%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM926+6 : TPTP v9.3.1. Released v5.3.0.
% 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 : n016.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 10:35:47 AM UTC 2026
% Result : Theorem 221.41s 37.38s
% Output : CNFRefutation 37.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 542
% Syntax : Number of formulae : 5358 (2872 unt; 0 typ; 0 def)
% Number of atoms : 30903 (12521 equ; 0 cnn)
% Maximal formula atoms : 7 ( 5 avg)
% Number of connectives : 91681 (8531 ~;7989 |; 126 &;73463 @)
% ( 333 <=>;1239 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 76 ( 73 usr; 18 con; 0-4 aty)
% Number of variables : 13428 ( 0 ^;13397 !; 31 ?;13428 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_ab_group_add,type,
ab_group_add: $i > $o ).
thf(tp_bit0,type,
bit0: $i > $i ).
thf(tp_bit1,type,
bit1: $i > $i ).
thf(tp_bool,type,
bool: $i ).
thf(tp_comm_monoid_mult,type,
comm_monoid_mult: $i > $o ).
thf(tp_comm_ring_1,type,
comm_ring_1: $i > $o ).
thf(tp_comm_semiring,type,
comm_semiring: $i > $o ).
thf(tp_comm_semiring_1,type,
comm_semiring_1: $i > $o ).
thf(tp_dvd,type,
dvd: $i > $o ).
thf(tp_dvd_dvd,type,
dvd_dvd: $i > $i > $i > $o ).
thf(tp_int,type,
int: $i ).
thf(tp_legendre,type,
legendre: $i > $i > $i ).
thf(tp_linord219039673up_add,type,
linord219039673up_add: $i > $o ).
thf(tp_linord581940658strict,type,
linord581940658strict: $i > $o ).
thf(tp_linord626643107strict,type,
linord626643107strict: $i > $o ).
thf(tp_linorder,type,
linorder: $i > $o ).
thf(tp_linordered_idom,type,
linordered_idom: $i > $o ).
thf(tp_linordered_ring,type,
linordered_ring: $i > $o ).
thf(tp_linordered_semidom,type,
linordered_semidom: $i > $o ).
thf(tp_m,type,
m: $i ).
thf(tp_min,type,
min: $i ).
thf(tp_minus_minus,type,
minus_minus: $i > $i > $i > $i ).
thf(tp_monoid_mult,type,
monoid_mult: $i > $o ).
thf(tp_mult_zero,type,
mult_zero: $i > $o ).
thf(tp_nat,type,
nat: $i ).
thf(tp_no_zero_divisors,type,
no_zero_divisors: $i > $o ).
thf(tp_number,type,
number: $i > $o ).
thf(tp_number_number_of,type,
number_number_of: $i > $i > $i ).
thf(tp_number_ring,type,
number_ring: $i > $o ).
thf(tp_number_semiring,type,
number_semiring: $i > $o ).
thf(tp_one_one,type,
one_one: $i > $i ).
thf(tp_ord_less,type,
ord_less: $i > $i > $i > $o ).
thf(tp_ord_less_eq,type,
ord_less_eq: $i > $i > $i > $o ).
thf(tp_order,type,
order: $i > $o ).
thf(tp_ordere453448008miring,type,
ordere453448008miring: $i > $o ).
thf(tp_pls,type,
pls: $i ).
thf(tp_plus_plus,type,
plus_plus: $i > $i > $i > $i ).
thf(tp_power,type,
power: $i > $o ).
thf(tp_power_power,type,
power_power: $i > $i > $i > $i ).
thf(tp_product_Pair,type,
product_Pair: $i > $i > $i > $i > $i ).
thf(tp_product_prod,type,
product_prod: $i > $i > $i ).
thf(tp_quadRes,type,
quadRes: $i > $i > $o ).
thf(tp_real,type,
real: $i ).
thf(tp_ring,type,
ring: $i > $o ).
thf(tp_ring_1,type,
ring_1: $i > $o ).
thf(tp_ring_11004092258visors,type,
ring_11004092258visors: $i > $o ).
thf(tp_ring_char_0,type,
ring_char_0: $i > $o ).
thf(tp_ring_n68954251visors,type,
ring_n68954251visors: $i > $o ).
thf(tp_s,type,
s: $i ).
thf(tp_s1,type,
s1: $i ).
thf(tp_sK1_S1,type,
sK1_S1: $i ).
thf(tp_sK2_SX0,type,
sK2_SX0: $i ).
thf(tp_sK3_SX0,type,
sK3_SX0: $i ).
thf(tp_sK4_SX0,type,
sK4_SX0: $i ).
thf(tp_sK5_SY1968,type,
sK5_SY1968: $i ).
thf(tp_sK6_SY2112,type,
sK6_SY2112: $i ).
thf(tp_sK7_SY1807,type,
sK7_SY1807: $i > $i > $i ).
thf(tp_sK8_SY1865,type,
sK8_SY1865: $i > $i > $i ).
thf(tp_sK9_SY1940,type,
sK9_SY1940: $i > $i > $i > $i ).
thf(tp_semiri456707255roduct,type,
semiri456707255roduct: $i > $o ).
thf(tp_semiring,type,
semiring: $i > $o ).
thf(tp_semiring_0,type,
semiring_0: $i > $o ).
thf(tp_semiring_1,type,
semiring_1: $i > $o ).
thf(tp_t,type,
t: $i ).
thf(tp_ti,type,
ti: $i > $i > $i ).
thf(tp_times_times,type,
times_times: $i > $i > $i > $i ).
thf(tp_twoSqu420862341sum2sq,type,
twoSqu420862341sum2sq: $i > $o ).
thf(tp_twoSqu579703163sum2sq,type,
twoSqu579703163sum2sq: $i > $i ).
thf(tp_undefined,type,
undefined: $i > $i ).
thf(tp_zcong,type,
zcong: $i > $i > $i > $o ).
thf(tp_zero_neq_one,type,
zero_neq_one: $i > $o ).
thf(tp_zero_zero,type,
zero_zero: $i > $i ).
thf(tp_zprime,type,
zprime: $i > $o ).
thf(35,axiom,
dvd @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Odvd) ).
thf(36,axiom,
number @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber) ).
thf(37,axiom,
power @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Power_Opower) ).
thf(38,axiom,
semiring @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring) ).
thf(39,axiom,
order @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Oorder) ).
thf(40,axiom,
mult_zero @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Omult__zero) ).
thf(41,axiom,
semiring_0 @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__0) ).
thf(42,axiom,
semiring_1 @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__1) ).
thf(43,axiom,
monoid_mult @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Omonoid__mult) ).
thf(44,axiom,
linorder @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Olinorder) ).
thf(45,axiom,
zero_neq_one @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ozero__neq__one) ).
thf(46,axiom,
number_semiring @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber__semiring) ).
thf(47,axiom,
comm_semiring @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ocomm__semiring) ).
thf(48,axiom,
comm_semiring_1 @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ocomm__semiring__1) ).
thf(49,axiom,
no_zero_divisors @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ono__zero__divisors) ).
thf(50,axiom,
comm_monoid_mult @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocomm__monoid__mult) ).
thf(51,axiom,
linordered_semidom @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Olinordered__semidom) ).
thf(52,axiom,
ordere453448008miring @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Oordered__cancel__semiring) ).
thf(53,axiom,
semiri456707255roduct @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduc) ).
thf(54,axiom,
dvd @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Odvd) ).
thf(55,axiom,
number @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber) ).
thf(56,axiom,
ring @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring) ).
thf(57,axiom,
power @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Power_Opower) ).
thf(58,axiom,
ring_1 @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring__1) ).
thf(59,axiom,
semiring @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring) ).
thf(60,axiom,
number_ring @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
thf(61,axiom,
ring_char_0 @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Oring__char__0) ).
thf(62,axiom,
order @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Oorder) ).
thf(63,axiom,
mult_zero @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Omult__zero) ).
thf(64,axiom,
semiring_0 @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring__0) ).
thf(65,axiom,
semiring_1 @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring__1) ).
thf(66,axiom,
comm_ring_1 @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ocomm__ring__1) ).
thf(67,axiom,
monoid_mult @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Omonoid__mult) ).
thf(68,axiom,
linorder @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Olinorder) ).
thf(69,axiom,
zero_neq_one @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ozero__neq__one) ).
thf(70,axiom,
ab_group_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oab__group__add) ).
thf(71,axiom,
number_semiring @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__semiring) ).
thf(72,axiom,
comm_semiring @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ocomm__semiring) ).
thf(73,axiom,
comm_semiring_1 @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ocomm__semiring__1) ).
thf(74,axiom,
linordered_idom @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__idom) ).
thf(75,axiom,
linordered_ring @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__ring) ).
thf(76,axiom,
no_zero_divisors @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ono__zero__divisors) ).
thf(77,axiom,
comm_monoid_mult @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocomm__monoid__mult) ).
thf(78,axiom,
linordered_semidom @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__semidom) ).
thf(79,axiom,
ring_n68954251visors @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring__no__zero__divisors) ).
thf(80,axiom,
linord581940658strict @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__ring__strict) ).
thf(81,axiom,
ordere453448008miring @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oordered__cancel__semiring) ).
thf(82,axiom,
ring_11004092258visors @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring__1__no__zero__divisors) ).
thf(83,axiom,
linord219039673up_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Olinordered__ab__group__add) ).
thf(84,axiom,
linord626643107strict @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__semiring__1__strict) ).
thf(85,axiom,
semiri456707255roduct @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduc) ).
thf(86,axiom,
! [X_a: $i] :
( ( ordere453448008miring @ X_a )
=> ! [B: $i,A_1: $i] :
( ( ord_less_eq @ X_a @ A_1 @ ( zero_zero @ X_a ) )
=> ( ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ B )
=> ( ord_less_eq @ X_a @ ( times_times @ X_a @ A_1 @ B ) @ ( zero_zero @ X_a ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_496_mult__nonpos__nonneg) ).
thf(87,axiom,
! [X_a: $i] :
( ( ordere453448008miring @ X_a )
=> ! [B: $i,A_1: $i] :
( ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ A_1 )
=> ( ( ord_less_eq @ X_a @ B @ ( zero_zero @ X_a ) )
=> ( ord_less_eq @ X_a @ ( times_times @ X_a @ B @ A_1 ) @ ( zero_zero @ X_a ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_495_mult__nonneg__nonpos2) ).
thf(88,axiom,
! [X_a: $i] :
( ( ordere453448008miring @ X_a )
=> ! [B: $i,A_1: $i] :
( ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ A_1 )
=> ( ( ord_less_eq @ X_a @ B @ ( zero_zero @ X_a ) )
=> ( ord_less_eq @ X_a @ ( times_times @ X_a @ A_1 @ B ) @ ( zero_zero @ X_a ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_494_mult__nonneg__nonpos) ).
thf(89,axiom,
! [X_a: $i] :
( ( ordere453448008miring @ X_a )
=> ! [B: $i,A_1: $i] :
( ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ A_1 )
=> ( ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ B )
=> ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ ( times_times @ X_a @ A_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_493_mult__nonneg__nonneg) ).
thf(90,axiom,
! [X_a: $i] :
( ( linord581940658strict @ X_a )
=> ! [A_2: $i,B_1: $i] :
( ( ord_less_eq @ X_a @ ( times_times @ X_a @ A_2 @ B_1 ) @ ( zero_zero @ X_a ) )
<=> ( ( ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ A_2 )
& ( ord_less_eq @ X_a @ B_1 @ ( zero_zero @ X_a ) ) )
| ( ( ord_less_eq @ X_a @ A_2 @ ( zero_zero @ X_a ) )
& ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ B_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_492_mult__le__0__iff) ).
thf(91,axiom,
! [X_a: $i] :
( ( linord581940658strict @ X_a )
=> ! [A_2: $i,B_1: $i] :
( ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ ( times_times @ X_a @ A_2 @ B_1 ) )
<=> ( ( ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ A_2 )
& ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ B_1 ) )
| ( ( ord_less_eq @ X_a @ A_2 @ ( zero_zero @ X_a ) )
& ( ord_less_eq @ X_a @ B_1 @ ( zero_zero @ X_a ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_491_zero__le__mult__iff) ).
thf(92,axiom,
! [X_a: $i] :
( ( linordered_ring @ X_a )
=> ! [A_1: $i] : ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ ( times_times @ X_a @ A_1 @ A_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_490_zero__le__square) ).
thf(94,axiom,
! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i] : ( dvd_dvd @ X_a @ ( one_one @ X_a ) @ A_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_488_one__dvd) ).
thf(95,axiom,
! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [C: $i,A_1: $i,B: $i] :
( ( dvd_dvd @ X_a @ A_1 @ B )
=> ( ( dvd_dvd @ X_a @ A_1 @ C )
=> ( dvd_dvd @ X_a @ A_1 @ ( plus_plus @ X_a @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_487_dvd__add) ).
thf(96,axiom,
! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i,B: $i,C: $i] :
( ( dvd_dvd @ X_a @ ( times_times @ X_a @ A_1 @ B ) @ C )
=> ( dvd_dvd @ X_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_486_dvd__mult__right) ).
thf(97,axiom,
! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i,B: $i,C: $i] :
( ( dvd_dvd @ X_a @ ( times_times @ X_a @ A_1 @ B ) @ C )
=> ( dvd_dvd @ X_a @ A_1 @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_485_dvd__mult__left) ).
thf(98,axiom,
! [X_a: $i] :
( ( dvd @ X_a )
=> ! [A_1: $i,B: $i,K: $i] :
( ( A_1
= ( times_times @ X_a @ B @ K ) )
=> ( dvd_dvd @ X_a @ B @ A_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_484_dvdI) ).
thf(99,axiom,
! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [C: $i,D: $i,A_1: $i,B: $i] :
( ( dvd_dvd @ X_a @ A_1 @ B )
=> ( ( dvd_dvd @ X_a @ C @ D )
=> ( dvd_dvd @ X_a @ ( times_times @ X_a @ A_1 @ C ) @ ( times_times @ X_a @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_483_mult__dvd__mono) ).
thf(100,axiom,
! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [B: $i,A_1: $i,C: $i] :
( ( dvd_dvd @ X_a @ A_1 @ C )
=> ( dvd_dvd @ X_a @ A_1 @ ( times_times @ X_a @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_482_dvd__mult) ).
thf(101,axiom,
! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [C: $i,A_1: $i,B: $i] :
( ( dvd_dvd @ X_a @ A_1 @ B )
=> ( dvd_dvd @ X_a @ A_1 @ ( times_times @ X_a @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_481_dvd__mult2) ).
thf(102,axiom,
! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i,B: $i] : ( dvd_dvd @ X_a @ A_1 @ ( times_times @ X_a @ B @ A_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_480_dvd__triv__right) ).
thf(103,axiom,
! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i,B: $i] : ( dvd_dvd @ X_a @ A_1 @ ( times_times @ X_a @ A_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_479_dvd__triv__left) ).
thf(105,axiom,
! [X_a: $i] :
( ( semiring @ X_a )
=> ! [A_1: $i,E: $i,B: $i,C: $i] :
( ( plus_plus @ X_a @ ( times_times @ X_a @ A_1 @ E ) @ ( plus_plus @ X_a @ ( times_times @ X_a @ B @ E ) @ C ) )
= ( plus_plus @ X_a @ ( times_times @ X_a @ ( plus_plus @ X_a @ A_1 @ B ) @ E ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_477_combine__common__factor) ).
thf(106,axiom,
! [X_a: $i] :
( ( comm_semiring @ X_a )
=> ! [A_1: $i,B: $i,C: $i] :
( ( times_times @ X_a @ ( plus_plus @ X_a @ A_1 @ B ) @ C )
= ( plus_plus @ X_a @ ( times_times @ X_a @ A_1 @ C ) @ ( times_times @ X_a @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_476_comm__semiring__class_Odistrib) ).
thf(107,axiom,
! [X_a: $i] :
( ( zero_neq_one @ X_a )
=> ( ( zero_zero @ X_a )
!= ( one_one @ X_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_475_zero__neq__one) ).
thf(108,axiom,
! [X_a: $i] :
( ( zero_neq_one @ X_a )
=> ( ( one_one @ X_a )
!= ( zero_zero @ X_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_474_one__neq__zero) ).
thf(109,axiom,
! [X_a: $i] :
( ( no_zero_divisors @ X_a )
=> ! [A_1: $i,B: $i] :
( ( ( times_times @ X_a @ A_1 @ B )
= ( zero_zero @ X_a ) )
=> ( ( ( ti @ X_a @ A_1 )
= ( zero_zero @ X_a ) )
| ( ( ti @ X_a @ B )
= ( zero_zero @ X_a ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_473_divisors__zero) ).
thf(110,axiom,
! [X_a: $i] :
( ( no_zero_divisors @ X_a )
=> ! [B: $i,A_1: $i] :
( ( ( ti @ X_a @ A_1 )
!= ( zero_zero @ X_a ) )
=> ( ( ( ti @ X_a @ B )
!= ( zero_zero @ X_a ) )
=> ( ( times_times @ X_a @ A_1 @ B )
!= ( zero_zero @ X_a ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_472_no__zero__divisors) ).
thf(111,axiom,
! [X_a: $i] :
( ( ring_n68954251visors @ X_a )
=> ! [A_2: $i,B_1: $i] :
( ( ( times_times @ X_a @ A_2 @ B_1 )
= ( zero_zero @ X_a ) )
<=> ( ( ( ti @ X_a @ A_2 )
= ( zero_zero @ X_a ) )
| ( ( ti @ X_a @ B_1 )
= ( zero_zero @ X_a ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_471_mult__eq__0__iff) ).
thf(112,axiom,
! [X_a: $i] :
( ( mult_zero @ X_a )
=> ! [A_1: $i] :
( ( times_times @ X_a @ A_1 @ ( zero_zero @ X_a ) )
= ( zero_zero @ X_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_470_mult__zero__right) ).
thf(113,axiom,
! [X_a: $i] :
( ( mult_zero @ X_a )
=> ! [A_1: $i] :
( ( times_times @ X_a @ ( zero_zero @ X_a ) @ A_1 )
= ( zero_zero @ X_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_469_mult__zero__left) ).
thf(118,axiom,
! [A_1: $i,N: $i] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
=> ( ( ord_less @ real @ ( zero_zero @ real ) @ A_1 )
=> ? [R: $i] :
( ( ord_less @ real @ ( zero_zero @ real ) @ R )
& ( ( power_power @ real @ R @ N )
= A_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_464_realpow__pos__nth) ).
thf(120,axiom,
ord_less_eq @ int @ ( zero_zero @ int ) @ ( number_number_of @ int @ ( bit1 @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_462_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J) ).
thf(121,axiom,
! [N: $i,X_1: $i] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ X_1 )
=> ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( power_power @ int @ X_1 @ N ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_461_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) ).
thf(122,axiom,
! [Y_1: $i,X_1: $i] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ X_1 )
=> ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ Y_1 )
=> ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ X_1 @ Y_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_460_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) ).
thf(123,axiom,
! [Y_1: $i,X_1: $i] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ X_1 )
=> ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ Y_1 )
=> ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( times_times @ int @ X_1 @ Y_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_459_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) ).
thf(124,axiom,
ord_less_eq @ int @ ( zero_zero @ int ) @ ( one_one @ int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_458_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).
thf(125,axiom,
ord_less_eq @ int @ ( zero_zero @ int ) @ ( zero_zero @ int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_457_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).
thf(130,axiom,
! [X_a: $i] :
( ( power @ X_a )
=> ! [M: $i,N: $i] :
( ( ( N
= ( zero_zero @ nat ) )
=> ( ( power_power @ X_a @ M @ N )
= ( one_one @ X_a ) ) )
& ( ( N
!= ( zero_zero @ nat ) )
=> ( ( power_power @ X_a @ M @ N )
= ( times_times @ X_a @ M @ ( power_power @ X_a @ M @ ( minus_minus @ nat @ N @ ( one_one @ nat ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_452_realpow__num__eq__if) ).
thf(131,axiom,
ord_less_eq @ int @ ( zero_zero @ int ) @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_451_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J) ).
thf(133,axiom,
! [B: $i,Q: $i,R_1: $i,B_2: $i,Q_1: $i,R_2: $i] :
( ( ( plus_plus @ int @ ( times_times @ int @ B @ Q ) @ R_1 )
= ( plus_plus @ int @ ( times_times @ int @ B_2 @ Q_1 ) @ R_2 ) )
=> ( ( ord_less @ int @ ( plus_plus @ int @ ( times_times @ int @ B_2 @ Q_1 ) @ R_2 ) @ ( zero_zero @ int ) )
=> ( ( ord_less @ int @ R_1 @ B )
=> ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ R_2 )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ B_2 )
=> ( ( ord_less_eq @ int @ B_2 @ B )
=> ( ord_less_eq @ int @ Q_1 @ Q ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_449_zdiv__mono2__neg__lemma) ).
thf(134,axiom,
! [B: $i,Q_1: $i,R_2: $i,Q: $i,R_1: $i] :
( ( ord_less_eq @ int @ ( plus_plus @ int @ ( times_times @ int @ B @ Q_1 ) @ R_2 ) @ ( plus_plus @ int @ ( times_times @ int @ B @ Q ) @ R_1 ) )
=> ( ( ord_less_eq @ int @ R_1 @ ( zero_zero @ int ) )
=> ( ( ord_less @ int @ B @ R_1 )
=> ( ( ord_less @ int @ B @ R_2 )
=> ( ord_less_eq @ int @ Q @ Q_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_448_unique__quotient__lemma__neg) ).
thf(135,axiom,
! [B: $i,Q: $i,R_1: $i,B_2: $i,Q_1: $i,R_2: $i] :
( ( ( plus_plus @ int @ ( times_times @ int @ B @ Q ) @ R_1 )
= ( plus_plus @ int @ ( times_times @ int @ B_2 @ Q_1 ) @ R_2 ) )
=> ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( times_times @ int @ B_2 @ Q_1 ) @ R_2 ) )
=> ( ( ord_less @ int @ R_2 @ B_2 )
=> ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ R_1 )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ B_2 )
=> ( ( ord_less_eq @ int @ B_2 @ B )
=> ( ord_less_eq @ int @ Q @ Q_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_447_zdiv__mono2__lemma) ).
thf(136,axiom,
! [B: $i,Q_1: $i,R_2: $i,Q: $i,R_1: $i] :
( ( ord_less_eq @ int @ ( plus_plus @ int @ ( times_times @ int @ B @ Q_1 ) @ R_2 ) @ ( plus_plus @ int @ ( times_times @ int @ B @ Q ) @ R_1 ) )
=> ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ R_2 )
=> ( ( ord_less @ int @ R_2 @ B )
=> ( ( ord_less @ int @ R_1 @ B )
=> ( ord_less_eq @ int @ Q_1 @ Q ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_446_unique__quotient__lemma) ).
thf(137,axiom,
! [B_2: $i,Q_1: $i,R_2: $i] :
( ( ord_less @ int @ ( plus_plus @ int @ ( times_times @ int @ B_2 @ Q_1 ) @ R_2 ) @ ( zero_zero @ int ) )
=> ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ R_2 )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ B_2 )
=> ( ord_less_eq @ int @ Q_1 @ ( zero_zero @ int ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_445_q__neg__lemma) ).
thf(138,axiom,
! [B_2: $i,Q_1: $i,R_2: $i] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( times_times @ int @ B_2 @ Q_1 ) @ R_2 ) )
=> ( ( ord_less @ int @ R_2 @ B_2 )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ B_2 )
=> ( ord_less_eq @ int @ ( zero_zero @ int ) @ Q_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_444_q__pos__lemma) ).
thf(139,axiom,
! [N: $i] : ( ord_less_eq @ real @ ( one_one @ real ) @ ( power_power @ real @ ( number_number_of @ real @ ( bit0 @ ( bit1 @ pls ) ) ) @ N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_443_two__realpow__ge__one) ).
thf(141,axiom,
! [X_a: $i] :
( ( ring_1 @ X_a )
=> ! [X_1: $i] :
( ( minus_minus @ X_a @ ( times_times @ X_a @ X_1 @ X_1 ) @ ( one_one @ X_a ) )
= ( times_times @ X_a @ ( plus_plus @ X_a @ X_1 @ ( one_one @ X_a ) ) @ ( minus_minus @ X_a @ X_1 @ ( one_one @ X_a ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_441_real__squared__diff__one__factored) ).
thf(142,axiom,
! [X_2: $i,Y_2: $i] :
( ( ( plus_plus @ real @ ( times_times @ real @ X_2 @ X_2 ) @ ( times_times @ real @ Y_2 @ Y_2 ) )
= ( zero_zero @ real ) )
<=> ( ( X_2
= ( zero_zero @ real ) )
& ( Y_2
= ( zero_zero @ real ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_440_real__two__squares__add__zero__iff) ).
thf(143,axiom,
! [X_2: $i,Y_2: $i,Z_1: $i] :
( ( ord_less @ real @ ( zero_zero @ real ) @ Z_1 )
=> ( ( ord_less @ real @ ( times_times @ real @ X_2 @ Z_1 ) @ ( times_times @ real @ Y_2 @ Z_1 ) )
<=> ( ord_less @ real @ X_2 @ Y_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_439_real__mult__less__iff1) ).
thf(146,axiom,
! [Y_1: $i,X_1: $i] :
( ( ord_less @ real @ ( zero_zero @ real ) @ X_1 )
=> ( ( ord_less @ real @ ( zero_zero @ real ) @ Y_1 )
=> ( ord_less @ real @ ( zero_zero @ real ) @ ( times_times @ real @ X_1 @ Y_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_436_real__mult__order) ).
thf(147,axiom,
! [X_1: $i,Y_1: $i,Z: $i] :
( ( ord_less @ real @ ( zero_zero @ real ) @ Z )
=> ( ( ord_less @ real @ X_1 @ Y_1 )
=> ( ord_less @ real @ ( times_times @ real @ Z @ X_1 ) @ ( times_times @ real @ Z @ Y_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_435_real__mult__less__mono2) ).
thf(148,axiom,
! [X_a: $i] :
( ( ring @ X_a )
=> ! [X_1: $i,Y_1: $i,A_1: $i,B: $i] :
( ( minus_minus @ X_a @ ( times_times @ X_a @ X_1 @ Y_1 ) @ ( times_times @ X_a @ A_1 @ B ) )
= ( plus_plus @ X_a @ ( times_times @ X_a @ X_1 @ ( minus_minus @ X_a @ Y_1 @ B ) ) @ ( times_times @ X_a @ ( minus_minus @ X_a @ X_1 @ A_1 ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_434_mult__diff__mult) ).
thf(149,axiom,
! [Z1: $i,Z2: $i,W: $i] :
( ( times_times @ real @ ( plus_plus @ real @ Z1 @ Z2 ) @ W )
= ( plus_plus @ real @ ( times_times @ real @ Z1 @ W ) @ ( times_times @ real @ Z2 @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_433_real__add__mult__distrib) ).
thf(150,axiom,
! [A_2: $i,B_1: $i,C_1: $i] :
( ( C_1
!= ( zero_zero @ real ) )
=> ( ( ( times_times @ real @ A_2 @ C_1 )
= ( times_times @ real @ B_1 @ C_1 ) )
<=> ( A_2 = B_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_432_real__mult__right__cancel) ).
thf(151,axiom,
! [A_2: $i,B_1: $i,C_1: $i] :
( ( C_1
!= ( zero_zero @ real ) )
=> ( ( ( times_times @ real @ C_1 @ A_2 )
= ( times_times @ real @ C_1 @ B_1 ) )
<=> ( A_2 = B_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_431_real__mult__left__cancel) ).
thf(152,axiom,
! [X_a: $i] :
( ( ab_group_add @ X_a )
=> ! [A_1: $i,C: $i,B: $i,D: $i] :
( ( minus_minus @ X_a @ ( plus_plus @ X_a @ A_1 @ C ) @ ( plus_plus @ X_a @ B @ D ) )
= ( plus_plus @ X_a @ ( minus_minus @ X_a @ A_1 @ B ) @ ( minus_minus @ X_a @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_430_add__diff__add) ).
thf(153,axiom,
! [Z: $i,X_1: $i,Y_1: $i] :
( ( ord_less_eq @ real @ X_1 @ Y_1 )
=> ( ord_less_eq @ real @ ( plus_plus @ real @ Z @ X_1 ) @ ( plus_plus @ real @ Z @ Y_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_429_real__add__left__mono) ).
thf(154,axiom,
! [Z1: $i,Z2: $i,Z3: $i] :
( ( times_times @ real @ ( times_times @ real @ Z1 @ Z2 ) @ Z3 )
= ( times_times @ real @ Z1 @ ( times_times @ real @ Z2 @ Z3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_428_real__mult__assoc) ).
thf(155,axiom,
! [Z: $i,W: $i] :
( ( times_times @ real @ Z @ W )
= ( times_times @ real @ W @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_427_real__mult__commute) ).
thf(156,axiom,
! [Z: $i] :
( ( times_times @ real @ ( one_one @ real ) @ Z )
= Z ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_426_real__mult__1) ).
thf(160,axiom,
( ( zero_zero @ real )
!= ( one_one @ real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_422_real__zero__not__eq__one) ).
thf(162,axiom,
! [X_2: $i,Y_2: $i] :
( ( ( plus_plus @ real @ ( power_power @ real @ X_2 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ real @ Y_2 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ real ) )
<=> ( ( X_2
= ( zero_zero @ real ) )
& ( Y_2
= ( zero_zero @ real ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_420_realpow__two__sum__zero__iff) ).
thf(163,axiom,
! [Ma: $i,X_2: $i] :
( ( quadRes @ Ma @ X_2 )
<=> ? [Y: $i] : ( zcong @ ( power_power @ int @ Y @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ X_2 @ Ma ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_419_QuadRes__def) ).
thf(167,axiom,
! [X_1: $i,Q: $i,N: $i,R_1: $i] :
( ( X_1
= ( plus_plus @ nat @ ( times_times @ nat @ Q @ N ) @ R_1 ) )
=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ R_1 )
=> ( ( ord_less @ nat @ R_1 @ N )
=> ~ ( dvd_dvd @ nat @ N @ X_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_415_divides__div__not) ).
thf(168,axiom,
! [Y_1: $i,X_1: $i,P: $i] :
( ( zprime @ P )
=> ( ~ ( zcong @ X_1 @ ( zero_zero @ int ) @ P )
=> ( ~ ( zcong @ Y_1 @ ( zero_zero @ int ) @ P )
=> ~ ( zcong @ ( times_times @ int @ X_1 @ Y_1 ) @ ( zero_zero @ int ) @ P ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_414_zcong__zmult__prop3) ).
thf(169,axiom,
! [P: $i,Y_1: $i,N: $i] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
=> ( ( dvd_dvd @ int @ P @ Y_1 )
=> ( dvd_dvd @ int @ P @ ( power_power @ int @ Y_1 @ N ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_413_zpower__zdvd__prop1) ).
thf(171,axiom,
! [M: $i,N: $i,P: $i] :
( ( zprime @ P )
=> ( ( dvd_dvd @ int @ P @ ( times_times @ int @ M @ N ) )
=> ( ( dvd_dvd @ int @ P @ M )
| ( dvd_dvd @ int @ P @ N ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_411_zprime__zdvd__zmult__better) ).
thf(172,axiom,
! [X_2: $i,N_1: $i] :
( ( ( power_power @ nat @ X_2 @ N_1 )
= ( one_one @ nat ) )
<=> ( ( X_2
= ( one_one @ nat ) )
| ( N_1
= ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_410_exp__eq__1) ).
thf(173,axiom,
! [X_2: $i,P_1: $i] :
( ( zcong @ X_2 @ ( zero_zero @ int ) @ P_1 )
<=> ( dvd_dvd @ int @ P_1 @ X_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_409_zcong__eq__zdvd__prop) ).
thf(174,axiom,
! [A_2: $i,Ma: $i] :
( ( zcong @ A_2 @ ( zero_zero @ int ) @ Ma )
<=> ( dvd_dvd @ int @ Ma @ A_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_408_zcong__zero__equiv__div) ).
thf(175,axiom,
! [A_1: $i,N: $i,B: $i] :
( ( dvd_dvd @ nat @ ( power_power @ nat @ A_1 @ N ) @ ( power_power @ nat @ B @ N ) )
=> ( ( N
!= ( zero_zero @ nat ) )
=> ( dvd_dvd @ nat @ A_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_407_divides__rev) ).
thf(176,axiom,
! [X_1: $i,Y_1: $i,N: $i] :
( ( N
!= ( zero_zero @ nat ) )
=> ( ( dvd_dvd @ nat @ ( power_power @ nat @ X_1 @ N ) @ Y_1 )
=> ( dvd_dvd @ nat @ X_1 @ Y_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_406_divides__exp2) ).
thf(177,axiom,
! [N: $i,M: $i] :
( ( dvd_dvd @ int @ N @ M )
=> ( ( ord_less_eq @ int @ M @ ( zero_zero @ int ) )
| ( ord_less_eq @ int @ N @ M ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_405_zdvd__bounds) ).
thf(179,axiom,
! [M: $i,X_1: $i] :
( ( ord_less @ int @ ( zero_zero @ int ) @ X_1 )
=> ( ( ord_less @ int @ X_1 @ M )
=> ~ ( zcong @ X_1 @ ( zero_zero @ int ) @ M ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_403_zcong__not__zero) ).
thf(180,axiom,
! [Ma: $i,K_1: $i,N_1: $i] :
( ( dvd_dvd @ nat @ ( times_times @ nat @ Ma @ K_1 ) @ ( times_times @ nat @ N_1 @ K_1 ) )
<=> ( ( K_1
= ( zero_zero @ nat ) )
| ( dvd_dvd @ nat @ Ma @ N_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_402_nat__mult__dvd__cancel__disj_H) ).
thf(181,axiom,
! [A_1: $i,B: $i] :
( ( dvd_dvd @ nat @ A_1 @ B )
=> ( ( B
= ( zero_zero @ nat ) )
| ( ord_less_eq @ nat @ A_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_401_divides__ge) ).
thf(182,axiom,
! [Z: $i,X_1: $i,Y_1: $i,M: $i] :
( ( zcong @ X_1 @ Y_1 @ M )
=> ( zcong @ ( power_power @ int @ X_1 @ Z ) @ ( power_power @ int @ Y_1 @ Z ) @ M ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_400_zcong__zpower) ).
thf(183,axiom,
! [N: $i,X_1: $i,Y_1: $i] :
( ( dvd_dvd @ nat @ X_1 @ Y_1 )
=> ( dvd_dvd @ nat @ ( power_power @ nat @ X_1 @ N ) @ ( power_power @ nat @ Y_1 @ N ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_399_divides__exp) ).
thf(184,axiom,
! [Ma: $i,N_1: $i] :
( ( ( power_power @ nat @ Ma @ N_1 )
= ( zero_zero @ nat ) )
<=> ( ( N_1
!= ( zero_zero @ nat ) )
& ( Ma
= ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_398_nat__power__eq__0__iff) ).
thf(185,axiom,
! [C: $i,A_1: $i,B: $i,M: $i] :
( ( zcong @ A_1 @ B @ M )
=> ( zcong @ ( plus_plus @ int @ A_1 @ C ) @ ( plus_plus @ int @ B @ C ) @ M ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_397_zcong__shift) ).
thf(186,axiom,
! [C_1: $i,D_1: $i,A_2: $i,B_1: $i,Ma: $i] :
( ( zcong @ A_2 @ B_1 @ Ma )
=> ( ( zcong @ C_1 @ ( times_times @ int @ A_2 @ D_1 ) @ Ma )
<=> ( zcong @ C_1 @ ( times_times @ int @ B_1 @ D_1 ) @ Ma ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_396_zcong__zmult__prop1) ).
thf(187,axiom,
! [C_1: $i,D_1: $i,A_2: $i,B_1: $i,Ma: $i] :
( ( zcong @ A_2 @ B_1 @ Ma )
=> ( ( zcong @ C_1 @ ( times_times @ int @ D_1 @ A_2 ) @ Ma )
<=> ( zcong @ C_1 @ ( times_times @ int @ D_1 @ B_1 ) @ Ma ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_395_zcong__zmult__prop2) ).
thf(188,axiom,
! [A_1: $i,B: $i,C: $i] :
( ( ( minus_minus @ int @ A_1 @ B )
= ( ti @ int @ C ) )
=> ( ( ti @ int @ A_1 )
= ( plus_plus @ int @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_394_Int2_Oaux1) ).
thf(189,axiom,
! [N_1: $i,Ma: $i] :
( ( ( times_times @ nat @ N_1 @ Ma )
= ( one_one @ nat ) )
<=> ( ( N_1
= ( one_one @ nat ) )
& ( Ma
= ( one_one @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_393_nat__mult__eq__one) ).
thf(190,axiom,
! [M: $i] : ( zcong @ M @ ( zero_zero @ int ) @ M ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_392_zcong__id) ).
thf(191,axiom,
! [C: $i,A_1: $i,B: $i] :
( ( dvd_dvd @ nat @ A_1 @ B )
=> ( dvd_dvd @ nat @ ( times_times @ nat @ A_1 @ C ) @ ( times_times @ nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_391_divides__mul__r) ).
thf(192,axiom,
! [C: $i,A_1: $i,B: $i] :
( ( dvd_dvd @ nat @ A_1 @ B )
=> ( dvd_dvd @ nat @ ( times_times @ nat @ C @ A_1 ) @ ( times_times @ nat @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_390_divides__mul__l) ).
thf(193,axiom,
! [B: $i,D: $i,A_1: $i] :
( ( dvd_dvd @ nat @ D @ A_1 )
=> ( ( dvd_dvd @ nat @ D @ ( plus_plus @ nat @ A_1 @ B ) )
=> ( dvd_dvd @ nat @ D @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_389_divides__add__revr) ).
thf(194,axiom,
! [X_1: $i,Y_1: $i] :
( ( minus_minus @ nat @ ( power_power @ nat @ X_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ nat @ Y_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( times_times @ nat @ ( plus_plus @ nat @ X_1 @ Y_1 ) @ ( minus_minus @ nat @ X_1 @ Y_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_388_diff__square) ).
thf(195,axiom,
! [P: $i,M: $i] :
( ( ( M
= ( zero_zero @ nat ) )
=> ( ( power_power @ nat @ P @ M )
= ( one_one @ nat ) ) )
& ( ( M
!= ( zero_zero @ nat ) )
=> ( ( power_power @ nat @ P @ M )
= ( times_times @ nat @ P @ ( power_power @ nat @ P @ ( minus_minus @ nat @ M @ ( one_one @ nat ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_387_power__eq__if) ).
thf(196,axiom,
! [N: $i,M: $i] :
( ( ( M
= ( zero_zero @ nat ) )
=> ( ( times_times @ nat @ M @ N )
= ( zero_zero @ nat ) ) )
& ( ( M
!= ( zero_zero @ nat ) )
=> ( ( times_times @ nat @ M @ N )
= ( plus_plus @ nat @ N @ ( times_times @ nat @ ( minus_minus @ nat @ M @ ( one_one @ nat ) ) @ N ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_386_mult__eq__if) ).
thf(197,axiom,
! [D: $i,C: $i,A_1: $i,B: $i,M: $i] :
( ( zcong @ A_1 @ B @ M )
=> ( ( ( ti @ int @ B )
= ( ti @ int @ C ) )
=> ( ( zcong @ C @ D @ M )
=> ( zcong @ A_1 @ D @ M ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_385_zcong__eq__trans) ).
thf(198,axiom,
! [X_2: $i,Y_2: $i] :
( ( ( dvd_dvd @ nat @ X_2 @ Y_2 )
& ( dvd_dvd @ nat @ Y_2 @ X_2 ) )
<=> ( X_2 = Y_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_384_divides__antisym) ).
thf(199,axiom,
! [N: $i,M: $i] :
( ( dvd_dvd @ nat @ N @ M )
=> ( ( M
= ( zero_zero @ nat ) )
| ( M = N )
| ( ord_less_eq @ nat @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ N ) @ M ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_383_divides__cases) ).
thf(201,axiom,
! [X_1: $i,P: $i] :
( ( ord_less @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ P )
=> ( ( zcong @ X_1 @ ( number_number_of @ int @ min ) @ P )
=> ~ ( zcong @ X_1 @ ( one_one @ int ) @ P ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_381_zcong__neg__1__impl__ne__1) ).
thf(202,axiom,
! [M: $i] :
( ( ord_less @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ M )
=> ~ ( zcong @ ( one_one @ int ) @ ( number_number_of @ int @ min ) @ M ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_380_one__not__neg__one__mod__m) ).
thf(203,axiom,
! [M: $i] :
( ( zprime @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ M ) @ ( one_one @ int ) ) )
=> ( ( legendre @ ( number_number_of @ int @ min ) @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ M ) @ ( one_one @ int ) ) )
= ( one_one @ int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_379_Legendre__1mod4) ).
thf(204,axiom,
! [N: $i] :
( ( ( power_power @ int @ ( number_number_of @ int @ min ) @ N )
= ( one_one @ int ) )
| ( ( power_power @ int @ ( number_number_of @ int @ min ) @ N )
= ( number_number_of @ int @ min ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_378_neg__one__power) ).
thf(205,axiom,
! [A_1: $i,B: $i] :
( ( power_power @ int @ ( minus_minus @ int @ A_1 @ B ) @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( minus_minus @ int @ ( plus_plus @ int @ ( minus_minus @ int @ ( power_power @ int @ A_1 @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) @ ( times_times @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit1 @ ( bit1 @ pls ) ) ) @ ( power_power @ int @ A_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ B ) ) @ ( times_times @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit1 @ ( bit1 @ pls ) ) ) @ A_1 ) @ ( power_power @ int @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ ( power_power @ int @ B @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_377_zdiff__power3) ).
thf(206,axiom,
! [A_1: $i,B: $i] :
( ( power_power @ int @ ( minus_minus @ int @ A_1 @ B ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ int @ ( minus_minus @ int @ ( power_power @ int @ A_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( times_times @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A_1 ) @ B ) ) @ ( power_power @ int @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_376_zdiff__power2) ).
thf(207,axiom,
! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [X_1: $i,Y_1: $i] :
( ( power_power @ X_a @ ( minus_minus @ X_a @ X_1 @ Y_1 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( minus_minus @ X_a @ ( plus_plus @ X_a @ ( power_power @ X_a @ X_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ X_a @ Y_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times @ X_a @ ( times_times @ X_a @ ( number_number_of @ X_a @ ( bit0 @ ( bit1 @ pls ) ) ) @ X_1 ) @ Y_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_375_power2__diff) ).
thf(208,axiom,
! [A_1: $i,B: $i] :
( ( times_times @ int @ ( plus_plus @ int @ A_1 @ B ) @ ( minus_minus @ int @ A_1 @ B ) )
= ( minus_minus @ int @ ( power_power @ int @ A_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_374_zspecial__product) ).
thf(211,axiom,
! [A_1: $i,B: $i,P: $i,Q: $i] :
( ( times_times @ int @ ( twoSqu579703163sum2sq @ ( product_Pair @ int @ int @ A_1 @ B ) ) @ ( twoSqu579703163sum2sq @ ( product_Pair @ int @ int @ P @ Q ) ) )
= ( twoSqu579703163sum2sq @ ( product_Pair @ int @ int @ ( plus_plus @ int @ ( times_times @ int @ A_1 @ P ) @ ( times_times @ int @ B @ Q ) ) @ ( minus_minus @ int @ ( times_times @ int @ A_1 @ Q ) @ ( times_times @ int @ B @ P ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_371_mult__sum2sq) ).
thf(212,axiom,
! [A_2: $i,P_1: $i] :
( ( zcong @ ( times_times @ int @ A_2 @ ( minus_minus @ int @ P_1 @ ( one_one @ int ) ) ) @ ( one_one @ int ) @ P_1 )
<=> ( zcong @ A_2 @ ( minus_minus @ int @ P_1 @ ( one_one @ int ) ) @ P_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_370_inv__not__p__minus__1__aux) ).
thf(213,axiom,
! [L: $i] :
( ( minus_minus @ int @ min @ ( bit0 @ L ) )
= ( bit1 @ ( minus_minus @ int @ min @ L ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_369_diff__bin__simps_I5_J) ).
thf(214,axiom,
! [L: $i] :
( ( minus_minus @ int @ min @ ( bit1 @ L ) )
= ( bit0 @ ( minus_minus @ int @ min @ L ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_368_diff__bin__simps_I6_J) ).
thf(215,axiom,
! [L: $i] :
( ( minus_minus @ int @ pls @ ( bit1 @ L ) )
= ( bit1 @ ( minus_minus @ int @ min @ L ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_367_diff__bin__simps_I4_J) ).
thf(216,axiom,
! [W_1: $i,Z_1: $i] :
( ( ord_less_eq @ int @ W_1 @ ( minus_minus @ int @ Z_1 @ ( one_one @ int ) ) )
<=> ( ord_less @ int @ W_1 @ Z_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_366_zle__diff1__eq) ).
thf(218,axiom,
! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [V: $i,W: $i,C: $i] :
( ( plus_plus @ X_a @ ( number_number_of @ X_a @ V ) @ ( minus_minus @ X_a @ ( number_number_of @ X_a @ W ) @ C ) )
= ( minus_minus @ X_a @ ( number_number_of @ X_a @ ( plus_plus @ int @ V @ W ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_364_add__number__of__diff1) ).
thf(219,axiom,
! [A_2: $i,B_1: $i,Ma: $i] :
( ( zcong @ A_2 @ B_1 @ Ma )
<=> ( dvd_dvd @ int @ Ma @ ( minus_minus @ int @ A_2 @ B_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_363_zcong__def) ).
thf(220,axiom,
! [A_1: $i,R_1: $i,B: $i,M: $i,C: $i,D: $i,N: $i] :
( ( plus_plus @ int @ ( times_times @ int @ ( minus_minus @ int @ A_1 @ ( times_times @ int @ R_1 @ B ) ) @ M ) @ ( times_times @ int @ ( minus_minus @ int @ C @ ( times_times @ int @ R_1 @ D ) ) @ N ) )
= ( minus_minus @ int @ ( plus_plus @ int @ ( times_times @ int @ A_1 @ M ) @ ( times_times @ int @ C @ N ) ) @ ( times_times @ int @ R_1 @ ( plus_plus @ int @ ( times_times @ int @ B @ M ) @ ( times_times @ int @ D @ N ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_362_xzgcda__linear__aux1) ).
thf(221,axiom,
! [K_1: $i,L_1: $i] :
( ( ord_less @ int @ K_1 @ L_1 )
<=> ( ord_less @ int @ ( minus_minus @ int @ K_1 @ L_1 ) @ ( zero_zero @ int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_361_less__bin__lemma) ).
thf(222,axiom,
! [L: $i] :
( ( minus_minus @ int @ pls @ ( bit0 @ L ) )
= ( bit0 @ ( minus_minus @ int @ pls @ L ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_360_diff__bin__simps_I3_J) ).
thf(223,axiom,
! [K: $i,L: $i] :
( ( minus_minus @ int @ ( bit1 @ K ) @ ( bit1 @ L ) )
= ( bit0 @ ( minus_minus @ int @ K @ L ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_359_diff__bin__simps_I10_J) ).
thf(224,axiom,
! [K: $i,L: $i] :
( ( minus_minus @ int @ ( bit1 @ K ) @ ( bit0 @ L ) )
= ( bit1 @ ( minus_minus @ int @ K @ L ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_358_diff__bin__simps_I9_J) ).
thf(225,axiom,
! [X_b: $i] :
( ( ( number @ X_b )
& ( ring @ X_b ) )
=> ! [A_1: $i,B: $i,V: $i] :
( ( times_times @ X_b @ ( minus_minus @ X_b @ A_1 @ B ) @ ( number_number_of @ X_b @ V ) )
= ( minus_minus @ X_b @ ( times_times @ X_b @ A_1 @ ( number_number_of @ X_b @ V ) ) @ ( times_times @ X_b @ B @ ( number_number_of @ X_b @ V ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_357_left__diff__distrib__number__of) ).
thf(226,axiom,
! [X_b: $i] :
( ( ( number @ X_b )
& ( ring @ X_b ) )
=> ! [V: $i,B: $i,C: $i] :
( ( times_times @ X_b @ ( number_number_of @ X_b @ V ) @ ( minus_minus @ X_b @ B @ C ) )
= ( minus_minus @ X_b @ ( times_times @ X_b @ ( number_number_of @ X_b @ V ) @ B ) @ ( times_times @ X_b @ ( number_number_of @ X_b @ V ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_356_right__diff__distrib__number__of) ).
thf(227,axiom,
! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [V: $i,W: $i] :
( ( number_number_of @ X_a @ ( minus_minus @ int @ V @ W ) )
= ( minus_minus @ X_a @ ( number_number_of @ X_a @ V ) @ ( number_number_of @ X_a @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_355_number__of__diff) ).
thf(228,axiom,
! [K: $i,M: $i,N: $i] :
( ( dvd_dvd @ int @ K @ ( minus_minus @ int @ M @ N ) )
=> ( ( dvd_dvd @ int @ K @ N )
=> ( dvd_dvd @ int @ K @ M ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_354_zdvd__zdiffD) ).
thf(229,axiom,
! [W: $i,Z1: $i,Z2: $i] :
( ( times_times @ int @ W @ ( minus_minus @ int @ Z1 @ Z2 ) )
= ( minus_minus @ int @ ( times_times @ int @ W @ Z1 ) @ ( times_times @ int @ W @ Z2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_353_zdiff__zmult__distrib2) ).
thf(230,axiom,
! [Z1: $i,Z2: $i,W: $i] :
( ( times_times @ int @ ( minus_minus @ int @ Z1 @ Z2 ) @ W )
= ( minus_minus @ int @ ( times_times @ int @ Z1 @ W ) @ ( times_times @ int @ Z2 @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_352_zdiff__zmult__distrib) ).
thf(231,axiom,
! [K: $i,L: $i] :
( ( minus_minus @ int @ ( bit0 @ K ) @ ( bit0 @ L ) )
= ( bit0 @ ( minus_minus @ int @ K @ L ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_351_diff__bin__simps_I7_J) ).
thf(232,axiom,
! [K: $i] :
( ( minus_minus @ int @ K @ pls )
= ( ti @ int @ K ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_350_diff__bin__simps_I1_J) ).
thf(233,axiom,
! [C: $i,D: $i,A_1: $i,B: $i,M: $i] :
( ( zcong @ A_1 @ B @ M )
=> ( ( zcong @ C @ D @ M )
=> ( zcong @ ( minus_minus @ int @ A_1 @ C ) @ ( minus_minus @ int @ B @ D ) @ M ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_349_zcong__zdiff) ).
thf(234,axiom,
( ~ ( quadRes @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) @ ( number_number_of @ int @ min ) )
=> ( ( legendre @ ( number_number_of @ int @ min ) @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) )
!= ( one_one @ int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_348__096_126_AQuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_A_061_061_062_ALegendre_A_N) ).
thf(235,axiom,
( ( minus_minus @ int @ ( power_power @ int @ s @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of @ int @ min ) )
= ( plus_plus @ int @ ( power_power @ int @ s @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( one_one @ int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_347__096s_A_094_A2_A_N_A_N1_A_061_As_A_094_A2_A_L_A1_096) ).
thf(236,axiom,
! [J: $i,K: $i,M: $i] :
( ( ord_less @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ M )
=> ( ( zcong @ ( power_power @ int @ ( number_number_of @ int @ min ) @ J ) @ ( power_power @ int @ ( number_number_of @ int @ min ) @ K ) @ M )
=> ( ( power_power @ int @ ( number_number_of @ int @ min ) @ J )
= ( power_power @ int @ ( number_number_of @ int @ min ) @ K ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_346_neg__one__power__eq__mod__m) ).
thf(238,axiom,
quadRes @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) @ ( number_number_of @ int @ min ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_344__096QuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_096) ).
thf(242,axiom,
! [X_a: $i] :
( ( ( power @ X_a )
& ( semiring_0 @ X_a ) )
=> ! [W: $i] :
( ( ( ( number_number_of @ nat @ W )
= ( zero_zero @ nat ) )
=> ( ( power_power @ X_a @ ( zero_zero @ X_a ) @ ( number_number_of @ nat @ W ) )
= ( one_one @ X_a ) ) )
& ( ( ( number_number_of @ nat @ W )
!= ( zero_zero @ nat ) )
=> ( ( power_power @ X_a @ ( zero_zero @ X_a ) @ ( number_number_of @ nat @ W ) )
= ( zero_zero @ X_a ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_340_power__0__left__number__of) ).
thf(243,axiom,
! [A_2: $i,B_1: $i,Ma: $i] :
( ( zcong @ A_2 @ B_1 @ Ma )
<=> ? [K_2: $i] :
( ( ti @ int @ B_1 )
= ( plus_plus @ int @ A_2 @ ( times_times @ int @ Ma @ K_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_339_zcong__iff__lin) ).
thf(244,axiom,
! [B: $i,M: $i,A_1: $i] :
( ( ord_less @ int @ ( zero_zero @ int ) @ A_1 )
=> ( ( ord_less @ int @ A_1 @ M )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ B )
=> ( ( ord_less @ int @ B @ A_1 )
=> ~ ( zcong @ A_1 @ B @ M ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_338_zcong__not) ).
thf(246,axiom,
! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [N: $i] :
( ( power_power @ X_a @ ( number_number_of @ X_a @ min ) @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ N ) )
= ( one_one @ X_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_336_power__m1__even) ).
thf(247,axiom,
! [C: $i,D: $i,A_1: $i,B: $i,M: $i] :
( ( zcong @ A_1 @ B @ M )
=> ( ( zcong @ C @ D @ M )
=> ( zcong @ ( plus_plus @ int @ A_1 @ C ) @ ( plus_plus @ int @ B @ D ) @ M ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_335_zcong__zadd) ).
thf(248,axiom,
! [A_1: $i,M: $i,B: $i] : ( zcong @ ( times_times @ int @ A_1 @ M ) @ ( times_times @ int @ B @ M ) @ M ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_334_zcong__zmult__self) ).
thf(249,axiom,
! [K: $i,A_1: $i,B: $i,M: $i] :
( ( zcong @ A_1 @ B @ M )
=> ( zcong @ ( times_times @ int @ A_1 @ K ) @ ( times_times @ int @ B @ K ) @ M ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_333_zcong__scalar) ).
thf(250,axiom,
! [K: $i,A_1: $i,B: $i,M: $i] :
( ( zcong @ A_1 @ B @ M )
=> ( zcong @ ( times_times @ int @ K @ A_1 ) @ ( times_times @ int @ K @ B ) @ M ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_332_zcong__scalar2) ).
thf(251,axiom,
! [C: $i,D: $i,A_1: $i,B: $i,M: $i] :
( ( zcong @ A_1 @ B @ M )
=> ( ( zcong @ C @ D @ M )
=> ( zcong @ ( times_times @ int @ A_1 @ C ) @ ( times_times @ int @ B @ D ) @ M ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_331_zcong__zmult) ).
thf(252,axiom,
! [A_1: $i,B: $i] : ( zcong @ A_1 @ B @ ( one_one @ int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_330_zcong__1) ).
thf(253,axiom,
! [A_2: $i,B_1: $i] :
( ( zcong @ A_2 @ B_1 @ ( zero_zero @ int ) )
<=> ( ( ti @ int @ A_2 )
= ( ti @ int @ B_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_329_IntPrimes_Ozcong__zero) ).
thf(254,axiom,
! [B: $i,A_1: $i,C: $i] :
( ( ord_less @ int @ A_1 @ C )
=> ( ( ord_less @ int @ B @ C )
=> ( ( ord_less_eq @ int @ A_1 @ B )
| ( ord_less_eq @ int @ B @ A_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_328_Euler_Oaux2) ).
thf(256,axiom,
! [V_1: $i,V: $i] :
( ( ( ord_less @ int @ V @ pls )
=> ( ( times_times @ nat @ ( number_number_of @ nat @ V ) @ ( number_number_of @ nat @ V_1 ) )
= ( zero_zero @ nat ) ) )
& ( ~ ( ord_less @ int @ V @ pls )
=> ( ( times_times @ nat @ ( number_number_of @ nat @ V ) @ ( number_number_of @ nat @ V_1 ) )
= ( number_number_of @ nat @ ( times_times @ int @ V @ V_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_326_mult__nat__number__of) ).
thf(257,axiom,
! [V_1: $i,K: $i,V: $i] :
( ( ( ord_less @ int @ V @ pls )
=> ( ( times_times @ nat @ ( number_number_of @ nat @ V ) @ ( times_times @ nat @ ( number_number_of @ nat @ V_1 ) @ K ) )
= ( zero_zero @ nat ) ) )
& ( ~ ( ord_less @ int @ V @ pls )
=> ( ( times_times @ nat @ ( number_number_of @ nat @ V ) @ ( times_times @ nat @ ( number_number_of @ nat @ V_1 ) @ K ) )
= ( times_times @ nat @ ( number_number_of @ nat @ ( times_times @ int @ V @ V_1 ) ) @ K ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_325_nat__number__of__mult__left) ).
thf(258,axiom,
ord_less @ nat @ ( zero_zero @ nat ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_324_pos2) ).
thf(262,axiom,
! [V_2: $i] :
( ( ( zero_zero @ nat )
= ( number_number_of @ nat @ V_2 ) )
<=> ( ord_less_eq @ int @ V_2 @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_320_eq__0__number__of) ).
thf(263,axiom,
! [V_2: $i] :
( ( ( number_number_of @ nat @ V_2 )
= ( zero_zero @ nat ) )
<=> ( ord_less_eq @ int @ V_2 @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_319_eq__number__of__0) ).
thf(264,axiom,
! [V_2: $i] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( number_number_of @ nat @ V_2 ) )
<=> ( ord_less @ int @ pls @ V_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_318_less__0__number__of) ).
thf(266,axiom,
! [X_a: $i] :
( ( linordered_semidom @ X_a )
=> ! [N: $i,A_1: $i] :
( ( ord_less @ X_a @ ( one_one @ X_a ) @ A_1 )
=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
=> ( ord_less @ X_a @ ( one_one @ X_a ) @ ( power_power @ X_a @ A_1 @ N ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_316_one__less__power) ).
thf(267,axiom,
! [Ma: $i,N_1: $i] :
( ( ( times_times @ int @ Ma @ N_1 )
= ( one_one @ int ) )
<=> ( ( ( ( ti @ int @ Ma )
= ( one_one @ int ) )
& ( ( ti @ int @ N_1 )
= ( one_one @ int ) ) )
| ( ( ( ti @ int @ Ma )
= ( number_number_of @ int @ min ) )
& ( ( ti @ int @ N_1 )
= ( number_number_of @ int @ min ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_315_zmult__eq__1__iff) ).
thf(268,axiom,
! [M: $i,N: $i] :
( ( ( times_times @ int @ M @ N )
= ( one_one @ int ) )
=> ( ( ( ti @ int @ M )
= ( one_one @ int ) )
| ( ( ti @ int @ M )
= ( number_number_of @ int @ min ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_314_pos__zmult__eq__1__iff__lemma) ).
thf(269,axiom,
! [K_1: $i] :
( ( ord_less @ int @ ( bit0 @ K_1 ) @ min )
<=> ( ord_less_eq @ int @ K_1 @ min ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_313_rel__simps_I11_J) ).
thf(270,axiom,
! [K_1: $i] :
( ( ord_less_eq @ int @ min @ ( bit0 @ K_1 ) )
<=> ( ord_less @ int @ min @ K_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_312_rel__simps_I25_J) ).
thf(271,axiom,
( ( zero_zero @ nat )
= ( number_number_of @ nat @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_311_semiring__norm_I113_J) ).
thf(272,axiom,
( ( number_number_of @ nat @ pls )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_310_nat__number__of__Pls) ).
thf(273,axiom,
! [X_a: $i] :
( ( power @ X_a )
=> ! [A_1: $i] :
( ( power_power @ X_a @ A_1 @ ( zero_zero @ nat ) )
= ( one_one @ X_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_309_power__0) ).
thf(274,axiom,
! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [X_1: $i] :
( ( power_power @ X_a @ X_1 @ ( zero_zero @ nat ) )
= ( one_one @ X_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_308_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
thf(275,axiom,
! [I: $i,M: $i,N: $i] :
( ( dvd_dvd @ nat @ ( power_power @ nat @ I @ M ) @ ( power_power @ nat @ I @ N ) )
=> ( ( ord_less @ nat @ ( one_one @ nat ) @ I )
=> ( ord_less_eq @ nat @ M @ N ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_307_power__dvd__imp__le) ).
thf(276,axiom,
( ( number_number_of @ int @ pls )
!= ( number_number_of @ int @ min ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_306_eq__number__of__Pls__Min) ).
thf(277,axiom,
! [K_1: $i] :
( ( ord_less_eq @ int @ ( bit0 @ K_1 ) @ min )
<=> ( ord_less_eq @ int @ K_1 @ min ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_305_rel__simps_I28_J) ).
thf(278,axiom,
ord_less_eq @ int @ min @ pls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_304_rel__simps_I23_J) ).
thf(279,axiom,
~ ( ord_less_eq @ int @ pls @ min ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_303_rel__simps_I20_J) ).
thf(280,axiom,
! [K_1: $i] :
( ( ord_less_eq @ int @ min @ ( bit1 @ K_1 ) )
<=> ( ord_less_eq @ int @ min @ K_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_302_rel__simps_I26_J) ).
thf(281,axiom,
! [K_1: $i] :
( ( ord_less_eq @ int @ ( bit1 @ K_1 ) @ min )
<=> ( ord_less_eq @ int @ K_1 @ min ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_301_rel__simps_I30_J) ).
thf(282,axiom,
ord_less @ int @ min @ ( zero_zero @ int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_300_bin__less__0__simps_I2_J) ).
thf(283,axiom,
! [K_1: $i] :
( ( ord_less @ int @ min @ ( bit0 @ K_1 ) )
<=> ( ord_less @ int @ min @ K_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_299_rel__simps_I8_J) ).
thf(284,axiom,
ord_less @ int @ min @ pls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_298_rel__simps_I6_J) ).
thf(285,axiom,
~ ( ord_less @ int @ pls @ min ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_297_rel__simps_I3_J) ).
thf(286,axiom,
! [K_1: $i] :
( ( ord_less @ int @ min @ ( bit1 @ K_1 ) )
<=> ( ord_less @ int @ min @ K_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_296_rel__simps_I9_J) ).
thf(287,axiom,
! [K_1: $i] :
( ( ord_less @ int @ ( bit1 @ K_1 ) @ min )
<=> ( ord_less @ int @ K_1 @ min ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_295_rel__simps_I13_J) ).
thf(288,axiom,
! [X_2: $i] :
( ~ ( ord_less @ real @ ( zero_zero @ real ) @ ( times_times @ real @ X_2 @ X_2 ) )
<=> ( X_2
= ( zero_zero @ real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_not__real__square__gt__zero) ).
thf(289,axiom,
ord_less_eq @ int @ min @ min,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_293_rel__simps_I24_J) ).
thf(290,axiom,
~ ( ord_less @ int @ min @ min ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_292_rel__simps_I7_J) ).
thf(291,axiom,
! [L: $i] :
( min
!= ( bit0 @ L ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_291_rel__simps_I42_J) ).
thf(292,axiom,
! [K: $i] :
( ( bit0 @ K )
!= min ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_290_rel__simps_I45_J) ).
thf(293,axiom,
min != pls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_289_rel__simps_I40_J) ).
thf(294,axiom,
pls != min,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_288_rel__simps_I37_J) ).
thf(295,axiom,
( ( bit1 @ min )
= min ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_287_Bit1__Min) ).
thf(296,axiom,
! [L_1: $i] :
( ( min
= ( bit1 @ L_1 ) )
<=> ( min
= ( ti @ int @ L_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_286_rel__simps_I43_J) ).
thf(297,axiom,
! [K_1: $i] :
( ( ( bit1 @ K_1 )
= min )
<=> ( ( ti @ int @ K_1 )
= min ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_285_rel__simps_I47_J) ).
thf(298,axiom,
! [M: $i,N: $i,I: $i] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ I )
=> ( ( ord_less @ nat @ ( power_power @ nat @ I @ M ) @ ( power_power @ nat @ I @ N ) )
=> ( ord_less @ nat @ M @ N ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_nat__power__less__imp__less) ).
thf(299,axiom,
! [X_2: $i,W_1: $i] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ X_2 @ ( number_number_of @ nat @ W_1 ) ) )
<=> ( ( ( number_number_of @ nat @ W_1 )
= ( zero_zero @ nat ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ X_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_283_zero__less__power__nat__eq__number__of) ).
thf(300,axiom,
! [X_2: $i,N_1: $i] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ X_2 @ N_1 ) )
<=> ( ( N_1
= ( zero_zero @ nat ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ X_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_282_zero__less__power__nat__eq) ).
thf(301,axiom,
! [X_2: $i,N_1: $i] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ X_2 @ N_1 ) )
<=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ X_2 )
| ( N_1
= ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_281_nat__zero__less__power__iff) ).
thf(302,axiom,
( ( legendre @ ( number_number_of @ int @ min ) @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) )
= ( one_one @ int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_280__096Legendre_A_N1_A_I4_A_K_Am_A_L_A1_J_A_061_A1_096) ).
thf(303,axiom,
~ ! [S1: $i] :
~ ( zcong @ ( power_power @ int @ S1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of @ int @ min ) @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_279__096_B_Bthesis_O_A_I_B_Bs1_O_A_091s1_A_094_A2_A_061_A_N1_093_A_Imod_A4_) ).
thf(307,axiom,
! [Y_1: $i,X_1: $i,P: $i] :
( ~ ( zcong @ X_1 @ ( zero_zero @ int ) @ P )
=> ( ( zcong @ ( power_power @ int @ Y_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ X_1 @ P )
=> ~ ( dvd_dvd @ int @ P @ Y_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_275_Euler_Oaux____1) ).
thf(308,axiom,
zcong @ ( power_power @ int @ s @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of @ int @ min ) @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_274_s) ).
thf(309,axiom,
! [X_a: $i] :
( ( linordered_semidom @ X_a )
=> ! [A_1: $i,N: $i,N_2: $i] :
( ( ord_less @ nat @ N @ N_2 )
=> ( ( ord_less @ X_a @ ( one_one @ X_a ) @ A_1 )
=> ( ord_less @ X_a @ ( power_power @ X_a @ A_1 @ N ) @ ( power_power @ X_a @ A_1 @ N_2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_273_power__strict__increasing) ).
thf(310,axiom,
! [X_a: $i] :
( ( linordered_semidom @ X_a )
=> ! [M: $i,N: $i,A_1: $i] :
( ( ord_less @ X_a @ ( one_one @ X_a ) @ A_1 )
=> ( ( ord_less @ X_a @ ( power_power @ X_a @ A_1 @ M ) @ ( power_power @ X_a @ A_1 @ N ) )
=> ( ord_less @ nat @ M @ N ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_272_power__less__imp__less__exp) ).
thf(311,axiom,
! [X_a: $i] :
( ( linordered_semidom @ X_a )
=> ! [X_2: $i,Y_2: $i,B_1: $i] :
( ( ord_less @ X_a @ ( one_one @ X_a ) @ B_1 )
=> ( ( ord_less @ X_a @ ( power_power @ X_a @ B_1 @ X_2 ) @ ( power_power @ X_a @ B_1 @ Y_2 ) )
<=> ( ord_less @ nat @ X_2 @ Y_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_271_power__strict__increasing__iff) ).
thf(312,axiom,
! [X_a: $i] :
( ( linordered_semidom @ X_a )
=> ! [Ma: $i,N_1: $i,A_2: $i] :
( ( ord_less @ X_a @ ( one_one @ X_a ) @ A_2 )
=> ( ( ( power_power @ X_a @ A_2 @ Ma )
= ( power_power @ X_a @ A_2 @ N_1 ) )
<=> ( Ma = N_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_270_power__inject__exp) ).
thf(313,axiom,
! [X_a: $i] :
( ( linordered_semidom @ X_a )
=> ! [A_1: $i,N: $i,N_2: $i] :
( ( ord_less_eq @ nat @ N @ N_2 )
=> ( ( ord_less_eq @ X_a @ ( one_one @ X_a ) @ A_1 )
=> ( ord_less_eq @ X_a @ ( power_power @ X_a @ A_1 @ N ) @ ( power_power @ X_a @ A_1 @ N_2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_269_power__increasing) ).
thf(314,axiom,
! [X_a: $i] :
( ( linordered_semidom @ X_a )
=> ! [N: $i,A_1: $i] :
( ( ord_less_eq @ X_a @ ( one_one @ X_a ) @ A_1 )
=> ( ord_less_eq @ X_a @ ( one_one @ X_a ) @ ( power_power @ X_a @ A_1 @ N ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_one__le__power) ).
thf(315,axiom,
! [X_a: $i] :
( ( linordered_idom @ X_a )
=> ! [A_1: $i,N: $i] : ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ ( power_power @ X_a @ A_1 @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ N ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_267_zero__le__even__power_H) ).
thf(317,axiom,
! [X_a: $i] :
( ( linordered_idom @ X_a )
=> ! [X_1: $i,Y_1: $i] :
~ ( ord_less @ X_a @ ( plus_plus @ X_a @ ( power_power @ X_a @ X_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ X_a @ Y_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( zero_zero @ X_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_not__sum__power2__lt__zero) ).
thf(319,axiom,
! [X_a: $i] :
( ( linordered_idom @ X_a )
=> ! [X_1: $i,Y_1: $i] : ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ ( plus_plus @ X_a @ ( power_power @ X_a @ X_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ X_a @ Y_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_sum__power2__ge__zero) ).
thf(321,axiom,
! [X_a: $i] :
( ( monoid_mult @ X_a )
=> ! [A_1: $i,M: $i,N: $i] :
( ( power_power @ X_a @ A_1 @ ( times_times @ nat @ M @ N ) )
= ( power_power @ X_a @ ( power_power @ X_a @ A_1 @ M ) @ N ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_power__mult) ).
thf(322,axiom,
! [X_a: $i] :
( ( monoid_mult @ X_a )
=> ! [N: $i] :
( ( power_power @ X_a @ ( one_one @ X_a ) @ N )
= ( one_one @ X_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_power__one) ).
thf(323,axiom,
! [X_a: $i] :
( ( monoid_mult @ X_a )
=> ! [A_1: $i,M: $i,N: $i] :
( ( power_power @ X_a @ A_1 @ ( plus_plus @ nat @ M @ N ) )
= ( times_times @ X_a @ ( power_power @ X_a @ A_1 @ M ) @ ( power_power @ X_a @ A_1 @ N ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_power__add) ).
thf(324,axiom,
! [X_a: $i] :
( ( comm_monoid_mult @ X_a )
=> ! [A_1: $i,B: $i,N: $i] :
( ( power_power @ X_a @ ( times_times @ X_a @ A_1 @ B ) @ N )
= ( times_times @ X_a @ ( power_power @ X_a @ A_1 @ N ) @ ( power_power @ X_a @ B @ N ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_power__mult__distrib) ).
thf(325,axiom,
! [X_a: $i] :
( ( monoid_mult @ X_a )
=> ! [A_1: $i,N: $i] :
( ( times_times @ X_a @ ( power_power @ X_a @ A_1 @ N ) @ A_1 )
= ( times_times @ X_a @ A_1 @ ( power_power @ X_a @ A_1 @ N ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_257_power__commutes) ).
thf(326,axiom,
! [X_a: $i] :
( ( linordered_idom @ X_a )
=> ! [X_2: $i,Y_2: $i] :
( ( ( plus_plus @ X_a @ ( power_power @ X_a @ X_2 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ X_a @ Y_2 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ X_a ) )
<=> ( ( ( ti @ X_a @ X_2 )
= ( zero_zero @ X_a ) )
& ( ( ti @ X_a @ Y_2 )
= ( zero_zero @ X_a ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_256_sum__power2__eq__zero__iff) ).
thf(328,axiom,
! [X_a: $i] :
( ( linordered_idom @ X_a )
=> ! [A_1: $i] :
~ ( ord_less @ X_a @ ( power_power @ X_a @ A_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( zero_zero @ X_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_power2__less__0) ).
thf(330,axiom,
! [X_a: $i] :
( ( linordered_semidom @ X_a )
=> ! [X_1: $i,Y_1: $i] :
( ( ord_less_eq @ X_a @ ( power_power @ X_a @ X_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ X_a @ Y_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ Y_1 )
=> ( ord_less_eq @ X_a @ X_1 @ Y_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_power2__le__imp__le) ).
thf(331,axiom,
! [X_a: $i] :
( ( linordered_idom @ X_a )
=> ! [A_1: $i] : ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ ( power_power @ X_a @ A_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_zero__le__power2) ).
thf(332,axiom,
! [X_a: $i] :
( ( ring_11004092258visors @ X_a )
=> ! [A_2: $i] :
( ( ( power_power @ X_a @ A_2 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ X_a ) )
<=> ( ( ti @ X_a @ A_2 )
= ( zero_zero @ X_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_zero__eq__power2) ).
thf(333,axiom,
! [X_a: $i] :
( ( semiring_1 @ X_a )
=> ( ( power_power @ X_a @ ( zero_zero @ X_a ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ X_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_zero__power2) ).
thf(334,axiom,
! [Z: $i] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ Z )
=> ( ord_less @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( one_one @ int ) @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_le__imp__0__less) ).
thf(339,axiom,
! [Z_1: $i] :
( ( ord_less @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ Z_1 ) @ Z_1 ) @ ( zero_zero @ int ) )
<=> ( ord_less @ int @ Z_1 @ ( zero_zero @ int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_odd__less__0) ).
thf(340,axiom,
! [N_1: $i,Ma: $i] :
( ( ord_less @ int @ ( zero_zero @ int ) @ Ma )
=> ( ( ( times_times @ int @ Ma @ N_1 )
= ( one_one @ int ) )
<=> ( ( ( ti @ int @ Ma )
= ( one_one @ int ) )
& ( ( ti @ int @ N_1 )
= ( one_one @ int ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_pos__zmult__eq__1__iff) ).
thf(341,axiom,
! [Z_1: $i] :
( ( ord_less_eq @ int @ ( one_one @ int ) @ Z_1 )
<=> ( ord_less @ int @ ( zero_zero @ int ) @ Z_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_int__one__le__iff__zero__less) ).
thf(342,axiom,
! [X_a: $i] :
( ( monoid_mult @ X_a )
=> ! [A_1: $i] :
( ( power_power @ X_a @ A_1 @ ( one_one @ nat ) )
= ( ti @ X_a @ A_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_power__one__right) ).
thf(343,axiom,
! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [W: $i] :
( ( number_number_of @ X_a @ ( bit0 @ W ) )
= ( plus_plus @ X_a @ ( plus_plus @ X_a @ ( zero_zero @ X_a ) @ ( number_number_of @ X_a @ W ) ) @ ( number_number_of @ X_a @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_number__of__Bit0) ).
thf(344,axiom,
! [V_2: $i,V_3: $i] :
( ( ord_less_eq @ nat @ ( number_number_of @ nat @ V_2 ) @ ( number_number_of @ nat @ V_3 ) )
<=> ( ~ ( ord_less_eq @ int @ V_2 @ V_3 )
=> ( ord_less_eq @ int @ V_2 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_le__nat__number__of) ).
thf(346,axiom,
! [X_a: $i] :
( ( linordered_ring @ X_a )
=> ! [X_1: $i,Y_1: $i] :
~ ( ord_less @ X_a @ ( plus_plus @ X_a @ ( times_times @ X_a @ X_1 @ X_1 ) @ ( times_times @ X_a @ Y_1 @ Y_1 ) ) @ ( zero_zero @ X_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_not__sum__squares__lt__zero) ).
thf(347,axiom,
! [V_2: $i,V_3: $i] :
( ( ord_less @ nat @ ( number_number_of @ nat @ V_2 ) @ ( number_number_of @ nat @ V_3 ) )
<=> ( ( ( ord_less @ int @ V_2 @ V_3 )
=> ( ord_less @ int @ pls @ V_3 ) )
& ( ord_less @ int @ V_2 @ V_3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_less__nat__number__of) ).
thf(349,axiom,
! [X_a: $i] :
( ( linordered_ring @ X_a )
=> ! [X_1: $i,Y_1: $i] : ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ ( plus_plus @ X_a @ ( times_times @ X_a @ X_1 @ X_1 ) @ ( times_times @ X_a @ Y_1 @ Y_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_sum__squares__ge__zero) ).
thf(350,axiom,
! [N: $i,A_1: $i,B: $i,P: $i] :
( ( zprime @ P )
=> ( ~ ( dvd_dvd @ int @ P @ B )
=> ( ( dvd_dvd @ int @ ( power_power @ int @ P @ N ) @ ( times_times @ int @ A_1 @ B ) )
=> ( dvd_dvd @ int @ ( power_power @ int @ P @ N ) @ A_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_zprime__power__zdvd__cancel__right) ).
thf(351,axiom,
! [N: $i,B: $i,A_1: $i,P: $i] :
( ( zprime @ P )
=> ( ~ ( dvd_dvd @ int @ P @ A_1 )
=> ( ( dvd_dvd @ int @ ( power_power @ int @ P @ N ) @ ( times_times @ int @ A_1 @ B ) )
=> ( dvd_dvd @ int @ ( power_power @ int @ P @ N ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_zprime__power__zdvd__cancel__left) ).
thf(352,axiom,
! [X_a: $i] :
( ( linordered_semidom @ X_a )
=> ! [N: $i,A_1: $i] :
( ( ord_less @ X_a @ ( zero_zero @ X_a ) @ A_1 )
=> ( ( ord_less @ X_a @ A_1 @ ( one_one @ X_a ) )
=> ( ord_less @ X_a @ ( times_times @ X_a @ A_1 @ ( power_power @ X_a @ A_1 @ N ) ) @ ( power_power @ X_a @ A_1 @ N ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_power__Suc__less) ).
thf(353,axiom,
! [Z: $i] :
( ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ Z ) @ Z )
!= ( zero_zero @ int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_odd__nonzero) ).
thf(354,axiom,
! [K: $i,I: $i,J: $i] :
( ( ord_less @ int @ I @ J )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ K )
=> ( ord_less @ int @ ( times_times @ int @ K @ I ) @ ( times_times @ int @ K @ J ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_zmult__zless__mono2) ).
thf(355,axiom,
! [B: $i,A_1: $i] :
( ( ord_less @ int @ ( zero_zero @ int ) @ A_1 )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ ( times_times @ int @ A_1 @ B ) )
=> ( ord_less @ int @ ( zero_zero @ int ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_pos__zmult__pos) ).
thf(356,axiom,
ord_less @ int @ ( zero_zero @ int ) @ ( one_one @ int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_int__0__less__1) ).
thf(357,axiom,
( ( zero_zero @ int )
= ( number_number_of @ int @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_zero__is__num__zero) ).
thf(358,axiom,
! [W_1: $i] :
( ( ord_less @ int @ ( bit0 @ W_1 ) @ ( zero_zero @ int ) )
<=> ( ord_less @ int @ W_1 @ ( zero_zero @ int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_bin__less__0__simps_I3_J) ).
thf(359,axiom,
~ ( ord_less @ int @ pls @ ( zero_zero @ int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_bin__less__0__simps_I1_J) ).
thf(360,axiom,
! [W_1: $i] :
( ( ord_less @ int @ ( bit1 @ W_1 ) @ ( zero_zero @ int ) )
<=> ( ord_less @ int @ W_1 @ ( zero_zero @ int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_bin__less__0__simps_I4_J) ).
thf(361,axiom,
! [X_a: $i] :
( ( number_semiring @ X_a )
=> ( ( number_number_of @ X_a @ pls )
= ( zero_zero @ X_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_semiring__numeral__0__eq__0) ).
thf(362,axiom,
! [X_a: $i] :
( ( number_ring @ X_a )
=> ( ( number_number_of @ X_a @ pls )
= ( zero_zero @ X_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_number__of__Pls) ).
thf(363,axiom,
! [X_a: $i] :
( ( number_ring @ X_a )
=> ( ( zero_zero @ X_a )
= ( number_number_of @ X_a @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_semiring__norm_I112_J) ).
thf(364,axiom,
! [A_1: $i,N: $i,P: $i] :
( ( zprime @ P )
=> ( ( dvd_dvd @ int @ P @ ( power_power @ int @ A_1 @ N ) )
=> ( dvd_dvd @ int @ P @ A_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_zprime__zdvd__power) ).
thf(365,axiom,
! [X_a: $i] :
( ( semiri456707255roduct @ X_a )
=> ! [C: $i,D: $i,A_1: $i,B: $i,R_1: $i] :
( ( ( ti @ X_a @ R_1 )
!= ( zero_zero @ X_a ) )
=> ( ( ( ( ti @ X_a @ A_1 )
= ( ti @ X_a @ B ) )
& ( ( ti @ X_a @ C )
!= ( ti @ X_a @ D ) ) )
=> ( ( plus_plus @ X_a @ A_1 @ ( times_times @ X_a @ R_1 @ C ) )
!= ( plus_plus @ X_a @ B @ ( times_times @ X_a @ R_1 @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_add__scale__eq__noteq) ).
thf(366,axiom,
! [X_a: $i] :
( ( linord581940658strict @ X_a )
=> ! [X_2: $i,Y_2: $i] :
( ( ( plus_plus @ X_a @ ( times_times @ X_a @ X_2 @ X_2 ) @ ( times_times @ X_a @ Y_2 @ Y_2 ) )
= ( zero_zero @ X_a ) )
<=> ( ( ( ti @ X_a @ X_2 )
= ( zero_zero @ X_a ) )
& ( ( ti @ X_a @ Y_2 )
= ( zero_zero @ X_a ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_sum__squares__eq__zero__iff) ).
thf(367,axiom,
! [X_a: $i] :
( ( linordered_idom @ X_a )
=> ! [A_2: $i] :
( ( ord_less @ X_a @ ( plus_plus @ X_a @ A_2 @ A_2 ) @ ( zero_zero @ X_a ) )
<=> ( ord_less @ X_a @ A_2 @ ( zero_zero @ X_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_even__less__0__iff) ).
thf(368,axiom,
! [X_a: $i] :
( ( linordered_semidom @ X_a )
=> ! [A_1: $i,N: $i,N_2: $i] :
( ( ord_less @ nat @ N @ N_2 )
=> ( ( ord_less @ X_a @ ( zero_zero @ X_a ) @ A_1 )
=> ( ( ord_less @ X_a @ A_1 @ ( one_one @ X_a ) )
=> ( ord_less @ X_a @ ( power_power @ X_a @ A_1 @ N_2 ) @ ( power_power @ X_a @ A_1 @ N ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_power__strict__decreasing) ).
thf(369,axiom,
! [X_a: $i] :
( ( linordered_semidom @ X_a )
=> ! [A_1: $i,N: $i,N_2: $i] :
( ( ord_less_eq @ nat @ N @ N_2 )
=> ( ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ A_1 )
=> ( ( ord_less_eq @ X_a @ A_1 @ ( one_one @ X_a ) )
=> ( ord_less_eq @ X_a @ ( power_power @ X_a @ A_1 @ N_2 ) @ ( power_power @ X_a @ A_1 @ N ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_power__decreasing) ).
thf(371,axiom,
! [C_1: $i,X_2: $i,Ta: $i,A_2: $i,D_1: $i] :
( ( dvd_dvd @ int @ A_2 @ D_1 )
=> ( ( dvd_dvd @ int @ A_2 @ ( plus_plus @ int @ X_2 @ Ta ) )
<=> ( dvd_dvd @ int @ A_2 @ ( plus_plus @ int @ ( plus_plus @ int @ X_2 @ ( times_times @ int @ C_1 @ D_1 ) ) @ Ta ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_zdvd__period) ).
thf(372,axiom,
! [K_1: $i,N_1: $i,Ma: $i] :
( ( dvd_dvd @ int @ K_1 @ ( plus_plus @ int @ N_1 @ ( times_times @ int @ K_1 @ Ma ) ) )
<=> ( dvd_dvd @ int @ K_1 @ N_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_zdvd__reduce) ).
thf(373,axiom,
! [Z: $i,X_1: $i,Y_1: $i,P: $i] :
( ( zcong @ ( power_power @ int @ X_1 @ Y_1 ) @ ( one_one @ int ) @ P )
=> ( zcong @ ( power_power @ int @ X_1 @ ( times_times @ nat @ Y_1 @ Z ) ) @ ( one_one @ int ) @ P ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_zcong__zpower__zmult) ).
thf(374,axiom,
! [X_a: $i] :
( ( linordered_semidom @ X_a )
=> ! [N: $i,A_1: $i] :
( ( ord_less @ X_a @ ( zero_zero @ X_a ) @ A_1 )
=> ( ord_less @ X_a @ ( zero_zero @ X_a ) @ ( power_power @ X_a @ A_1 @ N ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_zero__less__power) ).
thf(375,axiom,
! [X_a: $i] :
( ( linordered_semidom @ X_a )
=> ! [N: $i,A_1: $i,B: $i] :
( ( ord_less_eq @ X_a @ A_1 @ B )
=> ( ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ A_1 )
=> ( ord_less_eq @ X_a @ ( power_power @ X_a @ A_1 @ N ) @ ( power_power @ X_a @ B @ N ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_power__mono) ).
thf(376,axiom,
! [X_a: $i] :
( ( linordered_semidom @ X_a )
=> ! [N: $i,A_1: $i] :
( ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ A_1 )
=> ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ ( power_power @ X_a @ A_1 @ N ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_zero__le__power) ).
thf(377,axiom,
! [Z: $i] :
( ( plus_plus @ int @ Z @ ( zero_zero @ int ) )
= ( ti @ int @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_zadd__0__right) ).
thf(378,axiom,
! [Z: $i] :
( ( plus_plus @ int @ ( zero_zero @ int ) @ Z )
= ( ti @ int @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_zadd__0) ).
thf(379,axiom,
( ( zero_zero @ int )
!= ( one_one @ int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_int__0__neq__1) ).
thf(380,axiom,
( pls
= ( zero_zero @ int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_Pls__def) ).
thf(381,axiom,
! [X_a: $i] :
( ( linord219039673up_add @ X_a )
=> ! [A_2: $i] :
( ( ( plus_plus @ X_a @ A_2 @ A_2 )
= ( zero_zero @ X_a ) )
<=> ( ( ti @ X_a @ A_2 )
= ( zero_zero @ X_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_double__eq__0__iff) ).
thf(382,axiom,
! [X_a: $i] :
( ( semiri456707255roduct @ X_a )
=> ! [B_1: $i,A_2: $i] :
( ( ( ti @ X_a @ B_1 )
= ( plus_plus @ X_a @ B_1 @ A_2 ) )
<=> ( ( ti @ X_a @ A_2 )
= ( zero_zero @ X_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_add__0__iff) ).
thf(383,axiom,
! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i] :
( ( plus_plus @ X_a @ A_1 @ ( zero_zero @ X_a ) )
= ( ti @ X_a @ A_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
thf(384,axiom,
! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i] :
( ( plus_plus @ X_a @ ( zero_zero @ X_a ) @ A_1 )
= ( ti @ X_a @ A_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
thf(385,axiom,
! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i] :
( ( times_times @ X_a @ A_1 @ ( zero_zero @ X_a ) )
= ( zero_zero @ X_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
thf(386,axiom,
! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i] :
( ( times_times @ X_a @ ( zero_zero @ X_a ) @ A_1 )
= ( zero_zero @ X_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
thf(389,axiom,
! [X_a: $i] :
( ( ( power @ X_a )
& ( semiring_0 @ X_a ) )
=> ! [N: $i] :
( ( ( N
= ( zero_zero @ nat ) )
=> ( ( power_power @ X_a @ ( zero_zero @ X_a ) @ N )
= ( one_one @ X_a ) ) )
& ( ( N
!= ( zero_zero @ nat ) )
=> ( ( power_power @ X_a @ ( zero_zero @ X_a ) @ N )
= ( zero_zero @ X_a ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_power__0__left) ).
thf(390,axiom,
! [X_a: $i] :
( ( ring_11004092258visors @ X_a )
=> ! [N: $i,A_1: $i] :
( ( ( ti @ X_a @ A_1 )
!= ( zero_zero @ X_a ) )
=> ( ( power_power @ X_a @ A_1 @ N )
!= ( zero_zero @ X_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_field__power__not__zero) ).
thf(391,axiom,
! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [N: $i,X_1: $i,Y_1: $i] :
( ( dvd_dvd @ X_a @ X_1 @ Y_1 )
=> ( dvd_dvd @ X_a @ ( power_power @ X_a @ X_1 @ N ) @ ( power_power @ X_a @ Y_1 @ N ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_dvd__power__same) ).
thf(392,axiom,
! [K: $i,M: $i,N: $i] :
( ( dvd_dvd @ int @ ( times_times @ int @ K @ M ) @ ( times_times @ int @ K @ N ) )
=> ( ( ( ti @ int @ K )
!= ( zero_zero @ int ) )
=> ( dvd_dvd @ int @ M @ N ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_zdvd__mult__cancel) ).
thf(394,axiom,
! [N: $i,M: $i] :
( ( ord_less @ int @ ( zero_zero @ int ) @ M )
=> ( ( ord_less @ int @ M @ N )
=> ~ ( dvd_dvd @ int @ N @ M ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_zdvd__not__zless) ).
thf(396,axiom,
! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [M: $i,A_1: $i,N: $i,B: $i] :
( ( dvd_dvd @ X_a @ ( power_power @ X_a @ A_1 @ N ) @ B )
=> ( ( ord_less_eq @ nat @ M @ N )
=> ( dvd_dvd @ X_a @ ( power_power @ X_a @ A_1 @ M ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_power__le__dvd) ).
thf(397,axiom,
! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [N: $i,M: $i,X_1: $i,Y_1: $i] :
( ( dvd_dvd @ X_a @ X_1 @ Y_1 )
=> ( ( ord_less_eq @ nat @ N @ M )
=> ( dvd_dvd @ X_a @ ( power_power @ X_a @ X_1 @ N ) @ ( power_power @ X_a @ Y_1 @ M ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_dvd__power__le) ).
thf(398,axiom,
! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i,M: $i,N: $i] :
( ( ord_less_eq @ nat @ M @ N )
=> ( dvd_dvd @ X_a @ ( power_power @ X_a @ A_1 @ M ) @ ( power_power @ X_a @ A_1 @ N ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_le__imp__power__dvd) ).
thf(400,axiom,
zcong @ ( power_power @ int @ s1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of @ int @ min ) @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_s1) ).
thf(404,axiom,
zcong @ ( power_power @ int @ s @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ s1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178__096_091s_A_094_A2_A_061_As1_A_094_A2_093_A_Imod_A4_A_K_Am_A_L_A1_J_096) ).
thf(405,axiom,
! [X_a: $i] :
( ( linordered_semidom @ X_a )
=> ! [X_2: $i,Y_2: $i,B_1: $i] :
( ( ord_less @ X_a @ ( one_one @ X_a ) @ B_1 )
=> ( ( ord_less_eq @ X_a @ ( power_power @ X_a @ B_1 @ X_2 ) @ ( power_power @ X_a @ B_1 @ Y_2 ) )
<=> ( ord_less_eq @ nat @ X_2 @ Y_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_power__increasing__iff) ).
thf(406,axiom,
! [X_a: $i] :
( ( linordered_semidom @ X_a )
=> ! [M: $i,N: $i,A_1: $i] :
( ( ord_less @ X_a @ ( one_one @ X_a ) @ A_1 )
=> ( ( ord_less_eq @ X_a @ ( power_power @ X_a @ A_1 @ M ) @ ( power_power @ X_a @ A_1 @ N ) )
=> ( ord_less_eq @ nat @ M @ N ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_power__le__imp__le__exp) ).
thf(407,axiom,
! [X_a: $i] :
( ( linordered_semidom @ X_a )
=> ! [N: $i,A_1: $i] :
( ( ord_less @ X_a @ ( one_one @ X_a ) @ A_1 )
=> ( ord_less @ X_a @ ( one_one @ X_a ) @ ( times_times @ X_a @ A_1 @ ( power_power @ X_a @ A_1 @ N ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_power__gt1__lemma) ).
thf(408,axiom,
! [X_a: $i] :
( ( linordered_semidom @ X_a )
=> ! [N: $i,A_1: $i] :
( ( ord_less @ X_a @ ( one_one @ X_a ) @ A_1 )
=> ( ord_less @ X_a @ ( power_power @ X_a @ A_1 @ N ) @ ( times_times @ X_a @ A_1 @ ( power_power @ X_a @ A_1 @ N ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_power__less__power__Suc) ).
thf(409,axiom,
! [X_1: $i] :
( ( times_times @ real @ ( number_number_of @ real @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ real @ X_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( power_power @ real @ ( times_times @ real @ ( number_number_of @ real @ ( bit0 @ ( bit1 @ pls ) ) ) @ X_1 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_four__x__squared) ).
thf(410,axiom,
! [X_1: $i,Y_1: $i] :
( ( power_power @ real @ ( plus_plus @ real @ X_1 @ Y_1 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ real @ ( plus_plus @ real @ ( power_power @ real @ X_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ real @ Y_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times @ real @ ( times_times @ real @ ( number_number_of @ real @ ( bit0 @ ( bit1 @ pls ) ) ) @ X_1 ) @ Y_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_real__sum__squared__expand) ).
thf(412,axiom,
! [P: $i] :
( ( zprime @ P )
=> ( ( ( ti @ int @ P )
!= ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) )
=> ( ( ( ti @ int @ P )
!= ( number_number_of @ int @ ( bit1 @ ( bit1 @ pls ) ) ) )
=> ( ord_less_eq @ int @ ( number_number_of @ int @ ( bit1 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ P ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_prime__g__5) ).
thf(413,axiom,
dvd_dvd @ int @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) @ ( plus_plus @ int @ ( power_power @ int @ s @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( one_one @ int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169__0964_A_K_Am_A_L_A1_Advd_As_A_094_A2_A_L_A1_096) ).
thf(414,axiom,
ord_less @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_p0) ).
thf(415,axiom,
! [X_a: $i] :
( ( number_semiring @ X_a )
=> ( ( plus_plus @ X_a @ ( one_one @ X_a ) @ ( one_one @ X_a ) )
= ( number_number_of @ X_a @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_semiring__one__add__one__is__two) ).
thf(416,axiom,
! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [Z: $i] :
( ( times_times @ X_a @ Z @ ( number_number_of @ X_a @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ X_a @ Z @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_mult__2__right) ).
thf(417,axiom,
! [X_a: $i] :
( ( number_semiring @ X_a )
=> ! [Z: $i] :
( ( times_times @ X_a @ Z @ ( number_number_of @ X_a @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ X_a @ Z @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_semiring__mult__2__right) ).
thf(418,axiom,
! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [Z: $i] :
( ( times_times @ X_a @ ( number_number_of @ X_a @ ( bit0 @ ( bit1 @ pls ) ) ) @ Z )
= ( plus_plus @ X_a @ Z @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_mult__2) ).
thf(419,axiom,
! [X_a: $i] :
( ( number_semiring @ X_a )
=> ! [Z: $i] :
( ( times_times @ X_a @ ( number_number_of @ X_a @ ( bit0 @ ( bit1 @ pls ) ) ) @ Z )
= ( plus_plus @ X_a @ Z @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_semiring__mult__2) ).
thf(420,axiom,
! [X_1: $i] :
( ( power_power @ int @ ( power_power @ int @ X_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power @ int @ X_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_quartic__square__square) ).
thf(421,axiom,
! [X_a: $i] :
( ( monoid_mult @ X_a )
=> ! [A_1: $i] :
( ( power_power @ X_a @ A_1 @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( times_times @ X_a @ ( times_times @ X_a @ A_1 @ A_1 ) @ A_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_power3__eq__cube) ).
thf(422,axiom,
! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [W: $i] :
( ( times_times @ X_a @ ( plus_plus @ X_a @ ( one_one @ X_a ) @ ( one_one @ X_a ) ) @ ( number_number_of @ X_a @ W ) )
= ( number_number_of @ X_a @ ( bit0 @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_double__number__of__Bit0) ).
thf(423,axiom,
! [K: $i,L: $i] :
( ( times_times @ int @ ( bit1 @ K ) @ L )
= ( plus_plus @ int @ ( bit0 @ ( times_times @ int @ K @ L ) ) @ L ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_mult__Bit1) ).
thf(424,axiom,
( ( one_one @ int )
= ( number_number_of @ int @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_one__is__num__one) ).
thf(425,axiom,
! [X_a: $i] :
( ( number_ring @ X_a )
=> ( ( one_one @ X_a )
= ( number_number_of @ X_a @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_semiring__norm_I110_J) ).
thf(426,axiom,
! [X_a: $i] :
( ( number_ring @ X_a )
=> ( ( number_number_of @ X_a @ ( bit1 @ pls ) )
= ( one_one @ X_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_numeral__1__eq__1) ).
thf(427,axiom,
! [X_a: $i] :
( ( number_semiring @ X_a )
=> ( ( number_number_of @ X_a @ ( bit1 @ pls ) )
= ( one_one @ X_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_semiring__numeral__1__eq__1) ).
thf(428,axiom,
! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [A_1: $i] :
( ( times_times @ X_a @ A_1 @ ( number_number_of @ X_a @ ( bit1 @ pls ) ) )
= ( ti @ X_a @ A_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_mult__numeral__1__right) ).
thf(429,axiom,
! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [A_1: $i] :
( ( times_times @ X_a @ ( number_number_of @ X_a @ ( bit1 @ pls ) ) @ A_1 )
= ( ti @ X_a @ A_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_mult__numeral__1) ).
thf(430,axiom,
! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [W: $i] :
( ( number_number_of @ X_a @ ( bit1 @ W ) )
= ( plus_plus @ X_a @ ( plus_plus @ X_a @ ( one_one @ X_a ) @ ( number_number_of @ X_a @ W ) ) @ ( number_number_of @ X_a @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_number__of__Bit1) ).
thf(431,axiom,
! [K: $i] :
( ( bit1 @ K )
= ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ K ) @ K ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_Bit1__def) ).
thf(432,axiom,
! [K: $i,L: $i] :
( ( plus_plus @ int @ ( bit0 @ K ) @ ( bit1 @ L ) )
= ( bit1 @ ( plus_plus @ int @ K @ L ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_add__Bit0__Bit1) ).
thf(433,axiom,
! [K: $i,L: $i] :
( ( plus_plus @ int @ ( bit1 @ K ) @ ( bit0 @ L ) )
= ( bit1 @ ( plus_plus @ int @ K @ L ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_add__Bit1__Bit0) ).
thf(434,axiom,
! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [V: $i,W: $i] :
( ( number_number_of @ X_a @ ( plus_plus @ int @ V @ W ) )
= ( plus_plus @ X_a @ ( number_number_of @ X_a @ V ) @ ( number_number_of @ X_a @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_number__of__add) ).
thf(435,axiom,
! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [V: $i,W: $i] :
( ( plus_plus @ X_a @ ( number_number_of @ X_a @ V ) @ ( number_number_of @ X_a @ W ) )
= ( number_number_of @ X_a @ ( plus_plus @ int @ V @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_add__number__of__eq) ).
thf(436,axiom,
! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [V: $i,W: $i,Z: $i] :
( ( plus_plus @ X_a @ ( number_number_of @ X_a @ V ) @ ( plus_plus @ X_a @ ( number_number_of @ X_a @ W ) @ Z ) )
= ( plus_plus @ X_a @ ( number_number_of @ X_a @ ( plus_plus @ int @ V @ W ) ) @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_add__number__of__left) ).
thf(437,axiom,
! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [V: $i,W: $i] :
( ( number_number_of @ X_a @ ( times_times @ int @ V @ W ) )
= ( times_times @ X_a @ ( number_number_of @ X_a @ V ) @ ( number_number_of @ X_a @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_number__of__mult) ).
thf(438,axiom,
! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [V: $i,W: $i] :
( ( times_times @ X_a @ ( number_number_of @ X_a @ V ) @ ( number_number_of @ X_a @ W ) )
= ( number_number_of @ X_a @ ( times_times @ int @ V @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_arith__simps_I32_J) ).
thf(439,axiom,
! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [V: $i,W: $i,Z: $i] :
( ( times_times @ X_a @ ( number_number_of @ X_a @ V ) @ ( times_times @ X_a @ ( number_number_of @ X_a @ W ) @ Z ) )
= ( times_times @ X_a @ ( number_number_of @ X_a @ ( times_times @ int @ V @ W ) ) @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_mult__number__of__left) ).
thf(440,axiom,
! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [A_1: $i] :
( ( plus_plus @ X_a @ A_1 @ ( number_number_of @ X_a @ pls ) )
= ( ti @ X_a @ A_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_add__numeral__0__right) ).
thf(441,axiom,
! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [A_1: $i] :
( ( plus_plus @ X_a @ ( number_number_of @ X_a @ pls ) @ A_1 )
= ( ti @ X_a @ A_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_add__numeral__0) ).
thf(442,axiom,
! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [M: $i] :
( ( plus_plus @ X_a @ M @ M )
= ( times_times @ X_a @ ( plus_plus @ X_a @ ( one_one @ X_a ) @ ( one_one @ X_a ) ) @ M ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
thf(443,axiom,
! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [M: $i,A_1: $i] :
( ( plus_plus @ X_a @ M @ ( times_times @ X_a @ A_1 @ M ) )
= ( times_times @ X_a @ ( plus_plus @ X_a @ A_1 @ ( one_one @ X_a ) ) @ M ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
thf(444,axiom,
! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i,M: $i] :
( ( plus_plus @ X_a @ ( times_times @ X_a @ A_1 @ M ) @ M )
= ( times_times @ X_a @ ( plus_plus @ X_a @ A_1 @ ( one_one @ X_a ) ) @ M ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
thf(445,axiom,
! [X_b: $i] :
( ( ( number @ X_b )
& ( semiring @ X_b ) )
=> ! [V: $i,B: $i,C: $i] :
( ( times_times @ X_b @ ( number_number_of @ X_b @ V ) @ ( plus_plus @ X_b @ B @ C ) )
= ( plus_plus @ X_b @ ( times_times @ X_b @ ( number_number_of @ X_b @ V ) @ B ) @ ( times_times @ X_b @ ( number_number_of @ X_b @ V ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_right__distrib__number__of) ).
thf(446,axiom,
! [X_b: $i] :
( ( ( number @ X_b )
& ( semiring @ X_b ) )
=> ! [A_1: $i,B: $i,V: $i] :
( ( times_times @ X_b @ ( plus_plus @ X_b @ A_1 @ B ) @ ( number_number_of @ X_b @ V ) )
= ( plus_plus @ X_b @ ( times_times @ X_b @ A_1 @ ( number_number_of @ X_b @ V ) ) @ ( times_times @ X_b @ B @ ( number_number_of @ X_b @ V ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_left__distrib__number__of) ).
thf(447,axiom,
! [X_1: $i] : ( ord_less_eq @ int @ X_1 @ ( power_power @ int @ X_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_power2__ge__self) ).
thf(448,axiom,
! [X_a: $i] :
( ( number_semiring @ X_a )
=> ! [V_1: $i,V: $i] :
( ( ord_less_eq @ int @ pls @ V )
=> ( ( ord_less_eq @ int @ pls @ V_1 )
=> ( ( plus_plus @ X_a @ ( number_number_of @ X_a @ V ) @ ( number_number_of @ X_a @ V_1 ) )
= ( number_number_of @ X_a @ ( plus_plus @ int @ V @ V_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_semiring__add__number__of) ).
thf(449,axiom,
! [X_a: $i] :
( ( number_semiring @ X_a )
=> ! [V_1: $i,V: $i] :
( ( ord_less_eq @ int @ pls @ V )
=> ( ( ord_less_eq @ int @ pls @ V_1 )
=> ( ( times_times @ X_a @ ( number_number_of @ X_a @ V ) @ ( number_number_of @ X_a @ V_1 ) )
= ( number_number_of @ X_a @ ( times_times @ int @ V @ V_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_semiring__mult__number__of) ).
thf(450,axiom,
! [V: $i,W: $i] :
( ( plus_plus @ int @ ( number_number_of @ int @ V ) @ ( number_number_of @ int @ W ) )
= ( number_number_of @ int @ ( plus_plus @ int @ V @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_plus__numeral__code_I9_J) ).
thf(451,axiom,
! [W: $i,Z1: $i,Z2: $i] :
( ( times_times @ int @ W @ ( plus_plus @ int @ Z1 @ Z2 ) )
= ( plus_plus @ int @ ( times_times @ int @ W @ Z1 ) @ ( times_times @ int @ W @ Z2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_zadd__zmult__distrib2) ).
thf(452,axiom,
! [Z1: $i,Z2: $i,W: $i] :
( ( times_times @ int @ ( plus_plus @ int @ Z1 @ Z2 ) @ W )
= ( plus_plus @ int @ ( times_times @ int @ Z1 @ W ) @ ( times_times @ int @ Z2 @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_zadd__zmult__distrib) ).
thf(453,axiom,
! [V: $i,W: $i] :
( ( times_times @ int @ ( number_number_of @ int @ V ) @ ( number_number_of @ int @ W ) )
= ( number_number_of @ int @ ( times_times @ int @ V @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_times__numeral__code_I5_J) ).
thf(454,axiom,
! [Z: $i] :
( ( times_times @ int @ ( one_one @ int ) @ Z )
= ( ti @ int @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_zmult__1) ).
thf(455,axiom,
! [Z: $i] :
( ( times_times @ int @ Z @ ( one_one @ int ) )
= ( ti @ int @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_zmult__1__right) ).
thf(456,axiom,
! [K: $i] :
( ( bit0 @ K )
= ( plus_plus @ int @ K @ K ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_Bit0__def) ).
thf(457,axiom,
! [K: $i,L: $i] :
( ( plus_plus @ int @ ( bit0 @ K ) @ ( bit0 @ L ) )
= ( bit0 @ ( plus_plus @ int @ K @ L ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_add__Bit0__Bit0) ).
thf(458,axiom,
! [K: $i] :
( ( plus_plus @ int @ pls @ K )
= ( ti @ int @ K ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_add__Pls) ).
thf(459,axiom,
! [K: $i] :
( ( plus_plus @ int @ K @ pls )
= ( ti @ int @ K ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_add__Pls__right) ).
thf(460,axiom,
! [K: $i,L: $i] :
( ( times_times @ int @ ( bit0 @ K ) @ L )
= ( bit0 @ ( times_times @ int @ K @ L ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_mult__Bit0) ).
thf(461,axiom,
! [W: $i] :
( ( times_times @ int @ pls @ W )
= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_mult__Pls) ).
thf(462,axiom,
( ( bit0 @ pls )
= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_Bit0__Pls) ).
thf(463,axiom,
! [L_1: $i] :
( ( pls
= ( bit0 @ L_1 ) )
<=> ( pls
= ( ti @ int @ L_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_rel__simps_I38_J) ).
thf(464,axiom,
! [K_1: $i] :
( ( ( bit0 @ K_1 )
= pls )
<=> ( ( ti @ int @ K_1 )
= pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_rel__simps_I44_J) ).
thf(465,axiom,
! [K: $i,L: $i] :
( ( bit0 @ K )
!= ( bit1 @ L ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_rel__simps_I49_J) ).
thf(466,axiom,
! [K: $i,L: $i] :
( ( bit1 @ K )
!= ( bit0 @ L ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_rel__simps_I50_J) ).
thf(467,axiom,
! [L: $i] :
( pls
!= ( bit1 @ L ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_rel__simps_I39_J) ).
thf(468,axiom,
! [K: $i] :
( ( bit1 @ K )
!= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_rel__simps_I46_J) ).
thf(469,axiom,
! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [X_1: $i,Y_1: $i,Q: $i] :
( ( power_power @ X_a @ ( times_times @ X_a @ X_1 @ Y_1 ) @ Q )
= ( times_times @ X_a @ ( power_power @ X_a @ X_1 @ Q ) @ ( power_power @ X_a @ Y_1 @ Q ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
thf(470,axiom,
! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i] :
( ( times_times @ X_a @ ( one_one @ X_a ) @ A_1 )
= ( ti @ X_a @ A_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
thf(471,axiom,
! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i] :
( ( times_times @ X_a @ A_1 @ ( one_one @ X_a ) )
= ( ti @ X_a @ A_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
thf(472,axiom,
! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [X_1: $i,Y_1: $i,Z: $i] :
( ( times_times @ X_a @ X_1 @ ( plus_plus @ X_a @ Y_1 @ Z ) )
= ( plus_plus @ X_a @ ( times_times @ X_a @ X_1 @ Y_1 ) @ ( times_times @ X_a @ X_1 @ Z ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
thf(473,axiom,
! [X_a: $i] :
( ( semiri456707255roduct @ X_a )
=> ! [C_1: $i,D_1: $i,A_2: $i,B_1: $i] :
( ( ( ( ti @ X_a @ A_2 )
!= ( ti @ X_a @ B_1 ) )
& ( ( ti @ X_a @ C_1 )
!= ( ti @ X_a @ D_1 ) ) )
<=> ( ( plus_plus @ X_a @ ( times_times @ X_a @ A_2 @ C_1 ) @ ( times_times @ X_a @ B_1 @ D_1 ) )
!= ( plus_plus @ X_a @ ( times_times @ X_a @ A_2 @ D_1 ) @ ( times_times @ X_a @ B_1 @ C_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_crossproduct__noteq) ).
thf(474,axiom,
! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i,B: $i,C: $i] :
( ( times_times @ X_a @ ( plus_plus @ X_a @ A_1 @ B ) @ C )
= ( plus_plus @ X_a @ ( times_times @ X_a @ A_1 @ C ) @ ( times_times @ X_a @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
thf(475,axiom,
! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i,M: $i,B: $i] :
( ( plus_plus @ X_a @ ( times_times @ X_a @ A_1 @ M ) @ ( times_times @ X_a @ B @ M ) )
= ( times_times @ X_a @ ( plus_plus @ X_a @ A_1 @ B ) @ M ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
thf(476,axiom,
! [X_a: $i] :
( ( semiri456707255roduct @ X_a )
=> ! [W_1: $i,Y_2: $i,X_2: $i,Z_1: $i] :
( ( ( plus_plus @ X_a @ ( times_times @ X_a @ W_1 @ Y_2 ) @ ( times_times @ X_a @ X_2 @ Z_1 ) )
= ( plus_plus @ X_a @ ( times_times @ X_a @ W_1 @ Z_1 ) @ ( times_times @ X_a @ X_2 @ Y_2 ) ) )
<=> ( ( ( ti @ X_a @ W_1 )
= ( ti @ X_a @ X_2 ) )
| ( ( ti @ X_a @ Y_2 )
= ( ti @ X_a @ Z_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_crossproduct__eq) ).
thf(477,axiom,
! [X_a: $i] :
( ( ( number_ring @ X_a )
& ( linordered_idom @ X_a ) )
=> ! [Y_2: $i] :
( ( ord_less_eq @ X_a @ ( one_one @ X_a ) @ ( number_number_of @ X_a @ Y_2 ) )
<=> ( ord_less_eq @ int @ ( bit1 @ pls ) @ Y_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_le__special_I2_J) ).
thf(478,axiom,
! [X_a: $i] :
( ( ( number_ring @ X_a )
& ( linordered_idom @ X_a ) )
=> ! [X_2: $i] :
( ( ord_less_eq @ X_a @ ( number_number_of @ X_a @ X_2 ) @ ( one_one @ X_a ) )
<=> ( ord_less_eq @ int @ X_2 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_le__special_I4_J) ).
thf(479,axiom,
! [X_a: $i] :
( ( ( number_ring @ X_a )
& ( linordered_idom @ X_a ) )
=> ! [Y_2: $i] :
( ( ord_less @ X_a @ ( one_one @ X_a ) @ ( number_number_of @ X_a @ Y_2 ) )
<=> ( ord_less @ int @ ( bit1 @ pls ) @ Y_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_less__special_I2_J) ).
thf(480,axiom,
! [X_a: $i] :
( ( ( number_ring @ X_a )
& ( linordered_idom @ X_a ) )
=> ! [X_2: $i] :
( ( ord_less @ X_a @ ( number_number_of @ X_a @ X_2 ) @ ( one_one @ X_a ) )
<=> ( ord_less @ int @ X_2 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_less__special_I4_J) ).
thf(481,axiom,
! [X_a: $i] :
( ( monoid_mult @ X_a )
=> ! [A_1: $i,N: $i] :
( ( power_power @ X_a @ A_1 @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ N ) )
= ( power_power @ X_a @ ( power_power @ X_a @ A_1 @ N ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_power__even__eq) ).
thf(482,axiom,
! [W_1: $i,Z_1: $i] :
( ( ord_less @ int @ W_1 @ ( plus_plus @ int @ Z_1 @ ( one_one @ int ) ) )
<=> ( ( ord_less @ int @ W_1 @ Z_1 )
| ( ( ti @ int @ W_1 )
= ( ti @ int @ Z_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_zless__add1__eq) ).
thf(483,axiom,
! [K_1: $i] :
( ( ord_less_eq @ int @ pls @ ( bit0 @ K_1 ) )
<=> ( ord_less_eq @ int @ pls @ K_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_rel__simps_I21_J) ).
thf(484,axiom,
! [K_1: $i] :
( ( ord_less_eq @ int @ ( bit0 @ K_1 ) @ pls )
<=> ( ord_less_eq @ int @ K_1 @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_rel__simps_I27_J) ).
thf(485,axiom,
! [K_1: $i,L_1: $i] :
( ( ord_less_eq @ int @ ( bit0 @ K_1 ) @ ( bit1 @ L_1 ) )
<=> ( ord_less_eq @ int @ K_1 @ L_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_rel__simps_I32_J) ).
thf(486,axiom,
! [K1: $i,K2: $i] :
( ( ord_less_eq @ int @ ( bit0 @ K1 ) @ ( bit1 @ K2 ) )
<=> ( ord_less_eq @ int @ K1 @ K2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_less__eq__int__code_I14_J) ).
thf(487,axiom,
! [K_1: $i] :
( ( ord_less_eq @ int @ pls @ ( bit1 @ K_1 ) )
<=> ( ord_less_eq @ int @ pls @ K_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_rel__simps_I22_J) ).
thf(488,axiom,
! [K_1: $i] :
( ( ord_less @ int @ pls @ ( bit0 @ K_1 ) )
<=> ( ord_less @ int @ pls @ K_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_rel__simps_I4_J) ).
thf(489,axiom,
! [K_1: $i] :
( ( ord_less @ int @ ( bit0 @ K_1 ) @ pls )
<=> ( ord_less @ int @ K_1 @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_rel__simps_I10_J) ).
thf(490,axiom,
! [K_1: $i,L_1: $i] :
( ( ord_less @ int @ ( bit1 @ K_1 ) @ ( bit0 @ L_1 ) )
<=> ( ord_less @ int @ K_1 @ L_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_rel__simps_I16_J) ).
thf(491,axiom,
! [K1: $i,K2: $i] :
( ( ord_less @ int @ ( bit1 @ K1 ) @ ( bit0 @ K2 ) )
<=> ( ord_less @ int @ K1 @ K2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_less__int__code_I15_J) ).
thf(492,axiom,
! [K_1: $i] :
( ( ord_less @ int @ ( bit1 @ K_1 ) @ pls )
<=> ( ord_less @ int @ K_1 @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_rel__simps_I12_J) ).
thf(493,axiom,
! [Z: $i,W: $i] :
( ( plus_plus @ int @ Z @ W )
= ( plus_plus @ int @ W @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_zadd__commute) ).
thf(494,axiom,
! [X_1: $i,Y_1: $i,Z: $i] :
( ( plus_plus @ int @ X_1 @ ( plus_plus @ int @ Y_1 @ Z ) )
= ( plus_plus @ int @ Y_1 @ ( plus_plus @ int @ X_1 @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_zadd__left__commute) ).
thf(495,axiom,
! [Z1: $i,Z2: $i,Z3: $i] :
( ( plus_plus @ int @ ( plus_plus @ int @ Z1 @ Z2 ) @ Z3 )
= ( plus_plus @ int @ Z1 @ ( plus_plus @ int @ Z2 @ Z3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_zadd__assoc) ).
thf(496,axiom,
! [K: $i] :
( ( number_number_of @ int @ K )
= ( ti @ int @ K ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_number__of__is__id) ).
thf(497,axiom,
! [Z: $i,W: $i] :
( ( times_times @ int @ Z @ W )
= ( times_times @ int @ W @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_zmult__commute) ).
thf(498,axiom,
! [Z1: $i,Z2: $i,Z3: $i] :
( ( times_times @ int @ ( times_times @ int @ Z1 @ Z2 ) @ Z3 )
= ( times_times @ int @ Z1 @ ( times_times @ int @ Z2 @ Z3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_zmult__assoc) ).
thf(499,axiom,
! [K_1: $i,L_1: $i] :
( ( ( bit0 @ K_1 )
= ( bit0 @ L_1 ) )
<=> ( ( ti @ int @ K_1 )
= ( ti @ int @ L_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_rel__simps_I48_J) ).
thf(500,axiom,
! [K_1: $i,L_1: $i] :
( ( ( bit1 @ K_1 )
= ( bit1 @ L_1 ) )
<=> ( ( ti @ int @ K_1 )
= ( ti @ int @ L_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_rel__simps_I51_J) ).
thf(501,axiom,
! [X_a: $i] :
( ( number @ X_a )
=> ! [W_1: $i,X_2: $i] :
( ( ( number_number_of @ X_a @ W_1 )
= ( ti @ X_a @ X_2 ) )
<=> ( ( ti @ X_a @ X_2 )
= ( number_number_of @ X_a @ W_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_number__of__reorient) ).
thf(502,axiom,
! [X_a: $i] :
( ( ( number_ring @ X_a )
& ( ring_char_0 @ X_a ) )
=> ! [X_2: $i,Y_2: $i] :
( ( ( number_number_of @ X_a @ X_2 )
= ( number_number_of @ X_a @ Y_2 ) )
<=> ( ( ti @ int @ X_2 )
= ( ti @ int @ Y_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_eq__number__of) ).
thf(503,axiom,
! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i,C: $i] :
( ( plus_plus @ X_a @ A_1 @ C )
= ( plus_plus @ X_a @ C @ A_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(504,axiom,
! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i,C: $i,D: $i] :
( ( plus_plus @ X_a @ A_1 @ ( plus_plus @ X_a @ C @ D ) )
= ( plus_plus @ X_a @ C @ ( plus_plus @ X_a @ A_1 @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(505,axiom,
! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i,C: $i,D: $i] :
( ( plus_plus @ X_a @ A_1 @ ( plus_plus @ X_a @ C @ D ) )
= ( plus_plus @ X_a @ ( plus_plus @ X_a @ A_1 @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(506,axiom,
! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i,B: $i,C: $i] :
( ( plus_plus @ X_a @ ( plus_plus @ X_a @ A_1 @ B ) @ C )
= ( plus_plus @ X_a @ A_1 @ ( plus_plus @ X_a @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(507,axiom,
! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i,B: $i,C: $i] :
( ( plus_plus @ X_a @ ( plus_plus @ X_a @ A_1 @ B ) @ C )
= ( plus_plus @ X_a @ ( plus_plus @ X_a @ A_1 @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(508,axiom,
! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i,B: $i,C: $i,D: $i] :
( ( plus_plus @ X_a @ ( plus_plus @ X_a @ A_1 @ B ) @ ( plus_plus @ X_a @ C @ D ) )
= ( plus_plus @ X_a @ ( plus_plus @ X_a @ A_1 @ C ) @ ( plus_plus @ X_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(509,axiom,
! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i,B: $i] :
( ( times_times @ X_a @ A_1 @ B )
= ( times_times @ X_a @ B @ A_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
thf(510,axiom,
! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [Lx: $i,Rx: $i,Ry: $i] :
( ( times_times @ X_a @ Lx @ ( times_times @ X_a @ Rx @ Ry ) )
= ( times_times @ X_a @ Rx @ ( times_times @ X_a @ Lx @ Ry ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
thf(511,axiom,
! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [Lx: $i,Rx: $i,Ry: $i] :
( ( times_times @ X_a @ Lx @ ( times_times @ X_a @ Rx @ Ry ) )
= ( times_times @ X_a @ ( times_times @ X_a @ Lx @ Rx ) @ Ry ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
thf(512,axiom,
! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [Lx: $i,Ly: $i,Rx: $i] :
( ( times_times @ X_a @ ( times_times @ X_a @ Lx @ Ly ) @ Rx )
= ( times_times @ X_a @ Lx @ ( times_times @ X_a @ Ly @ Rx ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
thf(513,axiom,
! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [Lx: $i,Ly: $i,Rx: $i] :
( ( times_times @ X_a @ ( times_times @ X_a @ Lx @ Ly ) @ Rx )
= ( times_times @ X_a @ ( times_times @ X_a @ Lx @ Rx ) @ Ly ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
thf(514,axiom,
! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [Lx: $i,Ly: $i,Rx: $i,Ry: $i] :
( ( times_times @ X_a @ ( times_times @ X_a @ Lx @ Ly ) @ ( times_times @ X_a @ Rx @ Ry ) )
= ( times_times @ X_a @ Lx @ ( times_times @ X_a @ Ly @ ( times_times @ X_a @ Rx @ Ry ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
thf(515,axiom,
! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [Lx: $i,Ly: $i,Rx: $i,Ry: $i] :
( ( times_times @ X_a @ ( times_times @ X_a @ Lx @ Ly ) @ ( times_times @ X_a @ Rx @ Ry ) )
= ( times_times @ X_a @ Rx @ ( times_times @ X_a @ ( times_times @ X_a @ Lx @ Ly ) @ Ry ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
thf(516,axiom,
! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [Lx: $i,Ly: $i,Rx: $i,Ry: $i] :
( ( times_times @ X_a @ ( times_times @ X_a @ Lx @ Ly ) @ ( times_times @ X_a @ Rx @ Ry ) )
= ( times_times @ X_a @ ( times_times @ X_a @ Lx @ Rx ) @ ( times_times @ X_a @ Ly @ Ry ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
thf(517,axiom,
! [Y_1: $i,X_1: $i] :
( ( twoSqu420862341sum2sq @ X_1 )
=> ( ( twoSqu420862341sum2sq @ Y_1 )
=> ( twoSqu420862341sum2sq @ ( times_times @ int @ X_1 @ Y_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_is__mult__sum2sq) ).
thf(518,axiom,
zprime @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_zprime__2) ).
thf(519,axiom,
! [W_1: $i,Z_1: $i] :
( ( ord_less @ int @ W_1 @ ( plus_plus @ int @ Z_1 @ ( one_one @ int ) ) )
<=> ( ord_less_eq @ int @ W_1 @ Z_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_zle__add1__eq__le) ).
thf(520,axiom,
! [W_1: $i,Z_1: $i] :
( ( ord_less_eq @ int @ ( plus_plus @ int @ W_1 @ ( one_one @ int ) ) @ Z_1 )
<=> ( ord_less @ int @ W_1 @ Z_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_add1__zle__eq) ).
thf(521,axiom,
! [W: $i,Z: $i] :
( ( ord_less @ int @ W @ Z )
=> ( ord_less_eq @ int @ ( plus_plus @ int @ W @ ( one_one @ int ) ) @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_zless__imp__add1__zle) ).
thf(522,axiom,
! [K_1: $i,L_1: $i] :
( ( ord_less @ int @ ( bit0 @ K_1 ) @ ( bit1 @ L_1 ) )
<=> ( ord_less_eq @ int @ K_1 @ L_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_rel__simps_I15_J) ).
thf(523,axiom,
! [K1: $i,K2: $i] :
( ( ord_less @ int @ ( bit0 @ K1 ) @ ( bit1 @ K2 ) )
<=> ( ord_less_eq @ int @ K1 @ K2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_less__int__code_I14_J) ).
thf(524,axiom,
! [K_1: $i,L_1: $i] :
( ( ord_less_eq @ int @ ( bit1 @ K_1 ) @ ( bit0 @ L_1 ) )
<=> ( ord_less @ int @ K_1 @ L_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_rel__simps_I33_J) ).
thf(525,axiom,
! [K1: $i,K2: $i] :
( ( ord_less_eq @ int @ ( bit1 @ K1 ) @ ( bit0 @ K2 ) )
<=> ( ord_less @ int @ K1 @ K2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_less__eq__int__code_I15_J) ).
thf(526,axiom,
! [K_1: $i] :
( ( ord_less @ int @ pls @ ( bit1 @ K_1 ) )
<=> ( ord_less_eq @ int @ pls @ K_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_rel__simps_I5_J) ).
thf(527,axiom,
! [K_1: $i] :
( ( ord_less_eq @ int @ ( bit1 @ K_1 ) @ pls )
<=> ( ord_less @ int @ K_1 @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_rel__simps_I29_J) ).
thf(528,axiom,
( ( one_one @ nat )
= ( number_number_of @ nat @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_Numeral1__eq1__nat) ).
thf(529,axiom,
( ( number_number_of @ nat @ ( bit1 @ pls ) )
= ( one_one @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_nat__numeral__1__eq__1) ).
thf(530,axiom,
! [V_1: $i,V: $i] :
( ( ( ord_less @ int @ V @ pls )
=> ( ( plus_plus @ nat @ ( number_number_of @ nat @ V ) @ ( number_number_of @ nat @ V_1 ) )
= ( number_number_of @ nat @ V_1 ) ) )
& ( ~ ( ord_less @ int @ V @ pls )
=> ( ( ( ord_less @ int @ V_1 @ pls )
=> ( ( plus_plus @ nat @ ( number_number_of @ nat @ V ) @ ( number_number_of @ nat @ V_1 ) )
= ( number_number_of @ nat @ V ) ) )
& ( ~ ( ord_less @ int @ V_1 @ pls )
=> ( ( plus_plus @ nat @ ( number_number_of @ nat @ V ) @ ( number_number_of @ nat @ V_1 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ V @ V_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_add__nat__number__of) ).
thf(531,axiom,
! [K: $i,I: $i,J: $i] :
( ( ord_less_eq @ int @ I @ J )
=> ( ord_less_eq @ int @ ( plus_plus @ int @ K @ I ) @ ( plus_plus @ int @ K @ J ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_zadd__left__mono) ).
thf(532,axiom,
! [K: $i,I: $i,J: $i] :
( ( ord_less @ int @ I @ J )
=> ( ord_less @ int @ ( plus_plus @ int @ I @ K ) @ ( plus_plus @ int @ J @ K ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_zadd__strict__right__mono) ).
thf(533,axiom,
! [K_1: $i,L_1: $i] :
( ( ord_less_eq @ int @ ( number_number_of @ int @ K_1 ) @ ( number_number_of @ int @ L_1 ) )
<=> ( ord_less_eq @ int @ K_1 @ L_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_less__eq__number__of__int__code) ).
thf(534,axiom,
! [K_1: $i,L_1: $i] :
( ( ord_less @ int @ ( number_number_of @ int @ K_1 ) @ ( number_number_of @ int @ L_1 ) )
<=> ( ord_less @ int @ K_1 @ L_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_less__number__of__int__code) ).
thf(535,axiom,
! [K_1: $i,L_1: $i] :
( ( ord_less_eq @ int @ ( bit0 @ K_1 ) @ ( bit0 @ L_1 ) )
<=> ( ord_less_eq @ int @ K_1 @ L_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_rel__simps_I31_J) ).
thf(536,axiom,
! [K1: $i,K2: $i] :
( ( ord_less_eq @ int @ ( bit0 @ K1 ) @ ( bit0 @ K2 ) )
<=> ( ord_less_eq @ int @ K1 @ K2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_less__eq__int__code_I13_J) ).
thf(537,axiom,
ord_less_eq @ int @ pls @ pls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_rel__simps_I19_J) ).
thf(538,axiom,
! [K_1: $i,L_1: $i] :
( ( ord_less @ int @ ( bit0 @ K_1 ) @ ( bit0 @ L_1 ) )
<=> ( ord_less @ int @ K_1 @ L_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_rel__simps_I14_J) ).
thf(539,axiom,
! [K1: $i,K2: $i] :
( ( ord_less @ int @ ( bit0 @ K1 ) @ ( bit0 @ K2 ) )
<=> ( ord_less @ int @ K1 @ K2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_less__int__code_I13_J) ).
thf(540,axiom,
~ ( ord_less @ int @ pls @ pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_rel__simps_I2_J) ).
thf(541,axiom,
! [K_1: $i,L_1: $i] :
( ( ord_less_eq @ int @ ( bit1 @ K_1 ) @ ( bit1 @ L_1 ) )
<=> ( ord_less_eq @ int @ K_1 @ L_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_rel__simps_I34_J) ).
thf(542,axiom,
! [K1: $i,K2: $i] :
( ( ord_less_eq @ int @ ( bit1 @ K1 ) @ ( bit1 @ K2 ) )
<=> ( ord_less_eq @ int @ K1 @ K2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_less__eq__int__code_I16_J) ).
thf(543,axiom,
! [K_1: $i,L_1: $i] :
( ( ord_less @ int @ ( bit1 @ K_1 ) @ ( bit1 @ L_1 ) )
<=> ( ord_less @ int @ K_1 @ L_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_rel__simps_I17_J) ).
thf(544,axiom,
! [K1: $i,K2: $i] :
( ( ord_less @ int @ ( bit1 @ K1 ) @ ( bit1 @ K2 ) )
<=> ( ord_less @ int @ K1 @ K2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_less__int__code_I16_J) ).
thf(545,axiom,
( ( plus_plus @ nat @ ( one_one @ nat ) @ ( one_one @ nat ) )
= ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_nat__1__add__1) ).
thf(546,axiom,
! [Z: $i] :
( ( times_times @ nat @ Z @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ nat @ Z @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_nat__mult__2__right) ).
thf(547,axiom,
! [Z: $i] :
( ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ Z )
= ( plus_plus @ nat @ Z @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_nat__mult__2) ).
thf(548,axiom,
! [X_1: $i,Y_1: $i,Z: $i] :
( ( power_power @ int @ X_1 @ ( plus_plus @ nat @ Y_1 @ Z ) )
= ( times_times @ int @ ( power_power @ int @ X_1 @ Y_1 ) @ ( power_power @ int @ X_1 @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_zpower__zadd__distrib) ).
thf(549,axiom,
! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [X_1: $i,P: $i,Q: $i] :
( ( times_times @ X_a @ ( power_power @ X_a @ X_1 @ P ) @ ( power_power @ X_a @ X_1 @ Q ) )
= ( power_power @ X_a @ X_1 @ ( plus_plus @ nat @ P @ Q ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
thf(550,axiom,
! [Z_2: $i,Z: $i,W_2: $i,W: $i] :
( ( ord_less @ int @ W_2 @ W )
=> ( ( ord_less_eq @ int @ Z_2 @ Z )
=> ( ord_less @ int @ ( plus_plus @ int @ W_2 @ Z_2 ) @ ( plus_plus @ int @ W @ Z ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_zadd__zless__mono) ).
thf(551,axiom,
! [X_a: $i] :
( ( ( number_ring @ X_a )
& ( linordered_idom @ X_a ) )
=> ! [X_2: $i,Y_2: $i] :
( ( ord_less_eq @ X_a @ ( number_number_of @ X_a @ X_2 ) @ ( number_number_of @ X_a @ Y_2 ) )
<=> ( ord_less_eq @ int @ X_2 @ Y_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_le__number__of) ).
thf(552,axiom,
! [X_a: $i] :
( ( ( number_ring @ X_a )
& ( linordered_idom @ X_a ) )
=> ! [X_2: $i,Y_2: $i] :
( ( ord_less @ X_a @ ( number_number_of @ X_a @ X_2 ) @ ( number_number_of @ X_a @ Y_2 ) )
<=> ( ord_less @ int @ X_2 @ Y_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_less__number__of) ).
thf(554,axiom,
! [X_1: $i,Y_1: $i,Z: $i] :
( ( power_power @ int @ ( power_power @ int @ X_1 @ Y_1 ) @ Z )
= ( power_power @ int @ X_1 @ ( times_times @ nat @ Y_1 @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_zpower__zpower) ).
thf(555,axiom,
! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [X_1: $i] :
( ( power_power @ X_a @ X_1 @ ( one_one @ nat ) )
= ( ti @ X_a @ X_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
thf(556,axiom,
! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [X_1: $i,P: $i,Q: $i] :
( ( power_power @ X_a @ ( power_power @ X_a @ X_1 @ P ) @ Q )
= ( power_power @ X_a @ X_1 @ ( times_times @ nat @ P @ Q ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
thf(557,axiom,
! [Z: $i,W: $i] :
( ( ord_less_eq @ int @ Z @ W )
=> ( ( ord_less_eq @ int @ W @ Z )
=> ( ( ti @ int @ Z )
= ( ti @ int @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_zle__antisym) ).
thf(558,axiom,
! [K: $i,I: $i,J: $i] :
( ( ord_less_eq @ int @ I @ J )
=> ( ( ord_less_eq @ int @ J @ K )
=> ( ord_less_eq @ int @ I @ K ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_zle__trans) ).
thf(559,axiom,
! [X_1: $i,Y_1: $i] :
( ( ord_less @ int @ X_1 @ Y_1 )
| ( ( ti @ int @ X_1 )
= ( ti @ int @ Y_1 ) )
| ( ord_less @ int @ Y_1 @ X_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_zless__linear) ).
thf(560,axiom,
! [Z_1: $i,W_1: $i] :
( ( ord_less @ int @ Z_1 @ W_1 )
<=> ( ( ord_less_eq @ int @ Z_1 @ W_1 )
& ( ( ti @ int @ Z_1 )
!= ( ti @ int @ W_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_zless__le) ).
thf(561,axiom,
! [Z: $i,W: $i] :
( ( ord_less_eq @ int @ Z @ W )
| ( ord_less_eq @ int @ W @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_zle__linear) ).
thf(562,axiom,
! [W: $i] : ( ord_less_eq @ int @ W @ W ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_zle__refl) ).
thf(563,axiom,
~ ! [T_1: $i] :
( ( plus_plus @ int @ ( power_power @ int @ s @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( one_one @ int ) )
!= ( times_times @ int @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19__096_B_Bthesis_O_A_I_B_Bt_O_As_A_094_A2_A_L_A1_A_061_A_I4_A_K_Am_A_L_A1_) ).
thf(564,axiom,
! [X_a: $i] :
( ( number_ring @ X_a )
=> ( ( plus_plus @ X_a @ ( one_one @ X_a ) @ ( one_one @ X_a ) )
= ( number_number_of @ X_a @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_one__add__one__is__two) ).
thf(565,axiom,
! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [V: $i] :
( ( plus_plus @ X_a @ ( number_number_of @ X_a @ V ) @ ( one_one @ X_a ) )
= ( number_number_of @ X_a @ ( plus_plus @ int @ V @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_add__special_I3_J) ).
thf(566,axiom,
! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [W: $i] :
( ( plus_plus @ X_a @ ( one_one @ X_a ) @ ( number_number_of @ X_a @ W ) )
= ( number_number_of @ X_a @ ( plus_plus @ int @ ( bit1 @ pls ) @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_add__special_I2_J) ).
thf(567,axiom,
! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [X_1: $i,N: $i] :
( ( power_power @ X_a @ X_1 @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ N ) )
= ( times_times @ X_a @ ( power_power @ X_a @ X_1 @ N ) @ ( power_power @ X_a @ X_1 @ N ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).
thf(568,axiom,
! [X_a: $i] :
( ( monoid_mult @ X_a )
=> ! [A_1: $i] :
( ( power_power @ X_a @ A_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times @ X_a @ A_1 @ A_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_power2__eq__square) ).
thf(569,axiom,
! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [X_1: $i] :
( ( times_times @ X_a @ X_1 @ X_1 )
= ( power_power @ X_a @ X_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
thf(570,axiom,
! [X_a: $i] :
( ( semiring_1 @ X_a )
=> ( ( power_power @ X_a @ ( one_one @ X_a ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( one_one @ X_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_one__power2) ).
thf(571,axiom,
! [A_1: $i] :
( ( times_times @ int @ A_1 @ ( power_power @ int @ A_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( power_power @ int @ A_1 @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_cube__square) ).
thf(572,axiom,
! [X_b: $i] :
( ( ( monoid_mult @ X_b )
& ( number @ X_b ) )
=> ! [W: $i] :
( ( power_power @ X_b @ ( number_number_of @ X_b @ W ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times @ X_b @ ( number_number_of @ X_b @ W ) @ ( number_number_of @ X_b @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_power2__eq__square__number__of) ).
thf(573,axiom,
! [X_a: $i] :
( ( number_semiring @ X_a )
=> ! [X_1: $i,Y_1: $i] :
( ( power_power @ X_a @ ( plus_plus @ X_a @ X_1 @ Y_1 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ X_a @ ( plus_plus @ X_a @ ( power_power @ X_a @ X_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ X_a @ Y_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times @ X_a @ ( times_times @ X_a @ ( number_number_of @ X_a @ ( bit0 @ ( bit1 @ pls ) ) ) @ X_1 ) @ Y_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_power2__sum) ).
thf(574,axiom,
! [A_1: $i,B: $i] :
( ( power_power @ int @ ( plus_plus @ int @ A_1 @ B ) @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( power_power @ int @ A_1 @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) @ ( times_times @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit1 @ ( bit1 @ pls ) ) ) @ ( power_power @ int @ A_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ B ) ) @ ( times_times @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit1 @ ( bit1 @ pls ) ) ) @ A_1 ) @ ( power_power @ int @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ ( power_power @ int @ B @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_zadd__power3) ).
thf(575,axiom,
! [A_1: $i,B: $i] :
( ( power_power @ int @ ( plus_plus @ int @ A_1 @ B ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ int @ ( plus_plus @ int @ ( power_power @ int @ A_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( times_times @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A_1 ) @ B ) ) @ ( power_power @ int @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_zadd__power2) ).
thf(576,axiom,
twoSqu420862341sum2sq @ ( times_times @ int @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) @ t ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_qf1pt) ).
thf(577,axiom,
( ( plus_plus @ int @ ( power_power @ int @ s @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( one_one @ int ) )
= ( times_times @ int @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) @ t ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_t) ).
thf(578,axiom,
zprime @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_p) ).
thf(579,axiom,
ord_less @ int @ t @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_t__l__p) ).
thf(580,axiom,
( ( ord_less @ int @ ( one_one @ int ) @ t )
=> ? [X: $i,Y: $i] :
( ( plus_plus @ int @ ( power_power @ int @ X @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ Y @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) ).
thf(581,axiom,
( ( t
= ( one_one @ int ) )
=> ? [X: $i,Y: $i] :
( ( plus_plus @ int @ ( power_power @ int @ X @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ Y @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) ).
thf(582,axiom,
ord_less_eq @ int @ ( one_one @ int ) @ t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_tpos) ).
thf(583,axiom,
( ( ti @ int @ t )
= t ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_t_____res) ).
thf(584,axiom,
( ( ti @ int @ s )
= s ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_s_____res) ).
thf(585,axiom,
( ( ti @ int @ s1 )
= s1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_s1_____res) ).
thf(586,axiom,
! [B_1_1: $i] :
( ( ti @ int @ ( twoSqu579703163sum2sq @ B_1_1 ) )
= ( twoSqu579703163sum2sq @ B_1_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_TwoSquares__Mirabelle__iprzenvtji_Osum2sq_res) ).
thf(587,axiom,
! [B_1_1: $i] :
( ( twoSqu579703163sum2sq @ ( ti @ ( product_prod @ int @ int ) @ B_1_1 ) )
= ( twoSqu579703163sum2sq @ B_1_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_TwoSquares__Mirabelle__iprzenvtji_Osum2sq_arg1) ).
thf(588,axiom,
! [B_1_1: $i] :
( ( twoSqu420862341sum2sq @ ( ti @ int @ B_1_1 ) )
<=> ( twoSqu420862341sum2sq @ B_1_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_TwoSquares__Mirabelle__iprzenvtji_Ois__sum2sq_arg1) ).
thf(591,axiom,
! [B_1_1: $i,B_2_1: $i] :
( ( quadRes @ B_1_1 @ ( ti @ int @ B_2_1 ) )
<=> ( quadRes @ B_1_1 @ B_2_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Residues_OQuadRes_arg2) ).
thf(592,axiom,
! [B_1_1: $i,B_2_1: $i] :
( ( quadRes @ ( ti @ int @ B_1_1 ) @ B_2_1 )
<=> ( quadRes @ B_1_1 @ B_2_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Residues_OQuadRes_arg1) ).
thf(593,axiom,
! [B_1_1: $i,B_2_1: $i] :
( ( ti @ int @ ( legendre @ B_1_1 @ B_2_1 ) )
= ( legendre @ B_1_1 @ B_2_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Residues_OLegendre_res) ).
thf(594,axiom,
! [B_1_1: $i,B_2_1: $i] :
( ( legendre @ B_1_1 @ ( ti @ int @ B_2_1 ) )
= ( legendre @ B_1_1 @ B_2_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Residues_OLegendre_arg2) ).
thf(595,axiom,
! [B_1_1: $i,B_2_1: $i] :
( ( legendre @ ( ti @ int @ B_1_1 ) @ B_2_1 )
= ( legendre @ B_1_1 @ B_2_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Residues_OLegendre_arg1) ).
thf(596,axiom,
! [B_1_1: $i,B_2_1: $i] :
( ( ti @ ( product_prod @ int @ int ) @ ( product_Pair @ int @ int @ B_1_1 @ B_2_1 ) )
= ( product_Pair @ int @ int @ B_1_1 @ B_2_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Product__Type_OPair_res) ).
thf(597,axiom,
! [B_1_1: $i,B_2_1: $i] :
( ( product_Pair @ int @ int @ B_1_1 @ ( ti @ int @ B_2_1 ) )
= ( product_Pair @ int @ int @ B_1_1 @ B_2_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Product__Type_OPair_arg2) ).
thf(598,axiom,
! [B_1_1: $i,B_2_1: $i] :
( ( product_Pair @ int @ int @ ( ti @ int @ B_1_1 ) @ B_2_1 )
= ( product_Pair @ int @ int @ B_1_1 @ B_2_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Product__Type_OPair_arg1) ).
thf(599,axiom,
! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( power @ X_a )
=> ( ( ti @ X_a @ ( power_power @ X_a @ B_1_1 @ B_2_1 ) )
= ( power_power @ X_a @ B_1_1 @ B_2_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Power_Opower__class_Opower_res) ).
thf(600,axiom,
! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( power @ X_a )
=> ( ( power_power @ X_a @ B_1_1 @ ( ti @ nat @ B_2_1 ) )
= ( power_power @ X_a @ B_1_1 @ B_2_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Power_Opower__class_Opower_arg2) ).
thf(601,axiom,
! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( power @ X_a )
=> ( ( power_power @ X_a @ ( ti @ X_a @ B_1_1 ) @ B_2_1 )
= ( power_power @ X_a @ B_1_1 @ B_2_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Power_Opower__class_Opower_arg1) ).
thf(606,axiom,
! [B_1_1: $i,X_a: $i] :
( ( number @ X_a )
=> ( ( ti @ X_a @ ( number_number_of @ X_a @ B_1_1 ) )
= ( number_number_of @ X_a @ B_1_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Int_Onumber__class_Onumber__of_res) ).
thf(607,axiom,
! [B_1_1: $i,X_a: $i] :
( ( number @ X_a )
=> ( ( number_number_of @ X_a @ ( ti @ int @ B_1_1 ) )
= ( number_number_of @ X_a @ B_1_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Int_Onumber__class_Onumber__of_arg1) ).
thf(608,axiom,
( ( ti @ int @ min )
= min ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Int_OMin_res) ).
thf(609,axiom,
! [B_1_1: $i] :
( ( zprime @ ( ti @ int @ B_1_1 ) )
<=> ( zprime @ B_1_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_IntPrimes_Ozprime_arg1) ).
thf(610,axiom,
! [B_1_1: $i,B_2_1: $i,B_3: $i] :
( ( zcong @ B_1_1 @ B_2_1 @ ( ti @ int @ B_3 ) )
<=> ( zcong @ B_1_1 @ B_2_1 @ B_3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_IntPrimes_Ozcong_arg3) ).
thf(611,axiom,
! [B_1_1: $i,B_2_1: $i,B_3: $i] :
( ( zcong @ B_1_1 @ ( ti @ int @ B_2_1 ) @ B_3 )
<=> ( zcong @ B_1_1 @ B_2_1 @ B_3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_IntPrimes_Ozcong_arg2) ).
thf(612,axiom,
! [B_1_1: $i,B_2_1: $i,B_3: $i] :
( ( zcong @ ( ti @ int @ B_1_1 ) @ B_2_1 @ B_3 )
<=> ( zcong @ B_1_1 @ B_2_1 @ B_3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_IntPrimes_Ozcong_arg1) ).
thf(618,axiom,
! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( power @ X_a )
=> ( ( ti @ X_a @ ( times_times @ X_a @ B_1_1 @ B_2_1 ) )
= ( times_times @ X_a @ B_1_1 @ B_2_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_4_res) ).
thf(619,axiom,
! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( power @ X_a )
=> ( ( times_times @ X_a @ B_1_1 @ ( ti @ X_a @ B_2_1 ) )
= ( times_times @ X_a @ B_1_1 @ B_2_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_4_arg2) ).
thf(620,axiom,
! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( power @ X_a )
=> ( ( times_times @ X_a @ ( ti @ X_a @ B_1_1 ) @ B_2_1 )
= ( times_times @ X_a @ B_1_1 @ B_2_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_4_arg1) ).
thf(621,axiom,
! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( mult_zero @ X_a )
=> ( ( ti @ X_a @ ( times_times @ X_a @ B_1_1 @ B_2_1 ) )
= ( times_times @ X_a @ B_1_1 @ B_2_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_3_res) ).
thf(622,axiom,
! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( mult_zero @ X_a )
=> ( ( times_times @ X_a @ B_1_1 @ ( ti @ X_a @ B_2_1 ) )
= ( times_times @ X_a @ B_1_1 @ B_2_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_3_arg2) ).
thf(623,axiom,
! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( mult_zero @ X_a )
=> ( ( times_times @ X_a @ ( ti @ X_a @ B_1_1 ) @ B_2_1 )
= ( times_times @ X_a @ B_1_1 @ B_2_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_3_arg1) ).
thf(624,axiom,
! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( no_zero_divisors @ X_a )
=> ( ( ti @ X_a @ ( times_times @ X_a @ B_1_1 @ B_2_1 ) )
= ( times_times @ X_a @ B_1_1 @ B_2_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_2_res) ).
thf(625,axiom,
! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( no_zero_divisors @ X_a )
=> ( ( times_times @ X_a @ B_1_1 @ ( ti @ X_a @ B_2_1 ) )
= ( times_times @ X_a @ B_1_1 @ B_2_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_2_arg2) ).
thf(626,axiom,
! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( no_zero_divisors @ X_a )
=> ( ( times_times @ X_a @ ( ti @ X_a @ B_1_1 ) @ B_2_1 )
= ( times_times @ X_a @ B_1_1 @ B_2_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_2_arg1) ).
thf(627,axiom,
! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( semiring @ X_a )
=> ( ( ti @ X_a @ ( times_times @ X_a @ B_1_1 @ B_2_1 ) )
= ( times_times @ X_a @ B_1_1 @ B_2_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_1_res) ).
thf(628,axiom,
! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( semiring @ X_a )
=> ( ( times_times @ X_a @ B_1_1 @ ( ti @ X_a @ B_2_1 ) )
= ( times_times @ X_a @ B_1_1 @ B_2_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_1_arg2) ).
thf(629,axiom,
! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( semiring @ X_a )
=> ( ( times_times @ X_a @ ( ti @ X_a @ B_1_1 ) @ B_2_1 )
= ( times_times @ X_a @ B_1_1 @ B_2_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_1_arg1) ).
thf(630,axiom,
! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( dvd @ X_a )
=> ( ( ti @ X_a @ ( times_times @ X_a @ B_1_1 @ B_2_1 ) )
= ( times_times @ X_a @ B_1_1 @ B_2_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_0_res) ).
thf(631,axiom,
! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( dvd @ X_a )
=> ( ( times_times @ X_a @ B_1_1 @ ( ti @ X_a @ B_2_1 ) )
= ( times_times @ X_a @ B_1_1 @ B_2_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_0_arg2) ).
thf(632,axiom,
! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( dvd @ X_a )
=> ( ( times_times @ X_a @ ( ti @ X_a @ B_1_1 ) @ B_2_1 )
= ( times_times @ X_a @ B_1_1 @ B_2_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_0_arg1) ).
thf(633,axiom,
! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( ab_group_add @ X_a )
=> ( ( ti @ X_a @ ( plus_plus @ X_a @ B_1_1 @ B_2_1 ) )
= ( plus_plus @ X_a @ B_1_1 @ B_2_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_1_res) ).
thf(634,axiom,
! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( ab_group_add @ X_a )
=> ( ( plus_plus @ X_a @ B_1_1 @ ( ti @ X_a @ B_2_1 ) )
= ( plus_plus @ X_a @ B_1_1 @ B_2_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_1_arg2) ).
thf(635,axiom,
! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( ab_group_add @ X_a )
=> ( ( plus_plus @ X_a @ ( ti @ X_a @ B_1_1 ) @ B_2_1 )
= ( plus_plus @ X_a @ B_1_1 @ B_2_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_1_arg1) ).
thf(636,axiom,
! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( semiring @ X_a )
=> ( ( ti @ X_a @ ( plus_plus @ X_a @ B_1_1 @ B_2_1 ) )
= ( plus_plus @ X_a @ B_1_1 @ B_2_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_0_res) ).
thf(637,axiom,
! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( semiring @ X_a )
=> ( ( plus_plus @ X_a @ B_1_1 @ ( ti @ X_a @ B_2_1 ) )
= ( plus_plus @ X_a @ B_1_1 @ B_2_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_0_arg2) ).
thf(638,axiom,
! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( semiring @ X_a )
=> ( ( plus_plus @ X_a @ ( ti @ X_a @ B_1_1 ) @ B_2_1 )
= ( plus_plus @ X_a @ B_1_1 @ B_2_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_0_arg1) ).
thf(639,axiom,
! [X_a: $i] :
( ( power @ X_a )
=> ( ( ti @ X_a @ ( one_one @ X_a ) )
= ( one_one @ X_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Oone__class_Oone_1_res) ).
thf(640,axiom,
! [X_a: $i] :
( ( zero_neq_one @ X_a )
=> ( ( ti @ X_a @ ( one_one @ X_a ) )
= ( one_one @ X_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Oone__class_Oone_0_res) ).
thf(641,axiom,
! [B_1_1: $i,B_2_1: $i] :
( ( ti @ nat @ ( minus_minus @ nat @ B_1_1 @ B_2_1 ) )
= ( minus_minus @ nat @ B_1_1 @ B_2_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Ominus__class_Ominus_1_res) ).
thf(642,axiom,
! [B_1_1: $i,B_2_1: $i] :
( ( minus_minus @ nat @ B_1_1 @ ( ti @ nat @ B_2_1 ) )
= ( minus_minus @ nat @ B_1_1 @ B_2_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Ominus__class_Ominus_1_arg2) ).
thf(643,axiom,
! [B_1_1: $i,B_2_1: $i] :
( ( minus_minus @ nat @ ( ti @ nat @ B_1_1 ) @ B_2_1 )
= ( minus_minus @ nat @ B_1_1 @ B_2_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Ominus__class_Ominus_1_arg1) ).
thf(647,axiom,
( ( ti @ int @ m )
= m ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_m_res) ).
thf(648,axiom,
( ( ti @ int @ pls )
= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Int_OPls_res) ).
thf(649,axiom,
! [B_1_1: $i] :
( ( ti @ int @ ( bit1 @ B_1_1 ) )
= ( bit1 @ B_1_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Int_OBit1_res) ).
thf(650,axiom,
! [B_1_1: $i] :
( ( bit1 @ ( ti @ int @ B_1_1 ) )
= ( bit1 @ B_1_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Int_OBit1_arg1) ).
thf(651,axiom,
! [B_1_1: $i] :
( ( ti @ int @ ( bit0 @ B_1_1 ) )
= ( bit0 @ B_1_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Int_OBit0_res) ).
thf(652,axiom,
! [B_1_1: $i] :
( ( bit0 @ ( ti @ int @ B_1_1 ) )
= ( bit0 @ B_1_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Int_OBit0_arg1) ).
thf(653,conjecture,
? [X: $i,Y: $i] :
( ( plus_plus @ int @ ( power_power @ int @ X @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ Y @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(654,negated_conjecture,
( ( ? [X: $i,Y: $i] :
( ( plus_plus @ int @ ( power_power @ int @ X @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ Y @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[653]) ).
thf(655,plain,
( ( ? [X: $i,Y: $i] :
( ( plus_plus @ int @ ( power_power @ int @ X @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ Y @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[654]) ).
thf(656,plain,
( ( dvd @ nat )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(657,plain,
( ( number @ nat )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(658,plain,
( ( power @ nat )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(659,plain,
( ( semiring @ nat )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(660,plain,
( ( order @ nat )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(661,plain,
( ( mult_zero @ nat )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(662,plain,
( ( semiring_0 @ nat )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(663,plain,
( ( semiring_1 @ nat )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(664,plain,
( ( monoid_mult @ nat )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(665,plain,
( ( linorder @ nat )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(666,plain,
( ( zero_neq_one @ nat )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(667,plain,
( ( number_semiring @ nat )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(668,plain,
( ( comm_semiring @ nat )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(669,plain,
( ( comm_semiring_1 @ nat )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(670,plain,
( ( no_zero_divisors @ nat )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(671,plain,
( ( comm_monoid_mult @ nat )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(672,plain,
( ( linordered_semidom @ nat )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(673,plain,
( ( ordere453448008miring @ nat )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(674,plain,
( ( semiri456707255roduct @ nat )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(675,plain,
( ( dvd @ int )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(676,plain,
( ( number @ int )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(677,plain,
( ( ring @ int )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(678,plain,
( ( power @ int )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(679,plain,
( ( ring_1 @ int )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(680,plain,
( ( semiring @ int )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(681,plain,
( ( number_ring @ int )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(682,plain,
( ( ring_char_0 @ int )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(683,plain,
( ( order @ int )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(684,plain,
( ( mult_zero @ int )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(685,plain,
( ( semiring_0 @ int )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(686,plain,
( ( semiring_1 @ int )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(687,plain,
( ( comm_ring_1 @ int )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(688,plain,
( ( monoid_mult @ int )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(689,plain,
( ( linorder @ int )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(690,plain,
( ( zero_neq_one @ int )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(691,plain,
( ( ab_group_add @ int )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(692,plain,
( ( number_semiring @ int )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(693,plain,
( ( comm_semiring @ int )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(694,plain,
( ( comm_semiring_1 @ int )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(695,plain,
( ( linordered_idom @ int )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(696,plain,
( ( linordered_ring @ int )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(697,plain,
( ( no_zero_divisors @ int )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(698,plain,
( ( comm_monoid_mult @ int )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(699,plain,
( ( linordered_semidom @ int )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(700,plain,
( ( ring_n68954251visors @ int )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(701,plain,
( ( linord581940658strict @ int )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(702,plain,
( ( ordere453448008miring @ int )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(703,plain,
( ( ring_11004092258visors @ int )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(704,plain,
( ( linord219039673up_add @ int )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(705,plain,
( ( linord626643107strict @ int )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(706,plain,
( ( semiri456707255roduct @ int )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(707,plain,
( ( ! [X_a: $i] :
( ( ordere453448008miring @ X_a )
=> ! [B: $i,A_1: $i] :
( ( ord_less_eq @ X_a @ A_1 @ ( zero_zero @ X_a ) )
=> ( ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ B )
=> ( ord_less_eq @ X_a @ ( times_times @ X_a @ A_1 @ B ) @ ( zero_zero @ X_a ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(708,plain,
( ( ! [X_a: $i] :
( ( ordere453448008miring @ X_a )
=> ! [B: $i,A_1: $i] :
( ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ A_1 )
=> ( ( ord_less_eq @ X_a @ B @ ( zero_zero @ X_a ) )
=> ( ord_less_eq @ X_a @ ( times_times @ X_a @ B @ A_1 ) @ ( zero_zero @ X_a ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(709,plain,
( ( ! [X_a: $i] :
( ( ordere453448008miring @ X_a )
=> ! [B: $i,A_1: $i] :
( ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ A_1 )
=> ( ( ord_less_eq @ X_a @ B @ ( zero_zero @ X_a ) )
=> ( ord_less_eq @ X_a @ ( times_times @ X_a @ A_1 @ B ) @ ( zero_zero @ X_a ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(710,plain,
( ( ! [X_a: $i] :
( ( ordere453448008miring @ X_a )
=> ! [B: $i,A_1: $i] :
( ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ A_1 )
=> ( ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ B )
=> ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ ( times_times @ X_a @ A_1 @ B ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(711,plain,
( ( ! [X_a: $i] :
( ( linord581940658strict @ X_a )
=> ! [A_2: $i,B_1: $i] :
( ( ord_less_eq @ X_a @ ( times_times @ X_a @ A_2 @ B_1 ) @ ( zero_zero @ X_a ) )
<=> ( ( ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ A_2 )
& ( ord_less_eq @ X_a @ B_1 @ ( zero_zero @ X_a ) ) )
| ( ( ord_less_eq @ X_a @ A_2 @ ( zero_zero @ X_a ) )
& ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ B_1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(712,plain,
( ( ! [X_a: $i] :
( ( linord581940658strict @ X_a )
=> ! [A_2: $i,B_1: $i] :
( ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ ( times_times @ X_a @ A_2 @ B_1 ) )
<=> ( ( ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ A_2 )
& ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ B_1 ) )
| ( ( ord_less_eq @ X_a @ A_2 @ ( zero_zero @ X_a ) )
& ( ord_less_eq @ X_a @ B_1 @ ( zero_zero @ X_a ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(713,plain,
( ( ! [X_a: $i] :
( ( linordered_ring @ X_a )
=> ! [A_1: $i] : ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ ( times_times @ X_a @ A_1 @ A_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(714,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i] : ( dvd_dvd @ X_a @ ( one_one @ X_a ) @ A_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(715,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [C: $i,A_1: $i,B: $i] :
( ( dvd_dvd @ X_a @ A_1 @ B )
=> ( ( dvd_dvd @ X_a @ A_1 @ C )
=> ( dvd_dvd @ X_a @ A_1 @ ( plus_plus @ X_a @ B @ C ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(716,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i,B: $i,C: $i] :
( ( dvd_dvd @ X_a @ ( times_times @ X_a @ A_1 @ B ) @ C )
=> ( dvd_dvd @ X_a @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(717,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i,B: $i,C: $i] :
( ( dvd_dvd @ X_a @ ( times_times @ X_a @ A_1 @ B ) @ C )
=> ( dvd_dvd @ X_a @ A_1 @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(718,plain,
( ( ! [X_a: $i] :
( ( dvd @ X_a )
=> ! [A_1: $i,B: $i,K: $i] :
( ( A_1
= ( times_times @ X_a @ B @ K ) )
=> ( dvd_dvd @ X_a @ B @ A_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(719,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [C: $i,D: $i,A_1: $i,B: $i] :
( ( dvd_dvd @ X_a @ A_1 @ B )
=> ( ( dvd_dvd @ X_a @ C @ D )
=> ( dvd_dvd @ X_a @ ( times_times @ X_a @ A_1 @ C ) @ ( times_times @ X_a @ B @ D ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(720,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [B: $i,A_1: $i,C: $i] :
( ( dvd_dvd @ X_a @ A_1 @ C )
=> ( dvd_dvd @ X_a @ A_1 @ ( times_times @ X_a @ B @ C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(721,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [C: $i,A_1: $i,B: $i] :
( ( dvd_dvd @ X_a @ A_1 @ B )
=> ( dvd_dvd @ X_a @ A_1 @ ( times_times @ X_a @ B @ C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(722,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i,B: $i] : ( dvd_dvd @ X_a @ A_1 @ ( times_times @ X_a @ B @ A_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(723,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i,B: $i] : ( dvd_dvd @ X_a @ A_1 @ ( times_times @ X_a @ A_1 @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(724,plain,
( ( ! [X_a: $i] :
( ( semiring @ X_a )
=> ! [A_1: $i,E: $i,B: $i,C: $i] :
( ( plus_plus @ X_a @ ( times_times @ X_a @ A_1 @ E ) @ ( plus_plus @ X_a @ ( times_times @ X_a @ B @ E ) @ C ) )
= ( plus_plus @ X_a @ ( times_times @ X_a @ ( plus_plus @ X_a @ A_1 @ B ) @ E ) @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[105]) ).
thf(725,plain,
( ( ! [X_a: $i] :
( ( comm_semiring @ X_a )
=> ! [A_1: $i,B: $i,C: $i] :
( ( times_times @ X_a @ ( plus_plus @ X_a @ A_1 @ B ) @ C )
= ( plus_plus @ X_a @ ( times_times @ X_a @ A_1 @ C ) @ ( times_times @ X_a @ B @ C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(726,plain,
( ( ! [X_a: $i] :
( ( zero_neq_one @ X_a )
=> ( ( zero_zero @ X_a )
!= ( one_one @ X_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(727,plain,
( ( ! [X_a: $i] :
( ( zero_neq_one @ X_a )
=> ( ( one_one @ X_a )
!= ( zero_zero @ X_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[108]) ).
thf(728,plain,
( ( ! [X_a: $i] :
( ( no_zero_divisors @ X_a )
=> ! [A_1: $i,B: $i] :
( ( ( times_times @ X_a @ A_1 @ B )
= ( zero_zero @ X_a ) )
=> ( ( ( ti @ X_a @ A_1 )
= ( zero_zero @ X_a ) )
| ( ( ti @ X_a @ B )
= ( zero_zero @ X_a ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(729,plain,
( ( ! [X_a: $i] :
( ( no_zero_divisors @ X_a )
=> ! [B: $i,A_1: $i] :
( ( ( ti @ X_a @ A_1 )
!= ( zero_zero @ X_a ) )
=> ( ( ( ti @ X_a @ B )
!= ( zero_zero @ X_a ) )
=> ( ( times_times @ X_a @ A_1 @ B )
!= ( zero_zero @ X_a ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[110]) ).
thf(730,plain,
( ( ! [X_a: $i] :
( ( ring_n68954251visors @ X_a )
=> ! [A_2: $i,B_1: $i] :
( ( ( times_times @ X_a @ A_2 @ B_1 )
= ( zero_zero @ X_a ) )
<=> ( ( ( ti @ X_a @ A_2 )
= ( zero_zero @ X_a ) )
| ( ( ti @ X_a @ B_1 )
= ( zero_zero @ X_a ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[111]) ).
thf(731,plain,
( ( ! [X_a: $i] :
( ( mult_zero @ X_a )
=> ! [A_1: $i] :
( ( times_times @ X_a @ A_1 @ ( zero_zero @ X_a ) )
= ( zero_zero @ X_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[112]) ).
thf(732,plain,
( ( ! [X_a: $i] :
( ( mult_zero @ X_a )
=> ! [A_1: $i] :
( ( times_times @ X_a @ ( zero_zero @ X_a ) @ A_1 )
= ( zero_zero @ X_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[113]) ).
thf(733,plain,
( ( ! [A_1: $i,N: $i] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
=> ( ( ord_less @ real @ ( zero_zero @ real ) @ A_1 )
=> ? [R: $i] :
( ( ord_less @ real @ ( zero_zero @ real ) @ R )
& ( ( power_power @ real @ R @ N )
= A_1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[118]) ).
thf(734,plain,
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( number_number_of @ int @ ( bit1 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[120]) ).
thf(735,plain,
( ( ! [N: $i,X_1: $i] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ X_1 )
=> ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( power_power @ int @ X_1 @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[121]) ).
thf(736,plain,
( ( ! [Y_1: $i,X_1: $i] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ X_1 )
=> ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ Y_1 )
=> ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ X_1 @ Y_1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[122]) ).
thf(737,plain,
( ( ! [Y_1: $i,X_1: $i] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ X_1 )
=> ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ Y_1 )
=> ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( times_times @ int @ X_1 @ Y_1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[123]) ).
thf(738,plain,
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( one_one @ int ) )
= $true ),
inference(unfold_def,[status(thm)],[124]) ).
thf(739,plain,
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( zero_zero @ int ) )
= $true ),
inference(unfold_def,[status(thm)],[125]) ).
thf(740,plain,
( ( ! [X_a: $i] :
( ( power @ X_a )
=> ! [M: $i,N: $i] :
( ( ( N
= ( zero_zero @ nat ) )
=> ( ( power_power @ X_a @ M @ N )
= ( one_one @ X_a ) ) )
& ( ( N
!= ( zero_zero @ nat ) )
=> ( ( power_power @ X_a @ M @ N )
= ( times_times @ X_a @ M @ ( power_power @ X_a @ M @ ( minus_minus @ nat @ N @ ( one_one @ nat ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[130]) ).
thf(741,plain,
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[131]) ).
thf(742,plain,
( ( ! [B: $i,Q: $i,R_1: $i,B_2: $i,Q_1: $i,R_2: $i] :
( ( ( plus_plus @ int @ ( times_times @ int @ B @ Q ) @ R_1 )
= ( plus_plus @ int @ ( times_times @ int @ B_2 @ Q_1 ) @ R_2 ) )
=> ( ( ord_less @ int @ ( plus_plus @ int @ ( times_times @ int @ B_2 @ Q_1 ) @ R_2 ) @ ( zero_zero @ int ) )
=> ( ( ord_less @ int @ R_1 @ B )
=> ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ R_2 )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ B_2 )
=> ( ( ord_less_eq @ int @ B_2 @ B )
=> ( ord_less_eq @ int @ Q_1 @ Q ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[133]) ).
thf(743,plain,
( ( ! [B: $i,Q_1: $i,R_2: $i,Q: $i,R_1: $i] :
( ( ord_less_eq @ int @ ( plus_plus @ int @ ( times_times @ int @ B @ Q_1 ) @ R_2 ) @ ( plus_plus @ int @ ( times_times @ int @ B @ Q ) @ R_1 ) )
=> ( ( ord_less_eq @ int @ R_1 @ ( zero_zero @ int ) )
=> ( ( ord_less @ int @ B @ R_1 )
=> ( ( ord_less @ int @ B @ R_2 )
=> ( ord_less_eq @ int @ Q @ Q_1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[134]) ).
thf(744,plain,
( ( ! [B: $i,Q: $i,R_1: $i,B_2: $i,Q_1: $i,R_2: $i] :
( ( ( plus_plus @ int @ ( times_times @ int @ B @ Q ) @ R_1 )
= ( plus_plus @ int @ ( times_times @ int @ B_2 @ Q_1 ) @ R_2 ) )
=> ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( times_times @ int @ B_2 @ Q_1 ) @ R_2 ) )
=> ( ( ord_less @ int @ R_2 @ B_2 )
=> ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ R_1 )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ B_2 )
=> ( ( ord_less_eq @ int @ B_2 @ B )
=> ( ord_less_eq @ int @ Q @ Q_1 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[135]) ).
thf(745,plain,
( ( ! [B: $i,Q_1: $i,R_2: $i,Q: $i,R_1: $i] :
( ( ord_less_eq @ int @ ( plus_plus @ int @ ( times_times @ int @ B @ Q_1 ) @ R_2 ) @ ( plus_plus @ int @ ( times_times @ int @ B @ Q ) @ R_1 ) )
=> ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ R_2 )
=> ( ( ord_less @ int @ R_2 @ B )
=> ( ( ord_less @ int @ R_1 @ B )
=> ( ord_less_eq @ int @ Q_1 @ Q ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[136]) ).
thf(746,plain,
( ( ! [B_2: $i,Q_1: $i,R_2: $i] :
( ( ord_less @ int @ ( plus_plus @ int @ ( times_times @ int @ B_2 @ Q_1 ) @ R_2 ) @ ( zero_zero @ int ) )
=> ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ R_2 )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ B_2 )
=> ( ord_less_eq @ int @ Q_1 @ ( zero_zero @ int ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[137]) ).
thf(747,plain,
( ( ! [B_2: $i,Q_1: $i,R_2: $i] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( times_times @ int @ B_2 @ Q_1 ) @ R_2 ) )
=> ( ( ord_less @ int @ R_2 @ B_2 )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ B_2 )
=> ( ord_less_eq @ int @ ( zero_zero @ int ) @ Q_1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[138]) ).
thf(748,plain,
( ( ! [N: $i] : ( ord_less_eq @ real @ ( one_one @ real ) @ ( power_power @ real @ ( number_number_of @ real @ ( bit0 @ ( bit1 @ pls ) ) ) @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[139]) ).
thf(749,plain,
( ( ! [X_a: $i] :
( ( ring_1 @ X_a )
=> ! [X_1: $i] :
( ( minus_minus @ X_a @ ( times_times @ X_a @ X_1 @ X_1 ) @ ( one_one @ X_a ) )
= ( times_times @ X_a @ ( plus_plus @ X_a @ X_1 @ ( one_one @ X_a ) ) @ ( minus_minus @ X_a @ X_1 @ ( one_one @ X_a ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[141]) ).
thf(750,plain,
( ( ! [X_2: $i,Y_2: $i] :
( ( ( plus_plus @ real @ ( times_times @ real @ X_2 @ X_2 ) @ ( times_times @ real @ Y_2 @ Y_2 ) )
= ( zero_zero @ real ) )
<=> ( ( X_2
= ( zero_zero @ real ) )
& ( Y_2
= ( zero_zero @ real ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[142]) ).
thf(751,plain,
( ( ! [X_2: $i,Y_2: $i,Z_1: $i] :
( ( ord_less @ real @ ( zero_zero @ real ) @ Z_1 )
=> ( ( ord_less @ real @ ( times_times @ real @ X_2 @ Z_1 ) @ ( times_times @ real @ Y_2 @ Z_1 ) )
<=> ( ord_less @ real @ X_2 @ Y_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[143]) ).
thf(752,plain,
( ( ! [Y_1: $i,X_1: $i] :
( ( ord_less @ real @ ( zero_zero @ real ) @ X_1 )
=> ( ( ord_less @ real @ ( zero_zero @ real ) @ Y_1 )
=> ( ord_less @ real @ ( zero_zero @ real ) @ ( times_times @ real @ X_1 @ Y_1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[146]) ).
thf(753,plain,
( ( ! [X_1: $i,Y_1: $i,Z: $i] :
( ( ord_less @ real @ ( zero_zero @ real ) @ Z )
=> ( ( ord_less @ real @ X_1 @ Y_1 )
=> ( ord_less @ real @ ( times_times @ real @ Z @ X_1 ) @ ( times_times @ real @ Z @ Y_1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[147]) ).
thf(754,plain,
( ( ! [X_a: $i] :
( ( ring @ X_a )
=> ! [X_1: $i,Y_1: $i,A_1: $i,B: $i] :
( ( minus_minus @ X_a @ ( times_times @ X_a @ X_1 @ Y_1 ) @ ( times_times @ X_a @ A_1 @ B ) )
= ( plus_plus @ X_a @ ( times_times @ X_a @ X_1 @ ( minus_minus @ X_a @ Y_1 @ B ) ) @ ( times_times @ X_a @ ( minus_minus @ X_a @ X_1 @ A_1 ) @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[148]) ).
thf(755,plain,
( ( ! [Z1: $i,Z2: $i,W: $i] :
( ( times_times @ real @ ( plus_plus @ real @ Z1 @ Z2 ) @ W )
= ( plus_plus @ real @ ( times_times @ real @ Z1 @ W ) @ ( times_times @ real @ Z2 @ W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[149]) ).
thf(756,plain,
( ( ! [A_2: $i,B_1: $i,C_1: $i] :
( ( C_1
!= ( zero_zero @ real ) )
=> ( ( ( times_times @ real @ A_2 @ C_1 )
= ( times_times @ real @ B_1 @ C_1 ) )
<=> ( A_2 = B_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[150]) ).
thf(757,plain,
( ( ! [A_2: $i,B_1: $i,C_1: $i] :
( ( C_1
!= ( zero_zero @ real ) )
=> ( ( ( times_times @ real @ C_1 @ A_2 )
= ( times_times @ real @ C_1 @ B_1 ) )
<=> ( A_2 = B_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[151]) ).
thf(758,plain,
( ( ! [X_a: $i] :
( ( ab_group_add @ X_a )
=> ! [A_1: $i,C: $i,B: $i,D: $i] :
( ( minus_minus @ X_a @ ( plus_plus @ X_a @ A_1 @ C ) @ ( plus_plus @ X_a @ B @ D ) )
= ( plus_plus @ X_a @ ( minus_minus @ X_a @ A_1 @ B ) @ ( minus_minus @ X_a @ C @ D ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[152]) ).
thf(759,plain,
( ( ! [Z: $i,X_1: $i,Y_1: $i] :
( ( ord_less_eq @ real @ X_1 @ Y_1 )
=> ( ord_less_eq @ real @ ( plus_plus @ real @ Z @ X_1 ) @ ( plus_plus @ real @ Z @ Y_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[153]) ).
thf(760,plain,
( ( ! [Z1: $i,Z2: $i,Z3: $i] :
( ( times_times @ real @ ( times_times @ real @ Z1 @ Z2 ) @ Z3 )
= ( times_times @ real @ Z1 @ ( times_times @ real @ Z2 @ Z3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[154]) ).
thf(761,plain,
( ( ! [Z: $i,W: $i] :
( ( times_times @ real @ Z @ W )
= ( times_times @ real @ W @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[155]) ).
thf(762,plain,
( ( ! [Z: $i] :
( ( times_times @ real @ ( one_one @ real ) @ Z )
= Z ) )
= $true ),
inference(unfold_def,[status(thm)],[156]) ).
thf(763,plain,
( ( ( zero_zero @ real )
!= ( one_one @ real ) )
= $true ),
inference(unfold_def,[status(thm)],[160]) ).
thf(764,plain,
( ( ! [X_2: $i,Y_2: $i] :
( ( ( plus_plus @ real @ ( power_power @ real @ X_2 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ real @ Y_2 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ real ) )
<=> ( ( X_2
= ( zero_zero @ real ) )
& ( Y_2
= ( zero_zero @ real ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[162]) ).
thf(765,plain,
( ( ! [Ma: $i,X_2: $i] :
( ( quadRes @ Ma @ X_2 )
<=> ? [Y: $i] : ( zcong @ ( power_power @ int @ Y @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ X_2 @ Ma ) ) )
= $true ),
inference(unfold_def,[status(thm)],[163]) ).
thf(766,plain,
( ( ! [X_1: $i,Q: $i,N: $i,R_1: $i] :
( ( X_1
= ( plus_plus @ nat @ ( times_times @ nat @ Q @ N ) @ R_1 ) )
=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ R_1 )
=> ( ( ord_less @ nat @ R_1 @ N )
=> ~ ( dvd_dvd @ nat @ N @ X_1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[167]) ).
thf(767,plain,
( ( ! [Y_1: $i,X_1: $i,P: $i] :
( ( zprime @ P )
=> ( ~ ( zcong @ X_1 @ ( zero_zero @ int ) @ P )
=> ( ~ ( zcong @ Y_1 @ ( zero_zero @ int ) @ P )
=> ~ ( zcong @ ( times_times @ int @ X_1 @ Y_1 ) @ ( zero_zero @ int ) @ P ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[168]) ).
thf(768,plain,
( ( ! [P: $i,Y_1: $i,N: $i] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
=> ( ( dvd_dvd @ int @ P @ Y_1 )
=> ( dvd_dvd @ int @ P @ ( power_power @ int @ Y_1 @ N ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[169]) ).
thf(769,plain,
( ( ! [M: $i,N: $i,P: $i] :
( ( zprime @ P )
=> ( ( dvd_dvd @ int @ P @ ( times_times @ int @ M @ N ) )
=> ( ( dvd_dvd @ int @ P @ M )
| ( dvd_dvd @ int @ P @ N ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[171]) ).
thf(770,plain,
( ( ! [X_2: $i,N_1: $i] :
( ( ( power_power @ nat @ X_2 @ N_1 )
= ( one_one @ nat ) )
<=> ( ( X_2
= ( one_one @ nat ) )
| ( N_1
= ( zero_zero @ nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[172]) ).
thf(771,plain,
( ( ! [X_2: $i,P_1: $i] :
( ( zcong @ X_2 @ ( zero_zero @ int ) @ P_1 )
<=> ( dvd_dvd @ int @ P_1 @ X_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[173]) ).
thf(772,plain,
( ( ! [A_2: $i,Ma: $i] :
( ( zcong @ A_2 @ ( zero_zero @ int ) @ Ma )
<=> ( dvd_dvd @ int @ Ma @ A_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[174]) ).
thf(773,plain,
( ( ! [A_1: $i,N: $i,B: $i] :
( ( dvd_dvd @ nat @ ( power_power @ nat @ A_1 @ N ) @ ( power_power @ nat @ B @ N ) )
=> ( ( N
!= ( zero_zero @ nat ) )
=> ( dvd_dvd @ nat @ A_1 @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[175]) ).
thf(774,plain,
( ( ! [X_1: $i,Y_1: $i,N: $i] :
( ( N
!= ( zero_zero @ nat ) )
=> ( ( dvd_dvd @ nat @ ( power_power @ nat @ X_1 @ N ) @ Y_1 )
=> ( dvd_dvd @ nat @ X_1 @ Y_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[176]) ).
thf(775,plain,
( ( ! [N: $i,M: $i] :
( ( dvd_dvd @ int @ N @ M )
=> ( ( ord_less_eq @ int @ M @ ( zero_zero @ int ) )
| ( ord_less_eq @ int @ N @ M ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[177]) ).
thf(776,plain,
( ( ! [M: $i,X_1: $i] :
( ( ord_less @ int @ ( zero_zero @ int ) @ X_1 )
=> ( ( ord_less @ int @ X_1 @ M )
=> ~ ( zcong @ X_1 @ ( zero_zero @ int ) @ M ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[179]) ).
thf(777,plain,
( ( ! [Ma: $i,K_1: $i,N_1: $i] :
( ( dvd_dvd @ nat @ ( times_times @ nat @ Ma @ K_1 ) @ ( times_times @ nat @ N_1 @ K_1 ) )
<=> ( ( K_1
= ( zero_zero @ nat ) )
| ( dvd_dvd @ nat @ Ma @ N_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[180]) ).
thf(778,plain,
( ( ! [A_1: $i,B: $i] :
( ( dvd_dvd @ nat @ A_1 @ B )
=> ( ( B
= ( zero_zero @ nat ) )
| ( ord_less_eq @ nat @ A_1 @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[181]) ).
thf(779,plain,
( ( ! [Z: $i,X_1: $i,Y_1: $i,M: $i] :
( ( zcong @ X_1 @ Y_1 @ M )
=> ( zcong @ ( power_power @ int @ X_1 @ Z ) @ ( power_power @ int @ Y_1 @ Z ) @ M ) ) )
= $true ),
inference(unfold_def,[status(thm)],[182]) ).
thf(780,plain,
( ( ! [N: $i,X_1: $i,Y_1: $i] :
( ( dvd_dvd @ nat @ X_1 @ Y_1 )
=> ( dvd_dvd @ nat @ ( power_power @ nat @ X_1 @ N ) @ ( power_power @ nat @ Y_1 @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[183]) ).
thf(781,plain,
( ( ! [Ma: $i,N_1: $i] :
( ( ( power_power @ nat @ Ma @ N_1 )
= ( zero_zero @ nat ) )
<=> ( ( N_1
!= ( zero_zero @ nat ) )
& ( Ma
= ( zero_zero @ nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[184]) ).
thf(782,plain,
( ( ! [C: $i,A_1: $i,B: $i,M: $i] :
( ( zcong @ A_1 @ B @ M )
=> ( zcong @ ( plus_plus @ int @ A_1 @ C ) @ ( plus_plus @ int @ B @ C ) @ M ) ) )
= $true ),
inference(unfold_def,[status(thm)],[185]) ).
thf(783,plain,
( ( ! [C_1: $i,D_1: $i,A_2: $i,B_1: $i,Ma: $i] :
( ( zcong @ A_2 @ B_1 @ Ma )
=> ( ( zcong @ C_1 @ ( times_times @ int @ A_2 @ D_1 ) @ Ma )
<=> ( zcong @ C_1 @ ( times_times @ int @ B_1 @ D_1 ) @ Ma ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[186]) ).
thf(784,plain,
( ( ! [C_1: $i,D_1: $i,A_2: $i,B_1: $i,Ma: $i] :
( ( zcong @ A_2 @ B_1 @ Ma )
=> ( ( zcong @ C_1 @ ( times_times @ int @ D_1 @ A_2 ) @ Ma )
<=> ( zcong @ C_1 @ ( times_times @ int @ D_1 @ B_1 ) @ Ma ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[187]) ).
thf(785,plain,
( ( ! [A_1: $i,B: $i,C: $i] :
( ( ( minus_minus @ int @ A_1 @ B )
= ( ti @ int @ C ) )
=> ( ( ti @ int @ A_1 )
= ( plus_plus @ int @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[188]) ).
thf(786,plain,
( ( ! [N_1: $i,Ma: $i] :
( ( ( times_times @ nat @ N_1 @ Ma )
= ( one_one @ nat ) )
<=> ( ( N_1
= ( one_one @ nat ) )
& ( Ma
= ( one_one @ nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[189]) ).
thf(787,plain,
( ( ! [M: $i] : ( zcong @ M @ ( zero_zero @ int ) @ M ) )
= $true ),
inference(unfold_def,[status(thm)],[190]) ).
thf(788,plain,
( ( ! [C: $i,A_1: $i,B: $i] :
( ( dvd_dvd @ nat @ A_1 @ B )
=> ( dvd_dvd @ nat @ ( times_times @ nat @ A_1 @ C ) @ ( times_times @ nat @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[191]) ).
thf(789,plain,
( ( ! [C: $i,A_1: $i,B: $i] :
( ( dvd_dvd @ nat @ A_1 @ B )
=> ( dvd_dvd @ nat @ ( times_times @ nat @ C @ A_1 ) @ ( times_times @ nat @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[192]) ).
thf(790,plain,
( ( ! [B: $i,D: $i,A_1: $i] :
( ( dvd_dvd @ nat @ D @ A_1 )
=> ( ( dvd_dvd @ nat @ D @ ( plus_plus @ nat @ A_1 @ B ) )
=> ( dvd_dvd @ nat @ D @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[193]) ).
thf(791,plain,
( ( ! [X_1: $i,Y_1: $i] :
( ( minus_minus @ nat @ ( power_power @ nat @ X_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ nat @ Y_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( times_times @ nat @ ( plus_plus @ nat @ X_1 @ Y_1 ) @ ( minus_minus @ nat @ X_1 @ Y_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[194]) ).
thf(792,plain,
( ( ! [P: $i,M: $i] :
( ( ( M
= ( zero_zero @ nat ) )
=> ( ( power_power @ nat @ P @ M )
= ( one_one @ nat ) ) )
& ( ( M
!= ( zero_zero @ nat ) )
=> ( ( power_power @ nat @ P @ M )
= ( times_times @ nat @ P @ ( power_power @ nat @ P @ ( minus_minus @ nat @ M @ ( one_one @ nat ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[195]) ).
thf(793,plain,
( ( ! [N: $i,M: $i] :
( ( ( M
= ( zero_zero @ nat ) )
=> ( ( times_times @ nat @ M @ N )
= ( zero_zero @ nat ) ) )
& ( ( M
!= ( zero_zero @ nat ) )
=> ( ( times_times @ nat @ M @ N )
= ( plus_plus @ nat @ N @ ( times_times @ nat @ ( minus_minus @ nat @ M @ ( one_one @ nat ) ) @ N ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[196]) ).
thf(794,plain,
( ( ! [D: $i,C: $i,A_1: $i,B: $i,M: $i] :
( ( zcong @ A_1 @ B @ M )
=> ( ( ( ti @ int @ B )
= ( ti @ int @ C ) )
=> ( ( zcong @ C @ D @ M )
=> ( zcong @ A_1 @ D @ M ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[197]) ).
thf(795,plain,
( ( ! [X_2: $i,Y_2: $i] :
( ( ( dvd_dvd @ nat @ X_2 @ Y_2 )
& ( dvd_dvd @ nat @ Y_2 @ X_2 ) )
<=> ( X_2 = Y_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[198]) ).
thf(796,plain,
( ( ! [N: $i,M: $i] :
( ( dvd_dvd @ nat @ N @ M )
=> ( ( M
= ( zero_zero @ nat ) )
| ( M = N )
| ( ord_less_eq @ nat @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ N ) @ M ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[199]) ).
thf(797,plain,
( ( ! [X_1: $i,P: $i] :
( ( ord_less @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ P )
=> ( ( zcong @ X_1 @ ( number_number_of @ int @ min ) @ P )
=> ~ ( zcong @ X_1 @ ( one_one @ int ) @ P ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[201]) ).
thf(798,plain,
( ( ! [M: $i] :
( ( ord_less @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ M )
=> ~ ( zcong @ ( one_one @ int ) @ ( number_number_of @ int @ min ) @ M ) ) )
= $true ),
inference(unfold_def,[status(thm)],[202]) ).
thf(799,plain,
( ( ! [M: $i] :
( ( zprime @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ M ) @ ( one_one @ int ) ) )
=> ( ( legendre @ ( number_number_of @ int @ min ) @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ M ) @ ( one_one @ int ) ) )
= ( one_one @ int ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[203]) ).
thf(800,plain,
( ( ! [N: $i] :
( ( ( power_power @ int @ ( number_number_of @ int @ min ) @ N )
= ( one_one @ int ) )
| ( ( power_power @ int @ ( number_number_of @ int @ min ) @ N )
= ( number_number_of @ int @ min ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[204]) ).
thf(801,plain,
( ( ! [A_1: $i,B: $i] :
( ( power_power @ int @ ( minus_minus @ int @ A_1 @ B ) @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( minus_minus @ int @ ( plus_plus @ int @ ( minus_minus @ int @ ( power_power @ int @ A_1 @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) @ ( times_times @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit1 @ ( bit1 @ pls ) ) ) @ ( power_power @ int @ A_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ B ) ) @ ( times_times @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit1 @ ( bit1 @ pls ) ) ) @ A_1 ) @ ( power_power @ int @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ ( power_power @ int @ B @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[205]) ).
thf(802,plain,
( ( ! [A_1: $i,B: $i] :
( ( power_power @ int @ ( minus_minus @ int @ A_1 @ B ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ int @ ( minus_minus @ int @ ( power_power @ int @ A_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( times_times @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A_1 ) @ B ) ) @ ( power_power @ int @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[206]) ).
thf(803,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [X_1: $i,Y_1: $i] :
( ( power_power @ X_a @ ( minus_minus @ X_a @ X_1 @ Y_1 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( minus_minus @ X_a @ ( plus_plus @ X_a @ ( power_power @ X_a @ X_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ X_a @ Y_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times @ X_a @ ( times_times @ X_a @ ( number_number_of @ X_a @ ( bit0 @ ( bit1 @ pls ) ) ) @ X_1 ) @ Y_1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[207]) ).
thf(804,plain,
( ( ! [A_1: $i,B: $i] :
( ( times_times @ int @ ( plus_plus @ int @ A_1 @ B ) @ ( minus_minus @ int @ A_1 @ B ) )
= ( minus_minus @ int @ ( power_power @ int @ A_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[208]) ).
thf(805,plain,
( ( ! [A_1: $i,B: $i,P: $i,Q: $i] :
( ( times_times @ int @ ( twoSqu579703163sum2sq @ ( product_Pair @ int @ int @ A_1 @ B ) ) @ ( twoSqu579703163sum2sq @ ( product_Pair @ int @ int @ P @ Q ) ) )
= ( twoSqu579703163sum2sq @ ( product_Pair @ int @ int @ ( plus_plus @ int @ ( times_times @ int @ A_1 @ P ) @ ( times_times @ int @ B @ Q ) ) @ ( minus_minus @ int @ ( times_times @ int @ A_1 @ Q ) @ ( times_times @ int @ B @ P ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[211]) ).
thf(806,plain,
( ( ! [A_2: $i,P_1: $i] :
( ( zcong @ ( times_times @ int @ A_2 @ ( minus_minus @ int @ P_1 @ ( one_one @ int ) ) ) @ ( one_one @ int ) @ P_1 )
<=> ( zcong @ A_2 @ ( minus_minus @ int @ P_1 @ ( one_one @ int ) ) @ P_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[212]) ).
thf(807,plain,
( ( ! [L: $i] :
( ( minus_minus @ int @ min @ ( bit0 @ L ) )
= ( bit1 @ ( minus_minus @ int @ min @ L ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[213]) ).
thf(808,plain,
( ( ! [L: $i] :
( ( minus_minus @ int @ min @ ( bit1 @ L ) )
= ( bit0 @ ( minus_minus @ int @ min @ L ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[214]) ).
thf(809,plain,
( ( ! [L: $i] :
( ( minus_minus @ int @ pls @ ( bit1 @ L ) )
= ( bit1 @ ( minus_minus @ int @ min @ L ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[215]) ).
thf(810,plain,
( ( ! [W_1: $i,Z_1: $i] :
( ( ord_less_eq @ int @ W_1 @ ( minus_minus @ int @ Z_1 @ ( one_one @ int ) ) )
<=> ( ord_less @ int @ W_1 @ Z_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[216]) ).
thf(811,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [V: $i,W: $i,C: $i] :
( ( plus_plus @ X_a @ ( number_number_of @ X_a @ V ) @ ( minus_minus @ X_a @ ( number_number_of @ X_a @ W ) @ C ) )
= ( minus_minus @ X_a @ ( number_number_of @ X_a @ ( plus_plus @ int @ V @ W ) ) @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[218]) ).
thf(812,plain,
( ( ! [A_2: $i,B_1: $i,Ma: $i] :
( ( zcong @ A_2 @ B_1 @ Ma )
<=> ( dvd_dvd @ int @ Ma @ ( minus_minus @ int @ A_2 @ B_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[219]) ).
thf(813,plain,
( ( ! [A_1: $i,R_1: $i,B: $i,M: $i,C: $i,D: $i,N: $i] :
( ( plus_plus @ int @ ( times_times @ int @ ( minus_minus @ int @ A_1 @ ( times_times @ int @ R_1 @ B ) ) @ M ) @ ( times_times @ int @ ( minus_minus @ int @ C @ ( times_times @ int @ R_1 @ D ) ) @ N ) )
= ( minus_minus @ int @ ( plus_plus @ int @ ( times_times @ int @ A_1 @ M ) @ ( times_times @ int @ C @ N ) ) @ ( times_times @ int @ R_1 @ ( plus_plus @ int @ ( times_times @ int @ B @ M ) @ ( times_times @ int @ D @ N ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[220]) ).
thf(814,plain,
( ( ! [K_1: $i,L_1: $i] :
( ( ord_less @ int @ K_1 @ L_1 )
<=> ( ord_less @ int @ ( minus_minus @ int @ K_1 @ L_1 ) @ ( zero_zero @ int ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[221]) ).
thf(815,plain,
( ( ! [L: $i] :
( ( minus_minus @ int @ pls @ ( bit0 @ L ) )
= ( bit0 @ ( minus_minus @ int @ pls @ L ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[222]) ).
thf(816,plain,
( ( ! [K: $i,L: $i] :
( ( minus_minus @ int @ ( bit1 @ K ) @ ( bit1 @ L ) )
= ( bit0 @ ( minus_minus @ int @ K @ L ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[223]) ).
thf(817,plain,
( ( ! [K: $i,L: $i] :
( ( minus_minus @ int @ ( bit1 @ K ) @ ( bit0 @ L ) )
= ( bit1 @ ( minus_minus @ int @ K @ L ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[224]) ).
thf(818,plain,
( ( ! [X_b: $i] :
( ( ( number @ X_b )
& ( ring @ X_b ) )
=> ! [A_1: $i,B: $i,V: $i] :
( ( times_times @ X_b @ ( minus_minus @ X_b @ A_1 @ B ) @ ( number_number_of @ X_b @ V ) )
= ( minus_minus @ X_b @ ( times_times @ X_b @ A_1 @ ( number_number_of @ X_b @ V ) ) @ ( times_times @ X_b @ B @ ( number_number_of @ X_b @ V ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[225]) ).
thf(819,plain,
( ( ! [X_b: $i] :
( ( ( number @ X_b )
& ( ring @ X_b ) )
=> ! [V: $i,B: $i,C: $i] :
( ( times_times @ X_b @ ( number_number_of @ X_b @ V ) @ ( minus_minus @ X_b @ B @ C ) )
= ( minus_minus @ X_b @ ( times_times @ X_b @ ( number_number_of @ X_b @ V ) @ B ) @ ( times_times @ X_b @ ( number_number_of @ X_b @ V ) @ C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[226]) ).
thf(820,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [V: $i,W: $i] :
( ( number_number_of @ X_a @ ( minus_minus @ int @ V @ W ) )
= ( minus_minus @ X_a @ ( number_number_of @ X_a @ V ) @ ( number_number_of @ X_a @ W ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[227]) ).
thf(821,plain,
( ( ! [K: $i,M: $i,N: $i] :
( ( dvd_dvd @ int @ K @ ( minus_minus @ int @ M @ N ) )
=> ( ( dvd_dvd @ int @ K @ N )
=> ( dvd_dvd @ int @ K @ M ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[228]) ).
thf(822,plain,
( ( ! [W: $i,Z1: $i,Z2: $i] :
( ( times_times @ int @ W @ ( minus_minus @ int @ Z1 @ Z2 ) )
= ( minus_minus @ int @ ( times_times @ int @ W @ Z1 ) @ ( times_times @ int @ W @ Z2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[229]) ).
thf(823,plain,
( ( ! [Z1: $i,Z2: $i,W: $i] :
( ( times_times @ int @ ( minus_minus @ int @ Z1 @ Z2 ) @ W )
= ( minus_minus @ int @ ( times_times @ int @ Z1 @ W ) @ ( times_times @ int @ Z2 @ W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[230]) ).
thf(824,plain,
( ( ! [K: $i,L: $i] :
( ( minus_minus @ int @ ( bit0 @ K ) @ ( bit0 @ L ) )
= ( bit0 @ ( minus_minus @ int @ K @ L ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[231]) ).
thf(825,plain,
( ( ! [K: $i] :
( ( minus_minus @ int @ K @ pls )
= ( ti @ int @ K ) ) )
= $true ),
inference(unfold_def,[status(thm)],[232]) ).
thf(826,plain,
( ( ! [C: $i,D: $i,A_1: $i,B: $i,M: $i] :
( ( zcong @ A_1 @ B @ M )
=> ( ( zcong @ C @ D @ M )
=> ( zcong @ ( minus_minus @ int @ A_1 @ C ) @ ( minus_minus @ int @ B @ D ) @ M ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[233]) ).
thf(827,plain,
( ( ~ ( quadRes @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) @ ( number_number_of @ int @ min ) )
=> ( ( legendre @ ( number_number_of @ int @ min ) @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) )
!= ( one_one @ int ) ) )
= $true ),
inference(unfold_def,[status(thm)],[234]) ).
thf(828,plain,
( ( ( minus_minus @ int @ ( power_power @ int @ s @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of @ int @ min ) )
= ( plus_plus @ int @ ( power_power @ int @ s @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( one_one @ int ) ) )
= $true ),
inference(unfold_def,[status(thm)],[235]) ).
thf(829,plain,
( ( ! [J: $i,K: $i,M: $i] :
( ( ord_less @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ M )
=> ( ( zcong @ ( power_power @ int @ ( number_number_of @ int @ min ) @ J ) @ ( power_power @ int @ ( number_number_of @ int @ min ) @ K ) @ M )
=> ( ( power_power @ int @ ( number_number_of @ int @ min ) @ J )
= ( power_power @ int @ ( number_number_of @ int @ min ) @ K ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[236]) ).
thf(830,plain,
( ( quadRes @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) @ ( number_number_of @ int @ min ) )
= $true ),
inference(unfold_def,[status(thm)],[238]) ).
thf(831,plain,
( ( ! [X_a: $i] :
( ( ( power @ X_a )
& ( semiring_0 @ X_a ) )
=> ! [W: $i] :
( ( ( ( number_number_of @ nat @ W )
= ( zero_zero @ nat ) )
=> ( ( power_power @ X_a @ ( zero_zero @ X_a ) @ ( number_number_of @ nat @ W ) )
= ( one_one @ X_a ) ) )
& ( ( ( number_number_of @ nat @ W )
!= ( zero_zero @ nat ) )
=> ( ( power_power @ X_a @ ( zero_zero @ X_a ) @ ( number_number_of @ nat @ W ) )
= ( zero_zero @ X_a ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[242]) ).
thf(832,plain,
( ( ! [A_2: $i,B_1: $i,Ma: $i] :
( ( zcong @ A_2 @ B_1 @ Ma )
<=> ? [K_2: $i] :
( ( ti @ int @ B_1 )
= ( plus_plus @ int @ A_2 @ ( times_times @ int @ Ma @ K_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[243]) ).
thf(833,plain,
( ( ! [B: $i,M: $i,A_1: $i] :
( ( ord_less @ int @ ( zero_zero @ int ) @ A_1 )
=> ( ( ord_less @ int @ A_1 @ M )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ B )
=> ( ( ord_less @ int @ B @ A_1 )
=> ~ ( zcong @ A_1 @ B @ M ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[244]) ).
thf(834,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [N: $i] :
( ( power_power @ X_a @ ( number_number_of @ X_a @ min ) @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ N ) )
= ( one_one @ X_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[246]) ).
thf(835,plain,
( ( ! [C: $i,D: $i,A_1: $i,B: $i,M: $i] :
( ( zcong @ A_1 @ B @ M )
=> ( ( zcong @ C @ D @ M )
=> ( zcong @ ( plus_plus @ int @ A_1 @ C ) @ ( plus_plus @ int @ B @ D ) @ M ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[247]) ).
thf(836,plain,
( ( ! [A_1: $i,M: $i,B: $i] : ( zcong @ ( times_times @ int @ A_1 @ M ) @ ( times_times @ int @ B @ M ) @ M ) )
= $true ),
inference(unfold_def,[status(thm)],[248]) ).
thf(837,plain,
( ( ! [K: $i,A_1: $i,B: $i,M: $i] :
( ( zcong @ A_1 @ B @ M )
=> ( zcong @ ( times_times @ int @ A_1 @ K ) @ ( times_times @ int @ B @ K ) @ M ) ) )
= $true ),
inference(unfold_def,[status(thm)],[249]) ).
thf(838,plain,
( ( ! [K: $i,A_1: $i,B: $i,M: $i] :
( ( zcong @ A_1 @ B @ M )
=> ( zcong @ ( times_times @ int @ K @ A_1 ) @ ( times_times @ int @ K @ B ) @ M ) ) )
= $true ),
inference(unfold_def,[status(thm)],[250]) ).
thf(839,plain,
( ( ! [C: $i,D: $i,A_1: $i,B: $i,M: $i] :
( ( zcong @ A_1 @ B @ M )
=> ( ( zcong @ C @ D @ M )
=> ( zcong @ ( times_times @ int @ A_1 @ C ) @ ( times_times @ int @ B @ D ) @ M ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[251]) ).
thf(840,plain,
( ( ! [A_1: $i,B: $i] : ( zcong @ A_1 @ B @ ( one_one @ int ) ) )
= $true ),
inference(unfold_def,[status(thm)],[252]) ).
thf(841,plain,
( ( ! [A_2: $i,B_1: $i] :
( ( zcong @ A_2 @ B_1 @ ( zero_zero @ int ) )
<=> ( ( ti @ int @ A_2 )
= ( ti @ int @ B_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[253]) ).
thf(842,plain,
( ( ! [B: $i,A_1: $i,C: $i] :
( ( ord_less @ int @ A_1 @ C )
=> ( ( ord_less @ int @ B @ C )
=> ( ( ord_less_eq @ int @ A_1 @ B )
| ( ord_less_eq @ int @ B @ A_1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[254]) ).
thf(843,plain,
( ( ! [V_1: $i,V: $i] :
( ( ( ord_less @ int @ V @ pls )
=> ( ( times_times @ nat @ ( number_number_of @ nat @ V ) @ ( number_number_of @ nat @ V_1 ) )
= ( zero_zero @ nat ) ) )
& ( ~ ( ord_less @ int @ V @ pls )
=> ( ( times_times @ nat @ ( number_number_of @ nat @ V ) @ ( number_number_of @ nat @ V_1 ) )
= ( number_number_of @ nat @ ( times_times @ int @ V @ V_1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[256]) ).
thf(844,plain,
( ( ! [V_1: $i,K: $i,V: $i] :
( ( ( ord_less @ int @ V @ pls )
=> ( ( times_times @ nat @ ( number_number_of @ nat @ V ) @ ( times_times @ nat @ ( number_number_of @ nat @ V_1 ) @ K ) )
= ( zero_zero @ nat ) ) )
& ( ~ ( ord_less @ int @ V @ pls )
=> ( ( times_times @ nat @ ( number_number_of @ nat @ V ) @ ( times_times @ nat @ ( number_number_of @ nat @ V_1 ) @ K ) )
= ( times_times @ nat @ ( number_number_of @ nat @ ( times_times @ int @ V @ V_1 ) ) @ K ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[257]) ).
thf(845,plain,
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[258]) ).
thf(846,plain,
( ( ! [V_2: $i] :
( ( ( zero_zero @ nat )
= ( number_number_of @ nat @ V_2 ) )
<=> ( ord_less_eq @ int @ V_2 @ pls ) ) )
= $true ),
inference(unfold_def,[status(thm)],[262]) ).
thf(847,plain,
( ( ! [V_2: $i] :
( ( ( number_number_of @ nat @ V_2 )
= ( zero_zero @ nat ) )
<=> ( ord_less_eq @ int @ V_2 @ pls ) ) )
= $true ),
inference(unfold_def,[status(thm)],[263]) ).
thf(848,plain,
( ( ! [V_2: $i] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( number_number_of @ nat @ V_2 ) )
<=> ( ord_less @ int @ pls @ V_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[264]) ).
thf(849,plain,
( ( ! [X_a: $i] :
( ( linordered_semidom @ X_a )
=> ! [N: $i,A_1: $i] :
( ( ord_less @ X_a @ ( one_one @ X_a ) @ A_1 )
=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
=> ( ord_less @ X_a @ ( one_one @ X_a ) @ ( power_power @ X_a @ A_1 @ N ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[266]) ).
thf(850,plain,
( ( ! [Ma: $i,N_1: $i] :
( ( ( times_times @ int @ Ma @ N_1 )
= ( one_one @ int ) )
<=> ( ( ( ( ti @ int @ Ma )
= ( one_one @ int ) )
& ( ( ti @ int @ N_1 )
= ( one_one @ int ) ) )
| ( ( ( ti @ int @ Ma )
= ( number_number_of @ int @ min ) )
& ( ( ti @ int @ N_1 )
= ( number_number_of @ int @ min ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[267]) ).
thf(851,plain,
( ( ! [M: $i,N: $i] :
( ( ( times_times @ int @ M @ N )
= ( one_one @ int ) )
=> ( ( ( ti @ int @ M )
= ( one_one @ int ) )
| ( ( ti @ int @ M )
= ( number_number_of @ int @ min ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[268]) ).
thf(852,plain,
( ( ! [K_1: $i] :
( ( ord_less @ int @ ( bit0 @ K_1 ) @ min )
<=> ( ord_less_eq @ int @ K_1 @ min ) ) )
= $true ),
inference(unfold_def,[status(thm)],[269]) ).
thf(853,plain,
( ( ! [K_1: $i] :
( ( ord_less_eq @ int @ min @ ( bit0 @ K_1 ) )
<=> ( ord_less @ int @ min @ K_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[270]) ).
thf(854,plain,
( ( ( zero_zero @ nat )
= ( number_number_of @ nat @ pls ) )
= $true ),
inference(unfold_def,[status(thm)],[271]) ).
thf(855,plain,
( ( ( number_number_of @ nat @ pls )
= ( zero_zero @ nat ) )
= $true ),
inference(unfold_def,[status(thm)],[272]) ).
thf(856,plain,
( ( ! [X_a: $i] :
( ( power @ X_a )
=> ! [A_1: $i] :
( ( power_power @ X_a @ A_1 @ ( zero_zero @ nat ) )
= ( one_one @ X_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[273]) ).
thf(857,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [X_1: $i] :
( ( power_power @ X_a @ X_1 @ ( zero_zero @ nat ) )
= ( one_one @ X_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[274]) ).
thf(858,plain,
( ( ! [I: $i,M: $i,N: $i] :
( ( dvd_dvd @ nat @ ( power_power @ nat @ I @ M ) @ ( power_power @ nat @ I @ N ) )
=> ( ( ord_less @ nat @ ( one_one @ nat ) @ I )
=> ( ord_less_eq @ nat @ M @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[275]) ).
thf(859,plain,
( ( ( number_number_of @ int @ pls )
!= ( number_number_of @ int @ min ) )
= $true ),
inference(unfold_def,[status(thm)],[276]) ).
thf(860,plain,
( ( ! [K_1: $i] :
( ( ord_less_eq @ int @ ( bit0 @ K_1 ) @ min )
<=> ( ord_less_eq @ int @ K_1 @ min ) ) )
= $true ),
inference(unfold_def,[status(thm)],[277]) ).
thf(861,plain,
( ( ord_less_eq @ int @ min @ pls )
= $true ),
inference(unfold_def,[status(thm)],[278]) ).
thf(862,plain,
( ( ~ ( ord_less_eq @ int @ pls @ min ) )
= $true ),
inference(unfold_def,[status(thm)],[279]) ).
thf(863,plain,
( ( ! [K_1: $i] :
( ( ord_less_eq @ int @ min @ ( bit1 @ K_1 ) )
<=> ( ord_less_eq @ int @ min @ K_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[280]) ).
thf(864,plain,
( ( ! [K_1: $i] :
( ( ord_less_eq @ int @ ( bit1 @ K_1 ) @ min )
<=> ( ord_less_eq @ int @ K_1 @ min ) ) )
= $true ),
inference(unfold_def,[status(thm)],[281]) ).
thf(865,plain,
( ( ord_less @ int @ min @ ( zero_zero @ int ) )
= $true ),
inference(unfold_def,[status(thm)],[282]) ).
thf(866,plain,
( ( ! [K_1: $i] :
( ( ord_less @ int @ min @ ( bit0 @ K_1 ) )
<=> ( ord_less @ int @ min @ K_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[283]) ).
thf(867,plain,
( ( ord_less @ int @ min @ pls )
= $true ),
inference(unfold_def,[status(thm)],[284]) ).
thf(868,plain,
( ( ~ ( ord_less @ int @ pls @ min ) )
= $true ),
inference(unfold_def,[status(thm)],[285]) ).
thf(869,plain,
( ( ! [K_1: $i] :
( ( ord_less @ int @ min @ ( bit1 @ K_1 ) )
<=> ( ord_less @ int @ min @ K_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[286]) ).
thf(870,plain,
( ( ! [K_1: $i] :
( ( ord_less @ int @ ( bit1 @ K_1 ) @ min )
<=> ( ord_less @ int @ K_1 @ min ) ) )
= $true ),
inference(unfold_def,[status(thm)],[287]) ).
thf(871,plain,
( ( ! [X_2: $i] :
( ~ ( ord_less @ real @ ( zero_zero @ real ) @ ( times_times @ real @ X_2 @ X_2 ) )
<=> ( X_2
= ( zero_zero @ real ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[288]) ).
thf(872,plain,
( ( ord_less_eq @ int @ min @ min )
= $true ),
inference(unfold_def,[status(thm)],[289]) ).
thf(873,plain,
( ( ~ ( ord_less @ int @ min @ min ) )
= $true ),
inference(unfold_def,[status(thm)],[290]) ).
thf(874,plain,
( ( ! [L: $i] :
( min
!= ( bit0 @ L ) ) )
= $true ),
inference(unfold_def,[status(thm)],[291]) ).
thf(875,plain,
( ( ! [K: $i] :
( ( bit0 @ K )
!= min ) )
= $true ),
inference(unfold_def,[status(thm)],[292]) ).
thf(876,plain,
( ( min != pls )
= $true ),
inference(unfold_def,[status(thm)],[293]) ).
thf(877,plain,
( ( pls != min )
= $true ),
inference(unfold_def,[status(thm)],[294]) ).
thf(878,plain,
( ( ( bit1 @ min )
= min )
= $true ),
inference(unfold_def,[status(thm)],[295]) ).
thf(879,plain,
( ( ! [L_1: $i] :
( ( min
= ( bit1 @ L_1 ) )
<=> ( min
= ( ti @ int @ L_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[296]) ).
thf(880,plain,
( ( ! [K_1: $i] :
( ( ( bit1 @ K_1 )
= min )
<=> ( ( ti @ int @ K_1 )
= min ) ) )
= $true ),
inference(unfold_def,[status(thm)],[297]) ).
thf(881,plain,
( ( ! [M: $i,N: $i,I: $i] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ I )
=> ( ( ord_less @ nat @ ( power_power @ nat @ I @ M ) @ ( power_power @ nat @ I @ N ) )
=> ( ord_less @ nat @ M @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[298]) ).
thf(882,plain,
( ( ! [X_2: $i,W_1: $i] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ X_2 @ ( number_number_of @ nat @ W_1 ) ) )
<=> ( ( ( number_number_of @ nat @ W_1 )
= ( zero_zero @ nat ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ X_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[299]) ).
thf(883,plain,
( ( ! [X_2: $i,N_1: $i] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ X_2 @ N_1 ) )
<=> ( ( N_1
= ( zero_zero @ nat ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ X_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[300]) ).
thf(884,plain,
( ( ! [X_2: $i,N_1: $i] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ X_2 @ N_1 ) )
<=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ X_2 )
| ( N_1
= ( zero_zero @ nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[301]) ).
thf(885,plain,
( ( ( legendre @ ( number_number_of @ int @ min ) @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) )
= ( one_one @ int ) )
= $true ),
inference(unfold_def,[status(thm)],[302]) ).
thf(886,plain,
( ( ~ ! [S1: $i] :
~ ( zcong @ ( power_power @ int @ S1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of @ int @ min ) @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[303]) ).
thf(887,plain,
( ( ! [Y_1: $i,X_1: $i,P: $i] :
( ~ ( zcong @ X_1 @ ( zero_zero @ int ) @ P )
=> ( ( zcong @ ( power_power @ int @ Y_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ X_1 @ P )
=> ~ ( dvd_dvd @ int @ P @ Y_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[307]) ).
thf(888,plain,
( ( zcong @ ( power_power @ int @ s @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of @ int @ min ) @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) )
= $true ),
inference(unfold_def,[status(thm)],[308]) ).
thf(889,plain,
( ( ! [X_a: $i] :
( ( linordered_semidom @ X_a )
=> ! [A_1: $i,N: $i,N_2: $i] :
( ( ord_less @ nat @ N @ N_2 )
=> ( ( ord_less @ X_a @ ( one_one @ X_a ) @ A_1 )
=> ( ord_less @ X_a @ ( power_power @ X_a @ A_1 @ N ) @ ( power_power @ X_a @ A_1 @ N_2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[309]) ).
thf(890,plain,
( ( ! [X_a: $i] :
( ( linordered_semidom @ X_a )
=> ! [M: $i,N: $i,A_1: $i] :
( ( ord_less @ X_a @ ( one_one @ X_a ) @ A_1 )
=> ( ( ord_less @ X_a @ ( power_power @ X_a @ A_1 @ M ) @ ( power_power @ X_a @ A_1 @ N ) )
=> ( ord_less @ nat @ M @ N ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[310]) ).
thf(891,plain,
( ( ! [X_a: $i] :
( ( linordered_semidom @ X_a )
=> ! [X_2: $i,Y_2: $i,B_1: $i] :
( ( ord_less @ X_a @ ( one_one @ X_a ) @ B_1 )
=> ( ( ord_less @ X_a @ ( power_power @ X_a @ B_1 @ X_2 ) @ ( power_power @ X_a @ B_1 @ Y_2 ) )
<=> ( ord_less @ nat @ X_2 @ Y_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[311]) ).
thf(892,plain,
( ( ! [X_a: $i] :
( ( linordered_semidom @ X_a )
=> ! [Ma: $i,N_1: $i,A_2: $i] :
( ( ord_less @ X_a @ ( one_one @ X_a ) @ A_2 )
=> ( ( ( power_power @ X_a @ A_2 @ Ma )
= ( power_power @ X_a @ A_2 @ N_1 ) )
<=> ( Ma = N_1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[312]) ).
thf(893,plain,
( ( ! [X_a: $i] :
( ( linordered_semidom @ X_a )
=> ! [A_1: $i,N: $i,N_2: $i] :
( ( ord_less_eq @ nat @ N @ N_2 )
=> ( ( ord_less_eq @ X_a @ ( one_one @ X_a ) @ A_1 )
=> ( ord_less_eq @ X_a @ ( power_power @ X_a @ A_1 @ N ) @ ( power_power @ X_a @ A_1 @ N_2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[313]) ).
thf(894,plain,
( ( ! [X_a: $i] :
( ( linordered_semidom @ X_a )
=> ! [N: $i,A_1: $i] :
( ( ord_less_eq @ X_a @ ( one_one @ X_a ) @ A_1 )
=> ( ord_less_eq @ X_a @ ( one_one @ X_a ) @ ( power_power @ X_a @ A_1 @ N ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[314]) ).
thf(895,plain,
( ( ! [X_a: $i] :
( ( linordered_idom @ X_a )
=> ! [A_1: $i,N: $i] : ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ ( power_power @ X_a @ A_1 @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ N ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[315]) ).
thf(896,plain,
( ( ! [X_a: $i] :
( ( linordered_idom @ X_a )
=> ! [X_1: $i,Y_1: $i] :
~ ( ord_less @ X_a @ ( plus_plus @ X_a @ ( power_power @ X_a @ X_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ X_a @ Y_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( zero_zero @ X_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[317]) ).
thf(897,plain,
( ( ! [X_a: $i] :
( ( linordered_idom @ X_a )
=> ! [X_1: $i,Y_1: $i] : ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ ( plus_plus @ X_a @ ( power_power @ X_a @ X_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ X_a @ Y_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[319]) ).
thf(898,plain,
( ( ! [X_a: $i] :
( ( monoid_mult @ X_a )
=> ! [A_1: $i,M: $i,N: $i] :
( ( power_power @ X_a @ A_1 @ ( times_times @ nat @ M @ N ) )
= ( power_power @ X_a @ ( power_power @ X_a @ A_1 @ M ) @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[321]) ).
thf(899,plain,
( ( ! [X_a: $i] :
( ( monoid_mult @ X_a )
=> ! [N: $i] :
( ( power_power @ X_a @ ( one_one @ X_a ) @ N )
= ( one_one @ X_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[322]) ).
thf(900,plain,
( ( ! [X_a: $i] :
( ( monoid_mult @ X_a )
=> ! [A_1: $i,M: $i,N: $i] :
( ( power_power @ X_a @ A_1 @ ( plus_plus @ nat @ M @ N ) )
= ( times_times @ X_a @ ( power_power @ X_a @ A_1 @ M ) @ ( power_power @ X_a @ A_1 @ N ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[323]) ).
thf(901,plain,
( ( ! [X_a: $i] :
( ( comm_monoid_mult @ X_a )
=> ! [A_1: $i,B: $i,N: $i] :
( ( power_power @ X_a @ ( times_times @ X_a @ A_1 @ B ) @ N )
= ( times_times @ X_a @ ( power_power @ X_a @ A_1 @ N ) @ ( power_power @ X_a @ B @ N ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[324]) ).
thf(902,plain,
( ( ! [X_a: $i] :
( ( monoid_mult @ X_a )
=> ! [A_1: $i,N: $i] :
( ( times_times @ X_a @ ( power_power @ X_a @ A_1 @ N ) @ A_1 )
= ( times_times @ X_a @ A_1 @ ( power_power @ X_a @ A_1 @ N ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[325]) ).
thf(903,plain,
( ( ! [X_a: $i] :
( ( linordered_idom @ X_a )
=> ! [X_2: $i,Y_2: $i] :
( ( ( plus_plus @ X_a @ ( power_power @ X_a @ X_2 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ X_a @ Y_2 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ X_a ) )
<=> ( ( ( ti @ X_a @ X_2 )
= ( zero_zero @ X_a ) )
& ( ( ti @ X_a @ Y_2 )
= ( zero_zero @ X_a ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[326]) ).
thf(904,plain,
( ( ! [X_a: $i] :
( ( linordered_idom @ X_a )
=> ! [A_1: $i] :
~ ( ord_less @ X_a @ ( power_power @ X_a @ A_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( zero_zero @ X_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[328]) ).
thf(905,plain,
( ( ! [X_a: $i] :
( ( linordered_semidom @ X_a )
=> ! [X_1: $i,Y_1: $i] :
( ( ord_less_eq @ X_a @ ( power_power @ X_a @ X_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ X_a @ Y_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ Y_1 )
=> ( ord_less_eq @ X_a @ X_1 @ Y_1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[330]) ).
thf(906,plain,
( ( ! [X_a: $i] :
( ( linordered_idom @ X_a )
=> ! [A_1: $i] : ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ ( power_power @ X_a @ A_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[331]) ).
thf(907,plain,
( ( ! [X_a: $i] :
( ( ring_11004092258visors @ X_a )
=> ! [A_2: $i] :
( ( ( power_power @ X_a @ A_2 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ X_a ) )
<=> ( ( ti @ X_a @ A_2 )
= ( zero_zero @ X_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[332]) ).
thf(908,plain,
( ( ! [X_a: $i] :
( ( semiring_1 @ X_a )
=> ( ( power_power @ X_a @ ( zero_zero @ X_a ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ X_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[333]) ).
thf(909,plain,
( ( ! [Z: $i] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ Z )
=> ( ord_less @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( one_one @ int ) @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[334]) ).
thf(910,plain,
( ( ! [Z_1: $i] :
( ( ord_less @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ Z_1 ) @ Z_1 ) @ ( zero_zero @ int ) )
<=> ( ord_less @ int @ Z_1 @ ( zero_zero @ int ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[339]) ).
thf(911,plain,
( ( ! [N_1: $i,Ma: $i] :
( ( ord_less @ int @ ( zero_zero @ int ) @ Ma )
=> ( ( ( times_times @ int @ Ma @ N_1 )
= ( one_one @ int ) )
<=> ( ( ( ti @ int @ Ma )
= ( one_one @ int ) )
& ( ( ti @ int @ N_1 )
= ( one_one @ int ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[340]) ).
thf(912,plain,
( ( ! [Z_1: $i] :
( ( ord_less_eq @ int @ ( one_one @ int ) @ Z_1 )
<=> ( ord_less @ int @ ( zero_zero @ int ) @ Z_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[341]) ).
thf(913,plain,
( ( ! [X_a: $i] :
( ( monoid_mult @ X_a )
=> ! [A_1: $i] :
( ( power_power @ X_a @ A_1 @ ( one_one @ nat ) )
= ( ti @ X_a @ A_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[342]) ).
thf(914,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [W: $i] :
( ( number_number_of @ X_a @ ( bit0 @ W ) )
= ( plus_plus @ X_a @ ( plus_plus @ X_a @ ( zero_zero @ X_a ) @ ( number_number_of @ X_a @ W ) ) @ ( number_number_of @ X_a @ W ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[343]) ).
thf(915,plain,
( ( ! [V_2: $i,V_3: $i] :
( ( ord_less_eq @ nat @ ( number_number_of @ nat @ V_2 ) @ ( number_number_of @ nat @ V_3 ) )
<=> ( ~ ( ord_less_eq @ int @ V_2 @ V_3 )
=> ( ord_less_eq @ int @ V_2 @ pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[344]) ).
thf(916,plain,
( ( ! [X_a: $i] :
( ( linordered_ring @ X_a )
=> ! [X_1: $i,Y_1: $i] :
~ ( ord_less @ X_a @ ( plus_plus @ X_a @ ( times_times @ X_a @ X_1 @ X_1 ) @ ( times_times @ X_a @ Y_1 @ Y_1 ) ) @ ( zero_zero @ X_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[346]) ).
thf(917,plain,
( ( ! [V_2: $i,V_3: $i] :
( ( ord_less @ nat @ ( number_number_of @ nat @ V_2 ) @ ( number_number_of @ nat @ V_3 ) )
<=> ( ( ( ord_less @ int @ V_2 @ V_3 )
=> ( ord_less @ int @ pls @ V_3 ) )
& ( ord_less @ int @ V_2 @ V_3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[347]) ).
thf(918,plain,
( ( ! [X_a: $i] :
( ( linordered_ring @ X_a )
=> ! [X_1: $i,Y_1: $i] : ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ ( plus_plus @ X_a @ ( times_times @ X_a @ X_1 @ X_1 ) @ ( times_times @ X_a @ Y_1 @ Y_1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[349]) ).
thf(919,plain,
( ( ! [N: $i,A_1: $i,B: $i,P: $i] :
( ( zprime @ P )
=> ( ~ ( dvd_dvd @ int @ P @ B )
=> ( ( dvd_dvd @ int @ ( power_power @ int @ P @ N ) @ ( times_times @ int @ A_1 @ B ) )
=> ( dvd_dvd @ int @ ( power_power @ int @ P @ N ) @ A_1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[350]) ).
thf(920,plain,
( ( ! [N: $i,B: $i,A_1: $i,P: $i] :
( ( zprime @ P )
=> ( ~ ( dvd_dvd @ int @ P @ A_1 )
=> ( ( dvd_dvd @ int @ ( power_power @ int @ P @ N ) @ ( times_times @ int @ A_1 @ B ) )
=> ( dvd_dvd @ int @ ( power_power @ int @ P @ N ) @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[351]) ).
thf(921,plain,
( ( ! [X_a: $i] :
( ( linordered_semidom @ X_a )
=> ! [N: $i,A_1: $i] :
( ( ord_less @ X_a @ ( zero_zero @ X_a ) @ A_1 )
=> ( ( ord_less @ X_a @ A_1 @ ( one_one @ X_a ) )
=> ( ord_less @ X_a @ ( times_times @ X_a @ A_1 @ ( power_power @ X_a @ A_1 @ N ) ) @ ( power_power @ X_a @ A_1 @ N ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[352]) ).
thf(922,plain,
( ( ! [Z: $i] :
( ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ Z ) @ Z )
!= ( zero_zero @ int ) ) )
= $true ),
inference(unfold_def,[status(thm)],[353]) ).
thf(923,plain,
( ( ! [K: $i,I: $i,J: $i] :
( ( ord_less @ int @ I @ J )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ K )
=> ( ord_less @ int @ ( times_times @ int @ K @ I ) @ ( times_times @ int @ K @ J ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[354]) ).
thf(924,plain,
( ( ! [B: $i,A_1: $i] :
( ( ord_less @ int @ ( zero_zero @ int ) @ A_1 )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ ( times_times @ int @ A_1 @ B ) )
=> ( ord_less @ int @ ( zero_zero @ int ) @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[355]) ).
thf(925,plain,
( ( ord_less @ int @ ( zero_zero @ int ) @ ( one_one @ int ) )
= $true ),
inference(unfold_def,[status(thm)],[356]) ).
thf(926,plain,
( ( ( zero_zero @ int )
= ( number_number_of @ int @ pls ) )
= $true ),
inference(unfold_def,[status(thm)],[357]) ).
thf(927,plain,
( ( ! [W_1: $i] :
( ( ord_less @ int @ ( bit0 @ W_1 ) @ ( zero_zero @ int ) )
<=> ( ord_less @ int @ W_1 @ ( zero_zero @ int ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[358]) ).
thf(928,plain,
( ( ~ ( ord_less @ int @ pls @ ( zero_zero @ int ) ) )
= $true ),
inference(unfold_def,[status(thm)],[359]) ).
thf(929,plain,
( ( ! [W_1: $i] :
( ( ord_less @ int @ ( bit1 @ W_1 ) @ ( zero_zero @ int ) )
<=> ( ord_less @ int @ W_1 @ ( zero_zero @ int ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[360]) ).
thf(930,plain,
( ( ! [X_a: $i] :
( ( number_semiring @ X_a )
=> ( ( number_number_of @ X_a @ pls )
= ( zero_zero @ X_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[361]) ).
thf(931,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ( ( number_number_of @ X_a @ pls )
= ( zero_zero @ X_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[362]) ).
thf(932,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ( ( zero_zero @ X_a )
= ( number_number_of @ X_a @ pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[363]) ).
thf(933,plain,
( ( ! [A_1: $i,N: $i,P: $i] :
( ( zprime @ P )
=> ( ( dvd_dvd @ int @ P @ ( power_power @ int @ A_1 @ N ) )
=> ( dvd_dvd @ int @ P @ A_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[364]) ).
thf(934,plain,
( ( ! [X_a: $i] :
( ( semiri456707255roduct @ X_a )
=> ! [C: $i,D: $i,A_1: $i,B: $i,R_1: $i] :
( ( ( ti @ X_a @ R_1 )
!= ( zero_zero @ X_a ) )
=> ( ( ( ( ti @ X_a @ A_1 )
= ( ti @ X_a @ B ) )
& ( ( ti @ X_a @ C )
!= ( ti @ X_a @ D ) ) )
=> ( ( plus_plus @ X_a @ A_1 @ ( times_times @ X_a @ R_1 @ C ) )
!= ( plus_plus @ X_a @ B @ ( times_times @ X_a @ R_1 @ D ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[365]) ).
thf(935,plain,
( ( ! [X_a: $i] :
( ( linord581940658strict @ X_a )
=> ! [X_2: $i,Y_2: $i] :
( ( ( plus_plus @ X_a @ ( times_times @ X_a @ X_2 @ X_2 ) @ ( times_times @ X_a @ Y_2 @ Y_2 ) )
= ( zero_zero @ X_a ) )
<=> ( ( ( ti @ X_a @ X_2 )
= ( zero_zero @ X_a ) )
& ( ( ti @ X_a @ Y_2 )
= ( zero_zero @ X_a ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[366]) ).
thf(936,plain,
( ( ! [X_a: $i] :
( ( linordered_idom @ X_a )
=> ! [A_2: $i] :
( ( ord_less @ X_a @ ( plus_plus @ X_a @ A_2 @ A_2 ) @ ( zero_zero @ X_a ) )
<=> ( ord_less @ X_a @ A_2 @ ( zero_zero @ X_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[367]) ).
thf(937,plain,
( ( ! [X_a: $i] :
( ( linordered_semidom @ X_a )
=> ! [A_1: $i,N: $i,N_2: $i] :
( ( ord_less @ nat @ N @ N_2 )
=> ( ( ord_less @ X_a @ ( zero_zero @ X_a ) @ A_1 )
=> ( ( ord_less @ X_a @ A_1 @ ( one_one @ X_a ) )
=> ( ord_less @ X_a @ ( power_power @ X_a @ A_1 @ N_2 ) @ ( power_power @ X_a @ A_1 @ N ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[368]) ).
thf(938,plain,
( ( ! [X_a: $i] :
( ( linordered_semidom @ X_a )
=> ! [A_1: $i,N: $i,N_2: $i] :
( ( ord_less_eq @ nat @ N @ N_2 )
=> ( ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ A_1 )
=> ( ( ord_less_eq @ X_a @ A_1 @ ( one_one @ X_a ) )
=> ( ord_less_eq @ X_a @ ( power_power @ X_a @ A_1 @ N_2 ) @ ( power_power @ X_a @ A_1 @ N ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[369]) ).
thf(939,plain,
( ( ! [C_1: $i,X_2: $i,Ta: $i,A_2: $i,D_1: $i] :
( ( dvd_dvd @ int @ A_2 @ D_1 )
=> ( ( dvd_dvd @ int @ A_2 @ ( plus_plus @ int @ X_2 @ Ta ) )
<=> ( dvd_dvd @ int @ A_2 @ ( plus_plus @ int @ ( plus_plus @ int @ X_2 @ ( times_times @ int @ C_1 @ D_1 ) ) @ Ta ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[371]) ).
thf(940,plain,
( ( ! [K_1: $i,N_1: $i,Ma: $i] :
( ( dvd_dvd @ int @ K_1 @ ( plus_plus @ int @ N_1 @ ( times_times @ int @ K_1 @ Ma ) ) )
<=> ( dvd_dvd @ int @ K_1 @ N_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[372]) ).
thf(941,plain,
( ( ! [Z: $i,X_1: $i,Y_1: $i,P: $i] :
( ( zcong @ ( power_power @ int @ X_1 @ Y_1 ) @ ( one_one @ int ) @ P )
=> ( zcong @ ( power_power @ int @ X_1 @ ( times_times @ nat @ Y_1 @ Z ) ) @ ( one_one @ int ) @ P ) ) )
= $true ),
inference(unfold_def,[status(thm)],[373]) ).
thf(942,plain,
( ( ! [X_a: $i] :
( ( linordered_semidom @ X_a )
=> ! [N: $i,A_1: $i] :
( ( ord_less @ X_a @ ( zero_zero @ X_a ) @ A_1 )
=> ( ord_less @ X_a @ ( zero_zero @ X_a ) @ ( power_power @ X_a @ A_1 @ N ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[374]) ).
thf(943,plain,
( ( ! [X_a: $i] :
( ( linordered_semidom @ X_a )
=> ! [N: $i,A_1: $i,B: $i] :
( ( ord_less_eq @ X_a @ A_1 @ B )
=> ( ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ A_1 )
=> ( ord_less_eq @ X_a @ ( power_power @ X_a @ A_1 @ N ) @ ( power_power @ X_a @ B @ N ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[375]) ).
thf(944,plain,
( ( ! [X_a: $i] :
( ( linordered_semidom @ X_a )
=> ! [N: $i,A_1: $i] :
( ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ A_1 )
=> ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ ( power_power @ X_a @ A_1 @ N ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[376]) ).
thf(945,plain,
( ( ! [Z: $i] :
( ( plus_plus @ int @ Z @ ( zero_zero @ int ) )
= ( ti @ int @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[377]) ).
thf(946,plain,
( ( ! [Z: $i] :
( ( plus_plus @ int @ ( zero_zero @ int ) @ Z )
= ( ti @ int @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[378]) ).
thf(947,plain,
( ( ( zero_zero @ int )
!= ( one_one @ int ) )
= $true ),
inference(unfold_def,[status(thm)],[379]) ).
thf(948,plain,
( ( pls
= ( zero_zero @ int ) )
= $true ),
inference(unfold_def,[status(thm)],[380]) ).
thf(949,plain,
( ( ! [X_a: $i] :
( ( linord219039673up_add @ X_a )
=> ! [A_2: $i] :
( ( ( plus_plus @ X_a @ A_2 @ A_2 )
= ( zero_zero @ X_a ) )
<=> ( ( ti @ X_a @ A_2 )
= ( zero_zero @ X_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[381]) ).
thf(950,plain,
( ( ! [X_a: $i] :
( ( semiri456707255roduct @ X_a )
=> ! [B_1: $i,A_2: $i] :
( ( ( ti @ X_a @ B_1 )
= ( plus_plus @ X_a @ B_1 @ A_2 ) )
<=> ( ( ti @ X_a @ A_2 )
= ( zero_zero @ X_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[382]) ).
thf(951,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i] :
( ( plus_plus @ X_a @ A_1 @ ( zero_zero @ X_a ) )
= ( ti @ X_a @ A_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[383]) ).
thf(952,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i] :
( ( plus_plus @ X_a @ ( zero_zero @ X_a ) @ A_1 )
= ( ti @ X_a @ A_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[384]) ).
thf(953,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i] :
( ( times_times @ X_a @ A_1 @ ( zero_zero @ X_a ) )
= ( zero_zero @ X_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[385]) ).
thf(954,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i] :
( ( times_times @ X_a @ ( zero_zero @ X_a ) @ A_1 )
= ( zero_zero @ X_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[386]) ).
thf(955,plain,
( ( ! [X_a: $i] :
( ( ( power @ X_a )
& ( semiring_0 @ X_a ) )
=> ! [N: $i] :
( ( ( N
= ( zero_zero @ nat ) )
=> ( ( power_power @ X_a @ ( zero_zero @ X_a ) @ N )
= ( one_one @ X_a ) ) )
& ( ( N
!= ( zero_zero @ nat ) )
=> ( ( power_power @ X_a @ ( zero_zero @ X_a ) @ N )
= ( zero_zero @ X_a ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[389]) ).
thf(956,plain,
( ( ! [X_a: $i] :
( ( ring_11004092258visors @ X_a )
=> ! [N: $i,A_1: $i] :
( ( ( ti @ X_a @ A_1 )
!= ( zero_zero @ X_a ) )
=> ( ( power_power @ X_a @ A_1 @ N )
!= ( zero_zero @ X_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[390]) ).
thf(957,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [N: $i,X_1: $i,Y_1: $i] :
( ( dvd_dvd @ X_a @ X_1 @ Y_1 )
=> ( dvd_dvd @ X_a @ ( power_power @ X_a @ X_1 @ N ) @ ( power_power @ X_a @ Y_1 @ N ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[391]) ).
thf(958,plain,
( ( ! [K: $i,M: $i,N: $i] :
( ( dvd_dvd @ int @ ( times_times @ int @ K @ M ) @ ( times_times @ int @ K @ N ) )
=> ( ( ( ti @ int @ K )
!= ( zero_zero @ int ) )
=> ( dvd_dvd @ int @ M @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[392]) ).
thf(959,plain,
( ( ! [N: $i,M: $i] :
( ( ord_less @ int @ ( zero_zero @ int ) @ M )
=> ( ( ord_less @ int @ M @ N )
=> ~ ( dvd_dvd @ int @ N @ M ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[394]) ).
thf(960,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [M: $i,A_1: $i,N: $i,B: $i] :
( ( dvd_dvd @ X_a @ ( power_power @ X_a @ A_1 @ N ) @ B )
=> ( ( ord_less_eq @ nat @ M @ N )
=> ( dvd_dvd @ X_a @ ( power_power @ X_a @ A_1 @ M ) @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[396]) ).
thf(961,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [N: $i,M: $i,X_1: $i,Y_1: $i] :
( ( dvd_dvd @ X_a @ X_1 @ Y_1 )
=> ( ( ord_less_eq @ nat @ N @ M )
=> ( dvd_dvd @ X_a @ ( power_power @ X_a @ X_1 @ N ) @ ( power_power @ X_a @ Y_1 @ M ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[397]) ).
thf(962,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i,M: $i,N: $i] :
( ( ord_less_eq @ nat @ M @ N )
=> ( dvd_dvd @ X_a @ ( power_power @ X_a @ A_1 @ M ) @ ( power_power @ X_a @ A_1 @ N ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[398]) ).
thf(963,plain,
( ( zcong @ ( power_power @ int @ s1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of @ int @ min ) @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) )
= $true ),
inference(unfold_def,[status(thm)],[400]) ).
thf(964,plain,
( ( zcong @ ( power_power @ int @ s @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ s1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) )
= $true ),
inference(unfold_def,[status(thm)],[404]) ).
thf(965,plain,
( ( ! [X_a: $i] :
( ( linordered_semidom @ X_a )
=> ! [X_2: $i,Y_2: $i,B_1: $i] :
( ( ord_less @ X_a @ ( one_one @ X_a ) @ B_1 )
=> ( ( ord_less_eq @ X_a @ ( power_power @ X_a @ B_1 @ X_2 ) @ ( power_power @ X_a @ B_1 @ Y_2 ) )
<=> ( ord_less_eq @ nat @ X_2 @ Y_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[405]) ).
thf(966,plain,
( ( ! [X_a: $i] :
( ( linordered_semidom @ X_a )
=> ! [M: $i,N: $i,A_1: $i] :
( ( ord_less @ X_a @ ( one_one @ X_a ) @ A_1 )
=> ( ( ord_less_eq @ X_a @ ( power_power @ X_a @ A_1 @ M ) @ ( power_power @ X_a @ A_1 @ N ) )
=> ( ord_less_eq @ nat @ M @ N ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[406]) ).
thf(967,plain,
( ( ! [X_a: $i] :
( ( linordered_semidom @ X_a )
=> ! [N: $i,A_1: $i] :
( ( ord_less @ X_a @ ( one_one @ X_a ) @ A_1 )
=> ( ord_less @ X_a @ ( one_one @ X_a ) @ ( times_times @ X_a @ A_1 @ ( power_power @ X_a @ A_1 @ N ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[407]) ).
thf(968,plain,
( ( ! [X_a: $i] :
( ( linordered_semidom @ X_a )
=> ! [N: $i,A_1: $i] :
( ( ord_less @ X_a @ ( one_one @ X_a ) @ A_1 )
=> ( ord_less @ X_a @ ( power_power @ X_a @ A_1 @ N ) @ ( times_times @ X_a @ A_1 @ ( power_power @ X_a @ A_1 @ N ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[408]) ).
thf(969,plain,
( ( ! [X_1: $i] :
( ( times_times @ real @ ( number_number_of @ real @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ real @ X_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( power_power @ real @ ( times_times @ real @ ( number_number_of @ real @ ( bit0 @ ( bit1 @ pls ) ) ) @ X_1 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[409]) ).
thf(970,plain,
( ( ! [X_1: $i,Y_1: $i] :
( ( power_power @ real @ ( plus_plus @ real @ X_1 @ Y_1 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ real @ ( plus_plus @ real @ ( power_power @ real @ X_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ real @ Y_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times @ real @ ( times_times @ real @ ( number_number_of @ real @ ( bit0 @ ( bit1 @ pls ) ) ) @ X_1 ) @ Y_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[410]) ).
thf(971,plain,
( ( ! [P: $i] :
( ( zprime @ P )
=> ( ( ( ti @ int @ P )
!= ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) )
=> ( ( ( ti @ int @ P )
!= ( number_number_of @ int @ ( bit1 @ ( bit1 @ pls ) ) ) )
=> ( ord_less_eq @ int @ ( number_number_of @ int @ ( bit1 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ P ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[412]) ).
thf(972,plain,
( ( dvd_dvd @ int @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) @ ( plus_plus @ int @ ( power_power @ int @ s @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( one_one @ int ) ) )
= $true ),
inference(unfold_def,[status(thm)],[413]) ).
thf(973,plain,
( ( ord_less @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) )
= $true ),
inference(unfold_def,[status(thm)],[414]) ).
thf(974,plain,
( ( ! [X_a: $i] :
( ( number_semiring @ X_a )
=> ( ( plus_plus @ X_a @ ( one_one @ X_a ) @ ( one_one @ X_a ) )
= ( number_number_of @ X_a @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[415]) ).
thf(975,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [Z: $i] :
( ( times_times @ X_a @ Z @ ( number_number_of @ X_a @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ X_a @ Z @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[416]) ).
thf(976,plain,
( ( ! [X_a: $i] :
( ( number_semiring @ X_a )
=> ! [Z: $i] :
( ( times_times @ X_a @ Z @ ( number_number_of @ X_a @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ X_a @ Z @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[417]) ).
thf(977,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [Z: $i] :
( ( times_times @ X_a @ ( number_number_of @ X_a @ ( bit0 @ ( bit1 @ pls ) ) ) @ Z )
= ( plus_plus @ X_a @ Z @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[418]) ).
thf(978,plain,
( ( ! [X_a: $i] :
( ( number_semiring @ X_a )
=> ! [Z: $i] :
( ( times_times @ X_a @ ( number_number_of @ X_a @ ( bit0 @ ( bit1 @ pls ) ) ) @ Z )
= ( plus_plus @ X_a @ Z @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[419]) ).
thf(979,plain,
( ( ! [X_1: $i] :
( ( power_power @ int @ ( power_power @ int @ X_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power @ int @ X_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[420]) ).
thf(980,plain,
( ( ! [X_a: $i] :
( ( monoid_mult @ X_a )
=> ! [A_1: $i] :
( ( power_power @ X_a @ A_1 @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( times_times @ X_a @ ( times_times @ X_a @ A_1 @ A_1 ) @ A_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[421]) ).
thf(981,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [W: $i] :
( ( times_times @ X_a @ ( plus_plus @ X_a @ ( one_one @ X_a ) @ ( one_one @ X_a ) ) @ ( number_number_of @ X_a @ W ) )
= ( number_number_of @ X_a @ ( bit0 @ W ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[422]) ).
thf(982,plain,
( ( ! [K: $i,L: $i] :
( ( times_times @ int @ ( bit1 @ K ) @ L )
= ( plus_plus @ int @ ( bit0 @ ( times_times @ int @ K @ L ) ) @ L ) ) )
= $true ),
inference(unfold_def,[status(thm)],[423]) ).
thf(983,plain,
( ( ( one_one @ int )
= ( number_number_of @ int @ ( bit1 @ pls ) ) )
= $true ),
inference(unfold_def,[status(thm)],[424]) ).
thf(984,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ( ( one_one @ X_a )
= ( number_number_of @ X_a @ ( bit1 @ pls ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[425]) ).
thf(985,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ( ( number_number_of @ X_a @ ( bit1 @ pls ) )
= ( one_one @ X_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[426]) ).
thf(986,plain,
( ( ! [X_a: $i] :
( ( number_semiring @ X_a )
=> ( ( number_number_of @ X_a @ ( bit1 @ pls ) )
= ( one_one @ X_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[427]) ).
thf(987,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [A_1: $i] :
( ( times_times @ X_a @ A_1 @ ( number_number_of @ X_a @ ( bit1 @ pls ) ) )
= ( ti @ X_a @ A_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[428]) ).
thf(988,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [A_1: $i] :
( ( times_times @ X_a @ ( number_number_of @ X_a @ ( bit1 @ pls ) ) @ A_1 )
= ( ti @ X_a @ A_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[429]) ).
thf(989,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [W: $i] :
( ( number_number_of @ X_a @ ( bit1 @ W ) )
= ( plus_plus @ X_a @ ( plus_plus @ X_a @ ( one_one @ X_a ) @ ( number_number_of @ X_a @ W ) ) @ ( number_number_of @ X_a @ W ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[430]) ).
thf(990,plain,
( ( ! [K: $i] :
( ( bit1 @ K )
= ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ K ) @ K ) ) )
= $true ),
inference(unfold_def,[status(thm)],[431]) ).
thf(991,plain,
( ( ! [K: $i,L: $i] :
( ( plus_plus @ int @ ( bit0 @ K ) @ ( bit1 @ L ) )
= ( bit1 @ ( plus_plus @ int @ K @ L ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[432]) ).
thf(992,plain,
( ( ! [K: $i,L: $i] :
( ( plus_plus @ int @ ( bit1 @ K ) @ ( bit0 @ L ) )
= ( bit1 @ ( plus_plus @ int @ K @ L ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[433]) ).
thf(993,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [V: $i,W: $i] :
( ( number_number_of @ X_a @ ( plus_plus @ int @ V @ W ) )
= ( plus_plus @ X_a @ ( number_number_of @ X_a @ V ) @ ( number_number_of @ X_a @ W ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[434]) ).
thf(994,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [V: $i,W: $i] :
( ( plus_plus @ X_a @ ( number_number_of @ X_a @ V ) @ ( number_number_of @ X_a @ W ) )
= ( number_number_of @ X_a @ ( plus_plus @ int @ V @ W ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[435]) ).
thf(995,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [V: $i,W: $i,Z: $i] :
( ( plus_plus @ X_a @ ( number_number_of @ X_a @ V ) @ ( plus_plus @ X_a @ ( number_number_of @ X_a @ W ) @ Z ) )
= ( plus_plus @ X_a @ ( number_number_of @ X_a @ ( plus_plus @ int @ V @ W ) ) @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[436]) ).
thf(996,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [V: $i,W: $i] :
( ( number_number_of @ X_a @ ( times_times @ int @ V @ W ) )
= ( times_times @ X_a @ ( number_number_of @ X_a @ V ) @ ( number_number_of @ X_a @ W ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[437]) ).
thf(997,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [V: $i,W: $i] :
( ( times_times @ X_a @ ( number_number_of @ X_a @ V ) @ ( number_number_of @ X_a @ W ) )
= ( number_number_of @ X_a @ ( times_times @ int @ V @ W ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[438]) ).
thf(998,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [V: $i,W: $i,Z: $i] :
( ( times_times @ X_a @ ( number_number_of @ X_a @ V ) @ ( times_times @ X_a @ ( number_number_of @ X_a @ W ) @ Z ) )
= ( times_times @ X_a @ ( number_number_of @ X_a @ ( times_times @ int @ V @ W ) ) @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[439]) ).
thf(999,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [A_1: $i] :
( ( plus_plus @ X_a @ A_1 @ ( number_number_of @ X_a @ pls ) )
= ( ti @ X_a @ A_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[440]) ).
thf(1000,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [A_1: $i] :
( ( plus_plus @ X_a @ ( number_number_of @ X_a @ pls ) @ A_1 )
= ( ti @ X_a @ A_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[441]) ).
thf(1001,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [M: $i] :
( ( plus_plus @ X_a @ M @ M )
= ( times_times @ X_a @ ( plus_plus @ X_a @ ( one_one @ X_a ) @ ( one_one @ X_a ) ) @ M ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[442]) ).
thf(1002,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [M: $i,A_1: $i] :
( ( plus_plus @ X_a @ M @ ( times_times @ X_a @ A_1 @ M ) )
= ( times_times @ X_a @ ( plus_plus @ X_a @ A_1 @ ( one_one @ X_a ) ) @ M ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[443]) ).
thf(1003,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i,M: $i] :
( ( plus_plus @ X_a @ ( times_times @ X_a @ A_1 @ M ) @ M )
= ( times_times @ X_a @ ( plus_plus @ X_a @ A_1 @ ( one_one @ X_a ) ) @ M ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[444]) ).
thf(1004,plain,
( ( ! [X_b: $i] :
( ( ( number @ X_b )
& ( semiring @ X_b ) )
=> ! [V: $i,B: $i,C: $i] :
( ( times_times @ X_b @ ( number_number_of @ X_b @ V ) @ ( plus_plus @ X_b @ B @ C ) )
= ( plus_plus @ X_b @ ( times_times @ X_b @ ( number_number_of @ X_b @ V ) @ B ) @ ( times_times @ X_b @ ( number_number_of @ X_b @ V ) @ C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[445]) ).
thf(1005,plain,
( ( ! [X_b: $i] :
( ( ( number @ X_b )
& ( semiring @ X_b ) )
=> ! [A_1: $i,B: $i,V: $i] :
( ( times_times @ X_b @ ( plus_plus @ X_b @ A_1 @ B ) @ ( number_number_of @ X_b @ V ) )
= ( plus_plus @ X_b @ ( times_times @ X_b @ A_1 @ ( number_number_of @ X_b @ V ) ) @ ( times_times @ X_b @ B @ ( number_number_of @ X_b @ V ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[446]) ).
thf(1006,plain,
( ( ! [X_1: $i] : ( ord_less_eq @ int @ X_1 @ ( power_power @ int @ X_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[447]) ).
thf(1007,plain,
( ( ! [X_a: $i] :
( ( number_semiring @ X_a )
=> ! [V_1: $i,V: $i] :
( ( ord_less_eq @ int @ pls @ V )
=> ( ( ord_less_eq @ int @ pls @ V_1 )
=> ( ( plus_plus @ X_a @ ( number_number_of @ X_a @ V ) @ ( number_number_of @ X_a @ V_1 ) )
= ( number_number_of @ X_a @ ( plus_plus @ int @ V @ V_1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[448]) ).
thf(1008,plain,
( ( ! [X_a: $i] :
( ( number_semiring @ X_a )
=> ! [V_1: $i,V: $i] :
( ( ord_less_eq @ int @ pls @ V )
=> ( ( ord_less_eq @ int @ pls @ V_1 )
=> ( ( times_times @ X_a @ ( number_number_of @ X_a @ V ) @ ( number_number_of @ X_a @ V_1 ) )
= ( number_number_of @ X_a @ ( times_times @ int @ V @ V_1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[449]) ).
thf(1009,plain,
( ( ! [V: $i,W: $i] :
( ( plus_plus @ int @ ( number_number_of @ int @ V ) @ ( number_number_of @ int @ W ) )
= ( number_number_of @ int @ ( plus_plus @ int @ V @ W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[450]) ).
thf(1010,plain,
( ( ! [W: $i,Z1: $i,Z2: $i] :
( ( times_times @ int @ W @ ( plus_plus @ int @ Z1 @ Z2 ) )
= ( plus_plus @ int @ ( times_times @ int @ W @ Z1 ) @ ( times_times @ int @ W @ Z2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[451]) ).
thf(1011,plain,
( ( ! [Z1: $i,Z2: $i,W: $i] :
( ( times_times @ int @ ( plus_plus @ int @ Z1 @ Z2 ) @ W )
= ( plus_plus @ int @ ( times_times @ int @ Z1 @ W ) @ ( times_times @ int @ Z2 @ W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[452]) ).
thf(1012,plain,
( ( ! [V: $i,W: $i] :
( ( times_times @ int @ ( number_number_of @ int @ V ) @ ( number_number_of @ int @ W ) )
= ( number_number_of @ int @ ( times_times @ int @ V @ W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[453]) ).
thf(1013,plain,
( ( ! [Z: $i] :
( ( times_times @ int @ ( one_one @ int ) @ Z )
= ( ti @ int @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[454]) ).
thf(1014,plain,
( ( ! [Z: $i] :
( ( times_times @ int @ Z @ ( one_one @ int ) )
= ( ti @ int @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[455]) ).
thf(1015,plain,
( ( ! [K: $i] :
( ( bit0 @ K )
= ( plus_plus @ int @ K @ K ) ) )
= $true ),
inference(unfold_def,[status(thm)],[456]) ).
thf(1016,plain,
( ( ! [K: $i,L: $i] :
( ( plus_plus @ int @ ( bit0 @ K ) @ ( bit0 @ L ) )
= ( bit0 @ ( plus_plus @ int @ K @ L ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[457]) ).
thf(1017,plain,
( ( ! [K: $i] :
( ( plus_plus @ int @ pls @ K )
= ( ti @ int @ K ) ) )
= $true ),
inference(unfold_def,[status(thm)],[458]) ).
thf(1018,plain,
( ( ! [K: $i] :
( ( plus_plus @ int @ K @ pls )
= ( ti @ int @ K ) ) )
= $true ),
inference(unfold_def,[status(thm)],[459]) ).
thf(1019,plain,
( ( ! [K: $i,L: $i] :
( ( times_times @ int @ ( bit0 @ K ) @ L )
= ( bit0 @ ( times_times @ int @ K @ L ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[460]) ).
thf(1020,plain,
( ( ! [W: $i] :
( ( times_times @ int @ pls @ W )
= pls ) )
= $true ),
inference(unfold_def,[status(thm)],[461]) ).
thf(1021,plain,
( ( ( bit0 @ pls )
= pls )
= $true ),
inference(unfold_def,[status(thm)],[462]) ).
thf(1022,plain,
( ( ! [L_1: $i] :
( ( pls
= ( bit0 @ L_1 ) )
<=> ( pls
= ( ti @ int @ L_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[463]) ).
thf(1023,plain,
( ( ! [K_1: $i] :
( ( ( bit0 @ K_1 )
= pls )
<=> ( ( ti @ int @ K_1 )
= pls ) ) )
= $true ),
inference(unfold_def,[status(thm)],[464]) ).
thf(1024,plain,
( ( ! [K: $i,L: $i] :
( ( bit0 @ K )
!= ( bit1 @ L ) ) )
= $true ),
inference(unfold_def,[status(thm)],[465]) ).
thf(1025,plain,
( ( ! [K: $i,L: $i] :
( ( bit1 @ K )
!= ( bit0 @ L ) ) )
= $true ),
inference(unfold_def,[status(thm)],[466]) ).
thf(1026,plain,
( ( ! [L: $i] :
( pls
!= ( bit1 @ L ) ) )
= $true ),
inference(unfold_def,[status(thm)],[467]) ).
thf(1027,plain,
( ( ! [K: $i] :
( ( bit1 @ K )
!= pls ) )
= $true ),
inference(unfold_def,[status(thm)],[468]) ).
thf(1028,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [X_1: $i,Y_1: $i,Q: $i] :
( ( power_power @ X_a @ ( times_times @ X_a @ X_1 @ Y_1 ) @ Q )
= ( times_times @ X_a @ ( power_power @ X_a @ X_1 @ Q ) @ ( power_power @ X_a @ Y_1 @ Q ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[469]) ).
thf(1029,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i] :
( ( times_times @ X_a @ ( one_one @ X_a ) @ A_1 )
= ( ti @ X_a @ A_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[470]) ).
thf(1030,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i] :
( ( times_times @ X_a @ A_1 @ ( one_one @ X_a ) )
= ( ti @ X_a @ A_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[471]) ).
thf(1031,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [X_1: $i,Y_1: $i,Z: $i] :
( ( times_times @ X_a @ X_1 @ ( plus_plus @ X_a @ Y_1 @ Z ) )
= ( plus_plus @ X_a @ ( times_times @ X_a @ X_1 @ Y_1 ) @ ( times_times @ X_a @ X_1 @ Z ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[472]) ).
thf(1032,plain,
( ( ! [X_a: $i] :
( ( semiri456707255roduct @ X_a )
=> ! [C_1: $i,D_1: $i,A_2: $i,B_1: $i] :
( ( ( ( ti @ X_a @ A_2 )
!= ( ti @ X_a @ B_1 ) )
& ( ( ti @ X_a @ C_1 )
!= ( ti @ X_a @ D_1 ) ) )
<=> ( ( plus_plus @ X_a @ ( times_times @ X_a @ A_2 @ C_1 ) @ ( times_times @ X_a @ B_1 @ D_1 ) )
!= ( plus_plus @ X_a @ ( times_times @ X_a @ A_2 @ D_1 ) @ ( times_times @ X_a @ B_1 @ C_1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[473]) ).
thf(1033,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i,B: $i,C: $i] :
( ( times_times @ X_a @ ( plus_plus @ X_a @ A_1 @ B ) @ C )
= ( plus_plus @ X_a @ ( times_times @ X_a @ A_1 @ C ) @ ( times_times @ X_a @ B @ C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[474]) ).
thf(1034,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i,M: $i,B: $i] :
( ( plus_plus @ X_a @ ( times_times @ X_a @ A_1 @ M ) @ ( times_times @ X_a @ B @ M ) )
= ( times_times @ X_a @ ( plus_plus @ X_a @ A_1 @ B ) @ M ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[475]) ).
thf(1035,plain,
( ( ! [X_a: $i] :
( ( semiri456707255roduct @ X_a )
=> ! [W_1: $i,Y_2: $i,X_2: $i,Z_1: $i] :
( ( ( plus_plus @ X_a @ ( times_times @ X_a @ W_1 @ Y_2 ) @ ( times_times @ X_a @ X_2 @ Z_1 ) )
= ( plus_plus @ X_a @ ( times_times @ X_a @ W_1 @ Z_1 ) @ ( times_times @ X_a @ X_2 @ Y_2 ) ) )
<=> ( ( ( ti @ X_a @ W_1 )
= ( ti @ X_a @ X_2 ) )
| ( ( ti @ X_a @ Y_2 )
= ( ti @ X_a @ Z_1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[476]) ).
thf(1036,plain,
( ( ! [X_a: $i] :
( ( ( number_ring @ X_a )
& ( linordered_idom @ X_a ) )
=> ! [Y_2: $i] :
( ( ord_less_eq @ X_a @ ( one_one @ X_a ) @ ( number_number_of @ X_a @ Y_2 ) )
<=> ( ord_less_eq @ int @ ( bit1 @ pls ) @ Y_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[477]) ).
thf(1037,plain,
( ( ! [X_a: $i] :
( ( ( number_ring @ X_a )
& ( linordered_idom @ X_a ) )
=> ! [X_2: $i] :
( ( ord_less_eq @ X_a @ ( number_number_of @ X_a @ X_2 ) @ ( one_one @ X_a ) )
<=> ( ord_less_eq @ int @ X_2 @ ( bit1 @ pls ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[478]) ).
thf(1038,plain,
( ( ! [X_a: $i] :
( ( ( number_ring @ X_a )
& ( linordered_idom @ X_a ) )
=> ! [Y_2: $i] :
( ( ord_less @ X_a @ ( one_one @ X_a ) @ ( number_number_of @ X_a @ Y_2 ) )
<=> ( ord_less @ int @ ( bit1 @ pls ) @ Y_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[479]) ).
thf(1039,plain,
( ( ! [X_a: $i] :
( ( ( number_ring @ X_a )
& ( linordered_idom @ X_a ) )
=> ! [X_2: $i] :
( ( ord_less @ X_a @ ( number_number_of @ X_a @ X_2 ) @ ( one_one @ X_a ) )
<=> ( ord_less @ int @ X_2 @ ( bit1 @ pls ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[480]) ).
thf(1040,plain,
( ( ! [X_a: $i] :
( ( monoid_mult @ X_a )
=> ! [A_1: $i,N: $i] :
( ( power_power @ X_a @ A_1 @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ N ) )
= ( power_power @ X_a @ ( power_power @ X_a @ A_1 @ N ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[481]) ).
thf(1041,plain,
( ( ! [W_1: $i,Z_1: $i] :
( ( ord_less @ int @ W_1 @ ( plus_plus @ int @ Z_1 @ ( one_one @ int ) ) )
<=> ( ( ord_less @ int @ W_1 @ Z_1 )
| ( ( ti @ int @ W_1 )
= ( ti @ int @ Z_1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[482]) ).
thf(1042,plain,
( ( ! [K_1: $i] :
( ( ord_less_eq @ int @ pls @ ( bit0 @ K_1 ) )
<=> ( ord_less_eq @ int @ pls @ K_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[483]) ).
thf(1043,plain,
( ( ! [K_1: $i] :
( ( ord_less_eq @ int @ ( bit0 @ K_1 ) @ pls )
<=> ( ord_less_eq @ int @ K_1 @ pls ) ) )
= $true ),
inference(unfold_def,[status(thm)],[484]) ).
thf(1044,plain,
( ( ! [K_1: $i,L_1: $i] :
( ( ord_less_eq @ int @ ( bit0 @ K_1 ) @ ( bit1 @ L_1 ) )
<=> ( ord_less_eq @ int @ K_1 @ L_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[485]) ).
thf(1045,plain,
( ( ! [K1: $i,K2: $i] :
( ( ord_less_eq @ int @ ( bit0 @ K1 ) @ ( bit1 @ K2 ) )
<=> ( ord_less_eq @ int @ K1 @ K2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[486]) ).
thf(1046,plain,
( ( ! [K_1: $i] :
( ( ord_less_eq @ int @ pls @ ( bit1 @ K_1 ) )
<=> ( ord_less_eq @ int @ pls @ K_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[487]) ).
thf(1047,plain,
( ( ! [K_1: $i] :
( ( ord_less @ int @ pls @ ( bit0 @ K_1 ) )
<=> ( ord_less @ int @ pls @ K_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[488]) ).
thf(1048,plain,
( ( ! [K_1: $i] :
( ( ord_less @ int @ ( bit0 @ K_1 ) @ pls )
<=> ( ord_less @ int @ K_1 @ pls ) ) )
= $true ),
inference(unfold_def,[status(thm)],[489]) ).
thf(1049,plain,
( ( ! [K_1: $i,L_1: $i] :
( ( ord_less @ int @ ( bit1 @ K_1 ) @ ( bit0 @ L_1 ) )
<=> ( ord_less @ int @ K_1 @ L_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[490]) ).
thf(1050,plain,
( ( ! [K1: $i,K2: $i] :
( ( ord_less @ int @ ( bit1 @ K1 ) @ ( bit0 @ K2 ) )
<=> ( ord_less @ int @ K1 @ K2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[491]) ).
thf(1051,plain,
( ( ! [K_1: $i] :
( ( ord_less @ int @ ( bit1 @ K_1 ) @ pls )
<=> ( ord_less @ int @ K_1 @ pls ) ) )
= $true ),
inference(unfold_def,[status(thm)],[492]) ).
thf(1052,plain,
( ( ! [Z: $i,W: $i] :
( ( plus_plus @ int @ Z @ W )
= ( plus_plus @ int @ W @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[493]) ).
thf(1053,plain,
( ( ! [X_1: $i,Y_1: $i,Z: $i] :
( ( plus_plus @ int @ X_1 @ ( plus_plus @ int @ Y_1 @ Z ) )
= ( plus_plus @ int @ Y_1 @ ( plus_plus @ int @ X_1 @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[494]) ).
thf(1054,plain,
( ( ! [Z1: $i,Z2: $i,Z3: $i] :
( ( plus_plus @ int @ ( plus_plus @ int @ Z1 @ Z2 ) @ Z3 )
= ( plus_plus @ int @ Z1 @ ( plus_plus @ int @ Z2 @ Z3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[495]) ).
thf(1055,plain,
( ( ! [K: $i] :
( ( number_number_of @ int @ K )
= ( ti @ int @ K ) ) )
= $true ),
inference(unfold_def,[status(thm)],[496]) ).
thf(1056,plain,
( ( ! [Z: $i,W: $i] :
( ( times_times @ int @ Z @ W )
= ( times_times @ int @ W @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[497]) ).
thf(1057,plain,
( ( ! [Z1: $i,Z2: $i,Z3: $i] :
( ( times_times @ int @ ( times_times @ int @ Z1 @ Z2 ) @ Z3 )
= ( times_times @ int @ Z1 @ ( times_times @ int @ Z2 @ Z3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[498]) ).
thf(1058,plain,
( ( ! [K_1: $i,L_1: $i] :
( ( ( bit0 @ K_1 )
= ( bit0 @ L_1 ) )
<=> ( ( ti @ int @ K_1 )
= ( ti @ int @ L_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[499]) ).
thf(1059,plain,
( ( ! [K_1: $i,L_1: $i] :
( ( ( bit1 @ K_1 )
= ( bit1 @ L_1 ) )
<=> ( ( ti @ int @ K_1 )
= ( ti @ int @ L_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[500]) ).
thf(1060,plain,
( ( ! [X_a: $i] :
( ( number @ X_a )
=> ! [W_1: $i,X_2: $i] :
( ( ( number_number_of @ X_a @ W_1 )
= ( ti @ X_a @ X_2 ) )
<=> ( ( ti @ X_a @ X_2 )
= ( number_number_of @ X_a @ W_1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[501]) ).
thf(1061,plain,
( ( ! [X_a: $i] :
( ( ( number_ring @ X_a )
& ( ring_char_0 @ X_a ) )
=> ! [X_2: $i,Y_2: $i] :
( ( ( number_number_of @ X_a @ X_2 )
= ( number_number_of @ X_a @ Y_2 ) )
<=> ( ( ti @ int @ X_2 )
= ( ti @ int @ Y_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[502]) ).
thf(1062,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i,C: $i] :
( ( plus_plus @ X_a @ A_1 @ C )
= ( plus_plus @ X_a @ C @ A_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[503]) ).
thf(1063,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i,C: $i,D: $i] :
( ( plus_plus @ X_a @ A_1 @ ( plus_plus @ X_a @ C @ D ) )
= ( plus_plus @ X_a @ C @ ( plus_plus @ X_a @ A_1 @ D ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[504]) ).
thf(1064,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i,C: $i,D: $i] :
( ( plus_plus @ X_a @ A_1 @ ( plus_plus @ X_a @ C @ D ) )
= ( plus_plus @ X_a @ ( plus_plus @ X_a @ A_1 @ C ) @ D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[505]) ).
thf(1065,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i,B: $i,C: $i] :
( ( plus_plus @ X_a @ ( plus_plus @ X_a @ A_1 @ B ) @ C )
= ( plus_plus @ X_a @ A_1 @ ( plus_plus @ X_a @ B @ C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[506]) ).
thf(1066,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i,B: $i,C: $i] :
( ( plus_plus @ X_a @ ( plus_plus @ X_a @ A_1 @ B ) @ C )
= ( plus_plus @ X_a @ ( plus_plus @ X_a @ A_1 @ C ) @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[507]) ).
thf(1067,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i,B: $i,C: $i,D: $i] :
( ( plus_plus @ X_a @ ( plus_plus @ X_a @ A_1 @ B ) @ ( plus_plus @ X_a @ C @ D ) )
= ( plus_plus @ X_a @ ( plus_plus @ X_a @ A_1 @ C ) @ ( plus_plus @ X_a @ B @ D ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[508]) ).
thf(1068,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i,B: $i] :
( ( times_times @ X_a @ A_1 @ B )
= ( times_times @ X_a @ B @ A_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[509]) ).
thf(1069,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [Lx: $i,Rx: $i,Ry: $i] :
( ( times_times @ X_a @ Lx @ ( times_times @ X_a @ Rx @ Ry ) )
= ( times_times @ X_a @ Rx @ ( times_times @ X_a @ Lx @ Ry ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[510]) ).
thf(1070,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [Lx: $i,Rx: $i,Ry: $i] :
( ( times_times @ X_a @ Lx @ ( times_times @ X_a @ Rx @ Ry ) )
= ( times_times @ X_a @ ( times_times @ X_a @ Lx @ Rx ) @ Ry ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[511]) ).
thf(1071,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [Lx: $i,Ly: $i,Rx: $i] :
( ( times_times @ X_a @ ( times_times @ X_a @ Lx @ Ly ) @ Rx )
= ( times_times @ X_a @ Lx @ ( times_times @ X_a @ Ly @ Rx ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[512]) ).
thf(1072,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [Lx: $i,Ly: $i,Rx: $i] :
( ( times_times @ X_a @ ( times_times @ X_a @ Lx @ Ly ) @ Rx )
= ( times_times @ X_a @ ( times_times @ X_a @ Lx @ Rx ) @ Ly ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[513]) ).
thf(1073,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [Lx: $i,Ly: $i,Rx: $i,Ry: $i] :
( ( times_times @ X_a @ ( times_times @ X_a @ Lx @ Ly ) @ ( times_times @ X_a @ Rx @ Ry ) )
= ( times_times @ X_a @ Lx @ ( times_times @ X_a @ Ly @ ( times_times @ X_a @ Rx @ Ry ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[514]) ).
thf(1074,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [Lx: $i,Ly: $i,Rx: $i,Ry: $i] :
( ( times_times @ X_a @ ( times_times @ X_a @ Lx @ Ly ) @ ( times_times @ X_a @ Rx @ Ry ) )
= ( times_times @ X_a @ Rx @ ( times_times @ X_a @ ( times_times @ X_a @ Lx @ Ly ) @ Ry ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[515]) ).
thf(1075,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [Lx: $i,Ly: $i,Rx: $i,Ry: $i] :
( ( times_times @ X_a @ ( times_times @ X_a @ Lx @ Ly ) @ ( times_times @ X_a @ Rx @ Ry ) )
= ( times_times @ X_a @ ( times_times @ X_a @ Lx @ Rx ) @ ( times_times @ X_a @ Ly @ Ry ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[516]) ).
thf(1076,plain,
( ( ! [Y_1: $i,X_1: $i] :
( ( twoSqu420862341sum2sq @ X_1 )
=> ( ( twoSqu420862341sum2sq @ Y_1 )
=> ( twoSqu420862341sum2sq @ ( times_times @ int @ X_1 @ Y_1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[517]) ).
thf(1077,plain,
( ( zprime @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[518]) ).
thf(1078,plain,
( ( ! [W_1: $i,Z_1: $i] :
( ( ord_less @ int @ W_1 @ ( plus_plus @ int @ Z_1 @ ( one_one @ int ) ) )
<=> ( ord_less_eq @ int @ W_1 @ Z_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[519]) ).
thf(1079,plain,
( ( ! [W_1: $i,Z_1: $i] :
( ( ord_less_eq @ int @ ( plus_plus @ int @ W_1 @ ( one_one @ int ) ) @ Z_1 )
<=> ( ord_less @ int @ W_1 @ Z_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[520]) ).
thf(1080,plain,
( ( ! [W: $i,Z: $i] :
( ( ord_less @ int @ W @ Z )
=> ( ord_less_eq @ int @ ( plus_plus @ int @ W @ ( one_one @ int ) ) @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[521]) ).
thf(1081,plain,
( ( ! [K_1: $i,L_1: $i] :
( ( ord_less @ int @ ( bit0 @ K_1 ) @ ( bit1 @ L_1 ) )
<=> ( ord_less_eq @ int @ K_1 @ L_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[522]) ).
thf(1082,plain,
( ( ! [K1: $i,K2: $i] :
( ( ord_less @ int @ ( bit0 @ K1 ) @ ( bit1 @ K2 ) )
<=> ( ord_less_eq @ int @ K1 @ K2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[523]) ).
thf(1083,plain,
( ( ! [K_1: $i,L_1: $i] :
( ( ord_less_eq @ int @ ( bit1 @ K_1 ) @ ( bit0 @ L_1 ) )
<=> ( ord_less @ int @ K_1 @ L_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[524]) ).
thf(1084,plain,
( ( ! [K1: $i,K2: $i] :
( ( ord_less_eq @ int @ ( bit1 @ K1 ) @ ( bit0 @ K2 ) )
<=> ( ord_less @ int @ K1 @ K2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[525]) ).
thf(1085,plain,
( ( ! [K_1: $i] :
( ( ord_less @ int @ pls @ ( bit1 @ K_1 ) )
<=> ( ord_less_eq @ int @ pls @ K_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[526]) ).
thf(1086,plain,
( ( ! [K_1: $i] :
( ( ord_less_eq @ int @ ( bit1 @ K_1 ) @ pls )
<=> ( ord_less @ int @ K_1 @ pls ) ) )
= $true ),
inference(unfold_def,[status(thm)],[527]) ).
thf(1087,plain,
( ( ( one_one @ nat )
= ( number_number_of @ nat @ ( bit1 @ pls ) ) )
= $true ),
inference(unfold_def,[status(thm)],[528]) ).
thf(1088,plain,
( ( ( number_number_of @ nat @ ( bit1 @ pls ) )
= ( one_one @ nat ) )
= $true ),
inference(unfold_def,[status(thm)],[529]) ).
thf(1089,plain,
( ( ! [V_1: $i,V: $i] :
( ( ( ord_less @ int @ V @ pls )
=> ( ( plus_plus @ nat @ ( number_number_of @ nat @ V ) @ ( number_number_of @ nat @ V_1 ) )
= ( number_number_of @ nat @ V_1 ) ) )
& ( ~ ( ord_less @ int @ V @ pls )
=> ( ( ( ord_less @ int @ V_1 @ pls )
=> ( ( plus_plus @ nat @ ( number_number_of @ nat @ V ) @ ( number_number_of @ nat @ V_1 ) )
= ( number_number_of @ nat @ V ) ) )
& ( ~ ( ord_less @ int @ V_1 @ pls )
=> ( ( plus_plus @ nat @ ( number_number_of @ nat @ V ) @ ( number_number_of @ nat @ V_1 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ V @ V_1 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[530]) ).
thf(1090,plain,
( ( ! [K: $i,I: $i,J: $i] :
( ( ord_less_eq @ int @ I @ J )
=> ( ord_less_eq @ int @ ( plus_plus @ int @ K @ I ) @ ( plus_plus @ int @ K @ J ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[531]) ).
thf(1091,plain,
( ( ! [K: $i,I: $i,J: $i] :
( ( ord_less @ int @ I @ J )
=> ( ord_less @ int @ ( plus_plus @ int @ I @ K ) @ ( plus_plus @ int @ J @ K ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[532]) ).
thf(1092,plain,
( ( ! [K_1: $i,L_1: $i] :
( ( ord_less_eq @ int @ ( number_number_of @ int @ K_1 ) @ ( number_number_of @ int @ L_1 ) )
<=> ( ord_less_eq @ int @ K_1 @ L_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[533]) ).
thf(1093,plain,
( ( ! [K_1: $i,L_1: $i] :
( ( ord_less @ int @ ( number_number_of @ int @ K_1 ) @ ( number_number_of @ int @ L_1 ) )
<=> ( ord_less @ int @ K_1 @ L_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[534]) ).
thf(1094,plain,
( ( ! [K_1: $i,L_1: $i] :
( ( ord_less_eq @ int @ ( bit0 @ K_1 ) @ ( bit0 @ L_1 ) )
<=> ( ord_less_eq @ int @ K_1 @ L_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[535]) ).
thf(1095,plain,
( ( ! [K1: $i,K2: $i] :
( ( ord_less_eq @ int @ ( bit0 @ K1 ) @ ( bit0 @ K2 ) )
<=> ( ord_less_eq @ int @ K1 @ K2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[536]) ).
thf(1096,plain,
( ( ord_less_eq @ int @ pls @ pls )
= $true ),
inference(unfold_def,[status(thm)],[537]) ).
thf(1097,plain,
( ( ! [K_1: $i,L_1: $i] :
( ( ord_less @ int @ ( bit0 @ K_1 ) @ ( bit0 @ L_1 ) )
<=> ( ord_less @ int @ K_1 @ L_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[538]) ).
thf(1098,plain,
( ( ! [K1: $i,K2: $i] :
( ( ord_less @ int @ ( bit0 @ K1 ) @ ( bit0 @ K2 ) )
<=> ( ord_less @ int @ K1 @ K2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[539]) ).
thf(1099,plain,
( ( ~ ( ord_less @ int @ pls @ pls ) )
= $true ),
inference(unfold_def,[status(thm)],[540]) ).
thf(1100,plain,
( ( ! [K_1: $i,L_1: $i] :
( ( ord_less_eq @ int @ ( bit1 @ K_1 ) @ ( bit1 @ L_1 ) )
<=> ( ord_less_eq @ int @ K_1 @ L_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[541]) ).
thf(1101,plain,
( ( ! [K1: $i,K2: $i] :
( ( ord_less_eq @ int @ ( bit1 @ K1 ) @ ( bit1 @ K2 ) )
<=> ( ord_less_eq @ int @ K1 @ K2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[542]) ).
thf(1102,plain,
( ( ! [K_1: $i,L_1: $i] :
( ( ord_less @ int @ ( bit1 @ K_1 ) @ ( bit1 @ L_1 ) )
<=> ( ord_less @ int @ K_1 @ L_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[543]) ).
thf(1103,plain,
( ( ! [K1: $i,K2: $i] :
( ( ord_less @ int @ ( bit1 @ K1 ) @ ( bit1 @ K2 ) )
<=> ( ord_less @ int @ K1 @ K2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[544]) ).
thf(1104,plain,
( ( ( plus_plus @ nat @ ( one_one @ nat ) @ ( one_one @ nat ) )
= ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[545]) ).
thf(1105,plain,
( ( ! [Z: $i] :
( ( times_times @ nat @ Z @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ nat @ Z @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[546]) ).
thf(1106,plain,
( ( ! [Z: $i] :
( ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ Z )
= ( plus_plus @ nat @ Z @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[547]) ).
thf(1107,plain,
( ( ! [X_1: $i,Y_1: $i,Z: $i] :
( ( power_power @ int @ X_1 @ ( plus_plus @ nat @ Y_1 @ Z ) )
= ( times_times @ int @ ( power_power @ int @ X_1 @ Y_1 ) @ ( power_power @ int @ X_1 @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[548]) ).
thf(1108,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [X_1: $i,P: $i,Q: $i] :
( ( times_times @ X_a @ ( power_power @ X_a @ X_1 @ P ) @ ( power_power @ X_a @ X_1 @ Q ) )
= ( power_power @ X_a @ X_1 @ ( plus_plus @ nat @ P @ Q ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[549]) ).
thf(1109,plain,
( ( ! [Z_2: $i,Z: $i,W_2: $i,W: $i] :
( ( ord_less @ int @ W_2 @ W )
=> ( ( ord_less_eq @ int @ Z_2 @ Z )
=> ( ord_less @ int @ ( plus_plus @ int @ W_2 @ Z_2 ) @ ( plus_plus @ int @ W @ Z ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[550]) ).
thf(1110,plain,
( ( ! [X_a: $i] :
( ( ( number_ring @ X_a )
& ( linordered_idom @ X_a ) )
=> ! [X_2: $i,Y_2: $i] :
( ( ord_less_eq @ X_a @ ( number_number_of @ X_a @ X_2 ) @ ( number_number_of @ X_a @ Y_2 ) )
<=> ( ord_less_eq @ int @ X_2 @ Y_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[551]) ).
thf(1111,plain,
( ( ! [X_a: $i] :
( ( ( number_ring @ X_a )
& ( linordered_idom @ X_a ) )
=> ! [X_2: $i,Y_2: $i] :
( ( ord_less @ X_a @ ( number_number_of @ X_a @ X_2 ) @ ( number_number_of @ X_a @ Y_2 ) )
<=> ( ord_less @ int @ X_2 @ Y_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[552]) ).
thf(1112,plain,
( ( ! [X_1: $i,Y_1: $i,Z: $i] :
( ( power_power @ int @ ( power_power @ int @ X_1 @ Y_1 ) @ Z )
= ( power_power @ int @ X_1 @ ( times_times @ nat @ Y_1 @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[554]) ).
thf(1113,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [X_1: $i] :
( ( power_power @ X_a @ X_1 @ ( one_one @ nat ) )
= ( ti @ X_a @ X_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[555]) ).
thf(1114,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [X_1: $i,P: $i,Q: $i] :
( ( power_power @ X_a @ ( power_power @ X_a @ X_1 @ P ) @ Q )
= ( power_power @ X_a @ X_1 @ ( times_times @ nat @ P @ Q ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[556]) ).
thf(1115,plain,
( ( ! [Z: $i,W: $i] :
( ( ord_less_eq @ int @ Z @ W )
=> ( ( ord_less_eq @ int @ W @ Z )
=> ( ( ti @ int @ Z )
= ( ti @ int @ W ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[557]) ).
thf(1116,plain,
( ( ! [K: $i,I: $i,J: $i] :
( ( ord_less_eq @ int @ I @ J )
=> ( ( ord_less_eq @ int @ J @ K )
=> ( ord_less_eq @ int @ I @ K ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[558]) ).
thf(1117,plain,
( ( ! [X_1: $i,Y_1: $i] :
( ( ord_less @ int @ X_1 @ Y_1 )
| ( ( ti @ int @ X_1 )
= ( ti @ int @ Y_1 ) )
| ( ord_less @ int @ Y_1 @ X_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[559]) ).
thf(1118,plain,
( ( ! [Z_1: $i,W_1: $i] :
( ( ord_less @ int @ Z_1 @ W_1 )
<=> ( ( ord_less_eq @ int @ Z_1 @ W_1 )
& ( ( ti @ int @ Z_1 )
!= ( ti @ int @ W_1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[560]) ).
thf(1119,plain,
( ( ! [Z: $i,W: $i] :
( ( ord_less_eq @ int @ Z @ W )
| ( ord_less_eq @ int @ W @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[561]) ).
thf(1120,plain,
( ( ! [W: $i] : ( ord_less_eq @ int @ W @ W ) )
= $true ),
inference(unfold_def,[status(thm)],[562]) ).
thf(1121,plain,
( ( ~ ! [T_1: $i] :
( ( plus_plus @ int @ ( power_power @ int @ s @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( one_one @ int ) )
!= ( times_times @ int @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[563]) ).
thf(1122,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ( ( plus_plus @ X_a @ ( one_one @ X_a ) @ ( one_one @ X_a ) )
= ( number_number_of @ X_a @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[564]) ).
thf(1123,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [V: $i] :
( ( plus_plus @ X_a @ ( number_number_of @ X_a @ V ) @ ( one_one @ X_a ) )
= ( number_number_of @ X_a @ ( plus_plus @ int @ V @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[565]) ).
thf(1124,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [W: $i] :
( ( plus_plus @ X_a @ ( one_one @ X_a ) @ ( number_number_of @ X_a @ W ) )
= ( number_number_of @ X_a @ ( plus_plus @ int @ ( bit1 @ pls ) @ W ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[566]) ).
thf(1125,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [X_1: $i,N: $i] :
( ( power_power @ X_a @ X_1 @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ N ) )
= ( times_times @ X_a @ ( power_power @ X_a @ X_1 @ N ) @ ( power_power @ X_a @ X_1 @ N ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[567]) ).
thf(1126,plain,
( ( ! [X_a: $i] :
( ( monoid_mult @ X_a )
=> ! [A_1: $i] :
( ( power_power @ X_a @ A_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times @ X_a @ A_1 @ A_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[568]) ).
thf(1127,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [X_1: $i] :
( ( times_times @ X_a @ X_1 @ X_1 )
= ( power_power @ X_a @ X_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[569]) ).
thf(1128,plain,
( ( ! [X_a: $i] :
( ( semiring_1 @ X_a )
=> ( ( power_power @ X_a @ ( one_one @ X_a ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( one_one @ X_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[570]) ).
thf(1129,plain,
( ( ! [A_1: $i] :
( ( times_times @ int @ A_1 @ ( power_power @ int @ A_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( power_power @ int @ A_1 @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[571]) ).
thf(1130,plain,
( ( ! [X_b: $i] :
( ( ( monoid_mult @ X_b )
& ( number @ X_b ) )
=> ! [W: $i] :
( ( power_power @ X_b @ ( number_number_of @ X_b @ W ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times @ X_b @ ( number_number_of @ X_b @ W ) @ ( number_number_of @ X_b @ W ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[572]) ).
thf(1131,plain,
( ( ! [X_a: $i] :
( ( number_semiring @ X_a )
=> ! [X_1: $i,Y_1: $i] :
( ( power_power @ X_a @ ( plus_plus @ X_a @ X_1 @ Y_1 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ X_a @ ( plus_plus @ X_a @ ( power_power @ X_a @ X_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ X_a @ Y_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times @ X_a @ ( times_times @ X_a @ ( number_number_of @ X_a @ ( bit0 @ ( bit1 @ pls ) ) ) @ X_1 ) @ Y_1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[573]) ).
thf(1132,plain,
( ( ! [A_1: $i,B: $i] :
( ( power_power @ int @ ( plus_plus @ int @ A_1 @ B ) @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( power_power @ int @ A_1 @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) @ ( times_times @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit1 @ ( bit1 @ pls ) ) ) @ ( power_power @ int @ A_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ B ) ) @ ( times_times @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit1 @ ( bit1 @ pls ) ) ) @ A_1 ) @ ( power_power @ int @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ ( power_power @ int @ B @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[574]) ).
thf(1133,plain,
( ( ! [A_1: $i,B: $i] :
( ( power_power @ int @ ( plus_plus @ int @ A_1 @ B ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ int @ ( plus_plus @ int @ ( power_power @ int @ A_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( times_times @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A_1 ) @ B ) ) @ ( power_power @ int @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[575]) ).
thf(1134,plain,
( ( twoSqu420862341sum2sq @ ( times_times @ int @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) @ t ) )
= $true ),
inference(unfold_def,[status(thm)],[576]) ).
thf(1135,plain,
( ( ( plus_plus @ int @ ( power_power @ int @ s @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( one_one @ int ) )
= ( times_times @ int @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) @ t ) )
= $true ),
inference(unfold_def,[status(thm)],[577]) ).
thf(1136,plain,
( ( zprime @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) )
= $true ),
inference(unfold_def,[status(thm)],[578]) ).
thf(1137,plain,
( ( ord_less @ int @ t @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) )
= $true ),
inference(unfold_def,[status(thm)],[579]) ).
thf(1138,plain,
( ( ( ord_less @ int @ ( one_one @ int ) @ t )
=> ? [X: $i,Y: $i] :
( ( plus_plus @ int @ ( power_power @ int @ X @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ Y @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[580]) ).
thf(1139,plain,
( ( ( t
= ( one_one @ int ) )
=> ? [X: $i,Y: $i] :
( ( plus_plus @ int @ ( power_power @ int @ X @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ Y @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[581]) ).
thf(1140,plain,
( ( ord_less_eq @ int @ ( one_one @ int ) @ t )
= $true ),
inference(unfold_def,[status(thm)],[582]) ).
thf(1141,plain,
( ( ( ti @ int @ t )
= t )
= $true ),
inference(unfold_def,[status(thm)],[583]) ).
thf(1142,plain,
( ( ( ti @ int @ s )
= s )
= $true ),
inference(unfold_def,[status(thm)],[584]) ).
thf(1143,plain,
( ( ( ti @ int @ s1 )
= s1 )
= $true ),
inference(unfold_def,[status(thm)],[585]) ).
thf(1144,plain,
( ( ! [B_1_1: $i] :
( ( ti @ int @ ( twoSqu579703163sum2sq @ B_1_1 ) )
= ( twoSqu579703163sum2sq @ B_1_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[586]) ).
thf(1145,plain,
( ( ! [B_1_1: $i] :
( ( twoSqu579703163sum2sq @ ( ti @ ( product_prod @ int @ int ) @ B_1_1 ) )
= ( twoSqu579703163sum2sq @ B_1_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[587]) ).
thf(1146,plain,
( ( ! [B_1_1: $i] :
( ( twoSqu420862341sum2sq @ ( ti @ int @ B_1_1 ) )
<=> ( twoSqu420862341sum2sq @ B_1_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[588]) ).
thf(1147,plain,
( ( ! [B_1_1: $i,B_2_1: $i] :
( ( quadRes @ B_1_1 @ ( ti @ int @ B_2_1 ) )
<=> ( quadRes @ B_1_1 @ B_2_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[591]) ).
thf(1148,plain,
( ( ! [B_1_1: $i,B_2_1: $i] :
( ( quadRes @ ( ti @ int @ B_1_1 ) @ B_2_1 )
<=> ( quadRes @ B_1_1 @ B_2_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[592]) ).
thf(1149,plain,
( ( ! [B_1_1: $i,B_2_1: $i] :
( ( ti @ int @ ( legendre @ B_1_1 @ B_2_1 ) )
= ( legendre @ B_1_1 @ B_2_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[593]) ).
thf(1150,plain,
( ( ! [B_1_1: $i,B_2_1: $i] :
( ( legendre @ B_1_1 @ ( ti @ int @ B_2_1 ) )
= ( legendre @ B_1_1 @ B_2_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[594]) ).
thf(1151,plain,
( ( ! [B_1_1: $i,B_2_1: $i] :
( ( legendre @ ( ti @ int @ B_1_1 ) @ B_2_1 )
= ( legendre @ B_1_1 @ B_2_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[595]) ).
thf(1152,plain,
( ( ! [B_1_1: $i,B_2_1: $i] :
( ( ti @ ( product_prod @ int @ int ) @ ( product_Pair @ int @ int @ B_1_1 @ B_2_1 ) )
= ( product_Pair @ int @ int @ B_1_1 @ B_2_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[596]) ).
thf(1153,plain,
( ( ! [B_1_1: $i,B_2_1: $i] :
( ( product_Pair @ int @ int @ B_1_1 @ ( ti @ int @ B_2_1 ) )
= ( product_Pair @ int @ int @ B_1_1 @ B_2_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[597]) ).
thf(1154,plain,
( ( ! [B_1_1: $i,B_2_1: $i] :
( ( product_Pair @ int @ int @ ( ti @ int @ B_1_1 ) @ B_2_1 )
= ( product_Pair @ int @ int @ B_1_1 @ B_2_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[598]) ).
thf(1155,plain,
( ( ! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( power @ X_a )
=> ( ( ti @ X_a @ ( power_power @ X_a @ B_1_1 @ B_2_1 ) )
= ( power_power @ X_a @ B_1_1 @ B_2_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[599]) ).
thf(1156,plain,
( ( ! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( power @ X_a )
=> ( ( power_power @ X_a @ B_1_1 @ ( ti @ nat @ B_2_1 ) )
= ( power_power @ X_a @ B_1_1 @ B_2_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[600]) ).
thf(1157,plain,
( ( ! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( power @ X_a )
=> ( ( power_power @ X_a @ ( ti @ X_a @ B_1_1 ) @ B_2_1 )
= ( power_power @ X_a @ B_1_1 @ B_2_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[601]) ).
thf(1158,plain,
( ( ! [B_1_1: $i,X_a: $i] :
( ( number @ X_a )
=> ( ( ti @ X_a @ ( number_number_of @ X_a @ B_1_1 ) )
= ( number_number_of @ X_a @ B_1_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[606]) ).
thf(1159,plain,
( ( ! [B_1_1: $i,X_a: $i] :
( ( number @ X_a )
=> ( ( number_number_of @ X_a @ ( ti @ int @ B_1_1 ) )
= ( number_number_of @ X_a @ B_1_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[607]) ).
thf(1160,plain,
( ( ( ti @ int @ min )
= min )
= $true ),
inference(unfold_def,[status(thm)],[608]) ).
thf(1161,plain,
( ( ! [B_1_1: $i] :
( ( zprime @ ( ti @ int @ B_1_1 ) )
<=> ( zprime @ B_1_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[609]) ).
thf(1162,plain,
( ( ! [B_1_1: $i,B_2_1: $i,B_3: $i] :
( ( zcong @ B_1_1 @ B_2_1 @ ( ti @ int @ B_3 ) )
<=> ( zcong @ B_1_1 @ B_2_1 @ B_3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[610]) ).
thf(1163,plain,
( ( ! [B_1_1: $i,B_2_1: $i,B_3: $i] :
( ( zcong @ B_1_1 @ ( ti @ int @ B_2_1 ) @ B_3 )
<=> ( zcong @ B_1_1 @ B_2_1 @ B_3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[611]) ).
thf(1164,plain,
( ( ! [B_1_1: $i,B_2_1: $i,B_3: $i] :
( ( zcong @ ( ti @ int @ B_1_1 ) @ B_2_1 @ B_3 )
<=> ( zcong @ B_1_1 @ B_2_1 @ B_3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[612]) ).
thf(1165,plain,
( ( ! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( power @ X_a )
=> ( ( ti @ X_a @ ( times_times @ X_a @ B_1_1 @ B_2_1 ) )
= ( times_times @ X_a @ B_1_1 @ B_2_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[618]) ).
thf(1166,plain,
( ( ! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( power @ X_a )
=> ( ( times_times @ X_a @ B_1_1 @ ( ti @ X_a @ B_2_1 ) )
= ( times_times @ X_a @ B_1_1 @ B_2_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[619]) ).
thf(1167,plain,
( ( ! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( power @ X_a )
=> ( ( times_times @ X_a @ ( ti @ X_a @ B_1_1 ) @ B_2_1 )
= ( times_times @ X_a @ B_1_1 @ B_2_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[620]) ).
thf(1168,plain,
( ( ! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( mult_zero @ X_a )
=> ( ( ti @ X_a @ ( times_times @ X_a @ B_1_1 @ B_2_1 ) )
= ( times_times @ X_a @ B_1_1 @ B_2_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[621]) ).
thf(1169,plain,
( ( ! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( mult_zero @ X_a )
=> ( ( times_times @ X_a @ B_1_1 @ ( ti @ X_a @ B_2_1 ) )
= ( times_times @ X_a @ B_1_1 @ B_2_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[622]) ).
thf(1170,plain,
( ( ! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( mult_zero @ X_a )
=> ( ( times_times @ X_a @ ( ti @ X_a @ B_1_1 ) @ B_2_1 )
= ( times_times @ X_a @ B_1_1 @ B_2_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[623]) ).
thf(1171,plain,
( ( ! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( no_zero_divisors @ X_a )
=> ( ( ti @ X_a @ ( times_times @ X_a @ B_1_1 @ B_2_1 ) )
= ( times_times @ X_a @ B_1_1 @ B_2_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[624]) ).
thf(1172,plain,
( ( ! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( no_zero_divisors @ X_a )
=> ( ( times_times @ X_a @ B_1_1 @ ( ti @ X_a @ B_2_1 ) )
= ( times_times @ X_a @ B_1_1 @ B_2_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[625]) ).
thf(1173,plain,
( ( ! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( no_zero_divisors @ X_a )
=> ( ( times_times @ X_a @ ( ti @ X_a @ B_1_1 ) @ B_2_1 )
= ( times_times @ X_a @ B_1_1 @ B_2_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[626]) ).
thf(1174,plain,
( ( ! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( semiring @ X_a )
=> ( ( ti @ X_a @ ( times_times @ X_a @ B_1_1 @ B_2_1 ) )
= ( times_times @ X_a @ B_1_1 @ B_2_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[627]) ).
thf(1175,plain,
( ( ! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( semiring @ X_a )
=> ( ( times_times @ X_a @ B_1_1 @ ( ti @ X_a @ B_2_1 ) )
= ( times_times @ X_a @ B_1_1 @ B_2_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[628]) ).
thf(1176,plain,
( ( ! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( semiring @ X_a )
=> ( ( times_times @ X_a @ ( ti @ X_a @ B_1_1 ) @ B_2_1 )
= ( times_times @ X_a @ B_1_1 @ B_2_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[629]) ).
thf(1177,plain,
( ( ! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( dvd @ X_a )
=> ( ( ti @ X_a @ ( times_times @ X_a @ B_1_1 @ B_2_1 ) )
= ( times_times @ X_a @ B_1_1 @ B_2_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[630]) ).
thf(1178,plain,
( ( ! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( dvd @ X_a )
=> ( ( times_times @ X_a @ B_1_1 @ ( ti @ X_a @ B_2_1 ) )
= ( times_times @ X_a @ B_1_1 @ B_2_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[631]) ).
thf(1179,plain,
( ( ! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( dvd @ X_a )
=> ( ( times_times @ X_a @ ( ti @ X_a @ B_1_1 ) @ B_2_1 )
= ( times_times @ X_a @ B_1_1 @ B_2_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[632]) ).
thf(1180,plain,
( ( ! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( ab_group_add @ X_a )
=> ( ( ti @ X_a @ ( plus_plus @ X_a @ B_1_1 @ B_2_1 ) )
= ( plus_plus @ X_a @ B_1_1 @ B_2_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[633]) ).
thf(1181,plain,
( ( ! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( ab_group_add @ X_a )
=> ( ( plus_plus @ X_a @ B_1_1 @ ( ti @ X_a @ B_2_1 ) )
= ( plus_plus @ X_a @ B_1_1 @ B_2_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[634]) ).
thf(1182,plain,
( ( ! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( ab_group_add @ X_a )
=> ( ( plus_plus @ X_a @ ( ti @ X_a @ B_1_1 ) @ B_2_1 )
= ( plus_plus @ X_a @ B_1_1 @ B_2_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[635]) ).
thf(1183,plain,
( ( ! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( semiring @ X_a )
=> ( ( ti @ X_a @ ( plus_plus @ X_a @ B_1_1 @ B_2_1 ) )
= ( plus_plus @ X_a @ B_1_1 @ B_2_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[636]) ).
thf(1184,plain,
( ( ! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( semiring @ X_a )
=> ( ( plus_plus @ X_a @ B_1_1 @ ( ti @ X_a @ B_2_1 ) )
= ( plus_plus @ X_a @ B_1_1 @ B_2_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[637]) ).
thf(1185,plain,
( ( ! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( semiring @ X_a )
=> ( ( plus_plus @ X_a @ ( ti @ X_a @ B_1_1 ) @ B_2_1 )
= ( plus_plus @ X_a @ B_1_1 @ B_2_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[638]) ).
thf(1186,plain,
( ( ! [X_a: $i] :
( ( power @ X_a )
=> ( ( ti @ X_a @ ( one_one @ X_a ) )
= ( one_one @ X_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[639]) ).
thf(1187,plain,
( ( ! [X_a: $i] :
( ( zero_neq_one @ X_a )
=> ( ( ti @ X_a @ ( one_one @ X_a ) )
= ( one_one @ X_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[640]) ).
thf(1188,plain,
( ( ! [B_1_1: $i,B_2_1: $i] :
( ( ti @ nat @ ( minus_minus @ nat @ B_1_1 @ B_2_1 ) )
= ( minus_minus @ nat @ B_1_1 @ B_2_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[641]) ).
thf(1189,plain,
( ( ! [B_1_1: $i,B_2_1: $i] :
( ( minus_minus @ nat @ B_1_1 @ ( ti @ nat @ B_2_1 ) )
= ( minus_minus @ nat @ B_1_1 @ B_2_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[642]) ).
thf(1190,plain,
( ( ! [B_1_1: $i,B_2_1: $i] :
( ( minus_minus @ nat @ ( ti @ nat @ B_1_1 ) @ B_2_1 )
= ( minus_minus @ nat @ B_1_1 @ B_2_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[643]) ).
thf(1191,plain,
( ( ( ti @ int @ m )
= m )
= $true ),
inference(unfold_def,[status(thm)],[647]) ).
thf(1192,plain,
( ( ( ti @ int @ pls )
= pls )
= $true ),
inference(unfold_def,[status(thm)],[648]) ).
thf(1193,plain,
( ( ! [B_1_1: $i] :
( ( ti @ int @ ( bit1 @ B_1_1 ) )
= ( bit1 @ B_1_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[649]) ).
thf(1194,plain,
( ( ! [B_1_1: $i] :
( ( bit1 @ ( ti @ int @ B_1_1 ) )
= ( bit1 @ B_1_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[650]) ).
thf(1195,plain,
( ( ! [B_1_1: $i] :
( ( ti @ int @ ( bit0 @ B_1_1 ) )
= ( bit0 @ B_1_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[651]) ).
thf(1196,plain,
( ( ! [B_1_1: $i] :
( ( bit0 @ ( ti @ int @ B_1_1 ) )
= ( bit0 @ B_1_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[652]) ).
thf(1197,plain,
( ( ~ ? [X: $i,Y: $i] :
( ( plus_plus @ int @ ( power_power @ int @ X @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ Y @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[655]) ).
thf(1198,plain,
( ( ! [B_1_1: $i] :
( ( bit0 @ ( ti @ int @ B_1_1 ) )
= ( bit0 @ B_1_1 ) ) )
= $true ),
inference(copy,[status(thm)],[1196]) ).
thf(1199,plain,
( ( ! [B_1_1: $i] :
( ( ti @ int @ ( bit0 @ B_1_1 ) )
= ( bit0 @ B_1_1 ) ) )
= $true ),
inference(copy,[status(thm)],[1195]) ).
thf(1200,plain,
( ( ! [B_1_1: $i] :
( ( bit1 @ ( ti @ int @ B_1_1 ) )
= ( bit1 @ B_1_1 ) ) )
= $true ),
inference(copy,[status(thm)],[1194]) ).
thf(1201,plain,
( ( ! [B_1_1: $i] :
( ( ti @ int @ ( bit1 @ B_1_1 ) )
= ( bit1 @ B_1_1 ) ) )
= $true ),
inference(copy,[status(thm)],[1193]) ).
thf(1202,plain,
( ( ( ti @ int @ pls )
= pls )
= $true ),
inference(copy,[status(thm)],[1192]) ).
thf(1203,plain,
( ( ( ti @ int @ m )
= m )
= $true ),
inference(copy,[status(thm)],[1191]) ).
thf(1204,plain,
( ( ! [B_1_1: $i,B_2_1: $i] :
( ( minus_minus @ nat @ ( ti @ nat @ B_1_1 ) @ B_2_1 )
= ( minus_minus @ nat @ B_1_1 @ B_2_1 ) ) )
= $true ),
inference(copy,[status(thm)],[1190]) ).
thf(1205,plain,
( ( ! [B_1_1: $i,B_2_1: $i] :
( ( minus_minus @ nat @ B_1_1 @ ( ti @ nat @ B_2_1 ) )
= ( minus_minus @ nat @ B_1_1 @ B_2_1 ) ) )
= $true ),
inference(copy,[status(thm)],[1189]) ).
thf(1206,plain,
( ( ! [B_1_1: $i,B_2_1: $i] :
( ( ti @ nat @ ( minus_minus @ nat @ B_1_1 @ B_2_1 ) )
= ( minus_minus @ nat @ B_1_1 @ B_2_1 ) ) )
= $true ),
inference(copy,[status(thm)],[1188]) ).
thf(1207,plain,
( ( ! [X_a: $i] :
( ( zero_neq_one @ X_a )
=> ( ( ti @ X_a @ ( one_one @ X_a ) )
= ( one_one @ X_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1187]) ).
thf(1208,plain,
( ( ! [X_a: $i] :
( ( power @ X_a )
=> ( ( ti @ X_a @ ( one_one @ X_a ) )
= ( one_one @ X_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1186]) ).
thf(1209,plain,
( ( ! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( semiring @ X_a )
=> ( ( plus_plus @ X_a @ ( ti @ X_a @ B_1_1 ) @ B_2_1 )
= ( plus_plus @ X_a @ B_1_1 @ B_2_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1185]) ).
thf(1210,plain,
( ( ! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( semiring @ X_a )
=> ( ( plus_plus @ X_a @ B_1_1 @ ( ti @ X_a @ B_2_1 ) )
= ( plus_plus @ X_a @ B_1_1 @ B_2_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1184]) ).
thf(1211,plain,
( ( ! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( semiring @ X_a )
=> ( ( ti @ X_a @ ( plus_plus @ X_a @ B_1_1 @ B_2_1 ) )
= ( plus_plus @ X_a @ B_1_1 @ B_2_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1183]) ).
thf(1212,plain,
( ( ! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( ab_group_add @ X_a )
=> ( ( plus_plus @ X_a @ ( ti @ X_a @ B_1_1 ) @ B_2_1 )
= ( plus_plus @ X_a @ B_1_1 @ B_2_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1182]) ).
thf(1213,plain,
( ( ! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( ab_group_add @ X_a )
=> ( ( plus_plus @ X_a @ B_1_1 @ ( ti @ X_a @ B_2_1 ) )
= ( plus_plus @ X_a @ B_1_1 @ B_2_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1181]) ).
thf(1214,plain,
( ( ! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( ab_group_add @ X_a )
=> ( ( ti @ X_a @ ( plus_plus @ X_a @ B_1_1 @ B_2_1 ) )
= ( plus_plus @ X_a @ B_1_1 @ B_2_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1180]) ).
thf(1215,plain,
( ( ! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( dvd @ X_a )
=> ( ( times_times @ X_a @ ( ti @ X_a @ B_1_1 ) @ B_2_1 )
= ( times_times @ X_a @ B_1_1 @ B_2_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1179]) ).
thf(1216,plain,
( ( ! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( dvd @ X_a )
=> ( ( times_times @ X_a @ B_1_1 @ ( ti @ X_a @ B_2_1 ) )
= ( times_times @ X_a @ B_1_1 @ B_2_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1178]) ).
thf(1217,plain,
( ( ! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( dvd @ X_a )
=> ( ( ti @ X_a @ ( times_times @ X_a @ B_1_1 @ B_2_1 ) )
= ( times_times @ X_a @ B_1_1 @ B_2_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1177]) ).
thf(1218,plain,
( ( ! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( semiring @ X_a )
=> ( ( times_times @ X_a @ ( ti @ X_a @ B_1_1 ) @ B_2_1 )
= ( times_times @ X_a @ B_1_1 @ B_2_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1176]) ).
thf(1219,plain,
( ( ! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( semiring @ X_a )
=> ( ( times_times @ X_a @ B_1_1 @ ( ti @ X_a @ B_2_1 ) )
= ( times_times @ X_a @ B_1_1 @ B_2_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1175]) ).
thf(1220,plain,
( ( ! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( semiring @ X_a )
=> ( ( ti @ X_a @ ( times_times @ X_a @ B_1_1 @ B_2_1 ) )
= ( times_times @ X_a @ B_1_1 @ B_2_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1174]) ).
thf(1221,plain,
( ( ! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( no_zero_divisors @ X_a )
=> ( ( times_times @ X_a @ ( ti @ X_a @ B_1_1 ) @ B_2_1 )
= ( times_times @ X_a @ B_1_1 @ B_2_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1173]) ).
thf(1222,plain,
( ( ! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( no_zero_divisors @ X_a )
=> ( ( times_times @ X_a @ B_1_1 @ ( ti @ X_a @ B_2_1 ) )
= ( times_times @ X_a @ B_1_1 @ B_2_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1172]) ).
thf(1223,plain,
( ( ! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( no_zero_divisors @ X_a )
=> ( ( ti @ X_a @ ( times_times @ X_a @ B_1_1 @ B_2_1 ) )
= ( times_times @ X_a @ B_1_1 @ B_2_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1171]) ).
thf(1224,plain,
( ( ! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( mult_zero @ X_a )
=> ( ( times_times @ X_a @ ( ti @ X_a @ B_1_1 ) @ B_2_1 )
= ( times_times @ X_a @ B_1_1 @ B_2_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1170]) ).
thf(1225,plain,
( ( ! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( mult_zero @ X_a )
=> ( ( times_times @ X_a @ B_1_1 @ ( ti @ X_a @ B_2_1 ) )
= ( times_times @ X_a @ B_1_1 @ B_2_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1169]) ).
thf(1226,plain,
( ( ! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( mult_zero @ X_a )
=> ( ( ti @ X_a @ ( times_times @ X_a @ B_1_1 @ B_2_1 ) )
= ( times_times @ X_a @ B_1_1 @ B_2_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1168]) ).
thf(1227,plain,
( ( ! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( power @ X_a )
=> ( ( times_times @ X_a @ ( ti @ X_a @ B_1_1 ) @ B_2_1 )
= ( times_times @ X_a @ B_1_1 @ B_2_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1167]) ).
thf(1228,plain,
( ( ! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( power @ X_a )
=> ( ( times_times @ X_a @ B_1_1 @ ( ti @ X_a @ B_2_1 ) )
= ( times_times @ X_a @ B_1_1 @ B_2_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1166]) ).
thf(1229,plain,
( ( ! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( power @ X_a )
=> ( ( ti @ X_a @ ( times_times @ X_a @ B_1_1 @ B_2_1 ) )
= ( times_times @ X_a @ B_1_1 @ B_2_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1165]) ).
thf(1230,plain,
( ( ! [B_1_1: $i,B_2_1: $i,B_3: $i] :
( ( zcong @ ( ti @ int @ B_1_1 ) @ B_2_1 @ B_3 )
<=> ( zcong @ B_1_1 @ B_2_1 @ B_3 ) ) )
= $true ),
inference(copy,[status(thm)],[1164]) ).
thf(1231,plain,
( ( ! [B_1_1: $i,B_2_1: $i,B_3: $i] :
( ( zcong @ B_1_1 @ ( ti @ int @ B_2_1 ) @ B_3 )
<=> ( zcong @ B_1_1 @ B_2_1 @ B_3 ) ) )
= $true ),
inference(copy,[status(thm)],[1163]) ).
thf(1232,plain,
( ( ! [B_1_1: $i,B_2_1: $i,B_3: $i] :
( ( zcong @ B_1_1 @ B_2_1 @ ( ti @ int @ B_3 ) )
<=> ( zcong @ B_1_1 @ B_2_1 @ B_3 ) ) )
= $true ),
inference(copy,[status(thm)],[1162]) ).
thf(1233,plain,
( ( ! [B_1_1: $i] :
( ( zprime @ ( ti @ int @ B_1_1 ) )
<=> ( zprime @ B_1_1 ) ) )
= $true ),
inference(copy,[status(thm)],[1161]) ).
thf(1234,plain,
( ( ( ti @ int @ min )
= min )
= $true ),
inference(copy,[status(thm)],[1160]) ).
thf(1235,plain,
( ( ! [B_1_1: $i,X_a: $i] :
( ( number @ X_a )
=> ( ( number_number_of @ X_a @ ( ti @ int @ B_1_1 ) )
= ( number_number_of @ X_a @ B_1_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1159]) ).
thf(1236,plain,
( ( ! [B_1_1: $i,X_a: $i] :
( ( number @ X_a )
=> ( ( ti @ X_a @ ( number_number_of @ X_a @ B_1_1 ) )
= ( number_number_of @ X_a @ B_1_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1158]) ).
thf(1237,plain,
( ( ! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( power @ X_a )
=> ( ( power_power @ X_a @ ( ti @ X_a @ B_1_1 ) @ B_2_1 )
= ( power_power @ X_a @ B_1_1 @ B_2_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1157]) ).
thf(1238,plain,
( ( ! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( power @ X_a )
=> ( ( power_power @ X_a @ B_1_1 @ ( ti @ nat @ B_2_1 ) )
= ( power_power @ X_a @ B_1_1 @ B_2_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1156]) ).
thf(1239,plain,
( ( ! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ( power @ X_a )
=> ( ( ti @ X_a @ ( power_power @ X_a @ B_1_1 @ B_2_1 ) )
= ( power_power @ X_a @ B_1_1 @ B_2_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1155]) ).
thf(1240,plain,
( ( ! [B_1_1: $i,B_2_1: $i] :
( ( product_Pair @ int @ int @ ( ti @ int @ B_1_1 ) @ B_2_1 )
= ( product_Pair @ int @ int @ B_1_1 @ B_2_1 ) ) )
= $true ),
inference(copy,[status(thm)],[1154]) ).
thf(1241,plain,
( ( ! [B_1_1: $i,B_2_1: $i] :
( ( product_Pair @ int @ int @ B_1_1 @ ( ti @ int @ B_2_1 ) )
= ( product_Pair @ int @ int @ B_1_1 @ B_2_1 ) ) )
= $true ),
inference(copy,[status(thm)],[1153]) ).
thf(1242,plain,
( ( ! [B_1_1: $i,B_2_1: $i] :
( ( ti @ ( product_prod @ int @ int ) @ ( product_Pair @ int @ int @ B_1_1 @ B_2_1 ) )
= ( product_Pair @ int @ int @ B_1_1 @ B_2_1 ) ) )
= $true ),
inference(copy,[status(thm)],[1152]) ).
thf(1243,plain,
( ( ! [B_1_1: $i,B_2_1: $i] :
( ( legendre @ ( ti @ int @ B_1_1 ) @ B_2_1 )
= ( legendre @ B_1_1 @ B_2_1 ) ) )
= $true ),
inference(copy,[status(thm)],[1151]) ).
thf(1244,plain,
( ( ! [B_1_1: $i,B_2_1: $i] :
( ( legendre @ B_1_1 @ ( ti @ int @ B_2_1 ) )
= ( legendre @ B_1_1 @ B_2_1 ) ) )
= $true ),
inference(copy,[status(thm)],[1150]) ).
thf(1245,plain,
( ( ! [B_1_1: $i,B_2_1: $i] :
( ( ti @ int @ ( legendre @ B_1_1 @ B_2_1 ) )
= ( legendre @ B_1_1 @ B_2_1 ) ) )
= $true ),
inference(copy,[status(thm)],[1149]) ).
thf(1246,plain,
( ( ! [B_1_1: $i,B_2_1: $i] :
( ( quadRes @ ( ti @ int @ B_1_1 ) @ B_2_1 )
<=> ( quadRes @ B_1_1 @ B_2_1 ) ) )
= $true ),
inference(copy,[status(thm)],[1148]) ).
thf(1247,plain,
( ( ! [B_1_1: $i,B_2_1: $i] :
( ( quadRes @ B_1_1 @ ( ti @ int @ B_2_1 ) )
<=> ( quadRes @ B_1_1 @ B_2_1 ) ) )
= $true ),
inference(copy,[status(thm)],[1147]) ).
thf(1248,plain,
( ( ! [B_1_1: $i] :
( ( twoSqu420862341sum2sq @ ( ti @ int @ B_1_1 ) )
<=> ( twoSqu420862341sum2sq @ B_1_1 ) ) )
= $true ),
inference(copy,[status(thm)],[1146]) ).
thf(1249,plain,
( ( ! [B_1_1: $i] :
( ( twoSqu579703163sum2sq @ ( ti @ ( product_prod @ int @ int ) @ B_1_1 ) )
= ( twoSqu579703163sum2sq @ B_1_1 ) ) )
= $true ),
inference(copy,[status(thm)],[1145]) ).
thf(1250,plain,
( ( ! [B_1_1: $i] :
( ( ti @ int @ ( twoSqu579703163sum2sq @ B_1_1 ) )
= ( twoSqu579703163sum2sq @ B_1_1 ) ) )
= $true ),
inference(copy,[status(thm)],[1144]) ).
thf(1251,plain,
( ( ( ti @ int @ s1 )
= s1 )
= $true ),
inference(copy,[status(thm)],[1143]) ).
thf(1252,plain,
( ( ( ti @ int @ s )
= s )
= $true ),
inference(copy,[status(thm)],[1142]) ).
thf(1253,plain,
( ( ( ti @ int @ t )
= t )
= $true ),
inference(copy,[status(thm)],[1141]) ).
thf(1254,plain,
( ( ord_less_eq @ int @ ( one_one @ int ) @ t )
= $true ),
inference(copy,[status(thm)],[1140]) ).
thf(1255,plain,
( ( ( t
= ( one_one @ int ) )
=> ? [X: $i,Y: $i] :
( ( plus_plus @ int @ ( power_power @ int @ X @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ Y @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ) )
= $true ),
inference(copy,[status(thm)],[1139]) ).
thf(1256,plain,
( ( ( ord_less @ int @ ( one_one @ int ) @ t )
=> ? [X: $i,Y: $i] :
( ( plus_plus @ int @ ( power_power @ int @ X @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ Y @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ) )
= $true ),
inference(copy,[status(thm)],[1138]) ).
thf(1257,plain,
( ( ord_less @ int @ t @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) )
= $true ),
inference(copy,[status(thm)],[1137]) ).
thf(1258,plain,
( ( zprime @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) )
= $true ),
inference(copy,[status(thm)],[1136]) ).
thf(1259,plain,
( ( ( plus_plus @ int @ ( power_power @ int @ s @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( one_one @ int ) )
= ( times_times @ int @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) @ t ) )
= $true ),
inference(copy,[status(thm)],[1135]) ).
thf(1260,plain,
( ( twoSqu420862341sum2sq @ ( times_times @ int @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) @ t ) )
= $true ),
inference(copy,[status(thm)],[1134]) ).
thf(1261,plain,
( ( ! [A_1: $i,B: $i] :
( ( power_power @ int @ ( plus_plus @ int @ A_1 @ B ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ int @ ( plus_plus @ int @ ( power_power @ int @ A_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( times_times @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A_1 ) @ B ) ) @ ( power_power @ int @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1133]) ).
thf(1262,plain,
( ( ! [A_1: $i,B: $i] :
( ( power_power @ int @ ( plus_plus @ int @ A_1 @ B ) @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( power_power @ int @ A_1 @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) @ ( times_times @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit1 @ ( bit1 @ pls ) ) ) @ ( power_power @ int @ A_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ B ) ) @ ( times_times @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit1 @ ( bit1 @ pls ) ) ) @ A_1 ) @ ( power_power @ int @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ ( power_power @ int @ B @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1132]) ).
thf(1263,plain,
( ( ! [X_a: $i] :
( ( number_semiring @ X_a )
=> ! [X_1: $i,Y_1: $i] :
( ( power_power @ X_a @ ( plus_plus @ X_a @ X_1 @ Y_1 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ X_a @ ( plus_plus @ X_a @ ( power_power @ X_a @ X_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ X_a @ Y_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times @ X_a @ ( times_times @ X_a @ ( number_number_of @ X_a @ ( bit0 @ ( bit1 @ pls ) ) ) @ X_1 ) @ Y_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1131]) ).
thf(1264,plain,
( ( ! [X_b: $i] :
( ( ( monoid_mult @ X_b )
& ( number @ X_b ) )
=> ! [W: $i] :
( ( power_power @ X_b @ ( number_number_of @ X_b @ W ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times @ X_b @ ( number_number_of @ X_b @ W ) @ ( number_number_of @ X_b @ W ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1130]) ).
thf(1265,plain,
( ( ! [A_1: $i] :
( ( times_times @ int @ A_1 @ ( power_power @ int @ A_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( power_power @ int @ A_1 @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1129]) ).
thf(1266,plain,
( ( ! [X_a: $i] :
( ( semiring_1 @ X_a )
=> ( ( power_power @ X_a @ ( one_one @ X_a ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( one_one @ X_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1128]) ).
thf(1267,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [X_1: $i] :
( ( times_times @ X_a @ X_1 @ X_1 )
= ( power_power @ X_a @ X_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1127]) ).
thf(1268,plain,
( ( ! [X_a: $i] :
( ( monoid_mult @ X_a )
=> ! [A_1: $i] :
( ( power_power @ X_a @ A_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times @ X_a @ A_1 @ A_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1126]) ).
thf(1269,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [X_1: $i,N: $i] :
( ( power_power @ X_a @ X_1 @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ N ) )
= ( times_times @ X_a @ ( power_power @ X_a @ X_1 @ N ) @ ( power_power @ X_a @ X_1 @ N ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1125]) ).
thf(1270,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [W: $i] :
( ( plus_plus @ X_a @ ( one_one @ X_a ) @ ( number_number_of @ X_a @ W ) )
= ( number_number_of @ X_a @ ( plus_plus @ int @ ( bit1 @ pls ) @ W ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1124]) ).
thf(1271,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [V: $i] :
( ( plus_plus @ X_a @ ( number_number_of @ X_a @ V ) @ ( one_one @ X_a ) )
= ( number_number_of @ X_a @ ( plus_plus @ int @ V @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1123]) ).
thf(1272,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ( ( plus_plus @ X_a @ ( one_one @ X_a ) @ ( one_one @ X_a ) )
= ( number_number_of @ X_a @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1122]) ).
thf(1273,plain,
( ( ~ ! [T_1: $i] :
( ( plus_plus @ int @ ( power_power @ int @ s @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( one_one @ int ) )
!= ( times_times @ int @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[1121]) ).
thf(1274,plain,
( ( ! [W: $i] : ( ord_less_eq @ int @ W @ W ) )
= $true ),
inference(copy,[status(thm)],[1120]) ).
thf(1275,plain,
( ( ! [Z: $i,W: $i] :
( ( ord_less_eq @ int @ Z @ W )
| ( ord_less_eq @ int @ W @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[1119]) ).
thf(1276,plain,
( ( ! [Z_1: $i,W_1: $i] :
( ( ord_less @ int @ Z_1 @ W_1 )
<=> ( ( ord_less_eq @ int @ Z_1 @ W_1 )
& ( ( ti @ int @ Z_1 )
!= ( ti @ int @ W_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1118]) ).
thf(1277,plain,
( ( ! [X_1: $i,Y_1: $i] :
( ( ord_less @ int @ X_1 @ Y_1 )
| ( ( ti @ int @ X_1 )
= ( ti @ int @ Y_1 ) )
| ( ord_less @ int @ Y_1 @ X_1 ) ) )
= $true ),
inference(copy,[status(thm)],[1117]) ).
thf(1278,plain,
( ( ! [K: $i,I: $i,J: $i] :
( ( ord_less_eq @ int @ I @ J )
=> ( ( ord_less_eq @ int @ J @ K )
=> ( ord_less_eq @ int @ I @ K ) ) ) )
= $true ),
inference(copy,[status(thm)],[1116]) ).
thf(1279,plain,
( ( ! [Z: $i,W: $i] :
( ( ord_less_eq @ int @ Z @ W )
=> ( ( ord_less_eq @ int @ W @ Z )
=> ( ( ti @ int @ Z )
= ( ti @ int @ W ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1115]) ).
thf(1280,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [X_1: $i,P: $i,Q: $i] :
( ( power_power @ X_a @ ( power_power @ X_a @ X_1 @ P ) @ Q )
= ( power_power @ X_a @ X_1 @ ( times_times @ nat @ P @ Q ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1114]) ).
thf(1281,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [X_1: $i] :
( ( power_power @ X_a @ X_1 @ ( one_one @ nat ) )
= ( ti @ X_a @ X_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1113]) ).
thf(1282,plain,
( ( ! [X_1: $i,Y_1: $i,Z: $i] :
( ( power_power @ int @ ( power_power @ int @ X_1 @ Y_1 ) @ Z )
= ( power_power @ int @ X_1 @ ( times_times @ nat @ Y_1 @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[1112]) ).
thf(1283,plain,
( ( ! [X_a: $i] :
( ( ( number_ring @ X_a )
& ( linordered_idom @ X_a ) )
=> ! [X_2: $i,Y_2: $i] :
( ( ord_less @ X_a @ ( number_number_of @ X_a @ X_2 ) @ ( number_number_of @ X_a @ Y_2 ) )
<=> ( ord_less @ int @ X_2 @ Y_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1111]) ).
thf(1284,plain,
( ( ! [X_a: $i] :
( ( ( number_ring @ X_a )
& ( linordered_idom @ X_a ) )
=> ! [X_2: $i,Y_2: $i] :
( ( ord_less_eq @ X_a @ ( number_number_of @ X_a @ X_2 ) @ ( number_number_of @ X_a @ Y_2 ) )
<=> ( ord_less_eq @ int @ X_2 @ Y_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1110]) ).
thf(1285,plain,
( ( ! [Z_2: $i,Z: $i,W_2: $i,W: $i] :
( ( ord_less @ int @ W_2 @ W )
=> ( ( ord_less_eq @ int @ Z_2 @ Z )
=> ( ord_less @ int @ ( plus_plus @ int @ W_2 @ Z_2 ) @ ( plus_plus @ int @ W @ Z ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1109]) ).
thf(1286,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [X_1: $i,P: $i,Q: $i] :
( ( times_times @ X_a @ ( power_power @ X_a @ X_1 @ P ) @ ( power_power @ X_a @ X_1 @ Q ) )
= ( power_power @ X_a @ X_1 @ ( plus_plus @ nat @ P @ Q ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1108]) ).
thf(1287,plain,
( ( ! [X_1: $i,Y_1: $i,Z: $i] :
( ( power_power @ int @ X_1 @ ( plus_plus @ nat @ Y_1 @ Z ) )
= ( times_times @ int @ ( power_power @ int @ X_1 @ Y_1 ) @ ( power_power @ int @ X_1 @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[1107]) ).
thf(1288,plain,
( ( ! [Z: $i] :
( ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ Z )
= ( plus_plus @ nat @ Z @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[1106]) ).
thf(1289,plain,
( ( ! [Z: $i] :
( ( times_times @ nat @ Z @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ nat @ Z @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[1105]) ).
thf(1290,plain,
( ( ( plus_plus @ nat @ ( one_one @ nat ) @ ( one_one @ nat ) )
= ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(copy,[status(thm)],[1104]) ).
thf(1291,plain,
( ( ! [K1: $i,K2: $i] :
( ( ord_less @ int @ ( bit1 @ K1 ) @ ( bit1 @ K2 ) )
<=> ( ord_less @ int @ K1 @ K2 ) ) )
= $true ),
inference(copy,[status(thm)],[1103]) ).
thf(1292,plain,
( ( ! [K_1: $i,L_1: $i] :
( ( ord_less @ int @ ( bit1 @ K_1 ) @ ( bit1 @ L_1 ) )
<=> ( ord_less @ int @ K_1 @ L_1 ) ) )
= $true ),
inference(copy,[status(thm)],[1102]) ).
thf(1293,plain,
( ( ! [K1: $i,K2: $i] :
( ( ord_less_eq @ int @ ( bit1 @ K1 ) @ ( bit1 @ K2 ) )
<=> ( ord_less_eq @ int @ K1 @ K2 ) ) )
= $true ),
inference(copy,[status(thm)],[1101]) ).
thf(1294,plain,
( ( ! [K_1: $i,L_1: $i] :
( ( ord_less_eq @ int @ ( bit1 @ K_1 ) @ ( bit1 @ L_1 ) )
<=> ( ord_less_eq @ int @ K_1 @ L_1 ) ) )
= $true ),
inference(copy,[status(thm)],[1100]) ).
thf(1295,plain,
( ( ~ ( ord_less @ int @ pls @ pls ) )
= $true ),
inference(copy,[status(thm)],[1099]) ).
thf(1296,plain,
( ( ! [K1: $i,K2: $i] :
( ( ord_less @ int @ ( bit0 @ K1 ) @ ( bit0 @ K2 ) )
<=> ( ord_less @ int @ K1 @ K2 ) ) )
= $true ),
inference(copy,[status(thm)],[1098]) ).
thf(1297,plain,
( ( ! [K_1: $i,L_1: $i] :
( ( ord_less @ int @ ( bit0 @ K_1 ) @ ( bit0 @ L_1 ) )
<=> ( ord_less @ int @ K_1 @ L_1 ) ) )
= $true ),
inference(copy,[status(thm)],[1097]) ).
thf(1298,plain,
( ( ord_less_eq @ int @ pls @ pls )
= $true ),
inference(copy,[status(thm)],[1096]) ).
thf(1299,plain,
( ( ! [K1: $i,K2: $i] :
( ( ord_less_eq @ int @ ( bit0 @ K1 ) @ ( bit0 @ K2 ) )
<=> ( ord_less_eq @ int @ K1 @ K2 ) ) )
= $true ),
inference(copy,[status(thm)],[1095]) ).
thf(1300,plain,
( ( ! [K_1: $i,L_1: $i] :
( ( ord_less_eq @ int @ ( bit0 @ K_1 ) @ ( bit0 @ L_1 ) )
<=> ( ord_less_eq @ int @ K_1 @ L_1 ) ) )
= $true ),
inference(copy,[status(thm)],[1094]) ).
thf(1301,plain,
( ( ! [K_1: $i,L_1: $i] :
( ( ord_less @ int @ ( number_number_of @ int @ K_1 ) @ ( number_number_of @ int @ L_1 ) )
<=> ( ord_less @ int @ K_1 @ L_1 ) ) )
= $true ),
inference(copy,[status(thm)],[1093]) ).
thf(1302,plain,
( ( ! [K_1: $i,L_1: $i] :
( ( ord_less_eq @ int @ ( number_number_of @ int @ K_1 ) @ ( number_number_of @ int @ L_1 ) )
<=> ( ord_less_eq @ int @ K_1 @ L_1 ) ) )
= $true ),
inference(copy,[status(thm)],[1092]) ).
thf(1303,plain,
( ( ! [K: $i,I: $i,J: $i] :
( ( ord_less @ int @ I @ J )
=> ( ord_less @ int @ ( plus_plus @ int @ I @ K ) @ ( plus_plus @ int @ J @ K ) ) ) )
= $true ),
inference(copy,[status(thm)],[1091]) ).
thf(1304,plain,
( ( ! [K: $i,I: $i,J: $i] :
( ( ord_less_eq @ int @ I @ J )
=> ( ord_less_eq @ int @ ( plus_plus @ int @ K @ I ) @ ( plus_plus @ int @ K @ J ) ) ) )
= $true ),
inference(copy,[status(thm)],[1090]) ).
thf(1305,plain,
( ( ! [V_1: $i,V: $i] :
( ( ( ord_less @ int @ V @ pls )
=> ( ( plus_plus @ nat @ ( number_number_of @ nat @ V ) @ ( number_number_of @ nat @ V_1 ) )
= ( number_number_of @ nat @ V_1 ) ) )
& ( ~ ( ord_less @ int @ V @ pls )
=> ( ( ( ord_less @ int @ V_1 @ pls )
=> ( ( plus_plus @ nat @ ( number_number_of @ nat @ V ) @ ( number_number_of @ nat @ V_1 ) )
= ( number_number_of @ nat @ V ) ) )
& ( ~ ( ord_less @ int @ V_1 @ pls )
=> ( ( plus_plus @ nat @ ( number_number_of @ nat @ V ) @ ( number_number_of @ nat @ V_1 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ V @ V_1 ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1089]) ).
thf(1306,plain,
( ( ( number_number_of @ nat @ ( bit1 @ pls ) )
= ( one_one @ nat ) )
= $true ),
inference(copy,[status(thm)],[1088]) ).
thf(1307,plain,
( ( ( one_one @ nat )
= ( number_number_of @ nat @ ( bit1 @ pls ) ) )
= $true ),
inference(copy,[status(thm)],[1087]) ).
thf(1308,plain,
( ( ! [K_1: $i] :
( ( ord_less_eq @ int @ ( bit1 @ K_1 ) @ pls )
<=> ( ord_less @ int @ K_1 @ pls ) ) )
= $true ),
inference(copy,[status(thm)],[1086]) ).
thf(1309,plain,
( ( ! [K_1: $i] :
( ( ord_less @ int @ pls @ ( bit1 @ K_1 ) )
<=> ( ord_less_eq @ int @ pls @ K_1 ) ) )
= $true ),
inference(copy,[status(thm)],[1085]) ).
thf(1310,plain,
( ( ! [K1: $i,K2: $i] :
( ( ord_less_eq @ int @ ( bit1 @ K1 ) @ ( bit0 @ K2 ) )
<=> ( ord_less @ int @ K1 @ K2 ) ) )
= $true ),
inference(copy,[status(thm)],[1084]) ).
thf(1311,plain,
( ( ! [K_1: $i,L_1: $i] :
( ( ord_less_eq @ int @ ( bit1 @ K_1 ) @ ( bit0 @ L_1 ) )
<=> ( ord_less @ int @ K_1 @ L_1 ) ) )
= $true ),
inference(copy,[status(thm)],[1083]) ).
thf(1312,plain,
( ( ! [K1: $i,K2: $i] :
( ( ord_less @ int @ ( bit0 @ K1 ) @ ( bit1 @ K2 ) )
<=> ( ord_less_eq @ int @ K1 @ K2 ) ) )
= $true ),
inference(copy,[status(thm)],[1082]) ).
thf(1313,plain,
( ( ! [K_1: $i,L_1: $i] :
( ( ord_less @ int @ ( bit0 @ K_1 ) @ ( bit1 @ L_1 ) )
<=> ( ord_less_eq @ int @ K_1 @ L_1 ) ) )
= $true ),
inference(copy,[status(thm)],[1081]) ).
thf(1314,plain,
( ( ! [W: $i,Z: $i] :
( ( ord_less @ int @ W @ Z )
=> ( ord_less_eq @ int @ ( plus_plus @ int @ W @ ( one_one @ int ) ) @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[1080]) ).
thf(1315,plain,
( ( ! [W_1: $i,Z_1: $i] :
( ( ord_less_eq @ int @ ( plus_plus @ int @ W_1 @ ( one_one @ int ) ) @ Z_1 )
<=> ( ord_less @ int @ W_1 @ Z_1 ) ) )
= $true ),
inference(copy,[status(thm)],[1079]) ).
thf(1316,plain,
( ( ! [W_1: $i,Z_1: $i] :
( ( ord_less @ int @ W_1 @ ( plus_plus @ int @ Z_1 @ ( one_one @ int ) ) )
<=> ( ord_less_eq @ int @ W_1 @ Z_1 ) ) )
= $true ),
inference(copy,[status(thm)],[1078]) ).
thf(1317,plain,
( ( zprime @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(copy,[status(thm)],[1077]) ).
thf(1318,plain,
( ( ! [Y_1: $i,X_1: $i] :
( ( twoSqu420862341sum2sq @ X_1 )
=> ( ( twoSqu420862341sum2sq @ Y_1 )
=> ( twoSqu420862341sum2sq @ ( times_times @ int @ X_1 @ Y_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1076]) ).
thf(1319,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [Lx: $i,Ly: $i,Rx: $i,Ry: $i] :
( ( times_times @ X_a @ ( times_times @ X_a @ Lx @ Ly ) @ ( times_times @ X_a @ Rx @ Ry ) )
= ( times_times @ X_a @ ( times_times @ X_a @ Lx @ Rx ) @ ( times_times @ X_a @ Ly @ Ry ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1075]) ).
thf(1320,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [Lx: $i,Ly: $i,Rx: $i,Ry: $i] :
( ( times_times @ X_a @ ( times_times @ X_a @ Lx @ Ly ) @ ( times_times @ X_a @ Rx @ Ry ) )
= ( times_times @ X_a @ Rx @ ( times_times @ X_a @ ( times_times @ X_a @ Lx @ Ly ) @ Ry ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1074]) ).
thf(1321,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [Lx: $i,Ly: $i,Rx: $i,Ry: $i] :
( ( times_times @ X_a @ ( times_times @ X_a @ Lx @ Ly ) @ ( times_times @ X_a @ Rx @ Ry ) )
= ( times_times @ X_a @ Lx @ ( times_times @ X_a @ Ly @ ( times_times @ X_a @ Rx @ Ry ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1073]) ).
thf(1322,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [Lx: $i,Ly: $i,Rx: $i] :
( ( times_times @ X_a @ ( times_times @ X_a @ Lx @ Ly ) @ Rx )
= ( times_times @ X_a @ ( times_times @ X_a @ Lx @ Rx ) @ Ly ) ) ) )
= $true ),
inference(copy,[status(thm)],[1072]) ).
thf(1323,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [Lx: $i,Ly: $i,Rx: $i] :
( ( times_times @ X_a @ ( times_times @ X_a @ Lx @ Ly ) @ Rx )
= ( times_times @ X_a @ Lx @ ( times_times @ X_a @ Ly @ Rx ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1071]) ).
thf(1324,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [Lx: $i,Rx: $i,Ry: $i] :
( ( times_times @ X_a @ Lx @ ( times_times @ X_a @ Rx @ Ry ) )
= ( times_times @ X_a @ ( times_times @ X_a @ Lx @ Rx ) @ Ry ) ) ) )
= $true ),
inference(copy,[status(thm)],[1070]) ).
thf(1325,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [Lx: $i,Rx: $i,Ry: $i] :
( ( times_times @ X_a @ Lx @ ( times_times @ X_a @ Rx @ Ry ) )
= ( times_times @ X_a @ Rx @ ( times_times @ X_a @ Lx @ Ry ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1069]) ).
thf(1326,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i,B: $i] :
( ( times_times @ X_a @ A_1 @ B )
= ( times_times @ X_a @ B @ A_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1068]) ).
thf(1327,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i,B: $i,C: $i,D: $i] :
( ( plus_plus @ X_a @ ( plus_plus @ X_a @ A_1 @ B ) @ ( plus_plus @ X_a @ C @ D ) )
= ( plus_plus @ X_a @ ( plus_plus @ X_a @ A_1 @ C ) @ ( plus_plus @ X_a @ B @ D ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1067]) ).
thf(1328,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i,B: $i,C: $i] :
( ( plus_plus @ X_a @ ( plus_plus @ X_a @ A_1 @ B ) @ C )
= ( plus_plus @ X_a @ ( plus_plus @ X_a @ A_1 @ C ) @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[1066]) ).
thf(1329,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i,B: $i,C: $i] :
( ( plus_plus @ X_a @ ( plus_plus @ X_a @ A_1 @ B ) @ C )
= ( plus_plus @ X_a @ A_1 @ ( plus_plus @ X_a @ B @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1065]) ).
thf(1330,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i,C: $i,D: $i] :
( ( plus_plus @ X_a @ A_1 @ ( plus_plus @ X_a @ C @ D ) )
= ( plus_plus @ X_a @ ( plus_plus @ X_a @ A_1 @ C ) @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[1064]) ).
thf(1331,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i,C: $i,D: $i] :
( ( plus_plus @ X_a @ A_1 @ ( plus_plus @ X_a @ C @ D ) )
= ( plus_plus @ X_a @ C @ ( plus_plus @ X_a @ A_1 @ D ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1063]) ).
thf(1332,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i,C: $i] :
( ( plus_plus @ X_a @ A_1 @ C )
= ( plus_plus @ X_a @ C @ A_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1062]) ).
thf(1333,plain,
( ( ! [X_a: $i] :
( ( ( number_ring @ X_a )
& ( ring_char_0 @ X_a ) )
=> ! [X_2: $i,Y_2: $i] :
( ( ( number_number_of @ X_a @ X_2 )
= ( number_number_of @ X_a @ Y_2 ) )
<=> ( ( ti @ int @ X_2 )
= ( ti @ int @ Y_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1061]) ).
thf(1334,plain,
( ( ! [X_a: $i] :
( ( number @ X_a )
=> ! [W_1: $i,X_2: $i] :
( ( ( number_number_of @ X_a @ W_1 )
= ( ti @ X_a @ X_2 ) )
<=> ( ( ti @ X_a @ X_2 )
= ( number_number_of @ X_a @ W_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1060]) ).
thf(1335,plain,
( ( ! [K_1: $i,L_1: $i] :
( ( ( bit1 @ K_1 )
= ( bit1 @ L_1 ) )
<=> ( ( ti @ int @ K_1 )
= ( ti @ int @ L_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1059]) ).
thf(1336,plain,
( ( ! [K_1: $i,L_1: $i] :
( ( ( bit0 @ K_1 )
= ( bit0 @ L_1 ) )
<=> ( ( ti @ int @ K_1 )
= ( ti @ int @ L_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1058]) ).
thf(1337,plain,
( ( ! [Z1: $i,Z2: $i,Z3: $i] :
( ( times_times @ int @ ( times_times @ int @ Z1 @ Z2 ) @ Z3 )
= ( times_times @ int @ Z1 @ ( times_times @ int @ Z2 @ Z3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1057]) ).
thf(1338,plain,
( ( ! [Z: $i,W: $i] :
( ( times_times @ int @ Z @ W )
= ( times_times @ int @ W @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[1056]) ).
thf(1339,plain,
( ( ! [K: $i] :
( ( number_number_of @ int @ K )
= ( ti @ int @ K ) ) )
= $true ),
inference(copy,[status(thm)],[1055]) ).
thf(1340,plain,
( ( ! [Z1: $i,Z2: $i,Z3: $i] :
( ( plus_plus @ int @ ( plus_plus @ int @ Z1 @ Z2 ) @ Z3 )
= ( plus_plus @ int @ Z1 @ ( plus_plus @ int @ Z2 @ Z3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1054]) ).
thf(1341,plain,
( ( ! [X_1: $i,Y_1: $i,Z: $i] :
( ( plus_plus @ int @ X_1 @ ( plus_plus @ int @ Y_1 @ Z ) )
= ( plus_plus @ int @ Y_1 @ ( plus_plus @ int @ X_1 @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[1053]) ).
thf(1342,plain,
( ( ! [Z: $i,W: $i] :
( ( plus_plus @ int @ Z @ W )
= ( plus_plus @ int @ W @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[1052]) ).
thf(1343,plain,
( ( ! [K_1: $i] :
( ( ord_less @ int @ ( bit1 @ K_1 ) @ pls )
<=> ( ord_less @ int @ K_1 @ pls ) ) )
= $true ),
inference(copy,[status(thm)],[1051]) ).
thf(1344,plain,
( ( ! [K1: $i,K2: $i] :
( ( ord_less @ int @ ( bit1 @ K1 ) @ ( bit0 @ K2 ) )
<=> ( ord_less @ int @ K1 @ K2 ) ) )
= $true ),
inference(copy,[status(thm)],[1050]) ).
thf(1345,plain,
( ( ! [K_1: $i,L_1: $i] :
( ( ord_less @ int @ ( bit1 @ K_1 ) @ ( bit0 @ L_1 ) )
<=> ( ord_less @ int @ K_1 @ L_1 ) ) )
= $true ),
inference(copy,[status(thm)],[1049]) ).
thf(1346,plain,
( ( ! [K_1: $i] :
( ( ord_less @ int @ ( bit0 @ K_1 ) @ pls )
<=> ( ord_less @ int @ K_1 @ pls ) ) )
= $true ),
inference(copy,[status(thm)],[1048]) ).
thf(1347,plain,
( ( ! [K_1: $i] :
( ( ord_less @ int @ pls @ ( bit0 @ K_1 ) )
<=> ( ord_less @ int @ pls @ K_1 ) ) )
= $true ),
inference(copy,[status(thm)],[1047]) ).
thf(1348,plain,
( ( ! [K_1: $i] :
( ( ord_less_eq @ int @ pls @ ( bit1 @ K_1 ) )
<=> ( ord_less_eq @ int @ pls @ K_1 ) ) )
= $true ),
inference(copy,[status(thm)],[1046]) ).
thf(1349,plain,
( ( ! [K1: $i,K2: $i] :
( ( ord_less_eq @ int @ ( bit0 @ K1 ) @ ( bit1 @ K2 ) )
<=> ( ord_less_eq @ int @ K1 @ K2 ) ) )
= $true ),
inference(copy,[status(thm)],[1045]) ).
thf(1350,plain,
( ( ! [K_1: $i,L_1: $i] :
( ( ord_less_eq @ int @ ( bit0 @ K_1 ) @ ( bit1 @ L_1 ) )
<=> ( ord_less_eq @ int @ K_1 @ L_1 ) ) )
= $true ),
inference(copy,[status(thm)],[1044]) ).
thf(1351,plain,
( ( ! [K_1: $i] :
( ( ord_less_eq @ int @ ( bit0 @ K_1 ) @ pls )
<=> ( ord_less_eq @ int @ K_1 @ pls ) ) )
= $true ),
inference(copy,[status(thm)],[1043]) ).
thf(1352,plain,
( ( ! [K_1: $i] :
( ( ord_less_eq @ int @ pls @ ( bit0 @ K_1 ) )
<=> ( ord_less_eq @ int @ pls @ K_1 ) ) )
= $true ),
inference(copy,[status(thm)],[1042]) ).
thf(1353,plain,
( ( ! [W_1: $i,Z_1: $i] :
( ( ord_less @ int @ W_1 @ ( plus_plus @ int @ Z_1 @ ( one_one @ int ) ) )
<=> ( ( ord_less @ int @ W_1 @ Z_1 )
| ( ( ti @ int @ W_1 )
= ( ti @ int @ Z_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1041]) ).
thf(1354,plain,
( ( ! [X_a: $i] :
( ( monoid_mult @ X_a )
=> ! [A_1: $i,N: $i] :
( ( power_power @ X_a @ A_1 @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ N ) )
= ( power_power @ X_a @ ( power_power @ X_a @ A_1 @ N ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1040]) ).
thf(1355,plain,
( ( ! [X_a: $i] :
( ( ( number_ring @ X_a )
& ( linordered_idom @ X_a ) )
=> ! [X_2: $i] :
( ( ord_less @ X_a @ ( number_number_of @ X_a @ X_2 ) @ ( one_one @ X_a ) )
<=> ( ord_less @ int @ X_2 @ ( bit1 @ pls ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1039]) ).
thf(1356,plain,
( ( ! [X_a: $i] :
( ( ( number_ring @ X_a )
& ( linordered_idom @ X_a ) )
=> ! [Y_2: $i] :
( ( ord_less @ X_a @ ( one_one @ X_a ) @ ( number_number_of @ X_a @ Y_2 ) )
<=> ( ord_less @ int @ ( bit1 @ pls ) @ Y_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1038]) ).
thf(1357,plain,
( ( ! [X_a: $i] :
( ( ( number_ring @ X_a )
& ( linordered_idom @ X_a ) )
=> ! [X_2: $i] :
( ( ord_less_eq @ X_a @ ( number_number_of @ X_a @ X_2 ) @ ( one_one @ X_a ) )
<=> ( ord_less_eq @ int @ X_2 @ ( bit1 @ pls ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1037]) ).
thf(1358,plain,
( ( ! [X_a: $i] :
( ( ( number_ring @ X_a )
& ( linordered_idom @ X_a ) )
=> ! [Y_2: $i] :
( ( ord_less_eq @ X_a @ ( one_one @ X_a ) @ ( number_number_of @ X_a @ Y_2 ) )
<=> ( ord_less_eq @ int @ ( bit1 @ pls ) @ Y_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1036]) ).
thf(1359,plain,
( ( ! [X_a: $i] :
( ( semiri456707255roduct @ X_a )
=> ! [W_1: $i,Y_2: $i,X_2: $i,Z_1: $i] :
( ( ( plus_plus @ X_a @ ( times_times @ X_a @ W_1 @ Y_2 ) @ ( times_times @ X_a @ X_2 @ Z_1 ) )
= ( plus_plus @ X_a @ ( times_times @ X_a @ W_1 @ Z_1 ) @ ( times_times @ X_a @ X_2 @ Y_2 ) ) )
<=> ( ( ( ti @ X_a @ W_1 )
= ( ti @ X_a @ X_2 ) )
| ( ( ti @ X_a @ Y_2 )
= ( ti @ X_a @ Z_1 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1035]) ).
thf(1360,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i,M: $i,B: $i] :
( ( plus_plus @ X_a @ ( times_times @ X_a @ A_1 @ M ) @ ( times_times @ X_a @ B @ M ) )
= ( times_times @ X_a @ ( plus_plus @ X_a @ A_1 @ B ) @ M ) ) ) )
= $true ),
inference(copy,[status(thm)],[1034]) ).
thf(1361,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i,B: $i,C: $i] :
( ( times_times @ X_a @ ( plus_plus @ X_a @ A_1 @ B ) @ C )
= ( plus_plus @ X_a @ ( times_times @ X_a @ A_1 @ C ) @ ( times_times @ X_a @ B @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1033]) ).
thf(1362,plain,
( ( ! [X_a: $i] :
( ( semiri456707255roduct @ X_a )
=> ! [C_1: $i,D_1: $i,A_2: $i,B_1: $i] :
( ( ( ( ti @ X_a @ A_2 )
!= ( ti @ X_a @ B_1 ) )
& ( ( ti @ X_a @ C_1 )
!= ( ti @ X_a @ D_1 ) ) )
<=> ( ( plus_plus @ X_a @ ( times_times @ X_a @ A_2 @ C_1 ) @ ( times_times @ X_a @ B_1 @ D_1 ) )
!= ( plus_plus @ X_a @ ( times_times @ X_a @ A_2 @ D_1 ) @ ( times_times @ X_a @ B_1 @ C_1 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1032]) ).
thf(1363,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [X_1: $i,Y_1: $i,Z: $i] :
( ( times_times @ X_a @ X_1 @ ( plus_plus @ X_a @ Y_1 @ Z ) )
= ( plus_plus @ X_a @ ( times_times @ X_a @ X_1 @ Y_1 ) @ ( times_times @ X_a @ X_1 @ Z ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1031]) ).
thf(1364,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i] :
( ( times_times @ X_a @ A_1 @ ( one_one @ X_a ) )
= ( ti @ X_a @ A_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1030]) ).
thf(1365,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i] :
( ( times_times @ X_a @ ( one_one @ X_a ) @ A_1 )
= ( ti @ X_a @ A_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1029]) ).
thf(1366,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [X_1: $i,Y_1: $i,Q: $i] :
( ( power_power @ X_a @ ( times_times @ X_a @ X_1 @ Y_1 ) @ Q )
= ( times_times @ X_a @ ( power_power @ X_a @ X_1 @ Q ) @ ( power_power @ X_a @ Y_1 @ Q ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1028]) ).
thf(1367,plain,
( ( ! [K: $i] :
( ( bit1 @ K )
!= pls ) )
= $true ),
inference(copy,[status(thm)],[1027]) ).
thf(1368,plain,
( ( ! [L: $i] :
( pls
!= ( bit1 @ L ) ) )
= $true ),
inference(copy,[status(thm)],[1026]) ).
thf(1369,plain,
( ( ! [K: $i,L: $i] :
( ( bit1 @ K )
!= ( bit0 @ L ) ) )
= $true ),
inference(copy,[status(thm)],[1025]) ).
thf(1370,plain,
( ( ! [K: $i,L: $i] :
( ( bit0 @ K )
!= ( bit1 @ L ) ) )
= $true ),
inference(copy,[status(thm)],[1024]) ).
thf(1371,plain,
( ( ! [K_1: $i] :
( ( ( bit0 @ K_1 )
= pls )
<=> ( ( ti @ int @ K_1 )
= pls ) ) )
= $true ),
inference(copy,[status(thm)],[1023]) ).
thf(1372,plain,
( ( ! [L_1: $i] :
( ( pls
= ( bit0 @ L_1 ) )
<=> ( pls
= ( ti @ int @ L_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1022]) ).
thf(1373,plain,
( ( ( bit0 @ pls )
= pls )
= $true ),
inference(copy,[status(thm)],[1021]) ).
thf(1374,plain,
( ( ! [W: $i] :
( ( times_times @ int @ pls @ W )
= pls ) )
= $true ),
inference(copy,[status(thm)],[1020]) ).
thf(1375,plain,
( ( ! [K: $i,L: $i] :
( ( times_times @ int @ ( bit0 @ K ) @ L )
= ( bit0 @ ( times_times @ int @ K @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[1019]) ).
thf(1376,plain,
( ( ! [K: $i] :
( ( plus_plus @ int @ K @ pls )
= ( ti @ int @ K ) ) )
= $true ),
inference(copy,[status(thm)],[1018]) ).
thf(1377,plain,
( ( ! [K: $i] :
( ( plus_plus @ int @ pls @ K )
= ( ti @ int @ K ) ) )
= $true ),
inference(copy,[status(thm)],[1017]) ).
thf(1378,plain,
( ( ! [K: $i,L: $i] :
( ( plus_plus @ int @ ( bit0 @ K ) @ ( bit0 @ L ) )
= ( bit0 @ ( plus_plus @ int @ K @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[1016]) ).
thf(1379,plain,
( ( ! [K: $i] :
( ( bit0 @ K )
= ( plus_plus @ int @ K @ K ) ) )
= $true ),
inference(copy,[status(thm)],[1015]) ).
thf(1380,plain,
( ( ! [Z: $i] :
( ( times_times @ int @ Z @ ( one_one @ int ) )
= ( ti @ int @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[1014]) ).
thf(1381,plain,
( ( ! [Z: $i] :
( ( times_times @ int @ ( one_one @ int ) @ Z )
= ( ti @ int @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[1013]) ).
thf(1382,plain,
( ( ! [V: $i,W: $i] :
( ( times_times @ int @ ( number_number_of @ int @ V ) @ ( number_number_of @ int @ W ) )
= ( number_number_of @ int @ ( times_times @ int @ V @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[1012]) ).
thf(1383,plain,
( ( ! [Z1: $i,Z2: $i,W: $i] :
( ( times_times @ int @ ( plus_plus @ int @ Z1 @ Z2 ) @ W )
= ( plus_plus @ int @ ( times_times @ int @ Z1 @ W ) @ ( times_times @ int @ Z2 @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[1011]) ).
thf(1384,plain,
( ( ! [W: $i,Z1: $i,Z2: $i] :
( ( times_times @ int @ W @ ( plus_plus @ int @ Z1 @ Z2 ) )
= ( plus_plus @ int @ ( times_times @ int @ W @ Z1 ) @ ( times_times @ int @ W @ Z2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1010]) ).
thf(1385,plain,
( ( ! [V: $i,W: $i] :
( ( plus_plus @ int @ ( number_number_of @ int @ V ) @ ( number_number_of @ int @ W ) )
= ( number_number_of @ int @ ( plus_plus @ int @ V @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[1009]) ).
thf(1386,plain,
( ( ! [X_a: $i] :
( ( number_semiring @ X_a )
=> ! [V_1: $i,V: $i] :
( ( ord_less_eq @ int @ pls @ V )
=> ( ( ord_less_eq @ int @ pls @ V_1 )
=> ( ( times_times @ X_a @ ( number_number_of @ X_a @ V ) @ ( number_number_of @ X_a @ V_1 ) )
= ( number_number_of @ X_a @ ( times_times @ int @ V @ V_1 ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1008]) ).
thf(1387,plain,
( ( ! [X_a: $i] :
( ( number_semiring @ X_a )
=> ! [V_1: $i,V: $i] :
( ( ord_less_eq @ int @ pls @ V )
=> ( ( ord_less_eq @ int @ pls @ V_1 )
=> ( ( plus_plus @ X_a @ ( number_number_of @ X_a @ V ) @ ( number_number_of @ X_a @ V_1 ) )
= ( number_number_of @ X_a @ ( plus_plus @ int @ V @ V_1 ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1007]) ).
thf(1388,plain,
( ( ! [X_1: $i] : ( ord_less_eq @ int @ X_1 @ ( power_power @ int @ X_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1006]) ).
thf(1389,plain,
( ( ! [X_b: $i] :
( ( ( number @ X_b )
& ( semiring @ X_b ) )
=> ! [A_1: $i,B: $i,V: $i] :
( ( times_times @ X_b @ ( plus_plus @ X_b @ A_1 @ B ) @ ( number_number_of @ X_b @ V ) )
= ( plus_plus @ X_b @ ( times_times @ X_b @ A_1 @ ( number_number_of @ X_b @ V ) ) @ ( times_times @ X_b @ B @ ( number_number_of @ X_b @ V ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1005]) ).
thf(1390,plain,
( ( ! [X_b: $i] :
( ( ( number @ X_b )
& ( semiring @ X_b ) )
=> ! [V: $i,B: $i,C: $i] :
( ( times_times @ X_b @ ( number_number_of @ X_b @ V ) @ ( plus_plus @ X_b @ B @ C ) )
= ( plus_plus @ X_b @ ( times_times @ X_b @ ( number_number_of @ X_b @ V ) @ B ) @ ( times_times @ X_b @ ( number_number_of @ X_b @ V ) @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1004]) ).
thf(1391,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i,M: $i] :
( ( plus_plus @ X_a @ ( times_times @ X_a @ A_1 @ M ) @ M )
= ( times_times @ X_a @ ( plus_plus @ X_a @ A_1 @ ( one_one @ X_a ) ) @ M ) ) ) )
= $true ),
inference(copy,[status(thm)],[1003]) ).
thf(1392,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [M: $i,A_1: $i] :
( ( plus_plus @ X_a @ M @ ( times_times @ X_a @ A_1 @ M ) )
= ( times_times @ X_a @ ( plus_plus @ X_a @ A_1 @ ( one_one @ X_a ) ) @ M ) ) ) )
= $true ),
inference(copy,[status(thm)],[1002]) ).
thf(1393,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [M: $i] :
( ( plus_plus @ X_a @ M @ M )
= ( times_times @ X_a @ ( plus_plus @ X_a @ ( one_one @ X_a ) @ ( one_one @ X_a ) ) @ M ) ) ) )
= $true ),
inference(copy,[status(thm)],[1001]) ).
thf(1394,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [A_1: $i] :
( ( plus_plus @ X_a @ ( number_number_of @ X_a @ pls ) @ A_1 )
= ( ti @ X_a @ A_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1000]) ).
thf(1395,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [A_1: $i] :
( ( plus_plus @ X_a @ A_1 @ ( number_number_of @ X_a @ pls ) )
= ( ti @ X_a @ A_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[999]) ).
thf(1396,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [V: $i,W: $i,Z: $i] :
( ( times_times @ X_a @ ( number_number_of @ X_a @ V ) @ ( times_times @ X_a @ ( number_number_of @ X_a @ W ) @ Z ) )
= ( times_times @ X_a @ ( number_number_of @ X_a @ ( times_times @ int @ V @ W ) ) @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[998]) ).
thf(1397,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [V: $i,W: $i] :
( ( times_times @ X_a @ ( number_number_of @ X_a @ V ) @ ( number_number_of @ X_a @ W ) )
= ( number_number_of @ X_a @ ( times_times @ int @ V @ W ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[997]) ).
thf(1398,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [V: $i,W: $i] :
( ( number_number_of @ X_a @ ( times_times @ int @ V @ W ) )
= ( times_times @ X_a @ ( number_number_of @ X_a @ V ) @ ( number_number_of @ X_a @ W ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[996]) ).
thf(1399,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [V: $i,W: $i,Z: $i] :
( ( plus_plus @ X_a @ ( number_number_of @ X_a @ V ) @ ( plus_plus @ X_a @ ( number_number_of @ X_a @ W ) @ Z ) )
= ( plus_plus @ X_a @ ( number_number_of @ X_a @ ( plus_plus @ int @ V @ W ) ) @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[995]) ).
thf(1400,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [V: $i,W: $i] :
( ( plus_plus @ X_a @ ( number_number_of @ X_a @ V ) @ ( number_number_of @ X_a @ W ) )
= ( number_number_of @ X_a @ ( plus_plus @ int @ V @ W ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[994]) ).
thf(1401,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [V: $i,W: $i] :
( ( number_number_of @ X_a @ ( plus_plus @ int @ V @ W ) )
= ( plus_plus @ X_a @ ( number_number_of @ X_a @ V ) @ ( number_number_of @ X_a @ W ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[993]) ).
thf(1402,plain,
( ( ! [K: $i,L: $i] :
( ( plus_plus @ int @ ( bit1 @ K ) @ ( bit0 @ L ) )
= ( bit1 @ ( plus_plus @ int @ K @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[992]) ).
thf(1403,plain,
( ( ! [K: $i,L: $i] :
( ( plus_plus @ int @ ( bit0 @ K ) @ ( bit1 @ L ) )
= ( bit1 @ ( plus_plus @ int @ K @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[991]) ).
thf(1404,plain,
( ( ! [K: $i] :
( ( bit1 @ K )
= ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ K ) @ K ) ) )
= $true ),
inference(copy,[status(thm)],[990]) ).
thf(1405,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [W: $i] :
( ( number_number_of @ X_a @ ( bit1 @ W ) )
= ( plus_plus @ X_a @ ( plus_plus @ X_a @ ( one_one @ X_a ) @ ( number_number_of @ X_a @ W ) ) @ ( number_number_of @ X_a @ W ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[989]) ).
thf(1406,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [A_1: $i] :
( ( times_times @ X_a @ ( number_number_of @ X_a @ ( bit1 @ pls ) ) @ A_1 )
= ( ti @ X_a @ A_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[988]) ).
thf(1407,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [A_1: $i] :
( ( times_times @ X_a @ A_1 @ ( number_number_of @ X_a @ ( bit1 @ pls ) ) )
= ( ti @ X_a @ A_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[987]) ).
thf(1408,plain,
( ( ! [X_a: $i] :
( ( number_semiring @ X_a )
=> ( ( number_number_of @ X_a @ ( bit1 @ pls ) )
= ( one_one @ X_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[986]) ).
thf(1409,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ( ( number_number_of @ X_a @ ( bit1 @ pls ) )
= ( one_one @ X_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[985]) ).
thf(1410,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ( ( one_one @ X_a )
= ( number_number_of @ X_a @ ( bit1 @ pls ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[984]) ).
thf(1411,plain,
( ( ( one_one @ int )
= ( number_number_of @ int @ ( bit1 @ pls ) ) )
= $true ),
inference(copy,[status(thm)],[983]) ).
thf(1412,plain,
( ( ! [K: $i,L: $i] :
( ( times_times @ int @ ( bit1 @ K ) @ L )
= ( plus_plus @ int @ ( bit0 @ ( times_times @ int @ K @ L ) ) @ L ) ) )
= $true ),
inference(copy,[status(thm)],[982]) ).
thf(1413,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [W: $i] :
( ( times_times @ X_a @ ( plus_plus @ X_a @ ( one_one @ X_a ) @ ( one_one @ X_a ) ) @ ( number_number_of @ X_a @ W ) )
= ( number_number_of @ X_a @ ( bit0 @ W ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[981]) ).
thf(1414,plain,
( ( ! [X_a: $i] :
( ( monoid_mult @ X_a )
=> ! [A_1: $i] :
( ( power_power @ X_a @ A_1 @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( times_times @ X_a @ ( times_times @ X_a @ A_1 @ A_1 ) @ A_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[980]) ).
thf(1415,plain,
( ( ! [X_1: $i] :
( ( power_power @ int @ ( power_power @ int @ X_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power @ int @ X_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[979]) ).
thf(1416,plain,
( ( ! [X_a: $i] :
( ( number_semiring @ X_a )
=> ! [Z: $i] :
( ( times_times @ X_a @ ( number_number_of @ X_a @ ( bit0 @ ( bit1 @ pls ) ) ) @ Z )
= ( plus_plus @ X_a @ Z @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[978]) ).
thf(1417,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [Z: $i] :
( ( times_times @ X_a @ ( number_number_of @ X_a @ ( bit0 @ ( bit1 @ pls ) ) ) @ Z )
= ( plus_plus @ X_a @ Z @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[977]) ).
thf(1418,plain,
( ( ! [X_a: $i] :
( ( number_semiring @ X_a )
=> ! [Z: $i] :
( ( times_times @ X_a @ Z @ ( number_number_of @ X_a @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ X_a @ Z @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[976]) ).
thf(1419,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [Z: $i] :
( ( times_times @ X_a @ Z @ ( number_number_of @ X_a @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ X_a @ Z @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[975]) ).
thf(1420,plain,
( ( ! [X_a: $i] :
( ( number_semiring @ X_a )
=> ( ( plus_plus @ X_a @ ( one_one @ X_a ) @ ( one_one @ X_a ) )
= ( number_number_of @ X_a @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[974]) ).
thf(1421,plain,
( ( ord_less @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) )
= $true ),
inference(copy,[status(thm)],[973]) ).
thf(1422,plain,
( ( dvd_dvd @ int @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) @ ( plus_plus @ int @ ( power_power @ int @ s @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( one_one @ int ) ) )
= $true ),
inference(copy,[status(thm)],[972]) ).
thf(1423,plain,
( ( ! [P: $i] :
( ( zprime @ P )
=> ( ( ( ti @ int @ P )
!= ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) )
=> ( ( ( ti @ int @ P )
!= ( number_number_of @ int @ ( bit1 @ ( bit1 @ pls ) ) ) )
=> ( ord_less_eq @ int @ ( number_number_of @ int @ ( bit1 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ P ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[971]) ).
thf(1424,plain,
( ( ! [X_1: $i,Y_1: $i] :
( ( power_power @ real @ ( plus_plus @ real @ X_1 @ Y_1 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ real @ ( plus_plus @ real @ ( power_power @ real @ X_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ real @ Y_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times @ real @ ( times_times @ real @ ( number_number_of @ real @ ( bit0 @ ( bit1 @ pls ) ) ) @ X_1 ) @ Y_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[970]) ).
thf(1425,plain,
( ( ! [X_1: $i] :
( ( times_times @ real @ ( number_number_of @ real @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ real @ X_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( power_power @ real @ ( times_times @ real @ ( number_number_of @ real @ ( bit0 @ ( bit1 @ pls ) ) ) @ X_1 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[969]) ).
thf(1426,plain,
( ( ! [X_a: $i] :
( ( linordered_semidom @ X_a )
=> ! [N: $i,A_1: $i] :
( ( ord_less @ X_a @ ( one_one @ X_a ) @ A_1 )
=> ( ord_less @ X_a @ ( power_power @ X_a @ A_1 @ N ) @ ( times_times @ X_a @ A_1 @ ( power_power @ X_a @ A_1 @ N ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[968]) ).
thf(1427,plain,
( ( ! [X_a: $i] :
( ( linordered_semidom @ X_a )
=> ! [N: $i,A_1: $i] :
( ( ord_less @ X_a @ ( one_one @ X_a ) @ A_1 )
=> ( ord_less @ X_a @ ( one_one @ X_a ) @ ( times_times @ X_a @ A_1 @ ( power_power @ X_a @ A_1 @ N ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[967]) ).
thf(1428,plain,
( ( ! [X_a: $i] :
( ( linordered_semidom @ X_a )
=> ! [M: $i,N: $i,A_1: $i] :
( ( ord_less @ X_a @ ( one_one @ X_a ) @ A_1 )
=> ( ( ord_less_eq @ X_a @ ( power_power @ X_a @ A_1 @ M ) @ ( power_power @ X_a @ A_1 @ N ) )
=> ( ord_less_eq @ nat @ M @ N ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[966]) ).
thf(1429,plain,
( ( ! [X_a: $i] :
( ( linordered_semidom @ X_a )
=> ! [X_2: $i,Y_2: $i,B_1: $i] :
( ( ord_less @ X_a @ ( one_one @ X_a ) @ B_1 )
=> ( ( ord_less_eq @ X_a @ ( power_power @ X_a @ B_1 @ X_2 ) @ ( power_power @ X_a @ B_1 @ Y_2 ) )
<=> ( ord_less_eq @ nat @ X_2 @ Y_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[965]) ).
thf(1430,plain,
( ( zcong @ ( power_power @ int @ s @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ s1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) )
= $true ),
inference(copy,[status(thm)],[964]) ).
thf(1431,plain,
( ( zcong @ ( power_power @ int @ s1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of @ int @ min ) @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) )
= $true ),
inference(copy,[status(thm)],[963]) ).
thf(1432,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i,M: $i,N: $i] :
( ( ord_less_eq @ nat @ M @ N )
=> ( dvd_dvd @ X_a @ ( power_power @ X_a @ A_1 @ M ) @ ( power_power @ X_a @ A_1 @ N ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[962]) ).
thf(1433,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [N: $i,M: $i,X_1: $i,Y_1: $i] :
( ( dvd_dvd @ X_a @ X_1 @ Y_1 )
=> ( ( ord_less_eq @ nat @ N @ M )
=> ( dvd_dvd @ X_a @ ( power_power @ X_a @ X_1 @ N ) @ ( power_power @ X_a @ Y_1 @ M ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[961]) ).
thf(1434,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [M: $i,A_1: $i,N: $i,B: $i] :
( ( dvd_dvd @ X_a @ ( power_power @ X_a @ A_1 @ N ) @ B )
=> ( ( ord_less_eq @ nat @ M @ N )
=> ( dvd_dvd @ X_a @ ( power_power @ X_a @ A_1 @ M ) @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[960]) ).
thf(1435,plain,
( ( ! [N: $i,M: $i] :
( ( ord_less @ int @ ( zero_zero @ int ) @ M )
=> ( ( ord_less @ int @ M @ N )
=> ~ ( dvd_dvd @ int @ N @ M ) ) ) )
= $true ),
inference(copy,[status(thm)],[959]) ).
thf(1436,plain,
( ( ! [K: $i,M: $i,N: $i] :
( ( dvd_dvd @ int @ ( times_times @ int @ K @ M ) @ ( times_times @ int @ K @ N ) )
=> ( ( ( ti @ int @ K )
!= ( zero_zero @ int ) )
=> ( dvd_dvd @ int @ M @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[958]) ).
thf(1437,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [N: $i,X_1: $i,Y_1: $i] :
( ( dvd_dvd @ X_a @ X_1 @ Y_1 )
=> ( dvd_dvd @ X_a @ ( power_power @ X_a @ X_1 @ N ) @ ( power_power @ X_a @ Y_1 @ N ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[957]) ).
thf(1438,plain,
( ( ! [X_a: $i] :
( ( ring_11004092258visors @ X_a )
=> ! [N: $i,A_1: $i] :
( ( ( ti @ X_a @ A_1 )
!= ( zero_zero @ X_a ) )
=> ( ( power_power @ X_a @ A_1 @ N )
!= ( zero_zero @ X_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[956]) ).
thf(1439,plain,
( ( ! [X_a: $i] :
( ( ( power @ X_a )
& ( semiring_0 @ X_a ) )
=> ! [N: $i] :
( ( ( N
= ( zero_zero @ nat ) )
=> ( ( power_power @ X_a @ ( zero_zero @ X_a ) @ N )
= ( one_one @ X_a ) ) )
& ( ( N
!= ( zero_zero @ nat ) )
=> ( ( power_power @ X_a @ ( zero_zero @ X_a ) @ N )
= ( zero_zero @ X_a ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[955]) ).
thf(1440,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i] :
( ( times_times @ X_a @ ( zero_zero @ X_a ) @ A_1 )
= ( zero_zero @ X_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[954]) ).
thf(1441,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i] :
( ( times_times @ X_a @ A_1 @ ( zero_zero @ X_a ) )
= ( zero_zero @ X_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[953]) ).
thf(1442,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i] :
( ( plus_plus @ X_a @ ( zero_zero @ X_a ) @ A_1 )
= ( ti @ X_a @ A_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[952]) ).
thf(1443,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i] :
( ( plus_plus @ X_a @ A_1 @ ( zero_zero @ X_a ) )
= ( ti @ X_a @ A_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[951]) ).
thf(1444,plain,
( ( ! [X_a: $i] :
( ( semiri456707255roduct @ X_a )
=> ! [B_1: $i,A_2: $i] :
( ( ( ti @ X_a @ B_1 )
= ( plus_plus @ X_a @ B_1 @ A_2 ) )
<=> ( ( ti @ X_a @ A_2 )
= ( zero_zero @ X_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[950]) ).
thf(1445,plain,
( ( ! [X_a: $i] :
( ( linord219039673up_add @ X_a )
=> ! [A_2: $i] :
( ( ( plus_plus @ X_a @ A_2 @ A_2 )
= ( zero_zero @ X_a ) )
<=> ( ( ti @ X_a @ A_2 )
= ( zero_zero @ X_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[949]) ).
thf(1446,plain,
( ( pls
= ( zero_zero @ int ) )
= $true ),
inference(copy,[status(thm)],[948]) ).
thf(1447,plain,
( ( ( zero_zero @ int )
!= ( one_one @ int ) )
= $true ),
inference(copy,[status(thm)],[947]) ).
thf(1448,plain,
( ( ! [Z: $i] :
( ( plus_plus @ int @ ( zero_zero @ int ) @ Z )
= ( ti @ int @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[946]) ).
thf(1449,plain,
( ( ! [Z: $i] :
( ( plus_plus @ int @ Z @ ( zero_zero @ int ) )
= ( ti @ int @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[945]) ).
thf(1450,plain,
( ( ! [X_a: $i] :
( ( linordered_semidom @ X_a )
=> ! [N: $i,A_1: $i] :
( ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ A_1 )
=> ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ ( power_power @ X_a @ A_1 @ N ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[944]) ).
thf(1451,plain,
( ( ! [X_a: $i] :
( ( linordered_semidom @ X_a )
=> ! [N: $i,A_1: $i,B: $i] :
( ( ord_less_eq @ X_a @ A_1 @ B )
=> ( ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ A_1 )
=> ( ord_less_eq @ X_a @ ( power_power @ X_a @ A_1 @ N ) @ ( power_power @ X_a @ B @ N ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[943]) ).
thf(1452,plain,
( ( ! [X_a: $i] :
( ( linordered_semidom @ X_a )
=> ! [N: $i,A_1: $i] :
( ( ord_less @ X_a @ ( zero_zero @ X_a ) @ A_1 )
=> ( ord_less @ X_a @ ( zero_zero @ X_a ) @ ( power_power @ X_a @ A_1 @ N ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[942]) ).
thf(1453,plain,
( ( ! [Z: $i,X_1: $i,Y_1: $i,P: $i] :
( ( zcong @ ( power_power @ int @ X_1 @ Y_1 ) @ ( one_one @ int ) @ P )
=> ( zcong @ ( power_power @ int @ X_1 @ ( times_times @ nat @ Y_1 @ Z ) ) @ ( one_one @ int ) @ P ) ) )
= $true ),
inference(copy,[status(thm)],[941]) ).
thf(1454,plain,
( ( ! [K_1: $i,N_1: $i,Ma: $i] :
( ( dvd_dvd @ int @ K_1 @ ( plus_plus @ int @ N_1 @ ( times_times @ int @ K_1 @ Ma ) ) )
<=> ( dvd_dvd @ int @ K_1 @ N_1 ) ) )
= $true ),
inference(copy,[status(thm)],[940]) ).
thf(1455,plain,
( ( ! [C_1: $i,X_2: $i,Ta: $i,A_2: $i,D_1: $i] :
( ( dvd_dvd @ int @ A_2 @ D_1 )
=> ( ( dvd_dvd @ int @ A_2 @ ( plus_plus @ int @ X_2 @ Ta ) )
<=> ( dvd_dvd @ int @ A_2 @ ( plus_plus @ int @ ( plus_plus @ int @ X_2 @ ( times_times @ int @ C_1 @ D_1 ) ) @ Ta ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[939]) ).
thf(1456,plain,
( ( ! [X_a: $i] :
( ( linordered_semidom @ X_a )
=> ! [A_1: $i,N: $i,N_2: $i] :
( ( ord_less_eq @ nat @ N @ N_2 )
=> ( ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ A_1 )
=> ( ( ord_less_eq @ X_a @ A_1 @ ( one_one @ X_a ) )
=> ( ord_less_eq @ X_a @ ( power_power @ X_a @ A_1 @ N_2 ) @ ( power_power @ X_a @ A_1 @ N ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[938]) ).
thf(1457,plain,
( ( ! [X_a: $i] :
( ( linordered_semidom @ X_a )
=> ! [A_1: $i,N: $i,N_2: $i] :
( ( ord_less @ nat @ N @ N_2 )
=> ( ( ord_less @ X_a @ ( zero_zero @ X_a ) @ A_1 )
=> ( ( ord_less @ X_a @ A_1 @ ( one_one @ X_a ) )
=> ( ord_less @ X_a @ ( power_power @ X_a @ A_1 @ N_2 ) @ ( power_power @ X_a @ A_1 @ N ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[937]) ).
thf(1458,plain,
( ( ! [X_a: $i] :
( ( linordered_idom @ X_a )
=> ! [A_2: $i] :
( ( ord_less @ X_a @ ( plus_plus @ X_a @ A_2 @ A_2 ) @ ( zero_zero @ X_a ) )
<=> ( ord_less @ X_a @ A_2 @ ( zero_zero @ X_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[936]) ).
thf(1459,plain,
( ( ! [X_a: $i] :
( ( linord581940658strict @ X_a )
=> ! [X_2: $i,Y_2: $i] :
( ( ( plus_plus @ X_a @ ( times_times @ X_a @ X_2 @ X_2 ) @ ( times_times @ X_a @ Y_2 @ Y_2 ) )
= ( zero_zero @ X_a ) )
<=> ( ( ( ti @ X_a @ X_2 )
= ( zero_zero @ X_a ) )
& ( ( ti @ X_a @ Y_2 )
= ( zero_zero @ X_a ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[935]) ).
thf(1460,plain,
( ( ! [X_a: $i] :
( ( semiri456707255roduct @ X_a )
=> ! [C: $i,D: $i,A_1: $i,B: $i,R_1: $i] :
( ( ( ti @ X_a @ R_1 )
!= ( zero_zero @ X_a ) )
=> ( ( ( ( ti @ X_a @ A_1 )
= ( ti @ X_a @ B ) )
& ( ( ti @ X_a @ C )
!= ( ti @ X_a @ D ) ) )
=> ( ( plus_plus @ X_a @ A_1 @ ( times_times @ X_a @ R_1 @ C ) )
!= ( plus_plus @ X_a @ B @ ( times_times @ X_a @ R_1 @ D ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[934]) ).
thf(1461,plain,
( ( ! [A_1: $i,N: $i,P: $i] :
( ( zprime @ P )
=> ( ( dvd_dvd @ int @ P @ ( power_power @ int @ A_1 @ N ) )
=> ( dvd_dvd @ int @ P @ A_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[933]) ).
thf(1462,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ( ( zero_zero @ X_a )
= ( number_number_of @ X_a @ pls ) ) ) )
= $true ),
inference(copy,[status(thm)],[932]) ).
thf(1463,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ( ( number_number_of @ X_a @ pls )
= ( zero_zero @ X_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[931]) ).
thf(1464,plain,
( ( ! [X_a: $i] :
( ( number_semiring @ X_a )
=> ( ( number_number_of @ X_a @ pls )
= ( zero_zero @ X_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[930]) ).
thf(1465,plain,
( ( ! [W_1: $i] :
( ( ord_less @ int @ ( bit1 @ W_1 ) @ ( zero_zero @ int ) )
<=> ( ord_less @ int @ W_1 @ ( zero_zero @ int ) ) ) )
= $true ),
inference(copy,[status(thm)],[929]) ).
thf(1466,plain,
( ( ~ ( ord_less @ int @ pls @ ( zero_zero @ int ) ) )
= $true ),
inference(copy,[status(thm)],[928]) ).
thf(1467,plain,
( ( ! [W_1: $i] :
( ( ord_less @ int @ ( bit0 @ W_1 ) @ ( zero_zero @ int ) )
<=> ( ord_less @ int @ W_1 @ ( zero_zero @ int ) ) ) )
= $true ),
inference(copy,[status(thm)],[927]) ).
thf(1468,plain,
( ( ( zero_zero @ int )
= ( number_number_of @ int @ pls ) )
= $true ),
inference(copy,[status(thm)],[926]) ).
thf(1469,plain,
( ( ord_less @ int @ ( zero_zero @ int ) @ ( one_one @ int ) )
= $true ),
inference(copy,[status(thm)],[925]) ).
thf(1470,plain,
( ( ! [B: $i,A_1: $i] :
( ( ord_less @ int @ ( zero_zero @ int ) @ A_1 )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ ( times_times @ int @ A_1 @ B ) )
=> ( ord_less @ int @ ( zero_zero @ int ) @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[924]) ).
thf(1471,plain,
( ( ! [K: $i,I: $i,J: $i] :
( ( ord_less @ int @ I @ J )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ K )
=> ( ord_less @ int @ ( times_times @ int @ K @ I ) @ ( times_times @ int @ K @ J ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[923]) ).
thf(1472,plain,
( ( ! [Z: $i] :
( ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ Z ) @ Z )
!= ( zero_zero @ int ) ) )
= $true ),
inference(copy,[status(thm)],[922]) ).
thf(1473,plain,
( ( ! [X_a: $i] :
( ( linordered_semidom @ X_a )
=> ! [N: $i,A_1: $i] :
( ( ord_less @ X_a @ ( zero_zero @ X_a ) @ A_1 )
=> ( ( ord_less @ X_a @ A_1 @ ( one_one @ X_a ) )
=> ( ord_less @ X_a @ ( times_times @ X_a @ A_1 @ ( power_power @ X_a @ A_1 @ N ) ) @ ( power_power @ X_a @ A_1 @ N ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[921]) ).
thf(1474,plain,
( ( ! [N: $i,B: $i,A_1: $i,P: $i] :
( ( zprime @ P )
=> ( ~ ( dvd_dvd @ int @ P @ A_1 )
=> ( ( dvd_dvd @ int @ ( power_power @ int @ P @ N ) @ ( times_times @ int @ A_1 @ B ) )
=> ( dvd_dvd @ int @ ( power_power @ int @ P @ N ) @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[920]) ).
thf(1475,plain,
( ( ! [N: $i,A_1: $i,B: $i,P: $i] :
( ( zprime @ P )
=> ( ~ ( dvd_dvd @ int @ P @ B )
=> ( ( dvd_dvd @ int @ ( power_power @ int @ P @ N ) @ ( times_times @ int @ A_1 @ B ) )
=> ( dvd_dvd @ int @ ( power_power @ int @ P @ N ) @ A_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[919]) ).
thf(1476,plain,
( ( ! [X_a: $i] :
( ( linordered_ring @ X_a )
=> ! [X_1: $i,Y_1: $i] : ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ ( plus_plus @ X_a @ ( times_times @ X_a @ X_1 @ X_1 ) @ ( times_times @ X_a @ Y_1 @ Y_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[918]) ).
thf(1477,plain,
( ( ! [V_2: $i,V_3: $i] :
( ( ord_less @ nat @ ( number_number_of @ nat @ V_2 ) @ ( number_number_of @ nat @ V_3 ) )
<=> ( ( ( ord_less @ int @ V_2 @ V_3 )
=> ( ord_less @ int @ pls @ V_3 ) )
& ( ord_less @ int @ V_2 @ V_3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[917]) ).
thf(1478,plain,
( ( ! [X_a: $i] :
( ( linordered_ring @ X_a )
=> ! [X_1: $i,Y_1: $i] :
~ ( ord_less @ X_a @ ( plus_plus @ X_a @ ( times_times @ X_a @ X_1 @ X_1 ) @ ( times_times @ X_a @ Y_1 @ Y_1 ) ) @ ( zero_zero @ X_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[916]) ).
thf(1479,plain,
( ( ! [V_2: $i,V_3: $i] :
( ( ord_less_eq @ nat @ ( number_number_of @ nat @ V_2 ) @ ( number_number_of @ nat @ V_3 ) )
<=> ( ~ ( ord_less_eq @ int @ V_2 @ V_3 )
=> ( ord_less_eq @ int @ V_2 @ pls ) ) ) )
= $true ),
inference(copy,[status(thm)],[915]) ).
thf(1480,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [W: $i] :
( ( number_number_of @ X_a @ ( bit0 @ W ) )
= ( plus_plus @ X_a @ ( plus_plus @ X_a @ ( zero_zero @ X_a ) @ ( number_number_of @ X_a @ W ) ) @ ( number_number_of @ X_a @ W ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[914]) ).
thf(1481,plain,
( ( ! [X_a: $i] :
( ( monoid_mult @ X_a )
=> ! [A_1: $i] :
( ( power_power @ X_a @ A_1 @ ( one_one @ nat ) )
= ( ti @ X_a @ A_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[913]) ).
thf(1482,plain,
( ( ! [Z_1: $i] :
( ( ord_less_eq @ int @ ( one_one @ int ) @ Z_1 )
<=> ( ord_less @ int @ ( zero_zero @ int ) @ Z_1 ) ) )
= $true ),
inference(copy,[status(thm)],[912]) ).
thf(1483,plain,
( ( ! [N_1: $i,Ma: $i] :
( ( ord_less @ int @ ( zero_zero @ int ) @ Ma )
=> ( ( ( times_times @ int @ Ma @ N_1 )
= ( one_one @ int ) )
<=> ( ( ( ti @ int @ Ma )
= ( one_one @ int ) )
& ( ( ti @ int @ N_1 )
= ( one_one @ int ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[911]) ).
thf(1484,plain,
( ( ! [Z_1: $i] :
( ( ord_less @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ Z_1 ) @ Z_1 ) @ ( zero_zero @ int ) )
<=> ( ord_less @ int @ Z_1 @ ( zero_zero @ int ) ) ) )
= $true ),
inference(copy,[status(thm)],[910]) ).
thf(1485,plain,
( ( ! [Z: $i] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ Z )
=> ( ord_less @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( one_one @ int ) @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[909]) ).
thf(1486,plain,
( ( ! [X_a: $i] :
( ( semiring_1 @ X_a )
=> ( ( power_power @ X_a @ ( zero_zero @ X_a ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ X_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[908]) ).
thf(1487,plain,
( ( ! [X_a: $i] :
( ( ring_11004092258visors @ X_a )
=> ! [A_2: $i] :
( ( ( power_power @ X_a @ A_2 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ X_a ) )
<=> ( ( ti @ X_a @ A_2 )
= ( zero_zero @ X_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[907]) ).
thf(1488,plain,
( ( ! [X_a: $i] :
( ( linordered_idom @ X_a )
=> ! [A_1: $i] : ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ ( power_power @ X_a @ A_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[906]) ).
thf(1489,plain,
( ( ! [X_a: $i] :
( ( linordered_semidom @ X_a )
=> ! [X_1: $i,Y_1: $i] :
( ( ord_less_eq @ X_a @ ( power_power @ X_a @ X_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ X_a @ Y_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ Y_1 )
=> ( ord_less_eq @ X_a @ X_1 @ Y_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[905]) ).
thf(1490,plain,
( ( ! [X_a: $i] :
( ( linordered_idom @ X_a )
=> ! [A_1: $i] :
~ ( ord_less @ X_a @ ( power_power @ X_a @ A_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( zero_zero @ X_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[904]) ).
thf(1491,plain,
( ( ! [X_a: $i] :
( ( linordered_idom @ X_a )
=> ! [X_2: $i,Y_2: $i] :
( ( ( plus_plus @ X_a @ ( power_power @ X_a @ X_2 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ X_a @ Y_2 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ X_a ) )
<=> ( ( ( ti @ X_a @ X_2 )
= ( zero_zero @ X_a ) )
& ( ( ti @ X_a @ Y_2 )
= ( zero_zero @ X_a ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[903]) ).
thf(1492,plain,
( ( ! [X_a: $i] :
( ( monoid_mult @ X_a )
=> ! [A_1: $i,N: $i] :
( ( times_times @ X_a @ ( power_power @ X_a @ A_1 @ N ) @ A_1 )
= ( times_times @ X_a @ A_1 @ ( power_power @ X_a @ A_1 @ N ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[902]) ).
thf(1493,plain,
( ( ! [X_a: $i] :
( ( comm_monoid_mult @ X_a )
=> ! [A_1: $i,B: $i,N: $i] :
( ( power_power @ X_a @ ( times_times @ X_a @ A_1 @ B ) @ N )
= ( times_times @ X_a @ ( power_power @ X_a @ A_1 @ N ) @ ( power_power @ X_a @ B @ N ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[901]) ).
thf(1494,plain,
( ( ! [X_a: $i] :
( ( monoid_mult @ X_a )
=> ! [A_1: $i,M: $i,N: $i] :
( ( power_power @ X_a @ A_1 @ ( plus_plus @ nat @ M @ N ) )
= ( times_times @ X_a @ ( power_power @ X_a @ A_1 @ M ) @ ( power_power @ X_a @ A_1 @ N ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[900]) ).
thf(1495,plain,
( ( ! [X_a: $i] :
( ( monoid_mult @ X_a )
=> ! [N: $i] :
( ( power_power @ X_a @ ( one_one @ X_a ) @ N )
= ( one_one @ X_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[899]) ).
thf(1496,plain,
( ( ! [X_a: $i] :
( ( monoid_mult @ X_a )
=> ! [A_1: $i,M: $i,N: $i] :
( ( power_power @ X_a @ A_1 @ ( times_times @ nat @ M @ N ) )
= ( power_power @ X_a @ ( power_power @ X_a @ A_1 @ M ) @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[898]) ).
thf(1497,plain,
( ( ! [X_a: $i] :
( ( linordered_idom @ X_a )
=> ! [X_1: $i,Y_1: $i] : ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ ( plus_plus @ X_a @ ( power_power @ X_a @ X_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ X_a @ Y_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[897]) ).
thf(1498,plain,
( ( ! [X_a: $i] :
( ( linordered_idom @ X_a )
=> ! [X_1: $i,Y_1: $i] :
~ ( ord_less @ X_a @ ( plus_plus @ X_a @ ( power_power @ X_a @ X_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ X_a @ Y_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( zero_zero @ X_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[896]) ).
thf(1499,plain,
( ( ! [X_a: $i] :
( ( linordered_idom @ X_a )
=> ! [A_1: $i,N: $i] : ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ ( power_power @ X_a @ A_1 @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ N ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[895]) ).
thf(1500,plain,
( ( ! [X_a: $i] :
( ( linordered_semidom @ X_a )
=> ! [N: $i,A_1: $i] :
( ( ord_less_eq @ X_a @ ( one_one @ X_a ) @ A_1 )
=> ( ord_less_eq @ X_a @ ( one_one @ X_a ) @ ( power_power @ X_a @ A_1 @ N ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[894]) ).
thf(1501,plain,
( ( ! [X_a: $i] :
( ( linordered_semidom @ X_a )
=> ! [A_1: $i,N: $i,N_2: $i] :
( ( ord_less_eq @ nat @ N @ N_2 )
=> ( ( ord_less_eq @ X_a @ ( one_one @ X_a ) @ A_1 )
=> ( ord_less_eq @ X_a @ ( power_power @ X_a @ A_1 @ N ) @ ( power_power @ X_a @ A_1 @ N_2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[893]) ).
thf(1502,plain,
( ( ! [X_a: $i] :
( ( linordered_semidom @ X_a )
=> ! [Ma: $i,N_1: $i,A_2: $i] :
( ( ord_less @ X_a @ ( one_one @ X_a ) @ A_2 )
=> ( ( ( power_power @ X_a @ A_2 @ Ma )
= ( power_power @ X_a @ A_2 @ N_1 ) )
<=> ( Ma = N_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[892]) ).
thf(1503,plain,
( ( ! [X_a: $i] :
( ( linordered_semidom @ X_a )
=> ! [X_2: $i,Y_2: $i,B_1: $i] :
( ( ord_less @ X_a @ ( one_one @ X_a ) @ B_1 )
=> ( ( ord_less @ X_a @ ( power_power @ X_a @ B_1 @ X_2 ) @ ( power_power @ X_a @ B_1 @ Y_2 ) )
<=> ( ord_less @ nat @ X_2 @ Y_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[891]) ).
thf(1504,plain,
( ( ! [X_a: $i] :
( ( linordered_semidom @ X_a )
=> ! [M: $i,N: $i,A_1: $i] :
( ( ord_less @ X_a @ ( one_one @ X_a ) @ A_1 )
=> ( ( ord_less @ X_a @ ( power_power @ X_a @ A_1 @ M ) @ ( power_power @ X_a @ A_1 @ N ) )
=> ( ord_less @ nat @ M @ N ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[890]) ).
thf(1505,plain,
( ( ! [X_a: $i] :
( ( linordered_semidom @ X_a )
=> ! [A_1: $i,N: $i,N_2: $i] :
( ( ord_less @ nat @ N @ N_2 )
=> ( ( ord_less @ X_a @ ( one_one @ X_a ) @ A_1 )
=> ( ord_less @ X_a @ ( power_power @ X_a @ A_1 @ N ) @ ( power_power @ X_a @ A_1 @ N_2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[889]) ).
thf(1506,plain,
( ( zcong @ ( power_power @ int @ s @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of @ int @ min ) @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) )
= $true ),
inference(copy,[status(thm)],[888]) ).
thf(1507,plain,
( ( ! [Y_1: $i,X_1: $i,P: $i] :
( ~ ( zcong @ X_1 @ ( zero_zero @ int ) @ P )
=> ( ( zcong @ ( power_power @ int @ Y_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ X_1 @ P )
=> ~ ( dvd_dvd @ int @ P @ Y_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[887]) ).
thf(1508,plain,
( ( ~ ! [S1: $i] :
~ ( zcong @ ( power_power @ int @ S1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of @ int @ min ) @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ) )
= $true ),
inference(copy,[status(thm)],[886]) ).
thf(1509,plain,
( ( ( legendre @ ( number_number_of @ int @ min ) @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) )
= ( one_one @ int ) )
= $true ),
inference(copy,[status(thm)],[885]) ).
thf(1510,plain,
( ( ! [X_2: $i,N_1: $i] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ X_2 @ N_1 ) )
<=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ X_2 )
| ( N_1
= ( zero_zero @ nat ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[884]) ).
thf(1511,plain,
( ( ! [X_2: $i,N_1: $i] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ X_2 @ N_1 ) )
<=> ( ( N_1
= ( zero_zero @ nat ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ X_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[883]) ).
thf(1512,plain,
( ( ! [X_2: $i,W_1: $i] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ X_2 @ ( number_number_of @ nat @ W_1 ) ) )
<=> ( ( ( number_number_of @ nat @ W_1 )
= ( zero_zero @ nat ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ X_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[882]) ).
thf(1513,plain,
( ( ! [M: $i,N: $i,I: $i] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ I )
=> ( ( ord_less @ nat @ ( power_power @ nat @ I @ M ) @ ( power_power @ nat @ I @ N ) )
=> ( ord_less @ nat @ M @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[881]) ).
thf(1514,plain,
( ( ! [K_1: $i] :
( ( ( bit1 @ K_1 )
= min )
<=> ( ( ti @ int @ K_1 )
= min ) ) )
= $true ),
inference(copy,[status(thm)],[880]) ).
thf(1515,plain,
( ( ! [L_1: $i] :
( ( min
= ( bit1 @ L_1 ) )
<=> ( min
= ( ti @ int @ L_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[879]) ).
thf(1516,plain,
( ( ( bit1 @ min )
= min )
= $true ),
inference(copy,[status(thm)],[878]) ).
thf(1517,plain,
( ( pls != min )
= $true ),
inference(copy,[status(thm)],[877]) ).
thf(1518,plain,
( ( min != pls )
= $true ),
inference(copy,[status(thm)],[876]) ).
thf(1519,plain,
( ( ! [K: $i] :
( ( bit0 @ K )
!= min ) )
= $true ),
inference(copy,[status(thm)],[875]) ).
thf(1520,plain,
( ( ! [L: $i] :
( min
!= ( bit0 @ L ) ) )
= $true ),
inference(copy,[status(thm)],[874]) ).
thf(1521,plain,
( ( ~ ( ord_less @ int @ min @ min ) )
= $true ),
inference(copy,[status(thm)],[873]) ).
thf(1522,plain,
( ( ord_less_eq @ int @ min @ min )
= $true ),
inference(copy,[status(thm)],[872]) ).
thf(1523,plain,
( ( ! [X_2: $i] :
( ~ ( ord_less @ real @ ( zero_zero @ real ) @ ( times_times @ real @ X_2 @ X_2 ) )
<=> ( X_2
= ( zero_zero @ real ) ) ) )
= $true ),
inference(copy,[status(thm)],[871]) ).
thf(1524,plain,
( ( ! [K_1: $i] :
( ( ord_less @ int @ ( bit1 @ K_1 ) @ min )
<=> ( ord_less @ int @ K_1 @ min ) ) )
= $true ),
inference(copy,[status(thm)],[870]) ).
thf(1525,plain,
( ( ! [K_1: $i] :
( ( ord_less @ int @ min @ ( bit1 @ K_1 ) )
<=> ( ord_less @ int @ min @ K_1 ) ) )
= $true ),
inference(copy,[status(thm)],[869]) ).
thf(1526,plain,
( ( ~ ( ord_less @ int @ pls @ min ) )
= $true ),
inference(copy,[status(thm)],[868]) ).
thf(1527,plain,
( ( ord_less @ int @ min @ pls )
= $true ),
inference(copy,[status(thm)],[867]) ).
thf(1528,plain,
( ( ! [K_1: $i] :
( ( ord_less @ int @ min @ ( bit0 @ K_1 ) )
<=> ( ord_less @ int @ min @ K_1 ) ) )
= $true ),
inference(copy,[status(thm)],[866]) ).
thf(1529,plain,
( ( ord_less @ int @ min @ ( zero_zero @ int ) )
= $true ),
inference(copy,[status(thm)],[865]) ).
thf(1530,plain,
( ( ! [K_1: $i] :
( ( ord_less_eq @ int @ ( bit1 @ K_1 ) @ min )
<=> ( ord_less_eq @ int @ K_1 @ min ) ) )
= $true ),
inference(copy,[status(thm)],[864]) ).
thf(1531,plain,
( ( ! [K_1: $i] :
( ( ord_less_eq @ int @ min @ ( bit1 @ K_1 ) )
<=> ( ord_less_eq @ int @ min @ K_1 ) ) )
= $true ),
inference(copy,[status(thm)],[863]) ).
thf(1532,plain,
( ( ~ ( ord_less_eq @ int @ pls @ min ) )
= $true ),
inference(copy,[status(thm)],[862]) ).
thf(1533,plain,
( ( ord_less_eq @ int @ min @ pls )
= $true ),
inference(copy,[status(thm)],[861]) ).
thf(1534,plain,
( ( ! [K_1: $i] :
( ( ord_less_eq @ int @ ( bit0 @ K_1 ) @ min )
<=> ( ord_less_eq @ int @ K_1 @ min ) ) )
= $true ),
inference(copy,[status(thm)],[860]) ).
thf(1535,plain,
( ( ( number_number_of @ int @ pls )
!= ( number_number_of @ int @ min ) )
= $true ),
inference(copy,[status(thm)],[859]) ).
thf(1536,plain,
( ( ! [I: $i,M: $i,N: $i] :
( ( dvd_dvd @ nat @ ( power_power @ nat @ I @ M ) @ ( power_power @ nat @ I @ N ) )
=> ( ( ord_less @ nat @ ( one_one @ nat ) @ I )
=> ( ord_less_eq @ nat @ M @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[858]) ).
thf(1537,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [X_1: $i] :
( ( power_power @ X_a @ X_1 @ ( zero_zero @ nat ) )
= ( one_one @ X_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[857]) ).
thf(1538,plain,
( ( ! [X_a: $i] :
( ( power @ X_a )
=> ! [A_1: $i] :
( ( power_power @ X_a @ A_1 @ ( zero_zero @ nat ) )
= ( one_one @ X_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[856]) ).
thf(1539,plain,
( ( ( number_number_of @ nat @ pls )
= ( zero_zero @ nat ) )
= $true ),
inference(copy,[status(thm)],[855]) ).
thf(1540,plain,
( ( ( zero_zero @ nat )
= ( number_number_of @ nat @ pls ) )
= $true ),
inference(copy,[status(thm)],[854]) ).
thf(1541,plain,
( ( ! [K_1: $i] :
( ( ord_less_eq @ int @ min @ ( bit0 @ K_1 ) )
<=> ( ord_less @ int @ min @ K_1 ) ) )
= $true ),
inference(copy,[status(thm)],[853]) ).
thf(1542,plain,
( ( ! [K_1: $i] :
( ( ord_less @ int @ ( bit0 @ K_1 ) @ min )
<=> ( ord_less_eq @ int @ K_1 @ min ) ) )
= $true ),
inference(copy,[status(thm)],[852]) ).
thf(1543,plain,
( ( ! [M: $i,N: $i] :
( ( ( times_times @ int @ M @ N )
= ( one_one @ int ) )
=> ( ( ( ti @ int @ M )
= ( one_one @ int ) )
| ( ( ti @ int @ M )
= ( number_number_of @ int @ min ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[851]) ).
thf(1544,plain,
( ( ! [Ma: $i,N_1: $i] :
( ( ( times_times @ int @ Ma @ N_1 )
= ( one_one @ int ) )
<=> ( ( ( ( ti @ int @ Ma )
= ( one_one @ int ) )
& ( ( ti @ int @ N_1 )
= ( one_one @ int ) ) )
| ( ( ( ti @ int @ Ma )
= ( number_number_of @ int @ min ) )
& ( ( ti @ int @ N_1 )
= ( number_number_of @ int @ min ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[850]) ).
thf(1545,plain,
( ( ! [X_a: $i] :
( ( linordered_semidom @ X_a )
=> ! [N: $i,A_1: $i] :
( ( ord_less @ X_a @ ( one_one @ X_a ) @ A_1 )
=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
=> ( ord_less @ X_a @ ( one_one @ X_a ) @ ( power_power @ X_a @ A_1 @ N ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[849]) ).
thf(1546,plain,
( ( ! [V_2: $i] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( number_number_of @ nat @ V_2 ) )
<=> ( ord_less @ int @ pls @ V_2 ) ) )
= $true ),
inference(copy,[status(thm)],[848]) ).
thf(1547,plain,
( ( ! [V_2: $i] :
( ( ( number_number_of @ nat @ V_2 )
= ( zero_zero @ nat ) )
<=> ( ord_less_eq @ int @ V_2 @ pls ) ) )
= $true ),
inference(copy,[status(thm)],[847]) ).
thf(1548,plain,
( ( ! [V_2: $i] :
( ( ( zero_zero @ nat )
= ( number_number_of @ nat @ V_2 ) )
<=> ( ord_less_eq @ int @ V_2 @ pls ) ) )
= $true ),
inference(copy,[status(thm)],[846]) ).
thf(1549,plain,
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(copy,[status(thm)],[845]) ).
thf(1550,plain,
( ( ! [V_1: $i,K: $i,V: $i] :
( ( ( ord_less @ int @ V @ pls )
=> ( ( times_times @ nat @ ( number_number_of @ nat @ V ) @ ( times_times @ nat @ ( number_number_of @ nat @ V_1 ) @ K ) )
= ( zero_zero @ nat ) ) )
& ( ~ ( ord_less @ int @ V @ pls )
=> ( ( times_times @ nat @ ( number_number_of @ nat @ V ) @ ( times_times @ nat @ ( number_number_of @ nat @ V_1 ) @ K ) )
= ( times_times @ nat @ ( number_number_of @ nat @ ( times_times @ int @ V @ V_1 ) ) @ K ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[844]) ).
thf(1551,plain,
( ( ! [V_1: $i,V: $i] :
( ( ( ord_less @ int @ V @ pls )
=> ( ( times_times @ nat @ ( number_number_of @ nat @ V ) @ ( number_number_of @ nat @ V_1 ) )
= ( zero_zero @ nat ) ) )
& ( ~ ( ord_less @ int @ V @ pls )
=> ( ( times_times @ nat @ ( number_number_of @ nat @ V ) @ ( number_number_of @ nat @ V_1 ) )
= ( number_number_of @ nat @ ( times_times @ int @ V @ V_1 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[843]) ).
thf(1552,plain,
( ( ! [B: $i,A_1: $i,C: $i] :
( ( ord_less @ int @ A_1 @ C )
=> ( ( ord_less @ int @ B @ C )
=> ( ( ord_less_eq @ int @ A_1 @ B )
| ( ord_less_eq @ int @ B @ A_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[842]) ).
thf(1553,plain,
( ( ! [A_2: $i,B_1: $i] :
( ( zcong @ A_2 @ B_1 @ ( zero_zero @ int ) )
<=> ( ( ti @ int @ A_2 )
= ( ti @ int @ B_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[841]) ).
thf(1554,plain,
( ( ! [A_1: $i,B: $i] : ( zcong @ A_1 @ B @ ( one_one @ int ) ) )
= $true ),
inference(copy,[status(thm)],[840]) ).
thf(1555,plain,
( ( ! [C: $i,D: $i,A_1: $i,B: $i,M: $i] :
( ( zcong @ A_1 @ B @ M )
=> ( ( zcong @ C @ D @ M )
=> ( zcong @ ( times_times @ int @ A_1 @ C ) @ ( times_times @ int @ B @ D ) @ M ) ) ) )
= $true ),
inference(copy,[status(thm)],[839]) ).
thf(1556,plain,
( ( ! [K: $i,A_1: $i,B: $i,M: $i] :
( ( zcong @ A_1 @ B @ M )
=> ( zcong @ ( times_times @ int @ K @ A_1 ) @ ( times_times @ int @ K @ B ) @ M ) ) )
= $true ),
inference(copy,[status(thm)],[838]) ).
thf(1557,plain,
( ( ! [K: $i,A_1: $i,B: $i,M: $i] :
( ( zcong @ A_1 @ B @ M )
=> ( zcong @ ( times_times @ int @ A_1 @ K ) @ ( times_times @ int @ B @ K ) @ M ) ) )
= $true ),
inference(copy,[status(thm)],[837]) ).
thf(1558,plain,
( ( ! [A_1: $i,M: $i,B: $i] : ( zcong @ ( times_times @ int @ A_1 @ M ) @ ( times_times @ int @ B @ M ) @ M ) )
= $true ),
inference(copy,[status(thm)],[836]) ).
thf(1559,plain,
( ( ! [C: $i,D: $i,A_1: $i,B: $i,M: $i] :
( ( zcong @ A_1 @ B @ M )
=> ( ( zcong @ C @ D @ M )
=> ( zcong @ ( plus_plus @ int @ A_1 @ C ) @ ( plus_plus @ int @ B @ D ) @ M ) ) ) )
= $true ),
inference(copy,[status(thm)],[835]) ).
thf(1560,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [N: $i] :
( ( power_power @ X_a @ ( number_number_of @ X_a @ min ) @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ N ) )
= ( one_one @ X_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[834]) ).
thf(1561,plain,
( ( ! [B: $i,M: $i,A_1: $i] :
( ( ord_less @ int @ ( zero_zero @ int ) @ A_1 )
=> ( ( ord_less @ int @ A_1 @ M )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ B )
=> ( ( ord_less @ int @ B @ A_1 )
=> ~ ( zcong @ A_1 @ B @ M ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[833]) ).
thf(1562,plain,
( ( ! [A_2: $i,B_1: $i,Ma: $i] :
( ( zcong @ A_2 @ B_1 @ Ma )
<=> ? [K_2: $i] :
( ( ti @ int @ B_1 )
= ( plus_plus @ int @ A_2 @ ( times_times @ int @ Ma @ K_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[832]) ).
thf(1563,plain,
( ( ! [X_a: $i] :
( ( ( power @ X_a )
& ( semiring_0 @ X_a ) )
=> ! [W: $i] :
( ( ( ( number_number_of @ nat @ W )
= ( zero_zero @ nat ) )
=> ( ( power_power @ X_a @ ( zero_zero @ X_a ) @ ( number_number_of @ nat @ W ) )
= ( one_one @ X_a ) ) )
& ( ( ( number_number_of @ nat @ W )
!= ( zero_zero @ nat ) )
=> ( ( power_power @ X_a @ ( zero_zero @ X_a ) @ ( number_number_of @ nat @ W ) )
= ( zero_zero @ X_a ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[831]) ).
thf(1564,plain,
( ( quadRes @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) @ ( number_number_of @ int @ min ) )
= $true ),
inference(copy,[status(thm)],[830]) ).
thf(1565,plain,
( ( ! [J: $i,K: $i,M: $i] :
( ( ord_less @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ M )
=> ( ( zcong @ ( power_power @ int @ ( number_number_of @ int @ min ) @ J ) @ ( power_power @ int @ ( number_number_of @ int @ min ) @ K ) @ M )
=> ( ( power_power @ int @ ( number_number_of @ int @ min ) @ J )
= ( power_power @ int @ ( number_number_of @ int @ min ) @ K ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[829]) ).
thf(1566,plain,
( ( ( minus_minus @ int @ ( power_power @ int @ s @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of @ int @ min ) )
= ( plus_plus @ int @ ( power_power @ int @ s @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( one_one @ int ) ) )
= $true ),
inference(copy,[status(thm)],[828]) ).
thf(1567,plain,
( ( ~ ( quadRes @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) @ ( number_number_of @ int @ min ) )
=> ( ( legendre @ ( number_number_of @ int @ min ) @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) )
!= ( one_one @ int ) ) )
= $true ),
inference(copy,[status(thm)],[827]) ).
thf(1568,plain,
( ( ! [C: $i,D: $i,A_1: $i,B: $i,M: $i] :
( ( zcong @ A_1 @ B @ M )
=> ( ( zcong @ C @ D @ M )
=> ( zcong @ ( minus_minus @ int @ A_1 @ C ) @ ( minus_minus @ int @ B @ D ) @ M ) ) ) )
= $true ),
inference(copy,[status(thm)],[826]) ).
thf(1569,plain,
( ( ! [K: $i] :
( ( minus_minus @ int @ K @ pls )
= ( ti @ int @ K ) ) )
= $true ),
inference(copy,[status(thm)],[825]) ).
thf(1570,plain,
( ( ! [K: $i,L: $i] :
( ( minus_minus @ int @ ( bit0 @ K ) @ ( bit0 @ L ) )
= ( bit0 @ ( minus_minus @ int @ K @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[824]) ).
thf(1571,plain,
( ( ! [Z1: $i,Z2: $i,W: $i] :
( ( times_times @ int @ ( minus_minus @ int @ Z1 @ Z2 ) @ W )
= ( minus_minus @ int @ ( times_times @ int @ Z1 @ W ) @ ( times_times @ int @ Z2 @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[823]) ).
thf(1572,plain,
( ( ! [W: $i,Z1: $i,Z2: $i] :
( ( times_times @ int @ W @ ( minus_minus @ int @ Z1 @ Z2 ) )
= ( minus_minus @ int @ ( times_times @ int @ W @ Z1 ) @ ( times_times @ int @ W @ Z2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[822]) ).
thf(1573,plain,
( ( ! [K: $i,M: $i,N: $i] :
( ( dvd_dvd @ int @ K @ ( minus_minus @ int @ M @ N ) )
=> ( ( dvd_dvd @ int @ K @ N )
=> ( dvd_dvd @ int @ K @ M ) ) ) )
= $true ),
inference(copy,[status(thm)],[821]) ).
thf(1574,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [V: $i,W: $i] :
( ( number_number_of @ X_a @ ( minus_minus @ int @ V @ W ) )
= ( minus_minus @ X_a @ ( number_number_of @ X_a @ V ) @ ( number_number_of @ X_a @ W ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[820]) ).
thf(1575,plain,
( ( ! [X_b: $i] :
( ( ( number @ X_b )
& ( ring @ X_b ) )
=> ! [V: $i,B: $i,C: $i] :
( ( times_times @ X_b @ ( number_number_of @ X_b @ V ) @ ( minus_minus @ X_b @ B @ C ) )
= ( minus_minus @ X_b @ ( times_times @ X_b @ ( number_number_of @ X_b @ V ) @ B ) @ ( times_times @ X_b @ ( number_number_of @ X_b @ V ) @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[819]) ).
thf(1576,plain,
( ( ! [X_b: $i] :
( ( ( number @ X_b )
& ( ring @ X_b ) )
=> ! [A_1: $i,B: $i,V: $i] :
( ( times_times @ X_b @ ( minus_minus @ X_b @ A_1 @ B ) @ ( number_number_of @ X_b @ V ) )
= ( minus_minus @ X_b @ ( times_times @ X_b @ A_1 @ ( number_number_of @ X_b @ V ) ) @ ( times_times @ X_b @ B @ ( number_number_of @ X_b @ V ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[818]) ).
thf(1577,plain,
( ( ! [K: $i,L: $i] :
( ( minus_minus @ int @ ( bit1 @ K ) @ ( bit0 @ L ) )
= ( bit1 @ ( minus_minus @ int @ K @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[817]) ).
thf(1578,plain,
( ( ! [K: $i,L: $i] :
( ( minus_minus @ int @ ( bit1 @ K ) @ ( bit1 @ L ) )
= ( bit0 @ ( minus_minus @ int @ K @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[816]) ).
thf(1579,plain,
( ( ! [L: $i] :
( ( minus_minus @ int @ pls @ ( bit0 @ L ) )
= ( bit0 @ ( minus_minus @ int @ pls @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[815]) ).
thf(1580,plain,
( ( ! [K_1: $i,L_1: $i] :
( ( ord_less @ int @ K_1 @ L_1 )
<=> ( ord_less @ int @ ( minus_minus @ int @ K_1 @ L_1 ) @ ( zero_zero @ int ) ) ) )
= $true ),
inference(copy,[status(thm)],[814]) ).
thf(1581,plain,
( ( ! [A_1: $i,R_1: $i,B: $i,M: $i,C: $i,D: $i,N: $i] :
( ( plus_plus @ int @ ( times_times @ int @ ( minus_minus @ int @ A_1 @ ( times_times @ int @ R_1 @ B ) ) @ M ) @ ( times_times @ int @ ( minus_minus @ int @ C @ ( times_times @ int @ R_1 @ D ) ) @ N ) )
= ( minus_minus @ int @ ( plus_plus @ int @ ( times_times @ int @ A_1 @ M ) @ ( times_times @ int @ C @ N ) ) @ ( times_times @ int @ R_1 @ ( plus_plus @ int @ ( times_times @ int @ B @ M ) @ ( times_times @ int @ D @ N ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[813]) ).
thf(1582,plain,
( ( ! [A_2: $i,B_1: $i,Ma: $i] :
( ( zcong @ A_2 @ B_1 @ Ma )
<=> ( dvd_dvd @ int @ Ma @ ( minus_minus @ int @ A_2 @ B_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[812]) ).
thf(1583,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [V: $i,W: $i,C: $i] :
( ( plus_plus @ X_a @ ( number_number_of @ X_a @ V ) @ ( minus_minus @ X_a @ ( number_number_of @ X_a @ W ) @ C ) )
= ( minus_minus @ X_a @ ( number_number_of @ X_a @ ( plus_plus @ int @ V @ W ) ) @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[811]) ).
thf(1584,plain,
( ( ! [W_1: $i,Z_1: $i] :
( ( ord_less_eq @ int @ W_1 @ ( minus_minus @ int @ Z_1 @ ( one_one @ int ) ) )
<=> ( ord_less @ int @ W_1 @ Z_1 ) ) )
= $true ),
inference(copy,[status(thm)],[810]) ).
thf(1585,plain,
( ( ! [L: $i] :
( ( minus_minus @ int @ pls @ ( bit1 @ L ) )
= ( bit1 @ ( minus_minus @ int @ min @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[809]) ).
thf(1586,plain,
( ( ! [L: $i] :
( ( minus_minus @ int @ min @ ( bit1 @ L ) )
= ( bit0 @ ( minus_minus @ int @ min @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[808]) ).
thf(1587,plain,
( ( ! [L: $i] :
( ( minus_minus @ int @ min @ ( bit0 @ L ) )
= ( bit1 @ ( minus_minus @ int @ min @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[807]) ).
thf(1588,plain,
( ( ! [A_2: $i,P_1: $i] :
( ( zcong @ ( times_times @ int @ A_2 @ ( minus_minus @ int @ P_1 @ ( one_one @ int ) ) ) @ ( one_one @ int ) @ P_1 )
<=> ( zcong @ A_2 @ ( minus_minus @ int @ P_1 @ ( one_one @ int ) ) @ P_1 ) ) )
= $true ),
inference(copy,[status(thm)],[806]) ).
thf(1589,plain,
( ( ! [A_1: $i,B: $i,P: $i,Q: $i] :
( ( times_times @ int @ ( twoSqu579703163sum2sq @ ( product_Pair @ int @ int @ A_1 @ B ) ) @ ( twoSqu579703163sum2sq @ ( product_Pair @ int @ int @ P @ Q ) ) )
= ( twoSqu579703163sum2sq @ ( product_Pair @ int @ int @ ( plus_plus @ int @ ( times_times @ int @ A_1 @ P ) @ ( times_times @ int @ B @ Q ) ) @ ( minus_minus @ int @ ( times_times @ int @ A_1 @ Q ) @ ( times_times @ int @ B @ P ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[805]) ).
thf(1590,plain,
( ( ! [A_1: $i,B: $i] :
( ( times_times @ int @ ( plus_plus @ int @ A_1 @ B ) @ ( minus_minus @ int @ A_1 @ B ) )
= ( minus_minus @ int @ ( power_power @ int @ A_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[804]) ).
thf(1591,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [X_1: $i,Y_1: $i] :
( ( power_power @ X_a @ ( minus_minus @ X_a @ X_1 @ Y_1 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( minus_minus @ X_a @ ( plus_plus @ X_a @ ( power_power @ X_a @ X_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ X_a @ Y_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times @ X_a @ ( times_times @ X_a @ ( number_number_of @ X_a @ ( bit0 @ ( bit1 @ pls ) ) ) @ X_1 ) @ Y_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[803]) ).
thf(1592,plain,
( ( ! [A_1: $i,B: $i] :
( ( power_power @ int @ ( minus_minus @ int @ A_1 @ B ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ int @ ( minus_minus @ int @ ( power_power @ int @ A_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( times_times @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A_1 ) @ B ) ) @ ( power_power @ int @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[802]) ).
thf(1593,plain,
( ( ! [A_1: $i,B: $i] :
( ( power_power @ int @ ( minus_minus @ int @ A_1 @ B ) @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( minus_minus @ int @ ( plus_plus @ int @ ( minus_minus @ int @ ( power_power @ int @ A_1 @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) @ ( times_times @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit1 @ ( bit1 @ pls ) ) ) @ ( power_power @ int @ A_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ B ) ) @ ( times_times @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit1 @ ( bit1 @ pls ) ) ) @ A_1 ) @ ( power_power @ int @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ ( power_power @ int @ B @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[801]) ).
thf(1594,plain,
( ( ! [N: $i] :
( ( ( power_power @ int @ ( number_number_of @ int @ min ) @ N )
= ( one_one @ int ) )
| ( ( power_power @ int @ ( number_number_of @ int @ min ) @ N )
= ( number_number_of @ int @ min ) ) ) )
= $true ),
inference(copy,[status(thm)],[800]) ).
thf(1595,plain,
( ( ! [M: $i] :
( ( zprime @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ M ) @ ( one_one @ int ) ) )
=> ( ( legendre @ ( number_number_of @ int @ min ) @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ M ) @ ( one_one @ int ) ) )
= ( one_one @ int ) ) ) )
= $true ),
inference(copy,[status(thm)],[799]) ).
thf(1596,plain,
( ( ! [M: $i] :
( ( ord_less @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ M )
=> ~ ( zcong @ ( one_one @ int ) @ ( number_number_of @ int @ min ) @ M ) ) )
= $true ),
inference(copy,[status(thm)],[798]) ).
thf(1597,plain,
( ( ! [X_1: $i,P: $i] :
( ( ord_less @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ P )
=> ( ( zcong @ X_1 @ ( number_number_of @ int @ min ) @ P )
=> ~ ( zcong @ X_1 @ ( one_one @ int ) @ P ) ) ) )
= $true ),
inference(copy,[status(thm)],[797]) ).
thf(1598,plain,
( ( ! [N: $i,M: $i] :
( ( dvd_dvd @ nat @ N @ M )
=> ( ( M
= ( zero_zero @ nat ) )
| ( M = N )
| ( ord_less_eq @ nat @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ N ) @ M ) ) ) )
= $true ),
inference(copy,[status(thm)],[796]) ).
thf(1599,plain,
( ( ! [X_2: $i,Y_2: $i] :
( ( ( dvd_dvd @ nat @ X_2 @ Y_2 )
& ( dvd_dvd @ nat @ Y_2 @ X_2 ) )
<=> ( X_2 = Y_2 ) ) )
= $true ),
inference(copy,[status(thm)],[795]) ).
thf(1600,plain,
( ( ! [D: $i,C: $i,A_1: $i,B: $i,M: $i] :
( ( zcong @ A_1 @ B @ M )
=> ( ( ( ti @ int @ B )
= ( ti @ int @ C ) )
=> ( ( zcong @ C @ D @ M )
=> ( zcong @ A_1 @ D @ M ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[794]) ).
thf(1601,plain,
( ( ! [N: $i,M: $i] :
( ( ( M
= ( zero_zero @ nat ) )
=> ( ( times_times @ nat @ M @ N )
= ( zero_zero @ nat ) ) )
& ( ( M
!= ( zero_zero @ nat ) )
=> ( ( times_times @ nat @ M @ N )
= ( plus_plus @ nat @ N @ ( times_times @ nat @ ( minus_minus @ nat @ M @ ( one_one @ nat ) ) @ N ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[793]) ).
thf(1602,plain,
( ( ! [P: $i,M: $i] :
( ( ( M
= ( zero_zero @ nat ) )
=> ( ( power_power @ nat @ P @ M )
= ( one_one @ nat ) ) )
& ( ( M
!= ( zero_zero @ nat ) )
=> ( ( power_power @ nat @ P @ M )
= ( times_times @ nat @ P @ ( power_power @ nat @ P @ ( minus_minus @ nat @ M @ ( one_one @ nat ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[792]) ).
thf(1603,plain,
( ( ! [X_1: $i,Y_1: $i] :
( ( minus_minus @ nat @ ( power_power @ nat @ X_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ nat @ Y_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( times_times @ nat @ ( plus_plus @ nat @ X_1 @ Y_1 ) @ ( minus_minus @ nat @ X_1 @ Y_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[791]) ).
thf(1604,plain,
( ( ! [B: $i,D: $i,A_1: $i] :
( ( dvd_dvd @ nat @ D @ A_1 )
=> ( ( dvd_dvd @ nat @ D @ ( plus_plus @ nat @ A_1 @ B ) )
=> ( dvd_dvd @ nat @ D @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[790]) ).
thf(1605,plain,
( ( ! [C: $i,A_1: $i,B: $i] :
( ( dvd_dvd @ nat @ A_1 @ B )
=> ( dvd_dvd @ nat @ ( times_times @ nat @ C @ A_1 ) @ ( times_times @ nat @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[789]) ).
thf(1606,plain,
( ( ! [C: $i,A_1: $i,B: $i] :
( ( dvd_dvd @ nat @ A_1 @ B )
=> ( dvd_dvd @ nat @ ( times_times @ nat @ A_1 @ C ) @ ( times_times @ nat @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[788]) ).
thf(1607,plain,
( ( ! [M: $i] : ( zcong @ M @ ( zero_zero @ int ) @ M ) )
= $true ),
inference(copy,[status(thm)],[787]) ).
thf(1608,plain,
( ( ! [N_1: $i,Ma: $i] :
( ( ( times_times @ nat @ N_1 @ Ma )
= ( one_one @ nat ) )
<=> ( ( N_1
= ( one_one @ nat ) )
& ( Ma
= ( one_one @ nat ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[786]) ).
thf(1609,plain,
( ( ! [A_1: $i,B: $i,C: $i] :
( ( ( minus_minus @ int @ A_1 @ B )
= ( ti @ int @ C ) )
=> ( ( ti @ int @ A_1 )
= ( plus_plus @ int @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[785]) ).
thf(1610,plain,
( ( ! [C_1: $i,D_1: $i,A_2: $i,B_1: $i,Ma: $i] :
( ( zcong @ A_2 @ B_1 @ Ma )
=> ( ( zcong @ C_1 @ ( times_times @ int @ D_1 @ A_2 ) @ Ma )
<=> ( zcong @ C_1 @ ( times_times @ int @ D_1 @ B_1 ) @ Ma ) ) ) )
= $true ),
inference(copy,[status(thm)],[784]) ).
thf(1611,plain,
( ( ! [C_1: $i,D_1: $i,A_2: $i,B_1: $i,Ma: $i] :
( ( zcong @ A_2 @ B_1 @ Ma )
=> ( ( zcong @ C_1 @ ( times_times @ int @ A_2 @ D_1 ) @ Ma )
<=> ( zcong @ C_1 @ ( times_times @ int @ B_1 @ D_1 ) @ Ma ) ) ) )
= $true ),
inference(copy,[status(thm)],[783]) ).
thf(1612,plain,
( ( ! [C: $i,A_1: $i,B: $i,M: $i] :
( ( zcong @ A_1 @ B @ M )
=> ( zcong @ ( plus_plus @ int @ A_1 @ C ) @ ( plus_plus @ int @ B @ C ) @ M ) ) )
= $true ),
inference(copy,[status(thm)],[782]) ).
thf(1613,plain,
( ( ! [Ma: $i,N_1: $i] :
( ( ( power_power @ nat @ Ma @ N_1 )
= ( zero_zero @ nat ) )
<=> ( ( N_1
!= ( zero_zero @ nat ) )
& ( Ma
= ( zero_zero @ nat ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[781]) ).
thf(1614,plain,
( ( ! [N: $i,X_1: $i,Y_1: $i] :
( ( dvd_dvd @ nat @ X_1 @ Y_1 )
=> ( dvd_dvd @ nat @ ( power_power @ nat @ X_1 @ N ) @ ( power_power @ nat @ Y_1 @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[780]) ).
thf(1615,plain,
( ( ! [Z: $i,X_1: $i,Y_1: $i,M: $i] :
( ( zcong @ X_1 @ Y_1 @ M )
=> ( zcong @ ( power_power @ int @ X_1 @ Z ) @ ( power_power @ int @ Y_1 @ Z ) @ M ) ) )
= $true ),
inference(copy,[status(thm)],[779]) ).
thf(1616,plain,
( ( ! [A_1: $i,B: $i] :
( ( dvd_dvd @ nat @ A_1 @ B )
=> ( ( B
= ( zero_zero @ nat ) )
| ( ord_less_eq @ nat @ A_1 @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[778]) ).
thf(1617,plain,
( ( ! [Ma: $i,K_1: $i,N_1: $i] :
( ( dvd_dvd @ nat @ ( times_times @ nat @ Ma @ K_1 ) @ ( times_times @ nat @ N_1 @ K_1 ) )
<=> ( ( K_1
= ( zero_zero @ nat ) )
| ( dvd_dvd @ nat @ Ma @ N_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[777]) ).
thf(1618,plain,
( ( ! [M: $i,X_1: $i] :
( ( ord_less @ int @ ( zero_zero @ int ) @ X_1 )
=> ( ( ord_less @ int @ X_1 @ M )
=> ~ ( zcong @ X_1 @ ( zero_zero @ int ) @ M ) ) ) )
= $true ),
inference(copy,[status(thm)],[776]) ).
thf(1619,plain,
( ( ! [N: $i,M: $i] :
( ( dvd_dvd @ int @ N @ M )
=> ( ( ord_less_eq @ int @ M @ ( zero_zero @ int ) )
| ( ord_less_eq @ int @ N @ M ) ) ) )
= $true ),
inference(copy,[status(thm)],[775]) ).
thf(1620,plain,
( ( ! [X_1: $i,Y_1: $i,N: $i] :
( ( N
!= ( zero_zero @ nat ) )
=> ( ( dvd_dvd @ nat @ ( power_power @ nat @ X_1 @ N ) @ Y_1 )
=> ( dvd_dvd @ nat @ X_1 @ Y_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[774]) ).
thf(1621,plain,
( ( ! [A_1: $i,N: $i,B: $i] :
( ( dvd_dvd @ nat @ ( power_power @ nat @ A_1 @ N ) @ ( power_power @ nat @ B @ N ) )
=> ( ( N
!= ( zero_zero @ nat ) )
=> ( dvd_dvd @ nat @ A_1 @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[773]) ).
thf(1622,plain,
( ( ! [A_2: $i,Ma: $i] :
( ( zcong @ A_2 @ ( zero_zero @ int ) @ Ma )
<=> ( dvd_dvd @ int @ Ma @ A_2 ) ) )
= $true ),
inference(copy,[status(thm)],[772]) ).
thf(1623,plain,
( ( ! [X_2: $i,P_1: $i] :
( ( zcong @ X_2 @ ( zero_zero @ int ) @ P_1 )
<=> ( dvd_dvd @ int @ P_1 @ X_2 ) ) )
= $true ),
inference(copy,[status(thm)],[771]) ).
thf(1624,plain,
( ( ! [X_2: $i,N_1: $i] :
( ( ( power_power @ nat @ X_2 @ N_1 )
= ( one_one @ nat ) )
<=> ( ( X_2
= ( one_one @ nat ) )
| ( N_1
= ( zero_zero @ nat ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[770]) ).
thf(1625,plain,
( ( ! [M: $i,N: $i,P: $i] :
( ( zprime @ P )
=> ( ( dvd_dvd @ int @ P @ ( times_times @ int @ M @ N ) )
=> ( ( dvd_dvd @ int @ P @ M )
| ( dvd_dvd @ int @ P @ N ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[769]) ).
thf(1626,plain,
( ( ! [P: $i,Y_1: $i,N: $i] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
=> ( ( dvd_dvd @ int @ P @ Y_1 )
=> ( dvd_dvd @ int @ P @ ( power_power @ int @ Y_1 @ N ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[768]) ).
thf(1627,plain,
( ( ! [Y_1: $i,X_1: $i,P: $i] :
( ( zprime @ P )
=> ( ~ ( zcong @ X_1 @ ( zero_zero @ int ) @ P )
=> ( ~ ( zcong @ Y_1 @ ( zero_zero @ int ) @ P )
=> ~ ( zcong @ ( times_times @ int @ X_1 @ Y_1 ) @ ( zero_zero @ int ) @ P ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[767]) ).
thf(1628,plain,
( ( ! [X_1: $i,Q: $i,N: $i,R_1: $i] :
( ( X_1
= ( plus_plus @ nat @ ( times_times @ nat @ Q @ N ) @ R_1 ) )
=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ R_1 )
=> ( ( ord_less @ nat @ R_1 @ N )
=> ~ ( dvd_dvd @ nat @ N @ X_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[766]) ).
thf(1629,plain,
( ( ! [Ma: $i,X_2: $i] :
( ( quadRes @ Ma @ X_2 )
<=> ? [Y: $i] : ( zcong @ ( power_power @ int @ Y @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ X_2 @ Ma ) ) )
= $true ),
inference(copy,[status(thm)],[765]) ).
thf(1630,plain,
( ( ! [X_2: $i,Y_2: $i] :
( ( ( plus_plus @ real @ ( power_power @ real @ X_2 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ real @ Y_2 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ real ) )
<=> ( ( X_2
= ( zero_zero @ real ) )
& ( Y_2
= ( zero_zero @ real ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[764]) ).
thf(1631,plain,
( ( ( zero_zero @ real )
!= ( one_one @ real ) )
= $true ),
inference(copy,[status(thm)],[763]) ).
thf(1632,plain,
( ( ! [Z: $i] :
( ( times_times @ real @ ( one_one @ real ) @ Z )
= Z ) )
= $true ),
inference(copy,[status(thm)],[762]) ).
thf(1633,plain,
( ( ! [Z: $i,W: $i] :
( ( times_times @ real @ Z @ W )
= ( times_times @ real @ W @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[761]) ).
thf(1634,plain,
( ( ! [Z1: $i,Z2: $i,Z3: $i] :
( ( times_times @ real @ ( times_times @ real @ Z1 @ Z2 ) @ Z3 )
= ( times_times @ real @ Z1 @ ( times_times @ real @ Z2 @ Z3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[760]) ).
thf(1635,plain,
( ( ! [Z: $i,X_1: $i,Y_1: $i] :
( ( ord_less_eq @ real @ X_1 @ Y_1 )
=> ( ord_less_eq @ real @ ( plus_plus @ real @ Z @ X_1 ) @ ( plus_plus @ real @ Z @ Y_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[759]) ).
thf(1636,plain,
( ( ! [X_a: $i] :
( ( ab_group_add @ X_a )
=> ! [A_1: $i,C: $i,B: $i,D: $i] :
( ( minus_minus @ X_a @ ( plus_plus @ X_a @ A_1 @ C ) @ ( plus_plus @ X_a @ B @ D ) )
= ( plus_plus @ X_a @ ( minus_minus @ X_a @ A_1 @ B ) @ ( minus_minus @ X_a @ C @ D ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[758]) ).
thf(1637,plain,
( ( ! [A_2: $i,B_1: $i,C_1: $i] :
( ( C_1
!= ( zero_zero @ real ) )
=> ( ( ( times_times @ real @ C_1 @ A_2 )
= ( times_times @ real @ C_1 @ B_1 ) )
<=> ( A_2 = B_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[757]) ).
thf(1638,plain,
( ( ! [A_2: $i,B_1: $i,C_1: $i] :
( ( C_1
!= ( zero_zero @ real ) )
=> ( ( ( times_times @ real @ A_2 @ C_1 )
= ( times_times @ real @ B_1 @ C_1 ) )
<=> ( A_2 = B_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[756]) ).
thf(1639,plain,
( ( ! [Z1: $i,Z2: $i,W: $i] :
( ( times_times @ real @ ( plus_plus @ real @ Z1 @ Z2 ) @ W )
= ( plus_plus @ real @ ( times_times @ real @ Z1 @ W ) @ ( times_times @ real @ Z2 @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[755]) ).
thf(1640,plain,
( ( ! [X_a: $i] :
( ( ring @ X_a )
=> ! [X_1: $i,Y_1: $i,A_1: $i,B: $i] :
( ( minus_minus @ X_a @ ( times_times @ X_a @ X_1 @ Y_1 ) @ ( times_times @ X_a @ A_1 @ B ) )
= ( plus_plus @ X_a @ ( times_times @ X_a @ X_1 @ ( minus_minus @ X_a @ Y_1 @ B ) ) @ ( times_times @ X_a @ ( minus_minus @ X_a @ X_1 @ A_1 ) @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[754]) ).
thf(1641,plain,
( ( ! [X_1: $i,Y_1: $i,Z: $i] :
( ( ord_less @ real @ ( zero_zero @ real ) @ Z )
=> ( ( ord_less @ real @ X_1 @ Y_1 )
=> ( ord_less @ real @ ( times_times @ real @ Z @ X_1 ) @ ( times_times @ real @ Z @ Y_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[753]) ).
thf(1642,plain,
( ( ! [Y_1: $i,X_1: $i] :
( ( ord_less @ real @ ( zero_zero @ real ) @ X_1 )
=> ( ( ord_less @ real @ ( zero_zero @ real ) @ Y_1 )
=> ( ord_less @ real @ ( zero_zero @ real ) @ ( times_times @ real @ X_1 @ Y_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[752]) ).
thf(1643,plain,
( ( ! [X_2: $i,Y_2: $i,Z_1: $i] :
( ( ord_less @ real @ ( zero_zero @ real ) @ Z_1 )
=> ( ( ord_less @ real @ ( times_times @ real @ X_2 @ Z_1 ) @ ( times_times @ real @ Y_2 @ Z_1 ) )
<=> ( ord_less @ real @ X_2 @ Y_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[751]) ).
thf(1644,plain,
( ( ! [X_2: $i,Y_2: $i] :
( ( ( plus_plus @ real @ ( times_times @ real @ X_2 @ X_2 ) @ ( times_times @ real @ Y_2 @ Y_2 ) )
= ( zero_zero @ real ) )
<=> ( ( X_2
= ( zero_zero @ real ) )
& ( Y_2
= ( zero_zero @ real ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[750]) ).
thf(1645,plain,
( ( ! [X_a: $i] :
( ( ring_1 @ X_a )
=> ! [X_1: $i] :
( ( minus_minus @ X_a @ ( times_times @ X_a @ X_1 @ X_1 ) @ ( one_one @ X_a ) )
= ( times_times @ X_a @ ( plus_plus @ X_a @ X_1 @ ( one_one @ X_a ) ) @ ( minus_minus @ X_a @ X_1 @ ( one_one @ X_a ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[749]) ).
thf(1646,plain,
( ( ! [N: $i] : ( ord_less_eq @ real @ ( one_one @ real ) @ ( power_power @ real @ ( number_number_of @ real @ ( bit0 @ ( bit1 @ pls ) ) ) @ N ) ) )
= $true ),
inference(copy,[status(thm)],[748]) ).
thf(1647,plain,
( ( ! [B_2: $i,Q_1: $i,R_2: $i] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( times_times @ int @ B_2 @ Q_1 ) @ R_2 ) )
=> ( ( ord_less @ int @ R_2 @ B_2 )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ B_2 )
=> ( ord_less_eq @ int @ ( zero_zero @ int ) @ Q_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[747]) ).
thf(1648,plain,
( ( ! [B_2: $i,Q_1: $i,R_2: $i] :
( ( ord_less @ int @ ( plus_plus @ int @ ( times_times @ int @ B_2 @ Q_1 ) @ R_2 ) @ ( zero_zero @ int ) )
=> ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ R_2 )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ B_2 )
=> ( ord_less_eq @ int @ Q_1 @ ( zero_zero @ int ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[746]) ).
thf(1649,plain,
( ( ! [B: $i,Q_1: $i,R_2: $i,Q: $i,R_1: $i] :
( ( ord_less_eq @ int @ ( plus_plus @ int @ ( times_times @ int @ B @ Q_1 ) @ R_2 ) @ ( plus_plus @ int @ ( times_times @ int @ B @ Q ) @ R_1 ) )
=> ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ R_2 )
=> ( ( ord_less @ int @ R_2 @ B )
=> ( ( ord_less @ int @ R_1 @ B )
=> ( ord_less_eq @ int @ Q_1 @ Q ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[745]) ).
thf(1650,plain,
( ( ! [B: $i,Q: $i,R_1: $i,B_2: $i,Q_1: $i,R_2: $i] :
( ( ( plus_plus @ int @ ( times_times @ int @ B @ Q ) @ R_1 )
= ( plus_plus @ int @ ( times_times @ int @ B_2 @ Q_1 ) @ R_2 ) )
=> ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( times_times @ int @ B_2 @ Q_1 ) @ R_2 ) )
=> ( ( ord_less @ int @ R_2 @ B_2 )
=> ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ R_1 )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ B_2 )
=> ( ( ord_less_eq @ int @ B_2 @ B )
=> ( ord_less_eq @ int @ Q @ Q_1 ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[744]) ).
thf(1651,plain,
( ( ! [B: $i,Q_1: $i,R_2: $i,Q: $i,R_1: $i] :
( ( ord_less_eq @ int @ ( plus_plus @ int @ ( times_times @ int @ B @ Q_1 ) @ R_2 ) @ ( plus_plus @ int @ ( times_times @ int @ B @ Q ) @ R_1 ) )
=> ( ( ord_less_eq @ int @ R_1 @ ( zero_zero @ int ) )
=> ( ( ord_less @ int @ B @ R_1 )
=> ( ( ord_less @ int @ B @ R_2 )
=> ( ord_less_eq @ int @ Q @ Q_1 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[743]) ).
thf(1652,plain,
( ( ! [B: $i,Q: $i,R_1: $i,B_2: $i,Q_1: $i,R_2: $i] :
( ( ( plus_plus @ int @ ( times_times @ int @ B @ Q ) @ R_1 )
= ( plus_plus @ int @ ( times_times @ int @ B_2 @ Q_1 ) @ R_2 ) )
=> ( ( ord_less @ int @ ( plus_plus @ int @ ( times_times @ int @ B_2 @ Q_1 ) @ R_2 ) @ ( zero_zero @ int ) )
=> ( ( ord_less @ int @ R_1 @ B )
=> ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ R_2 )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ B_2 )
=> ( ( ord_less_eq @ int @ B_2 @ B )
=> ( ord_less_eq @ int @ Q_1 @ Q ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[742]) ).
thf(1653,plain,
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(copy,[status(thm)],[741]) ).
thf(1654,plain,
( ( ! [X_a: $i] :
( ( power @ X_a )
=> ! [M: $i,N: $i] :
( ( ( N
= ( zero_zero @ nat ) )
=> ( ( power_power @ X_a @ M @ N )
= ( one_one @ X_a ) ) )
& ( ( N
!= ( zero_zero @ nat ) )
=> ( ( power_power @ X_a @ M @ N )
= ( times_times @ X_a @ M @ ( power_power @ X_a @ M @ ( minus_minus @ nat @ N @ ( one_one @ nat ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[740]) ).
thf(1655,plain,
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( zero_zero @ int ) )
= $true ),
inference(copy,[status(thm)],[739]) ).
thf(1656,plain,
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( one_one @ int ) )
= $true ),
inference(copy,[status(thm)],[738]) ).
thf(1657,plain,
( ( ! [Y_1: $i,X_1: $i] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ X_1 )
=> ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ Y_1 )
=> ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( times_times @ int @ X_1 @ Y_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[737]) ).
thf(1658,plain,
( ( ! [Y_1: $i,X_1: $i] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ X_1 )
=> ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ Y_1 )
=> ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ X_1 @ Y_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[736]) ).
thf(1659,plain,
( ( ! [N: $i,X_1: $i] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ X_1 )
=> ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( power_power @ int @ X_1 @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[735]) ).
thf(1660,plain,
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( number_number_of @ int @ ( bit1 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(copy,[status(thm)],[734]) ).
thf(1661,plain,
( ( ! [A_1: $i,N: $i] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
=> ( ( ord_less @ real @ ( zero_zero @ real ) @ A_1 )
=> ? [R: $i] :
( ( ord_less @ real @ ( zero_zero @ real ) @ R )
& ( ( power_power @ real @ R @ N )
= A_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[733]) ).
thf(1662,plain,
( ( ! [X_a: $i] :
( ( mult_zero @ X_a )
=> ! [A_1: $i] :
( ( times_times @ X_a @ ( zero_zero @ X_a ) @ A_1 )
= ( zero_zero @ X_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[732]) ).
thf(1663,plain,
( ( ! [X_a: $i] :
( ( mult_zero @ X_a )
=> ! [A_1: $i] :
( ( times_times @ X_a @ A_1 @ ( zero_zero @ X_a ) )
= ( zero_zero @ X_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[731]) ).
thf(1664,plain,
( ( ! [X_a: $i] :
( ( ring_n68954251visors @ X_a )
=> ! [A_2: $i,B_1: $i] :
( ( ( times_times @ X_a @ A_2 @ B_1 )
= ( zero_zero @ X_a ) )
<=> ( ( ( ti @ X_a @ A_2 )
= ( zero_zero @ X_a ) )
| ( ( ti @ X_a @ B_1 )
= ( zero_zero @ X_a ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[730]) ).
thf(1665,plain,
( ( ! [X_a: $i] :
( ( no_zero_divisors @ X_a )
=> ! [B: $i,A_1: $i] :
( ( ( ti @ X_a @ A_1 )
!= ( zero_zero @ X_a ) )
=> ( ( ( ti @ X_a @ B )
!= ( zero_zero @ X_a ) )
=> ( ( times_times @ X_a @ A_1 @ B )
!= ( zero_zero @ X_a ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[729]) ).
thf(1666,plain,
( ( ! [X_a: $i] :
( ( no_zero_divisors @ X_a )
=> ! [A_1: $i,B: $i] :
( ( ( times_times @ X_a @ A_1 @ B )
= ( zero_zero @ X_a ) )
=> ( ( ( ti @ X_a @ A_1 )
= ( zero_zero @ X_a ) )
| ( ( ti @ X_a @ B )
= ( zero_zero @ X_a ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[728]) ).
thf(1667,plain,
( ( ! [X_a: $i] :
( ( zero_neq_one @ X_a )
=> ( ( one_one @ X_a )
!= ( zero_zero @ X_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[727]) ).
thf(1668,plain,
( ( ! [X_a: $i] :
( ( zero_neq_one @ X_a )
=> ( ( zero_zero @ X_a )
!= ( one_one @ X_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[726]) ).
thf(1669,plain,
( ( ! [X_a: $i] :
( ( comm_semiring @ X_a )
=> ! [A_1: $i,B: $i,C: $i] :
( ( times_times @ X_a @ ( plus_plus @ X_a @ A_1 @ B ) @ C )
= ( plus_plus @ X_a @ ( times_times @ X_a @ A_1 @ C ) @ ( times_times @ X_a @ B @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[725]) ).
thf(1670,plain,
( ( ! [X_a: $i] :
( ( semiring @ X_a )
=> ! [A_1: $i,E: $i,B: $i,C: $i] :
( ( plus_plus @ X_a @ ( times_times @ X_a @ A_1 @ E ) @ ( plus_plus @ X_a @ ( times_times @ X_a @ B @ E ) @ C ) )
= ( plus_plus @ X_a @ ( times_times @ X_a @ ( plus_plus @ X_a @ A_1 @ B ) @ E ) @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[724]) ).
thf(1671,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i,B: $i] : ( dvd_dvd @ X_a @ A_1 @ ( times_times @ X_a @ A_1 @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[723]) ).
thf(1672,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i,B: $i] : ( dvd_dvd @ X_a @ A_1 @ ( times_times @ X_a @ B @ A_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[722]) ).
thf(1673,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [C: $i,A_1: $i,B: $i] :
( ( dvd_dvd @ X_a @ A_1 @ B )
=> ( dvd_dvd @ X_a @ A_1 @ ( times_times @ X_a @ B @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[721]) ).
thf(1674,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [B: $i,A_1: $i,C: $i] :
( ( dvd_dvd @ X_a @ A_1 @ C )
=> ( dvd_dvd @ X_a @ A_1 @ ( times_times @ X_a @ B @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[720]) ).
thf(1675,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [C: $i,D: $i,A_1: $i,B: $i] :
( ( dvd_dvd @ X_a @ A_1 @ B )
=> ( ( dvd_dvd @ X_a @ C @ D )
=> ( dvd_dvd @ X_a @ ( times_times @ X_a @ A_1 @ C ) @ ( times_times @ X_a @ B @ D ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[719]) ).
thf(1676,plain,
( ( ! [X_a: $i] :
( ( dvd @ X_a )
=> ! [A_1: $i,B: $i,K: $i] :
( ( A_1
= ( times_times @ X_a @ B @ K ) )
=> ( dvd_dvd @ X_a @ B @ A_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[718]) ).
thf(1677,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i,B: $i,C: $i] :
( ( dvd_dvd @ X_a @ ( times_times @ X_a @ A_1 @ B ) @ C )
=> ( dvd_dvd @ X_a @ A_1 @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[717]) ).
thf(1678,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i,B: $i,C: $i] :
( ( dvd_dvd @ X_a @ ( times_times @ X_a @ A_1 @ B ) @ C )
=> ( dvd_dvd @ X_a @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[716]) ).
thf(1679,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [C: $i,A_1: $i,B: $i] :
( ( dvd_dvd @ X_a @ A_1 @ B )
=> ( ( dvd_dvd @ X_a @ A_1 @ C )
=> ( dvd_dvd @ X_a @ A_1 @ ( plus_plus @ X_a @ B @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[715]) ).
thf(1680,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i] : ( dvd_dvd @ X_a @ ( one_one @ X_a ) @ A_1 ) ) )
= $true ),
inference(copy,[status(thm)],[714]) ).
thf(1681,plain,
( ( ! [X_a: $i] :
( ( linordered_ring @ X_a )
=> ! [A_1: $i] : ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ ( times_times @ X_a @ A_1 @ A_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[713]) ).
thf(1682,plain,
( ( ! [X_a: $i] :
( ( linord581940658strict @ X_a )
=> ! [A_2: $i,B_1: $i] :
( ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ ( times_times @ X_a @ A_2 @ B_1 ) )
<=> ( ( ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ A_2 )
& ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ B_1 ) )
| ( ( ord_less_eq @ X_a @ A_2 @ ( zero_zero @ X_a ) )
& ( ord_less_eq @ X_a @ B_1 @ ( zero_zero @ X_a ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[712]) ).
thf(1683,plain,
( ( ! [X_a: $i] :
( ( linord581940658strict @ X_a )
=> ! [A_2: $i,B_1: $i] :
( ( ord_less_eq @ X_a @ ( times_times @ X_a @ A_2 @ B_1 ) @ ( zero_zero @ X_a ) )
<=> ( ( ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ A_2 )
& ( ord_less_eq @ X_a @ B_1 @ ( zero_zero @ X_a ) ) )
| ( ( ord_less_eq @ X_a @ A_2 @ ( zero_zero @ X_a ) )
& ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ B_1 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[711]) ).
thf(1684,plain,
( ( ! [X_a: $i] :
( ( ordere453448008miring @ X_a )
=> ! [B: $i,A_1: $i] :
( ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ A_1 )
=> ( ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ B )
=> ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ ( times_times @ X_a @ A_1 @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[710]) ).
thf(1685,plain,
( ( ! [X_a: $i] :
( ( ordere453448008miring @ X_a )
=> ! [B: $i,A_1: $i] :
( ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ A_1 )
=> ( ( ord_less_eq @ X_a @ B @ ( zero_zero @ X_a ) )
=> ( ord_less_eq @ X_a @ ( times_times @ X_a @ A_1 @ B ) @ ( zero_zero @ X_a ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[709]) ).
thf(1686,plain,
( ( ! [X_a: $i] :
( ( ordere453448008miring @ X_a )
=> ! [B: $i,A_1: $i] :
( ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ A_1 )
=> ( ( ord_less_eq @ X_a @ B @ ( zero_zero @ X_a ) )
=> ( ord_less_eq @ X_a @ ( times_times @ X_a @ B @ A_1 ) @ ( zero_zero @ X_a ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[708]) ).
thf(1687,plain,
( ( ! [X_a: $i] :
( ( ordere453448008miring @ X_a )
=> ! [B: $i,A_1: $i] :
( ( ord_less_eq @ X_a @ A_1 @ ( zero_zero @ X_a ) )
=> ( ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ B )
=> ( ord_less_eq @ X_a @ ( times_times @ X_a @ A_1 @ B ) @ ( zero_zero @ X_a ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[707]) ).
thf(1688,plain,
( ( semiri456707255roduct @ int )
= $true ),
inference(copy,[status(thm)],[706]) ).
thf(1689,plain,
( ( linord626643107strict @ int )
= $true ),
inference(copy,[status(thm)],[705]) ).
thf(1690,plain,
( ( linord219039673up_add @ int )
= $true ),
inference(copy,[status(thm)],[704]) ).
thf(1691,plain,
( ( ring_11004092258visors @ int )
= $true ),
inference(copy,[status(thm)],[703]) ).
thf(1692,plain,
( ( ordere453448008miring @ int )
= $true ),
inference(copy,[status(thm)],[702]) ).
thf(1693,plain,
( ( linord581940658strict @ int )
= $true ),
inference(copy,[status(thm)],[701]) ).
thf(1694,plain,
( ( ring_n68954251visors @ int )
= $true ),
inference(copy,[status(thm)],[700]) ).
thf(1695,plain,
( ( linordered_semidom @ int )
= $true ),
inference(copy,[status(thm)],[699]) ).
thf(1696,plain,
( ( comm_monoid_mult @ int )
= $true ),
inference(copy,[status(thm)],[698]) ).
thf(1697,plain,
( ( no_zero_divisors @ int )
= $true ),
inference(copy,[status(thm)],[697]) ).
thf(1698,plain,
( ( linordered_ring @ int )
= $true ),
inference(copy,[status(thm)],[696]) ).
thf(1699,plain,
( ( linordered_idom @ int )
= $true ),
inference(copy,[status(thm)],[695]) ).
thf(1700,plain,
( ( comm_semiring_1 @ int )
= $true ),
inference(copy,[status(thm)],[694]) ).
thf(1701,plain,
( ( comm_semiring @ int )
= $true ),
inference(copy,[status(thm)],[693]) ).
thf(1702,plain,
( ( number_semiring @ int )
= $true ),
inference(copy,[status(thm)],[692]) ).
thf(1703,plain,
( ( ab_group_add @ int )
= $true ),
inference(copy,[status(thm)],[691]) ).
thf(1704,plain,
( ( zero_neq_one @ int )
= $true ),
inference(copy,[status(thm)],[690]) ).
thf(1705,plain,
( ( linorder @ int )
= $true ),
inference(copy,[status(thm)],[689]) ).
thf(1706,plain,
( ( monoid_mult @ int )
= $true ),
inference(copy,[status(thm)],[688]) ).
thf(1707,plain,
( ( comm_ring_1 @ int )
= $true ),
inference(copy,[status(thm)],[687]) ).
thf(1708,plain,
( ( semiring_1 @ int )
= $true ),
inference(copy,[status(thm)],[686]) ).
thf(1709,plain,
( ( semiring_0 @ int )
= $true ),
inference(copy,[status(thm)],[685]) ).
thf(1710,plain,
( ( mult_zero @ int )
= $true ),
inference(copy,[status(thm)],[684]) ).
thf(1711,plain,
( ( order @ int )
= $true ),
inference(copy,[status(thm)],[683]) ).
thf(1712,plain,
( ( ring_char_0 @ int )
= $true ),
inference(copy,[status(thm)],[682]) ).
thf(1713,plain,
( ( number_ring @ int )
= $true ),
inference(copy,[status(thm)],[681]) ).
thf(1714,plain,
( ( semiring @ int )
= $true ),
inference(copy,[status(thm)],[680]) ).
thf(1715,plain,
( ( ring_1 @ int )
= $true ),
inference(copy,[status(thm)],[679]) ).
thf(1716,plain,
( ( power @ int )
= $true ),
inference(copy,[status(thm)],[678]) ).
thf(1717,plain,
( ( ring @ int )
= $true ),
inference(copy,[status(thm)],[677]) ).
thf(1718,plain,
( ( number @ int )
= $true ),
inference(copy,[status(thm)],[676]) ).
thf(1719,plain,
( ( dvd @ int )
= $true ),
inference(copy,[status(thm)],[675]) ).
thf(1720,plain,
( ( semiri456707255roduct @ nat )
= $true ),
inference(copy,[status(thm)],[674]) ).
thf(1721,plain,
( ( ordere453448008miring @ nat )
= $true ),
inference(copy,[status(thm)],[673]) ).
thf(1722,plain,
( ( linordered_semidom @ nat )
= $true ),
inference(copy,[status(thm)],[672]) ).
thf(1723,plain,
( ( comm_monoid_mult @ nat )
= $true ),
inference(copy,[status(thm)],[671]) ).
thf(1724,plain,
( ( no_zero_divisors @ nat )
= $true ),
inference(copy,[status(thm)],[670]) ).
thf(1725,plain,
( ( comm_semiring_1 @ nat )
= $true ),
inference(copy,[status(thm)],[669]) ).
thf(1726,plain,
( ( comm_semiring @ nat )
= $true ),
inference(copy,[status(thm)],[668]) ).
thf(1727,plain,
( ( number_semiring @ nat )
= $true ),
inference(copy,[status(thm)],[667]) ).
thf(1728,plain,
( ( zero_neq_one @ nat )
= $true ),
inference(copy,[status(thm)],[666]) ).
thf(1729,plain,
( ( linorder @ nat )
= $true ),
inference(copy,[status(thm)],[665]) ).
thf(1730,plain,
( ( monoid_mult @ nat )
= $true ),
inference(copy,[status(thm)],[664]) ).
thf(1731,plain,
( ( semiring_1 @ nat )
= $true ),
inference(copy,[status(thm)],[663]) ).
thf(1732,plain,
( ( semiring_0 @ nat )
= $true ),
inference(copy,[status(thm)],[662]) ).
thf(1733,plain,
( ( mult_zero @ nat )
= $true ),
inference(copy,[status(thm)],[661]) ).
thf(1734,plain,
( ( order @ nat )
= $true ),
inference(copy,[status(thm)],[660]) ).
thf(1735,plain,
( ( semiring @ nat )
= $true ),
inference(copy,[status(thm)],[659]) ).
thf(1736,plain,
( ( power @ nat )
= $true ),
inference(copy,[status(thm)],[658]) ).
thf(1737,plain,
( ( number @ nat )
= $true ),
inference(copy,[status(thm)],[657]) ).
thf(1738,plain,
( ( dvd @ nat )
= $true ),
inference(copy,[status(thm)],[656]) ).
thf(1739,plain,
( ( ~ ? [X: $i,Y: $i] :
( ( plus_plus @ int @ ( power_power @ int @ X @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ Y @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ) )
= $true ),
inference(copy,[status(thm)],[1197]) ).
thf(1740,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( zcong @ SX2 @ SX3 @ SX4 )
| ~ ( ~ ( ~ ( zcong @ SX0 @ ( times_times @ int @ SX2 @ SX1 ) @ SX4 )
| ( zcong @ SX0 @ ( times_times @ int @ SX3 @ SX1 ) @ SX4 ) )
| ~ ( ~ ( zcong @ SX0 @ ( times_times @ int @ SX3 @ SX1 ) @ SX4 )
| ( zcong @ SX0 @ ( times_times @ int @ SX2 @ SX1 ) @ SX4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1611]) ).
thf(1741,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ord_less @ int @ SX0 @ ( plus_plus @ int @ SX1 @ ( one_one @ int ) ) )
| ( ord_less @ int @ SX0 @ SX1 )
| ( ( ti @ int @ SX0 )
= ( ti @ int @ SX1 ) ) )
| ~ ( ~ ( ( ord_less @ int @ SX0 @ SX1 )
| ( ( ti @ int @ SX0 )
= ( ti @ int @ SX1 ) ) )
| ( ord_less @ int @ SX0 @ ( plus_plus @ int @ SX1 @ ( one_one @ int ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1353]) ).
thf(1742,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( semiring @ SX2 )
| ( ( plus_plus @ SX2 @ SX0 @ ( ti @ SX2 @ SX1 ) )
= ( plus_plus @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1210]) ).
thf(1743,plain,
( ( ! [SX0: $i] :
( ~ ( ordere453448008miring @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ~ ( ord_less_eq @ SX0 @ ( zero_zero @ SX0 ) @ SX2 )
| ~ ( ord_less_eq @ SX0 @ SX1 @ ( zero_zero @ SX0 ) )
| ( ord_less_eq @ SX0 @ ( times_times @ SX0 @ SX2 @ SX1 ) @ ( zero_zero @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1685]) ).
thf(1744,plain,
( ( ! [SX0: $i] :
( ~ ( monoid_mult @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ( times_times @ SX0 @ ( power_power @ SX0 @ SX1 @ SX2 ) @ SX1 )
= ( times_times @ SX0 @ SX1 @ ( power_power @ SX0 @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1492]) ).
thf(1745,plain,
( ( ! [SX0: $i] :
( ~ ( comm_semiring_1 @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ( plus_plus @ SX0 @ ( plus_plus @ SX0 @ SX1 @ SX2 ) @ SX3 )
= ( plus_plus @ SX0 @ SX1 @ ( plus_plus @ SX0 @ SX2 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1329]) ).
thf(1746,plain,
( ( ! [SX0: $i] :
( ~ ( number_semiring @ SX0 )
| ( ( plus_plus @ SX0 @ ( one_one @ SX0 ) @ ( one_one @ SX0 ) )
= ( number_number_of @ SX0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1420]) ).
thf(1747,plain,
( ( ! [SX0: $i] :
( ~ ( linordered_ring @ SX0 )
| ! [SX1: $i] : ( ord_less_eq @ SX0 @ ( zero_zero @ SX0 ) @ ( times_times @ SX0 @ SX1 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1681]) ).
thf(1748,plain,
( ( ! [SX0: $i] :
( ~ ( ordere453448008miring @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ~ ( ord_less_eq @ SX0 @ ( zero_zero @ SX0 ) @ SX2 )
| ~ ( ord_less_eq @ SX0 @ SX1 @ ( zero_zero @ SX0 ) )
| ( ord_less_eq @ SX0 @ ( times_times @ SX0 @ SX1 @ SX2 ) @ ( zero_zero @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1686]) ).
thf(1749,plain,
( ( ! [SX0: $i] :
( ~ ( linordered_idom @ SX0 )
| ! [SX1: $i,SX2: $i] :
~ ( ord_less @ SX0 @ ( plus_plus @ SX0 @ ( power_power @ SX0 @ SX1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SX0 @ SX2 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( zero_zero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1498]) ).
thf(1750,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( no_zero_divisors @ SX2 )
| ( ( times_times @ SX2 @ ( ti @ SX2 @ SX0 ) @ SX1 )
= ( times_times @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1221]) ).
thf(1751,plain,
( ( ! [SX0: $i] :
( ~ ( no_zero_divisors @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ~ ( ( ( ti @ SX0 @ SX2 )
!= ( zero_zero @ SX0 ) ) )
| ~ ( ( ( ti @ SX0 @ SX1 )
!= ( zero_zero @ SX0 ) ) )
| ( ( times_times @ SX0 @ SX2 @ SX1 )
!= ( zero_zero @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1665]) ).
thf(1752,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( ord_less_eq @ int @ min @ ( bit1 @ SX0 ) )
| ( ord_less_eq @ int @ min @ SX0 ) )
| ~ ( ~ ( ord_less_eq @ int @ min @ SX0 )
| ( ord_less_eq @ int @ min @ ( bit1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1531]) ).
thf(1753,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( dvd_dvd @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ SX1 @ ( zero_zero @ int ) )
| ( ord_less_eq @ int @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1619]) ).
thf(1754,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ( min
!= ( bit1 @ SX0 ) )
| ( min
= ( ti @ int @ SX0 ) ) )
| ~ ( ( min
!= ( ti @ int @ SX0 ) )
| ( min
= ( bit1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1515]) ).
thf(1755,plain,
( ( ! [SX0: $i] :
( ~ ( comm_semiring_1 @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ( times_times @ SX0 @ SX1 @ ( times_times @ SX0 @ SX2 @ SX3 ) )
= ( times_times @ SX0 @ ( times_times @ SX0 @ SX1 @ SX2 ) @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1324]) ).
thf(1756,plain,
( ( ! [SX0: $i] :
( ~ ( comm_semiring_1 @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( times_times @ SX0 @ ( times_times @ SX0 @ SX1 @ SX2 ) @ ( times_times @ SX0 @ SX3 @ SX4 ) )
= ( times_times @ SX0 @ SX1 @ ( times_times @ SX0 @ SX2 @ ( times_times @ SX0 @ SX3 @ SX4 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1321]) ).
thf(1757,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ord_less @ int @ ( number_number_of @ int @ SX0 ) @ ( number_number_of @ int @ SX1 ) )
| ( ord_less @ int @ SX0 @ SX1 ) )
| ~ ( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ int @ ( number_number_of @ int @ SX0 ) @ ( number_number_of @ int @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1301]) ).
thf(1758,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( dvd_dvd @ nat @ SX0 @ SX1 )
| ( SX1
= ( zero_zero @ nat ) )
| ( ord_less_eq @ nat @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1616]) ).
thf(1759,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( ab_group_add @ SX2 )
| ( ( ti @ SX2 @ ( plus_plus @ SX2 @ SX0 @ SX1 ) )
= ( plus_plus @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1214]) ).
thf(1760,plain,
( ( ! [SX0: $i] :
( ~ ( comm_semiring_1 @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ( plus_plus @ SX0 @ SX1 @ ( plus_plus @ SX0 @ SX2 @ SX3 ) )
= ( plus_plus @ SX0 @ SX2 @ ( plus_plus @ SX0 @ SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1331]) ).
thf(1761,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( ord_less_eq @ int @ SX1 @ SX2 )
| ( ord_less_eq @ int @ ( plus_plus @ int @ SX0 @ SX1 ) @ ( plus_plus @ int @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1304]) ).
thf(1762,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( zcong @ SX1 @ ( zero_zero @ int ) @ SX2 )
| ~ ( zcong @ ( power_power @ int @ SX0 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SX1 @ SX2 )
| ~ ( dvd_dvd @ int @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1507]) ).
thf(1763,plain,
( ( ! [SX0: $i] :
( ~ ( linordered_semidom @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ~ ( ord_less @ SX0 @ ( zero_zero @ SX0 ) @ SX2 )
| ~ ( ord_less @ SX0 @ SX2 @ ( one_one @ SX0 ) )
| ( ord_less @ SX0 @ ( times_times @ SX0 @ SX2 @ ( power_power @ SX0 @ SX2 @ SX1 ) ) @ ( power_power @ SX0 @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1473]) ).
thf(1764,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( quadRes @ ( ti @ int @ SX0 ) @ SX1 )
| ( quadRes @ SX0 @ SX1 ) )
| ~ ( ~ ( quadRes @ SX0 @ SX1 )
| ( quadRes @ ( ti @ int @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1246]) ).
thf(1765,plain,
( ( ( zero_zero @ int )
!= ( one_one @ int ) )
= $true ),
inference(unfold_def,[status(thm)],[1447]) ).
thf(1766,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( semiring @ SX2 )
| ( ( times_times @ SX2 @ SX0 @ ( ti @ SX2 @ SX1 ) )
= ( times_times @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1219]) ).
thf(1767,plain,
( ( ! [SX0: $i] :
( ~ ( semiring_1 @ SX0 )
| ( ( power_power @ SX0 @ ( one_one @ SX0 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( one_one @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1266]) ).
thf(1768,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ( ( bit1 @ SX0 )
!= min )
| ( ( ti @ int @ SX0 )
= min ) )
| ~ ( ( ( ti @ int @ SX0 )
!= min )
| ( ( bit1 @ SX0 )
= min ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1514]) ).
thf(1769,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( power @ SX2 )
| ( ( times_times @ SX2 @ SX0 @ ( ti @ SX2 @ SX1 ) )
= ( times_times @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1228]) ).
thf(1770,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( zcong @ SX2 @ SX3 @ SX4 )
| ( ( ti @ int @ SX3 )
!= ( ti @ int @ SX1 ) )
| ~ ( zcong @ SX1 @ SX0 @ SX4 )
| ( zcong @ SX2 @ SX0 @ SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1600]) ).
thf(1771,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( dvd_dvd @ int @ ( times_times @ int @ SX0 @ SX1 ) @ ( times_times @ int @ SX0 @ SX2 ) )
| ~ ( ( ( ti @ int @ SX0 )
!= ( zero_zero @ int ) ) )
| ( dvd_dvd @ int @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1436]) ).
thf(1772,plain,
( ( ! [SX0: $i] :
( ~ ( power @ SX0 )
| ! [SX1: $i] :
( ( power_power @ SX0 @ SX1 @ ( zero_zero @ nat ) )
= ( one_one @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1538]) ).
thf(1773,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( twoSqu420862341sum2sq @ SX1 )
| ~ ( twoSqu420862341sum2sq @ SX0 )
| ( twoSqu420862341sum2sq @ ( times_times @ int @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1318]) ).
thf(1774,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit0 @ SX0 ) @ pls )
| ( ord_less_eq @ int @ SX0 @ pls ) )
| ~ ( ~ ( ord_less_eq @ int @ SX0 @ pls )
| ( ord_less_eq @ int @ ( bit0 @ SX0 ) @ pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1351]) ).
thf(1775,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SX1 )
| ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( power_power @ int @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1659]) ).
thf(1776,plain,
( ( ! [SX0: $i] :
( ~ ( zero_neq_one @ SX0 )
| ( ( ti @ SX0 @ ( one_one @ SX0 ) )
= ( one_one @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1207]) ).
thf(1777,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less @ int @ SX0 @ SX1 ) )
| ~ ( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1345]) ).
thf(1778,plain,
( ( ! [SX0: $i] :
( ~ ( semiring_1 @ SX0 )
| ( ( power_power @ SX0 @ ( zero_zero @ SX0 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1486]) ).
thf(1779,plain,
( ( ! [SX0: $i] :
( ~ ( linordered_semidom @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ~ ( ord_less_eq @ nat @ SX2 @ SX3 )
| ~ ( ord_less_eq @ SX0 @ ( zero_zero @ SX0 ) @ SX1 )
| ~ ( ord_less_eq @ SX0 @ SX1 @ ( one_one @ SX0 ) )
| ( ord_less_eq @ SX0 @ ( power_power @ SX0 @ SX1 @ SX3 ) @ ( power_power @ SX0 @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1456]) ).
thf(1780,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( dvd_dvd @ nat @ SX1 @ SX2 )
| ( dvd_dvd @ nat @ ( times_times @ nat @ SX0 @ SX1 ) @ ( times_times @ nat @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1605]) ).
thf(1781,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( zprime @ SX2 )
| ~ ( dvd_dvd @ int @ SX2 @ ( power_power @ int @ SX0 @ SX1 ) )
| ( dvd_dvd @ int @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1461]) ).
thf(1782,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( number_ring @ SX0 )
| ~ ( linordered_idom @ SX0 ) )
| ! [SX1: $i] :
~ ( ~ ( ~ ( ord_less @ SX0 @ ( one_one @ SX0 ) @ ( number_number_of @ SX0 @ SX1 ) )
| ( ord_less @ int @ ( bit1 @ pls ) @ SX1 ) )
| ~ ( ~ ( ord_less @ int @ ( bit1 @ pls ) @ SX1 )
| ( ord_less @ SX0 @ ( one_one @ SX0 ) @ ( number_number_of @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1356]) ).
thf(1783,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( ord_less_eq @ real @ SX1 @ SX2 )
| ( ord_less_eq @ real @ ( plus_plus @ real @ SX0 @ SX1 ) @ ( plus_plus @ real @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1635]) ).
thf(1784,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq @ int @ SX0 @ SX1 ) )
| ~ ( ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1294]) ).
thf(1785,plain,
( ( ~ ( ord_less @ int @ ( one_one @ int ) @ t )
| ~ ! [SX0: $i] :
~ ~ ! [SX1: $i] :
( ( plus_plus @ int @ ( power_power @ int @ SX0 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ SX1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1256]) ).
thf(1786,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( number_ring @ SX0 )
| ~ ( linordered_idom @ SX0 ) )
| ! [SX1: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SX0 @ ( number_number_of @ SX0 @ SX1 ) @ ( one_one @ SX0 ) )
| ( ord_less_eq @ int @ SX1 @ ( bit1 @ pls ) ) )
| ~ ( ~ ( ord_less_eq @ int @ SX1 @ ( bit1 @ pls ) )
| ( ord_less_eq @ SX0 @ ( number_number_of @ SX0 @ SX1 ) @ ( one_one @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1357]) ).
thf(1787,plain,
( ( ! [SX0: $i] :
( ~ ( comm_semiring_1 @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( dvd_dvd @ SX0 @ SX3 @ SX4 )
| ~ ( dvd_dvd @ SX0 @ SX1 @ SX2 )
| ( dvd_dvd @ SX0 @ ( times_times @ SX0 @ SX3 @ SX1 ) @ ( times_times @ SX0 @ SX4 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1675]) ).
thf(1788,plain,
( ( ! [SX0: $i] :
( ~ ( ab_group_add @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( minus_minus @ SX0 @ ( plus_plus @ SX0 @ SX1 @ SX2 ) @ ( plus_plus @ SX0 @ SX3 @ SX4 ) )
= ( plus_plus @ SX0 @ ( minus_minus @ SX0 @ SX1 @ SX3 ) @ ( minus_minus @ SX0 @ SX2 @ SX4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1636]) ).
thf(1789,plain,
( ( ! [SX0: $i] :
( ~ ( number_semiring @ SX0 )
| ! [SX1: $i] :
( ( times_times @ SX0 @ SX1 @ ( number_number_of @ SX0 @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ SX0 @ SX1 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1418]) ).
thf(1790,plain,
( ( ! [SX0: $i] :
( ~ ( number_ring @ SX0 )
| ( ( plus_plus @ SX0 @ ( one_one @ SX0 ) @ ( one_one @ SX0 ) )
= ( number_number_of @ SX0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1272]) ).
thf(1791,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ( ( number_number_of @ nat @ SX0 )
!= ( zero_zero @ nat ) )
| ( ord_less_eq @ int @ SX0 @ pls ) )
| ~ ( ~ ( ord_less_eq @ int @ SX0 @ pls )
| ( ( number_number_of @ nat @ SX0 )
= ( zero_zero @ nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1547]) ).
thf(1792,plain,
( ( ! [SX0: $i] :
( ~ ( number_semiring @ SX0 )
| ! [SX1: $i] :
( ( times_times @ SX0 @ ( number_number_of @ SX0 @ ( bit0 @ ( bit1 @ pls ) ) ) @ SX1 )
= ( plus_plus @ SX0 @ SX1 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1416]) ).
thf(1793,plain,
( ( ! [SX0: $i] :
( ~ ( comm_semiring_1 @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ( times_times @ SX0 @ ( times_times @ SX0 @ SX1 @ SX2 ) @ SX3 )
= ( times_times @ SX0 @ ( times_times @ SX0 @ SX1 @ SX3 ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1322]) ).
thf(1794,plain,
( ( ! [SX0: $i] :
( ~ ( comm_semiring @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ( times_times @ SX0 @ ( plus_plus @ SX0 @ SX1 @ SX2 ) @ SX3 )
= ( plus_plus @ SX0 @ ( times_times @ SX0 @ SX1 @ SX3 ) @ ( times_times @ SX0 @ SX2 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1669]) ).
thf(1795,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( ord_less_eq @ int @ ( plus_plus @ int @ ( times_times @ int @ SX0 @ SX1 ) @ SX2 ) @ ( plus_plus @ int @ ( times_times @ int @ SX0 @ SX3 ) @ SX4 ) )
| ~ ( ord_less_eq @ int @ SX4 @ ( zero_zero @ int ) )
| ~ ( ord_less @ int @ SX0 @ SX4 )
| ~ ( ord_less @ int @ SX0 @ SX2 )
| ( ord_less_eq @ int @ SX3 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1651]) ).
thf(1796,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( bit1 @ SX0 )
!= ( bit0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1369]) ).
thf(1797,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( number_ring @ SX0 )
| ~ ( linordered_idom @ SX0 ) )
| ! [SX1: $i] :
~ ( ~ ( ~ ( ord_less @ SX0 @ ( number_number_of @ SX0 @ SX1 ) @ ( one_one @ SX0 ) )
| ( ord_less @ int @ SX1 @ ( bit1 @ pls ) ) )
| ~ ( ~ ( ord_less @ int @ SX1 @ ( bit1 @ pls ) )
| ( ord_less @ SX0 @ ( number_number_of @ SX0 @ SX1 ) @ ( one_one @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1355]) ).
thf(1798,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ord_less_eq @ nat @ ( number_number_of @ nat @ SX0 ) @ ( number_number_of @ nat @ SX1 ) )
| ~ ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ SX0 @ pls ) )
| ~ ( ~ ( ~ ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ SX0 @ pls ) )
| ( ord_less_eq @ nat @ ( number_number_of @ nat @ SX0 ) @ ( number_number_of @ nat @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1479]) ).
thf(1799,plain,
( ( ! [SX0: $i] :
( ~ ( comm_semiring_1 @ SX0 )
| ! [SX1: $i] :
( ( power_power @ SX0 @ SX1 @ ( one_one @ nat ) )
= ( ti @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1281]) ).
thf(1800,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( zcong @ SX0 @ SX1 @ SX2 )
| ( dvd_dvd @ int @ SX2 @ ( minus_minus @ int @ SX0 @ SX1 ) ) )
| ~ ( ~ ( dvd_dvd @ int @ SX2 @ ( minus_minus @ int @ SX0 @ SX1 ) )
| ( zcong @ SX0 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1582]) ).
thf(1801,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ord_less_eq @ int @ ( number_number_of @ int @ SX0 ) @ ( number_number_of @ int @ SX1 ) )
| ( ord_less_eq @ int @ SX0 @ SX1 ) )
| ~ ( ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ ( number_number_of @ int @ SX0 ) @ ( number_number_of @ int @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1302]) ).
thf(1802,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( number @ SX0 )
| ~ ( ring @ SX0 ) )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ( times_times @ SX0 @ ( number_number_of @ SX0 @ SX1 ) @ ( minus_minus @ SX0 @ SX2 @ SX3 ) )
= ( minus_minus @ SX0 @ ( times_times @ SX0 @ ( number_number_of @ SX0 @ SX1 ) @ SX2 ) @ ( times_times @ SX0 @ ( number_number_of @ SX0 @ SX1 ) @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1575]) ).
thf(1803,plain,
( ( ! [SX0: $i] :
( ~ ( monoid_mult @ SX0 )
| ! [SX1: $i] :
( ( power_power @ SX0 @ SX1 @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( times_times @ SX0 @ ( times_times @ SX0 @ SX1 @ SX1 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1414]) ).
thf(1804,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ ( plus_plus @ int @ SX0 @ ( one_one @ int ) ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1314]) ).
thf(1805,plain,
( ( ! [SX0: $i] :
( ~ ( linordered_semidom @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ~ ( ord_less @ SX0 @ ( one_one @ SX0 ) @ SX2 )
| ( ord_less @ SX0 @ ( one_one @ SX0 ) @ ( times_times @ SX0 @ SX2 @ ( power_power @ SX0 @ SX2 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1427]) ).
thf(1806,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( ( power_power @ nat @ SX0 @ SX1 )
!= ( zero_zero @ nat ) )
| ~ ( ~ ( ( SX1
!= ( zero_zero @ nat ) ) )
| ( SX0
!= ( zero_zero @ nat ) ) ) )
| ~ ( ~ ~ ( ~ ( ( SX1
!= ( zero_zero @ nat ) ) )
| ( SX0
!= ( zero_zero @ nat ) ) )
| ( ( power_power @ nat @ SX0 @ SX1 )
= ( zero_zero @ nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1613]) ).
thf(1807,plain,
( ( ! [SX0: $i] :
( ~ ( number_ring @ SX0 )
| ! [SX1: $i] :
( ( times_times @ SX0 @ SX1 @ ( number_number_of @ SX0 @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ SX0 @ SX1 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1419]) ).
thf(1808,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( dvd_dvd @ int @ SX0 @ ( plus_plus @ int @ SX1 @ ( times_times @ int @ SX0 @ SX2 ) ) )
| ( dvd_dvd @ int @ SX0 @ SX1 ) )
| ~ ( ~ ( dvd_dvd @ int @ SX0 @ SX1 )
| ( dvd_dvd @ int @ SX0 @ ( plus_plus @ int @ SX1 @ ( times_times @ int @ SX0 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1454]) ).
thf(1809,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SX0 ) @ min )
| ( ord_less @ int @ SX0 @ min ) )
| ~ ( ~ ( ord_less @ int @ SX0 @ min )
| ( ord_less @ int @ ( bit1 @ SX0 ) @ min ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1524]) ).
thf(1810,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ SX0 @ SX1 ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ SX0 )
| ( SX1
= ( zero_zero @ nat ) ) )
| ~ ( ~ ( ( ord_less @ nat @ ( zero_zero @ nat ) @ SX0 )
| ( SX1
= ( zero_zero @ nat ) ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1510]) ).
thf(1811,plain,
( ( ! [SX0: $i] :
( ( bit0 @ SX0 )
!= min ) )
= $true ),
inference(unfold_def,[status(thm)],[1519]) ).
thf(1812,plain,
( ( ! [SX0: $i] :
( ~ ( number_ring @ SX0 )
| ! [SX1: $i] :
( ( plus_plus @ SX0 @ ( one_one @ SX0 ) @ ( number_number_of @ SX0 @ SX1 ) )
= ( number_number_of @ SX0 @ ( plus_plus @ int @ ( bit1 @ pls ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1270]) ).
thf(1813,plain,
( ( ! [SX0: $i] :
( ~ ( comm_semiring_1 @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ( plus_plus @ SX0 @ ( times_times @ SX0 @ SX1 @ SX2 ) @ ( times_times @ SX0 @ SX3 @ SX2 ) )
= ( times_times @ SX0 @ ( plus_plus @ SX0 @ SX1 @ SX3 ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1360]) ).
thf(1814,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ~ ( ~ ( dvd_dvd @ nat @ SX0 @ SX1 )
| ~ ( dvd_dvd @ nat @ SX1 @ SX0 ) )
| ( SX0 = SX1 ) )
| ~ ( ( SX0 != SX1 )
| ~ ( ~ ( dvd_dvd @ nat @ SX0 @ SX1 )
| ~ ( dvd_dvd @ nat @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1599]) ).
thf(1815,plain,
( ( ! [SX0: $i] :
( ~ ( ordere453448008miring @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ~ ( ord_less_eq @ SX0 @ ( zero_zero @ SX0 ) @ SX2 )
| ~ ( ord_less_eq @ SX0 @ ( zero_zero @ SX0 ) @ SX1 )
| ( ord_less_eq @ SX0 @ ( zero_zero @ SX0 ) @ ( times_times @ SX0 @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1684]) ).
thf(1816,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ SX1 )
| ~ ( ord_less @ real @ ( zero_zero @ real ) @ SX0 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( ord_less @ real @ ( zero_zero @ real ) @ SX2 )
| ( ( power_power @ real @ SX2 @ SX1 )
!= SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1661]) ).
thf(1817,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( zcong @ SX1 @ SX2 @ SX3 )
| ( zcong @ ( times_times @ int @ SX0 @ SX1 ) @ ( times_times @ int @ SX0 @ SX2 ) @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1556]) ).
thf(1818,plain,
( ( ! [SX0: $i] :
( ~ ( linordered_semidom @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ~ ( ord_less @ SX0 @ ( one_one @ SX0 ) @ SX3 )
| ~ ( ~ ( ~ ( ord_less @ SX0 @ ( power_power @ SX0 @ SX3 @ SX1 ) @ ( power_power @ SX0 @ SX3 @ SX2 ) )
| ( ord_less @ nat @ SX1 @ SX2 ) )
| ~ ( ~ ( ord_less @ nat @ SX1 @ SX2 )
| ( ord_less @ SX0 @ ( power_power @ SX0 @ SX3 @ SX1 ) @ ( power_power @ SX0 @ SX3 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1503]) ).
thf(1819,plain,
( ( ! [SX0: $i] :
( ~ ( comm_semiring_1 @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ( power_power @ SX0 @ SX1 @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SX2 ) )
= ( times_times @ SX0 @ ( power_power @ SX0 @ SX1 @ SX2 ) @ ( power_power @ SX0 @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1269]) ).
thf(1820,plain,
( ( ! [SX0: $i] :
( ~ ( comm_semiring_1 @ SX0 )
| ! [SX1: $i] :
( ( plus_plus @ SX0 @ SX1 @ ( zero_zero @ SX0 ) )
= ( ti @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1443]) ).
thf(1821,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( dvd_dvd @ nat @ SX1 @ SX2 )
| ( dvd_dvd @ nat @ ( times_times @ nat @ SX1 @ SX0 ) @ ( times_times @ nat @ SX2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1606]) ).
thf(1822,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less @ int @ SX0 @ SX1 ) )
| ~ ( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1310]) ).
thf(1823,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ord_less @ int @ SX0 @ ( plus_plus @ int @ SX1 @ ( one_one @ int ) ) )
| ( ord_less_eq @ int @ SX0 @ SX1 ) )
| ~ ( ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ( ord_less @ int @ SX0 @ ( plus_plus @ int @ SX1 @ ( one_one @ int ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1316]) ).
thf(1824,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( ord_less @ int @ ( plus_plus @ int @ ( times_times @ int @ SX0 @ SX1 ) @ SX2 ) @ ( zero_zero @ int ) )
| ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SX2 )
| ~ ( ord_less @ int @ ( zero_zero @ int ) @ SX0 )
| ( ord_less_eq @ int @ SX1 @ ( zero_zero @ int ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1648]) ).
thf(1825,plain,
( ( pls != min )
= $true ),
inference(unfold_def,[status(thm)],[1517]) ).
thf(1826,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( bit0 @ SX0 )
!= ( bit1 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1370]) ).
thf(1827,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( zcong @ SX0 @ SX1 @ ( ti @ int @ SX2 ) )
| ( zcong @ SX0 @ SX1 @ SX2 ) )
| ~ ( ~ ( zcong @ SX0 @ SX1 @ SX2 )
| ( zcong @ SX0 @ SX1 @ ( ti @ int @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1232]) ).
thf(1828,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( dvd_dvd @ int @ SX3 @ SX4 )
| ~ ( ~ ( ~ ( dvd_dvd @ int @ SX3 @ ( plus_plus @ int @ SX1 @ SX2 ) )
| ( dvd_dvd @ int @ SX3 @ ( plus_plus @ int @ ( plus_plus @ int @ SX1 @ ( times_times @ int @ SX0 @ SX4 ) ) @ SX2 ) ) )
| ~ ( ~ ( dvd_dvd @ int @ SX3 @ ( plus_plus @ int @ ( plus_plus @ int @ SX1 @ ( times_times @ int @ SX0 @ SX4 ) ) @ SX2 ) )
| ( dvd_dvd @ int @ SX3 @ ( plus_plus @ int @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1455]) ).
thf(1829,plain,
( ( ! [SX0: $i] :
( ~ ( number_ring @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ( plus_plus @ SX0 @ ( number_number_of @ SX0 @ SX1 ) @ ( plus_plus @ SX0 @ ( number_number_of @ SX0 @ SX2 ) @ SX3 ) )
= ( plus_plus @ SX0 @ ( number_number_of @ SX0 @ ( plus_plus @ int @ SX1 @ SX2 ) ) @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1399]) ).
thf(1830,plain,
( ( ! [SX0: $i] :
( ~ ( linordered_idom @ SX0 )
| ! [SX1: $i,SX2: $i] : ( ord_less_eq @ SX0 @ ( zero_zero @ SX0 ) @ ( power_power @ SX0 @ SX1 @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1499]) ).
thf(1831,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( zcong @ SX2 @ SX3 @ SX4 )
| ~ ( zcong @ SX0 @ SX1 @ SX4 )
| ( zcong @ ( minus_minus @ int @ SX2 @ SX0 ) @ ( minus_minus @ int @ SX3 @ SX1 ) @ SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1568]) ).
thf(1832,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( number @ SX0 )
| ~ ( semiring @ SX0 ) )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ( times_times @ SX0 @ ( plus_plus @ SX0 @ SX1 @ SX2 ) @ ( number_number_of @ SX0 @ SX3 ) )
= ( plus_plus @ SX0 @ ( times_times @ SX0 @ SX1 @ ( number_number_of @ SX0 @ SX3 ) ) @ ( times_times @ SX0 @ SX2 @ ( number_number_of @ SX0 @ SX3 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1389]) ).
thf(1833,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( ( plus_plus @ real @ ( power_power @ real @ SX0 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ real @ SX1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ real ) )
| ~ ( ( SX0
!= ( zero_zero @ real ) )
| ( SX1
!= ( zero_zero @ real ) ) ) )
| ~ ( ~ ~ ( ( SX0
!= ( zero_zero @ real ) )
| ( SX1
!= ( zero_zero @ real ) ) )
| ( ( plus_plus @ real @ ( power_power @ real @ SX0 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ real @ SX1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ real ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1630]) ).
thf(1834,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( dvd_dvd @ nat @ ( power_power @ nat @ SX0 @ SX1 ) @ ( power_power @ nat @ SX0 @ SX2 ) )
| ~ ( ord_less @ nat @ ( one_one @ nat ) @ SX0 )
| ( ord_less_eq @ nat @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1536]) ).
thf(1835,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( ord_less_eq @ int @ pls @ ( bit0 @ SX0 ) )
| ( ord_less_eq @ int @ pls @ SX0 ) )
| ~ ( ~ ( ord_less_eq @ int @ pls @ SX0 )
| ( ord_less_eq @ int @ pls @ ( bit0 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1352]) ).
thf(1836,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ int @ ( minus_minus @ int @ SX0 @ SX1 ) @ ( zero_zero @ int ) ) )
| ~ ( ~ ( ord_less @ int @ ( minus_minus @ int @ SX0 @ SX1 ) @ ( zero_zero @ int ) )
| ( ord_less @ int @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1580]) ).
thf(1837,plain,
( ( ! [SX0: $i] :
( ~ ( number_ring @ SX0 )
| ! [SX1: $i] :
( ( power_power @ SX0 @ ( number_number_of @ SX0 @ min ) @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SX1 ) )
= ( one_one @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1560]) ).
thf(1838,plain,
( ( ! [SX0: $i] :
( ~ ( ring @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( minus_minus @ SX0 @ ( times_times @ SX0 @ SX1 @ SX2 ) @ ( times_times @ SX0 @ SX3 @ SX4 ) )
= ( plus_plus @ SX0 @ ( times_times @ SX0 @ SX1 @ ( minus_minus @ SX0 @ SX2 @ SX4 ) ) @ ( times_times @ SX0 @ ( minus_minus @ SX0 @ SX1 @ SX3 ) @ SX4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1640]) ).
thf(1839,plain,
( ( ! [SX0: $i] :
( ~ ( semiri456707255roduct @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
~ ( ~ ( ~ ~ ( ~ ( ( ( ti @ SX0 @ SX3 )
!= ( ti @ SX0 @ SX4 ) ) )
| ~ ( ( ( ti @ SX0 @ SX1 )
!= ( ti @ SX0 @ SX2 ) ) ) )
| ( ( plus_plus @ SX0 @ ( times_times @ SX0 @ SX3 @ SX1 ) @ ( times_times @ SX0 @ SX4 @ SX2 ) )
!= ( plus_plus @ SX0 @ ( times_times @ SX0 @ SX3 @ SX2 ) @ ( times_times @ SX0 @ SX4 @ SX1 ) ) ) )
| ~ ( ~ ( ( ( plus_plus @ SX0 @ ( times_times @ SX0 @ SX3 @ SX1 ) @ ( times_times @ SX0 @ SX4 @ SX2 ) )
!= ( plus_plus @ SX0 @ ( times_times @ SX0 @ SX3 @ SX2 ) @ ( times_times @ SX0 @ SX4 @ SX1 ) ) ) )
| ~ ( ~ ( ( ( ti @ SX0 @ SX3 )
!= ( ti @ SX0 @ SX4 ) ) )
| ~ ( ( ( ti @ SX0 @ SX1 )
!= ( ti @ SX0 @ SX2 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1362]) ).
thf(1840,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( number @ SX1 )
| ( ( ti @ SX1 @ ( number_number_of @ SX1 @ SX0 ) )
= ( number_number_of @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1236]) ).
thf(1841,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( ord_less @ int @ pls @ ( bit0 @ SX0 ) )
| ( ord_less @ int @ pls @ SX0 ) )
| ~ ( ~ ( ord_less @ int @ pls @ SX0 )
| ( ord_less @ int @ pls @ ( bit0 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1347]) ).
thf(1842,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ ( zero_zero @ int ) @ SX1 )
| ~ ( ord_less @ int @ SX1 @ SX0 )
| ~ ( dvd_dvd @ int @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1435]) ).
thf(1843,plain,
( ( ! [SX0: $i] :
( ~ ( linordered_semidom @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ~ ( ord_less @ SX0 @ ( one_one @ SX0 ) @ SX3 )
| ~ ( ord_less @ SX0 @ ( power_power @ SX0 @ SX3 @ SX1 ) @ ( power_power @ SX0 @ SX3 @ SX2 ) )
| ( ord_less @ nat @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1504]) ).
thf(1844,plain,
( ( ! [SX0: $i] :
( ~ ( dvd @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ( SX1
!= ( times_times @ SX0 @ SX2 @ SX3 ) )
| ( dvd_dvd @ SX0 @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1676]) ).
thf(1845,plain,
( ( ! [SX0: $i] :
( min
!= ( bit0 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1520]) ).
thf(1846,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less @ int @ SX0 @ SX1 ) )
| ~ ( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1291]) ).
thf(1847,plain,
( ( ! [SX0: $i] :
( ~ ( number_ring @ SX0 )
| ( ( number_number_of @ SX0 @ pls )
= ( zero_zero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1463]) ).
thf(1848,plain,
( ( ! [SX0: $i] :
( ~ ( comm_semiring_1 @ SX0 )
| ! [SX1: $i] :
( ( times_times @ SX0 @ SX1 @ ( one_one @ SX0 ) )
= ( ti @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1364]) ).
thf(1849,plain,
( ( ! [SX0: $i] :
( ~ ( comm_semiring_1 @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ( times_times @ SX0 @ ( power_power @ SX0 @ SX1 @ SX2 ) @ ( power_power @ SX0 @ SX1 @ SX3 ) )
= ( power_power @ SX0 @ SX1 @ ( plus_plus @ nat @ SX2 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1286]) ).
thf(1850,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less @ int @ SX0 @ SX1 ) )
| ~ ( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1296]) ).
thf(1851,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ord_less @ int @ SX0 @ SX1 )
| ~ ( ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ~ ( ( ( ti @ int @ SX0 )
!= ( ti @ int @ SX1 ) ) ) ) )
| ~ ( ~ ~ ( ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ~ ( ( ( ti @ int @ SX0 )
!= ( ti @ int @ SX1 ) ) ) )
| ( ord_less @ int @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1276]) ).
thf(1852,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( number @ SX1 )
| ( ( number_number_of @ SX1 @ ( ti @ int @ SX0 ) )
= ( number_number_of @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1235]) ).
thf(1853,plain,
( ( ! [SX0: $i] :
( ~ ( linord219039673up_add @ SX0 )
| ! [SX1: $i] :
~ ( ~ ( ( ( plus_plus @ SX0 @ SX1 @ SX1 )
!= ( zero_zero @ SX0 ) )
| ( ( ti @ SX0 @ SX1 )
= ( zero_zero @ SX0 ) ) )
| ~ ( ( ( ti @ SX0 @ SX1 )
!= ( zero_zero @ SX0 ) )
| ( ( plus_plus @ SX0 @ SX1 @ SX1 )
= ( zero_zero @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1445]) ).
thf(1854,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( ord_less @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ SX2 )
| ~ ( zcong @ ( power_power @ int @ ( number_number_of @ int @ min ) @ SX0 ) @ ( power_power @ int @ ( number_number_of @ int @ min ) @ SX1 ) @ SX2 )
| ( ( power_power @ int @ ( number_number_of @ int @ min ) @ SX0 )
= ( power_power @ int @ ( number_number_of @ int @ min ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1565]) ).
thf(1855,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( dvd_dvd @ nat @ ( times_times @ nat @ SX0 @ SX1 ) @ ( times_times @ nat @ SX2 @ SX1 ) )
| ( SX1
= ( zero_zero @ nat ) )
| ( dvd_dvd @ nat @ SX0 @ SX2 ) )
| ~ ( ~ ( ( SX1
= ( zero_zero @ nat ) )
| ( dvd_dvd @ nat @ SX0 @ SX2 ) )
| ( dvd_dvd @ nat @ ( times_times @ nat @ SX0 @ SX1 ) @ ( times_times @ nat @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1617]) ).
thf(1856,plain,
( ( ! [SX0: $i] :
( ~ ( linordered_semidom @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ~ ( ord_less_eq @ SX0 @ ( zero_zero @ SX0 ) @ SX2 )
| ( ord_less_eq @ SX0 @ ( zero_zero @ SX0 ) @ ( power_power @ SX0 @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1450]) ).
thf(1857,plain,
( ( ! [SX0: $i] :
( ~ ( linord581940658strict @ SX0 )
| ! [SX1: $i,SX2: $i] :
~ ( ~ ( ( ( plus_plus @ SX0 @ ( times_times @ SX0 @ SX1 @ SX1 ) @ ( times_times @ SX0 @ SX2 @ SX2 ) )
!= ( zero_zero @ SX0 ) )
| ~ ( ( ( ti @ SX0 @ SX1 )
!= ( zero_zero @ SX0 ) )
| ( ( ti @ SX0 @ SX2 )
!= ( zero_zero @ SX0 ) ) ) )
| ~ ( ~ ~ ( ( ( ti @ SX0 @ SX1 )
!= ( zero_zero @ SX0 ) )
| ( ( ti @ SX0 @ SX2 )
!= ( zero_zero @ SX0 ) ) )
| ( ( plus_plus @ SX0 @ ( times_times @ SX0 @ SX1 @ SX1 ) @ ( times_times @ SX0 @ SX2 @ SX2 ) )
= ( zero_zero @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1459]) ).
thf(1858,plain,
( ( ! [SX0: $i] :
( ~ ( linordered_semidom @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ~ ( ord_less @ SX0 @ ( one_one @ SX0 ) @ SX3 )
| ~ ( ~ ( ( ( power_power @ SX0 @ SX3 @ SX1 )
!= ( power_power @ SX0 @ SX3 @ SX2 ) )
| ( SX1 = SX2 ) )
| ~ ( ( SX1 != SX2 )
| ( ( power_power @ SX0 @ SX3 @ SX1 )
= ( power_power @ SX0 @ SX3 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1502]) ).
thf(1859,plain,
( ( ! [SX0: $i] :
( ~ ( linordered_ring @ SX0 )
| ! [SX1: $i,SX2: $i] :
~ ( ord_less @ SX0 @ ( plus_plus @ SX0 @ ( times_times @ SX0 @ SX1 @ SX1 ) @ ( times_times @ SX0 @ SX2 @ SX2 ) ) @ ( zero_zero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1478]) ).
thf(1860,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( zprime @ SX2 )
| ~ ~ ( zcong @ SX1 @ ( zero_zero @ int ) @ SX2 )
| ~ ~ ( zcong @ SX0 @ ( zero_zero @ int ) @ SX2 )
| ~ ( zcong @ ( times_times @ int @ SX1 @ SX0 ) @ ( zero_zero @ int ) @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1627]) ).
thf(1861,plain,
( ( ! [SX0: $i] :
( ~ ( number_semiring @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ( power_power @ SX0 @ ( plus_plus @ SX0 @ SX1 @ SX2 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ SX0 @ ( plus_plus @ SX0 @ ( power_power @ SX0 @ SX1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SX0 @ SX2 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times @ SX0 @ ( times_times @ SX0 @ ( number_number_of @ SX0 @ ( bit0 @ ( bit1 @ pls ) ) ) @ SX1 ) @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1263]) ).
thf(1862,plain,
( ( ! [SX0: $i] :
( ~ ( number_ring @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ( times_times @ SX0 @ ( number_number_of @ SX0 @ SX1 ) @ ( number_number_of @ SX0 @ SX2 ) )
= ( number_number_of @ SX0 @ ( times_times @ int @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1397]) ).
thf(1863,plain,
( ( ! [SX0: $i] :
( ~ ( linord581940658strict @ SX0 )
| ! [SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SX0 @ ( zero_zero @ SX0 ) @ ( times_times @ SX0 @ SX1 @ SX2 ) )
| ~ ( ~ ( ord_less_eq @ SX0 @ ( zero_zero @ SX0 ) @ SX1 )
| ~ ( ord_less_eq @ SX0 @ ( zero_zero @ SX0 ) @ SX2 ) )
| ~ ( ~ ( ord_less_eq @ SX0 @ SX1 @ ( zero_zero @ SX0 ) )
| ~ ( ord_less_eq @ SX0 @ SX2 @ ( zero_zero @ SX0 ) ) ) )
| ~ ( ~ ( ~ ( ~ ( ord_less_eq @ SX0 @ ( zero_zero @ SX0 ) @ SX1 )
| ~ ( ord_less_eq @ SX0 @ ( zero_zero @ SX0 ) @ SX2 ) )
| ~ ( ~ ( ord_less_eq @ SX0 @ SX1 @ ( zero_zero @ SX0 ) )
| ~ ( ord_less_eq @ SX0 @ SX2 @ ( zero_zero @ SX0 ) ) ) )
| ( ord_less_eq @ SX0 @ ( zero_zero @ SX0 ) @ ( times_times @ SX0 @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1682]) ).
thf(1864,plain,
( ( ! [SX0: $i] :
( ~ ( number_ring @ SX0 )
| ! [SX1: $i] :
( ( times_times @ SX0 @ ( number_number_of @ SX0 @ ( bit1 @ pls ) ) @ SX1 )
= ( ti @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1406]) ).
thf(1865,plain,
( ( ! [SX0: $i] :
( ~ ( linordered_semidom @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ~ ( ord_less @ SX0 @ ( one_one @ SX0 ) @ SX2 )
| ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ SX1 )
| ( ord_less @ SX0 @ ( one_one @ SX0 ) @ ( power_power @ SX0 @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1545]) ).
thf(1866,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( number_ring @ SX0 )
| ~ ( linordered_idom @ SX0 ) )
| ! [SX1: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SX0 @ ( one_one @ SX0 ) @ ( number_number_of @ SX0 @ SX1 ) )
| ( ord_less_eq @ int @ ( bit1 @ pls ) @ SX1 ) )
| ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ pls ) @ SX1 )
| ( ord_less_eq @ SX0 @ ( one_one @ SX0 ) @ ( number_number_of @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1358]) ).
thf(1867,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( ord_less @ int @ ( zero_zero @ int ) @ SX2 )
| ~ ( ord_less @ int @ SX2 @ SX1 )
| ~ ( ord_less @ int @ ( zero_zero @ int ) @ SX0 )
| ~ ( ord_less @ int @ SX0 @ SX2 )
| ~ ( zcong @ SX2 @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1561]) ).
thf(1868,plain,
( ( ~ ! [SX0: $i] :
( ( plus_plus @ int @ ( power_power @ int @ s @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( one_one @ int ) )
!= ( times_times @ int @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1273]) ).
thf(1869,plain,
( ( ! [SX0: $i] :
( ~ ( monoid_mult @ SX0 )
| ! [SX1: $i] :
( ( power_power @ SX0 @ SX1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times @ SX0 @ SX1 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1268]) ).
thf(1870,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SX0 ) @ min )
| ( ord_less_eq @ int @ SX0 @ min ) )
| ~ ( ~ ( ord_less_eq @ int @ SX0 @ min )
| ( ord_less @ int @ ( bit0 @ SX0 ) @ min ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1542]) ).
thf(1871,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( zcong @ SX2 @ SX3 @ SX4 )
| ~ ( zcong @ SX0 @ SX1 @ SX4 )
| ( zcong @ ( plus_plus @ int @ SX2 @ SX0 ) @ ( plus_plus @ int @ SX3 @ SX1 ) @ SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1559]) ).
thf(1872,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( ord_less @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ SX0 ) @ SX0 ) @ ( zero_zero @ int ) )
| ( ord_less @ int @ SX0 @ ( zero_zero @ int ) ) )
| ~ ( ~ ( ord_less @ int @ SX0 @ ( zero_zero @ int ) )
| ( ord_less @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ SX0 ) @ SX0 ) @ ( zero_zero @ int ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1484]) ).
thf(1873,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( twoSqu420862341sum2sq @ ( ti @ int @ SX0 ) )
| ( twoSqu420862341sum2sq @ SX0 ) )
| ~ ( ~ ( twoSqu420862341sum2sq @ SX0 )
| ( twoSqu420862341sum2sq @ ( ti @ int @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1248]) ).
thf(1874,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( dvd_dvd @ nat @ SX1 @ SX2 )
| ~ ( dvd_dvd @ nat @ SX1 @ ( plus_plus @ nat @ SX2 @ SX0 ) )
| ( dvd_dvd @ nat @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1604]) ).
thf(1875,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ( ( bit0 @ SX0 )
!= pls )
| ( ( ti @ int @ SX0 )
= pls ) )
| ~ ( ( ( ti @ int @ SX0 )
!= pls )
| ( ( bit0 @ SX0 )
= pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1371]) ).
thf(1876,plain,
( ( ! [SX0: $i] :
( ~ ( comm_semiring_1 @ SX0 )
| ! [SX1: $i,SX2: $i] : ( dvd_dvd @ SX0 @ SX1 @ ( times_times @ SX0 @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1672]) ).
thf(1877,plain,
( ( ! [SX0: $i] :
( ~ ( number_ring @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ( plus_plus @ SX0 @ ( number_number_of @ SX0 @ SX1 ) @ ( number_number_of @ SX0 @ SX2 ) )
= ( number_number_of @ SX0 @ ( plus_plus @ int @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1400]) ).
thf(1878,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( number_ring @ SX0 )
| ~ ( ring_char_0 @ SX0 ) )
| ! [SX1: $i,SX2: $i] :
~ ( ~ ( ( ( number_number_of @ SX0 @ SX1 )
!= ( number_number_of @ SX0 @ SX2 ) )
| ( ( ti @ int @ SX1 )
= ( ti @ int @ SX2 ) ) )
| ~ ( ( ( ti @ int @ SX1 )
!= ( ti @ int @ SX2 ) )
| ( ( number_number_of @ SX0 @ SX1 )
= ( number_number_of @ SX0 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1333]) ).
thf(1879,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( SX0
!= ( plus_plus @ nat @ ( times_times @ nat @ SX1 @ SX2 ) @ SX3 ) )
| ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ SX3 )
| ~ ( ord_less @ nat @ SX3 @ SX2 )
| ~ ( dvd_dvd @ nat @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1628]) ).
thf(1880,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( dvd_dvd @ nat @ ( power_power @ nat @ SX0 @ SX1 ) @ ( power_power @ nat @ SX2 @ SX1 ) )
| ~ ( ( SX1
!= ( zero_zero @ nat ) ) )
| ( dvd_dvd @ nat @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1621]) ).
thf(1881,plain,
( ( ! [SX0: $i] :
( ~ ( zero_neq_one @ SX0 )
| ( ( zero_zero @ SX0 )
!= ( one_one @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1668]) ).
thf(1882,plain,
( ( ! [SX0: $i] :
( ~ ( comm_semiring_1 @ SX0 )
| ! [SX1: $i] :
( ( plus_plus @ SX0 @ ( zero_zero @ SX0 ) @ SX1 )
= ( ti @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1442]) ).
thf(1883,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( number_ring @ SX0 )
| ~ ( linordered_idom @ SX0 ) )
| ! [SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( ord_less @ SX0 @ ( number_number_of @ SX0 @ SX1 ) @ ( number_number_of @ SX0 @ SX2 ) )
| ( ord_less @ int @ SX1 @ SX2 ) )
| ~ ( ~ ( ord_less @ int @ SX1 @ SX2 )
| ( ord_less @ SX0 @ ( number_number_of @ SX0 @ SX1 ) @ ( number_number_of @ SX0 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1283]) ).
thf(1884,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit0 @ SX0 ) @ min )
| ( ord_less_eq @ int @ SX0 @ min ) )
| ~ ( ~ ( ord_less_eq @ int @ SX0 @ min )
| ( ord_less_eq @ int @ ( bit0 @ SX0 ) @ min ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1534]) ).
thf(1885,plain,
( ( ! [SX0: $i] :
( ~ ( comm_semiring_1 @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( dvd_dvd @ SX0 @ ( power_power @ SX0 @ SX2 @ SX3 ) @ SX4 )
| ~ ( ord_less_eq @ nat @ SX1 @ SX3 )
| ( dvd_dvd @ SX0 @ ( power_power @ SX0 @ SX2 @ SX1 ) @ SX4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1434]) ).
thf(1886,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( ord_less @ real @ ( zero_zero @ real ) @ SX2 )
| ~ ( ord_less @ real @ SX0 @ SX1 )
| ( ord_less @ real @ ( times_times @ real @ SX2 @ SX0 ) @ ( times_times @ real @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1641]) ).
thf(1887,plain,
( ( ! [SX0: $i] :
( ~ ( comm_semiring_1 @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ~ ( dvd_dvd @ SX0 @ SX2 @ SX3 )
| ( dvd_dvd @ SX0 @ SX2 @ ( times_times @ SX0 @ SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1674]) ).
thf(1888,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ SX2 )
| ~ ( ord_less @ nat @ ( power_power @ nat @ SX2 @ SX0 ) @ ( power_power @ nat @ SX2 @ SX1 ) )
| ( ord_less @ nat @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1513]) ).
thf(1889,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SX1 )
| ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SX0 )
| ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1658]) ).
thf(1890,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( ord_less_eq @ int @ ( one_one @ int ) @ SX0 )
| ( ord_less @ int @ ( zero_zero @ int ) @ SX0 ) )
| ~ ( ~ ( ord_less @ int @ ( zero_zero @ int ) @ SX0 )
| ( ord_less_eq @ int @ ( one_one @ int ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1482]) ).
thf(1891,plain,
( ( ! [SX0: $i] :
( ~ ( comm_semiring_1 @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ~ ( dvd_dvd @ SX0 @ ( times_times @ SX0 @ SX1 @ SX2 ) @ SX3 )
| ( dvd_dvd @ SX0 @ SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1677]) ).
thf(1892,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( mult_zero @ SX2 )
| ( ( times_times @ SX2 @ ( ti @ SX2 @ SX0 ) @ SX1 )
= ( times_times @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1224]) ).
thf(1893,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( power @ SX2 )
| ( ( ti @ SX2 @ ( times_times @ SX2 @ SX0 @ SX1 ) )
= ( times_times @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1229]) ).
thf(1894,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( semiring @ SX2 )
| ( ( plus_plus @ SX2 @ ( ti @ SX2 @ SX0 ) @ SX1 )
= ( plus_plus @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1209]) ).
thf(1895,plain,
( ( ! [SX0: $i] :
( ~ ( linordered_ring @ SX0 )
| ! [SX1: $i,SX2: $i] : ( ord_less_eq @ SX0 @ ( zero_zero @ SX0 ) @ ( plus_plus @ SX0 @ ( times_times @ SX0 @ SX1 @ SX1 ) @ ( times_times @ SX0 @ SX2 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1476]) ).
thf(1896,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq @ int @ SX0 @ SX1 ) )
| ~ ( ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ( ord_less @ int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1313]) ).
thf(1897,plain,
( ( ! [SX0: $i] :
( ~ ( zero_neq_one @ SX0 )
| ( ( one_one @ SX0 )
!= ( zero_zero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1667]) ).
thf(1898,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ SX0 @ ( number_number_of @ nat @ SX1 ) ) )
| ( ( number_number_of @ nat @ SX1 )
= ( zero_zero @ nat ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ SX0 ) )
| ~ ( ~ ( ( ( number_number_of @ nat @ SX1 )
= ( zero_zero @ nat ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ SX0 ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ SX0 @ ( number_number_of @ nat @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1512]) ).
thf(1899,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( number @ SX0 )
| ~ ( semiring @ SX0 ) )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ( times_times @ SX0 @ ( number_number_of @ SX0 @ SX1 ) @ ( plus_plus @ SX0 @ SX2 @ SX3 ) )
= ( plus_plus @ SX0 @ ( times_times @ SX0 @ ( number_number_of @ SX0 @ SX1 ) @ SX2 ) @ ( times_times @ SX0 @ ( number_number_of @ SX0 @ SX1 ) @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1390]) ).
thf(1900,plain,
( ( ! [SX0: $i] :
( ~ ( ring_1 @ SX0 )
| ! [SX1: $i] :
( ( minus_minus @ SX0 @ ( times_times @ SX0 @ SX1 @ SX1 ) @ ( one_one @ SX0 ) )
= ( times_times @ SX0 @ ( plus_plus @ SX0 @ SX1 @ ( one_one @ SX0 ) ) @ ( minus_minus @ SX0 @ SX1 @ ( one_one @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1645]) ).
thf(1901,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq @ int @ SX0 @ SX1 ) )
| ~ ( ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ( ord_less @ int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1312]) ).
thf(1902,plain,
( ( ! [SX0: $i] :
( ~ ( number @ SX0 )
| ! [SX1: $i,SX2: $i] :
~ ( ~ ( ( ( number_number_of @ SX0 @ SX1 )
!= ( ti @ SX0 @ SX2 ) )
| ( ( ti @ SX0 @ SX2 )
= ( number_number_of @ SX0 @ SX1 ) ) )
| ~ ( ( ( ti @ SX0 @ SX2 )
!= ( number_number_of @ SX0 @ SX1 ) )
| ( ( number_number_of @ SX0 @ SX1 )
= ( ti @ SX0 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1334]) ).
thf(1903,plain,
( ( min != pls )
= $true ),
inference(unfold_def,[status(thm)],[1518]) ).
thf(1904,plain,
( ( ! [SX0: $i] :
( ~ ( comm_semiring_1 @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ( plus_plus @ SX0 @ SX1 @ ( plus_plus @ SX0 @ SX2 @ SX3 ) )
= ( plus_plus @ SX0 @ ( plus_plus @ SX0 @ SX1 @ SX2 ) @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1330]) ).
thf(1905,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( ord_less_eq @ int @ min @ ( bit0 @ SX0 ) )
| ( ord_less @ int @ min @ SX0 ) )
| ~ ( ~ ( ord_less @ int @ min @ SX0 )
| ( ord_less_eq @ int @ min @ ( bit0 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1541]) ).
thf(1906,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( zprime @ SX3 )
| ~ ~ ( dvd_dvd @ int @ SX3 @ SX2 )
| ~ ( dvd_dvd @ int @ ( power_power @ int @ SX3 @ SX0 ) @ ( times_times @ int @ SX2 @ SX1 ) )
| ( dvd_dvd @ int @ ( power_power @ int @ SX3 @ SX0 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1474]) ).
thf(1907,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ ( number_number_of @ nat @ SX0 ) )
| ( ord_less @ int @ pls @ SX0 ) )
| ~ ( ~ ( ord_less @ int @ pls @ SX0 )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ ( number_number_of @ nat @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1546]) ).
thf(1908,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq @ int @ SX0 @ SX1 ) )
| ~ ( ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1349]) ).
thf(1909,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( power @ SX2 )
| ( ( times_times @ SX2 @ ( ti @ SX2 @ SX0 ) @ SX1 )
= ( times_times @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1227]) ).
thf(1910,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( ord_less @ int @ pls @ ( bit1 @ SX0 ) )
| ( ord_less_eq @ int @ pls @ SX0 ) )
| ~ ( ~ ( ord_less_eq @ int @ pls @ SX0 )
| ( ord_less @ int @ pls @ ( bit1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1309]) ).
thf(1911,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( ord_less @ int @ SX2 @ pls )
| ( ( times_times @ nat @ ( number_number_of @ nat @ SX2 ) @ ( times_times @ nat @ ( number_number_of @ nat @ SX0 ) @ SX1 ) )
= ( zero_zero @ nat ) ) )
| ~ ( ~ ~ ( ord_less @ int @ SX2 @ pls )
| ( ( times_times @ nat @ ( number_number_of @ nat @ SX2 ) @ ( times_times @ nat @ ( number_number_of @ nat @ SX0 ) @ SX1 ) )
= ( times_times @ nat @ ( number_number_of @ nat @ ( times_times @ int @ SX2 @ SX0 ) ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1550]) ).
thf(1912,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( dvd @ SX2 )
| ( ( times_times @ SX2 @ ( ti @ SX2 @ SX0 ) @ SX1 )
= ( times_times @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1215]) ).
thf(1913,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ SX0 @ SX1 ) )
| ( SX1
= ( zero_zero @ nat ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ SX0 ) )
| ~ ( ~ ( ( SX1
= ( zero_zero @ nat ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ SX0 ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1511]) ).
thf(1914,plain,
( ( ! [SX0: $i] :
( ~ ( number_ring @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ( times_times @ SX0 @ ( number_number_of @ SX0 @ SX1 ) @ ( times_times @ SX0 @ ( number_number_of @ SX0 @ SX2 ) @ SX3 ) )
= ( times_times @ SX0 @ ( number_number_of @ SX0 @ ( times_times @ int @ SX1 @ SX2 ) ) @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1396]) ).
thf(1915,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SX0 ) @ ( zero_zero @ int ) )
| ( ord_less @ int @ SX0 @ ( zero_zero @ int ) ) )
| ~ ( ~ ( ord_less @ int @ SX0 @ ( zero_zero @ int ) )
| ( ord_less @ int @ ( bit1 @ SX0 ) @ ( zero_zero @ int ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1465]) ).
thf(1916,plain,
( ( ! [SX0: $i] :
( ~ ( number_ring @ SX0 )
| ! [SX1: $i] :
( ( plus_plus @ SX0 @ SX1 @ ( number_number_of @ SX0 @ pls ) )
= ( ti @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1395]) ).
thf(1917,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( power @ SX2 )
| ( ( power_power @ SX2 @ SX0 @ ( ti @ nat @ SX1 ) )
= ( power_power @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1238]) ).
thf(1918,plain,
( ( ! [SX0: $i] :
( ~ ( comm_semiring_1 @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ( times_times @ SX0 @ ( times_times @ SX0 @ SX1 @ SX2 ) @ SX3 )
= ( times_times @ SX0 @ SX1 @ ( times_times @ SX0 @ SX2 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1323]) ).
thf(1919,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less @ int @ SX0 @ SX1 ) )
| ~ ( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1344]) ).
thf(1920,plain,
( ( ! [SX0: $i] :
( ~ ( comm_semiring_1 @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ( plus_plus @ SX0 @ SX1 @ ( times_times @ SX0 @ SX2 @ SX1 ) )
= ( times_times @ SX0 @ ( plus_plus @ SX0 @ SX2 @ ( one_one @ SX0 ) ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1392]) ).
thf(1921,plain,
( ( ! [SX0: $i] :
( ~ ( semiri456707255roduct @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
~ ( ~ ( ( ( plus_plus @ SX0 @ ( times_times @ SX0 @ SX1 @ SX2 ) @ ( times_times @ SX0 @ SX3 @ SX4 ) )
!= ( plus_plus @ SX0 @ ( times_times @ SX0 @ SX1 @ SX4 ) @ ( times_times @ SX0 @ SX3 @ SX2 ) ) )
| ( ( ti @ SX0 @ SX1 )
= ( ti @ SX0 @ SX3 ) )
| ( ( ti @ SX0 @ SX2 )
= ( ti @ SX0 @ SX4 ) ) )
| ~ ( ~ ( ( ( ti @ SX0 @ SX1 )
= ( ti @ SX0 @ SX3 ) )
| ( ( ti @ SX0 @ SX2 )
= ( ti @ SX0 @ SX4 ) ) )
| ( ( plus_plus @ SX0 @ ( times_times @ SX0 @ SX1 @ SX2 ) @ ( times_times @ SX0 @ SX3 @ SX4 ) )
= ( plus_plus @ SX0 @ ( times_times @ SX0 @ SX1 @ SX4 ) @ ( times_times @ SX0 @ SX3 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1359]) ).
thf(1922,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( ord_less_eq @ int @ pls @ ( bit1 @ SX0 ) )
| ( ord_less_eq @ int @ pls @ SX0 ) )
| ~ ( ~ ( ord_less_eq @ int @ pls @ SX0 )
| ( ord_less_eq @ int @ pls @ ( bit1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1348]) ).
thf(1923,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( zcong @ SX2 @ SX3 @ SX4 )
| ~ ( ~ ( ~ ( zcong @ SX0 @ ( times_times @ int @ SX1 @ SX2 ) @ SX4 )
| ( zcong @ SX0 @ ( times_times @ int @ SX1 @ SX3 ) @ SX4 ) )
| ~ ( ~ ( zcong @ SX0 @ ( times_times @ int @ SX1 @ SX3 ) @ SX4 )
| ( zcong @ SX0 @ ( times_times @ int @ SX1 @ SX2 ) @ SX4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1610]) ).
thf(1924,plain,
( ( ! [SX0: $i] :
( ~ ( number_ring @ SX0 )
| ( ( one_one @ SX0 )
= ( number_number_of @ SX0 @ ( bit1 @ pls ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1410]) ).
thf(1925,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( ( SX2
!= ( zero_zero @ nat ) ) )
| ~ ( dvd_dvd @ nat @ ( power_power @ nat @ SX0 @ SX2 ) @ SX1 )
| ( dvd_dvd @ nat @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1620]) ).
thf(1926,plain,
( ( ! [SX0: $i] :
( ~ ( number_ring @ SX0 )
| ( ( number_number_of @ SX0 @ ( bit1 @ pls ) )
= ( one_one @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1409]) ).
thf(1927,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( zcong @ SX0 @ ( ti @ int @ SX1 ) @ SX2 )
| ( zcong @ SX0 @ SX1 @ SX2 ) )
| ~ ( ~ ( zcong @ SX0 @ SX1 @ SX2 )
| ( zcong @ SX0 @ ( ti @ int @ SX1 ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1231]) ).
thf(1928,plain,
( ( ! [SX0: $i] :
( ~ ( zprime @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SX0 ) @ ( one_one @ int ) ) )
| ( ( legendre @ ( number_number_of @ int @ min ) @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SX0 ) @ ( one_one @ int ) ) )
= ( one_one @ int ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1595]) ).
thf(1929,plain,
( ( ! [SX0: $i] :
( ~ ( number_ring @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ( number_number_of @ SX0 @ ( plus_plus @ int @ SX1 @ SX2 ) )
= ( plus_plus @ SX0 @ ( number_number_of @ SX0 @ SX1 ) @ ( number_number_of @ SX0 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1401]) ).
thf(1930,plain,
( ( ! [SX0: $i] :
( ~ ( number_ring @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ( number_number_of @ SX0 @ ( times_times @ int @ SX1 @ SX2 ) )
= ( times_times @ SX0 @ ( number_number_of @ SX0 @ SX1 ) @ ( number_number_of @ SX0 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1398]) ).
thf(1931,plain,
( ( ! [SX0: $i] :
( ~ ( comm_semiring_1 @ SX0 )
| ! [SX1: $i] :
( ( power_power @ SX0 @ SX1 @ ( zero_zero @ nat ) )
= ( one_one @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1537]) ).
thf(1932,plain,
( ( ! [SX0: $i] :
( ~ ( comm_semiring_1 @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( plus_plus @ SX0 @ ( plus_plus @ SX0 @ SX1 @ SX2 ) @ ( plus_plus @ SX0 @ SX3 @ SX4 ) )
= ( plus_plus @ SX0 @ ( plus_plus @ SX0 @ SX1 @ SX3 ) @ ( plus_plus @ SX0 @ SX2 @ SX4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1327]) ).
thf(1933,plain,
( ( ! [SX0: $i] :
( pls
!= ( bit1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1368]) ).
thf(1934,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SX1 )
| ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SX0 )
| ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( times_times @ int @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1657]) ).
thf(1935,plain,
( ( ! [SX0: $i] :
( ~ ( linordered_idom @ SX0 )
| ! [SX1: $i] :
~ ( ~ ( ~ ( ord_less @ SX0 @ ( plus_plus @ SX0 @ SX1 @ SX1 ) @ ( zero_zero @ SX0 ) )
| ( ord_less @ SX0 @ SX1 @ ( zero_zero @ SX0 ) ) )
| ~ ( ~ ( ord_less @ SX0 @ SX1 @ ( zero_zero @ SX0 ) )
| ( ord_less @ SX0 @ ( plus_plus @ SX0 @ SX1 @ SX1 ) @ ( zero_zero @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1458]) ).
thf(1936,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ~ ( ord_less_eq @ int @ SX1 @ SX0 )
| ( ( ti @ int @ SX0 )
= ( ti @ int @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1279]) ).
thf(1937,plain,
( ( ! [SX0: $i] :
( ~ ( number_ring @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ( plus_plus @ SX0 @ ( number_number_of @ SX0 @ SX1 ) @ ( minus_minus @ SX0 @ ( number_number_of @ SX0 @ SX2 ) @ SX3 ) )
= ( minus_minus @ SX0 @ ( number_number_of @ SX0 @ ( plus_plus @ int @ SX1 @ SX2 ) ) @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1583]) ).
thf(1938,plain,
( ( ! [SX0: $i] :
( ~ ( number_ring @ SX0 )
| ! [SX1: $i] :
( ( number_number_of @ SX0 @ ( bit0 @ SX1 ) )
= ( plus_plus @ SX0 @ ( plus_plus @ SX0 @ ( zero_zero @ SX0 ) @ ( number_number_of @ SX0 @ SX1 ) ) @ ( number_number_of @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1480]) ).
thf(1939,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( ( SX2
!= ( zero_zero @ real ) ) )
| ~ ( ~ ( ( ( times_times @ real @ SX2 @ SX0 )
!= ( times_times @ real @ SX2 @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ( ( SX0 != SX1 )
| ( ( times_times @ real @ SX2 @ SX0 )
= ( times_times @ real @ SX2 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1637]) ).
thf(1940,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( ord_less @ int @ min @ ( bit1 @ SX0 ) )
| ( ord_less @ int @ min @ SX0 ) )
| ~ ( ~ ( ord_less @ int @ min @ SX0 )
| ( ord_less @ int @ min @ ( bit1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1525]) ).
thf(1941,plain,
( ( ! [SX0: $i] :
( ~ ( number_ring @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ( number_number_of @ SX0 @ ( minus_minus @ int @ SX1 @ SX2 ) )
= ( minus_minus @ SX0 @ ( number_number_of @ SX0 @ SX1 ) @ ( number_number_of @ SX0 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1574]) ).
thf(1942,plain,
( ( ! [SX0: $i] :
( ~ ( monoid_mult @ SX0 )
| ! [SX1: $i] :
( ( power_power @ SX0 @ ( one_one @ SX0 ) @ SX1 )
= ( one_one @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1495]) ).
thf(1943,plain,
( ( ! [SX0: $i] :
( ~ ( comm_semiring_1 @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ~ ( dvd_dvd @ SX0 @ SX2 @ SX3 )
| ~ ( dvd_dvd @ SX0 @ SX2 @ SX1 )
| ( dvd_dvd @ SX0 @ SX2 @ ( plus_plus @ SX0 @ SX3 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1679]) ).
thf(1944,plain,
( ( ! [SX0: $i] :
( ~ ( comm_semiring_1 @ SX0 )
| ! [SX1: $i] :
( ( times_times @ SX0 @ ( zero_zero @ SX0 ) @ SX1 )
= ( zero_zero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1440]) ).
thf(1945,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SX0 ) @ pls )
| ( ord_less @ int @ SX0 @ pls ) )
| ~ ( ~ ( ord_less @ int @ SX0 @ pls )
| ( ord_less @ int @ ( bit0 @ SX0 ) @ pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1346]) ).
thf(1946,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( semiring @ SX2 )
| ( ( ti @ SX2 @ ( times_times @ SX2 @ SX0 @ SX1 ) )
= ( times_times @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1220]) ).
thf(1947,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( ( bit0 @ SX0 )
!= ( bit0 @ SX1 ) )
| ( ( ti @ int @ SX0 )
= ( ti @ int @ SX1 ) ) )
| ~ ( ( ( ti @ int @ SX0 )
!= ( ti @ int @ SX1 ) )
| ( ( bit0 @ SX0 )
= ( bit0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1336]) ).
thf(1948,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SX0 ) @ min )
| ( ord_less_eq @ int @ SX0 @ min ) )
| ~ ( ~ ( ord_less_eq @ int @ SX0 @ min )
| ( ord_less_eq @ int @ ( bit1 @ SX0 ) @ min ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1530]) ).
thf(1949,plain,
( ( ! [SX0: $i] :
( ~ ( number_ring @ SX0 )
| ! [SX1: $i] :
( ( plus_plus @ SX0 @ ( number_number_of @ SX0 @ pls ) @ SX1 )
= ( ti @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1394]) ).
thf(1950,plain,
( ( ! [SX0: $i] :
( ~ ( comm_semiring_1 @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ~ ( dvd_dvd @ SX0 @ SX2 @ SX3 )
| ( dvd_dvd @ SX0 @ ( power_power @ SX0 @ SX2 @ SX1 ) @ ( power_power @ SX0 @ SX3 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1437]) ).
thf(1951,plain,
( ( ! [SX0: $i] :
( ~ ( number_semiring @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ~ ( ord_less_eq @ int @ pls @ SX2 )
| ~ ( ord_less_eq @ int @ pls @ SX1 )
| ( ( plus_plus @ SX0 @ ( number_number_of @ SX0 @ SX2 ) @ ( number_number_of @ SX0 @ SX1 ) )
= ( number_number_of @ SX0 @ ( plus_plus @ int @ SX2 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1387]) ).
thf(1952,plain,
( ( ! [SX0: $i] :
( ~ ( monoid_mult @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ( power_power @ SX0 @ SX1 @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SX2 ) )
= ( power_power @ SX0 @ ( power_power @ SX0 @ SX1 @ SX2 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1354]) ).
thf(1953,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( dvd @ SX2 )
| ( ( times_times @ SX2 @ SX0 @ ( ti @ SX2 @ SX1 ) )
= ( times_times @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1216]) ).
thf(1954,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( zprime @ SX3 )
| ~ ~ ( dvd_dvd @ int @ SX3 @ SX2 )
| ~ ( dvd_dvd @ int @ ( power_power @ int @ SX3 @ SX0 ) @ ( times_times @ int @ SX1 @ SX2 ) )
| ( dvd_dvd @ int @ ( power_power @ int @ SX3 @ SX0 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1475]) ).
thf(1955,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( ab_group_add @ SX2 )
| ( ( plus_plus @ SX2 @ ( ti @ SX2 @ SX0 ) @ SX1 )
= ( plus_plus @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1212]) ).
thf(1956,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SX0 ) @ ( zero_zero @ int ) )
| ( ord_less @ int @ SX0 @ ( zero_zero @ int ) ) )
| ~ ( ~ ( ord_less @ int @ SX0 @ ( zero_zero @ int ) )
| ( ord_less @ int @ ( bit0 @ SX0 ) @ ( zero_zero @ int ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1467]) ).
thf(1957,plain,
( ( ! [SX0: $i] :
( ~ ( comm_semiring_1 @ SX0 )
| ! [SX1: $i] :
( ( times_times @ SX0 @ SX1 @ SX1 )
= ( power_power @ SX0 @ SX1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1267]) ).
thf(1958,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( zcong @ ( times_times @ int @ SX0 @ ( minus_minus @ int @ SX1 @ ( one_one @ int ) ) ) @ ( one_one @ int ) @ SX1 )
| ( zcong @ SX0 @ ( minus_minus @ int @ SX1 @ ( one_one @ int ) ) @ SX1 ) )
| ~ ( ~ ( zcong @ SX0 @ ( minus_minus @ int @ SX1 @ ( one_one @ int ) ) @ SX1 )
| ( zcong @ ( times_times @ int @ SX0 @ ( minus_minus @ int @ SX1 @ ( one_one @ int ) ) ) @ ( one_one @ int ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1588]) ).
thf(1959,plain,
( ( ! [SX0: $i] :
( ~ ( linordered_idom @ SX0 )
| ! [SX1: $i] : ( ord_less_eq @ SX0 @ ( zero_zero @ SX0 ) @ ( power_power @ SX0 @ SX1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1488]) ).
thf(1960,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( ord_less_eq @ int @ SX1 @ SX2 )
| ~ ( ord_less_eq @ int @ SX2 @ SX0 )
| ( ord_less_eq @ int @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1278]) ).
thf(1961,plain,
( ( ! [SX0: $i] :
( ~ ( power @ SX0 )
| ( ( ti @ SX0 @ ( one_one @ SX0 ) )
= ( one_one @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1208]) ).
thf(1962,plain,
( ( ! [SX0: $i] :
( ~ ( comm_semiring_1 @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ( plus_plus @ SX0 @ ( plus_plus @ SX0 @ SX1 @ SX2 ) @ SX3 )
= ( plus_plus @ SX0 @ ( plus_plus @ SX0 @ SX1 @ SX3 ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1328]) ).
thf(1963,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( ord_less @ int @ SX1 @ SX2 )
| ~ ( ord_less @ int @ ( zero_zero @ int ) @ SX0 )
| ( ord_less @ int @ ( times_times @ int @ SX0 @ SX1 ) @ ( times_times @ int @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1471]) ).
thf(1964,plain,
( ( ! [SX0: $i] :
( ~ ( comm_monoid_mult @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ( power_power @ SX0 @ ( times_times @ SX0 @ SX1 @ SX2 ) @ SX3 )
= ( times_times @ SX0 @ ( power_power @ SX0 @ SX1 @ SX3 ) @ ( power_power @ SX0 @ SX2 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1493]) ).
thf(1965,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( dvd_dvd @ nat @ SX0 @ SX1 )
| ( SX1
= ( zero_zero @ nat ) )
| ( SX1 = SX0 )
| ( ord_less_eq @ nat @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SX0 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1598]) ).
thf(1966,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq @ int @ SX0 @ SX1 ) )
| ~ ( ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1293]) ).
thf(1967,plain,
( ( ! [SX0: $i] :
( ~ ( ring_n68954251visors @ SX0 )
| ! [SX1: $i,SX2: $i] :
~ ( ~ ( ( ( times_times @ SX0 @ SX1 @ SX2 )
!= ( zero_zero @ SX0 ) )
| ( ( ti @ SX0 @ SX1 )
= ( zero_zero @ SX0 ) )
| ( ( ti @ SX0 @ SX2 )
= ( zero_zero @ SX0 ) ) )
| ~ ( ~ ( ( ( ti @ SX0 @ SX1 )
= ( zero_zero @ SX0 ) )
| ( ( ti @ SX0 @ SX2 )
= ( zero_zero @ SX0 ) ) )
| ( ( times_times @ SX0 @ SX1 @ SX2 )
= ( zero_zero @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1664]) ).
thf(1968,plain,
( ( ! [SX0: $i] :
( ~ ( number_ring @ SX0 )
| ! [SX1: $i] :
( ( times_times @ SX0 @ ( plus_plus @ SX0 @ ( one_one @ SX0 ) @ ( one_one @ SX0 ) ) @ ( number_number_of @ SX0 @ SX1 ) )
= ( number_number_of @ SX0 @ ( bit0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1413]) ).
thf(1969,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ( pls
!= ( bit0 @ SX0 ) )
| ( pls
= ( ti @ int @ SX0 ) ) )
| ~ ( ( pls
!= ( ti @ int @ SX0 ) )
| ( pls
= ( bit0 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1372]) ).
thf(1970,plain,
( ( ! [SX0: $i] :
( ~ ( linordered_semidom @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ~ ( ord_less @ SX0 @ ( one_one @ SX0 ) @ SX3 )
| ~ ( ord_less_eq @ SX0 @ ( power_power @ SX0 @ SX3 @ SX1 ) @ ( power_power @ SX0 @ SX3 @ SX2 ) )
| ( ord_less_eq @ nat @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1428]) ).
thf(1971,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( ( plus_plus @ int @ ( times_times @ int @ SX0 @ SX1 ) @ SX2 )
!= ( plus_plus @ int @ ( times_times @ int @ SX3 @ SX4 ) @ SX5 ) )
| ~ ( ord_less @ int @ ( plus_plus @ int @ ( times_times @ int @ SX3 @ SX4 ) @ SX5 ) @ ( zero_zero @ int ) )
| ~ ( ord_less @ int @ SX2 @ SX0 )
| ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SX5 )
| ~ ( ord_less @ int @ ( zero_zero @ int ) @ SX3 )
| ~ ( ord_less_eq @ int @ SX3 @ SX0 )
| ( ord_less_eq @ int @ SX4 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1652]) ).
thf(1972,plain,
( ( ! [SX0: $i] :
( ~ ( comm_semiring_1 @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ( plus_plus @ SX0 @ ( times_times @ SX0 @ SX1 @ SX2 ) @ SX2 )
= ( times_times @ SX0 @ ( plus_plus @ SX0 @ SX1 @ ( one_one @ SX0 ) ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1391]) ).
thf(1973,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( dvd @ SX2 )
| ( ( ti @ SX2 @ ( times_times @ SX2 @ SX0 @ SX1 ) )
= ( times_times @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1217]) ).
thf(1974,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( zcong @ SX1 @ SX2 @ SX3 )
| ( zcong @ ( power_power @ int @ SX1 @ SX0 ) @ ( power_power @ int @ SX2 @ SX0 ) @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1615]) ).
thf(1975,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SX0 ) @ pls )
| ( ord_less @ int @ SX0 @ pls ) )
| ~ ( ~ ( ord_less @ int @ SX0 @ pls )
| ( ord_less_eq @ int @ ( bit1 @ SX0 ) @ pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1308]) ).
thf(1976,plain,
( ( ! [SX0: $i] :
( ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ SX0 ) @ SX0 )
!= ( zero_zero @ int ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1472]) ).
thf(1977,plain,
( ( ! [SX0: $i] :
( ~ ( comm_semiring_1 @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ( power_power @ SX0 @ ( power_power @ SX0 @ SX1 @ SX2 ) @ SX3 )
= ( power_power @ SX0 @ SX1 @ ( times_times @ nat @ SX2 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1280]) ).
thf(1978,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( ord_less_eq @ int @ ( plus_plus @ int @ ( times_times @ int @ SX0 @ SX1 ) @ SX2 ) @ ( plus_plus @ int @ ( times_times @ int @ SX0 @ SX3 ) @ SX4 ) )
| ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SX2 )
| ~ ( ord_less @ int @ SX2 @ SX0 )
| ~ ( ord_less @ int @ SX4 @ SX0 )
| ( ord_less_eq @ int @ SX1 @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1649]) ).
thf(1979,plain,
( ( ! [SX0: $i] :
( ~ ( semiri456707255roduct @ SX0 )
| ! [SX1: $i,SX2: $i] :
~ ( ~ ( ( ( ti @ SX0 @ SX1 )
!= ( plus_plus @ SX0 @ SX1 @ SX2 ) )
| ( ( ti @ SX0 @ SX2 )
= ( zero_zero @ SX0 ) ) )
| ~ ( ( ( ti @ SX0 @ SX2 )
!= ( zero_zero @ SX0 ) )
| ( ( ti @ SX0 @ SX1 )
= ( plus_plus @ SX0 @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1444]) ).
thf(1980,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( quadRes @ SX0 @ SX1 )
| ~ ! [SX2: $i] :
~ ( zcong @ ( power_power @ int @ SX2 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SX1 @ SX0 ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ( zcong @ ( power_power @ int @ SX2 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SX1 @ SX0 )
| ( quadRes @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1629]) ).
thf(1981,plain,
( ( ! [SX0: $i] :
( ~ ( linordered_semidom @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ~ ( ord_less_eq @ nat @ SX2 @ SX3 )
| ~ ( ord_less_eq @ SX0 @ ( one_one @ SX0 ) @ SX1 )
| ( ord_less_eq @ SX0 @ ( power_power @ SX0 @ SX1 @ SX2 ) @ ( power_power @ SX0 @ SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1501]) ).
thf(1982,plain,
( ( ! [SX0: $i] :
( ~ ( comm_semiring_1 @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ( times_times @ SX0 @ ( plus_plus @ SX0 @ SX1 @ SX2 ) @ SX3 )
= ( plus_plus @ SX0 @ ( times_times @ SX0 @ SX1 @ SX3 ) @ ( times_times @ SX0 @ SX2 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1361]) ).
thf(1983,plain,
( ( ! [SX0: $i] :
( ~ ( linordered_semidom @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ~ ( ord_less_eq @ SX0 @ ( one_one @ SX0 ) @ SX2 )
| ( ord_less_eq @ SX0 @ ( one_one @ SX0 ) @ ( power_power @ SX0 @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1500]) ).
thf(1984,plain,
( ( ! [SX0: $i] :
( ~ ( comm_semiring_1 @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ( times_times @ SX0 @ SX1 @ SX2 )
= ( times_times @ SX0 @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1326]) ).
thf(1985,plain,
( ( ! [SX0: $i] :
( ~ ( linord581940658strict @ SX0 )
| ! [SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SX0 @ ( times_times @ SX0 @ SX1 @ SX2 ) @ ( zero_zero @ SX0 ) )
| ~ ( ~ ( ord_less_eq @ SX0 @ ( zero_zero @ SX0 ) @ SX1 )
| ~ ( ord_less_eq @ SX0 @ SX2 @ ( zero_zero @ SX0 ) ) )
| ~ ( ~ ( ord_less_eq @ SX0 @ SX1 @ ( zero_zero @ SX0 ) )
| ~ ( ord_less_eq @ SX0 @ ( zero_zero @ SX0 ) @ SX2 ) ) )
| ~ ( ~ ( ~ ( ~ ( ord_less_eq @ SX0 @ ( zero_zero @ SX0 ) @ SX1 )
| ~ ( ord_less_eq @ SX0 @ SX2 @ ( zero_zero @ SX0 ) ) )
| ~ ( ~ ( ord_less_eq @ SX0 @ SX1 @ ( zero_zero @ SX0 ) )
| ~ ( ord_less_eq @ SX0 @ ( zero_zero @ SX0 ) @ SX2 ) ) )
| ( ord_less_eq @ SX0 @ ( times_times @ SX0 @ SX1 @ SX2 ) @ ( zero_zero @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1683]) ).
thf(1986,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ( ( zero_zero @ nat )
!= ( number_number_of @ nat @ SX0 ) )
| ( ord_less_eq @ int @ SX0 @ pls ) )
| ~ ( ~ ( ord_less_eq @ int @ SX0 @ pls )
| ( ( zero_zero @ nat )
= ( number_number_of @ nat @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1548]) ).
thf(1987,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( number_ring @ SX0 )
| ~ ( linordered_idom @ SX0 ) )
| ! [SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SX0 @ ( number_number_of @ SX0 @ SX1 ) @ ( number_number_of @ SX0 @ SX2 ) )
| ( ord_less_eq @ int @ SX1 @ SX2 ) )
| ~ ( ~ ( ord_less_eq @ int @ SX1 @ SX2 )
| ( ord_less_eq @ SX0 @ ( number_number_of @ SX0 @ SX1 ) @ ( number_number_of @ SX0 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1284]) ).
thf(1988,plain,
( ( ! [SX0: $i] :
( ~ ( comm_semiring_1 @ SX0 )
| ! [SX1: $i] :
( ( times_times @ SX0 @ SX1 @ ( zero_zero @ SX0 ) )
= ( zero_zero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1441]) ).
thf(1989,plain,
( ( ! [SX0: $i] :
( ~ ( comm_semiring_1 @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( dvd_dvd @ SX0 @ SX3 @ SX4 )
| ~ ( ord_less_eq @ nat @ SX1 @ SX2 )
| ( dvd_dvd @ SX0 @ ( power_power @ SX0 @ SX3 @ SX1 ) @ ( power_power @ SX0 @ SX4 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1433]) ).
thf(1990,plain,
( ( ! [SX0: $i] :
( ~ ( number_semiring @ SX0 )
| ( ( number_number_of @ SX0 @ ( bit1 @ pls ) )
= ( one_one @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1408]) ).
thf(1991,plain,
( ( ! [SX0: $i] :
( ~ ( linordered_semidom @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ~ ( ord_less_eq @ SX0 @ ( power_power @ SX0 @ SX1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SX0 @ SX2 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ~ ( ord_less_eq @ SX0 @ ( zero_zero @ SX0 ) @ SX2 )
| ( ord_less_eq @ SX0 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1489]) ).
thf(1992,plain,
( ( ! [SX0: $i] :
( ( bit1 @ SX0 )
!= pls ) )
= $true ),
inference(unfold_def,[status(thm)],[1367]) ).
thf(1993,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( times_times @ int @ SX0 @ SX1 )
!= ( one_one @ int ) )
| ( ( ti @ int @ SX0 )
= ( one_one @ int ) )
| ( ( ti @ int @ SX0 )
= ( number_number_of @ int @ min ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1543]) ).
thf(1994,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( ord_less @ int @ min @ ( bit0 @ SX0 ) )
| ( ord_less @ int @ min @ SX0 ) )
| ~ ( ~ ( ord_less @ int @ min @ SX0 )
| ( ord_less @ int @ min @ ( bit0 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1528]) ).
thf(1995,plain,
( ( ! [SX0: $i] :
( ~ ( monoid_mult @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ( power_power @ SX0 @ SX1 @ ( plus_plus @ nat @ SX2 @ SX3 ) )
= ( times_times @ SX0 @ ( power_power @ SX0 @ SX1 @ SX2 ) @ ( power_power @ SX0 @ SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1494]) ).
thf(1996,plain,
( ( ! [SX0: $i] :
( ~ ( comm_semiring_1 @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ~ ( dvd_dvd @ SX0 @ ( times_times @ SX0 @ SX1 @ SX2 ) @ SX3 )
| ( dvd_dvd @ SX0 @ SX2 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1678]) ).
thf(1997,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ SX0 )
| ~ ( zcong @ ( one_one @ int ) @ ( number_number_of @ int @ min ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1596]) ).
thf(1998,plain,
( ( ! [SX0: $i] :
( ~ ( comm_semiring_1 @ SX0 )
| ! [SX1: $i,SX2: $i] : ( dvd_dvd @ SX0 @ SX1 @ ( times_times @ SX0 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1671]) ).
thf(1999,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( power @ SX0 )
| ~ ( semiring_0 @ SX0 ) )
| ! [SX1: $i] :
~ ( ~ ( ( ( number_number_of @ nat @ SX1 )
!= ( zero_zero @ nat ) )
| ( ( power_power @ SX0 @ ( zero_zero @ SX0 ) @ ( number_number_of @ nat @ SX1 ) )
= ( one_one @ SX0 ) ) )
| ~ ( ~ ( ( ( number_number_of @ nat @ SX1 )
!= ( zero_zero @ nat ) ) )
| ( ( power_power @ SX0 @ ( zero_zero @ SX0 ) @ ( number_number_of @ nat @ SX1 ) )
= ( zero_zero @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1563]) ).
thf(2000,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( no_zero_divisors @ SX2 )
| ( ( ti @ SX2 @ ( times_times @ SX2 @ SX0 @ SX1 ) )
= ( times_times @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1223]) ).
thf(2001,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( ab_group_add @ SX2 )
| ( ( plus_plus @ SX2 @ SX0 @ ( ti @ SX2 @ SX1 ) )
= ( plus_plus @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1213]) ).
thf(2002,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_eq @ int @ SX0 @ SX1 ) )
| ~ ( ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1300]) ).
thf(2003,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( zcong @ SX2 @ SX3 @ SX4 )
| ~ ( zcong @ SX0 @ SX1 @ SX4 )
| ( zcong @ ( times_times @ int @ SX2 @ SX0 ) @ ( times_times @ int @ SX3 @ SX1 ) @ SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1555]) ).
thf(2004,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( ord_less @ real @ ( zero_zero @ real ) @ SX2 )
| ~ ( ~ ( ~ ( ord_less @ real @ ( times_times @ real @ SX0 @ SX2 ) @ ( times_times @ real @ SX1 @ SX2 ) )
| ( ord_less @ real @ SX0 @ SX1 ) )
| ~ ( ~ ( ord_less @ real @ SX0 @ SX1 )
| ( ord_less @ real @ ( times_times @ real @ SX0 @ SX2 ) @ ( times_times @ real @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1643]) ).
thf(2005,plain,
( ( ! [SX0: $i] :
( ~ ( mult_zero @ SX0 )
| ! [SX1: $i] :
( ( times_times @ SX0 @ SX1 @ ( zero_zero @ SX0 ) )
= ( zero_zero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1663]) ).
thf(2006,plain,
( ( ~ ~ ! [SX0: $i] :
~ ~ ! [SX1: $i] :
( ( plus_plus @ int @ ( power_power @ int @ SX0 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ SX1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1739]) ).
thf(2007,plain,
( ( ! [SX0: $i] :
( ~ ( comm_semiring_1 @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( times_times @ SX0 @ ( times_times @ SX0 @ SX1 @ SX2 ) @ ( times_times @ SX0 @ SX3 @ SX4 ) )
= ( times_times @ SX0 @ ( times_times @ SX0 @ SX1 @ SX3 ) @ ( times_times @ SX0 @ SX2 @ SX4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1319]) ).
thf(2008,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less @ int @ SX0 @ SX1 ) )
| ~ ( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1297]) ).
thf(2009,plain,
( ( ! [SX0: $i] :
( ~ ( mult_zero @ SX0 )
| ! [SX1: $i] :
( ( times_times @ SX0 @ ( zero_zero @ SX0 ) @ SX1 )
= ( zero_zero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1662]) ).
thf(2010,plain,
( ( ( number_number_of @ int @ pls )
!= ( number_number_of @ int @ min ) )
= $true ),
inference(unfold_def,[status(thm)],[1535]) ).
thf(2011,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( quadRes @ SX0 @ ( ti @ int @ SX1 ) )
| ( quadRes @ SX0 @ SX1 ) )
| ~ ( ~ ( quadRes @ SX0 @ SX1 )
| ( quadRes @ SX0 @ ( ti @ int @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1247]) ).
thf(2012,plain,
( ( ! [SX0: $i] :
( ~ ( comm_semiring_1 @ SX0 )
| ! [SX1: $i] :
( ( plus_plus @ SX0 @ SX1 @ SX1 )
= ( times_times @ SX0 @ ( plus_plus @ SX0 @ ( one_one @ SX0 ) @ ( one_one @ SX0 ) ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1393]) ).
thf(2013,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ord_less_eq @ int @ SX0 @ ( minus_minus @ int @ SX1 @ ( one_one @ int ) ) )
| ( ord_less @ int @ SX0 @ SX1 ) )
| ~ ( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ SX0 @ ( minus_minus @ int @ SX1 @ ( one_one @ int ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1584]) ).
thf(2014,plain,
( ( ! [SX0: $i] :
( ~ ( number_semiring @ SX0 )
| ( ( number_number_of @ SX0 @ pls )
= ( zero_zero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1464]) ).
thf(2015,plain,
( ( ! [SX0: $i] :
( ~ ( ring_11004092258visors @ SX0 )
| ! [SX1: $i] :
~ ( ~ ( ( ( power_power @ SX0 @ SX1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= ( zero_zero @ SX0 ) )
| ( ( ti @ SX0 @ SX1 )
= ( zero_zero @ SX0 ) ) )
| ~ ( ( ( ti @ SX0 @ SX1 )
!= ( zero_zero @ SX0 ) )
| ( ( power_power @ SX0 @ SX1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1487]) ).
thf(2016,plain,
( ( ! [SX0: $i] :
( ~ ( linordered_semidom @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ~ ( ord_less @ SX0 @ ( zero_zero @ SX0 ) @ SX2 )
| ( ord_less @ SX0 @ ( zero_zero @ SX0 ) @ ( power_power @ SX0 @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1452]) ).
thf(2017,plain,
( ( ! [SX0: $i] :
( ~ ( comm_semiring_1 @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ~ ( dvd_dvd @ SX0 @ SX2 @ SX3 )
| ( dvd_dvd @ SX0 @ SX2 @ ( times_times @ SX0 @ SX3 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1673]) ).
thf(2018,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ord_less_eq @ int @ ( plus_plus @ int @ SX0 @ ( one_one @ int ) ) @ SX1 )
| ( ord_less @ int @ SX0 @ SX1 ) )
| ~ ( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ ( plus_plus @ int @ SX0 @ ( one_one @ int ) ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1315]) ).
thf(2019,plain,
( ( ! [SX0: $i] :
( ~ ( no_zero_divisors @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ( ( times_times @ SX0 @ SX1 @ SX2 )
!= ( zero_zero @ SX0 ) )
| ( ( ti @ SX0 @ SX1 )
= ( zero_zero @ SX0 ) )
| ( ( ti @ SX0 @ SX2 )
= ( zero_zero @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1666]) ).
thf(2020,plain,
( ( ! [SX0: $i] :
( ~ ( linordered_idom @ SX0 )
| ! [SX1: $i,SX2: $i] :
~ ( ~ ( ( ( plus_plus @ SX0 @ ( power_power @ SX0 @ SX1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SX0 @ SX2 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SX0 ) )
| ~ ( ( ( ti @ SX0 @ SX1 )
!= ( zero_zero @ SX0 ) )
| ( ( ti @ SX0 @ SX2 )
!= ( zero_zero @ SX0 ) ) ) )
| ~ ( ~ ~ ( ( ( ti @ SX0 @ SX1 )
!= ( zero_zero @ SX0 ) )
| ( ( ti @ SX0 @ SX2 )
!= ( zero_zero @ SX0 ) ) )
| ( ( plus_plus @ SX0 @ ( power_power @ SX0 @ SX1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SX0 @ SX2 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1491]) ).
thf(2021,plain,
( ( ! [SX0: $i] :
( ~ ( linordered_semidom @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ~ ( ord_less_eq @ SX0 @ SX2 @ SX3 )
| ~ ( ord_less_eq @ SX0 @ ( zero_zero @ SX0 ) @ SX2 )
| ( ord_less_eq @ SX0 @ ( power_power @ SX0 @ SX2 @ SX1 ) @ ( power_power @ SX0 @ SX3 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1451]) ).
thf(2022,plain,
( ( ! [SX0: $i] :
( ~ ( comm_semiring_1 @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ( times_times @ SX0 @ SX1 @ ( times_times @ SX0 @ SX2 @ SX3 ) )
= ( times_times @ SX0 @ SX2 @ ( times_times @ SX0 @ SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1325]) ).
thf(2023,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( power @ SX0 )
| ~ ( semiring_0 @ SX0 ) )
| ! [SX1: $i] :
~ ( ~ ( ( SX1
!= ( zero_zero @ nat ) )
| ( ( power_power @ SX0 @ ( zero_zero @ SX0 ) @ SX1 )
= ( one_one @ SX0 ) ) )
| ~ ( ~ ( ( SX1
!= ( zero_zero @ nat ) ) )
| ( ( power_power @ SX0 @ ( zero_zero @ SX0 ) @ SX1 )
= ( zero_zero @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1439]) ).
thf(2024,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( power @ SX2 )
| ( ( power_power @ SX2 @ ( ti @ SX2 @ SX0 ) @ SX1 )
= ( power_power @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1237]) ).
thf(2025,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( no_zero_divisors @ SX2 )
| ( ( times_times @ SX2 @ SX0 @ ( ti @ SX2 @ SX1 ) )
= ( times_times @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1222]) ).
thf(2026,plain,
( ( ! [SX0: $i] :
( ~ ( linordered_semidom @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ~ ( ord_less @ SX0 @ ( one_one @ SX0 ) @ SX3 )
| ~ ( ~ ( ~ ( ord_less_eq @ SX0 @ ( power_power @ SX0 @ SX3 @ SX1 ) @ ( power_power @ SX0 @ SX3 @ SX2 ) )
| ( ord_less_eq @ nat @ SX1 @ SX2 ) )
| ~ ( ~ ( ord_less_eq @ nat @ SX1 @ SX2 )
| ( ord_less_eq @ SX0 @ ( power_power @ SX0 @ SX3 @ SX1 ) @ ( power_power @ SX0 @ SX3 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1429]) ).
thf(2027,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( power @ SX2 )
| ( ( ti @ SX2 @ ( power_power @ SX2 @ SX0 @ SX1 ) )
= ( power_power @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1239]) ).
thf(2028,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( zcong @ SX0 @ ( zero_zero @ int ) @ SX1 )
| ( dvd_dvd @ int @ SX1 @ SX0 ) )
| ~ ( ~ ( dvd_dvd @ int @ SX1 @ SX0 )
| ( zcong @ SX0 @ ( zero_zero @ int ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1622]) ).
thf(2029,plain,
( ( ! [SX0: $i] :
( ~ ( number_semiring @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ~ ( ord_less_eq @ int @ pls @ SX2 )
| ~ ( ord_less_eq @ int @ pls @ SX1 )
| ( ( times_times @ SX0 @ ( number_number_of @ SX0 @ SX2 ) @ ( number_number_of @ SX0 @ SX1 ) )
= ( number_number_of @ SX0 @ ( times_times @ int @ SX2 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1386]) ).
thf(2030,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( ( SX2
!= ( zero_zero @ real ) ) )
| ~ ( ~ ( ( ( times_times @ real @ SX0 @ SX2 )
!= ( times_times @ real @ SX1 @ SX2 ) )
| ( SX0 = SX1 ) )
| ~ ( ( SX0 != SX1 )
| ( ( times_times @ real @ SX0 @ SX2 )
= ( times_times @ real @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1638]) ).
thf(2031,plain,
( ( ~ ~ ( quadRes @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) @ ( number_number_of @ int @ min ) )
| ( ( legendre @ ( number_number_of @ int @ min ) @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) )
!= ( one_one @ int ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1567]) ).
thf(2032,plain,
( ( ! [SX0: $i] :
( ~ ( power @ SX0 )
| ! [SX1: $i,SX2: $i] :
~ ( ~ ( ( SX2
!= ( zero_zero @ nat ) )
| ( ( power_power @ SX0 @ SX1 @ SX2 )
= ( one_one @ SX0 ) ) )
| ~ ( ~ ( ( SX2
!= ( zero_zero @ nat ) ) )
| ( ( power_power @ SX0 @ SX1 @ SX2 )
= ( times_times @ SX0 @ SX1 @ ( power_power @ SX0 @ SX1 @ ( minus_minus @ nat @ SX2 @ ( one_one @ nat ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1654]) ).
thf(2033,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( dvd_dvd @ nat @ SX1 @ SX2 )
| ( dvd_dvd @ nat @ ( power_power @ nat @ SX1 @ SX0 ) @ ( power_power @ nat @ SX2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1614]) ).
thf(2034,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( ord_less @ int @ SX1 @ SX2 )
| ( ord_less @ int @ ( plus_plus @ int @ SX1 @ SX0 ) @ ( plus_plus @ int @ SX2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1303]) ).
thf(2035,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ord_less @ int @ SX1 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SX1 ) @ ( number_number_of @ nat @ SX0 ) )
= ( number_number_of @ nat @ SX0 ) ) )
| ~ ( ~ ~ ( ord_less @ int @ SX1 @ pls )
| ~ ( ~ ( ~ ( ord_less @ int @ SX0 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SX1 ) @ ( number_number_of @ nat @ SX0 ) )
= ( number_number_of @ nat @ SX1 ) ) )
| ~ ( ~ ~ ( ord_less @ int @ SX0 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SX1 ) @ ( number_number_of @ nat @ SX0 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SX1 @ SX0 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1305]) ).
thf(2036,plain,
( ( ( zero_zero @ real )
!= ( one_one @ real ) )
= $true ),
inference(unfold_def,[status(thm)],[1631]) ).
thf(2037,plain,
( ( ! [SX0: $i] :
( ~ ( comm_semiring_1 @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ~ ( ord_less_eq @ nat @ SX2 @ SX3 )
| ( dvd_dvd @ SX0 @ ( power_power @ SX0 @ SX1 @ SX2 ) @ ( power_power @ SX0 @ SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1432]) ).
thf(2038,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( SX1
!= ( zero_zero @ nat ) )
| ( ( times_times @ nat @ SX1 @ SX0 )
= ( zero_zero @ nat ) ) )
| ~ ( ~ ( ( SX1
!= ( zero_zero @ nat ) ) )
| ( ( times_times @ nat @ SX1 @ SX0 )
= ( plus_plus @ nat @ SX0 @ ( times_times @ nat @ ( minus_minus @ nat @ SX1 @ ( one_one @ nat ) ) @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1601]) ).
thf(2039,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( dvd_dvd @ int @ SX0 @ ( minus_minus @ int @ SX1 @ SX2 ) )
| ~ ( dvd_dvd @ int @ SX0 @ SX2 )
| ( dvd_dvd @ int @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1573]) ).
thf(2040,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( ( bit1 @ SX0 )
!= ( bit1 @ SX1 ) )
| ( ( ti @ int @ SX0 )
= ( ti @ int @ SX1 ) ) )
| ~ ( ( ( ti @ int @ SX0 )
!= ( ti @ int @ SX1 ) )
| ( ( bit1 @ SX0 )
= ( bit1 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1335]) ).
thf(2041,plain,
( ( ! [SX0: $i] :
( ~ ( comm_semiring_1 @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ( power_power @ SX0 @ ( times_times @ SX0 @ SX1 @ SX2 ) @ SX3 )
= ( times_times @ SX0 @ ( power_power @ SX0 @ SX1 @ SX3 ) @ ( power_power @ SX0 @ SX2 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1366]) ).
thf(2042,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( zcong @ SX1 @ SX2 @ SX3 )
| ( zcong @ ( times_times @ int @ SX1 @ SX0 ) @ ( times_times @ int @ SX2 @ SX0 ) @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1557]) ).
thf(2043,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_eq @ int @ SX0 @ SX1 ) )
| ~ ( ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1299]) ).
thf(2044,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( ( times_times @ nat @ SX0 @ SX1 )
!= ( one_one @ nat ) )
| ~ ( ( SX0
!= ( one_one @ nat ) )
| ( SX1
!= ( one_one @ nat ) ) ) )
| ~ ( ~ ~ ( ( SX0
!= ( one_one @ nat ) )
| ( SX1
!= ( one_one @ nat ) ) )
| ( ( times_times @ nat @ SX0 @ SX1 )
= ( one_one @ nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1608]) ).
thf(2045,plain,
( ( ! [SX0: $i] :
( ~ ( linordered_semidom @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ~ ( ord_less @ SX0 @ ( one_one @ SX0 ) @ SX2 )
| ( ord_less @ SX0 @ ( power_power @ SX0 @ SX2 @ SX1 ) @ ( times_times @ SX0 @ SX2 @ ( power_power @ SX0 @ SX2 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1426]) ).
thf(2046,plain,
( ( ! [SX0: $i] :
( ~ ( ring_11004092258visors @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ~ ( ( ( ti @ SX0 @ SX2 )
!= ( zero_zero @ SX0 ) ) )
| ( ( power_power @ SX0 @ SX2 @ SX1 )
!= ( zero_zero @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1438]) ).
thf(2047,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( mult_zero @ SX2 )
| ( ( times_times @ SX2 @ SX0 @ ( ti @ SX2 @ SX1 ) )
= ( times_times @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1225]) ).
thf(2048,plain,
( ( ! [SX0: $i] :
( ~ ( number_ring @ SX0 )
| ! [SX1: $i] :
( ( number_number_of @ SX0 @ ( bit1 @ SX1 ) )
= ( plus_plus @ SX0 @ ( plus_plus @ SX0 @ ( one_one @ SX0 ) @ ( number_number_of @ SX0 @ SX1 ) ) @ ( number_number_of @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1405]) ).
thf(2049,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ real @ ( zero_zero @ real ) @ SX1 )
| ~ ( ord_less @ real @ ( zero_zero @ real ) @ SX0 )
| ( ord_less @ real @ ( zero_zero @ real ) @ ( times_times @ real @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1642]) ).
thf(2050,plain,
( ( ! [SX0: $i] :
( ~ ( comm_semiring_1 @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( times_times @ SX0 @ ( times_times @ SX0 @ SX1 @ SX2 ) @ ( times_times @ SX0 @ SX3 @ SX4 ) )
= ( times_times @ SX0 @ SX3 @ ( times_times @ SX0 @ ( times_times @ SX0 @ SX1 @ SX2 ) @ SX4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1320]) ).
thf(2051,plain,
( ( ! [SX0: $i] :
( ~ ( number_ring @ SX0 )
| ! [SX1: $i] :
( ( times_times @ SX0 @ SX1 @ ( number_number_of @ SX0 @ ( bit1 @ pls ) ) )
= ( ti @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1407]) ).
thf(2052,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( zprime @ SX2 )
| ~ ( dvd_dvd @ int @ SX2 @ ( times_times @ int @ SX0 @ SX1 ) )
| ( dvd_dvd @ int @ SX2 @ SX0 )
| ( dvd_dvd @ int @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1625]) ).
thf(2053,plain,
( ( ! [SX0: $i] :
( ~ ( linordered_semidom @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ~ ( ord_less @ nat @ SX2 @ SX3 )
| ~ ( ord_less @ SX0 @ ( one_one @ SX0 ) @ SX1 )
| ( ord_less @ SX0 @ ( power_power @ SX0 @ SX1 @ SX2 ) @ ( power_power @ SX0 @ SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1505]) ).
thf(2054,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( ord_less @ int @ SX1 @ SX2 )
| ~ ( ord_less @ int @ SX0 @ SX2 )
| ( ord_less_eq @ int @ SX1 @ SX0 )
| ( ord_less_eq @ int @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1552]) ).
thf(2055,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( ord_less @ int @ SX2 @ SX3 )
| ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ( ord_less @ int @ ( plus_plus @ int @ SX2 @ SX0 ) @ ( plus_plus @ int @ SX3 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1285]) ).
thf(2056,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( number @ SX0 )
| ~ ( ring @ SX0 ) )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ( times_times @ SX0 @ ( minus_minus @ SX0 @ SX1 @ SX2 ) @ ( number_number_of @ SX0 @ SX3 ) )
= ( minus_minus @ SX0 @ ( times_times @ SX0 @ SX1 @ ( number_number_of @ SX0 @ SX3 ) ) @ ( times_times @ SX0 @ SX2 @ ( number_number_of @ SX0 @ SX3 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1576]) ).
thf(2057,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ ( zero_zero @ int ) @ SX1 )
| ~ ( ord_less @ int @ ( zero_zero @ int ) @ ( times_times @ int @ SX1 @ SX0 ) )
| ( ord_less @ int @ ( zero_zero @ int ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1470]) ).
thf(2058,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ SX1 )
| ~ ( zcong @ SX0 @ ( number_number_of @ int @ min ) @ SX1 )
| ~ ( zcong @ SX0 @ ( one_one @ int ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1597]) ).
thf(2059,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ ( zero_zero @ int ) @ SX1 )
| ~ ( ord_less @ int @ SX1 @ SX0 )
| ~ ( zcong @ SX1 @ ( zero_zero @ int ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1618]) ).
thf(2060,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( SX1
!= ( zero_zero @ nat ) )
| ( ( power_power @ nat @ SX0 @ SX1 )
= ( one_one @ nat ) ) )
| ~ ( ~ ( ( SX1
!= ( zero_zero @ nat ) ) )
| ( ( power_power @ nat @ SX0 @ SX1 )
= ( times_times @ nat @ SX0 @ ( power_power @ nat @ SX0 @ ( minus_minus @ nat @ SX1 @ ( one_one @ nat ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1602]) ).
thf(2061,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ SX2 )
| ~ ( dvd_dvd @ int @ SX0 @ SX1 )
| ( dvd_dvd @ int @ SX0 @ ( power_power @ int @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1626]) ).
thf(2062,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ord_less @ nat @ ( number_number_of @ nat @ SX0 ) @ ( number_number_of @ nat @ SX1 ) )
| ~ ( ~ ( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ int @ pls @ SX1 ) )
| ~ ( ord_less @ int @ SX0 @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ int @ pls @ SX1 ) )
| ~ ( ord_less @ int @ SX0 @ SX1 ) )
| ( ord_less @ nat @ ( number_number_of @ nat @ SX0 ) @ ( number_number_of @ nat @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1477]) ).
thf(2063,plain,
( ( ! [SX0: $i] :
( ~ ( number_ring @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ( power_power @ SX0 @ ( minus_minus @ SX0 @ SX1 @ SX2 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( minus_minus @ SX0 @ ( plus_plus @ SX0 @ ( power_power @ SX0 @ SX1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SX0 @ SX2 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times @ SX0 @ ( times_times @ SX0 @ ( number_number_of @ SX0 @ ( bit0 @ ( bit1 @ pls ) ) ) @ SX1 ) @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1591]) ).
thf(2064,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( zprime @ ( ti @ int @ SX0 ) )
| ( zprime @ SX0 ) )
| ~ ( ~ ( zprime @ SX0 )
| ( zprime @ ( ti @ int @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1233]) ).
thf(2065,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( zcong @ ( power_power @ int @ SX1 @ SX2 ) @ ( one_one @ int ) @ SX3 )
| ( zcong @ ( power_power @ int @ SX1 @ ( times_times @ nat @ SX2 @ SX0 ) ) @ ( one_one @ int ) @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1453]) ).
thf(2066,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( zcong @ SX0 @ SX1 @ ( zero_zero @ int ) )
| ( ( ti @ int @ SX0 )
= ( ti @ int @ SX1 ) ) )
| ~ ( ( ( ti @ int @ SX0 )
!= ( ti @ int @ SX1 ) )
| ( zcong @ SX0 @ SX1 @ ( zero_zero @ int ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1553]) ).
thf(2067,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( ( plus_plus @ real @ ( times_times @ real @ SX0 @ SX0 ) @ ( times_times @ real @ SX1 @ SX1 ) )
!= ( zero_zero @ real ) )
| ~ ( ( SX0
!= ( zero_zero @ real ) )
| ( SX1
!= ( zero_zero @ real ) ) ) )
| ~ ( ~ ~ ( ( SX0
!= ( zero_zero @ real ) )
| ( SX1
!= ( zero_zero @ real ) ) )
| ( ( plus_plus @ real @ ( times_times @ real @ SX0 @ SX0 ) @ ( times_times @ real @ SX1 @ SX1 ) )
= ( zero_zero @ real ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1644]) ).
thf(2068,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SX0 ) @ pls )
| ( ord_less @ int @ SX0 @ pls ) )
| ~ ( ~ ( ord_less @ int @ SX0 @ pls )
| ( ord_less @ int @ ( bit1 @ SX0 ) @ pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1343]) ).
thf(2069,plain,
( ( ! [SX0: $i] :
( ~ ( semiring @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( plus_plus @ SX0 @ ( times_times @ SX0 @ SX1 @ SX2 ) @ ( plus_plus @ SX0 @ ( times_times @ SX0 @ SX3 @ SX2 ) @ SX4 ) )
= ( plus_plus @ SX0 @ ( times_times @ SX0 @ ( plus_plus @ SX0 @ SX1 @ SX3 ) @ SX2 ) @ SX4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1670]) ).
thf(2070,plain,
( ( ! [SX0: $i] :
( ~ ( monoid_mult @ SX0 )
| ! [SX1: $i] :
( ( power_power @ SX0 @ SX1 @ ( one_one @ nat ) )
= ( ti @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1481]) ).
thf(2071,plain,
( ( ( t
!= ( one_one @ int ) )
| ~ ! [SX0: $i] :
~ ~ ! [SX1: $i] :
( ( plus_plus @ int @ ( power_power @ int @ SX0 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ SX1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1255]) ).
thf(2072,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( semiring @ SX2 )
| ( ( times_times @ SX2 @ ( ti @ SX2 @ SX0 ) @ SX1 )
= ( times_times @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1218]) ).
thf(2073,plain,
( ( ! [SX0: $i] :
( ~ ( comm_semiring_1 @ SX0 )
| ! [SX1: $i] :
( ( times_times @ SX0 @ ( one_one @ SX0 ) @ SX1 )
= ( ti @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1365]) ).
thf(2074,plain,
( ( ! [SX0: $i] :
( ~ ( comm_semiring_1 @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ( times_times @ SX0 @ SX1 @ ( plus_plus @ SX0 @ SX2 @ SX3 ) )
= ( plus_plus @ SX0 @ ( times_times @ SX0 @ SX1 @ SX2 ) @ ( times_times @ SX0 @ SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1363]) ).
thf(2075,plain,
( ( ! [SX0: $i] :
( ~ ( number_ring @ SX0 )
| ! [SX1: $i] :
( ( times_times @ SX0 @ ( number_number_of @ SX0 @ ( bit0 @ ( bit1 @ pls ) ) ) @ SX1 )
= ( plus_plus @ SX0 @ SX1 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1417]) ).
thf(2076,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( zcong @ SX0 @ SX1 @ SX2 )
| ~ ! [SX3: $i] :
( ( ti @ int @ SX1 )
!= ( plus_plus @ int @ SX0 @ ( times_times @ int @ SX2 @ SX3 ) ) ) )
| ~ ( ~ ~ ! [SX3: $i] :
( ( ti @ int @ SX1 )
!= ( plus_plus @ int @ SX0 @ ( times_times @ int @ SX2 @ SX3 ) ) )
| ( zcong @ SX0 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1562]) ).
thf(2077,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( minus_minus @ int @ SX0 @ SX1 )
!= ( ti @ int @ SX2 ) )
| ( ( ti @ int @ SX0 )
= ( plus_plus @ int @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1609]) ).
thf(2078,plain,
( ( ! [SX0: $i] :
( ~ ( zprime @ SX0 )
| ~ ( ( ( ti @ int @ SX0 )
!= ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ~ ( ( ( ti @ int @ SX0 )
!= ( number_number_of @ int @ ( bit1 @ ( bit1 @ pls ) ) ) ) )
| ( ord_less_eq @ int @ ( number_number_of @ int @ ( bit1 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1423]) ).
thf(2079,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( semiring @ SX2 )
| ( ( ti @ SX2 @ ( plus_plus @ SX2 @ SX0 @ SX1 ) )
= ( plus_plus @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1211]) ).
thf(2080,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SX0 )
| ( ord_less @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( one_one @ int ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1485]) ).
thf(2081,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( times_times @ int @ SX0 @ SX1 ) @ SX2 ) )
| ~ ( ord_less @ int @ SX2 @ SX0 )
| ~ ( ord_less @ int @ ( zero_zero @ int ) @ SX0 )
| ( ord_less_eq @ int @ ( zero_zero @ int ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1647]) ).
thf(2082,plain,
( ( ! [SX0: $i] :
( ~ ( linordered_idom @ SX0 )
| ! [SX1: $i] :
~ ( ord_less @ SX0 @ ( power_power @ SX0 @ SX1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( zero_zero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1490]) ).
thf(2083,plain,
( ( ! [SX0: $i] :
( ~ ( monoid_mult @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ( power_power @ SX0 @ SX1 @ ( times_times @ nat @ SX2 @ SX3 ) )
= ( power_power @ SX0 @ ( power_power @ SX0 @ SX1 @ SX2 ) @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1496]) ).
thf(2084,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( ( times_times @ int @ SX0 @ SX1 )
!= ( one_one @ int ) )
| ~ ( ( ( ti @ int @ SX0 )
!= ( one_one @ int ) )
| ( ( ti @ int @ SX1 )
!= ( one_one @ int ) ) )
| ~ ( ( ( ti @ int @ SX0 )
!= ( number_number_of @ int @ min ) )
| ( ( ti @ int @ SX1 )
!= ( number_number_of @ int @ min ) ) ) )
| ~ ( ~ ( ~ ( ( ( ti @ int @ SX0 )
!= ( one_one @ int ) )
| ( ( ti @ int @ SX1 )
!= ( one_one @ int ) ) )
| ~ ( ( ( ti @ int @ SX0 )
!= ( number_number_of @ int @ min ) )
| ( ( ti @ int @ SX1 )
!= ( number_number_of @ int @ min ) ) ) )
| ( ( times_times @ int @ SX0 @ SX1 )
= ( one_one @ int ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1544]) ).
thf(2085,plain,
( ( ! [SX0: $i] :
( ~ ( comm_semiring_1 @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ( plus_plus @ SX0 @ SX1 @ SX2 )
= ( plus_plus @ SX0 @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1332]) ).
thf(2086,plain,
( ( ! [SX0: $i] :
( ~ ( number_ring @ SX0 )
| ( ( zero_zero @ SX0 )
= ( number_number_of @ SX0 @ pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1462]) ).
thf(2087,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( monoid_mult @ SX0 )
| ~ ( number @ SX0 ) )
| ! [SX1: $i] :
( ( power_power @ SX0 @ ( number_number_of @ SX0 @ SX1 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times @ SX0 @ ( number_number_of @ SX0 @ SX1 ) @ ( number_number_of @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1264]) ).
thf(2088,plain,
( ( ! [SX0: $i] :
( ~ ( ordere453448008miring @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ~ ( ord_less_eq @ SX0 @ SX2 @ ( zero_zero @ SX0 ) )
| ~ ( ord_less_eq @ SX0 @ ( zero_zero @ SX0 ) @ SX1 )
| ( ord_less_eq @ SX0 @ ( times_times @ SX0 @ SX2 @ SX1 ) @ ( zero_zero @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1687]) ).
thf(2089,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less @ int @ SX0 @ SX1 ) )
| ~ ( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1311]) ).
thf(2090,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ ( zero_zero @ int ) @ SX1 )
| ~ ( ~ ( ( ( times_times @ int @ SX1 @ SX0 )
!= ( one_one @ int ) )
| ~ ( ( ( ti @ int @ SX1 )
!= ( one_one @ int ) )
| ( ( ti @ int @ SX0 )
!= ( one_one @ int ) ) ) )
| ~ ( ~ ~ ( ( ( ti @ int @ SX1 )
!= ( one_one @ int ) )
| ( ( ti @ int @ SX0 )
!= ( one_one @ int ) ) )
| ( ( times_times @ int @ SX1 @ SX0 )
= ( one_one @ int ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1483]) ).
thf(2091,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq @ int @ SX0 @ SX1 ) )
| ~ ( ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1350]) ).
thf(2092,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ord_less @ int @ SX1 @ pls )
| ( ( times_times @ nat @ ( number_number_of @ nat @ SX1 ) @ ( number_number_of @ nat @ SX0 ) )
= ( zero_zero @ nat ) ) )
| ~ ( ~ ~ ( ord_less @ int @ SX1 @ pls )
| ( ( times_times @ nat @ ( number_number_of @ nat @ SX1 ) @ ( number_number_of @ nat @ SX0 ) )
= ( number_number_of @ nat @ ( times_times @ int @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1551]) ).
thf(2093,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( ( plus_plus @ int @ ( times_times @ int @ SX0 @ SX1 ) @ SX2 )
!= ( plus_plus @ int @ ( times_times @ int @ SX3 @ SX4 ) @ SX5 ) )
| ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( times_times @ int @ SX3 @ SX4 ) @ SX5 ) )
| ~ ( ord_less @ int @ SX5 @ SX3 )
| ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SX2 )
| ~ ( ord_less @ int @ ( zero_zero @ int ) @ SX3 )
| ~ ( ord_less_eq @ int @ SX3 @ SX0 )
| ( ord_less_eq @ int @ SX1 @ SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1650]) ).
thf(2094,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ~ ( ord_less @ real @ ( zero_zero @ real ) @ ( times_times @ real @ SX0 @ SX0 ) )
| ( SX0
= ( zero_zero @ real ) ) )
| ~ ( ( SX0
!= ( zero_zero @ real ) )
| ~ ( ord_less @ real @ ( zero_zero @ real ) @ ( times_times @ real @ SX0 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1523]) ).
thf(2095,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less @ int @ SX0 @ SX1 ) )
| ~ ( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1292]) ).
thf(2096,plain,
( ( ! [SX0: $i] :
( ~ ( comm_semiring_1 @ SX0 )
| ! [SX1: $i] : ( dvd_dvd @ SX0 @ ( one_one @ SX0 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1680]) ).
thf(2097,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( mult_zero @ SX2 )
| ( ( ti @ SX2 @ ( times_times @ SX2 @ SX0 @ SX1 ) )
= ( times_times @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1226]) ).
thf(2098,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( zcong @ ( ti @ int @ SX0 ) @ SX1 @ SX2 )
| ( zcong @ SX0 @ SX1 @ SX2 ) )
| ~ ( ~ ( zcong @ SX0 @ SX1 @ SX2 )
| ( zcong @ ( ti @ int @ SX0 ) @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1230]) ).
thf(2099,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( zcong @ SX0 @ ( zero_zero @ int ) @ SX1 )
| ( dvd_dvd @ int @ SX1 @ SX0 ) )
| ~ ( ~ ( dvd_dvd @ int @ SX1 @ SX0 )
| ( zcong @ SX0 @ ( zero_zero @ int ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1623]) ).
thf(2100,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( ( power_power @ nat @ SX0 @ SX1 )
!= ( one_one @ nat ) )
| ( SX0
= ( one_one @ nat ) )
| ( SX1
= ( zero_zero @ nat ) ) )
| ~ ( ~ ( ( SX0
= ( one_one @ nat ) )
| ( SX1
= ( zero_zero @ nat ) ) )
| ( ( power_power @ nat @ SX0 @ SX1 )
= ( one_one @ nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1624]) ).
thf(2101,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( zcong @ SX1 @ SX2 @ SX3 )
| ( zcong @ ( plus_plus @ int @ SX1 @ SX0 ) @ ( plus_plus @ int @ SX2 @ SX0 ) @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1612]) ).
thf(2102,plain,
( ( ! [SX0: $i] :
( ~ ( linordered_idom @ SX0 )
| ! [SX1: $i,SX2: $i] : ( ord_less_eq @ SX0 @ ( zero_zero @ SX0 ) @ ( plus_plus @ SX0 @ ( power_power @ SX0 @ SX1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SX0 @ SX2 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1497]) ).
thf(2103,plain,
( ( ! [SX0: $i] :
( ~ ( number_ring @ SX0 )
| ! [SX1: $i] :
( ( plus_plus @ SX0 @ ( number_number_of @ SX0 @ SX1 ) @ ( one_one @ SX0 ) )
= ( number_number_of @ SX0 @ ( plus_plus @ int @ SX1 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1271]) ).
thf(2104,plain,
( ( ! [SX0: $i] :
( ~ ( linordered_semidom @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ~ ( ord_less @ nat @ SX2 @ SX3 )
| ~ ( ord_less @ SX0 @ ( zero_zero @ SX0 ) @ SX1 )
| ~ ( ord_less @ SX0 @ SX1 @ ( one_one @ SX0 ) )
| ( ord_less @ SX0 @ ( power_power @ SX0 @ SX1 @ SX3 ) @ ( power_power @ SX0 @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1457]) ).
thf(2105,plain,
( ( ! [SX0: $i] :
( ~ ( semiri456707255roduct @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ( ( ( ti @ SX0 @ SX5 )
!= ( zero_zero @ SX0 ) ) )
| ~ ~ ( ( ( ti @ SX0 @ SX3 )
!= ( ti @ SX0 @ SX4 ) )
| ~ ( ( ( ti @ SX0 @ SX1 )
!= ( ti @ SX0 @ SX2 ) ) ) )
| ( ( plus_plus @ SX0 @ SX3 @ ( times_times @ SX0 @ SX5 @ SX1 ) )
!= ( plus_plus @ SX0 @ SX4 @ ( times_times @ SX0 @ SX5 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1460]) ).
thf(2106,plain,
! [SV1: $i] :
( ( ( bit0 @ ( ti @ int @ SV1 ) )
= ( bit0 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1198]) ).
thf(2107,plain,
! [SV2: $i] :
( ( ( ti @ int @ ( bit0 @ SV2 ) )
= ( bit0 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1199]) ).
thf(2108,plain,
! [SV3: $i] :
( ( ( bit1 @ ( ti @ int @ SV3 ) )
= ( bit1 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1200]) ).
thf(2109,plain,
! [SV4: $i] :
( ( ( ti @ int @ ( bit1 @ SV4 ) )
= ( bit1 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1201]) ).
thf(2110,plain,
! [SV5: $i] :
( ( ! [SY1103: $i] :
( ( minus_minus @ nat @ ( ti @ nat @ SV5 ) @ SY1103 )
= ( minus_minus @ nat @ SV5 @ SY1103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1204]) ).
thf(2111,plain,
! [SV6: $i] :
( ( ! [SY1104: $i] :
( ( minus_minus @ nat @ SV6 @ ( ti @ nat @ SY1104 ) )
= ( minus_minus @ nat @ SV6 @ SY1104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1205]) ).
thf(2112,plain,
! [SV7: $i] :
( ( ! [SY1105: $i] :
( ( ti @ nat @ ( minus_minus @ nat @ SV7 @ SY1105 ) )
= ( minus_minus @ nat @ SV7 @ SY1105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1206]) ).
thf(2113,plain,
! [SV8: $i] :
( ( ! [SY1106: $i] :
( ( product_Pair @ int @ int @ ( ti @ int @ SV8 ) @ SY1106 )
= ( product_Pair @ int @ int @ SV8 @ SY1106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1240]) ).
thf(2114,plain,
! [SV9: $i] :
( ( ! [SY1107: $i] :
( ( product_Pair @ int @ int @ SV9 @ ( ti @ int @ SY1107 ) )
= ( product_Pair @ int @ int @ SV9 @ SY1107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1241]) ).
thf(2115,plain,
! [SV10: $i] :
( ( ! [SY1108: $i] :
( ( ti @ ( product_prod @ int @ int ) @ ( product_Pair @ int @ int @ SV10 @ SY1108 ) )
= ( product_Pair @ int @ int @ SV10 @ SY1108 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1242]) ).
thf(2116,plain,
! [SV11: $i] :
( ( ! [SY1109: $i] :
( ( legendre @ ( ti @ int @ SV11 ) @ SY1109 )
= ( legendre @ SV11 @ SY1109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1243]) ).
thf(2117,plain,
! [SV12: $i] :
( ( ! [SY1110: $i] :
( ( legendre @ SV12 @ ( ti @ int @ SY1110 ) )
= ( legendre @ SV12 @ SY1110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1244]) ).
thf(2118,plain,
! [SV13: $i] :
( ( ! [SY1111: $i] :
( ( ti @ int @ ( legendre @ SV13 @ SY1111 ) )
= ( legendre @ SV13 @ SY1111 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1245]) ).
thf(2119,plain,
! [SV14: $i] :
( ( ( twoSqu579703163sum2sq @ ( ti @ ( product_prod @ int @ int ) @ SV14 ) )
= ( twoSqu579703163sum2sq @ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1249]) ).
thf(2120,plain,
! [SV15: $i] :
( ( ( ti @ int @ ( twoSqu579703163sum2sq @ SV15 ) )
= ( twoSqu579703163sum2sq @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1250]) ).
thf(2121,plain,
! [SV16: $i] :
( ( ! [SY1112: $i] :
( ( power_power @ int @ ( plus_plus @ int @ SV16 @ SY1112 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ int @ ( plus_plus @ int @ ( power_power @ int @ SV16 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( times_times @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV16 ) @ SY1112 ) ) @ ( power_power @ int @ SY1112 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1261]) ).
thf(2122,plain,
! [SV17: $i] :
( ( ! [SY1113: $i] :
( ( power_power @ int @ ( plus_plus @ int @ SV17 @ SY1113 ) @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( power_power @ int @ SV17 @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) @ ( times_times @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit1 @ ( bit1 @ pls ) ) ) @ ( power_power @ int @ SV17 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ SY1113 ) ) @ ( times_times @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit1 @ ( bit1 @ pls ) ) ) @ SV17 ) @ ( power_power @ int @ SY1113 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ ( power_power @ int @ SY1113 @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1262]) ).
thf(2123,plain,
! [SV18: $i] :
( ( ( times_times @ int @ SV18 @ ( power_power @ int @ SV18 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( power_power @ int @ SV18 @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1265]) ).
thf(2124,plain,
! [SV19: $i] :
( ( ord_less_eq @ int @ SV19 @ SV19 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1274]) ).
thf(2125,plain,
! [SV20: $i] :
( ( ! [SY1114: $i] :
( ( ord_less_eq @ int @ SV20 @ SY1114 )
| ( ord_less_eq @ int @ SY1114 @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1275]) ).
thf(2126,plain,
! [SV21: $i] :
( ( ! [SY1115: $i] :
( ( ord_less @ int @ SV21 @ SY1115 )
| ( ( ti @ int @ SV21 )
= ( ti @ int @ SY1115 ) )
| ( ord_less @ int @ SY1115 @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1277]) ).
thf(2127,plain,
! [SV22: $i] :
( ( ! [SY1116: $i,SY1117: $i] :
( ( power_power @ int @ ( power_power @ int @ SV22 @ SY1116 ) @ SY1117 )
= ( power_power @ int @ SV22 @ ( times_times @ nat @ SY1116 @ SY1117 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1282]) ).
thf(2128,plain,
! [SV23: $i] :
( ( ! [SY1118: $i,SY1119: $i] :
( ( power_power @ int @ SV23 @ ( plus_plus @ nat @ SY1118 @ SY1119 ) )
= ( times_times @ int @ ( power_power @ int @ SV23 @ SY1118 ) @ ( power_power @ int @ SV23 @ SY1119 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1287]) ).
thf(2129,plain,
! [SV24: $i] :
( ( ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV24 )
= ( plus_plus @ nat @ SV24 @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1288]) ).
thf(2130,plain,
! [SV25: $i] :
( ( ( times_times @ nat @ SV25 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ nat @ SV25 @ SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1289]) ).
thf(2131,plain,
( ( ord_less @ int @ pls @ pls )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1295]) ).
thf(2132,plain,
! [SV26: $i] :
( ( ! [SY1120: $i,SY1121: $i] :
( ( times_times @ int @ ( times_times @ int @ SV26 @ SY1120 ) @ SY1121 )
= ( times_times @ int @ SV26 @ ( times_times @ int @ SY1120 @ SY1121 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1337]) ).
thf(2133,plain,
! [SV27: $i] :
( ( ! [SY1122: $i] :
( ( times_times @ int @ SV27 @ SY1122 )
= ( times_times @ int @ SY1122 @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1338]) ).
thf(2134,plain,
! [SV28: $i] :
( ( ( number_number_of @ int @ SV28 )
= ( ti @ int @ SV28 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1339]) ).
thf(2135,plain,
! [SV29: $i] :
( ( ! [SY1123: $i,SY1124: $i] :
( ( plus_plus @ int @ ( plus_plus @ int @ SV29 @ SY1123 ) @ SY1124 )
= ( plus_plus @ int @ SV29 @ ( plus_plus @ int @ SY1123 @ SY1124 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1340]) ).
thf(2136,plain,
! [SV30: $i] :
( ( ! [SY1125: $i,SY1126: $i] :
( ( plus_plus @ int @ SV30 @ ( plus_plus @ int @ SY1125 @ SY1126 ) )
= ( plus_plus @ int @ SY1125 @ ( plus_plus @ int @ SV30 @ SY1126 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1341]) ).
thf(2137,plain,
! [SV31: $i] :
( ( ! [SY1127: $i] :
( ( plus_plus @ int @ SV31 @ SY1127 )
= ( plus_plus @ int @ SY1127 @ SV31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1342]) ).
thf(2138,plain,
! [SV32: $i] :
( ( ( times_times @ int @ pls @ SV32 )
= pls )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1374]) ).
thf(2139,plain,
! [SV33: $i] :
( ( ! [SY1128: $i] :
( ( times_times @ int @ ( bit0 @ SV33 ) @ SY1128 )
= ( bit0 @ ( times_times @ int @ SV33 @ SY1128 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1375]) ).
thf(2140,plain,
! [SV34: $i] :
( ( ( plus_plus @ int @ SV34 @ pls )
= ( ti @ int @ SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1376]) ).
thf(2141,plain,
! [SV35: $i] :
( ( ( plus_plus @ int @ pls @ SV35 )
= ( ti @ int @ SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1377]) ).
thf(2142,plain,
! [SV36: $i] :
( ( ! [SY1129: $i] :
( ( plus_plus @ int @ ( bit0 @ SV36 ) @ ( bit0 @ SY1129 ) )
= ( bit0 @ ( plus_plus @ int @ SV36 @ SY1129 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1378]) ).
thf(2143,plain,
! [SV37: $i] :
( ( ( bit0 @ SV37 )
= ( plus_plus @ int @ SV37 @ SV37 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1379]) ).
thf(2144,plain,
! [SV38: $i] :
( ( ( times_times @ int @ SV38 @ ( one_one @ int ) )
= ( ti @ int @ SV38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1380]) ).
thf(2145,plain,
! [SV39: $i] :
( ( ( times_times @ int @ ( one_one @ int ) @ SV39 )
= ( ti @ int @ SV39 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1381]) ).
thf(2146,plain,
! [SV40: $i] :
( ( ! [SY1130: $i] :
( ( times_times @ int @ ( number_number_of @ int @ SV40 ) @ ( number_number_of @ int @ SY1130 ) )
= ( number_number_of @ int @ ( times_times @ int @ SV40 @ SY1130 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1382]) ).
thf(2147,plain,
! [SV41: $i] :
( ( ! [SY1131: $i,SY1132: $i] :
( ( times_times @ int @ ( plus_plus @ int @ SV41 @ SY1131 ) @ SY1132 )
= ( plus_plus @ int @ ( times_times @ int @ SV41 @ SY1132 ) @ ( times_times @ int @ SY1131 @ SY1132 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1383]) ).
thf(2148,plain,
! [SV42: $i] :
( ( ! [SY1133: $i,SY1134: $i] :
( ( times_times @ int @ SV42 @ ( plus_plus @ int @ SY1133 @ SY1134 ) )
= ( plus_plus @ int @ ( times_times @ int @ SV42 @ SY1133 ) @ ( times_times @ int @ SV42 @ SY1134 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1384]) ).
thf(2149,plain,
! [SV43: $i] :
( ( ! [SY1135: $i] :
( ( plus_plus @ int @ ( number_number_of @ int @ SV43 ) @ ( number_number_of @ int @ SY1135 ) )
= ( number_number_of @ int @ ( plus_plus @ int @ SV43 @ SY1135 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1385]) ).
thf(2150,plain,
! [SV44: $i] :
( ( ord_less_eq @ int @ SV44 @ ( power_power @ int @ SV44 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1388]) ).
thf(2151,plain,
! [SV45: $i] :
( ( ! [SY1136: $i] :
( ( plus_plus @ int @ ( bit1 @ SV45 ) @ ( bit0 @ SY1136 ) )
= ( bit1 @ ( plus_plus @ int @ SV45 @ SY1136 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1402]) ).
thf(2152,plain,
! [SV46: $i] :
( ( ! [SY1137: $i] :
( ( plus_plus @ int @ ( bit0 @ SV46 ) @ ( bit1 @ SY1137 ) )
= ( bit1 @ ( plus_plus @ int @ SV46 @ SY1137 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1403]) ).
thf(2153,plain,
! [SV47: $i] :
( ( ( bit1 @ SV47 )
= ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ SV47 ) @ SV47 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1404]) ).
thf(2154,plain,
! [SV48: $i] :
( ( ! [SY1138: $i] :
( ( times_times @ int @ ( bit1 @ SV48 ) @ SY1138 )
= ( plus_plus @ int @ ( bit0 @ ( times_times @ int @ SV48 @ SY1138 ) ) @ SY1138 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1412]) ).
thf(2155,plain,
! [SV49: $i] :
( ( ( power_power @ int @ ( power_power @ int @ SV49 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power @ int @ SV49 @ ( number_number_of @ nat @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1415]) ).
thf(2156,plain,
! [SV50: $i] :
( ( ! [SY1139: $i] :
( ( power_power @ real @ ( plus_plus @ real @ SV50 @ SY1139 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ real @ ( plus_plus @ real @ ( power_power @ real @ SV50 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ real @ SY1139 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times @ real @ ( times_times @ real @ ( number_number_of @ real @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV50 ) @ SY1139 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1424]) ).
thf(2157,plain,
! [SV51: $i] :
( ( ( times_times @ real @ ( number_number_of @ real @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ real @ SV51 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( power_power @ real @ ( times_times @ real @ ( number_number_of @ real @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV51 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1425]) ).
thf(2158,plain,
! [SV52: $i] :
( ( ( plus_plus @ int @ ( zero_zero @ int ) @ SV52 )
= ( ti @ int @ SV52 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1448]) ).
thf(2159,plain,
! [SV53: $i] :
( ( ( plus_plus @ int @ SV53 @ ( zero_zero @ int ) )
= ( ti @ int @ SV53 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1449]) ).
thf(2160,plain,
( ( ord_less @ int @ pls @ ( zero_zero @ int ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1466]) ).
thf(2161,plain,
( ( ! [S1: $i] :
~ ( zcong @ ( power_power @ int @ S1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of @ int @ min ) @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1508]) ).
thf(2162,plain,
( ( ord_less @ int @ min @ min )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1521]) ).
thf(2163,plain,
( ( ord_less @ int @ pls @ min )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1526]) ).
thf(2164,plain,
( ( ord_less_eq @ int @ pls @ min )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1532]) ).
thf(2165,plain,
! [SV54: $i] :
( ( ! [SY1140: $i] : ( zcong @ SV54 @ SY1140 @ ( one_one @ int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1554]) ).
thf(2166,plain,
! [SV55: $i] :
( ( ! [SY1141: $i,SY1142: $i] : ( zcong @ ( times_times @ int @ SV55 @ SY1141 ) @ ( times_times @ int @ SY1142 @ SY1141 ) @ SY1141 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1558]) ).
thf(2167,plain,
! [SV56: $i] :
( ( ( minus_minus @ int @ SV56 @ pls )
= ( ti @ int @ SV56 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1569]) ).
thf(2168,plain,
! [SV57: $i] :
( ( ! [SY1143: $i] :
( ( minus_minus @ int @ ( bit0 @ SV57 ) @ ( bit0 @ SY1143 ) )
= ( bit0 @ ( minus_minus @ int @ SV57 @ SY1143 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1570]) ).
thf(2169,plain,
! [SV58: $i] :
( ( ! [SY1144: $i,SY1145: $i] :
( ( times_times @ int @ ( minus_minus @ int @ SV58 @ SY1144 ) @ SY1145 )
= ( minus_minus @ int @ ( times_times @ int @ SV58 @ SY1145 ) @ ( times_times @ int @ SY1144 @ SY1145 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1571]) ).
thf(2170,plain,
! [SV59: $i] :
( ( ! [SY1146: $i,SY1147: $i] :
( ( times_times @ int @ SV59 @ ( minus_minus @ int @ SY1146 @ SY1147 ) )
= ( minus_minus @ int @ ( times_times @ int @ SV59 @ SY1146 ) @ ( times_times @ int @ SV59 @ SY1147 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1572]) ).
thf(2171,plain,
! [SV60: $i] :
( ( ! [SY1148: $i] :
( ( minus_minus @ int @ ( bit1 @ SV60 ) @ ( bit0 @ SY1148 ) )
= ( bit1 @ ( minus_minus @ int @ SV60 @ SY1148 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1577]) ).
thf(2172,plain,
! [SV61: $i] :
( ( ! [SY1149: $i] :
( ( minus_minus @ int @ ( bit1 @ SV61 ) @ ( bit1 @ SY1149 ) )
= ( bit0 @ ( minus_minus @ int @ SV61 @ SY1149 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1578]) ).
thf(2173,plain,
! [SV62: $i] :
( ( ( minus_minus @ int @ pls @ ( bit0 @ SV62 ) )
= ( bit0 @ ( minus_minus @ int @ pls @ SV62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1579]) ).
thf(2174,plain,
! [SV63: $i] :
( ( ! [SY1150: $i,SY1151: $i,SY1152: $i,SY1153: $i,SY1154: $i,SY1155: $i] :
( ( plus_plus @ int @ ( times_times @ int @ ( minus_minus @ int @ SV63 @ ( times_times @ int @ SY1150 @ SY1151 ) ) @ SY1152 ) @ ( times_times @ int @ ( minus_minus @ int @ SY1153 @ ( times_times @ int @ SY1150 @ SY1154 ) ) @ SY1155 ) )
= ( minus_minus @ int @ ( plus_plus @ int @ ( times_times @ int @ SV63 @ SY1152 ) @ ( times_times @ int @ SY1153 @ SY1155 ) ) @ ( times_times @ int @ SY1150 @ ( plus_plus @ int @ ( times_times @ int @ SY1151 @ SY1152 ) @ ( times_times @ int @ SY1154 @ SY1155 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1581]) ).
thf(2175,plain,
! [SV64: $i] :
( ( ( minus_minus @ int @ pls @ ( bit1 @ SV64 ) )
= ( bit1 @ ( minus_minus @ int @ min @ SV64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1585]) ).
thf(2176,plain,
! [SV65: $i] :
( ( ( minus_minus @ int @ min @ ( bit1 @ SV65 ) )
= ( bit0 @ ( minus_minus @ int @ min @ SV65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1586]) ).
thf(2177,plain,
! [SV66: $i] :
( ( ( minus_minus @ int @ min @ ( bit0 @ SV66 ) )
= ( bit1 @ ( minus_minus @ int @ min @ SV66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1587]) ).
thf(2178,plain,
! [SV67: $i] :
( ( ! [SY1156: $i,SY1157: $i,SY1158: $i] :
( ( times_times @ int @ ( twoSqu579703163sum2sq @ ( product_Pair @ int @ int @ SV67 @ SY1156 ) ) @ ( twoSqu579703163sum2sq @ ( product_Pair @ int @ int @ SY1157 @ SY1158 ) ) )
= ( twoSqu579703163sum2sq @ ( product_Pair @ int @ int @ ( plus_plus @ int @ ( times_times @ int @ SV67 @ SY1157 ) @ ( times_times @ int @ SY1156 @ SY1158 ) ) @ ( minus_minus @ int @ ( times_times @ int @ SV67 @ SY1158 ) @ ( times_times @ int @ SY1156 @ SY1157 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1589]) ).
thf(2179,plain,
! [SV68: $i] :
( ( ! [SY1159: $i] :
( ( times_times @ int @ ( plus_plus @ int @ SV68 @ SY1159 ) @ ( minus_minus @ int @ SV68 @ SY1159 ) )
= ( minus_minus @ int @ ( power_power @ int @ SV68 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ SY1159 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1590]) ).
thf(2180,plain,
! [SV69: $i] :
( ( ! [SY1160: $i] :
( ( power_power @ int @ ( minus_minus @ int @ SV69 @ SY1160 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ int @ ( minus_minus @ int @ ( power_power @ int @ SV69 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( times_times @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV69 ) @ SY1160 ) ) @ ( power_power @ int @ SY1160 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1592]) ).
thf(2181,plain,
! [SV70: $i] :
( ( ! [SY1161: $i] :
( ( power_power @ int @ ( minus_minus @ int @ SV70 @ SY1161 ) @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( minus_minus @ int @ ( plus_plus @ int @ ( minus_minus @ int @ ( power_power @ int @ SV70 @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) @ ( times_times @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit1 @ ( bit1 @ pls ) ) ) @ ( power_power @ int @ SV70 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ SY1161 ) ) @ ( times_times @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit1 @ ( bit1 @ pls ) ) ) @ SV70 ) @ ( power_power @ int @ SY1161 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ ( power_power @ int @ SY1161 @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1593]) ).
thf(2182,plain,
! [SV71: $i] :
( ( ( ( power_power @ int @ ( number_number_of @ int @ min ) @ SV71 )
= ( one_one @ int ) )
| ( ( power_power @ int @ ( number_number_of @ int @ min ) @ SV71 )
= ( number_number_of @ int @ min ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1594]) ).
thf(2183,plain,
! [SV72: $i] :
( ( ! [SY1162: $i] :
( ( minus_minus @ nat @ ( power_power @ nat @ SV72 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ nat @ SY1162 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( times_times @ nat @ ( plus_plus @ nat @ SV72 @ SY1162 ) @ ( minus_minus @ nat @ SV72 @ SY1162 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1603]) ).
thf(2184,plain,
! [SV73: $i] :
( ( zcong @ SV73 @ ( zero_zero @ int ) @ SV73 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1607]) ).
thf(2185,plain,
! [SV74: $i] :
( ( ( times_times @ real @ ( one_one @ real ) @ SV74 )
= SV74 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1632]) ).
thf(2186,plain,
! [SV75: $i] :
( ( ! [SY1163: $i] :
( ( times_times @ real @ SV75 @ SY1163 )
= ( times_times @ real @ SY1163 @ SV75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1633]) ).
thf(2187,plain,
! [SV76: $i] :
( ( ! [SY1164: $i,SY1165: $i] :
( ( times_times @ real @ ( times_times @ real @ SV76 @ SY1164 ) @ SY1165 )
= ( times_times @ real @ SV76 @ ( times_times @ real @ SY1164 @ SY1165 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1634]) ).
thf(2188,plain,
! [SV77: $i] :
( ( ! [SY1166: $i,SY1167: $i] :
( ( times_times @ real @ ( plus_plus @ real @ SV77 @ SY1166 ) @ SY1167 )
= ( plus_plus @ real @ ( times_times @ real @ SV77 @ SY1167 ) @ ( times_times @ real @ SY1166 @ SY1167 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1639]) ).
thf(2189,plain,
! [SV78: $i] :
( ( ord_less_eq @ real @ ( one_one @ real ) @ ( power_power @ real @ ( number_number_of @ real @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV78 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1646]) ).
thf(2190,plain,
! [SV79: $i] :
( ( ! [SY1168: $i,SY1169: $i,SY1170: $i,SY1171: $i] :
( ~ ( zcong @ SY1169 @ SY1170 @ SY1171 )
| ~ ( ~ ( ~ ( zcong @ SV79 @ ( times_times @ int @ SY1169 @ SY1168 ) @ SY1171 )
| ( zcong @ SV79 @ ( times_times @ int @ SY1170 @ SY1168 ) @ SY1171 ) )
| ~ ( ~ ( zcong @ SV79 @ ( times_times @ int @ SY1170 @ SY1168 ) @ SY1171 )
| ( zcong @ SV79 @ ( times_times @ int @ SY1169 @ SY1168 ) @ SY1171 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1740]) ).
thf(2191,plain,
! [SV80: $i] :
( ( ! [SY1172: $i] :
~ ( ~ ( ~ ( ord_less @ int @ SV80 @ ( plus_plus @ int @ SY1172 @ ( one_one @ int ) ) )
| ( ord_less @ int @ SV80 @ SY1172 )
| ( ( ti @ int @ SV80 )
= ( ti @ int @ SY1172 ) ) )
| ~ ( ~ ( ( ord_less @ int @ SV80 @ SY1172 )
| ( ( ti @ int @ SV80 )
= ( ti @ int @ SY1172 ) ) )
| ( ord_less @ int @ SV80 @ ( plus_plus @ int @ SY1172 @ ( one_one @ int ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1741]) ).
thf(2192,plain,
! [SV81: $i] :
( ( ! [SY1173: $i,SY1174: $i] :
( ~ ( semiring @ SY1174 )
| ( ( plus_plus @ SY1174 @ SV81 @ ( ti @ SY1174 @ SY1173 ) )
= ( plus_plus @ SY1174 @ SV81 @ SY1173 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1742]) ).
thf(2193,plain,
! [SV82: $i] :
( ( ~ ( ordere453448008miring @ SV82 )
| ! [SY1175: $i,SY1176: $i] :
( ~ ( ord_less_eq @ SV82 @ ( zero_zero @ SV82 ) @ SY1176 )
| ~ ( ord_less_eq @ SV82 @ SY1175 @ ( zero_zero @ SV82 ) )
| ( ord_less_eq @ SV82 @ ( times_times @ SV82 @ SY1176 @ SY1175 ) @ ( zero_zero @ SV82 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1743]) ).
thf(2194,plain,
! [SV83: $i] :
( ( ~ ( monoid_mult @ SV83 )
| ! [SY1177: $i,SY1178: $i] :
( ( times_times @ SV83 @ ( power_power @ SV83 @ SY1177 @ SY1178 ) @ SY1177 )
= ( times_times @ SV83 @ SY1177 @ ( power_power @ SV83 @ SY1177 @ SY1178 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1744]) ).
thf(2195,plain,
! [SV84: $i] :
( ( ~ ( comm_semiring_1 @ SV84 )
| ! [SY1179: $i,SY1180: $i,SY1181: $i] :
( ( plus_plus @ SV84 @ ( plus_plus @ SV84 @ SY1179 @ SY1180 ) @ SY1181 )
= ( plus_plus @ SV84 @ SY1179 @ ( plus_plus @ SV84 @ SY1180 @ SY1181 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1745]) ).
thf(2196,plain,
! [SV85: $i] :
( ( ~ ( number_semiring @ SV85 )
| ( ( plus_plus @ SV85 @ ( one_one @ SV85 ) @ ( one_one @ SV85 ) )
= ( number_number_of @ SV85 @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1746]) ).
thf(2197,plain,
! [SV86: $i] :
( ( ~ ( linordered_ring @ SV86 )
| ! [SY1182: $i] : ( ord_less_eq @ SV86 @ ( zero_zero @ SV86 ) @ ( times_times @ SV86 @ SY1182 @ SY1182 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1747]) ).
thf(2198,plain,
! [SV87: $i] :
( ( ~ ( ordere453448008miring @ SV87 )
| ! [SY1183: $i,SY1184: $i] :
( ~ ( ord_less_eq @ SV87 @ ( zero_zero @ SV87 ) @ SY1184 )
| ~ ( ord_less_eq @ SV87 @ SY1183 @ ( zero_zero @ SV87 ) )
| ( ord_less_eq @ SV87 @ ( times_times @ SV87 @ SY1183 @ SY1184 ) @ ( zero_zero @ SV87 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1748]) ).
thf(2199,plain,
! [SV88: $i] :
( ( ~ ( linordered_idom @ SV88 )
| ! [SY1185: $i,SY1186: $i] :
~ ( ord_less @ SV88 @ ( plus_plus @ SV88 @ ( power_power @ SV88 @ SY1185 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV88 @ SY1186 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( zero_zero @ SV88 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1749]) ).
thf(2200,plain,
! [SV89: $i] :
( ( ! [SY1187: $i,SY1188: $i] :
( ~ ( no_zero_divisors @ SY1188 )
| ( ( times_times @ SY1188 @ ( ti @ SY1188 @ SV89 ) @ SY1187 )
= ( times_times @ SY1188 @ SV89 @ SY1187 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1750]) ).
thf(2201,plain,
! [SV90: $i] :
( ( ~ ( no_zero_divisors @ SV90 )
| ! [SY1189: $i,SY1190: $i] :
( ~ ( ( ( ti @ SV90 @ SY1190 )
!= ( zero_zero @ SV90 ) ) )
| ~ ( ( ( ti @ SV90 @ SY1189 )
!= ( zero_zero @ SV90 ) ) )
| ( ( times_times @ SV90 @ SY1190 @ SY1189 )
!= ( zero_zero @ SV90 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1751]) ).
thf(2202,plain,
! [SV91: $i] :
( ( ~ ( ~ ( ~ ( ord_less_eq @ int @ min @ ( bit1 @ SV91 ) )
| ( ord_less_eq @ int @ min @ SV91 ) )
| ~ ( ~ ( ord_less_eq @ int @ min @ SV91 )
| ( ord_less_eq @ int @ min @ ( bit1 @ SV91 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1752]) ).
thf(2203,plain,
! [SV92: $i] :
( ( ! [SY1191: $i] :
( ~ ( dvd_dvd @ int @ SV92 @ SY1191 )
| ( ord_less_eq @ int @ SY1191 @ ( zero_zero @ int ) )
| ( ord_less_eq @ int @ SV92 @ SY1191 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1753]) ).
thf(2204,plain,
! [SV93: $i] :
( ( ~ ( ~ ( ( min
!= ( bit1 @ SV93 ) )
| ( min
= ( ti @ int @ SV93 ) ) )
| ~ ( ( min
!= ( ti @ int @ SV93 ) )
| ( min
= ( bit1 @ SV93 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1754]) ).
thf(2205,plain,
! [SV94: $i] :
( ( ~ ( comm_semiring_1 @ SV94 )
| ! [SY1192: $i,SY1193: $i,SY1194: $i] :
( ( times_times @ SV94 @ SY1192 @ ( times_times @ SV94 @ SY1193 @ SY1194 ) )
= ( times_times @ SV94 @ ( times_times @ SV94 @ SY1192 @ SY1193 ) @ SY1194 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1755]) ).
thf(2206,plain,
! [SV95: $i] :
( ( ~ ( comm_semiring_1 @ SV95 )
| ! [SY1195: $i,SY1196: $i,SY1197: $i,SY1198: $i] :
( ( times_times @ SV95 @ ( times_times @ SV95 @ SY1195 @ SY1196 ) @ ( times_times @ SV95 @ SY1197 @ SY1198 ) )
= ( times_times @ SV95 @ SY1195 @ ( times_times @ SV95 @ SY1196 @ ( times_times @ SV95 @ SY1197 @ SY1198 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1756]) ).
thf(2207,plain,
! [SV96: $i] :
( ( ! [SY1199: $i] :
~ ( ~ ( ~ ( ord_less @ int @ ( number_number_of @ int @ SV96 ) @ ( number_number_of @ int @ SY1199 ) )
| ( ord_less @ int @ SV96 @ SY1199 ) )
| ~ ( ~ ( ord_less @ int @ SV96 @ SY1199 )
| ( ord_less @ int @ ( number_number_of @ int @ SV96 ) @ ( number_number_of @ int @ SY1199 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1757]) ).
thf(2208,plain,
! [SV97: $i] :
( ( ! [SY1200: $i] :
( ~ ( dvd_dvd @ nat @ SV97 @ SY1200 )
| ( SY1200
= ( zero_zero @ nat ) )
| ( ord_less_eq @ nat @ SV97 @ SY1200 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1758]) ).
thf(2209,plain,
! [SV98: $i] :
( ( ! [SY1201: $i,SY1202: $i] :
( ~ ( ab_group_add @ SY1202 )
| ( ( ti @ SY1202 @ ( plus_plus @ SY1202 @ SV98 @ SY1201 ) )
= ( plus_plus @ SY1202 @ SV98 @ SY1201 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1759]) ).
thf(2210,plain,
! [SV99: $i] :
( ( ~ ( comm_semiring_1 @ SV99 )
| ! [SY1203: $i,SY1204: $i,SY1205: $i] :
( ( plus_plus @ SV99 @ SY1203 @ ( plus_plus @ SV99 @ SY1204 @ SY1205 ) )
= ( plus_plus @ SV99 @ SY1204 @ ( plus_plus @ SV99 @ SY1203 @ SY1205 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1760]) ).
thf(2211,plain,
! [SV100: $i] :
( ( ! [SY1206: $i,SY1207: $i] :
( ~ ( ord_less_eq @ int @ SY1206 @ SY1207 )
| ( ord_less_eq @ int @ ( plus_plus @ int @ SV100 @ SY1206 ) @ ( plus_plus @ int @ SV100 @ SY1207 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1761]) ).
thf(2212,plain,
! [SV101: $i] :
( ( ! [SY1208: $i,SY1209: $i] :
( ~ ~ ( zcong @ SY1208 @ ( zero_zero @ int ) @ SY1209 )
| ~ ( zcong @ ( power_power @ int @ SV101 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SY1208 @ SY1209 )
| ~ ( dvd_dvd @ int @ SY1209 @ SV101 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1762]) ).
thf(2213,plain,
! [SV102: $i] :
( ( ~ ( linordered_semidom @ SV102 )
| ! [SY1210: $i,SY1211: $i] :
( ~ ( ord_less @ SV102 @ ( zero_zero @ SV102 ) @ SY1211 )
| ~ ( ord_less @ SV102 @ SY1211 @ ( one_one @ SV102 ) )
| ( ord_less @ SV102 @ ( times_times @ SV102 @ SY1211 @ ( power_power @ SV102 @ SY1211 @ SY1210 ) ) @ ( power_power @ SV102 @ SY1211 @ SY1210 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1763]) ).
thf(2214,plain,
! [SV103: $i] :
( ( ! [SY1212: $i] :
~ ( ~ ( ~ ( quadRes @ ( ti @ int @ SV103 ) @ SY1212 )
| ( quadRes @ SV103 @ SY1212 ) )
| ~ ( ~ ( quadRes @ SV103 @ SY1212 )
| ( quadRes @ ( ti @ int @ SV103 ) @ SY1212 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1764]) ).
thf(2215,plain,
( ( ( zero_zero @ int )
= ( one_one @ int ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1765]) ).
thf(2216,plain,
! [SV104: $i] :
( ( ! [SY1213: $i,SY1214: $i] :
( ~ ( semiring @ SY1214 )
| ( ( times_times @ SY1214 @ SV104 @ ( ti @ SY1214 @ SY1213 ) )
= ( times_times @ SY1214 @ SV104 @ SY1213 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1766]) ).
thf(2217,plain,
! [SV105: $i] :
( ( ~ ( semiring_1 @ SV105 )
| ( ( power_power @ SV105 @ ( one_one @ SV105 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( one_one @ SV105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1767]) ).
thf(2218,plain,
! [SV106: $i] :
( ( ~ ( ~ ( ( ( bit1 @ SV106 )
!= min )
| ( ( ti @ int @ SV106 )
= min ) )
| ~ ( ( ( ti @ int @ SV106 )
!= min )
| ( ( bit1 @ SV106 )
= min ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1768]) ).
thf(2219,plain,
! [SV107: $i] :
( ( ! [SY1215: $i,SY1216: $i] :
( ~ ( power @ SY1216 )
| ( ( times_times @ SY1216 @ SV107 @ ( ti @ SY1216 @ SY1215 ) )
= ( times_times @ SY1216 @ SV107 @ SY1215 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1769]) ).
thf(2220,plain,
! [SV108: $i] :
( ( ! [SY1217: $i,SY1218: $i,SY1219: $i,SY1220: $i] :
( ~ ( zcong @ SY1218 @ SY1219 @ SY1220 )
| ( ( ti @ int @ SY1219 )
!= ( ti @ int @ SY1217 ) )
| ~ ( zcong @ SY1217 @ SV108 @ SY1220 )
| ( zcong @ SY1218 @ SV108 @ SY1220 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1770]) ).
thf(2221,plain,
! [SV109: $i] :
( ( ! [SY1221: $i,SY1222: $i] :
( ~ ( dvd_dvd @ int @ ( times_times @ int @ SV109 @ SY1221 ) @ ( times_times @ int @ SV109 @ SY1222 ) )
| ~ ( ( ( ti @ int @ SV109 )
!= ( zero_zero @ int ) ) )
| ( dvd_dvd @ int @ SY1221 @ SY1222 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1771]) ).
thf(2222,plain,
! [SV110: $i] :
( ( ~ ( power @ SV110 )
| ! [SY1223: $i] :
( ( power_power @ SV110 @ SY1223 @ ( zero_zero @ nat ) )
= ( one_one @ SV110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1772]) ).
thf(2223,plain,
! [SV111: $i] :
( ( ! [SY1224: $i] :
( ~ ( twoSqu420862341sum2sq @ SY1224 )
| ~ ( twoSqu420862341sum2sq @ SV111 )
| ( twoSqu420862341sum2sq @ ( times_times @ int @ SY1224 @ SV111 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1773]) ).
thf(2224,plain,
! [SV112: $i] :
( ( ~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit0 @ SV112 ) @ pls )
| ( ord_less_eq @ int @ SV112 @ pls ) )
| ~ ( ~ ( ord_less_eq @ int @ SV112 @ pls )
| ( ord_less_eq @ int @ ( bit0 @ SV112 ) @ pls ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1774]) ).
thf(2225,plain,
! [SV113: $i] :
( ( ! [SY1225: $i] :
( ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SY1225 )
| ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( power_power @ int @ SY1225 @ SV113 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1775]) ).
thf(2226,plain,
! [SV114: $i] :
( ( ~ ( zero_neq_one @ SV114 )
| ( ( ti @ SV114 @ ( one_one @ SV114 ) )
= ( one_one @ SV114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1776]) ).
thf(2227,plain,
! [SV115: $i] :
( ( ! [SY1226: $i] :
~ ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SV115 ) @ ( bit0 @ SY1226 ) )
| ( ord_less @ int @ SV115 @ SY1226 ) )
| ~ ( ~ ( ord_less @ int @ SV115 @ SY1226 )
| ( ord_less @ int @ ( bit1 @ SV115 ) @ ( bit0 @ SY1226 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1777]) ).
thf(2228,plain,
! [SV116: $i] :
( ( ~ ( semiring_1 @ SV116 )
| ( ( power_power @ SV116 @ ( zero_zero @ SV116 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SV116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1778]) ).
thf(2229,plain,
! [SV117: $i] :
( ( ~ ( linordered_semidom @ SV117 )
| ! [SY1227: $i,SY1228: $i,SY1229: $i] :
( ~ ( ord_less_eq @ nat @ SY1228 @ SY1229 )
| ~ ( ord_less_eq @ SV117 @ ( zero_zero @ SV117 ) @ SY1227 )
| ~ ( ord_less_eq @ SV117 @ SY1227 @ ( one_one @ SV117 ) )
| ( ord_less_eq @ SV117 @ ( power_power @ SV117 @ SY1227 @ SY1229 ) @ ( power_power @ SV117 @ SY1227 @ SY1228 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1779]) ).
thf(2230,plain,
! [SV118: $i] :
( ( ! [SY1230: $i,SY1231: $i] :
( ~ ( dvd_dvd @ nat @ SY1230 @ SY1231 )
| ( dvd_dvd @ nat @ ( times_times @ nat @ SV118 @ SY1230 ) @ ( times_times @ nat @ SV118 @ SY1231 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1780]) ).
thf(2231,plain,
! [SV119: $i] :
( ( ! [SY1232: $i,SY1233: $i] :
( ~ ( zprime @ SY1233 )
| ~ ( dvd_dvd @ int @ SY1233 @ ( power_power @ int @ SV119 @ SY1232 ) )
| ( dvd_dvd @ int @ SY1233 @ SV119 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1781]) ).
thf(2232,plain,
! [SV120: $i] :
( ( ~ ~ ( ~ ( number_ring @ SV120 )
| ~ ( linordered_idom @ SV120 ) )
| ! [SY1234: $i] :
~ ( ~ ( ~ ( ord_less @ SV120 @ ( one_one @ SV120 ) @ ( number_number_of @ SV120 @ SY1234 ) )
| ( ord_less @ int @ ( bit1 @ pls ) @ SY1234 ) )
| ~ ( ~ ( ord_less @ int @ ( bit1 @ pls ) @ SY1234 )
| ( ord_less @ SV120 @ ( one_one @ SV120 ) @ ( number_number_of @ SV120 @ SY1234 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1782]) ).
thf(2233,plain,
! [SV121: $i] :
( ( ! [SY1235: $i,SY1236: $i] :
( ~ ( ord_less_eq @ real @ SY1235 @ SY1236 )
| ( ord_less_eq @ real @ ( plus_plus @ real @ SV121 @ SY1235 ) @ ( plus_plus @ real @ SV121 @ SY1236 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1783]) ).
thf(2234,plain,
! [SV122: $i] :
( ( ! [SY1237: $i] :
~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SV122 ) @ ( bit1 @ SY1237 ) )
| ( ord_less_eq @ int @ SV122 @ SY1237 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV122 @ SY1237 )
| ( ord_less_eq @ int @ ( bit1 @ SV122 ) @ ( bit1 @ SY1237 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1784]) ).
thf(2235,plain,
( ( ( ~ ( ord_less @ int @ ( one_one @ int ) @ t ) )
= $true )
| ( ( ~ ! [SX0: $i] :
~ ~ ! [SX1: $i] :
( ( plus_plus @ int @ ( power_power @ int @ SX0 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ SX1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1785]) ).
thf(2236,plain,
! [SV123: $i] :
( ( ~ ~ ( ~ ( number_ring @ SV123 )
| ~ ( linordered_idom @ SV123 ) )
| ! [SY1238: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV123 @ ( number_number_of @ SV123 @ SY1238 ) @ ( one_one @ SV123 ) )
| ( ord_less_eq @ int @ SY1238 @ ( bit1 @ pls ) ) )
| ~ ( ~ ( ord_less_eq @ int @ SY1238 @ ( bit1 @ pls ) )
| ( ord_less_eq @ SV123 @ ( number_number_of @ SV123 @ SY1238 ) @ ( one_one @ SV123 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1786]) ).
thf(2237,plain,
! [SV124: $i] :
( ( ~ ( comm_semiring_1 @ SV124 )
| ! [SY1239: $i,SY1240: $i,SY1241: $i,SY1242: $i] :
( ~ ( dvd_dvd @ SV124 @ SY1241 @ SY1242 )
| ~ ( dvd_dvd @ SV124 @ SY1239 @ SY1240 )
| ( dvd_dvd @ SV124 @ ( times_times @ SV124 @ SY1241 @ SY1239 ) @ ( times_times @ SV124 @ SY1242 @ SY1240 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1787]) ).
thf(2238,plain,
! [SV125: $i] :
( ( ~ ( ab_group_add @ SV125 )
| ! [SY1243: $i,SY1244: $i,SY1245: $i,SY1246: $i] :
( ( minus_minus @ SV125 @ ( plus_plus @ SV125 @ SY1243 @ SY1244 ) @ ( plus_plus @ SV125 @ SY1245 @ SY1246 ) )
= ( plus_plus @ SV125 @ ( minus_minus @ SV125 @ SY1243 @ SY1245 ) @ ( minus_minus @ SV125 @ SY1244 @ SY1246 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1788]) ).
thf(2239,plain,
! [SV126: $i] :
( ( ~ ( number_semiring @ SV126 )
| ! [SY1247: $i] :
( ( times_times @ SV126 @ SY1247 @ ( number_number_of @ SV126 @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ SV126 @ SY1247 @ SY1247 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1789]) ).
thf(2240,plain,
! [SV127: $i] :
( ( ~ ( number_ring @ SV127 )
| ( ( plus_plus @ SV127 @ ( one_one @ SV127 ) @ ( one_one @ SV127 ) )
= ( number_number_of @ SV127 @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1790]) ).
thf(2241,plain,
! [SV128: $i] :
( ( ~ ( ~ ( ( ( number_number_of @ nat @ SV128 )
!= ( zero_zero @ nat ) )
| ( ord_less_eq @ int @ SV128 @ pls ) )
| ~ ( ~ ( ord_less_eq @ int @ SV128 @ pls )
| ( ( number_number_of @ nat @ SV128 )
= ( zero_zero @ nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1791]) ).
thf(2242,plain,
! [SV129: $i] :
( ( ~ ( number_semiring @ SV129 )
| ! [SY1248: $i] :
( ( times_times @ SV129 @ ( number_number_of @ SV129 @ ( bit0 @ ( bit1 @ pls ) ) ) @ SY1248 )
= ( plus_plus @ SV129 @ SY1248 @ SY1248 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1792]) ).
thf(2243,plain,
! [SV130: $i] :
( ( ~ ( comm_semiring_1 @ SV130 )
| ! [SY1249: $i,SY1250: $i,SY1251: $i] :
( ( times_times @ SV130 @ ( times_times @ SV130 @ SY1249 @ SY1250 ) @ SY1251 )
= ( times_times @ SV130 @ ( times_times @ SV130 @ SY1249 @ SY1251 ) @ SY1250 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1793]) ).
thf(2244,plain,
! [SV131: $i] :
( ( ~ ( comm_semiring @ SV131 )
| ! [SY1252: $i,SY1253: $i,SY1254: $i] :
( ( times_times @ SV131 @ ( plus_plus @ SV131 @ SY1252 @ SY1253 ) @ SY1254 )
= ( plus_plus @ SV131 @ ( times_times @ SV131 @ SY1252 @ SY1254 ) @ ( times_times @ SV131 @ SY1253 @ SY1254 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1794]) ).
thf(2245,plain,
! [SV132: $i] :
( ( ! [SY1255: $i,SY1256: $i,SY1257: $i,SY1258: $i] :
( ~ ( ord_less_eq @ int @ ( plus_plus @ int @ ( times_times @ int @ SV132 @ SY1255 ) @ SY1256 ) @ ( plus_plus @ int @ ( times_times @ int @ SV132 @ SY1257 ) @ SY1258 ) )
| ~ ( ord_less_eq @ int @ SY1258 @ ( zero_zero @ int ) )
| ~ ( ord_less @ int @ SV132 @ SY1258 )
| ~ ( ord_less @ int @ SV132 @ SY1256 )
| ( ord_less_eq @ int @ SY1257 @ SY1255 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1795]) ).
thf(2246,plain,
! [SV133: $i] :
( ( ! [SY1259: $i] :
( ( bit1 @ SV133 )
!= ( bit0 @ SY1259 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1796]) ).
thf(2247,plain,
! [SV134: $i] :
( ( ~ ~ ( ~ ( number_ring @ SV134 )
| ~ ( linordered_idom @ SV134 ) )
| ! [SY1260: $i] :
~ ( ~ ( ~ ( ord_less @ SV134 @ ( number_number_of @ SV134 @ SY1260 ) @ ( one_one @ SV134 ) )
| ( ord_less @ int @ SY1260 @ ( bit1 @ pls ) ) )
| ~ ( ~ ( ord_less @ int @ SY1260 @ ( bit1 @ pls ) )
| ( ord_less @ SV134 @ ( number_number_of @ SV134 @ SY1260 ) @ ( one_one @ SV134 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1797]) ).
thf(2248,plain,
! [SV135: $i] :
( ( ! [SY1261: $i] :
~ ( ~ ( ~ ( ord_less_eq @ nat @ ( number_number_of @ nat @ SV135 ) @ ( number_number_of @ nat @ SY1261 ) )
| ~ ~ ( ord_less_eq @ int @ SV135 @ SY1261 )
| ( ord_less_eq @ int @ SV135 @ pls ) )
| ~ ( ~ ( ~ ~ ( ord_less_eq @ int @ SV135 @ SY1261 )
| ( ord_less_eq @ int @ SV135 @ pls ) )
| ( ord_less_eq @ nat @ ( number_number_of @ nat @ SV135 ) @ ( number_number_of @ nat @ SY1261 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1798]) ).
thf(2249,plain,
! [SV136: $i] :
( ( ~ ( comm_semiring_1 @ SV136 )
| ! [SY1262: $i] :
( ( power_power @ SV136 @ SY1262 @ ( one_one @ nat ) )
= ( ti @ SV136 @ SY1262 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1799]) ).
thf(2250,plain,
! [SV137: $i] :
( ( ! [SY1263: $i,SY1264: $i] :
~ ( ~ ( ~ ( zcong @ SV137 @ SY1263 @ SY1264 )
| ( dvd_dvd @ int @ SY1264 @ ( minus_minus @ int @ SV137 @ SY1263 ) ) )
| ~ ( ~ ( dvd_dvd @ int @ SY1264 @ ( minus_minus @ int @ SV137 @ SY1263 ) )
| ( zcong @ SV137 @ SY1263 @ SY1264 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1800]) ).
thf(2251,plain,
! [SV138: $i] :
( ( ! [SY1265: $i] :
~ ( ~ ( ~ ( ord_less_eq @ int @ ( number_number_of @ int @ SV138 ) @ ( number_number_of @ int @ SY1265 ) )
| ( ord_less_eq @ int @ SV138 @ SY1265 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV138 @ SY1265 )
| ( ord_less_eq @ int @ ( number_number_of @ int @ SV138 ) @ ( number_number_of @ int @ SY1265 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1801]) ).
thf(2252,plain,
! [SV139: $i] :
( ( ~ ~ ( ~ ( number @ SV139 )
| ~ ( ring @ SV139 ) )
| ! [SY1266: $i,SY1267: $i,SY1268: $i] :
( ( times_times @ SV139 @ ( number_number_of @ SV139 @ SY1266 ) @ ( minus_minus @ SV139 @ SY1267 @ SY1268 ) )
= ( minus_minus @ SV139 @ ( times_times @ SV139 @ ( number_number_of @ SV139 @ SY1266 ) @ SY1267 ) @ ( times_times @ SV139 @ ( number_number_of @ SV139 @ SY1266 ) @ SY1268 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1802]) ).
thf(2253,plain,
! [SV140: $i] :
( ( ~ ( monoid_mult @ SV140 )
| ! [SY1269: $i] :
( ( power_power @ SV140 @ SY1269 @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( times_times @ SV140 @ ( times_times @ SV140 @ SY1269 @ SY1269 ) @ SY1269 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1803]) ).
thf(2254,plain,
! [SV141: $i] :
( ( ! [SY1270: $i] :
( ~ ( ord_less @ int @ SV141 @ SY1270 )
| ( ord_less_eq @ int @ ( plus_plus @ int @ SV141 @ ( one_one @ int ) ) @ SY1270 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1804]) ).
thf(2255,plain,
! [SV142: $i] :
( ( ~ ( linordered_semidom @ SV142 )
| ! [SY1271: $i,SY1272: $i] :
( ~ ( ord_less @ SV142 @ ( one_one @ SV142 ) @ SY1272 )
| ( ord_less @ SV142 @ ( one_one @ SV142 ) @ ( times_times @ SV142 @ SY1272 @ ( power_power @ SV142 @ SY1272 @ SY1271 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1805]) ).
thf(2256,plain,
! [SV143: $i] :
( ( ! [SY1273: $i] :
~ ( ~ ( ( ( power_power @ nat @ SV143 @ SY1273 )
!= ( zero_zero @ nat ) )
| ~ ( ~ ( ( SY1273
!= ( zero_zero @ nat ) ) )
| ( SV143
!= ( zero_zero @ nat ) ) ) )
| ~ ( ~ ~ ( ~ ( ( SY1273
!= ( zero_zero @ nat ) ) )
| ( SV143
!= ( zero_zero @ nat ) ) )
| ( ( power_power @ nat @ SV143 @ SY1273 )
= ( zero_zero @ nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1806]) ).
thf(2257,plain,
! [SV144: $i] :
( ( ~ ( number_ring @ SV144 )
| ! [SY1274: $i] :
( ( times_times @ SV144 @ SY1274 @ ( number_number_of @ SV144 @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ SV144 @ SY1274 @ SY1274 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1807]) ).
thf(2258,plain,
! [SV145: $i] :
( ( ! [SY1275: $i,SY1276: $i] :
~ ( ~ ( ~ ( dvd_dvd @ int @ SV145 @ ( plus_plus @ int @ SY1275 @ ( times_times @ int @ SV145 @ SY1276 ) ) )
| ( dvd_dvd @ int @ SV145 @ SY1275 ) )
| ~ ( ~ ( dvd_dvd @ int @ SV145 @ SY1275 )
| ( dvd_dvd @ int @ SV145 @ ( plus_plus @ int @ SY1275 @ ( times_times @ int @ SV145 @ SY1276 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1808]) ).
thf(2259,plain,
! [SV146: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SV146 ) @ min )
| ( ord_less @ int @ SV146 @ min ) )
| ~ ( ~ ( ord_less @ int @ SV146 @ min )
| ( ord_less @ int @ ( bit1 @ SV146 ) @ min ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1809]) ).
thf(2260,plain,
! [SV147: $i] :
( ( ! [SY1277: $i] :
~ ( ~ ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ SV147 @ SY1277 ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ SV147 )
| ( SY1277
= ( zero_zero @ nat ) ) )
| ~ ( ~ ( ( ord_less @ nat @ ( zero_zero @ nat ) @ SV147 )
| ( SY1277
= ( zero_zero @ nat ) ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ SV147 @ SY1277 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1810]) ).
thf(2261,plain,
! [SV148: $i] :
( ( ( bit0 @ SV148 )
!= min )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1811]) ).
thf(2262,plain,
! [SV149: $i] :
( ( ~ ( number_ring @ SV149 )
| ! [SY1278: $i] :
( ( plus_plus @ SV149 @ ( one_one @ SV149 ) @ ( number_number_of @ SV149 @ SY1278 ) )
= ( number_number_of @ SV149 @ ( plus_plus @ int @ ( bit1 @ pls ) @ SY1278 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1812]) ).
thf(2263,plain,
! [SV150: $i] :
( ( ~ ( comm_semiring_1 @ SV150 )
| ! [SY1279: $i,SY1280: $i,SY1281: $i] :
( ( plus_plus @ SV150 @ ( times_times @ SV150 @ SY1279 @ SY1280 ) @ ( times_times @ SV150 @ SY1281 @ SY1280 ) )
= ( times_times @ SV150 @ ( plus_plus @ SV150 @ SY1279 @ SY1281 ) @ SY1280 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1813]) ).
thf(2264,plain,
! [SV151: $i] :
( ( ! [SY1282: $i] :
~ ( ~ ( ~ ~ ( ~ ( dvd_dvd @ nat @ SV151 @ SY1282 )
| ~ ( dvd_dvd @ nat @ SY1282 @ SV151 ) )
| ( SV151 = SY1282 ) )
| ~ ( ( SV151 != SY1282 )
| ~ ( ~ ( dvd_dvd @ nat @ SV151 @ SY1282 )
| ~ ( dvd_dvd @ nat @ SY1282 @ SV151 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1814]) ).
thf(2265,plain,
! [SV152: $i] :
( ( ~ ( ordere453448008miring @ SV152 )
| ! [SY1283: $i,SY1284: $i] :
( ~ ( ord_less_eq @ SV152 @ ( zero_zero @ SV152 ) @ SY1284 )
| ~ ( ord_less_eq @ SV152 @ ( zero_zero @ SV152 ) @ SY1283 )
| ( ord_less_eq @ SV152 @ ( zero_zero @ SV152 ) @ ( times_times @ SV152 @ SY1284 @ SY1283 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1815]) ).
thf(2266,plain,
! [SV153: $i] :
( ( ! [SY1285: $i] :
( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ SY1285 )
| ~ ( ord_less @ real @ ( zero_zero @ real ) @ SV153 )
| ~ ! [SY1286: $i] :
~ ~ ( ~ ( ord_less @ real @ ( zero_zero @ real ) @ SY1286 )
| ( ( power_power @ real @ SY1286 @ SY1285 )
!= SV153 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1816]) ).
thf(2267,plain,
! [SV154: $i] :
( ( ! [SY1287: $i,SY1288: $i,SY1289: $i] :
( ~ ( zcong @ SY1287 @ SY1288 @ SY1289 )
| ( zcong @ ( times_times @ int @ SV154 @ SY1287 ) @ ( times_times @ int @ SV154 @ SY1288 ) @ SY1289 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1817]) ).
thf(2268,plain,
! [SV155: $i] :
( ( ~ ( linordered_semidom @ SV155 )
| ! [SY1290: $i,SY1291: $i,SY1292: $i] :
( ~ ( ord_less @ SV155 @ ( one_one @ SV155 ) @ SY1292 )
| ~ ( ~ ( ~ ( ord_less @ SV155 @ ( power_power @ SV155 @ SY1292 @ SY1290 ) @ ( power_power @ SV155 @ SY1292 @ SY1291 ) )
| ( ord_less @ nat @ SY1290 @ SY1291 ) )
| ~ ( ~ ( ord_less @ nat @ SY1290 @ SY1291 )
| ( ord_less @ SV155 @ ( power_power @ SV155 @ SY1292 @ SY1290 ) @ ( power_power @ SV155 @ SY1292 @ SY1291 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1818]) ).
thf(2269,plain,
! [SV156: $i] :
( ( ~ ( comm_semiring_1 @ SV156 )
| ! [SY1293: $i,SY1294: $i] :
( ( power_power @ SV156 @ SY1293 @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SY1294 ) )
= ( times_times @ SV156 @ ( power_power @ SV156 @ SY1293 @ SY1294 ) @ ( power_power @ SV156 @ SY1293 @ SY1294 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1819]) ).
thf(2270,plain,
! [SV157: $i] :
( ( ~ ( comm_semiring_1 @ SV157 )
| ! [SY1295: $i] :
( ( plus_plus @ SV157 @ SY1295 @ ( zero_zero @ SV157 ) )
= ( ti @ SV157 @ SY1295 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1820]) ).
thf(2271,plain,
! [SV158: $i] :
( ( ! [SY1296: $i,SY1297: $i] :
( ~ ( dvd_dvd @ nat @ SY1296 @ SY1297 )
| ( dvd_dvd @ nat @ ( times_times @ nat @ SY1296 @ SV158 ) @ ( times_times @ nat @ SY1297 @ SV158 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1821]) ).
thf(2272,plain,
! [SV159: $i] :
( ( ! [SY1298: $i] :
~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SV159 ) @ ( bit0 @ SY1298 ) )
| ( ord_less @ int @ SV159 @ SY1298 ) )
| ~ ( ~ ( ord_less @ int @ SV159 @ SY1298 )
| ( ord_less_eq @ int @ ( bit1 @ SV159 ) @ ( bit0 @ SY1298 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1822]) ).
thf(2273,plain,
! [SV160: $i] :
( ( ! [SY1299: $i] :
~ ( ~ ( ~ ( ord_less @ int @ SV160 @ ( plus_plus @ int @ SY1299 @ ( one_one @ int ) ) )
| ( ord_less_eq @ int @ SV160 @ SY1299 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV160 @ SY1299 )
| ( ord_less @ int @ SV160 @ ( plus_plus @ int @ SY1299 @ ( one_one @ int ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1823]) ).
thf(2274,plain,
! [SV161: $i] :
( ( ! [SY1300: $i,SY1301: $i] :
( ~ ( ord_less @ int @ ( plus_plus @ int @ ( times_times @ int @ SV161 @ SY1300 ) @ SY1301 ) @ ( zero_zero @ int ) )
| ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SY1301 )
| ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV161 )
| ( ord_less_eq @ int @ SY1300 @ ( zero_zero @ int ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1824]) ).
thf(2275,plain,
( ( pls = min )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1825]) ).
thf(2276,plain,
! [SV162: $i] :
( ( ! [SY1302: $i] :
( ( bit0 @ SV162 )
!= ( bit1 @ SY1302 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1826]) ).
thf(2277,plain,
! [SV163: $i] :
( ( ! [SY1303: $i,SY1304: $i] :
~ ( ~ ( ~ ( zcong @ SV163 @ SY1303 @ ( ti @ int @ SY1304 ) )
| ( zcong @ SV163 @ SY1303 @ SY1304 ) )
| ~ ( ~ ( zcong @ SV163 @ SY1303 @ SY1304 )
| ( zcong @ SV163 @ SY1303 @ ( ti @ int @ SY1304 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1827]) ).
thf(2278,plain,
! [SV164: $i] :
( ( ! [SY1305: $i,SY1306: $i,SY1307: $i,SY1308: $i] :
( ~ ( dvd_dvd @ int @ SY1307 @ SY1308 )
| ~ ( ~ ( ~ ( dvd_dvd @ int @ SY1307 @ ( plus_plus @ int @ SY1305 @ SY1306 ) )
| ( dvd_dvd @ int @ SY1307 @ ( plus_plus @ int @ ( plus_plus @ int @ SY1305 @ ( times_times @ int @ SV164 @ SY1308 ) ) @ SY1306 ) ) )
| ~ ( ~ ( dvd_dvd @ int @ SY1307 @ ( plus_plus @ int @ ( plus_plus @ int @ SY1305 @ ( times_times @ int @ SV164 @ SY1308 ) ) @ SY1306 ) )
| ( dvd_dvd @ int @ SY1307 @ ( plus_plus @ int @ SY1305 @ SY1306 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1828]) ).
thf(2279,plain,
! [SV165: $i] :
( ( ~ ( number_ring @ SV165 )
| ! [SY1309: $i,SY1310: $i,SY1311: $i] :
( ( plus_plus @ SV165 @ ( number_number_of @ SV165 @ SY1309 ) @ ( plus_plus @ SV165 @ ( number_number_of @ SV165 @ SY1310 ) @ SY1311 ) )
= ( plus_plus @ SV165 @ ( number_number_of @ SV165 @ ( plus_plus @ int @ SY1309 @ SY1310 ) ) @ SY1311 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1829]) ).
thf(2280,plain,
! [SV166: $i] :
( ( ~ ( linordered_idom @ SV166 )
| ! [SY1312: $i,SY1313: $i] : ( ord_less_eq @ SV166 @ ( zero_zero @ SV166 ) @ ( power_power @ SV166 @ SY1312 @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SY1313 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1830]) ).
thf(2281,plain,
! [SV167: $i] :
( ( ! [SY1314: $i,SY1315: $i,SY1316: $i,SY1317: $i] :
( ~ ( zcong @ SY1315 @ SY1316 @ SY1317 )
| ~ ( zcong @ SV167 @ SY1314 @ SY1317 )
| ( zcong @ ( minus_minus @ int @ SY1315 @ SV167 ) @ ( minus_minus @ int @ SY1316 @ SY1314 ) @ SY1317 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1831]) ).
thf(2282,plain,
! [SV168: $i] :
( ( ~ ~ ( ~ ( number @ SV168 )
| ~ ( semiring @ SV168 ) )
| ! [SY1318: $i,SY1319: $i,SY1320: $i] :
( ( times_times @ SV168 @ ( plus_plus @ SV168 @ SY1318 @ SY1319 ) @ ( number_number_of @ SV168 @ SY1320 ) )
= ( plus_plus @ SV168 @ ( times_times @ SV168 @ SY1318 @ ( number_number_of @ SV168 @ SY1320 ) ) @ ( times_times @ SV168 @ SY1319 @ ( number_number_of @ SV168 @ SY1320 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1832]) ).
thf(2283,plain,
! [SV169: $i] :
( ( ! [SY1321: $i] :
~ ( ~ ( ( ( plus_plus @ real @ ( power_power @ real @ SV169 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ real @ SY1321 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ real ) )
| ~ ( ( SV169
!= ( zero_zero @ real ) )
| ( SY1321
!= ( zero_zero @ real ) ) ) )
| ~ ( ~ ~ ( ( SV169
!= ( zero_zero @ real ) )
| ( SY1321
!= ( zero_zero @ real ) ) )
| ( ( plus_plus @ real @ ( power_power @ real @ SV169 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ real @ SY1321 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ real ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1833]) ).
thf(2284,plain,
! [SV170: $i] :
( ( ! [SY1322: $i,SY1323: $i] :
( ~ ( dvd_dvd @ nat @ ( power_power @ nat @ SV170 @ SY1322 ) @ ( power_power @ nat @ SV170 @ SY1323 ) )
| ~ ( ord_less @ nat @ ( one_one @ nat ) @ SV170 )
| ( ord_less_eq @ nat @ SY1322 @ SY1323 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1834]) ).
thf(2285,plain,
! [SV171: $i] :
( ( ~ ( ~ ( ~ ( ord_less_eq @ int @ pls @ ( bit0 @ SV171 ) )
| ( ord_less_eq @ int @ pls @ SV171 ) )
| ~ ( ~ ( ord_less_eq @ int @ pls @ SV171 )
| ( ord_less_eq @ int @ pls @ ( bit0 @ SV171 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1835]) ).
thf(2286,plain,
! [SV172: $i] :
( ( ! [SY1324: $i] :
~ ( ~ ( ~ ( ord_less @ int @ SV172 @ SY1324 )
| ( ord_less @ int @ ( minus_minus @ int @ SV172 @ SY1324 ) @ ( zero_zero @ int ) ) )
| ~ ( ~ ( ord_less @ int @ ( minus_minus @ int @ SV172 @ SY1324 ) @ ( zero_zero @ int ) )
| ( ord_less @ int @ SV172 @ SY1324 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1836]) ).
thf(2287,plain,
! [SV173: $i] :
( ( ~ ( number_ring @ SV173 )
| ! [SY1325: $i] :
( ( power_power @ SV173 @ ( number_number_of @ SV173 @ min ) @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SY1325 ) )
= ( one_one @ SV173 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1837]) ).
thf(2288,plain,
! [SV174: $i] :
( ( ~ ( ring @ SV174 )
| ! [SY1326: $i,SY1327: $i,SY1328: $i,SY1329: $i] :
( ( minus_minus @ SV174 @ ( times_times @ SV174 @ SY1326 @ SY1327 ) @ ( times_times @ SV174 @ SY1328 @ SY1329 ) )
= ( plus_plus @ SV174 @ ( times_times @ SV174 @ SY1326 @ ( minus_minus @ SV174 @ SY1327 @ SY1329 ) ) @ ( times_times @ SV174 @ ( minus_minus @ SV174 @ SY1326 @ SY1328 ) @ SY1329 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1838]) ).
thf(2289,plain,
! [SV175: $i] :
( ( ~ ( semiri456707255roduct @ SV175 )
| ! [SY1330: $i,SY1331: $i,SY1332: $i,SY1333: $i] :
~ ( ~ ( ~ ~ ( ~ ( ( ( ti @ SV175 @ SY1332 )
!= ( ti @ SV175 @ SY1333 ) ) )
| ~ ( ( ( ti @ SV175 @ SY1330 )
!= ( ti @ SV175 @ SY1331 ) ) ) )
| ( ( plus_plus @ SV175 @ ( times_times @ SV175 @ SY1332 @ SY1330 ) @ ( times_times @ SV175 @ SY1333 @ SY1331 ) )
!= ( plus_plus @ SV175 @ ( times_times @ SV175 @ SY1332 @ SY1331 ) @ ( times_times @ SV175 @ SY1333 @ SY1330 ) ) ) )
| ~ ( ~ ( ( ( plus_plus @ SV175 @ ( times_times @ SV175 @ SY1332 @ SY1330 ) @ ( times_times @ SV175 @ SY1333 @ SY1331 ) )
!= ( plus_plus @ SV175 @ ( times_times @ SV175 @ SY1332 @ SY1331 ) @ ( times_times @ SV175 @ SY1333 @ SY1330 ) ) ) )
| ~ ( ~ ( ( ( ti @ SV175 @ SY1332 )
!= ( ti @ SV175 @ SY1333 ) ) )
| ~ ( ( ( ti @ SV175 @ SY1330 )
!= ( ti @ SV175 @ SY1331 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1839]) ).
thf(2290,plain,
! [SV176: $i] :
( ( ! [SY1334: $i] :
( ~ ( number @ SY1334 )
| ( ( ti @ SY1334 @ ( number_number_of @ SY1334 @ SV176 ) )
= ( number_number_of @ SY1334 @ SV176 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1840]) ).
thf(2291,plain,
! [SV177: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ int @ pls @ ( bit0 @ SV177 ) )
| ( ord_less @ int @ pls @ SV177 ) )
| ~ ( ~ ( ord_less @ int @ pls @ SV177 )
| ( ord_less @ int @ pls @ ( bit0 @ SV177 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1841]) ).
thf(2292,plain,
! [SV178: $i] :
( ( ! [SY1335: $i] :
( ~ ( ord_less @ int @ ( zero_zero @ int ) @ SY1335 )
| ~ ( ord_less @ int @ SY1335 @ SV178 )
| ~ ( dvd_dvd @ int @ SV178 @ SY1335 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1842]) ).
thf(2293,plain,
! [SV179: $i] :
( ( ~ ( linordered_semidom @ SV179 )
| ! [SY1336: $i,SY1337: $i,SY1338: $i] :
( ~ ( ord_less @ SV179 @ ( one_one @ SV179 ) @ SY1338 )
| ~ ( ord_less @ SV179 @ ( power_power @ SV179 @ SY1338 @ SY1336 ) @ ( power_power @ SV179 @ SY1338 @ SY1337 ) )
| ( ord_less @ nat @ SY1336 @ SY1337 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1843]) ).
thf(2294,plain,
! [SV180: $i] :
( ( ~ ( dvd @ SV180 )
| ! [SY1339: $i,SY1340: $i,SY1341: $i] :
( ( SY1339
!= ( times_times @ SV180 @ SY1340 @ SY1341 ) )
| ( dvd_dvd @ SV180 @ SY1340 @ SY1339 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1844]) ).
thf(2295,plain,
! [SV181: $i] :
( ( min
!= ( bit0 @ SV181 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1845]) ).
thf(2296,plain,
! [SV182: $i] :
( ( ! [SY1342: $i] :
~ ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SV182 ) @ ( bit1 @ SY1342 ) )
| ( ord_less @ int @ SV182 @ SY1342 ) )
| ~ ( ~ ( ord_less @ int @ SV182 @ SY1342 )
| ( ord_less @ int @ ( bit1 @ SV182 ) @ ( bit1 @ SY1342 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1846]) ).
thf(2297,plain,
! [SV183: $i] :
( ( ~ ( number_ring @ SV183 )
| ( ( number_number_of @ SV183 @ pls )
= ( zero_zero @ SV183 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1847]) ).
thf(2298,plain,
! [SV184: $i] :
( ( ~ ( comm_semiring_1 @ SV184 )
| ! [SY1343: $i] :
( ( times_times @ SV184 @ SY1343 @ ( one_one @ SV184 ) )
= ( ti @ SV184 @ SY1343 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1848]) ).
thf(2299,plain,
! [SV185: $i] :
( ( ~ ( comm_semiring_1 @ SV185 )
| ! [SY1344: $i,SY1345: $i,SY1346: $i] :
( ( times_times @ SV185 @ ( power_power @ SV185 @ SY1344 @ SY1345 ) @ ( power_power @ SV185 @ SY1344 @ SY1346 ) )
= ( power_power @ SV185 @ SY1344 @ ( plus_plus @ nat @ SY1345 @ SY1346 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1849]) ).
thf(2300,plain,
! [SV186: $i] :
( ( ! [SY1347: $i] :
~ ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SV186 ) @ ( bit0 @ SY1347 ) )
| ( ord_less @ int @ SV186 @ SY1347 ) )
| ~ ( ~ ( ord_less @ int @ SV186 @ SY1347 )
| ( ord_less @ int @ ( bit0 @ SV186 ) @ ( bit0 @ SY1347 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1850]) ).
thf(2301,plain,
! [SV187: $i] :
( ( ! [SY1348: $i] :
~ ( ~ ( ~ ( ord_less @ int @ SV187 @ SY1348 )
| ~ ( ~ ( ord_less_eq @ int @ SV187 @ SY1348 )
| ~ ( ( ( ti @ int @ SV187 )
!= ( ti @ int @ SY1348 ) ) ) ) )
| ~ ( ~ ~ ( ~ ( ord_less_eq @ int @ SV187 @ SY1348 )
| ~ ( ( ( ti @ int @ SV187 )
!= ( ti @ int @ SY1348 ) ) ) )
| ( ord_less @ int @ SV187 @ SY1348 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1851]) ).
thf(2302,plain,
! [SV188: $i] :
( ( ! [SY1349: $i] :
( ~ ( number @ SY1349 )
| ( ( number_number_of @ SY1349 @ ( ti @ int @ SV188 ) )
= ( number_number_of @ SY1349 @ SV188 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1852]) ).
thf(2303,plain,
! [SV189: $i] :
( ( ~ ( linord219039673up_add @ SV189 )
| ! [SY1350: $i] :
~ ( ~ ( ( ( plus_plus @ SV189 @ SY1350 @ SY1350 )
!= ( zero_zero @ SV189 ) )
| ( ( ti @ SV189 @ SY1350 )
= ( zero_zero @ SV189 ) ) )
| ~ ( ( ( ti @ SV189 @ SY1350 )
!= ( zero_zero @ SV189 ) )
| ( ( plus_plus @ SV189 @ SY1350 @ SY1350 )
= ( zero_zero @ SV189 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1853]) ).
thf(2304,plain,
! [SV190: $i] :
( ( ! [SY1351: $i,SY1352: $i] :
( ~ ( ord_less @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ SY1352 )
| ~ ( zcong @ ( power_power @ int @ ( number_number_of @ int @ min ) @ SV190 ) @ ( power_power @ int @ ( number_number_of @ int @ min ) @ SY1351 ) @ SY1352 )
| ( ( power_power @ int @ ( number_number_of @ int @ min ) @ SV190 )
= ( power_power @ int @ ( number_number_of @ int @ min ) @ SY1351 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1854]) ).
thf(2305,plain,
! [SV191: $i] :
( ( ! [SY1353: $i,SY1354: $i] :
~ ( ~ ( ~ ( dvd_dvd @ nat @ ( times_times @ nat @ SV191 @ SY1353 ) @ ( times_times @ nat @ SY1354 @ SY1353 ) )
| ( SY1353
= ( zero_zero @ nat ) )
| ( dvd_dvd @ nat @ SV191 @ SY1354 ) )
| ~ ( ~ ( ( SY1353
= ( zero_zero @ nat ) )
| ( dvd_dvd @ nat @ SV191 @ SY1354 ) )
| ( dvd_dvd @ nat @ ( times_times @ nat @ SV191 @ SY1353 ) @ ( times_times @ nat @ SY1354 @ SY1353 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1855]) ).
thf(2306,plain,
! [SV192: $i] :
( ( ~ ( linordered_semidom @ SV192 )
| ! [SY1355: $i,SY1356: $i] :
( ~ ( ord_less_eq @ SV192 @ ( zero_zero @ SV192 ) @ SY1356 )
| ( ord_less_eq @ SV192 @ ( zero_zero @ SV192 ) @ ( power_power @ SV192 @ SY1356 @ SY1355 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1856]) ).
thf(2307,plain,
! [SV193: $i] :
( ( ~ ( linord581940658strict @ SV193 )
| ! [SY1357: $i,SY1358: $i] :
~ ( ~ ( ( ( plus_plus @ SV193 @ ( times_times @ SV193 @ SY1357 @ SY1357 ) @ ( times_times @ SV193 @ SY1358 @ SY1358 ) )
!= ( zero_zero @ SV193 ) )
| ~ ( ( ( ti @ SV193 @ SY1357 )
!= ( zero_zero @ SV193 ) )
| ( ( ti @ SV193 @ SY1358 )
!= ( zero_zero @ SV193 ) ) ) )
| ~ ( ~ ~ ( ( ( ti @ SV193 @ SY1357 )
!= ( zero_zero @ SV193 ) )
| ( ( ti @ SV193 @ SY1358 )
!= ( zero_zero @ SV193 ) ) )
| ( ( plus_plus @ SV193 @ ( times_times @ SV193 @ SY1357 @ SY1357 ) @ ( times_times @ SV193 @ SY1358 @ SY1358 ) )
= ( zero_zero @ SV193 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1857]) ).
thf(2308,plain,
! [SV194: $i] :
( ( ~ ( linordered_semidom @ SV194 )
| ! [SY1359: $i,SY1360: $i,SY1361: $i] :
( ~ ( ord_less @ SV194 @ ( one_one @ SV194 ) @ SY1361 )
| ~ ( ~ ( ( ( power_power @ SV194 @ SY1361 @ SY1359 )
!= ( power_power @ SV194 @ SY1361 @ SY1360 ) )
| ( SY1359 = SY1360 ) )
| ~ ( ( SY1359 != SY1360 )
| ( ( power_power @ SV194 @ SY1361 @ SY1359 )
= ( power_power @ SV194 @ SY1361 @ SY1360 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1858]) ).
thf(2309,plain,
! [SV195: $i] :
( ( ~ ( linordered_ring @ SV195 )
| ! [SY1362: $i,SY1363: $i] :
~ ( ord_less @ SV195 @ ( plus_plus @ SV195 @ ( times_times @ SV195 @ SY1362 @ SY1362 ) @ ( times_times @ SV195 @ SY1363 @ SY1363 ) ) @ ( zero_zero @ SV195 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1859]) ).
thf(2310,plain,
! [SV196: $i] :
( ( ! [SY1364: $i,SY1365: $i] :
( ~ ( zprime @ SY1365 )
| ~ ~ ( zcong @ SY1364 @ ( zero_zero @ int ) @ SY1365 )
| ~ ~ ( zcong @ SV196 @ ( zero_zero @ int ) @ SY1365 )
| ~ ( zcong @ ( times_times @ int @ SY1364 @ SV196 ) @ ( zero_zero @ int ) @ SY1365 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1860]) ).
thf(2311,plain,
! [SV197: $i] :
( ( ~ ( number_semiring @ SV197 )
| ! [SY1366: $i,SY1367: $i] :
( ( power_power @ SV197 @ ( plus_plus @ SV197 @ SY1366 @ SY1367 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ SV197 @ ( plus_plus @ SV197 @ ( power_power @ SV197 @ SY1366 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV197 @ SY1367 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times @ SV197 @ ( times_times @ SV197 @ ( number_number_of @ SV197 @ ( bit0 @ ( bit1 @ pls ) ) ) @ SY1366 ) @ SY1367 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1861]) ).
thf(2312,plain,
! [SV198: $i] :
( ( ~ ( number_ring @ SV198 )
| ! [SY1368: $i,SY1369: $i] :
( ( times_times @ SV198 @ ( number_number_of @ SV198 @ SY1368 ) @ ( number_number_of @ SV198 @ SY1369 ) )
= ( number_number_of @ SV198 @ ( times_times @ int @ SY1368 @ SY1369 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1862]) ).
thf(2313,plain,
! [SV199: $i] :
( ( ~ ( linord581940658strict @ SV199 )
| ! [SY1370: $i,SY1371: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ ( times_times @ SV199 @ SY1370 @ SY1371 ) )
| ~ ( ~ ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ SY1370 )
| ~ ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ SY1371 ) )
| ~ ( ~ ( ord_less_eq @ SV199 @ SY1370 @ ( zero_zero @ SV199 ) )
| ~ ( ord_less_eq @ SV199 @ SY1371 @ ( zero_zero @ SV199 ) ) ) )
| ~ ( ~ ( ~ ( ~ ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ SY1370 )
| ~ ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ SY1371 ) )
| ~ ( ~ ( ord_less_eq @ SV199 @ SY1370 @ ( zero_zero @ SV199 ) )
| ~ ( ord_less_eq @ SV199 @ SY1371 @ ( zero_zero @ SV199 ) ) ) )
| ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ ( times_times @ SV199 @ SY1370 @ SY1371 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1863]) ).
thf(2314,plain,
! [SV200: $i] :
( ( ~ ( number_ring @ SV200 )
| ! [SY1372: $i] :
( ( times_times @ SV200 @ ( number_number_of @ SV200 @ ( bit1 @ pls ) ) @ SY1372 )
= ( ti @ SV200 @ SY1372 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1864]) ).
thf(2315,plain,
! [SV201: $i] :
( ( ~ ( linordered_semidom @ SV201 )
| ! [SY1373: $i,SY1374: $i] :
( ~ ( ord_less @ SV201 @ ( one_one @ SV201 ) @ SY1374 )
| ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ SY1373 )
| ( ord_less @ SV201 @ ( one_one @ SV201 ) @ ( power_power @ SV201 @ SY1374 @ SY1373 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1865]) ).
thf(2316,plain,
! [SV202: $i] :
( ( ~ ~ ( ~ ( number_ring @ SV202 )
| ~ ( linordered_idom @ SV202 ) )
| ! [SY1375: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV202 @ ( one_one @ SV202 ) @ ( number_number_of @ SV202 @ SY1375 ) )
| ( ord_less_eq @ int @ ( bit1 @ pls ) @ SY1375 ) )
| ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ pls ) @ SY1375 )
| ( ord_less_eq @ SV202 @ ( one_one @ SV202 ) @ ( number_number_of @ SV202 @ SY1375 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1866]) ).
thf(2317,plain,
! [SV203: $i] :
( ( ! [SY1376: $i,SY1377: $i] :
( ~ ( ord_less @ int @ ( zero_zero @ int ) @ SY1377 )
| ~ ( ord_less @ int @ SY1377 @ SY1376 )
| ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV203 )
| ~ ( ord_less @ int @ SV203 @ SY1377 )
| ~ ( zcong @ SY1377 @ SV203 @ SY1376 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1867]) ).
thf(2318,plain,
( ( ! [SX0: $i] :
( ( plus_plus @ int @ ( power_power @ int @ s @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( one_one @ int ) )
!= ( times_times @ int @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1868]) ).
thf(2319,plain,
! [SV204: $i] :
( ( ~ ( monoid_mult @ SV204 )
| ! [SY1378: $i] :
( ( power_power @ SV204 @ SY1378 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times @ SV204 @ SY1378 @ SY1378 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1869]) ).
thf(2320,plain,
! [SV205: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SV205 ) @ min )
| ( ord_less_eq @ int @ SV205 @ min ) )
| ~ ( ~ ( ord_less_eq @ int @ SV205 @ min )
| ( ord_less @ int @ ( bit0 @ SV205 ) @ min ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1870]) ).
thf(2321,plain,
! [SV206: $i] :
( ( ! [SY1379: $i,SY1380: $i,SY1381: $i,SY1382: $i] :
( ~ ( zcong @ SY1380 @ SY1381 @ SY1382 )
| ~ ( zcong @ SV206 @ SY1379 @ SY1382 )
| ( zcong @ ( plus_plus @ int @ SY1380 @ SV206 ) @ ( plus_plus @ int @ SY1381 @ SY1379 ) @ SY1382 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1871]) ).
thf(2322,plain,
! [SV207: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ SV207 ) @ SV207 ) @ ( zero_zero @ int ) )
| ( ord_less @ int @ SV207 @ ( zero_zero @ int ) ) )
| ~ ( ~ ( ord_less @ int @ SV207 @ ( zero_zero @ int ) )
| ( ord_less @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ SV207 ) @ SV207 ) @ ( zero_zero @ int ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1872]) ).
thf(2323,plain,
! [SV208: $i] :
( ( ~ ( ~ ( ~ ( twoSqu420862341sum2sq @ ( ti @ int @ SV208 ) )
| ( twoSqu420862341sum2sq @ SV208 ) )
| ~ ( ~ ( twoSqu420862341sum2sq @ SV208 )
| ( twoSqu420862341sum2sq @ ( ti @ int @ SV208 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1873]) ).
thf(2324,plain,
! [SV209: $i] :
( ( ! [SY1383: $i,SY1384: $i] :
( ~ ( dvd_dvd @ nat @ SY1383 @ SY1384 )
| ~ ( dvd_dvd @ nat @ SY1383 @ ( plus_plus @ nat @ SY1384 @ SV209 ) )
| ( dvd_dvd @ nat @ SY1383 @ SV209 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1874]) ).
thf(2325,plain,
! [SV210: $i] :
( ( ~ ( ~ ( ( ( bit0 @ SV210 )
!= pls )
| ( ( ti @ int @ SV210 )
= pls ) )
| ~ ( ( ( ti @ int @ SV210 )
!= pls )
| ( ( bit0 @ SV210 )
= pls ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1875]) ).
thf(2326,plain,
! [SV211: $i] :
( ( ~ ( comm_semiring_1 @ SV211 )
| ! [SY1385: $i,SY1386: $i] : ( dvd_dvd @ SV211 @ SY1385 @ ( times_times @ SV211 @ SY1386 @ SY1385 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1876]) ).
thf(2327,plain,
! [SV212: $i] :
( ( ~ ( number_ring @ SV212 )
| ! [SY1387: $i,SY1388: $i] :
( ( plus_plus @ SV212 @ ( number_number_of @ SV212 @ SY1387 ) @ ( number_number_of @ SV212 @ SY1388 ) )
= ( number_number_of @ SV212 @ ( plus_plus @ int @ SY1387 @ SY1388 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1877]) ).
thf(2328,plain,
! [SV213: $i] :
( ( ~ ~ ( ~ ( number_ring @ SV213 )
| ~ ( ring_char_0 @ SV213 ) )
| ! [SY1389: $i,SY1390: $i] :
~ ( ~ ( ( ( number_number_of @ SV213 @ SY1389 )
!= ( number_number_of @ SV213 @ SY1390 ) )
| ( ( ti @ int @ SY1389 )
= ( ti @ int @ SY1390 ) ) )
| ~ ( ( ( ti @ int @ SY1389 )
!= ( ti @ int @ SY1390 ) )
| ( ( number_number_of @ SV213 @ SY1389 )
= ( number_number_of @ SV213 @ SY1390 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1878]) ).
thf(2329,plain,
! [SV214: $i] :
( ( ! [SY1391: $i,SY1392: $i,SY1393: $i] :
( ( SV214
!= ( plus_plus @ nat @ ( times_times @ nat @ SY1391 @ SY1392 ) @ SY1393 ) )
| ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ SY1393 )
| ~ ( ord_less @ nat @ SY1393 @ SY1392 )
| ~ ( dvd_dvd @ nat @ SY1392 @ SV214 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1879]) ).
thf(2330,plain,
! [SV215: $i] :
( ( ! [SY1394: $i,SY1395: $i] :
( ~ ( dvd_dvd @ nat @ ( power_power @ nat @ SV215 @ SY1394 ) @ ( power_power @ nat @ SY1395 @ SY1394 ) )
| ~ ( ( SY1394
!= ( zero_zero @ nat ) ) )
| ( dvd_dvd @ nat @ SV215 @ SY1395 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1880]) ).
thf(2331,plain,
! [SV216: $i] :
( ( ~ ( zero_neq_one @ SV216 )
| ( ( zero_zero @ SV216 )
!= ( one_one @ SV216 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1881]) ).
thf(2332,plain,
! [SV217: $i] :
( ( ~ ( comm_semiring_1 @ SV217 )
| ! [SY1396: $i] :
( ( plus_plus @ SV217 @ ( zero_zero @ SV217 ) @ SY1396 )
= ( ti @ SV217 @ SY1396 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1882]) ).
thf(2333,plain,
! [SV218: $i] :
( ( ~ ~ ( ~ ( number_ring @ SV218 )
| ~ ( linordered_idom @ SV218 ) )
| ! [SY1397: $i,SY1398: $i] :
~ ( ~ ( ~ ( ord_less @ SV218 @ ( number_number_of @ SV218 @ SY1397 ) @ ( number_number_of @ SV218 @ SY1398 ) )
| ( ord_less @ int @ SY1397 @ SY1398 ) )
| ~ ( ~ ( ord_less @ int @ SY1397 @ SY1398 )
| ( ord_less @ SV218 @ ( number_number_of @ SV218 @ SY1397 ) @ ( number_number_of @ SV218 @ SY1398 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1883]) ).
thf(2334,plain,
! [SV219: $i] :
( ( ~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit0 @ SV219 ) @ min )
| ( ord_less_eq @ int @ SV219 @ min ) )
| ~ ( ~ ( ord_less_eq @ int @ SV219 @ min )
| ( ord_less_eq @ int @ ( bit0 @ SV219 ) @ min ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1884]) ).
thf(2335,plain,
! [SV220: $i] :
( ( ~ ( comm_semiring_1 @ SV220 )
| ! [SY1399: $i,SY1400: $i,SY1401: $i,SY1402: $i] :
( ~ ( dvd_dvd @ SV220 @ ( power_power @ SV220 @ SY1400 @ SY1401 ) @ SY1402 )
| ~ ( ord_less_eq @ nat @ SY1399 @ SY1401 )
| ( dvd_dvd @ SV220 @ ( power_power @ SV220 @ SY1400 @ SY1399 ) @ SY1402 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1885]) ).
thf(2336,plain,
! [SV221: $i] :
( ( ! [SY1403: $i,SY1404: $i] :
( ~ ( ord_less @ real @ ( zero_zero @ real ) @ SY1404 )
| ~ ( ord_less @ real @ SV221 @ SY1403 )
| ( ord_less @ real @ ( times_times @ real @ SY1404 @ SV221 ) @ ( times_times @ real @ SY1404 @ SY1403 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1886]) ).
thf(2337,plain,
! [SV222: $i] :
( ( ~ ( comm_semiring_1 @ SV222 )
| ! [SY1405: $i,SY1406: $i,SY1407: $i] :
( ~ ( dvd_dvd @ SV222 @ SY1406 @ SY1407 )
| ( dvd_dvd @ SV222 @ SY1406 @ ( times_times @ SV222 @ SY1405 @ SY1407 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1887]) ).
thf(2338,plain,
! [SV223: $i] :
( ( ! [SY1408: $i,SY1409: $i] :
( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ SY1409 )
| ~ ( ord_less @ nat @ ( power_power @ nat @ SY1409 @ SV223 ) @ ( power_power @ nat @ SY1409 @ SY1408 ) )
| ( ord_less @ nat @ SV223 @ SY1408 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1888]) ).
thf(2339,plain,
! [SV224: $i] :
( ( ! [SY1410: $i] :
( ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SY1410 )
| ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV224 )
| ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ SY1410 @ SV224 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1889]) ).
thf(2340,plain,
! [SV225: $i] :
( ( ~ ( ~ ( ~ ( ord_less_eq @ int @ ( one_one @ int ) @ SV225 )
| ( ord_less @ int @ ( zero_zero @ int ) @ SV225 ) )
| ~ ( ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV225 )
| ( ord_less_eq @ int @ ( one_one @ int ) @ SV225 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1890]) ).
thf(2341,plain,
! [SV226: $i] :
( ( ~ ( comm_semiring_1 @ SV226 )
| ! [SY1411: $i,SY1412: $i,SY1413: $i] :
( ~ ( dvd_dvd @ SV226 @ ( times_times @ SV226 @ SY1411 @ SY1412 ) @ SY1413 )
| ( dvd_dvd @ SV226 @ SY1411 @ SY1413 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1891]) ).
thf(2342,plain,
! [SV227: $i] :
( ( ! [SY1414: $i,SY1415: $i] :
( ~ ( mult_zero @ SY1415 )
| ( ( times_times @ SY1415 @ ( ti @ SY1415 @ SV227 ) @ SY1414 )
= ( times_times @ SY1415 @ SV227 @ SY1414 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1892]) ).
thf(2343,plain,
! [SV228: $i] :
( ( ! [SY1416: $i,SY1417: $i] :
( ~ ( power @ SY1417 )
| ( ( ti @ SY1417 @ ( times_times @ SY1417 @ SV228 @ SY1416 ) )
= ( times_times @ SY1417 @ SV228 @ SY1416 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1893]) ).
thf(2344,plain,
! [SV229: $i] :
( ( ! [SY1418: $i,SY1419: $i] :
( ~ ( semiring @ SY1419 )
| ( ( plus_plus @ SY1419 @ ( ti @ SY1419 @ SV229 ) @ SY1418 )
= ( plus_plus @ SY1419 @ SV229 @ SY1418 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1894]) ).
thf(2345,plain,
! [SV230: $i] :
( ( ~ ( linordered_ring @ SV230 )
| ! [SY1420: $i,SY1421: $i] : ( ord_less_eq @ SV230 @ ( zero_zero @ SV230 ) @ ( plus_plus @ SV230 @ ( times_times @ SV230 @ SY1420 @ SY1420 ) @ ( times_times @ SV230 @ SY1421 @ SY1421 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1895]) ).
thf(2346,plain,
! [SV231: $i] :
( ( ! [SY1422: $i] :
~ ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SV231 ) @ ( bit1 @ SY1422 ) )
| ( ord_less_eq @ int @ SV231 @ SY1422 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV231 @ SY1422 )
| ( ord_less @ int @ ( bit0 @ SV231 ) @ ( bit1 @ SY1422 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1896]) ).
thf(2347,plain,
! [SV232: $i] :
( ( ~ ( zero_neq_one @ SV232 )
| ( ( one_one @ SV232 )
!= ( zero_zero @ SV232 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1897]) ).
thf(2348,plain,
! [SV233: $i] :
( ( ! [SY1423: $i] :
~ ( ~ ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ SV233 @ ( number_number_of @ nat @ SY1423 ) ) )
| ( ( number_number_of @ nat @ SY1423 )
= ( zero_zero @ nat ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ SV233 ) )
| ~ ( ~ ( ( ( number_number_of @ nat @ SY1423 )
= ( zero_zero @ nat ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ SV233 ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ SV233 @ ( number_number_of @ nat @ SY1423 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1898]) ).
thf(2349,plain,
! [SV234: $i] :
( ( ~ ~ ( ~ ( number @ SV234 )
| ~ ( semiring @ SV234 ) )
| ! [SY1424: $i,SY1425: $i,SY1426: $i] :
( ( times_times @ SV234 @ ( number_number_of @ SV234 @ SY1424 ) @ ( plus_plus @ SV234 @ SY1425 @ SY1426 ) )
= ( plus_plus @ SV234 @ ( times_times @ SV234 @ ( number_number_of @ SV234 @ SY1424 ) @ SY1425 ) @ ( times_times @ SV234 @ ( number_number_of @ SV234 @ SY1424 ) @ SY1426 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1899]) ).
thf(2350,plain,
! [SV235: $i] :
( ( ~ ( ring_1 @ SV235 )
| ! [SY1427: $i] :
( ( minus_minus @ SV235 @ ( times_times @ SV235 @ SY1427 @ SY1427 ) @ ( one_one @ SV235 ) )
= ( times_times @ SV235 @ ( plus_plus @ SV235 @ SY1427 @ ( one_one @ SV235 ) ) @ ( minus_minus @ SV235 @ SY1427 @ ( one_one @ SV235 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1900]) ).
thf(2351,plain,
! [SV236: $i] :
( ( ! [SY1428: $i] :
~ ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SV236 ) @ ( bit1 @ SY1428 ) )
| ( ord_less_eq @ int @ SV236 @ SY1428 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV236 @ SY1428 )
| ( ord_less @ int @ ( bit0 @ SV236 ) @ ( bit1 @ SY1428 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1901]) ).
thf(2352,plain,
! [SV237: $i] :
( ( ~ ( number @ SV237 )
| ! [SY1429: $i,SY1430: $i] :
~ ( ~ ( ( ( number_number_of @ SV237 @ SY1429 )
!= ( ti @ SV237 @ SY1430 ) )
| ( ( ti @ SV237 @ SY1430 )
= ( number_number_of @ SV237 @ SY1429 ) ) )
| ~ ( ( ( ti @ SV237 @ SY1430 )
!= ( number_number_of @ SV237 @ SY1429 ) )
| ( ( number_number_of @ SV237 @ SY1429 )
= ( ti @ SV237 @ SY1430 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1902]) ).
thf(2353,plain,
( ( min = pls )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1903]) ).
thf(2354,plain,
! [SV238: $i] :
( ( ~ ( comm_semiring_1 @ SV238 )
| ! [SY1431: $i,SY1432: $i,SY1433: $i] :
( ( plus_plus @ SV238 @ SY1431 @ ( plus_plus @ SV238 @ SY1432 @ SY1433 ) )
= ( plus_plus @ SV238 @ ( plus_plus @ SV238 @ SY1431 @ SY1432 ) @ SY1433 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1904]) ).
thf(2355,plain,
! [SV239: $i] :
( ( ~ ( ~ ( ~ ( ord_less_eq @ int @ min @ ( bit0 @ SV239 ) )
| ( ord_less @ int @ min @ SV239 ) )
| ~ ( ~ ( ord_less @ int @ min @ SV239 )
| ( ord_less_eq @ int @ min @ ( bit0 @ SV239 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1905]) ).
thf(2356,plain,
! [SV240: $i] :
( ( ! [SY1434: $i,SY1435: $i,SY1436: $i] :
( ~ ( zprime @ SY1436 )
| ~ ~ ( dvd_dvd @ int @ SY1436 @ SY1435 )
| ~ ( dvd_dvd @ int @ ( power_power @ int @ SY1436 @ SV240 ) @ ( times_times @ int @ SY1435 @ SY1434 ) )
| ( dvd_dvd @ int @ ( power_power @ int @ SY1436 @ SV240 ) @ SY1434 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1906]) ).
thf(2357,plain,
! [SV241: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ ( number_number_of @ nat @ SV241 ) )
| ( ord_less @ int @ pls @ SV241 ) )
| ~ ( ~ ( ord_less @ int @ pls @ SV241 )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ ( number_number_of @ nat @ SV241 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1907]) ).
thf(2358,plain,
! [SV242: $i] :
( ( ! [SY1437: $i] :
~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit0 @ SV242 ) @ ( bit1 @ SY1437 ) )
| ( ord_less_eq @ int @ SV242 @ SY1437 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV242 @ SY1437 )
| ( ord_less_eq @ int @ ( bit0 @ SV242 ) @ ( bit1 @ SY1437 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1908]) ).
thf(2359,plain,
! [SV243: $i] :
( ( ! [SY1438: $i,SY1439: $i] :
( ~ ( power @ SY1439 )
| ( ( times_times @ SY1439 @ ( ti @ SY1439 @ SV243 ) @ SY1438 )
= ( times_times @ SY1439 @ SV243 @ SY1438 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1909]) ).
thf(2360,plain,
! [SV244: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ int @ pls @ ( bit1 @ SV244 ) )
| ( ord_less_eq @ int @ pls @ SV244 ) )
| ~ ( ~ ( ord_less_eq @ int @ pls @ SV244 )
| ( ord_less @ int @ pls @ ( bit1 @ SV244 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1910]) ).
thf(2361,plain,
! [SV245: $i] :
( ( ! [SY1440: $i,SY1441: $i] :
~ ( ~ ( ~ ( ord_less @ int @ SY1441 @ pls )
| ( ( times_times @ nat @ ( number_number_of @ nat @ SY1441 ) @ ( times_times @ nat @ ( number_number_of @ nat @ SV245 ) @ SY1440 ) )
= ( zero_zero @ nat ) ) )
| ~ ( ~ ~ ( ord_less @ int @ SY1441 @ pls )
| ( ( times_times @ nat @ ( number_number_of @ nat @ SY1441 ) @ ( times_times @ nat @ ( number_number_of @ nat @ SV245 ) @ SY1440 ) )
= ( times_times @ nat @ ( number_number_of @ nat @ ( times_times @ int @ SY1441 @ SV245 ) ) @ SY1440 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1911]) ).
thf(2362,plain,
! [SV246: $i] :
( ( ! [SY1442: $i,SY1443: $i] :
( ~ ( dvd @ SY1443 )
| ( ( times_times @ SY1443 @ ( ti @ SY1443 @ SV246 ) @ SY1442 )
= ( times_times @ SY1443 @ SV246 @ SY1442 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1912]) ).
thf(2363,plain,
! [SV247: $i] :
( ( ! [SY1444: $i] :
~ ( ~ ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ SV247 @ SY1444 ) )
| ( SY1444
= ( zero_zero @ nat ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ SV247 ) )
| ~ ( ~ ( ( SY1444
= ( zero_zero @ nat ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ SV247 ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ SV247 @ SY1444 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1913]) ).
thf(2364,plain,
! [SV248: $i] :
( ( ~ ( number_ring @ SV248 )
| ! [SY1445: $i,SY1446: $i,SY1447: $i] :
( ( times_times @ SV248 @ ( number_number_of @ SV248 @ SY1445 ) @ ( times_times @ SV248 @ ( number_number_of @ SV248 @ SY1446 ) @ SY1447 ) )
= ( times_times @ SV248 @ ( number_number_of @ SV248 @ ( times_times @ int @ SY1445 @ SY1446 ) ) @ SY1447 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1914]) ).
thf(2365,plain,
! [SV249: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SV249 ) @ ( zero_zero @ int ) )
| ( ord_less @ int @ SV249 @ ( zero_zero @ int ) ) )
| ~ ( ~ ( ord_less @ int @ SV249 @ ( zero_zero @ int ) )
| ( ord_less @ int @ ( bit1 @ SV249 ) @ ( zero_zero @ int ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1915]) ).
thf(2366,plain,
! [SV250: $i] :
( ( ~ ( number_ring @ SV250 )
| ! [SY1448: $i] :
( ( plus_plus @ SV250 @ SY1448 @ ( number_number_of @ SV250 @ pls ) )
= ( ti @ SV250 @ SY1448 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1916]) ).
thf(2367,plain,
! [SV251: $i] :
( ( ! [SY1449: $i,SY1450: $i] :
( ~ ( power @ SY1450 )
| ( ( power_power @ SY1450 @ SV251 @ ( ti @ nat @ SY1449 ) )
= ( power_power @ SY1450 @ SV251 @ SY1449 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1917]) ).
thf(2368,plain,
! [SV252: $i] :
( ( ~ ( comm_semiring_1 @ SV252 )
| ! [SY1451: $i,SY1452: $i,SY1453: $i] :
( ( times_times @ SV252 @ ( times_times @ SV252 @ SY1451 @ SY1452 ) @ SY1453 )
= ( times_times @ SV252 @ SY1451 @ ( times_times @ SV252 @ SY1452 @ SY1453 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1918]) ).
thf(2369,plain,
! [SV253: $i] :
( ( ! [SY1454: $i] :
~ ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SV253 ) @ ( bit0 @ SY1454 ) )
| ( ord_less @ int @ SV253 @ SY1454 ) )
| ~ ( ~ ( ord_less @ int @ SV253 @ SY1454 )
| ( ord_less @ int @ ( bit1 @ SV253 ) @ ( bit0 @ SY1454 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1919]) ).
thf(2370,plain,
! [SV254: $i] :
( ( ~ ( comm_semiring_1 @ SV254 )
| ! [SY1455: $i,SY1456: $i] :
( ( plus_plus @ SV254 @ SY1455 @ ( times_times @ SV254 @ SY1456 @ SY1455 ) )
= ( times_times @ SV254 @ ( plus_plus @ SV254 @ SY1456 @ ( one_one @ SV254 ) ) @ SY1455 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1920]) ).
thf(2371,plain,
! [SV255: $i] :
( ( ~ ( semiri456707255roduct @ SV255 )
| ! [SY1457: $i,SY1458: $i,SY1459: $i,SY1460: $i] :
~ ( ~ ( ( ( plus_plus @ SV255 @ ( times_times @ SV255 @ SY1457 @ SY1458 ) @ ( times_times @ SV255 @ SY1459 @ SY1460 ) )
!= ( plus_plus @ SV255 @ ( times_times @ SV255 @ SY1457 @ SY1460 ) @ ( times_times @ SV255 @ SY1459 @ SY1458 ) ) )
| ( ( ti @ SV255 @ SY1457 )
= ( ti @ SV255 @ SY1459 ) )
| ( ( ti @ SV255 @ SY1458 )
= ( ti @ SV255 @ SY1460 ) ) )
| ~ ( ~ ( ( ( ti @ SV255 @ SY1457 )
= ( ti @ SV255 @ SY1459 ) )
| ( ( ti @ SV255 @ SY1458 )
= ( ti @ SV255 @ SY1460 ) ) )
| ( ( plus_plus @ SV255 @ ( times_times @ SV255 @ SY1457 @ SY1458 ) @ ( times_times @ SV255 @ SY1459 @ SY1460 ) )
= ( plus_plus @ SV255 @ ( times_times @ SV255 @ SY1457 @ SY1460 ) @ ( times_times @ SV255 @ SY1459 @ SY1458 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1921]) ).
thf(2372,plain,
! [SV256: $i] :
( ( ~ ( ~ ( ~ ( ord_less_eq @ int @ pls @ ( bit1 @ SV256 ) )
| ( ord_less_eq @ int @ pls @ SV256 ) )
| ~ ( ~ ( ord_less_eq @ int @ pls @ SV256 )
| ( ord_less_eq @ int @ pls @ ( bit1 @ SV256 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1922]) ).
thf(2373,plain,
! [SV257: $i] :
( ( ! [SY1461: $i,SY1462: $i,SY1463: $i,SY1464: $i] :
( ~ ( zcong @ SY1462 @ SY1463 @ SY1464 )
| ~ ( ~ ( ~ ( zcong @ SV257 @ ( times_times @ int @ SY1461 @ SY1462 ) @ SY1464 )
| ( zcong @ SV257 @ ( times_times @ int @ SY1461 @ SY1463 ) @ SY1464 ) )
| ~ ( ~ ( zcong @ SV257 @ ( times_times @ int @ SY1461 @ SY1463 ) @ SY1464 )
| ( zcong @ SV257 @ ( times_times @ int @ SY1461 @ SY1462 ) @ SY1464 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1923]) ).
thf(2374,plain,
! [SV258: $i] :
( ( ~ ( number_ring @ SV258 )
| ( ( one_one @ SV258 )
= ( number_number_of @ SV258 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1924]) ).
thf(2375,plain,
! [SV259: $i] :
( ( ! [SY1465: $i,SY1466: $i] :
( ~ ( ( SY1466
!= ( zero_zero @ nat ) ) )
| ~ ( dvd_dvd @ nat @ ( power_power @ nat @ SV259 @ SY1466 ) @ SY1465 )
| ( dvd_dvd @ nat @ SV259 @ SY1465 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1925]) ).
thf(2376,plain,
! [SV260: $i] :
( ( ~ ( number_ring @ SV260 )
| ( ( number_number_of @ SV260 @ ( bit1 @ pls ) )
= ( one_one @ SV260 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1926]) ).
thf(2377,plain,
! [SV261: $i] :
( ( ! [SY1467: $i,SY1468: $i] :
~ ( ~ ( ~ ( zcong @ SV261 @ ( ti @ int @ SY1467 ) @ SY1468 )
| ( zcong @ SV261 @ SY1467 @ SY1468 ) )
| ~ ( ~ ( zcong @ SV261 @ SY1467 @ SY1468 )
| ( zcong @ SV261 @ ( ti @ int @ SY1467 ) @ SY1468 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1927]) ).
thf(2378,plain,
! [SV262: $i] :
( ( ~ ( zprime @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SV262 ) @ ( one_one @ int ) ) )
| ( ( legendre @ ( number_number_of @ int @ min ) @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SV262 ) @ ( one_one @ int ) ) )
= ( one_one @ int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1928]) ).
thf(2379,plain,
! [SV263: $i] :
( ( ~ ( number_ring @ SV263 )
| ! [SY1469: $i,SY1470: $i] :
( ( number_number_of @ SV263 @ ( plus_plus @ int @ SY1469 @ SY1470 ) )
= ( plus_plus @ SV263 @ ( number_number_of @ SV263 @ SY1469 ) @ ( number_number_of @ SV263 @ SY1470 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1929]) ).
thf(2380,plain,
! [SV264: $i] :
( ( ~ ( number_ring @ SV264 )
| ! [SY1471: $i,SY1472: $i] :
( ( number_number_of @ SV264 @ ( times_times @ int @ SY1471 @ SY1472 ) )
= ( times_times @ SV264 @ ( number_number_of @ SV264 @ SY1471 ) @ ( number_number_of @ SV264 @ SY1472 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1930]) ).
thf(2381,plain,
! [SV265: $i] :
( ( ~ ( comm_semiring_1 @ SV265 )
| ! [SY1473: $i] :
( ( power_power @ SV265 @ SY1473 @ ( zero_zero @ nat ) )
= ( one_one @ SV265 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1931]) ).
thf(2382,plain,
! [SV266: $i] :
( ( ~ ( comm_semiring_1 @ SV266 )
| ! [SY1474: $i,SY1475: $i,SY1476: $i,SY1477: $i] :
( ( plus_plus @ SV266 @ ( plus_plus @ SV266 @ SY1474 @ SY1475 ) @ ( plus_plus @ SV266 @ SY1476 @ SY1477 ) )
= ( plus_plus @ SV266 @ ( plus_plus @ SV266 @ SY1474 @ SY1476 ) @ ( plus_plus @ SV266 @ SY1475 @ SY1477 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1932]) ).
thf(2383,plain,
! [SV267: $i] :
( ( pls
!= ( bit1 @ SV267 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1933]) ).
thf(2384,plain,
! [SV268: $i] :
( ( ! [SY1478: $i] :
( ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SY1478 )
| ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV268 )
| ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( times_times @ int @ SY1478 @ SV268 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1934]) ).
thf(2385,plain,
! [SV269: $i] :
( ( ~ ( linordered_idom @ SV269 )
| ! [SY1479: $i] :
~ ( ~ ( ~ ( ord_less @ SV269 @ ( plus_plus @ SV269 @ SY1479 @ SY1479 ) @ ( zero_zero @ SV269 ) )
| ( ord_less @ SV269 @ SY1479 @ ( zero_zero @ SV269 ) ) )
| ~ ( ~ ( ord_less @ SV269 @ SY1479 @ ( zero_zero @ SV269 ) )
| ( ord_less @ SV269 @ ( plus_plus @ SV269 @ SY1479 @ SY1479 ) @ ( zero_zero @ SV269 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1935]) ).
thf(2386,plain,
! [SV270: $i] :
( ( ! [SY1480: $i] :
( ~ ( ord_less_eq @ int @ SV270 @ SY1480 )
| ~ ( ord_less_eq @ int @ SY1480 @ SV270 )
| ( ( ti @ int @ SV270 )
= ( ti @ int @ SY1480 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1936]) ).
thf(2387,plain,
! [SV271: $i] :
( ( ~ ( number_ring @ SV271 )
| ! [SY1481: $i,SY1482: $i,SY1483: $i] :
( ( plus_plus @ SV271 @ ( number_number_of @ SV271 @ SY1481 ) @ ( minus_minus @ SV271 @ ( number_number_of @ SV271 @ SY1482 ) @ SY1483 ) )
= ( minus_minus @ SV271 @ ( number_number_of @ SV271 @ ( plus_plus @ int @ SY1481 @ SY1482 ) ) @ SY1483 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1937]) ).
thf(2388,plain,
! [SV272: $i] :
( ( ~ ( number_ring @ SV272 )
| ! [SY1484: $i] :
( ( number_number_of @ SV272 @ ( bit0 @ SY1484 ) )
= ( plus_plus @ SV272 @ ( plus_plus @ SV272 @ ( zero_zero @ SV272 ) @ ( number_number_of @ SV272 @ SY1484 ) ) @ ( number_number_of @ SV272 @ SY1484 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1938]) ).
thf(2389,plain,
! [SV273: $i] :
( ( ! [SY1485: $i,SY1486: $i] :
( ~ ( ( SY1486
!= ( zero_zero @ real ) ) )
| ~ ( ~ ( ( ( times_times @ real @ SY1486 @ SV273 )
!= ( times_times @ real @ SY1486 @ SY1485 ) )
| ( SV273 = SY1485 ) )
| ~ ( ( SV273 != SY1485 )
| ( ( times_times @ real @ SY1486 @ SV273 )
= ( times_times @ real @ SY1486 @ SY1485 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1939]) ).
thf(2390,plain,
! [SV274: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ int @ min @ ( bit1 @ SV274 ) )
| ( ord_less @ int @ min @ SV274 ) )
| ~ ( ~ ( ord_less @ int @ min @ SV274 )
| ( ord_less @ int @ min @ ( bit1 @ SV274 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1940]) ).
thf(2391,plain,
! [SV275: $i] :
( ( ~ ( number_ring @ SV275 )
| ! [SY1487: $i,SY1488: $i] :
( ( number_number_of @ SV275 @ ( minus_minus @ int @ SY1487 @ SY1488 ) )
= ( minus_minus @ SV275 @ ( number_number_of @ SV275 @ SY1487 ) @ ( number_number_of @ SV275 @ SY1488 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1941]) ).
thf(2392,plain,
! [SV276: $i] :
( ( ~ ( monoid_mult @ SV276 )
| ! [SY1489: $i] :
( ( power_power @ SV276 @ ( one_one @ SV276 ) @ SY1489 )
= ( one_one @ SV276 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1942]) ).
thf(2393,plain,
! [SV277: $i] :
( ( ~ ( comm_semiring_1 @ SV277 )
| ! [SY1490: $i,SY1491: $i,SY1492: $i] :
( ~ ( dvd_dvd @ SV277 @ SY1491 @ SY1492 )
| ~ ( dvd_dvd @ SV277 @ SY1491 @ SY1490 )
| ( dvd_dvd @ SV277 @ SY1491 @ ( plus_plus @ SV277 @ SY1492 @ SY1490 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1943]) ).
thf(2394,plain,
! [SV278: $i] :
( ( ~ ( comm_semiring_1 @ SV278 )
| ! [SY1493: $i] :
( ( times_times @ SV278 @ ( zero_zero @ SV278 ) @ SY1493 )
= ( zero_zero @ SV278 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1944]) ).
thf(2395,plain,
! [SV279: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SV279 ) @ pls )
| ( ord_less @ int @ SV279 @ pls ) )
| ~ ( ~ ( ord_less @ int @ SV279 @ pls )
| ( ord_less @ int @ ( bit0 @ SV279 ) @ pls ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1945]) ).
thf(2396,plain,
! [SV280: $i] :
( ( ! [SY1494: $i,SY1495: $i] :
( ~ ( semiring @ SY1495 )
| ( ( ti @ SY1495 @ ( times_times @ SY1495 @ SV280 @ SY1494 ) )
= ( times_times @ SY1495 @ SV280 @ SY1494 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1946]) ).
thf(2397,plain,
! [SV281: $i] :
( ( ! [SY1496: $i] :
~ ( ~ ( ( ( bit0 @ SV281 )
!= ( bit0 @ SY1496 ) )
| ( ( ti @ int @ SV281 )
= ( ti @ int @ SY1496 ) ) )
| ~ ( ( ( ti @ int @ SV281 )
!= ( ti @ int @ SY1496 ) )
| ( ( bit0 @ SV281 )
= ( bit0 @ SY1496 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1947]) ).
thf(2398,plain,
! [SV282: $i] :
( ( ~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SV282 ) @ min )
| ( ord_less_eq @ int @ SV282 @ min ) )
| ~ ( ~ ( ord_less_eq @ int @ SV282 @ min )
| ( ord_less_eq @ int @ ( bit1 @ SV282 ) @ min ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1948]) ).
thf(2399,plain,
! [SV283: $i] :
( ( ~ ( number_ring @ SV283 )
| ! [SY1497: $i] :
( ( plus_plus @ SV283 @ ( number_number_of @ SV283 @ pls ) @ SY1497 )
= ( ti @ SV283 @ SY1497 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1949]) ).
thf(2400,plain,
! [SV284: $i] :
( ( ~ ( comm_semiring_1 @ SV284 )
| ! [SY1498: $i,SY1499: $i,SY1500: $i] :
( ~ ( dvd_dvd @ SV284 @ SY1499 @ SY1500 )
| ( dvd_dvd @ SV284 @ ( power_power @ SV284 @ SY1499 @ SY1498 ) @ ( power_power @ SV284 @ SY1500 @ SY1498 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1950]) ).
thf(2401,plain,
! [SV285: $i] :
( ( ~ ( number_semiring @ SV285 )
| ! [SY1501: $i,SY1502: $i] :
( ~ ( ord_less_eq @ int @ pls @ SY1502 )
| ~ ( ord_less_eq @ int @ pls @ SY1501 )
| ( ( plus_plus @ SV285 @ ( number_number_of @ SV285 @ SY1502 ) @ ( number_number_of @ SV285 @ SY1501 ) )
= ( number_number_of @ SV285 @ ( plus_plus @ int @ SY1502 @ SY1501 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1951]) ).
thf(2402,plain,
! [SV286: $i] :
( ( ~ ( monoid_mult @ SV286 )
| ! [SY1503: $i,SY1504: $i] :
( ( power_power @ SV286 @ SY1503 @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SY1504 ) )
= ( power_power @ SV286 @ ( power_power @ SV286 @ SY1503 @ SY1504 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1952]) ).
thf(2403,plain,
! [SV287: $i] :
( ( ! [SY1505: $i,SY1506: $i] :
( ~ ( dvd @ SY1506 )
| ( ( times_times @ SY1506 @ SV287 @ ( ti @ SY1506 @ SY1505 ) )
= ( times_times @ SY1506 @ SV287 @ SY1505 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1953]) ).
thf(2404,plain,
! [SV288: $i] :
( ( ! [SY1507: $i,SY1508: $i,SY1509: $i] :
( ~ ( zprime @ SY1509 )
| ~ ~ ( dvd_dvd @ int @ SY1509 @ SY1508 )
| ~ ( dvd_dvd @ int @ ( power_power @ int @ SY1509 @ SV288 ) @ ( times_times @ int @ SY1507 @ SY1508 ) )
| ( dvd_dvd @ int @ ( power_power @ int @ SY1509 @ SV288 ) @ SY1507 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1954]) ).
thf(2405,plain,
! [SV289: $i] :
( ( ! [SY1510: $i,SY1511: $i] :
( ~ ( ab_group_add @ SY1511 )
| ( ( plus_plus @ SY1511 @ ( ti @ SY1511 @ SV289 ) @ SY1510 )
= ( plus_plus @ SY1511 @ SV289 @ SY1510 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1955]) ).
thf(2406,plain,
! [SV290: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SV290 ) @ ( zero_zero @ int ) )
| ( ord_less @ int @ SV290 @ ( zero_zero @ int ) ) )
| ~ ( ~ ( ord_less @ int @ SV290 @ ( zero_zero @ int ) )
| ( ord_less @ int @ ( bit0 @ SV290 ) @ ( zero_zero @ int ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1956]) ).
thf(2407,plain,
! [SV291: $i] :
( ( ~ ( comm_semiring_1 @ SV291 )
| ! [SY1512: $i] :
( ( times_times @ SV291 @ SY1512 @ SY1512 )
= ( power_power @ SV291 @ SY1512 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1957]) ).
thf(2408,plain,
! [SV292: $i] :
( ( ! [SY1513: $i] :
~ ( ~ ( ~ ( zcong @ ( times_times @ int @ SV292 @ ( minus_minus @ int @ SY1513 @ ( one_one @ int ) ) ) @ ( one_one @ int ) @ SY1513 )
| ( zcong @ SV292 @ ( minus_minus @ int @ SY1513 @ ( one_one @ int ) ) @ SY1513 ) )
| ~ ( ~ ( zcong @ SV292 @ ( minus_minus @ int @ SY1513 @ ( one_one @ int ) ) @ SY1513 )
| ( zcong @ ( times_times @ int @ SV292 @ ( minus_minus @ int @ SY1513 @ ( one_one @ int ) ) ) @ ( one_one @ int ) @ SY1513 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1958]) ).
thf(2409,plain,
! [SV293: $i] :
( ( ~ ( linordered_idom @ SV293 )
| ! [SY1514: $i] : ( ord_less_eq @ SV293 @ ( zero_zero @ SV293 ) @ ( power_power @ SV293 @ SY1514 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1959]) ).
thf(2410,plain,
! [SV294: $i] :
( ( ! [SY1515: $i,SY1516: $i] :
( ~ ( ord_less_eq @ int @ SY1515 @ SY1516 )
| ~ ( ord_less_eq @ int @ SY1516 @ SV294 )
| ( ord_less_eq @ int @ SY1515 @ SV294 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1960]) ).
thf(2411,plain,
! [SV295: $i] :
( ( ~ ( power @ SV295 )
| ( ( ti @ SV295 @ ( one_one @ SV295 ) )
= ( one_one @ SV295 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1961]) ).
thf(2412,plain,
! [SV296: $i] :
( ( ~ ( comm_semiring_1 @ SV296 )
| ! [SY1517: $i,SY1518: $i,SY1519: $i] :
( ( plus_plus @ SV296 @ ( plus_plus @ SV296 @ SY1517 @ SY1518 ) @ SY1519 )
= ( plus_plus @ SV296 @ ( plus_plus @ SV296 @ SY1517 @ SY1519 ) @ SY1518 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1962]) ).
thf(2413,plain,
! [SV297: $i] :
( ( ! [SY1520: $i,SY1521: $i] :
( ~ ( ord_less @ int @ SY1520 @ SY1521 )
| ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV297 )
| ( ord_less @ int @ ( times_times @ int @ SV297 @ SY1520 ) @ ( times_times @ int @ SV297 @ SY1521 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1963]) ).
thf(2414,plain,
! [SV298: $i] :
( ( ~ ( comm_monoid_mult @ SV298 )
| ! [SY1522: $i,SY1523: $i,SY1524: $i] :
( ( power_power @ SV298 @ ( times_times @ SV298 @ SY1522 @ SY1523 ) @ SY1524 )
= ( times_times @ SV298 @ ( power_power @ SV298 @ SY1522 @ SY1524 ) @ ( power_power @ SV298 @ SY1523 @ SY1524 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1964]) ).
thf(2415,plain,
! [SV299: $i] :
( ( ! [SY1525: $i] :
( ~ ( dvd_dvd @ nat @ SV299 @ SY1525 )
| ( SY1525
= ( zero_zero @ nat ) )
| ( SY1525 = SV299 )
| ( ord_less_eq @ nat @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV299 ) @ SY1525 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1965]) ).
thf(2416,plain,
! [SV300: $i] :
( ( ! [SY1526: $i] :
~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SV300 ) @ ( bit1 @ SY1526 ) )
| ( ord_less_eq @ int @ SV300 @ SY1526 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV300 @ SY1526 )
| ( ord_less_eq @ int @ ( bit1 @ SV300 ) @ ( bit1 @ SY1526 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1966]) ).
thf(2417,plain,
! [SV301: $i] :
( ( ~ ( ring_n68954251visors @ SV301 )
| ! [SY1527: $i,SY1528: $i] :
~ ( ~ ( ( ( times_times @ SV301 @ SY1527 @ SY1528 )
!= ( zero_zero @ SV301 ) )
| ( ( ti @ SV301 @ SY1527 )
= ( zero_zero @ SV301 ) )
| ( ( ti @ SV301 @ SY1528 )
= ( zero_zero @ SV301 ) ) )
| ~ ( ~ ( ( ( ti @ SV301 @ SY1527 )
= ( zero_zero @ SV301 ) )
| ( ( ti @ SV301 @ SY1528 )
= ( zero_zero @ SV301 ) ) )
| ( ( times_times @ SV301 @ SY1527 @ SY1528 )
= ( zero_zero @ SV301 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1967]) ).
thf(2418,plain,
! [SV302: $i] :
( ( ~ ( number_ring @ SV302 )
| ! [SY1529: $i] :
( ( times_times @ SV302 @ ( plus_plus @ SV302 @ ( one_one @ SV302 ) @ ( one_one @ SV302 ) ) @ ( number_number_of @ SV302 @ SY1529 ) )
= ( number_number_of @ SV302 @ ( bit0 @ SY1529 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1968]) ).
thf(2419,plain,
! [SV303: $i] :
( ( ~ ( ~ ( ( pls
!= ( bit0 @ SV303 ) )
| ( pls
= ( ti @ int @ SV303 ) ) )
| ~ ( ( pls
!= ( ti @ int @ SV303 ) )
| ( pls
= ( bit0 @ SV303 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1969]) ).
thf(2420,plain,
! [SV304: $i] :
( ( ~ ( linordered_semidom @ SV304 )
| ! [SY1530: $i,SY1531: $i,SY1532: $i] :
( ~ ( ord_less @ SV304 @ ( one_one @ SV304 ) @ SY1532 )
| ~ ( ord_less_eq @ SV304 @ ( power_power @ SV304 @ SY1532 @ SY1530 ) @ ( power_power @ SV304 @ SY1532 @ SY1531 ) )
| ( ord_less_eq @ nat @ SY1530 @ SY1531 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1970]) ).
thf(2421,plain,
! [SV305: $i] :
( ( ! [SY1533: $i,SY1534: $i,SY1535: $i,SY1536: $i,SY1537: $i] :
( ( ( plus_plus @ int @ ( times_times @ int @ SV305 @ SY1533 ) @ SY1534 )
!= ( plus_plus @ int @ ( times_times @ int @ SY1535 @ SY1536 ) @ SY1537 ) )
| ~ ( ord_less @ int @ ( plus_plus @ int @ ( times_times @ int @ SY1535 @ SY1536 ) @ SY1537 ) @ ( zero_zero @ int ) )
| ~ ( ord_less @ int @ SY1534 @ SV305 )
| ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SY1537 )
| ~ ( ord_less @ int @ ( zero_zero @ int ) @ SY1535 )
| ~ ( ord_less_eq @ int @ SY1535 @ SV305 )
| ( ord_less_eq @ int @ SY1536 @ SY1533 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1971]) ).
thf(2422,plain,
! [SV306: $i] :
( ( ~ ( comm_semiring_1 @ SV306 )
| ! [SY1538: $i,SY1539: $i] :
( ( plus_plus @ SV306 @ ( times_times @ SV306 @ SY1538 @ SY1539 ) @ SY1539 )
= ( times_times @ SV306 @ ( plus_plus @ SV306 @ SY1538 @ ( one_one @ SV306 ) ) @ SY1539 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1972]) ).
thf(2423,plain,
! [SV307: $i] :
( ( ! [SY1540: $i,SY1541: $i] :
( ~ ( dvd @ SY1541 )
| ( ( ti @ SY1541 @ ( times_times @ SY1541 @ SV307 @ SY1540 ) )
= ( times_times @ SY1541 @ SV307 @ SY1540 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1973]) ).
thf(2424,plain,
! [SV308: $i] :
( ( ! [SY1542: $i,SY1543: $i,SY1544: $i] :
( ~ ( zcong @ SY1542 @ SY1543 @ SY1544 )
| ( zcong @ ( power_power @ int @ SY1542 @ SV308 ) @ ( power_power @ int @ SY1543 @ SV308 ) @ SY1544 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1974]) ).
thf(2425,plain,
! [SV309: $i] :
( ( ~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SV309 ) @ pls )
| ( ord_less @ int @ SV309 @ pls ) )
| ~ ( ~ ( ord_less @ int @ SV309 @ pls )
| ( ord_less_eq @ int @ ( bit1 @ SV309 ) @ pls ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1975]) ).
thf(2426,plain,
! [SV310: $i] :
( ( ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ SV310 ) @ SV310 )
!= ( zero_zero @ int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1976]) ).
thf(2427,plain,
! [SV311: $i] :
( ( ~ ( comm_semiring_1 @ SV311 )
| ! [SY1545: $i,SY1546: $i,SY1547: $i] :
( ( power_power @ SV311 @ ( power_power @ SV311 @ SY1545 @ SY1546 ) @ SY1547 )
= ( power_power @ SV311 @ SY1545 @ ( times_times @ nat @ SY1546 @ SY1547 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1977]) ).
thf(2428,plain,
! [SV312: $i] :
( ( ! [SY1548: $i,SY1549: $i,SY1550: $i,SY1551: $i] :
( ~ ( ord_less_eq @ int @ ( plus_plus @ int @ ( times_times @ int @ SV312 @ SY1548 ) @ SY1549 ) @ ( plus_plus @ int @ ( times_times @ int @ SV312 @ SY1550 ) @ SY1551 ) )
| ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SY1549 )
| ~ ( ord_less @ int @ SY1549 @ SV312 )
| ~ ( ord_less @ int @ SY1551 @ SV312 )
| ( ord_less_eq @ int @ SY1548 @ SY1550 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1978]) ).
thf(2429,plain,
! [SV313: $i] :
( ( ~ ( semiri456707255roduct @ SV313 )
| ! [SY1552: $i,SY1553: $i] :
~ ( ~ ( ( ( ti @ SV313 @ SY1552 )
!= ( plus_plus @ SV313 @ SY1552 @ SY1553 ) )
| ( ( ti @ SV313 @ SY1553 )
= ( zero_zero @ SV313 ) ) )
| ~ ( ( ( ti @ SV313 @ SY1553 )
!= ( zero_zero @ SV313 ) )
| ( ( ti @ SV313 @ SY1552 )
= ( plus_plus @ SV313 @ SY1552 @ SY1553 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1979]) ).
thf(2430,plain,
! [SV314: $i] :
( ( ! [SY1554: $i] :
~ ( ~ ( ~ ( quadRes @ SV314 @ SY1554 )
| ~ ! [SY1555: $i] :
~ ( zcong @ ( power_power @ int @ SY1555 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SY1554 @ SV314 ) )
| ~ ( ~ ~ ! [SY1556: $i] :
~ ( zcong @ ( power_power @ int @ SY1556 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SY1554 @ SV314 )
| ( quadRes @ SV314 @ SY1554 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1980]) ).
thf(2431,plain,
! [SV315: $i] :
( ( ~ ( linordered_semidom @ SV315 )
| ! [SY1557: $i,SY1558: $i,SY1559: $i] :
( ~ ( ord_less_eq @ nat @ SY1558 @ SY1559 )
| ~ ( ord_less_eq @ SV315 @ ( one_one @ SV315 ) @ SY1557 )
| ( ord_less_eq @ SV315 @ ( power_power @ SV315 @ SY1557 @ SY1558 ) @ ( power_power @ SV315 @ SY1557 @ SY1559 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1981]) ).
thf(2432,plain,
! [SV316: $i] :
( ( ~ ( comm_semiring_1 @ SV316 )
| ! [SY1560: $i,SY1561: $i,SY1562: $i] :
( ( times_times @ SV316 @ ( plus_plus @ SV316 @ SY1560 @ SY1561 ) @ SY1562 )
= ( plus_plus @ SV316 @ ( times_times @ SV316 @ SY1560 @ SY1562 ) @ ( times_times @ SV316 @ SY1561 @ SY1562 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1982]) ).
thf(2433,plain,
! [SV317: $i] :
( ( ~ ( linordered_semidom @ SV317 )
| ! [SY1563: $i,SY1564: $i] :
( ~ ( ord_less_eq @ SV317 @ ( one_one @ SV317 ) @ SY1564 )
| ( ord_less_eq @ SV317 @ ( one_one @ SV317 ) @ ( power_power @ SV317 @ SY1564 @ SY1563 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1983]) ).
thf(2434,plain,
! [SV318: $i] :
( ( ~ ( comm_semiring_1 @ SV318 )
| ! [SY1565: $i,SY1566: $i] :
( ( times_times @ SV318 @ SY1565 @ SY1566 )
= ( times_times @ SV318 @ SY1566 @ SY1565 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1984]) ).
thf(2435,plain,
! [SV319: $i] :
( ( ~ ( linord581940658strict @ SV319 )
| ! [SY1567: $i,SY1568: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV319 @ ( times_times @ SV319 @ SY1567 @ SY1568 ) @ ( zero_zero @ SV319 ) )
| ~ ( ~ ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SY1567 )
| ~ ( ord_less_eq @ SV319 @ SY1568 @ ( zero_zero @ SV319 ) ) )
| ~ ( ~ ( ord_less_eq @ SV319 @ SY1567 @ ( zero_zero @ SV319 ) )
| ~ ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SY1568 ) ) )
| ~ ( ~ ( ~ ( ~ ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SY1567 )
| ~ ( ord_less_eq @ SV319 @ SY1568 @ ( zero_zero @ SV319 ) ) )
| ~ ( ~ ( ord_less_eq @ SV319 @ SY1567 @ ( zero_zero @ SV319 ) )
| ~ ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SY1568 ) ) )
| ( ord_less_eq @ SV319 @ ( times_times @ SV319 @ SY1567 @ SY1568 ) @ ( zero_zero @ SV319 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1985]) ).
thf(2436,plain,
! [SV320: $i] :
( ( ~ ( ~ ( ( ( zero_zero @ nat )
!= ( number_number_of @ nat @ SV320 ) )
| ( ord_less_eq @ int @ SV320 @ pls ) )
| ~ ( ~ ( ord_less_eq @ int @ SV320 @ pls )
| ( ( zero_zero @ nat )
= ( number_number_of @ nat @ SV320 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1986]) ).
thf(2437,plain,
! [SV321: $i] :
( ( ~ ~ ( ~ ( number_ring @ SV321 )
| ~ ( linordered_idom @ SV321 ) )
| ! [SY1569: $i,SY1570: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV321 @ ( number_number_of @ SV321 @ SY1569 ) @ ( number_number_of @ SV321 @ SY1570 ) )
| ( ord_less_eq @ int @ SY1569 @ SY1570 ) )
| ~ ( ~ ( ord_less_eq @ int @ SY1569 @ SY1570 )
| ( ord_less_eq @ SV321 @ ( number_number_of @ SV321 @ SY1569 ) @ ( number_number_of @ SV321 @ SY1570 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1987]) ).
thf(2438,plain,
! [SV322: $i] :
( ( ~ ( comm_semiring_1 @ SV322 )
| ! [SY1571: $i] :
( ( times_times @ SV322 @ SY1571 @ ( zero_zero @ SV322 ) )
= ( zero_zero @ SV322 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1988]) ).
thf(2439,plain,
! [SV323: $i] :
( ( ~ ( comm_semiring_1 @ SV323 )
| ! [SY1572: $i,SY1573: $i,SY1574: $i,SY1575: $i] :
( ~ ( dvd_dvd @ SV323 @ SY1574 @ SY1575 )
| ~ ( ord_less_eq @ nat @ SY1572 @ SY1573 )
| ( dvd_dvd @ SV323 @ ( power_power @ SV323 @ SY1574 @ SY1572 ) @ ( power_power @ SV323 @ SY1575 @ SY1573 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1989]) ).
thf(2440,plain,
! [SV324: $i] :
( ( ~ ( number_semiring @ SV324 )
| ( ( number_number_of @ SV324 @ ( bit1 @ pls ) )
= ( one_one @ SV324 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1990]) ).
thf(2441,plain,
! [SV325: $i] :
( ( ~ ( linordered_semidom @ SV325 )
| ! [SY1576: $i,SY1577: $i] :
( ~ ( ord_less_eq @ SV325 @ ( power_power @ SV325 @ SY1576 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV325 @ SY1577 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ~ ( ord_less_eq @ SV325 @ ( zero_zero @ SV325 ) @ SY1577 )
| ( ord_less_eq @ SV325 @ SY1576 @ SY1577 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1991]) ).
thf(2442,plain,
! [SV326: $i] :
( ( ( bit1 @ SV326 )
!= pls )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1992]) ).
thf(2443,plain,
! [SV327: $i] :
( ( ! [SY1578: $i] :
( ( ( times_times @ int @ SV327 @ SY1578 )
!= ( one_one @ int ) )
| ( ( ti @ int @ SV327 )
= ( one_one @ int ) )
| ( ( ti @ int @ SV327 )
= ( number_number_of @ int @ min ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1993]) ).
thf(2444,plain,
! [SV328: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ int @ min @ ( bit0 @ SV328 ) )
| ( ord_less @ int @ min @ SV328 ) )
| ~ ( ~ ( ord_less @ int @ min @ SV328 )
| ( ord_less @ int @ min @ ( bit0 @ SV328 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1994]) ).
thf(2445,plain,
! [SV329: $i] :
( ( ~ ( monoid_mult @ SV329 )
| ! [SY1579: $i,SY1580: $i,SY1581: $i] :
( ( power_power @ SV329 @ SY1579 @ ( plus_plus @ nat @ SY1580 @ SY1581 ) )
= ( times_times @ SV329 @ ( power_power @ SV329 @ SY1579 @ SY1580 ) @ ( power_power @ SV329 @ SY1579 @ SY1581 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1995]) ).
thf(2446,plain,
! [SV330: $i] :
( ( ~ ( comm_semiring_1 @ SV330 )
| ! [SY1582: $i,SY1583: $i,SY1584: $i] :
( ~ ( dvd_dvd @ SV330 @ ( times_times @ SV330 @ SY1582 @ SY1583 ) @ SY1584 )
| ( dvd_dvd @ SV330 @ SY1583 @ SY1584 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1996]) ).
thf(2447,plain,
! [SV331: $i] :
( ( ~ ( ord_less @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV331 )
| ~ ( zcong @ ( one_one @ int ) @ ( number_number_of @ int @ min ) @ SV331 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1997]) ).
thf(2448,plain,
! [SV332: $i] :
( ( ~ ( comm_semiring_1 @ SV332 )
| ! [SY1585: $i,SY1586: $i] : ( dvd_dvd @ SV332 @ SY1585 @ ( times_times @ SV332 @ SY1585 @ SY1586 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1998]) ).
thf(2449,plain,
! [SV333: $i] :
( ( ~ ~ ( ~ ( power @ SV333 )
| ~ ( semiring_0 @ SV333 ) )
| ! [SY1587: $i] :
~ ( ~ ( ( ( number_number_of @ nat @ SY1587 )
!= ( zero_zero @ nat ) )
| ( ( power_power @ SV333 @ ( zero_zero @ SV333 ) @ ( number_number_of @ nat @ SY1587 ) )
= ( one_one @ SV333 ) ) )
| ~ ( ~ ( ( ( number_number_of @ nat @ SY1587 )
!= ( zero_zero @ nat ) ) )
| ( ( power_power @ SV333 @ ( zero_zero @ SV333 ) @ ( number_number_of @ nat @ SY1587 ) )
= ( zero_zero @ SV333 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1999]) ).
thf(2450,plain,
! [SV334: $i] :
( ( ! [SY1588: $i,SY1589: $i] :
( ~ ( no_zero_divisors @ SY1589 )
| ( ( ti @ SY1589 @ ( times_times @ SY1589 @ SV334 @ SY1588 ) )
= ( times_times @ SY1589 @ SV334 @ SY1588 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2000]) ).
thf(2451,plain,
! [SV335: $i] :
( ( ! [SY1590: $i,SY1591: $i] :
( ~ ( ab_group_add @ SY1591 )
| ( ( plus_plus @ SY1591 @ SV335 @ ( ti @ SY1591 @ SY1590 ) )
= ( plus_plus @ SY1591 @ SV335 @ SY1590 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2001]) ).
thf(2452,plain,
! [SV336: $i] :
( ( ! [SY1592: $i] :
~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit0 @ SV336 ) @ ( bit0 @ SY1592 ) )
| ( ord_less_eq @ int @ SV336 @ SY1592 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV336 @ SY1592 )
| ( ord_less_eq @ int @ ( bit0 @ SV336 ) @ ( bit0 @ SY1592 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2002]) ).
thf(2453,plain,
! [SV337: $i] :
( ( ! [SY1593: $i,SY1594: $i,SY1595: $i,SY1596: $i] :
( ~ ( zcong @ SY1594 @ SY1595 @ SY1596 )
| ~ ( zcong @ SV337 @ SY1593 @ SY1596 )
| ( zcong @ ( times_times @ int @ SY1594 @ SV337 ) @ ( times_times @ int @ SY1595 @ SY1593 ) @ SY1596 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2003]) ).
thf(2454,plain,
! [SV338: $i] :
( ( ! [SY1597: $i,SY1598: $i] :
( ~ ( ord_less @ real @ ( zero_zero @ real ) @ SY1598 )
| ~ ( ~ ( ~ ( ord_less @ real @ ( times_times @ real @ SV338 @ SY1598 ) @ ( times_times @ real @ SY1597 @ SY1598 ) )
| ( ord_less @ real @ SV338 @ SY1597 ) )
| ~ ( ~ ( ord_less @ real @ SV338 @ SY1597 )
| ( ord_less @ real @ ( times_times @ real @ SV338 @ SY1598 ) @ ( times_times @ real @ SY1597 @ SY1598 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2004]) ).
thf(2455,plain,
! [SV339: $i] :
( ( ~ ( mult_zero @ SV339 )
| ! [SY1599: $i] :
( ( times_times @ SV339 @ SY1599 @ ( zero_zero @ SV339 ) )
= ( zero_zero @ SV339 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2005]) ).
thf(2456,plain,
( ( ~ ! [SX0: $i] :
~ ~ ! [SX1: $i] :
( ( plus_plus @ int @ ( power_power @ int @ SX0 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ SX1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2006]) ).
thf(2457,plain,
! [SV340: $i] :
( ( ~ ( comm_semiring_1 @ SV340 )
| ! [SY1600: $i,SY1601: $i,SY1602: $i,SY1603: $i] :
( ( times_times @ SV340 @ ( times_times @ SV340 @ SY1600 @ SY1601 ) @ ( times_times @ SV340 @ SY1602 @ SY1603 ) )
= ( times_times @ SV340 @ ( times_times @ SV340 @ SY1600 @ SY1602 ) @ ( times_times @ SV340 @ SY1601 @ SY1603 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2007]) ).
thf(2458,plain,
! [SV341: $i] :
( ( ! [SY1604: $i] :
~ ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SV341 ) @ ( bit0 @ SY1604 ) )
| ( ord_less @ int @ SV341 @ SY1604 ) )
| ~ ( ~ ( ord_less @ int @ SV341 @ SY1604 )
| ( ord_less @ int @ ( bit0 @ SV341 ) @ ( bit0 @ SY1604 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2008]) ).
thf(2459,plain,
! [SV342: $i] :
( ( ~ ( mult_zero @ SV342 )
| ! [SY1605: $i] :
( ( times_times @ SV342 @ ( zero_zero @ SV342 ) @ SY1605 )
= ( zero_zero @ SV342 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2009]) ).
thf(2460,plain,
( ( ( number_number_of @ int @ pls )
= ( number_number_of @ int @ min ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2010]) ).
thf(2461,plain,
! [SV343: $i] :
( ( ! [SY1606: $i] :
~ ( ~ ( ~ ( quadRes @ SV343 @ ( ti @ int @ SY1606 ) )
| ( quadRes @ SV343 @ SY1606 ) )
| ~ ( ~ ( quadRes @ SV343 @ SY1606 )
| ( quadRes @ SV343 @ ( ti @ int @ SY1606 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2011]) ).
thf(2462,plain,
! [SV344: $i] :
( ( ~ ( comm_semiring_1 @ SV344 )
| ! [SY1607: $i] :
( ( plus_plus @ SV344 @ SY1607 @ SY1607 )
= ( times_times @ SV344 @ ( plus_plus @ SV344 @ ( one_one @ SV344 ) @ ( one_one @ SV344 ) ) @ SY1607 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2012]) ).
thf(2463,plain,
! [SV345: $i] :
( ( ! [SY1608: $i] :
~ ( ~ ( ~ ( ord_less_eq @ int @ SV345 @ ( minus_minus @ int @ SY1608 @ ( one_one @ int ) ) )
| ( ord_less @ int @ SV345 @ SY1608 ) )
| ~ ( ~ ( ord_less @ int @ SV345 @ SY1608 )
| ( ord_less_eq @ int @ SV345 @ ( minus_minus @ int @ SY1608 @ ( one_one @ int ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2013]) ).
thf(2464,plain,
! [SV346: $i] :
( ( ~ ( number_semiring @ SV346 )
| ( ( number_number_of @ SV346 @ pls )
= ( zero_zero @ SV346 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2014]) ).
thf(2465,plain,
! [SV347: $i] :
( ( ~ ( ring_11004092258visors @ SV347 )
| ! [SY1609: $i] :
~ ( ~ ( ( ( power_power @ SV347 @ SY1609 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= ( zero_zero @ SV347 ) )
| ( ( ti @ SV347 @ SY1609 )
= ( zero_zero @ SV347 ) ) )
| ~ ( ( ( ti @ SV347 @ SY1609 )
!= ( zero_zero @ SV347 ) )
| ( ( power_power @ SV347 @ SY1609 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SV347 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2015]) ).
thf(2466,plain,
! [SV348: $i] :
( ( ~ ( linordered_semidom @ SV348 )
| ! [SY1610: $i,SY1611: $i] :
( ~ ( ord_less @ SV348 @ ( zero_zero @ SV348 ) @ SY1611 )
| ( ord_less @ SV348 @ ( zero_zero @ SV348 ) @ ( power_power @ SV348 @ SY1611 @ SY1610 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2016]) ).
thf(2467,plain,
! [SV349: $i] :
( ( ~ ( comm_semiring_1 @ SV349 )
| ! [SY1612: $i,SY1613: $i,SY1614: $i] :
( ~ ( dvd_dvd @ SV349 @ SY1613 @ SY1614 )
| ( dvd_dvd @ SV349 @ SY1613 @ ( times_times @ SV349 @ SY1614 @ SY1612 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2017]) ).
thf(2468,plain,
! [SV350: $i] :
( ( ! [SY1615: $i] :
~ ( ~ ( ~ ( ord_less_eq @ int @ ( plus_plus @ int @ SV350 @ ( one_one @ int ) ) @ SY1615 )
| ( ord_less @ int @ SV350 @ SY1615 ) )
| ~ ( ~ ( ord_less @ int @ SV350 @ SY1615 )
| ( ord_less_eq @ int @ ( plus_plus @ int @ SV350 @ ( one_one @ int ) ) @ SY1615 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2018]) ).
thf(2469,plain,
! [SV351: $i] :
( ( ~ ( no_zero_divisors @ SV351 )
| ! [SY1616: $i,SY1617: $i] :
( ( ( times_times @ SV351 @ SY1616 @ SY1617 )
!= ( zero_zero @ SV351 ) )
| ( ( ti @ SV351 @ SY1616 )
= ( zero_zero @ SV351 ) )
| ( ( ti @ SV351 @ SY1617 )
= ( zero_zero @ SV351 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2019]) ).
thf(2470,plain,
! [SV352: $i] :
( ( ~ ( linordered_idom @ SV352 )
| ! [SY1618: $i,SY1619: $i] :
~ ( ~ ( ( ( plus_plus @ SV352 @ ( power_power @ SV352 @ SY1618 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV352 @ SY1619 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV352 ) )
| ~ ( ( ( ti @ SV352 @ SY1618 )
!= ( zero_zero @ SV352 ) )
| ( ( ti @ SV352 @ SY1619 )
!= ( zero_zero @ SV352 ) ) ) )
| ~ ( ~ ~ ( ( ( ti @ SV352 @ SY1618 )
!= ( zero_zero @ SV352 ) )
| ( ( ti @ SV352 @ SY1619 )
!= ( zero_zero @ SV352 ) ) )
| ( ( plus_plus @ SV352 @ ( power_power @ SV352 @ SY1618 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV352 @ SY1619 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV352 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2020]) ).
thf(2471,plain,
! [SV353: $i] :
( ( ~ ( linordered_semidom @ SV353 )
| ! [SY1620: $i,SY1621: $i,SY1622: $i] :
( ~ ( ord_less_eq @ SV353 @ SY1621 @ SY1622 )
| ~ ( ord_less_eq @ SV353 @ ( zero_zero @ SV353 ) @ SY1621 )
| ( ord_less_eq @ SV353 @ ( power_power @ SV353 @ SY1621 @ SY1620 ) @ ( power_power @ SV353 @ SY1622 @ SY1620 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2021]) ).
thf(2472,plain,
! [SV354: $i] :
( ( ~ ( comm_semiring_1 @ SV354 )
| ! [SY1623: $i,SY1624: $i,SY1625: $i] :
( ( times_times @ SV354 @ SY1623 @ ( times_times @ SV354 @ SY1624 @ SY1625 ) )
= ( times_times @ SV354 @ SY1624 @ ( times_times @ SV354 @ SY1623 @ SY1625 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2022]) ).
thf(2473,plain,
! [SV355: $i] :
( ( ~ ~ ( ~ ( power @ SV355 )
| ~ ( semiring_0 @ SV355 ) )
| ! [SY1626: $i] :
~ ( ~ ( ( SY1626
!= ( zero_zero @ nat ) )
| ( ( power_power @ SV355 @ ( zero_zero @ SV355 ) @ SY1626 )
= ( one_one @ SV355 ) ) )
| ~ ( ~ ( ( SY1626
!= ( zero_zero @ nat ) ) )
| ( ( power_power @ SV355 @ ( zero_zero @ SV355 ) @ SY1626 )
= ( zero_zero @ SV355 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2023]) ).
thf(2474,plain,
! [SV356: $i] :
( ( ! [SY1627: $i,SY1628: $i] :
( ~ ( power @ SY1628 )
| ( ( power_power @ SY1628 @ ( ti @ SY1628 @ SV356 ) @ SY1627 )
= ( power_power @ SY1628 @ SV356 @ SY1627 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2024]) ).
thf(2475,plain,
! [SV357: $i] :
( ( ! [SY1629: $i,SY1630: $i] :
( ~ ( no_zero_divisors @ SY1630 )
| ( ( times_times @ SY1630 @ SV357 @ ( ti @ SY1630 @ SY1629 ) )
= ( times_times @ SY1630 @ SV357 @ SY1629 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2025]) ).
thf(2476,plain,
! [SV358: $i] :
( ( ~ ( linordered_semidom @ SV358 )
| ! [SY1631: $i,SY1632: $i,SY1633: $i] :
( ~ ( ord_less @ SV358 @ ( one_one @ SV358 ) @ SY1633 )
| ~ ( ~ ( ~ ( ord_less_eq @ SV358 @ ( power_power @ SV358 @ SY1633 @ SY1631 ) @ ( power_power @ SV358 @ SY1633 @ SY1632 ) )
| ( ord_less_eq @ nat @ SY1631 @ SY1632 ) )
| ~ ( ~ ( ord_less_eq @ nat @ SY1631 @ SY1632 )
| ( ord_less_eq @ SV358 @ ( power_power @ SV358 @ SY1633 @ SY1631 ) @ ( power_power @ SV358 @ SY1633 @ SY1632 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2026]) ).
thf(2477,plain,
! [SV359: $i] :
( ( ! [SY1634: $i,SY1635: $i] :
( ~ ( power @ SY1635 )
| ( ( ti @ SY1635 @ ( power_power @ SY1635 @ SV359 @ SY1634 ) )
= ( power_power @ SY1635 @ SV359 @ SY1634 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2027]) ).
thf(2478,plain,
! [SV360: $i] :
( ( ! [SY1636: $i] :
~ ( ~ ( ~ ( zcong @ SV360 @ ( zero_zero @ int ) @ SY1636 )
| ( dvd_dvd @ int @ SY1636 @ SV360 ) )
| ~ ( ~ ( dvd_dvd @ int @ SY1636 @ SV360 )
| ( zcong @ SV360 @ ( zero_zero @ int ) @ SY1636 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2028]) ).
thf(2479,plain,
! [SV361: $i] :
( ( ~ ( number_semiring @ SV361 )
| ! [SY1637: $i,SY1638: $i] :
( ~ ( ord_less_eq @ int @ pls @ SY1638 )
| ~ ( ord_less_eq @ int @ pls @ SY1637 )
| ( ( times_times @ SV361 @ ( number_number_of @ SV361 @ SY1638 ) @ ( number_number_of @ SV361 @ SY1637 ) )
= ( number_number_of @ SV361 @ ( times_times @ int @ SY1638 @ SY1637 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2029]) ).
thf(2480,plain,
! [SV362: $i] :
( ( ! [SY1639: $i,SY1640: $i] :
( ~ ( ( SY1640
!= ( zero_zero @ real ) ) )
| ~ ( ~ ( ( ( times_times @ real @ SV362 @ SY1640 )
!= ( times_times @ real @ SY1639 @ SY1640 ) )
| ( SV362 = SY1639 ) )
| ~ ( ( SV362 != SY1639 )
| ( ( times_times @ real @ SV362 @ SY1640 )
= ( times_times @ real @ SY1639 @ SY1640 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2030]) ).
thf(2481,plain,
( ( ( ~ ~ ( quadRes @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) @ ( number_number_of @ int @ min ) ) )
= $true )
| ( ( ( legendre @ ( number_number_of @ int @ min ) @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) )
!= ( one_one @ int ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2031]) ).
thf(2482,plain,
! [SV363: $i] :
( ( ~ ( power @ SV363 )
| ! [SY1641: $i,SY1642: $i] :
~ ( ~ ( ( SY1642
!= ( zero_zero @ nat ) )
| ( ( power_power @ SV363 @ SY1641 @ SY1642 )
= ( one_one @ SV363 ) ) )
| ~ ( ~ ( ( SY1642
!= ( zero_zero @ nat ) ) )
| ( ( power_power @ SV363 @ SY1641 @ SY1642 )
= ( times_times @ SV363 @ SY1641 @ ( power_power @ SV363 @ SY1641 @ ( minus_minus @ nat @ SY1642 @ ( one_one @ nat ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2032]) ).
thf(2483,plain,
! [SV364: $i] :
( ( ! [SY1643: $i,SY1644: $i] :
( ~ ( dvd_dvd @ nat @ SY1643 @ SY1644 )
| ( dvd_dvd @ nat @ ( power_power @ nat @ SY1643 @ SV364 ) @ ( power_power @ nat @ SY1644 @ SV364 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2033]) ).
thf(2484,plain,
! [SV365: $i] :
( ( ! [SY1645: $i,SY1646: $i] :
( ~ ( ord_less @ int @ SY1645 @ SY1646 )
| ( ord_less @ int @ ( plus_plus @ int @ SY1645 @ SV365 ) @ ( plus_plus @ int @ SY1646 @ SV365 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2034]) ).
thf(2485,plain,
! [SV366: $i] :
( ( ! [SY1647: $i] :
~ ( ~ ( ~ ( ord_less @ int @ SY1647 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SY1647 ) @ ( number_number_of @ nat @ SV366 ) )
= ( number_number_of @ nat @ SV366 ) ) )
| ~ ( ~ ~ ( ord_less @ int @ SY1647 @ pls )
| ~ ( ~ ( ~ ( ord_less @ int @ SV366 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SY1647 ) @ ( number_number_of @ nat @ SV366 ) )
= ( number_number_of @ nat @ SY1647 ) ) )
| ~ ( ~ ~ ( ord_less @ int @ SV366 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SY1647 ) @ ( number_number_of @ nat @ SV366 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SY1647 @ SV366 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2035]) ).
thf(2486,plain,
( ( ( zero_zero @ real )
= ( one_one @ real ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2036]) ).
thf(2487,plain,
! [SV367: $i] :
( ( ~ ( comm_semiring_1 @ SV367 )
| ! [SY1648: $i,SY1649: $i,SY1650: $i] :
( ~ ( ord_less_eq @ nat @ SY1649 @ SY1650 )
| ( dvd_dvd @ SV367 @ ( power_power @ SV367 @ SY1648 @ SY1649 ) @ ( power_power @ SV367 @ SY1648 @ SY1650 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2037]) ).
thf(2488,plain,
! [SV368: $i] :
( ( ! [SY1651: $i] :
~ ( ~ ( ( SY1651
!= ( zero_zero @ nat ) )
| ( ( times_times @ nat @ SY1651 @ SV368 )
= ( zero_zero @ nat ) ) )
| ~ ( ~ ( ( SY1651
!= ( zero_zero @ nat ) ) )
| ( ( times_times @ nat @ SY1651 @ SV368 )
= ( plus_plus @ nat @ SV368 @ ( times_times @ nat @ ( minus_minus @ nat @ SY1651 @ ( one_one @ nat ) ) @ SV368 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2038]) ).
thf(2489,plain,
! [SV369: $i] :
( ( ! [SY1652: $i,SY1653: $i] :
( ~ ( dvd_dvd @ int @ SV369 @ ( minus_minus @ int @ SY1652 @ SY1653 ) )
| ~ ( dvd_dvd @ int @ SV369 @ SY1653 )
| ( dvd_dvd @ int @ SV369 @ SY1652 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2039]) ).
thf(2490,plain,
! [SV370: $i] :
( ( ! [SY1654: $i] :
~ ( ~ ( ( ( bit1 @ SV370 )
!= ( bit1 @ SY1654 ) )
| ( ( ti @ int @ SV370 )
= ( ti @ int @ SY1654 ) ) )
| ~ ( ( ( ti @ int @ SV370 )
!= ( ti @ int @ SY1654 ) )
| ( ( bit1 @ SV370 )
= ( bit1 @ SY1654 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2040]) ).
thf(2491,plain,
! [SV371: $i] :
( ( ~ ( comm_semiring_1 @ SV371 )
| ! [SY1655: $i,SY1656: $i,SY1657: $i] :
( ( power_power @ SV371 @ ( times_times @ SV371 @ SY1655 @ SY1656 ) @ SY1657 )
= ( times_times @ SV371 @ ( power_power @ SV371 @ SY1655 @ SY1657 ) @ ( power_power @ SV371 @ SY1656 @ SY1657 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2041]) ).
thf(2492,plain,
! [SV372: $i] :
( ( ! [SY1658: $i,SY1659: $i,SY1660: $i] :
( ~ ( zcong @ SY1658 @ SY1659 @ SY1660 )
| ( zcong @ ( times_times @ int @ SY1658 @ SV372 ) @ ( times_times @ int @ SY1659 @ SV372 ) @ SY1660 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2042]) ).
thf(2493,plain,
! [SV373: $i] :
( ( ! [SY1661: $i] :
~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit0 @ SV373 ) @ ( bit0 @ SY1661 ) )
| ( ord_less_eq @ int @ SV373 @ SY1661 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV373 @ SY1661 )
| ( ord_less_eq @ int @ ( bit0 @ SV373 ) @ ( bit0 @ SY1661 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2043]) ).
thf(2494,plain,
! [SV374: $i] :
( ( ! [SY1662: $i] :
~ ( ~ ( ( ( times_times @ nat @ SV374 @ SY1662 )
!= ( one_one @ nat ) )
| ~ ( ( SV374
!= ( one_one @ nat ) )
| ( SY1662
!= ( one_one @ nat ) ) ) )
| ~ ( ~ ~ ( ( SV374
!= ( one_one @ nat ) )
| ( SY1662
!= ( one_one @ nat ) ) )
| ( ( times_times @ nat @ SV374 @ SY1662 )
= ( one_one @ nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2044]) ).
thf(2495,plain,
! [SV375: $i] :
( ( ~ ( linordered_semidom @ SV375 )
| ! [SY1663: $i,SY1664: $i] :
( ~ ( ord_less @ SV375 @ ( one_one @ SV375 ) @ SY1664 )
| ( ord_less @ SV375 @ ( power_power @ SV375 @ SY1664 @ SY1663 ) @ ( times_times @ SV375 @ SY1664 @ ( power_power @ SV375 @ SY1664 @ SY1663 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2045]) ).
thf(2496,plain,
! [SV376: $i] :
( ( ~ ( ring_11004092258visors @ SV376 )
| ! [SY1665: $i,SY1666: $i] :
( ~ ( ( ( ti @ SV376 @ SY1666 )
!= ( zero_zero @ SV376 ) ) )
| ( ( power_power @ SV376 @ SY1666 @ SY1665 )
!= ( zero_zero @ SV376 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2046]) ).
thf(2497,plain,
! [SV377: $i] :
( ( ! [SY1667: $i,SY1668: $i] :
( ~ ( mult_zero @ SY1668 )
| ( ( times_times @ SY1668 @ SV377 @ ( ti @ SY1668 @ SY1667 ) )
= ( times_times @ SY1668 @ SV377 @ SY1667 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2047]) ).
thf(2498,plain,
! [SV378: $i] :
( ( ~ ( number_ring @ SV378 )
| ! [SY1669: $i] :
( ( number_number_of @ SV378 @ ( bit1 @ SY1669 ) )
= ( plus_plus @ SV378 @ ( plus_plus @ SV378 @ ( one_one @ SV378 ) @ ( number_number_of @ SV378 @ SY1669 ) ) @ ( number_number_of @ SV378 @ SY1669 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2048]) ).
thf(2499,plain,
! [SV379: $i] :
( ( ! [SY1670: $i] :
( ~ ( ord_less @ real @ ( zero_zero @ real ) @ SY1670 )
| ~ ( ord_less @ real @ ( zero_zero @ real ) @ SV379 )
| ( ord_less @ real @ ( zero_zero @ real ) @ ( times_times @ real @ SY1670 @ SV379 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2049]) ).
thf(2500,plain,
! [SV380: $i] :
( ( ~ ( comm_semiring_1 @ SV380 )
| ! [SY1671: $i,SY1672: $i,SY1673: $i,SY1674: $i] :
( ( times_times @ SV380 @ ( times_times @ SV380 @ SY1671 @ SY1672 ) @ ( times_times @ SV380 @ SY1673 @ SY1674 ) )
= ( times_times @ SV380 @ SY1673 @ ( times_times @ SV380 @ ( times_times @ SV380 @ SY1671 @ SY1672 ) @ SY1674 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2050]) ).
thf(2501,plain,
! [SV381: $i] :
( ( ~ ( number_ring @ SV381 )
| ! [SY1675: $i] :
( ( times_times @ SV381 @ SY1675 @ ( number_number_of @ SV381 @ ( bit1 @ pls ) ) )
= ( ti @ SV381 @ SY1675 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2051]) ).
thf(2502,plain,
! [SV382: $i] :
( ( ! [SY1676: $i,SY1677: $i] :
( ~ ( zprime @ SY1677 )
| ~ ( dvd_dvd @ int @ SY1677 @ ( times_times @ int @ SV382 @ SY1676 ) )
| ( dvd_dvd @ int @ SY1677 @ SV382 )
| ( dvd_dvd @ int @ SY1677 @ SY1676 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2052]) ).
thf(2503,plain,
! [SV383: $i] :
( ( ~ ( linordered_semidom @ SV383 )
| ! [SY1678: $i,SY1679: $i,SY1680: $i] :
( ~ ( ord_less @ nat @ SY1679 @ SY1680 )
| ~ ( ord_less @ SV383 @ ( one_one @ SV383 ) @ SY1678 )
| ( ord_less @ SV383 @ ( power_power @ SV383 @ SY1678 @ SY1679 ) @ ( power_power @ SV383 @ SY1678 @ SY1680 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2053]) ).
thf(2504,plain,
! [SV384: $i] :
( ( ! [SY1681: $i,SY1682: $i] :
( ~ ( ord_less @ int @ SY1681 @ SY1682 )
| ~ ( ord_less @ int @ SV384 @ SY1682 )
| ( ord_less_eq @ int @ SY1681 @ SV384 )
| ( ord_less_eq @ int @ SV384 @ SY1681 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2054]) ).
thf(2505,plain,
! [SV385: $i] :
( ( ! [SY1683: $i,SY1684: $i,SY1685: $i] :
( ~ ( ord_less @ int @ SY1684 @ SY1685 )
| ~ ( ord_less_eq @ int @ SV385 @ SY1683 )
| ( ord_less @ int @ ( plus_plus @ int @ SY1684 @ SV385 ) @ ( plus_plus @ int @ SY1685 @ SY1683 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2055]) ).
thf(2506,plain,
! [SV386: $i] :
( ( ~ ~ ( ~ ( number @ SV386 )
| ~ ( ring @ SV386 ) )
| ! [SY1686: $i,SY1687: $i,SY1688: $i] :
( ( times_times @ SV386 @ ( minus_minus @ SV386 @ SY1686 @ SY1687 ) @ ( number_number_of @ SV386 @ SY1688 ) )
= ( minus_minus @ SV386 @ ( times_times @ SV386 @ SY1686 @ ( number_number_of @ SV386 @ SY1688 ) ) @ ( times_times @ SV386 @ SY1687 @ ( number_number_of @ SV386 @ SY1688 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2056]) ).
thf(2507,plain,
! [SV387: $i] :
( ( ! [SY1689: $i] :
( ~ ( ord_less @ int @ ( zero_zero @ int ) @ SY1689 )
| ~ ( ord_less @ int @ ( zero_zero @ int ) @ ( times_times @ int @ SY1689 @ SV387 ) )
| ( ord_less @ int @ ( zero_zero @ int ) @ SV387 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2057]) ).
thf(2508,plain,
! [SV388: $i] :
( ( ! [SY1690: $i] :
( ~ ( ord_less @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ SY1690 )
| ~ ( zcong @ SV388 @ ( number_number_of @ int @ min ) @ SY1690 )
| ~ ( zcong @ SV388 @ ( one_one @ int ) @ SY1690 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2058]) ).
thf(2509,plain,
! [SV389: $i] :
( ( ! [SY1691: $i] :
( ~ ( ord_less @ int @ ( zero_zero @ int ) @ SY1691 )
| ~ ( ord_less @ int @ SY1691 @ SV389 )
| ~ ( zcong @ SY1691 @ ( zero_zero @ int ) @ SV389 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2059]) ).
thf(2510,plain,
! [SV390: $i] :
( ( ! [SY1692: $i] :
~ ( ~ ( ( SY1692
!= ( zero_zero @ nat ) )
| ( ( power_power @ nat @ SV390 @ SY1692 )
= ( one_one @ nat ) ) )
| ~ ( ~ ( ( SY1692
!= ( zero_zero @ nat ) ) )
| ( ( power_power @ nat @ SV390 @ SY1692 )
= ( times_times @ nat @ SV390 @ ( power_power @ nat @ SV390 @ ( minus_minus @ nat @ SY1692 @ ( one_one @ nat ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2060]) ).
thf(2511,plain,
! [SV391: $i] :
( ( ! [SY1693: $i,SY1694: $i] :
( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ SY1694 )
| ~ ( dvd_dvd @ int @ SV391 @ SY1693 )
| ( dvd_dvd @ int @ SV391 @ ( power_power @ int @ SY1693 @ SY1694 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2061]) ).
thf(2512,plain,
! [SV392: $i] :
( ( ! [SY1695: $i] :
~ ( ~ ( ~ ( ord_less @ nat @ ( number_number_of @ nat @ SV392 ) @ ( number_number_of @ nat @ SY1695 ) )
| ~ ( ~ ( ~ ( ord_less @ int @ SV392 @ SY1695 )
| ( ord_less @ int @ pls @ SY1695 ) )
| ~ ( ord_less @ int @ SV392 @ SY1695 ) ) )
| ~ ( ~ ~ ( ~ ( ~ ( ord_less @ int @ SV392 @ SY1695 )
| ( ord_less @ int @ pls @ SY1695 ) )
| ~ ( ord_less @ int @ SV392 @ SY1695 ) )
| ( ord_less @ nat @ ( number_number_of @ nat @ SV392 ) @ ( number_number_of @ nat @ SY1695 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2062]) ).
thf(2513,plain,
! [SV393: $i] :
( ( ~ ( number_ring @ SV393 )
| ! [SY1696: $i,SY1697: $i] :
( ( power_power @ SV393 @ ( minus_minus @ SV393 @ SY1696 @ SY1697 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( minus_minus @ SV393 @ ( plus_plus @ SV393 @ ( power_power @ SV393 @ SY1696 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV393 @ SY1697 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times @ SV393 @ ( times_times @ SV393 @ ( number_number_of @ SV393 @ ( bit0 @ ( bit1 @ pls ) ) ) @ SY1696 ) @ SY1697 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2063]) ).
thf(2514,plain,
! [SV394: $i] :
( ( ~ ( ~ ( ~ ( zprime @ ( ti @ int @ SV394 ) )
| ( zprime @ SV394 ) )
| ~ ( ~ ( zprime @ SV394 )
| ( zprime @ ( ti @ int @ SV394 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2064]) ).
thf(2515,plain,
! [SV395: $i] :
( ( ! [SY1698: $i,SY1699: $i,SY1700: $i] :
( ~ ( zcong @ ( power_power @ int @ SY1698 @ SY1699 ) @ ( one_one @ int ) @ SY1700 )
| ( zcong @ ( power_power @ int @ SY1698 @ ( times_times @ nat @ SY1699 @ SV395 ) ) @ ( one_one @ int ) @ SY1700 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2065]) ).
thf(2516,plain,
! [SV396: $i] :
( ( ! [SY1701: $i] :
~ ( ~ ( ~ ( zcong @ SV396 @ SY1701 @ ( zero_zero @ int ) )
| ( ( ti @ int @ SV396 )
= ( ti @ int @ SY1701 ) ) )
| ~ ( ( ( ti @ int @ SV396 )
!= ( ti @ int @ SY1701 ) )
| ( zcong @ SV396 @ SY1701 @ ( zero_zero @ int ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2066]) ).
thf(2517,plain,
! [SV397: $i] :
( ( ! [SY1702: $i] :
~ ( ~ ( ( ( plus_plus @ real @ ( times_times @ real @ SV397 @ SV397 ) @ ( times_times @ real @ SY1702 @ SY1702 ) )
!= ( zero_zero @ real ) )
| ~ ( ( SV397
!= ( zero_zero @ real ) )
| ( SY1702
!= ( zero_zero @ real ) ) ) )
| ~ ( ~ ~ ( ( SV397
!= ( zero_zero @ real ) )
| ( SY1702
!= ( zero_zero @ real ) ) )
| ( ( plus_plus @ real @ ( times_times @ real @ SV397 @ SV397 ) @ ( times_times @ real @ SY1702 @ SY1702 ) )
= ( zero_zero @ real ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2067]) ).
thf(2518,plain,
! [SV398: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SV398 ) @ pls )
| ( ord_less @ int @ SV398 @ pls ) )
| ~ ( ~ ( ord_less @ int @ SV398 @ pls )
| ( ord_less @ int @ ( bit1 @ SV398 ) @ pls ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2068]) ).
thf(2519,plain,
! [SV399: $i] :
( ( ~ ( semiring @ SV399 )
| ! [SY1703: $i,SY1704: $i,SY1705: $i,SY1706: $i] :
( ( plus_plus @ SV399 @ ( times_times @ SV399 @ SY1703 @ SY1704 ) @ ( plus_plus @ SV399 @ ( times_times @ SV399 @ SY1705 @ SY1704 ) @ SY1706 ) )
= ( plus_plus @ SV399 @ ( times_times @ SV399 @ ( plus_plus @ SV399 @ SY1703 @ SY1705 ) @ SY1704 ) @ SY1706 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2069]) ).
thf(2520,plain,
! [SV400: $i] :
( ( ~ ( monoid_mult @ SV400 )
| ! [SY1707: $i] :
( ( power_power @ SV400 @ SY1707 @ ( one_one @ nat ) )
= ( ti @ SV400 @ SY1707 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2070]) ).
thf(2521,plain,
( ( ( t
!= ( one_one @ int ) )
= $true )
| ( ( ~ ! [SX0: $i] :
~ ~ ! [SX1: $i] :
( ( plus_plus @ int @ ( power_power @ int @ SX0 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ SX1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2071]) ).
thf(2522,plain,
! [SV401: $i] :
( ( ! [SY1708: $i,SY1709: $i] :
( ~ ( semiring @ SY1709 )
| ( ( times_times @ SY1709 @ ( ti @ SY1709 @ SV401 ) @ SY1708 )
= ( times_times @ SY1709 @ SV401 @ SY1708 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2072]) ).
thf(2523,plain,
! [SV402: $i] :
( ( ~ ( comm_semiring_1 @ SV402 )
| ! [SY1710: $i] :
( ( times_times @ SV402 @ ( one_one @ SV402 ) @ SY1710 )
= ( ti @ SV402 @ SY1710 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2073]) ).
thf(2524,plain,
! [SV403: $i] :
( ( ~ ( comm_semiring_1 @ SV403 )
| ! [SY1711: $i,SY1712: $i,SY1713: $i] :
( ( times_times @ SV403 @ SY1711 @ ( plus_plus @ SV403 @ SY1712 @ SY1713 ) )
= ( plus_plus @ SV403 @ ( times_times @ SV403 @ SY1711 @ SY1712 ) @ ( times_times @ SV403 @ SY1711 @ SY1713 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2074]) ).
thf(2525,plain,
! [SV404: $i] :
( ( ~ ( number_ring @ SV404 )
| ! [SY1714: $i] :
( ( times_times @ SV404 @ ( number_number_of @ SV404 @ ( bit0 @ ( bit1 @ pls ) ) ) @ SY1714 )
= ( plus_plus @ SV404 @ SY1714 @ SY1714 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2075]) ).
thf(2526,plain,
! [SV405: $i] :
( ( ! [SY1715: $i,SY1716: $i] :
~ ( ~ ( ~ ( zcong @ SV405 @ SY1715 @ SY1716 )
| ~ ! [SY1717: $i] :
( ( ti @ int @ SY1715 )
!= ( plus_plus @ int @ SV405 @ ( times_times @ int @ SY1716 @ SY1717 ) ) ) )
| ~ ( ~ ~ ! [SY1718: $i] :
( ( ti @ int @ SY1715 )
!= ( plus_plus @ int @ SV405 @ ( times_times @ int @ SY1716 @ SY1718 ) ) )
| ( zcong @ SV405 @ SY1715 @ SY1716 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2076]) ).
thf(2527,plain,
! [SV406: $i] :
( ( ! [SY1719: $i,SY1720: $i] :
( ( ( minus_minus @ int @ SV406 @ SY1719 )
!= ( ti @ int @ SY1720 ) )
| ( ( ti @ int @ SV406 )
= ( plus_plus @ int @ SY1720 @ SY1719 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2077]) ).
thf(2528,plain,
! [SV407: $i] :
( ( ~ ( zprime @ SV407 )
| ~ ( ( ( ti @ int @ SV407 )
!= ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ~ ( ( ( ti @ int @ SV407 )
!= ( number_number_of @ int @ ( bit1 @ ( bit1 @ pls ) ) ) ) )
| ( ord_less_eq @ int @ ( number_number_of @ int @ ( bit1 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SV407 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2078]) ).
thf(2529,plain,
! [SV408: $i] :
( ( ! [SY1721: $i,SY1722: $i] :
( ~ ( semiring @ SY1722 )
| ( ( ti @ SY1722 @ ( plus_plus @ SY1722 @ SV408 @ SY1721 ) )
= ( plus_plus @ SY1722 @ SV408 @ SY1721 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2079]) ).
thf(2530,plain,
! [SV409: $i] :
( ( ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV409 )
| ( ord_less @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( one_one @ int ) @ SV409 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2080]) ).
thf(2531,plain,
! [SV410: $i] :
( ( ! [SY1723: $i,SY1724: $i] :
( ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( times_times @ int @ SV410 @ SY1723 ) @ SY1724 ) )
| ~ ( ord_less @ int @ SY1724 @ SV410 )
| ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV410 )
| ( ord_less_eq @ int @ ( zero_zero @ int ) @ SY1723 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2081]) ).
thf(2532,plain,
! [SV411: $i] :
( ( ~ ( linordered_idom @ SV411 )
| ! [SY1725: $i] :
~ ( ord_less @ SV411 @ ( power_power @ SV411 @ SY1725 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( zero_zero @ SV411 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2082]) ).
thf(2533,plain,
! [SV412: $i] :
( ( ~ ( monoid_mult @ SV412 )
| ! [SY1726: $i,SY1727: $i,SY1728: $i] :
( ( power_power @ SV412 @ SY1726 @ ( times_times @ nat @ SY1727 @ SY1728 ) )
= ( power_power @ SV412 @ ( power_power @ SV412 @ SY1726 @ SY1727 ) @ SY1728 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2083]) ).
thf(2534,plain,
! [SV413: $i] :
( ( ! [SY1729: $i] :
~ ( ~ ( ( ( times_times @ int @ SV413 @ SY1729 )
!= ( one_one @ int ) )
| ~ ( ( ( ti @ int @ SV413 )
!= ( one_one @ int ) )
| ( ( ti @ int @ SY1729 )
!= ( one_one @ int ) ) )
| ~ ( ( ( ti @ int @ SV413 )
!= ( number_number_of @ int @ min ) )
| ( ( ti @ int @ SY1729 )
!= ( number_number_of @ int @ min ) ) ) )
| ~ ( ~ ( ~ ( ( ( ti @ int @ SV413 )
!= ( one_one @ int ) )
| ( ( ti @ int @ SY1729 )
!= ( one_one @ int ) ) )
| ~ ( ( ( ti @ int @ SV413 )
!= ( number_number_of @ int @ min ) )
| ( ( ti @ int @ SY1729 )
!= ( number_number_of @ int @ min ) ) ) )
| ( ( times_times @ int @ SV413 @ SY1729 )
= ( one_one @ int ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2084]) ).
thf(2535,plain,
! [SV414: $i] :
( ( ~ ( comm_semiring_1 @ SV414 )
| ! [SY1730: $i,SY1731: $i] :
( ( plus_plus @ SV414 @ SY1730 @ SY1731 )
= ( plus_plus @ SV414 @ SY1731 @ SY1730 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2085]) ).
thf(2536,plain,
! [SV415: $i] :
( ( ~ ( number_ring @ SV415 )
| ( ( zero_zero @ SV415 )
= ( number_number_of @ SV415 @ pls ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2086]) ).
thf(2537,plain,
! [SV416: $i] :
( ( ~ ~ ( ~ ( monoid_mult @ SV416 )
| ~ ( number @ SV416 ) )
| ! [SY1732: $i] :
( ( power_power @ SV416 @ ( number_number_of @ SV416 @ SY1732 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times @ SV416 @ ( number_number_of @ SV416 @ SY1732 ) @ ( number_number_of @ SV416 @ SY1732 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2087]) ).
thf(2538,plain,
! [SV417: $i] :
( ( ~ ( ordere453448008miring @ SV417 )
| ! [SY1733: $i,SY1734: $i] :
( ~ ( ord_less_eq @ SV417 @ SY1734 @ ( zero_zero @ SV417 ) )
| ~ ( ord_less_eq @ SV417 @ ( zero_zero @ SV417 ) @ SY1733 )
| ( ord_less_eq @ SV417 @ ( times_times @ SV417 @ SY1734 @ SY1733 ) @ ( zero_zero @ SV417 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2088]) ).
thf(2539,plain,
! [SV418: $i] :
( ( ! [SY1735: $i] :
~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SV418 ) @ ( bit0 @ SY1735 ) )
| ( ord_less @ int @ SV418 @ SY1735 ) )
| ~ ( ~ ( ord_less @ int @ SV418 @ SY1735 )
| ( ord_less_eq @ int @ ( bit1 @ SV418 ) @ ( bit0 @ SY1735 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2089]) ).
thf(2540,plain,
! [SV419: $i] :
( ( ! [SY1736: $i] :
( ~ ( ord_less @ int @ ( zero_zero @ int ) @ SY1736 )
| ~ ( ~ ( ( ( times_times @ int @ SY1736 @ SV419 )
!= ( one_one @ int ) )
| ~ ( ( ( ti @ int @ SY1736 )
!= ( one_one @ int ) )
| ( ( ti @ int @ SV419 )
!= ( one_one @ int ) ) ) )
| ~ ( ~ ~ ( ( ( ti @ int @ SY1736 )
!= ( one_one @ int ) )
| ( ( ti @ int @ SV419 )
!= ( one_one @ int ) ) )
| ( ( times_times @ int @ SY1736 @ SV419 )
= ( one_one @ int ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2090]) ).
thf(2541,plain,
! [SV420: $i] :
( ( ! [SY1737: $i] :
~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit0 @ SV420 ) @ ( bit1 @ SY1737 ) )
| ( ord_less_eq @ int @ SV420 @ SY1737 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV420 @ SY1737 )
| ( ord_less_eq @ int @ ( bit0 @ SV420 ) @ ( bit1 @ SY1737 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2091]) ).
thf(2542,plain,
! [SV421: $i] :
( ( ! [SY1738: $i] :
~ ( ~ ( ~ ( ord_less @ int @ SY1738 @ pls )
| ( ( times_times @ nat @ ( number_number_of @ nat @ SY1738 ) @ ( number_number_of @ nat @ SV421 ) )
= ( zero_zero @ nat ) ) )
| ~ ( ~ ~ ( ord_less @ int @ SY1738 @ pls )
| ( ( times_times @ nat @ ( number_number_of @ nat @ SY1738 ) @ ( number_number_of @ nat @ SV421 ) )
= ( number_number_of @ nat @ ( times_times @ int @ SY1738 @ SV421 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2092]) ).
thf(2543,plain,
! [SV422: $i] :
( ( ! [SY1739: $i,SY1740: $i,SY1741: $i,SY1742: $i,SY1743: $i] :
( ( ( plus_plus @ int @ ( times_times @ int @ SV422 @ SY1739 ) @ SY1740 )
!= ( plus_plus @ int @ ( times_times @ int @ SY1741 @ SY1742 ) @ SY1743 ) )
| ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( times_times @ int @ SY1741 @ SY1742 ) @ SY1743 ) )
| ~ ( ord_less @ int @ SY1743 @ SY1741 )
| ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SY1740 )
| ~ ( ord_less @ int @ ( zero_zero @ int ) @ SY1741 )
| ~ ( ord_less_eq @ int @ SY1741 @ SV422 )
| ( ord_less_eq @ int @ SY1739 @ SY1742 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2093]) ).
thf(2544,plain,
! [SV423: $i] :
( ( ~ ( ~ ( ~ ~ ( ord_less @ real @ ( zero_zero @ real ) @ ( times_times @ real @ SV423 @ SV423 ) )
| ( SV423
= ( zero_zero @ real ) ) )
| ~ ( ( SV423
!= ( zero_zero @ real ) )
| ~ ( ord_less @ real @ ( zero_zero @ real ) @ ( times_times @ real @ SV423 @ SV423 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2094]) ).
thf(2545,plain,
! [SV424: $i] :
( ( ! [SY1744: $i] :
~ ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SV424 ) @ ( bit1 @ SY1744 ) )
| ( ord_less @ int @ SV424 @ SY1744 ) )
| ~ ( ~ ( ord_less @ int @ SV424 @ SY1744 )
| ( ord_less @ int @ ( bit1 @ SV424 ) @ ( bit1 @ SY1744 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2095]) ).
thf(2546,plain,
! [SV425: $i] :
( ( ~ ( comm_semiring_1 @ SV425 )
| ! [SY1745: $i] : ( dvd_dvd @ SV425 @ ( one_one @ SV425 ) @ SY1745 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2096]) ).
thf(2547,plain,
! [SV426: $i] :
( ( ! [SY1746: $i,SY1747: $i] :
( ~ ( mult_zero @ SY1747 )
| ( ( ti @ SY1747 @ ( times_times @ SY1747 @ SV426 @ SY1746 ) )
= ( times_times @ SY1747 @ SV426 @ SY1746 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2097]) ).
thf(2548,plain,
! [SV427: $i] :
( ( ! [SY1748: $i,SY1749: $i] :
~ ( ~ ( ~ ( zcong @ ( ti @ int @ SV427 ) @ SY1748 @ SY1749 )
| ( zcong @ SV427 @ SY1748 @ SY1749 ) )
| ~ ( ~ ( zcong @ SV427 @ SY1748 @ SY1749 )
| ( zcong @ ( ti @ int @ SV427 ) @ SY1748 @ SY1749 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2098]) ).
thf(2549,plain,
! [SV428: $i] :
( ( ! [SY1750: $i] :
~ ( ~ ( ~ ( zcong @ SV428 @ ( zero_zero @ int ) @ SY1750 )
| ( dvd_dvd @ int @ SY1750 @ SV428 ) )
| ~ ( ~ ( dvd_dvd @ int @ SY1750 @ SV428 )
| ( zcong @ SV428 @ ( zero_zero @ int ) @ SY1750 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2099]) ).
thf(2550,plain,
! [SV429: $i] :
( ( ! [SY1751: $i] :
~ ( ~ ( ( ( power_power @ nat @ SV429 @ SY1751 )
!= ( one_one @ nat ) )
| ( SV429
= ( one_one @ nat ) )
| ( SY1751
= ( zero_zero @ nat ) ) )
| ~ ( ~ ( ( SV429
= ( one_one @ nat ) )
| ( SY1751
= ( zero_zero @ nat ) ) )
| ( ( power_power @ nat @ SV429 @ SY1751 )
= ( one_one @ nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2100]) ).
thf(2551,plain,
! [SV430: $i] :
( ( ! [SY1752: $i,SY1753: $i,SY1754: $i] :
( ~ ( zcong @ SY1752 @ SY1753 @ SY1754 )
| ( zcong @ ( plus_plus @ int @ SY1752 @ SV430 ) @ ( plus_plus @ int @ SY1753 @ SV430 ) @ SY1754 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2101]) ).
thf(2552,plain,
! [SV431: $i] :
( ( ~ ( linordered_idom @ SV431 )
| ! [SY1755: $i,SY1756: $i] : ( ord_less_eq @ SV431 @ ( zero_zero @ SV431 ) @ ( plus_plus @ SV431 @ ( power_power @ SV431 @ SY1755 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV431 @ SY1756 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2102]) ).
thf(2553,plain,
! [SV432: $i] :
( ( ~ ( number_ring @ SV432 )
| ! [SY1757: $i] :
( ( plus_plus @ SV432 @ ( number_number_of @ SV432 @ SY1757 ) @ ( one_one @ SV432 ) )
= ( number_number_of @ SV432 @ ( plus_plus @ int @ SY1757 @ ( bit1 @ pls ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2103]) ).
thf(2554,plain,
! [SV433: $i] :
( ( ~ ( linordered_semidom @ SV433 )
| ! [SY1758: $i,SY1759: $i,SY1760: $i] :
( ~ ( ord_less @ nat @ SY1759 @ SY1760 )
| ~ ( ord_less @ SV433 @ ( zero_zero @ SV433 ) @ SY1758 )
| ~ ( ord_less @ SV433 @ SY1758 @ ( one_one @ SV433 ) )
| ( ord_less @ SV433 @ ( power_power @ SV433 @ SY1758 @ SY1760 ) @ ( power_power @ SV433 @ SY1758 @ SY1759 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2104]) ).
thf(2555,plain,
! [SV434: $i] :
( ( ~ ( semiri456707255roduct @ SV434 )
| ! [SY1761: $i,SY1762: $i,SY1763: $i,SY1764: $i,SY1765: $i] :
( ~ ( ( ( ti @ SV434 @ SY1765 )
!= ( zero_zero @ SV434 ) ) )
| ~ ~ ( ( ( ti @ SV434 @ SY1763 )
!= ( ti @ SV434 @ SY1764 ) )
| ~ ( ( ( ti @ SV434 @ SY1761 )
!= ( ti @ SV434 @ SY1762 ) ) ) )
| ( ( plus_plus @ SV434 @ SY1763 @ ( times_times @ SV434 @ SY1765 @ SY1761 ) )
!= ( plus_plus @ SV434 @ SY1764 @ ( times_times @ SV434 @ SY1765 @ SY1762 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2105]) ).
thf(2556,plain,
! [SV435: $i,SV5: $i] :
( ( ( minus_minus @ nat @ ( ti @ nat @ SV5 ) @ SV435 )
= ( minus_minus @ nat @ SV5 @ SV435 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2110]) ).
thf(2557,plain,
! [SV436: $i,SV6: $i] :
( ( ( minus_minus @ nat @ SV6 @ ( ti @ nat @ SV436 ) )
= ( minus_minus @ nat @ SV6 @ SV436 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2111]) ).
thf(2558,plain,
! [SV437: $i,SV7: $i] :
( ( ( ti @ nat @ ( minus_minus @ nat @ SV7 @ SV437 ) )
= ( minus_minus @ nat @ SV7 @ SV437 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2112]) ).
thf(2559,plain,
! [SV438: $i,SV8: $i] :
( ( ( product_Pair @ int @ int @ ( ti @ int @ SV8 ) @ SV438 )
= ( product_Pair @ int @ int @ SV8 @ SV438 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2113]) ).
thf(2560,plain,
! [SV439: $i,SV9: $i] :
( ( ( product_Pair @ int @ int @ SV9 @ ( ti @ int @ SV439 ) )
= ( product_Pair @ int @ int @ SV9 @ SV439 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2114]) ).
thf(2561,plain,
! [SV440: $i,SV10: $i] :
( ( ( ti @ ( product_prod @ int @ int ) @ ( product_Pair @ int @ int @ SV10 @ SV440 ) )
= ( product_Pair @ int @ int @ SV10 @ SV440 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2115]) ).
thf(2562,plain,
! [SV441: $i,SV11: $i] :
( ( ( legendre @ ( ti @ int @ SV11 ) @ SV441 )
= ( legendre @ SV11 @ SV441 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2116]) ).
thf(2563,plain,
! [SV442: $i,SV12: $i] :
( ( ( legendre @ SV12 @ ( ti @ int @ SV442 ) )
= ( legendre @ SV12 @ SV442 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2117]) ).
thf(2564,plain,
! [SV443: $i,SV13: $i] :
( ( ( ti @ int @ ( legendre @ SV13 @ SV443 ) )
= ( legendre @ SV13 @ SV443 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2118]) ).
thf(2565,plain,
! [SV444: $i,SV16: $i] :
( ( ( power_power @ int @ ( plus_plus @ int @ SV16 @ SV444 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ int @ ( plus_plus @ int @ ( power_power @ int @ SV16 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( times_times @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV16 ) @ SV444 ) ) @ ( power_power @ int @ SV444 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2121]) ).
thf(2566,plain,
! [SV445: $i,SV17: $i] :
( ( ( power_power @ int @ ( plus_plus @ int @ SV17 @ SV445 ) @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( power_power @ int @ SV17 @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) @ ( times_times @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit1 @ ( bit1 @ pls ) ) ) @ ( power_power @ int @ SV17 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ SV445 ) ) @ ( times_times @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit1 @ ( bit1 @ pls ) ) ) @ SV17 ) @ ( power_power @ int @ SV445 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ ( power_power @ int @ SV445 @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2122]) ).
thf(2567,plain,
! [SV446: $i,SV20: $i] :
( ( ( ord_less_eq @ int @ SV20 @ SV446 )
| ( ord_less_eq @ int @ SV446 @ SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2125]) ).
thf(2568,plain,
! [SV447: $i,SV21: $i] :
( ( ( ord_less @ int @ SV21 @ SV447 )
| ( ( ti @ int @ SV21 )
= ( ti @ int @ SV447 ) )
| ( ord_less @ int @ SV447 @ SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2126]) ).
thf(2569,plain,
! [SV448: $i,SV22: $i] :
( ( ! [SY1766: $i] :
( ( power_power @ int @ ( power_power @ int @ SV22 @ SV448 ) @ SY1766 )
= ( power_power @ int @ SV22 @ ( times_times @ nat @ SV448 @ SY1766 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2127]) ).
thf(2570,plain,
! [SV449: $i,SV23: $i] :
( ( ! [SY1767: $i] :
( ( power_power @ int @ SV23 @ ( plus_plus @ nat @ SV449 @ SY1767 ) )
= ( times_times @ int @ ( power_power @ int @ SV23 @ SV449 ) @ ( power_power @ int @ SV23 @ SY1767 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2128]) ).
thf(2571,plain,
! [SV450: $i,SV26: $i] :
( ( ! [SY1768: $i] :
( ( times_times @ int @ ( times_times @ int @ SV26 @ SV450 ) @ SY1768 )
= ( times_times @ int @ SV26 @ ( times_times @ int @ SV450 @ SY1768 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2132]) ).
thf(2572,plain,
! [SV451: $i,SV27: $i] :
( ( ( times_times @ int @ SV27 @ SV451 )
= ( times_times @ int @ SV451 @ SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2133]) ).
thf(2573,plain,
! [SV452: $i,SV29: $i] :
( ( ! [SY1769: $i] :
( ( plus_plus @ int @ ( plus_plus @ int @ SV29 @ SV452 ) @ SY1769 )
= ( plus_plus @ int @ SV29 @ ( plus_plus @ int @ SV452 @ SY1769 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2135]) ).
thf(2574,plain,
! [SV453: $i,SV30: $i] :
( ( ! [SY1770: $i] :
( ( plus_plus @ int @ SV30 @ ( plus_plus @ int @ SV453 @ SY1770 ) )
= ( plus_plus @ int @ SV453 @ ( plus_plus @ int @ SV30 @ SY1770 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2136]) ).
thf(2575,plain,
! [SV454: $i,SV31: $i] :
( ( ( plus_plus @ int @ SV31 @ SV454 )
= ( plus_plus @ int @ SV454 @ SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2137]) ).
thf(2576,plain,
! [SV455: $i,SV33: $i] :
( ( ( times_times @ int @ ( bit0 @ SV33 ) @ SV455 )
= ( bit0 @ ( times_times @ int @ SV33 @ SV455 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2139]) ).
thf(2577,plain,
! [SV456: $i,SV36: $i] :
( ( ( plus_plus @ int @ ( bit0 @ SV36 ) @ ( bit0 @ SV456 ) )
= ( bit0 @ ( plus_plus @ int @ SV36 @ SV456 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2142]) ).
thf(2578,plain,
! [SV457: $i,SV40: $i] :
( ( ( times_times @ int @ ( number_number_of @ int @ SV40 ) @ ( number_number_of @ int @ SV457 ) )
= ( number_number_of @ int @ ( times_times @ int @ SV40 @ SV457 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2146]) ).
thf(2579,plain,
! [SV458: $i,SV41: $i] :
( ( ! [SY1771: $i] :
( ( times_times @ int @ ( plus_plus @ int @ SV41 @ SV458 ) @ SY1771 )
= ( plus_plus @ int @ ( times_times @ int @ SV41 @ SY1771 ) @ ( times_times @ int @ SV458 @ SY1771 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2147]) ).
thf(2580,plain,
! [SV459: $i,SV42: $i] :
( ( ! [SY1772: $i] :
( ( times_times @ int @ SV42 @ ( plus_plus @ int @ SV459 @ SY1772 ) )
= ( plus_plus @ int @ ( times_times @ int @ SV42 @ SV459 ) @ ( times_times @ int @ SV42 @ SY1772 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2148]) ).
thf(2581,plain,
! [SV460: $i,SV43: $i] :
( ( ( plus_plus @ int @ ( number_number_of @ int @ SV43 ) @ ( number_number_of @ int @ SV460 ) )
= ( number_number_of @ int @ ( plus_plus @ int @ SV43 @ SV460 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2149]) ).
thf(2582,plain,
! [SV461: $i,SV45: $i] :
( ( ( plus_plus @ int @ ( bit1 @ SV45 ) @ ( bit0 @ SV461 ) )
= ( bit1 @ ( plus_plus @ int @ SV45 @ SV461 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2151]) ).
thf(2583,plain,
! [SV462: $i,SV46: $i] :
( ( ( plus_plus @ int @ ( bit0 @ SV46 ) @ ( bit1 @ SV462 ) )
= ( bit1 @ ( plus_plus @ int @ SV46 @ SV462 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2152]) ).
thf(2584,plain,
! [SV463: $i,SV48: $i] :
( ( ( times_times @ int @ ( bit1 @ SV48 ) @ SV463 )
= ( plus_plus @ int @ ( bit0 @ ( times_times @ int @ SV48 @ SV463 ) ) @ SV463 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2154]) ).
thf(2585,plain,
! [SV464: $i,SV50: $i] :
( ( ( power_power @ real @ ( plus_plus @ real @ SV50 @ SV464 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ real @ ( plus_plus @ real @ ( power_power @ real @ SV50 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ real @ SV464 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times @ real @ ( times_times @ real @ ( number_number_of @ real @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV50 ) @ SV464 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2156]) ).
thf(2586,plain,
( ( ~ ( zcong @ ( power_power @ int @ sK1_S1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of @ int @ min ) @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[2161]) ).
thf(2587,plain,
! [SV465: $i,SV54: $i] :
( ( zcong @ SV54 @ SV465 @ ( one_one @ int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2165]) ).
thf(2588,plain,
! [SV466: $i,SV55: $i] :
( ( ! [SY1773: $i] : ( zcong @ ( times_times @ int @ SV55 @ SV466 ) @ ( times_times @ int @ SY1773 @ SV466 ) @ SV466 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2166]) ).
thf(2589,plain,
! [SV467: $i,SV57: $i] :
( ( ( minus_minus @ int @ ( bit0 @ SV57 ) @ ( bit0 @ SV467 ) )
= ( bit0 @ ( minus_minus @ int @ SV57 @ SV467 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2168]) ).
thf(2590,plain,
! [SV468: $i,SV58: $i] :
( ( ! [SY1774: $i] :
( ( times_times @ int @ ( minus_minus @ int @ SV58 @ SV468 ) @ SY1774 )
= ( minus_minus @ int @ ( times_times @ int @ SV58 @ SY1774 ) @ ( times_times @ int @ SV468 @ SY1774 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2169]) ).
thf(2591,plain,
! [SV469: $i,SV59: $i] :
( ( ! [SY1775: $i] :
( ( times_times @ int @ SV59 @ ( minus_minus @ int @ SV469 @ SY1775 ) )
= ( minus_minus @ int @ ( times_times @ int @ SV59 @ SV469 ) @ ( times_times @ int @ SV59 @ SY1775 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2170]) ).
thf(2592,plain,
! [SV470: $i,SV60: $i] :
( ( ( minus_minus @ int @ ( bit1 @ SV60 ) @ ( bit0 @ SV470 ) )
= ( bit1 @ ( minus_minus @ int @ SV60 @ SV470 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2171]) ).
thf(2593,plain,
! [SV471: $i,SV61: $i] :
( ( ( minus_minus @ int @ ( bit1 @ SV61 ) @ ( bit1 @ SV471 ) )
= ( bit0 @ ( minus_minus @ int @ SV61 @ SV471 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2172]) ).
thf(2594,plain,
! [SV472: $i,SV63: $i] :
( ( ! [SY1776: $i,SY1777: $i,SY1778: $i,SY1779: $i,SY1780: $i] :
( ( plus_plus @ int @ ( times_times @ int @ ( minus_minus @ int @ SV63 @ ( times_times @ int @ SV472 @ SY1776 ) ) @ SY1777 ) @ ( times_times @ int @ ( minus_minus @ int @ SY1778 @ ( times_times @ int @ SV472 @ SY1779 ) ) @ SY1780 ) )
= ( minus_minus @ int @ ( plus_plus @ int @ ( times_times @ int @ SV63 @ SY1777 ) @ ( times_times @ int @ SY1778 @ SY1780 ) ) @ ( times_times @ int @ SV472 @ ( plus_plus @ int @ ( times_times @ int @ SY1776 @ SY1777 ) @ ( times_times @ int @ SY1779 @ SY1780 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2174]) ).
thf(2595,plain,
! [SV473: $i,SV67: $i] :
( ( ! [SY1781: $i,SY1782: $i] :
( ( times_times @ int @ ( twoSqu579703163sum2sq @ ( product_Pair @ int @ int @ SV67 @ SV473 ) ) @ ( twoSqu579703163sum2sq @ ( product_Pair @ int @ int @ SY1781 @ SY1782 ) ) )
= ( twoSqu579703163sum2sq @ ( product_Pair @ int @ int @ ( plus_plus @ int @ ( times_times @ int @ SV67 @ SY1781 ) @ ( times_times @ int @ SV473 @ SY1782 ) ) @ ( minus_minus @ int @ ( times_times @ int @ SV67 @ SY1782 ) @ ( times_times @ int @ SV473 @ SY1781 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2178]) ).
thf(2596,plain,
! [SV474: $i,SV68: $i] :
( ( ( times_times @ int @ ( plus_plus @ int @ SV68 @ SV474 ) @ ( minus_minus @ int @ SV68 @ SV474 ) )
= ( minus_minus @ int @ ( power_power @ int @ SV68 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ SV474 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2179]) ).
thf(2597,plain,
! [SV475: $i,SV69: $i] :
( ( ( power_power @ int @ ( minus_minus @ int @ SV69 @ SV475 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ int @ ( minus_minus @ int @ ( power_power @ int @ SV69 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( times_times @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV69 ) @ SV475 ) ) @ ( power_power @ int @ SV475 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2180]) ).
thf(2598,plain,
! [SV476: $i,SV70: $i] :
( ( ( power_power @ int @ ( minus_minus @ int @ SV70 @ SV476 ) @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( minus_minus @ int @ ( plus_plus @ int @ ( minus_minus @ int @ ( power_power @ int @ SV70 @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) @ ( times_times @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit1 @ ( bit1 @ pls ) ) ) @ ( power_power @ int @ SV70 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ SV476 ) ) @ ( times_times @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit1 @ ( bit1 @ pls ) ) ) @ SV70 ) @ ( power_power @ int @ SV476 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ ( power_power @ int @ SV476 @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2181]) ).
thf(2599,plain,
! [SV71: $i] :
( ( ( ( power_power @ int @ ( number_number_of @ int @ min ) @ SV71 )
= ( one_one @ int ) )
= $true )
| ( ( ( power_power @ int @ ( number_number_of @ int @ min ) @ SV71 )
= ( number_number_of @ int @ min ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2182]) ).
thf(2600,plain,
! [SV477: $i,SV72: $i] :
( ( ( minus_minus @ nat @ ( power_power @ nat @ SV72 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ nat @ SV477 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( times_times @ nat @ ( plus_plus @ nat @ SV72 @ SV477 ) @ ( minus_minus @ nat @ SV72 @ SV477 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2183]) ).
thf(2601,plain,
! [SV478: $i,SV75: $i] :
( ( ( times_times @ real @ SV75 @ SV478 )
= ( times_times @ real @ SV478 @ SV75 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2186]) ).
thf(2602,plain,
! [SV479: $i,SV76: $i] :
( ( ! [SY1783: $i] :
( ( times_times @ real @ ( times_times @ real @ SV76 @ SV479 ) @ SY1783 )
= ( times_times @ real @ SV76 @ ( times_times @ real @ SV479 @ SY1783 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2187]) ).
thf(2603,plain,
! [SV480: $i,SV77: $i] :
( ( ! [SY1784: $i] :
( ( times_times @ real @ ( plus_plus @ real @ SV77 @ SV480 ) @ SY1784 )
= ( plus_plus @ real @ ( times_times @ real @ SV77 @ SY1784 ) @ ( times_times @ real @ SV480 @ SY1784 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2188]) ).
thf(2604,plain,
! [SV481: $i,SV79: $i] :
( ( ! [SY1785: $i,SY1786: $i,SY1787: $i] :
( ~ ( zcong @ SY1785 @ SY1786 @ SY1787 )
| ~ ( ~ ( ~ ( zcong @ SV79 @ ( times_times @ int @ SY1785 @ SV481 ) @ SY1787 )
| ( zcong @ SV79 @ ( times_times @ int @ SY1786 @ SV481 ) @ SY1787 ) )
| ~ ( ~ ( zcong @ SV79 @ ( times_times @ int @ SY1786 @ SV481 ) @ SY1787 )
| ( zcong @ SV79 @ ( times_times @ int @ SY1785 @ SV481 ) @ SY1787 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2190]) ).
thf(2605,plain,
! [SV482: $i,SV80: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ int @ SV80 @ ( plus_plus @ int @ SV482 @ ( one_one @ int ) ) )
| ( ord_less @ int @ SV80 @ SV482 )
| ( ( ti @ int @ SV80 )
= ( ti @ int @ SV482 ) ) )
| ~ ( ~ ( ( ord_less @ int @ SV80 @ SV482 )
| ( ( ti @ int @ SV80 )
= ( ti @ int @ SV482 ) ) )
| ( ord_less @ int @ SV80 @ ( plus_plus @ int @ SV482 @ ( one_one @ int ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2191]) ).
thf(2606,plain,
! [SV483: $i,SV81: $i] :
( ( ! [SY1788: $i] :
( ~ ( semiring @ SY1788 )
| ( ( plus_plus @ SY1788 @ SV81 @ ( ti @ SY1788 @ SV483 ) )
= ( plus_plus @ SY1788 @ SV81 @ SV483 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2192]) ).
thf(2607,plain,
! [SV82: $i] :
( ( ( ~ ( ordere453448008miring @ SV82 ) )
= $true )
| ( ( ! [SY1175: $i,SY1176: $i] :
( ~ ( ord_less_eq @ SV82 @ ( zero_zero @ SV82 ) @ SY1176 )
| ~ ( ord_less_eq @ SV82 @ SY1175 @ ( zero_zero @ SV82 ) )
| ( ord_less_eq @ SV82 @ ( times_times @ SV82 @ SY1176 @ SY1175 ) @ ( zero_zero @ SV82 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2193]) ).
thf(2608,plain,
! [SV83: $i] :
( ( ( ~ ( monoid_mult @ SV83 ) )
= $true )
| ( ( ! [SY1177: $i,SY1178: $i] :
( ( times_times @ SV83 @ ( power_power @ SV83 @ SY1177 @ SY1178 ) @ SY1177 )
= ( times_times @ SV83 @ SY1177 @ ( power_power @ SV83 @ SY1177 @ SY1178 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2194]) ).
thf(2609,plain,
! [SV84: $i] :
( ( ( ~ ( comm_semiring_1 @ SV84 ) )
= $true )
| ( ( ! [SY1179: $i,SY1180: $i,SY1181: $i] :
( ( plus_plus @ SV84 @ ( plus_plus @ SV84 @ SY1179 @ SY1180 ) @ SY1181 )
= ( plus_plus @ SV84 @ SY1179 @ ( plus_plus @ SV84 @ SY1180 @ SY1181 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2195]) ).
thf(2610,plain,
! [SV85: $i] :
( ( ( ~ ( number_semiring @ SV85 ) )
= $true )
| ( ( ( plus_plus @ SV85 @ ( one_one @ SV85 ) @ ( one_one @ SV85 ) )
= ( number_number_of @ SV85 @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2196]) ).
thf(2611,plain,
! [SV86: $i] :
( ( ( ~ ( linordered_ring @ SV86 ) )
= $true )
| ( ( ! [SY1182: $i] : ( ord_less_eq @ SV86 @ ( zero_zero @ SV86 ) @ ( times_times @ SV86 @ SY1182 @ SY1182 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2197]) ).
thf(2612,plain,
! [SV87: $i] :
( ( ( ~ ( ordere453448008miring @ SV87 ) )
= $true )
| ( ( ! [SY1183: $i,SY1184: $i] :
( ~ ( ord_less_eq @ SV87 @ ( zero_zero @ SV87 ) @ SY1184 )
| ~ ( ord_less_eq @ SV87 @ SY1183 @ ( zero_zero @ SV87 ) )
| ( ord_less_eq @ SV87 @ ( times_times @ SV87 @ SY1183 @ SY1184 ) @ ( zero_zero @ SV87 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2198]) ).
thf(2613,plain,
! [SV88: $i] :
( ( ( ~ ( linordered_idom @ SV88 ) )
= $true )
| ( ( ! [SY1185: $i,SY1186: $i] :
~ ( ord_less @ SV88 @ ( plus_plus @ SV88 @ ( power_power @ SV88 @ SY1185 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV88 @ SY1186 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( zero_zero @ SV88 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2199]) ).
thf(2614,plain,
! [SV484: $i,SV89: $i] :
( ( ! [SY1789: $i] :
( ~ ( no_zero_divisors @ SY1789 )
| ( ( times_times @ SY1789 @ ( ti @ SY1789 @ SV89 ) @ SV484 )
= ( times_times @ SY1789 @ SV89 @ SV484 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2200]) ).
thf(2615,plain,
! [SV90: $i] :
( ( ( ~ ( no_zero_divisors @ SV90 ) )
= $true )
| ( ( ! [SY1189: $i,SY1190: $i] :
( ~ ( ( ( ti @ SV90 @ SY1190 )
!= ( zero_zero @ SV90 ) ) )
| ~ ( ( ( ti @ SV90 @ SY1189 )
!= ( zero_zero @ SV90 ) ) )
| ( ( times_times @ SV90 @ SY1190 @ SY1189 )
!= ( zero_zero @ SV90 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2201]) ).
thf(2616,plain,
! [SV91: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ min @ ( bit1 @ SV91 ) )
| ( ord_less_eq @ int @ min @ SV91 ) )
| ~ ( ~ ( ord_less_eq @ int @ min @ SV91 )
| ( ord_less_eq @ int @ min @ ( bit1 @ SV91 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2202]) ).
thf(2617,plain,
! [SV485: $i,SV92: $i] :
( ( ~ ( dvd_dvd @ int @ SV92 @ SV485 )
| ( ord_less_eq @ int @ SV485 @ ( zero_zero @ int ) )
| ( ord_less_eq @ int @ SV92 @ SV485 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2203]) ).
thf(2618,plain,
! [SV93: $i] :
( ( ~ ( ( min
!= ( bit1 @ SV93 ) )
| ( min
= ( ti @ int @ SV93 ) ) )
| ~ ( ( min
!= ( ti @ int @ SV93 ) )
| ( min
= ( bit1 @ SV93 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2204]) ).
thf(2619,plain,
! [SV94: $i] :
( ( ( ~ ( comm_semiring_1 @ SV94 ) )
= $true )
| ( ( ! [SY1192: $i,SY1193: $i,SY1194: $i] :
( ( times_times @ SV94 @ SY1192 @ ( times_times @ SV94 @ SY1193 @ SY1194 ) )
= ( times_times @ SV94 @ ( times_times @ SV94 @ SY1192 @ SY1193 ) @ SY1194 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2205]) ).
thf(2620,plain,
! [SV95: $i] :
( ( ( ~ ( comm_semiring_1 @ SV95 ) )
= $true )
| ( ( ! [SY1195: $i,SY1196: $i,SY1197: $i,SY1198: $i] :
( ( times_times @ SV95 @ ( times_times @ SV95 @ SY1195 @ SY1196 ) @ ( times_times @ SV95 @ SY1197 @ SY1198 ) )
= ( times_times @ SV95 @ SY1195 @ ( times_times @ SV95 @ SY1196 @ ( times_times @ SV95 @ SY1197 @ SY1198 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2206]) ).
thf(2621,plain,
! [SV486: $i,SV96: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ int @ ( number_number_of @ int @ SV96 ) @ ( number_number_of @ int @ SV486 ) )
| ( ord_less @ int @ SV96 @ SV486 ) )
| ~ ( ~ ( ord_less @ int @ SV96 @ SV486 )
| ( ord_less @ int @ ( number_number_of @ int @ SV96 ) @ ( number_number_of @ int @ SV486 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2207]) ).
thf(2622,plain,
! [SV487: $i,SV97: $i] :
( ( ~ ( dvd_dvd @ nat @ SV97 @ SV487 )
| ( SV487
= ( zero_zero @ nat ) )
| ( ord_less_eq @ nat @ SV97 @ SV487 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2208]) ).
thf(2623,plain,
! [SV488: $i,SV98: $i] :
( ( ! [SY1790: $i] :
( ~ ( ab_group_add @ SY1790 )
| ( ( ti @ SY1790 @ ( plus_plus @ SY1790 @ SV98 @ SV488 ) )
= ( plus_plus @ SY1790 @ SV98 @ SV488 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2209]) ).
thf(2624,plain,
! [SV99: $i] :
( ( ( ~ ( comm_semiring_1 @ SV99 ) )
= $true )
| ( ( ! [SY1203: $i,SY1204: $i,SY1205: $i] :
( ( plus_plus @ SV99 @ SY1203 @ ( plus_plus @ SV99 @ SY1204 @ SY1205 ) )
= ( plus_plus @ SV99 @ SY1204 @ ( plus_plus @ SV99 @ SY1203 @ SY1205 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2210]) ).
thf(2625,plain,
! [SV100: $i,SV489: $i] :
( ( ! [SY1791: $i] :
( ~ ( ord_less_eq @ int @ SV489 @ SY1791 )
| ( ord_less_eq @ int @ ( plus_plus @ int @ SV100 @ SV489 ) @ ( plus_plus @ int @ SV100 @ SY1791 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2211]) ).
thf(2626,plain,
! [SV101: $i,SV490: $i] :
( ( ! [SY1792: $i] :
( ~ ~ ( zcong @ SV490 @ ( zero_zero @ int ) @ SY1792 )
| ~ ( zcong @ ( power_power @ int @ SV101 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SV490 @ SY1792 )
| ~ ( dvd_dvd @ int @ SY1792 @ SV101 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2212]) ).
thf(2627,plain,
! [SV102: $i] :
( ( ( ~ ( linordered_semidom @ SV102 ) )
= $true )
| ( ( ! [SY1210: $i,SY1211: $i] :
( ~ ( ord_less @ SV102 @ ( zero_zero @ SV102 ) @ SY1211 )
| ~ ( ord_less @ SV102 @ SY1211 @ ( one_one @ SV102 ) )
| ( ord_less @ SV102 @ ( times_times @ SV102 @ SY1211 @ ( power_power @ SV102 @ SY1211 @ SY1210 ) ) @ ( power_power @ SV102 @ SY1211 @ SY1210 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2213]) ).
thf(2628,plain,
! [SV491: $i,SV103: $i] :
( ( ~ ( ~ ( ~ ( quadRes @ ( ti @ int @ SV103 ) @ SV491 )
| ( quadRes @ SV103 @ SV491 ) )
| ~ ( ~ ( quadRes @ SV103 @ SV491 )
| ( quadRes @ ( ti @ int @ SV103 ) @ SV491 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2214]) ).
thf(2629,plain,
! [SV492: $i,SV104: $i] :
( ( ! [SY1793: $i] :
( ~ ( semiring @ SY1793 )
| ( ( times_times @ SY1793 @ SV104 @ ( ti @ SY1793 @ SV492 ) )
= ( times_times @ SY1793 @ SV104 @ SV492 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2216]) ).
thf(2630,plain,
! [SV105: $i] :
( ( ( ~ ( semiring_1 @ SV105 ) )
= $true )
| ( ( ( power_power @ SV105 @ ( one_one @ SV105 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( one_one @ SV105 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2217]) ).
thf(2631,plain,
! [SV106: $i] :
( ( ~ ( ( ( bit1 @ SV106 )
!= min )
| ( ( ti @ int @ SV106 )
= min ) )
| ~ ( ( ( ti @ int @ SV106 )
!= min )
| ( ( bit1 @ SV106 )
= min ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2218]) ).
thf(2632,plain,
! [SV493: $i,SV107: $i] :
( ( ! [SY1794: $i] :
( ~ ( power @ SY1794 )
| ( ( times_times @ SY1794 @ SV107 @ ( ti @ SY1794 @ SV493 ) )
= ( times_times @ SY1794 @ SV107 @ SV493 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2219]) ).
thf(2633,plain,
! [SV108: $i,SV494: $i] :
( ( ! [SY1795: $i,SY1796: $i,SY1797: $i] :
( ~ ( zcong @ SY1795 @ SY1796 @ SY1797 )
| ( ( ti @ int @ SY1796 )
!= ( ti @ int @ SV494 ) )
| ~ ( zcong @ SV494 @ SV108 @ SY1797 )
| ( zcong @ SY1795 @ SV108 @ SY1797 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2220]) ).
thf(2634,plain,
! [SV495: $i,SV109: $i] :
( ( ! [SY1798: $i] :
( ~ ( dvd_dvd @ int @ ( times_times @ int @ SV109 @ SV495 ) @ ( times_times @ int @ SV109 @ SY1798 ) )
| ~ ( ( ( ti @ int @ SV109 )
!= ( zero_zero @ int ) ) )
| ( dvd_dvd @ int @ SV495 @ SY1798 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2221]) ).
thf(2635,plain,
! [SV110: $i] :
( ( ( ~ ( power @ SV110 ) )
= $true )
| ( ( ! [SY1223: $i] :
( ( power_power @ SV110 @ SY1223 @ ( zero_zero @ nat ) )
= ( one_one @ SV110 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2222]) ).
thf(2636,plain,
! [SV111: $i,SV496: $i] :
( ( ~ ( twoSqu420862341sum2sq @ SV496 )
| ~ ( twoSqu420862341sum2sq @ SV111 )
| ( twoSqu420862341sum2sq @ ( times_times @ int @ SV496 @ SV111 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2223]) ).
thf(2637,plain,
! [SV112: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( bit0 @ SV112 ) @ pls )
| ( ord_less_eq @ int @ SV112 @ pls ) )
| ~ ( ~ ( ord_less_eq @ int @ SV112 @ pls )
| ( ord_less_eq @ int @ ( bit0 @ SV112 ) @ pls ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2224]) ).
thf(2638,plain,
! [SV113: $i,SV497: $i] :
( ( ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV497 )
| ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( power_power @ int @ SV497 @ SV113 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2225]) ).
thf(2639,plain,
! [SV114: $i] :
( ( ( ~ ( zero_neq_one @ SV114 ) )
= $true )
| ( ( ( ti @ SV114 @ ( one_one @ SV114 ) )
= ( one_one @ SV114 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2226]) ).
thf(2640,plain,
! [SV498: $i,SV115: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SV115 ) @ ( bit0 @ SV498 ) )
| ( ord_less @ int @ SV115 @ SV498 ) )
| ~ ( ~ ( ord_less @ int @ SV115 @ SV498 )
| ( ord_less @ int @ ( bit1 @ SV115 ) @ ( bit0 @ SV498 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2227]) ).
thf(2641,plain,
! [SV116: $i] :
( ( ( ~ ( semiring_1 @ SV116 ) )
= $true )
| ( ( ( power_power @ SV116 @ ( zero_zero @ SV116 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SV116 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2228]) ).
thf(2642,plain,
! [SV117: $i] :
( ( ( ~ ( linordered_semidom @ SV117 ) )
= $true )
| ( ( ! [SY1227: $i,SY1228: $i,SY1229: $i] :
( ~ ( ord_less_eq @ nat @ SY1228 @ SY1229 )
| ~ ( ord_less_eq @ SV117 @ ( zero_zero @ SV117 ) @ SY1227 )
| ~ ( ord_less_eq @ SV117 @ SY1227 @ ( one_one @ SV117 ) )
| ( ord_less_eq @ SV117 @ ( power_power @ SV117 @ SY1227 @ SY1229 ) @ ( power_power @ SV117 @ SY1227 @ SY1228 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2229]) ).
thf(2643,plain,
! [SV118: $i,SV499: $i] :
( ( ! [SY1799: $i] :
( ~ ( dvd_dvd @ nat @ SV499 @ SY1799 )
| ( dvd_dvd @ nat @ ( times_times @ nat @ SV118 @ SV499 ) @ ( times_times @ nat @ SV118 @ SY1799 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2230]) ).
thf(2644,plain,
! [SV500: $i,SV119: $i] :
( ( ! [SY1800: $i] :
( ~ ( zprime @ SY1800 )
| ~ ( dvd_dvd @ int @ SY1800 @ ( power_power @ int @ SV119 @ SV500 ) )
| ( dvd_dvd @ int @ SY1800 @ SV119 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2231]) ).
thf(2645,plain,
! [SV120: $i] :
( ( ( ~ ~ ( ~ ( number_ring @ SV120 )
| ~ ( linordered_idom @ SV120 ) ) )
= $true )
| ( ( ! [SY1234: $i] :
~ ( ~ ( ~ ( ord_less @ SV120 @ ( one_one @ SV120 ) @ ( number_number_of @ SV120 @ SY1234 ) )
| ( ord_less @ int @ ( bit1 @ pls ) @ SY1234 ) )
| ~ ( ~ ( ord_less @ int @ ( bit1 @ pls ) @ SY1234 )
| ( ord_less @ SV120 @ ( one_one @ SV120 ) @ ( number_number_of @ SV120 @ SY1234 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2232]) ).
thf(2646,plain,
! [SV121: $i,SV501: $i] :
( ( ! [SY1801: $i] :
( ~ ( ord_less_eq @ real @ SV501 @ SY1801 )
| ( ord_less_eq @ real @ ( plus_plus @ real @ SV121 @ SV501 ) @ ( plus_plus @ real @ SV121 @ SY1801 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2233]) ).
thf(2647,plain,
! [SV502: $i,SV122: $i] :
( ( ~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SV122 ) @ ( bit1 @ SV502 ) )
| ( ord_less_eq @ int @ SV122 @ SV502 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV122 @ SV502 )
| ( ord_less_eq @ int @ ( bit1 @ SV122 ) @ ( bit1 @ SV502 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2234]) ).
thf(2648,plain,
( ( ( ord_less @ int @ ( one_one @ int ) @ t )
= $false )
| ( ( ~ ! [SX0: $i] :
~ ~ ! [SX1: $i] :
( ( plus_plus @ int @ ( power_power @ int @ SX0 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ SX1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2235]) ).
thf(2649,plain,
! [SV123: $i] :
( ( ( ~ ~ ( ~ ( number_ring @ SV123 )
| ~ ( linordered_idom @ SV123 ) ) )
= $true )
| ( ( ! [SY1238: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV123 @ ( number_number_of @ SV123 @ SY1238 ) @ ( one_one @ SV123 ) )
| ( ord_less_eq @ int @ SY1238 @ ( bit1 @ pls ) ) )
| ~ ( ~ ( ord_less_eq @ int @ SY1238 @ ( bit1 @ pls ) )
| ( ord_less_eq @ SV123 @ ( number_number_of @ SV123 @ SY1238 ) @ ( one_one @ SV123 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2236]) ).
thf(2650,plain,
! [SV124: $i] :
( ( ( ~ ( comm_semiring_1 @ SV124 ) )
= $true )
| ( ( ! [SY1239: $i,SY1240: $i,SY1241: $i,SY1242: $i] :
( ~ ( dvd_dvd @ SV124 @ SY1241 @ SY1242 )
| ~ ( dvd_dvd @ SV124 @ SY1239 @ SY1240 )
| ( dvd_dvd @ SV124 @ ( times_times @ SV124 @ SY1241 @ SY1239 ) @ ( times_times @ SV124 @ SY1242 @ SY1240 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2237]) ).
thf(2651,plain,
! [SV125: $i] :
( ( ( ~ ( ab_group_add @ SV125 ) )
= $true )
| ( ( ! [SY1243: $i,SY1244: $i,SY1245: $i,SY1246: $i] :
( ( minus_minus @ SV125 @ ( plus_plus @ SV125 @ SY1243 @ SY1244 ) @ ( plus_plus @ SV125 @ SY1245 @ SY1246 ) )
= ( plus_plus @ SV125 @ ( minus_minus @ SV125 @ SY1243 @ SY1245 ) @ ( minus_minus @ SV125 @ SY1244 @ SY1246 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2238]) ).
thf(2652,plain,
! [SV126: $i] :
( ( ( ~ ( number_semiring @ SV126 ) )
= $true )
| ( ( ! [SY1247: $i] :
( ( times_times @ SV126 @ SY1247 @ ( number_number_of @ SV126 @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ SV126 @ SY1247 @ SY1247 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2239]) ).
thf(2653,plain,
! [SV127: $i] :
( ( ( ~ ( number_ring @ SV127 ) )
= $true )
| ( ( ( plus_plus @ SV127 @ ( one_one @ SV127 ) @ ( one_one @ SV127 ) )
= ( number_number_of @ SV127 @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2240]) ).
thf(2654,plain,
! [SV128: $i] :
( ( ~ ( ( ( number_number_of @ nat @ SV128 )
!= ( zero_zero @ nat ) )
| ( ord_less_eq @ int @ SV128 @ pls ) )
| ~ ( ~ ( ord_less_eq @ int @ SV128 @ pls )
| ( ( number_number_of @ nat @ SV128 )
= ( zero_zero @ nat ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2241]) ).
thf(2655,plain,
! [SV129: $i] :
( ( ( ~ ( number_semiring @ SV129 ) )
= $true )
| ( ( ! [SY1248: $i] :
( ( times_times @ SV129 @ ( number_number_of @ SV129 @ ( bit0 @ ( bit1 @ pls ) ) ) @ SY1248 )
= ( plus_plus @ SV129 @ SY1248 @ SY1248 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2242]) ).
thf(2656,plain,
! [SV130: $i] :
( ( ( ~ ( comm_semiring_1 @ SV130 ) )
= $true )
| ( ( ! [SY1249: $i,SY1250: $i,SY1251: $i] :
( ( times_times @ SV130 @ ( times_times @ SV130 @ SY1249 @ SY1250 ) @ SY1251 )
= ( times_times @ SV130 @ ( times_times @ SV130 @ SY1249 @ SY1251 ) @ SY1250 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2243]) ).
thf(2657,plain,
! [SV131: $i] :
( ( ( ~ ( comm_semiring @ SV131 ) )
= $true )
| ( ( ! [SY1252: $i,SY1253: $i,SY1254: $i] :
( ( times_times @ SV131 @ ( plus_plus @ SV131 @ SY1252 @ SY1253 ) @ SY1254 )
= ( plus_plus @ SV131 @ ( times_times @ SV131 @ SY1252 @ SY1254 ) @ ( times_times @ SV131 @ SY1253 @ SY1254 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2244]) ).
thf(2658,plain,
! [SV503: $i,SV132: $i] :
( ( ! [SY1802: $i,SY1803: $i,SY1804: $i] :
( ~ ( ord_less_eq @ int @ ( plus_plus @ int @ ( times_times @ int @ SV132 @ SV503 ) @ SY1802 ) @ ( plus_plus @ int @ ( times_times @ int @ SV132 @ SY1803 ) @ SY1804 ) )
| ~ ( ord_less_eq @ int @ SY1804 @ ( zero_zero @ int ) )
| ~ ( ord_less @ int @ SV132 @ SY1804 )
| ~ ( ord_less @ int @ SV132 @ SY1802 )
| ( ord_less_eq @ int @ SY1803 @ SV503 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2245]) ).
thf(2659,plain,
! [SV504: $i,SV133: $i] :
( ( ( bit1 @ SV133 )
!= ( bit0 @ SV504 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2246]) ).
thf(2660,plain,
! [SV134: $i] :
( ( ( ~ ~ ( ~ ( number_ring @ SV134 )
| ~ ( linordered_idom @ SV134 ) ) )
= $true )
| ( ( ! [SY1260: $i] :
~ ( ~ ( ~ ( ord_less @ SV134 @ ( number_number_of @ SV134 @ SY1260 ) @ ( one_one @ SV134 ) )
| ( ord_less @ int @ SY1260 @ ( bit1 @ pls ) ) )
| ~ ( ~ ( ord_less @ int @ SY1260 @ ( bit1 @ pls ) )
| ( ord_less @ SV134 @ ( number_number_of @ SV134 @ SY1260 ) @ ( one_one @ SV134 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2247]) ).
thf(2661,plain,
! [SV505: $i,SV135: $i] :
( ( ~ ( ~ ( ~ ( ord_less_eq @ nat @ ( number_number_of @ nat @ SV135 ) @ ( number_number_of @ nat @ SV505 ) )
| ~ ~ ( ord_less_eq @ int @ SV135 @ SV505 )
| ( ord_less_eq @ int @ SV135 @ pls ) )
| ~ ( ~ ( ~ ~ ( ord_less_eq @ int @ SV135 @ SV505 )
| ( ord_less_eq @ int @ SV135 @ pls ) )
| ( ord_less_eq @ nat @ ( number_number_of @ nat @ SV135 ) @ ( number_number_of @ nat @ SV505 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2248]) ).
thf(2662,plain,
! [SV136: $i] :
( ( ( ~ ( comm_semiring_1 @ SV136 ) )
= $true )
| ( ( ! [SY1262: $i] :
( ( power_power @ SV136 @ SY1262 @ ( one_one @ nat ) )
= ( ti @ SV136 @ SY1262 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2249]) ).
thf(2663,plain,
! [SV506: $i,SV137: $i] :
( ( ! [SY1805: $i] :
~ ( ~ ( ~ ( zcong @ SV137 @ SV506 @ SY1805 )
| ( dvd_dvd @ int @ SY1805 @ ( minus_minus @ int @ SV137 @ SV506 ) ) )
| ~ ( ~ ( dvd_dvd @ int @ SY1805 @ ( minus_minus @ int @ SV137 @ SV506 ) )
| ( zcong @ SV137 @ SV506 @ SY1805 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2250]) ).
thf(2664,plain,
! [SV507: $i,SV138: $i] :
( ( ~ ( ~ ( ~ ( ord_less_eq @ int @ ( number_number_of @ int @ SV138 ) @ ( number_number_of @ int @ SV507 ) )
| ( ord_less_eq @ int @ SV138 @ SV507 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV138 @ SV507 )
| ( ord_less_eq @ int @ ( number_number_of @ int @ SV138 ) @ ( number_number_of @ int @ SV507 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2251]) ).
thf(2665,plain,
! [SV139: $i] :
( ( ( ~ ~ ( ~ ( number @ SV139 )
| ~ ( ring @ SV139 ) ) )
= $true )
| ( ( ! [SY1266: $i,SY1267: $i,SY1268: $i] :
( ( times_times @ SV139 @ ( number_number_of @ SV139 @ SY1266 ) @ ( minus_minus @ SV139 @ SY1267 @ SY1268 ) )
= ( minus_minus @ SV139 @ ( times_times @ SV139 @ ( number_number_of @ SV139 @ SY1266 ) @ SY1267 ) @ ( times_times @ SV139 @ ( number_number_of @ SV139 @ SY1266 ) @ SY1268 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2252]) ).
thf(2666,plain,
! [SV140: $i] :
( ( ( ~ ( monoid_mult @ SV140 ) )
= $true )
| ( ( ! [SY1269: $i] :
( ( power_power @ SV140 @ SY1269 @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( times_times @ SV140 @ ( times_times @ SV140 @ SY1269 @ SY1269 ) @ SY1269 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2253]) ).
thf(2667,plain,
! [SV508: $i,SV141: $i] :
( ( ~ ( ord_less @ int @ SV141 @ SV508 )
| ( ord_less_eq @ int @ ( plus_plus @ int @ SV141 @ ( one_one @ int ) ) @ SV508 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2254]) ).
thf(2668,plain,
! [SV142: $i] :
( ( ( ~ ( linordered_semidom @ SV142 ) )
= $true )
| ( ( ! [SY1271: $i,SY1272: $i] :
( ~ ( ord_less @ SV142 @ ( one_one @ SV142 ) @ SY1272 )
| ( ord_less @ SV142 @ ( one_one @ SV142 ) @ ( times_times @ SV142 @ SY1272 @ ( power_power @ SV142 @ SY1272 @ SY1271 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2255]) ).
thf(2669,plain,
! [SV509: $i,SV143: $i] :
( ( ~ ( ~ ( ( ( power_power @ nat @ SV143 @ SV509 )
!= ( zero_zero @ nat ) )
| ~ ( ~ ( ( SV509
!= ( zero_zero @ nat ) ) )
| ( SV143
!= ( zero_zero @ nat ) ) ) )
| ~ ( ~ ~ ( ~ ( ( SV509
!= ( zero_zero @ nat ) ) )
| ( SV143
!= ( zero_zero @ nat ) ) )
| ( ( power_power @ nat @ SV143 @ SV509 )
= ( zero_zero @ nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2256]) ).
thf(2670,plain,
! [SV144: $i] :
( ( ( ~ ( number_ring @ SV144 ) )
= $true )
| ( ( ! [SY1274: $i] :
( ( times_times @ SV144 @ SY1274 @ ( number_number_of @ SV144 @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ SV144 @ SY1274 @ SY1274 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2257]) ).
thf(2671,plain,
! [SV510: $i,SV145: $i] :
( ( ! [SY1806: $i] :
~ ( ~ ( ~ ( dvd_dvd @ int @ SV145 @ ( plus_plus @ int @ SV510 @ ( times_times @ int @ SV145 @ SY1806 ) ) )
| ( dvd_dvd @ int @ SV145 @ SV510 ) )
| ~ ( ~ ( dvd_dvd @ int @ SV145 @ SV510 )
| ( dvd_dvd @ int @ SV145 @ ( plus_plus @ int @ SV510 @ ( times_times @ int @ SV145 @ SY1806 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2258]) ).
thf(2672,plain,
! [SV146: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SV146 ) @ min )
| ( ord_less @ int @ SV146 @ min ) )
| ~ ( ~ ( ord_less @ int @ SV146 @ min )
| ( ord_less @ int @ ( bit1 @ SV146 ) @ min ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2259]) ).
thf(2673,plain,
! [SV511: $i,SV147: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ SV147 @ SV511 ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ SV147 )
| ( SV511
= ( zero_zero @ nat ) ) )
| ~ ( ~ ( ( ord_less @ nat @ ( zero_zero @ nat ) @ SV147 )
| ( SV511
= ( zero_zero @ nat ) ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ SV147 @ SV511 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2260]) ).
thf(2674,plain,
! [SV148: $i] :
( ( ( bit0 @ SV148 )
= min )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2261]) ).
thf(2675,plain,
! [SV149: $i] :
( ( ( ~ ( number_ring @ SV149 ) )
= $true )
| ( ( ! [SY1278: $i] :
( ( plus_plus @ SV149 @ ( one_one @ SV149 ) @ ( number_number_of @ SV149 @ SY1278 ) )
= ( number_number_of @ SV149 @ ( plus_plus @ int @ ( bit1 @ pls ) @ SY1278 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2262]) ).
thf(2676,plain,
! [SV150: $i] :
( ( ( ~ ( comm_semiring_1 @ SV150 ) )
= $true )
| ( ( ! [SY1279: $i,SY1280: $i,SY1281: $i] :
( ( plus_plus @ SV150 @ ( times_times @ SV150 @ SY1279 @ SY1280 ) @ ( times_times @ SV150 @ SY1281 @ SY1280 ) )
= ( times_times @ SV150 @ ( plus_plus @ SV150 @ SY1279 @ SY1281 ) @ SY1280 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2263]) ).
thf(2677,plain,
! [SV512: $i,SV151: $i] :
( ( ~ ( ~ ( ~ ~ ( ~ ( dvd_dvd @ nat @ SV151 @ SV512 )
| ~ ( dvd_dvd @ nat @ SV512 @ SV151 ) )
| ( SV151 = SV512 ) )
| ~ ( ( SV151 != SV512 )
| ~ ( ~ ( dvd_dvd @ nat @ SV151 @ SV512 )
| ~ ( dvd_dvd @ nat @ SV512 @ SV151 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2264]) ).
thf(2678,plain,
! [SV152: $i] :
( ( ( ~ ( ordere453448008miring @ SV152 ) )
= $true )
| ( ( ! [SY1283: $i,SY1284: $i] :
( ~ ( ord_less_eq @ SV152 @ ( zero_zero @ SV152 ) @ SY1284 )
| ~ ( ord_less_eq @ SV152 @ ( zero_zero @ SV152 ) @ SY1283 )
| ( ord_less_eq @ SV152 @ ( zero_zero @ SV152 ) @ ( times_times @ SV152 @ SY1284 @ SY1283 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2265]) ).
thf(2679,plain,
! [SV153: $i,SV513: $i] :
( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ SV513 )
| ~ ( ord_less @ real @ ( zero_zero @ real ) @ SV153 )
| ~ ! [SY1807: $i] :
~ ~ ( ~ ( ord_less @ real @ ( zero_zero @ real ) @ SY1807 )
| ( ( power_power @ real @ SY1807 @ SV513 )
!= SV153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2266]) ).
thf(2680,plain,
! [SV154: $i,SV514: $i] :
( ( ! [SY1808: $i,SY1809: $i] :
( ~ ( zcong @ SV514 @ SY1808 @ SY1809 )
| ( zcong @ ( times_times @ int @ SV154 @ SV514 ) @ ( times_times @ int @ SV154 @ SY1808 ) @ SY1809 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2267]) ).
thf(2681,plain,
! [SV155: $i] :
( ( ( ~ ( linordered_semidom @ SV155 ) )
= $true )
| ( ( ! [SY1290: $i,SY1291: $i,SY1292: $i] :
( ~ ( ord_less @ SV155 @ ( one_one @ SV155 ) @ SY1292 )
| ~ ( ~ ( ~ ( ord_less @ SV155 @ ( power_power @ SV155 @ SY1292 @ SY1290 ) @ ( power_power @ SV155 @ SY1292 @ SY1291 ) )
| ( ord_less @ nat @ SY1290 @ SY1291 ) )
| ~ ( ~ ( ord_less @ nat @ SY1290 @ SY1291 )
| ( ord_less @ SV155 @ ( power_power @ SV155 @ SY1292 @ SY1290 ) @ ( power_power @ SV155 @ SY1292 @ SY1291 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2268]) ).
thf(2682,plain,
! [SV156: $i] :
( ( ( ~ ( comm_semiring_1 @ SV156 ) )
= $true )
| ( ( ! [SY1293: $i,SY1294: $i] :
( ( power_power @ SV156 @ SY1293 @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SY1294 ) )
= ( times_times @ SV156 @ ( power_power @ SV156 @ SY1293 @ SY1294 ) @ ( power_power @ SV156 @ SY1293 @ SY1294 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2269]) ).
thf(2683,plain,
! [SV157: $i] :
( ( ( ~ ( comm_semiring_1 @ SV157 ) )
= $true )
| ( ( ! [SY1295: $i] :
( ( plus_plus @ SV157 @ SY1295 @ ( zero_zero @ SV157 ) )
= ( ti @ SV157 @ SY1295 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2270]) ).
thf(2684,plain,
! [SV158: $i,SV515: $i] :
( ( ! [SY1810: $i] :
( ~ ( dvd_dvd @ nat @ SV515 @ SY1810 )
| ( dvd_dvd @ nat @ ( times_times @ nat @ SV515 @ SV158 ) @ ( times_times @ nat @ SY1810 @ SV158 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2271]) ).
thf(2685,plain,
! [SV516: $i,SV159: $i] :
( ( ~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SV159 ) @ ( bit0 @ SV516 ) )
| ( ord_less @ int @ SV159 @ SV516 ) )
| ~ ( ~ ( ord_less @ int @ SV159 @ SV516 )
| ( ord_less_eq @ int @ ( bit1 @ SV159 ) @ ( bit0 @ SV516 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2272]) ).
thf(2686,plain,
! [SV517: $i,SV160: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ int @ SV160 @ ( plus_plus @ int @ SV517 @ ( one_one @ int ) ) )
| ( ord_less_eq @ int @ SV160 @ SV517 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV160 @ SV517 )
| ( ord_less @ int @ SV160 @ ( plus_plus @ int @ SV517 @ ( one_one @ int ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2273]) ).
thf(2687,plain,
! [SV518: $i,SV161: $i] :
( ( ! [SY1811: $i] :
( ~ ( ord_less @ int @ ( plus_plus @ int @ ( times_times @ int @ SV161 @ SV518 ) @ SY1811 ) @ ( zero_zero @ int ) )
| ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SY1811 )
| ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV161 )
| ( ord_less_eq @ int @ SV518 @ ( zero_zero @ int ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2274]) ).
thf(2688,plain,
! [SV519: $i,SV162: $i] :
( ( ( bit0 @ SV162 )
!= ( bit1 @ SV519 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2276]) ).
thf(2689,plain,
! [SV520: $i,SV163: $i] :
( ( ! [SY1812: $i] :
~ ( ~ ( ~ ( zcong @ SV163 @ SV520 @ ( ti @ int @ SY1812 ) )
| ( zcong @ SV163 @ SV520 @ SY1812 ) )
| ~ ( ~ ( zcong @ SV163 @ SV520 @ SY1812 )
| ( zcong @ SV163 @ SV520 @ ( ti @ int @ SY1812 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2277]) ).
thf(2690,plain,
! [SV164: $i,SV521: $i] :
( ( ! [SY1813: $i,SY1814: $i,SY1815: $i] :
( ~ ( dvd_dvd @ int @ SY1814 @ SY1815 )
| ~ ( ~ ( ~ ( dvd_dvd @ int @ SY1814 @ ( plus_plus @ int @ SV521 @ SY1813 ) )
| ( dvd_dvd @ int @ SY1814 @ ( plus_plus @ int @ ( plus_plus @ int @ SV521 @ ( times_times @ int @ SV164 @ SY1815 ) ) @ SY1813 ) ) )
| ~ ( ~ ( dvd_dvd @ int @ SY1814 @ ( plus_plus @ int @ ( plus_plus @ int @ SV521 @ ( times_times @ int @ SV164 @ SY1815 ) ) @ SY1813 ) )
| ( dvd_dvd @ int @ SY1814 @ ( plus_plus @ int @ SV521 @ SY1813 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2278]) ).
thf(2691,plain,
! [SV165: $i] :
( ( ( ~ ( number_ring @ SV165 ) )
= $true )
| ( ( ! [SY1309: $i,SY1310: $i,SY1311: $i] :
( ( plus_plus @ SV165 @ ( number_number_of @ SV165 @ SY1309 ) @ ( plus_plus @ SV165 @ ( number_number_of @ SV165 @ SY1310 ) @ SY1311 ) )
= ( plus_plus @ SV165 @ ( number_number_of @ SV165 @ ( plus_plus @ int @ SY1309 @ SY1310 ) ) @ SY1311 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2279]) ).
thf(2692,plain,
! [SV166: $i] :
( ( ( ~ ( linordered_idom @ SV166 ) )
= $true )
| ( ( ! [SY1312: $i,SY1313: $i] : ( ord_less_eq @ SV166 @ ( zero_zero @ SV166 ) @ ( power_power @ SV166 @ SY1312 @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SY1313 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2280]) ).
thf(2693,plain,
! [SV522: $i,SV167: $i] :
( ( ! [SY1816: $i,SY1817: $i,SY1818: $i] :
( ~ ( zcong @ SY1816 @ SY1817 @ SY1818 )
| ~ ( zcong @ SV167 @ SV522 @ SY1818 )
| ( zcong @ ( minus_minus @ int @ SY1816 @ SV167 ) @ ( minus_minus @ int @ SY1817 @ SV522 ) @ SY1818 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2281]) ).
thf(2694,plain,
! [SV168: $i] :
( ( ( ~ ~ ( ~ ( number @ SV168 )
| ~ ( semiring @ SV168 ) ) )
= $true )
| ( ( ! [SY1318: $i,SY1319: $i,SY1320: $i] :
( ( times_times @ SV168 @ ( plus_plus @ SV168 @ SY1318 @ SY1319 ) @ ( number_number_of @ SV168 @ SY1320 ) )
= ( plus_plus @ SV168 @ ( times_times @ SV168 @ SY1318 @ ( number_number_of @ SV168 @ SY1320 ) ) @ ( times_times @ SV168 @ SY1319 @ ( number_number_of @ SV168 @ SY1320 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2282]) ).
thf(2695,plain,
! [SV523: $i,SV169: $i] :
( ( ~ ( ~ ( ( ( plus_plus @ real @ ( power_power @ real @ SV169 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ real @ SV523 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ real ) )
| ~ ( ( SV169
!= ( zero_zero @ real ) )
| ( SV523
!= ( zero_zero @ real ) ) ) )
| ~ ( ~ ~ ( ( SV169
!= ( zero_zero @ real ) )
| ( SV523
!= ( zero_zero @ real ) ) )
| ( ( plus_plus @ real @ ( power_power @ real @ SV169 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ real @ SV523 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ real ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2283]) ).
thf(2696,plain,
! [SV524: $i,SV170: $i] :
( ( ! [SY1819: $i] :
( ~ ( dvd_dvd @ nat @ ( power_power @ nat @ SV170 @ SV524 ) @ ( power_power @ nat @ SV170 @ SY1819 ) )
| ~ ( ord_less @ nat @ ( one_one @ nat ) @ SV170 )
| ( ord_less_eq @ nat @ SV524 @ SY1819 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2284]) ).
thf(2697,plain,
! [SV171: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ pls @ ( bit0 @ SV171 ) )
| ( ord_less_eq @ int @ pls @ SV171 ) )
| ~ ( ~ ( ord_less_eq @ int @ pls @ SV171 )
| ( ord_less_eq @ int @ pls @ ( bit0 @ SV171 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2285]) ).
thf(2698,plain,
! [SV525: $i,SV172: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ int @ SV172 @ SV525 )
| ( ord_less @ int @ ( minus_minus @ int @ SV172 @ SV525 ) @ ( zero_zero @ int ) ) )
| ~ ( ~ ( ord_less @ int @ ( minus_minus @ int @ SV172 @ SV525 ) @ ( zero_zero @ int ) )
| ( ord_less @ int @ SV172 @ SV525 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2286]) ).
thf(2699,plain,
! [SV173: $i] :
( ( ( ~ ( number_ring @ SV173 ) )
= $true )
| ( ( ! [SY1325: $i] :
( ( power_power @ SV173 @ ( number_number_of @ SV173 @ min ) @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SY1325 ) )
= ( one_one @ SV173 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2287]) ).
thf(2700,plain,
! [SV174: $i] :
( ( ( ~ ( ring @ SV174 ) )
= $true )
| ( ( ! [SY1326: $i,SY1327: $i,SY1328: $i,SY1329: $i] :
( ( minus_minus @ SV174 @ ( times_times @ SV174 @ SY1326 @ SY1327 ) @ ( times_times @ SV174 @ SY1328 @ SY1329 ) )
= ( plus_plus @ SV174 @ ( times_times @ SV174 @ SY1326 @ ( minus_minus @ SV174 @ SY1327 @ SY1329 ) ) @ ( times_times @ SV174 @ ( minus_minus @ SV174 @ SY1326 @ SY1328 ) @ SY1329 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2288]) ).
thf(2701,plain,
! [SV175: $i] :
( ( ( ~ ( semiri456707255roduct @ SV175 ) )
= $true )
| ( ( ! [SY1330: $i,SY1331: $i,SY1332: $i,SY1333: $i] :
~ ( ~ ( ~ ~ ( ~ ( ( ( ti @ SV175 @ SY1332 )
!= ( ti @ SV175 @ SY1333 ) ) )
| ~ ( ( ( ti @ SV175 @ SY1330 )
!= ( ti @ SV175 @ SY1331 ) ) ) )
| ( ( plus_plus @ SV175 @ ( times_times @ SV175 @ SY1332 @ SY1330 ) @ ( times_times @ SV175 @ SY1333 @ SY1331 ) )
!= ( plus_plus @ SV175 @ ( times_times @ SV175 @ SY1332 @ SY1331 ) @ ( times_times @ SV175 @ SY1333 @ SY1330 ) ) ) )
| ~ ( ~ ( ( ( plus_plus @ SV175 @ ( times_times @ SV175 @ SY1332 @ SY1330 ) @ ( times_times @ SV175 @ SY1333 @ SY1331 ) )
!= ( plus_plus @ SV175 @ ( times_times @ SV175 @ SY1332 @ SY1331 ) @ ( times_times @ SV175 @ SY1333 @ SY1330 ) ) ) )
| ~ ( ~ ( ( ( ti @ SV175 @ SY1332 )
!= ( ti @ SV175 @ SY1333 ) ) )
| ~ ( ( ( ti @ SV175 @ SY1330 )
!= ( ti @ SV175 @ SY1331 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2289]) ).
thf(2702,plain,
! [SV176: $i,SV526: $i] :
( ( ~ ( number @ SV526 )
| ( ( ti @ SV526 @ ( number_number_of @ SV526 @ SV176 ) )
= ( number_number_of @ SV526 @ SV176 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2290]) ).
thf(2703,plain,
! [SV177: $i] :
( ( ~ ( ~ ( ord_less @ int @ pls @ ( bit0 @ SV177 ) )
| ( ord_less @ int @ pls @ SV177 ) )
| ~ ( ~ ( ord_less @ int @ pls @ SV177 )
| ( ord_less @ int @ pls @ ( bit0 @ SV177 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2291]) ).
thf(2704,plain,
! [SV178: $i,SV527: $i] :
( ( ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV527 )
| ~ ( ord_less @ int @ SV527 @ SV178 )
| ~ ( dvd_dvd @ int @ SV178 @ SV527 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2292]) ).
thf(2705,plain,
! [SV179: $i] :
( ( ( ~ ( linordered_semidom @ SV179 ) )
= $true )
| ( ( ! [SY1336: $i,SY1337: $i,SY1338: $i] :
( ~ ( ord_less @ SV179 @ ( one_one @ SV179 ) @ SY1338 )
| ~ ( ord_less @ SV179 @ ( power_power @ SV179 @ SY1338 @ SY1336 ) @ ( power_power @ SV179 @ SY1338 @ SY1337 ) )
| ( ord_less @ nat @ SY1336 @ SY1337 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2293]) ).
thf(2706,plain,
! [SV180: $i] :
( ( ( ~ ( dvd @ SV180 ) )
= $true )
| ( ( ! [SY1339: $i,SY1340: $i,SY1341: $i] :
( ( SY1339
!= ( times_times @ SV180 @ SY1340 @ SY1341 ) )
| ( dvd_dvd @ SV180 @ SY1340 @ SY1339 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2294]) ).
thf(2707,plain,
! [SV181: $i] :
( ( min
= ( bit0 @ SV181 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2295]) ).
thf(2708,plain,
! [SV528: $i,SV182: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SV182 ) @ ( bit1 @ SV528 ) )
| ( ord_less @ int @ SV182 @ SV528 ) )
| ~ ( ~ ( ord_less @ int @ SV182 @ SV528 )
| ( ord_less @ int @ ( bit1 @ SV182 ) @ ( bit1 @ SV528 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2296]) ).
thf(2709,plain,
! [SV183: $i] :
( ( ( ~ ( number_ring @ SV183 ) )
= $true )
| ( ( ( number_number_of @ SV183 @ pls )
= ( zero_zero @ SV183 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2297]) ).
thf(2710,plain,
! [SV184: $i] :
( ( ( ~ ( comm_semiring_1 @ SV184 ) )
= $true )
| ( ( ! [SY1343: $i] :
( ( times_times @ SV184 @ SY1343 @ ( one_one @ SV184 ) )
= ( ti @ SV184 @ SY1343 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2298]) ).
thf(2711,plain,
! [SV185: $i] :
( ( ( ~ ( comm_semiring_1 @ SV185 ) )
= $true )
| ( ( ! [SY1344: $i,SY1345: $i,SY1346: $i] :
( ( times_times @ SV185 @ ( power_power @ SV185 @ SY1344 @ SY1345 ) @ ( power_power @ SV185 @ SY1344 @ SY1346 ) )
= ( power_power @ SV185 @ SY1344 @ ( plus_plus @ nat @ SY1345 @ SY1346 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2299]) ).
thf(2712,plain,
! [SV529: $i,SV186: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SV186 ) @ ( bit0 @ SV529 ) )
| ( ord_less @ int @ SV186 @ SV529 ) )
| ~ ( ~ ( ord_less @ int @ SV186 @ SV529 )
| ( ord_less @ int @ ( bit0 @ SV186 ) @ ( bit0 @ SV529 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2300]) ).
thf(2713,plain,
! [SV530: $i,SV187: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ int @ SV187 @ SV530 )
| ~ ( ~ ( ord_less_eq @ int @ SV187 @ SV530 )
| ~ ( ( ( ti @ int @ SV187 )
!= ( ti @ int @ SV530 ) ) ) ) )
| ~ ( ~ ~ ( ~ ( ord_less_eq @ int @ SV187 @ SV530 )
| ~ ( ( ( ti @ int @ SV187 )
!= ( ti @ int @ SV530 ) ) ) )
| ( ord_less @ int @ SV187 @ SV530 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2301]) ).
thf(2714,plain,
! [SV188: $i,SV531: $i] :
( ( ~ ( number @ SV531 )
| ( ( number_number_of @ SV531 @ ( ti @ int @ SV188 ) )
= ( number_number_of @ SV531 @ SV188 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2302]) ).
thf(2715,plain,
! [SV189: $i] :
( ( ( ~ ( linord219039673up_add @ SV189 ) )
= $true )
| ( ( ! [SY1350: $i] :
~ ( ~ ( ( ( plus_plus @ SV189 @ SY1350 @ SY1350 )
!= ( zero_zero @ SV189 ) )
| ( ( ti @ SV189 @ SY1350 )
= ( zero_zero @ SV189 ) ) )
| ~ ( ( ( ti @ SV189 @ SY1350 )
!= ( zero_zero @ SV189 ) )
| ( ( plus_plus @ SV189 @ SY1350 @ SY1350 )
= ( zero_zero @ SV189 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2303]) ).
thf(2716,plain,
! [SV532: $i,SV190: $i] :
( ( ! [SY1820: $i] :
( ~ ( ord_less @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ SY1820 )
| ~ ( zcong @ ( power_power @ int @ ( number_number_of @ int @ min ) @ SV190 ) @ ( power_power @ int @ ( number_number_of @ int @ min ) @ SV532 ) @ SY1820 )
| ( ( power_power @ int @ ( number_number_of @ int @ min ) @ SV190 )
= ( power_power @ int @ ( number_number_of @ int @ min ) @ SV532 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2304]) ).
thf(2717,plain,
! [SV533: $i,SV191: $i] :
( ( ! [SY1821: $i] :
~ ( ~ ( ~ ( dvd_dvd @ nat @ ( times_times @ nat @ SV191 @ SV533 ) @ ( times_times @ nat @ SY1821 @ SV533 ) )
| ( SV533
= ( zero_zero @ nat ) )
| ( dvd_dvd @ nat @ SV191 @ SY1821 ) )
| ~ ( ~ ( ( SV533
= ( zero_zero @ nat ) )
| ( dvd_dvd @ nat @ SV191 @ SY1821 ) )
| ( dvd_dvd @ nat @ ( times_times @ nat @ SV191 @ SV533 ) @ ( times_times @ nat @ SY1821 @ SV533 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2305]) ).
thf(2718,plain,
! [SV192: $i] :
( ( ( ~ ( linordered_semidom @ SV192 ) )
= $true )
| ( ( ! [SY1355: $i,SY1356: $i] :
( ~ ( ord_less_eq @ SV192 @ ( zero_zero @ SV192 ) @ SY1356 )
| ( ord_less_eq @ SV192 @ ( zero_zero @ SV192 ) @ ( power_power @ SV192 @ SY1356 @ SY1355 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2306]) ).
thf(2719,plain,
! [SV193: $i] :
( ( ( ~ ( linord581940658strict @ SV193 ) )
= $true )
| ( ( ! [SY1357: $i,SY1358: $i] :
~ ( ~ ( ( ( plus_plus @ SV193 @ ( times_times @ SV193 @ SY1357 @ SY1357 ) @ ( times_times @ SV193 @ SY1358 @ SY1358 ) )
!= ( zero_zero @ SV193 ) )
| ~ ( ( ( ti @ SV193 @ SY1357 )
!= ( zero_zero @ SV193 ) )
| ( ( ti @ SV193 @ SY1358 )
!= ( zero_zero @ SV193 ) ) ) )
| ~ ( ~ ~ ( ( ( ti @ SV193 @ SY1357 )
!= ( zero_zero @ SV193 ) )
| ( ( ti @ SV193 @ SY1358 )
!= ( zero_zero @ SV193 ) ) )
| ( ( plus_plus @ SV193 @ ( times_times @ SV193 @ SY1357 @ SY1357 ) @ ( times_times @ SV193 @ SY1358 @ SY1358 ) )
= ( zero_zero @ SV193 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2307]) ).
thf(2720,plain,
! [SV194: $i] :
( ( ( ~ ( linordered_semidom @ SV194 ) )
= $true )
| ( ( ! [SY1359: $i,SY1360: $i,SY1361: $i] :
( ~ ( ord_less @ SV194 @ ( one_one @ SV194 ) @ SY1361 )
| ~ ( ~ ( ( ( power_power @ SV194 @ SY1361 @ SY1359 )
!= ( power_power @ SV194 @ SY1361 @ SY1360 ) )
| ( SY1359 = SY1360 ) )
| ~ ( ( SY1359 != SY1360 )
| ( ( power_power @ SV194 @ SY1361 @ SY1359 )
= ( power_power @ SV194 @ SY1361 @ SY1360 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2308]) ).
thf(2721,plain,
! [SV195: $i] :
( ( ( ~ ( linordered_ring @ SV195 ) )
= $true )
| ( ( ! [SY1362: $i,SY1363: $i] :
~ ( ord_less @ SV195 @ ( plus_plus @ SV195 @ ( times_times @ SV195 @ SY1362 @ SY1362 ) @ ( times_times @ SV195 @ SY1363 @ SY1363 ) ) @ ( zero_zero @ SV195 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2309]) ).
thf(2722,plain,
! [SV196: $i,SV534: $i] :
( ( ! [SY1822: $i] :
( ~ ( zprime @ SY1822 )
| ~ ~ ( zcong @ SV534 @ ( zero_zero @ int ) @ SY1822 )
| ~ ~ ( zcong @ SV196 @ ( zero_zero @ int ) @ SY1822 )
| ~ ( zcong @ ( times_times @ int @ SV534 @ SV196 ) @ ( zero_zero @ int ) @ SY1822 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2310]) ).
thf(2723,plain,
! [SV197: $i] :
( ( ( ~ ( number_semiring @ SV197 ) )
= $true )
| ( ( ! [SY1366: $i,SY1367: $i] :
( ( power_power @ SV197 @ ( plus_plus @ SV197 @ SY1366 @ SY1367 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ SV197 @ ( plus_plus @ SV197 @ ( power_power @ SV197 @ SY1366 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV197 @ SY1367 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times @ SV197 @ ( times_times @ SV197 @ ( number_number_of @ SV197 @ ( bit0 @ ( bit1 @ pls ) ) ) @ SY1366 ) @ SY1367 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2311]) ).
thf(2724,plain,
! [SV198: $i] :
( ( ( ~ ( number_ring @ SV198 ) )
= $true )
| ( ( ! [SY1368: $i,SY1369: $i] :
( ( times_times @ SV198 @ ( number_number_of @ SV198 @ SY1368 ) @ ( number_number_of @ SV198 @ SY1369 ) )
= ( number_number_of @ SV198 @ ( times_times @ int @ SY1368 @ SY1369 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2312]) ).
thf(2725,plain,
! [SV199: $i] :
( ( ( ~ ( linord581940658strict @ SV199 ) )
= $true )
| ( ( ! [SY1370: $i,SY1371: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ ( times_times @ SV199 @ SY1370 @ SY1371 ) )
| ~ ( ~ ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ SY1370 )
| ~ ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ SY1371 ) )
| ~ ( ~ ( ord_less_eq @ SV199 @ SY1370 @ ( zero_zero @ SV199 ) )
| ~ ( ord_less_eq @ SV199 @ SY1371 @ ( zero_zero @ SV199 ) ) ) )
| ~ ( ~ ( ~ ( ~ ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ SY1370 )
| ~ ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ SY1371 ) )
| ~ ( ~ ( ord_less_eq @ SV199 @ SY1370 @ ( zero_zero @ SV199 ) )
| ~ ( ord_less_eq @ SV199 @ SY1371 @ ( zero_zero @ SV199 ) ) ) )
| ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ ( times_times @ SV199 @ SY1370 @ SY1371 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2313]) ).
thf(2726,plain,
! [SV200: $i] :
( ( ( ~ ( number_ring @ SV200 ) )
= $true )
| ( ( ! [SY1372: $i] :
( ( times_times @ SV200 @ ( number_number_of @ SV200 @ ( bit1 @ pls ) ) @ SY1372 )
= ( ti @ SV200 @ SY1372 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2314]) ).
thf(2727,plain,
! [SV201: $i] :
( ( ( ~ ( linordered_semidom @ SV201 ) )
= $true )
| ( ( ! [SY1373: $i,SY1374: $i] :
( ~ ( ord_less @ SV201 @ ( one_one @ SV201 ) @ SY1374 )
| ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ SY1373 )
| ( ord_less @ SV201 @ ( one_one @ SV201 ) @ ( power_power @ SV201 @ SY1374 @ SY1373 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2315]) ).
thf(2728,plain,
! [SV202: $i] :
( ( ( ~ ~ ( ~ ( number_ring @ SV202 )
| ~ ( linordered_idom @ SV202 ) ) )
= $true )
| ( ( ! [SY1375: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV202 @ ( one_one @ SV202 ) @ ( number_number_of @ SV202 @ SY1375 ) )
| ( ord_less_eq @ int @ ( bit1 @ pls ) @ SY1375 ) )
| ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ pls ) @ SY1375 )
| ( ord_less_eq @ SV202 @ ( one_one @ SV202 ) @ ( number_number_of @ SV202 @ SY1375 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2316]) ).
thf(2729,plain,
! [SV203: $i,SV535: $i] :
( ( ! [SY1823: $i] :
( ~ ( ord_less @ int @ ( zero_zero @ int ) @ SY1823 )
| ~ ( ord_less @ int @ SY1823 @ SV535 )
| ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV203 )
| ~ ( ord_less @ int @ SV203 @ SY1823 )
| ~ ( zcong @ SY1823 @ SV203 @ SV535 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2317]) ).
thf(2730,plain,
( ( ( plus_plus @ int @ ( power_power @ int @ s @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( one_one @ int ) )
!= ( times_times @ int @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) @ sK2_SX0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[2318]) ).
thf(2731,plain,
! [SV204: $i] :
( ( ( ~ ( monoid_mult @ SV204 ) )
= $true )
| ( ( ! [SY1378: $i] :
( ( power_power @ SV204 @ SY1378 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times @ SV204 @ SY1378 @ SY1378 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2319]) ).
thf(2732,plain,
! [SV205: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SV205 ) @ min )
| ( ord_less_eq @ int @ SV205 @ min ) )
| ~ ( ~ ( ord_less_eq @ int @ SV205 @ min )
| ( ord_less @ int @ ( bit0 @ SV205 ) @ min ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2320]) ).
thf(2733,plain,
! [SV536: $i,SV206: $i] :
( ( ! [SY1824: $i,SY1825: $i,SY1826: $i] :
( ~ ( zcong @ SY1824 @ SY1825 @ SY1826 )
| ~ ( zcong @ SV206 @ SV536 @ SY1826 )
| ( zcong @ ( plus_plus @ int @ SY1824 @ SV206 ) @ ( plus_plus @ int @ SY1825 @ SV536 ) @ SY1826 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2321]) ).
thf(2734,plain,
! [SV207: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ SV207 ) @ SV207 ) @ ( zero_zero @ int ) )
| ( ord_less @ int @ SV207 @ ( zero_zero @ int ) ) )
| ~ ( ~ ( ord_less @ int @ SV207 @ ( zero_zero @ int ) )
| ( ord_less @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ SV207 ) @ SV207 ) @ ( zero_zero @ int ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2322]) ).
thf(2735,plain,
! [SV208: $i] :
( ( ~ ( ~ ( twoSqu420862341sum2sq @ ( ti @ int @ SV208 ) )
| ( twoSqu420862341sum2sq @ SV208 ) )
| ~ ( ~ ( twoSqu420862341sum2sq @ SV208 )
| ( twoSqu420862341sum2sq @ ( ti @ int @ SV208 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2323]) ).
thf(2736,plain,
! [SV209: $i,SV537: $i] :
( ( ! [SY1827: $i] :
( ~ ( dvd_dvd @ nat @ SV537 @ SY1827 )
| ~ ( dvd_dvd @ nat @ SV537 @ ( plus_plus @ nat @ SY1827 @ SV209 ) )
| ( dvd_dvd @ nat @ SV537 @ SV209 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2324]) ).
thf(2737,plain,
! [SV210: $i] :
( ( ~ ( ( ( bit0 @ SV210 )
!= pls )
| ( ( ti @ int @ SV210 )
= pls ) )
| ~ ( ( ( ti @ int @ SV210 )
!= pls )
| ( ( bit0 @ SV210 )
= pls ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2325]) ).
thf(2738,plain,
! [SV211: $i] :
( ( ( ~ ( comm_semiring_1 @ SV211 ) )
= $true )
| ( ( ! [SY1385: $i,SY1386: $i] : ( dvd_dvd @ SV211 @ SY1385 @ ( times_times @ SV211 @ SY1386 @ SY1385 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2326]) ).
thf(2739,plain,
! [SV212: $i] :
( ( ( ~ ( number_ring @ SV212 ) )
= $true )
| ( ( ! [SY1387: $i,SY1388: $i] :
( ( plus_plus @ SV212 @ ( number_number_of @ SV212 @ SY1387 ) @ ( number_number_of @ SV212 @ SY1388 ) )
= ( number_number_of @ SV212 @ ( plus_plus @ int @ SY1387 @ SY1388 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2327]) ).
thf(2740,plain,
! [SV213: $i] :
( ( ( ~ ~ ( ~ ( number_ring @ SV213 )
| ~ ( ring_char_0 @ SV213 ) ) )
= $true )
| ( ( ! [SY1389: $i,SY1390: $i] :
~ ( ~ ( ( ( number_number_of @ SV213 @ SY1389 )
!= ( number_number_of @ SV213 @ SY1390 ) )
| ( ( ti @ int @ SY1389 )
= ( ti @ int @ SY1390 ) ) )
| ~ ( ( ( ti @ int @ SY1389 )
!= ( ti @ int @ SY1390 ) )
| ( ( number_number_of @ SV213 @ SY1389 )
= ( number_number_of @ SV213 @ SY1390 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2328]) ).
thf(2741,plain,
! [SV538: $i,SV214: $i] :
( ( ! [SY1828: $i,SY1829: $i] :
( ( SV214
!= ( plus_plus @ nat @ ( times_times @ nat @ SV538 @ SY1828 ) @ SY1829 ) )
| ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ SY1829 )
| ~ ( ord_less @ nat @ SY1829 @ SY1828 )
| ~ ( dvd_dvd @ nat @ SY1828 @ SV214 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2329]) ).
thf(2742,plain,
! [SV539: $i,SV215: $i] :
( ( ! [SY1830: $i] :
( ~ ( dvd_dvd @ nat @ ( power_power @ nat @ SV215 @ SV539 ) @ ( power_power @ nat @ SY1830 @ SV539 ) )
| ~ ( ( SV539
!= ( zero_zero @ nat ) ) )
| ( dvd_dvd @ nat @ SV215 @ SY1830 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2330]) ).
thf(2743,plain,
! [SV216: $i] :
( ( ( ~ ( zero_neq_one @ SV216 ) )
= $true )
| ( ( ( zero_zero @ SV216 )
!= ( one_one @ SV216 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2331]) ).
thf(2744,plain,
! [SV217: $i] :
( ( ( ~ ( comm_semiring_1 @ SV217 ) )
= $true )
| ( ( ! [SY1396: $i] :
( ( plus_plus @ SV217 @ ( zero_zero @ SV217 ) @ SY1396 )
= ( ti @ SV217 @ SY1396 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2332]) ).
thf(2745,plain,
! [SV218: $i] :
( ( ( ~ ~ ( ~ ( number_ring @ SV218 )
| ~ ( linordered_idom @ SV218 ) ) )
= $true )
| ( ( ! [SY1397: $i,SY1398: $i] :
~ ( ~ ( ~ ( ord_less @ SV218 @ ( number_number_of @ SV218 @ SY1397 ) @ ( number_number_of @ SV218 @ SY1398 ) )
| ( ord_less @ int @ SY1397 @ SY1398 ) )
| ~ ( ~ ( ord_less @ int @ SY1397 @ SY1398 )
| ( ord_less @ SV218 @ ( number_number_of @ SV218 @ SY1397 ) @ ( number_number_of @ SV218 @ SY1398 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2333]) ).
thf(2746,plain,
! [SV219: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( bit0 @ SV219 ) @ min )
| ( ord_less_eq @ int @ SV219 @ min ) )
| ~ ( ~ ( ord_less_eq @ int @ SV219 @ min )
| ( ord_less_eq @ int @ ( bit0 @ SV219 ) @ min ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2334]) ).
thf(2747,plain,
! [SV220: $i] :
( ( ( ~ ( comm_semiring_1 @ SV220 ) )
= $true )
| ( ( ! [SY1399: $i,SY1400: $i,SY1401: $i,SY1402: $i] :
( ~ ( dvd_dvd @ SV220 @ ( power_power @ SV220 @ SY1400 @ SY1401 ) @ SY1402 )
| ~ ( ord_less_eq @ nat @ SY1399 @ SY1401 )
| ( dvd_dvd @ SV220 @ ( power_power @ SV220 @ SY1400 @ SY1399 ) @ SY1402 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2335]) ).
thf(2748,plain,
! [SV540: $i,SV221: $i] :
( ( ! [SY1831: $i] :
( ~ ( ord_less @ real @ ( zero_zero @ real ) @ SY1831 )
| ~ ( ord_less @ real @ SV221 @ SV540 )
| ( ord_less @ real @ ( times_times @ real @ SY1831 @ SV221 ) @ ( times_times @ real @ SY1831 @ SV540 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2336]) ).
thf(2749,plain,
! [SV222: $i] :
( ( ( ~ ( comm_semiring_1 @ SV222 ) )
= $true )
| ( ( ! [SY1405: $i,SY1406: $i,SY1407: $i] :
( ~ ( dvd_dvd @ SV222 @ SY1406 @ SY1407 )
| ( dvd_dvd @ SV222 @ SY1406 @ ( times_times @ SV222 @ SY1405 @ SY1407 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2337]) ).
thf(2750,plain,
! [SV541: $i,SV223: $i] :
( ( ! [SY1832: $i] :
( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ SY1832 )
| ~ ( ord_less @ nat @ ( power_power @ nat @ SY1832 @ SV223 ) @ ( power_power @ nat @ SY1832 @ SV541 ) )
| ( ord_less @ nat @ SV223 @ SV541 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2338]) ).
thf(2751,plain,
! [SV224: $i,SV542: $i] :
( ( ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV542 )
| ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV224 )
| ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ SV542 @ SV224 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2339]) ).
thf(2752,plain,
! [SV225: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( one_one @ int ) @ SV225 )
| ( ord_less @ int @ ( zero_zero @ int ) @ SV225 ) )
| ~ ( ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV225 )
| ( ord_less_eq @ int @ ( one_one @ int ) @ SV225 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2340]) ).
thf(2753,plain,
! [SV226: $i] :
( ( ( ~ ( comm_semiring_1 @ SV226 ) )
= $true )
| ( ( ! [SY1411: $i,SY1412: $i,SY1413: $i] :
( ~ ( dvd_dvd @ SV226 @ ( times_times @ SV226 @ SY1411 @ SY1412 ) @ SY1413 )
| ( dvd_dvd @ SV226 @ SY1411 @ SY1413 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2341]) ).
thf(2754,plain,
! [SV543: $i,SV227: $i] :
( ( ! [SY1833: $i] :
( ~ ( mult_zero @ SY1833 )
| ( ( times_times @ SY1833 @ ( ti @ SY1833 @ SV227 ) @ SV543 )
= ( times_times @ SY1833 @ SV227 @ SV543 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2342]) ).
thf(2755,plain,
! [SV544: $i,SV228: $i] :
( ( ! [SY1834: $i] :
( ~ ( power @ SY1834 )
| ( ( ti @ SY1834 @ ( times_times @ SY1834 @ SV228 @ SV544 ) )
= ( times_times @ SY1834 @ SV228 @ SV544 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2343]) ).
thf(2756,plain,
! [SV545: $i,SV229: $i] :
( ( ! [SY1835: $i] :
( ~ ( semiring @ SY1835 )
| ( ( plus_plus @ SY1835 @ ( ti @ SY1835 @ SV229 ) @ SV545 )
= ( plus_plus @ SY1835 @ SV229 @ SV545 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2344]) ).
thf(2757,plain,
! [SV230: $i] :
( ( ( ~ ( linordered_ring @ SV230 ) )
= $true )
| ( ( ! [SY1420: $i,SY1421: $i] : ( ord_less_eq @ SV230 @ ( zero_zero @ SV230 ) @ ( plus_plus @ SV230 @ ( times_times @ SV230 @ SY1420 @ SY1420 ) @ ( times_times @ SV230 @ SY1421 @ SY1421 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2345]) ).
thf(2758,plain,
! [SV546: $i,SV231: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SV231 ) @ ( bit1 @ SV546 ) )
| ( ord_less_eq @ int @ SV231 @ SV546 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV231 @ SV546 )
| ( ord_less @ int @ ( bit0 @ SV231 ) @ ( bit1 @ SV546 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2346]) ).
thf(2759,plain,
! [SV232: $i] :
( ( ( ~ ( zero_neq_one @ SV232 ) )
= $true )
| ( ( ( one_one @ SV232 )
!= ( zero_zero @ SV232 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2347]) ).
thf(2760,plain,
! [SV547: $i,SV233: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ SV233 @ ( number_number_of @ nat @ SV547 ) ) )
| ( ( number_number_of @ nat @ SV547 )
= ( zero_zero @ nat ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ SV233 ) )
| ~ ( ~ ( ( ( number_number_of @ nat @ SV547 )
= ( zero_zero @ nat ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ SV233 ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ SV233 @ ( number_number_of @ nat @ SV547 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2348]) ).
thf(2761,plain,
! [SV234: $i] :
( ( ( ~ ~ ( ~ ( number @ SV234 )
| ~ ( semiring @ SV234 ) ) )
= $true )
| ( ( ! [SY1424: $i,SY1425: $i,SY1426: $i] :
( ( times_times @ SV234 @ ( number_number_of @ SV234 @ SY1424 ) @ ( plus_plus @ SV234 @ SY1425 @ SY1426 ) )
= ( plus_plus @ SV234 @ ( times_times @ SV234 @ ( number_number_of @ SV234 @ SY1424 ) @ SY1425 ) @ ( times_times @ SV234 @ ( number_number_of @ SV234 @ SY1424 ) @ SY1426 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2349]) ).
thf(2762,plain,
! [SV235: $i] :
( ( ( ~ ( ring_1 @ SV235 ) )
= $true )
| ( ( ! [SY1427: $i] :
( ( minus_minus @ SV235 @ ( times_times @ SV235 @ SY1427 @ SY1427 ) @ ( one_one @ SV235 ) )
= ( times_times @ SV235 @ ( plus_plus @ SV235 @ SY1427 @ ( one_one @ SV235 ) ) @ ( minus_minus @ SV235 @ SY1427 @ ( one_one @ SV235 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2350]) ).
thf(2763,plain,
! [SV548: $i,SV236: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SV236 ) @ ( bit1 @ SV548 ) )
| ( ord_less_eq @ int @ SV236 @ SV548 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV236 @ SV548 )
| ( ord_less @ int @ ( bit0 @ SV236 ) @ ( bit1 @ SV548 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2351]) ).
thf(2764,plain,
! [SV237: $i] :
( ( ( ~ ( number @ SV237 ) )
= $true )
| ( ( ! [SY1429: $i,SY1430: $i] :
~ ( ~ ( ( ( number_number_of @ SV237 @ SY1429 )
!= ( ti @ SV237 @ SY1430 ) )
| ( ( ti @ SV237 @ SY1430 )
= ( number_number_of @ SV237 @ SY1429 ) ) )
| ~ ( ( ( ti @ SV237 @ SY1430 )
!= ( number_number_of @ SV237 @ SY1429 ) )
| ( ( number_number_of @ SV237 @ SY1429 )
= ( ti @ SV237 @ SY1430 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2352]) ).
thf(2765,plain,
! [SV238: $i] :
( ( ( ~ ( comm_semiring_1 @ SV238 ) )
= $true )
| ( ( ! [SY1431: $i,SY1432: $i,SY1433: $i] :
( ( plus_plus @ SV238 @ SY1431 @ ( plus_plus @ SV238 @ SY1432 @ SY1433 ) )
= ( plus_plus @ SV238 @ ( plus_plus @ SV238 @ SY1431 @ SY1432 ) @ SY1433 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2354]) ).
thf(2766,plain,
! [SV239: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ min @ ( bit0 @ SV239 ) )
| ( ord_less @ int @ min @ SV239 ) )
| ~ ( ~ ( ord_less @ int @ min @ SV239 )
| ( ord_less_eq @ int @ min @ ( bit0 @ SV239 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2355]) ).
thf(2767,plain,
! [SV549: $i,SV240: $i] :
( ( ! [SY1836: $i,SY1837: $i] :
( ~ ( zprime @ SY1837 )
| ~ ~ ( dvd_dvd @ int @ SY1837 @ SY1836 )
| ~ ( dvd_dvd @ int @ ( power_power @ int @ SY1837 @ SV240 ) @ ( times_times @ int @ SY1836 @ SV549 ) )
| ( dvd_dvd @ int @ ( power_power @ int @ SY1837 @ SV240 ) @ SV549 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2356]) ).
thf(2768,plain,
! [SV241: $i] :
( ( ~ ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ ( number_number_of @ nat @ SV241 ) )
| ( ord_less @ int @ pls @ SV241 ) )
| ~ ( ~ ( ord_less @ int @ pls @ SV241 )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ ( number_number_of @ nat @ SV241 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2357]) ).
thf(2769,plain,
! [SV550: $i,SV242: $i] :
( ( ~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit0 @ SV242 ) @ ( bit1 @ SV550 ) )
| ( ord_less_eq @ int @ SV242 @ SV550 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV242 @ SV550 )
| ( ord_less_eq @ int @ ( bit0 @ SV242 ) @ ( bit1 @ SV550 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2358]) ).
thf(2770,plain,
! [SV551: $i,SV243: $i] :
( ( ! [SY1838: $i] :
( ~ ( power @ SY1838 )
| ( ( times_times @ SY1838 @ ( ti @ SY1838 @ SV243 ) @ SV551 )
= ( times_times @ SY1838 @ SV243 @ SV551 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2359]) ).
thf(2771,plain,
! [SV244: $i] :
( ( ~ ( ~ ( ord_less @ int @ pls @ ( bit1 @ SV244 ) )
| ( ord_less_eq @ int @ pls @ SV244 ) )
| ~ ( ~ ( ord_less_eq @ int @ pls @ SV244 )
| ( ord_less @ int @ pls @ ( bit1 @ SV244 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2360]) ).
thf(2772,plain,
! [SV552: $i,SV245: $i] :
( ( ! [SY1839: $i] :
~ ( ~ ( ~ ( ord_less @ int @ SY1839 @ pls )
| ( ( times_times @ nat @ ( number_number_of @ nat @ SY1839 ) @ ( times_times @ nat @ ( number_number_of @ nat @ SV245 ) @ SV552 ) )
= ( zero_zero @ nat ) ) )
| ~ ( ~ ~ ( ord_less @ int @ SY1839 @ pls )
| ( ( times_times @ nat @ ( number_number_of @ nat @ SY1839 ) @ ( times_times @ nat @ ( number_number_of @ nat @ SV245 ) @ SV552 ) )
= ( times_times @ nat @ ( number_number_of @ nat @ ( times_times @ int @ SY1839 @ SV245 ) ) @ SV552 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2361]) ).
thf(2773,plain,
! [SV553: $i,SV246: $i] :
( ( ! [SY1840: $i] :
( ~ ( dvd @ SY1840 )
| ( ( times_times @ SY1840 @ ( ti @ SY1840 @ SV246 ) @ SV553 )
= ( times_times @ SY1840 @ SV246 @ SV553 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2362]) ).
thf(2774,plain,
! [SV554: $i,SV247: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ SV247 @ SV554 ) )
| ( SV554
= ( zero_zero @ nat ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ SV247 ) )
| ~ ( ~ ( ( SV554
= ( zero_zero @ nat ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ SV247 ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ SV247 @ SV554 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2363]) ).
thf(2775,plain,
! [SV248: $i] :
( ( ( ~ ( number_ring @ SV248 ) )
= $true )
| ( ( ! [SY1445: $i,SY1446: $i,SY1447: $i] :
( ( times_times @ SV248 @ ( number_number_of @ SV248 @ SY1445 ) @ ( times_times @ SV248 @ ( number_number_of @ SV248 @ SY1446 ) @ SY1447 ) )
= ( times_times @ SV248 @ ( number_number_of @ SV248 @ ( times_times @ int @ SY1445 @ SY1446 ) ) @ SY1447 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2364]) ).
thf(2776,plain,
! [SV249: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SV249 ) @ ( zero_zero @ int ) )
| ( ord_less @ int @ SV249 @ ( zero_zero @ int ) ) )
| ~ ( ~ ( ord_less @ int @ SV249 @ ( zero_zero @ int ) )
| ( ord_less @ int @ ( bit1 @ SV249 ) @ ( zero_zero @ int ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2365]) ).
thf(2777,plain,
! [SV250: $i] :
( ( ( ~ ( number_ring @ SV250 ) )
= $true )
| ( ( ! [SY1448: $i] :
( ( plus_plus @ SV250 @ SY1448 @ ( number_number_of @ SV250 @ pls ) )
= ( ti @ SV250 @ SY1448 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2366]) ).
thf(2778,plain,
! [SV555: $i,SV251: $i] :
( ( ! [SY1841: $i] :
( ~ ( power @ SY1841 )
| ( ( power_power @ SY1841 @ SV251 @ ( ti @ nat @ SV555 ) )
= ( power_power @ SY1841 @ SV251 @ SV555 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2367]) ).
thf(2779,plain,
! [SV252: $i] :
( ( ( ~ ( comm_semiring_1 @ SV252 ) )
= $true )
| ( ( ! [SY1451: $i,SY1452: $i,SY1453: $i] :
( ( times_times @ SV252 @ ( times_times @ SV252 @ SY1451 @ SY1452 ) @ SY1453 )
= ( times_times @ SV252 @ SY1451 @ ( times_times @ SV252 @ SY1452 @ SY1453 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2368]) ).
thf(2780,plain,
! [SV556: $i,SV253: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SV253 ) @ ( bit0 @ SV556 ) )
| ( ord_less @ int @ SV253 @ SV556 ) )
| ~ ( ~ ( ord_less @ int @ SV253 @ SV556 )
| ( ord_less @ int @ ( bit1 @ SV253 ) @ ( bit0 @ SV556 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2369]) ).
thf(2781,plain,
! [SV254: $i] :
( ( ( ~ ( comm_semiring_1 @ SV254 ) )
= $true )
| ( ( ! [SY1455: $i,SY1456: $i] :
( ( plus_plus @ SV254 @ SY1455 @ ( times_times @ SV254 @ SY1456 @ SY1455 ) )
= ( times_times @ SV254 @ ( plus_plus @ SV254 @ SY1456 @ ( one_one @ SV254 ) ) @ SY1455 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2370]) ).
thf(2782,plain,
! [SV255: $i] :
( ( ( ~ ( semiri456707255roduct @ SV255 ) )
= $true )
| ( ( ! [SY1457: $i,SY1458: $i,SY1459: $i,SY1460: $i] :
~ ( ~ ( ( ( plus_plus @ SV255 @ ( times_times @ SV255 @ SY1457 @ SY1458 ) @ ( times_times @ SV255 @ SY1459 @ SY1460 ) )
!= ( plus_plus @ SV255 @ ( times_times @ SV255 @ SY1457 @ SY1460 ) @ ( times_times @ SV255 @ SY1459 @ SY1458 ) ) )
| ( ( ti @ SV255 @ SY1457 )
= ( ti @ SV255 @ SY1459 ) )
| ( ( ti @ SV255 @ SY1458 )
= ( ti @ SV255 @ SY1460 ) ) )
| ~ ( ~ ( ( ( ti @ SV255 @ SY1457 )
= ( ti @ SV255 @ SY1459 ) )
| ( ( ti @ SV255 @ SY1458 )
= ( ti @ SV255 @ SY1460 ) ) )
| ( ( plus_plus @ SV255 @ ( times_times @ SV255 @ SY1457 @ SY1458 ) @ ( times_times @ SV255 @ SY1459 @ SY1460 ) )
= ( plus_plus @ SV255 @ ( times_times @ SV255 @ SY1457 @ SY1460 ) @ ( times_times @ SV255 @ SY1459 @ SY1458 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2371]) ).
thf(2783,plain,
! [SV256: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ pls @ ( bit1 @ SV256 ) )
| ( ord_less_eq @ int @ pls @ SV256 ) )
| ~ ( ~ ( ord_less_eq @ int @ pls @ SV256 )
| ( ord_less_eq @ int @ pls @ ( bit1 @ SV256 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2372]) ).
thf(2784,plain,
! [SV557: $i,SV257: $i] :
( ( ! [SY1842: $i,SY1843: $i,SY1844: $i] :
( ~ ( zcong @ SY1842 @ SY1843 @ SY1844 )
| ~ ( ~ ( ~ ( zcong @ SV257 @ ( times_times @ int @ SV557 @ SY1842 ) @ SY1844 )
| ( zcong @ SV257 @ ( times_times @ int @ SV557 @ SY1843 ) @ SY1844 ) )
| ~ ( ~ ( zcong @ SV257 @ ( times_times @ int @ SV557 @ SY1843 ) @ SY1844 )
| ( zcong @ SV257 @ ( times_times @ int @ SV557 @ SY1842 ) @ SY1844 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2373]) ).
thf(2785,plain,
! [SV258: $i] :
( ( ( ~ ( number_ring @ SV258 ) )
= $true )
| ( ( ( one_one @ SV258 )
= ( number_number_of @ SV258 @ ( bit1 @ pls ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2374]) ).
thf(2786,plain,
! [SV558: $i,SV259: $i] :
( ( ! [SY1845: $i] :
( ~ ( ( SY1845
!= ( zero_zero @ nat ) ) )
| ~ ( dvd_dvd @ nat @ ( power_power @ nat @ SV259 @ SY1845 ) @ SV558 )
| ( dvd_dvd @ nat @ SV259 @ SV558 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2375]) ).
thf(2787,plain,
! [SV260: $i] :
( ( ( ~ ( number_ring @ SV260 ) )
= $true )
| ( ( ( number_number_of @ SV260 @ ( bit1 @ pls ) )
= ( one_one @ SV260 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2376]) ).
thf(2788,plain,
! [SV559: $i,SV261: $i] :
( ( ! [SY1846: $i] :
~ ( ~ ( ~ ( zcong @ SV261 @ ( ti @ int @ SV559 ) @ SY1846 )
| ( zcong @ SV261 @ SV559 @ SY1846 ) )
| ~ ( ~ ( zcong @ SV261 @ SV559 @ SY1846 )
| ( zcong @ SV261 @ ( ti @ int @ SV559 ) @ SY1846 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2377]) ).
thf(2789,plain,
! [SV262: $i] :
( ( ( ~ ( zprime @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SV262 ) @ ( one_one @ int ) ) ) )
= $true )
| ( ( ( legendre @ ( number_number_of @ int @ min ) @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SV262 ) @ ( one_one @ int ) ) )
= ( one_one @ int ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2378]) ).
thf(2790,plain,
! [SV263: $i] :
( ( ( ~ ( number_ring @ SV263 ) )
= $true )
| ( ( ! [SY1469: $i,SY1470: $i] :
( ( number_number_of @ SV263 @ ( plus_plus @ int @ SY1469 @ SY1470 ) )
= ( plus_plus @ SV263 @ ( number_number_of @ SV263 @ SY1469 ) @ ( number_number_of @ SV263 @ SY1470 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2379]) ).
thf(2791,plain,
! [SV264: $i] :
( ( ( ~ ( number_ring @ SV264 ) )
= $true )
| ( ( ! [SY1471: $i,SY1472: $i] :
( ( number_number_of @ SV264 @ ( times_times @ int @ SY1471 @ SY1472 ) )
= ( times_times @ SV264 @ ( number_number_of @ SV264 @ SY1471 ) @ ( number_number_of @ SV264 @ SY1472 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2380]) ).
thf(2792,plain,
! [SV265: $i] :
( ( ( ~ ( comm_semiring_1 @ SV265 ) )
= $true )
| ( ( ! [SY1473: $i] :
( ( power_power @ SV265 @ SY1473 @ ( zero_zero @ nat ) )
= ( one_one @ SV265 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2381]) ).
thf(2793,plain,
! [SV266: $i] :
( ( ( ~ ( comm_semiring_1 @ SV266 ) )
= $true )
| ( ( ! [SY1474: $i,SY1475: $i,SY1476: $i,SY1477: $i] :
( ( plus_plus @ SV266 @ ( plus_plus @ SV266 @ SY1474 @ SY1475 ) @ ( plus_plus @ SV266 @ SY1476 @ SY1477 ) )
= ( plus_plus @ SV266 @ ( plus_plus @ SV266 @ SY1474 @ SY1476 ) @ ( plus_plus @ SV266 @ SY1475 @ SY1477 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2382]) ).
thf(2794,plain,
! [SV267: $i] :
( ( pls
= ( bit1 @ SV267 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2383]) ).
thf(2795,plain,
! [SV268: $i,SV560: $i] :
( ( ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV560 )
| ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV268 )
| ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( times_times @ int @ SV560 @ SV268 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2384]) ).
thf(2796,plain,
! [SV269: $i] :
( ( ( ~ ( linordered_idom @ SV269 ) )
= $true )
| ( ( ! [SY1479: $i] :
~ ( ~ ( ~ ( ord_less @ SV269 @ ( plus_plus @ SV269 @ SY1479 @ SY1479 ) @ ( zero_zero @ SV269 ) )
| ( ord_less @ SV269 @ SY1479 @ ( zero_zero @ SV269 ) ) )
| ~ ( ~ ( ord_less @ SV269 @ SY1479 @ ( zero_zero @ SV269 ) )
| ( ord_less @ SV269 @ ( plus_plus @ SV269 @ SY1479 @ SY1479 ) @ ( zero_zero @ SV269 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2385]) ).
thf(2797,plain,
! [SV561: $i,SV270: $i] :
( ( ~ ( ord_less_eq @ int @ SV270 @ SV561 )
| ~ ( ord_less_eq @ int @ SV561 @ SV270 )
| ( ( ti @ int @ SV270 )
= ( ti @ int @ SV561 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2386]) ).
thf(2798,plain,
! [SV271: $i] :
( ( ( ~ ( number_ring @ SV271 ) )
= $true )
| ( ( ! [SY1481: $i,SY1482: $i,SY1483: $i] :
( ( plus_plus @ SV271 @ ( number_number_of @ SV271 @ SY1481 ) @ ( minus_minus @ SV271 @ ( number_number_of @ SV271 @ SY1482 ) @ SY1483 ) )
= ( minus_minus @ SV271 @ ( number_number_of @ SV271 @ ( plus_plus @ int @ SY1481 @ SY1482 ) ) @ SY1483 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2387]) ).
thf(2799,plain,
! [SV272: $i] :
( ( ( ~ ( number_ring @ SV272 ) )
= $true )
| ( ( ! [SY1484: $i] :
( ( number_number_of @ SV272 @ ( bit0 @ SY1484 ) )
= ( plus_plus @ SV272 @ ( plus_plus @ SV272 @ ( zero_zero @ SV272 ) @ ( number_number_of @ SV272 @ SY1484 ) ) @ ( number_number_of @ SV272 @ SY1484 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2388]) ).
thf(2800,plain,
! [SV562: $i,SV273: $i] :
( ( ! [SY1847: $i] :
( ~ ( ( SY1847
!= ( zero_zero @ real ) ) )
| ~ ( ~ ( ( ( times_times @ real @ SY1847 @ SV273 )
!= ( times_times @ real @ SY1847 @ SV562 ) )
| ( SV273 = SV562 ) )
| ~ ( ( SV273 != SV562 )
| ( ( times_times @ real @ SY1847 @ SV273 )
= ( times_times @ real @ SY1847 @ SV562 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2389]) ).
thf(2801,plain,
! [SV274: $i] :
( ( ~ ( ~ ( ord_less @ int @ min @ ( bit1 @ SV274 ) )
| ( ord_less @ int @ min @ SV274 ) )
| ~ ( ~ ( ord_less @ int @ min @ SV274 )
| ( ord_less @ int @ min @ ( bit1 @ SV274 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2390]) ).
thf(2802,plain,
! [SV275: $i] :
( ( ( ~ ( number_ring @ SV275 ) )
= $true )
| ( ( ! [SY1487: $i,SY1488: $i] :
( ( number_number_of @ SV275 @ ( minus_minus @ int @ SY1487 @ SY1488 ) )
= ( minus_minus @ SV275 @ ( number_number_of @ SV275 @ SY1487 ) @ ( number_number_of @ SV275 @ SY1488 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2391]) ).
thf(2803,plain,
! [SV276: $i] :
( ( ( ~ ( monoid_mult @ SV276 ) )
= $true )
| ( ( ! [SY1489: $i] :
( ( power_power @ SV276 @ ( one_one @ SV276 ) @ SY1489 )
= ( one_one @ SV276 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2392]) ).
thf(2804,plain,
! [SV277: $i] :
( ( ( ~ ( comm_semiring_1 @ SV277 ) )
= $true )
| ( ( ! [SY1490: $i,SY1491: $i,SY1492: $i] :
( ~ ( dvd_dvd @ SV277 @ SY1491 @ SY1492 )
| ~ ( dvd_dvd @ SV277 @ SY1491 @ SY1490 )
| ( dvd_dvd @ SV277 @ SY1491 @ ( plus_plus @ SV277 @ SY1492 @ SY1490 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2393]) ).
thf(2805,plain,
! [SV278: $i] :
( ( ( ~ ( comm_semiring_1 @ SV278 ) )
= $true )
| ( ( ! [SY1493: $i] :
( ( times_times @ SV278 @ ( zero_zero @ SV278 ) @ SY1493 )
= ( zero_zero @ SV278 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2394]) ).
thf(2806,plain,
! [SV279: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SV279 ) @ pls )
| ( ord_less @ int @ SV279 @ pls ) )
| ~ ( ~ ( ord_less @ int @ SV279 @ pls )
| ( ord_less @ int @ ( bit0 @ SV279 ) @ pls ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2395]) ).
thf(2807,plain,
! [SV563: $i,SV280: $i] :
( ( ! [SY1848: $i] :
( ~ ( semiring @ SY1848 )
| ( ( ti @ SY1848 @ ( times_times @ SY1848 @ SV280 @ SV563 ) )
= ( times_times @ SY1848 @ SV280 @ SV563 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2396]) ).
thf(2808,plain,
! [SV564: $i,SV281: $i] :
( ( ~ ( ~ ( ( ( bit0 @ SV281 )
!= ( bit0 @ SV564 ) )
| ( ( ti @ int @ SV281 )
= ( ti @ int @ SV564 ) ) )
| ~ ( ( ( ti @ int @ SV281 )
!= ( ti @ int @ SV564 ) )
| ( ( bit0 @ SV281 )
= ( bit0 @ SV564 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2397]) ).
thf(2809,plain,
! [SV282: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SV282 ) @ min )
| ( ord_less_eq @ int @ SV282 @ min ) )
| ~ ( ~ ( ord_less_eq @ int @ SV282 @ min )
| ( ord_less_eq @ int @ ( bit1 @ SV282 ) @ min ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2398]) ).
thf(2810,plain,
! [SV283: $i] :
( ( ( ~ ( number_ring @ SV283 ) )
= $true )
| ( ( ! [SY1497: $i] :
( ( plus_plus @ SV283 @ ( number_number_of @ SV283 @ pls ) @ SY1497 )
= ( ti @ SV283 @ SY1497 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2399]) ).
thf(2811,plain,
! [SV284: $i] :
( ( ( ~ ( comm_semiring_1 @ SV284 ) )
= $true )
| ( ( ! [SY1498: $i,SY1499: $i,SY1500: $i] :
( ~ ( dvd_dvd @ SV284 @ SY1499 @ SY1500 )
| ( dvd_dvd @ SV284 @ ( power_power @ SV284 @ SY1499 @ SY1498 ) @ ( power_power @ SV284 @ SY1500 @ SY1498 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2400]) ).
thf(2812,plain,
! [SV285: $i] :
( ( ( ~ ( number_semiring @ SV285 ) )
= $true )
| ( ( ! [SY1501: $i,SY1502: $i] :
( ~ ( ord_less_eq @ int @ pls @ SY1502 )
| ~ ( ord_less_eq @ int @ pls @ SY1501 )
| ( ( plus_plus @ SV285 @ ( number_number_of @ SV285 @ SY1502 ) @ ( number_number_of @ SV285 @ SY1501 ) )
= ( number_number_of @ SV285 @ ( plus_plus @ int @ SY1502 @ SY1501 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2401]) ).
thf(2813,plain,
! [SV286: $i] :
( ( ( ~ ( monoid_mult @ SV286 ) )
= $true )
| ( ( ! [SY1503: $i,SY1504: $i] :
( ( power_power @ SV286 @ SY1503 @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SY1504 ) )
= ( power_power @ SV286 @ ( power_power @ SV286 @ SY1503 @ SY1504 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2402]) ).
thf(2814,plain,
! [SV565: $i,SV287: $i] :
( ( ! [SY1849: $i] :
( ~ ( dvd @ SY1849 )
| ( ( times_times @ SY1849 @ SV287 @ ( ti @ SY1849 @ SV565 ) )
= ( times_times @ SY1849 @ SV287 @ SV565 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2403]) ).
thf(2815,plain,
! [SV566: $i,SV288: $i] :
( ( ! [SY1850: $i,SY1851: $i] :
( ~ ( zprime @ SY1851 )
| ~ ~ ( dvd_dvd @ int @ SY1851 @ SY1850 )
| ~ ( dvd_dvd @ int @ ( power_power @ int @ SY1851 @ SV288 ) @ ( times_times @ int @ SV566 @ SY1850 ) )
| ( dvd_dvd @ int @ ( power_power @ int @ SY1851 @ SV288 ) @ SV566 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2404]) ).
thf(2816,plain,
! [SV567: $i,SV289: $i] :
( ( ! [SY1852: $i] :
( ~ ( ab_group_add @ SY1852 )
| ( ( plus_plus @ SY1852 @ ( ti @ SY1852 @ SV289 ) @ SV567 )
= ( plus_plus @ SY1852 @ SV289 @ SV567 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2405]) ).
thf(2817,plain,
! [SV290: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SV290 ) @ ( zero_zero @ int ) )
| ( ord_less @ int @ SV290 @ ( zero_zero @ int ) ) )
| ~ ( ~ ( ord_less @ int @ SV290 @ ( zero_zero @ int ) )
| ( ord_less @ int @ ( bit0 @ SV290 ) @ ( zero_zero @ int ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2406]) ).
thf(2818,plain,
! [SV291: $i] :
( ( ( ~ ( comm_semiring_1 @ SV291 ) )
= $true )
| ( ( ! [SY1512: $i] :
( ( times_times @ SV291 @ SY1512 @ SY1512 )
= ( power_power @ SV291 @ SY1512 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2407]) ).
thf(2819,plain,
! [SV568: $i,SV292: $i] :
( ( ~ ( ~ ( ~ ( zcong @ ( times_times @ int @ SV292 @ ( minus_minus @ int @ SV568 @ ( one_one @ int ) ) ) @ ( one_one @ int ) @ SV568 )
| ( zcong @ SV292 @ ( minus_minus @ int @ SV568 @ ( one_one @ int ) ) @ SV568 ) )
| ~ ( ~ ( zcong @ SV292 @ ( minus_minus @ int @ SV568 @ ( one_one @ int ) ) @ SV568 )
| ( zcong @ ( times_times @ int @ SV292 @ ( minus_minus @ int @ SV568 @ ( one_one @ int ) ) ) @ ( one_one @ int ) @ SV568 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2408]) ).
thf(2820,plain,
! [SV293: $i] :
( ( ( ~ ( linordered_idom @ SV293 ) )
= $true )
| ( ( ! [SY1514: $i] : ( ord_less_eq @ SV293 @ ( zero_zero @ SV293 ) @ ( power_power @ SV293 @ SY1514 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2409]) ).
thf(2821,plain,
! [SV294: $i,SV569: $i] :
( ( ! [SY1853: $i] :
( ~ ( ord_less_eq @ int @ SV569 @ SY1853 )
| ~ ( ord_less_eq @ int @ SY1853 @ SV294 )
| ( ord_less_eq @ int @ SV569 @ SV294 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2410]) ).
thf(2822,plain,
! [SV295: $i] :
( ( ( ~ ( power @ SV295 ) )
= $true )
| ( ( ( ti @ SV295 @ ( one_one @ SV295 ) )
= ( one_one @ SV295 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2411]) ).
thf(2823,plain,
! [SV296: $i] :
( ( ( ~ ( comm_semiring_1 @ SV296 ) )
= $true )
| ( ( ! [SY1517: $i,SY1518: $i,SY1519: $i] :
( ( plus_plus @ SV296 @ ( plus_plus @ SV296 @ SY1517 @ SY1518 ) @ SY1519 )
= ( plus_plus @ SV296 @ ( plus_plus @ SV296 @ SY1517 @ SY1519 ) @ SY1518 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2412]) ).
thf(2824,plain,
! [SV297: $i,SV570: $i] :
( ( ! [SY1854: $i] :
( ~ ( ord_less @ int @ SV570 @ SY1854 )
| ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV297 )
| ( ord_less @ int @ ( times_times @ int @ SV297 @ SV570 ) @ ( times_times @ int @ SV297 @ SY1854 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2413]) ).
thf(2825,plain,
! [SV298: $i] :
( ( ( ~ ( comm_monoid_mult @ SV298 ) )
= $true )
| ( ( ! [SY1522: $i,SY1523: $i,SY1524: $i] :
( ( power_power @ SV298 @ ( times_times @ SV298 @ SY1522 @ SY1523 ) @ SY1524 )
= ( times_times @ SV298 @ ( power_power @ SV298 @ SY1522 @ SY1524 ) @ ( power_power @ SV298 @ SY1523 @ SY1524 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2414]) ).
thf(2826,plain,
! [SV571: $i,SV299: $i] :
( ( ~ ( dvd_dvd @ nat @ SV299 @ SV571 )
| ( SV571
= ( zero_zero @ nat ) )
| ( SV571 = SV299 )
| ( ord_less_eq @ nat @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV299 ) @ SV571 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2415]) ).
thf(2827,plain,
! [SV572: $i,SV300: $i] :
( ( ~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SV300 ) @ ( bit1 @ SV572 ) )
| ( ord_less_eq @ int @ SV300 @ SV572 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV300 @ SV572 )
| ( ord_less_eq @ int @ ( bit1 @ SV300 ) @ ( bit1 @ SV572 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2416]) ).
thf(2828,plain,
! [SV301: $i] :
( ( ( ~ ( ring_n68954251visors @ SV301 ) )
= $true )
| ( ( ! [SY1527: $i,SY1528: $i] :
~ ( ~ ( ( ( times_times @ SV301 @ SY1527 @ SY1528 )
!= ( zero_zero @ SV301 ) )
| ( ( ti @ SV301 @ SY1527 )
= ( zero_zero @ SV301 ) )
| ( ( ti @ SV301 @ SY1528 )
= ( zero_zero @ SV301 ) ) )
| ~ ( ~ ( ( ( ti @ SV301 @ SY1527 )
= ( zero_zero @ SV301 ) )
| ( ( ti @ SV301 @ SY1528 )
= ( zero_zero @ SV301 ) ) )
| ( ( times_times @ SV301 @ SY1527 @ SY1528 )
= ( zero_zero @ SV301 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2417]) ).
thf(2829,plain,
! [SV302: $i] :
( ( ( ~ ( number_ring @ SV302 ) )
= $true )
| ( ( ! [SY1529: $i] :
( ( times_times @ SV302 @ ( plus_plus @ SV302 @ ( one_one @ SV302 ) @ ( one_one @ SV302 ) ) @ ( number_number_of @ SV302 @ SY1529 ) )
= ( number_number_of @ SV302 @ ( bit0 @ SY1529 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2418]) ).
thf(2830,plain,
! [SV303: $i] :
( ( ~ ( ( pls
!= ( bit0 @ SV303 ) )
| ( pls
= ( ti @ int @ SV303 ) ) )
| ~ ( ( pls
!= ( ti @ int @ SV303 ) )
| ( pls
= ( bit0 @ SV303 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2419]) ).
thf(2831,plain,
! [SV304: $i] :
( ( ( ~ ( linordered_semidom @ SV304 ) )
= $true )
| ( ( ! [SY1530: $i,SY1531: $i,SY1532: $i] :
( ~ ( ord_less @ SV304 @ ( one_one @ SV304 ) @ SY1532 )
| ~ ( ord_less_eq @ SV304 @ ( power_power @ SV304 @ SY1532 @ SY1530 ) @ ( power_power @ SV304 @ SY1532 @ SY1531 ) )
| ( ord_less_eq @ nat @ SY1530 @ SY1531 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2420]) ).
thf(2832,plain,
! [SV573: $i,SV305: $i] :
( ( ! [SY1855: $i,SY1856: $i,SY1857: $i,SY1858: $i] :
( ( ( plus_plus @ int @ ( times_times @ int @ SV305 @ SV573 ) @ SY1855 )
!= ( plus_plus @ int @ ( times_times @ int @ SY1856 @ SY1857 ) @ SY1858 ) )
| ~ ( ord_less @ int @ ( plus_plus @ int @ ( times_times @ int @ SY1856 @ SY1857 ) @ SY1858 ) @ ( zero_zero @ int ) )
| ~ ( ord_less @ int @ SY1855 @ SV305 )
| ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SY1858 )
| ~ ( ord_less @ int @ ( zero_zero @ int ) @ SY1856 )
| ~ ( ord_less_eq @ int @ SY1856 @ SV305 )
| ( ord_less_eq @ int @ SY1857 @ SV573 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2421]) ).
thf(2833,plain,
! [SV306: $i] :
( ( ( ~ ( comm_semiring_1 @ SV306 ) )
= $true )
| ( ( ! [SY1538: $i,SY1539: $i] :
( ( plus_plus @ SV306 @ ( times_times @ SV306 @ SY1538 @ SY1539 ) @ SY1539 )
= ( times_times @ SV306 @ ( plus_plus @ SV306 @ SY1538 @ ( one_one @ SV306 ) ) @ SY1539 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2422]) ).
thf(2834,plain,
! [SV574: $i,SV307: $i] :
( ( ! [SY1859: $i] :
( ~ ( dvd @ SY1859 )
| ( ( ti @ SY1859 @ ( times_times @ SY1859 @ SV307 @ SV574 ) )
= ( times_times @ SY1859 @ SV307 @ SV574 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2423]) ).
thf(2835,plain,
! [SV308: $i,SV575: $i] :
( ( ! [SY1860: $i,SY1861: $i] :
( ~ ( zcong @ SV575 @ SY1860 @ SY1861 )
| ( zcong @ ( power_power @ int @ SV575 @ SV308 ) @ ( power_power @ int @ SY1860 @ SV308 ) @ SY1861 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2424]) ).
thf(2836,plain,
! [SV309: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SV309 ) @ pls )
| ( ord_less @ int @ SV309 @ pls ) )
| ~ ( ~ ( ord_less @ int @ SV309 @ pls )
| ( ord_less_eq @ int @ ( bit1 @ SV309 ) @ pls ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2425]) ).
thf(2837,plain,
! [SV310: $i] :
( ( ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ SV310 ) @ SV310 )
= ( zero_zero @ int ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2426]) ).
thf(2838,plain,
! [SV311: $i] :
( ( ( ~ ( comm_semiring_1 @ SV311 ) )
= $true )
| ( ( ! [SY1545: $i,SY1546: $i,SY1547: $i] :
( ( power_power @ SV311 @ ( power_power @ SV311 @ SY1545 @ SY1546 ) @ SY1547 )
= ( power_power @ SV311 @ SY1545 @ ( times_times @ nat @ SY1546 @ SY1547 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2427]) ).
thf(2839,plain,
! [SV576: $i,SV312: $i] :
( ( ! [SY1862: $i,SY1863: $i,SY1864: $i] :
( ~ ( ord_less_eq @ int @ ( plus_plus @ int @ ( times_times @ int @ SV312 @ SV576 ) @ SY1862 ) @ ( plus_plus @ int @ ( times_times @ int @ SV312 @ SY1863 ) @ SY1864 ) )
| ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SY1862 )
| ~ ( ord_less @ int @ SY1862 @ SV312 )
| ~ ( ord_less @ int @ SY1864 @ SV312 )
| ( ord_less_eq @ int @ SV576 @ SY1863 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2428]) ).
thf(2840,plain,
! [SV313: $i] :
( ( ( ~ ( semiri456707255roduct @ SV313 ) )
= $true )
| ( ( ! [SY1552: $i,SY1553: $i] :
~ ( ~ ( ( ( ti @ SV313 @ SY1552 )
!= ( plus_plus @ SV313 @ SY1552 @ SY1553 ) )
| ( ( ti @ SV313 @ SY1553 )
= ( zero_zero @ SV313 ) ) )
| ~ ( ( ( ti @ SV313 @ SY1553 )
!= ( zero_zero @ SV313 ) )
| ( ( ti @ SV313 @ SY1552 )
= ( plus_plus @ SV313 @ SY1552 @ SY1553 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2429]) ).
thf(2841,plain,
! [SV577: $i,SV314: $i] :
( ( ~ ( ~ ( ~ ( quadRes @ SV314 @ SV577 )
| ~ ! [SY1865: $i] :
~ ( zcong @ ( power_power @ int @ SY1865 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SV577 @ SV314 ) )
| ~ ( ~ ~ ! [SY1866: $i] :
~ ( zcong @ ( power_power @ int @ SY1866 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SV577 @ SV314 )
| ( quadRes @ SV314 @ SV577 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2430]) ).
thf(2842,plain,
! [SV315: $i] :
( ( ( ~ ( linordered_semidom @ SV315 ) )
= $true )
| ( ( ! [SY1557: $i,SY1558: $i,SY1559: $i] :
( ~ ( ord_less_eq @ nat @ SY1558 @ SY1559 )
| ~ ( ord_less_eq @ SV315 @ ( one_one @ SV315 ) @ SY1557 )
| ( ord_less_eq @ SV315 @ ( power_power @ SV315 @ SY1557 @ SY1558 ) @ ( power_power @ SV315 @ SY1557 @ SY1559 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2431]) ).
thf(2843,plain,
! [SV316: $i] :
( ( ( ~ ( comm_semiring_1 @ SV316 ) )
= $true )
| ( ( ! [SY1560: $i,SY1561: $i,SY1562: $i] :
( ( times_times @ SV316 @ ( plus_plus @ SV316 @ SY1560 @ SY1561 ) @ SY1562 )
= ( plus_plus @ SV316 @ ( times_times @ SV316 @ SY1560 @ SY1562 ) @ ( times_times @ SV316 @ SY1561 @ SY1562 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2432]) ).
thf(2844,plain,
! [SV317: $i] :
( ( ( ~ ( linordered_semidom @ SV317 ) )
= $true )
| ( ( ! [SY1563: $i,SY1564: $i] :
( ~ ( ord_less_eq @ SV317 @ ( one_one @ SV317 ) @ SY1564 )
| ( ord_less_eq @ SV317 @ ( one_one @ SV317 ) @ ( power_power @ SV317 @ SY1564 @ SY1563 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2433]) ).
thf(2845,plain,
! [SV318: $i] :
( ( ( ~ ( comm_semiring_1 @ SV318 ) )
= $true )
| ( ( ! [SY1565: $i,SY1566: $i] :
( ( times_times @ SV318 @ SY1565 @ SY1566 )
= ( times_times @ SV318 @ SY1566 @ SY1565 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2434]) ).
thf(2846,plain,
! [SV319: $i] :
( ( ( ~ ( linord581940658strict @ SV319 ) )
= $true )
| ( ( ! [SY1567: $i,SY1568: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV319 @ ( times_times @ SV319 @ SY1567 @ SY1568 ) @ ( zero_zero @ SV319 ) )
| ~ ( ~ ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SY1567 )
| ~ ( ord_less_eq @ SV319 @ SY1568 @ ( zero_zero @ SV319 ) ) )
| ~ ( ~ ( ord_less_eq @ SV319 @ SY1567 @ ( zero_zero @ SV319 ) )
| ~ ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SY1568 ) ) )
| ~ ( ~ ( ~ ( ~ ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SY1567 )
| ~ ( ord_less_eq @ SV319 @ SY1568 @ ( zero_zero @ SV319 ) ) )
| ~ ( ~ ( ord_less_eq @ SV319 @ SY1567 @ ( zero_zero @ SV319 ) )
| ~ ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SY1568 ) ) )
| ( ord_less_eq @ SV319 @ ( times_times @ SV319 @ SY1567 @ SY1568 ) @ ( zero_zero @ SV319 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2435]) ).
thf(2847,plain,
! [SV320: $i] :
( ( ~ ( ( ( zero_zero @ nat )
!= ( number_number_of @ nat @ SV320 ) )
| ( ord_less_eq @ int @ SV320 @ pls ) )
| ~ ( ~ ( ord_less_eq @ int @ SV320 @ pls )
| ( ( zero_zero @ nat )
= ( number_number_of @ nat @ SV320 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2436]) ).
thf(2848,plain,
! [SV321: $i] :
( ( ( ~ ~ ( ~ ( number_ring @ SV321 )
| ~ ( linordered_idom @ SV321 ) ) )
= $true )
| ( ( ! [SY1569: $i,SY1570: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV321 @ ( number_number_of @ SV321 @ SY1569 ) @ ( number_number_of @ SV321 @ SY1570 ) )
| ( ord_less_eq @ int @ SY1569 @ SY1570 ) )
| ~ ( ~ ( ord_less_eq @ int @ SY1569 @ SY1570 )
| ( ord_less_eq @ SV321 @ ( number_number_of @ SV321 @ SY1569 ) @ ( number_number_of @ SV321 @ SY1570 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2437]) ).
thf(2849,plain,
! [SV322: $i] :
( ( ( ~ ( comm_semiring_1 @ SV322 ) )
= $true )
| ( ( ! [SY1571: $i] :
( ( times_times @ SV322 @ SY1571 @ ( zero_zero @ SV322 ) )
= ( zero_zero @ SV322 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2438]) ).
thf(2850,plain,
! [SV323: $i] :
( ( ( ~ ( comm_semiring_1 @ SV323 ) )
= $true )
| ( ( ! [SY1572: $i,SY1573: $i,SY1574: $i,SY1575: $i] :
( ~ ( dvd_dvd @ SV323 @ SY1574 @ SY1575 )
| ~ ( ord_less_eq @ nat @ SY1572 @ SY1573 )
| ( dvd_dvd @ SV323 @ ( power_power @ SV323 @ SY1574 @ SY1572 ) @ ( power_power @ SV323 @ SY1575 @ SY1573 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2439]) ).
thf(2851,plain,
! [SV324: $i] :
( ( ( ~ ( number_semiring @ SV324 ) )
= $true )
| ( ( ( number_number_of @ SV324 @ ( bit1 @ pls ) )
= ( one_one @ SV324 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2440]) ).
thf(2852,plain,
! [SV325: $i] :
( ( ( ~ ( linordered_semidom @ SV325 ) )
= $true )
| ( ( ! [SY1576: $i,SY1577: $i] :
( ~ ( ord_less_eq @ SV325 @ ( power_power @ SV325 @ SY1576 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV325 @ SY1577 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ~ ( ord_less_eq @ SV325 @ ( zero_zero @ SV325 ) @ SY1577 )
| ( ord_less_eq @ SV325 @ SY1576 @ SY1577 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2441]) ).
thf(2853,plain,
! [SV326: $i] :
( ( ( bit1 @ SV326 )
= pls )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2442]) ).
thf(2854,plain,
! [SV578: $i,SV327: $i] :
( ( ( ( times_times @ int @ SV327 @ SV578 )
!= ( one_one @ int ) )
| ( ( ti @ int @ SV327 )
= ( one_one @ int ) )
| ( ( ti @ int @ SV327 )
= ( number_number_of @ int @ min ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2443]) ).
thf(2855,plain,
! [SV328: $i] :
( ( ~ ( ~ ( ord_less @ int @ min @ ( bit0 @ SV328 ) )
| ( ord_less @ int @ min @ SV328 ) )
| ~ ( ~ ( ord_less @ int @ min @ SV328 )
| ( ord_less @ int @ min @ ( bit0 @ SV328 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2444]) ).
thf(2856,plain,
! [SV329: $i] :
( ( ( ~ ( monoid_mult @ SV329 ) )
= $true )
| ( ( ! [SY1579: $i,SY1580: $i,SY1581: $i] :
( ( power_power @ SV329 @ SY1579 @ ( plus_plus @ nat @ SY1580 @ SY1581 ) )
= ( times_times @ SV329 @ ( power_power @ SV329 @ SY1579 @ SY1580 ) @ ( power_power @ SV329 @ SY1579 @ SY1581 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2445]) ).
thf(2857,plain,
! [SV330: $i] :
( ( ( ~ ( comm_semiring_1 @ SV330 ) )
= $true )
| ( ( ! [SY1582: $i,SY1583: $i,SY1584: $i] :
( ~ ( dvd_dvd @ SV330 @ ( times_times @ SV330 @ SY1582 @ SY1583 ) @ SY1584 )
| ( dvd_dvd @ SV330 @ SY1583 @ SY1584 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2446]) ).
thf(2858,plain,
! [SV331: $i] :
( ( ( ~ ( ord_less @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV331 ) )
= $true )
| ( ( ~ ( zcong @ ( one_one @ int ) @ ( number_number_of @ int @ min ) @ SV331 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2447]) ).
thf(2859,plain,
! [SV332: $i] :
( ( ( ~ ( comm_semiring_1 @ SV332 ) )
= $true )
| ( ( ! [SY1585: $i,SY1586: $i] : ( dvd_dvd @ SV332 @ SY1585 @ ( times_times @ SV332 @ SY1585 @ SY1586 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2448]) ).
thf(2860,plain,
! [SV333: $i] :
( ( ( ~ ~ ( ~ ( power @ SV333 )
| ~ ( semiring_0 @ SV333 ) ) )
= $true )
| ( ( ! [SY1587: $i] :
~ ( ~ ( ( ( number_number_of @ nat @ SY1587 )
!= ( zero_zero @ nat ) )
| ( ( power_power @ SV333 @ ( zero_zero @ SV333 ) @ ( number_number_of @ nat @ SY1587 ) )
= ( one_one @ SV333 ) ) )
| ~ ( ~ ( ( ( number_number_of @ nat @ SY1587 )
!= ( zero_zero @ nat ) ) )
| ( ( power_power @ SV333 @ ( zero_zero @ SV333 ) @ ( number_number_of @ nat @ SY1587 ) )
= ( zero_zero @ SV333 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2449]) ).
thf(2861,plain,
! [SV579: $i,SV334: $i] :
( ( ! [SY1867: $i] :
( ~ ( no_zero_divisors @ SY1867 )
| ( ( ti @ SY1867 @ ( times_times @ SY1867 @ SV334 @ SV579 ) )
= ( times_times @ SY1867 @ SV334 @ SV579 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2450]) ).
thf(2862,plain,
! [SV580: $i,SV335: $i] :
( ( ! [SY1868: $i] :
( ~ ( ab_group_add @ SY1868 )
| ( ( plus_plus @ SY1868 @ SV335 @ ( ti @ SY1868 @ SV580 ) )
= ( plus_plus @ SY1868 @ SV335 @ SV580 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2451]) ).
thf(2863,plain,
! [SV581: $i,SV336: $i] :
( ( ~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit0 @ SV336 ) @ ( bit0 @ SV581 ) )
| ( ord_less_eq @ int @ SV336 @ SV581 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV336 @ SV581 )
| ( ord_less_eq @ int @ ( bit0 @ SV336 ) @ ( bit0 @ SV581 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2452]) ).
thf(2864,plain,
! [SV582: $i,SV337: $i] :
( ( ! [SY1869: $i,SY1870: $i,SY1871: $i] :
( ~ ( zcong @ SY1869 @ SY1870 @ SY1871 )
| ~ ( zcong @ SV337 @ SV582 @ SY1871 )
| ( zcong @ ( times_times @ int @ SY1869 @ SV337 ) @ ( times_times @ int @ SY1870 @ SV582 ) @ SY1871 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2453]) ).
thf(2865,plain,
! [SV583: $i,SV338: $i] :
( ( ! [SY1872: $i] :
( ~ ( ord_less @ real @ ( zero_zero @ real ) @ SY1872 )
| ~ ( ~ ( ~ ( ord_less @ real @ ( times_times @ real @ SV338 @ SY1872 ) @ ( times_times @ real @ SV583 @ SY1872 ) )
| ( ord_less @ real @ SV338 @ SV583 ) )
| ~ ( ~ ( ord_less @ real @ SV338 @ SV583 )
| ( ord_less @ real @ ( times_times @ real @ SV338 @ SY1872 ) @ ( times_times @ real @ SV583 @ SY1872 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2454]) ).
thf(2866,plain,
! [SV339: $i] :
( ( ( ~ ( mult_zero @ SV339 ) )
= $true )
| ( ( ! [SY1599: $i] :
( ( times_times @ SV339 @ SY1599 @ ( zero_zero @ SV339 ) )
= ( zero_zero @ SV339 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2455]) ).
thf(2867,plain,
( ( ! [SX0: $i] :
~ ~ ! [SX1: $i] :
( ( plus_plus @ int @ ( power_power @ int @ SX0 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ SX1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2456]) ).
thf(2868,plain,
! [SV340: $i] :
( ( ( ~ ( comm_semiring_1 @ SV340 ) )
= $true )
| ( ( ! [SY1600: $i,SY1601: $i,SY1602: $i,SY1603: $i] :
( ( times_times @ SV340 @ ( times_times @ SV340 @ SY1600 @ SY1601 ) @ ( times_times @ SV340 @ SY1602 @ SY1603 ) )
= ( times_times @ SV340 @ ( times_times @ SV340 @ SY1600 @ SY1602 ) @ ( times_times @ SV340 @ SY1601 @ SY1603 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2457]) ).
thf(2869,plain,
! [SV584: $i,SV341: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SV341 ) @ ( bit0 @ SV584 ) )
| ( ord_less @ int @ SV341 @ SV584 ) )
| ~ ( ~ ( ord_less @ int @ SV341 @ SV584 )
| ( ord_less @ int @ ( bit0 @ SV341 ) @ ( bit0 @ SV584 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2458]) ).
thf(2870,plain,
! [SV342: $i] :
( ( ( ~ ( mult_zero @ SV342 ) )
= $true )
| ( ( ! [SY1605: $i] :
( ( times_times @ SV342 @ ( zero_zero @ SV342 ) @ SY1605 )
= ( zero_zero @ SV342 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2459]) ).
thf(2871,plain,
! [SV585: $i,SV343: $i] :
( ( ~ ( ~ ( ~ ( quadRes @ SV343 @ ( ti @ int @ SV585 ) )
| ( quadRes @ SV343 @ SV585 ) )
| ~ ( ~ ( quadRes @ SV343 @ SV585 )
| ( quadRes @ SV343 @ ( ti @ int @ SV585 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2461]) ).
thf(2872,plain,
! [SV344: $i] :
( ( ( ~ ( comm_semiring_1 @ SV344 ) )
= $true )
| ( ( ! [SY1607: $i] :
( ( plus_plus @ SV344 @ SY1607 @ SY1607 )
= ( times_times @ SV344 @ ( plus_plus @ SV344 @ ( one_one @ SV344 ) @ ( one_one @ SV344 ) ) @ SY1607 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2462]) ).
thf(2873,plain,
! [SV586: $i,SV345: $i] :
( ( ~ ( ~ ( ~ ( ord_less_eq @ int @ SV345 @ ( minus_minus @ int @ SV586 @ ( one_one @ int ) ) )
| ( ord_less @ int @ SV345 @ SV586 ) )
| ~ ( ~ ( ord_less @ int @ SV345 @ SV586 )
| ( ord_less_eq @ int @ SV345 @ ( minus_minus @ int @ SV586 @ ( one_one @ int ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2463]) ).
thf(2874,plain,
! [SV346: $i] :
( ( ( ~ ( number_semiring @ SV346 ) )
= $true )
| ( ( ( number_number_of @ SV346 @ pls )
= ( zero_zero @ SV346 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2464]) ).
thf(2875,plain,
! [SV347: $i] :
( ( ( ~ ( ring_11004092258visors @ SV347 ) )
= $true )
| ( ( ! [SY1609: $i] :
~ ( ~ ( ( ( power_power @ SV347 @ SY1609 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= ( zero_zero @ SV347 ) )
| ( ( ti @ SV347 @ SY1609 )
= ( zero_zero @ SV347 ) ) )
| ~ ( ( ( ti @ SV347 @ SY1609 )
!= ( zero_zero @ SV347 ) )
| ( ( power_power @ SV347 @ SY1609 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SV347 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2465]) ).
thf(2876,plain,
! [SV348: $i] :
( ( ( ~ ( linordered_semidom @ SV348 ) )
= $true )
| ( ( ! [SY1610: $i,SY1611: $i] :
( ~ ( ord_less @ SV348 @ ( zero_zero @ SV348 ) @ SY1611 )
| ( ord_less @ SV348 @ ( zero_zero @ SV348 ) @ ( power_power @ SV348 @ SY1611 @ SY1610 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2466]) ).
thf(2877,plain,
! [SV349: $i] :
( ( ( ~ ( comm_semiring_1 @ SV349 ) )
= $true )
| ( ( ! [SY1612: $i,SY1613: $i,SY1614: $i] :
( ~ ( dvd_dvd @ SV349 @ SY1613 @ SY1614 )
| ( dvd_dvd @ SV349 @ SY1613 @ ( times_times @ SV349 @ SY1614 @ SY1612 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2467]) ).
thf(2878,plain,
! [SV587: $i,SV350: $i] :
( ( ~ ( ~ ( ~ ( ord_less_eq @ int @ ( plus_plus @ int @ SV350 @ ( one_one @ int ) ) @ SV587 )
| ( ord_less @ int @ SV350 @ SV587 ) )
| ~ ( ~ ( ord_less @ int @ SV350 @ SV587 )
| ( ord_less_eq @ int @ ( plus_plus @ int @ SV350 @ ( one_one @ int ) ) @ SV587 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2468]) ).
thf(2879,plain,
! [SV351: $i] :
( ( ( ~ ( no_zero_divisors @ SV351 ) )
= $true )
| ( ( ! [SY1616: $i,SY1617: $i] :
( ( ( times_times @ SV351 @ SY1616 @ SY1617 )
!= ( zero_zero @ SV351 ) )
| ( ( ti @ SV351 @ SY1616 )
= ( zero_zero @ SV351 ) )
| ( ( ti @ SV351 @ SY1617 )
= ( zero_zero @ SV351 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2469]) ).
thf(2880,plain,
! [SV352: $i] :
( ( ( ~ ( linordered_idom @ SV352 ) )
= $true )
| ( ( ! [SY1618: $i,SY1619: $i] :
~ ( ~ ( ( ( plus_plus @ SV352 @ ( power_power @ SV352 @ SY1618 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV352 @ SY1619 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV352 ) )
| ~ ( ( ( ti @ SV352 @ SY1618 )
!= ( zero_zero @ SV352 ) )
| ( ( ti @ SV352 @ SY1619 )
!= ( zero_zero @ SV352 ) ) ) )
| ~ ( ~ ~ ( ( ( ti @ SV352 @ SY1618 )
!= ( zero_zero @ SV352 ) )
| ( ( ti @ SV352 @ SY1619 )
!= ( zero_zero @ SV352 ) ) )
| ( ( plus_plus @ SV352 @ ( power_power @ SV352 @ SY1618 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV352 @ SY1619 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV352 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2470]) ).
thf(2881,plain,
! [SV353: $i] :
( ( ( ~ ( linordered_semidom @ SV353 ) )
= $true )
| ( ( ! [SY1620: $i,SY1621: $i,SY1622: $i] :
( ~ ( ord_less_eq @ SV353 @ SY1621 @ SY1622 )
| ~ ( ord_less_eq @ SV353 @ ( zero_zero @ SV353 ) @ SY1621 )
| ( ord_less_eq @ SV353 @ ( power_power @ SV353 @ SY1621 @ SY1620 ) @ ( power_power @ SV353 @ SY1622 @ SY1620 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2471]) ).
thf(2882,plain,
! [SV354: $i] :
( ( ( ~ ( comm_semiring_1 @ SV354 ) )
= $true )
| ( ( ! [SY1623: $i,SY1624: $i,SY1625: $i] :
( ( times_times @ SV354 @ SY1623 @ ( times_times @ SV354 @ SY1624 @ SY1625 ) )
= ( times_times @ SV354 @ SY1624 @ ( times_times @ SV354 @ SY1623 @ SY1625 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2472]) ).
thf(2883,plain,
! [SV355: $i] :
( ( ( ~ ~ ( ~ ( power @ SV355 )
| ~ ( semiring_0 @ SV355 ) ) )
= $true )
| ( ( ! [SY1626: $i] :
~ ( ~ ( ( SY1626
!= ( zero_zero @ nat ) )
| ( ( power_power @ SV355 @ ( zero_zero @ SV355 ) @ SY1626 )
= ( one_one @ SV355 ) ) )
| ~ ( ~ ( ( SY1626
!= ( zero_zero @ nat ) ) )
| ( ( power_power @ SV355 @ ( zero_zero @ SV355 ) @ SY1626 )
= ( zero_zero @ SV355 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2473]) ).
thf(2884,plain,
! [SV588: $i,SV356: $i] :
( ( ! [SY1873: $i] :
( ~ ( power @ SY1873 )
| ( ( power_power @ SY1873 @ ( ti @ SY1873 @ SV356 ) @ SV588 )
= ( power_power @ SY1873 @ SV356 @ SV588 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2474]) ).
thf(2885,plain,
! [SV589: $i,SV357: $i] :
( ( ! [SY1874: $i] :
( ~ ( no_zero_divisors @ SY1874 )
| ( ( times_times @ SY1874 @ SV357 @ ( ti @ SY1874 @ SV589 ) )
= ( times_times @ SY1874 @ SV357 @ SV589 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2475]) ).
thf(2886,plain,
! [SV358: $i] :
( ( ( ~ ( linordered_semidom @ SV358 ) )
= $true )
| ( ( ! [SY1631: $i,SY1632: $i,SY1633: $i] :
( ~ ( ord_less @ SV358 @ ( one_one @ SV358 ) @ SY1633 )
| ~ ( ~ ( ~ ( ord_less_eq @ SV358 @ ( power_power @ SV358 @ SY1633 @ SY1631 ) @ ( power_power @ SV358 @ SY1633 @ SY1632 ) )
| ( ord_less_eq @ nat @ SY1631 @ SY1632 ) )
| ~ ( ~ ( ord_less_eq @ nat @ SY1631 @ SY1632 )
| ( ord_less_eq @ SV358 @ ( power_power @ SV358 @ SY1633 @ SY1631 ) @ ( power_power @ SV358 @ SY1633 @ SY1632 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2476]) ).
thf(2887,plain,
! [SV590: $i,SV359: $i] :
( ( ! [SY1875: $i] :
( ~ ( power @ SY1875 )
| ( ( ti @ SY1875 @ ( power_power @ SY1875 @ SV359 @ SV590 ) )
= ( power_power @ SY1875 @ SV359 @ SV590 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2477]) ).
thf(2888,plain,
! [SV591: $i,SV360: $i] :
( ( ~ ( ~ ( ~ ( zcong @ SV360 @ ( zero_zero @ int ) @ SV591 )
| ( dvd_dvd @ int @ SV591 @ SV360 ) )
| ~ ( ~ ( dvd_dvd @ int @ SV591 @ SV360 )
| ( zcong @ SV360 @ ( zero_zero @ int ) @ SV591 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2478]) ).
thf(2889,plain,
! [SV361: $i] :
( ( ( ~ ( number_semiring @ SV361 ) )
= $true )
| ( ( ! [SY1637: $i,SY1638: $i] :
( ~ ( ord_less_eq @ int @ pls @ SY1638 )
| ~ ( ord_less_eq @ int @ pls @ SY1637 )
| ( ( times_times @ SV361 @ ( number_number_of @ SV361 @ SY1638 ) @ ( number_number_of @ SV361 @ SY1637 ) )
= ( number_number_of @ SV361 @ ( times_times @ int @ SY1638 @ SY1637 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2479]) ).
thf(2890,plain,
! [SV592: $i,SV362: $i] :
( ( ! [SY1876: $i] :
( ~ ( ( SY1876
!= ( zero_zero @ real ) ) )
| ~ ( ~ ( ( ( times_times @ real @ SV362 @ SY1876 )
!= ( times_times @ real @ SV592 @ SY1876 ) )
| ( SV362 = SV592 ) )
| ~ ( ( SV362 != SV592 )
| ( ( times_times @ real @ SV362 @ SY1876 )
= ( times_times @ real @ SV592 @ SY1876 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2480]) ).
thf(2891,plain,
( ( ( ~ ( quadRes @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) @ ( number_number_of @ int @ min ) ) )
= $false )
| ( ( ( legendre @ ( number_number_of @ int @ min ) @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) )
!= ( one_one @ int ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2481]) ).
thf(2892,plain,
! [SV363: $i] :
( ( ( ~ ( power @ SV363 ) )
= $true )
| ( ( ! [SY1641: $i,SY1642: $i] :
~ ( ~ ( ( SY1642
!= ( zero_zero @ nat ) )
| ( ( power_power @ SV363 @ SY1641 @ SY1642 )
= ( one_one @ SV363 ) ) )
| ~ ( ~ ( ( SY1642
!= ( zero_zero @ nat ) ) )
| ( ( power_power @ SV363 @ SY1641 @ SY1642 )
= ( times_times @ SV363 @ SY1641 @ ( power_power @ SV363 @ SY1641 @ ( minus_minus @ nat @ SY1642 @ ( one_one @ nat ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2482]) ).
thf(2893,plain,
! [SV364: $i,SV593: $i] :
( ( ! [SY1877: $i] :
( ~ ( dvd_dvd @ nat @ SV593 @ SY1877 )
| ( dvd_dvd @ nat @ ( power_power @ nat @ SV593 @ SV364 ) @ ( power_power @ nat @ SY1877 @ SV364 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2483]) ).
thf(2894,plain,
! [SV365: $i,SV594: $i] :
( ( ! [SY1878: $i] :
( ~ ( ord_less @ int @ SV594 @ SY1878 )
| ( ord_less @ int @ ( plus_plus @ int @ SV594 @ SV365 ) @ ( plus_plus @ int @ SY1878 @ SV365 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2484]) ).
thf(2895,plain,
! [SV366: $i,SV595: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ int @ SV595 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV595 ) @ ( number_number_of @ nat @ SV366 ) )
= ( number_number_of @ nat @ SV366 ) ) )
| ~ ( ~ ~ ( ord_less @ int @ SV595 @ pls )
| ~ ( ~ ( ~ ( ord_less @ int @ SV366 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV595 ) @ ( number_number_of @ nat @ SV366 ) )
= ( number_number_of @ nat @ SV595 ) ) )
| ~ ( ~ ~ ( ord_less @ int @ SV366 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV595 ) @ ( number_number_of @ nat @ SV366 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SV595 @ SV366 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2485]) ).
thf(2896,plain,
! [SV367: $i] :
( ( ( ~ ( comm_semiring_1 @ SV367 ) )
= $true )
| ( ( ! [SY1648: $i,SY1649: $i,SY1650: $i] :
( ~ ( ord_less_eq @ nat @ SY1649 @ SY1650 )
| ( dvd_dvd @ SV367 @ ( power_power @ SV367 @ SY1648 @ SY1649 ) @ ( power_power @ SV367 @ SY1648 @ SY1650 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2487]) ).
thf(2897,plain,
! [SV368: $i,SV596: $i] :
( ( ~ ( ~ ( ( SV596
!= ( zero_zero @ nat ) )
| ( ( times_times @ nat @ SV596 @ SV368 )
= ( zero_zero @ nat ) ) )
| ~ ( ~ ( ( SV596
!= ( zero_zero @ nat ) ) )
| ( ( times_times @ nat @ SV596 @ SV368 )
= ( plus_plus @ nat @ SV368 @ ( times_times @ nat @ ( minus_minus @ nat @ SV596 @ ( one_one @ nat ) ) @ SV368 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2488]) ).
thf(2898,plain,
! [SV597: $i,SV369: $i] :
( ( ! [SY1879: $i] :
( ~ ( dvd_dvd @ int @ SV369 @ ( minus_minus @ int @ SV597 @ SY1879 ) )
| ~ ( dvd_dvd @ int @ SV369 @ SY1879 )
| ( dvd_dvd @ int @ SV369 @ SV597 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2489]) ).
thf(2899,plain,
! [SV598: $i,SV370: $i] :
( ( ~ ( ~ ( ( ( bit1 @ SV370 )
!= ( bit1 @ SV598 ) )
| ( ( ti @ int @ SV370 )
= ( ti @ int @ SV598 ) ) )
| ~ ( ( ( ti @ int @ SV370 )
!= ( ti @ int @ SV598 ) )
| ( ( bit1 @ SV370 )
= ( bit1 @ SV598 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2490]) ).
thf(2900,plain,
! [SV371: $i] :
( ( ( ~ ( comm_semiring_1 @ SV371 ) )
= $true )
| ( ( ! [SY1655: $i,SY1656: $i,SY1657: $i] :
( ( power_power @ SV371 @ ( times_times @ SV371 @ SY1655 @ SY1656 ) @ SY1657 )
= ( times_times @ SV371 @ ( power_power @ SV371 @ SY1655 @ SY1657 ) @ ( power_power @ SV371 @ SY1656 @ SY1657 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2491]) ).
thf(2901,plain,
! [SV372: $i,SV599: $i] :
( ( ! [SY1880: $i,SY1881: $i] :
( ~ ( zcong @ SV599 @ SY1880 @ SY1881 )
| ( zcong @ ( times_times @ int @ SV599 @ SV372 ) @ ( times_times @ int @ SY1880 @ SV372 ) @ SY1881 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2492]) ).
thf(2902,plain,
! [SV600: $i,SV373: $i] :
( ( ~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit0 @ SV373 ) @ ( bit0 @ SV600 ) )
| ( ord_less_eq @ int @ SV373 @ SV600 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV373 @ SV600 )
| ( ord_less_eq @ int @ ( bit0 @ SV373 ) @ ( bit0 @ SV600 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2493]) ).
thf(2903,plain,
! [SV601: $i,SV374: $i] :
( ( ~ ( ~ ( ( ( times_times @ nat @ SV374 @ SV601 )
!= ( one_one @ nat ) )
| ~ ( ( SV374
!= ( one_one @ nat ) )
| ( SV601
!= ( one_one @ nat ) ) ) )
| ~ ( ~ ~ ( ( SV374
!= ( one_one @ nat ) )
| ( SV601
!= ( one_one @ nat ) ) )
| ( ( times_times @ nat @ SV374 @ SV601 )
= ( one_one @ nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2494]) ).
thf(2904,plain,
! [SV375: $i] :
( ( ( ~ ( linordered_semidom @ SV375 ) )
= $true )
| ( ( ! [SY1663: $i,SY1664: $i] :
( ~ ( ord_less @ SV375 @ ( one_one @ SV375 ) @ SY1664 )
| ( ord_less @ SV375 @ ( power_power @ SV375 @ SY1664 @ SY1663 ) @ ( times_times @ SV375 @ SY1664 @ ( power_power @ SV375 @ SY1664 @ SY1663 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2495]) ).
thf(2905,plain,
! [SV376: $i] :
( ( ( ~ ( ring_11004092258visors @ SV376 ) )
= $true )
| ( ( ! [SY1665: $i,SY1666: $i] :
( ~ ( ( ( ti @ SV376 @ SY1666 )
!= ( zero_zero @ SV376 ) ) )
| ( ( power_power @ SV376 @ SY1666 @ SY1665 )
!= ( zero_zero @ SV376 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2496]) ).
thf(2906,plain,
! [SV602: $i,SV377: $i] :
( ( ! [SY1882: $i] :
( ~ ( mult_zero @ SY1882 )
| ( ( times_times @ SY1882 @ SV377 @ ( ti @ SY1882 @ SV602 ) )
= ( times_times @ SY1882 @ SV377 @ SV602 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2497]) ).
thf(2907,plain,
! [SV378: $i] :
( ( ( ~ ( number_ring @ SV378 ) )
= $true )
| ( ( ! [SY1669: $i] :
( ( number_number_of @ SV378 @ ( bit1 @ SY1669 ) )
= ( plus_plus @ SV378 @ ( plus_plus @ SV378 @ ( one_one @ SV378 ) @ ( number_number_of @ SV378 @ SY1669 ) ) @ ( number_number_of @ SV378 @ SY1669 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2498]) ).
thf(2908,plain,
! [SV379: $i,SV603: $i] :
( ( ~ ( ord_less @ real @ ( zero_zero @ real ) @ SV603 )
| ~ ( ord_less @ real @ ( zero_zero @ real ) @ SV379 )
| ( ord_less @ real @ ( zero_zero @ real ) @ ( times_times @ real @ SV603 @ SV379 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2499]) ).
thf(2909,plain,
! [SV380: $i] :
( ( ( ~ ( comm_semiring_1 @ SV380 ) )
= $true )
| ( ( ! [SY1671: $i,SY1672: $i,SY1673: $i,SY1674: $i] :
( ( times_times @ SV380 @ ( times_times @ SV380 @ SY1671 @ SY1672 ) @ ( times_times @ SV380 @ SY1673 @ SY1674 ) )
= ( times_times @ SV380 @ SY1673 @ ( times_times @ SV380 @ ( times_times @ SV380 @ SY1671 @ SY1672 ) @ SY1674 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2500]) ).
thf(2910,plain,
! [SV381: $i] :
( ( ( ~ ( number_ring @ SV381 ) )
= $true )
| ( ( ! [SY1675: $i] :
( ( times_times @ SV381 @ SY1675 @ ( number_number_of @ SV381 @ ( bit1 @ pls ) ) )
= ( ti @ SV381 @ SY1675 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2501]) ).
thf(2911,plain,
! [SV604: $i,SV382: $i] :
( ( ! [SY1883: $i] :
( ~ ( zprime @ SY1883 )
| ~ ( dvd_dvd @ int @ SY1883 @ ( times_times @ int @ SV382 @ SV604 ) )
| ( dvd_dvd @ int @ SY1883 @ SV382 )
| ( dvd_dvd @ int @ SY1883 @ SV604 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2502]) ).
thf(2912,plain,
! [SV383: $i] :
( ( ( ~ ( linordered_semidom @ SV383 ) )
= $true )
| ( ( ! [SY1678: $i,SY1679: $i,SY1680: $i] :
( ~ ( ord_less @ nat @ SY1679 @ SY1680 )
| ~ ( ord_less @ SV383 @ ( one_one @ SV383 ) @ SY1678 )
| ( ord_less @ SV383 @ ( power_power @ SV383 @ SY1678 @ SY1679 ) @ ( power_power @ SV383 @ SY1678 @ SY1680 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2503]) ).
thf(2913,plain,
! [SV384: $i,SV605: $i] :
( ( ! [SY1884: $i] :
( ~ ( ord_less @ int @ SV605 @ SY1884 )
| ~ ( ord_less @ int @ SV384 @ SY1884 )
| ( ord_less_eq @ int @ SV605 @ SV384 )
| ( ord_less_eq @ int @ SV384 @ SV605 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2504]) ).
thf(2914,plain,
! [SV606: $i,SV385: $i] :
( ( ! [SY1885: $i,SY1886: $i] :
( ~ ( ord_less @ int @ SY1885 @ SY1886 )
| ~ ( ord_less_eq @ int @ SV385 @ SV606 )
| ( ord_less @ int @ ( plus_plus @ int @ SY1885 @ SV385 ) @ ( plus_plus @ int @ SY1886 @ SV606 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2505]) ).
thf(2915,plain,
! [SV386: $i] :
( ( ( ~ ~ ( ~ ( number @ SV386 )
| ~ ( ring @ SV386 ) ) )
= $true )
| ( ( ! [SY1686: $i,SY1687: $i,SY1688: $i] :
( ( times_times @ SV386 @ ( minus_minus @ SV386 @ SY1686 @ SY1687 ) @ ( number_number_of @ SV386 @ SY1688 ) )
= ( minus_minus @ SV386 @ ( times_times @ SV386 @ SY1686 @ ( number_number_of @ SV386 @ SY1688 ) ) @ ( times_times @ SV386 @ SY1687 @ ( number_number_of @ SV386 @ SY1688 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2506]) ).
thf(2916,plain,
! [SV387: $i,SV607: $i] :
( ( ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV607 )
| ~ ( ord_less @ int @ ( zero_zero @ int ) @ ( times_times @ int @ SV607 @ SV387 ) )
| ( ord_less @ int @ ( zero_zero @ int ) @ SV387 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2507]) ).
thf(2917,plain,
! [SV388: $i,SV608: $i] :
( ( ~ ( ord_less @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV608 )
| ~ ( zcong @ SV388 @ ( number_number_of @ int @ min ) @ SV608 )
| ~ ( zcong @ SV388 @ ( one_one @ int ) @ SV608 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2508]) ).
thf(2918,plain,
! [SV389: $i,SV609: $i] :
( ( ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV609 )
| ~ ( ord_less @ int @ SV609 @ SV389 )
| ~ ( zcong @ SV609 @ ( zero_zero @ int ) @ SV389 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2509]) ).
thf(2919,plain,
! [SV390: $i,SV610: $i] :
( ( ~ ( ~ ( ( SV610
!= ( zero_zero @ nat ) )
| ( ( power_power @ nat @ SV390 @ SV610 )
= ( one_one @ nat ) ) )
| ~ ( ~ ( ( SV610
!= ( zero_zero @ nat ) ) )
| ( ( power_power @ nat @ SV390 @ SV610 )
= ( times_times @ nat @ SV390 @ ( power_power @ nat @ SV390 @ ( minus_minus @ nat @ SV610 @ ( one_one @ nat ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2510]) ).
thf(2920,plain,
! [SV611: $i,SV391: $i] :
( ( ! [SY1887: $i] :
( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ SY1887 )
| ~ ( dvd_dvd @ int @ SV391 @ SV611 )
| ( dvd_dvd @ int @ SV391 @ ( power_power @ int @ SV611 @ SY1887 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2511]) ).
thf(2921,plain,
! [SV612: $i,SV392: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ nat @ ( number_number_of @ nat @ SV392 ) @ ( number_number_of @ nat @ SV612 ) )
| ~ ( ~ ( ~ ( ord_less @ int @ SV392 @ SV612 )
| ( ord_less @ int @ pls @ SV612 ) )
| ~ ( ord_less @ int @ SV392 @ SV612 ) ) )
| ~ ( ~ ~ ( ~ ( ~ ( ord_less @ int @ SV392 @ SV612 )
| ( ord_less @ int @ pls @ SV612 ) )
| ~ ( ord_less @ int @ SV392 @ SV612 ) )
| ( ord_less @ nat @ ( number_number_of @ nat @ SV392 ) @ ( number_number_of @ nat @ SV612 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2512]) ).
thf(2922,plain,
! [SV393: $i] :
( ( ( ~ ( number_ring @ SV393 ) )
= $true )
| ( ( ! [SY1696: $i,SY1697: $i] :
( ( power_power @ SV393 @ ( minus_minus @ SV393 @ SY1696 @ SY1697 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( minus_minus @ SV393 @ ( plus_plus @ SV393 @ ( power_power @ SV393 @ SY1696 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV393 @ SY1697 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times @ SV393 @ ( times_times @ SV393 @ ( number_number_of @ SV393 @ ( bit0 @ ( bit1 @ pls ) ) ) @ SY1696 ) @ SY1697 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2513]) ).
thf(2923,plain,
! [SV394: $i] :
( ( ~ ( ~ ( zprime @ ( ti @ int @ SV394 ) )
| ( zprime @ SV394 ) )
| ~ ( ~ ( zprime @ SV394 )
| ( zprime @ ( ti @ int @ SV394 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2514]) ).
thf(2924,plain,
! [SV395: $i,SV613: $i] :
( ( ! [SY1888: $i,SY1889: $i] :
( ~ ( zcong @ ( power_power @ int @ SV613 @ SY1888 ) @ ( one_one @ int ) @ SY1889 )
| ( zcong @ ( power_power @ int @ SV613 @ ( times_times @ nat @ SY1888 @ SV395 ) ) @ ( one_one @ int ) @ SY1889 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2515]) ).
thf(2925,plain,
! [SV614: $i,SV396: $i] :
( ( ~ ( ~ ( ~ ( zcong @ SV396 @ SV614 @ ( zero_zero @ int ) )
| ( ( ti @ int @ SV396 )
= ( ti @ int @ SV614 ) ) )
| ~ ( ( ( ti @ int @ SV396 )
!= ( ti @ int @ SV614 ) )
| ( zcong @ SV396 @ SV614 @ ( zero_zero @ int ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2516]) ).
thf(2926,plain,
! [SV615: $i,SV397: $i] :
( ( ~ ( ~ ( ( ( plus_plus @ real @ ( times_times @ real @ SV397 @ SV397 ) @ ( times_times @ real @ SV615 @ SV615 ) )
!= ( zero_zero @ real ) )
| ~ ( ( SV397
!= ( zero_zero @ real ) )
| ( SV615
!= ( zero_zero @ real ) ) ) )
| ~ ( ~ ~ ( ( SV397
!= ( zero_zero @ real ) )
| ( SV615
!= ( zero_zero @ real ) ) )
| ( ( plus_plus @ real @ ( times_times @ real @ SV397 @ SV397 ) @ ( times_times @ real @ SV615 @ SV615 ) )
= ( zero_zero @ real ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2517]) ).
thf(2927,plain,
! [SV398: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SV398 ) @ pls )
| ( ord_less @ int @ SV398 @ pls ) )
| ~ ( ~ ( ord_less @ int @ SV398 @ pls )
| ( ord_less @ int @ ( bit1 @ SV398 ) @ pls ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2518]) ).
thf(2928,plain,
! [SV399: $i] :
( ( ( ~ ( semiring @ SV399 ) )
= $true )
| ( ( ! [SY1703: $i,SY1704: $i,SY1705: $i,SY1706: $i] :
( ( plus_plus @ SV399 @ ( times_times @ SV399 @ SY1703 @ SY1704 ) @ ( plus_plus @ SV399 @ ( times_times @ SV399 @ SY1705 @ SY1704 ) @ SY1706 ) )
= ( plus_plus @ SV399 @ ( times_times @ SV399 @ ( plus_plus @ SV399 @ SY1703 @ SY1705 ) @ SY1704 ) @ SY1706 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2519]) ).
thf(2929,plain,
! [SV400: $i] :
( ( ( ~ ( monoid_mult @ SV400 ) )
= $true )
| ( ( ! [SY1707: $i] :
( ( power_power @ SV400 @ SY1707 @ ( one_one @ nat ) )
= ( ti @ SV400 @ SY1707 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2520]) ).
thf(2930,plain,
( ( ( t
= ( one_one @ int ) )
= $false )
| ( ( ~ ! [SX0: $i] :
~ ~ ! [SX1: $i] :
( ( plus_plus @ int @ ( power_power @ int @ SX0 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ SX1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2521]) ).
thf(2931,plain,
! [SV616: $i,SV401: $i] :
( ( ! [SY1890: $i] :
( ~ ( semiring @ SY1890 )
| ( ( times_times @ SY1890 @ ( ti @ SY1890 @ SV401 ) @ SV616 )
= ( times_times @ SY1890 @ SV401 @ SV616 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2522]) ).
thf(2932,plain,
! [SV402: $i] :
( ( ( ~ ( comm_semiring_1 @ SV402 ) )
= $true )
| ( ( ! [SY1710: $i] :
( ( times_times @ SV402 @ ( one_one @ SV402 ) @ SY1710 )
= ( ti @ SV402 @ SY1710 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2523]) ).
thf(2933,plain,
! [SV403: $i] :
( ( ( ~ ( comm_semiring_1 @ SV403 ) )
= $true )
| ( ( ! [SY1711: $i,SY1712: $i,SY1713: $i] :
( ( times_times @ SV403 @ SY1711 @ ( plus_plus @ SV403 @ SY1712 @ SY1713 ) )
= ( plus_plus @ SV403 @ ( times_times @ SV403 @ SY1711 @ SY1712 ) @ ( times_times @ SV403 @ SY1711 @ SY1713 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2524]) ).
thf(2934,plain,
! [SV404: $i] :
( ( ( ~ ( number_ring @ SV404 ) )
= $true )
| ( ( ! [SY1714: $i] :
( ( times_times @ SV404 @ ( number_number_of @ SV404 @ ( bit0 @ ( bit1 @ pls ) ) ) @ SY1714 )
= ( plus_plus @ SV404 @ SY1714 @ SY1714 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2525]) ).
thf(2935,plain,
! [SV617: $i,SV405: $i] :
( ( ! [SY1891: $i] :
~ ( ~ ( ~ ( zcong @ SV405 @ SV617 @ SY1891 )
| ~ ! [SY1892: $i] :
( ( ti @ int @ SV617 )
!= ( plus_plus @ int @ SV405 @ ( times_times @ int @ SY1891 @ SY1892 ) ) ) )
| ~ ( ~ ~ ! [SY1893: $i] :
( ( ti @ int @ SV617 )
!= ( plus_plus @ int @ SV405 @ ( times_times @ int @ SY1891 @ SY1893 ) ) )
| ( zcong @ SV405 @ SV617 @ SY1891 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2526]) ).
thf(2936,plain,
! [SV618: $i,SV406: $i] :
( ( ! [SY1894: $i] :
( ( ( minus_minus @ int @ SV406 @ SV618 )
!= ( ti @ int @ SY1894 ) )
| ( ( ti @ int @ SV406 )
= ( plus_plus @ int @ SY1894 @ SV618 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2527]) ).
thf(2937,plain,
! [SV407: $i] :
( ( ( ~ ( zprime @ SV407 ) )
= $true )
| ( ( ~ ( ( ( ti @ int @ SV407 )
!= ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ~ ( ( ( ti @ int @ SV407 )
!= ( number_number_of @ int @ ( bit1 @ ( bit1 @ pls ) ) ) ) )
| ( ord_less_eq @ int @ ( number_number_of @ int @ ( bit1 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SV407 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2528]) ).
thf(2938,plain,
! [SV619: $i,SV408: $i] :
( ( ! [SY1895: $i] :
( ~ ( semiring @ SY1895 )
| ( ( ti @ SY1895 @ ( plus_plus @ SY1895 @ SV408 @ SV619 ) )
= ( plus_plus @ SY1895 @ SV408 @ SV619 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2529]) ).
thf(2939,plain,
! [SV409: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV409 ) )
= $true )
| ( ( ord_less @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( one_one @ int ) @ SV409 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2530]) ).
thf(2940,plain,
! [SV620: $i,SV410: $i] :
( ( ! [SY1896: $i] :
( ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( times_times @ int @ SV410 @ SV620 ) @ SY1896 ) )
| ~ ( ord_less @ int @ SY1896 @ SV410 )
| ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV410 )
| ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV620 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2531]) ).
thf(2941,plain,
! [SV411: $i] :
( ( ( ~ ( linordered_idom @ SV411 ) )
= $true )
| ( ( ! [SY1725: $i] :
~ ( ord_less @ SV411 @ ( power_power @ SV411 @ SY1725 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( zero_zero @ SV411 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2532]) ).
thf(2942,plain,
! [SV412: $i] :
( ( ( ~ ( monoid_mult @ SV412 ) )
= $true )
| ( ( ! [SY1726: $i,SY1727: $i,SY1728: $i] :
( ( power_power @ SV412 @ SY1726 @ ( times_times @ nat @ SY1727 @ SY1728 ) )
= ( power_power @ SV412 @ ( power_power @ SV412 @ SY1726 @ SY1727 ) @ SY1728 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2533]) ).
thf(2943,plain,
! [SV621: $i,SV413: $i] :
( ( ~ ( ~ ( ( ( times_times @ int @ SV413 @ SV621 )
!= ( one_one @ int ) )
| ~ ( ( ( ti @ int @ SV413 )
!= ( one_one @ int ) )
| ( ( ti @ int @ SV621 )
!= ( one_one @ int ) ) )
| ~ ( ( ( ti @ int @ SV413 )
!= ( number_number_of @ int @ min ) )
| ( ( ti @ int @ SV621 )
!= ( number_number_of @ int @ min ) ) ) )
| ~ ( ~ ( ~ ( ( ( ti @ int @ SV413 )
!= ( one_one @ int ) )
| ( ( ti @ int @ SV621 )
!= ( one_one @ int ) ) )
| ~ ( ( ( ti @ int @ SV413 )
!= ( number_number_of @ int @ min ) )
| ( ( ti @ int @ SV621 )
!= ( number_number_of @ int @ min ) ) ) )
| ( ( times_times @ int @ SV413 @ SV621 )
= ( one_one @ int ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2534]) ).
thf(2944,plain,
! [SV414: $i] :
( ( ( ~ ( comm_semiring_1 @ SV414 ) )
= $true )
| ( ( ! [SY1730: $i,SY1731: $i] :
( ( plus_plus @ SV414 @ SY1730 @ SY1731 )
= ( plus_plus @ SV414 @ SY1731 @ SY1730 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2535]) ).
thf(2945,plain,
! [SV415: $i] :
( ( ( ~ ( number_ring @ SV415 ) )
= $true )
| ( ( ( zero_zero @ SV415 )
= ( number_number_of @ SV415 @ pls ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2536]) ).
thf(2946,plain,
! [SV416: $i] :
( ( ( ~ ~ ( ~ ( monoid_mult @ SV416 )
| ~ ( number @ SV416 ) ) )
= $true )
| ( ( ! [SY1732: $i] :
( ( power_power @ SV416 @ ( number_number_of @ SV416 @ SY1732 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times @ SV416 @ ( number_number_of @ SV416 @ SY1732 ) @ ( number_number_of @ SV416 @ SY1732 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2537]) ).
thf(2947,plain,
! [SV417: $i] :
( ( ( ~ ( ordere453448008miring @ SV417 ) )
= $true )
| ( ( ! [SY1733: $i,SY1734: $i] :
( ~ ( ord_less_eq @ SV417 @ SY1734 @ ( zero_zero @ SV417 ) )
| ~ ( ord_less_eq @ SV417 @ ( zero_zero @ SV417 ) @ SY1733 )
| ( ord_less_eq @ SV417 @ ( times_times @ SV417 @ SY1734 @ SY1733 ) @ ( zero_zero @ SV417 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2538]) ).
thf(2948,plain,
! [SV622: $i,SV418: $i] :
( ( ~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SV418 ) @ ( bit0 @ SV622 ) )
| ( ord_less @ int @ SV418 @ SV622 ) )
| ~ ( ~ ( ord_less @ int @ SV418 @ SV622 )
| ( ord_less_eq @ int @ ( bit1 @ SV418 ) @ ( bit0 @ SV622 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2539]) ).
thf(2949,plain,
! [SV419: $i,SV623: $i] :
( ( ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV623 )
| ~ ( ~ ( ( ( times_times @ int @ SV623 @ SV419 )
!= ( one_one @ int ) )
| ~ ( ( ( ti @ int @ SV623 )
!= ( one_one @ int ) )
| ( ( ti @ int @ SV419 )
!= ( one_one @ int ) ) ) )
| ~ ( ~ ~ ( ( ( ti @ int @ SV623 )
!= ( one_one @ int ) )
| ( ( ti @ int @ SV419 )
!= ( one_one @ int ) ) )
| ( ( times_times @ int @ SV623 @ SV419 )
= ( one_one @ int ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2540]) ).
thf(2950,plain,
! [SV624: $i,SV420: $i] :
( ( ~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit0 @ SV420 ) @ ( bit1 @ SV624 ) )
| ( ord_less_eq @ int @ SV420 @ SV624 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV420 @ SV624 )
| ( ord_less_eq @ int @ ( bit0 @ SV420 ) @ ( bit1 @ SV624 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2541]) ).
thf(2951,plain,
! [SV421: $i,SV625: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ int @ SV625 @ pls )
| ( ( times_times @ nat @ ( number_number_of @ nat @ SV625 ) @ ( number_number_of @ nat @ SV421 ) )
= ( zero_zero @ nat ) ) )
| ~ ( ~ ~ ( ord_less @ int @ SV625 @ pls )
| ( ( times_times @ nat @ ( number_number_of @ nat @ SV625 ) @ ( number_number_of @ nat @ SV421 ) )
= ( number_number_of @ nat @ ( times_times @ int @ SV625 @ SV421 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2542]) ).
thf(2952,plain,
! [SV626: $i,SV422: $i] :
( ( ! [SY1897: $i,SY1898: $i,SY1899: $i,SY1900: $i] :
( ( ( plus_plus @ int @ ( times_times @ int @ SV422 @ SV626 ) @ SY1897 )
!= ( plus_plus @ int @ ( times_times @ int @ SY1898 @ SY1899 ) @ SY1900 ) )
| ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( times_times @ int @ SY1898 @ SY1899 ) @ SY1900 ) )
| ~ ( ord_less @ int @ SY1900 @ SY1898 )
| ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SY1897 )
| ~ ( ord_less @ int @ ( zero_zero @ int ) @ SY1898 )
| ~ ( ord_less_eq @ int @ SY1898 @ SV422 )
| ( ord_less_eq @ int @ SV626 @ SY1899 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2543]) ).
thf(2953,plain,
! [SV423: $i] :
( ( ~ ( ~ ~ ( ord_less @ real @ ( zero_zero @ real ) @ ( times_times @ real @ SV423 @ SV423 ) )
| ( SV423
= ( zero_zero @ real ) ) )
| ~ ( ( SV423
!= ( zero_zero @ real ) )
| ~ ( ord_less @ real @ ( zero_zero @ real ) @ ( times_times @ real @ SV423 @ SV423 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2544]) ).
thf(2954,plain,
! [SV627: $i,SV424: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SV424 ) @ ( bit1 @ SV627 ) )
| ( ord_less @ int @ SV424 @ SV627 ) )
| ~ ( ~ ( ord_less @ int @ SV424 @ SV627 )
| ( ord_less @ int @ ( bit1 @ SV424 ) @ ( bit1 @ SV627 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2545]) ).
thf(2955,plain,
! [SV425: $i] :
( ( ( ~ ( comm_semiring_1 @ SV425 ) )
= $true )
| ( ( ! [SY1745: $i] : ( dvd_dvd @ SV425 @ ( one_one @ SV425 ) @ SY1745 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2546]) ).
thf(2956,plain,
! [SV628: $i,SV426: $i] :
( ( ! [SY1901: $i] :
( ~ ( mult_zero @ SY1901 )
| ( ( ti @ SY1901 @ ( times_times @ SY1901 @ SV426 @ SV628 ) )
= ( times_times @ SY1901 @ SV426 @ SV628 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2547]) ).
thf(2957,plain,
! [SV629: $i,SV427: $i] :
( ( ! [SY1902: $i] :
~ ( ~ ( ~ ( zcong @ ( ti @ int @ SV427 ) @ SV629 @ SY1902 )
| ( zcong @ SV427 @ SV629 @ SY1902 ) )
| ~ ( ~ ( zcong @ SV427 @ SV629 @ SY1902 )
| ( zcong @ ( ti @ int @ SV427 ) @ SV629 @ SY1902 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2548]) ).
thf(2958,plain,
! [SV630: $i,SV428: $i] :
( ( ~ ( ~ ( ~ ( zcong @ SV428 @ ( zero_zero @ int ) @ SV630 )
| ( dvd_dvd @ int @ SV630 @ SV428 ) )
| ~ ( ~ ( dvd_dvd @ int @ SV630 @ SV428 )
| ( zcong @ SV428 @ ( zero_zero @ int ) @ SV630 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2549]) ).
thf(2959,plain,
! [SV631: $i,SV429: $i] :
( ( ~ ( ~ ( ( ( power_power @ nat @ SV429 @ SV631 )
!= ( one_one @ nat ) )
| ( SV429
= ( one_one @ nat ) )
| ( SV631
= ( zero_zero @ nat ) ) )
| ~ ( ~ ( ( SV429
= ( one_one @ nat ) )
| ( SV631
= ( zero_zero @ nat ) ) )
| ( ( power_power @ nat @ SV429 @ SV631 )
= ( one_one @ nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2550]) ).
thf(2960,plain,
! [SV430: $i,SV632: $i] :
( ( ! [SY1903: $i,SY1904: $i] :
( ~ ( zcong @ SV632 @ SY1903 @ SY1904 )
| ( zcong @ ( plus_plus @ int @ SV632 @ SV430 ) @ ( plus_plus @ int @ SY1903 @ SV430 ) @ SY1904 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2551]) ).
thf(2961,plain,
! [SV431: $i] :
( ( ( ~ ( linordered_idom @ SV431 ) )
= $true )
| ( ( ! [SY1755: $i,SY1756: $i] : ( ord_less_eq @ SV431 @ ( zero_zero @ SV431 ) @ ( plus_plus @ SV431 @ ( power_power @ SV431 @ SY1755 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV431 @ SY1756 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2552]) ).
thf(2962,plain,
! [SV432: $i] :
( ( ( ~ ( number_ring @ SV432 ) )
= $true )
| ( ( ! [SY1757: $i] :
( ( plus_plus @ SV432 @ ( number_number_of @ SV432 @ SY1757 ) @ ( one_one @ SV432 ) )
= ( number_number_of @ SV432 @ ( plus_plus @ int @ SY1757 @ ( bit1 @ pls ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2553]) ).
thf(2963,plain,
! [SV433: $i] :
( ( ( ~ ( linordered_semidom @ SV433 ) )
= $true )
| ( ( ! [SY1758: $i,SY1759: $i,SY1760: $i] :
( ~ ( ord_less @ nat @ SY1759 @ SY1760 )
| ~ ( ord_less @ SV433 @ ( zero_zero @ SV433 ) @ SY1758 )
| ~ ( ord_less @ SV433 @ SY1758 @ ( one_one @ SV433 ) )
| ( ord_less @ SV433 @ ( power_power @ SV433 @ SY1758 @ SY1760 ) @ ( power_power @ SV433 @ SY1758 @ SY1759 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2554]) ).
thf(2964,plain,
! [SV434: $i] :
( ( ( ~ ( semiri456707255roduct @ SV434 ) )
= $true )
| ( ( ! [SY1761: $i,SY1762: $i,SY1763: $i,SY1764: $i,SY1765: $i] :
( ~ ( ( ( ti @ SV434 @ SY1765 )
!= ( zero_zero @ SV434 ) ) )
| ~ ~ ( ( ( ti @ SV434 @ SY1763 )
!= ( ti @ SV434 @ SY1764 ) )
| ~ ( ( ( ti @ SV434 @ SY1761 )
!= ( ti @ SV434 @ SY1762 ) ) ) )
| ( ( plus_plus @ SV434 @ SY1763 @ ( times_times @ SV434 @ SY1765 @ SY1761 ) )
!= ( plus_plus @ SV434 @ SY1764 @ ( times_times @ SV434 @ SY1765 @ SY1762 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2555]) ).
thf(2965,plain,
! [SV446: $i,SV20: $i] :
( ( ( ord_less_eq @ int @ SV20 @ SV446 )
= $true )
| ( ( ord_less_eq @ int @ SV446 @ SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2567]) ).
thf(2966,plain,
! [SV447: $i,SV21: $i] :
( ( ( ( ord_less @ int @ SV21 @ SV447 )
| ( ( ti @ int @ SV21 )
= ( ti @ int @ SV447 ) ) )
= $true )
| ( ( ord_less @ int @ SV447 @ SV21 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2568]) ).
thf(2967,plain,
! [SV633: $i,SV448: $i,SV22: $i] :
( ( ( power_power @ int @ ( power_power @ int @ SV22 @ SV448 ) @ SV633 )
= ( power_power @ int @ SV22 @ ( times_times @ nat @ SV448 @ SV633 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2569]) ).
thf(2968,plain,
! [SV634: $i,SV449: $i,SV23: $i] :
( ( ( power_power @ int @ SV23 @ ( plus_plus @ nat @ SV449 @ SV634 ) )
= ( times_times @ int @ ( power_power @ int @ SV23 @ SV449 ) @ ( power_power @ int @ SV23 @ SV634 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2570]) ).
thf(2969,plain,
! [SV635: $i,SV450: $i,SV26: $i] :
( ( ( times_times @ int @ ( times_times @ int @ SV26 @ SV450 ) @ SV635 )
= ( times_times @ int @ SV26 @ ( times_times @ int @ SV450 @ SV635 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2571]) ).
thf(2970,plain,
! [SV636: $i,SV452: $i,SV29: $i] :
( ( ( plus_plus @ int @ ( plus_plus @ int @ SV29 @ SV452 ) @ SV636 )
= ( plus_plus @ int @ SV29 @ ( plus_plus @ int @ SV452 @ SV636 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2573]) ).
thf(2971,plain,
! [SV637: $i,SV453: $i,SV30: $i] :
( ( ( plus_plus @ int @ SV30 @ ( plus_plus @ int @ SV453 @ SV637 ) )
= ( plus_plus @ int @ SV453 @ ( plus_plus @ int @ SV30 @ SV637 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2574]) ).
thf(2972,plain,
! [SV638: $i,SV458: $i,SV41: $i] :
( ( ( times_times @ int @ ( plus_plus @ int @ SV41 @ SV458 ) @ SV638 )
= ( plus_plus @ int @ ( times_times @ int @ SV41 @ SV638 ) @ ( times_times @ int @ SV458 @ SV638 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2579]) ).
thf(2973,plain,
! [SV639: $i,SV459: $i,SV42: $i] :
( ( ( times_times @ int @ SV42 @ ( plus_plus @ int @ SV459 @ SV639 ) )
= ( plus_plus @ int @ ( times_times @ int @ SV42 @ SV459 ) @ ( times_times @ int @ SV42 @ SV639 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2580]) ).
thf(2974,plain,
( ( zcong @ ( power_power @ int @ sK1_S1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of @ int @ min ) @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2586]) ).
thf(2975,plain,
! [SV640: $i,SV466: $i,SV55: $i] :
( ( zcong @ ( times_times @ int @ SV55 @ SV466 ) @ ( times_times @ int @ SV640 @ SV466 ) @ SV466 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2588]) ).
thf(2976,plain,
! [SV641: $i,SV468: $i,SV58: $i] :
( ( ( times_times @ int @ ( minus_minus @ int @ SV58 @ SV468 ) @ SV641 )
= ( minus_minus @ int @ ( times_times @ int @ SV58 @ SV641 ) @ ( times_times @ int @ SV468 @ SV641 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2590]) ).
thf(2977,plain,
! [SV642: $i,SV469: $i,SV59: $i] :
( ( ( times_times @ int @ SV59 @ ( minus_minus @ int @ SV469 @ SV642 ) )
= ( minus_minus @ int @ ( times_times @ int @ SV59 @ SV469 ) @ ( times_times @ int @ SV59 @ SV642 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2591]) ).
thf(2978,plain,
! [SV643: $i,SV472: $i,SV63: $i] :
( ( ! [SY1905: $i,SY1906: $i,SY1907: $i,SY1908: $i] :
( ( plus_plus @ int @ ( times_times @ int @ ( minus_minus @ int @ SV63 @ ( times_times @ int @ SV472 @ SV643 ) ) @ SY1905 ) @ ( times_times @ int @ ( minus_minus @ int @ SY1906 @ ( times_times @ int @ SV472 @ SY1907 ) ) @ SY1908 ) )
= ( minus_minus @ int @ ( plus_plus @ int @ ( times_times @ int @ SV63 @ SY1905 ) @ ( times_times @ int @ SY1906 @ SY1908 ) ) @ ( times_times @ int @ SV472 @ ( plus_plus @ int @ ( times_times @ int @ SV643 @ SY1905 ) @ ( times_times @ int @ SY1907 @ SY1908 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2594]) ).
thf(2979,plain,
! [SV644: $i,SV473: $i,SV67: $i] :
( ( ! [SY1909: $i] :
( ( times_times @ int @ ( twoSqu579703163sum2sq @ ( product_Pair @ int @ int @ SV67 @ SV473 ) ) @ ( twoSqu579703163sum2sq @ ( product_Pair @ int @ int @ SV644 @ SY1909 ) ) )
= ( twoSqu579703163sum2sq @ ( product_Pair @ int @ int @ ( plus_plus @ int @ ( times_times @ int @ SV67 @ SV644 ) @ ( times_times @ int @ SV473 @ SY1909 ) ) @ ( minus_minus @ int @ ( times_times @ int @ SV67 @ SY1909 ) @ ( times_times @ int @ SV473 @ SV644 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2595]) ).
thf(2980,plain,
! [SV645: $i,SV479: $i,SV76: $i] :
( ( ( times_times @ real @ ( times_times @ real @ SV76 @ SV479 ) @ SV645 )
= ( times_times @ real @ SV76 @ ( times_times @ real @ SV479 @ SV645 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2602]) ).
thf(2981,plain,
! [SV646: $i,SV480: $i,SV77: $i] :
( ( ( times_times @ real @ ( plus_plus @ real @ SV77 @ SV480 ) @ SV646 )
= ( plus_plus @ real @ ( times_times @ real @ SV77 @ SV646 ) @ ( times_times @ real @ SV480 @ SV646 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2603]) ).
thf(2982,plain,
! [SV481: $i,SV79: $i,SV647: $i] :
( ( ! [SY1910: $i,SY1911: $i] :
( ~ ( zcong @ SV647 @ SY1910 @ SY1911 )
| ~ ( ~ ( ~ ( zcong @ SV79 @ ( times_times @ int @ SV647 @ SV481 ) @ SY1911 )
| ( zcong @ SV79 @ ( times_times @ int @ SY1910 @ SV481 ) @ SY1911 ) )
| ~ ( ~ ( zcong @ SV79 @ ( times_times @ int @ SY1910 @ SV481 ) @ SY1911 )
| ( zcong @ SV79 @ ( times_times @ int @ SV647 @ SV481 ) @ SY1911 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2604]) ).
thf(2983,plain,
! [SV482: $i,SV80: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV80 @ ( plus_plus @ int @ SV482 @ ( one_one @ int ) ) )
| ( ord_less @ int @ SV80 @ SV482 )
| ( ( ti @ int @ SV80 )
= ( ti @ int @ SV482 ) ) )
| ~ ( ~ ( ( ord_less @ int @ SV80 @ SV482 )
| ( ( ti @ int @ SV80 )
= ( ti @ int @ SV482 ) ) )
| ( ord_less @ int @ SV80 @ ( plus_plus @ int @ SV482 @ ( one_one @ int ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2605]) ).
thf(2984,plain,
! [SV483: $i,SV81: $i,SV648: $i] :
( ( ~ ( semiring @ SV648 )
| ( ( plus_plus @ SV648 @ SV81 @ ( ti @ SV648 @ SV483 ) )
= ( plus_plus @ SV648 @ SV81 @ SV483 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2606]) ).
thf(2985,plain,
! [SV82: $i] :
( ( ( ordere453448008miring @ SV82 )
= $false )
| ( ( ! [SY1175: $i,SY1176: $i] :
( ~ ( ord_less_eq @ SV82 @ ( zero_zero @ SV82 ) @ SY1176 )
| ~ ( ord_less_eq @ SV82 @ SY1175 @ ( zero_zero @ SV82 ) )
| ( ord_less_eq @ SV82 @ ( times_times @ SV82 @ SY1176 @ SY1175 ) @ ( zero_zero @ SV82 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2607]) ).
thf(2986,plain,
! [SV83: $i] :
( ( ( monoid_mult @ SV83 )
= $false )
| ( ( ! [SY1177: $i,SY1178: $i] :
( ( times_times @ SV83 @ ( power_power @ SV83 @ SY1177 @ SY1178 ) @ SY1177 )
= ( times_times @ SV83 @ SY1177 @ ( power_power @ SV83 @ SY1177 @ SY1178 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2608]) ).
thf(2987,plain,
! [SV84: $i] :
( ( ( comm_semiring_1 @ SV84 )
= $false )
| ( ( ! [SY1179: $i,SY1180: $i,SY1181: $i] :
( ( plus_plus @ SV84 @ ( plus_plus @ SV84 @ SY1179 @ SY1180 ) @ SY1181 )
= ( plus_plus @ SV84 @ SY1179 @ ( plus_plus @ SV84 @ SY1180 @ SY1181 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2609]) ).
thf(2988,plain,
! [SV85: $i] :
( ( ( number_semiring @ SV85 )
= $false )
| ( ( ( plus_plus @ SV85 @ ( one_one @ SV85 ) @ ( one_one @ SV85 ) )
= ( number_number_of @ SV85 @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2610]) ).
thf(2989,plain,
! [SV86: $i] :
( ( ( linordered_ring @ SV86 )
= $false )
| ( ( ! [SY1182: $i] : ( ord_less_eq @ SV86 @ ( zero_zero @ SV86 ) @ ( times_times @ SV86 @ SY1182 @ SY1182 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2611]) ).
thf(2990,plain,
! [SV87: $i] :
( ( ( ordere453448008miring @ SV87 )
= $false )
| ( ( ! [SY1183: $i,SY1184: $i] :
( ~ ( ord_less_eq @ SV87 @ ( zero_zero @ SV87 ) @ SY1184 )
| ~ ( ord_less_eq @ SV87 @ SY1183 @ ( zero_zero @ SV87 ) )
| ( ord_less_eq @ SV87 @ ( times_times @ SV87 @ SY1183 @ SY1184 ) @ ( zero_zero @ SV87 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2612]) ).
thf(2991,plain,
! [SV88: $i] :
( ( ( linordered_idom @ SV88 )
= $false )
| ( ( ! [SY1185: $i,SY1186: $i] :
~ ( ord_less @ SV88 @ ( plus_plus @ SV88 @ ( power_power @ SV88 @ SY1185 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV88 @ SY1186 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( zero_zero @ SV88 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2613]) ).
thf(2992,plain,
! [SV484: $i,SV89: $i,SV649: $i] :
( ( ~ ( no_zero_divisors @ SV649 )
| ( ( times_times @ SV649 @ ( ti @ SV649 @ SV89 ) @ SV484 )
= ( times_times @ SV649 @ SV89 @ SV484 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2614]) ).
thf(2993,plain,
! [SV90: $i] :
( ( ( no_zero_divisors @ SV90 )
= $false )
| ( ( ! [SY1189: $i,SY1190: $i] :
( ~ ( ( ( ti @ SV90 @ SY1190 )
!= ( zero_zero @ SV90 ) ) )
| ~ ( ( ( ti @ SV90 @ SY1189 )
!= ( zero_zero @ SV90 ) ) )
| ( ( times_times @ SV90 @ SY1190 @ SY1189 )
!= ( zero_zero @ SV90 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2615]) ).
thf(2994,plain,
! [SV91: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ min @ ( bit1 @ SV91 ) )
| ( ord_less_eq @ int @ min @ SV91 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2616]) ).
thf(2995,plain,
! [SV91: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ min @ SV91 )
| ( ord_less_eq @ int @ min @ ( bit1 @ SV91 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2616]) ).
thf(2996,plain,
! [SV485: $i,SV92: $i] :
( ( ( ~ ( dvd_dvd @ int @ SV92 @ SV485 ) )
= $true )
| ( ( ( ord_less_eq @ int @ SV485 @ ( zero_zero @ int ) )
| ( ord_less_eq @ int @ SV92 @ SV485 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2617]) ).
thf(2997,plain,
! [SV93: $i] :
( ( ~ ( ( min
!= ( bit1 @ SV93 ) )
| ( min
= ( ti @ int @ SV93 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2618]) ).
thf(2998,plain,
! [SV93: $i] :
( ( ~ ( ( min
!= ( ti @ int @ SV93 ) )
| ( min
= ( bit1 @ SV93 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2618]) ).
thf(2999,plain,
! [SV94: $i] :
( ( ( comm_semiring_1 @ SV94 )
= $false )
| ( ( ! [SY1192: $i,SY1193: $i,SY1194: $i] :
( ( times_times @ SV94 @ SY1192 @ ( times_times @ SV94 @ SY1193 @ SY1194 ) )
= ( times_times @ SV94 @ ( times_times @ SV94 @ SY1192 @ SY1193 ) @ SY1194 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2619]) ).
thf(3000,plain,
! [SV95: $i] :
( ( ( comm_semiring_1 @ SV95 )
= $false )
| ( ( ! [SY1195: $i,SY1196: $i,SY1197: $i,SY1198: $i] :
( ( times_times @ SV95 @ ( times_times @ SV95 @ SY1195 @ SY1196 ) @ ( times_times @ SV95 @ SY1197 @ SY1198 ) )
= ( times_times @ SV95 @ SY1195 @ ( times_times @ SV95 @ SY1196 @ ( times_times @ SV95 @ SY1197 @ SY1198 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2620]) ).
thf(3001,plain,
! [SV486: $i,SV96: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( number_number_of @ int @ SV96 ) @ ( number_number_of @ int @ SV486 ) )
| ( ord_less @ int @ SV96 @ SV486 ) )
| ~ ( ~ ( ord_less @ int @ SV96 @ SV486 )
| ( ord_less @ int @ ( number_number_of @ int @ SV96 ) @ ( number_number_of @ int @ SV486 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2621]) ).
thf(3002,plain,
! [SV487: $i,SV97: $i] :
( ( ( ~ ( dvd_dvd @ nat @ SV97 @ SV487 ) )
= $true )
| ( ( ( SV487
= ( zero_zero @ nat ) )
| ( ord_less_eq @ nat @ SV97 @ SV487 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2622]) ).
thf(3003,plain,
! [SV488: $i,SV98: $i,SV650: $i] :
( ( ~ ( ab_group_add @ SV650 )
| ( ( ti @ SV650 @ ( plus_plus @ SV650 @ SV98 @ SV488 ) )
= ( plus_plus @ SV650 @ SV98 @ SV488 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2623]) ).
thf(3004,plain,
! [SV99: $i] :
( ( ( comm_semiring_1 @ SV99 )
= $false )
| ( ( ! [SY1203: $i,SY1204: $i,SY1205: $i] :
( ( plus_plus @ SV99 @ SY1203 @ ( plus_plus @ SV99 @ SY1204 @ SY1205 ) )
= ( plus_plus @ SV99 @ SY1204 @ ( plus_plus @ SV99 @ SY1203 @ SY1205 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2624]) ).
thf(3005,plain,
! [SV100: $i,SV651: $i,SV489: $i] :
( ( ~ ( ord_less_eq @ int @ SV489 @ SV651 )
| ( ord_less_eq @ int @ ( plus_plus @ int @ SV100 @ SV489 ) @ ( plus_plus @ int @ SV100 @ SV651 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2625]) ).
thf(3006,plain,
! [SV101: $i,SV652: $i,SV490: $i] :
( ( ~ ~ ( zcong @ SV490 @ ( zero_zero @ int ) @ SV652 )
| ~ ( zcong @ ( power_power @ int @ SV101 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SV490 @ SV652 )
| ~ ( dvd_dvd @ int @ SV652 @ SV101 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2626]) ).
thf(3007,plain,
! [SV102: $i] :
( ( ( linordered_semidom @ SV102 )
= $false )
| ( ( ! [SY1210: $i,SY1211: $i] :
( ~ ( ord_less @ SV102 @ ( zero_zero @ SV102 ) @ SY1211 )
| ~ ( ord_less @ SV102 @ SY1211 @ ( one_one @ SV102 ) )
| ( ord_less @ SV102 @ ( times_times @ SV102 @ SY1211 @ ( power_power @ SV102 @ SY1211 @ SY1210 ) ) @ ( power_power @ SV102 @ SY1211 @ SY1210 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2627]) ).
thf(3008,plain,
! [SV491: $i,SV103: $i] :
( ( ~ ( ~ ( quadRes @ ( ti @ int @ SV103 ) @ SV491 )
| ( quadRes @ SV103 @ SV491 ) )
| ~ ( ~ ( quadRes @ SV103 @ SV491 )
| ( quadRes @ ( ti @ int @ SV103 ) @ SV491 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2628]) ).
thf(3009,plain,
! [SV492: $i,SV104: $i,SV653: $i] :
( ( ~ ( semiring @ SV653 )
| ( ( times_times @ SV653 @ SV104 @ ( ti @ SV653 @ SV492 ) )
= ( times_times @ SV653 @ SV104 @ SV492 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2629]) ).
thf(3010,plain,
! [SV105: $i] :
( ( ( semiring_1 @ SV105 )
= $false )
| ( ( ( power_power @ SV105 @ ( one_one @ SV105 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( one_one @ SV105 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2630]) ).
thf(3011,plain,
! [SV106: $i] :
( ( ~ ( ( ( bit1 @ SV106 )
!= min )
| ( ( ti @ int @ SV106 )
= min ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2631]) ).
thf(3012,plain,
! [SV106: $i] :
( ( ~ ( ( ( ti @ int @ SV106 )
!= min )
| ( ( bit1 @ SV106 )
= min ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2631]) ).
thf(3013,plain,
! [SV493: $i,SV107: $i,SV654: $i] :
( ( ~ ( power @ SV654 )
| ( ( times_times @ SV654 @ SV107 @ ( ti @ SV654 @ SV493 ) )
= ( times_times @ SV654 @ SV107 @ SV493 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2632]) ).
thf(3014,plain,
! [SV108: $i,SV494: $i,SV655: $i] :
( ( ! [SY1912: $i,SY1913: $i] :
( ~ ( zcong @ SV655 @ SY1912 @ SY1913 )
| ( ( ti @ int @ SY1912 )
!= ( ti @ int @ SV494 ) )
| ~ ( zcong @ SV494 @ SV108 @ SY1913 )
| ( zcong @ SV655 @ SV108 @ SY1913 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2633]) ).
thf(3015,plain,
! [SV656: $i,SV495: $i,SV109: $i] :
( ( ~ ( dvd_dvd @ int @ ( times_times @ int @ SV109 @ SV495 ) @ ( times_times @ int @ SV109 @ SV656 ) )
| ~ ( ( ( ti @ int @ SV109 )
!= ( zero_zero @ int ) ) )
| ( dvd_dvd @ int @ SV495 @ SV656 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2634]) ).
thf(3016,plain,
! [SV110: $i] :
( ( ( power @ SV110 )
= $false )
| ( ( ! [SY1223: $i] :
( ( power_power @ SV110 @ SY1223 @ ( zero_zero @ nat ) )
= ( one_one @ SV110 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2635]) ).
thf(3017,plain,
! [SV111: $i,SV496: $i] :
( ( ( ~ ( twoSqu420862341sum2sq @ SV496 ) )
= $true )
| ( ( ~ ( twoSqu420862341sum2sq @ SV111 )
| ( twoSqu420862341sum2sq @ ( times_times @ int @ SV496 @ SV111 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2636]) ).
thf(3018,plain,
! [SV112: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( bit0 @ SV112 ) @ pls )
| ( ord_less_eq @ int @ SV112 @ pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2637]) ).
thf(3019,plain,
! [SV112: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ SV112 @ pls )
| ( ord_less_eq @ int @ ( bit0 @ SV112 ) @ pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2637]) ).
thf(3020,plain,
! [SV113: $i,SV497: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV497 ) )
= $true )
| ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( power_power @ int @ SV497 @ SV113 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2638]) ).
thf(3021,plain,
! [SV114: $i] :
( ( ( zero_neq_one @ SV114 )
= $false )
| ( ( ( ti @ SV114 @ ( one_one @ SV114 ) )
= ( one_one @ SV114 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2639]) ).
thf(3022,plain,
! [SV498: $i,SV115: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SV115 ) @ ( bit0 @ SV498 ) )
| ( ord_less @ int @ SV115 @ SV498 ) )
| ~ ( ~ ( ord_less @ int @ SV115 @ SV498 )
| ( ord_less @ int @ ( bit1 @ SV115 ) @ ( bit0 @ SV498 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2640]) ).
thf(3023,plain,
! [SV116: $i] :
( ( ( semiring_1 @ SV116 )
= $false )
| ( ( ( power_power @ SV116 @ ( zero_zero @ SV116 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SV116 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2641]) ).
thf(3024,plain,
! [SV117: $i] :
( ( ( linordered_semidom @ SV117 )
= $false )
| ( ( ! [SY1227: $i,SY1228: $i,SY1229: $i] :
( ~ ( ord_less_eq @ nat @ SY1228 @ SY1229 )
| ~ ( ord_less_eq @ SV117 @ ( zero_zero @ SV117 ) @ SY1227 )
| ~ ( ord_less_eq @ SV117 @ SY1227 @ ( one_one @ SV117 ) )
| ( ord_less_eq @ SV117 @ ( power_power @ SV117 @ SY1227 @ SY1229 ) @ ( power_power @ SV117 @ SY1227 @ SY1228 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2642]) ).
thf(3025,plain,
! [SV118: $i,SV657: $i,SV499: $i] :
( ( ~ ( dvd_dvd @ nat @ SV499 @ SV657 )
| ( dvd_dvd @ nat @ ( times_times @ nat @ SV118 @ SV499 ) @ ( times_times @ nat @ SV118 @ SV657 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2643]) ).
thf(3026,plain,
! [SV500: $i,SV119: $i,SV658: $i] :
( ( ~ ( zprime @ SV658 )
| ~ ( dvd_dvd @ int @ SV658 @ ( power_power @ int @ SV119 @ SV500 ) )
| ( dvd_dvd @ int @ SV658 @ SV119 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2644]) ).
thf(3027,plain,
! [SV120: $i] :
( ( ( ~ ( ~ ( number_ring @ SV120 )
| ~ ( linordered_idom @ SV120 ) ) )
= $false )
| ( ( ! [SY1234: $i] :
~ ( ~ ( ~ ( ord_less @ SV120 @ ( one_one @ SV120 ) @ ( number_number_of @ SV120 @ SY1234 ) )
| ( ord_less @ int @ ( bit1 @ pls ) @ SY1234 ) )
| ~ ( ~ ( ord_less @ int @ ( bit1 @ pls ) @ SY1234 )
| ( ord_less @ SV120 @ ( one_one @ SV120 ) @ ( number_number_of @ SV120 @ SY1234 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2645]) ).
thf(3028,plain,
! [SV121: $i,SV659: $i,SV501: $i] :
( ( ~ ( ord_less_eq @ real @ SV501 @ SV659 )
| ( ord_less_eq @ real @ ( plus_plus @ real @ SV121 @ SV501 ) @ ( plus_plus @ real @ SV121 @ SV659 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2646]) ).
thf(3029,plain,
! [SV502: $i,SV122: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SV122 ) @ ( bit1 @ SV502 ) )
| ( ord_less_eq @ int @ SV122 @ SV502 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV122 @ SV502 )
| ( ord_less_eq @ int @ ( bit1 @ SV122 ) @ ( bit1 @ SV502 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2647]) ).
thf(3030,plain,
( ( ( ! [SX0: $i] :
~ ~ ! [SX1: $i] :
( ( plus_plus @ int @ ( power_power @ int @ SX0 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ SX1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ) )
= $false )
| ( ( ord_less @ int @ ( one_one @ int ) @ t )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2648]) ).
thf(3031,plain,
! [SV123: $i] :
( ( ( ~ ( ~ ( number_ring @ SV123 )
| ~ ( linordered_idom @ SV123 ) ) )
= $false )
| ( ( ! [SY1238: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV123 @ ( number_number_of @ SV123 @ SY1238 ) @ ( one_one @ SV123 ) )
| ( ord_less_eq @ int @ SY1238 @ ( bit1 @ pls ) ) )
| ~ ( ~ ( ord_less_eq @ int @ SY1238 @ ( bit1 @ pls ) )
| ( ord_less_eq @ SV123 @ ( number_number_of @ SV123 @ SY1238 ) @ ( one_one @ SV123 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2649]) ).
thf(3032,plain,
! [SV124: $i] :
( ( ( comm_semiring_1 @ SV124 )
= $false )
| ( ( ! [SY1239: $i,SY1240: $i,SY1241: $i,SY1242: $i] :
( ~ ( dvd_dvd @ SV124 @ SY1241 @ SY1242 )
| ~ ( dvd_dvd @ SV124 @ SY1239 @ SY1240 )
| ( dvd_dvd @ SV124 @ ( times_times @ SV124 @ SY1241 @ SY1239 ) @ ( times_times @ SV124 @ SY1242 @ SY1240 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2650]) ).
thf(3033,plain,
! [SV125: $i] :
( ( ( ab_group_add @ SV125 )
= $false )
| ( ( ! [SY1243: $i,SY1244: $i,SY1245: $i,SY1246: $i] :
( ( minus_minus @ SV125 @ ( plus_plus @ SV125 @ SY1243 @ SY1244 ) @ ( plus_plus @ SV125 @ SY1245 @ SY1246 ) )
= ( plus_plus @ SV125 @ ( minus_minus @ SV125 @ SY1243 @ SY1245 ) @ ( minus_minus @ SV125 @ SY1244 @ SY1246 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2651]) ).
thf(3034,plain,
! [SV126: $i] :
( ( ( number_semiring @ SV126 )
= $false )
| ( ( ! [SY1247: $i] :
( ( times_times @ SV126 @ SY1247 @ ( number_number_of @ SV126 @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ SV126 @ SY1247 @ SY1247 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2652]) ).
thf(3035,plain,
! [SV127: $i] :
( ( ( number_ring @ SV127 )
= $false )
| ( ( ( plus_plus @ SV127 @ ( one_one @ SV127 ) @ ( one_one @ SV127 ) )
= ( number_number_of @ SV127 @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2653]) ).
thf(3036,plain,
! [SV128: $i] :
( ( ~ ( ( ( number_number_of @ nat @ SV128 )
!= ( zero_zero @ nat ) )
| ( ord_less_eq @ int @ SV128 @ pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2654]) ).
thf(3037,plain,
! [SV128: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ SV128 @ pls )
| ( ( number_number_of @ nat @ SV128 )
= ( zero_zero @ nat ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2654]) ).
thf(3038,plain,
! [SV129: $i] :
( ( ( number_semiring @ SV129 )
= $false )
| ( ( ! [SY1248: $i] :
( ( times_times @ SV129 @ ( number_number_of @ SV129 @ ( bit0 @ ( bit1 @ pls ) ) ) @ SY1248 )
= ( plus_plus @ SV129 @ SY1248 @ SY1248 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2655]) ).
thf(3039,plain,
! [SV130: $i] :
( ( ( comm_semiring_1 @ SV130 )
= $false )
| ( ( ! [SY1249: $i,SY1250: $i,SY1251: $i] :
( ( times_times @ SV130 @ ( times_times @ SV130 @ SY1249 @ SY1250 ) @ SY1251 )
= ( times_times @ SV130 @ ( times_times @ SV130 @ SY1249 @ SY1251 ) @ SY1250 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2656]) ).
thf(3040,plain,
! [SV131: $i] :
( ( ( comm_semiring @ SV131 )
= $false )
| ( ( ! [SY1252: $i,SY1253: $i,SY1254: $i] :
( ( times_times @ SV131 @ ( plus_plus @ SV131 @ SY1252 @ SY1253 ) @ SY1254 )
= ( plus_plus @ SV131 @ ( times_times @ SV131 @ SY1252 @ SY1254 ) @ ( times_times @ SV131 @ SY1253 @ SY1254 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2657]) ).
thf(3041,plain,
! [SV660: $i,SV503: $i,SV132: $i] :
( ( ! [SY1914: $i,SY1915: $i] :
( ~ ( ord_less_eq @ int @ ( plus_plus @ int @ ( times_times @ int @ SV132 @ SV503 ) @ SV660 ) @ ( plus_plus @ int @ ( times_times @ int @ SV132 @ SY1914 ) @ SY1915 ) )
| ~ ( ord_less_eq @ int @ SY1915 @ ( zero_zero @ int ) )
| ~ ( ord_less @ int @ SV132 @ SY1915 )
| ~ ( ord_less @ int @ SV132 @ SV660 )
| ( ord_less_eq @ int @ SY1914 @ SV503 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2658]) ).
thf(3042,plain,
! [SV504: $i,SV133: $i] :
( ( ( bit1 @ SV133 )
= ( bit0 @ SV504 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2659]) ).
thf(3043,plain,
! [SV134: $i] :
( ( ( ~ ( ~ ( number_ring @ SV134 )
| ~ ( linordered_idom @ SV134 ) ) )
= $false )
| ( ( ! [SY1260: $i] :
~ ( ~ ( ~ ( ord_less @ SV134 @ ( number_number_of @ SV134 @ SY1260 ) @ ( one_one @ SV134 ) )
| ( ord_less @ int @ SY1260 @ ( bit1 @ pls ) ) )
| ~ ( ~ ( ord_less @ int @ SY1260 @ ( bit1 @ pls ) )
| ( ord_less @ SV134 @ ( number_number_of @ SV134 @ SY1260 ) @ ( one_one @ SV134 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2660]) ).
thf(3044,plain,
! [SV505: $i,SV135: $i] :
( ( ~ ( ~ ( ord_less_eq @ nat @ ( number_number_of @ nat @ SV135 ) @ ( number_number_of @ nat @ SV505 ) )
| ~ ~ ( ord_less_eq @ int @ SV135 @ SV505 )
| ( ord_less_eq @ int @ SV135 @ pls ) )
| ~ ( ~ ( ~ ~ ( ord_less_eq @ int @ SV135 @ SV505 )
| ( ord_less_eq @ int @ SV135 @ pls ) )
| ( ord_less_eq @ nat @ ( number_number_of @ nat @ SV135 ) @ ( number_number_of @ nat @ SV505 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2661]) ).
thf(3045,plain,
! [SV136: $i] :
( ( ( comm_semiring_1 @ SV136 )
= $false )
| ( ( ! [SY1262: $i] :
( ( power_power @ SV136 @ SY1262 @ ( one_one @ nat ) )
= ( ti @ SV136 @ SY1262 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2662]) ).
thf(3046,plain,
! [SV661: $i,SV506: $i,SV137: $i] :
( ( ~ ( ~ ( ~ ( zcong @ SV137 @ SV506 @ SV661 )
| ( dvd_dvd @ int @ SV661 @ ( minus_minus @ int @ SV137 @ SV506 ) ) )
| ~ ( ~ ( dvd_dvd @ int @ SV661 @ ( minus_minus @ int @ SV137 @ SV506 ) )
| ( zcong @ SV137 @ SV506 @ SV661 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2663]) ).
thf(3047,plain,
! [SV507: $i,SV138: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( number_number_of @ int @ SV138 ) @ ( number_number_of @ int @ SV507 ) )
| ( ord_less_eq @ int @ SV138 @ SV507 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV138 @ SV507 )
| ( ord_less_eq @ int @ ( number_number_of @ int @ SV138 ) @ ( number_number_of @ int @ SV507 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2664]) ).
thf(3048,plain,
! [SV139: $i] :
( ( ( ~ ( ~ ( number @ SV139 )
| ~ ( ring @ SV139 ) ) )
= $false )
| ( ( ! [SY1266: $i,SY1267: $i,SY1268: $i] :
( ( times_times @ SV139 @ ( number_number_of @ SV139 @ SY1266 ) @ ( minus_minus @ SV139 @ SY1267 @ SY1268 ) )
= ( minus_minus @ SV139 @ ( times_times @ SV139 @ ( number_number_of @ SV139 @ SY1266 ) @ SY1267 ) @ ( times_times @ SV139 @ ( number_number_of @ SV139 @ SY1266 ) @ SY1268 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2665]) ).
thf(3049,plain,
! [SV140: $i] :
( ( ( monoid_mult @ SV140 )
= $false )
| ( ( ! [SY1269: $i] :
( ( power_power @ SV140 @ SY1269 @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( times_times @ SV140 @ ( times_times @ SV140 @ SY1269 @ SY1269 ) @ SY1269 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2666]) ).
thf(3050,plain,
! [SV508: $i,SV141: $i] :
( ( ( ~ ( ord_less @ int @ SV141 @ SV508 ) )
= $true )
| ( ( ord_less_eq @ int @ ( plus_plus @ int @ SV141 @ ( one_one @ int ) ) @ SV508 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2667]) ).
thf(3051,plain,
! [SV142: $i] :
( ( ( linordered_semidom @ SV142 )
= $false )
| ( ( ! [SY1271: $i,SY1272: $i] :
( ~ ( ord_less @ SV142 @ ( one_one @ SV142 ) @ SY1272 )
| ( ord_less @ SV142 @ ( one_one @ SV142 ) @ ( times_times @ SV142 @ SY1272 @ ( power_power @ SV142 @ SY1272 @ SY1271 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2668]) ).
thf(3052,plain,
! [SV509: $i,SV143: $i] :
( ( ~ ( ( ( power_power @ nat @ SV143 @ SV509 )
!= ( zero_zero @ nat ) )
| ~ ( ~ ( ( SV509
!= ( zero_zero @ nat ) ) )
| ( SV143
!= ( zero_zero @ nat ) ) ) )
| ~ ( ~ ~ ( ~ ( ( SV509
!= ( zero_zero @ nat ) ) )
| ( SV143
!= ( zero_zero @ nat ) ) )
| ( ( power_power @ nat @ SV143 @ SV509 )
= ( zero_zero @ nat ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2669]) ).
thf(3053,plain,
! [SV144: $i] :
( ( ( number_ring @ SV144 )
= $false )
| ( ( ! [SY1274: $i] :
( ( times_times @ SV144 @ SY1274 @ ( number_number_of @ SV144 @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ SV144 @ SY1274 @ SY1274 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2670]) ).
thf(3054,plain,
! [SV662: $i,SV510: $i,SV145: $i] :
( ( ~ ( ~ ( ~ ( dvd_dvd @ int @ SV145 @ ( plus_plus @ int @ SV510 @ ( times_times @ int @ SV145 @ SV662 ) ) )
| ( dvd_dvd @ int @ SV145 @ SV510 ) )
| ~ ( ~ ( dvd_dvd @ int @ SV145 @ SV510 )
| ( dvd_dvd @ int @ SV145 @ ( plus_plus @ int @ SV510 @ ( times_times @ int @ SV145 @ SV662 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2671]) ).
thf(3055,plain,
! [SV146: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SV146 ) @ min )
| ( ord_less @ int @ SV146 @ min ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2672]) ).
thf(3056,plain,
! [SV146: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV146 @ min )
| ( ord_less @ int @ ( bit1 @ SV146 ) @ min ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2672]) ).
thf(3057,plain,
! [SV511: $i,SV147: $i] :
( ( ~ ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ SV147 @ SV511 ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ SV147 )
| ( SV511
= ( zero_zero @ nat ) ) )
| ~ ( ~ ( ( ord_less @ nat @ ( zero_zero @ nat ) @ SV147 )
| ( SV511
= ( zero_zero @ nat ) ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ SV147 @ SV511 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2673]) ).
thf(3058,plain,
! [SV149: $i] :
( ( ( number_ring @ SV149 )
= $false )
| ( ( ! [SY1278: $i] :
( ( plus_plus @ SV149 @ ( one_one @ SV149 ) @ ( number_number_of @ SV149 @ SY1278 ) )
= ( number_number_of @ SV149 @ ( plus_plus @ int @ ( bit1 @ pls ) @ SY1278 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2675]) ).
thf(3059,plain,
! [SV150: $i] :
( ( ( comm_semiring_1 @ SV150 )
= $false )
| ( ( ! [SY1279: $i,SY1280: $i,SY1281: $i] :
( ( plus_plus @ SV150 @ ( times_times @ SV150 @ SY1279 @ SY1280 ) @ ( times_times @ SV150 @ SY1281 @ SY1280 ) )
= ( times_times @ SV150 @ ( plus_plus @ SV150 @ SY1279 @ SY1281 ) @ SY1280 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2676]) ).
thf(3060,plain,
! [SV512: $i,SV151: $i] :
( ( ~ ( ~ ~ ( ~ ( dvd_dvd @ nat @ SV151 @ SV512 )
| ~ ( dvd_dvd @ nat @ SV512 @ SV151 ) )
| ( SV151 = SV512 ) )
| ~ ( ( SV151 != SV512 )
| ~ ( ~ ( dvd_dvd @ nat @ SV151 @ SV512 )
| ~ ( dvd_dvd @ nat @ SV512 @ SV151 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2677]) ).
thf(3061,plain,
! [SV152: $i] :
( ( ( ordere453448008miring @ SV152 )
= $false )
| ( ( ! [SY1283: $i,SY1284: $i] :
( ~ ( ord_less_eq @ SV152 @ ( zero_zero @ SV152 ) @ SY1284 )
| ~ ( ord_less_eq @ SV152 @ ( zero_zero @ SV152 ) @ SY1283 )
| ( ord_less_eq @ SV152 @ ( zero_zero @ SV152 ) @ ( times_times @ SV152 @ SY1284 @ SY1283 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2678]) ).
thf(3062,plain,
! [SV153: $i,SV513: $i] :
( ( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ SV513 ) )
= $true )
| ( ( ~ ( ord_less @ real @ ( zero_zero @ real ) @ SV153 )
| ~ ! [SY1807: $i] :
~ ~ ( ~ ( ord_less @ real @ ( zero_zero @ real ) @ SY1807 )
| ( ( power_power @ real @ SY1807 @ SV513 )
!= SV153 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2679]) ).
thf(3063,plain,
! [SV154: $i,SV663: $i,SV514: $i] :
( ( ! [SY1916: $i] :
( ~ ( zcong @ SV514 @ SV663 @ SY1916 )
| ( zcong @ ( times_times @ int @ SV154 @ SV514 ) @ ( times_times @ int @ SV154 @ SV663 ) @ SY1916 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2680]) ).
thf(3064,plain,
! [SV155: $i] :
( ( ( linordered_semidom @ SV155 )
= $false )
| ( ( ! [SY1290: $i,SY1291: $i,SY1292: $i] :
( ~ ( ord_less @ SV155 @ ( one_one @ SV155 ) @ SY1292 )
| ~ ( ~ ( ~ ( ord_less @ SV155 @ ( power_power @ SV155 @ SY1292 @ SY1290 ) @ ( power_power @ SV155 @ SY1292 @ SY1291 ) )
| ( ord_less @ nat @ SY1290 @ SY1291 ) )
| ~ ( ~ ( ord_less @ nat @ SY1290 @ SY1291 )
| ( ord_less @ SV155 @ ( power_power @ SV155 @ SY1292 @ SY1290 ) @ ( power_power @ SV155 @ SY1292 @ SY1291 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2681]) ).
thf(3065,plain,
! [SV156: $i] :
( ( ( comm_semiring_1 @ SV156 )
= $false )
| ( ( ! [SY1293: $i,SY1294: $i] :
( ( power_power @ SV156 @ SY1293 @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SY1294 ) )
= ( times_times @ SV156 @ ( power_power @ SV156 @ SY1293 @ SY1294 ) @ ( power_power @ SV156 @ SY1293 @ SY1294 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2682]) ).
thf(3066,plain,
! [SV157: $i] :
( ( ( comm_semiring_1 @ SV157 )
= $false )
| ( ( ! [SY1295: $i] :
( ( plus_plus @ SV157 @ SY1295 @ ( zero_zero @ SV157 ) )
= ( ti @ SV157 @ SY1295 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2683]) ).
thf(3067,plain,
! [SV158: $i,SV664: $i,SV515: $i] :
( ( ~ ( dvd_dvd @ nat @ SV515 @ SV664 )
| ( dvd_dvd @ nat @ ( times_times @ nat @ SV515 @ SV158 ) @ ( times_times @ nat @ SV664 @ SV158 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2684]) ).
thf(3068,plain,
! [SV516: $i,SV159: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SV159 ) @ ( bit0 @ SV516 ) )
| ( ord_less @ int @ SV159 @ SV516 ) )
| ~ ( ~ ( ord_less @ int @ SV159 @ SV516 )
| ( ord_less_eq @ int @ ( bit1 @ SV159 ) @ ( bit0 @ SV516 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2685]) ).
thf(3069,plain,
! [SV517: $i,SV160: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV160 @ ( plus_plus @ int @ SV517 @ ( one_one @ int ) ) )
| ( ord_less_eq @ int @ SV160 @ SV517 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV160 @ SV517 )
| ( ord_less @ int @ SV160 @ ( plus_plus @ int @ SV517 @ ( one_one @ int ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2686]) ).
thf(3070,plain,
! [SV665: $i,SV518: $i,SV161: $i] :
( ( ~ ( ord_less @ int @ ( plus_plus @ int @ ( times_times @ int @ SV161 @ SV518 ) @ SV665 ) @ ( zero_zero @ int ) )
| ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV665 )
| ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV161 )
| ( ord_less_eq @ int @ SV518 @ ( zero_zero @ int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2687]) ).
thf(3071,plain,
! [SV519: $i,SV162: $i] :
( ( ( bit0 @ SV162 )
= ( bit1 @ SV519 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2688]) ).
thf(3072,plain,
! [SV666: $i,SV520: $i,SV163: $i] :
( ( ~ ( ~ ( ~ ( zcong @ SV163 @ SV520 @ ( ti @ int @ SV666 ) )
| ( zcong @ SV163 @ SV520 @ SV666 ) )
| ~ ( ~ ( zcong @ SV163 @ SV520 @ SV666 )
| ( zcong @ SV163 @ SV520 @ ( ti @ int @ SV666 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2689]) ).
thf(3073,plain,
! [SV164: $i,SV667: $i,SV521: $i] :
( ( ! [SY1917: $i,SY1918: $i] :
( ~ ( dvd_dvd @ int @ SY1917 @ SY1918 )
| ~ ( ~ ( ~ ( dvd_dvd @ int @ SY1917 @ ( plus_plus @ int @ SV521 @ SV667 ) )
| ( dvd_dvd @ int @ SY1917 @ ( plus_plus @ int @ ( plus_plus @ int @ SV521 @ ( times_times @ int @ SV164 @ SY1918 ) ) @ SV667 ) ) )
| ~ ( ~ ( dvd_dvd @ int @ SY1917 @ ( plus_plus @ int @ ( plus_plus @ int @ SV521 @ ( times_times @ int @ SV164 @ SY1918 ) ) @ SV667 ) )
| ( dvd_dvd @ int @ SY1917 @ ( plus_plus @ int @ SV521 @ SV667 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2690]) ).
thf(3074,plain,
! [SV165: $i] :
( ( ( number_ring @ SV165 )
= $false )
| ( ( ! [SY1309: $i,SY1310: $i,SY1311: $i] :
( ( plus_plus @ SV165 @ ( number_number_of @ SV165 @ SY1309 ) @ ( plus_plus @ SV165 @ ( number_number_of @ SV165 @ SY1310 ) @ SY1311 ) )
= ( plus_plus @ SV165 @ ( number_number_of @ SV165 @ ( plus_plus @ int @ SY1309 @ SY1310 ) ) @ SY1311 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2691]) ).
thf(3075,plain,
! [SV166: $i] :
( ( ( linordered_idom @ SV166 )
= $false )
| ( ( ! [SY1312: $i,SY1313: $i] : ( ord_less_eq @ SV166 @ ( zero_zero @ SV166 ) @ ( power_power @ SV166 @ SY1312 @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SY1313 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2692]) ).
thf(3076,plain,
! [SV522: $i,SV167: $i,SV668: $i] :
( ( ! [SY1919: $i,SY1920: $i] :
( ~ ( zcong @ SV668 @ SY1919 @ SY1920 )
| ~ ( zcong @ SV167 @ SV522 @ SY1920 )
| ( zcong @ ( minus_minus @ int @ SV668 @ SV167 ) @ ( minus_minus @ int @ SY1919 @ SV522 ) @ SY1920 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2693]) ).
thf(3077,plain,
! [SV168: $i] :
( ( ( ~ ( ~ ( number @ SV168 )
| ~ ( semiring @ SV168 ) ) )
= $false )
| ( ( ! [SY1318: $i,SY1319: $i,SY1320: $i] :
( ( times_times @ SV168 @ ( plus_plus @ SV168 @ SY1318 @ SY1319 ) @ ( number_number_of @ SV168 @ SY1320 ) )
= ( plus_plus @ SV168 @ ( times_times @ SV168 @ SY1318 @ ( number_number_of @ SV168 @ SY1320 ) ) @ ( times_times @ SV168 @ SY1319 @ ( number_number_of @ SV168 @ SY1320 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2694]) ).
thf(3078,plain,
! [SV523: $i,SV169: $i] :
( ( ~ ( ( ( plus_plus @ real @ ( power_power @ real @ SV169 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ real @ SV523 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ real ) )
| ~ ( ( SV169
!= ( zero_zero @ real ) )
| ( SV523
!= ( zero_zero @ real ) ) ) )
| ~ ( ~ ~ ( ( SV169
!= ( zero_zero @ real ) )
| ( SV523
!= ( zero_zero @ real ) ) )
| ( ( plus_plus @ real @ ( power_power @ real @ SV169 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ real @ SV523 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ real ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2695]) ).
thf(3079,plain,
! [SV669: $i,SV524: $i,SV170: $i] :
( ( ~ ( dvd_dvd @ nat @ ( power_power @ nat @ SV170 @ SV524 ) @ ( power_power @ nat @ SV170 @ SV669 ) )
| ~ ( ord_less @ nat @ ( one_one @ nat ) @ SV170 )
| ( ord_less_eq @ nat @ SV524 @ SV669 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2696]) ).
thf(3080,plain,
! [SV171: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ pls @ ( bit0 @ SV171 ) )
| ( ord_less_eq @ int @ pls @ SV171 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2697]) ).
thf(3081,plain,
! [SV171: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ pls @ SV171 )
| ( ord_less_eq @ int @ pls @ ( bit0 @ SV171 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2697]) ).
thf(3082,plain,
! [SV525: $i,SV172: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV172 @ SV525 )
| ( ord_less @ int @ ( minus_minus @ int @ SV172 @ SV525 ) @ ( zero_zero @ int ) ) )
| ~ ( ~ ( ord_less @ int @ ( minus_minus @ int @ SV172 @ SV525 ) @ ( zero_zero @ int ) )
| ( ord_less @ int @ SV172 @ SV525 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2698]) ).
thf(3083,plain,
! [SV173: $i] :
( ( ( number_ring @ SV173 )
= $false )
| ( ( ! [SY1325: $i] :
( ( power_power @ SV173 @ ( number_number_of @ SV173 @ min ) @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SY1325 ) )
= ( one_one @ SV173 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2699]) ).
thf(3084,plain,
! [SV174: $i] :
( ( ( ring @ SV174 )
= $false )
| ( ( ! [SY1326: $i,SY1327: $i,SY1328: $i,SY1329: $i] :
( ( minus_minus @ SV174 @ ( times_times @ SV174 @ SY1326 @ SY1327 ) @ ( times_times @ SV174 @ SY1328 @ SY1329 ) )
= ( plus_plus @ SV174 @ ( times_times @ SV174 @ SY1326 @ ( minus_minus @ SV174 @ SY1327 @ SY1329 ) ) @ ( times_times @ SV174 @ ( minus_minus @ SV174 @ SY1326 @ SY1328 ) @ SY1329 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2700]) ).
thf(3085,plain,
! [SV175: $i] :
( ( ( semiri456707255roduct @ SV175 )
= $false )
| ( ( ! [SY1330: $i,SY1331: $i,SY1332: $i,SY1333: $i] :
~ ( ~ ( ~ ~ ( ~ ( ( ( ti @ SV175 @ SY1332 )
!= ( ti @ SV175 @ SY1333 ) ) )
| ~ ( ( ( ti @ SV175 @ SY1330 )
!= ( ti @ SV175 @ SY1331 ) ) ) )
| ( ( plus_plus @ SV175 @ ( times_times @ SV175 @ SY1332 @ SY1330 ) @ ( times_times @ SV175 @ SY1333 @ SY1331 ) )
!= ( plus_plus @ SV175 @ ( times_times @ SV175 @ SY1332 @ SY1331 ) @ ( times_times @ SV175 @ SY1333 @ SY1330 ) ) ) )
| ~ ( ~ ( ( ( plus_plus @ SV175 @ ( times_times @ SV175 @ SY1332 @ SY1330 ) @ ( times_times @ SV175 @ SY1333 @ SY1331 ) )
!= ( plus_plus @ SV175 @ ( times_times @ SV175 @ SY1332 @ SY1331 ) @ ( times_times @ SV175 @ SY1333 @ SY1330 ) ) ) )
| ~ ( ~ ( ( ( ti @ SV175 @ SY1332 )
!= ( ti @ SV175 @ SY1333 ) ) )
| ~ ( ( ( ti @ SV175 @ SY1330 )
!= ( ti @ SV175 @ SY1331 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2701]) ).
thf(3086,plain,
! [SV176: $i,SV526: $i] :
( ( ( ~ ( number @ SV526 ) )
= $true )
| ( ( ( ti @ SV526 @ ( number_number_of @ SV526 @ SV176 ) )
= ( number_number_of @ SV526 @ SV176 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2702]) ).
thf(3087,plain,
! [SV177: $i] :
( ( ~ ( ~ ( ord_less @ int @ pls @ ( bit0 @ SV177 ) )
| ( ord_less @ int @ pls @ SV177 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2703]) ).
thf(3088,plain,
! [SV177: $i] :
( ( ~ ( ~ ( ord_less @ int @ pls @ SV177 )
| ( ord_less @ int @ pls @ ( bit0 @ SV177 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2703]) ).
thf(3089,plain,
! [SV178: $i,SV527: $i] :
( ( ( ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV527 ) )
= $true )
| ( ( ~ ( ord_less @ int @ SV527 @ SV178 )
| ~ ( dvd_dvd @ int @ SV178 @ SV527 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2704]) ).
thf(3090,plain,
! [SV179: $i] :
( ( ( linordered_semidom @ SV179 )
= $false )
| ( ( ! [SY1336: $i,SY1337: $i,SY1338: $i] :
( ~ ( ord_less @ SV179 @ ( one_one @ SV179 ) @ SY1338 )
| ~ ( ord_less @ SV179 @ ( power_power @ SV179 @ SY1338 @ SY1336 ) @ ( power_power @ SV179 @ SY1338 @ SY1337 ) )
| ( ord_less @ nat @ SY1336 @ SY1337 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2705]) ).
thf(3091,plain,
! [SV180: $i] :
( ( ( dvd @ SV180 )
= $false )
| ( ( ! [SY1339: $i,SY1340: $i,SY1341: $i] :
( ( SY1339
!= ( times_times @ SV180 @ SY1340 @ SY1341 ) )
| ( dvd_dvd @ SV180 @ SY1340 @ SY1339 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2706]) ).
thf(3092,plain,
! [SV528: $i,SV182: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SV182 ) @ ( bit1 @ SV528 ) )
| ( ord_less @ int @ SV182 @ SV528 ) )
| ~ ( ~ ( ord_less @ int @ SV182 @ SV528 )
| ( ord_less @ int @ ( bit1 @ SV182 ) @ ( bit1 @ SV528 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2708]) ).
thf(3093,plain,
! [SV183: $i] :
( ( ( number_ring @ SV183 )
= $false )
| ( ( ( number_number_of @ SV183 @ pls )
= ( zero_zero @ SV183 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2709]) ).
thf(3094,plain,
! [SV184: $i] :
( ( ( comm_semiring_1 @ SV184 )
= $false )
| ( ( ! [SY1343: $i] :
( ( times_times @ SV184 @ SY1343 @ ( one_one @ SV184 ) )
= ( ti @ SV184 @ SY1343 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2710]) ).
thf(3095,plain,
! [SV185: $i] :
( ( ( comm_semiring_1 @ SV185 )
= $false )
| ( ( ! [SY1344: $i,SY1345: $i,SY1346: $i] :
( ( times_times @ SV185 @ ( power_power @ SV185 @ SY1344 @ SY1345 ) @ ( power_power @ SV185 @ SY1344 @ SY1346 ) )
= ( power_power @ SV185 @ SY1344 @ ( plus_plus @ nat @ SY1345 @ SY1346 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2711]) ).
thf(3096,plain,
! [SV529: $i,SV186: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SV186 ) @ ( bit0 @ SV529 ) )
| ( ord_less @ int @ SV186 @ SV529 ) )
| ~ ( ~ ( ord_less @ int @ SV186 @ SV529 )
| ( ord_less @ int @ ( bit0 @ SV186 ) @ ( bit0 @ SV529 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2712]) ).
thf(3097,plain,
! [SV530: $i,SV187: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV187 @ SV530 )
| ~ ( ~ ( ord_less_eq @ int @ SV187 @ SV530 )
| ~ ( ( ( ti @ int @ SV187 )
!= ( ti @ int @ SV530 ) ) ) ) )
| ~ ( ~ ~ ( ~ ( ord_less_eq @ int @ SV187 @ SV530 )
| ~ ( ( ( ti @ int @ SV187 )
!= ( ti @ int @ SV530 ) ) ) )
| ( ord_less @ int @ SV187 @ SV530 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2713]) ).
thf(3098,plain,
! [SV188: $i,SV531: $i] :
( ( ( ~ ( number @ SV531 ) )
= $true )
| ( ( ( number_number_of @ SV531 @ ( ti @ int @ SV188 ) )
= ( number_number_of @ SV531 @ SV188 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2714]) ).
thf(3099,plain,
! [SV189: $i] :
( ( ( linord219039673up_add @ SV189 )
= $false )
| ( ( ! [SY1350: $i] :
~ ( ~ ( ( ( plus_plus @ SV189 @ SY1350 @ SY1350 )
!= ( zero_zero @ SV189 ) )
| ( ( ti @ SV189 @ SY1350 )
= ( zero_zero @ SV189 ) ) )
| ~ ( ( ( ti @ SV189 @ SY1350 )
!= ( zero_zero @ SV189 ) )
| ( ( plus_plus @ SV189 @ SY1350 @ SY1350 )
= ( zero_zero @ SV189 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2715]) ).
thf(3100,plain,
! [SV532: $i,SV190: $i,SV670: $i] :
( ( ~ ( ord_less @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV670 )
| ~ ( zcong @ ( power_power @ int @ ( number_number_of @ int @ min ) @ SV190 ) @ ( power_power @ int @ ( number_number_of @ int @ min ) @ SV532 ) @ SV670 )
| ( ( power_power @ int @ ( number_number_of @ int @ min ) @ SV190 )
= ( power_power @ int @ ( number_number_of @ int @ min ) @ SV532 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2716]) ).
thf(3101,plain,
! [SV671: $i,SV533: $i,SV191: $i] :
( ( ~ ( ~ ( ~ ( dvd_dvd @ nat @ ( times_times @ nat @ SV191 @ SV533 ) @ ( times_times @ nat @ SV671 @ SV533 ) )
| ( SV533
= ( zero_zero @ nat ) )
| ( dvd_dvd @ nat @ SV191 @ SV671 ) )
| ~ ( ~ ( ( SV533
= ( zero_zero @ nat ) )
| ( dvd_dvd @ nat @ SV191 @ SV671 ) )
| ( dvd_dvd @ nat @ ( times_times @ nat @ SV191 @ SV533 ) @ ( times_times @ nat @ SV671 @ SV533 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2717]) ).
thf(3102,plain,
! [SV192: $i] :
( ( ( linordered_semidom @ SV192 )
= $false )
| ( ( ! [SY1355: $i,SY1356: $i] :
( ~ ( ord_less_eq @ SV192 @ ( zero_zero @ SV192 ) @ SY1356 )
| ( ord_less_eq @ SV192 @ ( zero_zero @ SV192 ) @ ( power_power @ SV192 @ SY1356 @ SY1355 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2718]) ).
thf(3103,plain,
! [SV193: $i] :
( ( ( linord581940658strict @ SV193 )
= $false )
| ( ( ! [SY1357: $i,SY1358: $i] :
~ ( ~ ( ( ( plus_plus @ SV193 @ ( times_times @ SV193 @ SY1357 @ SY1357 ) @ ( times_times @ SV193 @ SY1358 @ SY1358 ) )
!= ( zero_zero @ SV193 ) )
| ~ ( ( ( ti @ SV193 @ SY1357 )
!= ( zero_zero @ SV193 ) )
| ( ( ti @ SV193 @ SY1358 )
!= ( zero_zero @ SV193 ) ) ) )
| ~ ( ~ ~ ( ( ( ti @ SV193 @ SY1357 )
!= ( zero_zero @ SV193 ) )
| ( ( ti @ SV193 @ SY1358 )
!= ( zero_zero @ SV193 ) ) )
| ( ( plus_plus @ SV193 @ ( times_times @ SV193 @ SY1357 @ SY1357 ) @ ( times_times @ SV193 @ SY1358 @ SY1358 ) )
= ( zero_zero @ SV193 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2719]) ).
thf(3104,plain,
! [SV194: $i] :
( ( ( linordered_semidom @ SV194 )
= $false )
| ( ( ! [SY1359: $i,SY1360: $i,SY1361: $i] :
( ~ ( ord_less @ SV194 @ ( one_one @ SV194 ) @ SY1361 )
| ~ ( ~ ( ( ( power_power @ SV194 @ SY1361 @ SY1359 )
!= ( power_power @ SV194 @ SY1361 @ SY1360 ) )
| ( SY1359 = SY1360 ) )
| ~ ( ( SY1359 != SY1360 )
| ( ( power_power @ SV194 @ SY1361 @ SY1359 )
= ( power_power @ SV194 @ SY1361 @ SY1360 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2720]) ).
thf(3105,plain,
! [SV195: $i] :
( ( ( linordered_ring @ SV195 )
= $false )
| ( ( ! [SY1362: $i,SY1363: $i] :
~ ( ord_less @ SV195 @ ( plus_plus @ SV195 @ ( times_times @ SV195 @ SY1362 @ SY1362 ) @ ( times_times @ SV195 @ SY1363 @ SY1363 ) ) @ ( zero_zero @ SV195 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2721]) ).
thf(3106,plain,
! [SV196: $i,SV534: $i,SV672: $i] :
( ( ~ ( zprime @ SV672 )
| ~ ~ ( zcong @ SV534 @ ( zero_zero @ int ) @ SV672 )
| ~ ~ ( zcong @ SV196 @ ( zero_zero @ int ) @ SV672 )
| ~ ( zcong @ ( times_times @ int @ SV534 @ SV196 ) @ ( zero_zero @ int ) @ SV672 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2722]) ).
thf(3107,plain,
! [SV197: $i] :
( ( ( number_semiring @ SV197 )
= $false )
| ( ( ! [SY1366: $i,SY1367: $i] :
( ( power_power @ SV197 @ ( plus_plus @ SV197 @ SY1366 @ SY1367 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ SV197 @ ( plus_plus @ SV197 @ ( power_power @ SV197 @ SY1366 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV197 @ SY1367 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times @ SV197 @ ( times_times @ SV197 @ ( number_number_of @ SV197 @ ( bit0 @ ( bit1 @ pls ) ) ) @ SY1366 ) @ SY1367 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2723]) ).
thf(3108,plain,
! [SV198: $i] :
( ( ( number_ring @ SV198 )
= $false )
| ( ( ! [SY1368: $i,SY1369: $i] :
( ( times_times @ SV198 @ ( number_number_of @ SV198 @ SY1368 ) @ ( number_number_of @ SV198 @ SY1369 ) )
= ( number_number_of @ SV198 @ ( times_times @ int @ SY1368 @ SY1369 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2724]) ).
thf(3109,plain,
! [SV199: $i] :
( ( ( linord581940658strict @ SV199 )
= $false )
| ( ( ! [SY1370: $i,SY1371: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ ( times_times @ SV199 @ SY1370 @ SY1371 ) )
| ~ ( ~ ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ SY1370 )
| ~ ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ SY1371 ) )
| ~ ( ~ ( ord_less_eq @ SV199 @ SY1370 @ ( zero_zero @ SV199 ) )
| ~ ( ord_less_eq @ SV199 @ SY1371 @ ( zero_zero @ SV199 ) ) ) )
| ~ ( ~ ( ~ ( ~ ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ SY1370 )
| ~ ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ SY1371 ) )
| ~ ( ~ ( ord_less_eq @ SV199 @ SY1370 @ ( zero_zero @ SV199 ) )
| ~ ( ord_less_eq @ SV199 @ SY1371 @ ( zero_zero @ SV199 ) ) ) )
| ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ ( times_times @ SV199 @ SY1370 @ SY1371 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2725]) ).
thf(3110,plain,
! [SV200: $i] :
( ( ( number_ring @ SV200 )
= $false )
| ( ( ! [SY1372: $i] :
( ( times_times @ SV200 @ ( number_number_of @ SV200 @ ( bit1 @ pls ) ) @ SY1372 )
= ( ti @ SV200 @ SY1372 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2726]) ).
thf(3111,plain,
! [SV201: $i] :
( ( ( linordered_semidom @ SV201 )
= $false )
| ( ( ! [SY1373: $i,SY1374: $i] :
( ~ ( ord_less @ SV201 @ ( one_one @ SV201 ) @ SY1374 )
| ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ SY1373 )
| ( ord_less @ SV201 @ ( one_one @ SV201 ) @ ( power_power @ SV201 @ SY1374 @ SY1373 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2727]) ).
thf(3112,plain,
! [SV202: $i] :
( ( ( ~ ( ~ ( number_ring @ SV202 )
| ~ ( linordered_idom @ SV202 ) ) )
= $false )
| ( ( ! [SY1375: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV202 @ ( one_one @ SV202 ) @ ( number_number_of @ SV202 @ SY1375 ) )
| ( ord_less_eq @ int @ ( bit1 @ pls ) @ SY1375 ) )
| ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ pls ) @ SY1375 )
| ( ord_less_eq @ SV202 @ ( one_one @ SV202 ) @ ( number_number_of @ SV202 @ SY1375 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2728]) ).
thf(3113,plain,
! [SV203: $i,SV535: $i,SV673: $i] :
( ( ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV673 )
| ~ ( ord_less @ int @ SV673 @ SV535 )
| ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV203 )
| ~ ( ord_less @ int @ SV203 @ SV673 )
| ~ ( zcong @ SV673 @ SV203 @ SV535 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2729]) ).
thf(3114,plain,
( ( ( plus_plus @ int @ ( power_power @ int @ s @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( one_one @ int ) )
= ( times_times @ int @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) @ sK2_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2730]) ).
thf(3115,plain,
! [SV204: $i] :
( ( ( monoid_mult @ SV204 )
= $false )
| ( ( ! [SY1378: $i] :
( ( power_power @ SV204 @ SY1378 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times @ SV204 @ SY1378 @ SY1378 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2731]) ).
thf(3116,plain,
! [SV205: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SV205 ) @ min )
| ( ord_less_eq @ int @ SV205 @ min ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2732]) ).
thf(3117,plain,
! [SV205: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ SV205 @ min )
| ( ord_less @ int @ ( bit0 @ SV205 ) @ min ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2732]) ).
thf(3118,plain,
! [SV536: $i,SV206: $i,SV674: $i] :
( ( ! [SY1921: $i,SY1922: $i] :
( ~ ( zcong @ SV674 @ SY1921 @ SY1922 )
| ~ ( zcong @ SV206 @ SV536 @ SY1922 )
| ( zcong @ ( plus_plus @ int @ SV674 @ SV206 ) @ ( plus_plus @ int @ SY1921 @ SV536 ) @ SY1922 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2733]) ).
thf(3119,plain,
! [SV207: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ SV207 ) @ SV207 ) @ ( zero_zero @ int ) )
| ( ord_less @ int @ SV207 @ ( zero_zero @ int ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2734]) ).
thf(3120,plain,
! [SV207: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV207 @ ( zero_zero @ int ) )
| ( ord_less @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ SV207 ) @ SV207 ) @ ( zero_zero @ int ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2734]) ).
thf(3121,plain,
! [SV208: $i] :
( ( ~ ( ~ ( twoSqu420862341sum2sq @ ( ti @ int @ SV208 ) )
| ( twoSqu420862341sum2sq @ SV208 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2735]) ).
thf(3122,plain,
! [SV208: $i] :
( ( ~ ( ~ ( twoSqu420862341sum2sq @ SV208 )
| ( twoSqu420862341sum2sq @ ( ti @ int @ SV208 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2735]) ).
thf(3123,plain,
! [SV209: $i,SV675: $i,SV537: $i] :
( ( ~ ( dvd_dvd @ nat @ SV537 @ SV675 )
| ~ ( dvd_dvd @ nat @ SV537 @ ( plus_plus @ nat @ SV675 @ SV209 ) )
| ( dvd_dvd @ nat @ SV537 @ SV209 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2736]) ).
thf(3124,plain,
! [SV210: $i] :
( ( ~ ( ( ( bit0 @ SV210 )
!= pls )
| ( ( ti @ int @ SV210 )
= pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2737]) ).
thf(3125,plain,
! [SV210: $i] :
( ( ~ ( ( ( ti @ int @ SV210 )
!= pls )
| ( ( bit0 @ SV210 )
= pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2737]) ).
thf(3126,plain,
! [SV211: $i] :
( ( ( comm_semiring_1 @ SV211 )
= $false )
| ( ( ! [SY1385: $i,SY1386: $i] : ( dvd_dvd @ SV211 @ SY1385 @ ( times_times @ SV211 @ SY1386 @ SY1385 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2738]) ).
thf(3127,plain,
! [SV212: $i] :
( ( ( number_ring @ SV212 )
= $false )
| ( ( ! [SY1387: $i,SY1388: $i] :
( ( plus_plus @ SV212 @ ( number_number_of @ SV212 @ SY1387 ) @ ( number_number_of @ SV212 @ SY1388 ) )
= ( number_number_of @ SV212 @ ( plus_plus @ int @ SY1387 @ SY1388 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2739]) ).
thf(3128,plain,
! [SV213: $i] :
( ( ( ~ ( ~ ( number_ring @ SV213 )
| ~ ( ring_char_0 @ SV213 ) ) )
= $false )
| ( ( ! [SY1389: $i,SY1390: $i] :
~ ( ~ ( ( ( number_number_of @ SV213 @ SY1389 )
!= ( number_number_of @ SV213 @ SY1390 ) )
| ( ( ti @ int @ SY1389 )
= ( ti @ int @ SY1390 ) ) )
| ~ ( ( ( ti @ int @ SY1389 )
!= ( ti @ int @ SY1390 ) )
| ( ( number_number_of @ SV213 @ SY1389 )
= ( number_number_of @ SV213 @ SY1390 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2740]) ).
thf(3129,plain,
! [SV676: $i,SV538: $i,SV214: $i] :
( ( ! [SY1923: $i] :
( ( SV214
!= ( plus_plus @ nat @ ( times_times @ nat @ SV538 @ SV676 ) @ SY1923 ) )
| ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ SY1923 )
| ~ ( ord_less @ nat @ SY1923 @ SV676 )
| ~ ( dvd_dvd @ nat @ SV676 @ SV214 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2741]) ).
thf(3130,plain,
! [SV677: $i,SV539: $i,SV215: $i] :
( ( ~ ( dvd_dvd @ nat @ ( power_power @ nat @ SV215 @ SV539 ) @ ( power_power @ nat @ SV677 @ SV539 ) )
| ~ ( ( SV539
!= ( zero_zero @ nat ) ) )
| ( dvd_dvd @ nat @ SV215 @ SV677 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2742]) ).
thf(3131,plain,
! [SV216: $i] :
( ( ( zero_neq_one @ SV216 )
= $false )
| ( ( ( zero_zero @ SV216 )
!= ( one_one @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2743]) ).
thf(3132,plain,
! [SV217: $i] :
( ( ( comm_semiring_1 @ SV217 )
= $false )
| ( ( ! [SY1396: $i] :
( ( plus_plus @ SV217 @ ( zero_zero @ SV217 ) @ SY1396 )
= ( ti @ SV217 @ SY1396 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2744]) ).
thf(3133,plain,
! [SV218: $i] :
( ( ( ~ ( ~ ( number_ring @ SV218 )
| ~ ( linordered_idom @ SV218 ) ) )
= $false )
| ( ( ! [SY1397: $i,SY1398: $i] :
~ ( ~ ( ~ ( ord_less @ SV218 @ ( number_number_of @ SV218 @ SY1397 ) @ ( number_number_of @ SV218 @ SY1398 ) )
| ( ord_less @ int @ SY1397 @ SY1398 ) )
| ~ ( ~ ( ord_less @ int @ SY1397 @ SY1398 )
| ( ord_less @ SV218 @ ( number_number_of @ SV218 @ SY1397 ) @ ( number_number_of @ SV218 @ SY1398 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2745]) ).
thf(3134,plain,
! [SV219: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( bit0 @ SV219 ) @ min )
| ( ord_less_eq @ int @ SV219 @ min ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2746]) ).
thf(3135,plain,
! [SV219: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ SV219 @ min )
| ( ord_less_eq @ int @ ( bit0 @ SV219 ) @ min ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2746]) ).
thf(3136,plain,
! [SV220: $i] :
( ( ( comm_semiring_1 @ SV220 )
= $false )
| ( ( ! [SY1399: $i,SY1400: $i,SY1401: $i,SY1402: $i] :
( ~ ( dvd_dvd @ SV220 @ ( power_power @ SV220 @ SY1400 @ SY1401 ) @ SY1402 )
| ~ ( ord_less_eq @ nat @ SY1399 @ SY1401 )
| ( dvd_dvd @ SV220 @ ( power_power @ SV220 @ SY1400 @ SY1399 ) @ SY1402 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2747]) ).
thf(3137,plain,
! [SV540: $i,SV221: $i,SV678: $i] :
( ( ~ ( ord_less @ real @ ( zero_zero @ real ) @ SV678 )
| ~ ( ord_less @ real @ SV221 @ SV540 )
| ( ord_less @ real @ ( times_times @ real @ SV678 @ SV221 ) @ ( times_times @ real @ SV678 @ SV540 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2748]) ).
thf(3138,plain,
! [SV222: $i] :
( ( ( comm_semiring_1 @ SV222 )
= $false )
| ( ( ! [SY1405: $i,SY1406: $i,SY1407: $i] :
( ~ ( dvd_dvd @ SV222 @ SY1406 @ SY1407 )
| ( dvd_dvd @ SV222 @ SY1406 @ ( times_times @ SV222 @ SY1405 @ SY1407 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2749]) ).
thf(3139,plain,
! [SV541: $i,SV223: $i,SV679: $i] :
( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ SV679 )
| ~ ( ord_less @ nat @ ( power_power @ nat @ SV679 @ SV223 ) @ ( power_power @ nat @ SV679 @ SV541 ) )
| ( ord_less @ nat @ SV223 @ SV541 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2750]) ).
thf(3140,plain,
! [SV224: $i,SV542: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV542 ) )
= $true )
| ( ( ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV224 )
| ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ SV542 @ SV224 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2751]) ).
thf(3141,plain,
! [SV225: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( one_one @ int ) @ SV225 )
| ( ord_less @ int @ ( zero_zero @ int ) @ SV225 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2752]) ).
thf(3142,plain,
! [SV225: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV225 )
| ( ord_less_eq @ int @ ( one_one @ int ) @ SV225 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2752]) ).
thf(3143,plain,
! [SV226: $i] :
( ( ( comm_semiring_1 @ SV226 )
= $false )
| ( ( ! [SY1411: $i,SY1412: $i,SY1413: $i] :
( ~ ( dvd_dvd @ SV226 @ ( times_times @ SV226 @ SY1411 @ SY1412 ) @ SY1413 )
| ( dvd_dvd @ SV226 @ SY1411 @ SY1413 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2753]) ).
thf(3144,plain,
! [SV543: $i,SV227: $i,SV680: $i] :
( ( ~ ( mult_zero @ SV680 )
| ( ( times_times @ SV680 @ ( ti @ SV680 @ SV227 ) @ SV543 )
= ( times_times @ SV680 @ SV227 @ SV543 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2754]) ).
thf(3145,plain,
! [SV544: $i,SV228: $i,SV681: $i] :
( ( ~ ( power @ SV681 )
| ( ( ti @ SV681 @ ( times_times @ SV681 @ SV228 @ SV544 ) )
= ( times_times @ SV681 @ SV228 @ SV544 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2755]) ).
thf(3146,plain,
! [SV545: $i,SV229: $i,SV682: $i] :
( ( ~ ( semiring @ SV682 )
| ( ( plus_plus @ SV682 @ ( ti @ SV682 @ SV229 ) @ SV545 )
= ( plus_plus @ SV682 @ SV229 @ SV545 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2756]) ).
thf(3147,plain,
! [SV230: $i] :
( ( ( linordered_ring @ SV230 )
= $false )
| ( ( ! [SY1420: $i,SY1421: $i] : ( ord_less_eq @ SV230 @ ( zero_zero @ SV230 ) @ ( plus_plus @ SV230 @ ( times_times @ SV230 @ SY1420 @ SY1420 ) @ ( times_times @ SV230 @ SY1421 @ SY1421 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2757]) ).
thf(3148,plain,
! [SV546: $i,SV231: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SV231 ) @ ( bit1 @ SV546 ) )
| ( ord_less_eq @ int @ SV231 @ SV546 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV231 @ SV546 )
| ( ord_less @ int @ ( bit0 @ SV231 ) @ ( bit1 @ SV546 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2758]) ).
thf(3149,plain,
! [SV232: $i] :
( ( ( zero_neq_one @ SV232 )
= $false )
| ( ( ( one_one @ SV232 )
!= ( zero_zero @ SV232 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2759]) ).
thf(3150,plain,
! [SV547: $i,SV233: $i] :
( ( ~ ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ SV233 @ ( number_number_of @ nat @ SV547 ) ) )
| ( ( number_number_of @ nat @ SV547 )
= ( zero_zero @ nat ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ SV233 ) )
| ~ ( ~ ( ( ( number_number_of @ nat @ SV547 )
= ( zero_zero @ nat ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ SV233 ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ SV233 @ ( number_number_of @ nat @ SV547 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2760]) ).
thf(3151,plain,
! [SV234: $i] :
( ( ( ~ ( ~ ( number @ SV234 )
| ~ ( semiring @ SV234 ) ) )
= $false )
| ( ( ! [SY1424: $i,SY1425: $i,SY1426: $i] :
( ( times_times @ SV234 @ ( number_number_of @ SV234 @ SY1424 ) @ ( plus_plus @ SV234 @ SY1425 @ SY1426 ) )
= ( plus_plus @ SV234 @ ( times_times @ SV234 @ ( number_number_of @ SV234 @ SY1424 ) @ SY1425 ) @ ( times_times @ SV234 @ ( number_number_of @ SV234 @ SY1424 ) @ SY1426 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2761]) ).
thf(3152,plain,
! [SV235: $i] :
( ( ( ring_1 @ SV235 )
= $false )
| ( ( ! [SY1427: $i] :
( ( minus_minus @ SV235 @ ( times_times @ SV235 @ SY1427 @ SY1427 ) @ ( one_one @ SV235 ) )
= ( times_times @ SV235 @ ( plus_plus @ SV235 @ SY1427 @ ( one_one @ SV235 ) ) @ ( minus_minus @ SV235 @ SY1427 @ ( one_one @ SV235 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2762]) ).
thf(3153,plain,
! [SV548: $i,SV236: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SV236 ) @ ( bit1 @ SV548 ) )
| ( ord_less_eq @ int @ SV236 @ SV548 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV236 @ SV548 )
| ( ord_less @ int @ ( bit0 @ SV236 ) @ ( bit1 @ SV548 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2763]) ).
thf(3154,plain,
! [SV237: $i] :
( ( ( number @ SV237 )
= $false )
| ( ( ! [SY1429: $i,SY1430: $i] :
~ ( ~ ( ( ( number_number_of @ SV237 @ SY1429 )
!= ( ti @ SV237 @ SY1430 ) )
| ( ( ti @ SV237 @ SY1430 )
= ( number_number_of @ SV237 @ SY1429 ) ) )
| ~ ( ( ( ti @ SV237 @ SY1430 )
!= ( number_number_of @ SV237 @ SY1429 ) )
| ( ( number_number_of @ SV237 @ SY1429 )
= ( ti @ SV237 @ SY1430 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2764]) ).
thf(3155,plain,
! [SV238: $i] :
( ( ( comm_semiring_1 @ SV238 )
= $false )
| ( ( ! [SY1431: $i,SY1432: $i,SY1433: $i] :
( ( plus_plus @ SV238 @ SY1431 @ ( plus_plus @ SV238 @ SY1432 @ SY1433 ) )
= ( plus_plus @ SV238 @ ( plus_plus @ SV238 @ SY1431 @ SY1432 ) @ SY1433 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2765]) ).
thf(3156,plain,
! [SV239: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ min @ ( bit0 @ SV239 ) )
| ( ord_less @ int @ min @ SV239 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2766]) ).
thf(3157,plain,
! [SV239: $i] :
( ( ~ ( ~ ( ord_less @ int @ min @ SV239 )
| ( ord_less_eq @ int @ min @ ( bit0 @ SV239 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2766]) ).
thf(3158,plain,
! [SV549: $i,SV240: $i,SV683: $i] :
( ( ! [SY1924: $i] :
( ~ ( zprime @ SY1924 )
| ~ ~ ( dvd_dvd @ int @ SY1924 @ SV683 )
| ~ ( dvd_dvd @ int @ ( power_power @ int @ SY1924 @ SV240 ) @ ( times_times @ int @ SV683 @ SV549 ) )
| ( dvd_dvd @ int @ ( power_power @ int @ SY1924 @ SV240 ) @ SV549 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2767]) ).
thf(3159,plain,
! [SV241: $i] :
( ( ~ ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ ( number_number_of @ nat @ SV241 ) )
| ( ord_less @ int @ pls @ SV241 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2768]) ).
thf(3160,plain,
! [SV241: $i] :
( ( ~ ( ~ ( ord_less @ int @ pls @ SV241 )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ ( number_number_of @ nat @ SV241 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2768]) ).
thf(3161,plain,
! [SV550: $i,SV242: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( bit0 @ SV242 ) @ ( bit1 @ SV550 ) )
| ( ord_less_eq @ int @ SV242 @ SV550 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV242 @ SV550 )
| ( ord_less_eq @ int @ ( bit0 @ SV242 ) @ ( bit1 @ SV550 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2769]) ).
thf(3162,plain,
! [SV551: $i,SV243: $i,SV684: $i] :
( ( ~ ( power @ SV684 )
| ( ( times_times @ SV684 @ ( ti @ SV684 @ SV243 ) @ SV551 )
= ( times_times @ SV684 @ SV243 @ SV551 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2770]) ).
thf(3163,plain,
! [SV244: $i] :
( ( ~ ( ~ ( ord_less @ int @ pls @ ( bit1 @ SV244 ) )
| ( ord_less_eq @ int @ pls @ SV244 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2771]) ).
thf(3164,plain,
! [SV244: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ pls @ SV244 )
| ( ord_less @ int @ pls @ ( bit1 @ SV244 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2771]) ).
thf(3165,plain,
! [SV552: $i,SV245: $i,SV685: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ int @ SV685 @ pls )
| ( ( times_times @ nat @ ( number_number_of @ nat @ SV685 ) @ ( times_times @ nat @ ( number_number_of @ nat @ SV245 ) @ SV552 ) )
= ( zero_zero @ nat ) ) )
| ~ ( ~ ~ ( ord_less @ int @ SV685 @ pls )
| ( ( times_times @ nat @ ( number_number_of @ nat @ SV685 ) @ ( times_times @ nat @ ( number_number_of @ nat @ SV245 ) @ SV552 ) )
= ( times_times @ nat @ ( number_number_of @ nat @ ( times_times @ int @ SV685 @ SV245 ) ) @ SV552 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2772]) ).
thf(3166,plain,
! [SV553: $i,SV246: $i,SV686: $i] :
( ( ~ ( dvd @ SV686 )
| ( ( times_times @ SV686 @ ( ti @ SV686 @ SV246 ) @ SV553 )
= ( times_times @ SV686 @ SV246 @ SV553 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2773]) ).
thf(3167,plain,
! [SV554: $i,SV247: $i] :
( ( ~ ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ SV247 @ SV554 ) )
| ( SV554
= ( zero_zero @ nat ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ SV247 ) )
| ~ ( ~ ( ( SV554
= ( zero_zero @ nat ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ SV247 ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ SV247 @ SV554 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2774]) ).
thf(3168,plain,
! [SV248: $i] :
( ( ( number_ring @ SV248 )
= $false )
| ( ( ! [SY1445: $i,SY1446: $i,SY1447: $i] :
( ( times_times @ SV248 @ ( number_number_of @ SV248 @ SY1445 ) @ ( times_times @ SV248 @ ( number_number_of @ SV248 @ SY1446 ) @ SY1447 ) )
= ( times_times @ SV248 @ ( number_number_of @ SV248 @ ( times_times @ int @ SY1445 @ SY1446 ) ) @ SY1447 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2775]) ).
thf(3169,plain,
! [SV249: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SV249 ) @ ( zero_zero @ int ) )
| ( ord_less @ int @ SV249 @ ( zero_zero @ int ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2776]) ).
thf(3170,plain,
! [SV249: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV249 @ ( zero_zero @ int ) )
| ( ord_less @ int @ ( bit1 @ SV249 ) @ ( zero_zero @ int ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2776]) ).
thf(3171,plain,
! [SV250: $i] :
( ( ( number_ring @ SV250 )
= $false )
| ( ( ! [SY1448: $i] :
( ( plus_plus @ SV250 @ SY1448 @ ( number_number_of @ SV250 @ pls ) )
= ( ti @ SV250 @ SY1448 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2777]) ).
thf(3172,plain,
! [SV555: $i,SV251: $i,SV687: $i] :
( ( ~ ( power @ SV687 )
| ( ( power_power @ SV687 @ SV251 @ ( ti @ nat @ SV555 ) )
= ( power_power @ SV687 @ SV251 @ SV555 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2778]) ).
thf(3173,plain,
! [SV252: $i] :
( ( ( comm_semiring_1 @ SV252 )
= $false )
| ( ( ! [SY1451: $i,SY1452: $i,SY1453: $i] :
( ( times_times @ SV252 @ ( times_times @ SV252 @ SY1451 @ SY1452 ) @ SY1453 )
= ( times_times @ SV252 @ SY1451 @ ( times_times @ SV252 @ SY1452 @ SY1453 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2779]) ).
thf(3174,plain,
! [SV556: $i,SV253: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SV253 ) @ ( bit0 @ SV556 ) )
| ( ord_less @ int @ SV253 @ SV556 ) )
| ~ ( ~ ( ord_less @ int @ SV253 @ SV556 )
| ( ord_less @ int @ ( bit1 @ SV253 ) @ ( bit0 @ SV556 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2780]) ).
thf(3175,plain,
! [SV254: $i] :
( ( ( comm_semiring_1 @ SV254 )
= $false )
| ( ( ! [SY1455: $i,SY1456: $i] :
( ( plus_plus @ SV254 @ SY1455 @ ( times_times @ SV254 @ SY1456 @ SY1455 ) )
= ( times_times @ SV254 @ ( plus_plus @ SV254 @ SY1456 @ ( one_one @ SV254 ) ) @ SY1455 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2781]) ).
thf(3176,plain,
! [SV255: $i] :
( ( ( semiri456707255roduct @ SV255 )
= $false )
| ( ( ! [SY1457: $i,SY1458: $i,SY1459: $i,SY1460: $i] :
~ ( ~ ( ( ( plus_plus @ SV255 @ ( times_times @ SV255 @ SY1457 @ SY1458 ) @ ( times_times @ SV255 @ SY1459 @ SY1460 ) )
!= ( plus_plus @ SV255 @ ( times_times @ SV255 @ SY1457 @ SY1460 ) @ ( times_times @ SV255 @ SY1459 @ SY1458 ) ) )
| ( ( ti @ SV255 @ SY1457 )
= ( ti @ SV255 @ SY1459 ) )
| ( ( ti @ SV255 @ SY1458 )
= ( ti @ SV255 @ SY1460 ) ) )
| ~ ( ~ ( ( ( ti @ SV255 @ SY1457 )
= ( ti @ SV255 @ SY1459 ) )
| ( ( ti @ SV255 @ SY1458 )
= ( ti @ SV255 @ SY1460 ) ) )
| ( ( plus_plus @ SV255 @ ( times_times @ SV255 @ SY1457 @ SY1458 ) @ ( times_times @ SV255 @ SY1459 @ SY1460 ) )
= ( plus_plus @ SV255 @ ( times_times @ SV255 @ SY1457 @ SY1460 ) @ ( times_times @ SV255 @ SY1459 @ SY1458 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2782]) ).
thf(3177,plain,
! [SV256: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ pls @ ( bit1 @ SV256 ) )
| ( ord_less_eq @ int @ pls @ SV256 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2783]) ).
thf(3178,plain,
! [SV256: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ pls @ SV256 )
| ( ord_less_eq @ int @ pls @ ( bit1 @ SV256 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2783]) ).
thf(3179,plain,
! [SV557: $i,SV257: $i,SV688: $i] :
( ( ! [SY1925: $i,SY1926: $i] :
( ~ ( zcong @ SV688 @ SY1925 @ SY1926 )
| ~ ( ~ ( ~ ( zcong @ SV257 @ ( times_times @ int @ SV557 @ SV688 ) @ SY1926 )
| ( zcong @ SV257 @ ( times_times @ int @ SV557 @ SY1925 ) @ SY1926 ) )
| ~ ( ~ ( zcong @ SV257 @ ( times_times @ int @ SV557 @ SY1925 ) @ SY1926 )
| ( zcong @ SV257 @ ( times_times @ int @ SV557 @ SV688 ) @ SY1926 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2784]) ).
thf(3180,plain,
! [SV258: $i] :
( ( ( number_ring @ SV258 )
= $false )
| ( ( ( one_one @ SV258 )
= ( number_number_of @ SV258 @ ( bit1 @ pls ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2785]) ).
thf(3181,plain,
! [SV558: $i,SV259: $i,SV689: $i] :
( ( ~ ( ( SV689
!= ( zero_zero @ nat ) ) )
| ~ ( dvd_dvd @ nat @ ( power_power @ nat @ SV259 @ SV689 ) @ SV558 )
| ( dvd_dvd @ nat @ SV259 @ SV558 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2786]) ).
thf(3182,plain,
! [SV260: $i] :
( ( ( number_ring @ SV260 )
= $false )
| ( ( ( number_number_of @ SV260 @ ( bit1 @ pls ) )
= ( one_one @ SV260 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2787]) ).
thf(3183,plain,
! [SV690: $i,SV559: $i,SV261: $i] :
( ( ~ ( ~ ( ~ ( zcong @ SV261 @ ( ti @ int @ SV559 ) @ SV690 )
| ( zcong @ SV261 @ SV559 @ SV690 ) )
| ~ ( ~ ( zcong @ SV261 @ SV559 @ SV690 )
| ( zcong @ SV261 @ ( ti @ int @ SV559 ) @ SV690 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2788]) ).
thf(3184,plain,
! [SV262: $i] :
( ( ( zprime @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SV262 ) @ ( one_one @ int ) ) )
= $false )
| ( ( ( legendre @ ( number_number_of @ int @ min ) @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SV262 ) @ ( one_one @ int ) ) )
= ( one_one @ int ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2789]) ).
thf(3185,plain,
! [SV263: $i] :
( ( ( number_ring @ SV263 )
= $false )
| ( ( ! [SY1469: $i,SY1470: $i] :
( ( number_number_of @ SV263 @ ( plus_plus @ int @ SY1469 @ SY1470 ) )
= ( plus_plus @ SV263 @ ( number_number_of @ SV263 @ SY1469 ) @ ( number_number_of @ SV263 @ SY1470 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2790]) ).
thf(3186,plain,
! [SV264: $i] :
( ( ( number_ring @ SV264 )
= $false )
| ( ( ! [SY1471: $i,SY1472: $i] :
( ( number_number_of @ SV264 @ ( times_times @ int @ SY1471 @ SY1472 ) )
= ( times_times @ SV264 @ ( number_number_of @ SV264 @ SY1471 ) @ ( number_number_of @ SV264 @ SY1472 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2791]) ).
thf(3187,plain,
! [SV265: $i] :
( ( ( comm_semiring_1 @ SV265 )
= $false )
| ( ( ! [SY1473: $i] :
( ( power_power @ SV265 @ SY1473 @ ( zero_zero @ nat ) )
= ( one_one @ SV265 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2792]) ).
thf(3188,plain,
! [SV266: $i] :
( ( ( comm_semiring_1 @ SV266 )
= $false )
| ( ( ! [SY1474: $i,SY1475: $i,SY1476: $i,SY1477: $i] :
( ( plus_plus @ SV266 @ ( plus_plus @ SV266 @ SY1474 @ SY1475 ) @ ( plus_plus @ SV266 @ SY1476 @ SY1477 ) )
= ( plus_plus @ SV266 @ ( plus_plus @ SV266 @ SY1474 @ SY1476 ) @ ( plus_plus @ SV266 @ SY1475 @ SY1477 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2793]) ).
thf(3189,plain,
! [SV268: $i,SV560: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV560 ) )
= $true )
| ( ( ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV268 )
| ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( times_times @ int @ SV560 @ SV268 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2795]) ).
thf(3190,plain,
! [SV269: $i] :
( ( ( linordered_idom @ SV269 )
= $false )
| ( ( ! [SY1479: $i] :
~ ( ~ ( ~ ( ord_less @ SV269 @ ( plus_plus @ SV269 @ SY1479 @ SY1479 ) @ ( zero_zero @ SV269 ) )
| ( ord_less @ SV269 @ SY1479 @ ( zero_zero @ SV269 ) ) )
| ~ ( ~ ( ord_less @ SV269 @ SY1479 @ ( zero_zero @ SV269 ) )
| ( ord_less @ SV269 @ ( plus_plus @ SV269 @ SY1479 @ SY1479 ) @ ( zero_zero @ SV269 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2796]) ).
thf(3191,plain,
! [SV561: $i,SV270: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV270 @ SV561 ) )
= $true )
| ( ( ~ ( ord_less_eq @ int @ SV561 @ SV270 )
| ( ( ti @ int @ SV270 )
= ( ti @ int @ SV561 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2797]) ).
thf(3192,plain,
! [SV271: $i] :
( ( ( number_ring @ SV271 )
= $false )
| ( ( ! [SY1481: $i,SY1482: $i,SY1483: $i] :
( ( plus_plus @ SV271 @ ( number_number_of @ SV271 @ SY1481 ) @ ( minus_minus @ SV271 @ ( number_number_of @ SV271 @ SY1482 ) @ SY1483 ) )
= ( minus_minus @ SV271 @ ( number_number_of @ SV271 @ ( plus_plus @ int @ SY1481 @ SY1482 ) ) @ SY1483 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2798]) ).
thf(3193,plain,
! [SV272: $i] :
( ( ( number_ring @ SV272 )
= $false )
| ( ( ! [SY1484: $i] :
( ( number_number_of @ SV272 @ ( bit0 @ SY1484 ) )
= ( plus_plus @ SV272 @ ( plus_plus @ SV272 @ ( zero_zero @ SV272 ) @ ( number_number_of @ SV272 @ SY1484 ) ) @ ( number_number_of @ SV272 @ SY1484 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2799]) ).
thf(3194,plain,
! [SV562: $i,SV273: $i,SV691: $i] :
( ( ~ ( ( SV691
!= ( zero_zero @ real ) ) )
| ~ ( ~ ( ( ( times_times @ real @ SV691 @ SV273 )
!= ( times_times @ real @ SV691 @ SV562 ) )
| ( SV273 = SV562 ) )
| ~ ( ( SV273 != SV562 )
| ( ( times_times @ real @ SV691 @ SV273 )
= ( times_times @ real @ SV691 @ SV562 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2800]) ).
thf(3195,plain,
! [SV274: $i] :
( ( ~ ( ~ ( ord_less @ int @ min @ ( bit1 @ SV274 ) )
| ( ord_less @ int @ min @ SV274 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2801]) ).
thf(3196,plain,
! [SV274: $i] :
( ( ~ ( ~ ( ord_less @ int @ min @ SV274 )
| ( ord_less @ int @ min @ ( bit1 @ SV274 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2801]) ).
thf(3197,plain,
! [SV275: $i] :
( ( ( number_ring @ SV275 )
= $false )
| ( ( ! [SY1487: $i,SY1488: $i] :
( ( number_number_of @ SV275 @ ( minus_minus @ int @ SY1487 @ SY1488 ) )
= ( minus_minus @ SV275 @ ( number_number_of @ SV275 @ SY1487 ) @ ( number_number_of @ SV275 @ SY1488 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2802]) ).
thf(3198,plain,
! [SV276: $i] :
( ( ( monoid_mult @ SV276 )
= $false )
| ( ( ! [SY1489: $i] :
( ( power_power @ SV276 @ ( one_one @ SV276 ) @ SY1489 )
= ( one_one @ SV276 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2803]) ).
thf(3199,plain,
! [SV277: $i] :
( ( ( comm_semiring_1 @ SV277 )
= $false )
| ( ( ! [SY1490: $i,SY1491: $i,SY1492: $i] :
( ~ ( dvd_dvd @ SV277 @ SY1491 @ SY1492 )
| ~ ( dvd_dvd @ SV277 @ SY1491 @ SY1490 )
| ( dvd_dvd @ SV277 @ SY1491 @ ( plus_plus @ SV277 @ SY1492 @ SY1490 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2804]) ).
thf(3200,plain,
! [SV278: $i] :
( ( ( comm_semiring_1 @ SV278 )
= $false )
| ( ( ! [SY1493: $i] :
( ( times_times @ SV278 @ ( zero_zero @ SV278 ) @ SY1493 )
= ( zero_zero @ SV278 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2805]) ).
thf(3201,plain,
! [SV279: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SV279 ) @ pls )
| ( ord_less @ int @ SV279 @ pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2806]) ).
thf(3202,plain,
! [SV279: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV279 @ pls )
| ( ord_less @ int @ ( bit0 @ SV279 ) @ pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2806]) ).
thf(3203,plain,
! [SV563: $i,SV280: $i,SV692: $i] :
( ( ~ ( semiring @ SV692 )
| ( ( ti @ SV692 @ ( times_times @ SV692 @ SV280 @ SV563 ) )
= ( times_times @ SV692 @ SV280 @ SV563 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2807]) ).
thf(3204,plain,
! [SV564: $i,SV281: $i] :
( ( ~ ( ( ( bit0 @ SV281 )
!= ( bit0 @ SV564 ) )
| ( ( ti @ int @ SV281 )
= ( ti @ int @ SV564 ) ) )
| ~ ( ( ( ti @ int @ SV281 )
!= ( ti @ int @ SV564 ) )
| ( ( bit0 @ SV281 )
= ( bit0 @ SV564 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2808]) ).
thf(3205,plain,
! [SV282: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SV282 ) @ min )
| ( ord_less_eq @ int @ SV282 @ min ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2809]) ).
thf(3206,plain,
! [SV282: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ SV282 @ min )
| ( ord_less_eq @ int @ ( bit1 @ SV282 ) @ min ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2809]) ).
thf(3207,plain,
! [SV283: $i] :
( ( ( number_ring @ SV283 )
= $false )
| ( ( ! [SY1497: $i] :
( ( plus_plus @ SV283 @ ( number_number_of @ SV283 @ pls ) @ SY1497 )
= ( ti @ SV283 @ SY1497 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2810]) ).
thf(3208,plain,
! [SV284: $i] :
( ( ( comm_semiring_1 @ SV284 )
= $false )
| ( ( ! [SY1498: $i,SY1499: $i,SY1500: $i] :
( ~ ( dvd_dvd @ SV284 @ SY1499 @ SY1500 )
| ( dvd_dvd @ SV284 @ ( power_power @ SV284 @ SY1499 @ SY1498 ) @ ( power_power @ SV284 @ SY1500 @ SY1498 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2811]) ).
thf(3209,plain,
! [SV285: $i] :
( ( ( number_semiring @ SV285 )
= $false )
| ( ( ! [SY1501: $i,SY1502: $i] :
( ~ ( ord_less_eq @ int @ pls @ SY1502 )
| ~ ( ord_less_eq @ int @ pls @ SY1501 )
| ( ( plus_plus @ SV285 @ ( number_number_of @ SV285 @ SY1502 ) @ ( number_number_of @ SV285 @ SY1501 ) )
= ( number_number_of @ SV285 @ ( plus_plus @ int @ SY1502 @ SY1501 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2812]) ).
thf(3210,plain,
! [SV286: $i] :
( ( ( monoid_mult @ SV286 )
= $false )
| ( ( ! [SY1503: $i,SY1504: $i] :
( ( power_power @ SV286 @ SY1503 @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SY1504 ) )
= ( power_power @ SV286 @ ( power_power @ SV286 @ SY1503 @ SY1504 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2813]) ).
thf(3211,plain,
! [SV565: $i,SV287: $i,SV693: $i] :
( ( ~ ( dvd @ SV693 )
| ( ( times_times @ SV693 @ SV287 @ ( ti @ SV693 @ SV565 ) )
= ( times_times @ SV693 @ SV287 @ SV565 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2814]) ).
thf(3212,plain,
! [SV566: $i,SV288: $i,SV694: $i] :
( ( ! [SY1927: $i] :
( ~ ( zprime @ SY1927 )
| ~ ~ ( dvd_dvd @ int @ SY1927 @ SV694 )
| ~ ( dvd_dvd @ int @ ( power_power @ int @ SY1927 @ SV288 ) @ ( times_times @ int @ SV566 @ SV694 ) )
| ( dvd_dvd @ int @ ( power_power @ int @ SY1927 @ SV288 ) @ SV566 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2815]) ).
thf(3213,plain,
! [SV567: $i,SV289: $i,SV695: $i] :
( ( ~ ( ab_group_add @ SV695 )
| ( ( plus_plus @ SV695 @ ( ti @ SV695 @ SV289 ) @ SV567 )
= ( plus_plus @ SV695 @ SV289 @ SV567 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2816]) ).
thf(3214,plain,
! [SV290: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SV290 ) @ ( zero_zero @ int ) )
| ( ord_less @ int @ SV290 @ ( zero_zero @ int ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2817]) ).
thf(3215,plain,
! [SV290: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV290 @ ( zero_zero @ int ) )
| ( ord_less @ int @ ( bit0 @ SV290 ) @ ( zero_zero @ int ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2817]) ).
thf(3216,plain,
! [SV291: $i] :
( ( ( comm_semiring_1 @ SV291 )
= $false )
| ( ( ! [SY1512: $i] :
( ( times_times @ SV291 @ SY1512 @ SY1512 )
= ( power_power @ SV291 @ SY1512 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2818]) ).
thf(3217,plain,
! [SV568: $i,SV292: $i] :
( ( ~ ( ~ ( zcong @ ( times_times @ int @ SV292 @ ( minus_minus @ int @ SV568 @ ( one_one @ int ) ) ) @ ( one_one @ int ) @ SV568 )
| ( zcong @ SV292 @ ( minus_minus @ int @ SV568 @ ( one_one @ int ) ) @ SV568 ) )
| ~ ( ~ ( zcong @ SV292 @ ( minus_minus @ int @ SV568 @ ( one_one @ int ) ) @ SV568 )
| ( zcong @ ( times_times @ int @ SV292 @ ( minus_minus @ int @ SV568 @ ( one_one @ int ) ) ) @ ( one_one @ int ) @ SV568 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2819]) ).
thf(3218,plain,
! [SV293: $i] :
( ( ( linordered_idom @ SV293 )
= $false )
| ( ( ! [SY1514: $i] : ( ord_less_eq @ SV293 @ ( zero_zero @ SV293 ) @ ( power_power @ SV293 @ SY1514 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2820]) ).
thf(3219,plain,
! [SV294: $i,SV696: $i,SV569: $i] :
( ( ~ ( ord_less_eq @ int @ SV569 @ SV696 )
| ~ ( ord_less_eq @ int @ SV696 @ SV294 )
| ( ord_less_eq @ int @ SV569 @ SV294 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2821]) ).
thf(3220,plain,
! [SV295: $i] :
( ( ( power @ SV295 )
= $false )
| ( ( ( ti @ SV295 @ ( one_one @ SV295 ) )
= ( one_one @ SV295 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2822]) ).
thf(3221,plain,
! [SV296: $i] :
( ( ( comm_semiring_1 @ SV296 )
= $false )
| ( ( ! [SY1517: $i,SY1518: $i,SY1519: $i] :
( ( plus_plus @ SV296 @ ( plus_plus @ SV296 @ SY1517 @ SY1518 ) @ SY1519 )
= ( plus_plus @ SV296 @ ( plus_plus @ SV296 @ SY1517 @ SY1519 ) @ SY1518 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2823]) ).
thf(3222,plain,
! [SV297: $i,SV697: $i,SV570: $i] :
( ( ~ ( ord_less @ int @ SV570 @ SV697 )
| ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV297 )
| ( ord_less @ int @ ( times_times @ int @ SV297 @ SV570 ) @ ( times_times @ int @ SV297 @ SV697 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2824]) ).
thf(3223,plain,
! [SV298: $i] :
( ( ( comm_monoid_mult @ SV298 )
= $false )
| ( ( ! [SY1522: $i,SY1523: $i,SY1524: $i] :
( ( power_power @ SV298 @ ( times_times @ SV298 @ SY1522 @ SY1523 ) @ SY1524 )
= ( times_times @ SV298 @ ( power_power @ SV298 @ SY1522 @ SY1524 ) @ ( power_power @ SV298 @ SY1523 @ SY1524 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2825]) ).
thf(3224,plain,
! [SV571: $i,SV299: $i] :
( ( ( ~ ( dvd_dvd @ nat @ SV299 @ SV571 ) )
= $true )
| ( ( ( SV571
= ( zero_zero @ nat ) )
| ( SV571 = SV299 )
| ( ord_less_eq @ nat @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV299 ) @ SV571 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2826]) ).
thf(3225,plain,
! [SV572: $i,SV300: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SV300 ) @ ( bit1 @ SV572 ) )
| ( ord_less_eq @ int @ SV300 @ SV572 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV300 @ SV572 )
| ( ord_less_eq @ int @ ( bit1 @ SV300 ) @ ( bit1 @ SV572 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2827]) ).
thf(3226,plain,
! [SV301: $i] :
( ( ( ring_n68954251visors @ SV301 )
= $false )
| ( ( ! [SY1527: $i,SY1528: $i] :
~ ( ~ ( ( ( times_times @ SV301 @ SY1527 @ SY1528 )
!= ( zero_zero @ SV301 ) )
| ( ( ti @ SV301 @ SY1527 )
= ( zero_zero @ SV301 ) )
| ( ( ti @ SV301 @ SY1528 )
= ( zero_zero @ SV301 ) ) )
| ~ ( ~ ( ( ( ti @ SV301 @ SY1527 )
= ( zero_zero @ SV301 ) )
| ( ( ti @ SV301 @ SY1528 )
= ( zero_zero @ SV301 ) ) )
| ( ( times_times @ SV301 @ SY1527 @ SY1528 )
= ( zero_zero @ SV301 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2828]) ).
thf(3227,plain,
! [SV302: $i] :
( ( ( number_ring @ SV302 )
= $false )
| ( ( ! [SY1529: $i] :
( ( times_times @ SV302 @ ( plus_plus @ SV302 @ ( one_one @ SV302 ) @ ( one_one @ SV302 ) ) @ ( number_number_of @ SV302 @ SY1529 ) )
= ( number_number_of @ SV302 @ ( bit0 @ SY1529 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2829]) ).
thf(3228,plain,
! [SV303: $i] :
( ( ~ ( ( pls
!= ( bit0 @ SV303 ) )
| ( pls
= ( ti @ int @ SV303 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2830]) ).
thf(3229,plain,
! [SV303: $i] :
( ( ~ ( ( pls
!= ( ti @ int @ SV303 ) )
| ( pls
= ( bit0 @ SV303 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2830]) ).
thf(3230,plain,
! [SV304: $i] :
( ( ( linordered_semidom @ SV304 )
= $false )
| ( ( ! [SY1530: $i,SY1531: $i,SY1532: $i] :
( ~ ( ord_less @ SV304 @ ( one_one @ SV304 ) @ SY1532 )
| ~ ( ord_less_eq @ SV304 @ ( power_power @ SV304 @ SY1532 @ SY1530 ) @ ( power_power @ SV304 @ SY1532 @ SY1531 ) )
| ( ord_less_eq @ nat @ SY1530 @ SY1531 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2831]) ).
thf(3231,plain,
! [SV698: $i,SV573: $i,SV305: $i] :
( ( ! [SY1928: $i,SY1929: $i,SY1930: $i] :
( ( ( plus_plus @ int @ ( times_times @ int @ SV305 @ SV573 ) @ SV698 )
!= ( plus_plus @ int @ ( times_times @ int @ SY1928 @ SY1929 ) @ SY1930 ) )
| ~ ( ord_less @ int @ ( plus_plus @ int @ ( times_times @ int @ SY1928 @ SY1929 ) @ SY1930 ) @ ( zero_zero @ int ) )
| ~ ( ord_less @ int @ SV698 @ SV305 )
| ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SY1930 )
| ~ ( ord_less @ int @ ( zero_zero @ int ) @ SY1928 )
| ~ ( ord_less_eq @ int @ SY1928 @ SV305 )
| ( ord_less_eq @ int @ SY1929 @ SV573 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2832]) ).
thf(3232,plain,
! [SV306: $i] :
( ( ( comm_semiring_1 @ SV306 )
= $false )
| ( ( ! [SY1538: $i,SY1539: $i] :
( ( plus_plus @ SV306 @ ( times_times @ SV306 @ SY1538 @ SY1539 ) @ SY1539 )
= ( times_times @ SV306 @ ( plus_plus @ SV306 @ SY1538 @ ( one_one @ SV306 ) ) @ SY1539 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2833]) ).
thf(3233,plain,
! [SV574: $i,SV307: $i,SV699: $i] :
( ( ~ ( dvd @ SV699 )
| ( ( ti @ SV699 @ ( times_times @ SV699 @ SV307 @ SV574 ) )
= ( times_times @ SV699 @ SV307 @ SV574 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2834]) ).
thf(3234,plain,
! [SV308: $i,SV700: $i,SV575: $i] :
( ( ! [SY1931: $i] :
( ~ ( zcong @ SV575 @ SV700 @ SY1931 )
| ( zcong @ ( power_power @ int @ SV575 @ SV308 ) @ ( power_power @ int @ SV700 @ SV308 ) @ SY1931 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2835]) ).
thf(3235,plain,
! [SV309: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SV309 ) @ pls )
| ( ord_less @ int @ SV309 @ pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2836]) ).
thf(3236,plain,
! [SV309: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV309 @ pls )
| ( ord_less_eq @ int @ ( bit1 @ SV309 ) @ pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2836]) ).
thf(3237,plain,
! [SV311: $i] :
( ( ( comm_semiring_1 @ SV311 )
= $false )
| ( ( ! [SY1545: $i,SY1546: $i,SY1547: $i] :
( ( power_power @ SV311 @ ( power_power @ SV311 @ SY1545 @ SY1546 ) @ SY1547 )
= ( power_power @ SV311 @ SY1545 @ ( times_times @ nat @ SY1546 @ SY1547 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2838]) ).
thf(3238,plain,
! [SV701: $i,SV576: $i,SV312: $i] :
( ( ! [SY1932: $i,SY1933: $i] :
( ~ ( ord_less_eq @ int @ ( plus_plus @ int @ ( times_times @ int @ SV312 @ SV576 ) @ SV701 ) @ ( plus_plus @ int @ ( times_times @ int @ SV312 @ SY1932 ) @ SY1933 ) )
| ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV701 )
| ~ ( ord_less @ int @ SV701 @ SV312 )
| ~ ( ord_less @ int @ SY1933 @ SV312 )
| ( ord_less_eq @ int @ SV576 @ SY1932 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2839]) ).
thf(3239,plain,
! [SV313: $i] :
( ( ( semiri456707255roduct @ SV313 )
= $false )
| ( ( ! [SY1552: $i,SY1553: $i] :
~ ( ~ ( ( ( ti @ SV313 @ SY1552 )
!= ( plus_plus @ SV313 @ SY1552 @ SY1553 ) )
| ( ( ti @ SV313 @ SY1553 )
= ( zero_zero @ SV313 ) ) )
| ~ ( ( ( ti @ SV313 @ SY1553 )
!= ( zero_zero @ SV313 ) )
| ( ( ti @ SV313 @ SY1552 )
= ( plus_plus @ SV313 @ SY1552 @ SY1553 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2840]) ).
thf(3240,plain,
! [SV577: $i,SV314: $i] :
( ( ~ ( ~ ( quadRes @ SV314 @ SV577 )
| ~ ! [SY1865: $i] :
~ ( zcong @ ( power_power @ int @ SY1865 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SV577 @ SV314 ) )
| ~ ( ~ ~ ! [SY1866: $i] :
~ ( zcong @ ( power_power @ int @ SY1866 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SV577 @ SV314 )
| ( quadRes @ SV314 @ SV577 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2841]) ).
thf(3241,plain,
! [SV315: $i] :
( ( ( linordered_semidom @ SV315 )
= $false )
| ( ( ! [SY1557: $i,SY1558: $i,SY1559: $i] :
( ~ ( ord_less_eq @ nat @ SY1558 @ SY1559 )
| ~ ( ord_less_eq @ SV315 @ ( one_one @ SV315 ) @ SY1557 )
| ( ord_less_eq @ SV315 @ ( power_power @ SV315 @ SY1557 @ SY1558 ) @ ( power_power @ SV315 @ SY1557 @ SY1559 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2842]) ).
thf(3242,plain,
! [SV316: $i] :
( ( ( comm_semiring_1 @ SV316 )
= $false )
| ( ( ! [SY1560: $i,SY1561: $i,SY1562: $i] :
( ( times_times @ SV316 @ ( plus_plus @ SV316 @ SY1560 @ SY1561 ) @ SY1562 )
= ( plus_plus @ SV316 @ ( times_times @ SV316 @ SY1560 @ SY1562 ) @ ( times_times @ SV316 @ SY1561 @ SY1562 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2843]) ).
thf(3243,plain,
! [SV317: $i] :
( ( ( linordered_semidom @ SV317 )
= $false )
| ( ( ! [SY1563: $i,SY1564: $i] :
( ~ ( ord_less_eq @ SV317 @ ( one_one @ SV317 ) @ SY1564 )
| ( ord_less_eq @ SV317 @ ( one_one @ SV317 ) @ ( power_power @ SV317 @ SY1564 @ SY1563 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2844]) ).
thf(3244,plain,
! [SV318: $i] :
( ( ( comm_semiring_1 @ SV318 )
= $false )
| ( ( ! [SY1565: $i,SY1566: $i] :
( ( times_times @ SV318 @ SY1565 @ SY1566 )
= ( times_times @ SV318 @ SY1566 @ SY1565 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2845]) ).
thf(3245,plain,
! [SV319: $i] :
( ( ( linord581940658strict @ SV319 )
= $false )
| ( ( ! [SY1567: $i,SY1568: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV319 @ ( times_times @ SV319 @ SY1567 @ SY1568 ) @ ( zero_zero @ SV319 ) )
| ~ ( ~ ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SY1567 )
| ~ ( ord_less_eq @ SV319 @ SY1568 @ ( zero_zero @ SV319 ) ) )
| ~ ( ~ ( ord_less_eq @ SV319 @ SY1567 @ ( zero_zero @ SV319 ) )
| ~ ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SY1568 ) ) )
| ~ ( ~ ( ~ ( ~ ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SY1567 )
| ~ ( ord_less_eq @ SV319 @ SY1568 @ ( zero_zero @ SV319 ) ) )
| ~ ( ~ ( ord_less_eq @ SV319 @ SY1567 @ ( zero_zero @ SV319 ) )
| ~ ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SY1568 ) ) )
| ( ord_less_eq @ SV319 @ ( times_times @ SV319 @ SY1567 @ SY1568 ) @ ( zero_zero @ SV319 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2846]) ).
thf(3246,plain,
! [SV320: $i] :
( ( ~ ( ( ( zero_zero @ nat )
!= ( number_number_of @ nat @ SV320 ) )
| ( ord_less_eq @ int @ SV320 @ pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2847]) ).
thf(3247,plain,
! [SV320: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ SV320 @ pls )
| ( ( zero_zero @ nat )
= ( number_number_of @ nat @ SV320 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2847]) ).
thf(3248,plain,
! [SV321: $i] :
( ( ( ~ ( ~ ( number_ring @ SV321 )
| ~ ( linordered_idom @ SV321 ) ) )
= $false )
| ( ( ! [SY1569: $i,SY1570: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV321 @ ( number_number_of @ SV321 @ SY1569 ) @ ( number_number_of @ SV321 @ SY1570 ) )
| ( ord_less_eq @ int @ SY1569 @ SY1570 ) )
| ~ ( ~ ( ord_less_eq @ int @ SY1569 @ SY1570 )
| ( ord_less_eq @ SV321 @ ( number_number_of @ SV321 @ SY1569 ) @ ( number_number_of @ SV321 @ SY1570 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2848]) ).
thf(3249,plain,
! [SV322: $i] :
( ( ( comm_semiring_1 @ SV322 )
= $false )
| ( ( ! [SY1571: $i] :
( ( times_times @ SV322 @ SY1571 @ ( zero_zero @ SV322 ) )
= ( zero_zero @ SV322 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2849]) ).
thf(3250,plain,
! [SV323: $i] :
( ( ( comm_semiring_1 @ SV323 )
= $false )
| ( ( ! [SY1572: $i,SY1573: $i,SY1574: $i,SY1575: $i] :
( ~ ( dvd_dvd @ SV323 @ SY1574 @ SY1575 )
| ~ ( ord_less_eq @ nat @ SY1572 @ SY1573 )
| ( dvd_dvd @ SV323 @ ( power_power @ SV323 @ SY1574 @ SY1572 ) @ ( power_power @ SV323 @ SY1575 @ SY1573 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2850]) ).
thf(3251,plain,
! [SV324: $i] :
( ( ( number_semiring @ SV324 )
= $false )
| ( ( ( number_number_of @ SV324 @ ( bit1 @ pls ) )
= ( one_one @ SV324 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2851]) ).
thf(3252,plain,
! [SV325: $i] :
( ( ( linordered_semidom @ SV325 )
= $false )
| ( ( ! [SY1576: $i,SY1577: $i] :
( ~ ( ord_less_eq @ SV325 @ ( power_power @ SV325 @ SY1576 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV325 @ SY1577 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ~ ( ord_less_eq @ SV325 @ ( zero_zero @ SV325 ) @ SY1577 )
| ( ord_less_eq @ SV325 @ SY1576 @ SY1577 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2852]) ).
thf(3253,plain,
! [SV578: $i,SV327: $i] :
( ( ( ( times_times @ int @ SV327 @ SV578 )
!= ( one_one @ int ) )
= $true )
| ( ( ( ( ti @ int @ SV327 )
= ( one_one @ int ) )
| ( ( ti @ int @ SV327 )
= ( number_number_of @ int @ min ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2854]) ).
thf(3254,plain,
! [SV328: $i] :
( ( ~ ( ~ ( ord_less @ int @ min @ ( bit0 @ SV328 ) )
| ( ord_less @ int @ min @ SV328 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2855]) ).
thf(3255,plain,
! [SV328: $i] :
( ( ~ ( ~ ( ord_less @ int @ min @ SV328 )
| ( ord_less @ int @ min @ ( bit0 @ SV328 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2855]) ).
thf(3256,plain,
! [SV329: $i] :
( ( ( monoid_mult @ SV329 )
= $false )
| ( ( ! [SY1579: $i,SY1580: $i,SY1581: $i] :
( ( power_power @ SV329 @ SY1579 @ ( plus_plus @ nat @ SY1580 @ SY1581 ) )
= ( times_times @ SV329 @ ( power_power @ SV329 @ SY1579 @ SY1580 ) @ ( power_power @ SV329 @ SY1579 @ SY1581 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2856]) ).
thf(3257,plain,
! [SV330: $i] :
( ( ( comm_semiring_1 @ SV330 )
= $false )
| ( ( ! [SY1582: $i,SY1583: $i,SY1584: $i] :
( ~ ( dvd_dvd @ SV330 @ ( times_times @ SV330 @ SY1582 @ SY1583 ) @ SY1584 )
| ( dvd_dvd @ SV330 @ SY1583 @ SY1584 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2857]) ).
thf(3258,plain,
! [SV331: $i] :
( ( ( ord_less @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV331 )
= $false )
| ( ( ~ ( zcong @ ( one_one @ int ) @ ( number_number_of @ int @ min ) @ SV331 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2858]) ).
thf(3259,plain,
! [SV332: $i] :
( ( ( comm_semiring_1 @ SV332 )
= $false )
| ( ( ! [SY1585: $i,SY1586: $i] : ( dvd_dvd @ SV332 @ SY1585 @ ( times_times @ SV332 @ SY1585 @ SY1586 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2859]) ).
thf(3260,plain,
! [SV333: $i] :
( ( ( ~ ( ~ ( power @ SV333 )
| ~ ( semiring_0 @ SV333 ) ) )
= $false )
| ( ( ! [SY1587: $i] :
~ ( ~ ( ( ( number_number_of @ nat @ SY1587 )
!= ( zero_zero @ nat ) )
| ( ( power_power @ SV333 @ ( zero_zero @ SV333 ) @ ( number_number_of @ nat @ SY1587 ) )
= ( one_one @ SV333 ) ) )
| ~ ( ~ ( ( ( number_number_of @ nat @ SY1587 )
!= ( zero_zero @ nat ) ) )
| ( ( power_power @ SV333 @ ( zero_zero @ SV333 ) @ ( number_number_of @ nat @ SY1587 ) )
= ( zero_zero @ SV333 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2860]) ).
thf(3261,plain,
! [SV579: $i,SV334: $i,SV702: $i] :
( ( ~ ( no_zero_divisors @ SV702 )
| ( ( ti @ SV702 @ ( times_times @ SV702 @ SV334 @ SV579 ) )
= ( times_times @ SV702 @ SV334 @ SV579 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2861]) ).
thf(3262,plain,
! [SV580: $i,SV335: $i,SV703: $i] :
( ( ~ ( ab_group_add @ SV703 )
| ( ( plus_plus @ SV703 @ SV335 @ ( ti @ SV703 @ SV580 ) )
= ( plus_plus @ SV703 @ SV335 @ SV580 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2862]) ).
thf(3263,plain,
! [SV581: $i,SV336: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( bit0 @ SV336 ) @ ( bit0 @ SV581 ) )
| ( ord_less_eq @ int @ SV336 @ SV581 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV336 @ SV581 )
| ( ord_less_eq @ int @ ( bit0 @ SV336 ) @ ( bit0 @ SV581 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2863]) ).
thf(3264,plain,
! [SV582: $i,SV337: $i,SV704: $i] :
( ( ! [SY1934: $i,SY1935: $i] :
( ~ ( zcong @ SV704 @ SY1934 @ SY1935 )
| ~ ( zcong @ SV337 @ SV582 @ SY1935 )
| ( zcong @ ( times_times @ int @ SV704 @ SV337 ) @ ( times_times @ int @ SY1934 @ SV582 ) @ SY1935 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2864]) ).
thf(3265,plain,
! [SV583: $i,SV338: $i,SV705: $i] :
( ( ~ ( ord_less @ real @ ( zero_zero @ real ) @ SV705 )
| ~ ( ~ ( ~ ( ord_less @ real @ ( times_times @ real @ SV338 @ SV705 ) @ ( times_times @ real @ SV583 @ SV705 ) )
| ( ord_less @ real @ SV338 @ SV583 ) )
| ~ ( ~ ( ord_less @ real @ SV338 @ SV583 )
| ( ord_less @ real @ ( times_times @ real @ SV338 @ SV705 ) @ ( times_times @ real @ SV583 @ SV705 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2865]) ).
thf(3266,plain,
! [SV339: $i] :
( ( ( mult_zero @ SV339 )
= $false )
| ( ( ! [SY1599: $i] :
( ( times_times @ SV339 @ SY1599 @ ( zero_zero @ SV339 ) )
= ( zero_zero @ SV339 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2866]) ).
thf(3267,plain,
! [SV706: $i] :
( ( ~ ~ ! [SY1936: $i] :
( ( plus_plus @ int @ ( power_power @ int @ SV706 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ SY1936 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2867]) ).
thf(3268,plain,
! [SV340: $i] :
( ( ( comm_semiring_1 @ SV340 )
= $false )
| ( ( ! [SY1600: $i,SY1601: $i,SY1602: $i,SY1603: $i] :
( ( times_times @ SV340 @ ( times_times @ SV340 @ SY1600 @ SY1601 ) @ ( times_times @ SV340 @ SY1602 @ SY1603 ) )
= ( times_times @ SV340 @ ( times_times @ SV340 @ SY1600 @ SY1602 ) @ ( times_times @ SV340 @ SY1601 @ SY1603 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2868]) ).
thf(3269,plain,
! [SV584: $i,SV341: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SV341 ) @ ( bit0 @ SV584 ) )
| ( ord_less @ int @ SV341 @ SV584 ) )
| ~ ( ~ ( ord_less @ int @ SV341 @ SV584 )
| ( ord_less @ int @ ( bit0 @ SV341 ) @ ( bit0 @ SV584 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2869]) ).
thf(3270,plain,
! [SV342: $i] :
( ( ( mult_zero @ SV342 )
= $false )
| ( ( ! [SY1605: $i] :
( ( times_times @ SV342 @ ( zero_zero @ SV342 ) @ SY1605 )
= ( zero_zero @ SV342 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2870]) ).
thf(3271,plain,
! [SV585: $i,SV343: $i] :
( ( ~ ( ~ ( quadRes @ SV343 @ ( ti @ int @ SV585 ) )
| ( quadRes @ SV343 @ SV585 ) )
| ~ ( ~ ( quadRes @ SV343 @ SV585 )
| ( quadRes @ SV343 @ ( ti @ int @ SV585 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2871]) ).
thf(3272,plain,
! [SV344: $i] :
( ( ( comm_semiring_1 @ SV344 )
= $false )
| ( ( ! [SY1607: $i] :
( ( plus_plus @ SV344 @ SY1607 @ SY1607 )
= ( times_times @ SV344 @ ( plus_plus @ SV344 @ ( one_one @ SV344 ) @ ( one_one @ SV344 ) ) @ SY1607 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2872]) ).
thf(3273,plain,
! [SV586: $i,SV345: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ SV345 @ ( minus_minus @ int @ SV586 @ ( one_one @ int ) ) )
| ( ord_less @ int @ SV345 @ SV586 ) )
| ~ ( ~ ( ord_less @ int @ SV345 @ SV586 )
| ( ord_less_eq @ int @ SV345 @ ( minus_minus @ int @ SV586 @ ( one_one @ int ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2873]) ).
thf(3274,plain,
! [SV346: $i] :
( ( ( number_semiring @ SV346 )
= $false )
| ( ( ( number_number_of @ SV346 @ pls )
= ( zero_zero @ SV346 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2874]) ).
thf(3275,plain,
! [SV347: $i] :
( ( ( ring_11004092258visors @ SV347 )
= $false )
| ( ( ! [SY1609: $i] :
~ ( ~ ( ( ( power_power @ SV347 @ SY1609 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= ( zero_zero @ SV347 ) )
| ( ( ti @ SV347 @ SY1609 )
= ( zero_zero @ SV347 ) ) )
| ~ ( ( ( ti @ SV347 @ SY1609 )
!= ( zero_zero @ SV347 ) )
| ( ( power_power @ SV347 @ SY1609 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SV347 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2875]) ).
thf(3276,plain,
! [SV348: $i] :
( ( ( linordered_semidom @ SV348 )
= $false )
| ( ( ! [SY1610: $i,SY1611: $i] :
( ~ ( ord_less @ SV348 @ ( zero_zero @ SV348 ) @ SY1611 )
| ( ord_less @ SV348 @ ( zero_zero @ SV348 ) @ ( power_power @ SV348 @ SY1611 @ SY1610 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2876]) ).
thf(3277,plain,
! [SV349: $i] :
( ( ( comm_semiring_1 @ SV349 )
= $false )
| ( ( ! [SY1612: $i,SY1613: $i,SY1614: $i] :
( ~ ( dvd_dvd @ SV349 @ SY1613 @ SY1614 )
| ( dvd_dvd @ SV349 @ SY1613 @ ( times_times @ SV349 @ SY1614 @ SY1612 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2877]) ).
thf(3278,plain,
! [SV587: $i,SV350: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( plus_plus @ int @ SV350 @ ( one_one @ int ) ) @ SV587 )
| ( ord_less @ int @ SV350 @ SV587 ) )
| ~ ( ~ ( ord_less @ int @ SV350 @ SV587 )
| ( ord_less_eq @ int @ ( plus_plus @ int @ SV350 @ ( one_one @ int ) ) @ SV587 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2878]) ).
thf(3279,plain,
! [SV351: $i] :
( ( ( no_zero_divisors @ SV351 )
= $false )
| ( ( ! [SY1616: $i,SY1617: $i] :
( ( ( times_times @ SV351 @ SY1616 @ SY1617 )
!= ( zero_zero @ SV351 ) )
| ( ( ti @ SV351 @ SY1616 )
= ( zero_zero @ SV351 ) )
| ( ( ti @ SV351 @ SY1617 )
= ( zero_zero @ SV351 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2879]) ).
thf(3280,plain,
! [SV352: $i] :
( ( ( linordered_idom @ SV352 )
= $false )
| ( ( ! [SY1618: $i,SY1619: $i] :
~ ( ~ ( ( ( plus_plus @ SV352 @ ( power_power @ SV352 @ SY1618 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV352 @ SY1619 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV352 ) )
| ~ ( ( ( ti @ SV352 @ SY1618 )
!= ( zero_zero @ SV352 ) )
| ( ( ti @ SV352 @ SY1619 )
!= ( zero_zero @ SV352 ) ) ) )
| ~ ( ~ ~ ( ( ( ti @ SV352 @ SY1618 )
!= ( zero_zero @ SV352 ) )
| ( ( ti @ SV352 @ SY1619 )
!= ( zero_zero @ SV352 ) ) )
| ( ( plus_plus @ SV352 @ ( power_power @ SV352 @ SY1618 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV352 @ SY1619 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV352 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2880]) ).
thf(3281,plain,
! [SV353: $i] :
( ( ( linordered_semidom @ SV353 )
= $false )
| ( ( ! [SY1620: $i,SY1621: $i,SY1622: $i] :
( ~ ( ord_less_eq @ SV353 @ SY1621 @ SY1622 )
| ~ ( ord_less_eq @ SV353 @ ( zero_zero @ SV353 ) @ SY1621 )
| ( ord_less_eq @ SV353 @ ( power_power @ SV353 @ SY1621 @ SY1620 ) @ ( power_power @ SV353 @ SY1622 @ SY1620 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2881]) ).
thf(3282,plain,
! [SV354: $i] :
( ( ( comm_semiring_1 @ SV354 )
= $false )
| ( ( ! [SY1623: $i,SY1624: $i,SY1625: $i] :
( ( times_times @ SV354 @ SY1623 @ ( times_times @ SV354 @ SY1624 @ SY1625 ) )
= ( times_times @ SV354 @ SY1624 @ ( times_times @ SV354 @ SY1623 @ SY1625 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2882]) ).
thf(3283,plain,
! [SV355: $i] :
( ( ( ~ ( ~ ( power @ SV355 )
| ~ ( semiring_0 @ SV355 ) ) )
= $false )
| ( ( ! [SY1626: $i] :
~ ( ~ ( ( SY1626
!= ( zero_zero @ nat ) )
| ( ( power_power @ SV355 @ ( zero_zero @ SV355 ) @ SY1626 )
= ( one_one @ SV355 ) ) )
| ~ ( ~ ( ( SY1626
!= ( zero_zero @ nat ) ) )
| ( ( power_power @ SV355 @ ( zero_zero @ SV355 ) @ SY1626 )
= ( zero_zero @ SV355 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2883]) ).
thf(3284,plain,
! [SV588: $i,SV356: $i,SV707: $i] :
( ( ~ ( power @ SV707 )
| ( ( power_power @ SV707 @ ( ti @ SV707 @ SV356 ) @ SV588 )
= ( power_power @ SV707 @ SV356 @ SV588 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2884]) ).
thf(3285,plain,
! [SV589: $i,SV357: $i,SV708: $i] :
( ( ~ ( no_zero_divisors @ SV708 )
| ( ( times_times @ SV708 @ SV357 @ ( ti @ SV708 @ SV589 ) )
= ( times_times @ SV708 @ SV357 @ SV589 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2885]) ).
thf(3286,plain,
! [SV358: $i] :
( ( ( linordered_semidom @ SV358 )
= $false )
| ( ( ! [SY1631: $i,SY1632: $i,SY1633: $i] :
( ~ ( ord_less @ SV358 @ ( one_one @ SV358 ) @ SY1633 )
| ~ ( ~ ( ~ ( ord_less_eq @ SV358 @ ( power_power @ SV358 @ SY1633 @ SY1631 ) @ ( power_power @ SV358 @ SY1633 @ SY1632 ) )
| ( ord_less_eq @ nat @ SY1631 @ SY1632 ) )
| ~ ( ~ ( ord_less_eq @ nat @ SY1631 @ SY1632 )
| ( ord_less_eq @ SV358 @ ( power_power @ SV358 @ SY1633 @ SY1631 ) @ ( power_power @ SV358 @ SY1633 @ SY1632 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2886]) ).
thf(3287,plain,
! [SV590: $i,SV359: $i,SV709: $i] :
( ( ~ ( power @ SV709 )
| ( ( ti @ SV709 @ ( power_power @ SV709 @ SV359 @ SV590 ) )
= ( power_power @ SV709 @ SV359 @ SV590 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2887]) ).
thf(3288,plain,
! [SV591: $i,SV360: $i] :
( ( ~ ( ~ ( zcong @ SV360 @ ( zero_zero @ int ) @ SV591 )
| ( dvd_dvd @ int @ SV591 @ SV360 ) )
| ~ ( ~ ( dvd_dvd @ int @ SV591 @ SV360 )
| ( zcong @ SV360 @ ( zero_zero @ int ) @ SV591 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2888]) ).
thf(3289,plain,
! [SV361: $i] :
( ( ( number_semiring @ SV361 )
= $false )
| ( ( ! [SY1637: $i,SY1638: $i] :
( ~ ( ord_less_eq @ int @ pls @ SY1638 )
| ~ ( ord_less_eq @ int @ pls @ SY1637 )
| ( ( times_times @ SV361 @ ( number_number_of @ SV361 @ SY1638 ) @ ( number_number_of @ SV361 @ SY1637 ) )
= ( number_number_of @ SV361 @ ( times_times @ int @ SY1638 @ SY1637 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2889]) ).
thf(3290,plain,
! [SV592: $i,SV362: $i,SV710: $i] :
( ( ~ ( ( SV710
!= ( zero_zero @ real ) ) )
| ~ ( ~ ( ( ( times_times @ real @ SV362 @ SV710 )
!= ( times_times @ real @ SV592 @ SV710 ) )
| ( SV362 = SV592 ) )
| ~ ( ( SV362 != SV592 )
| ( ( times_times @ real @ SV362 @ SV710 )
= ( times_times @ real @ SV592 @ SV710 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2890]) ).
thf(3291,plain,
( ( ( quadRes @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) @ ( number_number_of @ int @ min ) )
= $true )
| ( ( ( legendre @ ( number_number_of @ int @ min ) @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) )
!= ( one_one @ int ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2891]) ).
thf(3292,plain,
! [SV363: $i] :
( ( ( power @ SV363 )
= $false )
| ( ( ! [SY1641: $i,SY1642: $i] :
~ ( ~ ( ( SY1642
!= ( zero_zero @ nat ) )
| ( ( power_power @ SV363 @ SY1641 @ SY1642 )
= ( one_one @ SV363 ) ) )
| ~ ( ~ ( ( SY1642
!= ( zero_zero @ nat ) ) )
| ( ( power_power @ SV363 @ SY1641 @ SY1642 )
= ( times_times @ SV363 @ SY1641 @ ( power_power @ SV363 @ SY1641 @ ( minus_minus @ nat @ SY1642 @ ( one_one @ nat ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2892]) ).
thf(3293,plain,
! [SV364: $i,SV711: $i,SV593: $i] :
( ( ~ ( dvd_dvd @ nat @ SV593 @ SV711 )
| ( dvd_dvd @ nat @ ( power_power @ nat @ SV593 @ SV364 ) @ ( power_power @ nat @ SV711 @ SV364 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2893]) ).
thf(3294,plain,
! [SV365: $i,SV712: $i,SV594: $i] :
( ( ~ ( ord_less @ int @ SV594 @ SV712 )
| ( ord_less @ int @ ( plus_plus @ int @ SV594 @ SV365 ) @ ( plus_plus @ int @ SV712 @ SV365 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2894]) ).
thf(3295,plain,
! [SV366: $i,SV595: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV595 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV595 ) @ ( number_number_of @ nat @ SV366 ) )
= ( number_number_of @ nat @ SV366 ) ) )
| ~ ( ~ ~ ( ord_less @ int @ SV595 @ pls )
| ~ ( ~ ( ~ ( ord_less @ int @ SV366 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV595 ) @ ( number_number_of @ nat @ SV366 ) )
= ( number_number_of @ nat @ SV595 ) ) )
| ~ ( ~ ~ ( ord_less @ int @ SV366 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV595 ) @ ( number_number_of @ nat @ SV366 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SV595 @ SV366 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2895]) ).
thf(3296,plain,
! [SV367: $i] :
( ( ( comm_semiring_1 @ SV367 )
= $false )
| ( ( ! [SY1648: $i,SY1649: $i,SY1650: $i] :
( ~ ( ord_less_eq @ nat @ SY1649 @ SY1650 )
| ( dvd_dvd @ SV367 @ ( power_power @ SV367 @ SY1648 @ SY1649 ) @ ( power_power @ SV367 @ SY1648 @ SY1650 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2896]) ).
thf(3297,plain,
! [SV368: $i,SV596: $i] :
( ( ~ ( ( SV596
!= ( zero_zero @ nat ) )
| ( ( times_times @ nat @ SV596 @ SV368 )
= ( zero_zero @ nat ) ) )
| ~ ( ~ ( ( SV596
!= ( zero_zero @ nat ) ) )
| ( ( times_times @ nat @ SV596 @ SV368 )
= ( plus_plus @ nat @ SV368 @ ( times_times @ nat @ ( minus_minus @ nat @ SV596 @ ( one_one @ nat ) ) @ SV368 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2897]) ).
thf(3298,plain,
! [SV713: $i,SV597: $i,SV369: $i] :
( ( ~ ( dvd_dvd @ int @ SV369 @ ( minus_minus @ int @ SV597 @ SV713 ) )
| ~ ( dvd_dvd @ int @ SV369 @ SV713 )
| ( dvd_dvd @ int @ SV369 @ SV597 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2898]) ).
thf(3299,plain,
! [SV598: $i,SV370: $i] :
( ( ~ ( ( ( bit1 @ SV370 )
!= ( bit1 @ SV598 ) )
| ( ( ti @ int @ SV370 )
= ( ti @ int @ SV598 ) ) )
| ~ ( ( ( ti @ int @ SV370 )
!= ( ti @ int @ SV598 ) )
| ( ( bit1 @ SV370 )
= ( bit1 @ SV598 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2899]) ).
thf(3300,plain,
! [SV371: $i] :
( ( ( comm_semiring_1 @ SV371 )
= $false )
| ( ( ! [SY1655: $i,SY1656: $i,SY1657: $i] :
( ( power_power @ SV371 @ ( times_times @ SV371 @ SY1655 @ SY1656 ) @ SY1657 )
= ( times_times @ SV371 @ ( power_power @ SV371 @ SY1655 @ SY1657 ) @ ( power_power @ SV371 @ SY1656 @ SY1657 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2900]) ).
thf(3301,plain,
! [SV372: $i,SV714: $i,SV599: $i] :
( ( ! [SY1937: $i] :
( ~ ( zcong @ SV599 @ SV714 @ SY1937 )
| ( zcong @ ( times_times @ int @ SV599 @ SV372 ) @ ( times_times @ int @ SV714 @ SV372 ) @ SY1937 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2901]) ).
thf(3302,plain,
! [SV600: $i,SV373: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( bit0 @ SV373 ) @ ( bit0 @ SV600 ) )
| ( ord_less_eq @ int @ SV373 @ SV600 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV373 @ SV600 )
| ( ord_less_eq @ int @ ( bit0 @ SV373 ) @ ( bit0 @ SV600 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2902]) ).
thf(3303,plain,
! [SV601: $i,SV374: $i] :
( ( ~ ( ( ( times_times @ nat @ SV374 @ SV601 )
!= ( one_one @ nat ) )
| ~ ( ( SV374
!= ( one_one @ nat ) )
| ( SV601
!= ( one_one @ nat ) ) ) )
| ~ ( ~ ~ ( ( SV374
!= ( one_one @ nat ) )
| ( SV601
!= ( one_one @ nat ) ) )
| ( ( times_times @ nat @ SV374 @ SV601 )
= ( one_one @ nat ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2903]) ).
thf(3304,plain,
! [SV375: $i] :
( ( ( linordered_semidom @ SV375 )
= $false )
| ( ( ! [SY1663: $i,SY1664: $i] :
( ~ ( ord_less @ SV375 @ ( one_one @ SV375 ) @ SY1664 )
| ( ord_less @ SV375 @ ( power_power @ SV375 @ SY1664 @ SY1663 ) @ ( times_times @ SV375 @ SY1664 @ ( power_power @ SV375 @ SY1664 @ SY1663 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2904]) ).
thf(3305,plain,
! [SV376: $i] :
( ( ( ring_11004092258visors @ SV376 )
= $false )
| ( ( ! [SY1665: $i,SY1666: $i] :
( ~ ( ( ( ti @ SV376 @ SY1666 )
!= ( zero_zero @ SV376 ) ) )
| ( ( power_power @ SV376 @ SY1666 @ SY1665 )
!= ( zero_zero @ SV376 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2905]) ).
thf(3306,plain,
! [SV602: $i,SV377: $i,SV715: $i] :
( ( ~ ( mult_zero @ SV715 )
| ( ( times_times @ SV715 @ SV377 @ ( ti @ SV715 @ SV602 ) )
= ( times_times @ SV715 @ SV377 @ SV602 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2906]) ).
thf(3307,plain,
! [SV378: $i] :
( ( ( number_ring @ SV378 )
= $false )
| ( ( ! [SY1669: $i] :
( ( number_number_of @ SV378 @ ( bit1 @ SY1669 ) )
= ( plus_plus @ SV378 @ ( plus_plus @ SV378 @ ( one_one @ SV378 ) @ ( number_number_of @ SV378 @ SY1669 ) ) @ ( number_number_of @ SV378 @ SY1669 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2907]) ).
thf(3308,plain,
! [SV379: $i,SV603: $i] :
( ( ( ~ ( ord_less @ real @ ( zero_zero @ real ) @ SV603 ) )
= $true )
| ( ( ~ ( ord_less @ real @ ( zero_zero @ real ) @ SV379 )
| ( ord_less @ real @ ( zero_zero @ real ) @ ( times_times @ real @ SV603 @ SV379 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2908]) ).
thf(3309,plain,
! [SV380: $i] :
( ( ( comm_semiring_1 @ SV380 )
= $false )
| ( ( ! [SY1671: $i,SY1672: $i,SY1673: $i,SY1674: $i] :
( ( times_times @ SV380 @ ( times_times @ SV380 @ SY1671 @ SY1672 ) @ ( times_times @ SV380 @ SY1673 @ SY1674 ) )
= ( times_times @ SV380 @ SY1673 @ ( times_times @ SV380 @ ( times_times @ SV380 @ SY1671 @ SY1672 ) @ SY1674 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2909]) ).
thf(3310,plain,
! [SV381: $i] :
( ( ( number_ring @ SV381 )
= $false )
| ( ( ! [SY1675: $i] :
( ( times_times @ SV381 @ SY1675 @ ( number_number_of @ SV381 @ ( bit1 @ pls ) ) )
= ( ti @ SV381 @ SY1675 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2910]) ).
thf(3311,plain,
! [SV604: $i,SV382: $i,SV716: $i] :
( ( ~ ( zprime @ SV716 )
| ~ ( dvd_dvd @ int @ SV716 @ ( times_times @ int @ SV382 @ SV604 ) )
| ( dvd_dvd @ int @ SV716 @ SV382 )
| ( dvd_dvd @ int @ SV716 @ SV604 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2911]) ).
thf(3312,plain,
! [SV383: $i] :
( ( ( linordered_semidom @ SV383 )
= $false )
| ( ( ! [SY1678: $i,SY1679: $i,SY1680: $i] :
( ~ ( ord_less @ nat @ SY1679 @ SY1680 )
| ~ ( ord_less @ SV383 @ ( one_one @ SV383 ) @ SY1678 )
| ( ord_less @ SV383 @ ( power_power @ SV383 @ SY1678 @ SY1679 ) @ ( power_power @ SV383 @ SY1678 @ SY1680 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2912]) ).
thf(3313,plain,
! [SV384: $i,SV717: $i,SV605: $i] :
( ( ~ ( ord_less @ int @ SV605 @ SV717 )
| ~ ( ord_less @ int @ SV384 @ SV717 )
| ( ord_less_eq @ int @ SV605 @ SV384 )
| ( ord_less_eq @ int @ SV384 @ SV605 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2913]) ).
thf(3314,plain,
! [SV606: $i,SV385: $i,SV718: $i] :
( ( ! [SY1938: $i] :
( ~ ( ord_less @ int @ SV718 @ SY1938 )
| ~ ( ord_less_eq @ int @ SV385 @ SV606 )
| ( ord_less @ int @ ( plus_plus @ int @ SV718 @ SV385 ) @ ( plus_plus @ int @ SY1938 @ SV606 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2914]) ).
thf(3315,plain,
! [SV386: $i] :
( ( ( ~ ( ~ ( number @ SV386 )
| ~ ( ring @ SV386 ) ) )
= $false )
| ( ( ! [SY1686: $i,SY1687: $i,SY1688: $i] :
( ( times_times @ SV386 @ ( minus_minus @ SV386 @ SY1686 @ SY1687 ) @ ( number_number_of @ SV386 @ SY1688 ) )
= ( minus_minus @ SV386 @ ( times_times @ SV386 @ SY1686 @ ( number_number_of @ SV386 @ SY1688 ) ) @ ( times_times @ SV386 @ SY1687 @ ( number_number_of @ SV386 @ SY1688 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2915]) ).
thf(3316,plain,
! [SV387: $i,SV607: $i] :
( ( ( ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV607 ) )
= $true )
| ( ( ~ ( ord_less @ int @ ( zero_zero @ int ) @ ( times_times @ int @ SV607 @ SV387 ) )
| ( ord_less @ int @ ( zero_zero @ int ) @ SV387 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2916]) ).
thf(3317,plain,
! [SV388: $i,SV608: $i] :
( ( ( ~ ( ord_less @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV608 ) )
= $true )
| ( ( ~ ( zcong @ SV388 @ ( number_number_of @ int @ min ) @ SV608 )
| ~ ( zcong @ SV388 @ ( one_one @ int ) @ SV608 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2917]) ).
thf(3318,plain,
! [SV389: $i,SV609: $i] :
( ( ( ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV609 ) )
= $true )
| ( ( ~ ( ord_less @ int @ SV609 @ SV389 )
| ~ ( zcong @ SV609 @ ( zero_zero @ int ) @ SV389 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2918]) ).
thf(3319,plain,
! [SV390: $i,SV610: $i] :
( ( ~ ( ( SV610
!= ( zero_zero @ nat ) )
| ( ( power_power @ nat @ SV390 @ SV610 )
= ( one_one @ nat ) ) )
| ~ ( ~ ( ( SV610
!= ( zero_zero @ nat ) ) )
| ( ( power_power @ nat @ SV390 @ SV610 )
= ( times_times @ nat @ SV390 @ ( power_power @ nat @ SV390 @ ( minus_minus @ nat @ SV610 @ ( one_one @ nat ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2919]) ).
thf(3320,plain,
! [SV611: $i,SV391: $i,SV719: $i] :
( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ SV719 )
| ~ ( dvd_dvd @ int @ SV391 @ SV611 )
| ( dvd_dvd @ int @ SV391 @ ( power_power @ int @ SV611 @ SV719 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2920]) ).
thf(3321,plain,
! [SV612: $i,SV392: $i] :
( ( ~ ( ~ ( ord_less @ nat @ ( number_number_of @ nat @ SV392 ) @ ( number_number_of @ nat @ SV612 ) )
| ~ ( ~ ( ~ ( ord_less @ int @ SV392 @ SV612 )
| ( ord_less @ int @ pls @ SV612 ) )
| ~ ( ord_less @ int @ SV392 @ SV612 ) ) )
| ~ ( ~ ~ ( ~ ( ~ ( ord_less @ int @ SV392 @ SV612 )
| ( ord_less @ int @ pls @ SV612 ) )
| ~ ( ord_less @ int @ SV392 @ SV612 ) )
| ( ord_less @ nat @ ( number_number_of @ nat @ SV392 ) @ ( number_number_of @ nat @ SV612 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2921]) ).
thf(3322,plain,
! [SV393: $i] :
( ( ( number_ring @ SV393 )
= $false )
| ( ( ! [SY1696: $i,SY1697: $i] :
( ( power_power @ SV393 @ ( minus_minus @ SV393 @ SY1696 @ SY1697 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( minus_minus @ SV393 @ ( plus_plus @ SV393 @ ( power_power @ SV393 @ SY1696 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV393 @ SY1697 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times @ SV393 @ ( times_times @ SV393 @ ( number_number_of @ SV393 @ ( bit0 @ ( bit1 @ pls ) ) ) @ SY1696 ) @ SY1697 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2922]) ).
thf(3323,plain,
! [SV394: $i] :
( ( ~ ( ~ ( zprime @ ( ti @ int @ SV394 ) )
| ( zprime @ SV394 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2923]) ).
thf(3324,plain,
! [SV394: $i] :
( ( ~ ( ~ ( zprime @ SV394 )
| ( zprime @ ( ti @ int @ SV394 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2923]) ).
thf(3325,plain,
! [SV395: $i,SV720: $i,SV613: $i] :
( ( ! [SY1939: $i] :
( ~ ( zcong @ ( power_power @ int @ SV613 @ SV720 ) @ ( one_one @ int ) @ SY1939 )
| ( zcong @ ( power_power @ int @ SV613 @ ( times_times @ nat @ SV720 @ SV395 ) ) @ ( one_one @ int ) @ SY1939 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2924]) ).
thf(3326,plain,
! [SV614: $i,SV396: $i] :
( ( ~ ( ~ ( zcong @ SV396 @ SV614 @ ( zero_zero @ int ) )
| ( ( ti @ int @ SV396 )
= ( ti @ int @ SV614 ) ) )
| ~ ( ( ( ti @ int @ SV396 )
!= ( ti @ int @ SV614 ) )
| ( zcong @ SV396 @ SV614 @ ( zero_zero @ int ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2925]) ).
thf(3327,plain,
! [SV615: $i,SV397: $i] :
( ( ~ ( ( ( plus_plus @ real @ ( times_times @ real @ SV397 @ SV397 ) @ ( times_times @ real @ SV615 @ SV615 ) )
!= ( zero_zero @ real ) )
| ~ ( ( SV397
!= ( zero_zero @ real ) )
| ( SV615
!= ( zero_zero @ real ) ) ) )
| ~ ( ~ ~ ( ( SV397
!= ( zero_zero @ real ) )
| ( SV615
!= ( zero_zero @ real ) ) )
| ( ( plus_plus @ real @ ( times_times @ real @ SV397 @ SV397 ) @ ( times_times @ real @ SV615 @ SV615 ) )
= ( zero_zero @ real ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2926]) ).
thf(3328,plain,
! [SV398: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SV398 ) @ pls )
| ( ord_less @ int @ SV398 @ pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2927]) ).
thf(3329,plain,
! [SV398: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV398 @ pls )
| ( ord_less @ int @ ( bit1 @ SV398 ) @ pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2927]) ).
thf(3330,plain,
! [SV399: $i] :
( ( ( semiring @ SV399 )
= $false )
| ( ( ! [SY1703: $i,SY1704: $i,SY1705: $i,SY1706: $i] :
( ( plus_plus @ SV399 @ ( times_times @ SV399 @ SY1703 @ SY1704 ) @ ( plus_plus @ SV399 @ ( times_times @ SV399 @ SY1705 @ SY1704 ) @ SY1706 ) )
= ( plus_plus @ SV399 @ ( times_times @ SV399 @ ( plus_plus @ SV399 @ SY1703 @ SY1705 ) @ SY1704 ) @ SY1706 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2928]) ).
thf(3331,plain,
! [SV400: $i] :
( ( ( monoid_mult @ SV400 )
= $false )
| ( ( ! [SY1707: $i] :
( ( power_power @ SV400 @ SY1707 @ ( one_one @ nat ) )
= ( ti @ SV400 @ SY1707 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2929]) ).
thf(3332,plain,
( ( ( ! [SX0: $i] :
~ ~ ! [SX1: $i] :
( ( plus_plus @ int @ ( power_power @ int @ SX0 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ SX1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ) )
= $false )
| ( ( t
= ( one_one @ int ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2930]) ).
thf(3333,plain,
! [SV616: $i,SV401: $i,SV721: $i] :
( ( ~ ( semiring @ SV721 )
| ( ( times_times @ SV721 @ ( ti @ SV721 @ SV401 ) @ SV616 )
= ( times_times @ SV721 @ SV401 @ SV616 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2931]) ).
thf(3334,plain,
! [SV402: $i] :
( ( ( comm_semiring_1 @ SV402 )
= $false )
| ( ( ! [SY1710: $i] :
( ( times_times @ SV402 @ ( one_one @ SV402 ) @ SY1710 )
= ( ti @ SV402 @ SY1710 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2932]) ).
thf(3335,plain,
! [SV403: $i] :
( ( ( comm_semiring_1 @ SV403 )
= $false )
| ( ( ! [SY1711: $i,SY1712: $i,SY1713: $i] :
( ( times_times @ SV403 @ SY1711 @ ( plus_plus @ SV403 @ SY1712 @ SY1713 ) )
= ( plus_plus @ SV403 @ ( times_times @ SV403 @ SY1711 @ SY1712 ) @ ( times_times @ SV403 @ SY1711 @ SY1713 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2933]) ).
thf(3336,plain,
! [SV404: $i] :
( ( ( number_ring @ SV404 )
= $false )
| ( ( ! [SY1714: $i] :
( ( times_times @ SV404 @ ( number_number_of @ SV404 @ ( bit0 @ ( bit1 @ pls ) ) ) @ SY1714 )
= ( plus_plus @ SV404 @ SY1714 @ SY1714 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2934]) ).
thf(3337,plain,
! [SV722: $i,SV617: $i,SV405: $i] :
( ( ~ ( ~ ( ~ ( zcong @ SV405 @ SV617 @ SV722 )
| ~ ! [SY1940: $i] :
( ( ti @ int @ SV617 )
!= ( plus_plus @ int @ SV405 @ ( times_times @ int @ SV722 @ SY1940 ) ) ) )
| ~ ( ~ ~ ! [SY1941: $i] :
( ( ti @ int @ SV617 )
!= ( plus_plus @ int @ SV405 @ ( times_times @ int @ SV722 @ SY1941 ) ) )
| ( zcong @ SV405 @ SV617 @ SV722 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2935]) ).
thf(3338,plain,
! [SV723: $i,SV618: $i,SV406: $i] :
( ( ( ( minus_minus @ int @ SV406 @ SV618 )
!= ( ti @ int @ SV723 ) )
| ( ( ti @ int @ SV406 )
= ( plus_plus @ int @ SV723 @ SV618 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2936]) ).
thf(3339,plain,
! [SV407: $i] :
( ( ( zprime @ SV407 )
= $false )
| ( ( ~ ( ( ( ti @ int @ SV407 )
!= ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ~ ( ( ( ti @ int @ SV407 )
!= ( number_number_of @ int @ ( bit1 @ ( bit1 @ pls ) ) ) ) )
| ( ord_less_eq @ int @ ( number_number_of @ int @ ( bit1 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SV407 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2937]) ).
thf(3340,plain,
! [SV619: $i,SV408: $i,SV724: $i] :
( ( ~ ( semiring @ SV724 )
| ( ( ti @ SV724 @ ( plus_plus @ SV724 @ SV408 @ SV619 ) )
= ( plus_plus @ SV724 @ SV408 @ SV619 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2938]) ).
thf(3341,plain,
! [SV409: $i] :
( ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV409 )
= $false )
| ( ( ord_less @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( one_one @ int ) @ SV409 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2939]) ).
thf(3342,plain,
! [SV725: $i,SV620: $i,SV410: $i] :
( ( ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( times_times @ int @ SV410 @ SV620 ) @ SV725 ) )
| ~ ( ord_less @ int @ SV725 @ SV410 )
| ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV410 )
| ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV620 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2940]) ).
thf(3343,plain,
! [SV411: $i] :
( ( ( linordered_idom @ SV411 )
= $false )
| ( ( ! [SY1725: $i] :
~ ( ord_less @ SV411 @ ( power_power @ SV411 @ SY1725 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( zero_zero @ SV411 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2941]) ).
thf(3344,plain,
! [SV412: $i] :
( ( ( monoid_mult @ SV412 )
= $false )
| ( ( ! [SY1726: $i,SY1727: $i,SY1728: $i] :
( ( power_power @ SV412 @ SY1726 @ ( times_times @ nat @ SY1727 @ SY1728 ) )
= ( power_power @ SV412 @ ( power_power @ SV412 @ SY1726 @ SY1727 ) @ SY1728 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2942]) ).
thf(3345,plain,
! [SV621: $i,SV413: $i] :
( ( ~ ( ( ( times_times @ int @ SV413 @ SV621 )
!= ( one_one @ int ) )
| ~ ( ( ( ti @ int @ SV413 )
!= ( one_one @ int ) )
| ( ( ti @ int @ SV621 )
!= ( one_one @ int ) ) )
| ~ ( ( ( ti @ int @ SV413 )
!= ( number_number_of @ int @ min ) )
| ( ( ti @ int @ SV621 )
!= ( number_number_of @ int @ min ) ) ) )
| ~ ( ~ ( ~ ( ( ( ti @ int @ SV413 )
!= ( one_one @ int ) )
| ( ( ti @ int @ SV621 )
!= ( one_one @ int ) ) )
| ~ ( ( ( ti @ int @ SV413 )
!= ( number_number_of @ int @ min ) )
| ( ( ti @ int @ SV621 )
!= ( number_number_of @ int @ min ) ) ) )
| ( ( times_times @ int @ SV413 @ SV621 )
= ( one_one @ int ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2943]) ).
thf(3346,plain,
! [SV414: $i] :
( ( ( comm_semiring_1 @ SV414 )
= $false )
| ( ( ! [SY1730: $i,SY1731: $i] :
( ( plus_plus @ SV414 @ SY1730 @ SY1731 )
= ( plus_plus @ SV414 @ SY1731 @ SY1730 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2944]) ).
thf(3347,plain,
! [SV415: $i] :
( ( ( number_ring @ SV415 )
= $false )
| ( ( ( zero_zero @ SV415 )
= ( number_number_of @ SV415 @ pls ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2945]) ).
thf(3348,plain,
! [SV416: $i] :
( ( ( ~ ( ~ ( monoid_mult @ SV416 )
| ~ ( number @ SV416 ) ) )
= $false )
| ( ( ! [SY1732: $i] :
( ( power_power @ SV416 @ ( number_number_of @ SV416 @ SY1732 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times @ SV416 @ ( number_number_of @ SV416 @ SY1732 ) @ ( number_number_of @ SV416 @ SY1732 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2946]) ).
thf(3349,plain,
! [SV417: $i] :
( ( ( ordere453448008miring @ SV417 )
= $false )
| ( ( ! [SY1733: $i,SY1734: $i] :
( ~ ( ord_less_eq @ SV417 @ SY1734 @ ( zero_zero @ SV417 ) )
| ~ ( ord_less_eq @ SV417 @ ( zero_zero @ SV417 ) @ SY1733 )
| ( ord_less_eq @ SV417 @ ( times_times @ SV417 @ SY1734 @ SY1733 ) @ ( zero_zero @ SV417 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2947]) ).
thf(3350,plain,
! [SV622: $i,SV418: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SV418 ) @ ( bit0 @ SV622 ) )
| ( ord_less @ int @ SV418 @ SV622 ) )
| ~ ( ~ ( ord_less @ int @ SV418 @ SV622 )
| ( ord_less_eq @ int @ ( bit1 @ SV418 ) @ ( bit0 @ SV622 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2948]) ).
thf(3351,plain,
! [SV419: $i,SV623: $i] :
( ( ( ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV623 ) )
= $true )
| ( ( ~ ( ~ ( ( ( times_times @ int @ SV623 @ SV419 )
!= ( one_one @ int ) )
| ~ ( ( ( ti @ int @ SV623 )
!= ( one_one @ int ) )
| ( ( ti @ int @ SV419 )
!= ( one_one @ int ) ) ) )
| ~ ( ~ ~ ( ( ( ti @ int @ SV623 )
!= ( one_one @ int ) )
| ( ( ti @ int @ SV419 )
!= ( one_one @ int ) ) )
| ( ( times_times @ int @ SV623 @ SV419 )
= ( one_one @ int ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2949]) ).
thf(3352,plain,
! [SV624: $i,SV420: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( bit0 @ SV420 ) @ ( bit1 @ SV624 ) )
| ( ord_less_eq @ int @ SV420 @ SV624 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV420 @ SV624 )
| ( ord_less_eq @ int @ ( bit0 @ SV420 ) @ ( bit1 @ SV624 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2950]) ).
thf(3353,plain,
! [SV421: $i,SV625: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV625 @ pls )
| ( ( times_times @ nat @ ( number_number_of @ nat @ SV625 ) @ ( number_number_of @ nat @ SV421 ) )
= ( zero_zero @ nat ) ) )
| ~ ( ~ ~ ( ord_less @ int @ SV625 @ pls )
| ( ( times_times @ nat @ ( number_number_of @ nat @ SV625 ) @ ( number_number_of @ nat @ SV421 ) )
= ( number_number_of @ nat @ ( times_times @ int @ SV625 @ SV421 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2951]) ).
thf(3354,plain,
! [SV726: $i,SV626: $i,SV422: $i] :
( ( ! [SY1942: $i,SY1943: $i,SY1944: $i] :
( ( ( plus_plus @ int @ ( times_times @ int @ SV422 @ SV626 ) @ SV726 )
!= ( plus_plus @ int @ ( times_times @ int @ SY1942 @ SY1943 ) @ SY1944 ) )
| ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( times_times @ int @ SY1942 @ SY1943 ) @ SY1944 ) )
| ~ ( ord_less @ int @ SY1944 @ SY1942 )
| ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV726 )
| ~ ( ord_less @ int @ ( zero_zero @ int ) @ SY1942 )
| ~ ( ord_less_eq @ int @ SY1942 @ SV422 )
| ( ord_less_eq @ int @ SV626 @ SY1943 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2952]) ).
thf(3355,plain,
! [SV423: $i] :
( ( ~ ( ~ ~ ( ord_less @ real @ ( zero_zero @ real ) @ ( times_times @ real @ SV423 @ SV423 ) )
| ( SV423
= ( zero_zero @ real ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2953]) ).
thf(3356,plain,
! [SV423: $i] :
( ( ~ ( ( SV423
!= ( zero_zero @ real ) )
| ~ ( ord_less @ real @ ( zero_zero @ real ) @ ( times_times @ real @ SV423 @ SV423 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2953]) ).
thf(3357,plain,
! [SV627: $i,SV424: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SV424 ) @ ( bit1 @ SV627 ) )
| ( ord_less @ int @ SV424 @ SV627 ) )
| ~ ( ~ ( ord_less @ int @ SV424 @ SV627 )
| ( ord_less @ int @ ( bit1 @ SV424 ) @ ( bit1 @ SV627 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2954]) ).
thf(3358,plain,
! [SV425: $i] :
( ( ( comm_semiring_1 @ SV425 )
= $false )
| ( ( ! [SY1745: $i] : ( dvd_dvd @ SV425 @ ( one_one @ SV425 ) @ SY1745 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2955]) ).
thf(3359,plain,
! [SV628: $i,SV426: $i,SV727: $i] :
( ( ~ ( mult_zero @ SV727 )
| ( ( ti @ SV727 @ ( times_times @ SV727 @ SV426 @ SV628 ) )
= ( times_times @ SV727 @ SV426 @ SV628 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2956]) ).
thf(3360,plain,
! [SV728: $i,SV629: $i,SV427: $i] :
( ( ~ ( ~ ( ~ ( zcong @ ( ti @ int @ SV427 ) @ SV629 @ SV728 )
| ( zcong @ SV427 @ SV629 @ SV728 ) )
| ~ ( ~ ( zcong @ SV427 @ SV629 @ SV728 )
| ( zcong @ ( ti @ int @ SV427 ) @ SV629 @ SV728 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2957]) ).
thf(3361,plain,
! [SV630: $i,SV428: $i] :
( ( ~ ( ~ ( zcong @ SV428 @ ( zero_zero @ int ) @ SV630 )
| ( dvd_dvd @ int @ SV630 @ SV428 ) )
| ~ ( ~ ( dvd_dvd @ int @ SV630 @ SV428 )
| ( zcong @ SV428 @ ( zero_zero @ int ) @ SV630 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2958]) ).
thf(3362,plain,
! [SV631: $i,SV429: $i] :
( ( ~ ( ( ( power_power @ nat @ SV429 @ SV631 )
!= ( one_one @ nat ) )
| ( SV429
= ( one_one @ nat ) )
| ( SV631
= ( zero_zero @ nat ) ) )
| ~ ( ~ ( ( SV429
= ( one_one @ nat ) )
| ( SV631
= ( zero_zero @ nat ) ) )
| ( ( power_power @ nat @ SV429 @ SV631 )
= ( one_one @ nat ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2959]) ).
thf(3363,plain,
! [SV430: $i,SV729: $i,SV632: $i] :
( ( ! [SY1945: $i] :
( ~ ( zcong @ SV632 @ SV729 @ SY1945 )
| ( zcong @ ( plus_plus @ int @ SV632 @ SV430 ) @ ( plus_plus @ int @ SV729 @ SV430 ) @ SY1945 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2960]) ).
thf(3364,plain,
! [SV431: $i] :
( ( ( linordered_idom @ SV431 )
= $false )
| ( ( ! [SY1755: $i,SY1756: $i] : ( ord_less_eq @ SV431 @ ( zero_zero @ SV431 ) @ ( plus_plus @ SV431 @ ( power_power @ SV431 @ SY1755 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV431 @ SY1756 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2961]) ).
thf(3365,plain,
! [SV432: $i] :
( ( ( number_ring @ SV432 )
= $false )
| ( ( ! [SY1757: $i] :
( ( plus_plus @ SV432 @ ( number_number_of @ SV432 @ SY1757 ) @ ( one_one @ SV432 ) )
= ( number_number_of @ SV432 @ ( plus_plus @ int @ SY1757 @ ( bit1 @ pls ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2962]) ).
thf(3366,plain,
! [SV433: $i] :
( ( ( linordered_semidom @ SV433 )
= $false )
| ( ( ! [SY1758: $i,SY1759: $i,SY1760: $i] :
( ~ ( ord_less @ nat @ SY1759 @ SY1760 )
| ~ ( ord_less @ SV433 @ ( zero_zero @ SV433 ) @ SY1758 )
| ~ ( ord_less @ SV433 @ SY1758 @ ( one_one @ SV433 ) )
| ( ord_less @ SV433 @ ( power_power @ SV433 @ SY1758 @ SY1760 ) @ ( power_power @ SV433 @ SY1758 @ SY1759 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2963]) ).
thf(3367,plain,
! [SV434: $i] :
( ( ( semiri456707255roduct @ SV434 )
= $false )
| ( ( ! [SY1761: $i,SY1762: $i,SY1763: $i,SY1764: $i,SY1765: $i] :
( ~ ( ( ( ti @ SV434 @ SY1765 )
!= ( zero_zero @ SV434 ) ) )
| ~ ~ ( ( ( ti @ SV434 @ SY1763 )
!= ( ti @ SV434 @ SY1764 ) )
| ~ ( ( ( ti @ SV434 @ SY1761 )
!= ( ti @ SV434 @ SY1762 ) ) ) )
| ( ( plus_plus @ SV434 @ SY1763 @ ( times_times @ SV434 @ SY1765 @ SY1761 ) )
!= ( plus_plus @ SV434 @ SY1764 @ ( times_times @ SV434 @ SY1765 @ SY1762 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2964]) ).
thf(3368,plain,
! [SV447: $i,SV21: $i] :
( ( ( ord_less @ int @ SV21 @ SV447 )
= $true )
| ( ( ( ti @ int @ SV21 )
= ( ti @ int @ SV447 ) )
= $true )
| ( ( ord_less @ int @ SV447 @ SV21 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2966]) ).
thf(3369,plain,
! [SV730: $i,SV643: $i,SV472: $i,SV63: $i] :
( ( ! [SY1946: $i,SY1947: $i,SY1948: $i] :
( ( plus_plus @ int @ ( times_times @ int @ ( minus_minus @ int @ SV63 @ ( times_times @ int @ SV472 @ SV643 ) ) @ SV730 ) @ ( times_times @ int @ ( minus_minus @ int @ SY1946 @ ( times_times @ int @ SV472 @ SY1947 ) ) @ SY1948 ) )
= ( minus_minus @ int @ ( plus_plus @ int @ ( times_times @ int @ SV63 @ SV730 ) @ ( times_times @ int @ SY1946 @ SY1948 ) ) @ ( times_times @ int @ SV472 @ ( plus_plus @ int @ ( times_times @ int @ SV643 @ SV730 ) @ ( times_times @ int @ SY1947 @ SY1948 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2978]) ).
thf(3370,plain,
! [SV731: $i,SV644: $i,SV473: $i,SV67: $i] :
( ( ( times_times @ int @ ( twoSqu579703163sum2sq @ ( product_Pair @ int @ int @ SV67 @ SV473 ) ) @ ( twoSqu579703163sum2sq @ ( product_Pair @ int @ int @ SV644 @ SV731 ) ) )
= ( twoSqu579703163sum2sq @ ( product_Pair @ int @ int @ ( plus_plus @ int @ ( times_times @ int @ SV67 @ SV644 ) @ ( times_times @ int @ SV473 @ SV731 ) ) @ ( minus_minus @ int @ ( times_times @ int @ SV67 @ SV731 ) @ ( times_times @ int @ SV473 @ SV644 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2979]) ).
thf(3371,plain,
! [SV481: $i,SV79: $i,SV732: $i,SV647: $i] :
( ( ! [SY1949: $i] :
( ~ ( zcong @ SV647 @ SV732 @ SY1949 )
| ~ ( ~ ( ~ ( zcong @ SV79 @ ( times_times @ int @ SV647 @ SV481 ) @ SY1949 )
| ( zcong @ SV79 @ ( times_times @ int @ SV732 @ SV481 ) @ SY1949 ) )
| ~ ( ~ ( zcong @ SV79 @ ( times_times @ int @ SV732 @ SV481 ) @ SY1949 )
| ( zcong @ SV79 @ ( times_times @ int @ SV647 @ SV481 ) @ SY1949 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2982]) ).
thf(3372,plain,
! [SV482: $i,SV80: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV80 @ ( plus_plus @ int @ SV482 @ ( one_one @ int ) ) )
| ( ord_less @ int @ SV80 @ SV482 )
| ( ( ti @ int @ SV80 )
= ( ti @ int @ SV482 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2983]) ).
thf(3373,plain,
! [SV482: $i,SV80: $i] :
( ( ~ ( ~ ( ( ord_less @ int @ SV80 @ SV482 )
| ( ( ti @ int @ SV80 )
= ( ti @ int @ SV482 ) ) )
| ( ord_less @ int @ SV80 @ ( plus_plus @ int @ SV482 @ ( one_one @ int ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2983]) ).
thf(3374,plain,
! [SV483: $i,SV81: $i,SV648: $i] :
( ( ( ~ ( semiring @ SV648 ) )
= $true )
| ( ( ( plus_plus @ SV648 @ SV81 @ ( ti @ SV648 @ SV483 ) )
= ( plus_plus @ SV648 @ SV81 @ SV483 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2984]) ).
thf(3375,plain,
! [SV733: $i,SV82: $i] :
( ( ( ! [SY1950: $i] :
( ~ ( ord_less_eq @ SV82 @ ( zero_zero @ SV82 ) @ SY1950 )
| ~ ( ord_less_eq @ SV82 @ SV733 @ ( zero_zero @ SV82 ) )
| ( ord_less_eq @ SV82 @ ( times_times @ SV82 @ SY1950 @ SV733 ) @ ( zero_zero @ SV82 ) ) ) )
= $true )
| ( ( ordere453448008miring @ SV82 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2985]) ).
thf(3376,plain,
! [SV734: $i,SV83: $i] :
( ( ( ! [SY1951: $i] :
( ( times_times @ SV83 @ ( power_power @ SV83 @ SV734 @ SY1951 ) @ SV734 )
= ( times_times @ SV83 @ SV734 @ ( power_power @ SV83 @ SV734 @ SY1951 ) ) ) )
= $true )
| ( ( monoid_mult @ SV83 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2986]) ).
thf(3377,plain,
! [SV735: $i,SV84: $i] :
( ( ( ! [SY1952: $i,SY1953: $i] :
( ( plus_plus @ SV84 @ ( plus_plus @ SV84 @ SV735 @ SY1952 ) @ SY1953 )
= ( plus_plus @ SV84 @ SV735 @ ( plus_plus @ SV84 @ SY1952 @ SY1953 ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV84 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2987]) ).
thf(3378,plain,
! [SV736: $i,SV86: $i] :
( ( ( ord_less_eq @ SV86 @ ( zero_zero @ SV86 ) @ ( times_times @ SV86 @ SV736 @ SV736 ) )
= $true )
| ( ( linordered_ring @ SV86 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2989]) ).
thf(3379,plain,
! [SV737: $i,SV87: $i] :
( ( ( ! [SY1954: $i] :
( ~ ( ord_less_eq @ SV87 @ ( zero_zero @ SV87 ) @ SY1954 )
| ~ ( ord_less_eq @ SV87 @ SV737 @ ( zero_zero @ SV87 ) )
| ( ord_less_eq @ SV87 @ ( times_times @ SV87 @ SV737 @ SY1954 ) @ ( zero_zero @ SV87 ) ) ) )
= $true )
| ( ( ordere453448008miring @ SV87 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2990]) ).
thf(3380,plain,
! [SV738: $i,SV88: $i] :
( ( ( ! [SY1955: $i] :
~ ( ord_less @ SV88 @ ( plus_plus @ SV88 @ ( power_power @ SV88 @ SV738 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV88 @ SY1955 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( zero_zero @ SV88 ) ) )
= $true )
| ( ( linordered_idom @ SV88 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2991]) ).
thf(3381,plain,
! [SV484: $i,SV89: $i,SV649: $i] :
( ( ( ~ ( no_zero_divisors @ SV649 ) )
= $true )
| ( ( ( times_times @ SV649 @ ( ti @ SV649 @ SV89 ) @ SV484 )
= ( times_times @ SV649 @ SV89 @ SV484 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2992]) ).
thf(3382,plain,
! [SV739: $i,SV90: $i] :
( ( ( ! [SY1956: $i] :
( ~ ( ( ( ti @ SV90 @ SY1956 )
!= ( zero_zero @ SV90 ) ) )
| ~ ( ( ( ti @ SV90 @ SV739 )
!= ( zero_zero @ SV90 ) ) )
| ( ( times_times @ SV90 @ SY1956 @ SV739 )
!= ( zero_zero @ SV90 ) ) ) )
= $true )
| ( ( no_zero_divisors @ SV90 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2993]) ).
thf(3383,plain,
! [SV91: $i] :
( ( ~ ( ord_less_eq @ int @ min @ ( bit1 @ SV91 ) )
| ( ord_less_eq @ int @ min @ SV91 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2994]) ).
thf(3384,plain,
! [SV91: $i] :
( ( ~ ( ord_less_eq @ int @ min @ SV91 )
| ( ord_less_eq @ int @ min @ ( bit1 @ SV91 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2995]) ).
thf(3385,plain,
! [SV485: $i,SV92: $i] :
( ( ( dvd_dvd @ int @ SV92 @ SV485 )
= $false )
| ( ( ( ord_less_eq @ int @ SV485 @ ( zero_zero @ int ) )
| ( ord_less_eq @ int @ SV92 @ SV485 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2996]) ).
thf(3386,plain,
! [SV93: $i] :
( ( ( min
!= ( bit1 @ SV93 ) )
| ( min
= ( ti @ int @ SV93 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2997]) ).
thf(3387,plain,
! [SV93: $i] :
( ( ( min
!= ( ti @ int @ SV93 ) )
| ( min
= ( bit1 @ SV93 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2998]) ).
thf(3388,plain,
! [SV740: $i,SV94: $i] :
( ( ( ! [SY1957: $i,SY1958: $i] :
( ( times_times @ SV94 @ SV740 @ ( times_times @ SV94 @ SY1957 @ SY1958 ) )
= ( times_times @ SV94 @ ( times_times @ SV94 @ SV740 @ SY1957 ) @ SY1958 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV94 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2999]) ).
thf(3389,plain,
! [SV741: $i,SV95: $i] :
( ( ( ! [SY1959: $i,SY1960: $i,SY1961: $i] :
( ( times_times @ SV95 @ ( times_times @ SV95 @ SV741 @ SY1959 ) @ ( times_times @ SV95 @ SY1960 @ SY1961 ) )
= ( times_times @ SV95 @ SV741 @ ( times_times @ SV95 @ SY1959 @ ( times_times @ SV95 @ SY1960 @ SY1961 ) ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV95 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3000]) ).
thf(3390,plain,
! [SV486: $i,SV96: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( number_number_of @ int @ SV96 ) @ ( number_number_of @ int @ SV486 ) )
| ( ord_less @ int @ SV96 @ SV486 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3001]) ).
thf(3391,plain,
! [SV486: $i,SV96: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV96 @ SV486 )
| ( ord_less @ int @ ( number_number_of @ int @ SV96 ) @ ( number_number_of @ int @ SV486 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3001]) ).
thf(3392,plain,
! [SV487: $i,SV97: $i] :
( ( ( dvd_dvd @ nat @ SV97 @ SV487 )
= $false )
| ( ( ( SV487
= ( zero_zero @ nat ) )
| ( ord_less_eq @ nat @ SV97 @ SV487 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3002]) ).
thf(3393,plain,
! [SV488: $i,SV98: $i,SV650: $i] :
( ( ( ~ ( ab_group_add @ SV650 ) )
= $true )
| ( ( ( ti @ SV650 @ ( plus_plus @ SV650 @ SV98 @ SV488 ) )
= ( plus_plus @ SV650 @ SV98 @ SV488 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3003]) ).
thf(3394,plain,
! [SV742: $i,SV99: $i] :
( ( ( ! [SY1962: $i,SY1963: $i] :
( ( plus_plus @ SV99 @ SV742 @ ( plus_plus @ SV99 @ SY1962 @ SY1963 ) )
= ( plus_plus @ SV99 @ SY1962 @ ( plus_plus @ SV99 @ SV742 @ SY1963 ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV99 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3004]) ).
thf(3395,plain,
! [SV100: $i,SV651: $i,SV489: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV489 @ SV651 ) )
= $true )
| ( ( ord_less_eq @ int @ ( plus_plus @ int @ SV100 @ SV489 ) @ ( plus_plus @ int @ SV100 @ SV651 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3005]) ).
thf(3396,plain,
! [SV101: $i,SV652: $i,SV490: $i] :
( ( ( ~ ~ ( zcong @ SV490 @ ( zero_zero @ int ) @ SV652 ) )
= $true )
| ( ( ~ ( zcong @ ( power_power @ int @ SV101 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SV490 @ SV652 )
| ~ ( dvd_dvd @ int @ SV652 @ SV101 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3006]) ).
thf(3397,plain,
! [SV743: $i,SV102: $i] :
( ( ( ! [SY1964: $i] :
( ~ ( ord_less @ SV102 @ ( zero_zero @ SV102 ) @ SY1964 )
| ~ ( ord_less @ SV102 @ SY1964 @ ( one_one @ SV102 ) )
| ( ord_less @ SV102 @ ( times_times @ SV102 @ SY1964 @ ( power_power @ SV102 @ SY1964 @ SV743 ) ) @ ( power_power @ SV102 @ SY1964 @ SV743 ) ) ) )
= $true )
| ( ( linordered_semidom @ SV102 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3007]) ).
thf(3398,plain,
! [SV491: $i,SV103: $i] :
( ( ~ ( ~ ( quadRes @ ( ti @ int @ SV103 ) @ SV491 )
| ( quadRes @ SV103 @ SV491 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3008]) ).
thf(3399,plain,
! [SV491: $i,SV103: $i] :
( ( ~ ( ~ ( quadRes @ SV103 @ SV491 )
| ( quadRes @ ( ti @ int @ SV103 ) @ SV491 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3008]) ).
thf(3400,plain,
! [SV492: $i,SV104: $i,SV653: $i] :
( ( ( ~ ( semiring @ SV653 ) )
= $true )
| ( ( ( times_times @ SV653 @ SV104 @ ( ti @ SV653 @ SV492 ) )
= ( times_times @ SV653 @ SV104 @ SV492 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3009]) ).
thf(3401,plain,
! [SV106: $i] :
( ( ( ( bit1 @ SV106 )
!= min )
| ( ( ti @ int @ SV106 )
= min ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3011]) ).
thf(3402,plain,
! [SV106: $i] :
( ( ( ( ti @ int @ SV106 )
!= min )
| ( ( bit1 @ SV106 )
= min ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3012]) ).
thf(3403,plain,
! [SV493: $i,SV107: $i,SV654: $i] :
( ( ( ~ ( power @ SV654 ) )
= $true )
| ( ( ( times_times @ SV654 @ SV107 @ ( ti @ SV654 @ SV493 ) )
= ( times_times @ SV654 @ SV107 @ SV493 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3013]) ).
thf(3404,plain,
! [SV108: $i,SV494: $i,SV744: $i,SV655: $i] :
( ( ! [SY1965: $i] :
( ~ ( zcong @ SV655 @ SV744 @ SY1965 )
| ( ( ti @ int @ SV744 )
!= ( ti @ int @ SV494 ) )
| ~ ( zcong @ SV494 @ SV108 @ SY1965 )
| ( zcong @ SV655 @ SV108 @ SY1965 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3014]) ).
thf(3405,plain,
! [SV656: $i,SV495: $i,SV109: $i] :
( ( ( ~ ( dvd_dvd @ int @ ( times_times @ int @ SV109 @ SV495 ) @ ( times_times @ int @ SV109 @ SV656 ) ) )
= $true )
| ( ( ~ ( ( ( ti @ int @ SV109 )
!= ( zero_zero @ int ) ) )
| ( dvd_dvd @ int @ SV495 @ SV656 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3015]) ).
thf(3406,plain,
! [SV745: $i,SV110: $i] :
( ( ( ( power_power @ SV110 @ SV745 @ ( zero_zero @ nat ) )
= ( one_one @ SV110 ) )
= $true )
| ( ( power @ SV110 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3016]) ).
thf(3407,plain,
! [SV111: $i,SV496: $i] :
( ( ( twoSqu420862341sum2sq @ SV496 )
= $false )
| ( ( ~ ( twoSqu420862341sum2sq @ SV111 )
| ( twoSqu420862341sum2sq @ ( times_times @ int @ SV496 @ SV111 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3017]) ).
thf(3408,plain,
! [SV112: $i] :
( ( ~ ( ord_less_eq @ int @ ( bit0 @ SV112 ) @ pls )
| ( ord_less_eq @ int @ SV112 @ pls ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3018]) ).
thf(3409,plain,
! [SV112: $i] :
( ( ~ ( ord_less_eq @ int @ SV112 @ pls )
| ( ord_less_eq @ int @ ( bit0 @ SV112 ) @ pls ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3019]) ).
thf(3410,plain,
! [SV113: $i,SV497: $i] :
( ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV497 )
= $false )
| ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( power_power @ int @ SV497 @ SV113 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3020]) ).
thf(3411,plain,
! [SV498: $i,SV115: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SV115 ) @ ( bit0 @ SV498 ) )
| ( ord_less @ int @ SV115 @ SV498 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3022]) ).
thf(3412,plain,
! [SV498: $i,SV115: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV115 @ SV498 )
| ( ord_less @ int @ ( bit1 @ SV115 ) @ ( bit0 @ SV498 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3022]) ).
thf(3413,plain,
! [SV746: $i,SV117: $i] :
( ( ( ! [SY1966: $i,SY1967: $i] :
( ~ ( ord_less_eq @ nat @ SY1966 @ SY1967 )
| ~ ( ord_less_eq @ SV117 @ ( zero_zero @ SV117 ) @ SV746 )
| ~ ( ord_less_eq @ SV117 @ SV746 @ ( one_one @ SV117 ) )
| ( ord_less_eq @ SV117 @ ( power_power @ SV117 @ SV746 @ SY1967 ) @ ( power_power @ SV117 @ SV746 @ SY1966 ) ) ) )
= $true )
| ( ( linordered_semidom @ SV117 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3024]) ).
thf(3414,plain,
! [SV118: $i,SV657: $i,SV499: $i] :
( ( ( ~ ( dvd_dvd @ nat @ SV499 @ SV657 ) )
= $true )
| ( ( dvd_dvd @ nat @ ( times_times @ nat @ SV118 @ SV499 ) @ ( times_times @ nat @ SV118 @ SV657 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3025]) ).
thf(3415,plain,
! [SV500: $i,SV119: $i,SV658: $i] :
( ( ( ~ ( zprime @ SV658 ) )
= $true )
| ( ( ~ ( dvd_dvd @ int @ SV658 @ ( power_power @ int @ SV119 @ SV500 ) )
| ( dvd_dvd @ int @ SV658 @ SV119 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3026]) ).
thf(3416,plain,
! [SV120: $i] :
( ( ( ~ ( number_ring @ SV120 )
| ~ ( linordered_idom @ SV120 ) )
= $true )
| ( ( ! [SY1234: $i] :
~ ( ~ ( ~ ( ord_less @ SV120 @ ( one_one @ SV120 ) @ ( number_number_of @ SV120 @ SY1234 ) )
| ( ord_less @ int @ ( bit1 @ pls ) @ SY1234 ) )
| ~ ( ~ ( ord_less @ int @ ( bit1 @ pls ) @ SY1234 )
| ( ord_less @ SV120 @ ( one_one @ SV120 ) @ ( number_number_of @ SV120 @ SY1234 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3027]) ).
thf(3417,plain,
! [SV121: $i,SV659: $i,SV501: $i] :
( ( ( ~ ( ord_less_eq @ real @ SV501 @ SV659 ) )
= $true )
| ( ( ord_less_eq @ real @ ( plus_plus @ real @ SV121 @ SV501 ) @ ( plus_plus @ real @ SV121 @ SV659 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3028]) ).
thf(3418,plain,
! [SV502: $i,SV122: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SV122 ) @ ( bit1 @ SV502 ) )
| ( ord_less_eq @ int @ SV122 @ SV502 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3029]) ).
thf(3419,plain,
! [SV502: $i,SV122: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ SV122 @ SV502 )
| ( ord_less_eq @ int @ ( bit1 @ SV122 ) @ ( bit1 @ SV502 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3029]) ).
thf(3420,plain,
( ( ( ~ ~ ! [SY1968: $i] :
( ( plus_plus @ int @ ( power_power @ int @ sK3_SX0 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ SY1968 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ) )
= $false )
| ( ( ord_less @ int @ ( one_one @ int ) @ t )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3030]) ).
thf(3421,plain,
! [SV123: $i] :
( ( ( ~ ( number_ring @ SV123 )
| ~ ( linordered_idom @ SV123 ) )
= $true )
| ( ( ! [SY1238: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV123 @ ( number_number_of @ SV123 @ SY1238 ) @ ( one_one @ SV123 ) )
| ( ord_less_eq @ int @ SY1238 @ ( bit1 @ pls ) ) )
| ~ ( ~ ( ord_less_eq @ int @ SY1238 @ ( bit1 @ pls ) )
| ( ord_less_eq @ SV123 @ ( number_number_of @ SV123 @ SY1238 ) @ ( one_one @ SV123 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3031]) ).
thf(3422,plain,
! [SV747: $i,SV124: $i] :
( ( ( ! [SY1969: $i,SY1970: $i,SY1971: $i] :
( ~ ( dvd_dvd @ SV124 @ SY1970 @ SY1971 )
| ~ ( dvd_dvd @ SV124 @ SV747 @ SY1969 )
| ( dvd_dvd @ SV124 @ ( times_times @ SV124 @ SY1970 @ SV747 ) @ ( times_times @ SV124 @ SY1971 @ SY1969 ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV124 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3032]) ).
thf(3423,plain,
! [SV748: $i,SV125: $i] :
( ( ( ! [SY1972: $i,SY1973: $i,SY1974: $i] :
( ( minus_minus @ SV125 @ ( plus_plus @ SV125 @ SV748 @ SY1972 ) @ ( plus_plus @ SV125 @ SY1973 @ SY1974 ) )
= ( plus_plus @ SV125 @ ( minus_minus @ SV125 @ SV748 @ SY1973 ) @ ( minus_minus @ SV125 @ SY1972 @ SY1974 ) ) ) )
= $true )
| ( ( ab_group_add @ SV125 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3033]) ).
thf(3424,plain,
! [SV749: $i,SV126: $i] :
( ( ( ( times_times @ SV126 @ SV749 @ ( number_number_of @ SV126 @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ SV126 @ SV749 @ SV749 ) )
= $true )
| ( ( number_semiring @ SV126 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3034]) ).
thf(3425,plain,
! [SV128: $i] :
( ( ( ( number_number_of @ nat @ SV128 )
!= ( zero_zero @ nat ) )
| ( ord_less_eq @ int @ SV128 @ pls ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3036]) ).
thf(3426,plain,
! [SV128: $i] :
( ( ~ ( ord_less_eq @ int @ SV128 @ pls )
| ( ( number_number_of @ nat @ SV128 )
= ( zero_zero @ nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3037]) ).
thf(3427,plain,
! [SV750: $i,SV129: $i] :
( ( ( ( times_times @ SV129 @ ( number_number_of @ SV129 @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV750 )
= ( plus_plus @ SV129 @ SV750 @ SV750 ) )
= $true )
| ( ( number_semiring @ SV129 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3038]) ).
thf(3428,plain,
! [SV751: $i,SV130: $i] :
( ( ( ! [SY1975: $i,SY1976: $i] :
( ( times_times @ SV130 @ ( times_times @ SV130 @ SV751 @ SY1975 ) @ SY1976 )
= ( times_times @ SV130 @ ( times_times @ SV130 @ SV751 @ SY1976 ) @ SY1975 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV130 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3039]) ).
thf(3429,plain,
! [SV752: $i,SV131: $i] :
( ( ( ! [SY1977: $i,SY1978: $i] :
( ( times_times @ SV131 @ ( plus_plus @ SV131 @ SV752 @ SY1977 ) @ SY1978 )
= ( plus_plus @ SV131 @ ( times_times @ SV131 @ SV752 @ SY1978 ) @ ( times_times @ SV131 @ SY1977 @ SY1978 ) ) ) )
= $true )
| ( ( comm_semiring @ SV131 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3040]) ).
thf(3430,plain,
! [SV753: $i,SV660: $i,SV503: $i,SV132: $i] :
( ( ! [SY1979: $i] :
( ~ ( ord_less_eq @ int @ ( plus_plus @ int @ ( times_times @ int @ SV132 @ SV503 ) @ SV660 ) @ ( plus_plus @ int @ ( times_times @ int @ SV132 @ SV753 ) @ SY1979 ) )
| ~ ( ord_less_eq @ int @ SY1979 @ ( zero_zero @ int ) )
| ~ ( ord_less @ int @ SV132 @ SY1979 )
| ~ ( ord_less @ int @ SV132 @ SV660 )
| ( ord_less_eq @ int @ SV753 @ SV503 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3041]) ).
thf(3431,plain,
! [SV134: $i] :
( ( ( ~ ( number_ring @ SV134 )
| ~ ( linordered_idom @ SV134 ) )
= $true )
| ( ( ! [SY1260: $i] :
~ ( ~ ( ~ ( ord_less @ SV134 @ ( number_number_of @ SV134 @ SY1260 ) @ ( one_one @ SV134 ) )
| ( ord_less @ int @ SY1260 @ ( bit1 @ pls ) ) )
| ~ ( ~ ( ord_less @ int @ SY1260 @ ( bit1 @ pls ) )
| ( ord_less @ SV134 @ ( number_number_of @ SV134 @ SY1260 ) @ ( one_one @ SV134 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3043]) ).
thf(3432,plain,
! [SV505: $i,SV135: $i] :
( ( ~ ( ~ ( ord_less_eq @ nat @ ( number_number_of @ nat @ SV135 ) @ ( number_number_of @ nat @ SV505 ) )
| ~ ~ ( ord_less_eq @ int @ SV135 @ SV505 )
| ( ord_less_eq @ int @ SV135 @ pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3044]) ).
thf(3433,plain,
! [SV505: $i,SV135: $i] :
( ( ~ ( ~ ( ~ ~ ( ord_less_eq @ int @ SV135 @ SV505 )
| ( ord_less_eq @ int @ SV135 @ pls ) )
| ( ord_less_eq @ nat @ ( number_number_of @ nat @ SV135 ) @ ( number_number_of @ nat @ SV505 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3044]) ).
thf(3434,plain,
! [SV754: $i,SV136: $i] :
( ( ( ( power_power @ SV136 @ SV754 @ ( one_one @ nat ) )
= ( ti @ SV136 @ SV754 ) )
= $true )
| ( ( comm_semiring_1 @ SV136 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3045]) ).
thf(3435,plain,
! [SV661: $i,SV506: $i,SV137: $i] :
( ( ~ ( ~ ( zcong @ SV137 @ SV506 @ SV661 )
| ( dvd_dvd @ int @ SV661 @ ( minus_minus @ int @ SV137 @ SV506 ) ) )
| ~ ( ~ ( dvd_dvd @ int @ SV661 @ ( minus_minus @ int @ SV137 @ SV506 ) )
| ( zcong @ SV137 @ SV506 @ SV661 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3046]) ).
thf(3436,plain,
! [SV507: $i,SV138: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( number_number_of @ int @ SV138 ) @ ( number_number_of @ int @ SV507 ) )
| ( ord_less_eq @ int @ SV138 @ SV507 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3047]) ).
thf(3437,plain,
! [SV507: $i,SV138: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ SV138 @ SV507 )
| ( ord_less_eq @ int @ ( number_number_of @ int @ SV138 ) @ ( number_number_of @ int @ SV507 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3047]) ).
thf(3438,plain,
! [SV139: $i] :
( ( ( ~ ( number @ SV139 )
| ~ ( ring @ SV139 ) )
= $true )
| ( ( ! [SY1266: $i,SY1267: $i,SY1268: $i] :
( ( times_times @ SV139 @ ( number_number_of @ SV139 @ SY1266 ) @ ( minus_minus @ SV139 @ SY1267 @ SY1268 ) )
= ( minus_minus @ SV139 @ ( times_times @ SV139 @ ( number_number_of @ SV139 @ SY1266 ) @ SY1267 ) @ ( times_times @ SV139 @ ( number_number_of @ SV139 @ SY1266 ) @ SY1268 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3048]) ).
thf(3439,plain,
! [SV755: $i,SV140: $i] :
( ( ( ( power_power @ SV140 @ SV755 @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( times_times @ SV140 @ ( times_times @ SV140 @ SV755 @ SV755 ) @ SV755 ) )
= $true )
| ( ( monoid_mult @ SV140 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3049]) ).
thf(3440,plain,
! [SV508: $i,SV141: $i] :
( ( ( ord_less @ int @ SV141 @ SV508 )
= $false )
| ( ( ord_less_eq @ int @ ( plus_plus @ int @ SV141 @ ( one_one @ int ) ) @ SV508 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3050]) ).
thf(3441,plain,
! [SV756: $i,SV142: $i] :
( ( ( ! [SY1980: $i] :
( ~ ( ord_less @ SV142 @ ( one_one @ SV142 ) @ SY1980 )
| ( ord_less @ SV142 @ ( one_one @ SV142 ) @ ( times_times @ SV142 @ SY1980 @ ( power_power @ SV142 @ SY1980 @ SV756 ) ) ) ) )
= $true )
| ( ( linordered_semidom @ SV142 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3051]) ).
thf(3442,plain,
! [SV509: $i,SV143: $i] :
( ( ~ ( ( ( power_power @ nat @ SV143 @ SV509 )
!= ( zero_zero @ nat ) )
| ~ ( ~ ( ( SV509
!= ( zero_zero @ nat ) ) )
| ( SV143
!= ( zero_zero @ nat ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3052]) ).
thf(3443,plain,
! [SV143: $i,SV509: $i] :
( ( ~ ( ~ ~ ( ~ ( ( SV509
!= ( zero_zero @ nat ) ) )
| ( SV143
!= ( zero_zero @ nat ) ) )
| ( ( power_power @ nat @ SV143 @ SV509 )
= ( zero_zero @ nat ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3052]) ).
thf(3444,plain,
! [SV757: $i,SV144: $i] :
( ( ( ( times_times @ SV144 @ SV757 @ ( number_number_of @ SV144 @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ SV144 @ SV757 @ SV757 ) )
= $true )
| ( ( number_ring @ SV144 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3053]) ).
thf(3445,plain,
! [SV662: $i,SV510: $i,SV145: $i] :
( ( ~ ( ~ ( dvd_dvd @ int @ SV145 @ ( plus_plus @ int @ SV510 @ ( times_times @ int @ SV145 @ SV662 ) ) )
| ( dvd_dvd @ int @ SV145 @ SV510 ) )
| ~ ( ~ ( dvd_dvd @ int @ SV145 @ SV510 )
| ( dvd_dvd @ int @ SV145 @ ( plus_plus @ int @ SV510 @ ( times_times @ int @ SV145 @ SV662 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3054]) ).
thf(3446,plain,
! [SV146: $i] :
( ( ~ ( ord_less @ int @ ( bit1 @ SV146 ) @ min )
| ( ord_less @ int @ SV146 @ min ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3055]) ).
thf(3447,plain,
! [SV146: $i] :
( ( ~ ( ord_less @ int @ SV146 @ min )
| ( ord_less @ int @ ( bit1 @ SV146 ) @ min ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3056]) ).
thf(3448,plain,
! [SV511: $i,SV147: $i] :
( ( ~ ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ SV147 @ SV511 ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ SV147 )
| ( SV511
= ( zero_zero @ nat ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3057]) ).
thf(3449,plain,
! [SV511: $i,SV147: $i] :
( ( ~ ( ~ ( ( ord_less @ nat @ ( zero_zero @ nat ) @ SV147 )
| ( SV511
= ( zero_zero @ nat ) ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ SV147 @ SV511 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3057]) ).
thf(3450,plain,
! [SV758: $i,SV149: $i] :
( ( ( ( plus_plus @ SV149 @ ( one_one @ SV149 ) @ ( number_number_of @ SV149 @ SV758 ) )
= ( number_number_of @ SV149 @ ( plus_plus @ int @ ( bit1 @ pls ) @ SV758 ) ) )
= $true )
| ( ( number_ring @ SV149 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3058]) ).
thf(3451,plain,
! [SV759: $i,SV150: $i] :
( ( ( ! [SY1981: $i,SY1982: $i] :
( ( plus_plus @ SV150 @ ( times_times @ SV150 @ SV759 @ SY1981 ) @ ( times_times @ SV150 @ SY1982 @ SY1981 ) )
= ( times_times @ SV150 @ ( plus_plus @ SV150 @ SV759 @ SY1982 ) @ SY1981 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV150 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3059]) ).
thf(3452,plain,
! [SV512: $i,SV151: $i] :
( ( ~ ( ~ ~ ( ~ ( dvd_dvd @ nat @ SV151 @ SV512 )
| ~ ( dvd_dvd @ nat @ SV512 @ SV151 ) )
| ( SV151 = SV512 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3060]) ).
thf(3453,plain,
! [SV512: $i,SV151: $i] :
( ( ~ ( ( SV151 != SV512 )
| ~ ( ~ ( dvd_dvd @ nat @ SV151 @ SV512 )
| ~ ( dvd_dvd @ nat @ SV512 @ SV151 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3060]) ).
thf(3454,plain,
! [SV760: $i,SV152: $i] :
( ( ( ! [SY1983: $i] :
( ~ ( ord_less_eq @ SV152 @ ( zero_zero @ SV152 ) @ SY1983 )
| ~ ( ord_less_eq @ SV152 @ ( zero_zero @ SV152 ) @ SV760 )
| ( ord_less_eq @ SV152 @ ( zero_zero @ SV152 ) @ ( times_times @ SV152 @ SY1983 @ SV760 ) ) ) )
= $true )
| ( ( ordere453448008miring @ SV152 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3061]) ).
thf(3455,plain,
! [SV153: $i,SV513: $i] :
( ( ( ord_less @ nat @ ( zero_zero @ nat ) @ SV513 )
= $false )
| ( ( ~ ( ord_less @ real @ ( zero_zero @ real ) @ SV153 )
| ~ ! [SY1807: $i] :
~ ~ ( ~ ( ord_less @ real @ ( zero_zero @ real ) @ SY1807 )
| ( ( power_power @ real @ SY1807 @ SV513 )
!= SV153 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3062]) ).
thf(3456,plain,
! [SV154: $i,SV761: $i,SV663: $i,SV514: $i] :
( ( ~ ( zcong @ SV514 @ SV663 @ SV761 )
| ( zcong @ ( times_times @ int @ SV154 @ SV514 ) @ ( times_times @ int @ SV154 @ SV663 ) @ SV761 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3063]) ).
thf(3457,plain,
! [SV762: $i,SV155: $i] :
( ( ( ! [SY1984: $i,SY1985: $i] :
( ~ ( ord_less @ SV155 @ ( one_one @ SV155 ) @ SY1985 )
| ~ ( ~ ( ~ ( ord_less @ SV155 @ ( power_power @ SV155 @ SY1985 @ SV762 ) @ ( power_power @ SV155 @ SY1985 @ SY1984 ) )
| ( ord_less @ nat @ SV762 @ SY1984 ) )
| ~ ( ~ ( ord_less @ nat @ SV762 @ SY1984 )
| ( ord_less @ SV155 @ ( power_power @ SV155 @ SY1985 @ SV762 ) @ ( power_power @ SV155 @ SY1985 @ SY1984 ) ) ) ) ) )
= $true )
| ( ( linordered_semidom @ SV155 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3064]) ).
thf(3458,plain,
! [SV763: $i,SV156: $i] :
( ( ( ! [SY1986: $i] :
( ( power_power @ SV156 @ SV763 @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SY1986 ) )
= ( times_times @ SV156 @ ( power_power @ SV156 @ SV763 @ SY1986 ) @ ( power_power @ SV156 @ SV763 @ SY1986 ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV156 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3065]) ).
thf(3459,plain,
! [SV764: $i,SV157: $i] :
( ( ( ( plus_plus @ SV157 @ SV764 @ ( zero_zero @ SV157 ) )
= ( ti @ SV157 @ SV764 ) )
= $true )
| ( ( comm_semiring_1 @ SV157 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3066]) ).
thf(3460,plain,
! [SV158: $i,SV664: $i,SV515: $i] :
( ( ( ~ ( dvd_dvd @ nat @ SV515 @ SV664 ) )
= $true )
| ( ( dvd_dvd @ nat @ ( times_times @ nat @ SV515 @ SV158 ) @ ( times_times @ nat @ SV664 @ SV158 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3067]) ).
thf(3461,plain,
! [SV516: $i,SV159: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SV159 ) @ ( bit0 @ SV516 ) )
| ( ord_less @ int @ SV159 @ SV516 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3068]) ).
thf(3462,plain,
! [SV516: $i,SV159: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV159 @ SV516 )
| ( ord_less_eq @ int @ ( bit1 @ SV159 ) @ ( bit0 @ SV516 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3068]) ).
thf(3463,plain,
! [SV517: $i,SV160: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV160 @ ( plus_plus @ int @ SV517 @ ( one_one @ int ) ) )
| ( ord_less_eq @ int @ SV160 @ SV517 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3069]) ).
thf(3464,plain,
! [SV517: $i,SV160: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ SV160 @ SV517 )
| ( ord_less @ int @ SV160 @ ( plus_plus @ int @ SV517 @ ( one_one @ int ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3069]) ).
thf(3465,plain,
! [SV665: $i,SV518: $i,SV161: $i] :
( ( ( ~ ( ord_less @ int @ ( plus_plus @ int @ ( times_times @ int @ SV161 @ SV518 ) @ SV665 ) @ ( zero_zero @ int ) ) )
= $true )
| ( ( ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV665 )
| ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV161 )
| ( ord_less_eq @ int @ SV518 @ ( zero_zero @ int ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3070]) ).
thf(3466,plain,
! [SV666: $i,SV520: $i,SV163: $i] :
( ( ~ ( ~ ( zcong @ SV163 @ SV520 @ ( ti @ int @ SV666 ) )
| ( zcong @ SV163 @ SV520 @ SV666 ) )
| ~ ( ~ ( zcong @ SV163 @ SV520 @ SV666 )
| ( zcong @ SV163 @ SV520 @ ( ti @ int @ SV666 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3072]) ).
thf(3467,plain,
! [SV164: $i,SV667: $i,SV521: $i,SV765: $i] :
( ( ! [SY1987: $i] :
( ~ ( dvd_dvd @ int @ SV765 @ SY1987 )
| ~ ( ~ ( ~ ( dvd_dvd @ int @ SV765 @ ( plus_plus @ int @ SV521 @ SV667 ) )
| ( dvd_dvd @ int @ SV765 @ ( plus_plus @ int @ ( plus_plus @ int @ SV521 @ ( times_times @ int @ SV164 @ SY1987 ) ) @ SV667 ) ) )
| ~ ( ~ ( dvd_dvd @ int @ SV765 @ ( plus_plus @ int @ ( plus_plus @ int @ SV521 @ ( times_times @ int @ SV164 @ SY1987 ) ) @ SV667 ) )
| ( dvd_dvd @ int @ SV765 @ ( plus_plus @ int @ SV521 @ SV667 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3073]) ).
thf(3468,plain,
! [SV766: $i,SV165: $i] :
( ( ( ! [SY1988: $i,SY1989: $i] :
( ( plus_plus @ SV165 @ ( number_number_of @ SV165 @ SV766 ) @ ( plus_plus @ SV165 @ ( number_number_of @ SV165 @ SY1988 ) @ SY1989 ) )
= ( plus_plus @ SV165 @ ( number_number_of @ SV165 @ ( plus_plus @ int @ SV766 @ SY1988 ) ) @ SY1989 ) ) )
= $true )
| ( ( number_ring @ SV165 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3074]) ).
thf(3469,plain,
! [SV767: $i,SV166: $i] :
( ( ( ! [SY1990: $i] : ( ord_less_eq @ SV166 @ ( zero_zero @ SV166 ) @ ( power_power @ SV166 @ SV767 @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SY1990 ) ) ) )
= $true )
| ( ( linordered_idom @ SV166 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3075]) ).
thf(3470,plain,
! [SV522: $i,SV167: $i,SV768: $i,SV668: $i] :
( ( ! [SY1991: $i] :
( ~ ( zcong @ SV668 @ SV768 @ SY1991 )
| ~ ( zcong @ SV167 @ SV522 @ SY1991 )
| ( zcong @ ( minus_minus @ int @ SV668 @ SV167 ) @ ( minus_minus @ int @ SV768 @ SV522 ) @ SY1991 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3076]) ).
thf(3471,plain,
! [SV168: $i] :
( ( ( ~ ( number @ SV168 )
| ~ ( semiring @ SV168 ) )
= $true )
| ( ( ! [SY1318: $i,SY1319: $i,SY1320: $i] :
( ( times_times @ SV168 @ ( plus_plus @ SV168 @ SY1318 @ SY1319 ) @ ( number_number_of @ SV168 @ SY1320 ) )
= ( plus_plus @ SV168 @ ( times_times @ SV168 @ SY1318 @ ( number_number_of @ SV168 @ SY1320 ) ) @ ( times_times @ SV168 @ SY1319 @ ( number_number_of @ SV168 @ SY1320 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3077]) ).
thf(3472,plain,
! [SV523: $i,SV169: $i] :
( ( ~ ( ( ( plus_plus @ real @ ( power_power @ real @ SV169 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ real @ SV523 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ real ) )
| ~ ( ( SV169
!= ( zero_zero @ real ) )
| ( SV523
!= ( zero_zero @ real ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3078]) ).
thf(3473,plain,
! [SV523: $i,SV169: $i] :
( ( ~ ( ~ ~ ( ( SV169
!= ( zero_zero @ real ) )
| ( SV523
!= ( zero_zero @ real ) ) )
| ( ( plus_plus @ real @ ( power_power @ real @ SV169 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ real @ SV523 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ real ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3078]) ).
thf(3474,plain,
! [SV669: $i,SV524: $i,SV170: $i] :
( ( ( ~ ( dvd_dvd @ nat @ ( power_power @ nat @ SV170 @ SV524 ) @ ( power_power @ nat @ SV170 @ SV669 ) ) )
= $true )
| ( ( ~ ( ord_less @ nat @ ( one_one @ nat ) @ SV170 )
| ( ord_less_eq @ nat @ SV524 @ SV669 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3079]) ).
thf(3475,plain,
! [SV171: $i] :
( ( ~ ( ord_less_eq @ int @ pls @ ( bit0 @ SV171 ) )
| ( ord_less_eq @ int @ pls @ SV171 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3080]) ).
thf(3476,plain,
! [SV171: $i] :
( ( ~ ( ord_less_eq @ int @ pls @ SV171 )
| ( ord_less_eq @ int @ pls @ ( bit0 @ SV171 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3081]) ).
thf(3477,plain,
! [SV525: $i,SV172: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV172 @ SV525 )
| ( ord_less @ int @ ( minus_minus @ int @ SV172 @ SV525 ) @ ( zero_zero @ int ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3082]) ).
thf(3478,plain,
! [SV525: $i,SV172: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( minus_minus @ int @ SV172 @ SV525 ) @ ( zero_zero @ int ) )
| ( ord_less @ int @ SV172 @ SV525 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3082]) ).
thf(3479,plain,
! [SV769: $i,SV173: $i] :
( ( ( ( power_power @ SV173 @ ( number_number_of @ SV173 @ min ) @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV769 ) )
= ( one_one @ SV173 ) )
= $true )
| ( ( number_ring @ SV173 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3083]) ).
thf(3480,plain,
! [SV770: $i,SV174: $i] :
( ( ( ! [SY1992: $i,SY1993: $i,SY1994: $i] :
( ( minus_minus @ SV174 @ ( times_times @ SV174 @ SV770 @ SY1992 ) @ ( times_times @ SV174 @ SY1993 @ SY1994 ) )
= ( plus_plus @ SV174 @ ( times_times @ SV174 @ SV770 @ ( minus_minus @ SV174 @ SY1992 @ SY1994 ) ) @ ( times_times @ SV174 @ ( minus_minus @ SV174 @ SV770 @ SY1993 ) @ SY1994 ) ) ) )
= $true )
| ( ( ring @ SV174 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3084]) ).
thf(3481,plain,
! [SV771: $i,SV175: $i] :
( ( ( ! [SY1995: $i,SY1996: $i,SY1997: $i] :
~ ( ~ ( ~ ~ ( ~ ( ( ( ti @ SV175 @ SY1996 )
!= ( ti @ SV175 @ SY1997 ) ) )
| ~ ( ( ( ti @ SV175 @ SV771 )
!= ( ti @ SV175 @ SY1995 ) ) ) )
| ( ( plus_plus @ SV175 @ ( times_times @ SV175 @ SY1996 @ SV771 ) @ ( times_times @ SV175 @ SY1997 @ SY1995 ) )
!= ( plus_plus @ SV175 @ ( times_times @ SV175 @ SY1996 @ SY1995 ) @ ( times_times @ SV175 @ SY1997 @ SV771 ) ) ) )
| ~ ( ~ ( ( ( plus_plus @ SV175 @ ( times_times @ SV175 @ SY1996 @ SV771 ) @ ( times_times @ SV175 @ SY1997 @ SY1995 ) )
!= ( plus_plus @ SV175 @ ( times_times @ SV175 @ SY1996 @ SY1995 ) @ ( times_times @ SV175 @ SY1997 @ SV771 ) ) ) )
| ~ ( ~ ( ( ( ti @ SV175 @ SY1996 )
!= ( ti @ SV175 @ SY1997 ) ) )
| ~ ( ( ( ti @ SV175 @ SV771 )
!= ( ti @ SV175 @ SY1995 ) ) ) ) ) ) )
= $true )
| ( ( semiri456707255roduct @ SV175 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3085]) ).
thf(3482,plain,
! [SV176: $i,SV526: $i] :
( ( ( number @ SV526 )
= $false )
| ( ( ( ti @ SV526 @ ( number_number_of @ SV526 @ SV176 ) )
= ( number_number_of @ SV526 @ SV176 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3086]) ).
thf(3483,plain,
! [SV177: $i] :
( ( ~ ( ord_less @ int @ pls @ ( bit0 @ SV177 ) )
| ( ord_less @ int @ pls @ SV177 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3087]) ).
thf(3484,plain,
! [SV177: $i] :
( ( ~ ( ord_less @ int @ pls @ SV177 )
| ( ord_less @ int @ pls @ ( bit0 @ SV177 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3088]) ).
thf(3485,plain,
! [SV178: $i,SV527: $i] :
( ( ( ord_less @ int @ ( zero_zero @ int ) @ SV527 )
= $false )
| ( ( ~ ( ord_less @ int @ SV527 @ SV178 )
| ~ ( dvd_dvd @ int @ SV178 @ SV527 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3089]) ).
thf(3486,plain,
! [SV772: $i,SV179: $i] :
( ( ( ! [SY1998: $i,SY1999: $i] :
( ~ ( ord_less @ SV179 @ ( one_one @ SV179 ) @ SY1999 )
| ~ ( ord_less @ SV179 @ ( power_power @ SV179 @ SY1999 @ SV772 ) @ ( power_power @ SV179 @ SY1999 @ SY1998 ) )
| ( ord_less @ nat @ SV772 @ SY1998 ) ) )
= $true )
| ( ( linordered_semidom @ SV179 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3090]) ).
thf(3487,plain,
! [SV180: $i,SV773: $i] :
( ( ( ! [SY2000: $i,SY2001: $i] :
( ( SV773
!= ( times_times @ SV180 @ SY2000 @ SY2001 ) )
| ( dvd_dvd @ SV180 @ SY2000 @ SV773 ) ) )
= $true )
| ( ( dvd @ SV180 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3091]) ).
thf(3488,plain,
! [SV528: $i,SV182: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SV182 ) @ ( bit1 @ SV528 ) )
| ( ord_less @ int @ SV182 @ SV528 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3092]) ).
thf(3489,plain,
! [SV528: $i,SV182: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV182 @ SV528 )
| ( ord_less @ int @ ( bit1 @ SV182 ) @ ( bit1 @ SV528 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3092]) ).
thf(3490,plain,
! [SV774: $i,SV184: $i] :
( ( ( ( times_times @ SV184 @ SV774 @ ( one_one @ SV184 ) )
= ( ti @ SV184 @ SV774 ) )
= $true )
| ( ( comm_semiring_1 @ SV184 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3094]) ).
thf(3491,plain,
! [SV775: $i,SV185: $i] :
( ( ( ! [SY2002: $i,SY2003: $i] :
( ( times_times @ SV185 @ ( power_power @ SV185 @ SV775 @ SY2002 ) @ ( power_power @ SV185 @ SV775 @ SY2003 ) )
= ( power_power @ SV185 @ SV775 @ ( plus_plus @ nat @ SY2002 @ SY2003 ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV185 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3095]) ).
thf(3492,plain,
! [SV529: $i,SV186: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SV186 ) @ ( bit0 @ SV529 ) )
| ( ord_less @ int @ SV186 @ SV529 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3096]) ).
thf(3493,plain,
! [SV529: $i,SV186: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV186 @ SV529 )
| ( ord_less @ int @ ( bit0 @ SV186 ) @ ( bit0 @ SV529 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3096]) ).
thf(3494,plain,
! [SV530: $i,SV187: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV187 @ SV530 )
| ~ ( ~ ( ord_less_eq @ int @ SV187 @ SV530 )
| ~ ( ( ( ti @ int @ SV187 )
!= ( ti @ int @ SV530 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3097]) ).
thf(3495,plain,
! [SV530: $i,SV187: $i] :
( ( ~ ( ~ ~ ( ~ ( ord_less_eq @ int @ SV187 @ SV530 )
| ~ ( ( ( ti @ int @ SV187 )
!= ( ti @ int @ SV530 ) ) ) )
| ( ord_less @ int @ SV187 @ SV530 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3097]) ).
thf(3496,plain,
! [SV188: $i,SV531: $i] :
( ( ( number @ SV531 )
= $false )
| ( ( ( number_number_of @ SV531 @ ( ti @ int @ SV188 ) )
= ( number_number_of @ SV531 @ SV188 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3098]) ).
thf(3497,plain,
! [SV776: $i,SV189: $i] :
( ( ( ~ ( ~ ( ( ( plus_plus @ SV189 @ SV776 @ SV776 )
!= ( zero_zero @ SV189 ) )
| ( ( ti @ SV189 @ SV776 )
= ( zero_zero @ SV189 ) ) )
| ~ ( ( ( ti @ SV189 @ SV776 )
!= ( zero_zero @ SV189 ) )
| ( ( plus_plus @ SV189 @ SV776 @ SV776 )
= ( zero_zero @ SV189 ) ) ) ) )
= $true )
| ( ( linord219039673up_add @ SV189 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3099]) ).
thf(3498,plain,
! [SV532: $i,SV190: $i,SV670: $i] :
( ( ( ~ ( ord_less @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV670 ) )
= $true )
| ( ( ~ ( zcong @ ( power_power @ int @ ( number_number_of @ int @ min ) @ SV190 ) @ ( power_power @ int @ ( number_number_of @ int @ min ) @ SV532 ) @ SV670 )
| ( ( power_power @ int @ ( number_number_of @ int @ min ) @ SV190 )
= ( power_power @ int @ ( number_number_of @ int @ min ) @ SV532 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3100]) ).
thf(3499,plain,
! [SV671: $i,SV533: $i,SV191: $i] :
( ( ~ ( ~ ( dvd_dvd @ nat @ ( times_times @ nat @ SV191 @ SV533 ) @ ( times_times @ nat @ SV671 @ SV533 ) )
| ( SV533
= ( zero_zero @ nat ) )
| ( dvd_dvd @ nat @ SV191 @ SV671 ) )
| ~ ( ~ ( ( SV533
= ( zero_zero @ nat ) )
| ( dvd_dvd @ nat @ SV191 @ SV671 ) )
| ( dvd_dvd @ nat @ ( times_times @ nat @ SV191 @ SV533 ) @ ( times_times @ nat @ SV671 @ SV533 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3101]) ).
thf(3500,plain,
! [SV777: $i,SV192: $i] :
( ( ( ! [SY2004: $i] :
( ~ ( ord_less_eq @ SV192 @ ( zero_zero @ SV192 ) @ SY2004 )
| ( ord_less_eq @ SV192 @ ( zero_zero @ SV192 ) @ ( power_power @ SV192 @ SY2004 @ SV777 ) ) ) )
= $true )
| ( ( linordered_semidom @ SV192 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3102]) ).
thf(3501,plain,
! [SV778: $i,SV193: $i] :
( ( ( ! [SY2005: $i] :
~ ( ~ ( ( ( plus_plus @ SV193 @ ( times_times @ SV193 @ SV778 @ SV778 ) @ ( times_times @ SV193 @ SY2005 @ SY2005 ) )
!= ( zero_zero @ SV193 ) )
| ~ ( ( ( ti @ SV193 @ SV778 )
!= ( zero_zero @ SV193 ) )
| ( ( ti @ SV193 @ SY2005 )
!= ( zero_zero @ SV193 ) ) ) )
| ~ ( ~ ~ ( ( ( ti @ SV193 @ SV778 )
!= ( zero_zero @ SV193 ) )
| ( ( ti @ SV193 @ SY2005 )
!= ( zero_zero @ SV193 ) ) )
| ( ( plus_plus @ SV193 @ ( times_times @ SV193 @ SV778 @ SV778 ) @ ( times_times @ SV193 @ SY2005 @ SY2005 ) )
= ( zero_zero @ SV193 ) ) ) ) )
= $true )
| ( ( linord581940658strict @ SV193 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3103]) ).
thf(3502,plain,
! [SV779: $i,SV194: $i] :
( ( ( ! [SY2006: $i,SY2007: $i] :
( ~ ( ord_less @ SV194 @ ( one_one @ SV194 ) @ SY2007 )
| ~ ( ~ ( ( ( power_power @ SV194 @ SY2007 @ SV779 )
!= ( power_power @ SV194 @ SY2007 @ SY2006 ) )
| ( SV779 = SY2006 ) )
| ~ ( ( SV779 != SY2006 )
| ( ( power_power @ SV194 @ SY2007 @ SV779 )
= ( power_power @ SV194 @ SY2007 @ SY2006 ) ) ) ) ) )
= $true )
| ( ( linordered_semidom @ SV194 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3104]) ).
thf(3503,plain,
! [SV780: $i,SV195: $i] :
( ( ( ! [SY2008: $i] :
~ ( ord_less @ SV195 @ ( plus_plus @ SV195 @ ( times_times @ SV195 @ SV780 @ SV780 ) @ ( times_times @ SV195 @ SY2008 @ SY2008 ) ) @ ( zero_zero @ SV195 ) ) )
= $true )
| ( ( linordered_ring @ SV195 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3105]) ).
thf(3504,plain,
! [SV196: $i,SV534: $i,SV672: $i] :
( ( ( ~ ( zprime @ SV672 ) )
= $true )
| ( ( ~ ~ ( zcong @ SV534 @ ( zero_zero @ int ) @ SV672 )
| ~ ~ ( zcong @ SV196 @ ( zero_zero @ int ) @ SV672 )
| ~ ( zcong @ ( times_times @ int @ SV534 @ SV196 ) @ ( zero_zero @ int ) @ SV672 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3106]) ).
thf(3505,plain,
! [SV781: $i,SV197: $i] :
( ( ( ! [SY2009: $i] :
( ( power_power @ SV197 @ ( plus_plus @ SV197 @ SV781 @ SY2009 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ SV197 @ ( plus_plus @ SV197 @ ( power_power @ SV197 @ SV781 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV197 @ SY2009 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times @ SV197 @ ( times_times @ SV197 @ ( number_number_of @ SV197 @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV781 ) @ SY2009 ) ) ) )
= $true )
| ( ( number_semiring @ SV197 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3107]) ).
thf(3506,plain,
! [SV782: $i,SV198: $i] :
( ( ( ! [SY2010: $i] :
( ( times_times @ SV198 @ ( number_number_of @ SV198 @ SV782 ) @ ( number_number_of @ SV198 @ SY2010 ) )
= ( number_number_of @ SV198 @ ( times_times @ int @ SV782 @ SY2010 ) ) ) )
= $true )
| ( ( number_ring @ SV198 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3108]) ).
thf(3507,plain,
! [SV783: $i,SV199: $i] :
( ( ( ! [SY2011: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ ( times_times @ SV199 @ SV783 @ SY2011 ) )
| ~ ( ~ ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ SV783 )
| ~ ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ SY2011 ) )
| ~ ( ~ ( ord_less_eq @ SV199 @ SV783 @ ( zero_zero @ SV199 ) )
| ~ ( ord_less_eq @ SV199 @ SY2011 @ ( zero_zero @ SV199 ) ) ) )
| ~ ( ~ ( ~ ( ~ ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ SV783 )
| ~ ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ SY2011 ) )
| ~ ( ~ ( ord_less_eq @ SV199 @ SV783 @ ( zero_zero @ SV199 ) )
| ~ ( ord_less_eq @ SV199 @ SY2011 @ ( zero_zero @ SV199 ) ) ) )
| ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ ( times_times @ SV199 @ SV783 @ SY2011 ) ) ) ) )
= $true )
| ( ( linord581940658strict @ SV199 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3109]) ).
thf(3508,plain,
! [SV784: $i,SV200: $i] :
( ( ( ( times_times @ SV200 @ ( number_number_of @ SV200 @ ( bit1 @ pls ) ) @ SV784 )
= ( ti @ SV200 @ SV784 ) )
= $true )
| ( ( number_ring @ SV200 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3110]) ).
thf(3509,plain,
! [SV785: $i,SV201: $i] :
( ( ( ! [SY2012: $i] :
( ~ ( ord_less @ SV201 @ ( one_one @ SV201 ) @ SY2012 )
| ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ SV785 )
| ( ord_less @ SV201 @ ( one_one @ SV201 ) @ ( power_power @ SV201 @ SY2012 @ SV785 ) ) ) )
= $true )
| ( ( linordered_semidom @ SV201 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3111]) ).
thf(3510,plain,
! [SV202: $i] :
( ( ( ~ ( number_ring @ SV202 )
| ~ ( linordered_idom @ SV202 ) )
= $true )
| ( ( ! [SY1375: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV202 @ ( one_one @ SV202 ) @ ( number_number_of @ SV202 @ SY1375 ) )
| ( ord_less_eq @ int @ ( bit1 @ pls ) @ SY1375 ) )
| ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ pls ) @ SY1375 )
| ( ord_less_eq @ SV202 @ ( one_one @ SV202 ) @ ( number_number_of @ SV202 @ SY1375 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3112]) ).
thf(3511,plain,
! [SV203: $i,SV535: $i,SV673: $i] :
( ( ( ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV673 ) )
= $true )
| ( ( ~ ( ord_less @ int @ SV673 @ SV535 )
| ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV203 )
| ~ ( ord_less @ int @ SV203 @ SV673 )
| ~ ( zcong @ SV673 @ SV203 @ SV535 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3113]) ).
thf(3512,plain,
! [SV786: $i,SV204: $i] :
( ( ( ( power_power @ SV204 @ SV786 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times @ SV204 @ SV786 @ SV786 ) )
= $true )
| ( ( monoid_mult @ SV204 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3115]) ).
thf(3513,plain,
! [SV205: $i] :
( ( ~ ( ord_less @ int @ ( bit0 @ SV205 ) @ min )
| ( ord_less_eq @ int @ SV205 @ min ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3116]) ).
thf(3514,plain,
! [SV205: $i] :
( ( ~ ( ord_less_eq @ int @ SV205 @ min )
| ( ord_less @ int @ ( bit0 @ SV205 ) @ min ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3117]) ).
thf(3515,plain,
! [SV536: $i,SV206: $i,SV787: $i,SV674: $i] :
( ( ! [SY2013: $i] :
( ~ ( zcong @ SV674 @ SV787 @ SY2013 )
| ~ ( zcong @ SV206 @ SV536 @ SY2013 )
| ( zcong @ ( plus_plus @ int @ SV674 @ SV206 ) @ ( plus_plus @ int @ SV787 @ SV536 ) @ SY2013 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3118]) ).
thf(3516,plain,
! [SV207: $i] :
( ( ~ ( ord_less @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ SV207 ) @ SV207 ) @ ( zero_zero @ int ) )
| ( ord_less @ int @ SV207 @ ( zero_zero @ int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3119]) ).
thf(3517,plain,
! [SV207: $i] :
( ( ~ ( ord_less @ int @ SV207 @ ( zero_zero @ int ) )
| ( ord_less @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ SV207 ) @ SV207 ) @ ( zero_zero @ int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3120]) ).
thf(3518,plain,
! [SV208: $i] :
( ( ~ ( twoSqu420862341sum2sq @ ( ti @ int @ SV208 ) )
| ( twoSqu420862341sum2sq @ SV208 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3121]) ).
thf(3519,plain,
! [SV208: $i] :
( ( ~ ( twoSqu420862341sum2sq @ SV208 )
| ( twoSqu420862341sum2sq @ ( ti @ int @ SV208 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3122]) ).
thf(3520,plain,
! [SV209: $i,SV675: $i,SV537: $i] :
( ( ( ~ ( dvd_dvd @ nat @ SV537 @ SV675 ) )
= $true )
| ( ( ~ ( dvd_dvd @ nat @ SV537 @ ( plus_plus @ nat @ SV675 @ SV209 ) )
| ( dvd_dvd @ nat @ SV537 @ SV209 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3123]) ).
thf(3521,plain,
! [SV210: $i] :
( ( ( ( bit0 @ SV210 )
!= pls )
| ( ( ti @ int @ SV210 )
= pls ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3124]) ).
thf(3522,plain,
! [SV210: $i] :
( ( ( ( ti @ int @ SV210 )
!= pls )
| ( ( bit0 @ SV210 )
= pls ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3125]) ).
thf(3523,plain,
! [SV788: $i,SV211: $i] :
( ( ( ! [SY2014: $i] : ( dvd_dvd @ SV211 @ SV788 @ ( times_times @ SV211 @ SY2014 @ SV788 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV211 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3126]) ).
thf(3524,plain,
! [SV789: $i,SV212: $i] :
( ( ( ! [SY2015: $i] :
( ( plus_plus @ SV212 @ ( number_number_of @ SV212 @ SV789 ) @ ( number_number_of @ SV212 @ SY2015 ) )
= ( number_number_of @ SV212 @ ( plus_plus @ int @ SV789 @ SY2015 ) ) ) )
= $true )
| ( ( number_ring @ SV212 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3127]) ).
thf(3525,plain,
! [SV213: $i] :
( ( ( ~ ( number_ring @ SV213 )
| ~ ( ring_char_0 @ SV213 ) )
= $true )
| ( ( ! [SY1389: $i,SY1390: $i] :
~ ( ~ ( ( ( number_number_of @ SV213 @ SY1389 )
!= ( number_number_of @ SV213 @ SY1390 ) )
| ( ( ti @ int @ SY1389 )
= ( ti @ int @ SY1390 ) ) )
| ~ ( ( ( ti @ int @ SY1389 )
!= ( ti @ int @ SY1390 ) )
| ( ( number_number_of @ SV213 @ SY1389 )
= ( number_number_of @ SV213 @ SY1390 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3128]) ).
thf(3526,plain,
! [SV790: $i,SV676: $i,SV538: $i,SV214: $i] :
( ( ( SV214
!= ( plus_plus @ nat @ ( times_times @ nat @ SV538 @ SV676 ) @ SV790 ) )
| ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ SV790 )
| ~ ( ord_less @ nat @ SV790 @ SV676 )
| ~ ( dvd_dvd @ nat @ SV676 @ SV214 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3129]) ).
thf(3527,plain,
! [SV677: $i,SV539: $i,SV215: $i] :
( ( ( ~ ( dvd_dvd @ nat @ ( power_power @ nat @ SV215 @ SV539 ) @ ( power_power @ nat @ SV677 @ SV539 ) ) )
= $true )
| ( ( ~ ( ( SV539
!= ( zero_zero @ nat ) ) )
| ( dvd_dvd @ nat @ SV215 @ SV677 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3130]) ).
thf(3528,plain,
! [SV216: $i] :
( ( ( ( zero_zero @ SV216 )
= ( one_one @ SV216 ) )
= $false )
| ( ( zero_neq_one @ SV216 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3131]) ).
thf(3529,plain,
! [SV791: $i,SV217: $i] :
( ( ( ( plus_plus @ SV217 @ ( zero_zero @ SV217 ) @ SV791 )
= ( ti @ SV217 @ SV791 ) )
= $true )
| ( ( comm_semiring_1 @ SV217 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3132]) ).
thf(3530,plain,
! [SV218: $i] :
( ( ( ~ ( number_ring @ SV218 )
| ~ ( linordered_idom @ SV218 ) )
= $true )
| ( ( ! [SY1397: $i,SY1398: $i] :
~ ( ~ ( ~ ( ord_less @ SV218 @ ( number_number_of @ SV218 @ SY1397 ) @ ( number_number_of @ SV218 @ SY1398 ) )
| ( ord_less @ int @ SY1397 @ SY1398 ) )
| ~ ( ~ ( ord_less @ int @ SY1397 @ SY1398 )
| ( ord_less @ SV218 @ ( number_number_of @ SV218 @ SY1397 ) @ ( number_number_of @ SV218 @ SY1398 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3133]) ).
thf(3531,plain,
! [SV219: $i] :
( ( ~ ( ord_less_eq @ int @ ( bit0 @ SV219 ) @ min )
| ( ord_less_eq @ int @ SV219 @ min ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3134]) ).
thf(3532,plain,
! [SV219: $i] :
( ( ~ ( ord_less_eq @ int @ SV219 @ min )
| ( ord_less_eq @ int @ ( bit0 @ SV219 ) @ min ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3135]) ).
thf(3533,plain,
! [SV792: $i,SV220: $i] :
( ( ( ! [SY2016: $i,SY2017: $i,SY2018: $i] :
( ~ ( dvd_dvd @ SV220 @ ( power_power @ SV220 @ SY2016 @ SY2017 ) @ SY2018 )
| ~ ( ord_less_eq @ nat @ SV792 @ SY2017 )
| ( dvd_dvd @ SV220 @ ( power_power @ SV220 @ SY2016 @ SV792 ) @ SY2018 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV220 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3136]) ).
thf(3534,plain,
! [SV540: $i,SV221: $i,SV678: $i] :
( ( ( ~ ( ord_less @ real @ ( zero_zero @ real ) @ SV678 ) )
= $true )
| ( ( ~ ( ord_less @ real @ SV221 @ SV540 )
| ( ord_less @ real @ ( times_times @ real @ SV678 @ SV221 ) @ ( times_times @ real @ SV678 @ SV540 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3137]) ).
thf(3535,plain,
! [SV793: $i,SV222: $i] :
( ( ( ! [SY2019: $i,SY2020: $i] :
( ~ ( dvd_dvd @ SV222 @ SY2019 @ SY2020 )
| ( dvd_dvd @ SV222 @ SY2019 @ ( times_times @ SV222 @ SV793 @ SY2020 ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV222 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3138]) ).
thf(3536,plain,
! [SV541: $i,SV223: $i,SV679: $i] :
( ( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ SV679 ) )
= $true )
| ( ( ~ ( ord_less @ nat @ ( power_power @ nat @ SV679 @ SV223 ) @ ( power_power @ nat @ SV679 @ SV541 ) )
| ( ord_less @ nat @ SV223 @ SV541 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3139]) ).
thf(3537,plain,
! [SV224: $i,SV542: $i] :
( ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV542 )
= $false )
| ( ( ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV224 )
| ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ SV542 @ SV224 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3140]) ).
thf(3538,plain,
! [SV225: $i] :
( ( ~ ( ord_less_eq @ int @ ( one_one @ int ) @ SV225 )
| ( ord_less @ int @ ( zero_zero @ int ) @ SV225 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3141]) ).
thf(3539,plain,
! [SV225: $i] :
( ( ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV225 )
| ( ord_less_eq @ int @ ( one_one @ int ) @ SV225 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3142]) ).
thf(3540,plain,
! [SV794: $i,SV226: $i] :
( ( ( ! [SY2021: $i,SY2022: $i] :
( ~ ( dvd_dvd @ SV226 @ ( times_times @ SV226 @ SV794 @ SY2021 ) @ SY2022 )
| ( dvd_dvd @ SV226 @ SV794 @ SY2022 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV226 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3143]) ).
thf(3541,plain,
! [SV543: $i,SV227: $i,SV680: $i] :
( ( ( ~ ( mult_zero @ SV680 ) )
= $true )
| ( ( ( times_times @ SV680 @ ( ti @ SV680 @ SV227 ) @ SV543 )
= ( times_times @ SV680 @ SV227 @ SV543 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3144]) ).
thf(3542,plain,
! [SV544: $i,SV228: $i,SV681: $i] :
( ( ( ~ ( power @ SV681 ) )
= $true )
| ( ( ( ti @ SV681 @ ( times_times @ SV681 @ SV228 @ SV544 ) )
= ( times_times @ SV681 @ SV228 @ SV544 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3145]) ).
thf(3543,plain,
! [SV545: $i,SV229: $i,SV682: $i] :
( ( ( ~ ( semiring @ SV682 ) )
= $true )
| ( ( ( plus_plus @ SV682 @ ( ti @ SV682 @ SV229 ) @ SV545 )
= ( plus_plus @ SV682 @ SV229 @ SV545 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3146]) ).
thf(3544,plain,
! [SV795: $i,SV230: $i] :
( ( ( ! [SY2023: $i] : ( ord_less_eq @ SV230 @ ( zero_zero @ SV230 ) @ ( plus_plus @ SV230 @ ( times_times @ SV230 @ SV795 @ SV795 ) @ ( times_times @ SV230 @ SY2023 @ SY2023 ) ) ) )
= $true )
| ( ( linordered_ring @ SV230 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3147]) ).
thf(3545,plain,
! [SV546: $i,SV231: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SV231 ) @ ( bit1 @ SV546 ) )
| ( ord_less_eq @ int @ SV231 @ SV546 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3148]) ).
thf(3546,plain,
! [SV546: $i,SV231: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ SV231 @ SV546 )
| ( ord_less @ int @ ( bit0 @ SV231 ) @ ( bit1 @ SV546 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3148]) ).
thf(3547,plain,
! [SV232: $i] :
( ( ( ( one_one @ SV232 )
= ( zero_zero @ SV232 ) )
= $false )
| ( ( zero_neq_one @ SV232 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3149]) ).
thf(3548,plain,
! [SV547: $i,SV233: $i] :
( ( ~ ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ SV233 @ ( number_number_of @ nat @ SV547 ) ) )
| ( ( number_number_of @ nat @ SV547 )
= ( zero_zero @ nat ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ SV233 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3150]) ).
thf(3549,plain,
! [SV233: $i,SV547: $i] :
( ( ~ ( ~ ( ( ( number_number_of @ nat @ SV547 )
= ( zero_zero @ nat ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ SV233 ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ SV233 @ ( number_number_of @ nat @ SV547 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3150]) ).
thf(3550,plain,
! [SV234: $i] :
( ( ( ~ ( number @ SV234 )
| ~ ( semiring @ SV234 ) )
= $true )
| ( ( ! [SY1424: $i,SY1425: $i,SY1426: $i] :
( ( times_times @ SV234 @ ( number_number_of @ SV234 @ SY1424 ) @ ( plus_plus @ SV234 @ SY1425 @ SY1426 ) )
= ( plus_plus @ SV234 @ ( times_times @ SV234 @ ( number_number_of @ SV234 @ SY1424 ) @ SY1425 ) @ ( times_times @ SV234 @ ( number_number_of @ SV234 @ SY1424 ) @ SY1426 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3151]) ).
thf(3551,plain,
! [SV796: $i,SV235: $i] :
( ( ( ( minus_minus @ SV235 @ ( times_times @ SV235 @ SV796 @ SV796 ) @ ( one_one @ SV235 ) )
= ( times_times @ SV235 @ ( plus_plus @ SV235 @ SV796 @ ( one_one @ SV235 ) ) @ ( minus_minus @ SV235 @ SV796 @ ( one_one @ SV235 ) ) ) )
= $true )
| ( ( ring_1 @ SV235 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3152]) ).
thf(3552,plain,
! [SV548: $i,SV236: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SV236 ) @ ( bit1 @ SV548 ) )
| ( ord_less_eq @ int @ SV236 @ SV548 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3153]) ).
thf(3553,plain,
! [SV548: $i,SV236: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ SV236 @ SV548 )
| ( ord_less @ int @ ( bit0 @ SV236 ) @ ( bit1 @ SV548 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3153]) ).
thf(3554,plain,
! [SV797: $i,SV237: $i] :
( ( ( ! [SY2024: $i] :
~ ( ~ ( ( ( number_number_of @ SV237 @ SV797 )
!= ( ti @ SV237 @ SY2024 ) )
| ( ( ti @ SV237 @ SY2024 )
= ( number_number_of @ SV237 @ SV797 ) ) )
| ~ ( ( ( ti @ SV237 @ SY2024 )
!= ( number_number_of @ SV237 @ SV797 ) )
| ( ( number_number_of @ SV237 @ SV797 )
= ( ti @ SV237 @ SY2024 ) ) ) ) )
= $true )
| ( ( number @ SV237 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3154]) ).
thf(3555,plain,
! [SV798: $i,SV238: $i] :
( ( ( ! [SY2025: $i,SY2026: $i] :
( ( plus_plus @ SV238 @ SV798 @ ( plus_plus @ SV238 @ SY2025 @ SY2026 ) )
= ( plus_plus @ SV238 @ ( plus_plus @ SV238 @ SV798 @ SY2025 ) @ SY2026 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV238 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3155]) ).
thf(3556,plain,
! [SV239: $i] :
( ( ~ ( ord_less_eq @ int @ min @ ( bit0 @ SV239 ) )
| ( ord_less @ int @ min @ SV239 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3156]) ).
thf(3557,plain,
! [SV239: $i] :
( ( ~ ( ord_less @ int @ min @ SV239 )
| ( ord_less_eq @ int @ min @ ( bit0 @ SV239 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3157]) ).
thf(3558,plain,
! [SV549: $i,SV240: $i,SV683: $i,SV799: $i] :
( ( ~ ( zprime @ SV799 )
| ~ ~ ( dvd_dvd @ int @ SV799 @ SV683 )
| ~ ( dvd_dvd @ int @ ( power_power @ int @ SV799 @ SV240 ) @ ( times_times @ int @ SV683 @ SV549 ) )
| ( dvd_dvd @ int @ ( power_power @ int @ SV799 @ SV240 ) @ SV549 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3158]) ).
thf(3559,plain,
! [SV241: $i] :
( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ ( number_number_of @ nat @ SV241 ) )
| ( ord_less @ int @ pls @ SV241 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3159]) ).
thf(3560,plain,
! [SV241: $i] :
( ( ~ ( ord_less @ int @ pls @ SV241 )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ ( number_number_of @ nat @ SV241 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3160]) ).
thf(3561,plain,
! [SV550: $i,SV242: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( bit0 @ SV242 ) @ ( bit1 @ SV550 ) )
| ( ord_less_eq @ int @ SV242 @ SV550 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3161]) ).
thf(3562,plain,
! [SV550: $i,SV242: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ SV242 @ SV550 )
| ( ord_less_eq @ int @ ( bit0 @ SV242 ) @ ( bit1 @ SV550 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3161]) ).
thf(3563,plain,
! [SV551: $i,SV243: $i,SV684: $i] :
( ( ( ~ ( power @ SV684 ) )
= $true )
| ( ( ( times_times @ SV684 @ ( ti @ SV684 @ SV243 ) @ SV551 )
= ( times_times @ SV684 @ SV243 @ SV551 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3162]) ).
thf(3564,plain,
! [SV244: $i] :
( ( ~ ( ord_less @ int @ pls @ ( bit1 @ SV244 ) )
| ( ord_less_eq @ int @ pls @ SV244 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3163]) ).
thf(3565,plain,
! [SV244: $i] :
( ( ~ ( ord_less_eq @ int @ pls @ SV244 )
| ( ord_less @ int @ pls @ ( bit1 @ SV244 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3164]) ).
thf(3566,plain,
! [SV552: $i,SV245: $i,SV685: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV685 @ pls )
| ( ( times_times @ nat @ ( number_number_of @ nat @ SV685 ) @ ( times_times @ nat @ ( number_number_of @ nat @ SV245 ) @ SV552 ) )
= ( zero_zero @ nat ) ) )
| ~ ( ~ ~ ( ord_less @ int @ SV685 @ pls )
| ( ( times_times @ nat @ ( number_number_of @ nat @ SV685 ) @ ( times_times @ nat @ ( number_number_of @ nat @ SV245 ) @ SV552 ) )
= ( times_times @ nat @ ( number_number_of @ nat @ ( times_times @ int @ SV685 @ SV245 ) ) @ SV552 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3165]) ).
thf(3567,plain,
! [SV553: $i,SV246: $i,SV686: $i] :
( ( ( ~ ( dvd @ SV686 ) )
= $true )
| ( ( ( times_times @ SV686 @ ( ti @ SV686 @ SV246 ) @ SV553 )
= ( times_times @ SV686 @ SV246 @ SV553 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3166]) ).
thf(3568,plain,
! [SV554: $i,SV247: $i] :
( ( ~ ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ SV247 @ SV554 ) )
| ( SV554
= ( zero_zero @ nat ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ SV247 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3167]) ).
thf(3569,plain,
! [SV247: $i,SV554: $i] :
( ( ~ ( ~ ( ( SV554
= ( zero_zero @ nat ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ SV247 ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ SV247 @ SV554 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3167]) ).
thf(3570,plain,
! [SV800: $i,SV248: $i] :
( ( ( ! [SY2027: $i,SY2028: $i] :
( ( times_times @ SV248 @ ( number_number_of @ SV248 @ SV800 ) @ ( times_times @ SV248 @ ( number_number_of @ SV248 @ SY2027 ) @ SY2028 ) )
= ( times_times @ SV248 @ ( number_number_of @ SV248 @ ( times_times @ int @ SV800 @ SY2027 ) ) @ SY2028 ) ) )
= $true )
| ( ( number_ring @ SV248 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3168]) ).
thf(3571,plain,
! [SV249: $i] :
( ( ~ ( ord_less @ int @ ( bit1 @ SV249 ) @ ( zero_zero @ int ) )
| ( ord_less @ int @ SV249 @ ( zero_zero @ int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3169]) ).
thf(3572,plain,
! [SV249: $i] :
( ( ~ ( ord_less @ int @ SV249 @ ( zero_zero @ int ) )
| ( ord_less @ int @ ( bit1 @ SV249 ) @ ( zero_zero @ int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3170]) ).
thf(3573,plain,
! [SV801: $i,SV250: $i] :
( ( ( ( plus_plus @ SV250 @ SV801 @ ( number_number_of @ SV250 @ pls ) )
= ( ti @ SV250 @ SV801 ) )
= $true )
| ( ( number_ring @ SV250 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3171]) ).
thf(3574,plain,
! [SV555: $i,SV251: $i,SV687: $i] :
( ( ( ~ ( power @ SV687 ) )
= $true )
| ( ( ( power_power @ SV687 @ SV251 @ ( ti @ nat @ SV555 ) )
= ( power_power @ SV687 @ SV251 @ SV555 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3172]) ).
thf(3575,plain,
! [SV802: $i,SV252: $i] :
( ( ( ! [SY2029: $i,SY2030: $i] :
( ( times_times @ SV252 @ ( times_times @ SV252 @ SV802 @ SY2029 ) @ SY2030 )
= ( times_times @ SV252 @ SV802 @ ( times_times @ SV252 @ SY2029 @ SY2030 ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV252 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3173]) ).
thf(3576,plain,
! [SV556: $i,SV253: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SV253 ) @ ( bit0 @ SV556 ) )
| ( ord_less @ int @ SV253 @ SV556 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3174]) ).
thf(3577,plain,
! [SV556: $i,SV253: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV253 @ SV556 )
| ( ord_less @ int @ ( bit1 @ SV253 ) @ ( bit0 @ SV556 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3174]) ).
thf(3578,plain,
! [SV803: $i,SV254: $i] :
( ( ( ! [SY2031: $i] :
( ( plus_plus @ SV254 @ SV803 @ ( times_times @ SV254 @ SY2031 @ SV803 ) )
= ( times_times @ SV254 @ ( plus_plus @ SV254 @ SY2031 @ ( one_one @ SV254 ) ) @ SV803 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV254 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3175]) ).
thf(3579,plain,
! [SV804: $i,SV255: $i] :
( ( ( ! [SY2032: $i,SY2033: $i,SY2034: $i] :
~ ( ~ ( ( ( plus_plus @ SV255 @ ( times_times @ SV255 @ SV804 @ SY2032 ) @ ( times_times @ SV255 @ SY2033 @ SY2034 ) )
!= ( plus_plus @ SV255 @ ( times_times @ SV255 @ SV804 @ SY2034 ) @ ( times_times @ SV255 @ SY2033 @ SY2032 ) ) )
| ( ( ti @ SV255 @ SV804 )
= ( ti @ SV255 @ SY2033 ) )
| ( ( ti @ SV255 @ SY2032 )
= ( ti @ SV255 @ SY2034 ) ) )
| ~ ( ~ ( ( ( ti @ SV255 @ SV804 )
= ( ti @ SV255 @ SY2033 ) )
| ( ( ti @ SV255 @ SY2032 )
= ( ti @ SV255 @ SY2034 ) ) )
| ( ( plus_plus @ SV255 @ ( times_times @ SV255 @ SV804 @ SY2032 ) @ ( times_times @ SV255 @ SY2033 @ SY2034 ) )
= ( plus_plus @ SV255 @ ( times_times @ SV255 @ SV804 @ SY2034 ) @ ( times_times @ SV255 @ SY2033 @ SY2032 ) ) ) ) ) )
= $true )
| ( ( semiri456707255roduct @ SV255 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3176]) ).
thf(3580,plain,
! [SV256: $i] :
( ( ~ ( ord_less_eq @ int @ pls @ ( bit1 @ SV256 ) )
| ( ord_less_eq @ int @ pls @ SV256 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3177]) ).
thf(3581,plain,
! [SV256: $i] :
( ( ~ ( ord_less_eq @ int @ pls @ SV256 )
| ( ord_less_eq @ int @ pls @ ( bit1 @ SV256 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3178]) ).
thf(3582,plain,
! [SV557: $i,SV257: $i,SV805: $i,SV688: $i] :
( ( ! [SY2035: $i] :
( ~ ( zcong @ SV688 @ SV805 @ SY2035 )
| ~ ( ~ ( ~ ( zcong @ SV257 @ ( times_times @ int @ SV557 @ SV688 ) @ SY2035 )
| ( zcong @ SV257 @ ( times_times @ int @ SV557 @ SV805 ) @ SY2035 ) )
| ~ ( ~ ( zcong @ SV257 @ ( times_times @ int @ SV557 @ SV805 ) @ SY2035 )
| ( zcong @ SV257 @ ( times_times @ int @ SV557 @ SV688 ) @ SY2035 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3179]) ).
thf(3583,plain,
! [SV558: $i,SV259: $i,SV689: $i] :
( ( ( ~ ( ( SV689
!= ( zero_zero @ nat ) ) ) )
= $true )
| ( ( ~ ( dvd_dvd @ nat @ ( power_power @ nat @ SV259 @ SV689 ) @ SV558 )
| ( dvd_dvd @ nat @ SV259 @ SV558 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3181]) ).
thf(3584,plain,
! [SV690: $i,SV559: $i,SV261: $i] :
( ( ~ ( ~ ( zcong @ SV261 @ ( ti @ int @ SV559 ) @ SV690 )
| ( zcong @ SV261 @ SV559 @ SV690 ) )
| ~ ( ~ ( zcong @ SV261 @ SV559 @ SV690 )
| ( zcong @ SV261 @ ( ti @ int @ SV559 ) @ SV690 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3183]) ).
thf(3585,plain,
! [SV806: $i,SV263: $i] :
( ( ( ! [SY2036: $i] :
( ( number_number_of @ SV263 @ ( plus_plus @ int @ SV806 @ SY2036 ) )
= ( plus_plus @ SV263 @ ( number_number_of @ SV263 @ SV806 ) @ ( number_number_of @ SV263 @ SY2036 ) ) ) )
= $true )
| ( ( number_ring @ SV263 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3185]) ).
thf(3586,plain,
! [SV807: $i,SV264: $i] :
( ( ( ! [SY2037: $i] :
( ( number_number_of @ SV264 @ ( times_times @ int @ SV807 @ SY2037 ) )
= ( times_times @ SV264 @ ( number_number_of @ SV264 @ SV807 ) @ ( number_number_of @ SV264 @ SY2037 ) ) ) )
= $true )
| ( ( number_ring @ SV264 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3186]) ).
thf(3587,plain,
! [SV808: $i,SV265: $i] :
( ( ( ( power_power @ SV265 @ SV808 @ ( zero_zero @ nat ) )
= ( one_one @ SV265 ) )
= $true )
| ( ( comm_semiring_1 @ SV265 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3187]) ).
thf(3588,plain,
! [SV809: $i,SV266: $i] :
( ( ( ! [SY2038: $i,SY2039: $i,SY2040: $i] :
( ( plus_plus @ SV266 @ ( plus_plus @ SV266 @ SV809 @ SY2038 ) @ ( plus_plus @ SV266 @ SY2039 @ SY2040 ) )
= ( plus_plus @ SV266 @ ( plus_plus @ SV266 @ SV809 @ SY2039 ) @ ( plus_plus @ SV266 @ SY2038 @ SY2040 ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV266 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3188]) ).
thf(3589,plain,
! [SV268: $i,SV560: $i] :
( ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV560 )
= $false )
| ( ( ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV268 )
| ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( times_times @ int @ SV560 @ SV268 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3189]) ).
thf(3590,plain,
! [SV810: $i,SV269: $i] :
( ( ( ~ ( ~ ( ~ ( ord_less @ SV269 @ ( plus_plus @ SV269 @ SV810 @ SV810 ) @ ( zero_zero @ SV269 ) )
| ( ord_less @ SV269 @ SV810 @ ( zero_zero @ SV269 ) ) )
| ~ ( ~ ( ord_less @ SV269 @ SV810 @ ( zero_zero @ SV269 ) )
| ( ord_less @ SV269 @ ( plus_plus @ SV269 @ SV810 @ SV810 ) @ ( zero_zero @ SV269 ) ) ) ) )
= $true )
| ( ( linordered_idom @ SV269 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3190]) ).
thf(3591,plain,
! [SV561: $i,SV270: $i] :
( ( ( ord_less_eq @ int @ SV270 @ SV561 )
= $false )
| ( ( ~ ( ord_less_eq @ int @ SV561 @ SV270 )
| ( ( ti @ int @ SV270 )
= ( ti @ int @ SV561 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3191]) ).
thf(3592,plain,
! [SV811: $i,SV271: $i] :
( ( ( ! [SY2041: $i,SY2042: $i] :
( ( plus_plus @ SV271 @ ( number_number_of @ SV271 @ SV811 ) @ ( minus_minus @ SV271 @ ( number_number_of @ SV271 @ SY2041 ) @ SY2042 ) )
= ( minus_minus @ SV271 @ ( number_number_of @ SV271 @ ( plus_plus @ int @ SV811 @ SY2041 ) ) @ SY2042 ) ) )
= $true )
| ( ( number_ring @ SV271 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3192]) ).
thf(3593,plain,
! [SV812: $i,SV272: $i] :
( ( ( ( number_number_of @ SV272 @ ( bit0 @ SV812 ) )
= ( plus_plus @ SV272 @ ( plus_plus @ SV272 @ ( zero_zero @ SV272 ) @ ( number_number_of @ SV272 @ SV812 ) ) @ ( number_number_of @ SV272 @ SV812 ) ) )
= $true )
| ( ( number_ring @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3193]) ).
thf(3594,plain,
! [SV562: $i,SV273: $i,SV691: $i] :
( ( ( ~ ( ( SV691
!= ( zero_zero @ real ) ) ) )
= $true )
| ( ( ~ ( ~ ( ( ( times_times @ real @ SV691 @ SV273 )
!= ( times_times @ real @ SV691 @ SV562 ) )
| ( SV273 = SV562 ) )
| ~ ( ( SV273 != SV562 )
| ( ( times_times @ real @ SV691 @ SV273 )
= ( times_times @ real @ SV691 @ SV562 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3194]) ).
thf(3595,plain,
! [SV274: $i] :
( ( ~ ( ord_less @ int @ min @ ( bit1 @ SV274 ) )
| ( ord_less @ int @ min @ SV274 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3195]) ).
thf(3596,plain,
! [SV274: $i] :
( ( ~ ( ord_less @ int @ min @ SV274 )
| ( ord_less @ int @ min @ ( bit1 @ SV274 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3196]) ).
thf(3597,plain,
! [SV813: $i,SV275: $i] :
( ( ( ! [SY2043: $i] :
( ( number_number_of @ SV275 @ ( minus_minus @ int @ SV813 @ SY2043 ) )
= ( minus_minus @ SV275 @ ( number_number_of @ SV275 @ SV813 ) @ ( number_number_of @ SV275 @ SY2043 ) ) ) )
= $true )
| ( ( number_ring @ SV275 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3197]) ).
thf(3598,plain,
! [SV814: $i,SV276: $i] :
( ( ( ( power_power @ SV276 @ ( one_one @ SV276 ) @ SV814 )
= ( one_one @ SV276 ) )
= $true )
| ( ( monoid_mult @ SV276 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3198]) ).
thf(3599,plain,
! [SV815: $i,SV277: $i] :
( ( ( ! [SY2044: $i,SY2045: $i] :
( ~ ( dvd_dvd @ SV277 @ SY2044 @ SY2045 )
| ~ ( dvd_dvd @ SV277 @ SY2044 @ SV815 )
| ( dvd_dvd @ SV277 @ SY2044 @ ( plus_plus @ SV277 @ SY2045 @ SV815 ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV277 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3199]) ).
thf(3600,plain,
! [SV816: $i,SV278: $i] :
( ( ( ( times_times @ SV278 @ ( zero_zero @ SV278 ) @ SV816 )
= ( zero_zero @ SV278 ) )
= $true )
| ( ( comm_semiring_1 @ SV278 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3200]) ).
thf(3601,plain,
! [SV279: $i] :
( ( ~ ( ord_less @ int @ ( bit0 @ SV279 ) @ pls )
| ( ord_less @ int @ SV279 @ pls ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3201]) ).
thf(3602,plain,
! [SV279: $i] :
( ( ~ ( ord_less @ int @ SV279 @ pls )
| ( ord_less @ int @ ( bit0 @ SV279 ) @ pls ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3202]) ).
thf(3603,plain,
! [SV563: $i,SV280: $i,SV692: $i] :
( ( ( ~ ( semiring @ SV692 ) )
= $true )
| ( ( ( ti @ SV692 @ ( times_times @ SV692 @ SV280 @ SV563 ) )
= ( times_times @ SV692 @ SV280 @ SV563 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3203]) ).
thf(3604,plain,
! [SV564: $i,SV281: $i] :
( ( ~ ( ( ( bit0 @ SV281 )
!= ( bit0 @ SV564 ) )
| ( ( ti @ int @ SV281 )
= ( ti @ int @ SV564 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3204]) ).
thf(3605,plain,
! [SV564: $i,SV281: $i] :
( ( ~ ( ( ( ti @ int @ SV281 )
!= ( ti @ int @ SV564 ) )
| ( ( bit0 @ SV281 )
= ( bit0 @ SV564 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3204]) ).
thf(3606,plain,
! [SV282: $i] :
( ( ~ ( ord_less_eq @ int @ ( bit1 @ SV282 ) @ min )
| ( ord_less_eq @ int @ SV282 @ min ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3205]) ).
thf(3607,plain,
! [SV282: $i] :
( ( ~ ( ord_less_eq @ int @ SV282 @ min )
| ( ord_less_eq @ int @ ( bit1 @ SV282 ) @ min ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3206]) ).
thf(3608,plain,
! [SV817: $i,SV283: $i] :
( ( ( ( plus_plus @ SV283 @ ( number_number_of @ SV283 @ pls ) @ SV817 )
= ( ti @ SV283 @ SV817 ) )
= $true )
| ( ( number_ring @ SV283 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3207]) ).
thf(3609,plain,
! [SV818: $i,SV284: $i] :
( ( ( ! [SY2046: $i,SY2047: $i] :
( ~ ( dvd_dvd @ SV284 @ SY2046 @ SY2047 )
| ( dvd_dvd @ SV284 @ ( power_power @ SV284 @ SY2046 @ SV818 ) @ ( power_power @ SV284 @ SY2047 @ SV818 ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV284 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3208]) ).
thf(3610,plain,
! [SV285: $i,SV819: $i] :
( ( ( ! [SY2048: $i] :
( ~ ( ord_less_eq @ int @ pls @ SY2048 )
| ~ ( ord_less_eq @ int @ pls @ SV819 )
| ( ( plus_plus @ SV285 @ ( number_number_of @ SV285 @ SY2048 ) @ ( number_number_of @ SV285 @ SV819 ) )
= ( number_number_of @ SV285 @ ( plus_plus @ int @ SY2048 @ SV819 ) ) ) ) )
= $true )
| ( ( number_semiring @ SV285 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3209]) ).
thf(3611,plain,
! [SV820: $i,SV286: $i] :
( ( ( ! [SY2049: $i] :
( ( power_power @ SV286 @ SV820 @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SY2049 ) )
= ( power_power @ SV286 @ ( power_power @ SV286 @ SV820 @ SY2049 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true )
| ( ( monoid_mult @ SV286 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3210]) ).
thf(3612,plain,
! [SV565: $i,SV287: $i,SV693: $i] :
( ( ( ~ ( dvd @ SV693 ) )
= $true )
| ( ( ( times_times @ SV693 @ SV287 @ ( ti @ SV693 @ SV565 ) )
= ( times_times @ SV693 @ SV287 @ SV565 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3211]) ).
thf(3613,plain,
! [SV566: $i,SV288: $i,SV694: $i,SV821: $i] :
( ( ~ ( zprime @ SV821 )
| ~ ~ ( dvd_dvd @ int @ SV821 @ SV694 )
| ~ ( dvd_dvd @ int @ ( power_power @ int @ SV821 @ SV288 ) @ ( times_times @ int @ SV566 @ SV694 ) )
| ( dvd_dvd @ int @ ( power_power @ int @ SV821 @ SV288 ) @ SV566 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3212]) ).
thf(3614,plain,
! [SV567: $i,SV289: $i,SV695: $i] :
( ( ( ~ ( ab_group_add @ SV695 ) )
= $true )
| ( ( ( plus_plus @ SV695 @ ( ti @ SV695 @ SV289 ) @ SV567 )
= ( plus_plus @ SV695 @ SV289 @ SV567 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3213]) ).
thf(3615,plain,
! [SV290: $i] :
( ( ~ ( ord_less @ int @ ( bit0 @ SV290 ) @ ( zero_zero @ int ) )
| ( ord_less @ int @ SV290 @ ( zero_zero @ int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3214]) ).
thf(3616,plain,
! [SV290: $i] :
( ( ~ ( ord_less @ int @ SV290 @ ( zero_zero @ int ) )
| ( ord_less @ int @ ( bit0 @ SV290 ) @ ( zero_zero @ int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3215]) ).
thf(3617,plain,
! [SV822: $i,SV291: $i] :
( ( ( ( times_times @ SV291 @ SV822 @ SV822 )
= ( power_power @ SV291 @ SV822 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV291 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3216]) ).
thf(3618,plain,
! [SV568: $i,SV292: $i] :
( ( ~ ( ~ ( zcong @ ( times_times @ int @ SV292 @ ( minus_minus @ int @ SV568 @ ( one_one @ int ) ) ) @ ( one_one @ int ) @ SV568 )
| ( zcong @ SV292 @ ( minus_minus @ int @ SV568 @ ( one_one @ int ) ) @ SV568 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3217]) ).
thf(3619,plain,
! [SV568: $i,SV292: $i] :
( ( ~ ( ~ ( zcong @ SV292 @ ( minus_minus @ int @ SV568 @ ( one_one @ int ) ) @ SV568 )
| ( zcong @ ( times_times @ int @ SV292 @ ( minus_minus @ int @ SV568 @ ( one_one @ int ) ) ) @ ( one_one @ int ) @ SV568 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3217]) ).
thf(3620,plain,
! [SV823: $i,SV293: $i] :
( ( ( ord_less_eq @ SV293 @ ( zero_zero @ SV293 ) @ ( power_power @ SV293 @ SV823 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $true )
| ( ( linordered_idom @ SV293 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3218]) ).
thf(3621,plain,
! [SV294: $i,SV696: $i,SV569: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV569 @ SV696 ) )
= $true )
| ( ( ~ ( ord_less_eq @ int @ SV696 @ SV294 )
| ( ord_less_eq @ int @ SV569 @ SV294 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3219]) ).
thf(3622,plain,
! [SV824: $i,SV296: $i] :
( ( ( ! [SY2050: $i,SY2051: $i] :
( ( plus_plus @ SV296 @ ( plus_plus @ SV296 @ SV824 @ SY2050 ) @ SY2051 )
= ( plus_plus @ SV296 @ ( plus_plus @ SV296 @ SV824 @ SY2051 ) @ SY2050 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV296 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3221]) ).
thf(3623,plain,
! [SV297: $i,SV697: $i,SV570: $i] :
( ( ( ~ ( ord_less @ int @ SV570 @ SV697 ) )
= $true )
| ( ( ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV297 )
| ( ord_less @ int @ ( times_times @ int @ SV297 @ SV570 ) @ ( times_times @ int @ SV297 @ SV697 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3222]) ).
thf(3624,plain,
! [SV825: $i,SV298: $i] :
( ( ( ! [SY2052: $i,SY2053: $i] :
( ( power_power @ SV298 @ ( times_times @ SV298 @ SV825 @ SY2052 ) @ SY2053 )
= ( times_times @ SV298 @ ( power_power @ SV298 @ SV825 @ SY2053 ) @ ( power_power @ SV298 @ SY2052 @ SY2053 ) ) ) )
= $true )
| ( ( comm_monoid_mult @ SV298 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3223]) ).
thf(3625,plain,
! [SV571: $i,SV299: $i] :
( ( ( dvd_dvd @ nat @ SV299 @ SV571 )
= $false )
| ( ( ( SV571
= ( zero_zero @ nat ) )
| ( SV571 = SV299 )
| ( ord_less_eq @ nat @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV299 ) @ SV571 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3224]) ).
thf(3626,plain,
! [SV572: $i,SV300: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SV300 ) @ ( bit1 @ SV572 ) )
| ( ord_less_eq @ int @ SV300 @ SV572 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3225]) ).
thf(3627,plain,
! [SV572: $i,SV300: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ SV300 @ SV572 )
| ( ord_less_eq @ int @ ( bit1 @ SV300 ) @ ( bit1 @ SV572 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3225]) ).
thf(3628,plain,
! [SV826: $i,SV301: $i] :
( ( ( ! [SY2054: $i] :
~ ( ~ ( ( ( times_times @ SV301 @ SV826 @ SY2054 )
!= ( zero_zero @ SV301 ) )
| ( ( ti @ SV301 @ SV826 )
= ( zero_zero @ SV301 ) )
| ( ( ti @ SV301 @ SY2054 )
= ( zero_zero @ SV301 ) ) )
| ~ ( ~ ( ( ( ti @ SV301 @ SV826 )
= ( zero_zero @ SV301 ) )
| ( ( ti @ SV301 @ SY2054 )
= ( zero_zero @ SV301 ) ) )
| ( ( times_times @ SV301 @ SV826 @ SY2054 )
= ( zero_zero @ SV301 ) ) ) ) )
= $true )
| ( ( ring_n68954251visors @ SV301 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3226]) ).
thf(3629,plain,
! [SV827: $i,SV302: $i] :
( ( ( ( times_times @ SV302 @ ( plus_plus @ SV302 @ ( one_one @ SV302 ) @ ( one_one @ SV302 ) ) @ ( number_number_of @ SV302 @ SV827 ) )
= ( number_number_of @ SV302 @ ( bit0 @ SV827 ) ) )
= $true )
| ( ( number_ring @ SV302 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3227]) ).
thf(3630,plain,
! [SV303: $i] :
( ( ( pls
!= ( bit0 @ SV303 ) )
| ( pls
= ( ti @ int @ SV303 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3228]) ).
thf(3631,plain,
! [SV303: $i] :
( ( ( pls
!= ( ti @ int @ SV303 ) )
| ( pls
= ( bit0 @ SV303 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3229]) ).
thf(3632,plain,
! [SV828: $i,SV304: $i] :
( ( ( ! [SY2055: $i,SY2056: $i] :
( ~ ( ord_less @ SV304 @ ( one_one @ SV304 ) @ SY2056 )
| ~ ( ord_less_eq @ SV304 @ ( power_power @ SV304 @ SY2056 @ SV828 ) @ ( power_power @ SV304 @ SY2056 @ SY2055 ) )
| ( ord_less_eq @ nat @ SV828 @ SY2055 ) ) )
= $true )
| ( ( linordered_semidom @ SV304 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3230]) ).
thf(3633,plain,
! [SV829: $i,SV698: $i,SV573: $i,SV305: $i] :
( ( ! [SY2057: $i,SY2058: $i] :
( ( ( plus_plus @ int @ ( times_times @ int @ SV305 @ SV573 ) @ SV698 )
!= ( plus_plus @ int @ ( times_times @ int @ SV829 @ SY2057 ) @ SY2058 ) )
| ~ ( ord_less @ int @ ( plus_plus @ int @ ( times_times @ int @ SV829 @ SY2057 ) @ SY2058 ) @ ( zero_zero @ int ) )
| ~ ( ord_less @ int @ SV698 @ SV305 )
| ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SY2058 )
| ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV829 )
| ~ ( ord_less_eq @ int @ SV829 @ SV305 )
| ( ord_less_eq @ int @ SY2057 @ SV573 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3231]) ).
thf(3634,plain,
! [SV830: $i,SV306: $i] :
( ( ( ! [SY2059: $i] :
( ( plus_plus @ SV306 @ ( times_times @ SV306 @ SV830 @ SY2059 ) @ SY2059 )
= ( times_times @ SV306 @ ( plus_plus @ SV306 @ SV830 @ ( one_one @ SV306 ) ) @ SY2059 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV306 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3232]) ).
thf(3635,plain,
! [SV574: $i,SV307: $i,SV699: $i] :
( ( ( ~ ( dvd @ SV699 ) )
= $true )
| ( ( ( ti @ SV699 @ ( times_times @ SV699 @ SV307 @ SV574 ) )
= ( times_times @ SV699 @ SV307 @ SV574 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3233]) ).
thf(3636,plain,
! [SV308: $i,SV831: $i,SV700: $i,SV575: $i] :
( ( ~ ( zcong @ SV575 @ SV700 @ SV831 )
| ( zcong @ ( power_power @ int @ SV575 @ SV308 ) @ ( power_power @ int @ SV700 @ SV308 ) @ SV831 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3234]) ).
thf(3637,plain,
! [SV309: $i] :
( ( ~ ( ord_less_eq @ int @ ( bit1 @ SV309 ) @ pls )
| ( ord_less @ int @ SV309 @ pls ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3235]) ).
thf(3638,plain,
! [SV309: $i] :
( ( ~ ( ord_less @ int @ SV309 @ pls )
| ( ord_less_eq @ int @ ( bit1 @ SV309 ) @ pls ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3236]) ).
thf(3639,plain,
! [SV832: $i,SV311: $i] :
( ( ( ! [SY2060: $i,SY2061: $i] :
( ( power_power @ SV311 @ ( power_power @ SV311 @ SV832 @ SY2060 ) @ SY2061 )
= ( power_power @ SV311 @ SV832 @ ( times_times @ nat @ SY2060 @ SY2061 ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV311 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3237]) ).
thf(3640,plain,
! [SV833: $i,SV701: $i,SV576: $i,SV312: $i] :
( ( ! [SY2062: $i] :
( ~ ( ord_less_eq @ int @ ( plus_plus @ int @ ( times_times @ int @ SV312 @ SV576 ) @ SV701 ) @ ( plus_plus @ int @ ( times_times @ int @ SV312 @ SV833 ) @ SY2062 ) )
| ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV701 )
| ~ ( ord_less @ int @ SV701 @ SV312 )
| ~ ( ord_less @ int @ SY2062 @ SV312 )
| ( ord_less_eq @ int @ SV576 @ SV833 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3238]) ).
thf(3641,plain,
! [SV834: $i,SV313: $i] :
( ( ( ! [SY2063: $i] :
~ ( ~ ( ( ( ti @ SV313 @ SV834 )
!= ( plus_plus @ SV313 @ SV834 @ SY2063 ) )
| ( ( ti @ SV313 @ SY2063 )
= ( zero_zero @ SV313 ) ) )
| ~ ( ( ( ti @ SV313 @ SY2063 )
!= ( zero_zero @ SV313 ) )
| ( ( ti @ SV313 @ SV834 )
= ( plus_plus @ SV313 @ SV834 @ SY2063 ) ) ) ) )
= $true )
| ( ( semiri456707255roduct @ SV313 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3239]) ).
thf(3642,plain,
! [SV577: $i,SV314: $i] :
( ( ~ ( ~ ( quadRes @ SV314 @ SV577 )
| ~ ! [SY1865: $i] :
~ ( zcong @ ( power_power @ int @ SY1865 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SV577 @ SV314 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3240]) ).
thf(3643,plain,
! [SV314: $i,SV577: $i] :
( ( ~ ( ~ ~ ! [SY1866: $i] :
~ ( zcong @ ( power_power @ int @ SY1866 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SV577 @ SV314 )
| ( quadRes @ SV314 @ SV577 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3240]) ).
thf(3644,plain,
! [SV835: $i,SV315: $i] :
( ( ( ! [SY2064: $i,SY2065: $i] :
( ~ ( ord_less_eq @ nat @ SY2064 @ SY2065 )
| ~ ( ord_less_eq @ SV315 @ ( one_one @ SV315 ) @ SV835 )
| ( ord_less_eq @ SV315 @ ( power_power @ SV315 @ SV835 @ SY2064 ) @ ( power_power @ SV315 @ SV835 @ SY2065 ) ) ) )
= $true )
| ( ( linordered_semidom @ SV315 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3241]) ).
thf(3645,plain,
! [SV836: $i,SV316: $i] :
( ( ( ! [SY2066: $i,SY2067: $i] :
( ( times_times @ SV316 @ ( plus_plus @ SV316 @ SV836 @ SY2066 ) @ SY2067 )
= ( plus_plus @ SV316 @ ( times_times @ SV316 @ SV836 @ SY2067 ) @ ( times_times @ SV316 @ SY2066 @ SY2067 ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV316 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3242]) ).
thf(3646,plain,
! [SV837: $i,SV317: $i] :
( ( ( ! [SY2068: $i] :
( ~ ( ord_less_eq @ SV317 @ ( one_one @ SV317 ) @ SY2068 )
| ( ord_less_eq @ SV317 @ ( one_one @ SV317 ) @ ( power_power @ SV317 @ SY2068 @ SV837 ) ) ) )
= $true )
| ( ( linordered_semidom @ SV317 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3243]) ).
thf(3647,plain,
! [SV838: $i,SV318: $i] :
( ( ( ! [SY2069: $i] :
( ( times_times @ SV318 @ SV838 @ SY2069 )
= ( times_times @ SV318 @ SY2069 @ SV838 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV318 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3244]) ).
thf(3648,plain,
! [SV839: $i,SV319: $i] :
( ( ( ! [SY2070: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV319 @ ( times_times @ SV319 @ SV839 @ SY2070 ) @ ( zero_zero @ SV319 ) )
| ~ ( ~ ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SV839 )
| ~ ( ord_less_eq @ SV319 @ SY2070 @ ( zero_zero @ SV319 ) ) )
| ~ ( ~ ( ord_less_eq @ SV319 @ SV839 @ ( zero_zero @ SV319 ) )
| ~ ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SY2070 ) ) )
| ~ ( ~ ( ~ ( ~ ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SV839 )
| ~ ( ord_less_eq @ SV319 @ SY2070 @ ( zero_zero @ SV319 ) ) )
| ~ ( ~ ( ord_less_eq @ SV319 @ SV839 @ ( zero_zero @ SV319 ) )
| ~ ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SY2070 ) ) )
| ( ord_less_eq @ SV319 @ ( times_times @ SV319 @ SV839 @ SY2070 ) @ ( zero_zero @ SV319 ) ) ) ) )
= $true )
| ( ( linord581940658strict @ SV319 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3245]) ).
thf(3649,plain,
! [SV320: $i] :
( ( ( ( zero_zero @ nat )
!= ( number_number_of @ nat @ SV320 ) )
| ( ord_less_eq @ int @ SV320 @ pls ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3246]) ).
thf(3650,plain,
! [SV320: $i] :
( ( ~ ( ord_less_eq @ int @ SV320 @ pls )
| ( ( zero_zero @ nat )
= ( number_number_of @ nat @ SV320 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3247]) ).
thf(3651,plain,
! [SV321: $i] :
( ( ( ~ ( number_ring @ SV321 )
| ~ ( linordered_idom @ SV321 ) )
= $true )
| ( ( ! [SY1569: $i,SY1570: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV321 @ ( number_number_of @ SV321 @ SY1569 ) @ ( number_number_of @ SV321 @ SY1570 ) )
| ( ord_less_eq @ int @ SY1569 @ SY1570 ) )
| ~ ( ~ ( ord_less_eq @ int @ SY1569 @ SY1570 )
| ( ord_less_eq @ SV321 @ ( number_number_of @ SV321 @ SY1569 ) @ ( number_number_of @ SV321 @ SY1570 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3248]) ).
thf(3652,plain,
! [SV840: $i,SV322: $i] :
( ( ( ( times_times @ SV322 @ SV840 @ ( zero_zero @ SV322 ) )
= ( zero_zero @ SV322 ) )
= $true )
| ( ( comm_semiring_1 @ SV322 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3249]) ).
thf(3653,plain,
! [SV841: $i,SV323: $i] :
( ( ( ! [SY2071: $i,SY2072: $i,SY2073: $i] :
( ~ ( dvd_dvd @ SV323 @ SY2072 @ SY2073 )
| ~ ( ord_less_eq @ nat @ SV841 @ SY2071 )
| ( dvd_dvd @ SV323 @ ( power_power @ SV323 @ SY2072 @ SV841 ) @ ( power_power @ SV323 @ SY2073 @ SY2071 ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV323 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3250]) ).
thf(3654,plain,
! [SV842: $i,SV325: $i] :
( ( ( ! [SY2074: $i] :
( ~ ( ord_less_eq @ SV325 @ ( power_power @ SV325 @ SV842 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV325 @ SY2074 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ~ ( ord_less_eq @ SV325 @ ( zero_zero @ SV325 ) @ SY2074 )
| ( ord_less_eq @ SV325 @ SV842 @ SY2074 ) ) )
= $true )
| ( ( linordered_semidom @ SV325 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3252]) ).
thf(3655,plain,
! [SV578: $i,SV327: $i] :
( ( ( ( times_times @ int @ SV327 @ SV578 )
= ( one_one @ int ) )
= $false )
| ( ( ( ( ti @ int @ SV327 )
= ( one_one @ int ) )
| ( ( ti @ int @ SV327 )
= ( number_number_of @ int @ min ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3253]) ).
thf(3656,plain,
! [SV328: $i] :
( ( ~ ( ord_less @ int @ min @ ( bit0 @ SV328 ) )
| ( ord_less @ int @ min @ SV328 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3254]) ).
thf(3657,plain,
! [SV328: $i] :
( ( ~ ( ord_less @ int @ min @ SV328 )
| ( ord_less @ int @ min @ ( bit0 @ SV328 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3255]) ).
thf(3658,plain,
! [SV843: $i,SV329: $i] :
( ( ( ! [SY2075: $i,SY2076: $i] :
( ( power_power @ SV329 @ SV843 @ ( plus_plus @ nat @ SY2075 @ SY2076 ) )
= ( times_times @ SV329 @ ( power_power @ SV329 @ SV843 @ SY2075 ) @ ( power_power @ SV329 @ SV843 @ SY2076 ) ) ) )
= $true )
| ( ( monoid_mult @ SV329 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3256]) ).
thf(3659,plain,
! [SV844: $i,SV330: $i] :
( ( ( ! [SY2077: $i,SY2078: $i] :
( ~ ( dvd_dvd @ SV330 @ ( times_times @ SV330 @ SV844 @ SY2077 ) @ SY2078 )
| ( dvd_dvd @ SV330 @ SY2077 @ SY2078 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV330 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3257]) ).
thf(3660,plain,
! [SV331: $i] :
( ( ( zcong @ ( one_one @ int ) @ ( number_number_of @ int @ min ) @ SV331 )
= $false )
| ( ( ord_less @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV331 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3258]) ).
thf(3661,plain,
! [SV845: $i,SV332: $i] :
( ( ( ! [SY2079: $i] : ( dvd_dvd @ SV332 @ SV845 @ ( times_times @ SV332 @ SV845 @ SY2079 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV332 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3259]) ).
thf(3662,plain,
! [SV333: $i] :
( ( ( ~ ( power @ SV333 )
| ~ ( semiring_0 @ SV333 ) )
= $true )
| ( ( ! [SY1587: $i] :
~ ( ~ ( ( ( number_number_of @ nat @ SY1587 )
!= ( zero_zero @ nat ) )
| ( ( power_power @ SV333 @ ( zero_zero @ SV333 ) @ ( number_number_of @ nat @ SY1587 ) )
= ( one_one @ SV333 ) ) )
| ~ ( ~ ( ( ( number_number_of @ nat @ SY1587 )
!= ( zero_zero @ nat ) ) )
| ( ( power_power @ SV333 @ ( zero_zero @ SV333 ) @ ( number_number_of @ nat @ SY1587 ) )
= ( zero_zero @ SV333 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3260]) ).
thf(3663,plain,
! [SV579: $i,SV334: $i,SV702: $i] :
( ( ( ~ ( no_zero_divisors @ SV702 ) )
= $true )
| ( ( ( ti @ SV702 @ ( times_times @ SV702 @ SV334 @ SV579 ) )
= ( times_times @ SV702 @ SV334 @ SV579 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3261]) ).
thf(3664,plain,
! [SV580: $i,SV335: $i,SV703: $i] :
( ( ( ~ ( ab_group_add @ SV703 ) )
= $true )
| ( ( ( plus_plus @ SV703 @ SV335 @ ( ti @ SV703 @ SV580 ) )
= ( plus_plus @ SV703 @ SV335 @ SV580 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3262]) ).
thf(3665,plain,
! [SV581: $i,SV336: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( bit0 @ SV336 ) @ ( bit0 @ SV581 ) )
| ( ord_less_eq @ int @ SV336 @ SV581 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3263]) ).
thf(3666,plain,
! [SV581: $i,SV336: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ SV336 @ SV581 )
| ( ord_less_eq @ int @ ( bit0 @ SV336 ) @ ( bit0 @ SV581 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3263]) ).
thf(3667,plain,
! [SV582: $i,SV337: $i,SV846: $i,SV704: $i] :
( ( ! [SY2080: $i] :
( ~ ( zcong @ SV704 @ SV846 @ SY2080 )
| ~ ( zcong @ SV337 @ SV582 @ SY2080 )
| ( zcong @ ( times_times @ int @ SV704 @ SV337 ) @ ( times_times @ int @ SV846 @ SV582 ) @ SY2080 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3264]) ).
thf(3668,plain,
! [SV583: $i,SV338: $i,SV705: $i] :
( ( ( ~ ( ord_less @ real @ ( zero_zero @ real ) @ SV705 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( ord_less @ real @ ( times_times @ real @ SV338 @ SV705 ) @ ( times_times @ real @ SV583 @ SV705 ) )
| ( ord_less @ real @ SV338 @ SV583 ) )
| ~ ( ~ ( ord_less @ real @ SV338 @ SV583 )
| ( ord_less @ real @ ( times_times @ real @ SV338 @ SV705 ) @ ( times_times @ real @ SV583 @ SV705 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3265]) ).
thf(3669,plain,
! [SV847: $i,SV339: $i] :
( ( ( ( times_times @ SV339 @ SV847 @ ( zero_zero @ SV339 ) )
= ( zero_zero @ SV339 ) )
= $true )
| ( ( mult_zero @ SV339 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3266]) ).
thf(3670,plain,
! [SV706: $i] :
( ( ~ ! [SY1936: $i] :
( ( plus_plus @ int @ ( power_power @ int @ SV706 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ SY1936 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3267]) ).
thf(3671,plain,
! [SV848: $i,SV340: $i] :
( ( ( ! [SY2081: $i,SY2082: $i,SY2083: $i] :
( ( times_times @ SV340 @ ( times_times @ SV340 @ SV848 @ SY2081 ) @ ( times_times @ SV340 @ SY2082 @ SY2083 ) )
= ( times_times @ SV340 @ ( times_times @ SV340 @ SV848 @ SY2082 ) @ ( times_times @ SV340 @ SY2081 @ SY2083 ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV340 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3268]) ).
thf(3672,plain,
! [SV584: $i,SV341: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SV341 ) @ ( bit0 @ SV584 ) )
| ( ord_less @ int @ SV341 @ SV584 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3269]) ).
thf(3673,plain,
! [SV584: $i,SV341: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV341 @ SV584 )
| ( ord_less @ int @ ( bit0 @ SV341 ) @ ( bit0 @ SV584 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3269]) ).
thf(3674,plain,
! [SV849: $i,SV342: $i] :
( ( ( ( times_times @ SV342 @ ( zero_zero @ SV342 ) @ SV849 )
= ( zero_zero @ SV342 ) )
= $true )
| ( ( mult_zero @ SV342 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3270]) ).
thf(3675,plain,
! [SV585: $i,SV343: $i] :
( ( ~ ( ~ ( quadRes @ SV343 @ ( ti @ int @ SV585 ) )
| ( quadRes @ SV343 @ SV585 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3271]) ).
thf(3676,plain,
! [SV585: $i,SV343: $i] :
( ( ~ ( ~ ( quadRes @ SV343 @ SV585 )
| ( quadRes @ SV343 @ ( ti @ int @ SV585 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3271]) ).
thf(3677,plain,
! [SV850: $i,SV344: $i] :
( ( ( ( plus_plus @ SV344 @ SV850 @ SV850 )
= ( times_times @ SV344 @ ( plus_plus @ SV344 @ ( one_one @ SV344 ) @ ( one_one @ SV344 ) ) @ SV850 ) )
= $true )
| ( ( comm_semiring_1 @ SV344 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3272]) ).
thf(3678,plain,
! [SV586: $i,SV345: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ SV345 @ ( minus_minus @ int @ SV586 @ ( one_one @ int ) ) )
| ( ord_less @ int @ SV345 @ SV586 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3273]) ).
thf(3679,plain,
! [SV586: $i,SV345: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV345 @ SV586 )
| ( ord_less_eq @ int @ SV345 @ ( minus_minus @ int @ SV586 @ ( one_one @ int ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3273]) ).
thf(3680,plain,
! [SV851: $i,SV347: $i] :
( ( ( ~ ( ~ ( ( ( power_power @ SV347 @ SV851 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= ( zero_zero @ SV347 ) )
| ( ( ti @ SV347 @ SV851 )
= ( zero_zero @ SV347 ) ) )
| ~ ( ( ( ti @ SV347 @ SV851 )
!= ( zero_zero @ SV347 ) )
| ( ( power_power @ SV347 @ SV851 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SV347 ) ) ) ) )
= $true )
| ( ( ring_11004092258visors @ SV347 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3275]) ).
thf(3681,plain,
! [SV852: $i,SV348: $i] :
( ( ( ! [SY2084: $i] :
( ~ ( ord_less @ SV348 @ ( zero_zero @ SV348 ) @ SY2084 )
| ( ord_less @ SV348 @ ( zero_zero @ SV348 ) @ ( power_power @ SV348 @ SY2084 @ SV852 ) ) ) )
= $true )
| ( ( linordered_semidom @ SV348 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3276]) ).
thf(3682,plain,
! [SV853: $i,SV349: $i] :
( ( ( ! [SY2085: $i,SY2086: $i] :
( ~ ( dvd_dvd @ SV349 @ SY2085 @ SY2086 )
| ( dvd_dvd @ SV349 @ SY2085 @ ( times_times @ SV349 @ SY2086 @ SV853 ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV349 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3277]) ).
thf(3683,plain,
! [SV587: $i,SV350: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( plus_plus @ int @ SV350 @ ( one_one @ int ) ) @ SV587 )
| ( ord_less @ int @ SV350 @ SV587 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3278]) ).
thf(3684,plain,
! [SV587: $i,SV350: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV350 @ SV587 )
| ( ord_less_eq @ int @ ( plus_plus @ int @ SV350 @ ( one_one @ int ) ) @ SV587 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3278]) ).
thf(3685,plain,
! [SV854: $i,SV351: $i] :
( ( ( ! [SY2087: $i] :
( ( ( times_times @ SV351 @ SV854 @ SY2087 )
!= ( zero_zero @ SV351 ) )
| ( ( ti @ SV351 @ SV854 )
= ( zero_zero @ SV351 ) )
| ( ( ti @ SV351 @ SY2087 )
= ( zero_zero @ SV351 ) ) ) )
= $true )
| ( ( no_zero_divisors @ SV351 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3279]) ).
thf(3686,plain,
! [SV855: $i,SV352: $i] :
( ( ( ! [SY2088: $i] :
~ ( ~ ( ( ( plus_plus @ SV352 @ ( power_power @ SV352 @ SV855 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV352 @ SY2088 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV352 ) )
| ~ ( ( ( ti @ SV352 @ SV855 )
!= ( zero_zero @ SV352 ) )
| ( ( ti @ SV352 @ SY2088 )
!= ( zero_zero @ SV352 ) ) ) )
| ~ ( ~ ~ ( ( ( ti @ SV352 @ SV855 )
!= ( zero_zero @ SV352 ) )
| ( ( ti @ SV352 @ SY2088 )
!= ( zero_zero @ SV352 ) ) )
| ( ( plus_plus @ SV352 @ ( power_power @ SV352 @ SV855 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV352 @ SY2088 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV352 ) ) ) ) )
= $true )
| ( ( linordered_idom @ SV352 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3280]) ).
thf(3687,plain,
! [SV856: $i,SV353: $i] :
( ( ( ! [SY2089: $i,SY2090: $i] :
( ~ ( ord_less_eq @ SV353 @ SY2089 @ SY2090 )
| ~ ( ord_less_eq @ SV353 @ ( zero_zero @ SV353 ) @ SY2089 )
| ( ord_less_eq @ SV353 @ ( power_power @ SV353 @ SY2089 @ SV856 ) @ ( power_power @ SV353 @ SY2090 @ SV856 ) ) ) )
= $true )
| ( ( linordered_semidom @ SV353 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3281]) ).
thf(3688,plain,
! [SV857: $i,SV354: $i] :
( ( ( ! [SY2091: $i,SY2092: $i] :
( ( times_times @ SV354 @ SV857 @ ( times_times @ SV354 @ SY2091 @ SY2092 ) )
= ( times_times @ SV354 @ SY2091 @ ( times_times @ SV354 @ SV857 @ SY2092 ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV354 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3282]) ).
thf(3689,plain,
! [SV355: $i] :
( ( ( ~ ( power @ SV355 )
| ~ ( semiring_0 @ SV355 ) )
= $true )
| ( ( ! [SY1626: $i] :
~ ( ~ ( ( SY1626
!= ( zero_zero @ nat ) )
| ( ( power_power @ SV355 @ ( zero_zero @ SV355 ) @ SY1626 )
= ( one_one @ SV355 ) ) )
| ~ ( ~ ( ( SY1626
!= ( zero_zero @ nat ) ) )
| ( ( power_power @ SV355 @ ( zero_zero @ SV355 ) @ SY1626 )
= ( zero_zero @ SV355 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3283]) ).
thf(3690,plain,
! [SV588: $i,SV356: $i,SV707: $i] :
( ( ( ~ ( power @ SV707 ) )
= $true )
| ( ( ( power_power @ SV707 @ ( ti @ SV707 @ SV356 ) @ SV588 )
= ( power_power @ SV707 @ SV356 @ SV588 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3284]) ).
thf(3691,plain,
! [SV589: $i,SV357: $i,SV708: $i] :
( ( ( ~ ( no_zero_divisors @ SV708 ) )
= $true )
| ( ( ( times_times @ SV708 @ SV357 @ ( ti @ SV708 @ SV589 ) )
= ( times_times @ SV708 @ SV357 @ SV589 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3285]) ).
thf(3692,plain,
! [SV858: $i,SV358: $i] :
( ( ( ! [SY2093: $i,SY2094: $i] :
( ~ ( ord_less @ SV358 @ ( one_one @ SV358 ) @ SY2094 )
| ~ ( ~ ( ~ ( ord_less_eq @ SV358 @ ( power_power @ SV358 @ SY2094 @ SV858 ) @ ( power_power @ SV358 @ SY2094 @ SY2093 ) )
| ( ord_less_eq @ nat @ SV858 @ SY2093 ) )
| ~ ( ~ ( ord_less_eq @ nat @ SV858 @ SY2093 )
| ( ord_less_eq @ SV358 @ ( power_power @ SV358 @ SY2094 @ SV858 ) @ ( power_power @ SV358 @ SY2094 @ SY2093 ) ) ) ) ) )
= $true )
| ( ( linordered_semidom @ SV358 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3286]) ).
thf(3693,plain,
! [SV590: $i,SV359: $i,SV709: $i] :
( ( ( ~ ( power @ SV709 ) )
= $true )
| ( ( ( ti @ SV709 @ ( power_power @ SV709 @ SV359 @ SV590 ) )
= ( power_power @ SV709 @ SV359 @ SV590 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3287]) ).
thf(3694,plain,
! [SV591: $i,SV360: $i] :
( ( ~ ( ~ ( zcong @ SV360 @ ( zero_zero @ int ) @ SV591 )
| ( dvd_dvd @ int @ SV591 @ SV360 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3288]) ).
thf(3695,plain,
! [SV360: $i,SV591: $i] :
( ( ~ ( ~ ( dvd_dvd @ int @ SV591 @ SV360 )
| ( zcong @ SV360 @ ( zero_zero @ int ) @ SV591 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3288]) ).
thf(3696,plain,
! [SV361: $i,SV859: $i] :
( ( ( ! [SY2095: $i] :
( ~ ( ord_less_eq @ int @ pls @ SY2095 )
| ~ ( ord_less_eq @ int @ pls @ SV859 )
| ( ( times_times @ SV361 @ ( number_number_of @ SV361 @ SY2095 ) @ ( number_number_of @ SV361 @ SV859 ) )
= ( number_number_of @ SV361 @ ( times_times @ int @ SY2095 @ SV859 ) ) ) ) )
= $true )
| ( ( number_semiring @ SV361 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3289]) ).
thf(3697,plain,
! [SV592: $i,SV362: $i,SV710: $i] :
( ( ( ~ ( ( SV710
!= ( zero_zero @ real ) ) ) )
= $true )
| ( ( ~ ( ~ ( ( ( times_times @ real @ SV362 @ SV710 )
!= ( times_times @ real @ SV592 @ SV710 ) )
| ( SV362 = SV592 ) )
| ~ ( ( SV362 != SV592 )
| ( ( times_times @ real @ SV362 @ SV710 )
= ( times_times @ real @ SV592 @ SV710 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3290]) ).
thf(3698,plain,
( ( ( ( legendre @ ( number_number_of @ int @ min ) @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) )
= ( one_one @ int ) )
= $false )
| ( ( quadRes @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) @ ( number_number_of @ int @ min ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3291]) ).
thf(3699,plain,
! [SV860: $i,SV363: $i] :
( ( ( ! [SY2096: $i] :
~ ( ~ ( ( SY2096
!= ( zero_zero @ nat ) )
| ( ( power_power @ SV363 @ SV860 @ SY2096 )
= ( one_one @ SV363 ) ) )
| ~ ( ~ ( ( SY2096
!= ( zero_zero @ nat ) ) )
| ( ( power_power @ SV363 @ SV860 @ SY2096 )
= ( times_times @ SV363 @ SV860 @ ( power_power @ SV363 @ SV860 @ ( minus_minus @ nat @ SY2096 @ ( one_one @ nat ) ) ) ) ) ) ) )
= $true )
| ( ( power @ SV363 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3292]) ).
thf(3700,plain,
! [SV364: $i,SV711: $i,SV593: $i] :
( ( ( ~ ( dvd_dvd @ nat @ SV593 @ SV711 ) )
= $true )
| ( ( dvd_dvd @ nat @ ( power_power @ nat @ SV593 @ SV364 ) @ ( power_power @ nat @ SV711 @ SV364 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3293]) ).
thf(3701,plain,
! [SV365: $i,SV712: $i,SV594: $i] :
( ( ( ~ ( ord_less @ int @ SV594 @ SV712 ) )
= $true )
| ( ( ord_less @ int @ ( plus_plus @ int @ SV594 @ SV365 ) @ ( plus_plus @ int @ SV712 @ SV365 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3294]) ).
thf(3702,plain,
! [SV366: $i,SV595: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV595 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV595 ) @ ( number_number_of @ nat @ SV366 ) )
= ( number_number_of @ nat @ SV366 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3295]) ).
thf(3703,plain,
! [SV366: $i,SV595: $i] :
( ( ~ ( ~ ~ ( ord_less @ int @ SV595 @ pls )
| ~ ( ~ ( ~ ( ord_less @ int @ SV366 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV595 ) @ ( number_number_of @ nat @ SV366 ) )
= ( number_number_of @ nat @ SV595 ) ) )
| ~ ( ~ ~ ( ord_less @ int @ SV366 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV595 ) @ ( number_number_of @ nat @ SV366 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SV595 @ SV366 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3295]) ).
thf(3704,plain,
! [SV861: $i,SV367: $i] :
( ( ( ! [SY2097: $i,SY2098: $i] :
( ~ ( ord_less_eq @ nat @ SY2097 @ SY2098 )
| ( dvd_dvd @ SV367 @ ( power_power @ SV367 @ SV861 @ SY2097 ) @ ( power_power @ SV367 @ SV861 @ SY2098 ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV367 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3296]) ).
thf(3705,plain,
! [SV368: $i,SV596: $i] :
( ( ~ ( ( SV596
!= ( zero_zero @ nat ) )
| ( ( times_times @ nat @ SV596 @ SV368 )
= ( zero_zero @ nat ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3297]) ).
thf(3706,plain,
! [SV368: $i,SV596: $i] :
( ( ~ ( ~ ( ( SV596
!= ( zero_zero @ nat ) ) )
| ( ( times_times @ nat @ SV596 @ SV368 )
= ( plus_plus @ nat @ SV368 @ ( times_times @ nat @ ( minus_minus @ nat @ SV596 @ ( one_one @ nat ) ) @ SV368 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3297]) ).
thf(3707,plain,
! [SV713: $i,SV597: $i,SV369: $i] :
( ( ( ~ ( dvd_dvd @ int @ SV369 @ ( minus_minus @ int @ SV597 @ SV713 ) ) )
= $true )
| ( ( ~ ( dvd_dvd @ int @ SV369 @ SV713 )
| ( dvd_dvd @ int @ SV369 @ SV597 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3298]) ).
thf(3708,plain,
! [SV598: $i,SV370: $i] :
( ( ~ ( ( ( bit1 @ SV370 )
!= ( bit1 @ SV598 ) )
| ( ( ti @ int @ SV370 )
= ( ti @ int @ SV598 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3299]) ).
thf(3709,plain,
! [SV598: $i,SV370: $i] :
( ( ~ ( ( ( ti @ int @ SV370 )
!= ( ti @ int @ SV598 ) )
| ( ( bit1 @ SV370 )
= ( bit1 @ SV598 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3299]) ).
thf(3710,plain,
! [SV862: $i,SV371: $i] :
( ( ( ! [SY2099: $i,SY2100: $i] :
( ( power_power @ SV371 @ ( times_times @ SV371 @ SV862 @ SY2099 ) @ SY2100 )
= ( times_times @ SV371 @ ( power_power @ SV371 @ SV862 @ SY2100 ) @ ( power_power @ SV371 @ SY2099 @ SY2100 ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV371 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3300]) ).
thf(3711,plain,
! [SV372: $i,SV863: $i,SV714: $i,SV599: $i] :
( ( ~ ( zcong @ SV599 @ SV714 @ SV863 )
| ( zcong @ ( times_times @ int @ SV599 @ SV372 ) @ ( times_times @ int @ SV714 @ SV372 ) @ SV863 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3301]) ).
thf(3712,plain,
! [SV600: $i,SV373: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( bit0 @ SV373 ) @ ( bit0 @ SV600 ) )
| ( ord_less_eq @ int @ SV373 @ SV600 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3302]) ).
thf(3713,plain,
! [SV600: $i,SV373: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ SV373 @ SV600 )
| ( ord_less_eq @ int @ ( bit0 @ SV373 ) @ ( bit0 @ SV600 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3302]) ).
thf(3714,plain,
! [SV601: $i,SV374: $i] :
( ( ~ ( ( ( times_times @ nat @ SV374 @ SV601 )
!= ( one_one @ nat ) )
| ~ ( ( SV374
!= ( one_one @ nat ) )
| ( SV601
!= ( one_one @ nat ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3303]) ).
thf(3715,plain,
! [SV601: $i,SV374: $i] :
( ( ~ ( ~ ~ ( ( SV374
!= ( one_one @ nat ) )
| ( SV601
!= ( one_one @ nat ) ) )
| ( ( times_times @ nat @ SV374 @ SV601 )
= ( one_one @ nat ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3303]) ).
thf(3716,plain,
! [SV864: $i,SV375: $i] :
( ( ( ! [SY2101: $i] :
( ~ ( ord_less @ SV375 @ ( one_one @ SV375 ) @ SY2101 )
| ( ord_less @ SV375 @ ( power_power @ SV375 @ SY2101 @ SV864 ) @ ( times_times @ SV375 @ SY2101 @ ( power_power @ SV375 @ SY2101 @ SV864 ) ) ) ) )
= $true )
| ( ( linordered_semidom @ SV375 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3304]) ).
thf(3717,plain,
! [SV865: $i,SV376: $i] :
( ( ( ! [SY2102: $i] :
( ~ ( ( ( ti @ SV376 @ SY2102 )
!= ( zero_zero @ SV376 ) ) )
| ( ( power_power @ SV376 @ SY2102 @ SV865 )
!= ( zero_zero @ SV376 ) ) ) )
= $true )
| ( ( ring_11004092258visors @ SV376 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3305]) ).
thf(3718,plain,
! [SV602: $i,SV377: $i,SV715: $i] :
( ( ( ~ ( mult_zero @ SV715 ) )
= $true )
| ( ( ( times_times @ SV715 @ SV377 @ ( ti @ SV715 @ SV602 ) )
= ( times_times @ SV715 @ SV377 @ SV602 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3306]) ).
thf(3719,plain,
! [SV866: $i,SV378: $i] :
( ( ( ( number_number_of @ SV378 @ ( bit1 @ SV866 ) )
= ( plus_plus @ SV378 @ ( plus_plus @ SV378 @ ( one_one @ SV378 ) @ ( number_number_of @ SV378 @ SV866 ) ) @ ( number_number_of @ SV378 @ SV866 ) ) )
= $true )
| ( ( number_ring @ SV378 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3307]) ).
thf(3720,plain,
! [SV379: $i,SV603: $i] :
( ( ( ord_less @ real @ ( zero_zero @ real ) @ SV603 )
= $false )
| ( ( ~ ( ord_less @ real @ ( zero_zero @ real ) @ SV379 )
| ( ord_less @ real @ ( zero_zero @ real ) @ ( times_times @ real @ SV603 @ SV379 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3308]) ).
thf(3721,plain,
! [SV867: $i,SV380: $i] :
( ( ( ! [SY2103: $i,SY2104: $i,SY2105: $i] :
( ( times_times @ SV380 @ ( times_times @ SV380 @ SV867 @ SY2103 ) @ ( times_times @ SV380 @ SY2104 @ SY2105 ) )
= ( times_times @ SV380 @ SY2104 @ ( times_times @ SV380 @ ( times_times @ SV380 @ SV867 @ SY2103 ) @ SY2105 ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV380 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3309]) ).
thf(3722,plain,
! [SV868: $i,SV381: $i] :
( ( ( ( times_times @ SV381 @ SV868 @ ( number_number_of @ SV381 @ ( bit1 @ pls ) ) )
= ( ti @ SV381 @ SV868 ) )
= $true )
| ( ( number_ring @ SV381 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3310]) ).
thf(3723,plain,
! [SV604: $i,SV382: $i,SV716: $i] :
( ( ( ~ ( zprime @ SV716 ) )
= $true )
| ( ( ~ ( dvd_dvd @ int @ SV716 @ ( times_times @ int @ SV382 @ SV604 ) )
| ( dvd_dvd @ int @ SV716 @ SV382 )
| ( dvd_dvd @ int @ SV716 @ SV604 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3311]) ).
thf(3724,plain,
! [SV869: $i,SV383: $i] :
( ( ( ! [SY2106: $i,SY2107: $i] :
( ~ ( ord_less @ nat @ SY2106 @ SY2107 )
| ~ ( ord_less @ SV383 @ ( one_one @ SV383 ) @ SV869 )
| ( ord_less @ SV383 @ ( power_power @ SV383 @ SV869 @ SY2106 ) @ ( power_power @ SV383 @ SV869 @ SY2107 ) ) ) )
= $true )
| ( ( linordered_semidom @ SV383 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3312]) ).
thf(3725,plain,
! [SV384: $i,SV717: $i,SV605: $i] :
( ( ( ~ ( ord_less @ int @ SV605 @ SV717 ) )
= $true )
| ( ( ~ ( ord_less @ int @ SV384 @ SV717 )
| ( ord_less_eq @ int @ SV605 @ SV384 )
| ( ord_less_eq @ int @ SV384 @ SV605 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3313]) ).
thf(3726,plain,
! [SV606: $i,SV385: $i,SV870: $i,SV718: $i] :
( ( ~ ( ord_less @ int @ SV718 @ SV870 )
| ~ ( ord_less_eq @ int @ SV385 @ SV606 )
| ( ord_less @ int @ ( plus_plus @ int @ SV718 @ SV385 ) @ ( plus_plus @ int @ SV870 @ SV606 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3314]) ).
thf(3727,plain,
! [SV386: $i] :
( ( ( ~ ( number @ SV386 )
| ~ ( ring @ SV386 ) )
= $true )
| ( ( ! [SY1686: $i,SY1687: $i,SY1688: $i] :
( ( times_times @ SV386 @ ( minus_minus @ SV386 @ SY1686 @ SY1687 ) @ ( number_number_of @ SV386 @ SY1688 ) )
= ( minus_minus @ SV386 @ ( times_times @ SV386 @ SY1686 @ ( number_number_of @ SV386 @ SY1688 ) ) @ ( times_times @ SV386 @ SY1687 @ ( number_number_of @ SV386 @ SY1688 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3315]) ).
thf(3728,plain,
! [SV387: $i,SV607: $i] :
( ( ( ord_less @ int @ ( zero_zero @ int ) @ SV607 )
= $false )
| ( ( ~ ( ord_less @ int @ ( zero_zero @ int ) @ ( times_times @ int @ SV607 @ SV387 ) )
| ( ord_less @ int @ ( zero_zero @ int ) @ SV387 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3316]) ).
thf(3729,plain,
! [SV388: $i,SV608: $i] :
( ( ( ord_less @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV608 )
= $false )
| ( ( ~ ( zcong @ SV388 @ ( number_number_of @ int @ min ) @ SV608 )
| ~ ( zcong @ SV388 @ ( one_one @ int ) @ SV608 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3317]) ).
thf(3730,plain,
! [SV389: $i,SV609: $i] :
( ( ( ord_less @ int @ ( zero_zero @ int ) @ SV609 )
= $false )
| ( ( ~ ( ord_less @ int @ SV609 @ SV389 )
| ~ ( zcong @ SV609 @ ( zero_zero @ int ) @ SV389 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3318]) ).
thf(3731,plain,
! [SV390: $i,SV610: $i] :
( ( ~ ( ( SV610
!= ( zero_zero @ nat ) )
| ( ( power_power @ nat @ SV390 @ SV610 )
= ( one_one @ nat ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3319]) ).
thf(3732,plain,
! [SV390: $i,SV610: $i] :
( ( ~ ( ~ ( ( SV610
!= ( zero_zero @ nat ) ) )
| ( ( power_power @ nat @ SV390 @ SV610 )
= ( times_times @ nat @ SV390 @ ( power_power @ nat @ SV390 @ ( minus_minus @ nat @ SV610 @ ( one_one @ nat ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3319]) ).
thf(3733,plain,
! [SV611: $i,SV391: $i,SV719: $i] :
( ( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ SV719 ) )
= $true )
| ( ( ~ ( dvd_dvd @ int @ SV391 @ SV611 )
| ( dvd_dvd @ int @ SV391 @ ( power_power @ int @ SV611 @ SV719 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3320]) ).
thf(3734,plain,
! [SV612: $i,SV392: $i] :
( ( ~ ( ~ ( ord_less @ nat @ ( number_number_of @ nat @ SV392 ) @ ( number_number_of @ nat @ SV612 ) )
| ~ ( ~ ( ~ ( ord_less @ int @ SV392 @ SV612 )
| ( ord_less @ int @ pls @ SV612 ) )
| ~ ( ord_less @ int @ SV392 @ SV612 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3321]) ).
thf(3735,plain,
! [SV612: $i,SV392: $i] :
( ( ~ ( ~ ~ ( ~ ( ~ ( ord_less @ int @ SV392 @ SV612 )
| ( ord_less @ int @ pls @ SV612 ) )
| ~ ( ord_less @ int @ SV392 @ SV612 ) )
| ( ord_less @ nat @ ( number_number_of @ nat @ SV392 ) @ ( number_number_of @ nat @ SV612 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3321]) ).
thf(3736,plain,
! [SV871: $i,SV393: $i] :
( ( ( ! [SY2108: $i] :
( ( power_power @ SV393 @ ( minus_minus @ SV393 @ SV871 @ SY2108 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( minus_minus @ SV393 @ ( plus_plus @ SV393 @ ( power_power @ SV393 @ SV871 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV393 @ SY2108 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times @ SV393 @ ( times_times @ SV393 @ ( number_number_of @ SV393 @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV871 ) @ SY2108 ) ) ) )
= $true )
| ( ( number_ring @ SV393 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3322]) ).
thf(3737,plain,
! [SV394: $i] :
( ( ~ ( zprime @ ( ti @ int @ SV394 ) )
| ( zprime @ SV394 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3323]) ).
thf(3738,plain,
! [SV394: $i] :
( ( ~ ( zprime @ SV394 )
| ( zprime @ ( ti @ int @ SV394 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3324]) ).
thf(3739,plain,
! [SV395: $i,SV872: $i,SV720: $i,SV613: $i] :
( ( ~ ( zcong @ ( power_power @ int @ SV613 @ SV720 ) @ ( one_one @ int ) @ SV872 )
| ( zcong @ ( power_power @ int @ SV613 @ ( times_times @ nat @ SV720 @ SV395 ) ) @ ( one_one @ int ) @ SV872 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3325]) ).
thf(3740,plain,
! [SV614: $i,SV396: $i] :
( ( ~ ( ~ ( zcong @ SV396 @ SV614 @ ( zero_zero @ int ) )
| ( ( ti @ int @ SV396 )
= ( ti @ int @ SV614 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3326]) ).
thf(3741,plain,
! [SV614: $i,SV396: $i] :
( ( ~ ( ( ( ti @ int @ SV396 )
!= ( ti @ int @ SV614 ) )
| ( zcong @ SV396 @ SV614 @ ( zero_zero @ int ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3326]) ).
thf(3742,plain,
! [SV615: $i,SV397: $i] :
( ( ~ ( ( ( plus_plus @ real @ ( times_times @ real @ SV397 @ SV397 ) @ ( times_times @ real @ SV615 @ SV615 ) )
!= ( zero_zero @ real ) )
| ~ ( ( SV397
!= ( zero_zero @ real ) )
| ( SV615
!= ( zero_zero @ real ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3327]) ).
thf(3743,plain,
! [SV615: $i,SV397: $i] :
( ( ~ ( ~ ~ ( ( SV397
!= ( zero_zero @ real ) )
| ( SV615
!= ( zero_zero @ real ) ) )
| ( ( plus_plus @ real @ ( times_times @ real @ SV397 @ SV397 ) @ ( times_times @ real @ SV615 @ SV615 ) )
= ( zero_zero @ real ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3327]) ).
thf(3744,plain,
! [SV398: $i] :
( ( ~ ( ord_less @ int @ ( bit1 @ SV398 ) @ pls )
| ( ord_less @ int @ SV398 @ pls ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3328]) ).
thf(3745,plain,
! [SV398: $i] :
( ( ~ ( ord_less @ int @ SV398 @ pls )
| ( ord_less @ int @ ( bit1 @ SV398 ) @ pls ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3329]) ).
thf(3746,plain,
! [SV873: $i,SV399: $i] :
( ( ( ! [SY2109: $i,SY2110: $i,SY2111: $i] :
( ( plus_plus @ SV399 @ ( times_times @ SV399 @ SV873 @ SY2109 ) @ ( plus_plus @ SV399 @ ( times_times @ SV399 @ SY2110 @ SY2109 ) @ SY2111 ) )
= ( plus_plus @ SV399 @ ( times_times @ SV399 @ ( plus_plus @ SV399 @ SV873 @ SY2110 ) @ SY2109 ) @ SY2111 ) ) )
= $true )
| ( ( semiring @ SV399 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3330]) ).
thf(3747,plain,
! [SV874: $i,SV400: $i] :
( ( ( ( power_power @ SV400 @ SV874 @ ( one_one @ nat ) )
= ( ti @ SV400 @ SV874 ) )
= $true )
| ( ( monoid_mult @ SV400 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3331]) ).
thf(3748,plain,
( ( ( ~ ~ ! [SY2112: $i] :
( ( plus_plus @ int @ ( power_power @ int @ sK4_SX0 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ SY2112 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ) )
= $false )
| ( ( t
= ( one_one @ int ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3332]) ).
thf(3749,plain,
! [SV616: $i,SV401: $i,SV721: $i] :
( ( ( ~ ( semiring @ SV721 ) )
= $true )
| ( ( ( times_times @ SV721 @ ( ti @ SV721 @ SV401 ) @ SV616 )
= ( times_times @ SV721 @ SV401 @ SV616 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3333]) ).
thf(3750,plain,
! [SV875: $i,SV402: $i] :
( ( ( ( times_times @ SV402 @ ( one_one @ SV402 ) @ SV875 )
= ( ti @ SV402 @ SV875 ) )
= $true )
| ( ( comm_semiring_1 @ SV402 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3334]) ).
thf(3751,plain,
! [SV876: $i,SV403: $i] :
( ( ( ! [SY2113: $i,SY2114: $i] :
( ( times_times @ SV403 @ SV876 @ ( plus_plus @ SV403 @ SY2113 @ SY2114 ) )
= ( plus_plus @ SV403 @ ( times_times @ SV403 @ SV876 @ SY2113 ) @ ( times_times @ SV403 @ SV876 @ SY2114 ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV403 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3335]) ).
thf(3752,plain,
! [SV877: $i,SV404: $i] :
( ( ( ( times_times @ SV404 @ ( number_number_of @ SV404 @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV877 )
= ( plus_plus @ SV404 @ SV877 @ SV877 ) )
= $true )
| ( ( number_ring @ SV404 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3336]) ).
thf(3753,plain,
! [SV722: $i,SV617: $i,SV405: $i] :
( ( ~ ( ~ ( zcong @ SV405 @ SV617 @ SV722 )
| ~ ! [SY1940: $i] :
( ( ti @ int @ SV617 )
!= ( plus_plus @ int @ SV405 @ ( times_times @ int @ SV722 @ SY1940 ) ) ) )
| ~ ( ~ ~ ! [SY1941: $i] :
( ( ti @ int @ SV617 )
!= ( plus_plus @ int @ SV405 @ ( times_times @ int @ SV722 @ SY1941 ) ) )
| ( zcong @ SV405 @ SV617 @ SV722 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3337]) ).
thf(3754,plain,
! [SV723: $i,SV618: $i,SV406: $i] :
( ( ( ( minus_minus @ int @ SV406 @ SV618 )
!= ( ti @ int @ SV723 ) )
= $true )
| ( ( ( ti @ int @ SV406 )
= ( plus_plus @ int @ SV723 @ SV618 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3338]) ).
thf(3755,plain,
! [SV407: $i] :
( ( ( ~ ( ( ( ti @ int @ SV407 )
!= ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true )
| ( ( ~ ( ( ( ti @ int @ SV407 )
!= ( number_number_of @ int @ ( bit1 @ ( bit1 @ pls ) ) ) ) )
| ( ord_less_eq @ int @ ( number_number_of @ int @ ( bit1 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SV407 ) )
= $true )
| ( ( zprime @ SV407 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3339]) ).
thf(3756,plain,
! [SV619: $i,SV408: $i,SV724: $i] :
( ( ( ~ ( semiring @ SV724 ) )
= $true )
| ( ( ( ti @ SV724 @ ( plus_plus @ SV724 @ SV408 @ SV619 ) )
= ( plus_plus @ SV724 @ SV408 @ SV619 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3340]) ).
thf(3757,plain,
! [SV725: $i,SV620: $i,SV410: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( times_times @ int @ SV410 @ SV620 ) @ SV725 ) ) )
= $true )
| ( ( ~ ( ord_less @ int @ SV725 @ SV410 )
| ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV410 )
| ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV620 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3342]) ).
thf(3758,plain,
! [SV878: $i,SV411: $i] :
( ( ( ~ ( ord_less @ SV411 @ ( power_power @ SV411 @ SV878 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( zero_zero @ SV411 ) ) )
= $true )
| ( ( linordered_idom @ SV411 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3343]) ).
thf(3759,plain,
! [SV879: $i,SV412: $i] :
( ( ( ! [SY2115: $i,SY2116: $i] :
( ( power_power @ SV412 @ SV879 @ ( times_times @ nat @ SY2115 @ SY2116 ) )
= ( power_power @ SV412 @ ( power_power @ SV412 @ SV879 @ SY2115 ) @ SY2116 ) ) )
= $true )
| ( ( monoid_mult @ SV412 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3344]) ).
thf(3760,plain,
! [SV621: $i,SV413: $i] :
( ( ~ ( ( ( times_times @ int @ SV413 @ SV621 )
!= ( one_one @ int ) )
| ~ ( ( ( ti @ int @ SV413 )
!= ( one_one @ int ) )
| ( ( ti @ int @ SV621 )
!= ( one_one @ int ) ) )
| ~ ( ( ( ti @ int @ SV413 )
!= ( number_number_of @ int @ min ) )
| ( ( ti @ int @ SV621 )
!= ( number_number_of @ int @ min ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3345]) ).
thf(3761,plain,
! [SV621: $i,SV413: $i] :
( ( ~ ( ~ ( ~ ( ( ( ti @ int @ SV413 )
!= ( one_one @ int ) )
| ( ( ti @ int @ SV621 )
!= ( one_one @ int ) ) )
| ~ ( ( ( ti @ int @ SV413 )
!= ( number_number_of @ int @ min ) )
| ( ( ti @ int @ SV621 )
!= ( number_number_of @ int @ min ) ) ) )
| ( ( times_times @ int @ SV413 @ SV621 )
= ( one_one @ int ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3345]) ).
thf(3762,plain,
! [SV880: $i,SV414: $i] :
( ( ( ! [SY2117: $i] :
( ( plus_plus @ SV414 @ SV880 @ SY2117 )
= ( plus_plus @ SV414 @ SY2117 @ SV880 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV414 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3346]) ).
thf(3763,plain,
! [SV416: $i] :
( ( ( ~ ( monoid_mult @ SV416 )
| ~ ( number @ SV416 ) )
= $true )
| ( ( ! [SY1732: $i] :
( ( power_power @ SV416 @ ( number_number_of @ SV416 @ SY1732 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times @ SV416 @ ( number_number_of @ SV416 @ SY1732 ) @ ( number_number_of @ SV416 @ SY1732 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3348]) ).
thf(3764,plain,
! [SV881: $i,SV417: $i] :
( ( ( ! [SY2118: $i] :
( ~ ( ord_less_eq @ SV417 @ SY2118 @ ( zero_zero @ SV417 ) )
| ~ ( ord_less_eq @ SV417 @ ( zero_zero @ SV417 ) @ SV881 )
| ( ord_less_eq @ SV417 @ ( times_times @ SV417 @ SY2118 @ SV881 ) @ ( zero_zero @ SV417 ) ) ) )
= $true )
| ( ( ordere453448008miring @ SV417 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3349]) ).
thf(3765,plain,
! [SV622: $i,SV418: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SV418 ) @ ( bit0 @ SV622 ) )
| ( ord_less @ int @ SV418 @ SV622 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3350]) ).
thf(3766,plain,
! [SV622: $i,SV418: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV418 @ SV622 )
| ( ord_less_eq @ int @ ( bit1 @ SV418 ) @ ( bit0 @ SV622 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3350]) ).
thf(3767,plain,
! [SV419: $i,SV623: $i] :
( ( ( ord_less @ int @ ( zero_zero @ int ) @ SV623 )
= $false )
| ( ( ~ ( ~ ( ( ( times_times @ int @ SV623 @ SV419 )
!= ( one_one @ int ) )
| ~ ( ( ( ti @ int @ SV623 )
!= ( one_one @ int ) )
| ( ( ti @ int @ SV419 )
!= ( one_one @ int ) ) ) )
| ~ ( ~ ~ ( ( ( ti @ int @ SV623 )
!= ( one_one @ int ) )
| ( ( ti @ int @ SV419 )
!= ( one_one @ int ) ) )
| ( ( times_times @ int @ SV623 @ SV419 )
= ( one_one @ int ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3351]) ).
thf(3768,plain,
! [SV624: $i,SV420: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( bit0 @ SV420 ) @ ( bit1 @ SV624 ) )
| ( ord_less_eq @ int @ SV420 @ SV624 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3352]) ).
thf(3769,plain,
! [SV624: $i,SV420: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ SV420 @ SV624 )
| ( ord_less_eq @ int @ ( bit0 @ SV420 ) @ ( bit1 @ SV624 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3352]) ).
thf(3770,plain,
! [SV421: $i,SV625: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV625 @ pls )
| ( ( times_times @ nat @ ( number_number_of @ nat @ SV625 ) @ ( number_number_of @ nat @ SV421 ) )
= ( zero_zero @ nat ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3353]) ).
thf(3771,plain,
! [SV421: $i,SV625: $i] :
( ( ~ ( ~ ~ ( ord_less @ int @ SV625 @ pls )
| ( ( times_times @ nat @ ( number_number_of @ nat @ SV625 ) @ ( number_number_of @ nat @ SV421 ) )
= ( number_number_of @ nat @ ( times_times @ int @ SV625 @ SV421 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3353]) ).
thf(3772,plain,
! [SV882: $i,SV726: $i,SV626: $i,SV422: $i] :
( ( ! [SY2119: $i,SY2120: $i] :
( ( ( plus_plus @ int @ ( times_times @ int @ SV422 @ SV626 ) @ SV726 )
!= ( plus_plus @ int @ ( times_times @ int @ SV882 @ SY2119 ) @ SY2120 ) )
| ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( times_times @ int @ SV882 @ SY2119 ) @ SY2120 ) )
| ~ ( ord_less @ int @ SY2120 @ SV882 )
| ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV726 )
| ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV882 )
| ~ ( ord_less_eq @ int @ SV882 @ SV422 )
| ( ord_less_eq @ int @ SV626 @ SY2119 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3354]) ).
thf(3773,plain,
! [SV423: $i] :
( ( ~ ~ ( ord_less @ real @ ( zero_zero @ real ) @ ( times_times @ real @ SV423 @ SV423 ) )
| ( SV423
= ( zero_zero @ real ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3355]) ).
thf(3774,plain,
! [SV423: $i] :
( ( ( SV423
!= ( zero_zero @ real ) )
| ~ ( ord_less @ real @ ( zero_zero @ real ) @ ( times_times @ real @ SV423 @ SV423 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3356]) ).
thf(3775,plain,
! [SV627: $i,SV424: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SV424 ) @ ( bit1 @ SV627 ) )
| ( ord_less @ int @ SV424 @ SV627 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3357]) ).
thf(3776,plain,
! [SV627: $i,SV424: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV424 @ SV627 )
| ( ord_less @ int @ ( bit1 @ SV424 ) @ ( bit1 @ SV627 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3357]) ).
thf(3777,plain,
! [SV883: $i,SV425: $i] :
( ( ( dvd_dvd @ SV425 @ ( one_one @ SV425 ) @ SV883 )
= $true )
| ( ( comm_semiring_1 @ SV425 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3358]) ).
thf(3778,plain,
! [SV628: $i,SV426: $i,SV727: $i] :
( ( ( ~ ( mult_zero @ SV727 ) )
= $true )
| ( ( ( ti @ SV727 @ ( times_times @ SV727 @ SV426 @ SV628 ) )
= ( times_times @ SV727 @ SV426 @ SV628 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3359]) ).
thf(3779,plain,
! [SV728: $i,SV629: $i,SV427: $i] :
( ( ~ ( ~ ( zcong @ ( ti @ int @ SV427 ) @ SV629 @ SV728 )
| ( zcong @ SV427 @ SV629 @ SV728 ) )
| ~ ( ~ ( zcong @ SV427 @ SV629 @ SV728 )
| ( zcong @ ( ti @ int @ SV427 ) @ SV629 @ SV728 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3360]) ).
thf(3780,plain,
! [SV630: $i,SV428: $i] :
( ( ~ ( ~ ( zcong @ SV428 @ ( zero_zero @ int ) @ SV630 )
| ( dvd_dvd @ int @ SV630 @ SV428 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3361]) ).
thf(3781,plain,
! [SV428: $i,SV630: $i] :
( ( ~ ( ~ ( dvd_dvd @ int @ SV630 @ SV428 )
| ( zcong @ SV428 @ ( zero_zero @ int ) @ SV630 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3361]) ).
thf(3782,plain,
! [SV631: $i,SV429: $i] :
( ( ~ ( ( ( power_power @ nat @ SV429 @ SV631 )
!= ( one_one @ nat ) )
| ( SV429
= ( one_one @ nat ) )
| ( SV631
= ( zero_zero @ nat ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3362]) ).
thf(3783,plain,
! [SV631: $i,SV429: $i] :
( ( ~ ( ~ ( ( SV429
= ( one_one @ nat ) )
| ( SV631
= ( zero_zero @ nat ) ) )
| ( ( power_power @ nat @ SV429 @ SV631 )
= ( one_one @ nat ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3362]) ).
thf(3784,plain,
! [SV430: $i,SV884: $i,SV729: $i,SV632: $i] :
( ( ~ ( zcong @ SV632 @ SV729 @ SV884 )
| ( zcong @ ( plus_plus @ int @ SV632 @ SV430 ) @ ( plus_plus @ int @ SV729 @ SV430 ) @ SV884 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3363]) ).
thf(3785,plain,
! [SV885: $i,SV431: $i] :
( ( ( ! [SY2121: $i] : ( ord_less_eq @ SV431 @ ( zero_zero @ SV431 ) @ ( plus_plus @ SV431 @ ( power_power @ SV431 @ SV885 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV431 @ SY2121 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true )
| ( ( linordered_idom @ SV431 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3364]) ).
thf(3786,plain,
! [SV886: $i,SV432: $i] :
( ( ( ( plus_plus @ SV432 @ ( number_number_of @ SV432 @ SV886 ) @ ( one_one @ SV432 ) )
= ( number_number_of @ SV432 @ ( plus_plus @ int @ SV886 @ ( bit1 @ pls ) ) ) )
= $true )
| ( ( number_ring @ SV432 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3365]) ).
thf(3787,plain,
! [SV887: $i,SV433: $i] :
( ( ( ! [SY2122: $i,SY2123: $i] :
( ~ ( ord_less @ nat @ SY2122 @ SY2123 )
| ~ ( ord_less @ SV433 @ ( zero_zero @ SV433 ) @ SV887 )
| ~ ( ord_less @ SV433 @ SV887 @ ( one_one @ SV433 ) )
| ( ord_less @ SV433 @ ( power_power @ SV433 @ SV887 @ SY2123 ) @ ( power_power @ SV433 @ SV887 @ SY2122 ) ) ) )
= $true )
| ( ( linordered_semidom @ SV433 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3366]) ).
thf(3788,plain,
! [SV888: $i,SV434: $i] :
( ( ( ! [SY2124: $i,SY2125: $i,SY2126: $i,SY2127: $i] :
( ~ ( ( ( ti @ SV434 @ SY2127 )
!= ( zero_zero @ SV434 ) ) )
| ~ ~ ( ( ( ti @ SV434 @ SY2125 )
!= ( ti @ SV434 @ SY2126 ) )
| ~ ( ( ( ti @ SV434 @ SV888 )
!= ( ti @ SV434 @ SY2124 ) ) ) )
| ( ( plus_plus @ SV434 @ SY2125 @ ( times_times @ SV434 @ SY2127 @ SV888 ) )
!= ( plus_plus @ SV434 @ SY2126 @ ( times_times @ SV434 @ SY2127 @ SY2124 ) ) ) ) )
= $true )
| ( ( semiri456707255roduct @ SV434 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3367]) ).
thf(3789,plain,
! [SV889: $i,SV730: $i,SV643: $i,SV472: $i,SV63: $i] :
( ( ! [SY2128: $i,SY2129: $i] :
( ( plus_plus @ int @ ( times_times @ int @ ( minus_minus @ int @ SV63 @ ( times_times @ int @ SV472 @ SV643 ) ) @ SV730 ) @ ( times_times @ int @ ( minus_minus @ int @ SV889 @ ( times_times @ int @ SV472 @ SY2128 ) ) @ SY2129 ) )
= ( minus_minus @ int @ ( plus_plus @ int @ ( times_times @ int @ SV63 @ SV730 ) @ ( times_times @ int @ SV889 @ SY2129 ) ) @ ( times_times @ int @ SV472 @ ( plus_plus @ int @ ( times_times @ int @ SV643 @ SV730 ) @ ( times_times @ int @ SY2128 @ SY2129 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3369]) ).
thf(3790,plain,
! [SV481: $i,SV79: $i,SV890: $i,SV732: $i,SV647: $i] :
( ( ~ ( zcong @ SV647 @ SV732 @ SV890 )
| ~ ( ~ ( ~ ( zcong @ SV79 @ ( times_times @ int @ SV647 @ SV481 ) @ SV890 )
| ( zcong @ SV79 @ ( times_times @ int @ SV732 @ SV481 ) @ SV890 ) )
| ~ ( ~ ( zcong @ SV79 @ ( times_times @ int @ SV732 @ SV481 ) @ SV890 )
| ( zcong @ SV79 @ ( times_times @ int @ SV647 @ SV481 ) @ SV890 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3371]) ).
thf(3791,plain,
! [SV482: $i,SV80: $i] :
( ( ~ ( ord_less @ int @ SV80 @ ( plus_plus @ int @ SV482 @ ( one_one @ int ) ) )
| ( ord_less @ int @ SV80 @ SV482 )
| ( ( ti @ int @ SV80 )
= ( ti @ int @ SV482 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3372]) ).
thf(3792,plain,
! [SV482: $i,SV80: $i] :
( ( ~ ( ( ord_less @ int @ SV80 @ SV482 )
| ( ( ti @ int @ SV80 )
= ( ti @ int @ SV482 ) ) )
| ( ord_less @ int @ SV80 @ ( plus_plus @ int @ SV482 @ ( one_one @ int ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3373]) ).
thf(3793,plain,
! [SV483: $i,SV81: $i,SV648: $i] :
( ( ( semiring @ SV648 )
= $false )
| ( ( ( plus_plus @ SV648 @ SV81 @ ( ti @ SV648 @ SV483 ) )
= ( plus_plus @ SV648 @ SV81 @ SV483 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3374]) ).
thf(3794,plain,
! [SV733: $i,SV891: $i,SV82: $i] :
( ( ( ~ ( ord_less_eq @ SV82 @ ( zero_zero @ SV82 ) @ SV891 )
| ~ ( ord_less_eq @ SV82 @ SV733 @ ( zero_zero @ SV82 ) )
| ( ord_less_eq @ SV82 @ ( times_times @ SV82 @ SV891 @ SV733 ) @ ( zero_zero @ SV82 ) ) )
= $true )
| ( ( ordere453448008miring @ SV82 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3375]) ).
thf(3795,plain,
! [SV892: $i,SV734: $i,SV83: $i] :
( ( ( ( times_times @ SV83 @ ( power_power @ SV83 @ SV734 @ SV892 ) @ SV734 )
= ( times_times @ SV83 @ SV734 @ ( power_power @ SV83 @ SV734 @ SV892 ) ) )
= $true )
| ( ( monoid_mult @ SV83 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3376]) ).
thf(3796,plain,
! [SV893: $i,SV735: $i,SV84: $i] :
( ( ( ! [SY2130: $i] :
( ( plus_plus @ SV84 @ ( plus_plus @ SV84 @ SV735 @ SV893 ) @ SY2130 )
= ( plus_plus @ SV84 @ SV735 @ ( plus_plus @ SV84 @ SV893 @ SY2130 ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV84 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3377]) ).
thf(3797,plain,
! [SV737: $i,SV894: $i,SV87: $i] :
( ( ( ~ ( ord_less_eq @ SV87 @ ( zero_zero @ SV87 ) @ SV894 )
| ~ ( ord_less_eq @ SV87 @ SV737 @ ( zero_zero @ SV87 ) )
| ( ord_less_eq @ SV87 @ ( times_times @ SV87 @ SV737 @ SV894 ) @ ( zero_zero @ SV87 ) ) )
= $true )
| ( ( ordere453448008miring @ SV87 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3379]) ).
thf(3798,plain,
! [SV895: $i,SV738: $i,SV88: $i] :
( ( ( ~ ( ord_less @ SV88 @ ( plus_plus @ SV88 @ ( power_power @ SV88 @ SV738 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV88 @ SV895 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( zero_zero @ SV88 ) ) )
= $true )
| ( ( linordered_idom @ SV88 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3380]) ).
thf(3799,plain,
! [SV484: $i,SV89: $i,SV649: $i] :
( ( ( no_zero_divisors @ SV649 )
= $false )
| ( ( ( times_times @ SV649 @ ( ti @ SV649 @ SV89 ) @ SV484 )
= ( times_times @ SV649 @ SV89 @ SV484 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3381]) ).
thf(3800,plain,
! [SV739: $i,SV896: $i,SV90: $i] :
( ( ( ~ ( ( ( ti @ SV90 @ SV896 )
!= ( zero_zero @ SV90 ) ) )
| ~ ( ( ( ti @ SV90 @ SV739 )
!= ( zero_zero @ SV90 ) ) )
| ( ( times_times @ SV90 @ SV896 @ SV739 )
!= ( zero_zero @ SV90 ) ) )
= $true )
| ( ( no_zero_divisors @ SV90 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3382]) ).
thf(3801,plain,
! [SV91: $i] :
( ( ( ~ ( ord_less_eq @ int @ min @ ( bit1 @ SV91 ) ) )
= $true )
| ( ( ord_less_eq @ int @ min @ SV91 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3383]) ).
thf(3802,plain,
! [SV91: $i] :
( ( ( ~ ( ord_less_eq @ int @ min @ SV91 ) )
= $true )
| ( ( ord_less_eq @ int @ min @ ( bit1 @ SV91 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3384]) ).
thf(3803,plain,
! [SV92: $i,SV485: $i] :
( ( ( ord_less_eq @ int @ SV485 @ ( zero_zero @ int ) )
= $true )
| ( ( ord_less_eq @ int @ SV92 @ SV485 )
= $true )
| ( ( dvd_dvd @ int @ SV92 @ SV485 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3385]) ).
thf(3804,plain,
! [SV93: $i] :
( ( ( min
!= ( bit1 @ SV93 ) )
= $true )
| ( ( min
= ( ti @ int @ SV93 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3386]) ).
thf(3805,plain,
! [SV93: $i] :
( ( ( min
!= ( ti @ int @ SV93 ) )
= $true )
| ( ( min
= ( bit1 @ SV93 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3387]) ).
thf(3806,plain,
! [SV897: $i,SV740: $i,SV94: $i] :
( ( ( ! [SY2131: $i] :
( ( times_times @ SV94 @ SV740 @ ( times_times @ SV94 @ SV897 @ SY2131 ) )
= ( times_times @ SV94 @ ( times_times @ SV94 @ SV740 @ SV897 ) @ SY2131 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV94 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3388]) ).
thf(3807,plain,
! [SV898: $i,SV741: $i,SV95: $i] :
( ( ( ! [SY2132: $i,SY2133: $i] :
( ( times_times @ SV95 @ ( times_times @ SV95 @ SV741 @ SV898 ) @ ( times_times @ SV95 @ SY2132 @ SY2133 ) )
= ( times_times @ SV95 @ SV741 @ ( times_times @ SV95 @ SV898 @ ( times_times @ SV95 @ SY2132 @ SY2133 ) ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV95 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3389]) ).
thf(3808,plain,
! [SV486: $i,SV96: $i] :
( ( ~ ( ord_less @ int @ ( number_number_of @ int @ SV96 ) @ ( number_number_of @ int @ SV486 ) )
| ( ord_less @ int @ SV96 @ SV486 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3390]) ).
thf(3809,plain,
! [SV486: $i,SV96: $i] :
( ( ~ ( ord_less @ int @ SV96 @ SV486 )
| ( ord_less @ int @ ( number_number_of @ int @ SV96 ) @ ( number_number_of @ int @ SV486 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3391]) ).
thf(3810,plain,
! [SV97: $i,SV487: $i] :
( ( ( SV487
= ( zero_zero @ nat ) )
= $true )
| ( ( ord_less_eq @ nat @ SV97 @ SV487 )
= $true )
| ( ( dvd_dvd @ nat @ SV97 @ SV487 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3392]) ).
thf(3811,plain,
! [SV488: $i,SV98: $i,SV650: $i] :
( ( ( ab_group_add @ SV650 )
= $false )
| ( ( ( ti @ SV650 @ ( plus_plus @ SV650 @ SV98 @ SV488 ) )
= ( plus_plus @ SV650 @ SV98 @ SV488 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3393]) ).
thf(3812,plain,
! [SV899: $i,SV742: $i,SV99: $i] :
( ( ( ! [SY2134: $i] :
( ( plus_plus @ SV99 @ SV742 @ ( plus_plus @ SV99 @ SV899 @ SY2134 ) )
= ( plus_plus @ SV99 @ SV899 @ ( plus_plus @ SV99 @ SV742 @ SY2134 ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV99 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3394]) ).
thf(3813,plain,
! [SV100: $i,SV651: $i,SV489: $i] :
( ( ( ord_less_eq @ int @ SV489 @ SV651 )
= $false )
| ( ( ord_less_eq @ int @ ( plus_plus @ int @ SV100 @ SV489 ) @ ( plus_plus @ int @ SV100 @ SV651 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3395]) ).
thf(3814,plain,
! [SV101: $i,SV652: $i,SV490: $i] :
( ( ( ~ ( zcong @ SV490 @ ( zero_zero @ int ) @ SV652 ) )
= $false )
| ( ( ~ ( zcong @ ( power_power @ int @ SV101 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SV490 @ SV652 )
| ~ ( dvd_dvd @ int @ SV652 @ SV101 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3396]) ).
thf(3815,plain,
! [SV743: $i,SV900: $i,SV102: $i] :
( ( ( ~ ( ord_less @ SV102 @ ( zero_zero @ SV102 ) @ SV900 )
| ~ ( ord_less @ SV102 @ SV900 @ ( one_one @ SV102 ) )
| ( ord_less @ SV102 @ ( times_times @ SV102 @ SV900 @ ( power_power @ SV102 @ SV900 @ SV743 ) ) @ ( power_power @ SV102 @ SV900 @ SV743 ) ) )
= $true )
| ( ( linordered_semidom @ SV102 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3397]) ).
thf(3816,plain,
! [SV491: $i,SV103: $i] :
( ( ~ ( quadRes @ ( ti @ int @ SV103 ) @ SV491 )
| ( quadRes @ SV103 @ SV491 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3398]) ).
thf(3817,plain,
! [SV491: $i,SV103: $i] :
( ( ~ ( quadRes @ SV103 @ SV491 )
| ( quadRes @ ( ti @ int @ SV103 ) @ SV491 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3399]) ).
thf(3818,plain,
! [SV492: $i,SV104: $i,SV653: $i] :
( ( ( semiring @ SV653 )
= $false )
| ( ( ( times_times @ SV653 @ SV104 @ ( ti @ SV653 @ SV492 ) )
= ( times_times @ SV653 @ SV104 @ SV492 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3400]) ).
thf(3819,plain,
! [SV106: $i] :
( ( ( ( bit1 @ SV106 )
!= min )
= $true )
| ( ( ( ti @ int @ SV106 )
= min )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3401]) ).
thf(3820,plain,
! [SV106: $i] :
( ( ( ( ti @ int @ SV106 )
!= min )
= $true )
| ( ( ( bit1 @ SV106 )
= min )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3402]) ).
thf(3821,plain,
! [SV493: $i,SV107: $i,SV654: $i] :
( ( ( power @ SV654 )
= $false )
| ( ( ( times_times @ SV654 @ SV107 @ ( ti @ SV654 @ SV493 ) )
= ( times_times @ SV654 @ SV107 @ SV493 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3403]) ).
thf(3822,plain,
! [SV108: $i,SV494: $i,SV901: $i,SV744: $i,SV655: $i] :
( ( ~ ( zcong @ SV655 @ SV744 @ SV901 )
| ( ( ti @ int @ SV744 )
!= ( ti @ int @ SV494 ) )
| ~ ( zcong @ SV494 @ SV108 @ SV901 )
| ( zcong @ SV655 @ SV108 @ SV901 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3404]) ).
thf(3823,plain,
! [SV656: $i,SV495: $i,SV109: $i] :
( ( ( dvd_dvd @ int @ ( times_times @ int @ SV109 @ SV495 ) @ ( times_times @ int @ SV109 @ SV656 ) )
= $false )
| ( ( ~ ( ( ( ti @ int @ SV109 )
!= ( zero_zero @ int ) ) )
| ( dvd_dvd @ int @ SV495 @ SV656 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3405]) ).
thf(3824,plain,
! [SV496: $i,SV111: $i] :
( ( ( ~ ( twoSqu420862341sum2sq @ SV111 ) )
= $true )
| ( ( twoSqu420862341sum2sq @ ( times_times @ int @ SV496 @ SV111 ) )
= $true )
| ( ( twoSqu420862341sum2sq @ SV496 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3407]) ).
thf(3825,plain,
! [SV112: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( bit0 @ SV112 ) @ pls ) )
= $true )
| ( ( ord_less_eq @ int @ SV112 @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3408]) ).
thf(3826,plain,
! [SV112: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV112 @ pls ) )
= $true )
| ( ( ord_less_eq @ int @ ( bit0 @ SV112 ) @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3409]) ).
thf(3827,plain,
! [SV498: $i,SV115: $i] :
( ( ~ ( ord_less @ int @ ( bit1 @ SV115 ) @ ( bit0 @ SV498 ) )
| ( ord_less @ int @ SV115 @ SV498 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3411]) ).
thf(3828,plain,
! [SV498: $i,SV115: $i] :
( ( ~ ( ord_less @ int @ SV115 @ SV498 )
| ( ord_less @ int @ ( bit1 @ SV115 ) @ ( bit0 @ SV498 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3412]) ).
thf(3829,plain,
! [SV746: $i,SV117: $i,SV902: $i] :
( ( ( ! [SY2135: $i] :
( ~ ( ord_less_eq @ nat @ SV902 @ SY2135 )
| ~ ( ord_less_eq @ SV117 @ ( zero_zero @ SV117 ) @ SV746 )
| ~ ( ord_less_eq @ SV117 @ SV746 @ ( one_one @ SV117 ) )
| ( ord_less_eq @ SV117 @ ( power_power @ SV117 @ SV746 @ SY2135 ) @ ( power_power @ SV117 @ SV746 @ SV902 ) ) ) )
= $true )
| ( ( linordered_semidom @ SV117 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3413]) ).
thf(3830,plain,
! [SV118: $i,SV657: $i,SV499: $i] :
( ( ( dvd_dvd @ nat @ SV499 @ SV657 )
= $false )
| ( ( dvd_dvd @ nat @ ( times_times @ nat @ SV118 @ SV499 ) @ ( times_times @ nat @ SV118 @ SV657 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3414]) ).
thf(3831,plain,
! [SV500: $i,SV119: $i,SV658: $i] :
( ( ( zprime @ SV658 )
= $false )
| ( ( ~ ( dvd_dvd @ int @ SV658 @ ( power_power @ int @ SV119 @ SV500 ) )
| ( dvd_dvd @ int @ SV658 @ SV119 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3415]) ).
thf(3832,plain,
! [SV120: $i] :
( ( ( ~ ( number_ring @ SV120 ) )
= $true )
| ( ( ~ ( linordered_idom @ SV120 ) )
= $true )
| ( ( ! [SY1234: $i] :
~ ( ~ ( ~ ( ord_less @ SV120 @ ( one_one @ SV120 ) @ ( number_number_of @ SV120 @ SY1234 ) )
| ( ord_less @ int @ ( bit1 @ pls ) @ SY1234 ) )
| ~ ( ~ ( ord_less @ int @ ( bit1 @ pls ) @ SY1234 )
| ( ord_less @ SV120 @ ( one_one @ SV120 ) @ ( number_number_of @ SV120 @ SY1234 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3416]) ).
thf(3833,plain,
! [SV121: $i,SV659: $i,SV501: $i] :
( ( ( ord_less_eq @ real @ SV501 @ SV659 )
= $false )
| ( ( ord_less_eq @ real @ ( plus_plus @ real @ SV121 @ SV501 ) @ ( plus_plus @ real @ SV121 @ SV659 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3417]) ).
thf(3834,plain,
! [SV502: $i,SV122: $i] :
( ( ~ ( ord_less_eq @ int @ ( bit1 @ SV122 ) @ ( bit1 @ SV502 ) )
| ( ord_less_eq @ int @ SV122 @ SV502 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3418]) ).
thf(3835,plain,
! [SV502: $i,SV122: $i] :
( ( ~ ( ord_less_eq @ int @ SV122 @ SV502 )
| ( ord_less_eq @ int @ ( bit1 @ SV122 ) @ ( bit1 @ SV502 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3419]) ).
thf(3836,plain,
( ( ( ~ ! [SY1968: $i] :
( ( plus_plus @ int @ ( power_power @ int @ sK3_SX0 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ SY1968 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ) )
= $true )
| ( ( ord_less @ int @ ( one_one @ int ) @ t )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3420]) ).
thf(3837,plain,
! [SV123: $i] :
( ( ( ~ ( number_ring @ SV123 ) )
= $true )
| ( ( ~ ( linordered_idom @ SV123 ) )
= $true )
| ( ( ! [SY1238: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV123 @ ( number_number_of @ SV123 @ SY1238 ) @ ( one_one @ SV123 ) )
| ( ord_less_eq @ int @ SY1238 @ ( bit1 @ pls ) ) )
| ~ ( ~ ( ord_less_eq @ int @ SY1238 @ ( bit1 @ pls ) )
| ( ord_less_eq @ SV123 @ ( number_number_of @ SV123 @ SY1238 ) @ ( one_one @ SV123 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3421]) ).
thf(3838,plain,
! [SV903: $i,SV747: $i,SV124: $i] :
( ( ( ! [SY2136: $i,SY2137: $i] :
( ~ ( dvd_dvd @ SV124 @ SY2136 @ SY2137 )
| ~ ( dvd_dvd @ SV124 @ SV747 @ SV903 )
| ( dvd_dvd @ SV124 @ ( times_times @ SV124 @ SY2136 @ SV747 ) @ ( times_times @ SV124 @ SY2137 @ SV903 ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV124 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3422]) ).
thf(3839,plain,
! [SV904: $i,SV748: $i,SV125: $i] :
( ( ( ! [SY2138: $i,SY2139: $i] :
( ( minus_minus @ SV125 @ ( plus_plus @ SV125 @ SV748 @ SV904 ) @ ( plus_plus @ SV125 @ SY2138 @ SY2139 ) )
= ( plus_plus @ SV125 @ ( minus_minus @ SV125 @ SV748 @ SY2138 ) @ ( minus_minus @ SV125 @ SV904 @ SY2139 ) ) ) )
= $true )
| ( ( ab_group_add @ SV125 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3423]) ).
thf(3840,plain,
! [SV128: $i] :
( ( ( ( number_number_of @ nat @ SV128 )
!= ( zero_zero @ nat ) )
= $true )
| ( ( ord_less_eq @ int @ SV128 @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3425]) ).
thf(3841,plain,
! [SV128: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV128 @ pls ) )
= $true )
| ( ( ( number_number_of @ nat @ SV128 )
= ( zero_zero @ nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3426]) ).
thf(3842,plain,
! [SV905: $i,SV751: $i,SV130: $i] :
( ( ( ! [SY2140: $i] :
( ( times_times @ SV130 @ ( times_times @ SV130 @ SV751 @ SV905 ) @ SY2140 )
= ( times_times @ SV130 @ ( times_times @ SV130 @ SV751 @ SY2140 ) @ SV905 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV130 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3428]) ).
thf(3843,plain,
! [SV906: $i,SV752: $i,SV131: $i] :
( ( ( ! [SY2141: $i] :
( ( times_times @ SV131 @ ( plus_plus @ SV131 @ SV752 @ SV906 ) @ SY2141 )
= ( plus_plus @ SV131 @ ( times_times @ SV131 @ SV752 @ SY2141 ) @ ( times_times @ SV131 @ SV906 @ SY2141 ) ) ) )
= $true )
| ( ( comm_semiring @ SV131 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3429]) ).
thf(3844,plain,
! [SV907: $i,SV753: $i,SV660: $i,SV503: $i,SV132: $i] :
( ( ~ ( ord_less_eq @ int @ ( plus_plus @ int @ ( times_times @ int @ SV132 @ SV503 ) @ SV660 ) @ ( plus_plus @ int @ ( times_times @ int @ SV132 @ SV753 ) @ SV907 ) )
| ~ ( ord_less_eq @ int @ SV907 @ ( zero_zero @ int ) )
| ~ ( ord_less @ int @ SV132 @ SV907 )
| ~ ( ord_less @ int @ SV132 @ SV660 )
| ( ord_less_eq @ int @ SV753 @ SV503 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3430]) ).
thf(3845,plain,
! [SV134: $i] :
( ( ( ~ ( number_ring @ SV134 ) )
= $true )
| ( ( ~ ( linordered_idom @ SV134 ) )
= $true )
| ( ( ! [SY1260: $i] :
~ ( ~ ( ~ ( ord_less @ SV134 @ ( number_number_of @ SV134 @ SY1260 ) @ ( one_one @ SV134 ) )
| ( ord_less @ int @ SY1260 @ ( bit1 @ pls ) ) )
| ~ ( ~ ( ord_less @ int @ SY1260 @ ( bit1 @ pls ) )
| ( ord_less @ SV134 @ ( number_number_of @ SV134 @ SY1260 ) @ ( one_one @ SV134 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3431]) ).
thf(3846,plain,
! [SV505: $i,SV135: $i] :
( ( ~ ( ord_less_eq @ nat @ ( number_number_of @ nat @ SV135 ) @ ( number_number_of @ nat @ SV505 ) )
| ~ ~ ( ord_less_eq @ int @ SV135 @ SV505 )
| ( ord_less_eq @ int @ SV135 @ pls ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3432]) ).
thf(3847,plain,
! [SV505: $i,SV135: $i] :
( ( ~ ( ~ ~ ( ord_less_eq @ int @ SV135 @ SV505 )
| ( ord_less_eq @ int @ SV135 @ pls ) )
| ( ord_less_eq @ nat @ ( number_number_of @ nat @ SV135 ) @ ( number_number_of @ nat @ SV505 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3433]) ).
thf(3848,plain,
! [SV661: $i,SV506: $i,SV137: $i] :
( ( ~ ( ~ ( zcong @ SV137 @ SV506 @ SV661 )
| ( dvd_dvd @ int @ SV661 @ ( minus_minus @ int @ SV137 @ SV506 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3435]) ).
thf(3849,plain,
! [SV506: $i,SV137: $i,SV661: $i] :
( ( ~ ( ~ ( dvd_dvd @ int @ SV661 @ ( minus_minus @ int @ SV137 @ SV506 ) )
| ( zcong @ SV137 @ SV506 @ SV661 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3435]) ).
thf(3850,plain,
! [SV507: $i,SV138: $i] :
( ( ~ ( ord_less_eq @ int @ ( number_number_of @ int @ SV138 ) @ ( number_number_of @ int @ SV507 ) )
| ( ord_less_eq @ int @ SV138 @ SV507 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3436]) ).
thf(3851,plain,
! [SV507: $i,SV138: $i] :
( ( ~ ( ord_less_eq @ int @ SV138 @ SV507 )
| ( ord_less_eq @ int @ ( number_number_of @ int @ SV138 ) @ ( number_number_of @ int @ SV507 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3437]) ).
thf(3852,plain,
! [SV139: $i] :
( ( ( ~ ( number @ SV139 ) )
= $true )
| ( ( ~ ( ring @ SV139 ) )
= $true )
| ( ( ! [SY1266: $i,SY1267: $i,SY1268: $i] :
( ( times_times @ SV139 @ ( number_number_of @ SV139 @ SY1266 ) @ ( minus_minus @ SV139 @ SY1267 @ SY1268 ) )
= ( minus_minus @ SV139 @ ( times_times @ SV139 @ ( number_number_of @ SV139 @ SY1266 ) @ SY1267 ) @ ( times_times @ SV139 @ ( number_number_of @ SV139 @ SY1266 ) @ SY1268 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3438]) ).
thf(3853,plain,
! [SV756: $i,SV908: $i,SV142: $i] :
( ( ( ~ ( ord_less @ SV142 @ ( one_one @ SV142 ) @ SV908 )
| ( ord_less @ SV142 @ ( one_one @ SV142 ) @ ( times_times @ SV142 @ SV908 @ ( power_power @ SV142 @ SV908 @ SV756 ) ) ) )
= $true )
| ( ( linordered_semidom @ SV142 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3441]) ).
thf(3854,plain,
! [SV509: $i,SV143: $i] :
( ( ( ( power_power @ nat @ SV143 @ SV509 )
!= ( zero_zero @ nat ) )
| ~ ( ~ ( ( SV509
!= ( zero_zero @ nat ) ) )
| ( SV143
!= ( zero_zero @ nat ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3442]) ).
thf(3855,plain,
! [SV143: $i,SV509: $i] :
( ( ~ ~ ( ~ ( ( SV509
!= ( zero_zero @ nat ) ) )
| ( SV143
!= ( zero_zero @ nat ) ) )
| ( ( power_power @ nat @ SV143 @ SV509 )
= ( zero_zero @ nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3443]) ).
thf(3856,plain,
! [SV662: $i,SV510: $i,SV145: $i] :
( ( ~ ( ~ ( dvd_dvd @ int @ SV145 @ ( plus_plus @ int @ SV510 @ ( times_times @ int @ SV145 @ SV662 ) ) )
| ( dvd_dvd @ int @ SV145 @ SV510 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3445]) ).
thf(3857,plain,
! [SV662: $i,SV510: $i,SV145: $i] :
( ( ~ ( ~ ( dvd_dvd @ int @ SV145 @ SV510 )
| ( dvd_dvd @ int @ SV145 @ ( plus_plus @ int @ SV510 @ ( times_times @ int @ SV145 @ SV662 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3445]) ).
thf(3858,plain,
! [SV146: $i] :
( ( ( ~ ( ord_less @ int @ ( bit1 @ SV146 ) @ min ) )
= $true )
| ( ( ord_less @ int @ SV146 @ min )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3446]) ).
thf(3859,plain,
! [SV146: $i] :
( ( ( ~ ( ord_less @ int @ SV146 @ min ) )
= $true )
| ( ( ord_less @ int @ ( bit1 @ SV146 ) @ min )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3447]) ).
thf(3860,plain,
! [SV511: $i,SV147: $i] :
( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ SV147 @ SV511 ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ SV147 )
| ( SV511
= ( zero_zero @ nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3448]) ).
thf(3861,plain,
! [SV511: $i,SV147: $i] :
( ( ~ ( ( ord_less @ nat @ ( zero_zero @ nat ) @ SV147 )
| ( SV511
= ( zero_zero @ nat ) ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ SV147 @ SV511 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3449]) ).
thf(3862,plain,
! [SV909: $i,SV759: $i,SV150: $i] :
( ( ( ! [SY2142: $i] :
( ( plus_plus @ SV150 @ ( times_times @ SV150 @ SV759 @ SV909 ) @ ( times_times @ SV150 @ SY2142 @ SV909 ) )
= ( times_times @ SV150 @ ( plus_plus @ SV150 @ SV759 @ SY2142 ) @ SV909 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV150 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3451]) ).
thf(3863,plain,
! [SV512: $i,SV151: $i] :
( ( ~ ~ ( ~ ( dvd_dvd @ nat @ SV151 @ SV512 )
| ~ ( dvd_dvd @ nat @ SV512 @ SV151 ) )
| ( SV151 = SV512 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3452]) ).
thf(3864,plain,
! [SV512: $i,SV151: $i] :
( ( ( SV151 != SV512 )
| ~ ( ~ ( dvd_dvd @ nat @ SV151 @ SV512 )
| ~ ( dvd_dvd @ nat @ SV512 @ SV151 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3453]) ).
thf(3865,plain,
! [SV760: $i,SV910: $i,SV152: $i] :
( ( ( ~ ( ord_less_eq @ SV152 @ ( zero_zero @ SV152 ) @ SV910 )
| ~ ( ord_less_eq @ SV152 @ ( zero_zero @ SV152 ) @ SV760 )
| ( ord_less_eq @ SV152 @ ( zero_zero @ SV152 ) @ ( times_times @ SV152 @ SV910 @ SV760 ) ) )
= $true )
| ( ( ordere453448008miring @ SV152 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3454]) ).
thf(3866,plain,
! [SV513: $i,SV153: $i] :
( ( ( ~ ( ord_less @ real @ ( zero_zero @ real ) @ SV153 ) )
= $true )
| ( ( ~ ! [SY1807: $i] :
~ ~ ( ~ ( ord_less @ real @ ( zero_zero @ real ) @ SY1807 )
| ( ( power_power @ real @ SY1807 @ SV513 )
!= SV153 ) ) )
= $true )
| ( ( ord_less @ nat @ ( zero_zero @ nat ) @ SV513 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3455]) ).
thf(3867,plain,
! [SV154: $i,SV761: $i,SV663: $i,SV514: $i] :
( ( ( ~ ( zcong @ SV514 @ SV663 @ SV761 ) )
= $true )
| ( ( zcong @ ( times_times @ int @ SV154 @ SV514 ) @ ( times_times @ int @ SV154 @ SV663 ) @ SV761 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3456]) ).
thf(3868,plain,
! [SV911: $i,SV762: $i,SV155: $i] :
( ( ( ! [SY2143: $i] :
( ~ ( ord_less @ SV155 @ ( one_one @ SV155 ) @ SY2143 )
| ~ ( ~ ( ~ ( ord_less @ SV155 @ ( power_power @ SV155 @ SY2143 @ SV762 ) @ ( power_power @ SV155 @ SY2143 @ SV911 ) )
| ( ord_less @ nat @ SV762 @ SV911 ) )
| ~ ( ~ ( ord_less @ nat @ SV762 @ SV911 )
| ( ord_less @ SV155 @ ( power_power @ SV155 @ SY2143 @ SV762 ) @ ( power_power @ SV155 @ SY2143 @ SV911 ) ) ) ) ) )
= $true )
| ( ( linordered_semidom @ SV155 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3457]) ).
thf(3869,plain,
! [SV912: $i,SV763: $i,SV156: $i] :
( ( ( ( power_power @ SV156 @ SV763 @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV912 ) )
= ( times_times @ SV156 @ ( power_power @ SV156 @ SV763 @ SV912 ) @ ( power_power @ SV156 @ SV763 @ SV912 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV156 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3458]) ).
thf(3870,plain,
! [SV158: $i,SV664: $i,SV515: $i] :
( ( ( dvd_dvd @ nat @ SV515 @ SV664 )
= $false )
| ( ( dvd_dvd @ nat @ ( times_times @ nat @ SV515 @ SV158 ) @ ( times_times @ nat @ SV664 @ SV158 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3460]) ).
thf(3871,plain,
! [SV516: $i,SV159: $i] :
( ( ~ ( ord_less_eq @ int @ ( bit1 @ SV159 ) @ ( bit0 @ SV516 ) )
| ( ord_less @ int @ SV159 @ SV516 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3461]) ).
thf(3872,plain,
! [SV516: $i,SV159: $i] :
( ( ~ ( ord_less @ int @ SV159 @ SV516 )
| ( ord_less_eq @ int @ ( bit1 @ SV159 ) @ ( bit0 @ SV516 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3462]) ).
thf(3873,plain,
! [SV517: $i,SV160: $i] :
( ( ~ ( ord_less @ int @ SV160 @ ( plus_plus @ int @ SV517 @ ( one_one @ int ) ) )
| ( ord_less_eq @ int @ SV160 @ SV517 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3463]) ).
thf(3874,plain,
! [SV517: $i,SV160: $i] :
( ( ~ ( ord_less_eq @ int @ SV160 @ SV517 )
| ( ord_less @ int @ SV160 @ ( plus_plus @ int @ SV517 @ ( one_one @ int ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3464]) ).
thf(3875,plain,
! [SV665: $i,SV518: $i,SV161: $i] :
( ( ( ord_less @ int @ ( plus_plus @ int @ ( times_times @ int @ SV161 @ SV518 ) @ SV665 ) @ ( zero_zero @ int ) )
= $false )
| ( ( ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV665 )
| ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV161 )
| ( ord_less_eq @ int @ SV518 @ ( zero_zero @ int ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3465]) ).
thf(3876,plain,
! [SV666: $i,SV520: $i,SV163: $i] :
( ( ~ ( ~ ( zcong @ SV163 @ SV520 @ ( ti @ int @ SV666 ) )
| ( zcong @ SV163 @ SV520 @ SV666 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3466]) ).
thf(3877,plain,
! [SV666: $i,SV520: $i,SV163: $i] :
( ( ~ ( ~ ( zcong @ SV163 @ SV520 @ SV666 )
| ( zcong @ SV163 @ SV520 @ ( ti @ int @ SV666 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3466]) ).
thf(3878,plain,
! [SV164: $i,SV667: $i,SV521: $i,SV913: $i,SV765: $i] :
( ( ~ ( dvd_dvd @ int @ SV765 @ SV913 )
| ~ ( ~ ( ~ ( dvd_dvd @ int @ SV765 @ ( plus_plus @ int @ SV521 @ SV667 ) )
| ( dvd_dvd @ int @ SV765 @ ( plus_plus @ int @ ( plus_plus @ int @ SV521 @ ( times_times @ int @ SV164 @ SV913 ) ) @ SV667 ) ) )
| ~ ( ~ ( dvd_dvd @ int @ SV765 @ ( plus_plus @ int @ ( plus_plus @ int @ SV521 @ ( times_times @ int @ SV164 @ SV913 ) ) @ SV667 ) )
| ( dvd_dvd @ int @ SV765 @ ( plus_plus @ int @ SV521 @ SV667 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3467]) ).
thf(3879,plain,
! [SV914: $i,SV766: $i,SV165: $i] :
( ( ( ! [SY2144: $i] :
( ( plus_plus @ SV165 @ ( number_number_of @ SV165 @ SV766 ) @ ( plus_plus @ SV165 @ ( number_number_of @ SV165 @ SV914 ) @ SY2144 ) )
= ( plus_plus @ SV165 @ ( number_number_of @ SV165 @ ( plus_plus @ int @ SV766 @ SV914 ) ) @ SY2144 ) ) )
= $true )
| ( ( number_ring @ SV165 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3468]) ).
thf(3880,plain,
! [SV915: $i,SV767: $i,SV166: $i] :
( ( ( ord_less_eq @ SV166 @ ( zero_zero @ SV166 ) @ ( power_power @ SV166 @ SV767 @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV915 ) ) )
= $true )
| ( ( linordered_idom @ SV166 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3469]) ).
thf(3881,plain,
! [SV522: $i,SV167: $i,SV916: $i,SV768: $i,SV668: $i] :
( ( ~ ( zcong @ SV668 @ SV768 @ SV916 )
| ~ ( zcong @ SV167 @ SV522 @ SV916 )
| ( zcong @ ( minus_minus @ int @ SV668 @ SV167 ) @ ( minus_minus @ int @ SV768 @ SV522 ) @ SV916 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3470]) ).
thf(3882,plain,
! [SV168: $i] :
( ( ( ~ ( number @ SV168 ) )
= $true )
| ( ( ~ ( semiring @ SV168 ) )
= $true )
| ( ( ! [SY1318: $i,SY1319: $i,SY1320: $i] :
( ( times_times @ SV168 @ ( plus_plus @ SV168 @ SY1318 @ SY1319 ) @ ( number_number_of @ SV168 @ SY1320 ) )
= ( plus_plus @ SV168 @ ( times_times @ SV168 @ SY1318 @ ( number_number_of @ SV168 @ SY1320 ) ) @ ( times_times @ SV168 @ SY1319 @ ( number_number_of @ SV168 @ SY1320 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3471]) ).
thf(3883,plain,
! [SV523: $i,SV169: $i] :
( ( ( ( plus_plus @ real @ ( power_power @ real @ SV169 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ real @ SV523 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ real ) )
| ~ ( ( SV169
!= ( zero_zero @ real ) )
| ( SV523
!= ( zero_zero @ real ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3472]) ).
thf(3884,plain,
! [SV523: $i,SV169: $i] :
( ( ~ ~ ( ( SV169
!= ( zero_zero @ real ) )
| ( SV523
!= ( zero_zero @ real ) ) )
| ( ( plus_plus @ real @ ( power_power @ real @ SV169 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ real @ SV523 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ real ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3473]) ).
thf(3885,plain,
! [SV669: $i,SV524: $i,SV170: $i] :
( ( ( dvd_dvd @ nat @ ( power_power @ nat @ SV170 @ SV524 ) @ ( power_power @ nat @ SV170 @ SV669 ) )
= $false )
| ( ( ~ ( ord_less @ nat @ ( one_one @ nat ) @ SV170 )
| ( ord_less_eq @ nat @ SV524 @ SV669 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3474]) ).
thf(3886,plain,
! [SV171: $i] :
( ( ( ~ ( ord_less_eq @ int @ pls @ ( bit0 @ SV171 ) ) )
= $true )
| ( ( ord_less_eq @ int @ pls @ SV171 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3475]) ).
thf(3887,plain,
! [SV171: $i] :
( ( ( ~ ( ord_less_eq @ int @ pls @ SV171 ) )
= $true )
| ( ( ord_less_eq @ int @ pls @ ( bit0 @ SV171 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3476]) ).
thf(3888,plain,
! [SV525: $i,SV172: $i] :
( ( ~ ( ord_less @ int @ SV172 @ SV525 )
| ( ord_less @ int @ ( minus_minus @ int @ SV172 @ SV525 ) @ ( zero_zero @ int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3477]) ).
thf(3889,plain,
! [SV525: $i,SV172: $i] :
( ( ~ ( ord_less @ int @ ( minus_minus @ int @ SV172 @ SV525 ) @ ( zero_zero @ int ) )
| ( ord_less @ int @ SV172 @ SV525 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3478]) ).
thf(3890,plain,
! [SV917: $i,SV770: $i,SV174: $i] :
( ( ( ! [SY2145: $i,SY2146: $i] :
( ( minus_minus @ SV174 @ ( times_times @ SV174 @ SV770 @ SV917 ) @ ( times_times @ SV174 @ SY2145 @ SY2146 ) )
= ( plus_plus @ SV174 @ ( times_times @ SV174 @ SV770 @ ( minus_minus @ SV174 @ SV917 @ SY2146 ) ) @ ( times_times @ SV174 @ ( minus_minus @ SV174 @ SV770 @ SY2145 ) @ SY2146 ) ) ) )
= $true )
| ( ( ring @ SV174 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3480]) ).
thf(3891,plain,
! [SV918: $i,SV771: $i,SV175: $i] :
( ( ( ! [SY2147: $i,SY2148: $i] :
~ ( ~ ( ~ ~ ( ~ ( ( ( ti @ SV175 @ SY2147 )
!= ( ti @ SV175 @ SY2148 ) ) )
| ~ ( ( ( ti @ SV175 @ SV771 )
!= ( ti @ SV175 @ SV918 ) ) ) )
| ( ( plus_plus @ SV175 @ ( times_times @ SV175 @ SY2147 @ SV771 ) @ ( times_times @ SV175 @ SY2148 @ SV918 ) )
!= ( plus_plus @ SV175 @ ( times_times @ SV175 @ SY2147 @ SV918 ) @ ( times_times @ SV175 @ SY2148 @ SV771 ) ) ) )
| ~ ( ~ ( ( ( plus_plus @ SV175 @ ( times_times @ SV175 @ SY2147 @ SV771 ) @ ( times_times @ SV175 @ SY2148 @ SV918 ) )
!= ( plus_plus @ SV175 @ ( times_times @ SV175 @ SY2147 @ SV918 ) @ ( times_times @ SV175 @ SY2148 @ SV771 ) ) ) )
| ~ ( ~ ( ( ( ti @ SV175 @ SY2147 )
!= ( ti @ SV175 @ SY2148 ) ) )
| ~ ( ( ( ti @ SV175 @ SV771 )
!= ( ti @ SV175 @ SV918 ) ) ) ) ) ) )
= $true )
| ( ( semiri456707255roduct @ SV175 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3481]) ).
thf(3892,plain,
! [SV177: $i] :
( ( ( ~ ( ord_less @ int @ pls @ ( bit0 @ SV177 ) ) )
= $true )
| ( ( ord_less @ int @ pls @ SV177 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3483]) ).
thf(3893,plain,
! [SV177: $i] :
( ( ( ~ ( ord_less @ int @ pls @ SV177 ) )
= $true )
| ( ( ord_less @ int @ pls @ ( bit0 @ SV177 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3484]) ).
thf(3894,plain,
! [SV178: $i,SV527: $i] :
( ( ( ~ ( ord_less @ int @ SV527 @ SV178 ) )
= $true )
| ( ( ~ ( dvd_dvd @ int @ SV178 @ SV527 ) )
= $true )
| ( ( ord_less @ int @ ( zero_zero @ int ) @ SV527 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3485]) ).
thf(3895,plain,
! [SV919: $i,SV772: $i,SV179: $i] :
( ( ( ! [SY2149: $i] :
( ~ ( ord_less @ SV179 @ ( one_one @ SV179 ) @ SY2149 )
| ~ ( ord_less @ SV179 @ ( power_power @ SV179 @ SY2149 @ SV772 ) @ ( power_power @ SV179 @ SY2149 @ SV919 ) )
| ( ord_less @ nat @ SV772 @ SV919 ) ) )
= $true )
| ( ( linordered_semidom @ SV179 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3486]) ).
thf(3896,plain,
! [SV920: $i,SV180: $i,SV773: $i] :
( ( ( ! [SY2150: $i] :
( ( SV773
!= ( times_times @ SV180 @ SV920 @ SY2150 ) )
| ( dvd_dvd @ SV180 @ SV920 @ SV773 ) ) )
= $true )
| ( ( dvd @ SV180 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3487]) ).
thf(3897,plain,
! [SV528: $i,SV182: $i] :
( ( ~ ( ord_less @ int @ ( bit1 @ SV182 ) @ ( bit1 @ SV528 ) )
| ( ord_less @ int @ SV182 @ SV528 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3488]) ).
thf(3898,plain,
! [SV528: $i,SV182: $i] :
( ( ~ ( ord_less @ int @ SV182 @ SV528 )
| ( ord_less @ int @ ( bit1 @ SV182 ) @ ( bit1 @ SV528 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3489]) ).
thf(3899,plain,
! [SV921: $i,SV775: $i,SV185: $i] :
( ( ( ! [SY2151: $i] :
( ( times_times @ SV185 @ ( power_power @ SV185 @ SV775 @ SV921 ) @ ( power_power @ SV185 @ SV775 @ SY2151 ) )
= ( power_power @ SV185 @ SV775 @ ( plus_plus @ nat @ SV921 @ SY2151 ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV185 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3491]) ).
thf(3900,plain,
! [SV529: $i,SV186: $i] :
( ( ~ ( ord_less @ int @ ( bit0 @ SV186 ) @ ( bit0 @ SV529 ) )
| ( ord_less @ int @ SV186 @ SV529 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3492]) ).
thf(3901,plain,
! [SV529: $i,SV186: $i] :
( ( ~ ( ord_less @ int @ SV186 @ SV529 )
| ( ord_less @ int @ ( bit0 @ SV186 ) @ ( bit0 @ SV529 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3493]) ).
thf(3902,plain,
! [SV530: $i,SV187: $i] :
( ( ~ ( ord_less @ int @ SV187 @ SV530 )
| ~ ( ~ ( ord_less_eq @ int @ SV187 @ SV530 )
| ~ ( ( ( ti @ int @ SV187 )
!= ( ti @ int @ SV530 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3494]) ).
thf(3903,plain,
! [SV530: $i,SV187: $i] :
( ( ~ ~ ( ~ ( ord_less_eq @ int @ SV187 @ SV530 )
| ~ ( ( ( ti @ int @ SV187 )
!= ( ti @ int @ SV530 ) ) ) )
| ( ord_less @ int @ SV187 @ SV530 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3495]) ).
thf(3904,plain,
! [SV776: $i,SV189: $i] :
( ( ( ~ ( ( ( plus_plus @ SV189 @ SV776 @ SV776 )
!= ( zero_zero @ SV189 ) )
| ( ( ti @ SV189 @ SV776 )
= ( zero_zero @ SV189 ) ) )
| ~ ( ( ( ti @ SV189 @ SV776 )
!= ( zero_zero @ SV189 ) )
| ( ( plus_plus @ SV189 @ SV776 @ SV776 )
= ( zero_zero @ SV189 ) ) ) )
= $false )
| ( ( linord219039673up_add @ SV189 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3497]) ).
thf(3905,plain,
! [SV532: $i,SV190: $i,SV670: $i] :
( ( ( ord_less @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV670 )
= $false )
| ( ( ~ ( zcong @ ( power_power @ int @ ( number_number_of @ int @ min ) @ SV190 ) @ ( power_power @ int @ ( number_number_of @ int @ min ) @ SV532 ) @ SV670 )
| ( ( power_power @ int @ ( number_number_of @ int @ min ) @ SV190 )
= ( power_power @ int @ ( number_number_of @ int @ min ) @ SV532 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3498]) ).
thf(3906,plain,
! [SV671: $i,SV533: $i,SV191: $i] :
( ( ~ ( ~ ( dvd_dvd @ nat @ ( times_times @ nat @ SV191 @ SV533 ) @ ( times_times @ nat @ SV671 @ SV533 ) )
| ( SV533
= ( zero_zero @ nat ) )
| ( dvd_dvd @ nat @ SV191 @ SV671 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3499]) ).
thf(3907,plain,
! [SV671: $i,SV191: $i,SV533: $i] :
( ( ~ ( ~ ( ( SV533
= ( zero_zero @ nat ) )
| ( dvd_dvd @ nat @ SV191 @ SV671 ) )
| ( dvd_dvd @ nat @ ( times_times @ nat @ SV191 @ SV533 ) @ ( times_times @ nat @ SV671 @ SV533 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3499]) ).
thf(3908,plain,
! [SV777: $i,SV922: $i,SV192: $i] :
( ( ( ~ ( ord_less_eq @ SV192 @ ( zero_zero @ SV192 ) @ SV922 )
| ( ord_less_eq @ SV192 @ ( zero_zero @ SV192 ) @ ( power_power @ SV192 @ SV922 @ SV777 ) ) )
= $true )
| ( ( linordered_semidom @ SV192 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3500]) ).
thf(3909,plain,
! [SV923: $i,SV778: $i,SV193: $i] :
( ( ( ~ ( ~ ( ( ( plus_plus @ SV193 @ ( times_times @ SV193 @ SV778 @ SV778 ) @ ( times_times @ SV193 @ SV923 @ SV923 ) )
!= ( zero_zero @ SV193 ) )
| ~ ( ( ( ti @ SV193 @ SV778 )
!= ( zero_zero @ SV193 ) )
| ( ( ti @ SV193 @ SV923 )
!= ( zero_zero @ SV193 ) ) ) )
| ~ ( ~ ~ ( ( ( ti @ SV193 @ SV778 )
!= ( zero_zero @ SV193 ) )
| ( ( ti @ SV193 @ SV923 )
!= ( zero_zero @ SV193 ) ) )
| ( ( plus_plus @ SV193 @ ( times_times @ SV193 @ SV778 @ SV778 ) @ ( times_times @ SV193 @ SV923 @ SV923 ) )
= ( zero_zero @ SV193 ) ) ) ) )
= $true )
| ( ( linord581940658strict @ SV193 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3501]) ).
thf(3910,plain,
! [SV924: $i,SV779: $i,SV194: $i] :
( ( ( ! [SY2152: $i] :
( ~ ( ord_less @ SV194 @ ( one_one @ SV194 ) @ SY2152 )
| ~ ( ~ ( ( ( power_power @ SV194 @ SY2152 @ SV779 )
!= ( power_power @ SV194 @ SY2152 @ SV924 ) )
| ( SV779 = SV924 ) )
| ~ ( ( SV779 != SV924 )
| ( ( power_power @ SV194 @ SY2152 @ SV779 )
= ( power_power @ SV194 @ SY2152 @ SV924 ) ) ) ) ) )
= $true )
| ( ( linordered_semidom @ SV194 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3502]) ).
thf(3911,plain,
! [SV925: $i,SV780: $i,SV195: $i] :
( ( ( ~ ( ord_less @ SV195 @ ( plus_plus @ SV195 @ ( times_times @ SV195 @ SV780 @ SV780 ) @ ( times_times @ SV195 @ SV925 @ SV925 ) ) @ ( zero_zero @ SV195 ) ) )
= $true )
| ( ( linordered_ring @ SV195 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3503]) ).
thf(3912,plain,
! [SV196: $i,SV534: $i,SV672: $i] :
( ( ( zprime @ SV672 )
= $false )
| ( ( ~ ~ ( zcong @ SV534 @ ( zero_zero @ int ) @ SV672 )
| ~ ~ ( zcong @ SV196 @ ( zero_zero @ int ) @ SV672 )
| ~ ( zcong @ ( times_times @ int @ SV534 @ SV196 ) @ ( zero_zero @ int ) @ SV672 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3504]) ).
thf(3913,plain,
! [SV926: $i,SV781: $i,SV197: $i] :
( ( ( ( power_power @ SV197 @ ( plus_plus @ SV197 @ SV781 @ SV926 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ SV197 @ ( plus_plus @ SV197 @ ( power_power @ SV197 @ SV781 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV197 @ SV926 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times @ SV197 @ ( times_times @ SV197 @ ( number_number_of @ SV197 @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV781 ) @ SV926 ) ) )
= $true )
| ( ( number_semiring @ SV197 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3505]) ).
thf(3914,plain,
! [SV927: $i,SV782: $i,SV198: $i] :
( ( ( ( times_times @ SV198 @ ( number_number_of @ SV198 @ SV782 ) @ ( number_number_of @ SV198 @ SV927 ) )
= ( number_number_of @ SV198 @ ( times_times @ int @ SV782 @ SV927 ) ) )
= $true )
| ( ( number_ring @ SV198 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3506]) ).
thf(3915,plain,
! [SV928: $i,SV783: $i,SV199: $i] :
( ( ( ~ ( ~ ( ~ ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ ( times_times @ SV199 @ SV783 @ SV928 ) )
| ~ ( ~ ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ SV783 )
| ~ ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ SV928 ) )
| ~ ( ~ ( ord_less_eq @ SV199 @ SV783 @ ( zero_zero @ SV199 ) )
| ~ ( ord_less_eq @ SV199 @ SV928 @ ( zero_zero @ SV199 ) ) ) )
| ~ ( ~ ( ~ ( ~ ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ SV783 )
| ~ ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ SV928 ) )
| ~ ( ~ ( ord_less_eq @ SV199 @ SV783 @ ( zero_zero @ SV199 ) )
| ~ ( ord_less_eq @ SV199 @ SV928 @ ( zero_zero @ SV199 ) ) ) )
| ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ ( times_times @ SV199 @ SV783 @ SV928 ) ) ) ) )
= $true )
| ( ( linord581940658strict @ SV199 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3507]) ).
thf(3916,plain,
! [SV785: $i,SV929: $i,SV201: $i] :
( ( ( ~ ( ord_less @ SV201 @ ( one_one @ SV201 ) @ SV929 )
| ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ SV785 )
| ( ord_less @ SV201 @ ( one_one @ SV201 ) @ ( power_power @ SV201 @ SV929 @ SV785 ) ) )
= $true )
| ( ( linordered_semidom @ SV201 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3509]) ).
thf(3917,plain,
! [SV202: $i] :
( ( ( ~ ( number_ring @ SV202 ) )
= $true )
| ( ( ~ ( linordered_idom @ SV202 ) )
= $true )
| ( ( ! [SY1375: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV202 @ ( one_one @ SV202 ) @ ( number_number_of @ SV202 @ SY1375 ) )
| ( ord_less_eq @ int @ ( bit1 @ pls ) @ SY1375 ) )
| ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ pls ) @ SY1375 )
| ( ord_less_eq @ SV202 @ ( one_one @ SV202 ) @ ( number_number_of @ SV202 @ SY1375 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3510]) ).
thf(3918,plain,
! [SV203: $i,SV535: $i,SV673: $i] :
( ( ( ord_less @ int @ ( zero_zero @ int ) @ SV673 )
= $false )
| ( ( ~ ( ord_less @ int @ SV673 @ SV535 )
| ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV203 )
| ~ ( ord_less @ int @ SV203 @ SV673 )
| ~ ( zcong @ SV673 @ SV203 @ SV535 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3511]) ).
thf(3919,plain,
! [SV205: $i] :
( ( ( ~ ( ord_less @ int @ ( bit0 @ SV205 ) @ min ) )
= $true )
| ( ( ord_less_eq @ int @ SV205 @ min )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3513]) ).
thf(3920,plain,
! [SV205: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV205 @ min ) )
= $true )
| ( ( ord_less @ int @ ( bit0 @ SV205 ) @ min )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3514]) ).
thf(3921,plain,
! [SV536: $i,SV206: $i,SV930: $i,SV787: $i,SV674: $i] :
( ( ~ ( zcong @ SV674 @ SV787 @ SV930 )
| ~ ( zcong @ SV206 @ SV536 @ SV930 )
| ( zcong @ ( plus_plus @ int @ SV674 @ SV206 ) @ ( plus_plus @ int @ SV787 @ SV536 ) @ SV930 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3515]) ).
thf(3922,plain,
! [SV207: $i] :
( ( ( ~ ( ord_less @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ SV207 ) @ SV207 ) @ ( zero_zero @ int ) ) )
= $true )
| ( ( ord_less @ int @ SV207 @ ( zero_zero @ int ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3516]) ).
thf(3923,plain,
! [SV207: $i] :
( ( ( ~ ( ord_less @ int @ SV207 @ ( zero_zero @ int ) ) )
= $true )
| ( ( ord_less @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ SV207 ) @ SV207 ) @ ( zero_zero @ int ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3517]) ).
thf(3924,plain,
! [SV208: $i] :
( ( ( ~ ( twoSqu420862341sum2sq @ ( ti @ int @ SV208 ) ) )
= $true )
| ( ( twoSqu420862341sum2sq @ SV208 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3518]) ).
thf(3925,plain,
! [SV208: $i] :
( ( ( ~ ( twoSqu420862341sum2sq @ SV208 ) )
= $true )
| ( ( twoSqu420862341sum2sq @ ( ti @ int @ SV208 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3519]) ).
thf(3926,plain,
! [SV209: $i,SV675: $i,SV537: $i] :
( ( ( dvd_dvd @ nat @ SV537 @ SV675 )
= $false )
| ( ( ~ ( dvd_dvd @ nat @ SV537 @ ( plus_plus @ nat @ SV675 @ SV209 ) )
| ( dvd_dvd @ nat @ SV537 @ SV209 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3520]) ).
thf(3927,plain,
! [SV210: $i] :
( ( ( ( bit0 @ SV210 )
!= pls )
= $true )
| ( ( ( ti @ int @ SV210 )
= pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3521]) ).
thf(3928,plain,
! [SV210: $i] :
( ( ( ( ti @ int @ SV210 )
!= pls )
= $true )
| ( ( ( bit0 @ SV210 )
= pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3522]) ).
thf(3929,plain,
! [SV931: $i,SV788: $i,SV211: $i] :
( ( ( dvd_dvd @ SV211 @ SV788 @ ( times_times @ SV211 @ SV931 @ SV788 ) )
= $true )
| ( ( comm_semiring_1 @ SV211 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3523]) ).
thf(3930,plain,
! [SV932: $i,SV789: $i,SV212: $i] :
( ( ( ( plus_plus @ SV212 @ ( number_number_of @ SV212 @ SV789 ) @ ( number_number_of @ SV212 @ SV932 ) )
= ( number_number_of @ SV212 @ ( plus_plus @ int @ SV789 @ SV932 ) ) )
= $true )
| ( ( number_ring @ SV212 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3524]) ).
thf(3931,plain,
! [SV213: $i] :
( ( ( ~ ( number_ring @ SV213 ) )
= $true )
| ( ( ~ ( ring_char_0 @ SV213 ) )
= $true )
| ( ( ! [SY1389: $i,SY1390: $i] :
~ ( ~ ( ( ( number_number_of @ SV213 @ SY1389 )
!= ( number_number_of @ SV213 @ SY1390 ) )
| ( ( ti @ int @ SY1389 )
= ( ti @ int @ SY1390 ) ) )
| ~ ( ( ( ti @ int @ SY1389 )
!= ( ti @ int @ SY1390 ) )
| ( ( number_number_of @ SV213 @ SY1389 )
= ( number_number_of @ SV213 @ SY1390 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3525]) ).
thf(3932,plain,
! [SV790: $i,SV676: $i,SV538: $i,SV214: $i] :
( ( ( SV214
!= ( plus_plus @ nat @ ( times_times @ nat @ SV538 @ SV676 ) @ SV790 ) )
= $true )
| ( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ SV790 )
| ~ ( ord_less @ nat @ SV790 @ SV676 )
| ~ ( dvd_dvd @ nat @ SV676 @ SV214 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3526]) ).
thf(3933,plain,
! [SV677: $i,SV539: $i,SV215: $i] :
( ( ( dvd_dvd @ nat @ ( power_power @ nat @ SV215 @ SV539 ) @ ( power_power @ nat @ SV677 @ SV539 ) )
= $false )
| ( ( ~ ( ( SV539
!= ( zero_zero @ nat ) ) )
| ( dvd_dvd @ nat @ SV215 @ SV677 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3527]) ).
thf(3934,plain,
! [SV218: $i] :
( ( ( ~ ( number_ring @ SV218 ) )
= $true )
| ( ( ~ ( linordered_idom @ SV218 ) )
= $true )
| ( ( ! [SY1397: $i,SY1398: $i] :
~ ( ~ ( ~ ( ord_less @ SV218 @ ( number_number_of @ SV218 @ SY1397 ) @ ( number_number_of @ SV218 @ SY1398 ) )
| ( ord_less @ int @ SY1397 @ SY1398 ) )
| ~ ( ~ ( ord_less @ int @ SY1397 @ SY1398 )
| ( ord_less @ SV218 @ ( number_number_of @ SV218 @ SY1397 ) @ ( number_number_of @ SV218 @ SY1398 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3530]) ).
thf(3935,plain,
! [SV219: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( bit0 @ SV219 ) @ min ) )
= $true )
| ( ( ord_less_eq @ int @ SV219 @ min )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3531]) ).
thf(3936,plain,
! [SV219: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV219 @ min ) )
= $true )
| ( ( ord_less_eq @ int @ ( bit0 @ SV219 ) @ min )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3532]) ).
thf(3937,plain,
! [SV792: $i,SV933: $i,SV220: $i] :
( ( ( ! [SY2153: $i,SY2154: $i] :
( ~ ( dvd_dvd @ SV220 @ ( power_power @ SV220 @ SV933 @ SY2153 ) @ SY2154 )
| ~ ( ord_less_eq @ nat @ SV792 @ SY2153 )
| ( dvd_dvd @ SV220 @ ( power_power @ SV220 @ SV933 @ SV792 ) @ SY2154 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV220 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3533]) ).
thf(3938,plain,
! [SV540: $i,SV221: $i,SV678: $i] :
( ( ( ord_less @ real @ ( zero_zero @ real ) @ SV678 )
= $false )
| ( ( ~ ( ord_less @ real @ SV221 @ SV540 )
| ( ord_less @ real @ ( times_times @ real @ SV678 @ SV221 ) @ ( times_times @ real @ SV678 @ SV540 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3534]) ).
thf(3939,plain,
! [SV793: $i,SV934: $i,SV222: $i] :
( ( ( ! [SY2155: $i] :
( ~ ( dvd_dvd @ SV222 @ SV934 @ SY2155 )
| ( dvd_dvd @ SV222 @ SV934 @ ( times_times @ SV222 @ SV793 @ SY2155 ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV222 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3535]) ).
thf(3940,plain,
! [SV541: $i,SV223: $i,SV679: $i] :
( ( ( ord_less @ nat @ ( zero_zero @ nat ) @ SV679 )
= $false )
| ( ( ~ ( ord_less @ nat @ ( power_power @ nat @ SV679 @ SV223 ) @ ( power_power @ nat @ SV679 @ SV541 ) )
| ( ord_less @ nat @ SV223 @ SV541 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3536]) ).
thf(3941,plain,
! [SV542: $i,SV224: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV224 ) )
= $true )
| ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ SV542 @ SV224 ) )
= $true )
| ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV542 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3537]) ).
thf(3942,plain,
! [SV225: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( one_one @ int ) @ SV225 ) )
= $true )
| ( ( ord_less @ int @ ( zero_zero @ int ) @ SV225 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3538]) ).
thf(3943,plain,
! [SV225: $i] :
( ( ( ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV225 ) )
= $true )
| ( ( ord_less_eq @ int @ ( one_one @ int ) @ SV225 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3539]) ).
thf(3944,plain,
! [SV935: $i,SV794: $i,SV226: $i] :
( ( ( ! [SY2156: $i] :
( ~ ( dvd_dvd @ SV226 @ ( times_times @ SV226 @ SV794 @ SV935 ) @ SY2156 )
| ( dvd_dvd @ SV226 @ SV794 @ SY2156 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV226 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3540]) ).
thf(3945,plain,
! [SV543: $i,SV227: $i,SV680: $i] :
( ( ( mult_zero @ SV680 )
= $false )
| ( ( ( times_times @ SV680 @ ( ti @ SV680 @ SV227 ) @ SV543 )
= ( times_times @ SV680 @ SV227 @ SV543 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3541]) ).
thf(3946,plain,
! [SV544: $i,SV228: $i,SV681: $i] :
( ( ( power @ SV681 )
= $false )
| ( ( ( ti @ SV681 @ ( times_times @ SV681 @ SV228 @ SV544 ) )
= ( times_times @ SV681 @ SV228 @ SV544 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3542]) ).
thf(3947,plain,
! [SV545: $i,SV229: $i,SV682: $i] :
( ( ( semiring @ SV682 )
= $false )
| ( ( ( plus_plus @ SV682 @ ( ti @ SV682 @ SV229 ) @ SV545 )
= ( plus_plus @ SV682 @ SV229 @ SV545 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3543]) ).
thf(3948,plain,
! [SV936: $i,SV795: $i,SV230: $i] :
( ( ( ord_less_eq @ SV230 @ ( zero_zero @ SV230 ) @ ( plus_plus @ SV230 @ ( times_times @ SV230 @ SV795 @ SV795 ) @ ( times_times @ SV230 @ SV936 @ SV936 ) ) )
= $true )
| ( ( linordered_ring @ SV230 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3544]) ).
thf(3949,plain,
! [SV546: $i,SV231: $i] :
( ( ~ ( ord_less @ int @ ( bit0 @ SV231 ) @ ( bit1 @ SV546 ) )
| ( ord_less_eq @ int @ SV231 @ SV546 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3545]) ).
thf(3950,plain,
! [SV546: $i,SV231: $i] :
( ( ~ ( ord_less_eq @ int @ SV231 @ SV546 )
| ( ord_less @ int @ ( bit0 @ SV231 ) @ ( bit1 @ SV546 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3546]) ).
thf(3951,plain,
! [SV547: $i,SV233: $i] :
( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ SV233 @ ( number_number_of @ nat @ SV547 ) ) )
| ( ( number_number_of @ nat @ SV547 )
= ( zero_zero @ nat ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ SV233 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3548]) ).
thf(3952,plain,
! [SV233: $i,SV547: $i] :
( ( ~ ( ( ( number_number_of @ nat @ SV547 )
= ( zero_zero @ nat ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ SV233 ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ SV233 @ ( number_number_of @ nat @ SV547 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3549]) ).
thf(3953,plain,
! [SV234: $i] :
( ( ( ~ ( number @ SV234 ) )
= $true )
| ( ( ~ ( semiring @ SV234 ) )
= $true )
| ( ( ! [SY1424: $i,SY1425: $i,SY1426: $i] :
( ( times_times @ SV234 @ ( number_number_of @ SV234 @ SY1424 ) @ ( plus_plus @ SV234 @ SY1425 @ SY1426 ) )
= ( plus_plus @ SV234 @ ( times_times @ SV234 @ ( number_number_of @ SV234 @ SY1424 ) @ SY1425 ) @ ( times_times @ SV234 @ ( number_number_of @ SV234 @ SY1424 ) @ SY1426 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3550]) ).
thf(3954,plain,
! [SV548: $i,SV236: $i] :
( ( ~ ( ord_less @ int @ ( bit0 @ SV236 ) @ ( bit1 @ SV548 ) )
| ( ord_less_eq @ int @ SV236 @ SV548 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3552]) ).
thf(3955,plain,
! [SV548: $i,SV236: $i] :
( ( ~ ( ord_less_eq @ int @ SV236 @ SV548 )
| ( ord_less @ int @ ( bit0 @ SV236 ) @ ( bit1 @ SV548 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3553]) ).
thf(3956,plain,
! [SV937: $i,SV797: $i,SV237: $i] :
( ( ( ~ ( ~ ( ( ( number_number_of @ SV237 @ SV797 )
!= ( ti @ SV237 @ SV937 ) )
| ( ( ti @ SV237 @ SV937 )
= ( number_number_of @ SV237 @ SV797 ) ) )
| ~ ( ( ( ti @ SV237 @ SV937 )
!= ( number_number_of @ SV237 @ SV797 ) )
| ( ( number_number_of @ SV237 @ SV797 )
= ( ti @ SV237 @ SV937 ) ) ) ) )
= $true )
| ( ( number @ SV237 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3554]) ).
thf(3957,plain,
! [SV938: $i,SV798: $i,SV238: $i] :
( ( ( ! [SY2157: $i] :
( ( plus_plus @ SV238 @ SV798 @ ( plus_plus @ SV238 @ SV938 @ SY2157 ) )
= ( plus_plus @ SV238 @ ( plus_plus @ SV238 @ SV798 @ SV938 ) @ SY2157 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV238 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3555]) ).
thf(3958,plain,
! [SV239: $i] :
( ( ( ~ ( ord_less_eq @ int @ min @ ( bit0 @ SV239 ) ) )
= $true )
| ( ( ord_less @ int @ min @ SV239 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3556]) ).
thf(3959,plain,
! [SV239: $i] :
( ( ( ~ ( ord_less @ int @ min @ SV239 ) )
= $true )
| ( ( ord_less_eq @ int @ min @ ( bit0 @ SV239 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3557]) ).
thf(3960,plain,
! [SV549: $i,SV240: $i,SV683: $i,SV799: $i] :
( ( ( ~ ( zprime @ SV799 ) )
= $true )
| ( ( ~ ~ ( dvd_dvd @ int @ SV799 @ SV683 )
| ~ ( dvd_dvd @ int @ ( power_power @ int @ SV799 @ SV240 ) @ ( times_times @ int @ SV683 @ SV549 ) )
| ( dvd_dvd @ int @ ( power_power @ int @ SV799 @ SV240 ) @ SV549 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3558]) ).
thf(3961,plain,
! [SV241: $i] :
( ( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ ( number_number_of @ nat @ SV241 ) ) )
= $true )
| ( ( ord_less @ int @ pls @ SV241 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3559]) ).
thf(3962,plain,
! [SV241: $i] :
( ( ( ~ ( ord_less @ int @ pls @ SV241 ) )
= $true )
| ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( number_number_of @ nat @ SV241 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3560]) ).
thf(3963,plain,
! [SV550: $i,SV242: $i] :
( ( ~ ( ord_less_eq @ int @ ( bit0 @ SV242 ) @ ( bit1 @ SV550 ) )
| ( ord_less_eq @ int @ SV242 @ SV550 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3561]) ).
thf(3964,plain,
! [SV550: $i,SV242: $i] :
( ( ~ ( ord_less_eq @ int @ SV242 @ SV550 )
| ( ord_less_eq @ int @ ( bit0 @ SV242 ) @ ( bit1 @ SV550 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3562]) ).
thf(3965,plain,
! [SV551: $i,SV243: $i,SV684: $i] :
( ( ( power @ SV684 )
= $false )
| ( ( ( times_times @ SV684 @ ( ti @ SV684 @ SV243 ) @ SV551 )
= ( times_times @ SV684 @ SV243 @ SV551 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3563]) ).
thf(3966,plain,
! [SV244: $i] :
( ( ( ~ ( ord_less @ int @ pls @ ( bit1 @ SV244 ) ) )
= $true )
| ( ( ord_less_eq @ int @ pls @ SV244 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3564]) ).
thf(3967,plain,
! [SV244: $i] :
( ( ( ~ ( ord_less_eq @ int @ pls @ SV244 ) )
= $true )
| ( ( ord_less @ int @ pls @ ( bit1 @ SV244 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3565]) ).
thf(3968,plain,
! [SV552: $i,SV245: $i,SV685: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV685 @ pls )
| ( ( times_times @ nat @ ( number_number_of @ nat @ SV685 ) @ ( times_times @ nat @ ( number_number_of @ nat @ SV245 ) @ SV552 ) )
= ( zero_zero @ nat ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3566]) ).
thf(3969,plain,
! [SV552: $i,SV245: $i,SV685: $i] :
( ( ~ ( ~ ~ ( ord_less @ int @ SV685 @ pls )
| ( ( times_times @ nat @ ( number_number_of @ nat @ SV685 ) @ ( times_times @ nat @ ( number_number_of @ nat @ SV245 ) @ SV552 ) )
= ( times_times @ nat @ ( number_number_of @ nat @ ( times_times @ int @ SV685 @ SV245 ) ) @ SV552 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3566]) ).
thf(3970,plain,
! [SV553: $i,SV246: $i,SV686: $i] :
( ( ( dvd @ SV686 )
= $false )
| ( ( ( times_times @ SV686 @ ( ti @ SV686 @ SV246 ) @ SV553 )
= ( times_times @ SV686 @ SV246 @ SV553 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3567]) ).
thf(3971,plain,
! [SV554: $i,SV247: $i] :
( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ SV247 @ SV554 ) )
| ( SV554
= ( zero_zero @ nat ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ SV247 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3568]) ).
thf(3972,plain,
! [SV247: $i,SV554: $i] :
( ( ~ ( ( SV554
= ( zero_zero @ nat ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ SV247 ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ SV247 @ SV554 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3569]) ).
thf(3973,plain,
! [SV939: $i,SV800: $i,SV248: $i] :
( ( ( ! [SY2158: $i] :
( ( times_times @ SV248 @ ( number_number_of @ SV248 @ SV800 ) @ ( times_times @ SV248 @ ( number_number_of @ SV248 @ SV939 ) @ SY2158 ) )
= ( times_times @ SV248 @ ( number_number_of @ SV248 @ ( times_times @ int @ SV800 @ SV939 ) ) @ SY2158 ) ) )
= $true )
| ( ( number_ring @ SV248 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3570]) ).
thf(3974,plain,
! [SV249: $i] :
( ( ( ~ ( ord_less @ int @ ( bit1 @ SV249 ) @ ( zero_zero @ int ) ) )
= $true )
| ( ( ord_less @ int @ SV249 @ ( zero_zero @ int ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3571]) ).
thf(3975,plain,
! [SV249: $i] :
( ( ( ~ ( ord_less @ int @ SV249 @ ( zero_zero @ int ) ) )
= $true )
| ( ( ord_less @ int @ ( bit1 @ SV249 ) @ ( zero_zero @ int ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3572]) ).
thf(3976,plain,
! [SV555: $i,SV251: $i,SV687: $i] :
( ( ( power @ SV687 )
= $false )
| ( ( ( power_power @ SV687 @ SV251 @ ( ti @ nat @ SV555 ) )
= ( power_power @ SV687 @ SV251 @ SV555 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3574]) ).
thf(3977,plain,
! [SV940: $i,SV802: $i,SV252: $i] :
( ( ( ! [SY2159: $i] :
( ( times_times @ SV252 @ ( times_times @ SV252 @ SV802 @ SV940 ) @ SY2159 )
= ( times_times @ SV252 @ SV802 @ ( times_times @ SV252 @ SV940 @ SY2159 ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV252 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3575]) ).
thf(3978,plain,
! [SV556: $i,SV253: $i] :
( ( ~ ( ord_less @ int @ ( bit1 @ SV253 ) @ ( bit0 @ SV556 ) )
| ( ord_less @ int @ SV253 @ SV556 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3576]) ).
thf(3979,plain,
! [SV556: $i,SV253: $i] :
( ( ~ ( ord_less @ int @ SV253 @ SV556 )
| ( ord_less @ int @ ( bit1 @ SV253 ) @ ( bit0 @ SV556 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3577]) ).
thf(3980,plain,
! [SV941: $i,SV803: $i,SV254: $i] :
( ( ( ( plus_plus @ SV254 @ SV803 @ ( times_times @ SV254 @ SV941 @ SV803 ) )
= ( times_times @ SV254 @ ( plus_plus @ SV254 @ SV941 @ ( one_one @ SV254 ) ) @ SV803 ) )
= $true )
| ( ( comm_semiring_1 @ SV254 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3578]) ).
thf(3981,plain,
! [SV942: $i,SV804: $i,SV255: $i] :
( ( ( ! [SY2160: $i,SY2161: $i] :
~ ( ~ ( ( ( plus_plus @ SV255 @ ( times_times @ SV255 @ SV804 @ SV942 ) @ ( times_times @ SV255 @ SY2160 @ SY2161 ) )
!= ( plus_plus @ SV255 @ ( times_times @ SV255 @ SV804 @ SY2161 ) @ ( times_times @ SV255 @ SY2160 @ SV942 ) ) )
| ( ( ti @ SV255 @ SV804 )
= ( ti @ SV255 @ SY2160 ) )
| ( ( ti @ SV255 @ SV942 )
= ( ti @ SV255 @ SY2161 ) ) )
| ~ ( ~ ( ( ( ti @ SV255 @ SV804 )
= ( ti @ SV255 @ SY2160 ) )
| ( ( ti @ SV255 @ SV942 )
= ( ti @ SV255 @ SY2161 ) ) )
| ( ( plus_plus @ SV255 @ ( times_times @ SV255 @ SV804 @ SV942 ) @ ( times_times @ SV255 @ SY2160 @ SY2161 ) )
= ( plus_plus @ SV255 @ ( times_times @ SV255 @ SV804 @ SY2161 ) @ ( times_times @ SV255 @ SY2160 @ SV942 ) ) ) ) ) )
= $true )
| ( ( semiri456707255roduct @ SV255 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3579]) ).
thf(3982,plain,
! [SV256: $i] :
( ( ( ~ ( ord_less_eq @ int @ pls @ ( bit1 @ SV256 ) ) )
= $true )
| ( ( ord_less_eq @ int @ pls @ SV256 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3580]) ).
thf(3983,plain,
! [SV256: $i] :
( ( ( ~ ( ord_less_eq @ int @ pls @ SV256 ) )
= $true )
| ( ( ord_less_eq @ int @ pls @ ( bit1 @ SV256 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3581]) ).
thf(3984,plain,
! [SV557: $i,SV257: $i,SV943: $i,SV805: $i,SV688: $i] :
( ( ~ ( zcong @ SV688 @ SV805 @ SV943 )
| ~ ( ~ ( ~ ( zcong @ SV257 @ ( times_times @ int @ SV557 @ SV688 ) @ SV943 )
| ( zcong @ SV257 @ ( times_times @ int @ SV557 @ SV805 ) @ SV943 ) )
| ~ ( ~ ( zcong @ SV257 @ ( times_times @ int @ SV557 @ SV805 ) @ SV943 )
| ( zcong @ SV257 @ ( times_times @ int @ SV557 @ SV688 ) @ SV943 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3582]) ).
thf(3985,plain,
! [SV558: $i,SV259: $i,SV689: $i] :
( ( ( SV689
!= ( zero_zero @ nat ) )
= $false )
| ( ( ~ ( dvd_dvd @ nat @ ( power_power @ nat @ SV259 @ SV689 ) @ SV558 )
| ( dvd_dvd @ nat @ SV259 @ SV558 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3583]) ).
thf(3986,plain,
! [SV690: $i,SV559: $i,SV261: $i] :
( ( ~ ( ~ ( zcong @ SV261 @ ( ti @ int @ SV559 ) @ SV690 )
| ( zcong @ SV261 @ SV559 @ SV690 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3584]) ).
thf(3987,plain,
! [SV690: $i,SV559: $i,SV261: $i] :
( ( ~ ( ~ ( zcong @ SV261 @ SV559 @ SV690 )
| ( zcong @ SV261 @ ( ti @ int @ SV559 ) @ SV690 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3584]) ).
thf(3988,plain,
! [SV944: $i,SV806: $i,SV263: $i] :
( ( ( ( number_number_of @ SV263 @ ( plus_plus @ int @ SV806 @ SV944 ) )
= ( plus_plus @ SV263 @ ( number_number_of @ SV263 @ SV806 ) @ ( number_number_of @ SV263 @ SV944 ) ) )
= $true )
| ( ( number_ring @ SV263 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3585]) ).
thf(3989,plain,
! [SV945: $i,SV807: $i,SV264: $i] :
( ( ( ( number_number_of @ SV264 @ ( times_times @ int @ SV807 @ SV945 ) )
= ( times_times @ SV264 @ ( number_number_of @ SV264 @ SV807 ) @ ( number_number_of @ SV264 @ SV945 ) ) )
= $true )
| ( ( number_ring @ SV264 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3586]) ).
thf(3990,plain,
! [SV946: $i,SV809: $i,SV266: $i] :
( ( ( ! [SY2162: $i,SY2163: $i] :
( ( plus_plus @ SV266 @ ( plus_plus @ SV266 @ SV809 @ SV946 ) @ ( plus_plus @ SV266 @ SY2162 @ SY2163 ) )
= ( plus_plus @ SV266 @ ( plus_plus @ SV266 @ SV809 @ SY2162 ) @ ( plus_plus @ SV266 @ SV946 @ SY2163 ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV266 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3588]) ).
thf(3991,plain,
! [SV560: $i,SV268: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV268 ) )
= $true )
| ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( times_times @ int @ SV560 @ SV268 ) )
= $true )
| ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV560 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3589]) ).
thf(3992,plain,
! [SV810: $i,SV269: $i] :
( ( ( ~ ( ~ ( ord_less @ SV269 @ ( plus_plus @ SV269 @ SV810 @ SV810 ) @ ( zero_zero @ SV269 ) )
| ( ord_less @ SV269 @ SV810 @ ( zero_zero @ SV269 ) ) )
| ~ ( ~ ( ord_less @ SV269 @ SV810 @ ( zero_zero @ SV269 ) )
| ( ord_less @ SV269 @ ( plus_plus @ SV269 @ SV810 @ SV810 ) @ ( zero_zero @ SV269 ) ) ) )
= $false )
| ( ( linordered_idom @ SV269 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3590]) ).
thf(3993,plain,
! [SV270: $i,SV561: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV561 @ SV270 ) )
= $true )
| ( ( ( ti @ int @ SV270 )
= ( ti @ int @ SV561 ) )
= $true )
| ( ( ord_less_eq @ int @ SV270 @ SV561 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3591]) ).
thf(3994,plain,
! [SV947: $i,SV811: $i,SV271: $i] :
( ( ( ! [SY2164: $i] :
( ( plus_plus @ SV271 @ ( number_number_of @ SV271 @ SV811 ) @ ( minus_minus @ SV271 @ ( number_number_of @ SV271 @ SV947 ) @ SY2164 ) )
= ( minus_minus @ SV271 @ ( number_number_of @ SV271 @ ( plus_plus @ int @ SV811 @ SV947 ) ) @ SY2164 ) ) )
= $true )
| ( ( number_ring @ SV271 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3592]) ).
thf(3995,plain,
! [SV562: $i,SV273: $i,SV691: $i] :
( ( ( SV691
!= ( zero_zero @ real ) )
= $false )
| ( ( ~ ( ~ ( ( ( times_times @ real @ SV691 @ SV273 )
!= ( times_times @ real @ SV691 @ SV562 ) )
| ( SV273 = SV562 ) )
| ~ ( ( SV273 != SV562 )
| ( ( times_times @ real @ SV691 @ SV273 )
= ( times_times @ real @ SV691 @ SV562 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3594]) ).
thf(3996,plain,
! [SV274: $i] :
( ( ( ~ ( ord_less @ int @ min @ ( bit1 @ SV274 ) ) )
= $true )
| ( ( ord_less @ int @ min @ SV274 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3595]) ).
thf(3997,plain,
! [SV274: $i] :
( ( ( ~ ( ord_less @ int @ min @ SV274 ) )
= $true )
| ( ( ord_less @ int @ min @ ( bit1 @ SV274 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3596]) ).
thf(3998,plain,
! [SV948: $i,SV813: $i,SV275: $i] :
( ( ( ( number_number_of @ SV275 @ ( minus_minus @ int @ SV813 @ SV948 ) )
= ( minus_minus @ SV275 @ ( number_number_of @ SV275 @ SV813 ) @ ( number_number_of @ SV275 @ SV948 ) ) )
= $true )
| ( ( number_ring @ SV275 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3597]) ).
thf(3999,plain,
! [SV815: $i,SV949: $i,SV277: $i] :
( ( ( ! [SY2165: $i] :
( ~ ( dvd_dvd @ SV277 @ SV949 @ SY2165 )
| ~ ( dvd_dvd @ SV277 @ SV949 @ SV815 )
| ( dvd_dvd @ SV277 @ SV949 @ ( plus_plus @ SV277 @ SY2165 @ SV815 ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV277 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3599]) ).
thf(4000,plain,
! [SV279: $i] :
( ( ( ~ ( ord_less @ int @ ( bit0 @ SV279 ) @ pls ) )
= $true )
| ( ( ord_less @ int @ SV279 @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3601]) ).
thf(4001,plain,
! [SV279: $i] :
( ( ( ~ ( ord_less @ int @ SV279 @ pls ) )
= $true )
| ( ( ord_less @ int @ ( bit0 @ SV279 ) @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3602]) ).
thf(4002,plain,
! [SV563: $i,SV280: $i,SV692: $i] :
( ( ( semiring @ SV692 )
= $false )
| ( ( ( ti @ SV692 @ ( times_times @ SV692 @ SV280 @ SV563 ) )
= ( times_times @ SV692 @ SV280 @ SV563 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3603]) ).
thf(4003,plain,
! [SV564: $i,SV281: $i] :
( ( ( ( bit0 @ SV281 )
!= ( bit0 @ SV564 ) )
| ( ( ti @ int @ SV281 )
= ( ti @ int @ SV564 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3604]) ).
thf(4004,plain,
! [SV564: $i,SV281: $i] :
( ( ( ( ti @ int @ SV281 )
!= ( ti @ int @ SV564 ) )
| ( ( bit0 @ SV281 )
= ( bit0 @ SV564 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3605]) ).
thf(4005,plain,
! [SV282: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( bit1 @ SV282 ) @ min ) )
= $true )
| ( ( ord_less_eq @ int @ SV282 @ min )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3606]) ).
thf(4006,plain,
! [SV282: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV282 @ min ) )
= $true )
| ( ( ord_less_eq @ int @ ( bit1 @ SV282 ) @ min )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3607]) ).
thf(4007,plain,
! [SV818: $i,SV950: $i,SV284: $i] :
( ( ( ! [SY2166: $i] :
( ~ ( dvd_dvd @ SV284 @ SV950 @ SY2166 )
| ( dvd_dvd @ SV284 @ ( power_power @ SV284 @ SV950 @ SV818 ) @ ( power_power @ SV284 @ SY2166 @ SV818 ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV284 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3609]) ).
thf(4008,plain,
! [SV285: $i,SV819: $i,SV951: $i] :
( ( ( ~ ( ord_less_eq @ int @ pls @ SV951 )
| ~ ( ord_less_eq @ int @ pls @ SV819 )
| ( ( plus_plus @ SV285 @ ( number_number_of @ SV285 @ SV951 ) @ ( number_number_of @ SV285 @ SV819 ) )
= ( number_number_of @ SV285 @ ( plus_plus @ int @ SV951 @ SV819 ) ) ) )
= $true )
| ( ( number_semiring @ SV285 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3610]) ).
thf(4009,plain,
! [SV952: $i,SV820: $i,SV286: $i] :
( ( ( ( power_power @ SV286 @ SV820 @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV952 ) )
= ( power_power @ SV286 @ ( power_power @ SV286 @ SV820 @ SV952 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $true )
| ( ( monoid_mult @ SV286 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3611]) ).
thf(4010,plain,
! [SV565: $i,SV287: $i,SV693: $i] :
( ( ( dvd @ SV693 )
= $false )
| ( ( ( times_times @ SV693 @ SV287 @ ( ti @ SV693 @ SV565 ) )
= ( times_times @ SV693 @ SV287 @ SV565 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3612]) ).
thf(4011,plain,
! [SV566: $i,SV288: $i,SV694: $i,SV821: $i] :
( ( ( ~ ( zprime @ SV821 ) )
= $true )
| ( ( ~ ~ ( dvd_dvd @ int @ SV821 @ SV694 )
| ~ ( dvd_dvd @ int @ ( power_power @ int @ SV821 @ SV288 ) @ ( times_times @ int @ SV566 @ SV694 ) )
| ( dvd_dvd @ int @ ( power_power @ int @ SV821 @ SV288 ) @ SV566 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3613]) ).
thf(4012,plain,
! [SV567: $i,SV289: $i,SV695: $i] :
( ( ( ab_group_add @ SV695 )
= $false )
| ( ( ( plus_plus @ SV695 @ ( ti @ SV695 @ SV289 ) @ SV567 )
= ( plus_plus @ SV695 @ SV289 @ SV567 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3614]) ).
thf(4013,plain,
! [SV290: $i] :
( ( ( ~ ( ord_less @ int @ ( bit0 @ SV290 ) @ ( zero_zero @ int ) ) )
= $true )
| ( ( ord_less @ int @ SV290 @ ( zero_zero @ int ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3615]) ).
thf(4014,plain,
! [SV290: $i] :
( ( ( ~ ( ord_less @ int @ SV290 @ ( zero_zero @ int ) ) )
= $true )
| ( ( ord_less @ int @ ( bit0 @ SV290 ) @ ( zero_zero @ int ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3616]) ).
thf(4015,plain,
! [SV568: $i,SV292: $i] :
( ( ~ ( zcong @ ( times_times @ int @ SV292 @ ( minus_minus @ int @ SV568 @ ( one_one @ int ) ) ) @ ( one_one @ int ) @ SV568 )
| ( zcong @ SV292 @ ( minus_minus @ int @ SV568 @ ( one_one @ int ) ) @ SV568 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3618]) ).
thf(4016,plain,
! [SV568: $i,SV292: $i] :
( ( ~ ( zcong @ SV292 @ ( minus_minus @ int @ SV568 @ ( one_one @ int ) ) @ SV568 )
| ( zcong @ ( times_times @ int @ SV292 @ ( minus_minus @ int @ SV568 @ ( one_one @ int ) ) ) @ ( one_one @ int ) @ SV568 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3619]) ).
thf(4017,plain,
! [SV294: $i,SV696: $i,SV569: $i] :
( ( ( ord_less_eq @ int @ SV569 @ SV696 )
= $false )
| ( ( ~ ( ord_less_eq @ int @ SV696 @ SV294 )
| ( ord_less_eq @ int @ SV569 @ SV294 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3621]) ).
thf(4018,plain,
! [SV953: $i,SV824: $i,SV296: $i] :
( ( ( ! [SY2167: $i] :
( ( plus_plus @ SV296 @ ( plus_plus @ SV296 @ SV824 @ SV953 ) @ SY2167 )
= ( plus_plus @ SV296 @ ( plus_plus @ SV296 @ SV824 @ SY2167 ) @ SV953 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV296 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3622]) ).
thf(4019,plain,
! [SV297: $i,SV697: $i,SV570: $i] :
( ( ( ord_less @ int @ SV570 @ SV697 )
= $false )
| ( ( ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV297 )
| ( ord_less @ int @ ( times_times @ int @ SV297 @ SV570 ) @ ( times_times @ int @ SV297 @ SV697 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3623]) ).
thf(4020,plain,
! [SV954: $i,SV825: $i,SV298: $i] :
( ( ( ! [SY2168: $i] :
( ( power_power @ SV298 @ ( times_times @ SV298 @ SV825 @ SV954 ) @ SY2168 )
= ( times_times @ SV298 @ ( power_power @ SV298 @ SV825 @ SY2168 ) @ ( power_power @ SV298 @ SV954 @ SY2168 ) ) ) )
= $true )
| ( ( comm_monoid_mult @ SV298 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3624]) ).
thf(4021,plain,
! [SV299: $i,SV571: $i] :
( ( ( ( SV571
= ( zero_zero @ nat ) )
| ( SV571 = SV299 ) )
= $true )
| ( ( ord_less_eq @ nat @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV299 ) @ SV571 )
= $true )
| ( ( dvd_dvd @ nat @ SV299 @ SV571 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3625]) ).
thf(4022,plain,
! [SV572: $i,SV300: $i] :
( ( ~ ( ord_less_eq @ int @ ( bit1 @ SV300 ) @ ( bit1 @ SV572 ) )
| ( ord_less_eq @ int @ SV300 @ SV572 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3626]) ).
thf(4023,plain,
! [SV572: $i,SV300: $i] :
( ( ~ ( ord_less_eq @ int @ SV300 @ SV572 )
| ( ord_less_eq @ int @ ( bit1 @ SV300 ) @ ( bit1 @ SV572 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3627]) ).
thf(4024,plain,
! [SV955: $i,SV826: $i,SV301: $i] :
( ( ( ~ ( ~ ( ( ( times_times @ SV301 @ SV826 @ SV955 )
!= ( zero_zero @ SV301 ) )
| ( ( ti @ SV301 @ SV826 )
= ( zero_zero @ SV301 ) )
| ( ( ti @ SV301 @ SV955 )
= ( zero_zero @ SV301 ) ) )
| ~ ( ~ ( ( ( ti @ SV301 @ SV826 )
= ( zero_zero @ SV301 ) )
| ( ( ti @ SV301 @ SV955 )
= ( zero_zero @ SV301 ) ) )
| ( ( times_times @ SV301 @ SV826 @ SV955 )
= ( zero_zero @ SV301 ) ) ) ) )
= $true )
| ( ( ring_n68954251visors @ SV301 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3628]) ).
thf(4025,plain,
! [SV303: $i] :
( ( ( pls
!= ( bit0 @ SV303 ) )
= $true )
| ( ( pls
= ( ti @ int @ SV303 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3630]) ).
thf(4026,plain,
! [SV303: $i] :
( ( ( pls
!= ( ti @ int @ SV303 ) )
= $true )
| ( ( pls
= ( bit0 @ SV303 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3631]) ).
thf(4027,plain,
! [SV956: $i,SV828: $i,SV304: $i] :
( ( ( ! [SY2169: $i] :
( ~ ( ord_less @ SV304 @ ( one_one @ SV304 ) @ SY2169 )
| ~ ( ord_less_eq @ SV304 @ ( power_power @ SV304 @ SY2169 @ SV828 ) @ ( power_power @ SV304 @ SY2169 @ SV956 ) )
| ( ord_less_eq @ nat @ SV828 @ SV956 ) ) )
= $true )
| ( ( linordered_semidom @ SV304 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3632]) ).
thf(4028,plain,
! [SV957: $i,SV829: $i,SV698: $i,SV573: $i,SV305: $i] :
( ( ! [SY2170: $i] :
( ( ( plus_plus @ int @ ( times_times @ int @ SV305 @ SV573 ) @ SV698 )
!= ( plus_plus @ int @ ( times_times @ int @ SV829 @ SV957 ) @ SY2170 ) )
| ~ ( ord_less @ int @ ( plus_plus @ int @ ( times_times @ int @ SV829 @ SV957 ) @ SY2170 ) @ ( zero_zero @ int ) )
| ~ ( ord_less @ int @ SV698 @ SV305 )
| ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SY2170 )
| ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV829 )
| ~ ( ord_less_eq @ int @ SV829 @ SV305 )
| ( ord_less_eq @ int @ SV957 @ SV573 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3633]) ).
thf(4029,plain,
! [SV958: $i,SV830: $i,SV306: $i] :
( ( ( ( plus_plus @ SV306 @ ( times_times @ SV306 @ SV830 @ SV958 ) @ SV958 )
= ( times_times @ SV306 @ ( plus_plus @ SV306 @ SV830 @ ( one_one @ SV306 ) ) @ SV958 ) )
= $true )
| ( ( comm_semiring_1 @ SV306 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3634]) ).
thf(4030,plain,
! [SV574: $i,SV307: $i,SV699: $i] :
( ( ( dvd @ SV699 )
= $false )
| ( ( ( ti @ SV699 @ ( times_times @ SV699 @ SV307 @ SV574 ) )
= ( times_times @ SV699 @ SV307 @ SV574 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3635]) ).
thf(4031,plain,
! [SV308: $i,SV831: $i,SV700: $i,SV575: $i] :
( ( ( ~ ( zcong @ SV575 @ SV700 @ SV831 ) )
= $true )
| ( ( zcong @ ( power_power @ int @ SV575 @ SV308 ) @ ( power_power @ int @ SV700 @ SV308 ) @ SV831 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3636]) ).
thf(4032,plain,
! [SV309: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( bit1 @ SV309 ) @ pls ) )
= $true )
| ( ( ord_less @ int @ SV309 @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3637]) ).
thf(4033,plain,
! [SV309: $i] :
( ( ( ~ ( ord_less @ int @ SV309 @ pls ) )
= $true )
| ( ( ord_less_eq @ int @ ( bit1 @ SV309 ) @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3638]) ).
thf(4034,plain,
! [SV959: $i,SV832: $i,SV311: $i] :
( ( ( ! [SY2171: $i] :
( ( power_power @ SV311 @ ( power_power @ SV311 @ SV832 @ SV959 ) @ SY2171 )
= ( power_power @ SV311 @ SV832 @ ( times_times @ nat @ SV959 @ SY2171 ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV311 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3639]) ).
thf(4035,plain,
! [SV960: $i,SV833: $i,SV701: $i,SV576: $i,SV312: $i] :
( ( ~ ( ord_less_eq @ int @ ( plus_plus @ int @ ( times_times @ int @ SV312 @ SV576 ) @ SV701 ) @ ( plus_plus @ int @ ( times_times @ int @ SV312 @ SV833 ) @ SV960 ) )
| ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV701 )
| ~ ( ord_less @ int @ SV701 @ SV312 )
| ~ ( ord_less @ int @ SV960 @ SV312 )
| ( ord_less_eq @ int @ SV576 @ SV833 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3640]) ).
thf(4036,plain,
! [SV961: $i,SV834: $i,SV313: $i] :
( ( ( ~ ( ~ ( ( ( ti @ SV313 @ SV834 )
!= ( plus_plus @ SV313 @ SV834 @ SV961 ) )
| ( ( ti @ SV313 @ SV961 )
= ( zero_zero @ SV313 ) ) )
| ~ ( ( ( ti @ SV313 @ SV961 )
!= ( zero_zero @ SV313 ) )
| ( ( ti @ SV313 @ SV834 )
= ( plus_plus @ SV313 @ SV834 @ SV961 ) ) ) ) )
= $true )
| ( ( semiri456707255roduct @ SV313 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3641]) ).
thf(4037,plain,
! [SV577: $i,SV314: $i] :
( ( ~ ( quadRes @ SV314 @ SV577 )
| ~ ! [SY1865: $i] :
~ ( zcong @ ( power_power @ int @ SY1865 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SV577 @ SV314 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3642]) ).
thf(4038,plain,
! [SV314: $i,SV577: $i] :
( ( ~ ~ ! [SY1866: $i] :
~ ( zcong @ ( power_power @ int @ SY1866 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SV577 @ SV314 )
| ( quadRes @ SV314 @ SV577 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3643]) ).
thf(4039,plain,
! [SV835: $i,SV315: $i,SV962: $i] :
( ( ( ! [SY2172: $i] :
( ~ ( ord_less_eq @ nat @ SV962 @ SY2172 )
| ~ ( ord_less_eq @ SV315 @ ( one_one @ SV315 ) @ SV835 )
| ( ord_less_eq @ SV315 @ ( power_power @ SV315 @ SV835 @ SV962 ) @ ( power_power @ SV315 @ SV835 @ SY2172 ) ) ) )
= $true )
| ( ( linordered_semidom @ SV315 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3644]) ).
thf(4040,plain,
! [SV963: $i,SV836: $i,SV316: $i] :
( ( ( ! [SY2173: $i] :
( ( times_times @ SV316 @ ( plus_plus @ SV316 @ SV836 @ SV963 ) @ SY2173 )
= ( plus_plus @ SV316 @ ( times_times @ SV316 @ SV836 @ SY2173 ) @ ( times_times @ SV316 @ SV963 @ SY2173 ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV316 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3645]) ).
thf(4041,plain,
! [SV837: $i,SV964: $i,SV317: $i] :
( ( ( ~ ( ord_less_eq @ SV317 @ ( one_one @ SV317 ) @ SV964 )
| ( ord_less_eq @ SV317 @ ( one_one @ SV317 ) @ ( power_power @ SV317 @ SV964 @ SV837 ) ) )
= $true )
| ( ( linordered_semidom @ SV317 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3646]) ).
thf(4042,plain,
! [SV965: $i,SV838: $i,SV318: $i] :
( ( ( ( times_times @ SV318 @ SV838 @ SV965 )
= ( times_times @ SV318 @ SV965 @ SV838 ) )
= $true )
| ( ( comm_semiring_1 @ SV318 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3647]) ).
thf(4043,plain,
! [SV966: $i,SV839: $i,SV319: $i] :
( ( ( ~ ( ~ ( ~ ( ord_less_eq @ SV319 @ ( times_times @ SV319 @ SV839 @ SV966 ) @ ( zero_zero @ SV319 ) )
| ~ ( ~ ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SV839 )
| ~ ( ord_less_eq @ SV319 @ SV966 @ ( zero_zero @ SV319 ) ) )
| ~ ( ~ ( ord_less_eq @ SV319 @ SV839 @ ( zero_zero @ SV319 ) )
| ~ ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SV966 ) ) )
| ~ ( ~ ( ~ ( ~ ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SV839 )
| ~ ( ord_less_eq @ SV319 @ SV966 @ ( zero_zero @ SV319 ) ) )
| ~ ( ~ ( ord_less_eq @ SV319 @ SV839 @ ( zero_zero @ SV319 ) )
| ~ ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SV966 ) ) )
| ( ord_less_eq @ SV319 @ ( times_times @ SV319 @ SV839 @ SV966 ) @ ( zero_zero @ SV319 ) ) ) ) )
= $true )
| ( ( linord581940658strict @ SV319 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3648]) ).
thf(4044,plain,
! [SV320: $i] :
( ( ( ( zero_zero @ nat )
!= ( number_number_of @ nat @ SV320 ) )
= $true )
| ( ( ord_less_eq @ int @ SV320 @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3649]) ).
thf(4045,plain,
! [SV320: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV320 @ pls ) )
= $true )
| ( ( ( zero_zero @ nat )
= ( number_number_of @ nat @ SV320 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3650]) ).
thf(4046,plain,
! [SV321: $i] :
( ( ( ~ ( number_ring @ SV321 ) )
= $true )
| ( ( ~ ( linordered_idom @ SV321 ) )
= $true )
| ( ( ! [SY1569: $i,SY1570: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV321 @ ( number_number_of @ SV321 @ SY1569 ) @ ( number_number_of @ SV321 @ SY1570 ) )
| ( ord_less_eq @ int @ SY1569 @ SY1570 ) )
| ~ ( ~ ( ord_less_eq @ int @ SY1569 @ SY1570 )
| ( ord_less_eq @ SV321 @ ( number_number_of @ SV321 @ SY1569 ) @ ( number_number_of @ SV321 @ SY1570 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3651]) ).
thf(4047,plain,
! [SV967: $i,SV841: $i,SV323: $i] :
( ( ( ! [SY2174: $i,SY2175: $i] :
( ~ ( dvd_dvd @ SV323 @ SY2174 @ SY2175 )
| ~ ( ord_less_eq @ nat @ SV841 @ SV967 )
| ( dvd_dvd @ SV323 @ ( power_power @ SV323 @ SY2174 @ SV841 ) @ ( power_power @ SV323 @ SY2175 @ SV967 ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV323 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3653]) ).
thf(4048,plain,
! [SV968: $i,SV842: $i,SV325: $i] :
( ( ( ~ ( ord_less_eq @ SV325 @ ( power_power @ SV325 @ SV842 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV325 @ SV968 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ~ ( ord_less_eq @ SV325 @ ( zero_zero @ SV325 ) @ SV968 )
| ( ord_less_eq @ SV325 @ SV842 @ SV968 ) )
= $true )
| ( ( linordered_semidom @ SV325 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3654]) ).
thf(4049,plain,
! [SV578: $i,SV327: $i] :
( ( ( ( ti @ int @ SV327 )
= ( one_one @ int ) )
= $true )
| ( ( ( ti @ int @ SV327 )
= ( number_number_of @ int @ min ) )
= $true )
| ( ( ( times_times @ int @ SV327 @ SV578 )
= ( one_one @ int ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3655]) ).
thf(4050,plain,
! [SV328: $i] :
( ( ( ~ ( ord_less @ int @ min @ ( bit0 @ SV328 ) ) )
= $true )
| ( ( ord_less @ int @ min @ SV328 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3656]) ).
thf(4051,plain,
! [SV328: $i] :
( ( ( ~ ( ord_less @ int @ min @ SV328 ) )
= $true )
| ( ( ord_less @ int @ min @ ( bit0 @ SV328 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3657]) ).
thf(4052,plain,
! [SV969: $i,SV843: $i,SV329: $i] :
( ( ( ! [SY2176: $i] :
( ( power_power @ SV329 @ SV843 @ ( plus_plus @ nat @ SV969 @ SY2176 ) )
= ( times_times @ SV329 @ ( power_power @ SV329 @ SV843 @ SV969 ) @ ( power_power @ SV329 @ SV843 @ SY2176 ) ) ) )
= $true )
| ( ( monoid_mult @ SV329 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3658]) ).
thf(4053,plain,
! [SV970: $i,SV844: $i,SV330: $i] :
( ( ( ! [SY2177: $i] :
( ~ ( dvd_dvd @ SV330 @ ( times_times @ SV330 @ SV844 @ SV970 ) @ SY2177 )
| ( dvd_dvd @ SV330 @ SV970 @ SY2177 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV330 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3659]) ).
thf(4054,plain,
! [SV971: $i,SV845: $i,SV332: $i] :
( ( ( dvd_dvd @ SV332 @ SV845 @ ( times_times @ SV332 @ SV845 @ SV971 ) )
= $true )
| ( ( comm_semiring_1 @ SV332 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3661]) ).
thf(4055,plain,
! [SV333: $i] :
( ( ( ~ ( power @ SV333 ) )
= $true )
| ( ( ~ ( semiring_0 @ SV333 ) )
= $true )
| ( ( ! [SY1587: $i] :
~ ( ~ ( ( ( number_number_of @ nat @ SY1587 )
!= ( zero_zero @ nat ) )
| ( ( power_power @ SV333 @ ( zero_zero @ SV333 ) @ ( number_number_of @ nat @ SY1587 ) )
= ( one_one @ SV333 ) ) )
| ~ ( ~ ( ( ( number_number_of @ nat @ SY1587 )
!= ( zero_zero @ nat ) ) )
| ( ( power_power @ SV333 @ ( zero_zero @ SV333 ) @ ( number_number_of @ nat @ SY1587 ) )
= ( zero_zero @ SV333 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3662]) ).
thf(4056,plain,
! [SV579: $i,SV334: $i,SV702: $i] :
( ( ( no_zero_divisors @ SV702 )
= $false )
| ( ( ( ti @ SV702 @ ( times_times @ SV702 @ SV334 @ SV579 ) )
= ( times_times @ SV702 @ SV334 @ SV579 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3663]) ).
thf(4057,plain,
! [SV580: $i,SV335: $i,SV703: $i] :
( ( ( ab_group_add @ SV703 )
= $false )
| ( ( ( plus_plus @ SV703 @ SV335 @ ( ti @ SV703 @ SV580 ) )
= ( plus_plus @ SV703 @ SV335 @ SV580 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3664]) ).
thf(4058,plain,
! [SV581: $i,SV336: $i] :
( ( ~ ( ord_less_eq @ int @ ( bit0 @ SV336 ) @ ( bit0 @ SV581 ) )
| ( ord_less_eq @ int @ SV336 @ SV581 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3665]) ).
thf(4059,plain,
! [SV581: $i,SV336: $i] :
( ( ~ ( ord_less_eq @ int @ SV336 @ SV581 )
| ( ord_less_eq @ int @ ( bit0 @ SV336 ) @ ( bit0 @ SV581 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3666]) ).
thf(4060,plain,
! [SV582: $i,SV337: $i,SV972: $i,SV846: $i,SV704: $i] :
( ( ~ ( zcong @ SV704 @ SV846 @ SV972 )
| ~ ( zcong @ SV337 @ SV582 @ SV972 )
| ( zcong @ ( times_times @ int @ SV704 @ SV337 ) @ ( times_times @ int @ SV846 @ SV582 ) @ SV972 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3667]) ).
thf(4061,plain,
! [SV583: $i,SV338: $i,SV705: $i] :
( ( ( ord_less @ real @ ( zero_zero @ real ) @ SV705 )
= $false )
| ( ( ~ ( ~ ( ~ ( ord_less @ real @ ( times_times @ real @ SV338 @ SV705 ) @ ( times_times @ real @ SV583 @ SV705 ) )
| ( ord_less @ real @ SV338 @ SV583 ) )
| ~ ( ~ ( ord_less @ real @ SV338 @ SV583 )
| ( ord_less @ real @ ( times_times @ real @ SV338 @ SV705 ) @ ( times_times @ real @ SV583 @ SV705 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3668]) ).
thf(4062,plain,
! [SV706: $i] :
( ( ! [SY1936: $i] :
( ( plus_plus @ int @ ( power_power @ int @ SV706 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ SY1936 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3670]) ).
thf(4063,plain,
! [SV973: $i,SV848: $i,SV340: $i] :
( ( ( ! [SY2178: $i,SY2179: $i] :
( ( times_times @ SV340 @ ( times_times @ SV340 @ SV848 @ SV973 ) @ ( times_times @ SV340 @ SY2178 @ SY2179 ) )
= ( times_times @ SV340 @ ( times_times @ SV340 @ SV848 @ SY2178 ) @ ( times_times @ SV340 @ SV973 @ SY2179 ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV340 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3671]) ).
thf(4064,plain,
! [SV584: $i,SV341: $i] :
( ( ~ ( ord_less @ int @ ( bit0 @ SV341 ) @ ( bit0 @ SV584 ) )
| ( ord_less @ int @ SV341 @ SV584 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3672]) ).
thf(4065,plain,
! [SV584: $i,SV341: $i] :
( ( ~ ( ord_less @ int @ SV341 @ SV584 )
| ( ord_less @ int @ ( bit0 @ SV341 ) @ ( bit0 @ SV584 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3673]) ).
thf(4066,plain,
! [SV585: $i,SV343: $i] :
( ( ~ ( quadRes @ SV343 @ ( ti @ int @ SV585 ) )
| ( quadRes @ SV343 @ SV585 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3675]) ).
thf(4067,plain,
! [SV585: $i,SV343: $i] :
( ( ~ ( quadRes @ SV343 @ SV585 )
| ( quadRes @ SV343 @ ( ti @ int @ SV585 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3676]) ).
thf(4068,plain,
! [SV586: $i,SV345: $i] :
( ( ~ ( ord_less_eq @ int @ SV345 @ ( minus_minus @ int @ SV586 @ ( one_one @ int ) ) )
| ( ord_less @ int @ SV345 @ SV586 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3678]) ).
thf(4069,plain,
! [SV586: $i,SV345: $i] :
( ( ~ ( ord_less @ int @ SV345 @ SV586 )
| ( ord_less_eq @ int @ SV345 @ ( minus_minus @ int @ SV586 @ ( one_one @ int ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3679]) ).
thf(4070,plain,
! [SV851: $i,SV347: $i] :
( ( ( ~ ( ( ( power_power @ SV347 @ SV851 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= ( zero_zero @ SV347 ) )
| ( ( ti @ SV347 @ SV851 )
= ( zero_zero @ SV347 ) ) )
| ~ ( ( ( ti @ SV347 @ SV851 )
!= ( zero_zero @ SV347 ) )
| ( ( power_power @ SV347 @ SV851 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SV347 ) ) ) )
= $false )
| ( ( ring_11004092258visors @ SV347 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3680]) ).
thf(4071,plain,
! [SV852: $i,SV974: $i,SV348: $i] :
( ( ( ~ ( ord_less @ SV348 @ ( zero_zero @ SV348 ) @ SV974 )
| ( ord_less @ SV348 @ ( zero_zero @ SV348 ) @ ( power_power @ SV348 @ SV974 @ SV852 ) ) )
= $true )
| ( ( linordered_semidom @ SV348 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3681]) ).
thf(4072,plain,
! [SV853: $i,SV975: $i,SV349: $i] :
( ( ( ! [SY2180: $i] :
( ~ ( dvd_dvd @ SV349 @ SV975 @ SY2180 )
| ( dvd_dvd @ SV349 @ SV975 @ ( times_times @ SV349 @ SY2180 @ SV853 ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV349 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3682]) ).
thf(4073,plain,
! [SV587: $i,SV350: $i] :
( ( ~ ( ord_less_eq @ int @ ( plus_plus @ int @ SV350 @ ( one_one @ int ) ) @ SV587 )
| ( ord_less @ int @ SV350 @ SV587 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3683]) ).
thf(4074,plain,
! [SV587: $i,SV350: $i] :
( ( ~ ( ord_less @ int @ SV350 @ SV587 )
| ( ord_less_eq @ int @ ( plus_plus @ int @ SV350 @ ( one_one @ int ) ) @ SV587 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3684]) ).
thf(4075,plain,
! [SV976: $i,SV854: $i,SV351: $i] :
( ( ( ( ( times_times @ SV351 @ SV854 @ SV976 )
!= ( zero_zero @ SV351 ) )
| ( ( ti @ SV351 @ SV854 )
= ( zero_zero @ SV351 ) )
| ( ( ti @ SV351 @ SV976 )
= ( zero_zero @ SV351 ) ) )
= $true )
| ( ( no_zero_divisors @ SV351 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3685]) ).
thf(4076,plain,
! [SV977: $i,SV855: $i,SV352: $i] :
( ( ( ~ ( ~ ( ( ( plus_plus @ SV352 @ ( power_power @ SV352 @ SV855 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV352 @ SV977 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV352 ) )
| ~ ( ( ( ti @ SV352 @ SV855 )
!= ( zero_zero @ SV352 ) )
| ( ( ti @ SV352 @ SV977 )
!= ( zero_zero @ SV352 ) ) ) )
| ~ ( ~ ~ ( ( ( ti @ SV352 @ SV855 )
!= ( zero_zero @ SV352 ) )
| ( ( ti @ SV352 @ SV977 )
!= ( zero_zero @ SV352 ) ) )
| ( ( plus_plus @ SV352 @ ( power_power @ SV352 @ SV855 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV352 @ SV977 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV352 ) ) ) ) )
= $true )
| ( ( linordered_idom @ SV352 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3686]) ).
thf(4077,plain,
! [SV856: $i,SV978: $i,SV353: $i] :
( ( ( ! [SY2181: $i] :
( ~ ( ord_less_eq @ SV353 @ SV978 @ SY2181 )
| ~ ( ord_less_eq @ SV353 @ ( zero_zero @ SV353 ) @ SV978 )
| ( ord_less_eq @ SV353 @ ( power_power @ SV353 @ SV978 @ SV856 ) @ ( power_power @ SV353 @ SY2181 @ SV856 ) ) ) )
= $true )
| ( ( linordered_semidom @ SV353 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3687]) ).
thf(4078,plain,
! [SV979: $i,SV857: $i,SV354: $i] :
( ( ( ! [SY2182: $i] :
( ( times_times @ SV354 @ SV857 @ ( times_times @ SV354 @ SV979 @ SY2182 ) )
= ( times_times @ SV354 @ SV979 @ ( times_times @ SV354 @ SV857 @ SY2182 ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV354 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3688]) ).
thf(4079,plain,
! [SV355: $i] :
( ( ( ~ ( power @ SV355 ) )
= $true )
| ( ( ~ ( semiring_0 @ SV355 ) )
= $true )
| ( ( ! [SY1626: $i] :
~ ( ~ ( ( SY1626
!= ( zero_zero @ nat ) )
| ( ( power_power @ SV355 @ ( zero_zero @ SV355 ) @ SY1626 )
= ( one_one @ SV355 ) ) )
| ~ ( ~ ( ( SY1626
!= ( zero_zero @ nat ) ) )
| ( ( power_power @ SV355 @ ( zero_zero @ SV355 ) @ SY1626 )
= ( zero_zero @ SV355 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3689]) ).
thf(4080,plain,
! [SV588: $i,SV356: $i,SV707: $i] :
( ( ( power @ SV707 )
= $false )
| ( ( ( power_power @ SV707 @ ( ti @ SV707 @ SV356 ) @ SV588 )
= ( power_power @ SV707 @ SV356 @ SV588 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3690]) ).
thf(4081,plain,
! [SV589: $i,SV357: $i,SV708: $i] :
( ( ( no_zero_divisors @ SV708 )
= $false )
| ( ( ( times_times @ SV708 @ SV357 @ ( ti @ SV708 @ SV589 ) )
= ( times_times @ SV708 @ SV357 @ SV589 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3691]) ).
thf(4082,plain,
! [SV980: $i,SV858: $i,SV358: $i] :
( ( ( ! [SY2183: $i] :
( ~ ( ord_less @ SV358 @ ( one_one @ SV358 ) @ SY2183 )
| ~ ( ~ ( ~ ( ord_less_eq @ SV358 @ ( power_power @ SV358 @ SY2183 @ SV858 ) @ ( power_power @ SV358 @ SY2183 @ SV980 ) )
| ( ord_less_eq @ nat @ SV858 @ SV980 ) )
| ~ ( ~ ( ord_less_eq @ nat @ SV858 @ SV980 )
| ( ord_less_eq @ SV358 @ ( power_power @ SV358 @ SY2183 @ SV858 ) @ ( power_power @ SV358 @ SY2183 @ SV980 ) ) ) ) ) )
= $true )
| ( ( linordered_semidom @ SV358 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3692]) ).
thf(4083,plain,
! [SV590: $i,SV359: $i,SV709: $i] :
( ( ( power @ SV709 )
= $false )
| ( ( ( ti @ SV709 @ ( power_power @ SV709 @ SV359 @ SV590 ) )
= ( power_power @ SV709 @ SV359 @ SV590 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3693]) ).
thf(4084,plain,
! [SV591: $i,SV360: $i] :
( ( ~ ( zcong @ SV360 @ ( zero_zero @ int ) @ SV591 )
| ( dvd_dvd @ int @ SV591 @ SV360 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3694]) ).
thf(4085,plain,
! [SV360: $i,SV591: $i] :
( ( ~ ( dvd_dvd @ int @ SV591 @ SV360 )
| ( zcong @ SV360 @ ( zero_zero @ int ) @ SV591 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3695]) ).
thf(4086,plain,
! [SV361: $i,SV859: $i,SV981: $i] :
( ( ( ~ ( ord_less_eq @ int @ pls @ SV981 )
| ~ ( ord_less_eq @ int @ pls @ SV859 )
| ( ( times_times @ SV361 @ ( number_number_of @ SV361 @ SV981 ) @ ( number_number_of @ SV361 @ SV859 ) )
= ( number_number_of @ SV361 @ ( times_times @ int @ SV981 @ SV859 ) ) ) )
= $true )
| ( ( number_semiring @ SV361 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3696]) ).
thf(4087,plain,
! [SV592: $i,SV362: $i,SV710: $i] :
( ( ( SV710
!= ( zero_zero @ real ) )
= $false )
| ( ( ~ ( ~ ( ( ( times_times @ real @ SV362 @ SV710 )
!= ( times_times @ real @ SV592 @ SV710 ) )
| ( SV362 = SV592 ) )
| ~ ( ( SV362 != SV592 )
| ( ( times_times @ real @ SV362 @ SV710 )
= ( times_times @ real @ SV592 @ SV710 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3697]) ).
thf(4088,plain,
! [SV860: $i,SV363: $i,SV982: $i] :
( ( ( ~ ( ~ ( ( SV982
!= ( zero_zero @ nat ) )
| ( ( power_power @ SV363 @ SV860 @ SV982 )
= ( one_one @ SV363 ) ) )
| ~ ( ~ ( ( SV982
!= ( zero_zero @ nat ) ) )
| ( ( power_power @ SV363 @ SV860 @ SV982 )
= ( times_times @ SV363 @ SV860 @ ( power_power @ SV363 @ SV860 @ ( minus_minus @ nat @ SV982 @ ( one_one @ nat ) ) ) ) ) ) ) )
= $true )
| ( ( power @ SV363 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3699]) ).
thf(4089,plain,
! [SV364: $i,SV711: $i,SV593: $i] :
( ( ( dvd_dvd @ nat @ SV593 @ SV711 )
= $false )
| ( ( dvd_dvd @ nat @ ( power_power @ nat @ SV593 @ SV364 ) @ ( power_power @ nat @ SV711 @ SV364 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3700]) ).
thf(4090,plain,
! [SV365: $i,SV712: $i,SV594: $i] :
( ( ( ord_less @ int @ SV594 @ SV712 )
= $false )
| ( ( ord_less @ int @ ( plus_plus @ int @ SV594 @ SV365 ) @ ( plus_plus @ int @ SV712 @ SV365 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3701]) ).
thf(4091,plain,
! [SV366: $i,SV595: $i] :
( ( ~ ( ord_less @ int @ SV595 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV595 ) @ ( number_number_of @ nat @ SV366 ) )
= ( number_number_of @ nat @ SV366 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3702]) ).
thf(4092,plain,
! [SV366: $i,SV595: $i] :
( ( ~ ~ ( ord_less @ int @ SV595 @ pls )
| ~ ( ~ ( ~ ( ord_less @ int @ SV366 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV595 ) @ ( number_number_of @ nat @ SV366 ) )
= ( number_number_of @ nat @ SV595 ) ) )
| ~ ( ~ ~ ( ord_less @ int @ SV366 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV595 ) @ ( number_number_of @ nat @ SV366 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SV595 @ SV366 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3703]) ).
thf(4093,plain,
! [SV861: $i,SV367: $i,SV983: $i] :
( ( ( ! [SY2184: $i] :
( ~ ( ord_less_eq @ nat @ SV983 @ SY2184 )
| ( dvd_dvd @ SV367 @ ( power_power @ SV367 @ SV861 @ SV983 ) @ ( power_power @ SV367 @ SV861 @ SY2184 ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV367 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3704]) ).
thf(4094,plain,
! [SV368: $i,SV596: $i] :
( ( ( SV596
!= ( zero_zero @ nat ) )
| ( ( times_times @ nat @ SV596 @ SV368 )
= ( zero_zero @ nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3705]) ).
thf(4095,plain,
! [SV368: $i,SV596: $i] :
( ( ~ ( ( SV596
!= ( zero_zero @ nat ) ) )
| ( ( times_times @ nat @ SV596 @ SV368 )
= ( plus_plus @ nat @ SV368 @ ( times_times @ nat @ ( minus_minus @ nat @ SV596 @ ( one_one @ nat ) ) @ SV368 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3706]) ).
thf(4096,plain,
! [SV713: $i,SV597: $i,SV369: $i] :
( ( ( dvd_dvd @ int @ SV369 @ ( minus_minus @ int @ SV597 @ SV713 ) )
= $false )
| ( ( ~ ( dvd_dvd @ int @ SV369 @ SV713 )
| ( dvd_dvd @ int @ SV369 @ SV597 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3707]) ).
thf(4097,plain,
! [SV598: $i,SV370: $i] :
( ( ( ( bit1 @ SV370 )
!= ( bit1 @ SV598 ) )
| ( ( ti @ int @ SV370 )
= ( ti @ int @ SV598 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3708]) ).
thf(4098,plain,
! [SV598: $i,SV370: $i] :
( ( ( ( ti @ int @ SV370 )
!= ( ti @ int @ SV598 ) )
| ( ( bit1 @ SV370 )
= ( bit1 @ SV598 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3709]) ).
thf(4099,plain,
! [SV984: $i,SV862: $i,SV371: $i] :
( ( ( ! [SY2185: $i] :
( ( power_power @ SV371 @ ( times_times @ SV371 @ SV862 @ SV984 ) @ SY2185 )
= ( times_times @ SV371 @ ( power_power @ SV371 @ SV862 @ SY2185 ) @ ( power_power @ SV371 @ SV984 @ SY2185 ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV371 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3710]) ).
thf(4100,plain,
! [SV372: $i,SV863: $i,SV714: $i,SV599: $i] :
( ( ( ~ ( zcong @ SV599 @ SV714 @ SV863 ) )
= $true )
| ( ( zcong @ ( times_times @ int @ SV599 @ SV372 ) @ ( times_times @ int @ SV714 @ SV372 ) @ SV863 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3711]) ).
thf(4101,plain,
! [SV600: $i,SV373: $i] :
( ( ~ ( ord_less_eq @ int @ ( bit0 @ SV373 ) @ ( bit0 @ SV600 ) )
| ( ord_less_eq @ int @ SV373 @ SV600 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3712]) ).
thf(4102,plain,
! [SV600: $i,SV373: $i] :
( ( ~ ( ord_less_eq @ int @ SV373 @ SV600 )
| ( ord_less_eq @ int @ ( bit0 @ SV373 ) @ ( bit0 @ SV600 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3713]) ).
thf(4103,plain,
! [SV601: $i,SV374: $i] :
( ( ( ( times_times @ nat @ SV374 @ SV601 )
!= ( one_one @ nat ) )
| ~ ( ( SV374
!= ( one_one @ nat ) )
| ( SV601
!= ( one_one @ nat ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3714]) ).
thf(4104,plain,
! [SV601: $i,SV374: $i] :
( ( ~ ~ ( ( SV374
!= ( one_one @ nat ) )
| ( SV601
!= ( one_one @ nat ) ) )
| ( ( times_times @ nat @ SV374 @ SV601 )
= ( one_one @ nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3715]) ).
thf(4105,plain,
! [SV864: $i,SV985: $i,SV375: $i] :
( ( ( ~ ( ord_less @ SV375 @ ( one_one @ SV375 ) @ SV985 )
| ( ord_less @ SV375 @ ( power_power @ SV375 @ SV985 @ SV864 ) @ ( times_times @ SV375 @ SV985 @ ( power_power @ SV375 @ SV985 @ SV864 ) ) ) )
= $true )
| ( ( linordered_semidom @ SV375 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3716]) ).
thf(4106,plain,
! [SV865: $i,SV986: $i,SV376: $i] :
( ( ( ~ ( ( ( ti @ SV376 @ SV986 )
!= ( zero_zero @ SV376 ) ) )
| ( ( power_power @ SV376 @ SV986 @ SV865 )
!= ( zero_zero @ SV376 ) ) )
= $true )
| ( ( ring_11004092258visors @ SV376 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3717]) ).
thf(4107,plain,
! [SV602: $i,SV377: $i,SV715: $i] :
( ( ( mult_zero @ SV715 )
= $false )
| ( ( ( times_times @ SV715 @ SV377 @ ( ti @ SV715 @ SV602 ) )
= ( times_times @ SV715 @ SV377 @ SV602 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3718]) ).
thf(4108,plain,
! [SV603: $i,SV379: $i] :
( ( ( ~ ( ord_less @ real @ ( zero_zero @ real ) @ SV379 ) )
= $true )
| ( ( ord_less @ real @ ( zero_zero @ real ) @ ( times_times @ real @ SV603 @ SV379 ) )
= $true )
| ( ( ord_less @ real @ ( zero_zero @ real ) @ SV603 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3720]) ).
thf(4109,plain,
! [SV987: $i,SV867: $i,SV380: $i] :
( ( ( ! [SY2186: $i,SY2187: $i] :
( ( times_times @ SV380 @ ( times_times @ SV380 @ SV867 @ SV987 ) @ ( times_times @ SV380 @ SY2186 @ SY2187 ) )
= ( times_times @ SV380 @ SY2186 @ ( times_times @ SV380 @ ( times_times @ SV380 @ SV867 @ SV987 ) @ SY2187 ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV380 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3721]) ).
thf(4110,plain,
! [SV604: $i,SV382: $i,SV716: $i] :
( ( ( zprime @ SV716 )
= $false )
| ( ( ~ ( dvd_dvd @ int @ SV716 @ ( times_times @ int @ SV382 @ SV604 ) )
| ( dvd_dvd @ int @ SV716 @ SV382 )
| ( dvd_dvd @ int @ SV716 @ SV604 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3723]) ).
thf(4111,plain,
! [SV869: $i,SV383: $i,SV988: $i] :
( ( ( ! [SY2188: $i] :
( ~ ( ord_less @ nat @ SV988 @ SY2188 )
| ~ ( ord_less @ SV383 @ ( one_one @ SV383 ) @ SV869 )
| ( ord_less @ SV383 @ ( power_power @ SV383 @ SV869 @ SV988 ) @ ( power_power @ SV383 @ SV869 @ SY2188 ) ) ) )
= $true )
| ( ( linordered_semidom @ SV383 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3724]) ).
thf(4112,plain,
! [SV384: $i,SV717: $i,SV605: $i] :
( ( ( ord_less @ int @ SV605 @ SV717 )
= $false )
| ( ( ~ ( ord_less @ int @ SV384 @ SV717 )
| ( ord_less_eq @ int @ SV605 @ SV384 )
| ( ord_less_eq @ int @ SV384 @ SV605 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3725]) ).
thf(4113,plain,
! [SV606: $i,SV385: $i,SV870: $i,SV718: $i] :
( ( ( ~ ( ord_less @ int @ SV718 @ SV870 ) )
= $true )
| ( ( ~ ( ord_less_eq @ int @ SV385 @ SV606 )
| ( ord_less @ int @ ( plus_plus @ int @ SV718 @ SV385 ) @ ( plus_plus @ int @ SV870 @ SV606 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3726]) ).
thf(4114,plain,
! [SV386: $i] :
( ( ( ~ ( number @ SV386 ) )
= $true )
| ( ( ~ ( ring @ SV386 ) )
= $true )
| ( ( ! [SY1686: $i,SY1687: $i,SY1688: $i] :
( ( times_times @ SV386 @ ( minus_minus @ SV386 @ SY1686 @ SY1687 ) @ ( number_number_of @ SV386 @ SY1688 ) )
= ( minus_minus @ SV386 @ ( times_times @ SV386 @ SY1686 @ ( number_number_of @ SV386 @ SY1688 ) ) @ ( times_times @ SV386 @ SY1687 @ ( number_number_of @ SV386 @ SY1688 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3727]) ).
thf(4115,plain,
! [SV387: $i,SV607: $i] :
( ( ( ~ ( ord_less @ int @ ( zero_zero @ int ) @ ( times_times @ int @ SV607 @ SV387 ) ) )
= $true )
| ( ( ord_less @ int @ ( zero_zero @ int ) @ SV387 )
= $true )
| ( ( ord_less @ int @ ( zero_zero @ int ) @ SV607 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3728]) ).
thf(4116,plain,
! [SV608: $i,SV388: $i] :
( ( ( ~ ( zcong @ SV388 @ ( number_number_of @ int @ min ) @ SV608 ) )
= $true )
| ( ( ~ ( zcong @ SV388 @ ( one_one @ int ) @ SV608 ) )
= $true )
| ( ( ord_less @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV608 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3729]) ).
thf(4117,plain,
! [SV389: $i,SV609: $i] :
( ( ( ~ ( ord_less @ int @ SV609 @ SV389 ) )
= $true )
| ( ( ~ ( zcong @ SV609 @ ( zero_zero @ int ) @ SV389 ) )
= $true )
| ( ( ord_less @ int @ ( zero_zero @ int ) @ SV609 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3730]) ).
thf(4118,plain,
! [SV390: $i,SV610: $i] :
( ( ( SV610
!= ( zero_zero @ nat ) )
| ( ( power_power @ nat @ SV390 @ SV610 )
= ( one_one @ nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3731]) ).
thf(4119,plain,
! [SV390: $i,SV610: $i] :
( ( ~ ( ( SV610
!= ( zero_zero @ nat ) ) )
| ( ( power_power @ nat @ SV390 @ SV610 )
= ( times_times @ nat @ SV390 @ ( power_power @ nat @ SV390 @ ( minus_minus @ nat @ SV610 @ ( one_one @ nat ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3732]) ).
thf(4120,plain,
! [SV611: $i,SV391: $i,SV719: $i] :
( ( ( ord_less @ nat @ ( zero_zero @ nat ) @ SV719 )
= $false )
| ( ( ~ ( dvd_dvd @ int @ SV391 @ SV611 )
| ( dvd_dvd @ int @ SV391 @ ( power_power @ int @ SV611 @ SV719 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3733]) ).
thf(4121,plain,
! [SV612: $i,SV392: $i] :
( ( ~ ( ord_less @ nat @ ( number_number_of @ nat @ SV392 ) @ ( number_number_of @ nat @ SV612 ) )
| ~ ( ~ ( ~ ( ord_less @ int @ SV392 @ SV612 )
| ( ord_less @ int @ pls @ SV612 ) )
| ~ ( ord_less @ int @ SV392 @ SV612 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3734]) ).
thf(4122,plain,
! [SV612: $i,SV392: $i] :
( ( ~ ~ ( ~ ( ~ ( ord_less @ int @ SV392 @ SV612 )
| ( ord_less @ int @ pls @ SV612 ) )
| ~ ( ord_less @ int @ SV392 @ SV612 ) )
| ( ord_less @ nat @ ( number_number_of @ nat @ SV392 ) @ ( number_number_of @ nat @ SV612 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3735]) ).
thf(4123,plain,
! [SV989: $i,SV871: $i,SV393: $i] :
( ( ( ( power_power @ SV393 @ ( minus_minus @ SV393 @ SV871 @ SV989 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( minus_minus @ SV393 @ ( plus_plus @ SV393 @ ( power_power @ SV393 @ SV871 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV393 @ SV989 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times @ SV393 @ ( times_times @ SV393 @ ( number_number_of @ SV393 @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV871 ) @ SV989 ) ) )
= $true )
| ( ( number_ring @ SV393 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3736]) ).
thf(4124,plain,
! [SV394: $i] :
( ( ( ~ ( zprime @ ( ti @ int @ SV394 ) ) )
= $true )
| ( ( zprime @ SV394 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3737]) ).
thf(4125,plain,
! [SV394: $i] :
( ( ( ~ ( zprime @ SV394 ) )
= $true )
| ( ( zprime @ ( ti @ int @ SV394 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3738]) ).
thf(4126,plain,
! [SV395: $i,SV872: $i,SV720: $i,SV613: $i] :
( ( ( ~ ( zcong @ ( power_power @ int @ SV613 @ SV720 ) @ ( one_one @ int ) @ SV872 ) )
= $true )
| ( ( zcong @ ( power_power @ int @ SV613 @ ( times_times @ nat @ SV720 @ SV395 ) ) @ ( one_one @ int ) @ SV872 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3739]) ).
thf(4127,plain,
! [SV614: $i,SV396: $i] :
( ( ~ ( zcong @ SV396 @ SV614 @ ( zero_zero @ int ) )
| ( ( ti @ int @ SV396 )
= ( ti @ int @ SV614 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3740]) ).
thf(4128,plain,
! [SV614: $i,SV396: $i] :
( ( ( ( ti @ int @ SV396 )
!= ( ti @ int @ SV614 ) )
| ( zcong @ SV396 @ SV614 @ ( zero_zero @ int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3741]) ).
thf(4129,plain,
! [SV615: $i,SV397: $i] :
( ( ( ( plus_plus @ real @ ( times_times @ real @ SV397 @ SV397 ) @ ( times_times @ real @ SV615 @ SV615 ) )
!= ( zero_zero @ real ) )
| ~ ( ( SV397
!= ( zero_zero @ real ) )
| ( SV615
!= ( zero_zero @ real ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3742]) ).
thf(4130,plain,
! [SV615: $i,SV397: $i] :
( ( ~ ~ ( ( SV397
!= ( zero_zero @ real ) )
| ( SV615
!= ( zero_zero @ real ) ) )
| ( ( plus_plus @ real @ ( times_times @ real @ SV397 @ SV397 ) @ ( times_times @ real @ SV615 @ SV615 ) )
= ( zero_zero @ real ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3743]) ).
thf(4131,plain,
! [SV398: $i] :
( ( ( ~ ( ord_less @ int @ ( bit1 @ SV398 ) @ pls ) )
= $true )
| ( ( ord_less @ int @ SV398 @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3744]) ).
thf(4132,plain,
! [SV398: $i] :
( ( ( ~ ( ord_less @ int @ SV398 @ pls ) )
= $true )
| ( ( ord_less @ int @ ( bit1 @ SV398 ) @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3745]) ).
thf(4133,plain,
! [SV990: $i,SV873: $i,SV399: $i] :
( ( ( ! [SY2189: $i,SY2190: $i] :
( ( plus_plus @ SV399 @ ( times_times @ SV399 @ SV873 @ SV990 ) @ ( plus_plus @ SV399 @ ( times_times @ SV399 @ SY2189 @ SV990 ) @ SY2190 ) )
= ( plus_plus @ SV399 @ ( times_times @ SV399 @ ( plus_plus @ SV399 @ SV873 @ SY2189 ) @ SV990 ) @ SY2190 ) ) )
= $true )
| ( ( semiring @ SV399 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3746]) ).
thf(4134,plain,
( ( ( ~ ! [SY2112: $i] :
( ( plus_plus @ int @ ( power_power @ int @ sK4_SX0 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ SY2112 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ) )
= $true )
| ( ( t
= ( one_one @ int ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3748]) ).
thf(4135,plain,
! [SV616: $i,SV401: $i,SV721: $i] :
( ( ( semiring @ SV721 )
= $false )
| ( ( ( times_times @ SV721 @ ( ti @ SV721 @ SV401 ) @ SV616 )
= ( times_times @ SV721 @ SV401 @ SV616 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3749]) ).
thf(4136,plain,
! [SV991: $i,SV876: $i,SV403: $i] :
( ( ( ! [SY2191: $i] :
( ( times_times @ SV403 @ SV876 @ ( plus_plus @ SV403 @ SV991 @ SY2191 ) )
= ( plus_plus @ SV403 @ ( times_times @ SV403 @ SV876 @ SV991 ) @ ( times_times @ SV403 @ SV876 @ SY2191 ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV403 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3751]) ).
thf(4137,plain,
! [SV722: $i,SV617: $i,SV405: $i] :
( ( ~ ( ~ ( zcong @ SV405 @ SV617 @ SV722 )
| ~ ! [SY1940: $i] :
( ( ti @ int @ SV617 )
!= ( plus_plus @ int @ SV405 @ ( times_times @ int @ SV722 @ SY1940 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3753]) ).
thf(4138,plain,
! [SV722: $i,SV405: $i,SV617: $i] :
( ( ~ ( ~ ~ ! [SY1941: $i] :
( ( ti @ int @ SV617 )
!= ( plus_plus @ int @ SV405 @ ( times_times @ int @ SV722 @ SY1941 ) ) )
| ( zcong @ SV405 @ SV617 @ SV722 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3753]) ).
thf(4139,plain,
! [SV723: $i,SV618: $i,SV406: $i] :
( ( ( ( minus_minus @ int @ SV406 @ SV618 )
= ( ti @ int @ SV723 ) )
= $false )
| ( ( ( ti @ int @ SV406 )
= ( plus_plus @ int @ SV723 @ SV618 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3754]) ).
thf(4140,plain,
! [SV407: $i] :
( ( ( ( ti @ int @ SV407 )
!= ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $false )
| ( ( ~ ( ( ( ti @ int @ SV407 )
!= ( number_number_of @ int @ ( bit1 @ ( bit1 @ pls ) ) ) ) )
| ( ord_less_eq @ int @ ( number_number_of @ int @ ( bit1 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SV407 ) )
= $true )
| ( ( zprime @ SV407 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3755]) ).
thf(4141,plain,
! [SV619: $i,SV408: $i,SV724: $i] :
( ( ( semiring @ SV724 )
= $false )
| ( ( ( ti @ SV724 @ ( plus_plus @ SV724 @ SV408 @ SV619 ) )
= ( plus_plus @ SV724 @ SV408 @ SV619 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3756]) ).
thf(4142,plain,
! [SV725: $i,SV620: $i,SV410: $i] :
( ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( times_times @ int @ SV410 @ SV620 ) @ SV725 ) )
= $false )
| ( ( ~ ( ord_less @ int @ SV725 @ SV410 )
| ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV410 )
| ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV620 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3757]) ).
thf(4143,plain,
! [SV878: $i,SV411: $i] :
( ( ( ord_less @ SV411 @ ( power_power @ SV411 @ SV878 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( zero_zero @ SV411 ) )
= $false )
| ( ( linordered_idom @ SV411 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3758]) ).
thf(4144,plain,
! [SV992: $i,SV879: $i,SV412: $i] :
( ( ( ! [SY2192: $i] :
( ( power_power @ SV412 @ SV879 @ ( times_times @ nat @ SV992 @ SY2192 ) )
= ( power_power @ SV412 @ ( power_power @ SV412 @ SV879 @ SV992 ) @ SY2192 ) ) )
= $true )
| ( ( monoid_mult @ SV412 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3759]) ).
thf(4145,plain,
! [SV621: $i,SV413: $i] :
( ( ( ( times_times @ int @ SV413 @ SV621 )
!= ( one_one @ int ) )
| ~ ( ( ( ti @ int @ SV413 )
!= ( one_one @ int ) )
| ( ( ti @ int @ SV621 )
!= ( one_one @ int ) ) )
| ~ ( ( ( ti @ int @ SV413 )
!= ( number_number_of @ int @ min ) )
| ( ( ti @ int @ SV621 )
!= ( number_number_of @ int @ min ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3760]) ).
thf(4146,plain,
! [SV621: $i,SV413: $i] :
( ( ~ ( ~ ( ( ( ti @ int @ SV413 )
!= ( one_one @ int ) )
| ( ( ti @ int @ SV621 )
!= ( one_one @ int ) ) )
| ~ ( ( ( ti @ int @ SV413 )
!= ( number_number_of @ int @ min ) )
| ( ( ti @ int @ SV621 )
!= ( number_number_of @ int @ min ) ) ) )
| ( ( times_times @ int @ SV413 @ SV621 )
= ( one_one @ int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3761]) ).
thf(4147,plain,
! [SV993: $i,SV880: $i,SV414: $i] :
( ( ( ( plus_plus @ SV414 @ SV880 @ SV993 )
= ( plus_plus @ SV414 @ SV993 @ SV880 ) )
= $true )
| ( ( comm_semiring_1 @ SV414 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3762]) ).
thf(4148,plain,
! [SV416: $i] :
( ( ( ~ ( monoid_mult @ SV416 ) )
= $true )
| ( ( ~ ( number @ SV416 ) )
= $true )
| ( ( ! [SY1732: $i] :
( ( power_power @ SV416 @ ( number_number_of @ SV416 @ SY1732 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times @ SV416 @ ( number_number_of @ SV416 @ SY1732 ) @ ( number_number_of @ SV416 @ SY1732 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3763]) ).
thf(4149,plain,
! [SV881: $i,SV994: $i,SV417: $i] :
( ( ( ~ ( ord_less_eq @ SV417 @ SV994 @ ( zero_zero @ SV417 ) )
| ~ ( ord_less_eq @ SV417 @ ( zero_zero @ SV417 ) @ SV881 )
| ( ord_less_eq @ SV417 @ ( times_times @ SV417 @ SV994 @ SV881 ) @ ( zero_zero @ SV417 ) ) )
= $true )
| ( ( ordere453448008miring @ SV417 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3764]) ).
thf(4150,plain,
! [SV622: $i,SV418: $i] :
( ( ~ ( ord_less_eq @ int @ ( bit1 @ SV418 ) @ ( bit0 @ SV622 ) )
| ( ord_less @ int @ SV418 @ SV622 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3765]) ).
thf(4151,plain,
! [SV622: $i,SV418: $i] :
( ( ~ ( ord_less @ int @ SV418 @ SV622 )
| ( ord_less_eq @ int @ ( bit1 @ SV418 ) @ ( bit0 @ SV622 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3766]) ).
thf(4152,plain,
! [SV419: $i,SV623: $i] :
( ( ( ~ ( ( ( times_times @ int @ SV623 @ SV419 )
!= ( one_one @ int ) )
| ~ ( ( ( ti @ int @ SV623 )
!= ( one_one @ int ) )
| ( ( ti @ int @ SV419 )
!= ( one_one @ int ) ) ) )
| ~ ( ~ ~ ( ( ( ti @ int @ SV623 )
!= ( one_one @ int ) )
| ( ( ti @ int @ SV419 )
!= ( one_one @ int ) ) )
| ( ( times_times @ int @ SV623 @ SV419 )
= ( one_one @ int ) ) ) )
= $false )
| ( ( ord_less @ int @ ( zero_zero @ int ) @ SV623 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3767]) ).
thf(4153,plain,
! [SV624: $i,SV420: $i] :
( ( ~ ( ord_less_eq @ int @ ( bit0 @ SV420 ) @ ( bit1 @ SV624 ) )
| ( ord_less_eq @ int @ SV420 @ SV624 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3768]) ).
thf(4154,plain,
! [SV624: $i,SV420: $i] :
( ( ~ ( ord_less_eq @ int @ SV420 @ SV624 )
| ( ord_less_eq @ int @ ( bit0 @ SV420 ) @ ( bit1 @ SV624 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3769]) ).
thf(4155,plain,
! [SV421: $i,SV625: $i] :
( ( ~ ( ord_less @ int @ SV625 @ pls )
| ( ( times_times @ nat @ ( number_number_of @ nat @ SV625 ) @ ( number_number_of @ nat @ SV421 ) )
= ( zero_zero @ nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3770]) ).
thf(4156,plain,
! [SV421: $i,SV625: $i] :
( ( ~ ~ ( ord_less @ int @ SV625 @ pls )
| ( ( times_times @ nat @ ( number_number_of @ nat @ SV625 ) @ ( number_number_of @ nat @ SV421 ) )
= ( number_number_of @ nat @ ( times_times @ int @ SV625 @ SV421 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3771]) ).
thf(4157,plain,
! [SV995: $i,SV882: $i,SV726: $i,SV626: $i,SV422: $i] :
( ( ! [SY2193: $i] :
( ( ( plus_plus @ int @ ( times_times @ int @ SV422 @ SV626 ) @ SV726 )
!= ( plus_plus @ int @ ( times_times @ int @ SV882 @ SV995 ) @ SY2193 ) )
| ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( times_times @ int @ SV882 @ SV995 ) @ SY2193 ) )
| ~ ( ord_less @ int @ SY2193 @ SV882 )
| ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV726 )
| ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV882 )
| ~ ( ord_less_eq @ int @ SV882 @ SV422 )
| ( ord_less_eq @ int @ SV626 @ SV995 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3772]) ).
thf(4158,plain,
! [SV423: $i] :
( ( ( ~ ~ ( ord_less @ real @ ( zero_zero @ real ) @ ( times_times @ real @ SV423 @ SV423 ) ) )
= $true )
| ( ( SV423
= ( zero_zero @ real ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3773]) ).
thf(4159,plain,
! [SV423: $i] :
( ( ( SV423
!= ( zero_zero @ real ) )
= $true )
| ( ( ~ ( ord_less @ real @ ( zero_zero @ real ) @ ( times_times @ real @ SV423 @ SV423 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3774]) ).
thf(4160,plain,
! [SV627: $i,SV424: $i] :
( ( ~ ( ord_less @ int @ ( bit1 @ SV424 ) @ ( bit1 @ SV627 ) )
| ( ord_less @ int @ SV424 @ SV627 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3775]) ).
thf(4161,plain,
! [SV627: $i,SV424: $i] :
( ( ~ ( ord_less @ int @ SV424 @ SV627 )
| ( ord_less @ int @ ( bit1 @ SV424 ) @ ( bit1 @ SV627 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3776]) ).
thf(4162,plain,
! [SV628: $i,SV426: $i,SV727: $i] :
( ( ( mult_zero @ SV727 )
= $false )
| ( ( ( ti @ SV727 @ ( times_times @ SV727 @ SV426 @ SV628 ) )
= ( times_times @ SV727 @ SV426 @ SV628 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3778]) ).
thf(4163,plain,
! [SV728: $i,SV629: $i,SV427: $i] :
( ( ~ ( ~ ( zcong @ ( ti @ int @ SV427 ) @ SV629 @ SV728 )
| ( zcong @ SV427 @ SV629 @ SV728 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3779]) ).
thf(4164,plain,
! [SV728: $i,SV629: $i,SV427: $i] :
( ( ~ ( ~ ( zcong @ SV427 @ SV629 @ SV728 )
| ( zcong @ ( ti @ int @ SV427 ) @ SV629 @ SV728 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3779]) ).
thf(4165,plain,
! [SV630: $i,SV428: $i] :
( ( ~ ( zcong @ SV428 @ ( zero_zero @ int ) @ SV630 )
| ( dvd_dvd @ int @ SV630 @ SV428 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3780]) ).
thf(4166,plain,
! [SV428: $i,SV630: $i] :
( ( ~ ( dvd_dvd @ int @ SV630 @ SV428 )
| ( zcong @ SV428 @ ( zero_zero @ int ) @ SV630 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3781]) ).
thf(4167,plain,
! [SV631: $i,SV429: $i] :
( ( ( ( power_power @ nat @ SV429 @ SV631 )
!= ( one_one @ nat ) )
| ( SV429
= ( one_one @ nat ) )
| ( SV631
= ( zero_zero @ nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3782]) ).
thf(4168,plain,
! [SV631: $i,SV429: $i] :
( ( ~ ( ( SV429
= ( one_one @ nat ) )
| ( SV631
= ( zero_zero @ nat ) ) )
| ( ( power_power @ nat @ SV429 @ SV631 )
= ( one_one @ nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3783]) ).
thf(4169,plain,
! [SV430: $i,SV884: $i,SV729: $i,SV632: $i] :
( ( ( ~ ( zcong @ SV632 @ SV729 @ SV884 ) )
= $true )
| ( ( zcong @ ( plus_plus @ int @ SV632 @ SV430 ) @ ( plus_plus @ int @ SV729 @ SV430 ) @ SV884 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3784]) ).
thf(4170,plain,
! [SV996: $i,SV885: $i,SV431: $i] :
( ( ( ord_less_eq @ SV431 @ ( zero_zero @ SV431 ) @ ( plus_plus @ SV431 @ ( power_power @ SV431 @ SV885 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV431 @ SV996 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true )
| ( ( linordered_idom @ SV431 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3785]) ).
thf(4171,plain,
! [SV887: $i,SV433: $i,SV997: $i] :
( ( ( ! [SY2194: $i] :
( ~ ( ord_less @ nat @ SV997 @ SY2194 )
| ~ ( ord_less @ SV433 @ ( zero_zero @ SV433 ) @ SV887 )
| ~ ( ord_less @ SV433 @ SV887 @ ( one_one @ SV433 ) )
| ( ord_less @ SV433 @ ( power_power @ SV433 @ SV887 @ SY2194 ) @ ( power_power @ SV433 @ SV887 @ SV997 ) ) ) )
= $true )
| ( ( linordered_semidom @ SV433 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3787]) ).
thf(4172,plain,
! [SV998: $i,SV888: $i,SV434: $i] :
( ( ( ! [SY2195: $i,SY2196: $i,SY2197: $i] :
( ~ ( ( ( ti @ SV434 @ SY2197 )
!= ( zero_zero @ SV434 ) ) )
| ~ ~ ( ( ( ti @ SV434 @ SY2195 )
!= ( ti @ SV434 @ SY2196 ) )
| ~ ( ( ( ti @ SV434 @ SV888 )
!= ( ti @ SV434 @ SV998 ) ) ) )
| ( ( plus_plus @ SV434 @ SY2195 @ ( times_times @ SV434 @ SY2197 @ SV888 ) )
!= ( plus_plus @ SV434 @ SY2196 @ ( times_times @ SV434 @ SY2197 @ SV998 ) ) ) ) )
= $true )
| ( ( semiri456707255roduct @ SV434 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3788]) ).
thf(4173,plain,
! [SV999: $i,SV889: $i,SV730: $i,SV643: $i,SV472: $i,SV63: $i] :
( ( ! [SY2198: $i] :
( ( plus_plus @ int @ ( times_times @ int @ ( minus_minus @ int @ SV63 @ ( times_times @ int @ SV472 @ SV643 ) ) @ SV730 ) @ ( times_times @ int @ ( minus_minus @ int @ SV889 @ ( times_times @ int @ SV472 @ SV999 ) ) @ SY2198 ) )
= ( minus_minus @ int @ ( plus_plus @ int @ ( times_times @ int @ SV63 @ SV730 ) @ ( times_times @ int @ SV889 @ SY2198 ) ) @ ( times_times @ int @ SV472 @ ( plus_plus @ int @ ( times_times @ int @ SV643 @ SV730 ) @ ( times_times @ int @ SV999 @ SY2198 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3789]) ).
thf(4174,plain,
! [SV481: $i,SV79: $i,SV890: $i,SV732: $i,SV647: $i] :
( ( ( ~ ( zcong @ SV647 @ SV732 @ SV890 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( zcong @ SV79 @ ( times_times @ int @ SV647 @ SV481 ) @ SV890 )
| ( zcong @ SV79 @ ( times_times @ int @ SV732 @ SV481 ) @ SV890 ) )
| ~ ( ~ ( zcong @ SV79 @ ( times_times @ int @ SV732 @ SV481 ) @ SV890 )
| ( zcong @ SV79 @ ( times_times @ int @ SV647 @ SV481 ) @ SV890 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3790]) ).
thf(4175,plain,
! [SV482: $i,SV80: $i] :
( ( ( ~ ( ord_less @ int @ SV80 @ ( plus_plus @ int @ SV482 @ ( one_one @ int ) ) ) )
= $true )
| ( ( ( ord_less @ int @ SV80 @ SV482 )
| ( ( ti @ int @ SV80 )
= ( ti @ int @ SV482 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3791]) ).
thf(4176,plain,
! [SV482: $i,SV80: $i] :
( ( ( ~ ( ( ord_less @ int @ SV80 @ SV482 )
| ( ( ti @ int @ SV80 )
= ( ti @ int @ SV482 ) ) ) )
= $true )
| ( ( ord_less @ int @ SV80 @ ( plus_plus @ int @ SV482 @ ( one_one @ int ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3792]) ).
thf(4177,plain,
! [SV733: $i,SV891: $i,SV82: $i] :
( ( ( ~ ( ord_less_eq @ SV82 @ ( zero_zero @ SV82 ) @ SV891 ) )
= $true )
| ( ( ~ ( ord_less_eq @ SV82 @ SV733 @ ( zero_zero @ SV82 ) )
| ( ord_less_eq @ SV82 @ ( times_times @ SV82 @ SV891 @ SV733 ) @ ( zero_zero @ SV82 ) ) )
= $true )
| ( ( ordere453448008miring @ SV82 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3794]) ).
thf(4178,plain,
! [SV1000: $i,SV893: $i,SV735: $i,SV84: $i] :
( ( ( ( plus_plus @ SV84 @ ( plus_plus @ SV84 @ SV735 @ SV893 ) @ SV1000 )
= ( plus_plus @ SV84 @ SV735 @ ( plus_plus @ SV84 @ SV893 @ SV1000 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV84 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3796]) ).
thf(4179,plain,
! [SV737: $i,SV894: $i,SV87: $i] :
( ( ( ~ ( ord_less_eq @ SV87 @ ( zero_zero @ SV87 ) @ SV894 ) )
= $true )
| ( ( ~ ( ord_less_eq @ SV87 @ SV737 @ ( zero_zero @ SV87 ) )
| ( ord_less_eq @ SV87 @ ( times_times @ SV87 @ SV737 @ SV894 ) @ ( zero_zero @ SV87 ) ) )
= $true )
| ( ( ordere453448008miring @ SV87 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3797]) ).
thf(4180,plain,
! [SV895: $i,SV738: $i,SV88: $i] :
( ( ( ord_less @ SV88 @ ( plus_plus @ SV88 @ ( power_power @ SV88 @ SV738 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV88 @ SV895 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( zero_zero @ SV88 ) )
= $false )
| ( ( linordered_idom @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3798]) ).
thf(4181,plain,
! [SV739: $i,SV896: $i,SV90: $i] :
( ( ( ~ ( ( ( ti @ SV90 @ SV896 )
!= ( zero_zero @ SV90 ) ) ) )
= $true )
| ( ( ~ ( ( ( ti @ SV90 @ SV739 )
!= ( zero_zero @ SV90 ) ) )
| ( ( times_times @ SV90 @ SV896 @ SV739 )
!= ( zero_zero @ SV90 ) ) )
= $true )
| ( ( no_zero_divisors @ SV90 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3800]) ).
thf(4182,plain,
! [SV91: $i] :
( ( ( ord_less_eq @ int @ min @ ( bit1 @ SV91 ) )
= $false )
| ( ( ord_less_eq @ int @ min @ SV91 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3801]) ).
thf(4183,plain,
! [SV91: $i] :
( ( ( ord_less_eq @ int @ min @ SV91 )
= $false )
| ( ( ord_less_eq @ int @ min @ ( bit1 @ SV91 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3802]) ).
thf(4184,plain,
! [SV93: $i] :
( ( ( min
= ( bit1 @ SV93 ) )
= $false )
| ( ( min
= ( ti @ int @ SV93 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3804]) ).
thf(4185,plain,
! [SV93: $i] :
( ( ( min
= ( ti @ int @ SV93 ) )
= $false )
| ( ( min
= ( bit1 @ SV93 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3805]) ).
thf(4186,plain,
! [SV1001: $i,SV897: $i,SV740: $i,SV94: $i] :
( ( ( ( times_times @ SV94 @ SV740 @ ( times_times @ SV94 @ SV897 @ SV1001 ) )
= ( times_times @ SV94 @ ( times_times @ SV94 @ SV740 @ SV897 ) @ SV1001 ) )
= $true )
| ( ( comm_semiring_1 @ SV94 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3806]) ).
thf(4187,plain,
! [SV1002: $i,SV898: $i,SV741: $i,SV95: $i] :
( ( ( ! [SY2199: $i] :
( ( times_times @ SV95 @ ( times_times @ SV95 @ SV741 @ SV898 ) @ ( times_times @ SV95 @ SV1002 @ SY2199 ) )
= ( times_times @ SV95 @ SV741 @ ( times_times @ SV95 @ SV898 @ ( times_times @ SV95 @ SV1002 @ SY2199 ) ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV95 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3807]) ).
thf(4188,plain,
! [SV486: $i,SV96: $i] :
( ( ( ~ ( ord_less @ int @ ( number_number_of @ int @ SV96 ) @ ( number_number_of @ int @ SV486 ) ) )
= $true )
| ( ( ord_less @ int @ SV96 @ SV486 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3808]) ).
thf(4189,plain,
! [SV486: $i,SV96: $i] :
( ( ( ~ ( ord_less @ int @ SV96 @ SV486 ) )
= $true )
| ( ( ord_less @ int @ ( number_number_of @ int @ SV96 ) @ ( number_number_of @ int @ SV486 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3809]) ).
thf(4190,plain,
! [SV1003: $i,SV899: $i,SV742: $i,SV99: $i] :
( ( ( ( plus_plus @ SV99 @ SV742 @ ( plus_plus @ SV99 @ SV899 @ SV1003 ) )
= ( plus_plus @ SV99 @ SV899 @ ( plus_plus @ SV99 @ SV742 @ SV1003 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV99 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3812]) ).
thf(4191,plain,
! [SV101: $i,SV652: $i,SV490: $i] :
( ( ( zcong @ SV490 @ ( zero_zero @ int ) @ SV652 )
= $true )
| ( ( ~ ( zcong @ ( power_power @ int @ SV101 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SV490 @ SV652 )
| ~ ( dvd_dvd @ int @ SV652 @ SV101 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3814]) ).
thf(4192,plain,
! [SV743: $i,SV900: $i,SV102: $i] :
( ( ( ~ ( ord_less @ SV102 @ ( zero_zero @ SV102 ) @ SV900 ) )
= $true )
| ( ( ~ ( ord_less @ SV102 @ SV900 @ ( one_one @ SV102 ) )
| ( ord_less @ SV102 @ ( times_times @ SV102 @ SV900 @ ( power_power @ SV102 @ SV900 @ SV743 ) ) @ ( power_power @ SV102 @ SV900 @ SV743 ) ) )
= $true )
| ( ( linordered_semidom @ SV102 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3815]) ).
thf(4193,plain,
! [SV491: $i,SV103: $i] :
( ( ( ~ ( quadRes @ ( ti @ int @ SV103 ) @ SV491 ) )
= $true )
| ( ( quadRes @ SV103 @ SV491 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3816]) ).
thf(4194,plain,
! [SV491: $i,SV103: $i] :
( ( ( ~ ( quadRes @ SV103 @ SV491 ) )
= $true )
| ( ( quadRes @ ( ti @ int @ SV103 ) @ SV491 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3817]) ).
thf(4195,plain,
! [SV106: $i] :
( ( ( ( bit1 @ SV106 )
= min )
= $false )
| ( ( ( ti @ int @ SV106 )
= min )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3819]) ).
thf(4196,plain,
! [SV106: $i] :
( ( ( ( ti @ int @ SV106 )
= min )
= $false )
| ( ( ( bit1 @ SV106 )
= min )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3820]) ).
thf(4197,plain,
! [SV108: $i,SV494: $i,SV901: $i,SV744: $i,SV655: $i] :
( ( ( ~ ( zcong @ SV655 @ SV744 @ SV901 ) )
= $true )
| ( ( ( ( ti @ int @ SV744 )
!= ( ti @ int @ SV494 ) )
| ~ ( zcong @ SV494 @ SV108 @ SV901 )
| ( zcong @ SV655 @ SV108 @ SV901 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3822]) ).
thf(4198,plain,
! [SV656: $i,SV495: $i,SV109: $i] :
( ( ( ~ ( ( ( ti @ int @ SV109 )
!= ( zero_zero @ int ) ) ) )
= $true )
| ( ( dvd_dvd @ int @ SV495 @ SV656 )
= $true )
| ( ( dvd_dvd @ int @ ( times_times @ int @ SV109 @ SV495 ) @ ( times_times @ int @ SV109 @ SV656 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3823]) ).
thf(4199,plain,
! [SV496: $i,SV111: $i] :
( ( ( twoSqu420862341sum2sq @ SV111 )
= $false )
| ( ( twoSqu420862341sum2sq @ ( times_times @ int @ SV496 @ SV111 ) )
= $true )
| ( ( twoSqu420862341sum2sq @ SV496 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3824]) ).
thf(4200,plain,
! [SV112: $i] :
( ( ( ord_less_eq @ int @ ( bit0 @ SV112 ) @ pls )
= $false )
| ( ( ord_less_eq @ int @ SV112 @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3825]) ).
thf(4201,plain,
! [SV112: $i] :
( ( ( ord_less_eq @ int @ SV112 @ pls )
= $false )
| ( ( ord_less_eq @ int @ ( bit0 @ SV112 ) @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3826]) ).
thf(4202,plain,
! [SV498: $i,SV115: $i] :
( ( ( ~ ( ord_less @ int @ ( bit1 @ SV115 ) @ ( bit0 @ SV498 ) ) )
= $true )
| ( ( ord_less @ int @ SV115 @ SV498 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3827]) ).
thf(4203,plain,
! [SV498: $i,SV115: $i] :
( ( ( ~ ( ord_less @ int @ SV115 @ SV498 ) )
= $true )
| ( ( ord_less @ int @ ( bit1 @ SV115 ) @ ( bit0 @ SV498 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3828]) ).
thf(4204,plain,
! [SV746: $i,SV117: $i,SV1004: $i,SV902: $i] :
( ( ( ~ ( ord_less_eq @ nat @ SV902 @ SV1004 )
| ~ ( ord_less_eq @ SV117 @ ( zero_zero @ SV117 ) @ SV746 )
| ~ ( ord_less_eq @ SV117 @ SV746 @ ( one_one @ SV117 ) )
| ( ord_less_eq @ SV117 @ ( power_power @ SV117 @ SV746 @ SV1004 ) @ ( power_power @ SV117 @ SV746 @ SV902 ) ) )
= $true )
| ( ( linordered_semidom @ SV117 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3829]) ).
thf(4205,plain,
! [SV500: $i,SV119: $i,SV658: $i] :
( ( ( ~ ( dvd_dvd @ int @ SV658 @ ( power_power @ int @ SV119 @ SV500 ) ) )
= $true )
| ( ( dvd_dvd @ int @ SV658 @ SV119 )
= $true )
| ( ( zprime @ SV658 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3831]) ).
thf(4206,plain,
! [SV120: $i] :
( ( ( number_ring @ SV120 )
= $false )
| ( ( ~ ( linordered_idom @ SV120 ) )
= $true )
| ( ( ! [SY1234: $i] :
~ ( ~ ( ~ ( ord_less @ SV120 @ ( one_one @ SV120 ) @ ( number_number_of @ SV120 @ SY1234 ) )
| ( ord_less @ int @ ( bit1 @ pls ) @ SY1234 ) )
| ~ ( ~ ( ord_less @ int @ ( bit1 @ pls ) @ SY1234 )
| ( ord_less @ SV120 @ ( one_one @ SV120 ) @ ( number_number_of @ SV120 @ SY1234 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3832]) ).
thf(4207,plain,
! [SV502: $i,SV122: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( bit1 @ SV122 ) @ ( bit1 @ SV502 ) ) )
= $true )
| ( ( ord_less_eq @ int @ SV122 @ SV502 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3834]) ).
thf(4208,plain,
! [SV502: $i,SV122: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV122 @ SV502 ) )
= $true )
| ( ( ord_less_eq @ int @ ( bit1 @ SV122 ) @ ( bit1 @ SV502 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3835]) ).
thf(4209,plain,
( ( ( ! [SY1968: $i] :
( ( plus_plus @ int @ ( power_power @ int @ sK3_SX0 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ SY1968 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ) )
= $false )
| ( ( ord_less @ int @ ( one_one @ int ) @ t )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3836]) ).
thf(4210,plain,
! [SV123: $i] :
( ( ( number_ring @ SV123 )
= $false )
| ( ( ~ ( linordered_idom @ SV123 ) )
= $true )
| ( ( ! [SY1238: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV123 @ ( number_number_of @ SV123 @ SY1238 ) @ ( one_one @ SV123 ) )
| ( ord_less_eq @ int @ SY1238 @ ( bit1 @ pls ) ) )
| ~ ( ~ ( ord_less_eq @ int @ SY1238 @ ( bit1 @ pls ) )
| ( ord_less_eq @ SV123 @ ( number_number_of @ SV123 @ SY1238 ) @ ( one_one @ SV123 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3837]) ).
thf(4211,plain,
! [SV903: $i,SV747: $i,SV1005: $i,SV124: $i] :
( ( ( ! [SY2200: $i] :
( ~ ( dvd_dvd @ SV124 @ SV1005 @ SY2200 )
| ~ ( dvd_dvd @ SV124 @ SV747 @ SV903 )
| ( dvd_dvd @ SV124 @ ( times_times @ SV124 @ SV1005 @ SV747 ) @ ( times_times @ SV124 @ SY2200 @ SV903 ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV124 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3838]) ).
thf(4212,plain,
! [SV1006: $i,SV904: $i,SV748: $i,SV125: $i] :
( ( ( ! [SY2201: $i] :
( ( minus_minus @ SV125 @ ( plus_plus @ SV125 @ SV748 @ SV904 ) @ ( plus_plus @ SV125 @ SV1006 @ SY2201 ) )
= ( plus_plus @ SV125 @ ( minus_minus @ SV125 @ SV748 @ SV1006 ) @ ( minus_minus @ SV125 @ SV904 @ SY2201 ) ) ) )
= $true )
| ( ( ab_group_add @ SV125 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3839]) ).
thf(4213,plain,
! [SV128: $i] :
( ( ( ( number_number_of @ nat @ SV128 )
= ( zero_zero @ nat ) )
= $false )
| ( ( ord_less_eq @ int @ SV128 @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3840]) ).
thf(4214,plain,
! [SV128: $i] :
( ( ( ord_less_eq @ int @ SV128 @ pls )
= $false )
| ( ( ( number_number_of @ nat @ SV128 )
= ( zero_zero @ nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3841]) ).
thf(4215,plain,
! [SV1007: $i,SV905: $i,SV751: $i,SV130: $i] :
( ( ( ( times_times @ SV130 @ ( times_times @ SV130 @ SV751 @ SV905 ) @ SV1007 )
= ( times_times @ SV130 @ ( times_times @ SV130 @ SV751 @ SV1007 ) @ SV905 ) )
= $true )
| ( ( comm_semiring_1 @ SV130 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3842]) ).
thf(4216,plain,
! [SV1008: $i,SV906: $i,SV752: $i,SV131: $i] :
( ( ( ( times_times @ SV131 @ ( plus_plus @ SV131 @ SV752 @ SV906 ) @ SV1008 )
= ( plus_plus @ SV131 @ ( times_times @ SV131 @ SV752 @ SV1008 ) @ ( times_times @ SV131 @ SV906 @ SV1008 ) ) )
= $true )
| ( ( comm_semiring @ SV131 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3843]) ).
thf(4217,plain,
! [SV907: $i,SV753: $i,SV660: $i,SV503: $i,SV132: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( plus_plus @ int @ ( times_times @ int @ SV132 @ SV503 ) @ SV660 ) @ ( plus_plus @ int @ ( times_times @ int @ SV132 @ SV753 ) @ SV907 ) ) )
= $true )
| ( ( ~ ( ord_less_eq @ int @ SV907 @ ( zero_zero @ int ) )
| ~ ( ord_less @ int @ SV132 @ SV907 )
| ~ ( ord_less @ int @ SV132 @ SV660 )
| ( ord_less_eq @ int @ SV753 @ SV503 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3844]) ).
thf(4218,plain,
! [SV134: $i] :
( ( ( number_ring @ SV134 )
= $false )
| ( ( ~ ( linordered_idom @ SV134 ) )
= $true )
| ( ( ! [SY1260: $i] :
~ ( ~ ( ~ ( ord_less @ SV134 @ ( number_number_of @ SV134 @ SY1260 ) @ ( one_one @ SV134 ) )
| ( ord_less @ int @ SY1260 @ ( bit1 @ pls ) ) )
| ~ ( ~ ( ord_less @ int @ SY1260 @ ( bit1 @ pls ) )
| ( ord_less @ SV134 @ ( number_number_of @ SV134 @ SY1260 ) @ ( one_one @ SV134 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3845]) ).
thf(4219,plain,
! [SV505: $i,SV135: $i] :
( ( ( ~ ( ord_less_eq @ nat @ ( number_number_of @ nat @ SV135 ) @ ( number_number_of @ nat @ SV505 ) ) )
= $true )
| ( ( ~ ~ ( ord_less_eq @ int @ SV135 @ SV505 )
| ( ord_less_eq @ int @ SV135 @ pls ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3846]) ).
thf(4220,plain,
! [SV505: $i,SV135: $i] :
( ( ( ~ ( ~ ~ ( ord_less_eq @ int @ SV135 @ SV505 )
| ( ord_less_eq @ int @ SV135 @ pls ) ) )
= $true )
| ( ( ord_less_eq @ nat @ ( number_number_of @ nat @ SV135 ) @ ( number_number_of @ nat @ SV505 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3847]) ).
thf(4221,plain,
! [SV661: $i,SV506: $i,SV137: $i] :
( ( ~ ( zcong @ SV137 @ SV506 @ SV661 )
| ( dvd_dvd @ int @ SV661 @ ( minus_minus @ int @ SV137 @ SV506 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3848]) ).
thf(4222,plain,
! [SV506: $i,SV137: $i,SV661: $i] :
( ( ~ ( dvd_dvd @ int @ SV661 @ ( minus_minus @ int @ SV137 @ SV506 ) )
| ( zcong @ SV137 @ SV506 @ SV661 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3849]) ).
thf(4223,plain,
! [SV507: $i,SV138: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( number_number_of @ int @ SV138 ) @ ( number_number_of @ int @ SV507 ) ) )
= $true )
| ( ( ord_less_eq @ int @ SV138 @ SV507 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3850]) ).
thf(4224,plain,
! [SV507: $i,SV138: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV138 @ SV507 ) )
= $true )
| ( ( ord_less_eq @ int @ ( number_number_of @ int @ SV138 ) @ ( number_number_of @ int @ SV507 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3851]) ).
thf(4225,plain,
! [SV139: $i] :
( ( ( number @ SV139 )
= $false )
| ( ( ~ ( ring @ SV139 ) )
= $true )
| ( ( ! [SY1266: $i,SY1267: $i,SY1268: $i] :
( ( times_times @ SV139 @ ( number_number_of @ SV139 @ SY1266 ) @ ( minus_minus @ SV139 @ SY1267 @ SY1268 ) )
= ( minus_minus @ SV139 @ ( times_times @ SV139 @ ( number_number_of @ SV139 @ SY1266 ) @ SY1267 ) @ ( times_times @ SV139 @ ( number_number_of @ SV139 @ SY1266 ) @ SY1268 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3852]) ).
thf(4226,plain,
! [SV756: $i,SV908: $i,SV142: $i] :
( ( ( ~ ( ord_less @ SV142 @ ( one_one @ SV142 ) @ SV908 ) )
= $true )
| ( ( ord_less @ SV142 @ ( one_one @ SV142 ) @ ( times_times @ SV142 @ SV908 @ ( power_power @ SV142 @ SV908 @ SV756 ) ) )
= $true )
| ( ( linordered_semidom @ SV142 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3853]) ).
thf(4227,plain,
! [SV509: $i,SV143: $i] :
( ( ( ( power_power @ nat @ SV143 @ SV509 )
!= ( zero_zero @ nat ) )
= $true )
| ( ( ~ ( ~ ( ( SV509
!= ( zero_zero @ nat ) ) )
| ( SV143
!= ( zero_zero @ nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3854]) ).
thf(4228,plain,
! [SV143: $i,SV509: $i] :
( ( ( ~ ~ ( ~ ( ( SV509
!= ( zero_zero @ nat ) ) )
| ( SV143
!= ( zero_zero @ nat ) ) ) )
= $true )
| ( ( ( power_power @ nat @ SV143 @ SV509 )
= ( zero_zero @ nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3855]) ).
thf(4229,plain,
! [SV662: $i,SV510: $i,SV145: $i] :
( ( ~ ( dvd_dvd @ int @ SV145 @ ( plus_plus @ int @ SV510 @ ( times_times @ int @ SV145 @ SV662 ) ) )
| ( dvd_dvd @ int @ SV145 @ SV510 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3856]) ).
thf(4230,plain,
! [SV662: $i,SV510: $i,SV145: $i] :
( ( ~ ( dvd_dvd @ int @ SV145 @ SV510 )
| ( dvd_dvd @ int @ SV145 @ ( plus_plus @ int @ SV510 @ ( times_times @ int @ SV145 @ SV662 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3857]) ).
thf(4231,plain,
! [SV146: $i] :
( ( ( ord_less @ int @ ( bit1 @ SV146 ) @ min )
= $false )
| ( ( ord_less @ int @ SV146 @ min )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3858]) ).
thf(4232,plain,
! [SV146: $i] :
( ( ( ord_less @ int @ SV146 @ min )
= $false )
| ( ( ord_less @ int @ ( bit1 @ SV146 ) @ min )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3859]) ).
thf(4233,plain,
! [SV511: $i,SV147: $i] :
( ( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ SV147 @ SV511 ) ) )
= $true )
| ( ( ( ord_less @ nat @ ( zero_zero @ nat ) @ SV147 )
| ( SV511
= ( zero_zero @ nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3860]) ).
thf(4234,plain,
! [SV511: $i,SV147: $i] :
( ( ( ~ ( ( ord_less @ nat @ ( zero_zero @ nat ) @ SV147 )
| ( SV511
= ( zero_zero @ nat ) ) ) )
= $true )
| ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ SV147 @ SV511 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3861]) ).
thf(4235,plain,
! [SV1009: $i,SV909: $i,SV759: $i,SV150: $i] :
( ( ( ( plus_plus @ SV150 @ ( times_times @ SV150 @ SV759 @ SV909 ) @ ( times_times @ SV150 @ SV1009 @ SV909 ) )
= ( times_times @ SV150 @ ( plus_plus @ SV150 @ SV759 @ SV1009 ) @ SV909 ) )
= $true )
| ( ( comm_semiring_1 @ SV150 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3862]) ).
thf(4236,plain,
! [SV512: $i,SV151: $i] :
( ( ( ~ ~ ( ~ ( dvd_dvd @ nat @ SV151 @ SV512 )
| ~ ( dvd_dvd @ nat @ SV512 @ SV151 ) ) )
= $true )
| ( ( SV151 = SV512 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3863]) ).
thf(4237,plain,
! [SV512: $i,SV151: $i] :
( ( ( SV151 != SV512 )
= $true )
| ( ( ~ ( ~ ( dvd_dvd @ nat @ SV151 @ SV512 )
| ~ ( dvd_dvd @ nat @ SV512 @ SV151 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3864]) ).
thf(4238,plain,
! [SV760: $i,SV910: $i,SV152: $i] :
( ( ( ~ ( ord_less_eq @ SV152 @ ( zero_zero @ SV152 ) @ SV910 ) )
= $true )
| ( ( ~ ( ord_less_eq @ SV152 @ ( zero_zero @ SV152 ) @ SV760 )
| ( ord_less_eq @ SV152 @ ( zero_zero @ SV152 ) @ ( times_times @ SV152 @ SV910 @ SV760 ) ) )
= $true )
| ( ( ordere453448008miring @ SV152 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3865]) ).
thf(4239,plain,
! [SV513: $i,SV153: $i] :
( ( ( ord_less @ real @ ( zero_zero @ real ) @ SV153 )
= $false )
| ( ( ~ ! [SY1807: $i] :
~ ~ ( ~ ( ord_less @ real @ ( zero_zero @ real ) @ SY1807 )
| ( ( power_power @ real @ SY1807 @ SV513 )
!= SV153 ) ) )
= $true )
| ( ( ord_less @ nat @ ( zero_zero @ nat ) @ SV513 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3866]) ).
thf(4240,plain,
! [SV154: $i,SV761: $i,SV663: $i,SV514: $i] :
( ( ( zcong @ SV514 @ SV663 @ SV761 )
= $false )
| ( ( zcong @ ( times_times @ int @ SV154 @ SV514 ) @ ( times_times @ int @ SV154 @ SV663 ) @ SV761 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3867]) ).
thf(4241,plain,
! [SV911: $i,SV762: $i,SV1010: $i,SV155: $i] :
( ( ( ~ ( ord_less @ SV155 @ ( one_one @ SV155 ) @ SV1010 )
| ~ ( ~ ( ~ ( ord_less @ SV155 @ ( power_power @ SV155 @ SV1010 @ SV762 ) @ ( power_power @ SV155 @ SV1010 @ SV911 ) )
| ( ord_less @ nat @ SV762 @ SV911 ) )
| ~ ( ~ ( ord_less @ nat @ SV762 @ SV911 )
| ( ord_less @ SV155 @ ( power_power @ SV155 @ SV1010 @ SV762 ) @ ( power_power @ SV155 @ SV1010 @ SV911 ) ) ) ) )
= $true )
| ( ( linordered_semidom @ SV155 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3868]) ).
thf(4242,plain,
! [SV516: $i,SV159: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( bit1 @ SV159 ) @ ( bit0 @ SV516 ) ) )
= $true )
| ( ( ord_less @ int @ SV159 @ SV516 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3871]) ).
thf(4243,plain,
! [SV516: $i,SV159: $i] :
( ( ( ~ ( ord_less @ int @ SV159 @ SV516 ) )
= $true )
| ( ( ord_less_eq @ int @ ( bit1 @ SV159 ) @ ( bit0 @ SV516 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3872]) ).
thf(4244,plain,
! [SV517: $i,SV160: $i] :
( ( ( ~ ( ord_less @ int @ SV160 @ ( plus_plus @ int @ SV517 @ ( one_one @ int ) ) ) )
= $true )
| ( ( ord_less_eq @ int @ SV160 @ SV517 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3873]) ).
thf(4245,plain,
! [SV517: $i,SV160: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV160 @ SV517 ) )
= $true )
| ( ( ord_less @ int @ SV160 @ ( plus_plus @ int @ SV517 @ ( one_one @ int ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3874]) ).
thf(4246,plain,
! [SV518: $i,SV161: $i,SV665: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV665 ) )
= $true )
| ( ( ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV161 )
| ( ord_less_eq @ int @ SV518 @ ( zero_zero @ int ) ) )
= $true )
| ( ( ord_less @ int @ ( plus_plus @ int @ ( times_times @ int @ SV161 @ SV518 ) @ SV665 ) @ ( zero_zero @ int ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3875]) ).
thf(4247,plain,
! [SV666: $i,SV520: $i,SV163: $i] :
( ( ~ ( zcong @ SV163 @ SV520 @ ( ti @ int @ SV666 ) )
| ( zcong @ SV163 @ SV520 @ SV666 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3876]) ).
thf(4248,plain,
! [SV666: $i,SV520: $i,SV163: $i] :
( ( ~ ( zcong @ SV163 @ SV520 @ SV666 )
| ( zcong @ SV163 @ SV520 @ ( ti @ int @ SV666 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3877]) ).
thf(4249,plain,
! [SV164: $i,SV667: $i,SV521: $i,SV913: $i,SV765: $i] :
( ( ( ~ ( dvd_dvd @ int @ SV765 @ SV913 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( dvd_dvd @ int @ SV765 @ ( plus_plus @ int @ SV521 @ SV667 ) )
| ( dvd_dvd @ int @ SV765 @ ( plus_plus @ int @ ( plus_plus @ int @ SV521 @ ( times_times @ int @ SV164 @ SV913 ) ) @ SV667 ) ) )
| ~ ( ~ ( dvd_dvd @ int @ SV765 @ ( plus_plus @ int @ ( plus_plus @ int @ SV521 @ ( times_times @ int @ SV164 @ SV913 ) ) @ SV667 ) )
| ( dvd_dvd @ int @ SV765 @ ( plus_plus @ int @ SV521 @ SV667 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3878]) ).
thf(4250,plain,
! [SV1011: $i,SV914: $i,SV766: $i,SV165: $i] :
( ( ( ( plus_plus @ SV165 @ ( number_number_of @ SV165 @ SV766 ) @ ( plus_plus @ SV165 @ ( number_number_of @ SV165 @ SV914 ) @ SV1011 ) )
= ( plus_plus @ SV165 @ ( number_number_of @ SV165 @ ( plus_plus @ int @ SV766 @ SV914 ) ) @ SV1011 ) )
= $true )
| ( ( number_ring @ SV165 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3879]) ).
thf(4251,plain,
! [SV522: $i,SV167: $i,SV916: $i,SV768: $i,SV668: $i] :
( ( ( ~ ( zcong @ SV668 @ SV768 @ SV916 ) )
= $true )
| ( ( ~ ( zcong @ SV167 @ SV522 @ SV916 )
| ( zcong @ ( minus_minus @ int @ SV668 @ SV167 ) @ ( minus_minus @ int @ SV768 @ SV522 ) @ SV916 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3881]) ).
thf(4252,plain,
! [SV168: $i] :
( ( ( number @ SV168 )
= $false )
| ( ( ~ ( semiring @ SV168 ) )
= $true )
| ( ( ! [SY1318: $i,SY1319: $i,SY1320: $i] :
( ( times_times @ SV168 @ ( plus_plus @ SV168 @ SY1318 @ SY1319 ) @ ( number_number_of @ SV168 @ SY1320 ) )
= ( plus_plus @ SV168 @ ( times_times @ SV168 @ SY1318 @ ( number_number_of @ SV168 @ SY1320 ) ) @ ( times_times @ SV168 @ SY1319 @ ( number_number_of @ SV168 @ SY1320 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3882]) ).
thf(4253,plain,
! [SV523: $i,SV169: $i] :
( ( ( ( plus_plus @ real @ ( power_power @ real @ SV169 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ real @ SV523 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ real ) )
= $true )
| ( ( ~ ( ( SV169
!= ( zero_zero @ real ) )
| ( SV523
!= ( zero_zero @ real ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3883]) ).
thf(4254,plain,
! [SV523: $i,SV169: $i] :
( ( ( ~ ~ ( ( SV169
!= ( zero_zero @ real ) )
| ( SV523
!= ( zero_zero @ real ) ) ) )
= $true )
| ( ( ( plus_plus @ real @ ( power_power @ real @ SV169 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ real @ SV523 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ real ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3884]) ).
thf(4255,plain,
! [SV669: $i,SV524: $i,SV170: $i] :
( ( ( ~ ( ord_less @ nat @ ( one_one @ nat ) @ SV170 ) )
= $true )
| ( ( ord_less_eq @ nat @ SV524 @ SV669 )
= $true )
| ( ( dvd_dvd @ nat @ ( power_power @ nat @ SV170 @ SV524 ) @ ( power_power @ nat @ SV170 @ SV669 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3885]) ).
thf(4256,plain,
! [SV171: $i] :
( ( ( ord_less_eq @ int @ pls @ ( bit0 @ SV171 ) )
= $false )
| ( ( ord_less_eq @ int @ pls @ SV171 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3886]) ).
thf(4257,plain,
! [SV171: $i] :
( ( ( ord_less_eq @ int @ pls @ SV171 )
= $false )
| ( ( ord_less_eq @ int @ pls @ ( bit0 @ SV171 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3887]) ).
thf(4258,plain,
! [SV525: $i,SV172: $i] :
( ( ( ~ ( ord_less @ int @ SV172 @ SV525 ) )
= $true )
| ( ( ord_less @ int @ ( minus_minus @ int @ SV172 @ SV525 ) @ ( zero_zero @ int ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3888]) ).
thf(4259,plain,
! [SV525: $i,SV172: $i] :
( ( ( ~ ( ord_less @ int @ ( minus_minus @ int @ SV172 @ SV525 ) @ ( zero_zero @ int ) ) )
= $true )
| ( ( ord_less @ int @ SV172 @ SV525 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3889]) ).
thf(4260,plain,
! [SV1012: $i,SV917: $i,SV770: $i,SV174: $i] :
( ( ( ! [SY2202: $i] :
( ( minus_minus @ SV174 @ ( times_times @ SV174 @ SV770 @ SV917 ) @ ( times_times @ SV174 @ SV1012 @ SY2202 ) )
= ( plus_plus @ SV174 @ ( times_times @ SV174 @ SV770 @ ( minus_minus @ SV174 @ SV917 @ SY2202 ) ) @ ( times_times @ SV174 @ ( minus_minus @ SV174 @ SV770 @ SV1012 ) @ SY2202 ) ) ) )
= $true )
| ( ( ring @ SV174 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3890]) ).
thf(4261,plain,
! [SV918: $i,SV771: $i,SV1013: $i,SV175: $i] :
( ( ( ! [SY2203: $i] :
~ ( ~ ( ~ ~ ( ~ ( ( ( ti @ SV175 @ SV1013 )
!= ( ti @ SV175 @ SY2203 ) ) )
| ~ ( ( ( ti @ SV175 @ SV771 )
!= ( ti @ SV175 @ SV918 ) ) ) )
| ( ( plus_plus @ SV175 @ ( times_times @ SV175 @ SV1013 @ SV771 ) @ ( times_times @ SV175 @ SY2203 @ SV918 ) )
!= ( plus_plus @ SV175 @ ( times_times @ SV175 @ SV1013 @ SV918 ) @ ( times_times @ SV175 @ SY2203 @ SV771 ) ) ) )
| ~ ( ~ ( ( ( plus_plus @ SV175 @ ( times_times @ SV175 @ SV1013 @ SV771 ) @ ( times_times @ SV175 @ SY2203 @ SV918 ) )
!= ( plus_plus @ SV175 @ ( times_times @ SV175 @ SV1013 @ SV918 ) @ ( times_times @ SV175 @ SY2203 @ SV771 ) ) ) )
| ~ ( ~ ( ( ( ti @ SV175 @ SV1013 )
!= ( ti @ SV175 @ SY2203 ) ) )
| ~ ( ( ( ti @ SV175 @ SV771 )
!= ( ti @ SV175 @ SV918 ) ) ) ) ) ) )
= $true )
| ( ( semiri456707255roduct @ SV175 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3891]) ).
thf(4262,plain,
! [SV177: $i] :
( ( ( ord_less @ int @ pls @ ( bit0 @ SV177 ) )
= $false )
| ( ( ord_less @ int @ pls @ SV177 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3892]) ).
thf(4263,plain,
! [SV177: $i] :
( ( ( ord_less @ int @ pls @ SV177 )
= $false )
| ( ( ord_less @ int @ pls @ ( bit0 @ SV177 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3893]) ).
thf(4264,plain,
! [SV178: $i,SV527: $i] :
( ( ( ord_less @ int @ SV527 @ SV178 )
= $false )
| ( ( ~ ( dvd_dvd @ int @ SV178 @ SV527 ) )
= $true )
| ( ( ord_less @ int @ ( zero_zero @ int ) @ SV527 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3894]) ).
thf(4265,plain,
! [SV919: $i,SV772: $i,SV1014: $i,SV179: $i] :
( ( ( ~ ( ord_less @ SV179 @ ( one_one @ SV179 ) @ SV1014 )
| ~ ( ord_less @ SV179 @ ( power_power @ SV179 @ SV1014 @ SV772 ) @ ( power_power @ SV179 @ SV1014 @ SV919 ) )
| ( ord_less @ nat @ SV772 @ SV919 ) )
= $true )
| ( ( linordered_semidom @ SV179 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3895]) ).
thf(4266,plain,
! [SV1015: $i,SV920: $i,SV180: $i,SV773: $i] :
( ( ( ( SV773
!= ( times_times @ SV180 @ SV920 @ SV1015 ) )
| ( dvd_dvd @ SV180 @ SV920 @ SV773 ) )
= $true )
| ( ( dvd @ SV180 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3896]) ).
thf(4267,plain,
! [SV528: $i,SV182: $i] :
( ( ( ~ ( ord_less @ int @ ( bit1 @ SV182 ) @ ( bit1 @ SV528 ) ) )
= $true )
| ( ( ord_less @ int @ SV182 @ SV528 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3897]) ).
thf(4268,plain,
! [SV528: $i,SV182: $i] :
( ( ( ~ ( ord_less @ int @ SV182 @ SV528 ) )
= $true )
| ( ( ord_less @ int @ ( bit1 @ SV182 ) @ ( bit1 @ SV528 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3898]) ).
thf(4269,plain,
! [SV1016: $i,SV921: $i,SV775: $i,SV185: $i] :
( ( ( ( times_times @ SV185 @ ( power_power @ SV185 @ SV775 @ SV921 ) @ ( power_power @ SV185 @ SV775 @ SV1016 ) )
= ( power_power @ SV185 @ SV775 @ ( plus_plus @ nat @ SV921 @ SV1016 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV185 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3899]) ).
thf(4270,plain,
! [SV529: $i,SV186: $i] :
( ( ( ~ ( ord_less @ int @ ( bit0 @ SV186 ) @ ( bit0 @ SV529 ) ) )
= $true )
| ( ( ord_less @ int @ SV186 @ SV529 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3900]) ).
thf(4271,plain,
! [SV529: $i,SV186: $i] :
( ( ( ~ ( ord_less @ int @ SV186 @ SV529 ) )
= $true )
| ( ( ord_less @ int @ ( bit0 @ SV186 ) @ ( bit0 @ SV529 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3901]) ).
thf(4272,plain,
! [SV530: $i,SV187: $i] :
( ( ( ~ ( ord_less @ int @ SV187 @ SV530 ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq @ int @ SV187 @ SV530 )
| ~ ( ( ( ti @ int @ SV187 )
!= ( ti @ int @ SV530 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3902]) ).
thf(4273,plain,
! [SV530: $i,SV187: $i] :
( ( ( ~ ~ ( ~ ( ord_less_eq @ int @ SV187 @ SV530 )
| ~ ( ( ( ti @ int @ SV187 )
!= ( ti @ int @ SV530 ) ) ) ) )
= $true )
| ( ( ord_less @ int @ SV187 @ SV530 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3903]) ).
thf(4274,plain,
! [SV776: $i,SV189: $i] :
( ( ( ~ ( ( ( plus_plus @ SV189 @ SV776 @ SV776 )
!= ( zero_zero @ SV189 ) )
| ( ( ti @ SV189 @ SV776 )
= ( zero_zero @ SV189 ) ) ) )
= $false )
| ( ( linord219039673up_add @ SV189 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3904]) ).
thf(4275,plain,
! [SV776: $i,SV189: $i] :
( ( ( ~ ( ( ( ti @ SV189 @ SV776 )
!= ( zero_zero @ SV189 ) )
| ( ( plus_plus @ SV189 @ SV776 @ SV776 )
= ( zero_zero @ SV189 ) ) ) )
= $false )
| ( ( linord219039673up_add @ SV189 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3904]) ).
thf(4276,plain,
! [SV670: $i,SV532: $i,SV190: $i] :
( ( ( ~ ( zcong @ ( power_power @ int @ ( number_number_of @ int @ min ) @ SV190 ) @ ( power_power @ int @ ( number_number_of @ int @ min ) @ SV532 ) @ SV670 ) )
= $true )
| ( ( ( power_power @ int @ ( number_number_of @ int @ min ) @ SV190 )
= ( power_power @ int @ ( number_number_of @ int @ min ) @ SV532 ) )
= $true )
| ( ( ord_less @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV670 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3905]) ).
thf(4277,plain,
! [SV671: $i,SV533: $i,SV191: $i] :
( ( ~ ( dvd_dvd @ nat @ ( times_times @ nat @ SV191 @ SV533 ) @ ( times_times @ nat @ SV671 @ SV533 ) )
| ( SV533
= ( zero_zero @ nat ) )
| ( dvd_dvd @ nat @ SV191 @ SV671 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3906]) ).
thf(4278,plain,
! [SV671: $i,SV191: $i,SV533: $i] :
( ( ~ ( ( SV533
= ( zero_zero @ nat ) )
| ( dvd_dvd @ nat @ SV191 @ SV671 ) )
| ( dvd_dvd @ nat @ ( times_times @ nat @ SV191 @ SV533 ) @ ( times_times @ nat @ SV671 @ SV533 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3907]) ).
thf(4279,plain,
! [SV777: $i,SV922: $i,SV192: $i] :
( ( ( ~ ( ord_less_eq @ SV192 @ ( zero_zero @ SV192 ) @ SV922 ) )
= $true )
| ( ( ord_less_eq @ SV192 @ ( zero_zero @ SV192 ) @ ( power_power @ SV192 @ SV922 @ SV777 ) )
= $true )
| ( ( linordered_semidom @ SV192 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3908]) ).
thf(4280,plain,
! [SV923: $i,SV778: $i,SV193: $i] :
( ( ( ~ ( ( ( plus_plus @ SV193 @ ( times_times @ SV193 @ SV778 @ SV778 ) @ ( times_times @ SV193 @ SV923 @ SV923 ) )
!= ( zero_zero @ SV193 ) )
| ~ ( ( ( ti @ SV193 @ SV778 )
!= ( zero_zero @ SV193 ) )
| ( ( ti @ SV193 @ SV923 )
!= ( zero_zero @ SV193 ) ) ) )
| ~ ( ~ ~ ( ( ( ti @ SV193 @ SV778 )
!= ( zero_zero @ SV193 ) )
| ( ( ti @ SV193 @ SV923 )
!= ( zero_zero @ SV193 ) ) )
| ( ( plus_plus @ SV193 @ ( times_times @ SV193 @ SV778 @ SV778 ) @ ( times_times @ SV193 @ SV923 @ SV923 ) )
= ( zero_zero @ SV193 ) ) ) )
= $false )
| ( ( linord581940658strict @ SV193 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3909]) ).
thf(4281,plain,
! [SV924: $i,SV779: $i,SV1017: $i,SV194: $i] :
( ( ( ~ ( ord_less @ SV194 @ ( one_one @ SV194 ) @ SV1017 )
| ~ ( ~ ( ( ( power_power @ SV194 @ SV1017 @ SV779 )
!= ( power_power @ SV194 @ SV1017 @ SV924 ) )
| ( SV779 = SV924 ) )
| ~ ( ( SV779 != SV924 )
| ( ( power_power @ SV194 @ SV1017 @ SV779 )
= ( power_power @ SV194 @ SV1017 @ SV924 ) ) ) ) )
= $true )
| ( ( linordered_semidom @ SV194 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3910]) ).
thf(4282,plain,
! [SV925: $i,SV780: $i,SV195: $i] :
( ( ( ord_less @ SV195 @ ( plus_plus @ SV195 @ ( times_times @ SV195 @ SV780 @ SV780 ) @ ( times_times @ SV195 @ SV925 @ SV925 ) ) @ ( zero_zero @ SV195 ) )
= $false )
| ( ( linordered_ring @ SV195 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3911]) ).
thf(4283,plain,
! [SV196: $i,SV672: $i,SV534: $i] :
( ( ( ~ ~ ( zcong @ SV534 @ ( zero_zero @ int ) @ SV672 ) )
= $true )
| ( ( ~ ~ ( zcong @ SV196 @ ( zero_zero @ int ) @ SV672 )
| ~ ( zcong @ ( times_times @ int @ SV534 @ SV196 ) @ ( zero_zero @ int ) @ SV672 ) )
= $true )
| ( ( zprime @ SV672 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3912]) ).
thf(4284,plain,
! [SV928: $i,SV783: $i,SV199: $i] :
( ( ( ~ ( ~ ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ ( times_times @ SV199 @ SV783 @ SV928 ) )
| ~ ( ~ ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ SV783 )
| ~ ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ SV928 ) )
| ~ ( ~ ( ord_less_eq @ SV199 @ SV783 @ ( zero_zero @ SV199 ) )
| ~ ( ord_less_eq @ SV199 @ SV928 @ ( zero_zero @ SV199 ) ) ) )
| ~ ( ~ ( ~ ( ~ ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ SV783 )
| ~ ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ SV928 ) )
| ~ ( ~ ( ord_less_eq @ SV199 @ SV783 @ ( zero_zero @ SV199 ) )
| ~ ( ord_less_eq @ SV199 @ SV928 @ ( zero_zero @ SV199 ) ) ) )
| ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ ( times_times @ SV199 @ SV783 @ SV928 ) ) ) )
= $false )
| ( ( linord581940658strict @ SV199 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3915]) ).
thf(4285,plain,
! [SV785: $i,SV929: $i,SV201: $i] :
( ( ( ~ ( ord_less @ SV201 @ ( one_one @ SV201 ) @ SV929 ) )
= $true )
| ( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ SV785 )
| ( ord_less @ SV201 @ ( one_one @ SV201 ) @ ( power_power @ SV201 @ SV929 @ SV785 ) ) )
= $true )
| ( ( linordered_semidom @ SV201 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3916]) ).
thf(4286,plain,
! [SV202: $i] :
( ( ( number_ring @ SV202 )
= $false )
| ( ( ~ ( linordered_idom @ SV202 ) )
= $true )
| ( ( ! [SY1375: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV202 @ ( one_one @ SV202 ) @ ( number_number_of @ SV202 @ SY1375 ) )
| ( ord_less_eq @ int @ ( bit1 @ pls ) @ SY1375 ) )
| ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ pls ) @ SY1375 )
| ( ord_less_eq @ SV202 @ ( one_one @ SV202 ) @ ( number_number_of @ SV202 @ SY1375 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3917]) ).
thf(4287,plain,
! [SV203: $i,SV535: $i,SV673: $i] :
( ( ( ~ ( ord_less @ int @ SV673 @ SV535 ) )
= $true )
| ( ( ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV203 )
| ~ ( ord_less @ int @ SV203 @ SV673 )
| ~ ( zcong @ SV673 @ SV203 @ SV535 ) )
= $true )
| ( ( ord_less @ int @ ( zero_zero @ int ) @ SV673 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3918]) ).
thf(4288,plain,
! [SV205: $i] :
( ( ( ord_less @ int @ ( bit0 @ SV205 ) @ min )
= $false )
| ( ( ord_less_eq @ int @ SV205 @ min )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3919]) ).
thf(4289,plain,
! [SV205: $i] :
( ( ( ord_less_eq @ int @ SV205 @ min )
= $false )
| ( ( ord_less @ int @ ( bit0 @ SV205 ) @ min )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3920]) ).
thf(4290,plain,
! [SV536: $i,SV206: $i,SV930: $i,SV787: $i,SV674: $i] :
( ( ( ~ ( zcong @ SV674 @ SV787 @ SV930 ) )
= $true )
| ( ( ~ ( zcong @ SV206 @ SV536 @ SV930 )
| ( zcong @ ( plus_plus @ int @ SV674 @ SV206 ) @ ( plus_plus @ int @ SV787 @ SV536 ) @ SV930 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3921]) ).
thf(4291,plain,
! [SV207: $i] :
( ( ( ord_less @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ SV207 ) @ SV207 ) @ ( zero_zero @ int ) )
= $false )
| ( ( ord_less @ int @ SV207 @ ( zero_zero @ int ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3922]) ).
thf(4292,plain,
! [SV207: $i] :
( ( ( ord_less @ int @ SV207 @ ( zero_zero @ int ) )
= $false )
| ( ( ord_less @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ SV207 ) @ SV207 ) @ ( zero_zero @ int ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3923]) ).
thf(4293,plain,
! [SV208: $i] :
( ( ( twoSqu420862341sum2sq @ ( ti @ int @ SV208 ) )
= $false )
| ( ( twoSqu420862341sum2sq @ SV208 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3924]) ).
thf(4294,plain,
! [SV208: $i] :
( ( ( twoSqu420862341sum2sq @ SV208 )
= $false )
| ( ( twoSqu420862341sum2sq @ ( ti @ int @ SV208 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3925]) ).
thf(4295,plain,
! [SV209: $i,SV675: $i,SV537: $i] :
( ( ( ~ ( dvd_dvd @ nat @ SV537 @ ( plus_plus @ nat @ SV675 @ SV209 ) ) )
= $true )
| ( ( dvd_dvd @ nat @ SV537 @ SV209 )
= $true )
| ( ( dvd_dvd @ nat @ SV537 @ SV675 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3926]) ).
thf(4296,plain,
! [SV210: $i] :
( ( ( ( bit0 @ SV210 )
= pls )
= $false )
| ( ( ( ti @ int @ SV210 )
= pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3927]) ).
thf(4297,plain,
! [SV210: $i] :
( ( ( ( ti @ int @ SV210 )
= pls )
= $false )
| ( ( ( bit0 @ SV210 )
= pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3928]) ).
thf(4298,plain,
! [SV213: $i] :
( ( ( number_ring @ SV213 )
= $false )
| ( ( ~ ( ring_char_0 @ SV213 ) )
= $true )
| ( ( ! [SY1389: $i,SY1390: $i] :
~ ( ~ ( ( ( number_number_of @ SV213 @ SY1389 )
!= ( number_number_of @ SV213 @ SY1390 ) )
| ( ( ti @ int @ SY1389 )
= ( ti @ int @ SY1390 ) ) )
| ~ ( ( ( ti @ int @ SY1389 )
!= ( ti @ int @ SY1390 ) )
| ( ( number_number_of @ SV213 @ SY1389 )
= ( number_number_of @ SV213 @ SY1390 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3931]) ).
thf(4299,plain,
! [SV790: $i,SV676: $i,SV538: $i,SV214: $i] :
( ( ( SV214
= ( plus_plus @ nat @ ( times_times @ nat @ SV538 @ SV676 ) @ SV790 ) )
= $false )
| ( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ SV790 )
| ~ ( ord_less @ nat @ SV790 @ SV676 )
| ~ ( dvd_dvd @ nat @ SV676 @ SV214 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3932]) ).
thf(4300,plain,
! [SV677: $i,SV215: $i,SV539: $i] :
( ( ( ~ ( ( SV539
!= ( zero_zero @ nat ) ) ) )
= $true )
| ( ( dvd_dvd @ nat @ SV215 @ SV677 )
= $true )
| ( ( dvd_dvd @ nat @ ( power_power @ nat @ SV215 @ SV539 ) @ ( power_power @ nat @ SV677 @ SV539 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3933]) ).
thf(4301,plain,
! [SV218: $i] :
( ( ( number_ring @ SV218 )
= $false )
| ( ( ~ ( linordered_idom @ SV218 ) )
= $true )
| ( ( ! [SY1397: $i,SY1398: $i] :
~ ( ~ ( ~ ( ord_less @ SV218 @ ( number_number_of @ SV218 @ SY1397 ) @ ( number_number_of @ SV218 @ SY1398 ) )
| ( ord_less @ int @ SY1397 @ SY1398 ) )
| ~ ( ~ ( ord_less @ int @ SY1397 @ SY1398 )
| ( ord_less @ SV218 @ ( number_number_of @ SV218 @ SY1397 ) @ ( number_number_of @ SV218 @ SY1398 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3934]) ).
thf(4302,plain,
! [SV219: $i] :
( ( ( ord_less_eq @ int @ ( bit0 @ SV219 ) @ min )
= $false )
| ( ( ord_less_eq @ int @ SV219 @ min )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3935]) ).
thf(4303,plain,
! [SV219: $i] :
( ( ( ord_less_eq @ int @ SV219 @ min )
= $false )
| ( ( ord_less_eq @ int @ ( bit0 @ SV219 ) @ min )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3936]) ).
thf(4304,plain,
! [SV792: $i,SV1018: $i,SV933: $i,SV220: $i] :
( ( ( ! [SY2204: $i] :
( ~ ( dvd_dvd @ SV220 @ ( power_power @ SV220 @ SV933 @ SV1018 ) @ SY2204 )
| ~ ( ord_less_eq @ nat @ SV792 @ SV1018 )
| ( dvd_dvd @ SV220 @ ( power_power @ SV220 @ SV933 @ SV792 ) @ SY2204 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV220 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3937]) ).
thf(4305,plain,
! [SV678: $i,SV540: $i,SV221: $i] :
( ( ( ~ ( ord_less @ real @ SV221 @ SV540 ) )
= $true )
| ( ( ord_less @ real @ ( times_times @ real @ SV678 @ SV221 ) @ ( times_times @ real @ SV678 @ SV540 ) )
= $true )
| ( ( ord_less @ real @ ( zero_zero @ real ) @ SV678 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3938]) ).
thf(4306,plain,
! [SV793: $i,SV1019: $i,SV934: $i,SV222: $i] :
( ( ( ~ ( dvd_dvd @ SV222 @ SV934 @ SV1019 )
| ( dvd_dvd @ SV222 @ SV934 @ ( times_times @ SV222 @ SV793 @ SV1019 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV222 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3939]) ).
thf(4307,plain,
! [SV541: $i,SV223: $i,SV679: $i] :
( ( ( ~ ( ord_less @ nat @ ( power_power @ nat @ SV679 @ SV223 ) @ ( power_power @ nat @ SV679 @ SV541 ) ) )
= $true )
| ( ( ord_less @ nat @ SV223 @ SV541 )
= $true )
| ( ( ord_less @ nat @ ( zero_zero @ nat ) @ SV679 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3940]) ).
thf(4308,plain,
! [SV542: $i,SV224: $i] :
( ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV224 )
= $false )
| ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ SV542 @ SV224 ) )
= $true )
| ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV542 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3941]) ).
thf(4309,plain,
! [SV225: $i] :
( ( ( ord_less_eq @ int @ ( one_one @ int ) @ SV225 )
= $false )
| ( ( ord_less @ int @ ( zero_zero @ int ) @ SV225 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3942]) ).
thf(4310,plain,
! [SV225: $i] :
( ( ( ord_less @ int @ ( zero_zero @ int ) @ SV225 )
= $false )
| ( ( ord_less_eq @ int @ ( one_one @ int ) @ SV225 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3943]) ).
thf(4311,plain,
! [SV1020: $i,SV935: $i,SV794: $i,SV226: $i] :
( ( ( ~ ( dvd_dvd @ SV226 @ ( times_times @ SV226 @ SV794 @ SV935 ) @ SV1020 )
| ( dvd_dvd @ SV226 @ SV794 @ SV1020 ) )
= $true )
| ( ( comm_semiring_1 @ SV226 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3944]) ).
thf(4312,plain,
! [SV546: $i,SV231: $i] :
( ( ( ~ ( ord_less @ int @ ( bit0 @ SV231 ) @ ( bit1 @ SV546 ) ) )
= $true )
| ( ( ord_less_eq @ int @ SV231 @ SV546 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3949]) ).
thf(4313,plain,
! [SV546: $i,SV231: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV231 @ SV546 ) )
= $true )
| ( ( ord_less @ int @ ( bit0 @ SV231 ) @ ( bit1 @ SV546 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3950]) ).
thf(4314,plain,
! [SV547: $i,SV233: $i] :
( ( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ SV233 @ ( number_number_of @ nat @ SV547 ) ) ) )
= $true )
| ( ( ( ( number_number_of @ nat @ SV547 )
= ( zero_zero @ nat ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ SV233 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3951]) ).
thf(4315,plain,
! [SV233: $i,SV547: $i] :
( ( ( ~ ( ( ( number_number_of @ nat @ SV547 )
= ( zero_zero @ nat ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ SV233 ) ) )
= $true )
| ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ SV233 @ ( number_number_of @ nat @ SV547 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3952]) ).
thf(4316,plain,
! [SV234: $i] :
( ( ( number @ SV234 )
= $false )
| ( ( ~ ( semiring @ SV234 ) )
= $true )
| ( ( ! [SY1424: $i,SY1425: $i,SY1426: $i] :
( ( times_times @ SV234 @ ( number_number_of @ SV234 @ SY1424 ) @ ( plus_plus @ SV234 @ SY1425 @ SY1426 ) )
= ( plus_plus @ SV234 @ ( times_times @ SV234 @ ( number_number_of @ SV234 @ SY1424 ) @ SY1425 ) @ ( times_times @ SV234 @ ( number_number_of @ SV234 @ SY1424 ) @ SY1426 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3953]) ).
thf(4317,plain,
! [SV548: $i,SV236: $i] :
( ( ( ~ ( ord_less @ int @ ( bit0 @ SV236 ) @ ( bit1 @ SV548 ) ) )
= $true )
| ( ( ord_less_eq @ int @ SV236 @ SV548 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3954]) ).
thf(4318,plain,
! [SV548: $i,SV236: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV236 @ SV548 ) )
= $true )
| ( ( ord_less @ int @ ( bit0 @ SV236 ) @ ( bit1 @ SV548 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3955]) ).
thf(4319,plain,
! [SV937: $i,SV797: $i,SV237: $i] :
( ( ( ~ ( ( ( number_number_of @ SV237 @ SV797 )
!= ( ti @ SV237 @ SV937 ) )
| ( ( ti @ SV237 @ SV937 )
= ( number_number_of @ SV237 @ SV797 ) ) )
| ~ ( ( ( ti @ SV237 @ SV937 )
!= ( number_number_of @ SV237 @ SV797 ) )
| ( ( number_number_of @ SV237 @ SV797 )
= ( ti @ SV237 @ SV937 ) ) ) )
= $false )
| ( ( number @ SV237 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3956]) ).
thf(4320,plain,
! [SV1021: $i,SV938: $i,SV798: $i,SV238: $i] :
( ( ( ( plus_plus @ SV238 @ SV798 @ ( plus_plus @ SV238 @ SV938 @ SV1021 ) )
= ( plus_plus @ SV238 @ ( plus_plus @ SV238 @ SV798 @ SV938 ) @ SV1021 ) )
= $true )
| ( ( comm_semiring_1 @ SV238 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3957]) ).
thf(4321,plain,
! [SV239: $i] :
( ( ( ord_less_eq @ int @ min @ ( bit0 @ SV239 ) )
= $false )
| ( ( ord_less @ int @ min @ SV239 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3958]) ).
thf(4322,plain,
! [SV239: $i] :
( ( ( ord_less @ int @ min @ SV239 )
= $false )
| ( ( ord_less_eq @ int @ min @ ( bit0 @ SV239 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3959]) ).
thf(4323,plain,
! [SV549: $i,SV240: $i,SV683: $i,SV799: $i] :
( ( ( zprime @ SV799 )
= $false )
| ( ( ~ ~ ( dvd_dvd @ int @ SV799 @ SV683 )
| ~ ( dvd_dvd @ int @ ( power_power @ int @ SV799 @ SV240 ) @ ( times_times @ int @ SV683 @ SV549 ) )
| ( dvd_dvd @ int @ ( power_power @ int @ SV799 @ SV240 ) @ SV549 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3960]) ).
thf(4324,plain,
! [SV241: $i] :
( ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( number_number_of @ nat @ SV241 ) )
= $false )
| ( ( ord_less @ int @ pls @ SV241 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3961]) ).
thf(4325,plain,
! [SV241: $i] :
( ( ( ord_less @ int @ pls @ SV241 )
= $false )
| ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( number_number_of @ nat @ SV241 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3962]) ).
thf(4326,plain,
! [SV550: $i,SV242: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( bit0 @ SV242 ) @ ( bit1 @ SV550 ) ) )
= $true )
| ( ( ord_less_eq @ int @ SV242 @ SV550 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3963]) ).
thf(4327,plain,
! [SV550: $i,SV242: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV242 @ SV550 ) )
= $true )
| ( ( ord_less_eq @ int @ ( bit0 @ SV242 ) @ ( bit1 @ SV550 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3964]) ).
thf(4328,plain,
! [SV244: $i] :
( ( ( ord_less @ int @ pls @ ( bit1 @ SV244 ) )
= $false )
| ( ( ord_less_eq @ int @ pls @ SV244 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3966]) ).
thf(4329,plain,
! [SV244: $i] :
( ( ( ord_less_eq @ int @ pls @ SV244 )
= $false )
| ( ( ord_less @ int @ pls @ ( bit1 @ SV244 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3967]) ).
thf(4330,plain,
! [SV552: $i,SV245: $i,SV685: $i] :
( ( ~ ( ord_less @ int @ SV685 @ pls )
| ( ( times_times @ nat @ ( number_number_of @ nat @ SV685 ) @ ( times_times @ nat @ ( number_number_of @ nat @ SV245 ) @ SV552 ) )
= ( zero_zero @ nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3968]) ).
thf(4331,plain,
! [SV552: $i,SV245: $i,SV685: $i] :
( ( ~ ~ ( ord_less @ int @ SV685 @ pls )
| ( ( times_times @ nat @ ( number_number_of @ nat @ SV685 ) @ ( times_times @ nat @ ( number_number_of @ nat @ SV245 ) @ SV552 ) )
= ( times_times @ nat @ ( number_number_of @ nat @ ( times_times @ int @ SV685 @ SV245 ) ) @ SV552 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3969]) ).
thf(4332,plain,
! [SV554: $i,SV247: $i] :
( ( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ SV247 @ SV554 ) ) )
= $true )
| ( ( ( SV554
= ( zero_zero @ nat ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ SV247 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3971]) ).
thf(4333,plain,
! [SV247: $i,SV554: $i] :
( ( ( ~ ( ( SV554
= ( zero_zero @ nat ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ SV247 ) ) )
= $true )
| ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ SV247 @ SV554 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3972]) ).
thf(4334,plain,
! [SV1022: $i,SV939: $i,SV800: $i,SV248: $i] :
( ( ( ( times_times @ SV248 @ ( number_number_of @ SV248 @ SV800 ) @ ( times_times @ SV248 @ ( number_number_of @ SV248 @ SV939 ) @ SV1022 ) )
= ( times_times @ SV248 @ ( number_number_of @ SV248 @ ( times_times @ int @ SV800 @ SV939 ) ) @ SV1022 ) )
= $true )
| ( ( number_ring @ SV248 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3973]) ).
thf(4335,plain,
! [SV249: $i] :
( ( ( ord_less @ int @ ( bit1 @ SV249 ) @ ( zero_zero @ int ) )
= $false )
| ( ( ord_less @ int @ SV249 @ ( zero_zero @ int ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3974]) ).
thf(4336,plain,
! [SV249: $i] :
( ( ( ord_less @ int @ SV249 @ ( zero_zero @ int ) )
= $false )
| ( ( ord_less @ int @ ( bit1 @ SV249 ) @ ( zero_zero @ int ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3975]) ).
thf(4337,plain,
! [SV1023: $i,SV940: $i,SV802: $i,SV252: $i] :
( ( ( ( times_times @ SV252 @ ( times_times @ SV252 @ SV802 @ SV940 ) @ SV1023 )
= ( times_times @ SV252 @ SV802 @ ( times_times @ SV252 @ SV940 @ SV1023 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV252 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3977]) ).
thf(4338,plain,
! [SV556: $i,SV253: $i] :
( ( ( ~ ( ord_less @ int @ ( bit1 @ SV253 ) @ ( bit0 @ SV556 ) ) )
= $true )
| ( ( ord_less @ int @ SV253 @ SV556 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3978]) ).
thf(4339,plain,
! [SV556: $i,SV253: $i] :
( ( ( ~ ( ord_less @ int @ SV253 @ SV556 ) )
= $true )
| ( ( ord_less @ int @ ( bit1 @ SV253 ) @ ( bit0 @ SV556 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3979]) ).
thf(4340,plain,
! [SV1024: $i,SV942: $i,SV804: $i,SV255: $i] :
( ( ( ! [SY2205: $i] :
~ ( ~ ( ( ( plus_plus @ SV255 @ ( times_times @ SV255 @ SV804 @ SV942 ) @ ( times_times @ SV255 @ SV1024 @ SY2205 ) )
!= ( plus_plus @ SV255 @ ( times_times @ SV255 @ SV804 @ SY2205 ) @ ( times_times @ SV255 @ SV1024 @ SV942 ) ) )
| ( ( ti @ SV255 @ SV804 )
= ( ti @ SV255 @ SV1024 ) )
| ( ( ti @ SV255 @ SV942 )
= ( ti @ SV255 @ SY2205 ) ) )
| ~ ( ~ ( ( ( ti @ SV255 @ SV804 )
= ( ti @ SV255 @ SV1024 ) )
| ( ( ti @ SV255 @ SV942 )
= ( ti @ SV255 @ SY2205 ) ) )
| ( ( plus_plus @ SV255 @ ( times_times @ SV255 @ SV804 @ SV942 ) @ ( times_times @ SV255 @ SV1024 @ SY2205 ) )
= ( plus_plus @ SV255 @ ( times_times @ SV255 @ SV804 @ SY2205 ) @ ( times_times @ SV255 @ SV1024 @ SV942 ) ) ) ) ) )
= $true )
| ( ( semiri456707255roduct @ SV255 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3981]) ).
thf(4341,plain,
! [SV256: $i] :
( ( ( ord_less_eq @ int @ pls @ ( bit1 @ SV256 ) )
= $false )
| ( ( ord_less_eq @ int @ pls @ SV256 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3982]) ).
thf(4342,plain,
! [SV256: $i] :
( ( ( ord_less_eq @ int @ pls @ SV256 )
= $false )
| ( ( ord_less_eq @ int @ pls @ ( bit1 @ SV256 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3983]) ).
thf(4343,plain,
! [SV557: $i,SV257: $i,SV943: $i,SV805: $i,SV688: $i] :
( ( ( ~ ( zcong @ SV688 @ SV805 @ SV943 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( zcong @ SV257 @ ( times_times @ int @ SV557 @ SV688 ) @ SV943 )
| ( zcong @ SV257 @ ( times_times @ int @ SV557 @ SV805 ) @ SV943 ) )
| ~ ( ~ ( zcong @ SV257 @ ( times_times @ int @ SV557 @ SV805 ) @ SV943 )
| ( zcong @ SV257 @ ( times_times @ int @ SV557 @ SV688 ) @ SV943 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3984]) ).
thf(4344,plain,
! [SV558: $i,SV259: $i,SV689: $i] :
( ( ( SV689
= ( zero_zero @ nat ) )
= $true )
| ( ( ~ ( dvd_dvd @ nat @ ( power_power @ nat @ SV259 @ SV689 ) @ SV558 )
| ( dvd_dvd @ nat @ SV259 @ SV558 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3985]) ).
thf(4345,plain,
! [SV690: $i,SV559: $i,SV261: $i] :
( ( ~ ( zcong @ SV261 @ ( ti @ int @ SV559 ) @ SV690 )
| ( zcong @ SV261 @ SV559 @ SV690 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3986]) ).
thf(4346,plain,
! [SV690: $i,SV559: $i,SV261: $i] :
( ( ~ ( zcong @ SV261 @ SV559 @ SV690 )
| ( zcong @ SV261 @ ( ti @ int @ SV559 ) @ SV690 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3987]) ).
thf(4347,plain,
! [SV1025: $i,SV946: $i,SV809: $i,SV266: $i] :
( ( ( ! [SY2206: $i] :
( ( plus_plus @ SV266 @ ( plus_plus @ SV266 @ SV809 @ SV946 ) @ ( plus_plus @ SV266 @ SV1025 @ SY2206 ) )
= ( plus_plus @ SV266 @ ( plus_plus @ SV266 @ SV809 @ SV1025 ) @ ( plus_plus @ SV266 @ SV946 @ SY2206 ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV266 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3990]) ).
thf(4348,plain,
! [SV560: $i,SV268: $i] :
( ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV268 )
= $false )
| ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( times_times @ int @ SV560 @ SV268 ) )
= $true )
| ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV560 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3991]) ).
thf(4349,plain,
! [SV810: $i,SV269: $i] :
( ( ( ~ ( ~ ( ord_less @ SV269 @ ( plus_plus @ SV269 @ SV810 @ SV810 ) @ ( zero_zero @ SV269 ) )
| ( ord_less @ SV269 @ SV810 @ ( zero_zero @ SV269 ) ) ) )
= $false )
| ( ( linordered_idom @ SV269 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3992]) ).
thf(4350,plain,
! [SV810: $i,SV269: $i] :
( ( ( ~ ( ~ ( ord_less @ SV269 @ SV810 @ ( zero_zero @ SV269 ) )
| ( ord_less @ SV269 @ ( plus_plus @ SV269 @ SV810 @ SV810 ) @ ( zero_zero @ SV269 ) ) ) )
= $false )
| ( ( linordered_idom @ SV269 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3992]) ).
thf(4351,plain,
! [SV270: $i,SV561: $i] :
( ( ( ord_less_eq @ int @ SV561 @ SV270 )
= $false )
| ( ( ( ti @ int @ SV270 )
= ( ti @ int @ SV561 ) )
= $true )
| ( ( ord_less_eq @ int @ SV270 @ SV561 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3993]) ).
thf(4352,plain,
! [SV1026: $i,SV947: $i,SV811: $i,SV271: $i] :
( ( ( ( plus_plus @ SV271 @ ( number_number_of @ SV271 @ SV811 ) @ ( minus_minus @ SV271 @ ( number_number_of @ SV271 @ SV947 ) @ SV1026 ) )
= ( minus_minus @ SV271 @ ( number_number_of @ SV271 @ ( plus_plus @ int @ SV811 @ SV947 ) ) @ SV1026 ) )
= $true )
| ( ( number_ring @ SV271 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3994]) ).
thf(4353,plain,
! [SV562: $i,SV273: $i,SV691: $i] :
( ( ( SV691
= ( zero_zero @ real ) )
= $true )
| ( ( ~ ( ~ ( ( ( times_times @ real @ SV691 @ SV273 )
!= ( times_times @ real @ SV691 @ SV562 ) )
| ( SV273 = SV562 ) )
| ~ ( ( SV273 != SV562 )
| ( ( times_times @ real @ SV691 @ SV273 )
= ( times_times @ real @ SV691 @ SV562 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3995]) ).
thf(4354,plain,
! [SV274: $i] :
( ( ( ord_less @ int @ min @ ( bit1 @ SV274 ) )
= $false )
| ( ( ord_less @ int @ min @ SV274 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3996]) ).
thf(4355,plain,
! [SV274: $i] :
( ( ( ord_less @ int @ min @ SV274 )
= $false )
| ( ( ord_less @ int @ min @ ( bit1 @ SV274 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3997]) ).
thf(4356,plain,
! [SV815: $i,SV1027: $i,SV949: $i,SV277: $i] :
( ( ( ~ ( dvd_dvd @ SV277 @ SV949 @ SV1027 )
| ~ ( dvd_dvd @ SV277 @ SV949 @ SV815 )
| ( dvd_dvd @ SV277 @ SV949 @ ( plus_plus @ SV277 @ SV1027 @ SV815 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV277 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3999]) ).
thf(4357,plain,
! [SV279: $i] :
( ( ( ord_less @ int @ ( bit0 @ SV279 ) @ pls )
= $false )
| ( ( ord_less @ int @ SV279 @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4000]) ).
thf(4358,plain,
! [SV279: $i] :
( ( ( ord_less @ int @ SV279 @ pls )
= $false )
| ( ( ord_less @ int @ ( bit0 @ SV279 ) @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4001]) ).
thf(4359,plain,
! [SV564: $i,SV281: $i] :
( ( ( ( bit0 @ SV281 )
!= ( bit0 @ SV564 ) )
= $true )
| ( ( ( ti @ int @ SV281 )
= ( ti @ int @ SV564 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4003]) ).
thf(4360,plain,
! [SV564: $i,SV281: $i] :
( ( ( ( ti @ int @ SV281 )
!= ( ti @ int @ SV564 ) )
= $true )
| ( ( ( bit0 @ SV281 )
= ( bit0 @ SV564 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4004]) ).
thf(4361,plain,
! [SV282: $i] :
( ( ( ord_less_eq @ int @ ( bit1 @ SV282 ) @ min )
= $false )
| ( ( ord_less_eq @ int @ SV282 @ min )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4005]) ).
thf(4362,plain,
! [SV282: $i] :
( ( ( ord_less_eq @ int @ SV282 @ min )
= $false )
| ( ( ord_less_eq @ int @ ( bit1 @ SV282 ) @ min )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4006]) ).
thf(4363,plain,
! [SV818: $i,SV1028: $i,SV950: $i,SV284: $i] :
( ( ( ~ ( dvd_dvd @ SV284 @ SV950 @ SV1028 )
| ( dvd_dvd @ SV284 @ ( power_power @ SV284 @ SV950 @ SV818 ) @ ( power_power @ SV284 @ SV1028 @ SV818 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV284 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4007]) ).
thf(4364,plain,
! [SV285: $i,SV819: $i,SV951: $i] :
( ( ( ~ ( ord_less_eq @ int @ pls @ SV951 ) )
= $true )
| ( ( ~ ( ord_less_eq @ int @ pls @ SV819 )
| ( ( plus_plus @ SV285 @ ( number_number_of @ SV285 @ SV951 ) @ ( number_number_of @ SV285 @ SV819 ) )
= ( number_number_of @ SV285 @ ( plus_plus @ int @ SV951 @ SV819 ) ) ) )
= $true )
| ( ( number_semiring @ SV285 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4008]) ).
thf(4365,plain,
! [SV566: $i,SV288: $i,SV694: $i,SV821: $i] :
( ( ( zprime @ SV821 )
= $false )
| ( ( ~ ~ ( dvd_dvd @ int @ SV821 @ SV694 )
| ~ ( dvd_dvd @ int @ ( power_power @ int @ SV821 @ SV288 ) @ ( times_times @ int @ SV566 @ SV694 ) )
| ( dvd_dvd @ int @ ( power_power @ int @ SV821 @ SV288 ) @ SV566 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4011]) ).
thf(4366,plain,
! [SV290: $i] :
( ( ( ord_less @ int @ ( bit0 @ SV290 ) @ ( zero_zero @ int ) )
= $false )
| ( ( ord_less @ int @ SV290 @ ( zero_zero @ int ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4013]) ).
thf(4367,plain,
! [SV290: $i] :
( ( ( ord_less @ int @ SV290 @ ( zero_zero @ int ) )
= $false )
| ( ( ord_less @ int @ ( bit0 @ SV290 ) @ ( zero_zero @ int ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4014]) ).
thf(4368,plain,
! [SV568: $i,SV292: $i] :
( ( ( ~ ( zcong @ ( times_times @ int @ SV292 @ ( minus_minus @ int @ SV568 @ ( one_one @ int ) ) ) @ ( one_one @ int ) @ SV568 ) )
= $true )
| ( ( zcong @ SV292 @ ( minus_minus @ int @ SV568 @ ( one_one @ int ) ) @ SV568 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4015]) ).
thf(4369,plain,
! [SV568: $i,SV292: $i] :
( ( ( ~ ( zcong @ SV292 @ ( minus_minus @ int @ SV568 @ ( one_one @ int ) ) @ SV568 ) )
= $true )
| ( ( zcong @ ( times_times @ int @ SV292 @ ( minus_minus @ int @ SV568 @ ( one_one @ int ) ) ) @ ( one_one @ int ) @ SV568 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4016]) ).
thf(4370,plain,
! [SV569: $i,SV294: $i,SV696: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV696 @ SV294 ) )
= $true )
| ( ( ord_less_eq @ int @ SV569 @ SV294 )
= $true )
| ( ( ord_less_eq @ int @ SV569 @ SV696 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4017]) ).
thf(4371,plain,
! [SV1029: $i,SV953: $i,SV824: $i,SV296: $i] :
( ( ( ( plus_plus @ SV296 @ ( plus_plus @ SV296 @ SV824 @ SV953 ) @ SV1029 )
= ( plus_plus @ SV296 @ ( plus_plus @ SV296 @ SV824 @ SV1029 ) @ SV953 ) )
= $true )
| ( ( comm_semiring_1 @ SV296 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4018]) ).
thf(4372,plain,
! [SV697: $i,SV570: $i,SV297: $i] :
( ( ( ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV297 ) )
= $true )
| ( ( ord_less @ int @ ( times_times @ int @ SV297 @ SV570 ) @ ( times_times @ int @ SV297 @ SV697 ) )
= $true )
| ( ( ord_less @ int @ SV570 @ SV697 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4019]) ).
thf(4373,plain,
! [SV1030: $i,SV954: $i,SV825: $i,SV298: $i] :
( ( ( ( power_power @ SV298 @ ( times_times @ SV298 @ SV825 @ SV954 ) @ SV1030 )
= ( times_times @ SV298 @ ( power_power @ SV298 @ SV825 @ SV1030 ) @ ( power_power @ SV298 @ SV954 @ SV1030 ) ) )
= $true )
| ( ( comm_monoid_mult @ SV298 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4020]) ).
thf(4374,plain,
! [SV299: $i,SV571: $i] :
( ( ( SV571
= ( zero_zero @ nat ) )
= $true )
| ( ( SV571 = SV299 )
= $true )
| ( ( ord_less_eq @ nat @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV299 ) @ SV571 )
= $true )
| ( ( dvd_dvd @ nat @ SV299 @ SV571 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4021]) ).
thf(4375,plain,
! [SV572: $i,SV300: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( bit1 @ SV300 ) @ ( bit1 @ SV572 ) ) )
= $true )
| ( ( ord_less_eq @ int @ SV300 @ SV572 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4022]) ).
thf(4376,plain,
! [SV572: $i,SV300: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV300 @ SV572 ) )
= $true )
| ( ( ord_less_eq @ int @ ( bit1 @ SV300 ) @ ( bit1 @ SV572 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4023]) ).
thf(4377,plain,
! [SV955: $i,SV826: $i,SV301: $i] :
( ( ( ~ ( ( ( times_times @ SV301 @ SV826 @ SV955 )
!= ( zero_zero @ SV301 ) )
| ( ( ti @ SV301 @ SV826 )
= ( zero_zero @ SV301 ) )
| ( ( ti @ SV301 @ SV955 )
= ( zero_zero @ SV301 ) ) )
| ~ ( ~ ( ( ( ti @ SV301 @ SV826 )
= ( zero_zero @ SV301 ) )
| ( ( ti @ SV301 @ SV955 )
= ( zero_zero @ SV301 ) ) )
| ( ( times_times @ SV301 @ SV826 @ SV955 )
= ( zero_zero @ SV301 ) ) ) )
= $false )
| ( ( ring_n68954251visors @ SV301 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4024]) ).
thf(4378,plain,
! [SV303: $i] :
( ( ( pls
= ( bit0 @ SV303 ) )
= $false )
| ( ( pls
= ( ti @ int @ SV303 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4025]) ).
thf(4379,plain,
! [SV303: $i] :
( ( ( pls
= ( ti @ int @ SV303 ) )
= $false )
| ( ( pls
= ( bit0 @ SV303 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4026]) ).
thf(4380,plain,
! [SV956: $i,SV828: $i,SV1031: $i,SV304: $i] :
( ( ( ~ ( ord_less @ SV304 @ ( one_one @ SV304 ) @ SV1031 )
| ~ ( ord_less_eq @ SV304 @ ( power_power @ SV304 @ SV1031 @ SV828 ) @ ( power_power @ SV304 @ SV1031 @ SV956 ) )
| ( ord_less_eq @ nat @ SV828 @ SV956 ) )
= $true )
| ( ( linordered_semidom @ SV304 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4027]) ).
thf(4381,plain,
! [SV1032: $i,SV957: $i,SV829: $i,SV698: $i,SV573: $i,SV305: $i] :
( ( ( ( plus_plus @ int @ ( times_times @ int @ SV305 @ SV573 ) @ SV698 )
!= ( plus_plus @ int @ ( times_times @ int @ SV829 @ SV957 ) @ SV1032 ) )
| ~ ( ord_less @ int @ ( plus_plus @ int @ ( times_times @ int @ SV829 @ SV957 ) @ SV1032 ) @ ( zero_zero @ int ) )
| ~ ( ord_less @ int @ SV698 @ SV305 )
| ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV1032 )
| ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV829 )
| ~ ( ord_less_eq @ int @ SV829 @ SV305 )
| ( ord_less_eq @ int @ SV957 @ SV573 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4028]) ).
thf(4382,plain,
! [SV308: $i,SV831: $i,SV700: $i,SV575: $i] :
( ( ( zcong @ SV575 @ SV700 @ SV831 )
= $false )
| ( ( zcong @ ( power_power @ int @ SV575 @ SV308 ) @ ( power_power @ int @ SV700 @ SV308 ) @ SV831 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4031]) ).
thf(4383,plain,
! [SV309: $i] :
( ( ( ord_less_eq @ int @ ( bit1 @ SV309 ) @ pls )
= $false )
| ( ( ord_less @ int @ SV309 @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4032]) ).
thf(4384,plain,
! [SV309: $i] :
( ( ( ord_less @ int @ SV309 @ pls )
= $false )
| ( ( ord_less_eq @ int @ ( bit1 @ SV309 ) @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4033]) ).
thf(4385,plain,
! [SV1033: $i,SV959: $i,SV832: $i,SV311: $i] :
( ( ( ( power_power @ SV311 @ ( power_power @ SV311 @ SV832 @ SV959 ) @ SV1033 )
= ( power_power @ SV311 @ SV832 @ ( times_times @ nat @ SV959 @ SV1033 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV311 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4034]) ).
thf(4386,plain,
! [SV960: $i,SV833: $i,SV701: $i,SV576: $i,SV312: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( plus_plus @ int @ ( times_times @ int @ SV312 @ SV576 ) @ SV701 ) @ ( plus_plus @ int @ ( times_times @ int @ SV312 @ SV833 ) @ SV960 ) ) )
= $true )
| ( ( ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV701 )
| ~ ( ord_less @ int @ SV701 @ SV312 )
| ~ ( ord_less @ int @ SV960 @ SV312 )
| ( ord_less_eq @ int @ SV576 @ SV833 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4035]) ).
thf(4387,plain,
! [SV961: $i,SV834: $i,SV313: $i] :
( ( ( ~ ( ( ( ti @ SV313 @ SV834 )
!= ( plus_plus @ SV313 @ SV834 @ SV961 ) )
| ( ( ti @ SV313 @ SV961 )
= ( zero_zero @ SV313 ) ) )
| ~ ( ( ( ti @ SV313 @ SV961 )
!= ( zero_zero @ SV313 ) )
| ( ( ti @ SV313 @ SV834 )
= ( plus_plus @ SV313 @ SV834 @ SV961 ) ) ) )
= $false )
| ( ( semiri456707255roduct @ SV313 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4036]) ).
thf(4388,plain,
! [SV577: $i,SV314: $i] :
( ( ( ~ ( quadRes @ SV314 @ SV577 ) )
= $true )
| ( ( ~ ! [SY1865: $i] :
~ ( zcong @ ( power_power @ int @ SY1865 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SV577 @ SV314 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4037]) ).
thf(4389,plain,
! [SV314: $i,SV577: $i] :
( ( ( ~ ~ ! [SY1866: $i] :
~ ( zcong @ ( power_power @ int @ SY1866 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SV577 @ SV314 ) )
= $true )
| ( ( quadRes @ SV314 @ SV577 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4038]) ).
thf(4390,plain,
! [SV835: $i,SV315: $i,SV1034: $i,SV962: $i] :
( ( ( ~ ( ord_less_eq @ nat @ SV962 @ SV1034 )
| ~ ( ord_less_eq @ SV315 @ ( one_one @ SV315 ) @ SV835 )
| ( ord_less_eq @ SV315 @ ( power_power @ SV315 @ SV835 @ SV962 ) @ ( power_power @ SV315 @ SV835 @ SV1034 ) ) )
= $true )
| ( ( linordered_semidom @ SV315 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4039]) ).
thf(4391,plain,
! [SV1035: $i,SV963: $i,SV836: $i,SV316: $i] :
( ( ( ( times_times @ SV316 @ ( plus_plus @ SV316 @ SV836 @ SV963 ) @ SV1035 )
= ( plus_plus @ SV316 @ ( times_times @ SV316 @ SV836 @ SV1035 ) @ ( times_times @ SV316 @ SV963 @ SV1035 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV316 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4040]) ).
thf(4392,plain,
! [SV837: $i,SV964: $i,SV317: $i] :
( ( ( ~ ( ord_less_eq @ SV317 @ ( one_one @ SV317 ) @ SV964 ) )
= $true )
| ( ( ord_less_eq @ SV317 @ ( one_one @ SV317 ) @ ( power_power @ SV317 @ SV964 @ SV837 ) )
= $true )
| ( ( linordered_semidom @ SV317 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4041]) ).
thf(4393,plain,
! [SV966: $i,SV839: $i,SV319: $i] :
( ( ( ~ ( ~ ( ord_less_eq @ SV319 @ ( times_times @ SV319 @ SV839 @ SV966 ) @ ( zero_zero @ SV319 ) )
| ~ ( ~ ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SV839 )
| ~ ( ord_less_eq @ SV319 @ SV966 @ ( zero_zero @ SV319 ) ) )
| ~ ( ~ ( ord_less_eq @ SV319 @ SV839 @ ( zero_zero @ SV319 ) )
| ~ ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SV966 ) ) )
| ~ ( ~ ( ~ ( ~ ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SV839 )
| ~ ( ord_less_eq @ SV319 @ SV966 @ ( zero_zero @ SV319 ) ) )
| ~ ( ~ ( ord_less_eq @ SV319 @ SV839 @ ( zero_zero @ SV319 ) )
| ~ ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SV966 ) ) )
| ( ord_less_eq @ SV319 @ ( times_times @ SV319 @ SV839 @ SV966 ) @ ( zero_zero @ SV319 ) ) ) )
= $false )
| ( ( linord581940658strict @ SV319 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4043]) ).
thf(4394,plain,
! [SV320: $i] :
( ( ( ( zero_zero @ nat )
= ( number_number_of @ nat @ SV320 ) )
= $false )
| ( ( ord_less_eq @ int @ SV320 @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4044]) ).
thf(4395,plain,
! [SV320: $i] :
( ( ( ord_less_eq @ int @ SV320 @ pls )
= $false )
| ( ( ( zero_zero @ nat )
= ( number_number_of @ nat @ SV320 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4045]) ).
thf(4396,plain,
! [SV321: $i] :
( ( ( number_ring @ SV321 )
= $false )
| ( ( ~ ( linordered_idom @ SV321 ) )
= $true )
| ( ( ! [SY1569: $i,SY1570: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV321 @ ( number_number_of @ SV321 @ SY1569 ) @ ( number_number_of @ SV321 @ SY1570 ) )
| ( ord_less_eq @ int @ SY1569 @ SY1570 ) )
| ~ ( ~ ( ord_less_eq @ int @ SY1569 @ SY1570 )
| ( ord_less_eq @ SV321 @ ( number_number_of @ SV321 @ SY1569 ) @ ( number_number_of @ SV321 @ SY1570 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4046]) ).
thf(4397,plain,
! [SV967: $i,SV841: $i,SV1036: $i,SV323: $i] :
( ( ( ! [SY2207: $i] :
( ~ ( dvd_dvd @ SV323 @ SV1036 @ SY2207 )
| ~ ( ord_less_eq @ nat @ SV841 @ SV967 )
| ( dvd_dvd @ SV323 @ ( power_power @ SV323 @ SV1036 @ SV841 ) @ ( power_power @ SV323 @ SY2207 @ SV967 ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV323 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4047]) ).
thf(4398,plain,
! [SV968: $i,SV842: $i,SV325: $i] :
( ( ( ~ ( ord_less_eq @ SV325 @ ( power_power @ SV325 @ SV842 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV325 @ SV968 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true )
| ( ( ~ ( ord_less_eq @ SV325 @ ( zero_zero @ SV325 ) @ SV968 )
| ( ord_less_eq @ SV325 @ SV842 @ SV968 ) )
= $true )
| ( ( linordered_semidom @ SV325 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4048]) ).
thf(4399,plain,
! [SV328: $i] :
( ( ( ord_less @ int @ min @ ( bit0 @ SV328 ) )
= $false )
| ( ( ord_less @ int @ min @ SV328 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4050]) ).
thf(4400,plain,
! [SV328: $i] :
( ( ( ord_less @ int @ min @ SV328 )
= $false )
| ( ( ord_less @ int @ min @ ( bit0 @ SV328 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4051]) ).
thf(4401,plain,
! [SV1037: $i,SV969: $i,SV843: $i,SV329: $i] :
( ( ( ( power_power @ SV329 @ SV843 @ ( plus_plus @ nat @ SV969 @ SV1037 ) )
= ( times_times @ SV329 @ ( power_power @ SV329 @ SV843 @ SV969 ) @ ( power_power @ SV329 @ SV843 @ SV1037 ) ) )
= $true )
| ( ( monoid_mult @ SV329 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4052]) ).
thf(4402,plain,
! [SV1038: $i,SV970: $i,SV844: $i,SV330: $i] :
( ( ( ~ ( dvd_dvd @ SV330 @ ( times_times @ SV330 @ SV844 @ SV970 ) @ SV1038 )
| ( dvd_dvd @ SV330 @ SV970 @ SV1038 ) )
= $true )
| ( ( comm_semiring_1 @ SV330 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4053]) ).
thf(4403,plain,
! [SV333: $i] :
( ( ( power @ SV333 )
= $false )
| ( ( ~ ( semiring_0 @ SV333 ) )
= $true )
| ( ( ! [SY1587: $i] :
~ ( ~ ( ( ( number_number_of @ nat @ SY1587 )
!= ( zero_zero @ nat ) )
| ( ( power_power @ SV333 @ ( zero_zero @ SV333 ) @ ( number_number_of @ nat @ SY1587 ) )
= ( one_one @ SV333 ) ) )
| ~ ( ~ ( ( ( number_number_of @ nat @ SY1587 )
!= ( zero_zero @ nat ) ) )
| ( ( power_power @ SV333 @ ( zero_zero @ SV333 ) @ ( number_number_of @ nat @ SY1587 ) )
= ( zero_zero @ SV333 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4055]) ).
thf(4404,plain,
! [SV581: $i,SV336: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( bit0 @ SV336 ) @ ( bit0 @ SV581 ) ) )
= $true )
| ( ( ord_less_eq @ int @ SV336 @ SV581 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4058]) ).
thf(4405,plain,
! [SV581: $i,SV336: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV336 @ SV581 ) )
= $true )
| ( ( ord_less_eq @ int @ ( bit0 @ SV336 ) @ ( bit0 @ SV581 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4059]) ).
thf(4406,plain,
! [SV582: $i,SV337: $i,SV972: $i,SV846: $i,SV704: $i] :
( ( ( ~ ( zcong @ SV704 @ SV846 @ SV972 ) )
= $true )
| ( ( ~ ( zcong @ SV337 @ SV582 @ SV972 )
| ( zcong @ ( times_times @ int @ SV704 @ SV337 ) @ ( times_times @ int @ SV846 @ SV582 ) @ SV972 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4060]) ).
thf(4407,plain,
! [SV583: $i,SV705: $i,SV338: $i] :
( ( ( ~ ( ~ ( ord_less @ real @ ( times_times @ real @ SV338 @ SV705 ) @ ( times_times @ real @ SV583 @ SV705 ) )
| ( ord_less @ real @ SV338 @ SV583 ) )
| ~ ( ~ ( ord_less @ real @ SV338 @ SV583 )
| ( ord_less @ real @ ( times_times @ real @ SV338 @ SV705 ) @ ( times_times @ real @ SV583 @ SV705 ) ) ) )
= $false )
| ( ( ord_less @ real @ ( zero_zero @ real ) @ SV705 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4061]) ).
thf(4408,plain,
! [SV1039: $i,SV706: $i] :
( ( ( plus_plus @ int @ ( power_power @ int @ SV706 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ SV1039 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4062]) ).
thf(4409,plain,
! [SV1040: $i,SV973: $i,SV848: $i,SV340: $i] :
( ( ( ! [SY2208: $i] :
( ( times_times @ SV340 @ ( times_times @ SV340 @ SV848 @ SV973 ) @ ( times_times @ SV340 @ SV1040 @ SY2208 ) )
= ( times_times @ SV340 @ ( times_times @ SV340 @ SV848 @ SV1040 ) @ ( times_times @ SV340 @ SV973 @ SY2208 ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV340 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4063]) ).
thf(4410,plain,
! [SV584: $i,SV341: $i] :
( ( ( ~ ( ord_less @ int @ ( bit0 @ SV341 ) @ ( bit0 @ SV584 ) ) )
= $true )
| ( ( ord_less @ int @ SV341 @ SV584 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4064]) ).
thf(4411,plain,
! [SV584: $i,SV341: $i] :
( ( ( ~ ( ord_less @ int @ SV341 @ SV584 ) )
= $true )
| ( ( ord_less @ int @ ( bit0 @ SV341 ) @ ( bit0 @ SV584 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4065]) ).
thf(4412,plain,
! [SV585: $i,SV343: $i] :
( ( ( ~ ( quadRes @ SV343 @ ( ti @ int @ SV585 ) ) )
= $true )
| ( ( quadRes @ SV343 @ SV585 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4066]) ).
thf(4413,plain,
! [SV585: $i,SV343: $i] :
( ( ( ~ ( quadRes @ SV343 @ SV585 ) )
= $true )
| ( ( quadRes @ SV343 @ ( ti @ int @ SV585 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4067]) ).
thf(4414,plain,
! [SV586: $i,SV345: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV345 @ ( minus_minus @ int @ SV586 @ ( one_one @ int ) ) ) )
= $true )
| ( ( ord_less @ int @ SV345 @ SV586 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4068]) ).
thf(4415,plain,
! [SV586: $i,SV345: $i] :
( ( ( ~ ( ord_less @ int @ SV345 @ SV586 ) )
= $true )
| ( ( ord_less_eq @ int @ SV345 @ ( minus_minus @ int @ SV586 @ ( one_one @ int ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4069]) ).
thf(4416,plain,
! [SV851: $i,SV347: $i] :
( ( ( ~ ( ( ( power_power @ SV347 @ SV851 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= ( zero_zero @ SV347 ) )
| ( ( ti @ SV347 @ SV851 )
= ( zero_zero @ SV347 ) ) ) )
= $false )
| ( ( ring_11004092258visors @ SV347 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4070]) ).
thf(4417,plain,
! [SV851: $i,SV347: $i] :
( ( ( ~ ( ( ( ti @ SV347 @ SV851 )
!= ( zero_zero @ SV347 ) )
| ( ( power_power @ SV347 @ SV851 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SV347 ) ) ) )
= $false )
| ( ( ring_11004092258visors @ SV347 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4070]) ).
thf(4418,plain,
! [SV852: $i,SV974: $i,SV348: $i] :
( ( ( ~ ( ord_less @ SV348 @ ( zero_zero @ SV348 ) @ SV974 ) )
= $true )
| ( ( ord_less @ SV348 @ ( zero_zero @ SV348 ) @ ( power_power @ SV348 @ SV974 @ SV852 ) )
= $true )
| ( ( linordered_semidom @ SV348 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4071]) ).
thf(4419,plain,
! [SV853: $i,SV1041: $i,SV975: $i,SV349: $i] :
( ( ( ~ ( dvd_dvd @ SV349 @ SV975 @ SV1041 )
| ( dvd_dvd @ SV349 @ SV975 @ ( times_times @ SV349 @ SV1041 @ SV853 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV349 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4072]) ).
thf(4420,plain,
! [SV587: $i,SV350: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( plus_plus @ int @ SV350 @ ( one_one @ int ) ) @ SV587 ) )
= $true )
| ( ( ord_less @ int @ SV350 @ SV587 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4073]) ).
thf(4421,plain,
! [SV587: $i,SV350: $i] :
( ( ( ~ ( ord_less @ int @ SV350 @ SV587 ) )
= $true )
| ( ( ord_less_eq @ int @ ( plus_plus @ int @ SV350 @ ( one_one @ int ) ) @ SV587 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4074]) ).
thf(4422,plain,
! [SV976: $i,SV854: $i,SV351: $i] :
( ( ( ( times_times @ SV351 @ SV854 @ SV976 )
!= ( zero_zero @ SV351 ) )
= $true )
| ( ( ( ( ti @ SV351 @ SV854 )
= ( zero_zero @ SV351 ) )
| ( ( ti @ SV351 @ SV976 )
= ( zero_zero @ SV351 ) ) )
= $true )
| ( ( no_zero_divisors @ SV351 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4075]) ).
thf(4423,plain,
! [SV977: $i,SV855: $i,SV352: $i] :
( ( ( ~ ( ( ( plus_plus @ SV352 @ ( power_power @ SV352 @ SV855 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV352 @ SV977 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV352 ) )
| ~ ( ( ( ti @ SV352 @ SV855 )
!= ( zero_zero @ SV352 ) )
| ( ( ti @ SV352 @ SV977 )
!= ( zero_zero @ SV352 ) ) ) )
| ~ ( ~ ~ ( ( ( ti @ SV352 @ SV855 )
!= ( zero_zero @ SV352 ) )
| ( ( ti @ SV352 @ SV977 )
!= ( zero_zero @ SV352 ) ) )
| ( ( plus_plus @ SV352 @ ( power_power @ SV352 @ SV855 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV352 @ SV977 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV352 ) ) ) )
= $false )
| ( ( linordered_idom @ SV352 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4076]) ).
thf(4424,plain,
! [SV856: $i,SV1042: $i,SV978: $i,SV353: $i] :
( ( ( ~ ( ord_less_eq @ SV353 @ SV978 @ SV1042 )
| ~ ( ord_less_eq @ SV353 @ ( zero_zero @ SV353 ) @ SV978 )
| ( ord_less_eq @ SV353 @ ( power_power @ SV353 @ SV978 @ SV856 ) @ ( power_power @ SV353 @ SV1042 @ SV856 ) ) )
= $true )
| ( ( linordered_semidom @ SV353 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4077]) ).
thf(4425,plain,
! [SV1043: $i,SV979: $i,SV857: $i,SV354: $i] :
( ( ( ( times_times @ SV354 @ SV857 @ ( times_times @ SV354 @ SV979 @ SV1043 ) )
= ( times_times @ SV354 @ SV979 @ ( times_times @ SV354 @ SV857 @ SV1043 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV354 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4078]) ).
thf(4426,plain,
! [SV355: $i] :
( ( ( power @ SV355 )
= $false )
| ( ( ~ ( semiring_0 @ SV355 ) )
= $true )
| ( ( ! [SY1626: $i] :
~ ( ~ ( ( SY1626
!= ( zero_zero @ nat ) )
| ( ( power_power @ SV355 @ ( zero_zero @ SV355 ) @ SY1626 )
= ( one_one @ SV355 ) ) )
| ~ ( ~ ( ( SY1626
!= ( zero_zero @ nat ) ) )
| ( ( power_power @ SV355 @ ( zero_zero @ SV355 ) @ SY1626 )
= ( zero_zero @ SV355 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4079]) ).
thf(4427,plain,
! [SV980: $i,SV858: $i,SV1044: $i,SV358: $i] :
( ( ( ~ ( ord_less @ SV358 @ ( one_one @ SV358 ) @ SV1044 )
| ~ ( ~ ( ~ ( ord_less_eq @ SV358 @ ( power_power @ SV358 @ SV1044 @ SV858 ) @ ( power_power @ SV358 @ SV1044 @ SV980 ) )
| ( ord_less_eq @ nat @ SV858 @ SV980 ) )
| ~ ( ~ ( ord_less_eq @ nat @ SV858 @ SV980 )
| ( ord_less_eq @ SV358 @ ( power_power @ SV358 @ SV1044 @ SV858 ) @ ( power_power @ SV358 @ SV1044 @ SV980 ) ) ) ) )
= $true )
| ( ( linordered_semidom @ SV358 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4082]) ).
thf(4428,plain,
! [SV591: $i,SV360: $i] :
( ( ( ~ ( zcong @ SV360 @ ( zero_zero @ int ) @ SV591 ) )
= $true )
| ( ( dvd_dvd @ int @ SV591 @ SV360 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4084]) ).
thf(4429,plain,
! [SV360: $i,SV591: $i] :
( ( ( ~ ( dvd_dvd @ int @ SV591 @ SV360 ) )
= $true )
| ( ( zcong @ SV360 @ ( zero_zero @ int ) @ SV591 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4085]) ).
thf(4430,plain,
! [SV361: $i,SV859: $i,SV981: $i] :
( ( ( ~ ( ord_less_eq @ int @ pls @ SV981 ) )
= $true )
| ( ( ~ ( ord_less_eq @ int @ pls @ SV859 )
| ( ( times_times @ SV361 @ ( number_number_of @ SV361 @ SV981 ) @ ( number_number_of @ SV361 @ SV859 ) )
= ( number_number_of @ SV361 @ ( times_times @ int @ SV981 @ SV859 ) ) ) )
= $true )
| ( ( number_semiring @ SV361 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4086]) ).
thf(4431,plain,
! [SV592: $i,SV362: $i,SV710: $i] :
( ( ( SV710
= ( zero_zero @ real ) )
= $true )
| ( ( ~ ( ~ ( ( ( times_times @ real @ SV362 @ SV710 )
!= ( times_times @ real @ SV592 @ SV710 ) )
| ( SV362 = SV592 ) )
| ~ ( ( SV362 != SV592 )
| ( ( times_times @ real @ SV362 @ SV710 )
= ( times_times @ real @ SV592 @ SV710 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4087]) ).
thf(4432,plain,
! [SV860: $i,SV363: $i,SV982: $i] :
( ( ( ~ ( ( SV982
!= ( zero_zero @ nat ) )
| ( ( power_power @ SV363 @ SV860 @ SV982 )
= ( one_one @ SV363 ) ) )
| ~ ( ~ ( ( SV982
!= ( zero_zero @ nat ) ) )
| ( ( power_power @ SV363 @ SV860 @ SV982 )
= ( times_times @ SV363 @ SV860 @ ( power_power @ SV363 @ SV860 @ ( minus_minus @ nat @ SV982 @ ( one_one @ nat ) ) ) ) ) ) )
= $false )
| ( ( power @ SV363 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4088]) ).
thf(4433,plain,
! [SV366: $i,SV595: $i] :
( ( ( ~ ( ord_less @ int @ SV595 @ pls ) )
= $true )
| ( ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV595 ) @ ( number_number_of @ nat @ SV366 ) )
= ( number_number_of @ nat @ SV366 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4091]) ).
thf(4434,plain,
! [SV366: $i,SV595: $i] :
( ( ( ~ ~ ( ord_less @ int @ SV595 @ pls ) )
= $true )
| ( ( ~ ( ~ ( ~ ( ord_less @ int @ SV366 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV595 ) @ ( number_number_of @ nat @ SV366 ) )
= ( number_number_of @ nat @ SV595 ) ) )
| ~ ( ~ ~ ( ord_less @ int @ SV366 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV595 ) @ ( number_number_of @ nat @ SV366 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SV595 @ SV366 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4092]) ).
thf(4435,plain,
! [SV861: $i,SV367: $i,SV1045: $i,SV983: $i] :
( ( ( ~ ( ord_less_eq @ nat @ SV983 @ SV1045 )
| ( dvd_dvd @ SV367 @ ( power_power @ SV367 @ SV861 @ SV983 ) @ ( power_power @ SV367 @ SV861 @ SV1045 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV367 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4093]) ).
thf(4436,plain,
! [SV368: $i,SV596: $i] :
( ( ( SV596
!= ( zero_zero @ nat ) )
= $true )
| ( ( ( times_times @ nat @ SV596 @ SV368 )
= ( zero_zero @ nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4094]) ).
thf(4437,plain,
! [SV368: $i,SV596: $i] :
( ( ( ~ ( ( SV596
!= ( zero_zero @ nat ) ) ) )
= $true )
| ( ( ( times_times @ nat @ SV596 @ SV368 )
= ( plus_plus @ nat @ SV368 @ ( times_times @ nat @ ( minus_minus @ nat @ SV596 @ ( one_one @ nat ) ) @ SV368 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4095]) ).
thf(4438,plain,
! [SV597: $i,SV713: $i,SV369: $i] :
( ( ( ~ ( dvd_dvd @ int @ SV369 @ SV713 ) )
= $true )
| ( ( dvd_dvd @ int @ SV369 @ SV597 )
= $true )
| ( ( dvd_dvd @ int @ SV369 @ ( minus_minus @ int @ SV597 @ SV713 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4096]) ).
thf(4439,plain,
! [SV598: $i,SV370: $i] :
( ( ( ( bit1 @ SV370 )
!= ( bit1 @ SV598 ) )
= $true )
| ( ( ( ti @ int @ SV370 )
= ( ti @ int @ SV598 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4097]) ).
thf(4440,plain,
! [SV598: $i,SV370: $i] :
( ( ( ( ti @ int @ SV370 )
!= ( ti @ int @ SV598 ) )
= $true )
| ( ( ( bit1 @ SV370 )
= ( bit1 @ SV598 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4098]) ).
thf(4441,plain,
! [SV1046: $i,SV984: $i,SV862: $i,SV371: $i] :
( ( ( ( power_power @ SV371 @ ( times_times @ SV371 @ SV862 @ SV984 ) @ SV1046 )
= ( times_times @ SV371 @ ( power_power @ SV371 @ SV862 @ SV1046 ) @ ( power_power @ SV371 @ SV984 @ SV1046 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV371 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4099]) ).
thf(4442,plain,
! [SV372: $i,SV863: $i,SV714: $i,SV599: $i] :
( ( ( zcong @ SV599 @ SV714 @ SV863 )
= $false )
| ( ( zcong @ ( times_times @ int @ SV599 @ SV372 ) @ ( times_times @ int @ SV714 @ SV372 ) @ SV863 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4100]) ).
thf(4443,plain,
! [SV600: $i,SV373: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( bit0 @ SV373 ) @ ( bit0 @ SV600 ) ) )
= $true )
| ( ( ord_less_eq @ int @ SV373 @ SV600 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4101]) ).
thf(4444,plain,
! [SV600: $i,SV373: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV373 @ SV600 ) )
= $true )
| ( ( ord_less_eq @ int @ ( bit0 @ SV373 ) @ ( bit0 @ SV600 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4102]) ).
thf(4445,plain,
! [SV601: $i,SV374: $i] :
( ( ( ( times_times @ nat @ SV374 @ SV601 )
!= ( one_one @ nat ) )
= $true )
| ( ( ~ ( ( SV374
!= ( one_one @ nat ) )
| ( SV601
!= ( one_one @ nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4103]) ).
thf(4446,plain,
! [SV601: $i,SV374: $i] :
( ( ( ~ ~ ( ( SV374
!= ( one_one @ nat ) )
| ( SV601
!= ( one_one @ nat ) ) ) )
= $true )
| ( ( ( times_times @ nat @ SV374 @ SV601 )
= ( one_one @ nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4104]) ).
thf(4447,plain,
! [SV864: $i,SV985: $i,SV375: $i] :
( ( ( ~ ( ord_less @ SV375 @ ( one_one @ SV375 ) @ SV985 ) )
= $true )
| ( ( ord_less @ SV375 @ ( power_power @ SV375 @ SV985 @ SV864 ) @ ( times_times @ SV375 @ SV985 @ ( power_power @ SV375 @ SV985 @ SV864 ) ) )
= $true )
| ( ( linordered_semidom @ SV375 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4105]) ).
thf(4448,plain,
! [SV865: $i,SV986: $i,SV376: $i] :
( ( ( ~ ( ( ( ti @ SV376 @ SV986 )
!= ( zero_zero @ SV376 ) ) ) )
= $true )
| ( ( ( power_power @ SV376 @ SV986 @ SV865 )
!= ( zero_zero @ SV376 ) )
= $true )
| ( ( ring_11004092258visors @ SV376 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4106]) ).
thf(4449,plain,
! [SV603: $i,SV379: $i] :
( ( ( ord_less @ real @ ( zero_zero @ real ) @ SV379 )
= $false )
| ( ( ord_less @ real @ ( zero_zero @ real ) @ ( times_times @ real @ SV603 @ SV379 ) )
= $true )
| ( ( ord_less @ real @ ( zero_zero @ real ) @ SV603 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4108]) ).
thf(4450,plain,
! [SV1047: $i,SV987: $i,SV867: $i,SV380: $i] :
( ( ( ! [SY2209: $i] :
( ( times_times @ SV380 @ ( times_times @ SV380 @ SV867 @ SV987 ) @ ( times_times @ SV380 @ SV1047 @ SY2209 ) )
= ( times_times @ SV380 @ SV1047 @ ( times_times @ SV380 @ ( times_times @ SV380 @ SV867 @ SV987 ) @ SY2209 ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV380 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4109]) ).
thf(4451,plain,
! [SV604: $i,SV382: $i,SV716: $i] :
( ( ( ~ ( dvd_dvd @ int @ SV716 @ ( times_times @ int @ SV382 @ SV604 ) ) )
= $true )
| ( ( ( dvd_dvd @ int @ SV716 @ SV382 )
| ( dvd_dvd @ int @ SV716 @ SV604 ) )
= $true )
| ( ( zprime @ SV716 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4110]) ).
thf(4452,plain,
! [SV869: $i,SV383: $i,SV1048: $i,SV988: $i] :
( ( ( ~ ( ord_less @ nat @ SV988 @ SV1048 )
| ~ ( ord_less @ SV383 @ ( one_one @ SV383 ) @ SV869 )
| ( ord_less @ SV383 @ ( power_power @ SV383 @ SV869 @ SV988 ) @ ( power_power @ SV383 @ SV869 @ SV1048 ) ) )
= $true )
| ( ( linordered_semidom @ SV383 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4111]) ).
thf(4453,plain,
! [SV605: $i,SV717: $i,SV384: $i] :
( ( ( ~ ( ord_less @ int @ SV384 @ SV717 ) )
= $true )
| ( ( ( ord_less_eq @ int @ SV605 @ SV384 )
| ( ord_less_eq @ int @ SV384 @ SV605 ) )
= $true )
| ( ( ord_less @ int @ SV605 @ SV717 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4112]) ).
thf(4454,plain,
! [SV606: $i,SV385: $i,SV870: $i,SV718: $i] :
( ( ( ord_less @ int @ SV718 @ SV870 )
= $false )
| ( ( ~ ( ord_less_eq @ int @ SV385 @ SV606 )
| ( ord_less @ int @ ( plus_plus @ int @ SV718 @ SV385 ) @ ( plus_plus @ int @ SV870 @ SV606 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4113]) ).
thf(4455,plain,
! [SV386: $i] :
( ( ( number @ SV386 )
= $false )
| ( ( ~ ( ring @ SV386 ) )
= $true )
| ( ( ! [SY1686: $i,SY1687: $i,SY1688: $i] :
( ( times_times @ SV386 @ ( minus_minus @ SV386 @ SY1686 @ SY1687 ) @ ( number_number_of @ SV386 @ SY1688 ) )
= ( minus_minus @ SV386 @ ( times_times @ SV386 @ SY1686 @ ( number_number_of @ SV386 @ SY1688 ) ) @ ( times_times @ SV386 @ SY1687 @ ( number_number_of @ SV386 @ SY1688 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4114]) ).
thf(4456,plain,
! [SV387: $i,SV607: $i] :
( ( ( ord_less @ int @ ( zero_zero @ int ) @ ( times_times @ int @ SV607 @ SV387 ) )
= $false )
| ( ( ord_less @ int @ ( zero_zero @ int ) @ SV387 )
= $true )
| ( ( ord_less @ int @ ( zero_zero @ int ) @ SV607 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4115]) ).
thf(4457,plain,
! [SV608: $i,SV388: $i] :
( ( ( zcong @ SV388 @ ( number_number_of @ int @ min ) @ SV608 )
= $false )
| ( ( ~ ( zcong @ SV388 @ ( one_one @ int ) @ SV608 ) )
= $true )
| ( ( ord_less @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV608 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4116]) ).
thf(4458,plain,
! [SV389: $i,SV609: $i] :
( ( ( ord_less @ int @ SV609 @ SV389 )
= $false )
| ( ( ~ ( zcong @ SV609 @ ( zero_zero @ int ) @ SV389 ) )
= $true )
| ( ( ord_less @ int @ ( zero_zero @ int ) @ SV609 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4117]) ).
thf(4459,plain,
! [SV390: $i,SV610: $i] :
( ( ( SV610
!= ( zero_zero @ nat ) )
= $true )
| ( ( ( power_power @ nat @ SV390 @ SV610 )
= ( one_one @ nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4118]) ).
thf(4460,plain,
! [SV390: $i,SV610: $i] :
( ( ( ~ ( ( SV610
!= ( zero_zero @ nat ) ) ) )
= $true )
| ( ( ( power_power @ nat @ SV390 @ SV610 )
= ( times_times @ nat @ SV390 @ ( power_power @ nat @ SV390 @ ( minus_minus @ nat @ SV610 @ ( one_one @ nat ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4119]) ).
thf(4461,plain,
! [SV719: $i,SV611: $i,SV391: $i] :
( ( ( ~ ( dvd_dvd @ int @ SV391 @ SV611 ) )
= $true )
| ( ( dvd_dvd @ int @ SV391 @ ( power_power @ int @ SV611 @ SV719 ) )
= $true )
| ( ( ord_less @ nat @ ( zero_zero @ nat ) @ SV719 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4120]) ).
thf(4462,plain,
! [SV612: $i,SV392: $i] :
( ( ( ~ ( ord_less @ nat @ ( number_number_of @ nat @ SV392 ) @ ( number_number_of @ nat @ SV612 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( ord_less @ int @ SV392 @ SV612 )
| ( ord_less @ int @ pls @ SV612 ) )
| ~ ( ord_less @ int @ SV392 @ SV612 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4121]) ).
thf(4463,plain,
! [SV612: $i,SV392: $i] :
( ( ( ~ ~ ( ~ ( ~ ( ord_less @ int @ SV392 @ SV612 )
| ( ord_less @ int @ pls @ SV612 ) )
| ~ ( ord_less @ int @ SV392 @ SV612 ) ) )
= $true )
| ( ( ord_less @ nat @ ( number_number_of @ nat @ SV392 ) @ ( number_number_of @ nat @ SV612 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4122]) ).
thf(4464,plain,
! [SV394: $i] :
( ( ( zprime @ ( ti @ int @ SV394 ) )
= $false )
| ( ( zprime @ SV394 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4124]) ).
thf(4465,plain,
! [SV394: $i] :
( ( ( zprime @ SV394 )
= $false )
| ( ( zprime @ ( ti @ int @ SV394 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4125]) ).
thf(4466,plain,
! [SV395: $i,SV872: $i,SV720: $i,SV613: $i] :
( ( ( zcong @ ( power_power @ int @ SV613 @ SV720 ) @ ( one_one @ int ) @ SV872 )
= $false )
| ( ( zcong @ ( power_power @ int @ SV613 @ ( times_times @ nat @ SV720 @ SV395 ) ) @ ( one_one @ int ) @ SV872 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4126]) ).
thf(4467,plain,
! [SV614: $i,SV396: $i] :
( ( ( ~ ( zcong @ SV396 @ SV614 @ ( zero_zero @ int ) ) )
= $true )
| ( ( ( ti @ int @ SV396 )
= ( ti @ int @ SV614 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4127]) ).
thf(4468,plain,
! [SV614: $i,SV396: $i] :
( ( ( ( ti @ int @ SV396 )
!= ( ti @ int @ SV614 ) )
= $true )
| ( ( zcong @ SV396 @ SV614 @ ( zero_zero @ int ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4128]) ).
thf(4469,plain,
! [SV615: $i,SV397: $i] :
( ( ( ( plus_plus @ real @ ( times_times @ real @ SV397 @ SV397 ) @ ( times_times @ real @ SV615 @ SV615 ) )
!= ( zero_zero @ real ) )
= $true )
| ( ( ~ ( ( SV397
!= ( zero_zero @ real ) )
| ( SV615
!= ( zero_zero @ real ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4129]) ).
thf(4470,plain,
! [SV615: $i,SV397: $i] :
( ( ( ~ ~ ( ( SV397
!= ( zero_zero @ real ) )
| ( SV615
!= ( zero_zero @ real ) ) ) )
= $true )
| ( ( ( plus_plus @ real @ ( times_times @ real @ SV397 @ SV397 ) @ ( times_times @ real @ SV615 @ SV615 ) )
= ( zero_zero @ real ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4130]) ).
thf(4471,plain,
! [SV398: $i] :
( ( ( ord_less @ int @ ( bit1 @ SV398 ) @ pls )
= $false )
| ( ( ord_less @ int @ SV398 @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4131]) ).
thf(4472,plain,
! [SV398: $i] :
( ( ( ord_less @ int @ SV398 @ pls )
= $false )
| ( ( ord_less @ int @ ( bit1 @ SV398 ) @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4132]) ).
thf(4473,plain,
! [SV1049: $i,SV990: $i,SV873: $i,SV399: $i] :
( ( ( ! [SY2210: $i] :
( ( plus_plus @ SV399 @ ( times_times @ SV399 @ SV873 @ SV990 ) @ ( plus_plus @ SV399 @ ( times_times @ SV399 @ SV1049 @ SV990 ) @ SY2210 ) )
= ( plus_plus @ SV399 @ ( times_times @ SV399 @ ( plus_plus @ SV399 @ SV873 @ SV1049 ) @ SV990 ) @ SY2210 ) ) )
= $true )
| ( ( semiring @ SV399 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4133]) ).
thf(4474,plain,
( ( ( ! [SY2112: $i] :
( ( plus_plus @ int @ ( power_power @ int @ sK4_SX0 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ SY2112 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ) )
= $false )
| ( ( t
= ( one_one @ int ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4134]) ).
thf(4475,plain,
! [SV1050: $i,SV991: $i,SV876: $i,SV403: $i] :
( ( ( ( times_times @ SV403 @ SV876 @ ( plus_plus @ SV403 @ SV991 @ SV1050 ) )
= ( plus_plus @ SV403 @ ( times_times @ SV403 @ SV876 @ SV991 ) @ ( times_times @ SV403 @ SV876 @ SV1050 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV403 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4136]) ).
thf(4476,plain,
! [SV722: $i,SV617: $i,SV405: $i] :
( ( ~ ( zcong @ SV405 @ SV617 @ SV722 )
| ~ ! [SY1940: $i] :
( ( ti @ int @ SV617 )
!= ( plus_plus @ int @ SV405 @ ( times_times @ int @ SV722 @ SY1940 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4137]) ).
thf(4477,plain,
! [SV722: $i,SV405: $i,SV617: $i] :
( ( ~ ~ ! [SY1941: $i] :
( ( ti @ int @ SV617 )
!= ( plus_plus @ int @ SV405 @ ( times_times @ int @ SV722 @ SY1941 ) ) )
| ( zcong @ SV405 @ SV617 @ SV722 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4138]) ).
thf(4478,plain,
! [SV407: $i] :
( ( ( ( ti @ int @ SV407 )
= ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true )
| ( ( ~ ( ( ( ti @ int @ SV407 )
!= ( number_number_of @ int @ ( bit1 @ ( bit1 @ pls ) ) ) ) )
| ( ord_less_eq @ int @ ( number_number_of @ int @ ( bit1 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SV407 ) )
= $true )
| ( ( zprime @ SV407 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4140]) ).
thf(4479,plain,
! [SV620: $i,SV410: $i,SV725: $i] :
( ( ( ~ ( ord_less @ int @ SV725 @ SV410 ) )
= $true )
| ( ( ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV410 )
| ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV620 ) )
= $true )
| ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( times_times @ int @ SV410 @ SV620 ) @ SV725 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4142]) ).
thf(4480,plain,
! [SV1051: $i,SV992: $i,SV879: $i,SV412: $i] :
( ( ( ( power_power @ SV412 @ SV879 @ ( times_times @ nat @ SV992 @ SV1051 ) )
= ( power_power @ SV412 @ ( power_power @ SV412 @ SV879 @ SV992 ) @ SV1051 ) )
= $true )
| ( ( monoid_mult @ SV412 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4144]) ).
thf(4481,plain,
! [SV621: $i,SV413: $i] :
( ( ( ( times_times @ int @ SV413 @ SV621 )
!= ( one_one @ int ) )
= $true )
| ( ( ~ ( ( ( ti @ int @ SV413 )
!= ( one_one @ int ) )
| ( ( ti @ int @ SV621 )
!= ( one_one @ int ) ) )
| ~ ( ( ( ti @ int @ SV413 )
!= ( number_number_of @ int @ min ) )
| ( ( ti @ int @ SV621 )
!= ( number_number_of @ int @ min ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4145]) ).
thf(4482,plain,
! [SV621: $i,SV413: $i] :
( ( ( ~ ( ~ ( ( ( ti @ int @ SV413 )
!= ( one_one @ int ) )
| ( ( ti @ int @ SV621 )
!= ( one_one @ int ) ) )
| ~ ( ( ( ti @ int @ SV413 )
!= ( number_number_of @ int @ min ) )
| ( ( ti @ int @ SV621 )
!= ( number_number_of @ int @ min ) ) ) ) )
= $true )
| ( ( ( times_times @ int @ SV413 @ SV621 )
= ( one_one @ int ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4146]) ).
thf(4483,plain,
! [SV416: $i] :
( ( ( monoid_mult @ SV416 )
= $false )
| ( ( ~ ( number @ SV416 ) )
= $true )
| ( ( ! [SY1732: $i] :
( ( power_power @ SV416 @ ( number_number_of @ SV416 @ SY1732 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times @ SV416 @ ( number_number_of @ SV416 @ SY1732 ) @ ( number_number_of @ SV416 @ SY1732 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4148]) ).
thf(4484,plain,
! [SV881: $i,SV994: $i,SV417: $i] :
( ( ( ~ ( ord_less_eq @ SV417 @ SV994 @ ( zero_zero @ SV417 ) ) )
= $true )
| ( ( ~ ( ord_less_eq @ SV417 @ ( zero_zero @ SV417 ) @ SV881 )
| ( ord_less_eq @ SV417 @ ( times_times @ SV417 @ SV994 @ SV881 ) @ ( zero_zero @ SV417 ) ) )
= $true )
| ( ( ordere453448008miring @ SV417 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4149]) ).
thf(4485,plain,
! [SV622: $i,SV418: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( bit1 @ SV418 ) @ ( bit0 @ SV622 ) ) )
= $true )
| ( ( ord_less @ int @ SV418 @ SV622 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4150]) ).
thf(4486,plain,
! [SV622: $i,SV418: $i] :
( ( ( ~ ( ord_less @ int @ SV418 @ SV622 ) )
= $true )
| ( ( ord_less_eq @ int @ ( bit1 @ SV418 ) @ ( bit0 @ SV622 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4151]) ).
thf(4487,plain,
! [SV419: $i,SV623: $i] :
( ( ( ~ ( ( ( times_times @ int @ SV623 @ SV419 )
!= ( one_one @ int ) )
| ~ ( ( ( ti @ int @ SV623 )
!= ( one_one @ int ) )
| ( ( ti @ int @ SV419 )
!= ( one_one @ int ) ) ) ) )
= $false )
| ( ( ord_less @ int @ ( zero_zero @ int ) @ SV623 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4152]) ).
thf(4488,plain,
! [SV419: $i,SV623: $i] :
( ( ( ~ ( ~ ~ ( ( ( ti @ int @ SV623 )
!= ( one_one @ int ) )
| ( ( ti @ int @ SV419 )
!= ( one_one @ int ) ) )
| ( ( times_times @ int @ SV623 @ SV419 )
= ( one_one @ int ) ) ) )
= $false )
| ( ( ord_less @ int @ ( zero_zero @ int ) @ SV623 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4152]) ).
thf(4489,plain,
! [SV624: $i,SV420: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( bit0 @ SV420 ) @ ( bit1 @ SV624 ) ) )
= $true )
| ( ( ord_less_eq @ int @ SV420 @ SV624 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4153]) ).
thf(4490,plain,
! [SV624: $i,SV420: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV420 @ SV624 ) )
= $true )
| ( ( ord_less_eq @ int @ ( bit0 @ SV420 ) @ ( bit1 @ SV624 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4154]) ).
thf(4491,plain,
! [SV421: $i,SV625: $i] :
( ( ( ~ ( ord_less @ int @ SV625 @ pls ) )
= $true )
| ( ( ( times_times @ nat @ ( number_number_of @ nat @ SV625 ) @ ( number_number_of @ nat @ SV421 ) )
= ( zero_zero @ nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4155]) ).
thf(4492,plain,
! [SV421: $i,SV625: $i] :
( ( ( ~ ~ ( ord_less @ int @ SV625 @ pls ) )
= $true )
| ( ( ( times_times @ nat @ ( number_number_of @ nat @ SV625 ) @ ( number_number_of @ nat @ SV421 ) )
= ( number_number_of @ nat @ ( times_times @ int @ SV625 @ SV421 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4156]) ).
thf(4493,plain,
! [SV1052: $i,SV995: $i,SV882: $i,SV726: $i,SV626: $i,SV422: $i] :
( ( ( ( plus_plus @ int @ ( times_times @ int @ SV422 @ SV626 ) @ SV726 )
!= ( plus_plus @ int @ ( times_times @ int @ SV882 @ SV995 ) @ SV1052 ) )
| ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( times_times @ int @ SV882 @ SV995 ) @ SV1052 ) )
| ~ ( ord_less @ int @ SV1052 @ SV882 )
| ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV726 )
| ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV882 )
| ~ ( ord_less_eq @ int @ SV882 @ SV422 )
| ( ord_less_eq @ int @ SV626 @ SV995 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4157]) ).
thf(4494,plain,
! [SV423: $i] :
( ( ( ~ ( ord_less @ real @ ( zero_zero @ real ) @ ( times_times @ real @ SV423 @ SV423 ) ) )
= $false )
| ( ( SV423
= ( zero_zero @ real ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4158]) ).
thf(4495,plain,
! [SV423: $i] :
( ( ( SV423
= ( zero_zero @ real ) )
= $false )
| ( ( ~ ( ord_less @ real @ ( zero_zero @ real ) @ ( times_times @ real @ SV423 @ SV423 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4159]) ).
thf(4496,plain,
! [SV627: $i,SV424: $i] :
( ( ( ~ ( ord_less @ int @ ( bit1 @ SV424 ) @ ( bit1 @ SV627 ) ) )
= $true )
| ( ( ord_less @ int @ SV424 @ SV627 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4160]) ).
thf(4497,plain,
! [SV627: $i,SV424: $i] :
( ( ( ~ ( ord_less @ int @ SV424 @ SV627 ) )
= $true )
| ( ( ord_less @ int @ ( bit1 @ SV424 ) @ ( bit1 @ SV627 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4161]) ).
thf(4498,plain,
! [SV728: $i,SV629: $i,SV427: $i] :
( ( ~ ( zcong @ ( ti @ int @ SV427 ) @ SV629 @ SV728 )
| ( zcong @ SV427 @ SV629 @ SV728 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4163]) ).
thf(4499,plain,
! [SV728: $i,SV629: $i,SV427: $i] :
( ( ~ ( zcong @ SV427 @ SV629 @ SV728 )
| ( zcong @ ( ti @ int @ SV427 ) @ SV629 @ SV728 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4164]) ).
thf(4500,plain,
! [SV630: $i,SV428: $i] :
( ( ( ~ ( zcong @ SV428 @ ( zero_zero @ int ) @ SV630 ) )
= $true )
| ( ( dvd_dvd @ int @ SV630 @ SV428 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4165]) ).
thf(4501,plain,
! [SV428: $i,SV630: $i] :
( ( ( ~ ( dvd_dvd @ int @ SV630 @ SV428 ) )
= $true )
| ( ( zcong @ SV428 @ ( zero_zero @ int ) @ SV630 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4166]) ).
thf(4502,plain,
! [SV631: $i,SV429: $i] :
( ( ( ( power_power @ nat @ SV429 @ SV631 )
!= ( one_one @ nat ) )
= $true )
| ( ( ( SV429
= ( one_one @ nat ) )
| ( SV631
= ( zero_zero @ nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4167]) ).
thf(4503,plain,
! [SV631: $i,SV429: $i] :
( ( ( ~ ( ( SV429
= ( one_one @ nat ) )
| ( SV631
= ( zero_zero @ nat ) ) ) )
= $true )
| ( ( ( power_power @ nat @ SV429 @ SV631 )
= ( one_one @ nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4168]) ).
thf(4504,plain,
! [SV430: $i,SV884: $i,SV729: $i,SV632: $i] :
( ( ( zcong @ SV632 @ SV729 @ SV884 )
= $false )
| ( ( zcong @ ( plus_plus @ int @ SV632 @ SV430 ) @ ( plus_plus @ int @ SV729 @ SV430 ) @ SV884 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4169]) ).
thf(4505,plain,
! [SV887: $i,SV433: $i,SV1053: $i,SV997: $i] :
( ( ( ~ ( ord_less @ nat @ SV997 @ SV1053 )
| ~ ( ord_less @ SV433 @ ( zero_zero @ SV433 ) @ SV887 )
| ~ ( ord_less @ SV433 @ SV887 @ ( one_one @ SV433 ) )
| ( ord_less @ SV433 @ ( power_power @ SV433 @ SV887 @ SV1053 ) @ ( power_power @ SV433 @ SV887 @ SV997 ) ) )
= $true )
| ( ( linordered_semidom @ SV433 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4171]) ).
thf(4506,plain,
! [SV998: $i,SV888: $i,SV1054: $i,SV434: $i] :
( ( ( ! [SY2211: $i,SY2212: $i] :
( ~ ( ( ( ti @ SV434 @ SY2212 )
!= ( zero_zero @ SV434 ) ) )
| ~ ~ ( ( ( ti @ SV434 @ SV1054 )
!= ( ti @ SV434 @ SY2211 ) )
| ~ ( ( ( ti @ SV434 @ SV888 )
!= ( ti @ SV434 @ SV998 ) ) ) )
| ( ( plus_plus @ SV434 @ SV1054 @ ( times_times @ SV434 @ SY2212 @ SV888 ) )
!= ( plus_plus @ SV434 @ SY2211 @ ( times_times @ SV434 @ SY2212 @ SV998 ) ) ) ) )
= $true )
| ( ( semiri456707255roduct @ SV434 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4172]) ).
thf(4507,plain,
! [SV1055: $i,SV999: $i,SV889: $i,SV730: $i,SV643: $i,SV472: $i,SV63: $i] :
( ( ( plus_plus @ int @ ( times_times @ int @ ( minus_minus @ int @ SV63 @ ( times_times @ int @ SV472 @ SV643 ) ) @ SV730 ) @ ( times_times @ int @ ( minus_minus @ int @ SV889 @ ( times_times @ int @ SV472 @ SV999 ) ) @ SV1055 ) )
= ( minus_minus @ int @ ( plus_plus @ int @ ( times_times @ int @ SV63 @ SV730 ) @ ( times_times @ int @ SV889 @ SV1055 ) ) @ ( times_times @ int @ SV472 @ ( plus_plus @ int @ ( times_times @ int @ SV643 @ SV730 ) @ ( times_times @ int @ SV999 @ SV1055 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4173]) ).
thf(4508,plain,
! [SV481: $i,SV79: $i,SV890: $i,SV732: $i,SV647: $i] :
( ( ( zcong @ SV647 @ SV732 @ SV890 )
= $false )
| ( ( ~ ( ~ ( ~ ( zcong @ SV79 @ ( times_times @ int @ SV647 @ SV481 ) @ SV890 )
| ( zcong @ SV79 @ ( times_times @ int @ SV732 @ SV481 ) @ SV890 ) )
| ~ ( ~ ( zcong @ SV79 @ ( times_times @ int @ SV732 @ SV481 ) @ SV890 )
| ( zcong @ SV79 @ ( times_times @ int @ SV647 @ SV481 ) @ SV890 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4174]) ).
thf(4509,plain,
! [SV482: $i,SV80: $i] :
( ( ( ord_less @ int @ SV80 @ ( plus_plus @ int @ SV482 @ ( one_one @ int ) ) )
= $false )
| ( ( ( ord_less @ int @ SV80 @ SV482 )
| ( ( ti @ int @ SV80 )
= ( ti @ int @ SV482 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4175]) ).
thf(4510,plain,
! [SV482: $i,SV80: $i] :
( ( ( ( ord_less @ int @ SV80 @ SV482 )
| ( ( ti @ int @ SV80 )
= ( ti @ int @ SV482 ) ) )
= $false )
| ( ( ord_less @ int @ SV80 @ ( plus_plus @ int @ SV482 @ ( one_one @ int ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4176]) ).
thf(4511,plain,
! [SV733: $i,SV891: $i,SV82: $i] :
( ( ( ord_less_eq @ SV82 @ ( zero_zero @ SV82 ) @ SV891 )
= $false )
| ( ( ~ ( ord_less_eq @ SV82 @ SV733 @ ( zero_zero @ SV82 ) )
| ( ord_less_eq @ SV82 @ ( times_times @ SV82 @ SV891 @ SV733 ) @ ( zero_zero @ SV82 ) ) )
= $true )
| ( ( ordere453448008miring @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4177]) ).
thf(4512,plain,
! [SV737: $i,SV894: $i,SV87: $i] :
( ( ( ord_less_eq @ SV87 @ ( zero_zero @ SV87 ) @ SV894 )
= $false )
| ( ( ~ ( ord_less_eq @ SV87 @ SV737 @ ( zero_zero @ SV87 ) )
| ( ord_less_eq @ SV87 @ ( times_times @ SV87 @ SV737 @ SV894 ) @ ( zero_zero @ SV87 ) ) )
= $true )
| ( ( ordere453448008miring @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4179]) ).
thf(4513,plain,
! [SV739: $i,SV896: $i,SV90: $i] :
( ( ( ( ti @ SV90 @ SV896 )
!= ( zero_zero @ SV90 ) )
= $false )
| ( ( ~ ( ( ( ti @ SV90 @ SV739 )
!= ( zero_zero @ SV90 ) ) )
| ( ( times_times @ SV90 @ SV896 @ SV739 )
!= ( zero_zero @ SV90 ) ) )
= $true )
| ( ( no_zero_divisors @ SV90 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4181]) ).
thf(4514,plain,
! [SV1056: $i,SV1002: $i,SV898: $i,SV741: $i,SV95: $i] :
( ( ( ( times_times @ SV95 @ ( times_times @ SV95 @ SV741 @ SV898 ) @ ( times_times @ SV95 @ SV1002 @ SV1056 ) )
= ( times_times @ SV95 @ SV741 @ ( times_times @ SV95 @ SV898 @ ( times_times @ SV95 @ SV1002 @ SV1056 ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV95 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4187]) ).
thf(4515,plain,
! [SV486: $i,SV96: $i] :
( ( ( ord_less @ int @ ( number_number_of @ int @ SV96 ) @ ( number_number_of @ int @ SV486 ) )
= $false )
| ( ( ord_less @ int @ SV96 @ SV486 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4188]) ).
thf(4516,plain,
! [SV486: $i,SV96: $i] :
( ( ( ord_less @ int @ SV96 @ SV486 )
= $false )
| ( ( ord_less @ int @ ( number_number_of @ int @ SV96 ) @ ( number_number_of @ int @ SV486 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4189]) ).
thf(4517,plain,
! [SV652: $i,SV490: $i,SV101: $i] :
( ( ( ~ ( zcong @ ( power_power @ int @ SV101 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SV490 @ SV652 ) )
= $true )
| ( ( ~ ( dvd_dvd @ int @ SV652 @ SV101 ) )
= $true )
| ( ( zcong @ SV490 @ ( zero_zero @ int ) @ SV652 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4191]) ).
thf(4518,plain,
! [SV743: $i,SV900: $i,SV102: $i] :
( ( ( ord_less @ SV102 @ ( zero_zero @ SV102 ) @ SV900 )
= $false )
| ( ( ~ ( ord_less @ SV102 @ SV900 @ ( one_one @ SV102 ) )
| ( ord_less @ SV102 @ ( times_times @ SV102 @ SV900 @ ( power_power @ SV102 @ SV900 @ SV743 ) ) @ ( power_power @ SV102 @ SV900 @ SV743 ) ) )
= $true )
| ( ( linordered_semidom @ SV102 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4192]) ).
thf(4519,plain,
! [SV491: $i,SV103: $i] :
( ( ( quadRes @ ( ti @ int @ SV103 ) @ SV491 )
= $false )
| ( ( quadRes @ SV103 @ SV491 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4193]) ).
thf(4520,plain,
! [SV491: $i,SV103: $i] :
( ( ( quadRes @ SV103 @ SV491 )
= $false )
| ( ( quadRes @ ( ti @ int @ SV103 ) @ SV491 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4194]) ).
thf(4521,plain,
! [SV108: $i,SV494: $i,SV901: $i,SV744: $i,SV655: $i] :
( ( ( zcong @ SV655 @ SV744 @ SV901 )
= $false )
| ( ( ( ( ti @ int @ SV744 )
!= ( ti @ int @ SV494 ) )
| ~ ( zcong @ SV494 @ SV108 @ SV901 )
| ( zcong @ SV655 @ SV108 @ SV901 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4197]) ).
thf(4522,plain,
! [SV656: $i,SV495: $i,SV109: $i] :
( ( ( ( ti @ int @ SV109 )
!= ( zero_zero @ int ) )
= $false )
| ( ( dvd_dvd @ int @ SV495 @ SV656 )
= $true )
| ( ( dvd_dvd @ int @ ( times_times @ int @ SV109 @ SV495 ) @ ( times_times @ int @ SV109 @ SV656 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4198]) ).
thf(4523,plain,
! [SV498: $i,SV115: $i] :
( ( ( ord_less @ int @ ( bit1 @ SV115 ) @ ( bit0 @ SV498 ) )
= $false )
| ( ( ord_less @ int @ SV115 @ SV498 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4202]) ).
thf(4524,plain,
! [SV498: $i,SV115: $i] :
( ( ( ord_less @ int @ SV115 @ SV498 )
= $false )
| ( ( ord_less @ int @ ( bit1 @ SV115 ) @ ( bit0 @ SV498 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4203]) ).
thf(4525,plain,
! [SV746: $i,SV117: $i,SV1004: $i,SV902: $i] :
( ( ( ~ ( ord_less_eq @ nat @ SV902 @ SV1004 ) )
= $true )
| ( ( ~ ( ord_less_eq @ SV117 @ ( zero_zero @ SV117 ) @ SV746 )
| ~ ( ord_less_eq @ SV117 @ SV746 @ ( one_one @ SV117 ) )
| ( ord_less_eq @ SV117 @ ( power_power @ SV117 @ SV746 @ SV1004 ) @ ( power_power @ SV117 @ SV746 @ SV902 ) ) )
= $true )
| ( ( linordered_semidom @ SV117 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4204]) ).
thf(4526,plain,
! [SV500: $i,SV119: $i,SV658: $i] :
( ( ( dvd_dvd @ int @ SV658 @ ( power_power @ int @ SV119 @ SV500 ) )
= $false )
| ( ( dvd_dvd @ int @ SV658 @ SV119 )
= $true )
| ( ( zprime @ SV658 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4205]) ).
thf(4527,plain,
! [SV120: $i] :
( ( ( linordered_idom @ SV120 )
= $false )
| ( ( number_ring @ SV120 )
= $false )
| ( ( ! [SY1234: $i] :
~ ( ~ ( ~ ( ord_less @ SV120 @ ( one_one @ SV120 ) @ ( number_number_of @ SV120 @ SY1234 ) )
| ( ord_less @ int @ ( bit1 @ pls ) @ SY1234 ) )
| ~ ( ~ ( ord_less @ int @ ( bit1 @ pls ) @ SY1234 )
| ( ord_less @ SV120 @ ( one_one @ SV120 ) @ ( number_number_of @ SV120 @ SY1234 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4206]) ).
thf(4528,plain,
! [SV502: $i,SV122: $i] :
( ( ( ord_less_eq @ int @ ( bit1 @ SV122 ) @ ( bit1 @ SV502 ) )
= $false )
| ( ( ord_less_eq @ int @ SV122 @ SV502 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4207]) ).
thf(4529,plain,
! [SV502: $i,SV122: $i] :
( ( ( ord_less_eq @ int @ SV122 @ SV502 )
= $false )
| ( ( ord_less_eq @ int @ ( bit1 @ SV122 ) @ ( bit1 @ SV502 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4208]) ).
thf(4530,plain,
( ( ( ( plus_plus @ int @ ( power_power @ int @ sK3_SX0 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ sK5_SY1968 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) )
= $false )
| ( ( ord_less @ int @ ( one_one @ int ) @ t )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4209]) ).
thf(4531,plain,
! [SV123: $i] :
( ( ( linordered_idom @ SV123 )
= $false )
| ( ( number_ring @ SV123 )
= $false )
| ( ( ! [SY1238: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV123 @ ( number_number_of @ SV123 @ SY1238 ) @ ( one_one @ SV123 ) )
| ( ord_less_eq @ int @ SY1238 @ ( bit1 @ pls ) ) )
| ~ ( ~ ( ord_less_eq @ int @ SY1238 @ ( bit1 @ pls ) )
| ( ord_less_eq @ SV123 @ ( number_number_of @ SV123 @ SY1238 ) @ ( one_one @ SV123 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4210]) ).
thf(4532,plain,
! [SV903: $i,SV747: $i,SV1057: $i,SV1005: $i,SV124: $i] :
( ( ( ~ ( dvd_dvd @ SV124 @ SV1005 @ SV1057 )
| ~ ( dvd_dvd @ SV124 @ SV747 @ SV903 )
| ( dvd_dvd @ SV124 @ ( times_times @ SV124 @ SV1005 @ SV747 ) @ ( times_times @ SV124 @ SV1057 @ SV903 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV124 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4211]) ).
thf(4533,plain,
! [SV1058: $i,SV1006: $i,SV904: $i,SV748: $i,SV125: $i] :
( ( ( ( minus_minus @ SV125 @ ( plus_plus @ SV125 @ SV748 @ SV904 ) @ ( plus_plus @ SV125 @ SV1006 @ SV1058 ) )
= ( plus_plus @ SV125 @ ( minus_minus @ SV125 @ SV748 @ SV1006 ) @ ( minus_minus @ SV125 @ SV904 @ SV1058 ) ) )
= $true )
| ( ( ab_group_add @ SV125 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4212]) ).
thf(4534,plain,
! [SV907: $i,SV753: $i,SV660: $i,SV503: $i,SV132: $i] :
( ( ( ord_less_eq @ int @ ( plus_plus @ int @ ( times_times @ int @ SV132 @ SV503 ) @ SV660 ) @ ( plus_plus @ int @ ( times_times @ int @ SV132 @ SV753 ) @ SV907 ) )
= $false )
| ( ( ~ ( ord_less_eq @ int @ SV907 @ ( zero_zero @ int ) )
| ~ ( ord_less @ int @ SV132 @ SV907 )
| ~ ( ord_less @ int @ SV132 @ SV660 )
| ( ord_less_eq @ int @ SV753 @ SV503 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4217]) ).
thf(4535,plain,
! [SV134: $i] :
( ( ( linordered_idom @ SV134 )
= $false )
| ( ( number_ring @ SV134 )
= $false )
| ( ( ! [SY1260: $i] :
~ ( ~ ( ~ ( ord_less @ SV134 @ ( number_number_of @ SV134 @ SY1260 ) @ ( one_one @ SV134 ) )
| ( ord_less @ int @ SY1260 @ ( bit1 @ pls ) ) )
| ~ ( ~ ( ord_less @ int @ SY1260 @ ( bit1 @ pls ) )
| ( ord_less @ SV134 @ ( number_number_of @ SV134 @ SY1260 ) @ ( one_one @ SV134 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4218]) ).
thf(4536,plain,
! [SV505: $i,SV135: $i] :
( ( ( ord_less_eq @ nat @ ( number_number_of @ nat @ SV135 ) @ ( number_number_of @ nat @ SV505 ) )
= $false )
| ( ( ~ ~ ( ord_less_eq @ int @ SV135 @ SV505 )
| ( ord_less_eq @ int @ SV135 @ pls ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4219]) ).
thf(4537,plain,
! [SV505: $i,SV135: $i] :
( ( ( ~ ~ ( ord_less_eq @ int @ SV135 @ SV505 )
| ( ord_less_eq @ int @ SV135 @ pls ) )
= $false )
| ( ( ord_less_eq @ nat @ ( number_number_of @ nat @ SV135 ) @ ( number_number_of @ nat @ SV505 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4220]) ).
thf(4538,plain,
! [SV661: $i,SV506: $i,SV137: $i] :
( ( ( ~ ( zcong @ SV137 @ SV506 @ SV661 ) )
= $true )
| ( ( dvd_dvd @ int @ SV661 @ ( minus_minus @ int @ SV137 @ SV506 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4221]) ).
thf(4539,plain,
! [SV506: $i,SV137: $i,SV661: $i] :
( ( ( ~ ( dvd_dvd @ int @ SV661 @ ( minus_minus @ int @ SV137 @ SV506 ) ) )
= $true )
| ( ( zcong @ SV137 @ SV506 @ SV661 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4222]) ).
thf(4540,plain,
! [SV507: $i,SV138: $i] :
( ( ( ord_less_eq @ int @ ( number_number_of @ int @ SV138 ) @ ( number_number_of @ int @ SV507 ) )
= $false )
| ( ( ord_less_eq @ int @ SV138 @ SV507 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4223]) ).
thf(4541,plain,
! [SV507: $i,SV138: $i] :
( ( ( ord_less_eq @ int @ SV138 @ SV507 )
= $false )
| ( ( ord_less_eq @ int @ ( number_number_of @ int @ SV138 ) @ ( number_number_of @ int @ SV507 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4224]) ).
thf(4542,plain,
! [SV139: $i] :
( ( ( ring @ SV139 )
= $false )
| ( ( number @ SV139 )
= $false )
| ( ( ! [SY1266: $i,SY1267: $i,SY1268: $i] :
( ( times_times @ SV139 @ ( number_number_of @ SV139 @ SY1266 ) @ ( minus_minus @ SV139 @ SY1267 @ SY1268 ) )
= ( minus_minus @ SV139 @ ( times_times @ SV139 @ ( number_number_of @ SV139 @ SY1266 ) @ SY1267 ) @ ( times_times @ SV139 @ ( number_number_of @ SV139 @ SY1266 ) @ SY1268 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4225]) ).
thf(4543,plain,
! [SV756: $i,SV908: $i,SV142: $i] :
( ( ( ord_less @ SV142 @ ( one_one @ SV142 ) @ SV908 )
= $false )
| ( ( ord_less @ SV142 @ ( one_one @ SV142 ) @ ( times_times @ SV142 @ SV908 @ ( power_power @ SV142 @ SV908 @ SV756 ) ) )
= $true )
| ( ( linordered_semidom @ SV142 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4226]) ).
thf(4544,plain,
! [SV509: $i,SV143: $i] :
( ( ( ( power_power @ nat @ SV143 @ SV509 )
= ( zero_zero @ nat ) )
= $false )
| ( ( ~ ( ~ ( ( SV509
!= ( zero_zero @ nat ) ) )
| ( SV143
!= ( zero_zero @ nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4227]) ).
thf(4545,plain,
! [SV143: $i,SV509: $i] :
( ( ( ~ ( ~ ( ( SV509
!= ( zero_zero @ nat ) ) )
| ( SV143
!= ( zero_zero @ nat ) ) ) )
= $false )
| ( ( ( power_power @ nat @ SV143 @ SV509 )
= ( zero_zero @ nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4228]) ).
thf(4546,plain,
! [SV662: $i,SV510: $i,SV145: $i] :
( ( ( ~ ( dvd_dvd @ int @ SV145 @ ( plus_plus @ int @ SV510 @ ( times_times @ int @ SV145 @ SV662 ) ) ) )
= $true )
| ( ( dvd_dvd @ int @ SV145 @ SV510 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4229]) ).
thf(4547,plain,
! [SV662: $i,SV510: $i,SV145: $i] :
( ( ( ~ ( dvd_dvd @ int @ SV145 @ SV510 ) )
= $true )
| ( ( dvd_dvd @ int @ SV145 @ ( plus_plus @ int @ SV510 @ ( times_times @ int @ SV145 @ SV662 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4230]) ).
thf(4548,plain,
! [SV511: $i,SV147: $i] :
( ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ SV147 @ SV511 ) )
= $false )
| ( ( ( ord_less @ nat @ ( zero_zero @ nat ) @ SV147 )
| ( SV511
= ( zero_zero @ nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4233]) ).
thf(4549,plain,
! [SV511: $i,SV147: $i] :
( ( ( ( ord_less @ nat @ ( zero_zero @ nat ) @ SV147 )
| ( SV511
= ( zero_zero @ nat ) ) )
= $false )
| ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ SV147 @ SV511 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4234]) ).
thf(4550,plain,
! [SV512: $i,SV151: $i] :
( ( ( ~ ( ~ ( dvd_dvd @ nat @ SV151 @ SV512 )
| ~ ( dvd_dvd @ nat @ SV512 @ SV151 ) ) )
= $false )
| ( ( SV151 = SV512 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4236]) ).
thf(4551,plain,
! [SV512: $i,SV151: $i] :
( ( ( SV151 = SV512 )
= $false )
| ( ( ~ ( ~ ( dvd_dvd @ nat @ SV151 @ SV512 )
| ~ ( dvd_dvd @ nat @ SV512 @ SV151 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4237]) ).
thf(4552,plain,
! [SV760: $i,SV910: $i,SV152: $i] :
( ( ( ord_less_eq @ SV152 @ ( zero_zero @ SV152 ) @ SV910 )
= $false )
| ( ( ~ ( ord_less_eq @ SV152 @ ( zero_zero @ SV152 ) @ SV760 )
| ( ord_less_eq @ SV152 @ ( zero_zero @ SV152 ) @ ( times_times @ SV152 @ SV910 @ SV760 ) ) )
= $true )
| ( ( ordere453448008miring @ SV152 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4238]) ).
thf(4553,plain,
! [SV153: $i,SV513: $i] :
( ( ( ! [SY1807: $i] :
~ ~ ( ~ ( ord_less @ real @ ( zero_zero @ real ) @ SY1807 )
| ( ( power_power @ real @ SY1807 @ SV513 )
!= SV153 ) ) )
= $false )
| ( ( ord_less @ real @ ( zero_zero @ real ) @ SV153 )
= $false )
| ( ( ord_less @ nat @ ( zero_zero @ nat ) @ SV513 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4239]) ).
thf(4554,plain,
! [SV911: $i,SV762: $i,SV1010: $i,SV155: $i] :
( ( ( ~ ( ord_less @ SV155 @ ( one_one @ SV155 ) @ SV1010 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( ord_less @ SV155 @ ( power_power @ SV155 @ SV1010 @ SV762 ) @ ( power_power @ SV155 @ SV1010 @ SV911 ) )
| ( ord_less @ nat @ SV762 @ SV911 ) )
| ~ ( ~ ( ord_less @ nat @ SV762 @ SV911 )
| ( ord_less @ SV155 @ ( power_power @ SV155 @ SV1010 @ SV762 ) @ ( power_power @ SV155 @ SV1010 @ SV911 ) ) ) ) )
= $true )
| ( ( linordered_semidom @ SV155 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4241]) ).
thf(4555,plain,
! [SV516: $i,SV159: $i] :
( ( ( ord_less_eq @ int @ ( bit1 @ SV159 ) @ ( bit0 @ SV516 ) )
= $false )
| ( ( ord_less @ int @ SV159 @ SV516 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4242]) ).
thf(4556,plain,
! [SV516: $i,SV159: $i] :
( ( ( ord_less @ int @ SV159 @ SV516 )
= $false )
| ( ( ord_less_eq @ int @ ( bit1 @ SV159 ) @ ( bit0 @ SV516 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4243]) ).
thf(4557,plain,
! [SV517: $i,SV160: $i] :
( ( ( ord_less @ int @ SV160 @ ( plus_plus @ int @ SV517 @ ( one_one @ int ) ) )
= $false )
| ( ( ord_less_eq @ int @ SV160 @ SV517 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4244]) ).
thf(4558,plain,
! [SV517: $i,SV160: $i] :
( ( ( ord_less_eq @ int @ SV160 @ SV517 )
= $false )
| ( ( ord_less @ int @ SV160 @ ( plus_plus @ int @ SV517 @ ( one_one @ int ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4245]) ).
thf(4559,plain,
! [SV518: $i,SV161: $i,SV665: $i] :
( ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV665 )
= $false )
| ( ( ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV161 )
| ( ord_less_eq @ int @ SV518 @ ( zero_zero @ int ) ) )
= $true )
| ( ( ord_less @ int @ ( plus_plus @ int @ ( times_times @ int @ SV161 @ SV518 ) @ SV665 ) @ ( zero_zero @ int ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4246]) ).
thf(4560,plain,
! [SV666: $i,SV520: $i,SV163: $i] :
( ( ( ~ ( zcong @ SV163 @ SV520 @ ( ti @ int @ SV666 ) ) )
= $true )
| ( ( zcong @ SV163 @ SV520 @ SV666 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4247]) ).
thf(4561,plain,
! [SV666: $i,SV520: $i,SV163: $i] :
( ( ( ~ ( zcong @ SV163 @ SV520 @ SV666 ) )
= $true )
| ( ( zcong @ SV163 @ SV520 @ ( ti @ int @ SV666 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4248]) ).
thf(4562,plain,
! [SV164: $i,SV667: $i,SV521: $i,SV913: $i,SV765: $i] :
( ( ( dvd_dvd @ int @ SV765 @ SV913 )
= $false )
| ( ( ~ ( ~ ( ~ ( dvd_dvd @ int @ SV765 @ ( plus_plus @ int @ SV521 @ SV667 ) )
| ( dvd_dvd @ int @ SV765 @ ( plus_plus @ int @ ( plus_plus @ int @ SV521 @ ( times_times @ int @ SV164 @ SV913 ) ) @ SV667 ) ) )
| ~ ( ~ ( dvd_dvd @ int @ SV765 @ ( plus_plus @ int @ ( plus_plus @ int @ SV521 @ ( times_times @ int @ SV164 @ SV913 ) ) @ SV667 ) )
| ( dvd_dvd @ int @ SV765 @ ( plus_plus @ int @ SV521 @ SV667 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4249]) ).
thf(4563,plain,
! [SV522: $i,SV167: $i,SV916: $i,SV768: $i,SV668: $i] :
( ( ( zcong @ SV668 @ SV768 @ SV916 )
= $false )
| ( ( ~ ( zcong @ SV167 @ SV522 @ SV916 )
| ( zcong @ ( minus_minus @ int @ SV668 @ SV167 ) @ ( minus_minus @ int @ SV768 @ SV522 ) @ SV916 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4251]) ).
thf(4564,plain,
! [SV168: $i] :
( ( ( semiring @ SV168 )
= $false )
| ( ( number @ SV168 )
= $false )
| ( ( ! [SY1318: $i,SY1319: $i,SY1320: $i] :
( ( times_times @ SV168 @ ( plus_plus @ SV168 @ SY1318 @ SY1319 ) @ ( number_number_of @ SV168 @ SY1320 ) )
= ( plus_plus @ SV168 @ ( times_times @ SV168 @ SY1318 @ ( number_number_of @ SV168 @ SY1320 ) ) @ ( times_times @ SV168 @ SY1319 @ ( number_number_of @ SV168 @ SY1320 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4252]) ).
thf(4565,plain,
! [SV523: $i,SV169: $i] :
( ( ( ( plus_plus @ real @ ( power_power @ real @ SV169 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ real @ SV523 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ real ) )
= $false )
| ( ( ~ ( ( SV169
!= ( zero_zero @ real ) )
| ( SV523
!= ( zero_zero @ real ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4253]) ).
thf(4566,plain,
! [SV523: $i,SV169: $i] :
( ( ( ~ ( ( SV169
!= ( zero_zero @ real ) )
| ( SV523
!= ( zero_zero @ real ) ) ) )
= $false )
| ( ( ( plus_plus @ real @ ( power_power @ real @ SV169 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ real @ SV523 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ real ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4254]) ).
thf(4567,plain,
! [SV669: $i,SV524: $i,SV170: $i] :
( ( ( ord_less @ nat @ ( one_one @ nat ) @ SV170 )
= $false )
| ( ( ord_less_eq @ nat @ SV524 @ SV669 )
= $true )
| ( ( dvd_dvd @ nat @ ( power_power @ nat @ SV170 @ SV524 ) @ ( power_power @ nat @ SV170 @ SV669 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4255]) ).
thf(4568,plain,
! [SV525: $i,SV172: $i] :
( ( ( ord_less @ int @ SV172 @ SV525 )
= $false )
| ( ( ord_less @ int @ ( minus_minus @ int @ SV172 @ SV525 ) @ ( zero_zero @ int ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4258]) ).
thf(4569,plain,
! [SV525: $i,SV172: $i] :
( ( ( ord_less @ int @ ( minus_minus @ int @ SV172 @ SV525 ) @ ( zero_zero @ int ) )
= $false )
| ( ( ord_less @ int @ SV172 @ SV525 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4259]) ).
thf(4570,plain,
! [SV1059: $i,SV1012: $i,SV917: $i,SV770: $i,SV174: $i] :
( ( ( ( minus_minus @ SV174 @ ( times_times @ SV174 @ SV770 @ SV917 ) @ ( times_times @ SV174 @ SV1012 @ SV1059 ) )
= ( plus_plus @ SV174 @ ( times_times @ SV174 @ SV770 @ ( minus_minus @ SV174 @ SV917 @ SV1059 ) ) @ ( times_times @ SV174 @ ( minus_minus @ SV174 @ SV770 @ SV1012 ) @ SV1059 ) ) )
= $true )
| ( ( ring @ SV174 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4260]) ).
thf(4571,plain,
! [SV918: $i,SV771: $i,SV1060: $i,SV1013: $i,SV175: $i] :
( ( ( ~ ( ~ ( ~ ~ ( ~ ( ( ( ti @ SV175 @ SV1013 )
!= ( ti @ SV175 @ SV1060 ) ) )
| ~ ( ( ( ti @ SV175 @ SV771 )
!= ( ti @ SV175 @ SV918 ) ) ) )
| ( ( plus_plus @ SV175 @ ( times_times @ SV175 @ SV1013 @ SV771 ) @ ( times_times @ SV175 @ SV1060 @ SV918 ) )
!= ( plus_plus @ SV175 @ ( times_times @ SV175 @ SV1013 @ SV918 ) @ ( times_times @ SV175 @ SV1060 @ SV771 ) ) ) )
| ~ ( ~ ( ( ( plus_plus @ SV175 @ ( times_times @ SV175 @ SV1013 @ SV771 ) @ ( times_times @ SV175 @ SV1060 @ SV918 ) )
!= ( plus_plus @ SV175 @ ( times_times @ SV175 @ SV1013 @ SV918 ) @ ( times_times @ SV175 @ SV1060 @ SV771 ) ) ) )
| ~ ( ~ ( ( ( ti @ SV175 @ SV1013 )
!= ( ti @ SV175 @ SV1060 ) ) )
| ~ ( ( ( ti @ SV175 @ SV771 )
!= ( ti @ SV175 @ SV918 ) ) ) ) ) ) )
= $true )
| ( ( semiri456707255roduct @ SV175 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4261]) ).
thf(4572,plain,
! [SV527: $i,SV178: $i] :
( ( ( dvd_dvd @ int @ SV178 @ SV527 )
= $false )
| ( ( ord_less @ int @ SV527 @ SV178 )
= $false )
| ( ( ord_less @ int @ ( zero_zero @ int ) @ SV527 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4264]) ).
thf(4573,plain,
! [SV919: $i,SV772: $i,SV1014: $i,SV179: $i] :
( ( ( ~ ( ord_less @ SV179 @ ( one_one @ SV179 ) @ SV1014 ) )
= $true )
| ( ( ~ ( ord_less @ SV179 @ ( power_power @ SV179 @ SV1014 @ SV772 ) @ ( power_power @ SV179 @ SV1014 @ SV919 ) )
| ( ord_less @ nat @ SV772 @ SV919 ) )
= $true )
| ( ( linordered_semidom @ SV179 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4265]) ).
thf(4574,plain,
! [SV1015: $i,SV920: $i,SV180: $i,SV773: $i] :
( ( ( SV773
!= ( times_times @ SV180 @ SV920 @ SV1015 ) )
= $true )
| ( ( dvd_dvd @ SV180 @ SV920 @ SV773 )
= $true )
| ( ( dvd @ SV180 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4266]) ).
thf(4575,plain,
! [SV528: $i,SV182: $i] :
( ( ( ord_less @ int @ ( bit1 @ SV182 ) @ ( bit1 @ SV528 ) )
= $false )
| ( ( ord_less @ int @ SV182 @ SV528 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4267]) ).
thf(4576,plain,
! [SV528: $i,SV182: $i] :
( ( ( ord_less @ int @ SV182 @ SV528 )
= $false )
| ( ( ord_less @ int @ ( bit1 @ SV182 ) @ ( bit1 @ SV528 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4268]) ).
thf(4577,plain,
! [SV529: $i,SV186: $i] :
( ( ( ord_less @ int @ ( bit0 @ SV186 ) @ ( bit0 @ SV529 ) )
= $false )
| ( ( ord_less @ int @ SV186 @ SV529 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4270]) ).
thf(4578,plain,
! [SV529: $i,SV186: $i] :
( ( ( ord_less @ int @ SV186 @ SV529 )
= $false )
| ( ( ord_less @ int @ ( bit0 @ SV186 ) @ ( bit0 @ SV529 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4271]) ).
thf(4579,plain,
! [SV530: $i,SV187: $i] :
( ( ( ord_less @ int @ SV187 @ SV530 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq @ int @ SV187 @ SV530 )
| ~ ( ( ( ti @ int @ SV187 )
!= ( ti @ int @ SV530 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4272]) ).
thf(4580,plain,
! [SV530: $i,SV187: $i] :
( ( ( ~ ( ~ ( ord_less_eq @ int @ SV187 @ SV530 )
| ~ ( ( ( ti @ int @ SV187 )
!= ( ti @ int @ SV530 ) ) ) ) )
= $false )
| ( ( ord_less @ int @ SV187 @ SV530 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4273]) ).
thf(4581,plain,
! [SV776: $i,SV189: $i] :
( ( ( ( ( plus_plus @ SV189 @ SV776 @ SV776 )
!= ( zero_zero @ SV189 ) )
| ( ( ti @ SV189 @ SV776 )
= ( zero_zero @ SV189 ) ) )
= $true )
| ( ( linord219039673up_add @ SV189 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4274]) ).
thf(4582,plain,
! [SV776: $i,SV189: $i] :
( ( ( ( ( ti @ SV189 @ SV776 )
!= ( zero_zero @ SV189 ) )
| ( ( plus_plus @ SV189 @ SV776 @ SV776 )
= ( zero_zero @ SV189 ) ) )
= $true )
| ( ( linord219039673up_add @ SV189 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4275]) ).
thf(4583,plain,
! [SV670: $i,SV532: $i,SV190: $i] :
( ( ( zcong @ ( power_power @ int @ ( number_number_of @ int @ min ) @ SV190 ) @ ( power_power @ int @ ( number_number_of @ int @ min ) @ SV532 ) @ SV670 )
= $false )
| ( ( ( power_power @ int @ ( number_number_of @ int @ min ) @ SV190 )
= ( power_power @ int @ ( number_number_of @ int @ min ) @ SV532 ) )
= $true )
| ( ( ord_less @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV670 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4276]) ).
thf(4584,plain,
! [SV671: $i,SV533: $i,SV191: $i] :
( ( ( ~ ( dvd_dvd @ nat @ ( times_times @ nat @ SV191 @ SV533 ) @ ( times_times @ nat @ SV671 @ SV533 ) ) )
= $true )
| ( ( ( SV533
= ( zero_zero @ nat ) )
| ( dvd_dvd @ nat @ SV191 @ SV671 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4277]) ).
thf(4585,plain,
! [SV671: $i,SV191: $i,SV533: $i] :
( ( ( ~ ( ( SV533
= ( zero_zero @ nat ) )
| ( dvd_dvd @ nat @ SV191 @ SV671 ) ) )
= $true )
| ( ( dvd_dvd @ nat @ ( times_times @ nat @ SV191 @ SV533 ) @ ( times_times @ nat @ SV671 @ SV533 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4278]) ).
thf(4586,plain,
! [SV777: $i,SV922: $i,SV192: $i] :
( ( ( ord_less_eq @ SV192 @ ( zero_zero @ SV192 ) @ SV922 )
= $false )
| ( ( ord_less_eq @ SV192 @ ( zero_zero @ SV192 ) @ ( power_power @ SV192 @ SV922 @ SV777 ) )
= $true )
| ( ( linordered_semidom @ SV192 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4279]) ).
thf(4587,plain,
! [SV923: $i,SV778: $i,SV193: $i] :
( ( ( ~ ( ( ( plus_plus @ SV193 @ ( times_times @ SV193 @ SV778 @ SV778 ) @ ( times_times @ SV193 @ SV923 @ SV923 ) )
!= ( zero_zero @ SV193 ) )
| ~ ( ( ( ti @ SV193 @ SV778 )
!= ( zero_zero @ SV193 ) )
| ( ( ti @ SV193 @ SV923 )
!= ( zero_zero @ SV193 ) ) ) ) )
= $false )
| ( ( linord581940658strict @ SV193 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4280]) ).
thf(4588,plain,
! [SV923: $i,SV778: $i,SV193: $i] :
( ( ( ~ ( ~ ~ ( ( ( ti @ SV193 @ SV778 )
!= ( zero_zero @ SV193 ) )
| ( ( ti @ SV193 @ SV923 )
!= ( zero_zero @ SV193 ) ) )
| ( ( plus_plus @ SV193 @ ( times_times @ SV193 @ SV778 @ SV778 ) @ ( times_times @ SV193 @ SV923 @ SV923 ) )
= ( zero_zero @ SV193 ) ) ) )
= $false )
| ( ( linord581940658strict @ SV193 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4280]) ).
thf(4589,plain,
! [SV924: $i,SV779: $i,SV1017: $i,SV194: $i] :
( ( ( ~ ( ord_less @ SV194 @ ( one_one @ SV194 ) @ SV1017 ) )
= $true )
| ( ( ~ ( ~ ( ( ( power_power @ SV194 @ SV1017 @ SV779 )
!= ( power_power @ SV194 @ SV1017 @ SV924 ) )
| ( SV779 = SV924 ) )
| ~ ( ( SV779 != SV924 )
| ( ( power_power @ SV194 @ SV1017 @ SV779 )
= ( power_power @ SV194 @ SV1017 @ SV924 ) ) ) ) )
= $true )
| ( ( linordered_semidom @ SV194 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4281]) ).
thf(4590,plain,
! [SV196: $i,SV672: $i,SV534: $i] :
( ( ( ~ ( zcong @ SV534 @ ( zero_zero @ int ) @ SV672 ) )
= $false )
| ( ( ~ ~ ( zcong @ SV196 @ ( zero_zero @ int ) @ SV672 )
| ~ ( zcong @ ( times_times @ int @ SV534 @ SV196 ) @ ( zero_zero @ int ) @ SV672 ) )
= $true )
| ( ( zprime @ SV672 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4283]) ).
thf(4591,plain,
! [SV928: $i,SV783: $i,SV199: $i] :
( ( ( ~ ( ~ ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ ( times_times @ SV199 @ SV783 @ SV928 ) )
| ~ ( ~ ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ SV783 )
| ~ ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ SV928 ) )
| ~ ( ~ ( ord_less_eq @ SV199 @ SV783 @ ( zero_zero @ SV199 ) )
| ~ ( ord_less_eq @ SV199 @ SV928 @ ( zero_zero @ SV199 ) ) ) ) )
= $false )
| ( ( linord581940658strict @ SV199 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4284]) ).
thf(4592,plain,
! [SV928: $i,SV783: $i,SV199: $i] :
( ( ( ~ ( ~ ( ~ ( ~ ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ SV783 )
| ~ ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ SV928 ) )
| ~ ( ~ ( ord_less_eq @ SV199 @ SV783 @ ( zero_zero @ SV199 ) )
| ~ ( ord_less_eq @ SV199 @ SV928 @ ( zero_zero @ SV199 ) ) ) )
| ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ ( times_times @ SV199 @ SV783 @ SV928 ) ) ) )
= $false )
| ( ( linord581940658strict @ SV199 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4284]) ).
thf(4593,plain,
! [SV785: $i,SV929: $i,SV201: $i] :
( ( ( ord_less @ SV201 @ ( one_one @ SV201 ) @ SV929 )
= $false )
| ( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ SV785 )
| ( ord_less @ SV201 @ ( one_one @ SV201 ) @ ( power_power @ SV201 @ SV929 @ SV785 ) ) )
= $true )
| ( ( linordered_semidom @ SV201 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4285]) ).
thf(4594,plain,
! [SV202: $i] :
( ( ( linordered_idom @ SV202 )
= $false )
| ( ( number_ring @ SV202 )
= $false )
| ( ( ! [SY1375: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV202 @ ( one_one @ SV202 ) @ ( number_number_of @ SV202 @ SY1375 ) )
| ( ord_less_eq @ int @ ( bit1 @ pls ) @ SY1375 ) )
| ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ pls ) @ SY1375 )
| ( ord_less_eq @ SV202 @ ( one_one @ SV202 ) @ ( number_number_of @ SV202 @ SY1375 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4286]) ).
thf(4595,plain,
! [SV203: $i,SV535: $i,SV673: $i] :
( ( ( ord_less @ int @ SV673 @ SV535 )
= $false )
| ( ( ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV203 )
| ~ ( ord_less @ int @ SV203 @ SV673 )
| ~ ( zcong @ SV673 @ SV203 @ SV535 ) )
= $true )
| ( ( ord_less @ int @ ( zero_zero @ int ) @ SV673 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4287]) ).
thf(4596,plain,
! [SV536: $i,SV206: $i,SV930: $i,SV787: $i,SV674: $i] :
( ( ( zcong @ SV674 @ SV787 @ SV930 )
= $false )
| ( ( ~ ( zcong @ SV206 @ SV536 @ SV930 )
| ( zcong @ ( plus_plus @ int @ SV674 @ SV206 ) @ ( plus_plus @ int @ SV787 @ SV536 ) @ SV930 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4290]) ).
thf(4597,plain,
! [SV209: $i,SV675: $i,SV537: $i] :
( ( ( dvd_dvd @ nat @ SV537 @ ( plus_plus @ nat @ SV675 @ SV209 ) )
= $false )
| ( ( dvd_dvd @ nat @ SV537 @ SV209 )
= $true )
| ( ( dvd_dvd @ nat @ SV537 @ SV675 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4295]) ).
thf(4598,plain,
! [SV213: $i] :
( ( ( ring_char_0 @ SV213 )
= $false )
| ( ( number_ring @ SV213 )
= $false )
| ( ( ! [SY1389: $i,SY1390: $i] :
~ ( ~ ( ( ( number_number_of @ SV213 @ SY1389 )
!= ( number_number_of @ SV213 @ SY1390 ) )
| ( ( ti @ int @ SY1389 )
= ( ti @ int @ SY1390 ) ) )
| ~ ( ( ( ti @ int @ SY1389 )
!= ( ti @ int @ SY1390 ) )
| ( ( number_number_of @ SV213 @ SY1389 )
= ( number_number_of @ SV213 @ SY1390 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4298]) ).
thf(4599,plain,
! [SV538: $i,SV214: $i,SV676: $i,SV790: $i] :
( ( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ SV790 ) )
= $true )
| ( ( ~ ( ord_less @ nat @ SV790 @ SV676 )
| ~ ( dvd_dvd @ nat @ SV676 @ SV214 ) )
= $true )
| ( ( SV214
= ( plus_plus @ nat @ ( times_times @ nat @ SV538 @ SV676 ) @ SV790 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4299]) ).
thf(4600,plain,
! [SV677: $i,SV215: $i,SV539: $i] :
( ( ( SV539
!= ( zero_zero @ nat ) )
= $false )
| ( ( dvd_dvd @ nat @ SV215 @ SV677 )
= $true )
| ( ( dvd_dvd @ nat @ ( power_power @ nat @ SV215 @ SV539 ) @ ( power_power @ nat @ SV677 @ SV539 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4300]) ).
thf(4601,plain,
! [SV218: $i] :
( ( ( linordered_idom @ SV218 )
= $false )
| ( ( number_ring @ SV218 )
= $false )
| ( ( ! [SY1397: $i,SY1398: $i] :
~ ( ~ ( ~ ( ord_less @ SV218 @ ( number_number_of @ SV218 @ SY1397 ) @ ( number_number_of @ SV218 @ SY1398 ) )
| ( ord_less @ int @ SY1397 @ SY1398 ) )
| ~ ( ~ ( ord_less @ int @ SY1397 @ SY1398 )
| ( ord_less @ SV218 @ ( number_number_of @ SV218 @ SY1397 ) @ ( number_number_of @ SV218 @ SY1398 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4301]) ).
thf(4602,plain,
! [SV792: $i,SV1061: $i,SV1018: $i,SV933: $i,SV220: $i] :
( ( ( ~ ( dvd_dvd @ SV220 @ ( power_power @ SV220 @ SV933 @ SV1018 ) @ SV1061 )
| ~ ( ord_less_eq @ nat @ SV792 @ SV1018 )
| ( dvd_dvd @ SV220 @ ( power_power @ SV220 @ SV933 @ SV792 ) @ SV1061 ) )
= $true )
| ( ( comm_semiring_1 @ SV220 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4304]) ).
thf(4603,plain,
! [SV678: $i,SV540: $i,SV221: $i] :
( ( ( ord_less @ real @ SV221 @ SV540 )
= $false )
| ( ( ord_less @ real @ ( times_times @ real @ SV678 @ SV221 ) @ ( times_times @ real @ SV678 @ SV540 ) )
= $true )
| ( ( ord_less @ real @ ( zero_zero @ real ) @ SV678 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4305]) ).
thf(4604,plain,
! [SV793: $i,SV1019: $i,SV934: $i,SV222: $i] :
( ( ( ~ ( dvd_dvd @ SV222 @ SV934 @ SV1019 ) )
= $true )
| ( ( dvd_dvd @ SV222 @ SV934 @ ( times_times @ SV222 @ SV793 @ SV1019 ) )
= $true )
| ( ( comm_semiring_1 @ SV222 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4306]) ).
thf(4605,plain,
! [SV541: $i,SV223: $i,SV679: $i] :
( ( ( ord_less @ nat @ ( power_power @ nat @ SV679 @ SV223 ) @ ( power_power @ nat @ SV679 @ SV541 ) )
= $false )
| ( ( ord_less @ nat @ SV223 @ SV541 )
= $true )
| ( ( ord_less @ nat @ ( zero_zero @ nat ) @ SV679 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4307]) ).
thf(4606,plain,
! [SV1020: $i,SV935: $i,SV794: $i,SV226: $i] :
( ( ( ~ ( dvd_dvd @ SV226 @ ( times_times @ SV226 @ SV794 @ SV935 ) @ SV1020 ) )
= $true )
| ( ( dvd_dvd @ SV226 @ SV794 @ SV1020 )
= $true )
| ( ( comm_semiring_1 @ SV226 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4311]) ).
thf(4607,plain,
! [SV546: $i,SV231: $i] :
( ( ( ord_less @ int @ ( bit0 @ SV231 ) @ ( bit1 @ SV546 ) )
= $false )
| ( ( ord_less_eq @ int @ SV231 @ SV546 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4312]) ).
thf(4608,plain,
! [SV546: $i,SV231: $i] :
( ( ( ord_less_eq @ int @ SV231 @ SV546 )
= $false )
| ( ( ord_less @ int @ ( bit0 @ SV231 ) @ ( bit1 @ SV546 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4313]) ).
thf(4609,plain,
! [SV547: $i,SV233: $i] :
( ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ SV233 @ ( number_number_of @ nat @ SV547 ) ) )
= $false )
| ( ( ( ( number_number_of @ nat @ SV547 )
= ( zero_zero @ nat ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ SV233 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4314]) ).
thf(4610,plain,
! [SV233: $i,SV547: $i] :
( ( ( ( ( number_number_of @ nat @ SV547 )
= ( zero_zero @ nat ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ SV233 ) )
= $false )
| ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ SV233 @ ( number_number_of @ nat @ SV547 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4315]) ).
thf(4611,plain,
! [SV234: $i] :
( ( ( semiring @ SV234 )
= $false )
| ( ( number @ SV234 )
= $false )
| ( ( ! [SY1424: $i,SY1425: $i,SY1426: $i] :
( ( times_times @ SV234 @ ( number_number_of @ SV234 @ SY1424 ) @ ( plus_plus @ SV234 @ SY1425 @ SY1426 ) )
= ( plus_plus @ SV234 @ ( times_times @ SV234 @ ( number_number_of @ SV234 @ SY1424 ) @ SY1425 ) @ ( times_times @ SV234 @ ( number_number_of @ SV234 @ SY1424 ) @ SY1426 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4316]) ).
thf(4612,plain,
! [SV548: $i,SV236: $i] :
( ( ( ord_less @ int @ ( bit0 @ SV236 ) @ ( bit1 @ SV548 ) )
= $false )
| ( ( ord_less_eq @ int @ SV236 @ SV548 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4317]) ).
thf(4613,plain,
! [SV548: $i,SV236: $i] :
( ( ( ord_less_eq @ int @ SV236 @ SV548 )
= $false )
| ( ( ord_less @ int @ ( bit0 @ SV236 ) @ ( bit1 @ SV548 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4318]) ).
thf(4614,plain,
! [SV937: $i,SV797: $i,SV237: $i] :
( ( ( ~ ( ( ( number_number_of @ SV237 @ SV797 )
!= ( ti @ SV237 @ SV937 ) )
| ( ( ti @ SV237 @ SV937 )
= ( number_number_of @ SV237 @ SV797 ) ) ) )
= $false )
| ( ( number @ SV237 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4319]) ).
thf(4615,plain,
! [SV797: $i,SV937: $i,SV237: $i] :
( ( ( ~ ( ( ( ti @ SV237 @ SV937 )
!= ( number_number_of @ SV237 @ SV797 ) )
| ( ( number_number_of @ SV237 @ SV797 )
= ( ti @ SV237 @ SV937 ) ) ) )
= $false )
| ( ( number @ SV237 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4319]) ).
thf(4616,plain,
! [SV549: $i,SV240: $i,SV683: $i,SV799: $i] :
( ( ( ~ ~ ( dvd_dvd @ int @ SV799 @ SV683 ) )
= $true )
| ( ( ~ ( dvd_dvd @ int @ ( power_power @ int @ SV799 @ SV240 ) @ ( times_times @ int @ SV683 @ SV549 ) )
| ( dvd_dvd @ int @ ( power_power @ int @ SV799 @ SV240 ) @ SV549 ) )
= $true )
| ( ( zprime @ SV799 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4323]) ).
thf(4617,plain,
! [SV550: $i,SV242: $i] :
( ( ( ord_less_eq @ int @ ( bit0 @ SV242 ) @ ( bit1 @ SV550 ) )
= $false )
| ( ( ord_less_eq @ int @ SV242 @ SV550 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4326]) ).
thf(4618,plain,
! [SV550: $i,SV242: $i] :
( ( ( ord_less_eq @ int @ SV242 @ SV550 )
= $false )
| ( ( ord_less_eq @ int @ ( bit0 @ SV242 ) @ ( bit1 @ SV550 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4327]) ).
thf(4619,plain,
! [SV552: $i,SV245: $i,SV685: $i] :
( ( ( ~ ( ord_less @ int @ SV685 @ pls ) )
= $true )
| ( ( ( times_times @ nat @ ( number_number_of @ nat @ SV685 ) @ ( times_times @ nat @ ( number_number_of @ nat @ SV245 ) @ SV552 ) )
= ( zero_zero @ nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4330]) ).
thf(4620,plain,
! [SV552: $i,SV245: $i,SV685: $i] :
( ( ( ~ ~ ( ord_less @ int @ SV685 @ pls ) )
= $true )
| ( ( ( times_times @ nat @ ( number_number_of @ nat @ SV685 ) @ ( times_times @ nat @ ( number_number_of @ nat @ SV245 ) @ SV552 ) )
= ( times_times @ nat @ ( number_number_of @ nat @ ( times_times @ int @ SV685 @ SV245 ) ) @ SV552 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4331]) ).
thf(4621,plain,
! [SV554: $i,SV247: $i] :
( ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ SV247 @ SV554 ) )
= $false )
| ( ( ( SV554
= ( zero_zero @ nat ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ SV247 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4332]) ).
thf(4622,plain,
! [SV247: $i,SV554: $i] :
( ( ( ( SV554
= ( zero_zero @ nat ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ SV247 ) )
= $false )
| ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ SV247 @ SV554 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4333]) ).
thf(4623,plain,
! [SV556: $i,SV253: $i] :
( ( ( ord_less @ int @ ( bit1 @ SV253 ) @ ( bit0 @ SV556 ) )
= $false )
| ( ( ord_less @ int @ SV253 @ SV556 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4338]) ).
thf(4624,plain,
! [SV556: $i,SV253: $i] :
( ( ( ord_less @ int @ SV253 @ SV556 )
= $false )
| ( ( ord_less @ int @ ( bit1 @ SV253 ) @ ( bit0 @ SV556 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4339]) ).
thf(4625,plain,
! [SV1062: $i,SV1024: $i,SV942: $i,SV804: $i,SV255: $i] :
( ( ( ~ ( ~ ( ( ( plus_plus @ SV255 @ ( times_times @ SV255 @ SV804 @ SV942 ) @ ( times_times @ SV255 @ SV1024 @ SV1062 ) )
!= ( plus_plus @ SV255 @ ( times_times @ SV255 @ SV804 @ SV1062 ) @ ( times_times @ SV255 @ SV1024 @ SV942 ) ) )
| ( ( ti @ SV255 @ SV804 )
= ( ti @ SV255 @ SV1024 ) )
| ( ( ti @ SV255 @ SV942 )
= ( ti @ SV255 @ SV1062 ) ) )
| ~ ( ~ ( ( ( ti @ SV255 @ SV804 )
= ( ti @ SV255 @ SV1024 ) )
| ( ( ti @ SV255 @ SV942 )
= ( ti @ SV255 @ SV1062 ) ) )
| ( ( plus_plus @ SV255 @ ( times_times @ SV255 @ SV804 @ SV942 ) @ ( times_times @ SV255 @ SV1024 @ SV1062 ) )
= ( plus_plus @ SV255 @ ( times_times @ SV255 @ SV804 @ SV1062 ) @ ( times_times @ SV255 @ SV1024 @ SV942 ) ) ) ) ) )
= $true )
| ( ( semiri456707255roduct @ SV255 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4340]) ).
thf(4626,plain,
! [SV557: $i,SV257: $i,SV943: $i,SV805: $i,SV688: $i] :
( ( ( zcong @ SV688 @ SV805 @ SV943 )
= $false )
| ( ( ~ ( ~ ( ~ ( zcong @ SV257 @ ( times_times @ int @ SV557 @ SV688 ) @ SV943 )
| ( zcong @ SV257 @ ( times_times @ int @ SV557 @ SV805 ) @ SV943 ) )
| ~ ( ~ ( zcong @ SV257 @ ( times_times @ int @ SV557 @ SV805 ) @ SV943 )
| ( zcong @ SV257 @ ( times_times @ int @ SV557 @ SV688 ) @ SV943 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4343]) ).
thf(4627,plain,
! [SV558: $i,SV689: $i,SV259: $i] :
( ( ( ~ ( dvd_dvd @ nat @ ( power_power @ nat @ SV259 @ SV689 ) @ SV558 ) )
= $true )
| ( ( dvd_dvd @ nat @ SV259 @ SV558 )
= $true )
| ( ( SV689
= ( zero_zero @ nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4344]) ).
thf(4628,plain,
! [SV690: $i,SV559: $i,SV261: $i] :
( ( ( ~ ( zcong @ SV261 @ ( ti @ int @ SV559 ) @ SV690 ) )
= $true )
| ( ( zcong @ SV261 @ SV559 @ SV690 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4345]) ).
thf(4629,plain,
! [SV690: $i,SV559: $i,SV261: $i] :
( ( ( ~ ( zcong @ SV261 @ SV559 @ SV690 ) )
= $true )
| ( ( zcong @ SV261 @ ( ti @ int @ SV559 ) @ SV690 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4346]) ).
thf(4630,plain,
! [SV1063: $i,SV1025: $i,SV946: $i,SV809: $i,SV266: $i] :
( ( ( ( plus_plus @ SV266 @ ( plus_plus @ SV266 @ SV809 @ SV946 ) @ ( plus_plus @ SV266 @ SV1025 @ SV1063 ) )
= ( plus_plus @ SV266 @ ( plus_plus @ SV266 @ SV809 @ SV1025 ) @ ( plus_plus @ SV266 @ SV946 @ SV1063 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV266 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4347]) ).
thf(4631,plain,
! [SV810: $i,SV269: $i] :
( ( ( ~ ( ord_less @ SV269 @ ( plus_plus @ SV269 @ SV810 @ SV810 ) @ ( zero_zero @ SV269 ) )
| ( ord_less @ SV269 @ SV810 @ ( zero_zero @ SV269 ) ) )
= $true )
| ( ( linordered_idom @ SV269 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4349]) ).
thf(4632,plain,
! [SV810: $i,SV269: $i] :
( ( ( ~ ( ord_less @ SV269 @ SV810 @ ( zero_zero @ SV269 ) )
| ( ord_less @ SV269 @ ( plus_plus @ SV269 @ SV810 @ SV810 ) @ ( zero_zero @ SV269 ) ) )
= $true )
| ( ( linordered_idom @ SV269 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4350]) ).
thf(4633,plain,
! [SV562: $i,SV273: $i,SV691: $i] :
( ( ( ~ ( ( ( times_times @ real @ SV691 @ SV273 )
!= ( times_times @ real @ SV691 @ SV562 ) )
| ( SV273 = SV562 ) )
| ~ ( ( SV273 != SV562 )
| ( ( times_times @ real @ SV691 @ SV273 )
= ( times_times @ real @ SV691 @ SV562 ) ) ) )
= $false )
| ( ( SV691
= ( zero_zero @ real ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4353]) ).
thf(4634,plain,
! [SV815: $i,SV1027: $i,SV949: $i,SV277: $i] :
( ( ( ~ ( dvd_dvd @ SV277 @ SV949 @ SV1027 ) )
= $true )
| ( ( ~ ( dvd_dvd @ SV277 @ SV949 @ SV815 )
| ( dvd_dvd @ SV277 @ SV949 @ ( plus_plus @ SV277 @ SV1027 @ SV815 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV277 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4356]) ).
thf(4635,plain,
! [SV564: $i,SV281: $i] :
( ( ( ( bit0 @ SV281 )
= ( bit0 @ SV564 ) )
= $false )
| ( ( ( ti @ int @ SV281 )
= ( ti @ int @ SV564 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4359]) ).
thf(4636,plain,
! [SV564: $i,SV281: $i] :
( ( ( ( ti @ int @ SV281 )
= ( ti @ int @ SV564 ) )
= $false )
| ( ( ( bit0 @ SV281 )
= ( bit0 @ SV564 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4360]) ).
thf(4637,plain,
! [SV818: $i,SV1028: $i,SV950: $i,SV284: $i] :
( ( ( ~ ( dvd_dvd @ SV284 @ SV950 @ SV1028 ) )
= $true )
| ( ( dvd_dvd @ SV284 @ ( power_power @ SV284 @ SV950 @ SV818 ) @ ( power_power @ SV284 @ SV1028 @ SV818 ) )
= $true )
| ( ( comm_semiring_1 @ SV284 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4363]) ).
thf(4638,plain,
! [SV285: $i,SV819: $i,SV951: $i] :
( ( ( ord_less_eq @ int @ pls @ SV951 )
= $false )
| ( ( ~ ( ord_less_eq @ int @ pls @ SV819 )
| ( ( plus_plus @ SV285 @ ( number_number_of @ SV285 @ SV951 ) @ ( number_number_of @ SV285 @ SV819 ) )
= ( number_number_of @ SV285 @ ( plus_plus @ int @ SV951 @ SV819 ) ) ) )
= $true )
| ( ( number_semiring @ SV285 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4364]) ).
thf(4639,plain,
! [SV566: $i,SV288: $i,SV694: $i,SV821: $i] :
( ( ( ~ ~ ( dvd_dvd @ int @ SV821 @ SV694 ) )
= $true )
| ( ( ~ ( dvd_dvd @ int @ ( power_power @ int @ SV821 @ SV288 ) @ ( times_times @ int @ SV566 @ SV694 ) )
| ( dvd_dvd @ int @ ( power_power @ int @ SV821 @ SV288 ) @ SV566 ) )
= $true )
| ( ( zprime @ SV821 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4365]) ).
thf(4640,plain,
! [SV568: $i,SV292: $i] :
( ( ( zcong @ ( times_times @ int @ SV292 @ ( minus_minus @ int @ SV568 @ ( one_one @ int ) ) ) @ ( one_one @ int ) @ SV568 )
= $false )
| ( ( zcong @ SV292 @ ( minus_minus @ int @ SV568 @ ( one_one @ int ) ) @ SV568 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4368]) ).
thf(4641,plain,
! [SV568: $i,SV292: $i] :
( ( ( zcong @ SV292 @ ( minus_minus @ int @ SV568 @ ( one_one @ int ) ) @ SV568 )
= $false )
| ( ( zcong @ ( times_times @ int @ SV292 @ ( minus_minus @ int @ SV568 @ ( one_one @ int ) ) ) @ ( one_one @ int ) @ SV568 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4369]) ).
thf(4642,plain,
! [SV569: $i,SV294: $i,SV696: $i] :
( ( ( ord_less_eq @ int @ SV696 @ SV294 )
= $false )
| ( ( ord_less_eq @ int @ SV569 @ SV294 )
= $true )
| ( ( ord_less_eq @ int @ SV569 @ SV696 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4370]) ).
thf(4643,plain,
! [SV697: $i,SV570: $i,SV297: $i] :
( ( ( ord_less @ int @ ( zero_zero @ int ) @ SV297 )
= $false )
| ( ( ord_less @ int @ ( times_times @ int @ SV297 @ SV570 ) @ ( times_times @ int @ SV297 @ SV697 ) )
= $true )
| ( ( ord_less @ int @ SV570 @ SV697 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4372]) ).
thf(4644,plain,
! [SV572: $i,SV300: $i] :
( ( ( ord_less_eq @ int @ ( bit1 @ SV300 ) @ ( bit1 @ SV572 ) )
= $false )
| ( ( ord_less_eq @ int @ SV300 @ SV572 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4375]) ).
thf(4645,plain,
! [SV572: $i,SV300: $i] :
( ( ( ord_less_eq @ int @ SV300 @ SV572 )
= $false )
| ( ( ord_less_eq @ int @ ( bit1 @ SV300 ) @ ( bit1 @ SV572 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4376]) ).
thf(4646,plain,
! [SV955: $i,SV826: $i,SV301: $i] :
( ( ( ~ ( ( ( times_times @ SV301 @ SV826 @ SV955 )
!= ( zero_zero @ SV301 ) )
| ( ( ti @ SV301 @ SV826 )
= ( zero_zero @ SV301 ) )
| ( ( ti @ SV301 @ SV955 )
= ( zero_zero @ SV301 ) ) ) )
= $false )
| ( ( ring_n68954251visors @ SV301 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4377]) ).
thf(4647,plain,
! [SV955: $i,SV826: $i,SV301: $i] :
( ( ( ~ ( ~ ( ( ( ti @ SV301 @ SV826 )
= ( zero_zero @ SV301 ) )
| ( ( ti @ SV301 @ SV955 )
= ( zero_zero @ SV301 ) ) )
| ( ( times_times @ SV301 @ SV826 @ SV955 )
= ( zero_zero @ SV301 ) ) ) )
= $false )
| ( ( ring_n68954251visors @ SV301 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4377]) ).
thf(4648,plain,
! [SV956: $i,SV828: $i,SV1031: $i,SV304: $i] :
( ( ( ~ ( ord_less @ SV304 @ ( one_one @ SV304 ) @ SV1031 ) )
= $true )
| ( ( ~ ( ord_less_eq @ SV304 @ ( power_power @ SV304 @ SV1031 @ SV828 ) @ ( power_power @ SV304 @ SV1031 @ SV956 ) )
| ( ord_less_eq @ nat @ SV828 @ SV956 ) )
= $true )
| ( ( linordered_semidom @ SV304 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4380]) ).
thf(4649,plain,
! [SV1032: $i,SV957: $i,SV829: $i,SV698: $i,SV573: $i,SV305: $i] :
( ( ( ( plus_plus @ int @ ( times_times @ int @ SV305 @ SV573 ) @ SV698 )
!= ( plus_plus @ int @ ( times_times @ int @ SV829 @ SV957 ) @ SV1032 ) )
= $true )
| ( ( ~ ( ord_less @ int @ ( plus_plus @ int @ ( times_times @ int @ SV829 @ SV957 ) @ SV1032 ) @ ( zero_zero @ int ) )
| ~ ( ord_less @ int @ SV698 @ SV305 )
| ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV1032 )
| ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV829 )
| ~ ( ord_less_eq @ int @ SV829 @ SV305 )
| ( ord_less_eq @ int @ SV957 @ SV573 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4381]) ).
thf(4650,plain,
! [SV960: $i,SV833: $i,SV701: $i,SV576: $i,SV312: $i] :
( ( ( ord_less_eq @ int @ ( plus_plus @ int @ ( times_times @ int @ SV312 @ SV576 ) @ SV701 ) @ ( plus_plus @ int @ ( times_times @ int @ SV312 @ SV833 ) @ SV960 ) )
= $false )
| ( ( ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV701 )
| ~ ( ord_less @ int @ SV701 @ SV312 )
| ~ ( ord_less @ int @ SV960 @ SV312 )
| ( ord_less_eq @ int @ SV576 @ SV833 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4386]) ).
thf(4651,plain,
! [SV961: $i,SV834: $i,SV313: $i] :
( ( ( ~ ( ( ( ti @ SV313 @ SV834 )
!= ( plus_plus @ SV313 @ SV834 @ SV961 ) )
| ( ( ti @ SV313 @ SV961 )
= ( zero_zero @ SV313 ) ) ) )
= $false )
| ( ( semiri456707255roduct @ SV313 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4387]) ).
thf(4652,plain,
! [SV834: $i,SV961: $i,SV313: $i] :
( ( ( ~ ( ( ( ti @ SV313 @ SV961 )
!= ( zero_zero @ SV313 ) )
| ( ( ti @ SV313 @ SV834 )
= ( plus_plus @ SV313 @ SV834 @ SV961 ) ) ) )
= $false )
| ( ( semiri456707255roduct @ SV313 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4387]) ).
thf(4653,plain,
! [SV577: $i,SV314: $i] :
( ( ( quadRes @ SV314 @ SV577 )
= $false )
| ( ( ~ ! [SY1865: $i] :
~ ( zcong @ ( power_power @ int @ SY1865 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SV577 @ SV314 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4388]) ).
thf(4654,plain,
! [SV314: $i,SV577: $i] :
( ( ( ~ ! [SY1866: $i] :
~ ( zcong @ ( power_power @ int @ SY1866 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SV577 @ SV314 ) )
= $false )
| ( ( quadRes @ SV314 @ SV577 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4389]) ).
thf(4655,plain,
! [SV835: $i,SV315: $i,SV1034: $i,SV962: $i] :
( ( ( ~ ( ord_less_eq @ nat @ SV962 @ SV1034 ) )
= $true )
| ( ( ~ ( ord_less_eq @ SV315 @ ( one_one @ SV315 ) @ SV835 )
| ( ord_less_eq @ SV315 @ ( power_power @ SV315 @ SV835 @ SV962 ) @ ( power_power @ SV315 @ SV835 @ SV1034 ) ) )
= $true )
| ( ( linordered_semidom @ SV315 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4390]) ).
thf(4656,plain,
! [SV837: $i,SV964: $i,SV317: $i] :
( ( ( ord_less_eq @ SV317 @ ( one_one @ SV317 ) @ SV964 )
= $false )
| ( ( ord_less_eq @ SV317 @ ( one_one @ SV317 ) @ ( power_power @ SV317 @ SV964 @ SV837 ) )
= $true )
| ( ( linordered_semidom @ SV317 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4392]) ).
thf(4657,plain,
! [SV966: $i,SV839: $i,SV319: $i] :
( ( ( ~ ( ~ ( ord_less_eq @ SV319 @ ( times_times @ SV319 @ SV839 @ SV966 ) @ ( zero_zero @ SV319 ) )
| ~ ( ~ ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SV839 )
| ~ ( ord_less_eq @ SV319 @ SV966 @ ( zero_zero @ SV319 ) ) )
| ~ ( ~ ( ord_less_eq @ SV319 @ SV839 @ ( zero_zero @ SV319 ) )
| ~ ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SV966 ) ) ) )
= $false )
| ( ( linord581940658strict @ SV319 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4393]) ).
thf(4658,plain,
! [SV966: $i,SV839: $i,SV319: $i] :
( ( ( ~ ( ~ ( ~ ( ~ ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SV839 )
| ~ ( ord_less_eq @ SV319 @ SV966 @ ( zero_zero @ SV319 ) ) )
| ~ ( ~ ( ord_less_eq @ SV319 @ SV839 @ ( zero_zero @ SV319 ) )
| ~ ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SV966 ) ) )
| ( ord_less_eq @ SV319 @ ( times_times @ SV319 @ SV839 @ SV966 ) @ ( zero_zero @ SV319 ) ) ) )
= $false )
| ( ( linord581940658strict @ SV319 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4393]) ).
thf(4659,plain,
! [SV321: $i] :
( ( ( linordered_idom @ SV321 )
= $false )
| ( ( number_ring @ SV321 )
= $false )
| ( ( ! [SY1569: $i,SY1570: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV321 @ ( number_number_of @ SV321 @ SY1569 ) @ ( number_number_of @ SV321 @ SY1570 ) )
| ( ord_less_eq @ int @ SY1569 @ SY1570 ) )
| ~ ( ~ ( ord_less_eq @ int @ SY1569 @ SY1570 )
| ( ord_less_eq @ SV321 @ ( number_number_of @ SV321 @ SY1569 ) @ ( number_number_of @ SV321 @ SY1570 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4396]) ).
thf(4660,plain,
! [SV967: $i,SV841: $i,SV1064: $i,SV1036: $i,SV323: $i] :
( ( ( ~ ( dvd_dvd @ SV323 @ SV1036 @ SV1064 )
| ~ ( ord_less_eq @ nat @ SV841 @ SV967 )
| ( dvd_dvd @ SV323 @ ( power_power @ SV323 @ SV1036 @ SV841 ) @ ( power_power @ SV323 @ SV1064 @ SV967 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV323 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4397]) ).
thf(4661,plain,
! [SV968: $i,SV842: $i,SV325: $i] :
( ( ( ord_less_eq @ SV325 @ ( power_power @ SV325 @ SV842 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV325 @ SV968 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $false )
| ( ( ~ ( ord_less_eq @ SV325 @ ( zero_zero @ SV325 ) @ SV968 )
| ( ord_less_eq @ SV325 @ SV842 @ SV968 ) )
= $true )
| ( ( linordered_semidom @ SV325 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4398]) ).
thf(4662,plain,
! [SV1038: $i,SV970: $i,SV844: $i,SV330: $i] :
( ( ( ~ ( dvd_dvd @ SV330 @ ( times_times @ SV330 @ SV844 @ SV970 ) @ SV1038 ) )
= $true )
| ( ( dvd_dvd @ SV330 @ SV970 @ SV1038 )
= $true )
| ( ( comm_semiring_1 @ SV330 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4402]) ).
thf(4663,plain,
! [SV333: $i] :
( ( ( semiring_0 @ SV333 )
= $false )
| ( ( power @ SV333 )
= $false )
| ( ( ! [SY1587: $i] :
~ ( ~ ( ( ( number_number_of @ nat @ SY1587 )
!= ( zero_zero @ nat ) )
| ( ( power_power @ SV333 @ ( zero_zero @ SV333 ) @ ( number_number_of @ nat @ SY1587 ) )
= ( one_one @ SV333 ) ) )
| ~ ( ~ ( ( ( number_number_of @ nat @ SY1587 )
!= ( zero_zero @ nat ) ) )
| ( ( power_power @ SV333 @ ( zero_zero @ SV333 ) @ ( number_number_of @ nat @ SY1587 ) )
= ( zero_zero @ SV333 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4403]) ).
thf(4664,plain,
! [SV581: $i,SV336: $i] :
( ( ( ord_less_eq @ int @ ( bit0 @ SV336 ) @ ( bit0 @ SV581 ) )
= $false )
| ( ( ord_less_eq @ int @ SV336 @ SV581 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4404]) ).
thf(4665,plain,
! [SV581: $i,SV336: $i] :
( ( ( ord_less_eq @ int @ SV336 @ SV581 )
= $false )
| ( ( ord_less_eq @ int @ ( bit0 @ SV336 ) @ ( bit0 @ SV581 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4405]) ).
thf(4666,plain,
! [SV582: $i,SV337: $i,SV972: $i,SV846: $i,SV704: $i] :
( ( ( zcong @ SV704 @ SV846 @ SV972 )
= $false )
| ( ( ~ ( zcong @ SV337 @ SV582 @ SV972 )
| ( zcong @ ( times_times @ int @ SV704 @ SV337 ) @ ( times_times @ int @ SV846 @ SV582 ) @ SV972 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4406]) ).
thf(4667,plain,
! [SV583: $i,SV705: $i,SV338: $i] :
( ( ( ~ ( ~ ( ord_less @ real @ ( times_times @ real @ SV338 @ SV705 ) @ ( times_times @ real @ SV583 @ SV705 ) )
| ( ord_less @ real @ SV338 @ SV583 ) ) )
= $false )
| ( ( ord_less @ real @ ( zero_zero @ real ) @ SV705 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4407]) ).
thf(4668,plain,
! [SV705: $i,SV583: $i,SV338: $i] :
( ( ( ~ ( ~ ( ord_less @ real @ SV338 @ SV583 )
| ( ord_less @ real @ ( times_times @ real @ SV338 @ SV705 ) @ ( times_times @ real @ SV583 @ SV705 ) ) ) )
= $false )
| ( ( ord_less @ real @ ( zero_zero @ real ) @ SV705 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4407]) ).
thf(4669,plain,
! [SV1039: $i,SV706: $i] :
( ( ( plus_plus @ int @ ( power_power @ int @ SV706 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ SV1039 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4408]) ).
thf(4670,plain,
! [SV1065: $i,SV1040: $i,SV973: $i,SV848: $i,SV340: $i] :
( ( ( ( times_times @ SV340 @ ( times_times @ SV340 @ SV848 @ SV973 ) @ ( times_times @ SV340 @ SV1040 @ SV1065 ) )
= ( times_times @ SV340 @ ( times_times @ SV340 @ SV848 @ SV1040 ) @ ( times_times @ SV340 @ SV973 @ SV1065 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV340 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4409]) ).
thf(4671,plain,
! [SV584: $i,SV341: $i] :
( ( ( ord_less @ int @ ( bit0 @ SV341 ) @ ( bit0 @ SV584 ) )
= $false )
| ( ( ord_less @ int @ SV341 @ SV584 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4410]) ).
thf(4672,plain,
! [SV584: $i,SV341: $i] :
( ( ( ord_less @ int @ SV341 @ SV584 )
= $false )
| ( ( ord_less @ int @ ( bit0 @ SV341 ) @ ( bit0 @ SV584 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4411]) ).
thf(4673,plain,
! [SV585: $i,SV343: $i] :
( ( ( quadRes @ SV343 @ ( ti @ int @ SV585 ) )
= $false )
| ( ( quadRes @ SV343 @ SV585 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4412]) ).
thf(4674,plain,
! [SV585: $i,SV343: $i] :
( ( ( quadRes @ SV343 @ SV585 )
= $false )
| ( ( quadRes @ SV343 @ ( ti @ int @ SV585 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4413]) ).
thf(4675,plain,
! [SV586: $i,SV345: $i] :
( ( ( ord_less_eq @ int @ SV345 @ ( minus_minus @ int @ SV586 @ ( one_one @ int ) ) )
= $false )
| ( ( ord_less @ int @ SV345 @ SV586 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4414]) ).
thf(4676,plain,
! [SV586: $i,SV345: $i] :
( ( ( ord_less @ int @ SV345 @ SV586 )
= $false )
| ( ( ord_less_eq @ int @ SV345 @ ( minus_minus @ int @ SV586 @ ( one_one @ int ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4415]) ).
thf(4677,plain,
! [SV851: $i,SV347: $i] :
( ( ( ( ( power_power @ SV347 @ SV851 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= ( zero_zero @ SV347 ) )
| ( ( ti @ SV347 @ SV851 )
= ( zero_zero @ SV347 ) ) )
= $true )
| ( ( ring_11004092258visors @ SV347 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4416]) ).
thf(4678,plain,
! [SV851: $i,SV347: $i] :
( ( ( ( ( ti @ SV347 @ SV851 )
!= ( zero_zero @ SV347 ) )
| ( ( power_power @ SV347 @ SV851 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SV347 ) ) )
= $true )
| ( ( ring_11004092258visors @ SV347 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4417]) ).
thf(4679,plain,
! [SV852: $i,SV974: $i,SV348: $i] :
( ( ( ord_less @ SV348 @ ( zero_zero @ SV348 ) @ SV974 )
= $false )
| ( ( ord_less @ SV348 @ ( zero_zero @ SV348 ) @ ( power_power @ SV348 @ SV974 @ SV852 ) )
= $true )
| ( ( linordered_semidom @ SV348 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4418]) ).
thf(4680,plain,
! [SV853: $i,SV1041: $i,SV975: $i,SV349: $i] :
( ( ( ~ ( dvd_dvd @ SV349 @ SV975 @ SV1041 ) )
= $true )
| ( ( dvd_dvd @ SV349 @ SV975 @ ( times_times @ SV349 @ SV1041 @ SV853 ) )
= $true )
| ( ( comm_semiring_1 @ SV349 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4419]) ).
thf(4681,plain,
! [SV587: $i,SV350: $i] :
( ( ( ord_less_eq @ int @ ( plus_plus @ int @ SV350 @ ( one_one @ int ) ) @ SV587 )
= $false )
| ( ( ord_less @ int @ SV350 @ SV587 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4420]) ).
thf(4682,plain,
! [SV587: $i,SV350: $i] :
( ( ( ord_less @ int @ SV350 @ SV587 )
= $false )
| ( ( ord_less_eq @ int @ ( plus_plus @ int @ SV350 @ ( one_one @ int ) ) @ SV587 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4421]) ).
thf(4683,plain,
! [SV976: $i,SV854: $i,SV351: $i] :
( ( ( ( times_times @ SV351 @ SV854 @ SV976 )
= ( zero_zero @ SV351 ) )
= $false )
| ( ( ( ( ti @ SV351 @ SV854 )
= ( zero_zero @ SV351 ) )
| ( ( ti @ SV351 @ SV976 )
= ( zero_zero @ SV351 ) ) )
= $true )
| ( ( no_zero_divisors @ SV351 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4422]) ).
thf(4684,plain,
! [SV977: $i,SV855: $i,SV352: $i] :
( ( ( ~ ( ( ( plus_plus @ SV352 @ ( power_power @ SV352 @ SV855 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV352 @ SV977 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV352 ) )
| ~ ( ( ( ti @ SV352 @ SV855 )
!= ( zero_zero @ SV352 ) )
| ( ( ti @ SV352 @ SV977 )
!= ( zero_zero @ SV352 ) ) ) ) )
= $false )
| ( ( linordered_idom @ SV352 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4423]) ).
thf(4685,plain,
! [SV977: $i,SV855: $i,SV352: $i] :
( ( ( ~ ( ~ ~ ( ( ( ti @ SV352 @ SV855 )
!= ( zero_zero @ SV352 ) )
| ( ( ti @ SV352 @ SV977 )
!= ( zero_zero @ SV352 ) ) )
| ( ( plus_plus @ SV352 @ ( power_power @ SV352 @ SV855 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV352 @ SV977 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV352 ) ) ) )
= $false )
| ( ( linordered_idom @ SV352 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4423]) ).
thf(4686,plain,
! [SV856: $i,SV1042: $i,SV978: $i,SV353: $i] :
( ( ( ~ ( ord_less_eq @ SV353 @ SV978 @ SV1042 ) )
= $true )
| ( ( ~ ( ord_less_eq @ SV353 @ ( zero_zero @ SV353 ) @ SV978 )
| ( ord_less_eq @ SV353 @ ( power_power @ SV353 @ SV978 @ SV856 ) @ ( power_power @ SV353 @ SV1042 @ SV856 ) ) )
= $true )
| ( ( linordered_semidom @ SV353 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4424]) ).
thf(4687,plain,
! [SV355: $i] :
( ( ( semiring_0 @ SV355 )
= $false )
| ( ( power @ SV355 )
= $false )
| ( ( ! [SY1626: $i] :
~ ( ~ ( ( SY1626
!= ( zero_zero @ nat ) )
| ( ( power_power @ SV355 @ ( zero_zero @ SV355 ) @ SY1626 )
= ( one_one @ SV355 ) ) )
| ~ ( ~ ( ( SY1626
!= ( zero_zero @ nat ) ) )
| ( ( power_power @ SV355 @ ( zero_zero @ SV355 ) @ SY1626 )
= ( zero_zero @ SV355 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4426]) ).
thf(4688,plain,
! [SV980: $i,SV858: $i,SV1044: $i,SV358: $i] :
( ( ( ~ ( ord_less @ SV358 @ ( one_one @ SV358 ) @ SV1044 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( ord_less_eq @ SV358 @ ( power_power @ SV358 @ SV1044 @ SV858 ) @ ( power_power @ SV358 @ SV1044 @ SV980 ) )
| ( ord_less_eq @ nat @ SV858 @ SV980 ) )
| ~ ( ~ ( ord_less_eq @ nat @ SV858 @ SV980 )
| ( ord_less_eq @ SV358 @ ( power_power @ SV358 @ SV1044 @ SV858 ) @ ( power_power @ SV358 @ SV1044 @ SV980 ) ) ) ) )
= $true )
| ( ( linordered_semidom @ SV358 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4427]) ).
thf(4689,plain,
! [SV591: $i,SV360: $i] :
( ( ( zcong @ SV360 @ ( zero_zero @ int ) @ SV591 )
= $false )
| ( ( dvd_dvd @ int @ SV591 @ SV360 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4428]) ).
thf(4690,plain,
! [SV360: $i,SV591: $i] :
( ( ( dvd_dvd @ int @ SV591 @ SV360 )
= $false )
| ( ( zcong @ SV360 @ ( zero_zero @ int ) @ SV591 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4429]) ).
thf(4691,plain,
! [SV361: $i,SV859: $i,SV981: $i] :
( ( ( ord_less_eq @ int @ pls @ SV981 )
= $false )
| ( ( ~ ( ord_less_eq @ int @ pls @ SV859 )
| ( ( times_times @ SV361 @ ( number_number_of @ SV361 @ SV981 ) @ ( number_number_of @ SV361 @ SV859 ) )
= ( number_number_of @ SV361 @ ( times_times @ int @ SV981 @ SV859 ) ) ) )
= $true )
| ( ( number_semiring @ SV361 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4430]) ).
thf(4692,plain,
! [SV592: $i,SV710: $i,SV362: $i] :
( ( ( ~ ( ( ( times_times @ real @ SV362 @ SV710 )
!= ( times_times @ real @ SV592 @ SV710 ) )
| ( SV362 = SV592 ) )
| ~ ( ( SV362 != SV592 )
| ( ( times_times @ real @ SV362 @ SV710 )
= ( times_times @ real @ SV592 @ SV710 ) ) ) )
= $false )
| ( ( SV710
= ( zero_zero @ real ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4431]) ).
thf(4693,plain,
! [SV860: $i,SV363: $i,SV982: $i] :
( ( ( ~ ( ( SV982
!= ( zero_zero @ nat ) )
| ( ( power_power @ SV363 @ SV860 @ SV982 )
= ( one_one @ SV363 ) ) ) )
= $false )
| ( ( power @ SV363 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4432]) ).
thf(4694,plain,
! [SV860: $i,SV363: $i,SV982: $i] :
( ( ( ~ ( ~ ( ( SV982
!= ( zero_zero @ nat ) ) )
| ( ( power_power @ SV363 @ SV860 @ SV982 )
= ( times_times @ SV363 @ SV860 @ ( power_power @ SV363 @ SV860 @ ( minus_minus @ nat @ SV982 @ ( one_one @ nat ) ) ) ) ) ) )
= $false )
| ( ( power @ SV363 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4432]) ).
thf(4695,plain,
! [SV366: $i,SV595: $i] :
( ( ( ord_less @ int @ SV595 @ pls )
= $false )
| ( ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV595 ) @ ( number_number_of @ nat @ SV366 ) )
= ( number_number_of @ nat @ SV366 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4433]) ).
thf(4696,plain,
! [SV366: $i,SV595: $i] :
( ( ( ~ ( ord_less @ int @ SV595 @ pls ) )
= $false )
| ( ( ~ ( ~ ( ~ ( ord_less @ int @ SV366 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV595 ) @ ( number_number_of @ nat @ SV366 ) )
= ( number_number_of @ nat @ SV595 ) ) )
| ~ ( ~ ~ ( ord_less @ int @ SV366 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV595 ) @ ( number_number_of @ nat @ SV366 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SV595 @ SV366 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4434]) ).
thf(4697,plain,
! [SV861: $i,SV367: $i,SV1045: $i,SV983: $i] :
( ( ( ~ ( ord_less_eq @ nat @ SV983 @ SV1045 ) )
= $true )
| ( ( dvd_dvd @ SV367 @ ( power_power @ SV367 @ SV861 @ SV983 ) @ ( power_power @ SV367 @ SV861 @ SV1045 ) )
= $true )
| ( ( comm_semiring_1 @ SV367 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4435]) ).
thf(4698,plain,
! [SV368: $i,SV596: $i] :
( ( ( SV596
= ( zero_zero @ nat ) )
= $false )
| ( ( ( times_times @ nat @ SV596 @ SV368 )
= ( zero_zero @ nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4436]) ).
thf(4699,plain,
! [SV368: $i,SV596: $i] :
( ( ( SV596
!= ( zero_zero @ nat ) )
= $false )
| ( ( ( times_times @ nat @ SV596 @ SV368 )
= ( plus_plus @ nat @ SV368 @ ( times_times @ nat @ ( minus_minus @ nat @ SV596 @ ( one_one @ nat ) ) @ SV368 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4437]) ).
thf(4700,plain,
! [SV597: $i,SV713: $i,SV369: $i] :
( ( ( dvd_dvd @ int @ SV369 @ SV713 )
= $false )
| ( ( dvd_dvd @ int @ SV369 @ SV597 )
= $true )
| ( ( dvd_dvd @ int @ SV369 @ ( minus_minus @ int @ SV597 @ SV713 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4438]) ).
thf(4701,plain,
! [SV598: $i,SV370: $i] :
( ( ( ( bit1 @ SV370 )
= ( bit1 @ SV598 ) )
= $false )
| ( ( ( ti @ int @ SV370 )
= ( ti @ int @ SV598 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4439]) ).
thf(4702,plain,
! [SV598: $i,SV370: $i] :
( ( ( ( ti @ int @ SV370 )
= ( ti @ int @ SV598 ) )
= $false )
| ( ( ( bit1 @ SV370 )
= ( bit1 @ SV598 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4440]) ).
thf(4703,plain,
! [SV600: $i,SV373: $i] :
( ( ( ord_less_eq @ int @ ( bit0 @ SV373 ) @ ( bit0 @ SV600 ) )
= $false )
| ( ( ord_less_eq @ int @ SV373 @ SV600 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4443]) ).
thf(4704,plain,
! [SV600: $i,SV373: $i] :
( ( ( ord_less_eq @ int @ SV373 @ SV600 )
= $false )
| ( ( ord_less_eq @ int @ ( bit0 @ SV373 ) @ ( bit0 @ SV600 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4444]) ).
thf(4705,plain,
! [SV601: $i,SV374: $i] :
( ( ( ( times_times @ nat @ SV374 @ SV601 )
= ( one_one @ nat ) )
= $false )
| ( ( ~ ( ( SV374
!= ( one_one @ nat ) )
| ( SV601
!= ( one_one @ nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4445]) ).
thf(4706,plain,
! [SV601: $i,SV374: $i] :
( ( ( ~ ( ( SV374
!= ( one_one @ nat ) )
| ( SV601
!= ( one_one @ nat ) ) ) )
= $false )
| ( ( ( times_times @ nat @ SV374 @ SV601 )
= ( one_one @ nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4446]) ).
thf(4707,plain,
! [SV864: $i,SV985: $i,SV375: $i] :
( ( ( ord_less @ SV375 @ ( one_one @ SV375 ) @ SV985 )
= $false )
| ( ( ord_less @ SV375 @ ( power_power @ SV375 @ SV985 @ SV864 ) @ ( times_times @ SV375 @ SV985 @ ( power_power @ SV375 @ SV985 @ SV864 ) ) )
= $true )
| ( ( linordered_semidom @ SV375 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4447]) ).
thf(4708,plain,
! [SV865: $i,SV986: $i,SV376: $i] :
( ( ( ( ti @ SV376 @ SV986 )
!= ( zero_zero @ SV376 ) )
= $false )
| ( ( ( power_power @ SV376 @ SV986 @ SV865 )
!= ( zero_zero @ SV376 ) )
= $true )
| ( ( ring_11004092258visors @ SV376 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4448]) ).
thf(4709,plain,
! [SV1066: $i,SV1047: $i,SV987: $i,SV867: $i,SV380: $i] :
( ( ( ( times_times @ SV380 @ ( times_times @ SV380 @ SV867 @ SV987 ) @ ( times_times @ SV380 @ SV1047 @ SV1066 ) )
= ( times_times @ SV380 @ SV1047 @ ( times_times @ SV380 @ ( times_times @ SV380 @ SV867 @ SV987 ) @ SV1066 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV380 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4450]) ).
thf(4710,plain,
! [SV604: $i,SV382: $i,SV716: $i] :
( ( ( dvd_dvd @ int @ SV716 @ ( times_times @ int @ SV382 @ SV604 ) )
= $false )
| ( ( ( dvd_dvd @ int @ SV716 @ SV382 )
| ( dvd_dvd @ int @ SV716 @ SV604 ) )
= $true )
| ( ( zprime @ SV716 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4451]) ).
thf(4711,plain,
! [SV869: $i,SV383: $i,SV1048: $i,SV988: $i] :
( ( ( ~ ( ord_less @ nat @ SV988 @ SV1048 ) )
= $true )
| ( ( ~ ( ord_less @ SV383 @ ( one_one @ SV383 ) @ SV869 )
| ( ord_less @ SV383 @ ( power_power @ SV383 @ SV869 @ SV988 ) @ ( power_power @ SV383 @ SV869 @ SV1048 ) ) )
= $true )
| ( ( linordered_semidom @ SV383 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4452]) ).
thf(4712,plain,
! [SV605: $i,SV717: $i,SV384: $i] :
( ( ( ord_less @ int @ SV384 @ SV717 )
= $false )
| ( ( ( ord_less_eq @ int @ SV605 @ SV384 )
| ( ord_less_eq @ int @ SV384 @ SV605 ) )
= $true )
| ( ( ord_less @ int @ SV605 @ SV717 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4453]) ).
thf(4713,plain,
! [SV870: $i,SV718: $i,SV606: $i,SV385: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV385 @ SV606 ) )
= $true )
| ( ( ord_less @ int @ ( plus_plus @ int @ SV718 @ SV385 ) @ ( plus_plus @ int @ SV870 @ SV606 ) )
= $true )
| ( ( ord_less @ int @ SV718 @ SV870 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4454]) ).
thf(4714,plain,
! [SV386: $i] :
( ( ( ring @ SV386 )
= $false )
| ( ( number @ SV386 )
= $false )
| ( ( ! [SY1686: $i,SY1687: $i,SY1688: $i] :
( ( times_times @ SV386 @ ( minus_minus @ SV386 @ SY1686 @ SY1687 ) @ ( number_number_of @ SV386 @ SY1688 ) )
= ( minus_minus @ SV386 @ ( times_times @ SV386 @ SY1686 @ ( number_number_of @ SV386 @ SY1688 ) ) @ ( times_times @ SV386 @ SY1687 @ ( number_number_of @ SV386 @ SY1688 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4455]) ).
thf(4715,plain,
! [SV608: $i,SV388: $i] :
( ( ( zcong @ SV388 @ ( one_one @ int ) @ SV608 )
= $false )
| ( ( zcong @ SV388 @ ( number_number_of @ int @ min ) @ SV608 )
= $false )
| ( ( ord_less @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV608 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4457]) ).
thf(4716,plain,
! [SV389: $i,SV609: $i] :
( ( ( zcong @ SV609 @ ( zero_zero @ int ) @ SV389 )
= $false )
| ( ( ord_less @ int @ SV609 @ SV389 )
= $false )
| ( ( ord_less @ int @ ( zero_zero @ int ) @ SV609 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4458]) ).
thf(4717,plain,
! [SV390: $i,SV610: $i] :
( ( ( SV610
= ( zero_zero @ nat ) )
= $false )
| ( ( ( power_power @ nat @ SV390 @ SV610 )
= ( one_one @ nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4459]) ).
thf(4718,plain,
! [SV390: $i,SV610: $i] :
( ( ( SV610
!= ( zero_zero @ nat ) )
= $false )
| ( ( ( power_power @ nat @ SV390 @ SV610 )
= ( times_times @ nat @ SV390 @ ( power_power @ nat @ SV390 @ ( minus_minus @ nat @ SV610 @ ( one_one @ nat ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4460]) ).
thf(4719,plain,
! [SV719: $i,SV611: $i,SV391: $i] :
( ( ( dvd_dvd @ int @ SV391 @ SV611 )
= $false )
| ( ( dvd_dvd @ int @ SV391 @ ( power_power @ int @ SV611 @ SV719 ) )
= $true )
| ( ( ord_less @ nat @ ( zero_zero @ nat ) @ SV719 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4461]) ).
thf(4720,plain,
! [SV612: $i,SV392: $i] :
( ( ( ord_less @ nat @ ( number_number_of @ nat @ SV392 ) @ ( number_number_of @ nat @ SV612 ) )
= $false )
| ( ( ~ ( ~ ( ~ ( ord_less @ int @ SV392 @ SV612 )
| ( ord_less @ int @ pls @ SV612 ) )
| ~ ( ord_less @ int @ SV392 @ SV612 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4462]) ).
thf(4721,plain,
! [SV612: $i,SV392: $i] :
( ( ( ~ ( ~ ( ~ ( ord_less @ int @ SV392 @ SV612 )
| ( ord_less @ int @ pls @ SV612 ) )
| ~ ( ord_less @ int @ SV392 @ SV612 ) ) )
= $false )
| ( ( ord_less @ nat @ ( number_number_of @ nat @ SV392 ) @ ( number_number_of @ nat @ SV612 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4463]) ).
thf(4722,plain,
! [SV614: $i,SV396: $i] :
( ( ( zcong @ SV396 @ SV614 @ ( zero_zero @ int ) )
= $false )
| ( ( ( ti @ int @ SV396 )
= ( ti @ int @ SV614 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4467]) ).
thf(4723,plain,
! [SV614: $i,SV396: $i] :
( ( ( ( ti @ int @ SV396 )
= ( ti @ int @ SV614 ) )
= $false )
| ( ( zcong @ SV396 @ SV614 @ ( zero_zero @ int ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4468]) ).
thf(4724,plain,
! [SV615: $i,SV397: $i] :
( ( ( ( plus_plus @ real @ ( times_times @ real @ SV397 @ SV397 ) @ ( times_times @ real @ SV615 @ SV615 ) )
= ( zero_zero @ real ) )
= $false )
| ( ( ~ ( ( SV397
!= ( zero_zero @ real ) )
| ( SV615
!= ( zero_zero @ real ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4469]) ).
thf(4725,plain,
! [SV615: $i,SV397: $i] :
( ( ( ~ ( ( SV397
!= ( zero_zero @ real ) )
| ( SV615
!= ( zero_zero @ real ) ) ) )
= $false )
| ( ( ( plus_plus @ real @ ( times_times @ real @ SV397 @ SV397 ) @ ( times_times @ real @ SV615 @ SV615 ) )
= ( zero_zero @ real ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4470]) ).
thf(4726,plain,
! [SV1067: $i,SV1049: $i,SV990: $i,SV873: $i,SV399: $i] :
( ( ( ( plus_plus @ SV399 @ ( times_times @ SV399 @ SV873 @ SV990 ) @ ( plus_plus @ SV399 @ ( times_times @ SV399 @ SV1049 @ SV990 ) @ SV1067 ) )
= ( plus_plus @ SV399 @ ( times_times @ SV399 @ ( plus_plus @ SV399 @ SV873 @ SV1049 ) @ SV990 ) @ SV1067 ) )
= $true )
| ( ( semiring @ SV399 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4473]) ).
thf(4727,plain,
( ( ( ( plus_plus @ int @ ( power_power @ int @ sK4_SX0 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ sK6_SY2112 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) )
= $false )
| ( ( t
= ( one_one @ int ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4474]) ).
thf(4728,plain,
! [SV722: $i,SV617: $i,SV405: $i] :
( ( ( ~ ( zcong @ SV405 @ SV617 @ SV722 ) )
= $true )
| ( ( ~ ! [SY1940: $i] :
( ( ti @ int @ SV617 )
!= ( plus_plus @ int @ SV405 @ ( times_times @ int @ SV722 @ SY1940 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4476]) ).
thf(4729,plain,
! [SV722: $i,SV405: $i,SV617: $i] :
( ( ( ~ ~ ! [SY1941: $i] :
( ( ti @ int @ SV617 )
!= ( plus_plus @ int @ SV405 @ ( times_times @ int @ SV722 @ SY1941 ) ) ) )
= $true )
| ( ( zcong @ SV405 @ SV617 @ SV722 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4477]) ).
thf(4730,plain,
! [SV407: $i] :
( ( ( ~ ( ( ( ti @ int @ SV407 )
!= ( number_number_of @ int @ ( bit1 @ ( bit1 @ pls ) ) ) ) ) )
= $true )
| ( ( ord_less_eq @ int @ ( number_number_of @ int @ ( bit1 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SV407 )
= $true )
| ( ( ( ti @ int @ SV407 )
= ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true )
| ( ( zprime @ SV407 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4478]) ).
thf(4731,plain,
! [SV620: $i,SV410: $i,SV725: $i] :
( ( ( ord_less @ int @ SV725 @ SV410 )
= $false )
| ( ( ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV410 )
| ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV620 ) )
= $true )
| ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( times_times @ int @ SV410 @ SV620 ) @ SV725 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4479]) ).
thf(4732,plain,
! [SV621: $i,SV413: $i] :
( ( ( ( times_times @ int @ SV413 @ SV621 )
= ( one_one @ int ) )
= $false )
| ( ( ~ ( ( ( ti @ int @ SV413 )
!= ( one_one @ int ) )
| ( ( ti @ int @ SV621 )
!= ( one_one @ int ) ) )
| ~ ( ( ( ti @ int @ SV413 )
!= ( number_number_of @ int @ min ) )
| ( ( ti @ int @ SV621 )
!= ( number_number_of @ int @ min ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4481]) ).
thf(4733,plain,
! [SV621: $i,SV413: $i] :
( ( ( ~ ( ( ( ti @ int @ SV413 )
!= ( one_one @ int ) )
| ( ( ti @ int @ SV621 )
!= ( one_one @ int ) ) )
| ~ ( ( ( ti @ int @ SV413 )
!= ( number_number_of @ int @ min ) )
| ( ( ti @ int @ SV621 )
!= ( number_number_of @ int @ min ) ) ) )
= $false )
| ( ( ( times_times @ int @ SV413 @ SV621 )
= ( one_one @ int ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4482]) ).
thf(4734,plain,
! [SV416: $i] :
( ( ( number @ SV416 )
= $false )
| ( ( monoid_mult @ SV416 )
= $false )
| ( ( ! [SY1732: $i] :
( ( power_power @ SV416 @ ( number_number_of @ SV416 @ SY1732 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times @ SV416 @ ( number_number_of @ SV416 @ SY1732 ) @ ( number_number_of @ SV416 @ SY1732 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4483]) ).
thf(4735,plain,
! [SV881: $i,SV994: $i,SV417: $i] :
( ( ( ord_less_eq @ SV417 @ SV994 @ ( zero_zero @ SV417 ) )
= $false )
| ( ( ~ ( ord_less_eq @ SV417 @ ( zero_zero @ SV417 ) @ SV881 )
| ( ord_less_eq @ SV417 @ ( times_times @ SV417 @ SV994 @ SV881 ) @ ( zero_zero @ SV417 ) ) )
= $true )
| ( ( ordere453448008miring @ SV417 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4484]) ).
thf(4736,plain,
! [SV622: $i,SV418: $i] :
( ( ( ord_less_eq @ int @ ( bit1 @ SV418 ) @ ( bit0 @ SV622 ) )
= $false )
| ( ( ord_less @ int @ SV418 @ SV622 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4485]) ).
thf(4737,plain,
! [SV622: $i,SV418: $i] :
( ( ( ord_less @ int @ SV418 @ SV622 )
= $false )
| ( ( ord_less_eq @ int @ ( bit1 @ SV418 ) @ ( bit0 @ SV622 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4486]) ).
thf(4738,plain,
! [SV419: $i,SV623: $i] :
( ( ( ( ( times_times @ int @ SV623 @ SV419 )
!= ( one_one @ int ) )
| ~ ( ( ( ti @ int @ SV623 )
!= ( one_one @ int ) )
| ( ( ti @ int @ SV419 )
!= ( one_one @ int ) ) ) )
= $true )
| ( ( ord_less @ int @ ( zero_zero @ int ) @ SV623 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4487]) ).
thf(4739,plain,
! [SV419: $i,SV623: $i] :
( ( ( ~ ~ ( ( ( ti @ int @ SV623 )
!= ( one_one @ int ) )
| ( ( ti @ int @ SV419 )
!= ( one_one @ int ) ) )
| ( ( times_times @ int @ SV623 @ SV419 )
= ( one_one @ int ) ) )
= $true )
| ( ( ord_less @ int @ ( zero_zero @ int ) @ SV623 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4488]) ).
thf(4740,plain,
! [SV624: $i,SV420: $i] :
( ( ( ord_less_eq @ int @ ( bit0 @ SV420 ) @ ( bit1 @ SV624 ) )
= $false )
| ( ( ord_less_eq @ int @ SV420 @ SV624 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4489]) ).
thf(4741,plain,
! [SV624: $i,SV420: $i] :
( ( ( ord_less_eq @ int @ SV420 @ SV624 )
= $false )
| ( ( ord_less_eq @ int @ ( bit0 @ SV420 ) @ ( bit1 @ SV624 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4490]) ).
thf(4742,plain,
! [SV421: $i,SV625: $i] :
( ( ( ord_less @ int @ SV625 @ pls )
= $false )
| ( ( ( times_times @ nat @ ( number_number_of @ nat @ SV625 ) @ ( number_number_of @ nat @ SV421 ) )
= ( zero_zero @ nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4491]) ).
thf(4743,plain,
! [SV421: $i,SV625: $i] :
( ( ( ~ ( ord_less @ int @ SV625 @ pls ) )
= $false )
| ( ( ( times_times @ nat @ ( number_number_of @ nat @ SV625 ) @ ( number_number_of @ nat @ SV421 ) )
= ( number_number_of @ nat @ ( times_times @ int @ SV625 @ SV421 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4492]) ).
thf(4744,plain,
! [SV1052: $i,SV995: $i,SV882: $i,SV726: $i,SV626: $i,SV422: $i] :
( ( ( ( plus_plus @ int @ ( times_times @ int @ SV422 @ SV626 ) @ SV726 )
!= ( plus_plus @ int @ ( times_times @ int @ SV882 @ SV995 ) @ SV1052 ) )
= $true )
| ( ( ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( times_times @ int @ SV882 @ SV995 ) @ SV1052 ) )
| ~ ( ord_less @ int @ SV1052 @ SV882 )
| ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV726 )
| ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV882 )
| ~ ( ord_less_eq @ int @ SV882 @ SV422 )
| ( ord_less_eq @ int @ SV626 @ SV995 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4493]) ).
thf(4745,plain,
! [SV423: $i] :
( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( times_times @ real @ SV423 @ SV423 ) )
= $true )
| ( ( SV423
= ( zero_zero @ real ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4494]) ).
thf(4746,plain,
! [SV423: $i] :
( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( times_times @ real @ SV423 @ SV423 ) )
= $false )
| ( ( SV423
= ( zero_zero @ real ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4495]) ).
thf(4747,plain,
! [SV627: $i,SV424: $i] :
( ( ( ord_less @ int @ ( bit1 @ SV424 ) @ ( bit1 @ SV627 ) )
= $false )
| ( ( ord_less @ int @ SV424 @ SV627 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4496]) ).
thf(4748,plain,
! [SV627: $i,SV424: $i] :
( ( ( ord_less @ int @ SV424 @ SV627 )
= $false )
| ( ( ord_less @ int @ ( bit1 @ SV424 ) @ ( bit1 @ SV627 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4497]) ).
thf(4749,plain,
! [SV728: $i,SV629: $i,SV427: $i] :
( ( ( ~ ( zcong @ ( ti @ int @ SV427 ) @ SV629 @ SV728 ) )
= $true )
| ( ( zcong @ SV427 @ SV629 @ SV728 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4498]) ).
thf(4750,plain,
! [SV728: $i,SV629: $i,SV427: $i] :
( ( ( ~ ( zcong @ SV427 @ SV629 @ SV728 ) )
= $true )
| ( ( zcong @ ( ti @ int @ SV427 ) @ SV629 @ SV728 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4499]) ).
thf(4751,plain,
! [SV630: $i,SV428: $i] :
( ( ( zcong @ SV428 @ ( zero_zero @ int ) @ SV630 )
= $false )
| ( ( dvd_dvd @ int @ SV630 @ SV428 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4500]) ).
thf(4752,plain,
! [SV428: $i,SV630: $i] :
( ( ( dvd_dvd @ int @ SV630 @ SV428 )
= $false )
| ( ( zcong @ SV428 @ ( zero_zero @ int ) @ SV630 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4501]) ).
thf(4753,plain,
! [SV631: $i,SV429: $i] :
( ( ( ( power_power @ nat @ SV429 @ SV631 )
= ( one_one @ nat ) )
= $false )
| ( ( ( SV429
= ( one_one @ nat ) )
| ( SV631
= ( zero_zero @ nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4502]) ).
thf(4754,plain,
! [SV631: $i,SV429: $i] :
( ( ( ( SV429
= ( one_one @ nat ) )
| ( SV631
= ( zero_zero @ nat ) ) )
= $false )
| ( ( ( power_power @ nat @ SV429 @ SV631 )
= ( one_one @ nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4503]) ).
thf(4755,plain,
! [SV887: $i,SV433: $i,SV1053: $i,SV997: $i] :
( ( ( ~ ( ord_less @ nat @ SV997 @ SV1053 ) )
= $true )
| ( ( ~ ( ord_less @ SV433 @ ( zero_zero @ SV433 ) @ SV887 )
| ~ ( ord_less @ SV433 @ SV887 @ ( one_one @ SV433 ) )
| ( ord_less @ SV433 @ ( power_power @ SV433 @ SV887 @ SV1053 ) @ ( power_power @ SV433 @ SV887 @ SV997 ) ) )
= $true )
| ( ( linordered_semidom @ SV433 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4505]) ).
thf(4756,plain,
! [SV998: $i,SV888: $i,SV1068: $i,SV1054: $i,SV434: $i] :
( ( ( ! [SY2213: $i] :
( ~ ( ( ( ti @ SV434 @ SY2213 )
!= ( zero_zero @ SV434 ) ) )
| ~ ~ ( ( ( ti @ SV434 @ SV1054 )
!= ( ti @ SV434 @ SV1068 ) )
| ~ ( ( ( ti @ SV434 @ SV888 )
!= ( ti @ SV434 @ SV998 ) ) ) )
| ( ( plus_plus @ SV434 @ SV1054 @ ( times_times @ SV434 @ SY2213 @ SV888 ) )
!= ( plus_plus @ SV434 @ SV1068 @ ( times_times @ SV434 @ SY2213 @ SV998 ) ) ) ) )
= $true )
| ( ( semiri456707255roduct @ SV434 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4506]) ).
thf(4757,plain,
! [SV732: $i,SV890: $i,SV481: $i,SV647: $i,SV79: $i] :
( ( ( ~ ( ~ ( zcong @ SV79 @ ( times_times @ int @ SV647 @ SV481 ) @ SV890 )
| ( zcong @ SV79 @ ( times_times @ int @ SV732 @ SV481 ) @ SV890 ) )
| ~ ( ~ ( zcong @ SV79 @ ( times_times @ int @ SV732 @ SV481 ) @ SV890 )
| ( zcong @ SV79 @ ( times_times @ int @ SV647 @ SV481 ) @ SV890 ) ) )
= $false )
| ( ( zcong @ SV647 @ SV732 @ SV890 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4508]) ).
thf(4758,plain,
! [SV482: $i,SV80: $i] :
( ( ( ord_less @ int @ SV80 @ SV482 )
= $true )
| ( ( ( ti @ int @ SV80 )
= ( ti @ int @ SV482 ) )
= $true )
| ( ( ord_less @ int @ SV80 @ ( plus_plus @ int @ SV482 @ ( one_one @ int ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4509]) ).
thf(4759,plain,
! [SV482: $i,SV80: $i] :
( ( ( ord_less @ int @ SV80 @ SV482 )
= $false )
| ( ( ord_less @ int @ SV80 @ ( plus_plus @ int @ SV482 @ ( one_one @ int ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4510]) ).
thf(4760,plain,
! [SV482: $i,SV80: $i] :
( ( ( ( ti @ int @ SV80 )
= ( ti @ int @ SV482 ) )
= $false )
| ( ( ord_less @ int @ SV80 @ ( plus_plus @ int @ SV482 @ ( one_one @ int ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4510]) ).
thf(4761,plain,
! [SV891: $i,SV733: $i,SV82: $i] :
( ( ( ~ ( ord_less_eq @ SV82 @ SV733 @ ( zero_zero @ SV82 ) ) )
= $true )
| ( ( ord_less_eq @ SV82 @ ( times_times @ SV82 @ SV891 @ SV733 ) @ ( zero_zero @ SV82 ) )
= $true )
| ( ( ord_less_eq @ SV82 @ ( zero_zero @ SV82 ) @ SV891 )
= $false )
| ( ( ordere453448008miring @ SV82 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4511]) ).
thf(4762,plain,
! [SV894: $i,SV737: $i,SV87: $i] :
( ( ( ~ ( ord_less_eq @ SV87 @ SV737 @ ( zero_zero @ SV87 ) ) )
= $true )
| ( ( ord_less_eq @ SV87 @ ( times_times @ SV87 @ SV737 @ SV894 ) @ ( zero_zero @ SV87 ) )
= $true )
| ( ( ord_less_eq @ SV87 @ ( zero_zero @ SV87 ) @ SV894 )
= $false )
| ( ( ordere453448008miring @ SV87 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4512]) ).
thf(4763,plain,
! [SV739: $i,SV896: $i,SV90: $i] :
( ( ( ( ti @ SV90 @ SV896 )
= ( zero_zero @ SV90 ) )
= $true )
| ( ( ~ ( ( ( ti @ SV90 @ SV739 )
!= ( zero_zero @ SV90 ) ) )
| ( ( times_times @ SV90 @ SV896 @ SV739 )
!= ( zero_zero @ SV90 ) ) )
= $true )
| ( ( no_zero_divisors @ SV90 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4513]) ).
thf(4764,plain,
! [SV652: $i,SV490: $i,SV101: $i] :
( ( ( zcong @ ( power_power @ int @ SV101 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SV490 @ SV652 )
= $false )
| ( ( ~ ( dvd_dvd @ int @ SV652 @ SV101 ) )
= $true )
| ( ( zcong @ SV490 @ ( zero_zero @ int ) @ SV652 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4517]) ).
thf(4765,plain,
! [SV743: $i,SV900: $i,SV102: $i] :
( ( ( ~ ( ord_less @ SV102 @ SV900 @ ( one_one @ SV102 ) ) )
= $true )
| ( ( ord_less @ SV102 @ ( times_times @ SV102 @ SV900 @ ( power_power @ SV102 @ SV900 @ SV743 ) ) @ ( power_power @ SV102 @ SV900 @ SV743 ) )
= $true )
| ( ( ord_less @ SV102 @ ( zero_zero @ SV102 ) @ SV900 )
= $false )
| ( ( linordered_semidom @ SV102 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4518]) ).
thf(4766,plain,
! [SV655: $i,SV901: $i,SV108: $i,SV494: $i,SV744: $i] :
( ( ( ( ti @ int @ SV744 )
!= ( ti @ int @ SV494 ) )
= $true )
| ( ( ~ ( zcong @ SV494 @ SV108 @ SV901 )
| ( zcong @ SV655 @ SV108 @ SV901 ) )
= $true )
| ( ( zcong @ SV655 @ SV744 @ SV901 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4521]) ).
thf(4767,plain,
! [SV656: $i,SV495: $i,SV109: $i] :
( ( ( ( ti @ int @ SV109 )
= ( zero_zero @ int ) )
= $true )
| ( ( dvd_dvd @ int @ SV495 @ SV656 )
= $true )
| ( ( dvd_dvd @ int @ ( times_times @ int @ SV109 @ SV495 ) @ ( times_times @ int @ SV109 @ SV656 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4522]) ).
thf(4768,plain,
! [SV746: $i,SV117: $i,SV1004: $i,SV902: $i] :
( ( ( ord_less_eq @ nat @ SV902 @ SV1004 )
= $false )
| ( ( ~ ( ord_less_eq @ SV117 @ ( zero_zero @ SV117 ) @ SV746 )
| ~ ( ord_less_eq @ SV117 @ SV746 @ ( one_one @ SV117 ) )
| ( ord_less_eq @ SV117 @ ( power_power @ SV117 @ SV746 @ SV1004 ) @ ( power_power @ SV117 @ SV746 @ SV902 ) ) )
= $true )
| ( ( linordered_semidom @ SV117 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4525]) ).
thf(4769,plain,
! [SV1069: $i,SV120: $i] :
( ( ( ~ ( ~ ( ~ ( ord_less @ SV120 @ ( one_one @ SV120 ) @ ( number_number_of @ SV120 @ SV1069 ) )
| ( ord_less @ int @ ( bit1 @ pls ) @ SV1069 ) )
| ~ ( ~ ( ord_less @ int @ ( bit1 @ pls ) @ SV1069 )
| ( ord_less @ SV120 @ ( one_one @ SV120 ) @ ( number_number_of @ SV120 @ SV1069 ) ) ) ) )
= $true )
| ( ( number_ring @ SV120 )
= $false )
| ( ( linordered_idom @ SV120 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4527]) ).
thf(4770,plain,
( ( ( ( plus_plus @ int @ ( power_power @ int @ sK3_SX0 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ sK5_SY1968 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) )
= $true )
| ( ( ord_less @ int @ ( one_one @ int ) @ t )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4530]) ).
thf(4771,plain,
! [SV1070: $i,SV123: $i] :
( ( ( ~ ( ~ ( ~ ( ord_less_eq @ SV123 @ ( number_number_of @ SV123 @ SV1070 ) @ ( one_one @ SV123 ) )
| ( ord_less_eq @ int @ SV1070 @ ( bit1 @ pls ) ) )
| ~ ( ~ ( ord_less_eq @ int @ SV1070 @ ( bit1 @ pls ) )
| ( ord_less_eq @ SV123 @ ( number_number_of @ SV123 @ SV1070 ) @ ( one_one @ SV123 ) ) ) ) )
= $true )
| ( ( number_ring @ SV123 )
= $false )
| ( ( linordered_idom @ SV123 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4531]) ).
thf(4772,plain,
! [SV903: $i,SV747: $i,SV1057: $i,SV1005: $i,SV124: $i] :
( ( ( ~ ( dvd_dvd @ SV124 @ SV1005 @ SV1057 ) )
= $true )
| ( ( ~ ( dvd_dvd @ SV124 @ SV747 @ SV903 )
| ( dvd_dvd @ SV124 @ ( times_times @ SV124 @ SV1005 @ SV747 ) @ ( times_times @ SV124 @ SV1057 @ SV903 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV124 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4532]) ).
thf(4773,plain,
! [SV503: $i,SV753: $i,SV660: $i,SV132: $i,SV907: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV907 @ ( zero_zero @ int ) ) )
= $true )
| ( ( ~ ( ord_less @ int @ SV132 @ SV907 )
| ~ ( ord_less @ int @ SV132 @ SV660 )
| ( ord_less_eq @ int @ SV753 @ SV503 ) )
= $true )
| ( ( ord_less_eq @ int @ ( plus_plus @ int @ ( times_times @ int @ SV132 @ SV503 ) @ SV660 ) @ ( plus_plus @ int @ ( times_times @ int @ SV132 @ SV753 ) @ SV907 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4534]) ).
thf(4774,plain,
! [SV1071: $i,SV134: $i] :
( ( ( ~ ( ~ ( ~ ( ord_less @ SV134 @ ( number_number_of @ SV134 @ SV1071 ) @ ( one_one @ SV134 ) )
| ( ord_less @ int @ SV1071 @ ( bit1 @ pls ) ) )
| ~ ( ~ ( ord_less @ int @ SV1071 @ ( bit1 @ pls ) )
| ( ord_less @ SV134 @ ( number_number_of @ SV134 @ SV1071 ) @ ( one_one @ SV134 ) ) ) ) )
= $true )
| ( ( number_ring @ SV134 )
= $false )
| ( ( linordered_idom @ SV134 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4535]) ).
thf(4775,plain,
! [SV505: $i,SV135: $i] :
( ( ( ~ ~ ( ord_less_eq @ int @ SV135 @ SV505 ) )
= $true )
| ( ( ord_less_eq @ int @ SV135 @ pls )
= $true )
| ( ( ord_less_eq @ nat @ ( number_number_of @ nat @ SV135 ) @ ( number_number_of @ nat @ SV505 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4536]) ).
thf(4776,plain,
! [SV505: $i,SV135: $i] :
( ( ( ~ ~ ( ord_less_eq @ int @ SV135 @ SV505 ) )
= $false )
| ( ( ord_less_eq @ nat @ ( number_number_of @ nat @ SV135 ) @ ( number_number_of @ nat @ SV505 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4537]) ).
thf(4777,plain,
! [SV505: $i,SV135: $i] :
( ( ( ord_less_eq @ int @ SV135 @ pls )
= $false )
| ( ( ord_less_eq @ nat @ ( number_number_of @ nat @ SV135 ) @ ( number_number_of @ nat @ SV505 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4537]) ).
thf(4778,plain,
! [SV661: $i,SV506: $i,SV137: $i] :
( ( ( zcong @ SV137 @ SV506 @ SV661 )
= $false )
| ( ( dvd_dvd @ int @ SV661 @ ( minus_minus @ int @ SV137 @ SV506 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4538]) ).
thf(4779,plain,
! [SV506: $i,SV137: $i,SV661: $i] :
( ( ( dvd_dvd @ int @ SV661 @ ( minus_minus @ int @ SV137 @ SV506 ) )
= $false )
| ( ( zcong @ SV137 @ SV506 @ SV661 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4539]) ).
thf(4780,plain,
! [SV1072: $i,SV139: $i] :
( ( ( ! [SY2214: $i,SY2215: $i] :
( ( times_times @ SV139 @ ( number_number_of @ SV139 @ SV1072 ) @ ( minus_minus @ SV139 @ SY2214 @ SY2215 ) )
= ( minus_minus @ SV139 @ ( times_times @ SV139 @ ( number_number_of @ SV139 @ SV1072 ) @ SY2214 ) @ ( times_times @ SV139 @ ( number_number_of @ SV139 @ SV1072 ) @ SY2215 ) ) ) )
= $true )
| ( ( number @ SV139 )
= $false )
| ( ( ring @ SV139 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4542]) ).
thf(4781,plain,
! [SV143: $i,SV509: $i] :
( ( ( ~ ( ( SV509
!= ( zero_zero @ nat ) ) )
| ( SV143
!= ( zero_zero @ nat ) ) )
= $false )
| ( ( ( power_power @ nat @ SV143 @ SV509 )
= ( zero_zero @ nat ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4544]) ).
thf(4782,plain,
! [SV143: $i,SV509: $i] :
( ( ( ~ ( ( SV509
!= ( zero_zero @ nat ) ) )
| ( SV143
!= ( zero_zero @ nat ) ) )
= $true )
| ( ( ( power_power @ nat @ SV143 @ SV509 )
= ( zero_zero @ nat ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4545]) ).
thf(4783,plain,
! [SV662: $i,SV510: $i,SV145: $i] :
( ( ( dvd_dvd @ int @ SV145 @ ( plus_plus @ int @ SV510 @ ( times_times @ int @ SV145 @ SV662 ) ) )
= $false )
| ( ( dvd_dvd @ int @ SV145 @ SV510 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4546]) ).
thf(4784,plain,
! [SV662: $i,SV510: $i,SV145: $i] :
( ( ( dvd_dvd @ int @ SV145 @ SV510 )
= $false )
| ( ( dvd_dvd @ int @ SV145 @ ( plus_plus @ int @ SV510 @ ( times_times @ int @ SV145 @ SV662 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4547]) ).
thf(4785,plain,
! [SV511: $i,SV147: $i] :
( ( ( ord_less @ nat @ ( zero_zero @ nat ) @ SV147 )
= $true )
| ( ( SV511
= ( zero_zero @ nat ) )
= $true )
| ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ SV147 @ SV511 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4548]) ).
thf(4786,plain,
! [SV511: $i,SV147: $i] :
( ( ( ord_less @ nat @ ( zero_zero @ nat ) @ SV147 )
= $false )
| ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ SV147 @ SV511 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4549]) ).
thf(4787,plain,
! [SV147: $i,SV511: $i] :
( ( ( SV511
= ( zero_zero @ nat ) )
= $false )
| ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ SV147 @ SV511 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4549]) ).
thf(4788,plain,
! [SV512: $i,SV151: $i] :
( ( ( ~ ( dvd_dvd @ nat @ SV151 @ SV512 )
| ~ ( dvd_dvd @ nat @ SV512 @ SV151 ) )
= $true )
| ( ( SV151 = SV512 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4550]) ).
thf(4789,plain,
! [SV512: $i,SV151: $i] :
( ( ( ~ ( dvd_dvd @ nat @ SV151 @ SV512 )
| ~ ( dvd_dvd @ nat @ SV512 @ SV151 ) )
= $false )
| ( ( SV151 = SV512 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4551]) ).
thf(4790,plain,
! [SV910: $i,SV760: $i,SV152: $i] :
( ( ( ~ ( ord_less_eq @ SV152 @ ( zero_zero @ SV152 ) @ SV760 ) )
= $true )
| ( ( ord_less_eq @ SV152 @ ( zero_zero @ SV152 ) @ ( times_times @ SV152 @ SV910 @ SV760 ) )
= $true )
| ( ( ord_less_eq @ SV152 @ ( zero_zero @ SV152 ) @ SV910 )
= $false )
| ( ( ordere453448008miring @ SV152 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4552]) ).
thf(4791,plain,
! [SV513: $i,SV153: $i] :
( ( ( ~ ~ ( ~ ( ord_less @ real @ ( zero_zero @ real ) @ ( sK7_SY1807 @ SV153 @ SV513 ) )
| ( ( power_power @ real @ ( sK7_SY1807 @ SV153 @ SV513 ) @ SV513 )
!= SV153 ) ) )
= $false )
| ( ( ord_less @ real @ ( zero_zero @ real ) @ SV153 )
= $false )
| ( ( ord_less @ nat @ ( zero_zero @ nat ) @ SV513 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4553]) ).
thf(4792,plain,
! [SV911: $i,SV762: $i,SV1010: $i,SV155: $i] :
( ( ( ord_less @ SV155 @ ( one_one @ SV155 ) @ SV1010 )
= $false )
| ( ( ~ ( ~ ( ~ ( ord_less @ SV155 @ ( power_power @ SV155 @ SV1010 @ SV762 ) @ ( power_power @ SV155 @ SV1010 @ SV911 ) )
| ( ord_less @ nat @ SV762 @ SV911 ) )
| ~ ( ~ ( ord_less @ nat @ SV762 @ SV911 )
| ( ord_less @ SV155 @ ( power_power @ SV155 @ SV1010 @ SV762 ) @ ( power_power @ SV155 @ SV1010 @ SV911 ) ) ) ) )
= $true )
| ( ( linordered_semidom @ SV155 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4554]) ).
thf(4793,plain,
! [SV665: $i,SV518: $i,SV161: $i] :
( ( ( ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV161 ) )
= $true )
| ( ( ord_less_eq @ int @ SV518 @ ( zero_zero @ int ) )
= $true )
| ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV665 )
= $false )
| ( ( ord_less @ int @ ( plus_plus @ int @ ( times_times @ int @ SV161 @ SV518 ) @ SV665 ) @ ( zero_zero @ int ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4559]) ).
thf(4794,plain,
! [SV666: $i,SV520: $i,SV163: $i] :
( ( ( zcong @ SV163 @ SV520 @ ( ti @ int @ SV666 ) )
= $false )
| ( ( zcong @ SV163 @ SV520 @ SV666 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4560]) ).
thf(4795,plain,
! [SV666: $i,SV520: $i,SV163: $i] :
( ( ( zcong @ SV163 @ SV520 @ SV666 )
= $false )
| ( ( zcong @ SV163 @ SV520 @ ( ti @ int @ SV666 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4561]) ).
thf(4796,plain,
! [SV913: $i,SV164: $i,SV667: $i,SV521: $i,SV765: $i] :
( ( ( ~ ( ~ ( dvd_dvd @ int @ SV765 @ ( plus_plus @ int @ SV521 @ SV667 ) )
| ( dvd_dvd @ int @ SV765 @ ( plus_plus @ int @ ( plus_plus @ int @ SV521 @ ( times_times @ int @ SV164 @ SV913 ) ) @ SV667 ) ) )
| ~ ( ~ ( dvd_dvd @ int @ SV765 @ ( plus_plus @ int @ ( plus_plus @ int @ SV521 @ ( times_times @ int @ SV164 @ SV913 ) ) @ SV667 ) )
| ( dvd_dvd @ int @ SV765 @ ( plus_plus @ int @ SV521 @ SV667 ) ) ) )
= $false )
| ( ( dvd_dvd @ int @ SV765 @ SV913 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4562]) ).
thf(4797,plain,
! [SV768: $i,SV668: $i,SV916: $i,SV522: $i,SV167: $i] :
( ( ( ~ ( zcong @ SV167 @ SV522 @ SV916 ) )
= $true )
| ( ( zcong @ ( minus_minus @ int @ SV668 @ SV167 ) @ ( minus_minus @ int @ SV768 @ SV522 ) @ SV916 )
= $true )
| ( ( zcong @ SV668 @ SV768 @ SV916 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4563]) ).
thf(4798,plain,
! [SV1073: $i,SV168: $i] :
( ( ( ! [SY2216: $i,SY2217: $i] :
( ( times_times @ SV168 @ ( plus_plus @ SV168 @ SV1073 @ SY2216 ) @ ( number_number_of @ SV168 @ SY2217 ) )
= ( plus_plus @ SV168 @ ( times_times @ SV168 @ SV1073 @ ( number_number_of @ SV168 @ SY2217 ) ) @ ( times_times @ SV168 @ SY2216 @ ( number_number_of @ SV168 @ SY2217 ) ) ) ) )
= $true )
| ( ( number @ SV168 )
= $false )
| ( ( semiring @ SV168 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4564]) ).
thf(4799,plain,
! [SV523: $i,SV169: $i] :
( ( ( ( SV169
!= ( zero_zero @ real ) )
| ( SV523
!= ( zero_zero @ real ) ) )
= $false )
| ( ( ( plus_plus @ real @ ( power_power @ real @ SV169 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ real @ SV523 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ real ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4565]) ).
thf(4800,plain,
! [SV523: $i,SV169: $i] :
( ( ( ( SV169
!= ( zero_zero @ real ) )
| ( SV523
!= ( zero_zero @ real ) ) )
= $true )
| ( ( ( plus_plus @ real @ ( power_power @ real @ SV169 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ real @ SV523 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ real ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4566]) ).
thf(4801,plain,
! [SV918: $i,SV771: $i,SV1060: $i,SV1013: $i,SV175: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( ( ti @ SV175 @ SV1013 )
!= ( ti @ SV175 @ SV1060 ) ) )
| ~ ( ( ( ti @ SV175 @ SV771 )
!= ( ti @ SV175 @ SV918 ) ) ) )
| ( ( plus_plus @ SV175 @ ( times_times @ SV175 @ SV1013 @ SV771 ) @ ( times_times @ SV175 @ SV1060 @ SV918 ) )
!= ( plus_plus @ SV175 @ ( times_times @ SV175 @ SV1013 @ SV918 ) @ ( times_times @ SV175 @ SV1060 @ SV771 ) ) ) )
| ~ ( ~ ( ( ( plus_plus @ SV175 @ ( times_times @ SV175 @ SV1013 @ SV771 ) @ ( times_times @ SV175 @ SV1060 @ SV918 ) )
!= ( plus_plus @ SV175 @ ( times_times @ SV175 @ SV1013 @ SV918 ) @ ( times_times @ SV175 @ SV1060 @ SV771 ) ) ) )
| ~ ( ~ ( ( ( ti @ SV175 @ SV1013 )
!= ( ti @ SV175 @ SV1060 ) ) )
| ~ ( ( ( ti @ SV175 @ SV771 )
!= ( ti @ SV175 @ SV918 ) ) ) ) ) )
= $false )
| ( ( semiri456707255roduct @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4571]) ).
thf(4802,plain,
! [SV919: $i,SV772: $i,SV1014: $i,SV179: $i] :
( ( ( ord_less @ SV179 @ ( one_one @ SV179 ) @ SV1014 )
= $false )
| ( ( ~ ( ord_less @ SV179 @ ( power_power @ SV179 @ SV1014 @ SV772 ) @ ( power_power @ SV179 @ SV1014 @ SV919 ) )
| ( ord_less @ nat @ SV772 @ SV919 ) )
= $true )
| ( ( linordered_semidom @ SV179 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4573]) ).
thf(4803,plain,
! [SV1015: $i,SV920: $i,SV180: $i,SV773: $i] :
( ( ( SV773
= ( times_times @ SV180 @ SV920 @ SV1015 ) )
= $false )
| ( ( dvd_dvd @ SV180 @ SV920 @ SV773 )
= $true )
| ( ( dvd @ SV180 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4574]) ).
thf(4804,plain,
! [SV530: $i,SV187: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV187 @ SV530 )
| ~ ( ( ( ti @ int @ SV187 )
!= ( ti @ int @ SV530 ) ) ) )
= $false )
| ( ( ord_less @ int @ SV187 @ SV530 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4579]) ).
thf(4805,plain,
! [SV530: $i,SV187: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV187 @ SV530 )
| ~ ( ( ( ti @ int @ SV187 )
!= ( ti @ int @ SV530 ) ) ) )
= $true )
| ( ( ord_less @ int @ SV187 @ SV530 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4580]) ).
thf(4806,plain,
! [SV776: $i,SV189: $i] :
( ( ( ( plus_plus @ SV189 @ SV776 @ SV776 )
!= ( zero_zero @ SV189 ) )
= $true )
| ( ( ( ti @ SV189 @ SV776 )
= ( zero_zero @ SV189 ) )
= $true )
| ( ( linord219039673up_add @ SV189 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4581]) ).
thf(4807,plain,
! [SV776: $i,SV189: $i] :
( ( ( ( ti @ SV189 @ SV776 )
!= ( zero_zero @ SV189 ) )
= $true )
| ( ( ( plus_plus @ SV189 @ SV776 @ SV776 )
= ( zero_zero @ SV189 ) )
= $true )
| ( ( linord219039673up_add @ SV189 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4582]) ).
thf(4808,plain,
! [SV671: $i,SV533: $i,SV191: $i] :
( ( ( dvd_dvd @ nat @ ( times_times @ nat @ SV191 @ SV533 ) @ ( times_times @ nat @ SV671 @ SV533 ) )
= $false )
| ( ( ( SV533
= ( zero_zero @ nat ) )
| ( dvd_dvd @ nat @ SV191 @ SV671 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4584]) ).
thf(4809,plain,
! [SV671: $i,SV191: $i,SV533: $i] :
( ( ( ( SV533
= ( zero_zero @ nat ) )
| ( dvd_dvd @ nat @ SV191 @ SV671 ) )
= $false )
| ( ( dvd_dvd @ nat @ ( times_times @ nat @ SV191 @ SV533 ) @ ( times_times @ nat @ SV671 @ SV533 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4585]) ).
thf(4810,plain,
! [SV923: $i,SV778: $i,SV193: $i] :
( ( ( ( ( plus_plus @ SV193 @ ( times_times @ SV193 @ SV778 @ SV778 ) @ ( times_times @ SV193 @ SV923 @ SV923 ) )
!= ( zero_zero @ SV193 ) )
| ~ ( ( ( ti @ SV193 @ SV778 )
!= ( zero_zero @ SV193 ) )
| ( ( ti @ SV193 @ SV923 )
!= ( zero_zero @ SV193 ) ) ) )
= $true )
| ( ( linord581940658strict @ SV193 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4587]) ).
thf(4811,plain,
! [SV923: $i,SV778: $i,SV193: $i] :
( ( ( ~ ~ ( ( ( ti @ SV193 @ SV778 )
!= ( zero_zero @ SV193 ) )
| ( ( ti @ SV193 @ SV923 )
!= ( zero_zero @ SV193 ) ) )
| ( ( plus_plus @ SV193 @ ( times_times @ SV193 @ SV778 @ SV778 ) @ ( times_times @ SV193 @ SV923 @ SV923 ) )
= ( zero_zero @ SV193 ) ) )
= $true )
| ( ( linord581940658strict @ SV193 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4588]) ).
thf(4812,plain,
! [SV924: $i,SV779: $i,SV1017: $i,SV194: $i] :
( ( ( ord_less @ SV194 @ ( one_one @ SV194 ) @ SV1017 )
= $false )
| ( ( ~ ( ~ ( ( ( power_power @ SV194 @ SV1017 @ SV779 )
!= ( power_power @ SV194 @ SV1017 @ SV924 ) )
| ( SV779 = SV924 ) )
| ~ ( ( SV779 != SV924 )
| ( ( power_power @ SV194 @ SV1017 @ SV779 )
= ( power_power @ SV194 @ SV1017 @ SV924 ) ) ) ) )
= $true )
| ( ( linordered_semidom @ SV194 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4589]) ).
thf(4813,plain,
! [SV196: $i,SV672: $i,SV534: $i] :
( ( ( zcong @ SV534 @ ( zero_zero @ int ) @ SV672 )
= $true )
| ( ( ~ ~ ( zcong @ SV196 @ ( zero_zero @ int ) @ SV672 )
| ~ ( zcong @ ( times_times @ int @ SV534 @ SV196 ) @ ( zero_zero @ int ) @ SV672 ) )
= $true )
| ( ( zprime @ SV672 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4590]) ).
thf(4814,plain,
! [SV928: $i,SV783: $i,SV199: $i] :
( ( ( ~ ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ ( times_times @ SV199 @ SV783 @ SV928 ) )
| ~ ( ~ ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ SV783 )
| ~ ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ SV928 ) )
| ~ ( ~ ( ord_less_eq @ SV199 @ SV783 @ ( zero_zero @ SV199 ) )
| ~ ( ord_less_eq @ SV199 @ SV928 @ ( zero_zero @ SV199 ) ) ) )
= $true )
| ( ( linord581940658strict @ SV199 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4591]) ).
thf(4815,plain,
! [SV928: $i,SV783: $i,SV199: $i] :
( ( ( ~ ( ~ ( ~ ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ SV783 )
| ~ ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ SV928 ) )
| ~ ( ~ ( ord_less_eq @ SV199 @ SV783 @ ( zero_zero @ SV199 ) )
| ~ ( ord_less_eq @ SV199 @ SV928 @ ( zero_zero @ SV199 ) ) ) )
| ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ ( times_times @ SV199 @ SV783 @ SV928 ) ) )
= $true )
| ( ( linord581940658strict @ SV199 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4592]) ).
thf(4816,plain,
! [SV929: $i,SV201: $i,SV785: $i] :
( ( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ SV785 ) )
= $true )
| ( ( ord_less @ SV201 @ ( one_one @ SV201 ) @ ( power_power @ SV201 @ SV929 @ SV785 ) )
= $true )
| ( ( ord_less @ SV201 @ ( one_one @ SV201 ) @ SV929 )
= $false )
| ( ( linordered_semidom @ SV201 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4593]) ).
thf(4817,plain,
! [SV1074: $i,SV202: $i] :
( ( ( ~ ( ~ ( ~ ( ord_less_eq @ SV202 @ ( one_one @ SV202 ) @ ( number_number_of @ SV202 @ SV1074 ) )
| ( ord_less_eq @ int @ ( bit1 @ pls ) @ SV1074 ) )
| ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ pls ) @ SV1074 )
| ( ord_less_eq @ SV202 @ ( one_one @ SV202 ) @ ( number_number_of @ SV202 @ SV1074 ) ) ) ) )
= $true )
| ( ( number_ring @ SV202 )
= $false )
| ( ( linordered_idom @ SV202 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4594]) ).
thf(4818,plain,
! [SV535: $i,SV673: $i,SV203: $i] :
( ( ( ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV203 ) )
= $true )
| ( ( ~ ( ord_less @ int @ SV203 @ SV673 )
| ~ ( zcong @ SV673 @ SV203 @ SV535 ) )
= $true )
| ( ( ord_less @ int @ SV673 @ SV535 )
= $false )
| ( ( ord_less @ int @ ( zero_zero @ int ) @ SV673 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4595]) ).
thf(4819,plain,
! [SV787: $i,SV674: $i,SV930: $i,SV536: $i,SV206: $i] :
( ( ( ~ ( zcong @ SV206 @ SV536 @ SV930 ) )
= $true )
| ( ( zcong @ ( plus_plus @ int @ SV674 @ SV206 ) @ ( plus_plus @ int @ SV787 @ SV536 ) @ SV930 )
= $true )
| ( ( zcong @ SV674 @ SV787 @ SV930 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4596]) ).
thf(4820,plain,
! [SV1075: $i,SV213: $i] :
( ( ( ! [SY2218: $i] :
~ ( ~ ( ( ( number_number_of @ SV213 @ SV1075 )
!= ( number_number_of @ SV213 @ SY2218 ) )
| ( ( ti @ int @ SV1075 )
= ( ti @ int @ SY2218 ) ) )
| ~ ( ( ( ti @ int @ SV1075 )
!= ( ti @ int @ SY2218 ) )
| ( ( number_number_of @ SV213 @ SV1075 )
= ( number_number_of @ SV213 @ SY2218 ) ) ) ) )
= $true )
| ( ( number_ring @ SV213 )
= $false )
| ( ( ring_char_0 @ SV213 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4598]) ).
thf(4821,plain,
! [SV538: $i,SV214: $i,SV676: $i,SV790: $i] :
( ( ( ord_less @ nat @ ( zero_zero @ nat ) @ SV790 )
= $false )
| ( ( ~ ( ord_less @ nat @ SV790 @ SV676 )
| ~ ( dvd_dvd @ nat @ SV676 @ SV214 ) )
= $true )
| ( ( SV214
= ( plus_plus @ nat @ ( times_times @ nat @ SV538 @ SV676 ) @ SV790 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4599]) ).
thf(4822,plain,
! [SV677: $i,SV215: $i,SV539: $i] :
( ( ( SV539
= ( zero_zero @ nat ) )
= $true )
| ( ( dvd_dvd @ nat @ SV215 @ SV677 )
= $true )
| ( ( dvd_dvd @ nat @ ( power_power @ nat @ SV215 @ SV539 ) @ ( power_power @ nat @ SV677 @ SV539 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4600]) ).
thf(4823,plain,
! [SV1076: $i,SV218: $i] :
( ( ( ! [SY2219: $i] :
~ ( ~ ( ~ ( ord_less @ SV218 @ ( number_number_of @ SV218 @ SV1076 ) @ ( number_number_of @ SV218 @ SY2219 ) )
| ( ord_less @ int @ SV1076 @ SY2219 ) )
| ~ ( ~ ( ord_less @ int @ SV1076 @ SY2219 )
| ( ord_less @ SV218 @ ( number_number_of @ SV218 @ SV1076 ) @ ( number_number_of @ SV218 @ SY2219 ) ) ) ) )
= $true )
| ( ( number_ring @ SV218 )
= $false )
| ( ( linordered_idom @ SV218 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4601]) ).
thf(4824,plain,
! [SV792: $i,SV1061: $i,SV1018: $i,SV933: $i,SV220: $i] :
( ( ( ~ ( dvd_dvd @ SV220 @ ( power_power @ SV220 @ SV933 @ SV1018 ) @ SV1061 ) )
= $true )
| ( ( ~ ( ord_less_eq @ nat @ SV792 @ SV1018 )
| ( dvd_dvd @ SV220 @ ( power_power @ SV220 @ SV933 @ SV792 ) @ SV1061 ) )
= $true )
| ( ( comm_semiring_1 @ SV220 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4602]) ).
thf(4825,plain,
! [SV793: $i,SV1019: $i,SV934: $i,SV222: $i] :
( ( ( dvd_dvd @ SV222 @ SV934 @ SV1019 )
= $false )
| ( ( dvd_dvd @ SV222 @ SV934 @ ( times_times @ SV222 @ SV793 @ SV1019 ) )
= $true )
| ( ( comm_semiring_1 @ SV222 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4604]) ).
thf(4826,plain,
! [SV1020: $i,SV935: $i,SV794: $i,SV226: $i] :
( ( ( dvd_dvd @ SV226 @ ( times_times @ SV226 @ SV794 @ SV935 ) @ SV1020 )
= $false )
| ( ( dvd_dvd @ SV226 @ SV794 @ SV1020 )
= $true )
| ( ( comm_semiring_1 @ SV226 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4606]) ).
thf(4827,plain,
! [SV233: $i,SV547: $i] :
( ( ( ( number_number_of @ nat @ SV547 )
= ( zero_zero @ nat ) )
= $true )
| ( ( ord_less @ nat @ ( zero_zero @ nat ) @ SV233 )
= $true )
| ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ SV233 @ ( number_number_of @ nat @ SV547 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4609]) ).
thf(4828,plain,
! [SV233: $i,SV547: $i] :
( ( ( ( number_number_of @ nat @ SV547 )
= ( zero_zero @ nat ) )
= $false )
| ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ SV233 @ ( number_number_of @ nat @ SV547 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4610]) ).
thf(4829,plain,
! [SV547: $i,SV233: $i] :
( ( ( ord_less @ nat @ ( zero_zero @ nat ) @ SV233 )
= $false )
| ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ SV233 @ ( number_number_of @ nat @ SV547 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4610]) ).
thf(4830,plain,
! [SV1077: $i,SV234: $i] :
( ( ( ! [SY2220: $i,SY2221: $i] :
( ( times_times @ SV234 @ ( number_number_of @ SV234 @ SV1077 ) @ ( plus_plus @ SV234 @ SY2220 @ SY2221 ) )
= ( plus_plus @ SV234 @ ( times_times @ SV234 @ ( number_number_of @ SV234 @ SV1077 ) @ SY2220 ) @ ( times_times @ SV234 @ ( number_number_of @ SV234 @ SV1077 ) @ SY2221 ) ) ) )
= $true )
| ( ( number @ SV234 )
= $false )
| ( ( semiring @ SV234 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4611]) ).
thf(4831,plain,
! [SV937: $i,SV797: $i,SV237: $i] :
( ( ( ( ( number_number_of @ SV237 @ SV797 )
!= ( ti @ SV237 @ SV937 ) )
| ( ( ti @ SV237 @ SV937 )
= ( number_number_of @ SV237 @ SV797 ) ) )
= $true )
| ( ( number @ SV237 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4614]) ).
thf(4832,plain,
! [SV797: $i,SV937: $i,SV237: $i] :
( ( ( ( ( ti @ SV237 @ SV937 )
!= ( number_number_of @ SV237 @ SV797 ) )
| ( ( number_number_of @ SV237 @ SV797 )
= ( ti @ SV237 @ SV937 ) ) )
= $true )
| ( ( number @ SV237 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4615]) ).
thf(4833,plain,
! [SV549: $i,SV240: $i,SV683: $i,SV799: $i] :
( ( ( ~ ( dvd_dvd @ int @ SV799 @ SV683 ) )
= $false )
| ( ( ~ ( dvd_dvd @ int @ ( power_power @ int @ SV799 @ SV240 ) @ ( times_times @ int @ SV683 @ SV549 ) )
| ( dvd_dvd @ int @ ( power_power @ int @ SV799 @ SV240 ) @ SV549 ) )
= $true )
| ( ( zprime @ SV799 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4616]) ).
thf(4834,plain,
! [SV552: $i,SV245: $i,SV685: $i] :
( ( ( ord_less @ int @ SV685 @ pls )
= $false )
| ( ( ( times_times @ nat @ ( number_number_of @ nat @ SV685 ) @ ( times_times @ nat @ ( number_number_of @ nat @ SV245 ) @ SV552 ) )
= ( zero_zero @ nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4619]) ).
thf(4835,plain,
! [SV552: $i,SV245: $i,SV685: $i] :
( ( ( ~ ( ord_less @ int @ SV685 @ pls ) )
= $false )
| ( ( ( times_times @ nat @ ( number_number_of @ nat @ SV685 ) @ ( times_times @ nat @ ( number_number_of @ nat @ SV245 ) @ SV552 ) )
= ( times_times @ nat @ ( number_number_of @ nat @ ( times_times @ int @ SV685 @ SV245 ) ) @ SV552 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4620]) ).
thf(4836,plain,
! [SV247: $i,SV554: $i] :
( ( ( SV554
= ( zero_zero @ nat ) )
= $true )
| ( ( ord_less @ nat @ ( zero_zero @ nat ) @ SV247 )
= $true )
| ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ SV247 @ SV554 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4621]) ).
thf(4837,plain,
! [SV247: $i,SV554: $i] :
( ( ( SV554
= ( zero_zero @ nat ) )
= $false )
| ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ SV247 @ SV554 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4622]) ).
thf(4838,plain,
! [SV554: $i,SV247: $i] :
( ( ( ord_less @ nat @ ( zero_zero @ nat ) @ SV247 )
= $false )
| ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ SV247 @ SV554 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4622]) ).
thf(4839,plain,
! [SV1062: $i,SV1024: $i,SV942: $i,SV804: $i,SV255: $i] :
( ( ( ~ ( ( ( plus_plus @ SV255 @ ( times_times @ SV255 @ SV804 @ SV942 ) @ ( times_times @ SV255 @ SV1024 @ SV1062 ) )
!= ( plus_plus @ SV255 @ ( times_times @ SV255 @ SV804 @ SV1062 ) @ ( times_times @ SV255 @ SV1024 @ SV942 ) ) )
| ( ( ti @ SV255 @ SV804 )
= ( ti @ SV255 @ SV1024 ) )
| ( ( ti @ SV255 @ SV942 )
= ( ti @ SV255 @ SV1062 ) ) )
| ~ ( ~ ( ( ( ti @ SV255 @ SV804 )
= ( ti @ SV255 @ SV1024 ) )
| ( ( ti @ SV255 @ SV942 )
= ( ti @ SV255 @ SV1062 ) ) )
| ( ( plus_plus @ SV255 @ ( times_times @ SV255 @ SV804 @ SV942 ) @ ( times_times @ SV255 @ SV1024 @ SV1062 ) )
= ( plus_plus @ SV255 @ ( times_times @ SV255 @ SV804 @ SV1062 ) @ ( times_times @ SV255 @ SV1024 @ SV942 ) ) ) ) )
= $false )
| ( ( semiri456707255roduct @ SV255 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4625]) ).
thf(4840,plain,
! [SV805: $i,SV943: $i,SV688: $i,SV557: $i,SV257: $i] :
( ( ( ~ ( ~ ( zcong @ SV257 @ ( times_times @ int @ SV557 @ SV688 ) @ SV943 )
| ( zcong @ SV257 @ ( times_times @ int @ SV557 @ SV805 ) @ SV943 ) )
| ~ ( ~ ( zcong @ SV257 @ ( times_times @ int @ SV557 @ SV805 ) @ SV943 )
| ( zcong @ SV257 @ ( times_times @ int @ SV557 @ SV688 ) @ SV943 ) ) )
= $false )
| ( ( zcong @ SV688 @ SV805 @ SV943 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4626]) ).
thf(4841,plain,
! [SV558: $i,SV689: $i,SV259: $i] :
( ( ( dvd_dvd @ nat @ ( power_power @ nat @ SV259 @ SV689 ) @ SV558 )
= $false )
| ( ( dvd_dvd @ nat @ SV259 @ SV558 )
= $true )
| ( ( SV689
= ( zero_zero @ nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4627]) ).
thf(4842,plain,
! [SV690: $i,SV559: $i,SV261: $i] :
( ( ( zcong @ SV261 @ ( ti @ int @ SV559 ) @ SV690 )
= $false )
| ( ( zcong @ SV261 @ SV559 @ SV690 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4628]) ).
thf(4843,plain,
! [SV690: $i,SV559: $i,SV261: $i] :
( ( ( zcong @ SV261 @ SV559 @ SV690 )
= $false )
| ( ( zcong @ SV261 @ ( ti @ int @ SV559 ) @ SV690 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4629]) ).
thf(4844,plain,
! [SV810: $i,SV269: $i] :
( ( ( ~ ( ord_less @ SV269 @ ( plus_plus @ SV269 @ SV810 @ SV810 ) @ ( zero_zero @ SV269 ) ) )
= $true )
| ( ( ord_less @ SV269 @ SV810 @ ( zero_zero @ SV269 ) )
= $true )
| ( ( linordered_idom @ SV269 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4631]) ).
thf(4845,plain,
! [SV810: $i,SV269: $i] :
( ( ( ~ ( ord_less @ SV269 @ SV810 @ ( zero_zero @ SV269 ) ) )
= $true )
| ( ( ord_less @ SV269 @ ( plus_plus @ SV269 @ SV810 @ SV810 ) @ ( zero_zero @ SV269 ) )
= $true )
| ( ( linordered_idom @ SV269 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4632]) ).
thf(4846,plain,
! [SV562: $i,SV273: $i,SV691: $i] :
( ( ( ~ ( ( ( times_times @ real @ SV691 @ SV273 )
!= ( times_times @ real @ SV691 @ SV562 ) )
| ( SV273 = SV562 ) ) )
= $false )
| ( ( SV691
= ( zero_zero @ real ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4633]) ).
thf(4847,plain,
! [SV691: $i,SV562: $i,SV273: $i] :
( ( ( ~ ( ( SV273 != SV562 )
| ( ( times_times @ real @ SV691 @ SV273 )
= ( times_times @ real @ SV691 @ SV562 ) ) ) )
= $false )
| ( ( SV691
= ( zero_zero @ real ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4633]) ).
thf(4848,plain,
! [SV815: $i,SV1027: $i,SV949: $i,SV277: $i] :
( ( ( dvd_dvd @ SV277 @ SV949 @ SV1027 )
= $false )
| ( ( ~ ( dvd_dvd @ SV277 @ SV949 @ SV815 )
| ( dvd_dvd @ SV277 @ SV949 @ ( plus_plus @ SV277 @ SV1027 @ SV815 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV277 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4634]) ).
thf(4849,plain,
! [SV818: $i,SV1028: $i,SV950: $i,SV284: $i] :
( ( ( dvd_dvd @ SV284 @ SV950 @ SV1028 )
= $false )
| ( ( dvd_dvd @ SV284 @ ( power_power @ SV284 @ SV950 @ SV818 ) @ ( power_power @ SV284 @ SV1028 @ SV818 ) )
= $true )
| ( ( comm_semiring_1 @ SV284 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4637]) ).
thf(4850,plain,
! [SV951: $i,SV285: $i,SV819: $i] :
( ( ( ~ ( ord_less_eq @ int @ pls @ SV819 ) )
= $true )
| ( ( ( plus_plus @ SV285 @ ( number_number_of @ SV285 @ SV951 ) @ ( number_number_of @ SV285 @ SV819 ) )
= ( number_number_of @ SV285 @ ( plus_plus @ int @ SV951 @ SV819 ) ) )
= $true )
| ( ( ord_less_eq @ int @ pls @ SV951 )
= $false )
| ( ( number_semiring @ SV285 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4638]) ).
thf(4851,plain,
! [SV566: $i,SV288: $i,SV694: $i,SV821: $i] :
( ( ( ~ ( dvd_dvd @ int @ SV821 @ SV694 ) )
= $false )
| ( ( ~ ( dvd_dvd @ int @ ( power_power @ int @ SV821 @ SV288 ) @ ( times_times @ int @ SV566 @ SV694 ) )
| ( dvd_dvd @ int @ ( power_power @ int @ SV821 @ SV288 ) @ SV566 ) )
= $true )
| ( ( zprime @ SV821 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4639]) ).
thf(4852,plain,
! [SV955: $i,SV826: $i,SV301: $i] :
( ( ( ( ( times_times @ SV301 @ SV826 @ SV955 )
!= ( zero_zero @ SV301 ) )
| ( ( ti @ SV301 @ SV826 )
= ( zero_zero @ SV301 ) )
| ( ( ti @ SV301 @ SV955 )
= ( zero_zero @ SV301 ) ) )
= $true )
| ( ( ring_n68954251visors @ SV301 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4646]) ).
thf(4853,plain,
! [SV955: $i,SV826: $i,SV301: $i] :
( ( ( ~ ( ( ( ti @ SV301 @ SV826 )
= ( zero_zero @ SV301 ) )
| ( ( ti @ SV301 @ SV955 )
= ( zero_zero @ SV301 ) ) )
| ( ( times_times @ SV301 @ SV826 @ SV955 )
= ( zero_zero @ SV301 ) ) )
= $true )
| ( ( ring_n68954251visors @ SV301 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4647]) ).
thf(4854,plain,
! [SV956: $i,SV828: $i,SV1031: $i,SV304: $i] :
( ( ( ord_less @ SV304 @ ( one_one @ SV304 ) @ SV1031 )
= $false )
| ( ( ~ ( ord_less_eq @ SV304 @ ( power_power @ SV304 @ SV1031 @ SV828 ) @ ( power_power @ SV304 @ SV1031 @ SV956 ) )
| ( ord_less_eq @ nat @ SV828 @ SV956 ) )
= $true )
| ( ( linordered_semidom @ SV304 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4648]) ).
thf(4855,plain,
! [SV1032: $i,SV957: $i,SV829: $i,SV698: $i,SV573: $i,SV305: $i] :
( ( ( ( plus_plus @ int @ ( times_times @ int @ SV305 @ SV573 ) @ SV698 )
= ( plus_plus @ int @ ( times_times @ int @ SV829 @ SV957 ) @ SV1032 ) )
= $false )
| ( ( ~ ( ord_less @ int @ ( plus_plus @ int @ ( times_times @ int @ SV829 @ SV957 ) @ SV1032 ) @ ( zero_zero @ int ) )
| ~ ( ord_less @ int @ SV698 @ SV305 )
| ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV1032 )
| ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV829 )
| ~ ( ord_less_eq @ int @ SV829 @ SV305 )
| ( ord_less_eq @ int @ SV957 @ SV573 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4649]) ).
thf(4856,plain,
! [SV833: $i,SV576: $i,SV960: $i,SV312: $i,SV701: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV701 ) )
= $true )
| ( ( ~ ( ord_less @ int @ SV701 @ SV312 )
| ~ ( ord_less @ int @ SV960 @ SV312 )
| ( ord_less_eq @ int @ SV576 @ SV833 ) )
= $true )
| ( ( ord_less_eq @ int @ ( plus_plus @ int @ ( times_times @ int @ SV312 @ SV576 ) @ SV701 ) @ ( plus_plus @ int @ ( times_times @ int @ SV312 @ SV833 ) @ SV960 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4650]) ).
thf(4857,plain,
! [SV961: $i,SV834: $i,SV313: $i] :
( ( ( ( ( ti @ SV313 @ SV834 )
!= ( plus_plus @ SV313 @ SV834 @ SV961 ) )
| ( ( ti @ SV313 @ SV961 )
= ( zero_zero @ SV313 ) ) )
= $true )
| ( ( semiri456707255roduct @ SV313 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4651]) ).
thf(4858,plain,
! [SV834: $i,SV961: $i,SV313: $i] :
( ( ( ( ( ti @ SV313 @ SV961 )
!= ( zero_zero @ SV313 ) )
| ( ( ti @ SV313 @ SV834 )
= ( plus_plus @ SV313 @ SV834 @ SV961 ) ) )
= $true )
| ( ( semiri456707255roduct @ SV313 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4652]) ).
thf(4859,plain,
! [SV314: $i,SV577: $i] :
( ( ( ! [SY1865: $i] :
~ ( zcong @ ( power_power @ int @ SY1865 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SV577 @ SV314 ) )
= $false )
| ( ( quadRes @ SV314 @ SV577 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4653]) ).
thf(4860,plain,
! [SV314: $i,SV577: $i] :
( ( ( ! [SY1866: $i] :
~ ( zcong @ ( power_power @ int @ SY1866 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SV577 @ SV314 ) )
= $true )
| ( ( quadRes @ SV314 @ SV577 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4654]) ).
thf(4861,plain,
! [SV835: $i,SV315: $i,SV1034: $i,SV962: $i] :
( ( ( ord_less_eq @ nat @ SV962 @ SV1034 )
= $false )
| ( ( ~ ( ord_less_eq @ SV315 @ ( one_one @ SV315 ) @ SV835 )
| ( ord_less_eq @ SV315 @ ( power_power @ SV315 @ SV835 @ SV962 ) @ ( power_power @ SV315 @ SV835 @ SV1034 ) ) )
= $true )
| ( ( linordered_semidom @ SV315 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4655]) ).
thf(4862,plain,
! [SV966: $i,SV839: $i,SV319: $i] :
( ( ( ~ ( ord_less_eq @ SV319 @ ( times_times @ SV319 @ SV839 @ SV966 ) @ ( zero_zero @ SV319 ) )
| ~ ( ~ ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SV839 )
| ~ ( ord_less_eq @ SV319 @ SV966 @ ( zero_zero @ SV319 ) ) )
| ~ ( ~ ( ord_less_eq @ SV319 @ SV839 @ ( zero_zero @ SV319 ) )
| ~ ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SV966 ) ) )
= $true )
| ( ( linord581940658strict @ SV319 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4657]) ).
thf(4863,plain,
! [SV966: $i,SV839: $i,SV319: $i] :
( ( ( ~ ( ~ ( ~ ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SV839 )
| ~ ( ord_less_eq @ SV319 @ SV966 @ ( zero_zero @ SV319 ) ) )
| ~ ( ~ ( ord_less_eq @ SV319 @ SV839 @ ( zero_zero @ SV319 ) )
| ~ ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SV966 ) ) )
| ( ord_less_eq @ SV319 @ ( times_times @ SV319 @ SV839 @ SV966 ) @ ( zero_zero @ SV319 ) ) )
= $true )
| ( ( linord581940658strict @ SV319 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4658]) ).
thf(4864,plain,
! [SV1078: $i,SV321: $i] :
( ( ( ! [SY2222: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV321 @ ( number_number_of @ SV321 @ SV1078 ) @ ( number_number_of @ SV321 @ SY2222 ) )
| ( ord_less_eq @ int @ SV1078 @ SY2222 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV1078 @ SY2222 )
| ( ord_less_eq @ SV321 @ ( number_number_of @ SV321 @ SV1078 ) @ ( number_number_of @ SV321 @ SY2222 ) ) ) ) )
= $true )
| ( ( number_ring @ SV321 )
= $false )
| ( ( linordered_idom @ SV321 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4659]) ).
thf(4865,plain,
! [SV967: $i,SV841: $i,SV1064: $i,SV1036: $i,SV323: $i] :
( ( ( ~ ( dvd_dvd @ SV323 @ SV1036 @ SV1064 ) )
= $true )
| ( ( ~ ( ord_less_eq @ nat @ SV841 @ SV967 )
| ( dvd_dvd @ SV323 @ ( power_power @ SV323 @ SV1036 @ SV841 ) @ ( power_power @ SV323 @ SV1064 @ SV967 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV323 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4660]) ).
thf(4866,plain,
! [SV842: $i,SV968: $i,SV325: $i] :
( ( ( ~ ( ord_less_eq @ SV325 @ ( zero_zero @ SV325 ) @ SV968 ) )
= $true )
| ( ( ord_less_eq @ SV325 @ SV842 @ SV968 )
= $true )
| ( ( ord_less_eq @ SV325 @ ( power_power @ SV325 @ SV842 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV325 @ SV968 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $false )
| ( ( linordered_semidom @ SV325 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4661]) ).
thf(4867,plain,
! [SV1038: $i,SV970: $i,SV844: $i,SV330: $i] :
( ( ( dvd_dvd @ SV330 @ ( times_times @ SV330 @ SV844 @ SV970 ) @ SV1038 )
= $false )
| ( ( dvd_dvd @ SV330 @ SV970 @ SV1038 )
= $true )
| ( ( comm_semiring_1 @ SV330 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4662]) ).
thf(4868,plain,
! [SV333: $i,SV1079: $i] :
( ( ( ~ ( ~ ( ( ( number_number_of @ nat @ SV1079 )
!= ( zero_zero @ nat ) )
| ( ( power_power @ SV333 @ ( zero_zero @ SV333 ) @ ( number_number_of @ nat @ SV1079 ) )
= ( one_one @ SV333 ) ) )
| ~ ( ~ ( ( ( number_number_of @ nat @ SV1079 )
!= ( zero_zero @ nat ) ) )
| ( ( power_power @ SV333 @ ( zero_zero @ SV333 ) @ ( number_number_of @ nat @ SV1079 ) )
= ( zero_zero @ SV333 ) ) ) ) )
= $true )
| ( ( power @ SV333 )
= $false )
| ( ( semiring_0 @ SV333 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4663]) ).
thf(4869,plain,
! [SV846: $i,SV704: $i,SV972: $i,SV582: $i,SV337: $i] :
( ( ( ~ ( zcong @ SV337 @ SV582 @ SV972 ) )
= $true )
| ( ( zcong @ ( times_times @ int @ SV704 @ SV337 ) @ ( times_times @ int @ SV846 @ SV582 ) @ SV972 )
= $true )
| ( ( zcong @ SV704 @ SV846 @ SV972 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4666]) ).
thf(4870,plain,
! [SV583: $i,SV705: $i,SV338: $i] :
( ( ( ~ ( ord_less @ real @ ( times_times @ real @ SV338 @ SV705 ) @ ( times_times @ real @ SV583 @ SV705 ) )
| ( ord_less @ real @ SV338 @ SV583 ) )
= $true )
| ( ( ord_less @ real @ ( zero_zero @ real ) @ SV705 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4667]) ).
thf(4871,plain,
! [SV705: $i,SV583: $i,SV338: $i] :
( ( ( ~ ( ord_less @ real @ SV338 @ SV583 )
| ( ord_less @ real @ ( times_times @ real @ SV338 @ SV705 ) @ ( times_times @ real @ SV583 @ SV705 ) ) )
= $true )
| ( ( ord_less @ real @ ( zero_zero @ real ) @ SV705 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4668]) ).
thf(4872,plain,
! [SV851: $i,SV347: $i] :
( ( ( ( power_power @ SV347 @ SV851 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= ( zero_zero @ SV347 ) )
= $true )
| ( ( ( ti @ SV347 @ SV851 )
= ( zero_zero @ SV347 ) )
= $true )
| ( ( ring_11004092258visors @ SV347 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4677]) ).
thf(4873,plain,
! [SV851: $i,SV347: $i] :
( ( ( ( ti @ SV347 @ SV851 )
!= ( zero_zero @ SV347 ) )
= $true )
| ( ( ( power_power @ SV347 @ SV851 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SV347 ) )
= $true )
| ( ( ring_11004092258visors @ SV347 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4678]) ).
thf(4874,plain,
! [SV853: $i,SV1041: $i,SV975: $i,SV349: $i] :
( ( ( dvd_dvd @ SV349 @ SV975 @ SV1041 )
= $false )
| ( ( dvd_dvd @ SV349 @ SV975 @ ( times_times @ SV349 @ SV1041 @ SV853 ) )
= $true )
| ( ( comm_semiring_1 @ SV349 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4680]) ).
thf(4875,plain,
! [SV976: $i,SV854: $i,SV351: $i] :
( ( ( ( ti @ SV351 @ SV854 )
= ( zero_zero @ SV351 ) )
= $true )
| ( ( ( ti @ SV351 @ SV976 )
= ( zero_zero @ SV351 ) )
= $true )
| ( ( ( times_times @ SV351 @ SV854 @ SV976 )
= ( zero_zero @ SV351 ) )
= $false )
| ( ( no_zero_divisors @ SV351 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4683]) ).
thf(4876,plain,
! [SV977: $i,SV855: $i,SV352: $i] :
( ( ( ( ( plus_plus @ SV352 @ ( power_power @ SV352 @ SV855 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV352 @ SV977 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV352 ) )
| ~ ( ( ( ti @ SV352 @ SV855 )
!= ( zero_zero @ SV352 ) )
| ( ( ti @ SV352 @ SV977 )
!= ( zero_zero @ SV352 ) ) ) )
= $true )
| ( ( linordered_idom @ SV352 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4684]) ).
thf(4877,plain,
! [SV977: $i,SV855: $i,SV352: $i] :
( ( ( ~ ~ ( ( ( ti @ SV352 @ SV855 )
!= ( zero_zero @ SV352 ) )
| ( ( ti @ SV352 @ SV977 )
!= ( zero_zero @ SV352 ) ) )
| ( ( plus_plus @ SV352 @ ( power_power @ SV352 @ SV855 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV352 @ SV977 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV352 ) ) )
= $true )
| ( ( linordered_idom @ SV352 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4685]) ).
thf(4878,plain,
! [SV856: $i,SV1042: $i,SV978: $i,SV353: $i] :
( ( ( ord_less_eq @ SV353 @ SV978 @ SV1042 )
= $false )
| ( ( ~ ( ord_less_eq @ SV353 @ ( zero_zero @ SV353 ) @ SV978 )
| ( ord_less_eq @ SV353 @ ( power_power @ SV353 @ SV978 @ SV856 ) @ ( power_power @ SV353 @ SV1042 @ SV856 ) ) )
= $true )
| ( ( linordered_semidom @ SV353 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4686]) ).
thf(4879,plain,
! [SV355: $i,SV1080: $i] :
( ( ( ~ ( ~ ( ( SV1080
!= ( zero_zero @ nat ) )
| ( ( power_power @ SV355 @ ( zero_zero @ SV355 ) @ SV1080 )
= ( one_one @ SV355 ) ) )
| ~ ( ~ ( ( SV1080
!= ( zero_zero @ nat ) ) )
| ( ( power_power @ SV355 @ ( zero_zero @ SV355 ) @ SV1080 )
= ( zero_zero @ SV355 ) ) ) ) )
= $true )
| ( ( power @ SV355 )
= $false )
| ( ( semiring_0 @ SV355 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4687]) ).
thf(4880,plain,
! [SV980: $i,SV858: $i,SV1044: $i,SV358: $i] :
( ( ( ord_less @ SV358 @ ( one_one @ SV358 ) @ SV1044 )
= $false )
| ( ( ~ ( ~ ( ~ ( ord_less_eq @ SV358 @ ( power_power @ SV358 @ SV1044 @ SV858 ) @ ( power_power @ SV358 @ SV1044 @ SV980 ) )
| ( ord_less_eq @ nat @ SV858 @ SV980 ) )
| ~ ( ~ ( ord_less_eq @ nat @ SV858 @ SV980 )
| ( ord_less_eq @ SV358 @ ( power_power @ SV358 @ SV1044 @ SV858 ) @ ( power_power @ SV358 @ SV1044 @ SV980 ) ) ) ) )
= $true )
| ( ( linordered_semidom @ SV358 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4688]) ).
thf(4881,plain,
! [SV981: $i,SV361: $i,SV859: $i] :
( ( ( ~ ( ord_less_eq @ int @ pls @ SV859 ) )
= $true )
| ( ( ( times_times @ SV361 @ ( number_number_of @ SV361 @ SV981 ) @ ( number_number_of @ SV361 @ SV859 ) )
= ( number_number_of @ SV361 @ ( times_times @ int @ SV981 @ SV859 ) ) )
= $true )
| ( ( ord_less_eq @ int @ pls @ SV981 )
= $false )
| ( ( number_semiring @ SV361 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4691]) ).
thf(4882,plain,
! [SV592: $i,SV710: $i,SV362: $i] :
( ( ( ~ ( ( ( times_times @ real @ SV362 @ SV710 )
!= ( times_times @ real @ SV592 @ SV710 ) )
| ( SV362 = SV592 ) ) )
= $false )
| ( ( SV710
= ( zero_zero @ real ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4692]) ).
thf(4883,plain,
! [SV710: $i,SV592: $i,SV362: $i] :
( ( ( ~ ( ( SV362 != SV592 )
| ( ( times_times @ real @ SV362 @ SV710 )
= ( times_times @ real @ SV592 @ SV710 ) ) ) )
= $false )
| ( ( SV710
= ( zero_zero @ real ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4692]) ).
thf(4884,plain,
! [SV860: $i,SV363: $i,SV982: $i] :
( ( ( ( SV982
!= ( zero_zero @ nat ) )
| ( ( power_power @ SV363 @ SV860 @ SV982 )
= ( one_one @ SV363 ) ) )
= $true )
| ( ( power @ SV363 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4693]) ).
thf(4885,plain,
! [SV860: $i,SV363: $i,SV982: $i] :
( ( ( ~ ( ( SV982
!= ( zero_zero @ nat ) ) )
| ( ( power_power @ SV363 @ SV860 @ SV982 )
= ( times_times @ SV363 @ SV860 @ ( power_power @ SV363 @ SV860 @ ( minus_minus @ nat @ SV982 @ ( one_one @ nat ) ) ) ) ) )
= $true )
| ( ( power @ SV363 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4694]) ).
thf(4886,plain,
! [SV366: $i,SV595: $i] :
( ( ( ord_less @ int @ SV595 @ pls )
= $true )
| ( ( ~ ( ~ ( ~ ( ord_less @ int @ SV366 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV595 ) @ ( number_number_of @ nat @ SV366 ) )
= ( number_number_of @ nat @ SV595 ) ) )
| ~ ( ~ ~ ( ord_less @ int @ SV366 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV595 ) @ ( number_number_of @ nat @ SV366 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SV595 @ SV366 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4696]) ).
thf(4887,plain,
! [SV861: $i,SV367: $i,SV1045: $i,SV983: $i] :
( ( ( ord_less_eq @ nat @ SV983 @ SV1045 )
= $false )
| ( ( dvd_dvd @ SV367 @ ( power_power @ SV367 @ SV861 @ SV983 ) @ ( power_power @ SV367 @ SV861 @ SV1045 ) )
= $true )
| ( ( comm_semiring_1 @ SV367 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4697]) ).
thf(4888,plain,
! [SV368: $i,SV596: $i] :
( ( ( SV596
= ( zero_zero @ nat ) )
= $true )
| ( ( ( times_times @ nat @ SV596 @ SV368 )
= ( plus_plus @ nat @ SV368 @ ( times_times @ nat @ ( minus_minus @ nat @ SV596 @ ( one_one @ nat ) ) @ SV368 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4699]) ).
thf(4889,plain,
! [SV601: $i,SV374: $i] :
( ( ( ( SV374
!= ( one_one @ nat ) )
| ( SV601
!= ( one_one @ nat ) ) )
= $false )
| ( ( ( times_times @ nat @ SV374 @ SV601 )
= ( one_one @ nat ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4705]) ).
thf(4890,plain,
! [SV601: $i,SV374: $i] :
( ( ( ( SV374
!= ( one_one @ nat ) )
| ( SV601
!= ( one_one @ nat ) ) )
= $true )
| ( ( ( times_times @ nat @ SV374 @ SV601 )
= ( one_one @ nat ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4706]) ).
thf(4891,plain,
! [SV865: $i,SV986: $i,SV376: $i] :
( ( ( ( ti @ SV376 @ SV986 )
= ( zero_zero @ SV376 ) )
= $true )
| ( ( ( power_power @ SV376 @ SV986 @ SV865 )
!= ( zero_zero @ SV376 ) )
= $true )
| ( ( ring_11004092258visors @ SV376 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4708]) ).
thf(4892,plain,
! [SV604: $i,SV382: $i,SV716: $i] :
( ( ( dvd_dvd @ int @ SV716 @ SV382 )
= $true )
| ( ( dvd_dvd @ int @ SV716 @ SV604 )
= $true )
| ( ( dvd_dvd @ int @ SV716 @ ( times_times @ int @ SV382 @ SV604 ) )
= $false )
| ( ( zprime @ SV716 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4710]) ).
thf(4893,plain,
! [SV869: $i,SV383: $i,SV1048: $i,SV988: $i] :
( ( ( ord_less @ nat @ SV988 @ SV1048 )
= $false )
| ( ( ~ ( ord_less @ SV383 @ ( one_one @ SV383 ) @ SV869 )
| ( ord_less @ SV383 @ ( power_power @ SV383 @ SV869 @ SV988 ) @ ( power_power @ SV383 @ SV869 @ SV1048 ) ) )
= $true )
| ( ( linordered_semidom @ SV383 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4711]) ).
thf(4894,plain,
! [SV717: $i,SV384: $i,SV605: $i] :
( ( ( ord_less_eq @ int @ SV605 @ SV384 )
= $true )
| ( ( ord_less_eq @ int @ SV384 @ SV605 )
= $true )
| ( ( ord_less @ int @ SV384 @ SV717 )
= $false )
| ( ( ord_less @ int @ SV605 @ SV717 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4712]) ).
thf(4895,plain,
! [SV870: $i,SV718: $i,SV606: $i,SV385: $i] :
( ( ( ord_less_eq @ int @ SV385 @ SV606 )
= $false )
| ( ( ord_less @ int @ ( plus_plus @ int @ SV718 @ SV385 ) @ ( plus_plus @ int @ SV870 @ SV606 ) )
= $true )
| ( ( ord_less @ int @ SV718 @ SV870 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4713]) ).
thf(4896,plain,
! [SV1081: $i,SV386: $i] :
( ( ( ! [SY2223: $i,SY2224: $i] :
( ( times_times @ SV386 @ ( minus_minus @ SV386 @ SV1081 @ SY2223 ) @ ( number_number_of @ SV386 @ SY2224 ) )
= ( minus_minus @ SV386 @ ( times_times @ SV386 @ SV1081 @ ( number_number_of @ SV386 @ SY2224 ) ) @ ( times_times @ SV386 @ SY2223 @ ( number_number_of @ SV386 @ SY2224 ) ) ) ) )
= $true )
| ( ( number @ SV386 )
= $false )
| ( ( ring @ SV386 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4714]) ).
thf(4897,plain,
! [SV390: $i,SV610: $i] :
( ( ( SV610
= ( zero_zero @ nat ) )
= $true )
| ( ( ( power_power @ nat @ SV390 @ SV610 )
= ( times_times @ nat @ SV390 @ ( power_power @ nat @ SV390 @ ( minus_minus @ nat @ SV610 @ ( one_one @ nat ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4718]) ).
thf(4898,plain,
! [SV612: $i,SV392: $i] :
( ( ( ~ ( ~ ( ord_less @ int @ SV392 @ SV612 )
| ( ord_less @ int @ pls @ SV612 ) )
| ~ ( ord_less @ int @ SV392 @ SV612 ) )
= $false )
| ( ( ord_less @ nat @ ( number_number_of @ nat @ SV392 ) @ ( number_number_of @ nat @ SV612 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4720]) ).
thf(4899,plain,
! [SV612: $i,SV392: $i] :
( ( ( ~ ( ~ ( ord_less @ int @ SV392 @ SV612 )
| ( ord_less @ int @ pls @ SV612 ) )
| ~ ( ord_less @ int @ SV392 @ SV612 ) )
= $true )
| ( ( ord_less @ nat @ ( number_number_of @ nat @ SV392 ) @ ( number_number_of @ nat @ SV612 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4721]) ).
thf(4900,plain,
! [SV615: $i,SV397: $i] :
( ( ( ( SV397
!= ( zero_zero @ real ) )
| ( SV615
!= ( zero_zero @ real ) ) )
= $false )
| ( ( ( plus_plus @ real @ ( times_times @ real @ SV397 @ SV397 ) @ ( times_times @ real @ SV615 @ SV615 ) )
= ( zero_zero @ real ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4724]) ).
thf(4901,plain,
! [SV615: $i,SV397: $i] :
( ( ( ( SV397
!= ( zero_zero @ real ) )
| ( SV615
!= ( zero_zero @ real ) ) )
= $true )
| ( ( ( plus_plus @ real @ ( times_times @ real @ SV397 @ SV397 ) @ ( times_times @ real @ SV615 @ SV615 ) )
= ( zero_zero @ real ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4725]) ).
thf(4902,plain,
( ( ( ( plus_plus @ int @ ( power_power @ int @ sK4_SX0 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ sK6_SY2112 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) )
= $true )
| ( ( t
= ( one_one @ int ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4727]) ).
thf(4903,plain,
! [SV722: $i,SV617: $i,SV405: $i] :
( ( ( zcong @ SV405 @ SV617 @ SV722 )
= $false )
| ( ( ~ ! [SY1940: $i] :
( ( ti @ int @ SV617 )
!= ( plus_plus @ int @ SV405 @ ( times_times @ int @ SV722 @ SY1940 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4728]) ).
thf(4904,plain,
! [SV722: $i,SV405: $i,SV617: $i] :
( ( ( ~ ! [SY1941: $i] :
( ( ti @ int @ SV617 )
!= ( plus_plus @ int @ SV405 @ ( times_times @ int @ SV722 @ SY1941 ) ) ) )
= $false )
| ( ( zcong @ SV405 @ SV617 @ SV722 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4729]) ).
thf(4905,plain,
! [SV407: $i] :
( ( ( ( ti @ int @ SV407 )
!= ( number_number_of @ int @ ( bit1 @ ( bit1 @ pls ) ) ) )
= $false )
| ( ( ord_less_eq @ int @ ( number_number_of @ int @ ( bit1 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SV407 )
= $true )
| ( ( ( ti @ int @ SV407 )
= ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true )
| ( ( zprime @ SV407 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4730]) ).
thf(4906,plain,
! [SV725: $i,SV620: $i,SV410: $i] :
( ( ( ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV410 ) )
= $true )
| ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV620 )
= $true )
| ( ( ord_less @ int @ SV725 @ SV410 )
= $false )
| ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( times_times @ int @ SV410 @ SV620 ) @ SV725 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4731]) ).
thf(4907,plain,
! [SV621: $i,SV413: $i] :
( ( ( ~ ( ( ( ti @ int @ SV413 )
!= ( one_one @ int ) )
| ( ( ti @ int @ SV621 )
!= ( one_one @ int ) ) ) )
= $true )
| ( ( ~ ( ( ( ti @ int @ SV413 )
!= ( number_number_of @ int @ min ) )
| ( ( ti @ int @ SV621 )
!= ( number_number_of @ int @ min ) ) ) )
= $true )
| ( ( ( times_times @ int @ SV413 @ SV621 )
= ( one_one @ int ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4732]) ).
thf(4908,plain,
! [SV621: $i,SV413: $i] :
( ( ( ~ ( ( ( ti @ int @ SV413 )
!= ( one_one @ int ) )
| ( ( ti @ int @ SV621 )
!= ( one_one @ int ) ) ) )
= $false )
| ( ( ( times_times @ int @ SV413 @ SV621 )
= ( one_one @ int ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4733]) ).
thf(4909,plain,
! [SV621: $i,SV413: $i] :
( ( ( ~ ( ( ( ti @ int @ SV413 )
!= ( number_number_of @ int @ min ) )
| ( ( ti @ int @ SV621 )
!= ( number_number_of @ int @ min ) ) ) )
= $false )
| ( ( ( times_times @ int @ SV413 @ SV621 )
= ( one_one @ int ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4733]) ).
thf(4910,plain,
! [SV1082: $i,SV416: $i] :
( ( ( ( power_power @ SV416 @ ( number_number_of @ SV416 @ SV1082 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times @ SV416 @ ( number_number_of @ SV416 @ SV1082 ) @ ( number_number_of @ SV416 @ SV1082 ) ) )
= $true )
| ( ( monoid_mult @ SV416 )
= $false )
| ( ( number @ SV416 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4734]) ).
thf(4911,plain,
! [SV994: $i,SV881: $i,SV417: $i] :
( ( ( ~ ( ord_less_eq @ SV417 @ ( zero_zero @ SV417 ) @ SV881 ) )
= $true )
| ( ( ord_less_eq @ SV417 @ ( times_times @ SV417 @ SV994 @ SV881 ) @ ( zero_zero @ SV417 ) )
= $true )
| ( ( ord_less_eq @ SV417 @ SV994 @ ( zero_zero @ SV417 ) )
= $false )
| ( ( ordere453448008miring @ SV417 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4735]) ).
thf(4912,plain,
! [SV419: $i,SV623: $i] :
( ( ( ( times_times @ int @ SV623 @ SV419 )
!= ( one_one @ int ) )
= $true )
| ( ( ~ ( ( ( ti @ int @ SV623 )
!= ( one_one @ int ) )
| ( ( ti @ int @ SV419 )
!= ( one_one @ int ) ) ) )
= $true )
| ( ( ord_less @ int @ ( zero_zero @ int ) @ SV623 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4738]) ).
thf(4913,plain,
! [SV419: $i,SV623: $i] :
( ( ( ~ ~ ( ( ( ti @ int @ SV623 )
!= ( one_one @ int ) )
| ( ( ti @ int @ SV419 )
!= ( one_one @ int ) ) ) )
= $true )
| ( ( ( times_times @ int @ SV623 @ SV419 )
= ( one_one @ int ) )
= $true )
| ( ( ord_less @ int @ ( zero_zero @ int ) @ SV623 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4739]) ).
thf(4914,plain,
! [SV421: $i,SV625: $i] :
( ( ( ord_less @ int @ SV625 @ pls )
= $true )
| ( ( ( times_times @ nat @ ( number_number_of @ nat @ SV625 ) @ ( number_number_of @ nat @ SV421 ) )
= ( number_number_of @ nat @ ( times_times @ int @ SV625 @ SV421 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4743]) ).
thf(4915,plain,
! [SV1052: $i,SV995: $i,SV882: $i,SV726: $i,SV626: $i,SV422: $i] :
( ( ( ( plus_plus @ int @ ( times_times @ int @ SV422 @ SV626 ) @ SV726 )
= ( plus_plus @ int @ ( times_times @ int @ SV882 @ SV995 ) @ SV1052 ) )
= $false )
| ( ( ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( times_times @ int @ SV882 @ SV995 ) @ SV1052 ) )
| ~ ( ord_less @ int @ SV1052 @ SV882 )
| ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV726 )
| ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV882 )
| ~ ( ord_less_eq @ int @ SV882 @ SV422 )
| ( ord_less_eq @ int @ SV626 @ SV995 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4744]) ).
thf(4916,plain,
! [SV728: $i,SV629: $i,SV427: $i] :
( ( ( zcong @ ( ti @ int @ SV427 ) @ SV629 @ SV728 )
= $false )
| ( ( zcong @ SV427 @ SV629 @ SV728 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4749]) ).
thf(4917,plain,
! [SV728: $i,SV629: $i,SV427: $i] :
( ( ( zcong @ SV427 @ SV629 @ SV728 )
= $false )
| ( ( zcong @ ( ti @ int @ SV427 ) @ SV629 @ SV728 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4750]) ).
thf(4918,plain,
! [SV631: $i,SV429: $i] :
( ( ( SV429
= ( one_one @ nat ) )
= $true )
| ( ( SV631
= ( zero_zero @ nat ) )
= $true )
| ( ( ( power_power @ nat @ SV429 @ SV631 )
= ( one_one @ nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4753]) ).
thf(4919,plain,
! [SV631: $i,SV429: $i] :
( ( ( SV429
= ( one_one @ nat ) )
= $false )
| ( ( ( power_power @ nat @ SV429 @ SV631 )
= ( one_one @ nat ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4754]) ).
thf(4920,plain,
! [SV429: $i,SV631: $i] :
( ( ( SV631
= ( zero_zero @ nat ) )
= $false )
| ( ( ( power_power @ nat @ SV429 @ SV631 )
= ( one_one @ nat ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4754]) ).
thf(4921,plain,
! [SV887: $i,SV433: $i,SV1053: $i,SV997: $i] :
( ( ( ord_less @ nat @ SV997 @ SV1053 )
= $false )
| ( ( ~ ( ord_less @ SV433 @ ( zero_zero @ SV433 ) @ SV887 )
| ~ ( ord_less @ SV433 @ SV887 @ ( one_one @ SV433 ) )
| ( ord_less @ SV433 @ ( power_power @ SV433 @ SV887 @ SV1053 ) @ ( power_power @ SV433 @ SV887 @ SV997 ) ) )
= $true )
| ( ( linordered_semidom @ SV433 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4755]) ).
thf(4922,plain,
! [SV998: $i,SV888: $i,SV1068: $i,SV1054: $i,SV1083: $i,SV434: $i] :
( ( ( ~ ( ( ( ti @ SV434 @ SV1083 )
!= ( zero_zero @ SV434 ) ) )
| ~ ~ ( ( ( ti @ SV434 @ SV1054 )
!= ( ti @ SV434 @ SV1068 ) )
| ~ ( ( ( ti @ SV434 @ SV888 )
!= ( ti @ SV434 @ SV998 ) ) ) )
| ( ( plus_plus @ SV434 @ SV1054 @ ( times_times @ SV434 @ SV1083 @ SV888 ) )
!= ( plus_plus @ SV434 @ SV1068 @ ( times_times @ SV434 @ SV1083 @ SV998 ) ) ) )
= $true )
| ( ( semiri456707255roduct @ SV434 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4756]) ).
thf(4923,plain,
! [SV732: $i,SV890: $i,SV481: $i,SV647: $i,SV79: $i] :
( ( ( ~ ( ~ ( zcong @ SV79 @ ( times_times @ int @ SV647 @ SV481 ) @ SV890 )
| ( zcong @ SV79 @ ( times_times @ int @ SV732 @ SV481 ) @ SV890 ) ) )
= $false )
| ( ( zcong @ SV647 @ SV732 @ SV890 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4757]) ).
thf(4924,plain,
! [SV647: $i,SV890: $i,SV481: $i,SV732: $i,SV79: $i] :
( ( ( ~ ( ~ ( zcong @ SV79 @ ( times_times @ int @ SV732 @ SV481 ) @ SV890 )
| ( zcong @ SV79 @ ( times_times @ int @ SV647 @ SV481 ) @ SV890 ) ) )
= $false )
| ( ( zcong @ SV647 @ SV732 @ SV890 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4757]) ).
thf(4925,plain,
! [SV891: $i,SV733: $i,SV82: $i] :
( ( ( ord_less_eq @ SV82 @ SV733 @ ( zero_zero @ SV82 ) )
= $false )
| ( ( ord_less_eq @ SV82 @ ( times_times @ SV82 @ SV891 @ SV733 ) @ ( zero_zero @ SV82 ) )
= $true )
| ( ( ord_less_eq @ SV82 @ ( zero_zero @ SV82 ) @ SV891 )
= $false )
| ( ( ordere453448008miring @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4761]) ).
thf(4926,plain,
! [SV894: $i,SV737: $i,SV87: $i] :
( ( ( ord_less_eq @ SV87 @ SV737 @ ( zero_zero @ SV87 ) )
= $false )
| ( ( ord_less_eq @ SV87 @ ( times_times @ SV87 @ SV737 @ SV894 ) @ ( zero_zero @ SV87 ) )
= $true )
| ( ( ord_less_eq @ SV87 @ ( zero_zero @ SV87 ) @ SV894 )
= $false )
| ( ( ordere453448008miring @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4762]) ).
thf(4927,plain,
! [SV896: $i,SV739: $i,SV90: $i] :
( ( ( ~ ( ( ( ti @ SV90 @ SV739 )
!= ( zero_zero @ SV90 ) ) ) )
= $true )
| ( ( ( times_times @ SV90 @ SV896 @ SV739 )
!= ( zero_zero @ SV90 ) )
= $true )
| ( ( ( ti @ SV90 @ SV896 )
= ( zero_zero @ SV90 ) )
= $true )
| ( ( no_zero_divisors @ SV90 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4763]) ).
thf(4928,plain,
! [SV490: $i,SV101: $i,SV652: $i] :
( ( ( dvd_dvd @ int @ SV652 @ SV101 )
= $false )
| ( ( zcong @ ( power_power @ int @ SV101 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SV490 @ SV652 )
= $false )
| ( ( zcong @ SV490 @ ( zero_zero @ int ) @ SV652 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4764]) ).
thf(4929,plain,
! [SV743: $i,SV900: $i,SV102: $i] :
( ( ( ord_less @ SV102 @ SV900 @ ( one_one @ SV102 ) )
= $false )
| ( ( ord_less @ SV102 @ ( times_times @ SV102 @ SV900 @ ( power_power @ SV102 @ SV900 @ SV743 ) ) @ ( power_power @ SV102 @ SV900 @ SV743 ) )
= $true )
| ( ( ord_less @ SV102 @ ( zero_zero @ SV102 ) @ SV900 )
= $false )
| ( ( linordered_semidom @ SV102 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4765]) ).
thf(4930,plain,
! [SV655: $i,SV901: $i,SV108: $i,SV494: $i,SV744: $i] :
( ( ( ( ti @ int @ SV744 )
= ( ti @ int @ SV494 ) )
= $false )
| ( ( ~ ( zcong @ SV494 @ SV108 @ SV901 )
| ( zcong @ SV655 @ SV108 @ SV901 ) )
= $true )
| ( ( zcong @ SV655 @ SV744 @ SV901 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4766]) ).
thf(4931,plain,
! [SV902: $i,SV1004: $i,SV746: $i,SV117: $i] :
( ( ( ~ ( ord_less_eq @ SV117 @ ( zero_zero @ SV117 ) @ SV746 ) )
= $true )
| ( ( ~ ( ord_less_eq @ SV117 @ SV746 @ ( one_one @ SV117 ) )
| ( ord_less_eq @ SV117 @ ( power_power @ SV117 @ SV746 @ SV1004 ) @ ( power_power @ SV117 @ SV746 @ SV902 ) ) )
= $true )
| ( ( ord_less_eq @ nat @ SV902 @ SV1004 )
= $false )
| ( ( linordered_semidom @ SV117 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4768]) ).
thf(4932,plain,
! [SV1069: $i,SV120: $i] :
( ( ( ~ ( ~ ( ord_less @ SV120 @ ( one_one @ SV120 ) @ ( number_number_of @ SV120 @ SV1069 ) )
| ( ord_less @ int @ ( bit1 @ pls ) @ SV1069 ) )
| ~ ( ~ ( ord_less @ int @ ( bit1 @ pls ) @ SV1069 )
| ( ord_less @ SV120 @ ( one_one @ SV120 ) @ ( number_number_of @ SV120 @ SV1069 ) ) ) )
= $false )
| ( ( number_ring @ SV120 )
= $false )
| ( ( linordered_idom @ SV120 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4769]) ).
thf(4933,plain,
! [SV1070: $i,SV123: $i] :
( ( ( ~ ( ~ ( ord_less_eq @ SV123 @ ( number_number_of @ SV123 @ SV1070 ) @ ( one_one @ SV123 ) )
| ( ord_less_eq @ int @ SV1070 @ ( bit1 @ pls ) ) )
| ~ ( ~ ( ord_less_eq @ int @ SV1070 @ ( bit1 @ pls ) )
| ( ord_less_eq @ SV123 @ ( number_number_of @ SV123 @ SV1070 ) @ ( one_one @ SV123 ) ) ) )
= $false )
| ( ( number_ring @ SV123 )
= $false )
| ( ( linordered_idom @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4771]) ).
thf(4934,plain,
! [SV903: $i,SV747: $i,SV1057: $i,SV1005: $i,SV124: $i] :
( ( ( dvd_dvd @ SV124 @ SV1005 @ SV1057 )
= $false )
| ( ( ~ ( dvd_dvd @ SV124 @ SV747 @ SV903 )
| ( dvd_dvd @ SV124 @ ( times_times @ SV124 @ SV1005 @ SV747 ) @ ( times_times @ SV124 @ SV1057 @ SV903 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV124 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4772]) ).
thf(4935,plain,
! [SV503: $i,SV753: $i,SV660: $i,SV132: $i,SV907: $i] :
( ( ( ord_less_eq @ int @ SV907 @ ( zero_zero @ int ) )
= $false )
| ( ( ~ ( ord_less @ int @ SV132 @ SV907 )
| ~ ( ord_less @ int @ SV132 @ SV660 )
| ( ord_less_eq @ int @ SV753 @ SV503 ) )
= $true )
| ( ( ord_less_eq @ int @ ( plus_plus @ int @ ( times_times @ int @ SV132 @ SV503 ) @ SV660 ) @ ( plus_plus @ int @ ( times_times @ int @ SV132 @ SV753 ) @ SV907 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4773]) ).
thf(4936,plain,
! [SV1071: $i,SV134: $i] :
( ( ( ~ ( ~ ( ord_less @ SV134 @ ( number_number_of @ SV134 @ SV1071 ) @ ( one_one @ SV134 ) )
| ( ord_less @ int @ SV1071 @ ( bit1 @ pls ) ) )
| ~ ( ~ ( ord_less @ int @ SV1071 @ ( bit1 @ pls ) )
| ( ord_less @ SV134 @ ( number_number_of @ SV134 @ SV1071 ) @ ( one_one @ SV134 ) ) ) )
= $false )
| ( ( number_ring @ SV134 )
= $false )
| ( ( linordered_idom @ SV134 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4774]) ).
thf(4937,plain,
! [SV505: $i,SV135: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV135 @ SV505 ) )
= $false )
| ( ( ord_less_eq @ int @ SV135 @ pls )
= $true )
| ( ( ord_less_eq @ nat @ ( number_number_of @ nat @ SV135 ) @ ( number_number_of @ nat @ SV505 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4775]) ).
thf(4938,plain,
! [SV505: $i,SV135: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV135 @ SV505 ) )
= $true )
| ( ( ord_less_eq @ nat @ ( number_number_of @ nat @ SV135 ) @ ( number_number_of @ nat @ SV505 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4776]) ).
thf(4939,plain,
! [SV1084: $i,SV1072: $i,SV139: $i] :
( ( ( ! [SY2225: $i] :
( ( times_times @ SV139 @ ( number_number_of @ SV139 @ SV1072 ) @ ( minus_minus @ SV139 @ SV1084 @ SY2225 ) )
= ( minus_minus @ SV139 @ ( times_times @ SV139 @ ( number_number_of @ SV139 @ SV1072 ) @ SV1084 ) @ ( times_times @ SV139 @ ( number_number_of @ SV139 @ SV1072 ) @ SY2225 ) ) ) )
= $true )
| ( ( number @ SV139 )
= $false )
| ( ( ring @ SV139 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4780]) ).
thf(4940,plain,
! [SV143: $i,SV509: $i] :
( ( ( ~ ( ( SV509
!= ( zero_zero @ nat ) ) ) )
= $false )
| ( ( ( power_power @ nat @ SV143 @ SV509 )
= ( zero_zero @ nat ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4781]) ).
thf(4941,plain,
! [SV509: $i,SV143: $i] :
( ( ( SV143
!= ( zero_zero @ nat ) )
= $false )
| ( ( ( power_power @ nat @ SV143 @ SV509 )
= ( zero_zero @ nat ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4781]) ).
thf(4942,plain,
! [SV143: $i,SV509: $i] :
( ( ( ~ ( ( SV509
!= ( zero_zero @ nat ) ) ) )
= $true )
| ( ( SV143
!= ( zero_zero @ nat ) )
= $true )
| ( ( ( power_power @ nat @ SV143 @ SV509 )
= ( zero_zero @ nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4782]) ).
thf(4943,plain,
! [SV512: $i,SV151: $i] :
( ( ( ~ ( dvd_dvd @ nat @ SV151 @ SV512 ) )
= $true )
| ( ( ~ ( dvd_dvd @ nat @ SV512 @ SV151 ) )
= $true )
| ( ( SV151 = SV512 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4788]) ).
thf(4944,plain,
! [SV512: $i,SV151: $i] :
( ( ( ~ ( dvd_dvd @ nat @ SV151 @ SV512 ) )
= $false )
| ( ( SV151 = SV512 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4789]) ).
thf(4945,plain,
! [SV151: $i,SV512: $i] :
( ( ( ~ ( dvd_dvd @ nat @ SV512 @ SV151 ) )
= $false )
| ( ( SV151 = SV512 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4789]) ).
thf(4946,plain,
! [SV910: $i,SV760: $i,SV152: $i] :
( ( ( ord_less_eq @ SV152 @ ( zero_zero @ SV152 ) @ SV760 )
= $false )
| ( ( ord_less_eq @ SV152 @ ( zero_zero @ SV152 ) @ ( times_times @ SV152 @ SV910 @ SV760 ) )
= $true )
| ( ( ord_less_eq @ SV152 @ ( zero_zero @ SV152 ) @ SV910 )
= $false )
| ( ( ordere453448008miring @ SV152 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4790]) ).
thf(4947,plain,
! [SV513: $i,SV153: $i] :
( ( ( ~ ( ~ ( ord_less @ real @ ( zero_zero @ real ) @ ( sK7_SY1807 @ SV153 @ SV513 ) )
| ( ( power_power @ real @ ( sK7_SY1807 @ SV153 @ SV513 ) @ SV513 )
!= SV153 ) ) )
= $true )
| ( ( ord_less @ real @ ( zero_zero @ real ) @ SV153 )
= $false )
| ( ( ord_less @ nat @ ( zero_zero @ nat ) @ SV513 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4791]) ).
thf(4948,plain,
! [SV911: $i,SV762: $i,SV1010: $i,SV155: $i] :
( ( ( ~ ( ~ ( ord_less @ SV155 @ ( power_power @ SV155 @ SV1010 @ SV762 ) @ ( power_power @ SV155 @ SV1010 @ SV911 ) )
| ( ord_less @ nat @ SV762 @ SV911 ) )
| ~ ( ~ ( ord_less @ nat @ SV762 @ SV911 )
| ( ord_less @ SV155 @ ( power_power @ SV155 @ SV1010 @ SV762 ) @ ( power_power @ SV155 @ SV1010 @ SV911 ) ) ) )
= $false )
| ( ( ord_less @ SV155 @ ( one_one @ SV155 ) @ SV1010 )
= $false )
| ( ( linordered_semidom @ SV155 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4792]) ).
thf(4949,plain,
! [SV665: $i,SV518: $i,SV161: $i] :
( ( ( ord_less @ int @ ( zero_zero @ int ) @ SV161 )
= $false )
| ( ( ord_less_eq @ int @ SV518 @ ( zero_zero @ int ) )
= $true )
| ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV665 )
= $false )
| ( ( ord_less @ int @ ( plus_plus @ int @ ( times_times @ int @ SV161 @ SV518 ) @ SV665 ) @ ( zero_zero @ int ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4793]) ).
thf(4950,plain,
! [SV913: $i,SV164: $i,SV667: $i,SV521: $i,SV765: $i] :
( ( ( ~ ( ~ ( dvd_dvd @ int @ SV765 @ ( plus_plus @ int @ SV521 @ SV667 ) )
| ( dvd_dvd @ int @ SV765 @ ( plus_plus @ int @ ( plus_plus @ int @ SV521 @ ( times_times @ int @ SV164 @ SV913 ) ) @ SV667 ) ) ) )
= $false )
| ( ( dvd_dvd @ int @ SV765 @ SV913 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4796]) ).
thf(4951,plain,
! [SV667: $i,SV913: $i,SV164: $i,SV521: $i,SV765: $i] :
( ( ( ~ ( ~ ( dvd_dvd @ int @ SV765 @ ( plus_plus @ int @ ( plus_plus @ int @ SV521 @ ( times_times @ int @ SV164 @ SV913 ) ) @ SV667 ) )
| ( dvd_dvd @ int @ SV765 @ ( plus_plus @ int @ SV521 @ SV667 ) ) ) )
= $false )
| ( ( dvd_dvd @ int @ SV765 @ SV913 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4796]) ).
thf(4952,plain,
! [SV768: $i,SV668: $i,SV916: $i,SV522: $i,SV167: $i] :
( ( ( zcong @ SV167 @ SV522 @ SV916 )
= $false )
| ( ( zcong @ ( minus_minus @ int @ SV668 @ SV167 ) @ ( minus_minus @ int @ SV768 @ SV522 ) @ SV916 )
= $true )
| ( ( zcong @ SV668 @ SV768 @ SV916 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4797]) ).
thf(4953,plain,
! [SV1085: $i,SV1073: $i,SV168: $i] :
( ( ( ! [SY2226: $i] :
( ( times_times @ SV168 @ ( plus_plus @ SV168 @ SV1073 @ SV1085 ) @ ( number_number_of @ SV168 @ SY2226 ) )
= ( plus_plus @ SV168 @ ( times_times @ SV168 @ SV1073 @ ( number_number_of @ SV168 @ SY2226 ) ) @ ( times_times @ SV168 @ SV1085 @ ( number_number_of @ SV168 @ SY2226 ) ) ) ) )
= $true )
| ( ( number @ SV168 )
= $false )
| ( ( semiring @ SV168 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4798]) ).
thf(4954,plain,
! [SV523: $i,SV169: $i] :
( ( ( SV169
!= ( zero_zero @ real ) )
= $false )
| ( ( ( plus_plus @ real @ ( power_power @ real @ SV169 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ real @ SV523 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ real ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4799]) ).
thf(4955,plain,
! [SV169: $i,SV523: $i] :
( ( ( SV523
!= ( zero_zero @ real ) )
= $false )
| ( ( ( plus_plus @ real @ ( power_power @ real @ SV169 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ real @ SV523 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ real ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4799]) ).
thf(4956,plain,
! [SV523: $i,SV169: $i] :
( ( ( SV169
!= ( zero_zero @ real ) )
= $true )
| ( ( SV523
!= ( zero_zero @ real ) )
= $true )
| ( ( ( plus_plus @ real @ ( power_power @ real @ SV169 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ real @ SV523 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ real ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4800]) ).
thf(4957,plain,
! [SV918: $i,SV771: $i,SV1060: $i,SV1013: $i,SV175: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( ( ti @ SV175 @ SV1013 )
!= ( ti @ SV175 @ SV1060 ) ) )
| ~ ( ( ( ti @ SV175 @ SV771 )
!= ( ti @ SV175 @ SV918 ) ) ) )
| ( ( plus_plus @ SV175 @ ( times_times @ SV175 @ SV1013 @ SV771 ) @ ( times_times @ SV175 @ SV1060 @ SV918 ) )
!= ( plus_plus @ SV175 @ ( times_times @ SV175 @ SV1013 @ SV918 ) @ ( times_times @ SV175 @ SV1060 @ SV771 ) ) ) ) )
= $false )
| ( ( semiri456707255roduct @ SV175 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4801]) ).
thf(4958,plain,
! [SV918: $i,SV1060: $i,SV771: $i,SV1013: $i,SV175: $i] :
( ( ( ~ ( ~ ( ( ( plus_plus @ SV175 @ ( times_times @ SV175 @ SV1013 @ SV771 ) @ ( times_times @ SV175 @ SV1060 @ SV918 ) )
!= ( plus_plus @ SV175 @ ( times_times @ SV175 @ SV1013 @ SV918 ) @ ( times_times @ SV175 @ SV1060 @ SV771 ) ) ) )
| ~ ( ~ ( ( ( ti @ SV175 @ SV1013 )
!= ( ti @ SV175 @ SV1060 ) ) )
| ~ ( ( ( ti @ SV175 @ SV771 )
!= ( ti @ SV175 @ SV918 ) ) ) ) ) )
= $false )
| ( ( semiri456707255roduct @ SV175 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4801]) ).
thf(4959,plain,
! [SV919: $i,SV772: $i,SV1014: $i,SV179: $i] :
( ( ( ~ ( ord_less @ SV179 @ ( power_power @ SV179 @ SV1014 @ SV772 ) @ ( power_power @ SV179 @ SV1014 @ SV919 ) ) )
= $true )
| ( ( ord_less @ nat @ SV772 @ SV919 )
= $true )
| ( ( ord_less @ SV179 @ ( one_one @ SV179 ) @ SV1014 )
= $false )
| ( ( linordered_semidom @ SV179 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4802]) ).
thf(4960,plain,
! [SV530: $i,SV187: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV187 @ SV530 ) )
= $false )
| ( ( ord_less @ int @ SV187 @ SV530 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4804]) ).
thf(4961,plain,
! [SV530: $i,SV187: $i] :
( ( ( ~ ( ( ( ti @ int @ SV187 )
!= ( ti @ int @ SV530 ) ) ) )
= $false )
| ( ( ord_less @ int @ SV187 @ SV530 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4804]) ).
thf(4962,plain,
! [SV530: $i,SV187: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV187 @ SV530 ) )
= $true )
| ( ( ~ ( ( ( ti @ int @ SV187 )
!= ( ti @ int @ SV530 ) ) ) )
= $true )
| ( ( ord_less @ int @ SV187 @ SV530 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4805]) ).
thf(4963,plain,
! [SV776: $i,SV189: $i] :
( ( ( ( plus_plus @ SV189 @ SV776 @ SV776 )
= ( zero_zero @ SV189 ) )
= $false )
| ( ( ( ti @ SV189 @ SV776 )
= ( zero_zero @ SV189 ) )
= $true )
| ( ( linord219039673up_add @ SV189 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4806]) ).
thf(4964,plain,
! [SV776: $i,SV189: $i] :
( ( ( ( ti @ SV189 @ SV776 )
= ( zero_zero @ SV189 ) )
= $false )
| ( ( ( plus_plus @ SV189 @ SV776 @ SV776 )
= ( zero_zero @ SV189 ) )
= $true )
| ( ( linord219039673up_add @ SV189 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4807]) ).
thf(4965,plain,
! [SV671: $i,SV191: $i,SV533: $i] :
( ( ( SV533
= ( zero_zero @ nat ) )
= $true )
| ( ( dvd_dvd @ nat @ SV191 @ SV671 )
= $true )
| ( ( dvd_dvd @ nat @ ( times_times @ nat @ SV191 @ SV533 ) @ ( times_times @ nat @ SV671 @ SV533 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4808]) ).
thf(4966,plain,
! [SV671: $i,SV191: $i,SV533: $i] :
( ( ( SV533
= ( zero_zero @ nat ) )
= $false )
| ( ( dvd_dvd @ nat @ ( times_times @ nat @ SV191 @ SV533 ) @ ( times_times @ nat @ SV671 @ SV533 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4809]) ).
thf(4967,plain,
! [SV533: $i,SV671: $i,SV191: $i] :
( ( ( dvd_dvd @ nat @ SV191 @ SV671 )
= $false )
| ( ( dvd_dvd @ nat @ ( times_times @ nat @ SV191 @ SV533 ) @ ( times_times @ nat @ SV671 @ SV533 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4809]) ).
thf(4968,plain,
! [SV923: $i,SV778: $i,SV193: $i] :
( ( ( ( plus_plus @ SV193 @ ( times_times @ SV193 @ SV778 @ SV778 ) @ ( times_times @ SV193 @ SV923 @ SV923 ) )
!= ( zero_zero @ SV193 ) )
= $true )
| ( ( ~ ( ( ( ti @ SV193 @ SV778 )
!= ( zero_zero @ SV193 ) )
| ( ( ti @ SV193 @ SV923 )
!= ( zero_zero @ SV193 ) ) ) )
= $true )
| ( ( linord581940658strict @ SV193 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4810]) ).
thf(4969,plain,
! [SV923: $i,SV778: $i,SV193: $i] :
( ( ( ~ ~ ( ( ( ti @ SV193 @ SV778 )
!= ( zero_zero @ SV193 ) )
| ( ( ti @ SV193 @ SV923 )
!= ( zero_zero @ SV193 ) ) ) )
= $true )
| ( ( ( plus_plus @ SV193 @ ( times_times @ SV193 @ SV778 @ SV778 ) @ ( times_times @ SV193 @ SV923 @ SV923 ) )
= ( zero_zero @ SV193 ) )
= $true )
| ( ( linord581940658strict @ SV193 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4811]) ).
thf(4970,plain,
! [SV924: $i,SV779: $i,SV1017: $i,SV194: $i] :
( ( ( ~ ( ( ( power_power @ SV194 @ SV1017 @ SV779 )
!= ( power_power @ SV194 @ SV1017 @ SV924 ) )
| ( SV779 = SV924 ) )
| ~ ( ( SV779 != SV924 )
| ( ( power_power @ SV194 @ SV1017 @ SV779 )
= ( power_power @ SV194 @ SV1017 @ SV924 ) ) ) )
= $false )
| ( ( ord_less @ SV194 @ ( one_one @ SV194 ) @ SV1017 )
= $false )
| ( ( linordered_semidom @ SV194 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4812]) ).
thf(4971,plain,
! [SV534: $i,SV672: $i,SV196: $i] :
( ( ( ~ ~ ( zcong @ SV196 @ ( zero_zero @ int ) @ SV672 ) )
= $true )
| ( ( ~ ( zcong @ ( times_times @ int @ SV534 @ SV196 ) @ ( zero_zero @ int ) @ SV672 ) )
= $true )
| ( ( zcong @ SV534 @ ( zero_zero @ int ) @ SV672 )
= $true )
| ( ( zprime @ SV672 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4813]) ).
thf(4972,plain,
! [SV928: $i,SV783: $i,SV199: $i] :
( ( ( ~ ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ ( times_times @ SV199 @ SV783 @ SV928 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ SV783 )
| ~ ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ SV928 ) )
| ~ ( ~ ( ord_less_eq @ SV199 @ SV783 @ ( zero_zero @ SV199 ) )
| ~ ( ord_less_eq @ SV199 @ SV928 @ ( zero_zero @ SV199 ) ) ) )
= $true )
| ( ( linord581940658strict @ SV199 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4814]) ).
thf(4973,plain,
! [SV928: $i,SV783: $i,SV199: $i] :
( ( ( ~ ( ~ ( ~ ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ SV783 )
| ~ ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ SV928 ) )
| ~ ( ~ ( ord_less_eq @ SV199 @ SV783 @ ( zero_zero @ SV199 ) )
| ~ ( ord_less_eq @ SV199 @ SV928 @ ( zero_zero @ SV199 ) ) ) ) )
= $true )
| ( ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ ( times_times @ SV199 @ SV783 @ SV928 ) )
= $true )
| ( ( linord581940658strict @ SV199 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4815]) ).
thf(4974,plain,
! [SV929: $i,SV201: $i,SV785: $i] :
( ( ( ord_less @ nat @ ( zero_zero @ nat ) @ SV785 )
= $false )
| ( ( ord_less @ SV201 @ ( one_one @ SV201 ) @ ( power_power @ SV201 @ SV929 @ SV785 ) )
= $true )
| ( ( ord_less @ SV201 @ ( one_one @ SV201 ) @ SV929 )
= $false )
| ( ( linordered_semidom @ SV201 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4816]) ).
thf(4975,plain,
! [SV1074: $i,SV202: $i] :
( ( ( ~ ( ~ ( ord_less_eq @ SV202 @ ( one_one @ SV202 ) @ ( number_number_of @ SV202 @ SV1074 ) )
| ( ord_less_eq @ int @ ( bit1 @ pls ) @ SV1074 ) )
| ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ pls ) @ SV1074 )
| ( ord_less_eq @ SV202 @ ( one_one @ SV202 ) @ ( number_number_of @ SV202 @ SV1074 ) ) ) )
= $false )
| ( ( number_ring @ SV202 )
= $false )
| ( ( linordered_idom @ SV202 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4817]) ).
thf(4976,plain,
! [SV535: $i,SV673: $i,SV203: $i] :
( ( ( ord_less @ int @ ( zero_zero @ int ) @ SV203 )
= $false )
| ( ( ~ ( ord_less @ int @ SV203 @ SV673 )
| ~ ( zcong @ SV673 @ SV203 @ SV535 ) )
= $true )
| ( ( ord_less @ int @ SV673 @ SV535 )
= $false )
| ( ( ord_less @ int @ ( zero_zero @ int ) @ SV673 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4818]) ).
thf(4977,plain,
! [SV787: $i,SV674: $i,SV930: $i,SV536: $i,SV206: $i] :
( ( ( zcong @ SV206 @ SV536 @ SV930 )
= $false )
| ( ( zcong @ ( plus_plus @ int @ SV674 @ SV206 ) @ ( plus_plus @ int @ SV787 @ SV536 ) @ SV930 )
= $true )
| ( ( zcong @ SV674 @ SV787 @ SV930 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4819]) ).
thf(4978,plain,
! [SV1086: $i,SV1075: $i,SV213: $i] :
( ( ( ~ ( ~ ( ( ( number_number_of @ SV213 @ SV1075 )
!= ( number_number_of @ SV213 @ SV1086 ) )
| ( ( ti @ int @ SV1075 )
= ( ti @ int @ SV1086 ) ) )
| ~ ( ( ( ti @ int @ SV1075 )
!= ( ti @ int @ SV1086 ) )
| ( ( number_number_of @ SV213 @ SV1075 )
= ( number_number_of @ SV213 @ SV1086 ) ) ) ) )
= $true )
| ( ( number_ring @ SV213 )
= $false )
| ( ( ring_char_0 @ SV213 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4820]) ).
thf(4979,plain,
! [SV538: $i,SV214: $i,SV676: $i,SV790: $i] :
( ( ( ~ ( ord_less @ nat @ SV790 @ SV676 ) )
= $true )
| ( ( ~ ( dvd_dvd @ nat @ SV676 @ SV214 ) )
= $true )
| ( ( ord_less @ nat @ ( zero_zero @ nat ) @ SV790 )
= $false )
| ( ( SV214
= ( plus_plus @ nat @ ( times_times @ nat @ SV538 @ SV676 ) @ SV790 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4821]) ).
thf(4980,plain,
! [SV1087: $i,SV1076: $i,SV218: $i] :
( ( ( ~ ( ~ ( ~ ( ord_less @ SV218 @ ( number_number_of @ SV218 @ SV1076 ) @ ( number_number_of @ SV218 @ SV1087 ) )
| ( ord_less @ int @ SV1076 @ SV1087 ) )
| ~ ( ~ ( ord_less @ int @ SV1076 @ SV1087 )
| ( ord_less @ SV218 @ ( number_number_of @ SV218 @ SV1076 ) @ ( number_number_of @ SV218 @ SV1087 ) ) ) ) )
= $true )
| ( ( number_ring @ SV218 )
= $false )
| ( ( linordered_idom @ SV218 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4823]) ).
thf(4981,plain,
! [SV792: $i,SV1061: $i,SV1018: $i,SV933: $i,SV220: $i] :
( ( ( dvd_dvd @ SV220 @ ( power_power @ SV220 @ SV933 @ SV1018 ) @ SV1061 )
= $false )
| ( ( ~ ( ord_less_eq @ nat @ SV792 @ SV1018 )
| ( dvd_dvd @ SV220 @ ( power_power @ SV220 @ SV933 @ SV792 ) @ SV1061 ) )
= $true )
| ( ( comm_semiring_1 @ SV220 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4824]) ).
thf(4982,plain,
! [SV1088: $i,SV1077: $i,SV234: $i] :
( ( ( ! [SY2227: $i] :
( ( times_times @ SV234 @ ( number_number_of @ SV234 @ SV1077 ) @ ( plus_plus @ SV234 @ SV1088 @ SY2227 ) )
= ( plus_plus @ SV234 @ ( times_times @ SV234 @ ( number_number_of @ SV234 @ SV1077 ) @ SV1088 ) @ ( times_times @ SV234 @ ( number_number_of @ SV234 @ SV1077 ) @ SY2227 ) ) ) )
= $true )
| ( ( number @ SV234 )
= $false )
| ( ( semiring @ SV234 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4830]) ).
thf(4983,plain,
! [SV937: $i,SV797: $i,SV237: $i] :
( ( ( ( number_number_of @ SV237 @ SV797 )
!= ( ti @ SV237 @ SV937 ) )
= $true )
| ( ( ( ti @ SV237 @ SV937 )
= ( number_number_of @ SV237 @ SV797 ) )
= $true )
| ( ( number @ SV237 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4831]) ).
thf(4984,plain,
! [SV797: $i,SV937: $i,SV237: $i] :
( ( ( ( ti @ SV237 @ SV937 )
!= ( number_number_of @ SV237 @ SV797 ) )
= $true )
| ( ( ( number_number_of @ SV237 @ SV797 )
= ( ti @ SV237 @ SV937 ) )
= $true )
| ( ( number @ SV237 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4832]) ).
thf(4985,plain,
! [SV549: $i,SV240: $i,SV683: $i,SV799: $i] :
( ( ( dvd_dvd @ int @ SV799 @ SV683 )
= $true )
| ( ( ~ ( dvd_dvd @ int @ ( power_power @ int @ SV799 @ SV240 ) @ ( times_times @ int @ SV683 @ SV549 ) )
| ( dvd_dvd @ int @ ( power_power @ int @ SV799 @ SV240 ) @ SV549 ) )
= $true )
| ( ( zprime @ SV799 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4833]) ).
thf(4986,plain,
! [SV552: $i,SV245: $i,SV685: $i] :
( ( ( ord_less @ int @ SV685 @ pls )
= $true )
| ( ( ( times_times @ nat @ ( number_number_of @ nat @ SV685 ) @ ( times_times @ nat @ ( number_number_of @ nat @ SV245 ) @ SV552 ) )
= ( times_times @ nat @ ( number_number_of @ nat @ ( times_times @ int @ SV685 @ SV245 ) ) @ SV552 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4835]) ).
thf(4987,plain,
! [SV1062: $i,SV1024: $i,SV942: $i,SV804: $i,SV255: $i] :
( ( ( ~ ( ( ( plus_plus @ SV255 @ ( times_times @ SV255 @ SV804 @ SV942 ) @ ( times_times @ SV255 @ SV1024 @ SV1062 ) )
!= ( plus_plus @ SV255 @ ( times_times @ SV255 @ SV804 @ SV1062 ) @ ( times_times @ SV255 @ SV1024 @ SV942 ) ) )
| ( ( ti @ SV255 @ SV804 )
= ( ti @ SV255 @ SV1024 ) )
| ( ( ti @ SV255 @ SV942 )
= ( ti @ SV255 @ SV1062 ) ) ) )
= $false )
| ( ( semiri456707255roduct @ SV255 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4839]) ).
thf(4988,plain,
! [SV1062: $i,SV942: $i,SV1024: $i,SV804: $i,SV255: $i] :
( ( ( ~ ( ~ ( ( ( ti @ SV255 @ SV804 )
= ( ti @ SV255 @ SV1024 ) )
| ( ( ti @ SV255 @ SV942 )
= ( ti @ SV255 @ SV1062 ) ) )
| ( ( plus_plus @ SV255 @ ( times_times @ SV255 @ SV804 @ SV942 ) @ ( times_times @ SV255 @ SV1024 @ SV1062 ) )
= ( plus_plus @ SV255 @ ( times_times @ SV255 @ SV804 @ SV1062 ) @ ( times_times @ SV255 @ SV1024 @ SV942 ) ) ) ) )
= $false )
| ( ( semiri456707255roduct @ SV255 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4839]) ).
thf(4989,plain,
! [SV805: $i,SV943: $i,SV688: $i,SV557: $i,SV257: $i] :
( ( ( ~ ( ~ ( zcong @ SV257 @ ( times_times @ int @ SV557 @ SV688 ) @ SV943 )
| ( zcong @ SV257 @ ( times_times @ int @ SV557 @ SV805 ) @ SV943 ) ) )
= $false )
| ( ( zcong @ SV688 @ SV805 @ SV943 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4840]) ).
thf(4990,plain,
! [SV688: $i,SV943: $i,SV805: $i,SV557: $i,SV257: $i] :
( ( ( ~ ( ~ ( zcong @ SV257 @ ( times_times @ int @ SV557 @ SV805 ) @ SV943 )
| ( zcong @ SV257 @ ( times_times @ int @ SV557 @ SV688 ) @ SV943 ) ) )
= $false )
| ( ( zcong @ SV688 @ SV805 @ SV943 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4840]) ).
thf(4991,plain,
! [SV810: $i,SV269: $i] :
( ( ( ord_less @ SV269 @ ( plus_plus @ SV269 @ SV810 @ SV810 ) @ ( zero_zero @ SV269 ) )
= $false )
| ( ( ord_less @ SV269 @ SV810 @ ( zero_zero @ SV269 ) )
= $true )
| ( ( linordered_idom @ SV269 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4844]) ).
thf(4992,plain,
! [SV810: $i,SV269: $i] :
( ( ( ord_less @ SV269 @ SV810 @ ( zero_zero @ SV269 ) )
= $false )
| ( ( ord_less @ SV269 @ ( plus_plus @ SV269 @ SV810 @ SV810 ) @ ( zero_zero @ SV269 ) )
= $true )
| ( ( linordered_idom @ SV269 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4845]) ).
thf(4993,plain,
! [SV562: $i,SV273: $i,SV691: $i] :
( ( ( ( ( times_times @ real @ SV691 @ SV273 )
!= ( times_times @ real @ SV691 @ SV562 ) )
| ( SV273 = SV562 ) )
= $true )
| ( ( SV691
= ( zero_zero @ real ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4846]) ).
thf(4994,plain,
! [SV691: $i,SV562: $i,SV273: $i] :
( ( ( ( SV273 != SV562 )
| ( ( times_times @ real @ SV691 @ SV273 )
= ( times_times @ real @ SV691 @ SV562 ) ) )
= $true )
| ( ( SV691
= ( zero_zero @ real ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4847]) ).
thf(4995,plain,
! [SV1027: $i,SV815: $i,SV949: $i,SV277: $i] :
( ( ( ~ ( dvd_dvd @ SV277 @ SV949 @ SV815 ) )
= $true )
| ( ( dvd_dvd @ SV277 @ SV949 @ ( plus_plus @ SV277 @ SV1027 @ SV815 ) )
= $true )
| ( ( dvd_dvd @ SV277 @ SV949 @ SV1027 )
= $false )
| ( ( comm_semiring_1 @ SV277 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4848]) ).
thf(4996,plain,
! [SV951: $i,SV285: $i,SV819: $i] :
( ( ( ord_less_eq @ int @ pls @ SV819 )
= $false )
| ( ( ( plus_plus @ SV285 @ ( number_number_of @ SV285 @ SV951 ) @ ( number_number_of @ SV285 @ SV819 ) )
= ( number_number_of @ SV285 @ ( plus_plus @ int @ SV951 @ SV819 ) ) )
= $true )
| ( ( ord_less_eq @ int @ pls @ SV951 )
= $false )
| ( ( number_semiring @ SV285 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4850]) ).
thf(4997,plain,
! [SV566: $i,SV288: $i,SV694: $i,SV821: $i] :
( ( ( dvd_dvd @ int @ SV821 @ SV694 )
= $true )
| ( ( ~ ( dvd_dvd @ int @ ( power_power @ int @ SV821 @ SV288 ) @ ( times_times @ int @ SV566 @ SV694 ) )
| ( dvd_dvd @ int @ ( power_power @ int @ SV821 @ SV288 ) @ SV566 ) )
= $true )
| ( ( zprime @ SV821 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4851]) ).
thf(4998,plain,
! [SV955: $i,SV826: $i,SV301: $i] :
( ( ( ( times_times @ SV301 @ SV826 @ SV955 )
!= ( zero_zero @ SV301 ) )
= $true )
| ( ( ( ( ti @ SV301 @ SV826 )
= ( zero_zero @ SV301 ) )
| ( ( ti @ SV301 @ SV955 )
= ( zero_zero @ SV301 ) ) )
= $true )
| ( ( ring_n68954251visors @ SV301 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4852]) ).
thf(4999,plain,
! [SV955: $i,SV826: $i,SV301: $i] :
( ( ( ~ ( ( ( ti @ SV301 @ SV826 )
= ( zero_zero @ SV301 ) )
| ( ( ti @ SV301 @ SV955 )
= ( zero_zero @ SV301 ) ) ) )
= $true )
| ( ( ( times_times @ SV301 @ SV826 @ SV955 )
= ( zero_zero @ SV301 ) )
= $true )
| ( ( ring_n68954251visors @ SV301 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4853]) ).
thf(5000,plain,
! [SV956: $i,SV828: $i,SV1031: $i,SV304: $i] :
( ( ( ~ ( ord_less_eq @ SV304 @ ( power_power @ SV304 @ SV1031 @ SV828 ) @ ( power_power @ SV304 @ SV1031 @ SV956 ) ) )
= $true )
| ( ( ord_less_eq @ nat @ SV828 @ SV956 )
= $true )
| ( ( ord_less @ SV304 @ ( one_one @ SV304 ) @ SV1031 )
= $false )
| ( ( linordered_semidom @ SV304 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4854]) ).
thf(5001,plain,
! [SV573: $i,SV305: $i,SV698: $i,SV1032: $i,SV957: $i,SV829: $i] :
( ( ( ~ ( ord_less @ int @ ( plus_plus @ int @ ( times_times @ int @ SV829 @ SV957 ) @ SV1032 ) @ ( zero_zero @ int ) ) )
= $true )
| ( ( ~ ( ord_less @ int @ SV698 @ SV305 )
| ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV1032 )
| ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV829 )
| ~ ( ord_less_eq @ int @ SV829 @ SV305 )
| ( ord_less_eq @ int @ SV957 @ SV573 ) )
= $true )
| ( ( ( plus_plus @ int @ ( times_times @ int @ SV305 @ SV573 ) @ SV698 )
= ( plus_plus @ int @ ( times_times @ int @ SV829 @ SV957 ) @ SV1032 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4855]) ).
thf(5002,plain,
! [SV833: $i,SV576: $i,SV960: $i,SV312: $i,SV701: $i] :
( ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV701 )
= $false )
| ( ( ~ ( ord_less @ int @ SV701 @ SV312 )
| ~ ( ord_less @ int @ SV960 @ SV312 )
| ( ord_less_eq @ int @ SV576 @ SV833 ) )
= $true )
| ( ( ord_less_eq @ int @ ( plus_plus @ int @ ( times_times @ int @ SV312 @ SV576 ) @ SV701 ) @ ( plus_plus @ int @ ( times_times @ int @ SV312 @ SV833 ) @ SV960 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4856]) ).
thf(5003,plain,
! [SV961: $i,SV834: $i,SV313: $i] :
( ( ( ( ti @ SV313 @ SV834 )
!= ( plus_plus @ SV313 @ SV834 @ SV961 ) )
= $true )
| ( ( ( ti @ SV313 @ SV961 )
= ( zero_zero @ SV313 ) )
= $true )
| ( ( semiri456707255roduct @ SV313 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4857]) ).
thf(5004,plain,
! [SV834: $i,SV961: $i,SV313: $i] :
( ( ( ( ti @ SV313 @ SV961 )
!= ( zero_zero @ SV313 ) )
= $true )
| ( ( ( ti @ SV313 @ SV834 )
= ( plus_plus @ SV313 @ SV834 @ SV961 ) )
= $true )
| ( ( semiri456707255roduct @ SV313 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4858]) ).
thf(5005,plain,
! [SV577: $i,SV314: $i] :
( ( ( ~ ( zcong @ ( power_power @ int @ ( sK8_SY1865 @ SV314 @ SV577 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SV577 @ SV314 ) )
= $false )
| ( ( quadRes @ SV314 @ SV577 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4859]) ).
thf(5006,plain,
! [SV314: $i,SV577: $i,SV1089: $i] :
( ( ( ~ ( zcong @ ( power_power @ int @ SV1089 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SV577 @ SV314 ) )
= $true )
| ( ( quadRes @ SV314 @ SV577 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4860]) ).
thf(5007,plain,
! [SV1034: $i,SV962: $i,SV835: $i,SV315: $i] :
( ( ( ~ ( ord_less_eq @ SV315 @ ( one_one @ SV315 ) @ SV835 ) )
= $true )
| ( ( ord_less_eq @ SV315 @ ( power_power @ SV315 @ SV835 @ SV962 ) @ ( power_power @ SV315 @ SV835 @ SV1034 ) )
= $true )
| ( ( ord_less_eq @ nat @ SV962 @ SV1034 )
= $false )
| ( ( linordered_semidom @ SV315 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4861]) ).
thf(5008,plain,
! [SV966: $i,SV839: $i,SV319: $i] :
( ( ( ~ ( ord_less_eq @ SV319 @ ( times_times @ SV319 @ SV839 @ SV966 ) @ ( zero_zero @ SV319 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SV839 )
| ~ ( ord_less_eq @ SV319 @ SV966 @ ( zero_zero @ SV319 ) ) )
| ~ ( ~ ( ord_less_eq @ SV319 @ SV839 @ ( zero_zero @ SV319 ) )
| ~ ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SV966 ) ) )
= $true )
| ( ( linord581940658strict @ SV319 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4862]) ).
thf(5009,plain,
! [SV966: $i,SV839: $i,SV319: $i] :
( ( ( ~ ( ~ ( ~ ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SV839 )
| ~ ( ord_less_eq @ SV319 @ SV966 @ ( zero_zero @ SV319 ) ) )
| ~ ( ~ ( ord_less_eq @ SV319 @ SV839 @ ( zero_zero @ SV319 ) )
| ~ ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SV966 ) ) ) )
= $true )
| ( ( ord_less_eq @ SV319 @ ( times_times @ SV319 @ SV839 @ SV966 ) @ ( zero_zero @ SV319 ) )
= $true )
| ( ( linord581940658strict @ SV319 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4863]) ).
thf(5010,plain,
! [SV1090: $i,SV1078: $i,SV321: $i] :
( ( ( ~ ( ~ ( ~ ( ord_less_eq @ SV321 @ ( number_number_of @ SV321 @ SV1078 ) @ ( number_number_of @ SV321 @ SV1090 ) )
| ( ord_less_eq @ int @ SV1078 @ SV1090 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV1078 @ SV1090 )
| ( ord_less_eq @ SV321 @ ( number_number_of @ SV321 @ SV1078 ) @ ( number_number_of @ SV321 @ SV1090 ) ) ) ) )
= $true )
| ( ( number_ring @ SV321 )
= $false )
| ( ( linordered_idom @ SV321 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4864]) ).
thf(5011,plain,
! [SV967: $i,SV841: $i,SV1064: $i,SV1036: $i,SV323: $i] :
( ( ( dvd_dvd @ SV323 @ SV1036 @ SV1064 )
= $false )
| ( ( ~ ( ord_less_eq @ nat @ SV841 @ SV967 )
| ( dvd_dvd @ SV323 @ ( power_power @ SV323 @ SV1036 @ SV841 ) @ ( power_power @ SV323 @ SV1064 @ SV967 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV323 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4865]) ).
thf(5012,plain,
! [SV842: $i,SV968: $i,SV325: $i] :
( ( ( ord_less_eq @ SV325 @ ( zero_zero @ SV325 ) @ SV968 )
= $false )
| ( ( ord_less_eq @ SV325 @ SV842 @ SV968 )
= $true )
| ( ( ord_less_eq @ SV325 @ ( power_power @ SV325 @ SV842 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV325 @ SV968 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $false )
| ( ( linordered_semidom @ SV325 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4866]) ).
thf(5013,plain,
! [SV333: $i,SV1079: $i] :
( ( ( ~ ( ( ( number_number_of @ nat @ SV1079 )
!= ( zero_zero @ nat ) )
| ( ( power_power @ SV333 @ ( zero_zero @ SV333 ) @ ( number_number_of @ nat @ SV1079 ) )
= ( one_one @ SV333 ) ) )
| ~ ( ~ ( ( ( number_number_of @ nat @ SV1079 )
!= ( zero_zero @ nat ) ) )
| ( ( power_power @ SV333 @ ( zero_zero @ SV333 ) @ ( number_number_of @ nat @ SV1079 ) )
= ( zero_zero @ SV333 ) ) ) )
= $false )
| ( ( power @ SV333 )
= $false )
| ( ( semiring_0 @ SV333 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4868]) ).
thf(5014,plain,
! [SV846: $i,SV704: $i,SV972: $i,SV582: $i,SV337: $i] :
( ( ( zcong @ SV337 @ SV582 @ SV972 )
= $false )
| ( ( zcong @ ( times_times @ int @ SV704 @ SV337 ) @ ( times_times @ int @ SV846 @ SV582 ) @ SV972 )
= $true )
| ( ( zcong @ SV704 @ SV846 @ SV972 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4869]) ).
thf(5015,plain,
! [SV583: $i,SV705: $i,SV338: $i] :
( ( ( ~ ( ord_less @ real @ ( times_times @ real @ SV338 @ SV705 ) @ ( times_times @ real @ SV583 @ SV705 ) ) )
= $true )
| ( ( ord_less @ real @ SV338 @ SV583 )
= $true )
| ( ( ord_less @ real @ ( zero_zero @ real ) @ SV705 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4870]) ).
thf(5016,plain,
! [SV705: $i,SV583: $i,SV338: $i] :
( ( ( ~ ( ord_less @ real @ SV338 @ SV583 ) )
= $true )
| ( ( ord_less @ real @ ( times_times @ real @ SV338 @ SV705 ) @ ( times_times @ real @ SV583 @ SV705 ) )
= $true )
| ( ( ord_less @ real @ ( zero_zero @ real ) @ SV705 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4871]) ).
thf(5017,plain,
! [SV851: $i,SV347: $i] :
( ( ( ( power_power @ SV347 @ SV851 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SV347 ) )
= $false )
| ( ( ( ti @ SV347 @ SV851 )
= ( zero_zero @ SV347 ) )
= $true )
| ( ( ring_11004092258visors @ SV347 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4872]) ).
thf(5018,plain,
! [SV851: $i,SV347: $i] :
( ( ( ( ti @ SV347 @ SV851 )
= ( zero_zero @ SV347 ) )
= $false )
| ( ( ( power_power @ SV347 @ SV851 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SV347 ) )
= $true )
| ( ( ring_11004092258visors @ SV347 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4873]) ).
thf(5019,plain,
! [SV977: $i,SV855: $i,SV352: $i] :
( ( ( ( plus_plus @ SV352 @ ( power_power @ SV352 @ SV855 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV352 @ SV977 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV352 ) )
= $true )
| ( ( ~ ( ( ( ti @ SV352 @ SV855 )
!= ( zero_zero @ SV352 ) )
| ( ( ti @ SV352 @ SV977 )
!= ( zero_zero @ SV352 ) ) ) )
= $true )
| ( ( linordered_idom @ SV352 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4876]) ).
thf(5020,plain,
! [SV977: $i,SV855: $i,SV352: $i] :
( ( ( ~ ~ ( ( ( ti @ SV352 @ SV855 )
!= ( zero_zero @ SV352 ) )
| ( ( ti @ SV352 @ SV977 )
!= ( zero_zero @ SV352 ) ) ) )
= $true )
| ( ( ( plus_plus @ SV352 @ ( power_power @ SV352 @ SV855 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV352 @ SV977 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV352 ) )
= $true )
| ( ( linordered_idom @ SV352 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4877]) ).
thf(5021,plain,
! [SV1042: $i,SV856: $i,SV978: $i,SV353: $i] :
( ( ( ~ ( ord_less_eq @ SV353 @ ( zero_zero @ SV353 ) @ SV978 ) )
= $true )
| ( ( ord_less_eq @ SV353 @ ( power_power @ SV353 @ SV978 @ SV856 ) @ ( power_power @ SV353 @ SV1042 @ SV856 ) )
= $true )
| ( ( ord_less_eq @ SV353 @ SV978 @ SV1042 )
= $false )
| ( ( linordered_semidom @ SV353 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4878]) ).
thf(5022,plain,
! [SV355: $i,SV1080: $i] :
( ( ( ~ ( ( SV1080
!= ( zero_zero @ nat ) )
| ( ( power_power @ SV355 @ ( zero_zero @ SV355 ) @ SV1080 )
= ( one_one @ SV355 ) ) )
| ~ ( ~ ( ( SV1080
!= ( zero_zero @ nat ) ) )
| ( ( power_power @ SV355 @ ( zero_zero @ SV355 ) @ SV1080 )
= ( zero_zero @ SV355 ) ) ) )
= $false )
| ( ( power @ SV355 )
= $false )
| ( ( semiring_0 @ SV355 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4879]) ).
thf(5023,plain,
! [SV980: $i,SV858: $i,SV1044: $i,SV358: $i] :
( ( ( ~ ( ~ ( ord_less_eq @ SV358 @ ( power_power @ SV358 @ SV1044 @ SV858 ) @ ( power_power @ SV358 @ SV1044 @ SV980 ) )
| ( ord_less_eq @ nat @ SV858 @ SV980 ) )
| ~ ( ~ ( ord_less_eq @ nat @ SV858 @ SV980 )
| ( ord_less_eq @ SV358 @ ( power_power @ SV358 @ SV1044 @ SV858 ) @ ( power_power @ SV358 @ SV1044 @ SV980 ) ) ) )
= $false )
| ( ( ord_less @ SV358 @ ( one_one @ SV358 ) @ SV1044 )
= $false )
| ( ( linordered_semidom @ SV358 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4880]) ).
thf(5024,plain,
! [SV981: $i,SV361: $i,SV859: $i] :
( ( ( ord_less_eq @ int @ pls @ SV859 )
= $false )
| ( ( ( times_times @ SV361 @ ( number_number_of @ SV361 @ SV981 ) @ ( number_number_of @ SV361 @ SV859 ) )
= ( number_number_of @ SV361 @ ( times_times @ int @ SV981 @ SV859 ) ) )
= $true )
| ( ( ord_less_eq @ int @ pls @ SV981 )
= $false )
| ( ( number_semiring @ SV361 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4881]) ).
thf(5025,plain,
! [SV592: $i,SV710: $i,SV362: $i] :
( ( ( ( ( times_times @ real @ SV362 @ SV710 )
!= ( times_times @ real @ SV592 @ SV710 ) )
| ( SV362 = SV592 ) )
= $true )
| ( ( SV710
= ( zero_zero @ real ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4882]) ).
thf(5026,plain,
! [SV710: $i,SV592: $i,SV362: $i] :
( ( ( ( SV362 != SV592 )
| ( ( times_times @ real @ SV362 @ SV710 )
= ( times_times @ real @ SV592 @ SV710 ) ) )
= $true )
| ( ( SV710
= ( zero_zero @ real ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4883]) ).
thf(5027,plain,
! [SV860: $i,SV363: $i,SV982: $i] :
( ( ( SV982
!= ( zero_zero @ nat ) )
= $true )
| ( ( ( power_power @ SV363 @ SV860 @ SV982 )
= ( one_one @ SV363 ) )
= $true )
| ( ( power @ SV363 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4884]) ).
thf(5028,plain,
! [SV860: $i,SV363: $i,SV982: $i] :
( ( ( ~ ( ( SV982
!= ( zero_zero @ nat ) ) ) )
= $true )
| ( ( ( power_power @ SV363 @ SV860 @ SV982 )
= ( times_times @ SV363 @ SV860 @ ( power_power @ SV363 @ SV860 @ ( minus_minus @ nat @ SV982 @ ( one_one @ nat ) ) ) ) )
= $true )
| ( ( power @ SV363 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4885]) ).
thf(5029,plain,
! [SV595: $i,SV366: $i] :
( ( ( ~ ( ~ ( ord_less @ int @ SV366 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV595 ) @ ( number_number_of @ nat @ SV366 ) )
= ( number_number_of @ nat @ SV595 ) ) )
| ~ ( ~ ~ ( ord_less @ int @ SV366 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV595 ) @ ( number_number_of @ nat @ SV366 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SV595 @ SV366 ) ) ) ) )
= $false )
| ( ( ord_less @ int @ SV595 @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4886]) ).
thf(5030,plain,
! [SV601: $i,SV374: $i] :
( ( ( SV374
!= ( one_one @ nat ) )
= $false )
| ( ( ( times_times @ nat @ SV374 @ SV601 )
= ( one_one @ nat ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4889]) ).
thf(5031,plain,
! [SV374: $i,SV601: $i] :
( ( ( SV601
!= ( one_one @ nat ) )
= $false )
| ( ( ( times_times @ nat @ SV374 @ SV601 )
= ( one_one @ nat ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4889]) ).
thf(5032,plain,
! [SV601: $i,SV374: $i] :
( ( ( SV374
!= ( one_one @ nat ) )
= $true )
| ( ( SV601
!= ( one_one @ nat ) )
= $true )
| ( ( ( times_times @ nat @ SV374 @ SV601 )
= ( one_one @ nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4890]) ).
thf(5033,plain,
! [SV865: $i,SV986: $i,SV376: $i] :
( ( ( ( power_power @ SV376 @ SV986 @ SV865 )
= ( zero_zero @ SV376 ) )
= $false )
| ( ( ( ti @ SV376 @ SV986 )
= ( zero_zero @ SV376 ) )
= $true )
| ( ( ring_11004092258visors @ SV376 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4891]) ).
thf(5034,plain,
! [SV1048: $i,SV988: $i,SV869: $i,SV383: $i] :
( ( ( ~ ( ord_less @ SV383 @ ( one_one @ SV383 ) @ SV869 ) )
= $true )
| ( ( ord_less @ SV383 @ ( power_power @ SV383 @ SV869 @ SV988 ) @ ( power_power @ SV383 @ SV869 @ SV1048 ) )
= $true )
| ( ( ord_less @ nat @ SV988 @ SV1048 )
= $false )
| ( ( linordered_semidom @ SV383 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4893]) ).
thf(5035,plain,
! [SV1091: $i,SV1081: $i,SV386: $i] :
( ( ( ! [SY2228: $i] :
( ( times_times @ SV386 @ ( minus_minus @ SV386 @ SV1081 @ SV1091 ) @ ( number_number_of @ SV386 @ SY2228 ) )
= ( minus_minus @ SV386 @ ( times_times @ SV386 @ SV1081 @ ( number_number_of @ SV386 @ SY2228 ) ) @ ( times_times @ SV386 @ SV1091 @ ( number_number_of @ SV386 @ SY2228 ) ) ) ) )
= $true )
| ( ( number @ SV386 )
= $false )
| ( ( ring @ SV386 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4896]) ).
thf(5036,plain,
! [SV612: $i,SV392: $i] :
( ( ( ~ ( ~ ( ord_less @ int @ SV392 @ SV612 )
| ( ord_less @ int @ pls @ SV612 ) ) )
= $false )
| ( ( ord_less @ nat @ ( number_number_of @ nat @ SV392 ) @ ( number_number_of @ nat @ SV612 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4898]) ).
thf(5037,plain,
! [SV612: $i,SV392: $i] :
( ( ( ~ ( ord_less @ int @ SV392 @ SV612 ) )
= $false )
| ( ( ord_less @ nat @ ( number_number_of @ nat @ SV392 ) @ ( number_number_of @ nat @ SV612 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4898]) ).
thf(5038,plain,
! [SV612: $i,SV392: $i] :
( ( ( ~ ( ~ ( ord_less @ int @ SV392 @ SV612 )
| ( ord_less @ int @ pls @ SV612 ) ) )
= $true )
| ( ( ~ ( ord_less @ int @ SV392 @ SV612 ) )
= $true )
| ( ( ord_less @ nat @ ( number_number_of @ nat @ SV392 ) @ ( number_number_of @ nat @ SV612 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4899]) ).
thf(5039,plain,
! [SV615: $i,SV397: $i] :
( ( ( SV397
!= ( zero_zero @ real ) )
= $false )
| ( ( ( plus_plus @ real @ ( times_times @ real @ SV397 @ SV397 ) @ ( times_times @ real @ SV615 @ SV615 ) )
= ( zero_zero @ real ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4900]) ).
thf(5040,plain,
! [SV397: $i,SV615: $i] :
( ( ( SV615
!= ( zero_zero @ real ) )
= $false )
| ( ( ( plus_plus @ real @ ( times_times @ real @ SV397 @ SV397 ) @ ( times_times @ real @ SV615 @ SV615 ) )
= ( zero_zero @ real ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4900]) ).
thf(5041,plain,
! [SV615: $i,SV397: $i] :
( ( ( SV397
!= ( zero_zero @ real ) )
= $true )
| ( ( SV615
!= ( zero_zero @ real ) )
= $true )
| ( ( ( plus_plus @ real @ ( times_times @ real @ SV397 @ SV397 ) @ ( times_times @ real @ SV615 @ SV615 ) )
= ( zero_zero @ real ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4901]) ).
thf(5042,plain,
! [SV722: $i,SV405: $i,SV617: $i] :
( ( ( ! [SY1940: $i] :
( ( ti @ int @ SV617 )
!= ( plus_plus @ int @ SV405 @ ( times_times @ int @ SV722 @ SY1940 ) ) ) )
= $false )
| ( ( zcong @ SV405 @ SV617 @ SV722 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4903]) ).
thf(5043,plain,
! [SV722: $i,SV405: $i,SV617: $i] :
( ( ( ! [SY1941: $i] :
( ( ti @ int @ SV617 )
!= ( plus_plus @ int @ SV405 @ ( times_times @ int @ SV722 @ SY1941 ) ) ) )
= $true )
| ( ( zcong @ SV405 @ SV617 @ SV722 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4904]) ).
thf(5044,plain,
! [SV407: $i] :
( ( ( ( ti @ int @ SV407 )
= ( number_number_of @ int @ ( bit1 @ ( bit1 @ pls ) ) ) )
= $true )
| ( ( ord_less_eq @ int @ ( number_number_of @ int @ ( bit1 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SV407 )
= $true )
| ( ( ( ti @ int @ SV407 )
= ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true )
| ( ( zprime @ SV407 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4905]) ).
thf(5045,plain,
! [SV725: $i,SV620: $i,SV410: $i] :
( ( ( ord_less @ int @ ( zero_zero @ int ) @ SV410 )
= $false )
| ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV620 )
= $true )
| ( ( ord_less @ int @ SV725 @ SV410 )
= $false )
| ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( times_times @ int @ SV410 @ SV620 ) @ SV725 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4906]) ).
thf(5046,plain,
! [SV621: $i,SV413: $i] :
( ( ( ( ( ti @ int @ SV413 )
!= ( one_one @ int ) )
| ( ( ti @ int @ SV621 )
!= ( one_one @ int ) ) )
= $false )
| ( ( ~ ( ( ( ti @ int @ SV413 )
!= ( number_number_of @ int @ min ) )
| ( ( ti @ int @ SV621 )
!= ( number_number_of @ int @ min ) ) ) )
= $true )
| ( ( ( times_times @ int @ SV413 @ SV621 )
= ( one_one @ int ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4907]) ).
thf(5047,plain,
! [SV621: $i,SV413: $i] :
( ( ( ( ( ti @ int @ SV413 )
!= ( one_one @ int ) )
| ( ( ti @ int @ SV621 )
!= ( one_one @ int ) ) )
= $true )
| ( ( ( times_times @ int @ SV413 @ SV621 )
= ( one_one @ int ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4908]) ).
thf(5048,plain,
! [SV621: $i,SV413: $i] :
( ( ( ( ( ti @ int @ SV413 )
!= ( number_number_of @ int @ min ) )
| ( ( ti @ int @ SV621 )
!= ( number_number_of @ int @ min ) ) )
= $true )
| ( ( ( times_times @ int @ SV413 @ SV621 )
= ( one_one @ int ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4909]) ).
thf(5049,plain,
! [SV994: $i,SV881: $i,SV417: $i] :
( ( ( ord_less_eq @ SV417 @ ( zero_zero @ SV417 ) @ SV881 )
= $false )
| ( ( ord_less_eq @ SV417 @ ( times_times @ SV417 @ SV994 @ SV881 ) @ ( zero_zero @ SV417 ) )
= $true )
| ( ( ord_less_eq @ SV417 @ SV994 @ ( zero_zero @ SV417 ) )
= $false )
| ( ( ordere453448008miring @ SV417 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4911]) ).
thf(5050,plain,
! [SV419: $i,SV623: $i] :
( ( ( ( times_times @ int @ SV623 @ SV419 )
= ( one_one @ int ) )
= $false )
| ( ( ~ ( ( ( ti @ int @ SV623 )
!= ( one_one @ int ) )
| ( ( ti @ int @ SV419 )
!= ( one_one @ int ) ) ) )
= $true )
| ( ( ord_less @ int @ ( zero_zero @ int ) @ SV623 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4912]) ).
thf(5051,plain,
! [SV419: $i,SV623: $i] :
( ( ( ~ ( ( ( ti @ int @ SV623 )
!= ( one_one @ int ) )
| ( ( ti @ int @ SV419 )
!= ( one_one @ int ) ) ) )
= $false )
| ( ( ( times_times @ int @ SV623 @ SV419 )
= ( one_one @ int ) )
= $true )
| ( ( ord_less @ int @ ( zero_zero @ int ) @ SV623 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4913]) ).
thf(5052,plain,
! [SV626: $i,SV422: $i,SV726: $i,SV1052: $i,SV995: $i,SV882: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( times_times @ int @ SV882 @ SV995 ) @ SV1052 ) ) )
= $true )
| ( ( ~ ( ord_less @ int @ SV1052 @ SV882 )
| ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV726 )
| ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV882 )
| ~ ( ord_less_eq @ int @ SV882 @ SV422 )
| ( ord_less_eq @ int @ SV626 @ SV995 ) )
= $true )
| ( ( ( plus_plus @ int @ ( times_times @ int @ SV422 @ SV626 ) @ SV726 )
= ( plus_plus @ int @ ( times_times @ int @ SV882 @ SV995 ) @ SV1052 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4915]) ).
thf(5053,plain,
! [SV997: $i,SV1053: $i,SV887: $i,SV433: $i] :
( ( ( ~ ( ord_less @ SV433 @ ( zero_zero @ SV433 ) @ SV887 ) )
= $true )
| ( ( ~ ( ord_less @ SV433 @ SV887 @ ( one_one @ SV433 ) )
| ( ord_less @ SV433 @ ( power_power @ SV433 @ SV887 @ SV1053 ) @ ( power_power @ SV433 @ SV887 @ SV997 ) ) )
= $true )
| ( ( ord_less @ nat @ SV997 @ SV1053 )
= $false )
| ( ( linordered_semidom @ SV433 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4921]) ).
thf(5054,plain,
! [SV998: $i,SV888: $i,SV1068: $i,SV1054: $i,SV1083: $i,SV434: $i] :
( ( ( ~ ( ( ( ti @ SV434 @ SV1083 )
!= ( zero_zero @ SV434 ) ) ) )
= $true )
| ( ( ~ ~ ( ( ( ti @ SV434 @ SV1054 )
!= ( ti @ SV434 @ SV1068 ) )
| ~ ( ( ( ti @ SV434 @ SV888 )
!= ( ti @ SV434 @ SV998 ) ) ) )
| ( ( plus_plus @ SV434 @ SV1054 @ ( times_times @ SV434 @ SV1083 @ SV888 ) )
!= ( plus_plus @ SV434 @ SV1068 @ ( times_times @ SV434 @ SV1083 @ SV998 ) ) ) )
= $true )
| ( ( semiri456707255roduct @ SV434 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4922]) ).
thf(5055,plain,
! [SV732: $i,SV890: $i,SV481: $i,SV647: $i,SV79: $i] :
( ( ( ~ ( zcong @ SV79 @ ( times_times @ int @ SV647 @ SV481 ) @ SV890 )
| ( zcong @ SV79 @ ( times_times @ int @ SV732 @ SV481 ) @ SV890 ) )
= $true )
| ( ( zcong @ SV647 @ SV732 @ SV890 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4923]) ).
thf(5056,plain,
! [SV647: $i,SV890: $i,SV481: $i,SV732: $i,SV79: $i] :
( ( ( ~ ( zcong @ SV79 @ ( times_times @ int @ SV732 @ SV481 ) @ SV890 )
| ( zcong @ SV79 @ ( times_times @ int @ SV647 @ SV481 ) @ SV890 ) )
= $true )
| ( ( zcong @ SV647 @ SV732 @ SV890 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4924]) ).
thf(5057,plain,
! [SV896: $i,SV739: $i,SV90: $i] :
( ( ( ( ti @ SV90 @ SV739 )
!= ( zero_zero @ SV90 ) )
= $false )
| ( ( ( times_times @ SV90 @ SV896 @ SV739 )
!= ( zero_zero @ SV90 ) )
= $true )
| ( ( ( ti @ SV90 @ SV896 )
= ( zero_zero @ SV90 ) )
= $true )
| ( ( no_zero_divisors @ SV90 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4927]) ).
thf(5058,plain,
! [SV744: $i,SV655: $i,SV901: $i,SV108: $i,SV494: $i] :
( ( ( ~ ( zcong @ SV494 @ SV108 @ SV901 ) )
= $true )
| ( ( zcong @ SV655 @ SV108 @ SV901 )
= $true )
| ( ( ( ti @ int @ SV744 )
= ( ti @ int @ SV494 ) )
= $false )
| ( ( zcong @ SV655 @ SV744 @ SV901 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4930]) ).
thf(5059,plain,
! [SV902: $i,SV1004: $i,SV746: $i,SV117: $i] :
( ( ( ord_less_eq @ SV117 @ ( zero_zero @ SV117 ) @ SV746 )
= $false )
| ( ( ~ ( ord_less_eq @ SV117 @ SV746 @ ( one_one @ SV117 ) )
| ( ord_less_eq @ SV117 @ ( power_power @ SV117 @ SV746 @ SV1004 ) @ ( power_power @ SV117 @ SV746 @ SV902 ) ) )
= $true )
| ( ( ord_less_eq @ nat @ SV902 @ SV1004 )
= $false )
| ( ( linordered_semidom @ SV117 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4931]) ).
thf(5060,plain,
! [SV1069: $i,SV120: $i] :
( ( ( ~ ( ~ ( ord_less @ SV120 @ ( one_one @ SV120 ) @ ( number_number_of @ SV120 @ SV1069 ) )
| ( ord_less @ int @ ( bit1 @ pls ) @ SV1069 ) ) )
= $false )
| ( ( number_ring @ SV120 )
= $false )
| ( ( linordered_idom @ SV120 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4932]) ).
thf(5061,plain,
! [SV120: $i,SV1069: $i] :
( ( ( ~ ( ~ ( ord_less @ int @ ( bit1 @ pls ) @ SV1069 )
| ( ord_less @ SV120 @ ( one_one @ SV120 ) @ ( number_number_of @ SV120 @ SV1069 ) ) ) )
= $false )
| ( ( number_ring @ SV120 )
= $false )
| ( ( linordered_idom @ SV120 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4932]) ).
thf(5062,plain,
! [SV1070: $i,SV123: $i] :
( ( ( ~ ( ~ ( ord_less_eq @ SV123 @ ( number_number_of @ SV123 @ SV1070 ) @ ( one_one @ SV123 ) )
| ( ord_less_eq @ int @ SV1070 @ ( bit1 @ pls ) ) ) )
= $false )
| ( ( number_ring @ SV123 )
= $false )
| ( ( linordered_idom @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4933]) ).
thf(5063,plain,
! [SV123: $i,SV1070: $i] :
( ( ( ~ ( ~ ( ord_less_eq @ int @ SV1070 @ ( bit1 @ pls ) )
| ( ord_less_eq @ SV123 @ ( number_number_of @ SV123 @ SV1070 ) @ ( one_one @ SV123 ) ) ) )
= $false )
| ( ( number_ring @ SV123 )
= $false )
| ( ( linordered_idom @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4933]) ).
thf(5064,plain,
! [SV1057: $i,SV1005: $i,SV903: $i,SV747: $i,SV124: $i] :
( ( ( ~ ( dvd_dvd @ SV124 @ SV747 @ SV903 ) )
= $true )
| ( ( dvd_dvd @ SV124 @ ( times_times @ SV124 @ SV1005 @ SV747 ) @ ( times_times @ SV124 @ SV1057 @ SV903 ) )
= $true )
| ( ( dvd_dvd @ SV124 @ SV1005 @ SV1057 )
= $false )
| ( ( comm_semiring_1 @ SV124 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4934]) ).
thf(5065,plain,
! [SV503: $i,SV753: $i,SV660: $i,SV907: $i,SV132: $i] :
( ( ( ~ ( ord_less @ int @ SV132 @ SV907 ) )
= $true )
| ( ( ~ ( ord_less @ int @ SV132 @ SV660 )
| ( ord_less_eq @ int @ SV753 @ SV503 ) )
= $true )
| ( ( ord_less_eq @ int @ SV907 @ ( zero_zero @ int ) )
= $false )
| ( ( ord_less_eq @ int @ ( plus_plus @ int @ ( times_times @ int @ SV132 @ SV503 ) @ SV660 ) @ ( plus_plus @ int @ ( times_times @ int @ SV132 @ SV753 ) @ SV907 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4935]) ).
thf(5066,plain,
! [SV1071: $i,SV134: $i] :
( ( ( ~ ( ~ ( ord_less @ SV134 @ ( number_number_of @ SV134 @ SV1071 ) @ ( one_one @ SV134 ) )
| ( ord_less @ int @ SV1071 @ ( bit1 @ pls ) ) ) )
= $false )
| ( ( number_ring @ SV134 )
= $false )
| ( ( linordered_idom @ SV134 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4936]) ).
thf(5067,plain,
! [SV134: $i,SV1071: $i] :
( ( ( ~ ( ~ ( ord_less @ int @ SV1071 @ ( bit1 @ pls ) )
| ( ord_less @ SV134 @ ( number_number_of @ SV134 @ SV1071 ) @ ( one_one @ SV134 ) ) ) )
= $false )
| ( ( number_ring @ SV134 )
= $false )
| ( ( linordered_idom @ SV134 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4936]) ).
thf(5068,plain,
! [SV505: $i,SV135: $i] :
( ( ( ord_less_eq @ int @ SV135 @ SV505 )
= $true )
| ( ( ord_less_eq @ int @ SV135 @ pls )
= $true )
| ( ( ord_less_eq @ nat @ ( number_number_of @ nat @ SV135 ) @ ( number_number_of @ nat @ SV505 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4937]) ).
thf(5069,plain,
! [SV505: $i,SV135: $i] :
( ( ( ord_less_eq @ int @ SV135 @ SV505 )
= $false )
| ( ( ord_less_eq @ nat @ ( number_number_of @ nat @ SV135 ) @ ( number_number_of @ nat @ SV505 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4938]) ).
thf(5070,plain,
! [SV1092: $i,SV1084: $i,SV1072: $i,SV139: $i] :
( ( ( ( times_times @ SV139 @ ( number_number_of @ SV139 @ SV1072 ) @ ( minus_minus @ SV139 @ SV1084 @ SV1092 ) )
= ( minus_minus @ SV139 @ ( times_times @ SV139 @ ( number_number_of @ SV139 @ SV1072 ) @ SV1084 ) @ ( times_times @ SV139 @ ( number_number_of @ SV139 @ SV1072 ) @ SV1092 ) ) )
= $true )
| ( ( number @ SV139 )
= $false )
| ( ( ring @ SV139 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4939]) ).
thf(5071,plain,
! [SV143: $i,SV509: $i] :
( ( ( SV509
!= ( zero_zero @ nat ) )
= $true )
| ( ( ( power_power @ nat @ SV143 @ SV509 )
= ( zero_zero @ nat ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4940]) ).
thf(5072,plain,
! [SV509: $i,SV143: $i] :
( ( ( SV143
= ( zero_zero @ nat ) )
= $true )
| ( ( ( power_power @ nat @ SV143 @ SV509 )
= ( zero_zero @ nat ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4941]) ).
thf(5073,plain,
! [SV143: $i,SV509: $i] :
( ( ( SV509
!= ( zero_zero @ nat ) )
= $false )
| ( ( SV143
!= ( zero_zero @ nat ) )
= $true )
| ( ( ( power_power @ nat @ SV143 @ SV509 )
= ( zero_zero @ nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4942]) ).
thf(5074,plain,
! [SV512: $i,SV151: $i] :
( ( ( dvd_dvd @ nat @ SV151 @ SV512 )
= $false )
| ( ( ~ ( dvd_dvd @ nat @ SV512 @ SV151 ) )
= $true )
| ( ( SV151 = SV512 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4943]) ).
thf(5075,plain,
! [SV512: $i,SV151: $i] :
( ( ( dvd_dvd @ nat @ SV151 @ SV512 )
= $true )
| ( ( SV151 = SV512 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4944]) ).
thf(5076,plain,
! [SV151: $i,SV512: $i] :
( ( ( dvd_dvd @ nat @ SV512 @ SV151 )
= $true )
| ( ( SV151 = SV512 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4945]) ).
thf(5077,plain,
! [SV513: $i,SV153: $i] :
( ( ( ~ ( ord_less @ real @ ( zero_zero @ real ) @ ( sK7_SY1807 @ SV153 @ SV513 ) )
| ( ( power_power @ real @ ( sK7_SY1807 @ SV153 @ SV513 ) @ SV513 )
!= SV153 ) )
= $false )
| ( ( ord_less @ real @ ( zero_zero @ real ) @ SV153 )
= $false )
| ( ( ord_less @ nat @ ( zero_zero @ nat ) @ SV513 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4947]) ).
thf(5078,plain,
! [SV911: $i,SV762: $i,SV1010: $i,SV155: $i] :
( ( ( ~ ( ~ ( ord_less @ SV155 @ ( power_power @ SV155 @ SV1010 @ SV762 ) @ ( power_power @ SV155 @ SV1010 @ SV911 ) )
| ( ord_less @ nat @ SV762 @ SV911 ) ) )
= $false )
| ( ( ord_less @ SV155 @ ( one_one @ SV155 ) @ SV1010 )
= $false )
| ( ( linordered_semidom @ SV155 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4948]) ).
thf(5079,plain,
! [SV1010: $i,SV155: $i,SV911: $i,SV762: $i] :
( ( ( ~ ( ~ ( ord_less @ nat @ SV762 @ SV911 )
| ( ord_less @ SV155 @ ( power_power @ SV155 @ SV1010 @ SV762 ) @ ( power_power @ SV155 @ SV1010 @ SV911 ) ) ) )
= $false )
| ( ( ord_less @ SV155 @ ( one_one @ SV155 ) @ SV1010 )
= $false )
| ( ( linordered_semidom @ SV155 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4948]) ).
thf(5080,plain,
! [SV913: $i,SV164: $i,SV667: $i,SV521: $i,SV765: $i] :
( ( ( ~ ( dvd_dvd @ int @ SV765 @ ( plus_plus @ int @ SV521 @ SV667 ) )
| ( dvd_dvd @ int @ SV765 @ ( plus_plus @ int @ ( plus_plus @ int @ SV521 @ ( times_times @ int @ SV164 @ SV913 ) ) @ SV667 ) ) )
= $true )
| ( ( dvd_dvd @ int @ SV765 @ SV913 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4950]) ).
thf(5081,plain,
! [SV667: $i,SV913: $i,SV164: $i,SV521: $i,SV765: $i] :
( ( ( ~ ( dvd_dvd @ int @ SV765 @ ( plus_plus @ int @ ( plus_plus @ int @ SV521 @ ( times_times @ int @ SV164 @ SV913 ) ) @ SV667 ) )
| ( dvd_dvd @ int @ SV765 @ ( plus_plus @ int @ SV521 @ SV667 ) ) )
= $true )
| ( ( dvd_dvd @ int @ SV765 @ SV913 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4951]) ).
thf(5082,plain,
! [SV1093: $i,SV1085: $i,SV1073: $i,SV168: $i] :
( ( ( ( times_times @ SV168 @ ( plus_plus @ SV168 @ SV1073 @ SV1085 ) @ ( number_number_of @ SV168 @ SV1093 ) )
= ( plus_plus @ SV168 @ ( times_times @ SV168 @ SV1073 @ ( number_number_of @ SV168 @ SV1093 ) ) @ ( times_times @ SV168 @ SV1085 @ ( number_number_of @ SV168 @ SV1093 ) ) ) )
= $true )
| ( ( number @ SV168 )
= $false )
| ( ( semiring @ SV168 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4953]) ).
thf(5083,plain,
! [SV523: $i,SV169: $i] :
( ( ( SV169
= ( zero_zero @ real ) )
= $true )
| ( ( ( plus_plus @ real @ ( power_power @ real @ SV169 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ real @ SV523 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ real ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4954]) ).
thf(5084,plain,
! [SV169: $i,SV523: $i] :
( ( ( SV523
= ( zero_zero @ real ) )
= $true )
| ( ( ( plus_plus @ real @ ( power_power @ real @ SV169 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ real @ SV523 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ real ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4955]) ).
thf(5085,plain,
! [SV523: $i,SV169: $i] :
( ( ( SV169
= ( zero_zero @ real ) )
= $false )
| ( ( SV523
!= ( zero_zero @ real ) )
= $true )
| ( ( ( plus_plus @ real @ ( power_power @ real @ SV169 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ real @ SV523 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ real ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4956]) ).
thf(5086,plain,
! [SV918: $i,SV771: $i,SV1060: $i,SV1013: $i,SV175: $i] :
( ( ( ~ ~ ( ~ ( ( ( ti @ SV175 @ SV1013 )
!= ( ti @ SV175 @ SV1060 ) ) )
| ~ ( ( ( ti @ SV175 @ SV771 )
!= ( ti @ SV175 @ SV918 ) ) ) )
| ( ( plus_plus @ SV175 @ ( times_times @ SV175 @ SV1013 @ SV771 ) @ ( times_times @ SV175 @ SV1060 @ SV918 ) )
!= ( plus_plus @ SV175 @ ( times_times @ SV175 @ SV1013 @ SV918 ) @ ( times_times @ SV175 @ SV1060 @ SV771 ) ) ) )
= $true )
| ( ( semiri456707255roduct @ SV175 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4957]) ).
thf(5087,plain,
! [SV918: $i,SV1060: $i,SV771: $i,SV1013: $i,SV175: $i] :
( ( ( ~ ( ( ( plus_plus @ SV175 @ ( times_times @ SV175 @ SV1013 @ SV771 ) @ ( times_times @ SV175 @ SV1060 @ SV918 ) )
!= ( plus_plus @ SV175 @ ( times_times @ SV175 @ SV1013 @ SV918 ) @ ( times_times @ SV175 @ SV1060 @ SV771 ) ) ) )
| ~ ( ~ ( ( ( ti @ SV175 @ SV1013 )
!= ( ti @ SV175 @ SV1060 ) ) )
| ~ ( ( ( ti @ SV175 @ SV771 )
!= ( ti @ SV175 @ SV918 ) ) ) ) )
= $true )
| ( ( semiri456707255roduct @ SV175 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4958]) ).
thf(5088,plain,
! [SV919: $i,SV772: $i,SV1014: $i,SV179: $i] :
( ( ( ord_less @ SV179 @ ( power_power @ SV179 @ SV1014 @ SV772 ) @ ( power_power @ SV179 @ SV1014 @ SV919 ) )
= $false )
| ( ( ord_less @ nat @ SV772 @ SV919 )
= $true )
| ( ( ord_less @ SV179 @ ( one_one @ SV179 ) @ SV1014 )
= $false )
| ( ( linordered_semidom @ SV179 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4959]) ).
thf(5089,plain,
! [SV530: $i,SV187: $i] :
( ( ( ord_less_eq @ int @ SV187 @ SV530 )
= $true )
| ( ( ord_less @ int @ SV187 @ SV530 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4960]) ).
thf(5090,plain,
! [SV530: $i,SV187: $i] :
( ( ( ( ti @ int @ SV187 )
!= ( ti @ int @ SV530 ) )
= $true )
| ( ( ord_less @ int @ SV187 @ SV530 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4961]) ).
thf(5091,plain,
! [SV530: $i,SV187: $i] :
( ( ( ord_less_eq @ int @ SV187 @ SV530 )
= $false )
| ( ( ~ ( ( ( ti @ int @ SV187 )
!= ( ti @ int @ SV530 ) ) ) )
= $true )
| ( ( ord_less @ int @ SV187 @ SV530 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4962]) ).
thf(5092,plain,
! [SV923: $i,SV778: $i,SV193: $i] :
( ( ( ( plus_plus @ SV193 @ ( times_times @ SV193 @ SV778 @ SV778 ) @ ( times_times @ SV193 @ SV923 @ SV923 ) )
= ( zero_zero @ SV193 ) )
= $false )
| ( ( ~ ( ( ( ti @ SV193 @ SV778 )
!= ( zero_zero @ SV193 ) )
| ( ( ti @ SV193 @ SV923 )
!= ( zero_zero @ SV193 ) ) ) )
= $true )
| ( ( linord581940658strict @ SV193 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4968]) ).
thf(5093,plain,
! [SV923: $i,SV778: $i,SV193: $i] :
( ( ( ~ ( ( ( ti @ SV193 @ SV778 )
!= ( zero_zero @ SV193 ) )
| ( ( ti @ SV193 @ SV923 )
!= ( zero_zero @ SV193 ) ) ) )
= $false )
| ( ( ( plus_plus @ SV193 @ ( times_times @ SV193 @ SV778 @ SV778 ) @ ( times_times @ SV193 @ SV923 @ SV923 ) )
= ( zero_zero @ SV193 ) )
= $true )
| ( ( linord581940658strict @ SV193 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4969]) ).
thf(5094,plain,
! [SV924: $i,SV779: $i,SV1017: $i,SV194: $i] :
( ( ( ~ ( ( ( power_power @ SV194 @ SV1017 @ SV779 )
!= ( power_power @ SV194 @ SV1017 @ SV924 ) )
| ( SV779 = SV924 ) ) )
= $false )
| ( ( ord_less @ SV194 @ ( one_one @ SV194 ) @ SV1017 )
= $false )
| ( ( linordered_semidom @ SV194 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4970]) ).
thf(5095,plain,
! [SV1017: $i,SV194: $i,SV924: $i,SV779: $i] :
( ( ( ~ ( ( SV779 != SV924 )
| ( ( power_power @ SV194 @ SV1017 @ SV779 )
= ( power_power @ SV194 @ SV1017 @ SV924 ) ) ) )
= $false )
| ( ( ord_less @ SV194 @ ( one_one @ SV194 ) @ SV1017 )
= $false )
| ( ( linordered_semidom @ SV194 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4970]) ).
thf(5096,plain,
! [SV534: $i,SV672: $i,SV196: $i] :
( ( ( ~ ( zcong @ SV196 @ ( zero_zero @ int ) @ SV672 ) )
= $false )
| ( ( ~ ( zcong @ ( times_times @ int @ SV534 @ SV196 ) @ ( zero_zero @ int ) @ SV672 ) )
= $true )
| ( ( zcong @ SV534 @ ( zero_zero @ int ) @ SV672 )
= $true )
| ( ( zprime @ SV672 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4971]) ).
thf(5097,plain,
! [SV928: $i,SV783: $i,SV199: $i] :
( ( ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ ( times_times @ SV199 @ SV783 @ SV928 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ SV783 )
| ~ ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ SV928 ) )
| ~ ( ~ ( ord_less_eq @ SV199 @ SV783 @ ( zero_zero @ SV199 ) )
| ~ ( ord_less_eq @ SV199 @ SV928 @ ( zero_zero @ SV199 ) ) ) )
= $true )
| ( ( linord581940658strict @ SV199 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4972]) ).
thf(5098,plain,
! [SV928: $i,SV783: $i,SV199: $i] :
( ( ( ~ ( ~ ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ SV783 )
| ~ ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ SV928 ) )
| ~ ( ~ ( ord_less_eq @ SV199 @ SV783 @ ( zero_zero @ SV199 ) )
| ~ ( ord_less_eq @ SV199 @ SV928 @ ( zero_zero @ SV199 ) ) ) )
= $false )
| ( ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ ( times_times @ SV199 @ SV783 @ SV928 ) )
= $true )
| ( ( linord581940658strict @ SV199 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4973]) ).
thf(5099,plain,
! [SV1074: $i,SV202: $i] :
( ( ( ~ ( ~ ( ord_less_eq @ SV202 @ ( one_one @ SV202 ) @ ( number_number_of @ SV202 @ SV1074 ) )
| ( ord_less_eq @ int @ ( bit1 @ pls ) @ SV1074 ) ) )
= $false )
| ( ( number_ring @ SV202 )
= $false )
| ( ( linordered_idom @ SV202 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4975]) ).
thf(5100,plain,
! [SV202: $i,SV1074: $i] :
( ( ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ pls ) @ SV1074 )
| ( ord_less_eq @ SV202 @ ( one_one @ SV202 ) @ ( number_number_of @ SV202 @ SV1074 ) ) ) )
= $false )
| ( ( number_ring @ SV202 )
= $false )
| ( ( linordered_idom @ SV202 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4975]) ).
thf(5101,plain,
! [SV535: $i,SV673: $i,SV203: $i] :
( ( ( ~ ( ord_less @ int @ SV203 @ SV673 ) )
= $true )
| ( ( ~ ( zcong @ SV673 @ SV203 @ SV535 ) )
= $true )
| ( ( ord_less @ int @ ( zero_zero @ int ) @ SV203 )
= $false )
| ( ( ord_less @ int @ SV673 @ SV535 )
= $false )
| ( ( ord_less @ int @ ( zero_zero @ int ) @ SV673 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4976]) ).
thf(5102,plain,
! [SV1086: $i,SV1075: $i,SV213: $i] :
( ( ( ~ ( ( ( number_number_of @ SV213 @ SV1075 )
!= ( number_number_of @ SV213 @ SV1086 ) )
| ( ( ti @ int @ SV1075 )
= ( ti @ int @ SV1086 ) ) )
| ~ ( ( ( ti @ int @ SV1075 )
!= ( ti @ int @ SV1086 ) )
| ( ( number_number_of @ SV213 @ SV1075 )
= ( number_number_of @ SV213 @ SV1086 ) ) ) )
= $false )
| ( ( number_ring @ SV213 )
= $false )
| ( ( ring_char_0 @ SV213 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4978]) ).
thf(5103,plain,
! [SV538: $i,SV214: $i,SV676: $i,SV790: $i] :
( ( ( ord_less @ nat @ SV790 @ SV676 )
= $false )
| ( ( ~ ( dvd_dvd @ nat @ SV676 @ SV214 ) )
= $true )
| ( ( ord_less @ nat @ ( zero_zero @ nat ) @ SV790 )
= $false )
| ( ( SV214
= ( plus_plus @ nat @ ( times_times @ nat @ SV538 @ SV676 ) @ SV790 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4979]) ).
thf(5104,plain,
! [SV1087: $i,SV1076: $i,SV218: $i] :
( ( ( ~ ( ~ ( ord_less @ SV218 @ ( number_number_of @ SV218 @ SV1076 ) @ ( number_number_of @ SV218 @ SV1087 ) )
| ( ord_less @ int @ SV1076 @ SV1087 ) )
| ~ ( ~ ( ord_less @ int @ SV1076 @ SV1087 )
| ( ord_less @ SV218 @ ( number_number_of @ SV218 @ SV1076 ) @ ( number_number_of @ SV218 @ SV1087 ) ) ) )
= $false )
| ( ( number_ring @ SV218 )
= $false )
| ( ( linordered_idom @ SV218 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4980]) ).
thf(5105,plain,
! [SV1061: $i,SV933: $i,SV220: $i,SV1018: $i,SV792: $i] :
( ( ( ~ ( ord_less_eq @ nat @ SV792 @ SV1018 ) )
= $true )
| ( ( dvd_dvd @ SV220 @ ( power_power @ SV220 @ SV933 @ SV792 ) @ SV1061 )
= $true )
| ( ( dvd_dvd @ SV220 @ ( power_power @ SV220 @ SV933 @ SV1018 ) @ SV1061 )
= $false )
| ( ( comm_semiring_1 @ SV220 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4981]) ).
thf(5106,plain,
! [SV1094: $i,SV1088: $i,SV1077: $i,SV234: $i] :
( ( ( ( times_times @ SV234 @ ( number_number_of @ SV234 @ SV1077 ) @ ( plus_plus @ SV234 @ SV1088 @ SV1094 ) )
= ( plus_plus @ SV234 @ ( times_times @ SV234 @ ( number_number_of @ SV234 @ SV1077 ) @ SV1088 ) @ ( times_times @ SV234 @ ( number_number_of @ SV234 @ SV1077 ) @ SV1094 ) ) )
= $true )
| ( ( number @ SV234 )
= $false )
| ( ( semiring @ SV234 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4982]) ).
thf(5107,plain,
! [SV937: $i,SV797: $i,SV237: $i] :
( ( ( ( number_number_of @ SV237 @ SV797 )
= ( ti @ SV237 @ SV937 ) )
= $false )
| ( ( ( ti @ SV237 @ SV937 )
= ( number_number_of @ SV237 @ SV797 ) )
= $true )
| ( ( number @ SV237 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4983]) ).
thf(5108,plain,
! [SV797: $i,SV937: $i,SV237: $i] :
( ( ( ( ti @ SV237 @ SV937 )
= ( number_number_of @ SV237 @ SV797 ) )
= $false )
| ( ( ( number_number_of @ SV237 @ SV797 )
= ( ti @ SV237 @ SV937 ) )
= $true )
| ( ( number @ SV237 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4984]) ).
thf(5109,plain,
! [SV549: $i,SV683: $i,SV240: $i,SV799: $i] :
( ( ( ~ ( dvd_dvd @ int @ ( power_power @ int @ SV799 @ SV240 ) @ ( times_times @ int @ SV683 @ SV549 ) ) )
= $true )
| ( ( dvd_dvd @ int @ ( power_power @ int @ SV799 @ SV240 ) @ SV549 )
= $true )
| ( ( dvd_dvd @ int @ SV799 @ SV683 )
= $true )
| ( ( zprime @ SV799 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4985]) ).
thf(5110,plain,
! [SV1062: $i,SV1024: $i,SV942: $i,SV804: $i,SV255: $i] :
( ( ( ( ( plus_plus @ SV255 @ ( times_times @ SV255 @ SV804 @ SV942 ) @ ( times_times @ SV255 @ SV1024 @ SV1062 ) )
!= ( plus_plus @ SV255 @ ( times_times @ SV255 @ SV804 @ SV1062 ) @ ( times_times @ SV255 @ SV1024 @ SV942 ) ) )
| ( ( ti @ SV255 @ SV804 )
= ( ti @ SV255 @ SV1024 ) )
| ( ( ti @ SV255 @ SV942 )
= ( ti @ SV255 @ SV1062 ) ) )
= $true )
| ( ( semiri456707255roduct @ SV255 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4987]) ).
thf(5111,plain,
! [SV1062: $i,SV942: $i,SV1024: $i,SV804: $i,SV255: $i] :
( ( ( ~ ( ( ( ti @ SV255 @ SV804 )
= ( ti @ SV255 @ SV1024 ) )
| ( ( ti @ SV255 @ SV942 )
= ( ti @ SV255 @ SV1062 ) ) )
| ( ( plus_plus @ SV255 @ ( times_times @ SV255 @ SV804 @ SV942 ) @ ( times_times @ SV255 @ SV1024 @ SV1062 ) )
= ( plus_plus @ SV255 @ ( times_times @ SV255 @ SV804 @ SV1062 ) @ ( times_times @ SV255 @ SV1024 @ SV942 ) ) ) )
= $true )
| ( ( semiri456707255roduct @ SV255 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4988]) ).
thf(5112,plain,
! [SV805: $i,SV943: $i,SV688: $i,SV557: $i,SV257: $i] :
( ( ( ~ ( zcong @ SV257 @ ( times_times @ int @ SV557 @ SV688 ) @ SV943 )
| ( zcong @ SV257 @ ( times_times @ int @ SV557 @ SV805 ) @ SV943 ) )
= $true )
| ( ( zcong @ SV688 @ SV805 @ SV943 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4989]) ).
thf(5113,plain,
! [SV688: $i,SV943: $i,SV805: $i,SV557: $i,SV257: $i] :
( ( ( ~ ( zcong @ SV257 @ ( times_times @ int @ SV557 @ SV805 ) @ SV943 )
| ( zcong @ SV257 @ ( times_times @ int @ SV557 @ SV688 ) @ SV943 ) )
= $true )
| ( ( zcong @ SV688 @ SV805 @ SV943 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4990]) ).
thf(5114,plain,
! [SV562: $i,SV273: $i,SV691: $i] :
( ( ( ( times_times @ real @ SV691 @ SV273 )
!= ( times_times @ real @ SV691 @ SV562 ) )
= $true )
| ( ( SV273 = SV562 )
= $true )
| ( ( SV691
= ( zero_zero @ real ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4993]) ).
thf(5115,plain,
! [SV691: $i,SV562: $i,SV273: $i] :
( ( ( SV273 != SV562 )
= $true )
| ( ( ( times_times @ real @ SV691 @ SV273 )
= ( times_times @ real @ SV691 @ SV562 ) )
= $true )
| ( ( SV691
= ( zero_zero @ real ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4994]) ).
thf(5116,plain,
! [SV1027: $i,SV815: $i,SV949: $i,SV277: $i] :
( ( ( dvd_dvd @ SV277 @ SV949 @ SV815 )
= $false )
| ( ( dvd_dvd @ SV277 @ SV949 @ ( plus_plus @ SV277 @ SV1027 @ SV815 ) )
= $true )
| ( ( dvd_dvd @ SV277 @ SV949 @ SV1027 )
= $false )
| ( ( comm_semiring_1 @ SV277 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4995]) ).
thf(5117,plain,
! [SV694: $i,SV566: $i,SV288: $i,SV821: $i] :
( ( ( ~ ( dvd_dvd @ int @ ( power_power @ int @ SV821 @ SV288 ) @ ( times_times @ int @ SV566 @ SV694 ) ) )
= $true )
| ( ( dvd_dvd @ int @ ( power_power @ int @ SV821 @ SV288 ) @ SV566 )
= $true )
| ( ( dvd_dvd @ int @ SV821 @ SV694 )
= $true )
| ( ( zprime @ SV821 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4997]) ).
thf(5118,plain,
! [SV955: $i,SV826: $i,SV301: $i] :
( ( ( ( times_times @ SV301 @ SV826 @ SV955 )
= ( zero_zero @ SV301 ) )
= $false )
| ( ( ( ( ti @ SV301 @ SV826 )
= ( zero_zero @ SV301 ) )
| ( ( ti @ SV301 @ SV955 )
= ( zero_zero @ SV301 ) ) )
= $true )
| ( ( ring_n68954251visors @ SV301 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4998]) ).
thf(5119,plain,
! [SV955: $i,SV826: $i,SV301: $i] :
( ( ( ( ( ti @ SV301 @ SV826 )
= ( zero_zero @ SV301 ) )
| ( ( ti @ SV301 @ SV955 )
= ( zero_zero @ SV301 ) ) )
= $false )
| ( ( ( times_times @ SV301 @ SV826 @ SV955 )
= ( zero_zero @ SV301 ) )
= $true )
| ( ( ring_n68954251visors @ SV301 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4999]) ).
thf(5120,plain,
! [SV956: $i,SV828: $i,SV1031: $i,SV304: $i] :
( ( ( ord_less_eq @ SV304 @ ( power_power @ SV304 @ SV1031 @ SV828 ) @ ( power_power @ SV304 @ SV1031 @ SV956 ) )
= $false )
| ( ( ord_less_eq @ nat @ SV828 @ SV956 )
= $true )
| ( ( ord_less @ SV304 @ ( one_one @ SV304 ) @ SV1031 )
= $false )
| ( ( linordered_semidom @ SV304 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5000]) ).
thf(5121,plain,
! [SV573: $i,SV305: $i,SV698: $i,SV1032: $i,SV957: $i,SV829: $i] :
( ( ( ord_less @ int @ ( plus_plus @ int @ ( times_times @ int @ SV829 @ SV957 ) @ SV1032 ) @ ( zero_zero @ int ) )
= $false )
| ( ( ~ ( ord_less @ int @ SV698 @ SV305 )
| ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV1032 )
| ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV829 )
| ~ ( ord_less_eq @ int @ SV829 @ SV305 )
| ( ord_less_eq @ int @ SV957 @ SV573 ) )
= $true )
| ( ( ( plus_plus @ int @ ( times_times @ int @ SV305 @ SV573 ) @ SV698 )
= ( plus_plus @ int @ ( times_times @ int @ SV829 @ SV957 ) @ SV1032 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5001]) ).
thf(5122,plain,
! [SV833: $i,SV576: $i,SV960: $i,SV312: $i,SV701: $i] :
( ( ( ~ ( ord_less @ int @ SV701 @ SV312 ) )
= $true )
| ( ( ~ ( ord_less @ int @ SV960 @ SV312 )
| ( ord_less_eq @ int @ SV576 @ SV833 ) )
= $true )
| ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV701 )
= $false )
| ( ( ord_less_eq @ int @ ( plus_plus @ int @ ( times_times @ int @ SV312 @ SV576 ) @ SV701 ) @ ( plus_plus @ int @ ( times_times @ int @ SV312 @ SV833 ) @ SV960 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5002]) ).
thf(5123,plain,
! [SV961: $i,SV834: $i,SV313: $i] :
( ( ( ( ti @ SV313 @ SV834 )
= ( plus_plus @ SV313 @ SV834 @ SV961 ) )
= $false )
| ( ( ( ti @ SV313 @ SV961 )
= ( zero_zero @ SV313 ) )
= $true )
| ( ( semiri456707255roduct @ SV313 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5003]) ).
thf(5124,plain,
! [SV834: $i,SV961: $i,SV313: $i] :
( ( ( ( ti @ SV313 @ SV961 )
= ( zero_zero @ SV313 ) )
= $false )
| ( ( ( ti @ SV313 @ SV834 )
= ( plus_plus @ SV313 @ SV834 @ SV961 ) )
= $true )
| ( ( semiri456707255roduct @ SV313 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5004]) ).
thf(5125,plain,
! [SV577: $i,SV314: $i] :
( ( ( zcong @ ( power_power @ int @ ( sK8_SY1865 @ SV314 @ SV577 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SV577 @ SV314 )
= $true )
| ( ( quadRes @ SV314 @ SV577 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5005]) ).
thf(5126,plain,
! [SV314: $i,SV577: $i,SV1089: $i] :
( ( ( zcong @ ( power_power @ int @ SV1089 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SV577 @ SV314 )
= $false )
| ( ( quadRes @ SV314 @ SV577 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5006]) ).
thf(5127,plain,
! [SV1034: $i,SV962: $i,SV835: $i,SV315: $i] :
( ( ( ord_less_eq @ SV315 @ ( one_one @ SV315 ) @ SV835 )
= $false )
| ( ( ord_less_eq @ SV315 @ ( power_power @ SV315 @ SV835 @ SV962 ) @ ( power_power @ SV315 @ SV835 @ SV1034 ) )
= $true )
| ( ( ord_less_eq @ nat @ SV962 @ SV1034 )
= $false )
| ( ( linordered_semidom @ SV315 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5007]) ).
thf(5128,plain,
! [SV966: $i,SV839: $i,SV319: $i] :
( ( ( ord_less_eq @ SV319 @ ( times_times @ SV319 @ SV839 @ SV966 ) @ ( zero_zero @ SV319 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SV839 )
| ~ ( ord_less_eq @ SV319 @ SV966 @ ( zero_zero @ SV319 ) ) )
| ~ ( ~ ( ord_less_eq @ SV319 @ SV839 @ ( zero_zero @ SV319 ) )
| ~ ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SV966 ) ) )
= $true )
| ( ( linord581940658strict @ SV319 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5008]) ).
thf(5129,plain,
! [SV966: $i,SV839: $i,SV319: $i] :
( ( ( ~ ( ~ ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SV839 )
| ~ ( ord_less_eq @ SV319 @ SV966 @ ( zero_zero @ SV319 ) ) )
| ~ ( ~ ( ord_less_eq @ SV319 @ SV839 @ ( zero_zero @ SV319 ) )
| ~ ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SV966 ) ) )
= $false )
| ( ( ord_less_eq @ SV319 @ ( times_times @ SV319 @ SV839 @ SV966 ) @ ( zero_zero @ SV319 ) )
= $true )
| ( ( linord581940658strict @ SV319 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5009]) ).
thf(5130,plain,
! [SV1090: $i,SV1078: $i,SV321: $i] :
( ( ( ~ ( ~ ( ord_less_eq @ SV321 @ ( number_number_of @ SV321 @ SV1078 ) @ ( number_number_of @ SV321 @ SV1090 ) )
| ( ord_less_eq @ int @ SV1078 @ SV1090 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV1078 @ SV1090 )
| ( ord_less_eq @ SV321 @ ( number_number_of @ SV321 @ SV1078 ) @ ( number_number_of @ SV321 @ SV1090 ) ) ) )
= $false )
| ( ( number_ring @ SV321 )
= $false )
| ( ( linordered_idom @ SV321 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5010]) ).
thf(5131,plain,
! [SV1064: $i,SV1036: $i,SV323: $i,SV967: $i,SV841: $i] :
( ( ( ~ ( ord_less_eq @ nat @ SV841 @ SV967 ) )
= $true )
| ( ( dvd_dvd @ SV323 @ ( power_power @ SV323 @ SV1036 @ SV841 ) @ ( power_power @ SV323 @ SV1064 @ SV967 ) )
= $true )
| ( ( dvd_dvd @ SV323 @ SV1036 @ SV1064 )
= $false )
| ( ( comm_semiring_1 @ SV323 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5011]) ).
thf(5132,plain,
! [SV333: $i,SV1079: $i] :
( ( ( ~ ( ( ( number_number_of @ nat @ SV1079 )
!= ( zero_zero @ nat ) )
| ( ( power_power @ SV333 @ ( zero_zero @ SV333 ) @ ( number_number_of @ nat @ SV1079 ) )
= ( one_one @ SV333 ) ) ) )
= $false )
| ( ( power @ SV333 )
= $false )
| ( ( semiring_0 @ SV333 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5013]) ).
thf(5133,plain,
! [SV333: $i,SV1079: $i] :
( ( ( ~ ( ~ ( ( ( number_number_of @ nat @ SV1079 )
!= ( zero_zero @ nat ) ) )
| ( ( power_power @ SV333 @ ( zero_zero @ SV333 ) @ ( number_number_of @ nat @ SV1079 ) )
= ( zero_zero @ SV333 ) ) ) )
= $false )
| ( ( power @ SV333 )
= $false )
| ( ( semiring_0 @ SV333 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5013]) ).
thf(5134,plain,
! [SV583: $i,SV705: $i,SV338: $i] :
( ( ( ord_less @ real @ ( times_times @ real @ SV338 @ SV705 ) @ ( times_times @ real @ SV583 @ SV705 ) )
= $false )
| ( ( ord_less @ real @ SV338 @ SV583 )
= $true )
| ( ( ord_less @ real @ ( zero_zero @ real ) @ SV705 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5015]) ).
thf(5135,plain,
! [SV705: $i,SV583: $i,SV338: $i] :
( ( ( ord_less @ real @ SV338 @ SV583 )
= $false )
| ( ( ord_less @ real @ ( times_times @ real @ SV338 @ SV705 ) @ ( times_times @ real @ SV583 @ SV705 ) )
= $true )
| ( ( ord_less @ real @ ( zero_zero @ real ) @ SV705 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5016]) ).
thf(5136,plain,
! [SV977: $i,SV855: $i,SV352: $i] :
( ( ( ( plus_plus @ SV352 @ ( power_power @ SV352 @ SV855 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV352 @ SV977 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV352 ) )
= $false )
| ( ( ~ ( ( ( ti @ SV352 @ SV855 )
!= ( zero_zero @ SV352 ) )
| ( ( ti @ SV352 @ SV977 )
!= ( zero_zero @ SV352 ) ) ) )
= $true )
| ( ( linordered_idom @ SV352 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5019]) ).
thf(5137,plain,
! [SV977: $i,SV855: $i,SV352: $i] :
( ( ( ~ ( ( ( ti @ SV352 @ SV855 )
!= ( zero_zero @ SV352 ) )
| ( ( ti @ SV352 @ SV977 )
!= ( zero_zero @ SV352 ) ) ) )
= $false )
| ( ( ( plus_plus @ SV352 @ ( power_power @ SV352 @ SV855 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV352 @ SV977 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV352 ) )
= $true )
| ( ( linordered_idom @ SV352 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5020]) ).
thf(5138,plain,
! [SV1042: $i,SV856: $i,SV978: $i,SV353: $i] :
( ( ( ord_less_eq @ SV353 @ ( zero_zero @ SV353 ) @ SV978 )
= $false )
| ( ( ord_less_eq @ SV353 @ ( power_power @ SV353 @ SV978 @ SV856 ) @ ( power_power @ SV353 @ SV1042 @ SV856 ) )
= $true )
| ( ( ord_less_eq @ SV353 @ SV978 @ SV1042 )
= $false )
| ( ( linordered_semidom @ SV353 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5021]) ).
thf(5139,plain,
! [SV355: $i,SV1080: $i] :
( ( ( ~ ( ( SV1080
!= ( zero_zero @ nat ) )
| ( ( power_power @ SV355 @ ( zero_zero @ SV355 ) @ SV1080 )
= ( one_one @ SV355 ) ) ) )
= $false )
| ( ( power @ SV355 )
= $false )
| ( ( semiring_0 @ SV355 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5022]) ).
thf(5140,plain,
! [SV355: $i,SV1080: $i] :
( ( ( ~ ( ~ ( ( SV1080
!= ( zero_zero @ nat ) ) )
| ( ( power_power @ SV355 @ ( zero_zero @ SV355 ) @ SV1080 )
= ( zero_zero @ SV355 ) ) ) )
= $false )
| ( ( power @ SV355 )
= $false )
| ( ( semiring_0 @ SV355 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5022]) ).
thf(5141,plain,
! [SV980: $i,SV858: $i,SV1044: $i,SV358: $i] :
( ( ( ~ ( ~ ( ord_less_eq @ SV358 @ ( power_power @ SV358 @ SV1044 @ SV858 ) @ ( power_power @ SV358 @ SV1044 @ SV980 ) )
| ( ord_less_eq @ nat @ SV858 @ SV980 ) ) )
= $false )
| ( ( ord_less @ SV358 @ ( one_one @ SV358 ) @ SV1044 )
= $false )
| ( ( linordered_semidom @ SV358 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5023]) ).
thf(5142,plain,
! [SV1044: $i,SV358: $i,SV980: $i,SV858: $i] :
( ( ( ~ ( ~ ( ord_less_eq @ nat @ SV858 @ SV980 )
| ( ord_less_eq @ SV358 @ ( power_power @ SV358 @ SV1044 @ SV858 ) @ ( power_power @ SV358 @ SV1044 @ SV980 ) ) ) )
= $false )
| ( ( ord_less @ SV358 @ ( one_one @ SV358 ) @ SV1044 )
= $false )
| ( ( linordered_semidom @ SV358 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5023]) ).
thf(5143,plain,
! [SV592: $i,SV710: $i,SV362: $i] :
( ( ( ( times_times @ real @ SV362 @ SV710 )
!= ( times_times @ real @ SV592 @ SV710 ) )
= $true )
| ( ( SV362 = SV592 )
= $true )
| ( ( SV710
= ( zero_zero @ real ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5025]) ).
thf(5144,plain,
! [SV710: $i,SV592: $i,SV362: $i] :
( ( ( SV362 != SV592 )
= $true )
| ( ( ( times_times @ real @ SV362 @ SV710 )
= ( times_times @ real @ SV592 @ SV710 ) )
= $true )
| ( ( SV710
= ( zero_zero @ real ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5026]) ).
thf(5145,plain,
! [SV860: $i,SV363: $i,SV982: $i] :
( ( ( SV982
= ( zero_zero @ nat ) )
= $false )
| ( ( ( power_power @ SV363 @ SV860 @ SV982 )
= ( one_one @ SV363 ) )
= $true )
| ( ( power @ SV363 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5027]) ).
thf(5146,plain,
! [SV860: $i,SV363: $i,SV982: $i] :
( ( ( SV982
!= ( zero_zero @ nat ) )
= $false )
| ( ( ( power_power @ SV363 @ SV860 @ SV982 )
= ( times_times @ SV363 @ SV860 @ ( power_power @ SV363 @ SV860 @ ( minus_minus @ nat @ SV982 @ ( one_one @ nat ) ) ) ) )
= $true )
| ( ( power @ SV363 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5028]) ).
thf(5147,plain,
! [SV595: $i,SV366: $i] :
( ( ( ~ ( ~ ( ord_less @ int @ SV366 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV595 ) @ ( number_number_of @ nat @ SV366 ) )
= ( number_number_of @ nat @ SV595 ) ) ) )
= $false )
| ( ( ord_less @ int @ SV595 @ pls )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5029]) ).
thf(5148,plain,
! [SV595: $i,SV366: $i] :
( ( ( ~ ( ~ ~ ( ord_less @ int @ SV366 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV595 ) @ ( number_number_of @ nat @ SV366 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SV595 @ SV366 ) ) ) ) )
= $false )
| ( ( ord_less @ int @ SV595 @ pls )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5029]) ).
thf(5149,plain,
! [SV601: $i,SV374: $i] :
( ( ( SV374
= ( one_one @ nat ) )
= $true )
| ( ( ( times_times @ nat @ SV374 @ SV601 )
= ( one_one @ nat ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5030]) ).
thf(5150,plain,
! [SV374: $i,SV601: $i] :
( ( ( SV601
= ( one_one @ nat ) )
= $true )
| ( ( ( times_times @ nat @ SV374 @ SV601 )
= ( one_one @ nat ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5031]) ).
thf(5151,plain,
! [SV601: $i,SV374: $i] :
( ( ( SV374
= ( one_one @ nat ) )
= $false )
| ( ( SV601
!= ( one_one @ nat ) )
= $true )
| ( ( ( times_times @ nat @ SV374 @ SV601 )
= ( one_one @ nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5032]) ).
thf(5152,plain,
! [SV1048: $i,SV988: $i,SV869: $i,SV383: $i] :
( ( ( ord_less @ SV383 @ ( one_one @ SV383 ) @ SV869 )
= $false )
| ( ( ord_less @ SV383 @ ( power_power @ SV383 @ SV869 @ SV988 ) @ ( power_power @ SV383 @ SV869 @ SV1048 ) )
= $true )
| ( ( ord_less @ nat @ SV988 @ SV1048 )
= $false )
| ( ( linordered_semidom @ SV383 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5034]) ).
thf(5153,plain,
! [SV1095: $i,SV1091: $i,SV1081: $i,SV386: $i] :
( ( ( ( times_times @ SV386 @ ( minus_minus @ SV386 @ SV1081 @ SV1091 ) @ ( number_number_of @ SV386 @ SV1095 ) )
= ( minus_minus @ SV386 @ ( times_times @ SV386 @ SV1081 @ ( number_number_of @ SV386 @ SV1095 ) ) @ ( times_times @ SV386 @ SV1091 @ ( number_number_of @ SV386 @ SV1095 ) ) ) )
= $true )
| ( ( number @ SV386 )
= $false )
| ( ( ring @ SV386 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5035]) ).
thf(5154,plain,
! [SV612: $i,SV392: $i] :
( ( ( ~ ( ord_less @ int @ SV392 @ SV612 )
| ( ord_less @ int @ pls @ SV612 ) )
= $true )
| ( ( ord_less @ nat @ ( number_number_of @ nat @ SV392 ) @ ( number_number_of @ nat @ SV612 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5036]) ).
thf(5155,plain,
! [SV612: $i,SV392: $i] :
( ( ( ord_less @ int @ SV392 @ SV612 )
= $true )
| ( ( ord_less @ nat @ ( number_number_of @ nat @ SV392 ) @ ( number_number_of @ nat @ SV612 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5037]) ).
thf(5156,plain,
! [SV612: $i,SV392: $i] :
( ( ( ~ ( ord_less @ int @ SV392 @ SV612 )
| ( ord_less @ int @ pls @ SV612 ) )
= $false )
| ( ( ~ ( ord_less @ int @ SV392 @ SV612 ) )
= $true )
| ( ( ord_less @ nat @ ( number_number_of @ nat @ SV392 ) @ ( number_number_of @ nat @ SV612 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5038]) ).
thf(5157,plain,
! [SV615: $i,SV397: $i] :
( ( ( SV397
= ( zero_zero @ real ) )
= $true )
| ( ( ( plus_plus @ real @ ( times_times @ real @ SV397 @ SV397 ) @ ( times_times @ real @ SV615 @ SV615 ) )
= ( zero_zero @ real ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5039]) ).
thf(5158,plain,
! [SV397: $i,SV615: $i] :
( ( ( SV615
= ( zero_zero @ real ) )
= $true )
| ( ( ( plus_plus @ real @ ( times_times @ real @ SV397 @ SV397 ) @ ( times_times @ real @ SV615 @ SV615 ) )
= ( zero_zero @ real ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5040]) ).
thf(5159,plain,
! [SV615: $i,SV397: $i] :
( ( ( SV397
= ( zero_zero @ real ) )
= $false )
| ( ( SV615
!= ( zero_zero @ real ) )
= $true )
| ( ( ( plus_plus @ real @ ( times_times @ real @ SV397 @ SV397 ) @ ( times_times @ real @ SV615 @ SV615 ) )
= ( zero_zero @ real ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5041]) ).
thf(5160,plain,
! [SV722: $i,SV405: $i,SV617: $i] :
( ( ( ( ti @ int @ SV617 )
!= ( plus_plus @ int @ SV405 @ ( times_times @ int @ SV722 @ ( sK9_SY1940 @ SV722 @ SV405 @ SV617 ) ) ) )
= $false )
| ( ( zcong @ SV405 @ SV617 @ SV722 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[5042]) ).
thf(5161,plain,
! [SV1096: $i,SV722: $i,SV405: $i,SV617: $i] :
( ( ( ( ti @ int @ SV617 )
!= ( plus_plus @ int @ SV405 @ ( times_times @ int @ SV722 @ SV1096 ) ) )
= $true )
| ( ( zcong @ SV405 @ SV617 @ SV722 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5043]) ).
thf(5162,plain,
! [SV621: $i,SV413: $i] :
( ( ( ( ti @ int @ SV413 )
!= ( one_one @ int ) )
= $false )
| ( ( ~ ( ( ( ti @ int @ SV413 )
!= ( number_number_of @ int @ min ) )
| ( ( ti @ int @ SV621 )
!= ( number_number_of @ int @ min ) ) ) )
= $true )
| ( ( ( times_times @ int @ SV413 @ SV621 )
= ( one_one @ int ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5046]) ).
thf(5163,plain,
! [SV413: $i,SV621: $i] :
( ( ( ( ti @ int @ SV621 )
!= ( one_one @ int ) )
= $false )
| ( ( ~ ( ( ( ti @ int @ SV413 )
!= ( number_number_of @ int @ min ) )
| ( ( ti @ int @ SV621 )
!= ( number_number_of @ int @ min ) ) ) )
= $true )
| ( ( ( times_times @ int @ SV413 @ SV621 )
= ( one_one @ int ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5046]) ).
thf(5164,plain,
! [SV621: $i,SV413: $i] :
( ( ( ( ti @ int @ SV413 )
!= ( one_one @ int ) )
= $true )
| ( ( ( ti @ int @ SV621 )
!= ( one_one @ int ) )
= $true )
| ( ( ( times_times @ int @ SV413 @ SV621 )
= ( one_one @ int ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5047]) ).
thf(5165,plain,
! [SV621: $i,SV413: $i] :
( ( ( ( ti @ int @ SV413 )
!= ( number_number_of @ int @ min ) )
= $true )
| ( ( ( ti @ int @ SV621 )
!= ( number_number_of @ int @ min ) )
= $true )
| ( ( ( times_times @ int @ SV413 @ SV621 )
= ( one_one @ int ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5048]) ).
thf(5166,plain,
! [SV419: $i,SV623: $i] :
( ( ( ( ( ti @ int @ SV623 )
!= ( one_one @ int ) )
| ( ( ti @ int @ SV419 )
!= ( one_one @ int ) ) )
= $false )
| ( ( ( times_times @ int @ SV623 @ SV419 )
= ( one_one @ int ) )
= $false )
| ( ( ord_less @ int @ ( zero_zero @ int ) @ SV623 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5050]) ).
thf(5167,plain,
! [SV419: $i,SV623: $i] :
( ( ( ( ( ti @ int @ SV623 )
!= ( one_one @ int ) )
| ( ( ti @ int @ SV419 )
!= ( one_one @ int ) ) )
= $true )
| ( ( ( times_times @ int @ SV623 @ SV419 )
= ( one_one @ int ) )
= $true )
| ( ( ord_less @ int @ ( zero_zero @ int ) @ SV623 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5051]) ).
thf(5168,plain,
! [SV626: $i,SV422: $i,SV726: $i,SV1052: $i,SV995: $i,SV882: $i] :
( ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( times_times @ int @ SV882 @ SV995 ) @ SV1052 ) )
= $false )
| ( ( ~ ( ord_less @ int @ SV1052 @ SV882 )
| ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV726 )
| ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV882 )
| ~ ( ord_less_eq @ int @ SV882 @ SV422 )
| ( ord_less_eq @ int @ SV626 @ SV995 ) )
= $true )
| ( ( ( plus_plus @ int @ ( times_times @ int @ SV422 @ SV626 ) @ SV726 )
= ( plus_plus @ int @ ( times_times @ int @ SV882 @ SV995 ) @ SV1052 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5052]) ).
thf(5169,plain,
! [SV997: $i,SV1053: $i,SV887: $i,SV433: $i] :
( ( ( ord_less @ SV433 @ ( zero_zero @ SV433 ) @ SV887 )
= $false )
| ( ( ~ ( ord_less @ SV433 @ SV887 @ ( one_one @ SV433 ) )
| ( ord_less @ SV433 @ ( power_power @ SV433 @ SV887 @ SV1053 ) @ ( power_power @ SV433 @ SV887 @ SV997 ) ) )
= $true )
| ( ( ord_less @ nat @ SV997 @ SV1053 )
= $false )
| ( ( linordered_semidom @ SV433 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5053]) ).
thf(5170,plain,
! [SV998: $i,SV888: $i,SV1068: $i,SV1054: $i,SV1083: $i,SV434: $i] :
( ( ( ( ti @ SV434 @ SV1083 )
!= ( zero_zero @ SV434 ) )
= $false )
| ( ( ~ ~ ( ( ( ti @ SV434 @ SV1054 )
!= ( ti @ SV434 @ SV1068 ) )
| ~ ( ( ( ti @ SV434 @ SV888 )
!= ( ti @ SV434 @ SV998 ) ) ) )
| ( ( plus_plus @ SV434 @ SV1054 @ ( times_times @ SV434 @ SV1083 @ SV888 ) )
!= ( plus_plus @ SV434 @ SV1068 @ ( times_times @ SV434 @ SV1083 @ SV998 ) ) ) )
= $true )
| ( ( semiri456707255roduct @ SV434 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5054]) ).
thf(5171,plain,
! [SV732: $i,SV890: $i,SV481: $i,SV647: $i,SV79: $i] :
( ( ( ~ ( zcong @ SV79 @ ( times_times @ int @ SV647 @ SV481 ) @ SV890 ) )
= $true )
| ( ( zcong @ SV79 @ ( times_times @ int @ SV732 @ SV481 ) @ SV890 )
= $true )
| ( ( zcong @ SV647 @ SV732 @ SV890 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5055]) ).
thf(5172,plain,
! [SV647: $i,SV890: $i,SV481: $i,SV732: $i,SV79: $i] :
( ( ( ~ ( zcong @ SV79 @ ( times_times @ int @ SV732 @ SV481 ) @ SV890 ) )
= $true )
| ( ( zcong @ SV79 @ ( times_times @ int @ SV647 @ SV481 ) @ SV890 )
= $true )
| ( ( zcong @ SV647 @ SV732 @ SV890 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5056]) ).
thf(5173,plain,
! [SV896: $i,SV739: $i,SV90: $i] :
( ( ( ( ti @ SV90 @ SV739 )
= ( zero_zero @ SV90 ) )
= $true )
| ( ( ( times_times @ SV90 @ SV896 @ SV739 )
!= ( zero_zero @ SV90 ) )
= $true )
| ( ( ( ti @ SV90 @ SV896 )
= ( zero_zero @ SV90 ) )
= $true )
| ( ( no_zero_divisors @ SV90 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5057]) ).
thf(5174,plain,
! [SV744: $i,SV655: $i,SV901: $i,SV108: $i,SV494: $i] :
( ( ( zcong @ SV494 @ SV108 @ SV901 )
= $false )
| ( ( zcong @ SV655 @ SV108 @ SV901 )
= $true )
| ( ( ( ti @ int @ SV744 )
= ( ti @ int @ SV494 ) )
= $false )
| ( ( zcong @ SV655 @ SV744 @ SV901 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5058]) ).
thf(5175,plain,
! [SV902: $i,SV1004: $i,SV746: $i,SV117: $i] :
( ( ( ~ ( ord_less_eq @ SV117 @ SV746 @ ( one_one @ SV117 ) ) )
= $true )
| ( ( ord_less_eq @ SV117 @ ( power_power @ SV117 @ SV746 @ SV1004 ) @ ( power_power @ SV117 @ SV746 @ SV902 ) )
= $true )
| ( ( ord_less_eq @ SV117 @ ( zero_zero @ SV117 ) @ SV746 )
= $false )
| ( ( ord_less_eq @ nat @ SV902 @ SV1004 )
= $false )
| ( ( linordered_semidom @ SV117 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5059]) ).
thf(5176,plain,
! [SV1069: $i,SV120: $i] :
( ( ( ~ ( ord_less @ SV120 @ ( one_one @ SV120 ) @ ( number_number_of @ SV120 @ SV1069 ) )
| ( ord_less @ int @ ( bit1 @ pls ) @ SV1069 ) )
= $true )
| ( ( number_ring @ SV120 )
= $false )
| ( ( linordered_idom @ SV120 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5060]) ).
thf(5177,plain,
! [SV120: $i,SV1069: $i] :
( ( ( ~ ( ord_less @ int @ ( bit1 @ pls ) @ SV1069 )
| ( ord_less @ SV120 @ ( one_one @ SV120 ) @ ( number_number_of @ SV120 @ SV1069 ) ) )
= $true )
| ( ( number_ring @ SV120 )
= $false )
| ( ( linordered_idom @ SV120 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5061]) ).
thf(5178,plain,
! [SV1070: $i,SV123: $i] :
( ( ( ~ ( ord_less_eq @ SV123 @ ( number_number_of @ SV123 @ SV1070 ) @ ( one_one @ SV123 ) )
| ( ord_less_eq @ int @ SV1070 @ ( bit1 @ pls ) ) )
= $true )
| ( ( number_ring @ SV123 )
= $false )
| ( ( linordered_idom @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5062]) ).
thf(5179,plain,
! [SV123: $i,SV1070: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV1070 @ ( bit1 @ pls ) )
| ( ord_less_eq @ SV123 @ ( number_number_of @ SV123 @ SV1070 ) @ ( one_one @ SV123 ) ) )
= $true )
| ( ( number_ring @ SV123 )
= $false )
| ( ( linordered_idom @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5063]) ).
thf(5180,plain,
! [SV1057: $i,SV1005: $i,SV903: $i,SV747: $i,SV124: $i] :
( ( ( dvd_dvd @ SV124 @ SV747 @ SV903 )
= $false )
| ( ( dvd_dvd @ SV124 @ ( times_times @ SV124 @ SV1005 @ SV747 ) @ ( times_times @ SV124 @ SV1057 @ SV903 ) )
= $true )
| ( ( dvd_dvd @ SV124 @ SV1005 @ SV1057 )
= $false )
| ( ( comm_semiring_1 @ SV124 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5064]) ).
thf(5181,plain,
! [SV503: $i,SV753: $i,SV660: $i,SV907: $i,SV132: $i] :
( ( ( ord_less @ int @ SV132 @ SV907 )
= $false )
| ( ( ~ ( ord_less @ int @ SV132 @ SV660 )
| ( ord_less_eq @ int @ SV753 @ SV503 ) )
= $true )
| ( ( ord_less_eq @ int @ SV907 @ ( zero_zero @ int ) )
= $false )
| ( ( ord_less_eq @ int @ ( plus_plus @ int @ ( times_times @ int @ SV132 @ SV503 ) @ SV660 ) @ ( plus_plus @ int @ ( times_times @ int @ SV132 @ SV753 ) @ SV907 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5065]) ).
thf(5182,plain,
! [SV1071: $i,SV134: $i] :
( ( ( ~ ( ord_less @ SV134 @ ( number_number_of @ SV134 @ SV1071 ) @ ( one_one @ SV134 ) )
| ( ord_less @ int @ SV1071 @ ( bit1 @ pls ) ) )
= $true )
| ( ( number_ring @ SV134 )
= $false )
| ( ( linordered_idom @ SV134 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5066]) ).
thf(5183,plain,
! [SV134: $i,SV1071: $i] :
( ( ( ~ ( ord_less @ int @ SV1071 @ ( bit1 @ pls ) )
| ( ord_less @ SV134 @ ( number_number_of @ SV134 @ SV1071 ) @ ( one_one @ SV134 ) ) )
= $true )
| ( ( number_ring @ SV134 )
= $false )
| ( ( linordered_idom @ SV134 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5067]) ).
thf(5184,plain,
! [SV143: $i,SV509: $i] :
( ( ( SV509
= ( zero_zero @ nat ) )
= $false )
| ( ( ( power_power @ nat @ SV143 @ SV509 )
= ( zero_zero @ nat ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5071]) ).
thf(5185,plain,
! [SV143: $i,SV509: $i] :
( ( ( SV509
= ( zero_zero @ nat ) )
= $true )
| ( ( SV143
!= ( zero_zero @ nat ) )
= $true )
| ( ( ( power_power @ nat @ SV143 @ SV509 )
= ( zero_zero @ nat ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5073]) ).
thf(5186,plain,
! [SV151: $i,SV512: $i] :
( ( ( dvd_dvd @ nat @ SV512 @ SV151 )
= $false )
| ( ( dvd_dvd @ nat @ SV151 @ SV512 )
= $false )
| ( ( SV151 = SV512 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5074]) ).
thf(5187,plain,
! [SV513: $i,SV153: $i] :
( ( ( ~ ( ord_less @ real @ ( zero_zero @ real ) @ ( sK7_SY1807 @ SV153 @ SV513 ) ) )
= $false )
| ( ( ord_less @ real @ ( zero_zero @ real ) @ SV153 )
= $false )
| ( ( ord_less @ nat @ ( zero_zero @ nat ) @ SV513 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5077]) ).
thf(5188,plain,
! [SV513: $i,SV153: $i] :
( ( ( ( power_power @ real @ ( sK7_SY1807 @ SV153 @ SV513 ) @ SV513 )
!= SV153 )
= $false )
| ( ( ord_less @ real @ ( zero_zero @ real ) @ SV153 )
= $false )
| ( ( ord_less @ nat @ ( zero_zero @ nat ) @ SV513 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5077]) ).
thf(5189,plain,
! [SV911: $i,SV762: $i,SV1010: $i,SV155: $i] :
( ( ( ~ ( ord_less @ SV155 @ ( power_power @ SV155 @ SV1010 @ SV762 ) @ ( power_power @ SV155 @ SV1010 @ SV911 ) )
| ( ord_less @ nat @ SV762 @ SV911 ) )
= $true )
| ( ( ord_less @ SV155 @ ( one_one @ SV155 ) @ SV1010 )
= $false )
| ( ( linordered_semidom @ SV155 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5078]) ).
thf(5190,plain,
! [SV1010: $i,SV155: $i,SV911: $i,SV762: $i] :
( ( ( ~ ( ord_less @ nat @ SV762 @ SV911 )
| ( ord_less @ SV155 @ ( power_power @ SV155 @ SV1010 @ SV762 ) @ ( power_power @ SV155 @ SV1010 @ SV911 ) ) )
= $true )
| ( ( ord_less @ SV155 @ ( one_one @ SV155 ) @ SV1010 )
= $false )
| ( ( linordered_semidom @ SV155 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5079]) ).
thf(5191,plain,
! [SV913: $i,SV164: $i,SV667: $i,SV521: $i,SV765: $i] :
( ( ( ~ ( dvd_dvd @ int @ SV765 @ ( plus_plus @ int @ SV521 @ SV667 ) ) )
= $true )
| ( ( dvd_dvd @ int @ SV765 @ ( plus_plus @ int @ ( plus_plus @ int @ SV521 @ ( times_times @ int @ SV164 @ SV913 ) ) @ SV667 ) )
= $true )
| ( ( dvd_dvd @ int @ SV765 @ SV913 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5080]) ).
thf(5192,plain,
! [SV667: $i,SV913: $i,SV164: $i,SV521: $i,SV765: $i] :
( ( ( ~ ( dvd_dvd @ int @ SV765 @ ( plus_plus @ int @ ( plus_plus @ int @ SV521 @ ( times_times @ int @ SV164 @ SV913 ) ) @ SV667 ) ) )
= $true )
| ( ( dvd_dvd @ int @ SV765 @ ( plus_plus @ int @ SV521 @ SV667 ) )
= $true )
| ( ( dvd_dvd @ int @ SV765 @ SV913 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5081]) ).
thf(5193,plain,
! [SV169: $i,SV523: $i] :
( ( ( SV523
= ( zero_zero @ real ) )
= $false )
| ( ( SV169
= ( zero_zero @ real ) )
= $false )
| ( ( ( plus_plus @ real @ ( power_power @ real @ SV169 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ real @ SV523 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ real ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5085]) ).
thf(5194,plain,
! [SV918: $i,SV771: $i,SV1060: $i,SV1013: $i,SV175: $i] :
( ( ( ~ ~ ( ~ ( ( ( ti @ SV175 @ SV1013 )
!= ( ti @ SV175 @ SV1060 ) ) )
| ~ ( ( ( ti @ SV175 @ SV771 )
!= ( ti @ SV175 @ SV918 ) ) ) ) )
= $true )
| ( ( ( plus_plus @ SV175 @ ( times_times @ SV175 @ SV1013 @ SV771 ) @ ( times_times @ SV175 @ SV1060 @ SV918 ) )
!= ( plus_plus @ SV175 @ ( times_times @ SV175 @ SV1013 @ SV918 ) @ ( times_times @ SV175 @ SV1060 @ SV771 ) ) )
= $true )
| ( ( semiri456707255roduct @ SV175 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5086]) ).
thf(5195,plain,
! [SV918: $i,SV1060: $i,SV771: $i,SV1013: $i,SV175: $i] :
( ( ( ~ ( ( ( plus_plus @ SV175 @ ( times_times @ SV175 @ SV1013 @ SV771 ) @ ( times_times @ SV175 @ SV1060 @ SV918 ) )
!= ( plus_plus @ SV175 @ ( times_times @ SV175 @ SV1013 @ SV918 ) @ ( times_times @ SV175 @ SV1060 @ SV771 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( ( ( ti @ SV175 @ SV1013 )
!= ( ti @ SV175 @ SV1060 ) ) )
| ~ ( ( ( ti @ SV175 @ SV771 )
!= ( ti @ SV175 @ SV918 ) ) ) ) )
= $true )
| ( ( semiri456707255roduct @ SV175 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5087]) ).
thf(5196,plain,
! [SV530: $i,SV187: $i] :
( ( ( ( ti @ int @ SV187 )
= ( ti @ int @ SV530 ) )
= $false )
| ( ( ord_less @ int @ SV187 @ SV530 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5090]) ).
thf(5197,plain,
! [SV530: $i,SV187: $i] :
( ( ( ( ti @ int @ SV187 )
!= ( ti @ int @ SV530 ) )
= $false )
| ( ( ord_less_eq @ int @ SV187 @ SV530 )
= $false )
| ( ( ord_less @ int @ SV187 @ SV530 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5091]) ).
thf(5198,plain,
! [SV923: $i,SV778: $i,SV193: $i] :
( ( ( ( ( ti @ SV193 @ SV778 )
!= ( zero_zero @ SV193 ) )
| ( ( ti @ SV193 @ SV923 )
!= ( zero_zero @ SV193 ) ) )
= $false )
| ( ( ( plus_plus @ SV193 @ ( times_times @ SV193 @ SV778 @ SV778 ) @ ( times_times @ SV193 @ SV923 @ SV923 ) )
= ( zero_zero @ SV193 ) )
= $false )
| ( ( linord581940658strict @ SV193 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5092]) ).
thf(5199,plain,
! [SV923: $i,SV778: $i,SV193: $i] :
( ( ( ( ( ti @ SV193 @ SV778 )
!= ( zero_zero @ SV193 ) )
| ( ( ti @ SV193 @ SV923 )
!= ( zero_zero @ SV193 ) ) )
= $true )
| ( ( ( plus_plus @ SV193 @ ( times_times @ SV193 @ SV778 @ SV778 ) @ ( times_times @ SV193 @ SV923 @ SV923 ) )
= ( zero_zero @ SV193 ) )
= $true )
| ( ( linord581940658strict @ SV193 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5093]) ).
thf(5200,plain,
! [SV924: $i,SV779: $i,SV1017: $i,SV194: $i] :
( ( ( ( ( power_power @ SV194 @ SV1017 @ SV779 )
!= ( power_power @ SV194 @ SV1017 @ SV924 ) )
| ( SV779 = SV924 ) )
= $true )
| ( ( ord_less @ SV194 @ ( one_one @ SV194 ) @ SV1017 )
= $false )
| ( ( linordered_semidom @ SV194 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5094]) ).
thf(5201,plain,
! [SV1017: $i,SV194: $i,SV924: $i,SV779: $i] :
( ( ( ( SV779 != SV924 )
| ( ( power_power @ SV194 @ SV1017 @ SV779 )
= ( power_power @ SV194 @ SV1017 @ SV924 ) ) )
= $true )
| ( ( ord_less @ SV194 @ ( one_one @ SV194 ) @ SV1017 )
= $false )
| ( ( linordered_semidom @ SV194 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5095]) ).
thf(5202,plain,
! [SV534: $i,SV672: $i,SV196: $i] :
( ( ( zcong @ SV196 @ ( zero_zero @ int ) @ SV672 )
= $true )
| ( ( ~ ( zcong @ ( times_times @ int @ SV534 @ SV196 ) @ ( zero_zero @ int ) @ SV672 ) )
= $true )
| ( ( zcong @ SV534 @ ( zero_zero @ int ) @ SV672 )
= $true )
| ( ( zprime @ SV672 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5096]) ).
thf(5203,plain,
! [SV928: $i,SV783: $i,SV199: $i] :
( ( ( ~ ( ~ ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ SV783 )
| ~ ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ SV928 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq @ SV199 @ SV783 @ ( zero_zero @ SV199 ) )
| ~ ( ord_less_eq @ SV199 @ SV928 @ ( zero_zero @ SV199 ) ) ) )
= $true )
| ( ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ ( times_times @ SV199 @ SV783 @ SV928 ) )
= $false )
| ( ( linord581940658strict @ SV199 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5097]) ).
thf(5204,plain,
! [SV928: $i,SV783: $i,SV199: $i] :
( ( ( ~ ( ~ ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ SV783 )
| ~ ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ SV928 ) ) )
= $false )
| ( ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ ( times_times @ SV199 @ SV783 @ SV928 ) )
= $true )
| ( ( linord581940658strict @ SV199 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5098]) ).
thf(5205,plain,
! [SV928: $i,SV783: $i,SV199: $i] :
( ( ( ~ ( ~ ( ord_less_eq @ SV199 @ SV783 @ ( zero_zero @ SV199 ) )
| ~ ( ord_less_eq @ SV199 @ SV928 @ ( zero_zero @ SV199 ) ) ) )
= $false )
| ( ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ ( times_times @ SV199 @ SV783 @ SV928 ) )
= $true )
| ( ( linord581940658strict @ SV199 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5098]) ).
thf(5206,plain,
! [SV1074: $i,SV202: $i] :
( ( ( ~ ( ord_less_eq @ SV202 @ ( one_one @ SV202 ) @ ( number_number_of @ SV202 @ SV1074 ) )
| ( ord_less_eq @ int @ ( bit1 @ pls ) @ SV1074 ) )
= $true )
| ( ( number_ring @ SV202 )
= $false )
| ( ( linordered_idom @ SV202 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5099]) ).
thf(5207,plain,
! [SV202: $i,SV1074: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( bit1 @ pls ) @ SV1074 )
| ( ord_less_eq @ SV202 @ ( one_one @ SV202 ) @ ( number_number_of @ SV202 @ SV1074 ) ) )
= $true )
| ( ( number_ring @ SV202 )
= $false )
| ( ( linordered_idom @ SV202 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5100]) ).
thf(5208,plain,
! [SV535: $i,SV673: $i,SV203: $i] :
( ( ( ord_less @ int @ SV203 @ SV673 )
= $false )
| ( ( ~ ( zcong @ SV673 @ SV203 @ SV535 ) )
= $true )
| ( ( ord_less @ int @ ( zero_zero @ int ) @ SV203 )
= $false )
| ( ( ord_less @ int @ SV673 @ SV535 )
= $false )
| ( ( ord_less @ int @ ( zero_zero @ int ) @ SV673 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5101]) ).
thf(5209,plain,
! [SV1086: $i,SV1075: $i,SV213: $i] :
( ( ( ~ ( ( ( number_number_of @ SV213 @ SV1075 )
!= ( number_number_of @ SV213 @ SV1086 ) )
| ( ( ti @ int @ SV1075 )
= ( ti @ int @ SV1086 ) ) ) )
= $false )
| ( ( number_ring @ SV213 )
= $false )
| ( ( ring_char_0 @ SV213 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5102]) ).
thf(5210,plain,
! [SV213: $i,SV1086: $i,SV1075: $i] :
( ( ( ~ ( ( ( ti @ int @ SV1075 )
!= ( ti @ int @ SV1086 ) )
| ( ( number_number_of @ SV213 @ SV1075 )
= ( number_number_of @ SV213 @ SV1086 ) ) ) )
= $false )
| ( ( number_ring @ SV213 )
= $false )
| ( ( ring_char_0 @ SV213 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5102]) ).
thf(5211,plain,
! [SV538: $i,SV790: $i,SV214: $i,SV676: $i] :
( ( ( dvd_dvd @ nat @ SV676 @ SV214 )
= $false )
| ( ( ord_less @ nat @ SV790 @ SV676 )
= $false )
| ( ( ord_less @ nat @ ( zero_zero @ nat ) @ SV790 )
= $false )
| ( ( SV214
= ( plus_plus @ nat @ ( times_times @ nat @ SV538 @ SV676 ) @ SV790 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5103]) ).
thf(5212,plain,
! [SV1087: $i,SV1076: $i,SV218: $i] :
( ( ( ~ ( ~ ( ord_less @ SV218 @ ( number_number_of @ SV218 @ SV1076 ) @ ( number_number_of @ SV218 @ SV1087 ) )
| ( ord_less @ int @ SV1076 @ SV1087 ) ) )
= $false )
| ( ( number_ring @ SV218 )
= $false )
| ( ( linordered_idom @ SV218 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5104]) ).
thf(5213,plain,
! [SV218: $i,SV1087: $i,SV1076: $i] :
( ( ( ~ ( ~ ( ord_less @ int @ SV1076 @ SV1087 )
| ( ord_less @ SV218 @ ( number_number_of @ SV218 @ SV1076 ) @ ( number_number_of @ SV218 @ SV1087 ) ) ) )
= $false )
| ( ( number_ring @ SV218 )
= $false )
| ( ( linordered_idom @ SV218 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5104]) ).
thf(5214,plain,
! [SV1061: $i,SV933: $i,SV220: $i,SV1018: $i,SV792: $i] :
( ( ( ord_less_eq @ nat @ SV792 @ SV1018 )
= $false )
| ( ( dvd_dvd @ SV220 @ ( power_power @ SV220 @ SV933 @ SV792 ) @ SV1061 )
= $true )
| ( ( dvd_dvd @ SV220 @ ( power_power @ SV220 @ SV933 @ SV1018 ) @ SV1061 )
= $false )
| ( ( comm_semiring_1 @ SV220 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5105]) ).
thf(5215,plain,
! [SV549: $i,SV683: $i,SV240: $i,SV799: $i] :
( ( ( dvd_dvd @ int @ ( power_power @ int @ SV799 @ SV240 ) @ ( times_times @ int @ SV683 @ SV549 ) )
= $false )
| ( ( dvd_dvd @ int @ ( power_power @ int @ SV799 @ SV240 ) @ SV549 )
= $true )
| ( ( dvd_dvd @ int @ SV799 @ SV683 )
= $true )
| ( ( zprime @ SV799 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5109]) ).
thf(5216,plain,
! [SV1062: $i,SV1024: $i,SV942: $i,SV804: $i,SV255: $i] :
( ( ( ( plus_plus @ SV255 @ ( times_times @ SV255 @ SV804 @ SV942 ) @ ( times_times @ SV255 @ SV1024 @ SV1062 ) )
!= ( plus_plus @ SV255 @ ( times_times @ SV255 @ SV804 @ SV1062 ) @ ( times_times @ SV255 @ SV1024 @ SV942 ) ) )
= $true )
| ( ( ( ( ti @ SV255 @ SV804 )
= ( ti @ SV255 @ SV1024 ) )
| ( ( ti @ SV255 @ SV942 )
= ( ti @ SV255 @ SV1062 ) ) )
= $true )
| ( ( semiri456707255roduct @ SV255 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5110]) ).
thf(5217,plain,
! [SV1062: $i,SV942: $i,SV1024: $i,SV804: $i,SV255: $i] :
( ( ( ~ ( ( ( ti @ SV255 @ SV804 )
= ( ti @ SV255 @ SV1024 ) )
| ( ( ti @ SV255 @ SV942 )
= ( ti @ SV255 @ SV1062 ) ) ) )
= $true )
| ( ( ( plus_plus @ SV255 @ ( times_times @ SV255 @ SV804 @ SV942 ) @ ( times_times @ SV255 @ SV1024 @ SV1062 ) )
= ( plus_plus @ SV255 @ ( times_times @ SV255 @ SV804 @ SV1062 ) @ ( times_times @ SV255 @ SV1024 @ SV942 ) ) )
= $true )
| ( ( semiri456707255roduct @ SV255 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5111]) ).
thf(5218,plain,
! [SV805: $i,SV943: $i,SV688: $i,SV557: $i,SV257: $i] :
( ( ( ~ ( zcong @ SV257 @ ( times_times @ int @ SV557 @ SV688 ) @ SV943 ) )
= $true )
| ( ( zcong @ SV257 @ ( times_times @ int @ SV557 @ SV805 ) @ SV943 )
= $true )
| ( ( zcong @ SV688 @ SV805 @ SV943 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5112]) ).
thf(5219,plain,
! [SV688: $i,SV943: $i,SV805: $i,SV557: $i,SV257: $i] :
( ( ( ~ ( zcong @ SV257 @ ( times_times @ int @ SV557 @ SV805 ) @ SV943 ) )
= $true )
| ( ( zcong @ SV257 @ ( times_times @ int @ SV557 @ SV688 ) @ SV943 )
= $true )
| ( ( zcong @ SV688 @ SV805 @ SV943 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5113]) ).
thf(5220,plain,
! [SV562: $i,SV273: $i,SV691: $i] :
( ( ( ( times_times @ real @ SV691 @ SV273 )
= ( times_times @ real @ SV691 @ SV562 ) )
= $false )
| ( ( SV273 = SV562 )
= $true )
| ( ( SV691
= ( zero_zero @ real ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5114]) ).
thf(5221,plain,
! [SV691: $i,SV562: $i,SV273: $i] :
( ( ( SV273 = SV562 )
= $false )
| ( ( ( times_times @ real @ SV691 @ SV273 )
= ( times_times @ real @ SV691 @ SV562 ) )
= $true )
| ( ( SV691
= ( zero_zero @ real ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5115]) ).
thf(5222,plain,
! [SV694: $i,SV566: $i,SV288: $i,SV821: $i] :
( ( ( dvd_dvd @ int @ ( power_power @ int @ SV821 @ SV288 ) @ ( times_times @ int @ SV566 @ SV694 ) )
= $false )
| ( ( dvd_dvd @ int @ ( power_power @ int @ SV821 @ SV288 ) @ SV566 )
= $true )
| ( ( dvd_dvd @ int @ SV821 @ SV694 )
= $true )
| ( ( zprime @ SV821 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5117]) ).
thf(5223,plain,
! [SV955: $i,SV826: $i,SV301: $i] :
( ( ( ( ti @ SV301 @ SV826 )
= ( zero_zero @ SV301 ) )
= $true )
| ( ( ( ti @ SV301 @ SV955 )
= ( zero_zero @ SV301 ) )
= $true )
| ( ( ( times_times @ SV301 @ SV826 @ SV955 )
= ( zero_zero @ SV301 ) )
= $false )
| ( ( ring_n68954251visors @ SV301 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5118]) ).
thf(5224,plain,
! [SV955: $i,SV826: $i,SV301: $i] :
( ( ( ( ti @ SV301 @ SV826 )
= ( zero_zero @ SV301 ) )
= $false )
| ( ( ( times_times @ SV301 @ SV826 @ SV955 )
= ( zero_zero @ SV301 ) )
= $true )
| ( ( ring_n68954251visors @ SV301 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5119]) ).
thf(5225,plain,
! [SV826: $i,SV955: $i,SV301: $i] :
( ( ( ( ti @ SV301 @ SV955 )
= ( zero_zero @ SV301 ) )
= $false )
| ( ( ( times_times @ SV301 @ SV826 @ SV955 )
= ( zero_zero @ SV301 ) )
= $true )
| ( ( ring_n68954251visors @ SV301 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5119]) ).
thf(5226,plain,
! [SV573: $i,SV957: $i,SV829: $i,SV1032: $i,SV305: $i,SV698: $i] :
( ( ( ~ ( ord_less @ int @ SV698 @ SV305 ) )
= $true )
| ( ( ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV1032 )
| ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV829 )
| ~ ( ord_less_eq @ int @ SV829 @ SV305 )
| ( ord_less_eq @ int @ SV957 @ SV573 ) )
= $true )
| ( ( ord_less @ int @ ( plus_plus @ int @ ( times_times @ int @ SV829 @ SV957 ) @ SV1032 ) @ ( zero_zero @ int ) )
= $false )
| ( ( ( plus_plus @ int @ ( times_times @ int @ SV305 @ SV573 ) @ SV698 )
= ( plus_plus @ int @ ( times_times @ int @ SV829 @ SV957 ) @ SV1032 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5121]) ).
thf(5227,plain,
! [SV833: $i,SV576: $i,SV960: $i,SV312: $i,SV701: $i] :
( ( ( ord_less @ int @ SV701 @ SV312 )
= $false )
| ( ( ~ ( ord_less @ int @ SV960 @ SV312 )
| ( ord_less_eq @ int @ SV576 @ SV833 ) )
= $true )
| ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV701 )
= $false )
| ( ( ord_less_eq @ int @ ( plus_plus @ int @ ( times_times @ int @ SV312 @ SV576 ) @ SV701 ) @ ( plus_plus @ int @ ( times_times @ int @ SV312 @ SV833 ) @ SV960 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5122]) ).
thf(5228,plain,
! [SV966: $i,SV839: $i,SV319: $i] :
( ( ( ~ ( ~ ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SV839 )
| ~ ( ord_less_eq @ SV319 @ SV966 @ ( zero_zero @ SV319 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq @ SV319 @ SV839 @ ( zero_zero @ SV319 ) )
| ~ ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SV966 ) ) )
= $true )
| ( ( ord_less_eq @ SV319 @ ( times_times @ SV319 @ SV839 @ SV966 ) @ ( zero_zero @ SV319 ) )
= $false )
| ( ( linord581940658strict @ SV319 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5128]) ).
thf(5229,plain,
! [SV966: $i,SV839: $i,SV319: $i] :
( ( ( ~ ( ~ ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SV839 )
| ~ ( ord_less_eq @ SV319 @ SV966 @ ( zero_zero @ SV319 ) ) ) )
= $false )
| ( ( ord_less_eq @ SV319 @ ( times_times @ SV319 @ SV839 @ SV966 ) @ ( zero_zero @ SV319 ) )
= $true )
| ( ( linord581940658strict @ SV319 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5129]) ).
thf(5230,plain,
! [SV966: $i,SV839: $i,SV319: $i] :
( ( ( ~ ( ~ ( ord_less_eq @ SV319 @ SV839 @ ( zero_zero @ SV319 ) )
| ~ ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SV966 ) ) )
= $false )
| ( ( ord_less_eq @ SV319 @ ( times_times @ SV319 @ SV839 @ SV966 ) @ ( zero_zero @ SV319 ) )
= $true )
| ( ( linord581940658strict @ SV319 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5129]) ).
thf(5231,plain,
! [SV1090: $i,SV1078: $i,SV321: $i] :
( ( ( ~ ( ~ ( ord_less_eq @ SV321 @ ( number_number_of @ SV321 @ SV1078 ) @ ( number_number_of @ SV321 @ SV1090 ) )
| ( ord_less_eq @ int @ SV1078 @ SV1090 ) ) )
= $false )
| ( ( number_ring @ SV321 )
= $false )
| ( ( linordered_idom @ SV321 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5130]) ).
thf(5232,plain,
! [SV321: $i,SV1090: $i,SV1078: $i] :
( ( ( ~ ( ~ ( ord_less_eq @ int @ SV1078 @ SV1090 )
| ( ord_less_eq @ SV321 @ ( number_number_of @ SV321 @ SV1078 ) @ ( number_number_of @ SV321 @ SV1090 ) ) ) )
= $false )
| ( ( number_ring @ SV321 )
= $false )
| ( ( linordered_idom @ SV321 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5130]) ).
thf(5233,plain,
! [SV1064: $i,SV1036: $i,SV323: $i,SV967: $i,SV841: $i] :
( ( ( ord_less_eq @ nat @ SV841 @ SV967 )
= $false )
| ( ( dvd_dvd @ SV323 @ ( power_power @ SV323 @ SV1036 @ SV841 ) @ ( power_power @ SV323 @ SV1064 @ SV967 ) )
= $true )
| ( ( dvd_dvd @ SV323 @ SV1036 @ SV1064 )
= $false )
| ( ( comm_semiring_1 @ SV323 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5131]) ).
thf(5234,plain,
! [SV333: $i,SV1079: $i] :
( ( ( ( ( number_number_of @ nat @ SV1079 )
!= ( zero_zero @ nat ) )
| ( ( power_power @ SV333 @ ( zero_zero @ SV333 ) @ ( number_number_of @ nat @ SV1079 ) )
= ( one_one @ SV333 ) ) )
= $true )
| ( ( power @ SV333 )
= $false )
| ( ( semiring_0 @ SV333 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5132]) ).
thf(5235,plain,
! [SV333: $i,SV1079: $i] :
( ( ( ~ ( ( ( number_number_of @ nat @ SV1079 )
!= ( zero_zero @ nat ) ) )
| ( ( power_power @ SV333 @ ( zero_zero @ SV333 ) @ ( number_number_of @ nat @ SV1079 ) )
= ( zero_zero @ SV333 ) ) )
= $true )
| ( ( power @ SV333 )
= $false )
| ( ( semiring_0 @ SV333 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5133]) ).
thf(5236,plain,
! [SV977: $i,SV855: $i,SV352: $i] :
( ( ( ( ( ti @ SV352 @ SV855 )
!= ( zero_zero @ SV352 ) )
| ( ( ti @ SV352 @ SV977 )
!= ( zero_zero @ SV352 ) ) )
= $false )
| ( ( ( plus_plus @ SV352 @ ( power_power @ SV352 @ SV855 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV352 @ SV977 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV352 ) )
= $false )
| ( ( linordered_idom @ SV352 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5136]) ).
thf(5237,plain,
! [SV977: $i,SV855: $i,SV352: $i] :
( ( ( ( ( ti @ SV352 @ SV855 )
!= ( zero_zero @ SV352 ) )
| ( ( ti @ SV352 @ SV977 )
!= ( zero_zero @ SV352 ) ) )
= $true )
| ( ( ( plus_plus @ SV352 @ ( power_power @ SV352 @ SV855 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV352 @ SV977 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV352 ) )
= $true )
| ( ( linordered_idom @ SV352 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5137]) ).
thf(5238,plain,
! [SV355: $i,SV1080: $i] :
( ( ( ( SV1080
!= ( zero_zero @ nat ) )
| ( ( power_power @ SV355 @ ( zero_zero @ SV355 ) @ SV1080 )
= ( one_one @ SV355 ) ) )
= $true )
| ( ( power @ SV355 )
= $false )
| ( ( semiring_0 @ SV355 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5139]) ).
thf(5239,plain,
! [SV355: $i,SV1080: $i] :
( ( ( ~ ( ( SV1080
!= ( zero_zero @ nat ) ) )
| ( ( power_power @ SV355 @ ( zero_zero @ SV355 ) @ SV1080 )
= ( zero_zero @ SV355 ) ) )
= $true )
| ( ( power @ SV355 )
= $false )
| ( ( semiring_0 @ SV355 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5140]) ).
thf(5240,plain,
! [SV980: $i,SV858: $i,SV1044: $i,SV358: $i] :
( ( ( ~ ( ord_less_eq @ SV358 @ ( power_power @ SV358 @ SV1044 @ SV858 ) @ ( power_power @ SV358 @ SV1044 @ SV980 ) )
| ( ord_less_eq @ nat @ SV858 @ SV980 ) )
= $true )
| ( ( ord_less @ SV358 @ ( one_one @ SV358 ) @ SV1044 )
= $false )
| ( ( linordered_semidom @ SV358 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5141]) ).
thf(5241,plain,
! [SV1044: $i,SV358: $i,SV980: $i,SV858: $i] :
( ( ( ~ ( ord_less_eq @ nat @ SV858 @ SV980 )
| ( ord_less_eq @ SV358 @ ( power_power @ SV358 @ SV1044 @ SV858 ) @ ( power_power @ SV358 @ SV1044 @ SV980 ) ) )
= $true )
| ( ( ord_less @ SV358 @ ( one_one @ SV358 ) @ SV1044 )
= $false )
| ( ( linordered_semidom @ SV358 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5142]) ).
thf(5242,plain,
! [SV592: $i,SV710: $i,SV362: $i] :
( ( ( ( times_times @ real @ SV362 @ SV710 )
= ( times_times @ real @ SV592 @ SV710 ) )
= $false )
| ( ( SV362 = SV592 )
= $true )
| ( ( SV710
= ( zero_zero @ real ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5143]) ).
thf(5243,plain,
! [SV710: $i,SV592: $i,SV362: $i] :
( ( ( SV362 = SV592 )
= $false )
| ( ( ( times_times @ real @ SV362 @ SV710 )
= ( times_times @ real @ SV592 @ SV710 ) )
= $true )
| ( ( SV710
= ( zero_zero @ real ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5144]) ).
thf(5244,plain,
! [SV860: $i,SV363: $i,SV982: $i] :
( ( ( SV982
= ( zero_zero @ nat ) )
= $true )
| ( ( ( power_power @ SV363 @ SV860 @ SV982 )
= ( times_times @ SV363 @ SV860 @ ( power_power @ SV363 @ SV860 @ ( minus_minus @ nat @ SV982 @ ( one_one @ nat ) ) ) ) )
= $true )
| ( ( power @ SV363 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5146]) ).
thf(5245,plain,
! [SV595: $i,SV366: $i] :
( ( ( ~ ( ord_less @ int @ SV366 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV595 ) @ ( number_number_of @ nat @ SV366 ) )
= ( number_number_of @ nat @ SV595 ) ) )
= $true )
| ( ( ord_less @ int @ SV595 @ pls )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5147]) ).
thf(5246,plain,
! [SV595: $i,SV366: $i] :
( ( ( ~ ~ ( ord_less @ int @ SV366 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV595 ) @ ( number_number_of @ nat @ SV366 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SV595 @ SV366 ) ) ) )
= $true )
| ( ( ord_less @ int @ SV595 @ pls )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5148]) ).
thf(5247,plain,
! [SV374: $i,SV601: $i] :
( ( ( SV601
= ( one_one @ nat ) )
= $false )
| ( ( SV374
= ( one_one @ nat ) )
= $false )
| ( ( ( times_times @ nat @ SV374 @ SV601 )
= ( one_one @ nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5151]) ).
thf(5248,plain,
! [SV612: $i,SV392: $i] :
( ( ( ~ ( ord_less @ int @ SV392 @ SV612 ) )
= $true )
| ( ( ord_less @ int @ pls @ SV612 )
= $true )
| ( ( ord_less @ nat @ ( number_number_of @ nat @ SV392 ) @ ( number_number_of @ nat @ SV612 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5154]) ).
thf(5249,plain,
! [SV612: $i,SV392: $i] :
( ( ( ~ ( ord_less @ int @ SV392 @ SV612 ) )
= $false )
| ( ( ~ ( ord_less @ int @ SV392 @ SV612 ) )
= $true )
| ( ( ord_less @ nat @ ( number_number_of @ nat @ SV392 ) @ ( number_number_of @ nat @ SV612 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5156]) ).
thf(5250,plain,
! [SV392: $i,SV612: $i] :
( ( ( ord_less @ int @ pls @ SV612 )
= $false )
| ( ( ~ ( ord_less @ int @ SV392 @ SV612 ) )
= $true )
| ( ( ord_less @ nat @ ( number_number_of @ nat @ SV392 ) @ ( number_number_of @ nat @ SV612 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5156]) ).
thf(5251,plain,
! [SV397: $i,SV615: $i] :
( ( ( SV615
= ( zero_zero @ real ) )
= $false )
| ( ( SV397
= ( zero_zero @ real ) )
= $false )
| ( ( ( plus_plus @ real @ ( times_times @ real @ SV397 @ SV397 ) @ ( times_times @ real @ SV615 @ SV615 ) )
= ( zero_zero @ real ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5159]) ).
thf(5252,plain,
! [SV722: $i,SV405: $i,SV617: $i] :
( ( ( ( ti @ int @ SV617 )
= ( plus_plus @ int @ SV405 @ ( times_times @ int @ SV722 @ ( sK9_SY1940 @ SV722 @ SV405 @ SV617 ) ) ) )
= $true )
| ( ( zcong @ SV405 @ SV617 @ SV722 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5160]) ).
thf(5253,plain,
! [SV1096: $i,SV722: $i,SV405: $i,SV617: $i] :
( ( ( ( ti @ int @ SV617 )
= ( plus_plus @ int @ SV405 @ ( times_times @ int @ SV722 @ SV1096 ) ) )
= $false )
| ( ( zcong @ SV405 @ SV617 @ SV722 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5161]) ).
thf(5254,plain,
! [SV621: $i,SV413: $i] :
( ( ( ( ti @ int @ SV413 )
= ( one_one @ int ) )
= $true )
| ( ( ~ ( ( ( ti @ int @ SV413 )
!= ( number_number_of @ int @ min ) )
| ( ( ti @ int @ SV621 )
!= ( number_number_of @ int @ min ) ) ) )
= $true )
| ( ( ( times_times @ int @ SV413 @ SV621 )
= ( one_one @ int ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5162]) ).
thf(5255,plain,
! [SV413: $i,SV621: $i] :
( ( ( ( ti @ int @ SV621 )
= ( one_one @ int ) )
= $true )
| ( ( ~ ( ( ( ti @ int @ SV413 )
!= ( number_number_of @ int @ min ) )
| ( ( ti @ int @ SV621 )
!= ( number_number_of @ int @ min ) ) ) )
= $true )
| ( ( ( times_times @ int @ SV413 @ SV621 )
= ( one_one @ int ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5163]) ).
thf(5256,plain,
! [SV621: $i,SV413: $i] :
( ( ( ( ti @ int @ SV413 )
= ( one_one @ int ) )
= $false )
| ( ( ( ti @ int @ SV621 )
!= ( one_one @ int ) )
= $true )
| ( ( ( times_times @ int @ SV413 @ SV621 )
= ( one_one @ int ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5164]) ).
thf(5257,plain,
! [SV621: $i,SV413: $i] :
( ( ( ( ti @ int @ SV413 )
= ( number_number_of @ int @ min ) )
= $false )
| ( ( ( ti @ int @ SV621 )
!= ( number_number_of @ int @ min ) )
= $true )
| ( ( ( times_times @ int @ SV413 @ SV621 )
= ( one_one @ int ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5165]) ).
thf(5258,plain,
! [SV419: $i,SV623: $i] :
( ( ( ( ti @ int @ SV623 )
!= ( one_one @ int ) )
= $false )
| ( ( ( times_times @ int @ SV623 @ SV419 )
= ( one_one @ int ) )
= $false )
| ( ( ord_less @ int @ ( zero_zero @ int ) @ SV623 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5166]) ).
thf(5259,plain,
! [SV623: $i,SV419: $i] :
( ( ( ( ti @ int @ SV419 )
!= ( one_one @ int ) )
= $false )
| ( ( ( times_times @ int @ SV623 @ SV419 )
= ( one_one @ int ) )
= $false )
| ( ( ord_less @ int @ ( zero_zero @ int ) @ SV623 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5166]) ).
thf(5260,plain,
! [SV419: $i,SV623: $i] :
( ( ( ( ti @ int @ SV623 )
!= ( one_one @ int ) )
= $true )
| ( ( ( ti @ int @ SV419 )
!= ( one_one @ int ) )
= $true )
| ( ( ( times_times @ int @ SV623 @ SV419 )
= ( one_one @ int ) )
= $true )
| ( ( ord_less @ int @ ( zero_zero @ int ) @ SV623 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5167]) ).
thf(5261,plain,
! [SV995: $i,SV626: $i,SV422: $i,SV726: $i,SV882: $i,SV1052: $i] :
( ( ( ~ ( ord_less @ int @ SV1052 @ SV882 ) )
= $true )
| ( ( ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV726 )
| ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV882 )
| ~ ( ord_less_eq @ int @ SV882 @ SV422 )
| ( ord_less_eq @ int @ SV626 @ SV995 ) )
= $true )
| ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( times_times @ int @ SV882 @ SV995 ) @ SV1052 ) )
= $false )
| ( ( ( plus_plus @ int @ ( times_times @ int @ SV422 @ SV626 ) @ SV726 )
= ( plus_plus @ int @ ( times_times @ int @ SV882 @ SV995 ) @ SV1052 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5168]) ).
thf(5262,plain,
! [SV997: $i,SV1053: $i,SV887: $i,SV433: $i] :
( ( ( ~ ( ord_less @ SV433 @ SV887 @ ( one_one @ SV433 ) ) )
= $true )
| ( ( ord_less @ SV433 @ ( power_power @ SV433 @ SV887 @ SV1053 ) @ ( power_power @ SV433 @ SV887 @ SV997 ) )
= $true )
| ( ( ord_less @ SV433 @ ( zero_zero @ SV433 ) @ SV887 )
= $false )
| ( ( ord_less @ nat @ SV997 @ SV1053 )
= $false )
| ( ( linordered_semidom @ SV433 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5169]) ).
thf(5263,plain,
! [SV998: $i,SV888: $i,SV1068: $i,SV1054: $i,SV1083: $i,SV434: $i] :
( ( ( ( ti @ SV434 @ SV1083 )
= ( zero_zero @ SV434 ) )
= $true )
| ( ( ~ ~ ( ( ( ti @ SV434 @ SV1054 )
!= ( ti @ SV434 @ SV1068 ) )
| ~ ( ( ( ti @ SV434 @ SV888 )
!= ( ti @ SV434 @ SV998 ) ) ) )
| ( ( plus_plus @ SV434 @ SV1054 @ ( times_times @ SV434 @ SV1083 @ SV888 ) )
!= ( plus_plus @ SV434 @ SV1068 @ ( times_times @ SV434 @ SV1083 @ SV998 ) ) ) )
= $true )
| ( ( semiri456707255roduct @ SV434 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5170]) ).
thf(5264,plain,
! [SV732: $i,SV890: $i,SV481: $i,SV647: $i,SV79: $i] :
( ( ( zcong @ SV79 @ ( times_times @ int @ SV647 @ SV481 ) @ SV890 )
= $false )
| ( ( zcong @ SV79 @ ( times_times @ int @ SV732 @ SV481 ) @ SV890 )
= $true )
| ( ( zcong @ SV647 @ SV732 @ SV890 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5171]) ).
thf(5265,plain,
! [SV647: $i,SV890: $i,SV481: $i,SV732: $i,SV79: $i] :
( ( ( zcong @ SV79 @ ( times_times @ int @ SV732 @ SV481 ) @ SV890 )
= $false )
| ( ( zcong @ SV79 @ ( times_times @ int @ SV647 @ SV481 ) @ SV890 )
= $true )
| ( ( zcong @ SV647 @ SV732 @ SV890 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5172]) ).
thf(5266,plain,
! [SV739: $i,SV896: $i,SV90: $i] :
( ( ( ( times_times @ SV90 @ SV896 @ SV739 )
= ( zero_zero @ SV90 ) )
= $false )
| ( ( ( ti @ SV90 @ SV739 )
= ( zero_zero @ SV90 ) )
= $true )
| ( ( ( ti @ SV90 @ SV896 )
= ( zero_zero @ SV90 ) )
= $true )
| ( ( no_zero_divisors @ SV90 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5173]) ).
thf(5267,plain,
! [SV902: $i,SV1004: $i,SV746: $i,SV117: $i] :
( ( ( ord_less_eq @ SV117 @ SV746 @ ( one_one @ SV117 ) )
= $false )
| ( ( ord_less_eq @ SV117 @ ( power_power @ SV117 @ SV746 @ SV1004 ) @ ( power_power @ SV117 @ SV746 @ SV902 ) )
= $true )
| ( ( ord_less_eq @ SV117 @ ( zero_zero @ SV117 ) @ SV746 )
= $false )
| ( ( ord_less_eq @ nat @ SV902 @ SV1004 )
= $false )
| ( ( linordered_semidom @ SV117 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5175]) ).
thf(5268,plain,
! [SV1069: $i,SV120: $i] :
( ( ( ~ ( ord_less @ SV120 @ ( one_one @ SV120 ) @ ( number_number_of @ SV120 @ SV1069 ) ) )
= $true )
| ( ( ord_less @ int @ ( bit1 @ pls ) @ SV1069 )
= $true )
| ( ( number_ring @ SV120 )
= $false )
| ( ( linordered_idom @ SV120 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5176]) ).
thf(5269,plain,
! [SV120: $i,SV1069: $i] :
( ( ( ~ ( ord_less @ int @ ( bit1 @ pls ) @ SV1069 ) )
= $true )
| ( ( ord_less @ SV120 @ ( one_one @ SV120 ) @ ( number_number_of @ SV120 @ SV1069 ) )
= $true )
| ( ( number_ring @ SV120 )
= $false )
| ( ( linordered_idom @ SV120 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5177]) ).
thf(5270,plain,
! [SV1070: $i,SV123: $i] :
( ( ( ~ ( ord_less_eq @ SV123 @ ( number_number_of @ SV123 @ SV1070 ) @ ( one_one @ SV123 ) ) )
= $true )
| ( ( ord_less_eq @ int @ SV1070 @ ( bit1 @ pls ) )
= $true )
| ( ( number_ring @ SV123 )
= $false )
| ( ( linordered_idom @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5178]) ).
thf(5271,plain,
! [SV123: $i,SV1070: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV1070 @ ( bit1 @ pls ) ) )
= $true )
| ( ( ord_less_eq @ SV123 @ ( number_number_of @ SV123 @ SV1070 ) @ ( one_one @ SV123 ) )
= $true )
| ( ( number_ring @ SV123 )
= $false )
| ( ( linordered_idom @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5179]) ).
thf(5272,plain,
! [SV907: $i,SV503: $i,SV753: $i,SV660: $i,SV132: $i] :
( ( ( ~ ( ord_less @ int @ SV132 @ SV660 ) )
= $true )
| ( ( ord_less_eq @ int @ SV753 @ SV503 )
= $true )
| ( ( ord_less @ int @ SV132 @ SV907 )
= $false )
| ( ( ord_less_eq @ int @ SV907 @ ( zero_zero @ int ) )
= $false )
| ( ( ord_less_eq @ int @ ( plus_plus @ int @ ( times_times @ int @ SV132 @ SV503 ) @ SV660 ) @ ( plus_plus @ int @ ( times_times @ int @ SV132 @ SV753 ) @ SV907 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5181]) ).
thf(5273,plain,
! [SV1071: $i,SV134: $i] :
( ( ( ~ ( ord_less @ SV134 @ ( number_number_of @ SV134 @ SV1071 ) @ ( one_one @ SV134 ) ) )
= $true )
| ( ( ord_less @ int @ SV1071 @ ( bit1 @ pls ) )
= $true )
| ( ( number_ring @ SV134 )
= $false )
| ( ( linordered_idom @ SV134 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5182]) ).
thf(5274,plain,
! [SV134: $i,SV1071: $i] :
( ( ( ~ ( ord_less @ int @ SV1071 @ ( bit1 @ pls ) ) )
= $true )
| ( ( ord_less @ SV134 @ ( number_number_of @ SV134 @ SV1071 ) @ ( one_one @ SV134 ) )
= $true )
| ( ( number_ring @ SV134 )
= $false )
| ( ( linordered_idom @ SV134 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5183]) ).
thf(5275,plain,
! [SV509: $i,SV143: $i] :
( ( ( SV143
= ( zero_zero @ nat ) )
= $false )
| ( ( SV509
= ( zero_zero @ nat ) )
= $true )
| ( ( ( power_power @ nat @ SV143 @ SV509 )
= ( zero_zero @ nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5185]) ).
thf(5276,plain,
! [SV513: $i,SV153: $i] :
( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( sK7_SY1807 @ SV153 @ SV513 ) )
= $true )
| ( ( ord_less @ real @ ( zero_zero @ real ) @ SV153 )
= $false )
| ( ( ord_less @ nat @ ( zero_zero @ nat ) @ SV513 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5187]) ).
thf(5277,plain,
! [SV513: $i,SV153: $i] :
( ( ( ( power_power @ real @ ( sK7_SY1807 @ SV153 @ SV513 ) @ SV513 )
= SV153 )
= $true )
| ( ( ord_less @ real @ ( zero_zero @ real ) @ SV153 )
= $false )
| ( ( ord_less @ nat @ ( zero_zero @ nat ) @ SV513 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5188]) ).
thf(5278,plain,
! [SV911: $i,SV762: $i,SV1010: $i,SV155: $i] :
( ( ( ~ ( ord_less @ SV155 @ ( power_power @ SV155 @ SV1010 @ SV762 ) @ ( power_power @ SV155 @ SV1010 @ SV911 ) ) )
= $true )
| ( ( ord_less @ nat @ SV762 @ SV911 )
= $true )
| ( ( ord_less @ SV155 @ ( one_one @ SV155 ) @ SV1010 )
= $false )
| ( ( linordered_semidom @ SV155 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5189]) ).
thf(5279,plain,
! [SV1010: $i,SV155: $i,SV911: $i,SV762: $i] :
( ( ( ~ ( ord_less @ nat @ SV762 @ SV911 ) )
= $true )
| ( ( ord_less @ SV155 @ ( power_power @ SV155 @ SV1010 @ SV762 ) @ ( power_power @ SV155 @ SV1010 @ SV911 ) )
= $true )
| ( ( ord_less @ SV155 @ ( one_one @ SV155 ) @ SV1010 )
= $false )
| ( ( linordered_semidom @ SV155 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5190]) ).
thf(5280,plain,
! [SV913: $i,SV164: $i,SV667: $i,SV521: $i,SV765: $i] :
( ( ( dvd_dvd @ int @ SV765 @ ( plus_plus @ int @ SV521 @ SV667 ) )
= $false )
| ( ( dvd_dvd @ int @ SV765 @ ( plus_plus @ int @ ( plus_plus @ int @ SV521 @ ( times_times @ int @ SV164 @ SV913 ) ) @ SV667 ) )
= $true )
| ( ( dvd_dvd @ int @ SV765 @ SV913 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5191]) ).
thf(5281,plain,
! [SV667: $i,SV913: $i,SV164: $i,SV521: $i,SV765: $i] :
( ( ( dvd_dvd @ int @ SV765 @ ( plus_plus @ int @ ( plus_plus @ int @ SV521 @ ( times_times @ int @ SV164 @ SV913 ) ) @ SV667 ) )
= $false )
| ( ( dvd_dvd @ int @ SV765 @ ( plus_plus @ int @ SV521 @ SV667 ) )
= $true )
| ( ( dvd_dvd @ int @ SV765 @ SV913 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5192]) ).
thf(5282,plain,
! [SV918: $i,SV771: $i,SV1060: $i,SV1013: $i,SV175: $i] :
( ( ( ~ ( ~ ( ( ( ti @ SV175 @ SV1013 )
!= ( ti @ SV175 @ SV1060 ) ) )
| ~ ( ( ( ti @ SV175 @ SV771 )
!= ( ti @ SV175 @ SV918 ) ) ) ) )
= $false )
| ( ( ( plus_plus @ SV175 @ ( times_times @ SV175 @ SV1013 @ SV771 ) @ ( times_times @ SV175 @ SV1060 @ SV918 ) )
!= ( plus_plus @ SV175 @ ( times_times @ SV175 @ SV1013 @ SV918 ) @ ( times_times @ SV175 @ SV1060 @ SV771 ) ) )
= $true )
| ( ( semiri456707255roduct @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5194]) ).
thf(5283,plain,
! [SV918: $i,SV1060: $i,SV771: $i,SV1013: $i,SV175: $i] :
( ( ( ( plus_plus @ SV175 @ ( times_times @ SV175 @ SV1013 @ SV771 ) @ ( times_times @ SV175 @ SV1060 @ SV918 ) )
!= ( plus_plus @ SV175 @ ( times_times @ SV175 @ SV1013 @ SV918 ) @ ( times_times @ SV175 @ SV1060 @ SV771 ) ) )
= $false )
| ( ( ~ ( ~ ( ( ( ti @ SV175 @ SV1013 )
!= ( ti @ SV175 @ SV1060 ) ) )
| ~ ( ( ( ti @ SV175 @ SV771 )
!= ( ti @ SV175 @ SV918 ) ) ) ) )
= $true )
| ( ( semiri456707255roduct @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5195]) ).
thf(5284,plain,
! [SV530: $i,SV187: $i] :
( ( ( ( ti @ int @ SV187 )
= ( ti @ int @ SV530 ) )
= $true )
| ( ( ord_less_eq @ int @ SV187 @ SV530 )
= $false )
| ( ( ord_less @ int @ SV187 @ SV530 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5197]) ).
thf(5285,plain,
! [SV923: $i,SV778: $i,SV193: $i] :
( ( ( ( ti @ SV193 @ SV778 )
!= ( zero_zero @ SV193 ) )
= $false )
| ( ( ( plus_plus @ SV193 @ ( times_times @ SV193 @ SV778 @ SV778 ) @ ( times_times @ SV193 @ SV923 @ SV923 ) )
= ( zero_zero @ SV193 ) )
= $false )
| ( ( linord581940658strict @ SV193 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5198]) ).
thf(5286,plain,
! [SV778: $i,SV923: $i,SV193: $i] :
( ( ( ( ti @ SV193 @ SV923 )
!= ( zero_zero @ SV193 ) )
= $false )
| ( ( ( plus_plus @ SV193 @ ( times_times @ SV193 @ SV778 @ SV778 ) @ ( times_times @ SV193 @ SV923 @ SV923 ) )
= ( zero_zero @ SV193 ) )
= $false )
| ( ( linord581940658strict @ SV193 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5198]) ).
thf(5287,plain,
! [SV923: $i,SV778: $i,SV193: $i] :
( ( ( ( ti @ SV193 @ SV778 )
!= ( zero_zero @ SV193 ) )
= $true )
| ( ( ( ti @ SV193 @ SV923 )
!= ( zero_zero @ SV193 ) )
= $true )
| ( ( ( plus_plus @ SV193 @ ( times_times @ SV193 @ SV778 @ SV778 ) @ ( times_times @ SV193 @ SV923 @ SV923 ) )
= ( zero_zero @ SV193 ) )
= $true )
| ( ( linord581940658strict @ SV193 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5199]) ).
thf(5288,plain,
! [SV924: $i,SV779: $i,SV1017: $i,SV194: $i] :
( ( ( ( power_power @ SV194 @ SV1017 @ SV779 )
!= ( power_power @ SV194 @ SV1017 @ SV924 ) )
= $true )
| ( ( SV779 = SV924 )
= $true )
| ( ( ord_less @ SV194 @ ( one_one @ SV194 ) @ SV1017 )
= $false )
| ( ( linordered_semidom @ SV194 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5200]) ).
thf(5289,plain,
! [SV1017: $i,SV194: $i,SV924: $i,SV779: $i] :
( ( ( SV779 != SV924 )
= $true )
| ( ( ( power_power @ SV194 @ SV1017 @ SV779 )
= ( power_power @ SV194 @ SV1017 @ SV924 ) )
= $true )
| ( ( ord_less @ SV194 @ ( one_one @ SV194 ) @ SV1017 )
= $false )
| ( ( linordered_semidom @ SV194 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5201]) ).
thf(5290,plain,
! [SV672: $i,SV196: $i,SV534: $i] :
( ( ( zcong @ ( times_times @ int @ SV534 @ SV196 ) @ ( zero_zero @ int ) @ SV672 )
= $false )
| ( ( zcong @ SV196 @ ( zero_zero @ int ) @ SV672 )
= $true )
| ( ( zcong @ SV534 @ ( zero_zero @ int ) @ SV672 )
= $true )
| ( ( zprime @ SV672 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5202]) ).
thf(5291,plain,
! [SV928: $i,SV783: $i,SV199: $i] :
( ( ( ~ ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ SV783 )
| ~ ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ SV928 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq @ SV199 @ SV783 @ ( zero_zero @ SV199 ) )
| ~ ( ord_less_eq @ SV199 @ SV928 @ ( zero_zero @ SV199 ) ) ) )
= $true )
| ( ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ ( times_times @ SV199 @ SV783 @ SV928 ) )
= $false )
| ( ( linord581940658strict @ SV199 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5203]) ).
thf(5292,plain,
! [SV928: $i,SV783: $i,SV199: $i] :
( ( ( ~ ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ SV783 )
| ~ ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ SV928 ) )
= $true )
| ( ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ ( times_times @ SV199 @ SV783 @ SV928 ) )
= $true )
| ( ( linord581940658strict @ SV199 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5204]) ).
thf(5293,plain,
! [SV928: $i,SV783: $i,SV199: $i] :
( ( ( ~ ( ord_less_eq @ SV199 @ SV783 @ ( zero_zero @ SV199 ) )
| ~ ( ord_less_eq @ SV199 @ SV928 @ ( zero_zero @ SV199 ) ) )
= $true )
| ( ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ ( times_times @ SV199 @ SV783 @ SV928 ) )
= $true )
| ( ( linord581940658strict @ SV199 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5205]) ).
thf(5294,plain,
! [SV1074: $i,SV202: $i] :
( ( ( ~ ( ord_less_eq @ SV202 @ ( one_one @ SV202 ) @ ( number_number_of @ SV202 @ SV1074 ) ) )
= $true )
| ( ( ord_less_eq @ int @ ( bit1 @ pls ) @ SV1074 )
= $true )
| ( ( number_ring @ SV202 )
= $false )
| ( ( linordered_idom @ SV202 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5206]) ).
thf(5295,plain,
! [SV202: $i,SV1074: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( bit1 @ pls ) @ SV1074 ) )
= $true )
| ( ( ord_less_eq @ SV202 @ ( one_one @ SV202 ) @ ( number_number_of @ SV202 @ SV1074 ) )
= $true )
| ( ( number_ring @ SV202 )
= $false )
| ( ( linordered_idom @ SV202 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5207]) ).
thf(5296,plain,
! [SV535: $i,SV203: $i,SV673: $i] :
( ( ( zcong @ SV673 @ SV203 @ SV535 )
= $false )
| ( ( ord_less @ int @ SV203 @ SV673 )
= $false )
| ( ( ord_less @ int @ ( zero_zero @ int ) @ SV203 )
= $false )
| ( ( ord_less @ int @ SV673 @ SV535 )
= $false )
| ( ( ord_less @ int @ ( zero_zero @ int ) @ SV673 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5208]) ).
thf(5297,plain,
! [SV1086: $i,SV1075: $i,SV213: $i] :
( ( ( ( ( number_number_of @ SV213 @ SV1075 )
!= ( number_number_of @ SV213 @ SV1086 ) )
| ( ( ti @ int @ SV1075 )
= ( ti @ int @ SV1086 ) ) )
= $true )
| ( ( number_ring @ SV213 )
= $false )
| ( ( ring_char_0 @ SV213 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5209]) ).
thf(5298,plain,
! [SV213: $i,SV1086: $i,SV1075: $i] :
( ( ( ( ( ti @ int @ SV1075 )
!= ( ti @ int @ SV1086 ) )
| ( ( number_number_of @ SV213 @ SV1075 )
= ( number_number_of @ SV213 @ SV1086 ) ) )
= $true )
| ( ( number_ring @ SV213 )
= $false )
| ( ( ring_char_0 @ SV213 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5210]) ).
thf(5299,plain,
! [SV1087: $i,SV1076: $i,SV218: $i] :
( ( ( ~ ( ord_less @ SV218 @ ( number_number_of @ SV218 @ SV1076 ) @ ( number_number_of @ SV218 @ SV1087 ) )
| ( ord_less @ int @ SV1076 @ SV1087 ) )
= $true )
| ( ( number_ring @ SV218 )
= $false )
| ( ( linordered_idom @ SV218 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5212]) ).
thf(5300,plain,
! [SV218: $i,SV1087: $i,SV1076: $i] :
( ( ( ~ ( ord_less @ int @ SV1076 @ SV1087 )
| ( ord_less @ SV218 @ ( number_number_of @ SV218 @ SV1076 ) @ ( number_number_of @ SV218 @ SV1087 ) ) )
= $true )
| ( ( number_ring @ SV218 )
= $false )
| ( ( linordered_idom @ SV218 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5213]) ).
thf(5301,plain,
! [SV1062: $i,SV1024: $i,SV942: $i,SV804: $i,SV255: $i] :
( ( ( ( plus_plus @ SV255 @ ( times_times @ SV255 @ SV804 @ SV942 ) @ ( times_times @ SV255 @ SV1024 @ SV1062 ) )
= ( plus_plus @ SV255 @ ( times_times @ SV255 @ SV804 @ SV1062 ) @ ( times_times @ SV255 @ SV1024 @ SV942 ) ) )
= $false )
| ( ( ( ( ti @ SV255 @ SV804 )
= ( ti @ SV255 @ SV1024 ) )
| ( ( ti @ SV255 @ SV942 )
= ( ti @ SV255 @ SV1062 ) ) )
= $true )
| ( ( semiri456707255roduct @ SV255 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5216]) ).
thf(5302,plain,
! [SV1062: $i,SV942: $i,SV1024: $i,SV804: $i,SV255: $i] :
( ( ( ( ( ti @ SV255 @ SV804 )
= ( ti @ SV255 @ SV1024 ) )
| ( ( ti @ SV255 @ SV942 )
= ( ti @ SV255 @ SV1062 ) ) )
= $false )
| ( ( ( plus_plus @ SV255 @ ( times_times @ SV255 @ SV804 @ SV942 ) @ ( times_times @ SV255 @ SV1024 @ SV1062 ) )
= ( plus_plus @ SV255 @ ( times_times @ SV255 @ SV804 @ SV1062 ) @ ( times_times @ SV255 @ SV1024 @ SV942 ) ) )
= $true )
| ( ( semiri456707255roduct @ SV255 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5217]) ).
thf(5303,plain,
! [SV805: $i,SV943: $i,SV688: $i,SV557: $i,SV257: $i] :
( ( ( zcong @ SV257 @ ( times_times @ int @ SV557 @ SV688 ) @ SV943 )
= $false )
| ( ( zcong @ SV257 @ ( times_times @ int @ SV557 @ SV805 ) @ SV943 )
= $true )
| ( ( zcong @ SV688 @ SV805 @ SV943 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5218]) ).
thf(5304,plain,
! [SV688: $i,SV943: $i,SV805: $i,SV557: $i,SV257: $i] :
( ( ( zcong @ SV257 @ ( times_times @ int @ SV557 @ SV805 ) @ SV943 )
= $false )
| ( ( zcong @ SV257 @ ( times_times @ int @ SV557 @ SV688 ) @ SV943 )
= $true )
| ( ( zcong @ SV688 @ SV805 @ SV943 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5219]) ).
thf(5305,plain,
! [SV573: $i,SV957: $i,SV829: $i,SV1032: $i,SV305: $i,SV698: $i] :
( ( ( ord_less @ int @ SV698 @ SV305 )
= $false )
| ( ( ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV1032 )
| ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV829 )
| ~ ( ord_less_eq @ int @ SV829 @ SV305 )
| ( ord_less_eq @ int @ SV957 @ SV573 ) )
= $true )
| ( ( ord_less @ int @ ( plus_plus @ int @ ( times_times @ int @ SV829 @ SV957 ) @ SV1032 ) @ ( zero_zero @ int ) )
= $false )
| ( ( ( plus_plus @ int @ ( times_times @ int @ SV305 @ SV573 ) @ SV698 )
= ( plus_plus @ int @ ( times_times @ int @ SV829 @ SV957 ) @ SV1032 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5226]) ).
thf(5306,plain,
! [SV701: $i,SV833: $i,SV576: $i,SV312: $i,SV960: $i] :
( ( ( ~ ( ord_less @ int @ SV960 @ SV312 ) )
= $true )
| ( ( ord_less_eq @ int @ SV576 @ SV833 )
= $true )
| ( ( ord_less @ int @ SV701 @ SV312 )
= $false )
| ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV701 )
= $false )
| ( ( ord_less_eq @ int @ ( plus_plus @ int @ ( times_times @ int @ SV312 @ SV576 ) @ SV701 ) @ ( plus_plus @ int @ ( times_times @ int @ SV312 @ SV833 ) @ SV960 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5227]) ).
thf(5307,plain,
! [SV966: $i,SV839: $i,SV319: $i] :
( ( ( ~ ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SV839 )
| ~ ( ord_less_eq @ SV319 @ SV966 @ ( zero_zero @ SV319 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq @ SV319 @ SV839 @ ( zero_zero @ SV319 ) )
| ~ ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SV966 ) ) )
= $true )
| ( ( ord_less_eq @ SV319 @ ( times_times @ SV319 @ SV839 @ SV966 ) @ ( zero_zero @ SV319 ) )
= $false )
| ( ( linord581940658strict @ SV319 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5228]) ).
thf(5308,plain,
! [SV966: $i,SV839: $i,SV319: $i] :
( ( ( ~ ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SV839 )
| ~ ( ord_less_eq @ SV319 @ SV966 @ ( zero_zero @ SV319 ) ) )
= $true )
| ( ( ord_less_eq @ SV319 @ ( times_times @ SV319 @ SV839 @ SV966 ) @ ( zero_zero @ SV319 ) )
= $true )
| ( ( linord581940658strict @ SV319 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5229]) ).
thf(5309,plain,
! [SV966: $i,SV839: $i,SV319: $i] :
( ( ( ~ ( ord_less_eq @ SV319 @ SV839 @ ( zero_zero @ SV319 ) )
| ~ ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SV966 ) )
= $true )
| ( ( ord_less_eq @ SV319 @ ( times_times @ SV319 @ SV839 @ SV966 ) @ ( zero_zero @ SV319 ) )
= $true )
| ( ( linord581940658strict @ SV319 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5230]) ).
thf(5310,plain,
! [SV1090: $i,SV1078: $i,SV321: $i] :
( ( ( ~ ( ord_less_eq @ SV321 @ ( number_number_of @ SV321 @ SV1078 ) @ ( number_number_of @ SV321 @ SV1090 ) )
| ( ord_less_eq @ int @ SV1078 @ SV1090 ) )
= $true )
| ( ( number_ring @ SV321 )
= $false )
| ( ( linordered_idom @ SV321 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5231]) ).
thf(5311,plain,
! [SV321: $i,SV1090: $i,SV1078: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV1078 @ SV1090 )
| ( ord_less_eq @ SV321 @ ( number_number_of @ SV321 @ SV1078 ) @ ( number_number_of @ SV321 @ SV1090 ) ) )
= $true )
| ( ( number_ring @ SV321 )
= $false )
| ( ( linordered_idom @ SV321 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5232]) ).
thf(5312,plain,
! [SV333: $i,SV1079: $i] :
( ( ( ( number_number_of @ nat @ SV1079 )
!= ( zero_zero @ nat ) )
= $true )
| ( ( ( power_power @ SV333 @ ( zero_zero @ SV333 ) @ ( number_number_of @ nat @ SV1079 ) )
= ( one_one @ SV333 ) )
= $true )
| ( ( power @ SV333 )
= $false )
| ( ( semiring_0 @ SV333 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5234]) ).
thf(5313,plain,
! [SV333: $i,SV1079: $i] :
( ( ( ~ ( ( ( number_number_of @ nat @ SV1079 )
!= ( zero_zero @ nat ) ) ) )
= $true )
| ( ( ( power_power @ SV333 @ ( zero_zero @ SV333 ) @ ( number_number_of @ nat @ SV1079 ) )
= ( zero_zero @ SV333 ) )
= $true )
| ( ( power @ SV333 )
= $false )
| ( ( semiring_0 @ SV333 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5235]) ).
thf(5314,plain,
! [SV977: $i,SV855: $i,SV352: $i] :
( ( ( ( ti @ SV352 @ SV855 )
!= ( zero_zero @ SV352 ) )
= $false )
| ( ( ( plus_plus @ SV352 @ ( power_power @ SV352 @ SV855 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV352 @ SV977 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV352 ) )
= $false )
| ( ( linordered_idom @ SV352 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5236]) ).
thf(5315,plain,
! [SV855: $i,SV977: $i,SV352: $i] :
( ( ( ( ti @ SV352 @ SV977 )
!= ( zero_zero @ SV352 ) )
= $false )
| ( ( ( plus_plus @ SV352 @ ( power_power @ SV352 @ SV855 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV352 @ SV977 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV352 ) )
= $false )
| ( ( linordered_idom @ SV352 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5236]) ).
thf(5316,plain,
! [SV977: $i,SV855: $i,SV352: $i] :
( ( ( ( ti @ SV352 @ SV855 )
!= ( zero_zero @ SV352 ) )
= $true )
| ( ( ( ti @ SV352 @ SV977 )
!= ( zero_zero @ SV352 ) )
= $true )
| ( ( ( plus_plus @ SV352 @ ( power_power @ SV352 @ SV855 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV352 @ SV977 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV352 ) )
= $true )
| ( ( linordered_idom @ SV352 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5237]) ).
thf(5317,plain,
! [SV355: $i,SV1080: $i] :
( ( ( SV1080
!= ( zero_zero @ nat ) )
= $true )
| ( ( ( power_power @ SV355 @ ( zero_zero @ SV355 ) @ SV1080 )
= ( one_one @ SV355 ) )
= $true )
| ( ( power @ SV355 )
= $false )
| ( ( semiring_0 @ SV355 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5238]) ).
thf(5318,plain,
! [SV355: $i,SV1080: $i] :
( ( ( ~ ( ( SV1080
!= ( zero_zero @ nat ) ) ) )
= $true )
| ( ( ( power_power @ SV355 @ ( zero_zero @ SV355 ) @ SV1080 )
= ( zero_zero @ SV355 ) )
= $true )
| ( ( power @ SV355 )
= $false )
| ( ( semiring_0 @ SV355 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5239]) ).
thf(5319,plain,
! [SV980: $i,SV858: $i,SV1044: $i,SV358: $i] :
( ( ( ~ ( ord_less_eq @ SV358 @ ( power_power @ SV358 @ SV1044 @ SV858 ) @ ( power_power @ SV358 @ SV1044 @ SV980 ) ) )
= $true )
| ( ( ord_less_eq @ nat @ SV858 @ SV980 )
= $true )
| ( ( ord_less @ SV358 @ ( one_one @ SV358 ) @ SV1044 )
= $false )
| ( ( linordered_semidom @ SV358 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5240]) ).
thf(5320,plain,
! [SV1044: $i,SV358: $i,SV980: $i,SV858: $i] :
( ( ( ~ ( ord_less_eq @ nat @ SV858 @ SV980 ) )
= $true )
| ( ( ord_less_eq @ SV358 @ ( power_power @ SV358 @ SV1044 @ SV858 ) @ ( power_power @ SV358 @ SV1044 @ SV980 ) )
= $true )
| ( ( ord_less @ SV358 @ ( one_one @ SV358 ) @ SV1044 )
= $false )
| ( ( linordered_semidom @ SV358 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5241]) ).
thf(5321,plain,
! [SV595: $i,SV366: $i] :
( ( ( ~ ( ord_less @ int @ SV366 @ pls ) )
= $true )
| ( ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV595 ) @ ( number_number_of @ nat @ SV366 ) )
= ( number_number_of @ nat @ SV595 ) )
= $true )
| ( ( ord_less @ int @ SV595 @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5245]) ).
thf(5322,plain,
! [SV595: $i,SV366: $i] :
( ( ( ~ ~ ( ord_less @ int @ SV366 @ pls ) )
= $true )
| ( ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV595 ) @ ( number_number_of @ nat @ SV366 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SV595 @ SV366 ) ) )
= $true )
| ( ( ord_less @ int @ SV595 @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5246]) ).
thf(5323,plain,
! [SV612: $i,SV392: $i] :
( ( ( ord_less @ int @ SV392 @ SV612 )
= $false )
| ( ( ord_less @ int @ pls @ SV612 )
= $true )
| ( ( ord_less @ nat @ ( number_number_of @ nat @ SV392 ) @ ( number_number_of @ nat @ SV612 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5248]) ).
thf(5324,plain,
! [SV612: $i,SV392: $i] :
( ( ( ord_less @ int @ SV392 @ SV612 )
= $true )
| ( ( ~ ( ord_less @ int @ SV392 @ SV612 ) )
= $true )
| ( ( ord_less @ nat @ ( number_number_of @ nat @ SV392 ) @ ( number_number_of @ nat @ SV612 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5249]) ).
thf(5325,plain,
! [SV612: $i,SV392: $i] :
( ( ( ord_less @ int @ SV392 @ SV612 )
= $false )
| ( ( ord_less @ int @ pls @ SV612 )
= $false )
| ( ( ord_less @ nat @ ( number_number_of @ nat @ SV392 ) @ ( number_number_of @ nat @ SV612 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5250]) ).
thf(5326,plain,
! [SV621: $i,SV413: $i] :
( ( ( ( ( ti @ int @ SV413 )
!= ( number_number_of @ int @ min ) )
| ( ( ti @ int @ SV621 )
!= ( number_number_of @ int @ min ) ) )
= $false )
| ( ( ( ti @ int @ SV413 )
= ( one_one @ int ) )
= $true )
| ( ( ( times_times @ int @ SV413 @ SV621 )
= ( one_one @ int ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5254]) ).
thf(5327,plain,
! [SV621: $i,SV413: $i] :
( ( ( ( ( ti @ int @ SV413 )
!= ( number_number_of @ int @ min ) )
| ( ( ti @ int @ SV621 )
!= ( number_number_of @ int @ min ) ) )
= $false )
| ( ( ( ti @ int @ SV621 )
= ( one_one @ int ) )
= $true )
| ( ( ( times_times @ int @ SV413 @ SV621 )
= ( one_one @ int ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5255]) ).
thf(5328,plain,
! [SV413: $i,SV621: $i] :
( ( ( ( ti @ int @ SV621 )
= ( one_one @ int ) )
= $false )
| ( ( ( ti @ int @ SV413 )
= ( one_one @ int ) )
= $false )
| ( ( ( times_times @ int @ SV413 @ SV621 )
= ( one_one @ int ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5256]) ).
thf(5329,plain,
! [SV413: $i,SV621: $i] :
( ( ( ( ti @ int @ SV621 )
= ( number_number_of @ int @ min ) )
= $false )
| ( ( ( ti @ int @ SV413 )
= ( number_number_of @ int @ min ) )
= $false )
| ( ( ( times_times @ int @ SV413 @ SV621 )
= ( one_one @ int ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5257]) ).
thf(5330,plain,
! [SV419: $i,SV623: $i] :
( ( ( ( ti @ int @ SV623 )
= ( one_one @ int ) )
= $true )
| ( ( ( times_times @ int @ SV623 @ SV419 )
= ( one_one @ int ) )
= $false )
| ( ( ord_less @ int @ ( zero_zero @ int ) @ SV623 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5258]) ).
thf(5331,plain,
! [SV623: $i,SV419: $i] :
( ( ( ( ti @ int @ SV419 )
= ( one_one @ int ) )
= $true )
| ( ( ( times_times @ int @ SV623 @ SV419 )
= ( one_one @ int ) )
= $false )
| ( ( ord_less @ int @ ( zero_zero @ int ) @ SV623 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5259]) ).
thf(5332,plain,
! [SV419: $i,SV623: $i] :
( ( ( ( ti @ int @ SV623 )
= ( one_one @ int ) )
= $false )
| ( ( ( ti @ int @ SV419 )
!= ( one_one @ int ) )
= $true )
| ( ( ( times_times @ int @ SV623 @ SV419 )
= ( one_one @ int ) )
= $true )
| ( ( ord_less @ int @ ( zero_zero @ int ) @ SV623 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5260]) ).
thf(5333,plain,
! [SV995: $i,SV626: $i,SV422: $i,SV726: $i,SV882: $i,SV1052: $i] :
( ( ( ord_less @ int @ SV1052 @ SV882 )
= $false )
| ( ( ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV726 )
| ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV882 )
| ~ ( ord_less_eq @ int @ SV882 @ SV422 )
| ( ord_less_eq @ int @ SV626 @ SV995 ) )
= $true )
| ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( times_times @ int @ SV882 @ SV995 ) @ SV1052 ) )
= $false )
| ( ( ( plus_plus @ int @ ( times_times @ int @ SV422 @ SV626 ) @ SV726 )
= ( plus_plus @ int @ ( times_times @ int @ SV882 @ SV995 ) @ SV1052 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5261]) ).
thf(5334,plain,
! [SV997: $i,SV1053: $i,SV887: $i,SV433: $i] :
( ( ( ord_less @ SV433 @ SV887 @ ( one_one @ SV433 ) )
= $false )
| ( ( ord_less @ SV433 @ ( power_power @ SV433 @ SV887 @ SV1053 ) @ ( power_power @ SV433 @ SV887 @ SV997 ) )
= $true )
| ( ( ord_less @ SV433 @ ( zero_zero @ SV433 ) @ SV887 )
= $false )
| ( ( ord_less @ nat @ SV997 @ SV1053 )
= $false )
| ( ( linordered_semidom @ SV433 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5262]) ).
thf(5335,plain,
! [SV1083: $i,SV998: $i,SV888: $i,SV1068: $i,SV1054: $i,SV434: $i] :
( ( ( ~ ~ ( ( ( ti @ SV434 @ SV1054 )
!= ( ti @ SV434 @ SV1068 ) )
| ~ ( ( ( ti @ SV434 @ SV888 )
!= ( ti @ SV434 @ SV998 ) ) ) ) )
= $true )
| ( ( ( plus_plus @ SV434 @ SV1054 @ ( times_times @ SV434 @ SV1083 @ SV888 ) )
!= ( plus_plus @ SV434 @ SV1068 @ ( times_times @ SV434 @ SV1083 @ SV998 ) ) )
= $true )
| ( ( ( ti @ SV434 @ SV1083 )
= ( zero_zero @ SV434 ) )
= $true )
| ( ( semiri456707255roduct @ SV434 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5263]) ).
thf(5336,plain,
! [SV1069: $i,SV120: $i] :
( ( ( ord_less @ SV120 @ ( one_one @ SV120 ) @ ( number_number_of @ SV120 @ SV1069 ) )
= $false )
| ( ( ord_less @ int @ ( bit1 @ pls ) @ SV1069 )
= $true )
| ( ( number_ring @ SV120 )
= $false )
| ( ( linordered_idom @ SV120 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5268]) ).
thf(5337,plain,
! [SV120: $i,SV1069: $i] :
( ( ( ord_less @ int @ ( bit1 @ pls ) @ SV1069 )
= $false )
| ( ( ord_less @ SV120 @ ( one_one @ SV120 ) @ ( number_number_of @ SV120 @ SV1069 ) )
= $true )
| ( ( number_ring @ SV120 )
= $false )
| ( ( linordered_idom @ SV120 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5269]) ).
thf(5338,plain,
! [SV1070: $i,SV123: $i] :
( ( ( ord_less_eq @ SV123 @ ( number_number_of @ SV123 @ SV1070 ) @ ( one_one @ SV123 ) )
= $false )
| ( ( ord_less_eq @ int @ SV1070 @ ( bit1 @ pls ) )
= $true )
| ( ( number_ring @ SV123 )
= $false )
| ( ( linordered_idom @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5270]) ).
thf(5339,plain,
! [SV123: $i,SV1070: $i] :
( ( ( ord_less_eq @ int @ SV1070 @ ( bit1 @ pls ) )
= $false )
| ( ( ord_less_eq @ SV123 @ ( number_number_of @ SV123 @ SV1070 ) @ ( one_one @ SV123 ) )
= $true )
| ( ( number_ring @ SV123 )
= $false )
| ( ( linordered_idom @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5271]) ).
thf(5340,plain,
! [SV907: $i,SV503: $i,SV753: $i,SV660: $i,SV132: $i] :
( ( ( ord_less @ int @ SV132 @ SV660 )
= $false )
| ( ( ord_less_eq @ int @ SV753 @ SV503 )
= $true )
| ( ( ord_less @ int @ SV132 @ SV907 )
= $false )
| ( ( ord_less_eq @ int @ SV907 @ ( zero_zero @ int ) )
= $false )
| ( ( ord_less_eq @ int @ ( plus_plus @ int @ ( times_times @ int @ SV132 @ SV503 ) @ SV660 ) @ ( plus_plus @ int @ ( times_times @ int @ SV132 @ SV753 ) @ SV907 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5272]) ).
thf(5341,plain,
! [SV1071: $i,SV134: $i] :
( ( ( ord_less @ SV134 @ ( number_number_of @ SV134 @ SV1071 ) @ ( one_one @ SV134 ) )
= $false )
| ( ( ord_less @ int @ SV1071 @ ( bit1 @ pls ) )
= $true )
| ( ( number_ring @ SV134 )
= $false )
| ( ( linordered_idom @ SV134 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5273]) ).
thf(5342,plain,
! [SV134: $i,SV1071: $i] :
( ( ( ord_less @ int @ SV1071 @ ( bit1 @ pls ) )
= $false )
| ( ( ord_less @ SV134 @ ( number_number_of @ SV134 @ SV1071 ) @ ( one_one @ SV134 ) )
= $true )
| ( ( number_ring @ SV134 )
= $false )
| ( ( linordered_idom @ SV134 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5274]) ).
thf(5343,plain,
! [SV911: $i,SV762: $i,SV1010: $i,SV155: $i] :
( ( ( ord_less @ SV155 @ ( power_power @ SV155 @ SV1010 @ SV762 ) @ ( power_power @ SV155 @ SV1010 @ SV911 ) )
= $false )
| ( ( ord_less @ nat @ SV762 @ SV911 )
= $true )
| ( ( ord_less @ SV155 @ ( one_one @ SV155 ) @ SV1010 )
= $false )
| ( ( linordered_semidom @ SV155 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5278]) ).
thf(5344,plain,
! [SV1010: $i,SV155: $i,SV911: $i,SV762: $i] :
( ( ( ord_less @ nat @ SV762 @ SV911 )
= $false )
| ( ( ord_less @ SV155 @ ( power_power @ SV155 @ SV1010 @ SV762 ) @ ( power_power @ SV155 @ SV1010 @ SV911 ) )
= $true )
| ( ( ord_less @ SV155 @ ( one_one @ SV155 ) @ SV1010 )
= $false )
| ( ( linordered_semidom @ SV155 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5279]) ).
thf(5345,plain,
! [SV918: $i,SV771: $i,SV1060: $i,SV1013: $i,SV175: $i] :
( ( ( ~ ( ( ( ti @ SV175 @ SV1013 )
!= ( ti @ SV175 @ SV1060 ) ) )
| ~ ( ( ( ti @ SV175 @ SV771 )
!= ( ti @ SV175 @ SV918 ) ) ) )
= $true )
| ( ( ( plus_plus @ SV175 @ ( times_times @ SV175 @ SV1013 @ SV771 ) @ ( times_times @ SV175 @ SV1060 @ SV918 ) )
!= ( plus_plus @ SV175 @ ( times_times @ SV175 @ SV1013 @ SV918 ) @ ( times_times @ SV175 @ SV1060 @ SV771 ) ) )
= $true )
| ( ( semiri456707255roduct @ SV175 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5282]) ).
thf(5346,plain,
! [SV918: $i,SV1060: $i,SV771: $i,SV1013: $i,SV175: $i] :
( ( ( ( plus_plus @ SV175 @ ( times_times @ SV175 @ SV1013 @ SV771 ) @ ( times_times @ SV175 @ SV1060 @ SV918 ) )
= ( plus_plus @ SV175 @ ( times_times @ SV175 @ SV1013 @ SV918 ) @ ( times_times @ SV175 @ SV1060 @ SV771 ) ) )
= $true )
| ( ( ~ ( ~ ( ( ( ti @ SV175 @ SV1013 )
!= ( ti @ SV175 @ SV1060 ) ) )
| ~ ( ( ( ti @ SV175 @ SV771 )
!= ( ti @ SV175 @ SV918 ) ) ) ) )
= $true )
| ( ( semiri456707255roduct @ SV175 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5283]) ).
thf(5347,plain,
! [SV923: $i,SV778: $i,SV193: $i] :
( ( ( ( ti @ SV193 @ SV778 )
= ( zero_zero @ SV193 ) )
= $true )
| ( ( ( plus_plus @ SV193 @ ( times_times @ SV193 @ SV778 @ SV778 ) @ ( times_times @ SV193 @ SV923 @ SV923 ) )
= ( zero_zero @ SV193 ) )
= $false )
| ( ( linord581940658strict @ SV193 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5285]) ).
thf(5348,plain,
! [SV778: $i,SV923: $i,SV193: $i] :
( ( ( ( ti @ SV193 @ SV923 )
= ( zero_zero @ SV193 ) )
= $true )
| ( ( ( plus_plus @ SV193 @ ( times_times @ SV193 @ SV778 @ SV778 ) @ ( times_times @ SV193 @ SV923 @ SV923 ) )
= ( zero_zero @ SV193 ) )
= $false )
| ( ( linord581940658strict @ SV193 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5286]) ).
thf(5349,plain,
! [SV923: $i,SV778: $i,SV193: $i] :
( ( ( ( ti @ SV193 @ SV778 )
= ( zero_zero @ SV193 ) )
= $false )
| ( ( ( ti @ SV193 @ SV923 )
!= ( zero_zero @ SV193 ) )
= $true )
| ( ( ( plus_plus @ SV193 @ ( times_times @ SV193 @ SV778 @ SV778 ) @ ( times_times @ SV193 @ SV923 @ SV923 ) )
= ( zero_zero @ SV193 ) )
= $true )
| ( ( linord581940658strict @ SV193 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5287]) ).
thf(5350,plain,
! [SV924: $i,SV779: $i,SV1017: $i,SV194: $i] :
( ( ( ( power_power @ SV194 @ SV1017 @ SV779 )
= ( power_power @ SV194 @ SV1017 @ SV924 ) )
= $false )
| ( ( SV779 = SV924 )
= $true )
| ( ( ord_less @ SV194 @ ( one_one @ SV194 ) @ SV1017 )
= $false )
| ( ( linordered_semidom @ SV194 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5288]) ).
thf(5351,plain,
! [SV1017: $i,SV194: $i,SV924: $i,SV779: $i] :
( ( ( SV779 = SV924 )
= $false )
| ( ( ( power_power @ SV194 @ SV1017 @ SV779 )
= ( power_power @ SV194 @ SV1017 @ SV924 ) )
= $true )
| ( ( ord_less @ SV194 @ ( one_one @ SV194 ) @ SV1017 )
= $false )
| ( ( linordered_semidom @ SV194 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5289]) ).
thf(5352,plain,
! [SV928: $i,SV783: $i,SV199: $i] :
( ( ( ~ ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ SV783 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq @ SV199 @ SV783 @ ( zero_zero @ SV199 ) )
| ~ ( ord_less_eq @ SV199 @ SV928 @ ( zero_zero @ SV199 ) ) ) )
= $true )
| ( ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ ( times_times @ SV199 @ SV783 @ SV928 ) )
= $false )
| ( ( linord581940658strict @ SV199 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5291]) ).
thf(5353,plain,
! [SV783: $i,SV928: $i,SV199: $i] :
( ( ( ~ ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ SV928 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq @ SV199 @ SV783 @ ( zero_zero @ SV199 ) )
| ~ ( ord_less_eq @ SV199 @ SV928 @ ( zero_zero @ SV199 ) ) ) )
= $true )
| ( ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ ( times_times @ SV199 @ SV783 @ SV928 ) )
= $false )
| ( ( linord581940658strict @ SV199 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5291]) ).
thf(5354,plain,
! [SV928: $i,SV783: $i,SV199: $i] :
( ( ( ~ ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ SV783 ) )
= $true )
| ( ( ~ ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ SV928 ) )
= $true )
| ( ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ ( times_times @ SV199 @ SV783 @ SV928 ) )
= $true )
| ( ( linord581940658strict @ SV199 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5292]) ).
thf(5355,plain,
! [SV928: $i,SV783: $i,SV199: $i] :
( ( ( ~ ( ord_less_eq @ SV199 @ SV783 @ ( zero_zero @ SV199 ) ) )
= $true )
| ( ( ~ ( ord_less_eq @ SV199 @ SV928 @ ( zero_zero @ SV199 ) ) )
= $true )
| ( ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ ( times_times @ SV199 @ SV783 @ SV928 ) )
= $true )
| ( ( linord581940658strict @ SV199 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5293]) ).
thf(5356,plain,
! [SV1074: $i,SV202: $i] :
( ( ( ord_less_eq @ SV202 @ ( one_one @ SV202 ) @ ( number_number_of @ SV202 @ SV1074 ) )
= $false )
| ( ( ord_less_eq @ int @ ( bit1 @ pls ) @ SV1074 )
= $true )
| ( ( number_ring @ SV202 )
= $false )
| ( ( linordered_idom @ SV202 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5294]) ).
thf(5357,plain,
! [SV202: $i,SV1074: $i] :
( ( ( ord_less_eq @ int @ ( bit1 @ pls ) @ SV1074 )
= $false )
| ( ( ord_less_eq @ SV202 @ ( one_one @ SV202 ) @ ( number_number_of @ SV202 @ SV1074 ) )
= $true )
| ( ( number_ring @ SV202 )
= $false )
| ( ( linordered_idom @ SV202 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5295]) ).
thf(5358,plain,
! [SV1086: $i,SV1075: $i,SV213: $i] :
( ( ( ( number_number_of @ SV213 @ SV1075 )
!= ( number_number_of @ SV213 @ SV1086 ) )
= $true )
| ( ( ( ti @ int @ SV1075 )
= ( ti @ int @ SV1086 ) )
= $true )
| ( ( number_ring @ SV213 )
= $false )
| ( ( ring_char_0 @ SV213 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5297]) ).
thf(5359,plain,
! [SV213: $i,SV1086: $i,SV1075: $i] :
( ( ( ( ti @ int @ SV1075 )
!= ( ti @ int @ SV1086 ) )
= $true )
| ( ( ( number_number_of @ SV213 @ SV1075 )
= ( number_number_of @ SV213 @ SV1086 ) )
= $true )
| ( ( number_ring @ SV213 )
= $false )
| ( ( ring_char_0 @ SV213 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5298]) ).
thf(5360,plain,
! [SV1087: $i,SV1076: $i,SV218: $i] :
( ( ( ~ ( ord_less @ SV218 @ ( number_number_of @ SV218 @ SV1076 ) @ ( number_number_of @ SV218 @ SV1087 ) ) )
= $true )
| ( ( ord_less @ int @ SV1076 @ SV1087 )
= $true )
| ( ( number_ring @ SV218 )
= $false )
| ( ( linordered_idom @ SV218 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5299]) ).
thf(5361,plain,
! [SV218: $i,SV1087: $i,SV1076: $i] :
( ( ( ~ ( ord_less @ int @ SV1076 @ SV1087 ) )
= $true )
| ( ( ord_less @ SV218 @ ( number_number_of @ SV218 @ SV1076 ) @ ( number_number_of @ SV218 @ SV1087 ) )
= $true )
| ( ( number_ring @ SV218 )
= $false )
| ( ( linordered_idom @ SV218 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5300]) ).
thf(5362,plain,
! [SV1062: $i,SV942: $i,SV1024: $i,SV804: $i,SV255: $i] :
( ( ( ( ti @ SV255 @ SV804 )
= ( ti @ SV255 @ SV1024 ) )
= $true )
| ( ( ( ti @ SV255 @ SV942 )
= ( ti @ SV255 @ SV1062 ) )
= $true )
| ( ( ( plus_plus @ SV255 @ ( times_times @ SV255 @ SV804 @ SV942 ) @ ( times_times @ SV255 @ SV1024 @ SV1062 ) )
= ( plus_plus @ SV255 @ ( times_times @ SV255 @ SV804 @ SV1062 ) @ ( times_times @ SV255 @ SV1024 @ SV942 ) ) )
= $false )
| ( ( semiri456707255roduct @ SV255 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5301]) ).
thf(5363,plain,
! [SV1062: $i,SV942: $i,SV1024: $i,SV804: $i,SV255: $i] :
( ( ( ( ti @ SV255 @ SV804 )
= ( ti @ SV255 @ SV1024 ) )
= $false )
| ( ( ( plus_plus @ SV255 @ ( times_times @ SV255 @ SV804 @ SV942 ) @ ( times_times @ SV255 @ SV1024 @ SV1062 ) )
= ( plus_plus @ SV255 @ ( times_times @ SV255 @ SV804 @ SV1062 ) @ ( times_times @ SV255 @ SV1024 @ SV942 ) ) )
= $true )
| ( ( semiri456707255roduct @ SV255 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5302]) ).
thf(5364,plain,
! [SV1024: $i,SV804: $i,SV1062: $i,SV942: $i,SV255: $i] :
( ( ( ( ti @ SV255 @ SV942 )
= ( ti @ SV255 @ SV1062 ) )
= $false )
| ( ( ( plus_plus @ SV255 @ ( times_times @ SV255 @ SV804 @ SV942 ) @ ( times_times @ SV255 @ SV1024 @ SV1062 ) )
= ( plus_plus @ SV255 @ ( times_times @ SV255 @ SV804 @ SV1062 ) @ ( times_times @ SV255 @ SV1024 @ SV942 ) ) )
= $true )
| ( ( semiri456707255roduct @ SV255 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5302]) ).
thf(5365,plain,
! [SV698: $i,SV573: $i,SV957: $i,SV305: $i,SV829: $i,SV1032: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV1032 ) )
= $true )
| ( ( ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV829 )
| ~ ( ord_less_eq @ int @ SV829 @ SV305 )
| ( ord_less_eq @ int @ SV957 @ SV573 ) )
= $true )
| ( ( ord_less @ int @ SV698 @ SV305 )
= $false )
| ( ( ord_less @ int @ ( plus_plus @ int @ ( times_times @ int @ SV829 @ SV957 ) @ SV1032 ) @ ( zero_zero @ int ) )
= $false )
| ( ( ( plus_plus @ int @ ( times_times @ int @ SV305 @ SV573 ) @ SV698 )
= ( plus_plus @ int @ ( times_times @ int @ SV829 @ SV957 ) @ SV1032 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5305]) ).
thf(5366,plain,
! [SV701: $i,SV833: $i,SV576: $i,SV312: $i,SV960: $i] :
( ( ( ord_less @ int @ SV960 @ SV312 )
= $false )
| ( ( ord_less_eq @ int @ SV576 @ SV833 )
= $true )
| ( ( ord_less @ int @ SV701 @ SV312 )
= $false )
| ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV701 )
= $false )
| ( ( ord_less_eq @ int @ ( plus_plus @ int @ ( times_times @ int @ SV312 @ SV576 ) @ SV701 ) @ ( plus_plus @ int @ ( times_times @ int @ SV312 @ SV833 ) @ SV960 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5306]) ).
thf(5367,plain,
! [SV966: $i,SV839: $i,SV319: $i] :
( ( ( ~ ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SV839 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq @ SV319 @ SV839 @ ( zero_zero @ SV319 ) )
| ~ ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SV966 ) ) )
= $true )
| ( ( ord_less_eq @ SV319 @ ( times_times @ SV319 @ SV839 @ SV966 ) @ ( zero_zero @ SV319 ) )
= $false )
| ( ( linord581940658strict @ SV319 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5307]) ).
thf(5368,plain,
! [SV839: $i,SV966: $i,SV319: $i] :
( ( ( ~ ( ord_less_eq @ SV319 @ SV966 @ ( zero_zero @ SV319 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq @ SV319 @ SV839 @ ( zero_zero @ SV319 ) )
| ~ ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SV966 ) ) )
= $true )
| ( ( ord_less_eq @ SV319 @ ( times_times @ SV319 @ SV839 @ SV966 ) @ ( zero_zero @ SV319 ) )
= $false )
| ( ( linord581940658strict @ SV319 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5307]) ).
thf(5369,plain,
! [SV966: $i,SV839: $i,SV319: $i] :
( ( ( ~ ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SV839 ) )
= $true )
| ( ( ~ ( ord_less_eq @ SV319 @ SV966 @ ( zero_zero @ SV319 ) ) )
= $true )
| ( ( ord_less_eq @ SV319 @ ( times_times @ SV319 @ SV839 @ SV966 ) @ ( zero_zero @ SV319 ) )
= $true )
| ( ( linord581940658strict @ SV319 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5308]) ).
thf(5370,plain,
! [SV966: $i,SV839: $i,SV319: $i] :
( ( ( ~ ( ord_less_eq @ SV319 @ SV839 @ ( zero_zero @ SV319 ) ) )
= $true )
| ( ( ~ ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SV966 ) )
= $true )
| ( ( ord_less_eq @ SV319 @ ( times_times @ SV319 @ SV839 @ SV966 ) @ ( zero_zero @ SV319 ) )
= $true )
| ( ( linord581940658strict @ SV319 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5309]) ).
thf(5371,plain,
! [SV1090: $i,SV1078: $i,SV321: $i] :
( ( ( ~ ( ord_less_eq @ SV321 @ ( number_number_of @ SV321 @ SV1078 ) @ ( number_number_of @ SV321 @ SV1090 ) ) )
= $true )
| ( ( ord_less_eq @ int @ SV1078 @ SV1090 )
= $true )
| ( ( number_ring @ SV321 )
= $false )
| ( ( linordered_idom @ SV321 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5310]) ).
thf(5372,plain,
! [SV321: $i,SV1090: $i,SV1078: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV1078 @ SV1090 ) )
= $true )
| ( ( ord_less_eq @ SV321 @ ( number_number_of @ SV321 @ SV1078 ) @ ( number_number_of @ SV321 @ SV1090 ) )
= $true )
| ( ( number_ring @ SV321 )
= $false )
| ( ( linordered_idom @ SV321 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5311]) ).
thf(5373,plain,
! [SV333: $i,SV1079: $i] :
( ( ( ( number_number_of @ nat @ SV1079 )
= ( zero_zero @ nat ) )
= $false )
| ( ( ( power_power @ SV333 @ ( zero_zero @ SV333 ) @ ( number_number_of @ nat @ SV1079 ) )
= ( one_one @ SV333 ) )
= $true )
| ( ( power @ SV333 )
= $false )
| ( ( semiring_0 @ SV333 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5312]) ).
thf(5374,plain,
! [SV333: $i,SV1079: $i] :
( ( ( ( number_number_of @ nat @ SV1079 )
!= ( zero_zero @ nat ) )
= $false )
| ( ( ( power_power @ SV333 @ ( zero_zero @ SV333 ) @ ( number_number_of @ nat @ SV1079 ) )
= ( zero_zero @ SV333 ) )
= $true )
| ( ( power @ SV333 )
= $false )
| ( ( semiring_0 @ SV333 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5313]) ).
thf(5375,plain,
! [SV977: $i,SV855: $i,SV352: $i] :
( ( ( ( ti @ SV352 @ SV855 )
= ( zero_zero @ SV352 ) )
= $true )
| ( ( ( plus_plus @ SV352 @ ( power_power @ SV352 @ SV855 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV352 @ SV977 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV352 ) )
= $false )
| ( ( linordered_idom @ SV352 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5314]) ).
thf(5376,plain,
! [SV855: $i,SV977: $i,SV352: $i] :
( ( ( ( ti @ SV352 @ SV977 )
= ( zero_zero @ SV352 ) )
= $true )
| ( ( ( plus_plus @ SV352 @ ( power_power @ SV352 @ SV855 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV352 @ SV977 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV352 ) )
= $false )
| ( ( linordered_idom @ SV352 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5315]) ).
thf(5377,plain,
! [SV977: $i,SV855: $i,SV352: $i] :
( ( ( ( ti @ SV352 @ SV855 )
= ( zero_zero @ SV352 ) )
= $false )
| ( ( ( ti @ SV352 @ SV977 )
!= ( zero_zero @ SV352 ) )
= $true )
| ( ( ( plus_plus @ SV352 @ ( power_power @ SV352 @ SV855 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV352 @ SV977 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV352 ) )
= $true )
| ( ( linordered_idom @ SV352 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5316]) ).
thf(5378,plain,
! [SV355: $i,SV1080: $i] :
( ( ( SV1080
= ( zero_zero @ nat ) )
= $false )
| ( ( ( power_power @ SV355 @ ( zero_zero @ SV355 ) @ SV1080 )
= ( one_one @ SV355 ) )
= $true )
| ( ( power @ SV355 )
= $false )
| ( ( semiring_0 @ SV355 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5317]) ).
thf(5379,plain,
! [SV355: $i,SV1080: $i] :
( ( ( SV1080
!= ( zero_zero @ nat ) )
= $false )
| ( ( ( power_power @ SV355 @ ( zero_zero @ SV355 ) @ SV1080 )
= ( zero_zero @ SV355 ) )
= $true )
| ( ( power @ SV355 )
= $false )
| ( ( semiring_0 @ SV355 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5318]) ).
thf(5380,plain,
! [SV980: $i,SV858: $i,SV1044: $i,SV358: $i] :
( ( ( ord_less_eq @ SV358 @ ( power_power @ SV358 @ SV1044 @ SV858 ) @ ( power_power @ SV358 @ SV1044 @ SV980 ) )
= $false )
| ( ( ord_less_eq @ nat @ SV858 @ SV980 )
= $true )
| ( ( ord_less @ SV358 @ ( one_one @ SV358 ) @ SV1044 )
= $false )
| ( ( linordered_semidom @ SV358 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5319]) ).
thf(5381,plain,
! [SV1044: $i,SV358: $i,SV980: $i,SV858: $i] :
( ( ( ord_less_eq @ nat @ SV858 @ SV980 )
= $false )
| ( ( ord_less_eq @ SV358 @ ( power_power @ SV358 @ SV1044 @ SV858 ) @ ( power_power @ SV358 @ SV1044 @ SV980 ) )
= $true )
| ( ( ord_less @ SV358 @ ( one_one @ SV358 ) @ SV1044 )
= $false )
| ( ( linordered_semidom @ SV358 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5320]) ).
thf(5382,plain,
! [SV595: $i,SV366: $i] :
( ( ( ord_less @ int @ SV366 @ pls )
= $false )
| ( ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV595 ) @ ( number_number_of @ nat @ SV366 ) )
= ( number_number_of @ nat @ SV595 ) )
= $true )
| ( ( ord_less @ int @ SV595 @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5321]) ).
thf(5383,plain,
! [SV595: $i,SV366: $i] :
( ( ( ~ ( ord_less @ int @ SV366 @ pls ) )
= $false )
| ( ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV595 ) @ ( number_number_of @ nat @ SV366 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SV595 @ SV366 ) ) )
= $true )
| ( ( ord_less @ int @ SV595 @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5322]) ).
thf(5384,plain,
! [SV612: $i,SV392: $i] :
( ( ( ord_less @ int @ SV392 @ SV612 )
= $false )
| ( ( ord_less @ int @ SV392 @ SV612 )
= $true )
| ( ( ord_less @ nat @ ( number_number_of @ nat @ SV392 ) @ ( number_number_of @ nat @ SV612 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5324]) ).
thf(5385,plain,
! [SV621: $i,SV413: $i] :
( ( ( ( ti @ int @ SV413 )
!= ( number_number_of @ int @ min ) )
= $false )
| ( ( ( ti @ int @ SV413 )
= ( one_one @ int ) )
= $true )
| ( ( ( times_times @ int @ SV413 @ SV621 )
= ( one_one @ int ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5326]) ).
thf(5386,plain,
! [SV413: $i,SV621: $i] :
( ( ( ( ti @ int @ SV621 )
!= ( number_number_of @ int @ min ) )
= $false )
| ( ( ( ti @ int @ SV413 )
= ( one_one @ int ) )
= $true )
| ( ( ( times_times @ int @ SV413 @ SV621 )
= ( one_one @ int ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5326]) ).
thf(5387,plain,
! [SV621: $i,SV413: $i] :
( ( ( ( ti @ int @ SV413 )
!= ( number_number_of @ int @ min ) )
= $false )
| ( ( ( ti @ int @ SV621 )
= ( one_one @ int ) )
= $true )
| ( ( ( times_times @ int @ SV413 @ SV621 )
= ( one_one @ int ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5327]) ).
thf(5388,plain,
! [SV413: $i,SV621: $i] :
( ( ( ( ti @ int @ SV621 )
!= ( number_number_of @ int @ min ) )
= $false )
| ( ( ( ti @ int @ SV621 )
= ( one_one @ int ) )
= $true )
| ( ( ( times_times @ int @ SV413 @ SV621 )
= ( one_one @ int ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5327]) ).
thf(5389,plain,
! [SV623: $i,SV419: $i] :
( ( ( ( ti @ int @ SV419 )
= ( one_one @ int ) )
= $false )
| ( ( ( ti @ int @ SV623 )
= ( one_one @ int ) )
= $false )
| ( ( ( times_times @ int @ SV623 @ SV419 )
= ( one_one @ int ) )
= $true )
| ( ( ord_less @ int @ ( zero_zero @ int ) @ SV623 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5332]) ).
thf(5390,plain,
! [SV1052: $i,SV995: $i,SV626: $i,SV422: $i,SV882: $i,SV726: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV726 ) )
= $true )
| ( ( ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV882 )
| ~ ( ord_less_eq @ int @ SV882 @ SV422 )
| ( ord_less_eq @ int @ SV626 @ SV995 ) )
= $true )
| ( ( ord_less @ int @ SV1052 @ SV882 )
= $false )
| ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( times_times @ int @ SV882 @ SV995 ) @ SV1052 ) )
= $false )
| ( ( ( plus_plus @ int @ ( times_times @ int @ SV422 @ SV626 ) @ SV726 )
= ( plus_plus @ int @ ( times_times @ int @ SV882 @ SV995 ) @ SV1052 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5333]) ).
thf(5391,plain,
! [SV1083: $i,SV998: $i,SV888: $i,SV1068: $i,SV1054: $i,SV434: $i] :
( ( ( ~ ( ( ( ti @ SV434 @ SV1054 )
!= ( ti @ SV434 @ SV1068 ) )
| ~ ( ( ( ti @ SV434 @ SV888 )
!= ( ti @ SV434 @ SV998 ) ) ) ) )
= $false )
| ( ( ( plus_plus @ SV434 @ SV1054 @ ( times_times @ SV434 @ SV1083 @ SV888 ) )
!= ( plus_plus @ SV434 @ SV1068 @ ( times_times @ SV434 @ SV1083 @ SV998 ) ) )
= $true )
| ( ( ( ti @ SV434 @ SV1083 )
= ( zero_zero @ SV434 ) )
= $true )
| ( ( semiri456707255roduct @ SV434 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5335]) ).
thf(5392,plain,
! [SV918: $i,SV771: $i,SV1060: $i,SV1013: $i,SV175: $i] :
( ( ( ~ ( ( ( ti @ SV175 @ SV1013 )
!= ( ti @ SV175 @ SV1060 ) ) ) )
= $true )
| ( ( ~ ( ( ( ti @ SV175 @ SV771 )
!= ( ti @ SV175 @ SV918 ) ) ) )
= $true )
| ( ( ( plus_plus @ SV175 @ ( times_times @ SV175 @ SV1013 @ SV771 ) @ ( times_times @ SV175 @ SV1060 @ SV918 ) )
!= ( plus_plus @ SV175 @ ( times_times @ SV175 @ SV1013 @ SV918 ) @ ( times_times @ SV175 @ SV1060 @ SV771 ) ) )
= $true )
| ( ( semiri456707255roduct @ SV175 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5345]) ).
thf(5393,plain,
! [SV918: $i,SV771: $i,SV1060: $i,SV1013: $i,SV175: $i] :
( ( ( ~ ( ( ( ti @ SV175 @ SV1013 )
!= ( ti @ SV175 @ SV1060 ) ) )
| ~ ( ( ( ti @ SV175 @ SV771 )
!= ( ti @ SV175 @ SV918 ) ) ) )
= $false )
| ( ( ( plus_plus @ SV175 @ ( times_times @ SV175 @ SV1013 @ SV771 ) @ ( times_times @ SV175 @ SV1060 @ SV918 ) )
= ( plus_plus @ SV175 @ ( times_times @ SV175 @ SV1013 @ SV918 ) @ ( times_times @ SV175 @ SV1060 @ SV771 ) ) )
= $true )
| ( ( semiri456707255roduct @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5346]) ).
thf(5394,plain,
! [SV778: $i,SV923: $i,SV193: $i] :
( ( ( ( ti @ SV193 @ SV923 )
= ( zero_zero @ SV193 ) )
= $false )
| ( ( ( ti @ SV193 @ SV778 )
= ( zero_zero @ SV193 ) )
= $false )
| ( ( ( plus_plus @ SV193 @ ( times_times @ SV193 @ SV778 @ SV778 ) @ ( times_times @ SV193 @ SV923 @ SV923 ) )
= ( zero_zero @ SV193 ) )
= $true )
| ( ( linord581940658strict @ SV193 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5349]) ).
thf(5395,plain,
! [SV928: $i,SV783: $i,SV199: $i] :
( ( ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ SV783 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq @ SV199 @ SV783 @ ( zero_zero @ SV199 ) )
| ~ ( ord_less_eq @ SV199 @ SV928 @ ( zero_zero @ SV199 ) ) ) )
= $true )
| ( ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ ( times_times @ SV199 @ SV783 @ SV928 ) )
= $false )
| ( ( linord581940658strict @ SV199 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5352]) ).
thf(5396,plain,
! [SV783: $i,SV928: $i,SV199: $i] :
( ( ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ SV928 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq @ SV199 @ SV783 @ ( zero_zero @ SV199 ) )
| ~ ( ord_less_eq @ SV199 @ SV928 @ ( zero_zero @ SV199 ) ) ) )
= $true )
| ( ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ ( times_times @ SV199 @ SV783 @ SV928 ) )
= $false )
| ( ( linord581940658strict @ SV199 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5353]) ).
thf(5397,plain,
! [SV928: $i,SV783: $i,SV199: $i] :
( ( ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ SV783 )
= $false )
| ( ( ~ ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ SV928 ) )
= $true )
| ( ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ ( times_times @ SV199 @ SV783 @ SV928 ) )
= $true )
| ( ( linord581940658strict @ SV199 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5354]) ).
thf(5398,plain,
! [SV928: $i,SV783: $i,SV199: $i] :
( ( ( ord_less_eq @ SV199 @ SV783 @ ( zero_zero @ SV199 ) )
= $false )
| ( ( ~ ( ord_less_eq @ SV199 @ SV928 @ ( zero_zero @ SV199 ) ) )
= $true )
| ( ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ ( times_times @ SV199 @ SV783 @ SV928 ) )
= $true )
| ( ( linord581940658strict @ SV199 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5355]) ).
thf(5399,plain,
! [SV1086: $i,SV1075: $i,SV213: $i] :
( ( ( ( number_number_of @ SV213 @ SV1075 )
= ( number_number_of @ SV213 @ SV1086 ) )
= $false )
| ( ( ( ti @ int @ SV1075 )
= ( ti @ int @ SV1086 ) )
= $true )
| ( ( number_ring @ SV213 )
= $false )
| ( ( ring_char_0 @ SV213 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5358]) ).
thf(5400,plain,
! [SV213: $i,SV1086: $i,SV1075: $i] :
( ( ( ( ti @ int @ SV1075 )
= ( ti @ int @ SV1086 ) )
= $false )
| ( ( ( number_number_of @ SV213 @ SV1075 )
= ( number_number_of @ SV213 @ SV1086 ) )
= $true )
| ( ( number_ring @ SV213 )
= $false )
| ( ( ring_char_0 @ SV213 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5359]) ).
thf(5401,plain,
! [SV1087: $i,SV1076: $i,SV218: $i] :
( ( ( ord_less @ SV218 @ ( number_number_of @ SV218 @ SV1076 ) @ ( number_number_of @ SV218 @ SV1087 ) )
= $false )
| ( ( ord_less @ int @ SV1076 @ SV1087 )
= $true )
| ( ( number_ring @ SV218 )
= $false )
| ( ( linordered_idom @ SV218 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5360]) ).
thf(5402,plain,
! [SV218: $i,SV1087: $i,SV1076: $i] :
( ( ( ord_less @ int @ SV1076 @ SV1087 )
= $false )
| ( ( ord_less @ SV218 @ ( number_number_of @ SV218 @ SV1076 ) @ ( number_number_of @ SV218 @ SV1087 ) )
= $true )
| ( ( number_ring @ SV218 )
= $false )
| ( ( linordered_idom @ SV218 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5361]) ).
thf(5403,plain,
! [SV698: $i,SV573: $i,SV957: $i,SV305: $i,SV829: $i,SV1032: $i] :
( ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV1032 )
= $false )
| ( ( ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV829 )
| ~ ( ord_less_eq @ int @ SV829 @ SV305 )
| ( ord_less_eq @ int @ SV957 @ SV573 ) )
= $true )
| ( ( ord_less @ int @ SV698 @ SV305 )
= $false )
| ( ( ord_less @ int @ ( plus_plus @ int @ ( times_times @ int @ SV829 @ SV957 ) @ SV1032 ) @ ( zero_zero @ int ) )
= $false )
| ( ( ( plus_plus @ int @ ( times_times @ int @ SV305 @ SV573 ) @ SV698 )
= ( plus_plus @ int @ ( times_times @ int @ SV829 @ SV957 ) @ SV1032 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5365]) ).
thf(5404,plain,
! [SV966: $i,SV839: $i,SV319: $i] :
( ( ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SV839 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq @ SV319 @ SV839 @ ( zero_zero @ SV319 ) )
| ~ ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SV966 ) ) )
= $true )
| ( ( ord_less_eq @ SV319 @ ( times_times @ SV319 @ SV839 @ SV966 ) @ ( zero_zero @ SV319 ) )
= $false )
| ( ( linord581940658strict @ SV319 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5367]) ).
thf(5405,plain,
! [SV839: $i,SV966: $i,SV319: $i] :
( ( ( ord_less_eq @ SV319 @ SV966 @ ( zero_zero @ SV319 ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq @ SV319 @ SV839 @ ( zero_zero @ SV319 ) )
| ~ ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SV966 ) ) )
= $true )
| ( ( ord_less_eq @ SV319 @ ( times_times @ SV319 @ SV839 @ SV966 ) @ ( zero_zero @ SV319 ) )
= $false )
| ( ( linord581940658strict @ SV319 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5368]) ).
thf(5406,plain,
! [SV966: $i,SV839: $i,SV319: $i] :
( ( ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SV839 )
= $false )
| ( ( ~ ( ord_less_eq @ SV319 @ SV966 @ ( zero_zero @ SV319 ) ) )
= $true )
| ( ( ord_less_eq @ SV319 @ ( times_times @ SV319 @ SV839 @ SV966 ) @ ( zero_zero @ SV319 ) )
= $true )
| ( ( linord581940658strict @ SV319 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5369]) ).
thf(5407,plain,
! [SV966: $i,SV839: $i,SV319: $i] :
( ( ( ord_less_eq @ SV319 @ SV839 @ ( zero_zero @ SV319 ) )
= $false )
| ( ( ~ ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SV966 ) )
= $true )
| ( ( ord_less_eq @ SV319 @ ( times_times @ SV319 @ SV839 @ SV966 ) @ ( zero_zero @ SV319 ) )
= $true )
| ( ( linord581940658strict @ SV319 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5370]) ).
thf(5408,plain,
! [SV1090: $i,SV1078: $i,SV321: $i] :
( ( ( ord_less_eq @ SV321 @ ( number_number_of @ SV321 @ SV1078 ) @ ( number_number_of @ SV321 @ SV1090 ) )
= $false )
| ( ( ord_less_eq @ int @ SV1078 @ SV1090 )
= $true )
| ( ( number_ring @ SV321 )
= $false )
| ( ( linordered_idom @ SV321 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5371]) ).
thf(5409,plain,
! [SV321: $i,SV1090: $i,SV1078: $i] :
( ( ( ord_less_eq @ int @ SV1078 @ SV1090 )
= $false )
| ( ( ord_less_eq @ SV321 @ ( number_number_of @ SV321 @ SV1078 ) @ ( number_number_of @ SV321 @ SV1090 ) )
= $true )
| ( ( number_ring @ SV321 )
= $false )
| ( ( linordered_idom @ SV321 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5372]) ).
thf(5410,plain,
! [SV333: $i,SV1079: $i] :
( ( ( ( number_number_of @ nat @ SV1079 )
= ( zero_zero @ nat ) )
= $true )
| ( ( ( power_power @ SV333 @ ( zero_zero @ SV333 ) @ ( number_number_of @ nat @ SV1079 ) )
= ( zero_zero @ SV333 ) )
= $true )
| ( ( power @ SV333 )
= $false )
| ( ( semiring_0 @ SV333 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5374]) ).
thf(5411,plain,
! [SV855: $i,SV977: $i,SV352: $i] :
( ( ( ( ti @ SV352 @ SV977 )
= ( zero_zero @ SV352 ) )
= $false )
| ( ( ( ti @ SV352 @ SV855 )
= ( zero_zero @ SV352 ) )
= $false )
| ( ( ( plus_plus @ SV352 @ ( power_power @ SV352 @ SV855 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV352 @ SV977 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV352 ) )
= $true )
| ( ( linordered_idom @ SV352 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5377]) ).
thf(5412,plain,
! [SV355: $i,SV1080: $i] :
( ( ( SV1080
= ( zero_zero @ nat ) )
= $true )
| ( ( ( power_power @ SV355 @ ( zero_zero @ SV355 ) @ SV1080 )
= ( zero_zero @ SV355 ) )
= $true )
| ( ( power @ SV355 )
= $false )
| ( ( semiring_0 @ SV355 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5379]) ).
thf(5413,plain,
! [SV595: $i,SV366: $i] :
( ( ( ord_less @ int @ SV366 @ pls )
= $true )
| ( ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV595 ) @ ( number_number_of @ nat @ SV366 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SV595 @ SV366 ) ) )
= $true )
| ( ( ord_less @ int @ SV595 @ pls )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5383]) ).
thf(5414,plain,
! [SV621: $i,SV413: $i] :
( ( ( ( ti @ int @ SV413 )
= ( number_number_of @ int @ min ) )
= $true )
| ( ( ( ti @ int @ SV413 )
= ( one_one @ int ) )
= $true )
| ( ( ( times_times @ int @ SV413 @ SV621 )
= ( one_one @ int ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5385]) ).
thf(5415,plain,
! [SV413: $i,SV621: $i] :
( ( ( ( ti @ int @ SV621 )
= ( number_number_of @ int @ min ) )
= $true )
| ( ( ( ti @ int @ SV413 )
= ( one_one @ int ) )
= $true )
| ( ( ( times_times @ int @ SV413 @ SV621 )
= ( one_one @ int ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5386]) ).
thf(5416,plain,
! [SV621: $i,SV413: $i] :
( ( ( ( ti @ int @ SV413 )
= ( number_number_of @ int @ min ) )
= $true )
| ( ( ( ti @ int @ SV621 )
= ( one_one @ int ) )
= $true )
| ( ( ( times_times @ int @ SV413 @ SV621 )
= ( one_one @ int ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5387]) ).
thf(5417,plain,
! [SV413: $i,SV621: $i] :
( ( ( ( ti @ int @ SV621 )
= ( number_number_of @ int @ min ) )
= $true )
| ( ( ( ti @ int @ SV621 )
= ( one_one @ int ) )
= $true )
| ( ( ( times_times @ int @ SV413 @ SV621 )
= ( one_one @ int ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5388]) ).
thf(5418,plain,
! [SV1052: $i,SV995: $i,SV626: $i,SV422: $i,SV882: $i,SV726: $i] :
( ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV726 )
= $false )
| ( ( ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV882 )
| ~ ( ord_less_eq @ int @ SV882 @ SV422 )
| ( ord_less_eq @ int @ SV626 @ SV995 ) )
= $true )
| ( ( ord_less @ int @ SV1052 @ SV882 )
= $false )
| ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( times_times @ int @ SV882 @ SV995 ) @ SV1052 ) )
= $false )
| ( ( ( plus_plus @ int @ ( times_times @ int @ SV422 @ SV626 ) @ SV726 )
= ( plus_plus @ int @ ( times_times @ int @ SV882 @ SV995 ) @ SV1052 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5390]) ).
thf(5419,plain,
! [SV1083: $i,SV998: $i,SV888: $i,SV1068: $i,SV1054: $i,SV434: $i] :
( ( ( ( ( ti @ SV434 @ SV1054 )
!= ( ti @ SV434 @ SV1068 ) )
| ~ ( ( ( ti @ SV434 @ SV888 )
!= ( ti @ SV434 @ SV998 ) ) ) )
= $true )
| ( ( ( plus_plus @ SV434 @ SV1054 @ ( times_times @ SV434 @ SV1083 @ SV888 ) )
!= ( plus_plus @ SV434 @ SV1068 @ ( times_times @ SV434 @ SV1083 @ SV998 ) ) )
= $true )
| ( ( ( ti @ SV434 @ SV1083 )
= ( zero_zero @ SV434 ) )
= $true )
| ( ( semiri456707255roduct @ SV434 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5391]) ).
thf(5420,plain,
! [SV918: $i,SV771: $i,SV1060: $i,SV1013: $i,SV175: $i] :
( ( ( ( ti @ SV175 @ SV1013 )
!= ( ti @ SV175 @ SV1060 ) )
= $false )
| ( ( ~ ( ( ( ti @ SV175 @ SV771 )
!= ( ti @ SV175 @ SV918 ) ) ) )
= $true )
| ( ( ( plus_plus @ SV175 @ ( times_times @ SV175 @ SV1013 @ SV771 ) @ ( times_times @ SV175 @ SV1060 @ SV918 ) )
!= ( plus_plus @ SV175 @ ( times_times @ SV175 @ SV1013 @ SV918 ) @ ( times_times @ SV175 @ SV1060 @ SV771 ) ) )
= $true )
| ( ( semiri456707255roduct @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5392]) ).
thf(5421,plain,
! [SV918: $i,SV771: $i,SV1060: $i,SV1013: $i,SV175: $i] :
( ( ( ~ ( ( ( ti @ SV175 @ SV1013 )
!= ( ti @ SV175 @ SV1060 ) ) ) )
= $false )
| ( ( ( plus_plus @ SV175 @ ( times_times @ SV175 @ SV1013 @ SV771 ) @ ( times_times @ SV175 @ SV1060 @ SV918 ) )
= ( plus_plus @ SV175 @ ( times_times @ SV175 @ SV1013 @ SV918 ) @ ( times_times @ SV175 @ SV1060 @ SV771 ) ) )
= $true )
| ( ( semiri456707255roduct @ SV175 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5393]) ).
thf(5422,plain,
! [SV1060: $i,SV1013: $i,SV918: $i,SV771: $i,SV175: $i] :
( ( ( ~ ( ( ( ti @ SV175 @ SV771 )
!= ( ti @ SV175 @ SV918 ) ) ) )
= $false )
| ( ( ( plus_plus @ SV175 @ ( times_times @ SV175 @ SV1013 @ SV771 ) @ ( times_times @ SV175 @ SV1060 @ SV918 ) )
= ( plus_plus @ SV175 @ ( times_times @ SV175 @ SV1013 @ SV918 ) @ ( times_times @ SV175 @ SV1060 @ SV771 ) ) )
= $true )
| ( ( semiri456707255roduct @ SV175 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5393]) ).
thf(5423,plain,
! [SV928: $i,SV783: $i,SV199: $i] :
( ( ( ~ ( ord_less_eq @ SV199 @ SV783 @ ( zero_zero @ SV199 ) )
| ~ ( ord_less_eq @ SV199 @ SV928 @ ( zero_zero @ SV199 ) ) )
= $false )
| ( ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ SV783 )
= $true )
| ( ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ ( times_times @ SV199 @ SV783 @ SV928 ) )
= $false )
| ( ( linord581940658strict @ SV199 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5395]) ).
thf(5424,plain,
! [SV928: $i,SV783: $i,SV199: $i] :
( ( ( ~ ( ord_less_eq @ SV199 @ SV783 @ ( zero_zero @ SV199 ) )
| ~ ( ord_less_eq @ SV199 @ SV928 @ ( zero_zero @ SV199 ) ) )
= $false )
| ( ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ SV928 )
= $true )
| ( ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ ( times_times @ SV199 @ SV783 @ SV928 ) )
= $false )
| ( ( linord581940658strict @ SV199 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5396]) ).
thf(5425,plain,
! [SV783: $i,SV928: $i,SV199: $i] :
( ( ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ SV928 )
= $false )
| ( ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ SV783 )
= $false )
| ( ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ ( times_times @ SV199 @ SV783 @ SV928 ) )
= $true )
| ( ( linord581940658strict @ SV199 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5397]) ).
thf(5426,plain,
! [SV783: $i,SV928: $i,SV199: $i] :
( ( ( ord_less_eq @ SV199 @ SV928 @ ( zero_zero @ SV199 ) )
= $false )
| ( ( ord_less_eq @ SV199 @ SV783 @ ( zero_zero @ SV199 ) )
= $false )
| ( ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ ( times_times @ SV199 @ SV783 @ SV928 ) )
= $true )
| ( ( linord581940658strict @ SV199 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5398]) ).
thf(5427,plain,
! [SV698: $i,SV1032: $i,SV573: $i,SV957: $i,SV305: $i,SV829: $i] :
( ( ( ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV829 ) )
= $true )
| ( ( ~ ( ord_less_eq @ int @ SV829 @ SV305 )
| ( ord_less_eq @ int @ SV957 @ SV573 ) )
= $true )
| ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV1032 )
= $false )
| ( ( ord_less @ int @ SV698 @ SV305 )
= $false )
| ( ( ord_less @ int @ ( plus_plus @ int @ ( times_times @ int @ SV829 @ SV957 ) @ SV1032 ) @ ( zero_zero @ int ) )
= $false )
| ( ( ( plus_plus @ int @ ( times_times @ int @ SV305 @ SV573 ) @ SV698 )
= ( plus_plus @ int @ ( times_times @ int @ SV829 @ SV957 ) @ SV1032 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5403]) ).
thf(5428,plain,
! [SV966: $i,SV839: $i,SV319: $i] :
( ( ( ~ ( ord_less_eq @ SV319 @ SV839 @ ( zero_zero @ SV319 ) )
| ~ ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SV966 ) )
= $false )
| ( ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SV839 )
= $true )
| ( ( ord_less_eq @ SV319 @ ( times_times @ SV319 @ SV839 @ SV966 ) @ ( zero_zero @ SV319 ) )
= $false )
| ( ( linord581940658strict @ SV319 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5404]) ).
thf(5429,plain,
! [SV966: $i,SV839: $i,SV319: $i] :
( ( ( ~ ( ord_less_eq @ SV319 @ SV839 @ ( zero_zero @ SV319 ) )
| ~ ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SV966 ) )
= $false )
| ( ( ord_less_eq @ SV319 @ SV966 @ ( zero_zero @ SV319 ) )
= $true )
| ( ( ord_less_eq @ SV319 @ ( times_times @ SV319 @ SV839 @ SV966 ) @ ( zero_zero @ SV319 ) )
= $false )
| ( ( linord581940658strict @ SV319 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5405]) ).
thf(5430,plain,
! [SV839: $i,SV966: $i,SV319: $i] :
( ( ( ord_less_eq @ SV319 @ SV966 @ ( zero_zero @ SV319 ) )
= $false )
| ( ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SV839 )
= $false )
| ( ( ord_less_eq @ SV319 @ ( times_times @ SV319 @ SV839 @ SV966 ) @ ( zero_zero @ SV319 ) )
= $true )
| ( ( linord581940658strict @ SV319 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5406]) ).
thf(5431,plain,
! [SV839: $i,SV966: $i,SV319: $i] :
( ( ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SV966 )
= $false )
| ( ( ord_less_eq @ SV319 @ SV839 @ ( zero_zero @ SV319 ) )
= $false )
| ( ( ord_less_eq @ SV319 @ ( times_times @ SV319 @ SV839 @ SV966 ) @ ( zero_zero @ SV319 ) )
= $true )
| ( ( linord581940658strict @ SV319 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5407]) ).
thf(5432,plain,
! [SV1052: $i,SV726: $i,SV995: $i,SV626: $i,SV422: $i,SV882: $i] :
( ( ( ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV882 ) )
= $true )
| ( ( ~ ( ord_less_eq @ int @ SV882 @ SV422 )
| ( ord_less_eq @ int @ SV626 @ SV995 ) )
= $true )
| ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV726 )
= $false )
| ( ( ord_less @ int @ SV1052 @ SV882 )
= $false )
| ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( times_times @ int @ SV882 @ SV995 ) @ SV1052 ) )
= $false )
| ( ( ( plus_plus @ int @ ( times_times @ int @ SV422 @ SV626 ) @ SV726 )
= ( plus_plus @ int @ ( times_times @ int @ SV882 @ SV995 ) @ SV1052 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5418]) ).
thf(5433,plain,
! [SV1083: $i,SV998: $i,SV888: $i,SV1068: $i,SV1054: $i,SV434: $i] :
( ( ( ( ti @ SV434 @ SV1054 )
!= ( ti @ SV434 @ SV1068 ) )
= $true )
| ( ( ~ ( ( ( ti @ SV434 @ SV888 )
!= ( ti @ SV434 @ SV998 ) ) ) )
= $true )
| ( ( ( plus_plus @ SV434 @ SV1054 @ ( times_times @ SV434 @ SV1083 @ SV888 ) )
!= ( plus_plus @ SV434 @ SV1068 @ ( times_times @ SV434 @ SV1083 @ SV998 ) ) )
= $true )
| ( ( ( ti @ SV434 @ SV1083 )
= ( zero_zero @ SV434 ) )
= $true )
| ( ( semiri456707255roduct @ SV434 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5419]) ).
thf(5434,plain,
! [SV918: $i,SV771: $i,SV1060: $i,SV1013: $i,SV175: $i] :
( ( ( ( ti @ SV175 @ SV1013 )
= ( ti @ SV175 @ SV1060 ) )
= $true )
| ( ( ~ ( ( ( ti @ SV175 @ SV771 )
!= ( ti @ SV175 @ SV918 ) ) ) )
= $true )
| ( ( ( plus_plus @ SV175 @ ( times_times @ SV175 @ SV1013 @ SV771 ) @ ( times_times @ SV175 @ SV1060 @ SV918 ) )
!= ( plus_plus @ SV175 @ ( times_times @ SV175 @ SV1013 @ SV918 ) @ ( times_times @ SV175 @ SV1060 @ SV771 ) ) )
= $true )
| ( ( semiri456707255roduct @ SV175 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5420]) ).
thf(5435,plain,
! [SV918: $i,SV771: $i,SV1060: $i,SV1013: $i,SV175: $i] :
( ( ( ( ti @ SV175 @ SV1013 )
!= ( ti @ SV175 @ SV1060 ) )
= $true )
| ( ( ( plus_plus @ SV175 @ ( times_times @ SV175 @ SV1013 @ SV771 ) @ ( times_times @ SV175 @ SV1060 @ SV918 ) )
= ( plus_plus @ SV175 @ ( times_times @ SV175 @ SV1013 @ SV918 ) @ ( times_times @ SV175 @ SV1060 @ SV771 ) ) )
= $true )
| ( ( semiri456707255roduct @ SV175 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5421]) ).
thf(5436,plain,
! [SV1060: $i,SV1013: $i,SV918: $i,SV771: $i,SV175: $i] :
( ( ( ( ti @ SV175 @ SV771 )
!= ( ti @ SV175 @ SV918 ) )
= $true )
| ( ( ( plus_plus @ SV175 @ ( times_times @ SV175 @ SV1013 @ SV771 ) @ ( times_times @ SV175 @ SV1060 @ SV918 ) )
= ( plus_plus @ SV175 @ ( times_times @ SV175 @ SV1013 @ SV918 ) @ ( times_times @ SV175 @ SV1060 @ SV771 ) ) )
= $true )
| ( ( semiri456707255roduct @ SV175 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5422]) ).
thf(5437,plain,
! [SV928: $i,SV783: $i,SV199: $i] :
( ( ( ~ ( ord_less_eq @ SV199 @ SV783 @ ( zero_zero @ SV199 ) ) )
= $false )
| ( ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ SV783 )
= $true )
| ( ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ ( times_times @ SV199 @ SV783 @ SV928 ) )
= $false )
| ( ( linord581940658strict @ SV199 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5423]) ).
thf(5438,plain,
! [SV783: $i,SV928: $i,SV199: $i] :
( ( ( ~ ( ord_less_eq @ SV199 @ SV928 @ ( zero_zero @ SV199 ) ) )
= $false )
| ( ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ SV783 )
= $true )
| ( ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ ( times_times @ SV199 @ SV783 @ SV928 ) )
= $false )
| ( ( linord581940658strict @ SV199 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5423]) ).
thf(5439,plain,
! [SV928: $i,SV783: $i,SV199: $i] :
( ( ( ~ ( ord_less_eq @ SV199 @ SV783 @ ( zero_zero @ SV199 ) ) )
= $false )
| ( ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ SV928 )
= $true )
| ( ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ ( times_times @ SV199 @ SV783 @ SV928 ) )
= $false )
| ( ( linord581940658strict @ SV199 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5424]) ).
thf(5440,plain,
! [SV783: $i,SV928: $i,SV199: $i] :
( ( ( ~ ( ord_less_eq @ SV199 @ SV928 @ ( zero_zero @ SV199 ) ) )
= $false )
| ( ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ SV928 )
= $true )
| ( ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ ( times_times @ SV199 @ SV783 @ SV928 ) )
= $false )
| ( ( linord581940658strict @ SV199 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5424]) ).
thf(5441,plain,
! [SV698: $i,SV1032: $i,SV573: $i,SV957: $i,SV305: $i,SV829: $i] :
( ( ( ord_less @ int @ ( zero_zero @ int ) @ SV829 )
= $false )
| ( ( ~ ( ord_less_eq @ int @ SV829 @ SV305 )
| ( ord_less_eq @ int @ SV957 @ SV573 ) )
= $true )
| ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV1032 )
= $false )
| ( ( ord_less @ int @ SV698 @ SV305 )
= $false )
| ( ( ord_less @ int @ ( plus_plus @ int @ ( times_times @ int @ SV829 @ SV957 ) @ SV1032 ) @ ( zero_zero @ int ) )
= $false )
| ( ( ( plus_plus @ int @ ( times_times @ int @ SV305 @ SV573 ) @ SV698 )
= ( plus_plus @ int @ ( times_times @ int @ SV829 @ SV957 ) @ SV1032 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5427]) ).
thf(5442,plain,
! [SV966: $i,SV839: $i,SV319: $i] :
( ( ( ~ ( ord_less_eq @ SV319 @ SV839 @ ( zero_zero @ SV319 ) ) )
= $false )
| ( ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SV839 )
= $true )
| ( ( ord_less_eq @ SV319 @ ( times_times @ SV319 @ SV839 @ SV966 ) @ ( zero_zero @ SV319 ) )
= $false )
| ( ( linord581940658strict @ SV319 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5428]) ).
thf(5443,plain,
! [SV839: $i,SV966: $i,SV319: $i] :
( ( ( ~ ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SV966 ) )
= $false )
| ( ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SV839 )
= $true )
| ( ( ord_less_eq @ SV319 @ ( times_times @ SV319 @ SV839 @ SV966 ) @ ( zero_zero @ SV319 ) )
= $false )
| ( ( linord581940658strict @ SV319 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5428]) ).
thf(5444,plain,
! [SV966: $i,SV839: $i,SV319: $i] :
( ( ( ~ ( ord_less_eq @ SV319 @ SV839 @ ( zero_zero @ SV319 ) ) )
= $false )
| ( ( ord_less_eq @ SV319 @ SV966 @ ( zero_zero @ SV319 ) )
= $true )
| ( ( ord_less_eq @ SV319 @ ( times_times @ SV319 @ SV839 @ SV966 ) @ ( zero_zero @ SV319 ) )
= $false )
| ( ( linord581940658strict @ SV319 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5429]) ).
thf(5445,plain,
! [SV839: $i,SV966: $i,SV319: $i] :
( ( ( ~ ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SV966 ) )
= $false )
| ( ( ord_less_eq @ SV319 @ SV966 @ ( zero_zero @ SV319 ) )
= $true )
| ( ( ord_less_eq @ SV319 @ ( times_times @ SV319 @ SV839 @ SV966 ) @ ( zero_zero @ SV319 ) )
= $false )
| ( ( linord581940658strict @ SV319 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5429]) ).
thf(5446,plain,
! [SV1052: $i,SV726: $i,SV995: $i,SV626: $i,SV422: $i,SV882: $i] :
( ( ( ord_less @ int @ ( zero_zero @ int ) @ SV882 )
= $false )
| ( ( ~ ( ord_less_eq @ int @ SV882 @ SV422 )
| ( ord_less_eq @ int @ SV626 @ SV995 ) )
= $true )
| ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV726 )
= $false )
| ( ( ord_less @ int @ SV1052 @ SV882 )
= $false )
| ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( times_times @ int @ SV882 @ SV995 ) @ SV1052 ) )
= $false )
| ( ( ( plus_plus @ int @ ( times_times @ int @ SV422 @ SV626 ) @ SV726 )
= ( plus_plus @ int @ ( times_times @ int @ SV882 @ SV995 ) @ SV1052 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5432]) ).
thf(5447,plain,
! [SV1083: $i,SV998: $i,SV888: $i,SV1068: $i,SV1054: $i,SV434: $i] :
( ( ( ( ti @ SV434 @ SV1054 )
= ( ti @ SV434 @ SV1068 ) )
= $false )
| ( ( ~ ( ( ( ti @ SV434 @ SV888 )
!= ( ti @ SV434 @ SV998 ) ) ) )
= $true )
| ( ( ( plus_plus @ SV434 @ SV1054 @ ( times_times @ SV434 @ SV1083 @ SV888 ) )
!= ( plus_plus @ SV434 @ SV1068 @ ( times_times @ SV434 @ SV1083 @ SV998 ) ) )
= $true )
| ( ( ( ti @ SV434 @ SV1083 )
= ( zero_zero @ SV434 ) )
= $true )
| ( ( semiri456707255roduct @ SV434 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5433]) ).
thf(5448,plain,
! [SV1060: $i,SV1013: $i,SV918: $i,SV771: $i,SV175: $i] :
( ( ( ( ti @ SV175 @ SV771 )
!= ( ti @ SV175 @ SV918 ) )
= $false )
| ( ( ( ti @ SV175 @ SV1013 )
= ( ti @ SV175 @ SV1060 ) )
= $true )
| ( ( ( plus_plus @ SV175 @ ( times_times @ SV175 @ SV1013 @ SV771 ) @ ( times_times @ SV175 @ SV1060 @ SV918 ) )
!= ( plus_plus @ SV175 @ ( times_times @ SV175 @ SV1013 @ SV918 ) @ ( times_times @ SV175 @ SV1060 @ SV771 ) ) )
= $true )
| ( ( semiri456707255roduct @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5434]) ).
thf(5449,plain,
! [SV918: $i,SV771: $i,SV1060: $i,SV1013: $i,SV175: $i] :
( ( ( ( ti @ SV175 @ SV1013 )
= ( ti @ SV175 @ SV1060 ) )
= $false )
| ( ( ( plus_plus @ SV175 @ ( times_times @ SV175 @ SV1013 @ SV771 ) @ ( times_times @ SV175 @ SV1060 @ SV918 ) )
= ( plus_plus @ SV175 @ ( times_times @ SV175 @ SV1013 @ SV918 ) @ ( times_times @ SV175 @ SV1060 @ SV771 ) ) )
= $true )
| ( ( semiri456707255roduct @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5435]) ).
thf(5450,plain,
! [SV1060: $i,SV1013: $i,SV918: $i,SV771: $i,SV175: $i] :
( ( ( ( ti @ SV175 @ SV771 )
= ( ti @ SV175 @ SV918 ) )
= $false )
| ( ( ( plus_plus @ SV175 @ ( times_times @ SV175 @ SV1013 @ SV771 ) @ ( times_times @ SV175 @ SV1060 @ SV918 ) )
= ( plus_plus @ SV175 @ ( times_times @ SV175 @ SV1013 @ SV918 ) @ ( times_times @ SV175 @ SV1060 @ SV771 ) ) )
= $true )
| ( ( semiri456707255roduct @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5436]) ).
thf(5451,plain,
! [SV928: $i,SV783: $i,SV199: $i] :
( ( ( ord_less_eq @ SV199 @ SV783 @ ( zero_zero @ SV199 ) )
= $true )
| ( ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ SV783 )
= $true )
| ( ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ ( times_times @ SV199 @ SV783 @ SV928 ) )
= $false )
| ( ( linord581940658strict @ SV199 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5437]) ).
thf(5452,plain,
! [SV783: $i,SV928: $i,SV199: $i] :
( ( ( ord_less_eq @ SV199 @ SV928 @ ( zero_zero @ SV199 ) )
= $true )
| ( ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ SV783 )
= $true )
| ( ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ ( times_times @ SV199 @ SV783 @ SV928 ) )
= $false )
| ( ( linord581940658strict @ SV199 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5438]) ).
thf(5453,plain,
! [SV928: $i,SV783: $i,SV199: $i] :
( ( ( ord_less_eq @ SV199 @ SV783 @ ( zero_zero @ SV199 ) )
= $true )
| ( ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ SV928 )
= $true )
| ( ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ ( times_times @ SV199 @ SV783 @ SV928 ) )
= $false )
| ( ( linord581940658strict @ SV199 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5439]) ).
thf(5454,plain,
! [SV783: $i,SV928: $i,SV199: $i] :
( ( ( ord_less_eq @ SV199 @ SV928 @ ( zero_zero @ SV199 ) )
= $true )
| ( ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ SV928 )
= $true )
| ( ( ord_less_eq @ SV199 @ ( zero_zero @ SV199 ) @ ( times_times @ SV199 @ SV783 @ SV928 ) )
= $false )
| ( ( linord581940658strict @ SV199 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5440]) ).
thf(5455,plain,
! [SV698: $i,SV1032: $i,SV573: $i,SV957: $i,SV305: $i,SV829: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV829 @ SV305 ) )
= $true )
| ( ( ord_less_eq @ int @ SV957 @ SV573 )
= $true )
| ( ( ord_less @ int @ ( zero_zero @ int ) @ SV829 )
= $false )
| ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV1032 )
= $false )
| ( ( ord_less @ int @ SV698 @ SV305 )
= $false )
| ( ( ord_less @ int @ ( plus_plus @ int @ ( times_times @ int @ SV829 @ SV957 ) @ SV1032 ) @ ( zero_zero @ int ) )
= $false )
| ( ( ( plus_plus @ int @ ( times_times @ int @ SV305 @ SV573 ) @ SV698 )
= ( plus_plus @ int @ ( times_times @ int @ SV829 @ SV957 ) @ SV1032 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5441]) ).
thf(5456,plain,
! [SV966: $i,SV839: $i,SV319: $i] :
( ( ( ord_less_eq @ SV319 @ SV839 @ ( zero_zero @ SV319 ) )
= $true )
| ( ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SV839 )
= $true )
| ( ( ord_less_eq @ SV319 @ ( times_times @ SV319 @ SV839 @ SV966 ) @ ( zero_zero @ SV319 ) )
= $false )
| ( ( linord581940658strict @ SV319 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5442]) ).
thf(5457,plain,
! [SV839: $i,SV966: $i,SV319: $i] :
( ( ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SV966 )
= $true )
| ( ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SV839 )
= $true )
| ( ( ord_less_eq @ SV319 @ ( times_times @ SV319 @ SV839 @ SV966 ) @ ( zero_zero @ SV319 ) )
= $false )
| ( ( linord581940658strict @ SV319 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5443]) ).
thf(5458,plain,
! [SV966: $i,SV839: $i,SV319: $i] :
( ( ( ord_less_eq @ SV319 @ SV839 @ ( zero_zero @ SV319 ) )
= $true )
| ( ( ord_less_eq @ SV319 @ SV966 @ ( zero_zero @ SV319 ) )
= $true )
| ( ( ord_less_eq @ SV319 @ ( times_times @ SV319 @ SV839 @ SV966 ) @ ( zero_zero @ SV319 ) )
= $false )
| ( ( linord581940658strict @ SV319 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5444]) ).
thf(5459,plain,
! [SV839: $i,SV966: $i,SV319: $i] :
( ( ( ord_less_eq @ SV319 @ ( zero_zero @ SV319 ) @ SV966 )
= $true )
| ( ( ord_less_eq @ SV319 @ SV966 @ ( zero_zero @ SV319 ) )
= $true )
| ( ( ord_less_eq @ SV319 @ ( times_times @ SV319 @ SV839 @ SV966 ) @ ( zero_zero @ SV319 ) )
= $false )
| ( ( linord581940658strict @ SV319 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5445]) ).
thf(5460,plain,
! [SV1052: $i,SV726: $i,SV995: $i,SV626: $i,SV422: $i,SV882: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV882 @ SV422 ) )
= $true )
| ( ( ord_less_eq @ int @ SV626 @ SV995 )
= $true )
| ( ( ord_less @ int @ ( zero_zero @ int ) @ SV882 )
= $false )
| ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV726 )
= $false )
| ( ( ord_less @ int @ SV1052 @ SV882 )
= $false )
| ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( times_times @ int @ SV882 @ SV995 ) @ SV1052 ) )
= $false )
| ( ( ( plus_plus @ int @ ( times_times @ int @ SV422 @ SV626 ) @ SV726 )
= ( plus_plus @ int @ ( times_times @ int @ SV882 @ SV995 ) @ SV1052 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5446]) ).
thf(5461,plain,
! [SV1083: $i,SV1068: $i,SV1054: $i,SV998: $i,SV888: $i,SV434: $i] :
( ( ( ( ti @ SV434 @ SV888 )
!= ( ti @ SV434 @ SV998 ) )
= $false )
| ( ( ( ti @ SV434 @ SV1054 )
= ( ti @ SV434 @ SV1068 ) )
= $false )
| ( ( ( plus_plus @ SV434 @ SV1054 @ ( times_times @ SV434 @ SV1083 @ SV888 ) )
!= ( plus_plus @ SV434 @ SV1068 @ ( times_times @ SV434 @ SV1083 @ SV998 ) ) )
= $true )
| ( ( ( ti @ SV434 @ SV1083 )
= ( zero_zero @ SV434 ) )
= $true )
| ( ( semiri456707255roduct @ SV434 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5447]) ).
thf(5462,plain,
! [SV1060: $i,SV1013: $i,SV918: $i,SV771: $i,SV175: $i] :
( ( ( ( ti @ SV175 @ SV771 )
= ( ti @ SV175 @ SV918 ) )
= $true )
| ( ( ( ti @ SV175 @ SV1013 )
= ( ti @ SV175 @ SV1060 ) )
= $true )
| ( ( ( plus_plus @ SV175 @ ( times_times @ SV175 @ SV1013 @ SV771 ) @ ( times_times @ SV175 @ SV1060 @ SV918 ) )
!= ( plus_plus @ SV175 @ ( times_times @ SV175 @ SV1013 @ SV918 ) @ ( times_times @ SV175 @ SV1060 @ SV771 ) ) )
= $true )
| ( ( semiri456707255roduct @ SV175 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5448]) ).
thf(5463,plain,
! [SV698: $i,SV1032: $i,SV573: $i,SV957: $i,SV305: $i,SV829: $i] :
( ( ( ord_less_eq @ int @ SV829 @ SV305 )
= $false )
| ( ( ord_less_eq @ int @ SV957 @ SV573 )
= $true )
| ( ( ord_less @ int @ ( zero_zero @ int ) @ SV829 )
= $false )
| ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV1032 )
= $false )
| ( ( ord_less @ int @ SV698 @ SV305 )
= $false )
| ( ( ord_less @ int @ ( plus_plus @ int @ ( times_times @ int @ SV829 @ SV957 ) @ SV1032 ) @ ( zero_zero @ int ) )
= $false )
| ( ( ( plus_plus @ int @ ( times_times @ int @ SV305 @ SV573 ) @ SV698 )
= ( plus_plus @ int @ ( times_times @ int @ SV829 @ SV957 ) @ SV1032 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5455]) ).
thf(5464,plain,
! [SV1052: $i,SV726: $i,SV995: $i,SV626: $i,SV422: $i,SV882: $i] :
( ( ( ord_less_eq @ int @ SV882 @ SV422 )
= $false )
| ( ( ord_less_eq @ int @ SV626 @ SV995 )
= $true )
| ( ( ord_less @ int @ ( zero_zero @ int ) @ SV882 )
= $false )
| ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV726 )
= $false )
| ( ( ord_less @ int @ SV1052 @ SV882 )
= $false )
| ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( times_times @ int @ SV882 @ SV995 ) @ SV1052 ) )
= $false )
| ( ( ( plus_plus @ int @ ( times_times @ int @ SV422 @ SV626 ) @ SV726 )
= ( plus_plus @ int @ ( times_times @ int @ SV882 @ SV995 ) @ SV1052 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5460]) ).
thf(5465,plain,
! [SV1083: $i,SV1068: $i,SV1054: $i,SV998: $i,SV888: $i,SV434: $i] :
( ( ( ( ti @ SV434 @ SV888 )
= ( ti @ SV434 @ SV998 ) )
= $true )
| ( ( ( ti @ SV434 @ SV1054 )
= ( ti @ SV434 @ SV1068 ) )
= $false )
| ( ( ( plus_plus @ SV434 @ SV1054 @ ( times_times @ SV434 @ SV1083 @ SV888 ) )
!= ( plus_plus @ SV434 @ SV1068 @ ( times_times @ SV434 @ SV1083 @ SV998 ) ) )
= $true )
| ( ( ( ti @ SV434 @ SV1083 )
= ( zero_zero @ SV434 ) )
= $true )
| ( ( semiri456707255roduct @ SV434 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5461]) ).
thf(5466,plain,
! [SV918: $i,SV1060: $i,SV771: $i,SV1013: $i,SV175: $i] :
( ( ( ( plus_plus @ SV175 @ ( times_times @ SV175 @ SV1013 @ SV771 ) @ ( times_times @ SV175 @ SV1060 @ SV918 ) )
= ( plus_plus @ SV175 @ ( times_times @ SV175 @ SV1013 @ SV918 ) @ ( times_times @ SV175 @ SV1060 @ SV771 ) ) )
= $false )
| ( ( ( ti @ SV175 @ SV1013 )
= ( ti @ SV175 @ SV1060 ) )
= $true )
| ( ( ( ti @ SV175 @ SV771 )
= ( ti @ SV175 @ SV918 ) )
= $true )
| ( ( semiri456707255roduct @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5462]) ).
thf(5467,plain,
! [SV998: $i,SV1068: $i,SV888: $i,SV1083: $i,SV1054: $i,SV434: $i] :
( ( ( ( plus_plus @ SV434 @ SV1054 @ ( times_times @ SV434 @ SV1083 @ SV888 ) )
= ( plus_plus @ SV434 @ SV1068 @ ( times_times @ SV434 @ SV1083 @ SV998 ) ) )
= $false )
| ( ( ( ti @ SV434 @ SV1054 )
= ( ti @ SV434 @ SV1068 ) )
= $false )
| ( ( ( ti @ SV434 @ SV888 )
= ( ti @ SV434 @ SV998 ) )
= $true )
| ( ( ( ti @ SV434 @ SV1083 )
= ( zero_zero @ SV434 ) )
= $true )
| ( ( semiri456707255roduct @ SV434 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5465]) ).
thf(5468,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[1202,5467,5466,5464,5463,5459,5458,5457,5456,5454,5453,5452,5451,5450,5449,5431,5430,5426,5425,5417,5416,5415,5414,5413,5412,5411,5410,5409,5408,5402,5401,5400,5399,5394,5389,5384,5382,5381,5380,5378,5376,5375,5373,5366,5364,5363,5362,5357,5356,5351,5350,5348,5347,5344,5343,5342,5341,5340,5339,5338,5337,5336,5334,5331,5330,5329,5328,5325,5323,5304,5303,5296,5290,5284,5281,5280,5277,5276,5275,5267,5266,5265,5264,5253,5252,5251,5247,5244,5243,5242,5233,5225,5224,5223,5222,5221,5220,5215,5214,5211,5196,5193,5186,5184,5180,5174,5158,5157,5155,5153,5152,5150,5149,5145,5138,5135,5134,5127,5126,5125,5124,5123,5120,5116,5108,5107,5106,5089,5088,5084,5083,5082,5076,5075,5072,5070,5069,5068,5049,5045,5044,5033,5024,5018,5017,5014,5012,4996,4992,4991,4986,4977,4974,4967,4966,4965,4964,4963,4952,4949,4946,4929,4928,4926,4925,4920,4919,4918,4917,4916,4914,4910,4902,4897,4895,4894,4892,4888,4887,4875,4874,4867,4849,4843,4842,4841,4838,4837,4836,4834,4829,4828,4827,4826,4825,4822,4803,4795,4794,4787,4786,4785,4784,4783,4779,4778,4777,4770,4767,4760,4759,4758,4752,4751,4748,4747,4746,4745,4742,4741,4740,4737,4736,4726,4723,4722,4719,4717,4716,4715,4709,4707,4704,4703,4702,4701,4700,4698,4695,4690,4689,4682,4681,4679,4676,4675,4674,4673,4672,4671,4670,4669,4665,4664,4656,4645,4644,4643,4642,4641,4640,4636,4635,4630,4624,4623,4618,4617,4613,4612,4608,4607,4605,4603,4597,4586,4583,4578,4577,4576,4575,4572,4570,4569,4568,4567,4558,4557,4556,4555,4543,4541,4540,4533,4529,4528,4526,4524,4523,4520,4519,4516,4515,4514,4507,4504,4480,4475,4472,4471,4466,4465,4464,4456,4449,4442,4441,4425,4401,4400,4399,4395,4394,4391,4385,4384,4383,4382,4379,4378,4374,4373,4371,4367,4366,4362,4361,4358,4357,4355,4354,4352,4351,4348,4342,4341,4337,4336,4335,4334,4329,4328,4325,4324,4322,4321,4320,4310,4309,4308,4303,4302,4297,4296,4294,4293,4292,4291,4289,4288,4282,4269,4263,4262,4257,4256,4250,4240,4235,4232,4231,4216,4215,4214,4213,4201,4200,4199,4196,4195,4190,4186,4185,4184,4183,4182,4180,4178,4170,4162,4147,4143,4141,4139,4135,4123,4107,4090,4089,4083,4081,4080,4057,4056,4054,4049,4042,4030,4029,4012,4010,4009,4002,3998,3989,3988,3980,3976,3970,3965,3948,3947,3946,3945,3930,3929,3914,3913,3880,3870,3869,3833,3830,3821,3818,3813,3811,3810,3803,3799,3795,3793,3786,3777,3752,3750,3747,3722,3719,3698,3677,3674,3669,3660,3652,3629,3620,3617,3608,3600,3598,3593,3587,3573,3551,3547,3529,3528,3512,3508,3496,3490,3482,3479,3459,3450,3444,3440,3439,3434,3427,3424,3410,3406,3378,3370,3368,3347,3341,3274,3251,3220,3184,3182,3180,3114,3093,3071,3042,3035,3023,3021,3010,2988,2981,2980,2977,2976,2975,2974,2973,2972,2971,2970,2969,2968,2967,2965,2853,2837,2794,2707,2674,2601,2600,2599,2598,2597,2596,2593,2592,2589,2587,2585,2584,2583,2582,2581,2578,2577,2576,2575,2572,2566,2565,2564,2563,2562,2561,2560,2559,2558,2557,2556,2486,2460,2353,2275,2215,2189,2185,2184,2177,2176,2175,2173,2167,2164,2163,2162,2160,2159,2158,2157,2155,2153,2150,2145,2144,2143,2141,2140,2138,2134,2131,2130,2129,2124,2123,2120,2119,2109,2108,2107,2106,1738,1737,1736,1735,1734,1733,1732,1731,1730,1729,1728,1727,1726,1725,1724,1723,1722,1721,1720,1719,1718,1717,1716,1715,1714,1713,1712,1711,1710,1709,1708,1707,1706,1705,1704,1703,1702,1701,1700,1699,1698,1697,1696,1695,1694,1693,1692,1691,1690,1689,1688,1660,1656,1655,1653,1566,1564,1549,1540,1539,1533,1529,1527,1522,1516,1509,1506,1469,1468,1446,1431,1430,1422,1421,1411,1373,1317,1307,1306,1298,1290,1260,1259,1258,1257,1254,1253,1252,1251,1234,1203]) ).
thf(5469,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[5468]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM926+6 : TPTP v9.3.1. Released v5.3.0.
% 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
% 0.09/0.22 % Computer : n016.cluster.edu
% 0.09/0.22 % Model : x86_64 x86_64
% 0.09/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.22 % Memory : 8046.5625MB
% 0.09/0.22 % OS : Linux 6.8.0-71-generic
% 0.09/0.22 % CPULimit : 300
% 0.09/0.22 % WCLimit : 300
% 0.09/0.22 % DateTime : Tue Oct 6 13:50:29 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.22 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 221.41/37.38 .....
% 221.41/37.38
% 221.41/37.38 No.of.Axioms: 541
% 221.41/37.38
% 221.41/37.38 Length.of.Defs: 0
% 221.41/37.38
% 221.41/37.38 Contains.Choice.Funs: false
% 221.41/37.38 .......................................................................................................................................................................................................................................
% 221.41/37.38
% 221.41/37.38 ********************************
% 221.41/37.38 * All subproblems solved! *
% 221.41/37.38 ********************************
% 221.41/37.38 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:541,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:298,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:5468,loop_count:0,foatp_calls:1,translation:fof_full)
% 221.41/37.38
% 221.41/37.38 %**** Beginning of derivation protocol ****
% 221.41/37.38 % SZS output start CNFRefutation
% See solution above
% 37.32/37.42
% 37.32/37.42 %**** End of derivation protocol ****
% 37.32/37.42 %**** no. of clauses in derivation: 5358 ****
% 37.32/37.42 %**** clause counter: 5468 ****
% 37.32/37.42
% 37.32/37.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:541,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:298,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:5468,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------