TSTP Solution File: SWV123+1 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SWV123+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Wed Jul 20 20:01:54 EDT 2022
% Result : Theorem 0.51s 0.66s
% Output : CNFRefutation 0.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 120
% Syntax : Number of formulae : 528 ( 374 unt; 35 typ; 0 def)
% Number of atoms : 2444 (1072 equ; 0 cnn)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 3059 ( 274 ~; 632 |; 36 &;2054 @)
% ( 10 <=>; 53 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 46 ( 46 >; 0 *; 0 +; 0 <<)
% Number of symbols : 38 ( 35 usr; 15 con; 0-4 aty)
% Number of variables : 573 ( 0 ^ 573 !; 0 ?; 573 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a_select2,type,
a_select2: $i > $i > $i ).
thf(tp_a_select3,type,
a_select3: $i > $i > $i > $i ).
thf(tp_def,type,
def: $i ).
thf(tp_dim,type,
dim: $i > $i > $i ).
thf(tp_geq,type,
geq: $i > $i > $o ).
thf(tp_gt,type,
gt: $i > $i > $o ).
thf(tp_inv,type,
inv: $i > $i ).
thf(tp_leq,type,
leq: $i > $i > $o ).
thf(tp_lt,type,
lt: $i > $i > $o ).
thf(tp_minus,type,
minus: $i > $i > $i ).
thf(tp_n0,type,
n0: $i ).
thf(tp_n1,type,
n1: $i ).
thf(tp_n2,type,
n2: $i ).
thf(tp_n3,type,
n3: $i ).
thf(tp_n4,type,
n4: $i ).
thf(tp_n5,type,
n5: $i ).
thf(tp_n6,type,
n6: $i ).
thf(tp_n999,type,
n999: $i ).
thf(tp_plus,type,
plus: $i > $i > $i ).
thf(tp_pred,type,
pred: $i > $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(1,axiom,
( ( succ @ ( succ @ ( succ @ n0 ) ) )
= n3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_3) ).
thf(2,axiom,
( ( succ @ ( succ @ n0 ) )
= n2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_2) ).
thf(3,axiom,
( ( succ @ n0 )
= n1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_1) ).
thf(4,axiom,
( ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ n0 ) ) ) ) ) )
= n6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_6) ).
thf(5,axiom,
( ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ n0 ) ) ) ) )
= n5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_5) ).
thf(6,axiom,
( ( succ @ ( succ @ ( succ @ ( succ @ n0 ) ) ) )
= n4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_4) ).
thf(7,axiom,
! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n3 ) )
=> ( ( X = n0 )
| ( X = n1 )
| ( X = n2 )
| ( X = n3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finite_domain_3) ).
thf(8,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(9,axiom,
! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n1 ) )
=> ( ( X = n0 )
| ( X = n1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finite_domain_1) ).
thf(10,axiom,
! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n0 ) )
=> ( X = n0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finite_domain_0) ).
thf(11,axiom,
! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n6 ) )
=> ( ( X = n0 )
| ( X = n1 )
| ( X = n2 )
| ( X = n3 )
| ( X = n4 )
| ( X = n5 )
| ( X = n6 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finite_domain_6) ).
thf(12,axiom,
! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n5 ) )
=> ( ( X = n0 )
| ( X = n1 )
| ( X = n2 )
| ( X = n3 )
| ( X = n4 )
| ( X = n5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finite_domain_5) ).
thf(13,axiom,
! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n4 ) )
=> ( ( X = n0 )
| ( X = n1 )
| ( X = n2 )
| ( X = n3 )
| ( X = n4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finite_domain_4) ).
thf(14,axiom,
gt @ n999 @ n3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_999_3) ).
thf(15,axiom,
gt @ n6 @ n3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_6_3) ).
thf(16,axiom,
gt @ n5 @ n3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_5_3) ).
thf(17,axiom,
gt @ n4 @ n3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_4_3) ).
thf(18,axiom,
gt @ n3 @ n2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_3_2) ).
thf(19,axiom,
gt @ n999 @ n2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_999_2) ).
thf(20,axiom,
gt @ n6 @ n2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_6_2) ).
thf(21,axiom,
gt @ n5 @ n2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_5_2) ).
thf(22,axiom,
gt @ n4 @ n2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_4_2) ).
thf(23,axiom,
gt @ n3 @ n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_3_1) ).
thf(24,axiom,
gt @ n2 @ n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_2_1) ).
thf(25,axiom,
gt @ n999 @ n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_999_1) ).
thf(26,axiom,
gt @ n6 @ n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_6_1) ).
thf(27,axiom,
gt @ n5 @ n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_5_1) ).
thf(28,axiom,
gt @ n4 @ n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_4_1) ).
thf(29,axiom,
gt @ n3 @ n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_3_0) ).
thf(30,axiom,
gt @ n2 @ n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_2_0) ).
thf(31,axiom,
gt @ n1 @ n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_1_0) ).
thf(32,axiom,
gt @ n999 @ n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_999_0) ).
thf(33,axiom,
gt @ n6 @ n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_6_0) ).
thf(34,axiom,
gt @ n5 @ n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_5_0) ).
thf(35,axiom,
gt @ n4 @ n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_4_0) ).
thf(36,axiom,
gt @ n3 @ tptp_minus_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_3_tptp_minus_1) ).
thf(37,axiom,
gt @ n2 @ tptp_minus_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_2_tptp_minus_1) ).
thf(38,axiom,
gt @ n1 @ tptp_minus_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_1_tptp_minus_1) ).
thf(39,axiom,
gt @ n0 @ tptp_minus_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_0_tptp_minus_1) ).
thf(40,axiom,
gt @ n999 @ tptp_minus_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_999_tptp_minus_1) ).
thf(41,axiom,
gt @ n6 @ tptp_minus_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_6_tptp_minus_1) ).
thf(42,axiom,
gt @ n5 @ tptp_minus_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_5_tptp_minus_1) ).
thf(43,axiom,
gt @ n4 @ tptp_minus_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_4_tptp_minus_1) ).
thf(44,axiom,
gt @ n999 @ n6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_999_6) ).
thf(45,axiom,
gt @ n999 @ n5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_999_5) ).
thf(46,axiom,
gt @ n6 @ n5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_6_5) ).
thf(47,axiom,
gt @ n999 @ n4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_999_4) ).
thf(48,axiom,
gt @ n6 @ n4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_6_4) ).
thf(49,axiom,
gt @ n5 @ n4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_5_4) ).
thf(51,axiom,
true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ttrue) ).
thf(58,axiom,
! [X: $i,Y: $i] :
( ( leq @ ( minus @ X @ Y ) @ X )
=> ( leq @ n0 @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_minus) ).
thf(59,axiom,
! [X: $i,Y: $i] :
( ( leq @ ( succ @ X ) @ Y )
=> ( gt @ Y @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_succ_gt) ).
thf(60,axiom,
! [X: $i,Y: $i] :
( ( leq @ ( succ @ X ) @ ( succ @ Y ) )
<=> ( leq @ X @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_succ_succ) ).
thf(61,axiom,
! [X: $i] :
( ( succ @ ( pred @ X ) )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_pred) ).
thf(62,axiom,
! [X: $i] :
( ( pred @ ( succ @ X ) )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pred_succ) ).
thf(63,axiom,
! [X: $i] :
( ( minus @ X @ n1 )
= ( pred @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pred_minus_1) ).
thf(64,axiom,
! [X: $i] :
( ( plus @ n5 @ X )
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ X ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_plus_5_l) ).
thf(65,axiom,
! [X: $i] :
( ( plus @ X @ n5 )
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ X ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_plus_5_r) ).
thf(66,axiom,
! [X: $i] :
( ( plus @ n4 @ X )
= ( succ @ ( succ @ ( succ @ ( succ @ X ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_plus_4_l) ).
thf(67,axiom,
! [X: $i] :
( ( plus @ X @ n4 )
= ( succ @ ( succ @ ( succ @ ( succ @ X ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_plus_4_r) ).
thf(68,axiom,
! [X: $i] :
( ( plus @ n3 @ X )
= ( succ @ ( succ @ ( succ @ X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_plus_3_l) ).
thf(69,axiom,
! [X: $i] :
( ( plus @ X @ n3 )
= ( succ @ ( succ @ ( succ @ X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_plus_3_r) ).
thf(70,axiom,
! [X: $i] :
( ( plus @ n2 @ X )
= ( succ @ ( succ @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_plus_2_l) ).
thf(71,axiom,
! [X: $i] :
( ( plus @ X @ n2 )
= ( succ @ ( succ @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_plus_2_r) ).
thf(72,axiom,
! [X: $i] :
( ( plus @ n1 @ X )
= ( succ @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_plus_1_l) ).
thf(73,axiom,
! [X: $i] :
( ( plus @ X @ n1 )
= ( succ @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_plus_1_r) ).
thf(74,axiom,
( ( succ @ tptp_minus_1 )
= n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_tptp_minus_1) ).
thf(75,axiom,
! [Body: $i] :
( tptp_float_0_0
= ( sum @ n0 @ tptp_minus_1 @ Body ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_plus_base_float) ).
thf(76,axiom,
! [Body: $i] :
( ( sum @ n0 @ tptp_minus_1 @ Body )
= n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_plus_base) ).
thf(87,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(88,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(89,axiom,
! [X: $i,Y: $i] :
( ( leq @ X @ Y )
<=> ( gt @ ( succ @ Y ) @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_succ_gt_equiv) ).
thf(90,axiom,
! [X: $i,Y: $i] :
( ( leq @ X @ Y )
=> ( leq @ X @ ( succ @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_succ) ).
thf(91,axiom,
! [X: $i] : ( gt @ ( succ @ X ) @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_succ) ).
thf(92,axiom,
! [X: $i,Y: $i] :
( ( leq @ X @ ( pred @ Y ) )
<=> ( gt @ Y @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_gt_pred) ).
thf(93,axiom,
! [X: $i,Y: $i] :
( ( ( leq @ X @ Y )
& ( X != Y ) )
=> ( gt @ Y @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_gt2) ).
thf(94,axiom,
! [X: $i,Y: $i] :
( ( gt @ Y @ X )
=> ( leq @ X @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_gt1) ).
thf(95,axiom,
! [X: $i,Y: $i] :
( ( geq @ X @ Y )
<=> ( leq @ Y @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_geq) ).
thf(96,axiom,
! [X: $i,Y: $i] :
( ( lt @ X @ Y )
<=> ( gt @ Y @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lt_gt) ).
thf(97,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(98,axiom,
! [X: $i] : ( leq @ X @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_leq) ).
thf(99,axiom,
! [X: $i] :
~ ( gt @ X @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',irreflexivity_gt) ).
thf(100,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( ( gt @ X @ Y )
& ( gt @ Y @ Z ) )
=> ( gt @ X @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_gt) ).
thf(101,axiom,
! [X: $i,Y: $i] :
( ( gt @ X @ Y )
| ( gt @ Y @ X )
| ( X = Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',totality) ).
thf(102,conjecture,
( ( geq @ ( minus @ n3 @ n1 ) @ n0 )
=> ( ( geq @ ( minus @ n6 @ n1 ) @ n0 )
=> ( ( ( geq @ n2 @ n0 )
& ( geq @ ( minus @ n999 @ n1 ) @ n0 ) )
=> ( ( geq @ ( minus @ n6 @ n1 ) @ n0 )
=> ( ( geq @ ( minus @ n6 @ n1 ) @ n0 )
=> ( ( geq @ ( minus @ n6 @ n1 ) @ n0 )
=> ( ( ( geq @ ( minus @ n3 @ n1 ) @ n0 )
& ( geq @ ( minus @ n999 @ n1 ) @ n0 ) )
=> true ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quaternion_ds1_symm_0016) ).
thf(103,negated_conjecture,
( ( ( geq @ ( minus @ n3 @ n1 ) @ n0 )
=> ( ( geq @ ( minus @ n6 @ n1 ) @ n0 )
=> ( ( ( geq @ n2 @ n0 )
& ( geq @ ( minus @ n999 @ n1 ) @ n0 ) )
=> ( ( geq @ ( minus @ n6 @ n1 ) @ n0 )
=> ( ( geq @ ( minus @ n6 @ n1 ) @ n0 )
=> ( ( geq @ ( minus @ n6 @ n1 ) @ n0 )
=> ( ( ( geq @ ( minus @ n3 @ n1 ) @ n0 )
& ( geq @ ( minus @ n999 @ n1 ) @ n0 ) )
=> true ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[102]) ).
thf(104,plain,
( ( ( geq @ ( minus @ n3 @ n1 ) @ n0 )
=> ( ( geq @ ( minus @ n6 @ n1 ) @ n0 )
=> ( ( ( geq @ n2 @ n0 )
& ( geq @ ( minus @ n999 @ n1 ) @ n0 ) )
=> ( ( geq @ ( minus @ n6 @ n1 ) @ n0 )
=> ( ( geq @ ( minus @ n6 @ n1 ) @ n0 )
=> ( ( geq @ ( minus @ n6 @ n1 ) @ n0 )
=> ( ( ( geq @ ( minus @ n3 @ n1 ) @ n0 )
& ( geq @ ( minus @ n999 @ n1 ) @ n0 ) )
=> true ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[103]) ).
thf(105,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n6 ) )
=> ( ( X = n0 )
| ( X = n1 )
| ( X = n2 )
| ( X = n3 )
| ( X = n4 )
| ( X = n5 )
| ( X = n6 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(106,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n5 ) )
=> ( ( X = n0 )
| ( X = n1 )
| ( X = n2 )
| ( X = n3 )
| ( X = n4 )
| ( X = n5 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(107,plain,
( ( gt @ n5 @ tptp_minus_1 )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(108,plain,
( ( gt @ n4 @ tptp_minus_1 )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(109,plain,
( ( gt @ n5 @ n4 )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(110,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ ( succ @ X ) @ Y )
=> ( gt @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(111,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ ( succ @ X ) @ ( succ @ Y ) )
<=> ( leq @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(112,plain,
( ( ! [X: $i] :
( ( succ @ ( pred @ X ) )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(113,plain,
( ( ! [X: $i] :
( ( pred @ ( succ @ X ) )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(114,plain,
( ( ! [X: $i] :
( ( plus @ n5 @ X )
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ X ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(115,plain,
( ( ! [X: $i] :
( ( plus @ X @ n5 )
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ X ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(116,plain,
( ( ! [X: $i] :
( ( plus @ n4 @ X )
= ( succ @ ( succ @ ( succ @ ( succ @ X ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(117,plain,
( ( ! [X: $i] :
( ( plus @ X @ n4 )
= ( succ @ ( succ @ ( succ @ ( succ @ X ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(118,plain,
( ( ! [Body: $i] :
( tptp_float_0_0
= ( sum @ n0 @ tptp_minus_1 @ Body ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(119,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ X @ Y )
<=> ( gt @ ( succ @ Y ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(120,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ X @ Y )
=> ( leq @ X @ ( succ @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(121,plain,
( ( ! [X: $i] : ( gt @ ( succ @ X ) @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(122,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ X @ ( pred @ Y ) )
<=> ( gt @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(123,plain,
( ( ! [X: $i,Y: $i] :
( ( ( leq @ X @ Y )
& ( X != Y ) )
=> ( gt @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(124,plain,
( ( ! [X: $i,Y: $i] :
( ( gt @ Y @ X )
=> ( leq @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(125,plain,
( ( ! [X: $i,Y: $i] :
( ( lt @ X @ Y )
<=> ( gt @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(126,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( leq @ X @ Y )
& ( leq @ Y @ Z ) )
=> ( leq @ X @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(127,plain,
( ( ! [X: $i] : ( leq @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(128,plain,
( ( ! [X: $i] :
~ ( gt @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(129,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( gt @ X @ Y )
& ( gt @ Y @ Z ) )
=> ( gt @ X @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(130,plain,
( ( ! [X: $i,Y: $i] :
( ( gt @ X @ Y )
| ( gt @ Y @ X )
| ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(131,plain,
( ( ( succ @ ( succ @ ( succ @ n0 ) ) )
= n3 )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(132,plain,
( ( ( succ @ ( succ @ n0 ) )
= n2 )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(133,plain,
( ( ( succ @ n0 )
= n1 )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(134,plain,
( ( ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ n0 ) ) ) ) ) )
= n6 )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(135,plain,
( ( ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ n0 ) ) ) ) )
= n5 )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(136,plain,
( ( ( succ @ ( succ @ ( succ @ ( succ @ n0 ) ) ) )
= n4 )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(137,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n3 ) )
=> ( ( X = n0 )
| ( X = n1 )
| ( X = n2 )
| ( X = n3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(138,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n2 ) )
=> ( ( X = n0 )
| ( X = n1 )
| ( X = n2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(139,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n1 ) )
=> ( ( X = n0 )
| ( X = n1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(140,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n0 ) )
=> ( X = n0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(141,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n4 ) )
=> ( ( X = n0 )
| ( X = n1 )
| ( X = n2 )
| ( X = n3 )
| ( X = n4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(142,plain,
( ( gt @ n999 @ n3 )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(143,plain,
( ( gt @ n6 @ n3 )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(144,plain,
( ( gt @ n5 @ n3 )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(145,plain,
( ( gt @ n4 @ n3 )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(146,plain,
( ( gt @ n3 @ n2 )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(147,plain,
( ( gt @ n999 @ n2 )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(148,plain,
( ( gt @ n6 @ n2 )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(149,plain,
( ( gt @ n5 @ n2 )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(150,plain,
( ( gt @ n4 @ n2 )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(151,plain,
( ( gt @ n3 @ n1 )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(152,plain,
( ( gt @ n2 @ n1 )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(153,plain,
( ( gt @ n999 @ n1 )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(154,plain,
( ( gt @ n6 @ n1 )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(155,plain,
( ( gt @ n5 @ n1 )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(156,plain,
( ( gt @ n4 @ n1 )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(157,plain,
( ( gt @ n3 @ n0 )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(158,plain,
( ( gt @ n2 @ n0 )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(159,plain,
( ( gt @ n1 @ n0 )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(160,plain,
( ( gt @ n999 @ n0 )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(161,plain,
( ( gt @ n6 @ n0 )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(162,plain,
( ( gt @ n5 @ n0 )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(163,plain,
( ( gt @ n4 @ n0 )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(164,plain,
( ( gt @ n3 @ tptp_minus_1 )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(165,plain,
( ( gt @ n2 @ tptp_minus_1 )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(166,plain,
( ( gt @ n1 @ tptp_minus_1 )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(167,plain,
( ( gt @ n0 @ tptp_minus_1 )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(168,plain,
( ( gt @ n999 @ tptp_minus_1 )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(169,plain,
( ( gt @ n6 @ tptp_minus_1 )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(170,plain,
( ( gt @ n999 @ n6 )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(171,plain,
( ( gt @ n999 @ n5 )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(172,plain,
( ( gt @ n6 @ n5 )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(173,plain,
( ( gt @ n999 @ n4 )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(174,plain,
( ( gt @ n6 @ n4 )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(175,plain,
true = $true,
inference(unfold_def,[status(thm)],[51]) ).
thf(176,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ ( minus @ X @ Y ) @ X )
=> ( leq @ n0 @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(177,plain,
( ( ! [X: $i] :
( ( minus @ X @ n1 )
= ( pred @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(178,plain,
( ( ! [X: $i] :
( ( plus @ n3 @ X )
= ( succ @ ( succ @ ( succ @ X ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(179,plain,
( ( ! [X: $i] :
( ( plus @ X @ n3 )
= ( succ @ ( succ @ ( succ @ X ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(180,plain,
( ( ! [X: $i] :
( ( plus @ n2 @ X )
= ( succ @ ( succ @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(181,plain,
( ( ! [X: $i] :
( ( plus @ X @ n2 )
= ( succ @ ( succ @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(182,plain,
( ( ! [X: $i] :
( ( plus @ n1 @ X )
= ( succ @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(183,plain,
( ( ! [X: $i] :
( ( plus @ X @ n1 )
= ( succ @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(184,plain,
( ( ( succ @ tptp_minus_1 )
= n0 )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(185,plain,
( ( ! [Body: $i] :
( ( sum @ n0 @ tptp_minus_1 @ Body )
= n0 ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(186,plain,
( ( ! [X: $i,C: $i] :
( ( leq @ n0 @ X )
=> ( leq @ n0 @ ( uniform_int_rnd @ C @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(187,plain,
( ( ! [X: $i,C: $i] :
( ( leq @ n0 @ X )
=> ( leq @ ( uniform_int_rnd @ C @ X ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(188,plain,
( ( ! [X: $i,Y: $i] :
( ( geq @ X @ Y )
<=> ( leq @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(189,plain,
( ( geq @ ( minus @ n3 @ n1 ) @ n0 )
= $true ),
inference(standard_cnf,[status(thm)],[104]) ).
thf(190,plain,
( ( geq @ ( minus @ n6 @ n1 ) @ n0 )
= $true ),
inference(standard_cnf,[status(thm)],[104]) ).
thf(191,plain,
( ( geq @ n2 @ n0 )
= $true ),
inference(standard_cnf,[status(thm)],[104]) ).
thf(192,plain,
( ( geq @ ( minus @ n999 @ n1 ) @ n0 )
= $true ),
inference(standard_cnf,[status(thm)],[104]) ).
thf(193,plain,
( ( geq @ ( minus @ n6 @ n1 ) @ n0 )
= $true ),
inference(standard_cnf,[status(thm)],[104]) ).
thf(194,plain,
( ( geq @ ( minus @ n6 @ n1 ) @ n0 )
= $true ),
inference(standard_cnf,[status(thm)],[104]) ).
thf(195,plain,
( ( geq @ ( minus @ n6 @ n1 ) @ n0 )
= $true ),
inference(standard_cnf,[status(thm)],[104]) ).
thf(196,plain,
( ( geq @ ( minus @ n3 @ n1 ) @ n0 )
= $true ),
inference(standard_cnf,[status(thm)],[104]) ).
thf(197,plain,
( ( geq @ ( minus @ n999 @ n1 ) @ n0 )
= $true ),
inference(standard_cnf,[status(thm)],[104]) ).
thf(198,plain,
true = $false,
inference(standard_cnf,[status(thm)],[104]) ).
thf(199,plain,
( ( ~ true )
= $true ),
inference(polarity_switch,[status(thm)],[198]) ).
thf(200,plain,
( ( ! [X: $i] :
( ~ ( leq @ n0 @ X )
| ~ ( leq @ X @ n6 )
| ( X = n6 )
| ( X = n5 )
| ( X = n4 )
| ( X = n3 )
| ( X = n2 )
| ( X = n0 )
| ( X = n1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[105]) ).
thf(201,plain,
( ( ! [X: $i] :
( ~ ( leq @ n0 @ X )
| ~ ( leq @ X @ n5 )
| ( X = n5 )
| ( X = n4 )
| ( X = n3 )
| ( X = n2 )
| ( X = n0 )
| ( X = n1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[106]) ).
thf(202,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( leq @ ( succ @ X ) @ Y )
| ( gt @ Y @ X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[110]) ).
thf(203,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( leq @ ( succ @ X ) @ ( succ @ Y ) )
| ( leq @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ~ ( leq @ X @ Y )
| ( leq @ ( succ @ X ) @ ( succ @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[111]) ).
thf(204,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( gt @ ( succ @ Y ) @ X )
| ( leq @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ~ ( leq @ X @ Y )
| ( gt @ ( succ @ Y ) @ X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[119]) ).
thf(205,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( leq @ X @ Y )
| ( leq @ X @ ( succ @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[120]) ).
thf(206,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( gt @ Y @ X )
| ( leq @ X @ ( pred @ Y ) ) )
& ! [X: $i,Y: $i] :
( ~ ( leq @ X @ ( pred @ Y ) )
| ( gt @ Y @ X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[122]) ).
thf(207,plain,
( ( ! [X: $i,Y: $i] :
( ( X = Y )
| ~ ( leq @ X @ Y )
| ( gt @ Y @ X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[123]) ).
thf(208,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( gt @ Y @ X )
| ( leq @ X @ Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[124]) ).
thf(209,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( gt @ Y @ X )
| ( lt @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ~ ( lt @ X @ Y )
| ( gt @ Y @ X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[125]) ).
thf(210,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( leq @ X @ Y )
| ~ ( leq @ Y @ Z )
| ( leq @ X @ Z ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[126]) ).
thf(211,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( gt @ X @ Y )
| ~ ( gt @ Y @ Z )
| ( gt @ X @ Z ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[129]) ).
thf(212,plain,
( ( ! [X: $i,Y: $i] :
( ( X = Y )
| ( gt @ X @ Y )
| ( gt @ Y @ X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[130]) ).
thf(213,plain,
( ( ! [X: $i] :
( ~ ( leq @ n0 @ X )
| ~ ( leq @ X @ n3 )
| ( X = n3 )
| ( X = n2 )
| ( X = n0 )
| ( X = n1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[137]) ).
thf(214,plain,
( ( ! [X: $i] :
( ~ ( leq @ n0 @ X )
| ~ ( leq @ X @ n2 )
| ( X = n2 )
| ( X = n0 )
| ( X = n1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[138]) ).
thf(215,plain,
( ( ! [X: $i] :
( ~ ( leq @ n0 @ X )
| ~ ( leq @ X @ n1 )
| ( X = n0 )
| ( X = n1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[139]) ).
thf(216,plain,
( ( ! [X: $i] :
( ~ ( leq @ n0 @ X )
| ~ ( leq @ X @ n0 )
| ( X = n0 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[140]) ).
thf(217,plain,
( ( ! [X: $i] :
( ~ ( leq @ n0 @ X )
| ~ ( leq @ X @ n4 )
| ( X = n4 )
| ( X = n3 )
| ( X = n2 )
| ( X = n0 )
| ( X = n1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[141]) ).
thf(218,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( leq @ ( minus @ X @ Y ) @ X )
| ( leq @ n0 @ Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[176]) ).
thf(219,plain,
( ( ! [X: $i] :
( ~ ( leq @ n0 @ X )
| ! [C: $i] : ( leq @ n0 @ ( uniform_int_rnd @ C @ X ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[186]) ).
thf(220,plain,
( ( ! [X: $i] :
( ~ ( leq @ n0 @ X )
| ! [C: $i] : ( leq @ ( uniform_int_rnd @ C @ X ) @ X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[187]) ).
thf(221,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( geq @ X @ Y )
| ( leq @ Y @ X ) )
& ! [X: $i,Y: $i] :
( ~ ( leq @ Y @ X )
| ( geq @ X @ Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[188]) ).
thf(222,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( geq @ X @ Y )
| ( leq @ Y @ X ) )
& ! [X: $i,Y: $i] :
( ~ ( leq @ Y @ X )
| ( geq @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[221]) ).
thf(223,plain,
( ( ! [X: $i] :
( ~ ( leq @ n0 @ X )
| ! [C: $i] : ( leq @ ( uniform_int_rnd @ C @ X ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[220]) ).
thf(224,plain,
( ( ! [X: $i] :
( ~ ( leq @ n0 @ X )
| ! [C: $i] : ( leq @ n0 @ ( uniform_int_rnd @ C @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[219]) ).
thf(225,plain,
( ( ! [Body: $i] :
( ( sum @ n0 @ tptp_minus_1 @ Body )
= n0 ) )
= $true ),
inference(copy,[status(thm)],[185]) ).
thf(226,plain,
( ( ( succ @ tptp_minus_1 )
= n0 )
= $true ),
inference(copy,[status(thm)],[184]) ).
thf(227,plain,
( ( ! [X: $i] :
( ( plus @ X @ n1 )
= ( succ @ X ) ) )
= $true ),
inference(copy,[status(thm)],[183]) ).
thf(228,plain,
( ( ! [X: $i] :
( ( plus @ n1 @ X )
= ( succ @ X ) ) )
= $true ),
inference(copy,[status(thm)],[182]) ).
thf(229,plain,
( ( ! [X: $i] :
( ( plus @ X @ n2 )
= ( succ @ ( succ @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[181]) ).
thf(230,plain,
( ( ! [X: $i] :
( ( plus @ n2 @ X )
= ( succ @ ( succ @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[180]) ).
thf(231,plain,
( ( ! [X: $i] :
( ( plus @ X @ n3 )
= ( succ @ ( succ @ ( succ @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[179]) ).
thf(232,plain,
( ( ! [X: $i] :
( ( plus @ n3 @ X )
= ( succ @ ( succ @ ( succ @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[178]) ).
thf(233,plain,
( ( ! [X: $i] :
( ( minus @ X @ n1 )
= ( pred @ X ) ) )
= $true ),
inference(copy,[status(thm)],[177]) ).
thf(234,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( leq @ ( minus @ X @ Y ) @ X )
| ( leq @ n0 @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[218]) ).
thf(235,plain,
true = $true,
inference(copy,[status(thm)],[175]) ).
thf(236,plain,
( ( gt @ n6 @ n4 )
= $true ),
inference(copy,[status(thm)],[174]) ).
thf(237,plain,
( ( gt @ n999 @ n4 )
= $true ),
inference(copy,[status(thm)],[173]) ).
thf(238,plain,
( ( gt @ n6 @ n5 )
= $true ),
inference(copy,[status(thm)],[172]) ).
thf(239,plain,
( ( gt @ n999 @ n5 )
= $true ),
inference(copy,[status(thm)],[171]) ).
thf(240,plain,
( ( gt @ n999 @ n6 )
= $true ),
inference(copy,[status(thm)],[170]) ).
thf(241,plain,
( ( gt @ n6 @ tptp_minus_1 )
= $true ),
inference(copy,[status(thm)],[169]) ).
thf(242,plain,
( ( gt @ n999 @ tptp_minus_1 )
= $true ),
inference(copy,[status(thm)],[168]) ).
thf(243,plain,
( ( gt @ n0 @ tptp_minus_1 )
= $true ),
inference(copy,[status(thm)],[167]) ).
thf(244,plain,
( ( gt @ n1 @ tptp_minus_1 )
= $true ),
inference(copy,[status(thm)],[166]) ).
thf(245,plain,
( ( gt @ n2 @ tptp_minus_1 )
= $true ),
inference(copy,[status(thm)],[165]) ).
thf(246,plain,
( ( gt @ n3 @ tptp_minus_1 )
= $true ),
inference(copy,[status(thm)],[164]) ).
thf(247,plain,
( ( gt @ n4 @ n0 )
= $true ),
inference(copy,[status(thm)],[163]) ).
thf(248,plain,
( ( gt @ n5 @ n0 )
= $true ),
inference(copy,[status(thm)],[162]) ).
thf(249,plain,
( ( gt @ n6 @ n0 )
= $true ),
inference(copy,[status(thm)],[161]) ).
thf(250,plain,
( ( gt @ n999 @ n0 )
= $true ),
inference(copy,[status(thm)],[160]) ).
thf(251,plain,
( ( gt @ n1 @ n0 )
= $true ),
inference(copy,[status(thm)],[159]) ).
thf(252,plain,
( ( gt @ n2 @ n0 )
= $true ),
inference(copy,[status(thm)],[158]) ).
thf(253,plain,
( ( gt @ n3 @ n0 )
= $true ),
inference(copy,[status(thm)],[157]) ).
thf(254,plain,
( ( gt @ n4 @ n1 )
= $true ),
inference(copy,[status(thm)],[156]) ).
thf(255,plain,
( ( gt @ n5 @ n1 )
= $true ),
inference(copy,[status(thm)],[155]) ).
thf(256,plain,
( ( gt @ n6 @ n1 )
= $true ),
inference(copy,[status(thm)],[154]) ).
thf(257,plain,
( ( gt @ n999 @ n1 )
= $true ),
inference(copy,[status(thm)],[153]) ).
thf(258,plain,
( ( gt @ n2 @ n1 )
= $true ),
inference(copy,[status(thm)],[152]) ).
thf(259,plain,
( ( gt @ n3 @ n1 )
= $true ),
inference(copy,[status(thm)],[151]) ).
thf(260,plain,
( ( gt @ n4 @ n2 )
= $true ),
inference(copy,[status(thm)],[150]) ).
thf(261,plain,
( ( gt @ n5 @ n2 )
= $true ),
inference(copy,[status(thm)],[149]) ).
thf(262,plain,
( ( gt @ n6 @ n2 )
= $true ),
inference(copy,[status(thm)],[148]) ).
thf(263,plain,
( ( gt @ n999 @ n2 )
= $true ),
inference(copy,[status(thm)],[147]) ).
thf(264,plain,
( ( gt @ n3 @ n2 )
= $true ),
inference(copy,[status(thm)],[146]) ).
thf(265,plain,
( ( gt @ n4 @ n3 )
= $true ),
inference(copy,[status(thm)],[145]) ).
thf(266,plain,
( ( gt @ n5 @ n3 )
= $true ),
inference(copy,[status(thm)],[144]) ).
thf(267,plain,
( ( gt @ n6 @ n3 )
= $true ),
inference(copy,[status(thm)],[143]) ).
thf(268,plain,
( ( gt @ n999 @ n3 )
= $true ),
inference(copy,[status(thm)],[142]) ).
thf(269,plain,
( ( ! [X: $i] :
( ~ ( leq @ n0 @ X )
| ~ ( leq @ X @ n4 )
| ( X = n4 )
| ( X = n3 )
| ( X = n2 )
| ( X = n0 )
| ( X = n1 ) ) )
= $true ),
inference(copy,[status(thm)],[217]) ).
thf(270,plain,
( ( ! [X: $i] :
( ~ ( leq @ n0 @ X )
| ~ ( leq @ X @ n0 )
| ( X = n0 ) ) )
= $true ),
inference(copy,[status(thm)],[216]) ).
thf(271,plain,
( ( ! [X: $i] :
( ~ ( leq @ n0 @ X )
| ~ ( leq @ X @ n1 )
| ( X = n0 )
| ( X = n1 ) ) )
= $true ),
inference(copy,[status(thm)],[215]) ).
thf(272,plain,
( ( ! [X: $i] :
( ~ ( leq @ n0 @ X )
| ~ ( leq @ X @ n2 )
| ( X = n2 )
| ( X = n0 )
| ( X = n1 ) ) )
= $true ),
inference(copy,[status(thm)],[214]) ).
thf(273,plain,
( ( ! [X: $i] :
( ~ ( leq @ n0 @ X )
| ~ ( leq @ X @ n3 )
| ( X = n3 )
| ( X = n2 )
| ( X = n0 )
| ( X = n1 ) ) )
= $true ),
inference(copy,[status(thm)],[213]) ).
thf(274,plain,
( ( ( succ @ ( succ @ ( succ @ ( succ @ n0 ) ) ) )
= n4 )
= $true ),
inference(copy,[status(thm)],[136]) ).
thf(275,plain,
( ( ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ n0 ) ) ) ) )
= n5 )
= $true ),
inference(copy,[status(thm)],[135]) ).
thf(276,plain,
( ( ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ n0 ) ) ) ) ) )
= n6 )
= $true ),
inference(copy,[status(thm)],[134]) ).
thf(277,plain,
( ( ( succ @ n0 )
= n1 )
= $true ),
inference(copy,[status(thm)],[133]) ).
thf(278,plain,
( ( ( succ @ ( succ @ n0 ) )
= n2 )
= $true ),
inference(copy,[status(thm)],[132]) ).
thf(279,plain,
( ( ( succ @ ( succ @ ( succ @ n0 ) ) )
= n3 )
= $true ),
inference(copy,[status(thm)],[131]) ).
thf(280,plain,
( ( ! [X: $i,Y: $i] :
( ( X = Y )
| ( gt @ X @ Y )
| ( gt @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[212]) ).
thf(281,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( gt @ X @ Y )
| ~ ( gt @ Y @ Z )
| ( gt @ X @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[211]) ).
thf(282,plain,
( ( ! [X: $i] :
~ ( gt @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[128]) ).
thf(283,plain,
( ( ! [X: $i] : ( leq @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[127]) ).
thf(284,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( leq @ X @ Y )
| ~ ( leq @ Y @ Z )
| ( leq @ X @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[210]) ).
thf(285,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( gt @ Y @ X )
| ( lt @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ~ ( lt @ X @ Y )
| ( gt @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[209]) ).
thf(286,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( gt @ Y @ X )
| ( leq @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[208]) ).
thf(287,plain,
( ( ! [X: $i,Y: $i] :
( ( X = Y )
| ~ ( leq @ X @ Y )
| ( gt @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[207]) ).
thf(288,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( gt @ Y @ X )
| ( leq @ X @ ( pred @ Y ) ) )
& ! [X: $i,Y: $i] :
( ~ ( leq @ X @ ( pred @ Y ) )
| ( gt @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[206]) ).
thf(289,plain,
( ( ! [X: $i] : ( gt @ ( succ @ X ) @ X ) )
= $true ),
inference(copy,[status(thm)],[121]) ).
thf(290,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( leq @ X @ Y )
| ( leq @ X @ ( succ @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[205]) ).
thf(291,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( gt @ ( succ @ Y ) @ X )
| ( leq @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ~ ( leq @ X @ Y )
| ( gt @ ( succ @ Y ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[204]) ).
thf(292,plain,
( ( ! [Body: $i] :
( tptp_float_0_0
= ( sum @ n0 @ tptp_minus_1 @ Body ) ) )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(293,plain,
( ( ! [X: $i] :
( ( plus @ X @ n4 )
= ( succ @ ( succ @ ( succ @ ( succ @ X ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(294,plain,
( ( ! [X: $i] :
( ( plus @ n4 @ X )
= ( succ @ ( succ @ ( succ @ ( succ @ X ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(295,plain,
( ( ! [X: $i] :
( ( plus @ X @ n5 )
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ X ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[115]) ).
thf(296,plain,
( ( ! [X: $i] :
( ( plus @ n5 @ X )
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ X ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(297,plain,
( ( ! [X: $i] :
( ( pred @ ( succ @ X ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(298,plain,
( ( ! [X: $i] :
( ( succ @ ( pred @ X ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(299,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( leq @ ( succ @ X ) @ ( succ @ Y ) )
| ( leq @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ~ ( leq @ X @ Y )
| ( leq @ ( succ @ X ) @ ( succ @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[203]) ).
thf(300,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( leq @ ( succ @ X ) @ Y )
| ( gt @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[202]) ).
thf(301,plain,
( ( gt @ n5 @ n4 )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(302,plain,
( ( gt @ n4 @ tptp_minus_1 )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(303,plain,
( ( gt @ n5 @ tptp_minus_1 )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(304,plain,
( ( ! [X: $i] :
( ~ ( leq @ n0 @ X )
| ~ ( leq @ X @ n5 )
| ( X = n5 )
| ( X = n4 )
| ( X = n3 )
| ( X = n2 )
| ( X = n0 )
| ( X = n1 ) ) )
= $true ),
inference(copy,[status(thm)],[201]) ).
thf(305,plain,
( ( ! [X: $i] :
( ~ ( leq @ n0 @ X )
| ~ ( leq @ X @ n6 )
| ( X = n6 )
| ( X = n5 )
| ( X = n4 )
| ( X = n3 )
| ( X = n2 )
| ( X = n0 )
| ( X = n1 ) ) )
= $true ),
inference(copy,[status(thm)],[200]) ).
thf(306,plain,
( ( geq @ ( minus @ n999 @ n1 ) @ n0 )
= $true ),
inference(copy,[status(thm)],[197]) ).
thf(307,plain,
( ( geq @ ( minus @ n3 @ n1 ) @ n0 )
= $true ),
inference(copy,[status(thm)],[196]) ).
thf(308,plain,
( ( geq @ ( minus @ n6 @ n1 ) @ n0 )
= $true ),
inference(copy,[status(thm)],[195]) ).
thf(309,plain,
( ( geq @ ( minus @ n6 @ n1 ) @ n0 )
= $true ),
inference(copy,[status(thm)],[194]) ).
thf(310,plain,
( ( geq @ ( minus @ n6 @ n1 ) @ n0 )
= $true ),
inference(copy,[status(thm)],[193]) ).
thf(311,plain,
( ( geq @ ( minus @ n999 @ n1 ) @ n0 )
= $true ),
inference(copy,[status(thm)],[192]) ).
thf(312,plain,
( ( geq @ n2 @ n0 )
= $true ),
inference(copy,[status(thm)],[191]) ).
thf(313,plain,
( ( geq @ ( minus @ n6 @ n1 ) @ n0 )
= $true ),
inference(copy,[status(thm)],[190]) ).
thf(314,plain,
( ( geq @ ( minus @ n3 @ n1 ) @ n0 )
= $true ),
inference(copy,[status(thm)],[189]) ).
thf(315,plain,
( ( ~ true )
= $true ),
inference(copy,[status(thm)],[199]) ).
thf(316,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( leq @ ( succ @ SX0 ) @ ( succ @ SX1 ) )
| ( leq @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX0 @ SX1 )
| ( leq @ ( succ @ SX0 ) @ ( succ @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[299]) ).
thf(317,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( gt @ SX1 @ SX0 )
| ( leq @ SX0 @ ( pred @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX0 @ ( pred @ SX1 ) )
| ( gt @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[288]) ).
thf(318,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( gt @ SX1 @ SX0 )
| ( lt @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( lt @ SX0 @ SX1 )
| ( gt @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[285]) ).
thf(319,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( gt @ ( succ @ SX1 ) @ SX0 )
| ( leq @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX0 @ SX1 )
| ( gt @ ( succ @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[291]) ).
thf(320,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( geq @ SX0 @ SX1 )
| ( leq @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX1 @ SX0 )
| ( geq @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[222]) ).
thf(321,plain,
! [SV1: $i] :
( ( ~ ( leq @ n0 @ SV1 )
| ! [SY57: $i] : ( leq @ ( uniform_int_rnd @ SY57 @ SV1 ) @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[223]) ).
thf(322,plain,
! [SV2: $i] :
( ( ~ ( leq @ n0 @ SV2 )
| ! [SY58: $i] : ( leq @ n0 @ ( uniform_int_rnd @ SY58 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[224]) ).
thf(323,plain,
! [SV3: $i] :
( ( ( sum @ n0 @ tptp_minus_1 @ SV3 )
= n0 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[225]) ).
thf(324,plain,
! [SV4: $i] :
( ( ( plus @ SV4 @ n1 )
= ( succ @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[227]) ).
thf(325,plain,
! [SV5: $i] :
( ( ( plus @ n1 @ SV5 )
= ( succ @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[228]) ).
thf(326,plain,
! [SV6: $i] :
( ( ( plus @ SV6 @ n2 )
= ( succ @ ( succ @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[229]) ).
thf(327,plain,
! [SV7: $i] :
( ( ( plus @ n2 @ SV7 )
= ( succ @ ( succ @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[230]) ).
thf(328,plain,
! [SV8: $i] :
( ( ( plus @ SV8 @ n3 )
= ( succ @ ( succ @ ( succ @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[231]) ).
thf(329,plain,
! [SV9: $i] :
( ( ( plus @ n3 @ SV9 )
= ( succ @ ( succ @ ( succ @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[232]) ).
thf(330,plain,
! [SV10: $i] :
( ( ( minus @ SV10 @ n1 )
= ( pred @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[233]) ).
thf(331,plain,
! [SV11: $i] :
( ( ! [SY59: $i] :
( ~ ( leq @ ( minus @ SV11 @ SY59 ) @ SV11 )
| ( leq @ n0 @ SY59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[234]) ).
thf(332,plain,
! [SV12: $i] :
( ( ~ ( leq @ n0 @ SV12 )
| ~ ( leq @ SV12 @ n4 )
| ( SV12 = n4 )
| ( SV12 = n3 )
| ( SV12 = n2 )
| ( SV12 = n0 )
| ( SV12 = n1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[269]) ).
thf(333,plain,
! [SV13: $i] :
( ( ~ ( leq @ n0 @ SV13 )
| ~ ( leq @ SV13 @ n0 )
| ( SV13 = n0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[270]) ).
thf(334,plain,
! [SV14: $i] :
( ( ~ ( leq @ n0 @ SV14 )
| ~ ( leq @ SV14 @ n1 )
| ( SV14 = n0 )
| ( SV14 = n1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[271]) ).
thf(335,plain,
! [SV15: $i] :
( ( ~ ( leq @ n0 @ SV15 )
| ~ ( leq @ SV15 @ n2 )
| ( SV15 = n2 )
| ( SV15 = n0 )
| ( SV15 = n1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[272]) ).
thf(336,plain,
! [SV16: $i] :
( ( ~ ( leq @ n0 @ SV16 )
| ~ ( leq @ SV16 @ n3 )
| ( SV16 = n3 )
| ( SV16 = n2 )
| ( SV16 = n0 )
| ( SV16 = n1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[273]) ).
thf(337,plain,
! [SV17: $i] :
( ( ! [SY60: $i] :
( ( SV17 = SY60 )
| ( gt @ SV17 @ SY60 )
| ( gt @ SY60 @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[280]) ).
thf(338,plain,
! [SV18: $i] :
( ( ! [SY61: $i,SY62: $i] :
( ~ ( gt @ SV18 @ SY61 )
| ~ ( gt @ SY61 @ SY62 )
| ( gt @ SV18 @ SY62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[281]) ).
thf(339,plain,
! [SV19: $i] :
( ( ~ ( gt @ SV19 @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[282]) ).
thf(340,plain,
! [SV20: $i] :
( ( leq @ SV20 @ SV20 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[283]) ).
thf(341,plain,
! [SV21: $i] :
( ( ! [SY63: $i,SY64: $i] :
( ~ ( leq @ SV21 @ SY63 )
| ~ ( leq @ SY63 @ SY64 )
| ( leq @ SV21 @ SY64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[284]) ).
thf(342,plain,
! [SV22: $i] :
( ( ! [SY65: $i] :
( ~ ( gt @ SY65 @ SV22 )
| ( leq @ SV22 @ SY65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[286]) ).
thf(343,plain,
! [SV23: $i] :
( ( ! [SY66: $i] :
( ( SV23 = SY66 )
| ~ ( leq @ SV23 @ SY66 )
| ( gt @ SY66 @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[287]) ).
thf(344,plain,
! [SV24: $i] :
( ( gt @ ( succ @ SV24 ) @ SV24 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[289]) ).
thf(345,plain,
! [SV25: $i] :
( ( ! [SY67: $i] :
( ~ ( leq @ SV25 @ SY67 )
| ( leq @ SV25 @ ( succ @ SY67 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[290]) ).
thf(346,plain,
! [SV26: $i] :
( ( tptp_float_0_0
= ( sum @ n0 @ tptp_minus_1 @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[292]) ).
thf(347,plain,
! [SV27: $i] :
( ( ( plus @ SV27 @ n4 )
= ( succ @ ( succ @ ( succ @ ( succ @ SV27 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[293]) ).
thf(348,plain,
! [SV28: $i] :
( ( ( plus @ n4 @ SV28 )
= ( succ @ ( succ @ ( succ @ ( succ @ SV28 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[294]) ).
thf(349,plain,
! [SV29: $i] :
( ( ( plus @ SV29 @ n5 )
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ SV29 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[295]) ).
thf(350,plain,
! [SV30: $i] :
( ( ( plus @ n5 @ SV30 )
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ SV30 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[296]) ).
thf(351,plain,
! [SV31: $i] :
( ( ( pred @ ( succ @ SV31 ) )
= SV31 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[297]) ).
thf(352,plain,
! [SV32: $i] :
( ( ( succ @ ( pred @ SV32 ) )
= SV32 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[298]) ).
thf(353,plain,
! [SV33: $i] :
( ( ! [SY68: $i] :
( ~ ( leq @ ( succ @ SV33 ) @ SY68 )
| ( gt @ SY68 @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[300]) ).
thf(354,plain,
! [SV34: $i] :
( ( ~ ( leq @ n0 @ SV34 )
| ~ ( leq @ SV34 @ n5 )
| ( SV34 = n5 )
| ( SV34 = n4 )
| ( SV34 = n3 )
| ( SV34 = n2 )
| ( SV34 = n0 )
| ( SV34 = n1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[304]) ).
thf(355,plain,
! [SV35: $i] :
( ( ~ ( leq @ n0 @ SV35 )
| ~ ( leq @ SV35 @ n6 )
| ( SV35 = n6 )
| ( SV35 = n5 )
| ( SV35 = n4 )
| ( SV35 = n3 )
| ( SV35 = n2 )
| ( SV35 = n0 )
| ( SV35 = n1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[305]) ).
thf(356,plain,
true = $false,
inference(extcnf_not_pos,[status(thm)],[315]) ).
thf(357,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( leq @ ( succ @ SX0 ) @ ( succ @ SX1 ) )
| ( leq @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX0 @ SX1 )
| ( leq @ ( succ @ SX0 ) @ ( succ @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[316]) ).
thf(358,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( gt @ SX1 @ SX0 )
| ( leq @ SX0 @ ( pred @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX0 @ ( pred @ SX1 ) )
| ( gt @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[317]) ).
thf(359,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( gt @ SX1 @ SX0 )
| ( lt @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( lt @ SX0 @ SX1 )
| ( gt @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[318]) ).
thf(360,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( gt @ ( succ @ SX1 ) @ SX0 )
| ( leq @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX0 @ SX1 )
| ( gt @ ( succ @ SX1 ) @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[319]) ).
thf(361,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( geq @ SX0 @ SX1 )
| ( leq @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX1 @ SX0 )
| ( geq @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[320]) ).
thf(362,plain,
! [SV1: $i] :
( ( ( ~ ( leq @ n0 @ SV1 ) )
= $true )
| ( ( ! [SY57: $i] : ( leq @ ( uniform_int_rnd @ SY57 @ SV1 ) @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[321]) ).
thf(363,plain,
! [SV2: $i] :
( ( ( ~ ( leq @ n0 @ SV2 ) )
= $true )
| ( ( ! [SY58: $i] : ( leq @ n0 @ ( uniform_int_rnd @ SY58 @ SV2 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[322]) ).
thf(364,plain,
! [SV36: $i,SV11: $i] :
( ( ~ ( leq @ ( minus @ SV11 @ SV36 ) @ SV11 )
| ( leq @ n0 @ SV36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[331]) ).
thf(365,plain,
! [SV12: $i] :
( ( ( ~ ( leq @ n0 @ SV12 )
| ~ ( leq @ SV12 @ n4 ) )
= $true )
| ( ( ( SV12 = n4 )
| ( SV12 = n3 )
| ( SV12 = n2 )
| ( SV12 = n0 )
| ( SV12 = n1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[332]) ).
thf(366,plain,
! [SV13: $i] :
( ( ( ~ ( leq @ n0 @ SV13 )
| ~ ( leq @ SV13 @ n0 ) )
= $true )
| ( ( SV13 = n0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[333]) ).
thf(367,plain,
! [SV14: $i] :
( ( ( ~ ( leq @ n0 @ SV14 )
| ~ ( leq @ SV14 @ n1 ) )
= $true )
| ( ( ( SV14 = n0 )
| ( SV14 = n1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[334]) ).
thf(368,plain,
! [SV15: $i] :
( ( ( ~ ( leq @ n0 @ SV15 )
| ~ ( leq @ SV15 @ n2 ) )
= $true )
| ( ( ( SV15 = n2 )
| ( SV15 = n0 )
| ( SV15 = n1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[335]) ).
thf(369,plain,
! [SV16: $i] :
( ( ( ~ ( leq @ n0 @ SV16 )
| ~ ( leq @ SV16 @ n3 ) )
= $true )
| ( ( ( SV16 = n3 )
| ( SV16 = n2 )
| ( SV16 = n0 )
| ( SV16 = n1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[336]) ).
thf(370,plain,
! [SV37: $i,SV17: $i] :
( ( ( SV17 = SV37 )
| ( gt @ SV17 @ SV37 )
| ( gt @ SV37 @ SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[337]) ).
thf(371,plain,
! [SV38: $i,SV18: $i] :
( ( ! [SY69: $i] :
( ~ ( gt @ SV18 @ SV38 )
| ~ ( gt @ SV38 @ SY69 )
| ( gt @ SV18 @ SY69 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[338]) ).
thf(372,plain,
! [SV19: $i] :
( ( gt @ SV19 @ SV19 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[339]) ).
thf(373,plain,
! [SV39: $i,SV21: $i] :
( ( ! [SY70: $i] :
( ~ ( leq @ SV21 @ SV39 )
| ~ ( leq @ SV39 @ SY70 )
| ( leq @ SV21 @ SY70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[341]) ).
thf(374,plain,
! [SV22: $i,SV40: $i] :
( ( ~ ( gt @ SV40 @ SV22 )
| ( leq @ SV22 @ SV40 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[342]) ).
thf(375,plain,
! [SV41: $i,SV23: $i] :
( ( ( SV23 = SV41 )
| ~ ( leq @ SV23 @ SV41 )
| ( gt @ SV41 @ SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[343]) ).
thf(376,plain,
! [SV42: $i,SV25: $i] :
( ( ~ ( leq @ SV25 @ SV42 )
| ( leq @ SV25 @ ( succ @ SV42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[345]) ).
thf(377,plain,
! [SV43: $i,SV33: $i] :
( ( ~ ( leq @ ( succ @ SV33 ) @ SV43 )
| ( gt @ SV43 @ SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[353]) ).
thf(378,plain,
! [SV34: $i] :
( ( ( ~ ( leq @ n0 @ SV34 )
| ~ ( leq @ SV34 @ n5 ) )
= $true )
| ( ( ( SV34 = n5 )
| ( SV34 = n4 )
| ( SV34 = n3 )
| ( SV34 = n2 )
| ( SV34 = n0 )
| ( SV34 = n1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[354]) ).
thf(379,plain,
! [SV35: $i] :
( ( ( ~ ( leq @ n0 @ SV35 )
| ~ ( leq @ SV35 @ n6 ) )
= $true )
| ( ( ( SV35 = n6 )
| ( SV35 = n5 )
| ( SV35 = n4 )
| ( SV35 = n3 )
| ( SV35 = n2 )
| ( SV35 = n0 )
| ( SV35 = n1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[355]) ).
thf(380,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( leq @ ( succ @ SX0 ) @ ( succ @ SX1 ) )
| ( leq @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[357]) ).
thf(381,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX0 @ SX1 )
| ( leq @ ( succ @ SX0 ) @ ( succ @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[357]) ).
thf(382,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( gt @ SX1 @ SX0 )
| ( leq @ SX0 @ ( pred @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[358]) ).
thf(383,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX0 @ ( pred @ SX1 ) )
| ( gt @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[358]) ).
thf(384,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( gt @ SX1 @ SX0 )
| ( lt @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[359]) ).
thf(385,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( lt @ SX0 @ SX1 )
| ( gt @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[359]) ).
thf(386,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( gt @ ( succ @ SX1 ) @ SX0 )
| ( leq @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[360]) ).
thf(387,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX0 @ SX1 )
| ( gt @ ( succ @ SX1 ) @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[360]) ).
thf(388,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( geq @ SX0 @ SX1 )
| ( leq @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[361]) ).
thf(389,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX1 @ SX0 )
| ( geq @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[361]) ).
thf(390,plain,
! [SV1: $i] :
( ( ( leq @ n0 @ SV1 )
= $false )
| ( ( ! [SY57: $i] : ( leq @ ( uniform_int_rnd @ SY57 @ SV1 ) @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[362]) ).
thf(391,plain,
! [SV2: $i] :
( ( ( leq @ n0 @ SV2 )
= $false )
| ( ( ! [SY58: $i] : ( leq @ n0 @ ( uniform_int_rnd @ SY58 @ SV2 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[363]) ).
thf(392,plain,
! [SV36: $i,SV11: $i] :
( ( ( ~ ( leq @ ( minus @ SV11 @ SV36 ) @ SV11 ) )
= $true )
| ( ( leq @ n0 @ SV36 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[364]) ).
thf(393,plain,
! [SV12: $i] :
( ( ( ~ ( leq @ n0 @ SV12 ) )
= $true )
| ( ( ~ ( leq @ SV12 @ n4 ) )
= $true )
| ( ( ( SV12 = n4 )
| ( SV12 = n3 )
| ( SV12 = n2 )
| ( SV12 = n0 )
| ( SV12 = n1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[365]) ).
thf(394,plain,
! [SV13: $i] :
( ( ( ~ ( leq @ n0 @ SV13 ) )
= $true )
| ( ( ~ ( leq @ SV13 @ n0 ) )
= $true )
| ( ( SV13 = n0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[366]) ).
thf(395,plain,
! [SV14: $i] :
( ( ( ~ ( leq @ n0 @ SV14 ) )
= $true )
| ( ( ~ ( leq @ SV14 @ n1 ) )
= $true )
| ( ( ( SV14 = n0 )
| ( SV14 = n1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[367]) ).
thf(396,plain,
! [SV15: $i] :
( ( ( ~ ( leq @ n0 @ SV15 ) )
= $true )
| ( ( ~ ( leq @ SV15 @ n2 ) )
= $true )
| ( ( ( SV15 = n2 )
| ( SV15 = n0 )
| ( SV15 = n1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[368]) ).
thf(397,plain,
! [SV16: $i] :
( ( ( ~ ( leq @ n0 @ SV16 ) )
= $true )
| ( ( ~ ( leq @ SV16 @ n3 ) )
= $true )
| ( ( ( SV16 = n3 )
| ( SV16 = n2 )
| ( SV16 = n0 )
| ( SV16 = n1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[369]) ).
thf(398,plain,
! [SV37: $i,SV17: $i] :
( ( ( SV17 = SV37 )
= $true )
| ( ( ( gt @ SV17 @ SV37 )
| ( gt @ SV37 @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[370]) ).
thf(399,plain,
! [SV44: $i,SV38: $i,SV18: $i] :
( ( ~ ( gt @ SV18 @ SV38 )
| ~ ( gt @ SV38 @ SV44 )
| ( gt @ SV18 @ SV44 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[371]) ).
thf(400,plain,
! [SV45: $i,SV39: $i,SV21: $i] :
( ( ~ ( leq @ SV21 @ SV39 )
| ~ ( leq @ SV39 @ SV45 )
| ( leq @ SV21 @ SV45 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[373]) ).
thf(401,plain,
! [SV22: $i,SV40: $i] :
( ( ( ~ ( gt @ SV40 @ SV22 ) )
= $true )
| ( ( leq @ SV22 @ SV40 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[374]) ).
thf(402,plain,
! [SV41: $i,SV23: $i] :
( ( ( ( SV23 = SV41 )
| ~ ( leq @ SV23 @ SV41 ) )
= $true )
| ( ( gt @ SV41 @ SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[375]) ).
thf(403,plain,
! [SV42: $i,SV25: $i] :
( ( ( ~ ( leq @ SV25 @ SV42 ) )
= $true )
| ( ( leq @ SV25 @ ( succ @ SV42 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[376]) ).
thf(404,plain,
! [SV43: $i,SV33: $i] :
( ( ( ~ ( leq @ ( succ @ SV33 ) @ SV43 ) )
= $true )
| ( ( gt @ SV43 @ SV33 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[377]) ).
thf(405,plain,
! [SV34: $i] :
( ( ( ~ ( leq @ n0 @ SV34 ) )
= $true )
| ( ( ~ ( leq @ SV34 @ n5 ) )
= $true )
| ( ( ( SV34 = n5 )
| ( SV34 = n4 )
| ( SV34 = n3 )
| ( SV34 = n2 )
| ( SV34 = n0 )
| ( SV34 = n1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[378]) ).
thf(406,plain,
! [SV35: $i] :
( ( ( ~ ( leq @ n0 @ SV35 ) )
= $true )
| ( ( ~ ( leq @ SV35 @ n6 ) )
= $true )
| ( ( ( SV35 = n6 )
| ( SV35 = n5 )
| ( SV35 = n4 )
| ( SV35 = n3 )
| ( SV35 = n2 )
| ( SV35 = n0 )
| ( SV35 = n1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[379]) ).
thf(407,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ ( succ @ SX0 ) @ ( succ @ SX1 ) )
| ( leq @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[380]) ).
thf(408,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX0 @ SX1 )
| ( leq @ ( succ @ SX0 ) @ ( succ @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[381]) ).
thf(409,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( gt @ SX1 @ SX0 )
| ( leq @ SX0 @ ( pred @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[382]) ).
thf(410,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX0 @ ( pred @ SX1 ) )
| ( gt @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[383]) ).
thf(411,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( gt @ SX1 @ SX0 )
| ( lt @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[384]) ).
thf(412,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( lt @ SX0 @ SX1 )
| ( gt @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[385]) ).
thf(413,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( gt @ ( succ @ SX1 ) @ SX0 )
| ( leq @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[386]) ).
thf(414,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX0 @ SX1 )
| ( gt @ ( succ @ SX1 ) @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[387]) ).
thf(415,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( geq @ SX0 @ SX1 )
| ( leq @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[388]) ).
thf(416,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX1 @ SX0 )
| ( geq @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[389]) ).
thf(417,plain,
! [SV1: $i,SV46: $i] :
( ( ( leq @ ( uniform_int_rnd @ SV46 @ SV1 ) @ SV1 )
= $true )
| ( ( leq @ n0 @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[390]) ).
thf(418,plain,
! [SV2: $i,SV47: $i] :
( ( ( leq @ n0 @ ( uniform_int_rnd @ SV47 @ SV2 ) )
= $true )
| ( ( leq @ n0 @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[391]) ).
thf(419,plain,
! [SV36: $i,SV11: $i] :
( ( ( leq @ ( minus @ SV11 @ SV36 ) @ SV11 )
= $false )
| ( ( leq @ n0 @ SV36 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[392]) ).
thf(420,plain,
! [SV12: $i] :
( ( ( leq @ n0 @ SV12 )
= $false )
| ( ( ~ ( leq @ SV12 @ n4 ) )
= $true )
| ( ( ( SV12 = n4 )
| ( SV12 = n3 )
| ( SV12 = n2 )
| ( SV12 = n0 )
| ( SV12 = n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[393]) ).
thf(421,plain,
! [SV13: $i] :
( ( ( leq @ n0 @ SV13 )
= $false )
| ( ( ~ ( leq @ SV13 @ n0 ) )
= $true )
| ( ( SV13 = n0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[394]) ).
thf(422,plain,
! [SV14: $i] :
( ( ( leq @ n0 @ SV14 )
= $false )
| ( ( ~ ( leq @ SV14 @ n1 ) )
= $true )
| ( ( ( SV14 = n0 )
| ( SV14 = n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[395]) ).
thf(423,plain,
! [SV15: $i] :
( ( ( leq @ n0 @ SV15 )
= $false )
| ( ( ~ ( leq @ SV15 @ n2 ) )
= $true )
| ( ( ( SV15 = n2 )
| ( SV15 = n0 )
| ( SV15 = n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[396]) ).
thf(424,plain,
! [SV16: $i] :
( ( ( leq @ n0 @ SV16 )
= $false )
| ( ( ~ ( leq @ SV16 @ n3 ) )
= $true )
| ( ( ( SV16 = n3 )
| ( SV16 = n2 )
| ( SV16 = n0 )
| ( SV16 = n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[397]) ).
thf(425,plain,
! [SV37: $i,SV17: $i] :
( ( ( gt @ SV17 @ SV37 )
= $true )
| ( ( gt @ SV37 @ SV17 )
= $true )
| ( ( SV17 = SV37 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[398]) ).
thf(426,plain,
! [SV44: $i,SV38: $i,SV18: $i] :
( ( ( ~ ( gt @ SV18 @ SV38 )
| ~ ( gt @ SV38 @ SV44 ) )
= $true )
| ( ( gt @ SV18 @ SV44 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[399]) ).
thf(427,plain,
! [SV45: $i,SV39: $i,SV21: $i] :
( ( ( ~ ( leq @ SV21 @ SV39 )
| ~ ( leq @ SV39 @ SV45 ) )
= $true )
| ( ( leq @ SV21 @ SV45 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[400]) ).
thf(428,plain,
! [SV22: $i,SV40: $i] :
( ( ( gt @ SV40 @ SV22 )
= $false )
| ( ( leq @ SV22 @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[401]) ).
thf(429,plain,
! [SV41: $i,SV23: $i] :
( ( ( SV23 = SV41 )
= $true )
| ( ( ~ ( leq @ SV23 @ SV41 ) )
= $true )
| ( ( gt @ SV41 @ SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[402]) ).
thf(430,plain,
! [SV42: $i,SV25: $i] :
( ( ( leq @ SV25 @ SV42 )
= $false )
| ( ( leq @ SV25 @ ( succ @ SV42 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[403]) ).
thf(431,plain,
! [SV43: $i,SV33: $i] :
( ( ( leq @ ( succ @ SV33 ) @ SV43 )
= $false )
| ( ( gt @ SV43 @ SV33 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[404]) ).
thf(432,plain,
! [SV34: $i] :
( ( ( leq @ n0 @ SV34 )
= $false )
| ( ( ~ ( leq @ SV34 @ n5 ) )
= $true )
| ( ( ( SV34 = n5 )
| ( SV34 = n4 )
| ( SV34 = n3 )
| ( SV34 = n2 )
| ( SV34 = n0 )
| ( SV34 = n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[405]) ).
thf(433,plain,
! [SV35: $i] :
( ( ( leq @ n0 @ SV35 )
= $false )
| ( ( ~ ( leq @ SV35 @ n6 ) )
= $true )
| ( ( ( SV35 = n6 )
| ( SV35 = n5 )
| ( SV35 = n4 )
| ( SV35 = n3 )
| ( SV35 = n2 )
| ( SV35 = n0 )
| ( SV35 = n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[406]) ).
thf(434,plain,
! [SV48: $i] :
( ( ! [SY71: $i] :
( ~ ( leq @ ( succ @ SV48 ) @ ( succ @ SY71 ) )
| ( leq @ SV48 @ SY71 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[407]) ).
thf(435,plain,
! [SV49: $i] :
( ( ! [SY72: $i] :
( ~ ( leq @ SV49 @ SY72 )
| ( leq @ ( succ @ SV49 ) @ ( succ @ SY72 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[408]) ).
thf(436,plain,
! [SV50: $i] :
( ( ! [SY73: $i] :
( ~ ( gt @ SY73 @ SV50 )
| ( leq @ SV50 @ ( pred @ SY73 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[409]) ).
thf(437,plain,
! [SV51: $i] :
( ( ! [SY74: $i] :
( ~ ( leq @ SV51 @ ( pred @ SY74 ) )
| ( gt @ SY74 @ SV51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[410]) ).
thf(438,plain,
! [SV52: $i] :
( ( ! [SY75: $i] :
( ~ ( gt @ SY75 @ SV52 )
| ( lt @ SV52 @ SY75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[411]) ).
thf(439,plain,
! [SV53: $i] :
( ( ! [SY76: $i] :
( ~ ( lt @ SV53 @ SY76 )
| ( gt @ SY76 @ SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[412]) ).
thf(440,plain,
! [SV54: $i] :
( ( ! [SY77: $i] :
( ~ ( gt @ ( succ @ SY77 ) @ SV54 )
| ( leq @ SV54 @ SY77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[413]) ).
thf(441,plain,
! [SV55: $i] :
( ( ! [SY78: $i] :
( ~ ( leq @ SV55 @ SY78 )
| ( gt @ ( succ @ SY78 ) @ SV55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[414]) ).
thf(442,plain,
! [SV56: $i] :
( ( ! [SY79: $i] :
( ~ ( geq @ SV56 @ SY79 )
| ( leq @ SY79 @ SV56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[415]) ).
thf(443,plain,
! [SV57: $i] :
( ( ! [SY80: $i] :
( ~ ( leq @ SY80 @ SV57 )
| ( geq @ SV57 @ SY80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[416]) ).
thf(444,plain,
! [SV12: $i] :
( ( ( leq @ SV12 @ n4 )
= $false )
| ( ( leq @ n0 @ SV12 )
= $false )
| ( ( ( SV12 = n4 )
| ( SV12 = n3 )
| ( SV12 = n2 )
| ( SV12 = n0 )
| ( SV12 = n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[420]) ).
thf(445,plain,
! [SV13: $i] :
( ( ( leq @ SV13 @ n0 )
= $false )
| ( ( leq @ n0 @ SV13 )
= $false )
| ( ( SV13 = n0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[421]) ).
thf(446,plain,
! [SV14: $i] :
( ( ( leq @ SV14 @ n1 )
= $false )
| ( ( leq @ n0 @ SV14 )
= $false )
| ( ( ( SV14 = n0 )
| ( SV14 = n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[422]) ).
thf(447,plain,
! [SV15: $i] :
( ( ( leq @ SV15 @ n2 )
= $false )
| ( ( leq @ n0 @ SV15 )
= $false )
| ( ( ( SV15 = n2 )
| ( SV15 = n0 )
| ( SV15 = n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[423]) ).
thf(448,plain,
! [SV16: $i] :
( ( ( leq @ SV16 @ n3 )
= $false )
| ( ( leq @ n0 @ SV16 )
= $false )
| ( ( ( SV16 = n3 )
| ( SV16 = n2 )
| ( SV16 = n0 )
| ( SV16 = n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[424]) ).
thf(449,plain,
! [SV44: $i,SV38: $i,SV18: $i] :
( ( ( ~ ( gt @ SV18 @ SV38 ) )
= $true )
| ( ( ~ ( gt @ SV38 @ SV44 ) )
= $true )
| ( ( gt @ SV18 @ SV44 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[426]) ).
thf(450,plain,
! [SV45: $i,SV39: $i,SV21: $i] :
( ( ( ~ ( leq @ SV21 @ SV39 ) )
= $true )
| ( ( ~ ( leq @ SV39 @ SV45 ) )
= $true )
| ( ( leq @ SV21 @ SV45 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[427]) ).
thf(451,plain,
! [SV41: $i,SV23: $i] :
( ( ( leq @ SV23 @ SV41 )
= $false )
| ( ( SV23 = SV41 )
= $true )
| ( ( gt @ SV41 @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[429]) ).
thf(452,plain,
! [SV34: $i] :
( ( ( leq @ SV34 @ n5 )
= $false )
| ( ( leq @ n0 @ SV34 )
= $false )
| ( ( ( SV34 = n5 )
| ( SV34 = n4 )
| ( SV34 = n3 )
| ( SV34 = n2 )
| ( SV34 = n0 )
| ( SV34 = n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[432]) ).
thf(453,plain,
! [SV35: $i] :
( ( ( leq @ SV35 @ n6 )
= $false )
| ( ( leq @ n0 @ SV35 )
= $false )
| ( ( ( SV35 = n6 )
| ( SV35 = n5 )
| ( SV35 = n4 )
| ( SV35 = n3 )
| ( SV35 = n2 )
| ( SV35 = n0 )
| ( SV35 = n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[433]) ).
thf(454,plain,
! [SV58: $i,SV48: $i] :
( ( ~ ( leq @ ( succ @ SV48 ) @ ( succ @ SV58 ) )
| ( leq @ SV48 @ SV58 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[434]) ).
thf(455,plain,
! [SV59: $i,SV49: $i] :
( ( ~ ( leq @ SV49 @ SV59 )
| ( leq @ ( succ @ SV49 ) @ ( succ @ SV59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[435]) ).
thf(456,plain,
! [SV50: $i,SV60: $i] :
( ( ~ ( gt @ SV60 @ SV50 )
| ( leq @ SV50 @ ( pred @ SV60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[436]) ).
thf(457,plain,
! [SV61: $i,SV51: $i] :
( ( ~ ( leq @ SV51 @ ( pred @ SV61 ) )
| ( gt @ SV61 @ SV51 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[437]) ).
thf(458,plain,
! [SV52: $i,SV62: $i] :
( ( ~ ( gt @ SV62 @ SV52 )
| ( lt @ SV52 @ SV62 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[438]) ).
thf(459,plain,
! [SV63: $i,SV53: $i] :
( ( ~ ( lt @ SV53 @ SV63 )
| ( gt @ SV63 @ SV53 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[439]) ).
thf(460,plain,
! [SV54: $i,SV64: $i] :
( ( ~ ( gt @ ( succ @ SV64 ) @ SV54 )
| ( leq @ SV54 @ SV64 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[440]) ).
thf(461,plain,
! [SV65: $i,SV55: $i] :
( ( ~ ( leq @ SV55 @ SV65 )
| ( gt @ ( succ @ SV65 ) @ SV55 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[441]) ).
thf(462,plain,
! [SV66: $i,SV56: $i] :
( ( ~ ( geq @ SV56 @ SV66 )
| ( leq @ SV66 @ SV56 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[442]) ).
thf(463,plain,
! [SV57: $i,SV67: $i] :
( ( ~ ( leq @ SV67 @ SV57 )
| ( geq @ SV57 @ SV67 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[443]) ).
thf(464,plain,
! [SV12: $i] :
( ( ( SV12 = n4 )
= $true )
| ( ( ( SV12 = n3 )
| ( SV12 = n2 )
| ( SV12 = n0 )
| ( SV12 = n1 ) )
= $true )
| ( ( leq @ n0 @ SV12 )
= $false )
| ( ( leq @ SV12 @ n4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[444]) ).
thf(465,plain,
! [SV14: $i] :
( ( ( SV14 = n0 )
= $true )
| ( ( SV14 = n1 )
= $true )
| ( ( leq @ n0 @ SV14 )
= $false )
| ( ( leq @ SV14 @ n1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[446]) ).
thf(466,plain,
! [SV15: $i] :
( ( ( SV15 = n2 )
= $true )
| ( ( ( SV15 = n0 )
| ( SV15 = n1 ) )
= $true )
| ( ( leq @ n0 @ SV15 )
= $false )
| ( ( leq @ SV15 @ n2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[447]) ).
thf(467,plain,
! [SV16: $i] :
( ( ( SV16 = n3 )
= $true )
| ( ( ( SV16 = n2 )
| ( SV16 = n0 )
| ( SV16 = n1 ) )
= $true )
| ( ( leq @ n0 @ SV16 )
= $false )
| ( ( leq @ SV16 @ n3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[448]) ).
thf(468,plain,
! [SV44: $i,SV38: $i,SV18: $i] :
( ( ( gt @ SV18 @ SV38 )
= $false )
| ( ( ~ ( gt @ SV38 @ SV44 ) )
= $true )
| ( ( gt @ SV18 @ SV44 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[449]) ).
thf(469,plain,
! [SV45: $i,SV39: $i,SV21: $i] :
( ( ( leq @ SV21 @ SV39 )
= $false )
| ( ( ~ ( leq @ SV39 @ SV45 ) )
= $true )
| ( ( leq @ SV21 @ SV45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[450]) ).
thf(470,plain,
! [SV34: $i] :
( ( ( SV34 = n5 )
= $true )
| ( ( ( SV34 = n4 )
| ( SV34 = n3 )
| ( SV34 = n2 )
| ( SV34 = n0 )
| ( SV34 = n1 ) )
= $true )
| ( ( leq @ n0 @ SV34 )
= $false )
| ( ( leq @ SV34 @ n5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[452]) ).
thf(471,plain,
! [SV35: $i] :
( ( ( SV35 = n6 )
= $true )
| ( ( ( SV35 = n5 )
| ( SV35 = n4 )
| ( SV35 = n3 )
| ( SV35 = n2 )
| ( SV35 = n0 )
| ( SV35 = n1 ) )
= $true )
| ( ( leq @ n0 @ SV35 )
= $false )
| ( ( leq @ SV35 @ n6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[453]) ).
thf(472,plain,
! [SV58: $i,SV48: $i] :
( ( ( ~ ( leq @ ( succ @ SV48 ) @ ( succ @ SV58 ) ) )
= $true )
| ( ( leq @ SV48 @ SV58 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[454]) ).
thf(473,plain,
! [SV59: $i,SV49: $i] :
( ( ( ~ ( leq @ SV49 @ SV59 ) )
= $true )
| ( ( leq @ ( succ @ SV49 ) @ ( succ @ SV59 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[455]) ).
thf(474,plain,
! [SV50: $i,SV60: $i] :
( ( ( ~ ( gt @ SV60 @ SV50 ) )
= $true )
| ( ( leq @ SV50 @ ( pred @ SV60 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[456]) ).
thf(475,plain,
! [SV61: $i,SV51: $i] :
( ( ( ~ ( leq @ SV51 @ ( pred @ SV61 ) ) )
= $true )
| ( ( gt @ SV61 @ SV51 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[457]) ).
thf(476,plain,
! [SV52: $i,SV62: $i] :
( ( ( ~ ( gt @ SV62 @ SV52 ) )
= $true )
| ( ( lt @ SV52 @ SV62 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[458]) ).
thf(477,plain,
! [SV63: $i,SV53: $i] :
( ( ( ~ ( lt @ SV53 @ SV63 ) )
= $true )
| ( ( gt @ SV63 @ SV53 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[459]) ).
thf(478,plain,
! [SV54: $i,SV64: $i] :
( ( ( ~ ( gt @ ( succ @ SV64 ) @ SV54 ) )
= $true )
| ( ( leq @ SV54 @ SV64 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[460]) ).
thf(479,plain,
! [SV65: $i,SV55: $i] :
( ( ( ~ ( leq @ SV55 @ SV65 ) )
= $true )
| ( ( gt @ ( succ @ SV65 ) @ SV55 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[461]) ).
thf(480,plain,
! [SV66: $i,SV56: $i] :
( ( ( ~ ( geq @ SV56 @ SV66 ) )
= $true )
| ( ( leq @ SV66 @ SV56 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[462]) ).
thf(481,plain,
! [SV57: $i,SV67: $i] :
( ( ( ~ ( leq @ SV67 @ SV57 ) )
= $true )
| ( ( geq @ SV57 @ SV67 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[463]) ).
thf(482,plain,
! [SV12: $i] :
( ( ( SV12 = n3 )
= $true )
| ( ( ( SV12 = n2 )
| ( SV12 = n0 )
| ( SV12 = n1 ) )
= $true )
| ( ( SV12 = n4 )
= $true )
| ( ( leq @ n0 @ SV12 )
= $false )
| ( ( leq @ SV12 @ n4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[464]) ).
thf(483,plain,
! [SV15: $i] :
( ( ( SV15 = n0 )
= $true )
| ( ( SV15 = n1 )
= $true )
| ( ( SV15 = n2 )
= $true )
| ( ( leq @ n0 @ SV15 )
= $false )
| ( ( leq @ SV15 @ n2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[466]) ).
thf(484,plain,
! [SV16: $i] :
( ( ( SV16 = n2 )
= $true )
| ( ( ( SV16 = n0 )
| ( SV16 = n1 ) )
= $true )
| ( ( SV16 = n3 )
= $true )
| ( ( leq @ n0 @ SV16 )
= $false )
| ( ( leq @ SV16 @ n3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[467]) ).
thf(485,plain,
! [SV18: $i,SV44: $i,SV38: $i] :
( ( ( gt @ SV38 @ SV44 )
= $false )
| ( ( gt @ SV18 @ SV38 )
= $false )
| ( ( gt @ SV18 @ SV44 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[468]) ).
thf(486,plain,
! [SV21: $i,SV45: $i,SV39: $i] :
( ( ( leq @ SV39 @ SV45 )
= $false )
| ( ( leq @ SV21 @ SV39 )
= $false )
| ( ( leq @ SV21 @ SV45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[469]) ).
thf(487,plain,
! [SV34: $i] :
( ( ( SV34 = n4 )
= $true )
| ( ( ( SV34 = n3 )
| ( SV34 = n2 )
| ( SV34 = n0 )
| ( SV34 = n1 ) )
= $true )
| ( ( SV34 = n5 )
= $true )
| ( ( leq @ n0 @ SV34 )
= $false )
| ( ( leq @ SV34 @ n5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[470]) ).
thf(488,plain,
! [SV35: $i] :
( ( ( SV35 = n5 )
= $true )
| ( ( ( SV35 = n4 )
| ( SV35 = n3 )
| ( SV35 = n2 )
| ( SV35 = n0 )
| ( SV35 = n1 ) )
= $true )
| ( ( SV35 = n6 )
= $true )
| ( ( leq @ n0 @ SV35 )
= $false )
| ( ( leq @ SV35 @ n6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[471]) ).
thf(489,plain,
! [SV58: $i,SV48: $i] :
( ( ( leq @ ( succ @ SV48 ) @ ( succ @ SV58 ) )
= $false )
| ( ( leq @ SV48 @ SV58 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[472]) ).
thf(490,plain,
! [SV59: $i,SV49: $i] :
( ( ( leq @ SV49 @ SV59 )
= $false )
| ( ( leq @ ( succ @ SV49 ) @ ( succ @ SV59 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[473]) ).
thf(491,plain,
! [SV50: $i,SV60: $i] :
( ( ( gt @ SV60 @ SV50 )
= $false )
| ( ( leq @ SV50 @ ( pred @ SV60 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[474]) ).
thf(492,plain,
! [SV61: $i,SV51: $i] :
( ( ( leq @ SV51 @ ( pred @ SV61 ) )
= $false )
| ( ( gt @ SV61 @ SV51 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[475]) ).
thf(493,plain,
! [SV52: $i,SV62: $i] :
( ( ( gt @ SV62 @ SV52 )
= $false )
| ( ( lt @ SV52 @ SV62 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[476]) ).
thf(494,plain,
! [SV63: $i,SV53: $i] :
( ( ( lt @ SV53 @ SV63 )
= $false )
| ( ( gt @ SV63 @ SV53 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[477]) ).
thf(495,plain,
! [SV54: $i,SV64: $i] :
( ( ( gt @ ( succ @ SV64 ) @ SV54 )
= $false )
| ( ( leq @ SV54 @ SV64 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[478]) ).
thf(496,plain,
! [SV65: $i,SV55: $i] :
( ( ( leq @ SV55 @ SV65 )
= $false )
| ( ( gt @ ( succ @ SV65 ) @ SV55 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[479]) ).
thf(497,plain,
! [SV66: $i,SV56: $i] :
( ( ( geq @ SV56 @ SV66 )
= $false )
| ( ( leq @ SV66 @ SV56 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[480]) ).
thf(498,plain,
! [SV57: $i,SV67: $i] :
( ( ( leq @ SV67 @ SV57 )
= $false )
| ( ( geq @ SV57 @ SV67 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[481]) ).
thf(499,plain,
! [SV12: $i] :
( ( ( SV12 = n2 )
= $true )
| ( ( ( SV12 = n0 )
| ( SV12 = n1 ) )
= $true )
| ( ( SV12 = n3 )
= $true )
| ( ( SV12 = n4 )
= $true )
| ( ( leq @ n0 @ SV12 )
= $false )
| ( ( leq @ SV12 @ n4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[482]) ).
thf(500,plain,
! [SV16: $i] :
( ( ( SV16 = n0 )
= $true )
| ( ( SV16 = n1 )
= $true )
| ( ( SV16 = n2 )
= $true )
| ( ( SV16 = n3 )
= $true )
| ( ( leq @ n0 @ SV16 )
= $false )
| ( ( leq @ SV16 @ n3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[484]) ).
thf(501,plain,
! [SV34: $i] :
( ( ( SV34 = n3 )
= $true )
| ( ( ( SV34 = n2 )
| ( SV34 = n0 )
| ( SV34 = n1 ) )
= $true )
| ( ( SV34 = n4 )
= $true )
| ( ( SV34 = n5 )
= $true )
| ( ( leq @ n0 @ SV34 )
= $false )
| ( ( leq @ SV34 @ n5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[487]) ).
thf(502,plain,
! [SV35: $i] :
( ( ( SV35 = n4 )
= $true )
| ( ( ( SV35 = n3 )
| ( SV35 = n2 )
| ( SV35 = n0 )
| ( SV35 = n1 ) )
= $true )
| ( ( SV35 = n5 )
= $true )
| ( ( SV35 = n6 )
= $true )
| ( ( leq @ n0 @ SV35 )
= $false )
| ( ( leq @ SV35 @ n6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[488]) ).
thf(503,plain,
! [SV12: $i] :
( ( ( SV12 = n0 )
= $true )
| ( ( SV12 = n1 )
= $true )
| ( ( SV12 = n2 )
= $true )
| ( ( SV12 = n3 )
= $true )
| ( ( SV12 = n4 )
= $true )
| ( ( leq @ n0 @ SV12 )
= $false )
| ( ( leq @ SV12 @ n4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[499]) ).
thf(504,plain,
! [SV34: $i] :
( ( ( SV34 = n2 )
= $true )
| ( ( ( SV34 = n0 )
| ( SV34 = n1 ) )
= $true )
| ( ( SV34 = n3 )
= $true )
| ( ( SV34 = n4 )
= $true )
| ( ( SV34 = n5 )
= $true )
| ( ( leq @ n0 @ SV34 )
= $false )
| ( ( leq @ SV34 @ n5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[501]) ).
thf(505,plain,
! [SV35: $i] :
( ( ( SV35 = n3 )
= $true )
| ( ( ( SV35 = n2 )
| ( SV35 = n0 )
| ( SV35 = n1 ) )
= $true )
| ( ( SV35 = n4 )
= $true )
| ( ( SV35 = n5 )
= $true )
| ( ( SV35 = n6 )
= $true )
| ( ( leq @ n0 @ SV35 )
= $false )
| ( ( leq @ SV35 @ n6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[502]) ).
thf(506,plain,
! [SV34: $i] :
( ( ( SV34 = n0 )
= $true )
| ( ( SV34 = n1 )
= $true )
| ( ( SV34 = n2 )
= $true )
| ( ( SV34 = n3 )
= $true )
| ( ( SV34 = n4 )
= $true )
| ( ( SV34 = n5 )
= $true )
| ( ( leq @ n0 @ SV34 )
= $false )
| ( ( leq @ SV34 @ n5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[504]) ).
thf(507,plain,
! [SV35: $i] :
( ( ( SV35 = n2 )
= $true )
| ( ( ( SV35 = n0 )
| ( SV35 = n1 ) )
= $true )
| ( ( SV35 = n3 )
= $true )
| ( ( SV35 = n4 )
= $true )
| ( ( SV35 = n5 )
= $true )
| ( ( SV35 = n6 )
= $true )
| ( ( leq @ n0 @ SV35 )
= $false )
| ( ( leq @ SV35 @ n6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[505]) ).
thf(508,plain,
! [SV35: $i] :
( ( ( SV35 = n0 )
= $true )
| ( ( SV35 = n1 )
= $true )
| ( ( SV35 = n2 )
= $true )
| ( ( SV35 = n3 )
= $true )
| ( ( SV35 = n4 )
= $true )
| ( ( SV35 = n5 )
= $true )
| ( ( SV35 = n6 )
= $true )
| ( ( leq @ n0 @ SV35 )
= $false )
| ( ( leq @ SV35 @ n6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[507]) ).
thf(509,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[226,508,506,503,500,498,497,496,495,494,493,492,491,490,489,486,485,483,465,451,445,431,430,428,425,419,418,417,372,356,352,351,350,349,348,347,346,344,340,330,329,328,327,326,325,324,323,314,313,312,311,310,309,308,307,306,303,302,301,279,278,277,276,275,274,268,267,266,265,264,263,262,261,260,259,258,257,256,255,254,253,252,251,250,249,248,247,246,245,244,243,242,241,240,239,238,237,236,235]) ).
thf(510,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[509]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV123+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.03/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.34 % Computer : n015.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Wed Jun 15 03:29:09 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.21/0.39 .
% 0.21/0.51
% 0.21/0.51 No.of.Axioms: 101
% 0.21/0.51
% 0.21/0.51 Length.of.Defs: 0
% 0.21/0.51
% 0.21/0.51 Contains.Choice.Funs: false
% 0.21/0.54 .....
% 0.40/0.56 (rf:2,axioms:84,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:103,loop_count:0,foatp_calls:0,translation:fof_full)...................
% 0.51/0.66
% 0.51/0.66 ********************************
% 0.51/0.66 * All subproblems solved! *
% 0.51/0.66 ********************************
% 0.51/0.66 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:2,axioms:93,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:509,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.51/0.71
% 0.51/0.71 %**** Beginning of derivation protocol ****
% 0.51/0.71 % SZS output start CNFRefutation
% See solution above
% 0.51/0.71
% 0.51/0.71 %**** End of derivation protocol ****
% 0.51/0.71 %**** no. of clauses in derivation: 493 ****
% 0.51/0.71 %**** clause counter: 509 ****
% 0.51/0.71
% 0.51/0.71 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:2,axioms:93,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:509,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------