%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWV062+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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 10:54:43 AM UTC 2026
% Result : Theorem 3.09s 0.78s
% Output : CNFRefutation 3.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 23
% Syntax : Number of formulae : 841 ( 516 unt; 0 typ; 0 def)
% Number of atoms : 4701 (1749 equ; 0 cnn)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 6544 (1190 ~;1152 |; 75 &;4028 @)
% ( 16 <=>; 83 =>; 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 : 40 ( 37 usr; 17 con; 0-4 aty)
% Number of variables : 1254 ( 0 ^;1254 !; 0 ?;1254 :)
% 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_n135300,type,
n135300: $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_pv10,type,
pv10: $i ).
thf(tp_pv41,type,
pv41: $i ).
thf(tp_pv43,type,
pv43: $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/sandbox/benchmark/theBenchmark.p',successor_1) ).
thf(4,axiom,
( ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ n0 ) ) ) ) )
= n5 ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',finite_domain_2) ).
thf(8,axiom,
! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n1 ) )
=> ( ( X = n0 )
| ( X = n1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finite_domain_1) ).
thf(9,axiom,
! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n0 ) )
=> ( X = n0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finite_domain_0) ).
thf(21,axiom,
gt @ n135300 @ n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_135300_1) ).
thf(22,axiom,
gt @ n5 @ n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_5_1) ).
thf(26,axiom,
gt @ n1 @ n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_1_0) ).
thf(27,axiom,
gt @ n135300 @ n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_135300_0) ).
thf(28,axiom,
gt @ n5 @ n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_5_0) ).
thf(37,axiom,
gt @ n135300 @ n5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_135300_5) ).
thf(48,axiom,
! [X: $i,Y: $i] :
( ( leq @ ( minus @ X @ Y ) @ X )
=> ( leq @ n0 @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_minus) ).
thf(50,axiom,
! [X: $i,Y: $i] :
( ( leq @ ( succ @ X ) @ ( succ @ Y ) )
<=> ( leq @ X @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_succ_succ) ).
thf(53,axiom,
! [X: $i] :
( ( minus @ X @ n1 )
= ( pred @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pred_minus_1) ).
thf(77,axiom,
! [X: $i,C: $i] :
( ( leq @ n0 @ X )
=> ( leq @ n0 @ ( uniform_int_rnd @ C @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',uniform_int_rand_ranges_lo) ).
thf(78,axiom,
! [X: $i,C: $i] :
( ( leq @ n0 @ X )
=> ( leq @ ( uniform_int_rnd @ C @ X ) @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',uniform_int_rand_ranges_hi) ).
thf(80,axiom,
! [X: $i,Y: $i] :
( ( leq @ X @ Y )
=> ( leq @ X @ ( succ @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_succ) ).
thf(83,axiom,
! [X: $i,Y: $i] :
( ( ( leq @ X @ Y )
& ( X != Y ) )
=> ( gt @ Y @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_gt2) ).
thf(84,axiom,
! [X: $i,Y: $i] :
( ( gt @ Y @ X )
=> ( leq @ X @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_gt1) ).
thf(85,axiom,
! [X: $i,Y: $i] :
( ( geq @ X @ Y )
<=> ( leq @ Y @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_geq) ).
thf(87,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( ( leq @ X @ Y )
& ( leq @ Y @ Z ) )
=> ( leq @ X @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_leq) ).
thf(88,axiom,
! [X: $i] : ( leq @ X @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_leq) ).
thf(92,conjecture,
( ( ( leq @ n0 @ pv10 )
& ( leq @ n0 @ pv41 )
& ( leq @ n0 @ pv43 )
& ( leq @ pv10 @ ( minus @ n135300 @ n1 ) )
& ( leq @ pv41 @ ( minus @ n5 @ n1 ) )
& ( leq @ pv43 @ ( minus @ n5 @ n1 ) ) )
=> ( ( leq @ n0 @ pv10 )
& ( leq @ n0 @ pv41 )
& ( leq @ n0 @ pv43 )
& ( leq @ pv10 @ ( minus @ n135300 @ n1 ) )
& ( leq @ pv41 @ ( minus @ n5 @ n1 ) )
& ( leq @ pv43 @ ( minus @ n5 @ n1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cl5_nebula_array_0003) ).
thf(93,negated_conjecture,
( ( ( ( leq @ n0 @ pv10 )
& ( leq @ n0 @ pv41 )
& ( leq @ n0 @ pv43 )
& ( leq @ pv10 @ ( minus @ n135300 @ n1 ) )
& ( leq @ pv41 @ ( minus @ n5 @ n1 ) )
& ( leq @ pv43 @ ( minus @ n5 @ n1 ) ) )
=> ( ( leq @ n0 @ pv10 )
& ( leq @ n0 @ pv41 )
& ( leq @ n0 @ pv43 )
& ( leq @ pv10 @ ( minus @ n135300 @ n1 ) )
& ( leq @ pv41 @ ( minus @ n5 @ n1 ) )
& ( leq @ pv43 @ ( minus @ n5 @ n1 ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[92]) ).
thf(94,plain,
( ( ( ( leq @ n0 @ pv10 )
& ( leq @ n0 @ pv41 )
& ( leq @ n0 @ pv43 )
& ( leq @ pv10 @ ( minus @ n135300 @ n1 ) )
& ( leq @ pv41 @ ( minus @ n5 @ n1 ) )
& ( leq @ pv43 @ ( minus @ n5 @ n1 ) ) )
=> ( ( leq @ n0 @ pv10 )
& ( leq @ n0 @ pv41 )
& ( leq @ n0 @ pv43 )
& ( leq @ pv10 @ ( minus @ n135300 @ n1 ) )
& ( leq @ pv41 @ ( minus @ n5 @ n1 ) )
& ( leq @ pv43 @ ( minus @ n5 @ n1 ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[93]) ).
thf(95,plain,
( ( ( succ @ n0 )
= n1 )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(96,plain,
( ( ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ n0 ) ) ) ) )
= n5 )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(97,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n2 ) )
=> ( ( X = n0 )
| ( X = n1 )
| ( X = n2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(98,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n1 ) )
=> ( ( X = n0 )
| ( X = n1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(99,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n0 ) )
=> ( X = n0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(100,plain,
( ( gt @ n135300 @ n1 )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(101,plain,
( ( gt @ n5 @ n1 )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(102,plain,
( ( gt @ n1 @ n0 )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(103,plain,
( ( gt @ n135300 @ n0 )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(104,plain,
( ( gt @ n5 @ n0 )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(105,plain,
( ( gt @ n135300 @ n5 )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(106,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ ( minus @ X @ Y ) @ X )
=> ( leq @ n0 @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(107,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ ( succ @ X ) @ ( succ @ Y ) )
<=> ( leq @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(108,plain,
( ( ! [X: $i] :
( ( minus @ X @ n1 )
= ( pred @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(109,plain,
( ( ! [X: $i,C: $i] :
( ( leq @ n0 @ X )
=> ( leq @ n0 @ ( uniform_int_rnd @ C @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(110,plain,
( ( ! [X: $i,C: $i] :
( ( leq @ n0 @ X )
=> ( leq @ ( uniform_int_rnd @ C @ X ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(111,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ X @ Y )
=> ( leq @ X @ ( succ @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(112,plain,
( ( ! [X: $i,Y: $i] :
( ( ( leq @ X @ Y )
& ( X != Y ) )
=> ( gt @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(113,plain,
( ( ! [X: $i,Y: $i] :
( ( gt @ Y @ X )
=> ( leq @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(114,plain,
( ( ! [X: $i,Y: $i] :
( ( geq @ X @ Y )
<=> ( leq @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(115,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( leq @ X @ Y )
& ( leq @ Y @ Z ) )
=> ( leq @ X @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(116,plain,
( ( ! [X: $i] : ( leq @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(117,plain,
( ( leq @ n0 @ pv10 )
= $true ),
inference(standard_cnf,[status(thm)],[94]) ).
thf(118,plain,
( ( leq @ n0 @ pv41 )
= $true ),
inference(standard_cnf,[status(thm)],[94]) ).
thf(119,plain,
( ( leq @ n0 @ pv43 )
= $true ),
inference(standard_cnf,[status(thm)],[94]) ).
thf(120,plain,
( ( leq @ pv10 @ ( minus @ n135300 @ n1 ) )
= $true ),
inference(standard_cnf,[status(thm)],[94]) ).
thf(121,plain,
( ( leq @ pv41 @ ( minus @ n5 @ n1 ) )
= $true ),
inference(standard_cnf,[status(thm)],[94]) ).
thf(122,plain,
( ( leq @ pv43 @ ( minus @ n5 @ n1 ) )
= $true ),
inference(standard_cnf,[status(thm)],[94]) ).
thf(123,plain,
( ( ( leq @ n0 @ pv10 )
& ( leq @ n0 @ pv41 )
& ( leq @ n0 @ pv43 )
& ( leq @ pv10 @ ( minus @ n135300 @ n1 ) )
& ( leq @ pv41 @ ( minus @ n5 @ n1 ) )
& ( leq @ pv43 @ ( minus @ n5 @ n1 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[94]) ).
thf(124,plain,
( ( leq @ n0 @ pv10 )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[123]) ).
thf(125,plain,
( ( leq @ n0 @ pv41 )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[123]) ).
thf(126,plain,
( ( leq @ n0 @ pv43 )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[123]) ).
thf(127,plain,
( ( leq @ pv10 @ ( minus @ n135300 @ n1 ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[123]) ).
thf(128,plain,
( ( leq @ pv41 @ ( minus @ n5 @ n1 ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[123]) ).
thf(129,plain,
( ( leq @ pv43 @ ( minus @ n5 @ n1 ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[123]) ).
thf(130,plain,
( ( ~ ( leq @ n0 @ pv10 ) )
= $true ),
inference(polarity_switch,[status(thm)],[124]) ).
thf(131,plain,
( ( ~ ( leq @ n0 @ pv41 ) )
= $true ),
inference(polarity_switch,[status(thm)],[125]) ).
thf(132,plain,
( ( ~ ( leq @ n0 @ pv43 ) )
= $true ),
inference(polarity_switch,[status(thm)],[126]) ).
thf(133,plain,
( ( ~ ( leq @ pv10 @ ( minus @ n135300 @ n1 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[127]) ).
thf(134,plain,
( ( ~ ( leq @ pv41 @ ( minus @ n5 @ n1 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[128]) ).
thf(135,plain,
( ( ~ ( leq @ pv43 @ ( minus @ n5 @ n1 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[129]) ).
thf(136,plain,
( ( ! [X: $i] : ( leq @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(137,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( leq @ X @ Y )
& ( leq @ Y @ Z ) )
=> ( leq @ X @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[115]) ).
thf(138,plain,
( ( ! [X: $i,Y: $i] :
( ( geq @ X @ Y )
<=> ( leq @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(139,plain,
( ( ! [X: $i,Y: $i] :
( ( gt @ Y @ X )
=> ( leq @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(140,plain,
( ( ! [X: $i,Y: $i] :
( ( ( leq @ X @ Y )
& ( X != Y ) )
=> ( gt @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(141,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ X @ Y )
=> ( leq @ X @ ( succ @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(142,plain,
( ( ! [X: $i,C: $i] :
( ( leq @ n0 @ X )
=> ( leq @ ( uniform_int_rnd @ C @ X ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(143,plain,
( ( ! [X: $i,C: $i] :
( ( leq @ n0 @ X )
=> ( leq @ n0 @ ( uniform_int_rnd @ C @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(144,plain,
( ( ! [X: $i] :
( ( minus @ X @ n1 )
= ( pred @ X ) ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(145,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ ( succ @ X ) @ ( succ @ Y ) )
<=> ( leq @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(146,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ ( minus @ X @ Y ) @ X )
=> ( leq @ n0 @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(147,plain,
( ( gt @ n135300 @ n5 )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(148,plain,
( ( gt @ n5 @ n0 )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(149,plain,
( ( gt @ n135300 @ n0 )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(150,plain,
( ( gt @ n1 @ n0 )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(151,plain,
( ( gt @ n5 @ n1 )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(152,plain,
( ( gt @ n135300 @ n1 )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(153,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n0 ) )
=> ( X = n0 ) ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(154,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n1 ) )
=> ( ( X = n0 )
| ( X = n1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(155,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n2 ) )
=> ( ( X = n0 )
| ( X = n1 )
| ( X = n2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(156,plain,
( ( ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ n0 ) ) ) ) )
= n5 )
= $true ),
inference(copy,[status(thm)],[96]) ).
thf(157,plain,
( ( ( succ @ n0 )
= n1 )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(158,plain,
( ( leq @ pv43 @ ( minus @ n5 @ n1 ) )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(159,plain,
( ( leq @ pv41 @ ( minus @ n5 @ n1 ) )
= $true ),
inference(copy,[status(thm)],[121]) ).
thf(160,plain,
( ( leq @ pv10 @ ( minus @ n135300 @ n1 ) )
= $true ),
inference(copy,[status(thm)],[120]) ).
thf(161,plain,
( ( leq @ n0 @ pv43 )
= $true ),
inference(copy,[status(thm)],[119]) ).
thf(162,plain,
( ( leq @ n0 @ pv41 )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(163,plain,
( ( leq @ n0 @ pv10 )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(164,plain,
( ( ~ ( leq @ n0 @ pv10 ) )
= $true ),
inference(copy,[status(thm)],[130]) ).
thf(165,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( gt @ SX1 @ SX0 )
| ( leq @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[139]) ).
thf(166,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( geq @ SX0 @ SX1 )
| ( leq @ SX1 @ SX0 ) )
| ~ ( ~ ( leq @ SX1 @ SX0 )
| ( geq @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[138]) ).
thf(167,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( leq @ n0 @ SX0 )
| ~ ( leq @ SX0 @ n1 ) )
| ( SX0 = n0 )
| ( SX0 = n1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[154]) ).
thf(168,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( leq @ n0 @ SX0 )
| ~ ( leq @ SX0 @ n2 ) )
| ( SX0 = n0 )
| ( SX0 = n1 )
| ( SX0 = n2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[155]) ).
thf(169,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ ( minus @ SX0 @ SX1 ) @ SX0 )
| ( leq @ n0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[146]) ).
thf(170,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( leq @ n0 @ SX0 )
| ~ ( leq @ SX0 @ n0 ) )
| ( SX0 = n0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[153]) ).
thf(171,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( leq @ SX0 @ SX1 )
| ~ ( leq @ SX1 @ SX2 ) )
| ( leq @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[137]) ).
thf(172,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ n0 @ SX0 )
| ( leq @ ( uniform_int_rnd @ SX1 @ SX0 ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[142]) ).
thf(173,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ n0 @ SX0 )
| ( leq @ n0 @ ( uniform_int_rnd @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[143]) ).
thf(174,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( leq @ SX0 @ SX1 )
| ~ ( ( SX0 != SX1 ) ) )
| ( gt @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[140]) ).
thf(175,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX0 @ SX1 )
| ( leq @ SX0 @ ( succ @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[141]) ).
thf(176,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)],[145]) ).
thf(177,plain,
! [SV1: $i] :
( ( leq @ SV1 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(178,plain,
! [SV2: $i] :
( ( ( minus @ SV2 @ n1 )
= ( pred @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(179,plain,
( ( leq @ n0 @ pv10 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(180,plain,
! [SV3: $i] :
( ( ! [SY24: $i] :
( ~ ( gt @ SY24 @ SV3 )
| ( leq @ SV3 @ SY24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(181,plain,
! [SV4: $i] :
( ( ! [SY25: $i] :
~ ( ~ ( ~ ( geq @ SV4 @ SY25 )
| ( leq @ SY25 @ SV4 ) )
| ~ ( ~ ( leq @ SY25 @ SV4 )
| ( geq @ SV4 @ SY25 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(182,plain,
! [SV5: $i] :
( ( ~ ~ ( ~ ( leq @ n0 @ SV5 )
| ~ ( leq @ SV5 @ n1 ) )
| ( SV5 = n0 )
| ( SV5 = n1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(183,plain,
! [SV6: $i] :
( ( ~ ~ ( ~ ( leq @ n0 @ SV6 )
| ~ ( leq @ SV6 @ n2 ) )
| ( SV6 = n0 )
| ( SV6 = n1 )
| ( SV6 = n2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(184,plain,
! [SV7: $i] :
( ( ! [SY26: $i] :
( ~ ( leq @ ( minus @ SV7 @ SY26 ) @ SV7 )
| ( leq @ n0 @ SY26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(185,plain,
! [SV8: $i] :
( ( ~ ~ ( ~ ( leq @ n0 @ SV8 )
| ~ ( leq @ SV8 @ n0 ) )
| ( SV8 = n0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(186,plain,
! [SV9: $i] :
( ( ! [SY27: $i,SY28: $i] :
( ~ ~ ( ~ ( leq @ SV9 @ SY27 )
| ~ ( leq @ SY27 @ SY28 ) )
| ( leq @ SV9 @ SY28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(187,plain,
! [SV10: $i] :
( ( ! [SY29: $i] :
( ~ ( leq @ n0 @ SV10 )
| ( leq @ ( uniform_int_rnd @ SY29 @ SV10 ) @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(188,plain,
! [SV11: $i] :
( ( ! [SY30: $i] :
( ~ ( leq @ n0 @ SV11 )
| ( leq @ n0 @ ( uniform_int_rnd @ SY30 @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(189,plain,
! [SV12: $i] :
( ( ! [SY31: $i] :
( ~ ~ ( ~ ( leq @ SV12 @ SY31 )
| ~ ( ( SV12 != SY31 ) ) )
| ( gt @ SY31 @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(190,plain,
! [SV13: $i] :
( ( ! [SY32: $i] :
( ~ ( leq @ SV13 @ SY32 )
| ( leq @ SV13 @ ( succ @ SY32 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(191,plain,
! [SV14: $i] :
( ( ! [SY33: $i] :
~ ( ~ ( ~ ( leq @ ( succ @ SV14 ) @ ( succ @ SY33 ) )
| ( leq @ SV14 @ SY33 ) )
| ~ ( ~ ( leq @ SV14 @ SY33 )
| ( leq @ ( succ @ SV14 ) @ ( succ @ SY33 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(192,plain,
! [SV3: $i,SV15: $i] :
( ( ~ ( gt @ SV15 @ SV3 )
| ( leq @ SV3 @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(193,plain,
! [SV16: $i,SV4: $i] :
( ( ~ ( ~ ( ~ ( geq @ SV4 @ SV16 )
| ( leq @ SV16 @ SV4 ) )
| ~ ( ~ ( leq @ SV16 @ SV4 )
| ( geq @ SV4 @ SV16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(194,plain,
! [SV5: $i] :
( ( ( ~ ~ ( ~ ( leq @ n0 @ SV5 )
| ~ ( leq @ SV5 @ n1 ) ) )
= $true )
| ( ( ( SV5 = n0 )
| ( SV5 = n1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[182]) ).
thf(195,plain,
! [SV6: $i] :
( ( ( ~ ~ ( ~ ( leq @ n0 @ SV6 )
| ~ ( leq @ SV6 @ n2 ) ) )
= $true )
| ( ( ( SV6 = n0 )
| ( SV6 = n1 )
| ( SV6 = n2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[183]) ).
thf(196,plain,
! [SV17: $i,SV7: $i] :
( ( ~ ( leq @ ( minus @ SV7 @ SV17 ) @ SV7 )
| ( leq @ n0 @ SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(197,plain,
! [SV8: $i] :
( ( ( ~ ~ ( ~ ( leq @ n0 @ SV8 )
| ~ ( leq @ SV8 @ n0 ) ) )
= $true )
| ( ( SV8 = n0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[185]) ).
thf(198,plain,
! [SV18: $i,SV9: $i] :
( ( ! [SY34: $i] :
( ~ ~ ( ~ ( leq @ SV9 @ SV18 )
| ~ ( leq @ SV18 @ SY34 ) )
| ( leq @ SV9 @ SY34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(199,plain,
! [SV19: $i,SV10: $i] :
( ( ~ ( leq @ n0 @ SV10 )
| ( leq @ ( uniform_int_rnd @ SV19 @ SV10 ) @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(200,plain,
! [SV20: $i,SV11: $i] :
( ( ~ ( leq @ n0 @ SV11 )
| ( leq @ n0 @ ( uniform_int_rnd @ SV20 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(201,plain,
! [SV21: $i,SV12: $i] :
( ( ~ ~ ( ~ ( leq @ SV12 @ SV21 )
| ~ ( ( SV12 != SV21 ) ) )
| ( gt @ SV21 @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(202,plain,
! [SV22: $i,SV13: $i] :
( ( ~ ( leq @ SV13 @ SV22 )
| ( leq @ SV13 @ ( succ @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(203,plain,
! [SV23: $i,SV14: $i] :
( ( ~ ( ~ ( ~ ( leq @ ( succ @ SV14 ) @ ( succ @ SV23 ) )
| ( leq @ SV14 @ SV23 ) )
| ~ ( ~ ( leq @ SV14 @ SV23 )
| ( leq @ ( succ @ SV14 ) @ ( succ @ SV23 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[191]) ).
thf(204,plain,
! [SV3: $i,SV15: $i] :
( ( ( ~ ( gt @ SV15 @ SV3 ) )
= $true )
| ( ( leq @ SV3 @ SV15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[192]) ).
thf(205,plain,
! [SV16: $i,SV4: $i] :
( ( ~ ( ~ ( geq @ SV4 @ SV16 )
| ( leq @ SV16 @ SV4 ) )
| ~ ( ~ ( leq @ SV16 @ SV4 )
| ( geq @ SV4 @ SV16 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(206,plain,
! [SV5: $i] :
( ( ( ~ ( ~ ( leq @ n0 @ SV5 )
| ~ ( leq @ SV5 @ n1 ) ) )
= $false )
| ( ( ( SV5 = n0 )
| ( SV5 = n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(207,plain,
! [SV6: $i] :
( ( ( ~ ( ~ ( leq @ n0 @ SV6 )
| ~ ( leq @ SV6 @ n2 ) ) )
= $false )
| ( ( ( SV6 = n0 )
| ( SV6 = n1 )
| ( SV6 = n2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(208,plain,
! [SV17: $i,SV7: $i] :
( ( ( ~ ( leq @ ( minus @ SV7 @ SV17 ) @ SV7 ) )
= $true )
| ( ( leq @ n0 @ SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[196]) ).
thf(209,plain,
! [SV8: $i] :
( ( ( ~ ( ~ ( leq @ n0 @ SV8 )
| ~ ( leq @ SV8 @ n0 ) ) )
= $false )
| ( ( SV8 = n0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(210,plain,
! [SV24: $i,SV18: $i,SV9: $i] :
( ( ~ ~ ( ~ ( leq @ SV9 @ SV18 )
| ~ ( leq @ SV18 @ SV24 ) )
| ( leq @ SV9 @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(211,plain,
! [SV19: $i,SV10: $i] :
( ( ( ~ ( leq @ n0 @ SV10 ) )
= $true )
| ( ( leq @ ( uniform_int_rnd @ SV19 @ SV10 ) @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[199]) ).
thf(212,plain,
! [SV20: $i,SV11: $i] :
( ( ( ~ ( leq @ n0 @ SV11 ) )
= $true )
| ( ( leq @ n0 @ ( uniform_int_rnd @ SV20 @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[200]) ).
thf(213,plain,
! [SV21: $i,SV12: $i] :
( ( ( ~ ~ ( ~ ( leq @ SV12 @ SV21 )
| ~ ( ( SV12 != SV21 ) ) ) )
= $true )
| ( ( gt @ SV21 @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[201]) ).
thf(214,plain,
! [SV22: $i,SV13: $i] :
( ( ( ~ ( leq @ SV13 @ SV22 ) )
= $true )
| ( ( leq @ SV13 @ ( succ @ SV22 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[202]) ).
thf(215,plain,
! [SV23: $i,SV14: $i] :
( ( ~ ( ~ ( leq @ ( succ @ SV14 ) @ ( succ @ SV23 ) )
| ( leq @ SV14 @ SV23 ) )
| ~ ( ~ ( leq @ SV14 @ SV23 )
| ( leq @ ( succ @ SV14 ) @ ( succ @ SV23 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(216,plain,
! [SV3: $i,SV15: $i] :
( ( ( gt @ SV15 @ SV3 )
= $false )
| ( ( leq @ SV3 @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(217,plain,
! [SV16: $i,SV4: $i] :
( ( ~ ( ~ ( geq @ SV4 @ SV16 )
| ( leq @ SV16 @ SV4 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[205]) ).
thf(218,plain,
! [SV4: $i,SV16: $i] :
( ( ~ ( ~ ( leq @ SV16 @ SV4 )
| ( geq @ SV4 @ SV16 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[205]) ).
thf(219,plain,
! [SV5: $i] :
( ( ( ~ ( leq @ n0 @ SV5 )
| ~ ( leq @ SV5 @ n1 ) )
= $true )
| ( ( ( SV5 = n0 )
| ( SV5 = n1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[206]) ).
thf(220,plain,
! [SV6: $i] :
( ( ( ~ ( leq @ n0 @ SV6 )
| ~ ( leq @ SV6 @ n2 ) )
= $true )
| ( ( ( SV6 = n0 )
| ( SV6 = n1 )
| ( SV6 = n2 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[207]) ).
thf(221,plain,
! [SV17: $i,SV7: $i] :
( ( ( leq @ ( minus @ SV7 @ SV17 ) @ SV7 )
= $false )
| ( ( leq @ n0 @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[208]) ).
thf(222,plain,
! [SV8: $i] :
( ( ( ~ ( leq @ n0 @ SV8 )
| ~ ( leq @ SV8 @ n0 ) )
= $true )
| ( ( SV8 = n0 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[209]) ).
thf(223,plain,
! [SV24: $i,SV18: $i,SV9: $i] :
( ( ( ~ ~ ( ~ ( leq @ SV9 @ SV18 )
| ~ ( leq @ SV18 @ SV24 ) ) )
= $true )
| ( ( leq @ SV9 @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[210]) ).
thf(224,plain,
! [SV19: $i,SV10: $i] :
( ( ( leq @ n0 @ SV10 )
= $false )
| ( ( leq @ ( uniform_int_rnd @ SV19 @ SV10 ) @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[211]) ).
thf(225,plain,
! [SV20: $i,SV11: $i] :
( ( ( leq @ n0 @ SV11 )
= $false )
| ( ( leq @ n0 @ ( uniform_int_rnd @ SV20 @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[212]) ).
thf(226,plain,
! [SV21: $i,SV12: $i] :
( ( ( ~ ( ~ ( leq @ SV12 @ SV21 )
| ~ ( ( SV12 != SV21 ) ) ) )
= $false )
| ( ( gt @ SV21 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[213]) ).
thf(227,plain,
! [SV22: $i,SV13: $i] :
( ( ( leq @ SV13 @ SV22 )
= $false )
| ( ( leq @ SV13 @ ( succ @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[214]) ).
thf(228,plain,
! [SV23: $i,SV14: $i] :
( ( ~ ( ~ ( leq @ ( succ @ SV14 ) @ ( succ @ SV23 ) )
| ( leq @ SV14 @ SV23 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[215]) ).
thf(229,plain,
! [SV23: $i,SV14: $i] :
( ( ~ ( ~ ( leq @ SV14 @ SV23 )
| ( leq @ ( succ @ SV14 ) @ ( succ @ SV23 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[215]) ).
thf(230,plain,
! [SV16: $i,SV4: $i] :
( ( ~ ( geq @ SV4 @ SV16 )
| ( leq @ SV16 @ SV4 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[217]) ).
thf(231,plain,
! [SV4: $i,SV16: $i] :
( ( ~ ( leq @ SV16 @ SV4 )
| ( geq @ SV4 @ SV16 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[218]) ).
thf(232,plain,
! [SV5: $i] :
( ( ( ~ ( leq @ n0 @ SV5 ) )
= $true )
| ( ( ~ ( leq @ SV5 @ n1 ) )
= $true )
| ( ( ( SV5 = n0 )
| ( SV5 = n1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[219]) ).
thf(233,plain,
! [SV6: $i] :
( ( ( ~ ( leq @ n0 @ SV6 ) )
= $true )
| ( ( ~ ( leq @ SV6 @ n2 ) )
= $true )
| ( ( ( SV6 = n0 )
| ( SV6 = n1 )
| ( SV6 = n2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[220]) ).
thf(234,plain,
! [SV8: $i] :
( ( ( ~ ( leq @ n0 @ SV8 ) )
= $true )
| ( ( ~ ( leq @ SV8 @ n0 ) )
= $true )
| ( ( SV8 = n0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[222]) ).
thf(235,plain,
! [SV24: $i,SV18: $i,SV9: $i] :
( ( ( ~ ( ~ ( leq @ SV9 @ SV18 )
| ~ ( leq @ SV18 @ SV24 ) ) )
= $false )
| ( ( leq @ SV9 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[223]) ).
thf(236,plain,
! [SV21: $i,SV12: $i] :
( ( ( ~ ( leq @ SV12 @ SV21 )
| ~ ( ( SV12 != SV21 ) ) )
= $true )
| ( ( gt @ SV21 @ SV12 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[226]) ).
thf(237,plain,
! [SV23: $i,SV14: $i] :
( ( ~ ( leq @ ( succ @ SV14 ) @ ( succ @ SV23 ) )
| ( leq @ SV14 @ SV23 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[228]) ).
thf(238,plain,
! [SV23: $i,SV14: $i] :
( ( ~ ( leq @ SV14 @ SV23 )
| ( leq @ ( succ @ SV14 ) @ ( succ @ SV23 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[229]) ).
thf(239,plain,
! [SV16: $i,SV4: $i] :
( ( ( ~ ( geq @ SV4 @ SV16 ) )
= $true )
| ( ( leq @ SV16 @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[230]) ).
thf(240,plain,
! [SV4: $i,SV16: $i] :
( ( ( ~ ( leq @ SV16 @ SV4 ) )
= $true )
| ( ( geq @ SV4 @ SV16 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[231]) ).
thf(241,plain,
! [SV5: $i] :
( ( ( leq @ n0 @ SV5 )
= $false )
| ( ( ~ ( leq @ SV5 @ n1 ) )
= $true )
| ( ( ( SV5 = n0 )
| ( SV5 = n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[232]) ).
thf(242,plain,
! [SV6: $i] :
( ( ( leq @ n0 @ SV6 )
= $false )
| ( ( ~ ( leq @ SV6 @ n2 ) )
= $true )
| ( ( ( SV6 = n0 )
| ( SV6 = n1 )
| ( SV6 = n2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[233]) ).
thf(243,plain,
! [SV8: $i] :
( ( ( leq @ n0 @ SV8 )
= $false )
| ( ( ~ ( leq @ SV8 @ n0 ) )
= $true )
| ( ( SV8 = n0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[234]) ).
thf(244,plain,
! [SV24: $i,SV18: $i,SV9: $i] :
( ( ( ~ ( leq @ SV9 @ SV18 )
| ~ ( leq @ SV18 @ SV24 ) )
= $true )
| ( ( leq @ SV9 @ SV24 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[235]) ).
thf(245,plain,
! [SV21: $i,SV12: $i] :
( ( ( ~ ( leq @ SV12 @ SV21 ) )
= $true )
| ( ( ~ ( ( SV12 != SV21 ) ) )
= $true )
| ( ( gt @ SV21 @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[236]) ).
thf(246,plain,
! [SV23: $i,SV14: $i] :
( ( ( ~ ( leq @ ( succ @ SV14 ) @ ( succ @ SV23 ) ) )
= $true )
| ( ( leq @ SV14 @ SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[237]) ).
thf(247,plain,
! [SV23: $i,SV14: $i] :
( ( ( ~ ( leq @ SV14 @ SV23 ) )
= $true )
| ( ( leq @ ( succ @ SV14 ) @ ( succ @ SV23 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[238]) ).
thf(248,plain,
! [SV16: $i,SV4: $i] :
( ( ( geq @ SV4 @ SV16 )
= $false )
| ( ( leq @ SV16 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[239]) ).
thf(249,plain,
! [SV4: $i,SV16: $i] :
( ( ( leq @ SV16 @ SV4 )
= $false )
| ( ( geq @ SV4 @ SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[240]) ).
thf(250,plain,
! [SV5: $i] :
( ( ( leq @ SV5 @ n1 )
= $false )
| ( ( leq @ n0 @ SV5 )
= $false )
| ( ( ( SV5 = n0 )
| ( SV5 = n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[241]) ).
thf(251,plain,
! [SV6: $i] :
( ( ( leq @ SV6 @ n2 )
= $false )
| ( ( leq @ n0 @ SV6 )
= $false )
| ( ( ( SV6 = n0 )
| ( SV6 = n1 )
| ( SV6 = n2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[242]) ).
thf(252,plain,
! [SV8: $i] :
( ( ( leq @ SV8 @ n0 )
= $false )
| ( ( leq @ n0 @ SV8 )
= $false )
| ( ( SV8 = n0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[243]) ).
thf(253,plain,
! [SV24: $i,SV18: $i,SV9: $i] :
( ( ( ~ ( leq @ SV9 @ SV18 ) )
= $true )
| ( ( ~ ( leq @ SV18 @ SV24 ) )
= $true )
| ( ( leq @ SV9 @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[244]) ).
thf(254,plain,
! [SV21: $i,SV12: $i] :
( ( ( leq @ SV12 @ SV21 )
= $false )
| ( ( ~ ( ( SV12 != SV21 ) ) )
= $true )
| ( ( gt @ SV21 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[245]) ).
thf(255,plain,
! [SV23: $i,SV14: $i] :
( ( ( leq @ ( succ @ SV14 ) @ ( succ @ SV23 ) )
= $false )
| ( ( leq @ SV14 @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[246]) ).
thf(256,plain,
! [SV23: $i,SV14: $i] :
( ( ( leq @ SV14 @ SV23 )
= $false )
| ( ( leq @ ( succ @ SV14 ) @ ( succ @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[247]) ).
thf(257,plain,
! [SV5: $i] :
( ( ( SV5 = n0 )
= $true )
| ( ( SV5 = n1 )
= $true )
| ( ( leq @ n0 @ SV5 )
= $false )
| ( ( leq @ SV5 @ n1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[250]) ).
thf(258,plain,
! [SV6: $i] :
( ( ( ( SV6 = n0 )
| ( SV6 = n1 ) )
= $true )
| ( ( SV6 = n2 )
= $true )
| ( ( leq @ n0 @ SV6 )
= $false )
| ( ( leq @ SV6 @ n2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[251]) ).
thf(259,plain,
! [SV24: $i,SV18: $i,SV9: $i] :
( ( ( leq @ SV9 @ SV18 )
= $false )
| ( ( ~ ( leq @ SV18 @ SV24 ) )
= $true )
| ( ( leq @ SV9 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[253]) ).
thf(260,plain,
! [SV21: $i,SV12: $i] :
( ( ( SV12 != SV21 )
= $false )
| ( ( leq @ SV12 @ SV21 )
= $false )
| ( ( gt @ SV21 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[254]) ).
thf(261,plain,
! [SV6: $i] :
( ( ( SV6 = n0 )
= $true )
| ( ( SV6 = n1 )
= $true )
| ( ( SV6 = n2 )
= $true )
| ( ( leq @ n0 @ SV6 )
= $false )
| ( ( leq @ SV6 @ n2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[258]) ).
thf(262,plain,
! [SV9: $i,SV24: $i,SV18: $i] :
( ( ( leq @ SV18 @ SV24 )
= $false )
| ( ( leq @ SV9 @ SV18 )
= $false )
| ( ( leq @ SV9 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[259]) ).
thf(263,plain,
! [SV21: $i,SV12: $i] :
( ( ( SV12 = SV21 )
= $true )
| ( ( leq @ SV12 @ SV21 )
= $false )
| ( ( gt @ SV21 @ SV12 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[260]) ).
thf(264,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[147,263,262,261,257,256,255,252,249,248,227,225,224,221,216,179,178,177,163,162,161,160,159,158,157,156,152,151,150,149,148]) ).
thf(265,plain,
( ( ! [X: $i] : ( leq @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(266,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( leq @ X @ Y )
& ( leq @ Y @ Z ) )
=> ( leq @ X @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[115]) ).
thf(267,plain,
( ( ! [X: $i,Y: $i] :
( ( geq @ X @ Y )
<=> ( leq @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(268,plain,
( ( ! [X: $i,Y: $i] :
( ( gt @ Y @ X )
=> ( leq @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(269,plain,
( ( ! [X: $i,Y: $i] :
( ( ( leq @ X @ Y )
& ( X != Y ) )
=> ( gt @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(270,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ X @ Y )
=> ( leq @ X @ ( succ @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(271,plain,
( ( ! [X: $i,C: $i] :
( ( leq @ n0 @ X )
=> ( leq @ ( uniform_int_rnd @ C @ X ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(272,plain,
( ( ! [X: $i,C: $i] :
( ( leq @ n0 @ X )
=> ( leq @ n0 @ ( uniform_int_rnd @ C @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(273,plain,
( ( ! [X: $i] :
( ( minus @ X @ n1 )
= ( pred @ X ) ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(274,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ ( succ @ X ) @ ( succ @ Y ) )
<=> ( leq @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(275,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ ( minus @ X @ Y ) @ X )
=> ( leq @ n0 @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(276,plain,
( ( gt @ n135300 @ n5 )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(277,plain,
( ( gt @ n5 @ n0 )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(278,plain,
( ( gt @ n135300 @ n0 )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(279,plain,
( ( gt @ n1 @ n0 )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(280,plain,
( ( gt @ n5 @ n1 )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(281,plain,
( ( gt @ n135300 @ n1 )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(282,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n0 ) )
=> ( X = n0 ) ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(283,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n1 ) )
=> ( ( X = n0 )
| ( X = n1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(284,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n2 ) )
=> ( ( X = n0 )
| ( X = n1 )
| ( X = n2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(285,plain,
( ( ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ n0 ) ) ) ) )
= n5 )
= $true ),
inference(copy,[status(thm)],[96]) ).
thf(286,plain,
( ( ( succ @ n0 )
= n1 )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(287,plain,
( ( leq @ pv43 @ ( minus @ n5 @ n1 ) )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(288,plain,
( ( leq @ pv41 @ ( minus @ n5 @ n1 ) )
= $true ),
inference(copy,[status(thm)],[121]) ).
thf(289,plain,
( ( leq @ pv10 @ ( minus @ n135300 @ n1 ) )
= $true ),
inference(copy,[status(thm)],[120]) ).
thf(290,plain,
( ( leq @ n0 @ pv43 )
= $true ),
inference(copy,[status(thm)],[119]) ).
thf(291,plain,
( ( leq @ n0 @ pv41 )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(292,plain,
( ( leq @ n0 @ pv10 )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(293,plain,
( ( ~ ( leq @ n0 @ pv41 ) )
= $true ),
inference(copy,[status(thm)],[131]) ).
thf(294,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( leq @ n0 @ SX0 )
| ~ ( leq @ SX0 @ n0 ) )
| ( SX0 = n0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[282]) ).
thf(295,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( geq @ SX0 @ SX1 )
| ( leq @ SX1 @ SX0 ) )
| ~ ( ~ ( leq @ SX1 @ SX0 )
| ( geq @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[267]) ).
thf(296,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( gt @ SX1 @ SX0 )
| ( leq @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[268]) ).
thf(297,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( leq @ SX0 @ SX1 )
| ~ ( leq @ SX1 @ SX2 ) )
| ( leq @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[266]) ).
thf(298,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( leq @ n0 @ SX0 )
| ~ ( leq @ SX0 @ n2 ) )
| ( SX0 = n0 )
| ( SX0 = n1 )
| ( SX0 = n2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[284]) ).
thf(299,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)],[274]) ).
thf(300,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( leq @ SX0 @ SX1 )
| ~ ( ( SX0 != SX1 ) ) )
| ( gt @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[269]) ).
thf(301,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ n0 @ SX0 )
| ( leq @ ( uniform_int_rnd @ SX1 @ SX0 ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[271]) ).
thf(302,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ ( minus @ SX0 @ SX1 ) @ SX0 )
| ( leq @ n0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[275]) ).
thf(303,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( leq @ n0 @ SX0 )
| ~ ( leq @ SX0 @ n1 ) )
| ( SX0 = n0 )
| ( SX0 = n1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[283]) ).
thf(304,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX0 @ SX1 )
| ( leq @ SX0 @ ( succ @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[270]) ).
thf(305,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ n0 @ SX0 )
| ( leq @ n0 @ ( uniform_int_rnd @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[272]) ).
thf(306,plain,
! [SV25: $i] :
( ( leq @ SV25 @ SV25 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[265]) ).
thf(307,plain,
! [SV26: $i] :
( ( ( minus @ SV26 @ n1 )
= ( pred @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[273]) ).
thf(308,plain,
( ( leq @ n0 @ pv41 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[293]) ).
thf(309,plain,
! [SV27: $i] :
( ( ~ ~ ( ~ ( leq @ n0 @ SV27 )
| ~ ( leq @ SV27 @ n0 ) )
| ( SV27 = n0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[294]) ).
thf(310,plain,
! [SV28: $i] :
( ( ! [SY35: $i] :
~ ( ~ ( ~ ( geq @ SV28 @ SY35 )
| ( leq @ SY35 @ SV28 ) )
| ~ ( ~ ( leq @ SY35 @ SV28 )
| ( geq @ SV28 @ SY35 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[295]) ).
thf(311,plain,
! [SV29: $i] :
( ( ! [SY36: $i] :
( ~ ( gt @ SY36 @ SV29 )
| ( leq @ SV29 @ SY36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[296]) ).
thf(312,plain,
! [SV30: $i] :
( ( ! [SY37: $i,SY38: $i] :
( ~ ~ ( ~ ( leq @ SV30 @ SY37 )
| ~ ( leq @ SY37 @ SY38 ) )
| ( leq @ SV30 @ SY38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[297]) ).
thf(313,plain,
! [SV31: $i] :
( ( ~ ~ ( ~ ( leq @ n0 @ SV31 )
| ~ ( leq @ SV31 @ n2 ) )
| ( SV31 = n0 )
| ( SV31 = n1 )
| ( SV31 = n2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[298]) ).
thf(314,plain,
! [SV32: $i] :
( ( ! [SY39: $i] :
~ ( ~ ( ~ ( leq @ ( succ @ SV32 ) @ ( succ @ SY39 ) )
| ( leq @ SV32 @ SY39 ) )
| ~ ( ~ ( leq @ SV32 @ SY39 )
| ( leq @ ( succ @ SV32 ) @ ( succ @ SY39 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[299]) ).
thf(315,plain,
! [SV33: $i] :
( ( ! [SY40: $i] :
( ~ ~ ( ~ ( leq @ SV33 @ SY40 )
| ~ ( ( SV33 != SY40 ) ) )
| ( gt @ SY40 @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[300]) ).
thf(316,plain,
! [SV34: $i] :
( ( ! [SY41: $i] :
( ~ ( leq @ n0 @ SV34 )
| ( leq @ ( uniform_int_rnd @ SY41 @ SV34 ) @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[301]) ).
thf(317,plain,
! [SV35: $i] :
( ( ! [SY42: $i] :
( ~ ( leq @ ( minus @ SV35 @ SY42 ) @ SV35 )
| ( leq @ n0 @ SY42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[302]) ).
thf(318,plain,
! [SV36: $i] :
( ( ~ ~ ( ~ ( leq @ n0 @ SV36 )
| ~ ( leq @ SV36 @ n1 ) )
| ( SV36 = n0 )
| ( SV36 = n1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[303]) ).
thf(319,plain,
! [SV37: $i] :
( ( ! [SY43: $i] :
( ~ ( leq @ SV37 @ SY43 )
| ( leq @ SV37 @ ( succ @ SY43 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[304]) ).
thf(320,plain,
! [SV38: $i] :
( ( ! [SY44: $i] :
( ~ ( leq @ n0 @ SV38 )
| ( leq @ n0 @ ( uniform_int_rnd @ SY44 @ SV38 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[305]) ).
thf(321,plain,
! [SV27: $i] :
( ( ( ~ ~ ( ~ ( leq @ n0 @ SV27 )
| ~ ( leq @ SV27 @ n0 ) ) )
= $true )
| ( ( SV27 = n0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[309]) ).
thf(322,plain,
! [SV39: $i,SV28: $i] :
( ( ~ ( ~ ( ~ ( geq @ SV28 @ SV39 )
| ( leq @ SV39 @ SV28 ) )
| ~ ( ~ ( leq @ SV39 @ SV28 )
| ( geq @ SV28 @ SV39 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[310]) ).
thf(323,plain,
! [SV29: $i,SV40: $i] :
( ( ~ ( gt @ SV40 @ SV29 )
| ( leq @ SV29 @ SV40 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[311]) ).
thf(324,plain,
! [SV41: $i,SV30: $i] :
( ( ! [SY45: $i] :
( ~ ~ ( ~ ( leq @ SV30 @ SV41 )
| ~ ( leq @ SV41 @ SY45 ) )
| ( leq @ SV30 @ SY45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[312]) ).
thf(325,plain,
! [SV31: $i] :
( ( ( ~ ~ ( ~ ( leq @ n0 @ SV31 )
| ~ ( leq @ SV31 @ n2 ) ) )
= $true )
| ( ( ( SV31 = n0 )
| ( SV31 = n1 )
| ( SV31 = n2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[313]) ).
thf(326,plain,
! [SV42: $i,SV32: $i] :
( ( ~ ( ~ ( ~ ( leq @ ( succ @ SV32 ) @ ( succ @ SV42 ) )
| ( leq @ SV32 @ SV42 ) )
| ~ ( ~ ( leq @ SV32 @ SV42 )
| ( leq @ ( succ @ SV32 ) @ ( succ @ SV42 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[314]) ).
thf(327,plain,
! [SV43: $i,SV33: $i] :
( ( ~ ~ ( ~ ( leq @ SV33 @ SV43 )
| ~ ( ( SV33 != SV43 ) ) )
| ( gt @ SV43 @ SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[315]) ).
thf(328,plain,
! [SV44: $i,SV34: $i] :
( ( ~ ( leq @ n0 @ SV34 )
| ( leq @ ( uniform_int_rnd @ SV44 @ SV34 ) @ SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[316]) ).
thf(329,plain,
! [SV45: $i,SV35: $i] :
( ( ~ ( leq @ ( minus @ SV35 @ SV45 ) @ SV35 )
| ( leq @ n0 @ SV45 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[317]) ).
thf(330,plain,
! [SV36: $i] :
( ( ( ~ ~ ( ~ ( leq @ n0 @ SV36 )
| ~ ( leq @ SV36 @ n1 ) ) )
= $true )
| ( ( ( SV36 = n0 )
| ( SV36 = n1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[318]) ).
thf(331,plain,
! [SV46: $i,SV37: $i] :
( ( ~ ( leq @ SV37 @ SV46 )
| ( leq @ SV37 @ ( succ @ SV46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[319]) ).
thf(332,plain,
! [SV47: $i,SV38: $i] :
( ( ~ ( leq @ n0 @ SV38 )
| ( leq @ n0 @ ( uniform_int_rnd @ SV47 @ SV38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[320]) ).
thf(333,plain,
! [SV27: $i] :
( ( ( ~ ( ~ ( leq @ n0 @ SV27 )
| ~ ( leq @ SV27 @ n0 ) ) )
= $false )
| ( ( SV27 = n0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[321]) ).
thf(334,plain,
! [SV39: $i,SV28: $i] :
( ( ~ ( ~ ( geq @ SV28 @ SV39 )
| ( leq @ SV39 @ SV28 ) )
| ~ ( ~ ( leq @ SV39 @ SV28 )
| ( geq @ SV28 @ SV39 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[322]) ).
thf(335,plain,
! [SV29: $i,SV40: $i] :
( ( ( ~ ( gt @ SV40 @ SV29 ) )
= $true )
| ( ( leq @ SV29 @ SV40 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[323]) ).
thf(336,plain,
! [SV48: $i,SV41: $i,SV30: $i] :
( ( ~ ~ ( ~ ( leq @ SV30 @ SV41 )
| ~ ( leq @ SV41 @ SV48 ) )
| ( leq @ SV30 @ SV48 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[324]) ).
thf(337,plain,
! [SV31: $i] :
( ( ( ~ ( ~ ( leq @ n0 @ SV31 )
| ~ ( leq @ SV31 @ n2 ) ) )
= $false )
| ( ( ( SV31 = n0 )
| ( SV31 = n1 )
| ( SV31 = n2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[325]) ).
thf(338,plain,
! [SV42: $i,SV32: $i] :
( ( ~ ( ~ ( leq @ ( succ @ SV32 ) @ ( succ @ SV42 ) )
| ( leq @ SV32 @ SV42 ) )
| ~ ( ~ ( leq @ SV32 @ SV42 )
| ( leq @ ( succ @ SV32 ) @ ( succ @ SV42 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[326]) ).
thf(339,plain,
! [SV43: $i,SV33: $i] :
( ( ( ~ ~ ( ~ ( leq @ SV33 @ SV43 )
| ~ ( ( SV33 != SV43 ) ) ) )
= $true )
| ( ( gt @ SV43 @ SV33 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[327]) ).
thf(340,plain,
! [SV44: $i,SV34: $i] :
( ( ( ~ ( leq @ n0 @ SV34 ) )
= $true )
| ( ( leq @ ( uniform_int_rnd @ SV44 @ SV34 ) @ SV34 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[328]) ).
thf(341,plain,
! [SV45: $i,SV35: $i] :
( ( ( ~ ( leq @ ( minus @ SV35 @ SV45 ) @ SV35 ) )
= $true )
| ( ( leq @ n0 @ SV45 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[329]) ).
thf(342,plain,
! [SV36: $i] :
( ( ( ~ ( ~ ( leq @ n0 @ SV36 )
| ~ ( leq @ SV36 @ n1 ) ) )
= $false )
| ( ( ( SV36 = n0 )
| ( SV36 = n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[330]) ).
thf(343,plain,
! [SV46: $i,SV37: $i] :
( ( ( ~ ( leq @ SV37 @ SV46 ) )
= $true )
| ( ( leq @ SV37 @ ( succ @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[331]) ).
thf(344,plain,
! [SV47: $i,SV38: $i] :
( ( ( ~ ( leq @ n0 @ SV38 ) )
= $true )
| ( ( leq @ n0 @ ( uniform_int_rnd @ SV47 @ SV38 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[332]) ).
thf(345,plain,
! [SV27: $i] :
( ( ( ~ ( leq @ n0 @ SV27 )
| ~ ( leq @ SV27 @ n0 ) )
= $true )
| ( ( SV27 = n0 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[333]) ).
thf(346,plain,
! [SV39: $i,SV28: $i] :
( ( ~ ( ~ ( geq @ SV28 @ SV39 )
| ( leq @ SV39 @ SV28 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[334]) ).
thf(347,plain,
! [SV28: $i,SV39: $i] :
( ( ~ ( ~ ( leq @ SV39 @ SV28 )
| ( geq @ SV28 @ SV39 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[334]) ).
thf(348,plain,
! [SV29: $i,SV40: $i] :
( ( ( gt @ SV40 @ SV29 )
= $false )
| ( ( leq @ SV29 @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[335]) ).
thf(349,plain,
! [SV48: $i,SV41: $i,SV30: $i] :
( ( ( ~ ~ ( ~ ( leq @ SV30 @ SV41 )
| ~ ( leq @ SV41 @ SV48 ) ) )
= $true )
| ( ( leq @ SV30 @ SV48 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[336]) ).
thf(350,plain,
! [SV31: $i] :
( ( ( ~ ( leq @ n0 @ SV31 )
| ~ ( leq @ SV31 @ n2 ) )
= $true )
| ( ( ( SV31 = n0 )
| ( SV31 = n1 )
| ( SV31 = n2 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[337]) ).
thf(351,plain,
! [SV42: $i,SV32: $i] :
( ( ~ ( ~ ( leq @ ( succ @ SV32 ) @ ( succ @ SV42 ) )
| ( leq @ SV32 @ SV42 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[338]) ).
thf(352,plain,
! [SV42: $i,SV32: $i] :
( ( ~ ( ~ ( leq @ SV32 @ SV42 )
| ( leq @ ( succ @ SV32 ) @ ( succ @ SV42 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[338]) ).
thf(353,plain,
! [SV43: $i,SV33: $i] :
( ( ( ~ ( ~ ( leq @ SV33 @ SV43 )
| ~ ( ( SV33 != SV43 ) ) ) )
= $false )
| ( ( gt @ SV43 @ SV33 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[339]) ).
thf(354,plain,
! [SV44: $i,SV34: $i] :
( ( ( leq @ n0 @ SV34 )
= $false )
| ( ( leq @ ( uniform_int_rnd @ SV44 @ SV34 ) @ SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[340]) ).
thf(355,plain,
! [SV45: $i,SV35: $i] :
( ( ( leq @ ( minus @ SV35 @ SV45 ) @ SV35 )
= $false )
| ( ( leq @ n0 @ SV45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[341]) ).
thf(356,plain,
! [SV36: $i] :
( ( ( ~ ( leq @ n0 @ SV36 )
| ~ ( leq @ SV36 @ n1 ) )
= $true )
| ( ( ( SV36 = n0 )
| ( SV36 = n1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[342]) ).
thf(357,plain,
! [SV46: $i,SV37: $i] :
( ( ( leq @ SV37 @ SV46 )
= $false )
| ( ( leq @ SV37 @ ( succ @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[343]) ).
thf(358,plain,
! [SV47: $i,SV38: $i] :
( ( ( leq @ n0 @ SV38 )
= $false )
| ( ( leq @ n0 @ ( uniform_int_rnd @ SV47 @ SV38 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[344]) ).
thf(359,plain,
! [SV27: $i] :
( ( ( ~ ( leq @ n0 @ SV27 ) )
= $true )
| ( ( ~ ( leq @ SV27 @ n0 ) )
= $true )
| ( ( SV27 = n0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[345]) ).
thf(360,plain,
! [SV39: $i,SV28: $i] :
( ( ~ ( geq @ SV28 @ SV39 )
| ( leq @ SV39 @ SV28 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[346]) ).
thf(361,plain,
! [SV28: $i,SV39: $i] :
( ( ~ ( leq @ SV39 @ SV28 )
| ( geq @ SV28 @ SV39 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[347]) ).
thf(362,plain,
! [SV48: $i,SV41: $i,SV30: $i] :
( ( ( ~ ( ~ ( leq @ SV30 @ SV41 )
| ~ ( leq @ SV41 @ SV48 ) ) )
= $false )
| ( ( leq @ SV30 @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[349]) ).
thf(363,plain,
! [SV31: $i] :
( ( ( ~ ( leq @ n0 @ SV31 ) )
= $true )
| ( ( ~ ( leq @ SV31 @ n2 ) )
= $true )
| ( ( ( SV31 = n0 )
| ( SV31 = n1 )
| ( SV31 = n2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[350]) ).
thf(364,plain,
! [SV42: $i,SV32: $i] :
( ( ~ ( leq @ ( succ @ SV32 ) @ ( succ @ SV42 ) )
| ( leq @ SV32 @ SV42 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[351]) ).
thf(365,plain,
! [SV42: $i,SV32: $i] :
( ( ~ ( leq @ SV32 @ SV42 )
| ( leq @ ( succ @ SV32 ) @ ( succ @ SV42 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[352]) ).
thf(366,plain,
! [SV43: $i,SV33: $i] :
( ( ( ~ ( leq @ SV33 @ SV43 )
| ~ ( ( SV33 != SV43 ) ) )
= $true )
| ( ( gt @ SV43 @ SV33 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[353]) ).
thf(367,plain,
! [SV36: $i] :
( ( ( ~ ( leq @ n0 @ SV36 ) )
= $true )
| ( ( ~ ( leq @ SV36 @ n1 ) )
= $true )
| ( ( ( SV36 = n0 )
| ( SV36 = n1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[356]) ).
thf(368,plain,
! [SV27: $i] :
( ( ( leq @ n0 @ SV27 )
= $false )
| ( ( ~ ( leq @ SV27 @ n0 ) )
= $true )
| ( ( SV27 = n0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[359]) ).
thf(369,plain,
! [SV39: $i,SV28: $i] :
( ( ( ~ ( geq @ SV28 @ SV39 ) )
= $true )
| ( ( leq @ SV39 @ SV28 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[360]) ).
thf(370,plain,
! [SV28: $i,SV39: $i] :
( ( ( ~ ( leq @ SV39 @ SV28 ) )
= $true )
| ( ( geq @ SV28 @ SV39 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[361]) ).
thf(371,plain,
! [SV48: $i,SV41: $i,SV30: $i] :
( ( ( ~ ( leq @ SV30 @ SV41 )
| ~ ( leq @ SV41 @ SV48 ) )
= $true )
| ( ( leq @ SV30 @ SV48 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[362]) ).
thf(372,plain,
! [SV31: $i] :
( ( ( leq @ n0 @ SV31 )
= $false )
| ( ( ~ ( leq @ SV31 @ n2 ) )
= $true )
| ( ( ( SV31 = n0 )
| ( SV31 = n1 )
| ( SV31 = n2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[363]) ).
thf(373,plain,
! [SV42: $i,SV32: $i] :
( ( ( ~ ( leq @ ( succ @ SV32 ) @ ( succ @ SV42 ) ) )
= $true )
| ( ( leq @ SV32 @ SV42 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[364]) ).
thf(374,plain,
! [SV42: $i,SV32: $i] :
( ( ( ~ ( leq @ SV32 @ SV42 ) )
= $true )
| ( ( leq @ ( succ @ SV32 ) @ ( succ @ SV42 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[365]) ).
thf(375,plain,
! [SV43: $i,SV33: $i] :
( ( ( ~ ( leq @ SV33 @ SV43 ) )
= $true )
| ( ( ~ ( ( SV33 != SV43 ) ) )
= $true )
| ( ( gt @ SV43 @ SV33 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[366]) ).
thf(376,plain,
! [SV36: $i] :
( ( ( leq @ n0 @ SV36 )
= $false )
| ( ( ~ ( leq @ SV36 @ n1 ) )
= $true )
| ( ( ( SV36 = n0 )
| ( SV36 = n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[367]) ).
thf(377,plain,
! [SV27: $i] :
( ( ( leq @ SV27 @ n0 )
= $false )
| ( ( leq @ n0 @ SV27 )
= $false )
| ( ( SV27 = n0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[368]) ).
thf(378,plain,
! [SV39: $i,SV28: $i] :
( ( ( geq @ SV28 @ SV39 )
= $false )
| ( ( leq @ SV39 @ SV28 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[369]) ).
thf(379,plain,
! [SV28: $i,SV39: $i] :
( ( ( leq @ SV39 @ SV28 )
= $false )
| ( ( geq @ SV28 @ SV39 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[370]) ).
thf(380,plain,
! [SV48: $i,SV41: $i,SV30: $i] :
( ( ( ~ ( leq @ SV30 @ SV41 ) )
= $true )
| ( ( ~ ( leq @ SV41 @ SV48 ) )
= $true )
| ( ( leq @ SV30 @ SV48 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[371]) ).
thf(381,plain,
! [SV31: $i] :
( ( ( leq @ SV31 @ n2 )
= $false )
| ( ( leq @ n0 @ SV31 )
= $false )
| ( ( ( SV31 = n0 )
| ( SV31 = n1 )
| ( SV31 = n2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[372]) ).
thf(382,plain,
! [SV42: $i,SV32: $i] :
( ( ( leq @ ( succ @ SV32 ) @ ( succ @ SV42 ) )
= $false )
| ( ( leq @ SV32 @ SV42 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[373]) ).
thf(383,plain,
! [SV42: $i,SV32: $i] :
( ( ( leq @ SV32 @ SV42 )
= $false )
| ( ( leq @ ( succ @ SV32 ) @ ( succ @ SV42 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[374]) ).
thf(384,plain,
! [SV43: $i,SV33: $i] :
( ( ( leq @ SV33 @ SV43 )
= $false )
| ( ( ~ ( ( SV33 != SV43 ) ) )
= $true )
| ( ( gt @ SV43 @ SV33 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[375]) ).
thf(385,plain,
! [SV36: $i] :
( ( ( leq @ SV36 @ n1 )
= $false )
| ( ( leq @ n0 @ SV36 )
= $false )
| ( ( ( SV36 = n0 )
| ( SV36 = n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[376]) ).
thf(386,plain,
! [SV48: $i,SV41: $i,SV30: $i] :
( ( ( leq @ SV30 @ SV41 )
= $false )
| ( ( ~ ( leq @ SV41 @ SV48 ) )
= $true )
| ( ( leq @ SV30 @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[380]) ).
thf(387,plain,
! [SV31: $i] :
( ( ( ( SV31 = n0 )
| ( SV31 = n1 ) )
= $true )
| ( ( SV31 = n2 )
= $true )
| ( ( leq @ n0 @ SV31 )
= $false )
| ( ( leq @ SV31 @ n2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[381]) ).
thf(388,plain,
! [SV43: $i,SV33: $i] :
( ( ( SV33 != SV43 )
= $false )
| ( ( leq @ SV33 @ SV43 )
= $false )
| ( ( gt @ SV43 @ SV33 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[384]) ).
thf(389,plain,
! [SV36: $i] :
( ( ( SV36 = n0 )
= $true )
| ( ( SV36 = n1 )
= $true )
| ( ( leq @ n0 @ SV36 )
= $false )
| ( ( leq @ SV36 @ n1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[385]) ).
thf(390,plain,
! [SV30: $i,SV48: $i,SV41: $i] :
( ( ( leq @ SV41 @ SV48 )
= $false )
| ( ( leq @ SV30 @ SV41 )
= $false )
| ( ( leq @ SV30 @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[386]) ).
thf(391,plain,
! [SV31: $i] :
( ( ( SV31 = n0 )
= $true )
| ( ( SV31 = n1 )
= $true )
| ( ( SV31 = n2 )
= $true )
| ( ( leq @ n0 @ SV31 )
= $false )
| ( ( leq @ SV31 @ n2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[387]) ).
thf(392,plain,
! [SV43: $i,SV33: $i] :
( ( ( SV33 = SV43 )
= $true )
| ( ( leq @ SV33 @ SV43 )
= $false )
| ( ( gt @ SV43 @ SV33 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[388]) ).
thf(393,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[276,392,391,390,389,383,382,379,378,377,358,357,355,354,348,308,307,306,292,291,290,289,288,287,286,285,281,280,279,278,277]) ).
thf(394,plain,
( ( ! [X: $i] : ( leq @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(395,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( leq @ X @ Y )
& ( leq @ Y @ Z ) )
=> ( leq @ X @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[115]) ).
thf(396,plain,
( ( ! [X: $i,Y: $i] :
( ( geq @ X @ Y )
<=> ( leq @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(397,plain,
( ( ! [X: $i,Y: $i] :
( ( gt @ Y @ X )
=> ( leq @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(398,plain,
( ( ! [X: $i,Y: $i] :
( ( ( leq @ X @ Y )
& ( X != Y ) )
=> ( gt @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(399,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ X @ Y )
=> ( leq @ X @ ( succ @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(400,plain,
( ( ! [X: $i,C: $i] :
( ( leq @ n0 @ X )
=> ( leq @ ( uniform_int_rnd @ C @ X ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(401,plain,
( ( ! [X: $i,C: $i] :
( ( leq @ n0 @ X )
=> ( leq @ n0 @ ( uniform_int_rnd @ C @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(402,plain,
( ( ! [X: $i] :
( ( minus @ X @ n1 )
= ( pred @ X ) ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(403,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ ( succ @ X ) @ ( succ @ Y ) )
<=> ( leq @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(404,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ ( minus @ X @ Y ) @ X )
=> ( leq @ n0 @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(405,plain,
( ( gt @ n135300 @ n5 )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(406,plain,
( ( gt @ n5 @ n0 )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(407,plain,
( ( gt @ n135300 @ n0 )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(408,plain,
( ( gt @ n1 @ n0 )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(409,plain,
( ( gt @ n5 @ n1 )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(410,plain,
( ( gt @ n135300 @ n1 )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(411,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n0 ) )
=> ( X = n0 ) ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(412,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n1 ) )
=> ( ( X = n0 )
| ( X = n1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(413,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n2 ) )
=> ( ( X = n0 )
| ( X = n1 )
| ( X = n2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(414,plain,
( ( ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ n0 ) ) ) ) )
= n5 )
= $true ),
inference(copy,[status(thm)],[96]) ).
thf(415,plain,
( ( ( succ @ n0 )
= n1 )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(416,plain,
( ( leq @ pv43 @ ( minus @ n5 @ n1 ) )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(417,plain,
( ( leq @ pv41 @ ( minus @ n5 @ n1 ) )
= $true ),
inference(copy,[status(thm)],[121]) ).
thf(418,plain,
( ( leq @ pv10 @ ( minus @ n135300 @ n1 ) )
= $true ),
inference(copy,[status(thm)],[120]) ).
thf(419,plain,
( ( leq @ n0 @ pv43 )
= $true ),
inference(copy,[status(thm)],[119]) ).
thf(420,plain,
( ( leq @ n0 @ pv41 )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(421,plain,
( ( leq @ n0 @ pv10 )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(422,plain,
( ( ~ ( leq @ n0 @ pv43 ) )
= $true ),
inference(copy,[status(thm)],[132]) ).
thf(423,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ n0 @ SX0 )
| ( leq @ n0 @ ( uniform_int_rnd @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[401]) ).
thf(424,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( leq @ n0 @ SX0 )
| ~ ( leq @ SX0 @ n0 ) )
| ( SX0 = n0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[411]) ).
thf(425,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( geq @ SX0 @ SX1 )
| ( leq @ SX1 @ SX0 ) )
| ~ ( ~ ( leq @ SX1 @ SX0 )
| ( geq @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[396]) ).
thf(426,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( gt @ SX1 @ SX0 )
| ( leq @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[397]) ).
thf(427,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( leq @ n0 @ SX0 )
| ~ ( leq @ SX0 @ n2 ) )
| ( SX0 = n0 )
| ( SX0 = n1 )
| ( SX0 = n2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[413]) ).
thf(428,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( leq @ n0 @ SX0 )
| ~ ( leq @ SX0 @ n1 ) )
| ( SX0 = n0 )
| ( SX0 = n1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[412]) ).
thf(429,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ n0 @ SX0 )
| ( leq @ ( uniform_int_rnd @ SX1 @ SX0 ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[400]) ).
thf(430,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX0 @ SX1 )
| ( leq @ SX0 @ ( succ @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[399]) ).
thf(431,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( leq @ SX0 @ SX1 )
| ~ ( ( SX0 != SX1 ) ) )
| ( gt @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[398]) ).
thf(432,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( leq @ SX0 @ SX1 )
| ~ ( leq @ SX1 @ SX2 ) )
| ( leq @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[395]) ).
thf(433,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ ( minus @ SX0 @ SX1 ) @ SX0 )
| ( leq @ n0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[404]) ).
thf(434,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)],[403]) ).
thf(435,plain,
! [SV49: $i] :
( ( leq @ SV49 @ SV49 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[394]) ).
thf(436,plain,
! [SV50: $i] :
( ( ( minus @ SV50 @ n1 )
= ( pred @ SV50 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[402]) ).
thf(437,plain,
( ( leq @ n0 @ pv43 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[422]) ).
thf(438,plain,
! [SV51: $i] :
( ( ! [SY46: $i] :
( ~ ( leq @ n0 @ SV51 )
| ( leq @ n0 @ ( uniform_int_rnd @ SY46 @ SV51 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[423]) ).
thf(439,plain,
! [SV52: $i] :
( ( ~ ~ ( ~ ( leq @ n0 @ SV52 )
| ~ ( leq @ SV52 @ n0 ) )
| ( SV52 = n0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[424]) ).
thf(440,plain,
! [SV53: $i] :
( ( ! [SY47: $i] :
~ ( ~ ( ~ ( geq @ SV53 @ SY47 )
| ( leq @ SY47 @ SV53 ) )
| ~ ( ~ ( leq @ SY47 @ SV53 )
| ( geq @ SV53 @ SY47 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[425]) ).
thf(441,plain,
! [SV54: $i] :
( ( ! [SY48: $i] :
( ~ ( gt @ SY48 @ SV54 )
| ( leq @ SV54 @ SY48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[426]) ).
thf(442,plain,
! [SV55: $i] :
( ( ~ ~ ( ~ ( leq @ n0 @ SV55 )
| ~ ( leq @ SV55 @ n2 ) )
| ( SV55 = n0 )
| ( SV55 = n1 )
| ( SV55 = n2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[427]) ).
thf(443,plain,
! [SV56: $i] :
( ( ~ ~ ( ~ ( leq @ n0 @ SV56 )
| ~ ( leq @ SV56 @ n1 ) )
| ( SV56 = n0 )
| ( SV56 = n1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[428]) ).
thf(444,plain,
! [SV57: $i] :
( ( ! [SY49: $i] :
( ~ ( leq @ n0 @ SV57 )
| ( leq @ ( uniform_int_rnd @ SY49 @ SV57 ) @ SV57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[429]) ).
thf(445,plain,
! [SV58: $i] :
( ( ! [SY50: $i] :
( ~ ( leq @ SV58 @ SY50 )
| ( leq @ SV58 @ ( succ @ SY50 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[430]) ).
thf(446,plain,
! [SV59: $i] :
( ( ! [SY51: $i] :
( ~ ~ ( ~ ( leq @ SV59 @ SY51 )
| ~ ( ( SV59 != SY51 ) ) )
| ( gt @ SY51 @ SV59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[431]) ).
thf(447,plain,
! [SV60: $i] :
( ( ! [SY52: $i,SY53: $i] :
( ~ ~ ( ~ ( leq @ SV60 @ SY52 )
| ~ ( leq @ SY52 @ SY53 ) )
| ( leq @ SV60 @ SY53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[432]) ).
thf(448,plain,
! [SV61: $i] :
( ( ! [SY54: $i] :
( ~ ( leq @ ( minus @ SV61 @ SY54 ) @ SV61 )
| ( leq @ n0 @ SY54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[433]) ).
thf(449,plain,
! [SV62: $i] :
( ( ! [SY55: $i] :
~ ( ~ ( ~ ( leq @ ( succ @ SV62 ) @ ( succ @ SY55 ) )
| ( leq @ SV62 @ SY55 ) )
| ~ ( ~ ( leq @ SV62 @ SY55 )
| ( leq @ ( succ @ SV62 ) @ ( succ @ SY55 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[434]) ).
thf(450,plain,
! [SV63: $i,SV51: $i] :
( ( ~ ( leq @ n0 @ SV51 )
| ( leq @ n0 @ ( uniform_int_rnd @ SV63 @ SV51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[438]) ).
thf(451,plain,
! [SV52: $i] :
( ( ( ~ ~ ( ~ ( leq @ n0 @ SV52 )
| ~ ( leq @ SV52 @ n0 ) ) )
= $true )
| ( ( SV52 = n0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[439]) ).
thf(452,plain,
! [SV64: $i,SV53: $i] :
( ( ~ ( ~ ( ~ ( geq @ SV53 @ SV64 )
| ( leq @ SV64 @ SV53 ) )
| ~ ( ~ ( leq @ SV64 @ SV53 )
| ( geq @ SV53 @ SV64 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[440]) ).
thf(453,plain,
! [SV54: $i,SV65: $i] :
( ( ~ ( gt @ SV65 @ SV54 )
| ( leq @ SV54 @ SV65 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[441]) ).
thf(454,plain,
! [SV55: $i] :
( ( ( ~ ~ ( ~ ( leq @ n0 @ SV55 )
| ~ ( leq @ SV55 @ n2 ) ) )
= $true )
| ( ( ( SV55 = n0 )
| ( SV55 = n1 )
| ( SV55 = n2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[442]) ).
thf(455,plain,
! [SV56: $i] :
( ( ( ~ ~ ( ~ ( leq @ n0 @ SV56 )
| ~ ( leq @ SV56 @ n1 ) ) )
= $true )
| ( ( ( SV56 = n0 )
| ( SV56 = n1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[443]) ).
thf(456,plain,
! [SV66: $i,SV57: $i] :
( ( ~ ( leq @ n0 @ SV57 )
| ( leq @ ( uniform_int_rnd @ SV66 @ SV57 ) @ SV57 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[444]) ).
thf(457,plain,
! [SV67: $i,SV58: $i] :
( ( ~ ( leq @ SV58 @ SV67 )
| ( leq @ SV58 @ ( succ @ SV67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[445]) ).
thf(458,plain,
! [SV68: $i,SV59: $i] :
( ( ~ ~ ( ~ ( leq @ SV59 @ SV68 )
| ~ ( ( SV59 != SV68 ) ) )
| ( gt @ SV68 @ SV59 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[446]) ).
thf(459,plain,
! [SV69: $i,SV60: $i] :
( ( ! [SY56: $i] :
( ~ ~ ( ~ ( leq @ SV60 @ SV69 )
| ~ ( leq @ SV69 @ SY56 ) )
| ( leq @ SV60 @ SY56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[447]) ).
thf(460,plain,
! [SV70: $i,SV61: $i] :
( ( ~ ( leq @ ( minus @ SV61 @ SV70 ) @ SV61 )
| ( leq @ n0 @ SV70 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[448]) ).
thf(461,plain,
! [SV71: $i,SV62: $i] :
( ( ~ ( ~ ( ~ ( leq @ ( succ @ SV62 ) @ ( succ @ SV71 ) )
| ( leq @ SV62 @ SV71 ) )
| ~ ( ~ ( leq @ SV62 @ SV71 )
| ( leq @ ( succ @ SV62 ) @ ( succ @ SV71 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[449]) ).
thf(462,plain,
! [SV63: $i,SV51: $i] :
( ( ( ~ ( leq @ n0 @ SV51 ) )
= $true )
| ( ( leq @ n0 @ ( uniform_int_rnd @ SV63 @ SV51 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[450]) ).
thf(463,plain,
! [SV52: $i] :
( ( ( ~ ( ~ ( leq @ n0 @ SV52 )
| ~ ( leq @ SV52 @ n0 ) ) )
= $false )
| ( ( SV52 = n0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[451]) ).
thf(464,plain,
! [SV64: $i,SV53: $i] :
( ( ~ ( ~ ( geq @ SV53 @ SV64 )
| ( leq @ SV64 @ SV53 ) )
| ~ ( ~ ( leq @ SV64 @ SV53 )
| ( geq @ SV53 @ SV64 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[452]) ).
thf(465,plain,
! [SV54: $i,SV65: $i] :
( ( ( ~ ( gt @ SV65 @ SV54 ) )
= $true )
| ( ( leq @ SV54 @ SV65 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[453]) ).
thf(466,plain,
! [SV55: $i] :
( ( ( ~ ( ~ ( leq @ n0 @ SV55 )
| ~ ( leq @ SV55 @ n2 ) ) )
= $false )
| ( ( ( SV55 = n0 )
| ( SV55 = n1 )
| ( SV55 = n2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[454]) ).
thf(467,plain,
! [SV56: $i] :
( ( ( ~ ( ~ ( leq @ n0 @ SV56 )
| ~ ( leq @ SV56 @ n1 ) ) )
= $false )
| ( ( ( SV56 = n0 )
| ( SV56 = n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[455]) ).
thf(468,plain,
! [SV66: $i,SV57: $i] :
( ( ( ~ ( leq @ n0 @ SV57 ) )
= $true )
| ( ( leq @ ( uniform_int_rnd @ SV66 @ SV57 ) @ SV57 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[456]) ).
thf(469,plain,
! [SV67: $i,SV58: $i] :
( ( ( ~ ( leq @ SV58 @ SV67 ) )
= $true )
| ( ( leq @ SV58 @ ( succ @ SV67 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[457]) ).
thf(470,plain,
! [SV68: $i,SV59: $i] :
( ( ( ~ ~ ( ~ ( leq @ SV59 @ SV68 )
| ~ ( ( SV59 != SV68 ) ) ) )
= $true )
| ( ( gt @ SV68 @ SV59 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[458]) ).
thf(471,plain,
! [SV72: $i,SV69: $i,SV60: $i] :
( ( ~ ~ ( ~ ( leq @ SV60 @ SV69 )
| ~ ( leq @ SV69 @ SV72 ) )
| ( leq @ SV60 @ SV72 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[459]) ).
thf(472,plain,
! [SV70: $i,SV61: $i] :
( ( ( ~ ( leq @ ( minus @ SV61 @ SV70 ) @ SV61 ) )
= $true )
| ( ( leq @ n0 @ SV70 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[460]) ).
thf(473,plain,
! [SV71: $i,SV62: $i] :
( ( ~ ( ~ ( leq @ ( succ @ SV62 ) @ ( succ @ SV71 ) )
| ( leq @ SV62 @ SV71 ) )
| ~ ( ~ ( leq @ SV62 @ SV71 )
| ( leq @ ( succ @ SV62 ) @ ( succ @ SV71 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[461]) ).
thf(474,plain,
! [SV63: $i,SV51: $i] :
( ( ( leq @ n0 @ SV51 )
= $false )
| ( ( leq @ n0 @ ( uniform_int_rnd @ SV63 @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[462]) ).
thf(475,plain,
! [SV52: $i] :
( ( ( ~ ( leq @ n0 @ SV52 )
| ~ ( leq @ SV52 @ n0 ) )
= $true )
| ( ( SV52 = n0 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[463]) ).
thf(476,plain,
! [SV64: $i,SV53: $i] :
( ( ~ ( ~ ( geq @ SV53 @ SV64 )
| ( leq @ SV64 @ SV53 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[464]) ).
thf(477,plain,
! [SV53: $i,SV64: $i] :
( ( ~ ( ~ ( leq @ SV64 @ SV53 )
| ( geq @ SV53 @ SV64 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[464]) ).
thf(478,plain,
! [SV54: $i,SV65: $i] :
( ( ( gt @ SV65 @ SV54 )
= $false )
| ( ( leq @ SV54 @ SV65 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[465]) ).
thf(479,plain,
! [SV55: $i] :
( ( ( ~ ( leq @ n0 @ SV55 )
| ~ ( leq @ SV55 @ n2 ) )
= $true )
| ( ( ( SV55 = n0 )
| ( SV55 = n1 )
| ( SV55 = n2 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[466]) ).
thf(480,plain,
! [SV56: $i] :
( ( ( ~ ( leq @ n0 @ SV56 )
| ~ ( leq @ SV56 @ n1 ) )
= $true )
| ( ( ( SV56 = n0 )
| ( SV56 = n1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[467]) ).
thf(481,plain,
! [SV66: $i,SV57: $i] :
( ( ( leq @ n0 @ SV57 )
= $false )
| ( ( leq @ ( uniform_int_rnd @ SV66 @ SV57 ) @ SV57 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[468]) ).
thf(482,plain,
! [SV67: $i,SV58: $i] :
( ( ( leq @ SV58 @ SV67 )
= $false )
| ( ( leq @ SV58 @ ( succ @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[469]) ).
thf(483,plain,
! [SV68: $i,SV59: $i] :
( ( ( ~ ( ~ ( leq @ SV59 @ SV68 )
| ~ ( ( SV59 != SV68 ) ) ) )
= $false )
| ( ( gt @ SV68 @ SV59 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[470]) ).
thf(484,plain,
! [SV72: $i,SV69: $i,SV60: $i] :
( ( ( ~ ~ ( ~ ( leq @ SV60 @ SV69 )
| ~ ( leq @ SV69 @ SV72 ) ) )
= $true )
| ( ( leq @ SV60 @ SV72 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[471]) ).
thf(485,plain,
! [SV70: $i,SV61: $i] :
( ( ( leq @ ( minus @ SV61 @ SV70 ) @ SV61 )
= $false )
| ( ( leq @ n0 @ SV70 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[472]) ).
thf(486,plain,
! [SV71: $i,SV62: $i] :
( ( ~ ( ~ ( leq @ ( succ @ SV62 ) @ ( succ @ SV71 ) )
| ( leq @ SV62 @ SV71 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[473]) ).
thf(487,plain,
! [SV71: $i,SV62: $i] :
( ( ~ ( ~ ( leq @ SV62 @ SV71 )
| ( leq @ ( succ @ SV62 ) @ ( succ @ SV71 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[473]) ).
thf(488,plain,
! [SV52: $i] :
( ( ( ~ ( leq @ n0 @ SV52 ) )
= $true )
| ( ( ~ ( leq @ SV52 @ n0 ) )
= $true )
| ( ( SV52 = n0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[475]) ).
thf(489,plain,
! [SV64: $i,SV53: $i] :
( ( ~ ( geq @ SV53 @ SV64 )
| ( leq @ SV64 @ SV53 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[476]) ).
thf(490,plain,
! [SV53: $i,SV64: $i] :
( ( ~ ( leq @ SV64 @ SV53 )
| ( geq @ SV53 @ SV64 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[477]) ).
thf(491,plain,
! [SV55: $i] :
( ( ( ~ ( leq @ n0 @ SV55 ) )
= $true )
| ( ( ~ ( leq @ SV55 @ n2 ) )
= $true )
| ( ( ( SV55 = n0 )
| ( SV55 = n1 )
| ( SV55 = n2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[479]) ).
thf(492,plain,
! [SV56: $i] :
( ( ( ~ ( leq @ n0 @ SV56 ) )
= $true )
| ( ( ~ ( leq @ SV56 @ n1 ) )
= $true )
| ( ( ( SV56 = n0 )
| ( SV56 = n1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[480]) ).
thf(493,plain,
! [SV68: $i,SV59: $i] :
( ( ( ~ ( leq @ SV59 @ SV68 )
| ~ ( ( SV59 != SV68 ) ) )
= $true )
| ( ( gt @ SV68 @ SV59 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[483]) ).
thf(494,plain,
! [SV72: $i,SV69: $i,SV60: $i] :
( ( ( ~ ( ~ ( leq @ SV60 @ SV69 )
| ~ ( leq @ SV69 @ SV72 ) ) )
= $false )
| ( ( leq @ SV60 @ SV72 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[484]) ).
thf(495,plain,
! [SV71: $i,SV62: $i] :
( ( ~ ( leq @ ( succ @ SV62 ) @ ( succ @ SV71 ) )
| ( leq @ SV62 @ SV71 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[486]) ).
thf(496,plain,
! [SV71: $i,SV62: $i] :
( ( ~ ( leq @ SV62 @ SV71 )
| ( leq @ ( succ @ SV62 ) @ ( succ @ SV71 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[487]) ).
thf(497,plain,
! [SV52: $i] :
( ( ( leq @ n0 @ SV52 )
= $false )
| ( ( ~ ( leq @ SV52 @ n0 ) )
= $true )
| ( ( SV52 = n0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[488]) ).
thf(498,plain,
! [SV64: $i,SV53: $i] :
( ( ( ~ ( geq @ SV53 @ SV64 ) )
= $true )
| ( ( leq @ SV64 @ SV53 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[489]) ).
thf(499,plain,
! [SV53: $i,SV64: $i] :
( ( ( ~ ( leq @ SV64 @ SV53 ) )
= $true )
| ( ( geq @ SV53 @ SV64 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[490]) ).
thf(500,plain,
! [SV55: $i] :
( ( ( leq @ n0 @ SV55 )
= $false )
| ( ( ~ ( leq @ SV55 @ n2 ) )
= $true )
| ( ( ( SV55 = n0 )
| ( SV55 = n1 )
| ( SV55 = n2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[491]) ).
thf(501,plain,
! [SV56: $i] :
( ( ( leq @ n0 @ SV56 )
= $false )
| ( ( ~ ( leq @ SV56 @ n1 ) )
= $true )
| ( ( ( SV56 = n0 )
| ( SV56 = n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[492]) ).
thf(502,plain,
! [SV68: $i,SV59: $i] :
( ( ( ~ ( leq @ SV59 @ SV68 ) )
= $true )
| ( ( ~ ( ( SV59 != SV68 ) ) )
= $true )
| ( ( gt @ SV68 @ SV59 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[493]) ).
thf(503,plain,
! [SV72: $i,SV69: $i,SV60: $i] :
( ( ( ~ ( leq @ SV60 @ SV69 )
| ~ ( leq @ SV69 @ SV72 ) )
= $true )
| ( ( leq @ SV60 @ SV72 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[494]) ).
thf(504,plain,
! [SV71: $i,SV62: $i] :
( ( ( ~ ( leq @ ( succ @ SV62 ) @ ( succ @ SV71 ) ) )
= $true )
| ( ( leq @ SV62 @ SV71 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[495]) ).
thf(505,plain,
! [SV71: $i,SV62: $i] :
( ( ( ~ ( leq @ SV62 @ SV71 ) )
= $true )
| ( ( leq @ ( succ @ SV62 ) @ ( succ @ SV71 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[496]) ).
thf(506,plain,
! [SV52: $i] :
( ( ( leq @ SV52 @ n0 )
= $false )
| ( ( leq @ n0 @ SV52 )
= $false )
| ( ( SV52 = n0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[497]) ).
thf(507,plain,
! [SV64: $i,SV53: $i] :
( ( ( geq @ SV53 @ SV64 )
= $false )
| ( ( leq @ SV64 @ SV53 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[498]) ).
thf(508,plain,
! [SV53: $i,SV64: $i] :
( ( ( leq @ SV64 @ SV53 )
= $false )
| ( ( geq @ SV53 @ SV64 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[499]) ).
thf(509,plain,
! [SV55: $i] :
( ( ( leq @ SV55 @ n2 )
= $false )
| ( ( leq @ n0 @ SV55 )
= $false )
| ( ( ( SV55 = n0 )
| ( SV55 = n1 )
| ( SV55 = n2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[500]) ).
thf(510,plain,
! [SV56: $i] :
( ( ( leq @ SV56 @ n1 )
= $false )
| ( ( leq @ n0 @ SV56 )
= $false )
| ( ( ( SV56 = n0 )
| ( SV56 = n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[501]) ).
thf(511,plain,
! [SV68: $i,SV59: $i] :
( ( ( leq @ SV59 @ SV68 )
= $false )
| ( ( ~ ( ( SV59 != SV68 ) ) )
= $true )
| ( ( gt @ SV68 @ SV59 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[502]) ).
thf(512,plain,
! [SV72: $i,SV69: $i,SV60: $i] :
( ( ( ~ ( leq @ SV60 @ SV69 ) )
= $true )
| ( ( ~ ( leq @ SV69 @ SV72 ) )
= $true )
| ( ( leq @ SV60 @ SV72 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[503]) ).
thf(513,plain,
! [SV71: $i,SV62: $i] :
( ( ( leq @ ( succ @ SV62 ) @ ( succ @ SV71 ) )
= $false )
| ( ( leq @ SV62 @ SV71 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[504]) ).
thf(514,plain,
! [SV71: $i,SV62: $i] :
( ( ( leq @ SV62 @ SV71 )
= $false )
| ( ( leq @ ( succ @ SV62 ) @ ( succ @ SV71 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[505]) ).
thf(515,plain,
! [SV55: $i] :
( ( ( ( SV55 = n0 )
| ( SV55 = n1 ) )
= $true )
| ( ( SV55 = n2 )
= $true )
| ( ( leq @ n0 @ SV55 )
= $false )
| ( ( leq @ SV55 @ n2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[509]) ).
thf(516,plain,
! [SV56: $i] :
( ( ( SV56 = n0 )
= $true )
| ( ( SV56 = n1 )
= $true )
| ( ( leq @ n0 @ SV56 )
= $false )
| ( ( leq @ SV56 @ n1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[510]) ).
thf(517,plain,
! [SV68: $i,SV59: $i] :
( ( ( SV59 != SV68 )
= $false )
| ( ( leq @ SV59 @ SV68 )
= $false )
| ( ( gt @ SV68 @ SV59 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[511]) ).
thf(518,plain,
! [SV72: $i,SV69: $i,SV60: $i] :
( ( ( leq @ SV60 @ SV69 )
= $false )
| ( ( ~ ( leq @ SV69 @ SV72 ) )
= $true )
| ( ( leq @ SV60 @ SV72 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[512]) ).
thf(519,plain,
! [SV55: $i] :
( ( ( SV55 = n0 )
= $true )
| ( ( SV55 = n1 )
= $true )
| ( ( SV55 = n2 )
= $true )
| ( ( leq @ n0 @ SV55 )
= $false )
| ( ( leq @ SV55 @ n2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[515]) ).
thf(520,plain,
! [SV68: $i,SV59: $i] :
( ( ( SV59 = SV68 )
= $true )
| ( ( leq @ SV59 @ SV68 )
= $false )
| ( ( gt @ SV68 @ SV59 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[517]) ).
thf(521,plain,
! [SV60: $i,SV72: $i,SV69: $i] :
( ( ( leq @ SV69 @ SV72 )
= $false )
| ( ( leq @ SV60 @ SV69 )
= $false )
| ( ( leq @ SV60 @ SV72 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[518]) ).
thf(522,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[405,521,520,519,516,514,513,508,507,506,485,482,481,478,474,437,436,435,421,420,419,418,417,416,415,414,410,409,408,407,406]) ).
thf(523,plain,
( ( ! [X: $i] : ( leq @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(524,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( leq @ X @ Y )
& ( leq @ Y @ Z ) )
=> ( leq @ X @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[115]) ).
thf(525,plain,
( ( ! [X: $i,Y: $i] :
( ( geq @ X @ Y )
<=> ( leq @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(526,plain,
( ( ! [X: $i,Y: $i] :
( ( gt @ Y @ X )
=> ( leq @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(527,plain,
( ( ! [X: $i,Y: $i] :
( ( ( leq @ X @ Y )
& ( X != Y ) )
=> ( gt @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(528,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ X @ Y )
=> ( leq @ X @ ( succ @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(529,plain,
( ( ! [X: $i,C: $i] :
( ( leq @ n0 @ X )
=> ( leq @ ( uniform_int_rnd @ C @ X ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(530,plain,
( ( ! [X: $i,C: $i] :
( ( leq @ n0 @ X )
=> ( leq @ n0 @ ( uniform_int_rnd @ C @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(531,plain,
( ( ! [X: $i] :
( ( minus @ X @ n1 )
= ( pred @ X ) ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(532,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ ( succ @ X ) @ ( succ @ Y ) )
<=> ( leq @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(533,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ ( minus @ X @ Y ) @ X )
=> ( leq @ n0 @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(534,plain,
( ( gt @ n135300 @ n5 )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(535,plain,
( ( gt @ n5 @ n0 )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(536,plain,
( ( gt @ n135300 @ n0 )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(537,plain,
( ( gt @ n1 @ n0 )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(538,plain,
( ( gt @ n5 @ n1 )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(539,plain,
( ( gt @ n135300 @ n1 )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(540,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n0 ) )
=> ( X = n0 ) ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(541,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n1 ) )
=> ( ( X = n0 )
| ( X = n1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(542,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n2 ) )
=> ( ( X = n0 )
| ( X = n1 )
| ( X = n2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(543,plain,
( ( ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ n0 ) ) ) ) )
= n5 )
= $true ),
inference(copy,[status(thm)],[96]) ).
thf(544,plain,
( ( ( succ @ n0 )
= n1 )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(545,plain,
( ( leq @ pv43 @ ( minus @ n5 @ n1 ) )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(546,plain,
( ( leq @ pv41 @ ( minus @ n5 @ n1 ) )
= $true ),
inference(copy,[status(thm)],[121]) ).
thf(547,plain,
( ( leq @ pv10 @ ( minus @ n135300 @ n1 ) )
= $true ),
inference(copy,[status(thm)],[120]) ).
thf(548,plain,
( ( leq @ n0 @ pv43 )
= $true ),
inference(copy,[status(thm)],[119]) ).
thf(549,plain,
( ( leq @ n0 @ pv41 )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(550,plain,
( ( leq @ n0 @ pv10 )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(551,plain,
( ( ~ ( leq @ pv10 @ ( minus @ n135300 @ n1 ) ) )
= $true ),
inference(copy,[status(thm)],[133]) ).
thf(552,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( leq @ SX0 @ SX1 )
| ~ ( leq @ SX1 @ SX2 ) )
| ( leq @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[524]) ).
thf(553,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( leq @ SX0 @ SX1 )
| ~ ( ( SX0 != SX1 ) ) )
| ( gt @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[527]) ).
thf(554,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( geq @ SX0 @ SX1 )
| ( leq @ SX1 @ SX0 ) )
| ~ ( ~ ( leq @ SX1 @ SX0 )
| ( geq @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[525]) ).
thf(555,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( leq @ n0 @ SX0 )
| ~ ( leq @ SX0 @ n2 ) )
| ( SX0 = n0 )
| ( SX0 = n1 )
| ( SX0 = n2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[542]) ).
thf(556,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( leq @ n0 @ SX0 )
| ~ ( leq @ SX0 @ n1 ) )
| ( SX0 = n0 )
| ( SX0 = n1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[541]) ).
thf(557,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX0 @ SX1 )
| ( leq @ SX0 @ ( succ @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[528]) ).
thf(558,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)],[532]) ).
thf(559,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ ( minus @ SX0 @ SX1 ) @ SX0 )
| ( leq @ n0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[533]) ).
thf(560,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ n0 @ SX0 )
| ( leq @ n0 @ ( uniform_int_rnd @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[530]) ).
thf(561,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( leq @ n0 @ SX0 )
| ~ ( leq @ SX0 @ n0 ) )
| ( SX0 = n0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[540]) ).
thf(562,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( gt @ SX1 @ SX0 )
| ( leq @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[526]) ).
thf(563,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ n0 @ SX0 )
| ( leq @ ( uniform_int_rnd @ SX1 @ SX0 ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[529]) ).
thf(564,plain,
! [SV73: $i] :
( ( leq @ SV73 @ SV73 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[523]) ).
thf(565,plain,
! [SV74: $i] :
( ( ( minus @ SV74 @ n1 )
= ( pred @ SV74 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[531]) ).
thf(566,plain,
( ( leq @ pv10 @ ( minus @ n135300 @ n1 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[551]) ).
thf(567,plain,
! [SV75: $i] :
( ( ! [SY57: $i,SY58: $i] :
( ~ ~ ( ~ ( leq @ SV75 @ SY57 )
| ~ ( leq @ SY57 @ SY58 ) )
| ( leq @ SV75 @ SY58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[552]) ).
thf(568,plain,
! [SV76: $i] :
( ( ! [SY59: $i] :
( ~ ~ ( ~ ( leq @ SV76 @ SY59 )
| ~ ( ( SV76 != SY59 ) ) )
| ( gt @ SY59 @ SV76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[553]) ).
thf(569,plain,
! [SV77: $i] :
( ( ! [SY60: $i] :
~ ( ~ ( ~ ( geq @ SV77 @ SY60 )
| ( leq @ SY60 @ SV77 ) )
| ~ ( ~ ( leq @ SY60 @ SV77 )
| ( geq @ SV77 @ SY60 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[554]) ).
thf(570,plain,
! [SV78: $i] :
( ( ~ ~ ( ~ ( leq @ n0 @ SV78 )
| ~ ( leq @ SV78 @ n2 ) )
| ( SV78 = n0 )
| ( SV78 = n1 )
| ( SV78 = n2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[555]) ).
thf(571,plain,
! [SV79: $i] :
( ( ~ ~ ( ~ ( leq @ n0 @ SV79 )
| ~ ( leq @ SV79 @ n1 ) )
| ( SV79 = n0 )
| ( SV79 = n1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[556]) ).
thf(572,plain,
! [SV80: $i] :
( ( ! [SY61: $i] :
( ~ ( leq @ SV80 @ SY61 )
| ( leq @ SV80 @ ( succ @ SY61 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[557]) ).
thf(573,plain,
! [SV81: $i] :
( ( ! [SY62: $i] :
~ ( ~ ( ~ ( leq @ ( succ @ SV81 ) @ ( succ @ SY62 ) )
| ( leq @ SV81 @ SY62 ) )
| ~ ( ~ ( leq @ SV81 @ SY62 )
| ( leq @ ( succ @ SV81 ) @ ( succ @ SY62 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[558]) ).
thf(574,plain,
! [SV82: $i] :
( ( ! [SY63: $i] :
( ~ ( leq @ ( minus @ SV82 @ SY63 ) @ SV82 )
| ( leq @ n0 @ SY63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[559]) ).
thf(575,plain,
! [SV83: $i] :
( ( ! [SY64: $i] :
( ~ ( leq @ n0 @ SV83 )
| ( leq @ n0 @ ( uniform_int_rnd @ SY64 @ SV83 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[560]) ).
thf(576,plain,
! [SV84: $i] :
( ( ~ ~ ( ~ ( leq @ n0 @ SV84 )
| ~ ( leq @ SV84 @ n0 ) )
| ( SV84 = n0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[561]) ).
thf(577,plain,
! [SV85: $i] :
( ( ! [SY65: $i] :
( ~ ( gt @ SY65 @ SV85 )
| ( leq @ SV85 @ SY65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[562]) ).
thf(578,plain,
! [SV86: $i] :
( ( ! [SY66: $i] :
( ~ ( leq @ n0 @ SV86 )
| ( leq @ ( uniform_int_rnd @ SY66 @ SV86 ) @ SV86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[563]) ).
thf(579,plain,
! [SV87: $i,SV75: $i] :
( ( ! [SY67: $i] :
( ~ ~ ( ~ ( leq @ SV75 @ SV87 )
| ~ ( leq @ SV87 @ SY67 ) )
| ( leq @ SV75 @ SY67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[567]) ).
thf(580,plain,
! [SV88: $i,SV76: $i] :
( ( ~ ~ ( ~ ( leq @ SV76 @ SV88 )
| ~ ( ( SV76 != SV88 ) ) )
| ( gt @ SV88 @ SV76 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[568]) ).
thf(581,plain,
! [SV89: $i,SV77: $i] :
( ( ~ ( ~ ( ~ ( geq @ SV77 @ SV89 )
| ( leq @ SV89 @ SV77 ) )
| ~ ( ~ ( leq @ SV89 @ SV77 )
| ( geq @ SV77 @ SV89 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[569]) ).
thf(582,plain,
! [SV78: $i] :
( ( ( ~ ~ ( ~ ( leq @ n0 @ SV78 )
| ~ ( leq @ SV78 @ n2 ) ) )
= $true )
| ( ( ( SV78 = n0 )
| ( SV78 = n1 )
| ( SV78 = n2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[570]) ).
thf(583,plain,
! [SV79: $i] :
( ( ( ~ ~ ( ~ ( leq @ n0 @ SV79 )
| ~ ( leq @ SV79 @ n1 ) ) )
= $true )
| ( ( ( SV79 = n0 )
| ( SV79 = n1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[571]) ).
thf(584,plain,
! [SV90: $i,SV80: $i] :
( ( ~ ( leq @ SV80 @ SV90 )
| ( leq @ SV80 @ ( succ @ SV90 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[572]) ).
thf(585,plain,
! [SV91: $i,SV81: $i] :
( ( ~ ( ~ ( ~ ( leq @ ( succ @ SV81 ) @ ( succ @ SV91 ) )
| ( leq @ SV81 @ SV91 ) )
| ~ ( ~ ( leq @ SV81 @ SV91 )
| ( leq @ ( succ @ SV81 ) @ ( succ @ SV91 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[573]) ).
thf(586,plain,
! [SV92: $i,SV82: $i] :
( ( ~ ( leq @ ( minus @ SV82 @ SV92 ) @ SV82 )
| ( leq @ n0 @ SV92 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[574]) ).
thf(587,plain,
! [SV93: $i,SV83: $i] :
( ( ~ ( leq @ n0 @ SV83 )
| ( leq @ n0 @ ( uniform_int_rnd @ SV93 @ SV83 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[575]) ).
thf(588,plain,
! [SV84: $i] :
( ( ( ~ ~ ( ~ ( leq @ n0 @ SV84 )
| ~ ( leq @ SV84 @ n0 ) ) )
= $true )
| ( ( SV84 = n0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[576]) ).
thf(589,plain,
! [SV85: $i,SV94: $i] :
( ( ~ ( gt @ SV94 @ SV85 )
| ( leq @ SV85 @ SV94 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[577]) ).
thf(590,plain,
! [SV95: $i,SV86: $i] :
( ( ~ ( leq @ n0 @ SV86 )
| ( leq @ ( uniform_int_rnd @ SV95 @ SV86 ) @ SV86 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[578]) ).
thf(591,plain,
! [SV96: $i,SV87: $i,SV75: $i] :
( ( ~ ~ ( ~ ( leq @ SV75 @ SV87 )
| ~ ( leq @ SV87 @ SV96 ) )
| ( leq @ SV75 @ SV96 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[579]) ).
thf(592,plain,
! [SV88: $i,SV76: $i] :
( ( ( ~ ~ ( ~ ( leq @ SV76 @ SV88 )
| ~ ( ( SV76 != SV88 ) ) ) )
= $true )
| ( ( gt @ SV88 @ SV76 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[580]) ).
thf(593,plain,
! [SV89: $i,SV77: $i] :
( ( ~ ( ~ ( geq @ SV77 @ SV89 )
| ( leq @ SV89 @ SV77 ) )
| ~ ( ~ ( leq @ SV89 @ SV77 )
| ( geq @ SV77 @ SV89 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[581]) ).
thf(594,plain,
! [SV78: $i] :
( ( ( ~ ( ~ ( leq @ n0 @ SV78 )
| ~ ( leq @ SV78 @ n2 ) ) )
= $false )
| ( ( ( SV78 = n0 )
| ( SV78 = n1 )
| ( SV78 = n2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[582]) ).
thf(595,plain,
! [SV79: $i] :
( ( ( ~ ( ~ ( leq @ n0 @ SV79 )
| ~ ( leq @ SV79 @ n1 ) ) )
= $false )
| ( ( ( SV79 = n0 )
| ( SV79 = n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[583]) ).
thf(596,plain,
! [SV90: $i,SV80: $i] :
( ( ( ~ ( leq @ SV80 @ SV90 ) )
= $true )
| ( ( leq @ SV80 @ ( succ @ SV90 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[584]) ).
thf(597,plain,
! [SV91: $i,SV81: $i] :
( ( ~ ( ~ ( leq @ ( succ @ SV81 ) @ ( succ @ SV91 ) )
| ( leq @ SV81 @ SV91 ) )
| ~ ( ~ ( leq @ SV81 @ SV91 )
| ( leq @ ( succ @ SV81 ) @ ( succ @ SV91 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[585]) ).
thf(598,plain,
! [SV92: $i,SV82: $i] :
( ( ( ~ ( leq @ ( minus @ SV82 @ SV92 ) @ SV82 ) )
= $true )
| ( ( leq @ n0 @ SV92 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[586]) ).
thf(599,plain,
! [SV93: $i,SV83: $i] :
( ( ( ~ ( leq @ n0 @ SV83 ) )
= $true )
| ( ( leq @ n0 @ ( uniform_int_rnd @ SV93 @ SV83 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[587]) ).
thf(600,plain,
! [SV84: $i] :
( ( ( ~ ( ~ ( leq @ n0 @ SV84 )
| ~ ( leq @ SV84 @ n0 ) ) )
= $false )
| ( ( SV84 = n0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[588]) ).
thf(601,plain,
! [SV85: $i,SV94: $i] :
( ( ( ~ ( gt @ SV94 @ SV85 ) )
= $true )
| ( ( leq @ SV85 @ SV94 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[589]) ).
thf(602,plain,
! [SV95: $i,SV86: $i] :
( ( ( ~ ( leq @ n0 @ SV86 ) )
= $true )
| ( ( leq @ ( uniform_int_rnd @ SV95 @ SV86 ) @ SV86 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[590]) ).
thf(603,plain,
! [SV96: $i,SV87: $i,SV75: $i] :
( ( ( ~ ~ ( ~ ( leq @ SV75 @ SV87 )
| ~ ( leq @ SV87 @ SV96 ) ) )
= $true )
| ( ( leq @ SV75 @ SV96 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[591]) ).
thf(604,plain,
! [SV88: $i,SV76: $i] :
( ( ( ~ ( ~ ( leq @ SV76 @ SV88 )
| ~ ( ( SV76 != SV88 ) ) ) )
= $false )
| ( ( gt @ SV88 @ SV76 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[592]) ).
thf(605,plain,
! [SV89: $i,SV77: $i] :
( ( ~ ( ~ ( geq @ SV77 @ SV89 )
| ( leq @ SV89 @ SV77 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[593]) ).
thf(606,plain,
! [SV77: $i,SV89: $i] :
( ( ~ ( ~ ( leq @ SV89 @ SV77 )
| ( geq @ SV77 @ SV89 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[593]) ).
thf(607,plain,
! [SV78: $i] :
( ( ( ~ ( leq @ n0 @ SV78 )
| ~ ( leq @ SV78 @ n2 ) )
= $true )
| ( ( ( SV78 = n0 )
| ( SV78 = n1 )
| ( SV78 = n2 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[594]) ).
thf(608,plain,
! [SV79: $i] :
( ( ( ~ ( leq @ n0 @ SV79 )
| ~ ( leq @ SV79 @ n1 ) )
= $true )
| ( ( ( SV79 = n0 )
| ( SV79 = n1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[595]) ).
thf(609,plain,
! [SV90: $i,SV80: $i] :
( ( ( leq @ SV80 @ SV90 )
= $false )
| ( ( leq @ SV80 @ ( succ @ SV90 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[596]) ).
thf(610,plain,
! [SV91: $i,SV81: $i] :
( ( ~ ( ~ ( leq @ ( succ @ SV81 ) @ ( succ @ SV91 ) )
| ( leq @ SV81 @ SV91 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[597]) ).
thf(611,plain,
! [SV91: $i,SV81: $i] :
( ( ~ ( ~ ( leq @ SV81 @ SV91 )
| ( leq @ ( succ @ SV81 ) @ ( succ @ SV91 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[597]) ).
thf(612,plain,
! [SV92: $i,SV82: $i] :
( ( ( leq @ ( minus @ SV82 @ SV92 ) @ SV82 )
= $false )
| ( ( leq @ n0 @ SV92 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[598]) ).
thf(613,plain,
! [SV93: $i,SV83: $i] :
( ( ( leq @ n0 @ SV83 )
= $false )
| ( ( leq @ n0 @ ( uniform_int_rnd @ SV93 @ SV83 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[599]) ).
thf(614,plain,
! [SV84: $i] :
( ( ( ~ ( leq @ n0 @ SV84 )
| ~ ( leq @ SV84 @ n0 ) )
= $true )
| ( ( SV84 = n0 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[600]) ).
thf(615,plain,
! [SV85: $i,SV94: $i] :
( ( ( gt @ SV94 @ SV85 )
= $false )
| ( ( leq @ SV85 @ SV94 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[601]) ).
thf(616,plain,
! [SV95: $i,SV86: $i] :
( ( ( leq @ n0 @ SV86 )
= $false )
| ( ( leq @ ( uniform_int_rnd @ SV95 @ SV86 ) @ SV86 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[602]) ).
thf(617,plain,
! [SV96: $i,SV87: $i,SV75: $i] :
( ( ( ~ ( ~ ( leq @ SV75 @ SV87 )
| ~ ( leq @ SV87 @ SV96 ) ) )
= $false )
| ( ( leq @ SV75 @ SV96 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[603]) ).
thf(618,plain,
! [SV88: $i,SV76: $i] :
( ( ( ~ ( leq @ SV76 @ SV88 )
| ~ ( ( SV76 != SV88 ) ) )
= $true )
| ( ( gt @ SV88 @ SV76 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[604]) ).
thf(619,plain,
! [SV89: $i,SV77: $i] :
( ( ~ ( geq @ SV77 @ SV89 )
| ( leq @ SV89 @ SV77 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[605]) ).
thf(620,plain,
! [SV77: $i,SV89: $i] :
( ( ~ ( leq @ SV89 @ SV77 )
| ( geq @ SV77 @ SV89 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[606]) ).
thf(621,plain,
! [SV78: $i] :
( ( ( ~ ( leq @ n0 @ SV78 ) )
= $true )
| ( ( ~ ( leq @ SV78 @ n2 ) )
= $true )
| ( ( ( SV78 = n0 )
| ( SV78 = n1 )
| ( SV78 = n2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[607]) ).
thf(622,plain,
! [SV79: $i] :
( ( ( ~ ( leq @ n0 @ SV79 ) )
= $true )
| ( ( ~ ( leq @ SV79 @ n1 ) )
= $true )
| ( ( ( SV79 = n0 )
| ( SV79 = n1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[608]) ).
thf(623,plain,
! [SV91: $i,SV81: $i] :
( ( ~ ( leq @ ( succ @ SV81 ) @ ( succ @ SV91 ) )
| ( leq @ SV81 @ SV91 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[610]) ).
thf(624,plain,
! [SV91: $i,SV81: $i] :
( ( ~ ( leq @ SV81 @ SV91 )
| ( leq @ ( succ @ SV81 ) @ ( succ @ SV91 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[611]) ).
thf(625,plain,
! [SV84: $i] :
( ( ( ~ ( leq @ n0 @ SV84 ) )
= $true )
| ( ( ~ ( leq @ SV84 @ n0 ) )
= $true )
| ( ( SV84 = n0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[614]) ).
thf(626,plain,
! [SV96: $i,SV87: $i,SV75: $i] :
( ( ( ~ ( leq @ SV75 @ SV87 )
| ~ ( leq @ SV87 @ SV96 ) )
= $true )
| ( ( leq @ SV75 @ SV96 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[617]) ).
thf(627,plain,
! [SV88: $i,SV76: $i] :
( ( ( ~ ( leq @ SV76 @ SV88 ) )
= $true )
| ( ( ~ ( ( SV76 != SV88 ) ) )
= $true )
| ( ( gt @ SV88 @ SV76 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[618]) ).
thf(628,plain,
! [SV89: $i,SV77: $i] :
( ( ( ~ ( geq @ SV77 @ SV89 ) )
= $true )
| ( ( leq @ SV89 @ SV77 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[619]) ).
thf(629,plain,
! [SV77: $i,SV89: $i] :
( ( ( ~ ( leq @ SV89 @ SV77 ) )
= $true )
| ( ( geq @ SV77 @ SV89 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[620]) ).
thf(630,plain,
! [SV78: $i] :
( ( ( leq @ n0 @ SV78 )
= $false )
| ( ( ~ ( leq @ SV78 @ n2 ) )
= $true )
| ( ( ( SV78 = n0 )
| ( SV78 = n1 )
| ( SV78 = n2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[621]) ).
thf(631,plain,
! [SV79: $i] :
( ( ( leq @ n0 @ SV79 )
= $false )
| ( ( ~ ( leq @ SV79 @ n1 ) )
= $true )
| ( ( ( SV79 = n0 )
| ( SV79 = n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[622]) ).
thf(632,plain,
! [SV91: $i,SV81: $i] :
( ( ( ~ ( leq @ ( succ @ SV81 ) @ ( succ @ SV91 ) ) )
= $true )
| ( ( leq @ SV81 @ SV91 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[623]) ).
thf(633,plain,
! [SV91: $i,SV81: $i] :
( ( ( ~ ( leq @ SV81 @ SV91 ) )
= $true )
| ( ( leq @ ( succ @ SV81 ) @ ( succ @ SV91 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[624]) ).
thf(634,plain,
! [SV84: $i] :
( ( ( leq @ n0 @ SV84 )
= $false )
| ( ( ~ ( leq @ SV84 @ n0 ) )
= $true )
| ( ( SV84 = n0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[625]) ).
thf(635,plain,
! [SV96: $i,SV87: $i,SV75: $i] :
( ( ( ~ ( leq @ SV75 @ SV87 ) )
= $true )
| ( ( ~ ( leq @ SV87 @ SV96 ) )
= $true )
| ( ( leq @ SV75 @ SV96 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[626]) ).
thf(636,plain,
! [SV88: $i,SV76: $i] :
( ( ( leq @ SV76 @ SV88 )
= $false )
| ( ( ~ ( ( SV76 != SV88 ) ) )
= $true )
| ( ( gt @ SV88 @ SV76 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[627]) ).
thf(637,plain,
! [SV89: $i,SV77: $i] :
( ( ( geq @ SV77 @ SV89 )
= $false )
| ( ( leq @ SV89 @ SV77 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[628]) ).
thf(638,plain,
! [SV77: $i,SV89: $i] :
( ( ( leq @ SV89 @ SV77 )
= $false )
| ( ( geq @ SV77 @ SV89 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[629]) ).
thf(639,plain,
! [SV78: $i] :
( ( ( leq @ SV78 @ n2 )
= $false )
| ( ( leq @ n0 @ SV78 )
= $false )
| ( ( ( SV78 = n0 )
| ( SV78 = n1 )
| ( SV78 = n2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[630]) ).
thf(640,plain,
! [SV79: $i] :
( ( ( leq @ SV79 @ n1 )
= $false )
| ( ( leq @ n0 @ SV79 )
= $false )
| ( ( ( SV79 = n0 )
| ( SV79 = n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[631]) ).
thf(641,plain,
! [SV91: $i,SV81: $i] :
( ( ( leq @ ( succ @ SV81 ) @ ( succ @ SV91 ) )
= $false )
| ( ( leq @ SV81 @ SV91 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[632]) ).
thf(642,plain,
! [SV91: $i,SV81: $i] :
( ( ( leq @ SV81 @ SV91 )
= $false )
| ( ( leq @ ( succ @ SV81 ) @ ( succ @ SV91 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[633]) ).
thf(643,plain,
! [SV84: $i] :
( ( ( leq @ SV84 @ n0 )
= $false )
| ( ( leq @ n0 @ SV84 )
= $false )
| ( ( SV84 = n0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[634]) ).
thf(644,plain,
! [SV96: $i,SV87: $i,SV75: $i] :
( ( ( leq @ SV75 @ SV87 )
= $false )
| ( ( ~ ( leq @ SV87 @ SV96 ) )
= $true )
| ( ( leq @ SV75 @ SV96 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[635]) ).
thf(645,plain,
! [SV88: $i,SV76: $i] :
( ( ( SV76 != SV88 )
= $false )
| ( ( leq @ SV76 @ SV88 )
= $false )
| ( ( gt @ SV88 @ SV76 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[636]) ).
thf(646,plain,
! [SV78: $i] :
( ( ( ( SV78 = n0 )
| ( SV78 = n1 ) )
= $true )
| ( ( SV78 = n2 )
= $true )
| ( ( leq @ n0 @ SV78 )
= $false )
| ( ( leq @ SV78 @ n2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[639]) ).
thf(647,plain,
! [SV79: $i] :
( ( ( SV79 = n0 )
= $true )
| ( ( SV79 = n1 )
= $true )
| ( ( leq @ n0 @ SV79 )
= $false )
| ( ( leq @ SV79 @ n1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[640]) ).
thf(648,plain,
! [SV75: $i,SV96: $i,SV87: $i] :
( ( ( leq @ SV87 @ SV96 )
= $false )
| ( ( leq @ SV75 @ SV87 )
= $false )
| ( ( leq @ SV75 @ SV96 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[644]) ).
thf(649,plain,
! [SV88: $i,SV76: $i] :
( ( ( SV76 = SV88 )
= $true )
| ( ( leq @ SV76 @ SV88 )
= $false )
| ( ( gt @ SV88 @ SV76 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[645]) ).
thf(650,plain,
! [SV78: $i] :
( ( ( SV78 = n0 )
= $true )
| ( ( SV78 = n1 )
= $true )
| ( ( SV78 = n2 )
= $true )
| ( ( leq @ n0 @ SV78 )
= $false )
| ( ( leq @ SV78 @ n2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[646]) ).
thf(651,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[534,650,649,648,647,643,642,641,638,637,616,615,613,612,609,566,565,564,550,549,548,547,546,545,544,543,539,538,537,536,535]) ).
thf(652,plain,
( ( ! [X: $i] : ( leq @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(653,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( leq @ X @ Y )
& ( leq @ Y @ Z ) )
=> ( leq @ X @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[115]) ).
thf(654,plain,
( ( ! [X: $i,Y: $i] :
( ( geq @ X @ Y )
<=> ( leq @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(655,plain,
( ( ! [X: $i,Y: $i] :
( ( gt @ Y @ X )
=> ( leq @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(656,plain,
( ( ! [X: $i,Y: $i] :
( ( ( leq @ X @ Y )
& ( X != Y ) )
=> ( gt @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(657,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ X @ Y )
=> ( leq @ X @ ( succ @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(658,plain,
( ( ! [X: $i,C: $i] :
( ( leq @ n0 @ X )
=> ( leq @ ( uniform_int_rnd @ C @ X ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(659,plain,
( ( ! [X: $i,C: $i] :
( ( leq @ n0 @ X )
=> ( leq @ n0 @ ( uniform_int_rnd @ C @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(660,plain,
( ( ! [X: $i] :
( ( minus @ X @ n1 )
= ( pred @ X ) ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(661,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ ( succ @ X ) @ ( succ @ Y ) )
<=> ( leq @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(662,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ ( minus @ X @ Y ) @ X )
=> ( leq @ n0 @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(663,plain,
( ( gt @ n135300 @ n5 )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(664,plain,
( ( gt @ n5 @ n0 )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(665,plain,
( ( gt @ n135300 @ n0 )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(666,plain,
( ( gt @ n1 @ n0 )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(667,plain,
( ( gt @ n5 @ n1 )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(668,plain,
( ( gt @ n135300 @ n1 )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(669,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n0 ) )
=> ( X = n0 ) ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(670,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n1 ) )
=> ( ( X = n0 )
| ( X = n1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(671,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n2 ) )
=> ( ( X = n0 )
| ( X = n1 )
| ( X = n2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(672,plain,
( ( ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ n0 ) ) ) ) )
= n5 )
= $true ),
inference(copy,[status(thm)],[96]) ).
thf(673,plain,
( ( ( succ @ n0 )
= n1 )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(674,plain,
( ( leq @ pv43 @ ( minus @ n5 @ n1 ) )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(675,plain,
( ( leq @ pv41 @ ( minus @ n5 @ n1 ) )
= $true ),
inference(copy,[status(thm)],[121]) ).
thf(676,plain,
( ( leq @ pv10 @ ( minus @ n135300 @ n1 ) )
= $true ),
inference(copy,[status(thm)],[120]) ).
thf(677,plain,
( ( leq @ n0 @ pv43 )
= $true ),
inference(copy,[status(thm)],[119]) ).
thf(678,plain,
( ( leq @ n0 @ pv41 )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(679,plain,
( ( leq @ n0 @ pv10 )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(680,plain,
( ( ~ ( leq @ pv41 @ ( minus @ n5 @ n1 ) ) )
= $true ),
inference(copy,[status(thm)],[134]) ).
thf(681,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( leq @ n0 @ SX0 )
| ~ ( leq @ SX0 @ n1 ) )
| ( SX0 = n0 )
| ( SX0 = n1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[670]) ).
thf(682,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ n0 @ SX0 )
| ( leq @ n0 @ ( uniform_int_rnd @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[659]) ).
thf(683,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)],[661]) ).
thf(684,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( leq @ SX0 @ SX1 )
| ~ ( ( SX0 != SX1 ) ) )
| ( gt @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[656]) ).
thf(685,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( leq @ n0 @ SX0 )
| ~ ( leq @ SX0 @ n0 ) )
| ( SX0 = n0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[669]) ).
thf(686,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX0 @ SX1 )
| ( leq @ SX0 @ ( succ @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[657]) ).
thf(687,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( leq @ SX0 @ SX1 )
| ~ ( leq @ SX1 @ SX2 ) )
| ( leq @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[653]) ).
thf(688,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( gt @ SX1 @ SX0 )
| ( leq @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[655]) ).
thf(689,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ n0 @ SX0 )
| ( leq @ ( uniform_int_rnd @ SX1 @ SX0 ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[658]) ).
thf(690,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ ( minus @ SX0 @ SX1 ) @ SX0 )
| ( leq @ n0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[662]) ).
thf(691,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( leq @ n0 @ SX0 )
| ~ ( leq @ SX0 @ n2 ) )
| ( SX0 = n0 )
| ( SX0 = n1 )
| ( SX0 = n2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[671]) ).
thf(692,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( geq @ SX0 @ SX1 )
| ( leq @ SX1 @ SX0 ) )
| ~ ( ~ ( leq @ SX1 @ SX0 )
| ( geq @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[654]) ).
thf(693,plain,
! [SV97: $i] :
( ( leq @ SV97 @ SV97 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[652]) ).
thf(694,plain,
! [SV98: $i] :
( ( ( minus @ SV98 @ n1 )
= ( pred @ SV98 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[660]) ).
thf(695,plain,
( ( leq @ pv41 @ ( minus @ n5 @ n1 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[680]) ).
thf(696,plain,
! [SV99: $i] :
( ( ~ ~ ( ~ ( leq @ n0 @ SV99 )
| ~ ( leq @ SV99 @ n1 ) )
| ( SV99 = n0 )
| ( SV99 = n1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[681]) ).
thf(697,plain,
! [SV100: $i] :
( ( ! [SY68: $i] :
( ~ ( leq @ n0 @ SV100 )
| ( leq @ n0 @ ( uniform_int_rnd @ SY68 @ SV100 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[682]) ).
thf(698,plain,
! [SV101: $i] :
( ( ! [SY69: $i] :
~ ( ~ ( ~ ( leq @ ( succ @ SV101 ) @ ( succ @ SY69 ) )
| ( leq @ SV101 @ SY69 ) )
| ~ ( ~ ( leq @ SV101 @ SY69 )
| ( leq @ ( succ @ SV101 ) @ ( succ @ SY69 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[683]) ).
thf(699,plain,
! [SV102: $i] :
( ( ! [SY70: $i] :
( ~ ~ ( ~ ( leq @ SV102 @ SY70 )
| ~ ( ( SV102 != SY70 ) ) )
| ( gt @ SY70 @ SV102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[684]) ).
thf(700,plain,
! [SV103: $i] :
( ( ~ ~ ( ~ ( leq @ n0 @ SV103 )
| ~ ( leq @ SV103 @ n0 ) )
| ( SV103 = n0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[685]) ).
thf(701,plain,
! [SV104: $i] :
( ( ! [SY71: $i] :
( ~ ( leq @ SV104 @ SY71 )
| ( leq @ SV104 @ ( succ @ SY71 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[686]) ).
thf(702,plain,
! [SV105: $i] :
( ( ! [SY72: $i,SY73: $i] :
( ~ ~ ( ~ ( leq @ SV105 @ SY72 )
| ~ ( leq @ SY72 @ SY73 ) )
| ( leq @ SV105 @ SY73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[687]) ).
thf(703,plain,
! [SV106: $i] :
( ( ! [SY74: $i] :
( ~ ( gt @ SY74 @ SV106 )
| ( leq @ SV106 @ SY74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[688]) ).
thf(704,plain,
! [SV107: $i] :
( ( ! [SY75: $i] :
( ~ ( leq @ n0 @ SV107 )
| ( leq @ ( uniform_int_rnd @ SY75 @ SV107 ) @ SV107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[689]) ).
thf(705,plain,
! [SV108: $i] :
( ( ! [SY76: $i] :
( ~ ( leq @ ( minus @ SV108 @ SY76 ) @ SV108 )
| ( leq @ n0 @ SY76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[690]) ).
thf(706,plain,
! [SV109: $i] :
( ( ~ ~ ( ~ ( leq @ n0 @ SV109 )
| ~ ( leq @ SV109 @ n2 ) )
| ( SV109 = n0 )
| ( SV109 = n1 )
| ( SV109 = n2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[691]) ).
thf(707,plain,
! [SV110: $i] :
( ( ! [SY77: $i] :
~ ( ~ ( ~ ( geq @ SV110 @ SY77 )
| ( leq @ SY77 @ SV110 ) )
| ~ ( ~ ( leq @ SY77 @ SV110 )
| ( geq @ SV110 @ SY77 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[692]) ).
thf(708,plain,
! [SV99: $i] :
( ( ( ~ ~ ( ~ ( leq @ n0 @ SV99 )
| ~ ( leq @ SV99 @ n1 ) ) )
= $true )
| ( ( ( SV99 = n0 )
| ( SV99 = n1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[696]) ).
thf(709,plain,
! [SV111: $i,SV100: $i] :
( ( ~ ( leq @ n0 @ SV100 )
| ( leq @ n0 @ ( uniform_int_rnd @ SV111 @ SV100 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[697]) ).
thf(710,plain,
! [SV112: $i,SV101: $i] :
( ( ~ ( ~ ( ~ ( leq @ ( succ @ SV101 ) @ ( succ @ SV112 ) )
| ( leq @ SV101 @ SV112 ) )
| ~ ( ~ ( leq @ SV101 @ SV112 )
| ( leq @ ( succ @ SV101 ) @ ( succ @ SV112 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[698]) ).
thf(711,plain,
! [SV113: $i,SV102: $i] :
( ( ~ ~ ( ~ ( leq @ SV102 @ SV113 )
| ~ ( ( SV102 != SV113 ) ) )
| ( gt @ SV113 @ SV102 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[699]) ).
thf(712,plain,
! [SV103: $i] :
( ( ( ~ ~ ( ~ ( leq @ n0 @ SV103 )
| ~ ( leq @ SV103 @ n0 ) ) )
= $true )
| ( ( SV103 = n0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[700]) ).
thf(713,plain,
! [SV114: $i,SV104: $i] :
( ( ~ ( leq @ SV104 @ SV114 )
| ( leq @ SV104 @ ( succ @ SV114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[701]) ).
thf(714,plain,
! [SV115: $i,SV105: $i] :
( ( ! [SY78: $i] :
( ~ ~ ( ~ ( leq @ SV105 @ SV115 )
| ~ ( leq @ SV115 @ SY78 ) )
| ( leq @ SV105 @ SY78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[702]) ).
thf(715,plain,
! [SV106: $i,SV116: $i] :
( ( ~ ( gt @ SV116 @ SV106 )
| ( leq @ SV106 @ SV116 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[703]) ).
thf(716,plain,
! [SV117: $i,SV107: $i] :
( ( ~ ( leq @ n0 @ SV107 )
| ( leq @ ( uniform_int_rnd @ SV117 @ SV107 ) @ SV107 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[704]) ).
thf(717,plain,
! [SV118: $i,SV108: $i] :
( ( ~ ( leq @ ( minus @ SV108 @ SV118 ) @ SV108 )
| ( leq @ n0 @ SV118 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[705]) ).
thf(718,plain,
! [SV109: $i] :
( ( ( ~ ~ ( ~ ( leq @ n0 @ SV109 )
| ~ ( leq @ SV109 @ n2 ) ) )
= $true )
| ( ( ( SV109 = n0 )
| ( SV109 = n1 )
| ( SV109 = n2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[706]) ).
thf(719,plain,
! [SV119: $i,SV110: $i] :
( ( ~ ( ~ ( ~ ( geq @ SV110 @ SV119 )
| ( leq @ SV119 @ SV110 ) )
| ~ ( ~ ( leq @ SV119 @ SV110 )
| ( geq @ SV110 @ SV119 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[707]) ).
thf(720,plain,
! [SV99: $i] :
( ( ( ~ ( ~ ( leq @ n0 @ SV99 )
| ~ ( leq @ SV99 @ n1 ) ) )
= $false )
| ( ( ( SV99 = n0 )
| ( SV99 = n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[708]) ).
thf(721,plain,
! [SV111: $i,SV100: $i] :
( ( ( ~ ( leq @ n0 @ SV100 ) )
= $true )
| ( ( leq @ n0 @ ( uniform_int_rnd @ SV111 @ SV100 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[709]) ).
thf(722,plain,
! [SV112: $i,SV101: $i] :
( ( ~ ( ~ ( leq @ ( succ @ SV101 ) @ ( succ @ SV112 ) )
| ( leq @ SV101 @ SV112 ) )
| ~ ( ~ ( leq @ SV101 @ SV112 )
| ( leq @ ( succ @ SV101 ) @ ( succ @ SV112 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[710]) ).
thf(723,plain,
! [SV113: $i,SV102: $i] :
( ( ( ~ ~ ( ~ ( leq @ SV102 @ SV113 )
| ~ ( ( SV102 != SV113 ) ) ) )
= $true )
| ( ( gt @ SV113 @ SV102 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[711]) ).
thf(724,plain,
! [SV103: $i] :
( ( ( ~ ( ~ ( leq @ n0 @ SV103 )
| ~ ( leq @ SV103 @ n0 ) ) )
= $false )
| ( ( SV103 = n0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[712]) ).
thf(725,plain,
! [SV114: $i,SV104: $i] :
( ( ( ~ ( leq @ SV104 @ SV114 ) )
= $true )
| ( ( leq @ SV104 @ ( succ @ SV114 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[713]) ).
thf(726,plain,
! [SV120: $i,SV115: $i,SV105: $i] :
( ( ~ ~ ( ~ ( leq @ SV105 @ SV115 )
| ~ ( leq @ SV115 @ SV120 ) )
| ( leq @ SV105 @ SV120 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[714]) ).
thf(727,plain,
! [SV106: $i,SV116: $i] :
( ( ( ~ ( gt @ SV116 @ SV106 ) )
= $true )
| ( ( leq @ SV106 @ SV116 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[715]) ).
thf(728,plain,
! [SV117: $i,SV107: $i] :
( ( ( ~ ( leq @ n0 @ SV107 ) )
= $true )
| ( ( leq @ ( uniform_int_rnd @ SV117 @ SV107 ) @ SV107 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[716]) ).
thf(729,plain,
! [SV118: $i,SV108: $i] :
( ( ( ~ ( leq @ ( minus @ SV108 @ SV118 ) @ SV108 ) )
= $true )
| ( ( leq @ n0 @ SV118 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[717]) ).
thf(730,plain,
! [SV109: $i] :
( ( ( ~ ( ~ ( leq @ n0 @ SV109 )
| ~ ( leq @ SV109 @ n2 ) ) )
= $false )
| ( ( ( SV109 = n0 )
| ( SV109 = n1 )
| ( SV109 = n2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[718]) ).
thf(731,plain,
! [SV119: $i,SV110: $i] :
( ( ~ ( ~ ( geq @ SV110 @ SV119 )
| ( leq @ SV119 @ SV110 ) )
| ~ ( ~ ( leq @ SV119 @ SV110 )
| ( geq @ SV110 @ SV119 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[719]) ).
thf(732,plain,
! [SV99: $i] :
( ( ( ~ ( leq @ n0 @ SV99 )
| ~ ( leq @ SV99 @ n1 ) )
= $true )
| ( ( ( SV99 = n0 )
| ( SV99 = n1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[720]) ).
thf(733,plain,
! [SV111: $i,SV100: $i] :
( ( ( leq @ n0 @ SV100 )
= $false )
| ( ( leq @ n0 @ ( uniform_int_rnd @ SV111 @ SV100 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[721]) ).
thf(734,plain,
! [SV112: $i,SV101: $i] :
( ( ~ ( ~ ( leq @ ( succ @ SV101 ) @ ( succ @ SV112 ) )
| ( leq @ SV101 @ SV112 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[722]) ).
thf(735,plain,
! [SV112: $i,SV101: $i] :
( ( ~ ( ~ ( leq @ SV101 @ SV112 )
| ( leq @ ( succ @ SV101 ) @ ( succ @ SV112 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[722]) ).
thf(736,plain,
! [SV113: $i,SV102: $i] :
( ( ( ~ ( ~ ( leq @ SV102 @ SV113 )
| ~ ( ( SV102 != SV113 ) ) ) )
= $false )
| ( ( gt @ SV113 @ SV102 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[723]) ).
thf(737,plain,
! [SV103: $i] :
( ( ( ~ ( leq @ n0 @ SV103 )
| ~ ( leq @ SV103 @ n0 ) )
= $true )
| ( ( SV103 = n0 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[724]) ).
thf(738,plain,
! [SV114: $i,SV104: $i] :
( ( ( leq @ SV104 @ SV114 )
= $false )
| ( ( leq @ SV104 @ ( succ @ SV114 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[725]) ).
thf(739,plain,
! [SV120: $i,SV115: $i,SV105: $i] :
( ( ( ~ ~ ( ~ ( leq @ SV105 @ SV115 )
| ~ ( leq @ SV115 @ SV120 ) ) )
= $true )
| ( ( leq @ SV105 @ SV120 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[726]) ).
thf(740,plain,
! [SV106: $i,SV116: $i] :
( ( ( gt @ SV116 @ SV106 )
= $false )
| ( ( leq @ SV106 @ SV116 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[727]) ).
thf(741,plain,
! [SV117: $i,SV107: $i] :
( ( ( leq @ n0 @ SV107 )
= $false )
| ( ( leq @ ( uniform_int_rnd @ SV117 @ SV107 ) @ SV107 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[728]) ).
thf(742,plain,
! [SV118: $i,SV108: $i] :
( ( ( leq @ ( minus @ SV108 @ SV118 ) @ SV108 )
= $false )
| ( ( leq @ n0 @ SV118 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[729]) ).
thf(743,plain,
! [SV109: $i] :
( ( ( ~ ( leq @ n0 @ SV109 )
| ~ ( leq @ SV109 @ n2 ) )
= $true )
| ( ( ( SV109 = n0 )
| ( SV109 = n1 )
| ( SV109 = n2 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[730]) ).
thf(744,plain,
! [SV119: $i,SV110: $i] :
( ( ~ ( ~ ( geq @ SV110 @ SV119 )
| ( leq @ SV119 @ SV110 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[731]) ).
thf(745,plain,
! [SV110: $i,SV119: $i] :
( ( ~ ( ~ ( leq @ SV119 @ SV110 )
| ( geq @ SV110 @ SV119 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[731]) ).
thf(746,plain,
! [SV99: $i] :
( ( ( ~ ( leq @ n0 @ SV99 ) )
= $true )
| ( ( ~ ( leq @ SV99 @ n1 ) )
= $true )
| ( ( ( SV99 = n0 )
| ( SV99 = n1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[732]) ).
thf(747,plain,
! [SV112: $i,SV101: $i] :
( ( ~ ( leq @ ( succ @ SV101 ) @ ( succ @ SV112 ) )
| ( leq @ SV101 @ SV112 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[734]) ).
thf(748,plain,
! [SV112: $i,SV101: $i] :
( ( ~ ( leq @ SV101 @ SV112 )
| ( leq @ ( succ @ SV101 ) @ ( succ @ SV112 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[735]) ).
thf(749,plain,
! [SV113: $i,SV102: $i] :
( ( ( ~ ( leq @ SV102 @ SV113 )
| ~ ( ( SV102 != SV113 ) ) )
= $true )
| ( ( gt @ SV113 @ SV102 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[736]) ).
thf(750,plain,
! [SV103: $i] :
( ( ( ~ ( leq @ n0 @ SV103 ) )
= $true )
| ( ( ~ ( leq @ SV103 @ n0 ) )
= $true )
| ( ( SV103 = n0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[737]) ).
thf(751,plain,
! [SV120: $i,SV115: $i,SV105: $i] :
( ( ( ~ ( ~ ( leq @ SV105 @ SV115 )
| ~ ( leq @ SV115 @ SV120 ) ) )
= $false )
| ( ( leq @ SV105 @ SV120 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[739]) ).
thf(752,plain,
! [SV109: $i] :
( ( ( ~ ( leq @ n0 @ SV109 ) )
= $true )
| ( ( ~ ( leq @ SV109 @ n2 ) )
= $true )
| ( ( ( SV109 = n0 )
| ( SV109 = n1 )
| ( SV109 = n2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[743]) ).
thf(753,plain,
! [SV119: $i,SV110: $i] :
( ( ~ ( geq @ SV110 @ SV119 )
| ( leq @ SV119 @ SV110 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[744]) ).
thf(754,plain,
! [SV110: $i,SV119: $i] :
( ( ~ ( leq @ SV119 @ SV110 )
| ( geq @ SV110 @ SV119 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[745]) ).
thf(755,plain,
! [SV99: $i] :
( ( ( leq @ n0 @ SV99 )
= $false )
| ( ( ~ ( leq @ SV99 @ n1 ) )
= $true )
| ( ( ( SV99 = n0 )
| ( SV99 = n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[746]) ).
thf(756,plain,
! [SV112: $i,SV101: $i] :
( ( ( ~ ( leq @ ( succ @ SV101 ) @ ( succ @ SV112 ) ) )
= $true )
| ( ( leq @ SV101 @ SV112 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[747]) ).
thf(757,plain,
! [SV112: $i,SV101: $i] :
( ( ( ~ ( leq @ SV101 @ SV112 ) )
= $true )
| ( ( leq @ ( succ @ SV101 ) @ ( succ @ SV112 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[748]) ).
thf(758,plain,
! [SV113: $i,SV102: $i] :
( ( ( ~ ( leq @ SV102 @ SV113 ) )
= $true )
| ( ( ~ ( ( SV102 != SV113 ) ) )
= $true )
| ( ( gt @ SV113 @ SV102 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[749]) ).
thf(759,plain,
! [SV103: $i] :
( ( ( leq @ n0 @ SV103 )
= $false )
| ( ( ~ ( leq @ SV103 @ n0 ) )
= $true )
| ( ( SV103 = n0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[750]) ).
thf(760,plain,
! [SV120: $i,SV115: $i,SV105: $i] :
( ( ( ~ ( leq @ SV105 @ SV115 )
| ~ ( leq @ SV115 @ SV120 ) )
= $true )
| ( ( leq @ SV105 @ SV120 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[751]) ).
thf(761,plain,
! [SV109: $i] :
( ( ( leq @ n0 @ SV109 )
= $false )
| ( ( ~ ( leq @ SV109 @ n2 ) )
= $true )
| ( ( ( SV109 = n0 )
| ( SV109 = n1 )
| ( SV109 = n2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[752]) ).
thf(762,plain,
! [SV119: $i,SV110: $i] :
( ( ( ~ ( geq @ SV110 @ SV119 ) )
= $true )
| ( ( leq @ SV119 @ SV110 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[753]) ).
thf(763,plain,
! [SV110: $i,SV119: $i] :
( ( ( ~ ( leq @ SV119 @ SV110 ) )
= $true )
| ( ( geq @ SV110 @ SV119 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[754]) ).
thf(764,plain,
! [SV99: $i] :
( ( ( leq @ SV99 @ n1 )
= $false )
| ( ( leq @ n0 @ SV99 )
= $false )
| ( ( ( SV99 = n0 )
| ( SV99 = n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[755]) ).
thf(765,plain,
! [SV112: $i,SV101: $i] :
( ( ( leq @ ( succ @ SV101 ) @ ( succ @ SV112 ) )
= $false )
| ( ( leq @ SV101 @ SV112 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[756]) ).
thf(766,plain,
! [SV112: $i,SV101: $i] :
( ( ( leq @ SV101 @ SV112 )
= $false )
| ( ( leq @ ( succ @ SV101 ) @ ( succ @ SV112 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[757]) ).
thf(767,plain,
! [SV113: $i,SV102: $i] :
( ( ( leq @ SV102 @ SV113 )
= $false )
| ( ( ~ ( ( SV102 != SV113 ) ) )
= $true )
| ( ( gt @ SV113 @ SV102 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[758]) ).
thf(768,plain,
! [SV103: $i] :
( ( ( leq @ SV103 @ n0 )
= $false )
| ( ( leq @ n0 @ SV103 )
= $false )
| ( ( SV103 = n0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[759]) ).
thf(769,plain,
! [SV120: $i,SV115: $i,SV105: $i] :
( ( ( ~ ( leq @ SV105 @ SV115 ) )
= $true )
| ( ( ~ ( leq @ SV115 @ SV120 ) )
= $true )
| ( ( leq @ SV105 @ SV120 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[760]) ).
thf(770,plain,
! [SV109: $i] :
( ( ( leq @ SV109 @ n2 )
= $false )
| ( ( leq @ n0 @ SV109 )
= $false )
| ( ( ( SV109 = n0 )
| ( SV109 = n1 )
| ( SV109 = n2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[761]) ).
thf(771,plain,
! [SV119: $i,SV110: $i] :
( ( ( geq @ SV110 @ SV119 )
= $false )
| ( ( leq @ SV119 @ SV110 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[762]) ).
thf(772,plain,
! [SV110: $i,SV119: $i] :
( ( ( leq @ SV119 @ SV110 )
= $false )
| ( ( geq @ SV110 @ SV119 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[763]) ).
thf(773,plain,
! [SV99: $i] :
( ( ( SV99 = n0 )
= $true )
| ( ( SV99 = n1 )
= $true )
| ( ( leq @ n0 @ SV99 )
= $false )
| ( ( leq @ SV99 @ n1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[764]) ).
thf(774,plain,
! [SV113: $i,SV102: $i] :
( ( ( SV102 != SV113 )
= $false )
| ( ( leq @ SV102 @ SV113 )
= $false )
| ( ( gt @ SV113 @ SV102 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[767]) ).
thf(775,plain,
! [SV120: $i,SV115: $i,SV105: $i] :
( ( ( leq @ SV105 @ SV115 )
= $false )
| ( ( ~ ( leq @ SV115 @ SV120 ) )
= $true )
| ( ( leq @ SV105 @ SV120 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[769]) ).
thf(776,plain,
! [SV109: $i] :
( ( ( ( SV109 = n0 )
| ( SV109 = n1 ) )
= $true )
| ( ( SV109 = n2 )
= $true )
| ( ( leq @ n0 @ SV109 )
= $false )
| ( ( leq @ SV109 @ n2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[770]) ).
thf(777,plain,
! [SV113: $i,SV102: $i] :
( ( ( SV102 = SV113 )
= $true )
| ( ( leq @ SV102 @ SV113 )
= $false )
| ( ( gt @ SV113 @ SV102 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[774]) ).
thf(778,plain,
! [SV105: $i,SV120: $i,SV115: $i] :
( ( ( leq @ SV115 @ SV120 )
= $false )
| ( ( leq @ SV105 @ SV115 )
= $false )
| ( ( leq @ SV105 @ SV120 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[775]) ).
thf(779,plain,
! [SV109: $i] :
( ( ( SV109 = n0 )
= $true )
| ( ( SV109 = n1 )
= $true )
| ( ( SV109 = n2 )
= $true )
| ( ( leq @ n0 @ SV109 )
= $false )
| ( ( leq @ SV109 @ n2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[776]) ).
thf(780,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[663,779,778,777,773,772,771,768,766,765,742,741,740,738,733,695,694,693,679,678,677,676,675,674,673,672,668,667,666,665,664]) ).
thf(781,plain,
( ( ! [X: $i] : ( leq @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(782,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( leq @ X @ Y )
& ( leq @ Y @ Z ) )
=> ( leq @ X @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[115]) ).
thf(783,plain,
( ( ! [X: $i,Y: $i] :
( ( geq @ X @ Y )
<=> ( leq @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(784,plain,
( ( ! [X: $i,Y: $i] :
( ( gt @ Y @ X )
=> ( leq @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(785,plain,
( ( ! [X: $i,Y: $i] :
( ( ( leq @ X @ Y )
& ( X != Y ) )
=> ( gt @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(786,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ X @ Y )
=> ( leq @ X @ ( succ @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(787,plain,
( ( ! [X: $i,C: $i] :
( ( leq @ n0 @ X )
=> ( leq @ ( uniform_int_rnd @ C @ X ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(788,plain,
( ( ! [X: $i,C: $i] :
( ( leq @ n0 @ X )
=> ( leq @ n0 @ ( uniform_int_rnd @ C @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(789,plain,
( ( ! [X: $i] :
( ( minus @ X @ n1 )
= ( pred @ X ) ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(790,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ ( succ @ X ) @ ( succ @ Y ) )
<=> ( leq @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(791,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ ( minus @ X @ Y ) @ X )
=> ( leq @ n0 @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(792,plain,
( ( gt @ n135300 @ n5 )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(793,plain,
( ( gt @ n5 @ n0 )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(794,plain,
( ( gt @ n135300 @ n0 )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(795,plain,
( ( gt @ n1 @ n0 )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(796,plain,
( ( gt @ n5 @ n1 )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(797,plain,
( ( gt @ n135300 @ n1 )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(798,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n0 ) )
=> ( X = n0 ) ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(799,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n1 ) )
=> ( ( X = n0 )
| ( X = n1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(800,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n2 ) )
=> ( ( X = n0 )
| ( X = n1 )
| ( X = n2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(801,plain,
( ( ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ n0 ) ) ) ) )
= n5 )
= $true ),
inference(copy,[status(thm)],[96]) ).
thf(802,plain,
( ( ( succ @ n0 )
= n1 )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(803,plain,
( ( leq @ pv43 @ ( minus @ n5 @ n1 ) )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(804,plain,
( ( leq @ pv41 @ ( minus @ n5 @ n1 ) )
= $true ),
inference(copy,[status(thm)],[121]) ).
thf(805,plain,
( ( leq @ pv10 @ ( minus @ n135300 @ n1 ) )
= $true ),
inference(copy,[status(thm)],[120]) ).
thf(806,plain,
( ( leq @ n0 @ pv43 )
= $true ),
inference(copy,[status(thm)],[119]) ).
thf(807,plain,
( ( leq @ n0 @ pv41 )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(808,plain,
( ( leq @ n0 @ pv10 )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(809,plain,
( ( ~ ( leq @ pv43 @ ( minus @ n5 @ n1 ) ) )
= $true ),
inference(copy,[status(thm)],[135]) ).
thf(810,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ n0 @ SX0 )
| ( leq @ n0 @ ( uniform_int_rnd @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[788]) ).
thf(811,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( leq @ SX0 @ SX1 )
| ~ ( leq @ SX1 @ SX2 ) )
| ( leq @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[782]) ).
thf(812,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( leq @ n0 @ SX0 )
| ~ ( leq @ SX0 @ n0 ) )
| ( SX0 = n0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[798]) ).
thf(813,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( geq @ SX0 @ SX1 )
| ( leq @ SX1 @ SX0 ) )
| ~ ( ~ ( leq @ SX1 @ SX0 )
| ( geq @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[783]) ).
thf(814,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( leq @ SX0 @ SX1 )
| ~ ( ( SX0 != SX1 ) ) )
| ( gt @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[785]) ).
thf(815,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX0 @ SX1 )
| ( leq @ SX0 @ ( succ @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[786]) ).
thf(816,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( leq @ n0 @ SX0 )
| ~ ( leq @ SX0 @ n1 ) )
| ( SX0 = n0 )
| ( SX0 = n1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[799]) ).
thf(817,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( gt @ SX1 @ SX0 )
| ( leq @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[784]) ).
thf(818,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( leq @ n0 @ SX0 )
| ~ ( leq @ SX0 @ n2 ) )
| ( SX0 = n0 )
| ( SX0 = n1 )
| ( SX0 = n2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[800]) ).
thf(819,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)],[790]) ).
thf(820,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ n0 @ SX0 )
| ( leq @ ( uniform_int_rnd @ SX1 @ SX0 ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[787]) ).
thf(821,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ ( minus @ SX0 @ SX1 ) @ SX0 )
| ( leq @ n0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[791]) ).
thf(822,plain,
! [SV121: $i] :
( ( leq @ SV121 @ SV121 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[781]) ).
thf(823,plain,
! [SV122: $i] :
( ( ( minus @ SV122 @ n1 )
= ( pred @ SV122 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[789]) ).
thf(824,plain,
( ( leq @ pv43 @ ( minus @ n5 @ n1 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[809]) ).
thf(825,plain,
! [SV123: $i] :
( ( ! [SY79: $i] :
( ~ ( leq @ n0 @ SV123 )
| ( leq @ n0 @ ( uniform_int_rnd @ SY79 @ SV123 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[810]) ).
thf(826,plain,
! [SV124: $i] :
( ( ! [SY80: $i,SY81: $i] :
( ~ ~ ( ~ ( leq @ SV124 @ SY80 )
| ~ ( leq @ SY80 @ SY81 ) )
| ( leq @ SV124 @ SY81 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[811]) ).
thf(827,plain,
! [SV125: $i] :
( ( ~ ~ ( ~ ( leq @ n0 @ SV125 )
| ~ ( leq @ SV125 @ n0 ) )
| ( SV125 = n0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[812]) ).
thf(828,plain,
! [SV126: $i] :
( ( ! [SY82: $i] :
~ ( ~ ( ~ ( geq @ SV126 @ SY82 )
| ( leq @ SY82 @ SV126 ) )
| ~ ( ~ ( leq @ SY82 @ SV126 )
| ( geq @ SV126 @ SY82 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[813]) ).
thf(829,plain,
! [SV127: $i] :
( ( ! [SY83: $i] :
( ~ ~ ( ~ ( leq @ SV127 @ SY83 )
| ~ ( ( SV127 != SY83 ) ) )
| ( gt @ SY83 @ SV127 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[814]) ).
thf(830,plain,
! [SV128: $i] :
( ( ! [SY84: $i] :
( ~ ( leq @ SV128 @ SY84 )
| ( leq @ SV128 @ ( succ @ SY84 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[815]) ).
thf(831,plain,
! [SV129: $i] :
( ( ~ ~ ( ~ ( leq @ n0 @ SV129 )
| ~ ( leq @ SV129 @ n1 ) )
| ( SV129 = n0 )
| ( SV129 = n1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[816]) ).
thf(832,plain,
! [SV130: $i] :
( ( ! [SY85: $i] :
( ~ ( gt @ SY85 @ SV130 )
| ( leq @ SV130 @ SY85 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[817]) ).
thf(833,plain,
! [SV131: $i] :
( ( ~ ~ ( ~ ( leq @ n0 @ SV131 )
| ~ ( leq @ SV131 @ n2 ) )
| ( SV131 = n0 )
| ( SV131 = n1 )
| ( SV131 = n2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[818]) ).
thf(834,plain,
! [SV132: $i] :
( ( ! [SY86: $i] :
~ ( ~ ( ~ ( leq @ ( succ @ SV132 ) @ ( succ @ SY86 ) )
| ( leq @ SV132 @ SY86 ) )
| ~ ( ~ ( leq @ SV132 @ SY86 )
| ( leq @ ( succ @ SV132 ) @ ( succ @ SY86 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[819]) ).
thf(835,plain,
! [SV133: $i] :
( ( ! [SY87: $i] :
( ~ ( leq @ n0 @ SV133 )
| ( leq @ ( uniform_int_rnd @ SY87 @ SV133 ) @ SV133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[820]) ).
thf(836,plain,
! [SV134: $i] :
( ( ! [SY88: $i] :
( ~ ( leq @ ( minus @ SV134 @ SY88 ) @ SV134 )
| ( leq @ n0 @ SY88 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[821]) ).
thf(837,plain,
! [SV135: $i,SV123: $i] :
( ( ~ ( leq @ n0 @ SV123 )
| ( leq @ n0 @ ( uniform_int_rnd @ SV135 @ SV123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[825]) ).
thf(838,plain,
! [SV136: $i,SV124: $i] :
( ( ! [SY89: $i] :
( ~ ~ ( ~ ( leq @ SV124 @ SV136 )
| ~ ( leq @ SV136 @ SY89 ) )
| ( leq @ SV124 @ SY89 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[826]) ).
thf(839,plain,
! [SV125: $i] :
( ( ( ~ ~ ( ~ ( leq @ n0 @ SV125 )
| ~ ( leq @ SV125 @ n0 ) ) )
= $true )
| ( ( SV125 = n0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[827]) ).
thf(840,plain,
! [SV137: $i,SV126: $i] :
( ( ~ ( ~ ( ~ ( geq @ SV126 @ SV137 )
| ( leq @ SV137 @ SV126 ) )
| ~ ( ~ ( leq @ SV137 @ SV126 )
| ( geq @ SV126 @ SV137 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[828]) ).
thf(841,plain,
! [SV138: $i,SV127: $i] :
( ( ~ ~ ( ~ ( leq @ SV127 @ SV138 )
| ~ ( ( SV127 != SV138 ) ) )
| ( gt @ SV138 @ SV127 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[829]) ).
thf(842,plain,
! [SV139: $i,SV128: $i] :
( ( ~ ( leq @ SV128 @ SV139 )
| ( leq @ SV128 @ ( succ @ SV139 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[830]) ).
thf(843,plain,
! [SV129: $i] :
( ( ( ~ ~ ( ~ ( leq @ n0 @ SV129 )
| ~ ( leq @ SV129 @ n1 ) ) )
= $true )
| ( ( ( SV129 = n0 )
| ( SV129 = n1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[831]) ).
thf(844,plain,
! [SV130: $i,SV140: $i] :
( ( ~ ( gt @ SV140 @ SV130 )
| ( leq @ SV130 @ SV140 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[832]) ).
thf(845,plain,
! [SV131: $i] :
( ( ( ~ ~ ( ~ ( leq @ n0 @ SV131 )
| ~ ( leq @ SV131 @ n2 ) ) )
= $true )
| ( ( ( SV131 = n0 )
| ( SV131 = n1 )
| ( SV131 = n2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[833]) ).
thf(846,plain,
! [SV141: $i,SV132: $i] :
( ( ~ ( ~ ( ~ ( leq @ ( succ @ SV132 ) @ ( succ @ SV141 ) )
| ( leq @ SV132 @ SV141 ) )
| ~ ( ~ ( leq @ SV132 @ SV141 )
| ( leq @ ( succ @ SV132 ) @ ( succ @ SV141 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[834]) ).
thf(847,plain,
! [SV142: $i,SV133: $i] :
( ( ~ ( leq @ n0 @ SV133 )
| ( leq @ ( uniform_int_rnd @ SV142 @ SV133 ) @ SV133 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[835]) ).
thf(848,plain,
! [SV143: $i,SV134: $i] :
( ( ~ ( leq @ ( minus @ SV134 @ SV143 ) @ SV134 )
| ( leq @ n0 @ SV143 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[836]) ).
thf(849,plain,
! [SV135: $i,SV123: $i] :
( ( ( ~ ( leq @ n0 @ SV123 ) )
= $true )
| ( ( leq @ n0 @ ( uniform_int_rnd @ SV135 @ SV123 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[837]) ).
thf(850,plain,
! [SV144: $i,SV136: $i,SV124: $i] :
( ( ~ ~ ( ~ ( leq @ SV124 @ SV136 )
| ~ ( leq @ SV136 @ SV144 ) )
| ( leq @ SV124 @ SV144 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[838]) ).
thf(851,plain,
! [SV125: $i] :
( ( ( ~ ( ~ ( leq @ n0 @ SV125 )
| ~ ( leq @ SV125 @ n0 ) ) )
= $false )
| ( ( SV125 = n0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[839]) ).
thf(852,plain,
! [SV137: $i,SV126: $i] :
( ( ~ ( ~ ( geq @ SV126 @ SV137 )
| ( leq @ SV137 @ SV126 ) )
| ~ ( ~ ( leq @ SV137 @ SV126 )
| ( geq @ SV126 @ SV137 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[840]) ).
thf(853,plain,
! [SV138: $i,SV127: $i] :
( ( ( ~ ~ ( ~ ( leq @ SV127 @ SV138 )
| ~ ( ( SV127 != SV138 ) ) ) )
= $true )
| ( ( gt @ SV138 @ SV127 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[841]) ).
thf(854,plain,
! [SV139: $i,SV128: $i] :
( ( ( ~ ( leq @ SV128 @ SV139 ) )
= $true )
| ( ( leq @ SV128 @ ( succ @ SV139 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[842]) ).
thf(855,plain,
! [SV129: $i] :
( ( ( ~ ( ~ ( leq @ n0 @ SV129 )
| ~ ( leq @ SV129 @ n1 ) ) )
= $false )
| ( ( ( SV129 = n0 )
| ( SV129 = n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[843]) ).
thf(856,plain,
! [SV130: $i,SV140: $i] :
( ( ( ~ ( gt @ SV140 @ SV130 ) )
= $true )
| ( ( leq @ SV130 @ SV140 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[844]) ).
thf(857,plain,
! [SV131: $i] :
( ( ( ~ ( ~ ( leq @ n0 @ SV131 )
| ~ ( leq @ SV131 @ n2 ) ) )
= $false )
| ( ( ( SV131 = n0 )
| ( SV131 = n1 )
| ( SV131 = n2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[845]) ).
thf(858,plain,
! [SV141: $i,SV132: $i] :
( ( ~ ( ~ ( leq @ ( succ @ SV132 ) @ ( succ @ SV141 ) )
| ( leq @ SV132 @ SV141 ) )
| ~ ( ~ ( leq @ SV132 @ SV141 )
| ( leq @ ( succ @ SV132 ) @ ( succ @ SV141 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[846]) ).
thf(859,plain,
! [SV142: $i,SV133: $i] :
( ( ( ~ ( leq @ n0 @ SV133 ) )
= $true )
| ( ( leq @ ( uniform_int_rnd @ SV142 @ SV133 ) @ SV133 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[847]) ).
thf(860,plain,
! [SV143: $i,SV134: $i] :
( ( ( ~ ( leq @ ( minus @ SV134 @ SV143 ) @ SV134 ) )
= $true )
| ( ( leq @ n0 @ SV143 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[848]) ).
thf(861,plain,
! [SV135: $i,SV123: $i] :
( ( ( leq @ n0 @ SV123 )
= $false )
| ( ( leq @ n0 @ ( uniform_int_rnd @ SV135 @ SV123 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[849]) ).
thf(862,plain,
! [SV144: $i,SV136: $i,SV124: $i] :
( ( ( ~ ~ ( ~ ( leq @ SV124 @ SV136 )
| ~ ( leq @ SV136 @ SV144 ) ) )
= $true )
| ( ( leq @ SV124 @ SV144 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[850]) ).
thf(863,plain,
! [SV125: $i] :
( ( ( ~ ( leq @ n0 @ SV125 )
| ~ ( leq @ SV125 @ n0 ) )
= $true )
| ( ( SV125 = n0 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[851]) ).
thf(864,plain,
! [SV137: $i,SV126: $i] :
( ( ~ ( ~ ( geq @ SV126 @ SV137 )
| ( leq @ SV137 @ SV126 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[852]) ).
thf(865,plain,
! [SV126: $i,SV137: $i] :
( ( ~ ( ~ ( leq @ SV137 @ SV126 )
| ( geq @ SV126 @ SV137 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[852]) ).
thf(866,plain,
! [SV138: $i,SV127: $i] :
( ( ( ~ ( ~ ( leq @ SV127 @ SV138 )
| ~ ( ( SV127 != SV138 ) ) ) )
= $false )
| ( ( gt @ SV138 @ SV127 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[853]) ).
thf(867,plain,
! [SV139: $i,SV128: $i] :
( ( ( leq @ SV128 @ SV139 )
= $false )
| ( ( leq @ SV128 @ ( succ @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[854]) ).
thf(868,plain,
! [SV129: $i] :
( ( ( ~ ( leq @ n0 @ SV129 )
| ~ ( leq @ SV129 @ n1 ) )
= $true )
| ( ( ( SV129 = n0 )
| ( SV129 = n1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[855]) ).
thf(869,plain,
! [SV130: $i,SV140: $i] :
( ( ( gt @ SV140 @ SV130 )
= $false )
| ( ( leq @ SV130 @ SV140 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[856]) ).
thf(870,plain,
! [SV131: $i] :
( ( ( ~ ( leq @ n0 @ SV131 )
| ~ ( leq @ SV131 @ n2 ) )
= $true )
| ( ( ( SV131 = n0 )
| ( SV131 = n1 )
| ( SV131 = n2 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[857]) ).
thf(871,plain,
! [SV141: $i,SV132: $i] :
( ( ~ ( ~ ( leq @ ( succ @ SV132 ) @ ( succ @ SV141 ) )
| ( leq @ SV132 @ SV141 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[858]) ).
thf(872,plain,
! [SV141: $i,SV132: $i] :
( ( ~ ( ~ ( leq @ SV132 @ SV141 )
| ( leq @ ( succ @ SV132 ) @ ( succ @ SV141 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[858]) ).
thf(873,plain,
! [SV142: $i,SV133: $i] :
( ( ( leq @ n0 @ SV133 )
= $false )
| ( ( leq @ ( uniform_int_rnd @ SV142 @ SV133 ) @ SV133 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[859]) ).
thf(874,plain,
! [SV143: $i,SV134: $i] :
( ( ( leq @ ( minus @ SV134 @ SV143 ) @ SV134 )
= $false )
| ( ( leq @ n0 @ SV143 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[860]) ).
thf(875,plain,
! [SV144: $i,SV136: $i,SV124: $i] :
( ( ( ~ ( ~ ( leq @ SV124 @ SV136 )
| ~ ( leq @ SV136 @ SV144 ) ) )
= $false )
| ( ( leq @ SV124 @ SV144 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[862]) ).
thf(876,plain,
! [SV125: $i] :
( ( ( ~ ( leq @ n0 @ SV125 ) )
= $true )
| ( ( ~ ( leq @ SV125 @ n0 ) )
= $true )
| ( ( SV125 = n0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[863]) ).
thf(877,plain,
! [SV137: $i,SV126: $i] :
( ( ~ ( geq @ SV126 @ SV137 )
| ( leq @ SV137 @ SV126 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[864]) ).
thf(878,plain,
! [SV126: $i,SV137: $i] :
( ( ~ ( leq @ SV137 @ SV126 )
| ( geq @ SV126 @ SV137 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[865]) ).
thf(879,plain,
! [SV138: $i,SV127: $i] :
( ( ( ~ ( leq @ SV127 @ SV138 )
| ~ ( ( SV127 != SV138 ) ) )
= $true )
| ( ( gt @ SV138 @ SV127 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[866]) ).
thf(880,plain,
! [SV129: $i] :
( ( ( ~ ( leq @ n0 @ SV129 ) )
= $true )
| ( ( ~ ( leq @ SV129 @ n1 ) )
= $true )
| ( ( ( SV129 = n0 )
| ( SV129 = n1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[868]) ).
thf(881,plain,
! [SV131: $i] :
( ( ( ~ ( leq @ n0 @ SV131 ) )
= $true )
| ( ( ~ ( leq @ SV131 @ n2 ) )
= $true )
| ( ( ( SV131 = n0 )
| ( SV131 = n1 )
| ( SV131 = n2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[870]) ).
thf(882,plain,
! [SV141: $i,SV132: $i] :
( ( ~ ( leq @ ( succ @ SV132 ) @ ( succ @ SV141 ) )
| ( leq @ SV132 @ SV141 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[871]) ).
thf(883,plain,
! [SV141: $i,SV132: $i] :
( ( ~ ( leq @ SV132 @ SV141 )
| ( leq @ ( succ @ SV132 ) @ ( succ @ SV141 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[872]) ).
thf(884,plain,
! [SV144: $i,SV136: $i,SV124: $i] :
( ( ( ~ ( leq @ SV124 @ SV136 )
| ~ ( leq @ SV136 @ SV144 ) )
= $true )
| ( ( leq @ SV124 @ SV144 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[875]) ).
thf(885,plain,
! [SV125: $i] :
( ( ( leq @ n0 @ SV125 )
= $false )
| ( ( ~ ( leq @ SV125 @ n0 ) )
= $true )
| ( ( SV125 = n0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[876]) ).
thf(886,plain,
! [SV137: $i,SV126: $i] :
( ( ( ~ ( geq @ SV126 @ SV137 ) )
= $true )
| ( ( leq @ SV137 @ SV126 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[877]) ).
thf(887,plain,
! [SV126: $i,SV137: $i] :
( ( ( ~ ( leq @ SV137 @ SV126 ) )
= $true )
| ( ( geq @ SV126 @ SV137 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[878]) ).
thf(888,plain,
! [SV138: $i,SV127: $i] :
( ( ( ~ ( leq @ SV127 @ SV138 ) )
= $true )
| ( ( ~ ( ( SV127 != SV138 ) ) )
= $true )
| ( ( gt @ SV138 @ SV127 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[879]) ).
thf(889,plain,
! [SV129: $i] :
( ( ( leq @ n0 @ SV129 )
= $false )
| ( ( ~ ( leq @ SV129 @ n1 ) )
= $true )
| ( ( ( SV129 = n0 )
| ( SV129 = n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[880]) ).
thf(890,plain,
! [SV131: $i] :
( ( ( leq @ n0 @ SV131 )
= $false )
| ( ( ~ ( leq @ SV131 @ n2 ) )
= $true )
| ( ( ( SV131 = n0 )
| ( SV131 = n1 )
| ( SV131 = n2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[881]) ).
thf(891,plain,
! [SV141: $i,SV132: $i] :
( ( ( ~ ( leq @ ( succ @ SV132 ) @ ( succ @ SV141 ) ) )
= $true )
| ( ( leq @ SV132 @ SV141 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[882]) ).
thf(892,plain,
! [SV141: $i,SV132: $i] :
( ( ( ~ ( leq @ SV132 @ SV141 ) )
= $true )
| ( ( leq @ ( succ @ SV132 ) @ ( succ @ SV141 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[883]) ).
thf(893,plain,
! [SV144: $i,SV136: $i,SV124: $i] :
( ( ( ~ ( leq @ SV124 @ SV136 ) )
= $true )
| ( ( ~ ( leq @ SV136 @ SV144 ) )
= $true )
| ( ( leq @ SV124 @ SV144 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[884]) ).
thf(894,plain,
! [SV125: $i] :
( ( ( leq @ SV125 @ n0 )
= $false )
| ( ( leq @ n0 @ SV125 )
= $false )
| ( ( SV125 = n0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[885]) ).
thf(895,plain,
! [SV137: $i,SV126: $i] :
( ( ( geq @ SV126 @ SV137 )
= $false )
| ( ( leq @ SV137 @ SV126 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[886]) ).
thf(896,plain,
! [SV126: $i,SV137: $i] :
( ( ( leq @ SV137 @ SV126 )
= $false )
| ( ( geq @ SV126 @ SV137 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[887]) ).
thf(897,plain,
! [SV138: $i,SV127: $i] :
( ( ( leq @ SV127 @ SV138 )
= $false )
| ( ( ~ ( ( SV127 != SV138 ) ) )
= $true )
| ( ( gt @ SV138 @ SV127 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[888]) ).
thf(898,plain,
! [SV129: $i] :
( ( ( leq @ SV129 @ n1 )
= $false )
| ( ( leq @ n0 @ SV129 )
= $false )
| ( ( ( SV129 = n0 )
| ( SV129 = n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[889]) ).
thf(899,plain,
! [SV131: $i] :
( ( ( leq @ SV131 @ n2 )
= $false )
| ( ( leq @ n0 @ SV131 )
= $false )
| ( ( ( SV131 = n0 )
| ( SV131 = n1 )
| ( SV131 = n2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[890]) ).
thf(900,plain,
! [SV141: $i,SV132: $i] :
( ( ( leq @ ( succ @ SV132 ) @ ( succ @ SV141 ) )
= $false )
| ( ( leq @ SV132 @ SV141 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[891]) ).
thf(901,plain,
! [SV141: $i,SV132: $i] :
( ( ( leq @ SV132 @ SV141 )
= $false )
| ( ( leq @ ( succ @ SV132 ) @ ( succ @ SV141 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[892]) ).
thf(902,plain,
! [SV144: $i,SV136: $i,SV124: $i] :
( ( ( leq @ SV124 @ SV136 )
= $false )
| ( ( ~ ( leq @ SV136 @ SV144 ) )
= $true )
| ( ( leq @ SV124 @ SV144 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[893]) ).
thf(903,plain,
! [SV138: $i,SV127: $i] :
( ( ( SV127 != SV138 )
= $false )
| ( ( leq @ SV127 @ SV138 )
= $false )
| ( ( gt @ SV138 @ SV127 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[897]) ).
thf(904,plain,
! [SV129: $i] :
( ( ( SV129 = n0 )
= $true )
| ( ( SV129 = n1 )
= $true )
| ( ( leq @ n0 @ SV129 )
= $false )
| ( ( leq @ SV129 @ n1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[898]) ).
thf(905,plain,
! [SV131: $i] :
( ( ( ( SV131 = n0 )
| ( SV131 = n1 ) )
= $true )
| ( ( SV131 = n2 )
= $true )
| ( ( leq @ n0 @ SV131 )
= $false )
| ( ( leq @ SV131 @ n2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[899]) ).
thf(906,plain,
! [SV124: $i,SV144: $i,SV136: $i] :
( ( ( leq @ SV136 @ SV144 )
= $false )
| ( ( leq @ SV124 @ SV136 )
= $false )
| ( ( leq @ SV124 @ SV144 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[902]) ).
thf(907,plain,
! [SV138: $i,SV127: $i] :
( ( ( SV127 = SV138 )
= $true )
| ( ( leq @ SV127 @ SV138 )
= $false )
| ( ( gt @ SV138 @ SV127 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[903]) ).
thf(908,plain,
! [SV131: $i] :
( ( ( SV131 = n0 )
= $true )
| ( ( SV131 = n1 )
= $true )
| ( ( SV131 = n2 )
= $true )
| ( ( leq @ n0 @ SV131 )
= $false )
| ( ( leq @ SV131 @ n2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[905]) ).
thf(909,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[792,908,907,906,904,901,900,896,895,894,874,873,869,867,861,824,823,822,808,807,806,805,804,803,802,801,797,796,795,794,793]) ).
thf(910,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[909,264,393,522,651,780]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV062+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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.18 % Computer : n019.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Oct 6 16:18:01 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.09/0.78
% 3.09/0.78 No.of.Axioms: 22
% 3.09/0.78
% 3.09/0.78 Length.of.Defs: 0
% 3.09/0.78
% 3.09/0.78 Contains.Choice.Funs: false
% 3.09/0.78 ....................
% 3.09/0.78
% 3.09/0.78 ********************************
% 3.09/0.78 * All subproblems solved! *
% 3.09/0.78 ********************************
% 3.09/0.78 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:28,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:909,loop_count:0,foatp_calls:1,translation:fof_full)
% 3.09/0.78
% 3.09/0.78 %**** Beginning of derivation protocol ****
% 3.09/0.78 % SZS output start CNFRefutation
% See solution above
% 3.09/0.79
% 3.09/0.79 %**** End of derivation protocol ****
% 3.09/0.79 %**** no. of clauses in derivation: 841 ****
% 3.09/0.79 %**** clause counter: 909 ****
% 3.09/0.79
% 3.09/0.79 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:28,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:909,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------