[447]) ).
thf(464,plain,
! [SV56: $i] :
( ( ( ~ ( leq @ n0 @ SV56 ) )
= $true )
| ( ( ~ ( leq @ SV56 @ n0 ) )
= $true )
| ( ( SV56 = n0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[450]) ).
thf(465,plain,
! [SV68: $i,SV58: $i] :
( ( ~ ( leq @ ( succ @ SV58 ) @ ( succ @ SV68 ) )
| ( leq @ SV58 @ SV68 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[452]) ).
thf(466,plain,
! [SV68: $i,SV58: $i] :
( ( ~ ( leq @ SV58 @ SV68 )
| ( leq @ ( succ @ SV58 ) @ ( succ @ SV68 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[453]) ).
thf(467,plain,
! [SV72: $i,SV70: $i,SV60: $i] :
( ( ( ~ ( ~ ( leq @ SV60 @ SV70 )
| ~ ( leq @ SV70 @ SV72 ) ) )
= $false )
| ( ( leq @ SV60 @ SV72 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[455]) ).
thf(468,plain,
( ( ( leq @ n0 @ pv31 )
= $false )
| ( ( ~ ( leq @ pv31 @ ( minus @ n5 @ n1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[458]) ).
thf(469,plain,
! [SV62: $i] :
( ( ( ~ ( leq @ n0 @ SV62 ) )
= $true )
| ( ( ~ ( leq @ SV62 @ n1 ) )
= $true )
| ( ( ( SV62 = n0 )
| ( SV62 = n1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[459]) ).
thf(470,plain,
! [SV63: $i,SV51: $i] :
( ( ( ~ ( leq @ SV51 @ SV63 ) )
= $true )
| ( ( ~ ( ( SV51 != SV63 ) ) )
= $true )
| ( ( gt @ SV63 @ SV51 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[460]) ).
thf(471,plain,
! [SV64: $i,SV52: $i] :
( ( ( ~ ( geq @ SV52 @ SV64 ) )
= $true )
| ( ( leq @ SV64 @ SV52 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[461]) ).
thf(472,plain,
! [SV52: $i,SV64: $i] :
( ( ( ~ ( leq @ SV64 @ SV52 ) )
= $true )
| ( ( geq @ SV52 @ SV64 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[462]) ).
thf(473,plain,
! [SV53: $i] :
( ( ( leq @ n0 @ SV53 )
= $false )
| ( ( ~ ( leq @ SV53 @ n2 ) )
= $true )
| ( ( ( SV53 = n0 )
| ( SV53 = n1 )
| ( SV53 = n2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[463]) ).
thf(474,plain,
! [SV56: $i] :
( ( ( leq @ n0 @ SV56 )
= $false )
| ( ( ~ ( leq @ SV56 @ n0 ) )
= $true )
| ( ( SV56 = n0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[464]) ).
thf(475,plain,
! [SV68: $i,SV58: $i] :
( ( ( ~ ( leq @ ( succ @ SV58 ) @ ( succ @ SV68 ) ) )
= $true )
| ( ( leq @ SV58 @ SV68 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[465]) ).
thf(476,plain,
! [SV68: $i,SV58: $i] :
( ( ( ~ ( leq @ SV58 @ SV68 ) )
= $true )
| ( ( leq @ ( succ @ SV58 ) @ ( succ @ SV68 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[466]) ).
thf(477,plain,
! [SV72: $i,SV70: $i,SV60: $i] :
( ( ( ~ ( leq @ SV60 @ SV70 )
| ~ ( leq @ SV70 @ SV72 ) )
= $true )
| ( ( leq @ SV60 @ SV72 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[467]) ).
thf(478,plain,
( ( ( leq @ pv31 @ ( minus @ n5 @ n1 ) )
= $false )
| ( ( leq @ n0 @ pv31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[468]) ).
thf(479,plain,
! [SV62: $i] :
( ( ( leq @ n0 @ SV62 )
= $false )
| ( ( ~ ( leq @ SV62 @ n1 ) )
= $true )
| ( ( ( SV62 = n0 )
| ( SV62 = n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[469]) ).
thf(480,plain,
! [SV63: $i,SV51: $i] :
( ( ( leq @ SV51 @ SV63 )
= $false )
| ( ( ~ ( ( SV51 != SV63 ) ) )
= $true )
| ( ( gt @ SV63 @ SV51 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[470]) ).
thf(481,plain,
! [SV64: $i,SV52: $i] :
( ( ( geq @ SV52 @ SV64 )
= $false )
| ( ( leq @ SV64 @ SV52 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[471]) ).
thf(482,plain,
! [SV52: $i,SV64: $i] :
( ( ( leq @ SV64 @ SV52 )
= $false )
| ( ( geq @ SV52 @ SV64 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[472]) ).
thf(483,plain,
! [SV53: $i] :
( ( ( leq @ SV53 @ n2 )
= $false )
| ( ( leq @ n0 @ SV53 )
= $false )
| ( ( ( SV53 = n0 )
| ( SV53 = n1 )
| ( SV53 = n2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[473]) ).
thf(484,plain,
! [SV56: $i] :
( ( ( leq @ SV56 @ n0 )
= $false )
| ( ( leq @ n0 @ SV56 )
= $false )
| ( ( SV56 = n0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[474]) ).
thf(485,plain,
! [SV68: $i,SV58: $i] :
( ( ( leq @ ( succ @ SV58 ) @ ( succ @ SV68 ) )
= $false )
| ( ( leq @ SV58 @ SV68 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[475]) ).
thf(486,plain,
! [SV68: $i,SV58: $i] :
( ( ( leq @ SV58 @ SV68 )
= $false )
| ( ( leq @ ( succ @ SV58 ) @ ( succ @ SV68 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[476]) ).
thf(487,plain,
! [SV72: $i,SV70: $i,SV60: $i] :
( ( ( ~ ( leq @ SV60 @ SV70 ) )
= $true )
| ( ( ~ ( leq @ SV70 @ SV72 ) )
= $true )
| ( ( leq @ SV60 @ SV72 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[477]) ).
thf(488,plain,
! [SV62: $i] :
( ( ( leq @ SV62 @ n1 )
= $false )
| ( ( leq @ n0 @ SV62 )
= $false )
| ( ( ( SV62 = n0 )
| ( SV62 = n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[479]) ).
thf(489,plain,
! [SV63: $i,SV51: $i] :
( ( ( SV51 != SV63 )
= $false )
| ( ( leq @ SV51 @ SV63 )
= $false )
| ( ( gt @ SV63 @ SV51 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[480]) ).
thf(490,plain,
! [SV53: $i] :
( ( ( ( SV53 = n0 )
| ( SV53 = n1 ) )
= $true )
| ( ( SV53 = n2 )
= $true )
| ( ( leq @ n0 @ SV53 )
= $false )
| ( ( leq @ SV53 @ n2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[483]) ).
thf(491,plain,
! [SV72: $i,SV70: $i,SV60: $i] :
( ( ( leq @ SV60 @ SV70 )
= $false )
| ( ( ~ ( leq @ SV70 @ SV72 ) )
= $true )
| ( ( leq @ SV60 @ SV72 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[487]) ).
thf(492,plain,
! [SV62: $i] :
( ( ( SV62 = n0 )
= $true )
| ( ( SV62 = n1 )
= $true )
| ( ( leq @ n0 @ SV62 )
= $false )
| ( ( leq @ SV62 @ n1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[488]) ).
thf(493,plain,
! [SV63: $i,SV51: $i] :
( ( ( SV51 = SV63 )
= $true )
| ( ( leq @ SV51 @ SV63 )
= $false )
| ( ( gt @ SV63 @ SV51 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[489]) ).
thf(494,plain,
! [SV53: $i] :
( ( ( SV53 = n0 )
= $true )
| ( ( SV53 = n1 )
= $true )
| ( ( SV53 = n2 )
= $true )
| ( ( leq @ n0 @ SV53 )
= $false )
| ( ( leq @ SV53 @ n2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[490]) ).
thf(495,plain,
! [SV60: $i,SV72: $i,SV70: $i] :
( ( ( leq @ SV70 @ SV72 )
= $false )
| ( ( leq @ SV60 @ SV70 )
= $false )
| ( ( leq @ SV60 @ SV72 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[491]) ).
thf(496,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[376,495,494,493,492,486,485,484,482,481,478,457,456,454,451,449,448,402,401,386,385,384,383,379,378,377]) ).
thf(497,plain,
( ( ! [X: $i] : ( leq @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(498,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( leq @ X @ Y )
& ( leq @ Y @ Z ) )
=> ( leq @ X @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(499,plain,
( ( ! [X: $i,Y: $i] :
( ( geq @ X @ Y )
<=> ( leq @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(500,plain,
( ( ! [X: $i,Y: $i] :
( ( gt @ Y @ X )
=> ( leq @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(501,plain,
( ( ! [X: $i,Y: $i] :
( ( ( leq @ X @ Y )
& ( X != Y ) )
=> ( gt @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(502,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ X @ Y )
=> ( leq @ X @ ( succ @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(503,plain,
( ( ! [X: $i,C: $i] :
( ( leq @ n0 @ X )
=> ( leq @ ( uniform_int_rnd @ C @ X ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(504,plain,
( ( ! [X: $i,C: $i] :
( ( leq @ n0 @ X )
=> ( leq @ n0 @ ( uniform_int_rnd @ C @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(505,plain,
( ( ! [X: $i] :
( ( minus @ X @ n1 )
= ( pred @ X ) ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(506,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ ( succ @ X ) @ ( succ @ Y ) )
<=> ( leq @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(507,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ ( minus @ X @ Y ) @ X )
=> ( leq @ n0 @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(508,plain,
true = $true,
inference(copy,[status(thm)],[96]) ).
thf(509,plain,
( ( gt @ n5 @ n0 )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(510,plain,
( ( gt @ n1 @ n0 )
= $true ),
inference(copy,[status(thm)],[94]) ).
thf(511,plain,
( ( gt @ n5 @ n1 )
= $true ),
inference(copy,[status(thm)],[93]) ).
thf(512,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n0 ) )
=> ( X = n0 ) ) )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(513,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n1 ) )
=> ( ( X = n0 )
| ( X = n1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(514,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n2 ) )
=> ( ( X = n0 )
| ( X = n1 )
| ( X = n2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(515,plain,
( ( ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ n0 ) ) ) ) )
= n5 )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(516,plain,
( ( ( succ @ n0 )
= n1 )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(517,plain,
( ( leq @ pv31 @ ( minus @ n5 @ n1 ) )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(518,plain,
( ( leq @ n0 @ pv31 )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(519,plain,
( ( ~ ( ( n0 = pv40 )
=> true ) )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(520,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( leq @ SX0 @ SX1 )
| ~ ( ( SX0 != SX1 ) ) )
| ( gt @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[501]) ).
thf(521,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( leq @ ( succ @ SX0 ) @ ( succ @ SX1 ) )
| ( leq @ SX0 @ SX1 ) )
| ~ ( ~ ( leq @ SX0 @ SX1 )
| ( leq @ ( succ @ SX0 ) @ ( succ @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[506]) ).
thf(522,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ n0 @ SX0 )
| ( leq @ n0 @ ( uniform_int_rnd @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[504]) ).
thf(523,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ ( minus @ SX0 @ SX1 ) @ SX0 )
| ( leq @ n0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[507]) ).
thf(524,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( leq @ SX0 @ SX1 )
| ~ ( leq @ SX1 @ SX2 ) )
| ( leq @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[498]) ).
thf(525,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( geq @ SX0 @ SX1 )
| ( leq @ SX1 @ SX0 ) )
| ~ ( ~ ( leq @ SX1 @ SX0 )
| ( geq @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[499]) ).
thf(526,plain,
( ( ~ ( ( n0 != pv40 )
| true ) )
= $true ),
inference(unfold_def,[status(thm)],[519]) ).
thf(527,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( gt @ SX1 @ SX0 )
| ( leq @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[500]) ).
thf(528,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( leq @ n0 @ SX0 )
| ~ ( leq @ SX0 @ n2 ) )
| ( SX0 = n0 )
| ( SX0 = n1 )
| ( SX0 = n2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[514]) ).
thf(529,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ n0 @ SX0 )
| ( leq @ ( uniform_int_rnd @ SX1 @ SX0 ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[503]) ).
thf(530,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( leq @ n0 @ SX0 )
| ~ ( leq @ SX0 @ n1 ) )
| ( SX0 = n0 )
| ( SX0 = n1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[513]) ).
thf(531,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX0 @ SX1 )
| ( leq @ SX0 @ ( succ @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[502]) ).
thf(532,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( leq @ n0 @ SX0 )
| ~ ( leq @ SX0 @ n0 ) )
| ( SX0 = n0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[512]) ).
thf(533,plain,
! [SV73: $i] :
( ( leq @ SV73 @ SV73 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[497]) ).
thf(534,plain,
! [SV74: $i] :
( ( ( minus @ SV74 @ n1 )
= ( pred @ SV74 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[505]) ).
thf(535,plain,
! [SV75: $i] :
( ( ! [SY57: $i] :
( ~ ~ ( ~ ( leq @ SV75 @ SY57 )
| ~ ( ( SV75 != SY57 ) ) )
| ( gt @ SY57 @ SV75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[520]) ).
thf(536,plain,
! [SV76: $i] :
( ( ! [SY58: $i] :
~ ( ~ ( ~ ( leq @ ( succ @ SV76 ) @ ( succ @ SY58 ) )
| ( leq @ SV76 @ SY58 ) )
| ~ ( ~ ( leq @ SV76 @ SY58 )
| ( leq @ ( succ @ SV76 ) @ ( succ @ SY58 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[521]) ).
thf(537,plain,
! [SV77: $i] :
( ( ! [SY59: $i] :
( ~ ( leq @ n0 @ SV77 )
| ( leq @ n0 @ ( uniform_int_rnd @ SY59 @ SV77 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[522]) ).
thf(538,plain,
! [SV78: $i] :
( ( ! [SY60: $i] :
( ~ ( leq @ ( minus @ SV78 @ SY60 ) @ SV78 )
| ( leq @ n0 @ SY60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[523]) ).
thf(539,plain,
! [SV79: $i] :
( ( ! [SY61: $i,SY62: $i] :
( ~ ~ ( ~ ( leq @ SV79 @ SY61 )
| ~ ( leq @ SY61 @ SY62 ) )
| ( leq @ SV79 @ SY62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[524]) ).
thf(540,plain,
! [SV80: $i] :
( ( ! [SY63: $i] :
~ ( ~ ( ~ ( geq @ SV80 @ SY63 )
| ( leq @ SY63 @ SV80 ) )
| ~ ( ~ ( leq @ SY63 @ SV80 )
| ( geq @ SV80 @ SY63 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[525]) ).
thf(541,plain,
( ( ( n0 != pv40 )
| true )
= $false ),
inference(extcnf_not_pos,[status(thm)],[526]) ).
thf(542,plain,
! [SV81: $i] :
( ( ! [SY64: $i] :
( ~ ( gt @ SY64 @ SV81 )
| ( leq @ SV81 @ SY64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[527]) ).
thf(543,plain,
! [SV82: $i] :
( ( ~ ~ ( ~ ( leq @ n0 @ SV82 )
| ~ ( leq @ SV82 @ n2 ) )
| ( SV82 = n0 )
| ( SV82 = n1 )
| ( SV82 = n2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[528]) ).
thf(544,plain,
! [SV83: $i] :
( ( ! [SY65: $i] :
( ~ ( leq @ n0 @ SV83 )
| ( leq @ ( uniform_int_rnd @ SY65 @ SV83 ) @ SV83 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[529]) ).
thf(545,plain,
! [SV84: $i] :
( ( ~ ~ ( ~ ( leq @ n0 @ SV84 )
| ~ ( leq @ SV84 @ n1 ) )
| ( SV84 = n0 )
| ( SV84 = n1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[530]) ).
thf(546,plain,
! [SV85: $i] :
( ( ! [SY66: $i] :
( ~ ( leq @ SV85 @ SY66 )
| ( leq @ SV85 @ ( succ @ SY66 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[531]) ).
thf(547,plain,
! [SV86: $i] :
( ( ~ ~ ( ~ ( leq @ n0 @ SV86 )
| ~ ( leq @ SV86 @ n0 ) )
| ( SV86 = n0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[532]) ).
thf(548,plain,
! [SV87: $i,SV75: $i] :
( ( ~ ~ ( ~ ( leq @ SV75 @ SV87 )
| ~ ( ( SV75 != SV87 ) ) )
| ( gt @ SV87 @ SV75 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[535]) ).
thf(549,plain,
! [SV88: $i,SV76: $i] :
( ( ~ ( ~ ( ~ ( leq @ ( succ @ SV76 ) @ ( succ @ SV88 ) )
| ( leq @ SV76 @ SV88 ) )
| ~ ( ~ ( leq @ SV76 @ SV88 )
| ( leq @ ( succ @ SV76 ) @ ( succ @ SV88 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[536]) ).
thf(550,plain,
! [SV89: $i,SV77: $i] :
( ( ~ ( leq @ n0 @ SV77 )
| ( leq @ n0 @ ( uniform_int_rnd @ SV89 @ SV77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[537]) ).
thf(551,plain,
! [SV90: $i,SV78: $i] :
( ( ~ ( leq @ ( minus @ SV78 @ SV90 ) @ SV78 )
| ( leq @ n0 @ SV90 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[538]) ).
thf(552,plain,
! [SV91: $i,SV79: $i] :
( ( ! [SY67: $i] :
( ~ ~ ( ~ ( leq @ SV79 @ SV91 )
| ~ ( leq @ SV91 @ SY67 ) )
| ( leq @ SV79 @ SY67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[539]) ).
thf(553,plain,
! [SV92: $i,SV80: $i] :
( ( ~ ( ~ ( ~ ( geq @ SV80 @ SV92 )
| ( leq @ SV92 @ SV80 ) )
| ~ ( ~ ( leq @ SV92 @ SV80 )
| ( geq @ SV80 @ SV92 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[540]) ).
thf(554,plain,
( ( n0 != pv40 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[541]) ).
thf(555,plain,
true = $false,
inference(extcnf_or_neg,[status(thm)],[541]) ).
thf(556,plain,
! [SV81: $i,SV93: $i] :
( ( ~ ( gt @ SV93 @ SV81 )
| ( leq @ SV81 @ SV93 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[542]) ).
thf(557,plain,
! [SV82: $i] :
( ( ( ~ ~ ( ~ ( leq @ n0 @ SV82 )
| ~ ( leq @ SV82 @ n2 ) ) )
= $true )
| ( ( ( SV82 = n0 )
| ( SV82 = n1 )
| ( SV82 = n2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[543]) ).
thf(558,plain,
! [SV94: $i,SV83: $i] :
( ( ~ ( leq @ n0 @ SV83 )
| ( leq @ ( uniform_int_rnd @ SV94 @ SV83 ) @ SV83 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[544]) ).
thf(559,plain,
! [SV84: $i] :
( ( ( ~ ~ ( ~ ( leq @ n0 @ SV84 )
| ~ ( leq @ SV84 @ n1 ) ) )
= $true )
| ( ( ( SV84 = n0 )
| ( SV84 = n1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[545]) ).
thf(560,plain,
! [SV95: $i,SV85: $i] :
( ( ~ ( leq @ SV85 @ SV95 )
| ( leq @ SV85 @ ( succ @ SV95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[546]) ).
thf(561,plain,
! [SV86: $i] :
( ( ( ~ ~ ( ~ ( leq @ n0 @ SV86 )
| ~ ( leq @ SV86 @ n0 ) ) )
= $true )
| ( ( SV86 = n0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[547]) ).
thf(562,plain,
! [SV87: $i,SV75: $i] :
( ( ( ~ ~ ( ~ ( leq @ SV75 @ SV87 )
| ~ ( ( SV75 != SV87 ) ) ) )
= $true )
| ( ( gt @ SV87 @ SV75 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[548]) ).
thf(563,plain,
! [SV88: $i,SV76: $i] :
( ( ~ ( ~ ( leq @ ( succ @ SV76 ) @ ( succ @ SV88 ) )
| ( leq @ SV76 @ SV88 ) )
| ~ ( ~ ( leq @ SV76 @ SV88 )
| ( leq @ ( succ @ SV76 ) @ ( succ @ SV88 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[549]) ).
thf(564,plain,
! [SV89: $i,SV77: $i] :
( ( ( ~ ( leq @ n0 @ SV77 ) )
= $true )
| ( ( leq @ n0 @ ( uniform_int_rnd @ SV89 @ SV77 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[550]) ).
thf(565,plain,
! [SV90: $i,SV78: $i] :
( ( ( ~ ( leq @ ( minus @ SV78 @ SV90 ) @ SV78 ) )
= $true )
| ( ( leq @ n0 @ SV90 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[551]) ).
thf(566,plain,
! [SV96: $i,SV91: $i,SV79: $i] :
( ( ~ ~ ( ~ ( leq @ SV79 @ SV91 )
| ~ ( leq @ SV91 @ SV96 ) )
| ( leq @ SV79 @ SV96 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[552]) ).
thf(567,plain,
! [SV92: $i,SV80: $i] :
( ( ~ ( ~ ( geq @ SV80 @ SV92 )
| ( leq @ SV92 @ SV80 ) )
| ~ ( ~ ( leq @ SV92 @ SV80 )
| ( geq @ SV80 @ SV92 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[553]) ).
thf(568,plain,
( ( n0 = pv40 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[554]) ).
thf(569,plain,
! [SV81: $i,SV93: $i] :
( ( ( ~ ( gt @ SV93 @ SV81 ) )
= $true )
| ( ( leq @ SV81 @ SV93 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[556]) ).
thf(570,plain,
! [SV82: $i] :
( ( ( ~ ( ~ ( leq @ n0 @ SV82 )
| ~ ( leq @ SV82 @ n2 ) ) )
= $false )
| ( ( ( SV82 = n0 )
| ( SV82 = n1 )
| ( SV82 = n2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[557]) ).
thf(571,plain,
! [SV94: $i,SV83: $i] :
( ( ( ~ ( leq @ n0 @ SV83 ) )
= $true )
| ( ( leq @ ( uniform_int_rnd @ SV94 @ SV83 ) @ SV83 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[558]) ).
thf(572,plain,
! [SV84: $i] :
( ( ( ~ ( ~ ( leq @ n0 @ SV84 )
| ~ ( leq @ SV84 @ n1 ) ) )
= $false )
| ( ( ( SV84 = n0 )
| ( SV84 = n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[559]) ).
thf(573,plain,
! [SV95: $i,SV85: $i] :
( ( ( ~ ( leq @ SV85 @ SV95 ) )
= $true )
| ( ( leq @ SV85 @ ( succ @ SV95 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[560]) ).
thf(574,plain,
! [SV86: $i] :
( ( ( ~ ( ~ ( leq @ n0 @ SV86 )
| ~ ( leq @ SV86 @ n0 ) ) )
= $false )
| ( ( SV86 = n0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[561]) ).
thf(575,plain,
! [SV87: $i,SV75: $i] :
( ( ( ~ ( ~ ( leq @ SV75 @ SV87 )
| ~ ( ( SV75 != SV87 ) ) ) )
= $false )
| ( ( gt @ SV87 @ SV75 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[562]) ).
thf(576,plain,
! [SV88: $i,SV76: $i] :
( ( ~ ( ~ ( leq @ ( succ @ SV76 ) @ ( succ @ SV88 ) )
| ( leq @ SV76 @ SV88 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[563]) ).
thf(577,plain,
! [SV88: $i,SV76: $i] :
( ( ~ ( ~ ( leq @ SV76 @ SV88 )
| ( leq @ ( succ @ SV76 ) @ ( succ @ SV88 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[563]) ).
thf(578,plain,
! [SV89: $i,SV77: $i] :
( ( ( leq @ n0 @ SV77 )
= $false )
| ( ( leq @ n0 @ ( uniform_int_rnd @ SV89 @ SV77 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[564]) ).
thf(579,plain,
! [SV90: $i,SV78: $i] :
( ( ( leq @ ( minus @ SV78 @ SV90 ) @ SV78 )
= $false )
| ( ( leq @ n0 @ SV90 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[565]) ).
thf(580,plain,
! [SV96: $i,SV91: $i,SV79: $i] :
( ( ( ~ ~ ( ~ ( leq @ SV79 @ SV91 )
| ~ ( leq @ SV91 @ SV96 ) ) )
= $true )
| ( ( leq @ SV79 @ SV96 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[566]) ).
thf(581,plain,
! [SV92: $i,SV80: $i] :
( ( ~ ( ~ ( geq @ SV80 @ SV92 )
| ( leq @ SV92 @ SV80 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[567]) ).
thf(582,plain,
! [SV80: $i,SV92: $i] :
( ( ~ ( ~ ( leq @ SV92 @ SV80 )
| ( geq @ SV80 @ SV92 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[567]) ).
thf(583,plain,
! [SV81: $i,SV93: $i] :
( ( ( gt @ SV93 @ SV81 )
= $false )
| ( ( leq @ SV81 @ SV93 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[569]) ).
thf(584,plain,
! [SV82: $i] :
( ( ( ~ ( leq @ n0 @ SV82 )
| ~ ( leq @ SV82 @ n2 ) )
= $true )
| ( ( ( SV82 = n0 )
| ( SV82 = n1 )
| ( SV82 = n2 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[570]) ).
thf(585,plain,
! [SV94: $i,SV83: $i] :
( ( ( leq @ n0 @ SV83 )
= $false )
| ( ( leq @ ( uniform_int_rnd @ SV94 @ SV83 ) @ SV83 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[571]) ).
thf(586,plain,
! [SV84: $i] :
( ( ( ~ ( leq @ n0 @ SV84 )
| ~ ( leq @ SV84 @ n1 ) )
= $true )
| ( ( ( SV84 = n0 )
| ( SV84 = n1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[572]) ).
thf(587,plain,
! [SV95: $i,SV85: $i] :
( ( ( leq @ SV85 @ SV95 )
= $false )
| ( ( leq @ SV85 @ ( succ @ SV95 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[573]) ).
thf(588,plain,
! [SV86: $i] :
( ( ( ~ ( leq @ n0 @ SV86 )
| ~ ( leq @ SV86 @ n0 ) )
= $true )
| ( ( SV86 = n0 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[574]) ).
thf(589,plain,
! [SV87: $i,SV75: $i] :
( ( ( ~ ( leq @ SV75 @ SV87 )
| ~ ( ( SV75 != SV87 ) ) )
= $true )
| ( ( gt @ SV87 @ SV75 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[575]) ).
thf(590,plain,
! [SV88: $i,SV76: $i] :
( ( ~ ( leq @ ( succ @ SV76 ) @ ( succ @ SV88 ) )
| ( leq @ SV76 @ SV88 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[576]) ).
thf(591,plain,
! [SV88: $i,SV76: $i] :
( ( ~ ( leq @ SV76 @ SV88 )
| ( leq @ ( succ @ SV76 ) @ ( succ @ SV88 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[577]) ).
thf(592,plain,
! [SV96: $i,SV91: $i,SV79: $i] :
( ( ( ~ ( ~ ( leq @ SV79 @ SV91 )
| ~ ( leq @ SV91 @ SV96 ) ) )
= $false )
| ( ( leq @ SV79 @ SV96 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[580]) ).
thf(593,plain,
! [SV92: $i,SV80: $i] :
( ( ~ ( geq @ SV80 @ SV92 )
| ( leq @ SV92 @ SV80 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[581]) ).
thf(594,plain,
! [SV80: $i,SV92: $i] :
( ( ~ ( leq @ SV92 @ SV80 )
| ( geq @ SV80 @ SV92 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[582]) ).
thf(595,plain,
! [SV82: $i] :
( ( ( ~ ( leq @ n0 @ SV82 ) )
= $true )
| ( ( ~ ( leq @ SV82 @ n2 ) )
= $true )
| ( ( ( SV82 = n0 )
| ( SV82 = n1 )
| ( SV82 = n2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[584]) ).
thf(596,plain,
! [SV84: $i] :
( ( ( ~ ( leq @ n0 @ SV84 ) )
= $true )
| ( ( ~ ( leq @ SV84 @ n1 ) )
= $true )
| ( ( ( SV84 = n0 )
| ( SV84 = n1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[586]) ).
thf(597,plain,
! [SV86: $i] :
( ( ( ~ ( leq @ n0 @ SV86 ) )
= $true )
| ( ( ~ ( leq @ SV86 @ n0 ) )
= $true )
| ( ( SV86 = n0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[588]) ).
thf(598,plain,
! [SV87: $i,SV75: $i] :
( ( ( ~ ( leq @ SV75 @ SV87 ) )
= $true )
| ( ( ~ ( ( SV75 != SV87 ) ) )
= $true )
| ( ( gt @ SV87 @ SV75 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[589]) ).
thf(599,plain,
! [SV88: $i,SV76: $i] :
( ( ( ~ ( leq @ ( succ @ SV76 ) @ ( succ @ SV88 ) ) )
= $true )
| ( ( leq @ SV76 @ SV88 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[590]) ).
thf(600,plain,
! [SV88: $i,SV76: $i] :
( ( ( ~ ( leq @ SV76 @ SV88 ) )
= $true )
| ( ( leq @ ( succ @ SV76 ) @ ( succ @ SV88 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[591]) ).
thf(601,plain,
! [SV96: $i,SV91: $i,SV79: $i] :
( ( ( ~ ( leq @ SV79 @ SV91 )
| ~ ( leq @ SV91 @ SV96 ) )
= $true )
| ( ( leq @ SV79 @ SV96 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[592]) ).
thf(602,plain,
! [SV92: $i,SV80: $i] :
( ( ( ~ ( geq @ SV80 @ SV92 ) )
= $true )
| ( ( leq @ SV92 @ SV80 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[593]) ).
thf(603,plain,
! [SV80: $i,SV92: $i] :
( ( ( ~ ( leq @ SV92 @ SV80 ) )
= $true )
| ( ( geq @ SV80 @ SV92 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[594]) ).
thf(604,plain,
! [SV82: $i] :
( ( ( leq @ n0 @ SV82 )
= $false )
| ( ( ~ ( leq @ SV82 @ n2 ) )
= $true )
| ( ( ( SV82 = n0 )
| ( SV82 = n1 )
| ( SV82 = n2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[595]) ).
thf(605,plain,
! [SV84: $i] :
( ( ( leq @ n0 @ SV84 )
= $false )
| ( ( ~ ( leq @ SV84 @ n1 ) )
= $true )
| ( ( ( SV84 = n0 )
| ( SV84 = n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[596]) ).
thf(606,plain,
! [SV86: $i] :
( ( ( leq @ n0 @ SV86 )
= $false )
| ( ( ~ ( leq @ SV86 @ n0 ) )
= $true )
| ( ( SV86 = n0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[597]) ).
thf(607,plain,
! [SV87: $i,SV75: $i] :
( ( ( leq @ SV75 @ SV87 )
= $false )
| ( ( ~ ( ( SV75 != SV87 ) ) )
= $true )
| ( ( gt @ SV87 @ SV75 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[598]) ).
thf(608,plain,
! [SV88: $i,SV76: $i] :
( ( ( leq @ ( succ @ SV76 ) @ ( succ @ SV88 ) )
= $false )
| ( ( leq @ SV76 @ SV88 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[599]) ).
thf(609,plain,
! [SV88: $i,SV76: $i] :
( ( ( leq @ SV76 @ SV88 )
= $false )
| ( ( leq @ ( succ @ SV76 ) @ ( succ @ SV88 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[600]) ).
thf(610,plain,
! [SV96: $i,SV91: $i,SV79: $i] :
( ( ( ~ ( leq @ SV79 @ SV91 ) )
= $true )
| ( ( ~ ( leq @ SV91 @ SV96 ) )
= $true )
| ( ( leq @ SV79 @ SV96 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[601]) ).
thf(611,plain,
! [SV92: $i,SV80: $i] :
( ( ( geq @ SV80 @ SV92 )
= $false )
| ( ( leq @ SV92 @ SV80 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[602]) ).
thf(612,plain,
! [SV80: $i,SV92: $i] :
( ( ( leq @ SV92 @ SV80 )
= $false )
| ( ( geq @ SV80 @ SV92 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[603]) ).
thf(613,plain,
! [SV82: $i] :
( ( ( leq @ SV82 @ n2 )
= $false )
| ( ( leq @ n0 @ SV82 )
= $false )
| ( ( ( SV82 = n0 )
| ( SV82 = n1 )
| ( SV82 = n2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[604]) ).
thf(614,plain,
! [SV84: $i] :
( ( ( leq @ SV84 @ n1 )
= $false )
| ( ( leq @ n0 @ SV84 )
= $false )
| ( ( ( SV84 = n0 )
| ( SV84 = n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[605]) ).
thf(615,plain,
! [SV86: $i] :
( ( ( leq @ SV86 @ n0 )
= $false )
| ( ( leq @ n0 @ SV86 )
= $false )
| ( ( SV86 = n0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[606]) ).
thf(616,plain,
! [SV87: $i,SV75: $i] :
( ( ( SV75 != SV87 )
= $false )
| ( ( leq @ SV75 @ SV87 )
= $false )
| ( ( gt @ SV87 @ SV75 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[607]) ).
thf(617,plain,
! [SV96: $i,SV91: $i,SV79: $i] :
( ( ( leq @ SV79 @ SV91 )
= $false )
| ( ( ~ ( leq @ SV91 @ SV96 ) )
= $true )
| ( ( leq @ SV79 @ SV96 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[610]) ).
thf(618,plain,
! [SV82: $i] :
( ( ( ( SV82 = n0 )
| ( SV82 = n1 ) )
= $true )
| ( ( SV82 = n2 )
= $true )
| ( ( leq @ n0 @ SV82 )
= $false )
| ( ( leq @ SV82 @ n2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[613]) ).
thf(619,plain,
! [SV84: $i] :
( ( ( SV84 = n0 )
= $true )
| ( ( SV84 = n1 )
= $true )
| ( ( leq @ n0 @ SV84 )
= $false )
| ( ( leq @ SV84 @ n1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[614]) ).
thf(620,plain,
! [SV87: $i,SV75: $i] :
( ( ( SV75 = SV87 )
= $true )
| ( ( leq @ SV75 @ SV87 )
= $false )
| ( ( gt @ SV87 @ SV75 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[616]) ).
thf(621,plain,
! [SV79: $i,SV96: $i,SV91: $i] :
( ( ( leq @ SV91 @ SV96 )
= $false )
| ( ( leq @ SV79 @ SV91 )
= $false )
| ( ( leq @ SV79 @ SV96 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[617]) ).
thf(622,plain,
! [SV82: $i] :
( ( ( SV82 = n0 )
= $true )
| ( ( SV82 = n1 )
= $true )
| ( ( SV82 = n2 )
= $true )
| ( ( leq @ n0 @ SV82 )
= $false )
| ( ( leq @ SV82 @ n2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[618]) ).
thf(623,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[508,622,621,620,619,615,612,611,609,608,587,585,583,579,578,568,555,534,533,518,517,516,515,511,510,509]) ).
thf(624,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[623,241,364,496]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV077+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.20 % Computer : n007.cluster.edu
% 0.06/0.20 % Model : x86_64 x86_64
% 0.06/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.20 % Memory : 8046.5625MB
% 0.06/0.20 % OS : Linux 6.8.0-71-generic
% 0.06/0.20 % CPULimit : 300
% 0.06/0.20 % WCLimit : 300
% 0.06/0.20 % DateTime : Tue Oct 6 16:16:01 UTC 2026
% 0.06/0.20 % CPUTime :
% 0.06/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.53/0.55
% 1.53/0.55 No.of.Axioms: 20
% 1.53/0.55
% 1.53/0.55 Length.of.Defs: 0
% 1.53/0.55
% 1.53/0.55 Contains.Choice.Funs: false
% 1.53/0.55 ..............
% 1.53/0.55
% 1.53/0.55 ********************************
% 1.53/0.55 * All subproblems solved! *
% 1.53/0.55 ********************************
% 1.53/0.55 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:22,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:623,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.53/0.55
% 1.53/0.55 %**** Beginning of derivation protocol ****
% 1.53/0.55 % SZS output start CNFRefutation
% See solution above
% 1.53/0.55
% 1.53/0.55 %**** End of derivation protocol ****
% 1.53/0.55 %**** no. of clauses in derivation: 560 ****
% 1.53/0.55 %**** clause counter: 623 ****
% 1.53/0.55
% 1.53/0.55 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:22,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:623,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------