%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM924^2 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 10:35:32 AM UTC 2026
% Result : Theorem 174.32s 29.38s
% Output : CNFRefutation 29.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 686
% Syntax : Number of formulae : 6997 (5027 unt; 0 typ; 0 def)
% Number of atoms : 35601 (16016 equ; 0 cnn)
% Maximal formula atoms : 7 ( 5 avg)
% Number of connectives : 81755 (9330 ~;9632 |; 554 &;61185 @)
% ( 312 <=>; 742 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 52 ( 49 usr; 16 con; 0-3 aty)
% Number of variables : 17320 ( 0 ^;17314 !; 6 ?;17320 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_int,type,
int: $tType ).
thf(tp_nat,type,
nat: $tType ).
thf(tp_real,type,
real: $tType ).
thf(tp_bit0,type,
bit0: int > int ).
thf(tp_bit1,type,
bit1: int > int ).
thf(tp_dvd_dvd_int,type,
dvd_dvd_int: int > int > $o ).
thf(tp_dvd_dvd_nat,type,
dvd_dvd_nat: nat > nat > $o ).
thf(tp_dvd_dvd_real,type,
dvd_dvd_real: real > real > $o ).
thf(tp_legendre,type,
legendre: int > int > int ).
thf(tp_m,type,
m: int ).
thf(tp_min,type,
min: int ).
thf(tp_minus_minus_int,type,
minus_minus_int: int > int > int ).
thf(tp_minus_minus_nat,type,
minus_minus_nat: nat > nat > nat ).
thf(tp_minus_minus_real,type,
minus_minus_real: real > real > real ).
thf(tp_number267125858f_real,type,
number267125858f_real: int > real ).
thf(tp_number_number_of_int,type,
number_number_of_int: int > int ).
thf(tp_number_number_of_nat,type,
number_number_of_nat: int > nat ).
thf(tp_one_one_int,type,
one_one_int: int ).
thf(tp_one_one_nat,type,
one_one_nat: nat ).
thf(tp_one_one_real,type,
one_one_real: real ).
thf(tp_ord_less_eq_int,type,
ord_less_eq_int: int > int > $o ).
thf(tp_ord_less_eq_nat,type,
ord_less_eq_nat: nat > nat > $o ).
thf(tp_ord_less_eq_real,type,
ord_less_eq_real: real > real > $o ).
thf(tp_ord_less_int,type,
ord_less_int: int > int > $o ).
thf(tp_ord_less_nat,type,
ord_less_nat: nat > nat > $o ).
thf(tp_ord_less_real,type,
ord_less_real: real > real > $o ).
thf(tp_pls,type,
pls: int ).
thf(tp_plus_plus_int,type,
plus_plus_int: int > int > int ).
thf(tp_plus_plus_nat,type,
plus_plus_nat: nat > nat > nat ).
thf(tp_plus_plus_real,type,
plus_plus_real: real > real > real ).
thf(tp_power_power_int,type,
power_power_int: int > nat > int ).
thf(tp_power_power_nat,type,
power_power_nat: nat > nat > nat ).
thf(tp_power_power_real,type,
power_power_real: real > nat > real ).
thf(tp_quadRes,type,
quadRes: int > int > $o ).
thf(tp_s,type,
s: int ).
thf(tp_s1,type,
s1: int ).
thf(tp_sK1_X_1,type,
sK1_X_1: nat > real > real ).
thf(tp_sK2_S1,type,
sK2_S1: int ).
thf(tp_sK3_M_9,type,
sK3_M_9: int > int ).
thf(tp_sK4_T_1,type,
sK4_T_1: int ).
thf(tp_sK5_Y_1,type,
sK5_Y_1: int > int > int ).
thf(tp_sK6_K_1,type,
sK6_K_1: int > int > int > int ).
thf(tp_t,type,
t: int ).
thf(tp_times_times_int,type,
times_times_int: int > int > int ).
thf(tp_times_times_nat,type,
times_times_nat: nat > nat > nat ).
thf(tp_times_times_real,type,
times_times_real: real > real > real ).
thf(tp_twoSqu362149276sum2sq,type,
twoSqu362149276sum2sq: int > $o ).
thf(tp_zcong,type,
zcong: int > int > int > $o ).
thf(tp_zero_zero_int,type,
zero_zero_int: int ).
thf(tp_zero_zero_nat,type,
zero_zero_nat: nat ).
thf(tp_zero_zero_real,type,
zero_zero_real: real ).
thf(tp_zprime,type,
zprime: int > $o ).
thf(1,axiom,
! [N: nat,M: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_697_divides__cases) ).
thf(2,axiom,
! [I: nat,M: nat,N: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_696_power__dvd__imp__le) ).
thf(3,axiom,
! [X: nat,Q: nat,N: nat,R: nat] :
( ( X
= ( plus_plus_nat @ ( times_times_nat @ Q @ N ) @ R ) )
=> ( ( ord_less_nat @ zero_zero_nat @ R )
=> ( ( ord_less_nat @ R @ N )
=> ~ ( dvd_dvd_nat @ N @ X ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_695_divides__div__not) ).
thf(4,axiom,
! [X: nat,Y: nat,N: nat] :
( ( N != zero_zero_nat )
=> ( ( dvd_dvd_nat @ ( power_power_nat @ X @ N ) @ Y )
=> ( dvd_dvd_nat @ X @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_694_divides__exp2) ).
thf(5,axiom,
! [A: nat,N: nat,B: nat] :
( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
=> ( ( N != zero_zero_nat )
=> ( dvd_dvd_nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_693_divides__rev) ).
thf(6,axiom,
! [M: nat,K: nat,N: nat] :
( ( dvd_dvd_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
<=> ( ( K = zero_zero_nat )
| ( dvd_dvd_nat @ M @ N ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_692_nat__mult__dvd__cancel__disj_H) ).
thf(7,axiom,
! [B: nat,D: nat,A: nat] :
( ( dvd_dvd_nat @ D @ A )
=> ( ( dvd_dvd_nat @ D @ ( plus_plus_nat @ A @ B ) )
=> ( dvd_dvd_nat @ D @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_691_divides__add__revr) ).
thf(8,axiom,
! [C: nat,A: nat,B: nat] :
( ( dvd_dvd_nat @ A @ B )
=> ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_690_divides__mul__r) ).
thf(9,axiom,
! [C: nat,A: nat,B: nat] :
( ( dvd_dvd_nat @ A @ B )
=> ( dvd_dvd_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_689_divides__mul__l) ).
thf(10,axiom,
! [N: nat,X: nat,Y: nat] :
( ( dvd_dvd_nat @ X @ Y )
=> ( dvd_dvd_nat @ ( power_power_nat @ X @ N ) @ ( power_power_nat @ Y @ N ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_688_divides__exp) ).
thf(11,axiom,
! [A: nat,B: nat] :
( ( dvd_dvd_nat @ A @ B )
=> ( ( B = zero_zero_nat )
| ( ord_less_eq_nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_687_divides__ge) ).
thf(12,axiom,
! [A: real,N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
=> ( ( ord_less_real @ zero_zero_real @ A )
=> ? [X_1: real] :
( ( ord_less_real @ zero_zero_real @ X_1 )
& ( ( power_power_real @ X_1 @ N )
= A )
& ! [Y_1: real] :
( ( ( ord_less_real @ zero_zero_real @ Y_1 )
& ( ( power_power_real @ Y_1 @ N )
= A ) )
=> ( Y_1 = X_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_686_realpow__pos__nth__unique) ).
thf(13,axiom,
! [A_1: int,N_2: nat,N_1: nat] :
( ( ord_less_nat @ N_2 @ N_1 )
=> ( ( ord_less_int @ zero_zero_int @ A_1 )
=> ( ( ord_less_int @ A_1 @ one_one_int )
=> ( ord_less_int @ ( power_power_int @ A_1 @ N_1 ) @ ( power_power_int @ A_1 @ N_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_685_power__strict__decreasing) ).
thf(14,axiom,
! [N_3: nat,A_2: int] :
( ( ord_less_int @ zero_zero_int @ A_2 )
=> ( ( ord_less_int @ A_2 @ one_one_int )
=> ( ord_less_int @ ( times_times_int @ A_2 @ ( power_power_int @ A_2 @ N_3 ) ) @ ( power_power_int @ A_2 @ N_3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_684_power__Suc__less) ).
thf(15,axiom,
! [N_3: nat,A_2: nat] :
( ( ord_less_nat @ zero_zero_nat @ A_2 )
=> ( ( ord_less_nat @ A_2 @ one_one_nat )
=> ( ord_less_nat @ ( times_times_nat @ A_2 @ ( power_power_nat @ A_2 @ N_3 ) ) @ ( power_power_nat @ A_2 @ N_3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_683_power__Suc__less) ).
thf(16,axiom,
! [N_3: nat,A_2: real] :
( ( ord_less_real @ zero_zero_real @ A_2 )
=> ( ( ord_less_real @ A_2 @ one_one_real )
=> ( ord_less_real @ ( times_times_real @ A_2 @ ( power_power_real @ A_2 @ N_3 ) ) @ ( power_power_real @ A_2 @ N_3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_682_power__Suc__less) ).
thf(17,axiom,
! [A_3: int,N_5: nat,N_4: nat] :
( ( ord_less_eq_nat @ N_5 @ N_4 )
=> ( ( ord_less_eq_int @ one_one_int @ A_3 )
=> ( ord_less_eq_int @ ( power_power_int @ A_3 @ N_5 ) @ ( power_power_int @ A_3 @ N_4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_681_power__increasing) ).
thf(18,axiom,
! [A_3: nat,N_5: nat,N_4: nat] :
( ( ord_less_eq_nat @ N_5 @ N_4 )
=> ( ( ord_less_eq_nat @ one_one_nat @ A_3 )
=> ( ord_less_eq_nat @ ( power_power_nat @ A_3 @ N_5 ) @ ( power_power_nat @ A_3 @ N_4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_680_power__increasing) ).
thf(19,axiom,
! [A_3: real,N_5: nat,N_4: nat] :
( ( ord_less_eq_nat @ N_5 @ N_4 )
=> ( ( ord_less_eq_real @ one_one_real @ A_3 )
=> ( ord_less_eq_real @ ( power_power_real @ A_3 @ N_5 ) @ ( power_power_real @ A_3 @ N_4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_679_power__increasing) ).
thf(20,axiom,
! [X_2: nat,Y_2: nat,B_1: int] :
( ( ord_less_int @ one_one_int @ B_1 )
=> ( ( ord_less_int @ ( power_power_int @ B_1 @ X_2 ) @ ( power_power_int @ B_1 @ Y_2 ) )
<=> ( ord_less_nat @ X_2 @ Y_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_678_power__strict__increasing__iff) ).
thf(21,axiom,
! [X_2: nat,Y_2: nat,B_1: nat] :
( ( ord_less_nat @ one_one_nat @ B_1 )
=> ( ( ord_less_nat @ ( power_power_nat @ B_1 @ X_2 ) @ ( power_power_nat @ B_1 @ Y_2 ) )
<=> ( ord_less_nat @ X_2 @ Y_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_677_power__strict__increasing__iff) ).
thf(22,axiom,
! [X_2: nat,Y_2: nat,B_1: real] :
( ( ord_less_real @ one_one_real @ B_1 )
=> ( ( ord_less_real @ ( power_power_real @ B_1 @ X_2 ) @ ( power_power_real @ B_1 @ Y_2 ) )
<=> ( ord_less_nat @ X_2 @ Y_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_676_power__strict__increasing__iff) ).
thf(23,axiom,
! [M_1: nat,N_6: nat,A_4: int] :
( ( ord_less_int @ one_one_int @ A_4 )
=> ( ( ord_less_int @ ( power_power_int @ A_4 @ M_1 ) @ ( power_power_int @ A_4 @ N_6 ) )
=> ( ord_less_nat @ M_1 @ N_6 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_675_power__less__imp__less__exp) ).
thf(24,axiom,
! [M_1: nat,N_6: nat,A_4: nat] :
( ( ord_less_nat @ one_one_nat @ A_4 )
=> ( ( ord_less_nat @ ( power_power_nat @ A_4 @ M_1 ) @ ( power_power_nat @ A_4 @ N_6 ) )
=> ( ord_less_nat @ M_1 @ N_6 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_674_power__less__imp__less__exp) ).
thf(25,axiom,
! [M_1: nat,N_6: nat,A_4: real] :
( ( ord_less_real @ one_one_real @ A_4 )
=> ( ( ord_less_real @ ( power_power_real @ A_4 @ M_1 ) @ ( power_power_real @ A_4 @ N_6 ) )
=> ( ord_less_nat @ M_1 @ N_6 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_673_power__less__imp__less__exp) ).
thf(26,axiom,
! [A_5: int,N_8: nat,N_7: nat] :
( ( ord_less_nat @ N_8 @ N_7 )
=> ( ( ord_less_int @ one_one_int @ A_5 )
=> ( ord_less_int @ ( power_power_int @ A_5 @ N_8 ) @ ( power_power_int @ A_5 @ N_7 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_672_power__strict__increasing) ).
thf(27,axiom,
! [A_5: nat,N_8: nat,N_7: nat] :
( ( ord_less_nat @ N_8 @ N_7 )
=> ( ( ord_less_nat @ one_one_nat @ A_5 )
=> ( ord_less_nat @ ( power_power_nat @ A_5 @ N_8 ) @ ( power_power_nat @ A_5 @ N_7 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_671_power__strict__increasing) ).
thf(28,axiom,
! [A_5: real,N_8: nat,N_7: nat] :
( ( ord_less_nat @ N_8 @ N_7 )
=> ( ( ord_less_real @ one_one_real @ A_5 )
=> ( ord_less_real @ ( power_power_real @ A_5 @ N_8 ) @ ( power_power_real @ A_5 @ N_7 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_670_power__strict__increasing) ).
thf(29,axiom,
! [N_9: nat] :
( ( ( N_9 = zero_zero_nat )
=> ( ( power_power_int @ zero_zero_int @ N_9 )
= one_one_int ) )
& ( ( N_9 != zero_zero_nat )
=> ( ( power_power_int @ zero_zero_int @ N_9 )
= zero_zero_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_669_power__0__left) ).
thf(30,axiom,
! [N_9: nat] :
( ( ( N_9 = zero_zero_nat )
=> ( ( power_power_nat @ zero_zero_nat @ N_9 )
= one_one_nat ) )
& ( ( N_9 != zero_zero_nat )
=> ( ( power_power_nat @ zero_zero_nat @ N_9 )
= zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_668_power__0__left) ).
thf(31,axiom,
! [N_9: nat] :
( ( ( N_9 = zero_zero_nat )
=> ( ( power_power_real @ zero_zero_real @ N_9 )
= one_one_real ) )
& ( ( N_9 != zero_zero_nat )
=> ( ( power_power_real @ zero_zero_real @ N_9 )
= zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_667_power__0__left) ).
thf(32,axiom,
! [N_10: nat,A_6: int] :
( ( ord_less_int @ one_one_int @ A_6 )
=> ( ord_less_int @ one_one_int @ ( times_times_int @ A_6 @ ( power_power_int @ A_6 @ N_10 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_666_power__gt1__lemma) ).
thf(33,axiom,
! [N_10: nat,A_6: nat] :
( ( ord_less_nat @ one_one_nat @ A_6 )
=> ( ord_less_nat @ one_one_nat @ ( times_times_nat @ A_6 @ ( power_power_nat @ A_6 @ N_10 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_665_power__gt1__lemma) ).
thf(34,axiom,
! [N_10: nat,A_6: real] :
( ( ord_less_real @ one_one_real @ A_6 )
=> ( ord_less_real @ one_one_real @ ( times_times_real @ A_6 @ ( power_power_real @ A_6 @ N_10 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_664_power__gt1__lemma) ).
thf(35,axiom,
! [N_11: nat,A_7: int] :
( ( ord_less_int @ one_one_int @ A_7 )
=> ( ord_less_int @ ( power_power_int @ A_7 @ N_11 ) @ ( times_times_int @ A_7 @ ( power_power_int @ A_7 @ N_11 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_663_power__less__power__Suc) ).
thf(36,axiom,
! [N_11: nat,A_7: nat] :
( ( ord_less_nat @ one_one_nat @ A_7 )
=> ( ord_less_nat @ ( power_power_nat @ A_7 @ N_11 ) @ ( times_times_nat @ A_7 @ ( power_power_nat @ A_7 @ N_11 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_662_power__less__power__Suc) ).
thf(37,axiom,
! [N_11: nat,A_7: real] :
( ( ord_less_real @ one_one_real @ A_7 )
=> ( ord_less_real @ ( power_power_real @ A_7 @ N_11 ) @ ( times_times_real @ A_7 @ ( power_power_real @ A_7 @ N_11 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_661_power__less__power__Suc) ).
thf(38,axiom,
! [A_8: int,N_12: nat,B_2: int] :
( ( ord_less_int @ ( power_power_int @ A_8 @ N_12 ) @ ( power_power_int @ B_2 @ N_12 ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ B_2 )
=> ( ord_less_int @ A_8 @ B_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_660_power__less__imp__less__base) ).
thf(39,axiom,
! [A_8: nat,N_12: nat,B_2: nat] :
( ( ord_less_nat @ ( power_power_nat @ A_8 @ N_12 ) @ ( power_power_nat @ B_2 @ N_12 ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B_2 )
=> ( ord_less_nat @ A_8 @ B_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_659_power__less__imp__less__base) ).
thf(40,axiom,
! [A_8: real,N_12: nat,B_2: real] :
( ( ord_less_real @ ( power_power_real @ A_8 @ N_12 ) @ ( power_power_real @ B_2 @ N_12 ) )
=> ( ( ord_less_eq_real @ zero_zero_real @ B_2 )
=> ( ord_less_real @ A_8 @ B_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_658_power__less__imp__less__base) ).
thf(41,axiom,
! [X: nat,N: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X @ N ) )
<=> ( ( ord_less_nat @ zero_zero_nat @ X )
| ( N = zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_657_nat__zero__less__power__iff) ).
thf(42,axiom,
! [M: nat,N: nat,I: nat] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_656_nat__power__less__imp__less) ).
thf(43,axiom,
! [A_9: real,M_2: nat,N_13: nat] :
( ( ord_less_eq_nat @ M_2 @ N_13 )
=> ( dvd_dvd_real @ ( power_power_real @ A_9 @ M_2 ) @ ( power_power_real @ A_9 @ N_13 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_655_le__imp__power__dvd) ).
thf(44,axiom,
! [A_9: int,M_2: nat,N_13: nat] :
( ( ord_less_eq_nat @ M_2 @ N_13 )
=> ( dvd_dvd_int @ ( power_power_int @ A_9 @ M_2 ) @ ( power_power_int @ A_9 @ N_13 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_654_le__imp__power__dvd) ).
thf(45,axiom,
! [A_9: nat,M_2: nat,N_13: nat] :
( ( ord_less_eq_nat @ M_2 @ N_13 )
=> ( dvd_dvd_nat @ ( power_power_nat @ A_9 @ M_2 ) @ ( power_power_nat @ A_9 @ N_13 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_653_le__imp__power__dvd) ).
thf(46,axiom,
! [N_14: nat,M_3: nat,X_3: real,Y_3: real] :
( ( dvd_dvd_real @ X_3 @ Y_3 )
=> ( ( ord_less_eq_nat @ N_14 @ M_3 )
=> ( dvd_dvd_real @ ( power_power_real @ X_3 @ N_14 ) @ ( power_power_real @ Y_3 @ M_3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_652_dvd__power__le) ).
thf(47,axiom,
! [N_14: nat,M_3: nat,X_3: int,Y_3: int] :
( ( dvd_dvd_int @ X_3 @ Y_3 )
=> ( ( ord_less_eq_nat @ N_14 @ M_3 )
=> ( dvd_dvd_int @ ( power_power_int @ X_3 @ N_14 ) @ ( power_power_int @ Y_3 @ M_3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_651_dvd__power__le) ).
thf(48,axiom,
! [N_14: nat,M_3: nat,X_3: nat,Y_3: nat] :
( ( dvd_dvd_nat @ X_3 @ Y_3 )
=> ( ( ord_less_eq_nat @ N_14 @ M_3 )
=> ( dvd_dvd_nat @ ( power_power_nat @ X_3 @ N_14 ) @ ( power_power_nat @ Y_3 @ M_3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_650_dvd__power__le) ).
thf(49,axiom,
! [M_4: nat,A_10: real,N_15: nat,B_3: real] :
( ( dvd_dvd_real @ ( power_power_real @ A_10 @ N_15 ) @ B_3 )
=> ( ( ord_less_eq_nat @ M_4 @ N_15 )
=> ( dvd_dvd_real @ ( power_power_real @ A_10 @ M_4 ) @ B_3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_649_power__le__dvd) ).
thf(50,axiom,
! [M_4: nat,A_10: int,N_15: nat,B_3: int] :
( ( dvd_dvd_int @ ( power_power_int @ A_10 @ N_15 ) @ B_3 )
=> ( ( ord_less_eq_nat @ M_4 @ N_15 )
=> ( dvd_dvd_int @ ( power_power_int @ A_10 @ M_4 ) @ B_3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_648_power__le__dvd) ).
thf(51,axiom,
! [M_4: nat,A_10: nat,N_15: nat,B_3: nat] :
( ( dvd_dvd_nat @ ( power_power_nat @ A_10 @ N_15 ) @ B_3 )
=> ( ( ord_less_eq_nat @ M_4 @ N_15 )
=> ( dvd_dvd_nat @ ( power_power_nat @ A_10 @ M_4 ) @ B_3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_647_power__le__dvd) ).
thf(52,axiom,
! [A_11: int,M_5: nat,N_16: nat] :
( ( power_power_int @ A_11 @ ( plus_plus_nat @ M_5 @ N_16 ) )
= ( times_times_int @ ( power_power_int @ A_11 @ M_5 ) @ ( power_power_int @ A_11 @ N_16 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_646_power__add) ).
thf(53,axiom,
! [A_11: nat,M_5: nat,N_16: nat] :
( ( power_power_nat @ A_11 @ ( plus_plus_nat @ M_5 @ N_16 ) )
= ( times_times_nat @ ( power_power_nat @ A_11 @ M_5 ) @ ( power_power_nat @ A_11 @ N_16 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_645_power__add) ).
thf(54,axiom,
! [A_11: real,M_5: nat,N_16: nat] :
( ( power_power_real @ A_11 @ ( plus_plus_nat @ M_5 @ N_16 ) )
= ( times_times_real @ ( power_power_real @ A_11 @ M_5 ) @ ( power_power_real @ A_11 @ N_16 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_644_power__add) ).
thf(55,axiom,
! [A_12: int] :
( ( power_power_int @ A_12 @ zero_zero_nat )
= one_one_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_643_power__0) ).
thf(56,axiom,
! [A_12: nat] :
( ( power_power_nat @ A_12 @ zero_zero_nat )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_642_power__0) ).
thf(57,axiom,
! [A_12: real] :
( ( power_power_real @ A_12 @ zero_zero_nat )
= one_one_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_641_power__0) ).
thf(58,axiom,
! [A_13: int,N_17: nat] :
( ( ( power_power_int @ A_13 @ N_17 )
= zero_zero_int )
<=> ( ( A_13 = zero_zero_int )
& ( N_17 != zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_640_power__eq__0__iff) ).
thf(59,axiom,
! [A_13: nat,N_17: nat] :
( ( ( power_power_nat @ A_13 @ N_17 )
= zero_zero_nat )
<=> ( ( A_13 = zero_zero_nat )
& ( N_17 != zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_639_power__eq__0__iff) ).
thf(60,axiom,
! [A_13: real,N_17: nat] :
( ( ( power_power_real @ A_13 @ N_17 )
= zero_zero_real )
<=> ( ( A_13 = zero_zero_real )
& ( N_17 != zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_638_power__eq__0__iff) ).
thf(61,axiom,
! [M_6: nat,N_18: nat,A_14: int] :
( ( ord_less_int @ one_one_int @ A_14 )
=> ( ( ( power_power_int @ A_14 @ M_6 )
= ( power_power_int @ A_14 @ N_18 ) )
<=> ( M_6 = N_18 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_637_power__inject__exp) ).
thf(62,axiom,
! [M_6: nat,N_18: nat,A_14: nat] :
( ( ord_less_nat @ one_one_nat @ A_14 )
=> ( ( ( power_power_nat @ A_14 @ M_6 )
= ( power_power_nat @ A_14 @ N_18 ) )
<=> ( M_6 = N_18 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_636_power__inject__exp) ).
thf(63,axiom,
! [M_6: nat,N_18: nat,A_14: real] :
( ( ord_less_real @ one_one_real @ A_14 )
=> ( ( ( power_power_real @ A_14 @ M_6 )
= ( power_power_real @ A_14 @ N_18 ) )
<=> ( M_6 = N_18 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_635_power__inject__exp) ).
thf(64,axiom,
! [N_19: nat,A_15: int] :
( ( ord_less_eq_int @ one_one_int @ A_15 )
=> ( ord_less_eq_int @ one_one_int @ ( power_power_int @ A_15 @ N_19 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_634_one__le__power) ).
thf(65,axiom,
! [N_19: nat,A_15: nat] :
( ( ord_less_eq_nat @ one_one_nat @ A_15 )
=> ( ord_less_eq_nat @ one_one_nat @ ( power_power_nat @ A_15 @ N_19 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_633_one__le__power) ).
thf(66,axiom,
! [N_19: nat,A_15: real] :
( ( ord_less_eq_real @ one_one_real @ A_15 )
=> ( ord_less_eq_real @ one_one_real @ ( power_power_real @ A_15 @ N_19 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_632_one__le__power) ).
thf(67,axiom,
! [N_20: nat,A_16: int] :
( ( ord_less_int @ zero_zero_int @ A_16 )
=> ( ord_less_int @ zero_zero_int @ ( power_power_int @ A_16 @ N_20 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_631_zero__less__power) ).
thf(68,axiom,
! [N_20: nat,A_16: nat] :
( ( ord_less_nat @ zero_zero_nat @ A_16 )
=> ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A_16 @ N_20 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_630_zero__less__power) ).
thf(69,axiom,
! [N_20: nat,A_16: real] :
( ( ord_less_real @ zero_zero_real @ A_16 )
=> ( ord_less_real @ zero_zero_real @ ( power_power_real @ A_16 @ N_20 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_629_zero__less__power) ).
thf(70,axiom,
! [N_21: nat,A_17: int] :
( ( ord_less_eq_int @ zero_zero_int @ A_17 )
=> ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A_17 @ N_21 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_628_zero__le__power) ).
thf(71,axiom,
! [N_21: nat,A_17: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ A_17 )
=> ( ord_less_eq_nat @ zero_zero_nat @ ( power_power_nat @ A_17 @ N_21 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_627_zero__le__power) ).
thf(72,axiom,
! [N_21: nat,A_17: real] :
( ( ord_less_eq_real @ zero_zero_real @ A_17 )
=> ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A_17 @ N_21 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_626_zero__le__power) ).
thf(73,axiom,
! [N_22: nat,A_18: int,B_4: int] :
( ( ord_less_eq_int @ A_18 @ B_4 )
=> ( ( ord_less_eq_int @ zero_zero_int @ A_18 )
=> ( ord_less_eq_int @ ( power_power_int @ A_18 @ N_22 ) @ ( power_power_int @ B_4 @ N_22 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_625_power__mono) ).
thf(74,axiom,
! [N_22: nat,A_18: nat,B_4: nat] :
( ( ord_less_eq_nat @ A_18 @ B_4 )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A_18 )
=> ( ord_less_eq_nat @ ( power_power_nat @ A_18 @ N_22 ) @ ( power_power_nat @ B_4 @ N_22 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_624_power__mono) ).
thf(75,axiom,
! [N_22: nat,A_18: real,B_4: real] :
( ( ord_less_eq_real @ A_18 @ B_4 )
=> ( ( ord_less_eq_real @ zero_zero_real @ A_18 )
=> ( ord_less_eq_real @ ( power_power_real @ A_18 @ N_22 ) @ ( power_power_real @ B_4 @ N_22 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_623_power__mono) ).
thf(76,axiom,
! [A_19: int] :
( ( power_power_int @ A_19 @ one_one_nat )
= A_19 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_622_power__one__right) ).
thf(77,axiom,
! [A_19: nat] :
( ( power_power_nat @ A_19 @ one_one_nat )
= A_19 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_621_power__one__right) ).
thf(78,axiom,
! [A_19: real] :
( ( power_power_real @ A_19 @ one_one_nat )
= A_19 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_620_power__one__right) ).
thf(79,axiom,
! [A_20: int,M_7: nat,N_23: nat] :
( ( power_power_int @ A_20 @ ( times_times_nat @ M_7 @ N_23 ) )
= ( power_power_int @ ( power_power_int @ A_20 @ M_7 ) @ N_23 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_619_power__mult) ).
thf(80,axiom,
! [A_20: nat,M_7: nat,N_23: nat] :
( ( power_power_nat @ A_20 @ ( times_times_nat @ M_7 @ N_23 ) )
= ( power_power_nat @ ( power_power_nat @ A_20 @ M_7 ) @ N_23 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_618_power__mult) ).
thf(81,axiom,
! [A_20: real,M_7: nat,N_23: nat] :
( ( power_power_real @ A_20 @ ( times_times_nat @ M_7 @ N_23 ) )
= ( power_power_real @ ( power_power_real @ A_20 @ M_7 ) @ N_23 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_617_power__mult) ).
thf(82,axiom,
! [N_24: nat,X_4: real,Y_4: real] :
( ( dvd_dvd_real @ X_4 @ Y_4 )
=> ( dvd_dvd_real @ ( power_power_real @ X_4 @ N_24 ) @ ( power_power_real @ Y_4 @ N_24 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_616_dvd__power__same) ).
thf(83,axiom,
! [N_24: nat,X_4: int,Y_4: int] :
( ( dvd_dvd_int @ X_4 @ Y_4 )
=> ( dvd_dvd_int @ ( power_power_int @ X_4 @ N_24 ) @ ( power_power_int @ Y_4 @ N_24 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_615_dvd__power__same) ).
thf(84,axiom,
! [N_24: nat,X_4: nat,Y_4: nat] :
( ( dvd_dvd_nat @ X_4 @ Y_4 )
=> ( dvd_dvd_nat @ ( power_power_nat @ X_4 @ N_24 ) @ ( power_power_nat @ Y_4 @ N_24 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_614_dvd__power__same) ).
thf(85,axiom,
! [N_25: nat] :
( ( power_power_int @ one_one_int @ N_25 )
= one_one_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_613_power__one) ).
thf(86,axiom,
! [N_25: nat] :
( ( power_power_nat @ one_one_nat @ N_25 )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_612_power__one) ).
thf(87,axiom,
! [N_25: nat] :
( ( power_power_real @ one_one_real @ N_25 )
= one_one_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_611_power__one) ).
thf(88,axiom,
! [A_21: int,N_26: nat] :
( ( times_times_int @ ( power_power_int @ A_21 @ N_26 ) @ A_21 )
= ( times_times_int @ A_21 @ ( power_power_int @ A_21 @ N_26 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_610_power__commutes) ).
thf(89,axiom,
! [A_21: nat,N_26: nat] :
( ( times_times_nat @ ( power_power_nat @ A_21 @ N_26 ) @ A_21 )
= ( times_times_nat @ A_21 @ ( power_power_nat @ A_21 @ N_26 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_609_power__commutes) ).
thf(90,axiom,
! [A_21: real,N_26: nat] :
( ( times_times_real @ ( power_power_real @ A_21 @ N_26 ) @ A_21 )
= ( times_times_real @ A_21 @ ( power_power_real @ A_21 @ N_26 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_608_power__commutes) ).
thf(91,axiom,
! [A_22: int,B_5: int,N_27: nat] :
( ( power_power_int @ ( times_times_int @ A_22 @ B_5 ) @ N_27 )
= ( times_times_int @ ( power_power_int @ A_22 @ N_27 ) @ ( power_power_int @ B_5 @ N_27 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_607_power__mult__distrib) ).
thf(92,axiom,
! [A_22: nat,B_5: nat,N_27: nat] :
( ( power_power_nat @ ( times_times_nat @ A_22 @ B_5 ) @ N_27 )
= ( times_times_nat @ ( power_power_nat @ A_22 @ N_27 ) @ ( power_power_nat @ B_5 @ N_27 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_606_power__mult__distrib) ).
thf(93,axiom,
! [A_22: real,B_5: real,N_27: nat] :
( ( power_power_real @ ( times_times_real @ A_22 @ B_5 ) @ N_27 )
= ( times_times_real @ ( power_power_real @ A_22 @ N_27 ) @ ( power_power_real @ B_5 @ N_27 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_605_power__mult__distrib) ).
thf(94,axiom,
! [N_28: nat,A_23: int] :
( ( A_23 != zero_zero_int )
=> ( ( power_power_int @ A_23 @ N_28 )
!= zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_604_field__power__not__zero) ).
thf(95,axiom,
! [N_28: nat,A_23: real] :
( ( A_23 != zero_zero_real )
=> ( ( power_power_real @ A_23 @ N_28 )
!= zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_603_field__power__not__zero) ).
thf(100,axiom,
! [N_29: nat,A_24: int,B_6: int] :
( ( ord_less_int @ A_24 @ B_6 )
=> ( ( ord_less_eq_int @ zero_zero_int @ A_24 )
=> ( ( ord_less_nat @ zero_zero_nat @ N_29 )
=> ( ord_less_int @ ( power_power_int @ A_24 @ N_29 ) @ ( power_power_int @ B_6 @ N_29 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_598_power__strict__mono) ).
thf(101,axiom,
! [N_29: nat,A_24: nat,B_6: nat] :
( ( ord_less_nat @ A_24 @ B_6 )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A_24 )
=> ( ( ord_less_nat @ zero_zero_nat @ N_29 )
=> ( ord_less_nat @ ( power_power_nat @ A_24 @ N_29 ) @ ( power_power_nat @ B_6 @ N_29 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_597_power__strict__mono) ).
thf(102,axiom,
! [N_29: nat,A_24: real,B_6: real] :
( ( ord_less_real @ A_24 @ B_6 )
=> ( ( ord_less_eq_real @ zero_zero_real @ A_24 )
=> ( ( ord_less_nat @ zero_zero_nat @ N_29 )
=> ( ord_less_real @ ( power_power_real @ A_24 @ N_29 ) @ ( power_power_real @ B_6 @ N_29 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_596_power__strict__mono) ).
thf(103,axiom,
! [M_8: int,N_30: nat] :
( ( ( N_30 = zero_zero_nat )
=> ( ( power_power_int @ M_8 @ N_30 )
= one_one_int ) )
& ( ( N_30 != zero_zero_nat )
=> ( ( power_power_int @ M_8 @ N_30 )
= ( times_times_int @ M_8 @ ( power_power_int @ M_8 @ ( minus_minus_nat @ N_30 @ one_one_nat ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_595_realpow__num__eq__if) ).
thf(104,axiom,
! [M_8: nat,N_30: nat] :
( ( ( N_30 = zero_zero_nat )
=> ( ( power_power_nat @ M_8 @ N_30 )
= one_one_nat ) )
& ( ( N_30 != zero_zero_nat )
=> ( ( power_power_nat @ M_8 @ N_30 )
= ( times_times_nat @ M_8 @ ( power_power_nat @ M_8 @ ( minus_minus_nat @ N_30 @ one_one_nat ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_594_realpow__num__eq__if) ).
thf(105,axiom,
! [M_8: real,N_30: nat] :
( ( ( N_30 = zero_zero_nat )
=> ( ( power_power_real @ M_8 @ N_30 )
= one_one_real ) )
& ( ( N_30 != zero_zero_nat )
=> ( ( power_power_real @ M_8 @ N_30 )
= ( times_times_real @ M_8 @ ( power_power_real @ M_8 @ ( minus_minus_nat @ N_30 @ one_one_nat ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_593_realpow__num__eq__if) ).
thf(106,axiom,
! [N: nat] : ( ord_less_eq_real @ one_one_real @ ( power_power_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ N ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_592_two__realpow__ge__one) ).
thf(107,axiom,
! [X_5: int,N_31: nat] :
( ( ord_less_nat @ zero_zero_nat @ N_31 )
=> ( ( times_times_int @ ( power_power_int @ X_5 @ ( minus_minus_nat @ N_31 @ one_one_nat ) ) @ X_5 )
= ( power_power_int @ X_5 @ N_31 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_591_realpow__minus__mult) ).
thf(108,axiom,
! [X_5: nat,N_31: nat] :
( ( ord_less_nat @ zero_zero_nat @ N_31 )
=> ( ( times_times_nat @ ( power_power_nat @ X_5 @ ( minus_minus_nat @ N_31 @ one_one_nat ) ) @ X_5 )
= ( power_power_nat @ X_5 @ N_31 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_590_realpow__minus__mult) ).
thf(109,axiom,
! [X_5: real,N_31: nat] :
( ( ord_less_nat @ zero_zero_nat @ N_31 )
=> ( ( times_times_real @ ( power_power_real @ X_5 @ ( minus_minus_nat @ N_31 @ one_one_nat ) ) @ X_5 )
= ( power_power_real @ X_5 @ N_31 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_589_realpow__minus__mult) ).
thf(110,axiom,
! [X_6: int] :
( ( minus_minus_int @ ( times_times_int @ X_6 @ X_6 ) @ one_one_int )
= ( times_times_int @ ( plus_plus_int @ X_6 @ one_one_int ) @ ( minus_minus_int @ X_6 @ one_one_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_588_real__squared__diff__one__factored) ).
thf(111,axiom,
! [X_6: real] :
( ( minus_minus_real @ ( times_times_real @ X_6 @ X_6 ) @ one_one_real )
= ( times_times_real @ ( plus_plus_real @ X_6 @ one_one_real ) @ ( minus_minus_real @ X_6 @ one_one_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_587_real__squared__diff__one__factored) ).
thf(112,axiom,
! [X: nat,N: nat] :
( ( ( power_power_nat @ X @ N )
= one_one_nat )
<=> ( ( X = one_one_nat )
| ( N = zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_586_exp__eq__1) ).
thf(113,axiom,
! [X: real,Y: real] :
( ( ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) )
= zero_zero_real )
<=> ( ( X = zero_zero_real )
& ( Y = zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_585_real__two__squares__add__zero__iff) ).
thf(114,axiom,
! [X: real,Y: real,Z: real] :
( ( ord_less_real @ zero_zero_real @ Z )
=> ( ( ord_less_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ Y @ Z ) )
<=> ( ord_less_real @ X @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_584_real__mult__less__iff1) ).
thf(115,axiom,
! [Y: real,X: real] :
( ( ord_less_real @ zero_zero_real @ X )
=> ( ( ord_less_real @ zero_zero_real @ Y )
=> ( ord_less_real @ zero_zero_real @ ( times_times_real @ X @ Y ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_583_real__mult__order) ).
thf(116,axiom,
! [X: real,Y: real,Z: real] :
( ( ord_less_real @ zero_zero_real @ Z )
=> ( ( ord_less_real @ X @ Y )
=> ( ord_less_real @ ( times_times_real @ Z @ X ) @ ( times_times_real @ Z @ Y ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_582_real__mult__less__mono2) ).
thf(117,axiom,
! [X: real,Y: real,Z: real] :
( ( ord_less_real @ zero_zero_real @ Z )
=> ( ( ord_less_eq_real @ ( times_times_real @ Z @ X ) @ ( times_times_real @ Z @ Y ) )
<=> ( ord_less_eq_real @ X @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_581_real__mult__le__cancel__iff2) ).
thf(118,axiom,
! [X: real,Y: real,Z: real] :
( ( ord_less_real @ zero_zero_real @ Z )
=> ( ( ord_less_eq_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ Y @ Z ) )
<=> ( ord_less_eq_real @ X @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_580_real__mult__le__cancel__iff1) ).
thf(119,axiom,
! [X_7: int,Y_5: int,A_25: int,B_7: int] :
( ( minus_minus_int @ ( times_times_int @ X_7 @ Y_5 ) @ ( times_times_int @ A_25 @ B_7 ) )
= ( plus_plus_int @ ( times_times_int @ X_7 @ ( minus_minus_int @ Y_5 @ B_7 ) ) @ ( times_times_int @ ( minus_minus_int @ X_7 @ A_25 ) @ B_7 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_579_mult__diff__mult) ).
thf(120,axiom,
! [X_7: real,Y_5: real,A_25: real,B_7: real] :
( ( minus_minus_real @ ( times_times_real @ X_7 @ Y_5 ) @ ( times_times_real @ A_25 @ B_7 ) )
= ( plus_plus_real @ ( times_times_real @ X_7 @ ( minus_minus_real @ Y_5 @ B_7 ) ) @ ( times_times_real @ ( minus_minus_real @ X_7 @ A_25 ) @ B_7 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_578_mult__diff__mult) ).
thf(121,axiom,
! [M: nat,N: nat] :
( ( ( power_power_nat @ M @ N )
= zero_zero_nat )
<=> ( ( N != zero_zero_nat )
& ( M = zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_577_nat__power__eq__0__iff) ).
thf(122,axiom,
! [Z1: real,Z2: real,W: real] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_576_real__add__mult__distrib) ).
thf(123,axiom,
! [N: nat,M: nat] :
( ( ( times_times_nat @ N @ M )
= one_one_nat )
<=> ( ( N = one_one_nat )
& ( M = one_one_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_575_nat__mult__eq__one) ).
thf(124,axiom,
! [A: real,B: real,C: real] :
( ( C != zero_zero_real )
=> ( ( ( times_times_real @ A @ C )
= ( times_times_real @ B @ C ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_574_real__mult__right__cancel) ).
thf(125,axiom,
! [A: real,B: real,C: real] :
( ( C != zero_zero_real )
=> ( ( ( times_times_real @ C @ A )
= ( times_times_real @ C @ B ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_573_real__mult__left__cancel) ).
thf(126,axiom,
! [A_26: int,C_1: int,B_8: int,D_1: int] :
( ( minus_minus_int @ ( plus_plus_int @ A_26 @ C_1 ) @ ( plus_plus_int @ B_8 @ D_1 ) )
= ( plus_plus_int @ ( minus_minus_int @ A_26 @ B_8 ) @ ( minus_minus_int @ C_1 @ D_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_572_add__diff__add) ).
thf(127,axiom,
! [A_26: real,C_1: real,B_8: real,D_1: real] :
( ( minus_minus_real @ ( plus_plus_real @ A_26 @ C_1 ) @ ( plus_plus_real @ B_8 @ D_1 ) )
= ( plus_plus_real @ ( minus_minus_real @ A_26 @ B_8 ) @ ( minus_minus_real @ C_1 @ D_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_571_add__diff__add) ).
thf(128,axiom,
! [Z: real,X: real,Y: real] :
( ( ord_less_eq_real @ X @ Y )
=> ( ord_less_eq_real @ ( plus_plus_real @ Z @ X ) @ ( plus_plus_real @ Z @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_570_real__add__left__mono) ).
thf(129,axiom,
! [Z: real] :
( ( times_times_real @ one_one_real @ Z )
= Z ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_569_real__mult__1) ).
thf(130,axiom,
! [Z: real,W: real] :
( ( times_times_real @ Z @ W )
= ( times_times_real @ W @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_568_real__mult__commute) ).
thf(131,axiom,
! [Z1: real,Z2: real,Z3: real] :
( ( times_times_real @ ( times_times_real @ Z1 @ Z2 ) @ Z3 )
= ( times_times_real @ Z1 @ ( times_times_real @ Z2 @ Z3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_567_real__mult__assoc) ).
thf(132,axiom,
! [X: real,Y: real] :
( ( ord_less_eq_real @ X @ Y )
<=> ( ( ord_less_real @ X @ Y )
| ( X = Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_566_less__eq__real__def) ).
thf(133,axiom,
! [X: real,Y: real] :
( ( ord_less_real @ X @ Y )
<=> ( ( ord_less_eq_real @ X @ Y )
& ( X != Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_565_real__less__def) ).
thf(135,axiom,
zero_zero_real != one_one_real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_563_real__zero__not__eq__one) ).
thf(136,axiom,
! [X: real,Y: real] :
( ( ( plus_plus_real @ ( power_power_real @ X @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_real )
<=> ( ( X = zero_zero_real )
& ( Y = zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_562_realpow__two__sum__zero__iff) ).
thf(137,axiom,
! [X: nat,Y: nat] :
( ( minus_minus_nat @ ( power_power_nat @ X @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_nat @ Y @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( times_times_nat @ ( plus_plus_nat @ X @ Y ) @ ( minus_minus_nat @ X @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_561_diff__square) ).
thf(138,axiom,
! [P: nat,M: nat] :
( ( ( 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/sandbox2/benchmark/theBenchmark.p',fact_560_power__eq__if) ).
thf(139,axiom,
! [N: nat,M: nat] :
( ( ( 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/sandbox2/benchmark/theBenchmark.p',fact_559_mult__eq__if) ).
thf(140,axiom,
! [X: real,Y: real] :
( ( power_power_real @ ( plus_plus_real @ X @ Y ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_real @ ( plus_plus_real @ ( power_power_real @ X @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ X ) @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_558_real__sum__squared__expand) ).
thf(141,axiom,
! [M: int,X: int] :
( ( quadRes @ M @ X )
<=> ? [Y_1: int] : ( zcong @ ( power_power_int @ Y_1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ X @ M ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_557_QuadRes__def) ).
thf(142,axiom,
! [A: int,P: int] :
( ( ( zcong @ A @ zero_zero_int @ P )
=> ( ( legendre @ A @ P )
= zero_zero_int ) )
& ( ~ ( zcong @ A @ zero_zero_int @ P )
=> ( ( ( quadRes @ P @ A )
=> ( ( legendre @ A @ P )
= one_one_int ) )
& ( ~ ( quadRes @ P @ A )
=> ( ( legendre @ A @ P )
= ( number_number_of_int @ min ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_556_Legendre__def) ).
thf(143,axiom,
! [M: int] :
( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ M )
=> ~ ( zcong @ one_one_int @ ( number_number_of_int @ min ) @ M ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_555_one__not__neg__one__mod__m) ).
thf(144,axiom,
! [M: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_554_Legendre__1mod4) ).
thf(145,axiom,
! [Y: int,N: nat,P: int] :
( ( zprime @ P )
=> ( ( dvd_dvd_int @ P @ ( power_power_int @ Y @ N ) )
=> ( ( ord_less_nat @ zero_zero_nat @ N )
=> ( dvd_dvd_int @ P @ Y ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_553_zpower__zdvd__prop2) ).
thf(146,axiom,
! [B: int,A: int,P: int] :
( ( zprime @ P )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ( zcong @ ( times_times_int @ A @ B ) @ zero_zero_int @ P )
=> ( ( zcong @ A @ zero_zero_int @ P )
| ( zcong @ B @ zero_zero_int @ P ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_552_zcong__zprime__prod__zero) ).
thf(147,axiom,
! [B: int,A: int,P: int] :
( ( zprime @ P )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ( ~ ( zcong @ A @ zero_zero_int @ P )
& ~ ( zcong @ B @ zero_zero_int @ P ) )
=> ~ ( zcong @ ( times_times_int @ A @ B ) @ zero_zero_int @ P ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_551_zcong__zprime__prod__zero__contra) ).
thf(148,axiom,
! [Y: int,X: int,P: int] :
( ( zprime @ P )
=> ( ~ ( zcong @ X @ zero_zero_int @ P )
=> ( ~ ( zcong @ Y @ zero_zero_int @ P )
=> ~ ( zcong @ ( times_times_int @ X @ Y ) @ zero_zero_int @ P ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_550_zcong__zmult__prop3) ).
thf(149,axiom,
! [N: nat] :
( ( ( 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/sandbox2/benchmark/theBenchmark.p',fact_549_neg__one__power) ).
thf(150,axiom,
! [P: int,Y: int,N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
=> ( ( dvd_dvd_int @ P @ Y )
=> ( dvd_dvd_int @ P @ ( power_power_int @ Y @ N ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_548_zpower__zdvd__prop1) ).
thf(151,axiom,
! [M: int,X: int] :
( ( ord_less_eq_int @ zero_zero_int @ X )
=> ( ( ord_less_int @ X @ M )
=> ( ( zcong @ X @ zero_zero_int @ M )
=> ( X = zero_zero_int ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_547_Int2_Ozcong__zero) ).
thf(152,axiom,
! [M: int,N: int,P: int] :
( ( zprime @ P )
=> ( ( dvd_dvd_int @ P @ ( times_times_int @ M @ N ) )
=> ( ( dvd_dvd_int @ P @ M )
| ( dvd_dvd_int @ P @ N ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_546_zprime__zdvd__zmult__better) ).
thf(153,axiom,
! [X: int,P: int] :
( ( zcong @ X @ zero_zero_int @ P )
<=> ( dvd_dvd_int @ P @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_545_zcong__eq__zdvd__prop) ).
thf(154,axiom,
! [A: int,M: int] :
( ( zcong @ A @ zero_zero_int @ M )
<=> ( dvd_dvd_int @ M @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_544_zcong__zero__equiv__div) ).
thf(155,axiom,
! [N: int,M: int] :
( ( dvd_dvd_int @ N @ M )
=> ( ( ord_less_eq_int @ M @ zero_zero_int )
| ( ord_less_eq_int @ N @ M ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_543_zdvd__bounds) ).
thf(156,axiom,
! [M: int,X: int] :
( ( ord_less_int @ zero_zero_int @ X )
=> ( ( ord_less_int @ X @ M )
=> ~ ( zcong @ X @ zero_zero_int @ M ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_542_zcong__not__zero) ).
thf(157,axiom,
! [M: int,Y: int,X: int] :
( ( ord_less_int @ zero_zero_int @ X )
=> ( ( ord_less_int @ zero_zero_int @ Y )
=> ( ( ord_less_int @ zero_zero_int @ M )
=> ( ( zcong @ X @ Y @ M )
=> ( ( ord_less_int @ X @ M )
=> ( ( ord_less_int @ Y @ M )
=> ( X = Y ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_541_zcong__less__eq) ).
thf(158,axiom,
! [A: int,B: int] :
( ( power_power_int @ ( minus_minus_int @ A @ B ) @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( minus_minus_int @ ( plus_plus_int @ ( minus_minus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ B ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) @ A ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_540_zdiff__power3) ).
thf(159,axiom,
! [A: int,B: int] :
( ( power_power_int @ ( minus_minus_int @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ ( minus_minus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_539_zdiff__power2) ).
thf(160,axiom,
! [X_8: int,Y_6: int] :
( ( power_power_int @ ( minus_minus_int @ X_8 @ Y_6 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( minus_minus_int @ ( plus_plus_int @ ( power_power_int @ X_8 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_6 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ X_8 ) @ Y_6 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_538_power2__diff) ).
thf(161,axiom,
! [X_8: real,Y_6: real] :
( ( power_power_real @ ( minus_minus_real @ X_8 @ Y_6 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( minus_minus_real @ ( plus_plus_real @ ( power_power_real @ X_8 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y_6 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ X_8 ) @ Y_6 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_537_power2__diff) ).
thf(162,axiom,
! [Z: nat,X: int,Y: int,M: int] :
( ( zcong @ X @ Y @ M )
=> ( zcong @ ( power_power_int @ X @ Z ) @ ( power_power_int @ Y @ Z ) @ M ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_536_zcong__zpower) ).
thf(163,axiom,
! [C: int,A: int,B: int,M: int] :
( ( zcong @ A @ B @ M )
=> ( zcong @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) @ M ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_535_zcong__shift) ).
thf(164,axiom,
! [C: int,D: int,A: int,B: int,M: int] :
( ( zcong @ A @ B @ M )
=> ( ( zcong @ C @ ( times_times_int @ A @ D ) @ M )
<=> ( zcong @ C @ ( times_times_int @ B @ D ) @ M ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_534_zcong__zmult__prop1) ).
thf(165,axiom,
! [C: int,D: int,A: int,B: int,M: int] :
( ( zcong @ A @ B @ M )
=> ( ( zcong @ C @ ( times_times_int @ D @ A ) @ M )
<=> ( zcong @ C @ ( times_times_int @ D @ B ) @ M ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_533_zcong__zmult__prop2) ).
thf(166,axiom,
! [M: int] : ( zcong @ M @ zero_zero_int @ M ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_532_zcong__id) ).
thf(167,axiom,
! [A: int,B: int] :
( ( times_times_int @ ( plus_plus_int @ A @ B ) @ ( minus_minus_int @ A @ B ) )
= ( minus_minus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_531_zspecial__product) ).
thf(168,axiom,
! [A: int,P: int] :
( ( zprime @ P )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ( zcong @ ( times_times_int @ A @ A ) @ one_one_int @ P )
=> ( ( zcong @ A @ one_one_int @ P )
| ( zcong @ A @ ( minus_minus_int @ P @ one_one_int ) @ P ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_530_zcong__square) ).
thf(169,axiom,
! [A: int,P: int] :
( ( zprime @ P )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ( ord_less_int @ A @ P )
=> ( ( zcong @ ( times_times_int @ A @ A ) @ one_one_int @ P )
=> ( ( A = one_one_int )
| ( A
= ( minus_minus_int @ P @ one_one_int ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_529_zcong__square__zless) ).
thf(170,axiom,
! [D: int,C: int,A: int,B: int,M: int] :
( ( zcong @ A @ B @ M )
=> ( ( B = C )
=> ( ( zcong @ C @ D @ M )
=> ( zcong @ A @ D @ M ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_528_zcong__eq__trans) ).
thf(171,axiom,
! [A: int,P: int] :
( ( zcong @ ( times_times_int @ A @ ( minus_minus_int @ P @ one_one_int ) ) @ one_one_int @ P )
<=> ( zcong @ A @ ( minus_minus_int @ P @ one_one_int ) @ P ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_527_inv__not__p__minus__1__aux) ).
thf(172,axiom,
! [L: int] :
( ( minus_minus_int @ min @ ( bit0 @ L ) )
= ( bit1 @ ( minus_minus_int @ min @ L ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_526_diff__bin__simps_I5_J) ).
thf(173,axiom,
! [L: int] :
( ( minus_minus_int @ min @ ( bit1 @ L ) )
= ( bit0 @ ( minus_minus_int @ min @ L ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_525_diff__bin__simps_I6_J) ).
thf(174,axiom,
! [L: int] :
( ( minus_minus_int @ pls @ ( bit1 @ L ) )
= ( bit1 @ ( minus_minus_int @ min @ L ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_524_diff__bin__simps_I4_J) ).
thf(175,axiom,
! [W: int,Z: int] :
( ( ord_less_eq_int @ W @ ( minus_minus_int @ Z @ one_one_int ) )
<=> ( ord_less_int @ W @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_523_zle__diff1__eq) ).
thf(176,axiom,
! [A: int,X: int] :
( ( ord_less_int @ zero_zero_int @ X )
=> ( ( ord_less_int @ X @ A )
=> ( ( X
!= ( minus_minus_int @ A @ one_one_int ) )
=> ( ord_less_int @ X @ ( minus_minus_int @ A @ one_one_int ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_522_Euler_Oaux1) ).
thf(177,axiom,
! [V: int,W_1: int,C_2: int] :
( ( plus_plus_int @ ( number_number_of_int @ V ) @ ( minus_minus_int @ ( number_number_of_int @ W_1 ) @ C_2 ) )
= ( minus_minus_int @ ( number_number_of_int @ ( plus_plus_int @ V @ W_1 ) ) @ C_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_521_add__number__of__diff1) ).
thf(178,axiom,
! [V: int,W_1: int,C_2: real] :
( ( plus_plus_real @ ( number267125858f_real @ V ) @ ( minus_minus_real @ ( number267125858f_real @ W_1 ) @ C_2 ) )
= ( minus_minus_real @ ( number267125858f_real @ ( plus_plus_int @ V @ W_1 ) ) @ C_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_520_add__number__of__diff1) ).
thf(179,axiom,
! [A: int,B: int,M: int] :
( ( zcong @ A @ B @ M )
<=> ( dvd_dvd_int @ M @ ( minus_minus_int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_519_zcong__def) ).
thf(180,axiom,
! [A: int,R: int,B: int,M: int,C: int,D: int,N: int] :
( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ ( times_times_int @ R @ B ) ) @ M ) @ ( times_times_int @ ( minus_minus_int @ C @ ( times_times_int @ R @ D ) ) @ N ) )
= ( minus_minus_int @ ( plus_plus_int @ ( times_times_int @ A @ M ) @ ( times_times_int @ C @ N ) ) @ ( times_times_int @ R @ ( plus_plus_int @ ( times_times_int @ B @ M ) @ ( times_times_int @ D @ N ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_518_xzgcda__linear__aux1) ).
thf(181,axiom,
! [K: int,L: int] :
( ( ord_less_int @ K @ L )
<=> ( ord_less_int @ ( minus_minus_int @ K @ L ) @ zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_517_less__bin__lemma) ).
thf(182,axiom,
! [L: int] :
( ( minus_minus_int @ pls @ ( bit0 @ L ) )
= ( bit0 @ ( minus_minus_int @ pls @ L ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_516_diff__bin__simps_I3_J) ).
thf(183,axiom,
! [K: int,L: int] :
( ( minus_minus_int @ ( bit1 @ K ) @ ( bit1 @ L ) )
= ( bit0 @ ( minus_minus_int @ K @ L ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_515_diff__bin__simps_I10_J) ).
thf(184,axiom,
! [K: int,L: int] :
( ( minus_minus_int @ ( bit1 @ K ) @ ( bit0 @ L ) )
= ( bit1 @ ( minus_minus_int @ K @ L ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_514_diff__bin__simps_I9_J) ).
thf(185,axiom,
! [A_27: int,B_9: int,V_1: int] :
( ( times_times_int @ ( minus_minus_int @ A_27 @ B_9 ) @ ( number_number_of_int @ V_1 ) )
= ( minus_minus_int @ ( times_times_int @ A_27 @ ( number_number_of_int @ V_1 ) ) @ ( times_times_int @ B_9 @ ( number_number_of_int @ V_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_513_left__diff__distrib__number__of) ).
thf(186,axiom,
! [A_27: real,B_9: real,V_1: int] :
( ( times_times_real @ ( minus_minus_real @ A_27 @ B_9 ) @ ( number267125858f_real @ V_1 ) )
= ( minus_minus_real @ ( times_times_real @ A_27 @ ( number267125858f_real @ V_1 ) ) @ ( times_times_real @ B_9 @ ( number267125858f_real @ V_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_512_left__diff__distrib__number__of) ).
thf(187,axiom,
! [V_2: int,B_10: int,C_3: int] :
( ( times_times_int @ ( number_number_of_int @ V_2 ) @ ( minus_minus_int @ B_10 @ C_3 ) )
= ( minus_minus_int @ ( times_times_int @ ( number_number_of_int @ V_2 ) @ B_10 ) @ ( times_times_int @ ( number_number_of_int @ V_2 ) @ C_3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_511_right__diff__distrib__number__of) ).
thf(188,axiom,
! [V_2: int,B_10: real,C_3: real] :
( ( times_times_real @ ( number267125858f_real @ V_2 ) @ ( minus_minus_real @ B_10 @ C_3 ) )
= ( minus_minus_real @ ( times_times_real @ ( number267125858f_real @ V_2 ) @ B_10 ) @ ( times_times_real @ ( number267125858f_real @ V_2 ) @ C_3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_510_right__diff__distrib__number__of) ).
thf(189,axiom,
! [V_3: int,W_2: int] :
( ( number_number_of_int @ ( minus_minus_int @ V_3 @ W_2 ) )
= ( minus_minus_int @ ( number_number_of_int @ V_3 ) @ ( number_number_of_int @ W_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_509_number__of__diff) ).
thf(190,axiom,
! [V_3: int,W_2: int] :
( ( number267125858f_real @ ( minus_minus_int @ V_3 @ W_2 ) )
= ( minus_minus_real @ ( number267125858f_real @ V_3 ) @ ( number267125858f_real @ W_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_508_number__of__diff) ).
thf(191,axiom,
! [A: int,B: int,C: int] :
( ( ( minus_minus_int @ A @ B )
= C )
=> ( A
= ( plus_plus_int @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_507_Int2_Oaux1) ).
thf(192,axiom,
! [K: int] :
( ( minus_minus_int @ K @ pls )
= K ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_506_diff__bin__simps_I1_J) ).
thf(193,axiom,
! [K: int,L: int] :
( ( minus_minus_int @ ( bit0 @ K ) @ ( bit0 @ L ) )
= ( bit0 @ ( minus_minus_int @ K @ L ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_505_diff__bin__simps_I7_J) ).
thf(194,axiom,
! [Z1: int,Z2: int,W: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_504_zdiff__zmult__distrib) ).
thf(195,axiom,
! [W: int,Z1: int,Z2: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_503_zdiff__zmult__distrib2) ).
thf(196,axiom,
! [K: int,M: int,N: int] :
( ( dvd_dvd_int @ K @ ( minus_minus_int @ M @ N ) )
=> ( ( dvd_dvd_int @ K @ N )
=> ( dvd_dvd_int @ K @ M ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_502_zdvd__zdiffD) ).
thf(197,axiom,
! [C: int,D: int,A: int,B: int,M: int] :
( ( zcong @ A @ B @ M )
=> ( ( zcong @ C @ D @ M )
=> ( zcong @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D ) @ M ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_501_zcong__zdiff) ).
thf(198,axiom,
! [X: real] :
( ~ ( ord_less_real @ zero_zero_real @ ( times_times_real @ X @ X ) )
<=> ( X = zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_500_not__real__square__gt__zero) ).
thf(200,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/sandbox2/benchmark/theBenchmark.p',fact_498__096s_A_094_A2_A_N_A_N1_A_061_As_A_094_A2_A_L_A1_096) ).
thf(201,axiom,
! [X: int,P: int] :
( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ P )
=> ( ( zcong @ X @ ( number_number_of_int @ min ) @ P )
=> ~ ( zcong @ X @ one_one_int @ P ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_497_zcong__neg__1__impl__ne__1) ).
thf(202,axiom,
! [J: nat,K: nat,M: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_496_neg__one__power__eq__mod__m) ).
thf(203,axiom,
dvd_dvd_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ ( minus_minus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_int @ min ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_495__0964_A_K_Am_A_L_A1_Advd_As_A_094_A2_A_N_A_N1_096) ).
thf(204,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/sandbox2/benchmark/theBenchmark.p',fact_494__096QuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_096) ).
thf(205,axiom,
! [N: int,P: int,M: int] :
( ( ord_less_eq_int @ zero_zero_int @ M )
=> ( ( zprime @ P )
=> ( ( dvd_dvd_int @ P @ ( times_times_int @ M @ N ) )
=> ( ( dvd_dvd_int @ P @ M )
| ( dvd_dvd_int @ P @ N ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_493_zprime__zdvd__zmult) ).
thf(206,axiom,
! [Z: nat,X: int,Y: nat,P: int] :
( ( zcong @ ( power_power_int @ X @ Y ) @ one_one_int @ P )
=> ( zcong @ ( power_power_int @ X @ ( times_times_nat @ Y @ Z ) ) @ one_one_int @ P ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_492_zcong__zpower__zmult) ).
thf(207,axiom,
! [B: int,M: int,A: int] :
( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( ord_less_int @ A @ M )
=> ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_int @ B @ M )
=> ( ( zcong @ A @ B @ M )
=> ( A = B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_491_zcong__zless__imp__eq) ).
thf(208,axiom,
! [M: int,A: int] :
( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( ord_less_int @ A @ M )
=> ( ( zcong @ A @ zero_zero_int @ M )
=> ( A = zero_zero_int ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_490_zcong__zless__0) ).
thf(209,axiom,
! [X: real] :
( ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ X @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( power_power_real @ ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ X ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_489_four__x__squared) ).
thf(210,axiom,
! [A: int,B: int,M: int] :
( ( zcong @ A @ B @ M )
<=> ? [K_1: int] :
( B
= ( plus_plus_int @ A @ ( times_times_int @ M @ K_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_488_zcong__iff__lin) ).
thf(211,axiom,
! [B: int,M: int,A: int] :
( ( ord_less_int @ zero_zero_int @ A )
=> ( ( ord_less_int @ A @ M )
=> ( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ord_less_int @ B @ A )
=> ~ ( zcong @ A @ B @ M ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_487_zcong__not) ).
thf(212,axiom,
! [N_32: nat] :
( ( power_power_int @ ( number_number_of_int @ min ) @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ N_32 ) )
= one_one_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_486_power__m1__even) ).
thf(213,axiom,
! [N_32: nat] :
( ( power_power_real @ ( number267125858f_real @ min ) @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ N_32 ) )
= one_one_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_485_power__m1__even) ).
thf(214,axiom,
! [C: int,D: int,A: int,B: int,M: int] :
( ( zcong @ A @ B @ M )
=> ( ( zcong @ C @ D @ M )
=> ( zcong @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) @ M ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_484_zcong__zadd) ).
thf(215,axiom,
! [C: int,D: int,A: int,B: int,M: int] :
( ( zcong @ A @ B @ M )
=> ( ( zcong @ C @ D @ M )
=> ( zcong @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) @ M ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_483_zcong__zmult) ).
thf(216,axiom,
! [K: int,A: int,B: int,M: int] :
( ( zcong @ A @ B @ M )
=> ( zcong @ ( times_times_int @ K @ A ) @ ( times_times_int @ K @ B ) @ M ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_482_zcong__scalar2) ).
thf(217,axiom,
! [K: int,A: int,B: int,M: int] :
( ( zcong @ A @ B @ M )
=> ( zcong @ ( times_times_int @ A @ K ) @ ( times_times_int @ B @ K ) @ M ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_481_zcong__scalar) ).
thf(218,axiom,
! [A: int,M: int,B: int] : ( zcong @ ( times_times_int @ A @ M ) @ ( times_times_int @ B @ M ) @ M ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_480_zcong__zmult__self) ).
thf(219,axiom,
! [A: int,B: int] : ( zcong @ A @ B @ one_one_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_479_zcong__1) ).
thf(220,axiom,
! [A: int,B: int] :
( ( zcong @ A @ B @ zero_zero_int )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_478_IntPrimes_Ozcong__zero) ).
thf(221,axiom,
! [B: int,A: int,C: int] :
( ( ord_less_int @ A @ C )
=> ( ( ord_less_int @ B @ C )
=> ( ( ord_less_eq_int @ A @ B )
| ( ord_less_eq_int @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_477_Euler_Oaux2) ).
thf(222,axiom,
! [X_9: int,Y_7: int] :
( ( ord_less_eq_int @ X_9 @ Y_7 )
=> ( ( X_9 != Y_7 )
=> ( ord_less_int @ X_9 @ Y_7 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_476_order__le__neq__implies__less) ).
thf(223,axiom,
! [X_9: nat,Y_7: nat] :
( ( ord_less_eq_nat @ X_9 @ Y_7 )
=> ( ( X_9 != Y_7 )
=> ( ord_less_nat @ X_9 @ Y_7 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_475_order__le__neq__implies__less) ).
thf(224,axiom,
! [X_9: real,Y_7: real] :
( ( ord_less_eq_real @ X_9 @ Y_7 )
=> ( ( X_9 != Y_7 )
=> ( ord_less_real @ X_9 @ Y_7 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_474_order__le__neq__implies__less) ).
thf(225,axiom,
! [C: int,A: int,B: int,M: int] :
( ( zcong @ A @ B @ M )
=> ( ( zcong @ B @ C @ M )
=> ( zcong @ A @ C @ M ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_473_zcong__trans) ).
thf(226,axiom,
! [K: int,M: int] : ( zcong @ K @ K @ M ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_472_zcong__refl) ).
thf(227,axiom,
! [A: int,B: int,M: int] :
( ( zcong @ A @ B @ M )
<=> ( zcong @ B @ A @ M ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_471_zcong__sym) ).
thf(228,axiom,
! [M: int,N: int] :
( ( ( times_times_int @ M @ N )
= one_one_int )
=> ( ( M = one_one_int )
| ( M
= ( number_number_of_int @ min ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_470_pos__zmult__eq__1__iff__lemma) ).
thf(229,axiom,
! [M: int,N: int] :
( ( ( times_times_int @ M @ N )
= one_one_int )
<=> ( ( ( M = one_one_int )
& ( N = one_one_int ) )
| ( ( M
= ( number_number_of_int @ min ) )
& ( N
= ( number_number_of_int @ min ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_469_zmult__eq__1__iff) ).
thf(230,axiom,
! [K: int] :
( ( ord_less_eq_int @ min @ ( bit0 @ K ) )
<=> ( ord_less_int @ min @ K ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_468_rel__simps_I25_J) ).
thf(231,axiom,
! [K: int] :
( ( ord_less_int @ ( bit0 @ K ) @ min )
<=> ( ord_less_eq_int @ K @ min ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_467_rel__simps_I11_J) ).
thf(232,axiom,
( ( number_number_of_int @ pls )
!= ( number_number_of_int @ min ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_466_eq__number__of__Pls__Min) ).
thf(233,axiom,
! [K: int] :
( ( ord_less_eq_int @ ( bit0 @ K ) @ min )
<=> ( ord_less_eq_int @ K @ min ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_465_rel__simps_I28_J) ).
thf(234,axiom,
~ ( ord_less_eq_int @ pls @ min ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_464_rel__simps_I20_J) ).
thf(235,axiom,
ord_less_eq_int @ min @ pls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_463_rel__simps_I23_J) ).
thf(236,axiom,
! [K: int] :
( ( ord_less_eq_int @ ( bit1 @ K ) @ min )
<=> ( ord_less_eq_int @ K @ min ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_462_rel__simps_I30_J) ).
thf(237,axiom,
! [K: int] :
( ( ord_less_eq_int @ min @ ( bit1 @ K ) )
<=> ( ord_less_eq_int @ min @ K ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_461_rel__simps_I26_J) ).
thf(238,axiom,
ord_less_int @ min @ zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_460_bin__less__0__simps_I2_J) ).
thf(239,axiom,
! [K: int] :
( ( ord_less_int @ min @ ( bit0 @ K ) )
<=> ( ord_less_int @ min @ K ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_459_rel__simps_I8_J) ).
thf(240,axiom,
ord_less_int @ min @ pls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_458_rel__simps_I6_J) ).
thf(241,axiom,
~ ( ord_less_int @ pls @ min ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_457_rel__simps_I3_J) ).
thf(242,axiom,
! [K: int] :
( ( ord_less_int @ min @ ( bit1 @ K ) )
<=> ( ord_less_int @ min @ K ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_456_rel__simps_I9_J) ).
thf(243,axiom,
! [K: int] :
( ( ord_less_int @ ( bit1 @ K ) @ min )
<=> ( ord_less_int @ K @ min ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_455_rel__simps_I13_J) ).
thf(244,axiom,
ord_less_eq_int @ min @ min,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_454_rel__simps_I24_J) ).
thf(245,axiom,
~ ( ord_less_int @ min @ min ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_453_rel__simps_I7_J) ).
thf(246,axiom,
! [K: int] :
( ( bit0 @ K )
!= min ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_452_rel__simps_I45_J) ).
thf(247,axiom,
! [L: int] :
( min
!= ( bit0 @ L ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_451_rel__simps_I42_J) ).
thf(248,axiom,
pls != min,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_450_rel__simps_I37_J) ).
thf(249,axiom,
min != pls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_449_rel__simps_I40_J) ).
thf(250,axiom,
! [K: int] :
( ( ( bit1 @ K )
= min )
<=> ( K = min ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_448_rel__simps_I47_J) ).
thf(251,axiom,
! [L: int] :
( ( min
= ( bit1 @ L ) )
<=> ( min = L ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_447_rel__simps_I43_J) ).
thf(252,axiom,
( ( bit1 @ min )
= min ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_446_Bit1__Min) ).
thf(254,axiom,
~ ! [S1: int] :
~ ( 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/sandbox2/benchmark/theBenchmark.p',fact_444__096_B_Bthesis_O_A_I_B_Bs1_O_A_091s1_A_094_A2_A_061_A_N1_093_A_Imod_A4_) ).
thf(255,axiom,
ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_443_pos2) ).
thf(256,axiom,
! [P: int] :
( ( zprime @ P )
=> ( ( P
!= ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
=> ( ( P
!= ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) )
=> ( ord_less_eq_int @ ( number_number_of_int @ ( bit1 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ P ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_442_prime__g__5) ).
thf(257,axiom,
! [P: int] :
( ( zprime @ P )
<=> ( ( ord_less_int @ one_one_int @ P )
& ! [M_9: int] :
( ( ( ord_less_eq_int @ zero_zero_int @ M_9 )
& ( dvd_dvd_int @ M_9 @ P ) )
=> ( ( M_9 = one_one_int )
| ( M_9 = P ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_441_zprime__def) ).
thf(258,axiom,
! [Y: int,X: int,P: int] :
( ~ ( zcong @ X @ zero_zero_int @ P )
=> ( ( zcong @ ( power_power_int @ Y @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ X @ P )
=> ~ ( dvd_dvd_int @ P @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_440_Euler_Oaux____1) ).
thf(259,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/sandbox2/benchmark/theBenchmark.p',fact_439_s) ).
thf(260,axiom,
! [X_10: int] :
( ( times_times_int @ X_10 @ X_10 )
= ( power_power_int @ X_10 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_438_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
thf(261,axiom,
! [X_10: nat] :
( ( times_times_nat @ X_10 @ X_10 )
= ( power_power_nat @ X_10 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_437_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
thf(262,axiom,
! [X_10: real] :
( ( times_times_real @ X_10 @ X_10 )
= ( power_power_real @ X_10 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_436_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
thf(263,axiom,
! [X: int] :
( ( power_power_int @ ( power_power_int @ X @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power_int @ X @ ( number_number_of_nat @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_435_quartic__square__square) ).
thf(264,axiom,
! [B: int,Q: int,R: int,B_11: int,Q_1: int,R_1: int] :
( ( ( plus_plus_int @ ( times_times_int @ B @ Q ) @ R )
= ( plus_plus_int @ ( times_times_int @ B_11 @ Q_1 ) @ R_1 ) )
=> ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ B_11 @ Q_1 ) @ R_1 ) @ zero_zero_int )
=> ( ( ord_less_int @ R @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ R_1 )
=> ( ( ord_less_int @ zero_zero_int @ B_11 )
=> ( ( ord_less_eq_int @ B_11 @ B )
=> ( ord_less_eq_int @ Q_1 @ Q ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_434_zdiv__mono2__neg__lemma) ).
thf(265,axiom,
! [B: int,Q_1: int,R_1: int,Q: int,R: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q_1 ) @ R_1 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q ) @ R ) )
=> ( ( ord_less_eq_int @ R @ zero_zero_int )
=> ( ( ord_less_int @ B @ R )
=> ( ( ord_less_int @ B @ R_1 )
=> ( ord_less_eq_int @ Q @ Q_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_433_unique__quotient__lemma__neg) ).
thf(266,axiom,
! [B: int,Q: int,R: int,B_11: int,Q_1: int,R_1: int] :
( ( ( plus_plus_int @ ( times_times_int @ B @ Q ) @ R )
= ( plus_plus_int @ ( times_times_int @ B_11 @ Q_1 ) @ R_1 ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B_11 @ Q_1 ) @ R_1 ) )
=> ( ( ord_less_int @ R_1 @ B_11 )
=> ( ( ord_less_eq_int @ zero_zero_int @ R )
=> ( ( ord_less_int @ zero_zero_int @ B_11 )
=> ( ( ord_less_eq_int @ B_11 @ B )
=> ( ord_less_eq_int @ Q @ Q_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_432_zdiv__mono2__lemma) ).
thf(267,axiom,
! [B: int,Q_1: int,R_1: int,Q: int,R: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q_1 ) @ R_1 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q ) @ R ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ R_1 )
=> ( ( ord_less_int @ R_1 @ B )
=> ( ( ord_less_int @ R @ B )
=> ( ord_less_eq_int @ Q_1 @ Q ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_431_unique__quotient__lemma) ).
thf(268,axiom,
! [B_11: int,Q_1: int,R_1: int] :
( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ B_11 @ Q_1 ) @ R_1 ) @ zero_zero_int )
=> ( ( ord_less_eq_int @ zero_zero_int @ R_1 )
=> ( ( ord_less_int @ zero_zero_int @ B_11 )
=> ( ord_less_eq_int @ Q_1 @ zero_zero_int ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_430_q__neg__lemma) ).
thf(269,axiom,
! [B_11: int,Q_1: int,R_1: int] :
( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B_11 @ Q_1 ) @ R_1 ) )
=> ( ( ord_less_int @ R_1 @ B_11 )
=> ( ( ord_less_int @ zero_zero_int @ B_11 )
=> ( ord_less_eq_int @ zero_zero_int @ Q_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_429_q__pos__lemma) ).
thf(270,axiom,
ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_428_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J) ).
thf(271,axiom,
! [W_3: int] :
( ( ( ( number_number_of_nat @ W_3 )
= zero_zero_nat )
=> ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ W_3 ) )
= one_one_int ) )
& ( ( ( number_number_of_nat @ W_3 )
!= zero_zero_nat )
=> ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ W_3 ) )
= zero_zero_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_427_power__0__left__number__of) ).
thf(272,axiom,
! [W_3: int] :
( ( ( ( number_number_of_nat @ W_3 )
= zero_zero_nat )
=> ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ W_3 ) )
= one_one_nat ) )
& ( ( ( number_number_of_nat @ W_3 )
!= zero_zero_nat )
=> ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ W_3 ) )
= zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_426_power__0__left__number__of) ).
thf(273,axiom,
! [W_3: int] :
( ( ( ( number_number_of_nat @ W_3 )
= zero_zero_nat )
=> ( ( power_power_real @ zero_zero_real @ ( number_number_of_nat @ W_3 ) )
= one_one_real ) )
& ( ( ( number_number_of_nat @ W_3 )
!= zero_zero_nat )
=> ( ( power_power_real @ zero_zero_real @ ( number_number_of_nat @ W_3 ) )
= zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_425_power__0__left__number__of) ).
thf(274,axiom,
! [N: nat,X: int] :
( ( ord_less_eq_int @ zero_zero_int @ X )
=> ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ X @ N ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_424_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) ).
thf(275,axiom,
! [Y: int,X: int] :
( ( ord_less_eq_int @ zero_zero_int @ X )
=> ( ( ord_less_eq_int @ zero_zero_int @ Y )
=> ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ X @ Y ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_423_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) ).
thf(276,axiom,
! [Y: int,X: int] :
( ( ord_less_eq_int @ zero_zero_int @ X )
=> ( ( ord_less_eq_int @ zero_zero_int @ Y )
=> ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ X @ Y ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_422_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) ).
thf(277,axiom,
ord_less_eq_int @ zero_zero_int @ one_one_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_421_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).
thf(278,axiom,
! [B: int,A: int] :
( ( ord_less_int @ zero_zero_int @ A )
=> ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
=> ( ord_less_int @ zero_zero_int @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_420_pos__zmult__pos) ).
thf(279,axiom,
! [A_28: int,W_4: int] :
( ( ( power_power_int @ A_28 @ ( number_number_of_nat @ W_4 ) )
= zero_zero_int )
<=> ( ( A_28 = zero_zero_int )
& ( ( number_number_of_nat @ W_4 )
!= zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_419_power__eq__0__iff__number__of) ).
thf(280,axiom,
! [A_28: nat,W_4: int] :
( ( ( power_power_nat @ A_28 @ ( number_number_of_nat @ W_4 ) )
= zero_zero_nat )
<=> ( ( A_28 = zero_zero_nat )
& ( ( number_number_of_nat @ W_4 )
!= zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_418_power__eq__0__iff__number__of) ).
thf(281,axiom,
! [A_28: real,W_4: int] :
( ( ( power_power_real @ A_28 @ ( number_number_of_nat @ W_4 ) )
= zero_zero_real )
<=> ( ( A_28 = zero_zero_real )
& ( ( number_number_of_nat @ W_4 )
!= zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_417_power__eq__0__iff__number__of) ).
thf(282,axiom,
! [A_29: int,M_10: int] :
( ( plus_plus_int @ ( times_times_int @ A_29 @ M_10 ) @ M_10 )
= ( times_times_int @ ( plus_plus_int @ A_29 @ one_one_int ) @ M_10 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_416_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
thf(283,axiom,
! [A_29: nat,M_10: nat] :
( ( plus_plus_nat @ ( times_times_nat @ A_29 @ M_10 ) @ M_10 )
= ( times_times_nat @ ( plus_plus_nat @ A_29 @ one_one_nat ) @ M_10 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_415_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
thf(284,axiom,
! [A_29: real,M_10: real] :
( ( plus_plus_real @ ( times_times_real @ A_29 @ M_10 ) @ M_10 )
= ( times_times_real @ ( plus_plus_real @ A_29 @ one_one_real ) @ M_10 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_414_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
thf(285,axiom,
! [M_11: int,A_30: int] :
( ( plus_plus_int @ M_11 @ ( times_times_int @ A_30 @ M_11 ) )
= ( times_times_int @ ( plus_plus_int @ A_30 @ one_one_int ) @ M_11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_413_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
thf(286,axiom,
! [M_11: nat,A_30: nat] :
( ( plus_plus_nat @ M_11 @ ( times_times_nat @ A_30 @ M_11 ) )
= ( times_times_nat @ ( plus_plus_nat @ A_30 @ one_one_nat ) @ M_11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_412_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
thf(287,axiom,
! [M_11: real,A_30: real] :
( ( plus_plus_real @ M_11 @ ( times_times_real @ A_30 @ M_11 ) )
= ( times_times_real @ ( plus_plus_real @ A_30 @ one_one_real ) @ M_11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_411_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
thf(288,axiom,
! [M_12: int] :
( ( plus_plus_int @ M_12 @ M_12 )
= ( times_times_int @ ( plus_plus_int @ one_one_int @ one_one_int ) @ M_12 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_410_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
thf(289,axiom,
! [M_12: nat] :
( ( plus_plus_nat @ M_12 @ M_12 )
= ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) @ M_12 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_409_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
thf(290,axiom,
! [M_12: real] :
( ( plus_plus_real @ M_12 @ M_12 )
= ( times_times_real @ ( plus_plus_real @ one_one_real @ one_one_real ) @ M_12 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_408_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
thf(291,axiom,
! [C_4: int,D_2: int,A_31: int,B_12: int,R_2: int] :
( ( R_2 != zero_zero_int )
=> ( ( ( A_31 = B_12 )
& ( C_4 != D_2 ) )
=> ( ( plus_plus_int @ A_31 @ ( times_times_int @ R_2 @ C_4 ) )
!= ( plus_plus_int @ B_12 @ ( times_times_int @ R_2 @ D_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_407_add__scale__eq__noteq) ).
thf(292,axiom,
! [C_4: nat,D_2: nat,A_31: nat,B_12: nat,R_2: nat] :
( ( R_2 != zero_zero_nat )
=> ( ( ( A_31 = B_12 )
& ( C_4 != D_2 ) )
=> ( ( plus_plus_nat @ A_31 @ ( times_times_nat @ R_2 @ C_4 ) )
!= ( plus_plus_nat @ B_12 @ ( times_times_nat @ R_2 @ D_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_406_add__scale__eq__noteq) ).
thf(293,axiom,
! [C_4: real,D_2: real,A_31: real,B_12: real,R_2: real] :
( ( R_2 != zero_zero_real )
=> ( ( ( A_31 = B_12 )
& ( C_4 != D_2 ) )
=> ( ( plus_plus_real @ A_31 @ ( times_times_real @ R_2 @ C_4 ) )
!= ( plus_plus_real @ B_12 @ ( times_times_real @ R_2 @ D_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_405_add__scale__eq__noteq) ).
thf(294,axiom,
! [A_32: int,N_33: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A_32 @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ N_33 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_404_zero__le__even__power_H) ).
thf(295,axiom,
! [A_32: real,N_33: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A_32 @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ N_33 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_403_zero__le__even__power_H) ).
thf(296,axiom,
ord_less_eq_int @ zero_zero_int @ zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_402_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).
thf(297,axiom,
! [X_11: int] :
( ( power_power_int @ X_11 @ zero_zero_nat )
= one_one_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_401_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
thf(298,axiom,
! [X_11: nat] :
( ( power_power_nat @ X_11 @ zero_zero_nat )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_400_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
thf(299,axiom,
! [X_11: real] :
( ( power_power_real @ X_11 @ zero_zero_nat )
= one_one_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_399_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
thf(300,axiom,
! [X_12: int,P_1: nat,Q_2: nat] :
( ( times_times_int @ ( power_power_int @ X_12 @ P_1 ) @ ( power_power_int @ X_12 @ Q_2 ) )
= ( power_power_int @ X_12 @ ( plus_plus_nat @ P_1 @ Q_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_398_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
thf(301,axiom,
! [X_12: nat,P_1: nat,Q_2: nat] :
( ( times_times_nat @ ( power_power_nat @ X_12 @ P_1 ) @ ( power_power_nat @ X_12 @ Q_2 ) )
= ( power_power_nat @ X_12 @ ( plus_plus_nat @ P_1 @ Q_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_397_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
thf(302,axiom,
! [X_12: real,P_1: nat,Q_2: nat] :
( ( times_times_real @ ( power_power_real @ X_12 @ P_1 ) @ ( power_power_real @ X_12 @ Q_2 ) )
= ( power_power_real @ X_12 @ ( plus_plus_nat @ P_1 @ Q_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_396_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
thf(303,axiom,
! [X_13: int,Y_8: int,Q_3: nat] :
( ( power_power_int @ ( times_times_int @ X_13 @ Y_8 ) @ Q_3 )
= ( times_times_int @ ( power_power_int @ X_13 @ Q_3 ) @ ( power_power_int @ Y_8 @ Q_3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_395_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
thf(304,axiom,
! [X_13: nat,Y_8: nat,Q_3: nat] :
( ( power_power_nat @ ( times_times_nat @ X_13 @ Y_8 ) @ Q_3 )
= ( times_times_nat @ ( power_power_nat @ X_13 @ Q_3 ) @ ( power_power_nat @ Y_8 @ Q_3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_394_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
thf(305,axiom,
! [X_13: real,Y_8: real,Q_3: nat] :
( ( power_power_real @ ( times_times_real @ X_13 @ Y_8 ) @ Q_3 )
= ( times_times_real @ ( power_power_real @ X_13 @ Q_3 ) @ ( power_power_real @ Y_8 @ Q_3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_393_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
thf(306,axiom,
! [A_33: int] :
( ( times_times_int @ A_33 @ one_one_int )
= A_33 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_392_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
thf(307,axiom,
! [A_33: nat] :
( ( times_times_nat @ A_33 @ one_one_nat )
= A_33 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_391_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
thf(308,axiom,
! [A_33: real] :
( ( times_times_real @ A_33 @ one_one_real )
= A_33 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_390_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
thf(309,axiom,
! [A_34: int] :
( ( times_times_int @ one_one_int @ A_34 )
= A_34 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_389_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
thf(310,axiom,
! [A_34: nat] :
( ( times_times_nat @ one_one_nat @ A_34 )
= A_34 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_388_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
thf(311,axiom,
! [A_34: real] :
( ( times_times_real @ one_one_real @ A_34 )
= A_34 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_387_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
thf(312,axiom,
! [W_5: int,Y_9: int,X_14: int,Z_1: int] :
( ( ( plus_plus_int @ ( times_times_int @ W_5 @ Y_9 ) @ ( times_times_int @ X_14 @ Z_1 ) )
= ( plus_plus_int @ ( times_times_int @ W_5 @ Z_1 ) @ ( times_times_int @ X_14 @ Y_9 ) ) )
<=> ( ( W_5 = X_14 )
| ( Y_9 = Z_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_386_crossproduct__eq) ).
thf(313,axiom,
! [W_5: nat,Y_9: nat,X_14: nat,Z_1: nat] :
( ( ( plus_plus_nat @ ( times_times_nat @ W_5 @ Y_9 ) @ ( times_times_nat @ X_14 @ Z_1 ) )
= ( plus_plus_nat @ ( times_times_nat @ W_5 @ Z_1 ) @ ( times_times_nat @ X_14 @ Y_9 ) ) )
<=> ( ( W_5 = X_14 )
| ( Y_9 = Z_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_385_crossproduct__eq) ).
thf(314,axiom,
! [W_5: real,Y_9: real,X_14: real,Z_1: real] :
( ( ( plus_plus_real @ ( times_times_real @ W_5 @ Y_9 ) @ ( times_times_real @ X_14 @ Z_1 ) )
= ( plus_plus_real @ ( times_times_real @ W_5 @ Z_1 ) @ ( times_times_real @ X_14 @ Y_9 ) ) )
<=> ( ( W_5 = X_14 )
| ( Y_9 = Z_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_384_crossproduct__eq) ).
thf(315,axiom,
! [A_35: int,M_13: int,B_13: int] :
( ( plus_plus_int @ ( times_times_int @ A_35 @ M_13 ) @ ( times_times_int @ B_13 @ M_13 ) )
= ( times_times_int @ ( plus_plus_int @ A_35 @ B_13 ) @ M_13 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_383_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
thf(316,axiom,
! [A_35: nat,M_13: nat,B_13: nat] :
( ( plus_plus_nat @ ( times_times_nat @ A_35 @ M_13 ) @ ( times_times_nat @ B_13 @ M_13 ) )
= ( times_times_nat @ ( plus_plus_nat @ A_35 @ B_13 ) @ M_13 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_382_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
thf(317,axiom,
! [A_35: real,M_13: real,B_13: real] :
( ( plus_plus_real @ ( times_times_real @ A_35 @ M_13 ) @ ( times_times_real @ B_13 @ M_13 ) )
= ( times_times_real @ ( plus_plus_real @ A_35 @ B_13 ) @ M_13 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_381_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
thf(318,axiom,
! [A_36: int,B_14: int,C_5: int] :
( ( times_times_int @ ( plus_plus_int @ A_36 @ B_14 ) @ C_5 )
= ( plus_plus_int @ ( times_times_int @ A_36 @ C_5 ) @ ( times_times_int @ B_14 @ C_5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_380_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
thf(319,axiom,
! [A_36: nat,B_14: nat,C_5: nat] :
( ( times_times_nat @ ( plus_plus_nat @ A_36 @ B_14 ) @ C_5 )
= ( plus_plus_nat @ ( times_times_nat @ A_36 @ C_5 ) @ ( times_times_nat @ B_14 @ C_5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_379_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
thf(320,axiom,
! [A_36: real,B_14: real,C_5: real] :
( ( times_times_real @ ( plus_plus_real @ A_36 @ B_14 ) @ C_5 )
= ( plus_plus_real @ ( times_times_real @ A_36 @ C_5 ) @ ( times_times_real @ B_14 @ C_5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_378_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
thf(321,axiom,
! [C_6: int,D_3: int,A_37: int,B_15: int] :
( ( ( A_37 != B_15 )
& ( C_6 != D_3 ) )
<=> ( ( plus_plus_int @ ( times_times_int @ A_37 @ C_6 ) @ ( times_times_int @ B_15 @ D_3 ) )
!= ( plus_plus_int @ ( times_times_int @ A_37 @ D_3 ) @ ( times_times_int @ B_15 @ C_6 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_377_crossproduct__noteq) ).
thf(322,axiom,
! [C_6: nat,D_3: nat,A_37: nat,B_15: nat] :
( ( ( A_37 != B_15 )
& ( C_6 != D_3 ) )
<=> ( ( plus_plus_nat @ ( times_times_nat @ A_37 @ C_6 ) @ ( times_times_nat @ B_15 @ D_3 ) )
!= ( plus_plus_nat @ ( times_times_nat @ A_37 @ D_3 ) @ ( times_times_nat @ B_15 @ C_6 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_376_crossproduct__noteq) ).
thf(323,axiom,
! [C_6: real,D_3: real,A_37: real,B_15: real] :
( ( ( A_37 != B_15 )
& ( C_6 != D_3 ) )
<=> ( ( plus_plus_real @ ( times_times_real @ A_37 @ C_6 ) @ ( times_times_real @ B_15 @ D_3 ) )
!= ( plus_plus_real @ ( times_times_real @ A_37 @ D_3 ) @ ( times_times_real @ B_15 @ C_6 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_375_crossproduct__noteq) ).
thf(324,axiom,
! [X_15: int,Y_10: int,Z_2: int] :
( ( times_times_int @ X_15 @ ( plus_plus_int @ Y_10 @ Z_2 ) )
= ( plus_plus_int @ ( times_times_int @ X_15 @ Y_10 ) @ ( times_times_int @ X_15 @ Z_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_374_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
thf(325,axiom,
! [X_15: nat,Y_10: nat,Z_2: nat] :
( ( times_times_nat @ X_15 @ ( plus_plus_nat @ Y_10 @ Z_2 ) )
= ( plus_plus_nat @ ( times_times_nat @ X_15 @ Y_10 ) @ ( times_times_nat @ X_15 @ Z_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_373_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
thf(326,axiom,
! [X_15: real,Y_10: real,Z_2: real] :
( ( times_times_real @ X_15 @ ( plus_plus_real @ Y_10 @ Z_2 ) )
= ( plus_plus_real @ ( times_times_real @ X_15 @ Y_10 ) @ ( times_times_real @ X_15 @ Z_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_372_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
thf(327,axiom,
! [B_16: int,A_38: int] :
( ( B_16
= ( plus_plus_int @ B_16 @ A_38 ) )
<=> ( A_38 = zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_371_add__0__iff) ).
thf(328,axiom,
! [B_16: nat,A_38: nat] :
( ( B_16
= ( plus_plus_nat @ B_16 @ A_38 ) )
<=> ( A_38 = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_370_add__0__iff) ).
thf(329,axiom,
! [B_16: real,A_38: real] :
( ( B_16
= ( plus_plus_real @ B_16 @ A_38 ) )
<=> ( A_38 = zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_369_add__0__iff) ).
thf(330,axiom,
! [A_39: int] :
( ( plus_plus_int @ A_39 @ zero_zero_int )
= A_39 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_368_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
thf(331,axiom,
! [A_39: nat] :
( ( plus_plus_nat @ A_39 @ zero_zero_nat )
= A_39 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_367_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
thf(332,axiom,
! [A_39: real] :
( ( plus_plus_real @ A_39 @ zero_zero_real )
= A_39 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_366_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
thf(333,axiom,
! [A_40: int] :
( ( plus_plus_int @ zero_zero_int @ A_40 )
= A_40 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_365_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
thf(334,axiom,
! [A_40: nat] :
( ( plus_plus_nat @ zero_zero_nat @ A_40 )
= A_40 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_364_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
thf(335,axiom,
! [A_40: real] :
( ( plus_plus_real @ zero_zero_real @ A_40 )
= A_40 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_363_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
thf(336,axiom,
! [A_41: int] :
( ( times_times_int @ A_41 @ zero_zero_int )
= zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_362_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
thf(337,axiom,
! [A_41: nat] :
( ( times_times_nat @ A_41 @ zero_zero_nat )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_361_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
thf(338,axiom,
! [A_41: real] :
( ( times_times_real @ A_41 @ zero_zero_real )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_360_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
thf(339,axiom,
! [A_42: int] :
( ( times_times_int @ zero_zero_int @ A_42 )
= zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_359_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
thf(340,axiom,
! [A_42: nat] :
( ( times_times_nat @ zero_zero_nat @ A_42 )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_358_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
thf(341,axiom,
! [A_42: real] :
( ( times_times_real @ zero_zero_real @ A_42 )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_357_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
thf(342,axiom,
! [A_43: int,K_2: nat] :
( ( ord_less_eq_int @ ( power_power_int @ A_43 @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ K_2 ) ) @ zero_zero_int )
=> ( A_43 = zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_356_even__power__le__0__imp__0) ).
thf(343,axiom,
! [A_43: real,K_2: nat] :
( ( ord_less_eq_real @ ( power_power_real @ A_43 @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ K_2 ) ) @ zero_zero_real )
=> ( A_43 = zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_355_even__power__le__0__imp__0) ).
thf(344,axiom,
! [A_44: int,N_34: nat] :
( ( power_power_int @ A_44 @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ N_34 ) )
= ( power_power_int @ ( power_power_int @ A_44 @ N_34 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_354_power__even__eq) ).
thf(345,axiom,
! [A_44: nat,N_34: nat] :
( ( power_power_nat @ A_44 @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ N_34 ) )
= ( power_power_nat @ ( power_power_nat @ A_44 @ N_34 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_353_power__even__eq) ).
thf(346,axiom,
! [A_44: real,N_34: nat] :
( ( power_power_real @ A_44 @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ N_34 ) )
= ( power_power_real @ ( power_power_real @ A_44 @ N_34 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_352_power__even__eq) ).
thf(347,axiom,
! [V_5: int,K: nat,V_4: int] :
( ( ( ord_less_int @ V_4 @ pls )
=> ( ( times_times_nat @ ( number_number_of_nat @ V_4 ) @ ( times_times_nat @ ( number_number_of_nat @ V_5 ) @ K ) )
= zero_zero_nat ) )
& ( ~ ( ord_less_int @ V_4 @ pls )
=> ( ( times_times_nat @ ( number_number_of_nat @ V_4 ) @ ( times_times_nat @ ( number_number_of_nat @ V_5 ) @ K ) )
= ( times_times_nat @ ( number_number_of_nat @ ( times_times_int @ V_4 @ V_5 ) ) @ K ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_351_nat__number__of__mult__left) ).
thf(348,axiom,
! [V_5: int,V_4: int] :
( ( ( ord_less_int @ V_4 @ pls )
=> ( ( times_times_nat @ ( number_number_of_nat @ V_4 ) @ ( number_number_of_nat @ V_5 ) )
= zero_zero_nat ) )
& ( ~ ( ord_less_int @ V_4 @ pls )
=> ( ( times_times_nat @ ( number_number_of_nat @ V_4 ) @ ( number_number_of_nat @ V_5 ) )
= ( number_number_of_nat @ ( times_times_int @ V_4 @ V_5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_350_mult__nat__number__of) ).
thf(349,axiom,
! [Z: nat] :
( ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ Z )
= ( plus_plus_nat @ Z @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_349_nat__mult__2) ).
thf(350,axiom,
! [Z: nat] :
( ( times_times_nat @ Z @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_nat @ Z @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_348_nat__mult__2__right) ).
thf(351,axiom,
! [X: nat,W: int] :
( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X @ ( number_number_of_nat @ W ) ) )
<=> ( ( ( number_number_of_nat @ W )
= zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_347_zero__less__power__nat__eq__number__of) ).
thf(352,axiom,
! [X_16: int] :
( ( power_power_int @ X_16 @ one_one_nat )
= X_16 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_346_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
thf(353,axiom,
! [X_16: nat] :
( ( power_power_nat @ X_16 @ one_one_nat )
= X_16 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_345_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
thf(354,axiom,
! [X_16: real] :
( ( power_power_real @ X_16 @ one_one_nat )
= X_16 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_344_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
thf(355,axiom,
! [A_45: int,B_17: int,C_7: int,D_4: int] :
( ( plus_plus_int @ ( plus_plus_int @ A_45 @ B_17 ) @ ( plus_plus_int @ C_7 @ D_4 ) )
= ( plus_plus_int @ ( plus_plus_int @ A_45 @ C_7 ) @ ( plus_plus_int @ B_17 @ D_4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_343_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(356,axiom,
! [A_45: nat,B_17: nat,C_7: nat,D_4: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ A_45 @ B_17 ) @ ( plus_plus_nat @ C_7 @ D_4 ) )
= ( plus_plus_nat @ ( plus_plus_nat @ A_45 @ C_7 ) @ ( plus_plus_nat @ B_17 @ D_4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_342_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(357,axiom,
! [A_45: real,B_17: real,C_7: real,D_4: real] :
( ( plus_plus_real @ ( plus_plus_real @ A_45 @ B_17 ) @ ( plus_plus_real @ C_7 @ D_4 ) )
= ( plus_plus_real @ ( plus_plus_real @ A_45 @ C_7 ) @ ( plus_plus_real @ B_17 @ D_4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_341_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(358,axiom,
! [A_46: int,B_18: int,C_8: int] :
( ( plus_plus_int @ ( plus_plus_int @ A_46 @ B_18 ) @ C_8 )
= ( plus_plus_int @ ( plus_plus_int @ A_46 @ C_8 ) @ B_18 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_340_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(359,axiom,
! [A_46: nat,B_18: nat,C_8: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ A_46 @ B_18 ) @ C_8 )
= ( plus_plus_nat @ ( plus_plus_nat @ A_46 @ C_8 ) @ B_18 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_339_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(360,axiom,
! [A_46: real,B_18: real,C_8: real] :
( ( plus_plus_real @ ( plus_plus_real @ A_46 @ B_18 ) @ C_8 )
= ( plus_plus_real @ ( plus_plus_real @ A_46 @ C_8 ) @ B_18 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_338_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(361,axiom,
! [A_47: int,B_19: int,C_9: int] :
( ( plus_plus_int @ ( plus_plus_int @ A_47 @ B_19 ) @ C_9 )
= ( plus_plus_int @ A_47 @ ( plus_plus_int @ B_19 @ C_9 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_337_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(362,axiom,
! [A_47: nat,B_19: nat,C_9: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ A_47 @ B_19 ) @ C_9 )
= ( plus_plus_nat @ A_47 @ ( plus_plus_nat @ B_19 @ C_9 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_336_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(363,axiom,
! [A_47: real,B_19: real,C_9: real] :
( ( plus_plus_real @ ( plus_plus_real @ A_47 @ B_19 ) @ C_9 )
= ( plus_plus_real @ A_47 @ ( plus_plus_real @ B_19 @ C_9 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(364,axiom,
! [A_48: int,C_10: int,D_5: int] :
( ( plus_plus_int @ A_48 @ ( plus_plus_int @ C_10 @ D_5 ) )
= ( plus_plus_int @ ( plus_plus_int @ A_48 @ C_10 ) @ D_5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_334_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(365,axiom,
! [A_48: nat,C_10: nat,D_5: nat] :
( ( plus_plus_nat @ A_48 @ ( plus_plus_nat @ C_10 @ D_5 ) )
= ( plus_plus_nat @ ( plus_plus_nat @ A_48 @ C_10 ) @ D_5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(366,axiom,
! [A_48: real,C_10: real,D_5: real] :
( ( plus_plus_real @ A_48 @ ( plus_plus_real @ C_10 @ D_5 ) )
= ( plus_plus_real @ ( plus_plus_real @ A_48 @ C_10 ) @ D_5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_332_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(367,axiom,
! [A_49: int,C_11: int,D_6: int] :
( ( plus_plus_int @ A_49 @ ( plus_plus_int @ C_11 @ D_6 ) )
= ( plus_plus_int @ C_11 @ ( plus_plus_int @ A_49 @ D_6 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_331_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(368,axiom,
! [A_49: nat,C_11: nat,D_6: nat] :
( ( plus_plus_nat @ A_49 @ ( plus_plus_nat @ C_11 @ D_6 ) )
= ( plus_plus_nat @ C_11 @ ( plus_plus_nat @ A_49 @ D_6 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_330_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(369,axiom,
! [A_49: real,C_11: real,D_6: real] :
( ( plus_plus_real @ A_49 @ ( plus_plus_real @ C_11 @ D_6 ) )
= ( plus_plus_real @ C_11 @ ( plus_plus_real @ A_49 @ D_6 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_329_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(370,axiom,
! [A_50: int,C_12: int] :
( ( plus_plus_int @ A_50 @ C_12 )
= ( plus_plus_int @ C_12 @ A_50 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_328_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(371,axiom,
! [A_50: nat,C_12: nat] :
( ( plus_plus_nat @ A_50 @ C_12 )
= ( plus_plus_nat @ C_12 @ A_50 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(372,axiom,
! [A_50: real,C_12: real] :
( ( plus_plus_real @ A_50 @ C_12 )
= ( plus_plus_real @ C_12 @ A_50 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_326_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(373,axiom,
! [A_51: int,B_20: int] :
( ( times_times_int @ A_51 @ B_20 )
= ( times_times_int @ B_20 @ A_51 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_325_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
thf(374,axiom,
! [A_51: nat,B_20: nat] :
( ( times_times_nat @ A_51 @ B_20 )
= ( times_times_nat @ B_20 @ A_51 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
thf(375,axiom,
! [A_51: real,B_20: real] :
( ( times_times_real @ A_51 @ B_20 )
= ( times_times_real @ B_20 @ A_51 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_323_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
thf(376,axiom,
! [Lx: int,Rx: int,Ry: int] :
( ( times_times_int @ Lx @ ( times_times_int @ Rx @ Ry ) )
= ( times_times_int @ Rx @ ( times_times_int @ Lx @ Ry ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_322_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
thf(377,axiom,
! [Lx: nat,Rx: nat,Ry: nat] :
( ( times_times_nat @ Lx @ ( times_times_nat @ Rx @ Ry ) )
= ( times_times_nat @ Rx @ ( times_times_nat @ Lx @ Ry ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
thf(378,axiom,
! [Lx: real,Rx: real,Ry: real] :
( ( times_times_real @ Lx @ ( times_times_real @ Rx @ Ry ) )
= ( times_times_real @ Rx @ ( times_times_real @ Lx @ Ry ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_320_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
thf(379,axiom,
! [Lx_1: int,Rx_1: int,Ry_1: int] :
( ( times_times_int @ Lx_1 @ ( times_times_int @ Rx_1 @ Ry_1 ) )
= ( times_times_int @ ( times_times_int @ Lx_1 @ Rx_1 ) @ Ry_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_319_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
thf(380,axiom,
! [Lx_1: nat,Rx_1: nat,Ry_1: nat] :
( ( times_times_nat @ Lx_1 @ ( times_times_nat @ Rx_1 @ Ry_1 ) )
= ( times_times_nat @ ( times_times_nat @ Lx_1 @ Rx_1 ) @ Ry_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_318_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
thf(381,axiom,
! [Lx_1: real,Rx_1: real,Ry_1: real] :
( ( times_times_real @ Lx_1 @ ( times_times_real @ Rx_1 @ Ry_1 ) )
= ( times_times_real @ ( times_times_real @ Lx_1 @ Rx_1 ) @ Ry_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_317_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
thf(382,axiom,
! [Lx_2: int,Ly: int,Rx_2: int] :
( ( times_times_int @ ( times_times_int @ Lx_2 @ Ly ) @ Rx_2 )
= ( times_times_int @ Lx_2 @ ( times_times_int @ Ly @ Rx_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_316_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
thf(383,axiom,
! [Lx_2: nat,Ly: nat,Rx_2: nat] :
( ( times_times_nat @ ( times_times_nat @ Lx_2 @ Ly ) @ Rx_2 )
= ( times_times_nat @ Lx_2 @ ( times_times_nat @ Ly @ Rx_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
thf(384,axiom,
! [Lx_2: real,Ly: real,Rx_2: real] :
( ( times_times_real @ ( times_times_real @ Lx_2 @ Ly ) @ Rx_2 )
= ( times_times_real @ Lx_2 @ ( times_times_real @ Ly @ Rx_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_314_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
thf(385,axiom,
! [Lx_3: int,Ly_1: int,Rx_3: int] :
( ( times_times_int @ ( times_times_int @ Lx_3 @ Ly_1 ) @ Rx_3 )
= ( times_times_int @ ( times_times_int @ Lx_3 @ Rx_3 ) @ Ly_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
thf(386,axiom,
! [Lx_3: nat,Ly_1: nat,Rx_3: nat] :
( ( times_times_nat @ ( times_times_nat @ Lx_3 @ Ly_1 ) @ Rx_3 )
= ( times_times_nat @ ( times_times_nat @ Lx_3 @ Rx_3 ) @ Ly_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_312_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
thf(387,axiom,
! [Lx_3: real,Ly_1: real,Rx_3: real] :
( ( times_times_real @ ( times_times_real @ Lx_3 @ Ly_1 ) @ Rx_3 )
= ( times_times_real @ ( times_times_real @ Lx_3 @ Rx_3 ) @ Ly_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_311_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
thf(388,axiom,
! [Lx_4: int,Ly_2: int,Rx_4: int,Ry_2: int] :
( ( times_times_int @ ( times_times_int @ Lx_4 @ Ly_2 ) @ ( times_times_int @ Rx_4 @ Ry_2 ) )
= ( times_times_int @ Lx_4 @ ( times_times_int @ Ly_2 @ ( times_times_int @ Rx_4 @ Ry_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
thf(389,axiom,
! [Lx_4: nat,Ly_2: nat,Rx_4: nat,Ry_2: nat] :
( ( times_times_nat @ ( times_times_nat @ Lx_4 @ Ly_2 ) @ ( times_times_nat @ Rx_4 @ Ry_2 ) )
= ( times_times_nat @ Lx_4 @ ( times_times_nat @ Ly_2 @ ( times_times_nat @ Rx_4 @ Ry_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_309_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
thf(390,axiom,
! [Lx_4: real,Ly_2: real,Rx_4: real,Ry_2: real] :
( ( times_times_real @ ( times_times_real @ Lx_4 @ Ly_2 ) @ ( times_times_real @ Rx_4 @ Ry_2 ) )
= ( times_times_real @ Lx_4 @ ( times_times_real @ Ly_2 @ ( times_times_real @ Rx_4 @ Ry_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_308_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
thf(391,axiom,
! [Lx_5: int,Ly_3: int,Rx_5: int,Ry_3: int] :
( ( times_times_int @ ( times_times_int @ Lx_5 @ Ly_3 ) @ ( times_times_int @ Rx_5 @ Ry_3 ) )
= ( times_times_int @ Rx_5 @ ( times_times_int @ ( times_times_int @ Lx_5 @ Ly_3 ) @ Ry_3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
thf(392,axiom,
! [Lx_5: nat,Ly_3: nat,Rx_5: nat,Ry_3: nat] :
( ( times_times_nat @ ( times_times_nat @ Lx_5 @ Ly_3 ) @ ( times_times_nat @ Rx_5 @ Ry_3 ) )
= ( times_times_nat @ Rx_5 @ ( times_times_nat @ ( times_times_nat @ Lx_5 @ Ly_3 ) @ Ry_3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_306_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
thf(393,axiom,
! [Lx_5: real,Ly_3: real,Rx_5: real,Ry_3: real] :
( ( times_times_real @ ( times_times_real @ Lx_5 @ Ly_3 ) @ ( times_times_real @ Rx_5 @ Ry_3 ) )
= ( times_times_real @ Rx_5 @ ( times_times_real @ ( times_times_real @ Lx_5 @ Ly_3 ) @ Ry_3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
thf(394,axiom,
! [Lx_6: int,Ly_4: int,Rx_6: int,Ry_4: int] :
( ( times_times_int @ ( times_times_int @ Lx_6 @ Ly_4 ) @ ( times_times_int @ Rx_6 @ Ry_4 ) )
= ( times_times_int @ ( times_times_int @ Lx_6 @ Rx_6 ) @ ( times_times_int @ Ly_4 @ Ry_4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_304_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
thf(395,axiom,
! [Lx_6: nat,Ly_4: nat,Rx_6: nat,Ry_4: nat] :
( ( times_times_nat @ ( times_times_nat @ Lx_6 @ Ly_4 ) @ ( times_times_nat @ Rx_6 @ Ry_4 ) )
= ( times_times_nat @ ( times_times_nat @ Lx_6 @ Rx_6 ) @ ( times_times_nat @ Ly_4 @ Ry_4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_303_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
thf(396,axiom,
! [Lx_6: real,Ly_4: real,Rx_6: real,Ry_4: real] :
( ( times_times_real @ ( times_times_real @ Lx_6 @ Ly_4 ) @ ( times_times_real @ Rx_6 @ Ry_4 ) )
= ( times_times_real @ ( times_times_real @ Lx_6 @ Rx_6 ) @ ( times_times_real @ Ly_4 @ Ry_4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
thf(397,axiom,
! [V_4: int,V_5: int] :
( ( ord_less_eq_nat @ ( number_number_of_nat @ V_4 ) @ ( number_number_of_nat @ V_5 ) )
<=> ( ~ ( ord_less_eq_int @ V_4 @ V_5 )
=> ( ord_less_eq_int @ V_4 @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_le__nat__number__of) ).
thf(398,axiom,
! [Y: int,X: int] :
( ( twoSqu362149276sum2sq @ X )
=> ( ( twoSqu362149276sum2sq @ Y )
=> ( twoSqu362149276sum2sq @ ( times_times_int @ X @ Y ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_is__mult__sum2sq) ).
thf(399,axiom,
! [Z: int,N: int] :
( ( dvd_dvd_int @ Z @ N )
=> ( ( ord_less_int @ zero_zero_int @ N )
=> ( ord_less_eq_int @ Z @ N ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_zdvd__imp__le) ).
thf(400,axiom,
zprime @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_zprime__2) ).
thf(401,axiom,
! [C: int,X: int,T: int,A: int,D: int] :
( ( dvd_dvd_int @ A @ D )
=> ( ( dvd_dvd_int @ A @ ( plus_plus_int @ X @ T ) )
<=> ( dvd_dvd_int @ A @ ( plus_plus_int @ ( plus_plus_int @ X @ ( times_times_int @ C @ D ) ) @ T ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_zdvd__period) ).
thf(402,axiom,
! [K: int,N: int,M: int] :
( ( dvd_dvd_int @ K @ ( plus_plus_int @ N @ ( times_times_int @ K @ M ) ) )
<=> ( dvd_dvd_int @ K @ N ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_zdvd__reduce) ).
thf(403,axiom,
! [K: int,M: int,N: int] :
( ( dvd_dvd_int @ ( times_times_int @ K @ M ) @ ( times_times_int @ K @ N ) )
=> ( ( K != zero_zero_int )
=> ( dvd_dvd_int @ M @ N ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_zdvd__mult__cancel) ).
thf(404,axiom,
! [N: int,M: int] :
( ( ord_less_eq_int @ zero_zero_int @ M )
=> ( ( ord_less_eq_int @ zero_zero_int @ N )
=> ( ( dvd_dvd_int @ M @ N )
=> ( ( dvd_dvd_int @ N @ M )
=> ( M = N ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_zdvd__antisym__nonneg) ).
thf(405,axiom,
! [N: int,M: int] :
( ( ord_less_int @ zero_zero_int @ M )
=> ( ( ord_less_int @ M @ N )
=> ~ ( dvd_dvd_int @ N @ M ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_zdvd__not__zless) ).
thf(406,axiom,
! [X: int,Y: nat,Z: nat] :
( ( power_power_int @ ( power_power_int @ X @ Y ) @ Z )
= ( power_power_int @ X @ ( times_times_nat @ Y @ Z ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_zpower__zpower) ).
thf(407,axiom,
! [N: nat,B: int,A: int,P: int] :
( ( zprime @ P )
=> ( ~ ( dvd_dvd_int @ P @ A )
=> ( ( dvd_dvd_int @ ( power_power_int @ P @ N ) @ ( times_times_int @ A @ B ) )
=> ( dvd_dvd_int @ ( power_power_int @ P @ N ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_zprime__power__zdvd__cancel__left) ).
thf(408,axiom,
! [N: nat,A: int,B: int,P: int] :
( ( zprime @ P )
=> ( ~ ( dvd_dvd_int @ P @ B )
=> ( ( dvd_dvd_int @ ( power_power_int @ P @ N ) @ ( times_times_int @ A @ B ) )
=> ( dvd_dvd_int @ ( power_power_int @ P @ N ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_zprime__power__zdvd__cancel__right) ).
thf(409,axiom,
! [X_17: int,P_2: nat,Q_4: nat] :
( ( power_power_int @ ( power_power_int @ X_17 @ P_2 ) @ Q_4 )
= ( power_power_int @ X_17 @ ( times_times_nat @ P_2 @ Q_4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
thf(410,axiom,
! [X_17: nat,P_2: nat,Q_4: nat] :
( ( power_power_nat @ ( power_power_nat @ X_17 @ P_2 ) @ Q_4 )
= ( power_power_nat @ X_17 @ ( times_times_nat @ P_2 @ Q_4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
thf(411,axiom,
! [X_17: real,P_2: nat,Q_4: nat] :
( ( power_power_real @ ( power_power_real @ X_17 @ P_2 ) @ Q_4 )
= ( power_power_real @ X_17 @ ( times_times_nat @ P_2 @ Q_4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
thf(412,axiom,
! [A: int,N: nat,P: int] :
( ( zprime @ P )
=> ( ( dvd_dvd_int @ P @ ( power_power_int @ A @ N ) )
=> ( dvd_dvd_int @ P @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_zprime__zdvd__power) ).
thf(413,axiom,
! [X: nat,N: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X @ N ) )
<=> ( ( N = zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_zero__less__power__nat__eq) ).
thf(418,axiom,
! [X_18: int,N_35: nat] :
( ( power_power_int @ X_18 @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ N_35 ) )
= ( times_times_int @ ( power_power_int @ X_18 @ N_35 ) @ ( power_power_int @ X_18 @ N_35 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).
thf(419,axiom,
! [X_18: nat,N_35: nat] :
( ( power_power_nat @ X_18 @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ N_35 ) )
= ( times_times_nat @ ( power_power_nat @ X_18 @ N_35 ) @ ( power_power_nat @ X_18 @ N_35 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).
thf(420,axiom,
! [X_18: real,N_35: nat] :
( ( power_power_real @ X_18 @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ N_35 ) )
= ( times_times_real @ ( power_power_real @ X_18 @ N_35 ) @ ( power_power_real @ X_18 @ N_35 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).
thf(421,axiom,
ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J) ).
thf(422,axiom,
! [R: int,Q: int,A: int] :
( ( ord_less_int @ zero_zero_int @ A )
=> ( ( A
= ( plus_plus_int @ R @ ( times_times_int @ A @ Q ) ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ R )
=> ( ord_less_eq_int @ Q @ one_one_int ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_self__quotient__aux2) ).
thf(423,axiom,
! [R: int,Q: int,A: int] :
( ( ord_less_int @ zero_zero_int @ A )
=> ( ( A
= ( plus_plus_int @ R @ ( times_times_int @ A @ Q ) ) )
=> ( ( ord_less_int @ R @ A )
=> ( ord_less_eq_int @ one_one_int @ Q ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_self__quotient__aux1) ).
thf(424,axiom,
! [X: int] : ( ord_less_eq_int @ X @ ( power_power_int @ X @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_power2__ge__self) ).
thf(425,axiom,
! [A: int] :
( ( times_times_int @ A @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( power_power_int @ A @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_cube__square) ).
thf(427,axiom,
! [X: int] :
( ( ord_less_eq_int @ zero_zero_int @ X )
=> ( ( ord_less_int @ X @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
=> ( ( X = zero_zero_int )
| ( X = one_one_int ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_int__pos__lt__two__imp__zero__or__one) ).
thf(428,axiom,
! [A: int,B: int] :
( ( power_power_int @ ( plus_plus_int @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_zadd__power2) ).
thf(429,axiom,
! [A: int,B: int] :
( ( power_power_int @ ( plus_plus_int @ A @ B ) @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ B ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) @ A ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_269_zadd__power3) ).
thf(430,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/sandbox2/benchmark/theBenchmark.p',fact_268__0964_A_K_Am_A_L_A1_Advd_As_A_094_A2_A_L_A1_096) ).
thf(431,axiom,
! [Y_11: int] :
( ( ord_less_int @ one_one_int @ ( number_number_of_int @ Y_11 ) )
<=> ( ord_less_int @ ( bit1 @ pls ) @ Y_11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_less__special_I2_J) ).
thf(432,axiom,
! [Y_11: int] :
( ( ord_less_real @ one_one_real @ ( number267125858f_real @ Y_11 ) )
<=> ( ord_less_int @ ( bit1 @ pls ) @ Y_11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_less__special_I2_J) ).
thf(433,axiom,
! [X_19: int] :
( ( ord_less_int @ ( number_number_of_int @ X_19 ) @ one_one_int )
<=> ( ord_less_int @ X_19 @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_less__special_I4_J) ).
thf(434,axiom,
! [X_19: int] :
( ( ord_less_real @ ( number267125858f_real @ X_19 ) @ one_one_real )
<=> ( ord_less_int @ X_19 @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_less__special_I4_J) ).
thf(435,axiom,
( ( plus_plus_int @ one_one_int @ one_one_int )
= ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_one__add__one__is__two) ).
thf(436,axiom,
( ( plus_plus_real @ one_one_real @ one_one_real )
= ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_one__add__one__is__two) ).
thf(437,axiom,
( ( plus_plus_int @ one_one_int @ one_one_int )
= ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_semiring__one__add__one__is__two) ).
thf(438,axiom,
( ( plus_plus_nat @ one_one_nat @ one_one_nat )
= ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_semiring__one__add__one__is__two) ).
thf(439,axiom,
( ( plus_plus_real @ one_one_real @ one_one_real )
= ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_semiring__one__add__one__is__two) ).
thf(440,axiom,
! [Y_12: int] :
( ( ord_less_int @ zero_zero_int @ ( number_number_of_int @ Y_12 ) )
<=> ( ord_less_int @ pls @ Y_12 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_less__special_I1_J) ).
thf(441,axiom,
! [Y_12: int] :
( ( ord_less_real @ zero_zero_real @ ( number267125858f_real @ Y_12 ) )
<=> ( ord_less_int @ pls @ Y_12 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_less__special_I1_J) ).
thf(442,axiom,
! [X_20: int] :
( ( ord_less_int @ ( number_number_of_int @ X_20 ) @ zero_zero_int )
<=> ( ord_less_int @ X_20 @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_less__special_I3_J) ).
thf(443,axiom,
! [X_20: int] :
( ( ord_less_real @ ( number267125858f_real @ X_20 ) @ zero_zero_real )
<=> ( ord_less_int @ X_20 @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_less__special_I3_J) ).
thf(444,axiom,
! [Z: int] :
( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z ) @ zero_zero_int )
<=> ( ord_less_int @ Z @ zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_odd__less__0) ).
thf(445,axiom,
( one_one_int
= ( number_number_of_int @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_semiring__norm_I110_J) ).
thf(446,axiom,
( one_one_real
= ( number267125858f_real @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_semiring__norm_I110_J) ).
thf(447,axiom,
( ( number_number_of_int @ ( bit1 @ pls ) )
= one_one_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_numeral__1__eq__1) ).
thf(448,axiom,
( ( number267125858f_real @ ( bit1 @ pls ) )
= one_one_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_numeral__1__eq__1) ).
thf(449,axiom,
( ( number_number_of_int @ ( bit1 @ pls ) )
= one_one_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_semiring__numeral__1__eq__1) ).
thf(450,axiom,
( ( number_number_of_nat @ ( bit1 @ pls ) )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_semiring__numeral__1__eq__1) ).
thf(451,axiom,
( ( number267125858f_real @ ( bit1 @ pls ) )
= one_one_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_semiring__numeral__1__eq__1) ).
thf(452,axiom,
! [W_6: int] :
( ( number_number_of_int @ ( bit1 @ W_6 ) )
= ( plus_plus_int @ ( plus_plus_int @ one_one_int @ ( number_number_of_int @ W_6 ) ) @ ( number_number_of_int @ W_6 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_number__of__Bit1) ).
thf(453,axiom,
! [W_6: int] :
( ( number267125858f_real @ ( bit1 @ W_6 ) )
= ( plus_plus_real @ ( plus_plus_real @ one_one_real @ ( number267125858f_real @ W_6 ) ) @ ( number267125858f_real @ W_6 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_number__of__Bit1) ).
thf(454,axiom,
! [W_7: int] :
( ( number_number_of_int @ ( bit0 @ W_7 ) )
= ( plus_plus_int @ ( plus_plus_int @ zero_zero_int @ ( number_number_of_int @ W_7 ) ) @ ( number_number_of_int @ W_7 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_number__of__Bit0) ).
thf(455,axiom,
! [W_7: int] :
( ( number267125858f_real @ ( bit0 @ W_7 ) )
= ( plus_plus_real @ ( plus_plus_real @ zero_zero_real @ ( number267125858f_real @ W_7 ) ) @ ( number267125858f_real @ W_7 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_number__of__Bit0) ).
thf(456,axiom,
! [X_21: int,Y_13: int] :
( ( power_power_int @ ( plus_plus_int @ X_21 @ Y_13 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ X_21 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_13 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ X_21 ) @ Y_13 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_power2__sum) ).
thf(457,axiom,
! [X_21: nat,Y_13: nat] :
( ( power_power_nat @ ( plus_plus_nat @ X_21 @ Y_13 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_nat @ ( plus_plus_nat @ ( power_power_nat @ X_21 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_nat @ Y_13 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_nat @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ X_21 ) @ Y_13 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_power2__sum) ).
thf(458,axiom,
! [X_21: real,Y_13: real] :
( ( power_power_real @ ( plus_plus_real @ X_21 @ Y_13 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_real @ ( plus_plus_real @ ( power_power_real @ X_21 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y_13 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ X_21 ) @ Y_13 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_power2__sum) ).
thf(459,axiom,
! [W_8: int] :
( ( power_power_int @ ( number_number_of_int @ W_8 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_int @ ( number_number_of_int @ W_8 ) @ ( number_number_of_int @ W_8 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_power2__eq__square__number__of) ).
thf(460,axiom,
! [W_8: int] :
( ( power_power_nat @ ( number_number_of_nat @ W_8 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_nat @ ( number_number_of_nat @ W_8 ) @ ( number_number_of_nat @ W_8 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_power2__eq__square__number__of) ).
thf(461,axiom,
! [W_8: int] :
( ( power_power_real @ ( number267125858f_real @ W_8 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_real @ ( number267125858f_real @ W_8 ) @ ( number267125858f_real @ W_8 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_power2__eq__square__number__of) ).
thf(462,axiom,
! [W: int,Z: int] :
( ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
<=> ( ( ord_less_int @ W @ Z )
| ( W = Z ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_zless__add1__eq) ).
thf(463,axiom,
! [Z: int] :
( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z )
!= zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_odd__nonzero) ).
thf(464,axiom,
! [K: int] :
( ( bit1 @ K )
= ( plus_plus_int @ ( plus_plus_int @ one_one_int @ K ) @ K ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_Bit1__def) ).
thf(465,axiom,
ord_less_int @ zero_zero_int @ one_one_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_int__0__less__1) ).
thf(466,axiom,
! [K: int,L: int] :
( ( plus_plus_int @ ( bit0 @ K ) @ ( bit1 @ L ) )
= ( bit1 @ ( plus_plus_int @ K @ L ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_add__Bit0__Bit1) ).
thf(467,axiom,
! [K: int,L: int] :
( ( plus_plus_int @ ( bit1 @ K ) @ ( bit0 @ L ) )
= ( bit1 @ ( plus_plus_int @ K @ L ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_add__Bit1__Bit0) ).
thf(468,axiom,
! [W: int] :
( ( ord_less_int @ ( bit0 @ W ) @ zero_zero_int )
<=> ( ord_less_int @ W @ zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_bin__less__0__simps_I3_J) ).
thf(469,axiom,
~ ( ord_less_int @ pls @ zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_bin__less__0__simps_I1_J) ).
thf(470,axiom,
! [K: int] :
( ( ord_less_int @ pls @ ( bit0 @ K ) )
<=> ( ord_less_int @ pls @ K ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_rel__simps_I4_J) ).
thf(471,axiom,
! [K: int] :
( ( ord_less_int @ ( bit0 @ K ) @ pls )
<=> ( ord_less_int @ K @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_rel__simps_I10_J) ).
thf(472,axiom,
! [W: int] :
( ( ord_less_int @ ( bit1 @ W ) @ zero_zero_int )
<=> ( ord_less_int @ W @ zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_bin__less__0__simps_I4_J) ).
thf(473,axiom,
! [K: int,L: int] :
( ( ord_less_int @ ( bit1 @ K ) @ ( bit0 @ L ) )
<=> ( ord_less_int @ K @ L ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_rel__simps_I16_J) ).
thf(474,axiom,
! [K1: int,K2: int] :
( ( ord_less_int @ ( bit1 @ K1 ) @ ( bit0 @ K2 ) )
<=> ( ord_less_int @ K1 @ K2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_less__int__code_I15_J) ).
thf(475,axiom,
! [K: int] :
( ( ord_less_int @ ( bit1 @ K ) @ pls )
<=> ( ord_less_int @ K @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_rel__simps_I12_J) ).
thf(476,axiom,
! [V_6: int,W_9: int] :
( ( number_number_of_int @ ( plus_plus_int @ V_6 @ W_9 ) )
= ( plus_plus_int @ ( number_number_of_int @ V_6 ) @ ( number_number_of_int @ W_9 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_number__of__add) ).
thf(477,axiom,
! [V_6: int,W_9: int] :
( ( number267125858f_real @ ( plus_plus_int @ V_6 @ W_9 ) )
= ( plus_plus_real @ ( number267125858f_real @ V_6 ) @ ( number267125858f_real @ W_9 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_number__of__add) ).
thf(478,axiom,
! [V_7: int,W_10: int] :
( ( plus_plus_int @ ( number_number_of_int @ V_7 ) @ ( number_number_of_int @ W_10 ) )
= ( number_number_of_int @ ( plus_plus_int @ V_7 @ W_10 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_add__number__of__eq) ).
thf(479,axiom,
! [V_7: int,W_10: int] :
( ( plus_plus_real @ ( number267125858f_real @ V_7 ) @ ( number267125858f_real @ W_10 ) )
= ( number267125858f_real @ ( plus_plus_int @ V_7 @ W_10 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_add__number__of__eq) ).
thf(480,axiom,
! [V_8: int,W_11: int,Z_3: int] :
( ( plus_plus_int @ ( number_number_of_int @ V_8 ) @ ( plus_plus_int @ ( number_number_of_int @ W_11 ) @ Z_3 ) )
= ( plus_plus_int @ ( number_number_of_int @ ( plus_plus_int @ V_8 @ W_11 ) ) @ Z_3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_add__number__of__left) ).
thf(481,axiom,
! [V_8: int,W_11: int,Z_3: real] :
( ( plus_plus_real @ ( number267125858f_real @ V_8 ) @ ( plus_plus_real @ ( number267125858f_real @ W_11 ) @ Z_3 ) )
= ( plus_plus_real @ ( number267125858f_real @ ( plus_plus_int @ V_8 @ W_11 ) ) @ Z_3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_add__number__of__left) ).
thf(482,axiom,
! [X_22: int,Y_14: int] :
( ( ord_less_int @ ( number_number_of_int @ X_22 ) @ ( number_number_of_int @ Y_14 ) )
<=> ( ord_less_int @ X_22 @ Y_14 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_less__number__of) ).
thf(483,axiom,
! [X_22: int,Y_14: int] :
( ( ord_less_real @ ( number267125858f_real @ X_22 ) @ ( number267125858f_real @ Y_14 ) )
<=> ( ord_less_int @ X_22 @ Y_14 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_less__number__of) ).
thf(484,axiom,
! [A_52: int] :
( ( plus_plus_int @ A_52 @ ( number_number_of_int @ pls ) )
= A_52 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_add__numeral__0__right) ).
thf(485,axiom,
! [A_52: real] :
( ( plus_plus_real @ A_52 @ ( number267125858f_real @ pls ) )
= A_52 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_add__numeral__0__right) ).
thf(486,axiom,
! [A_53: int] :
( ( plus_plus_int @ ( number_number_of_int @ pls ) @ A_53 )
= A_53 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_add__numeral__0) ).
thf(487,axiom,
! [A_53: real] :
( ( plus_plus_real @ ( number267125858f_real @ pls ) @ A_53 )
= A_53 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_add__numeral__0) ).
thf(488,axiom,
( zero_zero_int
= ( number_number_of_int @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_semiring__norm_I112_J) ).
thf(489,axiom,
( zero_zero_real
= ( number267125858f_real @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_semiring__norm_I112_J) ).
thf(490,axiom,
( ( number_number_of_int @ pls )
= zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_number__of__Pls) ).
thf(491,axiom,
( ( number267125858f_real @ pls )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_number__of__Pls) ).
thf(492,axiom,
( ( number_number_of_int @ pls )
= zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_semiring__numeral__0__eq__0) ).
thf(493,axiom,
( ( number_number_of_nat @ pls )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_semiring__numeral__0__eq__0) ).
thf(494,axiom,
( ( number267125858f_real @ pls )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_semiring__numeral__0__eq__0) ).
thf(495,axiom,
! [A_54: int] :
( ( ord_less_int @ ( plus_plus_int @ A_54 @ A_54 ) @ zero_zero_int )
<=> ( ord_less_int @ A_54 @ zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_even__less__0__iff) ).
thf(496,axiom,
! [A_54: real] :
( ( ord_less_real @ ( plus_plus_real @ A_54 @ A_54 ) @ zero_zero_real )
<=> ( ord_less_real @ A_54 @ zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_even__less__0__iff) ).
thf(497,axiom,
! [A_55: int] :
( ( power_power_int @ A_55 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_int @ A_55 @ A_55 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_power2__eq__square) ).
thf(498,axiom,
! [A_55: nat] :
( ( power_power_nat @ A_55 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_nat @ A_55 @ A_55 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_power2__eq__square) ).
thf(499,axiom,
! [A_55: real] :
( ( power_power_real @ A_55 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_real @ A_55 @ A_55 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_power2__eq__square) ).
thf(500,axiom,
! [Z_4: int] :
( ( times_times_int @ Z_4 @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ Z_4 @ Z_4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_mult__2__right) ).
thf(501,axiom,
! [Z_4: real] :
( ( times_times_real @ Z_4 @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_real @ Z_4 @ Z_4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_mult__2__right) ).
thf(502,axiom,
! [Z_5: int] :
( ( times_times_int @ Z_5 @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ Z_5 @ Z_5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_semiring__mult__2__right) ).
thf(503,axiom,
! [Z_5: nat] :
( ( times_times_nat @ Z_5 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_nat @ Z_5 @ Z_5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_semiring__mult__2__right) ).
thf(504,axiom,
! [Z_5: real] :
( ( times_times_real @ Z_5 @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_real @ Z_5 @ Z_5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_semiring__mult__2__right) ).
thf(505,axiom,
! [Z_6: int] :
( ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ Z_6 )
= ( plus_plus_int @ Z_6 @ Z_6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_mult__2) ).
thf(506,axiom,
! [Z_6: real] :
( ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ Z_6 )
= ( plus_plus_real @ Z_6 @ Z_6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_mult__2) ).
thf(507,axiom,
! [Z_7: int] :
( ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ Z_7 )
= ( plus_plus_int @ Z_7 @ Z_7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_semiring__mult__2) ).
thf(508,axiom,
! [Z_7: nat] :
( ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ Z_7 )
= ( plus_plus_nat @ Z_7 @ Z_7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_semiring__mult__2) ).
thf(509,axiom,
! [Z_7: real] :
( ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ Z_7 )
= ( plus_plus_real @ Z_7 @ Z_7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_semiring__mult__2) ).
thf(510,axiom,
! [A_56: int] :
( ( power_power_int @ A_56 @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( times_times_int @ ( times_times_int @ A_56 @ A_56 ) @ A_56 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_power3__eq__cube) ).
thf(511,axiom,
! [A_56: nat] :
( ( power_power_nat @ A_56 @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( times_times_nat @ ( times_times_nat @ A_56 @ A_56 ) @ A_56 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_power3__eq__cube) ).
thf(512,axiom,
! [A_56: real] :
( ( power_power_real @ A_56 @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( times_times_real @ ( times_times_real @ A_56 @ A_56 ) @ A_56 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_power3__eq__cube) ).
thf(513,axiom,
! [W_12: int] :
( ( times_times_int @ ( plus_plus_int @ one_one_int @ one_one_int ) @ ( number_number_of_int @ W_12 ) )
= ( number_number_of_int @ ( bit0 @ W_12 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_double__number__of__Bit0) ).
thf(514,axiom,
! [W_12: int] :
( ( times_times_real @ ( plus_plus_real @ one_one_real @ one_one_real ) @ ( number267125858f_real @ W_12 ) )
= ( number267125858f_real @ ( bit0 @ W_12 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_double__number__of__Bit0) ).
thf(515,axiom,
! [K: int,I: int,J: int] :
( ( ord_less_int @ I @ J )
=> ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ K ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_zadd__strict__right__mono) ).
thf(516,axiom,
! [Z: int] :
( ( plus_plus_int @ zero_zero_int @ Z )
= Z ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_zadd__0) ).
thf(517,axiom,
! [Z: int] :
( ( plus_plus_int @ Z @ zero_zero_int )
= Z ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_zadd__0__right) ).
thf(518,axiom,
! [K: int] :
( ( bit0 @ K )
= ( plus_plus_int @ K @ K ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_Bit0__def) ).
thf(519,axiom,
! [K: int,L: int] :
( ( plus_plus_int @ ( bit0 @ K ) @ ( bit0 @ L ) )
= ( bit0 @ ( plus_plus_int @ K @ L ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_add__Bit0__Bit0) ).
thf(520,axiom,
! [K: int] :
( ( plus_plus_int @ pls @ K )
= K ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_add__Pls) ).
thf(521,axiom,
! [K: int] :
( ( plus_plus_int @ K @ pls )
= K ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_add__Pls__right) ).
thf(522,axiom,
zero_zero_int != one_one_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_int__0__neq__1) ).
thf(523,axiom,
! [K: int,L: int] :
( ( ord_less_int @ ( bit0 @ K ) @ ( bit0 @ L ) )
<=> ( ord_less_int @ K @ L ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_rel__simps_I14_J) ).
thf(524,axiom,
! [K1: int,K2: int] :
( ( ord_less_int @ ( bit0 @ K1 ) @ ( bit0 @ K2 ) )
<=> ( ord_less_int @ K1 @ K2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_less__int__code_I13_J) ).
thf(525,axiom,
~ ( ord_less_int @ pls @ pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_rel__simps_I2_J) ).
thf(526,axiom,
! [K: int,L: int] :
( ( ord_less_int @ ( bit1 @ K ) @ ( bit1 @ L ) )
<=> ( ord_less_int @ K @ L ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_rel__simps_I17_J) ).
thf(527,axiom,
! [K1: int,K2: int] :
( ( ord_less_int @ ( bit1 @ K1 ) @ ( bit1 @ K2 ) )
<=> ( ord_less_int @ K1 @ K2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_less__int__code_I16_J) ).
thf(528,axiom,
pls = zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_Pls__def) ).
thf(529,axiom,
( ( bit0 @ pls )
= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_Bit0__Pls) ).
thf(530,axiom,
! [L: int] :
( ( pls
= ( bit0 @ L ) )
<=> ( pls = L ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_rel__simps_I38_J) ).
thf(531,axiom,
! [K: int] :
( ( ( bit0 @ K )
= pls )
<=> ( K = pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_rel__simps_I44_J) ).
thf(532,axiom,
! [K: int,L: int] :
( ( bit0 @ K )
!= ( bit1 @ L ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_rel__simps_I49_J) ).
thf(533,axiom,
! [K: int,L: int] :
( ( bit1 @ K )
!= ( bit0 @ L ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_rel__simps_I50_J) ).
thf(534,axiom,
! [L: int] :
( pls
!= ( bit1 @ L ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_rel__simps_I39_J) ).
thf(535,axiom,
! [K: int] :
( ( bit1 @ K )
!= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_rel__simps_I46_J) ).
thf(536,axiom,
! [A_57: int] :
( ( ( plus_plus_int @ A_57 @ A_57 )
= zero_zero_int )
<=> ( A_57 = zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_double__eq__0__iff) ).
thf(537,axiom,
! [A_57: real] :
( ( ( plus_plus_real @ A_57 @ A_57 )
= zero_zero_real )
<=> ( A_57 = zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_double__eq__0__iff) ).
thf(538,axiom,
! [N: int,M: int] :
( ( ord_less_int @ zero_zero_int @ M )
=> ( ( ( times_times_int @ M @ N )
= one_one_int )
<=> ( ( M = one_one_int )
& ( N = one_one_int ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_pos__zmult__eq__1__iff) ).
thf(539,axiom,
! [K: int,L: int] :
( ( times_times_int @ ( bit1 @ K ) @ L )
= ( plus_plus_int @ ( bit0 @ ( times_times_int @ K @ L ) ) @ L ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_mult__Bit1) ).
thf(540,axiom,
( one_one_int
= ( number_number_of_int @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_one__is__num__one) ).
thf(541,axiom,
! [A_58: int] :
( ( times_times_int @ A_58 @ ( number_number_of_int @ ( bit1 @ pls ) ) )
= A_58 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_mult__numeral__1__right) ).
thf(542,axiom,
! [A_58: real] :
( ( times_times_real @ A_58 @ ( number267125858f_real @ ( bit1 @ pls ) ) )
= A_58 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_mult__numeral__1__right) ).
thf(543,axiom,
! [A_59: int] :
( ( times_times_int @ ( number_number_of_int @ ( bit1 @ pls ) ) @ A_59 )
= A_59 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_mult__numeral__1) ).
thf(544,axiom,
! [A_59: real] :
( ( times_times_real @ ( number267125858f_real @ ( bit1 @ pls ) ) @ A_59 )
= A_59 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_mult__numeral__1) ).
thf(545,axiom,
! [X_23: int,Y_15: int] :
~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ X_23 @ X_23 ) @ ( times_times_int @ Y_15 @ Y_15 ) ) @ zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_not__sum__squares__lt__zero) ).
thf(546,axiom,
! [X_23: real,Y_15: real] :
~ ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ X_23 @ X_23 ) @ ( times_times_real @ Y_15 @ Y_15 ) ) @ zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_not__sum__squares__lt__zero) ).
thf(547,axiom,
! [X_24: int,Y_16: int] :
( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X_24 @ X_24 ) @ ( times_times_int @ Y_16 @ Y_16 ) ) )
<=> ( ( X_24 != zero_zero_int )
| ( Y_16 != zero_zero_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_sum__squares__gt__zero__iff) ).
thf(548,axiom,
! [X_24: real,Y_16: real] :
( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X_24 @ X_24 ) @ ( times_times_real @ Y_16 @ Y_16 ) ) )
<=> ( ( X_24 != zero_zero_real )
| ( Y_16 != zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_sum__squares__gt__zero__iff) ).
thf(549,axiom,
! [X_25: int,Y_17: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X_25 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_17 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_sum__power2__ge__zero) ).
thf(550,axiom,
! [X_25: real,Y_17: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X_25 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y_17 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_sum__power2__ge__zero) ).
thf(551,axiom,
! [X_26: int,Y_18: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ ( power_power_int @ X_26 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_18 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_int )
<=> ( ( X_26 = zero_zero_int )
& ( Y_18 = zero_zero_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_sum__power2__le__zero__iff) ).
thf(552,axiom,
! [X_26: real,Y_18: real] :
( ( ord_less_eq_real @ ( plus_plus_real @ ( power_power_real @ X_26 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y_18 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_real )
<=> ( ( X_26 = zero_zero_real )
& ( Y_18 = zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_sum__power2__le__zero__iff) ).
thf(553,axiom,
! [X_27: int,Y_19: int] :
( ( ord_less_int @ ( power_power_int @ X_27 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_19 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ Y_19 )
=> ( ord_less_int @ X_27 @ Y_19 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_power2__less__imp__less) ).
thf(554,axiom,
! [X_27: nat,Y_19: nat] :
( ( ord_less_nat @ ( power_power_nat @ X_27 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_nat @ Y_19 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ Y_19 )
=> ( ord_less_nat @ X_27 @ Y_19 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_power2__less__imp__less) ).
thf(555,axiom,
! [X_27: real,Y_19: real] :
( ( ord_less_real @ ( power_power_real @ X_27 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y_19 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_real @ zero_zero_real @ Y_19 )
=> ( ord_less_real @ X_27 @ Y_19 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_power2__less__imp__less) ).
thf(556,axiom,
! [A_60: int] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A_60 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_zero__le__power2) ).
thf(557,axiom,
! [A_60: real] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A_60 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_zero__le__power2) ).
thf(558,axiom,
! [X_28: int,Y_20: int] :
( ( ord_less_eq_int @ ( power_power_int @ X_28 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_20 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ Y_20 )
=> ( ord_less_eq_int @ X_28 @ Y_20 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_power2__le__imp__le) ).
thf(559,axiom,
! [X_28: nat,Y_20: nat] :
( ( ord_less_eq_nat @ ( power_power_nat @ X_28 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_nat @ Y_20 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ Y_20 )
=> ( ord_less_eq_nat @ X_28 @ Y_20 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_power2__le__imp__le) ).
thf(560,axiom,
! [X_28: real,Y_20: real] :
( ( ord_less_eq_real @ ( power_power_real @ X_28 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y_20 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_real @ zero_zero_real @ Y_20 )
=> ( ord_less_eq_real @ X_28 @ Y_20 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_power2__le__imp__le) ).
thf(561,axiom,
! [X_29: int,Y_21: int] :
( ( ( power_power_int @ X_29 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power_int @ Y_21 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ X_29 )
=> ( ( ord_less_eq_int @ zero_zero_int @ Y_21 )
=> ( X_29 = Y_21 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_power2__eq__imp__eq) ).
thf(562,axiom,
! [X_29: nat,Y_21: nat] :
( ( ( power_power_nat @ X_29 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power_nat @ Y_21 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ X_29 )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ Y_21 )
=> ( X_29 = Y_21 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_power2__eq__imp__eq) ).
thf(563,axiom,
! [X_29: real,Y_21: real] :
( ( ( power_power_real @ X_29 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power_real @ Y_21 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_real @ zero_zero_real @ X_29 )
=> ( ( ord_less_eq_real @ zero_zero_real @ Y_21 )
=> ( X_29 = Y_21 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_power2__eq__imp__eq) ).
thf(564,axiom,
! [K: int,I: int,J: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_134_zmult__zless__mono2) ).
thf(565,axiom,
( zero_zero_int
= ( number_number_of_int @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_zero__is__num__zero) ).
thf(566,axiom,
! [Z: int,W: int] :
( ( plus_plus_int @ Z @ W )
= ( plus_plus_int @ W @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_zadd__commute) ).
thf(567,axiom,
! [X: int,Y: int,Z: int] :
( ( plus_plus_int @ X @ ( plus_plus_int @ Y @ Z ) )
= ( plus_plus_int @ Y @ ( plus_plus_int @ X @ Z ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_zadd__left__commute) ).
thf(568,axiom,
! [Z1: int,Z2: int,Z3: int] :
( ( plus_plus_int @ ( plus_plus_int @ Z1 @ Z2 ) @ Z3 )
= ( plus_plus_int @ Z1 @ ( plus_plus_int @ Z2 @ Z3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_zadd__assoc) ).
thf(569,axiom,
! [V_9: int,B_21: int,C_13: int] :
( ( times_times_int @ ( number_number_of_int @ V_9 ) @ ( plus_plus_int @ B_21 @ C_13 ) )
= ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ V_9 ) @ B_21 ) @ ( times_times_int @ ( number_number_of_int @ V_9 ) @ C_13 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_right__distrib__number__of) ).
thf(570,axiom,
! [V_9: int,B_21: nat,C_13: nat] :
( ( times_times_nat @ ( number_number_of_nat @ V_9 ) @ ( plus_plus_nat @ B_21 @ C_13 ) )
= ( plus_plus_nat @ ( times_times_nat @ ( number_number_of_nat @ V_9 ) @ B_21 ) @ ( times_times_nat @ ( number_number_of_nat @ V_9 ) @ C_13 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_right__distrib__number__of) ).
thf(571,axiom,
! [V_9: int,B_21: real,C_13: real] :
( ( times_times_real @ ( number267125858f_real @ V_9 ) @ ( plus_plus_real @ B_21 @ C_13 ) )
= ( plus_plus_real @ ( times_times_real @ ( number267125858f_real @ V_9 ) @ B_21 ) @ ( times_times_real @ ( number267125858f_real @ V_9 ) @ C_13 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_right__distrib__number__of) ).
thf(572,axiom,
! [A_61: int,B_22: int,V_10: int] :
( ( times_times_int @ ( plus_plus_int @ A_61 @ B_22 ) @ ( number_number_of_int @ V_10 ) )
= ( plus_plus_int @ ( times_times_int @ A_61 @ ( number_number_of_int @ V_10 ) ) @ ( times_times_int @ B_22 @ ( number_number_of_int @ V_10 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_left__distrib__number__of) ).
thf(573,axiom,
! [A_61: nat,B_22: nat,V_10: int] :
( ( times_times_nat @ ( plus_plus_nat @ A_61 @ B_22 ) @ ( number_number_of_nat @ V_10 ) )
= ( plus_plus_nat @ ( times_times_nat @ A_61 @ ( number_number_of_nat @ V_10 ) ) @ ( times_times_nat @ B_22 @ ( number_number_of_nat @ V_10 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_left__distrib__number__of) ).
thf(574,axiom,
! [A_61: real,B_22: real,V_10: int] :
( ( times_times_real @ ( plus_plus_real @ A_61 @ B_22 ) @ ( number267125858f_real @ V_10 ) )
= ( plus_plus_real @ ( times_times_real @ A_61 @ ( number267125858f_real @ V_10 ) ) @ ( times_times_real @ B_22 @ ( number267125858f_real @ V_10 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_left__distrib__number__of) ).
thf(575,axiom,
! [X_30: int,Y_22: int] :
( ( ( plus_plus_int @ ( times_times_int @ X_30 @ X_30 ) @ ( times_times_int @ Y_22 @ Y_22 ) )
= zero_zero_int )
<=> ( ( X_30 = zero_zero_int )
& ( Y_22 = zero_zero_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_sum__squares__eq__zero__iff) ).
thf(576,axiom,
! [X_30: real,Y_22: real] :
( ( ( plus_plus_real @ ( times_times_real @ X_30 @ X_30 ) @ ( times_times_real @ Y_22 @ Y_22 ) )
= zero_zero_real )
<=> ( ( X_30 = zero_zero_real )
& ( Y_22 = zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_sum__squares__eq__zero__iff) ).
thf(577,axiom,
! [X: int,Y: int] :
( ( ord_less_int @ X @ Y )
| ( X = Y )
| ( ord_less_int @ Y @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_zless__linear) ).
thf(578,axiom,
! [K: int,L: int] :
( ( ( bit0 @ K )
= ( bit0 @ L ) )
<=> ( K = L ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_rel__simps_I48_J) ).
thf(579,axiom,
! [K: int,L: int] :
( ( ( bit1 @ K )
= ( bit1 @ L ) )
<=> ( K = L ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_rel__simps_I51_J) ).
thf(580,axiom,
! [W_13: int,X_31: nat] :
( ( ( number_number_of_nat @ W_13 )
= X_31 )
<=> ( X_31
= ( number_number_of_nat @ W_13 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_number__of__reorient) ).
thf(581,axiom,
! [W_13: int,X_31: int] :
( ( ( number_number_of_int @ W_13 )
= X_31 )
<=> ( X_31
= ( number_number_of_int @ W_13 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_number__of__reorient) ).
thf(582,axiom,
! [W_13: int,X_31: real] :
( ( ( number267125858f_real @ W_13 )
= X_31 )
<=> ( X_31
= ( number267125858f_real @ W_13 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_number__of__reorient) ).
thf(583,axiom,
! [X_32: int,Y_23: int] :
( ( ( number_number_of_int @ X_32 )
= ( number_number_of_int @ Y_23 ) )
<=> ( X_32 = Y_23 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_eq__number__of) ).
thf(584,axiom,
! [X_32: int,Y_23: int] :
( ( ( number267125858f_real @ X_32 )
= ( number267125858f_real @ Y_23 ) )
<=> ( X_32 = Y_23 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_eq__number__of) ).
thf(585,axiom,
! [Z: int] :
( ( ord_less_eq_int @ zero_zero_int @ Z )
=> ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ Z ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_le__imp__0__less) ).
thf(586,axiom,
! [V_5: int,V_4: int] :
( ( ( ord_less_int @ V_4 @ pls )
=> ( ( plus_plus_nat @ ( number_number_of_nat @ V_4 ) @ ( number_number_of_nat @ V_5 ) )
= ( number_number_of_nat @ V_5 ) ) )
& ( ~ ( ord_less_int @ V_4 @ pls )
=> ( ( ( ord_less_int @ V_5 @ pls )
=> ( ( plus_plus_nat @ ( number_number_of_nat @ V_4 ) @ ( number_number_of_nat @ V_5 ) )
= ( number_number_of_nat @ V_4 ) ) )
& ( ~ ( ord_less_int @ V_5 @ pls )
=> ( ( plus_plus_nat @ ( number_number_of_nat @ V_4 ) @ ( number_number_of_nat @ V_5 ) )
= ( number_number_of_nat @ ( plus_plus_int @ V_4 @ V_5 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_add__nat__number__of) ).
thf(587,axiom,
! [V_12: int,V_11: int] :
( ( ord_less_eq_int @ pls @ V_11 )
=> ( ( ord_less_eq_int @ pls @ V_12 )
=> ( ( plus_plus_int @ ( number_number_of_int @ V_11 ) @ ( number_number_of_int @ V_12 ) )
= ( number_number_of_int @ ( plus_plus_int @ V_11 @ V_12 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_semiring__add__number__of) ).
thf(588,axiom,
! [V_12: int,V_11: int] :
( ( ord_less_eq_int @ pls @ V_11 )
=> ( ( ord_less_eq_int @ pls @ V_12 )
=> ( ( plus_plus_nat @ ( number_number_of_nat @ V_11 ) @ ( number_number_of_nat @ V_12 ) )
= ( number_number_of_nat @ ( plus_plus_int @ V_11 @ V_12 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_semiring__add__number__of) ).
thf(589,axiom,
! [V_12: int,V_11: int] :
( ( ord_less_eq_int @ pls @ V_11 )
=> ( ( ord_less_eq_int @ pls @ V_12 )
=> ( ( plus_plus_real @ ( number267125858f_real @ V_11 ) @ ( number267125858f_real @ V_12 ) )
= ( number267125858f_real @ ( plus_plus_int @ V_11 @ V_12 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_semiring__add__number__of) ).
thf(590,axiom,
! [W: int,Z: int] :
( ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
<=> ( ord_less_eq_int @ W @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_zle__add1__eq__le) ).
thf(591,axiom,
! [W: int,Z: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z )
<=> ( ord_less_int @ W @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_add1__zle__eq) ).
thf(592,axiom,
! [W: int,Z: int] :
( ( ord_less_int @ W @ Z )
=> ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_zless__imp__add1__zle) ).
thf(593,axiom,
( one_one_nat
= ( number_number_of_nat @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_Numeral1__eq1__nat) ).
thf(594,axiom,
( ( number_number_of_nat @ ( bit1 @ pls ) )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_nat__numeral__1__eq__1) ).
thf(595,axiom,
! [Z: int] :
( ( ord_less_eq_int @ one_one_int @ Z )
<=> ( ord_less_int @ zero_zero_int @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_int__one__le__iff__zero__less) ).
thf(596,axiom,
! [V_4: int,V_5: int] :
( ( ord_less_nat @ ( number_number_of_nat @ V_4 ) @ ( number_number_of_nat @ V_5 ) )
<=> ( ( ( ord_less_int @ V_4 @ V_5 )
=> ( ord_less_int @ pls @ V_5 ) )
& ( ord_less_int @ V_4 @ V_5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_less__nat__number__of) ).
thf(597,axiom,
! [K: int,L: int] :
( ( ord_less_int @ ( bit0 @ K ) @ ( bit1 @ L ) )
<=> ( ord_less_eq_int @ K @ L ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_rel__simps_I15_J) ).
thf(598,axiom,
! [K1: int,K2: int] :
( ( ord_less_int @ ( bit0 @ K1 ) @ ( bit1 @ K2 ) )
<=> ( ord_less_eq_int @ K1 @ K2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_less__int__code_I14_J) ).
thf(599,axiom,
! [K: int,L: int] :
( ( ord_less_eq_int @ ( bit1 @ K ) @ ( bit0 @ L ) )
<=> ( ord_less_int @ K @ L ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_rel__simps_I33_J) ).
thf(600,axiom,
! [K1: int,K2: int] :
( ( ord_less_eq_int @ ( bit1 @ K1 ) @ ( bit0 @ K2 ) )
<=> ( ord_less_int @ K1 @ K2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_less__eq__int__code_I15_J) ).
thf(601,axiom,
! [K: int] :
( ( ord_less_int @ pls @ ( bit1 @ K ) )
<=> ( ord_less_eq_int @ pls @ K ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_rel__simps_I5_J) ).
thf(602,axiom,
! [K: int] :
( ( ord_less_eq_int @ ( bit1 @ K ) @ pls )
<=> ( ord_less_int @ K @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_rel__simps_I29_J) ).
thf(603,axiom,
! [W: int,Z1: int,Z2: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_95_zadd__zmult__distrib2) ).
thf(604,axiom,
! [Z1: int,Z2: int,W: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_94_zadd__zmult__distrib) ).
thf(605,axiom,
! [V_4: int,W: int] :
( ( plus_plus_int @ ( number_number_of_int @ V_4 ) @ ( number_number_of_int @ W ) )
= ( number_number_of_int @ ( plus_plus_int @ V_4 @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_plus__numeral__code_I9_J) ).
thf(606,axiom,
! [Z: int] :
( ( times_times_int @ one_one_int @ Z )
= Z ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_zmult__1) ).
thf(607,axiom,
! [Z: int] :
( ( times_times_int @ Z @ one_one_int )
= Z ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_zmult__1__right) ).
thf(608,axiom,
! [K: int,L: int] :
( ( ord_less_int @ ( number_number_of_int @ K ) @ ( number_number_of_int @ L ) )
<=> ( ord_less_int @ K @ L ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_less__number__of__int__code) ).
thf(609,axiom,
! [K: int,L: int] :
( ( times_times_int @ ( bit0 @ K ) @ L )
= ( bit0 @ ( times_times_int @ K @ L ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_mult__Bit0) ).
thf(610,axiom,
! [W: int] :
( ( times_times_int @ pls @ W )
= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_mult__Pls) ).
thf(611,axiom,
( ( plus_plus_nat @ one_one_nat @ one_one_nat )
= ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_nat__1__add__1) ).
thf(612,axiom,
! [Y_24: int] :
( ( ord_less_eq_int @ one_one_int @ ( number_number_of_int @ Y_24 ) )
<=> ( ord_less_eq_int @ ( bit1 @ pls ) @ Y_24 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_le__special_I2_J) ).
thf(613,axiom,
! [Y_24: int] :
( ( ord_less_eq_real @ one_one_real @ ( number267125858f_real @ Y_24 ) )
<=> ( ord_less_eq_int @ ( bit1 @ pls ) @ Y_24 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_le__special_I2_J) ).
thf(614,axiom,
! [X_33: int] :
( ( ord_less_eq_int @ ( number_number_of_int @ X_33 ) @ one_one_int )
<=> ( ord_less_eq_int @ X_33 @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_le__special_I4_J) ).
thf(615,axiom,
! [X_33: int] :
( ( ord_less_eq_real @ ( number267125858f_real @ X_33 ) @ one_one_real )
<=> ( ord_less_eq_int @ X_33 @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_le__special_I4_J) ).
thf(616,axiom,
( zero_zero_nat
= ( number_number_of_nat @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_semiring__norm_I113_J) ).
thf(617,axiom,
( ( number_number_of_nat @ pls )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_nat__number__of__Pls) ).
thf(618,axiom,
! [Z_8: int,Z: int,W_14: int,W: int] :
( ( ord_less_int @ W_14 @ W )
=> ( ( ord_less_eq_int @ Z_8 @ Z )
=> ( ord_less_int @ ( plus_plus_int @ W_14 @ Z_8 ) @ ( plus_plus_int @ W @ Z ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_zadd__zless__mono) ).
thf(619,axiom,
! [K: int] :
( ( ord_less_eq_int @ pls @ ( bit0 @ K ) )
<=> ( ord_less_eq_int @ pls @ K ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_rel__simps_I21_J) ).
thf(620,axiom,
! [K: int] :
( ( ord_less_eq_int @ ( bit0 @ K ) @ pls )
<=> ( ord_less_eq_int @ K @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_rel__simps_I27_J) ).
thf(621,axiom,
! [K: int,L: int] :
( ( ord_less_eq_int @ ( bit0 @ K ) @ ( bit1 @ L ) )
<=> ( ord_less_eq_int @ K @ L ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_rel__simps_I32_J) ).
thf(622,axiom,
! [K1: int,K2: int] :
( ( ord_less_eq_int @ ( bit0 @ K1 ) @ ( bit1 @ K2 ) )
<=> ( ord_less_eq_int @ K1 @ K2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_less__eq__int__code_I14_J) ).
thf(623,axiom,
! [K: int] :
( ( ord_less_eq_int @ pls @ ( bit1 @ K ) )
<=> ( ord_less_eq_int @ pls @ K ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_rel__simps_I22_J) ).
thf(624,axiom,
! [V_13: int,W_15: int] :
( ( ord_less_eq_int @ ( number_number_of_int @ V_13 ) @ ( number_number_of_int @ W_15 ) )
<=> ~ ( ord_less_int @ ( number_number_of_int @ W_15 ) @ ( number_number_of_int @ V_13 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_le__number__of__eq__not__less) ).
thf(625,axiom,
! [V_13: int,W_15: int] :
( ( ord_less_eq_nat @ ( number_number_of_nat @ V_13 ) @ ( number_number_of_nat @ W_15 ) )
<=> ~ ( ord_less_nat @ ( number_number_of_nat @ W_15 ) @ ( number_number_of_nat @ V_13 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_le__number__of__eq__not__less) ).
thf(626,axiom,
! [V_13: int,W_15: int] :
( ( ord_less_eq_real @ ( number267125858f_real @ V_13 ) @ ( number267125858f_real @ W_15 ) )
<=> ~ ( ord_less_real @ ( number267125858f_real @ W_15 ) @ ( number267125858f_real @ V_13 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_le__number__of__eq__not__less) ).
thf(627,axiom,
! [V_4: int] :
( ( ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ V_4 ) )
<=> ( ord_less_int @ pls @ V_4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_less__0__number__of) ).
thf(628,axiom,
! [Y_25: int] :
( ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ Y_25 ) )
<=> ( ord_less_eq_int @ pls @ Y_25 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_le__special_I1_J) ).
thf(629,axiom,
! [Y_25: int] :
( ( ord_less_eq_real @ zero_zero_real @ ( number267125858f_real @ Y_25 ) )
<=> ( ord_less_eq_int @ pls @ Y_25 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_le__special_I1_J) ).
thf(630,axiom,
! [X_34: int] :
( ( ord_less_eq_int @ ( number_number_of_int @ X_34 ) @ zero_zero_int )
<=> ( ord_less_eq_int @ X_34 @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_le__special_I3_J) ).
thf(631,axiom,
! [X_34: int] :
( ( ord_less_eq_real @ ( number267125858f_real @ X_34 ) @ zero_zero_real )
<=> ( ord_less_eq_int @ X_34 @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_le__special_I3_J) ).
thf(632,axiom,
! [X_35: int,Y_26: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X_35 @ X_35 ) @ ( times_times_int @ Y_26 @ Y_26 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_sum__squares__ge__zero) ).
thf(633,axiom,
! [X_35: real,Y_26: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X_35 @ X_35 ) @ ( times_times_real @ Y_26 @ Y_26 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_sum__squares__ge__zero) ).
thf(634,axiom,
! [X_36: int,Y_27: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ X_36 @ X_36 ) @ ( times_times_int @ Y_27 @ Y_27 ) ) @ zero_zero_int )
<=> ( ( X_36 = zero_zero_int )
& ( Y_27 = zero_zero_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_sum__squares__le__zero__iff) ).
thf(635,axiom,
! [X_36: real,Y_27: real] :
( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ X_36 @ X_36 ) @ ( times_times_real @ Y_27 @ Y_27 ) ) @ zero_zero_real )
<=> ( ( X_36 = zero_zero_real )
& ( Y_27 = zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_sum__squares__le__zero__iff) ).
thf(636,axiom,
! [V_14: int,W_16: int] :
( ( number_number_of_int @ ( times_times_int @ V_14 @ W_16 ) )
= ( times_times_int @ ( number_number_of_int @ V_14 ) @ ( number_number_of_int @ W_16 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_number__of__mult) ).
thf(637,axiom,
! [V_14: int,W_16: int] :
( ( number267125858f_real @ ( times_times_int @ V_14 @ W_16 ) )
= ( times_times_real @ ( number267125858f_real @ V_14 ) @ ( number267125858f_real @ W_16 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_number__of__mult) ).
thf(638,axiom,
! [V_15: int,W_17: int] :
( ( times_times_int @ ( number_number_of_int @ V_15 ) @ ( number_number_of_int @ W_17 ) )
= ( number_number_of_int @ ( times_times_int @ V_15 @ W_17 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_arith__simps_I32_J) ).
thf(639,axiom,
! [V_15: int,W_17: int] :
( ( times_times_real @ ( number267125858f_real @ V_15 ) @ ( number267125858f_real @ W_17 ) )
= ( number267125858f_real @ ( times_times_int @ V_15 @ W_17 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_arith__simps_I32_J) ).
thf(640,axiom,
! [V_16: int,W_18: int,Z_9: int] :
( ( times_times_int @ ( number_number_of_int @ V_16 ) @ ( times_times_int @ ( number_number_of_int @ W_18 ) @ Z_9 ) )
= ( times_times_int @ ( number_number_of_int @ ( times_times_int @ V_16 @ W_18 ) ) @ Z_9 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_mult__number__of__left) ).
thf(641,axiom,
! [V_16: int,W_18: int,Z_9: real] :
( ( times_times_real @ ( number267125858f_real @ V_16 ) @ ( times_times_real @ ( number267125858f_real @ W_18 ) @ Z_9 ) )
= ( times_times_real @ ( number267125858f_real @ ( times_times_int @ V_16 @ W_18 ) ) @ Z_9 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_mult__number__of__left) ).
thf(642,axiom,
! [V_18: int,V_17: int] :
( ( ord_less_eq_int @ pls @ V_17 )
=> ( ( ord_less_eq_int @ pls @ V_18 )
=> ( ( times_times_int @ ( number_number_of_int @ V_17 ) @ ( number_number_of_int @ V_18 ) )
= ( number_number_of_int @ ( times_times_int @ V_17 @ V_18 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_semiring__mult__number__of) ).
thf(643,axiom,
! [V_18: int,V_17: int] :
( ( ord_less_eq_int @ pls @ V_17 )
=> ( ( ord_less_eq_int @ pls @ V_18 )
=> ( ( times_times_nat @ ( number_number_of_nat @ V_17 ) @ ( number_number_of_nat @ V_18 ) )
= ( number_number_of_nat @ ( times_times_int @ V_17 @ V_18 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_semiring__mult__number__of) ).
thf(644,axiom,
! [V_18: int,V_17: int] :
( ( ord_less_eq_int @ pls @ V_17 )
=> ( ( ord_less_eq_int @ pls @ V_18 )
=> ( ( times_times_real @ ( number267125858f_real @ V_17 ) @ ( number267125858f_real @ V_18 ) )
= ( number267125858f_real @ ( times_times_int @ V_17 @ V_18 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_semiring__mult__number__of) ).
thf(645,axiom,
! [V_4: int] :
( ( zero_zero_nat
= ( number_number_of_nat @ V_4 ) )
<=> ( ord_less_eq_int @ V_4 @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_eq__0__number__of) ).
thf(646,axiom,
! [V_4: int] :
( ( ( number_number_of_nat @ V_4 )
= zero_zero_nat )
<=> ( ord_less_eq_int @ V_4 @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_eq__number__of__0) ).
thf(647,axiom,
! [K: int,I: int,J: int] :
( ( ord_less_eq_int @ I @ J )
=> ( ord_less_eq_int @ ( plus_plus_int @ K @ I ) @ ( plus_plus_int @ K @ J ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_zadd__left__mono) ).
thf(648,axiom,
! [Z: int,W: int] :
( ( ord_less_int @ Z @ W )
<=> ( ( ord_less_eq_int @ Z @ W )
& ( Z != W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_zless__le) ).
thf(649,axiom,
! [K: int,L: int] :
( ( ord_less_eq_int @ ( bit0 @ K ) @ ( bit0 @ L ) )
<=> ( ord_less_eq_int @ K @ L ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_rel__simps_I31_J) ).
thf(650,axiom,
! [K1: int,K2: int] :
( ( ord_less_eq_int @ ( bit0 @ K1 ) @ ( bit0 @ K2 ) )
<=> ( ord_less_eq_int @ K1 @ K2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_less__eq__int__code_I13_J) ).
thf(651,axiom,
ord_less_eq_int @ pls @ pls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_rel__simps_I19_J) ).
thf(652,axiom,
! [K: int,L: int] :
( ( ord_less_eq_int @ ( bit1 @ K ) @ ( bit1 @ L ) )
<=> ( ord_less_eq_int @ K @ L ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_rel__simps_I34_J) ).
thf(653,axiom,
! [K1: int,K2: int] :
( ( ord_less_eq_int @ ( bit1 @ K1 ) @ ( bit1 @ K2 ) )
<=> ( ord_less_eq_int @ K1 @ K2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_less__eq__int__code_I16_J) ).
thf(654,axiom,
! [X: int,Y: nat,Z: nat] :
( ( power_power_int @ X @ ( plus_plus_nat @ Y @ Z ) )
= ( times_times_int @ ( power_power_int @ X @ Y ) @ ( power_power_int @ X @ Z ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_zpower__zadd__distrib) ).
thf(655,axiom,
! [Z: int,W: int] :
( ( ord_less_eq_int @ Z @ W )
=> ( ( ord_less_eq_int @ W @ Z )
=> ( Z = W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_zle__antisym) ).
thf(656,axiom,
! [K: int,I: int,J: int] :
( ( ord_less_eq_int @ I @ J )
=> ( ( ord_less_eq_int @ J @ K )
=> ( ord_less_eq_int @ I @ K ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_zle__trans) ).
thf(657,axiom,
! [Z1: int,Z2: int,Z3: int] :
( ( times_times_int @ ( times_times_int @ Z1 @ Z2 ) @ Z3 )
= ( times_times_int @ Z1 @ ( times_times_int @ Z2 @ Z3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_zmult__assoc) ).
thf(658,axiom,
! [X_37: int,Y_28: int] :
( ( ord_less_eq_int @ ( number_number_of_int @ X_37 ) @ ( number_number_of_int @ Y_28 ) )
<=> ( ord_less_eq_int @ X_37 @ Y_28 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_le__number__of) ).
thf(659,axiom,
! [X_37: int,Y_28: int] :
( ( ord_less_eq_real @ ( number267125858f_real @ X_37 ) @ ( number267125858f_real @ Y_28 ) )
<=> ( ord_less_eq_int @ X_37 @ Y_28 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_le__number__of) ).
thf(660,axiom,
! [K: int,L: int] :
( ( ord_less_eq_int @ ( number_number_of_int @ K ) @ ( number_number_of_int @ L ) )
<=> ( ord_less_eq_int @ K @ L ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_less__eq__number__of__int__code) ).
thf(661,axiom,
! [V_4: int,W: int] :
( ( times_times_int @ ( number_number_of_int @ V_4 ) @ ( number_number_of_int @ W ) )
= ( number_number_of_int @ ( times_times_int @ V_4 @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_times__numeral__code_I5_J) ).
thf(662,axiom,
! [Z: int,W: int] :
( ( ord_less_eq_int @ Z @ W )
| ( ord_less_eq_int @ W @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_zle__linear) ).
thf(663,axiom,
! [Z: int,W: int] :
( ( times_times_int @ Z @ W )
= ( times_times_int @ W @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_zmult__commute) ).
thf(664,axiom,
! [K: int] :
( ( number_number_of_int @ K )
= K ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_number__of__is__id) ).
thf(665,axiom,
! [W: int] : ( ord_less_eq_int @ W @ W ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_zle__refl) ).
thf(667,axiom,
zprime @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_p) ).
thf(668,axiom,
~ ! [T_1: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_30__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(669,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/sandbox2/benchmark/theBenchmark.p',fact_29_t__l__p) ).
thf(670,axiom,
! [V_19: int] :
( ( plus_plus_int @ ( number_number_of_int @ V_19 ) @ one_one_int )
= ( number_number_of_int @ ( plus_plus_int @ V_19 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_add__special_I3_J) ).
thf(671,axiom,
! [V_19: int] :
( ( plus_plus_real @ ( number267125858f_real @ V_19 ) @ one_one_real )
= ( number267125858f_real @ ( plus_plus_int @ V_19 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_add__special_I3_J) ).
thf(672,axiom,
! [W_19: int] :
( ( plus_plus_int @ one_one_int @ ( number_number_of_int @ W_19 ) )
= ( number_number_of_int @ ( plus_plus_int @ ( bit1 @ pls ) @ W_19 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_add__special_I2_J) ).
thf(673,axiom,
! [W_19: int] :
( ( plus_plus_real @ one_one_real @ ( number267125858f_real @ W_19 ) )
= ( number267125858f_real @ ( plus_plus_int @ ( bit1 @ pls ) @ W_19 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_add__special_I2_J) ).
thf(674,axiom,
! [A_62: int] :
( ( ( power_power_int @ A_62 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int )
<=> ( A_62 = zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_zero__eq__power2) ).
thf(675,axiom,
! [A_62: real] :
( ( ( power_power_real @ A_62 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_real )
<=> ( A_62 = zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_zero__eq__power2) ).
thf(676,axiom,
( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_zero__power2) ).
thf(677,axiom,
( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_zero__power2) ).
thf(678,axiom,
( ( power_power_real @ zero_zero_real @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_zero__power2) ).
thf(679,axiom,
( ( power_power_int @ one_one_int @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_one__power2) ).
thf(680,axiom,
( ( power_power_nat @ one_one_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_one__power2) ).
thf(681,axiom,
( ( power_power_real @ one_one_real @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_one__power2) ).
thf(682,axiom,
! [A_63: int] :
( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A_63 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
<=> ( A_63 != zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_zero__less__power2) ).
thf(683,axiom,
! [A_63: real] :
( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A_63 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
<=> ( A_63 != zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_zero__less__power2) ).
thf(684,axiom,
! [A_64: int] :
~ ( ord_less_int @ ( power_power_int @ A_64 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_power2__less__0) ).
thf(685,axiom,
! [A_64: real] :
~ ( ord_less_real @ ( power_power_real @ A_64 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_power2__less__0) ).
thf(686,axiom,
! [X_38: int,Y_29: int] :
( ( ( plus_plus_int @ ( power_power_int @ X_38 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_29 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_int )
<=> ( ( X_38 = zero_zero_int )
& ( Y_29 = zero_zero_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_sum__power2__eq__zero__iff) ).
thf(687,axiom,
! [X_38: real,Y_29: real] :
( ( ( plus_plus_real @ ( power_power_real @ X_38 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y_29 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_real )
<=> ( ( X_38 = zero_zero_real )
& ( Y_29 = zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_sum__power2__eq__zero__iff) ).
thf(688,axiom,
! [X_39: int,Y_30: int] :
( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X_39 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_30 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
<=> ( ( X_39 != zero_zero_int )
| ( Y_30 != zero_zero_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_sum__power2__gt__zero__iff) ).
thf(689,axiom,
! [X_39: real,Y_30: real] :
( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X_39 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y_30 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
<=> ( ( X_39 != zero_zero_real )
| ( Y_30 != zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_sum__power2__gt__zero__iff) ).
thf(690,axiom,
! [X: int,Y: int] :
~ ( ord_less_int @ ( 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 ) ) ) ) ) @ zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_not__sum__power2__lt__zero) ).
thf(691,axiom,
! [X: real,Y: real] :
~ ( ord_less_real @ ( plus_plus_real @ ( power_power_real @ X @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_not__sum__power2__lt__zero) ).
thf(692,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/sandbox2/benchmark/theBenchmark.p',fact_6_p0) ).
thf(693,axiom,
~ ( ord_less_eq_int @ one_one_int @ t ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5__096_126_A1_A_060_061_At_096) ).
thf(694,axiom,
( ( t = zero_zero_int )
=> ( ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int )
= zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_calculation_I2_J) ).
thf(695,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/sandbox2/benchmark/theBenchmark.p',fact_3_t) ).
thf(696,axiom,
ord_less_int @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ t ) @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__096_I4_A_K_Am_A_L_A1_J_A_K_At_A_060_A_I4_A_K_Am_A_L_A1_J_A_K_A0_096) ).
thf(697,axiom,
ord_less_int @ t @ one_one_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_calculation_I1_J) ).
thf(698,axiom,
ord_less_int @ t @ zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__096t_A_060_A0_096) ).
thf(699,conjecture,
ord_less_int @ ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int ) @ zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(700,negated_conjecture,
( ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int ) @ zero_zero_int )
= $false ),
inference(negate_conjecture,[status(cth)],[699]) ).
thf(701,plain,
( ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int ) @ zero_zero_int )
= $false ),
inference(unfold_def,[status(thm)],[700]) ).
thf(702,plain,
( ( ! [N: nat,M: nat] :
( ( 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)],[1]) ).
thf(703,plain,
( ( ! [I: nat,M: nat,N: nat] :
( ( 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)],[2]) ).
thf(704,plain,
( ( ! [X: nat,Q: nat,N: nat,R: nat] :
( ( X
= ( plus_plus_nat @ ( times_times_nat @ Q @ N ) @ R ) )
=> ( ( ord_less_nat @ zero_zero_nat @ R )
=> ( ( ord_less_nat @ R @ N )
=> ~ ( dvd_dvd_nat @ N @ X ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(705,plain,
( ( ! [X: nat,Y: nat,N: nat] :
( ( N != zero_zero_nat )
=> ( ( dvd_dvd_nat @ ( power_power_nat @ X @ N ) @ Y )
=> ( dvd_dvd_nat @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(706,plain,
( ( ! [A: nat,N: nat,B: nat] :
( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
=> ( ( N != zero_zero_nat )
=> ( dvd_dvd_nat @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(707,plain,
( ( ! [M: nat,K: nat,N: nat] :
( ( dvd_dvd_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
<=> ( ( K = zero_zero_nat )
| ( dvd_dvd_nat @ M @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(708,plain,
( ( ! [B: nat,D: nat,A: nat] :
( ( dvd_dvd_nat @ D @ A )
=> ( ( dvd_dvd_nat @ D @ ( plus_plus_nat @ A @ B ) )
=> ( dvd_dvd_nat @ D @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(709,plain,
( ( ! [C: nat,A: nat,B: nat] :
( ( dvd_dvd_nat @ A @ B )
=> ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(710,plain,
( ( ! [C: nat,A: nat,B: nat] :
( ( dvd_dvd_nat @ A @ B )
=> ( dvd_dvd_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(711,plain,
( ( ! [N: nat,X: nat,Y: nat] :
( ( dvd_dvd_nat @ X @ Y )
=> ( dvd_dvd_nat @ ( power_power_nat @ X @ N ) @ ( power_power_nat @ Y @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(712,plain,
( ( ! [A: nat,B: nat] :
( ( dvd_dvd_nat @ A @ B )
=> ( ( B = zero_zero_nat )
| ( ord_less_eq_nat @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(713,plain,
( ( ! [A: real,N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
=> ( ( ord_less_real @ zero_zero_real @ A )
=> ? [X_1: real] :
( ( ord_less_real @ zero_zero_real @ X_1 )
& ( ( power_power_real @ X_1 @ N )
= A )
& ! [Y_1: real] :
( ( ( ord_less_real @ zero_zero_real @ Y_1 )
& ( ( power_power_real @ Y_1 @ N )
= A ) )
=> ( Y_1 = X_1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(714,plain,
( ( ! [N_3: nat,A_2: nat] :
( ( ord_less_nat @ zero_zero_nat @ A_2 )
=> ( ( ord_less_nat @ A_2 @ one_one_nat )
=> ( ord_less_nat @ ( times_times_nat @ A_2 @ ( power_power_nat @ A_2 @ N_3 ) ) @ ( power_power_nat @ A_2 @ N_3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(715,plain,
( ( ! [N_3: nat,A_2: real] :
( ( ord_less_real @ zero_zero_real @ A_2 )
=> ( ( ord_less_real @ A_2 @ one_one_real )
=> ( ord_less_real @ ( times_times_real @ A_2 @ ( power_power_real @ A_2 @ N_3 ) ) @ ( power_power_real @ A_2 @ N_3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(716,plain,
( ( ! [A_3: nat,N_5: nat,N_4: nat] :
( ( ord_less_eq_nat @ N_5 @ N_4 )
=> ( ( ord_less_eq_nat @ one_one_nat @ A_3 )
=> ( ord_less_eq_nat @ ( power_power_nat @ A_3 @ N_5 ) @ ( power_power_nat @ A_3 @ N_4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(717,plain,
( ( ! [A_3: real,N_5: nat,N_4: nat] :
( ( ord_less_eq_nat @ N_5 @ N_4 )
=> ( ( ord_less_eq_real @ one_one_real @ A_3 )
=> ( ord_less_eq_real @ ( power_power_real @ A_3 @ N_5 ) @ ( power_power_real @ A_3 @ N_4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(718,plain,
( ( ! [X_2: nat,Y_2: nat,B_1: nat] :
( ( ord_less_nat @ one_one_nat @ B_1 )
=> ( ( ord_less_nat @ ( power_power_nat @ B_1 @ X_2 ) @ ( power_power_nat @ B_1 @ Y_2 ) )
<=> ( ord_less_nat @ X_2 @ Y_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(719,plain,
( ( ! [X_2: nat,Y_2: nat,B_1: real] :
( ( ord_less_real @ one_one_real @ B_1 )
=> ( ( ord_less_real @ ( power_power_real @ B_1 @ X_2 ) @ ( power_power_real @ B_1 @ Y_2 ) )
<=> ( ord_less_nat @ X_2 @ Y_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(720,plain,
( ( ! [M_1: nat,N_6: nat,A_4: nat] :
( ( ord_less_nat @ one_one_nat @ A_4 )
=> ( ( ord_less_nat @ ( power_power_nat @ A_4 @ M_1 ) @ ( power_power_nat @ A_4 @ N_6 ) )
=> ( ord_less_nat @ M_1 @ N_6 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(721,plain,
( ( ! [M_1: nat,N_6: nat,A_4: real] :
( ( ord_less_real @ one_one_real @ A_4 )
=> ( ( ord_less_real @ ( power_power_real @ A_4 @ M_1 ) @ ( power_power_real @ A_4 @ N_6 ) )
=> ( ord_less_nat @ M_1 @ N_6 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(722,plain,
( ( ! [A_5: nat,N_8: nat,N_7: nat] :
( ( ord_less_nat @ N_8 @ N_7 )
=> ( ( ord_less_nat @ one_one_nat @ A_5 )
=> ( ord_less_nat @ ( power_power_nat @ A_5 @ N_8 ) @ ( power_power_nat @ A_5 @ N_7 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(723,plain,
( ( ! [A_5: real,N_8: nat,N_7: nat] :
( ( ord_less_nat @ N_8 @ N_7 )
=> ( ( ord_less_real @ one_one_real @ A_5 )
=> ( ord_less_real @ ( power_power_real @ A_5 @ N_8 ) @ ( power_power_real @ A_5 @ N_7 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(724,plain,
( ( ! [N_9: nat] :
( ( ( N_9 = zero_zero_nat )
=> ( ( power_power_nat @ zero_zero_nat @ N_9 )
= one_one_nat ) )
& ( ( N_9 != zero_zero_nat )
=> ( ( power_power_nat @ zero_zero_nat @ N_9 )
= zero_zero_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(725,plain,
( ( ! [N_9: nat] :
( ( ( N_9 = zero_zero_nat )
=> ( ( power_power_real @ zero_zero_real @ N_9 )
= one_one_real ) )
& ( ( N_9 != zero_zero_nat )
=> ( ( power_power_real @ zero_zero_real @ N_9 )
= zero_zero_real ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(726,plain,
( ( ! [N_10: nat,A_6: nat] :
( ( ord_less_nat @ one_one_nat @ A_6 )
=> ( ord_less_nat @ one_one_nat @ ( times_times_nat @ A_6 @ ( power_power_nat @ A_6 @ N_10 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(727,plain,
( ( ! [N_10: nat,A_6: real] :
( ( ord_less_real @ one_one_real @ A_6 )
=> ( ord_less_real @ one_one_real @ ( times_times_real @ A_6 @ ( power_power_real @ A_6 @ N_10 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(728,plain,
( ( ! [N_11: nat,A_7: nat] :
( ( ord_less_nat @ one_one_nat @ A_7 )
=> ( ord_less_nat @ ( power_power_nat @ A_7 @ N_11 ) @ ( times_times_nat @ A_7 @ ( power_power_nat @ A_7 @ N_11 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(729,plain,
( ( ! [N_11: nat,A_7: real] :
( ( ord_less_real @ one_one_real @ A_7 )
=> ( ord_less_real @ ( power_power_real @ A_7 @ N_11 ) @ ( times_times_real @ A_7 @ ( power_power_real @ A_7 @ N_11 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(730,plain,
( ( ! [A_8: nat,N_12: nat,B_2: nat] :
( ( ord_less_nat @ ( power_power_nat @ A_8 @ N_12 ) @ ( power_power_nat @ B_2 @ N_12 ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B_2 )
=> ( ord_less_nat @ A_8 @ B_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(731,plain,
( ( ! [A_8: real,N_12: nat,B_2: real] :
( ( ord_less_real @ ( power_power_real @ A_8 @ N_12 ) @ ( power_power_real @ B_2 @ N_12 ) )
=> ( ( ord_less_eq_real @ zero_zero_real @ B_2 )
=> ( ord_less_real @ A_8 @ B_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(732,plain,
( ( ! [X: nat,N: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X @ N ) )
<=> ( ( ord_less_nat @ zero_zero_nat @ X )
| ( N = zero_zero_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(733,plain,
( ( ! [M: nat,N: nat,I: nat] :
( ( 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)],[42]) ).
thf(734,plain,
( ( ! [A_9: real,M_2: nat,N_13: nat] :
( ( ord_less_eq_nat @ M_2 @ N_13 )
=> ( dvd_dvd_real @ ( power_power_real @ A_9 @ M_2 ) @ ( power_power_real @ A_9 @ N_13 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(735,plain,
( ( ! [A_9: nat,M_2: nat,N_13: nat] :
( ( ord_less_eq_nat @ M_2 @ N_13 )
=> ( dvd_dvd_nat @ ( power_power_nat @ A_9 @ M_2 ) @ ( power_power_nat @ A_9 @ N_13 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(736,plain,
( ( ! [N_14: nat,M_3: nat,X_3: real,Y_3: real] :
( ( dvd_dvd_real @ X_3 @ Y_3 )
=> ( ( ord_less_eq_nat @ N_14 @ M_3 )
=> ( dvd_dvd_real @ ( power_power_real @ X_3 @ N_14 ) @ ( power_power_real @ Y_3 @ M_3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(737,plain,
( ( ! [N_14: nat,M_3: nat,X_3: nat,Y_3: nat] :
( ( dvd_dvd_nat @ X_3 @ Y_3 )
=> ( ( ord_less_eq_nat @ N_14 @ M_3 )
=> ( dvd_dvd_nat @ ( power_power_nat @ X_3 @ N_14 ) @ ( power_power_nat @ Y_3 @ M_3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(738,plain,
( ( ! [M_4: nat,A_10: real,N_15: nat,B_3: real] :
( ( dvd_dvd_real @ ( power_power_real @ A_10 @ N_15 ) @ B_3 )
=> ( ( ord_less_eq_nat @ M_4 @ N_15 )
=> ( dvd_dvd_real @ ( power_power_real @ A_10 @ M_4 ) @ B_3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(739,plain,
( ( ! [M_4: nat,A_10: nat,N_15: nat,B_3: nat] :
( ( dvd_dvd_nat @ ( power_power_nat @ A_10 @ N_15 ) @ B_3 )
=> ( ( ord_less_eq_nat @ M_4 @ N_15 )
=> ( dvd_dvd_nat @ ( power_power_nat @ A_10 @ M_4 ) @ B_3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(740,plain,
( ( ! [A_11: nat,M_5: nat,N_16: nat] :
( ( power_power_nat @ A_11 @ ( plus_plus_nat @ M_5 @ N_16 ) )
= ( times_times_nat @ ( power_power_nat @ A_11 @ M_5 ) @ ( power_power_nat @ A_11 @ N_16 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(741,plain,
( ( ! [A_11: real,M_5: nat,N_16: nat] :
( ( power_power_real @ A_11 @ ( plus_plus_nat @ M_5 @ N_16 ) )
= ( times_times_real @ ( power_power_real @ A_11 @ M_5 ) @ ( power_power_real @ A_11 @ N_16 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(742,plain,
( ( ! [A_12: nat] :
( ( power_power_nat @ A_12 @ zero_zero_nat )
= one_one_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(743,plain,
( ( ! [A_12: real] :
( ( power_power_real @ A_12 @ zero_zero_nat )
= one_one_real ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(744,plain,
( ( ! [A_13: nat,N_17: nat] :
( ( ( power_power_nat @ A_13 @ N_17 )
= zero_zero_nat )
<=> ( ( A_13 = zero_zero_nat )
& ( N_17 != zero_zero_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(745,plain,
( ( ! [A_13: real,N_17: nat] :
( ( ( power_power_real @ A_13 @ N_17 )
= zero_zero_real )
<=> ( ( A_13 = zero_zero_real )
& ( N_17 != zero_zero_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(746,plain,
( ( ! [M_6: nat,N_18: nat,A_14: nat] :
( ( ord_less_nat @ one_one_nat @ A_14 )
=> ( ( ( power_power_nat @ A_14 @ M_6 )
= ( power_power_nat @ A_14 @ N_18 ) )
<=> ( M_6 = N_18 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(747,plain,
( ( ! [M_6: nat,N_18: nat,A_14: real] :
( ( ord_less_real @ one_one_real @ A_14 )
=> ( ( ( power_power_real @ A_14 @ M_6 )
= ( power_power_real @ A_14 @ N_18 ) )
<=> ( M_6 = N_18 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(748,plain,
( ( ! [N_19: nat,A_15: nat] :
( ( ord_less_eq_nat @ one_one_nat @ A_15 )
=> ( ord_less_eq_nat @ one_one_nat @ ( power_power_nat @ A_15 @ N_19 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(749,plain,
( ( ! [N_19: nat,A_15: real] :
( ( ord_less_eq_real @ one_one_real @ A_15 )
=> ( ord_less_eq_real @ one_one_real @ ( power_power_real @ A_15 @ N_19 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(750,plain,
( ( ! [N_20: nat,A_16: nat] :
( ( ord_less_nat @ zero_zero_nat @ A_16 )
=> ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A_16 @ N_20 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(751,plain,
( ( ! [N_20: nat,A_16: real] :
( ( ord_less_real @ zero_zero_real @ A_16 )
=> ( ord_less_real @ zero_zero_real @ ( power_power_real @ A_16 @ N_20 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(752,plain,
( ( ! [N_21: nat,A_17: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ A_17 )
=> ( ord_less_eq_nat @ zero_zero_nat @ ( power_power_nat @ A_17 @ N_21 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(753,plain,
( ( ! [N_21: nat,A_17: real] :
( ( ord_less_eq_real @ zero_zero_real @ A_17 )
=> ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A_17 @ N_21 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(754,plain,
( ( ! [N_22: nat,A_18: nat,B_4: nat] :
( ( ord_less_eq_nat @ A_18 @ B_4 )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A_18 )
=> ( ord_less_eq_nat @ ( power_power_nat @ A_18 @ N_22 ) @ ( power_power_nat @ B_4 @ N_22 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(755,plain,
( ( ! [N_22: nat,A_18: real,B_4: real] :
( ( ord_less_eq_real @ A_18 @ B_4 )
=> ( ( ord_less_eq_real @ zero_zero_real @ A_18 )
=> ( ord_less_eq_real @ ( power_power_real @ A_18 @ N_22 ) @ ( power_power_real @ B_4 @ N_22 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(756,plain,
( ( ! [A_19: nat] :
( ( power_power_nat @ A_19 @ one_one_nat )
= A_19 ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(757,plain,
( ( ! [A_19: real] :
( ( power_power_real @ A_19 @ one_one_nat )
= A_19 ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(758,plain,
( ( ! [A_20: nat,M_7: nat,N_23: nat] :
( ( power_power_nat @ A_20 @ ( times_times_nat @ M_7 @ N_23 ) )
= ( power_power_nat @ ( power_power_nat @ A_20 @ M_7 ) @ N_23 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(759,plain,
( ( ! [A_20: real,M_7: nat,N_23: nat] :
( ( power_power_real @ A_20 @ ( times_times_nat @ M_7 @ N_23 ) )
= ( power_power_real @ ( power_power_real @ A_20 @ M_7 ) @ N_23 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(760,plain,
( ( ! [N_24: nat,X_4: real,Y_4: real] :
( ( dvd_dvd_real @ X_4 @ Y_4 )
=> ( dvd_dvd_real @ ( power_power_real @ X_4 @ N_24 ) @ ( power_power_real @ Y_4 @ N_24 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(761,plain,
( ( ! [N_24: nat,X_4: nat,Y_4: nat] :
( ( dvd_dvd_nat @ X_4 @ Y_4 )
=> ( dvd_dvd_nat @ ( power_power_nat @ X_4 @ N_24 ) @ ( power_power_nat @ Y_4 @ N_24 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(762,plain,
( ( ! [N_25: nat] :
( ( power_power_nat @ one_one_nat @ N_25 )
= one_one_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(763,plain,
( ( ! [N_25: nat] :
( ( power_power_real @ one_one_real @ N_25 )
= one_one_real ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(764,plain,
( ( ! [A_21: nat,N_26: nat] :
( ( times_times_nat @ ( power_power_nat @ A_21 @ N_26 ) @ A_21 )
= ( times_times_nat @ A_21 @ ( power_power_nat @ A_21 @ N_26 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(765,plain,
( ( ! [A_21: real,N_26: nat] :
( ( times_times_real @ ( power_power_real @ A_21 @ N_26 ) @ A_21 )
= ( times_times_real @ A_21 @ ( power_power_real @ A_21 @ N_26 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(766,plain,
( ( ! [A_22: nat,B_5: nat,N_27: nat] :
( ( power_power_nat @ ( times_times_nat @ A_22 @ B_5 ) @ N_27 )
= ( times_times_nat @ ( power_power_nat @ A_22 @ N_27 ) @ ( power_power_nat @ B_5 @ N_27 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(767,plain,
( ( ! [A_22: real,B_5: real,N_27: nat] :
( ( power_power_real @ ( times_times_real @ A_22 @ B_5 ) @ N_27 )
= ( times_times_real @ ( power_power_real @ A_22 @ N_27 ) @ ( power_power_real @ B_5 @ N_27 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(768,plain,
( ( ! [N_28: nat,A_23: real] :
( ( A_23 != zero_zero_real )
=> ( ( power_power_real @ A_23 @ N_28 )
!= zero_zero_real ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(769,plain,
( ( ! [N_29: nat,A_24: int,B_6: int] :
( ( ord_less_int @ A_24 @ B_6 )
=> ( ( ord_less_eq_int @ zero_zero_int @ A_24 )
=> ( ( ord_less_nat @ zero_zero_nat @ N_29 )
=> ( ord_less_int @ ( power_power_int @ A_24 @ N_29 ) @ ( power_power_int @ B_6 @ N_29 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(770,plain,
( ( ! [N_29: nat,A_24: nat,B_6: nat] :
( ( ord_less_nat @ A_24 @ B_6 )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A_24 )
=> ( ( ord_less_nat @ zero_zero_nat @ N_29 )
=> ( ord_less_nat @ ( power_power_nat @ A_24 @ N_29 ) @ ( power_power_nat @ B_6 @ N_29 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(771,plain,
( ( ! [N_29: nat,A_24: real,B_6: real] :
( ( ord_less_real @ A_24 @ B_6 )
=> ( ( ord_less_eq_real @ zero_zero_real @ A_24 )
=> ( ( ord_less_nat @ zero_zero_nat @ N_29 )
=> ( ord_less_real @ ( power_power_real @ A_24 @ N_29 ) @ ( power_power_real @ B_6 @ N_29 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(772,plain,
( ( ! [M_8: int,N_30: nat] :
( ( ( N_30 = zero_zero_nat )
=> ( ( power_power_int @ M_8 @ N_30 )
= one_one_int ) )
& ( ( N_30 != zero_zero_nat )
=> ( ( power_power_int @ M_8 @ N_30 )
= ( times_times_int @ M_8 @ ( power_power_int @ M_8 @ ( minus_minus_nat @ N_30 @ one_one_nat ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(773,plain,
( ( ! [M_8: nat,N_30: nat] :
( ( ( N_30 = zero_zero_nat )
=> ( ( power_power_nat @ M_8 @ N_30 )
= one_one_nat ) )
& ( ( N_30 != zero_zero_nat )
=> ( ( power_power_nat @ M_8 @ N_30 )
= ( times_times_nat @ M_8 @ ( power_power_nat @ M_8 @ ( minus_minus_nat @ N_30 @ one_one_nat ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(774,plain,
( ( ! [M_8: real,N_30: nat] :
( ( ( N_30 = zero_zero_nat )
=> ( ( power_power_real @ M_8 @ N_30 )
= one_one_real ) )
& ( ( N_30 != zero_zero_nat )
=> ( ( power_power_real @ M_8 @ N_30 )
= ( times_times_real @ M_8 @ ( power_power_real @ M_8 @ ( minus_minus_nat @ N_30 @ one_one_nat ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[105]) ).
thf(775,plain,
( ( ! [N: nat] : ( ord_less_eq_real @ one_one_real @ ( power_power_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(776,plain,
( ( ! [X_5: int,N_31: nat] :
( ( ord_less_nat @ zero_zero_nat @ N_31 )
=> ( ( times_times_int @ ( power_power_int @ X_5 @ ( minus_minus_nat @ N_31 @ one_one_nat ) ) @ X_5 )
= ( power_power_int @ X_5 @ N_31 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(777,plain,
( ( ! [X_5: nat,N_31: nat] :
( ( ord_less_nat @ zero_zero_nat @ N_31 )
=> ( ( times_times_nat @ ( power_power_nat @ X_5 @ ( minus_minus_nat @ N_31 @ one_one_nat ) ) @ X_5 )
= ( power_power_nat @ X_5 @ N_31 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[108]) ).
thf(778,plain,
( ( ! [X_5: real,N_31: nat] :
( ( ord_less_nat @ zero_zero_nat @ N_31 )
=> ( ( times_times_real @ ( power_power_real @ X_5 @ ( minus_minus_nat @ N_31 @ one_one_nat ) ) @ X_5 )
= ( power_power_real @ X_5 @ N_31 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(779,plain,
( ( ! [X_6: real] :
( ( minus_minus_real @ ( times_times_real @ X_6 @ X_6 ) @ one_one_real )
= ( times_times_real @ ( plus_plus_real @ X_6 @ one_one_real ) @ ( minus_minus_real @ X_6 @ one_one_real ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[111]) ).
thf(780,plain,
( ( ! [X: nat,N: nat] :
( ( ( power_power_nat @ X @ N )
= one_one_nat )
<=> ( ( X = one_one_nat )
| ( N = zero_zero_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[112]) ).
thf(781,plain,
( ( ! [X: real,Y: real] :
( ( ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) )
= zero_zero_real )
<=> ( ( X = zero_zero_real )
& ( Y = zero_zero_real ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[113]) ).
thf(782,plain,
( ( ! [X: real,Y: real,Z: real] :
( ( ord_less_real @ zero_zero_real @ Z )
=> ( ( ord_less_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ Y @ Z ) )
<=> ( ord_less_real @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[114]) ).
thf(783,plain,
( ( ! [Y: real,X: real] :
( ( ord_less_real @ zero_zero_real @ X )
=> ( ( ord_less_real @ zero_zero_real @ Y )
=> ( ord_less_real @ zero_zero_real @ ( times_times_real @ X @ Y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[115]) ).
thf(784,plain,
( ( ! [X: real,Y: real,Z: real] :
( ( ord_less_real @ zero_zero_real @ Z )
=> ( ( ord_less_real @ X @ Y )
=> ( ord_less_real @ ( times_times_real @ Z @ X ) @ ( times_times_real @ Z @ Y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[116]) ).
thf(785,plain,
( ( ! [X: real,Y: real,Z: real] :
( ( ord_less_real @ zero_zero_real @ Z )
=> ( ( ord_less_eq_real @ ( times_times_real @ Z @ X ) @ ( times_times_real @ Z @ Y ) )
<=> ( ord_less_eq_real @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[117]) ).
thf(786,plain,
( ( ! [X: real,Y: real,Z: real] :
( ( ord_less_real @ zero_zero_real @ Z )
=> ( ( ord_less_eq_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ Y @ Z ) )
<=> ( ord_less_eq_real @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[118]) ).
thf(787,plain,
( ( ! [X_7: real,Y_5: real,A_25: real,B_7: real] :
( ( minus_minus_real @ ( times_times_real @ X_7 @ Y_5 ) @ ( times_times_real @ A_25 @ B_7 ) )
= ( plus_plus_real @ ( times_times_real @ X_7 @ ( minus_minus_real @ Y_5 @ B_7 ) ) @ ( times_times_real @ ( minus_minus_real @ X_7 @ A_25 ) @ B_7 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[120]) ).
thf(788,plain,
( ( ! [M: nat,N: nat] :
( ( ( power_power_nat @ M @ N )
= zero_zero_nat )
<=> ( ( N != zero_zero_nat )
& ( M = zero_zero_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[121]) ).
thf(789,plain,
( ( ! [Z1: real,Z2: real,W: real] :
( ( 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)],[122]) ).
thf(790,plain,
( ( ! [N: nat,M: nat] :
( ( ( times_times_nat @ N @ M )
= one_one_nat )
<=> ( ( N = one_one_nat )
& ( M = one_one_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[123]) ).
thf(791,plain,
( ( ! [A: real,B: real,C: real] :
( ( C != zero_zero_real )
=> ( ( ( times_times_real @ A @ C )
= ( times_times_real @ B @ C ) )
<=> ( A = B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[124]) ).
thf(792,plain,
( ( ! [A: real,B: real,C: real] :
( ( C != zero_zero_real )
=> ( ( ( times_times_real @ C @ A )
= ( times_times_real @ C @ B ) )
<=> ( A = B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[125]) ).
thf(793,plain,
( ( ! [A_26: real,C_1: real,B_8: real,D_1: real] :
( ( minus_minus_real @ ( plus_plus_real @ A_26 @ C_1 ) @ ( plus_plus_real @ B_8 @ D_1 ) )
= ( plus_plus_real @ ( minus_minus_real @ A_26 @ B_8 ) @ ( minus_minus_real @ C_1 @ D_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[127]) ).
thf(794,plain,
( ( ! [Z: real,X: real,Y: real] :
( ( ord_less_eq_real @ X @ Y )
=> ( ord_less_eq_real @ ( plus_plus_real @ Z @ X ) @ ( plus_plus_real @ Z @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[128]) ).
thf(795,plain,
( ( ! [Z: real] :
( ( times_times_real @ one_one_real @ Z )
= Z ) )
= $true ),
inference(unfold_def,[status(thm)],[129]) ).
thf(796,plain,
( ( ! [Z: real,W: real] :
( ( times_times_real @ Z @ W )
= ( times_times_real @ W @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[130]) ).
thf(797,plain,
( ( ! [Z1: real,Z2: real,Z3: real] :
( ( times_times_real @ ( times_times_real @ Z1 @ Z2 ) @ Z3 )
= ( times_times_real @ Z1 @ ( times_times_real @ Z2 @ Z3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[131]) ).
thf(798,plain,
( ( ! [X: real,Y: real] :
( ( ord_less_eq_real @ X @ Y )
<=> ( ( ord_less_real @ X @ Y )
| ( X = Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[132]) ).
thf(799,plain,
( ( ! [X: real,Y: real] :
( ( ord_less_real @ X @ Y )
<=> ( ( ord_less_eq_real @ X @ Y )
& ( X != Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[133]) ).
thf(800,plain,
( ( zero_zero_real != one_one_real )
= $true ),
inference(unfold_def,[status(thm)],[135]) ).
thf(801,plain,
( ( ! [X: real,Y: real] :
( ( ( plus_plus_real @ ( power_power_real @ X @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_real )
<=> ( ( X = zero_zero_real )
& ( Y = zero_zero_real ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[136]) ).
thf(802,plain,
( ( ! [X: nat,Y: nat] :
( ( minus_minus_nat @ ( power_power_nat @ X @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_nat @ Y @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( times_times_nat @ ( plus_plus_nat @ X @ Y ) @ ( minus_minus_nat @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[137]) ).
thf(803,plain,
( ( ! [P: nat,M: nat] :
( ( ( 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)],[138]) ).
thf(804,plain,
( ( ! [N: nat,M: nat] :
( ( ( 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)],[139]) ).
thf(805,plain,
( ( ! [X: real,Y: real] :
( ( power_power_real @ ( plus_plus_real @ X @ Y ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_real @ ( plus_plus_real @ ( power_power_real @ X @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ X ) @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[140]) ).
thf(806,plain,
( ( ! [A: int,P: int] :
( ( ( zcong @ A @ zero_zero_int @ P )
=> ( ( legendre @ A @ P )
= zero_zero_int ) )
& ( ~ ( zcong @ A @ zero_zero_int @ P )
=> ( ( ( quadRes @ P @ A )
=> ( ( legendre @ A @ P )
= one_one_int ) )
& ( ~ ( quadRes @ P @ A )
=> ( ( legendre @ A @ P )
= ( number_number_of_int @ min ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[142]) ).
thf(807,plain,
( ( ! [M: int] :
( ( 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)],[143]) ).
thf(808,plain,
( ( ! [M: int] :
( ( 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)],[144]) ).
thf(809,plain,
( ( ! [Y: int,N: nat,P: int] :
( ( zprime @ P )
=> ( ( dvd_dvd_int @ P @ ( power_power_int @ Y @ N ) )
=> ( ( ord_less_nat @ zero_zero_nat @ N )
=> ( dvd_dvd_int @ P @ Y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[145]) ).
thf(810,plain,
( ( ! [B: int,A: int,P: int] :
( ( zprime @ P )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ( zcong @ ( times_times_int @ A @ B ) @ zero_zero_int @ P )
=> ( ( zcong @ A @ zero_zero_int @ P )
| ( zcong @ B @ zero_zero_int @ P ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[146]) ).
thf(811,plain,
( ( ! [B: int,A: int,P: int] :
( ( zprime @ P )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ( ~ ( zcong @ A @ zero_zero_int @ P )
& ~ ( zcong @ B @ zero_zero_int @ P ) )
=> ~ ( zcong @ ( times_times_int @ A @ B ) @ zero_zero_int @ P ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[147]) ).
thf(812,plain,
( ( ! [Y: int,X: int,P: int] :
( ( zprime @ P )
=> ( ~ ( zcong @ X @ zero_zero_int @ P )
=> ( ~ ( zcong @ Y @ zero_zero_int @ P )
=> ~ ( zcong @ ( times_times_int @ X @ Y ) @ zero_zero_int @ P ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[148]) ).
thf(813,plain,
( ( ! [P: int,Y: int,N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
=> ( ( dvd_dvd_int @ P @ Y )
=> ( dvd_dvd_int @ P @ ( power_power_int @ Y @ N ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[150]) ).
thf(814,plain,
( ( ! [M: int,N: int,P: int] :
( ( 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)],[152]) ).
thf(815,plain,
( ( ! [A: int,B: int] :
( ( power_power_int @ ( minus_minus_int @ A @ B ) @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( minus_minus_int @ ( plus_plus_int @ ( minus_minus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ B ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) @ A ) @ ( 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)],[158]) ).
thf(816,plain,
( ( ! [A: int,B: int] :
( ( power_power_int @ ( minus_minus_int @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ ( minus_minus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[159]) ).
thf(817,plain,
( ( ! [X_8: int,Y_6: int] :
( ( power_power_int @ ( minus_minus_int @ X_8 @ Y_6 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( minus_minus_int @ ( plus_plus_int @ ( power_power_int @ X_8 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_6 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ X_8 ) @ Y_6 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[160]) ).
thf(818,plain,
( ( ! [X_8: real,Y_6: real] :
( ( power_power_real @ ( minus_minus_real @ X_8 @ Y_6 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( minus_minus_real @ ( plus_plus_real @ ( power_power_real @ X_8 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y_6 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ X_8 ) @ Y_6 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[161]) ).
thf(819,plain,
( ( ! [C: int,D: int,A: int,B: int,M: int] :
( ( zcong @ A @ B @ M )
=> ( ( zcong @ C @ ( times_times_int @ A @ D ) @ M )
<=> ( zcong @ C @ ( times_times_int @ B @ D ) @ M ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[164]) ).
thf(820,plain,
( ( ! [C: int,D: int,A: int,B: int,M: int] :
( ( zcong @ A @ B @ M )
=> ( ( zcong @ C @ ( times_times_int @ D @ A ) @ M )
<=> ( zcong @ C @ ( times_times_int @ D @ B ) @ M ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[165]) ).
thf(821,plain,
( ( ! [A: int,P: int] :
( ( zprime @ P )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ( zcong @ ( times_times_int @ A @ A ) @ one_one_int @ P )
=> ( ( zcong @ A @ one_one_int @ P )
| ( zcong @ A @ ( minus_minus_int @ P @ one_one_int ) @ P ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[168]) ).
thf(822,plain,
( ( ! [A: int,P: int] :
( ( zprime @ P )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ( ord_less_int @ A @ P )
=> ( ( zcong @ ( times_times_int @ A @ A ) @ one_one_int @ P )
=> ( ( A = one_one_int )
| ( A
= ( minus_minus_int @ P @ one_one_int ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[169]) ).
thf(823,plain,
( ( ! [D: int,C: int,A: int,B: int,M: int] :
( ( zcong @ A @ B @ M )
=> ( ( B = C )
=> ( ( zcong @ C @ D @ M )
=> ( zcong @ A @ D @ M ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[170]) ).
thf(824,plain,
( ( ! [A: int,P: int] :
( ( zcong @ ( times_times_int @ A @ ( minus_minus_int @ P @ one_one_int ) ) @ one_one_int @ P )
<=> ( zcong @ A @ ( minus_minus_int @ P @ one_one_int ) @ P ) ) )
= $true ),
inference(unfold_def,[status(thm)],[171]) ).
thf(825,plain,
( ( ! [V: int,W_1: int,C_2: real] :
( ( plus_plus_real @ ( number267125858f_real @ V ) @ ( minus_minus_real @ ( number267125858f_real @ W_1 ) @ C_2 ) )
= ( minus_minus_real @ ( number267125858f_real @ ( plus_plus_int @ V @ W_1 ) ) @ C_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[178]) ).
thf(826,plain,
( ( ! [A: int,B: int,M: int] :
( ( zcong @ A @ B @ M )
<=> ( dvd_dvd_int @ M @ ( minus_minus_int @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[179]) ).
thf(827,plain,
( ( ! [A_27: int,B_9: int,V_1: int] :
( ( times_times_int @ ( minus_minus_int @ A_27 @ B_9 ) @ ( number_number_of_int @ V_1 ) )
= ( minus_minus_int @ ( times_times_int @ A_27 @ ( number_number_of_int @ V_1 ) ) @ ( times_times_int @ B_9 @ ( number_number_of_int @ V_1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[185]) ).
thf(828,plain,
( ( ! [A_27: real,B_9: real,V_1: int] :
( ( times_times_real @ ( minus_minus_real @ A_27 @ B_9 ) @ ( number267125858f_real @ V_1 ) )
= ( minus_minus_real @ ( times_times_real @ A_27 @ ( number267125858f_real @ V_1 ) ) @ ( times_times_real @ B_9 @ ( number267125858f_real @ V_1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[186]) ).
thf(829,plain,
( ( ! [V_2: int,B_10: int,C_3: int] :
( ( times_times_int @ ( number_number_of_int @ V_2 ) @ ( minus_minus_int @ B_10 @ C_3 ) )
= ( minus_minus_int @ ( times_times_int @ ( number_number_of_int @ V_2 ) @ B_10 ) @ ( times_times_int @ ( number_number_of_int @ V_2 ) @ C_3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[187]) ).
thf(830,plain,
( ( ! [V_2: int,B_10: real,C_3: real] :
( ( times_times_real @ ( number267125858f_real @ V_2 ) @ ( minus_minus_real @ B_10 @ C_3 ) )
= ( minus_minus_real @ ( times_times_real @ ( number267125858f_real @ V_2 ) @ B_10 ) @ ( times_times_real @ ( number267125858f_real @ V_2 ) @ C_3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[188]) ).
thf(831,plain,
( ( ! [V_3: int,W_2: int] :
( ( number_number_of_int @ ( minus_minus_int @ V_3 @ W_2 ) )
= ( minus_minus_int @ ( number_number_of_int @ V_3 ) @ ( number_number_of_int @ W_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[189]) ).
thf(832,plain,
( ( ! [V_3: int,W_2: int] :
( ( number267125858f_real @ ( minus_minus_int @ V_3 @ W_2 ) )
= ( minus_minus_real @ ( number267125858f_real @ V_3 ) @ ( number267125858f_real @ W_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[190]) ).
thf(833,plain,
( ( ! [Z1: int,Z2: int,W: int] :
( ( 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)],[194]) ).
thf(834,plain,
( ( ! [W: int,Z1: int,Z2: int] :
( ( 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)],[195]) ).
thf(835,plain,
( ( ! [K: int,M: int,N: int] :
( ( 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)],[196]) ).
thf(836,plain,
( ( ! [C: int,D: int,A: int,B: int,M: int] :
( ( zcong @ A @ B @ M )
=> ( ( zcong @ C @ D @ M )
=> ( zcong @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D ) @ M ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[197]) ).
thf(837,plain,
( ( ! [X: real] :
( ~ ( ord_less_real @ zero_zero_real @ ( times_times_real @ X @ X ) )
<=> ( X = zero_zero_real ) ) )
= $true ),
inference(unfold_def,[status(thm)],[198]) ).
thf(838,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)],[200]) ).
thf(839,plain,
( ( ! [X: int,P: int] :
( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ P )
=> ( ( zcong @ X @ ( number_number_of_int @ min ) @ P )
=> ~ ( zcong @ X @ one_one_int @ P ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[201]) ).
thf(840,plain,
( ( ! [J: nat,K: nat,M: int] :
( ( 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)],[202]) ).
thf(841,plain,
( ( dvd_dvd_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ ( minus_minus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_int @ min ) ) )
= $true ),
inference(unfold_def,[status(thm)],[203]) ).
thf(842,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)],[204]) ).
thf(843,plain,
( ( ! [N: int,P: int,M: int] :
( ( ord_less_eq_int @ zero_zero_int @ M )
=> ( ( 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)],[205]) ).
thf(844,plain,
( ( ! [X: real] :
( ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ X @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( power_power_real @ ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ X ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[209]) ).
thf(845,plain,
( ( ! [N_32: nat] :
( ( power_power_int @ ( number_number_of_int @ min ) @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ N_32 ) )
= one_one_int ) )
= $true ),
inference(unfold_def,[status(thm)],[212]) ).
thf(846,plain,
( ( ! [N_32: nat] :
( ( power_power_real @ ( number267125858f_real @ min ) @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ N_32 ) )
= one_one_real ) )
= $true ),
inference(unfold_def,[status(thm)],[213]) ).
thf(847,plain,
( ( ! [C: int,D: int,A: int,B: int,M: int] :
( ( zcong @ A @ B @ M )
=> ( ( zcong @ C @ D @ M )
=> ( zcong @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) @ M ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[215]) ).
thf(848,plain,
( ( ! [K: int,A: int,B: int,M: int] :
( ( zcong @ A @ B @ M )
=> ( zcong @ ( times_times_int @ K @ A ) @ ( times_times_int @ K @ B ) @ M ) ) )
= $true ),
inference(unfold_def,[status(thm)],[216]) ).
thf(849,plain,
( ( ! [K: int,A: int,B: int,M: int] :
( ( zcong @ A @ B @ M )
=> ( zcong @ ( times_times_int @ A @ K ) @ ( times_times_int @ B @ K ) @ M ) ) )
= $true ),
inference(unfold_def,[status(thm)],[217]) ).
thf(850,plain,
( ( ! [A: int,M: int,B: int] : ( zcong @ ( times_times_int @ A @ M ) @ ( times_times_int @ B @ M ) @ M ) )
= $true ),
inference(unfold_def,[status(thm)],[218]) ).
thf(851,plain,
( ( ! [X_9: nat,Y_7: nat] :
( ( ord_less_eq_nat @ X_9 @ Y_7 )
=> ( ( X_9 != Y_7 )
=> ( ord_less_nat @ X_9 @ Y_7 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[223]) ).
thf(852,plain,
( ( ! [X_9: real,Y_7: real] :
( ( ord_less_eq_real @ X_9 @ Y_7 )
=> ( ( X_9 != Y_7 )
=> ( ord_less_real @ X_9 @ Y_7 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[224]) ).
thf(853,plain,
( ( ! [C: int,A: int,B: int,M: int] :
( ( zcong @ A @ B @ M )
=> ( ( zcong @ B @ C @ M )
=> ( zcong @ A @ C @ M ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[225]) ).
thf(854,plain,
( ( ! [K: int,M: int] : ( zcong @ K @ K @ M ) )
= $true ),
inference(unfold_def,[status(thm)],[226]) ).
thf(855,plain,
( ( ! [A: int,B: int,M: int] :
( ( zcong @ A @ B @ M )
<=> ( zcong @ B @ A @ M ) ) )
= $true ),
inference(unfold_def,[status(thm)],[227]) ).
thf(856,plain,
( ( ! [M: int,N: int] :
( ( ( times_times_int @ M @ N )
= one_one_int )
=> ( ( M = one_one_int )
| ( M
= ( number_number_of_int @ min ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[228]) ).
thf(857,plain,
( ( ! [M: int,N: int] :
( ( ( times_times_int @ M @ N )
= one_one_int )
<=> ( ( ( M = one_one_int )
& ( N = one_one_int ) )
| ( ( M
= ( number_number_of_int @ min ) )
& ( N
= ( number_number_of_int @ min ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[229]) ).
thf(858,plain,
( ( ord_less_eq_int @ min @ min )
= $true ),
inference(unfold_def,[status(thm)],[244]) ).
thf(859,plain,
( ( ~ ! [S1: int] :
~ ( 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)],[254]) ).
thf(860,plain,
( ( ! [P: int] :
( ( zprime @ P )
=> ( ( P
!= ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
=> ( ( 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)],[256]) ).
thf(861,plain,
( ( ! [P: int] :
( ( zprime @ P )
<=> ( ( ord_less_int @ one_one_int @ P )
& ! [M_9: int] :
( ( ( ord_less_eq_int @ zero_zero_int @ M_9 )
& ( dvd_dvd_int @ M_9 @ P ) )
=> ( ( M_9 = one_one_int )
| ( M_9 = P ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[257]) ).
thf(862,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)],[259]) ).
thf(863,plain,
( ( ! [W_3: int] :
( ( ( ( number_number_of_nat @ W_3 )
= zero_zero_nat )
=> ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ W_3 ) )
= one_one_nat ) )
& ( ( ( number_number_of_nat @ W_3 )
!= zero_zero_nat )
=> ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ W_3 ) )
= zero_zero_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[272]) ).
thf(864,plain,
( ( ! [W_3: int] :
( ( ( ( number_number_of_nat @ W_3 )
= zero_zero_nat )
=> ( ( power_power_real @ zero_zero_real @ ( number_number_of_nat @ W_3 ) )
= one_one_real ) )
& ( ( ( number_number_of_nat @ W_3 )
!= zero_zero_nat )
=> ( ( power_power_real @ zero_zero_real @ ( number_number_of_nat @ W_3 ) )
= zero_zero_real ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[273]) ).
thf(865,plain,
( ( ! [A_28: real,W_4: int] :
( ( ( power_power_real @ A_28 @ ( number_number_of_nat @ W_4 ) )
= zero_zero_real )
<=> ( ( A_28 = zero_zero_real )
& ( ( number_number_of_nat @ W_4 )
!= zero_zero_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[281]) ).
thf(866,plain,
( ( ! [A_29: nat,M_10: nat] :
( ( plus_plus_nat @ ( times_times_nat @ A_29 @ M_10 ) @ M_10 )
= ( times_times_nat @ ( plus_plus_nat @ A_29 @ one_one_nat ) @ M_10 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[283]) ).
thf(867,plain,
( ( ! [A_29: real,M_10: real] :
( ( plus_plus_real @ ( times_times_real @ A_29 @ M_10 ) @ M_10 )
= ( times_times_real @ ( plus_plus_real @ A_29 @ one_one_real ) @ M_10 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[284]) ).
thf(868,plain,
( ( ! [M_11: nat,A_30: nat] :
( ( plus_plus_nat @ M_11 @ ( times_times_nat @ A_30 @ M_11 ) )
= ( times_times_nat @ ( plus_plus_nat @ A_30 @ one_one_nat ) @ M_11 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[286]) ).
thf(869,plain,
( ( ! [M_11: real,A_30: real] :
( ( plus_plus_real @ M_11 @ ( times_times_real @ A_30 @ M_11 ) )
= ( times_times_real @ ( plus_plus_real @ A_30 @ one_one_real ) @ M_11 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[287]) ).
thf(870,plain,
( ( ! [M_12: nat] :
( ( plus_plus_nat @ M_12 @ M_12 )
= ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) @ M_12 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[289]) ).
thf(871,plain,
( ( ! [M_12: real] :
( ( plus_plus_real @ M_12 @ M_12 )
= ( times_times_real @ ( plus_plus_real @ one_one_real @ one_one_real ) @ M_12 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[290]) ).
thf(872,plain,
( ( ! [C_4: nat,D_2: nat,A_31: nat,B_12: nat,R_2: nat] :
( ( R_2 != zero_zero_nat )
=> ( ( ( A_31 = B_12 )
& ( C_4 != D_2 ) )
=> ( ( plus_plus_nat @ A_31 @ ( times_times_nat @ R_2 @ C_4 ) )
!= ( plus_plus_nat @ B_12 @ ( times_times_nat @ R_2 @ D_2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[292]) ).
thf(873,plain,
( ( ! [C_4: real,D_2: real,A_31: real,B_12: real,R_2: real] :
( ( R_2 != zero_zero_real )
=> ( ( ( A_31 = B_12 )
& ( C_4 != D_2 ) )
=> ( ( plus_plus_real @ A_31 @ ( times_times_real @ R_2 @ C_4 ) )
!= ( plus_plus_real @ B_12 @ ( times_times_real @ R_2 @ D_2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[293]) ).
thf(874,plain,
( ( ! [A_32: real,N_33: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A_32 @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ N_33 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[295]) ).
thf(875,plain,
( ( ! [X_11: nat] :
( ( power_power_nat @ X_11 @ zero_zero_nat )
= one_one_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[298]) ).
thf(876,plain,
( ( ! [X_11: real] :
( ( power_power_real @ X_11 @ zero_zero_nat )
= one_one_real ) )
= $true ),
inference(unfold_def,[status(thm)],[299]) ).
thf(877,plain,
( ( ! [X_12: nat,P_1: nat,Q_2: nat] :
( ( times_times_nat @ ( power_power_nat @ X_12 @ P_1 ) @ ( power_power_nat @ X_12 @ Q_2 ) )
= ( power_power_nat @ X_12 @ ( plus_plus_nat @ P_1 @ Q_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[301]) ).
thf(878,plain,
( ( ! [X_12: real,P_1: nat,Q_2: nat] :
( ( times_times_real @ ( power_power_real @ X_12 @ P_1 ) @ ( power_power_real @ X_12 @ Q_2 ) )
= ( power_power_real @ X_12 @ ( plus_plus_nat @ P_1 @ Q_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[302]) ).
thf(879,plain,
( ( ! [X_13: nat,Y_8: nat,Q_3: nat] :
( ( power_power_nat @ ( times_times_nat @ X_13 @ Y_8 ) @ Q_3 )
= ( times_times_nat @ ( power_power_nat @ X_13 @ Q_3 ) @ ( power_power_nat @ Y_8 @ Q_3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[304]) ).
thf(880,plain,
( ( ! [X_13: real,Y_8: real,Q_3: nat] :
( ( power_power_real @ ( times_times_real @ X_13 @ Y_8 ) @ Q_3 )
= ( times_times_real @ ( power_power_real @ X_13 @ Q_3 ) @ ( power_power_real @ Y_8 @ Q_3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[305]) ).
thf(881,plain,
( ( ! [A_33: nat] :
( ( times_times_nat @ A_33 @ one_one_nat )
= A_33 ) )
= $true ),
inference(unfold_def,[status(thm)],[307]) ).
thf(882,plain,
( ( ! [A_33: real] :
( ( times_times_real @ A_33 @ one_one_real )
= A_33 ) )
= $true ),
inference(unfold_def,[status(thm)],[308]) ).
thf(883,plain,
( ( ! [A_34: nat] :
( ( times_times_nat @ one_one_nat @ A_34 )
= A_34 ) )
= $true ),
inference(unfold_def,[status(thm)],[310]) ).
thf(884,plain,
( ( ! [A_34: real] :
( ( times_times_real @ one_one_real @ A_34 )
= A_34 ) )
= $true ),
inference(unfold_def,[status(thm)],[311]) ).
thf(885,plain,
( ( ! [W_5: nat,Y_9: nat,X_14: nat,Z_1: nat] :
( ( ( plus_plus_nat @ ( times_times_nat @ W_5 @ Y_9 ) @ ( times_times_nat @ X_14 @ Z_1 ) )
= ( plus_plus_nat @ ( times_times_nat @ W_5 @ Z_1 ) @ ( times_times_nat @ X_14 @ Y_9 ) ) )
<=> ( ( W_5 = X_14 )
| ( Y_9 = Z_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[313]) ).
thf(886,plain,
( ( ! [W_5: real,Y_9: real,X_14: real,Z_1: real] :
( ( ( plus_plus_real @ ( times_times_real @ W_5 @ Y_9 ) @ ( times_times_real @ X_14 @ Z_1 ) )
= ( plus_plus_real @ ( times_times_real @ W_5 @ Z_1 ) @ ( times_times_real @ X_14 @ Y_9 ) ) )
<=> ( ( W_5 = X_14 )
| ( Y_9 = Z_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[314]) ).
thf(887,plain,
( ( ! [A_35: nat,M_13: nat,B_13: nat] :
( ( plus_plus_nat @ ( times_times_nat @ A_35 @ M_13 ) @ ( times_times_nat @ B_13 @ M_13 ) )
= ( times_times_nat @ ( plus_plus_nat @ A_35 @ B_13 ) @ M_13 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[316]) ).
thf(888,plain,
( ( ! [A_35: real,M_13: real,B_13: real] :
( ( plus_plus_real @ ( times_times_real @ A_35 @ M_13 ) @ ( times_times_real @ B_13 @ M_13 ) )
= ( times_times_real @ ( plus_plus_real @ A_35 @ B_13 ) @ M_13 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[317]) ).
thf(889,plain,
( ( ! [A_36: nat,B_14: nat,C_5: nat] :
( ( times_times_nat @ ( plus_plus_nat @ A_36 @ B_14 ) @ C_5 )
= ( plus_plus_nat @ ( times_times_nat @ A_36 @ C_5 ) @ ( times_times_nat @ B_14 @ C_5 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[319]) ).
thf(890,plain,
( ( ! [A_36: real,B_14: real,C_5: real] :
( ( times_times_real @ ( plus_plus_real @ A_36 @ B_14 ) @ C_5 )
= ( plus_plus_real @ ( times_times_real @ A_36 @ C_5 ) @ ( times_times_real @ B_14 @ C_5 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[320]) ).
thf(891,plain,
( ( ! [C_6: nat,D_3: nat,A_37: nat,B_15: nat] :
( ( ( A_37 != B_15 )
& ( C_6 != D_3 ) )
<=> ( ( plus_plus_nat @ ( times_times_nat @ A_37 @ C_6 ) @ ( times_times_nat @ B_15 @ D_3 ) )
!= ( plus_plus_nat @ ( times_times_nat @ A_37 @ D_3 ) @ ( times_times_nat @ B_15 @ C_6 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[322]) ).
thf(892,plain,
( ( ! [C_6: real,D_3: real,A_37: real,B_15: real] :
( ( ( A_37 != B_15 )
& ( C_6 != D_3 ) )
<=> ( ( plus_plus_real @ ( times_times_real @ A_37 @ C_6 ) @ ( times_times_real @ B_15 @ D_3 ) )
!= ( plus_plus_real @ ( times_times_real @ A_37 @ D_3 ) @ ( times_times_real @ B_15 @ C_6 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[323]) ).
thf(893,plain,
( ( ! [X_15: nat,Y_10: nat,Z_2: nat] :
( ( times_times_nat @ X_15 @ ( plus_plus_nat @ Y_10 @ Z_2 ) )
= ( plus_plus_nat @ ( times_times_nat @ X_15 @ Y_10 ) @ ( times_times_nat @ X_15 @ Z_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[325]) ).
thf(894,plain,
( ( ! [X_15: real,Y_10: real,Z_2: real] :
( ( times_times_real @ X_15 @ ( plus_plus_real @ Y_10 @ Z_2 ) )
= ( plus_plus_real @ ( times_times_real @ X_15 @ Y_10 ) @ ( times_times_real @ X_15 @ Z_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[326]) ).
thf(895,plain,
( ( ! [B_16: nat,A_38: nat] :
( ( B_16
= ( plus_plus_nat @ B_16 @ A_38 ) )
<=> ( A_38 = zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[328]) ).
thf(896,plain,
( ( ! [B_16: real,A_38: real] :
( ( B_16
= ( plus_plus_real @ B_16 @ A_38 ) )
<=> ( A_38 = zero_zero_real ) ) )
= $true ),
inference(unfold_def,[status(thm)],[329]) ).
thf(897,plain,
( ( ! [A_39: nat] :
( ( plus_plus_nat @ A_39 @ zero_zero_nat )
= A_39 ) )
= $true ),
inference(unfold_def,[status(thm)],[331]) ).
thf(898,plain,
( ( ! [A_39: real] :
( ( plus_plus_real @ A_39 @ zero_zero_real )
= A_39 ) )
= $true ),
inference(unfold_def,[status(thm)],[332]) ).
thf(899,plain,
( ( ! [A_40: nat] :
( ( plus_plus_nat @ zero_zero_nat @ A_40 )
= A_40 ) )
= $true ),
inference(unfold_def,[status(thm)],[334]) ).
thf(900,plain,
( ( ! [A_40: real] :
( ( plus_plus_real @ zero_zero_real @ A_40 )
= A_40 ) )
= $true ),
inference(unfold_def,[status(thm)],[335]) ).
thf(901,plain,
( ( ! [A_41: nat] :
( ( times_times_nat @ A_41 @ zero_zero_nat )
= zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[337]) ).
thf(902,plain,
( ( ! [A_41: real] :
( ( times_times_real @ A_41 @ zero_zero_real )
= zero_zero_real ) )
= $true ),
inference(unfold_def,[status(thm)],[338]) ).
thf(903,plain,
( ( ! [A_42: nat] :
( ( times_times_nat @ zero_zero_nat @ A_42 )
= zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[340]) ).
thf(904,plain,
( ( ! [A_42: real] :
( ( times_times_real @ zero_zero_real @ A_42 )
= zero_zero_real ) )
= $true ),
inference(unfold_def,[status(thm)],[341]) ).
thf(905,plain,
( ( ! [A_43: real,K_2: nat] :
( ( ord_less_eq_real @ ( power_power_real @ A_43 @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ K_2 ) ) @ zero_zero_real )
=> ( A_43 = zero_zero_real ) ) )
= $true ),
inference(unfold_def,[status(thm)],[343]) ).
thf(906,plain,
( ( ! [V_5: int,K: nat,V_4: int] :
( ( ( ord_less_int @ V_4 @ pls )
=> ( ( times_times_nat @ ( number_number_of_nat @ V_4 ) @ ( times_times_nat @ ( number_number_of_nat @ V_5 ) @ K ) )
= zero_zero_nat ) )
& ( ~ ( ord_less_int @ V_4 @ pls )
=> ( ( times_times_nat @ ( number_number_of_nat @ V_4 ) @ ( times_times_nat @ ( number_number_of_nat @ V_5 ) @ K ) )
= ( times_times_nat @ ( number_number_of_nat @ ( times_times_int @ V_4 @ V_5 ) ) @ K ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[347]) ).
thf(907,plain,
( ( ! [V_5: int,V_4: int] :
( ( ( ord_less_int @ V_4 @ pls )
=> ( ( times_times_nat @ ( number_number_of_nat @ V_4 ) @ ( number_number_of_nat @ V_5 ) )
= zero_zero_nat ) )
& ( ~ ( ord_less_int @ V_4 @ pls )
=> ( ( times_times_nat @ ( number_number_of_nat @ V_4 ) @ ( number_number_of_nat @ V_5 ) )
= ( number_number_of_nat @ ( times_times_int @ V_4 @ V_5 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[348]) ).
thf(908,plain,
( ( ! [X: nat,W: int] :
( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X @ ( number_number_of_nat @ W ) ) )
<=> ( ( ( number_number_of_nat @ W )
= zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[351]) ).
thf(909,plain,
( ( ! [X_16: nat] :
( ( power_power_nat @ X_16 @ one_one_nat )
= X_16 ) )
= $true ),
inference(unfold_def,[status(thm)],[353]) ).
thf(910,plain,
( ( ! [X_16: real] :
( ( power_power_real @ X_16 @ one_one_nat )
= X_16 ) )
= $true ),
inference(unfold_def,[status(thm)],[354]) ).
thf(911,plain,
( ( ! [A_45: nat,B_17: nat,C_7: nat,D_4: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ A_45 @ B_17 ) @ ( plus_plus_nat @ C_7 @ D_4 ) )
= ( plus_plus_nat @ ( plus_plus_nat @ A_45 @ C_7 ) @ ( plus_plus_nat @ B_17 @ D_4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[356]) ).
thf(912,plain,
( ( ! [A_45: real,B_17: real,C_7: real,D_4: real] :
( ( plus_plus_real @ ( plus_plus_real @ A_45 @ B_17 ) @ ( plus_plus_real @ C_7 @ D_4 ) )
= ( plus_plus_real @ ( plus_plus_real @ A_45 @ C_7 ) @ ( plus_plus_real @ B_17 @ D_4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[357]) ).
thf(913,plain,
( ( ! [A_46: nat,B_18: nat,C_8: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ A_46 @ B_18 ) @ C_8 )
= ( plus_plus_nat @ ( plus_plus_nat @ A_46 @ C_8 ) @ B_18 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[359]) ).
thf(914,plain,
( ( ! [A_46: real,B_18: real,C_8: real] :
( ( plus_plus_real @ ( plus_plus_real @ A_46 @ B_18 ) @ C_8 )
= ( plus_plus_real @ ( plus_plus_real @ A_46 @ C_8 ) @ B_18 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[360]) ).
thf(915,plain,
( ( ! [A_47: nat,B_19: nat,C_9: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ A_47 @ B_19 ) @ C_9 )
= ( plus_plus_nat @ A_47 @ ( plus_plus_nat @ B_19 @ C_9 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[362]) ).
thf(916,plain,
( ( ! [A_47: real,B_19: real,C_9: real] :
( ( plus_plus_real @ ( plus_plus_real @ A_47 @ B_19 ) @ C_9 )
= ( plus_plus_real @ A_47 @ ( plus_plus_real @ B_19 @ C_9 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[363]) ).
thf(917,plain,
( ( ! [A_48: nat,C_10: nat,D_5: nat] :
( ( plus_plus_nat @ A_48 @ ( plus_plus_nat @ C_10 @ D_5 ) )
= ( plus_plus_nat @ ( plus_plus_nat @ A_48 @ C_10 ) @ D_5 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[365]) ).
thf(918,plain,
( ( ! [A_48: real,C_10: real,D_5: real] :
( ( plus_plus_real @ A_48 @ ( plus_plus_real @ C_10 @ D_5 ) )
= ( plus_plus_real @ ( plus_plus_real @ A_48 @ C_10 ) @ D_5 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[366]) ).
thf(919,plain,
( ( ! [A_49: nat,C_11: nat,D_6: nat] :
( ( plus_plus_nat @ A_49 @ ( plus_plus_nat @ C_11 @ D_6 ) )
= ( plus_plus_nat @ C_11 @ ( plus_plus_nat @ A_49 @ D_6 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[368]) ).
thf(920,plain,
( ( ! [A_49: real,C_11: real,D_6: real] :
( ( plus_plus_real @ A_49 @ ( plus_plus_real @ C_11 @ D_6 ) )
= ( plus_plus_real @ C_11 @ ( plus_plus_real @ A_49 @ D_6 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[369]) ).
thf(921,plain,
( ( ! [A_50: nat,C_12: nat] :
( ( plus_plus_nat @ A_50 @ C_12 )
= ( plus_plus_nat @ C_12 @ A_50 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[371]) ).
thf(922,plain,
( ( ! [A_50: real,C_12: real] :
( ( plus_plus_real @ A_50 @ C_12 )
= ( plus_plus_real @ C_12 @ A_50 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[372]) ).
thf(923,plain,
( ( ! [A_51: int,B_20: int] :
( ( times_times_int @ A_51 @ B_20 )
= ( times_times_int @ B_20 @ A_51 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[373]) ).
thf(924,plain,
( ( ! [A_51: nat,B_20: nat] :
( ( times_times_nat @ A_51 @ B_20 )
= ( times_times_nat @ B_20 @ A_51 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[374]) ).
thf(925,plain,
( ( ! [A_51: real,B_20: real] :
( ( times_times_real @ A_51 @ B_20 )
= ( times_times_real @ B_20 @ A_51 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[375]) ).
thf(926,plain,
( ( ! [Lx: int,Rx: int,Ry: int] :
( ( times_times_int @ Lx @ ( times_times_int @ Rx @ Ry ) )
= ( times_times_int @ Rx @ ( times_times_int @ Lx @ Ry ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[376]) ).
thf(927,plain,
( ( ! [Lx: nat,Rx: nat,Ry: nat] :
( ( times_times_nat @ Lx @ ( times_times_nat @ Rx @ Ry ) )
= ( times_times_nat @ Rx @ ( times_times_nat @ Lx @ Ry ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[377]) ).
thf(928,plain,
( ( ! [Lx: real,Rx: real,Ry: real] :
( ( times_times_real @ Lx @ ( times_times_real @ Rx @ Ry ) )
= ( times_times_real @ Rx @ ( times_times_real @ Lx @ Ry ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[378]) ).
thf(929,plain,
( ( ! [Lx_1: int,Rx_1: int,Ry_1: int] :
( ( times_times_int @ Lx_1 @ ( times_times_int @ Rx_1 @ Ry_1 ) )
= ( times_times_int @ ( times_times_int @ Lx_1 @ Rx_1 ) @ Ry_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[379]) ).
thf(930,plain,
( ( ! [Lx_1: nat,Rx_1: nat,Ry_1: nat] :
( ( times_times_nat @ Lx_1 @ ( times_times_nat @ Rx_1 @ Ry_1 ) )
= ( times_times_nat @ ( times_times_nat @ Lx_1 @ Rx_1 ) @ Ry_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[380]) ).
thf(931,plain,
( ( ! [Lx_1: real,Rx_1: real,Ry_1: real] :
( ( times_times_real @ Lx_1 @ ( times_times_real @ Rx_1 @ Ry_1 ) )
= ( times_times_real @ ( times_times_real @ Lx_1 @ Rx_1 ) @ Ry_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[381]) ).
thf(932,plain,
( ( ! [Lx_2: int,Ly: int,Rx_2: int] :
( ( times_times_int @ ( times_times_int @ Lx_2 @ Ly ) @ Rx_2 )
= ( times_times_int @ Lx_2 @ ( times_times_int @ Ly @ Rx_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[382]) ).
thf(933,plain,
( ( ! [Lx_2: nat,Ly: nat,Rx_2: nat] :
( ( times_times_nat @ ( times_times_nat @ Lx_2 @ Ly ) @ Rx_2 )
= ( times_times_nat @ Lx_2 @ ( times_times_nat @ Ly @ Rx_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[383]) ).
thf(934,plain,
( ( ! [Lx_2: real,Ly: real,Rx_2: real] :
( ( times_times_real @ ( times_times_real @ Lx_2 @ Ly ) @ Rx_2 )
= ( times_times_real @ Lx_2 @ ( times_times_real @ Ly @ Rx_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[384]) ).
thf(935,plain,
( ( ! [Lx_3: int,Ly_1: int,Rx_3: int] :
( ( times_times_int @ ( times_times_int @ Lx_3 @ Ly_1 ) @ Rx_3 )
= ( times_times_int @ ( times_times_int @ Lx_3 @ Rx_3 ) @ Ly_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[385]) ).
thf(936,plain,
( ( ! [Lx_3: nat,Ly_1: nat,Rx_3: nat] :
( ( times_times_nat @ ( times_times_nat @ Lx_3 @ Ly_1 ) @ Rx_3 )
= ( times_times_nat @ ( times_times_nat @ Lx_3 @ Rx_3 ) @ Ly_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[386]) ).
thf(937,plain,
( ( ! [Lx_3: real,Ly_1: real,Rx_3: real] :
( ( times_times_real @ ( times_times_real @ Lx_3 @ Ly_1 ) @ Rx_3 )
= ( times_times_real @ ( times_times_real @ Lx_3 @ Rx_3 ) @ Ly_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[387]) ).
thf(938,plain,
( ( ! [Lx_4: int,Ly_2: int,Rx_4: int,Ry_2: int] :
( ( times_times_int @ ( times_times_int @ Lx_4 @ Ly_2 ) @ ( times_times_int @ Rx_4 @ Ry_2 ) )
= ( times_times_int @ Lx_4 @ ( times_times_int @ Ly_2 @ ( times_times_int @ Rx_4 @ Ry_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[388]) ).
thf(939,plain,
( ( ! [Lx_4: nat,Ly_2: nat,Rx_4: nat,Ry_2: nat] :
( ( times_times_nat @ ( times_times_nat @ Lx_4 @ Ly_2 ) @ ( times_times_nat @ Rx_4 @ Ry_2 ) )
= ( times_times_nat @ Lx_4 @ ( times_times_nat @ Ly_2 @ ( times_times_nat @ Rx_4 @ Ry_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[389]) ).
thf(940,plain,
( ( ! [Lx_4: real,Ly_2: real,Rx_4: real,Ry_2: real] :
( ( times_times_real @ ( times_times_real @ Lx_4 @ Ly_2 ) @ ( times_times_real @ Rx_4 @ Ry_2 ) )
= ( times_times_real @ Lx_4 @ ( times_times_real @ Ly_2 @ ( times_times_real @ Rx_4 @ Ry_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[390]) ).
thf(941,plain,
( ( ! [Lx_5: int,Ly_3: int,Rx_5: int,Ry_3: int] :
( ( times_times_int @ ( times_times_int @ Lx_5 @ Ly_3 ) @ ( times_times_int @ Rx_5 @ Ry_3 ) )
= ( times_times_int @ Rx_5 @ ( times_times_int @ ( times_times_int @ Lx_5 @ Ly_3 ) @ Ry_3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[391]) ).
thf(942,plain,
( ( ! [Lx_5: nat,Ly_3: nat,Rx_5: nat,Ry_3: nat] :
( ( times_times_nat @ ( times_times_nat @ Lx_5 @ Ly_3 ) @ ( times_times_nat @ Rx_5 @ Ry_3 ) )
= ( times_times_nat @ Rx_5 @ ( times_times_nat @ ( times_times_nat @ Lx_5 @ Ly_3 ) @ Ry_3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[392]) ).
thf(943,plain,
( ( ! [Lx_5: real,Ly_3: real,Rx_5: real,Ry_3: real] :
( ( times_times_real @ ( times_times_real @ Lx_5 @ Ly_3 ) @ ( times_times_real @ Rx_5 @ Ry_3 ) )
= ( times_times_real @ Rx_5 @ ( times_times_real @ ( times_times_real @ Lx_5 @ Ly_3 ) @ Ry_3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[393]) ).
thf(944,plain,
( ( ! [Lx_6: int,Ly_4: int,Rx_6: int,Ry_4: int] :
( ( times_times_int @ ( times_times_int @ Lx_6 @ Ly_4 ) @ ( times_times_int @ Rx_6 @ Ry_4 ) )
= ( times_times_int @ ( times_times_int @ Lx_6 @ Rx_6 ) @ ( times_times_int @ Ly_4 @ Ry_4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[394]) ).
thf(945,plain,
( ( ! [Lx_6: nat,Ly_4: nat,Rx_6: nat,Ry_4: nat] :
( ( times_times_nat @ ( times_times_nat @ Lx_6 @ Ly_4 ) @ ( times_times_nat @ Rx_6 @ Ry_4 ) )
= ( times_times_nat @ ( times_times_nat @ Lx_6 @ Rx_6 ) @ ( times_times_nat @ Ly_4 @ Ry_4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[395]) ).
thf(946,plain,
( ( ! [Lx_6: real,Ly_4: real,Rx_6: real,Ry_4: real] :
( ( times_times_real @ ( times_times_real @ Lx_6 @ Ly_4 ) @ ( times_times_real @ Rx_6 @ Ry_4 ) )
= ( times_times_real @ ( times_times_real @ Lx_6 @ Rx_6 ) @ ( times_times_real @ Ly_4 @ Ry_4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[396]) ).
thf(947,plain,
( ( ! [Y: int,X: int] :
( ( twoSqu362149276sum2sq @ X )
=> ( ( twoSqu362149276sum2sq @ Y )
=> ( twoSqu362149276sum2sq @ ( times_times_int @ X @ Y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[398]) ).
thf(948,plain,
( ( ! [N: nat,B: int,A: int,P: int] :
( ( zprime @ P )
=> ( ~ ( dvd_dvd_int @ P @ A )
=> ( ( dvd_dvd_int @ ( power_power_int @ P @ N ) @ ( times_times_int @ A @ B ) )
=> ( dvd_dvd_int @ ( power_power_int @ P @ N ) @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[407]) ).
thf(949,plain,
( ( ! [N: nat,A: int,B: int,P: int] :
( ( zprime @ P )
=> ( ~ ( dvd_dvd_int @ P @ B )
=> ( ( dvd_dvd_int @ ( power_power_int @ P @ N ) @ ( times_times_int @ A @ B ) )
=> ( dvd_dvd_int @ ( power_power_int @ P @ N ) @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[408]) ).
thf(950,plain,
( ( ! [X_17: nat,P_2: nat,Q_4: nat] :
( ( power_power_nat @ ( power_power_nat @ X_17 @ P_2 ) @ Q_4 )
= ( power_power_nat @ X_17 @ ( times_times_nat @ P_2 @ Q_4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[410]) ).
thf(951,plain,
( ( ! [X_17: real,P_2: nat,Q_4: nat] :
( ( power_power_real @ ( power_power_real @ X_17 @ P_2 ) @ Q_4 )
= ( power_power_real @ X_17 @ ( times_times_nat @ P_2 @ Q_4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[411]) ).
thf(952,plain,
( ( ! [X: nat,N: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X @ N ) )
<=> ( ( N = zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[413]) ).
thf(953,plain,
( ( ! [X_18: real,N_35: nat] :
( ( power_power_real @ X_18 @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ N_35 ) )
= ( times_times_real @ ( power_power_real @ X_18 @ N_35 ) @ ( power_power_real @ X_18 @ N_35 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[420]) ).
thf(954,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)],[430]) ).
thf(955,plain,
( ( ! [Y_11: int] :
( ( ord_less_real @ one_one_real @ ( number267125858f_real @ Y_11 ) )
<=> ( ord_less_int @ ( bit1 @ pls ) @ Y_11 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[432]) ).
thf(956,plain,
( ( ! [X_19: int] :
( ( ord_less_real @ ( number267125858f_real @ X_19 ) @ one_one_real )
<=> ( ord_less_int @ X_19 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[434]) ).
thf(957,plain,
( ( ( plus_plus_real @ one_one_real @ one_one_real )
= ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[436]) ).
thf(958,plain,
( ( ( plus_plus_real @ one_one_real @ one_one_real )
= ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[439]) ).
thf(959,plain,
( ( ! [Y_12: int] :
( ( ord_less_real @ zero_zero_real @ ( number267125858f_real @ Y_12 ) )
<=> ( ord_less_int @ pls @ Y_12 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[441]) ).
thf(960,plain,
( ( ! [X_20: int] :
( ( ord_less_real @ ( number267125858f_real @ X_20 ) @ zero_zero_real )
<=> ( ord_less_int @ X_20 @ pls ) ) )
= $true ),
inference(unfold_def,[status(thm)],[443]) ).
thf(961,plain,
( ( ! [W_6: int] :
( ( number267125858f_real @ ( bit1 @ W_6 ) )
= ( plus_plus_real @ ( plus_plus_real @ one_one_real @ ( number267125858f_real @ W_6 ) ) @ ( number267125858f_real @ W_6 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[453]) ).
thf(962,plain,
( ( ! [W_7: int] :
( ( number267125858f_real @ ( bit0 @ W_7 ) )
= ( plus_plus_real @ ( plus_plus_real @ zero_zero_real @ ( number267125858f_real @ W_7 ) ) @ ( number267125858f_real @ W_7 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[455]) ).
thf(963,plain,
( ( ! [X_21: nat,Y_13: nat] :
( ( power_power_nat @ ( plus_plus_nat @ X_21 @ Y_13 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_nat @ ( plus_plus_nat @ ( power_power_nat @ X_21 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_nat @ Y_13 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_nat @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ X_21 ) @ Y_13 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[457]) ).
thf(964,plain,
( ( ! [X_21: real,Y_13: real] :
( ( power_power_real @ ( plus_plus_real @ X_21 @ Y_13 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_real @ ( plus_plus_real @ ( power_power_real @ X_21 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y_13 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ X_21 ) @ Y_13 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[458]) ).
thf(965,plain,
( ( ! [W_8: int] :
( ( power_power_real @ ( number267125858f_real @ W_8 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_real @ ( number267125858f_real @ W_8 ) @ ( number267125858f_real @ W_8 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[461]) ).
thf(966,plain,
( ( ! [A_54: real] :
( ( ord_less_real @ ( plus_plus_real @ A_54 @ A_54 ) @ zero_zero_real )
<=> ( ord_less_real @ A_54 @ zero_zero_real ) ) )
= $true ),
inference(unfold_def,[status(thm)],[496]) ).
thf(967,plain,
( ( ! [Z_4: real] :
( ( times_times_real @ Z_4 @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_real @ Z_4 @ Z_4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[501]) ).
thf(968,plain,
( ( ! [Z_5: real] :
( ( times_times_real @ Z_5 @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_real @ Z_5 @ Z_5 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[504]) ).
thf(969,plain,
( ( ! [Z_6: real] :
( ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ Z_6 )
= ( plus_plus_real @ Z_6 @ Z_6 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[506]) ).
thf(970,plain,
( ( ! [Z_7: real] :
( ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ Z_7 )
= ( plus_plus_real @ Z_7 @ Z_7 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[509]) ).
thf(971,plain,
( ( ! [W_12: int] :
( ( times_times_real @ ( plus_plus_real @ one_one_real @ one_one_real ) @ ( number267125858f_real @ W_12 ) )
= ( number267125858f_real @ ( bit0 @ W_12 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[514]) ).
thf(972,plain,
( ( ! [A_57: real] :
( ( ( plus_plus_real @ A_57 @ A_57 )
= zero_zero_real )
<=> ( A_57 = zero_zero_real ) ) )
= $true ),
inference(unfold_def,[status(thm)],[537]) ).
thf(973,plain,
( ( ! [X_23: real,Y_15: real] :
~ ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ X_23 @ X_23 ) @ ( times_times_real @ Y_15 @ Y_15 ) ) @ zero_zero_real ) )
= $true ),
inference(unfold_def,[status(thm)],[546]) ).
thf(974,plain,
( ( ! [X_24: real,Y_16: real] :
( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X_24 @ X_24 ) @ ( times_times_real @ Y_16 @ Y_16 ) ) )
<=> ( ( X_24 != zero_zero_real )
| ( Y_16 != zero_zero_real ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[548]) ).
thf(975,plain,
( ( ! [X_25: real,Y_17: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X_25 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y_17 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[550]) ).
thf(976,plain,
( ( ! [X_26: real,Y_18: real] :
( ( ord_less_eq_real @ ( plus_plus_real @ ( power_power_real @ X_26 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y_18 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_real )
<=> ( ( X_26 = zero_zero_real )
& ( Y_18 = zero_zero_real ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[552]) ).
thf(977,plain,
( ( ! [X_27: nat,Y_19: nat] :
( ( ord_less_nat @ ( power_power_nat @ X_27 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_nat @ Y_19 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ Y_19 )
=> ( ord_less_nat @ X_27 @ Y_19 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[554]) ).
thf(978,plain,
( ( ! [X_27: real,Y_19: real] :
( ( ord_less_real @ ( power_power_real @ X_27 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y_19 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_real @ zero_zero_real @ Y_19 )
=> ( ord_less_real @ X_27 @ Y_19 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[555]) ).
thf(979,plain,
( ( ! [A_60: real] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A_60 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[557]) ).
thf(980,plain,
( ( ! [X_28: nat,Y_20: nat] :
( ( ord_less_eq_nat @ ( power_power_nat @ X_28 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_nat @ Y_20 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ Y_20 )
=> ( ord_less_eq_nat @ X_28 @ Y_20 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[559]) ).
thf(981,plain,
( ( ! [X_28: real,Y_20: real] :
( ( ord_less_eq_real @ ( power_power_real @ X_28 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y_20 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_real @ zero_zero_real @ Y_20 )
=> ( ord_less_eq_real @ X_28 @ Y_20 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[560]) ).
thf(982,plain,
( ( ! [X_29: nat,Y_21: nat] :
( ( ( power_power_nat @ X_29 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power_nat @ Y_21 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ X_29 )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ Y_21 )
=> ( X_29 = Y_21 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[562]) ).
thf(983,plain,
( ( ! [X_29: real,Y_21: real] :
( ( ( power_power_real @ X_29 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power_real @ Y_21 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_real @ zero_zero_real @ X_29 )
=> ( ( ord_less_eq_real @ zero_zero_real @ Y_21 )
=> ( X_29 = Y_21 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[563]) ).
thf(984,plain,
( ( ! [V_9: int,B_21: real,C_13: real] :
( ( times_times_real @ ( number267125858f_real @ V_9 ) @ ( plus_plus_real @ B_21 @ C_13 ) )
= ( plus_plus_real @ ( times_times_real @ ( number267125858f_real @ V_9 ) @ B_21 ) @ ( times_times_real @ ( number267125858f_real @ V_9 ) @ C_13 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[571]) ).
thf(985,plain,
( ( ! [A_61: real,B_22: real,V_10: int] :
( ( times_times_real @ ( plus_plus_real @ A_61 @ B_22 ) @ ( number267125858f_real @ V_10 ) )
= ( plus_plus_real @ ( times_times_real @ A_61 @ ( number267125858f_real @ V_10 ) ) @ ( times_times_real @ B_22 @ ( number267125858f_real @ V_10 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[574]) ).
thf(986,plain,
( ( ! [X_30: real,Y_22: real] :
( ( ( plus_plus_real @ ( times_times_real @ X_30 @ X_30 ) @ ( times_times_real @ Y_22 @ Y_22 ) )
= zero_zero_real )
<=> ( ( X_30 = zero_zero_real )
& ( Y_22 = zero_zero_real ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[576]) ).
thf(987,plain,
( ( ! [W_13: int,X_31: int] :
( ( ( number_number_of_int @ W_13 )
= X_31 )
<=> ( X_31
= ( number_number_of_int @ W_13 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[581]) ).
thf(988,plain,
( ( ! [W_13: int,X_31: real] :
( ( ( number267125858f_real @ W_13 )
= X_31 )
<=> ( X_31
= ( number267125858f_real @ W_13 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[582]) ).
thf(989,plain,
( ( ! [X_32: int,Y_23: int] :
( ( ( number_number_of_int @ X_32 )
= ( number_number_of_int @ Y_23 ) )
<=> ( X_32 = Y_23 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[583]) ).
thf(990,plain,
( ( ! [X_32: int,Y_23: int] :
( ( ( number267125858f_real @ X_32 )
= ( number267125858f_real @ Y_23 ) )
<=> ( X_32 = Y_23 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[584]) ).
thf(991,plain,
( ( ! [V_12: int,V_11: int] :
( ( ord_less_eq_int @ pls @ V_11 )
=> ( ( ord_less_eq_int @ pls @ V_12 )
=> ( ( plus_plus_real @ ( number267125858f_real @ V_11 ) @ ( number267125858f_real @ V_12 ) )
= ( number267125858f_real @ ( plus_plus_int @ V_11 @ V_12 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[589]) ).
thf(992,plain,
( ( ! [Y_24: int] :
( ( ord_less_eq_real @ one_one_real @ ( number267125858f_real @ Y_24 ) )
<=> ( ord_less_eq_int @ ( bit1 @ pls ) @ Y_24 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[613]) ).
thf(993,plain,
( ( ! [X_33: int] :
( ( ord_less_eq_real @ ( number267125858f_real @ X_33 ) @ one_one_real )
<=> ( ord_less_eq_int @ X_33 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[615]) ).
thf(994,plain,
( ( ! [V_13: int,W_15: int] :
( ( ord_less_eq_real @ ( number267125858f_real @ V_13 ) @ ( number267125858f_real @ W_15 ) )
<=> ~ ( ord_less_real @ ( number267125858f_real @ W_15 ) @ ( number267125858f_real @ V_13 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[626]) ).
thf(995,plain,
( ( ! [Y_25: int] :
( ( ord_less_eq_real @ zero_zero_real @ ( number267125858f_real @ Y_25 ) )
<=> ( ord_less_eq_int @ pls @ Y_25 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[629]) ).
thf(996,plain,
( ( ! [X_34: int] :
( ( ord_less_eq_real @ ( number267125858f_real @ X_34 ) @ zero_zero_real )
<=> ( ord_less_eq_int @ X_34 @ pls ) ) )
= $true ),
inference(unfold_def,[status(thm)],[631]) ).
thf(997,plain,
( ( ! [X_35: real,Y_26: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X_35 @ X_35 ) @ ( times_times_real @ Y_26 @ Y_26 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[633]) ).
thf(998,plain,
( ( ! [X_36: real,Y_27: real] :
( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ X_36 @ X_36 ) @ ( times_times_real @ Y_27 @ Y_27 ) ) @ zero_zero_real )
<=> ( ( X_36 = zero_zero_real )
& ( Y_27 = zero_zero_real ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[635]) ).
thf(999,plain,
( ( ! [V_14: int,W_16: int] :
( ( number_number_of_int @ ( times_times_int @ V_14 @ W_16 ) )
= ( times_times_int @ ( number_number_of_int @ V_14 ) @ ( number_number_of_int @ W_16 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[636]) ).
thf(1000,plain,
( ( ! [V_14: int,W_16: int] :
( ( number267125858f_real @ ( times_times_int @ V_14 @ W_16 ) )
= ( times_times_real @ ( number267125858f_real @ V_14 ) @ ( number267125858f_real @ W_16 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[637]) ).
thf(1001,plain,
( ( ! [V_15: int,W_17: int] :
( ( times_times_int @ ( number_number_of_int @ V_15 ) @ ( number_number_of_int @ W_17 ) )
= ( number_number_of_int @ ( times_times_int @ V_15 @ W_17 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[638]) ).
thf(1002,plain,
( ( ! [V_15: int,W_17: int] :
( ( times_times_real @ ( number267125858f_real @ V_15 ) @ ( number267125858f_real @ W_17 ) )
= ( number267125858f_real @ ( times_times_int @ V_15 @ W_17 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[639]) ).
thf(1003,plain,
( ( ! [V_16: int,W_18: int,Z_9: int] :
( ( times_times_int @ ( number_number_of_int @ V_16 ) @ ( times_times_int @ ( number_number_of_int @ W_18 ) @ Z_9 ) )
= ( times_times_int @ ( number_number_of_int @ ( times_times_int @ V_16 @ W_18 ) ) @ Z_9 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[640]) ).
thf(1004,plain,
( ( ! [V_16: int,W_18: int,Z_9: real] :
( ( times_times_real @ ( number267125858f_real @ V_16 ) @ ( times_times_real @ ( number267125858f_real @ W_18 ) @ Z_9 ) )
= ( times_times_real @ ( number267125858f_real @ ( times_times_int @ V_16 @ W_18 ) ) @ Z_9 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[641]) ).
thf(1005,plain,
( ( ! [V_18: int,V_17: int] :
( ( ord_less_eq_int @ pls @ V_17 )
=> ( ( ord_less_eq_int @ pls @ V_18 )
=> ( ( times_times_int @ ( number_number_of_int @ V_17 ) @ ( number_number_of_int @ V_18 ) )
= ( number_number_of_int @ ( times_times_int @ V_17 @ V_18 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[642]) ).
thf(1006,plain,
( ( ! [V_18: int,V_17: int] :
( ( ord_less_eq_int @ pls @ V_17 )
=> ( ( ord_less_eq_int @ pls @ V_18 )
=> ( ( times_times_nat @ ( number_number_of_nat @ V_17 ) @ ( number_number_of_nat @ V_18 ) )
= ( number_number_of_nat @ ( times_times_int @ V_17 @ V_18 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[643]) ).
thf(1007,plain,
( ( ! [V_18: int,V_17: int] :
( ( ord_less_eq_int @ pls @ V_17 )
=> ( ( ord_less_eq_int @ pls @ V_18 )
=> ( ( times_times_real @ ( number267125858f_real @ V_17 ) @ ( number267125858f_real @ V_18 ) )
= ( number267125858f_real @ ( times_times_int @ V_17 @ V_18 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[644]) ).
thf(1008,plain,
( ( ! [Z: int,W: int] :
( ( ord_less_eq_int @ Z @ W )
=> ( ( ord_less_eq_int @ W @ Z )
=> ( Z = W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[655]) ).
thf(1009,plain,
( ( ! [K: int,I: int,J: int] :
( ( ord_less_eq_int @ I @ J )
=> ( ( ord_less_eq_int @ J @ K )
=> ( ord_less_eq_int @ I @ K ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[656]) ).
thf(1010,plain,
( ( ! [Z1: int,Z2: int,Z3: int] :
( ( times_times_int @ ( times_times_int @ Z1 @ Z2 ) @ Z3 )
= ( times_times_int @ Z1 @ ( times_times_int @ Z2 @ Z3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[657]) ).
thf(1011,plain,
( ( ! [X_37: int,Y_28: int] :
( ( ord_less_eq_int @ ( number_number_of_int @ X_37 ) @ ( number_number_of_int @ Y_28 ) )
<=> ( ord_less_eq_int @ X_37 @ Y_28 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[658]) ).
thf(1012,plain,
( ( ! [X_37: int,Y_28: int] :
( ( ord_less_eq_real @ ( number267125858f_real @ X_37 ) @ ( number267125858f_real @ Y_28 ) )
<=> ( ord_less_eq_int @ X_37 @ Y_28 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[659]) ).
thf(1013,plain,
( ( ! [K: int,L: int] :
( ( ord_less_eq_int @ ( number_number_of_int @ K ) @ ( number_number_of_int @ L ) )
<=> ( ord_less_eq_int @ K @ L ) ) )
= $true ),
inference(unfold_def,[status(thm)],[660]) ).
thf(1014,plain,
( ( ! [V_4: int,W: int] :
( ( times_times_int @ ( number_number_of_int @ V_4 ) @ ( number_number_of_int @ W ) )
= ( number_number_of_int @ ( times_times_int @ V_4 @ W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[661]) ).
thf(1015,plain,
( ( ! [Z: int,W: int] :
( ( ord_less_eq_int @ Z @ W )
| ( ord_less_eq_int @ W @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[662]) ).
thf(1016,plain,
( ( ! [Z: int,W: int] :
( ( times_times_int @ Z @ W )
= ( times_times_int @ W @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[663]) ).
thf(1017,plain,
( ( ! [K: int] :
( ( number_number_of_int @ K )
= K ) )
= $true ),
inference(unfold_def,[status(thm)],[664]) ).
thf(1018,plain,
( ( ! [W: int] : ( ord_less_eq_int @ W @ W ) )
= $true ),
inference(unfold_def,[status(thm)],[665]) ).
thf(1019,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)],[667]) ).
thf(1020,plain,
( ( ~ ! [T_1: int] :
( ( 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)],[668]) ).
thf(1021,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)],[669]) ).
thf(1022,plain,
( ( ! [V_19: int] :
( ( plus_plus_real @ ( number267125858f_real @ V_19 ) @ one_one_real )
= ( number267125858f_real @ ( plus_plus_int @ V_19 @ ( bit1 @ pls ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[671]) ).
thf(1023,plain,
( ( ! [W_19: int] :
( ( plus_plus_real @ one_one_real @ ( number267125858f_real @ W_19 ) )
= ( number267125858f_real @ ( plus_plus_int @ ( bit1 @ pls ) @ W_19 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[673]) ).
thf(1024,plain,
( ( ! [A_63: real] :
( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A_63 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
<=> ( A_63 != zero_zero_real ) ) )
= $true ),
inference(unfold_def,[status(thm)],[683]) ).
thf(1025,plain,
( ( ! [A_64: real] :
~ ( ord_less_real @ ( power_power_real @ A_64 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ zero_zero_real ) )
= $true ),
inference(unfold_def,[status(thm)],[685]) ).
thf(1026,plain,
( ( ! [X_38: real,Y_29: real] :
( ( ( plus_plus_real @ ( power_power_real @ X_38 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y_29 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_real )
<=> ( ( X_38 = zero_zero_real )
& ( Y_29 = zero_zero_real ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[687]) ).
thf(1027,plain,
( ( ! [X_39: real,Y_30: real] :
( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X_39 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y_30 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
<=> ( ( X_39 != zero_zero_real )
| ( Y_30 != zero_zero_real ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[689]) ).
thf(1028,plain,
( ( ! [X: real,Y: real] :
~ ( ord_less_real @ ( plus_plus_real @ ( power_power_real @ X @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_real ) )
= $true ),
inference(unfold_def,[status(thm)],[691]) ).
thf(1029,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)],[692]) ).
thf(1030,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)],[695]) ).
thf(1031,plain,
( ( ord_less_int @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ t ) @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ zero_zero_int ) )
= $true ),
inference(unfold_def,[status(thm)],[696]) ).
thf(1032,plain,
( ( ! [A_1: int,N_2: nat,N_1: nat] :
( ( ord_less_nat @ N_2 @ N_1 )
=> ( ( ord_less_int @ zero_zero_int @ A_1 )
=> ( ( ord_less_int @ A_1 @ one_one_int )
=> ( ord_less_int @ ( power_power_int @ A_1 @ N_1 ) @ ( power_power_int @ A_1 @ N_2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(1033,plain,
( ( ! [N_3: nat,A_2: int] :
( ( ord_less_int @ zero_zero_int @ A_2 )
=> ( ( ord_less_int @ A_2 @ one_one_int )
=> ( ord_less_int @ ( times_times_int @ A_2 @ ( power_power_int @ A_2 @ N_3 ) ) @ ( power_power_int @ A_2 @ N_3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(1034,plain,
( ( ! [A_3: int,N_5: nat,N_4: nat] :
( ( ord_less_eq_nat @ N_5 @ N_4 )
=> ( ( ord_less_eq_int @ one_one_int @ A_3 )
=> ( ord_less_eq_int @ ( power_power_int @ A_3 @ N_5 ) @ ( power_power_int @ A_3 @ N_4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(1035,plain,
( ( ! [X_2: nat,Y_2: nat,B_1: int] :
( ( ord_less_int @ one_one_int @ B_1 )
=> ( ( ord_less_int @ ( power_power_int @ B_1 @ X_2 ) @ ( power_power_int @ B_1 @ Y_2 ) )
<=> ( ord_less_nat @ X_2 @ Y_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(1036,plain,
( ( ! [M_1: nat,N_6: nat,A_4: int] :
( ( ord_less_int @ one_one_int @ A_4 )
=> ( ( ord_less_int @ ( power_power_int @ A_4 @ M_1 ) @ ( power_power_int @ A_4 @ N_6 ) )
=> ( ord_less_nat @ M_1 @ N_6 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(1037,plain,
( ( ! [A_5: int,N_8: nat,N_7: nat] :
( ( ord_less_nat @ N_8 @ N_7 )
=> ( ( ord_less_int @ one_one_int @ A_5 )
=> ( ord_less_int @ ( power_power_int @ A_5 @ N_8 ) @ ( power_power_int @ A_5 @ N_7 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(1038,plain,
( ( ! [N_9: nat] :
( ( ( N_9 = zero_zero_nat )
=> ( ( power_power_int @ zero_zero_int @ N_9 )
= one_one_int ) )
& ( ( N_9 != zero_zero_nat )
=> ( ( power_power_int @ zero_zero_int @ N_9 )
= zero_zero_int ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(1039,plain,
( ( ! [N_10: nat,A_6: int] :
( ( ord_less_int @ one_one_int @ A_6 )
=> ( ord_less_int @ one_one_int @ ( times_times_int @ A_6 @ ( power_power_int @ A_6 @ N_10 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(1040,plain,
( ( ! [N_11: nat,A_7: int] :
( ( ord_less_int @ one_one_int @ A_7 )
=> ( ord_less_int @ ( power_power_int @ A_7 @ N_11 ) @ ( times_times_int @ A_7 @ ( power_power_int @ A_7 @ N_11 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(1041,plain,
( ( ! [A_8: int,N_12: nat,B_2: int] :
( ( ord_less_int @ ( power_power_int @ A_8 @ N_12 ) @ ( power_power_int @ B_2 @ N_12 ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ B_2 )
=> ( ord_less_int @ A_8 @ B_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(1042,plain,
( ( ! [A_9: int,M_2: nat,N_13: nat] :
( ( ord_less_eq_nat @ M_2 @ N_13 )
=> ( dvd_dvd_int @ ( power_power_int @ A_9 @ M_2 ) @ ( power_power_int @ A_9 @ N_13 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(1043,plain,
( ( ! [N_14: nat,M_3: nat,X_3: int,Y_3: int] :
( ( dvd_dvd_int @ X_3 @ Y_3 )
=> ( ( ord_less_eq_nat @ N_14 @ M_3 )
=> ( dvd_dvd_int @ ( power_power_int @ X_3 @ N_14 ) @ ( power_power_int @ Y_3 @ M_3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(1044,plain,
( ( ! [M_4: nat,A_10: int,N_15: nat,B_3: int] :
( ( dvd_dvd_int @ ( power_power_int @ A_10 @ N_15 ) @ B_3 )
=> ( ( ord_less_eq_nat @ M_4 @ N_15 )
=> ( dvd_dvd_int @ ( power_power_int @ A_10 @ M_4 ) @ B_3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(1045,plain,
( ( ! [A_11: int,M_5: nat,N_16: nat] :
( ( power_power_int @ A_11 @ ( plus_plus_nat @ M_5 @ N_16 ) )
= ( times_times_int @ ( power_power_int @ A_11 @ M_5 ) @ ( power_power_int @ A_11 @ N_16 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(1046,plain,
( ( ! [A_12: int] :
( ( power_power_int @ A_12 @ zero_zero_nat )
= one_one_int ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(1047,plain,
( ( ! [A_13: int,N_17: nat] :
( ( ( power_power_int @ A_13 @ N_17 )
= zero_zero_int )
<=> ( ( A_13 = zero_zero_int )
& ( N_17 != zero_zero_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(1048,plain,
( ( ! [M_6: nat,N_18: nat,A_14: int] :
( ( ord_less_int @ one_one_int @ A_14 )
=> ( ( ( power_power_int @ A_14 @ M_6 )
= ( power_power_int @ A_14 @ N_18 ) )
<=> ( M_6 = N_18 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(1049,plain,
( ( ! [N_19: nat,A_15: int] :
( ( ord_less_eq_int @ one_one_int @ A_15 )
=> ( ord_less_eq_int @ one_one_int @ ( power_power_int @ A_15 @ N_19 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(1050,plain,
( ( ! [N_20: nat,A_16: int] :
( ( ord_less_int @ zero_zero_int @ A_16 )
=> ( ord_less_int @ zero_zero_int @ ( power_power_int @ A_16 @ N_20 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(1051,plain,
( ( ! [N_21: nat,A_17: int] :
( ( ord_less_eq_int @ zero_zero_int @ A_17 )
=> ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A_17 @ N_21 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(1052,plain,
( ( ! [N_22: nat,A_18: int,B_4: int] :
( ( ord_less_eq_int @ A_18 @ B_4 )
=> ( ( ord_less_eq_int @ zero_zero_int @ A_18 )
=> ( ord_less_eq_int @ ( power_power_int @ A_18 @ N_22 ) @ ( power_power_int @ B_4 @ N_22 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(1053,plain,
( ( ! [A_19: int] :
( ( power_power_int @ A_19 @ one_one_nat )
= A_19 ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(1054,plain,
( ( ! [A_20: int,M_7: nat,N_23: nat] :
( ( power_power_int @ A_20 @ ( times_times_nat @ M_7 @ N_23 ) )
= ( power_power_int @ ( power_power_int @ A_20 @ M_7 ) @ N_23 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(1055,plain,
( ( ! [N_24: nat,X_4: int,Y_4: int] :
( ( dvd_dvd_int @ X_4 @ Y_4 )
=> ( dvd_dvd_int @ ( power_power_int @ X_4 @ N_24 ) @ ( power_power_int @ Y_4 @ N_24 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(1056,plain,
( ( ! [N_25: nat] :
( ( power_power_int @ one_one_int @ N_25 )
= one_one_int ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(1057,plain,
( ( ! [A_21: int,N_26: nat] :
( ( times_times_int @ ( power_power_int @ A_21 @ N_26 ) @ A_21 )
= ( times_times_int @ A_21 @ ( power_power_int @ A_21 @ N_26 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(1058,plain,
( ( ! [A_22: int,B_5: int,N_27: nat] :
( ( power_power_int @ ( times_times_int @ A_22 @ B_5 ) @ N_27 )
= ( times_times_int @ ( power_power_int @ A_22 @ N_27 ) @ ( power_power_int @ B_5 @ N_27 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(1059,plain,
( ( ! [N_28: nat,A_23: int] :
( ( A_23 != zero_zero_int )
=> ( ( power_power_int @ A_23 @ N_28 )
!= zero_zero_int ) ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(1060,plain,
( ( ! [X_6: int] :
( ( minus_minus_int @ ( times_times_int @ X_6 @ X_6 ) @ one_one_int )
= ( times_times_int @ ( plus_plus_int @ X_6 @ one_one_int ) @ ( minus_minus_int @ X_6 @ one_one_int ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[110]) ).
thf(1061,plain,
( ( ! [X_7: int,Y_5: int,A_25: int,B_7: int] :
( ( minus_minus_int @ ( times_times_int @ X_7 @ Y_5 ) @ ( times_times_int @ A_25 @ B_7 ) )
= ( plus_plus_int @ ( times_times_int @ X_7 @ ( minus_minus_int @ Y_5 @ B_7 ) ) @ ( times_times_int @ ( minus_minus_int @ X_7 @ A_25 ) @ B_7 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[119]) ).
thf(1062,plain,
( ( ! [A_26: int,C_1: int,B_8: int,D_1: int] :
( ( minus_minus_int @ ( plus_plus_int @ A_26 @ C_1 ) @ ( plus_plus_int @ B_8 @ D_1 ) )
= ( plus_plus_int @ ( minus_minus_int @ A_26 @ B_8 ) @ ( minus_minus_int @ C_1 @ D_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[126]) ).
thf(1063,plain,
( ( ! [M: int,X: int] :
( ( quadRes @ M @ X )
<=> ? [Y_1: int] : ( zcong @ ( power_power_int @ Y_1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ X @ M ) ) )
= $true ),
inference(unfold_def,[status(thm)],[141]) ).
thf(1064,plain,
( ( ! [N: nat] :
( ( ( 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)],[149]) ).
thf(1065,plain,
( ( ! [M: int,X: int] :
( ( ord_less_eq_int @ zero_zero_int @ X )
=> ( ( ord_less_int @ X @ M )
=> ( ( zcong @ X @ zero_zero_int @ M )
=> ( X = zero_zero_int ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[151]) ).
thf(1066,plain,
( ( ! [X: int,P: int] :
( ( zcong @ X @ zero_zero_int @ P )
<=> ( dvd_dvd_int @ P @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[153]) ).
thf(1067,plain,
( ( ! [A: int,M: int] :
( ( zcong @ A @ zero_zero_int @ M )
<=> ( dvd_dvd_int @ M @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[154]) ).
thf(1068,plain,
( ( ! [N: int,M: int] :
( ( 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)],[155]) ).
thf(1069,plain,
( ( ! [M: int,X: int] :
( ( ord_less_int @ zero_zero_int @ X )
=> ( ( ord_less_int @ X @ M )
=> ~ ( zcong @ X @ zero_zero_int @ M ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[156]) ).
thf(1070,plain,
( ( ! [M: int,Y: int,X: int] :
( ( ord_less_int @ zero_zero_int @ X )
=> ( ( ord_less_int @ zero_zero_int @ Y )
=> ( ( ord_less_int @ zero_zero_int @ M )
=> ( ( zcong @ X @ Y @ M )
=> ( ( ord_less_int @ X @ M )
=> ( ( ord_less_int @ Y @ M )
=> ( X = Y ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[157]) ).
thf(1071,plain,
( ( ! [Z: nat,X: int,Y: int,M: int] :
( ( zcong @ X @ Y @ M )
=> ( zcong @ ( power_power_int @ X @ Z ) @ ( power_power_int @ Y @ Z ) @ M ) ) )
= $true ),
inference(unfold_def,[status(thm)],[162]) ).
thf(1072,plain,
( ( ! [C: int,A: int,B: int,M: int] :
( ( zcong @ A @ B @ M )
=> ( zcong @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) @ M ) ) )
= $true ),
inference(unfold_def,[status(thm)],[163]) ).
thf(1073,plain,
( ( ! [M: int] : ( zcong @ M @ zero_zero_int @ M ) )
= $true ),
inference(unfold_def,[status(thm)],[166]) ).
thf(1074,plain,
( ( ! [A: int,B: int] :
( ( times_times_int @ ( plus_plus_int @ A @ B ) @ ( minus_minus_int @ A @ B ) )
= ( minus_minus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[167]) ).
thf(1075,plain,
( ( ! [L: int] :
( ( minus_minus_int @ min @ ( bit0 @ L ) )
= ( bit1 @ ( minus_minus_int @ min @ L ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[172]) ).
thf(1076,plain,
( ( ! [L: int] :
( ( minus_minus_int @ min @ ( bit1 @ L ) )
= ( bit0 @ ( minus_minus_int @ min @ L ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[173]) ).
thf(1077,plain,
( ( ! [L: int] :
( ( minus_minus_int @ pls @ ( bit1 @ L ) )
= ( bit1 @ ( minus_minus_int @ min @ L ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[174]) ).
thf(1078,plain,
( ( ! [W: int,Z: int] :
( ( ord_less_eq_int @ W @ ( minus_minus_int @ Z @ one_one_int ) )
<=> ( ord_less_int @ W @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[175]) ).
thf(1079,plain,
( ( ! [A: int,X: int] :
( ( ord_less_int @ zero_zero_int @ X )
=> ( ( ord_less_int @ X @ A )
=> ( ( X
!= ( minus_minus_int @ A @ one_one_int ) )
=> ( ord_less_int @ X @ ( minus_minus_int @ A @ one_one_int ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[176]) ).
thf(1080,plain,
( ( ! [V: int,W_1: int,C_2: int] :
( ( plus_plus_int @ ( number_number_of_int @ V ) @ ( minus_minus_int @ ( number_number_of_int @ W_1 ) @ C_2 ) )
= ( minus_minus_int @ ( number_number_of_int @ ( plus_plus_int @ V @ W_1 ) ) @ C_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[177]) ).
thf(1081,plain,
( ( ! [A: int,R: int,B: int,M: int,C: int,D: int,N: int] :
( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ ( times_times_int @ R @ B ) ) @ M ) @ ( times_times_int @ ( minus_minus_int @ C @ ( times_times_int @ R @ D ) ) @ N ) )
= ( minus_minus_int @ ( plus_plus_int @ ( times_times_int @ A @ M ) @ ( times_times_int @ C @ N ) ) @ ( times_times_int @ R @ ( plus_plus_int @ ( times_times_int @ B @ M ) @ ( times_times_int @ D @ N ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[180]) ).
thf(1082,plain,
( ( ! [K: int,L: int] :
( ( ord_less_int @ K @ L )
<=> ( ord_less_int @ ( minus_minus_int @ K @ L ) @ zero_zero_int ) ) )
= $true ),
inference(unfold_def,[status(thm)],[181]) ).
thf(1083,plain,
( ( ! [L: int] :
( ( minus_minus_int @ pls @ ( bit0 @ L ) )
= ( bit0 @ ( minus_minus_int @ pls @ L ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[182]) ).
thf(1084,plain,
( ( ! [K: int,L: int] :
( ( minus_minus_int @ ( bit1 @ K ) @ ( bit1 @ L ) )
= ( bit0 @ ( minus_minus_int @ K @ L ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[183]) ).
thf(1085,plain,
( ( ! [K: int,L: int] :
( ( minus_minus_int @ ( bit1 @ K ) @ ( bit0 @ L ) )
= ( bit1 @ ( minus_minus_int @ K @ L ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[184]) ).
thf(1086,plain,
( ( ! [A: int,B: int,C: int] :
( ( ( minus_minus_int @ A @ B )
= C )
=> ( A
= ( plus_plus_int @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[191]) ).
thf(1087,plain,
( ( ! [K: int] :
( ( minus_minus_int @ K @ pls )
= K ) )
= $true ),
inference(unfold_def,[status(thm)],[192]) ).
thf(1088,plain,
( ( ! [K: int,L: int] :
( ( minus_minus_int @ ( bit0 @ K ) @ ( bit0 @ L ) )
= ( bit0 @ ( minus_minus_int @ K @ L ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[193]) ).
thf(1089,plain,
( ( ! [Z: nat,X: int,Y: nat,P: int] :
( ( zcong @ ( power_power_int @ X @ Y ) @ one_one_int @ P )
=> ( zcong @ ( power_power_int @ X @ ( times_times_nat @ Y @ Z ) ) @ one_one_int @ P ) ) )
= $true ),
inference(unfold_def,[status(thm)],[206]) ).
thf(1090,plain,
( ( ! [B: int,M: int,A: int] :
( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( ord_less_int @ A @ M )
=> ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ( ord_less_int @ B @ M )
=> ( ( zcong @ A @ B @ M )
=> ( A = B ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[207]) ).
thf(1091,plain,
( ( ! [M: int,A: int] :
( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( ord_less_int @ A @ M )
=> ( ( zcong @ A @ zero_zero_int @ M )
=> ( A = zero_zero_int ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[208]) ).
thf(1092,plain,
( ( ! [A: int,B: int,M: int] :
( ( zcong @ A @ B @ M )
<=> ? [K_1: int] :
( B
= ( plus_plus_int @ A @ ( times_times_int @ M @ K_1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[210]) ).
thf(1093,plain,
( ( ! [B: int,M: int,A: int] :
( ( ord_less_int @ zero_zero_int @ A )
=> ( ( ord_less_int @ A @ M )
=> ( ( ord_less_int @ zero_zero_int @ B )
=> ( ( ord_less_int @ B @ A )
=> ~ ( zcong @ A @ B @ M ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[211]) ).
thf(1094,plain,
( ( ! [C: int,D: int,A: int,B: int,M: int] :
( ( zcong @ A @ B @ M )
=> ( ( zcong @ C @ D @ M )
=> ( zcong @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) @ M ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[214]) ).
thf(1095,plain,
( ( ! [A: int,B: int] : ( zcong @ A @ B @ one_one_int ) )
= $true ),
inference(unfold_def,[status(thm)],[219]) ).
thf(1096,plain,
( ( ! [A: int,B: int] :
( ( zcong @ A @ B @ zero_zero_int )
<=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[220]) ).
thf(1097,plain,
( ( ! [B: int,A: int,C: int] :
( ( ord_less_int @ A @ C )
=> ( ( ord_less_int @ B @ C )
=> ( ( ord_less_eq_int @ A @ B )
| ( ord_less_eq_int @ B @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[221]) ).
thf(1098,plain,
( ( ! [X_9: int,Y_7: int] :
( ( ord_less_eq_int @ X_9 @ Y_7 )
=> ( ( X_9 != Y_7 )
=> ( ord_less_int @ X_9 @ Y_7 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[222]) ).
thf(1099,plain,
( ( ! [K: int] :
( ( ord_less_eq_int @ min @ ( bit0 @ K ) )
<=> ( ord_less_int @ min @ K ) ) )
= $true ),
inference(unfold_def,[status(thm)],[230]) ).
thf(1100,plain,
( ( ! [K: int] :
( ( ord_less_int @ ( bit0 @ K ) @ min )
<=> ( ord_less_eq_int @ K @ min ) ) )
= $true ),
inference(unfold_def,[status(thm)],[231]) ).
thf(1101,plain,
( ( ( number_number_of_int @ pls )
!= ( number_number_of_int @ min ) )
= $true ),
inference(unfold_def,[status(thm)],[232]) ).
thf(1102,plain,
( ( ! [K: int] :
( ( ord_less_eq_int @ ( bit0 @ K ) @ min )
<=> ( ord_less_eq_int @ K @ min ) ) )
= $true ),
inference(unfold_def,[status(thm)],[233]) ).
thf(1103,plain,
( ( ~ ( ord_less_eq_int @ pls @ min ) )
= $true ),
inference(unfold_def,[status(thm)],[234]) ).
thf(1104,plain,
( ( ord_less_eq_int @ min @ pls )
= $true ),
inference(unfold_def,[status(thm)],[235]) ).
thf(1105,plain,
( ( ! [K: int] :
( ( ord_less_eq_int @ ( bit1 @ K ) @ min )
<=> ( ord_less_eq_int @ K @ min ) ) )
= $true ),
inference(unfold_def,[status(thm)],[236]) ).
thf(1106,plain,
( ( ! [K: int] :
( ( ord_less_eq_int @ min @ ( bit1 @ K ) )
<=> ( ord_less_eq_int @ min @ K ) ) )
= $true ),
inference(unfold_def,[status(thm)],[237]) ).
thf(1107,plain,
( ( ord_less_int @ min @ zero_zero_int )
= $true ),
inference(unfold_def,[status(thm)],[238]) ).
thf(1108,plain,
( ( ! [K: int] :
( ( ord_less_int @ min @ ( bit0 @ K ) )
<=> ( ord_less_int @ min @ K ) ) )
= $true ),
inference(unfold_def,[status(thm)],[239]) ).
thf(1109,plain,
( ( ord_less_int @ min @ pls )
= $true ),
inference(unfold_def,[status(thm)],[240]) ).
thf(1110,plain,
( ( ~ ( ord_less_int @ pls @ min ) )
= $true ),
inference(unfold_def,[status(thm)],[241]) ).
thf(1111,plain,
( ( ! [K: int] :
( ( ord_less_int @ min @ ( bit1 @ K ) )
<=> ( ord_less_int @ min @ K ) ) )
= $true ),
inference(unfold_def,[status(thm)],[242]) ).
thf(1112,plain,
( ( ! [K: int] :
( ( ord_less_int @ ( bit1 @ K ) @ min )
<=> ( ord_less_int @ K @ min ) ) )
= $true ),
inference(unfold_def,[status(thm)],[243]) ).
thf(1113,plain,
( ( ~ ( ord_less_int @ min @ min ) )
= $true ),
inference(unfold_def,[status(thm)],[245]) ).
thf(1114,plain,
( ( ! [K: int] :
( ( bit0 @ K )
!= min ) )
= $true ),
inference(unfold_def,[status(thm)],[246]) ).
thf(1115,plain,
( ( ! [L: int] :
( min
!= ( bit0 @ L ) ) )
= $true ),
inference(unfold_def,[status(thm)],[247]) ).
thf(1116,plain,
( ( pls != min )
= $true ),
inference(unfold_def,[status(thm)],[248]) ).
thf(1117,plain,
( ( min != pls )
= $true ),
inference(unfold_def,[status(thm)],[249]) ).
thf(1118,plain,
( ( ! [K: int] :
( ( ( bit1 @ K )
= min )
<=> ( K = min ) ) )
= $true ),
inference(unfold_def,[status(thm)],[250]) ).
thf(1119,plain,
( ( ! [L: int] :
( ( min
= ( bit1 @ L ) )
<=> ( min = L ) ) )
= $true ),
inference(unfold_def,[status(thm)],[251]) ).
thf(1120,plain,
( ( ( bit1 @ min )
= min )
= $true ),
inference(unfold_def,[status(thm)],[252]) ).
thf(1121,plain,
( ( ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[255]) ).
thf(1122,plain,
( ( ! [Y: int,X: int,P: int] :
( ~ ( zcong @ X @ zero_zero_int @ P )
=> ( ( zcong @ ( power_power_int @ Y @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ X @ P )
=> ~ ( dvd_dvd_int @ P @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[258]) ).
thf(1123,plain,
( ( ! [X_10: int] :
( ( times_times_int @ X_10 @ X_10 )
= ( power_power_int @ X_10 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[260]) ).
thf(1124,plain,
( ( ! [X_10: nat] :
( ( times_times_nat @ X_10 @ X_10 )
= ( power_power_nat @ X_10 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[261]) ).
thf(1125,plain,
( ( ! [X_10: real] :
( ( times_times_real @ X_10 @ X_10 )
= ( power_power_real @ X_10 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[262]) ).
thf(1126,plain,
( ( ! [X: int] :
( ( power_power_int @ ( power_power_int @ X @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power_int @ X @ ( number_number_of_nat @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[263]) ).
thf(1127,plain,
( ( ! [B: int,Q: int,R: int,B_11: int,Q_1: int,R_1: int] :
( ( ( plus_plus_int @ ( times_times_int @ B @ Q ) @ R )
= ( plus_plus_int @ ( times_times_int @ B_11 @ Q_1 ) @ R_1 ) )
=> ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ B_11 @ Q_1 ) @ R_1 ) @ zero_zero_int )
=> ( ( ord_less_int @ R @ B )
=> ( ( ord_less_eq_int @ zero_zero_int @ R_1 )
=> ( ( ord_less_int @ zero_zero_int @ B_11 )
=> ( ( ord_less_eq_int @ B_11 @ B )
=> ( ord_less_eq_int @ Q_1 @ Q ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[264]) ).
thf(1128,plain,
( ( ! [B: int,Q_1: int,R_1: int,Q: int,R: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q_1 ) @ R_1 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q ) @ R ) )
=> ( ( ord_less_eq_int @ R @ zero_zero_int )
=> ( ( ord_less_int @ B @ R )
=> ( ( ord_less_int @ B @ R_1 )
=> ( ord_less_eq_int @ Q @ Q_1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[265]) ).
thf(1129,plain,
( ( ! [B: int,Q: int,R: int,B_11: int,Q_1: int,R_1: int] :
( ( ( plus_plus_int @ ( times_times_int @ B @ Q ) @ R )
= ( plus_plus_int @ ( times_times_int @ B_11 @ Q_1 ) @ R_1 ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B_11 @ Q_1 ) @ R_1 ) )
=> ( ( ord_less_int @ R_1 @ B_11 )
=> ( ( ord_less_eq_int @ zero_zero_int @ R )
=> ( ( ord_less_int @ zero_zero_int @ B_11 )
=> ( ( ord_less_eq_int @ B_11 @ B )
=> ( ord_less_eq_int @ Q @ Q_1 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[266]) ).
thf(1130,plain,
( ( ! [B: int,Q_1: int,R_1: int,Q: int,R: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q_1 ) @ R_1 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q ) @ R ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ R_1 )
=> ( ( ord_less_int @ R_1 @ B )
=> ( ( ord_less_int @ R @ B )
=> ( ord_less_eq_int @ Q_1 @ Q ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[267]) ).
thf(1131,plain,
( ( ! [B_11: int,Q_1: int,R_1: int] :
( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ B_11 @ Q_1 ) @ R_1 ) @ zero_zero_int )
=> ( ( ord_less_eq_int @ zero_zero_int @ R_1 )
=> ( ( ord_less_int @ zero_zero_int @ B_11 )
=> ( ord_less_eq_int @ Q_1 @ zero_zero_int ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[268]) ).
thf(1132,plain,
( ( ! [B_11: int,Q_1: int,R_1: int] :
( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B_11 @ Q_1 ) @ R_1 ) )
=> ( ( ord_less_int @ R_1 @ B_11 )
=> ( ( ord_less_int @ zero_zero_int @ B_11 )
=> ( ord_less_eq_int @ zero_zero_int @ Q_1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[269]) ).
thf(1133,plain,
( ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[270]) ).
thf(1134,plain,
( ( ! [W_3: int] :
( ( ( ( number_number_of_nat @ W_3 )
= zero_zero_nat )
=> ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ W_3 ) )
= one_one_int ) )
& ( ( ( number_number_of_nat @ W_3 )
!= zero_zero_nat )
=> ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ W_3 ) )
= zero_zero_int ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[271]) ).
thf(1135,plain,
( ( ! [N: nat,X: int] :
( ( ord_less_eq_int @ zero_zero_int @ X )
=> ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ X @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[274]) ).
thf(1136,plain,
( ( ! [Y: int,X: int] :
( ( ord_less_eq_int @ zero_zero_int @ X )
=> ( ( ord_less_eq_int @ zero_zero_int @ Y )
=> ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ X @ Y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[275]) ).
thf(1137,plain,
( ( ! [Y: int,X: int] :
( ( ord_less_eq_int @ zero_zero_int @ X )
=> ( ( ord_less_eq_int @ zero_zero_int @ Y )
=> ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ X @ Y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[276]) ).
thf(1138,plain,
( ( ord_less_eq_int @ zero_zero_int @ one_one_int )
= $true ),
inference(unfold_def,[status(thm)],[277]) ).
thf(1139,plain,
( ( ! [B: int,A: int] :
( ( ord_less_int @ zero_zero_int @ A )
=> ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
=> ( ord_less_int @ zero_zero_int @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[278]) ).
thf(1140,plain,
( ( ! [A_28: int,W_4: int] :
( ( ( power_power_int @ A_28 @ ( number_number_of_nat @ W_4 ) )
= zero_zero_int )
<=> ( ( A_28 = zero_zero_int )
& ( ( number_number_of_nat @ W_4 )
!= zero_zero_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[279]) ).
thf(1141,plain,
( ( ! [A_28: nat,W_4: int] :
( ( ( power_power_nat @ A_28 @ ( number_number_of_nat @ W_4 ) )
= zero_zero_nat )
<=> ( ( A_28 = zero_zero_nat )
& ( ( number_number_of_nat @ W_4 )
!= zero_zero_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[280]) ).
thf(1142,plain,
( ( ! [A_29: int,M_10: int] :
( ( plus_plus_int @ ( times_times_int @ A_29 @ M_10 ) @ M_10 )
= ( times_times_int @ ( plus_plus_int @ A_29 @ one_one_int ) @ M_10 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[282]) ).
thf(1143,plain,
( ( ! [M_11: int,A_30: int] :
( ( plus_plus_int @ M_11 @ ( times_times_int @ A_30 @ M_11 ) )
= ( times_times_int @ ( plus_plus_int @ A_30 @ one_one_int ) @ M_11 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[285]) ).
thf(1144,plain,
( ( ! [M_12: int] :
( ( plus_plus_int @ M_12 @ M_12 )
= ( times_times_int @ ( plus_plus_int @ one_one_int @ one_one_int ) @ M_12 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[288]) ).
thf(1145,plain,
( ( ! [C_4: int,D_2: int,A_31: int,B_12: int,R_2: int] :
( ( R_2 != zero_zero_int )
=> ( ( ( A_31 = B_12 )
& ( C_4 != D_2 ) )
=> ( ( plus_plus_int @ A_31 @ ( times_times_int @ R_2 @ C_4 ) )
!= ( plus_plus_int @ B_12 @ ( times_times_int @ R_2 @ D_2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[291]) ).
thf(1146,plain,
( ( ! [A_32: int,N_33: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A_32 @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ N_33 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[294]) ).
thf(1147,plain,
( ( ord_less_eq_int @ zero_zero_int @ zero_zero_int )
= $true ),
inference(unfold_def,[status(thm)],[296]) ).
thf(1148,plain,
( ( ! [X_11: int] :
( ( power_power_int @ X_11 @ zero_zero_nat )
= one_one_int ) )
= $true ),
inference(unfold_def,[status(thm)],[297]) ).
thf(1149,plain,
( ( ! [X_12: int,P_1: nat,Q_2: nat] :
( ( times_times_int @ ( power_power_int @ X_12 @ P_1 ) @ ( power_power_int @ X_12 @ Q_2 ) )
= ( power_power_int @ X_12 @ ( plus_plus_nat @ P_1 @ Q_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[300]) ).
thf(1150,plain,
( ( ! [X_13: int,Y_8: int,Q_3: nat] :
( ( power_power_int @ ( times_times_int @ X_13 @ Y_8 ) @ Q_3 )
= ( times_times_int @ ( power_power_int @ X_13 @ Q_3 ) @ ( power_power_int @ Y_8 @ Q_3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[303]) ).
thf(1151,plain,
( ( ! [A_33: int] :
( ( times_times_int @ A_33 @ one_one_int )
= A_33 ) )
= $true ),
inference(unfold_def,[status(thm)],[306]) ).
thf(1152,plain,
( ( ! [A_34: int] :
( ( times_times_int @ one_one_int @ A_34 )
= A_34 ) )
= $true ),
inference(unfold_def,[status(thm)],[309]) ).
thf(1153,plain,
( ( ! [W_5: int,Y_9: int,X_14: int,Z_1: int] :
( ( ( plus_plus_int @ ( times_times_int @ W_5 @ Y_9 ) @ ( times_times_int @ X_14 @ Z_1 ) )
= ( plus_plus_int @ ( times_times_int @ W_5 @ Z_1 ) @ ( times_times_int @ X_14 @ Y_9 ) ) )
<=> ( ( W_5 = X_14 )
| ( Y_9 = Z_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[312]) ).
thf(1154,plain,
( ( ! [A_35: int,M_13: int,B_13: int] :
( ( plus_plus_int @ ( times_times_int @ A_35 @ M_13 ) @ ( times_times_int @ B_13 @ M_13 ) )
= ( times_times_int @ ( plus_plus_int @ A_35 @ B_13 ) @ M_13 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[315]) ).
thf(1155,plain,
( ( ! [A_36: int,B_14: int,C_5: int] :
( ( times_times_int @ ( plus_plus_int @ A_36 @ B_14 ) @ C_5 )
= ( plus_plus_int @ ( times_times_int @ A_36 @ C_5 ) @ ( times_times_int @ B_14 @ C_5 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[318]) ).
thf(1156,plain,
( ( ! [C_6: int,D_3: int,A_37: int,B_15: int] :
( ( ( A_37 != B_15 )
& ( C_6 != D_3 ) )
<=> ( ( plus_plus_int @ ( times_times_int @ A_37 @ C_6 ) @ ( times_times_int @ B_15 @ D_3 ) )
!= ( plus_plus_int @ ( times_times_int @ A_37 @ D_3 ) @ ( times_times_int @ B_15 @ C_6 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[321]) ).
thf(1157,plain,
( ( ! [X_15: int,Y_10: int,Z_2: int] :
( ( times_times_int @ X_15 @ ( plus_plus_int @ Y_10 @ Z_2 ) )
= ( plus_plus_int @ ( times_times_int @ X_15 @ Y_10 ) @ ( times_times_int @ X_15 @ Z_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[324]) ).
thf(1158,plain,
( ( ! [B_16: int,A_38: int] :
( ( B_16
= ( plus_plus_int @ B_16 @ A_38 ) )
<=> ( A_38 = zero_zero_int ) ) )
= $true ),
inference(unfold_def,[status(thm)],[327]) ).
thf(1159,plain,
( ( ! [A_39: int] :
( ( plus_plus_int @ A_39 @ zero_zero_int )
= A_39 ) )
= $true ),
inference(unfold_def,[status(thm)],[330]) ).
thf(1160,plain,
( ( ! [A_40: int] :
( ( plus_plus_int @ zero_zero_int @ A_40 )
= A_40 ) )
= $true ),
inference(unfold_def,[status(thm)],[333]) ).
thf(1161,plain,
( ( ! [A_41: int] :
( ( times_times_int @ A_41 @ zero_zero_int )
= zero_zero_int ) )
= $true ),
inference(unfold_def,[status(thm)],[336]) ).
thf(1162,plain,
( ( ! [A_42: int] :
( ( times_times_int @ zero_zero_int @ A_42 )
= zero_zero_int ) )
= $true ),
inference(unfold_def,[status(thm)],[339]) ).
thf(1163,plain,
( ( ! [A_43: int,K_2: nat] :
( ( ord_less_eq_int @ ( power_power_int @ A_43 @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ K_2 ) ) @ zero_zero_int )
=> ( A_43 = zero_zero_int ) ) )
= $true ),
inference(unfold_def,[status(thm)],[342]) ).
thf(1164,plain,
( ( ! [A_44: int,N_34: nat] :
( ( power_power_int @ A_44 @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ N_34 ) )
= ( power_power_int @ ( power_power_int @ A_44 @ N_34 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[344]) ).
thf(1165,plain,
( ( ! [A_44: nat,N_34: nat] :
( ( power_power_nat @ A_44 @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ N_34 ) )
= ( power_power_nat @ ( power_power_nat @ A_44 @ N_34 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[345]) ).
thf(1166,plain,
( ( ! [A_44: real,N_34: nat] :
( ( power_power_real @ A_44 @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ N_34 ) )
= ( power_power_real @ ( power_power_real @ A_44 @ N_34 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[346]) ).
thf(1167,plain,
( ( ! [Z: nat] :
( ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ Z )
= ( plus_plus_nat @ Z @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[349]) ).
thf(1168,plain,
( ( ! [Z: nat] :
( ( times_times_nat @ Z @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_nat @ Z @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[350]) ).
thf(1169,plain,
( ( ! [X_16: int] :
( ( power_power_int @ X_16 @ one_one_nat )
= X_16 ) )
= $true ),
inference(unfold_def,[status(thm)],[352]) ).
thf(1170,plain,
( ( ! [A_45: int,B_17: int,C_7: int,D_4: int] :
( ( plus_plus_int @ ( plus_plus_int @ A_45 @ B_17 ) @ ( plus_plus_int @ C_7 @ D_4 ) )
= ( plus_plus_int @ ( plus_plus_int @ A_45 @ C_7 ) @ ( plus_plus_int @ B_17 @ D_4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[355]) ).
thf(1171,plain,
( ( ! [A_46: int,B_18: int,C_8: int] :
( ( plus_plus_int @ ( plus_plus_int @ A_46 @ B_18 ) @ C_8 )
= ( plus_plus_int @ ( plus_plus_int @ A_46 @ C_8 ) @ B_18 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[358]) ).
thf(1172,plain,
( ( ! [A_47: int,B_19: int,C_9: int] :
( ( plus_plus_int @ ( plus_plus_int @ A_47 @ B_19 ) @ C_9 )
= ( plus_plus_int @ A_47 @ ( plus_plus_int @ B_19 @ C_9 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[361]) ).
thf(1173,plain,
( ( ! [A_48: int,C_10: int,D_5: int] :
( ( plus_plus_int @ A_48 @ ( plus_plus_int @ C_10 @ D_5 ) )
= ( plus_plus_int @ ( plus_plus_int @ A_48 @ C_10 ) @ D_5 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[364]) ).
thf(1174,plain,
( ( ! [A_49: int,C_11: int,D_6: int] :
( ( plus_plus_int @ A_49 @ ( plus_plus_int @ C_11 @ D_6 ) )
= ( plus_plus_int @ C_11 @ ( plus_plus_int @ A_49 @ D_6 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[367]) ).
thf(1175,plain,
( ( ! [A_50: int,C_12: int] :
( ( plus_plus_int @ A_50 @ C_12 )
= ( plus_plus_int @ C_12 @ A_50 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[370]) ).
thf(1176,plain,
( ( ! [V_4: int,V_5: int] :
( ( ord_less_eq_nat @ ( number_number_of_nat @ V_4 ) @ ( number_number_of_nat @ V_5 ) )
<=> ( ~ ( ord_less_eq_int @ V_4 @ V_5 )
=> ( ord_less_eq_int @ V_4 @ pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[397]) ).
thf(1177,plain,
( ( ! [Z: int,N: int] :
( ( dvd_dvd_int @ Z @ N )
=> ( ( ord_less_int @ zero_zero_int @ N )
=> ( ord_less_eq_int @ Z @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[399]) ).
thf(1178,plain,
( ( zprime @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[400]) ).
thf(1179,plain,
( ( ! [C: int,X: int,T: int,A: int,D: int] :
( ( dvd_dvd_int @ A @ D )
=> ( ( dvd_dvd_int @ A @ ( plus_plus_int @ X @ T ) )
<=> ( dvd_dvd_int @ A @ ( plus_plus_int @ ( plus_plus_int @ X @ ( times_times_int @ C @ D ) ) @ T ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[401]) ).
thf(1180,plain,
( ( ! [K: int,N: int,M: int] :
( ( dvd_dvd_int @ K @ ( plus_plus_int @ N @ ( times_times_int @ K @ M ) ) )
<=> ( dvd_dvd_int @ K @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[402]) ).
thf(1181,plain,
( ( ! [K: int,M: int,N: int] :
( ( dvd_dvd_int @ ( times_times_int @ K @ M ) @ ( times_times_int @ K @ N ) )
=> ( ( K != zero_zero_int )
=> ( dvd_dvd_int @ M @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[403]) ).
thf(1182,plain,
( ( ! [N: int,M: int] :
( ( ord_less_eq_int @ zero_zero_int @ M )
=> ( ( ord_less_eq_int @ zero_zero_int @ N )
=> ( ( dvd_dvd_int @ M @ N )
=> ( ( dvd_dvd_int @ N @ M )
=> ( M = N ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[404]) ).
thf(1183,plain,
( ( ! [N: int,M: int] :
( ( ord_less_int @ zero_zero_int @ M )
=> ( ( ord_less_int @ M @ N )
=> ~ ( dvd_dvd_int @ N @ M ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[405]) ).
thf(1184,plain,
( ( ! [X: int,Y: nat,Z: nat] :
( ( power_power_int @ ( power_power_int @ X @ Y ) @ Z )
= ( power_power_int @ X @ ( times_times_nat @ Y @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[406]) ).
thf(1185,plain,
( ( ! [X_17: int,P_2: nat,Q_4: nat] :
( ( power_power_int @ ( power_power_int @ X_17 @ P_2 ) @ Q_4 )
= ( power_power_int @ X_17 @ ( times_times_nat @ P_2 @ Q_4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[409]) ).
thf(1186,plain,
( ( ! [A: int,N: nat,P: int] :
( ( zprime @ P )
=> ( ( dvd_dvd_int @ P @ ( power_power_int @ A @ N ) )
=> ( dvd_dvd_int @ P @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[412]) ).
thf(1187,plain,
( ( ! [X_18: int,N_35: nat] :
( ( power_power_int @ X_18 @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ N_35 ) )
= ( times_times_int @ ( power_power_int @ X_18 @ N_35 ) @ ( power_power_int @ X_18 @ N_35 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[418]) ).
thf(1188,plain,
( ( ! [X_18: nat,N_35: nat] :
( ( power_power_nat @ X_18 @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ N_35 ) )
= ( times_times_nat @ ( power_power_nat @ X_18 @ N_35 ) @ ( power_power_nat @ X_18 @ N_35 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[419]) ).
thf(1189,plain,
( ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[421]) ).
thf(1190,plain,
( ( ! [R: int,Q: int,A: int] :
( ( ord_less_int @ zero_zero_int @ A )
=> ( ( A
= ( plus_plus_int @ R @ ( times_times_int @ A @ Q ) ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ R )
=> ( ord_less_eq_int @ Q @ one_one_int ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[422]) ).
thf(1191,plain,
( ( ! [R: int,Q: int,A: int] :
( ( ord_less_int @ zero_zero_int @ A )
=> ( ( A
= ( plus_plus_int @ R @ ( times_times_int @ A @ Q ) ) )
=> ( ( ord_less_int @ R @ A )
=> ( ord_less_eq_int @ one_one_int @ Q ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[423]) ).
thf(1192,plain,
( ( ! [X: int] : ( ord_less_eq_int @ X @ ( power_power_int @ X @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[424]) ).
thf(1193,plain,
( ( ! [A: int] :
( ( times_times_int @ A @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( power_power_int @ A @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[425]) ).
thf(1194,plain,
( ( ! [X: int] :
( ( ord_less_eq_int @ zero_zero_int @ X )
=> ( ( ord_less_int @ X @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
=> ( ( X = zero_zero_int )
| ( X = one_one_int ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[427]) ).
thf(1195,plain,
( ( ! [A: int,B: int] :
( ( power_power_int @ ( plus_plus_int @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[428]) ).
thf(1196,plain,
( ( ! [A: int,B: int] :
( ( power_power_int @ ( plus_plus_int @ A @ B ) @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ B ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) @ A ) @ ( 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)],[429]) ).
thf(1197,plain,
( ( ! [Y_11: int] :
( ( ord_less_int @ one_one_int @ ( number_number_of_int @ Y_11 ) )
<=> ( ord_less_int @ ( bit1 @ pls ) @ Y_11 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[431]) ).
thf(1198,plain,
( ( ! [X_19: int] :
( ( ord_less_int @ ( number_number_of_int @ X_19 ) @ one_one_int )
<=> ( ord_less_int @ X_19 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[433]) ).
thf(1199,plain,
( ( ( plus_plus_int @ one_one_int @ one_one_int )
= ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[435]) ).
thf(1200,plain,
( ( ( plus_plus_int @ one_one_int @ one_one_int )
= ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[437]) ).
thf(1201,plain,
( ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
= ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[438]) ).
thf(1202,plain,
( ( ! [Y_12: int] :
( ( ord_less_int @ zero_zero_int @ ( number_number_of_int @ Y_12 ) )
<=> ( ord_less_int @ pls @ Y_12 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[440]) ).
thf(1203,plain,
( ( ! [X_20: int] :
( ( ord_less_int @ ( number_number_of_int @ X_20 ) @ zero_zero_int )
<=> ( ord_less_int @ X_20 @ pls ) ) )
= $true ),
inference(unfold_def,[status(thm)],[442]) ).
thf(1204,plain,
( ( ! [Z: int] :
( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z ) @ zero_zero_int )
<=> ( ord_less_int @ Z @ zero_zero_int ) ) )
= $true ),
inference(unfold_def,[status(thm)],[444]) ).
thf(1205,plain,
( ( one_one_int
= ( number_number_of_int @ ( bit1 @ pls ) ) )
= $true ),
inference(unfold_def,[status(thm)],[445]) ).
thf(1206,plain,
( ( one_one_real
= ( number267125858f_real @ ( bit1 @ pls ) ) )
= $true ),
inference(unfold_def,[status(thm)],[446]) ).
thf(1207,plain,
( ( ( number_number_of_int @ ( bit1 @ pls ) )
= one_one_int )
= $true ),
inference(unfold_def,[status(thm)],[447]) ).
thf(1208,plain,
( ( ( number267125858f_real @ ( bit1 @ pls ) )
= one_one_real )
= $true ),
inference(unfold_def,[status(thm)],[448]) ).
thf(1209,plain,
( ( ( number_number_of_int @ ( bit1 @ pls ) )
= one_one_int )
= $true ),
inference(unfold_def,[status(thm)],[449]) ).
thf(1210,plain,
( ( ( number_number_of_nat @ ( bit1 @ pls ) )
= one_one_nat )
= $true ),
inference(unfold_def,[status(thm)],[450]) ).
thf(1211,plain,
( ( ( number267125858f_real @ ( bit1 @ pls ) )
= one_one_real )
= $true ),
inference(unfold_def,[status(thm)],[451]) ).
thf(1212,plain,
( ( ! [W_6: int] :
( ( number_number_of_int @ ( bit1 @ W_6 ) )
= ( plus_plus_int @ ( plus_plus_int @ one_one_int @ ( number_number_of_int @ W_6 ) ) @ ( number_number_of_int @ W_6 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[452]) ).
thf(1213,plain,
( ( ! [W_7: int] :
( ( number_number_of_int @ ( bit0 @ W_7 ) )
= ( plus_plus_int @ ( plus_plus_int @ zero_zero_int @ ( number_number_of_int @ W_7 ) ) @ ( number_number_of_int @ W_7 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[454]) ).
thf(1214,plain,
( ( ! [X_21: int,Y_13: int] :
( ( power_power_int @ ( plus_plus_int @ X_21 @ Y_13 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ X_21 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_13 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ X_21 ) @ Y_13 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[456]) ).
thf(1215,plain,
( ( ! [W_8: int] :
( ( power_power_int @ ( number_number_of_int @ W_8 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_int @ ( number_number_of_int @ W_8 ) @ ( number_number_of_int @ W_8 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[459]) ).
thf(1216,plain,
( ( ! [W_8: int] :
( ( power_power_nat @ ( number_number_of_nat @ W_8 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_nat @ ( number_number_of_nat @ W_8 ) @ ( number_number_of_nat @ W_8 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[460]) ).
thf(1217,plain,
( ( ! [W: int,Z: int] :
( ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
<=> ( ( ord_less_int @ W @ Z )
| ( W = Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[462]) ).
thf(1218,plain,
( ( ! [Z: int] :
( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z )
!= zero_zero_int ) )
= $true ),
inference(unfold_def,[status(thm)],[463]) ).
thf(1219,plain,
( ( ! [K: int] :
( ( bit1 @ K )
= ( plus_plus_int @ ( plus_plus_int @ one_one_int @ K ) @ K ) ) )
= $true ),
inference(unfold_def,[status(thm)],[464]) ).
thf(1220,plain,
( ( ord_less_int @ zero_zero_int @ one_one_int )
= $true ),
inference(unfold_def,[status(thm)],[465]) ).
thf(1221,plain,
( ( ! [K: int,L: int] :
( ( plus_plus_int @ ( bit0 @ K ) @ ( bit1 @ L ) )
= ( bit1 @ ( plus_plus_int @ K @ L ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[466]) ).
thf(1222,plain,
( ( ! [K: int,L: int] :
( ( plus_plus_int @ ( bit1 @ K ) @ ( bit0 @ L ) )
= ( bit1 @ ( plus_plus_int @ K @ L ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[467]) ).
thf(1223,plain,
( ( ! [W: int] :
( ( ord_less_int @ ( bit0 @ W ) @ zero_zero_int )
<=> ( ord_less_int @ W @ zero_zero_int ) ) )
= $true ),
inference(unfold_def,[status(thm)],[468]) ).
thf(1224,plain,
( ( ~ ( ord_less_int @ pls @ zero_zero_int ) )
= $true ),
inference(unfold_def,[status(thm)],[469]) ).
thf(1225,plain,
( ( ! [K: int] :
( ( ord_less_int @ pls @ ( bit0 @ K ) )
<=> ( ord_less_int @ pls @ K ) ) )
= $true ),
inference(unfold_def,[status(thm)],[470]) ).
thf(1226,plain,
( ( ! [K: int] :
( ( ord_less_int @ ( bit0 @ K ) @ pls )
<=> ( ord_less_int @ K @ pls ) ) )
= $true ),
inference(unfold_def,[status(thm)],[471]) ).
thf(1227,plain,
( ( ! [W: int] :
( ( ord_less_int @ ( bit1 @ W ) @ zero_zero_int )
<=> ( ord_less_int @ W @ zero_zero_int ) ) )
= $true ),
inference(unfold_def,[status(thm)],[472]) ).
thf(1228,plain,
( ( ! [K: int,L: int] :
( ( ord_less_int @ ( bit1 @ K ) @ ( bit0 @ L ) )
<=> ( ord_less_int @ K @ L ) ) )
= $true ),
inference(unfold_def,[status(thm)],[473]) ).
thf(1229,plain,
( ( ! [K1: int,K2: int] :
( ( ord_less_int @ ( bit1 @ K1 ) @ ( bit0 @ K2 ) )
<=> ( ord_less_int @ K1 @ K2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[474]) ).
thf(1230,plain,
( ( ! [K: int] :
( ( ord_less_int @ ( bit1 @ K ) @ pls )
<=> ( ord_less_int @ K @ pls ) ) )
= $true ),
inference(unfold_def,[status(thm)],[475]) ).
thf(1231,plain,
( ( ! [V_6: int,W_9: int] :
( ( number_number_of_int @ ( plus_plus_int @ V_6 @ W_9 ) )
= ( plus_plus_int @ ( number_number_of_int @ V_6 ) @ ( number_number_of_int @ W_9 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[476]) ).
thf(1232,plain,
( ( ! [V_6: int,W_9: int] :
( ( number267125858f_real @ ( plus_plus_int @ V_6 @ W_9 ) )
= ( plus_plus_real @ ( number267125858f_real @ V_6 ) @ ( number267125858f_real @ W_9 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[477]) ).
thf(1233,plain,
( ( ! [V_7: int,W_10: int] :
( ( plus_plus_int @ ( number_number_of_int @ V_7 ) @ ( number_number_of_int @ W_10 ) )
= ( number_number_of_int @ ( plus_plus_int @ V_7 @ W_10 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[478]) ).
thf(1234,plain,
( ( ! [V_7: int,W_10: int] :
( ( plus_plus_real @ ( number267125858f_real @ V_7 ) @ ( number267125858f_real @ W_10 ) )
= ( number267125858f_real @ ( plus_plus_int @ V_7 @ W_10 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[479]) ).
thf(1235,plain,
( ( ! [V_8: int,W_11: int,Z_3: int] :
( ( plus_plus_int @ ( number_number_of_int @ V_8 ) @ ( plus_plus_int @ ( number_number_of_int @ W_11 ) @ Z_3 ) )
= ( plus_plus_int @ ( number_number_of_int @ ( plus_plus_int @ V_8 @ W_11 ) ) @ Z_3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[480]) ).
thf(1236,plain,
( ( ! [V_8: int,W_11: int,Z_3: real] :
( ( plus_plus_real @ ( number267125858f_real @ V_8 ) @ ( plus_plus_real @ ( number267125858f_real @ W_11 ) @ Z_3 ) )
= ( plus_plus_real @ ( number267125858f_real @ ( plus_plus_int @ V_8 @ W_11 ) ) @ Z_3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[481]) ).
thf(1237,plain,
( ( ! [X_22: int,Y_14: int] :
( ( ord_less_int @ ( number_number_of_int @ X_22 ) @ ( number_number_of_int @ Y_14 ) )
<=> ( ord_less_int @ X_22 @ Y_14 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[482]) ).
thf(1238,plain,
( ( ! [X_22: int,Y_14: int] :
( ( ord_less_real @ ( number267125858f_real @ X_22 ) @ ( number267125858f_real @ Y_14 ) )
<=> ( ord_less_int @ X_22 @ Y_14 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[483]) ).
thf(1239,plain,
( ( ! [A_52: int] :
( ( plus_plus_int @ A_52 @ ( number_number_of_int @ pls ) )
= A_52 ) )
= $true ),
inference(unfold_def,[status(thm)],[484]) ).
thf(1240,plain,
( ( ! [A_52: real] :
( ( plus_plus_real @ A_52 @ ( number267125858f_real @ pls ) )
= A_52 ) )
= $true ),
inference(unfold_def,[status(thm)],[485]) ).
thf(1241,plain,
( ( ! [A_53: int] :
( ( plus_plus_int @ ( number_number_of_int @ pls ) @ A_53 )
= A_53 ) )
= $true ),
inference(unfold_def,[status(thm)],[486]) ).
thf(1242,plain,
( ( ! [A_53: real] :
( ( plus_plus_real @ ( number267125858f_real @ pls ) @ A_53 )
= A_53 ) )
= $true ),
inference(unfold_def,[status(thm)],[487]) ).
thf(1243,plain,
( ( zero_zero_int
= ( number_number_of_int @ pls ) )
= $true ),
inference(unfold_def,[status(thm)],[488]) ).
thf(1244,plain,
( ( zero_zero_real
= ( number267125858f_real @ pls ) )
= $true ),
inference(unfold_def,[status(thm)],[489]) ).
thf(1245,plain,
( ( ( number_number_of_int @ pls )
= zero_zero_int )
= $true ),
inference(unfold_def,[status(thm)],[490]) ).
thf(1246,plain,
( ( ( number267125858f_real @ pls )
= zero_zero_real )
= $true ),
inference(unfold_def,[status(thm)],[491]) ).
thf(1247,plain,
( ( ( number_number_of_int @ pls )
= zero_zero_int )
= $true ),
inference(unfold_def,[status(thm)],[492]) ).
thf(1248,plain,
( ( ( number_number_of_nat @ pls )
= zero_zero_nat )
= $true ),
inference(unfold_def,[status(thm)],[493]) ).
thf(1249,plain,
( ( ( number267125858f_real @ pls )
= zero_zero_real )
= $true ),
inference(unfold_def,[status(thm)],[494]) ).
thf(1250,plain,
( ( ! [A_54: int] :
( ( ord_less_int @ ( plus_plus_int @ A_54 @ A_54 ) @ zero_zero_int )
<=> ( ord_less_int @ A_54 @ zero_zero_int ) ) )
= $true ),
inference(unfold_def,[status(thm)],[495]) ).
thf(1251,plain,
( ( ! [A_55: int] :
( ( power_power_int @ A_55 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_int @ A_55 @ A_55 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[497]) ).
thf(1252,plain,
( ( ! [A_55: nat] :
( ( power_power_nat @ A_55 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_nat @ A_55 @ A_55 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[498]) ).
thf(1253,plain,
( ( ! [A_55: real] :
( ( power_power_real @ A_55 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_real @ A_55 @ A_55 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[499]) ).
thf(1254,plain,
( ( ! [Z_4: int] :
( ( times_times_int @ Z_4 @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ Z_4 @ Z_4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[500]) ).
thf(1255,plain,
( ( ! [Z_5: int] :
( ( times_times_int @ Z_5 @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ Z_5 @ Z_5 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[502]) ).
thf(1256,plain,
( ( ! [Z_5: nat] :
( ( times_times_nat @ Z_5 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_nat @ Z_5 @ Z_5 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[503]) ).
thf(1257,plain,
( ( ! [Z_6: int] :
( ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ Z_6 )
= ( plus_plus_int @ Z_6 @ Z_6 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[505]) ).
thf(1258,plain,
( ( ! [Z_7: int] :
( ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ Z_7 )
= ( plus_plus_int @ Z_7 @ Z_7 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[507]) ).
thf(1259,plain,
( ( ! [Z_7: nat] :
( ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ Z_7 )
= ( plus_plus_nat @ Z_7 @ Z_7 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[508]) ).
thf(1260,plain,
( ( ! [A_56: int] :
( ( power_power_int @ A_56 @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( times_times_int @ ( times_times_int @ A_56 @ A_56 ) @ A_56 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[510]) ).
thf(1261,plain,
( ( ! [A_56: nat] :
( ( power_power_nat @ A_56 @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( times_times_nat @ ( times_times_nat @ A_56 @ A_56 ) @ A_56 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[511]) ).
thf(1262,plain,
( ( ! [A_56: real] :
( ( power_power_real @ A_56 @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( times_times_real @ ( times_times_real @ A_56 @ A_56 ) @ A_56 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[512]) ).
thf(1263,plain,
( ( ! [W_12: int] :
( ( times_times_int @ ( plus_plus_int @ one_one_int @ one_one_int ) @ ( number_number_of_int @ W_12 ) )
= ( number_number_of_int @ ( bit0 @ W_12 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[513]) ).
thf(1264,plain,
( ( ! [K: int,I: int,J: int] :
( ( ord_less_int @ I @ J )
=> ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ K ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[515]) ).
thf(1265,plain,
( ( ! [Z: int] :
( ( plus_plus_int @ zero_zero_int @ Z )
= Z ) )
= $true ),
inference(unfold_def,[status(thm)],[516]) ).
thf(1266,plain,
( ( ! [Z: int] :
( ( plus_plus_int @ Z @ zero_zero_int )
= Z ) )
= $true ),
inference(unfold_def,[status(thm)],[517]) ).
thf(1267,plain,
( ( ! [K: int] :
( ( bit0 @ K )
= ( plus_plus_int @ K @ K ) ) )
= $true ),
inference(unfold_def,[status(thm)],[518]) ).
thf(1268,plain,
( ( ! [K: int,L: int] :
( ( plus_plus_int @ ( bit0 @ K ) @ ( bit0 @ L ) )
= ( bit0 @ ( plus_plus_int @ K @ L ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[519]) ).
thf(1269,plain,
( ( ! [K: int] :
( ( plus_plus_int @ pls @ K )
= K ) )
= $true ),
inference(unfold_def,[status(thm)],[520]) ).
thf(1270,plain,
( ( ! [K: int] :
( ( plus_plus_int @ K @ pls )
= K ) )
= $true ),
inference(unfold_def,[status(thm)],[521]) ).
thf(1271,plain,
( ( zero_zero_int != one_one_int )
= $true ),
inference(unfold_def,[status(thm)],[522]) ).
thf(1272,plain,
( ( ! [K: int,L: int] :
( ( ord_less_int @ ( bit0 @ K ) @ ( bit0 @ L ) )
<=> ( ord_less_int @ K @ L ) ) )
= $true ),
inference(unfold_def,[status(thm)],[523]) ).
thf(1273,plain,
( ( ! [K1: int,K2: int] :
( ( ord_less_int @ ( bit0 @ K1 ) @ ( bit0 @ K2 ) )
<=> ( ord_less_int @ K1 @ K2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[524]) ).
thf(1274,plain,
( ( ~ ( ord_less_int @ pls @ pls ) )
= $true ),
inference(unfold_def,[status(thm)],[525]) ).
thf(1275,plain,
( ( ! [K: int,L: int] :
( ( ord_less_int @ ( bit1 @ K ) @ ( bit1 @ L ) )
<=> ( ord_less_int @ K @ L ) ) )
= $true ),
inference(unfold_def,[status(thm)],[526]) ).
thf(1276,plain,
( ( ! [K1: int,K2: int] :
( ( ord_less_int @ ( bit1 @ K1 ) @ ( bit1 @ K2 ) )
<=> ( ord_less_int @ K1 @ K2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[527]) ).
thf(1277,plain,
( ( pls = zero_zero_int )
= $true ),
inference(unfold_def,[status(thm)],[528]) ).
thf(1278,plain,
( ( ( bit0 @ pls )
= pls )
= $true ),
inference(unfold_def,[status(thm)],[529]) ).
thf(1279,plain,
( ( ! [L: int] :
( ( pls
= ( bit0 @ L ) )
<=> ( pls = L ) ) )
= $true ),
inference(unfold_def,[status(thm)],[530]) ).
thf(1280,plain,
( ( ! [K: int] :
( ( ( bit0 @ K )
= pls )
<=> ( K = pls ) ) )
= $true ),
inference(unfold_def,[status(thm)],[531]) ).
thf(1281,plain,
( ( ! [K: int,L: int] :
( ( bit0 @ K )
!= ( bit1 @ L ) ) )
= $true ),
inference(unfold_def,[status(thm)],[532]) ).
thf(1282,plain,
( ( ! [K: int,L: int] :
( ( bit1 @ K )
!= ( bit0 @ L ) ) )
= $true ),
inference(unfold_def,[status(thm)],[533]) ).
thf(1283,plain,
( ( ! [L: int] :
( pls
!= ( bit1 @ L ) ) )
= $true ),
inference(unfold_def,[status(thm)],[534]) ).
thf(1284,plain,
( ( ! [K: int] :
( ( bit1 @ K )
!= pls ) )
= $true ),
inference(unfold_def,[status(thm)],[535]) ).
thf(1285,plain,
( ( ! [A_57: int] :
( ( ( plus_plus_int @ A_57 @ A_57 )
= zero_zero_int )
<=> ( A_57 = zero_zero_int ) ) )
= $true ),
inference(unfold_def,[status(thm)],[536]) ).
thf(1286,plain,
( ( ! [N: int,M: int] :
( ( ord_less_int @ zero_zero_int @ M )
=> ( ( ( times_times_int @ M @ N )
= one_one_int )
<=> ( ( M = one_one_int )
& ( N = one_one_int ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[538]) ).
thf(1287,plain,
( ( ! [K: int,L: int] :
( ( times_times_int @ ( bit1 @ K ) @ L )
= ( plus_plus_int @ ( bit0 @ ( times_times_int @ K @ L ) ) @ L ) ) )
= $true ),
inference(unfold_def,[status(thm)],[539]) ).
thf(1288,plain,
( ( one_one_int
= ( number_number_of_int @ ( bit1 @ pls ) ) )
= $true ),
inference(unfold_def,[status(thm)],[540]) ).
thf(1289,plain,
( ( ! [A_58: int] :
( ( times_times_int @ A_58 @ ( number_number_of_int @ ( bit1 @ pls ) ) )
= A_58 ) )
= $true ),
inference(unfold_def,[status(thm)],[541]) ).
thf(1290,plain,
( ( ! [A_58: real] :
( ( times_times_real @ A_58 @ ( number267125858f_real @ ( bit1 @ pls ) ) )
= A_58 ) )
= $true ),
inference(unfold_def,[status(thm)],[542]) ).
thf(1291,plain,
( ( ! [A_59: int] :
( ( times_times_int @ ( number_number_of_int @ ( bit1 @ pls ) ) @ A_59 )
= A_59 ) )
= $true ),
inference(unfold_def,[status(thm)],[543]) ).
thf(1292,plain,
( ( ! [A_59: real] :
( ( times_times_real @ ( number267125858f_real @ ( bit1 @ pls ) ) @ A_59 )
= A_59 ) )
= $true ),
inference(unfold_def,[status(thm)],[544]) ).
thf(1293,plain,
( ( ! [X_23: int,Y_15: int] :
~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ X_23 @ X_23 ) @ ( times_times_int @ Y_15 @ Y_15 ) ) @ zero_zero_int ) )
= $true ),
inference(unfold_def,[status(thm)],[545]) ).
thf(1294,plain,
( ( ! [X_24: int,Y_16: int] :
( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X_24 @ X_24 ) @ ( times_times_int @ Y_16 @ Y_16 ) ) )
<=> ( ( X_24 != zero_zero_int )
| ( Y_16 != zero_zero_int ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[547]) ).
thf(1295,plain,
( ( ! [X_25: int,Y_17: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X_25 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_17 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[549]) ).
thf(1296,plain,
( ( ! [X_26: int,Y_18: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ ( power_power_int @ X_26 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_18 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_int )
<=> ( ( X_26 = zero_zero_int )
& ( Y_18 = zero_zero_int ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[551]) ).
thf(1297,plain,
( ( ! [X_27: int,Y_19: int] :
( ( ord_less_int @ ( power_power_int @ X_27 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_19 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ Y_19 )
=> ( ord_less_int @ X_27 @ Y_19 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[553]) ).
thf(1298,plain,
( ( ! [A_60: int] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A_60 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[556]) ).
thf(1299,plain,
( ( ! [X_28: int,Y_20: int] :
( ( ord_less_eq_int @ ( power_power_int @ X_28 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_20 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ Y_20 )
=> ( ord_less_eq_int @ X_28 @ Y_20 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[558]) ).
thf(1300,plain,
( ( ! [X_29: int,Y_21: int] :
( ( ( power_power_int @ X_29 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power_int @ Y_21 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ X_29 )
=> ( ( ord_less_eq_int @ zero_zero_int @ Y_21 )
=> ( X_29 = Y_21 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[561]) ).
thf(1301,plain,
( ( ! [K: int,I: int,J: int] :
( ( 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)],[564]) ).
thf(1302,plain,
( ( zero_zero_int
= ( number_number_of_int @ pls ) )
= $true ),
inference(unfold_def,[status(thm)],[565]) ).
thf(1303,plain,
( ( ! [Z: int,W: int] :
( ( plus_plus_int @ Z @ W )
= ( plus_plus_int @ W @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[566]) ).
thf(1304,plain,
( ( ! [X: int,Y: int,Z: int] :
( ( plus_plus_int @ X @ ( plus_plus_int @ Y @ Z ) )
= ( plus_plus_int @ Y @ ( plus_plus_int @ X @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[567]) ).
thf(1305,plain,
( ( ! [Z1: int,Z2: int,Z3: int] :
( ( plus_plus_int @ ( plus_plus_int @ Z1 @ Z2 ) @ Z3 )
= ( plus_plus_int @ Z1 @ ( plus_plus_int @ Z2 @ Z3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[568]) ).
thf(1306,plain,
( ( ! [V_9: int,B_21: int,C_13: int] :
( ( times_times_int @ ( number_number_of_int @ V_9 ) @ ( plus_plus_int @ B_21 @ C_13 ) )
= ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ V_9 ) @ B_21 ) @ ( times_times_int @ ( number_number_of_int @ V_9 ) @ C_13 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[569]) ).
thf(1307,plain,
( ( ! [V_9: int,B_21: nat,C_13: nat] :
( ( times_times_nat @ ( number_number_of_nat @ V_9 ) @ ( plus_plus_nat @ B_21 @ C_13 ) )
= ( plus_plus_nat @ ( times_times_nat @ ( number_number_of_nat @ V_9 ) @ B_21 ) @ ( times_times_nat @ ( number_number_of_nat @ V_9 ) @ C_13 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[570]) ).
thf(1308,plain,
( ( ! [A_61: int,B_22: int,V_10: int] :
( ( times_times_int @ ( plus_plus_int @ A_61 @ B_22 ) @ ( number_number_of_int @ V_10 ) )
= ( plus_plus_int @ ( times_times_int @ A_61 @ ( number_number_of_int @ V_10 ) ) @ ( times_times_int @ B_22 @ ( number_number_of_int @ V_10 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[572]) ).
thf(1309,plain,
( ( ! [A_61: nat,B_22: nat,V_10: int] :
( ( times_times_nat @ ( plus_plus_nat @ A_61 @ B_22 ) @ ( number_number_of_nat @ V_10 ) )
= ( plus_plus_nat @ ( times_times_nat @ A_61 @ ( number_number_of_nat @ V_10 ) ) @ ( times_times_nat @ B_22 @ ( number_number_of_nat @ V_10 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[573]) ).
thf(1310,plain,
( ( ! [X_30: int,Y_22: int] :
( ( ( plus_plus_int @ ( times_times_int @ X_30 @ X_30 ) @ ( times_times_int @ Y_22 @ Y_22 ) )
= zero_zero_int )
<=> ( ( X_30 = zero_zero_int )
& ( Y_22 = zero_zero_int ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[575]) ).
thf(1311,plain,
( ( ! [X: int,Y: int] :
( ( ord_less_int @ X @ Y )
| ( X = Y )
| ( ord_less_int @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[577]) ).
thf(1312,plain,
( ( ! [K: int,L: int] :
( ( ( bit0 @ K )
= ( bit0 @ L ) )
<=> ( K = L ) ) )
= $true ),
inference(unfold_def,[status(thm)],[578]) ).
thf(1313,plain,
( ( ! [K: int,L: int] :
( ( ( bit1 @ K )
= ( bit1 @ L ) )
<=> ( K = L ) ) )
= $true ),
inference(unfold_def,[status(thm)],[579]) ).
thf(1314,plain,
( ( ! [W_13: int,X_31: nat] :
( ( ( number_number_of_nat @ W_13 )
= X_31 )
<=> ( X_31
= ( number_number_of_nat @ W_13 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[580]) ).
thf(1315,plain,
( ( ! [Z: int] :
( ( 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)],[585]) ).
thf(1316,plain,
( ( ! [V_5: int,V_4: int] :
( ( ( ord_less_int @ V_4 @ pls )
=> ( ( plus_plus_nat @ ( number_number_of_nat @ V_4 ) @ ( number_number_of_nat @ V_5 ) )
= ( number_number_of_nat @ V_5 ) ) )
& ( ~ ( ord_less_int @ V_4 @ pls )
=> ( ( ( ord_less_int @ V_5 @ pls )
=> ( ( plus_plus_nat @ ( number_number_of_nat @ V_4 ) @ ( number_number_of_nat @ V_5 ) )
= ( number_number_of_nat @ V_4 ) ) )
& ( ~ ( ord_less_int @ V_5 @ pls )
=> ( ( plus_plus_nat @ ( number_number_of_nat @ V_4 ) @ ( number_number_of_nat @ V_5 ) )
= ( number_number_of_nat @ ( plus_plus_int @ V_4 @ V_5 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[586]) ).
thf(1317,plain,
( ( ! [V_12: int,V_11: int] :
( ( ord_less_eq_int @ pls @ V_11 )
=> ( ( ord_less_eq_int @ pls @ V_12 )
=> ( ( plus_plus_int @ ( number_number_of_int @ V_11 ) @ ( number_number_of_int @ V_12 ) )
= ( number_number_of_int @ ( plus_plus_int @ V_11 @ V_12 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[587]) ).
thf(1318,plain,
( ( ! [V_12: int,V_11: int] :
( ( ord_less_eq_int @ pls @ V_11 )
=> ( ( ord_less_eq_int @ pls @ V_12 )
=> ( ( plus_plus_nat @ ( number_number_of_nat @ V_11 ) @ ( number_number_of_nat @ V_12 ) )
= ( number_number_of_nat @ ( plus_plus_int @ V_11 @ V_12 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[588]) ).
thf(1319,plain,
( ( ! [W: int,Z: int] :
( ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
<=> ( ord_less_eq_int @ W @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[590]) ).
thf(1320,plain,
( ( ! [W: int,Z: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z )
<=> ( ord_less_int @ W @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[591]) ).
thf(1321,plain,
( ( ! [W: int,Z: int] :
( ( ord_less_int @ W @ Z )
=> ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[592]) ).
thf(1322,plain,
( ( one_one_nat
= ( number_number_of_nat @ ( bit1 @ pls ) ) )
= $true ),
inference(unfold_def,[status(thm)],[593]) ).
thf(1323,plain,
( ( ( number_number_of_nat @ ( bit1 @ pls ) )
= one_one_nat )
= $true ),
inference(unfold_def,[status(thm)],[594]) ).
thf(1324,plain,
( ( ! [Z: int] :
( ( ord_less_eq_int @ one_one_int @ Z )
<=> ( ord_less_int @ zero_zero_int @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[595]) ).
thf(1325,plain,
( ( ! [V_4: int,V_5: int] :
( ( ord_less_nat @ ( number_number_of_nat @ V_4 ) @ ( number_number_of_nat @ V_5 ) )
<=> ( ( ( ord_less_int @ V_4 @ V_5 )
=> ( ord_less_int @ pls @ V_5 ) )
& ( ord_less_int @ V_4 @ V_5 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[596]) ).
thf(1326,plain,
( ( ! [K: int,L: int] :
( ( ord_less_int @ ( bit0 @ K ) @ ( bit1 @ L ) )
<=> ( ord_less_eq_int @ K @ L ) ) )
= $true ),
inference(unfold_def,[status(thm)],[597]) ).
thf(1327,plain,
( ( ! [K1: int,K2: int] :
( ( ord_less_int @ ( bit0 @ K1 ) @ ( bit1 @ K2 ) )
<=> ( ord_less_eq_int @ K1 @ K2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[598]) ).
thf(1328,plain,
( ( ! [K: int,L: int] :
( ( ord_less_eq_int @ ( bit1 @ K ) @ ( bit0 @ L ) )
<=> ( ord_less_int @ K @ L ) ) )
= $true ),
inference(unfold_def,[status(thm)],[599]) ).
thf(1329,plain,
( ( ! [K1: int,K2: int] :
( ( ord_less_eq_int @ ( bit1 @ K1 ) @ ( bit0 @ K2 ) )
<=> ( ord_less_int @ K1 @ K2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[600]) ).
thf(1330,plain,
( ( ! [K: int] :
( ( ord_less_int @ pls @ ( bit1 @ K ) )
<=> ( ord_less_eq_int @ pls @ K ) ) )
= $true ),
inference(unfold_def,[status(thm)],[601]) ).
thf(1331,plain,
( ( ! [K: int] :
( ( ord_less_eq_int @ ( bit1 @ K ) @ pls )
<=> ( ord_less_int @ K @ pls ) ) )
= $true ),
inference(unfold_def,[status(thm)],[602]) ).
thf(1332,plain,
( ( ! [W: int,Z1: int,Z2: int] :
( ( 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)],[603]) ).
thf(1333,plain,
( ( ! [Z1: int,Z2: int,W: int] :
( ( 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)],[604]) ).
thf(1334,plain,
( ( ! [V_4: int,W: int] :
( ( plus_plus_int @ ( number_number_of_int @ V_4 ) @ ( number_number_of_int @ W ) )
= ( number_number_of_int @ ( plus_plus_int @ V_4 @ W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[605]) ).
thf(1335,plain,
( ( ! [Z: int] :
( ( times_times_int @ one_one_int @ Z )
= Z ) )
= $true ),
inference(unfold_def,[status(thm)],[606]) ).
thf(1336,plain,
( ( ! [Z: int] :
( ( times_times_int @ Z @ one_one_int )
= Z ) )
= $true ),
inference(unfold_def,[status(thm)],[607]) ).
thf(1337,plain,
( ( ! [K: int,L: int] :
( ( ord_less_int @ ( number_number_of_int @ K ) @ ( number_number_of_int @ L ) )
<=> ( ord_less_int @ K @ L ) ) )
= $true ),
inference(unfold_def,[status(thm)],[608]) ).
thf(1338,plain,
( ( ! [K: int,L: int] :
( ( times_times_int @ ( bit0 @ K ) @ L )
= ( bit0 @ ( times_times_int @ K @ L ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[609]) ).
thf(1339,plain,
( ( ! [W: int] :
( ( times_times_int @ pls @ W )
= pls ) )
= $true ),
inference(unfold_def,[status(thm)],[610]) ).
thf(1340,plain,
( ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
= ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[611]) ).
thf(1341,plain,
( ( ! [Y_24: int] :
( ( ord_less_eq_int @ one_one_int @ ( number_number_of_int @ Y_24 ) )
<=> ( ord_less_eq_int @ ( bit1 @ pls ) @ Y_24 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[612]) ).
thf(1342,plain,
( ( ! [X_33: int] :
( ( ord_less_eq_int @ ( number_number_of_int @ X_33 ) @ one_one_int )
<=> ( ord_less_eq_int @ X_33 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[614]) ).
thf(1343,plain,
( ( zero_zero_nat
= ( number_number_of_nat @ pls ) )
= $true ),
inference(unfold_def,[status(thm)],[616]) ).
thf(1344,plain,
( ( ( number_number_of_nat @ pls )
= zero_zero_nat )
= $true ),
inference(unfold_def,[status(thm)],[617]) ).
thf(1345,plain,
( ( ! [Z_8: int,Z: int,W_14: int,W: int] :
( ( ord_less_int @ W_14 @ W )
=> ( ( ord_less_eq_int @ Z_8 @ Z )
=> ( ord_less_int @ ( plus_plus_int @ W_14 @ Z_8 ) @ ( plus_plus_int @ W @ Z ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[618]) ).
thf(1346,plain,
( ( ! [K: int] :
( ( ord_less_eq_int @ pls @ ( bit0 @ K ) )
<=> ( ord_less_eq_int @ pls @ K ) ) )
= $true ),
inference(unfold_def,[status(thm)],[619]) ).
thf(1347,plain,
( ( ! [K: int] :
( ( ord_less_eq_int @ ( bit0 @ K ) @ pls )
<=> ( ord_less_eq_int @ K @ pls ) ) )
= $true ),
inference(unfold_def,[status(thm)],[620]) ).
thf(1348,plain,
( ( ! [K: int,L: int] :
( ( ord_less_eq_int @ ( bit0 @ K ) @ ( bit1 @ L ) )
<=> ( ord_less_eq_int @ K @ L ) ) )
= $true ),
inference(unfold_def,[status(thm)],[621]) ).
thf(1349,plain,
( ( ! [K1: int,K2: int] :
( ( ord_less_eq_int @ ( bit0 @ K1 ) @ ( bit1 @ K2 ) )
<=> ( ord_less_eq_int @ K1 @ K2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[622]) ).
thf(1350,plain,
( ( ! [K: int] :
( ( ord_less_eq_int @ pls @ ( bit1 @ K ) )
<=> ( ord_less_eq_int @ pls @ K ) ) )
= $true ),
inference(unfold_def,[status(thm)],[623]) ).
thf(1351,plain,
( ( ! [V_13: int,W_15: int] :
( ( ord_less_eq_int @ ( number_number_of_int @ V_13 ) @ ( number_number_of_int @ W_15 ) )
<=> ~ ( ord_less_int @ ( number_number_of_int @ W_15 ) @ ( number_number_of_int @ V_13 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[624]) ).
thf(1352,plain,
( ( ! [V_13: int,W_15: int] :
( ( ord_less_eq_nat @ ( number_number_of_nat @ V_13 ) @ ( number_number_of_nat @ W_15 ) )
<=> ~ ( ord_less_nat @ ( number_number_of_nat @ W_15 ) @ ( number_number_of_nat @ V_13 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[625]) ).
thf(1353,plain,
( ( ! [V_4: int] :
( ( ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ V_4 ) )
<=> ( ord_less_int @ pls @ V_4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[627]) ).
thf(1354,plain,
( ( ! [Y_25: int] :
( ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ Y_25 ) )
<=> ( ord_less_eq_int @ pls @ Y_25 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[628]) ).
thf(1355,plain,
( ( ! [X_34: int] :
( ( ord_less_eq_int @ ( number_number_of_int @ X_34 ) @ zero_zero_int )
<=> ( ord_less_eq_int @ X_34 @ pls ) ) )
= $true ),
inference(unfold_def,[status(thm)],[630]) ).
thf(1356,plain,
( ( ! [X_35: int,Y_26: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X_35 @ X_35 ) @ ( times_times_int @ Y_26 @ Y_26 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[632]) ).
thf(1357,plain,
( ( ! [X_36: int,Y_27: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ X_36 @ X_36 ) @ ( times_times_int @ Y_27 @ Y_27 ) ) @ zero_zero_int )
<=> ( ( X_36 = zero_zero_int )
& ( Y_27 = zero_zero_int ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[634]) ).
thf(1358,plain,
( ( ! [V_4: int] :
( ( zero_zero_nat
= ( number_number_of_nat @ V_4 ) )
<=> ( ord_less_eq_int @ V_4 @ pls ) ) )
= $true ),
inference(unfold_def,[status(thm)],[645]) ).
thf(1359,plain,
( ( ! [V_4: int] :
( ( ( number_number_of_nat @ V_4 )
= zero_zero_nat )
<=> ( ord_less_eq_int @ V_4 @ pls ) ) )
= $true ),
inference(unfold_def,[status(thm)],[646]) ).
thf(1360,plain,
( ( ! [K: int,I: int,J: int] :
( ( 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)],[647]) ).
thf(1361,plain,
( ( ! [Z: int,W: int] :
( ( ord_less_int @ Z @ W )
<=> ( ( ord_less_eq_int @ Z @ W )
& ( Z != W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[648]) ).
thf(1362,plain,
( ( ! [K: int,L: int] :
( ( ord_less_eq_int @ ( bit0 @ K ) @ ( bit0 @ L ) )
<=> ( ord_less_eq_int @ K @ L ) ) )
= $true ),
inference(unfold_def,[status(thm)],[649]) ).
thf(1363,plain,
( ( ! [K1: int,K2: int] :
( ( ord_less_eq_int @ ( bit0 @ K1 ) @ ( bit0 @ K2 ) )
<=> ( ord_less_eq_int @ K1 @ K2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[650]) ).
thf(1364,plain,
( ( ord_less_eq_int @ pls @ pls )
= $true ),
inference(unfold_def,[status(thm)],[651]) ).
thf(1365,plain,
( ( ! [K: int,L: int] :
( ( ord_less_eq_int @ ( bit1 @ K ) @ ( bit1 @ L ) )
<=> ( ord_less_eq_int @ K @ L ) ) )
= $true ),
inference(unfold_def,[status(thm)],[652]) ).
thf(1366,plain,
( ( ! [K1: int,K2: int] :
( ( ord_less_eq_int @ ( bit1 @ K1 ) @ ( bit1 @ K2 ) )
<=> ( ord_less_eq_int @ K1 @ K2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[653]) ).
thf(1367,plain,
( ( ! [X: int,Y: nat,Z: nat] :
( ( power_power_int @ X @ ( plus_plus_nat @ Y @ Z ) )
= ( times_times_int @ ( power_power_int @ X @ Y ) @ ( power_power_int @ X @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[654]) ).
thf(1368,plain,
( ( ! [V_19: int] :
( ( plus_plus_int @ ( number_number_of_int @ V_19 ) @ one_one_int )
= ( number_number_of_int @ ( plus_plus_int @ V_19 @ ( bit1 @ pls ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[670]) ).
thf(1369,plain,
( ( ! [W_19: int] :
( ( plus_plus_int @ one_one_int @ ( number_number_of_int @ W_19 ) )
= ( number_number_of_int @ ( plus_plus_int @ ( bit1 @ pls ) @ W_19 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[672]) ).
thf(1370,plain,
( ( ! [A_62: int] :
( ( ( power_power_int @ A_62 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int )
<=> ( A_62 = zero_zero_int ) ) )
= $true ),
inference(unfold_def,[status(thm)],[674]) ).
thf(1371,plain,
( ( ! [A_62: real] :
( ( ( power_power_real @ A_62 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_real )
<=> ( A_62 = zero_zero_real ) ) )
= $true ),
inference(unfold_def,[status(thm)],[675]) ).
thf(1372,plain,
( ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int )
= $true ),
inference(unfold_def,[status(thm)],[676]) ).
thf(1373,plain,
( ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_nat )
= $true ),
inference(unfold_def,[status(thm)],[677]) ).
thf(1374,plain,
( ( ( power_power_real @ zero_zero_real @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_real )
= $true ),
inference(unfold_def,[status(thm)],[678]) ).
thf(1375,plain,
( ( ( power_power_int @ one_one_int @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_int )
= $true ),
inference(unfold_def,[status(thm)],[679]) ).
thf(1376,plain,
( ( ( power_power_nat @ one_one_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_nat )
= $true ),
inference(unfold_def,[status(thm)],[680]) ).
thf(1377,plain,
( ( ( power_power_real @ one_one_real @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_real )
= $true ),
inference(unfold_def,[status(thm)],[681]) ).
thf(1378,plain,
( ( ! [A_63: int] :
( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A_63 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
<=> ( A_63 != zero_zero_int ) ) )
= $true ),
inference(unfold_def,[status(thm)],[682]) ).
thf(1379,plain,
( ( ! [A_64: int] :
~ ( ord_less_int @ ( power_power_int @ A_64 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ zero_zero_int ) )
= $true ),
inference(unfold_def,[status(thm)],[684]) ).
thf(1380,plain,
( ( ! [X_38: int,Y_29: int] :
( ( ( plus_plus_int @ ( power_power_int @ X_38 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_29 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_int )
<=> ( ( X_38 = zero_zero_int )
& ( Y_29 = zero_zero_int ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[686]) ).
thf(1381,plain,
( ( ! [X_39: int,Y_30: int] :
( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X_39 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_30 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
<=> ( ( X_39 != zero_zero_int )
| ( Y_30 != zero_zero_int ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[688]) ).
thf(1382,plain,
( ( ! [X: int,Y: int] :
~ ( ord_less_int @ ( 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 ) ) ) ) ) @ zero_zero_int ) )
= $true ),
inference(unfold_def,[status(thm)],[690]) ).
thf(1383,plain,
( ( ~ ( ord_less_eq_int @ one_one_int @ t ) )
= $true ),
inference(unfold_def,[status(thm)],[693]) ).
thf(1384,plain,
( ( ( t = zero_zero_int )
=> ( ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int )
= zero_zero_int ) )
= $true ),
inference(unfold_def,[status(thm)],[694]) ).
thf(1385,plain,
( ( ord_less_int @ t @ one_one_int )
= $true ),
inference(unfold_def,[status(thm)],[697]) ).
thf(1386,plain,
( ( ord_less_int @ t @ zero_zero_int )
= $true ),
inference(unfold_def,[status(thm)],[698]) ).
thf(1387,plain,
( ( ~ ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int ) @ zero_zero_int ) )
= $true ),
inference(polarity_switch,[status(thm)],[701]) ).
thf(1388,plain,
( ( ! [N: nat,M: nat] :
( ~ ( dvd_dvd_nat @ N @ M )
| ( ord_less_eq_nat @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ N ) @ M )
| ( M = zero_zero_nat )
| ( M = N ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[702]) ).
thf(1389,plain,
( ( ! [I: nat,M: nat,N: nat] :
( ~ ( 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(extcnf_combined,[status(esa)],[703]) ).
thf(1390,plain,
( ( ! [X: nat,Q: nat,N: nat,R: nat] :
( ( X
!= ( plus_plus_nat @ ( times_times_nat @ Q @ N ) @ R ) )
| ~ ( ord_less_nat @ zero_zero_nat @ R )
| ~ ( ord_less_nat @ R @ N )
| ~ ( dvd_dvd_nat @ N @ X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[704]) ).
thf(1391,plain,
( ( ! [X: nat,Y: nat,N: nat] :
( ( N = zero_zero_nat )
| ~ ( dvd_dvd_nat @ ( power_power_nat @ X @ N ) @ Y )
| ( dvd_dvd_nat @ X @ Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[705]) ).
thf(1392,plain,
( ( ! [A: nat,N: nat,B: nat] :
( ~ ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
| ( N = zero_zero_nat )
| ( dvd_dvd_nat @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[706]) ).
thf(1393,plain,
( ( ! [M: nat] :
( ! [K: nat,N: nat] :
( ~ ( dvd_dvd_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
| ( K = zero_zero_nat )
| ( dvd_dvd_nat @ M @ N ) )
& ! [K: nat] :
( ( K != zero_zero_nat )
| ! [N: nat] : ( dvd_dvd_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) ) )
& ! [K: nat,N: nat] :
( ~ ( dvd_dvd_nat @ M @ N )
| ( dvd_dvd_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[707]) ).
thf(1394,plain,
( ( ! [B: nat,D: nat,A: nat] :
( ~ ( dvd_dvd_nat @ D @ A )
| ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ A @ B ) )
| ( dvd_dvd_nat @ D @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[708]) ).
thf(1395,plain,
( ( ! [C: nat,A: nat,B: nat] :
( ~ ( dvd_dvd_nat @ A @ B )
| ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[709]) ).
thf(1396,plain,
( ( ! [C: nat,A: nat,B: nat] :
( ~ ( dvd_dvd_nat @ A @ B )
| ( dvd_dvd_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[710]) ).
thf(1397,plain,
( ( ! [N: nat,X: nat,Y: nat] :
( ~ ( dvd_dvd_nat @ X @ Y )
| ( dvd_dvd_nat @ ( power_power_nat @ X @ N ) @ ( power_power_nat @ Y @ N ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[711]) ).
thf(1398,plain,
( ( ! [A: nat,B: nat] :
( ~ ( dvd_dvd_nat @ A @ B )
| ( B = zero_zero_nat )
| ( ord_less_eq_nat @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[712]) ).
thf(1399,plain,
( ( ! [A: real,N: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ N )
| ~ ( ord_less_real @ zero_zero_real @ A )
| ( ! [SY1333: real] :
( ( ( power_power_real @ SY1333 @ N )
!= A )
| ~ ( ord_less_real @ zero_zero_real @ SY1333 )
| ( SY1333
= ( sK1_X_1 @ N @ A ) ) )
& ( ( power_power_real @ ( sK1_X_1 @ N @ A ) @ N )
= A )
& ( ord_less_real @ zero_zero_real @ ( sK1_X_1 @ N @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[713]) ).
thf(1400,plain,
( ( ! [N_3: nat,A_2: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ A_2 )
| ~ ( ord_less_nat @ A_2 @ one_one_nat )
| ( ord_less_nat @ ( times_times_nat @ A_2 @ ( power_power_nat @ A_2 @ N_3 ) ) @ ( power_power_nat @ A_2 @ N_3 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[714]) ).
thf(1401,plain,
( ( ! [N_3: nat,A_2: real] :
( ~ ( ord_less_real @ zero_zero_real @ A_2 )
| ~ ( ord_less_real @ A_2 @ one_one_real )
| ( ord_less_real @ ( times_times_real @ A_2 @ ( power_power_real @ A_2 @ N_3 ) ) @ ( power_power_real @ A_2 @ N_3 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[715]) ).
thf(1402,plain,
( ( ! [A_3: nat,N_5: nat,N_4: nat] :
( ~ ( ord_less_eq_nat @ N_5 @ N_4 )
| ~ ( ord_less_eq_nat @ one_one_nat @ A_3 )
| ( ord_less_eq_nat @ ( power_power_nat @ A_3 @ N_5 ) @ ( power_power_nat @ A_3 @ N_4 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[716]) ).
thf(1403,plain,
( ( ! [A_3: real,N_5: nat,N_4: nat] :
( ~ ( ord_less_eq_nat @ N_5 @ N_4 )
| ~ ( ord_less_eq_real @ one_one_real @ A_3 )
| ( ord_less_eq_real @ ( power_power_real @ A_3 @ N_5 ) @ ( power_power_real @ A_3 @ N_4 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[717]) ).
thf(1404,plain,
( ( ! [X_2: nat] :
( ! [Y_2: nat,B_1: nat] :
( ~ ( ord_less_nat @ one_one_nat @ B_1 )
| ~ ( ord_less_nat @ ( power_power_nat @ B_1 @ X_2 ) @ ( power_power_nat @ B_1 @ Y_2 ) )
| ( ord_less_nat @ X_2 @ Y_2 ) )
& ! [Y_2: nat,B_1: nat] :
( ~ ( ord_less_nat @ one_one_nat @ B_1 )
| ~ ( ord_less_nat @ X_2 @ Y_2 )
| ( ord_less_nat @ ( power_power_nat @ B_1 @ X_2 ) @ ( power_power_nat @ B_1 @ Y_2 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[718]) ).
thf(1405,plain,
( ( ! [X_2: nat] :
( ! [Y_2: nat,B_1: real] :
( ~ ( ord_less_real @ one_one_real @ B_1 )
| ~ ( ord_less_nat @ X_2 @ Y_2 )
| ( ord_less_real @ ( power_power_real @ B_1 @ X_2 ) @ ( power_power_real @ B_1 @ Y_2 ) ) )
& ! [Y_2: nat,B_1: real] :
( ~ ( ord_less_real @ one_one_real @ B_1 )
| ~ ( ord_less_real @ ( power_power_real @ B_1 @ X_2 ) @ ( power_power_real @ B_1 @ Y_2 ) )
| ( ord_less_nat @ X_2 @ Y_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[719]) ).
thf(1406,plain,
( ( ! [M_1: nat,N_6: nat,A_4: nat] :
( ~ ( ord_less_nat @ one_one_nat @ A_4 )
| ~ ( ord_less_nat @ ( power_power_nat @ A_4 @ M_1 ) @ ( power_power_nat @ A_4 @ N_6 ) )
| ( ord_less_nat @ M_1 @ N_6 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[720]) ).
thf(1407,plain,
( ( ! [M_1: nat,N_6: nat,A_4: real] :
( ~ ( ord_less_real @ one_one_real @ A_4 )
| ~ ( ord_less_real @ ( power_power_real @ A_4 @ M_1 ) @ ( power_power_real @ A_4 @ N_6 ) )
| ( ord_less_nat @ M_1 @ N_6 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[721]) ).
thf(1408,plain,
( ( ! [A_5: nat,N_8: nat,N_7: nat] :
( ~ ( ord_less_nat @ N_8 @ N_7 )
| ~ ( ord_less_nat @ one_one_nat @ A_5 )
| ( ord_less_nat @ ( power_power_nat @ A_5 @ N_8 ) @ ( power_power_nat @ A_5 @ N_7 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[722]) ).
thf(1409,plain,
( ( ! [A_5: real,N_8: nat,N_7: nat] :
( ~ ( ord_less_nat @ N_8 @ N_7 )
| ~ ( ord_less_real @ one_one_real @ A_5 )
| ( ord_less_real @ ( power_power_real @ A_5 @ N_8 ) @ ( power_power_real @ A_5 @ N_7 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[723]) ).
thf(1410,plain,
( ( ! [N_9: nat] :
( ( N_9 != zero_zero_nat )
| ( ( power_power_nat @ zero_zero_nat @ N_9 )
= one_one_nat ) )
& ! [N_9: nat] :
( ( N_9 = zero_zero_nat )
| ( ( power_power_nat @ zero_zero_nat @ N_9 )
= zero_zero_nat ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[724]) ).
thf(1411,plain,
( ( ! [N_9: nat] :
( ( N_9 != zero_zero_nat )
| ( ( power_power_real @ zero_zero_real @ N_9 )
= one_one_real ) )
& ! [N_9: nat] :
( ( N_9 = zero_zero_nat )
| ( ( power_power_real @ zero_zero_real @ N_9 )
= zero_zero_real ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[725]) ).
thf(1412,plain,
( ( ! [N_10: nat,A_6: nat] :
( ~ ( ord_less_nat @ one_one_nat @ A_6 )
| ( ord_less_nat @ one_one_nat @ ( times_times_nat @ A_6 @ ( power_power_nat @ A_6 @ N_10 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[726]) ).
thf(1413,plain,
( ( ! [N_10: nat,A_6: real] :
( ~ ( ord_less_real @ one_one_real @ A_6 )
| ( ord_less_real @ one_one_real @ ( times_times_real @ A_6 @ ( power_power_real @ A_6 @ N_10 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[727]) ).
thf(1414,plain,
( ( ! [N_11: nat,A_7: nat] :
( ~ ( ord_less_nat @ one_one_nat @ A_7 )
| ( ord_less_nat @ ( power_power_nat @ A_7 @ N_11 ) @ ( times_times_nat @ A_7 @ ( power_power_nat @ A_7 @ N_11 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[728]) ).
thf(1415,plain,
( ( ! [N_11: nat,A_7: real] :
( ~ ( ord_less_real @ one_one_real @ A_7 )
| ( ord_less_real @ ( power_power_real @ A_7 @ N_11 ) @ ( times_times_real @ A_7 @ ( power_power_real @ A_7 @ N_11 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[729]) ).
thf(1416,plain,
( ( ! [A_8: nat,N_12: nat,B_2: nat] :
( ~ ( ord_less_nat @ ( power_power_nat @ A_8 @ N_12 ) @ ( power_power_nat @ B_2 @ N_12 ) )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ B_2 )
| ( ord_less_nat @ A_8 @ B_2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[730]) ).
thf(1417,plain,
( ( ! [A_8: real,N_12: nat,B_2: real] :
( ~ ( ord_less_real @ ( power_power_real @ A_8 @ N_12 ) @ ( power_power_real @ B_2 @ N_12 ) )
| ~ ( ord_less_eq_real @ zero_zero_real @ B_2 )
| ( ord_less_real @ A_8 @ B_2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[731]) ).
thf(1418,plain,
( ( ! [X: nat,N: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X @ N ) )
| ( N = zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ X ) )
& ! [X: nat,N: nat] :
( ( N != zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X @ N ) ) )
& ! [X: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ X )
| ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X @ N ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[732]) ).
thf(1419,plain,
( ( ! [M: nat,N: nat,I: nat] :
( ~ ( 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(extcnf_combined,[status(esa)],[733]) ).
thf(1420,plain,
( ( ! [A_9: real,M_2: nat,N_13: nat] :
( ~ ( ord_less_eq_nat @ M_2 @ N_13 )
| ( dvd_dvd_real @ ( power_power_real @ A_9 @ M_2 ) @ ( power_power_real @ A_9 @ N_13 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[734]) ).
thf(1421,plain,
( ( ! [A_9: nat,M_2: nat,N_13: nat] :
( ~ ( ord_less_eq_nat @ M_2 @ N_13 )
| ( dvd_dvd_nat @ ( power_power_nat @ A_9 @ M_2 ) @ ( power_power_nat @ A_9 @ N_13 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[735]) ).
thf(1422,plain,
( ( ! [N_14: nat,M_3: nat,X_3: real,Y_3: real] :
( ~ ( dvd_dvd_real @ X_3 @ Y_3 )
| ~ ( ord_less_eq_nat @ N_14 @ M_3 )
| ( dvd_dvd_real @ ( power_power_real @ X_3 @ N_14 ) @ ( power_power_real @ Y_3 @ M_3 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[736]) ).
thf(1423,plain,
( ( ! [N_14: nat,M_3: nat,X_3: nat,Y_3: nat] :
( ~ ( dvd_dvd_nat @ X_3 @ Y_3 )
| ~ ( ord_less_eq_nat @ N_14 @ M_3 )
| ( dvd_dvd_nat @ ( power_power_nat @ X_3 @ N_14 ) @ ( power_power_nat @ Y_3 @ M_3 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[737]) ).
thf(1424,plain,
( ( ! [M_4: nat,A_10: real,N_15: nat,B_3: real] :
( ~ ( dvd_dvd_real @ ( power_power_real @ A_10 @ N_15 ) @ B_3 )
| ~ ( ord_less_eq_nat @ M_4 @ N_15 )
| ( dvd_dvd_real @ ( power_power_real @ A_10 @ M_4 ) @ B_3 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[738]) ).
thf(1425,plain,
( ( ! [M_4: nat,A_10: nat,N_15: nat,B_3: nat] :
( ~ ( dvd_dvd_nat @ ( power_power_nat @ A_10 @ N_15 ) @ B_3 )
| ~ ( ord_less_eq_nat @ M_4 @ N_15 )
| ( dvd_dvd_nat @ ( power_power_nat @ A_10 @ M_4 ) @ B_3 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[739]) ).
thf(1426,plain,
( ( ! [A_13: nat,N_17: nat] :
( ( N_17 = zero_zero_nat )
| ( A_13 != zero_zero_nat )
| ( ( power_power_nat @ A_13 @ N_17 )
= zero_zero_nat ) )
& ! [A_13: nat,N_17: nat] :
( ( ( power_power_nat @ A_13 @ N_17 )
!= zero_zero_nat )
| ( N_17 != zero_zero_nat ) )
& ! [A_13: nat] :
( ! [N_17: nat] :
( ( power_power_nat @ A_13 @ N_17 )
!= zero_zero_nat )
| ( A_13 = zero_zero_nat ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[744]) ).
thf(1427,plain,
( ( ! [A_13: real,N_17: nat] :
( ( N_17 = zero_zero_nat )
| ( A_13 != zero_zero_real )
| ( ( power_power_real @ A_13 @ N_17 )
= zero_zero_real ) )
& ! [A_13: real,N_17: nat] :
( ( ( power_power_real @ A_13 @ N_17 )
!= zero_zero_real )
| ( N_17 != zero_zero_nat ) )
& ! [A_13: real] :
( ! [N_17: nat] :
( ( power_power_real @ A_13 @ N_17 )
!= zero_zero_real )
| ( A_13 = zero_zero_real ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[745]) ).
thf(1428,plain,
( ( ! [M_6: nat] :
( ! [N_18: nat,A_14: nat] :
( ~ ( ord_less_nat @ one_one_nat @ A_14 )
| ( ( power_power_nat @ A_14 @ M_6 )
!= ( power_power_nat @ A_14 @ N_18 ) )
| ( M_6 = N_18 ) )
& ! [N_18: nat,A_14: nat] :
( ~ ( ord_less_nat @ one_one_nat @ A_14 )
| ( M_6 != N_18 )
| ( ( power_power_nat @ A_14 @ M_6 )
= ( power_power_nat @ A_14 @ N_18 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[746]) ).
thf(1429,plain,
( ( ! [M_6: nat] :
( ! [N_18: nat,A_14: real] :
( ~ ( ord_less_real @ one_one_real @ A_14 )
| ( ( power_power_real @ A_14 @ M_6 )
!= ( power_power_real @ A_14 @ N_18 ) )
| ( M_6 = N_18 ) )
& ! [N_18: nat,A_14: real] :
( ~ ( ord_less_real @ one_one_real @ A_14 )
| ( M_6 != N_18 )
| ( ( power_power_real @ A_14 @ M_6 )
= ( power_power_real @ A_14 @ N_18 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[747]) ).
thf(1430,plain,
( ( ! [N_19: nat,A_15: nat] :
( ~ ( ord_less_eq_nat @ one_one_nat @ A_15 )
| ( ord_less_eq_nat @ one_one_nat @ ( power_power_nat @ A_15 @ N_19 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[748]) ).
thf(1431,plain,
( ( ! [N_19: nat,A_15: real] :
( ~ ( ord_less_eq_real @ one_one_real @ A_15 )
| ( ord_less_eq_real @ one_one_real @ ( power_power_real @ A_15 @ N_19 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[749]) ).
thf(1432,plain,
( ( ! [N_20: nat,A_16: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ A_16 )
| ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A_16 @ N_20 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[750]) ).
thf(1433,plain,
( ( ! [N_20: nat,A_16: real] :
( ~ ( ord_less_real @ zero_zero_real @ A_16 )
| ( ord_less_real @ zero_zero_real @ ( power_power_real @ A_16 @ N_20 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[751]) ).
thf(1434,plain,
( ( ! [N_21: nat,A_17: nat] :
( ~ ( ord_less_eq_nat @ zero_zero_nat @ A_17 )
| ( ord_less_eq_nat @ zero_zero_nat @ ( power_power_nat @ A_17 @ N_21 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[752]) ).
thf(1435,plain,
( ( ! [N_21: nat,A_17: real] :
( ~ ( ord_less_eq_real @ zero_zero_real @ A_17 )
| ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A_17 @ N_21 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[753]) ).
thf(1436,plain,
( ( ! [N_22: nat,A_18: nat,B_4: nat] :
( ~ ( ord_less_eq_nat @ A_18 @ B_4 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ A_18 )
| ( ord_less_eq_nat @ ( power_power_nat @ A_18 @ N_22 ) @ ( power_power_nat @ B_4 @ N_22 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[754]) ).
thf(1437,plain,
( ( ! [N_22: nat,A_18: real,B_4: real] :
( ~ ( ord_less_eq_real @ A_18 @ B_4 )
| ~ ( ord_less_eq_real @ zero_zero_real @ A_18 )
| ( ord_less_eq_real @ ( power_power_real @ A_18 @ N_22 ) @ ( power_power_real @ B_4 @ N_22 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[755]) ).
thf(1438,plain,
( ( ! [N_24: nat,X_4: real,Y_4: real] :
( ~ ( dvd_dvd_real @ X_4 @ Y_4 )
| ( dvd_dvd_real @ ( power_power_real @ X_4 @ N_24 ) @ ( power_power_real @ Y_4 @ N_24 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[760]) ).
thf(1439,plain,
( ( ! [N_24: nat,X_4: nat,Y_4: nat] :
( ~ ( dvd_dvd_nat @ X_4 @ Y_4 )
| ( dvd_dvd_nat @ ( power_power_nat @ X_4 @ N_24 ) @ ( power_power_nat @ Y_4 @ N_24 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[761]) ).
thf(1440,plain,
( ( ! [N_28: nat,A_23: real] :
( ( A_23 = zero_zero_real )
| ( ( power_power_real @ A_23 @ N_28 )
!= zero_zero_real ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[768]) ).
thf(1441,plain,
( ( ! [N_29: nat,A_24: int,B_6: int] :
( ~ ( ord_less_int @ A_24 @ B_6 )
| ~ ( ord_less_eq_int @ zero_zero_int @ A_24 )
| ~ ( ord_less_nat @ zero_zero_nat @ N_29 )
| ( ord_less_int @ ( power_power_int @ A_24 @ N_29 ) @ ( power_power_int @ B_6 @ N_29 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[769]) ).
thf(1442,plain,
( ( ! [N_29: nat,A_24: nat,B_6: nat] :
( ~ ( ord_less_nat @ A_24 @ B_6 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ A_24 )
| ~ ( ord_less_nat @ zero_zero_nat @ N_29 )
| ( ord_less_nat @ ( power_power_nat @ A_24 @ N_29 ) @ ( power_power_nat @ B_6 @ N_29 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[770]) ).
thf(1443,plain,
( ( ! [N_29: nat,A_24: real,B_6: real] :
( ~ ( ord_less_real @ A_24 @ B_6 )
| ~ ( ord_less_eq_real @ zero_zero_real @ A_24 )
| ~ ( ord_less_nat @ zero_zero_nat @ N_29 )
| ( ord_less_real @ ( power_power_real @ A_24 @ N_29 ) @ ( power_power_real @ B_6 @ N_29 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[771]) ).
thf(1444,plain,
( ( ! [M_8: int,N_30: nat] :
( ( N_30 != zero_zero_nat )
| ( ( power_power_int @ M_8 @ N_30 )
= one_one_int ) )
& ! [M_8: int,N_30: nat] :
( ( N_30 = zero_zero_nat )
| ( ( power_power_int @ M_8 @ N_30 )
= ( times_times_int @ M_8 @ ( power_power_int @ M_8 @ ( minus_minus_nat @ N_30 @ one_one_nat ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[772]) ).
thf(1445,plain,
( ( ! [M_8: nat,N_30: nat] :
( ( N_30 != zero_zero_nat )
| ( ( power_power_nat @ M_8 @ N_30 )
= one_one_nat ) )
& ! [M_8: nat,N_30: nat] :
( ( N_30 = zero_zero_nat )
| ( ( power_power_nat @ M_8 @ N_30 )
= ( times_times_nat @ M_8 @ ( power_power_nat @ M_8 @ ( minus_minus_nat @ N_30 @ one_one_nat ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[773]) ).
thf(1446,plain,
( ( ! [M_8: real,N_30: nat] :
( ( N_30 != zero_zero_nat )
| ( ( power_power_real @ M_8 @ N_30 )
= one_one_real ) )
& ! [M_8: real,N_30: nat] :
( ( N_30 = zero_zero_nat )
| ( ( power_power_real @ M_8 @ N_30 )
= ( times_times_real @ M_8 @ ( power_power_real @ M_8 @ ( minus_minus_nat @ N_30 @ one_one_nat ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[774]) ).
thf(1447,plain,
( ( ! [X_5: int,N_31: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ N_31 )
| ( ( times_times_int @ ( power_power_int @ X_5 @ ( minus_minus_nat @ N_31 @ one_one_nat ) ) @ X_5 )
= ( power_power_int @ X_5 @ N_31 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[776]) ).
thf(1448,plain,
( ( ! [X_5: nat,N_31: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ N_31 )
| ( ( times_times_nat @ ( power_power_nat @ X_5 @ ( minus_minus_nat @ N_31 @ one_one_nat ) ) @ X_5 )
= ( power_power_nat @ X_5 @ N_31 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[777]) ).
thf(1449,plain,
( ( ! [X_5: real,N_31: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ N_31 )
| ( ( times_times_real @ ( power_power_real @ X_5 @ ( minus_minus_nat @ N_31 @ one_one_nat ) ) @ X_5 )
= ( power_power_real @ X_5 @ N_31 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[778]) ).
thf(1450,plain,
( ( ! [X: nat,N: nat] :
( ( ( power_power_nat @ X @ N )
!= one_one_nat )
| ( X = one_one_nat )
| ( N = zero_zero_nat ) )
& ! [X: nat] :
( ( X != one_one_nat )
| ! [N: nat] :
( ( power_power_nat @ X @ N )
= one_one_nat ) )
& ! [X: nat,N: nat] :
( ( N != zero_zero_nat )
| ( ( power_power_nat @ X @ N )
= one_one_nat ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[780]) ).
thf(1451,plain,
( ( ! [X: real,Y: real] :
( ( X != zero_zero_real )
| ( Y != zero_zero_real )
| ( ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) )
= zero_zero_real ) )
& ! [X: real] :
( ! [Y: real] :
( ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) )
!= zero_zero_real )
| ( X = zero_zero_real ) )
& ! [X: real,Y: real] :
( ( ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) )
!= zero_zero_real )
| ( Y = zero_zero_real ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[781]) ).
thf(1452,plain,
( ( ! [X: real] :
( ! [Y: real,Z: real] :
( ~ ( ord_less_real @ zero_zero_real @ Z )
| ~ ( ord_less_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ Y @ Z ) )
| ( ord_less_real @ X @ Y ) )
& ! [Y: real,Z: real] :
( ~ ( ord_less_real @ zero_zero_real @ Z )
| ~ ( ord_less_real @ X @ Y )
| ( ord_less_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ Y @ Z ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[782]) ).
thf(1453,plain,
( ( ! [Y: real,X: real] :
( ~ ( ord_less_real @ zero_zero_real @ X )
| ~ ( ord_less_real @ zero_zero_real @ Y )
| ( ord_less_real @ zero_zero_real @ ( times_times_real @ X @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[783]) ).
thf(1454,plain,
( ( ! [X: real,Y: real,Z: real] :
( ~ ( ord_less_real @ zero_zero_real @ Z )
| ~ ( ord_less_real @ X @ Y )
| ( ord_less_real @ ( times_times_real @ Z @ X ) @ ( times_times_real @ Z @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[784]) ).
thf(1455,plain,
( ( ! [X: real] :
( ! [Y: real,Z: real] :
( ~ ( ord_less_real @ zero_zero_real @ Z )
| ~ ( ord_less_eq_real @ ( times_times_real @ Z @ X ) @ ( times_times_real @ Z @ Y ) )
| ( ord_less_eq_real @ X @ Y ) )
& ! [Y: real,Z: real] :
( ~ ( ord_less_real @ zero_zero_real @ Z )
| ~ ( ord_less_eq_real @ X @ Y )
| ( ord_less_eq_real @ ( times_times_real @ Z @ X ) @ ( times_times_real @ Z @ Y ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[785]) ).
thf(1456,plain,
( ( ! [X: real] :
( ! [Y: real,Z: real] :
( ~ ( ord_less_real @ zero_zero_real @ Z )
| ~ ( ord_less_eq_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ Y @ Z ) )
| ( ord_less_eq_real @ X @ Y ) )
& ! [Y: real,Z: real] :
( ~ ( ord_less_real @ zero_zero_real @ Z )
| ~ ( ord_less_eq_real @ X @ Y )
| ( ord_less_eq_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ Y @ Z ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[786]) ).
thf(1457,plain,
( ( ! [M: nat,N: nat] :
( ( N = zero_zero_nat )
| ( M != zero_zero_nat )
| ( ( power_power_nat @ M @ N )
= zero_zero_nat ) )
& ! [M: nat,N: nat] :
( ( ( power_power_nat @ M @ N )
!= zero_zero_nat )
| ( N != zero_zero_nat ) )
& ! [M: nat] :
( ! [N: nat] :
( ( power_power_nat @ M @ N )
!= zero_zero_nat )
| ( M = zero_zero_nat ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[788]) ).
thf(1458,plain,
( ( ! [N: nat,M: nat] :
( ( N != one_one_nat )
| ( M != one_one_nat )
| ( ( times_times_nat @ N @ M )
= one_one_nat ) )
& ! [N: nat] :
( ! [M: nat] :
( ( times_times_nat @ N @ M )
!= one_one_nat )
| ( N = one_one_nat ) )
& ! [N: nat,M: nat] :
( ( ( times_times_nat @ N @ M )
!= one_one_nat )
| ( M = one_one_nat ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[790]) ).
thf(1459,plain,
( ( ! [A: real] :
( ! [B: real,C: real] :
( ( C = zero_zero_real )
| ( ( times_times_real @ A @ C )
!= ( times_times_real @ B @ C ) )
| ( A = B ) )
& ! [B: real,C: real] :
( ( C = zero_zero_real )
| ( A != B )
| ( ( times_times_real @ A @ C )
= ( times_times_real @ B @ C ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[791]) ).
thf(1460,plain,
( ( ! [A: real] :
( ! [B: real,C: real] :
( ( C = zero_zero_real )
| ( ( times_times_real @ C @ A )
!= ( times_times_real @ C @ B ) )
| ( A = B ) )
& ! [B: real,C: real] :
( ( C = zero_zero_real )
| ( A != B )
| ( ( times_times_real @ C @ A )
= ( times_times_real @ C @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[792]) ).
thf(1461,plain,
( ( ! [Z: real,X: real,Y: real] :
( ~ ( ord_less_eq_real @ X @ Y )
| ( ord_less_eq_real @ ( plus_plus_real @ Z @ X ) @ ( plus_plus_real @ Z @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[794]) ).
thf(1462,plain,
( ( ! [X: real,Y: real] :
( ~ ( ord_less_eq_real @ X @ Y )
| ( X = Y )
| ( ord_less_real @ X @ Y ) )
& ! [X: real,Y: real] :
( ( X != Y )
| ( ord_less_eq_real @ X @ Y ) )
& ! [X: real,Y: real] :
( ~ ( ord_less_real @ X @ Y )
| ( ord_less_eq_real @ X @ Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[798]) ).
thf(1463,plain,
( ( ! [X: real,Y: real] :
( ( X = Y )
| ~ ( ord_less_eq_real @ X @ Y )
| ( ord_less_real @ X @ Y ) )
& ! [X: real,Y: real] :
( ~ ( ord_less_real @ X @ Y )
| ( X != Y ) )
& ! [X: real,Y: real] :
( ~ ( ord_less_real @ X @ Y )
| ( ord_less_eq_real @ X @ Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[799]) ).
thf(1464,plain,
( ( zero_zero_real != one_one_real )
= $true ),
inference(extcnf_combined,[status(esa)],[800]) ).
thf(1465,plain,
( ( ! [X: real,Y: real] :
( ( X != zero_zero_real )
| ( Y != zero_zero_real )
| ( ( plus_plus_real @ ( power_power_real @ X @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_real ) )
& ! [X: real] :
( ! [Y: real] :
( ( plus_plus_real @ ( power_power_real @ X @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_real )
| ( X = zero_zero_real ) )
& ! [X: real,Y: real] :
( ( ( plus_plus_real @ ( power_power_real @ X @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_real )
| ( Y = zero_zero_real ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[801]) ).
thf(1466,plain,
( ( ! [P: nat,M: nat] :
( ( M != zero_zero_nat )
| ( ( power_power_nat @ P @ M )
= one_one_nat ) )
& ! [P: nat,M: 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(extcnf_combined,[status(esa)],[803]) ).
thf(1467,plain,
( ( ! [N: nat,M: nat] :
( ( M != zero_zero_nat )
| ( ( times_times_nat @ M @ N )
= zero_zero_nat ) )
& ! [N: nat,M: 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(extcnf_combined,[status(esa)],[804]) ).
thf(1468,plain,
( ( ! [A: int,P: int] :
( ~ ( zcong @ A @ zero_zero_int @ P )
| ( ( legendre @ A @ P )
= zero_zero_int ) )
& ! [A: int,P: int] :
( ( zcong @ A @ zero_zero_int @ P )
| ~ ( quadRes @ P @ A )
| ( ( legendre @ A @ P )
= one_one_int ) )
& ! [A: int,P: int] :
( ( zcong @ A @ zero_zero_int @ P )
| ( quadRes @ P @ A )
| ( ( legendre @ A @ P )
= ( number_number_of_int @ min ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[806]) ).
thf(1469,plain,
( ( ! [M: int] :
( ~ ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ M )
| ~ ( zcong @ one_one_int @ ( number_number_of_int @ min ) @ M ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[807]) ).
thf(1470,plain,
( ( ! [M: int] :
( ~ ( 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(extcnf_combined,[status(esa)],[808]) ).
thf(1471,plain,
( ( ! [Y: int,N: nat,P: int] :
( ~ ( zprime @ P )
| ~ ( dvd_dvd_int @ P @ ( power_power_int @ Y @ N ) )
| ~ ( ord_less_nat @ zero_zero_nat @ N )
| ( dvd_dvd_int @ P @ Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[809]) ).
thf(1472,plain,
( ( ! [B: int,A: int,P: int] :
( ~ ( zprime @ P )
| ~ ( ord_less_int @ zero_zero_int @ A )
| ~ ( zcong @ ( times_times_int @ A @ B ) @ zero_zero_int @ P )
| ( zcong @ A @ zero_zero_int @ P )
| ( zcong @ B @ zero_zero_int @ P ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[810]) ).
thf(1473,plain,
( ( ! [B: int,A: int,P: int] :
( ~ ( zprime @ P )
| ~ ( ord_less_int @ zero_zero_int @ A )
| ( zcong @ A @ zero_zero_int @ P )
| ( zcong @ B @ zero_zero_int @ P )
| ~ ( zcong @ ( times_times_int @ A @ B ) @ zero_zero_int @ P ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[811]) ).
thf(1474,plain,
( ( ! [Y: int,X: int,P: int] :
( ~ ( zprime @ P )
| ( zcong @ X @ zero_zero_int @ P )
| ( zcong @ Y @ zero_zero_int @ P )
| ~ ( zcong @ ( times_times_int @ X @ Y ) @ zero_zero_int @ P ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[812]) ).
thf(1475,plain,
( ( ! [P: int,Y: int,N: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ N )
| ~ ( dvd_dvd_int @ P @ Y )
| ( dvd_dvd_int @ P @ ( power_power_int @ Y @ N ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[813]) ).
thf(1476,plain,
( ( ! [M: int,N: int,P: int] :
( ~ ( zprime @ P )
| ~ ( dvd_dvd_int @ P @ ( times_times_int @ M @ N ) )
| ( dvd_dvd_int @ P @ M )
| ( dvd_dvd_int @ P @ N ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[814]) ).
thf(1477,plain,
( ( ! [C: int,D: int,A: int] :
( ! [B: int,M: int] :
( ~ ( zcong @ A @ B @ M )
| ~ ( zcong @ C @ ( times_times_int @ A @ D ) @ M )
| ( zcong @ C @ ( times_times_int @ B @ D ) @ M ) )
& ! [B: int,M: int] :
( ~ ( zcong @ A @ B @ M )
| ~ ( zcong @ C @ ( times_times_int @ B @ D ) @ M )
| ( zcong @ C @ ( times_times_int @ A @ D ) @ M ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[819]) ).
thf(1478,plain,
( ( ! [C: int,D: int,A: int] :
( ! [B: int,M: int] :
( ~ ( zcong @ A @ B @ M )
| ~ ( zcong @ C @ ( times_times_int @ D @ A ) @ M )
| ( zcong @ C @ ( times_times_int @ D @ B ) @ M ) )
& ! [B: int,M: int] :
( ~ ( zcong @ A @ B @ M )
| ~ ( zcong @ C @ ( times_times_int @ D @ B ) @ M )
| ( zcong @ C @ ( times_times_int @ D @ A ) @ M ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[820]) ).
thf(1479,plain,
( ( ! [A: int,P: int] :
( ~ ( zprime @ P )
| ~ ( ord_less_int @ zero_zero_int @ A )
| ~ ( zcong @ ( times_times_int @ A @ A ) @ one_one_int @ P )
| ( zcong @ A @ one_one_int @ P )
| ( zcong @ A @ ( minus_minus_int @ P @ one_one_int ) @ P ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[821]) ).
thf(1480,plain,
( ( ! [A: int,P: int] :
( ~ ( zprime @ P )
| ~ ( ord_less_int @ zero_zero_int @ A )
| ~ ( ord_less_int @ A @ P )
| ~ ( zcong @ ( times_times_int @ A @ A ) @ one_one_int @ P )
| ( A = one_one_int )
| ( A
= ( minus_minus_int @ P @ one_one_int ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[822]) ).
thf(1481,plain,
( ( ! [D: int,C: int,A: int,B: int,M: int] :
( ~ ( zcong @ A @ B @ M )
| ( B != C )
| ~ ( zcong @ C @ D @ M )
| ( zcong @ A @ D @ M ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[823]) ).
thf(1482,plain,
( ( ! [A: int,P: int] :
( ~ ( zcong @ ( times_times_int @ A @ ( minus_minus_int @ P @ one_one_int ) ) @ one_one_int @ P )
| ( zcong @ A @ ( minus_minus_int @ P @ one_one_int ) @ P ) )
& ! [A: int,P: int] :
( ~ ( zcong @ A @ ( minus_minus_int @ P @ one_one_int ) @ P )
| ( zcong @ ( times_times_int @ A @ ( minus_minus_int @ P @ one_one_int ) ) @ one_one_int @ P ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[824]) ).
thf(1483,plain,
( ( ! [A: int] :
( ! [B: int,M: int] :
( ~ ( dvd_dvd_int @ M @ ( minus_minus_int @ A @ B ) )
| ( zcong @ A @ B @ M ) )
& ! [B: int,M: int] :
( ~ ( zcong @ A @ B @ M )
| ( dvd_dvd_int @ M @ ( minus_minus_int @ A @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[826]) ).
thf(1484,plain,
( ( ! [K: int,M: int,N: int] :
( ~ ( dvd_dvd_int @ K @ ( minus_minus_int @ M @ N ) )
| ~ ( dvd_dvd_int @ K @ N )
| ( dvd_dvd_int @ K @ M ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[835]) ).
thf(1485,plain,
( ( ! [C: int,D: int,A: int,B: int,M: int] :
( ~ ( zcong @ A @ B @ M )
| ~ ( zcong @ C @ D @ M )
| ( zcong @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D ) @ M ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[836]) ).
thf(1486,plain,
( ( ! [X: real] :
( ( X != zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ ( times_times_real @ X @ X ) ) )
& ! [X: real] :
( ( ord_less_real @ zero_zero_real @ ( times_times_real @ X @ X ) )
| ( X = zero_zero_real ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[837]) ).
thf(1487,plain,
( ( ! [X: int,P: int] :
( ~ ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ P )
| ~ ( zcong @ X @ ( number_number_of_int @ min ) @ P )
| ~ ( zcong @ X @ one_one_int @ P ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[839]) ).
thf(1488,plain,
( ( ! [J: nat,K: nat,M: int] :
( ~ ( 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(extcnf_combined,[status(esa)],[840]) ).
thf(1489,plain,
( ( ! [N: int,P: int,M: int] :
( ~ ( ord_less_eq_int @ zero_zero_int @ M )
| ~ ( zprime @ P )
| ~ ( dvd_dvd_int @ P @ ( times_times_int @ M @ N ) )
| ( dvd_dvd_int @ P @ M )
| ( dvd_dvd_int @ P @ N ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[843]) ).
thf(1490,plain,
( ( ! [C: int,D: int,A: int,B: int,M: int] :
( ~ ( zcong @ A @ B @ M )
| ~ ( zcong @ C @ D @ M )
| ( zcong @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) @ M ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[847]) ).
thf(1491,plain,
( ( ! [K: int,A: int,B: int,M: int] :
( ~ ( zcong @ A @ B @ M )
| ( zcong @ ( times_times_int @ K @ A ) @ ( times_times_int @ K @ B ) @ M ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[848]) ).
thf(1492,plain,
( ( ! [K: int,A: int,B: int,M: int] :
( ~ ( zcong @ A @ B @ M )
| ( zcong @ ( times_times_int @ A @ K ) @ ( times_times_int @ B @ K ) @ M ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[849]) ).
thf(1493,plain,
( ( ! [X_9: nat,Y_7: nat] :
( ~ ( ord_less_eq_nat @ X_9 @ Y_7 )
| ( X_9 = Y_7 )
| ( ord_less_nat @ X_9 @ Y_7 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[851]) ).
thf(1494,plain,
( ( ! [X_9: real,Y_7: real] :
( ~ ( ord_less_eq_real @ X_9 @ Y_7 )
| ( X_9 = Y_7 )
| ( ord_less_real @ X_9 @ Y_7 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[852]) ).
thf(1495,plain,
( ( ! [C: int,A: int,B: int,M: int] :
( ~ ( zcong @ A @ B @ M )
| ~ ( zcong @ B @ C @ M )
| ( zcong @ A @ C @ M ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[853]) ).
thf(1496,plain,
( ( ! [A: int] :
( ! [B: int,M: int] :
( ~ ( zcong @ A @ B @ M )
| ( zcong @ B @ A @ M ) )
& ! [B: int,M: int] :
( ~ ( zcong @ B @ A @ M )
| ( zcong @ A @ B @ M ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[855]) ).
thf(1497,plain,
( ( ! [M: int] :
( ! [N: int] :
( ( times_times_int @ M @ N )
!= one_one_int )
| ( M = one_one_int )
| ( M
= ( number_number_of_int @ min ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[856]) ).
thf(1498,plain,
( ( ! [M: int] :
( ! [N: int] :
( ( times_times_int @ M @ N )
!= one_one_int )
| ( M = one_one_int )
| ( M
= ( number_number_of_int @ min ) ) )
& ! [M: int,N: int] :
( ( ( times_times_int @ M @ N )
!= one_one_int )
| ( M = one_one_int )
| ( N
= ( number_number_of_int @ min ) ) )
& ! [M: int,N: int] :
( ( ( times_times_int @ M @ N )
!= one_one_int )
| ( N = one_one_int )
| ( M
= ( number_number_of_int @ min ) ) )
& ! [M: int,N: int] :
( ( ( times_times_int @ M @ N )
!= one_one_int )
| ( N = one_one_int )
| ( N
= ( number_number_of_int @ min ) ) )
& ! [M: int,N: int] :
( ( M != one_one_int )
| ( N != one_one_int )
| ( ( times_times_int @ M @ N )
= one_one_int ) )
& ! [M: int,N: int] :
( ( M
!= ( number_number_of_int @ min ) )
| ( N
!= ( number_number_of_int @ min ) )
| ( ( times_times_int @ M @ N )
= one_one_int ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[857]) ).
thf(1499,plain,
( ( zcong @ ( power_power_int @ sK2_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_combined,[status(esa)],[859]) ).
thf(1500,plain,
( ( ! [P: int] :
( ~ ( zprime @ P )
| ( P
= ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
| ( P
= ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) )
| ( ord_less_eq_int @ ( number_number_of_int @ ( bit1 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ P ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[860]) ).
thf(1501,plain,
( ( ! [P: int] :
( ( ( dvd_dvd_int @ ( sK3_M_9 @ P ) @ P )
& ( ord_less_eq_int @ zero_zero_int @ ( sK3_M_9 @ P ) )
& ( ( sK3_M_9 @ P )
!= one_one_int )
& ( ( sK3_M_9 @ P )
!= P ) )
| ~ ( ord_less_int @ one_one_int @ P )
| ( zprime @ P ) )
& ! [P: int] :
( ~ ( zprime @ P )
| ! [M_9: int] :
( ~ ( dvd_dvd_int @ M_9 @ P )
| ~ ( ord_less_eq_int @ zero_zero_int @ M_9 )
| ( M_9 = one_one_int )
| ( M_9 = P ) ) )
& ! [P: int] :
( ~ ( zprime @ P )
| ( ord_less_int @ one_one_int @ P ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[861]) ).
thf(1502,plain,
( ( ! [W_3: int] :
( ( ( number_number_of_nat @ W_3 )
!= zero_zero_nat )
| ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ W_3 ) )
= one_one_nat ) )
& ! [W_3: int] :
( ( ( number_number_of_nat @ W_3 )
= zero_zero_nat )
| ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ W_3 ) )
= zero_zero_nat ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[863]) ).
thf(1503,plain,
( ( ! [W_3: int] :
( ( ( number_number_of_nat @ W_3 )
!= zero_zero_nat )
| ( ( power_power_real @ zero_zero_real @ ( number_number_of_nat @ W_3 ) )
= one_one_real ) )
& ! [W_3: int] :
( ( ( number_number_of_nat @ W_3 )
= zero_zero_nat )
| ( ( power_power_real @ zero_zero_real @ ( number_number_of_nat @ W_3 ) )
= zero_zero_real ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[864]) ).
thf(1504,plain,
( ( ! [A_28: real,W_4: int] :
( ( ( number_number_of_nat @ W_4 )
= zero_zero_nat )
| ( A_28 != zero_zero_real )
| ( ( power_power_real @ A_28 @ ( number_number_of_nat @ W_4 ) )
= zero_zero_real ) )
& ! [A_28: real,W_4: int] :
( ( ( power_power_real @ A_28 @ ( number_number_of_nat @ W_4 ) )
!= zero_zero_real )
| ( ( number_number_of_nat @ W_4 )
!= zero_zero_nat ) )
& ! [A_28: real] :
( ! [W_4: int] :
( ( power_power_real @ A_28 @ ( number_number_of_nat @ W_4 ) )
!= zero_zero_real )
| ( A_28 = zero_zero_real ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[865]) ).
thf(1505,plain,
( ( ! [C_4: nat,D_2: nat,A_31: nat,B_12: nat,R_2: nat] :
( ( R_2 = zero_zero_nat )
| ( C_4 = D_2 )
| ( A_31 != B_12 )
| ( ( plus_plus_nat @ A_31 @ ( times_times_nat @ R_2 @ C_4 ) )
!= ( plus_plus_nat @ B_12 @ ( times_times_nat @ R_2 @ D_2 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[872]) ).
thf(1506,plain,
( ( ! [C_4: real,D_2: real,A_31: real,B_12: real,R_2: real] :
( ( R_2 = zero_zero_real )
| ( C_4 = D_2 )
| ( A_31 != B_12 )
| ( ( plus_plus_real @ A_31 @ ( times_times_real @ R_2 @ C_4 ) )
!= ( plus_plus_real @ B_12 @ ( times_times_real @ R_2 @ D_2 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[873]) ).
thf(1507,plain,
( ( ! [W_5: nat,Y_9: nat] :
( ! [X_14: nat,Z_1: nat] :
( ( ( plus_plus_nat @ ( times_times_nat @ W_5 @ Y_9 ) @ ( times_times_nat @ X_14 @ Z_1 ) )
!= ( plus_plus_nat @ ( times_times_nat @ W_5 @ Z_1 ) @ ( times_times_nat @ X_14 @ Y_9 ) ) )
| ( W_5 = X_14 )
| ( Y_9 = Z_1 ) )
& ! [X_14: nat] :
( ( W_5 != X_14 )
| ! [Z_1: nat] :
( ( plus_plus_nat @ ( times_times_nat @ W_5 @ Y_9 ) @ ( times_times_nat @ X_14 @ Z_1 ) )
= ( plus_plus_nat @ ( times_times_nat @ W_5 @ Z_1 ) @ ( times_times_nat @ X_14 @ Y_9 ) ) ) )
& ! [X_14: nat,Z_1: nat] :
( ( Y_9 != Z_1 )
| ( ( plus_plus_nat @ ( times_times_nat @ W_5 @ Y_9 ) @ ( times_times_nat @ X_14 @ Z_1 ) )
= ( plus_plus_nat @ ( times_times_nat @ W_5 @ Z_1 ) @ ( times_times_nat @ X_14 @ Y_9 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[885]) ).
thf(1508,plain,
( ( ! [W_5: real,Y_9: real] :
( ! [X_14: real,Z_1: real] :
( ( ( plus_plus_real @ ( times_times_real @ W_5 @ Y_9 ) @ ( times_times_real @ X_14 @ Z_1 ) )
!= ( plus_plus_real @ ( times_times_real @ W_5 @ Z_1 ) @ ( times_times_real @ X_14 @ Y_9 ) ) )
| ( W_5 = X_14 )
| ( Y_9 = Z_1 ) )
& ! [X_14: real] :
( ( W_5 != X_14 )
| ! [Z_1: real] :
( ( plus_plus_real @ ( times_times_real @ W_5 @ Y_9 ) @ ( times_times_real @ X_14 @ Z_1 ) )
= ( plus_plus_real @ ( times_times_real @ W_5 @ Z_1 ) @ ( times_times_real @ X_14 @ Y_9 ) ) ) )
& ! [X_14: real,Z_1: real] :
( ( Y_9 != Z_1 )
| ( ( plus_plus_real @ ( times_times_real @ W_5 @ Y_9 ) @ ( times_times_real @ X_14 @ Z_1 ) )
= ( plus_plus_real @ ( times_times_real @ W_5 @ Z_1 ) @ ( times_times_real @ X_14 @ Y_9 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[886]) ).
thf(1509,plain,
( ( ! [C_6: nat,D_3: nat] :
( ! [A_37: nat,B_15: nat] :
( ( ( plus_plus_nat @ ( times_times_nat @ A_37 @ C_6 ) @ ( times_times_nat @ B_15 @ D_3 ) )
= ( plus_plus_nat @ ( times_times_nat @ A_37 @ D_3 ) @ ( times_times_nat @ B_15 @ C_6 ) ) )
| ( A_37 != B_15 ) )
& ( ! [A_37: nat,B_15: nat] :
( ( plus_plus_nat @ ( times_times_nat @ A_37 @ C_6 ) @ ( times_times_nat @ B_15 @ D_3 ) )
= ( plus_plus_nat @ ( times_times_nat @ A_37 @ D_3 ) @ ( times_times_nat @ B_15 @ C_6 ) ) )
| ( C_6 != D_3 ) )
& ! [A_37: nat,B_15: nat] :
( ( A_37 = B_15 )
| ( C_6 = D_3 )
| ( ( plus_plus_nat @ ( times_times_nat @ A_37 @ C_6 ) @ ( times_times_nat @ B_15 @ D_3 ) )
!= ( plus_plus_nat @ ( times_times_nat @ A_37 @ D_3 ) @ ( times_times_nat @ B_15 @ C_6 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[891]) ).
thf(1510,plain,
( ( ! [C_6: real,D_3: real] :
( ! [A_37: real,B_15: real] :
( ( ( plus_plus_real @ ( times_times_real @ A_37 @ C_6 ) @ ( times_times_real @ B_15 @ D_3 ) )
= ( plus_plus_real @ ( times_times_real @ A_37 @ D_3 ) @ ( times_times_real @ B_15 @ C_6 ) ) )
| ( A_37 != B_15 ) )
& ( ! [A_37: real,B_15: real] :
( ( plus_plus_real @ ( times_times_real @ A_37 @ C_6 ) @ ( times_times_real @ B_15 @ D_3 ) )
= ( plus_plus_real @ ( times_times_real @ A_37 @ D_3 ) @ ( times_times_real @ B_15 @ C_6 ) ) )
| ( C_6 != D_3 ) )
& ! [A_37: real,B_15: real] :
( ( A_37 = B_15 )
| ( C_6 = D_3 )
| ( ( plus_plus_real @ ( times_times_real @ A_37 @ C_6 ) @ ( times_times_real @ B_15 @ D_3 ) )
!= ( plus_plus_real @ ( times_times_real @ A_37 @ D_3 ) @ ( times_times_real @ B_15 @ C_6 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[892]) ).
thf(1511,plain,
( ( ! [B_16: nat,A_38: nat] :
( ( B_16
!= ( plus_plus_nat @ B_16 @ A_38 ) )
| ( A_38 = zero_zero_nat ) )
& ! [B_16: nat,A_38: nat] :
( ( A_38 != zero_zero_nat )
| ( B_16
= ( plus_plus_nat @ B_16 @ A_38 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[895]) ).
thf(1512,plain,
( ( ! [B_16: real,A_38: real] :
( ( B_16
!= ( plus_plus_real @ B_16 @ A_38 ) )
| ( A_38 = zero_zero_real ) )
& ! [B_16: real,A_38: real] :
( ( A_38 != zero_zero_real )
| ( B_16
= ( plus_plus_real @ B_16 @ A_38 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[896]) ).
thf(1513,plain,
( ( ! [A_43: real] :
( ! [K_2: nat] :
~ ( ord_less_eq_real @ ( power_power_real @ A_43 @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ K_2 ) ) @ zero_zero_real )
| ( A_43 = zero_zero_real ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[905]) ).
thf(1514,plain,
( ( ! [V_5: int] :
( ! [K: nat,V_4: int] :
( ~ ( ord_less_int @ V_4 @ pls )
| ( ( times_times_nat @ ( number_number_of_nat @ V_4 ) @ ( times_times_nat @ ( number_number_of_nat @ V_5 ) @ K ) )
= zero_zero_nat ) )
& ! [K: nat,V_4: int] :
( ( ord_less_int @ V_4 @ pls )
| ( ( times_times_nat @ ( number_number_of_nat @ V_4 ) @ ( times_times_nat @ ( number_number_of_nat @ V_5 ) @ K ) )
= ( times_times_nat @ ( number_number_of_nat @ ( times_times_int @ V_4 @ V_5 ) ) @ K ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[906]) ).
thf(1515,plain,
( ( ! [V_5: int,V_4: int] :
( ~ ( ord_less_int @ V_4 @ pls )
| ( ( times_times_nat @ ( number_number_of_nat @ V_4 ) @ ( number_number_of_nat @ V_5 ) )
= zero_zero_nat ) )
& ! [V_5: int,V_4: int] :
( ( ord_less_int @ V_4 @ pls )
| ( ( times_times_nat @ ( number_number_of_nat @ V_4 ) @ ( number_number_of_nat @ V_5 ) )
= ( number_number_of_nat @ ( times_times_int @ V_4 @ V_5 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[907]) ).
thf(1516,plain,
( ( ! [X: nat,W: int] :
( ~ ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X @ ( number_number_of_nat @ W ) ) )
| ( ( number_number_of_nat @ W )
= zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ X ) )
& ! [X: nat,W: int] :
( ( ( number_number_of_nat @ W )
!= zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X @ ( number_number_of_nat @ W ) ) ) )
& ! [X: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ X )
| ! [W: int] : ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X @ ( number_number_of_nat @ W ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[908]) ).
thf(1517,plain,
( ( ! [Y: int,X: int] :
( ~ ( twoSqu362149276sum2sq @ X )
| ~ ( twoSqu362149276sum2sq @ Y )
| ( twoSqu362149276sum2sq @ ( times_times_int @ X @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[947]) ).
thf(1518,plain,
( ( ! [N: nat,B: int,A: int,P: int] :
( ~ ( zprime @ P )
| ( dvd_dvd_int @ P @ A )
| ~ ( dvd_dvd_int @ ( power_power_int @ P @ N ) @ ( times_times_int @ A @ B ) )
| ( dvd_dvd_int @ ( power_power_int @ P @ N ) @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[948]) ).
thf(1519,plain,
( ( ! [N: nat,A: int,B: int,P: int] :
( ~ ( zprime @ P )
| ( dvd_dvd_int @ P @ B )
| ~ ( dvd_dvd_int @ ( power_power_int @ P @ N ) @ ( times_times_int @ A @ B ) )
| ( dvd_dvd_int @ ( power_power_int @ P @ N ) @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[949]) ).
thf(1520,plain,
( ( ! [X: nat,N: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X @ N ) )
| ( N = zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ X ) )
& ! [X: nat,N: nat] :
( ( N != zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X @ N ) ) )
& ! [X: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ X )
| ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X @ N ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[952]) ).
thf(1521,plain,
( ( ! [Y_11: int] :
( ~ ( ord_less_int @ ( bit1 @ pls ) @ Y_11 )
| ( ord_less_real @ one_one_real @ ( number267125858f_real @ Y_11 ) ) )
& ! [Y_11: int] :
( ~ ( ord_less_real @ one_one_real @ ( number267125858f_real @ Y_11 ) )
| ( ord_less_int @ ( bit1 @ pls ) @ Y_11 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[955]) ).
thf(1522,plain,
( ( ! [X_19: int] :
( ~ ( ord_less_int @ X_19 @ ( bit1 @ pls ) )
| ( ord_less_real @ ( number267125858f_real @ X_19 ) @ one_one_real ) )
& ! [X_19: int] :
( ~ ( ord_less_real @ ( number267125858f_real @ X_19 ) @ one_one_real )
| ( ord_less_int @ X_19 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[956]) ).
thf(1523,plain,
( ( ! [Y_12: int] :
( ~ ( ord_less_int @ pls @ Y_12 )
| ( ord_less_real @ zero_zero_real @ ( number267125858f_real @ Y_12 ) ) )
& ! [Y_12: int] :
( ~ ( ord_less_real @ zero_zero_real @ ( number267125858f_real @ Y_12 ) )
| ( ord_less_int @ pls @ Y_12 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[959]) ).
thf(1524,plain,
( ( ! [X_20: int] :
( ~ ( ord_less_int @ X_20 @ pls )
| ( ord_less_real @ ( number267125858f_real @ X_20 ) @ zero_zero_real ) )
& ! [X_20: int] :
( ~ ( ord_less_real @ ( number267125858f_real @ X_20 ) @ zero_zero_real )
| ( ord_less_int @ X_20 @ pls ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[960]) ).
thf(1525,plain,
( ( ! [A_54: real] :
( ~ ( ord_less_real @ ( plus_plus_real @ A_54 @ A_54 ) @ zero_zero_real )
| ( ord_less_real @ A_54 @ zero_zero_real ) )
& ! [A_54: real] :
( ~ ( ord_less_real @ A_54 @ zero_zero_real )
| ( ord_less_real @ ( plus_plus_real @ A_54 @ A_54 ) @ zero_zero_real ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[966]) ).
thf(1526,plain,
( ( ! [A_57: real] :
( ( ( plus_plus_real @ A_57 @ A_57 )
!= zero_zero_real )
| ( A_57 = zero_zero_real ) )
& ! [A_57: real] :
( ( A_57 != zero_zero_real )
| ( ( plus_plus_real @ A_57 @ A_57 )
= zero_zero_real ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[972]) ).
thf(1527,plain,
( ( ! [X_24: real,Y_16: real] :
( ~ ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X_24 @ X_24 ) @ ( times_times_real @ Y_16 @ Y_16 ) ) )
| ( X_24 != zero_zero_real )
| ( Y_16 != zero_zero_real ) )
& ! [X_24: real] :
( ( X_24 = zero_zero_real )
| ! [Y_16: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X_24 @ X_24 ) @ ( times_times_real @ Y_16 @ Y_16 ) ) ) )
& ! [X_24: real,Y_16: real] :
( ( Y_16 = zero_zero_real )
| ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X_24 @ X_24 ) @ ( times_times_real @ Y_16 @ Y_16 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[974]) ).
thf(1528,plain,
( ( ! [X_26: real,Y_18: real] :
( ( X_26 != zero_zero_real )
| ( Y_18 != zero_zero_real )
| ( ord_less_eq_real @ ( plus_plus_real @ ( power_power_real @ X_26 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y_18 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_real ) )
& ! [X_26: real] :
( ! [Y_18: real] :
~ ( ord_less_eq_real @ ( plus_plus_real @ ( power_power_real @ X_26 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y_18 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_real )
| ( X_26 = zero_zero_real ) )
& ! [X_26: real,Y_18: real] :
( ~ ( ord_less_eq_real @ ( plus_plus_real @ ( power_power_real @ X_26 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y_18 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_real )
| ( Y_18 = zero_zero_real ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[976]) ).
thf(1529,plain,
( ( ! [X_27: nat,Y_19: nat] :
( ~ ( ord_less_nat @ ( power_power_nat @ X_27 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_nat @ Y_19 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ Y_19 )
| ( ord_less_nat @ X_27 @ Y_19 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[977]) ).
thf(1530,plain,
( ( ! [X_27: real,Y_19: real] :
( ~ ( ord_less_real @ ( power_power_real @ X_27 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y_19 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ~ ( ord_less_eq_real @ zero_zero_real @ Y_19 )
| ( ord_less_real @ X_27 @ Y_19 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[978]) ).
thf(1531,plain,
( ( ! [X_28: nat,Y_20: nat] :
( ~ ( ord_less_eq_nat @ ( power_power_nat @ X_28 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_nat @ Y_20 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ Y_20 )
| ( ord_less_eq_nat @ X_28 @ Y_20 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[980]) ).
thf(1532,plain,
( ( ! [X_28: real,Y_20: real] :
( ~ ( ord_less_eq_real @ ( power_power_real @ X_28 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y_20 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ~ ( ord_less_eq_real @ zero_zero_real @ Y_20 )
| ( ord_less_eq_real @ X_28 @ Y_20 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[981]) ).
thf(1533,plain,
( ( ! [X_29: nat,Y_21: nat] :
( ( ( power_power_nat @ X_29 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= ( power_power_nat @ Y_21 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ X_29 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ Y_21 )
| ( X_29 = Y_21 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[982]) ).
thf(1534,plain,
( ( ! [X_29: real,Y_21: real] :
( ( ( power_power_real @ X_29 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= ( power_power_real @ Y_21 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ~ ( ord_less_eq_real @ zero_zero_real @ X_29 )
| ~ ( ord_less_eq_real @ zero_zero_real @ Y_21 )
| ( X_29 = Y_21 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[983]) ).
thf(1535,plain,
( ( ! [X_30: real,Y_22: real] :
( ( X_30 != zero_zero_real )
| ( Y_22 != zero_zero_real )
| ( ( plus_plus_real @ ( times_times_real @ X_30 @ X_30 ) @ ( times_times_real @ Y_22 @ Y_22 ) )
= zero_zero_real ) )
& ! [X_30: real] :
( ! [Y_22: real] :
( ( plus_plus_real @ ( times_times_real @ X_30 @ X_30 ) @ ( times_times_real @ Y_22 @ Y_22 ) )
!= zero_zero_real )
| ( X_30 = zero_zero_real ) )
& ! [X_30: real,Y_22: real] :
( ( ( plus_plus_real @ ( times_times_real @ X_30 @ X_30 ) @ ( times_times_real @ Y_22 @ Y_22 ) )
!= zero_zero_real )
| ( Y_22 = zero_zero_real ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[986]) ).
thf(1536,plain,
( ( ! [W_13: int,X_31: int] :
( ( ( number_number_of_int @ W_13 )
!= X_31 )
| ( X_31
= ( number_number_of_int @ W_13 ) ) )
& ! [W_13: int,X_31: int] :
( ( X_31
!= ( number_number_of_int @ W_13 ) )
| ( ( number_number_of_int @ W_13 )
= X_31 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[987]) ).
thf(1537,plain,
( ( ! [W_13: int,X_31: real] :
( ( ( number267125858f_real @ W_13 )
!= X_31 )
| ( X_31
= ( number267125858f_real @ W_13 ) ) )
& ! [W_13: int,X_31: real] :
( ( X_31
!= ( number267125858f_real @ W_13 ) )
| ( ( number267125858f_real @ W_13 )
= X_31 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[988]) ).
thf(1538,plain,
( ( ! [X_32: int,Y_23: int] :
( ( ( number_number_of_int @ X_32 )
!= ( number_number_of_int @ Y_23 ) )
| ( X_32 = Y_23 ) )
& ! [X_32: int,Y_23: int] :
( ( X_32 != Y_23 )
| ( ( number_number_of_int @ X_32 )
= ( number_number_of_int @ Y_23 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[989]) ).
thf(1539,plain,
( ( ! [X_32: int,Y_23: int] :
( ( ( number267125858f_real @ X_32 )
!= ( number267125858f_real @ Y_23 ) )
| ( X_32 = Y_23 ) )
& ! [X_32: int,Y_23: int] :
( ( X_32 != Y_23 )
| ( ( number267125858f_real @ X_32 )
= ( number267125858f_real @ Y_23 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[990]) ).
thf(1540,plain,
( ( ! [V_12: int,V_11: int] :
( ~ ( ord_less_eq_int @ pls @ V_11 )
| ~ ( ord_less_eq_int @ pls @ V_12 )
| ( ( plus_plus_real @ ( number267125858f_real @ V_11 ) @ ( number267125858f_real @ V_12 ) )
= ( number267125858f_real @ ( plus_plus_int @ V_11 @ V_12 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[991]) ).
thf(1541,plain,
( ( ! [Y_24: int] :
( ~ ( ord_less_eq_int @ ( bit1 @ pls ) @ Y_24 )
| ( ord_less_eq_real @ one_one_real @ ( number267125858f_real @ Y_24 ) ) )
& ! [Y_24: int] :
( ~ ( ord_less_eq_real @ one_one_real @ ( number267125858f_real @ Y_24 ) )
| ( ord_less_eq_int @ ( bit1 @ pls ) @ Y_24 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[992]) ).
thf(1542,plain,
( ( ! [X_33: int] :
( ~ ( ord_less_eq_int @ X_33 @ ( bit1 @ pls ) )
| ( ord_less_eq_real @ ( number267125858f_real @ X_33 ) @ one_one_real ) )
& ! [X_33: int] :
( ~ ( ord_less_eq_real @ ( number267125858f_real @ X_33 ) @ one_one_real )
| ( ord_less_eq_int @ X_33 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[993]) ).
thf(1543,plain,
( ( ! [V_13: int,W_15: int] :
( ~ ( ord_less_eq_real @ ( number267125858f_real @ V_13 ) @ ( number267125858f_real @ W_15 ) )
| ~ ( ord_less_real @ ( number267125858f_real @ W_15 ) @ ( number267125858f_real @ V_13 ) ) )
& ! [V_13: int,W_15: int] :
( ( ord_less_real @ ( number267125858f_real @ W_15 ) @ ( number267125858f_real @ V_13 ) )
| ( ord_less_eq_real @ ( number267125858f_real @ V_13 ) @ ( number267125858f_real @ W_15 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[994]) ).
thf(1544,plain,
( ( ! [Y_25: int] :
( ~ ( ord_less_eq_int @ pls @ Y_25 )
| ( ord_less_eq_real @ zero_zero_real @ ( number267125858f_real @ Y_25 ) ) )
& ! [Y_25: int] :
( ~ ( ord_less_eq_real @ zero_zero_real @ ( number267125858f_real @ Y_25 ) )
| ( ord_less_eq_int @ pls @ Y_25 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[995]) ).
thf(1545,plain,
( ( ! [X_34: int] :
( ~ ( ord_less_eq_int @ X_34 @ pls )
| ( ord_less_eq_real @ ( number267125858f_real @ X_34 ) @ zero_zero_real ) )
& ! [X_34: int] :
( ~ ( ord_less_eq_real @ ( number267125858f_real @ X_34 ) @ zero_zero_real )
| ( ord_less_eq_int @ X_34 @ pls ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[996]) ).
thf(1546,plain,
( ( ! [X_36: real,Y_27: real] :
( ( X_36 != zero_zero_real )
| ( Y_27 != zero_zero_real )
| ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ X_36 @ X_36 ) @ ( times_times_real @ Y_27 @ Y_27 ) ) @ zero_zero_real ) )
& ! [X_36: real] :
( ! [Y_27: real] :
~ ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ X_36 @ X_36 ) @ ( times_times_real @ Y_27 @ Y_27 ) ) @ zero_zero_real )
| ( X_36 = zero_zero_real ) )
& ! [X_36: real,Y_27: real] :
( ~ ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ X_36 @ X_36 ) @ ( times_times_real @ Y_27 @ Y_27 ) ) @ zero_zero_real )
| ( Y_27 = zero_zero_real ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[998]) ).
thf(1547,plain,
( ( ! [V_18: int,V_17: int] :
( ~ ( ord_less_eq_int @ pls @ V_17 )
| ~ ( ord_less_eq_int @ pls @ V_18 )
| ( ( times_times_int @ ( number_number_of_int @ V_17 ) @ ( number_number_of_int @ V_18 ) )
= ( number_number_of_int @ ( times_times_int @ V_17 @ V_18 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1005]) ).
thf(1548,plain,
( ( ! [V_18: int,V_17: int] :
( ~ ( ord_less_eq_int @ pls @ V_17 )
| ~ ( ord_less_eq_int @ pls @ V_18 )
| ( ( times_times_nat @ ( number_number_of_nat @ V_17 ) @ ( number_number_of_nat @ V_18 ) )
= ( number_number_of_nat @ ( times_times_int @ V_17 @ V_18 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1006]) ).
thf(1549,plain,
( ( ! [V_18: int,V_17: int] :
( ~ ( ord_less_eq_int @ pls @ V_17 )
| ~ ( ord_less_eq_int @ pls @ V_18 )
| ( ( times_times_real @ ( number267125858f_real @ V_17 ) @ ( number267125858f_real @ V_18 ) )
= ( number267125858f_real @ ( times_times_int @ V_17 @ V_18 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1007]) ).
thf(1550,plain,
( ( ! [Z: int,W: int] :
( ~ ( ord_less_eq_int @ Z @ W )
| ~ ( ord_less_eq_int @ W @ Z )
| ( Z = W ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1008]) ).
thf(1551,plain,
( ( ! [K: int,I: int,J: int] :
( ~ ( ord_less_eq_int @ I @ J )
| ~ ( ord_less_eq_int @ J @ K )
| ( ord_less_eq_int @ I @ K ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1009]) ).
thf(1552,plain,
( ( ! [X_37: int,Y_28: int] :
( ~ ( ord_less_eq_int @ ( number_number_of_int @ X_37 ) @ ( number_number_of_int @ Y_28 ) )
| ( ord_less_eq_int @ X_37 @ Y_28 ) )
& ! [X_37: int,Y_28: int] :
( ~ ( ord_less_eq_int @ X_37 @ Y_28 )
| ( ord_less_eq_int @ ( number_number_of_int @ X_37 ) @ ( number_number_of_int @ Y_28 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1011]) ).
thf(1553,plain,
( ( ! [X_37: int,Y_28: int] :
( ~ ( ord_less_eq_int @ X_37 @ Y_28 )
| ( ord_less_eq_real @ ( number267125858f_real @ X_37 ) @ ( number267125858f_real @ Y_28 ) ) )
& ! [X_37: int,Y_28: int] :
( ~ ( ord_less_eq_real @ ( number267125858f_real @ X_37 ) @ ( number267125858f_real @ Y_28 ) )
| ( ord_less_eq_int @ X_37 @ Y_28 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1012]) ).
thf(1554,plain,
( ( ! [K: int,L: int] :
( ~ ( ord_less_eq_int @ ( number_number_of_int @ K ) @ ( number_number_of_int @ L ) )
| ( ord_less_eq_int @ K @ L ) )
& ! [K: int,L: int] :
( ~ ( ord_less_eq_int @ K @ L )
| ( ord_less_eq_int @ ( number_number_of_int @ K ) @ ( number_number_of_int @ L ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1013]) ).
thf(1555,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 ) @ sK4_T_1 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1020]) ).
thf(1556,plain,
( ( ! [A_63: real] :
( ( A_63 = zero_zero_real )
| ( ord_less_real @ zero_zero_real @ ( power_power_real @ A_63 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
& ! [A_63: real] :
( ~ ( ord_less_real @ zero_zero_real @ ( power_power_real @ A_63 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ( A_63 != zero_zero_real ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1024]) ).
thf(1557,plain,
( ( ! [X_38: real,Y_29: real] :
( ( X_38 != zero_zero_real )
| ( Y_29 != zero_zero_real )
| ( ( plus_plus_real @ ( power_power_real @ X_38 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y_29 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_real ) )
& ! [X_38: real] :
( ! [Y_29: real] :
( ( plus_plus_real @ ( power_power_real @ X_38 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y_29 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_real )
| ( X_38 = zero_zero_real ) )
& ! [X_38: real,Y_29: real] :
( ( ( plus_plus_real @ ( power_power_real @ X_38 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y_29 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_real )
| ( Y_29 = zero_zero_real ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1026]) ).
thf(1558,plain,
( ( ! [X_39: real,Y_30: real] :
( ~ ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X_39 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y_30 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
| ( X_39 != zero_zero_real )
| ( Y_30 != zero_zero_real ) )
& ! [X_39: real] :
( ( X_39 = zero_zero_real )
| ! [Y_30: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X_39 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y_30 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
& ! [X_39: real,Y_30: real] :
( ( Y_30 = zero_zero_real )
| ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X_39 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y_30 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1027]) ).
thf(1559,plain,
( ( ! [A_1: int,N_2: nat,N_1: nat] :
( ~ ( ord_less_nat @ N_2 @ N_1 )
| ~ ( ord_less_int @ zero_zero_int @ A_1 )
| ~ ( ord_less_int @ A_1 @ one_one_int )
| ( ord_less_int @ ( power_power_int @ A_1 @ N_1 ) @ ( power_power_int @ A_1 @ N_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1032]) ).
thf(1560,plain,
( ( ! [N_3: nat,A_2: int] :
( ~ ( ord_less_int @ zero_zero_int @ A_2 )
| ~ ( ord_less_int @ A_2 @ one_one_int )
| ( ord_less_int @ ( times_times_int @ A_2 @ ( power_power_int @ A_2 @ N_3 ) ) @ ( power_power_int @ A_2 @ N_3 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1033]) ).
thf(1561,plain,
( ( ! [A_3: int,N_5: nat,N_4: nat] :
( ~ ( ord_less_eq_nat @ N_5 @ N_4 )
| ~ ( ord_less_eq_int @ one_one_int @ A_3 )
| ( ord_less_eq_int @ ( power_power_int @ A_3 @ N_5 ) @ ( power_power_int @ A_3 @ N_4 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1034]) ).
thf(1562,plain,
( ( ! [X_2: nat] :
( ! [Y_2: nat,B_1: int] :
( ~ ( ord_less_int @ one_one_int @ B_1 )
| ~ ( ord_less_int @ ( power_power_int @ B_1 @ X_2 ) @ ( power_power_int @ B_1 @ Y_2 ) )
| ( ord_less_nat @ X_2 @ Y_2 ) )
& ! [Y_2: nat,B_1: int] :
( ~ ( ord_less_int @ one_one_int @ B_1 )
| ~ ( ord_less_nat @ X_2 @ Y_2 )
| ( ord_less_int @ ( power_power_int @ B_1 @ X_2 ) @ ( power_power_int @ B_1 @ Y_2 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1035]) ).
thf(1563,plain,
( ( ! [M_1: nat,N_6: nat,A_4: int] :
( ~ ( ord_less_int @ one_one_int @ A_4 )
| ~ ( ord_less_int @ ( power_power_int @ A_4 @ M_1 ) @ ( power_power_int @ A_4 @ N_6 ) )
| ( ord_less_nat @ M_1 @ N_6 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1036]) ).
thf(1564,plain,
( ( ! [A_5: int,N_8: nat,N_7: nat] :
( ~ ( ord_less_nat @ N_8 @ N_7 )
| ~ ( ord_less_int @ one_one_int @ A_5 )
| ( ord_less_int @ ( power_power_int @ A_5 @ N_8 ) @ ( power_power_int @ A_5 @ N_7 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1037]) ).
thf(1565,plain,
( ( ! [N_9: nat] :
( ( N_9 != zero_zero_nat )
| ( ( power_power_int @ zero_zero_int @ N_9 )
= one_one_int ) )
& ! [N_9: nat] :
( ( N_9 = zero_zero_nat )
| ( ( power_power_int @ zero_zero_int @ N_9 )
= zero_zero_int ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1038]) ).
thf(1566,plain,
( ( ! [N_10: nat,A_6: int] :
( ~ ( ord_less_int @ one_one_int @ A_6 )
| ( ord_less_int @ one_one_int @ ( times_times_int @ A_6 @ ( power_power_int @ A_6 @ N_10 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1039]) ).
thf(1567,plain,
( ( ! [N_11: nat,A_7: int] :
( ~ ( ord_less_int @ one_one_int @ A_7 )
| ( ord_less_int @ ( power_power_int @ A_7 @ N_11 ) @ ( times_times_int @ A_7 @ ( power_power_int @ A_7 @ N_11 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1040]) ).
thf(1568,plain,
( ( ! [A_8: int,N_12: nat,B_2: int] :
( ~ ( ord_less_int @ ( power_power_int @ A_8 @ N_12 ) @ ( power_power_int @ B_2 @ N_12 ) )
| ~ ( ord_less_eq_int @ zero_zero_int @ B_2 )
| ( ord_less_int @ A_8 @ B_2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1041]) ).
thf(1569,plain,
( ( ! [A_9: int,M_2: nat,N_13: nat] :
( ~ ( ord_less_eq_nat @ M_2 @ N_13 )
| ( dvd_dvd_int @ ( power_power_int @ A_9 @ M_2 ) @ ( power_power_int @ A_9 @ N_13 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1042]) ).
thf(1570,plain,
( ( ! [N_14: nat,M_3: nat,X_3: int,Y_3: int] :
( ~ ( dvd_dvd_int @ X_3 @ Y_3 )
| ~ ( ord_less_eq_nat @ N_14 @ M_3 )
| ( dvd_dvd_int @ ( power_power_int @ X_3 @ N_14 ) @ ( power_power_int @ Y_3 @ M_3 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1043]) ).
thf(1571,plain,
( ( ! [M_4: nat,A_10: int,N_15: nat,B_3: int] :
( ~ ( dvd_dvd_int @ ( power_power_int @ A_10 @ N_15 ) @ B_3 )
| ~ ( ord_less_eq_nat @ M_4 @ N_15 )
| ( dvd_dvd_int @ ( power_power_int @ A_10 @ M_4 ) @ B_3 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1044]) ).
thf(1572,plain,
( ( ! [A_13: int,N_17: nat] :
( ( N_17 = zero_zero_nat )
| ( A_13 != zero_zero_int )
| ( ( power_power_int @ A_13 @ N_17 )
= zero_zero_int ) )
& ! [A_13: int,N_17: nat] :
( ( ( power_power_int @ A_13 @ N_17 )
!= zero_zero_int )
| ( N_17 != zero_zero_nat ) )
& ! [A_13: int] :
( ! [N_17: nat] :
( ( power_power_int @ A_13 @ N_17 )
!= zero_zero_int )
| ( A_13 = zero_zero_int ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1047]) ).
thf(1573,plain,
( ( ! [M_6: nat] :
( ! [N_18: nat,A_14: int] :
( ~ ( ord_less_int @ one_one_int @ A_14 )
| ( ( power_power_int @ A_14 @ M_6 )
!= ( power_power_int @ A_14 @ N_18 ) )
| ( M_6 = N_18 ) )
& ! [N_18: nat,A_14: int] :
( ~ ( ord_less_int @ one_one_int @ A_14 )
| ( M_6 != N_18 )
| ( ( power_power_int @ A_14 @ M_6 )
= ( power_power_int @ A_14 @ N_18 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1048]) ).
thf(1574,plain,
( ( ! [N_19: nat,A_15: int] :
( ~ ( ord_less_eq_int @ one_one_int @ A_15 )
| ( ord_less_eq_int @ one_one_int @ ( power_power_int @ A_15 @ N_19 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1049]) ).
thf(1575,plain,
( ( ! [N_20: nat,A_16: int] :
( ~ ( ord_less_int @ zero_zero_int @ A_16 )
| ( ord_less_int @ zero_zero_int @ ( power_power_int @ A_16 @ N_20 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1050]) ).
thf(1576,plain,
( ( ! [N_21: nat,A_17: int] :
( ~ ( ord_less_eq_int @ zero_zero_int @ A_17 )
| ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A_17 @ N_21 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1051]) ).
thf(1577,plain,
( ( ! [N_22: nat,A_18: int,B_4: int] :
( ~ ( ord_less_eq_int @ A_18 @ B_4 )
| ~ ( ord_less_eq_int @ zero_zero_int @ A_18 )
| ( ord_less_eq_int @ ( power_power_int @ A_18 @ N_22 ) @ ( power_power_int @ B_4 @ N_22 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1052]) ).
thf(1578,plain,
( ( ! [N_24: nat,X_4: int,Y_4: int] :
( ~ ( dvd_dvd_int @ X_4 @ Y_4 )
| ( dvd_dvd_int @ ( power_power_int @ X_4 @ N_24 ) @ ( power_power_int @ Y_4 @ N_24 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1055]) ).
thf(1579,plain,
( ( ! [N_28: nat,A_23: int] :
( ( A_23 = zero_zero_int )
| ( ( power_power_int @ A_23 @ N_28 )
!= zero_zero_int ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1059]) ).
thf(1580,plain,
( ( ! [M: int,X: int] :
( ! [Y_1: int] :
~ ( zcong @ ( power_power_int @ Y_1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ X @ M )
| ( quadRes @ M @ X ) )
& ! [M: int,X: int] :
( ~ ( quadRes @ M @ X )
| ( zcong @ ( power_power_int @ ( sK5_Y_1 @ X @ M ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ X @ M ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1063]) ).
thf(1581,plain,
( ( ! [M: int,X: int] :
( ~ ( ord_less_eq_int @ zero_zero_int @ X )
| ~ ( ord_less_int @ X @ M )
| ~ ( zcong @ X @ zero_zero_int @ M )
| ( X = zero_zero_int ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1065]) ).
thf(1582,plain,
( ( ! [X: int,P: int] :
( ~ ( dvd_dvd_int @ P @ X )
| ( zcong @ X @ zero_zero_int @ P ) )
& ! [X: int,P: int] :
( ~ ( zcong @ X @ zero_zero_int @ P )
| ( dvd_dvd_int @ P @ X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1066]) ).
thf(1583,plain,
( ( ! [A: int,M: int] :
( ~ ( dvd_dvd_int @ M @ A )
| ( zcong @ A @ zero_zero_int @ M ) )
& ! [A: int,M: int] :
( ~ ( zcong @ A @ zero_zero_int @ M )
| ( dvd_dvd_int @ M @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1067]) ).
thf(1584,plain,
( ( ! [N: int,M: int] :
( ~ ( dvd_dvd_int @ N @ M )
| ( ord_less_eq_int @ M @ zero_zero_int )
| ( ord_less_eq_int @ N @ M ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1068]) ).
thf(1585,plain,
( ( ! [M: int,X: int] :
( ~ ( ord_less_int @ zero_zero_int @ X )
| ~ ( ord_less_int @ X @ M )
| ~ ( zcong @ X @ zero_zero_int @ M ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1069]) ).
thf(1586,plain,
( ( ! [M: int,Y: int,X: int] :
( ~ ( ord_less_int @ zero_zero_int @ X )
| ~ ( ord_less_int @ zero_zero_int @ Y )
| ~ ( ord_less_int @ zero_zero_int @ M )
| ~ ( zcong @ X @ Y @ M )
| ~ ( ord_less_int @ X @ M )
| ~ ( ord_less_int @ Y @ M )
| ( X = Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1070]) ).
thf(1587,plain,
( ( ! [Z: nat,X: int,Y: int,M: int] :
( ~ ( zcong @ X @ Y @ M )
| ( zcong @ ( power_power_int @ X @ Z ) @ ( power_power_int @ Y @ Z ) @ M ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1071]) ).
thf(1588,plain,
( ( ! [C: int,A: int,B: int,M: int] :
( ~ ( zcong @ A @ B @ M )
| ( zcong @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) @ M ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1072]) ).
thf(1589,plain,
( ( ! [W: int,Z: int] :
( ~ ( ord_less_eq_int @ W @ ( minus_minus_int @ Z @ one_one_int ) )
| ( ord_less_int @ W @ Z ) )
& ! [W: int,Z: int] :
( ~ ( ord_less_int @ W @ Z )
| ( ord_less_eq_int @ W @ ( minus_minus_int @ Z @ one_one_int ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1078]) ).
thf(1590,plain,
( ( ! [A: int,X: int] :
( ~ ( ord_less_int @ zero_zero_int @ X )
| ~ ( ord_less_int @ X @ A )
| ( X
= ( minus_minus_int @ A @ one_one_int ) )
| ( ord_less_int @ X @ ( minus_minus_int @ A @ one_one_int ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1079]) ).
thf(1591,plain,
( ( ! [K: int,L: int] :
( ~ ( ord_less_int @ K @ L )
| ( ord_less_int @ ( minus_minus_int @ K @ L ) @ zero_zero_int ) )
& ! [K: int,L: int] :
( ~ ( ord_less_int @ ( minus_minus_int @ K @ L ) @ zero_zero_int )
| ( ord_less_int @ K @ L ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1082]) ).
thf(1592,plain,
( ( ! [A: int,B: int,C: int] :
( ( ( minus_minus_int @ A @ B )
!= C )
| ( A
= ( plus_plus_int @ C @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1086]) ).
thf(1593,plain,
( ( ! [Z: nat,X: int,Y: nat,P: int] :
( ~ ( zcong @ ( power_power_int @ X @ Y ) @ one_one_int @ P )
| ( zcong @ ( power_power_int @ X @ ( times_times_nat @ Y @ Z ) ) @ one_one_int @ P ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1089]) ).
thf(1594,plain,
( ( ! [B: int,M: int,A: int] :
( ~ ( ord_less_eq_int @ zero_zero_int @ A )
| ~ ( ord_less_int @ A @ M )
| ~ ( ord_less_eq_int @ zero_zero_int @ B )
| ~ ( ord_less_int @ B @ M )
| ~ ( zcong @ A @ B @ M )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1090]) ).
thf(1595,plain,
( ( ! [M: int,A: int] :
( ~ ( ord_less_eq_int @ zero_zero_int @ A )
| ~ ( ord_less_int @ A @ M )
| ~ ( zcong @ A @ zero_zero_int @ M )
| ( A = zero_zero_int ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1091]) ).
thf(1596,plain,
( ( ! [A: int] :
( ! [B: int,M: int] :
( ! [K_1: int] :
( B
!= ( plus_plus_int @ A @ ( times_times_int @ M @ K_1 ) ) )
| ( zcong @ A @ B @ M ) )
& ! [B: int,M: int] :
( ~ ( zcong @ A @ B @ M )
| ( B
= ( plus_plus_int @ A @ ( times_times_int @ M @ ( sK6_K_1 @ M @ B @ A ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1092]) ).
thf(1597,plain,
( ( ! [B: int,M: int,A: int] :
( ~ ( ord_less_int @ zero_zero_int @ A )
| ~ ( ord_less_int @ A @ M )
| ~ ( ord_less_int @ zero_zero_int @ B )
| ~ ( ord_less_int @ B @ A )
| ~ ( zcong @ A @ B @ M ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1093]) ).
thf(1598,plain,
( ( ! [C: int,D: int,A: int,B: int,M: int] :
( ~ ( zcong @ A @ B @ M )
| ~ ( zcong @ C @ D @ M )
| ( zcong @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) @ M ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1094]) ).
thf(1599,plain,
( ( ! [A: int,B: int] :
( ( A != B )
| ( zcong @ A @ B @ zero_zero_int ) )
& ! [A: int,B: int] :
( ~ ( zcong @ A @ B @ zero_zero_int )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1096]) ).
thf(1600,plain,
( ( ! [B: int,A: int,C: int] :
( ~ ( ord_less_int @ A @ C )
| ~ ( ord_less_int @ B @ C )
| ( ord_less_eq_int @ A @ B )
| ( ord_less_eq_int @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1097]) ).
thf(1601,plain,
( ( ! [X_9: int,Y_7: int] :
( ~ ( ord_less_eq_int @ X_9 @ Y_7 )
| ( X_9 = Y_7 )
| ( ord_less_int @ X_9 @ Y_7 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1098]) ).
thf(1602,plain,
( ( ! [K: int] :
( ~ ( ord_less_eq_int @ min @ ( bit0 @ K ) )
| ( ord_less_int @ min @ K ) )
& ! [K: int] :
( ~ ( ord_less_int @ min @ K )
| ( ord_less_eq_int @ min @ ( bit0 @ K ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1099]) ).
thf(1603,plain,
( ( ! [K: int] :
( ~ ( ord_less_eq_int @ K @ min )
| ( ord_less_int @ ( bit0 @ K ) @ min ) )
& ! [K: int] :
( ~ ( ord_less_int @ ( bit0 @ K ) @ min )
| ( ord_less_eq_int @ K @ min ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1100]) ).
thf(1604,plain,
( ( ( number_number_of_int @ pls )
!= ( number_number_of_int @ min ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1101]) ).
thf(1605,plain,
( ( ! [K: int] :
( ~ ( ord_less_eq_int @ ( bit0 @ K ) @ min )
| ( ord_less_eq_int @ K @ min ) )
& ! [K: int] :
( ~ ( ord_less_eq_int @ K @ min )
| ( ord_less_eq_int @ ( bit0 @ K ) @ min ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1102]) ).
thf(1606,plain,
( ( ! [K: int] :
( ~ ( ord_less_eq_int @ ( bit1 @ K ) @ min )
| ( ord_less_eq_int @ K @ min ) )
& ! [K: int] :
( ~ ( ord_less_eq_int @ K @ min )
| ( ord_less_eq_int @ ( bit1 @ K ) @ min ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1105]) ).
thf(1607,plain,
( ( ! [K: int] :
( ~ ( ord_less_eq_int @ min @ ( bit1 @ K ) )
| ( ord_less_eq_int @ min @ K ) )
& ! [K: int] :
( ~ ( ord_less_eq_int @ min @ K )
| ( ord_less_eq_int @ min @ ( bit1 @ K ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1106]) ).
thf(1608,plain,
( ( ! [K: int] :
( ~ ( ord_less_int @ min @ ( bit0 @ K ) )
| ( ord_less_int @ min @ K ) )
& ! [K: int] :
( ~ ( ord_less_int @ min @ K )
| ( ord_less_int @ min @ ( bit0 @ K ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1108]) ).
thf(1609,plain,
( ( ! [K: int] :
( ~ ( ord_less_int @ min @ ( bit1 @ K ) )
| ( ord_less_int @ min @ K ) )
& ! [K: int] :
( ~ ( ord_less_int @ min @ K )
| ( ord_less_int @ min @ ( bit1 @ K ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1111]) ).
thf(1610,plain,
( ( ! [K: int] :
( ~ ( ord_less_int @ ( bit1 @ K ) @ min )
| ( ord_less_int @ K @ min ) )
& ! [K: int] :
( ~ ( ord_less_int @ K @ min )
| ( ord_less_int @ ( bit1 @ K ) @ min ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1112]) ).
thf(1611,plain,
( ( ! [K: int] :
( ( bit0 @ K )
!= min ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1114]) ).
thf(1612,plain,
( ( ! [L: int] :
( min
!= ( bit0 @ L ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1115]) ).
thf(1613,plain,
( ( pls != min )
= $true ),
inference(extcnf_combined,[status(esa)],[1116]) ).
thf(1614,plain,
( ( min != pls )
= $true ),
inference(extcnf_combined,[status(esa)],[1117]) ).
thf(1615,plain,
( ( ! [K: int] :
( ( ( bit1 @ K )
!= min )
| ( K = min ) )
& ! [K: int] :
( ( K != min )
| ( ( bit1 @ K )
= min ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1118]) ).
thf(1616,plain,
( ( ! [L: int] :
( ( min
!= ( bit1 @ L ) )
| ( min = L ) )
& ! [L: int] :
( ( min != L )
| ( min
= ( bit1 @ L ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1119]) ).
thf(1617,plain,
( ( ! [Y: int,X: int,P: int] :
( ( zcong @ X @ zero_zero_int @ P )
| ~ ( zcong @ ( power_power_int @ Y @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ X @ P )
| ~ ( dvd_dvd_int @ P @ Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1122]) ).
thf(1618,plain,
( ( ! [B: int,Q: int,R: int,B_11: int,Q_1: int,R_1: int] :
( ( ( plus_plus_int @ ( times_times_int @ B @ Q ) @ R )
!= ( plus_plus_int @ ( times_times_int @ B_11 @ Q_1 ) @ R_1 ) )
| ~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ B_11 @ Q_1 ) @ R_1 ) @ zero_zero_int )
| ~ ( ord_less_int @ R @ B )
| ~ ( ord_less_eq_int @ zero_zero_int @ R_1 )
| ~ ( ord_less_int @ zero_zero_int @ B_11 )
| ~ ( ord_less_eq_int @ B_11 @ B )
| ( ord_less_eq_int @ Q_1 @ Q ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1127]) ).
thf(1619,plain,
( ( ! [B: int,Q_1: int,R_1: int,Q: int,R: int] :
( ~ ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q_1 ) @ R_1 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q ) @ R ) )
| ~ ( ord_less_eq_int @ R @ zero_zero_int )
| ~ ( ord_less_int @ B @ R )
| ~ ( ord_less_int @ B @ R_1 )
| ( ord_less_eq_int @ Q @ Q_1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1128]) ).
thf(1620,plain,
( ( ! [B: int,Q: int,R: int,B_11: int,Q_1: int,R_1: int] :
( ( ( plus_plus_int @ ( times_times_int @ B @ Q ) @ R )
!= ( plus_plus_int @ ( times_times_int @ B_11 @ Q_1 ) @ R_1 ) )
| ~ ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B_11 @ Q_1 ) @ R_1 ) )
| ~ ( ord_less_int @ R_1 @ B_11 )
| ~ ( ord_less_eq_int @ zero_zero_int @ R )
| ~ ( ord_less_int @ zero_zero_int @ B_11 )
| ~ ( ord_less_eq_int @ B_11 @ B )
| ( ord_less_eq_int @ Q @ Q_1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1129]) ).
thf(1621,plain,
( ( ! [B: int,Q_1: int,R_1: int,Q: int,R: int] :
( ~ ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q_1 ) @ R_1 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q ) @ R ) )
| ~ ( ord_less_eq_int @ zero_zero_int @ R_1 )
| ~ ( ord_less_int @ R_1 @ B )
| ~ ( ord_less_int @ R @ B )
| ( ord_less_eq_int @ Q_1 @ Q ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1130]) ).
thf(1622,plain,
( ( ! [B_11: int,Q_1: int,R_1: int] :
( ~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ B_11 @ Q_1 ) @ R_1 ) @ zero_zero_int )
| ~ ( ord_less_eq_int @ zero_zero_int @ R_1 )
| ~ ( ord_less_int @ zero_zero_int @ B_11 )
| ( ord_less_eq_int @ Q_1 @ zero_zero_int ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1131]) ).
thf(1623,plain,
( ( ! [B_11: int,Q_1: int,R_1: int] :
( ~ ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B_11 @ Q_1 ) @ R_1 ) )
| ~ ( ord_less_int @ R_1 @ B_11 )
| ~ ( ord_less_int @ zero_zero_int @ B_11 )
| ( ord_less_eq_int @ zero_zero_int @ Q_1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1132]) ).
thf(1624,plain,
( ( ! [W_3: int] :
( ( ( number_number_of_nat @ W_3 )
!= zero_zero_nat )
| ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ W_3 ) )
= one_one_int ) )
& ! [W_3: int] :
( ( ( number_number_of_nat @ W_3 )
= zero_zero_nat )
| ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ W_3 ) )
= zero_zero_int ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1134]) ).
thf(1625,plain,
( ( ! [N: nat,X: int] :
( ~ ( ord_less_eq_int @ zero_zero_int @ X )
| ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ X @ N ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1135]) ).
thf(1626,plain,
( ( ! [Y: int,X: int] :
( ~ ( ord_less_eq_int @ zero_zero_int @ X )
| ~ ( ord_less_eq_int @ zero_zero_int @ Y )
| ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ X @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1136]) ).
thf(1627,plain,
( ( ! [Y: int,X: int] :
( ~ ( ord_less_eq_int @ zero_zero_int @ X )
| ~ ( ord_less_eq_int @ zero_zero_int @ Y )
| ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ X @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1137]) ).
thf(1628,plain,
( ( ! [B: int,A: int] :
( ~ ( ord_less_int @ zero_zero_int @ A )
| ~ ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
| ( ord_less_int @ zero_zero_int @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1139]) ).
thf(1629,plain,
( ( ! [A_28: int,W_4: int] :
( ( ( number_number_of_nat @ W_4 )
= zero_zero_nat )
| ( A_28 != zero_zero_int )
| ( ( power_power_int @ A_28 @ ( number_number_of_nat @ W_4 ) )
= zero_zero_int ) )
& ! [A_28: int,W_4: int] :
( ( ( power_power_int @ A_28 @ ( number_number_of_nat @ W_4 ) )
!= zero_zero_int )
| ( ( number_number_of_nat @ W_4 )
!= zero_zero_nat ) )
& ! [A_28: int] :
( ! [W_4: int] :
( ( power_power_int @ A_28 @ ( number_number_of_nat @ W_4 ) )
!= zero_zero_int )
| ( A_28 = zero_zero_int ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1140]) ).
thf(1630,plain,
( ( ! [A_28: nat,W_4: int] :
( ( ( number_number_of_nat @ W_4 )
= zero_zero_nat )
| ( A_28 != zero_zero_nat )
| ( ( power_power_nat @ A_28 @ ( number_number_of_nat @ W_4 ) )
= zero_zero_nat ) )
& ! [A_28: nat,W_4: int] :
( ( ( power_power_nat @ A_28 @ ( number_number_of_nat @ W_4 ) )
!= zero_zero_nat )
| ( ( number_number_of_nat @ W_4 )
!= zero_zero_nat ) )
& ! [A_28: nat] :
( ! [W_4: int] :
( ( power_power_nat @ A_28 @ ( number_number_of_nat @ W_4 ) )
!= zero_zero_nat )
| ( A_28 = zero_zero_nat ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1141]) ).
thf(1631,plain,
( ( ! [C_4: int,D_2: int,A_31: int,B_12: int,R_2: int] :
( ( R_2 = zero_zero_int )
| ( C_4 = D_2 )
| ( A_31 != B_12 )
| ( ( plus_plus_int @ A_31 @ ( times_times_int @ R_2 @ C_4 ) )
!= ( plus_plus_int @ B_12 @ ( times_times_int @ R_2 @ D_2 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1145]) ).
thf(1632,plain,
( ( ! [W_5: int,Y_9: int] :
( ! [X_14: int,Z_1: int] :
( ( ( plus_plus_int @ ( times_times_int @ W_5 @ Y_9 ) @ ( times_times_int @ X_14 @ Z_1 ) )
!= ( plus_plus_int @ ( times_times_int @ W_5 @ Z_1 ) @ ( times_times_int @ X_14 @ Y_9 ) ) )
| ( W_5 = X_14 )
| ( Y_9 = Z_1 ) )
& ! [X_14: int] :
( ( W_5 != X_14 )
| ! [Z_1: int] :
( ( plus_plus_int @ ( times_times_int @ W_5 @ Y_9 ) @ ( times_times_int @ X_14 @ Z_1 ) )
= ( plus_plus_int @ ( times_times_int @ W_5 @ Z_1 ) @ ( times_times_int @ X_14 @ Y_9 ) ) ) )
& ! [X_14: int,Z_1: int] :
( ( Y_9 != Z_1 )
| ( ( plus_plus_int @ ( times_times_int @ W_5 @ Y_9 ) @ ( times_times_int @ X_14 @ Z_1 ) )
= ( plus_plus_int @ ( times_times_int @ W_5 @ Z_1 ) @ ( times_times_int @ X_14 @ Y_9 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1153]) ).
thf(1633,plain,
( ( ! [C_6: int,D_3: int] :
( ! [A_37: int,B_15: int] :
( ( ( plus_plus_int @ ( times_times_int @ A_37 @ C_6 ) @ ( times_times_int @ B_15 @ D_3 ) )
= ( plus_plus_int @ ( times_times_int @ A_37 @ D_3 ) @ ( times_times_int @ B_15 @ C_6 ) ) )
| ( A_37 != B_15 ) )
& ( ! [A_37: int,B_15: int] :
( ( plus_plus_int @ ( times_times_int @ A_37 @ C_6 ) @ ( times_times_int @ B_15 @ D_3 ) )
= ( plus_plus_int @ ( times_times_int @ A_37 @ D_3 ) @ ( times_times_int @ B_15 @ C_6 ) ) )
| ( C_6 != D_3 ) )
& ! [A_37: int,B_15: int] :
( ( A_37 = B_15 )
| ( C_6 = D_3 )
| ( ( plus_plus_int @ ( times_times_int @ A_37 @ C_6 ) @ ( times_times_int @ B_15 @ D_3 ) )
!= ( plus_plus_int @ ( times_times_int @ A_37 @ D_3 ) @ ( times_times_int @ B_15 @ C_6 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1156]) ).
thf(1634,plain,
( ( ! [B_16: int,A_38: int] :
( ( B_16
!= ( plus_plus_int @ B_16 @ A_38 ) )
| ( A_38 = zero_zero_int ) )
& ! [B_16: int,A_38: int] :
( ( A_38 != zero_zero_int )
| ( B_16
= ( plus_plus_int @ B_16 @ A_38 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1158]) ).
thf(1635,plain,
( ( ! [A_43: int] :
( ! [K_2: nat] :
~ ( ord_less_eq_int @ ( power_power_int @ A_43 @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ K_2 ) ) @ zero_zero_int )
| ( A_43 = zero_zero_int ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1163]) ).
thf(1636,plain,
( ( ! [V_4: int,V_5: int] :
( ~ ( ord_less_eq_int @ V_4 @ V_5 )
| ( ord_less_eq_nat @ ( number_number_of_nat @ V_4 ) @ ( number_number_of_nat @ V_5 ) ) )
& ! [V_4: int] :
( ~ ( ord_less_eq_int @ V_4 @ pls )
| ! [V_5: int] : ( ord_less_eq_nat @ ( number_number_of_nat @ V_4 ) @ ( number_number_of_nat @ V_5 ) ) )
& ! [V_4: int,V_5: int] :
( ~ ( ord_less_eq_nat @ ( number_number_of_nat @ V_4 ) @ ( number_number_of_nat @ V_5 ) )
| ( ord_less_eq_int @ V_4 @ V_5 )
| ( ord_less_eq_int @ V_4 @ pls ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1176]) ).
thf(1637,plain,
( ( ! [Z: int,N: int] :
( ~ ( dvd_dvd_int @ Z @ N )
| ~ ( ord_less_int @ zero_zero_int @ N )
| ( ord_less_eq_int @ Z @ N ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1177]) ).
thf(1638,plain,
( ( ! [C: int,X: int,T: int] :
( ! [A: int,D: int] :
( ~ ( dvd_dvd_int @ A @ D )
| ~ ( dvd_dvd_int @ A @ ( plus_plus_int @ X @ T ) )
| ( dvd_dvd_int @ A @ ( plus_plus_int @ ( plus_plus_int @ X @ ( times_times_int @ C @ D ) ) @ T ) ) )
& ! [A: int,D: int] :
( ~ ( dvd_dvd_int @ A @ D )
| ~ ( dvd_dvd_int @ A @ ( plus_plus_int @ ( plus_plus_int @ X @ ( times_times_int @ C @ D ) ) @ T ) )
| ( dvd_dvd_int @ A @ ( plus_plus_int @ X @ T ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1179]) ).
thf(1639,plain,
( ( ! [K: int] :
( ! [N: int] :
( ! [M: int] :
~ ( dvd_dvd_int @ K @ ( plus_plus_int @ N @ ( times_times_int @ K @ M ) ) )
| ( dvd_dvd_int @ K @ N ) )
& ! [N: int] :
( ~ ( dvd_dvd_int @ K @ N )
| ! [M: int] : ( dvd_dvd_int @ K @ ( plus_plus_int @ N @ ( times_times_int @ K @ M ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1180]) ).
thf(1640,plain,
( ( ! [K: int,M: int,N: int] :
( ~ ( dvd_dvd_int @ ( times_times_int @ K @ M ) @ ( times_times_int @ K @ N ) )
| ( K = zero_zero_int )
| ( dvd_dvd_int @ M @ N ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1181]) ).
thf(1641,plain,
( ( ! [N: int,M: int] :
( ~ ( ord_less_eq_int @ zero_zero_int @ M )
| ~ ( ord_less_eq_int @ zero_zero_int @ N )
| ~ ( dvd_dvd_int @ M @ N )
| ~ ( dvd_dvd_int @ N @ M )
| ( M = N ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1182]) ).
thf(1642,plain,
( ( ! [N: int,M: int] :
( ~ ( ord_less_int @ zero_zero_int @ M )
| ~ ( ord_less_int @ M @ N )
| ~ ( dvd_dvd_int @ N @ M ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1183]) ).
thf(1643,plain,
( ( ! [A: int,N: nat,P: int] :
( ~ ( zprime @ P )
| ~ ( dvd_dvd_int @ P @ ( power_power_int @ A @ N ) )
| ( dvd_dvd_int @ P @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1186]) ).
thf(1644,plain,
( ( ! [R: int,Q: int,A: int] :
( ~ ( ord_less_int @ zero_zero_int @ A )
| ( A
!= ( plus_plus_int @ R @ ( times_times_int @ A @ Q ) ) )
| ~ ( ord_less_eq_int @ zero_zero_int @ R )
| ( ord_less_eq_int @ Q @ one_one_int ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1190]) ).
thf(1645,plain,
( ( ! [R: int,Q: int,A: int] :
( ~ ( ord_less_int @ zero_zero_int @ A )
| ( A
!= ( plus_plus_int @ R @ ( times_times_int @ A @ Q ) ) )
| ~ ( ord_less_int @ R @ A )
| ( ord_less_eq_int @ one_one_int @ Q ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1191]) ).
thf(1646,plain,
( ( ! [X: int] :
( ~ ( ord_less_eq_int @ zero_zero_int @ X )
| ~ ( ord_less_int @ X @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
| ( X = zero_zero_int )
| ( X = one_one_int ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1194]) ).
thf(1647,plain,
( ( ! [Y_11: int] :
( ~ ( ord_less_int @ one_one_int @ ( number_number_of_int @ Y_11 ) )
| ( ord_less_int @ ( bit1 @ pls ) @ Y_11 ) )
& ! [Y_11: int] :
( ~ ( ord_less_int @ ( bit1 @ pls ) @ Y_11 )
| ( ord_less_int @ one_one_int @ ( number_number_of_int @ Y_11 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1197]) ).
thf(1648,plain,
( ( ! [X_19: int] :
( ~ ( ord_less_int @ ( number_number_of_int @ X_19 ) @ one_one_int )
| ( ord_less_int @ X_19 @ ( bit1 @ pls ) ) )
& ! [X_19: int] :
( ~ ( ord_less_int @ X_19 @ ( bit1 @ pls ) )
| ( ord_less_int @ ( number_number_of_int @ X_19 ) @ one_one_int ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1198]) ).
thf(1649,plain,
( ( ! [Y_12: int] :
( ~ ( ord_less_int @ zero_zero_int @ ( number_number_of_int @ Y_12 ) )
| ( ord_less_int @ pls @ Y_12 ) )
& ! [Y_12: int] :
( ~ ( ord_less_int @ pls @ Y_12 )
| ( ord_less_int @ zero_zero_int @ ( number_number_of_int @ Y_12 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1202]) ).
thf(1650,plain,
( ( ! [X_20: int] :
( ~ ( ord_less_int @ ( number_number_of_int @ X_20 ) @ zero_zero_int )
| ( ord_less_int @ X_20 @ pls ) )
& ! [X_20: int] :
( ~ ( ord_less_int @ X_20 @ pls )
| ( ord_less_int @ ( number_number_of_int @ X_20 ) @ zero_zero_int ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1203]) ).
thf(1651,plain,
( ( ! [Z: int] :
( ~ ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z ) @ zero_zero_int )
| ( ord_less_int @ Z @ zero_zero_int ) )
& ! [Z: int] :
( ~ ( ord_less_int @ Z @ zero_zero_int )
| ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z ) @ zero_zero_int ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1204]) ).
thf(1652,plain,
( ( ! [W: int,Z: int] :
( ~ ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
| ( W = Z )
| ( ord_less_int @ W @ Z ) )
& ! [W: int,Z: int] :
( ( W != Z )
| ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) ) )
& ! [W: int,Z: int] :
( ~ ( ord_less_int @ W @ Z )
| ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1217]) ).
thf(1653,plain,
( ( ! [Z: int] :
( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z )
!= zero_zero_int ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1218]) ).
thf(1654,plain,
( ( ! [W: int] :
( ~ ( ord_less_int @ ( bit0 @ W ) @ zero_zero_int )
| ( ord_less_int @ W @ zero_zero_int ) )
& ! [W: int] :
( ~ ( ord_less_int @ W @ zero_zero_int )
| ( ord_less_int @ ( bit0 @ W ) @ zero_zero_int ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1223]) ).
thf(1655,plain,
( ( ! [K: int] :
( ~ ( ord_less_int @ pls @ ( bit0 @ K ) )
| ( ord_less_int @ pls @ K ) )
& ! [K: int] :
( ~ ( ord_less_int @ pls @ K )
| ( ord_less_int @ pls @ ( bit0 @ K ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1225]) ).
thf(1656,plain,
( ( ! [K: int] :
( ~ ( ord_less_int @ ( bit0 @ K ) @ pls )
| ( ord_less_int @ K @ pls ) )
& ! [K: int] :
( ~ ( ord_less_int @ K @ pls )
| ( ord_less_int @ ( bit0 @ K ) @ pls ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1226]) ).
thf(1657,plain,
( ( ! [W: int] :
( ~ ( ord_less_int @ ( bit1 @ W ) @ zero_zero_int )
| ( ord_less_int @ W @ zero_zero_int ) )
& ! [W: int] :
( ~ ( ord_less_int @ W @ zero_zero_int )
| ( ord_less_int @ ( bit1 @ W ) @ zero_zero_int ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1227]) ).
thf(1658,plain,
( ( ! [K: int,L: int] :
( ~ ( ord_less_int @ ( bit1 @ K ) @ ( bit0 @ L ) )
| ( ord_less_int @ K @ L ) )
& ! [K: int,L: int] :
( ~ ( ord_less_int @ K @ L )
| ( ord_less_int @ ( bit1 @ K ) @ ( bit0 @ L ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1228]) ).
thf(1659,plain,
( ( ! [K1: int,K2: int] :
( ~ ( ord_less_int @ ( bit1 @ K1 ) @ ( bit0 @ K2 ) )
| ( ord_less_int @ K1 @ K2 ) )
& ! [K1: int,K2: int] :
( ~ ( ord_less_int @ K1 @ K2 )
| ( ord_less_int @ ( bit1 @ K1 ) @ ( bit0 @ K2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1229]) ).
thf(1660,plain,
( ( ! [K: int] :
( ~ ( ord_less_int @ ( bit1 @ K ) @ pls )
| ( ord_less_int @ K @ pls ) )
& ! [K: int] :
( ~ ( ord_less_int @ K @ pls )
| ( ord_less_int @ ( bit1 @ K ) @ pls ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1230]) ).
thf(1661,plain,
( ( ! [X_22: int,Y_14: int] :
( ~ ( ord_less_int @ ( number_number_of_int @ X_22 ) @ ( number_number_of_int @ Y_14 ) )
| ( ord_less_int @ X_22 @ Y_14 ) )
& ! [X_22: int,Y_14: int] :
( ~ ( ord_less_int @ X_22 @ Y_14 )
| ( ord_less_int @ ( number_number_of_int @ X_22 ) @ ( number_number_of_int @ Y_14 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1237]) ).
thf(1662,plain,
( ( ! [X_22: int,Y_14: int] :
( ~ ( ord_less_int @ X_22 @ Y_14 )
| ( ord_less_real @ ( number267125858f_real @ X_22 ) @ ( number267125858f_real @ Y_14 ) ) )
& ! [X_22: int,Y_14: int] :
( ~ ( ord_less_real @ ( number267125858f_real @ X_22 ) @ ( number267125858f_real @ Y_14 ) )
| ( ord_less_int @ X_22 @ Y_14 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1238]) ).
thf(1663,plain,
( ( ! [A_54: int] :
( ~ ( ord_less_int @ ( plus_plus_int @ A_54 @ A_54 ) @ zero_zero_int )
| ( ord_less_int @ A_54 @ zero_zero_int ) )
& ! [A_54: int] :
( ~ ( ord_less_int @ A_54 @ zero_zero_int )
| ( ord_less_int @ ( plus_plus_int @ A_54 @ A_54 ) @ zero_zero_int ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1250]) ).
thf(1664,plain,
( ( ! [K: int,I: int,J: int] :
( ~ ( ord_less_int @ I @ J )
| ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ K ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1264]) ).
thf(1665,plain,
( ( zero_zero_int != one_one_int )
= $true ),
inference(extcnf_combined,[status(esa)],[1271]) ).
thf(1666,plain,
( ( ! [K: int,L: int] :
( ~ ( ord_less_int @ ( bit0 @ K ) @ ( bit0 @ L ) )
| ( ord_less_int @ K @ L ) )
& ! [K: int,L: int] :
( ~ ( ord_less_int @ K @ L )
| ( ord_less_int @ ( bit0 @ K ) @ ( bit0 @ L ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1272]) ).
thf(1667,plain,
( ( ! [K1: int,K2: int] :
( ~ ( ord_less_int @ ( bit0 @ K1 ) @ ( bit0 @ K2 ) )
| ( ord_less_int @ K1 @ K2 ) )
& ! [K1: int,K2: int] :
( ~ ( ord_less_int @ K1 @ K2 )
| ( ord_less_int @ ( bit0 @ K1 ) @ ( bit0 @ K2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1273]) ).
thf(1668,plain,
( ( ! [K: int,L: int] :
( ~ ( ord_less_int @ ( bit1 @ K ) @ ( bit1 @ L ) )
| ( ord_less_int @ K @ L ) )
& ! [K: int,L: int] :
( ~ ( ord_less_int @ K @ L )
| ( ord_less_int @ ( bit1 @ K ) @ ( bit1 @ L ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1275]) ).
thf(1669,plain,
( ( ! [K1: int,K2: int] :
( ~ ( ord_less_int @ ( bit1 @ K1 ) @ ( bit1 @ K2 ) )
| ( ord_less_int @ K1 @ K2 ) )
& ! [K1: int,K2: int] :
( ~ ( ord_less_int @ K1 @ K2 )
| ( ord_less_int @ ( bit1 @ K1 ) @ ( bit1 @ K2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1276]) ).
thf(1670,plain,
( ( ! [L: int] :
( ( pls
!= ( bit0 @ L ) )
| ( pls = L ) )
& ! [L: int] :
( ( pls != L )
| ( pls
= ( bit0 @ L ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1279]) ).
thf(1671,plain,
( ( ! [K: int] :
( ( ( bit0 @ K )
!= pls )
| ( K = pls ) )
& ! [K: int] :
( ( K != pls )
| ( ( bit0 @ K )
= pls ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1280]) ).
thf(1672,plain,
( ( ! [K: int,L: int] :
( ( bit0 @ K )
!= ( bit1 @ L ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1281]) ).
thf(1673,plain,
( ( ! [K: int,L: int] :
( ( bit1 @ K )
!= ( bit0 @ L ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1282]) ).
thf(1674,plain,
( ( ! [L: int] :
( pls
!= ( bit1 @ L ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1283]) ).
thf(1675,plain,
( ( ! [K: int] :
( ( bit1 @ K )
!= pls ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1284]) ).
thf(1676,plain,
( ( ! [A_57: int] :
( ( ( plus_plus_int @ A_57 @ A_57 )
!= zero_zero_int )
| ( A_57 = zero_zero_int ) )
& ! [A_57: int] :
( ( A_57 != zero_zero_int )
| ( ( plus_plus_int @ A_57 @ A_57 )
= zero_zero_int ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1285]) ).
thf(1677,plain,
( ( ! [N: int,M: int] :
( ~ ( ord_less_int @ zero_zero_int @ M )
| ( M != one_one_int )
| ( N != one_one_int )
| ( ( times_times_int @ M @ N )
= one_one_int ) )
& ! [N: int,M: int] :
( ~ ( ord_less_int @ zero_zero_int @ M )
| ( ( times_times_int @ M @ N )
!= one_one_int )
| ( M = one_one_int ) )
& ! [N: int,M: int] :
( ~ ( ord_less_int @ zero_zero_int @ M )
| ( ( times_times_int @ M @ N )
!= one_one_int )
| ( N = one_one_int ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1286]) ).
thf(1678,plain,
( ( ! [X_24: int,Y_16: int] :
( ~ ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X_24 @ X_24 ) @ ( times_times_int @ Y_16 @ Y_16 ) ) )
| ( X_24 != zero_zero_int )
| ( Y_16 != zero_zero_int ) )
& ! [X_24: int] :
( ( X_24 = zero_zero_int )
| ! [Y_16: int] : ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X_24 @ X_24 ) @ ( times_times_int @ Y_16 @ Y_16 ) ) ) )
& ! [X_24: int,Y_16: int] :
( ( Y_16 = zero_zero_int )
| ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X_24 @ X_24 ) @ ( times_times_int @ Y_16 @ Y_16 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1294]) ).
thf(1679,plain,
( ( ! [X_26: int,Y_18: int] :
( ( X_26 != zero_zero_int )
| ( Y_18 != zero_zero_int )
| ( ord_less_eq_int @ ( plus_plus_int @ ( power_power_int @ X_26 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_18 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_int ) )
& ! [X_26: int] :
( ! [Y_18: int] :
~ ( ord_less_eq_int @ ( plus_plus_int @ ( power_power_int @ X_26 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_18 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_int )
| ( X_26 = zero_zero_int ) )
& ! [X_26: int,Y_18: int] :
( ~ ( ord_less_eq_int @ ( plus_plus_int @ ( power_power_int @ X_26 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_18 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_int )
| ( Y_18 = zero_zero_int ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1296]) ).
thf(1680,plain,
( ( ! [X_27: int,Y_19: int] :
( ~ ( ord_less_int @ ( power_power_int @ X_27 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_19 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ~ ( ord_less_eq_int @ zero_zero_int @ Y_19 )
| ( ord_less_int @ X_27 @ Y_19 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1297]) ).
thf(1681,plain,
( ( ! [X_28: int,Y_20: int] :
( ~ ( ord_less_eq_int @ ( power_power_int @ X_28 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_20 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ~ ( ord_less_eq_int @ zero_zero_int @ Y_20 )
| ( ord_less_eq_int @ X_28 @ Y_20 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1299]) ).
thf(1682,plain,
( ( ! [X_29: int,Y_21: int] :
( ( ( power_power_int @ X_29 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= ( power_power_int @ Y_21 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ~ ( ord_less_eq_int @ zero_zero_int @ X_29 )
| ~ ( ord_less_eq_int @ zero_zero_int @ Y_21 )
| ( X_29 = Y_21 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1300]) ).
thf(1683,plain,
( ( ! [K: int,I: int,J: int] :
( ~ ( 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(extcnf_combined,[status(esa)],[1301]) ).
thf(1684,plain,
( ( ! [X_30: int,Y_22: int] :
( ( X_30 != zero_zero_int )
| ( Y_22 != zero_zero_int )
| ( ( plus_plus_int @ ( times_times_int @ X_30 @ X_30 ) @ ( times_times_int @ Y_22 @ Y_22 ) )
= zero_zero_int ) )
& ! [X_30: int] :
( ! [Y_22: int] :
( ( plus_plus_int @ ( times_times_int @ X_30 @ X_30 ) @ ( times_times_int @ Y_22 @ Y_22 ) )
!= zero_zero_int )
| ( X_30 = zero_zero_int ) )
& ! [X_30: int,Y_22: int] :
( ( ( plus_plus_int @ ( times_times_int @ X_30 @ X_30 ) @ ( times_times_int @ Y_22 @ Y_22 ) )
!= zero_zero_int )
| ( Y_22 = zero_zero_int ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1310]) ).
thf(1685,plain,
( ( ! [X: int,Y: int] :
( ( ord_less_int @ Y @ X )
| ( X = Y )
| ( ord_less_int @ X @ Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1311]) ).
thf(1686,plain,
( ( ! [K: int,L: int] :
( ( ( bit0 @ K )
!= ( bit0 @ L ) )
| ( K = L ) )
& ! [K: int,L: int] :
( ( K != L )
| ( ( bit0 @ K )
= ( bit0 @ L ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1312]) ).
thf(1687,plain,
( ( ! [K: int,L: int] :
( ( ( bit1 @ K )
!= ( bit1 @ L ) )
| ( K = L ) )
& ! [K: int,L: int] :
( ( K != L )
| ( ( bit1 @ K )
= ( bit1 @ L ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1313]) ).
thf(1688,plain,
( ( ! [W_13: int,X_31: nat] :
( ( ( number_number_of_nat @ W_13 )
!= X_31 )
| ( X_31
= ( number_number_of_nat @ W_13 ) ) )
& ! [W_13: int,X_31: nat] :
( ( X_31
!= ( number_number_of_nat @ W_13 ) )
| ( ( number_number_of_nat @ W_13 )
= X_31 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1314]) ).
thf(1689,plain,
( ( ! [Z: int] :
( ~ ( ord_less_eq_int @ zero_zero_int @ Z )
| ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1315]) ).
thf(1690,plain,
( ( ! [V_5: int,V_4: int] :
( ~ ( ord_less_int @ V_4 @ pls )
| ( ( plus_plus_nat @ ( number_number_of_nat @ V_4 ) @ ( number_number_of_nat @ V_5 ) )
= ( number_number_of_nat @ V_5 ) ) )
& ! [V_5: int,V_4: int] :
( ( ord_less_int @ V_4 @ pls )
| ~ ( ord_less_int @ V_5 @ pls )
| ( ( plus_plus_nat @ ( number_number_of_nat @ V_4 ) @ ( number_number_of_nat @ V_5 ) )
= ( number_number_of_nat @ V_4 ) ) )
& ! [V_5: int,V_4: int] :
( ( ord_less_int @ V_4 @ pls )
| ( ord_less_int @ V_5 @ pls )
| ( ( plus_plus_nat @ ( number_number_of_nat @ V_4 ) @ ( number_number_of_nat @ V_5 ) )
= ( number_number_of_nat @ ( plus_plus_int @ V_4 @ V_5 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1316]) ).
thf(1691,plain,
( ( ! [V_12: int,V_11: int] :
( ~ ( ord_less_eq_int @ pls @ V_11 )
| ~ ( ord_less_eq_int @ pls @ V_12 )
| ( ( plus_plus_int @ ( number_number_of_int @ V_11 ) @ ( number_number_of_int @ V_12 ) )
= ( number_number_of_int @ ( plus_plus_int @ V_11 @ V_12 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1317]) ).
thf(1692,plain,
( ( ! [V_12: int,V_11: int] :
( ~ ( ord_less_eq_int @ pls @ V_11 )
| ~ ( ord_less_eq_int @ pls @ V_12 )
| ( ( plus_plus_nat @ ( number_number_of_nat @ V_11 ) @ ( number_number_of_nat @ V_12 ) )
= ( number_number_of_nat @ ( plus_plus_int @ V_11 @ V_12 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1318]) ).
thf(1693,plain,
( ( ! [W: int,Z: int] :
( ~ ( ord_less_eq_int @ W @ Z )
| ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) ) )
& ! [W: int,Z: int] :
( ~ ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
| ( ord_less_eq_int @ W @ Z ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1319]) ).
thf(1694,plain,
( ( ! [W: int,Z: int] :
( ~ ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z )
| ( ord_less_int @ W @ Z ) )
& ! [W: int,Z: int] :
( ~ ( ord_less_int @ W @ Z )
| ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1320]) ).
thf(1695,plain,
( ( ! [W: int,Z: int] :
( ~ ( ord_less_int @ W @ Z )
| ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1321]) ).
thf(1696,plain,
( ( ! [Z: int] :
( ~ ( ord_less_eq_int @ one_one_int @ Z )
| ( ord_less_int @ zero_zero_int @ Z ) )
& ! [Z: int] :
( ~ ( ord_less_int @ zero_zero_int @ Z )
| ( ord_less_eq_int @ one_one_int @ Z ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1324]) ).
thf(1697,plain,
( ( ! [V_4: int,V_5: int] :
( ( ord_less_int @ V_4 @ V_5 )
| ~ ( ord_less_int @ V_4 @ V_5 )
| ( ord_less_nat @ ( number_number_of_nat @ V_4 ) @ ( number_number_of_nat @ V_5 ) ) )
& ! [V_4: int,V_5: int] :
( ~ ( ord_less_int @ pls @ V_5 )
| ~ ( ord_less_int @ V_4 @ V_5 )
| ( ord_less_nat @ ( number_number_of_nat @ V_4 ) @ ( number_number_of_nat @ V_5 ) ) )
& ! [V_4: int,V_5: int] :
( ~ ( ord_less_nat @ ( number_number_of_nat @ V_4 ) @ ( number_number_of_nat @ V_5 ) )
| ~ ( ord_less_int @ V_4 @ V_5 )
| ( ord_less_int @ pls @ V_5 ) )
& ! [V_4: int,V_5: int] :
( ~ ( ord_less_nat @ ( number_number_of_nat @ V_4 ) @ ( number_number_of_nat @ V_5 ) )
| ( ord_less_int @ V_4 @ V_5 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1325]) ).
thf(1698,plain,
( ( ! [K: int,L: int] :
( ~ ( ord_less_eq_int @ K @ L )
| ( ord_less_int @ ( bit0 @ K ) @ ( bit1 @ L ) ) )
& ! [K: int,L: int] :
( ~ ( ord_less_int @ ( bit0 @ K ) @ ( bit1 @ L ) )
| ( ord_less_eq_int @ K @ L ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1326]) ).
thf(1699,plain,
( ( ! [K1: int,K2: int] :
( ~ ( ord_less_eq_int @ K1 @ K2 )
| ( ord_less_int @ ( bit0 @ K1 ) @ ( bit1 @ K2 ) ) )
& ! [K1: int,K2: int] :
( ~ ( ord_less_int @ ( bit0 @ K1 ) @ ( bit1 @ K2 ) )
| ( ord_less_eq_int @ K1 @ K2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1327]) ).
thf(1700,plain,
( ( ! [K: int,L: int] :
( ~ ( ord_less_eq_int @ ( bit1 @ K ) @ ( bit0 @ L ) )
| ( ord_less_int @ K @ L ) )
& ! [K: int,L: int] :
( ~ ( ord_less_int @ K @ L )
| ( ord_less_eq_int @ ( bit1 @ K ) @ ( bit0 @ L ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1328]) ).
thf(1701,plain,
( ( ! [K1: int,K2: int] :
( ~ ( ord_less_eq_int @ ( bit1 @ K1 ) @ ( bit0 @ K2 ) )
| ( ord_less_int @ K1 @ K2 ) )
& ! [K1: int,K2: int] :
( ~ ( ord_less_int @ K1 @ K2 )
| ( ord_less_eq_int @ ( bit1 @ K1 ) @ ( bit0 @ K2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1329]) ).
thf(1702,plain,
( ( ! [K: int] :
( ~ ( ord_less_eq_int @ pls @ K )
| ( ord_less_int @ pls @ ( bit1 @ K ) ) )
& ! [K: int] :
( ~ ( ord_less_int @ pls @ ( bit1 @ K ) )
| ( ord_less_eq_int @ pls @ K ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1330]) ).
thf(1703,plain,
( ( ! [K: int] :
( ~ ( ord_less_eq_int @ ( bit1 @ K ) @ pls )
| ( ord_less_int @ K @ pls ) )
& ! [K: int] :
( ~ ( ord_less_int @ K @ pls )
| ( ord_less_eq_int @ ( bit1 @ K ) @ pls ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1331]) ).
thf(1704,plain,
( ( ! [K: int,L: int] :
( ~ ( ord_less_int @ ( number_number_of_int @ K ) @ ( number_number_of_int @ L ) )
| ( ord_less_int @ K @ L ) )
& ! [K: int,L: int] :
( ~ ( ord_less_int @ K @ L )
| ( ord_less_int @ ( number_number_of_int @ K ) @ ( number_number_of_int @ L ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1337]) ).
thf(1705,plain,
( ( ! [Y_24: int] :
( ~ ( ord_less_eq_int @ one_one_int @ ( number_number_of_int @ Y_24 ) )
| ( ord_less_eq_int @ ( bit1 @ pls ) @ Y_24 ) )
& ! [Y_24: int] :
( ~ ( ord_less_eq_int @ ( bit1 @ pls ) @ Y_24 )
| ( ord_less_eq_int @ one_one_int @ ( number_number_of_int @ Y_24 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1341]) ).
thf(1706,plain,
( ( ! [X_33: int] :
( ~ ( ord_less_eq_int @ ( number_number_of_int @ X_33 ) @ one_one_int )
| ( ord_less_eq_int @ X_33 @ ( bit1 @ pls ) ) )
& ! [X_33: int] :
( ~ ( ord_less_eq_int @ X_33 @ ( bit1 @ pls ) )
| ( ord_less_eq_int @ ( number_number_of_int @ X_33 ) @ one_one_int ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1342]) ).
thf(1707,plain,
( ( ! [Z_8: int,Z: int,W_14: int,W: int] :
( ~ ( ord_less_int @ W_14 @ W )
| ~ ( ord_less_eq_int @ Z_8 @ Z )
| ( ord_less_int @ ( plus_plus_int @ W_14 @ Z_8 ) @ ( plus_plus_int @ W @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1345]) ).
thf(1708,plain,
( ( ! [K: int] :
( ~ ( ord_less_eq_int @ pls @ ( bit0 @ K ) )
| ( ord_less_eq_int @ pls @ K ) )
& ! [K: int] :
( ~ ( ord_less_eq_int @ pls @ K )
| ( ord_less_eq_int @ pls @ ( bit0 @ K ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1346]) ).
thf(1709,plain,
( ( ! [K: int] :
( ~ ( ord_less_eq_int @ ( bit0 @ K ) @ pls )
| ( ord_less_eq_int @ K @ pls ) )
& ! [K: int] :
( ~ ( ord_less_eq_int @ K @ pls )
| ( ord_less_eq_int @ ( bit0 @ K ) @ pls ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1347]) ).
thf(1710,plain,
( ( ! [K: int,L: int] :
( ~ ( ord_less_eq_int @ ( bit0 @ K ) @ ( bit1 @ L ) )
| ( ord_less_eq_int @ K @ L ) )
& ! [K: int,L: int] :
( ~ ( ord_less_eq_int @ K @ L )
| ( ord_less_eq_int @ ( bit0 @ K ) @ ( bit1 @ L ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1348]) ).
thf(1711,plain,
( ( ! [K1: int,K2: int] :
( ~ ( ord_less_eq_int @ ( bit0 @ K1 ) @ ( bit1 @ K2 ) )
| ( ord_less_eq_int @ K1 @ K2 ) )
& ! [K1: int,K2: int] :
( ~ ( ord_less_eq_int @ K1 @ K2 )
| ( ord_less_eq_int @ ( bit0 @ K1 ) @ ( bit1 @ K2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1349]) ).
thf(1712,plain,
( ( ! [K: int] :
( ~ ( ord_less_eq_int @ pls @ ( bit1 @ K ) )
| ( ord_less_eq_int @ pls @ K ) )
& ! [K: int] :
( ~ ( ord_less_eq_int @ pls @ K )
| ( ord_less_eq_int @ pls @ ( bit1 @ K ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1350]) ).
thf(1713,plain,
( ( ! [V_13: int,W_15: int] :
( ~ ( ord_less_eq_int @ ( number_number_of_int @ V_13 ) @ ( number_number_of_int @ W_15 ) )
| ~ ( ord_less_int @ ( number_number_of_int @ W_15 ) @ ( number_number_of_int @ V_13 ) ) )
& ! [V_13: int,W_15: int] :
( ( ord_less_int @ ( number_number_of_int @ W_15 ) @ ( number_number_of_int @ V_13 ) )
| ( ord_less_eq_int @ ( number_number_of_int @ V_13 ) @ ( number_number_of_int @ W_15 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1351]) ).
thf(1714,plain,
( ( ! [V_13: int,W_15: int] :
( ~ ( ord_less_eq_nat @ ( number_number_of_nat @ V_13 ) @ ( number_number_of_nat @ W_15 ) )
| ~ ( ord_less_nat @ ( number_number_of_nat @ W_15 ) @ ( number_number_of_nat @ V_13 ) ) )
& ! [V_13: int,W_15: int] :
( ( ord_less_nat @ ( number_number_of_nat @ W_15 ) @ ( number_number_of_nat @ V_13 ) )
| ( ord_less_eq_nat @ ( number_number_of_nat @ V_13 ) @ ( number_number_of_nat @ W_15 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1352]) ).
thf(1715,plain,
( ( ! [V_4: int] :
( ~ ( ord_less_int @ pls @ V_4 )
| ( ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ V_4 ) ) )
& ! [V_4: int] :
( ~ ( ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ V_4 ) )
| ( ord_less_int @ pls @ V_4 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1353]) ).
thf(1716,plain,
( ( ! [Y_25: int] :
( ~ ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ Y_25 ) )
| ( ord_less_eq_int @ pls @ Y_25 ) )
& ! [Y_25: int] :
( ~ ( ord_less_eq_int @ pls @ Y_25 )
| ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ Y_25 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1354]) ).
thf(1717,plain,
( ( ! [X_34: int] :
( ~ ( ord_less_eq_int @ ( number_number_of_int @ X_34 ) @ zero_zero_int )
| ( ord_less_eq_int @ X_34 @ pls ) )
& ! [X_34: int] :
( ~ ( ord_less_eq_int @ X_34 @ pls )
| ( ord_less_eq_int @ ( number_number_of_int @ X_34 ) @ zero_zero_int ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1355]) ).
thf(1718,plain,
( ( ! [X_36: int,Y_27: int] :
( ( X_36 != zero_zero_int )
| ( Y_27 != zero_zero_int )
| ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ X_36 @ X_36 ) @ ( times_times_int @ Y_27 @ Y_27 ) ) @ zero_zero_int ) )
& ! [X_36: int] :
( ! [Y_27: int] :
~ ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ X_36 @ X_36 ) @ ( times_times_int @ Y_27 @ Y_27 ) ) @ zero_zero_int )
| ( X_36 = zero_zero_int ) )
& ! [X_36: int,Y_27: int] :
( ~ ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ X_36 @ X_36 ) @ ( times_times_int @ Y_27 @ Y_27 ) ) @ zero_zero_int )
| ( Y_27 = zero_zero_int ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1357]) ).
thf(1719,plain,
( ( ! [V_4: int] :
( ( zero_zero_nat
!= ( number_number_of_nat @ V_4 ) )
| ( ord_less_eq_int @ V_4 @ pls ) )
& ! [V_4: int] :
( ~ ( ord_less_eq_int @ V_4 @ pls )
| ( zero_zero_nat
= ( number_number_of_nat @ V_4 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1358]) ).
thf(1720,plain,
( ( ! [V_4: int] :
( ( ( number_number_of_nat @ V_4 )
!= zero_zero_nat )
| ( ord_less_eq_int @ V_4 @ pls ) )
& ! [V_4: int] :
( ~ ( ord_less_eq_int @ V_4 @ pls )
| ( ( number_number_of_nat @ V_4 )
= zero_zero_nat ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1359]) ).
thf(1721,plain,
( ( ! [K: int,I: int,J: int] :
( ~ ( ord_less_eq_int @ I @ J )
| ( ord_less_eq_int @ ( plus_plus_int @ K @ I ) @ ( plus_plus_int @ K @ J ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1360]) ).
thf(1722,plain,
( ( ! [Z: int,W: int] :
( ( Z = W )
| ~ ( ord_less_eq_int @ Z @ W )
| ( ord_less_int @ Z @ W ) )
& ! [Z: int,W: int] :
( ~ ( ord_less_int @ Z @ W )
| ( Z != W ) )
& ! [Z: int,W: int] :
( ~ ( ord_less_int @ Z @ W )
| ( ord_less_eq_int @ Z @ W ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1361]) ).
thf(1723,plain,
( ( ! [K: int,L: int] :
( ~ ( ord_less_eq_int @ ( bit0 @ K ) @ ( bit0 @ L ) )
| ( ord_less_eq_int @ K @ L ) )
& ! [K: int,L: int] :
( ~ ( ord_less_eq_int @ K @ L )
| ( ord_less_eq_int @ ( bit0 @ K ) @ ( bit0 @ L ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1362]) ).
thf(1724,plain,
( ( ! [K1: int,K2: int] :
( ~ ( ord_less_eq_int @ ( bit0 @ K1 ) @ ( bit0 @ K2 ) )
| ( ord_less_eq_int @ K1 @ K2 ) )
& ! [K1: int,K2: int] :
( ~ ( ord_less_eq_int @ K1 @ K2 )
| ( ord_less_eq_int @ ( bit0 @ K1 ) @ ( bit0 @ K2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1363]) ).
thf(1725,plain,
( ( ! [K: int,L: int] :
( ~ ( ord_less_eq_int @ ( bit1 @ K ) @ ( bit1 @ L ) )
| ( ord_less_eq_int @ K @ L ) )
& ! [K: int,L: int] :
( ~ ( ord_less_eq_int @ K @ L )
| ( ord_less_eq_int @ ( bit1 @ K ) @ ( bit1 @ L ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1365]) ).
thf(1726,plain,
( ( ! [K1: int,K2: int] :
( ~ ( ord_less_eq_int @ ( bit1 @ K1 ) @ ( bit1 @ K2 ) )
| ( ord_less_eq_int @ K1 @ K2 ) )
& ! [K1: int,K2: int] :
( ~ ( ord_less_eq_int @ K1 @ K2 )
| ( ord_less_eq_int @ ( bit1 @ K1 ) @ ( bit1 @ K2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1366]) ).
thf(1727,plain,
( ( ! [A_62: int] :
( ( ( power_power_int @ A_62 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= zero_zero_int )
| ( A_62 = zero_zero_int ) )
& ! [A_62: int] :
( ( A_62 != zero_zero_int )
| ( ( power_power_int @ A_62 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1370]) ).
thf(1728,plain,
( ( ! [A_62: real] :
( ( ( power_power_real @ A_62 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= zero_zero_real )
| ( A_62 = zero_zero_real ) )
& ! [A_62: real] :
( ( A_62 != zero_zero_real )
| ( ( power_power_real @ A_62 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_real ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1371]) ).
thf(1729,plain,
( ( ! [A_63: int] :
( ( A_63 = zero_zero_int )
| ( ord_less_int @ zero_zero_int @ ( power_power_int @ A_63 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
& ! [A_63: int] :
( ~ ( ord_less_int @ zero_zero_int @ ( power_power_int @ A_63 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ( A_63 != zero_zero_int ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1378]) ).
thf(1730,plain,
( ( ! [X_38: int,Y_29: int] :
( ( X_38 != zero_zero_int )
| ( Y_29 != zero_zero_int )
| ( ( plus_plus_int @ ( power_power_int @ X_38 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_29 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_int ) )
& ! [X_38: int] :
( ! [Y_29: int] :
( ( plus_plus_int @ ( power_power_int @ X_38 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_29 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_int )
| ( X_38 = zero_zero_int ) )
& ! [X_38: int,Y_29: int] :
( ( ( plus_plus_int @ ( power_power_int @ X_38 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_29 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_int )
| ( Y_29 = zero_zero_int ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1380]) ).
thf(1731,plain,
( ( ! [X_39: int,Y_30: int] :
( ~ ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X_39 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_30 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
| ( X_39 != zero_zero_int )
| ( Y_30 != zero_zero_int ) )
& ! [X_39: int] :
( ( X_39 = zero_zero_int )
| ! [Y_30: int] : ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X_39 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_30 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
& ! [X_39: int,Y_30: int] :
( ( Y_30 = zero_zero_int )
| ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X_39 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_30 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1381]) ).
thf(1732,plain,
( ( ( t != zero_zero_int )
| ( ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int )
= zero_zero_int ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1384]) ).
thf(1733,plain,
( ( ord_less_int @ t @ zero_zero_int )
= $true ),
inference(copy,[status(thm)],[1386]) ).
thf(1734,plain,
( ( ord_less_int @ t @ one_one_int )
= $true ),
inference(copy,[status(thm)],[1385]) ).
thf(1735,plain,
( ( ( t != zero_zero_int )
| ( ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int )
= zero_zero_int ) )
= $true ),
inference(copy,[status(thm)],[1732]) ).
thf(1736,plain,
( ( ~ ( ord_less_eq_int @ one_one_int @ t ) )
= $true ),
inference(copy,[status(thm)],[1383]) ).
thf(1737,plain,
( ( ! [X: int,Y: int] :
~ ( ord_less_int @ ( 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 ) ) ) ) ) @ zero_zero_int ) )
= $true ),
inference(copy,[status(thm)],[1382]) ).
thf(1738,plain,
( ( ! [X_39: int,Y_30: int] :
( ~ ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X_39 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_30 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
| ( X_39 != zero_zero_int )
| ( Y_30 != zero_zero_int ) )
& ! [X_39: int] :
( ( X_39 = zero_zero_int )
| ! [Y_30: int] : ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X_39 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_30 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
& ! [X_39: int,Y_30: int] :
( ( Y_30 = zero_zero_int )
| ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X_39 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_30 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1731]) ).
thf(1739,plain,
( ( ! [X_38: int,Y_29: int] :
( ( X_38 != zero_zero_int )
| ( Y_29 != zero_zero_int )
| ( ( plus_plus_int @ ( power_power_int @ X_38 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_29 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_int ) )
& ! [X_38: int] :
( ! [Y_29: int] :
( ( plus_plus_int @ ( power_power_int @ X_38 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_29 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_int )
| ( X_38 = zero_zero_int ) )
& ! [X_38: int,Y_29: int] :
( ( ( plus_plus_int @ ( power_power_int @ X_38 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_29 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_int )
| ( Y_29 = zero_zero_int ) ) )
= $true ),
inference(copy,[status(thm)],[1730]) ).
thf(1740,plain,
( ( ! [A_64: int] :
~ ( ord_less_int @ ( power_power_int @ A_64 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ zero_zero_int ) )
= $true ),
inference(copy,[status(thm)],[1379]) ).
thf(1741,plain,
( ( ! [A_63: int] :
( ( A_63 = zero_zero_int )
| ( ord_less_int @ zero_zero_int @ ( power_power_int @ A_63 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
& ! [A_63: int] :
( ~ ( ord_less_int @ zero_zero_int @ ( power_power_int @ A_63 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ( A_63 != zero_zero_int ) ) )
= $true ),
inference(copy,[status(thm)],[1729]) ).
thf(1742,plain,
( ( ( power_power_real @ one_one_real @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_real )
= $true ),
inference(copy,[status(thm)],[1377]) ).
thf(1743,plain,
( ( ( power_power_nat @ one_one_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_nat )
= $true ),
inference(copy,[status(thm)],[1376]) ).
thf(1744,plain,
( ( ( power_power_int @ one_one_int @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_int )
= $true ),
inference(copy,[status(thm)],[1375]) ).
thf(1745,plain,
( ( ( power_power_real @ zero_zero_real @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_real )
= $true ),
inference(copy,[status(thm)],[1374]) ).
thf(1746,plain,
( ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_nat )
= $true ),
inference(copy,[status(thm)],[1373]) ).
thf(1747,plain,
( ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int )
= $true ),
inference(copy,[status(thm)],[1372]) ).
thf(1748,plain,
( ( ! [A_62: real] :
( ( ( power_power_real @ A_62 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= zero_zero_real )
| ( A_62 = zero_zero_real ) )
& ! [A_62: real] :
( ( A_62 != zero_zero_real )
| ( ( power_power_real @ A_62 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_real ) ) )
= $true ),
inference(copy,[status(thm)],[1728]) ).
thf(1749,plain,
( ( ! [A_62: int] :
( ( ( power_power_int @ A_62 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= zero_zero_int )
| ( A_62 = zero_zero_int ) )
& ! [A_62: int] :
( ( A_62 != zero_zero_int )
| ( ( power_power_int @ A_62 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int ) ) )
= $true ),
inference(copy,[status(thm)],[1727]) ).
thf(1750,plain,
( ( ! [W_19: int] :
( ( plus_plus_int @ one_one_int @ ( number_number_of_int @ W_19 ) )
= ( number_number_of_int @ ( plus_plus_int @ ( bit1 @ pls ) @ W_19 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1369]) ).
thf(1751,plain,
( ( ! [V_19: int] :
( ( plus_plus_int @ ( number_number_of_int @ V_19 ) @ one_one_int )
= ( number_number_of_int @ ( plus_plus_int @ V_19 @ ( bit1 @ pls ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1368]) ).
thf(1752,plain,
( ( ! [X: int,Y: nat,Z: nat] :
( ( power_power_int @ X @ ( plus_plus_nat @ Y @ Z ) )
= ( times_times_int @ ( power_power_int @ X @ Y ) @ ( power_power_int @ X @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[1367]) ).
thf(1753,plain,
( ( ! [K1: int,K2: int] :
( ~ ( ord_less_eq_int @ ( bit1 @ K1 ) @ ( bit1 @ K2 ) )
| ( ord_less_eq_int @ K1 @ K2 ) )
& ! [K1: int,K2: int] :
( ~ ( ord_less_eq_int @ K1 @ K2 )
| ( ord_less_eq_int @ ( bit1 @ K1 ) @ ( bit1 @ K2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1726]) ).
thf(1754,plain,
( ( ! [K: int,L: int] :
( ~ ( ord_less_eq_int @ ( bit1 @ K ) @ ( bit1 @ L ) )
| ( ord_less_eq_int @ K @ L ) )
& ! [K: int,L: int] :
( ~ ( ord_less_eq_int @ K @ L )
| ( ord_less_eq_int @ ( bit1 @ K ) @ ( bit1 @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[1725]) ).
thf(1755,plain,
( ( ord_less_eq_int @ pls @ pls )
= $true ),
inference(copy,[status(thm)],[1364]) ).
thf(1756,plain,
( ( ! [K1: int,K2: int] :
( ~ ( ord_less_eq_int @ ( bit0 @ K1 ) @ ( bit0 @ K2 ) )
| ( ord_less_eq_int @ K1 @ K2 ) )
& ! [K1: int,K2: int] :
( ~ ( ord_less_eq_int @ K1 @ K2 )
| ( ord_less_eq_int @ ( bit0 @ K1 ) @ ( bit0 @ K2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1724]) ).
thf(1757,plain,
( ( ! [K: int,L: int] :
( ~ ( ord_less_eq_int @ ( bit0 @ K ) @ ( bit0 @ L ) )
| ( ord_less_eq_int @ K @ L ) )
& ! [K: int,L: int] :
( ~ ( ord_less_eq_int @ K @ L )
| ( ord_less_eq_int @ ( bit0 @ K ) @ ( bit0 @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[1723]) ).
thf(1758,plain,
( ( ! [Z: int,W: int] :
( ( Z = W )
| ~ ( ord_less_eq_int @ Z @ W )
| ( ord_less_int @ Z @ W ) )
& ! [Z: int,W: int] :
( ~ ( ord_less_int @ Z @ W )
| ( Z != W ) )
& ! [Z: int,W: int] :
( ~ ( ord_less_int @ Z @ W )
| ( ord_less_eq_int @ Z @ W ) ) )
= $true ),
inference(copy,[status(thm)],[1722]) ).
thf(1759,plain,
( ( ! [K: int,I: int,J: int] :
( ~ ( 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)],[1721]) ).
thf(1760,plain,
( ( ! [V_4: int] :
( ( ( number_number_of_nat @ V_4 )
!= zero_zero_nat )
| ( ord_less_eq_int @ V_4 @ pls ) )
& ! [V_4: int] :
( ~ ( ord_less_eq_int @ V_4 @ pls )
| ( ( number_number_of_nat @ V_4 )
= zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1720]) ).
thf(1761,plain,
( ( ! [V_4: int] :
( ( zero_zero_nat
!= ( number_number_of_nat @ V_4 ) )
| ( ord_less_eq_int @ V_4 @ pls ) )
& ! [V_4: int] :
( ~ ( ord_less_eq_int @ V_4 @ pls )
| ( zero_zero_nat
= ( number_number_of_nat @ V_4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1719]) ).
thf(1762,plain,
( ( ! [X_36: int,Y_27: int] :
( ( X_36 != zero_zero_int )
| ( Y_27 != zero_zero_int )
| ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ X_36 @ X_36 ) @ ( times_times_int @ Y_27 @ Y_27 ) ) @ zero_zero_int ) )
& ! [X_36: int] :
( ! [Y_27: int] :
~ ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ X_36 @ X_36 ) @ ( times_times_int @ Y_27 @ Y_27 ) ) @ zero_zero_int )
| ( X_36 = zero_zero_int ) )
& ! [X_36: int,Y_27: int] :
( ~ ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ X_36 @ X_36 ) @ ( times_times_int @ Y_27 @ Y_27 ) ) @ zero_zero_int )
| ( Y_27 = zero_zero_int ) ) )
= $true ),
inference(copy,[status(thm)],[1718]) ).
thf(1763,plain,
( ( ! [X_35: int,Y_26: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X_35 @ X_35 ) @ ( times_times_int @ Y_26 @ Y_26 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1356]) ).
thf(1764,plain,
( ( ! [X_34: int] :
( ~ ( ord_less_eq_int @ ( number_number_of_int @ X_34 ) @ zero_zero_int )
| ( ord_less_eq_int @ X_34 @ pls ) )
& ! [X_34: int] :
( ~ ( ord_less_eq_int @ X_34 @ pls )
| ( ord_less_eq_int @ ( number_number_of_int @ X_34 ) @ zero_zero_int ) ) )
= $true ),
inference(copy,[status(thm)],[1717]) ).
thf(1765,plain,
( ( ! [Y_25: int] :
( ~ ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ Y_25 ) )
| ( ord_less_eq_int @ pls @ Y_25 ) )
& ! [Y_25: int] :
( ~ ( ord_less_eq_int @ pls @ Y_25 )
| ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ Y_25 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1716]) ).
thf(1766,plain,
( ( ! [V_4: int] :
( ~ ( ord_less_int @ pls @ V_4 )
| ( ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ V_4 ) ) )
& ! [V_4: int] :
( ~ ( ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ V_4 ) )
| ( ord_less_int @ pls @ V_4 ) ) )
= $true ),
inference(copy,[status(thm)],[1715]) ).
thf(1767,plain,
( ( ! [V_13: int,W_15: int] :
( ~ ( ord_less_eq_nat @ ( number_number_of_nat @ V_13 ) @ ( number_number_of_nat @ W_15 ) )
| ~ ( ord_less_nat @ ( number_number_of_nat @ W_15 ) @ ( number_number_of_nat @ V_13 ) ) )
& ! [V_13: int,W_15: int] :
( ( ord_less_nat @ ( number_number_of_nat @ W_15 ) @ ( number_number_of_nat @ V_13 ) )
| ( ord_less_eq_nat @ ( number_number_of_nat @ V_13 ) @ ( number_number_of_nat @ W_15 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1714]) ).
thf(1768,plain,
( ( ! [V_13: int,W_15: int] :
( ~ ( ord_less_eq_int @ ( number_number_of_int @ V_13 ) @ ( number_number_of_int @ W_15 ) )
| ~ ( ord_less_int @ ( number_number_of_int @ W_15 ) @ ( number_number_of_int @ V_13 ) ) )
& ! [V_13: int,W_15: int] :
( ( ord_less_int @ ( number_number_of_int @ W_15 ) @ ( number_number_of_int @ V_13 ) )
| ( ord_less_eq_int @ ( number_number_of_int @ V_13 ) @ ( number_number_of_int @ W_15 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1713]) ).
thf(1769,plain,
( ( ! [K: int] :
( ~ ( ord_less_eq_int @ pls @ ( bit1 @ K ) )
| ( ord_less_eq_int @ pls @ K ) )
& ! [K: int] :
( ~ ( ord_less_eq_int @ pls @ K )
| ( ord_less_eq_int @ pls @ ( bit1 @ K ) ) ) )
= $true ),
inference(copy,[status(thm)],[1712]) ).
thf(1770,plain,
( ( ! [K1: int,K2: int] :
( ~ ( ord_less_eq_int @ ( bit0 @ K1 ) @ ( bit1 @ K2 ) )
| ( ord_less_eq_int @ K1 @ K2 ) )
& ! [K1: int,K2: int] :
( ~ ( ord_less_eq_int @ K1 @ K2 )
| ( ord_less_eq_int @ ( bit0 @ K1 ) @ ( bit1 @ K2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1711]) ).
thf(1771,plain,
( ( ! [K: int,L: int] :
( ~ ( ord_less_eq_int @ ( bit0 @ K ) @ ( bit1 @ L ) )
| ( ord_less_eq_int @ K @ L ) )
& ! [K: int,L: int] :
( ~ ( ord_less_eq_int @ K @ L )
| ( ord_less_eq_int @ ( bit0 @ K ) @ ( bit1 @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[1710]) ).
thf(1772,plain,
( ( ! [K: int] :
( ~ ( ord_less_eq_int @ ( bit0 @ K ) @ pls )
| ( ord_less_eq_int @ K @ pls ) )
& ! [K: int] :
( ~ ( ord_less_eq_int @ K @ pls )
| ( ord_less_eq_int @ ( bit0 @ K ) @ pls ) ) )
= $true ),
inference(copy,[status(thm)],[1709]) ).
thf(1773,plain,
( ( ! [K: int] :
( ~ ( ord_less_eq_int @ pls @ ( bit0 @ K ) )
| ( ord_less_eq_int @ pls @ K ) )
& ! [K: int] :
( ~ ( ord_less_eq_int @ pls @ K )
| ( ord_less_eq_int @ pls @ ( bit0 @ K ) ) ) )
= $true ),
inference(copy,[status(thm)],[1708]) ).
thf(1774,plain,
( ( ! [Z_8: int,Z: int,W_14: int,W: int] :
( ~ ( ord_less_int @ W_14 @ W )
| ~ ( ord_less_eq_int @ Z_8 @ Z )
| ( ord_less_int @ ( plus_plus_int @ W_14 @ Z_8 ) @ ( plus_plus_int @ W @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[1707]) ).
thf(1775,plain,
( ( ( number_number_of_nat @ pls )
= zero_zero_nat )
= $true ),
inference(copy,[status(thm)],[1344]) ).
thf(1776,plain,
( ( zero_zero_nat
= ( number_number_of_nat @ pls ) )
= $true ),
inference(copy,[status(thm)],[1343]) ).
thf(1777,plain,
( ( ! [X_33: int] :
( ~ ( ord_less_eq_int @ ( number_number_of_int @ X_33 ) @ one_one_int )
| ( ord_less_eq_int @ X_33 @ ( bit1 @ pls ) ) )
& ! [X_33: int] :
( ~ ( ord_less_eq_int @ X_33 @ ( bit1 @ pls ) )
| ( ord_less_eq_int @ ( number_number_of_int @ X_33 ) @ one_one_int ) ) )
= $true ),
inference(copy,[status(thm)],[1706]) ).
thf(1778,plain,
( ( ! [Y_24: int] :
( ~ ( ord_less_eq_int @ one_one_int @ ( number_number_of_int @ Y_24 ) )
| ( ord_less_eq_int @ ( bit1 @ pls ) @ Y_24 ) )
& ! [Y_24: int] :
( ~ ( ord_less_eq_int @ ( bit1 @ pls ) @ Y_24 )
| ( ord_less_eq_int @ one_one_int @ ( number_number_of_int @ Y_24 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1705]) ).
thf(1779,plain,
( ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
= ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(copy,[status(thm)],[1340]) ).
thf(1780,plain,
( ( ! [W: int] :
( ( times_times_int @ pls @ W )
= pls ) )
= $true ),
inference(copy,[status(thm)],[1339]) ).
thf(1781,plain,
( ( ! [K: int,L: int] :
( ( times_times_int @ ( bit0 @ K ) @ L )
= ( bit0 @ ( times_times_int @ K @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[1338]) ).
thf(1782,plain,
( ( ! [K: int,L: int] :
( ~ ( ord_less_int @ ( number_number_of_int @ K ) @ ( number_number_of_int @ L ) )
| ( ord_less_int @ K @ L ) )
& ! [K: int,L: int] :
( ~ ( ord_less_int @ K @ L )
| ( ord_less_int @ ( number_number_of_int @ K ) @ ( number_number_of_int @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[1704]) ).
thf(1783,plain,
( ( ! [Z: int] :
( ( times_times_int @ Z @ one_one_int )
= Z ) )
= $true ),
inference(copy,[status(thm)],[1336]) ).
thf(1784,plain,
( ( ! [Z: int] :
( ( times_times_int @ one_one_int @ Z )
= Z ) )
= $true ),
inference(copy,[status(thm)],[1335]) ).
thf(1785,plain,
( ( ! [V_4: int,W: int] :
( ( plus_plus_int @ ( number_number_of_int @ V_4 ) @ ( number_number_of_int @ W ) )
= ( number_number_of_int @ ( plus_plus_int @ V_4 @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[1334]) ).
thf(1786,plain,
( ( ! [Z1: int,Z2: int,W: int] :
( ( 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)],[1333]) ).
thf(1787,plain,
( ( ! [W: int,Z1: int,Z2: int] :
( ( 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)],[1332]) ).
thf(1788,plain,
( ( ! [K: int] :
( ~ ( ord_less_eq_int @ ( bit1 @ K ) @ pls )
| ( ord_less_int @ K @ pls ) )
& ! [K: int] :
( ~ ( ord_less_int @ K @ pls )
| ( ord_less_eq_int @ ( bit1 @ K ) @ pls ) ) )
= $true ),
inference(copy,[status(thm)],[1703]) ).
thf(1789,plain,
( ( ! [K: int] :
( ~ ( ord_less_eq_int @ pls @ K )
| ( ord_less_int @ pls @ ( bit1 @ K ) ) )
& ! [K: int] :
( ~ ( ord_less_int @ pls @ ( bit1 @ K ) )
| ( ord_less_eq_int @ pls @ K ) ) )
= $true ),
inference(copy,[status(thm)],[1702]) ).
thf(1790,plain,
( ( ! [K1: int,K2: int] :
( ~ ( ord_less_eq_int @ ( bit1 @ K1 ) @ ( bit0 @ K2 ) )
| ( ord_less_int @ K1 @ K2 ) )
& ! [K1: int,K2: int] :
( ~ ( ord_less_int @ K1 @ K2 )
| ( ord_less_eq_int @ ( bit1 @ K1 ) @ ( bit0 @ K2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1701]) ).
thf(1791,plain,
( ( ! [K: int,L: int] :
( ~ ( ord_less_eq_int @ ( bit1 @ K ) @ ( bit0 @ L ) )
| ( ord_less_int @ K @ L ) )
& ! [K: int,L: int] :
( ~ ( ord_less_int @ K @ L )
| ( ord_less_eq_int @ ( bit1 @ K ) @ ( bit0 @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[1700]) ).
thf(1792,plain,
( ( ! [K1: int,K2: int] :
( ~ ( ord_less_eq_int @ K1 @ K2 )
| ( ord_less_int @ ( bit0 @ K1 ) @ ( bit1 @ K2 ) ) )
& ! [K1: int,K2: int] :
( ~ ( ord_less_int @ ( bit0 @ K1 ) @ ( bit1 @ K2 ) )
| ( ord_less_eq_int @ K1 @ K2 ) ) )
= $true ),
inference(copy,[status(thm)],[1699]) ).
thf(1793,plain,
( ( ! [K: int,L: int] :
( ~ ( ord_less_eq_int @ K @ L )
| ( ord_less_int @ ( bit0 @ K ) @ ( bit1 @ L ) ) )
& ! [K: int,L: int] :
( ~ ( ord_less_int @ ( bit0 @ K ) @ ( bit1 @ L ) )
| ( ord_less_eq_int @ K @ L ) ) )
= $true ),
inference(copy,[status(thm)],[1698]) ).
thf(1794,plain,
( ( ! [V_4: int,V_5: int] :
( ( ord_less_int @ V_4 @ V_5 )
| ~ ( ord_less_int @ V_4 @ V_5 )
| ( ord_less_nat @ ( number_number_of_nat @ V_4 ) @ ( number_number_of_nat @ V_5 ) ) )
& ! [V_4: int,V_5: int] :
( ~ ( ord_less_int @ pls @ V_5 )
| ~ ( ord_less_int @ V_4 @ V_5 )
| ( ord_less_nat @ ( number_number_of_nat @ V_4 ) @ ( number_number_of_nat @ V_5 ) ) )
& ! [V_4: int,V_5: int] :
( ~ ( ord_less_nat @ ( number_number_of_nat @ V_4 ) @ ( number_number_of_nat @ V_5 ) )
| ~ ( ord_less_int @ V_4 @ V_5 )
| ( ord_less_int @ pls @ V_5 ) )
& ! [V_4: int,V_5: int] :
( ~ ( ord_less_nat @ ( number_number_of_nat @ V_4 ) @ ( number_number_of_nat @ V_5 ) )
| ( ord_less_int @ V_4 @ V_5 ) ) )
= $true ),
inference(copy,[status(thm)],[1697]) ).
thf(1795,plain,
( ( ! [Z: int] :
( ~ ( ord_less_eq_int @ one_one_int @ Z )
| ( ord_less_int @ zero_zero_int @ Z ) )
& ! [Z: int] :
( ~ ( ord_less_int @ zero_zero_int @ Z )
| ( ord_less_eq_int @ one_one_int @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[1696]) ).
thf(1796,plain,
( ( ( number_number_of_nat @ ( bit1 @ pls ) )
= one_one_nat )
= $true ),
inference(copy,[status(thm)],[1323]) ).
thf(1797,plain,
( ( one_one_nat
= ( number_number_of_nat @ ( bit1 @ pls ) ) )
= $true ),
inference(copy,[status(thm)],[1322]) ).
thf(1798,plain,
( ( ! [W: int,Z: int] :
( ~ ( ord_less_int @ W @ Z )
| ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[1695]) ).
thf(1799,plain,
( ( ! [W: int,Z: int] :
( ~ ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z )
| ( ord_less_int @ W @ Z ) )
& ! [W: int,Z: int] :
( ~ ( ord_less_int @ W @ Z )
| ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[1694]) ).
thf(1800,plain,
( ( ! [W: int,Z: int] :
( ~ ( ord_less_eq_int @ W @ Z )
| ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) ) )
& ! [W: int,Z: int] :
( ~ ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
| ( ord_less_eq_int @ W @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[1693]) ).
thf(1801,plain,
( ( ! [V_12: int,V_11: int] :
( ~ ( ord_less_eq_int @ pls @ V_11 )
| ~ ( ord_less_eq_int @ pls @ V_12 )
| ( ( plus_plus_nat @ ( number_number_of_nat @ V_11 ) @ ( number_number_of_nat @ V_12 ) )
= ( number_number_of_nat @ ( plus_plus_int @ V_11 @ V_12 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1692]) ).
thf(1802,plain,
( ( ! [V_12: int,V_11: int] :
( ~ ( ord_less_eq_int @ pls @ V_11 )
| ~ ( ord_less_eq_int @ pls @ V_12 )
| ( ( plus_plus_int @ ( number_number_of_int @ V_11 ) @ ( number_number_of_int @ V_12 ) )
= ( number_number_of_int @ ( plus_plus_int @ V_11 @ V_12 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1691]) ).
thf(1803,plain,
( ( ! [V_5: int,V_4: int] :
( ~ ( ord_less_int @ V_4 @ pls )
| ( ( plus_plus_nat @ ( number_number_of_nat @ V_4 ) @ ( number_number_of_nat @ V_5 ) )
= ( number_number_of_nat @ V_5 ) ) )
& ! [V_5: int,V_4: int] :
( ( ord_less_int @ V_4 @ pls )
| ~ ( ord_less_int @ V_5 @ pls )
| ( ( plus_plus_nat @ ( number_number_of_nat @ V_4 ) @ ( number_number_of_nat @ V_5 ) )
= ( number_number_of_nat @ V_4 ) ) )
& ! [V_5: int,V_4: int] :
( ( ord_less_int @ V_4 @ pls )
| ( ord_less_int @ V_5 @ pls )
| ( ( plus_plus_nat @ ( number_number_of_nat @ V_4 ) @ ( number_number_of_nat @ V_5 ) )
= ( number_number_of_nat @ ( plus_plus_int @ V_4 @ V_5 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1690]) ).
thf(1804,plain,
( ( ! [Z: int] :
( ~ ( 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)],[1689]) ).
thf(1805,plain,
( ( ! [W_13: int,X_31: nat] :
( ( ( number_number_of_nat @ W_13 )
!= X_31 )
| ( X_31
= ( number_number_of_nat @ W_13 ) ) )
& ! [W_13: int,X_31: nat] :
( ( X_31
!= ( number_number_of_nat @ W_13 ) )
| ( ( number_number_of_nat @ W_13 )
= X_31 ) ) )
= $true ),
inference(copy,[status(thm)],[1688]) ).
thf(1806,plain,
( ( ! [K: int,L: int] :
( ( ( bit1 @ K )
!= ( bit1 @ L ) )
| ( K = L ) )
& ! [K: int,L: int] :
( ( K != L )
| ( ( bit1 @ K )
= ( bit1 @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[1687]) ).
thf(1807,plain,
( ( ! [K: int,L: int] :
( ( ( bit0 @ K )
!= ( bit0 @ L ) )
| ( K = L ) )
& ! [K: int,L: int] :
( ( K != L )
| ( ( bit0 @ K )
= ( bit0 @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[1686]) ).
thf(1808,plain,
( ( ! [X: int,Y: int] :
( ( ord_less_int @ Y @ X )
| ( X = Y )
| ( ord_less_int @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[1685]) ).
thf(1809,plain,
( ( ! [X_30: int,Y_22: int] :
( ( X_30 != zero_zero_int )
| ( Y_22 != zero_zero_int )
| ( ( plus_plus_int @ ( times_times_int @ X_30 @ X_30 ) @ ( times_times_int @ Y_22 @ Y_22 ) )
= zero_zero_int ) )
& ! [X_30: int] :
( ! [Y_22: int] :
( ( plus_plus_int @ ( times_times_int @ X_30 @ X_30 ) @ ( times_times_int @ Y_22 @ Y_22 ) )
!= zero_zero_int )
| ( X_30 = zero_zero_int ) )
& ! [X_30: int,Y_22: int] :
( ( ( plus_plus_int @ ( times_times_int @ X_30 @ X_30 ) @ ( times_times_int @ Y_22 @ Y_22 ) )
!= zero_zero_int )
| ( Y_22 = zero_zero_int ) ) )
= $true ),
inference(copy,[status(thm)],[1684]) ).
thf(1810,plain,
( ( ! [A_61: nat,B_22: nat,V_10: int] :
( ( times_times_nat @ ( plus_plus_nat @ A_61 @ B_22 ) @ ( number_number_of_nat @ V_10 ) )
= ( plus_plus_nat @ ( times_times_nat @ A_61 @ ( number_number_of_nat @ V_10 ) ) @ ( times_times_nat @ B_22 @ ( number_number_of_nat @ V_10 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1309]) ).
thf(1811,plain,
( ( ! [A_61: int,B_22: int,V_10: int] :
( ( times_times_int @ ( plus_plus_int @ A_61 @ B_22 ) @ ( number_number_of_int @ V_10 ) )
= ( plus_plus_int @ ( times_times_int @ A_61 @ ( number_number_of_int @ V_10 ) ) @ ( times_times_int @ B_22 @ ( number_number_of_int @ V_10 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1308]) ).
thf(1812,plain,
( ( ! [V_9: int,B_21: nat,C_13: nat] :
( ( times_times_nat @ ( number_number_of_nat @ V_9 ) @ ( plus_plus_nat @ B_21 @ C_13 ) )
= ( plus_plus_nat @ ( times_times_nat @ ( number_number_of_nat @ V_9 ) @ B_21 ) @ ( times_times_nat @ ( number_number_of_nat @ V_9 ) @ C_13 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1307]) ).
thf(1813,plain,
( ( ! [V_9: int,B_21: int,C_13: int] :
( ( times_times_int @ ( number_number_of_int @ V_9 ) @ ( plus_plus_int @ B_21 @ C_13 ) )
= ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ V_9 ) @ B_21 ) @ ( times_times_int @ ( number_number_of_int @ V_9 ) @ C_13 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1306]) ).
thf(1814,plain,
( ( ! [Z1: int,Z2: int,Z3: int] :
( ( plus_plus_int @ ( plus_plus_int @ Z1 @ Z2 ) @ Z3 )
= ( plus_plus_int @ Z1 @ ( plus_plus_int @ Z2 @ Z3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1305]) ).
thf(1815,plain,
( ( ! [X: int,Y: int,Z: int] :
( ( plus_plus_int @ X @ ( plus_plus_int @ Y @ Z ) )
= ( plus_plus_int @ Y @ ( plus_plus_int @ X @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[1304]) ).
thf(1816,plain,
( ( ! [Z: int,W: int] :
( ( plus_plus_int @ Z @ W )
= ( plus_plus_int @ W @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[1303]) ).
thf(1817,plain,
( ( zero_zero_int
= ( number_number_of_int @ pls ) )
= $true ),
inference(copy,[status(thm)],[1302]) ).
thf(1818,plain,
( ( ! [K: int,I: int,J: int] :
( ~ ( 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)],[1683]) ).
thf(1819,plain,
( ( ! [X_29: int,Y_21: int] :
( ( ( power_power_int @ X_29 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= ( power_power_int @ Y_21 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ~ ( ord_less_eq_int @ zero_zero_int @ X_29 )
| ~ ( ord_less_eq_int @ zero_zero_int @ Y_21 )
| ( X_29 = Y_21 ) ) )
= $true ),
inference(copy,[status(thm)],[1682]) ).
thf(1820,plain,
( ( ! [X_28: int,Y_20: int] :
( ~ ( ord_less_eq_int @ ( power_power_int @ X_28 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_20 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ~ ( ord_less_eq_int @ zero_zero_int @ Y_20 )
| ( ord_less_eq_int @ X_28 @ Y_20 ) ) )
= $true ),
inference(copy,[status(thm)],[1681]) ).
thf(1821,plain,
( ( ! [A_60: int] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A_60 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1298]) ).
thf(1822,plain,
( ( ! [X_27: int,Y_19: int] :
( ~ ( ord_less_int @ ( power_power_int @ X_27 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_19 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ~ ( ord_less_eq_int @ zero_zero_int @ Y_19 )
| ( ord_less_int @ X_27 @ Y_19 ) ) )
= $true ),
inference(copy,[status(thm)],[1680]) ).
thf(1823,plain,
( ( ! [X_26: int,Y_18: int] :
( ( X_26 != zero_zero_int )
| ( Y_18 != zero_zero_int )
| ( ord_less_eq_int @ ( plus_plus_int @ ( power_power_int @ X_26 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_18 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_int ) )
& ! [X_26: int] :
( ! [Y_18: int] :
~ ( ord_less_eq_int @ ( plus_plus_int @ ( power_power_int @ X_26 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_18 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_int )
| ( X_26 = zero_zero_int ) )
& ! [X_26: int,Y_18: int] :
( ~ ( ord_less_eq_int @ ( plus_plus_int @ ( power_power_int @ X_26 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_18 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_int )
| ( Y_18 = zero_zero_int ) ) )
= $true ),
inference(copy,[status(thm)],[1679]) ).
thf(1824,plain,
( ( ! [X_25: int,Y_17: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X_25 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_17 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1295]) ).
thf(1825,plain,
( ( ! [X_24: int,Y_16: int] :
( ~ ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X_24 @ X_24 ) @ ( times_times_int @ Y_16 @ Y_16 ) ) )
| ( X_24 != zero_zero_int )
| ( Y_16 != zero_zero_int ) )
& ! [X_24: int] :
( ( X_24 = zero_zero_int )
| ! [Y_16: int] : ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X_24 @ X_24 ) @ ( times_times_int @ Y_16 @ Y_16 ) ) ) )
& ! [X_24: int,Y_16: int] :
( ( Y_16 = zero_zero_int )
| ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X_24 @ X_24 ) @ ( times_times_int @ Y_16 @ Y_16 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1678]) ).
thf(1826,plain,
( ( ! [X_23: int,Y_15: int] :
~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ X_23 @ X_23 ) @ ( times_times_int @ Y_15 @ Y_15 ) ) @ zero_zero_int ) )
= $true ),
inference(copy,[status(thm)],[1293]) ).
thf(1827,plain,
( ( ! [A_59: real] :
( ( times_times_real @ ( number267125858f_real @ ( bit1 @ pls ) ) @ A_59 )
= A_59 ) )
= $true ),
inference(copy,[status(thm)],[1292]) ).
thf(1828,plain,
( ( ! [A_59: int] :
( ( times_times_int @ ( number_number_of_int @ ( bit1 @ pls ) ) @ A_59 )
= A_59 ) )
= $true ),
inference(copy,[status(thm)],[1291]) ).
thf(1829,plain,
( ( ! [A_58: real] :
( ( times_times_real @ A_58 @ ( number267125858f_real @ ( bit1 @ pls ) ) )
= A_58 ) )
= $true ),
inference(copy,[status(thm)],[1290]) ).
thf(1830,plain,
( ( ! [A_58: int] :
( ( times_times_int @ A_58 @ ( number_number_of_int @ ( bit1 @ pls ) ) )
= A_58 ) )
= $true ),
inference(copy,[status(thm)],[1289]) ).
thf(1831,plain,
( ( one_one_int
= ( number_number_of_int @ ( bit1 @ pls ) ) )
= $true ),
inference(copy,[status(thm)],[1288]) ).
thf(1832,plain,
( ( ! [K: int,L: int] :
( ( times_times_int @ ( bit1 @ K ) @ L )
= ( plus_plus_int @ ( bit0 @ ( times_times_int @ K @ L ) ) @ L ) ) )
= $true ),
inference(copy,[status(thm)],[1287]) ).
thf(1833,plain,
( ( ! [N: int,M: int] :
( ~ ( ord_less_int @ zero_zero_int @ M )
| ( M != one_one_int )
| ( N != one_one_int )
| ( ( times_times_int @ M @ N )
= one_one_int ) )
& ! [N: int,M: int] :
( ~ ( ord_less_int @ zero_zero_int @ M )
| ( ( times_times_int @ M @ N )
!= one_one_int )
| ( M = one_one_int ) )
& ! [N: int,M: int] :
( ~ ( ord_less_int @ zero_zero_int @ M )
| ( ( times_times_int @ M @ N )
!= one_one_int )
| ( N = one_one_int ) ) )
= $true ),
inference(copy,[status(thm)],[1677]) ).
thf(1834,plain,
( ( ! [A_57: int] :
( ( ( plus_plus_int @ A_57 @ A_57 )
!= zero_zero_int )
| ( A_57 = zero_zero_int ) )
& ! [A_57: int] :
( ( A_57 != zero_zero_int )
| ( ( plus_plus_int @ A_57 @ A_57 )
= zero_zero_int ) ) )
= $true ),
inference(copy,[status(thm)],[1676]) ).
thf(1835,plain,
( ( ! [K: int] :
( ( bit1 @ K )
!= pls ) )
= $true ),
inference(copy,[status(thm)],[1675]) ).
thf(1836,plain,
( ( ! [L: int] :
( pls
!= ( bit1 @ L ) ) )
= $true ),
inference(copy,[status(thm)],[1674]) ).
thf(1837,plain,
( ( ! [K: int,L: int] :
( ( bit1 @ K )
!= ( bit0 @ L ) ) )
= $true ),
inference(copy,[status(thm)],[1673]) ).
thf(1838,plain,
( ( ! [K: int,L: int] :
( ( bit0 @ K )
!= ( bit1 @ L ) ) )
= $true ),
inference(copy,[status(thm)],[1672]) ).
thf(1839,plain,
( ( ! [K: int] :
( ( ( bit0 @ K )
!= pls )
| ( K = pls ) )
& ! [K: int] :
( ( K != pls )
| ( ( bit0 @ K )
= pls ) ) )
= $true ),
inference(copy,[status(thm)],[1671]) ).
thf(1840,plain,
( ( ! [L: int] :
( ( pls
!= ( bit0 @ L ) )
| ( pls = L ) )
& ! [L: int] :
( ( pls != L )
| ( pls
= ( bit0 @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[1670]) ).
thf(1841,plain,
( ( ( bit0 @ pls )
= pls )
= $true ),
inference(copy,[status(thm)],[1278]) ).
thf(1842,plain,
( ( pls = zero_zero_int )
= $true ),
inference(copy,[status(thm)],[1277]) ).
thf(1843,plain,
( ( ! [K1: int,K2: int] :
( ~ ( ord_less_int @ ( bit1 @ K1 ) @ ( bit1 @ K2 ) )
| ( ord_less_int @ K1 @ K2 ) )
& ! [K1: int,K2: int] :
( ~ ( ord_less_int @ K1 @ K2 )
| ( ord_less_int @ ( bit1 @ K1 ) @ ( bit1 @ K2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1669]) ).
thf(1844,plain,
( ( ! [K: int,L: int] :
( ~ ( ord_less_int @ ( bit1 @ K ) @ ( bit1 @ L ) )
| ( ord_less_int @ K @ L ) )
& ! [K: int,L: int] :
( ~ ( ord_less_int @ K @ L )
| ( ord_less_int @ ( bit1 @ K ) @ ( bit1 @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[1668]) ).
thf(1845,plain,
( ( ~ ( ord_less_int @ pls @ pls ) )
= $true ),
inference(copy,[status(thm)],[1274]) ).
thf(1846,plain,
( ( ! [K1: int,K2: int] :
( ~ ( ord_less_int @ ( bit0 @ K1 ) @ ( bit0 @ K2 ) )
| ( ord_less_int @ K1 @ K2 ) )
& ! [K1: int,K2: int] :
( ~ ( ord_less_int @ K1 @ K2 )
| ( ord_less_int @ ( bit0 @ K1 ) @ ( bit0 @ K2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1667]) ).
thf(1847,plain,
( ( ! [K: int,L: int] :
( ~ ( ord_less_int @ ( bit0 @ K ) @ ( bit0 @ L ) )
| ( ord_less_int @ K @ L ) )
& ! [K: int,L: int] :
( ~ ( ord_less_int @ K @ L )
| ( ord_less_int @ ( bit0 @ K ) @ ( bit0 @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[1666]) ).
thf(1848,plain,
( ( zero_zero_int != one_one_int )
= $true ),
inference(copy,[status(thm)],[1665]) ).
thf(1849,plain,
( ( ! [K: int] :
( ( plus_plus_int @ K @ pls )
= K ) )
= $true ),
inference(copy,[status(thm)],[1270]) ).
thf(1850,plain,
( ( ! [K: int] :
( ( plus_plus_int @ pls @ K )
= K ) )
= $true ),
inference(copy,[status(thm)],[1269]) ).
thf(1851,plain,
( ( ! [K: int,L: int] :
( ( plus_plus_int @ ( bit0 @ K ) @ ( bit0 @ L ) )
= ( bit0 @ ( plus_plus_int @ K @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[1268]) ).
thf(1852,plain,
( ( ! [K: int] :
( ( bit0 @ K )
= ( plus_plus_int @ K @ K ) ) )
= $true ),
inference(copy,[status(thm)],[1267]) ).
thf(1853,plain,
( ( ! [Z: int] :
( ( plus_plus_int @ Z @ zero_zero_int )
= Z ) )
= $true ),
inference(copy,[status(thm)],[1266]) ).
thf(1854,plain,
( ( ! [Z: int] :
( ( plus_plus_int @ zero_zero_int @ Z )
= Z ) )
= $true ),
inference(copy,[status(thm)],[1265]) ).
thf(1855,plain,
( ( ! [K: int,I: int,J: int] :
( ~ ( ord_less_int @ I @ J )
| ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ K ) ) ) )
= $true ),
inference(copy,[status(thm)],[1664]) ).
thf(1856,plain,
( ( ! [W_12: int] :
( ( times_times_int @ ( plus_plus_int @ one_one_int @ one_one_int ) @ ( number_number_of_int @ W_12 ) )
= ( number_number_of_int @ ( bit0 @ W_12 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1263]) ).
thf(1857,plain,
( ( ! [A_56: real] :
( ( power_power_real @ A_56 @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( times_times_real @ ( times_times_real @ A_56 @ A_56 ) @ A_56 ) ) )
= $true ),
inference(copy,[status(thm)],[1262]) ).
thf(1858,plain,
( ( ! [A_56: nat] :
( ( power_power_nat @ A_56 @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( times_times_nat @ ( times_times_nat @ A_56 @ A_56 ) @ A_56 ) ) )
= $true ),
inference(copy,[status(thm)],[1261]) ).
thf(1859,plain,
( ( ! [A_56: int] :
( ( power_power_int @ A_56 @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( times_times_int @ ( times_times_int @ A_56 @ A_56 ) @ A_56 ) ) )
= $true ),
inference(copy,[status(thm)],[1260]) ).
thf(1860,plain,
( ( ! [Z_7: nat] :
( ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ Z_7 )
= ( plus_plus_nat @ Z_7 @ Z_7 ) ) )
= $true ),
inference(copy,[status(thm)],[1259]) ).
thf(1861,plain,
( ( ! [Z_7: int] :
( ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ Z_7 )
= ( plus_plus_int @ Z_7 @ Z_7 ) ) )
= $true ),
inference(copy,[status(thm)],[1258]) ).
thf(1862,plain,
( ( ! [Z_6: int] :
( ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ Z_6 )
= ( plus_plus_int @ Z_6 @ Z_6 ) ) )
= $true ),
inference(copy,[status(thm)],[1257]) ).
thf(1863,plain,
( ( ! [Z_5: nat] :
( ( times_times_nat @ Z_5 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_nat @ Z_5 @ Z_5 ) ) )
= $true ),
inference(copy,[status(thm)],[1256]) ).
thf(1864,plain,
( ( ! [Z_5: int] :
( ( times_times_int @ Z_5 @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ Z_5 @ Z_5 ) ) )
= $true ),
inference(copy,[status(thm)],[1255]) ).
thf(1865,plain,
( ( ! [Z_4: int] :
( ( times_times_int @ Z_4 @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ Z_4 @ Z_4 ) ) )
= $true ),
inference(copy,[status(thm)],[1254]) ).
thf(1866,plain,
( ( ! [A_55: real] :
( ( power_power_real @ A_55 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_real @ A_55 @ A_55 ) ) )
= $true ),
inference(copy,[status(thm)],[1253]) ).
thf(1867,plain,
( ( ! [A_55: nat] :
( ( power_power_nat @ A_55 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_nat @ A_55 @ A_55 ) ) )
= $true ),
inference(copy,[status(thm)],[1252]) ).
thf(1868,plain,
( ( ! [A_55: int] :
( ( power_power_int @ A_55 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_int @ A_55 @ A_55 ) ) )
= $true ),
inference(copy,[status(thm)],[1251]) ).
thf(1869,plain,
( ( ! [A_54: int] :
( ~ ( ord_less_int @ ( plus_plus_int @ A_54 @ A_54 ) @ zero_zero_int )
| ( ord_less_int @ A_54 @ zero_zero_int ) )
& ! [A_54: int] :
( ~ ( ord_less_int @ A_54 @ zero_zero_int )
| ( ord_less_int @ ( plus_plus_int @ A_54 @ A_54 ) @ zero_zero_int ) ) )
= $true ),
inference(copy,[status(thm)],[1663]) ).
thf(1870,plain,
( ( ( number267125858f_real @ pls )
= zero_zero_real )
= $true ),
inference(copy,[status(thm)],[1249]) ).
thf(1871,plain,
( ( ( number_number_of_nat @ pls )
= zero_zero_nat )
= $true ),
inference(copy,[status(thm)],[1248]) ).
thf(1872,plain,
( ( ( number_number_of_int @ pls )
= zero_zero_int )
= $true ),
inference(copy,[status(thm)],[1247]) ).
thf(1873,plain,
( ( ( number267125858f_real @ pls )
= zero_zero_real )
= $true ),
inference(copy,[status(thm)],[1246]) ).
thf(1874,plain,
( ( ( number_number_of_int @ pls )
= zero_zero_int )
= $true ),
inference(copy,[status(thm)],[1245]) ).
thf(1875,plain,
( ( zero_zero_real
= ( number267125858f_real @ pls ) )
= $true ),
inference(copy,[status(thm)],[1244]) ).
thf(1876,plain,
( ( zero_zero_int
= ( number_number_of_int @ pls ) )
= $true ),
inference(copy,[status(thm)],[1243]) ).
thf(1877,plain,
( ( ! [A_53: real] :
( ( plus_plus_real @ ( number267125858f_real @ pls ) @ A_53 )
= A_53 ) )
= $true ),
inference(copy,[status(thm)],[1242]) ).
thf(1878,plain,
( ( ! [A_53: int] :
( ( plus_plus_int @ ( number_number_of_int @ pls ) @ A_53 )
= A_53 ) )
= $true ),
inference(copy,[status(thm)],[1241]) ).
thf(1879,plain,
( ( ! [A_52: real] :
( ( plus_plus_real @ A_52 @ ( number267125858f_real @ pls ) )
= A_52 ) )
= $true ),
inference(copy,[status(thm)],[1240]) ).
thf(1880,plain,
( ( ! [A_52: int] :
( ( plus_plus_int @ A_52 @ ( number_number_of_int @ pls ) )
= A_52 ) )
= $true ),
inference(copy,[status(thm)],[1239]) ).
thf(1881,plain,
( ( ! [X_22: int,Y_14: int] :
( ~ ( ord_less_int @ X_22 @ Y_14 )
| ( ord_less_real @ ( number267125858f_real @ X_22 ) @ ( number267125858f_real @ Y_14 ) ) )
& ! [X_22: int,Y_14: int] :
( ~ ( ord_less_real @ ( number267125858f_real @ X_22 ) @ ( number267125858f_real @ Y_14 ) )
| ( ord_less_int @ X_22 @ Y_14 ) ) )
= $true ),
inference(copy,[status(thm)],[1662]) ).
thf(1882,plain,
( ( ! [X_22: int,Y_14: int] :
( ~ ( ord_less_int @ ( number_number_of_int @ X_22 ) @ ( number_number_of_int @ Y_14 ) )
| ( ord_less_int @ X_22 @ Y_14 ) )
& ! [X_22: int,Y_14: int] :
( ~ ( ord_less_int @ X_22 @ Y_14 )
| ( ord_less_int @ ( number_number_of_int @ X_22 ) @ ( number_number_of_int @ Y_14 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1661]) ).
thf(1883,plain,
( ( ! [V_8: int,W_11: int,Z_3: real] :
( ( plus_plus_real @ ( number267125858f_real @ V_8 ) @ ( plus_plus_real @ ( number267125858f_real @ W_11 ) @ Z_3 ) )
= ( plus_plus_real @ ( number267125858f_real @ ( plus_plus_int @ V_8 @ W_11 ) ) @ Z_3 ) ) )
= $true ),
inference(copy,[status(thm)],[1236]) ).
thf(1884,plain,
( ( ! [V_8: int,W_11: int,Z_3: int] :
( ( plus_plus_int @ ( number_number_of_int @ V_8 ) @ ( plus_plus_int @ ( number_number_of_int @ W_11 ) @ Z_3 ) )
= ( plus_plus_int @ ( number_number_of_int @ ( plus_plus_int @ V_8 @ W_11 ) ) @ Z_3 ) ) )
= $true ),
inference(copy,[status(thm)],[1235]) ).
thf(1885,plain,
( ( ! [V_7: int,W_10: int] :
( ( plus_plus_real @ ( number267125858f_real @ V_7 ) @ ( number267125858f_real @ W_10 ) )
= ( number267125858f_real @ ( plus_plus_int @ V_7 @ W_10 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1234]) ).
thf(1886,plain,
( ( ! [V_7: int,W_10: int] :
( ( plus_plus_int @ ( number_number_of_int @ V_7 ) @ ( number_number_of_int @ W_10 ) )
= ( number_number_of_int @ ( plus_plus_int @ V_7 @ W_10 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1233]) ).
thf(1887,plain,
( ( ! [V_6: int,W_9: int] :
( ( number267125858f_real @ ( plus_plus_int @ V_6 @ W_9 ) )
= ( plus_plus_real @ ( number267125858f_real @ V_6 ) @ ( number267125858f_real @ W_9 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1232]) ).
thf(1888,plain,
( ( ! [V_6: int,W_9: int] :
( ( number_number_of_int @ ( plus_plus_int @ V_6 @ W_9 ) )
= ( plus_plus_int @ ( number_number_of_int @ V_6 ) @ ( number_number_of_int @ W_9 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1231]) ).
thf(1889,plain,
( ( ! [K: int] :
( ~ ( ord_less_int @ ( bit1 @ K ) @ pls )
| ( ord_less_int @ K @ pls ) )
& ! [K: int] :
( ~ ( ord_less_int @ K @ pls )
| ( ord_less_int @ ( bit1 @ K ) @ pls ) ) )
= $true ),
inference(copy,[status(thm)],[1660]) ).
thf(1890,plain,
( ( ! [K1: int,K2: int] :
( ~ ( ord_less_int @ ( bit1 @ K1 ) @ ( bit0 @ K2 ) )
| ( ord_less_int @ K1 @ K2 ) )
& ! [K1: int,K2: int] :
( ~ ( ord_less_int @ K1 @ K2 )
| ( ord_less_int @ ( bit1 @ K1 ) @ ( bit0 @ K2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1659]) ).
thf(1891,plain,
( ( ! [K: int,L: int] :
( ~ ( ord_less_int @ ( bit1 @ K ) @ ( bit0 @ L ) )
| ( ord_less_int @ K @ L ) )
& ! [K: int,L: int] :
( ~ ( ord_less_int @ K @ L )
| ( ord_less_int @ ( bit1 @ K ) @ ( bit0 @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[1658]) ).
thf(1892,plain,
( ( ! [W: int] :
( ~ ( ord_less_int @ ( bit1 @ W ) @ zero_zero_int )
| ( ord_less_int @ W @ zero_zero_int ) )
& ! [W: int] :
( ~ ( ord_less_int @ W @ zero_zero_int )
| ( ord_less_int @ ( bit1 @ W ) @ zero_zero_int ) ) )
= $true ),
inference(copy,[status(thm)],[1657]) ).
thf(1893,plain,
( ( ! [K: int] :
( ~ ( ord_less_int @ ( bit0 @ K ) @ pls )
| ( ord_less_int @ K @ pls ) )
& ! [K: int] :
( ~ ( ord_less_int @ K @ pls )
| ( ord_less_int @ ( bit0 @ K ) @ pls ) ) )
= $true ),
inference(copy,[status(thm)],[1656]) ).
thf(1894,plain,
( ( ! [K: int] :
( ~ ( ord_less_int @ pls @ ( bit0 @ K ) )
| ( ord_less_int @ pls @ K ) )
& ! [K: int] :
( ~ ( ord_less_int @ pls @ K )
| ( ord_less_int @ pls @ ( bit0 @ K ) ) ) )
= $true ),
inference(copy,[status(thm)],[1655]) ).
thf(1895,plain,
( ( ~ ( ord_less_int @ pls @ zero_zero_int ) )
= $true ),
inference(copy,[status(thm)],[1224]) ).
thf(1896,plain,
( ( ! [W: int] :
( ~ ( ord_less_int @ ( bit0 @ W ) @ zero_zero_int )
| ( ord_less_int @ W @ zero_zero_int ) )
& ! [W: int] :
( ~ ( ord_less_int @ W @ zero_zero_int )
| ( ord_less_int @ ( bit0 @ W ) @ zero_zero_int ) ) )
= $true ),
inference(copy,[status(thm)],[1654]) ).
thf(1897,plain,
( ( ! [K: int,L: int] :
( ( plus_plus_int @ ( bit1 @ K ) @ ( bit0 @ L ) )
= ( bit1 @ ( plus_plus_int @ K @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[1222]) ).
thf(1898,plain,
( ( ! [K: int,L: int] :
( ( plus_plus_int @ ( bit0 @ K ) @ ( bit1 @ L ) )
= ( bit1 @ ( plus_plus_int @ K @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[1221]) ).
thf(1899,plain,
( ( ord_less_int @ zero_zero_int @ one_one_int )
= $true ),
inference(copy,[status(thm)],[1220]) ).
thf(1900,plain,
( ( ! [K: int] :
( ( bit1 @ K )
= ( plus_plus_int @ ( plus_plus_int @ one_one_int @ K ) @ K ) ) )
= $true ),
inference(copy,[status(thm)],[1219]) ).
thf(1901,plain,
( ( ! [Z: int] :
( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z )
!= zero_zero_int ) )
= $true ),
inference(copy,[status(thm)],[1653]) ).
thf(1902,plain,
( ( ! [W: int,Z: int] :
( ~ ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
| ( W = Z )
| ( ord_less_int @ W @ Z ) )
& ! [W: int,Z: int] :
( ( W != Z )
| ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) ) )
& ! [W: int,Z: int] :
( ~ ( ord_less_int @ W @ Z )
| ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) ) ) )
= $true ),
inference(copy,[status(thm)],[1652]) ).
thf(1903,plain,
( ( ! [W_8: int] :
( ( power_power_nat @ ( number_number_of_nat @ W_8 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_nat @ ( number_number_of_nat @ W_8 ) @ ( number_number_of_nat @ W_8 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1216]) ).
thf(1904,plain,
( ( ! [W_8: int] :
( ( power_power_int @ ( number_number_of_int @ W_8 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_int @ ( number_number_of_int @ W_8 ) @ ( number_number_of_int @ W_8 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1215]) ).
thf(1905,plain,
( ( ! [X_21: int,Y_13: int] :
( ( power_power_int @ ( plus_plus_int @ X_21 @ Y_13 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ X_21 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_13 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ X_21 ) @ Y_13 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1214]) ).
thf(1906,plain,
( ( ! [W_7: int] :
( ( number_number_of_int @ ( bit0 @ W_7 ) )
= ( plus_plus_int @ ( plus_plus_int @ zero_zero_int @ ( number_number_of_int @ W_7 ) ) @ ( number_number_of_int @ W_7 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1213]) ).
thf(1907,plain,
( ( ! [W_6: int] :
( ( number_number_of_int @ ( bit1 @ W_6 ) )
= ( plus_plus_int @ ( plus_plus_int @ one_one_int @ ( number_number_of_int @ W_6 ) ) @ ( number_number_of_int @ W_6 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1212]) ).
thf(1908,plain,
( ( ( number267125858f_real @ ( bit1 @ pls ) )
= one_one_real )
= $true ),
inference(copy,[status(thm)],[1211]) ).
thf(1909,plain,
( ( ( number_number_of_nat @ ( bit1 @ pls ) )
= one_one_nat )
= $true ),
inference(copy,[status(thm)],[1210]) ).
thf(1910,plain,
( ( ( number_number_of_int @ ( bit1 @ pls ) )
= one_one_int )
= $true ),
inference(copy,[status(thm)],[1209]) ).
thf(1911,plain,
( ( ( number267125858f_real @ ( bit1 @ pls ) )
= one_one_real )
= $true ),
inference(copy,[status(thm)],[1208]) ).
thf(1912,plain,
( ( ( number_number_of_int @ ( bit1 @ pls ) )
= one_one_int )
= $true ),
inference(copy,[status(thm)],[1207]) ).
thf(1913,plain,
( ( one_one_real
= ( number267125858f_real @ ( bit1 @ pls ) ) )
= $true ),
inference(copy,[status(thm)],[1206]) ).
thf(1914,plain,
( ( one_one_int
= ( number_number_of_int @ ( bit1 @ pls ) ) )
= $true ),
inference(copy,[status(thm)],[1205]) ).
thf(1915,plain,
( ( ! [Z: int] :
( ~ ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z ) @ zero_zero_int )
| ( ord_less_int @ Z @ zero_zero_int ) )
& ! [Z: int] :
( ~ ( ord_less_int @ Z @ zero_zero_int )
| ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z ) @ zero_zero_int ) ) )
= $true ),
inference(copy,[status(thm)],[1651]) ).
thf(1916,plain,
( ( ! [X_20: int] :
( ~ ( ord_less_int @ ( number_number_of_int @ X_20 ) @ zero_zero_int )
| ( ord_less_int @ X_20 @ pls ) )
& ! [X_20: int] :
( ~ ( ord_less_int @ X_20 @ pls )
| ( ord_less_int @ ( number_number_of_int @ X_20 ) @ zero_zero_int ) ) )
= $true ),
inference(copy,[status(thm)],[1650]) ).
thf(1917,plain,
( ( ! [Y_12: int] :
( ~ ( ord_less_int @ zero_zero_int @ ( number_number_of_int @ Y_12 ) )
| ( ord_less_int @ pls @ Y_12 ) )
& ! [Y_12: int] :
( ~ ( ord_less_int @ pls @ Y_12 )
| ( ord_less_int @ zero_zero_int @ ( number_number_of_int @ Y_12 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1649]) ).
thf(1918,plain,
( ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
= ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(copy,[status(thm)],[1201]) ).
thf(1919,plain,
( ( ( plus_plus_int @ one_one_int @ one_one_int )
= ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(copy,[status(thm)],[1200]) ).
thf(1920,plain,
( ( ( plus_plus_int @ one_one_int @ one_one_int )
= ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(copy,[status(thm)],[1199]) ).
thf(1921,plain,
( ( ! [X_19: int] :
( ~ ( ord_less_int @ ( number_number_of_int @ X_19 ) @ one_one_int )
| ( ord_less_int @ X_19 @ ( bit1 @ pls ) ) )
& ! [X_19: int] :
( ~ ( ord_less_int @ X_19 @ ( bit1 @ pls ) )
| ( ord_less_int @ ( number_number_of_int @ X_19 ) @ one_one_int ) ) )
= $true ),
inference(copy,[status(thm)],[1648]) ).
thf(1922,plain,
( ( ! [Y_11: int] :
( ~ ( ord_less_int @ one_one_int @ ( number_number_of_int @ Y_11 ) )
| ( ord_less_int @ ( bit1 @ pls ) @ Y_11 ) )
& ! [Y_11: int] :
( ~ ( ord_less_int @ ( bit1 @ pls ) @ Y_11 )
| ( ord_less_int @ one_one_int @ ( number_number_of_int @ Y_11 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1647]) ).
thf(1923,plain,
( ( ! [A: int,B: int] :
( ( power_power_int @ ( plus_plus_int @ A @ B ) @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ B ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) @ A ) @ ( 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)],[1196]) ).
thf(1924,plain,
( ( ! [A: int,B: int] :
( ( power_power_int @ ( plus_plus_int @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1195]) ).
thf(1925,plain,
( ( ! [X: int] :
( ~ ( ord_less_eq_int @ zero_zero_int @ X )
| ~ ( ord_less_int @ X @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
| ( X = zero_zero_int )
| ( X = one_one_int ) ) )
= $true ),
inference(copy,[status(thm)],[1646]) ).
thf(1926,plain,
( ( ! [A: int] :
( ( times_times_int @ A @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( power_power_int @ A @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1193]) ).
thf(1927,plain,
( ( ! [X: int] : ( ord_less_eq_int @ X @ ( power_power_int @ X @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1192]) ).
thf(1928,plain,
( ( ! [R: int,Q: int,A: int] :
( ~ ( ord_less_int @ zero_zero_int @ A )
| ( A
!= ( plus_plus_int @ R @ ( times_times_int @ A @ Q ) ) )
| ~ ( ord_less_int @ R @ A )
| ( ord_less_eq_int @ one_one_int @ Q ) ) )
= $true ),
inference(copy,[status(thm)],[1645]) ).
thf(1929,plain,
( ( ! [R: int,Q: int,A: int] :
( ~ ( ord_less_int @ zero_zero_int @ A )
| ( A
!= ( plus_plus_int @ R @ ( times_times_int @ A @ Q ) ) )
| ~ ( ord_less_eq_int @ zero_zero_int @ R )
| ( ord_less_eq_int @ Q @ one_one_int ) ) )
= $true ),
inference(copy,[status(thm)],[1644]) ).
thf(1930,plain,
( ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(copy,[status(thm)],[1189]) ).
thf(1931,plain,
( ( ! [X_18: nat,N_35: nat] :
( ( power_power_nat @ X_18 @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ N_35 ) )
= ( times_times_nat @ ( power_power_nat @ X_18 @ N_35 ) @ ( power_power_nat @ X_18 @ N_35 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1188]) ).
thf(1932,plain,
( ( ! [X_18: int,N_35: nat] :
( ( power_power_int @ X_18 @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ N_35 ) )
= ( times_times_int @ ( power_power_int @ X_18 @ N_35 ) @ ( power_power_int @ X_18 @ N_35 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1187]) ).
thf(1933,plain,
( ( ! [A: int,N: nat,P: int] :
( ~ ( zprime @ P )
| ~ ( dvd_dvd_int @ P @ ( power_power_int @ A @ N ) )
| ( dvd_dvd_int @ P @ A ) ) )
= $true ),
inference(copy,[status(thm)],[1643]) ).
thf(1934,plain,
( ( ! [X_17: int,P_2: nat,Q_4: nat] :
( ( power_power_int @ ( power_power_int @ X_17 @ P_2 ) @ Q_4 )
= ( power_power_int @ X_17 @ ( times_times_nat @ P_2 @ Q_4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1185]) ).
thf(1935,plain,
( ( ! [X: int,Y: nat,Z: nat] :
( ( power_power_int @ ( power_power_int @ X @ Y ) @ Z )
= ( power_power_int @ X @ ( times_times_nat @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[1184]) ).
thf(1936,plain,
( ( ! [N: int,M: int] :
( ~ ( ord_less_int @ zero_zero_int @ M )
| ~ ( ord_less_int @ M @ N )
| ~ ( dvd_dvd_int @ N @ M ) ) )
= $true ),
inference(copy,[status(thm)],[1642]) ).
thf(1937,plain,
( ( ! [N: int,M: int] :
( ~ ( ord_less_eq_int @ zero_zero_int @ M )
| ~ ( ord_less_eq_int @ zero_zero_int @ N )
| ~ ( dvd_dvd_int @ M @ N )
| ~ ( dvd_dvd_int @ N @ M )
| ( M = N ) ) )
= $true ),
inference(copy,[status(thm)],[1641]) ).
thf(1938,plain,
( ( ! [K: int,M: int,N: int] :
( ~ ( dvd_dvd_int @ ( times_times_int @ K @ M ) @ ( times_times_int @ K @ N ) )
| ( K = zero_zero_int )
| ( dvd_dvd_int @ M @ N ) ) )
= $true ),
inference(copy,[status(thm)],[1640]) ).
thf(1939,plain,
( ( ! [K: int] :
( ! [N: int] :
( ! [M: int] :
~ ( dvd_dvd_int @ K @ ( plus_plus_int @ N @ ( times_times_int @ K @ M ) ) )
| ( dvd_dvd_int @ K @ N ) )
& ! [N: int] :
( ~ ( dvd_dvd_int @ K @ N )
| ! [M: int] : ( dvd_dvd_int @ K @ ( plus_plus_int @ N @ ( times_times_int @ K @ M ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1639]) ).
thf(1940,plain,
( ( ! [C: int,X: int,T: int] :
( ! [A: int,D: int] :
( ~ ( dvd_dvd_int @ A @ D )
| ~ ( dvd_dvd_int @ A @ ( plus_plus_int @ X @ T ) )
| ( dvd_dvd_int @ A @ ( plus_plus_int @ ( plus_plus_int @ X @ ( times_times_int @ C @ D ) ) @ T ) ) )
& ! [A: int,D: int] :
( ~ ( dvd_dvd_int @ A @ D )
| ~ ( dvd_dvd_int @ A @ ( plus_plus_int @ ( plus_plus_int @ X @ ( times_times_int @ C @ D ) ) @ T ) )
| ( dvd_dvd_int @ A @ ( plus_plus_int @ X @ T ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1638]) ).
thf(1941,plain,
( ( zprime @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(copy,[status(thm)],[1178]) ).
thf(1942,plain,
( ( ! [Z: int,N: int] :
( ~ ( dvd_dvd_int @ Z @ N )
| ~ ( ord_less_int @ zero_zero_int @ N )
| ( ord_less_eq_int @ Z @ N ) ) )
= $true ),
inference(copy,[status(thm)],[1637]) ).
thf(1943,plain,
( ( ! [V_4: int,V_5: int] :
( ~ ( ord_less_eq_int @ V_4 @ V_5 )
| ( ord_less_eq_nat @ ( number_number_of_nat @ V_4 ) @ ( number_number_of_nat @ V_5 ) ) )
& ! [V_4: int] :
( ~ ( ord_less_eq_int @ V_4 @ pls )
| ! [V_5: int] : ( ord_less_eq_nat @ ( number_number_of_nat @ V_4 ) @ ( number_number_of_nat @ V_5 ) ) )
& ! [V_4: int,V_5: int] :
( ~ ( ord_less_eq_nat @ ( number_number_of_nat @ V_4 ) @ ( number_number_of_nat @ V_5 ) )
| ( ord_less_eq_int @ V_4 @ V_5 )
| ( ord_less_eq_int @ V_4 @ pls ) ) )
= $true ),
inference(copy,[status(thm)],[1636]) ).
thf(1944,plain,
( ( ! [A_50: int,C_12: int] :
( ( plus_plus_int @ A_50 @ C_12 )
= ( plus_plus_int @ C_12 @ A_50 ) ) )
= $true ),
inference(copy,[status(thm)],[1175]) ).
thf(1945,plain,
( ( ! [A_49: int,C_11: int,D_6: int] :
( ( plus_plus_int @ A_49 @ ( plus_plus_int @ C_11 @ D_6 ) )
= ( plus_plus_int @ C_11 @ ( plus_plus_int @ A_49 @ D_6 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1174]) ).
thf(1946,plain,
( ( ! [A_48: int,C_10: int,D_5: int] :
( ( plus_plus_int @ A_48 @ ( plus_plus_int @ C_10 @ D_5 ) )
= ( plus_plus_int @ ( plus_plus_int @ A_48 @ C_10 ) @ D_5 ) ) )
= $true ),
inference(copy,[status(thm)],[1173]) ).
thf(1947,plain,
( ( ! [A_47: int,B_19: int,C_9: int] :
( ( plus_plus_int @ ( plus_plus_int @ A_47 @ B_19 ) @ C_9 )
= ( plus_plus_int @ A_47 @ ( plus_plus_int @ B_19 @ C_9 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1172]) ).
thf(1948,plain,
( ( ! [A_46: int,B_18: int,C_8: int] :
( ( plus_plus_int @ ( plus_plus_int @ A_46 @ B_18 ) @ C_8 )
= ( plus_plus_int @ ( plus_plus_int @ A_46 @ C_8 ) @ B_18 ) ) )
= $true ),
inference(copy,[status(thm)],[1171]) ).
thf(1949,plain,
( ( ! [A_45: int,B_17: int,C_7: int,D_4: int] :
( ( plus_plus_int @ ( plus_plus_int @ A_45 @ B_17 ) @ ( plus_plus_int @ C_7 @ D_4 ) )
= ( plus_plus_int @ ( plus_plus_int @ A_45 @ C_7 ) @ ( plus_plus_int @ B_17 @ D_4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1170]) ).
thf(1950,plain,
( ( ! [X_16: int] :
( ( power_power_int @ X_16 @ one_one_nat )
= X_16 ) )
= $true ),
inference(copy,[status(thm)],[1169]) ).
thf(1951,plain,
( ( ! [Z: nat] :
( ( times_times_nat @ Z @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_nat @ Z @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[1168]) ).
thf(1952,plain,
( ( ! [Z: nat] :
( ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ Z )
= ( plus_plus_nat @ Z @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[1167]) ).
thf(1953,plain,
( ( ! [A_44: real,N_34: nat] :
( ( power_power_real @ A_44 @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ N_34 ) )
= ( power_power_real @ ( power_power_real @ A_44 @ N_34 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1166]) ).
thf(1954,plain,
( ( ! [A_44: nat,N_34: nat] :
( ( power_power_nat @ A_44 @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ N_34 ) )
= ( power_power_nat @ ( power_power_nat @ A_44 @ N_34 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1165]) ).
thf(1955,plain,
( ( ! [A_44: int,N_34: nat] :
( ( power_power_int @ A_44 @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ N_34 ) )
= ( power_power_int @ ( power_power_int @ A_44 @ N_34 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1164]) ).
thf(1956,plain,
( ( ! [A_43: int] :
( ! [K_2: nat] :
~ ( ord_less_eq_int @ ( power_power_int @ A_43 @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ K_2 ) ) @ zero_zero_int )
| ( A_43 = zero_zero_int ) ) )
= $true ),
inference(copy,[status(thm)],[1635]) ).
thf(1957,plain,
( ( ! [A_42: int] :
( ( times_times_int @ zero_zero_int @ A_42 )
= zero_zero_int ) )
= $true ),
inference(copy,[status(thm)],[1162]) ).
thf(1958,plain,
( ( ! [A_41: int] :
( ( times_times_int @ A_41 @ zero_zero_int )
= zero_zero_int ) )
= $true ),
inference(copy,[status(thm)],[1161]) ).
thf(1959,plain,
( ( ! [A_40: int] :
( ( plus_plus_int @ zero_zero_int @ A_40 )
= A_40 ) )
= $true ),
inference(copy,[status(thm)],[1160]) ).
thf(1960,plain,
( ( ! [A_39: int] :
( ( plus_plus_int @ A_39 @ zero_zero_int )
= A_39 ) )
= $true ),
inference(copy,[status(thm)],[1159]) ).
thf(1961,plain,
( ( ! [B_16: int,A_38: int] :
( ( B_16
!= ( plus_plus_int @ B_16 @ A_38 ) )
| ( A_38 = zero_zero_int ) )
& ! [B_16: int,A_38: int] :
( ( A_38 != zero_zero_int )
| ( B_16
= ( plus_plus_int @ B_16 @ A_38 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1634]) ).
thf(1962,plain,
( ( ! [X_15: int,Y_10: int,Z_2: int] :
( ( times_times_int @ X_15 @ ( plus_plus_int @ Y_10 @ Z_2 ) )
= ( plus_plus_int @ ( times_times_int @ X_15 @ Y_10 ) @ ( times_times_int @ X_15 @ Z_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1157]) ).
thf(1963,plain,
( ( ! [C_6: int,D_3: int] :
( ! [A_37: int,B_15: int] :
( ( ( plus_plus_int @ ( times_times_int @ A_37 @ C_6 ) @ ( times_times_int @ B_15 @ D_3 ) )
= ( plus_plus_int @ ( times_times_int @ A_37 @ D_3 ) @ ( times_times_int @ B_15 @ C_6 ) ) )
| ( A_37 != B_15 ) )
& ( ! [A_37: int,B_15: int] :
( ( plus_plus_int @ ( times_times_int @ A_37 @ C_6 ) @ ( times_times_int @ B_15 @ D_3 ) )
= ( plus_plus_int @ ( times_times_int @ A_37 @ D_3 ) @ ( times_times_int @ B_15 @ C_6 ) ) )
| ( C_6 != D_3 ) )
& ! [A_37: int,B_15: int] :
( ( A_37 = B_15 )
| ( C_6 = D_3 )
| ( ( plus_plus_int @ ( times_times_int @ A_37 @ C_6 ) @ ( times_times_int @ B_15 @ D_3 ) )
!= ( plus_plus_int @ ( times_times_int @ A_37 @ D_3 ) @ ( times_times_int @ B_15 @ C_6 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1633]) ).
thf(1964,plain,
( ( ! [A_36: int,B_14: int,C_5: int] :
( ( times_times_int @ ( plus_plus_int @ A_36 @ B_14 ) @ C_5 )
= ( plus_plus_int @ ( times_times_int @ A_36 @ C_5 ) @ ( times_times_int @ B_14 @ C_5 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1155]) ).
thf(1965,plain,
( ( ! [A_35: int,M_13: int,B_13: int] :
( ( plus_plus_int @ ( times_times_int @ A_35 @ M_13 ) @ ( times_times_int @ B_13 @ M_13 ) )
= ( times_times_int @ ( plus_plus_int @ A_35 @ B_13 ) @ M_13 ) ) )
= $true ),
inference(copy,[status(thm)],[1154]) ).
thf(1966,plain,
( ( ! [W_5: int,Y_9: int] :
( ! [X_14: int,Z_1: int] :
( ( ( plus_plus_int @ ( times_times_int @ W_5 @ Y_9 ) @ ( times_times_int @ X_14 @ Z_1 ) )
!= ( plus_plus_int @ ( times_times_int @ W_5 @ Z_1 ) @ ( times_times_int @ X_14 @ Y_9 ) ) )
| ( W_5 = X_14 )
| ( Y_9 = Z_1 ) )
& ! [X_14: int] :
( ( W_5 != X_14 )
| ! [Z_1: int] :
( ( plus_plus_int @ ( times_times_int @ W_5 @ Y_9 ) @ ( times_times_int @ X_14 @ Z_1 ) )
= ( plus_plus_int @ ( times_times_int @ W_5 @ Z_1 ) @ ( times_times_int @ X_14 @ Y_9 ) ) ) )
& ! [X_14: int,Z_1: int] :
( ( Y_9 != Z_1 )
| ( ( plus_plus_int @ ( times_times_int @ W_5 @ Y_9 ) @ ( times_times_int @ X_14 @ Z_1 ) )
= ( plus_plus_int @ ( times_times_int @ W_5 @ Z_1 ) @ ( times_times_int @ X_14 @ Y_9 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1632]) ).
thf(1967,plain,
( ( ! [A_34: int] :
( ( times_times_int @ one_one_int @ A_34 )
= A_34 ) )
= $true ),
inference(copy,[status(thm)],[1152]) ).
thf(1968,plain,
( ( ! [A_33: int] :
( ( times_times_int @ A_33 @ one_one_int )
= A_33 ) )
= $true ),
inference(copy,[status(thm)],[1151]) ).
thf(1969,plain,
( ( ! [X_13: int,Y_8: int,Q_3: nat] :
( ( power_power_int @ ( times_times_int @ X_13 @ Y_8 ) @ Q_3 )
= ( times_times_int @ ( power_power_int @ X_13 @ Q_3 ) @ ( power_power_int @ Y_8 @ Q_3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1150]) ).
thf(1970,plain,
( ( ! [X_12: int,P_1: nat,Q_2: nat] :
( ( times_times_int @ ( power_power_int @ X_12 @ P_1 ) @ ( power_power_int @ X_12 @ Q_2 ) )
= ( power_power_int @ X_12 @ ( plus_plus_nat @ P_1 @ Q_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1149]) ).
thf(1971,plain,
( ( ! [X_11: int] :
( ( power_power_int @ X_11 @ zero_zero_nat )
= one_one_int ) )
= $true ),
inference(copy,[status(thm)],[1148]) ).
thf(1972,plain,
( ( ord_less_eq_int @ zero_zero_int @ zero_zero_int )
= $true ),
inference(copy,[status(thm)],[1147]) ).
thf(1973,plain,
( ( ! [A_32: int,N_33: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A_32 @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ N_33 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1146]) ).
thf(1974,plain,
( ( ! [C_4: int,D_2: int,A_31: int,B_12: int,R_2: int] :
( ( R_2 = zero_zero_int )
| ( C_4 = D_2 )
| ( A_31 != B_12 )
| ( ( plus_plus_int @ A_31 @ ( times_times_int @ R_2 @ C_4 ) )
!= ( plus_plus_int @ B_12 @ ( times_times_int @ R_2 @ D_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1631]) ).
thf(1975,plain,
( ( ! [M_12: int] :
( ( plus_plus_int @ M_12 @ M_12 )
= ( times_times_int @ ( plus_plus_int @ one_one_int @ one_one_int ) @ M_12 ) ) )
= $true ),
inference(copy,[status(thm)],[1144]) ).
thf(1976,plain,
( ( ! [M_11: int,A_30: int] :
( ( plus_plus_int @ M_11 @ ( times_times_int @ A_30 @ M_11 ) )
= ( times_times_int @ ( plus_plus_int @ A_30 @ one_one_int ) @ M_11 ) ) )
= $true ),
inference(copy,[status(thm)],[1143]) ).
thf(1977,plain,
( ( ! [A_29: int,M_10: int] :
( ( plus_plus_int @ ( times_times_int @ A_29 @ M_10 ) @ M_10 )
= ( times_times_int @ ( plus_plus_int @ A_29 @ one_one_int ) @ M_10 ) ) )
= $true ),
inference(copy,[status(thm)],[1142]) ).
thf(1978,plain,
( ( ! [A_28: nat,W_4: int] :
( ( ( number_number_of_nat @ W_4 )
= zero_zero_nat )
| ( A_28 != zero_zero_nat )
| ( ( power_power_nat @ A_28 @ ( number_number_of_nat @ W_4 ) )
= zero_zero_nat ) )
& ! [A_28: nat,W_4: int] :
( ( ( power_power_nat @ A_28 @ ( number_number_of_nat @ W_4 ) )
!= zero_zero_nat )
| ( ( number_number_of_nat @ W_4 )
!= zero_zero_nat ) )
& ! [A_28: nat] :
( ! [W_4: int] :
( ( power_power_nat @ A_28 @ ( number_number_of_nat @ W_4 ) )
!= zero_zero_nat )
| ( A_28 = zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1630]) ).
thf(1979,plain,
( ( ! [A_28: int,W_4: int] :
( ( ( number_number_of_nat @ W_4 )
= zero_zero_nat )
| ( A_28 != zero_zero_int )
| ( ( power_power_int @ A_28 @ ( number_number_of_nat @ W_4 ) )
= zero_zero_int ) )
& ! [A_28: int,W_4: int] :
( ( ( power_power_int @ A_28 @ ( number_number_of_nat @ W_4 ) )
!= zero_zero_int )
| ( ( number_number_of_nat @ W_4 )
!= zero_zero_nat ) )
& ! [A_28: int] :
( ! [W_4: int] :
( ( power_power_int @ A_28 @ ( number_number_of_nat @ W_4 ) )
!= zero_zero_int )
| ( A_28 = zero_zero_int ) ) )
= $true ),
inference(copy,[status(thm)],[1629]) ).
thf(1980,plain,
( ( ! [B: int,A: int] :
( ~ ( ord_less_int @ zero_zero_int @ A )
| ~ ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
| ( ord_less_int @ zero_zero_int @ B ) ) )
= $true ),
inference(copy,[status(thm)],[1628]) ).
thf(1981,plain,
( ( ord_less_eq_int @ zero_zero_int @ one_one_int )
= $true ),
inference(copy,[status(thm)],[1138]) ).
thf(1982,plain,
( ( ! [Y: int,X: int] :
( ~ ( ord_less_eq_int @ zero_zero_int @ X )
| ~ ( ord_less_eq_int @ zero_zero_int @ Y )
| ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[1627]) ).
thf(1983,plain,
( ( ! [Y: int,X: int] :
( ~ ( ord_less_eq_int @ zero_zero_int @ X )
| ~ ( ord_less_eq_int @ zero_zero_int @ Y )
| ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[1626]) ).
thf(1984,plain,
( ( ! [N: nat,X: int] :
( ~ ( ord_less_eq_int @ zero_zero_int @ X )
| ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ X @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[1625]) ).
thf(1985,plain,
( ( ! [W_3: int] :
( ( ( number_number_of_nat @ W_3 )
!= zero_zero_nat )
| ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ W_3 ) )
= one_one_int ) )
& ! [W_3: int] :
( ( ( number_number_of_nat @ W_3 )
= zero_zero_nat )
| ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ W_3 ) )
= zero_zero_int ) ) )
= $true ),
inference(copy,[status(thm)],[1624]) ).
thf(1986,plain,
( ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(copy,[status(thm)],[1133]) ).
thf(1987,plain,
( ( ! [B_11: int,Q_1: int,R_1: int] :
( ~ ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B_11 @ Q_1 ) @ R_1 ) )
| ~ ( ord_less_int @ R_1 @ B_11 )
| ~ ( ord_less_int @ zero_zero_int @ B_11 )
| ( ord_less_eq_int @ zero_zero_int @ Q_1 ) ) )
= $true ),
inference(copy,[status(thm)],[1623]) ).
thf(1988,plain,
( ( ! [B_11: int,Q_1: int,R_1: int] :
( ~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ B_11 @ Q_1 ) @ R_1 ) @ zero_zero_int )
| ~ ( ord_less_eq_int @ zero_zero_int @ R_1 )
| ~ ( ord_less_int @ zero_zero_int @ B_11 )
| ( ord_less_eq_int @ Q_1 @ zero_zero_int ) ) )
= $true ),
inference(copy,[status(thm)],[1622]) ).
thf(1989,plain,
( ( ! [B: int,Q_1: int,R_1: int,Q: int,R: int] :
( ~ ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q_1 ) @ R_1 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q ) @ R ) )
| ~ ( ord_less_eq_int @ zero_zero_int @ R_1 )
| ~ ( ord_less_int @ R_1 @ B )
| ~ ( ord_less_int @ R @ B )
| ( ord_less_eq_int @ Q_1 @ Q ) ) )
= $true ),
inference(copy,[status(thm)],[1621]) ).
thf(1990,plain,
( ( ! [B: int,Q: int,R: int,B_11: int,Q_1: int,R_1: int] :
( ( ( plus_plus_int @ ( times_times_int @ B @ Q ) @ R )
!= ( plus_plus_int @ ( times_times_int @ B_11 @ Q_1 ) @ R_1 ) )
| ~ ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B_11 @ Q_1 ) @ R_1 ) )
| ~ ( ord_less_int @ R_1 @ B_11 )
| ~ ( ord_less_eq_int @ zero_zero_int @ R )
| ~ ( ord_less_int @ zero_zero_int @ B_11 )
| ~ ( ord_less_eq_int @ B_11 @ B )
| ( ord_less_eq_int @ Q @ Q_1 ) ) )
= $true ),
inference(copy,[status(thm)],[1620]) ).
thf(1991,plain,
( ( ! [B: int,Q_1: int,R_1: int,Q: int,R: int] :
( ~ ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q_1 ) @ R_1 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q ) @ R ) )
| ~ ( ord_less_eq_int @ R @ zero_zero_int )
| ~ ( ord_less_int @ B @ R )
| ~ ( ord_less_int @ B @ R_1 )
| ( ord_less_eq_int @ Q @ Q_1 ) ) )
= $true ),
inference(copy,[status(thm)],[1619]) ).
thf(1992,plain,
( ( ! [B: int,Q: int,R: int,B_11: int,Q_1: int,R_1: int] :
( ( ( plus_plus_int @ ( times_times_int @ B @ Q ) @ R )
!= ( plus_plus_int @ ( times_times_int @ B_11 @ Q_1 ) @ R_1 ) )
| ~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ B_11 @ Q_1 ) @ R_1 ) @ zero_zero_int )
| ~ ( ord_less_int @ R @ B )
| ~ ( ord_less_eq_int @ zero_zero_int @ R_1 )
| ~ ( ord_less_int @ zero_zero_int @ B_11 )
| ~ ( ord_less_eq_int @ B_11 @ B )
| ( ord_less_eq_int @ Q_1 @ Q ) ) )
= $true ),
inference(copy,[status(thm)],[1618]) ).
thf(1993,plain,
( ( ! [X: int] :
( ( power_power_int @ ( power_power_int @ X @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power_int @ X @ ( number_number_of_nat @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1126]) ).
thf(1994,plain,
( ( ! [X_10: real] :
( ( times_times_real @ X_10 @ X_10 )
= ( power_power_real @ X_10 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1125]) ).
thf(1995,plain,
( ( ! [X_10: nat] :
( ( times_times_nat @ X_10 @ X_10 )
= ( power_power_nat @ X_10 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1124]) ).
thf(1996,plain,
( ( ! [X_10: int] :
( ( times_times_int @ X_10 @ X_10 )
= ( power_power_int @ X_10 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1123]) ).
thf(1997,plain,
( ( ! [Y: int,X: int,P: int] :
( ( zcong @ X @ zero_zero_int @ P )
| ~ ( zcong @ ( power_power_int @ Y @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ X @ P )
| ~ ( dvd_dvd_int @ P @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[1617]) ).
thf(1998,plain,
( ( ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(copy,[status(thm)],[1121]) ).
thf(1999,plain,
( ( ( bit1 @ min )
= min )
= $true ),
inference(copy,[status(thm)],[1120]) ).
thf(2000,plain,
( ( ! [L: int] :
( ( min
!= ( bit1 @ L ) )
| ( min = L ) )
& ! [L: int] :
( ( min != L )
| ( min
= ( bit1 @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[1616]) ).
thf(2001,plain,
( ( ! [K: int] :
( ( ( bit1 @ K )
!= min )
| ( K = min ) )
& ! [K: int] :
( ( K != min )
| ( ( bit1 @ K )
= min ) ) )
= $true ),
inference(copy,[status(thm)],[1615]) ).
thf(2002,plain,
( ( min != pls )
= $true ),
inference(copy,[status(thm)],[1614]) ).
thf(2003,plain,
( ( pls != min )
= $true ),
inference(copy,[status(thm)],[1613]) ).
thf(2004,plain,
( ( ! [L: int] :
( min
!= ( bit0 @ L ) ) )
= $true ),
inference(copy,[status(thm)],[1612]) ).
thf(2005,plain,
( ( ! [K: int] :
( ( bit0 @ K )
!= min ) )
= $true ),
inference(copy,[status(thm)],[1611]) ).
thf(2006,plain,
( ( ~ ( ord_less_int @ min @ min ) )
= $true ),
inference(copy,[status(thm)],[1113]) ).
thf(2007,plain,
( ( ! [K: int] :
( ~ ( ord_less_int @ ( bit1 @ K ) @ min )
| ( ord_less_int @ K @ min ) )
& ! [K: int] :
( ~ ( ord_less_int @ K @ min )
| ( ord_less_int @ ( bit1 @ K ) @ min ) ) )
= $true ),
inference(copy,[status(thm)],[1610]) ).
thf(2008,plain,
( ( ! [K: int] :
( ~ ( ord_less_int @ min @ ( bit1 @ K ) )
| ( ord_less_int @ min @ K ) )
& ! [K: int] :
( ~ ( ord_less_int @ min @ K )
| ( ord_less_int @ min @ ( bit1 @ K ) ) ) )
= $true ),
inference(copy,[status(thm)],[1609]) ).
thf(2009,plain,
( ( ~ ( ord_less_int @ pls @ min ) )
= $true ),
inference(copy,[status(thm)],[1110]) ).
thf(2010,plain,
( ( ord_less_int @ min @ pls )
= $true ),
inference(copy,[status(thm)],[1109]) ).
thf(2011,plain,
( ( ! [K: int] :
( ~ ( ord_less_int @ min @ ( bit0 @ K ) )
| ( ord_less_int @ min @ K ) )
& ! [K: int] :
( ~ ( ord_less_int @ min @ K )
| ( ord_less_int @ min @ ( bit0 @ K ) ) ) )
= $true ),
inference(copy,[status(thm)],[1608]) ).
thf(2012,plain,
( ( ord_less_int @ min @ zero_zero_int )
= $true ),
inference(copy,[status(thm)],[1107]) ).
thf(2013,plain,
( ( ! [K: int] :
( ~ ( ord_less_eq_int @ min @ ( bit1 @ K ) )
| ( ord_less_eq_int @ min @ K ) )
& ! [K: int] :
( ~ ( ord_less_eq_int @ min @ K )
| ( ord_less_eq_int @ min @ ( bit1 @ K ) ) ) )
= $true ),
inference(copy,[status(thm)],[1607]) ).
thf(2014,plain,
( ( ! [K: int] :
( ~ ( ord_less_eq_int @ ( bit1 @ K ) @ min )
| ( ord_less_eq_int @ K @ min ) )
& ! [K: int] :
( ~ ( ord_less_eq_int @ K @ min )
| ( ord_less_eq_int @ ( bit1 @ K ) @ min ) ) )
= $true ),
inference(copy,[status(thm)],[1606]) ).
thf(2015,plain,
( ( ord_less_eq_int @ min @ pls )
= $true ),
inference(copy,[status(thm)],[1104]) ).
thf(2016,plain,
( ( ~ ( ord_less_eq_int @ pls @ min ) )
= $true ),
inference(copy,[status(thm)],[1103]) ).
thf(2017,plain,
( ( ! [K: int] :
( ~ ( ord_less_eq_int @ ( bit0 @ K ) @ min )
| ( ord_less_eq_int @ K @ min ) )
& ! [K: int] :
( ~ ( ord_less_eq_int @ K @ min )
| ( ord_less_eq_int @ ( bit0 @ K ) @ min ) ) )
= $true ),
inference(copy,[status(thm)],[1605]) ).
thf(2018,plain,
( ( ( number_number_of_int @ pls )
!= ( number_number_of_int @ min ) )
= $true ),
inference(copy,[status(thm)],[1604]) ).
thf(2019,plain,
( ( ! [K: int] :
( ~ ( ord_less_eq_int @ K @ min )
| ( ord_less_int @ ( bit0 @ K ) @ min ) )
& ! [K: int] :
( ~ ( ord_less_int @ ( bit0 @ K ) @ min )
| ( ord_less_eq_int @ K @ min ) ) )
= $true ),
inference(copy,[status(thm)],[1603]) ).
thf(2020,plain,
( ( ! [K: int] :
( ~ ( ord_less_eq_int @ min @ ( bit0 @ K ) )
| ( ord_less_int @ min @ K ) )
& ! [K: int] :
( ~ ( ord_less_int @ min @ K )
| ( ord_less_eq_int @ min @ ( bit0 @ K ) ) ) )
= $true ),
inference(copy,[status(thm)],[1602]) ).
thf(2021,plain,
( ( ! [X_9: int,Y_7: int] :
( ~ ( ord_less_eq_int @ X_9 @ Y_7 )
| ( X_9 = Y_7 )
| ( ord_less_int @ X_9 @ Y_7 ) ) )
= $true ),
inference(copy,[status(thm)],[1601]) ).
thf(2022,plain,
( ( ! [B: int,A: int,C: int] :
( ~ ( ord_less_int @ A @ C )
| ~ ( ord_less_int @ B @ C )
| ( ord_less_eq_int @ A @ B )
| ( ord_less_eq_int @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[1600]) ).
thf(2023,plain,
( ( ! [A: int,B: int] :
( ( A != B )
| ( zcong @ A @ B @ zero_zero_int ) )
& ! [A: int,B: int] :
( ~ ( zcong @ A @ B @ zero_zero_int )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[1599]) ).
thf(2024,plain,
( ( ! [A: int,B: int] : ( zcong @ A @ B @ one_one_int ) )
= $true ),
inference(copy,[status(thm)],[1095]) ).
thf(2025,plain,
( ( ! [C: int,D: int,A: int,B: int,M: int] :
( ~ ( zcong @ A @ B @ M )
| ~ ( zcong @ C @ D @ M )
| ( zcong @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) @ M ) ) )
= $true ),
inference(copy,[status(thm)],[1598]) ).
thf(2026,plain,
( ( ! [B: int,M: int,A: int] :
( ~ ( ord_less_int @ zero_zero_int @ A )
| ~ ( ord_less_int @ A @ M )
| ~ ( ord_less_int @ zero_zero_int @ B )
| ~ ( ord_less_int @ B @ A )
| ~ ( zcong @ A @ B @ M ) ) )
= $true ),
inference(copy,[status(thm)],[1597]) ).
thf(2027,plain,
( ( ! [A: int] :
( ! [B: int,M: int] :
( ! [K_1: int] :
( B
!= ( plus_plus_int @ A @ ( times_times_int @ M @ K_1 ) ) )
| ( zcong @ A @ B @ M ) )
& ! [B: int,M: int] :
( ~ ( zcong @ A @ B @ M )
| ( B
= ( plus_plus_int @ A @ ( times_times_int @ M @ ( sK6_K_1 @ M @ B @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1596]) ).
thf(2028,plain,
( ( ! [M: int,A: int] :
( ~ ( ord_less_eq_int @ zero_zero_int @ A )
| ~ ( ord_less_int @ A @ M )
| ~ ( zcong @ A @ zero_zero_int @ M )
| ( A = zero_zero_int ) ) )
= $true ),
inference(copy,[status(thm)],[1595]) ).
thf(2029,plain,
( ( ! [B: int,M: int,A: int] :
( ~ ( ord_less_eq_int @ zero_zero_int @ A )
| ~ ( ord_less_int @ A @ M )
| ~ ( ord_less_eq_int @ zero_zero_int @ B )
| ~ ( ord_less_int @ B @ M )
| ~ ( zcong @ A @ B @ M )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[1594]) ).
thf(2030,plain,
( ( ! [Z: nat,X: int,Y: nat,P: int] :
( ~ ( zcong @ ( power_power_int @ X @ Y ) @ one_one_int @ P )
| ( zcong @ ( power_power_int @ X @ ( times_times_nat @ Y @ Z ) ) @ one_one_int @ P ) ) )
= $true ),
inference(copy,[status(thm)],[1593]) ).
thf(2031,plain,
( ( ! [K: int,L: int] :
( ( minus_minus_int @ ( bit0 @ K ) @ ( bit0 @ L ) )
= ( bit0 @ ( minus_minus_int @ K @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[1088]) ).
thf(2032,plain,
( ( ! [K: int] :
( ( minus_minus_int @ K @ pls )
= K ) )
= $true ),
inference(copy,[status(thm)],[1087]) ).
thf(2033,plain,
( ( ! [A: int,B: int,C: int] :
( ( ( minus_minus_int @ A @ B )
!= C )
| ( A
= ( plus_plus_int @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[1592]) ).
thf(2034,plain,
( ( ! [K: int,L: int] :
( ( minus_minus_int @ ( bit1 @ K ) @ ( bit0 @ L ) )
= ( bit1 @ ( minus_minus_int @ K @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[1085]) ).
thf(2035,plain,
( ( ! [K: int,L: int] :
( ( minus_minus_int @ ( bit1 @ K ) @ ( bit1 @ L ) )
= ( bit0 @ ( minus_minus_int @ K @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[1084]) ).
thf(2036,plain,
( ( ! [L: int] :
( ( minus_minus_int @ pls @ ( bit0 @ L ) )
= ( bit0 @ ( minus_minus_int @ pls @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[1083]) ).
thf(2037,plain,
( ( ! [K: int,L: int] :
( ~ ( ord_less_int @ K @ L )
| ( ord_less_int @ ( minus_minus_int @ K @ L ) @ zero_zero_int ) )
& ! [K: int,L: int] :
( ~ ( ord_less_int @ ( minus_minus_int @ K @ L ) @ zero_zero_int )
| ( ord_less_int @ K @ L ) ) )
= $true ),
inference(copy,[status(thm)],[1591]) ).
thf(2038,plain,
( ( ! [A: int,R: int,B: int,M: int,C: int,D: int,N: int] :
( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ ( times_times_int @ R @ B ) ) @ M ) @ ( times_times_int @ ( minus_minus_int @ C @ ( times_times_int @ R @ D ) ) @ N ) )
= ( minus_minus_int @ ( plus_plus_int @ ( times_times_int @ A @ M ) @ ( times_times_int @ C @ N ) ) @ ( times_times_int @ R @ ( plus_plus_int @ ( times_times_int @ B @ M ) @ ( times_times_int @ D @ N ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1081]) ).
thf(2039,plain,
( ( ! [V: int,W_1: int,C_2: int] :
( ( plus_plus_int @ ( number_number_of_int @ V ) @ ( minus_minus_int @ ( number_number_of_int @ W_1 ) @ C_2 ) )
= ( minus_minus_int @ ( number_number_of_int @ ( plus_plus_int @ V @ W_1 ) ) @ C_2 ) ) )
= $true ),
inference(copy,[status(thm)],[1080]) ).
thf(2040,plain,
( ( ! [A: int,X: int] :
( ~ ( ord_less_int @ zero_zero_int @ X )
| ~ ( ord_less_int @ X @ A )
| ( X
= ( minus_minus_int @ A @ one_one_int ) )
| ( ord_less_int @ X @ ( minus_minus_int @ A @ one_one_int ) ) ) )
= $true ),
inference(copy,[status(thm)],[1590]) ).
thf(2041,plain,
( ( ! [W: int,Z: int] :
( ~ ( ord_less_eq_int @ W @ ( minus_minus_int @ Z @ one_one_int ) )
| ( ord_less_int @ W @ Z ) )
& ! [W: int,Z: int] :
( ~ ( ord_less_int @ W @ Z )
| ( ord_less_eq_int @ W @ ( minus_minus_int @ Z @ one_one_int ) ) ) )
= $true ),
inference(copy,[status(thm)],[1589]) ).
thf(2042,plain,
( ( ! [L: int] :
( ( minus_minus_int @ pls @ ( bit1 @ L ) )
= ( bit1 @ ( minus_minus_int @ min @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[1077]) ).
thf(2043,plain,
( ( ! [L: int] :
( ( minus_minus_int @ min @ ( bit1 @ L ) )
= ( bit0 @ ( minus_minus_int @ min @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[1076]) ).
thf(2044,plain,
( ( ! [L: int] :
( ( minus_minus_int @ min @ ( bit0 @ L ) )
= ( bit1 @ ( minus_minus_int @ min @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[1075]) ).
thf(2045,plain,
( ( ! [A: int,B: int] :
( ( times_times_int @ ( plus_plus_int @ A @ B ) @ ( minus_minus_int @ A @ B ) )
= ( minus_minus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1074]) ).
thf(2046,plain,
( ( ! [M: int] : ( zcong @ M @ zero_zero_int @ M ) )
= $true ),
inference(copy,[status(thm)],[1073]) ).
thf(2047,plain,
( ( ! [C: int,A: int,B: int,M: int] :
( ~ ( zcong @ A @ B @ M )
| ( zcong @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) @ M ) ) )
= $true ),
inference(copy,[status(thm)],[1588]) ).
thf(2048,plain,
( ( ! [Z: nat,X: int,Y: int,M: int] :
( ~ ( zcong @ X @ Y @ M )
| ( zcong @ ( power_power_int @ X @ Z ) @ ( power_power_int @ Y @ Z ) @ M ) ) )
= $true ),
inference(copy,[status(thm)],[1587]) ).
thf(2049,plain,
( ( ! [M: int,Y: int,X: int] :
( ~ ( ord_less_int @ zero_zero_int @ X )
| ~ ( ord_less_int @ zero_zero_int @ Y )
| ~ ( ord_less_int @ zero_zero_int @ M )
| ~ ( zcong @ X @ Y @ M )
| ~ ( ord_less_int @ X @ M )
| ~ ( ord_less_int @ Y @ M )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[1586]) ).
thf(2050,plain,
( ( ! [M: int,X: int] :
( ~ ( ord_less_int @ zero_zero_int @ X )
| ~ ( ord_less_int @ X @ M )
| ~ ( zcong @ X @ zero_zero_int @ M ) ) )
= $true ),
inference(copy,[status(thm)],[1585]) ).
thf(2051,plain,
( ( ! [N: int,M: int] :
( ~ ( dvd_dvd_int @ N @ M )
| ( ord_less_eq_int @ M @ zero_zero_int )
| ( ord_less_eq_int @ N @ M ) ) )
= $true ),
inference(copy,[status(thm)],[1584]) ).
thf(2052,plain,
( ( ! [A: int,M: int] :
( ~ ( dvd_dvd_int @ M @ A )
| ( zcong @ A @ zero_zero_int @ M ) )
& ! [A: int,M: int] :
( ~ ( zcong @ A @ zero_zero_int @ M )
| ( dvd_dvd_int @ M @ A ) ) )
= $true ),
inference(copy,[status(thm)],[1583]) ).
thf(2053,plain,
( ( ! [X: int,P: int] :
( ~ ( dvd_dvd_int @ P @ X )
| ( zcong @ X @ zero_zero_int @ P ) )
& ! [X: int,P: int] :
( ~ ( zcong @ X @ zero_zero_int @ P )
| ( dvd_dvd_int @ P @ X ) ) )
= $true ),
inference(copy,[status(thm)],[1582]) ).
thf(2054,plain,
( ( ! [M: int,X: int] :
( ~ ( ord_less_eq_int @ zero_zero_int @ X )
| ~ ( ord_less_int @ X @ M )
| ~ ( zcong @ X @ zero_zero_int @ M )
| ( X = zero_zero_int ) ) )
= $true ),
inference(copy,[status(thm)],[1581]) ).
thf(2055,plain,
( ( ! [N: nat] :
( ( ( 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)],[1064]) ).
thf(2056,plain,
( ( ! [M: int,X: int] :
( ! [Y_1: int] :
~ ( zcong @ ( power_power_int @ Y_1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ X @ M )
| ( quadRes @ M @ X ) )
& ! [M: int,X: int] :
( ~ ( quadRes @ M @ X )
| ( zcong @ ( power_power_int @ ( sK5_Y_1 @ X @ M ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ X @ M ) ) )
= $true ),
inference(copy,[status(thm)],[1580]) ).
thf(2057,plain,
( ( ! [A_26: int,C_1: int,B_8: int,D_1: int] :
( ( minus_minus_int @ ( plus_plus_int @ A_26 @ C_1 ) @ ( plus_plus_int @ B_8 @ D_1 ) )
= ( plus_plus_int @ ( minus_minus_int @ A_26 @ B_8 ) @ ( minus_minus_int @ C_1 @ D_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1062]) ).
thf(2058,plain,
( ( ! [X_7: int,Y_5: int,A_25: int,B_7: int] :
( ( minus_minus_int @ ( times_times_int @ X_7 @ Y_5 ) @ ( times_times_int @ A_25 @ B_7 ) )
= ( plus_plus_int @ ( times_times_int @ X_7 @ ( minus_minus_int @ Y_5 @ B_7 ) ) @ ( times_times_int @ ( minus_minus_int @ X_7 @ A_25 ) @ B_7 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1061]) ).
thf(2059,plain,
( ( ! [X_6: int] :
( ( minus_minus_int @ ( times_times_int @ X_6 @ X_6 ) @ one_one_int )
= ( times_times_int @ ( plus_plus_int @ X_6 @ one_one_int ) @ ( minus_minus_int @ X_6 @ one_one_int ) ) ) )
= $true ),
inference(copy,[status(thm)],[1060]) ).
thf(2060,plain,
( ( ! [N_28: nat,A_23: int] :
( ( A_23 = zero_zero_int )
| ( ( power_power_int @ A_23 @ N_28 )
!= zero_zero_int ) ) )
= $true ),
inference(copy,[status(thm)],[1579]) ).
thf(2061,plain,
( ( ! [A_22: int,B_5: int,N_27: nat] :
( ( power_power_int @ ( times_times_int @ A_22 @ B_5 ) @ N_27 )
= ( times_times_int @ ( power_power_int @ A_22 @ N_27 ) @ ( power_power_int @ B_5 @ N_27 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1058]) ).
thf(2062,plain,
( ( ! [A_21: int,N_26: nat] :
( ( times_times_int @ ( power_power_int @ A_21 @ N_26 ) @ A_21 )
= ( times_times_int @ A_21 @ ( power_power_int @ A_21 @ N_26 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1057]) ).
thf(2063,plain,
( ( ! [N_25: nat] :
( ( power_power_int @ one_one_int @ N_25 )
= one_one_int ) )
= $true ),
inference(copy,[status(thm)],[1056]) ).
thf(2064,plain,
( ( ! [N_24: nat,X_4: int,Y_4: int] :
( ~ ( dvd_dvd_int @ X_4 @ Y_4 )
| ( dvd_dvd_int @ ( power_power_int @ X_4 @ N_24 ) @ ( power_power_int @ Y_4 @ N_24 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1578]) ).
thf(2065,plain,
( ( ! [A_20: int,M_7: nat,N_23: nat] :
( ( power_power_int @ A_20 @ ( times_times_nat @ M_7 @ N_23 ) )
= ( power_power_int @ ( power_power_int @ A_20 @ M_7 ) @ N_23 ) ) )
= $true ),
inference(copy,[status(thm)],[1054]) ).
thf(2066,plain,
( ( ! [A_19: int] :
( ( power_power_int @ A_19 @ one_one_nat )
= A_19 ) )
= $true ),
inference(copy,[status(thm)],[1053]) ).
thf(2067,plain,
( ( ! [N_22: nat,A_18: int,B_4: int] :
( ~ ( ord_less_eq_int @ A_18 @ B_4 )
| ~ ( ord_less_eq_int @ zero_zero_int @ A_18 )
| ( ord_less_eq_int @ ( power_power_int @ A_18 @ N_22 ) @ ( power_power_int @ B_4 @ N_22 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1577]) ).
thf(2068,plain,
( ( ! [N_21: nat,A_17: int] :
( ~ ( ord_less_eq_int @ zero_zero_int @ A_17 )
| ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A_17 @ N_21 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1576]) ).
thf(2069,plain,
( ( ! [N_20: nat,A_16: int] :
( ~ ( ord_less_int @ zero_zero_int @ A_16 )
| ( ord_less_int @ zero_zero_int @ ( power_power_int @ A_16 @ N_20 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1575]) ).
thf(2070,plain,
( ( ! [N_19: nat,A_15: int] :
( ~ ( ord_less_eq_int @ one_one_int @ A_15 )
| ( ord_less_eq_int @ one_one_int @ ( power_power_int @ A_15 @ N_19 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1574]) ).
thf(2071,plain,
( ( ! [M_6: nat] :
( ! [N_18: nat,A_14: int] :
( ~ ( ord_less_int @ one_one_int @ A_14 )
| ( ( power_power_int @ A_14 @ M_6 )
!= ( power_power_int @ A_14 @ N_18 ) )
| ( M_6 = N_18 ) )
& ! [N_18: nat,A_14: int] :
( ~ ( ord_less_int @ one_one_int @ A_14 )
| ( M_6 != N_18 )
| ( ( power_power_int @ A_14 @ M_6 )
= ( power_power_int @ A_14 @ N_18 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1573]) ).
thf(2072,plain,
( ( ! [A_13: int,N_17: nat] :
( ( N_17 = zero_zero_nat )
| ( A_13 != zero_zero_int )
| ( ( power_power_int @ A_13 @ N_17 )
= zero_zero_int ) )
& ! [A_13: int,N_17: nat] :
( ( ( power_power_int @ A_13 @ N_17 )
!= zero_zero_int )
| ( N_17 != zero_zero_nat ) )
& ! [A_13: int] :
( ! [N_17: nat] :
( ( power_power_int @ A_13 @ N_17 )
!= zero_zero_int )
| ( A_13 = zero_zero_int ) ) )
= $true ),
inference(copy,[status(thm)],[1572]) ).
thf(2073,plain,
( ( ! [A_12: int] :
( ( power_power_int @ A_12 @ zero_zero_nat )
= one_one_int ) )
= $true ),
inference(copy,[status(thm)],[1046]) ).
thf(2074,plain,
( ( ! [A_11: int,M_5: nat,N_16: nat] :
( ( power_power_int @ A_11 @ ( plus_plus_nat @ M_5 @ N_16 ) )
= ( times_times_int @ ( power_power_int @ A_11 @ M_5 ) @ ( power_power_int @ A_11 @ N_16 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1045]) ).
thf(2075,plain,
( ( ! [M_4: nat,A_10: int,N_15: nat,B_3: int] :
( ~ ( dvd_dvd_int @ ( power_power_int @ A_10 @ N_15 ) @ B_3 )
| ~ ( ord_less_eq_nat @ M_4 @ N_15 )
| ( dvd_dvd_int @ ( power_power_int @ A_10 @ M_4 ) @ B_3 ) ) )
= $true ),
inference(copy,[status(thm)],[1571]) ).
thf(2076,plain,
( ( ! [N_14: nat,M_3: nat,X_3: int,Y_3: int] :
( ~ ( dvd_dvd_int @ X_3 @ Y_3 )
| ~ ( ord_less_eq_nat @ N_14 @ M_3 )
| ( dvd_dvd_int @ ( power_power_int @ X_3 @ N_14 ) @ ( power_power_int @ Y_3 @ M_3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1570]) ).
thf(2077,plain,
( ( ! [A_9: int,M_2: nat,N_13: nat] :
( ~ ( ord_less_eq_nat @ M_2 @ N_13 )
| ( dvd_dvd_int @ ( power_power_int @ A_9 @ M_2 ) @ ( power_power_int @ A_9 @ N_13 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1569]) ).
thf(2078,plain,
( ( ! [A_8: int,N_12: nat,B_2: int] :
( ~ ( ord_less_int @ ( power_power_int @ A_8 @ N_12 ) @ ( power_power_int @ B_2 @ N_12 ) )
| ~ ( ord_less_eq_int @ zero_zero_int @ B_2 )
| ( ord_less_int @ A_8 @ B_2 ) ) )
= $true ),
inference(copy,[status(thm)],[1568]) ).
thf(2079,plain,
( ( ! [N_11: nat,A_7: int] :
( ~ ( ord_less_int @ one_one_int @ A_7 )
| ( ord_less_int @ ( power_power_int @ A_7 @ N_11 ) @ ( times_times_int @ A_7 @ ( power_power_int @ A_7 @ N_11 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1567]) ).
thf(2080,plain,
( ( ! [N_10: nat,A_6: int] :
( ~ ( ord_less_int @ one_one_int @ A_6 )
| ( ord_less_int @ one_one_int @ ( times_times_int @ A_6 @ ( power_power_int @ A_6 @ N_10 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1566]) ).
thf(2081,plain,
( ( ! [N_9: nat] :
( ( N_9 != zero_zero_nat )
| ( ( power_power_int @ zero_zero_int @ N_9 )
= one_one_int ) )
& ! [N_9: nat] :
( ( N_9 = zero_zero_nat )
| ( ( power_power_int @ zero_zero_int @ N_9 )
= zero_zero_int ) ) )
= $true ),
inference(copy,[status(thm)],[1565]) ).
thf(2082,plain,
( ( ! [A_5: int,N_8: nat,N_7: nat] :
( ~ ( ord_less_nat @ N_8 @ N_7 )
| ~ ( ord_less_int @ one_one_int @ A_5 )
| ( ord_less_int @ ( power_power_int @ A_5 @ N_8 ) @ ( power_power_int @ A_5 @ N_7 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1564]) ).
thf(2083,plain,
( ( ! [M_1: nat,N_6: nat,A_4: int] :
( ~ ( ord_less_int @ one_one_int @ A_4 )
| ~ ( ord_less_int @ ( power_power_int @ A_4 @ M_1 ) @ ( power_power_int @ A_4 @ N_6 ) )
| ( ord_less_nat @ M_1 @ N_6 ) ) )
= $true ),
inference(copy,[status(thm)],[1563]) ).
thf(2084,plain,
( ( ! [X_2: nat] :
( ! [Y_2: nat,B_1: int] :
( ~ ( ord_less_int @ one_one_int @ B_1 )
| ~ ( ord_less_int @ ( power_power_int @ B_1 @ X_2 ) @ ( power_power_int @ B_1 @ Y_2 ) )
| ( ord_less_nat @ X_2 @ Y_2 ) )
& ! [Y_2: nat,B_1: int] :
( ~ ( ord_less_int @ one_one_int @ B_1 )
| ~ ( ord_less_nat @ X_2 @ Y_2 )
| ( ord_less_int @ ( power_power_int @ B_1 @ X_2 ) @ ( power_power_int @ B_1 @ Y_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1562]) ).
thf(2085,plain,
( ( ! [A_3: int,N_5: nat,N_4: nat] :
( ~ ( ord_less_eq_nat @ N_5 @ N_4 )
| ~ ( ord_less_eq_int @ one_one_int @ A_3 )
| ( ord_less_eq_int @ ( power_power_int @ A_3 @ N_5 ) @ ( power_power_int @ A_3 @ N_4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1561]) ).
thf(2086,plain,
( ( ! [N_3: nat,A_2: int] :
( ~ ( ord_less_int @ zero_zero_int @ A_2 )
| ~ ( ord_less_int @ A_2 @ one_one_int )
| ( ord_less_int @ ( times_times_int @ A_2 @ ( power_power_int @ A_2 @ N_3 ) ) @ ( power_power_int @ A_2 @ N_3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1560]) ).
thf(2087,plain,
( ( ! [A_1: int,N_2: nat,N_1: nat] :
( ~ ( ord_less_nat @ N_2 @ N_1 )
| ~ ( ord_less_int @ zero_zero_int @ A_1 )
| ~ ( ord_less_int @ A_1 @ one_one_int )
| ( ord_less_int @ ( power_power_int @ A_1 @ N_1 ) @ ( power_power_int @ A_1 @ N_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1559]) ).
thf(2088,plain,
( ( ord_less_int @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ t ) @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ zero_zero_int ) )
= $true ),
inference(copy,[status(thm)],[1031]) ).
thf(2089,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)],[1030]) ).
thf(2090,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)],[1029]) ).
thf(2091,plain,
( ( ! [X: real,Y: real] :
~ ( ord_less_real @ ( plus_plus_real @ ( power_power_real @ X @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_real ) )
= $true ),
inference(copy,[status(thm)],[1028]) ).
thf(2092,plain,
( ( ! [X_39: real,Y_30: real] :
( ~ ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X_39 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y_30 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
| ( X_39 != zero_zero_real )
| ( Y_30 != zero_zero_real ) )
& ! [X_39: real] :
( ( X_39 = zero_zero_real )
| ! [Y_30: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X_39 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y_30 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
& ! [X_39: real,Y_30: real] :
( ( Y_30 = zero_zero_real )
| ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X_39 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y_30 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1558]) ).
thf(2093,plain,
( ( ! [X_38: real,Y_29: real] :
( ( X_38 != zero_zero_real )
| ( Y_29 != zero_zero_real )
| ( ( plus_plus_real @ ( power_power_real @ X_38 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y_29 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_real ) )
& ! [X_38: real] :
( ! [Y_29: real] :
( ( plus_plus_real @ ( power_power_real @ X_38 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y_29 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_real )
| ( X_38 = zero_zero_real ) )
& ! [X_38: real,Y_29: real] :
( ( ( plus_plus_real @ ( power_power_real @ X_38 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y_29 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_real )
| ( Y_29 = zero_zero_real ) ) )
= $true ),
inference(copy,[status(thm)],[1557]) ).
thf(2094,plain,
( ( ! [A_64: real] :
~ ( ord_less_real @ ( power_power_real @ A_64 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ zero_zero_real ) )
= $true ),
inference(copy,[status(thm)],[1025]) ).
thf(2095,plain,
( ( ! [A_63: real] :
( ( A_63 = zero_zero_real )
| ( ord_less_real @ zero_zero_real @ ( power_power_real @ A_63 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
& ! [A_63: real] :
( ~ ( ord_less_real @ zero_zero_real @ ( power_power_real @ A_63 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ( A_63 != zero_zero_real ) ) )
= $true ),
inference(copy,[status(thm)],[1556]) ).
thf(2096,plain,
( ( ! [W_19: int] :
( ( plus_plus_real @ one_one_real @ ( number267125858f_real @ W_19 ) )
= ( number267125858f_real @ ( plus_plus_int @ ( bit1 @ pls ) @ W_19 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1023]) ).
thf(2097,plain,
( ( ! [V_19: int] :
( ( plus_plus_real @ ( number267125858f_real @ V_19 ) @ one_one_real )
= ( number267125858f_real @ ( plus_plus_int @ V_19 @ ( bit1 @ pls ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1022]) ).
thf(2098,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)],[1021]) ).
thf(2099,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 ) @ sK4_T_1 ) )
= $true ),
inference(copy,[status(thm)],[1555]) ).
thf(2100,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)],[1019]) ).
thf(2101,plain,
( ( ! [W: int] : ( ord_less_eq_int @ W @ W ) )
= $true ),
inference(copy,[status(thm)],[1018]) ).
thf(2102,plain,
( ( ! [K: int] :
( ( number_number_of_int @ K )
= K ) )
= $true ),
inference(copy,[status(thm)],[1017]) ).
thf(2103,plain,
( ( ! [Z: int,W: int] :
( ( times_times_int @ Z @ W )
= ( times_times_int @ W @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[1016]) ).
thf(2104,plain,
( ( ! [Z: int,W: int] :
( ( ord_less_eq_int @ Z @ W )
| ( ord_less_eq_int @ W @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[1015]) ).
thf(2105,plain,
( ( ! [V_4: int,W: int] :
( ( times_times_int @ ( number_number_of_int @ V_4 ) @ ( number_number_of_int @ W ) )
= ( number_number_of_int @ ( times_times_int @ V_4 @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[1014]) ).
thf(2106,plain,
( ( ! [K: int,L: int] :
( ~ ( ord_less_eq_int @ ( number_number_of_int @ K ) @ ( number_number_of_int @ L ) )
| ( ord_less_eq_int @ K @ L ) )
& ! [K: int,L: int] :
( ~ ( ord_less_eq_int @ K @ L )
| ( ord_less_eq_int @ ( number_number_of_int @ K ) @ ( number_number_of_int @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[1554]) ).
thf(2107,plain,
( ( ! [X_37: int,Y_28: int] :
( ~ ( ord_less_eq_int @ X_37 @ Y_28 )
| ( ord_less_eq_real @ ( number267125858f_real @ X_37 ) @ ( number267125858f_real @ Y_28 ) ) )
& ! [X_37: int,Y_28: int] :
( ~ ( ord_less_eq_real @ ( number267125858f_real @ X_37 ) @ ( number267125858f_real @ Y_28 ) )
| ( ord_less_eq_int @ X_37 @ Y_28 ) ) )
= $true ),
inference(copy,[status(thm)],[1553]) ).
thf(2108,plain,
( ( ! [X_37: int,Y_28: int] :
( ~ ( ord_less_eq_int @ ( number_number_of_int @ X_37 ) @ ( number_number_of_int @ Y_28 ) )
| ( ord_less_eq_int @ X_37 @ Y_28 ) )
& ! [X_37: int,Y_28: int] :
( ~ ( ord_less_eq_int @ X_37 @ Y_28 )
| ( ord_less_eq_int @ ( number_number_of_int @ X_37 ) @ ( number_number_of_int @ Y_28 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1552]) ).
thf(2109,plain,
( ( ! [Z1: int,Z2: int,Z3: int] :
( ( times_times_int @ ( times_times_int @ Z1 @ Z2 ) @ Z3 )
= ( times_times_int @ Z1 @ ( times_times_int @ Z2 @ Z3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1010]) ).
thf(2110,plain,
( ( ! [K: int,I: int,J: int] :
( ~ ( ord_less_eq_int @ I @ J )
| ~ ( ord_less_eq_int @ J @ K )
| ( ord_less_eq_int @ I @ K ) ) )
= $true ),
inference(copy,[status(thm)],[1551]) ).
thf(2111,plain,
( ( ! [Z: int,W: int] :
( ~ ( ord_less_eq_int @ Z @ W )
| ~ ( ord_less_eq_int @ W @ Z )
| ( Z = W ) ) )
= $true ),
inference(copy,[status(thm)],[1550]) ).
thf(2112,plain,
( ( ! [V_18: int,V_17: int] :
( ~ ( ord_less_eq_int @ pls @ V_17 )
| ~ ( ord_less_eq_int @ pls @ V_18 )
| ( ( times_times_real @ ( number267125858f_real @ V_17 ) @ ( number267125858f_real @ V_18 ) )
= ( number267125858f_real @ ( times_times_int @ V_17 @ V_18 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1549]) ).
thf(2113,plain,
( ( ! [V_18: int,V_17: int] :
( ~ ( ord_less_eq_int @ pls @ V_17 )
| ~ ( ord_less_eq_int @ pls @ V_18 )
| ( ( times_times_nat @ ( number_number_of_nat @ V_17 ) @ ( number_number_of_nat @ V_18 ) )
= ( number_number_of_nat @ ( times_times_int @ V_17 @ V_18 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1548]) ).
thf(2114,plain,
( ( ! [V_18: int,V_17: int] :
( ~ ( ord_less_eq_int @ pls @ V_17 )
| ~ ( ord_less_eq_int @ pls @ V_18 )
| ( ( times_times_int @ ( number_number_of_int @ V_17 ) @ ( number_number_of_int @ V_18 ) )
= ( number_number_of_int @ ( times_times_int @ V_17 @ V_18 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1547]) ).
thf(2115,plain,
( ( ! [V_16: int,W_18: int,Z_9: real] :
( ( times_times_real @ ( number267125858f_real @ V_16 ) @ ( times_times_real @ ( number267125858f_real @ W_18 ) @ Z_9 ) )
= ( times_times_real @ ( number267125858f_real @ ( times_times_int @ V_16 @ W_18 ) ) @ Z_9 ) ) )
= $true ),
inference(copy,[status(thm)],[1004]) ).
thf(2116,plain,
( ( ! [V_16: int,W_18: int,Z_9: int] :
( ( times_times_int @ ( number_number_of_int @ V_16 ) @ ( times_times_int @ ( number_number_of_int @ W_18 ) @ Z_9 ) )
= ( times_times_int @ ( number_number_of_int @ ( times_times_int @ V_16 @ W_18 ) ) @ Z_9 ) ) )
= $true ),
inference(copy,[status(thm)],[1003]) ).
thf(2117,plain,
( ( ! [V_15: int,W_17: int] :
( ( times_times_real @ ( number267125858f_real @ V_15 ) @ ( number267125858f_real @ W_17 ) )
= ( number267125858f_real @ ( times_times_int @ V_15 @ W_17 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1002]) ).
thf(2118,plain,
( ( ! [V_15: int,W_17: int] :
( ( times_times_int @ ( number_number_of_int @ V_15 ) @ ( number_number_of_int @ W_17 ) )
= ( number_number_of_int @ ( times_times_int @ V_15 @ W_17 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1001]) ).
thf(2119,plain,
( ( ! [V_14: int,W_16: int] :
( ( number267125858f_real @ ( times_times_int @ V_14 @ W_16 ) )
= ( times_times_real @ ( number267125858f_real @ V_14 ) @ ( number267125858f_real @ W_16 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1000]) ).
thf(2120,plain,
( ( ! [V_14: int,W_16: int] :
( ( number_number_of_int @ ( times_times_int @ V_14 @ W_16 ) )
= ( times_times_int @ ( number_number_of_int @ V_14 ) @ ( number_number_of_int @ W_16 ) ) ) )
= $true ),
inference(copy,[status(thm)],[999]) ).
thf(2121,plain,
( ( ! [X_36: real,Y_27: real] :
( ( X_36 != zero_zero_real )
| ( Y_27 != zero_zero_real )
| ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ X_36 @ X_36 ) @ ( times_times_real @ Y_27 @ Y_27 ) ) @ zero_zero_real ) )
& ! [X_36: real] :
( ! [Y_27: real] :
~ ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ X_36 @ X_36 ) @ ( times_times_real @ Y_27 @ Y_27 ) ) @ zero_zero_real )
| ( X_36 = zero_zero_real ) )
& ! [X_36: real,Y_27: real] :
( ~ ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ X_36 @ X_36 ) @ ( times_times_real @ Y_27 @ Y_27 ) ) @ zero_zero_real )
| ( Y_27 = zero_zero_real ) ) )
= $true ),
inference(copy,[status(thm)],[1546]) ).
thf(2122,plain,
( ( ! [X_35: real,Y_26: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X_35 @ X_35 ) @ ( times_times_real @ Y_26 @ Y_26 ) ) ) )
= $true ),
inference(copy,[status(thm)],[997]) ).
thf(2123,plain,
( ( ! [X_34: int] :
( ~ ( ord_less_eq_int @ X_34 @ pls )
| ( ord_less_eq_real @ ( number267125858f_real @ X_34 ) @ zero_zero_real ) )
& ! [X_34: int] :
( ~ ( ord_less_eq_real @ ( number267125858f_real @ X_34 ) @ zero_zero_real )
| ( ord_less_eq_int @ X_34 @ pls ) ) )
= $true ),
inference(copy,[status(thm)],[1545]) ).
thf(2124,plain,
( ( ! [Y_25: int] :
( ~ ( ord_less_eq_int @ pls @ Y_25 )
| ( ord_less_eq_real @ zero_zero_real @ ( number267125858f_real @ Y_25 ) ) )
& ! [Y_25: int] :
( ~ ( ord_less_eq_real @ zero_zero_real @ ( number267125858f_real @ Y_25 ) )
| ( ord_less_eq_int @ pls @ Y_25 ) ) )
= $true ),
inference(copy,[status(thm)],[1544]) ).
thf(2125,plain,
( ( ! [V_13: int,W_15: int] :
( ~ ( ord_less_eq_real @ ( number267125858f_real @ V_13 ) @ ( number267125858f_real @ W_15 ) )
| ~ ( ord_less_real @ ( number267125858f_real @ W_15 ) @ ( number267125858f_real @ V_13 ) ) )
& ! [V_13: int,W_15: int] :
( ( ord_less_real @ ( number267125858f_real @ W_15 ) @ ( number267125858f_real @ V_13 ) )
| ( ord_less_eq_real @ ( number267125858f_real @ V_13 ) @ ( number267125858f_real @ W_15 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1543]) ).
thf(2126,plain,
( ( ! [X_33: int] :
( ~ ( ord_less_eq_int @ X_33 @ ( bit1 @ pls ) )
| ( ord_less_eq_real @ ( number267125858f_real @ X_33 ) @ one_one_real ) )
& ! [X_33: int] :
( ~ ( ord_less_eq_real @ ( number267125858f_real @ X_33 ) @ one_one_real )
| ( ord_less_eq_int @ X_33 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(copy,[status(thm)],[1542]) ).
thf(2127,plain,
( ( ! [Y_24: int] :
( ~ ( ord_less_eq_int @ ( bit1 @ pls ) @ Y_24 )
| ( ord_less_eq_real @ one_one_real @ ( number267125858f_real @ Y_24 ) ) )
& ! [Y_24: int] :
( ~ ( ord_less_eq_real @ one_one_real @ ( number267125858f_real @ Y_24 ) )
| ( ord_less_eq_int @ ( bit1 @ pls ) @ Y_24 ) ) )
= $true ),
inference(copy,[status(thm)],[1541]) ).
thf(2128,plain,
( ( ! [V_12: int,V_11: int] :
( ~ ( ord_less_eq_int @ pls @ V_11 )
| ~ ( ord_less_eq_int @ pls @ V_12 )
| ( ( plus_plus_real @ ( number267125858f_real @ V_11 ) @ ( number267125858f_real @ V_12 ) )
= ( number267125858f_real @ ( plus_plus_int @ V_11 @ V_12 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1540]) ).
thf(2129,plain,
( ( ! [X_32: int,Y_23: int] :
( ( ( number267125858f_real @ X_32 )
!= ( number267125858f_real @ Y_23 ) )
| ( X_32 = Y_23 ) )
& ! [X_32: int,Y_23: int] :
( ( X_32 != Y_23 )
| ( ( number267125858f_real @ X_32 )
= ( number267125858f_real @ Y_23 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1539]) ).
thf(2130,plain,
( ( ! [X_32: int,Y_23: int] :
( ( ( number_number_of_int @ X_32 )
!= ( number_number_of_int @ Y_23 ) )
| ( X_32 = Y_23 ) )
& ! [X_32: int,Y_23: int] :
( ( X_32 != Y_23 )
| ( ( number_number_of_int @ X_32 )
= ( number_number_of_int @ Y_23 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1538]) ).
thf(2131,plain,
( ( ! [W_13: int,X_31: real] :
( ( ( number267125858f_real @ W_13 )
!= X_31 )
| ( X_31
= ( number267125858f_real @ W_13 ) ) )
& ! [W_13: int,X_31: real] :
( ( X_31
!= ( number267125858f_real @ W_13 ) )
| ( ( number267125858f_real @ W_13 )
= X_31 ) ) )
= $true ),
inference(copy,[status(thm)],[1537]) ).
thf(2132,plain,
( ( ! [W_13: int,X_31: int] :
( ( ( number_number_of_int @ W_13 )
!= X_31 )
| ( X_31
= ( number_number_of_int @ W_13 ) ) )
& ! [W_13: int,X_31: int] :
( ( X_31
!= ( number_number_of_int @ W_13 ) )
| ( ( number_number_of_int @ W_13 )
= X_31 ) ) )
= $true ),
inference(copy,[status(thm)],[1536]) ).
thf(2133,plain,
( ( ! [X_30: real,Y_22: real] :
( ( X_30 != zero_zero_real )
| ( Y_22 != zero_zero_real )
| ( ( plus_plus_real @ ( times_times_real @ X_30 @ X_30 ) @ ( times_times_real @ Y_22 @ Y_22 ) )
= zero_zero_real ) )
& ! [X_30: real] :
( ! [Y_22: real] :
( ( plus_plus_real @ ( times_times_real @ X_30 @ X_30 ) @ ( times_times_real @ Y_22 @ Y_22 ) )
!= zero_zero_real )
| ( X_30 = zero_zero_real ) )
& ! [X_30: real,Y_22: real] :
( ( ( plus_plus_real @ ( times_times_real @ X_30 @ X_30 ) @ ( times_times_real @ Y_22 @ Y_22 ) )
!= zero_zero_real )
| ( Y_22 = zero_zero_real ) ) )
= $true ),
inference(copy,[status(thm)],[1535]) ).
thf(2134,plain,
( ( ! [A_61: real,B_22: real,V_10: int] :
( ( times_times_real @ ( plus_plus_real @ A_61 @ B_22 ) @ ( number267125858f_real @ V_10 ) )
= ( plus_plus_real @ ( times_times_real @ A_61 @ ( number267125858f_real @ V_10 ) ) @ ( times_times_real @ B_22 @ ( number267125858f_real @ V_10 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[985]) ).
thf(2135,plain,
( ( ! [V_9: int,B_21: real,C_13: real] :
( ( times_times_real @ ( number267125858f_real @ V_9 ) @ ( plus_plus_real @ B_21 @ C_13 ) )
= ( plus_plus_real @ ( times_times_real @ ( number267125858f_real @ V_9 ) @ B_21 ) @ ( times_times_real @ ( number267125858f_real @ V_9 ) @ C_13 ) ) ) )
= $true ),
inference(copy,[status(thm)],[984]) ).
thf(2136,plain,
( ( ! [X_29: real,Y_21: real] :
( ( ( power_power_real @ X_29 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= ( power_power_real @ Y_21 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ~ ( ord_less_eq_real @ zero_zero_real @ X_29 )
| ~ ( ord_less_eq_real @ zero_zero_real @ Y_21 )
| ( X_29 = Y_21 ) ) )
= $true ),
inference(copy,[status(thm)],[1534]) ).
thf(2137,plain,
( ( ! [X_29: nat,Y_21: nat] :
( ( ( power_power_nat @ X_29 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= ( power_power_nat @ Y_21 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ X_29 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ Y_21 )
| ( X_29 = Y_21 ) ) )
= $true ),
inference(copy,[status(thm)],[1533]) ).
thf(2138,plain,
( ( ! [X_28: real,Y_20: real] :
( ~ ( ord_less_eq_real @ ( power_power_real @ X_28 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y_20 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ~ ( ord_less_eq_real @ zero_zero_real @ Y_20 )
| ( ord_less_eq_real @ X_28 @ Y_20 ) ) )
= $true ),
inference(copy,[status(thm)],[1532]) ).
thf(2139,plain,
( ( ! [X_28: nat,Y_20: nat] :
( ~ ( ord_less_eq_nat @ ( power_power_nat @ X_28 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_nat @ Y_20 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ Y_20 )
| ( ord_less_eq_nat @ X_28 @ Y_20 ) ) )
= $true ),
inference(copy,[status(thm)],[1531]) ).
thf(2140,plain,
( ( ! [A_60: real] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A_60 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[979]) ).
thf(2141,plain,
( ( ! [X_27: real,Y_19: real] :
( ~ ( ord_less_real @ ( power_power_real @ X_27 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y_19 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ~ ( ord_less_eq_real @ zero_zero_real @ Y_19 )
| ( ord_less_real @ X_27 @ Y_19 ) ) )
= $true ),
inference(copy,[status(thm)],[1530]) ).
thf(2142,plain,
( ( ! [X_27: nat,Y_19: nat] :
( ~ ( ord_less_nat @ ( power_power_nat @ X_27 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_nat @ Y_19 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ Y_19 )
| ( ord_less_nat @ X_27 @ Y_19 ) ) )
= $true ),
inference(copy,[status(thm)],[1529]) ).
thf(2143,plain,
( ( ! [X_26: real,Y_18: real] :
( ( X_26 != zero_zero_real )
| ( Y_18 != zero_zero_real )
| ( ord_less_eq_real @ ( plus_plus_real @ ( power_power_real @ X_26 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y_18 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_real ) )
& ! [X_26: real] :
( ! [Y_18: real] :
~ ( ord_less_eq_real @ ( plus_plus_real @ ( power_power_real @ X_26 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y_18 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_real )
| ( X_26 = zero_zero_real ) )
& ! [X_26: real,Y_18: real] :
( ~ ( ord_less_eq_real @ ( plus_plus_real @ ( power_power_real @ X_26 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y_18 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_real )
| ( Y_18 = zero_zero_real ) ) )
= $true ),
inference(copy,[status(thm)],[1528]) ).
thf(2144,plain,
( ( ! [X_25: real,Y_17: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X_25 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y_17 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[975]) ).
thf(2145,plain,
( ( ! [X_24: real,Y_16: real] :
( ~ ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X_24 @ X_24 ) @ ( times_times_real @ Y_16 @ Y_16 ) ) )
| ( X_24 != zero_zero_real )
| ( Y_16 != zero_zero_real ) )
& ! [X_24: real] :
( ( X_24 = zero_zero_real )
| ! [Y_16: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X_24 @ X_24 ) @ ( times_times_real @ Y_16 @ Y_16 ) ) ) )
& ! [X_24: real,Y_16: real] :
( ( Y_16 = zero_zero_real )
| ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X_24 @ X_24 ) @ ( times_times_real @ Y_16 @ Y_16 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1527]) ).
thf(2146,plain,
( ( ! [X_23: real,Y_15: real] :
~ ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ X_23 @ X_23 ) @ ( times_times_real @ Y_15 @ Y_15 ) ) @ zero_zero_real ) )
= $true ),
inference(copy,[status(thm)],[973]) ).
thf(2147,plain,
( ( ! [A_57: real] :
( ( ( plus_plus_real @ A_57 @ A_57 )
!= zero_zero_real )
| ( A_57 = zero_zero_real ) )
& ! [A_57: real] :
( ( A_57 != zero_zero_real )
| ( ( plus_plus_real @ A_57 @ A_57 )
= zero_zero_real ) ) )
= $true ),
inference(copy,[status(thm)],[1526]) ).
thf(2148,plain,
( ( ! [W_12: int] :
( ( times_times_real @ ( plus_plus_real @ one_one_real @ one_one_real ) @ ( number267125858f_real @ W_12 ) )
= ( number267125858f_real @ ( bit0 @ W_12 ) ) ) )
= $true ),
inference(copy,[status(thm)],[971]) ).
thf(2149,plain,
( ( ! [Z_7: real] :
( ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ Z_7 )
= ( plus_plus_real @ Z_7 @ Z_7 ) ) )
= $true ),
inference(copy,[status(thm)],[970]) ).
thf(2150,plain,
( ( ! [Z_6: real] :
( ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ Z_6 )
= ( plus_plus_real @ Z_6 @ Z_6 ) ) )
= $true ),
inference(copy,[status(thm)],[969]) ).
thf(2151,plain,
( ( ! [Z_5: real] :
( ( times_times_real @ Z_5 @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_real @ Z_5 @ Z_5 ) ) )
= $true ),
inference(copy,[status(thm)],[968]) ).
thf(2152,plain,
( ( ! [Z_4: real] :
( ( times_times_real @ Z_4 @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_real @ Z_4 @ Z_4 ) ) )
= $true ),
inference(copy,[status(thm)],[967]) ).
thf(2153,plain,
( ( ! [A_54: real] :
( ~ ( ord_less_real @ ( plus_plus_real @ A_54 @ A_54 ) @ zero_zero_real )
| ( ord_less_real @ A_54 @ zero_zero_real ) )
& ! [A_54: real] :
( ~ ( ord_less_real @ A_54 @ zero_zero_real )
| ( ord_less_real @ ( plus_plus_real @ A_54 @ A_54 ) @ zero_zero_real ) ) )
= $true ),
inference(copy,[status(thm)],[1525]) ).
thf(2154,plain,
( ( ! [W_8: int] :
( ( power_power_real @ ( number267125858f_real @ W_8 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_real @ ( number267125858f_real @ W_8 ) @ ( number267125858f_real @ W_8 ) ) ) )
= $true ),
inference(copy,[status(thm)],[965]) ).
thf(2155,plain,
( ( ! [X_21: real,Y_13: real] :
( ( power_power_real @ ( plus_plus_real @ X_21 @ Y_13 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_real @ ( plus_plus_real @ ( power_power_real @ X_21 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y_13 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ X_21 ) @ Y_13 ) ) ) )
= $true ),
inference(copy,[status(thm)],[964]) ).
thf(2156,plain,
( ( ! [X_21: nat,Y_13: nat] :
( ( power_power_nat @ ( plus_plus_nat @ X_21 @ Y_13 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_nat @ ( plus_plus_nat @ ( power_power_nat @ X_21 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_nat @ Y_13 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_nat @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ X_21 ) @ Y_13 ) ) ) )
= $true ),
inference(copy,[status(thm)],[963]) ).
thf(2157,plain,
( ( ! [W_7: int] :
( ( number267125858f_real @ ( bit0 @ W_7 ) )
= ( plus_plus_real @ ( plus_plus_real @ zero_zero_real @ ( number267125858f_real @ W_7 ) ) @ ( number267125858f_real @ W_7 ) ) ) )
= $true ),
inference(copy,[status(thm)],[962]) ).
thf(2158,plain,
( ( ! [W_6: int] :
( ( number267125858f_real @ ( bit1 @ W_6 ) )
= ( plus_plus_real @ ( plus_plus_real @ one_one_real @ ( number267125858f_real @ W_6 ) ) @ ( number267125858f_real @ W_6 ) ) ) )
= $true ),
inference(copy,[status(thm)],[961]) ).
thf(2159,plain,
( ( ! [X_20: int] :
( ~ ( ord_less_int @ X_20 @ pls )
| ( ord_less_real @ ( number267125858f_real @ X_20 ) @ zero_zero_real ) )
& ! [X_20: int] :
( ~ ( ord_less_real @ ( number267125858f_real @ X_20 ) @ zero_zero_real )
| ( ord_less_int @ X_20 @ pls ) ) )
= $true ),
inference(copy,[status(thm)],[1524]) ).
thf(2160,plain,
( ( ! [Y_12: int] :
( ~ ( ord_less_int @ pls @ Y_12 )
| ( ord_less_real @ zero_zero_real @ ( number267125858f_real @ Y_12 ) ) )
& ! [Y_12: int] :
( ~ ( ord_less_real @ zero_zero_real @ ( number267125858f_real @ Y_12 ) )
| ( ord_less_int @ pls @ Y_12 ) ) )
= $true ),
inference(copy,[status(thm)],[1523]) ).
thf(2161,plain,
( ( ( plus_plus_real @ one_one_real @ one_one_real )
= ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(copy,[status(thm)],[958]) ).
thf(2162,plain,
( ( ( plus_plus_real @ one_one_real @ one_one_real )
= ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(copy,[status(thm)],[957]) ).
thf(2163,plain,
( ( ! [X_19: int] :
( ~ ( ord_less_int @ X_19 @ ( bit1 @ pls ) )
| ( ord_less_real @ ( number267125858f_real @ X_19 ) @ one_one_real ) )
& ! [X_19: int] :
( ~ ( ord_less_real @ ( number267125858f_real @ X_19 ) @ one_one_real )
| ( ord_less_int @ X_19 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(copy,[status(thm)],[1522]) ).
thf(2164,plain,
( ( ! [Y_11: int] :
( ~ ( ord_less_int @ ( bit1 @ pls ) @ Y_11 )
| ( ord_less_real @ one_one_real @ ( number267125858f_real @ Y_11 ) ) )
& ! [Y_11: int] :
( ~ ( ord_less_real @ one_one_real @ ( number267125858f_real @ Y_11 ) )
| ( ord_less_int @ ( bit1 @ pls ) @ Y_11 ) ) )
= $true ),
inference(copy,[status(thm)],[1521]) ).
thf(2165,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)],[954]) ).
thf(2166,plain,
( ( ! [X_18: real,N_35: nat] :
( ( power_power_real @ X_18 @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ N_35 ) )
= ( times_times_real @ ( power_power_real @ X_18 @ N_35 ) @ ( power_power_real @ X_18 @ N_35 ) ) ) )
= $true ),
inference(copy,[status(thm)],[953]) ).
thf(2167,plain,
( ( ! [X: nat,N: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X @ N ) )
| ( N = zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ X ) )
& ! [X: nat,N: nat] :
( ( N != zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X @ N ) ) )
& ! [X: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ X )
| ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[1520]) ).
thf(2168,plain,
( ( ! [X_17: real,P_2: nat,Q_4: nat] :
( ( power_power_real @ ( power_power_real @ X_17 @ P_2 ) @ Q_4 )
= ( power_power_real @ X_17 @ ( times_times_nat @ P_2 @ Q_4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[951]) ).
thf(2169,plain,
( ( ! [X_17: nat,P_2: nat,Q_4: nat] :
( ( power_power_nat @ ( power_power_nat @ X_17 @ P_2 ) @ Q_4 )
= ( power_power_nat @ X_17 @ ( times_times_nat @ P_2 @ Q_4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[950]) ).
thf(2170,plain,
( ( ! [N: nat,A: int,B: int,P: int] :
( ~ ( zprime @ P )
| ( dvd_dvd_int @ P @ B )
| ~ ( dvd_dvd_int @ ( power_power_int @ P @ N ) @ ( times_times_int @ A @ B ) )
| ( dvd_dvd_int @ ( power_power_int @ P @ N ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[1519]) ).
thf(2171,plain,
( ( ! [N: nat,B: int,A: int,P: int] :
( ~ ( zprime @ P )
| ( dvd_dvd_int @ P @ A )
| ~ ( dvd_dvd_int @ ( power_power_int @ P @ N ) @ ( times_times_int @ A @ B ) )
| ( dvd_dvd_int @ ( power_power_int @ P @ N ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[1518]) ).
thf(2172,plain,
( ( ! [Y: int,X: int] :
( ~ ( twoSqu362149276sum2sq @ X )
| ~ ( twoSqu362149276sum2sq @ Y )
| ( twoSqu362149276sum2sq @ ( times_times_int @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[1517]) ).
thf(2173,plain,
( ( ! [Lx_6: real,Ly_4: real,Rx_6: real,Ry_4: real] :
( ( times_times_real @ ( times_times_real @ Lx_6 @ Ly_4 ) @ ( times_times_real @ Rx_6 @ Ry_4 ) )
= ( times_times_real @ ( times_times_real @ Lx_6 @ Rx_6 ) @ ( times_times_real @ Ly_4 @ Ry_4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[946]) ).
thf(2174,plain,
( ( ! [Lx_6: nat,Ly_4: nat,Rx_6: nat,Ry_4: nat] :
( ( times_times_nat @ ( times_times_nat @ Lx_6 @ Ly_4 ) @ ( times_times_nat @ Rx_6 @ Ry_4 ) )
= ( times_times_nat @ ( times_times_nat @ Lx_6 @ Rx_6 ) @ ( times_times_nat @ Ly_4 @ Ry_4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[945]) ).
thf(2175,plain,
( ( ! [Lx_6: int,Ly_4: int,Rx_6: int,Ry_4: int] :
( ( times_times_int @ ( times_times_int @ Lx_6 @ Ly_4 ) @ ( times_times_int @ Rx_6 @ Ry_4 ) )
= ( times_times_int @ ( times_times_int @ Lx_6 @ Rx_6 ) @ ( times_times_int @ Ly_4 @ Ry_4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[944]) ).
thf(2176,plain,
( ( ! [Lx_5: real,Ly_3: real,Rx_5: real,Ry_3: real] :
( ( times_times_real @ ( times_times_real @ Lx_5 @ Ly_3 ) @ ( times_times_real @ Rx_5 @ Ry_3 ) )
= ( times_times_real @ Rx_5 @ ( times_times_real @ ( times_times_real @ Lx_5 @ Ly_3 ) @ Ry_3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[943]) ).
thf(2177,plain,
( ( ! [Lx_5: nat,Ly_3: nat,Rx_5: nat,Ry_3: nat] :
( ( times_times_nat @ ( times_times_nat @ Lx_5 @ Ly_3 ) @ ( times_times_nat @ Rx_5 @ Ry_3 ) )
= ( times_times_nat @ Rx_5 @ ( times_times_nat @ ( times_times_nat @ Lx_5 @ Ly_3 ) @ Ry_3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[942]) ).
thf(2178,plain,
( ( ! [Lx_5: int,Ly_3: int,Rx_5: int,Ry_3: int] :
( ( times_times_int @ ( times_times_int @ Lx_5 @ Ly_3 ) @ ( times_times_int @ Rx_5 @ Ry_3 ) )
= ( times_times_int @ Rx_5 @ ( times_times_int @ ( times_times_int @ Lx_5 @ Ly_3 ) @ Ry_3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[941]) ).
thf(2179,plain,
( ( ! [Lx_4: real,Ly_2: real,Rx_4: real,Ry_2: real] :
( ( times_times_real @ ( times_times_real @ Lx_4 @ Ly_2 ) @ ( times_times_real @ Rx_4 @ Ry_2 ) )
= ( times_times_real @ Lx_4 @ ( times_times_real @ Ly_2 @ ( times_times_real @ Rx_4 @ Ry_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[940]) ).
thf(2180,plain,
( ( ! [Lx_4: nat,Ly_2: nat,Rx_4: nat,Ry_2: nat] :
( ( times_times_nat @ ( times_times_nat @ Lx_4 @ Ly_2 ) @ ( times_times_nat @ Rx_4 @ Ry_2 ) )
= ( times_times_nat @ Lx_4 @ ( times_times_nat @ Ly_2 @ ( times_times_nat @ Rx_4 @ Ry_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[939]) ).
thf(2181,plain,
( ( ! [Lx_4: int,Ly_2: int,Rx_4: int,Ry_2: int] :
( ( times_times_int @ ( times_times_int @ Lx_4 @ Ly_2 ) @ ( times_times_int @ Rx_4 @ Ry_2 ) )
= ( times_times_int @ Lx_4 @ ( times_times_int @ Ly_2 @ ( times_times_int @ Rx_4 @ Ry_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[938]) ).
thf(2182,plain,
( ( ! [Lx_3: real,Ly_1: real,Rx_3: real] :
( ( times_times_real @ ( times_times_real @ Lx_3 @ Ly_1 ) @ Rx_3 )
= ( times_times_real @ ( times_times_real @ Lx_3 @ Rx_3 ) @ Ly_1 ) ) )
= $true ),
inference(copy,[status(thm)],[937]) ).
thf(2183,plain,
( ( ! [Lx_3: nat,Ly_1: nat,Rx_3: nat] :
( ( times_times_nat @ ( times_times_nat @ Lx_3 @ Ly_1 ) @ Rx_3 )
= ( times_times_nat @ ( times_times_nat @ Lx_3 @ Rx_3 ) @ Ly_1 ) ) )
= $true ),
inference(copy,[status(thm)],[936]) ).
thf(2184,plain,
( ( ! [Lx_3: int,Ly_1: int,Rx_3: int] :
( ( times_times_int @ ( times_times_int @ Lx_3 @ Ly_1 ) @ Rx_3 )
= ( times_times_int @ ( times_times_int @ Lx_3 @ Rx_3 ) @ Ly_1 ) ) )
= $true ),
inference(copy,[status(thm)],[935]) ).
thf(2185,plain,
( ( ! [Lx_2: real,Ly: real,Rx_2: real] :
( ( times_times_real @ ( times_times_real @ Lx_2 @ Ly ) @ Rx_2 )
= ( times_times_real @ Lx_2 @ ( times_times_real @ Ly @ Rx_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[934]) ).
thf(2186,plain,
( ( ! [Lx_2: nat,Ly: nat,Rx_2: nat] :
( ( times_times_nat @ ( times_times_nat @ Lx_2 @ Ly ) @ Rx_2 )
= ( times_times_nat @ Lx_2 @ ( times_times_nat @ Ly @ Rx_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[933]) ).
thf(2187,plain,
( ( ! [Lx_2: int,Ly: int,Rx_2: int] :
( ( times_times_int @ ( times_times_int @ Lx_2 @ Ly ) @ Rx_2 )
= ( times_times_int @ Lx_2 @ ( times_times_int @ Ly @ Rx_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[932]) ).
thf(2188,plain,
( ( ! [Lx_1: real,Rx_1: real,Ry_1: real] :
( ( times_times_real @ Lx_1 @ ( times_times_real @ Rx_1 @ Ry_1 ) )
= ( times_times_real @ ( times_times_real @ Lx_1 @ Rx_1 ) @ Ry_1 ) ) )
= $true ),
inference(copy,[status(thm)],[931]) ).
thf(2189,plain,
( ( ! [Lx_1: nat,Rx_1: nat,Ry_1: nat] :
( ( times_times_nat @ Lx_1 @ ( times_times_nat @ Rx_1 @ Ry_1 ) )
= ( times_times_nat @ ( times_times_nat @ Lx_1 @ Rx_1 ) @ Ry_1 ) ) )
= $true ),
inference(copy,[status(thm)],[930]) ).
thf(2190,plain,
( ( ! [Lx_1: int,Rx_1: int,Ry_1: int] :
( ( times_times_int @ Lx_1 @ ( times_times_int @ Rx_1 @ Ry_1 ) )
= ( times_times_int @ ( times_times_int @ Lx_1 @ Rx_1 ) @ Ry_1 ) ) )
= $true ),
inference(copy,[status(thm)],[929]) ).
thf(2191,plain,
( ( ! [Lx: real,Rx: real,Ry: real] :
( ( times_times_real @ Lx @ ( times_times_real @ Rx @ Ry ) )
= ( times_times_real @ Rx @ ( times_times_real @ Lx @ Ry ) ) ) )
= $true ),
inference(copy,[status(thm)],[928]) ).
thf(2192,plain,
( ( ! [Lx: nat,Rx: nat,Ry: nat] :
( ( times_times_nat @ Lx @ ( times_times_nat @ Rx @ Ry ) )
= ( times_times_nat @ Rx @ ( times_times_nat @ Lx @ Ry ) ) ) )
= $true ),
inference(copy,[status(thm)],[927]) ).
thf(2193,plain,
( ( ! [Lx: int,Rx: int,Ry: int] :
( ( times_times_int @ Lx @ ( times_times_int @ Rx @ Ry ) )
= ( times_times_int @ Rx @ ( times_times_int @ Lx @ Ry ) ) ) )
= $true ),
inference(copy,[status(thm)],[926]) ).
thf(2194,plain,
( ( ! [A_51: real,B_20: real] :
( ( times_times_real @ A_51 @ B_20 )
= ( times_times_real @ B_20 @ A_51 ) ) )
= $true ),
inference(copy,[status(thm)],[925]) ).
thf(2195,plain,
( ( ! [A_51: nat,B_20: nat] :
( ( times_times_nat @ A_51 @ B_20 )
= ( times_times_nat @ B_20 @ A_51 ) ) )
= $true ),
inference(copy,[status(thm)],[924]) ).
thf(2196,plain,
( ( ! [A_51: int,B_20: int] :
( ( times_times_int @ A_51 @ B_20 )
= ( times_times_int @ B_20 @ A_51 ) ) )
= $true ),
inference(copy,[status(thm)],[923]) ).
thf(2197,plain,
( ( ! [A_50: real,C_12: real] :
( ( plus_plus_real @ A_50 @ C_12 )
= ( plus_plus_real @ C_12 @ A_50 ) ) )
= $true ),
inference(copy,[status(thm)],[922]) ).
thf(2198,plain,
( ( ! [A_50: nat,C_12: nat] :
( ( plus_plus_nat @ A_50 @ C_12 )
= ( plus_plus_nat @ C_12 @ A_50 ) ) )
= $true ),
inference(copy,[status(thm)],[921]) ).
thf(2199,plain,
( ( ! [A_49: real,C_11: real,D_6: real] :
( ( plus_plus_real @ A_49 @ ( plus_plus_real @ C_11 @ D_6 ) )
= ( plus_plus_real @ C_11 @ ( plus_plus_real @ A_49 @ D_6 ) ) ) )
= $true ),
inference(copy,[status(thm)],[920]) ).
thf(2200,plain,
( ( ! [A_49: nat,C_11: nat,D_6: nat] :
( ( plus_plus_nat @ A_49 @ ( plus_plus_nat @ C_11 @ D_6 ) )
= ( plus_plus_nat @ C_11 @ ( plus_plus_nat @ A_49 @ D_6 ) ) ) )
= $true ),
inference(copy,[status(thm)],[919]) ).
thf(2201,plain,
( ( ! [A_48: real,C_10: real,D_5: real] :
( ( plus_plus_real @ A_48 @ ( plus_plus_real @ C_10 @ D_5 ) )
= ( plus_plus_real @ ( plus_plus_real @ A_48 @ C_10 ) @ D_5 ) ) )
= $true ),
inference(copy,[status(thm)],[918]) ).
thf(2202,plain,
( ( ! [A_48: nat,C_10: nat,D_5: nat] :
( ( plus_plus_nat @ A_48 @ ( plus_plus_nat @ C_10 @ D_5 ) )
= ( plus_plus_nat @ ( plus_plus_nat @ A_48 @ C_10 ) @ D_5 ) ) )
= $true ),
inference(copy,[status(thm)],[917]) ).
thf(2203,plain,
( ( ! [A_47: real,B_19: real,C_9: real] :
( ( plus_plus_real @ ( plus_plus_real @ A_47 @ B_19 ) @ C_9 )
= ( plus_plus_real @ A_47 @ ( plus_plus_real @ B_19 @ C_9 ) ) ) )
= $true ),
inference(copy,[status(thm)],[916]) ).
thf(2204,plain,
( ( ! [A_47: nat,B_19: nat,C_9: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ A_47 @ B_19 ) @ C_9 )
= ( plus_plus_nat @ A_47 @ ( plus_plus_nat @ B_19 @ C_9 ) ) ) )
= $true ),
inference(copy,[status(thm)],[915]) ).
thf(2205,plain,
( ( ! [A_46: real,B_18: real,C_8: real] :
( ( plus_plus_real @ ( plus_plus_real @ A_46 @ B_18 ) @ C_8 )
= ( plus_plus_real @ ( plus_plus_real @ A_46 @ C_8 ) @ B_18 ) ) )
= $true ),
inference(copy,[status(thm)],[914]) ).
thf(2206,plain,
( ( ! [A_46: nat,B_18: nat,C_8: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ A_46 @ B_18 ) @ C_8 )
= ( plus_plus_nat @ ( plus_plus_nat @ A_46 @ C_8 ) @ B_18 ) ) )
= $true ),
inference(copy,[status(thm)],[913]) ).
thf(2207,plain,
( ( ! [A_45: real,B_17: real,C_7: real,D_4: real] :
( ( plus_plus_real @ ( plus_plus_real @ A_45 @ B_17 ) @ ( plus_plus_real @ C_7 @ D_4 ) )
= ( plus_plus_real @ ( plus_plus_real @ A_45 @ C_7 ) @ ( plus_plus_real @ B_17 @ D_4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[912]) ).
thf(2208,plain,
( ( ! [A_45: nat,B_17: nat,C_7: nat,D_4: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ A_45 @ B_17 ) @ ( plus_plus_nat @ C_7 @ D_4 ) )
= ( plus_plus_nat @ ( plus_plus_nat @ A_45 @ C_7 ) @ ( plus_plus_nat @ B_17 @ D_4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[911]) ).
thf(2209,plain,
( ( ! [X_16: real] :
( ( power_power_real @ X_16 @ one_one_nat )
= X_16 ) )
= $true ),
inference(copy,[status(thm)],[910]) ).
thf(2210,plain,
( ( ! [X_16: nat] :
( ( power_power_nat @ X_16 @ one_one_nat )
= X_16 ) )
= $true ),
inference(copy,[status(thm)],[909]) ).
thf(2211,plain,
( ( ! [X: nat,W: int] :
( ~ ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X @ ( number_number_of_nat @ W ) ) )
| ( ( number_number_of_nat @ W )
= zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ X ) )
& ! [X: nat,W: int] :
( ( ( number_number_of_nat @ W )
!= zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X @ ( number_number_of_nat @ W ) ) ) )
& ! [X: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ X )
| ! [W: int] : ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X @ ( number_number_of_nat @ W ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1516]) ).
thf(2212,plain,
( ( ! [V_5: int,V_4: int] :
( ~ ( ord_less_int @ V_4 @ pls )
| ( ( times_times_nat @ ( number_number_of_nat @ V_4 ) @ ( number_number_of_nat @ V_5 ) )
= zero_zero_nat ) )
& ! [V_5: int,V_4: int] :
( ( ord_less_int @ V_4 @ pls )
| ( ( times_times_nat @ ( number_number_of_nat @ V_4 ) @ ( number_number_of_nat @ V_5 ) )
= ( number_number_of_nat @ ( times_times_int @ V_4 @ V_5 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1515]) ).
thf(2213,plain,
( ( ! [V_5: int] :
( ! [K: nat,V_4: int] :
( ~ ( ord_less_int @ V_4 @ pls )
| ( ( times_times_nat @ ( number_number_of_nat @ V_4 ) @ ( times_times_nat @ ( number_number_of_nat @ V_5 ) @ K ) )
= zero_zero_nat ) )
& ! [K: nat,V_4: int] :
( ( ord_less_int @ V_4 @ pls )
| ( ( times_times_nat @ ( number_number_of_nat @ V_4 ) @ ( times_times_nat @ ( number_number_of_nat @ V_5 ) @ K ) )
= ( times_times_nat @ ( number_number_of_nat @ ( times_times_int @ V_4 @ V_5 ) ) @ K ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1514]) ).
thf(2214,plain,
( ( ! [A_43: real] :
( ! [K_2: nat] :
~ ( ord_less_eq_real @ ( power_power_real @ A_43 @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ K_2 ) ) @ zero_zero_real )
| ( A_43 = zero_zero_real ) ) )
= $true ),
inference(copy,[status(thm)],[1513]) ).
thf(2215,plain,
( ( ! [A_42: real] :
( ( times_times_real @ zero_zero_real @ A_42 )
= zero_zero_real ) )
= $true ),
inference(copy,[status(thm)],[904]) ).
thf(2216,plain,
( ( ! [A_42: nat] :
( ( times_times_nat @ zero_zero_nat @ A_42 )
= zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[903]) ).
thf(2217,plain,
( ( ! [A_41: real] :
( ( times_times_real @ A_41 @ zero_zero_real )
= zero_zero_real ) )
= $true ),
inference(copy,[status(thm)],[902]) ).
thf(2218,plain,
( ( ! [A_41: nat] :
( ( times_times_nat @ A_41 @ zero_zero_nat )
= zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[901]) ).
thf(2219,plain,
( ( ! [A_40: real] :
( ( plus_plus_real @ zero_zero_real @ A_40 )
= A_40 ) )
= $true ),
inference(copy,[status(thm)],[900]) ).
thf(2220,plain,
( ( ! [A_40: nat] :
( ( plus_plus_nat @ zero_zero_nat @ A_40 )
= A_40 ) )
= $true ),
inference(copy,[status(thm)],[899]) ).
thf(2221,plain,
( ( ! [A_39: real] :
( ( plus_plus_real @ A_39 @ zero_zero_real )
= A_39 ) )
= $true ),
inference(copy,[status(thm)],[898]) ).
thf(2222,plain,
( ( ! [A_39: nat] :
( ( plus_plus_nat @ A_39 @ zero_zero_nat )
= A_39 ) )
= $true ),
inference(copy,[status(thm)],[897]) ).
thf(2223,plain,
( ( ! [B_16: real,A_38: real] :
( ( B_16
!= ( plus_plus_real @ B_16 @ A_38 ) )
| ( A_38 = zero_zero_real ) )
& ! [B_16: real,A_38: real] :
( ( A_38 != zero_zero_real )
| ( B_16
= ( plus_plus_real @ B_16 @ A_38 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1512]) ).
thf(2224,plain,
( ( ! [B_16: nat,A_38: nat] :
( ( B_16
!= ( plus_plus_nat @ B_16 @ A_38 ) )
| ( A_38 = zero_zero_nat ) )
& ! [B_16: nat,A_38: nat] :
( ( A_38 != zero_zero_nat )
| ( B_16
= ( plus_plus_nat @ B_16 @ A_38 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1511]) ).
thf(2225,plain,
( ( ! [X_15: real,Y_10: real,Z_2: real] :
( ( times_times_real @ X_15 @ ( plus_plus_real @ Y_10 @ Z_2 ) )
= ( plus_plus_real @ ( times_times_real @ X_15 @ Y_10 ) @ ( times_times_real @ X_15 @ Z_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[894]) ).
thf(2226,plain,
( ( ! [X_15: nat,Y_10: nat,Z_2: nat] :
( ( times_times_nat @ X_15 @ ( plus_plus_nat @ Y_10 @ Z_2 ) )
= ( plus_plus_nat @ ( times_times_nat @ X_15 @ Y_10 ) @ ( times_times_nat @ X_15 @ Z_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[893]) ).
thf(2227,plain,
( ( ! [C_6: real,D_3: real] :
( ! [A_37: real,B_15: real] :
( ( ( plus_plus_real @ ( times_times_real @ A_37 @ C_6 ) @ ( times_times_real @ B_15 @ D_3 ) )
= ( plus_plus_real @ ( times_times_real @ A_37 @ D_3 ) @ ( times_times_real @ B_15 @ C_6 ) ) )
| ( A_37 != B_15 ) )
& ( ! [A_37: real,B_15: real] :
( ( plus_plus_real @ ( times_times_real @ A_37 @ C_6 ) @ ( times_times_real @ B_15 @ D_3 ) )
= ( plus_plus_real @ ( times_times_real @ A_37 @ D_3 ) @ ( times_times_real @ B_15 @ C_6 ) ) )
| ( C_6 != D_3 ) )
& ! [A_37: real,B_15: real] :
( ( A_37 = B_15 )
| ( C_6 = D_3 )
| ( ( plus_plus_real @ ( times_times_real @ A_37 @ C_6 ) @ ( times_times_real @ B_15 @ D_3 ) )
!= ( plus_plus_real @ ( times_times_real @ A_37 @ D_3 ) @ ( times_times_real @ B_15 @ C_6 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1510]) ).
thf(2228,plain,
( ( ! [C_6: nat,D_3: nat] :
( ! [A_37: nat,B_15: nat] :
( ( ( plus_plus_nat @ ( times_times_nat @ A_37 @ C_6 ) @ ( times_times_nat @ B_15 @ D_3 ) )
= ( plus_plus_nat @ ( times_times_nat @ A_37 @ D_3 ) @ ( times_times_nat @ B_15 @ C_6 ) ) )
| ( A_37 != B_15 ) )
& ( ! [A_37: nat,B_15: nat] :
( ( plus_plus_nat @ ( times_times_nat @ A_37 @ C_6 ) @ ( times_times_nat @ B_15 @ D_3 ) )
= ( plus_plus_nat @ ( times_times_nat @ A_37 @ D_3 ) @ ( times_times_nat @ B_15 @ C_6 ) ) )
| ( C_6 != D_3 ) )
& ! [A_37: nat,B_15: nat] :
( ( A_37 = B_15 )
| ( C_6 = D_3 )
| ( ( plus_plus_nat @ ( times_times_nat @ A_37 @ C_6 ) @ ( times_times_nat @ B_15 @ D_3 ) )
!= ( plus_plus_nat @ ( times_times_nat @ A_37 @ D_3 ) @ ( times_times_nat @ B_15 @ C_6 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1509]) ).
thf(2229,plain,
( ( ! [A_36: real,B_14: real,C_5: real] :
( ( times_times_real @ ( plus_plus_real @ A_36 @ B_14 ) @ C_5 )
= ( plus_plus_real @ ( times_times_real @ A_36 @ C_5 ) @ ( times_times_real @ B_14 @ C_5 ) ) ) )
= $true ),
inference(copy,[status(thm)],[890]) ).
thf(2230,plain,
( ( ! [A_36: nat,B_14: nat,C_5: nat] :
( ( times_times_nat @ ( plus_plus_nat @ A_36 @ B_14 ) @ C_5 )
= ( plus_plus_nat @ ( times_times_nat @ A_36 @ C_5 ) @ ( times_times_nat @ B_14 @ C_5 ) ) ) )
= $true ),
inference(copy,[status(thm)],[889]) ).
thf(2231,plain,
( ( ! [A_35: real,M_13: real,B_13: real] :
( ( plus_plus_real @ ( times_times_real @ A_35 @ M_13 ) @ ( times_times_real @ B_13 @ M_13 ) )
= ( times_times_real @ ( plus_plus_real @ A_35 @ B_13 ) @ M_13 ) ) )
= $true ),
inference(copy,[status(thm)],[888]) ).
thf(2232,plain,
( ( ! [A_35: nat,M_13: nat,B_13: nat] :
( ( plus_plus_nat @ ( times_times_nat @ A_35 @ M_13 ) @ ( times_times_nat @ B_13 @ M_13 ) )
= ( times_times_nat @ ( plus_plus_nat @ A_35 @ B_13 ) @ M_13 ) ) )
= $true ),
inference(copy,[status(thm)],[887]) ).
thf(2233,plain,
( ( ! [W_5: real,Y_9: real] :
( ! [X_14: real,Z_1: real] :
( ( ( plus_plus_real @ ( times_times_real @ W_5 @ Y_9 ) @ ( times_times_real @ X_14 @ Z_1 ) )
!= ( plus_plus_real @ ( times_times_real @ W_5 @ Z_1 ) @ ( times_times_real @ X_14 @ Y_9 ) ) )
| ( W_5 = X_14 )
| ( Y_9 = Z_1 ) )
& ! [X_14: real] :
( ( W_5 != X_14 )
| ! [Z_1: real] :
( ( plus_plus_real @ ( times_times_real @ W_5 @ Y_9 ) @ ( times_times_real @ X_14 @ Z_1 ) )
= ( plus_plus_real @ ( times_times_real @ W_5 @ Z_1 ) @ ( times_times_real @ X_14 @ Y_9 ) ) ) )
& ! [X_14: real,Z_1: real] :
( ( Y_9 != Z_1 )
| ( ( plus_plus_real @ ( times_times_real @ W_5 @ Y_9 ) @ ( times_times_real @ X_14 @ Z_1 ) )
= ( plus_plus_real @ ( times_times_real @ W_5 @ Z_1 ) @ ( times_times_real @ X_14 @ Y_9 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1508]) ).
thf(2234,plain,
( ( ! [W_5: nat,Y_9: nat] :
( ! [X_14: nat,Z_1: nat] :
( ( ( plus_plus_nat @ ( times_times_nat @ W_5 @ Y_9 ) @ ( times_times_nat @ X_14 @ Z_1 ) )
!= ( plus_plus_nat @ ( times_times_nat @ W_5 @ Z_1 ) @ ( times_times_nat @ X_14 @ Y_9 ) ) )
| ( W_5 = X_14 )
| ( Y_9 = Z_1 ) )
& ! [X_14: nat] :
( ( W_5 != X_14 )
| ! [Z_1: nat] :
( ( plus_plus_nat @ ( times_times_nat @ W_5 @ Y_9 ) @ ( times_times_nat @ X_14 @ Z_1 ) )
= ( plus_plus_nat @ ( times_times_nat @ W_5 @ Z_1 ) @ ( times_times_nat @ X_14 @ Y_9 ) ) ) )
& ! [X_14: nat,Z_1: nat] :
( ( Y_9 != Z_1 )
| ( ( plus_plus_nat @ ( times_times_nat @ W_5 @ Y_9 ) @ ( times_times_nat @ X_14 @ Z_1 ) )
= ( plus_plus_nat @ ( times_times_nat @ W_5 @ Z_1 ) @ ( times_times_nat @ X_14 @ Y_9 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1507]) ).
thf(2235,plain,
( ( ! [A_34: real] :
( ( times_times_real @ one_one_real @ A_34 )
= A_34 ) )
= $true ),
inference(copy,[status(thm)],[884]) ).
thf(2236,plain,
( ( ! [A_34: nat] :
( ( times_times_nat @ one_one_nat @ A_34 )
= A_34 ) )
= $true ),
inference(copy,[status(thm)],[883]) ).
thf(2237,plain,
( ( ! [A_33: real] :
( ( times_times_real @ A_33 @ one_one_real )
= A_33 ) )
= $true ),
inference(copy,[status(thm)],[882]) ).
thf(2238,plain,
( ( ! [A_33: nat] :
( ( times_times_nat @ A_33 @ one_one_nat )
= A_33 ) )
= $true ),
inference(copy,[status(thm)],[881]) ).
thf(2239,plain,
( ( ! [X_13: real,Y_8: real,Q_3: nat] :
( ( power_power_real @ ( times_times_real @ X_13 @ Y_8 ) @ Q_3 )
= ( times_times_real @ ( power_power_real @ X_13 @ Q_3 ) @ ( power_power_real @ Y_8 @ Q_3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[880]) ).
thf(2240,plain,
( ( ! [X_13: nat,Y_8: nat,Q_3: nat] :
( ( power_power_nat @ ( times_times_nat @ X_13 @ Y_8 ) @ Q_3 )
= ( times_times_nat @ ( power_power_nat @ X_13 @ Q_3 ) @ ( power_power_nat @ Y_8 @ Q_3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[879]) ).
thf(2241,plain,
( ( ! [X_12: real,P_1: nat,Q_2: nat] :
( ( times_times_real @ ( power_power_real @ X_12 @ P_1 ) @ ( power_power_real @ X_12 @ Q_2 ) )
= ( power_power_real @ X_12 @ ( plus_plus_nat @ P_1 @ Q_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[878]) ).
thf(2242,plain,
( ( ! [X_12: nat,P_1: nat,Q_2: nat] :
( ( times_times_nat @ ( power_power_nat @ X_12 @ P_1 ) @ ( power_power_nat @ X_12 @ Q_2 ) )
= ( power_power_nat @ X_12 @ ( plus_plus_nat @ P_1 @ Q_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[877]) ).
thf(2243,plain,
( ( ! [X_11: real] :
( ( power_power_real @ X_11 @ zero_zero_nat )
= one_one_real ) )
= $true ),
inference(copy,[status(thm)],[876]) ).
thf(2244,plain,
( ( ! [X_11: nat] :
( ( power_power_nat @ X_11 @ zero_zero_nat )
= one_one_nat ) )
= $true ),
inference(copy,[status(thm)],[875]) ).
thf(2245,plain,
( ( ! [A_32: real,N_33: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A_32 @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ N_33 ) ) ) )
= $true ),
inference(copy,[status(thm)],[874]) ).
thf(2246,plain,
( ( ! [C_4: real,D_2: real,A_31: real,B_12: real,R_2: real] :
( ( R_2 = zero_zero_real )
| ( C_4 = D_2 )
| ( A_31 != B_12 )
| ( ( plus_plus_real @ A_31 @ ( times_times_real @ R_2 @ C_4 ) )
!= ( plus_plus_real @ B_12 @ ( times_times_real @ R_2 @ D_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1506]) ).
thf(2247,plain,
( ( ! [C_4: nat,D_2: nat,A_31: nat,B_12: nat,R_2: nat] :
( ( R_2 = zero_zero_nat )
| ( C_4 = D_2 )
| ( A_31 != B_12 )
| ( ( plus_plus_nat @ A_31 @ ( times_times_nat @ R_2 @ C_4 ) )
!= ( plus_plus_nat @ B_12 @ ( times_times_nat @ R_2 @ D_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1505]) ).
thf(2248,plain,
( ( ! [M_12: real] :
( ( plus_plus_real @ M_12 @ M_12 )
= ( times_times_real @ ( plus_plus_real @ one_one_real @ one_one_real ) @ M_12 ) ) )
= $true ),
inference(copy,[status(thm)],[871]) ).
thf(2249,plain,
( ( ! [M_12: nat] :
( ( plus_plus_nat @ M_12 @ M_12 )
= ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) @ M_12 ) ) )
= $true ),
inference(copy,[status(thm)],[870]) ).
thf(2250,plain,
( ( ! [M_11: real,A_30: real] :
( ( plus_plus_real @ M_11 @ ( times_times_real @ A_30 @ M_11 ) )
= ( times_times_real @ ( plus_plus_real @ A_30 @ one_one_real ) @ M_11 ) ) )
= $true ),
inference(copy,[status(thm)],[869]) ).
thf(2251,plain,
( ( ! [M_11: nat,A_30: nat] :
( ( plus_plus_nat @ M_11 @ ( times_times_nat @ A_30 @ M_11 ) )
= ( times_times_nat @ ( plus_plus_nat @ A_30 @ one_one_nat ) @ M_11 ) ) )
= $true ),
inference(copy,[status(thm)],[868]) ).
thf(2252,plain,
( ( ! [A_29: real,M_10: real] :
( ( plus_plus_real @ ( times_times_real @ A_29 @ M_10 ) @ M_10 )
= ( times_times_real @ ( plus_plus_real @ A_29 @ one_one_real ) @ M_10 ) ) )
= $true ),
inference(copy,[status(thm)],[867]) ).
thf(2253,plain,
( ( ! [A_29: nat,M_10: nat] :
( ( plus_plus_nat @ ( times_times_nat @ A_29 @ M_10 ) @ M_10 )
= ( times_times_nat @ ( plus_plus_nat @ A_29 @ one_one_nat ) @ M_10 ) ) )
= $true ),
inference(copy,[status(thm)],[866]) ).
thf(2254,plain,
( ( ! [A_28: real,W_4: int] :
( ( ( number_number_of_nat @ W_4 )
= zero_zero_nat )
| ( A_28 != zero_zero_real )
| ( ( power_power_real @ A_28 @ ( number_number_of_nat @ W_4 ) )
= zero_zero_real ) )
& ! [A_28: real,W_4: int] :
( ( ( power_power_real @ A_28 @ ( number_number_of_nat @ W_4 ) )
!= zero_zero_real )
| ( ( number_number_of_nat @ W_4 )
!= zero_zero_nat ) )
& ! [A_28: real] :
( ! [W_4: int] :
( ( power_power_real @ A_28 @ ( number_number_of_nat @ W_4 ) )
!= zero_zero_real )
| ( A_28 = zero_zero_real ) ) )
= $true ),
inference(copy,[status(thm)],[1504]) ).
thf(2255,plain,
( ( ! [W_3: int] :
( ( ( number_number_of_nat @ W_3 )
!= zero_zero_nat )
| ( ( power_power_real @ zero_zero_real @ ( number_number_of_nat @ W_3 ) )
= one_one_real ) )
& ! [W_3: int] :
( ( ( number_number_of_nat @ W_3 )
= zero_zero_nat )
| ( ( power_power_real @ zero_zero_real @ ( number_number_of_nat @ W_3 ) )
= zero_zero_real ) ) )
= $true ),
inference(copy,[status(thm)],[1503]) ).
thf(2256,plain,
( ( ! [W_3: int] :
( ( ( number_number_of_nat @ W_3 )
!= zero_zero_nat )
| ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ W_3 ) )
= one_one_nat ) )
& ! [W_3: int] :
( ( ( number_number_of_nat @ W_3 )
= zero_zero_nat )
| ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ W_3 ) )
= zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1502]) ).
thf(2257,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)],[862]) ).
thf(2258,plain,
( ( ! [P: int] :
( ( ( dvd_dvd_int @ ( sK3_M_9 @ P ) @ P )
& ( ord_less_eq_int @ zero_zero_int @ ( sK3_M_9 @ P ) )
& ( ( sK3_M_9 @ P )
!= one_one_int )
& ( ( sK3_M_9 @ P )
!= P ) )
| ~ ( ord_less_int @ one_one_int @ P )
| ( zprime @ P ) )
& ! [P: int] :
( ~ ( zprime @ P )
| ! [M_9: int] :
( ~ ( dvd_dvd_int @ M_9 @ P )
| ~ ( ord_less_eq_int @ zero_zero_int @ M_9 )
| ( M_9 = one_one_int )
| ( M_9 = P ) ) )
& ! [P: int] :
( ~ ( zprime @ P )
| ( ord_less_int @ one_one_int @ P ) ) )
= $true ),
inference(copy,[status(thm)],[1501]) ).
thf(2259,plain,
( ( ! [P: int] :
( ~ ( zprime @ P )
| ( P
= ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
| ( 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)],[1500]) ).
thf(2260,plain,
( ( zcong @ ( power_power_int @ sK2_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)],[1499]) ).
thf(2261,plain,
( ( ord_less_eq_int @ min @ min )
= $true ),
inference(copy,[status(thm)],[858]) ).
thf(2262,plain,
( ( ! [M: int] :
( ! [N: int] :
( ( times_times_int @ M @ N )
!= one_one_int )
| ( M = one_one_int )
| ( M
= ( number_number_of_int @ min ) ) )
& ! [M: int,N: int] :
( ( ( times_times_int @ M @ N )
!= one_one_int )
| ( M = one_one_int )
| ( N
= ( number_number_of_int @ min ) ) )
& ! [M: int,N: int] :
( ( ( times_times_int @ M @ N )
!= one_one_int )
| ( N = one_one_int )
| ( M
= ( number_number_of_int @ min ) ) )
& ! [M: int,N: int] :
( ( ( times_times_int @ M @ N )
!= one_one_int )
| ( N = one_one_int )
| ( N
= ( number_number_of_int @ min ) ) )
& ! [M: int,N: int] :
( ( M != one_one_int )
| ( N != one_one_int )
| ( ( times_times_int @ M @ N )
= one_one_int ) )
& ! [M: int,N: int] :
( ( M
!= ( number_number_of_int @ min ) )
| ( N
!= ( number_number_of_int @ min ) )
| ( ( times_times_int @ M @ N )
= one_one_int ) ) )
= $true ),
inference(copy,[status(thm)],[1498]) ).
thf(2263,plain,
( ( ! [M: int] :
( ! [N: int] :
( ( times_times_int @ M @ N )
!= one_one_int )
| ( M = one_one_int )
| ( M
= ( number_number_of_int @ min ) ) ) )
= $true ),
inference(copy,[status(thm)],[1497]) ).
thf(2264,plain,
( ( ! [A: int] :
( ! [B: int,M: int] :
( ~ ( zcong @ A @ B @ M )
| ( zcong @ B @ A @ M ) )
& ! [B: int,M: int] :
( ~ ( zcong @ B @ A @ M )
| ( zcong @ A @ B @ M ) ) ) )
= $true ),
inference(copy,[status(thm)],[1496]) ).
thf(2265,plain,
( ( ! [K: int,M: int] : ( zcong @ K @ K @ M ) )
= $true ),
inference(copy,[status(thm)],[854]) ).
thf(2266,plain,
( ( ! [C: int,A: int,B: int,M: int] :
( ~ ( zcong @ A @ B @ M )
| ~ ( zcong @ B @ C @ M )
| ( zcong @ A @ C @ M ) ) )
= $true ),
inference(copy,[status(thm)],[1495]) ).
thf(2267,plain,
( ( ! [X_9: real,Y_7: real] :
( ~ ( ord_less_eq_real @ X_9 @ Y_7 )
| ( X_9 = Y_7 )
| ( ord_less_real @ X_9 @ Y_7 ) ) )
= $true ),
inference(copy,[status(thm)],[1494]) ).
thf(2268,plain,
( ( ! [X_9: nat,Y_7: nat] :
( ~ ( ord_less_eq_nat @ X_9 @ Y_7 )
| ( X_9 = Y_7 )
| ( ord_less_nat @ X_9 @ Y_7 ) ) )
= $true ),
inference(copy,[status(thm)],[1493]) ).
thf(2269,plain,
( ( ! [A: int,M: int,B: int] : ( zcong @ ( times_times_int @ A @ M ) @ ( times_times_int @ B @ M ) @ M ) )
= $true ),
inference(copy,[status(thm)],[850]) ).
thf(2270,plain,
( ( ! [K: int,A: int,B: int,M: int] :
( ~ ( zcong @ A @ B @ M )
| ( zcong @ ( times_times_int @ A @ K ) @ ( times_times_int @ B @ K ) @ M ) ) )
= $true ),
inference(copy,[status(thm)],[1492]) ).
thf(2271,plain,
( ( ! [K: int,A: int,B: int,M: int] :
( ~ ( zcong @ A @ B @ M )
| ( zcong @ ( times_times_int @ K @ A ) @ ( times_times_int @ K @ B ) @ M ) ) )
= $true ),
inference(copy,[status(thm)],[1491]) ).
thf(2272,plain,
( ( ! [C: int,D: int,A: int,B: int,M: int] :
( ~ ( zcong @ A @ B @ M )
| ~ ( zcong @ C @ D @ M )
| ( zcong @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) @ M ) ) )
= $true ),
inference(copy,[status(thm)],[1490]) ).
thf(2273,plain,
( ( ! [N_32: nat] :
( ( power_power_real @ ( number267125858f_real @ min ) @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ N_32 ) )
= one_one_real ) )
= $true ),
inference(copy,[status(thm)],[846]) ).
thf(2274,plain,
( ( ! [N_32: nat] :
( ( power_power_int @ ( number_number_of_int @ min ) @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ N_32 ) )
= one_one_int ) )
= $true ),
inference(copy,[status(thm)],[845]) ).
thf(2275,plain,
( ( ! [X: real] :
( ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ X @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( power_power_real @ ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ X ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[844]) ).
thf(2276,plain,
( ( ! [N: int,P: int,M: int] :
( ~ ( ord_less_eq_int @ zero_zero_int @ M )
| ~ ( 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)],[1489]) ).
thf(2277,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)],[842]) ).
thf(2278,plain,
( ( dvd_dvd_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ ( minus_minus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_int @ min ) ) )
= $true ),
inference(copy,[status(thm)],[841]) ).
thf(2279,plain,
( ( ! [J: nat,K: nat,M: int] :
( ~ ( 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)],[1488]) ).
thf(2280,plain,
( ( ! [X: int,P: int] :
( ~ ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ P )
| ~ ( zcong @ X @ ( number_number_of_int @ min ) @ P )
| ~ ( zcong @ X @ one_one_int @ P ) ) )
= $true ),
inference(copy,[status(thm)],[1487]) ).
thf(2281,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)],[838]) ).
thf(2282,plain,
( ( ! [X: real] :
( ( X != zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ ( times_times_real @ X @ X ) ) )
& ! [X: real] :
( ( ord_less_real @ zero_zero_real @ ( times_times_real @ X @ X ) )
| ( X = zero_zero_real ) ) )
= $true ),
inference(copy,[status(thm)],[1486]) ).
thf(2283,plain,
( ( ! [C: int,D: int,A: int,B: int,M: int] :
( ~ ( zcong @ A @ B @ M )
| ~ ( zcong @ C @ D @ M )
| ( zcong @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D ) @ M ) ) )
= $true ),
inference(copy,[status(thm)],[1485]) ).
thf(2284,plain,
( ( ! [K: int,M: int,N: int] :
( ~ ( dvd_dvd_int @ K @ ( minus_minus_int @ M @ N ) )
| ~ ( dvd_dvd_int @ K @ N )
| ( dvd_dvd_int @ K @ M ) ) )
= $true ),
inference(copy,[status(thm)],[1484]) ).
thf(2285,plain,
( ( ! [W: int,Z1: int,Z2: int] :
( ( 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)],[834]) ).
thf(2286,plain,
( ( ! [Z1: int,Z2: int,W: int] :
( ( 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)],[833]) ).
thf(2287,plain,
( ( ! [V_3: int,W_2: int] :
( ( number267125858f_real @ ( minus_minus_int @ V_3 @ W_2 ) )
= ( minus_minus_real @ ( number267125858f_real @ V_3 ) @ ( number267125858f_real @ W_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[832]) ).
thf(2288,plain,
( ( ! [V_3: int,W_2: int] :
( ( number_number_of_int @ ( minus_minus_int @ V_3 @ W_2 ) )
= ( minus_minus_int @ ( number_number_of_int @ V_3 ) @ ( number_number_of_int @ W_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[831]) ).
thf(2289,plain,
( ( ! [V_2: int,B_10: real,C_3: real] :
( ( times_times_real @ ( number267125858f_real @ V_2 ) @ ( minus_minus_real @ B_10 @ C_3 ) )
= ( minus_minus_real @ ( times_times_real @ ( number267125858f_real @ V_2 ) @ B_10 ) @ ( times_times_real @ ( number267125858f_real @ V_2 ) @ C_3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[830]) ).
thf(2290,plain,
( ( ! [V_2: int,B_10: int,C_3: int] :
( ( times_times_int @ ( number_number_of_int @ V_2 ) @ ( minus_minus_int @ B_10 @ C_3 ) )
= ( minus_minus_int @ ( times_times_int @ ( number_number_of_int @ V_2 ) @ B_10 ) @ ( times_times_int @ ( number_number_of_int @ V_2 ) @ C_3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[829]) ).
thf(2291,plain,
( ( ! [A_27: real,B_9: real,V_1: int] :
( ( times_times_real @ ( minus_minus_real @ A_27 @ B_9 ) @ ( number267125858f_real @ V_1 ) )
= ( minus_minus_real @ ( times_times_real @ A_27 @ ( number267125858f_real @ V_1 ) ) @ ( times_times_real @ B_9 @ ( number267125858f_real @ V_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[828]) ).
thf(2292,plain,
( ( ! [A_27: int,B_9: int,V_1: int] :
( ( times_times_int @ ( minus_minus_int @ A_27 @ B_9 ) @ ( number_number_of_int @ V_1 ) )
= ( minus_minus_int @ ( times_times_int @ A_27 @ ( number_number_of_int @ V_1 ) ) @ ( times_times_int @ B_9 @ ( number_number_of_int @ V_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[827]) ).
thf(2293,plain,
( ( ! [A: int] :
( ! [B: int,M: int] :
( ~ ( dvd_dvd_int @ M @ ( minus_minus_int @ A @ B ) )
| ( zcong @ A @ B @ M ) )
& ! [B: int,M: int] :
( ~ ( zcong @ A @ B @ M )
| ( dvd_dvd_int @ M @ ( minus_minus_int @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1483]) ).
thf(2294,plain,
( ( ! [V: int,W_1: int,C_2: real] :
( ( plus_plus_real @ ( number267125858f_real @ V ) @ ( minus_minus_real @ ( number267125858f_real @ W_1 ) @ C_2 ) )
= ( minus_minus_real @ ( number267125858f_real @ ( plus_plus_int @ V @ W_1 ) ) @ C_2 ) ) )
= $true ),
inference(copy,[status(thm)],[825]) ).
thf(2295,plain,
( ( ! [A: int,P: int] :
( ~ ( zcong @ ( times_times_int @ A @ ( minus_minus_int @ P @ one_one_int ) ) @ one_one_int @ P )
| ( zcong @ A @ ( minus_minus_int @ P @ one_one_int ) @ P ) )
& ! [A: int,P: int] :
( ~ ( zcong @ A @ ( minus_minus_int @ P @ one_one_int ) @ P )
| ( zcong @ ( times_times_int @ A @ ( minus_minus_int @ P @ one_one_int ) ) @ one_one_int @ P ) ) )
= $true ),
inference(copy,[status(thm)],[1482]) ).
thf(2296,plain,
( ( ! [D: int,C: int,A: int,B: int,M: int] :
( ~ ( zcong @ A @ B @ M )
| ( B != C )
| ~ ( zcong @ C @ D @ M )
| ( zcong @ A @ D @ M ) ) )
= $true ),
inference(copy,[status(thm)],[1481]) ).
thf(2297,plain,
( ( ! [A: int,P: int] :
( ~ ( zprime @ P )
| ~ ( ord_less_int @ zero_zero_int @ A )
| ~ ( ord_less_int @ A @ P )
| ~ ( zcong @ ( times_times_int @ A @ A ) @ one_one_int @ P )
| ( A = one_one_int )
| ( A
= ( minus_minus_int @ P @ one_one_int ) ) ) )
= $true ),
inference(copy,[status(thm)],[1480]) ).
thf(2298,plain,
( ( ! [A: int,P: int] :
( ~ ( zprime @ P )
| ~ ( ord_less_int @ zero_zero_int @ A )
| ~ ( zcong @ ( times_times_int @ A @ A ) @ one_one_int @ P )
| ( zcong @ A @ one_one_int @ P )
| ( zcong @ A @ ( minus_minus_int @ P @ one_one_int ) @ P ) ) )
= $true ),
inference(copy,[status(thm)],[1479]) ).
thf(2299,plain,
( ( ! [C: int,D: int,A: int] :
( ! [B: int,M: int] :
( ~ ( zcong @ A @ B @ M )
| ~ ( zcong @ C @ ( times_times_int @ D @ A ) @ M )
| ( zcong @ C @ ( times_times_int @ D @ B ) @ M ) )
& ! [B: int,M: int] :
( ~ ( zcong @ A @ B @ M )
| ~ ( zcong @ C @ ( times_times_int @ D @ B ) @ M )
| ( zcong @ C @ ( times_times_int @ D @ A ) @ M ) ) ) )
= $true ),
inference(copy,[status(thm)],[1478]) ).
thf(2300,plain,
( ( ! [C: int,D: int,A: int] :
( ! [B: int,M: int] :
( ~ ( zcong @ A @ B @ M )
| ~ ( zcong @ C @ ( times_times_int @ A @ D ) @ M )
| ( zcong @ C @ ( times_times_int @ B @ D ) @ M ) )
& ! [B: int,M: int] :
( ~ ( zcong @ A @ B @ M )
| ~ ( zcong @ C @ ( times_times_int @ B @ D ) @ M )
| ( zcong @ C @ ( times_times_int @ A @ D ) @ M ) ) ) )
= $true ),
inference(copy,[status(thm)],[1477]) ).
thf(2301,plain,
( ( ! [X_8: real,Y_6: real] :
( ( power_power_real @ ( minus_minus_real @ X_8 @ Y_6 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( minus_minus_real @ ( plus_plus_real @ ( power_power_real @ X_8 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y_6 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ X_8 ) @ Y_6 ) ) ) )
= $true ),
inference(copy,[status(thm)],[818]) ).
thf(2302,plain,
( ( ! [X_8: int,Y_6: int] :
( ( power_power_int @ ( minus_minus_int @ X_8 @ Y_6 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( minus_minus_int @ ( plus_plus_int @ ( power_power_int @ X_8 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_6 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ X_8 ) @ Y_6 ) ) ) )
= $true ),
inference(copy,[status(thm)],[817]) ).
thf(2303,plain,
( ( ! [A: int,B: int] :
( ( power_power_int @ ( minus_minus_int @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ ( minus_minus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[816]) ).
thf(2304,plain,
( ( ! [A: int,B: int] :
( ( power_power_int @ ( minus_minus_int @ A @ B ) @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( minus_minus_int @ ( plus_plus_int @ ( minus_minus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ B ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) @ A ) @ ( 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)],[815]) ).
thf(2305,plain,
( ( ! [M: int,N: int,P: int] :
( ~ ( 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)],[1476]) ).
thf(2306,plain,
( ( ! [P: int,Y: int,N: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ N )
| ~ ( dvd_dvd_int @ P @ Y )
| ( dvd_dvd_int @ P @ ( power_power_int @ Y @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[1475]) ).
thf(2307,plain,
( ( ! [Y: int,X: int,P: int] :
( ~ ( zprime @ P )
| ( zcong @ X @ zero_zero_int @ P )
| ( zcong @ Y @ zero_zero_int @ P )
| ~ ( zcong @ ( times_times_int @ X @ Y ) @ zero_zero_int @ P ) ) )
= $true ),
inference(copy,[status(thm)],[1474]) ).
thf(2308,plain,
( ( ! [B: int,A: int,P: int] :
( ~ ( zprime @ P )
| ~ ( ord_less_int @ zero_zero_int @ A )
| ( zcong @ A @ zero_zero_int @ P )
| ( zcong @ B @ zero_zero_int @ P )
| ~ ( zcong @ ( times_times_int @ A @ B ) @ zero_zero_int @ P ) ) )
= $true ),
inference(copy,[status(thm)],[1473]) ).
thf(2309,plain,
( ( ! [B: int,A: int,P: int] :
( ~ ( zprime @ P )
| ~ ( ord_less_int @ zero_zero_int @ A )
| ~ ( zcong @ ( times_times_int @ A @ B ) @ zero_zero_int @ P )
| ( zcong @ A @ zero_zero_int @ P )
| ( zcong @ B @ zero_zero_int @ P ) ) )
= $true ),
inference(copy,[status(thm)],[1472]) ).
thf(2310,plain,
( ( ! [Y: int,N: nat,P: int] :
( ~ ( zprime @ P )
| ~ ( dvd_dvd_int @ P @ ( power_power_int @ Y @ N ) )
| ~ ( ord_less_nat @ zero_zero_nat @ N )
| ( dvd_dvd_int @ P @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[1471]) ).
thf(2311,plain,
( ( ! [M: int] :
( ~ ( 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)],[1470]) ).
thf(2312,plain,
( ( ! [M: int] :
( ~ ( 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)],[1469]) ).
thf(2313,plain,
( ( ! [A: int,P: int] :
( ~ ( zcong @ A @ zero_zero_int @ P )
| ( ( legendre @ A @ P )
= zero_zero_int ) )
& ! [A: int,P: int] :
( ( zcong @ A @ zero_zero_int @ P )
| ~ ( quadRes @ P @ A )
| ( ( legendre @ A @ P )
= one_one_int ) )
& ! [A: int,P: int] :
( ( zcong @ A @ zero_zero_int @ P )
| ( quadRes @ P @ A )
| ( ( legendre @ A @ P )
= ( number_number_of_int @ min ) ) ) )
= $true ),
inference(copy,[status(thm)],[1468]) ).
thf(2314,plain,
( ( ! [X: real,Y: real] :
( ( power_power_real @ ( plus_plus_real @ X @ Y ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_real @ ( plus_plus_real @ ( power_power_real @ X @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ X ) @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[805]) ).
thf(2315,plain,
( ( ! [N: nat,M: nat] :
( ( M != zero_zero_nat )
| ( ( times_times_nat @ M @ N )
= zero_zero_nat ) )
& ! [N: nat,M: 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)],[1467]) ).
thf(2316,plain,
( ( ! [P: nat,M: nat] :
( ( M != zero_zero_nat )
| ( ( power_power_nat @ P @ M )
= one_one_nat ) )
& ! [P: nat,M: 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)],[1466]) ).
thf(2317,plain,
( ( ! [X: nat,Y: nat] :
( ( minus_minus_nat @ ( power_power_nat @ X @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_nat @ Y @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( times_times_nat @ ( plus_plus_nat @ X @ Y ) @ ( minus_minus_nat @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[802]) ).
thf(2318,plain,
( ( ! [X: real,Y: real] :
( ( X != zero_zero_real )
| ( Y != zero_zero_real )
| ( ( plus_plus_real @ ( power_power_real @ X @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_real ) )
& ! [X: real] :
( ! [Y: real] :
( ( plus_plus_real @ ( power_power_real @ X @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_real )
| ( X = zero_zero_real ) )
& ! [X: real,Y: real] :
( ( ( plus_plus_real @ ( power_power_real @ X @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_real )
| ( Y = zero_zero_real ) ) )
= $true ),
inference(copy,[status(thm)],[1465]) ).
thf(2319,plain,
( ( zero_zero_real != one_one_real )
= $true ),
inference(copy,[status(thm)],[1464]) ).
thf(2320,plain,
( ( ! [X: real,Y: real] :
( ( X = Y )
| ~ ( ord_less_eq_real @ X @ Y )
| ( ord_less_real @ X @ Y ) )
& ! [X: real,Y: real] :
( ~ ( ord_less_real @ X @ Y )
| ( X != Y ) )
& ! [X: real,Y: real] :
( ~ ( ord_less_real @ X @ Y )
| ( ord_less_eq_real @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[1463]) ).
thf(2321,plain,
( ( ! [X: real,Y: real] :
( ~ ( ord_less_eq_real @ X @ Y )
| ( X = Y )
| ( ord_less_real @ X @ Y ) )
& ! [X: real,Y: real] :
( ( X != Y )
| ( ord_less_eq_real @ X @ Y ) )
& ! [X: real,Y: real] :
( ~ ( ord_less_real @ X @ Y )
| ( ord_less_eq_real @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[1462]) ).
thf(2322,plain,
( ( ! [Z1: real,Z2: real,Z3: real] :
( ( times_times_real @ ( times_times_real @ Z1 @ Z2 ) @ Z3 )
= ( times_times_real @ Z1 @ ( times_times_real @ Z2 @ Z3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[797]) ).
thf(2323,plain,
( ( ! [Z: real,W: real] :
( ( times_times_real @ Z @ W )
= ( times_times_real @ W @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[796]) ).
thf(2324,plain,
( ( ! [Z: real] :
( ( times_times_real @ one_one_real @ Z )
= Z ) )
= $true ),
inference(copy,[status(thm)],[795]) ).
thf(2325,plain,
( ( ! [Z: real,X: real,Y: real] :
( ~ ( ord_less_eq_real @ X @ Y )
| ( ord_less_eq_real @ ( plus_plus_real @ Z @ X ) @ ( plus_plus_real @ Z @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[1461]) ).
thf(2326,plain,
( ( ! [A_26: real,C_1: real,B_8: real,D_1: real] :
( ( minus_minus_real @ ( plus_plus_real @ A_26 @ C_1 ) @ ( plus_plus_real @ B_8 @ D_1 ) )
= ( plus_plus_real @ ( minus_minus_real @ A_26 @ B_8 ) @ ( minus_minus_real @ C_1 @ D_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[793]) ).
thf(2327,plain,
( ( ! [A: real] :
( ! [B: real,C: real] :
( ( C = zero_zero_real )
| ( ( times_times_real @ C @ A )
!= ( times_times_real @ C @ B ) )
| ( A = B ) )
& ! [B: real,C: real] :
( ( C = zero_zero_real )
| ( A != B )
| ( ( times_times_real @ C @ A )
= ( times_times_real @ C @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1460]) ).
thf(2328,plain,
( ( ! [A: real] :
( ! [B: real,C: real] :
( ( C = zero_zero_real )
| ( ( times_times_real @ A @ C )
!= ( times_times_real @ B @ C ) )
| ( A = B ) )
& ! [B: real,C: real] :
( ( C = zero_zero_real )
| ( A != B )
| ( ( times_times_real @ A @ C )
= ( times_times_real @ B @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1459]) ).
thf(2329,plain,
( ( ! [N: nat,M: nat] :
( ( N != one_one_nat )
| ( M != one_one_nat )
| ( ( times_times_nat @ N @ M )
= one_one_nat ) )
& ! [N: nat] :
( ! [M: nat] :
( ( times_times_nat @ N @ M )
!= one_one_nat )
| ( N = one_one_nat ) )
& ! [N: nat,M: nat] :
( ( ( times_times_nat @ N @ M )
!= one_one_nat )
| ( M = one_one_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1458]) ).
thf(2330,plain,
( ( ! [Z1: real,Z2: real,W: real] :
( ( 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)],[789]) ).
thf(2331,plain,
( ( ! [M: nat,N: nat] :
( ( N = zero_zero_nat )
| ( M != zero_zero_nat )
| ( ( power_power_nat @ M @ N )
= zero_zero_nat ) )
& ! [M: nat,N: nat] :
( ( ( power_power_nat @ M @ N )
!= zero_zero_nat )
| ( N != zero_zero_nat ) )
& ! [M: nat] :
( ! [N: nat] :
( ( power_power_nat @ M @ N )
!= zero_zero_nat )
| ( M = zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1457]) ).
thf(2332,plain,
( ( ! [X_7: real,Y_5: real,A_25: real,B_7: real] :
( ( minus_minus_real @ ( times_times_real @ X_7 @ Y_5 ) @ ( times_times_real @ A_25 @ B_7 ) )
= ( plus_plus_real @ ( times_times_real @ X_7 @ ( minus_minus_real @ Y_5 @ B_7 ) ) @ ( times_times_real @ ( minus_minus_real @ X_7 @ A_25 ) @ B_7 ) ) ) )
= $true ),
inference(copy,[status(thm)],[787]) ).
thf(2333,plain,
( ( ! [X: real] :
( ! [Y: real,Z: real] :
( ~ ( ord_less_real @ zero_zero_real @ Z )
| ~ ( ord_less_eq_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ Y @ Z ) )
| ( ord_less_eq_real @ X @ Y ) )
& ! [Y: real,Z: real] :
( ~ ( ord_less_real @ zero_zero_real @ Z )
| ~ ( ord_less_eq_real @ X @ Y )
| ( ord_less_eq_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ Y @ Z ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1456]) ).
thf(2334,plain,
( ( ! [X: real] :
( ! [Y: real,Z: real] :
( ~ ( ord_less_real @ zero_zero_real @ Z )
| ~ ( ord_less_eq_real @ ( times_times_real @ Z @ X ) @ ( times_times_real @ Z @ Y ) )
| ( ord_less_eq_real @ X @ Y ) )
& ! [Y: real,Z: real] :
( ~ ( ord_less_real @ zero_zero_real @ Z )
| ~ ( ord_less_eq_real @ X @ Y )
| ( ord_less_eq_real @ ( times_times_real @ Z @ X ) @ ( times_times_real @ Z @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1455]) ).
thf(2335,plain,
( ( ! [X: real,Y: real,Z: real] :
( ~ ( ord_less_real @ zero_zero_real @ Z )
| ~ ( ord_less_real @ X @ Y )
| ( ord_less_real @ ( times_times_real @ Z @ X ) @ ( times_times_real @ Z @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[1454]) ).
thf(2336,plain,
( ( ! [Y: real,X: real] :
( ~ ( ord_less_real @ zero_zero_real @ X )
| ~ ( ord_less_real @ zero_zero_real @ Y )
| ( ord_less_real @ zero_zero_real @ ( times_times_real @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[1453]) ).
thf(2337,plain,
( ( ! [X: real] :
( ! [Y: real,Z: real] :
( ~ ( ord_less_real @ zero_zero_real @ Z )
| ~ ( ord_less_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ Y @ Z ) )
| ( ord_less_real @ X @ Y ) )
& ! [Y: real,Z: real] :
( ~ ( ord_less_real @ zero_zero_real @ Z )
| ~ ( ord_less_real @ X @ Y )
| ( ord_less_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ Y @ Z ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1452]) ).
thf(2338,plain,
( ( ! [X: real,Y: real] :
( ( X != zero_zero_real )
| ( Y != zero_zero_real )
| ( ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) )
= zero_zero_real ) )
& ! [X: real] :
( ! [Y: real] :
( ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) )
!= zero_zero_real )
| ( X = zero_zero_real ) )
& ! [X: real,Y: real] :
( ( ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) )
!= zero_zero_real )
| ( Y = zero_zero_real ) ) )
= $true ),
inference(copy,[status(thm)],[1451]) ).
thf(2339,plain,
( ( ! [X: nat,N: nat] :
( ( ( power_power_nat @ X @ N )
!= one_one_nat )
| ( X = one_one_nat )
| ( N = zero_zero_nat ) )
& ! [X: nat] :
( ( X != one_one_nat )
| ! [N: nat] :
( ( power_power_nat @ X @ N )
= one_one_nat ) )
& ! [X: nat,N: nat] :
( ( N != zero_zero_nat )
| ( ( power_power_nat @ X @ N )
= one_one_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1450]) ).
thf(2340,plain,
( ( ! [X_6: real] :
( ( minus_minus_real @ ( times_times_real @ X_6 @ X_6 ) @ one_one_real )
= ( times_times_real @ ( plus_plus_real @ X_6 @ one_one_real ) @ ( minus_minus_real @ X_6 @ one_one_real ) ) ) )
= $true ),
inference(copy,[status(thm)],[779]) ).
thf(2341,plain,
( ( ! [X_5: real,N_31: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ N_31 )
| ( ( times_times_real @ ( power_power_real @ X_5 @ ( minus_minus_nat @ N_31 @ one_one_nat ) ) @ X_5 )
= ( power_power_real @ X_5 @ N_31 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1449]) ).
thf(2342,plain,
( ( ! [X_5: nat,N_31: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ N_31 )
| ( ( times_times_nat @ ( power_power_nat @ X_5 @ ( minus_minus_nat @ N_31 @ one_one_nat ) ) @ X_5 )
= ( power_power_nat @ X_5 @ N_31 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1448]) ).
thf(2343,plain,
( ( ! [X_5: int,N_31: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ N_31 )
| ( ( times_times_int @ ( power_power_int @ X_5 @ ( minus_minus_nat @ N_31 @ one_one_nat ) ) @ X_5 )
= ( power_power_int @ X_5 @ N_31 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1447]) ).
thf(2344,plain,
( ( ! [N: nat] : ( ord_less_eq_real @ one_one_real @ ( power_power_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ N ) ) )
= $true ),
inference(copy,[status(thm)],[775]) ).
thf(2345,plain,
( ( ! [M_8: real,N_30: nat] :
( ( N_30 != zero_zero_nat )
| ( ( power_power_real @ M_8 @ N_30 )
= one_one_real ) )
& ! [M_8: real,N_30: nat] :
( ( N_30 = zero_zero_nat )
| ( ( power_power_real @ M_8 @ N_30 )
= ( times_times_real @ M_8 @ ( power_power_real @ M_8 @ ( minus_minus_nat @ N_30 @ one_one_nat ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1446]) ).
thf(2346,plain,
( ( ! [M_8: nat,N_30: nat] :
( ( N_30 != zero_zero_nat )
| ( ( power_power_nat @ M_8 @ N_30 )
= one_one_nat ) )
& ! [M_8: nat,N_30: nat] :
( ( N_30 = zero_zero_nat )
| ( ( power_power_nat @ M_8 @ N_30 )
= ( times_times_nat @ M_8 @ ( power_power_nat @ M_8 @ ( minus_minus_nat @ N_30 @ one_one_nat ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1445]) ).
thf(2347,plain,
( ( ! [M_8: int,N_30: nat] :
( ( N_30 != zero_zero_nat )
| ( ( power_power_int @ M_8 @ N_30 )
= one_one_int ) )
& ! [M_8: int,N_30: nat] :
( ( N_30 = zero_zero_nat )
| ( ( power_power_int @ M_8 @ N_30 )
= ( times_times_int @ M_8 @ ( power_power_int @ M_8 @ ( minus_minus_nat @ N_30 @ one_one_nat ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1444]) ).
thf(2348,plain,
( ( ! [N_29: nat,A_24: real,B_6: real] :
( ~ ( ord_less_real @ A_24 @ B_6 )
| ~ ( ord_less_eq_real @ zero_zero_real @ A_24 )
| ~ ( ord_less_nat @ zero_zero_nat @ N_29 )
| ( ord_less_real @ ( power_power_real @ A_24 @ N_29 ) @ ( power_power_real @ B_6 @ N_29 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1443]) ).
thf(2349,plain,
( ( ! [N_29: nat,A_24: nat,B_6: nat] :
( ~ ( ord_less_nat @ A_24 @ B_6 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ A_24 )
| ~ ( ord_less_nat @ zero_zero_nat @ N_29 )
| ( ord_less_nat @ ( power_power_nat @ A_24 @ N_29 ) @ ( power_power_nat @ B_6 @ N_29 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1442]) ).
thf(2350,plain,
( ( ! [N_29: nat,A_24: int,B_6: int] :
( ~ ( ord_less_int @ A_24 @ B_6 )
| ~ ( ord_less_eq_int @ zero_zero_int @ A_24 )
| ~ ( ord_less_nat @ zero_zero_nat @ N_29 )
| ( ord_less_int @ ( power_power_int @ A_24 @ N_29 ) @ ( power_power_int @ B_6 @ N_29 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1441]) ).
thf(2351,plain,
( ( ! [N_28: nat,A_23: real] :
( ( A_23 = zero_zero_real )
| ( ( power_power_real @ A_23 @ N_28 )
!= zero_zero_real ) ) )
= $true ),
inference(copy,[status(thm)],[1440]) ).
thf(2352,plain,
( ( ! [A_22: real,B_5: real,N_27: nat] :
( ( power_power_real @ ( times_times_real @ A_22 @ B_5 ) @ N_27 )
= ( times_times_real @ ( power_power_real @ A_22 @ N_27 ) @ ( power_power_real @ B_5 @ N_27 ) ) ) )
= $true ),
inference(copy,[status(thm)],[767]) ).
thf(2353,plain,
( ( ! [A_22: nat,B_5: nat,N_27: nat] :
( ( power_power_nat @ ( times_times_nat @ A_22 @ B_5 ) @ N_27 )
= ( times_times_nat @ ( power_power_nat @ A_22 @ N_27 ) @ ( power_power_nat @ B_5 @ N_27 ) ) ) )
= $true ),
inference(copy,[status(thm)],[766]) ).
thf(2354,plain,
( ( ! [A_21: real,N_26: nat] :
( ( times_times_real @ ( power_power_real @ A_21 @ N_26 ) @ A_21 )
= ( times_times_real @ A_21 @ ( power_power_real @ A_21 @ N_26 ) ) ) )
= $true ),
inference(copy,[status(thm)],[765]) ).
thf(2355,plain,
( ( ! [A_21: nat,N_26: nat] :
( ( times_times_nat @ ( power_power_nat @ A_21 @ N_26 ) @ A_21 )
= ( times_times_nat @ A_21 @ ( power_power_nat @ A_21 @ N_26 ) ) ) )
= $true ),
inference(copy,[status(thm)],[764]) ).
thf(2356,plain,
( ( ! [N_25: nat] :
( ( power_power_real @ one_one_real @ N_25 )
= one_one_real ) )
= $true ),
inference(copy,[status(thm)],[763]) ).
thf(2357,plain,
( ( ! [N_25: nat] :
( ( power_power_nat @ one_one_nat @ N_25 )
= one_one_nat ) )
= $true ),
inference(copy,[status(thm)],[762]) ).
thf(2358,plain,
( ( ! [N_24: nat,X_4: nat,Y_4: nat] :
( ~ ( dvd_dvd_nat @ X_4 @ Y_4 )
| ( dvd_dvd_nat @ ( power_power_nat @ X_4 @ N_24 ) @ ( power_power_nat @ Y_4 @ N_24 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1439]) ).
thf(2359,plain,
( ( ! [N_24: nat,X_4: real,Y_4: real] :
( ~ ( dvd_dvd_real @ X_4 @ Y_4 )
| ( dvd_dvd_real @ ( power_power_real @ X_4 @ N_24 ) @ ( power_power_real @ Y_4 @ N_24 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1438]) ).
thf(2360,plain,
( ( ! [A_20: real,M_7: nat,N_23: nat] :
( ( power_power_real @ A_20 @ ( times_times_nat @ M_7 @ N_23 ) )
= ( power_power_real @ ( power_power_real @ A_20 @ M_7 ) @ N_23 ) ) )
= $true ),
inference(copy,[status(thm)],[759]) ).
thf(2361,plain,
( ( ! [A_20: nat,M_7: nat,N_23: nat] :
( ( power_power_nat @ A_20 @ ( times_times_nat @ M_7 @ N_23 ) )
= ( power_power_nat @ ( power_power_nat @ A_20 @ M_7 ) @ N_23 ) ) )
= $true ),
inference(copy,[status(thm)],[758]) ).
thf(2362,plain,
( ( ! [A_19: real] :
( ( power_power_real @ A_19 @ one_one_nat )
= A_19 ) )
= $true ),
inference(copy,[status(thm)],[757]) ).
thf(2363,plain,
( ( ! [A_19: nat] :
( ( power_power_nat @ A_19 @ one_one_nat )
= A_19 ) )
= $true ),
inference(copy,[status(thm)],[756]) ).
thf(2364,plain,
( ( ! [N_22: nat,A_18: real,B_4: real] :
( ~ ( ord_less_eq_real @ A_18 @ B_4 )
| ~ ( ord_less_eq_real @ zero_zero_real @ A_18 )
| ( ord_less_eq_real @ ( power_power_real @ A_18 @ N_22 ) @ ( power_power_real @ B_4 @ N_22 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1437]) ).
thf(2365,plain,
( ( ! [N_22: nat,A_18: nat,B_4: nat] :
( ~ ( ord_less_eq_nat @ A_18 @ B_4 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ A_18 )
| ( ord_less_eq_nat @ ( power_power_nat @ A_18 @ N_22 ) @ ( power_power_nat @ B_4 @ N_22 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1436]) ).
thf(2366,plain,
( ( ! [N_21: nat,A_17: real] :
( ~ ( ord_less_eq_real @ zero_zero_real @ A_17 )
| ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A_17 @ N_21 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1435]) ).
thf(2367,plain,
( ( ! [N_21: nat,A_17: nat] :
( ~ ( ord_less_eq_nat @ zero_zero_nat @ A_17 )
| ( ord_less_eq_nat @ zero_zero_nat @ ( power_power_nat @ A_17 @ N_21 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1434]) ).
thf(2368,plain,
( ( ! [N_20: nat,A_16: real] :
( ~ ( ord_less_real @ zero_zero_real @ A_16 )
| ( ord_less_real @ zero_zero_real @ ( power_power_real @ A_16 @ N_20 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1433]) ).
thf(2369,plain,
( ( ! [N_20: nat,A_16: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ A_16 )
| ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A_16 @ N_20 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1432]) ).
thf(2370,plain,
( ( ! [N_19: nat,A_15: real] :
( ~ ( ord_less_eq_real @ one_one_real @ A_15 )
| ( ord_less_eq_real @ one_one_real @ ( power_power_real @ A_15 @ N_19 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1431]) ).
thf(2371,plain,
( ( ! [N_19: nat,A_15: nat] :
( ~ ( ord_less_eq_nat @ one_one_nat @ A_15 )
| ( ord_less_eq_nat @ one_one_nat @ ( power_power_nat @ A_15 @ N_19 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1430]) ).
thf(2372,plain,
( ( ! [M_6: nat] :
( ! [N_18: nat,A_14: real] :
( ~ ( ord_less_real @ one_one_real @ A_14 )
| ( ( power_power_real @ A_14 @ M_6 )
!= ( power_power_real @ A_14 @ N_18 ) )
| ( M_6 = N_18 ) )
& ! [N_18: nat,A_14: real] :
( ~ ( ord_less_real @ one_one_real @ A_14 )
| ( M_6 != N_18 )
| ( ( power_power_real @ A_14 @ M_6 )
= ( power_power_real @ A_14 @ N_18 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1429]) ).
thf(2373,plain,
( ( ! [M_6: nat] :
( ! [N_18: nat,A_14: nat] :
( ~ ( ord_less_nat @ one_one_nat @ A_14 )
| ( ( power_power_nat @ A_14 @ M_6 )
!= ( power_power_nat @ A_14 @ N_18 ) )
| ( M_6 = N_18 ) )
& ! [N_18: nat,A_14: nat] :
( ~ ( ord_less_nat @ one_one_nat @ A_14 )
| ( M_6 != N_18 )
| ( ( power_power_nat @ A_14 @ M_6 )
= ( power_power_nat @ A_14 @ N_18 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1428]) ).
thf(2374,plain,
( ( ! [A_13: real,N_17: nat] :
( ( N_17 = zero_zero_nat )
| ( A_13 != zero_zero_real )
| ( ( power_power_real @ A_13 @ N_17 )
= zero_zero_real ) )
& ! [A_13: real,N_17: nat] :
( ( ( power_power_real @ A_13 @ N_17 )
!= zero_zero_real )
| ( N_17 != zero_zero_nat ) )
& ! [A_13: real] :
( ! [N_17: nat] :
( ( power_power_real @ A_13 @ N_17 )
!= zero_zero_real )
| ( A_13 = zero_zero_real ) ) )
= $true ),
inference(copy,[status(thm)],[1427]) ).
thf(2375,plain,
( ( ! [A_13: nat,N_17: nat] :
( ( N_17 = zero_zero_nat )
| ( A_13 != zero_zero_nat )
| ( ( power_power_nat @ A_13 @ N_17 )
= zero_zero_nat ) )
& ! [A_13: nat,N_17: nat] :
( ( ( power_power_nat @ A_13 @ N_17 )
!= zero_zero_nat )
| ( N_17 != zero_zero_nat ) )
& ! [A_13: nat] :
( ! [N_17: nat] :
( ( power_power_nat @ A_13 @ N_17 )
!= zero_zero_nat )
| ( A_13 = zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1426]) ).
thf(2376,plain,
( ( ! [A_12: real] :
( ( power_power_real @ A_12 @ zero_zero_nat )
= one_one_real ) )
= $true ),
inference(copy,[status(thm)],[743]) ).
thf(2377,plain,
( ( ! [A_12: nat] :
( ( power_power_nat @ A_12 @ zero_zero_nat )
= one_one_nat ) )
= $true ),
inference(copy,[status(thm)],[742]) ).
thf(2378,plain,
( ( ! [A_11: real,M_5: nat,N_16: nat] :
( ( power_power_real @ A_11 @ ( plus_plus_nat @ M_5 @ N_16 ) )
= ( times_times_real @ ( power_power_real @ A_11 @ M_5 ) @ ( power_power_real @ A_11 @ N_16 ) ) ) )
= $true ),
inference(copy,[status(thm)],[741]) ).
thf(2379,plain,
( ( ! [A_11: nat,M_5: nat,N_16: nat] :
( ( power_power_nat @ A_11 @ ( plus_plus_nat @ M_5 @ N_16 ) )
= ( times_times_nat @ ( power_power_nat @ A_11 @ M_5 ) @ ( power_power_nat @ A_11 @ N_16 ) ) ) )
= $true ),
inference(copy,[status(thm)],[740]) ).
thf(2380,plain,
( ( ! [M_4: nat,A_10: nat,N_15: nat,B_3: nat] :
( ~ ( dvd_dvd_nat @ ( power_power_nat @ A_10 @ N_15 ) @ B_3 )
| ~ ( ord_less_eq_nat @ M_4 @ N_15 )
| ( dvd_dvd_nat @ ( power_power_nat @ A_10 @ M_4 ) @ B_3 ) ) )
= $true ),
inference(copy,[status(thm)],[1425]) ).
thf(2381,plain,
( ( ! [M_4: nat,A_10: real,N_15: nat,B_3: real] :
( ~ ( dvd_dvd_real @ ( power_power_real @ A_10 @ N_15 ) @ B_3 )
| ~ ( ord_less_eq_nat @ M_4 @ N_15 )
| ( dvd_dvd_real @ ( power_power_real @ A_10 @ M_4 ) @ B_3 ) ) )
= $true ),
inference(copy,[status(thm)],[1424]) ).
thf(2382,plain,
( ( ! [N_14: nat,M_3: nat,X_3: nat,Y_3: nat] :
( ~ ( dvd_dvd_nat @ X_3 @ Y_3 )
| ~ ( ord_less_eq_nat @ N_14 @ M_3 )
| ( dvd_dvd_nat @ ( power_power_nat @ X_3 @ N_14 ) @ ( power_power_nat @ Y_3 @ M_3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1423]) ).
thf(2383,plain,
( ( ! [N_14: nat,M_3: nat,X_3: real,Y_3: real] :
( ~ ( dvd_dvd_real @ X_3 @ Y_3 )
| ~ ( ord_less_eq_nat @ N_14 @ M_3 )
| ( dvd_dvd_real @ ( power_power_real @ X_3 @ N_14 ) @ ( power_power_real @ Y_3 @ M_3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1422]) ).
thf(2384,plain,
( ( ! [A_9: nat,M_2: nat,N_13: nat] :
( ~ ( ord_less_eq_nat @ M_2 @ N_13 )
| ( dvd_dvd_nat @ ( power_power_nat @ A_9 @ M_2 ) @ ( power_power_nat @ A_9 @ N_13 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1421]) ).
thf(2385,plain,
( ( ! [A_9: real,M_2: nat,N_13: nat] :
( ~ ( ord_less_eq_nat @ M_2 @ N_13 )
| ( dvd_dvd_real @ ( power_power_real @ A_9 @ M_2 ) @ ( power_power_real @ A_9 @ N_13 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1420]) ).
thf(2386,plain,
( ( ! [M: nat,N: nat,I: nat] :
( ~ ( 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)],[1419]) ).
thf(2387,plain,
( ( ! [X: nat,N: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X @ N ) )
| ( N = zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ X ) )
& ! [X: nat,N: nat] :
( ( N != zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X @ N ) ) )
& ! [X: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ X )
| ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[1418]) ).
thf(2388,plain,
( ( ! [A_8: real,N_12: nat,B_2: real] :
( ~ ( ord_less_real @ ( power_power_real @ A_8 @ N_12 ) @ ( power_power_real @ B_2 @ N_12 ) )
| ~ ( ord_less_eq_real @ zero_zero_real @ B_2 )
| ( ord_less_real @ A_8 @ B_2 ) ) )
= $true ),
inference(copy,[status(thm)],[1417]) ).
thf(2389,plain,
( ( ! [A_8: nat,N_12: nat,B_2: nat] :
( ~ ( ord_less_nat @ ( power_power_nat @ A_8 @ N_12 ) @ ( power_power_nat @ B_2 @ N_12 ) )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ B_2 )
| ( ord_less_nat @ A_8 @ B_2 ) ) )
= $true ),
inference(copy,[status(thm)],[1416]) ).
thf(2390,plain,
( ( ! [N_11: nat,A_7: real] :
( ~ ( ord_less_real @ one_one_real @ A_7 )
| ( ord_less_real @ ( power_power_real @ A_7 @ N_11 ) @ ( times_times_real @ A_7 @ ( power_power_real @ A_7 @ N_11 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1415]) ).
thf(2391,plain,
( ( ! [N_11: nat,A_7: nat] :
( ~ ( ord_less_nat @ one_one_nat @ A_7 )
| ( ord_less_nat @ ( power_power_nat @ A_7 @ N_11 ) @ ( times_times_nat @ A_7 @ ( power_power_nat @ A_7 @ N_11 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1414]) ).
thf(2392,plain,
( ( ! [N_10: nat,A_6: real] :
( ~ ( ord_less_real @ one_one_real @ A_6 )
| ( ord_less_real @ one_one_real @ ( times_times_real @ A_6 @ ( power_power_real @ A_6 @ N_10 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1413]) ).
thf(2393,plain,
( ( ! [N_10: nat,A_6: nat] :
( ~ ( ord_less_nat @ one_one_nat @ A_6 )
| ( ord_less_nat @ one_one_nat @ ( times_times_nat @ A_6 @ ( power_power_nat @ A_6 @ N_10 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1412]) ).
thf(2394,plain,
( ( ! [N_9: nat] :
( ( N_9 != zero_zero_nat )
| ( ( power_power_real @ zero_zero_real @ N_9 )
= one_one_real ) )
& ! [N_9: nat] :
( ( N_9 = zero_zero_nat )
| ( ( power_power_real @ zero_zero_real @ N_9 )
= zero_zero_real ) ) )
= $true ),
inference(copy,[status(thm)],[1411]) ).
thf(2395,plain,
( ( ! [N_9: nat] :
( ( N_9 != zero_zero_nat )
| ( ( power_power_nat @ zero_zero_nat @ N_9 )
= one_one_nat ) )
& ! [N_9: nat] :
( ( N_9 = zero_zero_nat )
| ( ( power_power_nat @ zero_zero_nat @ N_9 )
= zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1410]) ).
thf(2396,plain,
( ( ! [A_5: real,N_8: nat,N_7: nat] :
( ~ ( ord_less_nat @ N_8 @ N_7 )
| ~ ( ord_less_real @ one_one_real @ A_5 )
| ( ord_less_real @ ( power_power_real @ A_5 @ N_8 ) @ ( power_power_real @ A_5 @ N_7 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1409]) ).
thf(2397,plain,
( ( ! [A_5: nat,N_8: nat,N_7: nat] :
( ~ ( ord_less_nat @ N_8 @ N_7 )
| ~ ( ord_less_nat @ one_one_nat @ A_5 )
| ( ord_less_nat @ ( power_power_nat @ A_5 @ N_8 ) @ ( power_power_nat @ A_5 @ N_7 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1408]) ).
thf(2398,plain,
( ( ! [M_1: nat,N_6: nat,A_4: real] :
( ~ ( ord_less_real @ one_one_real @ A_4 )
| ~ ( ord_less_real @ ( power_power_real @ A_4 @ M_1 ) @ ( power_power_real @ A_4 @ N_6 ) )
| ( ord_less_nat @ M_1 @ N_6 ) ) )
= $true ),
inference(copy,[status(thm)],[1407]) ).
thf(2399,plain,
( ( ! [M_1: nat,N_6: nat,A_4: nat] :
( ~ ( ord_less_nat @ one_one_nat @ A_4 )
| ~ ( ord_less_nat @ ( power_power_nat @ A_4 @ M_1 ) @ ( power_power_nat @ A_4 @ N_6 ) )
| ( ord_less_nat @ M_1 @ N_6 ) ) )
= $true ),
inference(copy,[status(thm)],[1406]) ).
thf(2400,plain,
( ( ! [X_2: nat] :
( ! [Y_2: nat,B_1: real] :
( ~ ( ord_less_real @ one_one_real @ B_1 )
| ~ ( ord_less_nat @ X_2 @ Y_2 )
| ( ord_less_real @ ( power_power_real @ B_1 @ X_2 ) @ ( power_power_real @ B_1 @ Y_2 ) ) )
& ! [Y_2: nat,B_1: real] :
( ~ ( ord_less_real @ one_one_real @ B_1 )
| ~ ( ord_less_real @ ( power_power_real @ B_1 @ X_2 ) @ ( power_power_real @ B_1 @ Y_2 ) )
| ( ord_less_nat @ X_2 @ Y_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1405]) ).
thf(2401,plain,
( ( ! [X_2: nat] :
( ! [Y_2: nat,B_1: nat] :
( ~ ( ord_less_nat @ one_one_nat @ B_1 )
| ~ ( ord_less_nat @ ( power_power_nat @ B_1 @ X_2 ) @ ( power_power_nat @ B_1 @ Y_2 ) )
| ( ord_less_nat @ X_2 @ Y_2 ) )
& ! [Y_2: nat,B_1: nat] :
( ~ ( ord_less_nat @ one_one_nat @ B_1 )
| ~ ( ord_less_nat @ X_2 @ Y_2 )
| ( ord_less_nat @ ( power_power_nat @ B_1 @ X_2 ) @ ( power_power_nat @ B_1 @ Y_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1404]) ).
thf(2402,plain,
( ( ! [A_3: real,N_5: nat,N_4: nat] :
( ~ ( ord_less_eq_nat @ N_5 @ N_4 )
| ~ ( ord_less_eq_real @ one_one_real @ A_3 )
| ( ord_less_eq_real @ ( power_power_real @ A_3 @ N_5 ) @ ( power_power_real @ A_3 @ N_4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1403]) ).
thf(2403,plain,
( ( ! [A_3: nat,N_5: nat,N_4: nat] :
( ~ ( ord_less_eq_nat @ N_5 @ N_4 )
| ~ ( ord_less_eq_nat @ one_one_nat @ A_3 )
| ( ord_less_eq_nat @ ( power_power_nat @ A_3 @ N_5 ) @ ( power_power_nat @ A_3 @ N_4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1402]) ).
thf(2404,plain,
( ( ! [N_3: nat,A_2: real] :
( ~ ( ord_less_real @ zero_zero_real @ A_2 )
| ~ ( ord_less_real @ A_2 @ one_one_real )
| ( ord_less_real @ ( times_times_real @ A_2 @ ( power_power_real @ A_2 @ N_3 ) ) @ ( power_power_real @ A_2 @ N_3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1401]) ).
thf(2405,plain,
( ( ! [N_3: nat,A_2: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ A_2 )
| ~ ( ord_less_nat @ A_2 @ one_one_nat )
| ( ord_less_nat @ ( times_times_nat @ A_2 @ ( power_power_nat @ A_2 @ N_3 ) ) @ ( power_power_nat @ A_2 @ N_3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1400]) ).
thf(2406,plain,
( ( ! [A: real,N: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ N )
| ~ ( ord_less_real @ zero_zero_real @ A )
| ( ! [SY1333: real] :
( ( ( power_power_real @ SY1333 @ N )
!= A )
| ~ ( ord_less_real @ zero_zero_real @ SY1333 )
| ( SY1333
= ( sK1_X_1 @ N @ A ) ) )
& ( ( power_power_real @ ( sK1_X_1 @ N @ A ) @ N )
= A )
& ( ord_less_real @ zero_zero_real @ ( sK1_X_1 @ N @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1399]) ).
thf(2407,plain,
( ( ! [A: nat,B: nat] :
( ~ ( dvd_dvd_nat @ A @ B )
| ( B = zero_zero_nat )
| ( ord_less_eq_nat @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[1398]) ).
thf(2408,plain,
( ( ! [N: nat,X: nat,Y: nat] :
( ~ ( dvd_dvd_nat @ X @ Y )
| ( dvd_dvd_nat @ ( power_power_nat @ X @ N ) @ ( power_power_nat @ Y @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[1397]) ).
thf(2409,plain,
( ( ! [C: nat,A: nat,B: nat] :
( ~ ( dvd_dvd_nat @ A @ B )
| ( dvd_dvd_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[1396]) ).
thf(2410,plain,
( ( ! [C: nat,A: nat,B: nat] :
( ~ ( dvd_dvd_nat @ A @ B )
| ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[1395]) ).
thf(2411,plain,
( ( ! [B: nat,D: nat,A: nat] :
( ~ ( dvd_dvd_nat @ D @ A )
| ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ A @ B ) )
| ( dvd_dvd_nat @ D @ B ) ) )
= $true ),
inference(copy,[status(thm)],[1394]) ).
thf(2412,plain,
( ( ! [M: nat] :
( ! [K: nat,N: nat] :
( ~ ( dvd_dvd_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
| ( K = zero_zero_nat )
| ( dvd_dvd_nat @ M @ N ) )
& ! [K: nat] :
( ( K != zero_zero_nat )
| ! [N: nat] : ( dvd_dvd_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) ) )
& ! [K: nat,N: nat] :
( ~ ( dvd_dvd_nat @ M @ N )
| ( dvd_dvd_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1393]) ).
thf(2413,plain,
( ( ! [A: nat,N: nat,B: nat] :
( ~ ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
| ( N = zero_zero_nat )
| ( dvd_dvd_nat @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[1392]) ).
thf(2414,plain,
( ( ! [X: nat,Y: nat,N: nat] :
( ( N = zero_zero_nat )
| ~ ( dvd_dvd_nat @ ( power_power_nat @ X @ N ) @ Y )
| ( dvd_dvd_nat @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[1391]) ).
thf(2415,plain,
( ( ! [X: nat,Q: nat,N: nat,R: nat] :
( ( X
!= ( plus_plus_nat @ ( times_times_nat @ Q @ N ) @ R ) )
| ~ ( ord_less_nat @ zero_zero_nat @ R )
| ~ ( ord_less_nat @ R @ N )
| ~ ( dvd_dvd_nat @ N @ X ) ) )
= $true ),
inference(copy,[status(thm)],[1390]) ).
thf(2416,plain,
( ( ! [I: nat,M: nat,N: nat] :
( ~ ( 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)],[1389]) ).
thf(2417,plain,
( ( ! [N: nat,M: nat] :
( ~ ( dvd_dvd_nat @ N @ M )
| ( ord_less_eq_nat @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ N ) @ M )
| ( M = zero_zero_nat )
| ( M = N ) ) )
= $true ),
inference(copy,[status(thm)],[1388]) ).
thf(2418,plain,
( ( ~ ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int ) @ zero_zero_int ) )
= $true ),
inference(copy,[status(thm)],[1387]) ).
thf(2419,plain,
( ( ~ ( ~ ! [SX0: real] :
( ( ( power_power_real @ SX0 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= zero_zero_real )
| ( SX0 = zero_zero_real ) )
| ~ ! [SX0: real] :
( ( SX0 != zero_zero_real )
| ( ( power_power_real @ SX0 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_real ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1748]) ).
thf(2420,plain,
( ( ~ ( ~ ! [SX0: nat,SX1: nat] :
( ( SX1 = zero_zero_nat )
| ( SX0 != zero_zero_nat )
| ( ( power_power_nat @ SX0 @ SX1 )
= zero_zero_nat ) )
| ~ ~ ( ~ ! [SX0: nat,SX1: nat] :
( ( ( power_power_nat @ SX0 @ SX1 )
!= zero_zero_nat )
| ( SX1 != zero_zero_nat ) )
| ~ ! [SX0: nat] :
( ! [SX1: nat] :
( ( power_power_nat @ SX0 @ SX1 )
!= zero_zero_nat )
| ( SX0 = zero_zero_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2375]) ).
thf(2421,plain,
( ( ~ ( ~ ! [SX0: nat,SX1: int] :
( ( ( number_number_of_nat @ SX1 )
= zero_zero_nat )
| ( SX0 != zero_zero_nat )
| ( ( power_power_nat @ SX0 @ ( number_number_of_nat @ SX1 ) )
= zero_zero_nat ) )
| ~ ~ ( ~ ! [SX0: nat,SX1: int] :
( ( ( power_power_nat @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_nat )
| ( ( number_number_of_nat @ SX1 )
!= zero_zero_nat ) )
| ~ ! [SX0: nat] :
( ! [SX1: int] :
( ( power_power_nat @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_nat )
| ( SX0 = zero_zero_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1978]) ).
thf(2422,plain,
( ( ~ ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ min @ ( bit0 @ SX0 ) )
| ( ord_less_int @ min @ SX0 ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_int @ min @ SX0 )
| ( ord_less_eq_int @ min @ ( bit0 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2020]) ).
thf(2423,plain,
( ( ~ ( ~ ! [SX0: real,SX1: real] :
( ~ ( ord_less_real @ 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 ) ) ) ) ) )
| ( SX0 != zero_zero_real )
| ( SX1 != zero_zero_real ) )
| ~ ~ ( ~ ! [SX0: real] :
( ( SX0 = zero_zero_real )
| ! [SX1: real] : ( ord_less_real @ 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 ) ) ) ) ) ) )
| ~ ! [SX0: real,SX1: real] :
( ( SX1 = zero_zero_real )
| ( ord_less_real @ 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 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2092]) ).
thf(2424,plain,
( ( ~ ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ pls @ SX0 )
| ( ord_less_eq_real @ zero_zero_real @ ( number267125858f_real @ SX0 ) ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_eq_real @ zero_zero_real @ ( number267125858f_real @ SX0 ) )
| ( ord_less_eq_int @ pls @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2124]) ).
thf(2425,plain,
( ( ~ ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ pls @ SX0 )
| ( ord_less_int @ pls @ ( bit1 @ SX0 ) ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_int @ pls @ ( bit1 @ SX0 ) )
| ( ord_less_eq_int @ pls @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1789]) ).
thf(2426,plain,
( ( ~ ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1793]) ).
thf(2427,plain,
( ( ~ ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ min @ ( bit1 @ SX0 ) )
| ( ord_less_int @ min @ SX0 ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_int @ min @ SX0 )
| ( ord_less_int @ min @ ( bit1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2008]) ).
thf(2428,plain,
( ( ~ ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1844]) ).
thf(2429,plain,
( ( ~ ( ~ ! [SX0: nat,SX1: nat] :
( ( ( power_power_nat @ SX0 @ SX1 )
!= one_one_nat )
| ( SX0 = one_one_nat )
| ( SX1 = zero_zero_nat ) )
| ~ ~ ( ~ ! [SX0: nat] :
( ( SX0 != one_one_nat )
| ! [SX1: nat] :
( ( power_power_nat @ SX0 @ SX1 )
= one_one_nat ) )
| ~ ! [SX0: nat,SX1: nat] :
( ( SX1 != zero_zero_nat )
| ( ( power_power_nat @ SX0 @ SX1 )
= one_one_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2339]) ).
thf(2430,plain,
( ( ~ ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_eq_real @ ( number267125858f_real @ SX0 ) @ ( number267125858f_real @ SX1 ) ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_real @ ( number267125858f_real @ SX0 ) @ ( number267125858f_real @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2107]) ).
thf(2431,plain,
( ( ~ ( ~ ! [SX0: nat] :
( ( SX0 != zero_zero_nat )
| ( ( power_power_real @ zero_zero_real @ SX0 )
= one_one_real ) )
| ~ ! [SX0: nat] :
( ( SX0 = zero_zero_nat )
| ( ( power_power_real @ zero_zero_real @ SX0 )
= zero_zero_real ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2394]) ).
thf(2432,plain,
( ( ~ ( ~ ! [SX0: int,SX1: int] :
( ( ( bit1 @ SX0 )
!= ( bit1 @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: int,SX1: int] :
( ( SX0 != SX1 )
| ( ( bit1 @ SX0 )
= ( bit1 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1806]) ).
thf(2433,plain,
( ( ~ ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ ( number_number_of_int @ SX0 ) @ ( number_number_of_int @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ ( number_number_of_int @ SX0 ) @ ( number_number_of_int @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1882]) ).
thf(2434,plain,
( ( ~ ( ~ ! [SX0: real,SX1: real] :
( ( SX0 != zero_zero_real )
| ( SX1 != zero_zero_real )
| ( ord_less_eq_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 ) )
| ~ ~ ( ~ ! [SX0: real] :
( ! [SX1: real] :
~ ( ord_less_eq_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 )
| ( SX0 = zero_zero_real ) )
| ~ ! [SX0: real,SX1: real] :
( ~ ( ord_less_eq_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 )
| ( SX1 = zero_zero_real ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2143]) ).
thf(2435,plain,
( ( ~ ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ ( plus_plus_int @ SX1 @ one_one_int ) )
| ( SX0 = SX1 )
| ( ord_less_int @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: int,SX1: int] :
( ( SX0 != SX1 )
| ( ord_less_int @ SX0 @ ( plus_plus_int @ SX1 @ one_one_int ) ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ SX0 @ ( plus_plus_int @ SX1 @ one_one_int ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1902]) ).
thf(2436,plain,
( ( ~ ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ min @ ( bit1 @ SX0 ) )
| ( ord_less_eq_int @ min @ SX0 ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ min @ SX0 )
| ( ord_less_eq_int @ min @ ( bit1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2013]) ).
thf(2437,plain,
( ( ~ ( ~ ! [SX0: int] :
( ( ( number_number_of_nat @ SX0 )
!= zero_zero_nat )
| ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ SX0 ) )
= one_one_int ) )
| ~ ! [SX0: int] :
( ( ( number_number_of_nat @ SX0 )
= zero_zero_nat )
| ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ SX0 ) )
= zero_zero_int ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1985]) ).
thf(2438,plain,
( ( ! [SX0: nat,SX1: nat] :
~ ( ~ ~ ( ~ ! [SX2: nat,SX3: nat] :
( ( ( plus_plus_nat @ ( times_times_nat @ SX2 @ SX0 ) @ ( times_times_nat @ SX3 @ SX1 ) )
= ( plus_plus_nat @ ( times_times_nat @ SX2 @ SX1 ) @ ( times_times_nat @ SX3 @ SX0 ) ) )
| ( SX2 != SX3 ) )
| ~ ( ! [SX2: nat,SX3: nat] :
( ( plus_plus_nat @ ( times_times_nat @ SX2 @ SX0 ) @ ( times_times_nat @ SX3 @ SX1 ) )
= ( plus_plus_nat @ ( times_times_nat @ SX2 @ SX1 ) @ ( times_times_nat @ SX3 @ SX0 ) ) )
| ( SX0 != SX1 ) ) )
| ~ ! [SX2: nat,SX3: nat] :
( ( SX2 = SX3 )
| ( SX0 = SX1 )
| ( ( plus_plus_nat @ ( times_times_nat @ SX2 @ SX0 ) @ ( times_times_nat @ SX3 @ SX1 ) )
!= ( plus_plus_nat @ ( times_times_nat @ SX2 @ SX1 ) @ ( times_times_nat @ SX3 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2228]) ).
thf(2439,plain,
( ( ~ ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1754]) ).
thf(2440,plain,
( ( ~ ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1846]) ).
thf(2441,plain,
( ( ~ ( ~ ! [SX0: real,SX1: int] :
( ( ( number_number_of_nat @ SX1 )
= zero_zero_nat )
| ( SX0 != zero_zero_real )
| ( ( power_power_real @ SX0 @ ( number_number_of_nat @ SX1 ) )
= zero_zero_real ) )
| ~ ~ ( ~ ! [SX0: real,SX1: int] :
( ( ( power_power_real @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_real )
| ( ( number_number_of_nat @ SX1 )
!= zero_zero_nat ) )
| ~ ! [SX0: real] :
( ! [SX1: int] :
( ( power_power_real @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_real )
| ( SX0 = zero_zero_real ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2254]) ).
thf(2442,plain,
( ( ~ ( ~ ! [SX0: real,SX1: real] :
( ~ ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ SX0 @ SX0 ) @ ( times_times_real @ SX1 @ SX1 ) ) )
| ( SX0 != zero_zero_real )
| ( SX1 != zero_zero_real ) )
| ~ ~ ( ~ ! [SX0: real] :
( ( SX0 = zero_zero_real )
| ! [SX1: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ SX0 @ SX0 ) @ ( times_times_real @ SX1 @ SX1 ) ) ) )
| ~ ! [SX0: real,SX1: real] :
( ( SX1 = zero_zero_real )
| ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ SX0 @ SX0 ) @ ( times_times_real @ SX1 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2145]) ).
thf(2443,plain,
( ( ~ ( ~ ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SX0 @ SX1 ) )
| ( SX1 = zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SX0 ) )
| ~ ~ ( ~ ! [SX0: nat,SX1: nat] :
( ( SX1 != zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SX0 @ SX1 ) ) )
| ~ ! [SX0: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SX0 )
| ! [SX1: nat] : ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2167]) ).
thf(2444,plain,
( ( ! [SX0: real,SX1: real] :
~ ( ~ ~ ( ~ ! [SX2: real,SX3: real] :
( ( ( plus_plus_real @ ( times_times_real @ SX2 @ SX0 ) @ ( times_times_real @ SX3 @ SX1 ) )
= ( plus_plus_real @ ( times_times_real @ SX2 @ SX1 ) @ ( times_times_real @ SX3 @ SX0 ) ) )
| ( SX2 != SX3 ) )
| ~ ( ! [SX2: real,SX3: real] :
( ( plus_plus_real @ ( times_times_real @ SX2 @ SX0 ) @ ( times_times_real @ SX3 @ SX1 ) )
= ( plus_plus_real @ ( times_times_real @ SX2 @ SX1 ) @ ( times_times_real @ SX3 @ SX0 ) ) )
| ( SX0 != SX1 ) ) )
| ~ ! [SX2: real,SX3: real] :
( ( SX2 = SX3 )
| ( SX0 = SX1 )
| ( ( plus_plus_real @ ( times_times_real @ SX2 @ SX0 ) @ ( times_times_real @ SX3 @ SX1 ) )
!= ( plus_plus_real @ ( times_times_real @ SX2 @ SX1 ) @ ( times_times_real @ SX3 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2227]) ).
thf(2445,plain,
( ( ~ ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ ( bit0 @ SX0 ) @ pls )
| ( ord_less_eq_int @ SX0 @ pls ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ SX0 @ pls )
| ( ord_less_eq_int @ ( bit0 @ SX0 ) @ pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1772]) ).
thf(2446,plain,
( ( ~ ( ~ ! [SX0: int] :
( ( ( bit1 @ SX0 )
!= min )
| ( SX0 = min ) )
| ~ ! [SX0: int] :
( ( SX0 != min )
| ( ( bit1 @ SX0 )
= min ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2001]) ).
thf(2447,plain,
( ( ~ ( ~ ! [SX0: real,SX1: real] :
( ~ ( ord_less_eq_real @ SX0 @ SX1 )
| ( SX0 = SX1 )
| ( ord_less_real @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: real,SX1: real] :
( ( SX0 != SX1 )
| ( ord_less_eq_real @ SX0 @ SX1 ) )
| ~ ! [SX0: real,SX1: real] :
( ~ ( ord_less_real @ SX0 @ SX1 )
| ( ord_less_eq_real @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2321]) ).
thf(2448,plain,
( ( ~ ( ~ ! [SX0: real] :
( ( ( plus_plus_real @ SX0 @ SX0 )
!= zero_zero_real )
| ( SX0 = zero_zero_real ) )
| ~ ! [SX0: real] :
( ( SX0 != zero_zero_real )
| ( ( plus_plus_real @ SX0 @ SX0 )
= zero_zero_real ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2147]) ).
thf(2449,plain,
( ( ~ ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ zero_zero_int @ ( 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 ) ) ) ) ) )
| ( SX0 != zero_zero_int )
| ( SX1 != zero_zero_int ) )
| ~ ~ ( ~ ! [SX0: int] :
( ( SX0 = zero_zero_int )
| ! [SX1: int] : ( ord_less_int @ zero_zero_int @ ( 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 ) ) ) ) ) ) )
| ~ ! [SX0: int,SX1: int] :
( ( SX1 = zero_zero_int )
| ( ord_less_int @ zero_zero_int @ ( 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 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1738]) ).
thf(2450,plain,
( ( ~ ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ pls @ SX0 )
| ( ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ SX0 ) ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ SX0 ) )
| ( ord_less_int @ pls @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1766]) ).
thf(2451,plain,
( ( ~ ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ ( number_number_of_int @ SX0 ) @ ( number_number_of_int @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( 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)],[2106]) ).
thf(2452,plain,
( ( ~ ( ~ ! [SX0: real,SX1: 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 ) )
| ~ ~ ( ~ ! [SX0: real] :
( ! [SX1: 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 )
| ( SX0 = zero_zero_real ) )
| ~ ! [SX0: real,SX1: 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 )
| ( SX1 = zero_zero_real ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2093]) ).
thf(2453,plain,
( ( ~ ( ~ ! [SX0: int,SX1: nat] :
( ( SX1 != zero_zero_nat )
| ( ( power_power_int @ SX0 @ SX1 )
= one_one_int ) )
| ~ ! [SX0: int,SX1: nat] :
( ( SX1 = zero_zero_nat )
| ( ( power_power_int @ SX0 @ SX1 )
= ( times_times_int @ SX0 @ ( power_power_int @ SX0 @ ( minus_minus_nat @ SX1 @ one_one_nat ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2347]) ).
thf(2454,plain,
( ( ~ ( ~ ! [SX0: int] :
( ( ( number_number_of_nat @ SX0 )
!= zero_zero_nat )
| ( ord_less_eq_int @ SX0 @ pls ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ SX0 @ pls )
| ( ( number_number_of_nat @ SX0 )
= zero_zero_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1760]) ).
thf(2455,plain,
( ( ~ ( ~ ! [SX0: int,SX1: int] :
( ~ ( dvd_dvd_int @ SX1 @ SX0 )
| ( zcong @ SX0 @ zero_zero_int @ SX1 ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( zcong @ SX0 @ zero_zero_int @ SX1 )
| ( dvd_dvd_int @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2052]) ).
thf(2456,plain,
( ( ~ ( ~ ! [SX0: nat,SX1: nat] :
( ( SX1 != zero_zero_nat )
| ( ( power_power_nat @ SX0 @ SX1 )
= one_one_nat ) )
| ~ ! [SX0: nat,SX1: 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)],[2346]) ).
thf(2457,plain,
( ( ~ ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ ( bit1 @ SX0 ) @ min )
| ( ord_less_int @ SX0 @ min ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_int @ SX0 @ min )
| ( ord_less_int @ ( bit1 @ SX0 ) @ min ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2007]) ).
thf(2458,plain,
( ( ! [SX0: nat] :
~ ( ~ ! [SX1: nat,SX2: int] :
( ~ ( ord_less_int @ one_one_int @ SX2 )
| ~ ( ord_less_int @ ( power_power_int @ SX2 @ SX0 ) @ ( power_power_int @ SX2 @ SX1 ) )
| ( ord_less_nat @ SX0 @ SX1 ) )
| ~ ! [SX1: nat,SX2: int] :
( ~ ( ord_less_int @ one_one_int @ SX2 )
| ~ ( ord_less_nat @ SX0 @ SX1 )
| ( ord_less_int @ ( power_power_int @ SX2 @ SX0 ) @ ( power_power_int @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2084]) ).
thf(2459,plain,
( ( ~ ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ ( bit1 @ SX0 ) @ zero_zero_int )
| ( ord_less_int @ SX0 @ zero_zero_int ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_int @ SX0 @ zero_zero_int )
| ( ord_less_int @ ( bit1 @ SX0 ) @ zero_zero_int ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1892]) ).
thf(2460,plain,
( ( ~ ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ SX0 @ pls )
| ( ord_less_eq_real @ ( number267125858f_real @ SX0 ) @ zero_zero_real ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_eq_real @ ( number267125858f_real @ SX0 ) @ zero_zero_real )
| ( ord_less_eq_int @ SX0 @ pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2123]) ).
thf(2461,plain,
( ( ~ ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ min @ ( bit0 @ SX0 ) )
| ( ord_less_int @ min @ SX0 ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_int @ min @ SX0 )
| ( ord_less_int @ min @ ( bit0 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2011]) ).
thf(2462,plain,
( ( ~ ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ ( number_number_of_int @ SX0 ) @ ( number_number_of_int @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( 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)],[2108]) ).
thf(2463,plain,
( ( ! [SX0: int] :
~ ( ~ ! [SX1: int] :
( ! [SX2: int] :
~ ( dvd_dvd_int @ SX0 @ ( plus_plus_int @ SX1 @ ( times_times_int @ SX0 @ SX2 ) ) )
| ( dvd_dvd_int @ SX0 @ SX1 ) )
| ~ ! [SX1: int] :
( ~ ( dvd_dvd_int @ SX0 @ SX1 )
| ! [SX2: int] : ( dvd_dvd_int @ SX0 @ ( plus_plus_int @ SX1 @ ( times_times_int @ SX0 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1939]) ).
thf(2464,plain,
( ( ~ ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ SX0 @ ( minus_minus_int @ SX1 @ one_one_int ) )
| ( ord_less_int @ SX0 @ SX1 ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ SX0 @ ( minus_minus_int @ SX1 @ one_one_int ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2041]) ).
thf(2465,plain,
( ( ~ ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1757]) ).
thf(2466,plain,
( ( ~ ( ~ ! [SX0: int,SX1: int] :
( ( ( number_number_of_nat @ SX1 )
= zero_zero_nat )
| ( SX0 != zero_zero_int )
| ( ( power_power_int @ SX0 @ ( number_number_of_nat @ SX1 ) )
= zero_zero_int ) )
| ~ ~ ( ~ ! [SX0: int,SX1: int] :
( ( ( power_power_int @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_int )
| ( ( number_number_of_nat @ SX1 )
!= zero_zero_nat ) )
| ~ ! [SX0: int] :
( ! [SX1: int] :
( ( power_power_int @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1979]) ).
thf(2467,plain,
( ( ~ ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_real @ ( number267125858f_real @ SX0 ) @ ( number267125858f_real @ SX1 ) )
| ~ ( ord_less_real @ ( number267125858f_real @ SX1 ) @ ( number267125858f_real @ SX0 ) ) )
| ~ ! [SX0: int,SX1: int] :
( ( ord_less_real @ ( number267125858f_real @ SX1 ) @ ( number267125858f_real @ SX0 ) )
| ( ord_less_eq_real @ ( number267125858f_real @ SX0 ) @ ( number267125858f_real @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2125]) ).
thf(2468,plain,
( ( ~ ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ ( minus_minus_int @ SX0 @ SX1 ) @ zero_zero_int ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ ( minus_minus_int @ SX0 @ SX1 ) @ zero_zero_int )
| ( ord_less_int @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2037]) ).
thf(2469,plain,
( ( ~ ( ~ ! [SX0: int,SX1: int] :
( ~ ( 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 ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( 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)],[2295]) ).
thf(2470,plain,
( ( ~ ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ ( bit0 @ SX0 ) @ pls )
| ( ord_less_int @ SX0 @ pls ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_int @ SX0 @ pls )
| ( ord_less_int @ ( bit0 @ SX0 ) @ pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1893]) ).
thf(2471,plain,
( ( ~ ( ~ ! [SX0: nat,SX1: nat] :
( ( SX1 != zero_zero_nat )
| ( ( times_times_nat @ SX1 @ SX0 )
= zero_zero_nat ) )
| ~ ! [SX0: nat,SX1: 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)],[2315]) ).
thf(2472,plain,
( ( ~ ( ~ ! [SX0: real,SX1: 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 ) )
| ~ ~ ( ~ ! [SX0: real] :
( ! [SX1: 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 )
| ( SX0 = zero_zero_real ) )
| ~ ! [SX0: real,SX1: 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 )
| ( SX1 = zero_zero_real ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2318]) ).
thf(2473,plain,
( ( ~ ( ~ ! [SX0: int,SX1: int] :
( ( SX0 != zero_zero_int )
| ( SX1 != zero_zero_int )
| ( ( 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 ) ) ) ) )
= zero_zero_int ) )
| ~ ~ ( ~ ! [SX0: int] :
( ! [SX1: int] :
( ( 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 ) ) ) ) )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) )
| ~ ! [SX0: int,SX1: int] :
( ( ( 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 ) ) ) ) )
!= zero_zero_int )
| ( SX1 = zero_zero_int ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1739]) ).
thf(2474,plain,
( ( ~ ( ~ ! [SX0: int,SX1: int] :
( ~ ( dvd_dvd_int @ SX1 @ SX0 )
| ( zcong @ SX0 @ zero_zero_int @ SX1 ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( zcong @ SX0 @ zero_zero_int @ SX1 )
| ( dvd_dvd_int @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2053]) ).
thf(2475,plain,
( ( ~ ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1771]) ).
thf(2476,plain,
( ( ~ ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ ( plus_plus_int @ SX0 @ SX0 ) @ zero_zero_int )
| ( ord_less_int @ SX0 @ zero_zero_int ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_int @ SX0 @ zero_zero_int )
| ( ord_less_int @ ( plus_plus_int @ SX0 @ SX0 ) @ zero_zero_int ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1869]) ).
thf(2477,plain,
( ( ~ ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ one_one_int @ SX0 )
| ( ord_less_int @ zero_zero_int @ SX0 ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_int @ zero_zero_int @ SX0 )
| ( ord_less_eq_int @ one_one_int @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1795]) ).
thf(2478,plain,
( ( ! [SX0: real] :
~ ( ~ ! [SX1: real,SX2: real] :
( ~ ( ord_less_real @ zero_zero_real @ SX2 )
| ~ ( ord_less_eq_real @ ( times_times_real @ SX0 @ SX2 ) @ ( times_times_real @ SX1 @ SX2 ) )
| ( ord_less_eq_real @ SX0 @ SX1 ) )
| ~ ! [SX1: real,SX2: real] :
( ~ ( ord_less_real @ zero_zero_real @ SX2 )
| ~ ( ord_less_eq_real @ SX0 @ SX1 )
| ( ord_less_eq_real @ ( times_times_real @ SX0 @ SX2 ) @ ( times_times_real @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2333]) ).
thf(2479,plain,
( ( ~ ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ pls @ SX0 )
| ( ord_less_real @ zero_zero_real @ ( number267125858f_real @ SX0 ) ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_real @ zero_zero_real @ ( number267125858f_real @ SX0 ) )
| ( ord_less_int @ pls @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2160]) ).
thf(2480,plain,
( ( ~ ( ~ ! [SX0: real,SX1: real] :
( ( SX0 != zero_zero_real )
| ( SX1 != zero_zero_real )
| ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ SX0 @ SX0 ) @ ( times_times_real @ SX1 @ SX1 ) ) @ zero_zero_real ) )
| ~ ~ ( ~ ! [SX0: real] :
( ! [SX1: real] :
~ ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ SX0 @ SX0 ) @ ( times_times_real @ SX1 @ SX1 ) ) @ zero_zero_real )
| ( SX0 = zero_zero_real ) )
| ~ ! [SX0: real,SX1: real] :
( ~ ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ SX0 @ SX0 ) @ ( times_times_real @ SX1 @ SX1 ) ) @ zero_zero_real )
| ( SX1 = zero_zero_real ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2121]) ).
thf(2481,plain,
( ( ~ ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1791]) ).
thf(2482,plain,
( ( ~ ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ zero_zero_int @ ( number_number_of_int @ SX0 ) )
| ( ord_less_int @ pls @ SX0 ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_int @ pls @ SX0 )
| ( ord_less_int @ zero_zero_int @ ( number_number_of_int @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1917]) ).
thf(2483,plain,
( ( ~ ( ~ ! [SX0: int,SX1: int] :
( ( SX0 != zero_zero_int )
| ( SX1 != zero_zero_int )
| ( ord_less_eq_int @ ( 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 ) ) ) ) ) @ zero_zero_int ) )
| ~ ~ ( ~ ! [SX0: int] :
( ! [SX1: int] :
~ ( ord_less_eq_int @ ( 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 ) ) ) ) ) @ zero_zero_int )
| ( SX0 = zero_zero_int ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ ( 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 ) ) ) ) ) @ zero_zero_int )
| ( SX1 = zero_zero_int ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1823]) ).
thf(2484,plain,
( ( ~ ( ~ ! [SX0: int] :
( ( min
!= ( bit1 @ SX0 ) )
| ( min = SX0 ) )
| ~ ! [SX0: int] :
( ( min != SX0 )
| ( min
= ( bit1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2000]) ).
thf(2485,plain,
( ( ~ ( ~ ! [SX0: int,SX1: int] :
( ( SX0 != zero_zero_int )
| ( SX1 != zero_zero_int )
| ( ( plus_plus_int @ ( times_times_int @ SX0 @ SX0 ) @ ( times_times_int @ SX1 @ SX1 ) )
= zero_zero_int ) )
| ~ ~ ( ~ ! [SX0: int] :
( ! [SX1: int] :
( ( plus_plus_int @ ( times_times_int @ SX0 @ SX0 ) @ ( times_times_int @ SX1 @ SX1 ) )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) )
| ~ ! [SX0: int,SX1: int] :
( ( ( plus_plus_int @ ( times_times_int @ SX0 @ SX0 ) @ ( times_times_int @ SX1 @ SX1 ) )
!= zero_zero_int )
| ( SX1 = zero_zero_int ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1809]) ).
thf(2486,plain,
( ( ~ ( ~ ! [SX0: int,SX1: int] :
( ( SX0 = SX1 )
| ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_int @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1758]) ).
thf(2487,plain,
( ( ~ ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ ( number_number_of_int @ SX0 ) @ zero_zero_int )
| ( ord_less_eq_int @ SX0 @ pls ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ SX0 @ pls )
| ( ord_less_eq_int @ ( number_number_of_int @ SX0 ) @ zero_zero_int ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1764]) ).
thf(2488,plain,
( ( ! [SX0: nat] :
~ ( ~ ! [SX1: nat,SX2: nat] :
( ~ ( ord_less_nat @ one_one_nat @ SX2 )
| ~ ( ord_less_nat @ ( power_power_nat @ SX2 @ SX0 ) @ ( power_power_nat @ SX2 @ SX1 ) )
| ( ord_less_nat @ SX0 @ SX1 ) )
| ~ ! [SX1: nat,SX2: nat] :
( ~ ( ord_less_nat @ one_one_nat @ SX2 )
| ~ ( ord_less_nat @ SX0 @ SX1 )
| ( ord_less_nat @ ( power_power_nat @ SX2 @ SX0 ) @ ( power_power_nat @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2401]) ).
thf(2489,plain,
( ( ~ ( ~ ! [SX0: nat,SX1: nat] :
( ( SX0 != one_one_nat )
| ( SX1 != one_one_nat )
| ( ( times_times_nat @ SX0 @ SX1 )
= one_one_nat ) )
| ~ ~ ( ~ ! [SX0: nat] :
( ! [SX1: nat] :
( ( times_times_nat @ SX0 @ SX1 )
!= one_one_nat )
| ( SX0 = one_one_nat ) )
| ~ ! [SX0: nat,SX1: nat] :
( ( ( times_times_nat @ SX0 @ SX1 )
!= one_one_nat )
| ( SX1 = one_one_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2329]) ).
thf(2490,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: int] :
( ! [SX1: int] :
( ( times_times_int @ SX0 @ SX1 )
!= one_one_int )
| ( SX0 = one_one_int )
| ( SX0
= ( number_number_of_int @ min ) ) )
| ~ ! [SX0: int,SX1: int] :
( ( ( times_times_int @ SX0 @ SX1 )
!= one_one_int )
| ( SX0 = one_one_int )
| ( SX1
= ( number_number_of_int @ min ) ) ) )
| ~ ~ ( ~ ! [SX0: int,SX1: int] :
( ( ( times_times_int @ SX0 @ SX1 )
!= one_one_int )
| ( SX1 = one_one_int )
| ( SX0
= ( number_number_of_int @ min ) ) )
| ~ ! [SX0: int,SX1: int] :
( ( ( times_times_int @ SX0 @ SX1 )
!= one_one_int )
| ( SX1 = one_one_int )
| ( SX1
= ( number_number_of_int @ min ) ) ) ) )
| ~ ~ ( ~ ! [SX0: int,SX1: int] :
( ( SX0 != one_one_int )
| ( SX1 != one_one_int )
| ( ( times_times_int @ SX0 @ SX1 )
= one_one_int ) )
| ~ ! [SX0: int,SX1: int] :
( ( SX0
!= ( number_number_of_int @ min ) )
| ( SX1
!= ( number_number_of_int @ min ) )
| ( ( times_times_int @ SX0 @ SX1 )
= one_one_int ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2262]) ).
thf(2491,plain,
( ( ~ ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ SX0 @ ( bit1 @ pls ) )
| ( ord_less_real @ ( number267125858f_real @ SX0 ) @ one_one_real ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_real @ ( number267125858f_real @ SX0 ) @ one_one_real )
| ( ord_less_int @ SX0 @ ( bit1 @ pls ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2163]) ).
thf(2492,plain,
( ( ~ ( ~ ! [SX0: int,SX1: int] :
( ( ( number_number_of_int @ SX0 )
!= SX1 )
| ( SX1
= ( number_number_of_int @ SX0 ) ) )
| ~ ! [SX0: int,SX1: int] :
( ( SX1
!= ( number_number_of_int @ SX0 ) )
| ( ( number_number_of_int @ SX0 )
= SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2132]) ).
thf(2493,plain,
( ( ~ ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_int @ SX0 @ ( plus_plus_int @ SX1 @ one_one_int ) ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ ( plus_plus_int @ SX1 @ one_one_int ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1800]) ).
thf(2494,plain,
( ( ~ ( ~ ! [SX0: real,SX1: 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 ) )
| ~ ~ ( ~ ! [SX0: real] :
( ! [SX1: real] :
( ( plus_plus_real @ ( times_times_real @ SX0 @ SX0 ) @ ( times_times_real @ SX1 @ SX1 ) )
!= zero_zero_real )
| ( SX0 = zero_zero_real ) )
| ~ ! [SX0: real,SX1: real] :
( ( ( plus_plus_real @ ( times_times_real @ SX0 @ SX0 ) @ ( times_times_real @ SX1 @ SX1 ) )
!= zero_zero_real )
| ( SX1 = zero_zero_real ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2338]) ).
thf(2495,plain,
( ( ~ ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ ( bit1 @ SX0 ) @ pls )
| ( ord_less_int @ SX0 @ pls ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_int @ SX0 @ pls )
| ( ord_less_eq_int @ ( bit1 @ SX0 ) @ pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1788]) ).
thf(2496,plain,
( ( ! [SX0: nat] :
~ ( ~ ! [SX1: nat,SX2: real] :
( ~ ( ord_less_real @ one_one_real @ SX2 )
| ~ ( ord_less_nat @ SX0 @ SX1 )
| ( ord_less_real @ ( power_power_real @ SX2 @ SX0 ) @ ( power_power_real @ SX2 @ SX1 ) ) )
| ~ ! [SX1: nat,SX2: real] :
( ~ ( ord_less_real @ one_one_real @ SX2 )
| ~ ( ord_less_real @ ( power_power_real @ SX2 @ SX0 ) @ ( power_power_real @ SX2 @ SX1 ) )
| ( ord_less_nat @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2400]) ).
thf(2497,plain,
( ( ~ ( ~ ! [SX0: int] :
( ( ( bit0 @ SX0 )
!= pls )
| ( SX0 = pls ) )
| ~ ! [SX0: int] :
( ( SX0 != pls )
| ( ( bit0 @ SX0 )
= pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1839]) ).
thf(2498,plain,
( ( ~ ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ SX0 @ SX0 ) @ ( times_times_int @ SX1 @ SX1 ) ) )
| ( SX0 != zero_zero_int )
| ( SX1 != zero_zero_int ) )
| ~ ~ ( ~ ! [SX0: int] :
( ( SX0 = zero_zero_int )
| ! [SX1: int] : ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ SX0 @ SX0 ) @ ( times_times_int @ SX1 @ SX1 ) ) ) )
| ~ ! [SX0: int,SX1: int] :
( ( SX1 = zero_zero_int )
| ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ SX0 @ SX0 ) @ ( times_times_int @ SX1 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1825]) ).
thf(2499,plain,
( ( ~ ( ~ ! [SX0: int,SX1: nat] :
( ( ( number_number_of_nat @ SX0 )
!= SX1 )
| ( SX1
= ( number_number_of_nat @ SX0 ) ) )
| ~ ! [SX0: int,SX1: nat] :
( ( SX1
!= ( number_number_of_nat @ SX0 ) )
| ( ( number_number_of_nat @ SX0 )
= SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1805]) ).
thf(2500,plain,
( ( ~ ( ~ ! [SX0: real] :
( ( SX0 != zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ ( times_times_real @ SX0 @ SX0 ) ) )
| ~ ! [SX0: real] :
( ( ord_less_real @ zero_zero_real @ ( times_times_real @ SX0 @ SX0 ) )
| ( SX0 = zero_zero_real ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2282]) ).
thf(2501,plain,
( ( ~ ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ ( number_number_of_int @ SX0 ) @ one_one_int )
| ( ord_less_int @ SX0 @ ( bit1 @ pls ) ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_int @ SX0 @ ( bit1 @ pls ) )
| ( ord_less_int @ ( number_number_of_int @ SX0 ) @ one_one_int ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1921]) ).
thf(2502,plain,
( ( ! [SX0: real] :
~ ( ~ ! [SX1: real,SX2: real] :
( ( SX2 = zero_zero_real )
| ( ( times_times_real @ SX2 @ SX0 )
!= ( times_times_real @ SX2 @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX1: real,SX2: real] :
( ( SX2 = zero_zero_real )
| ( SX0 != SX1 )
| ( ( times_times_real @ SX2 @ SX0 )
= ( times_times_real @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2327]) ).
thf(2503,plain,
( ( ~ ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1770]) ).
thf(2504,plain,
( ( ~ ( ~ ! [SX0: int] :
( ( pls
!= ( bit0 @ SX0 ) )
| ( pls = SX0 ) )
| ~ ! [SX0: int] :
( ( pls != SX0 )
| ( pls
= ( bit0 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1840]) ).
thf(2505,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: int,SX1: int] :
( ( ord_less_int @ SX0 @ SX1 )
| ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_nat @ ( number_number_of_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ pls @ SX1 )
| ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_nat @ ( number_number_of_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) ) ) )
| ~ ~ ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_nat @ ( number_number_of_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) )
| ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ pls @ SX1 ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_nat @ ( number_number_of_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1794]) ).
thf(2506,plain,
( ( ~ ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1847]) ).
thf(2507,plain,
( ( ! [SX0: int,SX1: int,SX2: int] :
~ ( ~ ! [SX3: int,SX4: int] :
( ~ ( zcong @ SX2 @ SX3 @ SX4 )
| ~ ( zcong @ SX0 @ ( times_times_int @ SX2 @ SX1 ) @ SX4 )
| ( zcong @ SX0 @ ( times_times_int @ SX3 @ SX1 ) @ SX4 ) )
| ~ ! [SX3: int,SX4: int] :
( ~ ( zcong @ SX2 @ SX3 @ SX4 )
| ~ ( zcong @ SX0 @ ( times_times_int @ SX3 @ SX1 ) @ SX4 )
| ( zcong @ SX0 @ ( times_times_int @ SX2 @ SX1 ) @ SX4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2300]) ).
thf(2508,plain,
( ( ~ ( ~ ! [SX0: real,SX1: nat] :
( ( SX1 != zero_zero_nat )
| ( ( power_power_real @ SX0 @ SX1 )
= one_one_real ) )
| ~ ! [SX0: real,SX1: nat] :
( ( SX1 = zero_zero_nat )
| ( ( power_power_real @ SX0 @ SX1 )
= ( times_times_real @ SX0 @ ( power_power_real @ SX0 @ ( minus_minus_nat @ SX1 @ one_one_nat ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2345]) ).
thf(2509,plain,
( ( ! [SX0: int,SX1: int] :
~ ( ~ ~ ( ~ ! [SX2: int,SX3: int] :
( ( ( plus_plus_int @ ( times_times_int @ SX2 @ SX0 ) @ ( times_times_int @ SX3 @ SX1 ) )
= ( plus_plus_int @ ( times_times_int @ SX2 @ SX1 ) @ ( times_times_int @ SX3 @ SX0 ) ) )
| ( SX2 != SX3 ) )
| ~ ( ! [SX2: int,SX3: int] :
( ( plus_plus_int @ ( times_times_int @ SX2 @ SX0 ) @ ( times_times_int @ SX3 @ SX1 ) )
= ( plus_plus_int @ ( times_times_int @ SX2 @ SX1 ) @ ( times_times_int @ SX3 @ SX0 ) ) )
| ( SX0 != SX1 ) ) )
| ~ ! [SX2: int,SX3: int] :
( ( SX2 = SX3 )
| ( SX0 = SX1 )
| ( ( plus_plus_int @ ( times_times_int @ SX2 @ SX0 ) @ ( times_times_int @ SX3 @ SX1 ) )
!= ( plus_plus_int @ ( times_times_int @ SX2 @ SX1 ) @ ( times_times_int @ SX3 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1963]) ).
thf(2510,plain,
( ( ~ ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1792]) ).
thf(2511,plain,
( ( ~ ( ~ ! [SX0: int] :
( ( SX0 = zero_zero_int )
| ( ord_less_int @ zero_zero_int @ ( power_power_int @ SX0 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_int @ zero_zero_int @ ( power_power_int @ SX0 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ( SX0 != zero_zero_int ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1741]) ).
thf(2512,plain,
( ( ~ ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ SX0 @ pls )
| ( ord_less_real @ ( number267125858f_real @ SX0 ) @ zero_zero_real ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_real @ ( number267125858f_real @ SX0 ) @ zero_zero_real )
| ( ord_less_int @ SX0 @ pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2159]) ).
thf(2513,plain,
( ( ~ ( ~ ! [SX0: real,SX1: 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 ) )
| ~ ~ ( ~ ! [SX0: real] :
( ! [SX1: real] :
( ( plus_plus_real @ ( times_times_real @ SX0 @ SX0 ) @ ( times_times_real @ SX1 @ SX1 ) )
!= zero_zero_real )
| ( SX0 = zero_zero_real ) )
| ~ ! [SX0: real,SX1: real] :
( ( ( plus_plus_real @ ( times_times_real @ SX0 @ SX0 ) @ ( times_times_real @ SX1 @ SX1 ) )
!= zero_zero_real )
| ( SX1 = zero_zero_real ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2133]) ).
thf(2514,plain,
( ( ~ ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ ( bit1 @ pls ) @ SX0 )
| ( ord_less_eq_real @ one_one_real @ ( number267125858f_real @ SX0 ) ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_eq_real @ one_one_real @ ( number267125858f_real @ SX0 ) )
| ( ord_less_eq_int @ ( bit1 @ pls ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2127]) ).
thf(2515,plain,
( ( ! [SX0: int,SX1: int,SX2: int] :
~ ( ~ ! [SX3: int,SX4: int] :
( ~ ( zcong @ SX2 @ SX3 @ SX4 )
| ~ ( zcong @ SX0 @ ( times_times_int @ SX1 @ SX2 ) @ SX4 )
| ( zcong @ SX0 @ ( times_times_int @ SX1 @ SX3 ) @ SX4 ) )
| ~ ! [SX3: int,SX4: int] :
( ~ ( zcong @ SX2 @ SX3 @ SX4 )
| ~ ( zcong @ SX0 @ ( times_times_int @ SX1 @ SX3 ) @ SX4 )
| ( zcong @ SX0 @ ( times_times_int @ SX1 @ SX2 ) @ SX4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2299]) ).
thf(2516,plain,
( ( ~ ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ ( bit1 @ SX0 ) @ min )
| ( ord_less_eq_int @ SX0 @ min ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ SX0 @ min )
| ( ord_less_eq_int @ ( bit1 @ SX0 ) @ min ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2014]) ).
thf(2517,plain,
( ( ~ ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1753]) ).
thf(2518,plain,
( ( ~ ( ~ ! [SX0: int,SX1: int] :
( ( SX0 != SX1 )
| ( zcong @ SX0 @ SX1 @ zero_zero_int ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( zcong @ SX0 @ SX1 @ zero_zero_int )
| ( SX0 = SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2023]) ).
thf(2519,plain,
( ( ~ ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1790]) ).
thf(2520,plain,
( ( ! [SX0: nat,SX1: nat] :
~ ( ~ ! [SX2: nat,SX3: nat] :
( ( ( plus_plus_nat @ ( times_times_nat @ SX0 @ SX1 ) @ ( times_times_nat @ SX2 @ SX3 ) )
!= ( plus_plus_nat @ ( times_times_nat @ SX0 @ SX3 ) @ ( times_times_nat @ SX2 @ SX1 ) ) )
| ( SX0 = SX2 )
| ( SX1 = SX3 ) )
| ~ ~ ( ~ ! [SX2: nat] :
( ( SX0 != SX2 )
| ! [SX3: nat] :
( ( plus_plus_nat @ ( times_times_nat @ SX0 @ SX1 ) @ ( times_times_nat @ SX2 @ SX3 ) )
= ( plus_plus_nat @ ( times_times_nat @ SX0 @ SX3 ) @ ( times_times_nat @ SX2 @ SX1 ) ) ) )
| ~ ! [SX2: nat,SX3: nat] :
( ( SX1 != SX3 )
| ( ( plus_plus_nat @ ( times_times_nat @ SX0 @ SX1 ) @ ( times_times_nat @ SX2 @ SX3 ) )
= ( plus_plus_nat @ ( times_times_nat @ SX0 @ SX3 ) @ ( times_times_nat @ SX2 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2234]) ).
thf(2521,plain,
( ( ~ ( ~ ! [SX0: real,SX1: nat] :
( ( SX1 = zero_zero_nat )
| ( SX0 != zero_zero_real )
| ( ( power_power_real @ SX0 @ SX1 )
= zero_zero_real ) )
| ~ ~ ( ~ ! [SX0: real,SX1: nat] :
( ( ( power_power_real @ SX0 @ SX1 )
!= zero_zero_real )
| ( SX1 != zero_zero_nat ) )
| ~ ! [SX0: real] :
( ! [SX1: nat] :
( ( power_power_real @ SX0 @ SX1 )
!= zero_zero_real )
| ( SX0 = zero_zero_real ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2374]) ).
thf(2522,plain,
( ( ~ ( ~ ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SX0 @ SX1 ) )
| ( SX1 = zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SX0 ) )
| ~ ~ ( ~ ! [SX0: nat,SX1: nat] :
( ( SX1 != zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SX0 @ SX1 ) ) )
| ~ ! [SX0: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SX0 )
| ! [SX1: nat] : ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2387]) ).
thf(2523,plain,
( ( ! [SX0: int,SX1: int] :
~ ( ~ ! [SX2: int,SX3: int] :
( ( ( plus_plus_int @ ( times_times_int @ SX0 @ SX1 ) @ ( times_times_int @ SX2 @ SX3 ) )
!= ( plus_plus_int @ ( times_times_int @ SX0 @ SX3 ) @ ( times_times_int @ SX2 @ SX1 ) ) )
| ( SX0 = SX2 )
| ( SX1 = SX3 ) )
| ~ ~ ( ~ ! [SX2: int] :
( ( SX0 != SX2 )
| ! [SX3: int] :
( ( plus_plus_int @ ( times_times_int @ SX0 @ SX1 ) @ ( times_times_int @ SX2 @ SX3 ) )
= ( plus_plus_int @ ( times_times_int @ SX0 @ SX3 ) @ ( times_times_int @ SX2 @ SX1 ) ) ) )
| ~ ! [SX2: int,SX3: int] :
( ( SX1 != SX3 )
| ( ( plus_plus_int @ ( times_times_int @ SX0 @ SX1 ) @ ( times_times_int @ SX2 @ SX3 ) )
= ( plus_plus_int @ ( times_times_int @ SX0 @ SX3 ) @ ( times_times_int @ SX2 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1966]) ).
thf(2524,plain,
( ( ~ ( ~ ! [SX0: nat,SX1: nat] :
( ( SX1 != zero_zero_nat )
| ( ( power_power_nat @ SX0 @ SX1 )
= one_one_nat ) )
| ~ ! [SX0: nat,SX1: 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)],[2316]) ).
thf(2525,plain,
( ( ~ ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ zero_zero_int @ SX1 )
| ( SX1 != one_one_int )
| ( SX0 != one_one_int )
| ( ( times_times_int @ SX1 @ SX0 )
= one_one_int ) )
| ~ ~ ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ zero_zero_int @ SX1 )
| ( ( times_times_int @ SX1 @ SX0 )
!= one_one_int )
| ( SX1 = one_one_int ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ zero_zero_int @ SX1 )
| ( ( times_times_int @ SX1 @ SX0 )
!= one_one_int )
| ( SX0 = one_one_int ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1833]) ).
thf(2526,plain,
( ( ~ ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ ( plus_plus_int @ SX0 @ one_one_int ) @ SX1 )
| ( ord_less_int @ SX0 @ SX1 ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( plus_plus_int @ SX0 @ one_one_int ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1799]) ).
thf(2527,plain,
( ( ~ ( ~ ! [SX0: int] :
( ( ( number_number_of_nat @ SX0 )
!= zero_zero_nat )
| ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ SX0 ) )
= one_one_nat ) )
| ~ ! [SX0: int] :
( ( ( number_number_of_nat @ SX0 )
= zero_zero_nat )
| ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ SX0 ) )
= zero_zero_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2256]) ).
thf(2528,plain,
( ( ~ ( ~ ! [SX0: real,SX1: real] :
( ( SX0 = SX1 )
| ~ ( ord_less_eq_real @ SX0 @ SX1 )
| ( ord_less_real @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: real,SX1: real] :
( ~ ( ord_less_real @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: real,SX1: real] :
( ~ ( ord_less_real @ SX0 @ SX1 )
| ( ord_less_eq_real @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2320]) ).
thf(2529,plain,
( ( ~ ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_real @ ( number267125858f_real @ SX0 ) @ ( number267125858f_real @ SX1 ) ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_real @ ( number267125858f_real @ SX0 ) @ ( number267125858f_real @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1881]) ).
thf(2530,plain,
( ( ~ ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ ( number_number_of_int @ SX0 ) @ ( number_number_of_int @ SX1 ) )
| ~ ( ord_less_int @ ( number_number_of_int @ SX1 ) @ ( number_number_of_int @ SX0 ) ) )
| ~ ! [SX0: int,SX1: int] :
( ( ord_less_int @ ( number_number_of_int @ SX1 ) @ ( number_number_of_int @ SX0 ) )
| ( ord_less_eq_int @ ( number_number_of_int @ SX0 ) @ ( number_number_of_int @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1768]) ).
thf(2531,plain,
( ( ~ ( ~ ! [SX0: int] :
( ( ( plus_plus_int @ SX0 @ SX0 )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) )
| ~ ! [SX0: int] :
( ( SX0 != zero_zero_int )
| ( ( plus_plus_int @ SX0 @ SX0 )
= zero_zero_int ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1834]) ).
thf(2532,plain,
( ( ~ ( ~ ! [SX0: nat,SX1: int] :
( ~ ( 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 ) )
| ~ ~ ( ~ ! [SX0: nat,SX1: int] :
( ( ( number_number_of_nat @ SX1 )
!= zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SX0 @ ( number_number_of_nat @ SX1 ) ) ) )
| ~ ! [SX0: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SX0 )
| ! [SX1: int] : ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SX0 @ ( number_number_of_nat @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2211]) ).
thf(2533,plain,
( ( ~ ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ SX0 @ ( bit1 @ pls ) )
| ( ord_less_eq_real @ ( number267125858f_real @ SX0 ) @ one_one_real ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_eq_real @ ( number267125858f_real @ SX0 ) @ one_one_real )
| ( ord_less_eq_int @ SX0 @ ( bit1 @ pls ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2126]) ).
thf(2534,plain,
( ( ~ ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX1 @ pls )
| ( ( times_times_nat @ ( number_number_of_nat @ SX1 ) @ ( number_number_of_nat @ SX0 ) )
= zero_zero_nat ) )
| ~ ! [SX0: int,SX1: int] :
( ( 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)],[2212]) ).
thf(2535,plain,
( ( ~ ( ~ ! [SX0: real] :
( ( SX0 = zero_zero_real )
| ( ord_less_real @ zero_zero_real @ ( power_power_real @ SX0 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
| ~ ! [SX0: real] :
( ~ ( ord_less_real @ zero_zero_real @ ( power_power_real @ SX0 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ( SX0 != zero_zero_real ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2095]) ).
thf(2536,plain,
( ( ~ ( ~ ! [SX0: int] :
( ~ ( ~ ~ ( ~ ( dvd_dvd_int @ ( sK3_M_9 @ SX0 ) @ SX0 )
| ~ ( ord_less_eq_int @ zero_zero_int @ ( sK3_M_9 @ SX0 ) ) )
| ~ ~ ( ~ ( ( ( sK3_M_9 @ SX0 )
!= one_one_int ) )
| ~ ( ( ( sK3_M_9 @ SX0 )
!= SX0 ) ) ) )
| ~ ( ord_less_int @ one_one_int @ SX0 )
| ( zprime @ SX0 ) )
| ~ ~ ( ~ ! [SX0: int] :
( ~ ( zprime @ SX0 )
| ! [SX1: int] :
( ~ ( dvd_dvd_int @ SX1 @ SX0 )
| ~ ( ord_less_eq_int @ zero_zero_int @ SX1 )
| ( SX1 = one_one_int )
| ( SX1 = SX0 ) ) )
| ~ ! [SX0: int] :
( ~ ( zprime @ SX0 )
| ( ord_less_int @ one_one_int @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2258]) ).
thf(2537,plain,
( ( ! [SX0: int] :
~ ( ~ ! [SX1: nat,SX2: int] :
( ~ ( 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 ) )
| ~ ! [SX1: nat,SX2: int] :
( ( 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)],[2213]) ).
thf(2538,plain,
( ( ~ ( ~ ! [SX0: int,SX1: int] :
( ~ ( zcong @ SX0 @ zero_zero_int @ SX1 )
| ( ( legendre @ SX0 @ SX1 )
= zero_zero_int ) )
| ~ ~ ( ~ ! [SX0: int,SX1: int] :
( ( zcong @ SX0 @ zero_zero_int @ SX1 )
| ~ ( quadRes @ SX1 @ SX0 )
| ( ( legendre @ SX0 @ SX1 )
= one_one_int ) )
| ~ ! [SX0: int,SX1: int] :
( ( zcong @ SX0 @ zero_zero_int @ SX1 )
| ( quadRes @ SX1 @ SX0 )
| ( ( legendre @ SX0 @ SX1 )
= ( number_number_of_int @ min ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2313]) ).
thf(2539,plain,
( ( ~ ( ~ ! [SX0: nat] :
( ( SX0 != zero_zero_nat )
| ( ( power_power_int @ zero_zero_int @ SX0 )
= one_one_int ) )
| ~ ! [SX0: nat] :
( ( SX0 = zero_zero_nat )
| ( ( power_power_int @ zero_zero_int @ SX0 )
= zero_zero_int ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2081]) ).
thf(2540,plain,
( ( ! [SX0: real,SX1: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SX1 )
| ~ ( ord_less_real @ zero_zero_real @ SX0 )
| ~ ( ~ ! [SX2: real] :
( ( ( power_power_real @ SX2 @ SX1 )
!= SX0 )
| ~ ( ord_less_real @ zero_zero_real @ SX2 )
| ( SX2
= ( sK1_X_1 @ SX1 @ SX0 ) ) )
| ~ ~ ( ( ( power_power_real @ ( sK1_X_1 @ SX1 @ SX0 ) @ SX1 )
!= SX0 )
| ~ ( ord_less_real @ zero_zero_real @ ( sK1_X_1 @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2406]) ).
thf(2541,plain,
( ( ~ ( ~ ! [SX0: int] :
( ( zero_zero_nat
!= ( number_number_of_nat @ SX0 ) )
| ( ord_less_eq_int @ SX0 @ pls ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ SX0 @ pls )
| ( zero_zero_nat
= ( number_number_of_nat @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1761]) ).
thf(2542,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_eq_nat @ ( number_number_of_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ SX0 @ pls )
| ! [SX1: int] : ( ord_less_eq_nat @ ( number_number_of_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) ) ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( 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 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1943]) ).
thf(2543,plain,
( ( ~ ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ ( number_number_of_int @ SX0 ) @ zero_zero_int )
| ( ord_less_int @ SX0 @ pls ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_int @ SX0 @ pls )
| ( ord_less_int @ ( number_number_of_int @ SX0 ) @ zero_zero_int ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1916]) ).
thf(2544,plain,
( ( ~ ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ one_one_int @ ( number_number_of_int @ SX0 ) )
| ( ord_less_eq_int @ ( bit1 @ pls ) @ SX0 ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ ( bit1 @ pls ) @ SX0 )
| ( ord_less_eq_int @ one_one_int @ ( number_number_of_int @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1778]) ).
thf(2545,plain,
( ( ~ ( ~ ! [SX0: int,SX1: real] :
( ( ( number267125858f_real @ SX0 )
!= SX1 )
| ( SX1
= ( number267125858f_real @ SX0 ) ) )
| ~ ! [SX0: int,SX1: real] :
( ( SX1
!= ( number267125858f_real @ SX0 ) )
| ( ( number267125858f_real @ SX0 )
= SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2131]) ).
thf(2546,plain,
( ( ~ ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ SX0 ) @ SX0 ) @ zero_zero_int )
| ( ord_less_int @ SX0 @ zero_zero_int ) )
| ~ ! [SX0: 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)],[1915]) ).
thf(2547,plain,
( ( ! [SX0: int] :
~ ( ~ ! [SX1: int,SX2: int] :
( ~ ( zcong @ SX0 @ SX1 @ SX2 )
| ( zcong @ SX1 @ SX0 @ SX2 ) )
| ~ ! [SX1: int,SX2: int] :
( ~ ( zcong @ SX1 @ SX0 @ SX2 )
| ( zcong @ SX0 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2264]) ).
thf(2548,plain,
( ( ! [SX0: int,SX1: int,SX2: int] :
~ ( ~ ! [SX3: int,SX4: int] :
( ~ ( 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 ) ) )
| ~ ! [SX3: int,SX4: int] :
( ~ ( dvd_dvd_int @ SX3 @ SX4 )
| ~ ( 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)],[1940]) ).
thf(2549,plain,
( ( ~ ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ ( bit1 @ pls ) @ SX0 )
| ( ord_less_real @ one_one_real @ ( number267125858f_real @ SX0 ) ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_real @ one_one_real @ ( number267125858f_real @ SX0 ) )
| ( ord_less_int @ ( bit1 @ pls ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2164]) ).
thf(2550,plain,
( ( ~ ( ~ ! [SX0: real,SX1: real] :
( ( SX0
!= ( plus_plus_real @ SX0 @ SX1 ) )
| ( SX1 = zero_zero_real ) )
| ~ ! [SX0: real,SX1: real] :
( ( SX1 != zero_zero_real )
| ( SX0
= ( plus_plus_real @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2223]) ).
thf(2551,plain,
( ( ! [SX0: int] :
~ ( ~ ! [SX1: int,SX2: int] :
( ! [SX3: int] :
( SX1
!= ( plus_plus_int @ SX0 @ ( times_times_int @ SX2 @ SX3 ) ) )
| ( zcong @ SX0 @ SX1 @ SX2 ) )
| ~ ! [SX1: int,SX2: int] :
( ~ ( zcong @ SX0 @ SX1 @ SX2 )
| ( SX1
= ( plus_plus_int @ SX0 @ ( times_times_int @ SX2 @ ( sK6_K_1 @ SX2 @ SX1 @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2027]) ).
thf(2552,plain,
( ( ~ ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ pls @ ( bit0 @ SX0 ) )
| ( ord_less_eq_int @ pls @ SX0 ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ pls @ SX0 )
| ( ord_less_eq_int @ pls @ ( bit0 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1773]) ).
thf(2553,plain,
( ( ! [SX0: nat] :
~ ( ~ ! [SX1: nat,SX2: nat] :
( ~ ( ord_less_nat @ one_one_nat @ SX2 )
| ( ( power_power_nat @ SX2 @ SX0 )
!= ( power_power_nat @ SX2 @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX1: nat,SX2: nat] :
( ~ ( ord_less_nat @ one_one_nat @ SX2 )
| ( SX0 != SX1 )
| ( ( power_power_nat @ SX2 @ SX0 )
= ( power_power_nat @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2373]) ).
thf(2554,plain,
( ( ! [SX0: real,SX1: real] :
~ ( ~ ! [SX2: real,SX3: real] :
( ( ( plus_plus_real @ ( times_times_real @ SX0 @ SX1 ) @ ( times_times_real @ SX2 @ SX3 ) )
!= ( plus_plus_real @ ( times_times_real @ SX0 @ SX3 ) @ ( times_times_real @ SX2 @ SX1 ) ) )
| ( SX0 = SX2 )
| ( SX1 = SX3 ) )
| ~ ~ ( ~ ! [SX2: real] :
( ( SX0 != SX2 )
| ! [SX3: real] :
( ( plus_plus_real @ ( times_times_real @ SX0 @ SX1 ) @ ( times_times_real @ SX2 @ SX3 ) )
= ( plus_plus_real @ ( times_times_real @ SX0 @ SX3 ) @ ( times_times_real @ SX2 @ SX1 ) ) ) )
| ~ ! [SX2: real,SX3: real] :
( ( SX1 != SX3 )
| ( ( plus_plus_real @ ( times_times_real @ SX0 @ SX1 ) @ ( times_times_real @ SX2 @ SX3 ) )
= ( plus_plus_real @ ( times_times_real @ SX0 @ SX3 ) @ ( times_times_real @ SX2 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2233]) ).
thf(2555,plain,
( ( ~ ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ ( bit1 @ SX0 ) @ pls )
| ( ord_less_int @ SX0 @ pls ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_int @ SX0 @ pls )
| ( ord_less_int @ ( bit1 @ SX0 ) @ pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1889]) ).
thf(2556,plain,
( ( ~ ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ SX0 ) )
| ( ord_less_eq_int @ pls @ SX0 ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ pls @ SX0 )
| ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1765]) ).
thf(2557,plain,
( ( ! [SX0: nat] :
~ ( ~ ! [SX1: nat,SX2: nat] :
( ~ ( dvd_dvd_nat @ ( times_times_nat @ SX0 @ SX1 ) @ ( times_times_nat @ SX2 @ SX1 ) )
| ( SX1 = zero_zero_nat )
| ( dvd_dvd_nat @ SX0 @ SX2 ) )
| ~ ~ ( ~ ! [SX1: nat] :
( ( SX1 != zero_zero_nat )
| ! [SX2: nat] : ( dvd_dvd_nat @ ( times_times_nat @ SX0 @ SX1 ) @ ( times_times_nat @ SX2 @ SX1 ) ) )
| ~ ! [SX1: nat,SX2: 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)],[2412]) ).
thf(2558,plain,
( ( ~ ( ~ ! [SX0: int,SX1: int] :
( ( ( number267125858f_real @ SX0 )
!= ( number267125858f_real @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: int,SX1: int] :
( ( SX0 != SX1 )
| ( ( number267125858f_real @ SX0 )
= ( number267125858f_real @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2129]) ).
thf(2559,plain,
( ( ~ ( ~ ! [SX0: nat] :
( ( SX0 != zero_zero_nat )
| ( ( power_power_nat @ zero_zero_nat @ SX0 )
= one_one_nat ) )
| ~ ! [SX0: nat] :
( ( SX0 = zero_zero_nat )
| ( ( power_power_nat @ zero_zero_nat @ SX0 )
= zero_zero_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2395]) ).
thf(2560,plain,
( ( ~ ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ ( bit0 @ SX0 ) @ min )
| ( ord_less_eq_int @ SX0 @ min ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ SX0 @ min )
| ( ord_less_eq_int @ ( bit0 @ SX0 ) @ min ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2017]) ).
thf(2561,plain,
( ( ~ ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1890]) ).
thf(2562,plain,
( ( ~ ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1756]) ).
thf(2563,plain,
( ( ~ ( ~ ! [SX0: nat,SX1: nat] :
( ( SX0
!= ( plus_plus_nat @ SX0 @ SX1 ) )
| ( SX1 = zero_zero_nat ) )
| ~ ! [SX0: nat,SX1: nat] :
( ( SX1 != zero_zero_nat )
| ( SX0
= ( plus_plus_nat @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2224]) ).
thf(2564,plain,
( ( ~ ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1843]) ).
thf(2565,plain,
( ( ~ ( ~ ! [SX0: nat,SX1: nat] :
( ( SX1 = zero_zero_nat )
| ( SX0 != zero_zero_nat )
| ( ( power_power_nat @ SX0 @ SX1 )
= zero_zero_nat ) )
| ~ ~ ( ~ ! [SX0: nat,SX1: nat] :
( ( ( power_power_nat @ SX0 @ SX1 )
!= zero_zero_nat )
| ( SX1 != zero_zero_nat ) )
| ~ ! [SX0: nat] :
( ! [SX1: nat] :
( ( power_power_nat @ SX0 @ SX1 )
!= zero_zero_nat )
| ( SX0 = zero_zero_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2331]) ).
thf(2566,plain,
( ( ~ ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1891]) ).
thf(2567,plain,
( ( ~ ( ~ ! [SX0: int,SX1: int] :
( ( SX0
!= ( plus_plus_int @ SX0 @ SX1 ) )
| ( SX1 = zero_zero_int ) )
| ~ ! [SX0: int,SX1: int] :
( ( SX1 != zero_zero_int )
| ( SX0
= ( plus_plus_int @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1961]) ).
thf(2568,plain,
( ( ~ ( ~ ! [SX0: int,SX1: int] :
( ! [SX2: int] :
~ ( zcong @ ( power_power_int @ SX2 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SX1 @ SX0 )
| ( quadRes @ SX0 @ SX1 ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( quadRes @ SX0 @ SX1 )
| ( zcong @ ( power_power_int @ ( sK5_Y_1 @ SX1 @ SX0 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2056]) ).
thf(2569,plain,
( ( ~ ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ one_one_int @ ( number_number_of_int @ SX0 ) )
| ( ord_less_int @ ( bit1 @ pls ) @ SX0 ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_int @ ( bit1 @ pls ) @ SX0 )
| ( ord_less_int @ one_one_int @ ( number_number_of_int @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1922]) ).
thf(2570,plain,
( ( ! [SX0: nat] :
~ ( ~ ! [SX1: nat,SX2: real] :
( ~ ( ord_less_real @ one_one_real @ SX2 )
| ( ( power_power_real @ SX2 @ SX0 )
!= ( power_power_real @ SX2 @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX1: nat,SX2: real] :
( ~ ( ord_less_real @ one_one_real @ SX2 )
| ( SX0 != SX1 )
| ( ( power_power_real @ SX2 @ SX0 )
= ( power_power_real @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2372]) ).
thf(2571,plain,
( ( ~ ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX1 @ pls )
| ( ( plus_plus_nat @ ( number_number_of_nat @ SX1 ) @ ( number_number_of_nat @ SX0 ) )
= ( number_number_of_nat @ SX0 ) ) )
| ~ ~ ( ~ ! [SX0: int,SX1: int] :
( ( 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 ) ) )
| ~ ! [SX0: int,SX1: int] :
( ( 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 @ ( plus_plus_int @ SX1 @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1803]) ).
thf(2572,plain,
( ( ! [SX0: real] :
~ ( ~ ! [SX1: real,SX2: real] :
( ( SX2 = zero_zero_real )
| ( ( times_times_real @ SX0 @ SX2 )
!= ( times_times_real @ SX1 @ SX2 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX1: real,SX2: real] :
( ( SX2 = zero_zero_real )
| ( SX0 != SX1 )
| ( ( times_times_real @ SX0 @ SX2 )
= ( times_times_real @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2328]) ).
thf(2573,plain,
( ( ! [SX0: real] :
~ ( ~ ! [SX1: real,SX2: real] :
( ~ ( 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 ) )
| ~ ! [SX1: real,SX2: real] :
( ~ ( ord_less_real @ zero_zero_real @ SX2 )
| ~ ( ord_less_real @ SX0 @ SX1 )
| ( ord_less_real @ ( times_times_real @ SX0 @ SX2 ) @ ( times_times_real @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2337]) ).
thf(2574,plain,
( ( ! [SX0: real] :
~ ( ~ ! [SX1: real,SX2: real] :
( ~ ( ord_less_real @ zero_zero_real @ SX2 )
| ~ ( ord_less_eq_real @ ( times_times_real @ SX2 @ SX0 ) @ ( times_times_real @ SX2 @ SX1 ) )
| ( ord_less_eq_real @ SX0 @ SX1 ) )
| ~ ! [SX1: real,SX2: real] :
( ~ ( ord_less_real @ zero_zero_real @ SX2 )
| ~ ( ord_less_eq_real @ SX0 @ SX1 )
| ( ord_less_eq_real @ ( times_times_real @ SX2 @ SX0 ) @ ( times_times_real @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2334]) ).
thf(2575,plain,
( ( ~ ( ~ ! [SX0: int,SX1: int] :
( ( ( bit0 @ SX0 )
!= ( bit0 @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: int,SX1: int] :
( ( SX0 != SX1 )
| ( ( bit0 @ SX0 )
= ( bit0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1807]) ).
thf(2576,plain,
( ( ~ ( ~ ! [SX0: int] :
( ( ( power_power_int @ SX0 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) )
| ~ ! [SX0: int] :
( ( SX0 != zero_zero_int )
| ( ( power_power_int @ SX0 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1749]) ).
thf(2577,plain,
( ( ~ ( ~ ! [SX0: int,SX1: int] :
( ( SX0 != zero_zero_int )
| ( SX1 != zero_zero_int )
| ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SX0 @ SX0 ) @ ( times_times_int @ SX1 @ SX1 ) ) @ zero_zero_int ) )
| ~ ~ ( ~ ! [SX0: int] :
( ! [SX1: int] :
~ ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SX0 @ SX0 ) @ ( times_times_int @ SX1 @ SX1 ) ) @ zero_zero_int )
| ( SX0 = zero_zero_int ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SX0 @ SX0 ) @ ( times_times_int @ SX1 @ SX1 ) ) @ zero_zero_int )
| ( SX1 = zero_zero_int ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1762]) ).
thf(2578,plain,
( ( ~ ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ pls @ ( bit0 @ SX0 ) )
| ( ord_less_int @ pls @ SX0 ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_int @ pls @ SX0 )
| ( ord_less_int @ pls @ ( bit0 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1894]) ).
thf(2579,plain,
( ( ~ ( ~ ! [SX0: real] :
( ~ ( ord_less_real @ ( plus_plus_real @ SX0 @ SX0 ) @ zero_zero_real )
| ( ord_less_real @ SX0 @ zero_zero_real ) )
| ~ ! [SX0: real] :
( ~ ( ord_less_real @ SX0 @ zero_zero_real )
| ( ord_less_real @ ( plus_plus_real @ SX0 @ SX0 ) @ zero_zero_real ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2153]) ).
thf(2580,plain,
( ( ~ ( ~ ! [SX0: int,SX1: nat] :
( ( SX1 = zero_zero_nat )
| ( SX0 != zero_zero_int )
| ( ( power_power_int @ SX0 @ SX1 )
= zero_zero_int ) )
| ~ ~ ( ~ ! [SX0: int,SX1: nat] :
( ( ( power_power_int @ SX0 @ SX1 )
!= zero_zero_int )
| ( SX1 != zero_zero_nat ) )
| ~ ! [SX0: int] :
( ! [SX1: nat] :
( ( power_power_int @ SX0 @ SX1 )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2072]) ).
thf(2581,plain,
( ( ~ ( ~ ! [SX0: int,SX1: int] :
( ( ( number_number_of_int @ SX0 )
!= ( number_number_of_int @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: int,SX1: int] :
( ( SX0 != SX1 )
| ( ( number_number_of_int @ SX0 )
= ( number_number_of_int @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2130]) ).
thf(2582,plain,
( ( ~ ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ SX0 @ min )
| ( ord_less_int @ ( bit0 @ SX0 ) @ min ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_int @ ( bit0 @ SX0 ) @ min )
| ( ord_less_eq_int @ SX0 @ min ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2019]) ).
thf(2583,plain,
( ( ~ ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_nat @ ( number_number_of_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) )
| ~ ( ord_less_nat @ ( number_number_of_nat @ SX1 ) @ ( number_number_of_nat @ SX0 ) ) )
| ~ ! [SX0: int,SX1: int] :
( ( ord_less_nat @ ( number_number_of_nat @ SX1 ) @ ( number_number_of_nat @ SX0 ) )
| ( ord_less_eq_nat @ ( number_number_of_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1767]) ).
thf(2584,plain,
( ( ~ ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ ( number_number_of_int @ SX0 ) @ one_one_int )
| ( ord_less_eq_int @ SX0 @ ( bit1 @ pls ) ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ SX0 @ ( bit1 @ pls ) )
| ( ord_less_eq_int @ ( number_number_of_int @ SX0 ) @ one_one_int ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1777]) ).
thf(2585,plain,
( ( ! [SX0: int] :
~ ( ~ ! [SX1: int,SX2: int] :
( ~ ( dvd_dvd_int @ SX2 @ ( minus_minus_int @ SX0 @ SX1 ) )
| ( zcong @ SX0 @ SX1 @ SX2 ) )
| ~ ! [SX1: int,SX2: int] :
( ~ ( zcong @ SX0 @ SX1 @ SX2 )
| ( dvd_dvd_int @ SX2 @ ( minus_minus_int @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2293]) ).
thf(2586,plain,
( ( ~ ( ~ ! [SX0: int] :
( ( ( number_number_of_nat @ SX0 )
!= zero_zero_nat )
| ( ( power_power_real @ zero_zero_real @ ( number_number_of_nat @ SX0 ) )
= one_one_real ) )
| ~ ! [SX0: int] :
( ( ( number_number_of_nat @ SX0 )
= zero_zero_nat )
| ( ( power_power_real @ zero_zero_real @ ( number_number_of_nat @ SX0 ) )
= zero_zero_real ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2255]) ).
thf(2587,plain,
( ( ~ ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ ( bit0 @ SX0 ) @ zero_zero_int )
| ( ord_less_int @ SX0 @ zero_zero_int ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_int @ SX0 @ zero_zero_int )
| ( ord_less_int @ ( bit0 @ SX0 ) @ zero_zero_int ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1896]) ).
thf(2588,plain,
( ( ~ ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ pls @ ( bit1 @ SX0 ) )
| ( ord_less_eq_int @ pls @ SX0 ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ pls @ SX0 )
| ( ord_less_eq_int @ pls @ ( bit1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1769]) ).
thf(2589,plain,
( ( ~ ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ ( number_number_of_int @ SX0 ) @ ( number_number_of_int @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ ( number_number_of_int @ SX0 ) @ ( number_number_of_int @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1782]) ).
thf(2590,plain,
( ( ! [SX0: nat] :
~ ( ~ ! [SX1: nat,SX2: int] :
( ~ ( ord_less_int @ one_one_int @ SX2 )
| ( ( power_power_int @ SX2 @ SX0 )
!= ( power_power_int @ SX2 @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX1: nat,SX2: int] :
( ~ ( ord_less_int @ one_one_int @ SX2 )
| ( SX0 != SX1 )
| ( ( power_power_int @ SX2 @ SX0 )
= ( power_power_int @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2071]) ).
thf(2591,plain,
( ( ( t != zero_zero_int )
= $true )
| ( ( ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int )
= zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1735]) ).
thf(2592,plain,
( ( ord_less_eq_int @ one_one_int @ t )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1736]) ).
thf(2593,plain,
! [SV1: int] :
( ( ! [SY1334: int] :
~ ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ SV1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SY1334 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1737]) ).
thf(2594,plain,
! [SV2: int] :
( ( ~ ( ord_less_int @ ( power_power_int @ SV2 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1740]) ).
thf(2595,plain,
! [SV3: int] :
( ( ( plus_plus_int @ one_one_int @ ( number_number_of_int @ SV3 ) )
= ( number_number_of_int @ ( plus_plus_int @ ( bit1 @ pls ) @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1750]) ).
thf(2596,plain,
! [SV4: int] :
( ( ( plus_plus_int @ ( number_number_of_int @ SV4 ) @ one_one_int )
= ( number_number_of_int @ ( plus_plus_int @ SV4 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1751]) ).
thf(2597,plain,
! [SV5: int] :
( ( ! [SY1335: nat,SY1336: nat] :
( ( power_power_int @ SV5 @ ( plus_plus_nat @ SY1335 @ SY1336 ) )
= ( times_times_int @ ( power_power_int @ SV5 @ SY1335 ) @ ( power_power_int @ SV5 @ SY1336 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1752]) ).
thf(2598,plain,
! [SV6: int] :
( ( ! [SY1337: int,SY1338: int] :
( ~ ( ord_less_eq_int @ SY1337 @ SY1338 )
| ( ord_less_eq_int @ ( plus_plus_int @ SV6 @ SY1337 ) @ ( plus_plus_int @ SV6 @ SY1338 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1759]) ).
thf(2599,plain,
! [SV7: int] :
( ( ! [SY1339: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ SV7 @ SV7 ) @ ( times_times_int @ SY1339 @ SY1339 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1763]) ).
thf(2600,plain,
! [SV8: int] :
( ( ! [SY1340: int,SY1341: int,SY1342: int] :
( ~ ( ord_less_int @ SY1341 @ SY1342 )
| ~ ( ord_less_eq_int @ SV8 @ SY1340 )
| ( ord_less_int @ ( plus_plus_int @ SY1341 @ SV8 ) @ ( plus_plus_int @ SY1342 @ SY1340 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1774]) ).
thf(2601,plain,
! [SV9: int] :
( ( ( times_times_int @ pls @ SV9 )
= pls )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1780]) ).
thf(2602,plain,
! [SV10: int] :
( ( ! [SY1343: int] :
( ( times_times_int @ ( bit0 @ SV10 ) @ SY1343 )
= ( bit0 @ ( times_times_int @ SV10 @ SY1343 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1781]) ).
thf(2603,plain,
! [SV11: int] :
( ( ( times_times_int @ SV11 @ one_one_int )
= SV11 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1783]) ).
thf(2604,plain,
! [SV12: int] :
( ( ( times_times_int @ one_one_int @ SV12 )
= SV12 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1784]) ).
thf(2605,plain,
! [SV13: int] :
( ( ! [SY1344: int] :
( ( plus_plus_int @ ( number_number_of_int @ SV13 ) @ ( number_number_of_int @ SY1344 ) )
= ( number_number_of_int @ ( plus_plus_int @ SV13 @ SY1344 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1785]) ).
thf(2606,plain,
! [SV14: int] :
( ( ! [SY1345: int,SY1346: int] :
( ( times_times_int @ ( plus_plus_int @ SV14 @ SY1345 ) @ SY1346 )
= ( plus_plus_int @ ( times_times_int @ SV14 @ SY1346 ) @ ( times_times_int @ SY1345 @ SY1346 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1786]) ).
thf(2607,plain,
! [SV15: int] :
( ( ! [SY1347: int,SY1348: int] :
( ( times_times_int @ SV15 @ ( plus_plus_int @ SY1347 @ SY1348 ) )
= ( plus_plus_int @ ( times_times_int @ SV15 @ SY1347 ) @ ( times_times_int @ SV15 @ SY1348 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1787]) ).
thf(2608,plain,
! [SV16: int] :
( ( ! [SY1349: int] :
( ~ ( ord_less_int @ SV16 @ SY1349 )
| ( ord_less_eq_int @ ( plus_plus_int @ SV16 @ one_one_int ) @ SY1349 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1798]) ).
thf(2609,plain,
! [SV17: int] :
( ( ! [SY1350: int] :
( ~ ( ord_less_eq_int @ pls @ SY1350 )
| ~ ( ord_less_eq_int @ pls @ SV17 )
| ( ( plus_plus_nat @ ( number_number_of_nat @ SY1350 ) @ ( number_number_of_nat @ SV17 ) )
= ( number_number_of_nat @ ( plus_plus_int @ SY1350 @ SV17 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1801]) ).
thf(2610,plain,
! [SV18: int] :
( ( ! [SY1351: int] :
( ~ ( ord_less_eq_int @ pls @ SY1351 )
| ~ ( ord_less_eq_int @ pls @ SV18 )
| ( ( plus_plus_int @ ( number_number_of_int @ SY1351 ) @ ( number_number_of_int @ SV18 ) )
= ( number_number_of_int @ ( plus_plus_int @ SY1351 @ SV18 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1802]) ).
thf(2611,plain,
! [SV19: int] :
( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV19 )
| ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1804]) ).
thf(2612,plain,
! [SV20: int] :
( ( ! [SY1352: int] :
( ( ord_less_int @ SY1352 @ SV20 )
| ( SV20 = SY1352 )
| ( ord_less_int @ SV20 @ SY1352 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1808]) ).
thf(2613,plain,
! [SV21: nat] :
( ( ! [SY1353: nat,SY1354: int] :
( ( times_times_nat @ ( plus_plus_nat @ SV21 @ SY1353 ) @ ( number_number_of_nat @ SY1354 ) )
= ( plus_plus_nat @ ( times_times_nat @ SV21 @ ( number_number_of_nat @ SY1354 ) ) @ ( times_times_nat @ SY1353 @ ( number_number_of_nat @ SY1354 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1810]) ).
thf(2614,plain,
! [SV22: int] :
( ( ! [SY1355: int,SY1356: int] :
( ( times_times_int @ ( plus_plus_int @ SV22 @ SY1355 ) @ ( number_number_of_int @ SY1356 ) )
= ( plus_plus_int @ ( times_times_int @ SV22 @ ( number_number_of_int @ SY1356 ) ) @ ( times_times_int @ SY1355 @ ( number_number_of_int @ SY1356 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1811]) ).
thf(2615,plain,
! [SV23: int] :
( ( ! [SY1357: nat,SY1358: nat] :
( ( times_times_nat @ ( number_number_of_nat @ SV23 ) @ ( plus_plus_nat @ SY1357 @ SY1358 ) )
= ( plus_plus_nat @ ( times_times_nat @ ( number_number_of_nat @ SV23 ) @ SY1357 ) @ ( times_times_nat @ ( number_number_of_nat @ SV23 ) @ SY1358 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1812]) ).
thf(2616,plain,
! [SV24: int] :
( ( ! [SY1359: int,SY1360: int] :
( ( times_times_int @ ( number_number_of_int @ SV24 ) @ ( plus_plus_int @ SY1359 @ SY1360 ) )
= ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ SV24 ) @ SY1359 ) @ ( times_times_int @ ( number_number_of_int @ SV24 ) @ SY1360 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1813]) ).
thf(2617,plain,
! [SV25: int] :
( ( ! [SY1361: int,SY1362: int] :
( ( plus_plus_int @ ( plus_plus_int @ SV25 @ SY1361 ) @ SY1362 )
= ( plus_plus_int @ SV25 @ ( plus_plus_int @ SY1361 @ SY1362 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1814]) ).
thf(2618,plain,
! [SV26: int] :
( ( ! [SY1363: int,SY1364: int] :
( ( plus_plus_int @ SV26 @ ( plus_plus_int @ SY1363 @ SY1364 ) )
= ( plus_plus_int @ SY1363 @ ( plus_plus_int @ SV26 @ SY1364 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1815]) ).
thf(2619,plain,
! [SV27: int] :
( ( ! [SY1365: int] :
( ( plus_plus_int @ SV27 @ SY1365 )
= ( plus_plus_int @ SY1365 @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1816]) ).
thf(2620,plain,
! [SV28: int] :
( ( ! [SY1366: int,SY1367: int] :
( ~ ( ord_less_int @ SY1366 @ SY1367 )
| ~ ( ord_less_int @ zero_zero_int @ SV28 )
| ( ord_less_int @ ( times_times_int @ SV28 @ SY1366 ) @ ( times_times_int @ SV28 @ SY1367 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1818]) ).
thf(2621,plain,
! [SV29: int] :
( ( ! [SY1368: int] :
( ( ( power_power_int @ SV29 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= ( power_power_int @ SY1368 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ~ ( ord_less_eq_int @ zero_zero_int @ SV29 )
| ~ ( ord_less_eq_int @ zero_zero_int @ SY1368 )
| ( SV29 = SY1368 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1819]) ).
thf(2622,plain,
! [SV30: int] :
( ( ! [SY1369: int] :
( ~ ( ord_less_eq_int @ ( power_power_int @ SV30 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SY1369 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ~ ( ord_less_eq_int @ zero_zero_int @ SY1369 )
| ( ord_less_eq_int @ SV30 @ SY1369 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1820]) ).
thf(2623,plain,
! [SV31: int] :
( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ SV31 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1821]) ).
thf(2624,plain,
! [SV32: int] :
( ( ! [SY1370: int] :
( ~ ( ord_less_int @ ( power_power_int @ SV32 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SY1370 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ~ ( ord_less_eq_int @ zero_zero_int @ SY1370 )
| ( ord_less_int @ SV32 @ SY1370 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1822]) ).
thf(2625,plain,
! [SV33: int] :
( ( ! [SY1371: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ SV33 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SY1371 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1824]) ).
thf(2626,plain,
! [SV34: int] :
( ( ! [SY1372: int] :
~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ SV34 @ SV34 ) @ ( times_times_int @ SY1372 @ SY1372 ) ) @ zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1826]) ).
thf(2627,plain,
! [SV35: real] :
( ( ( times_times_real @ ( number267125858f_real @ ( bit1 @ pls ) ) @ SV35 )
= SV35 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1827]) ).
thf(2628,plain,
! [SV36: int] :
( ( ( times_times_int @ ( number_number_of_int @ ( bit1 @ pls ) ) @ SV36 )
= SV36 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1828]) ).
thf(2629,plain,
! [SV37: real] :
( ( ( times_times_real @ SV37 @ ( number267125858f_real @ ( bit1 @ pls ) ) )
= SV37 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1829]) ).
thf(2630,plain,
! [SV38: int] :
( ( ( times_times_int @ SV38 @ ( number_number_of_int @ ( bit1 @ pls ) ) )
= SV38 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1830]) ).
thf(2631,plain,
! [SV39: int] :
( ( ! [SY1373: int] :
( ( times_times_int @ ( bit1 @ SV39 ) @ SY1373 )
= ( plus_plus_int @ ( bit0 @ ( times_times_int @ SV39 @ SY1373 ) ) @ SY1373 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1832]) ).
thf(2632,plain,
! [SV40: int] :
( ( ( bit1 @ SV40 )
!= pls )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1835]) ).
thf(2633,plain,
! [SV41: int] :
( ( pls
!= ( bit1 @ SV41 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1836]) ).
thf(2634,plain,
! [SV42: int] :
( ( ! [SY1374: int] :
( ( bit1 @ SV42 )
!= ( bit0 @ SY1374 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1837]) ).
thf(2635,plain,
! [SV43: int] :
( ( ! [SY1375: int] :
( ( bit0 @ SV43 )
!= ( bit1 @ SY1375 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1838]) ).
thf(2636,plain,
( ( ord_less_int @ pls @ pls )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1845]) ).
thf(2637,plain,
( ( zero_zero_int = one_one_int )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1848]) ).
thf(2638,plain,
! [SV44: int] :
( ( ( plus_plus_int @ SV44 @ pls )
= SV44 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1849]) ).
thf(2639,plain,
! [SV45: int] :
( ( ( plus_plus_int @ pls @ SV45 )
= SV45 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1850]) ).
thf(2640,plain,
! [SV46: int] :
( ( ! [SY1376: int] :
( ( plus_plus_int @ ( bit0 @ SV46 ) @ ( bit0 @ SY1376 ) )
= ( bit0 @ ( plus_plus_int @ SV46 @ SY1376 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1851]) ).
thf(2641,plain,
! [SV47: int] :
( ( ( bit0 @ SV47 )
= ( plus_plus_int @ SV47 @ SV47 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1852]) ).
thf(2642,plain,
! [SV48: int] :
( ( ( plus_plus_int @ SV48 @ zero_zero_int )
= SV48 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1853]) ).
thf(2643,plain,
! [SV49: int] :
( ( ( plus_plus_int @ zero_zero_int @ SV49 )
= SV49 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1854]) ).
thf(2644,plain,
! [SV50: int] :
( ( ! [SY1377: int,SY1378: int] :
( ~ ( ord_less_int @ SY1377 @ SY1378 )
| ( ord_less_int @ ( plus_plus_int @ SY1377 @ SV50 ) @ ( plus_plus_int @ SY1378 @ SV50 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1855]) ).
thf(2645,plain,
! [SV51: int] :
( ( ( times_times_int @ ( plus_plus_int @ one_one_int @ one_one_int ) @ ( number_number_of_int @ SV51 ) )
= ( number_number_of_int @ ( bit0 @ SV51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1856]) ).
thf(2646,plain,
! [SV52: real] :
( ( ( power_power_real @ SV52 @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( times_times_real @ ( times_times_real @ SV52 @ SV52 ) @ SV52 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1857]) ).
thf(2647,plain,
! [SV53: nat] :
( ( ( power_power_nat @ SV53 @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( times_times_nat @ ( times_times_nat @ SV53 @ SV53 ) @ SV53 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1858]) ).
thf(2648,plain,
! [SV54: int] :
( ( ( power_power_int @ SV54 @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( times_times_int @ ( times_times_int @ SV54 @ SV54 ) @ SV54 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1859]) ).
thf(2649,plain,
! [SV55: nat] :
( ( ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV55 )
= ( plus_plus_nat @ SV55 @ SV55 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1860]) ).
thf(2650,plain,
! [SV56: int] :
( ( ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV56 )
= ( plus_plus_int @ SV56 @ SV56 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1861]) ).
thf(2651,plain,
! [SV57: int] :
( ( ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV57 )
= ( plus_plus_int @ SV57 @ SV57 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1862]) ).
thf(2652,plain,
! [SV58: nat] :
( ( ( times_times_nat @ SV58 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_nat @ SV58 @ SV58 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1863]) ).
thf(2653,plain,
! [SV59: int] :
( ( ( times_times_int @ SV59 @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ SV59 @ SV59 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1864]) ).
thf(2654,plain,
! [SV60: int] :
( ( ( times_times_int @ SV60 @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ SV60 @ SV60 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1865]) ).
thf(2655,plain,
! [SV61: real] :
( ( ( power_power_real @ SV61 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_real @ SV61 @ SV61 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1866]) ).
thf(2656,plain,
! [SV62: nat] :
( ( ( power_power_nat @ SV62 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_nat @ SV62 @ SV62 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1867]) ).
thf(2657,plain,
! [SV63: int] :
( ( ( power_power_int @ SV63 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_int @ SV63 @ SV63 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1868]) ).
thf(2658,plain,
! [SV64: real] :
( ( ( plus_plus_real @ ( number267125858f_real @ pls ) @ SV64 )
= SV64 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1877]) ).
thf(2659,plain,
! [SV65: int] :
( ( ( plus_plus_int @ ( number_number_of_int @ pls ) @ SV65 )
= SV65 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1878]) ).
thf(2660,plain,
! [SV66: real] :
( ( ( plus_plus_real @ SV66 @ ( number267125858f_real @ pls ) )
= SV66 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1879]) ).
thf(2661,plain,
! [SV67: int] :
( ( ( plus_plus_int @ SV67 @ ( number_number_of_int @ pls ) )
= SV67 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1880]) ).
thf(2662,plain,
! [SV68: int] :
( ( ! [SY1379: int,SY1380: real] :
( ( plus_plus_real @ ( number267125858f_real @ SV68 ) @ ( plus_plus_real @ ( number267125858f_real @ SY1379 ) @ SY1380 ) )
= ( plus_plus_real @ ( number267125858f_real @ ( plus_plus_int @ SV68 @ SY1379 ) ) @ SY1380 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1883]) ).
thf(2663,plain,
! [SV69: int] :
( ( ! [SY1381: int,SY1382: int] :
( ( plus_plus_int @ ( number_number_of_int @ SV69 ) @ ( plus_plus_int @ ( number_number_of_int @ SY1381 ) @ SY1382 ) )
= ( plus_plus_int @ ( number_number_of_int @ ( plus_plus_int @ SV69 @ SY1381 ) ) @ SY1382 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1884]) ).
thf(2664,plain,
! [SV70: int] :
( ( ! [SY1383: int] :
( ( plus_plus_real @ ( number267125858f_real @ SV70 ) @ ( number267125858f_real @ SY1383 ) )
= ( number267125858f_real @ ( plus_plus_int @ SV70 @ SY1383 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1885]) ).
thf(2665,plain,
! [SV71: int] :
( ( ! [SY1384: int] :
( ( plus_plus_int @ ( number_number_of_int @ SV71 ) @ ( number_number_of_int @ SY1384 ) )
= ( number_number_of_int @ ( plus_plus_int @ SV71 @ SY1384 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1886]) ).
thf(2666,plain,
! [SV72: int] :
( ( ! [SY1385: int] :
( ( number267125858f_real @ ( plus_plus_int @ SV72 @ SY1385 ) )
= ( plus_plus_real @ ( number267125858f_real @ SV72 ) @ ( number267125858f_real @ SY1385 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1887]) ).
thf(2667,plain,
! [SV73: int] :
( ( ! [SY1386: int] :
( ( number_number_of_int @ ( plus_plus_int @ SV73 @ SY1386 ) )
= ( plus_plus_int @ ( number_number_of_int @ SV73 ) @ ( number_number_of_int @ SY1386 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1888]) ).
thf(2668,plain,
( ( ord_less_int @ pls @ zero_zero_int )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1895]) ).
thf(2669,plain,
! [SV74: int] :
( ( ! [SY1387: int] :
( ( plus_plus_int @ ( bit1 @ SV74 ) @ ( bit0 @ SY1387 ) )
= ( bit1 @ ( plus_plus_int @ SV74 @ SY1387 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1897]) ).
thf(2670,plain,
! [SV75: int] :
( ( ! [SY1388: int] :
( ( plus_plus_int @ ( bit0 @ SV75 ) @ ( bit1 @ SY1388 ) )
= ( bit1 @ ( plus_plus_int @ SV75 @ SY1388 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1898]) ).
thf(2671,plain,
! [SV76: int] :
( ( ( bit1 @ SV76 )
= ( plus_plus_int @ ( plus_plus_int @ one_one_int @ SV76 ) @ SV76 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1900]) ).
thf(2672,plain,
! [SV77: int] :
( ( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ SV77 ) @ SV77 )
!= zero_zero_int )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1901]) ).
thf(2673,plain,
! [SV78: int] :
( ( ( power_power_nat @ ( number_number_of_nat @ SV78 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_nat @ ( number_number_of_nat @ SV78 ) @ ( number_number_of_nat @ SV78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1903]) ).
thf(2674,plain,
! [SV79: int] :
( ( ( power_power_int @ ( number_number_of_int @ SV79 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_int @ ( number_number_of_int @ SV79 ) @ ( number_number_of_int @ SV79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1904]) ).
thf(2675,plain,
! [SV80: int] :
( ( ! [SY1389: int] :
( ( power_power_int @ ( plus_plus_int @ SV80 @ SY1389 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ SV80 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SY1389 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV80 ) @ SY1389 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1905]) ).
thf(2676,plain,
! [SV81: int] :
( ( ( number_number_of_int @ ( bit0 @ SV81 ) )
= ( plus_plus_int @ ( plus_plus_int @ zero_zero_int @ ( number_number_of_int @ SV81 ) ) @ ( number_number_of_int @ SV81 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1906]) ).
thf(2677,plain,
! [SV82: int] :
( ( ( number_number_of_int @ ( bit1 @ SV82 ) )
= ( plus_plus_int @ ( plus_plus_int @ one_one_int @ ( number_number_of_int @ SV82 ) ) @ ( number_number_of_int @ SV82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1907]) ).
thf(2678,plain,
! [SV83: int] :
( ( ! [SY1390: int] :
( ( power_power_int @ ( plus_plus_int @ SV83 @ SY1390 ) @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ SV83 @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) @ ( power_power_int @ SV83 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ SY1390 ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) @ SV83 ) @ ( power_power_int @ SY1390 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ ( power_power_int @ SY1390 @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1923]) ).
thf(2679,plain,
! [SV84: int] :
( ( ! [SY1391: int] :
( ( power_power_int @ ( plus_plus_int @ SV84 @ SY1391 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ SV84 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV84 ) @ SY1391 ) ) @ ( power_power_int @ SY1391 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1924]) ).
thf(2680,plain,
! [SV85: int] :
( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV85 )
| ~ ( ord_less_int @ SV85 @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
| ( SV85 = zero_zero_int )
| ( SV85 = one_one_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1925]) ).
thf(2681,plain,
! [SV86: int] :
( ( ( times_times_int @ SV86 @ ( power_power_int @ SV86 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( power_power_int @ SV86 @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1926]) ).
thf(2682,plain,
! [SV87: int] :
( ( ord_less_eq_int @ SV87 @ ( power_power_int @ SV87 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1927]) ).
thf(2683,plain,
! [SV88: int] :
( ( ! [SY1392: int,SY1393: int] :
( ~ ( ord_less_int @ zero_zero_int @ SY1393 )
| ( SY1393
!= ( plus_plus_int @ SV88 @ ( times_times_int @ SY1393 @ SY1392 ) ) )
| ~ ( ord_less_int @ SV88 @ SY1393 )
| ( ord_less_eq_int @ one_one_int @ SY1392 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1928]) ).
thf(2684,plain,
! [SV89: int] :
( ( ! [SY1394: int,SY1395: int] :
( ~ ( ord_less_int @ zero_zero_int @ SY1395 )
| ( SY1395
!= ( plus_plus_int @ SV89 @ ( times_times_int @ SY1395 @ SY1394 ) ) )
| ~ ( ord_less_eq_int @ zero_zero_int @ SV89 )
| ( ord_less_eq_int @ SY1394 @ one_one_int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1929]) ).
thf(2685,plain,
! [SV90: nat] :
( ( ! [SY1396: nat] :
( ( power_power_nat @ SV90 @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SY1396 ) )
= ( times_times_nat @ ( power_power_nat @ SV90 @ SY1396 ) @ ( power_power_nat @ SV90 @ SY1396 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1931]) ).
thf(2686,plain,
! [SV91: int] :
( ( ! [SY1397: nat] :
( ( power_power_int @ SV91 @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SY1397 ) )
= ( times_times_int @ ( power_power_int @ SV91 @ SY1397 ) @ ( power_power_int @ SV91 @ SY1397 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1932]) ).
thf(2687,plain,
! [SV92: int] :
( ( ! [SY1398: nat,SY1399: int] :
( ~ ( zprime @ SY1399 )
| ~ ( dvd_dvd_int @ SY1399 @ ( power_power_int @ SV92 @ SY1398 ) )
| ( dvd_dvd_int @ SY1399 @ SV92 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1933]) ).
thf(2688,plain,
! [SV93: int] :
( ( ! [SY1400: nat,SY1401: nat] :
( ( power_power_int @ ( power_power_int @ SV93 @ SY1400 ) @ SY1401 )
= ( power_power_int @ SV93 @ ( times_times_nat @ SY1400 @ SY1401 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1934]) ).
thf(2689,plain,
! [SV94: int] :
( ( ! [SY1402: nat,SY1403: nat] :
( ( power_power_int @ ( power_power_int @ SV94 @ SY1402 ) @ SY1403 )
= ( power_power_int @ SV94 @ ( times_times_nat @ SY1402 @ SY1403 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1935]) ).
thf(2690,plain,
! [SV95: int] :
( ( ! [SY1404: int] :
( ~ ( ord_less_int @ zero_zero_int @ SY1404 )
| ~ ( ord_less_int @ SY1404 @ SV95 )
| ~ ( dvd_dvd_int @ SV95 @ SY1404 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1936]) ).
thf(2691,plain,
! [SV96: int] :
( ( ! [SY1405: int] :
( ~ ( ord_less_eq_int @ zero_zero_int @ SY1405 )
| ~ ( ord_less_eq_int @ zero_zero_int @ SV96 )
| ~ ( dvd_dvd_int @ SY1405 @ SV96 )
| ~ ( dvd_dvd_int @ SV96 @ SY1405 )
| ( SY1405 = SV96 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1937]) ).
thf(2692,plain,
! [SV97: int] :
( ( ! [SY1406: int,SY1407: int] :
( ~ ( dvd_dvd_int @ ( times_times_int @ SV97 @ SY1406 ) @ ( times_times_int @ SV97 @ SY1407 ) )
| ( SV97 = zero_zero_int )
| ( dvd_dvd_int @ SY1406 @ SY1407 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1938]) ).
thf(2693,plain,
! [SV98: int] :
( ( ! [SY1408: int] :
( ~ ( dvd_dvd_int @ SV98 @ SY1408 )
| ~ ( ord_less_int @ zero_zero_int @ SY1408 )
| ( ord_less_eq_int @ SV98 @ SY1408 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1942]) ).
thf(2694,plain,
! [SV99: int] :
( ( ! [SY1409: int] :
( ( plus_plus_int @ SV99 @ SY1409 )
= ( plus_plus_int @ SY1409 @ SV99 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1944]) ).
thf(2695,plain,
! [SV100: int] :
( ( ! [SY1410: int,SY1411: int] :
( ( plus_plus_int @ SV100 @ ( plus_plus_int @ SY1410 @ SY1411 ) )
= ( plus_plus_int @ SY1410 @ ( plus_plus_int @ SV100 @ SY1411 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1945]) ).
thf(2696,plain,
! [SV101: int] :
( ( ! [SY1412: int,SY1413: int] :
( ( plus_plus_int @ SV101 @ ( plus_plus_int @ SY1412 @ SY1413 ) )
= ( plus_plus_int @ ( plus_plus_int @ SV101 @ SY1412 ) @ SY1413 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1946]) ).
thf(2697,plain,
! [SV102: int] :
( ( ! [SY1414: int,SY1415: int] :
( ( plus_plus_int @ ( plus_plus_int @ SV102 @ SY1414 ) @ SY1415 )
= ( plus_plus_int @ SV102 @ ( plus_plus_int @ SY1414 @ SY1415 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1947]) ).
thf(2698,plain,
! [SV103: int] :
( ( ! [SY1416: int,SY1417: int] :
( ( plus_plus_int @ ( plus_plus_int @ SV103 @ SY1416 ) @ SY1417 )
= ( plus_plus_int @ ( plus_plus_int @ SV103 @ SY1417 ) @ SY1416 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1948]) ).
thf(2699,plain,
! [SV104: int] :
( ( ! [SY1418: int,SY1419: int,SY1420: int] :
( ( plus_plus_int @ ( plus_plus_int @ SV104 @ SY1418 ) @ ( plus_plus_int @ SY1419 @ SY1420 ) )
= ( plus_plus_int @ ( plus_plus_int @ SV104 @ SY1419 ) @ ( plus_plus_int @ SY1418 @ SY1420 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1949]) ).
thf(2700,plain,
! [SV105: int] :
( ( ( power_power_int @ SV105 @ one_one_nat )
= SV105 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1950]) ).
thf(2701,plain,
! [SV106: nat] :
( ( ( times_times_nat @ SV106 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_nat @ SV106 @ SV106 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1951]) ).
thf(2702,plain,
! [SV107: nat] :
( ( ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV107 )
= ( plus_plus_nat @ SV107 @ SV107 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1952]) ).
thf(2703,plain,
! [SV108: real] :
( ( ! [SY1421: nat] :
( ( power_power_real @ SV108 @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SY1421 ) )
= ( power_power_real @ ( power_power_real @ SV108 @ SY1421 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1953]) ).
thf(2704,plain,
! [SV109: nat] :
( ( ! [SY1422: nat] :
( ( power_power_nat @ SV109 @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SY1422 ) )
= ( power_power_nat @ ( power_power_nat @ SV109 @ SY1422 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1954]) ).
thf(2705,plain,
! [SV110: int] :
( ( ! [SY1423: nat] :
( ( power_power_int @ SV110 @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SY1423 ) )
= ( power_power_int @ ( power_power_int @ SV110 @ SY1423 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1955]) ).
thf(2706,plain,
! [SV111: int] :
( ( ! [SY1424: nat] :
~ ( ord_less_eq_int @ ( power_power_int @ SV111 @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SY1424 ) ) @ zero_zero_int )
| ( SV111 = zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1956]) ).
thf(2707,plain,
! [SV112: int] :
( ( ( times_times_int @ zero_zero_int @ SV112 )
= zero_zero_int )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1957]) ).
thf(2708,plain,
! [SV113: int] :
( ( ( times_times_int @ SV113 @ zero_zero_int )
= zero_zero_int )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1958]) ).
thf(2709,plain,
! [SV114: int] :
( ( ( plus_plus_int @ zero_zero_int @ SV114 )
= SV114 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1959]) ).
thf(2710,plain,
! [SV115: int] :
( ( ( plus_plus_int @ SV115 @ zero_zero_int )
= SV115 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1960]) ).
thf(2711,plain,
! [SV116: int] :
( ( ! [SY1425: int,SY1426: int] :
( ( times_times_int @ SV116 @ ( plus_plus_int @ SY1425 @ SY1426 ) )
= ( plus_plus_int @ ( times_times_int @ SV116 @ SY1425 ) @ ( times_times_int @ SV116 @ SY1426 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1962]) ).
thf(2712,plain,
! [SV117: int] :
( ( ! [SY1427: int,SY1428: int] :
( ( times_times_int @ ( plus_plus_int @ SV117 @ SY1427 ) @ SY1428 )
= ( plus_plus_int @ ( times_times_int @ SV117 @ SY1428 ) @ ( times_times_int @ SY1427 @ SY1428 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1964]) ).
thf(2713,plain,
! [SV118: int] :
( ( ! [SY1429: int,SY1430: int] :
( ( plus_plus_int @ ( times_times_int @ SV118 @ SY1429 ) @ ( times_times_int @ SY1430 @ SY1429 ) )
= ( times_times_int @ ( plus_plus_int @ SV118 @ SY1430 ) @ SY1429 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1965]) ).
thf(2714,plain,
! [SV119: int] :
( ( ( times_times_int @ one_one_int @ SV119 )
= SV119 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1967]) ).
thf(2715,plain,
! [SV120: int] :
( ( ( times_times_int @ SV120 @ one_one_int )
= SV120 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1968]) ).
thf(2716,plain,
! [SV121: int] :
( ( ! [SY1431: int,SY1432: nat] :
( ( power_power_int @ ( times_times_int @ SV121 @ SY1431 ) @ SY1432 )
= ( times_times_int @ ( power_power_int @ SV121 @ SY1432 ) @ ( power_power_int @ SY1431 @ SY1432 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1969]) ).
thf(2717,plain,
! [SV122: int] :
( ( ! [SY1433: nat,SY1434: nat] :
( ( times_times_int @ ( power_power_int @ SV122 @ SY1433 ) @ ( power_power_int @ SV122 @ SY1434 ) )
= ( power_power_int @ SV122 @ ( plus_plus_nat @ SY1433 @ SY1434 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1970]) ).
thf(2718,plain,
! [SV123: int] :
( ( ( power_power_int @ SV123 @ zero_zero_nat )
= one_one_int )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1971]) ).
thf(2719,plain,
! [SV124: int] :
( ( ! [SY1435: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ SV124 @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SY1435 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1973]) ).
thf(2720,plain,
! [SV125: int] :
( ( ! [SY1436: int,SY1437: int,SY1438: int,SY1439: int] :
( ( SY1439 = zero_zero_int )
| ( SV125 = SY1436 )
| ( SY1437 != SY1438 )
| ( ( plus_plus_int @ SY1437 @ ( times_times_int @ SY1439 @ SV125 ) )
!= ( plus_plus_int @ SY1438 @ ( times_times_int @ SY1439 @ SY1436 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1974]) ).
thf(2721,plain,
! [SV126: int] :
( ( ( plus_plus_int @ SV126 @ SV126 )
= ( times_times_int @ ( plus_plus_int @ one_one_int @ one_one_int ) @ SV126 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1975]) ).
thf(2722,plain,
! [SV127: int] :
( ( ! [SY1440: int] :
( ( plus_plus_int @ SV127 @ ( times_times_int @ SY1440 @ SV127 ) )
= ( times_times_int @ ( plus_plus_int @ SY1440 @ one_one_int ) @ SV127 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1976]) ).
thf(2723,plain,
! [SV128: int] :
( ( ! [SY1441: int] :
( ( plus_plus_int @ ( times_times_int @ SV128 @ SY1441 ) @ SY1441 )
= ( times_times_int @ ( plus_plus_int @ SV128 @ one_one_int ) @ SY1441 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1977]) ).
thf(2724,plain,
! [SV129: int] :
( ( ! [SY1442: int] :
( ~ ( ord_less_int @ zero_zero_int @ SY1442 )
| ~ ( ord_less_int @ zero_zero_int @ ( times_times_int @ SY1442 @ SV129 ) )
| ( ord_less_int @ zero_zero_int @ SV129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1980]) ).
thf(2725,plain,
! [SV130: int] :
( ( ! [SY1443: int] :
( ~ ( ord_less_eq_int @ zero_zero_int @ SY1443 )
| ~ ( ord_less_eq_int @ zero_zero_int @ SV130 )
| ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ SY1443 @ SV130 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1982]) ).
thf(2726,plain,
! [SV131: int] :
( ( ! [SY1444: int] :
( ~ ( ord_less_eq_int @ zero_zero_int @ SY1444 )
| ~ ( ord_less_eq_int @ zero_zero_int @ SV131 )
| ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ SY1444 @ SV131 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1983]) ).
thf(2727,plain,
! [SV132: nat] :
( ( ! [SY1445: int] :
( ~ ( ord_less_eq_int @ zero_zero_int @ SY1445 )
| ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ SY1445 @ SV132 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1984]) ).
thf(2728,plain,
! [SV133: int] :
( ( ! [SY1446: int,SY1447: int] :
( ~ ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ SV133 @ SY1446 ) @ SY1447 ) )
| ~ ( ord_less_int @ SY1447 @ SV133 )
| ~ ( ord_less_int @ zero_zero_int @ SV133 )
| ( ord_less_eq_int @ zero_zero_int @ SY1446 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1987]) ).
thf(2729,plain,
! [SV134: int] :
( ( ! [SY1448: int,SY1449: int] :
( ~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ SV134 @ SY1448 ) @ SY1449 ) @ zero_zero_int )
| ~ ( ord_less_eq_int @ zero_zero_int @ SY1449 )
| ~ ( ord_less_int @ zero_zero_int @ SV134 )
| ( ord_less_eq_int @ SY1448 @ zero_zero_int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1988]) ).
thf(2730,plain,
! [SV135: int] :
( ( ! [SY1450: int,SY1451: int,SY1452: int,SY1453: int] :
( ~ ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SV135 @ SY1450 ) @ SY1451 ) @ ( plus_plus_int @ ( times_times_int @ SV135 @ SY1452 ) @ SY1453 ) )
| ~ ( ord_less_eq_int @ zero_zero_int @ SY1451 )
| ~ ( ord_less_int @ SY1451 @ SV135 )
| ~ ( ord_less_int @ SY1453 @ SV135 )
| ( ord_less_eq_int @ SY1450 @ SY1452 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1989]) ).
thf(2731,plain,
! [SV136: int] :
( ( ! [SY1454: int,SY1455: int,SY1456: int,SY1457: int,SY1458: int] :
( ( ( plus_plus_int @ ( times_times_int @ SV136 @ SY1454 ) @ SY1455 )
!= ( plus_plus_int @ ( times_times_int @ SY1456 @ SY1457 ) @ SY1458 ) )
| ~ ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ SY1456 @ SY1457 ) @ SY1458 ) )
| ~ ( ord_less_int @ SY1458 @ SY1456 )
| ~ ( ord_less_eq_int @ zero_zero_int @ SY1455 )
| ~ ( ord_less_int @ zero_zero_int @ SY1456 )
| ~ ( ord_less_eq_int @ SY1456 @ SV136 )
| ( ord_less_eq_int @ SY1454 @ SY1457 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1990]) ).
thf(2732,plain,
! [SV137: int] :
( ( ! [SY1459: int,SY1460: int,SY1461: int,SY1462: int] :
( ~ ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SV137 @ SY1459 ) @ SY1460 ) @ ( plus_plus_int @ ( times_times_int @ SV137 @ SY1461 ) @ SY1462 ) )
| ~ ( ord_less_eq_int @ SY1462 @ zero_zero_int )
| ~ ( ord_less_int @ SV137 @ SY1462 )
| ~ ( ord_less_int @ SV137 @ SY1460 )
| ( ord_less_eq_int @ SY1461 @ SY1459 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1991]) ).
thf(2733,plain,
! [SV138: int] :
( ( ! [SY1463: int,SY1464: int,SY1465: int,SY1466: int,SY1467: int] :
( ( ( plus_plus_int @ ( times_times_int @ SV138 @ SY1463 ) @ SY1464 )
!= ( plus_plus_int @ ( times_times_int @ SY1465 @ SY1466 ) @ SY1467 ) )
| ~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ SY1465 @ SY1466 ) @ SY1467 ) @ zero_zero_int )
| ~ ( ord_less_int @ SY1464 @ SV138 )
| ~ ( ord_less_eq_int @ zero_zero_int @ SY1467 )
| ~ ( ord_less_int @ zero_zero_int @ SY1465 )
| ~ ( ord_less_eq_int @ SY1465 @ SV138 )
| ( ord_less_eq_int @ SY1466 @ SY1463 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1992]) ).
thf(2734,plain,
! [SV139: int] :
( ( ( power_power_int @ ( power_power_int @ SV139 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power_int @ SV139 @ ( number_number_of_nat @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1993]) ).
thf(2735,plain,
! [SV140: real] :
( ( ( times_times_real @ SV140 @ SV140 )
= ( power_power_real @ SV140 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1994]) ).
thf(2736,plain,
! [SV141: nat] :
( ( ( times_times_nat @ SV141 @ SV141 )
= ( power_power_nat @ SV141 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1995]) ).
thf(2737,plain,
! [SV142: int] :
( ( ( times_times_int @ SV142 @ SV142 )
= ( power_power_int @ SV142 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1996]) ).
thf(2738,plain,
! [SV143: int] :
( ( ! [SY1468: int,SY1469: int] :
( ( zcong @ SY1468 @ zero_zero_int @ SY1469 )
| ~ ( zcong @ ( power_power_int @ SV143 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SY1468 @ SY1469 )
| ~ ( dvd_dvd_int @ SY1469 @ SV143 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1997]) ).
thf(2739,plain,
( ( min = pls )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2002]) ).
thf(2740,plain,
( ( pls = min )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2003]) ).
thf(2741,plain,
! [SV144: int] :
( ( min
!= ( bit0 @ SV144 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2004]) ).
thf(2742,plain,
! [SV145: int] :
( ( ( bit0 @ SV145 )
!= min )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2005]) ).
thf(2743,plain,
( ( ord_less_int @ min @ min )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2006]) ).
thf(2744,plain,
( ( ord_less_int @ pls @ min )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2009]) ).
thf(2745,plain,
( ( ord_less_eq_int @ pls @ min )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2016]) ).
thf(2746,plain,
( ( ( number_number_of_int @ pls )
= ( number_number_of_int @ min ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2018]) ).
thf(2747,plain,
! [SV146: int] :
( ( ! [SY1470: int] :
( ~ ( ord_less_eq_int @ SV146 @ SY1470 )
| ( SV146 = SY1470 )
| ( ord_less_int @ SV146 @ SY1470 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2021]) ).
thf(2748,plain,
! [SV147: int] :
( ( ! [SY1471: int,SY1472: int] :
( ~ ( ord_less_int @ SY1471 @ SY1472 )
| ~ ( ord_less_int @ SV147 @ SY1472 )
| ( ord_less_eq_int @ SY1471 @ SV147 )
| ( ord_less_eq_int @ SV147 @ SY1471 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2022]) ).
thf(2749,plain,
! [SV148: int] :
( ( ! [SY1473: int] : ( zcong @ SV148 @ SY1473 @ one_one_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2024]) ).
thf(2750,plain,
! [SV149: int] :
( ( ! [SY1474: int,SY1475: int,SY1476: int,SY1477: int] :
( ~ ( zcong @ SY1475 @ SY1476 @ SY1477 )
| ~ ( zcong @ SV149 @ SY1474 @ SY1477 )
| ( zcong @ ( plus_plus_int @ SY1475 @ SV149 ) @ ( plus_plus_int @ SY1476 @ SY1474 ) @ SY1477 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2025]) ).
thf(2751,plain,
! [SV150: int] :
( ( ! [SY1478: int,SY1479: int] :
( ~ ( ord_less_int @ zero_zero_int @ SY1479 )
| ~ ( ord_less_int @ SY1479 @ SY1478 )
| ~ ( ord_less_int @ zero_zero_int @ SV150 )
| ~ ( ord_less_int @ SV150 @ SY1479 )
| ~ ( zcong @ SY1479 @ SV150 @ SY1478 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2026]) ).
thf(2752,plain,
! [SV151: int] :
( ( ! [SY1480: int] :
( ~ ( ord_less_eq_int @ zero_zero_int @ SY1480 )
| ~ ( ord_less_int @ SY1480 @ SV151 )
| ~ ( zcong @ SY1480 @ zero_zero_int @ SV151 )
| ( SY1480 = zero_zero_int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2028]) ).
thf(2753,plain,
! [SV152: int] :
( ( ! [SY1481: int,SY1482: int] :
( ~ ( ord_less_eq_int @ zero_zero_int @ SY1482 )
| ~ ( ord_less_int @ SY1482 @ SY1481 )
| ~ ( ord_less_eq_int @ zero_zero_int @ SV152 )
| ~ ( ord_less_int @ SV152 @ SY1481 )
| ~ ( zcong @ SY1482 @ SV152 @ SY1481 )
| ( SY1482 = SV152 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2029]) ).
thf(2754,plain,
! [SV153: nat] :
( ( ! [SY1483: int,SY1484: nat,SY1485: int] :
( ~ ( zcong @ ( power_power_int @ SY1483 @ SY1484 ) @ one_one_int @ SY1485 )
| ( zcong @ ( power_power_int @ SY1483 @ ( times_times_nat @ SY1484 @ SV153 ) ) @ one_one_int @ SY1485 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2030]) ).
thf(2755,plain,
! [SV154: int] :
( ( ! [SY1486: int] :
( ( minus_minus_int @ ( bit0 @ SV154 ) @ ( bit0 @ SY1486 ) )
= ( bit0 @ ( minus_minus_int @ SV154 @ SY1486 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2031]) ).
thf(2756,plain,
! [SV155: int] :
( ( ( minus_minus_int @ SV155 @ pls )
= SV155 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2032]) ).
thf(2757,plain,
! [SV156: int] :
( ( ! [SY1487: int,SY1488: int] :
( ( ( minus_minus_int @ SV156 @ SY1487 )
!= SY1488 )
| ( SV156
= ( plus_plus_int @ SY1488 @ SY1487 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2033]) ).
thf(2758,plain,
! [SV157: int] :
( ( ! [SY1489: int] :
( ( minus_minus_int @ ( bit1 @ SV157 ) @ ( bit0 @ SY1489 ) )
= ( bit1 @ ( minus_minus_int @ SV157 @ SY1489 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2034]) ).
thf(2759,plain,
! [SV158: int] :
( ( ! [SY1490: int] :
( ( minus_minus_int @ ( bit1 @ SV158 ) @ ( bit1 @ SY1490 ) )
= ( bit0 @ ( minus_minus_int @ SV158 @ SY1490 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2035]) ).
thf(2760,plain,
! [SV159: int] :
( ( ( minus_minus_int @ pls @ ( bit0 @ SV159 ) )
= ( bit0 @ ( minus_minus_int @ pls @ SV159 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2036]) ).
thf(2761,plain,
! [SV160: int] :
( ( ! [SY1491: int,SY1492: int,SY1493: int,SY1494: int,SY1495: int,SY1496: int] :
( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ SV160 @ ( times_times_int @ SY1491 @ SY1492 ) ) @ SY1493 ) @ ( times_times_int @ ( minus_minus_int @ SY1494 @ ( times_times_int @ SY1491 @ SY1495 ) ) @ SY1496 ) )
= ( minus_minus_int @ ( plus_plus_int @ ( times_times_int @ SV160 @ SY1493 ) @ ( times_times_int @ SY1494 @ SY1496 ) ) @ ( times_times_int @ SY1491 @ ( plus_plus_int @ ( times_times_int @ SY1492 @ SY1493 ) @ ( times_times_int @ SY1495 @ SY1496 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2038]) ).
thf(2762,plain,
! [SV161: int] :
( ( ! [SY1497: int,SY1498: int] :
( ( plus_plus_int @ ( number_number_of_int @ SV161 ) @ ( minus_minus_int @ ( number_number_of_int @ SY1497 ) @ SY1498 ) )
= ( minus_minus_int @ ( number_number_of_int @ ( plus_plus_int @ SV161 @ SY1497 ) ) @ SY1498 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2039]) ).
thf(2763,plain,
! [SV162: int] :
( ( ! [SY1499: int] :
( ~ ( ord_less_int @ zero_zero_int @ SY1499 )
| ~ ( ord_less_int @ SY1499 @ SV162 )
| ( SY1499
= ( minus_minus_int @ SV162 @ one_one_int ) )
| ( ord_less_int @ SY1499 @ ( minus_minus_int @ SV162 @ one_one_int ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2040]) ).
thf(2764,plain,
! [SV163: int] :
( ( ( minus_minus_int @ pls @ ( bit1 @ SV163 ) )
= ( bit1 @ ( minus_minus_int @ min @ SV163 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2042]) ).
thf(2765,plain,
! [SV164: int] :
( ( ( minus_minus_int @ min @ ( bit1 @ SV164 ) )
= ( bit0 @ ( minus_minus_int @ min @ SV164 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2043]) ).
thf(2766,plain,
! [SV165: int] :
( ( ( minus_minus_int @ min @ ( bit0 @ SV165 ) )
= ( bit1 @ ( minus_minus_int @ min @ SV165 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2044]) ).
thf(2767,plain,
! [SV166: int] :
( ( ! [SY1500: int] :
( ( times_times_int @ ( plus_plus_int @ SV166 @ SY1500 ) @ ( minus_minus_int @ SV166 @ SY1500 ) )
= ( minus_minus_int @ ( power_power_int @ SV166 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SY1500 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2045]) ).
thf(2768,plain,
! [SV167: int] :
( ( zcong @ SV167 @ zero_zero_int @ SV167 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2046]) ).
thf(2769,plain,
! [SV168: int] :
( ( ! [SY1501: int,SY1502: int,SY1503: int] :
( ~ ( zcong @ SY1501 @ SY1502 @ SY1503 )
| ( zcong @ ( plus_plus_int @ SY1501 @ SV168 ) @ ( plus_plus_int @ SY1502 @ SV168 ) @ SY1503 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2047]) ).
thf(2770,plain,
! [SV169: nat] :
( ( ! [SY1504: int,SY1505: int,SY1506: int] :
( ~ ( zcong @ SY1504 @ SY1505 @ SY1506 )
| ( zcong @ ( power_power_int @ SY1504 @ SV169 ) @ ( power_power_int @ SY1505 @ SV169 ) @ SY1506 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2048]) ).
thf(2771,plain,
! [SV170: int] :
( ( ! [SY1507: int,SY1508: int] :
( ~ ( ord_less_int @ zero_zero_int @ SY1508 )
| ~ ( ord_less_int @ zero_zero_int @ SY1507 )
| ~ ( ord_less_int @ zero_zero_int @ SV170 )
| ~ ( zcong @ SY1508 @ SY1507 @ SV170 )
| ~ ( ord_less_int @ SY1508 @ SV170 )
| ~ ( ord_less_int @ SY1507 @ SV170 )
| ( SY1508 = SY1507 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2049]) ).
thf(2772,plain,
! [SV171: int] :
( ( ! [SY1509: int] :
( ~ ( ord_less_int @ zero_zero_int @ SY1509 )
| ~ ( ord_less_int @ SY1509 @ SV171 )
| ~ ( zcong @ SY1509 @ zero_zero_int @ SV171 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2050]) ).
thf(2773,plain,
! [SV172: int] :
( ( ! [SY1510: int] :
( ~ ( dvd_dvd_int @ SV172 @ SY1510 )
| ( ord_less_eq_int @ SY1510 @ zero_zero_int )
| ( ord_less_eq_int @ SV172 @ SY1510 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2051]) ).
thf(2774,plain,
! [SV173: int] :
( ( ! [SY1511: int] :
( ~ ( ord_less_eq_int @ zero_zero_int @ SY1511 )
| ~ ( ord_less_int @ SY1511 @ SV173 )
| ~ ( zcong @ SY1511 @ zero_zero_int @ SV173 )
| ( SY1511 = zero_zero_int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2054]) ).
thf(2775,plain,
! [SV174: nat] :
( ( ( ( power_power_int @ ( number_number_of_int @ min ) @ SV174 )
= one_one_int )
| ( ( power_power_int @ ( number_number_of_int @ min ) @ SV174 )
= ( number_number_of_int @ min ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2055]) ).
thf(2776,plain,
! [SV175: int] :
( ( ! [SY1512: int,SY1513: int,SY1514: int] :
( ( minus_minus_int @ ( plus_plus_int @ SV175 @ SY1512 ) @ ( plus_plus_int @ SY1513 @ SY1514 ) )
= ( plus_plus_int @ ( minus_minus_int @ SV175 @ SY1513 ) @ ( minus_minus_int @ SY1512 @ SY1514 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2057]) ).
thf(2777,plain,
! [SV176: int] :
( ( ! [SY1515: int,SY1516: int,SY1517: int] :
( ( minus_minus_int @ ( times_times_int @ SV176 @ SY1515 ) @ ( times_times_int @ SY1516 @ SY1517 ) )
= ( plus_plus_int @ ( times_times_int @ SV176 @ ( minus_minus_int @ SY1515 @ SY1517 ) ) @ ( times_times_int @ ( minus_minus_int @ SV176 @ SY1516 ) @ SY1517 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2058]) ).
thf(2778,plain,
! [SV177: int] :
( ( ( minus_minus_int @ ( times_times_int @ SV177 @ SV177 ) @ one_one_int )
= ( times_times_int @ ( plus_plus_int @ SV177 @ one_one_int ) @ ( minus_minus_int @ SV177 @ one_one_int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2059]) ).
thf(2779,plain,
! [SV178: nat] :
( ( ! [SY1518: int] :
( ( SY1518 = zero_zero_int )
| ( ( power_power_int @ SY1518 @ SV178 )
!= zero_zero_int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2060]) ).
thf(2780,plain,
! [SV179: int] :
( ( ! [SY1519: int,SY1520: nat] :
( ( power_power_int @ ( times_times_int @ SV179 @ SY1519 ) @ SY1520 )
= ( times_times_int @ ( power_power_int @ SV179 @ SY1520 ) @ ( power_power_int @ SY1519 @ SY1520 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2061]) ).
thf(2781,plain,
! [SV180: int] :
( ( ! [SY1521: nat] :
( ( times_times_int @ ( power_power_int @ SV180 @ SY1521 ) @ SV180 )
= ( times_times_int @ SV180 @ ( power_power_int @ SV180 @ SY1521 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2062]) ).
thf(2782,plain,
! [SV181: nat] :
( ( ( power_power_int @ one_one_int @ SV181 )
= one_one_int )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2063]) ).
thf(2783,plain,
! [SV182: nat] :
( ( ! [SY1522: int,SY1523: int] :
( ~ ( dvd_dvd_int @ SY1522 @ SY1523 )
| ( dvd_dvd_int @ ( power_power_int @ SY1522 @ SV182 ) @ ( power_power_int @ SY1523 @ SV182 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2064]) ).
thf(2784,plain,
! [SV183: int] :
( ( ! [SY1524: nat,SY1525: nat] :
( ( power_power_int @ SV183 @ ( times_times_nat @ SY1524 @ SY1525 ) )
= ( power_power_int @ ( power_power_int @ SV183 @ SY1524 ) @ SY1525 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2065]) ).
thf(2785,plain,
! [SV184: int] :
( ( ( power_power_int @ SV184 @ one_one_nat )
= SV184 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2066]) ).
thf(2786,plain,
! [SV185: nat] :
( ( ! [SY1526: int,SY1527: int] :
( ~ ( ord_less_eq_int @ SY1526 @ SY1527 )
| ~ ( ord_less_eq_int @ zero_zero_int @ SY1526 )
| ( ord_less_eq_int @ ( power_power_int @ SY1526 @ SV185 ) @ ( power_power_int @ SY1527 @ SV185 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2067]) ).
thf(2787,plain,
! [SV186: nat] :
( ( ! [SY1528: int] :
( ~ ( ord_less_eq_int @ zero_zero_int @ SY1528 )
| ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ SY1528 @ SV186 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2068]) ).
thf(2788,plain,
! [SV187: nat] :
( ( ! [SY1529: int] :
( ~ ( ord_less_int @ zero_zero_int @ SY1529 )
| ( ord_less_int @ zero_zero_int @ ( power_power_int @ SY1529 @ SV187 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2069]) ).
thf(2789,plain,
! [SV188: nat] :
( ( ! [SY1530: int] :
( ~ ( ord_less_eq_int @ one_one_int @ SY1530 )
| ( ord_less_eq_int @ one_one_int @ ( power_power_int @ SY1530 @ SV188 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2070]) ).
thf(2790,plain,
! [SV189: int] :
( ( ( power_power_int @ SV189 @ zero_zero_nat )
= one_one_int )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2073]) ).
thf(2791,plain,
! [SV190: int] :
( ( ! [SY1531: nat,SY1532: nat] :
( ( power_power_int @ SV190 @ ( plus_plus_nat @ SY1531 @ SY1532 ) )
= ( times_times_int @ ( power_power_int @ SV190 @ SY1531 ) @ ( power_power_int @ SV190 @ SY1532 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2074]) ).
thf(2792,plain,
! [SV191: nat] :
( ( ! [SY1533: int,SY1534: nat,SY1535: int] :
( ~ ( dvd_dvd_int @ ( power_power_int @ SY1533 @ SY1534 ) @ SY1535 )
| ~ ( ord_less_eq_nat @ SV191 @ SY1534 )
| ( dvd_dvd_int @ ( power_power_int @ SY1533 @ SV191 ) @ SY1535 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2075]) ).
thf(2793,plain,
! [SV192: nat] :
( ( ! [SY1536: nat,SY1537: int,SY1538: int] :
( ~ ( dvd_dvd_int @ SY1537 @ SY1538 )
| ~ ( ord_less_eq_nat @ SV192 @ SY1536 )
| ( dvd_dvd_int @ ( power_power_int @ SY1537 @ SV192 ) @ ( power_power_int @ SY1538 @ SY1536 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2076]) ).
thf(2794,plain,
! [SV193: int] :
( ( ! [SY1539: nat,SY1540: nat] :
( ~ ( ord_less_eq_nat @ SY1539 @ SY1540 )
| ( dvd_dvd_int @ ( power_power_int @ SV193 @ SY1539 ) @ ( power_power_int @ SV193 @ SY1540 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2077]) ).
thf(2795,plain,
! [SV194: int] :
( ( ! [SY1541: nat,SY1542: int] :
( ~ ( ord_less_int @ ( power_power_int @ SV194 @ SY1541 ) @ ( power_power_int @ SY1542 @ SY1541 ) )
| ~ ( ord_less_eq_int @ zero_zero_int @ SY1542 )
| ( ord_less_int @ SV194 @ SY1542 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2078]) ).
thf(2796,plain,
! [SV195: nat] :
( ( ! [SY1543: int] :
( ~ ( ord_less_int @ one_one_int @ SY1543 )
| ( ord_less_int @ ( power_power_int @ SY1543 @ SV195 ) @ ( times_times_int @ SY1543 @ ( power_power_int @ SY1543 @ SV195 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2079]) ).
thf(2797,plain,
! [SV196: nat] :
( ( ! [SY1544: int] :
( ~ ( ord_less_int @ one_one_int @ SY1544 )
| ( ord_less_int @ one_one_int @ ( times_times_int @ SY1544 @ ( power_power_int @ SY1544 @ SV196 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2080]) ).
thf(2798,plain,
! [SV197: int] :
( ( ! [SY1545: nat,SY1546: nat] :
( ~ ( ord_less_nat @ SY1545 @ SY1546 )
| ~ ( ord_less_int @ one_one_int @ SV197 )
| ( ord_less_int @ ( power_power_int @ SV197 @ SY1545 ) @ ( power_power_int @ SV197 @ SY1546 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2082]) ).
thf(2799,plain,
! [SV198: nat] :
( ( ! [SY1547: nat,SY1548: int] :
( ~ ( ord_less_int @ one_one_int @ SY1548 )
| ~ ( ord_less_int @ ( power_power_int @ SY1548 @ SV198 ) @ ( power_power_int @ SY1548 @ SY1547 ) )
| ( ord_less_nat @ SV198 @ SY1547 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2083]) ).
thf(2800,plain,
! [SV199: int] :
( ( ! [SY1549: nat,SY1550: nat] :
( ~ ( ord_less_eq_nat @ SY1549 @ SY1550 )
| ~ ( ord_less_eq_int @ one_one_int @ SV199 )
| ( ord_less_eq_int @ ( power_power_int @ SV199 @ SY1549 ) @ ( power_power_int @ SV199 @ SY1550 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2085]) ).
thf(2801,plain,
! [SV200: nat] :
( ( ! [SY1551: int] :
( ~ ( ord_less_int @ zero_zero_int @ SY1551 )
| ~ ( ord_less_int @ SY1551 @ one_one_int )
| ( ord_less_int @ ( times_times_int @ SY1551 @ ( power_power_int @ SY1551 @ SV200 ) ) @ ( power_power_int @ SY1551 @ SV200 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2086]) ).
thf(2802,plain,
! [SV201: int] :
( ( ! [SY1552: nat,SY1553: nat] :
( ~ ( ord_less_nat @ SY1552 @ SY1553 )
| ~ ( ord_less_int @ zero_zero_int @ SV201 )
| ~ ( ord_less_int @ SV201 @ one_one_int )
| ( ord_less_int @ ( power_power_int @ SV201 @ SY1553 ) @ ( power_power_int @ SV201 @ SY1552 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2087]) ).
thf(2803,plain,
! [SV202: real] :
( ( ! [SY1554: real] :
~ ( ord_less_real @ ( plus_plus_real @ ( power_power_real @ SV202 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SY1554 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_real ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2091]) ).
thf(2804,plain,
! [SV203: real] :
( ( ~ ( ord_less_real @ ( power_power_real @ SV203 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ zero_zero_real ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2094]) ).
thf(2805,plain,
! [SV204: int] :
( ( ( plus_plus_real @ one_one_real @ ( number267125858f_real @ SV204 ) )
= ( number267125858f_real @ ( plus_plus_int @ ( bit1 @ pls ) @ SV204 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2096]) ).
thf(2806,plain,
! [SV205: int] :
( ( ( plus_plus_real @ ( number267125858f_real @ SV205 ) @ one_one_real )
= ( number267125858f_real @ ( plus_plus_int @ SV205 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2097]) ).
thf(2807,plain,
! [SV206: int] :
( ( ord_less_eq_int @ SV206 @ SV206 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2101]) ).
thf(2808,plain,
! [SV207: int] :
( ( ( number_number_of_int @ SV207 )
= SV207 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2102]) ).
thf(2809,plain,
! [SV208: int] :
( ( ! [SY1555: int] :
( ( times_times_int @ SV208 @ SY1555 )
= ( times_times_int @ SY1555 @ SV208 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2103]) ).
thf(2810,plain,
! [SV209: int] :
( ( ! [SY1556: int] :
( ( ord_less_eq_int @ SV209 @ SY1556 )
| ( ord_less_eq_int @ SY1556 @ SV209 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2104]) ).
thf(2811,plain,
! [SV210: int] :
( ( ! [SY1557: int] :
( ( times_times_int @ ( number_number_of_int @ SV210 ) @ ( number_number_of_int @ SY1557 ) )
= ( number_number_of_int @ ( times_times_int @ SV210 @ SY1557 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2105]) ).
thf(2812,plain,
! [SV211: int] :
( ( ! [SY1558: int,SY1559: int] :
( ( times_times_int @ ( times_times_int @ SV211 @ SY1558 ) @ SY1559 )
= ( times_times_int @ SV211 @ ( times_times_int @ SY1558 @ SY1559 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2109]) ).
thf(2813,plain,
! [SV212: int] :
( ( ! [SY1560: int,SY1561: int] :
( ~ ( ord_less_eq_int @ SY1560 @ SY1561 )
| ~ ( ord_less_eq_int @ SY1561 @ SV212 )
| ( ord_less_eq_int @ SY1560 @ SV212 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2110]) ).
thf(2814,plain,
! [SV213: int] :
( ( ! [SY1562: int] :
( ~ ( ord_less_eq_int @ SV213 @ SY1562 )
| ~ ( ord_less_eq_int @ SY1562 @ SV213 )
| ( SV213 = SY1562 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2111]) ).
thf(2815,plain,
! [SV214: int] :
( ( ! [SY1563: int] :
( ~ ( ord_less_eq_int @ pls @ SY1563 )
| ~ ( ord_less_eq_int @ pls @ SV214 )
| ( ( times_times_real @ ( number267125858f_real @ SY1563 ) @ ( number267125858f_real @ SV214 ) )
= ( number267125858f_real @ ( times_times_int @ SY1563 @ SV214 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2112]) ).
thf(2816,plain,
! [SV215: int] :
( ( ! [SY1564: int] :
( ~ ( ord_less_eq_int @ pls @ SY1564 )
| ~ ( ord_less_eq_int @ pls @ SV215 )
| ( ( times_times_nat @ ( number_number_of_nat @ SY1564 ) @ ( number_number_of_nat @ SV215 ) )
= ( number_number_of_nat @ ( times_times_int @ SY1564 @ SV215 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2113]) ).
thf(2817,plain,
! [SV216: int] :
( ( ! [SY1565: int] :
( ~ ( ord_less_eq_int @ pls @ SY1565 )
| ~ ( ord_less_eq_int @ pls @ SV216 )
| ( ( times_times_int @ ( number_number_of_int @ SY1565 ) @ ( number_number_of_int @ SV216 ) )
= ( number_number_of_int @ ( times_times_int @ SY1565 @ SV216 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2114]) ).
thf(2818,plain,
! [SV217: int] :
( ( ! [SY1566: int,SY1567: real] :
( ( times_times_real @ ( number267125858f_real @ SV217 ) @ ( times_times_real @ ( number267125858f_real @ SY1566 ) @ SY1567 ) )
= ( times_times_real @ ( number267125858f_real @ ( times_times_int @ SV217 @ SY1566 ) ) @ SY1567 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2115]) ).
thf(2819,plain,
! [SV218: int] :
( ( ! [SY1568: int,SY1569: int] :
( ( times_times_int @ ( number_number_of_int @ SV218 ) @ ( times_times_int @ ( number_number_of_int @ SY1568 ) @ SY1569 ) )
= ( times_times_int @ ( number_number_of_int @ ( times_times_int @ SV218 @ SY1568 ) ) @ SY1569 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2116]) ).
thf(2820,plain,
! [SV219: int] :
( ( ! [SY1570: int] :
( ( times_times_real @ ( number267125858f_real @ SV219 ) @ ( number267125858f_real @ SY1570 ) )
= ( number267125858f_real @ ( times_times_int @ SV219 @ SY1570 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2117]) ).
thf(2821,plain,
! [SV220: int] :
( ( ! [SY1571: int] :
( ( times_times_int @ ( number_number_of_int @ SV220 ) @ ( number_number_of_int @ SY1571 ) )
= ( number_number_of_int @ ( times_times_int @ SV220 @ SY1571 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2118]) ).
thf(2822,plain,
! [SV221: int] :
( ( ! [SY1572: int] :
( ( number267125858f_real @ ( times_times_int @ SV221 @ SY1572 ) )
= ( times_times_real @ ( number267125858f_real @ SV221 ) @ ( number267125858f_real @ SY1572 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2119]) ).
thf(2823,plain,
! [SV222: int] :
( ( ! [SY1573: int] :
( ( number_number_of_int @ ( times_times_int @ SV222 @ SY1573 ) )
= ( times_times_int @ ( number_number_of_int @ SV222 ) @ ( number_number_of_int @ SY1573 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2120]) ).
thf(2824,plain,
! [SV223: real] :
( ( ! [SY1574: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ SV223 @ SV223 ) @ ( times_times_real @ SY1574 @ SY1574 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2122]) ).
thf(2825,plain,
! [SV224: int] :
( ( ! [SY1575: int] :
( ~ ( ord_less_eq_int @ pls @ SY1575 )
| ~ ( ord_less_eq_int @ pls @ SV224 )
| ( ( plus_plus_real @ ( number267125858f_real @ SY1575 ) @ ( number267125858f_real @ SV224 ) )
= ( number267125858f_real @ ( plus_plus_int @ SY1575 @ SV224 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2128]) ).
thf(2826,plain,
! [SV225: real] :
( ( ! [SY1576: real,SY1577: int] :
( ( times_times_real @ ( plus_plus_real @ SV225 @ SY1576 ) @ ( number267125858f_real @ SY1577 ) )
= ( plus_plus_real @ ( times_times_real @ SV225 @ ( number267125858f_real @ SY1577 ) ) @ ( times_times_real @ SY1576 @ ( number267125858f_real @ SY1577 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2134]) ).
thf(2827,plain,
! [SV226: int] :
( ( ! [SY1578: real,SY1579: real] :
( ( times_times_real @ ( number267125858f_real @ SV226 ) @ ( plus_plus_real @ SY1578 @ SY1579 ) )
= ( plus_plus_real @ ( times_times_real @ ( number267125858f_real @ SV226 ) @ SY1578 ) @ ( times_times_real @ ( number267125858f_real @ SV226 ) @ SY1579 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2135]) ).
thf(2828,plain,
! [SV227: real] :
( ( ! [SY1580: real] :
( ( ( power_power_real @ SV227 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= ( power_power_real @ SY1580 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ~ ( ord_less_eq_real @ zero_zero_real @ SV227 )
| ~ ( ord_less_eq_real @ zero_zero_real @ SY1580 )
| ( SV227 = SY1580 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2136]) ).
thf(2829,plain,
! [SV228: nat] :
( ( ! [SY1581: nat] :
( ( ( power_power_nat @ SV228 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= ( power_power_nat @ SY1581 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV228 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SY1581 )
| ( SV228 = SY1581 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2137]) ).
thf(2830,plain,
! [SV229: real] :
( ( ! [SY1582: real] :
( ~ ( ord_less_eq_real @ ( power_power_real @ SV229 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SY1582 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ~ ( ord_less_eq_real @ zero_zero_real @ SY1582 )
| ( ord_less_eq_real @ SV229 @ SY1582 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2138]) ).
thf(2831,plain,
! [SV230: nat] :
( ( ! [SY1583: nat] :
( ~ ( ord_less_eq_nat @ ( power_power_nat @ SV230 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_nat @ SY1583 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SY1583 )
| ( ord_less_eq_nat @ SV230 @ SY1583 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2139]) ).
thf(2832,plain,
! [SV231: real] :
( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ SV231 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2140]) ).
thf(2833,plain,
! [SV232: real] :
( ( ! [SY1584: real] :
( ~ ( ord_less_real @ ( power_power_real @ SV232 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SY1584 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ~ ( ord_less_eq_real @ zero_zero_real @ SY1584 )
| ( ord_less_real @ SV232 @ SY1584 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2141]) ).
thf(2834,plain,
! [SV233: nat] :
( ( ! [SY1585: nat] :
( ~ ( ord_less_nat @ ( power_power_nat @ SV233 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_nat @ SY1585 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SY1585 )
| ( ord_less_nat @ SV233 @ SY1585 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2142]) ).
thf(2835,plain,
! [SV234: real] :
( ( ! [SY1586: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ SV234 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SY1586 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2144]) ).
thf(2836,plain,
! [SV235: real] :
( ( ! [SY1587: real] :
~ ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ SV235 @ SV235 ) @ ( times_times_real @ SY1587 @ SY1587 ) ) @ zero_zero_real ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2146]) ).
thf(2837,plain,
! [SV236: int] :
( ( ( times_times_real @ ( plus_plus_real @ one_one_real @ one_one_real ) @ ( number267125858f_real @ SV236 ) )
= ( number267125858f_real @ ( bit0 @ SV236 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2148]) ).
thf(2838,plain,
! [SV237: real] :
( ( ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV237 )
= ( plus_plus_real @ SV237 @ SV237 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2149]) ).
thf(2839,plain,
! [SV238: real] :
( ( ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV238 )
= ( plus_plus_real @ SV238 @ SV238 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2150]) ).
thf(2840,plain,
! [SV239: real] :
( ( ( times_times_real @ SV239 @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_real @ SV239 @ SV239 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2151]) ).
thf(2841,plain,
! [SV240: real] :
( ( ( times_times_real @ SV240 @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_real @ SV240 @ SV240 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2152]) ).
thf(2842,plain,
! [SV241: int] :
( ( ( power_power_real @ ( number267125858f_real @ SV241 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_real @ ( number267125858f_real @ SV241 ) @ ( number267125858f_real @ SV241 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2154]) ).
thf(2843,plain,
! [SV242: real] :
( ( ! [SY1588: real] :
( ( power_power_real @ ( plus_plus_real @ SV242 @ SY1588 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_real @ ( plus_plus_real @ ( power_power_real @ SV242 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SY1588 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV242 ) @ SY1588 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2155]) ).
thf(2844,plain,
! [SV243: nat] :
( ( ! [SY1589: nat] :
( ( power_power_nat @ ( plus_plus_nat @ SV243 @ SY1589 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_nat @ ( plus_plus_nat @ ( power_power_nat @ SV243 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_nat @ SY1589 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_nat @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV243 ) @ SY1589 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2156]) ).
thf(2845,plain,
! [SV244: int] :
( ( ( number267125858f_real @ ( bit0 @ SV244 ) )
= ( plus_plus_real @ ( plus_plus_real @ zero_zero_real @ ( number267125858f_real @ SV244 ) ) @ ( number267125858f_real @ SV244 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2157]) ).
thf(2846,plain,
! [SV245: int] :
( ( ( number267125858f_real @ ( bit1 @ SV245 ) )
= ( plus_plus_real @ ( plus_plus_real @ one_one_real @ ( number267125858f_real @ SV245 ) ) @ ( number267125858f_real @ SV245 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2158]) ).
thf(2847,plain,
! [SV246: real] :
( ( ! [SY1590: nat] :
( ( power_power_real @ SV246 @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SY1590 ) )
= ( times_times_real @ ( power_power_real @ SV246 @ SY1590 ) @ ( power_power_real @ SV246 @ SY1590 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2166]) ).
thf(2848,plain,
! [SV247: real] :
( ( ! [SY1591: nat,SY1592: nat] :
( ( power_power_real @ ( power_power_real @ SV247 @ SY1591 ) @ SY1592 )
= ( power_power_real @ SV247 @ ( times_times_nat @ SY1591 @ SY1592 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2168]) ).
thf(2849,plain,
! [SV248: nat] :
( ( ! [SY1593: nat,SY1594: nat] :
( ( power_power_nat @ ( power_power_nat @ SV248 @ SY1593 ) @ SY1594 )
= ( power_power_nat @ SV248 @ ( times_times_nat @ SY1593 @ SY1594 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2169]) ).
thf(2850,plain,
! [SV249: nat] :
( ( ! [SY1595: int,SY1596: int,SY1597: int] :
( ~ ( zprime @ SY1597 )
| ( dvd_dvd_int @ SY1597 @ SY1596 )
| ~ ( dvd_dvd_int @ ( power_power_int @ SY1597 @ SV249 ) @ ( times_times_int @ SY1595 @ SY1596 ) )
| ( dvd_dvd_int @ ( power_power_int @ SY1597 @ SV249 ) @ SY1595 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2170]) ).
thf(2851,plain,
! [SV250: nat] :
( ( ! [SY1598: int,SY1599: int,SY1600: int] :
( ~ ( zprime @ SY1600 )
| ( dvd_dvd_int @ SY1600 @ SY1599 )
| ~ ( dvd_dvd_int @ ( power_power_int @ SY1600 @ SV250 ) @ ( times_times_int @ SY1599 @ SY1598 ) )
| ( dvd_dvd_int @ ( power_power_int @ SY1600 @ SV250 ) @ SY1598 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2171]) ).
thf(2852,plain,
! [SV251: int] :
( ( ! [SY1601: int] :
( ~ ( twoSqu362149276sum2sq @ SY1601 )
| ~ ( twoSqu362149276sum2sq @ SV251 )
| ( twoSqu362149276sum2sq @ ( times_times_int @ SY1601 @ SV251 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2172]) ).
thf(2853,plain,
! [SV252: real] :
( ( ! [SY1602: real,SY1603: real,SY1604: real] :
( ( times_times_real @ ( times_times_real @ SV252 @ SY1602 ) @ ( times_times_real @ SY1603 @ SY1604 ) )
= ( times_times_real @ ( times_times_real @ SV252 @ SY1603 ) @ ( times_times_real @ SY1602 @ SY1604 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2173]) ).
thf(2854,plain,
! [SV253: nat] :
( ( ! [SY1605: nat,SY1606: nat,SY1607: nat] :
( ( times_times_nat @ ( times_times_nat @ SV253 @ SY1605 ) @ ( times_times_nat @ SY1606 @ SY1607 ) )
= ( times_times_nat @ ( times_times_nat @ SV253 @ SY1606 ) @ ( times_times_nat @ SY1605 @ SY1607 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2174]) ).
thf(2855,plain,
! [SV254: int] :
( ( ! [SY1608: int,SY1609: int,SY1610: int] :
( ( times_times_int @ ( times_times_int @ SV254 @ SY1608 ) @ ( times_times_int @ SY1609 @ SY1610 ) )
= ( times_times_int @ ( times_times_int @ SV254 @ SY1609 ) @ ( times_times_int @ SY1608 @ SY1610 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2175]) ).
thf(2856,plain,
! [SV255: real] :
( ( ! [SY1611: real,SY1612: real,SY1613: real] :
( ( times_times_real @ ( times_times_real @ SV255 @ SY1611 ) @ ( times_times_real @ SY1612 @ SY1613 ) )
= ( times_times_real @ SY1612 @ ( times_times_real @ ( times_times_real @ SV255 @ SY1611 ) @ SY1613 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2176]) ).
thf(2857,plain,
! [SV256: nat] :
( ( ! [SY1614: nat,SY1615: nat,SY1616: nat] :
( ( times_times_nat @ ( times_times_nat @ SV256 @ SY1614 ) @ ( times_times_nat @ SY1615 @ SY1616 ) )
= ( times_times_nat @ SY1615 @ ( times_times_nat @ ( times_times_nat @ SV256 @ SY1614 ) @ SY1616 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2177]) ).
thf(2858,plain,
! [SV257: int] :
( ( ! [SY1617: int,SY1618: int,SY1619: int] :
( ( times_times_int @ ( times_times_int @ SV257 @ SY1617 ) @ ( times_times_int @ SY1618 @ SY1619 ) )
= ( times_times_int @ SY1618 @ ( times_times_int @ ( times_times_int @ SV257 @ SY1617 ) @ SY1619 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2178]) ).
thf(2859,plain,
! [SV258: real] :
( ( ! [SY1620: real,SY1621: real,SY1622: real] :
( ( times_times_real @ ( times_times_real @ SV258 @ SY1620 ) @ ( times_times_real @ SY1621 @ SY1622 ) )
= ( times_times_real @ SV258 @ ( times_times_real @ SY1620 @ ( times_times_real @ SY1621 @ SY1622 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2179]) ).
thf(2860,plain,
! [SV259: nat] :
( ( ! [SY1623: nat,SY1624: nat,SY1625: nat] :
( ( times_times_nat @ ( times_times_nat @ SV259 @ SY1623 ) @ ( times_times_nat @ SY1624 @ SY1625 ) )
= ( times_times_nat @ SV259 @ ( times_times_nat @ SY1623 @ ( times_times_nat @ SY1624 @ SY1625 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2180]) ).
thf(2861,plain,
! [SV260: int] :
( ( ! [SY1626: int,SY1627: int,SY1628: int] :
( ( times_times_int @ ( times_times_int @ SV260 @ SY1626 ) @ ( times_times_int @ SY1627 @ SY1628 ) )
= ( times_times_int @ SV260 @ ( times_times_int @ SY1626 @ ( times_times_int @ SY1627 @ SY1628 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2181]) ).
thf(2862,plain,
! [SV261: real] :
( ( ! [SY1629: real,SY1630: real] :
( ( times_times_real @ ( times_times_real @ SV261 @ SY1629 ) @ SY1630 )
= ( times_times_real @ ( times_times_real @ SV261 @ SY1630 ) @ SY1629 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2182]) ).
thf(2863,plain,
! [SV262: nat] :
( ( ! [SY1631: nat,SY1632: nat] :
( ( times_times_nat @ ( times_times_nat @ SV262 @ SY1631 ) @ SY1632 )
= ( times_times_nat @ ( times_times_nat @ SV262 @ SY1632 ) @ SY1631 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2183]) ).
thf(2864,plain,
! [SV263: int] :
( ( ! [SY1633: int,SY1634: int] :
( ( times_times_int @ ( times_times_int @ SV263 @ SY1633 ) @ SY1634 )
= ( times_times_int @ ( times_times_int @ SV263 @ SY1634 ) @ SY1633 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2184]) ).
thf(2865,plain,
! [SV264: real] :
( ( ! [SY1635: real,SY1636: real] :
( ( times_times_real @ ( times_times_real @ SV264 @ SY1635 ) @ SY1636 )
= ( times_times_real @ SV264 @ ( times_times_real @ SY1635 @ SY1636 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2185]) ).
thf(2866,plain,
! [SV265: nat] :
( ( ! [SY1637: nat,SY1638: nat] :
( ( times_times_nat @ ( times_times_nat @ SV265 @ SY1637 ) @ SY1638 )
= ( times_times_nat @ SV265 @ ( times_times_nat @ SY1637 @ SY1638 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2186]) ).
thf(2867,plain,
! [SV266: int] :
( ( ! [SY1639: int,SY1640: int] :
( ( times_times_int @ ( times_times_int @ SV266 @ SY1639 ) @ SY1640 )
= ( times_times_int @ SV266 @ ( times_times_int @ SY1639 @ SY1640 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2187]) ).
thf(2868,plain,
! [SV267: real] :
( ( ! [SY1641: real,SY1642: real] :
( ( times_times_real @ SV267 @ ( times_times_real @ SY1641 @ SY1642 ) )
= ( times_times_real @ ( times_times_real @ SV267 @ SY1641 ) @ SY1642 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2188]) ).
thf(2869,plain,
! [SV268: nat] :
( ( ! [SY1643: nat,SY1644: nat] :
( ( times_times_nat @ SV268 @ ( times_times_nat @ SY1643 @ SY1644 ) )
= ( times_times_nat @ ( times_times_nat @ SV268 @ SY1643 ) @ SY1644 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2189]) ).
thf(2870,plain,
! [SV269: int] :
( ( ! [SY1645: int,SY1646: int] :
( ( times_times_int @ SV269 @ ( times_times_int @ SY1645 @ SY1646 ) )
= ( times_times_int @ ( times_times_int @ SV269 @ SY1645 ) @ SY1646 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2190]) ).
thf(2871,plain,
! [SV270: real] :
( ( ! [SY1647: real,SY1648: real] :
( ( times_times_real @ SV270 @ ( times_times_real @ SY1647 @ SY1648 ) )
= ( times_times_real @ SY1647 @ ( times_times_real @ SV270 @ SY1648 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2191]) ).
thf(2872,plain,
! [SV271: nat] :
( ( ! [SY1649: nat,SY1650: nat] :
( ( times_times_nat @ SV271 @ ( times_times_nat @ SY1649 @ SY1650 ) )
= ( times_times_nat @ SY1649 @ ( times_times_nat @ SV271 @ SY1650 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2192]) ).
thf(2873,plain,
! [SV272: int] :
( ( ! [SY1651: int,SY1652: int] :
( ( times_times_int @ SV272 @ ( times_times_int @ SY1651 @ SY1652 ) )
= ( times_times_int @ SY1651 @ ( times_times_int @ SV272 @ SY1652 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2193]) ).
thf(2874,plain,
! [SV273: real] :
( ( ! [SY1653: real] :
( ( times_times_real @ SV273 @ SY1653 )
= ( times_times_real @ SY1653 @ SV273 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2194]) ).
thf(2875,plain,
! [SV274: nat] :
( ( ! [SY1654: nat] :
( ( times_times_nat @ SV274 @ SY1654 )
= ( times_times_nat @ SY1654 @ SV274 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2195]) ).
thf(2876,plain,
! [SV275: int] :
( ( ! [SY1655: int] :
( ( times_times_int @ SV275 @ SY1655 )
= ( times_times_int @ SY1655 @ SV275 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2196]) ).
thf(2877,plain,
! [SV276: real] :
( ( ! [SY1656: real] :
( ( plus_plus_real @ SV276 @ SY1656 )
= ( plus_plus_real @ SY1656 @ SV276 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2197]) ).
thf(2878,plain,
! [SV277: nat] :
( ( ! [SY1657: nat] :
( ( plus_plus_nat @ SV277 @ SY1657 )
= ( plus_plus_nat @ SY1657 @ SV277 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2198]) ).
thf(2879,plain,
! [SV278: real] :
( ( ! [SY1658: real,SY1659: real] :
( ( plus_plus_real @ SV278 @ ( plus_plus_real @ SY1658 @ SY1659 ) )
= ( plus_plus_real @ SY1658 @ ( plus_plus_real @ SV278 @ SY1659 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2199]) ).
thf(2880,plain,
! [SV279: nat] :
( ( ! [SY1660: nat,SY1661: nat] :
( ( plus_plus_nat @ SV279 @ ( plus_plus_nat @ SY1660 @ SY1661 ) )
= ( plus_plus_nat @ SY1660 @ ( plus_plus_nat @ SV279 @ SY1661 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2200]) ).
thf(2881,plain,
! [SV280: real] :
( ( ! [SY1662: real,SY1663: real] :
( ( plus_plus_real @ SV280 @ ( plus_plus_real @ SY1662 @ SY1663 ) )
= ( plus_plus_real @ ( plus_plus_real @ SV280 @ SY1662 ) @ SY1663 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2201]) ).
thf(2882,plain,
! [SV281: nat] :
( ( ! [SY1664: nat,SY1665: nat] :
( ( plus_plus_nat @ SV281 @ ( plus_plus_nat @ SY1664 @ SY1665 ) )
= ( plus_plus_nat @ ( plus_plus_nat @ SV281 @ SY1664 ) @ SY1665 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2202]) ).
thf(2883,plain,
! [SV282: real] :
( ( ! [SY1666: real,SY1667: real] :
( ( plus_plus_real @ ( plus_plus_real @ SV282 @ SY1666 ) @ SY1667 )
= ( plus_plus_real @ SV282 @ ( plus_plus_real @ SY1666 @ SY1667 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2203]) ).
thf(2884,plain,
! [SV283: nat] :
( ( ! [SY1668: nat,SY1669: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ SV283 @ SY1668 ) @ SY1669 )
= ( plus_plus_nat @ SV283 @ ( plus_plus_nat @ SY1668 @ SY1669 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2204]) ).
thf(2885,plain,
! [SV284: real] :
( ( ! [SY1670: real,SY1671: real] :
( ( plus_plus_real @ ( plus_plus_real @ SV284 @ SY1670 ) @ SY1671 )
= ( plus_plus_real @ ( plus_plus_real @ SV284 @ SY1671 ) @ SY1670 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2205]) ).
thf(2886,plain,
! [SV285: nat] :
( ( ! [SY1672: nat,SY1673: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ SV285 @ SY1672 ) @ SY1673 )
= ( plus_plus_nat @ ( plus_plus_nat @ SV285 @ SY1673 ) @ SY1672 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2206]) ).
thf(2887,plain,
! [SV286: real] :
( ( ! [SY1674: real,SY1675: real,SY1676: real] :
( ( plus_plus_real @ ( plus_plus_real @ SV286 @ SY1674 ) @ ( plus_plus_real @ SY1675 @ SY1676 ) )
= ( plus_plus_real @ ( plus_plus_real @ SV286 @ SY1675 ) @ ( plus_plus_real @ SY1674 @ SY1676 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2207]) ).
thf(2888,plain,
! [SV287: nat] :
( ( ! [SY1677: nat,SY1678: nat,SY1679: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ SV287 @ SY1677 ) @ ( plus_plus_nat @ SY1678 @ SY1679 ) )
= ( plus_plus_nat @ ( plus_plus_nat @ SV287 @ SY1678 ) @ ( plus_plus_nat @ SY1677 @ SY1679 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2208]) ).
thf(2889,plain,
! [SV288: real] :
( ( ( power_power_real @ SV288 @ one_one_nat )
= SV288 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2209]) ).
thf(2890,plain,
! [SV289: nat] :
( ( ( power_power_nat @ SV289 @ one_one_nat )
= SV289 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2210]) ).
thf(2891,plain,
! [SV290: real] :
( ( ! [SY1680: nat] :
~ ( ord_less_eq_real @ ( power_power_real @ SV290 @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SY1680 ) ) @ zero_zero_real )
| ( SV290 = zero_zero_real ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2214]) ).
thf(2892,plain,
! [SV291: real] :
( ( ( times_times_real @ zero_zero_real @ SV291 )
= zero_zero_real )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2215]) ).
thf(2893,plain,
! [SV292: nat] :
( ( ( times_times_nat @ zero_zero_nat @ SV292 )
= zero_zero_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2216]) ).
thf(2894,plain,
! [SV293: real] :
( ( ( times_times_real @ SV293 @ zero_zero_real )
= zero_zero_real )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2217]) ).
thf(2895,plain,
! [SV294: nat] :
( ( ( times_times_nat @ SV294 @ zero_zero_nat )
= zero_zero_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2218]) ).
thf(2896,plain,
! [SV295: real] :
( ( ( plus_plus_real @ zero_zero_real @ SV295 )
= SV295 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2219]) ).
thf(2897,plain,
! [SV296: nat] :
( ( ( plus_plus_nat @ zero_zero_nat @ SV296 )
= SV296 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2220]) ).
thf(2898,plain,
! [SV297: real] :
( ( ( plus_plus_real @ SV297 @ zero_zero_real )
= SV297 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2221]) ).
thf(2899,plain,
! [SV298: nat] :
( ( ( plus_plus_nat @ SV298 @ zero_zero_nat )
= SV298 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2222]) ).
thf(2900,plain,
! [SV299: real] :
( ( ! [SY1681: real,SY1682: real] :
( ( times_times_real @ SV299 @ ( plus_plus_real @ SY1681 @ SY1682 ) )
= ( plus_plus_real @ ( times_times_real @ SV299 @ SY1681 ) @ ( times_times_real @ SV299 @ SY1682 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2225]) ).
thf(2901,plain,
! [SV300: nat] :
( ( ! [SY1683: nat,SY1684: nat] :
( ( times_times_nat @ SV300 @ ( plus_plus_nat @ SY1683 @ SY1684 ) )
= ( plus_plus_nat @ ( times_times_nat @ SV300 @ SY1683 ) @ ( times_times_nat @ SV300 @ SY1684 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2226]) ).
thf(2902,plain,
! [SV301: real] :
( ( ! [SY1685: real,SY1686: real] :
( ( times_times_real @ ( plus_plus_real @ SV301 @ SY1685 ) @ SY1686 )
= ( plus_plus_real @ ( times_times_real @ SV301 @ SY1686 ) @ ( times_times_real @ SY1685 @ SY1686 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2229]) ).
thf(2903,plain,
! [SV302: nat] :
( ( ! [SY1687: nat,SY1688: nat] :
( ( times_times_nat @ ( plus_plus_nat @ SV302 @ SY1687 ) @ SY1688 )
= ( plus_plus_nat @ ( times_times_nat @ SV302 @ SY1688 ) @ ( times_times_nat @ SY1687 @ SY1688 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2230]) ).
thf(2904,plain,
! [SV303: real] :
( ( ! [SY1689: real,SY1690: real] :
( ( plus_plus_real @ ( times_times_real @ SV303 @ SY1689 ) @ ( times_times_real @ SY1690 @ SY1689 ) )
= ( times_times_real @ ( plus_plus_real @ SV303 @ SY1690 ) @ SY1689 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2231]) ).
thf(2905,plain,
! [SV304: nat] :
( ( ! [SY1691: nat,SY1692: nat] :
( ( plus_plus_nat @ ( times_times_nat @ SV304 @ SY1691 ) @ ( times_times_nat @ SY1692 @ SY1691 ) )
= ( times_times_nat @ ( plus_plus_nat @ SV304 @ SY1692 ) @ SY1691 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2232]) ).
thf(2906,plain,
! [SV305: real] :
( ( ( times_times_real @ one_one_real @ SV305 )
= SV305 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2235]) ).
thf(2907,plain,
! [SV306: nat] :
( ( ( times_times_nat @ one_one_nat @ SV306 )
= SV306 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2236]) ).
thf(2908,plain,
! [SV307: real] :
( ( ( times_times_real @ SV307 @ one_one_real )
= SV307 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2237]) ).
thf(2909,plain,
! [SV308: nat] :
( ( ( times_times_nat @ SV308 @ one_one_nat )
= SV308 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2238]) ).
thf(2910,plain,
! [SV309: real] :
( ( ! [SY1693: real,SY1694: nat] :
( ( power_power_real @ ( times_times_real @ SV309 @ SY1693 ) @ SY1694 )
= ( times_times_real @ ( power_power_real @ SV309 @ SY1694 ) @ ( power_power_real @ SY1693 @ SY1694 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2239]) ).
thf(2911,plain,
! [SV310: nat] :
( ( ! [SY1695: nat,SY1696: nat] :
( ( power_power_nat @ ( times_times_nat @ SV310 @ SY1695 ) @ SY1696 )
= ( times_times_nat @ ( power_power_nat @ SV310 @ SY1696 ) @ ( power_power_nat @ SY1695 @ SY1696 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2240]) ).
thf(2912,plain,
! [SV311: real] :
( ( ! [SY1697: nat,SY1698: nat] :
( ( times_times_real @ ( power_power_real @ SV311 @ SY1697 ) @ ( power_power_real @ SV311 @ SY1698 ) )
= ( power_power_real @ SV311 @ ( plus_plus_nat @ SY1697 @ SY1698 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2241]) ).
thf(2913,plain,
! [SV312: nat] :
( ( ! [SY1699: nat,SY1700: nat] :
( ( times_times_nat @ ( power_power_nat @ SV312 @ SY1699 ) @ ( power_power_nat @ SV312 @ SY1700 ) )
= ( power_power_nat @ SV312 @ ( plus_plus_nat @ SY1699 @ SY1700 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2242]) ).
thf(2914,plain,
! [SV313: real] :
( ( ( power_power_real @ SV313 @ zero_zero_nat )
= one_one_real )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2243]) ).
thf(2915,plain,
! [SV314: nat] :
( ( ( power_power_nat @ SV314 @ zero_zero_nat )
= one_one_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2244]) ).
thf(2916,plain,
! [SV315: real] :
( ( ! [SY1701: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ SV315 @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SY1701 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2245]) ).
thf(2917,plain,
! [SV316: real] :
( ( ! [SY1702: real,SY1703: real,SY1704: real,SY1705: real] :
( ( SY1705 = zero_zero_real )
| ( SV316 = SY1702 )
| ( SY1703 != SY1704 )
| ( ( plus_plus_real @ SY1703 @ ( times_times_real @ SY1705 @ SV316 ) )
!= ( plus_plus_real @ SY1704 @ ( times_times_real @ SY1705 @ SY1702 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2246]) ).
thf(2918,plain,
! [SV317: nat] :
( ( ! [SY1706: nat,SY1707: nat,SY1708: nat,SY1709: nat] :
( ( SY1709 = zero_zero_nat )
| ( SV317 = SY1706 )
| ( SY1707 != SY1708 )
| ( ( plus_plus_nat @ SY1707 @ ( times_times_nat @ SY1709 @ SV317 ) )
!= ( plus_plus_nat @ SY1708 @ ( times_times_nat @ SY1709 @ SY1706 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2247]) ).
thf(2919,plain,
! [SV318: real] :
( ( ( plus_plus_real @ SV318 @ SV318 )
= ( times_times_real @ ( plus_plus_real @ one_one_real @ one_one_real ) @ SV318 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2248]) ).
thf(2920,plain,
! [SV319: nat] :
( ( ( plus_plus_nat @ SV319 @ SV319 )
= ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) @ SV319 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2249]) ).
thf(2921,plain,
! [SV320: real] :
( ( ! [SY1710: real] :
( ( plus_plus_real @ SV320 @ ( times_times_real @ SY1710 @ SV320 ) )
= ( times_times_real @ ( plus_plus_real @ SY1710 @ one_one_real ) @ SV320 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2250]) ).
thf(2922,plain,
! [SV321: nat] :
( ( ! [SY1711: nat] :
( ( plus_plus_nat @ SV321 @ ( times_times_nat @ SY1711 @ SV321 ) )
= ( times_times_nat @ ( plus_plus_nat @ SY1711 @ one_one_nat ) @ SV321 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2251]) ).
thf(2923,plain,
! [SV322: real] :
( ( ! [SY1712: real] :
( ( plus_plus_real @ ( times_times_real @ SV322 @ SY1712 ) @ SY1712 )
= ( times_times_real @ ( plus_plus_real @ SV322 @ one_one_real ) @ SY1712 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2252]) ).
thf(2924,plain,
! [SV323: nat] :
( ( ! [SY1713: nat] :
( ( plus_plus_nat @ ( times_times_nat @ SV323 @ SY1713 ) @ SY1713 )
= ( times_times_nat @ ( plus_plus_nat @ SV323 @ one_one_nat ) @ SY1713 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2253]) ).
thf(2925,plain,
! [SV324: int] :
( ( ~ ( zprime @ SV324 )
| ( SV324
= ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
| ( SV324
= ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) )
| ( ord_less_eq_int @ ( number_number_of_int @ ( bit1 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SV324 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2259]) ).
thf(2926,plain,
! [SV325: int] :
( ( ! [SY1714: int] :
( ( times_times_int @ SV325 @ SY1714 )
!= one_one_int )
| ( SV325 = one_one_int )
| ( SV325
= ( number_number_of_int @ min ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2263]) ).
thf(2927,plain,
! [SV326: int] :
( ( ! [SY1715: int] : ( zcong @ SV326 @ SV326 @ SY1715 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2265]) ).
thf(2928,plain,
! [SV327: int] :
( ( ! [SY1716: int,SY1717: int,SY1718: int] :
( ~ ( zcong @ SY1716 @ SY1717 @ SY1718 )
| ~ ( zcong @ SY1717 @ SV327 @ SY1718 )
| ( zcong @ SY1716 @ SV327 @ SY1718 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2266]) ).
thf(2929,plain,
! [SV328: real] :
( ( ! [SY1719: real] :
( ~ ( ord_less_eq_real @ SV328 @ SY1719 )
| ( SV328 = SY1719 )
| ( ord_less_real @ SV328 @ SY1719 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2267]) ).
thf(2930,plain,
! [SV329: nat] :
( ( ! [SY1720: nat] :
( ~ ( ord_less_eq_nat @ SV329 @ SY1720 )
| ( SV329 = SY1720 )
| ( ord_less_nat @ SV329 @ SY1720 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2268]) ).
thf(2931,plain,
! [SV330: int] :
( ( ! [SY1721: int,SY1722: int] : ( zcong @ ( times_times_int @ SV330 @ SY1721 ) @ ( times_times_int @ SY1722 @ SY1721 ) @ SY1721 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2269]) ).
thf(2932,plain,
! [SV331: int] :
( ( ! [SY1723: int,SY1724: int,SY1725: int] :
( ~ ( zcong @ SY1723 @ SY1724 @ SY1725 )
| ( zcong @ ( times_times_int @ SY1723 @ SV331 ) @ ( times_times_int @ SY1724 @ SV331 ) @ SY1725 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2270]) ).
thf(2933,plain,
! [SV332: int] :
( ( ! [SY1726: int,SY1727: int,SY1728: int] :
( ~ ( zcong @ SY1726 @ SY1727 @ SY1728 )
| ( zcong @ ( times_times_int @ SV332 @ SY1726 ) @ ( times_times_int @ SV332 @ SY1727 ) @ SY1728 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2271]) ).
thf(2934,plain,
! [SV333: int] :
( ( ! [SY1729: int,SY1730: int,SY1731: int,SY1732: int] :
( ~ ( zcong @ SY1730 @ SY1731 @ SY1732 )
| ~ ( zcong @ SV333 @ SY1729 @ SY1732 )
| ( zcong @ ( times_times_int @ SY1730 @ SV333 ) @ ( times_times_int @ SY1731 @ SY1729 ) @ SY1732 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2272]) ).
thf(2935,plain,
! [SV334: nat] :
( ( ( power_power_real @ ( number267125858f_real @ min ) @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV334 ) )
= one_one_real )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2273]) ).
thf(2936,plain,
! [SV335: nat] :
( ( ( power_power_int @ ( number_number_of_int @ min ) @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV335 ) )
= one_one_int )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2274]) ).
thf(2937,plain,
! [SV336: real] :
( ( ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SV336 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( power_power_real @ ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV336 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2275]) ).
thf(2938,plain,
! [SV337: int] :
( ( ! [SY1733: int,SY1734: int] :
( ~ ( ord_less_eq_int @ zero_zero_int @ SY1734 )
| ~ ( zprime @ SY1733 )
| ~ ( dvd_dvd_int @ SY1733 @ ( times_times_int @ SY1734 @ SV337 ) )
| ( dvd_dvd_int @ SY1733 @ SY1734 )
| ( dvd_dvd_int @ SY1733 @ SV337 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2276]) ).
thf(2939,plain,
! [SV338: nat] :
( ( ! [SY1735: nat,SY1736: int] :
( ~ ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ SY1736 )
| ~ ( zcong @ ( power_power_int @ ( number_number_of_int @ min ) @ SV338 ) @ ( power_power_int @ ( number_number_of_int @ min ) @ SY1735 ) @ SY1736 )
| ( ( power_power_int @ ( number_number_of_int @ min ) @ SV338 )
= ( power_power_int @ ( number_number_of_int @ min ) @ SY1735 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2279]) ).
thf(2940,plain,
! [SV339: int] :
( ( ! [SY1737: int] :
( ~ ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ SY1737 )
| ~ ( zcong @ SV339 @ ( number_number_of_int @ min ) @ SY1737 )
| ~ ( zcong @ SV339 @ one_one_int @ SY1737 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2280]) ).
thf(2941,plain,
! [SV340: int] :
( ( ! [SY1738: int,SY1739: int,SY1740: int,SY1741: int] :
( ~ ( zcong @ SY1739 @ SY1740 @ SY1741 )
| ~ ( zcong @ SV340 @ SY1738 @ SY1741 )
| ( zcong @ ( minus_minus_int @ SY1739 @ SV340 ) @ ( minus_minus_int @ SY1740 @ SY1738 ) @ SY1741 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2283]) ).
thf(2942,plain,
! [SV341: int] :
( ( ! [SY1742: int,SY1743: int] :
( ~ ( dvd_dvd_int @ SV341 @ ( minus_minus_int @ SY1742 @ SY1743 ) )
| ~ ( dvd_dvd_int @ SV341 @ SY1743 )
| ( dvd_dvd_int @ SV341 @ SY1742 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2284]) ).
thf(2943,plain,
! [SV342: int] :
( ( ! [SY1744: int,SY1745: int] :
( ( times_times_int @ SV342 @ ( minus_minus_int @ SY1744 @ SY1745 ) )
= ( minus_minus_int @ ( times_times_int @ SV342 @ SY1744 ) @ ( times_times_int @ SV342 @ SY1745 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2285]) ).
thf(2944,plain,
! [SV343: int] :
( ( ! [SY1746: int,SY1747: int] :
( ( times_times_int @ ( minus_minus_int @ SV343 @ SY1746 ) @ SY1747 )
= ( minus_minus_int @ ( times_times_int @ SV343 @ SY1747 ) @ ( times_times_int @ SY1746 @ SY1747 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2286]) ).
thf(2945,plain,
! [SV344: int] :
( ( ! [SY1748: int] :
( ( number267125858f_real @ ( minus_minus_int @ SV344 @ SY1748 ) )
= ( minus_minus_real @ ( number267125858f_real @ SV344 ) @ ( number267125858f_real @ SY1748 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2287]) ).
thf(2946,plain,
! [SV345: int] :
( ( ! [SY1749: int] :
( ( number_number_of_int @ ( minus_minus_int @ SV345 @ SY1749 ) )
= ( minus_minus_int @ ( number_number_of_int @ SV345 ) @ ( number_number_of_int @ SY1749 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2288]) ).
thf(2947,plain,
! [SV346: int] :
( ( ! [SY1750: real,SY1751: real] :
( ( times_times_real @ ( number267125858f_real @ SV346 ) @ ( minus_minus_real @ SY1750 @ SY1751 ) )
= ( minus_minus_real @ ( times_times_real @ ( number267125858f_real @ SV346 ) @ SY1750 ) @ ( times_times_real @ ( number267125858f_real @ SV346 ) @ SY1751 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2289]) ).
thf(2948,plain,
! [SV347: int] :
( ( ! [SY1752: int,SY1753: int] :
( ( times_times_int @ ( number_number_of_int @ SV347 ) @ ( minus_minus_int @ SY1752 @ SY1753 ) )
= ( minus_minus_int @ ( times_times_int @ ( number_number_of_int @ SV347 ) @ SY1752 ) @ ( times_times_int @ ( number_number_of_int @ SV347 ) @ SY1753 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2290]) ).
thf(2949,plain,
! [SV348: real] :
( ( ! [SY1754: real,SY1755: int] :
( ( times_times_real @ ( minus_minus_real @ SV348 @ SY1754 ) @ ( number267125858f_real @ SY1755 ) )
= ( minus_minus_real @ ( times_times_real @ SV348 @ ( number267125858f_real @ SY1755 ) ) @ ( times_times_real @ SY1754 @ ( number267125858f_real @ SY1755 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2291]) ).
thf(2950,plain,
! [SV349: int] :
( ( ! [SY1756: int,SY1757: int] :
( ( times_times_int @ ( minus_minus_int @ SV349 @ SY1756 ) @ ( number_number_of_int @ SY1757 ) )
= ( minus_minus_int @ ( times_times_int @ SV349 @ ( number_number_of_int @ SY1757 ) ) @ ( times_times_int @ SY1756 @ ( number_number_of_int @ SY1757 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2292]) ).
thf(2951,plain,
! [SV350: int] :
( ( ! [SY1758: int,SY1759: real] :
( ( plus_plus_real @ ( number267125858f_real @ SV350 ) @ ( minus_minus_real @ ( number267125858f_real @ SY1758 ) @ SY1759 ) )
= ( minus_minus_real @ ( number267125858f_real @ ( plus_plus_int @ SV350 @ SY1758 ) ) @ SY1759 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2294]) ).
thf(2952,plain,
! [SV351: int] :
( ( ! [SY1760: int,SY1761: int,SY1762: int,SY1763: int] :
( ~ ( zcong @ SY1761 @ SY1762 @ SY1763 )
| ( SY1762 != SY1760 )
| ~ ( zcong @ SY1760 @ SV351 @ SY1763 )
| ( zcong @ SY1761 @ SV351 @ SY1763 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2296]) ).
thf(2953,plain,
! [SV352: int] :
( ( ! [SY1764: int] :
( ~ ( zprime @ SY1764 )
| ~ ( ord_less_int @ zero_zero_int @ SV352 )
| ~ ( ord_less_int @ SV352 @ SY1764 )
| ~ ( zcong @ ( times_times_int @ SV352 @ SV352 ) @ one_one_int @ SY1764 )
| ( SV352 = one_one_int )
| ( SV352
= ( minus_minus_int @ SY1764 @ one_one_int ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2297]) ).
thf(2954,plain,
! [SV353: int] :
( ( ! [SY1765: int] :
( ~ ( zprime @ SY1765 )
| ~ ( ord_less_int @ zero_zero_int @ SV353 )
| ~ ( zcong @ ( times_times_int @ SV353 @ SV353 ) @ one_one_int @ SY1765 )
| ( zcong @ SV353 @ one_one_int @ SY1765 )
| ( zcong @ SV353 @ ( minus_minus_int @ SY1765 @ one_one_int ) @ SY1765 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2298]) ).
thf(2955,plain,
! [SV354: real] :
( ( ! [SY1766: real] :
( ( power_power_real @ ( minus_minus_real @ SV354 @ SY1766 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( minus_minus_real @ ( plus_plus_real @ ( power_power_real @ SV354 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SY1766 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV354 ) @ SY1766 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2301]) ).
thf(2956,plain,
! [SV355: int] :
( ( ! [SY1767: int] :
( ( power_power_int @ ( minus_minus_int @ SV355 @ SY1767 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( minus_minus_int @ ( plus_plus_int @ ( power_power_int @ SV355 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SY1767 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV355 ) @ SY1767 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2302]) ).
thf(2957,plain,
! [SV356: int] :
( ( ! [SY1768: int] :
( ( power_power_int @ ( minus_minus_int @ SV356 @ SY1768 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ ( minus_minus_int @ ( power_power_int @ SV356 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV356 ) @ SY1768 ) ) @ ( power_power_int @ SY1768 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2303]) ).
thf(2958,plain,
! [SV357: int] :
( ( ! [SY1769: int] :
( ( power_power_int @ ( minus_minus_int @ SV357 @ SY1769 ) @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( minus_minus_int @ ( plus_plus_int @ ( minus_minus_int @ ( power_power_int @ SV357 @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) @ ( power_power_int @ SV357 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ SY1769 ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) @ SV357 ) @ ( power_power_int @ SY1769 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ ( power_power_int @ SY1769 @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2304]) ).
thf(2959,plain,
! [SV358: int] :
( ( ! [SY1770: int,SY1771: int] :
( ~ ( zprime @ SY1771 )
| ~ ( dvd_dvd_int @ SY1771 @ ( times_times_int @ SV358 @ SY1770 ) )
| ( dvd_dvd_int @ SY1771 @ SV358 )
| ( dvd_dvd_int @ SY1771 @ SY1770 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2305]) ).
thf(2960,plain,
! [SV359: int] :
( ( ! [SY1772: int,SY1773: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SY1773 )
| ~ ( dvd_dvd_int @ SV359 @ SY1772 )
| ( dvd_dvd_int @ SV359 @ ( power_power_int @ SY1772 @ SY1773 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2306]) ).
thf(2961,plain,
! [SV360: int] :
( ( ! [SY1774: int,SY1775: int] :
( ~ ( zprime @ SY1775 )
| ( zcong @ SY1774 @ zero_zero_int @ SY1775 )
| ( zcong @ SV360 @ zero_zero_int @ SY1775 )
| ~ ( zcong @ ( times_times_int @ SY1774 @ SV360 ) @ zero_zero_int @ SY1775 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2307]) ).
thf(2962,plain,
! [SV361: int] :
( ( ! [SY1776: int,SY1777: int] :
( ~ ( zprime @ SY1777 )
| ~ ( ord_less_int @ zero_zero_int @ SY1776 )
| ( zcong @ SY1776 @ zero_zero_int @ SY1777 )
| ( zcong @ SV361 @ zero_zero_int @ SY1777 )
| ~ ( zcong @ ( times_times_int @ SY1776 @ SV361 ) @ zero_zero_int @ SY1777 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2308]) ).
thf(2963,plain,
! [SV362: int] :
( ( ! [SY1778: int,SY1779: int] :
( ~ ( zprime @ SY1779 )
| ~ ( ord_less_int @ zero_zero_int @ SY1778 )
| ~ ( zcong @ ( times_times_int @ SY1778 @ SV362 ) @ zero_zero_int @ SY1779 )
| ( zcong @ SY1778 @ zero_zero_int @ SY1779 )
| ( zcong @ SV362 @ zero_zero_int @ SY1779 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2309]) ).
thf(2964,plain,
! [SV363: int] :
( ( ! [SY1780: nat,SY1781: int] :
( ~ ( zprime @ SY1781 )
| ~ ( dvd_dvd_int @ SY1781 @ ( power_power_int @ SV363 @ SY1780 ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SY1780 )
| ( dvd_dvd_int @ SY1781 @ SV363 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2310]) ).
thf(2965,plain,
! [SV364: int] :
( ( ~ ( zprime @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SV364 ) @ one_one_int ) )
| ( ( legendre @ ( number_number_of_int @ min ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SV364 ) @ one_one_int ) )
= one_one_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2311]) ).
thf(2966,plain,
! [SV365: int] :
( ( ~ ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV365 )
| ~ ( zcong @ one_one_int @ ( number_number_of_int @ min ) @ SV365 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2312]) ).
thf(2967,plain,
! [SV366: real] :
( ( ! [SY1782: real] :
( ( power_power_real @ ( plus_plus_real @ SV366 @ SY1782 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_real @ ( plus_plus_real @ ( power_power_real @ SV366 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SY1782 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV366 ) @ SY1782 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2314]) ).
thf(2968,plain,
! [SV367: nat] :
( ( ! [SY1783: nat] :
( ( minus_minus_nat @ ( power_power_nat @ SV367 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_nat @ SY1783 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( times_times_nat @ ( plus_plus_nat @ SV367 @ SY1783 ) @ ( minus_minus_nat @ SV367 @ SY1783 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2317]) ).
thf(2969,plain,
( ( zero_zero_real = one_one_real )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2319]) ).
thf(2970,plain,
! [SV368: real] :
( ( ! [SY1784: real,SY1785: real] :
( ( times_times_real @ ( times_times_real @ SV368 @ SY1784 ) @ SY1785 )
= ( times_times_real @ SV368 @ ( times_times_real @ SY1784 @ SY1785 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2322]) ).
thf(2971,plain,
! [SV369: real] :
( ( ! [SY1786: real] :
( ( times_times_real @ SV369 @ SY1786 )
= ( times_times_real @ SY1786 @ SV369 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2323]) ).
thf(2972,plain,
! [SV370: real] :
( ( ( times_times_real @ one_one_real @ SV370 )
= SV370 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2324]) ).
thf(2973,plain,
! [SV371: real] :
( ( ! [SY1787: real,SY1788: real] :
( ~ ( ord_less_eq_real @ SY1787 @ SY1788 )
| ( ord_less_eq_real @ ( plus_plus_real @ SV371 @ SY1787 ) @ ( plus_plus_real @ SV371 @ SY1788 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2325]) ).
thf(2974,plain,
! [SV372: real] :
( ( ! [SY1789: real,SY1790: real,SY1791: real] :
( ( minus_minus_real @ ( plus_plus_real @ SV372 @ SY1789 ) @ ( plus_plus_real @ SY1790 @ SY1791 ) )
= ( plus_plus_real @ ( minus_minus_real @ SV372 @ SY1790 ) @ ( minus_minus_real @ SY1789 @ SY1791 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2326]) ).
thf(2975,plain,
! [SV373: real] :
( ( ! [SY1792: real,SY1793: real] :
( ( times_times_real @ ( plus_plus_real @ SV373 @ SY1792 ) @ SY1793 )
= ( plus_plus_real @ ( times_times_real @ SV373 @ SY1793 ) @ ( times_times_real @ SY1792 @ SY1793 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2330]) ).
thf(2976,plain,
! [SV374: real] :
( ( ! [SY1794: real,SY1795: real,SY1796: real] :
( ( minus_minus_real @ ( times_times_real @ SV374 @ SY1794 ) @ ( times_times_real @ SY1795 @ SY1796 ) )
= ( plus_plus_real @ ( times_times_real @ SV374 @ ( minus_minus_real @ SY1794 @ SY1796 ) ) @ ( times_times_real @ ( minus_minus_real @ SV374 @ SY1795 ) @ SY1796 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2332]) ).
thf(2977,plain,
! [SV375: real] :
( ( ! [SY1797: real,SY1798: real] :
( ~ ( ord_less_real @ zero_zero_real @ SY1798 )
| ~ ( ord_less_real @ SV375 @ SY1797 )
| ( ord_less_real @ ( times_times_real @ SY1798 @ SV375 ) @ ( times_times_real @ SY1798 @ SY1797 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2335]) ).
thf(2978,plain,
! [SV376: real] :
( ( ! [SY1799: real] :
( ~ ( ord_less_real @ zero_zero_real @ SY1799 )
| ~ ( ord_less_real @ zero_zero_real @ SV376 )
| ( ord_less_real @ zero_zero_real @ ( times_times_real @ SY1799 @ SV376 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2336]) ).
thf(2979,plain,
! [SV377: real] :
( ( ( minus_minus_real @ ( times_times_real @ SV377 @ SV377 ) @ one_one_real )
= ( times_times_real @ ( plus_plus_real @ SV377 @ one_one_real ) @ ( minus_minus_real @ SV377 @ one_one_real ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2340]) ).
thf(2980,plain,
! [SV378: real] :
( ( ! [SY1800: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SY1800 )
| ( ( times_times_real @ ( power_power_real @ SV378 @ ( minus_minus_nat @ SY1800 @ one_one_nat ) ) @ SV378 )
= ( power_power_real @ SV378 @ SY1800 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2341]) ).
thf(2981,plain,
! [SV379: nat] :
( ( ! [SY1801: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SY1801 )
| ( ( times_times_nat @ ( power_power_nat @ SV379 @ ( minus_minus_nat @ SY1801 @ one_one_nat ) ) @ SV379 )
= ( power_power_nat @ SV379 @ SY1801 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2342]) ).
thf(2982,plain,
! [SV380: int] :
( ( ! [SY1802: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SY1802 )
| ( ( times_times_int @ ( power_power_int @ SV380 @ ( minus_minus_nat @ SY1802 @ one_one_nat ) ) @ SV380 )
= ( power_power_int @ SV380 @ SY1802 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2343]) ).
thf(2983,plain,
! [SV381: nat] :
( ( ord_less_eq_real @ one_one_real @ ( power_power_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV381 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2344]) ).
thf(2984,plain,
! [SV382: nat] :
( ( ! [SY1803: real,SY1804: real] :
( ~ ( ord_less_real @ SY1803 @ SY1804 )
| ~ ( ord_less_eq_real @ zero_zero_real @ SY1803 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV382 )
| ( ord_less_real @ ( power_power_real @ SY1803 @ SV382 ) @ ( power_power_real @ SY1804 @ SV382 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2348]) ).
thf(2985,plain,
! [SV383: nat] :
( ( ! [SY1805: nat,SY1806: nat] :
( ~ ( ord_less_nat @ SY1805 @ SY1806 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SY1805 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV383 )
| ( ord_less_nat @ ( power_power_nat @ SY1805 @ SV383 ) @ ( power_power_nat @ SY1806 @ SV383 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2349]) ).
thf(2986,plain,
! [SV384: nat] :
( ( ! [SY1807: int,SY1808: int] :
( ~ ( ord_less_int @ SY1807 @ SY1808 )
| ~ ( ord_less_eq_int @ zero_zero_int @ SY1807 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV384 )
| ( ord_less_int @ ( power_power_int @ SY1807 @ SV384 ) @ ( power_power_int @ SY1808 @ SV384 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2350]) ).
thf(2987,plain,
! [SV385: nat] :
( ( ! [SY1809: real] :
( ( SY1809 = zero_zero_real )
| ( ( power_power_real @ SY1809 @ SV385 )
!= zero_zero_real ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2351]) ).
thf(2988,plain,
! [SV386: real] :
( ( ! [SY1810: real,SY1811: nat] :
( ( power_power_real @ ( times_times_real @ SV386 @ SY1810 ) @ SY1811 )
= ( times_times_real @ ( power_power_real @ SV386 @ SY1811 ) @ ( power_power_real @ SY1810 @ SY1811 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2352]) ).
thf(2989,plain,
! [SV387: nat] :
( ( ! [SY1812: nat,SY1813: nat] :
( ( power_power_nat @ ( times_times_nat @ SV387 @ SY1812 ) @ SY1813 )
= ( times_times_nat @ ( power_power_nat @ SV387 @ SY1813 ) @ ( power_power_nat @ SY1812 @ SY1813 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2353]) ).
thf(2990,plain,
! [SV388: real] :
( ( ! [SY1814: nat] :
( ( times_times_real @ ( power_power_real @ SV388 @ SY1814 ) @ SV388 )
= ( times_times_real @ SV388 @ ( power_power_real @ SV388 @ SY1814 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2354]) ).
thf(2991,plain,
! [SV389: nat] :
( ( ! [SY1815: nat] :
( ( times_times_nat @ ( power_power_nat @ SV389 @ SY1815 ) @ SV389 )
= ( times_times_nat @ SV389 @ ( power_power_nat @ SV389 @ SY1815 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2355]) ).
thf(2992,plain,
! [SV390: nat] :
( ( ( power_power_real @ one_one_real @ SV390 )
= one_one_real )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2356]) ).
thf(2993,plain,
! [SV391: nat] :
( ( ( power_power_nat @ one_one_nat @ SV391 )
= one_one_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2357]) ).
thf(2994,plain,
! [SV392: nat] :
( ( ! [SY1816: nat,SY1817: nat] :
( ~ ( dvd_dvd_nat @ SY1816 @ SY1817 )
| ( dvd_dvd_nat @ ( power_power_nat @ SY1816 @ SV392 ) @ ( power_power_nat @ SY1817 @ SV392 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2358]) ).
thf(2995,plain,
! [SV393: nat] :
( ( ! [SY1818: real,SY1819: real] :
( ~ ( dvd_dvd_real @ SY1818 @ SY1819 )
| ( dvd_dvd_real @ ( power_power_real @ SY1818 @ SV393 ) @ ( power_power_real @ SY1819 @ SV393 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2359]) ).
thf(2996,plain,
! [SV394: real] :
( ( ! [SY1820: nat,SY1821: nat] :
( ( power_power_real @ SV394 @ ( times_times_nat @ SY1820 @ SY1821 ) )
= ( power_power_real @ ( power_power_real @ SV394 @ SY1820 ) @ SY1821 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2360]) ).
thf(2997,plain,
! [SV395: nat] :
( ( ! [SY1822: nat,SY1823: nat] :
( ( power_power_nat @ SV395 @ ( times_times_nat @ SY1822 @ SY1823 ) )
= ( power_power_nat @ ( power_power_nat @ SV395 @ SY1822 ) @ SY1823 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2361]) ).
thf(2998,plain,
! [SV396: real] :
( ( ( power_power_real @ SV396 @ one_one_nat )
= SV396 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2362]) ).
thf(2999,plain,
! [SV397: nat] :
( ( ( power_power_nat @ SV397 @ one_one_nat )
= SV397 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2363]) ).
thf(3000,plain,
! [SV398: nat] :
( ( ! [SY1824: real,SY1825: real] :
( ~ ( ord_less_eq_real @ SY1824 @ SY1825 )
| ~ ( ord_less_eq_real @ zero_zero_real @ SY1824 )
| ( ord_less_eq_real @ ( power_power_real @ SY1824 @ SV398 ) @ ( power_power_real @ SY1825 @ SV398 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2364]) ).
thf(3001,plain,
! [SV399: nat] :
( ( ! [SY1826: nat,SY1827: nat] :
( ~ ( ord_less_eq_nat @ SY1826 @ SY1827 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SY1826 )
| ( ord_less_eq_nat @ ( power_power_nat @ SY1826 @ SV399 ) @ ( power_power_nat @ SY1827 @ SV399 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2365]) ).
thf(3002,plain,
! [SV400: nat] :
( ( ! [SY1828: real] :
( ~ ( ord_less_eq_real @ zero_zero_real @ SY1828 )
| ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ SY1828 @ SV400 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2366]) ).
thf(3003,plain,
! [SV401: nat] :
( ( ! [SY1829: nat] :
( ~ ( ord_less_eq_nat @ zero_zero_nat @ SY1829 )
| ( ord_less_eq_nat @ zero_zero_nat @ ( power_power_nat @ SY1829 @ SV401 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2367]) ).
thf(3004,plain,
! [SV402: nat] :
( ( ! [SY1830: real] :
( ~ ( ord_less_real @ zero_zero_real @ SY1830 )
| ( ord_less_real @ zero_zero_real @ ( power_power_real @ SY1830 @ SV402 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2368]) ).
thf(3005,plain,
! [SV403: nat] :
( ( ! [SY1831: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SY1831 )
| ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SY1831 @ SV403 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2369]) ).
thf(3006,plain,
! [SV404: nat] :
( ( ! [SY1832: real] :
( ~ ( ord_less_eq_real @ one_one_real @ SY1832 )
| ( ord_less_eq_real @ one_one_real @ ( power_power_real @ SY1832 @ SV404 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2370]) ).
thf(3007,plain,
! [SV405: nat] :
( ( ! [SY1833: nat] :
( ~ ( ord_less_eq_nat @ one_one_nat @ SY1833 )
| ( ord_less_eq_nat @ one_one_nat @ ( power_power_nat @ SY1833 @ SV405 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2371]) ).
thf(3008,plain,
! [SV406: real] :
( ( ( power_power_real @ SV406 @ zero_zero_nat )
= one_one_real )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2376]) ).
thf(3009,plain,
! [SV407: nat] :
( ( ( power_power_nat @ SV407 @ zero_zero_nat )
= one_one_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2377]) ).
thf(3010,plain,
! [SV408: real] :
( ( ! [SY1834: nat,SY1835: nat] :
( ( power_power_real @ SV408 @ ( plus_plus_nat @ SY1834 @ SY1835 ) )
= ( times_times_real @ ( power_power_real @ SV408 @ SY1834 ) @ ( power_power_real @ SV408 @ SY1835 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2378]) ).
thf(3011,plain,
! [SV409: nat] :
( ( ! [SY1836: nat,SY1837: nat] :
( ( power_power_nat @ SV409 @ ( plus_plus_nat @ SY1836 @ SY1837 ) )
= ( times_times_nat @ ( power_power_nat @ SV409 @ SY1836 ) @ ( power_power_nat @ SV409 @ SY1837 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2379]) ).
thf(3012,plain,
! [SV410: nat] :
( ( ! [SY1838: nat,SY1839: nat,SY1840: nat] :
( ~ ( dvd_dvd_nat @ ( power_power_nat @ SY1838 @ SY1839 ) @ SY1840 )
| ~ ( ord_less_eq_nat @ SV410 @ SY1839 )
| ( dvd_dvd_nat @ ( power_power_nat @ SY1838 @ SV410 ) @ SY1840 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2380]) ).
thf(3013,plain,
! [SV411: nat] :
( ( ! [SY1841: real,SY1842: nat,SY1843: real] :
( ~ ( dvd_dvd_real @ ( power_power_real @ SY1841 @ SY1842 ) @ SY1843 )
| ~ ( ord_less_eq_nat @ SV411 @ SY1842 )
| ( dvd_dvd_real @ ( power_power_real @ SY1841 @ SV411 ) @ SY1843 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2381]) ).
thf(3014,plain,
! [SV412: nat] :
( ( ! [SY1844: nat,SY1845: nat,SY1846: nat] :
( ~ ( dvd_dvd_nat @ SY1845 @ SY1846 )
| ~ ( ord_less_eq_nat @ SV412 @ SY1844 )
| ( dvd_dvd_nat @ ( power_power_nat @ SY1845 @ SV412 ) @ ( power_power_nat @ SY1846 @ SY1844 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2382]) ).
thf(3015,plain,
! [SV413: nat] :
( ( ! [SY1847: nat,SY1848: real,SY1849: real] :
( ~ ( dvd_dvd_real @ SY1848 @ SY1849 )
| ~ ( ord_less_eq_nat @ SV413 @ SY1847 )
| ( dvd_dvd_real @ ( power_power_real @ SY1848 @ SV413 ) @ ( power_power_real @ SY1849 @ SY1847 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2383]) ).
thf(3016,plain,
! [SV414: nat] :
( ( ! [SY1850: nat,SY1851: nat] :
( ~ ( ord_less_eq_nat @ SY1850 @ SY1851 )
| ( dvd_dvd_nat @ ( power_power_nat @ SV414 @ SY1850 ) @ ( power_power_nat @ SV414 @ SY1851 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2384]) ).
thf(3017,plain,
! [SV415: real] :
( ( ! [SY1852: nat,SY1853: nat] :
( ~ ( ord_less_eq_nat @ SY1852 @ SY1853 )
| ( dvd_dvd_real @ ( power_power_real @ SV415 @ SY1852 ) @ ( power_power_real @ SV415 @ SY1853 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2385]) ).
thf(3018,plain,
! [SV416: nat] :
( ( ! [SY1854: nat,SY1855: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SY1855 )
| ~ ( ord_less_nat @ ( power_power_nat @ SY1855 @ SV416 ) @ ( power_power_nat @ SY1855 @ SY1854 ) )
| ( ord_less_nat @ SV416 @ SY1854 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2386]) ).
thf(3019,plain,
! [SV417: real] :
( ( ! [SY1856: nat,SY1857: real] :
( ~ ( ord_less_real @ ( power_power_real @ SV417 @ SY1856 ) @ ( power_power_real @ SY1857 @ SY1856 ) )
| ~ ( ord_less_eq_real @ zero_zero_real @ SY1857 )
| ( ord_less_real @ SV417 @ SY1857 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2388]) ).
thf(3020,plain,
! [SV418: nat] :
( ( ! [SY1858: nat,SY1859: nat] :
( ~ ( ord_less_nat @ ( power_power_nat @ SV418 @ SY1858 ) @ ( power_power_nat @ SY1859 @ SY1858 ) )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SY1859 )
| ( ord_less_nat @ SV418 @ SY1859 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2389]) ).
thf(3021,plain,
! [SV419: nat] :
( ( ! [SY1860: real] :
( ~ ( ord_less_real @ one_one_real @ SY1860 )
| ( ord_less_real @ ( power_power_real @ SY1860 @ SV419 ) @ ( times_times_real @ SY1860 @ ( power_power_real @ SY1860 @ SV419 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2390]) ).
thf(3022,plain,
! [SV420: nat] :
( ( ! [SY1861: nat] :
( ~ ( ord_less_nat @ one_one_nat @ SY1861 )
| ( ord_less_nat @ ( power_power_nat @ SY1861 @ SV420 ) @ ( times_times_nat @ SY1861 @ ( power_power_nat @ SY1861 @ SV420 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2391]) ).
thf(3023,plain,
! [SV421: nat] :
( ( ! [SY1862: real] :
( ~ ( ord_less_real @ one_one_real @ SY1862 )
| ( ord_less_real @ one_one_real @ ( times_times_real @ SY1862 @ ( power_power_real @ SY1862 @ SV421 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2392]) ).
thf(3024,plain,
! [SV422: nat] :
( ( ! [SY1863: nat] :
( ~ ( ord_less_nat @ one_one_nat @ SY1863 )
| ( ord_less_nat @ one_one_nat @ ( times_times_nat @ SY1863 @ ( power_power_nat @ SY1863 @ SV422 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2393]) ).
thf(3025,plain,
! [SV423: real] :
( ( ! [SY1864: nat,SY1865: nat] :
( ~ ( ord_less_nat @ SY1864 @ SY1865 )
| ~ ( ord_less_real @ one_one_real @ SV423 )
| ( ord_less_real @ ( power_power_real @ SV423 @ SY1864 ) @ ( power_power_real @ SV423 @ SY1865 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2396]) ).
thf(3026,plain,
! [SV424: nat] :
( ( ! [SY1866: nat,SY1867: nat] :
( ~ ( ord_less_nat @ SY1866 @ SY1867 )
| ~ ( ord_less_nat @ one_one_nat @ SV424 )
| ( ord_less_nat @ ( power_power_nat @ SV424 @ SY1866 ) @ ( power_power_nat @ SV424 @ SY1867 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2397]) ).
thf(3027,plain,
! [SV425: nat] :
( ( ! [SY1868: nat,SY1869: real] :
( ~ ( ord_less_real @ one_one_real @ SY1869 )
| ~ ( ord_less_real @ ( power_power_real @ SY1869 @ SV425 ) @ ( power_power_real @ SY1869 @ SY1868 ) )
| ( ord_less_nat @ SV425 @ SY1868 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2398]) ).
thf(3028,plain,
! [SV426: nat] :
( ( ! [SY1870: nat,SY1871: nat] :
( ~ ( ord_less_nat @ one_one_nat @ SY1871 )
| ~ ( ord_less_nat @ ( power_power_nat @ SY1871 @ SV426 ) @ ( power_power_nat @ SY1871 @ SY1870 ) )
| ( ord_less_nat @ SV426 @ SY1870 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2399]) ).
thf(3029,plain,
! [SV427: real] :
( ( ! [SY1872: nat,SY1873: nat] :
( ~ ( ord_less_eq_nat @ SY1872 @ SY1873 )
| ~ ( ord_less_eq_real @ one_one_real @ SV427 )
| ( ord_less_eq_real @ ( power_power_real @ SV427 @ SY1872 ) @ ( power_power_real @ SV427 @ SY1873 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2402]) ).
thf(3030,plain,
! [SV428: nat] :
( ( ! [SY1874: nat,SY1875: nat] :
( ~ ( ord_less_eq_nat @ SY1874 @ SY1875 )
| ~ ( ord_less_eq_nat @ one_one_nat @ SV428 )
| ( ord_less_eq_nat @ ( power_power_nat @ SV428 @ SY1874 ) @ ( power_power_nat @ SV428 @ SY1875 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2403]) ).
thf(3031,plain,
! [SV429: nat] :
( ( ! [SY1876: real] :
( ~ ( ord_less_real @ zero_zero_real @ SY1876 )
| ~ ( ord_less_real @ SY1876 @ one_one_real )
| ( ord_less_real @ ( times_times_real @ SY1876 @ ( power_power_real @ SY1876 @ SV429 ) ) @ ( power_power_real @ SY1876 @ SV429 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2404]) ).
thf(3032,plain,
! [SV430: nat] :
( ( ! [SY1877: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SY1877 )
| ~ ( ord_less_nat @ SY1877 @ one_one_nat )
| ( ord_less_nat @ ( times_times_nat @ SY1877 @ ( power_power_nat @ SY1877 @ SV430 ) ) @ ( power_power_nat @ SY1877 @ SV430 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2405]) ).
thf(3033,plain,
! [SV431: nat] :
( ( ! [SY1878: nat] :
( ~ ( dvd_dvd_nat @ SV431 @ SY1878 )
| ( SY1878 = zero_zero_nat )
| ( ord_less_eq_nat @ SV431 @ SY1878 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2407]) ).
thf(3034,plain,
! [SV432: nat] :
( ( ! [SY1879: nat,SY1880: nat] :
( ~ ( dvd_dvd_nat @ SY1879 @ SY1880 )
| ( dvd_dvd_nat @ ( power_power_nat @ SY1879 @ SV432 ) @ ( power_power_nat @ SY1880 @ SV432 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2408]) ).
thf(3035,plain,
! [SV433: nat] :
( ( ! [SY1881: nat,SY1882: nat] :
( ~ ( dvd_dvd_nat @ SY1881 @ SY1882 )
| ( dvd_dvd_nat @ ( times_times_nat @ SV433 @ SY1881 ) @ ( times_times_nat @ SV433 @ SY1882 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2409]) ).
thf(3036,plain,
! [SV434: nat] :
( ( ! [SY1883: nat,SY1884: nat] :
( ~ ( dvd_dvd_nat @ SY1883 @ SY1884 )
| ( dvd_dvd_nat @ ( times_times_nat @ SY1883 @ SV434 ) @ ( times_times_nat @ SY1884 @ SV434 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2410]) ).
thf(3037,plain,
! [SV435: nat] :
( ( ! [SY1885: nat,SY1886: nat] :
( ~ ( dvd_dvd_nat @ SY1885 @ SY1886 )
| ~ ( dvd_dvd_nat @ SY1885 @ ( plus_plus_nat @ SY1886 @ SV435 ) )
| ( dvd_dvd_nat @ SY1885 @ SV435 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2411]) ).
thf(3038,plain,
! [SV436: nat] :
( ( ! [SY1887: nat,SY1888: nat] :
( ~ ( dvd_dvd_nat @ ( power_power_nat @ SV436 @ SY1887 ) @ ( power_power_nat @ SY1888 @ SY1887 ) )
| ( SY1887 = zero_zero_nat )
| ( dvd_dvd_nat @ SV436 @ SY1888 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2413]) ).
thf(3039,plain,
! [SV437: nat] :
( ( ! [SY1889: nat,SY1890: nat] :
( ( SY1890 = zero_zero_nat )
| ~ ( dvd_dvd_nat @ ( power_power_nat @ SV437 @ SY1890 ) @ SY1889 )
| ( dvd_dvd_nat @ SV437 @ SY1889 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2414]) ).
thf(3040,plain,
! [SV438: nat] :
( ( ! [SY1891: nat,SY1892: nat,SY1893: nat] :
( ( SV438
!= ( plus_plus_nat @ ( times_times_nat @ SY1891 @ SY1892 ) @ SY1893 ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SY1893 )
| ~ ( ord_less_nat @ SY1893 @ SY1892 )
| ~ ( dvd_dvd_nat @ SY1892 @ SV438 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2415]) ).
thf(3041,plain,
! [SV439: nat] :
( ( ! [SY1894: nat,SY1895: nat] :
( ~ ( dvd_dvd_nat @ ( power_power_nat @ SV439 @ SY1894 ) @ ( power_power_nat @ SV439 @ SY1895 ) )
| ~ ( ord_less_nat @ one_one_nat @ SV439 )
| ( ord_less_eq_nat @ SY1894 @ SY1895 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2416]) ).
thf(3042,plain,
! [SV440: nat] :
( ( ! [SY1896: nat] :
( ~ ( dvd_dvd_nat @ SV440 @ SY1896 )
| ( ord_less_eq_nat @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV440 ) @ SY1896 )
| ( SY1896 = zero_zero_nat )
| ( SY1896 = SV440 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2417]) ).
thf(3043,plain,
( ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int ) @ zero_zero_int )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2418]) ).
thf(3044,plain,
( ( ~ ! [SX0: real] :
( ( ( power_power_real @ SX0 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= zero_zero_real )
| ( SX0 = zero_zero_real ) )
| ~ ! [SX0: real] :
( ( SX0 != zero_zero_real )
| ( ( power_power_real @ SX0 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_real ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2419]) ).
thf(3045,plain,
( ( ~ ! [SX0: nat,SX1: nat] :
( ( SX1 = zero_zero_nat )
| ( SX0 != zero_zero_nat )
| ( ( power_power_nat @ SX0 @ SX1 )
= zero_zero_nat ) )
| ~ ~ ( ~ ! [SX0: nat,SX1: nat] :
( ( ( power_power_nat @ SX0 @ SX1 )
!= zero_zero_nat )
| ( SX1 != zero_zero_nat ) )
| ~ ! [SX0: nat] :
( ! [SX1: nat] :
( ( power_power_nat @ SX0 @ SX1 )
!= zero_zero_nat )
| ( SX0 = zero_zero_nat ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2420]) ).
thf(3046,plain,
( ( ~ ! [SX0: nat,SX1: int] :
( ( ( number_number_of_nat @ SX1 )
= zero_zero_nat )
| ( SX0 != zero_zero_nat )
| ( ( power_power_nat @ SX0 @ ( number_number_of_nat @ SX1 ) )
= zero_zero_nat ) )
| ~ ~ ( ~ ! [SX0: nat,SX1: int] :
( ( ( power_power_nat @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_nat )
| ( ( number_number_of_nat @ SX1 )
!= zero_zero_nat ) )
| ~ ! [SX0: nat] :
( ! [SX1: int] :
( ( power_power_nat @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_nat )
| ( SX0 = zero_zero_nat ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2421]) ).
thf(3047,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ min @ ( bit0 @ SX0 ) )
| ( ord_less_int @ min @ SX0 ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_int @ min @ SX0 )
| ( ord_less_eq_int @ min @ ( bit0 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2422]) ).
thf(3048,plain,
( ( ~ ! [SX0: real,SX1: real] :
( ~ ( ord_less_real @ 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 ) ) ) ) ) )
| ( SX0 != zero_zero_real )
| ( SX1 != zero_zero_real ) )
| ~ ~ ( ~ ! [SX0: real] :
( ( SX0 = zero_zero_real )
| ! [SX1: real] : ( ord_less_real @ 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 ) ) ) ) ) ) )
| ~ ! [SX0: real,SX1: real] :
( ( SX1 = zero_zero_real )
| ( ord_less_real @ 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 ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2423]) ).
thf(3049,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ pls @ SX0 )
| ( ord_less_eq_real @ zero_zero_real @ ( number267125858f_real @ SX0 ) ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_eq_real @ zero_zero_real @ ( number267125858f_real @ SX0 ) )
| ( ord_less_eq_int @ pls @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2424]) ).
thf(3050,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ pls @ SX0 )
| ( ord_less_int @ pls @ ( bit1 @ SX0 ) ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_int @ pls @ ( bit1 @ SX0 ) )
| ( ord_less_eq_int @ pls @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2425]) ).
thf(3051,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2426]) ).
thf(3052,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ min @ ( bit1 @ SX0 ) )
| ( ord_less_int @ min @ SX0 ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_int @ min @ SX0 )
| ( ord_less_int @ min @ ( bit1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2427]) ).
thf(3053,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2428]) ).
thf(3054,plain,
( ( ~ ! [SX0: nat,SX1: nat] :
( ( ( power_power_nat @ SX0 @ SX1 )
!= one_one_nat )
| ( SX0 = one_one_nat )
| ( SX1 = zero_zero_nat ) )
| ~ ~ ( ~ ! [SX0: nat] :
( ( SX0 != one_one_nat )
| ! [SX1: nat] :
( ( power_power_nat @ SX0 @ SX1 )
= one_one_nat ) )
| ~ ! [SX0: nat,SX1: nat] :
( ( SX1 != zero_zero_nat )
| ( ( power_power_nat @ SX0 @ SX1 )
= one_one_nat ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2429]) ).
thf(3055,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_eq_real @ ( number267125858f_real @ SX0 ) @ ( number267125858f_real @ SX1 ) ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_real @ ( number267125858f_real @ SX0 ) @ ( number267125858f_real @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2430]) ).
thf(3056,plain,
( ( ~ ! [SX0: nat] :
( ( SX0 != zero_zero_nat )
| ( ( power_power_real @ zero_zero_real @ SX0 )
= one_one_real ) )
| ~ ! [SX0: nat] :
( ( SX0 = zero_zero_nat )
| ( ( power_power_real @ zero_zero_real @ SX0 )
= zero_zero_real ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2431]) ).
thf(3057,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ( ( bit1 @ SX0 )
!= ( bit1 @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: int,SX1: int] :
( ( SX0 != SX1 )
| ( ( bit1 @ SX0 )
= ( bit1 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2432]) ).
thf(3058,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ ( number_number_of_int @ SX0 ) @ ( number_number_of_int @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ ( number_number_of_int @ SX0 ) @ ( number_number_of_int @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2433]) ).
thf(3059,plain,
( ( ~ ! [SX0: real,SX1: real] :
( ( SX0 != zero_zero_real )
| ( SX1 != zero_zero_real )
| ( ord_less_eq_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 ) )
| ~ ~ ( ~ ! [SX0: real] :
( ! [SX1: real] :
~ ( ord_less_eq_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 )
| ( SX0 = zero_zero_real ) )
| ~ ! [SX0: real,SX1: real] :
( ~ ( ord_less_eq_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 )
| ( SX1 = zero_zero_real ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2434]) ).
thf(3060,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ ( plus_plus_int @ SX1 @ one_one_int ) )
| ( SX0 = SX1 )
| ( ord_less_int @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: int,SX1: int] :
( ( SX0 != SX1 )
| ( ord_less_int @ SX0 @ ( plus_plus_int @ SX1 @ one_one_int ) ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ SX0 @ ( plus_plus_int @ SX1 @ one_one_int ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2435]) ).
thf(3061,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ min @ ( bit1 @ SX0 ) )
| ( ord_less_eq_int @ min @ SX0 ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ min @ SX0 )
| ( ord_less_eq_int @ min @ ( bit1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2436]) ).
thf(3062,plain,
( ( ~ ! [SX0: int] :
( ( ( number_number_of_nat @ SX0 )
!= zero_zero_nat )
| ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ SX0 ) )
= one_one_int ) )
| ~ ! [SX0: int] :
( ( ( number_number_of_nat @ SX0 )
= zero_zero_nat )
| ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ SX0 ) )
= zero_zero_int ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2437]) ).
thf(3063,plain,
! [SV441: nat] :
( ( ! [SY1897: nat] :
~ ( ~ ~ ( ~ ! [SY1898: nat,SY1899: nat] :
( ( ( plus_plus_nat @ ( times_times_nat @ SY1898 @ SV441 ) @ ( times_times_nat @ SY1899 @ SY1897 ) )
= ( plus_plus_nat @ ( times_times_nat @ SY1898 @ SY1897 ) @ ( times_times_nat @ SY1899 @ SV441 ) ) )
| ( SY1898 != SY1899 ) )
| ~ ( ! [SY1900: nat,SY1901: nat] :
( ( plus_plus_nat @ ( times_times_nat @ SY1900 @ SV441 ) @ ( times_times_nat @ SY1901 @ SY1897 ) )
= ( plus_plus_nat @ ( times_times_nat @ SY1900 @ SY1897 ) @ ( times_times_nat @ SY1901 @ SV441 ) ) )
| ( SV441 != SY1897 ) ) )
| ~ ! [SY1902: nat,SY1903: nat] :
( ( SY1902 = SY1903 )
| ( SV441 = SY1897 )
| ( ( plus_plus_nat @ ( times_times_nat @ SY1902 @ SV441 ) @ ( times_times_nat @ SY1903 @ SY1897 ) )
!= ( plus_plus_nat @ ( times_times_nat @ SY1902 @ SY1897 ) @ ( times_times_nat @ SY1903 @ SV441 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2438]) ).
thf(3064,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2439]) ).
thf(3065,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2440]) ).
thf(3066,plain,
( ( ~ ! [SX0: real,SX1: int] :
( ( ( number_number_of_nat @ SX1 )
= zero_zero_nat )
| ( SX0 != zero_zero_real )
| ( ( power_power_real @ SX0 @ ( number_number_of_nat @ SX1 ) )
= zero_zero_real ) )
| ~ ~ ( ~ ! [SX0: real,SX1: int] :
( ( ( power_power_real @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_real )
| ( ( number_number_of_nat @ SX1 )
!= zero_zero_nat ) )
| ~ ! [SX0: real] :
( ! [SX1: int] :
( ( power_power_real @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_real )
| ( SX0 = zero_zero_real ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2441]) ).
thf(3067,plain,
( ( ~ ! [SX0: real,SX1: real] :
( ~ ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ SX0 @ SX0 ) @ ( times_times_real @ SX1 @ SX1 ) ) )
| ( SX0 != zero_zero_real )
| ( SX1 != zero_zero_real ) )
| ~ ~ ( ~ ! [SX0: real] :
( ( SX0 = zero_zero_real )
| ! [SX1: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ SX0 @ SX0 ) @ ( times_times_real @ SX1 @ SX1 ) ) ) )
| ~ ! [SX0: real,SX1: real] :
( ( SX1 = zero_zero_real )
| ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ SX0 @ SX0 ) @ ( times_times_real @ SX1 @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2442]) ).
thf(3068,plain,
( ( ~ ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SX0 @ SX1 ) )
| ( SX1 = zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SX0 ) )
| ~ ~ ( ~ ! [SX0: nat,SX1: nat] :
( ( SX1 != zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SX0 @ SX1 ) ) )
| ~ ! [SX0: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SX0 )
| ! [SX1: nat] : ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SX0 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2443]) ).
thf(3069,plain,
! [SV442: real] :
( ( ! [SY1904: real] :
~ ( ~ ~ ( ~ ! [SY1905: real,SY1906: real] :
( ( ( plus_plus_real @ ( times_times_real @ SY1905 @ SV442 ) @ ( times_times_real @ SY1906 @ SY1904 ) )
= ( plus_plus_real @ ( times_times_real @ SY1905 @ SY1904 ) @ ( times_times_real @ SY1906 @ SV442 ) ) )
| ( SY1905 != SY1906 ) )
| ~ ( ! [SY1907: real,SY1908: real] :
( ( plus_plus_real @ ( times_times_real @ SY1907 @ SV442 ) @ ( times_times_real @ SY1908 @ SY1904 ) )
= ( plus_plus_real @ ( times_times_real @ SY1907 @ SY1904 ) @ ( times_times_real @ SY1908 @ SV442 ) ) )
| ( SV442 != SY1904 ) ) )
| ~ ! [SY1909: real,SY1910: real] :
( ( SY1909 = SY1910 )
| ( SV442 = SY1904 )
| ( ( plus_plus_real @ ( times_times_real @ SY1909 @ SV442 ) @ ( times_times_real @ SY1910 @ SY1904 ) )
!= ( plus_plus_real @ ( times_times_real @ SY1909 @ SY1904 ) @ ( times_times_real @ SY1910 @ SV442 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2444]) ).
thf(3070,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ ( bit0 @ SX0 ) @ pls )
| ( ord_less_eq_int @ SX0 @ pls ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ SX0 @ pls )
| ( ord_less_eq_int @ ( bit0 @ SX0 ) @ pls ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2445]) ).
thf(3071,plain,
( ( ~ ! [SX0: int] :
( ( ( bit1 @ SX0 )
!= min )
| ( SX0 = min ) )
| ~ ! [SX0: int] :
( ( SX0 != min )
| ( ( bit1 @ SX0 )
= min ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2446]) ).
thf(3072,plain,
( ( ~ ! [SX0: real,SX1: real] :
( ~ ( ord_less_eq_real @ SX0 @ SX1 )
| ( SX0 = SX1 )
| ( ord_less_real @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: real,SX1: real] :
( ( SX0 != SX1 )
| ( ord_less_eq_real @ SX0 @ SX1 ) )
| ~ ! [SX0: real,SX1: real] :
( ~ ( ord_less_real @ SX0 @ SX1 )
| ( ord_less_eq_real @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2447]) ).
thf(3073,plain,
( ( ~ ! [SX0: real] :
( ( ( plus_plus_real @ SX0 @ SX0 )
!= zero_zero_real )
| ( SX0 = zero_zero_real ) )
| ~ ! [SX0: real] :
( ( SX0 != zero_zero_real )
| ( ( plus_plus_real @ SX0 @ SX0 )
= zero_zero_real ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2448]) ).
thf(3074,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ zero_zero_int @ ( 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 ) ) ) ) ) )
| ( SX0 != zero_zero_int )
| ( SX1 != zero_zero_int ) )
| ~ ~ ( ~ ! [SX0: int] :
( ( SX0 = zero_zero_int )
| ! [SX1: int] : ( ord_less_int @ zero_zero_int @ ( 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 ) ) ) ) ) ) )
| ~ ! [SX0: int,SX1: int] :
( ( SX1 = zero_zero_int )
| ( ord_less_int @ zero_zero_int @ ( 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 ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2449]) ).
thf(3075,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ pls @ SX0 )
| ( ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ SX0 ) ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ SX0 ) )
| ( ord_less_int @ pls @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2450]) ).
thf(3076,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ ( number_number_of_int @ SX0 ) @ ( number_number_of_int @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( number_number_of_int @ SX0 ) @ ( number_number_of_int @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2451]) ).
thf(3077,plain,
( ( ~ ! [SX0: real,SX1: 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 ) )
| ~ ~ ( ~ ! [SX0: real] :
( ! [SX1: 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 )
| ( SX0 = zero_zero_real ) )
| ~ ! [SX0: real,SX1: 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 )
| ( SX1 = zero_zero_real ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2452]) ).
thf(3078,plain,
( ( ~ ! [SX0: int,SX1: nat] :
( ( SX1 != zero_zero_nat )
| ( ( power_power_int @ SX0 @ SX1 )
= one_one_int ) )
| ~ ! [SX0: int,SX1: nat] :
( ( SX1 = zero_zero_nat )
| ( ( power_power_int @ SX0 @ SX1 )
= ( times_times_int @ SX0 @ ( power_power_int @ SX0 @ ( minus_minus_nat @ SX1 @ one_one_nat ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2453]) ).
thf(3079,plain,
( ( ~ ! [SX0: int] :
( ( ( number_number_of_nat @ SX0 )
!= zero_zero_nat )
| ( ord_less_eq_int @ SX0 @ pls ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ SX0 @ pls )
| ( ( number_number_of_nat @ SX0 )
= zero_zero_nat ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2454]) ).
thf(3080,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( dvd_dvd_int @ SX1 @ SX0 )
| ( zcong @ SX0 @ zero_zero_int @ SX1 ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( zcong @ SX0 @ zero_zero_int @ SX1 )
| ( dvd_dvd_int @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2455]) ).
thf(3081,plain,
( ( ~ ! [SX0: nat,SX1: nat] :
( ( SX1 != zero_zero_nat )
| ( ( power_power_nat @ SX0 @ SX1 )
= one_one_nat ) )
| ~ ! [SX0: nat,SX1: 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 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2456]) ).
thf(3082,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ ( bit1 @ SX0 ) @ min )
| ( ord_less_int @ SX0 @ min ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_int @ SX0 @ min )
| ( ord_less_int @ ( bit1 @ SX0 ) @ min ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2457]) ).
thf(3083,plain,
! [SV443: nat] :
( ( ~ ( ~ ! [SY1911: nat,SY1912: int] :
( ~ ( ord_less_int @ one_one_int @ SY1912 )
| ~ ( ord_less_int @ ( power_power_int @ SY1912 @ SV443 ) @ ( power_power_int @ SY1912 @ SY1911 ) )
| ( ord_less_nat @ SV443 @ SY1911 ) )
| ~ ! [SY1913: nat,SY1914: int] :
( ~ ( ord_less_int @ one_one_int @ SY1914 )
| ~ ( ord_less_nat @ SV443 @ SY1913 )
| ( ord_less_int @ ( power_power_int @ SY1914 @ SV443 ) @ ( power_power_int @ SY1914 @ SY1913 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2458]) ).
thf(3084,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ ( bit1 @ SX0 ) @ zero_zero_int )
| ( ord_less_int @ SX0 @ zero_zero_int ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_int @ SX0 @ zero_zero_int )
| ( ord_less_int @ ( bit1 @ SX0 ) @ zero_zero_int ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2459]) ).
thf(3085,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ SX0 @ pls )
| ( ord_less_eq_real @ ( number267125858f_real @ SX0 ) @ zero_zero_real ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_eq_real @ ( number267125858f_real @ SX0 ) @ zero_zero_real )
| ( ord_less_eq_int @ SX0 @ pls ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2460]) ).
thf(3086,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ min @ ( bit0 @ SX0 ) )
| ( ord_less_int @ min @ SX0 ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_int @ min @ SX0 )
| ( ord_less_int @ min @ ( bit0 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2461]) ).
thf(3087,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ ( number_number_of_int @ SX0 ) @ ( number_number_of_int @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( number_number_of_int @ SX0 ) @ ( number_number_of_int @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2462]) ).
thf(3088,plain,
! [SV444: int] :
( ( ~ ( ~ ! [SY1915: int] :
( ! [SY1916: int] :
~ ( dvd_dvd_int @ SV444 @ ( plus_plus_int @ SY1915 @ ( times_times_int @ SV444 @ SY1916 ) ) )
| ( dvd_dvd_int @ SV444 @ SY1915 ) )
| ~ ! [SY1917: int] :
( ~ ( dvd_dvd_int @ SV444 @ SY1917 )
| ! [SY1918: int] : ( dvd_dvd_int @ SV444 @ ( plus_plus_int @ SY1917 @ ( times_times_int @ SV444 @ SY1918 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2463]) ).
thf(3089,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ SX0 @ ( minus_minus_int @ SX1 @ one_one_int ) )
| ( ord_less_int @ SX0 @ SX1 ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ SX0 @ ( minus_minus_int @ SX1 @ one_one_int ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2464]) ).
thf(3090,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2465]) ).
thf(3091,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ( ( number_number_of_nat @ SX1 )
= zero_zero_nat )
| ( SX0 != zero_zero_int )
| ( ( power_power_int @ SX0 @ ( number_number_of_nat @ SX1 ) )
= zero_zero_int ) )
| ~ ~ ( ~ ! [SX0: int,SX1: int] :
( ( ( power_power_int @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_int )
| ( ( number_number_of_nat @ SX1 )
!= zero_zero_nat ) )
| ~ ! [SX0: int] :
( ! [SX1: int] :
( ( power_power_int @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2466]) ).
thf(3092,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_real @ ( number267125858f_real @ SX0 ) @ ( number267125858f_real @ SX1 ) )
| ~ ( ord_less_real @ ( number267125858f_real @ SX1 ) @ ( number267125858f_real @ SX0 ) ) )
| ~ ! [SX0: int,SX1: int] :
( ( ord_less_real @ ( number267125858f_real @ SX1 ) @ ( number267125858f_real @ SX0 ) )
| ( ord_less_eq_real @ ( number267125858f_real @ SX0 ) @ ( number267125858f_real @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2467]) ).
thf(3093,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ ( minus_minus_int @ SX0 @ SX1 ) @ zero_zero_int ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ ( minus_minus_int @ SX0 @ SX1 ) @ zero_zero_int )
| ( ord_less_int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2468]) ).
thf(3094,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( 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 ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( 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 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2469]) ).
thf(3095,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ ( bit0 @ SX0 ) @ pls )
| ( ord_less_int @ SX0 @ pls ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_int @ SX0 @ pls )
| ( ord_less_int @ ( bit0 @ SX0 ) @ pls ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2470]) ).
thf(3096,plain,
( ( ~ ! [SX0: nat,SX1: nat] :
( ( SX1 != zero_zero_nat )
| ( ( times_times_nat @ SX1 @ SX0 )
= zero_zero_nat ) )
| ~ ! [SX0: nat,SX1: 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 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2471]) ).
thf(3097,plain,
( ( ~ ! [SX0: real,SX1: 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 ) )
| ~ ~ ( ~ ! [SX0: real] :
( ! [SX1: 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 )
| ( SX0 = zero_zero_real ) )
| ~ ! [SX0: real,SX1: 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 )
| ( SX1 = zero_zero_real ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2472]) ).
thf(3098,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ( SX0 != zero_zero_int )
| ( SX1 != zero_zero_int )
| ( ( 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 ) ) ) ) )
= zero_zero_int ) )
| ~ ~ ( ~ ! [SX0: int] :
( ! [SX1: int] :
( ( 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 ) ) ) ) )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) )
| ~ ! [SX0: int,SX1: int] :
( ( ( 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 ) ) ) ) )
!= zero_zero_int )
| ( SX1 = zero_zero_int ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2473]) ).
thf(3099,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( dvd_dvd_int @ SX1 @ SX0 )
| ( zcong @ SX0 @ zero_zero_int @ SX1 ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( zcong @ SX0 @ zero_zero_int @ SX1 )
| ( dvd_dvd_int @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2474]) ).
thf(3100,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2475]) ).
thf(3101,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ ( plus_plus_int @ SX0 @ SX0 ) @ zero_zero_int )
| ( ord_less_int @ SX0 @ zero_zero_int ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_int @ SX0 @ zero_zero_int )
| ( ord_less_int @ ( plus_plus_int @ SX0 @ SX0 ) @ zero_zero_int ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2476]) ).
thf(3102,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ one_one_int @ SX0 )
| ( ord_less_int @ zero_zero_int @ SX0 ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_int @ zero_zero_int @ SX0 )
| ( ord_less_eq_int @ one_one_int @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2477]) ).
thf(3103,plain,
! [SV445: real] :
( ( ~ ( ~ ! [SY1919: real,SY1920: real] :
( ~ ( ord_less_real @ zero_zero_real @ SY1920 )
| ~ ( ord_less_eq_real @ ( times_times_real @ SV445 @ SY1920 ) @ ( times_times_real @ SY1919 @ SY1920 ) )
| ( ord_less_eq_real @ SV445 @ SY1919 ) )
| ~ ! [SY1921: real,SY1922: real] :
( ~ ( ord_less_real @ zero_zero_real @ SY1922 )
| ~ ( ord_less_eq_real @ SV445 @ SY1921 )
| ( ord_less_eq_real @ ( times_times_real @ SV445 @ SY1922 ) @ ( times_times_real @ SY1921 @ SY1922 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2478]) ).
thf(3104,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ pls @ SX0 )
| ( ord_less_real @ zero_zero_real @ ( number267125858f_real @ SX0 ) ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_real @ zero_zero_real @ ( number267125858f_real @ SX0 ) )
| ( ord_less_int @ pls @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2479]) ).
thf(3105,plain,
( ( ~ ! [SX0: real,SX1: real] :
( ( SX0 != zero_zero_real )
| ( SX1 != zero_zero_real )
| ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ SX0 @ SX0 ) @ ( times_times_real @ SX1 @ SX1 ) ) @ zero_zero_real ) )
| ~ ~ ( ~ ! [SX0: real] :
( ! [SX1: real] :
~ ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ SX0 @ SX0 ) @ ( times_times_real @ SX1 @ SX1 ) ) @ zero_zero_real )
| ( SX0 = zero_zero_real ) )
| ~ ! [SX0: real,SX1: real] :
( ~ ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ SX0 @ SX0 ) @ ( times_times_real @ SX1 @ SX1 ) ) @ zero_zero_real )
| ( SX1 = zero_zero_real ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2480]) ).
thf(3106,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2481]) ).
thf(3107,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ zero_zero_int @ ( number_number_of_int @ SX0 ) )
| ( ord_less_int @ pls @ SX0 ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_int @ pls @ SX0 )
| ( ord_less_int @ zero_zero_int @ ( number_number_of_int @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2482]) ).
thf(3108,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ( SX0 != zero_zero_int )
| ( SX1 != zero_zero_int )
| ( ord_less_eq_int @ ( 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 ) ) ) ) ) @ zero_zero_int ) )
| ~ ~ ( ~ ! [SX0: int] :
( ! [SX1: int] :
~ ( ord_less_eq_int @ ( 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 ) ) ) ) ) @ zero_zero_int )
| ( SX0 = zero_zero_int ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ ( 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 ) ) ) ) ) @ zero_zero_int )
| ( SX1 = zero_zero_int ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2483]) ).
thf(3109,plain,
( ( ~ ! [SX0: int] :
( ( min
!= ( bit1 @ SX0 ) )
| ( min = SX0 ) )
| ~ ! [SX0: int] :
( ( min != SX0 )
| ( min
= ( bit1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2484]) ).
thf(3110,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ( SX0 != zero_zero_int )
| ( SX1 != zero_zero_int )
| ( ( plus_plus_int @ ( times_times_int @ SX0 @ SX0 ) @ ( times_times_int @ SX1 @ SX1 ) )
= zero_zero_int ) )
| ~ ~ ( ~ ! [SX0: int] :
( ! [SX1: int] :
( ( plus_plus_int @ ( times_times_int @ SX0 @ SX0 ) @ ( times_times_int @ SX1 @ SX1 ) )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) )
| ~ ! [SX0: int,SX1: int] :
( ( ( plus_plus_int @ ( times_times_int @ SX0 @ SX0 ) @ ( times_times_int @ SX1 @ SX1 ) )
!= zero_zero_int )
| ( SX1 = zero_zero_int ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2485]) ).
thf(3111,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ( SX0 = SX1 )
| ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_int @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2486]) ).
thf(3112,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ ( number_number_of_int @ SX0 ) @ zero_zero_int )
| ( ord_less_eq_int @ SX0 @ pls ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ SX0 @ pls )
| ( ord_less_eq_int @ ( number_number_of_int @ SX0 ) @ zero_zero_int ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2487]) ).
thf(3113,plain,
! [SV446: nat] :
( ( ~ ( ~ ! [SY1923: nat,SY1924: nat] :
( ~ ( ord_less_nat @ one_one_nat @ SY1924 )
| ~ ( ord_less_nat @ ( power_power_nat @ SY1924 @ SV446 ) @ ( power_power_nat @ SY1924 @ SY1923 ) )
| ( ord_less_nat @ SV446 @ SY1923 ) )
| ~ ! [SY1925: nat,SY1926: nat] :
( ~ ( ord_less_nat @ one_one_nat @ SY1926 )
| ~ ( ord_less_nat @ SV446 @ SY1925 )
| ( ord_less_nat @ ( power_power_nat @ SY1926 @ SV446 ) @ ( power_power_nat @ SY1926 @ SY1925 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2488]) ).
thf(3114,plain,
( ( ~ ! [SX0: nat,SX1: nat] :
( ( SX0 != one_one_nat )
| ( SX1 != one_one_nat )
| ( ( times_times_nat @ SX0 @ SX1 )
= one_one_nat ) )
| ~ ~ ( ~ ! [SX0: nat] :
( ! [SX1: nat] :
( ( times_times_nat @ SX0 @ SX1 )
!= one_one_nat )
| ( SX0 = one_one_nat ) )
| ~ ! [SX0: nat,SX1: nat] :
( ( ( times_times_nat @ SX0 @ SX1 )
!= one_one_nat )
| ( SX1 = one_one_nat ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2489]) ).
thf(3115,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: int] :
( ! [SX1: int] :
( ( times_times_int @ SX0 @ SX1 )
!= one_one_int )
| ( SX0 = one_one_int )
| ( SX0
= ( number_number_of_int @ min ) ) )
| ~ ! [SX0: int,SX1: int] :
( ( ( times_times_int @ SX0 @ SX1 )
!= one_one_int )
| ( SX0 = one_one_int )
| ( SX1
= ( number_number_of_int @ min ) ) ) )
| ~ ~ ( ~ ! [SX0: int,SX1: int] :
( ( ( times_times_int @ SX0 @ SX1 )
!= one_one_int )
| ( SX1 = one_one_int )
| ( SX0
= ( number_number_of_int @ min ) ) )
| ~ ! [SX0: int,SX1: int] :
( ( ( times_times_int @ SX0 @ SX1 )
!= one_one_int )
| ( SX1 = one_one_int )
| ( SX1
= ( number_number_of_int @ min ) ) ) ) )
| ~ ~ ( ~ ! [SX0: int,SX1: int] :
( ( SX0 != one_one_int )
| ( SX1 != one_one_int )
| ( ( times_times_int @ SX0 @ SX1 )
= one_one_int ) )
| ~ ! [SX0: int,SX1: int] :
( ( SX0
!= ( number_number_of_int @ min ) )
| ( SX1
!= ( number_number_of_int @ min ) )
| ( ( times_times_int @ SX0 @ SX1 )
= one_one_int ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2490]) ).
thf(3116,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ SX0 @ ( bit1 @ pls ) )
| ( ord_less_real @ ( number267125858f_real @ SX0 ) @ one_one_real ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_real @ ( number267125858f_real @ SX0 ) @ one_one_real )
| ( ord_less_int @ SX0 @ ( bit1 @ pls ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2491]) ).
thf(3117,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ( ( number_number_of_int @ SX0 )
!= SX1 )
| ( SX1
= ( number_number_of_int @ SX0 ) ) )
| ~ ! [SX0: int,SX1: int] :
( ( SX1
!= ( number_number_of_int @ SX0 ) )
| ( ( number_number_of_int @ SX0 )
= SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2492]) ).
thf(3118,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_int @ SX0 @ ( plus_plus_int @ SX1 @ one_one_int ) ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ ( plus_plus_int @ SX1 @ one_one_int ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2493]) ).
thf(3119,plain,
( ( ~ ! [SX0: real,SX1: 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 ) )
| ~ ~ ( ~ ! [SX0: real] :
( ! [SX1: real] :
( ( plus_plus_real @ ( times_times_real @ SX0 @ SX0 ) @ ( times_times_real @ SX1 @ SX1 ) )
!= zero_zero_real )
| ( SX0 = zero_zero_real ) )
| ~ ! [SX0: real,SX1: real] :
( ( ( plus_plus_real @ ( times_times_real @ SX0 @ SX0 ) @ ( times_times_real @ SX1 @ SX1 ) )
!= zero_zero_real )
| ( SX1 = zero_zero_real ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2494]) ).
thf(3120,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ ( bit1 @ SX0 ) @ pls )
| ( ord_less_int @ SX0 @ pls ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_int @ SX0 @ pls )
| ( ord_less_eq_int @ ( bit1 @ SX0 ) @ pls ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2495]) ).
thf(3121,plain,
! [SV447: nat] :
( ( ~ ( ~ ! [SY1927: nat,SY1928: real] :
( ~ ( ord_less_real @ one_one_real @ SY1928 )
| ~ ( ord_less_nat @ SV447 @ SY1927 )
| ( ord_less_real @ ( power_power_real @ SY1928 @ SV447 ) @ ( power_power_real @ SY1928 @ SY1927 ) ) )
| ~ ! [SY1929: nat,SY1930: real] :
( ~ ( ord_less_real @ one_one_real @ SY1930 )
| ~ ( ord_less_real @ ( power_power_real @ SY1930 @ SV447 ) @ ( power_power_real @ SY1930 @ SY1929 ) )
| ( ord_less_nat @ SV447 @ SY1929 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2496]) ).
thf(3122,plain,
( ( ~ ! [SX0: int] :
( ( ( bit0 @ SX0 )
!= pls )
| ( SX0 = pls ) )
| ~ ! [SX0: int] :
( ( SX0 != pls )
| ( ( bit0 @ SX0 )
= pls ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2497]) ).
thf(3123,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ SX0 @ SX0 ) @ ( times_times_int @ SX1 @ SX1 ) ) )
| ( SX0 != zero_zero_int )
| ( SX1 != zero_zero_int ) )
| ~ ~ ( ~ ! [SX0: int] :
( ( SX0 = zero_zero_int )
| ! [SX1: int] : ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ SX0 @ SX0 ) @ ( times_times_int @ SX1 @ SX1 ) ) ) )
| ~ ! [SX0: int,SX1: int] :
( ( SX1 = zero_zero_int )
| ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ SX0 @ SX0 ) @ ( times_times_int @ SX1 @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2498]) ).
thf(3124,plain,
( ( ~ ! [SX0: int,SX1: nat] :
( ( ( number_number_of_nat @ SX0 )
!= SX1 )
| ( SX1
= ( number_number_of_nat @ SX0 ) ) )
| ~ ! [SX0: int,SX1: nat] :
( ( SX1
!= ( number_number_of_nat @ SX0 ) )
| ( ( number_number_of_nat @ SX0 )
= SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2499]) ).
thf(3125,plain,
( ( ~ ! [SX0: real] :
( ( SX0 != zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ ( times_times_real @ SX0 @ SX0 ) ) )
| ~ ! [SX0: real] :
( ( ord_less_real @ zero_zero_real @ ( times_times_real @ SX0 @ SX0 ) )
| ( SX0 = zero_zero_real ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2500]) ).
thf(3126,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ ( number_number_of_int @ SX0 ) @ one_one_int )
| ( ord_less_int @ SX0 @ ( bit1 @ pls ) ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_int @ SX0 @ ( bit1 @ pls ) )
| ( ord_less_int @ ( number_number_of_int @ SX0 ) @ one_one_int ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2501]) ).
thf(3127,plain,
! [SV448: real] :
( ( ~ ( ~ ! [SY1931: real,SY1932: real] :
( ( SY1932 = zero_zero_real )
| ( ( times_times_real @ SY1932 @ SV448 )
!= ( times_times_real @ SY1932 @ SY1931 ) )
| ( SV448 = SY1931 ) )
| ~ ! [SY1933: real,SY1934: real] :
( ( SY1934 = zero_zero_real )
| ( SV448 != SY1933 )
| ( ( times_times_real @ SY1934 @ SV448 )
= ( times_times_real @ SY1934 @ SY1933 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2502]) ).
thf(3128,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2503]) ).
thf(3129,plain,
( ( ~ ! [SX0: int] :
( ( pls
!= ( bit0 @ SX0 ) )
| ( pls = SX0 ) )
| ~ ! [SX0: int] :
( ( pls != SX0 )
| ( pls
= ( bit0 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2504]) ).
thf(3130,plain,
( ( ~ ~ ( ~ ! [SX0: int,SX1: int] :
( ( ord_less_int @ SX0 @ SX1 )
| ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_nat @ ( number_number_of_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ pls @ SX1 )
| ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_nat @ ( number_number_of_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) ) ) )
| ~ ~ ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_nat @ ( number_number_of_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) )
| ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ pls @ SX1 ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_nat @ ( number_number_of_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2505]) ).
thf(3131,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2506]) ).
thf(3132,plain,
! [SV449: int] :
( ( ! [SY1935: int,SY1936: int] :
~ ( ~ ! [SY1937: int,SY1938: int] :
( ~ ( zcong @ SY1936 @ SY1937 @ SY1938 )
| ~ ( zcong @ SV449 @ ( times_times_int @ SY1936 @ SY1935 ) @ SY1938 )
| ( zcong @ SV449 @ ( times_times_int @ SY1937 @ SY1935 ) @ SY1938 ) )
| ~ ! [SY1939: int,SY1940: int] :
( ~ ( zcong @ SY1936 @ SY1939 @ SY1940 )
| ~ ( zcong @ SV449 @ ( times_times_int @ SY1939 @ SY1935 ) @ SY1940 )
| ( zcong @ SV449 @ ( times_times_int @ SY1936 @ SY1935 ) @ SY1940 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2507]) ).
thf(3133,plain,
( ( ~ ! [SX0: real,SX1: nat] :
( ( SX1 != zero_zero_nat )
| ( ( power_power_real @ SX0 @ SX1 )
= one_one_real ) )
| ~ ! [SX0: real,SX1: nat] :
( ( SX1 = zero_zero_nat )
| ( ( power_power_real @ SX0 @ SX1 )
= ( times_times_real @ SX0 @ ( power_power_real @ SX0 @ ( minus_minus_nat @ SX1 @ one_one_nat ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2508]) ).
thf(3134,plain,
! [SV450: int] :
( ( ! [SY1941: int] :
~ ( ~ ~ ( ~ ! [SY1942: int,SY1943: int] :
( ( ( plus_plus_int @ ( times_times_int @ SY1942 @ SV450 ) @ ( times_times_int @ SY1943 @ SY1941 ) )
= ( plus_plus_int @ ( times_times_int @ SY1942 @ SY1941 ) @ ( times_times_int @ SY1943 @ SV450 ) ) )
| ( SY1942 != SY1943 ) )
| ~ ( ! [SY1944: int,SY1945: int] :
( ( plus_plus_int @ ( times_times_int @ SY1944 @ SV450 ) @ ( times_times_int @ SY1945 @ SY1941 ) )
= ( plus_plus_int @ ( times_times_int @ SY1944 @ SY1941 ) @ ( times_times_int @ SY1945 @ SV450 ) ) )
| ( SV450 != SY1941 ) ) )
| ~ ! [SY1946: int,SY1947: int] :
( ( SY1946 = SY1947 )
| ( SV450 = SY1941 )
| ( ( plus_plus_int @ ( times_times_int @ SY1946 @ SV450 ) @ ( times_times_int @ SY1947 @ SY1941 ) )
!= ( plus_plus_int @ ( times_times_int @ SY1946 @ SY1941 ) @ ( times_times_int @ SY1947 @ SV450 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2509]) ).
thf(3135,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2510]) ).
thf(3136,plain,
( ( ~ ! [SX0: int] :
( ( SX0 = zero_zero_int )
| ( ord_less_int @ zero_zero_int @ ( power_power_int @ SX0 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_int @ zero_zero_int @ ( power_power_int @ SX0 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ( SX0 != zero_zero_int ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2511]) ).
thf(3137,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ SX0 @ pls )
| ( ord_less_real @ ( number267125858f_real @ SX0 ) @ zero_zero_real ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_real @ ( number267125858f_real @ SX0 ) @ zero_zero_real )
| ( ord_less_int @ SX0 @ pls ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2512]) ).
thf(3138,plain,
( ( ~ ! [SX0: real,SX1: 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 ) )
| ~ ~ ( ~ ! [SX0: real] :
( ! [SX1: real] :
( ( plus_plus_real @ ( times_times_real @ SX0 @ SX0 ) @ ( times_times_real @ SX1 @ SX1 ) )
!= zero_zero_real )
| ( SX0 = zero_zero_real ) )
| ~ ! [SX0: real,SX1: real] :
( ( ( plus_plus_real @ ( times_times_real @ SX0 @ SX0 ) @ ( times_times_real @ SX1 @ SX1 ) )
!= zero_zero_real )
| ( SX1 = zero_zero_real ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2513]) ).
thf(3139,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ ( bit1 @ pls ) @ SX0 )
| ( ord_less_eq_real @ one_one_real @ ( number267125858f_real @ SX0 ) ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_eq_real @ one_one_real @ ( number267125858f_real @ SX0 ) )
| ( ord_less_eq_int @ ( bit1 @ pls ) @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2514]) ).
thf(3140,plain,
! [SV451: int] :
( ( ! [SY1948: int,SY1949: int] :
~ ( ~ ! [SY1950: int,SY1951: int] :
( ~ ( zcong @ SY1949 @ SY1950 @ SY1951 )
| ~ ( zcong @ SV451 @ ( times_times_int @ SY1948 @ SY1949 ) @ SY1951 )
| ( zcong @ SV451 @ ( times_times_int @ SY1948 @ SY1950 ) @ SY1951 ) )
| ~ ! [SY1952: int,SY1953: int] :
( ~ ( zcong @ SY1949 @ SY1952 @ SY1953 )
| ~ ( zcong @ SV451 @ ( times_times_int @ SY1948 @ SY1952 ) @ SY1953 )
| ( zcong @ SV451 @ ( times_times_int @ SY1948 @ SY1949 ) @ SY1953 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2515]) ).
thf(3141,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ ( bit1 @ SX0 ) @ min )
| ( ord_less_eq_int @ SX0 @ min ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ SX0 @ min )
| ( ord_less_eq_int @ ( bit1 @ SX0 ) @ min ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2516]) ).
thf(3142,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2517]) ).
thf(3143,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ( SX0 != SX1 )
| ( zcong @ SX0 @ SX1 @ zero_zero_int ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( zcong @ SX0 @ SX1 @ zero_zero_int )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2518]) ).
thf(3144,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2519]) ).
thf(3145,plain,
! [SV452: nat] :
( ( ! [SY1954: nat] :
~ ( ~ ! [SY1955: nat,SY1956: nat] :
( ( ( plus_plus_nat @ ( times_times_nat @ SV452 @ SY1954 ) @ ( times_times_nat @ SY1955 @ SY1956 ) )
!= ( plus_plus_nat @ ( times_times_nat @ SV452 @ SY1956 ) @ ( times_times_nat @ SY1955 @ SY1954 ) ) )
| ( SV452 = SY1955 )
| ( SY1954 = SY1956 ) )
| ~ ~ ( ~ ! [SY1957: nat] :
( ( SV452 != SY1957 )
| ! [SY1958: nat] :
( ( plus_plus_nat @ ( times_times_nat @ SV452 @ SY1954 ) @ ( times_times_nat @ SY1957 @ SY1958 ) )
= ( plus_plus_nat @ ( times_times_nat @ SV452 @ SY1958 ) @ ( times_times_nat @ SY1957 @ SY1954 ) ) ) )
| ~ ! [SY1959: nat,SY1960: nat] :
( ( SY1954 != SY1960 )
| ( ( plus_plus_nat @ ( times_times_nat @ SV452 @ SY1954 ) @ ( times_times_nat @ SY1959 @ SY1960 ) )
= ( plus_plus_nat @ ( times_times_nat @ SV452 @ SY1960 ) @ ( times_times_nat @ SY1959 @ SY1954 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2520]) ).
thf(3146,plain,
( ( ~ ! [SX0: real,SX1: nat] :
( ( SX1 = zero_zero_nat )
| ( SX0 != zero_zero_real )
| ( ( power_power_real @ SX0 @ SX1 )
= zero_zero_real ) )
| ~ ~ ( ~ ! [SX0: real,SX1: nat] :
( ( ( power_power_real @ SX0 @ SX1 )
!= zero_zero_real )
| ( SX1 != zero_zero_nat ) )
| ~ ! [SX0: real] :
( ! [SX1: nat] :
( ( power_power_real @ SX0 @ SX1 )
!= zero_zero_real )
| ( SX0 = zero_zero_real ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2521]) ).
thf(3147,plain,
( ( ~ ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SX0 @ SX1 ) )
| ( SX1 = zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SX0 ) )
| ~ ~ ( ~ ! [SX0: nat,SX1: nat] :
( ( SX1 != zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SX0 @ SX1 ) ) )
| ~ ! [SX0: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SX0 )
| ! [SX1: nat] : ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SX0 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2522]) ).
thf(3148,plain,
! [SV453: int] :
( ( ! [SY1961: int] :
~ ( ~ ! [SY1962: int,SY1963: int] :
( ( ( plus_plus_int @ ( times_times_int @ SV453 @ SY1961 ) @ ( times_times_int @ SY1962 @ SY1963 ) )
!= ( plus_plus_int @ ( times_times_int @ SV453 @ SY1963 ) @ ( times_times_int @ SY1962 @ SY1961 ) ) )
| ( SV453 = SY1962 )
| ( SY1961 = SY1963 ) )
| ~ ~ ( ~ ! [SY1964: int] :
( ( SV453 != SY1964 )
| ! [SY1965: int] :
( ( plus_plus_int @ ( times_times_int @ SV453 @ SY1961 ) @ ( times_times_int @ SY1964 @ SY1965 ) )
= ( plus_plus_int @ ( times_times_int @ SV453 @ SY1965 ) @ ( times_times_int @ SY1964 @ SY1961 ) ) ) )
| ~ ! [SY1966: int,SY1967: int] :
( ( SY1961 != SY1967 )
| ( ( plus_plus_int @ ( times_times_int @ SV453 @ SY1961 ) @ ( times_times_int @ SY1966 @ SY1967 ) )
= ( plus_plus_int @ ( times_times_int @ SV453 @ SY1967 ) @ ( times_times_int @ SY1966 @ SY1961 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2523]) ).
thf(3149,plain,
( ( ~ ! [SX0: nat,SX1: nat] :
( ( SX1 != zero_zero_nat )
| ( ( power_power_nat @ SX0 @ SX1 )
= one_one_nat ) )
| ~ ! [SX0: nat,SX1: 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 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2524]) ).
thf(3150,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ zero_zero_int @ SX1 )
| ( SX1 != one_one_int )
| ( SX0 != one_one_int )
| ( ( times_times_int @ SX1 @ SX0 )
= one_one_int ) )
| ~ ~ ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ zero_zero_int @ SX1 )
| ( ( times_times_int @ SX1 @ SX0 )
!= one_one_int )
| ( SX1 = one_one_int ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ zero_zero_int @ SX1 )
| ( ( times_times_int @ SX1 @ SX0 )
!= one_one_int )
| ( SX0 = one_one_int ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2525]) ).
thf(3151,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ ( plus_plus_int @ SX0 @ one_one_int ) @ SX1 )
| ( ord_less_int @ SX0 @ SX1 ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( plus_plus_int @ SX0 @ one_one_int ) @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2526]) ).
thf(3152,plain,
( ( ~ ! [SX0: int] :
( ( ( number_number_of_nat @ SX0 )
!= zero_zero_nat )
| ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ SX0 ) )
= one_one_nat ) )
| ~ ! [SX0: int] :
( ( ( number_number_of_nat @ SX0 )
= zero_zero_nat )
| ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ SX0 ) )
= zero_zero_nat ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2527]) ).
thf(3153,plain,
( ( ~ ! [SX0: real,SX1: real] :
( ( SX0 = SX1 )
| ~ ( ord_less_eq_real @ SX0 @ SX1 )
| ( ord_less_real @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: real,SX1: real] :
( ~ ( ord_less_real @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: real,SX1: real] :
( ~ ( ord_less_real @ SX0 @ SX1 )
| ( ord_less_eq_real @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2528]) ).
thf(3154,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_real @ ( number267125858f_real @ SX0 ) @ ( number267125858f_real @ SX1 ) ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_real @ ( number267125858f_real @ SX0 ) @ ( number267125858f_real @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2529]) ).
thf(3155,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ ( number_number_of_int @ SX0 ) @ ( number_number_of_int @ SX1 ) )
| ~ ( ord_less_int @ ( number_number_of_int @ SX1 ) @ ( number_number_of_int @ SX0 ) ) )
| ~ ! [SX0: int,SX1: int] :
( ( ord_less_int @ ( number_number_of_int @ SX1 ) @ ( number_number_of_int @ SX0 ) )
| ( ord_less_eq_int @ ( number_number_of_int @ SX0 ) @ ( number_number_of_int @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2530]) ).
thf(3156,plain,
( ( ~ ! [SX0: int] :
( ( ( plus_plus_int @ SX0 @ SX0 )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) )
| ~ ! [SX0: int] :
( ( SX0 != zero_zero_int )
| ( ( plus_plus_int @ SX0 @ SX0 )
= zero_zero_int ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2531]) ).
thf(3157,plain,
( ( ~ ! [SX0: nat,SX1: int] :
( ~ ( 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 ) )
| ~ ~ ( ~ ! [SX0: nat,SX1: int] :
( ( ( number_number_of_nat @ SX1 )
!= zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SX0 @ ( number_number_of_nat @ SX1 ) ) ) )
| ~ ! [SX0: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SX0 )
| ! [SX1: int] : ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SX0 @ ( number_number_of_nat @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2532]) ).
thf(3158,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ SX0 @ ( bit1 @ pls ) )
| ( ord_less_eq_real @ ( number267125858f_real @ SX0 ) @ one_one_real ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_eq_real @ ( number267125858f_real @ SX0 ) @ one_one_real )
| ( ord_less_eq_int @ SX0 @ ( bit1 @ pls ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2533]) ).
thf(3159,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX1 @ pls )
| ( ( times_times_nat @ ( number_number_of_nat @ SX1 ) @ ( number_number_of_nat @ SX0 ) )
= zero_zero_nat ) )
| ~ ! [SX0: int,SX1: int] :
( ( 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 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2534]) ).
thf(3160,plain,
( ( ~ ! [SX0: real] :
( ( SX0 = zero_zero_real )
| ( ord_less_real @ zero_zero_real @ ( power_power_real @ SX0 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
| ~ ! [SX0: real] :
( ~ ( ord_less_real @ zero_zero_real @ ( power_power_real @ SX0 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ( SX0 != zero_zero_real ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2535]) ).
thf(3161,plain,
( ( ~ ! [SX0: int] :
( ~ ( ~ ~ ( ~ ( dvd_dvd_int @ ( sK3_M_9 @ SX0 ) @ SX0 )
| ~ ( ord_less_eq_int @ zero_zero_int @ ( sK3_M_9 @ SX0 ) ) )
| ~ ~ ( ~ ( ( ( sK3_M_9 @ SX0 )
!= one_one_int ) )
| ~ ( ( ( sK3_M_9 @ SX0 )
!= SX0 ) ) ) )
| ~ ( ord_less_int @ one_one_int @ SX0 )
| ( zprime @ SX0 ) )
| ~ ~ ( ~ ! [SX0: int] :
( ~ ( zprime @ SX0 )
| ! [SX1: int] :
( ~ ( dvd_dvd_int @ SX1 @ SX0 )
| ~ ( ord_less_eq_int @ zero_zero_int @ SX1 )
| ( SX1 = one_one_int )
| ( SX1 = SX0 ) ) )
| ~ ! [SX0: int] :
( ~ ( zprime @ SX0 )
| ( ord_less_int @ one_one_int @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2536]) ).
thf(3162,plain,
! [SV454: int] :
( ( ~ ( ~ ! [SY1968: nat,SY1969: int] :
( ~ ( ord_less_int @ SY1969 @ pls )
| ( ( times_times_nat @ ( number_number_of_nat @ SY1969 ) @ ( times_times_nat @ ( number_number_of_nat @ SV454 ) @ SY1968 ) )
= zero_zero_nat ) )
| ~ ! [SY1970: nat,SY1971: int] :
( ( ord_less_int @ SY1971 @ pls )
| ( ( times_times_nat @ ( number_number_of_nat @ SY1971 ) @ ( times_times_nat @ ( number_number_of_nat @ SV454 ) @ SY1970 ) )
= ( times_times_nat @ ( number_number_of_nat @ ( times_times_int @ SY1971 @ SV454 ) ) @ SY1970 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2537]) ).
thf(3163,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( zcong @ SX0 @ zero_zero_int @ SX1 )
| ( ( legendre @ SX0 @ SX1 )
= zero_zero_int ) )
| ~ ~ ( ~ ! [SX0: int,SX1: int] :
( ( zcong @ SX0 @ zero_zero_int @ SX1 )
| ~ ( quadRes @ SX1 @ SX0 )
| ( ( legendre @ SX0 @ SX1 )
= one_one_int ) )
| ~ ! [SX0: int,SX1: int] :
( ( zcong @ SX0 @ zero_zero_int @ SX1 )
| ( quadRes @ SX1 @ SX0 )
| ( ( legendre @ SX0 @ SX1 )
= ( number_number_of_int @ min ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2538]) ).
thf(3164,plain,
( ( ~ ! [SX0: nat] :
( ( SX0 != zero_zero_nat )
| ( ( power_power_int @ zero_zero_int @ SX0 )
= one_one_int ) )
| ~ ! [SX0: nat] :
( ( SX0 = zero_zero_nat )
| ( ( power_power_int @ zero_zero_int @ SX0 )
= zero_zero_int ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2539]) ).
thf(3165,plain,
! [SV455: real] :
( ( ! [SY1972: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SY1972 )
| ~ ( ord_less_real @ zero_zero_real @ SV455 )
| ~ ( ~ ! [SY1973: real] :
( ( ( power_power_real @ SY1973 @ SY1972 )
!= SV455 )
| ~ ( ord_less_real @ zero_zero_real @ SY1973 )
| ( SY1973
= ( sK1_X_1 @ SY1972 @ SV455 ) ) )
| ~ ~ ( ( ( power_power_real @ ( sK1_X_1 @ SY1972 @ SV455 ) @ SY1972 )
!= SV455 )
| ~ ( ord_less_real @ zero_zero_real @ ( sK1_X_1 @ SY1972 @ SV455 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2540]) ).
thf(3166,plain,
( ( ~ ! [SX0: int] :
( ( zero_zero_nat
!= ( number_number_of_nat @ SX0 ) )
| ( ord_less_eq_int @ SX0 @ pls ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ SX0 @ pls )
| ( zero_zero_nat
= ( number_number_of_nat @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2541]) ).
thf(3167,plain,
( ( ~ ~ ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_eq_nat @ ( number_number_of_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ SX0 @ pls )
| ! [SX1: int] : ( ord_less_eq_nat @ ( number_number_of_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) ) ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( 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 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2542]) ).
thf(3168,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ ( number_number_of_int @ SX0 ) @ zero_zero_int )
| ( ord_less_int @ SX0 @ pls ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_int @ SX0 @ pls )
| ( ord_less_int @ ( number_number_of_int @ SX0 ) @ zero_zero_int ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2543]) ).
thf(3169,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ one_one_int @ ( number_number_of_int @ SX0 ) )
| ( ord_less_eq_int @ ( bit1 @ pls ) @ SX0 ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ ( bit1 @ pls ) @ SX0 )
| ( ord_less_eq_int @ one_one_int @ ( number_number_of_int @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2544]) ).
thf(3170,plain,
( ( ~ ! [SX0: int,SX1: real] :
( ( ( number267125858f_real @ SX0 )
!= SX1 )
| ( SX1
= ( number267125858f_real @ SX0 ) ) )
| ~ ! [SX0: int,SX1: real] :
( ( SX1
!= ( number267125858f_real @ SX0 ) )
| ( ( number267125858f_real @ SX0 )
= SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2545]) ).
thf(3171,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ SX0 ) @ SX0 ) @ zero_zero_int )
| ( ord_less_int @ SX0 @ zero_zero_int ) )
| ~ ! [SX0: 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 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2546]) ).
thf(3172,plain,
! [SV456: int] :
( ( ~ ( ~ ! [SY1974: int,SY1975: int] :
( ~ ( zcong @ SV456 @ SY1974 @ SY1975 )
| ( zcong @ SY1974 @ SV456 @ SY1975 ) )
| ~ ! [SY1976: int,SY1977: int] :
( ~ ( zcong @ SY1976 @ SV456 @ SY1977 )
| ( zcong @ SV456 @ SY1976 @ SY1977 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2547]) ).
thf(3173,plain,
! [SV457: int] :
( ( ! [SY1978: int,SY1979: int] :
~ ( ~ ! [SY1980: int,SY1981: int] :
( ~ ( dvd_dvd_int @ SY1980 @ SY1981 )
| ~ ( dvd_dvd_int @ SY1980 @ ( plus_plus_int @ SY1978 @ SY1979 ) )
| ( dvd_dvd_int @ SY1980 @ ( plus_plus_int @ ( plus_plus_int @ SY1978 @ ( times_times_int @ SV457 @ SY1981 ) ) @ SY1979 ) ) )
| ~ ! [SY1982: int,SY1983: int] :
( ~ ( dvd_dvd_int @ SY1982 @ SY1983 )
| ~ ( dvd_dvd_int @ SY1982 @ ( plus_plus_int @ ( plus_plus_int @ SY1978 @ ( times_times_int @ SV457 @ SY1983 ) ) @ SY1979 ) )
| ( dvd_dvd_int @ SY1982 @ ( plus_plus_int @ SY1978 @ SY1979 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2548]) ).
thf(3174,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ ( bit1 @ pls ) @ SX0 )
| ( ord_less_real @ one_one_real @ ( number267125858f_real @ SX0 ) ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_real @ one_one_real @ ( number267125858f_real @ SX0 ) )
| ( ord_less_int @ ( bit1 @ pls ) @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2549]) ).
thf(3175,plain,
( ( ~ ! [SX0: real,SX1: real] :
( ( SX0
!= ( plus_plus_real @ SX0 @ SX1 ) )
| ( SX1 = zero_zero_real ) )
| ~ ! [SX0: real,SX1: real] :
( ( SX1 != zero_zero_real )
| ( SX0
= ( plus_plus_real @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2550]) ).
thf(3176,plain,
! [SV458: int] :
( ( ~ ( ~ ! [SY1984: int,SY1985: int] :
( ! [SY1986: int] :
( SY1984
!= ( plus_plus_int @ SV458 @ ( times_times_int @ SY1985 @ SY1986 ) ) )
| ( zcong @ SV458 @ SY1984 @ SY1985 ) )
| ~ ! [SY1987: int,SY1988: int] :
( ~ ( zcong @ SV458 @ SY1987 @ SY1988 )
| ( SY1987
= ( plus_plus_int @ SV458 @ ( times_times_int @ SY1988 @ ( sK6_K_1 @ SY1988 @ SY1987 @ SV458 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2551]) ).
thf(3177,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ pls @ ( bit0 @ SX0 ) )
| ( ord_less_eq_int @ pls @ SX0 ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ pls @ SX0 )
| ( ord_less_eq_int @ pls @ ( bit0 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2552]) ).
thf(3178,plain,
! [SV459: nat] :
( ( ~ ( ~ ! [SY1989: nat,SY1990: nat] :
( ~ ( ord_less_nat @ one_one_nat @ SY1990 )
| ( ( power_power_nat @ SY1990 @ SV459 )
!= ( power_power_nat @ SY1990 @ SY1989 ) )
| ( SV459 = SY1989 ) )
| ~ ! [SY1991: nat,SY1992: nat] :
( ~ ( ord_less_nat @ one_one_nat @ SY1992 )
| ( SV459 != SY1991 )
| ( ( power_power_nat @ SY1992 @ SV459 )
= ( power_power_nat @ SY1992 @ SY1991 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2553]) ).
thf(3179,plain,
! [SV460: real] :
( ( ! [SY1993: real] :
~ ( ~ ! [SY1994: real,SY1995: real] :
( ( ( plus_plus_real @ ( times_times_real @ SV460 @ SY1993 ) @ ( times_times_real @ SY1994 @ SY1995 ) )
!= ( plus_plus_real @ ( times_times_real @ SV460 @ SY1995 ) @ ( times_times_real @ SY1994 @ SY1993 ) ) )
| ( SV460 = SY1994 )
| ( SY1993 = SY1995 ) )
| ~ ~ ( ~ ! [SY1996: real] :
( ( SV460 != SY1996 )
| ! [SY1997: real] :
( ( plus_plus_real @ ( times_times_real @ SV460 @ SY1993 ) @ ( times_times_real @ SY1996 @ SY1997 ) )
= ( plus_plus_real @ ( times_times_real @ SV460 @ SY1997 ) @ ( times_times_real @ SY1996 @ SY1993 ) ) ) )
| ~ ! [SY1998: real,SY1999: real] :
( ( SY1993 != SY1999 )
| ( ( plus_plus_real @ ( times_times_real @ SV460 @ SY1993 ) @ ( times_times_real @ SY1998 @ SY1999 ) )
= ( plus_plus_real @ ( times_times_real @ SV460 @ SY1999 ) @ ( times_times_real @ SY1998 @ SY1993 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2554]) ).
thf(3180,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ ( bit1 @ SX0 ) @ pls )
| ( ord_less_int @ SX0 @ pls ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_int @ SX0 @ pls )
| ( ord_less_int @ ( bit1 @ SX0 ) @ pls ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2555]) ).
thf(3181,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ SX0 ) )
| ( ord_less_eq_int @ pls @ SX0 ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ pls @ SX0 )
| ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2556]) ).
thf(3182,plain,
! [SV461: nat] :
( ( ~ ( ~ ! [SY2000: nat,SY2001: nat] :
( ~ ( dvd_dvd_nat @ ( times_times_nat @ SV461 @ SY2000 ) @ ( times_times_nat @ SY2001 @ SY2000 ) )
| ( SY2000 = zero_zero_nat )
| ( dvd_dvd_nat @ SV461 @ SY2001 ) )
| ~ ~ ( ~ ! [SY2002: nat] :
( ( SY2002 != zero_zero_nat )
| ! [SY2003: nat] : ( dvd_dvd_nat @ ( times_times_nat @ SV461 @ SY2002 ) @ ( times_times_nat @ SY2003 @ SY2002 ) ) )
| ~ ! [SY2004: nat,SY2005: nat] :
( ~ ( dvd_dvd_nat @ SV461 @ SY2005 )
| ( dvd_dvd_nat @ ( times_times_nat @ SV461 @ SY2004 ) @ ( times_times_nat @ SY2005 @ SY2004 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2557]) ).
thf(3183,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ( ( number267125858f_real @ SX0 )
!= ( number267125858f_real @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: int,SX1: int] :
( ( SX0 != SX1 )
| ( ( number267125858f_real @ SX0 )
= ( number267125858f_real @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2558]) ).
thf(3184,plain,
( ( ~ ! [SX0: nat] :
( ( SX0 != zero_zero_nat )
| ( ( power_power_nat @ zero_zero_nat @ SX0 )
= one_one_nat ) )
| ~ ! [SX0: nat] :
( ( SX0 = zero_zero_nat )
| ( ( power_power_nat @ zero_zero_nat @ SX0 )
= zero_zero_nat ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2559]) ).
thf(3185,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ ( bit0 @ SX0 ) @ min )
| ( ord_less_eq_int @ SX0 @ min ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ SX0 @ min )
| ( ord_less_eq_int @ ( bit0 @ SX0 ) @ min ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2560]) ).
thf(3186,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2561]) ).
thf(3187,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2562]) ).
thf(3188,plain,
( ( ~ ! [SX0: nat,SX1: nat] :
( ( SX0
!= ( plus_plus_nat @ SX0 @ SX1 ) )
| ( SX1 = zero_zero_nat ) )
| ~ ! [SX0: nat,SX1: nat] :
( ( SX1 != zero_zero_nat )
| ( SX0
= ( plus_plus_nat @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2563]) ).
thf(3189,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2564]) ).
thf(3190,plain,
( ( ~ ! [SX0: nat,SX1: nat] :
( ( SX1 = zero_zero_nat )
| ( SX0 != zero_zero_nat )
| ( ( power_power_nat @ SX0 @ SX1 )
= zero_zero_nat ) )
| ~ ~ ( ~ ! [SX0: nat,SX1: nat] :
( ( ( power_power_nat @ SX0 @ SX1 )
!= zero_zero_nat )
| ( SX1 != zero_zero_nat ) )
| ~ ! [SX0: nat] :
( ! [SX1: nat] :
( ( power_power_nat @ SX0 @ SX1 )
!= zero_zero_nat )
| ( SX0 = zero_zero_nat ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2565]) ).
thf(3191,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2566]) ).
thf(3192,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ( SX0
!= ( plus_plus_int @ SX0 @ SX1 ) )
| ( SX1 = zero_zero_int ) )
| ~ ! [SX0: int,SX1: int] :
( ( SX1 != zero_zero_int )
| ( SX0
= ( plus_plus_int @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2567]) ).
thf(3193,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ! [SX2: int] :
~ ( zcong @ ( power_power_int @ SX2 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SX1 @ SX0 )
| ( quadRes @ SX0 @ SX1 ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( quadRes @ SX0 @ SX1 )
| ( zcong @ ( power_power_int @ ( sK5_Y_1 @ SX1 @ SX0 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2568]) ).
thf(3194,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ one_one_int @ ( number_number_of_int @ SX0 ) )
| ( ord_less_int @ ( bit1 @ pls ) @ SX0 ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_int @ ( bit1 @ pls ) @ SX0 )
| ( ord_less_int @ one_one_int @ ( number_number_of_int @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2569]) ).
thf(3195,plain,
! [SV462: nat] :
( ( ~ ( ~ ! [SY2006: nat,SY2007: real] :
( ~ ( ord_less_real @ one_one_real @ SY2007 )
| ( ( power_power_real @ SY2007 @ SV462 )
!= ( power_power_real @ SY2007 @ SY2006 ) )
| ( SV462 = SY2006 ) )
| ~ ! [SY2008: nat,SY2009: real] :
( ~ ( ord_less_real @ one_one_real @ SY2009 )
| ( SV462 != SY2008 )
| ( ( power_power_real @ SY2009 @ SV462 )
= ( power_power_real @ SY2009 @ SY2008 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2570]) ).
thf(3196,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX1 @ pls )
| ( ( plus_plus_nat @ ( number_number_of_nat @ SX1 ) @ ( number_number_of_nat @ SX0 ) )
= ( number_number_of_nat @ SX0 ) ) )
| ~ ~ ( ~ ! [SX0: int,SX1: int] :
( ( 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 ) ) )
| ~ ! [SX0: int,SX1: int] :
( ( 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 @ ( plus_plus_int @ SX1 @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2571]) ).
thf(3197,plain,
! [SV463: real] :
( ( ~ ( ~ ! [SY2010: real,SY2011: real] :
( ( SY2011 = zero_zero_real )
| ( ( times_times_real @ SV463 @ SY2011 )
!= ( times_times_real @ SY2010 @ SY2011 ) )
| ( SV463 = SY2010 ) )
| ~ ! [SY2012: real,SY2013: real] :
( ( SY2013 = zero_zero_real )
| ( SV463 != SY2012 )
| ( ( times_times_real @ SV463 @ SY2013 )
= ( times_times_real @ SY2012 @ SY2013 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2572]) ).
thf(3198,plain,
! [SV464: real] :
( ( ~ ( ~ ! [SY2014: real,SY2015: real] :
( ~ ( ord_less_real @ zero_zero_real @ SY2015 )
| ~ ( ord_less_real @ ( times_times_real @ SV464 @ SY2015 ) @ ( times_times_real @ SY2014 @ SY2015 ) )
| ( ord_less_real @ SV464 @ SY2014 ) )
| ~ ! [SY2016: real,SY2017: real] :
( ~ ( ord_less_real @ zero_zero_real @ SY2017 )
| ~ ( ord_less_real @ SV464 @ SY2016 )
| ( ord_less_real @ ( times_times_real @ SV464 @ SY2017 ) @ ( times_times_real @ SY2016 @ SY2017 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2573]) ).
thf(3199,plain,
! [SV465: real] :
( ( ~ ( ~ ! [SY2018: real,SY2019: real] :
( ~ ( ord_less_real @ zero_zero_real @ SY2019 )
| ~ ( ord_less_eq_real @ ( times_times_real @ SY2019 @ SV465 ) @ ( times_times_real @ SY2019 @ SY2018 ) )
| ( ord_less_eq_real @ SV465 @ SY2018 ) )
| ~ ! [SY2020: real,SY2021: real] :
( ~ ( ord_less_real @ zero_zero_real @ SY2021 )
| ~ ( ord_less_eq_real @ SV465 @ SY2020 )
| ( ord_less_eq_real @ ( times_times_real @ SY2021 @ SV465 ) @ ( times_times_real @ SY2021 @ SY2020 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2574]) ).
thf(3200,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ( ( bit0 @ SX0 )
!= ( bit0 @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: int,SX1: int] :
( ( SX0 != SX1 )
| ( ( bit0 @ SX0 )
= ( bit0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2575]) ).
thf(3201,plain,
( ( ~ ! [SX0: int] :
( ( ( power_power_int @ SX0 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) )
| ~ ! [SX0: int] :
( ( SX0 != zero_zero_int )
| ( ( power_power_int @ SX0 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2576]) ).
thf(3202,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ( SX0 != zero_zero_int )
| ( SX1 != zero_zero_int )
| ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SX0 @ SX0 ) @ ( times_times_int @ SX1 @ SX1 ) ) @ zero_zero_int ) )
| ~ ~ ( ~ ! [SX0: int] :
( ! [SX1: int] :
~ ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SX0 @ SX0 ) @ ( times_times_int @ SX1 @ SX1 ) ) @ zero_zero_int )
| ( SX0 = zero_zero_int ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SX0 @ SX0 ) @ ( times_times_int @ SX1 @ SX1 ) ) @ zero_zero_int )
| ( SX1 = zero_zero_int ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2577]) ).
thf(3203,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ pls @ ( bit0 @ SX0 ) )
| ( ord_less_int @ pls @ SX0 ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_int @ pls @ SX0 )
| ( ord_less_int @ pls @ ( bit0 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2578]) ).
thf(3204,plain,
( ( ~ ! [SX0: real] :
( ~ ( ord_less_real @ ( plus_plus_real @ SX0 @ SX0 ) @ zero_zero_real )
| ( ord_less_real @ SX0 @ zero_zero_real ) )
| ~ ! [SX0: real] :
( ~ ( ord_less_real @ SX0 @ zero_zero_real )
| ( ord_less_real @ ( plus_plus_real @ SX0 @ SX0 ) @ zero_zero_real ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2579]) ).
thf(3205,plain,
( ( ~ ! [SX0: int,SX1: nat] :
( ( SX1 = zero_zero_nat )
| ( SX0 != zero_zero_int )
| ( ( power_power_int @ SX0 @ SX1 )
= zero_zero_int ) )
| ~ ~ ( ~ ! [SX0: int,SX1: nat] :
( ( ( power_power_int @ SX0 @ SX1 )
!= zero_zero_int )
| ( SX1 != zero_zero_nat ) )
| ~ ! [SX0: int] :
( ! [SX1: nat] :
( ( power_power_int @ SX0 @ SX1 )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2580]) ).
thf(3206,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ( ( number_number_of_int @ SX0 )
!= ( number_number_of_int @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: int,SX1: int] :
( ( SX0 != SX1 )
| ( ( number_number_of_int @ SX0 )
= ( number_number_of_int @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2581]) ).
thf(3207,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ SX0 @ min )
| ( ord_less_int @ ( bit0 @ SX0 ) @ min ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_int @ ( bit0 @ SX0 ) @ min )
| ( ord_less_eq_int @ SX0 @ min ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2582]) ).
thf(3208,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_nat @ ( number_number_of_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) )
| ~ ( ord_less_nat @ ( number_number_of_nat @ SX1 ) @ ( number_number_of_nat @ SX0 ) ) )
| ~ ! [SX0: int,SX1: int] :
( ( ord_less_nat @ ( number_number_of_nat @ SX1 ) @ ( number_number_of_nat @ SX0 ) )
| ( ord_less_eq_nat @ ( number_number_of_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2583]) ).
thf(3209,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ ( number_number_of_int @ SX0 ) @ one_one_int )
| ( ord_less_eq_int @ SX0 @ ( bit1 @ pls ) ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ SX0 @ ( bit1 @ pls ) )
| ( ord_less_eq_int @ ( number_number_of_int @ SX0 ) @ one_one_int ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2584]) ).
thf(3210,plain,
! [SV466: int] :
( ( ~ ( ~ ! [SY2022: int,SY2023: int] :
( ~ ( dvd_dvd_int @ SY2023 @ ( minus_minus_int @ SV466 @ SY2022 ) )
| ( zcong @ SV466 @ SY2022 @ SY2023 ) )
| ~ ! [SY2024: int,SY2025: int] :
( ~ ( zcong @ SV466 @ SY2024 @ SY2025 )
| ( dvd_dvd_int @ SY2025 @ ( minus_minus_int @ SV466 @ SY2024 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2585]) ).
thf(3211,plain,
( ( ~ ! [SX0: int] :
( ( ( number_number_of_nat @ SX0 )
!= zero_zero_nat )
| ( ( power_power_real @ zero_zero_real @ ( number_number_of_nat @ SX0 ) )
= one_one_real ) )
| ~ ! [SX0: int] :
( ( ( number_number_of_nat @ SX0 )
= zero_zero_nat )
| ( ( power_power_real @ zero_zero_real @ ( number_number_of_nat @ SX0 ) )
= zero_zero_real ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2586]) ).
thf(3212,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ ( bit0 @ SX0 ) @ zero_zero_int )
| ( ord_less_int @ SX0 @ zero_zero_int ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_int @ SX0 @ zero_zero_int )
| ( ord_less_int @ ( bit0 @ SX0 ) @ zero_zero_int ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2587]) ).
thf(3213,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ pls @ ( bit1 @ SX0 ) )
| ( ord_less_eq_int @ pls @ SX0 ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ pls @ SX0 )
| ( ord_less_eq_int @ pls @ ( bit1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2588]) ).
thf(3214,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ ( number_number_of_int @ SX0 ) @ ( number_number_of_int @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ ( number_number_of_int @ SX0 ) @ ( number_number_of_int @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2589]) ).
thf(3215,plain,
! [SV467: nat] :
( ( ~ ( ~ ! [SY2026: nat,SY2027: int] :
( ~ ( ord_less_int @ one_one_int @ SY2027 )
| ( ( power_power_int @ SY2027 @ SV467 )
!= ( power_power_int @ SY2027 @ SY2026 ) )
| ( SV467 = SY2026 ) )
| ~ ! [SY2028: nat,SY2029: int] :
( ~ ( ord_less_int @ one_one_int @ SY2029 )
| ( SV467 != SY2028 )
| ( ( power_power_int @ SY2029 @ SV467 )
= ( power_power_int @ SY2029 @ SY2028 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2590]) ).
thf(3216,plain,
( ( ( t = zero_zero_int )
= $false )
| ( ( ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int )
= zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2591]) ).
thf(3217,plain,
! [SV468: int,SV1: int] :
( ( ~ ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ SV1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV468 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2593]) ).
thf(3218,plain,
! [SV2: int] :
( ( ord_less_int @ ( power_power_int @ SV2 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ zero_zero_int )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2594]) ).
thf(3219,plain,
! [SV469: nat,SV5: int] :
( ( ! [SY2030: nat] :
( ( power_power_int @ SV5 @ ( plus_plus_nat @ SV469 @ SY2030 ) )
= ( times_times_int @ ( power_power_int @ SV5 @ SV469 ) @ ( power_power_int @ SV5 @ SY2030 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2597]) ).
thf(3220,plain,
! [SV6: int,SV470: int] :
( ( ! [SY2031: int] :
( ~ ( ord_less_eq_int @ SV470 @ SY2031 )
| ( ord_less_eq_int @ ( plus_plus_int @ SV6 @ SV470 ) @ ( plus_plus_int @ SV6 @ SY2031 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2598]) ).
thf(3221,plain,
! [SV471: int,SV7: int] :
( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ SV7 @ SV7 ) @ ( times_times_int @ SV471 @ SV471 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2599]) ).
thf(3222,plain,
! [SV472: int,SV8: int] :
( ( ! [SY2032: int,SY2033: int] :
( ~ ( ord_less_int @ SY2032 @ SY2033 )
| ~ ( ord_less_eq_int @ SV8 @ SV472 )
| ( ord_less_int @ ( plus_plus_int @ SY2032 @ SV8 ) @ ( plus_plus_int @ SY2033 @ SV472 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2600]) ).
thf(3223,plain,
! [SV473: int,SV10: int] :
( ( ( times_times_int @ ( bit0 @ SV10 ) @ SV473 )
= ( bit0 @ ( times_times_int @ SV10 @ SV473 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2602]) ).
thf(3224,plain,
! [SV474: int,SV13: int] :
( ( ( plus_plus_int @ ( number_number_of_int @ SV13 ) @ ( number_number_of_int @ SV474 ) )
= ( number_number_of_int @ ( plus_plus_int @ SV13 @ SV474 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2605]) ).
thf(3225,plain,
! [SV475: int,SV14: int] :
( ( ! [SY2034: int] :
( ( times_times_int @ ( plus_plus_int @ SV14 @ SV475 ) @ SY2034 )
= ( plus_plus_int @ ( times_times_int @ SV14 @ SY2034 ) @ ( times_times_int @ SV475 @ SY2034 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2606]) ).
thf(3226,plain,
! [SV476: int,SV15: int] :
( ( ! [SY2035: int] :
( ( times_times_int @ SV15 @ ( plus_plus_int @ SV476 @ SY2035 ) )
= ( plus_plus_int @ ( times_times_int @ SV15 @ SV476 ) @ ( times_times_int @ SV15 @ SY2035 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2607]) ).
thf(3227,plain,
! [SV477: int,SV16: int] :
( ( ~ ( ord_less_int @ SV16 @ SV477 )
| ( ord_less_eq_int @ ( plus_plus_int @ SV16 @ one_one_int ) @ SV477 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2608]) ).
thf(3228,plain,
! [SV17: int,SV478: int] :
( ( ~ ( ord_less_eq_int @ pls @ SV478 )
| ~ ( ord_less_eq_int @ pls @ SV17 )
| ( ( plus_plus_nat @ ( number_number_of_nat @ SV478 ) @ ( number_number_of_nat @ SV17 ) )
= ( number_number_of_nat @ ( plus_plus_int @ SV478 @ SV17 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2609]) ).
thf(3229,plain,
! [SV18: int,SV479: int] :
( ( ~ ( ord_less_eq_int @ pls @ SV479 )
| ~ ( ord_less_eq_int @ pls @ SV18 )
| ( ( plus_plus_int @ ( number_number_of_int @ SV479 ) @ ( number_number_of_int @ SV18 ) )
= ( number_number_of_int @ ( plus_plus_int @ SV479 @ SV18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2610]) ).
thf(3230,plain,
! [SV19: int] :
( ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV19 ) )
= $true )
| ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2611]) ).
thf(3231,plain,
! [SV20: int,SV480: int] :
( ( ( ord_less_int @ SV480 @ SV20 )
| ( SV20 = SV480 )
| ( ord_less_int @ SV20 @ SV480 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2612]) ).
thf(3232,plain,
! [SV481: nat,SV21: nat] :
( ( ! [SY2036: int] :
( ( times_times_nat @ ( plus_plus_nat @ SV21 @ SV481 ) @ ( number_number_of_nat @ SY2036 ) )
= ( plus_plus_nat @ ( times_times_nat @ SV21 @ ( number_number_of_nat @ SY2036 ) ) @ ( times_times_nat @ SV481 @ ( number_number_of_nat @ SY2036 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2613]) ).
thf(3233,plain,
! [SV482: int,SV22: int] :
( ( ! [SY2037: int] :
( ( times_times_int @ ( plus_plus_int @ SV22 @ SV482 ) @ ( number_number_of_int @ SY2037 ) )
= ( plus_plus_int @ ( times_times_int @ SV22 @ ( number_number_of_int @ SY2037 ) ) @ ( times_times_int @ SV482 @ ( number_number_of_int @ SY2037 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2614]) ).
thf(3234,plain,
! [SV483: nat,SV23: int] :
( ( ! [SY2038: nat] :
( ( times_times_nat @ ( number_number_of_nat @ SV23 ) @ ( plus_plus_nat @ SV483 @ SY2038 ) )
= ( plus_plus_nat @ ( times_times_nat @ ( number_number_of_nat @ SV23 ) @ SV483 ) @ ( times_times_nat @ ( number_number_of_nat @ SV23 ) @ SY2038 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2615]) ).
thf(3235,plain,
! [SV484: int,SV24: int] :
( ( ! [SY2039: int] :
( ( times_times_int @ ( number_number_of_int @ SV24 ) @ ( plus_plus_int @ SV484 @ SY2039 ) )
= ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ SV24 ) @ SV484 ) @ ( times_times_int @ ( number_number_of_int @ SV24 ) @ SY2039 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2616]) ).
thf(3236,plain,
! [SV485: int,SV25: int] :
( ( ! [SY2040: int] :
( ( plus_plus_int @ ( plus_plus_int @ SV25 @ SV485 ) @ SY2040 )
= ( plus_plus_int @ SV25 @ ( plus_plus_int @ SV485 @ SY2040 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2617]) ).
thf(3237,plain,
! [SV486: int,SV26: int] :
( ( ! [SY2041: int] :
( ( plus_plus_int @ SV26 @ ( plus_plus_int @ SV486 @ SY2041 ) )
= ( plus_plus_int @ SV486 @ ( plus_plus_int @ SV26 @ SY2041 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2618]) ).
thf(3238,plain,
! [SV487: int,SV27: int] :
( ( ( plus_plus_int @ SV27 @ SV487 )
= ( plus_plus_int @ SV487 @ SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2619]) ).
thf(3239,plain,
! [SV28: int,SV488: int] :
( ( ! [SY2042: int] :
( ~ ( ord_less_int @ SV488 @ SY2042 )
| ~ ( ord_less_int @ zero_zero_int @ SV28 )
| ( ord_less_int @ ( times_times_int @ SV28 @ SV488 ) @ ( times_times_int @ SV28 @ SY2042 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2620]) ).
thf(3240,plain,
! [SV489: int,SV29: int] :
( ( ( ( power_power_int @ SV29 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= ( power_power_int @ SV489 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ~ ( ord_less_eq_int @ zero_zero_int @ SV29 )
| ~ ( ord_less_eq_int @ zero_zero_int @ SV489 )
| ( SV29 = SV489 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2621]) ).
thf(3241,plain,
! [SV490: int,SV30: int] :
( ( ~ ( ord_less_eq_int @ ( power_power_int @ SV30 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV490 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ~ ( ord_less_eq_int @ zero_zero_int @ SV490 )
| ( ord_less_eq_int @ SV30 @ SV490 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2622]) ).
thf(3242,plain,
! [SV491: int,SV32: int] :
( ( ~ ( ord_less_int @ ( power_power_int @ SV32 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV491 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ~ ( ord_less_eq_int @ zero_zero_int @ SV491 )
| ( ord_less_int @ SV32 @ SV491 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2624]) ).
thf(3243,plain,
! [SV492: int,SV33: int] :
( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ SV33 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV492 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2625]) ).
thf(3244,plain,
! [SV493: int,SV34: int] :
( ( ~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ SV34 @ SV34 ) @ ( times_times_int @ SV493 @ SV493 ) ) @ zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2626]) ).
thf(3245,plain,
! [SV494: int,SV39: int] :
( ( ( times_times_int @ ( bit1 @ SV39 ) @ SV494 )
= ( plus_plus_int @ ( bit0 @ ( times_times_int @ SV39 @ SV494 ) ) @ SV494 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2631]) ).
thf(3246,plain,
! [SV40: int] :
( ( ( bit1 @ SV40 )
= pls )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2632]) ).
thf(3247,plain,
! [SV41: int] :
( ( pls
= ( bit1 @ SV41 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2633]) ).
thf(3248,plain,
! [SV495: int,SV42: int] :
( ( ( bit1 @ SV42 )
!= ( bit0 @ SV495 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2634]) ).
thf(3249,plain,
! [SV496: int,SV43: int] :
( ( ( bit0 @ SV43 )
!= ( bit1 @ SV496 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2635]) ).
thf(3250,plain,
! [SV497: int,SV46: int] :
( ( ( plus_plus_int @ ( bit0 @ SV46 ) @ ( bit0 @ SV497 ) )
= ( bit0 @ ( plus_plus_int @ SV46 @ SV497 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2640]) ).
thf(3251,plain,
! [SV50: int,SV498: int] :
( ( ! [SY2043: int] :
( ~ ( ord_less_int @ SV498 @ SY2043 )
| ( ord_less_int @ ( plus_plus_int @ SV498 @ SV50 ) @ ( plus_plus_int @ SY2043 @ SV50 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2644]) ).
thf(3252,plain,
! [SV499: int,SV68: int] :
( ( ! [SY2044: real] :
( ( plus_plus_real @ ( number267125858f_real @ SV68 ) @ ( plus_plus_real @ ( number267125858f_real @ SV499 ) @ SY2044 ) )
= ( plus_plus_real @ ( number267125858f_real @ ( plus_plus_int @ SV68 @ SV499 ) ) @ SY2044 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2662]) ).
thf(3253,plain,
! [SV500: int,SV69: int] :
( ( ! [SY2045: int] :
( ( plus_plus_int @ ( number_number_of_int @ SV69 ) @ ( plus_plus_int @ ( number_number_of_int @ SV500 ) @ SY2045 ) )
= ( plus_plus_int @ ( number_number_of_int @ ( plus_plus_int @ SV69 @ SV500 ) ) @ SY2045 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2663]) ).
thf(3254,plain,
! [SV501: int,SV70: int] :
( ( ( plus_plus_real @ ( number267125858f_real @ SV70 ) @ ( number267125858f_real @ SV501 ) )
= ( number267125858f_real @ ( plus_plus_int @ SV70 @ SV501 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2664]) ).
thf(3255,plain,
! [SV502: int,SV71: int] :
( ( ( plus_plus_int @ ( number_number_of_int @ SV71 ) @ ( number_number_of_int @ SV502 ) )
= ( number_number_of_int @ ( plus_plus_int @ SV71 @ SV502 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2665]) ).
thf(3256,plain,
! [SV503: int,SV72: int] :
( ( ( number267125858f_real @ ( plus_plus_int @ SV72 @ SV503 ) )
= ( plus_plus_real @ ( number267125858f_real @ SV72 ) @ ( number267125858f_real @ SV503 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2666]) ).
thf(3257,plain,
! [SV504: int,SV73: int] :
( ( ( number_number_of_int @ ( plus_plus_int @ SV73 @ SV504 ) )
= ( plus_plus_int @ ( number_number_of_int @ SV73 ) @ ( number_number_of_int @ SV504 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2667]) ).
thf(3258,plain,
! [SV505: int,SV74: int] :
( ( ( plus_plus_int @ ( bit1 @ SV74 ) @ ( bit0 @ SV505 ) )
= ( bit1 @ ( plus_plus_int @ SV74 @ SV505 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2669]) ).
thf(3259,plain,
! [SV506: int,SV75: int] :
( ( ( plus_plus_int @ ( bit0 @ SV75 ) @ ( bit1 @ SV506 ) )
= ( bit1 @ ( plus_plus_int @ SV75 @ SV506 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2670]) ).
thf(3260,plain,
! [SV77: int] :
( ( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ SV77 ) @ SV77 )
= zero_zero_int )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2672]) ).
thf(3261,plain,
! [SV507: int,SV80: int] :
( ( ( power_power_int @ ( plus_plus_int @ SV80 @ SV507 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ SV80 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV507 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV80 ) @ SV507 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2675]) ).
thf(3262,plain,
! [SV508: int,SV83: int] :
( ( ( power_power_int @ ( plus_plus_int @ SV83 @ SV508 ) @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ SV83 @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) @ ( power_power_int @ SV83 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ SV508 ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) @ SV83 ) @ ( power_power_int @ SV508 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ ( power_power_int @ SV508 @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2678]) ).
thf(3263,plain,
! [SV509: int,SV84: int] :
( ( ( power_power_int @ ( plus_plus_int @ SV84 @ SV509 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ SV84 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV84 ) @ SV509 ) ) @ ( power_power_int @ SV509 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2679]) ).
thf(3264,plain,
! [SV85: int] :
( ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV85 ) )
= $true )
| ( ( ~ ( ord_less_int @ SV85 @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
| ( SV85 = zero_zero_int )
| ( SV85 = one_one_int ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2680]) ).
thf(3265,plain,
! [SV510: int,SV88: int] :
( ( ! [SY2046: int] :
( ~ ( ord_less_int @ zero_zero_int @ SY2046 )
| ( SY2046
!= ( plus_plus_int @ SV88 @ ( times_times_int @ SY2046 @ SV510 ) ) )
| ~ ( ord_less_int @ SV88 @ SY2046 )
| ( ord_less_eq_int @ one_one_int @ SV510 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2683]) ).
thf(3266,plain,
! [SV511: int,SV89: int] :
( ( ! [SY2047: int] :
( ~ ( ord_less_int @ zero_zero_int @ SY2047 )
| ( SY2047
!= ( plus_plus_int @ SV89 @ ( times_times_int @ SY2047 @ SV511 ) ) )
| ~ ( ord_less_eq_int @ zero_zero_int @ SV89 )
| ( ord_less_eq_int @ SV511 @ one_one_int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2684]) ).
thf(3267,plain,
! [SV512: nat,SV90: nat] :
( ( ( power_power_nat @ SV90 @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV512 ) )
= ( times_times_nat @ ( power_power_nat @ SV90 @ SV512 ) @ ( power_power_nat @ SV90 @ SV512 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2685]) ).
thf(3268,plain,
! [SV513: nat,SV91: int] :
( ( ( power_power_int @ SV91 @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV513 ) )
= ( times_times_int @ ( power_power_int @ SV91 @ SV513 ) @ ( power_power_int @ SV91 @ SV513 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2686]) ).
thf(3269,plain,
! [SV514: nat,SV92: int] :
( ( ! [SY2048: int] :
( ~ ( zprime @ SY2048 )
| ~ ( dvd_dvd_int @ SY2048 @ ( power_power_int @ SV92 @ SV514 ) )
| ( dvd_dvd_int @ SY2048 @ SV92 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2687]) ).
thf(3270,plain,
! [SV515: nat,SV93: int] :
( ( ! [SY2049: nat] :
( ( power_power_int @ ( power_power_int @ SV93 @ SV515 ) @ SY2049 )
= ( power_power_int @ SV93 @ ( times_times_nat @ SV515 @ SY2049 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2688]) ).
thf(3271,plain,
! [SV516: nat,SV94: int] :
( ( ! [SY2050: nat] :
( ( power_power_int @ ( power_power_int @ SV94 @ SV516 ) @ SY2050 )
= ( power_power_int @ SV94 @ ( times_times_nat @ SV516 @ SY2050 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2689]) ).
thf(3272,plain,
! [SV95: int,SV517: int] :
( ( ~ ( ord_less_int @ zero_zero_int @ SV517 )
| ~ ( ord_less_int @ SV517 @ SV95 )
| ~ ( dvd_dvd_int @ SV95 @ SV517 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2690]) ).
thf(3273,plain,
! [SV96: int,SV518: int] :
( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV518 )
| ~ ( ord_less_eq_int @ zero_zero_int @ SV96 )
| ~ ( dvd_dvd_int @ SV518 @ SV96 )
| ~ ( dvd_dvd_int @ SV96 @ SV518 )
| ( SV518 = SV96 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2691]) ).
thf(3274,plain,
! [SV519: int,SV97: int] :
( ( ! [SY2051: int] :
( ~ ( dvd_dvd_int @ ( times_times_int @ SV97 @ SV519 ) @ ( times_times_int @ SV97 @ SY2051 ) )
| ( SV97 = zero_zero_int )
| ( dvd_dvd_int @ SV519 @ SY2051 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2692]) ).
thf(3275,plain,
! [SV520: int,SV98: int] :
( ( ~ ( dvd_dvd_int @ SV98 @ SV520 )
| ~ ( ord_less_int @ zero_zero_int @ SV520 )
| ( ord_less_eq_int @ SV98 @ SV520 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2693]) ).
thf(3276,plain,
! [SV521: int,SV99: int] :
( ( ( plus_plus_int @ SV99 @ SV521 )
= ( plus_plus_int @ SV521 @ SV99 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2694]) ).
thf(3277,plain,
! [SV522: int,SV100: int] :
( ( ! [SY2052: int] :
( ( plus_plus_int @ SV100 @ ( plus_plus_int @ SV522 @ SY2052 ) )
= ( plus_plus_int @ SV522 @ ( plus_plus_int @ SV100 @ SY2052 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2695]) ).
thf(3278,plain,
! [SV523: int,SV101: int] :
( ( ! [SY2053: int] :
( ( plus_plus_int @ SV101 @ ( plus_plus_int @ SV523 @ SY2053 ) )
= ( plus_plus_int @ ( plus_plus_int @ SV101 @ SV523 ) @ SY2053 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2696]) ).
thf(3279,plain,
! [SV524: int,SV102: int] :
( ( ! [SY2054: int] :
( ( plus_plus_int @ ( plus_plus_int @ SV102 @ SV524 ) @ SY2054 )
= ( plus_plus_int @ SV102 @ ( plus_plus_int @ SV524 @ SY2054 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2697]) ).
thf(3280,plain,
! [SV525: int,SV103: int] :
( ( ! [SY2055: int] :
( ( plus_plus_int @ ( plus_plus_int @ SV103 @ SV525 ) @ SY2055 )
= ( plus_plus_int @ ( plus_plus_int @ SV103 @ SY2055 ) @ SV525 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2698]) ).
thf(3281,plain,
! [SV526: int,SV104: int] :
( ( ! [SY2056: int,SY2057: int] :
( ( plus_plus_int @ ( plus_plus_int @ SV104 @ SV526 ) @ ( plus_plus_int @ SY2056 @ SY2057 ) )
= ( plus_plus_int @ ( plus_plus_int @ SV104 @ SY2056 ) @ ( plus_plus_int @ SV526 @ SY2057 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2699]) ).
thf(3282,plain,
! [SV527: nat,SV108: real] :
( ( ( power_power_real @ SV108 @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV527 ) )
= ( power_power_real @ ( power_power_real @ SV108 @ SV527 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2703]) ).
thf(3283,plain,
! [SV528: nat,SV109: nat] :
( ( ( power_power_nat @ SV109 @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV528 ) )
= ( power_power_nat @ ( power_power_nat @ SV109 @ SV528 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2704]) ).
thf(3284,plain,
! [SV529: nat,SV110: int] :
( ( ( power_power_int @ SV110 @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV529 ) )
= ( power_power_int @ ( power_power_int @ SV110 @ SV529 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2705]) ).
thf(3285,plain,
! [SV111: int] :
( ( ( ! [SY1424: nat] :
~ ( ord_less_eq_int @ ( power_power_int @ SV111 @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SY1424 ) ) @ zero_zero_int ) )
= $true )
| ( ( SV111 = zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2706]) ).
thf(3286,plain,
! [SV530: int,SV116: int] :
( ( ! [SY2058: int] :
( ( times_times_int @ SV116 @ ( plus_plus_int @ SV530 @ SY2058 ) )
= ( plus_plus_int @ ( times_times_int @ SV116 @ SV530 ) @ ( times_times_int @ SV116 @ SY2058 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2711]) ).
thf(3287,plain,
! [SV531: int,SV117: int] :
( ( ! [SY2059: int] :
( ( times_times_int @ ( plus_plus_int @ SV117 @ SV531 ) @ SY2059 )
= ( plus_plus_int @ ( times_times_int @ SV117 @ SY2059 ) @ ( times_times_int @ SV531 @ SY2059 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2712]) ).
thf(3288,plain,
! [SV532: int,SV118: int] :
( ( ! [SY2060: int] :
( ( plus_plus_int @ ( times_times_int @ SV118 @ SV532 ) @ ( times_times_int @ SY2060 @ SV532 ) )
= ( times_times_int @ ( plus_plus_int @ SV118 @ SY2060 ) @ SV532 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2713]) ).
thf(3289,plain,
! [SV533: int,SV121: int] :
( ( ! [SY2061: nat] :
( ( power_power_int @ ( times_times_int @ SV121 @ SV533 ) @ SY2061 )
= ( times_times_int @ ( power_power_int @ SV121 @ SY2061 ) @ ( power_power_int @ SV533 @ SY2061 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2716]) ).
thf(3290,plain,
! [SV534: nat,SV122: int] :
( ( ! [SY2062: nat] :
( ( times_times_int @ ( power_power_int @ SV122 @ SV534 ) @ ( power_power_int @ SV122 @ SY2062 ) )
= ( power_power_int @ SV122 @ ( plus_plus_nat @ SV534 @ SY2062 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2717]) ).
thf(3291,plain,
! [SV535: nat,SV124: int] :
( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ SV124 @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV535 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2719]) ).
thf(3292,plain,
! [SV536: int,SV125: int] :
( ( ! [SY2063: int,SY2064: int,SY2065: int] :
( ( SY2065 = zero_zero_int )
| ( SV125 = SV536 )
| ( SY2063 != SY2064 )
| ( ( plus_plus_int @ SY2063 @ ( times_times_int @ SY2065 @ SV125 ) )
!= ( plus_plus_int @ SY2064 @ ( times_times_int @ SY2065 @ SV536 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2720]) ).
thf(3293,plain,
! [SV537: int,SV127: int] :
( ( ( plus_plus_int @ SV127 @ ( times_times_int @ SV537 @ SV127 ) )
= ( times_times_int @ ( plus_plus_int @ SV537 @ one_one_int ) @ SV127 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2722]) ).
thf(3294,plain,
! [SV538: int,SV128: int] :
( ( ( plus_plus_int @ ( times_times_int @ SV128 @ SV538 ) @ SV538 )
= ( times_times_int @ ( plus_plus_int @ SV128 @ one_one_int ) @ SV538 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2723]) ).
thf(3295,plain,
! [SV129: int,SV539: int] :
( ( ~ ( ord_less_int @ zero_zero_int @ SV539 )
| ~ ( ord_less_int @ zero_zero_int @ ( times_times_int @ SV539 @ SV129 ) )
| ( ord_less_int @ zero_zero_int @ SV129 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2724]) ).
thf(3296,plain,
! [SV130: int,SV540: int] :
( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV540 )
| ~ ( ord_less_eq_int @ zero_zero_int @ SV130 )
| ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ SV540 @ SV130 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2725]) ).
thf(3297,plain,
! [SV131: int,SV541: int] :
( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV541 )
| ~ ( ord_less_eq_int @ zero_zero_int @ SV131 )
| ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ SV541 @ SV131 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2726]) ).
thf(3298,plain,
! [SV132: nat,SV542: int] :
( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV542 )
| ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ SV542 @ SV132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2727]) ).
thf(3299,plain,
! [SV543: int,SV133: int] :
( ( ! [SY2066: int] :
( ~ ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ SV133 @ SV543 ) @ SY2066 ) )
| ~ ( ord_less_int @ SY2066 @ SV133 )
| ~ ( ord_less_int @ zero_zero_int @ SV133 )
| ( ord_less_eq_int @ zero_zero_int @ SV543 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2728]) ).
thf(3300,plain,
! [SV544: int,SV134: int] :
( ( ! [SY2067: int] :
( ~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ SV134 @ SV544 ) @ SY2067 ) @ zero_zero_int )
| ~ ( ord_less_eq_int @ zero_zero_int @ SY2067 )
| ~ ( ord_less_int @ zero_zero_int @ SV134 )
| ( ord_less_eq_int @ SV544 @ zero_zero_int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2729]) ).
thf(3301,plain,
! [SV545: int,SV135: int] :
( ( ! [SY2068: int,SY2069: int,SY2070: int] :
( ~ ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SV135 @ SV545 ) @ SY2068 ) @ ( plus_plus_int @ ( times_times_int @ SV135 @ SY2069 ) @ SY2070 ) )
| ~ ( ord_less_eq_int @ zero_zero_int @ SY2068 )
| ~ ( ord_less_int @ SY2068 @ SV135 )
| ~ ( ord_less_int @ SY2070 @ SV135 )
| ( ord_less_eq_int @ SV545 @ SY2069 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2730]) ).
thf(3302,plain,
! [SV546: int,SV136: int] :
( ( ! [SY2071: int,SY2072: int,SY2073: int,SY2074: int] :
( ( ( plus_plus_int @ ( times_times_int @ SV136 @ SV546 ) @ SY2071 )
!= ( plus_plus_int @ ( times_times_int @ SY2072 @ SY2073 ) @ SY2074 ) )
| ~ ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ SY2072 @ SY2073 ) @ SY2074 ) )
| ~ ( ord_less_int @ SY2074 @ SY2072 )
| ~ ( ord_less_eq_int @ zero_zero_int @ SY2071 )
| ~ ( ord_less_int @ zero_zero_int @ SY2072 )
| ~ ( ord_less_eq_int @ SY2072 @ SV136 )
| ( ord_less_eq_int @ SV546 @ SY2073 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2731]) ).
thf(3303,plain,
! [SV547: int,SV137: int] :
( ( ! [SY2075: int,SY2076: int,SY2077: int] :
( ~ ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SV137 @ SV547 ) @ SY2075 ) @ ( plus_plus_int @ ( times_times_int @ SV137 @ SY2076 ) @ SY2077 ) )
| ~ ( ord_less_eq_int @ SY2077 @ zero_zero_int )
| ~ ( ord_less_int @ SV137 @ SY2077 )
| ~ ( ord_less_int @ SV137 @ SY2075 )
| ( ord_less_eq_int @ SY2076 @ SV547 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2732]) ).
thf(3304,plain,
! [SV548: int,SV138: int] :
( ( ! [SY2078: int,SY2079: int,SY2080: int,SY2081: int] :
( ( ( plus_plus_int @ ( times_times_int @ SV138 @ SV548 ) @ SY2078 )
!= ( plus_plus_int @ ( times_times_int @ SY2079 @ SY2080 ) @ SY2081 ) )
| ~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ SY2079 @ SY2080 ) @ SY2081 ) @ zero_zero_int )
| ~ ( ord_less_int @ SY2078 @ SV138 )
| ~ ( ord_less_eq_int @ zero_zero_int @ SY2081 )
| ~ ( ord_less_int @ zero_zero_int @ SY2079 )
| ~ ( ord_less_eq_int @ SY2079 @ SV138 )
| ( ord_less_eq_int @ SY2080 @ SV548 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2733]) ).
thf(3305,plain,
! [SV143: int,SV549: int] :
( ( ! [SY2082: int] :
( ( zcong @ SV549 @ zero_zero_int @ SY2082 )
| ~ ( zcong @ ( power_power_int @ SV143 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SV549 @ SY2082 )
| ~ ( dvd_dvd_int @ SY2082 @ SV143 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2738]) ).
thf(3306,plain,
! [SV144: int] :
( ( min
= ( bit0 @ SV144 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2741]) ).
thf(3307,plain,
! [SV145: int] :
( ( ( bit0 @ SV145 )
= min )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2742]) ).
thf(3308,plain,
! [SV550: int,SV146: int] :
( ( ~ ( ord_less_eq_int @ SV146 @ SV550 )
| ( SV146 = SV550 )
| ( ord_less_int @ SV146 @ SV550 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2747]) ).
thf(3309,plain,
! [SV147: int,SV551: int] :
( ( ! [SY2083: int] :
( ~ ( ord_less_int @ SV551 @ SY2083 )
| ~ ( ord_less_int @ SV147 @ SY2083 )
| ( ord_less_eq_int @ SV551 @ SV147 )
| ( ord_less_eq_int @ SV147 @ SV551 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2748]) ).
thf(3310,plain,
! [SV552: int,SV148: int] :
( ( zcong @ SV148 @ SV552 @ one_one_int )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2749]) ).
thf(3311,plain,
! [SV553: int,SV149: int] :
( ( ! [SY2084: int,SY2085: int,SY2086: int] :
( ~ ( zcong @ SY2084 @ SY2085 @ SY2086 )
| ~ ( zcong @ SV149 @ SV553 @ SY2086 )
| ( zcong @ ( plus_plus_int @ SY2084 @ SV149 ) @ ( plus_plus_int @ SY2085 @ SV553 ) @ SY2086 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2750]) ).
thf(3312,plain,
! [SV150: int,SV554: int] :
( ( ! [SY2087: int] :
( ~ ( ord_less_int @ zero_zero_int @ SY2087 )
| ~ ( ord_less_int @ SY2087 @ SV554 )
| ~ ( ord_less_int @ zero_zero_int @ SV150 )
| ~ ( ord_less_int @ SV150 @ SY2087 )
| ~ ( zcong @ SY2087 @ SV150 @ SV554 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2751]) ).
thf(3313,plain,
! [SV151: int,SV555: int] :
( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV555 )
| ~ ( ord_less_int @ SV555 @ SV151 )
| ~ ( zcong @ SV555 @ zero_zero_int @ SV151 )
| ( SV555 = zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2752]) ).
thf(3314,plain,
! [SV152: int,SV556: int] :
( ( ! [SY2088: int] :
( ~ ( ord_less_eq_int @ zero_zero_int @ SY2088 )
| ~ ( ord_less_int @ SY2088 @ SV556 )
| ~ ( ord_less_eq_int @ zero_zero_int @ SV152 )
| ~ ( ord_less_int @ SV152 @ SV556 )
| ~ ( zcong @ SY2088 @ SV152 @ SV556 )
| ( SY2088 = SV152 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2753]) ).
thf(3315,plain,
! [SV153: nat,SV557: int] :
( ( ! [SY2089: nat,SY2090: int] :
( ~ ( zcong @ ( power_power_int @ SV557 @ SY2089 ) @ one_one_int @ SY2090 )
| ( zcong @ ( power_power_int @ SV557 @ ( times_times_nat @ SY2089 @ SV153 ) ) @ one_one_int @ SY2090 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2754]) ).
thf(3316,plain,
! [SV558: int,SV154: int] :
( ( ( minus_minus_int @ ( bit0 @ SV154 ) @ ( bit0 @ SV558 ) )
= ( bit0 @ ( minus_minus_int @ SV154 @ SV558 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2755]) ).
thf(3317,plain,
! [SV559: int,SV156: int] :
( ( ! [SY2091: int] :
( ( ( minus_minus_int @ SV156 @ SV559 )
!= SY2091 )
| ( SV156
= ( plus_plus_int @ SY2091 @ SV559 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2757]) ).
thf(3318,plain,
! [SV560: int,SV157: int] :
( ( ( minus_minus_int @ ( bit1 @ SV157 ) @ ( bit0 @ SV560 ) )
= ( bit1 @ ( minus_minus_int @ SV157 @ SV560 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2758]) ).
thf(3319,plain,
! [SV561: int,SV158: int] :
( ( ( minus_minus_int @ ( bit1 @ SV158 ) @ ( bit1 @ SV561 ) )
= ( bit0 @ ( minus_minus_int @ SV158 @ SV561 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2759]) ).
thf(3320,plain,
! [SV562: int,SV160: int] :
( ( ! [SY2092: int,SY2093: int,SY2094: int,SY2095: int,SY2096: int] :
( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ SV160 @ ( times_times_int @ SV562 @ SY2092 ) ) @ SY2093 ) @ ( times_times_int @ ( minus_minus_int @ SY2094 @ ( times_times_int @ SV562 @ SY2095 ) ) @ SY2096 ) )
= ( minus_minus_int @ ( plus_plus_int @ ( times_times_int @ SV160 @ SY2093 ) @ ( times_times_int @ SY2094 @ SY2096 ) ) @ ( times_times_int @ SV562 @ ( plus_plus_int @ ( times_times_int @ SY2092 @ SY2093 ) @ ( times_times_int @ SY2095 @ SY2096 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2761]) ).
thf(3321,plain,
! [SV563: int,SV161: int] :
( ( ! [SY2097: int] :
( ( plus_plus_int @ ( number_number_of_int @ SV161 ) @ ( minus_minus_int @ ( number_number_of_int @ SV563 ) @ SY2097 ) )
= ( minus_minus_int @ ( number_number_of_int @ ( plus_plus_int @ SV161 @ SV563 ) ) @ SY2097 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2762]) ).
thf(3322,plain,
! [SV162: int,SV564: int] :
( ( ~ ( ord_less_int @ zero_zero_int @ SV564 )
| ~ ( ord_less_int @ SV564 @ SV162 )
| ( SV564
= ( minus_minus_int @ SV162 @ one_one_int ) )
| ( ord_less_int @ SV564 @ ( minus_minus_int @ SV162 @ one_one_int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2763]) ).
thf(3323,plain,
! [SV565: int,SV166: int] :
( ( ( times_times_int @ ( plus_plus_int @ SV166 @ SV565 ) @ ( minus_minus_int @ SV166 @ SV565 ) )
= ( minus_minus_int @ ( power_power_int @ SV166 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV565 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2767]) ).
thf(3324,plain,
! [SV168: int,SV566: int] :
( ( ! [SY2098: int,SY2099: int] :
( ~ ( zcong @ SV566 @ SY2098 @ SY2099 )
| ( zcong @ ( plus_plus_int @ SV566 @ SV168 ) @ ( plus_plus_int @ SY2098 @ SV168 ) @ SY2099 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2769]) ).
thf(3325,plain,
! [SV169: nat,SV567: int] :
( ( ! [SY2100: int,SY2101: int] :
( ~ ( zcong @ SV567 @ SY2100 @ SY2101 )
| ( zcong @ ( power_power_int @ SV567 @ SV169 ) @ ( power_power_int @ SY2100 @ SV169 ) @ SY2101 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2770]) ).
thf(3326,plain,
! [SV170: int,SV568: int] :
( ( ! [SY2102: int] :
( ~ ( ord_less_int @ zero_zero_int @ SY2102 )
| ~ ( ord_less_int @ zero_zero_int @ SV568 )
| ~ ( ord_less_int @ zero_zero_int @ SV170 )
| ~ ( zcong @ SY2102 @ SV568 @ SV170 )
| ~ ( ord_less_int @ SY2102 @ SV170 )
| ~ ( ord_less_int @ SV568 @ SV170 )
| ( SY2102 = SV568 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2771]) ).
thf(3327,plain,
! [SV171: int,SV569: int] :
( ( ~ ( ord_less_int @ zero_zero_int @ SV569 )
| ~ ( ord_less_int @ SV569 @ SV171 )
| ~ ( zcong @ SV569 @ zero_zero_int @ SV171 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2772]) ).
thf(3328,plain,
! [SV570: int,SV172: int] :
( ( ~ ( dvd_dvd_int @ SV172 @ SV570 )
| ( ord_less_eq_int @ SV570 @ zero_zero_int )
| ( ord_less_eq_int @ SV172 @ SV570 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2773]) ).
thf(3329,plain,
! [SV173: int,SV571: int] :
( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV571 )
| ~ ( ord_less_int @ SV571 @ SV173 )
| ~ ( zcong @ SV571 @ zero_zero_int @ SV173 )
| ( SV571 = zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2774]) ).
thf(3330,plain,
! [SV174: nat] :
( ( ( ( power_power_int @ ( number_number_of_int @ min ) @ SV174 )
= one_one_int )
= $true )
| ( ( ( power_power_int @ ( number_number_of_int @ min ) @ SV174 )
= ( number_number_of_int @ min ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2775]) ).
thf(3331,plain,
! [SV572: int,SV175: int] :
( ( ! [SY2103: int,SY2104: int] :
( ( minus_minus_int @ ( plus_plus_int @ SV175 @ SV572 ) @ ( plus_plus_int @ SY2103 @ SY2104 ) )
= ( plus_plus_int @ ( minus_minus_int @ SV175 @ SY2103 ) @ ( minus_minus_int @ SV572 @ SY2104 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2776]) ).
thf(3332,plain,
! [SV573: int,SV176: int] :
( ( ! [SY2105: int,SY2106: int] :
( ( minus_minus_int @ ( times_times_int @ SV176 @ SV573 ) @ ( times_times_int @ SY2105 @ SY2106 ) )
= ( plus_plus_int @ ( times_times_int @ SV176 @ ( minus_minus_int @ SV573 @ SY2106 ) ) @ ( times_times_int @ ( minus_minus_int @ SV176 @ SY2105 ) @ SY2106 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2777]) ).
thf(3333,plain,
! [SV178: nat,SV574: int] :
( ( ( SV574 = zero_zero_int )
| ( ( power_power_int @ SV574 @ SV178 )
!= zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2779]) ).
thf(3334,plain,
! [SV575: int,SV179: int] :
( ( ! [SY2107: nat] :
( ( power_power_int @ ( times_times_int @ SV179 @ SV575 ) @ SY2107 )
= ( times_times_int @ ( power_power_int @ SV179 @ SY2107 ) @ ( power_power_int @ SV575 @ SY2107 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2780]) ).
thf(3335,plain,
! [SV576: nat,SV180: int] :
( ( ( times_times_int @ ( power_power_int @ SV180 @ SV576 ) @ SV180 )
= ( times_times_int @ SV180 @ ( power_power_int @ SV180 @ SV576 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2781]) ).
thf(3336,plain,
! [SV182: nat,SV577: int] :
( ( ! [SY2108: int] :
( ~ ( dvd_dvd_int @ SV577 @ SY2108 )
| ( dvd_dvd_int @ ( power_power_int @ SV577 @ SV182 ) @ ( power_power_int @ SY2108 @ SV182 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2783]) ).
thf(3337,plain,
! [SV578: nat,SV183: int] :
( ( ! [SY2109: nat] :
( ( power_power_int @ SV183 @ ( times_times_nat @ SV578 @ SY2109 ) )
= ( power_power_int @ ( power_power_int @ SV183 @ SV578 ) @ SY2109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2784]) ).
thf(3338,plain,
! [SV185: nat,SV579: int] :
( ( ! [SY2110: int] :
( ~ ( ord_less_eq_int @ SV579 @ SY2110 )
| ~ ( ord_less_eq_int @ zero_zero_int @ SV579 )
| ( ord_less_eq_int @ ( power_power_int @ SV579 @ SV185 ) @ ( power_power_int @ SY2110 @ SV185 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2786]) ).
thf(3339,plain,
! [SV186: nat,SV580: int] :
( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV580 )
| ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ SV580 @ SV186 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2787]) ).
thf(3340,plain,
! [SV187: nat,SV581: int] :
( ( ~ ( ord_less_int @ zero_zero_int @ SV581 )
| ( ord_less_int @ zero_zero_int @ ( power_power_int @ SV581 @ SV187 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2788]) ).
thf(3341,plain,
! [SV188: nat,SV582: int] :
( ( ~ ( ord_less_eq_int @ one_one_int @ SV582 )
| ( ord_less_eq_int @ one_one_int @ ( power_power_int @ SV582 @ SV188 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2789]) ).
thf(3342,plain,
! [SV583: nat,SV190: int] :
( ( ! [SY2111: nat] :
( ( power_power_int @ SV190 @ ( plus_plus_nat @ SV583 @ SY2111 ) )
= ( times_times_int @ ( power_power_int @ SV190 @ SV583 ) @ ( power_power_int @ SV190 @ SY2111 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2791]) ).
thf(3343,plain,
! [SV191: nat,SV584: int] :
( ( ! [SY2112: nat,SY2113: int] :
( ~ ( dvd_dvd_int @ ( power_power_int @ SV584 @ SY2112 ) @ SY2113 )
| ~ ( ord_less_eq_nat @ SV191 @ SY2112 )
| ( dvd_dvd_int @ ( power_power_int @ SV584 @ SV191 ) @ SY2113 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2792]) ).
thf(3344,plain,
! [SV585: nat,SV192: nat] :
( ( ! [SY2114: int,SY2115: int] :
( ~ ( dvd_dvd_int @ SY2114 @ SY2115 )
| ~ ( ord_less_eq_nat @ SV192 @ SV585 )
| ( dvd_dvd_int @ ( power_power_int @ SY2114 @ SV192 ) @ ( power_power_int @ SY2115 @ SV585 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2793]) ).
thf(3345,plain,
! [SV193: int,SV586: nat] :
( ( ! [SY2116: nat] :
( ~ ( ord_less_eq_nat @ SV586 @ SY2116 )
| ( dvd_dvd_int @ ( power_power_int @ SV193 @ SV586 ) @ ( power_power_int @ SV193 @ SY2116 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2794]) ).
thf(3346,plain,
! [SV587: nat,SV194: int] :
( ( ! [SY2117: int] :
( ~ ( ord_less_int @ ( power_power_int @ SV194 @ SV587 ) @ ( power_power_int @ SY2117 @ SV587 ) )
| ~ ( ord_less_eq_int @ zero_zero_int @ SY2117 )
| ( ord_less_int @ SV194 @ SY2117 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2795]) ).
thf(3347,plain,
! [SV195: nat,SV588: int] :
( ( ~ ( ord_less_int @ one_one_int @ SV588 )
| ( ord_less_int @ ( power_power_int @ SV588 @ SV195 ) @ ( times_times_int @ SV588 @ ( power_power_int @ SV588 @ SV195 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2796]) ).
thf(3348,plain,
! [SV196: nat,SV589: int] :
( ( ~ ( ord_less_int @ one_one_int @ SV589 )
| ( ord_less_int @ one_one_int @ ( times_times_int @ SV589 @ ( power_power_int @ SV589 @ SV196 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2797]) ).
thf(3349,plain,
! [SV197: int,SV590: nat] :
( ( ! [SY2118: nat] :
( ~ ( ord_less_nat @ SV590 @ SY2118 )
| ~ ( ord_less_int @ one_one_int @ SV197 )
| ( ord_less_int @ ( power_power_int @ SV197 @ SV590 ) @ ( power_power_int @ SV197 @ SY2118 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2798]) ).
thf(3350,plain,
! [SV591: nat,SV198: nat] :
( ( ! [SY2119: int] :
( ~ ( ord_less_int @ one_one_int @ SY2119 )
| ~ ( ord_less_int @ ( power_power_int @ SY2119 @ SV198 ) @ ( power_power_int @ SY2119 @ SV591 ) )
| ( ord_less_nat @ SV198 @ SV591 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2799]) ).
thf(3351,plain,
! [SV199: int,SV592: nat] :
( ( ! [SY2120: nat] :
( ~ ( ord_less_eq_nat @ SV592 @ SY2120 )
| ~ ( ord_less_eq_int @ one_one_int @ SV199 )
| ( ord_less_eq_int @ ( power_power_int @ SV199 @ SV592 ) @ ( power_power_int @ SV199 @ SY2120 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2800]) ).
thf(3352,plain,
! [SV200: nat,SV593: int] :
( ( ~ ( ord_less_int @ zero_zero_int @ SV593 )
| ~ ( ord_less_int @ SV593 @ one_one_int )
| ( ord_less_int @ ( times_times_int @ SV593 @ ( power_power_int @ SV593 @ SV200 ) ) @ ( power_power_int @ SV593 @ SV200 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2801]) ).
thf(3353,plain,
! [SV201: int,SV594: nat] :
( ( ! [SY2121: nat] :
( ~ ( ord_less_nat @ SV594 @ SY2121 )
| ~ ( ord_less_int @ zero_zero_int @ SV201 )
| ~ ( ord_less_int @ SV201 @ one_one_int )
| ( ord_less_int @ ( power_power_int @ SV201 @ SY2121 ) @ ( power_power_int @ SV201 @ SV594 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2802]) ).
thf(3354,plain,
! [SV595: real,SV202: real] :
( ( ~ ( ord_less_real @ ( plus_plus_real @ ( power_power_real @ SV202 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SV595 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_real ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2803]) ).
thf(3355,plain,
! [SV203: real] :
( ( ord_less_real @ ( power_power_real @ SV203 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ zero_zero_real )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2804]) ).
thf(3356,plain,
! [SV596: int,SV208: int] :
( ( ( times_times_int @ SV208 @ SV596 )
= ( times_times_int @ SV596 @ SV208 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2809]) ).
thf(3357,plain,
! [SV597: int,SV209: int] :
( ( ( ord_less_eq_int @ SV209 @ SV597 )
| ( ord_less_eq_int @ SV597 @ SV209 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2810]) ).
thf(3358,plain,
! [SV598: int,SV210: int] :
( ( ( times_times_int @ ( number_number_of_int @ SV210 ) @ ( number_number_of_int @ SV598 ) )
= ( number_number_of_int @ ( times_times_int @ SV210 @ SV598 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2811]) ).
thf(3359,plain,
! [SV599: int,SV211: int] :
( ( ! [SY2122: int] :
( ( times_times_int @ ( times_times_int @ SV211 @ SV599 ) @ SY2122 )
= ( times_times_int @ SV211 @ ( times_times_int @ SV599 @ SY2122 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2812]) ).
thf(3360,plain,
! [SV212: int,SV600: int] :
( ( ! [SY2123: int] :
( ~ ( ord_less_eq_int @ SV600 @ SY2123 )
| ~ ( ord_less_eq_int @ SY2123 @ SV212 )
| ( ord_less_eq_int @ SV600 @ SV212 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2813]) ).
thf(3361,plain,
! [SV601: int,SV213: int] :
( ( ~ ( ord_less_eq_int @ SV213 @ SV601 )
| ~ ( ord_less_eq_int @ SV601 @ SV213 )
| ( SV213 = SV601 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2814]) ).
thf(3362,plain,
! [SV214: int,SV602: int] :
( ( ~ ( ord_less_eq_int @ pls @ SV602 )
| ~ ( ord_less_eq_int @ pls @ SV214 )
| ( ( times_times_real @ ( number267125858f_real @ SV602 ) @ ( number267125858f_real @ SV214 ) )
= ( number267125858f_real @ ( times_times_int @ SV602 @ SV214 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2815]) ).
thf(3363,plain,
! [SV215: int,SV603: int] :
( ( ~ ( ord_less_eq_int @ pls @ SV603 )
| ~ ( ord_less_eq_int @ pls @ SV215 )
| ( ( times_times_nat @ ( number_number_of_nat @ SV603 ) @ ( number_number_of_nat @ SV215 ) )
= ( number_number_of_nat @ ( times_times_int @ SV603 @ SV215 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2816]) ).
thf(3364,plain,
! [SV216: int,SV604: int] :
( ( ~ ( ord_less_eq_int @ pls @ SV604 )
| ~ ( ord_less_eq_int @ pls @ SV216 )
| ( ( times_times_int @ ( number_number_of_int @ SV604 ) @ ( number_number_of_int @ SV216 ) )
= ( number_number_of_int @ ( times_times_int @ SV604 @ SV216 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2817]) ).
thf(3365,plain,
! [SV605: int,SV217: int] :
( ( ! [SY2124: real] :
( ( times_times_real @ ( number267125858f_real @ SV217 ) @ ( times_times_real @ ( number267125858f_real @ SV605 ) @ SY2124 ) )
= ( times_times_real @ ( number267125858f_real @ ( times_times_int @ SV217 @ SV605 ) ) @ SY2124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2818]) ).
thf(3366,plain,
! [SV606: int,SV218: int] :
( ( ! [SY2125: int] :
( ( times_times_int @ ( number_number_of_int @ SV218 ) @ ( times_times_int @ ( number_number_of_int @ SV606 ) @ SY2125 ) )
= ( times_times_int @ ( number_number_of_int @ ( times_times_int @ SV218 @ SV606 ) ) @ SY2125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2819]) ).
thf(3367,plain,
! [SV607: int,SV219: int] :
( ( ( times_times_real @ ( number267125858f_real @ SV219 ) @ ( number267125858f_real @ SV607 ) )
= ( number267125858f_real @ ( times_times_int @ SV219 @ SV607 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2820]) ).
thf(3368,plain,
! [SV608: int,SV220: int] :
( ( ( times_times_int @ ( number_number_of_int @ SV220 ) @ ( number_number_of_int @ SV608 ) )
= ( number_number_of_int @ ( times_times_int @ SV220 @ SV608 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2821]) ).
thf(3369,plain,
! [SV609: int,SV221: int] :
( ( ( number267125858f_real @ ( times_times_int @ SV221 @ SV609 ) )
= ( times_times_real @ ( number267125858f_real @ SV221 ) @ ( number267125858f_real @ SV609 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2822]) ).
thf(3370,plain,
! [SV610: int,SV222: int] :
( ( ( number_number_of_int @ ( times_times_int @ SV222 @ SV610 ) )
= ( times_times_int @ ( number_number_of_int @ SV222 ) @ ( number_number_of_int @ SV610 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2823]) ).
thf(3371,plain,
! [SV611: real,SV223: real] :
( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ SV223 @ SV223 ) @ ( times_times_real @ SV611 @ SV611 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2824]) ).
thf(3372,plain,
! [SV224: int,SV612: int] :
( ( ~ ( ord_less_eq_int @ pls @ SV612 )
| ~ ( ord_less_eq_int @ pls @ SV224 )
| ( ( plus_plus_real @ ( number267125858f_real @ SV612 ) @ ( number267125858f_real @ SV224 ) )
= ( number267125858f_real @ ( plus_plus_int @ SV612 @ SV224 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2825]) ).
thf(3373,plain,
! [SV613: real,SV225: real] :
( ( ! [SY2126: int] :
( ( times_times_real @ ( plus_plus_real @ SV225 @ SV613 ) @ ( number267125858f_real @ SY2126 ) )
= ( plus_plus_real @ ( times_times_real @ SV225 @ ( number267125858f_real @ SY2126 ) ) @ ( times_times_real @ SV613 @ ( number267125858f_real @ SY2126 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2826]) ).
thf(3374,plain,
! [SV614: real,SV226: int] :
( ( ! [SY2127: real] :
( ( times_times_real @ ( number267125858f_real @ SV226 ) @ ( plus_plus_real @ SV614 @ SY2127 ) )
= ( plus_plus_real @ ( times_times_real @ ( number267125858f_real @ SV226 ) @ SV614 ) @ ( times_times_real @ ( number267125858f_real @ SV226 ) @ SY2127 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2827]) ).
thf(3375,plain,
! [SV615: real,SV227: real] :
( ( ( ( power_power_real @ SV227 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= ( power_power_real @ SV615 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ~ ( ord_less_eq_real @ zero_zero_real @ SV227 )
| ~ ( ord_less_eq_real @ zero_zero_real @ SV615 )
| ( SV227 = SV615 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2828]) ).
thf(3376,plain,
! [SV616: nat,SV228: nat] :
( ( ( ( power_power_nat @ SV228 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= ( power_power_nat @ SV616 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV228 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV616 )
| ( SV228 = SV616 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2829]) ).
thf(3377,plain,
! [SV617: real,SV229: real] :
( ( ~ ( ord_less_eq_real @ ( power_power_real @ SV229 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SV617 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ~ ( ord_less_eq_real @ zero_zero_real @ SV617 )
| ( ord_less_eq_real @ SV229 @ SV617 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2830]) ).
thf(3378,plain,
! [SV618: nat,SV230: nat] :
( ( ~ ( ord_less_eq_nat @ ( power_power_nat @ SV230 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_nat @ SV618 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV618 )
| ( ord_less_eq_nat @ SV230 @ SV618 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2831]) ).
thf(3379,plain,
! [SV619: real,SV232: real] :
( ( ~ ( ord_less_real @ ( power_power_real @ SV232 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SV619 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ~ ( ord_less_eq_real @ zero_zero_real @ SV619 )
| ( ord_less_real @ SV232 @ SV619 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2833]) ).
thf(3380,plain,
! [SV620: nat,SV233: nat] :
( ( ~ ( ord_less_nat @ ( power_power_nat @ SV233 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_nat @ SV620 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV620 )
| ( ord_less_nat @ SV233 @ SV620 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2834]) ).
thf(3381,plain,
! [SV621: real,SV234: real] :
( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ SV234 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SV621 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2835]) ).
thf(3382,plain,
! [SV622: real,SV235: real] :
( ( ~ ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ SV235 @ SV235 ) @ ( times_times_real @ SV622 @ SV622 ) ) @ zero_zero_real ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2836]) ).
thf(3383,plain,
! [SV623: real,SV242: real] :
( ( ( power_power_real @ ( plus_plus_real @ SV242 @ SV623 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_real @ ( plus_plus_real @ ( power_power_real @ SV242 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SV623 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV242 ) @ SV623 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2843]) ).
thf(3384,plain,
! [SV624: nat,SV243: nat] :
( ( ( power_power_nat @ ( plus_plus_nat @ SV243 @ SV624 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_nat @ ( plus_plus_nat @ ( power_power_nat @ SV243 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_nat @ SV624 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_nat @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV243 ) @ SV624 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2844]) ).
thf(3385,plain,
! [SV625: nat,SV246: real] :
( ( ( power_power_real @ SV246 @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV625 ) )
= ( times_times_real @ ( power_power_real @ SV246 @ SV625 ) @ ( power_power_real @ SV246 @ SV625 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2847]) ).
thf(3386,plain,
! [SV626: nat,SV247: real] :
( ( ! [SY2128: nat] :
( ( power_power_real @ ( power_power_real @ SV247 @ SV626 ) @ SY2128 )
= ( power_power_real @ SV247 @ ( times_times_nat @ SV626 @ SY2128 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2848]) ).
thf(3387,plain,
! [SV627: nat,SV248: nat] :
( ( ! [SY2129: nat] :
( ( power_power_nat @ ( power_power_nat @ SV248 @ SV627 ) @ SY2129 )
= ( power_power_nat @ SV248 @ ( times_times_nat @ SV627 @ SY2129 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2849]) ).
thf(3388,plain,
! [SV628: int,SV249: nat] :
( ( ! [SY2130: int,SY2131: int] :
( ~ ( zprime @ SY2131 )
| ( dvd_dvd_int @ SY2131 @ SY2130 )
| ~ ( dvd_dvd_int @ ( power_power_int @ SY2131 @ SV249 ) @ ( times_times_int @ SV628 @ SY2130 ) )
| ( dvd_dvd_int @ ( power_power_int @ SY2131 @ SV249 ) @ SV628 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2850]) ).
thf(3389,plain,
! [SV629: int,SV250: nat] :
( ( ! [SY2132: int,SY2133: int] :
( ~ ( zprime @ SY2133 )
| ( dvd_dvd_int @ SY2133 @ SY2132 )
| ~ ( dvd_dvd_int @ ( power_power_int @ SY2133 @ SV250 ) @ ( times_times_int @ SY2132 @ SV629 ) )
| ( dvd_dvd_int @ ( power_power_int @ SY2133 @ SV250 ) @ SV629 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2851]) ).
thf(3390,plain,
! [SV251: int,SV630: int] :
( ( ~ ( twoSqu362149276sum2sq @ SV630 )
| ~ ( twoSqu362149276sum2sq @ SV251 )
| ( twoSqu362149276sum2sq @ ( times_times_int @ SV630 @ SV251 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2852]) ).
thf(3391,plain,
! [SV631: real,SV252: real] :
( ( ! [SY2134: real,SY2135: real] :
( ( times_times_real @ ( times_times_real @ SV252 @ SV631 ) @ ( times_times_real @ SY2134 @ SY2135 ) )
= ( times_times_real @ ( times_times_real @ SV252 @ SY2134 ) @ ( times_times_real @ SV631 @ SY2135 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2853]) ).
thf(3392,plain,
! [SV632: nat,SV253: nat] :
( ( ! [SY2136: nat,SY2137: nat] :
( ( times_times_nat @ ( times_times_nat @ SV253 @ SV632 ) @ ( times_times_nat @ SY2136 @ SY2137 ) )
= ( times_times_nat @ ( times_times_nat @ SV253 @ SY2136 ) @ ( times_times_nat @ SV632 @ SY2137 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2854]) ).
thf(3393,plain,
! [SV633: int,SV254: int] :
( ( ! [SY2138: int,SY2139: int] :
( ( times_times_int @ ( times_times_int @ SV254 @ SV633 ) @ ( times_times_int @ SY2138 @ SY2139 ) )
= ( times_times_int @ ( times_times_int @ SV254 @ SY2138 ) @ ( times_times_int @ SV633 @ SY2139 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2855]) ).
thf(3394,plain,
! [SV634: real,SV255: real] :
( ( ! [SY2140: real,SY2141: real] :
( ( times_times_real @ ( times_times_real @ SV255 @ SV634 ) @ ( times_times_real @ SY2140 @ SY2141 ) )
= ( times_times_real @ SY2140 @ ( times_times_real @ ( times_times_real @ SV255 @ SV634 ) @ SY2141 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2856]) ).
thf(3395,plain,
! [SV635: nat,SV256: nat] :
( ( ! [SY2142: nat,SY2143: nat] :
( ( times_times_nat @ ( times_times_nat @ SV256 @ SV635 ) @ ( times_times_nat @ SY2142 @ SY2143 ) )
= ( times_times_nat @ SY2142 @ ( times_times_nat @ ( times_times_nat @ SV256 @ SV635 ) @ SY2143 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2857]) ).
thf(3396,plain,
! [SV636: int,SV257: int] :
( ( ! [SY2144: int,SY2145: int] :
( ( times_times_int @ ( times_times_int @ SV257 @ SV636 ) @ ( times_times_int @ SY2144 @ SY2145 ) )
= ( times_times_int @ SY2144 @ ( times_times_int @ ( times_times_int @ SV257 @ SV636 ) @ SY2145 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2858]) ).
thf(3397,plain,
! [SV637: real,SV258: real] :
( ( ! [SY2146: real,SY2147: real] :
( ( times_times_real @ ( times_times_real @ SV258 @ SV637 ) @ ( times_times_real @ SY2146 @ SY2147 ) )
= ( times_times_real @ SV258 @ ( times_times_real @ SV637 @ ( times_times_real @ SY2146 @ SY2147 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2859]) ).
thf(3398,plain,
! [SV638: nat,SV259: nat] :
( ( ! [SY2148: nat,SY2149: nat] :
( ( times_times_nat @ ( times_times_nat @ SV259 @ SV638 ) @ ( times_times_nat @ SY2148 @ SY2149 ) )
= ( times_times_nat @ SV259 @ ( times_times_nat @ SV638 @ ( times_times_nat @ SY2148 @ SY2149 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2860]) ).
thf(3399,plain,
! [SV639: int,SV260: int] :
( ( ! [SY2150: int,SY2151: int] :
( ( times_times_int @ ( times_times_int @ SV260 @ SV639 ) @ ( times_times_int @ SY2150 @ SY2151 ) )
= ( times_times_int @ SV260 @ ( times_times_int @ SV639 @ ( times_times_int @ SY2150 @ SY2151 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2861]) ).
thf(3400,plain,
! [SV640: real,SV261: real] :
( ( ! [SY2152: real] :
( ( times_times_real @ ( times_times_real @ SV261 @ SV640 ) @ SY2152 )
= ( times_times_real @ ( times_times_real @ SV261 @ SY2152 ) @ SV640 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2862]) ).
thf(3401,plain,
! [SV641: nat,SV262: nat] :
( ( ! [SY2153: nat] :
( ( times_times_nat @ ( times_times_nat @ SV262 @ SV641 ) @ SY2153 )
= ( times_times_nat @ ( times_times_nat @ SV262 @ SY2153 ) @ SV641 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2863]) ).
thf(3402,plain,
! [SV642: int,SV263: int] :
( ( ! [SY2154: int] :
( ( times_times_int @ ( times_times_int @ SV263 @ SV642 ) @ SY2154 )
= ( times_times_int @ ( times_times_int @ SV263 @ SY2154 ) @ SV642 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2864]) ).
thf(3403,plain,
! [SV643: real,SV264: real] :
( ( ! [SY2155: real] :
( ( times_times_real @ ( times_times_real @ SV264 @ SV643 ) @ SY2155 )
= ( times_times_real @ SV264 @ ( times_times_real @ SV643 @ SY2155 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2865]) ).
thf(3404,plain,
! [SV644: nat,SV265: nat] :
( ( ! [SY2156: nat] :
( ( times_times_nat @ ( times_times_nat @ SV265 @ SV644 ) @ SY2156 )
= ( times_times_nat @ SV265 @ ( times_times_nat @ SV644 @ SY2156 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2866]) ).
thf(3405,plain,
! [SV645: int,SV266: int] :
( ( ! [SY2157: int] :
( ( times_times_int @ ( times_times_int @ SV266 @ SV645 ) @ SY2157 )
= ( times_times_int @ SV266 @ ( times_times_int @ SV645 @ SY2157 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2867]) ).
thf(3406,plain,
! [SV646: real,SV267: real] :
( ( ! [SY2158: real] :
( ( times_times_real @ SV267 @ ( times_times_real @ SV646 @ SY2158 ) )
= ( times_times_real @ ( times_times_real @ SV267 @ SV646 ) @ SY2158 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2868]) ).
thf(3407,plain,
! [SV647: nat,SV268: nat] :
( ( ! [SY2159: nat] :
( ( times_times_nat @ SV268 @ ( times_times_nat @ SV647 @ SY2159 ) )
= ( times_times_nat @ ( times_times_nat @ SV268 @ SV647 ) @ SY2159 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2869]) ).
thf(3408,plain,
! [SV648: int,SV269: int] :
( ( ! [SY2160: int] :
( ( times_times_int @ SV269 @ ( times_times_int @ SV648 @ SY2160 ) )
= ( times_times_int @ ( times_times_int @ SV269 @ SV648 ) @ SY2160 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2870]) ).
thf(3409,plain,
! [SV649: real,SV270: real] :
( ( ! [SY2161: real] :
( ( times_times_real @ SV270 @ ( times_times_real @ SV649 @ SY2161 ) )
= ( times_times_real @ SV649 @ ( times_times_real @ SV270 @ SY2161 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2871]) ).
thf(3410,plain,
! [SV650: nat,SV271: nat] :
( ( ! [SY2162: nat] :
( ( times_times_nat @ SV271 @ ( times_times_nat @ SV650 @ SY2162 ) )
= ( times_times_nat @ SV650 @ ( times_times_nat @ SV271 @ SY2162 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2872]) ).
thf(3411,plain,
! [SV651: int,SV272: int] :
( ( ! [SY2163: int] :
( ( times_times_int @ SV272 @ ( times_times_int @ SV651 @ SY2163 ) )
= ( times_times_int @ SV651 @ ( times_times_int @ SV272 @ SY2163 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2873]) ).
thf(3412,plain,
! [SV652: real,SV273: real] :
( ( ( times_times_real @ SV273 @ SV652 )
= ( times_times_real @ SV652 @ SV273 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2874]) ).
thf(3413,plain,
! [SV653: nat,SV274: nat] :
( ( ( times_times_nat @ SV274 @ SV653 )
= ( times_times_nat @ SV653 @ SV274 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2875]) ).
thf(3414,plain,
! [SV654: int,SV275: int] :
( ( ( times_times_int @ SV275 @ SV654 )
= ( times_times_int @ SV654 @ SV275 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2876]) ).
thf(3415,plain,
! [SV655: real,SV276: real] :
( ( ( plus_plus_real @ SV276 @ SV655 )
= ( plus_plus_real @ SV655 @ SV276 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2877]) ).
thf(3416,plain,
! [SV656: nat,SV277: nat] :
( ( ( plus_plus_nat @ SV277 @ SV656 )
= ( plus_plus_nat @ SV656 @ SV277 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2878]) ).
thf(3417,plain,
! [SV657: real,SV278: real] :
( ( ! [SY2164: real] :
( ( plus_plus_real @ SV278 @ ( plus_plus_real @ SV657 @ SY2164 ) )
= ( plus_plus_real @ SV657 @ ( plus_plus_real @ SV278 @ SY2164 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2879]) ).
thf(3418,plain,
! [SV658: nat,SV279: nat] :
( ( ! [SY2165: nat] :
( ( plus_plus_nat @ SV279 @ ( plus_plus_nat @ SV658 @ SY2165 ) )
= ( plus_plus_nat @ SV658 @ ( plus_plus_nat @ SV279 @ SY2165 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2880]) ).
thf(3419,plain,
! [SV659: real,SV280: real] :
( ( ! [SY2166: real] :
( ( plus_plus_real @ SV280 @ ( plus_plus_real @ SV659 @ SY2166 ) )
= ( plus_plus_real @ ( plus_plus_real @ SV280 @ SV659 ) @ SY2166 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2881]) ).
thf(3420,plain,
! [SV660: nat,SV281: nat] :
( ( ! [SY2167: nat] :
( ( plus_plus_nat @ SV281 @ ( plus_plus_nat @ SV660 @ SY2167 ) )
= ( plus_plus_nat @ ( plus_plus_nat @ SV281 @ SV660 ) @ SY2167 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2882]) ).
thf(3421,plain,
! [SV661: real,SV282: real] :
( ( ! [SY2168: real] :
( ( plus_plus_real @ ( plus_plus_real @ SV282 @ SV661 ) @ SY2168 )
= ( plus_plus_real @ SV282 @ ( plus_plus_real @ SV661 @ SY2168 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2883]) ).
thf(3422,plain,
! [SV662: nat,SV283: nat] :
( ( ! [SY2169: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ SV283 @ SV662 ) @ SY2169 )
= ( plus_plus_nat @ SV283 @ ( plus_plus_nat @ SV662 @ SY2169 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2884]) ).
thf(3423,plain,
! [SV663: real,SV284: real] :
( ( ! [SY2170: real] :
( ( plus_plus_real @ ( plus_plus_real @ SV284 @ SV663 ) @ SY2170 )
= ( plus_plus_real @ ( plus_plus_real @ SV284 @ SY2170 ) @ SV663 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2885]) ).
thf(3424,plain,
! [SV664: nat,SV285: nat] :
( ( ! [SY2171: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ SV285 @ SV664 ) @ SY2171 )
= ( plus_plus_nat @ ( plus_plus_nat @ SV285 @ SY2171 ) @ SV664 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2886]) ).
thf(3425,plain,
! [SV665: real,SV286: real] :
( ( ! [SY2172: real,SY2173: real] :
( ( plus_plus_real @ ( plus_plus_real @ SV286 @ SV665 ) @ ( plus_plus_real @ SY2172 @ SY2173 ) )
= ( plus_plus_real @ ( plus_plus_real @ SV286 @ SY2172 ) @ ( plus_plus_real @ SV665 @ SY2173 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2887]) ).
thf(3426,plain,
! [SV666: nat,SV287: nat] :
( ( ! [SY2174: nat,SY2175: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ SV287 @ SV666 ) @ ( plus_plus_nat @ SY2174 @ SY2175 ) )
= ( plus_plus_nat @ ( plus_plus_nat @ SV287 @ SY2174 ) @ ( plus_plus_nat @ SV666 @ SY2175 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2888]) ).
thf(3427,plain,
! [SV290: real] :
( ( ( ! [SY1680: nat] :
~ ( ord_less_eq_real @ ( power_power_real @ SV290 @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SY1680 ) ) @ zero_zero_real ) )
= $true )
| ( ( SV290 = zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2891]) ).
thf(3428,plain,
! [SV667: real,SV299: real] :
( ( ! [SY2176: real] :
( ( times_times_real @ SV299 @ ( plus_plus_real @ SV667 @ SY2176 ) )
= ( plus_plus_real @ ( times_times_real @ SV299 @ SV667 ) @ ( times_times_real @ SV299 @ SY2176 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2900]) ).
thf(3429,plain,
! [SV668: nat,SV300: nat] :
( ( ! [SY2177: nat] :
( ( times_times_nat @ SV300 @ ( plus_plus_nat @ SV668 @ SY2177 ) )
= ( plus_plus_nat @ ( times_times_nat @ SV300 @ SV668 ) @ ( times_times_nat @ SV300 @ SY2177 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2901]) ).
thf(3430,plain,
! [SV669: real,SV301: real] :
( ( ! [SY2178: real] :
( ( times_times_real @ ( plus_plus_real @ SV301 @ SV669 ) @ SY2178 )
= ( plus_plus_real @ ( times_times_real @ SV301 @ SY2178 ) @ ( times_times_real @ SV669 @ SY2178 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2902]) ).
thf(3431,plain,
! [SV670: nat,SV302: nat] :
( ( ! [SY2179: nat] :
( ( times_times_nat @ ( plus_plus_nat @ SV302 @ SV670 ) @ SY2179 )
= ( plus_plus_nat @ ( times_times_nat @ SV302 @ SY2179 ) @ ( times_times_nat @ SV670 @ SY2179 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2903]) ).
thf(3432,plain,
! [SV671: real,SV303: real] :
( ( ! [SY2180: real] :
( ( plus_plus_real @ ( times_times_real @ SV303 @ SV671 ) @ ( times_times_real @ SY2180 @ SV671 ) )
= ( times_times_real @ ( plus_plus_real @ SV303 @ SY2180 ) @ SV671 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2904]) ).
thf(3433,plain,
! [SV672: nat,SV304: nat] :
( ( ! [SY2181: nat] :
( ( plus_plus_nat @ ( times_times_nat @ SV304 @ SV672 ) @ ( times_times_nat @ SY2181 @ SV672 ) )
= ( times_times_nat @ ( plus_plus_nat @ SV304 @ SY2181 ) @ SV672 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2905]) ).
thf(3434,plain,
! [SV673: real,SV309: real] :
( ( ! [SY2182: nat] :
( ( power_power_real @ ( times_times_real @ SV309 @ SV673 ) @ SY2182 )
= ( times_times_real @ ( power_power_real @ SV309 @ SY2182 ) @ ( power_power_real @ SV673 @ SY2182 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2910]) ).
thf(3435,plain,
! [SV674: nat,SV310: nat] :
( ( ! [SY2183: nat] :
( ( power_power_nat @ ( times_times_nat @ SV310 @ SV674 ) @ SY2183 )
= ( times_times_nat @ ( power_power_nat @ SV310 @ SY2183 ) @ ( power_power_nat @ SV674 @ SY2183 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2911]) ).
thf(3436,plain,
! [SV675: nat,SV311: real] :
( ( ! [SY2184: nat] :
( ( times_times_real @ ( power_power_real @ SV311 @ SV675 ) @ ( power_power_real @ SV311 @ SY2184 ) )
= ( power_power_real @ SV311 @ ( plus_plus_nat @ SV675 @ SY2184 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2912]) ).
thf(3437,plain,
! [SV676: nat,SV312: nat] :
( ( ! [SY2185: nat] :
( ( times_times_nat @ ( power_power_nat @ SV312 @ SV676 ) @ ( power_power_nat @ SV312 @ SY2185 ) )
= ( power_power_nat @ SV312 @ ( plus_plus_nat @ SV676 @ SY2185 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2913]) ).
thf(3438,plain,
! [SV677: nat,SV315: real] :
( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ SV315 @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV677 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2916]) ).
thf(3439,plain,
! [SV678: real,SV316: real] :
( ( ! [SY2186: real,SY2187: real,SY2188: real] :
( ( SY2188 = zero_zero_real )
| ( SV316 = SV678 )
| ( SY2186 != SY2187 )
| ( ( plus_plus_real @ SY2186 @ ( times_times_real @ SY2188 @ SV316 ) )
!= ( plus_plus_real @ SY2187 @ ( times_times_real @ SY2188 @ SV678 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2917]) ).
thf(3440,plain,
! [SV679: nat,SV317: nat] :
( ( ! [SY2189: nat,SY2190: nat,SY2191: nat] :
( ( SY2191 = zero_zero_nat )
| ( SV317 = SV679 )
| ( SY2189 != SY2190 )
| ( ( plus_plus_nat @ SY2189 @ ( times_times_nat @ SY2191 @ SV317 ) )
!= ( plus_plus_nat @ SY2190 @ ( times_times_nat @ SY2191 @ SV679 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2918]) ).
thf(3441,plain,
! [SV680: real,SV320: real] :
( ( ( plus_plus_real @ SV320 @ ( times_times_real @ SV680 @ SV320 ) )
= ( times_times_real @ ( plus_plus_real @ SV680 @ one_one_real ) @ SV320 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2921]) ).
thf(3442,plain,
! [SV681: nat,SV321: nat] :
( ( ( plus_plus_nat @ SV321 @ ( times_times_nat @ SV681 @ SV321 ) )
= ( times_times_nat @ ( plus_plus_nat @ SV681 @ one_one_nat ) @ SV321 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2922]) ).
thf(3443,plain,
! [SV682: real,SV322: real] :
( ( ( plus_plus_real @ ( times_times_real @ SV322 @ SV682 ) @ SV682 )
= ( times_times_real @ ( plus_plus_real @ SV322 @ one_one_real ) @ SV682 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2923]) ).
thf(3444,plain,
! [SV683: nat,SV323: nat] :
( ( ( plus_plus_nat @ ( times_times_nat @ SV323 @ SV683 ) @ SV683 )
= ( times_times_nat @ ( plus_plus_nat @ SV323 @ one_one_nat ) @ SV683 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2924]) ).
thf(3445,plain,
! [SV324: int] :
( ( ( ~ ( zprime @ SV324 ) )
= $true )
| ( ( ( SV324
= ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
| ( SV324
= ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) )
| ( ord_less_eq_int @ ( number_number_of_int @ ( bit1 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SV324 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2925]) ).
thf(3446,plain,
! [SV325: int] :
( ( ( ! [SY1714: int] :
( ( times_times_int @ SV325 @ SY1714 )
!= one_one_int ) )
= $true )
| ( ( ( SV325 = one_one_int )
| ( SV325
= ( number_number_of_int @ min ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2926]) ).
thf(3447,plain,
! [SV684: int,SV326: int] :
( ( zcong @ SV326 @ SV326 @ SV684 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2927]) ).
thf(3448,plain,
! [SV327: int,SV685: int] :
( ( ! [SY2192: int,SY2193: int] :
( ~ ( zcong @ SV685 @ SY2192 @ SY2193 )
| ~ ( zcong @ SY2192 @ SV327 @ SY2193 )
| ( zcong @ SV685 @ SV327 @ SY2193 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2928]) ).
thf(3449,plain,
! [SV686: real,SV328: real] :
( ( ~ ( ord_less_eq_real @ SV328 @ SV686 )
| ( SV328 = SV686 )
| ( ord_less_real @ SV328 @ SV686 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2929]) ).
thf(3450,plain,
! [SV687: nat,SV329: nat] :
( ( ~ ( ord_less_eq_nat @ SV329 @ SV687 )
| ( SV329 = SV687 )
| ( ord_less_nat @ SV329 @ SV687 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2930]) ).
thf(3451,plain,
! [SV688: int,SV330: int] :
( ( ! [SY2194: int] : ( zcong @ ( times_times_int @ SV330 @ SV688 ) @ ( times_times_int @ SY2194 @ SV688 ) @ SV688 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2931]) ).
thf(3452,plain,
! [SV331: int,SV689: int] :
( ( ! [SY2195: int,SY2196: int] :
( ~ ( zcong @ SV689 @ SY2195 @ SY2196 )
| ( zcong @ ( times_times_int @ SV689 @ SV331 ) @ ( times_times_int @ SY2195 @ SV331 ) @ SY2196 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2932]) ).
thf(3453,plain,
! [SV332: int,SV690: int] :
( ( ! [SY2197: int,SY2198: int] :
( ~ ( zcong @ SV690 @ SY2197 @ SY2198 )
| ( zcong @ ( times_times_int @ SV332 @ SV690 ) @ ( times_times_int @ SV332 @ SY2197 ) @ SY2198 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2933]) ).
thf(3454,plain,
! [SV691: int,SV333: int] :
( ( ! [SY2199: int,SY2200: int,SY2201: int] :
( ~ ( zcong @ SY2199 @ SY2200 @ SY2201 )
| ~ ( zcong @ SV333 @ SV691 @ SY2201 )
| ( zcong @ ( times_times_int @ SY2199 @ SV333 ) @ ( times_times_int @ SY2200 @ SV691 ) @ SY2201 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2934]) ).
thf(3455,plain,
! [SV337: int,SV692: int] :
( ( ! [SY2202: int] :
( ~ ( ord_less_eq_int @ zero_zero_int @ SY2202 )
| ~ ( zprime @ SV692 )
| ~ ( dvd_dvd_int @ SV692 @ ( times_times_int @ SY2202 @ SV337 ) )
| ( dvd_dvd_int @ SV692 @ SY2202 )
| ( dvd_dvd_int @ SV692 @ SV337 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2938]) ).
thf(3456,plain,
! [SV693: nat,SV338: nat] :
( ( ! [SY2203: int] :
( ~ ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ SY2203 )
| ~ ( zcong @ ( power_power_int @ ( number_number_of_int @ min ) @ SV338 ) @ ( power_power_int @ ( number_number_of_int @ min ) @ SV693 ) @ SY2203 )
| ( ( power_power_int @ ( number_number_of_int @ min ) @ SV338 )
= ( power_power_int @ ( number_number_of_int @ min ) @ SV693 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2939]) ).
thf(3457,plain,
! [SV339: int,SV694: int] :
( ( ~ ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV694 )
| ~ ( zcong @ SV339 @ ( number_number_of_int @ min ) @ SV694 )
| ~ ( zcong @ SV339 @ one_one_int @ SV694 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2940]) ).
thf(3458,plain,
! [SV695: int,SV340: int] :
( ( ! [SY2204: int,SY2205: int,SY2206: int] :
( ~ ( zcong @ SY2204 @ SY2205 @ SY2206 )
| ~ ( zcong @ SV340 @ SV695 @ SY2206 )
| ( zcong @ ( minus_minus_int @ SY2204 @ SV340 ) @ ( minus_minus_int @ SY2205 @ SV695 ) @ SY2206 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2941]) ).
thf(3459,plain,
! [SV696: int,SV341: int] :
( ( ! [SY2207: int] :
( ~ ( dvd_dvd_int @ SV341 @ ( minus_minus_int @ SV696 @ SY2207 ) )
| ~ ( dvd_dvd_int @ SV341 @ SY2207 )
| ( dvd_dvd_int @ SV341 @ SV696 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2942]) ).
thf(3460,plain,
! [SV697: int,SV342: int] :
( ( ! [SY2208: int] :
( ( times_times_int @ SV342 @ ( minus_minus_int @ SV697 @ SY2208 ) )
= ( minus_minus_int @ ( times_times_int @ SV342 @ SV697 ) @ ( times_times_int @ SV342 @ SY2208 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2943]) ).
thf(3461,plain,
! [SV698: int,SV343: int] :
( ( ! [SY2209: int] :
( ( times_times_int @ ( minus_minus_int @ SV343 @ SV698 ) @ SY2209 )
= ( minus_minus_int @ ( times_times_int @ SV343 @ SY2209 ) @ ( times_times_int @ SV698 @ SY2209 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2944]) ).
thf(3462,plain,
! [SV699: int,SV344: int] :
( ( ( number267125858f_real @ ( minus_minus_int @ SV344 @ SV699 ) )
= ( minus_minus_real @ ( number267125858f_real @ SV344 ) @ ( number267125858f_real @ SV699 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2945]) ).
thf(3463,plain,
! [SV700: int,SV345: int] :
( ( ( number_number_of_int @ ( minus_minus_int @ SV345 @ SV700 ) )
= ( minus_minus_int @ ( number_number_of_int @ SV345 ) @ ( number_number_of_int @ SV700 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2946]) ).
thf(3464,plain,
! [SV701: real,SV346: int] :
( ( ! [SY2210: real] :
( ( times_times_real @ ( number267125858f_real @ SV346 ) @ ( minus_minus_real @ SV701 @ SY2210 ) )
= ( minus_minus_real @ ( times_times_real @ ( number267125858f_real @ SV346 ) @ SV701 ) @ ( times_times_real @ ( number267125858f_real @ SV346 ) @ SY2210 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2947]) ).
thf(3465,plain,
! [SV702: int,SV347: int] :
( ( ! [SY2211: int] :
( ( times_times_int @ ( number_number_of_int @ SV347 ) @ ( minus_minus_int @ SV702 @ SY2211 ) )
= ( minus_minus_int @ ( times_times_int @ ( number_number_of_int @ SV347 ) @ SV702 ) @ ( times_times_int @ ( number_number_of_int @ SV347 ) @ SY2211 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2948]) ).
thf(3466,plain,
! [SV703: real,SV348: real] :
( ( ! [SY2212: int] :
( ( times_times_real @ ( minus_minus_real @ SV348 @ SV703 ) @ ( number267125858f_real @ SY2212 ) )
= ( minus_minus_real @ ( times_times_real @ SV348 @ ( number267125858f_real @ SY2212 ) ) @ ( times_times_real @ SV703 @ ( number267125858f_real @ SY2212 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2949]) ).
thf(3467,plain,
! [SV704: int,SV349: int] :
( ( ! [SY2213: int] :
( ( times_times_int @ ( minus_minus_int @ SV349 @ SV704 ) @ ( number_number_of_int @ SY2213 ) )
= ( minus_minus_int @ ( times_times_int @ SV349 @ ( number_number_of_int @ SY2213 ) ) @ ( times_times_int @ SV704 @ ( number_number_of_int @ SY2213 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2950]) ).
thf(3468,plain,
! [SV705: int,SV350: int] :
( ( ! [SY2214: real] :
( ( plus_plus_real @ ( number267125858f_real @ SV350 ) @ ( minus_minus_real @ ( number267125858f_real @ SV705 ) @ SY2214 ) )
= ( minus_minus_real @ ( number267125858f_real @ ( plus_plus_int @ SV350 @ SV705 ) ) @ SY2214 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2951]) ).
thf(3469,plain,
! [SV351: int,SV706: int] :
( ( ! [SY2215: int,SY2216: int,SY2217: int] :
( ~ ( zcong @ SY2215 @ SY2216 @ SY2217 )
| ( SY2216 != SV706 )
| ~ ( zcong @ SV706 @ SV351 @ SY2217 )
| ( zcong @ SY2215 @ SV351 @ SY2217 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2952]) ).
thf(3470,plain,
! [SV352: int,SV707: int] :
( ( ~ ( zprime @ SV707 )
| ~ ( ord_less_int @ zero_zero_int @ SV352 )
| ~ ( ord_less_int @ SV352 @ SV707 )
| ~ ( zcong @ ( times_times_int @ SV352 @ SV352 ) @ one_one_int @ SV707 )
| ( SV352 = one_one_int )
| ( SV352
= ( minus_minus_int @ SV707 @ one_one_int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2953]) ).
thf(3471,plain,
! [SV353: int,SV708: int] :
( ( ~ ( zprime @ SV708 )
| ~ ( ord_less_int @ zero_zero_int @ SV353 )
| ~ ( zcong @ ( times_times_int @ SV353 @ SV353 ) @ one_one_int @ SV708 )
| ( zcong @ SV353 @ one_one_int @ SV708 )
| ( zcong @ SV353 @ ( minus_minus_int @ SV708 @ one_one_int ) @ SV708 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2954]) ).
thf(3472,plain,
! [SV709: real,SV354: real] :
( ( ( power_power_real @ ( minus_minus_real @ SV354 @ SV709 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( minus_minus_real @ ( plus_plus_real @ ( power_power_real @ SV354 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SV709 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV354 ) @ SV709 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2955]) ).
thf(3473,plain,
! [SV710: int,SV355: int] :
( ( ( power_power_int @ ( minus_minus_int @ SV355 @ SV710 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( minus_minus_int @ ( plus_plus_int @ ( power_power_int @ SV355 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV710 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV355 ) @ SV710 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2956]) ).
thf(3474,plain,
! [SV711: int,SV356: int] :
( ( ( power_power_int @ ( minus_minus_int @ SV356 @ SV711 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ ( minus_minus_int @ ( power_power_int @ SV356 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV356 ) @ SV711 ) ) @ ( power_power_int @ SV711 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2957]) ).
thf(3475,plain,
! [SV712: int,SV357: int] :
( ( ( power_power_int @ ( minus_minus_int @ SV357 @ SV712 ) @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( minus_minus_int @ ( plus_plus_int @ ( minus_minus_int @ ( power_power_int @ SV357 @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) @ ( power_power_int @ SV357 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ SV712 ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) @ SV357 ) @ ( power_power_int @ SV712 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ ( power_power_int @ SV712 @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2958]) ).
thf(3476,plain,
! [SV713: int,SV358: int] :
( ( ! [SY2218: int] :
( ~ ( zprime @ SY2218 )
| ~ ( dvd_dvd_int @ SY2218 @ ( times_times_int @ SV358 @ SV713 ) )
| ( dvd_dvd_int @ SY2218 @ SV358 )
| ( dvd_dvd_int @ SY2218 @ SV713 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2959]) ).
thf(3477,plain,
! [SV714: int,SV359: int] :
( ( ! [SY2219: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SY2219 )
| ~ ( dvd_dvd_int @ SV359 @ SV714 )
| ( dvd_dvd_int @ SV359 @ ( power_power_int @ SV714 @ SY2219 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2960]) ).
thf(3478,plain,
! [SV360: int,SV715: int] :
( ( ! [SY2220: int] :
( ~ ( zprime @ SY2220 )
| ( zcong @ SV715 @ zero_zero_int @ SY2220 )
| ( zcong @ SV360 @ zero_zero_int @ SY2220 )
| ~ ( zcong @ ( times_times_int @ SV715 @ SV360 ) @ zero_zero_int @ SY2220 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2961]) ).
thf(3479,plain,
! [SV361: int,SV716: int] :
( ( ! [SY2221: int] :
( ~ ( zprime @ SY2221 )
| ~ ( ord_less_int @ zero_zero_int @ SV716 )
| ( zcong @ SV716 @ zero_zero_int @ SY2221 )
| ( zcong @ SV361 @ zero_zero_int @ SY2221 )
| ~ ( zcong @ ( times_times_int @ SV716 @ SV361 ) @ zero_zero_int @ SY2221 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2962]) ).
thf(3480,plain,
! [SV362: int,SV717: int] :
( ( ! [SY2222: int] :
( ~ ( zprime @ SY2222 )
| ~ ( ord_less_int @ zero_zero_int @ SV717 )
| ~ ( zcong @ ( times_times_int @ SV717 @ SV362 ) @ zero_zero_int @ SY2222 )
| ( zcong @ SV717 @ zero_zero_int @ SY2222 )
| ( zcong @ SV362 @ zero_zero_int @ SY2222 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2963]) ).
thf(3481,plain,
! [SV718: nat,SV363: int] :
( ( ! [SY2223: int] :
( ~ ( zprime @ SY2223 )
| ~ ( dvd_dvd_int @ SY2223 @ ( power_power_int @ SV363 @ SV718 ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV718 )
| ( dvd_dvd_int @ SY2223 @ SV363 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2964]) ).
thf(3482,plain,
! [SV364: int] :
( ( ( ~ ( zprime @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SV364 ) @ one_one_int ) ) )
= $true )
| ( ( ( legendre @ ( number_number_of_int @ min ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SV364 ) @ one_one_int ) )
= one_one_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2965]) ).
thf(3483,plain,
! [SV365: int] :
( ( ( ~ ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV365 ) )
= $true )
| ( ( ~ ( zcong @ one_one_int @ ( number_number_of_int @ min ) @ SV365 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2966]) ).
thf(3484,plain,
! [SV719: real,SV366: real] :
( ( ( power_power_real @ ( plus_plus_real @ SV366 @ SV719 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_real @ ( plus_plus_real @ ( power_power_real @ SV366 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SV719 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV366 ) @ SV719 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2967]) ).
thf(3485,plain,
! [SV720: nat,SV367: nat] :
( ( ( minus_minus_nat @ ( power_power_nat @ SV367 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_nat @ SV720 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( times_times_nat @ ( plus_plus_nat @ SV367 @ SV720 ) @ ( minus_minus_nat @ SV367 @ SV720 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2968]) ).
thf(3486,plain,
! [SV721: real,SV368: real] :
( ( ! [SY2224: real] :
( ( times_times_real @ ( times_times_real @ SV368 @ SV721 ) @ SY2224 )
= ( times_times_real @ SV368 @ ( times_times_real @ SV721 @ SY2224 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2970]) ).
thf(3487,plain,
! [SV722: real,SV369: real] :
( ( ( times_times_real @ SV369 @ SV722 )
= ( times_times_real @ SV722 @ SV369 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2971]) ).
thf(3488,plain,
! [SV371: real,SV723: real] :
( ( ! [SY2225: real] :
( ~ ( ord_less_eq_real @ SV723 @ SY2225 )
| ( ord_less_eq_real @ ( plus_plus_real @ SV371 @ SV723 ) @ ( plus_plus_real @ SV371 @ SY2225 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2973]) ).
thf(3489,plain,
! [SV724: real,SV372: real] :
( ( ! [SY2226: real,SY2227: real] :
( ( minus_minus_real @ ( plus_plus_real @ SV372 @ SV724 ) @ ( plus_plus_real @ SY2226 @ SY2227 ) )
= ( plus_plus_real @ ( minus_minus_real @ SV372 @ SY2226 ) @ ( minus_minus_real @ SV724 @ SY2227 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2974]) ).
thf(3490,plain,
! [SV725: real,SV373: real] :
( ( ! [SY2228: real] :
( ( times_times_real @ ( plus_plus_real @ SV373 @ SV725 ) @ SY2228 )
= ( plus_plus_real @ ( times_times_real @ SV373 @ SY2228 ) @ ( times_times_real @ SV725 @ SY2228 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2975]) ).
thf(3491,plain,
! [SV726: real,SV374: real] :
( ( ! [SY2229: real,SY2230: real] :
( ( minus_minus_real @ ( times_times_real @ SV374 @ SV726 ) @ ( times_times_real @ SY2229 @ SY2230 ) )
= ( plus_plus_real @ ( times_times_real @ SV374 @ ( minus_minus_real @ SV726 @ SY2230 ) ) @ ( times_times_real @ ( minus_minus_real @ SV374 @ SY2229 ) @ SY2230 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2976]) ).
thf(3492,plain,
! [SV727: real,SV375: real] :
( ( ! [SY2231: real] :
( ~ ( ord_less_real @ zero_zero_real @ SY2231 )
| ~ ( ord_less_real @ SV375 @ SV727 )
| ( ord_less_real @ ( times_times_real @ SY2231 @ SV375 ) @ ( times_times_real @ SY2231 @ SV727 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2977]) ).
thf(3493,plain,
! [SV376: real,SV728: real] :
( ( ~ ( ord_less_real @ zero_zero_real @ SV728 )
| ~ ( ord_less_real @ zero_zero_real @ SV376 )
| ( ord_less_real @ zero_zero_real @ ( times_times_real @ SV728 @ SV376 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2978]) ).
thf(3494,plain,
! [SV378: real,SV729: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ SV729 )
| ( ( times_times_real @ ( power_power_real @ SV378 @ ( minus_minus_nat @ SV729 @ one_one_nat ) ) @ SV378 )
= ( power_power_real @ SV378 @ SV729 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2980]) ).
thf(3495,plain,
! [SV379: nat,SV730: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ SV730 )
| ( ( times_times_nat @ ( power_power_nat @ SV379 @ ( minus_minus_nat @ SV730 @ one_one_nat ) ) @ SV379 )
= ( power_power_nat @ SV379 @ SV730 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2981]) ).
thf(3496,plain,
! [SV380: int,SV731: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ SV731 )
| ( ( times_times_int @ ( power_power_int @ SV380 @ ( minus_minus_nat @ SV731 @ one_one_nat ) ) @ SV380 )
= ( power_power_int @ SV380 @ SV731 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2982]) ).
thf(3497,plain,
! [SV382: nat,SV732: real] :
( ( ! [SY2232: real] :
( ~ ( ord_less_real @ SV732 @ SY2232 )
| ~ ( ord_less_eq_real @ zero_zero_real @ SV732 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV382 )
| ( ord_less_real @ ( power_power_real @ SV732 @ SV382 ) @ ( power_power_real @ SY2232 @ SV382 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2984]) ).
thf(3498,plain,
! [SV383: nat,SV733: nat] :
( ( ! [SY2233: nat] :
( ~ ( ord_less_nat @ SV733 @ SY2233 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV733 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV383 )
| ( ord_less_nat @ ( power_power_nat @ SV733 @ SV383 ) @ ( power_power_nat @ SY2233 @ SV383 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2985]) ).
thf(3499,plain,
! [SV384: nat,SV734: int] :
( ( ! [SY2234: int] :
( ~ ( ord_less_int @ SV734 @ SY2234 )
| ~ ( ord_less_eq_int @ zero_zero_int @ SV734 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV384 )
| ( ord_less_int @ ( power_power_int @ SV734 @ SV384 ) @ ( power_power_int @ SY2234 @ SV384 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2986]) ).
thf(3500,plain,
! [SV385: nat,SV735: real] :
( ( ( SV735 = zero_zero_real )
| ( ( power_power_real @ SV735 @ SV385 )
!= zero_zero_real ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2987]) ).
thf(3501,plain,
! [SV736: real,SV386: real] :
( ( ! [SY2235: nat] :
( ( power_power_real @ ( times_times_real @ SV386 @ SV736 ) @ SY2235 )
= ( times_times_real @ ( power_power_real @ SV386 @ SY2235 ) @ ( power_power_real @ SV736 @ SY2235 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2988]) ).
thf(3502,plain,
! [SV737: nat,SV387: nat] :
( ( ! [SY2236: nat] :
( ( power_power_nat @ ( times_times_nat @ SV387 @ SV737 ) @ SY2236 )
= ( times_times_nat @ ( power_power_nat @ SV387 @ SY2236 ) @ ( power_power_nat @ SV737 @ SY2236 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2989]) ).
thf(3503,plain,
! [SV738: nat,SV388: real] :
( ( ( times_times_real @ ( power_power_real @ SV388 @ SV738 ) @ SV388 )
= ( times_times_real @ SV388 @ ( power_power_real @ SV388 @ SV738 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2990]) ).
thf(3504,plain,
! [SV739: nat,SV389: nat] :
( ( ( times_times_nat @ ( power_power_nat @ SV389 @ SV739 ) @ SV389 )
= ( times_times_nat @ SV389 @ ( power_power_nat @ SV389 @ SV739 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2991]) ).
thf(3505,plain,
! [SV392: nat,SV740: nat] :
( ( ! [SY2237: nat] :
( ~ ( dvd_dvd_nat @ SV740 @ SY2237 )
| ( dvd_dvd_nat @ ( power_power_nat @ SV740 @ SV392 ) @ ( power_power_nat @ SY2237 @ SV392 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2994]) ).
thf(3506,plain,
! [SV393: nat,SV741: real] :
( ( ! [SY2238: real] :
( ~ ( dvd_dvd_real @ SV741 @ SY2238 )
| ( dvd_dvd_real @ ( power_power_real @ SV741 @ SV393 ) @ ( power_power_real @ SY2238 @ SV393 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2995]) ).
thf(3507,plain,
! [SV742: nat,SV394: real] :
( ( ! [SY2239: nat] :
( ( power_power_real @ SV394 @ ( times_times_nat @ SV742 @ SY2239 ) )
= ( power_power_real @ ( power_power_real @ SV394 @ SV742 ) @ SY2239 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2996]) ).
thf(3508,plain,
! [SV743: nat,SV395: nat] :
( ( ! [SY2240: nat] :
( ( power_power_nat @ SV395 @ ( times_times_nat @ SV743 @ SY2240 ) )
= ( power_power_nat @ ( power_power_nat @ SV395 @ SV743 ) @ SY2240 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2997]) ).
thf(3509,plain,
! [SV398: nat,SV744: real] :
( ( ! [SY2241: real] :
( ~ ( ord_less_eq_real @ SV744 @ SY2241 )
| ~ ( ord_less_eq_real @ zero_zero_real @ SV744 )
| ( ord_less_eq_real @ ( power_power_real @ SV744 @ SV398 ) @ ( power_power_real @ SY2241 @ SV398 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3000]) ).
thf(3510,plain,
! [SV399: nat,SV745: nat] :
( ( ! [SY2242: nat] :
( ~ ( ord_less_eq_nat @ SV745 @ SY2242 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV745 )
| ( ord_less_eq_nat @ ( power_power_nat @ SV745 @ SV399 ) @ ( power_power_nat @ SY2242 @ SV399 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3001]) ).
thf(3511,plain,
! [SV400: nat,SV746: real] :
( ( ~ ( ord_less_eq_real @ zero_zero_real @ SV746 )
| ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ SV746 @ SV400 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3002]) ).
thf(3512,plain,
! [SV401: nat,SV747: nat] :
( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV747 )
| ( ord_less_eq_nat @ zero_zero_nat @ ( power_power_nat @ SV747 @ SV401 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3003]) ).
thf(3513,plain,
! [SV402: nat,SV748: real] :
( ( ~ ( ord_less_real @ zero_zero_real @ SV748 )
| ( ord_less_real @ zero_zero_real @ ( power_power_real @ SV748 @ SV402 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3004]) ).
thf(3514,plain,
! [SV403: nat,SV749: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ SV749 )
| ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV749 @ SV403 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3005]) ).
thf(3515,plain,
! [SV404: nat,SV750: real] :
( ( ~ ( ord_less_eq_real @ one_one_real @ SV750 )
| ( ord_less_eq_real @ one_one_real @ ( power_power_real @ SV750 @ SV404 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3006]) ).
thf(3516,plain,
! [SV405: nat,SV751: nat] :
( ( ~ ( ord_less_eq_nat @ one_one_nat @ SV751 )
| ( ord_less_eq_nat @ one_one_nat @ ( power_power_nat @ SV751 @ SV405 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3007]) ).
thf(3517,plain,
! [SV752: nat,SV408: real] :
( ( ! [SY2243: nat] :
( ( power_power_real @ SV408 @ ( plus_plus_nat @ SV752 @ SY2243 ) )
= ( times_times_real @ ( power_power_real @ SV408 @ SV752 ) @ ( power_power_real @ SV408 @ SY2243 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3010]) ).
thf(3518,plain,
! [SV753: nat,SV409: nat] :
( ( ! [SY2244: nat] :
( ( power_power_nat @ SV409 @ ( plus_plus_nat @ SV753 @ SY2244 ) )
= ( times_times_nat @ ( power_power_nat @ SV409 @ SV753 ) @ ( power_power_nat @ SV409 @ SY2244 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3011]) ).
thf(3519,plain,
! [SV410: nat,SV754: nat] :
( ( ! [SY2245: nat,SY2246: nat] :
( ~ ( dvd_dvd_nat @ ( power_power_nat @ SV754 @ SY2245 ) @ SY2246 )
| ~ ( ord_less_eq_nat @ SV410 @ SY2245 )
| ( dvd_dvd_nat @ ( power_power_nat @ SV754 @ SV410 ) @ SY2246 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3012]) ).
thf(3520,plain,
! [SV411: nat,SV755: real] :
( ( ! [SY2247: nat,SY2248: real] :
( ~ ( dvd_dvd_real @ ( power_power_real @ SV755 @ SY2247 ) @ SY2248 )
| ~ ( ord_less_eq_nat @ SV411 @ SY2247 )
| ( dvd_dvd_real @ ( power_power_real @ SV755 @ SV411 ) @ SY2248 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3013]) ).
thf(3521,plain,
! [SV756: nat,SV412: nat] :
( ( ! [SY2249: nat,SY2250: nat] :
( ~ ( dvd_dvd_nat @ SY2249 @ SY2250 )
| ~ ( ord_less_eq_nat @ SV412 @ SV756 )
| ( dvd_dvd_nat @ ( power_power_nat @ SY2249 @ SV412 ) @ ( power_power_nat @ SY2250 @ SV756 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3014]) ).
thf(3522,plain,
! [SV757: nat,SV413: nat] :
( ( ! [SY2251: real,SY2252: real] :
( ~ ( dvd_dvd_real @ SY2251 @ SY2252 )
| ~ ( ord_less_eq_nat @ SV413 @ SV757 )
| ( dvd_dvd_real @ ( power_power_real @ SY2251 @ SV413 ) @ ( power_power_real @ SY2252 @ SV757 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3015]) ).
thf(3523,plain,
! [SV414: nat,SV758: nat] :
( ( ! [SY2253: nat] :
( ~ ( ord_less_eq_nat @ SV758 @ SY2253 )
| ( dvd_dvd_nat @ ( power_power_nat @ SV414 @ SV758 ) @ ( power_power_nat @ SV414 @ SY2253 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3016]) ).
thf(3524,plain,
! [SV415: real,SV759: nat] :
( ( ! [SY2254: nat] :
( ~ ( ord_less_eq_nat @ SV759 @ SY2254 )
| ( dvd_dvd_real @ ( power_power_real @ SV415 @ SV759 ) @ ( power_power_real @ SV415 @ SY2254 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3017]) ).
thf(3525,plain,
! [SV760: nat,SV416: nat] :
( ( ! [SY2255: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SY2255 )
| ~ ( ord_less_nat @ ( power_power_nat @ SY2255 @ SV416 ) @ ( power_power_nat @ SY2255 @ SV760 ) )
| ( ord_less_nat @ SV416 @ SV760 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3018]) ).
thf(3526,plain,
! [SV761: nat,SV417: real] :
( ( ! [SY2256: real] :
( ~ ( ord_less_real @ ( power_power_real @ SV417 @ SV761 ) @ ( power_power_real @ SY2256 @ SV761 ) )
| ~ ( ord_less_eq_real @ zero_zero_real @ SY2256 )
| ( ord_less_real @ SV417 @ SY2256 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3019]) ).
thf(3527,plain,
! [SV762: nat,SV418: nat] :
( ( ! [SY2257: nat] :
( ~ ( ord_less_nat @ ( power_power_nat @ SV418 @ SV762 ) @ ( power_power_nat @ SY2257 @ SV762 ) )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SY2257 )
| ( ord_less_nat @ SV418 @ SY2257 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3020]) ).
thf(3528,plain,
! [SV419: nat,SV763: real] :
( ( ~ ( ord_less_real @ one_one_real @ SV763 )
| ( ord_less_real @ ( power_power_real @ SV763 @ SV419 ) @ ( times_times_real @ SV763 @ ( power_power_real @ SV763 @ SV419 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3021]) ).
thf(3529,plain,
! [SV420: nat,SV764: nat] :
( ( ~ ( ord_less_nat @ one_one_nat @ SV764 )
| ( ord_less_nat @ ( power_power_nat @ SV764 @ SV420 ) @ ( times_times_nat @ SV764 @ ( power_power_nat @ SV764 @ SV420 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3022]) ).
thf(3530,plain,
! [SV421: nat,SV765: real] :
( ( ~ ( ord_less_real @ one_one_real @ SV765 )
| ( ord_less_real @ one_one_real @ ( times_times_real @ SV765 @ ( power_power_real @ SV765 @ SV421 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3023]) ).
thf(3531,plain,
! [SV422: nat,SV766: nat] :
( ( ~ ( ord_less_nat @ one_one_nat @ SV766 )
| ( ord_less_nat @ one_one_nat @ ( times_times_nat @ SV766 @ ( power_power_nat @ SV766 @ SV422 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3024]) ).
thf(3532,plain,
! [SV423: real,SV767: nat] :
( ( ! [SY2258: nat] :
( ~ ( ord_less_nat @ SV767 @ SY2258 )
| ~ ( ord_less_real @ one_one_real @ SV423 )
| ( ord_less_real @ ( power_power_real @ SV423 @ SV767 ) @ ( power_power_real @ SV423 @ SY2258 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3025]) ).
thf(3533,plain,
! [SV424: nat,SV768: nat] :
( ( ! [SY2259: nat] :
( ~ ( ord_less_nat @ SV768 @ SY2259 )
| ~ ( ord_less_nat @ one_one_nat @ SV424 )
| ( ord_less_nat @ ( power_power_nat @ SV424 @ SV768 ) @ ( power_power_nat @ SV424 @ SY2259 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3026]) ).
thf(3534,plain,
! [SV769: nat,SV425: nat] :
( ( ! [SY2260: real] :
( ~ ( ord_less_real @ one_one_real @ SY2260 )
| ~ ( ord_less_real @ ( power_power_real @ SY2260 @ SV425 ) @ ( power_power_real @ SY2260 @ SV769 ) )
| ( ord_less_nat @ SV425 @ SV769 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3027]) ).
thf(3535,plain,
! [SV770: nat,SV426: nat] :
( ( ! [SY2261: nat] :
( ~ ( ord_less_nat @ one_one_nat @ SY2261 )
| ~ ( ord_less_nat @ ( power_power_nat @ SY2261 @ SV426 ) @ ( power_power_nat @ SY2261 @ SV770 ) )
| ( ord_less_nat @ SV426 @ SV770 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3028]) ).
thf(3536,plain,
! [SV427: real,SV771: nat] :
( ( ! [SY2262: nat] :
( ~ ( ord_less_eq_nat @ SV771 @ SY2262 )
| ~ ( ord_less_eq_real @ one_one_real @ SV427 )
| ( ord_less_eq_real @ ( power_power_real @ SV427 @ SV771 ) @ ( power_power_real @ SV427 @ SY2262 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3029]) ).
thf(3537,plain,
! [SV428: nat,SV772: nat] :
( ( ! [SY2263: nat] :
( ~ ( ord_less_eq_nat @ SV772 @ SY2263 )
| ~ ( ord_less_eq_nat @ one_one_nat @ SV428 )
| ( ord_less_eq_nat @ ( power_power_nat @ SV428 @ SV772 ) @ ( power_power_nat @ SV428 @ SY2263 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3030]) ).
thf(3538,plain,
! [SV429: nat,SV773: real] :
( ( ~ ( ord_less_real @ zero_zero_real @ SV773 )
| ~ ( ord_less_real @ SV773 @ one_one_real )
| ( ord_less_real @ ( times_times_real @ SV773 @ ( power_power_real @ SV773 @ SV429 ) ) @ ( power_power_real @ SV773 @ SV429 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3031]) ).
thf(3539,plain,
! [SV430: nat,SV774: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ SV774 )
| ~ ( ord_less_nat @ SV774 @ one_one_nat )
| ( ord_less_nat @ ( times_times_nat @ SV774 @ ( power_power_nat @ SV774 @ SV430 ) ) @ ( power_power_nat @ SV774 @ SV430 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3032]) ).
thf(3540,plain,
! [SV775: nat,SV431: nat] :
( ( ~ ( dvd_dvd_nat @ SV431 @ SV775 )
| ( SV775 = zero_zero_nat )
| ( ord_less_eq_nat @ SV431 @ SV775 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3033]) ).
thf(3541,plain,
! [SV432: nat,SV776: nat] :
( ( ! [SY2264: nat] :
( ~ ( dvd_dvd_nat @ SV776 @ SY2264 )
| ( dvd_dvd_nat @ ( power_power_nat @ SV776 @ SV432 ) @ ( power_power_nat @ SY2264 @ SV432 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3034]) ).
thf(3542,plain,
! [SV433: nat,SV777: nat] :
( ( ! [SY2265: nat] :
( ~ ( dvd_dvd_nat @ SV777 @ SY2265 )
| ( dvd_dvd_nat @ ( times_times_nat @ SV433 @ SV777 ) @ ( times_times_nat @ SV433 @ SY2265 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3035]) ).
thf(3543,plain,
! [SV434: nat,SV778: nat] :
( ( ! [SY2266: nat] :
( ~ ( dvd_dvd_nat @ SV778 @ SY2266 )
| ( dvd_dvd_nat @ ( times_times_nat @ SV778 @ SV434 ) @ ( times_times_nat @ SY2266 @ SV434 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3036]) ).
thf(3544,plain,
! [SV435: nat,SV779: nat] :
( ( ! [SY2267: nat] :
( ~ ( dvd_dvd_nat @ SV779 @ SY2267 )
| ~ ( dvd_dvd_nat @ SV779 @ ( plus_plus_nat @ SY2267 @ SV435 ) )
| ( dvd_dvd_nat @ SV779 @ SV435 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3037]) ).
thf(3545,plain,
! [SV780: nat,SV436: nat] :
( ( ! [SY2268: nat] :
( ~ ( dvd_dvd_nat @ ( power_power_nat @ SV436 @ SV780 ) @ ( power_power_nat @ SY2268 @ SV780 ) )
| ( SV780 = zero_zero_nat )
| ( dvd_dvd_nat @ SV436 @ SY2268 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3038]) ).
thf(3546,plain,
! [SV781: nat,SV437: nat] :
( ( ! [SY2269: nat] :
( ( SY2269 = zero_zero_nat )
| ~ ( dvd_dvd_nat @ ( power_power_nat @ SV437 @ SY2269 ) @ SV781 )
| ( dvd_dvd_nat @ SV437 @ SV781 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3039]) ).
thf(3547,plain,
! [SV782: nat,SV438: nat] :
( ( ! [SY2270: nat,SY2271: nat] :
( ( SV438
!= ( plus_plus_nat @ ( times_times_nat @ SV782 @ SY2270 ) @ SY2271 ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SY2271 )
| ~ ( ord_less_nat @ SY2271 @ SY2270 )
| ~ ( dvd_dvd_nat @ SY2270 @ SV438 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3040]) ).
thf(3548,plain,
! [SV783: nat,SV439: nat] :
( ( ! [SY2272: nat] :
( ~ ( dvd_dvd_nat @ ( power_power_nat @ SV439 @ SV783 ) @ ( power_power_nat @ SV439 @ SY2272 ) )
| ~ ( ord_less_nat @ one_one_nat @ SV439 )
| ( ord_less_eq_nat @ SV783 @ SY2272 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3041]) ).
thf(3549,plain,
! [SV784: nat,SV440: nat] :
( ( ~ ( dvd_dvd_nat @ SV440 @ SV784 )
| ( ord_less_eq_nat @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV440 ) @ SV784 )
| ( SV784 = zero_zero_nat )
| ( SV784 = SV440 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3042]) ).
thf(3550,plain,
( ( ~ ! [SX0: real] :
( ( ( power_power_real @ SX0 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= zero_zero_real )
| ( SX0 = zero_zero_real ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3044]) ).
thf(3551,plain,
( ( ~ ! [SX0: real] :
( ( SX0 != zero_zero_real )
| ( ( power_power_real @ SX0 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_real ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3044]) ).
thf(3552,plain,
( ( ~ ! [SX0: nat,SX1: nat] :
( ( SX1 = zero_zero_nat )
| ( SX0 != zero_zero_nat )
| ( ( power_power_nat @ SX0 @ SX1 )
= zero_zero_nat ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3045]) ).
thf(3553,plain,
( ( ~ ~ ( ~ ! [SX0: nat,SX1: nat] :
( ( ( power_power_nat @ SX0 @ SX1 )
!= zero_zero_nat )
| ( SX1 != zero_zero_nat ) )
| ~ ! [SX0: nat] :
( ! [SX1: nat] :
( ( power_power_nat @ SX0 @ SX1 )
!= zero_zero_nat )
| ( SX0 = zero_zero_nat ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3045]) ).
thf(3554,plain,
( ( ~ ! [SX0: nat,SX1: int] :
( ( ( number_number_of_nat @ SX1 )
= zero_zero_nat )
| ( SX0 != zero_zero_nat )
| ( ( power_power_nat @ SX0 @ ( number_number_of_nat @ SX1 ) )
= zero_zero_nat ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3046]) ).
thf(3555,plain,
( ( ~ ~ ( ~ ! [SX0: nat,SX1: int] :
( ( ( power_power_nat @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_nat )
| ( ( number_number_of_nat @ SX1 )
!= zero_zero_nat ) )
| ~ ! [SX0: nat] :
( ! [SX1: int] :
( ( power_power_nat @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_nat )
| ( SX0 = zero_zero_nat ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3046]) ).
thf(3556,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ min @ ( bit0 @ SX0 ) )
| ( ord_less_int @ min @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3047]) ).
thf(3557,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ min @ SX0 )
| ( ord_less_eq_int @ min @ ( bit0 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3047]) ).
thf(3558,plain,
( ( ~ ! [SX0: real,SX1: real] :
( ~ ( ord_less_real @ 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 ) ) ) ) ) )
| ( SX0 != zero_zero_real )
| ( SX1 != zero_zero_real ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3048]) ).
thf(3559,plain,
( ( ~ ~ ( ~ ! [SX0: real] :
( ( SX0 = zero_zero_real )
| ! [SX1: real] : ( ord_less_real @ 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 ) ) ) ) ) ) )
| ~ ! [SX0: real,SX1: real] :
( ( SX1 = zero_zero_real )
| ( ord_less_real @ 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 ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3048]) ).
thf(3560,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ pls @ SX0 )
| ( ord_less_eq_real @ zero_zero_real @ ( number267125858f_real @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3049]) ).
thf(3561,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_real @ zero_zero_real @ ( number267125858f_real @ SX0 ) )
| ( ord_less_eq_int @ pls @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3049]) ).
thf(3562,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ pls @ SX0 )
| ( ord_less_int @ pls @ ( bit1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3050]) ).
thf(3563,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ pls @ ( bit1 @ SX0 ) )
| ( ord_less_eq_int @ pls @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3050]) ).
thf(3564,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3051]) ).
thf(3565,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3051]) ).
thf(3566,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ min @ ( bit1 @ SX0 ) )
| ( ord_less_int @ min @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3052]) ).
thf(3567,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ min @ SX0 )
| ( ord_less_int @ min @ ( bit1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3052]) ).
thf(3568,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3053]) ).
thf(3569,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3053]) ).
thf(3570,plain,
( ( ~ ! [SX0: nat,SX1: nat] :
( ( ( power_power_nat @ SX0 @ SX1 )
!= one_one_nat )
| ( SX0 = one_one_nat )
| ( SX1 = zero_zero_nat ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3054]) ).
thf(3571,plain,
( ( ~ ~ ( ~ ! [SX0: nat] :
( ( SX0 != one_one_nat )
| ! [SX1: nat] :
( ( power_power_nat @ SX0 @ SX1 )
= one_one_nat ) )
| ~ ! [SX0: nat,SX1: nat] :
( ( SX1 != zero_zero_nat )
| ( ( power_power_nat @ SX0 @ SX1 )
= one_one_nat ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3054]) ).
thf(3572,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_eq_real @ ( number267125858f_real @ SX0 ) @ ( number267125858f_real @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3055]) ).
thf(3573,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_real @ ( number267125858f_real @ SX0 ) @ ( number267125858f_real @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3055]) ).
thf(3574,plain,
( ( ~ ! [SX0: nat] :
( ( SX0 != zero_zero_nat )
| ( ( power_power_real @ zero_zero_real @ SX0 )
= one_one_real ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3056]) ).
thf(3575,plain,
( ( ~ ! [SX0: nat] :
( ( SX0 = zero_zero_nat )
| ( ( power_power_real @ zero_zero_real @ SX0 )
= zero_zero_real ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3056]) ).
thf(3576,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ( ( bit1 @ SX0 )
!= ( bit1 @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3057]) ).
thf(3577,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ( SX0 != SX1 )
| ( ( bit1 @ SX0 )
= ( bit1 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3057]) ).
thf(3578,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ ( number_number_of_int @ SX0 ) @ ( number_number_of_int @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3058]) ).
thf(3579,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ ( number_number_of_int @ SX0 ) @ ( number_number_of_int @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3058]) ).
thf(3580,plain,
( ( ~ ! [SX0: real,SX1: real] :
( ( SX0 != zero_zero_real )
| ( SX1 != zero_zero_real )
| ( ord_less_eq_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 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3059]) ).
thf(3581,plain,
( ( ~ ~ ( ~ ! [SX0: real] :
( ! [SX1: real] :
~ ( ord_less_eq_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 )
| ( SX0 = zero_zero_real ) )
| ~ ! [SX0: real,SX1: real] :
( ~ ( ord_less_eq_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 )
| ( SX1 = zero_zero_real ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3059]) ).
thf(3582,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ ( plus_plus_int @ SX1 @ one_one_int ) )
| ( SX0 = SX1 )
| ( ord_less_int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3060]) ).
thf(3583,plain,
( ( ~ ~ ( ~ ! [SX0: int,SX1: int] :
( ( SX0 != SX1 )
| ( ord_less_int @ SX0 @ ( plus_plus_int @ SX1 @ one_one_int ) ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ SX0 @ ( plus_plus_int @ SX1 @ one_one_int ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3060]) ).
thf(3584,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ min @ ( bit1 @ SX0 ) )
| ( ord_less_eq_int @ min @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3061]) ).
thf(3585,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ min @ SX0 )
| ( ord_less_eq_int @ min @ ( bit1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3061]) ).
thf(3586,plain,
( ( ~ ! [SX0: int] :
( ( ( number_number_of_nat @ SX0 )
!= zero_zero_nat )
| ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ SX0 ) )
= one_one_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3062]) ).
thf(3587,plain,
( ( ~ ! [SX0: int] :
( ( ( number_number_of_nat @ SX0 )
= zero_zero_nat )
| ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ SX0 ) )
= zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3062]) ).
thf(3588,plain,
! [SV785: nat,SV441: nat] :
( ( ~ ( ~ ~ ( ~ ! [SY2273: nat,SY2274: nat] :
( ( ( plus_plus_nat @ ( times_times_nat @ SY2273 @ SV441 ) @ ( times_times_nat @ SY2274 @ SV785 ) )
= ( plus_plus_nat @ ( times_times_nat @ SY2273 @ SV785 ) @ ( times_times_nat @ SY2274 @ SV441 ) ) )
| ( SY2273 != SY2274 ) )
| ~ ( ! [SY2275: nat,SY2276: nat] :
( ( plus_plus_nat @ ( times_times_nat @ SY2275 @ SV441 ) @ ( times_times_nat @ SY2276 @ SV785 ) )
= ( plus_plus_nat @ ( times_times_nat @ SY2275 @ SV785 ) @ ( times_times_nat @ SY2276 @ SV441 ) ) )
| ( SV441 != SV785 ) ) )
| ~ ! [SY2277: nat,SY2278: nat] :
( ( SY2277 = SY2278 )
| ( SV441 = SV785 )
| ( ( plus_plus_nat @ ( times_times_nat @ SY2277 @ SV441 ) @ ( times_times_nat @ SY2278 @ SV785 ) )
!= ( plus_plus_nat @ ( times_times_nat @ SY2277 @ SV785 ) @ ( times_times_nat @ SY2278 @ SV441 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3063]) ).
thf(3589,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3064]) ).
thf(3590,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3064]) ).
thf(3591,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3065]) ).
thf(3592,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3065]) ).
thf(3593,plain,
( ( ~ ! [SX0: real,SX1: int] :
( ( ( number_number_of_nat @ SX1 )
= zero_zero_nat )
| ( SX0 != zero_zero_real )
| ( ( power_power_real @ SX0 @ ( number_number_of_nat @ SX1 ) )
= zero_zero_real ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3066]) ).
thf(3594,plain,
( ( ~ ~ ( ~ ! [SX0: real,SX1: int] :
( ( ( power_power_real @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_real )
| ( ( number_number_of_nat @ SX1 )
!= zero_zero_nat ) )
| ~ ! [SX0: real] :
( ! [SX1: int] :
( ( power_power_real @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_real )
| ( SX0 = zero_zero_real ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3066]) ).
thf(3595,plain,
( ( ~ ! [SX0: real,SX1: real] :
( ~ ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ SX0 @ SX0 ) @ ( times_times_real @ SX1 @ SX1 ) ) )
| ( SX0 != zero_zero_real )
| ( SX1 != zero_zero_real ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3067]) ).
thf(3596,plain,
( ( ~ ~ ( ~ ! [SX0: real] :
( ( SX0 = zero_zero_real )
| ! [SX1: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ SX0 @ SX0 ) @ ( times_times_real @ SX1 @ SX1 ) ) ) )
| ~ ! [SX0: real,SX1: real] :
( ( SX1 = zero_zero_real )
| ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ SX0 @ SX0 ) @ ( times_times_real @ SX1 @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3067]) ).
thf(3597,plain,
( ( ~ ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SX0 @ SX1 ) )
| ( SX1 = zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3068]) ).
thf(3598,plain,
( ( ~ ~ ( ~ ! [SX0: nat,SX1: nat] :
( ( SX1 != zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SX0 @ SX1 ) ) )
| ~ ! [SX0: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SX0 )
| ! [SX1: nat] : ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SX0 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3068]) ).
thf(3599,plain,
! [SV786: real,SV442: real] :
( ( ~ ( ~ ~ ( ~ ! [SY2279: real,SY2280: real] :
( ( ( plus_plus_real @ ( times_times_real @ SY2279 @ SV442 ) @ ( times_times_real @ SY2280 @ SV786 ) )
= ( plus_plus_real @ ( times_times_real @ SY2279 @ SV786 ) @ ( times_times_real @ SY2280 @ SV442 ) ) )
| ( SY2279 != SY2280 ) )
| ~ ( ! [SY2281: real,SY2282: real] :
( ( plus_plus_real @ ( times_times_real @ SY2281 @ SV442 ) @ ( times_times_real @ SY2282 @ SV786 ) )
= ( plus_plus_real @ ( times_times_real @ SY2281 @ SV786 ) @ ( times_times_real @ SY2282 @ SV442 ) ) )
| ( SV442 != SV786 ) ) )
| ~ ! [SY2283: real,SY2284: real] :
( ( SY2283 = SY2284 )
| ( SV442 = SV786 )
| ( ( plus_plus_real @ ( times_times_real @ SY2283 @ SV442 ) @ ( times_times_real @ SY2284 @ SV786 ) )
!= ( plus_plus_real @ ( times_times_real @ SY2283 @ SV786 ) @ ( times_times_real @ SY2284 @ SV442 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3069]) ).
thf(3600,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ ( bit0 @ SX0 ) @ pls )
| ( ord_less_eq_int @ SX0 @ pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3070]) ).
thf(3601,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ SX0 @ pls )
| ( ord_less_eq_int @ ( bit0 @ SX0 ) @ pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3070]) ).
thf(3602,plain,
( ( ~ ! [SX0: int] :
( ( ( bit1 @ SX0 )
!= min )
| ( SX0 = min ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3071]) ).
thf(3603,plain,
( ( ~ ! [SX0: int] :
( ( SX0 != min )
| ( ( bit1 @ SX0 )
= min ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3071]) ).
thf(3604,plain,
( ( ~ ! [SX0: real,SX1: real] :
( ~ ( ord_less_eq_real @ SX0 @ SX1 )
| ( SX0 = SX1 )
| ( ord_less_real @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3072]) ).
thf(3605,plain,
( ( ~ ~ ( ~ ! [SX0: real,SX1: real] :
( ( SX0 != SX1 )
| ( ord_less_eq_real @ SX0 @ SX1 ) )
| ~ ! [SX0: real,SX1: real] :
( ~ ( ord_less_real @ SX0 @ SX1 )
| ( ord_less_eq_real @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3072]) ).
thf(3606,plain,
( ( ~ ! [SX0: real] :
( ( ( plus_plus_real @ SX0 @ SX0 )
!= zero_zero_real )
| ( SX0 = zero_zero_real ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3073]) ).
thf(3607,plain,
( ( ~ ! [SX0: real] :
( ( SX0 != zero_zero_real )
| ( ( plus_plus_real @ SX0 @ SX0 )
= zero_zero_real ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3073]) ).
thf(3608,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ zero_zero_int @ ( 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 ) ) ) ) ) )
| ( SX0 != zero_zero_int )
| ( SX1 != zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3074]) ).
thf(3609,plain,
( ( ~ ~ ( ~ ! [SX0: int] :
( ( SX0 = zero_zero_int )
| ! [SX1: int] : ( ord_less_int @ zero_zero_int @ ( 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 ) ) ) ) ) ) )
| ~ ! [SX0: int,SX1: int] :
( ( SX1 = zero_zero_int )
| ( ord_less_int @ zero_zero_int @ ( 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 ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3074]) ).
thf(3610,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ pls @ SX0 )
| ( ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3075]) ).
thf(3611,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ SX0 ) )
| ( ord_less_int @ pls @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3075]) ).
thf(3612,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ ( number_number_of_int @ SX0 ) @ ( number_number_of_int @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3076]) ).
thf(3613,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( number_number_of_int @ SX0 ) @ ( number_number_of_int @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3076]) ).
thf(3614,plain,
( ( ~ ! [SX0: real,SX1: 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 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3077]) ).
thf(3615,plain,
( ( ~ ~ ( ~ ! [SX0: real] :
( ! [SX1: 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 )
| ( SX0 = zero_zero_real ) )
| ~ ! [SX0: real,SX1: 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 )
| ( SX1 = zero_zero_real ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3077]) ).
thf(3616,plain,
( ( ~ ! [SX0: int,SX1: nat] :
( ( SX1 != zero_zero_nat )
| ( ( power_power_int @ SX0 @ SX1 )
= one_one_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3078]) ).
thf(3617,plain,
( ( ~ ! [SX0: int,SX1: nat] :
( ( SX1 = zero_zero_nat )
| ( ( power_power_int @ SX0 @ SX1 )
= ( times_times_int @ SX0 @ ( power_power_int @ SX0 @ ( minus_minus_nat @ SX1 @ one_one_nat ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3078]) ).
thf(3618,plain,
( ( ~ ! [SX0: int] :
( ( ( number_number_of_nat @ SX0 )
!= zero_zero_nat )
| ( ord_less_eq_int @ SX0 @ pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3079]) ).
thf(3619,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ SX0 @ pls )
| ( ( number_number_of_nat @ SX0 )
= zero_zero_nat ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3079]) ).
thf(3620,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( dvd_dvd_int @ SX1 @ SX0 )
| ( zcong @ SX0 @ zero_zero_int @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3080]) ).
thf(3621,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( zcong @ SX0 @ zero_zero_int @ SX1 )
| ( dvd_dvd_int @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3080]) ).
thf(3622,plain,
( ( ~ ! [SX0: nat,SX1: nat] :
( ( SX1 != zero_zero_nat )
| ( ( power_power_nat @ SX0 @ SX1 )
= one_one_nat ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3081]) ).
thf(3623,plain,
( ( ~ ! [SX0: nat,SX1: 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 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3081]) ).
thf(3624,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ ( bit1 @ SX0 ) @ min )
| ( ord_less_int @ SX0 @ min ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3082]) ).
thf(3625,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ SX0 @ min )
| ( ord_less_int @ ( bit1 @ SX0 ) @ min ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3082]) ).
thf(3626,plain,
! [SV443: nat] :
( ( ~ ! [SY1911: nat,SY1912: int] :
( ~ ( ord_less_int @ one_one_int @ SY1912 )
| ~ ( ord_less_int @ ( power_power_int @ SY1912 @ SV443 ) @ ( power_power_int @ SY1912 @ SY1911 ) )
| ( ord_less_nat @ SV443 @ SY1911 ) )
| ~ ! [SY1913: nat,SY1914: int] :
( ~ ( ord_less_int @ one_one_int @ SY1914 )
| ~ ( ord_less_nat @ SV443 @ SY1913 )
| ( ord_less_int @ ( power_power_int @ SY1914 @ SV443 ) @ ( power_power_int @ SY1914 @ SY1913 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3083]) ).
thf(3627,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ ( bit1 @ SX0 ) @ zero_zero_int )
| ( ord_less_int @ SX0 @ zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3084]) ).
thf(3628,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ SX0 @ zero_zero_int )
| ( ord_less_int @ ( bit1 @ SX0 ) @ zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3084]) ).
thf(3629,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ SX0 @ pls )
| ( ord_less_eq_real @ ( number267125858f_real @ SX0 ) @ zero_zero_real ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3085]) ).
thf(3630,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_real @ ( number267125858f_real @ SX0 ) @ zero_zero_real )
| ( ord_less_eq_int @ SX0 @ pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3085]) ).
thf(3631,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ min @ ( bit0 @ SX0 ) )
| ( ord_less_int @ min @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3086]) ).
thf(3632,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ min @ SX0 )
| ( ord_less_int @ min @ ( bit0 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3086]) ).
thf(3633,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ ( number_number_of_int @ SX0 ) @ ( number_number_of_int @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3087]) ).
thf(3634,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( number_number_of_int @ SX0 ) @ ( number_number_of_int @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3087]) ).
thf(3635,plain,
! [SV444: int] :
( ( ~ ! [SY1915: int] :
( ! [SY1916: int] :
~ ( dvd_dvd_int @ SV444 @ ( plus_plus_int @ SY1915 @ ( times_times_int @ SV444 @ SY1916 ) ) )
| ( dvd_dvd_int @ SV444 @ SY1915 ) )
| ~ ! [SY1917: int] :
( ~ ( dvd_dvd_int @ SV444 @ SY1917 )
| ! [SY1918: int] : ( dvd_dvd_int @ SV444 @ ( plus_plus_int @ SY1917 @ ( times_times_int @ SV444 @ SY1918 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3088]) ).
thf(3636,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ SX0 @ ( minus_minus_int @ SX1 @ one_one_int ) )
| ( ord_less_int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3089]) ).
thf(3637,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ SX0 @ ( minus_minus_int @ SX1 @ one_one_int ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3089]) ).
thf(3638,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3090]) ).
thf(3639,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3090]) ).
thf(3640,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ( ( number_number_of_nat @ SX1 )
= zero_zero_nat )
| ( SX0 != zero_zero_int )
| ( ( power_power_int @ SX0 @ ( number_number_of_nat @ SX1 ) )
= zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3091]) ).
thf(3641,plain,
( ( ~ ~ ( ~ ! [SX0: int,SX1: int] :
( ( ( power_power_int @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_int )
| ( ( number_number_of_nat @ SX1 )
!= zero_zero_nat ) )
| ~ ! [SX0: int] :
( ! [SX1: int] :
( ( power_power_int @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3091]) ).
thf(3642,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_real @ ( number267125858f_real @ SX0 ) @ ( number267125858f_real @ SX1 ) )
| ~ ( ord_less_real @ ( number267125858f_real @ SX1 ) @ ( number267125858f_real @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3092]) ).
thf(3643,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ( ord_less_real @ ( number267125858f_real @ SX1 ) @ ( number267125858f_real @ SX0 ) )
| ( ord_less_eq_real @ ( number267125858f_real @ SX0 ) @ ( number267125858f_real @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3092]) ).
thf(3644,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ ( minus_minus_int @ SX0 @ SX1 ) @ zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3093]) ).
thf(3645,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ ( minus_minus_int @ SX0 @ SX1 ) @ zero_zero_int )
| ( ord_less_int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3093]) ).
thf(3646,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( 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 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3094]) ).
thf(3647,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( 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 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3094]) ).
thf(3648,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ ( bit0 @ SX0 ) @ pls )
| ( ord_less_int @ SX0 @ pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3095]) ).
thf(3649,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ SX0 @ pls )
| ( ord_less_int @ ( bit0 @ SX0 ) @ pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3095]) ).
thf(3650,plain,
( ( ~ ! [SX0: nat,SX1: nat] :
( ( SX1 != zero_zero_nat )
| ( ( times_times_nat @ SX1 @ SX0 )
= zero_zero_nat ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3096]) ).
thf(3651,plain,
( ( ~ ! [SX0: nat,SX1: 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 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3096]) ).
thf(3652,plain,
( ( ~ ! [SX0: real,SX1: 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 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3097]) ).
thf(3653,plain,
( ( ~ ~ ( ~ ! [SX0: real] :
( ! [SX1: 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 )
| ( SX0 = zero_zero_real ) )
| ~ ! [SX0: real,SX1: 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 )
| ( SX1 = zero_zero_real ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3097]) ).
thf(3654,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ( SX0 != zero_zero_int )
| ( SX1 != zero_zero_int )
| ( ( 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 ) ) ) ) )
= zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3098]) ).
thf(3655,plain,
( ( ~ ~ ( ~ ! [SX0: int] :
( ! [SX1: int] :
( ( 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 ) ) ) ) )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) )
| ~ ! [SX0: int,SX1: int] :
( ( ( 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 ) ) ) ) )
!= zero_zero_int )
| ( SX1 = zero_zero_int ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3098]) ).
thf(3656,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( dvd_dvd_int @ SX1 @ SX0 )
| ( zcong @ SX0 @ zero_zero_int @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3099]) ).
thf(3657,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( zcong @ SX0 @ zero_zero_int @ SX1 )
| ( dvd_dvd_int @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3099]) ).
thf(3658,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3100]) ).
thf(3659,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3100]) ).
thf(3660,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ ( plus_plus_int @ SX0 @ SX0 ) @ zero_zero_int )
| ( ord_less_int @ SX0 @ zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3101]) ).
thf(3661,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ SX0 @ zero_zero_int )
| ( ord_less_int @ ( plus_plus_int @ SX0 @ SX0 ) @ zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3101]) ).
thf(3662,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ one_one_int @ SX0 )
| ( ord_less_int @ zero_zero_int @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3102]) ).
thf(3663,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ zero_zero_int @ SX0 )
| ( ord_less_eq_int @ one_one_int @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3102]) ).
thf(3664,plain,
! [SV445: real] :
( ( ~ ! [SY1919: real,SY1920: real] :
( ~ ( ord_less_real @ zero_zero_real @ SY1920 )
| ~ ( ord_less_eq_real @ ( times_times_real @ SV445 @ SY1920 ) @ ( times_times_real @ SY1919 @ SY1920 ) )
| ( ord_less_eq_real @ SV445 @ SY1919 ) )
| ~ ! [SY1921: real,SY1922: real] :
( ~ ( ord_less_real @ zero_zero_real @ SY1922 )
| ~ ( ord_less_eq_real @ SV445 @ SY1921 )
| ( ord_less_eq_real @ ( times_times_real @ SV445 @ SY1922 ) @ ( times_times_real @ SY1921 @ SY1922 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3103]) ).
thf(3665,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ pls @ SX0 )
| ( ord_less_real @ zero_zero_real @ ( number267125858f_real @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3104]) ).
thf(3666,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_real @ zero_zero_real @ ( number267125858f_real @ SX0 ) )
| ( ord_less_int @ pls @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3104]) ).
thf(3667,plain,
( ( ~ ! [SX0: real,SX1: real] :
( ( SX0 != zero_zero_real )
| ( SX1 != zero_zero_real )
| ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ SX0 @ SX0 ) @ ( times_times_real @ SX1 @ SX1 ) ) @ zero_zero_real ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3105]) ).
thf(3668,plain,
( ( ~ ~ ( ~ ! [SX0: real] :
( ! [SX1: real] :
~ ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ SX0 @ SX0 ) @ ( times_times_real @ SX1 @ SX1 ) ) @ zero_zero_real )
| ( SX0 = zero_zero_real ) )
| ~ ! [SX0: real,SX1: real] :
( ~ ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ SX0 @ SX0 ) @ ( times_times_real @ SX1 @ SX1 ) ) @ zero_zero_real )
| ( SX1 = zero_zero_real ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3105]) ).
thf(3669,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3106]) ).
thf(3670,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3106]) ).
thf(3671,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ zero_zero_int @ ( number_number_of_int @ SX0 ) )
| ( ord_less_int @ pls @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3107]) ).
thf(3672,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ pls @ SX0 )
| ( ord_less_int @ zero_zero_int @ ( number_number_of_int @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3107]) ).
thf(3673,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ( SX0 != zero_zero_int )
| ( SX1 != zero_zero_int )
| ( ord_less_eq_int @ ( 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 ) ) ) ) ) @ zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3108]) ).
thf(3674,plain,
( ( ~ ~ ( ~ ! [SX0: int] :
( ! [SX1: int] :
~ ( ord_less_eq_int @ ( 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 ) ) ) ) ) @ zero_zero_int )
| ( SX0 = zero_zero_int ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ ( 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 ) ) ) ) ) @ zero_zero_int )
| ( SX1 = zero_zero_int ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3108]) ).
thf(3675,plain,
( ( ~ ! [SX0: int] :
( ( min
!= ( bit1 @ SX0 ) )
| ( min = SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3109]) ).
thf(3676,plain,
( ( ~ ! [SX0: int] :
( ( min != SX0 )
| ( min
= ( bit1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3109]) ).
thf(3677,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ( SX0 != zero_zero_int )
| ( SX1 != zero_zero_int )
| ( ( plus_plus_int @ ( times_times_int @ SX0 @ SX0 ) @ ( times_times_int @ SX1 @ SX1 ) )
= zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3110]) ).
thf(3678,plain,
( ( ~ ~ ( ~ ! [SX0: int] :
( ! [SX1: int] :
( ( plus_plus_int @ ( times_times_int @ SX0 @ SX0 ) @ ( times_times_int @ SX1 @ SX1 ) )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) )
| ~ ! [SX0: int,SX1: int] :
( ( ( plus_plus_int @ ( times_times_int @ SX0 @ SX0 ) @ ( times_times_int @ SX1 @ SX1 ) )
!= zero_zero_int )
| ( SX1 = zero_zero_int ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3110]) ).
thf(3679,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ( SX0 = SX1 )
| ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3111]) ).
thf(3680,plain,
( ( ~ ~ ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3111]) ).
thf(3681,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ ( number_number_of_int @ SX0 ) @ zero_zero_int )
| ( ord_less_eq_int @ SX0 @ pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3112]) ).
thf(3682,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ SX0 @ pls )
| ( ord_less_eq_int @ ( number_number_of_int @ SX0 ) @ zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3112]) ).
thf(3683,plain,
! [SV446: nat] :
( ( ~ ! [SY1923: nat,SY1924: nat] :
( ~ ( ord_less_nat @ one_one_nat @ SY1924 )
| ~ ( ord_less_nat @ ( power_power_nat @ SY1924 @ SV446 ) @ ( power_power_nat @ SY1924 @ SY1923 ) )
| ( ord_less_nat @ SV446 @ SY1923 ) )
| ~ ! [SY1925: nat,SY1926: nat] :
( ~ ( ord_less_nat @ one_one_nat @ SY1926 )
| ~ ( ord_less_nat @ SV446 @ SY1925 )
| ( ord_less_nat @ ( power_power_nat @ SY1926 @ SV446 ) @ ( power_power_nat @ SY1926 @ SY1925 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3113]) ).
thf(3684,plain,
( ( ~ ! [SX0: nat,SX1: nat] :
( ( SX0 != one_one_nat )
| ( SX1 != one_one_nat )
| ( ( times_times_nat @ SX0 @ SX1 )
= one_one_nat ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3114]) ).
thf(3685,plain,
( ( ~ ~ ( ~ ! [SX0: nat] :
( ! [SX1: nat] :
( ( times_times_nat @ SX0 @ SX1 )
!= one_one_nat )
| ( SX0 = one_one_nat ) )
| ~ ! [SX0: nat,SX1: nat] :
( ( ( times_times_nat @ SX0 @ SX1 )
!= one_one_nat )
| ( SX1 = one_one_nat ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3114]) ).
thf(3686,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: int] :
( ! [SX1: int] :
( ( times_times_int @ SX0 @ SX1 )
!= one_one_int )
| ( SX0 = one_one_int )
| ( SX0
= ( number_number_of_int @ min ) ) )
| ~ ! [SX0: int,SX1: int] :
( ( ( times_times_int @ SX0 @ SX1 )
!= one_one_int )
| ( SX0 = one_one_int )
| ( SX1
= ( number_number_of_int @ min ) ) ) )
| ~ ~ ( ~ ! [SX0: int,SX1: int] :
( ( ( times_times_int @ SX0 @ SX1 )
!= one_one_int )
| ( SX1 = one_one_int )
| ( SX0
= ( number_number_of_int @ min ) ) )
| ~ ! [SX0: int,SX1: int] :
( ( ( times_times_int @ SX0 @ SX1 )
!= one_one_int )
| ( SX1 = one_one_int )
| ( SX1
= ( number_number_of_int @ min ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3115]) ).
thf(3687,plain,
( ( ~ ~ ( ~ ! [SX0: int,SX1: int] :
( ( SX0 != one_one_int )
| ( SX1 != one_one_int )
| ( ( times_times_int @ SX0 @ SX1 )
= one_one_int ) )
| ~ ! [SX0: int,SX1: int] :
( ( SX0
!= ( number_number_of_int @ min ) )
| ( SX1
!= ( number_number_of_int @ min ) )
| ( ( times_times_int @ SX0 @ SX1 )
= one_one_int ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3115]) ).
thf(3688,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ SX0 @ ( bit1 @ pls ) )
| ( ord_less_real @ ( number267125858f_real @ SX0 ) @ one_one_real ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3116]) ).
thf(3689,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_real @ ( number267125858f_real @ SX0 ) @ one_one_real )
| ( ord_less_int @ SX0 @ ( bit1 @ pls ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3116]) ).
thf(3690,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ( ( number_number_of_int @ SX0 )
!= SX1 )
| ( SX1
= ( number_number_of_int @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3117]) ).
thf(3691,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ( SX1
!= ( number_number_of_int @ SX0 ) )
| ( ( number_number_of_int @ SX0 )
= SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3117]) ).
thf(3692,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_int @ SX0 @ ( plus_plus_int @ SX1 @ one_one_int ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3118]) ).
thf(3693,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ ( plus_plus_int @ SX1 @ one_one_int ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3118]) ).
thf(3694,plain,
( ( ~ ! [SX0: real,SX1: 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 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3119]) ).
thf(3695,plain,
( ( ~ ~ ( ~ ! [SX0: real] :
( ! [SX1: real] :
( ( plus_plus_real @ ( times_times_real @ SX0 @ SX0 ) @ ( times_times_real @ SX1 @ SX1 ) )
!= zero_zero_real )
| ( SX0 = zero_zero_real ) )
| ~ ! [SX0: real,SX1: real] :
( ( ( plus_plus_real @ ( times_times_real @ SX0 @ SX0 ) @ ( times_times_real @ SX1 @ SX1 ) )
!= zero_zero_real )
| ( SX1 = zero_zero_real ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3119]) ).
thf(3696,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ ( bit1 @ SX0 ) @ pls )
| ( ord_less_int @ SX0 @ pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3120]) ).
thf(3697,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ SX0 @ pls )
| ( ord_less_eq_int @ ( bit1 @ SX0 ) @ pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3120]) ).
thf(3698,plain,
! [SV447: nat] :
( ( ~ ! [SY1927: nat,SY1928: real] :
( ~ ( ord_less_real @ one_one_real @ SY1928 )
| ~ ( ord_less_nat @ SV447 @ SY1927 )
| ( ord_less_real @ ( power_power_real @ SY1928 @ SV447 ) @ ( power_power_real @ SY1928 @ SY1927 ) ) )
| ~ ! [SY1929: nat,SY1930: real] :
( ~ ( ord_less_real @ one_one_real @ SY1930 )
| ~ ( ord_less_real @ ( power_power_real @ SY1930 @ SV447 ) @ ( power_power_real @ SY1930 @ SY1929 ) )
| ( ord_less_nat @ SV447 @ SY1929 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3121]) ).
thf(3699,plain,
( ( ~ ! [SX0: int] :
( ( ( bit0 @ SX0 )
!= pls )
| ( SX0 = pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3122]) ).
thf(3700,plain,
( ( ~ ! [SX0: int] :
( ( SX0 != pls )
| ( ( bit0 @ SX0 )
= pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3122]) ).
thf(3701,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ SX0 @ SX0 ) @ ( times_times_int @ SX1 @ SX1 ) ) )
| ( SX0 != zero_zero_int )
| ( SX1 != zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3123]) ).
thf(3702,plain,
( ( ~ ~ ( ~ ! [SX0: int] :
( ( SX0 = zero_zero_int )
| ! [SX1: int] : ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ SX0 @ SX0 ) @ ( times_times_int @ SX1 @ SX1 ) ) ) )
| ~ ! [SX0: int,SX1: int] :
( ( SX1 = zero_zero_int )
| ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ SX0 @ SX0 ) @ ( times_times_int @ SX1 @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3123]) ).
thf(3703,plain,
( ( ~ ! [SX0: int,SX1: nat] :
( ( ( number_number_of_nat @ SX0 )
!= SX1 )
| ( SX1
= ( number_number_of_nat @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3124]) ).
thf(3704,plain,
( ( ~ ! [SX0: int,SX1: nat] :
( ( SX1
!= ( number_number_of_nat @ SX0 ) )
| ( ( number_number_of_nat @ SX0 )
= SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3124]) ).
thf(3705,plain,
( ( ~ ! [SX0: real] :
( ( SX0 != zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ ( times_times_real @ SX0 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3125]) ).
thf(3706,plain,
( ( ~ ! [SX0: real] :
( ( ord_less_real @ zero_zero_real @ ( times_times_real @ SX0 @ SX0 ) )
| ( SX0 = zero_zero_real ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3125]) ).
thf(3707,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ ( number_number_of_int @ SX0 ) @ one_one_int )
| ( ord_less_int @ SX0 @ ( bit1 @ pls ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3126]) ).
thf(3708,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ SX0 @ ( bit1 @ pls ) )
| ( ord_less_int @ ( number_number_of_int @ SX0 ) @ one_one_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3126]) ).
thf(3709,plain,
! [SV448: real] :
( ( ~ ! [SY1931: real,SY1932: real] :
( ( SY1932 = zero_zero_real )
| ( ( times_times_real @ SY1932 @ SV448 )
!= ( times_times_real @ SY1932 @ SY1931 ) )
| ( SV448 = SY1931 ) )
| ~ ! [SY1933: real,SY1934: real] :
( ( SY1934 = zero_zero_real )
| ( SV448 != SY1933 )
| ( ( times_times_real @ SY1934 @ SV448 )
= ( times_times_real @ SY1934 @ SY1933 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3127]) ).
thf(3710,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3128]) ).
thf(3711,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3128]) ).
thf(3712,plain,
( ( ~ ! [SX0: int] :
( ( pls
!= ( bit0 @ SX0 ) )
| ( pls = SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3129]) ).
thf(3713,plain,
( ( ~ ! [SX0: int] :
( ( pls != SX0 )
| ( pls
= ( bit0 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3129]) ).
thf(3714,plain,
( ( ~ ~ ( ~ ! [SX0: int,SX1: int] :
( ( ord_less_int @ SX0 @ SX1 )
| ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_nat @ ( number_number_of_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ pls @ SX1 )
| ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_nat @ ( number_number_of_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3130]) ).
thf(3715,plain,
( ( ~ ~ ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_nat @ ( number_number_of_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) )
| ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ pls @ SX1 ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_nat @ ( number_number_of_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3130]) ).
thf(3716,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3131]) ).
thf(3717,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3131]) ).
thf(3718,plain,
! [SV787: int,SV449: int] :
( ( ! [SY2285: int] :
~ ( ~ ! [SY2286: int,SY2287: int] :
( ~ ( zcong @ SY2285 @ SY2286 @ SY2287 )
| ~ ( zcong @ SV449 @ ( times_times_int @ SY2285 @ SV787 ) @ SY2287 )
| ( zcong @ SV449 @ ( times_times_int @ SY2286 @ SV787 ) @ SY2287 ) )
| ~ ! [SY2288: int,SY2289: int] :
( ~ ( zcong @ SY2285 @ SY2288 @ SY2289 )
| ~ ( zcong @ SV449 @ ( times_times_int @ SY2288 @ SV787 ) @ SY2289 )
| ( zcong @ SV449 @ ( times_times_int @ SY2285 @ SV787 ) @ SY2289 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3132]) ).
thf(3719,plain,
( ( ~ ! [SX0: real,SX1: nat] :
( ( SX1 != zero_zero_nat )
| ( ( power_power_real @ SX0 @ SX1 )
= one_one_real ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3133]) ).
thf(3720,plain,
( ( ~ ! [SX0: real,SX1: nat] :
( ( SX1 = zero_zero_nat )
| ( ( power_power_real @ SX0 @ SX1 )
= ( times_times_real @ SX0 @ ( power_power_real @ SX0 @ ( minus_minus_nat @ SX1 @ one_one_nat ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3133]) ).
thf(3721,plain,
! [SV788: int,SV450: int] :
( ( ~ ( ~ ~ ( ~ ! [SY2290: int,SY2291: int] :
( ( ( plus_plus_int @ ( times_times_int @ SY2290 @ SV450 ) @ ( times_times_int @ SY2291 @ SV788 ) )
= ( plus_plus_int @ ( times_times_int @ SY2290 @ SV788 ) @ ( times_times_int @ SY2291 @ SV450 ) ) )
| ( SY2290 != SY2291 ) )
| ~ ( ! [SY2292: int,SY2293: int] :
( ( plus_plus_int @ ( times_times_int @ SY2292 @ SV450 ) @ ( times_times_int @ SY2293 @ SV788 ) )
= ( plus_plus_int @ ( times_times_int @ SY2292 @ SV788 ) @ ( times_times_int @ SY2293 @ SV450 ) ) )
| ( SV450 != SV788 ) ) )
| ~ ! [SY2294: int,SY2295: int] :
( ( SY2294 = SY2295 )
| ( SV450 = SV788 )
| ( ( plus_plus_int @ ( times_times_int @ SY2294 @ SV450 ) @ ( times_times_int @ SY2295 @ SV788 ) )
!= ( plus_plus_int @ ( times_times_int @ SY2294 @ SV788 ) @ ( times_times_int @ SY2295 @ SV450 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3134]) ).
thf(3722,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3135]) ).
thf(3723,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3135]) ).
thf(3724,plain,
( ( ~ ! [SX0: int] :
( ( SX0 = zero_zero_int )
| ( ord_less_int @ zero_zero_int @ ( power_power_int @ SX0 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3136]) ).
thf(3725,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ zero_zero_int @ ( power_power_int @ SX0 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ( SX0 != zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3136]) ).
thf(3726,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ SX0 @ pls )
| ( ord_less_real @ ( number267125858f_real @ SX0 ) @ zero_zero_real ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3137]) ).
thf(3727,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_real @ ( number267125858f_real @ SX0 ) @ zero_zero_real )
| ( ord_less_int @ SX0 @ pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3137]) ).
thf(3728,plain,
( ( ~ ! [SX0: real,SX1: 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 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3138]) ).
thf(3729,plain,
( ( ~ ~ ( ~ ! [SX0: real] :
( ! [SX1: real] :
( ( plus_plus_real @ ( times_times_real @ SX0 @ SX0 ) @ ( times_times_real @ SX1 @ SX1 ) )
!= zero_zero_real )
| ( SX0 = zero_zero_real ) )
| ~ ! [SX0: real,SX1: real] :
( ( ( plus_plus_real @ ( times_times_real @ SX0 @ SX0 ) @ ( times_times_real @ SX1 @ SX1 ) )
!= zero_zero_real )
| ( SX1 = zero_zero_real ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3138]) ).
thf(3730,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ ( bit1 @ pls ) @ SX0 )
| ( ord_less_eq_real @ one_one_real @ ( number267125858f_real @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3139]) ).
thf(3731,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_real @ one_one_real @ ( number267125858f_real @ SX0 ) )
| ( ord_less_eq_int @ ( bit1 @ pls ) @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3139]) ).
thf(3732,plain,
! [SV789: int,SV451: int] :
( ( ! [SY2296: int] :
~ ( ~ ! [SY2297: int,SY2298: int] :
( ~ ( zcong @ SY2296 @ SY2297 @ SY2298 )
| ~ ( zcong @ SV451 @ ( times_times_int @ SV789 @ SY2296 ) @ SY2298 )
| ( zcong @ SV451 @ ( times_times_int @ SV789 @ SY2297 ) @ SY2298 ) )
| ~ ! [SY2299: int,SY2300: int] :
( ~ ( zcong @ SY2296 @ SY2299 @ SY2300 )
| ~ ( zcong @ SV451 @ ( times_times_int @ SV789 @ SY2299 ) @ SY2300 )
| ( zcong @ SV451 @ ( times_times_int @ SV789 @ SY2296 ) @ SY2300 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3140]) ).
thf(3733,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ ( bit1 @ SX0 ) @ min )
| ( ord_less_eq_int @ SX0 @ min ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3141]) ).
thf(3734,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ SX0 @ min )
| ( ord_less_eq_int @ ( bit1 @ SX0 ) @ min ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3141]) ).
thf(3735,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3142]) ).
thf(3736,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3142]) ).
thf(3737,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ( SX0 != SX1 )
| ( zcong @ SX0 @ SX1 @ zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3143]) ).
thf(3738,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( zcong @ SX0 @ SX1 @ zero_zero_int )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3143]) ).
thf(3739,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3144]) ).
thf(3740,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3144]) ).
thf(3741,plain,
! [SV790: nat,SV452: nat] :
( ( ~ ( ~ ! [SY2301: nat,SY2302: nat] :
( ( ( plus_plus_nat @ ( times_times_nat @ SV452 @ SV790 ) @ ( times_times_nat @ SY2301 @ SY2302 ) )
!= ( plus_plus_nat @ ( times_times_nat @ SV452 @ SY2302 ) @ ( times_times_nat @ SY2301 @ SV790 ) ) )
| ( SV452 = SY2301 )
| ( SV790 = SY2302 ) )
| ~ ~ ( ~ ! [SY2303: nat] :
( ( SV452 != SY2303 )
| ! [SY2304: nat] :
( ( plus_plus_nat @ ( times_times_nat @ SV452 @ SV790 ) @ ( times_times_nat @ SY2303 @ SY2304 ) )
= ( plus_plus_nat @ ( times_times_nat @ SV452 @ SY2304 ) @ ( times_times_nat @ SY2303 @ SV790 ) ) ) )
| ~ ! [SY2305: nat,SY2306: nat] :
( ( SV790 != SY2306 )
| ( ( plus_plus_nat @ ( times_times_nat @ SV452 @ SV790 ) @ ( times_times_nat @ SY2305 @ SY2306 ) )
= ( plus_plus_nat @ ( times_times_nat @ SV452 @ SY2306 ) @ ( times_times_nat @ SY2305 @ SV790 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3145]) ).
thf(3742,plain,
( ( ~ ! [SX0: real,SX1: nat] :
( ( SX1 = zero_zero_nat )
| ( SX0 != zero_zero_real )
| ( ( power_power_real @ SX0 @ SX1 )
= zero_zero_real ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3146]) ).
thf(3743,plain,
( ( ~ ~ ( ~ ! [SX0: real,SX1: nat] :
( ( ( power_power_real @ SX0 @ SX1 )
!= zero_zero_real )
| ( SX1 != zero_zero_nat ) )
| ~ ! [SX0: real] :
( ! [SX1: nat] :
( ( power_power_real @ SX0 @ SX1 )
!= zero_zero_real )
| ( SX0 = zero_zero_real ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3146]) ).
thf(3744,plain,
( ( ~ ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SX0 @ SX1 ) )
| ( SX1 = zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3147]) ).
thf(3745,plain,
( ( ~ ~ ( ~ ! [SX0: nat,SX1: nat] :
( ( SX1 != zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SX0 @ SX1 ) ) )
| ~ ! [SX0: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SX0 )
| ! [SX1: nat] : ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SX0 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3147]) ).
thf(3746,plain,
! [SV791: int,SV453: int] :
( ( ~ ( ~ ! [SY2307: int,SY2308: int] :
( ( ( plus_plus_int @ ( times_times_int @ SV453 @ SV791 ) @ ( times_times_int @ SY2307 @ SY2308 ) )
!= ( plus_plus_int @ ( times_times_int @ SV453 @ SY2308 ) @ ( times_times_int @ SY2307 @ SV791 ) ) )
| ( SV453 = SY2307 )
| ( SV791 = SY2308 ) )
| ~ ~ ( ~ ! [SY2309: int] :
( ( SV453 != SY2309 )
| ! [SY2310: int] :
( ( plus_plus_int @ ( times_times_int @ SV453 @ SV791 ) @ ( times_times_int @ SY2309 @ SY2310 ) )
= ( plus_plus_int @ ( times_times_int @ SV453 @ SY2310 ) @ ( times_times_int @ SY2309 @ SV791 ) ) ) )
| ~ ! [SY2311: int,SY2312: int] :
( ( SV791 != SY2312 )
| ( ( plus_plus_int @ ( times_times_int @ SV453 @ SV791 ) @ ( times_times_int @ SY2311 @ SY2312 ) )
= ( plus_plus_int @ ( times_times_int @ SV453 @ SY2312 ) @ ( times_times_int @ SY2311 @ SV791 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3148]) ).
thf(3747,plain,
( ( ~ ! [SX0: nat,SX1: nat] :
( ( SX1 != zero_zero_nat )
| ( ( power_power_nat @ SX0 @ SX1 )
= one_one_nat ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3149]) ).
thf(3748,plain,
( ( ~ ! [SX0: nat,SX1: 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 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3149]) ).
thf(3749,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ zero_zero_int @ SX1 )
| ( SX1 != one_one_int )
| ( SX0 != one_one_int )
| ( ( times_times_int @ SX1 @ SX0 )
= one_one_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3150]) ).
thf(3750,plain,
( ( ~ ~ ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ zero_zero_int @ SX1 )
| ( ( times_times_int @ SX1 @ SX0 )
!= one_one_int )
| ( SX1 = one_one_int ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ zero_zero_int @ SX1 )
| ( ( times_times_int @ SX1 @ SX0 )
!= one_one_int )
| ( SX0 = one_one_int ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3150]) ).
thf(3751,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ ( plus_plus_int @ SX0 @ one_one_int ) @ SX1 )
| ( ord_less_int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3151]) ).
thf(3752,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( plus_plus_int @ SX0 @ one_one_int ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3151]) ).
thf(3753,plain,
( ( ~ ! [SX0: int] :
( ( ( number_number_of_nat @ SX0 )
!= zero_zero_nat )
| ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ SX0 ) )
= one_one_nat ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3152]) ).
thf(3754,plain,
( ( ~ ! [SX0: int] :
( ( ( number_number_of_nat @ SX0 )
= zero_zero_nat )
| ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ SX0 ) )
= zero_zero_nat ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3152]) ).
thf(3755,plain,
( ( ~ ! [SX0: real,SX1: real] :
( ( SX0 = SX1 )
| ~ ( ord_less_eq_real @ SX0 @ SX1 )
| ( ord_less_real @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3153]) ).
thf(3756,plain,
( ( ~ ~ ( ~ ! [SX0: real,SX1: real] :
( ~ ( ord_less_real @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: real,SX1: real] :
( ~ ( ord_less_real @ SX0 @ SX1 )
| ( ord_less_eq_real @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3153]) ).
thf(3757,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_real @ ( number267125858f_real @ SX0 ) @ ( number267125858f_real @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3154]) ).
thf(3758,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_real @ ( number267125858f_real @ SX0 ) @ ( number267125858f_real @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3154]) ).
thf(3759,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ ( number_number_of_int @ SX0 ) @ ( number_number_of_int @ SX1 ) )
| ~ ( ord_less_int @ ( number_number_of_int @ SX1 ) @ ( number_number_of_int @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3155]) ).
thf(3760,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ( ord_less_int @ ( number_number_of_int @ SX1 ) @ ( number_number_of_int @ SX0 ) )
| ( ord_less_eq_int @ ( number_number_of_int @ SX0 ) @ ( number_number_of_int @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3155]) ).
thf(3761,plain,
( ( ~ ! [SX0: int] :
( ( ( plus_plus_int @ SX0 @ SX0 )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3156]) ).
thf(3762,plain,
( ( ~ ! [SX0: int] :
( ( SX0 != zero_zero_int )
| ( ( plus_plus_int @ SX0 @ SX0 )
= zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3156]) ).
thf(3763,plain,
( ( ~ ! [SX0: nat,SX1: int] :
( ~ ( 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 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3157]) ).
thf(3764,plain,
( ( ~ ~ ( ~ ! [SX0: nat,SX1: int] :
( ( ( number_number_of_nat @ SX1 )
!= zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SX0 @ ( number_number_of_nat @ SX1 ) ) ) )
| ~ ! [SX0: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SX0 )
| ! [SX1: int] : ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SX0 @ ( number_number_of_nat @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3157]) ).
thf(3765,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ SX0 @ ( bit1 @ pls ) )
| ( ord_less_eq_real @ ( number267125858f_real @ SX0 ) @ one_one_real ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3158]) ).
thf(3766,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_real @ ( number267125858f_real @ SX0 ) @ one_one_real )
| ( ord_less_eq_int @ SX0 @ ( bit1 @ pls ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3158]) ).
thf(3767,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX1 @ pls )
| ( ( times_times_nat @ ( number_number_of_nat @ SX1 ) @ ( number_number_of_nat @ SX0 ) )
= zero_zero_nat ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3159]) ).
thf(3768,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ( 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 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3159]) ).
thf(3769,plain,
( ( ~ ! [SX0: real] :
( ( SX0 = zero_zero_real )
| ( ord_less_real @ zero_zero_real @ ( power_power_real @ SX0 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3160]) ).
thf(3770,plain,
( ( ~ ! [SX0: real] :
( ~ ( ord_less_real @ zero_zero_real @ ( power_power_real @ SX0 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ( SX0 != zero_zero_real ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3160]) ).
thf(3771,plain,
( ( ~ ! [SX0: int] :
( ~ ( ~ ~ ( ~ ( dvd_dvd_int @ ( sK3_M_9 @ SX0 ) @ SX0 )
| ~ ( ord_less_eq_int @ zero_zero_int @ ( sK3_M_9 @ SX0 ) ) )
| ~ ~ ( ~ ( ( ( sK3_M_9 @ SX0 )
!= one_one_int ) )
| ~ ( ( ( sK3_M_9 @ SX0 )
!= SX0 ) ) ) )
| ~ ( ord_less_int @ one_one_int @ SX0 )
| ( zprime @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3161]) ).
thf(3772,plain,
( ( ~ ~ ( ~ ! [SX0: int] :
( ~ ( zprime @ SX0 )
| ! [SX1: int] :
( ~ ( dvd_dvd_int @ SX1 @ SX0 )
| ~ ( ord_less_eq_int @ zero_zero_int @ SX1 )
| ( SX1 = one_one_int )
| ( SX1 = SX0 ) ) )
| ~ ! [SX0: int] :
( ~ ( zprime @ SX0 )
| ( ord_less_int @ one_one_int @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3161]) ).
thf(3773,plain,
! [SV454: int] :
( ( ~ ! [SY1968: nat,SY1969: int] :
( ~ ( ord_less_int @ SY1969 @ pls )
| ( ( times_times_nat @ ( number_number_of_nat @ SY1969 ) @ ( times_times_nat @ ( number_number_of_nat @ SV454 ) @ SY1968 ) )
= zero_zero_nat ) )
| ~ ! [SY1970: nat,SY1971: int] :
( ( ord_less_int @ SY1971 @ pls )
| ( ( times_times_nat @ ( number_number_of_nat @ SY1971 ) @ ( times_times_nat @ ( number_number_of_nat @ SV454 ) @ SY1970 ) )
= ( times_times_nat @ ( number_number_of_nat @ ( times_times_int @ SY1971 @ SV454 ) ) @ SY1970 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3162]) ).
thf(3774,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( zcong @ SX0 @ zero_zero_int @ SX1 )
| ( ( legendre @ SX0 @ SX1 )
= zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3163]) ).
thf(3775,plain,
( ( ~ ~ ( ~ ! [SX0: int,SX1: int] :
( ( zcong @ SX0 @ zero_zero_int @ SX1 )
| ~ ( quadRes @ SX1 @ SX0 )
| ( ( legendre @ SX0 @ SX1 )
= one_one_int ) )
| ~ ! [SX0: int,SX1: int] :
( ( zcong @ SX0 @ zero_zero_int @ SX1 )
| ( quadRes @ SX1 @ SX0 )
| ( ( legendre @ SX0 @ SX1 )
= ( number_number_of_int @ min ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3163]) ).
thf(3776,plain,
( ( ~ ! [SX0: nat] :
( ( SX0 != zero_zero_nat )
| ( ( power_power_int @ zero_zero_int @ SX0 )
= one_one_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3164]) ).
thf(3777,plain,
( ( ~ ! [SX0: nat] :
( ( SX0 = zero_zero_nat )
| ( ( power_power_int @ zero_zero_int @ SX0 )
= zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3164]) ).
thf(3778,plain,
! [SV455: real,SV792: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ SV792 )
| ~ ( ord_less_real @ zero_zero_real @ SV455 )
| ~ ( ~ ! [SY2313: real] :
( ( ( power_power_real @ SY2313 @ SV792 )
!= SV455 )
| ~ ( ord_less_real @ zero_zero_real @ SY2313 )
| ( SY2313
= ( sK1_X_1 @ SV792 @ SV455 ) ) )
| ~ ~ ( ( ( power_power_real @ ( sK1_X_1 @ SV792 @ SV455 ) @ SV792 )
!= SV455 )
| ~ ( ord_less_real @ zero_zero_real @ ( sK1_X_1 @ SV792 @ SV455 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3165]) ).
thf(3779,plain,
( ( ~ ! [SX0: int] :
( ( zero_zero_nat
!= ( number_number_of_nat @ SX0 ) )
| ( ord_less_eq_int @ SX0 @ pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3166]) ).
thf(3780,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ SX0 @ pls )
| ( zero_zero_nat
= ( number_number_of_nat @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3166]) ).
thf(3781,plain,
( ( ~ ~ ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_eq_nat @ ( number_number_of_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ SX0 @ pls )
| ! [SX1: int] : ( ord_less_eq_nat @ ( number_number_of_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3167]) ).
thf(3782,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( 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 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3167]) ).
thf(3783,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ ( number_number_of_int @ SX0 ) @ zero_zero_int )
| ( ord_less_int @ SX0 @ pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3168]) ).
thf(3784,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ SX0 @ pls )
| ( ord_less_int @ ( number_number_of_int @ SX0 ) @ zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3168]) ).
thf(3785,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ one_one_int @ ( number_number_of_int @ SX0 ) )
| ( ord_less_eq_int @ ( bit1 @ pls ) @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3169]) ).
thf(3786,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ ( bit1 @ pls ) @ SX0 )
| ( ord_less_eq_int @ one_one_int @ ( number_number_of_int @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3169]) ).
thf(3787,plain,
( ( ~ ! [SX0: int,SX1: real] :
( ( ( number267125858f_real @ SX0 )
!= SX1 )
| ( SX1
= ( number267125858f_real @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3170]) ).
thf(3788,plain,
( ( ~ ! [SX0: int,SX1: real] :
( ( SX1
!= ( number267125858f_real @ SX0 ) )
| ( ( number267125858f_real @ SX0 )
= SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3170]) ).
thf(3789,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ SX0 ) @ SX0 ) @ zero_zero_int )
| ( ord_less_int @ SX0 @ zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3171]) ).
thf(3790,plain,
( ( ~ ! [SX0: 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 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3171]) ).
thf(3791,plain,
! [SV456: int] :
( ( ~ ! [SY1974: int,SY1975: int] :
( ~ ( zcong @ SV456 @ SY1974 @ SY1975 )
| ( zcong @ SY1974 @ SV456 @ SY1975 ) )
| ~ ! [SY1976: int,SY1977: int] :
( ~ ( zcong @ SY1976 @ SV456 @ SY1977 )
| ( zcong @ SV456 @ SY1976 @ SY1977 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3172]) ).
thf(3792,plain,
! [SV457: int,SV793: int] :
( ( ! [SY2314: int] :
~ ( ~ ! [SY2315: int,SY2316: int] :
( ~ ( dvd_dvd_int @ SY2315 @ SY2316 )
| ~ ( dvd_dvd_int @ SY2315 @ ( plus_plus_int @ SV793 @ SY2314 ) )
| ( dvd_dvd_int @ SY2315 @ ( plus_plus_int @ ( plus_plus_int @ SV793 @ ( times_times_int @ SV457 @ SY2316 ) ) @ SY2314 ) ) )
| ~ ! [SY2317: int,SY2318: int] :
( ~ ( dvd_dvd_int @ SY2317 @ SY2318 )
| ~ ( dvd_dvd_int @ SY2317 @ ( plus_plus_int @ ( plus_plus_int @ SV793 @ ( times_times_int @ SV457 @ SY2318 ) ) @ SY2314 ) )
| ( dvd_dvd_int @ SY2317 @ ( plus_plus_int @ SV793 @ SY2314 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3173]) ).
thf(3793,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ ( bit1 @ pls ) @ SX0 )
| ( ord_less_real @ one_one_real @ ( number267125858f_real @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3174]) ).
thf(3794,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_real @ one_one_real @ ( number267125858f_real @ SX0 ) )
| ( ord_less_int @ ( bit1 @ pls ) @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3174]) ).
thf(3795,plain,
( ( ~ ! [SX0: real,SX1: real] :
( ( SX0
!= ( plus_plus_real @ SX0 @ SX1 ) )
| ( SX1 = zero_zero_real ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3175]) ).
thf(3796,plain,
( ( ~ ! [SX0: real,SX1: real] :
( ( SX1 != zero_zero_real )
| ( SX0
= ( plus_plus_real @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3175]) ).
thf(3797,plain,
! [SV458: int] :
( ( ~ ! [SY1984: int,SY1985: int] :
( ! [SY1986: int] :
( SY1984
!= ( plus_plus_int @ SV458 @ ( times_times_int @ SY1985 @ SY1986 ) ) )
| ( zcong @ SV458 @ SY1984 @ SY1985 ) )
| ~ ! [SY1987: int,SY1988: int] :
( ~ ( zcong @ SV458 @ SY1987 @ SY1988 )
| ( SY1987
= ( plus_plus_int @ SV458 @ ( times_times_int @ SY1988 @ ( sK6_K_1 @ SY1988 @ SY1987 @ SV458 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3176]) ).
thf(3798,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ pls @ ( bit0 @ SX0 ) )
| ( ord_less_eq_int @ pls @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3177]) ).
thf(3799,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ pls @ SX0 )
| ( ord_less_eq_int @ pls @ ( bit0 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3177]) ).
thf(3800,plain,
! [SV459: nat] :
( ( ~ ! [SY1989: nat,SY1990: nat] :
( ~ ( ord_less_nat @ one_one_nat @ SY1990 )
| ( ( power_power_nat @ SY1990 @ SV459 )
!= ( power_power_nat @ SY1990 @ SY1989 ) )
| ( SV459 = SY1989 ) )
| ~ ! [SY1991: nat,SY1992: nat] :
( ~ ( ord_less_nat @ one_one_nat @ SY1992 )
| ( SV459 != SY1991 )
| ( ( power_power_nat @ SY1992 @ SV459 )
= ( power_power_nat @ SY1992 @ SY1991 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3178]) ).
thf(3801,plain,
! [SV794: real,SV460: real] :
( ( ~ ( ~ ! [SY2319: real,SY2320: real] :
( ( ( plus_plus_real @ ( times_times_real @ SV460 @ SV794 ) @ ( times_times_real @ SY2319 @ SY2320 ) )
!= ( plus_plus_real @ ( times_times_real @ SV460 @ SY2320 ) @ ( times_times_real @ SY2319 @ SV794 ) ) )
| ( SV460 = SY2319 )
| ( SV794 = SY2320 ) )
| ~ ~ ( ~ ! [SY2321: real] :
( ( SV460 != SY2321 )
| ! [SY2322: real] :
( ( plus_plus_real @ ( times_times_real @ SV460 @ SV794 ) @ ( times_times_real @ SY2321 @ SY2322 ) )
= ( plus_plus_real @ ( times_times_real @ SV460 @ SY2322 ) @ ( times_times_real @ SY2321 @ SV794 ) ) ) )
| ~ ! [SY2323: real,SY2324: real] :
( ( SV794 != SY2324 )
| ( ( plus_plus_real @ ( times_times_real @ SV460 @ SV794 ) @ ( times_times_real @ SY2323 @ SY2324 ) )
= ( plus_plus_real @ ( times_times_real @ SV460 @ SY2324 ) @ ( times_times_real @ SY2323 @ SV794 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3179]) ).
thf(3802,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ ( bit1 @ SX0 ) @ pls )
| ( ord_less_int @ SX0 @ pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3180]) ).
thf(3803,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ SX0 @ pls )
| ( ord_less_int @ ( bit1 @ SX0 ) @ pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3180]) ).
thf(3804,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ SX0 ) )
| ( ord_less_eq_int @ pls @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3181]) ).
thf(3805,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ pls @ SX0 )
| ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3181]) ).
thf(3806,plain,
! [SV461: nat] :
( ( ~ ! [SY2000: nat,SY2001: nat] :
( ~ ( dvd_dvd_nat @ ( times_times_nat @ SV461 @ SY2000 ) @ ( times_times_nat @ SY2001 @ SY2000 ) )
| ( SY2000 = zero_zero_nat )
| ( dvd_dvd_nat @ SV461 @ SY2001 ) )
| ~ ~ ( ~ ! [SY2002: nat] :
( ( SY2002 != zero_zero_nat )
| ! [SY2003: nat] : ( dvd_dvd_nat @ ( times_times_nat @ SV461 @ SY2002 ) @ ( times_times_nat @ SY2003 @ SY2002 ) ) )
| ~ ! [SY2004: nat,SY2005: nat] :
( ~ ( dvd_dvd_nat @ SV461 @ SY2005 )
| ( dvd_dvd_nat @ ( times_times_nat @ SV461 @ SY2004 ) @ ( times_times_nat @ SY2005 @ SY2004 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3182]) ).
thf(3807,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ( ( number267125858f_real @ SX0 )
!= ( number267125858f_real @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3183]) ).
thf(3808,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ( SX0 != SX1 )
| ( ( number267125858f_real @ SX0 )
= ( number267125858f_real @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3183]) ).
thf(3809,plain,
( ( ~ ! [SX0: nat] :
( ( SX0 != zero_zero_nat )
| ( ( power_power_nat @ zero_zero_nat @ SX0 )
= one_one_nat ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3184]) ).
thf(3810,plain,
( ( ~ ! [SX0: nat] :
( ( SX0 = zero_zero_nat )
| ( ( power_power_nat @ zero_zero_nat @ SX0 )
= zero_zero_nat ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3184]) ).
thf(3811,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ ( bit0 @ SX0 ) @ min )
| ( ord_less_eq_int @ SX0 @ min ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3185]) ).
thf(3812,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ SX0 @ min )
| ( ord_less_eq_int @ ( bit0 @ SX0 ) @ min ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3185]) ).
thf(3813,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3186]) ).
thf(3814,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3186]) ).
thf(3815,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3187]) ).
thf(3816,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3187]) ).
thf(3817,plain,
( ( ~ ! [SX0: nat,SX1: nat] :
( ( SX0
!= ( plus_plus_nat @ SX0 @ SX1 ) )
| ( SX1 = zero_zero_nat ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3188]) ).
thf(3818,plain,
( ( ~ ! [SX0: nat,SX1: nat] :
( ( SX1 != zero_zero_nat )
| ( SX0
= ( plus_plus_nat @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3188]) ).
thf(3819,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3189]) ).
thf(3820,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3189]) ).
thf(3821,plain,
( ( ~ ! [SX0: nat,SX1: nat] :
( ( SX1 = zero_zero_nat )
| ( SX0 != zero_zero_nat )
| ( ( power_power_nat @ SX0 @ SX1 )
= zero_zero_nat ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3190]) ).
thf(3822,plain,
( ( ~ ~ ( ~ ! [SX0: nat,SX1: nat] :
( ( ( power_power_nat @ SX0 @ SX1 )
!= zero_zero_nat )
| ( SX1 != zero_zero_nat ) )
| ~ ! [SX0: nat] :
( ! [SX1: nat] :
( ( power_power_nat @ SX0 @ SX1 )
!= zero_zero_nat )
| ( SX0 = zero_zero_nat ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3190]) ).
thf(3823,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3191]) ).
thf(3824,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3191]) ).
thf(3825,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ( SX0
!= ( plus_plus_int @ SX0 @ SX1 ) )
| ( SX1 = zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3192]) ).
thf(3826,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ( SX1 != zero_zero_int )
| ( SX0
= ( plus_plus_int @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3192]) ).
thf(3827,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ! [SX2: int] :
~ ( zcong @ ( power_power_int @ SX2 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SX1 @ SX0 )
| ( quadRes @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3193]) ).
thf(3828,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( quadRes @ SX0 @ SX1 )
| ( zcong @ ( power_power_int @ ( sK5_Y_1 @ SX1 @ SX0 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3193]) ).
thf(3829,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ one_one_int @ ( number_number_of_int @ SX0 ) )
| ( ord_less_int @ ( bit1 @ pls ) @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3194]) ).
thf(3830,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ ( bit1 @ pls ) @ SX0 )
| ( ord_less_int @ one_one_int @ ( number_number_of_int @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3194]) ).
thf(3831,plain,
! [SV462: nat] :
( ( ~ ! [SY2006: nat,SY2007: real] :
( ~ ( ord_less_real @ one_one_real @ SY2007 )
| ( ( power_power_real @ SY2007 @ SV462 )
!= ( power_power_real @ SY2007 @ SY2006 ) )
| ( SV462 = SY2006 ) )
| ~ ! [SY2008: nat,SY2009: real] :
( ~ ( ord_less_real @ one_one_real @ SY2009 )
| ( SV462 != SY2008 )
| ( ( power_power_real @ SY2009 @ SV462 )
= ( power_power_real @ SY2009 @ SY2008 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3195]) ).
thf(3832,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX1 @ pls )
| ( ( plus_plus_nat @ ( number_number_of_nat @ SX1 ) @ ( number_number_of_nat @ SX0 ) )
= ( number_number_of_nat @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3196]) ).
thf(3833,plain,
( ( ~ ~ ( ~ ! [SX0: int,SX1: int] :
( ( 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 ) ) )
| ~ ! [SX0: int,SX1: int] :
( ( 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 @ ( plus_plus_int @ SX1 @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3196]) ).
thf(3834,plain,
! [SV463: real] :
( ( ~ ! [SY2010: real,SY2011: real] :
( ( SY2011 = zero_zero_real )
| ( ( times_times_real @ SV463 @ SY2011 )
!= ( times_times_real @ SY2010 @ SY2011 ) )
| ( SV463 = SY2010 ) )
| ~ ! [SY2012: real,SY2013: real] :
( ( SY2013 = zero_zero_real )
| ( SV463 != SY2012 )
| ( ( times_times_real @ SV463 @ SY2013 )
= ( times_times_real @ SY2012 @ SY2013 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3197]) ).
thf(3835,plain,
! [SV464: real] :
( ( ~ ! [SY2014: real,SY2015: real] :
( ~ ( ord_less_real @ zero_zero_real @ SY2015 )
| ~ ( ord_less_real @ ( times_times_real @ SV464 @ SY2015 ) @ ( times_times_real @ SY2014 @ SY2015 ) )
| ( ord_less_real @ SV464 @ SY2014 ) )
| ~ ! [SY2016: real,SY2017: real] :
( ~ ( ord_less_real @ zero_zero_real @ SY2017 )
| ~ ( ord_less_real @ SV464 @ SY2016 )
| ( ord_less_real @ ( times_times_real @ SV464 @ SY2017 ) @ ( times_times_real @ SY2016 @ SY2017 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3198]) ).
thf(3836,plain,
! [SV465: real] :
( ( ~ ! [SY2018: real,SY2019: real] :
( ~ ( ord_less_real @ zero_zero_real @ SY2019 )
| ~ ( ord_less_eq_real @ ( times_times_real @ SY2019 @ SV465 ) @ ( times_times_real @ SY2019 @ SY2018 ) )
| ( ord_less_eq_real @ SV465 @ SY2018 ) )
| ~ ! [SY2020: real,SY2021: real] :
( ~ ( ord_less_real @ zero_zero_real @ SY2021 )
| ~ ( ord_less_eq_real @ SV465 @ SY2020 )
| ( ord_less_eq_real @ ( times_times_real @ SY2021 @ SV465 ) @ ( times_times_real @ SY2021 @ SY2020 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3199]) ).
thf(3837,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ( ( bit0 @ SX0 )
!= ( bit0 @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3200]) ).
thf(3838,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ( SX0 != SX1 )
| ( ( bit0 @ SX0 )
= ( bit0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3200]) ).
thf(3839,plain,
( ( ~ ! [SX0: int] :
( ( ( power_power_int @ SX0 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3201]) ).
thf(3840,plain,
( ( ~ ! [SX0: int] :
( ( SX0 != zero_zero_int )
| ( ( power_power_int @ SX0 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3201]) ).
thf(3841,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ( SX0 != zero_zero_int )
| ( SX1 != zero_zero_int )
| ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SX0 @ SX0 ) @ ( times_times_int @ SX1 @ SX1 ) ) @ zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3202]) ).
thf(3842,plain,
( ( ~ ~ ( ~ ! [SX0: int] :
( ! [SX1: int] :
~ ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SX0 @ SX0 ) @ ( times_times_int @ SX1 @ SX1 ) ) @ zero_zero_int )
| ( SX0 = zero_zero_int ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SX0 @ SX0 ) @ ( times_times_int @ SX1 @ SX1 ) ) @ zero_zero_int )
| ( SX1 = zero_zero_int ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3202]) ).
thf(3843,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ pls @ ( bit0 @ SX0 ) )
| ( ord_less_int @ pls @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3203]) ).
thf(3844,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ pls @ SX0 )
| ( ord_less_int @ pls @ ( bit0 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3203]) ).
thf(3845,plain,
( ( ~ ! [SX0: real] :
( ~ ( ord_less_real @ ( plus_plus_real @ SX0 @ SX0 ) @ zero_zero_real )
| ( ord_less_real @ SX0 @ zero_zero_real ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3204]) ).
thf(3846,plain,
( ( ~ ! [SX0: real] :
( ~ ( ord_less_real @ SX0 @ zero_zero_real )
| ( ord_less_real @ ( plus_plus_real @ SX0 @ SX0 ) @ zero_zero_real ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3204]) ).
thf(3847,plain,
( ( ~ ! [SX0: int,SX1: nat] :
( ( SX1 = zero_zero_nat )
| ( SX0 != zero_zero_int )
| ( ( power_power_int @ SX0 @ SX1 )
= zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3205]) ).
thf(3848,plain,
( ( ~ ~ ( ~ ! [SX0: int,SX1: nat] :
( ( ( power_power_int @ SX0 @ SX1 )
!= zero_zero_int )
| ( SX1 != zero_zero_nat ) )
| ~ ! [SX0: int] :
( ! [SX1: nat] :
( ( power_power_int @ SX0 @ SX1 )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3205]) ).
thf(3849,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ( ( number_number_of_int @ SX0 )
!= ( number_number_of_int @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3206]) ).
thf(3850,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ( SX0 != SX1 )
| ( ( number_number_of_int @ SX0 )
= ( number_number_of_int @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3206]) ).
thf(3851,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ SX0 @ min )
| ( ord_less_int @ ( bit0 @ SX0 ) @ min ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3207]) ).
thf(3852,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ ( bit0 @ SX0 ) @ min )
| ( ord_less_eq_int @ SX0 @ min ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3207]) ).
thf(3853,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_nat @ ( number_number_of_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) )
| ~ ( ord_less_nat @ ( number_number_of_nat @ SX1 ) @ ( number_number_of_nat @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3208]) ).
thf(3854,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ( ord_less_nat @ ( number_number_of_nat @ SX1 ) @ ( number_number_of_nat @ SX0 ) )
| ( ord_less_eq_nat @ ( number_number_of_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3208]) ).
thf(3855,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ ( number_number_of_int @ SX0 ) @ one_one_int )
| ( ord_less_eq_int @ SX0 @ ( bit1 @ pls ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3209]) ).
thf(3856,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ SX0 @ ( bit1 @ pls ) )
| ( ord_less_eq_int @ ( number_number_of_int @ SX0 ) @ one_one_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3209]) ).
thf(3857,plain,
! [SV466: int] :
( ( ~ ! [SY2022: int,SY2023: int] :
( ~ ( dvd_dvd_int @ SY2023 @ ( minus_minus_int @ SV466 @ SY2022 ) )
| ( zcong @ SV466 @ SY2022 @ SY2023 ) )
| ~ ! [SY2024: int,SY2025: int] :
( ~ ( zcong @ SV466 @ SY2024 @ SY2025 )
| ( dvd_dvd_int @ SY2025 @ ( minus_minus_int @ SV466 @ SY2024 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3210]) ).
thf(3858,plain,
( ( ~ ! [SX0: int] :
( ( ( number_number_of_nat @ SX0 )
!= zero_zero_nat )
| ( ( power_power_real @ zero_zero_real @ ( number_number_of_nat @ SX0 ) )
= one_one_real ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3211]) ).
thf(3859,plain,
( ( ~ ! [SX0: int] :
( ( ( number_number_of_nat @ SX0 )
= zero_zero_nat )
| ( ( power_power_real @ zero_zero_real @ ( number_number_of_nat @ SX0 ) )
= zero_zero_real ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3211]) ).
thf(3860,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ ( bit0 @ SX0 ) @ zero_zero_int )
| ( ord_less_int @ SX0 @ zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3212]) ).
thf(3861,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_int @ SX0 @ zero_zero_int )
| ( ord_less_int @ ( bit0 @ SX0 ) @ zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3212]) ).
thf(3862,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ pls @ ( bit1 @ SX0 ) )
| ( ord_less_eq_int @ pls @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3213]) ).
thf(3863,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ pls @ SX0 )
| ( ord_less_eq_int @ pls @ ( bit1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3213]) ).
thf(3864,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ ( number_number_of_int @ SX0 ) @ ( number_number_of_int @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3214]) ).
thf(3865,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ ( number_number_of_int @ SX0 ) @ ( number_number_of_int @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3214]) ).
thf(3866,plain,
! [SV467: nat] :
( ( ~ ! [SY2026: nat,SY2027: int] :
( ~ ( ord_less_int @ one_one_int @ SY2027 )
| ( ( power_power_int @ SY2027 @ SV467 )
!= ( power_power_int @ SY2027 @ SY2026 ) )
| ( SV467 = SY2026 ) )
| ~ ! [SY2028: nat,SY2029: int] :
( ~ ( ord_less_int @ one_one_int @ SY2029 )
| ( SV467 != SY2028 )
| ( ( power_power_int @ SY2029 @ SV467 )
= ( power_power_int @ SY2029 @ SY2028 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3215]) ).
thf(3867,plain,
! [SV468: int,SV1: int] :
( ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ SV1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV468 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_int )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3217]) ).
thf(3868,plain,
! [SV795: nat,SV469: nat,SV5: int] :
( ( ( power_power_int @ SV5 @ ( plus_plus_nat @ SV469 @ SV795 ) )
= ( times_times_int @ ( power_power_int @ SV5 @ SV469 ) @ ( power_power_int @ SV5 @ SV795 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3219]) ).
thf(3869,plain,
! [SV6: int,SV796: int,SV470: int] :
( ( ~ ( ord_less_eq_int @ SV470 @ SV796 )
| ( ord_less_eq_int @ ( plus_plus_int @ SV6 @ SV470 ) @ ( plus_plus_int @ SV6 @ SV796 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3220]) ).
thf(3870,plain,
! [SV472: int,SV8: int,SV797: int] :
( ( ! [SY2325: int] :
( ~ ( ord_less_int @ SV797 @ SY2325 )
| ~ ( ord_less_eq_int @ SV8 @ SV472 )
| ( ord_less_int @ ( plus_plus_int @ SV797 @ SV8 ) @ ( plus_plus_int @ SY2325 @ SV472 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3222]) ).
thf(3871,plain,
! [SV798: int,SV475: int,SV14: int] :
( ( ( times_times_int @ ( plus_plus_int @ SV14 @ SV475 ) @ SV798 )
= ( plus_plus_int @ ( times_times_int @ SV14 @ SV798 ) @ ( times_times_int @ SV475 @ SV798 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3225]) ).
thf(3872,plain,
! [SV799: int,SV476: int,SV15: int] :
( ( ( times_times_int @ SV15 @ ( plus_plus_int @ SV476 @ SV799 ) )
= ( plus_plus_int @ ( times_times_int @ SV15 @ SV476 ) @ ( times_times_int @ SV15 @ SV799 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3226]) ).
thf(3873,plain,
! [SV477: int,SV16: int] :
( ( ( ~ ( ord_less_int @ SV16 @ SV477 ) )
= $true )
| ( ( ord_less_eq_int @ ( plus_plus_int @ SV16 @ one_one_int ) @ SV477 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3227]) ).
thf(3874,plain,
! [SV17: int,SV478: int] :
( ( ( ~ ( ord_less_eq_int @ pls @ SV478 ) )
= $true )
| ( ( ~ ( ord_less_eq_int @ pls @ SV17 )
| ( ( plus_plus_nat @ ( number_number_of_nat @ SV478 ) @ ( number_number_of_nat @ SV17 ) )
= ( number_number_of_nat @ ( plus_plus_int @ SV478 @ SV17 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3228]) ).
thf(3875,plain,
! [SV18: int,SV479: int] :
( ( ( ~ ( ord_less_eq_int @ pls @ SV479 ) )
= $true )
| ( ( ~ ( ord_less_eq_int @ pls @ SV18 )
| ( ( plus_plus_int @ ( number_number_of_int @ SV479 ) @ ( number_number_of_int @ SV18 ) )
= ( number_number_of_int @ ( plus_plus_int @ SV479 @ SV18 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3229]) ).
thf(3876,plain,
! [SV19: int] :
( ( ( ord_less_eq_int @ zero_zero_int @ SV19 )
= $false )
| ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3230]) ).
thf(3877,plain,
! [SV20: int,SV480: int] :
( ( ( ord_less_int @ SV480 @ SV20 )
= $true )
| ( ( ( SV20 = SV480 )
| ( ord_less_int @ SV20 @ SV480 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3231]) ).
thf(3878,plain,
! [SV800: int,SV481: nat,SV21: nat] :
( ( ( times_times_nat @ ( plus_plus_nat @ SV21 @ SV481 ) @ ( number_number_of_nat @ SV800 ) )
= ( plus_plus_nat @ ( times_times_nat @ SV21 @ ( number_number_of_nat @ SV800 ) ) @ ( times_times_nat @ SV481 @ ( number_number_of_nat @ SV800 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3232]) ).
thf(3879,plain,
! [SV801: int,SV482: int,SV22: int] :
( ( ( times_times_int @ ( plus_plus_int @ SV22 @ SV482 ) @ ( number_number_of_int @ SV801 ) )
= ( plus_plus_int @ ( times_times_int @ SV22 @ ( number_number_of_int @ SV801 ) ) @ ( times_times_int @ SV482 @ ( number_number_of_int @ SV801 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3233]) ).
thf(3880,plain,
! [SV802: nat,SV483: nat,SV23: int] :
( ( ( times_times_nat @ ( number_number_of_nat @ SV23 ) @ ( plus_plus_nat @ SV483 @ SV802 ) )
= ( plus_plus_nat @ ( times_times_nat @ ( number_number_of_nat @ SV23 ) @ SV483 ) @ ( times_times_nat @ ( number_number_of_nat @ SV23 ) @ SV802 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3234]) ).
thf(3881,plain,
! [SV803: int,SV484: int,SV24: int] :
( ( ( times_times_int @ ( number_number_of_int @ SV24 ) @ ( plus_plus_int @ SV484 @ SV803 ) )
= ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ SV24 ) @ SV484 ) @ ( times_times_int @ ( number_number_of_int @ SV24 ) @ SV803 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3235]) ).
thf(3882,plain,
! [SV804: int,SV485: int,SV25: int] :
( ( ( plus_plus_int @ ( plus_plus_int @ SV25 @ SV485 ) @ SV804 )
= ( plus_plus_int @ SV25 @ ( plus_plus_int @ SV485 @ SV804 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3236]) ).
thf(3883,plain,
! [SV805: int,SV486: int,SV26: int] :
( ( ( plus_plus_int @ SV26 @ ( plus_plus_int @ SV486 @ SV805 ) )
= ( plus_plus_int @ SV486 @ ( plus_plus_int @ SV26 @ SV805 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3237]) ).
thf(3884,plain,
! [SV28: int,SV806: int,SV488: int] :
( ( ~ ( ord_less_int @ SV488 @ SV806 )
| ~ ( ord_less_int @ zero_zero_int @ SV28 )
| ( ord_less_int @ ( times_times_int @ SV28 @ SV488 ) @ ( times_times_int @ SV28 @ SV806 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3239]) ).
thf(3885,plain,
! [SV489: int,SV29: int] :
( ( ( ( power_power_int @ SV29 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= ( power_power_int @ SV489 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $true )
| ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV29 )
| ~ ( ord_less_eq_int @ zero_zero_int @ SV489 )
| ( SV29 = SV489 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3240]) ).
thf(3886,plain,
! [SV490: int,SV30: int] :
( ( ( ~ ( ord_less_eq_int @ ( power_power_int @ SV30 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV490 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true )
| ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV490 )
| ( ord_less_eq_int @ SV30 @ SV490 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3241]) ).
thf(3887,plain,
! [SV491: int,SV32: int] :
( ( ( ~ ( ord_less_int @ ( power_power_int @ SV32 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV491 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true )
| ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV491 )
| ( ord_less_int @ SV32 @ SV491 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3242]) ).
thf(3888,plain,
! [SV493: int,SV34: int] :
( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ SV34 @ SV34 ) @ ( times_times_int @ SV493 @ SV493 ) ) @ zero_zero_int )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3244]) ).
thf(3889,plain,
! [SV495: int,SV42: int] :
( ( ( bit1 @ SV42 )
= ( bit0 @ SV495 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3248]) ).
thf(3890,plain,
! [SV496: int,SV43: int] :
( ( ( bit0 @ SV43 )
= ( bit1 @ SV496 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3249]) ).
thf(3891,plain,
! [SV50: int,SV807: int,SV498: int] :
( ( ~ ( ord_less_int @ SV498 @ SV807 )
| ( ord_less_int @ ( plus_plus_int @ SV498 @ SV50 ) @ ( plus_plus_int @ SV807 @ SV50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3251]) ).
thf(3892,plain,
! [SV808: real,SV499: int,SV68: int] :
( ( ( plus_plus_real @ ( number267125858f_real @ SV68 ) @ ( plus_plus_real @ ( number267125858f_real @ SV499 ) @ SV808 ) )
= ( plus_plus_real @ ( number267125858f_real @ ( plus_plus_int @ SV68 @ SV499 ) ) @ SV808 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3252]) ).
thf(3893,plain,
! [SV809: int,SV500: int,SV69: int] :
( ( ( plus_plus_int @ ( number_number_of_int @ SV69 ) @ ( plus_plus_int @ ( number_number_of_int @ SV500 ) @ SV809 ) )
= ( plus_plus_int @ ( number_number_of_int @ ( plus_plus_int @ SV69 @ SV500 ) ) @ SV809 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3253]) ).
thf(3894,plain,
! [SV85: int] :
( ( ( ord_less_eq_int @ zero_zero_int @ SV85 )
= $false )
| ( ( ~ ( ord_less_int @ SV85 @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
| ( SV85 = zero_zero_int )
| ( SV85 = one_one_int ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3264]) ).
thf(3895,plain,
! [SV510: int,SV88: int,SV810: int] :
( ( ~ ( ord_less_int @ zero_zero_int @ SV810 )
| ( SV810
!= ( plus_plus_int @ SV88 @ ( times_times_int @ SV810 @ SV510 ) ) )
| ~ ( ord_less_int @ SV88 @ SV810 )
| ( ord_less_eq_int @ one_one_int @ SV510 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3265]) ).
thf(3896,plain,
! [SV511: int,SV89: int,SV811: int] :
( ( ~ ( ord_less_int @ zero_zero_int @ SV811 )
| ( SV811
!= ( plus_plus_int @ SV89 @ ( times_times_int @ SV811 @ SV511 ) ) )
| ~ ( ord_less_eq_int @ zero_zero_int @ SV89 )
| ( ord_less_eq_int @ SV511 @ one_one_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3266]) ).
thf(3897,plain,
! [SV514: nat,SV92: int,SV812: int] :
( ( ~ ( zprime @ SV812 )
| ~ ( dvd_dvd_int @ SV812 @ ( power_power_int @ SV92 @ SV514 ) )
| ( dvd_dvd_int @ SV812 @ SV92 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3269]) ).
thf(3898,plain,
! [SV813: nat,SV515: nat,SV93: int] :
( ( ( power_power_int @ ( power_power_int @ SV93 @ SV515 ) @ SV813 )
= ( power_power_int @ SV93 @ ( times_times_nat @ SV515 @ SV813 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3270]) ).
thf(3899,plain,
! [SV814: nat,SV516: nat,SV94: int] :
( ( ( power_power_int @ ( power_power_int @ SV94 @ SV516 ) @ SV814 )
= ( power_power_int @ SV94 @ ( times_times_nat @ SV516 @ SV814 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3271]) ).
thf(3900,plain,
! [SV95: int,SV517: int] :
( ( ( ~ ( ord_less_int @ zero_zero_int @ SV517 ) )
= $true )
| ( ( ~ ( ord_less_int @ SV517 @ SV95 )
| ~ ( dvd_dvd_int @ SV95 @ SV517 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3272]) ).
thf(3901,plain,
! [SV96: int,SV518: int] :
( ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV518 ) )
= $true )
| ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV96 )
| ~ ( dvd_dvd_int @ SV518 @ SV96 )
| ~ ( dvd_dvd_int @ SV96 @ SV518 )
| ( SV518 = SV96 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3273]) ).
thf(3902,plain,
! [SV815: int,SV519: int,SV97: int] :
( ( ~ ( dvd_dvd_int @ ( times_times_int @ SV97 @ SV519 ) @ ( times_times_int @ SV97 @ SV815 ) )
| ( SV97 = zero_zero_int )
| ( dvd_dvd_int @ SV519 @ SV815 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3274]) ).
thf(3903,plain,
! [SV520: int,SV98: int] :
( ( ( ~ ( dvd_dvd_int @ SV98 @ SV520 ) )
= $true )
| ( ( ~ ( ord_less_int @ zero_zero_int @ SV520 )
| ( ord_less_eq_int @ SV98 @ SV520 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3275]) ).
thf(3904,plain,
! [SV816: int,SV522: int,SV100: int] :
( ( ( plus_plus_int @ SV100 @ ( plus_plus_int @ SV522 @ SV816 ) )
= ( plus_plus_int @ SV522 @ ( plus_plus_int @ SV100 @ SV816 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3277]) ).
thf(3905,plain,
! [SV817: int,SV523: int,SV101: int] :
( ( ( plus_plus_int @ SV101 @ ( plus_plus_int @ SV523 @ SV817 ) )
= ( plus_plus_int @ ( plus_plus_int @ SV101 @ SV523 ) @ SV817 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3278]) ).
thf(3906,plain,
! [SV818: int,SV524: int,SV102: int] :
( ( ( plus_plus_int @ ( plus_plus_int @ SV102 @ SV524 ) @ SV818 )
= ( plus_plus_int @ SV102 @ ( plus_plus_int @ SV524 @ SV818 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3279]) ).
thf(3907,plain,
! [SV819: int,SV525: int,SV103: int] :
( ( ( plus_plus_int @ ( plus_plus_int @ SV103 @ SV525 ) @ SV819 )
= ( plus_plus_int @ ( plus_plus_int @ SV103 @ SV819 ) @ SV525 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3280]) ).
thf(3908,plain,
! [SV820: int,SV526: int,SV104: int] :
( ( ! [SY2326: int] :
( ( plus_plus_int @ ( plus_plus_int @ SV104 @ SV526 ) @ ( plus_plus_int @ SV820 @ SY2326 ) )
= ( plus_plus_int @ ( plus_plus_int @ SV104 @ SV820 ) @ ( plus_plus_int @ SV526 @ SY2326 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3281]) ).
thf(3909,plain,
! [SV821: nat,SV111: int] :
( ( ( ~ ( ord_less_eq_int @ ( power_power_int @ SV111 @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV821 ) ) @ zero_zero_int ) )
= $true )
| ( ( SV111 = zero_zero_int )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3285]) ).
thf(3910,plain,
! [SV822: int,SV530: int,SV116: int] :
( ( ( times_times_int @ SV116 @ ( plus_plus_int @ SV530 @ SV822 ) )
= ( plus_plus_int @ ( times_times_int @ SV116 @ SV530 ) @ ( times_times_int @ SV116 @ SV822 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3286]) ).
thf(3911,plain,
! [SV823: int,SV531: int,SV117: int] :
( ( ( times_times_int @ ( plus_plus_int @ SV117 @ SV531 ) @ SV823 )
= ( plus_plus_int @ ( times_times_int @ SV117 @ SV823 ) @ ( times_times_int @ SV531 @ SV823 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3287]) ).
thf(3912,plain,
! [SV824: int,SV532: int,SV118: int] :
( ( ( plus_plus_int @ ( times_times_int @ SV118 @ SV532 ) @ ( times_times_int @ SV824 @ SV532 ) )
= ( times_times_int @ ( plus_plus_int @ SV118 @ SV824 ) @ SV532 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3288]) ).
thf(3913,plain,
! [SV825: nat,SV533: int,SV121: int] :
( ( ( power_power_int @ ( times_times_int @ SV121 @ SV533 ) @ SV825 )
= ( times_times_int @ ( power_power_int @ SV121 @ SV825 ) @ ( power_power_int @ SV533 @ SV825 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3289]) ).
thf(3914,plain,
! [SV826: nat,SV534: nat,SV122: int] :
( ( ( times_times_int @ ( power_power_int @ SV122 @ SV534 ) @ ( power_power_int @ SV122 @ SV826 ) )
= ( power_power_int @ SV122 @ ( plus_plus_nat @ SV534 @ SV826 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3290]) ).
thf(3915,plain,
! [SV827: int,SV536: int,SV125: int] :
( ( ! [SY2327: int,SY2328: int] :
( ( SY2328 = zero_zero_int )
| ( SV125 = SV536 )
| ( SV827 != SY2327 )
| ( ( plus_plus_int @ SV827 @ ( times_times_int @ SY2328 @ SV125 ) )
!= ( plus_plus_int @ SY2327 @ ( times_times_int @ SY2328 @ SV536 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3292]) ).
thf(3916,plain,
! [SV129: int,SV539: int] :
( ( ( ~ ( ord_less_int @ zero_zero_int @ SV539 ) )
= $true )
| ( ( ~ ( ord_less_int @ zero_zero_int @ ( times_times_int @ SV539 @ SV129 ) )
| ( ord_less_int @ zero_zero_int @ SV129 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3295]) ).
thf(3917,plain,
! [SV130: int,SV540: int] :
( ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV540 ) )
= $true )
| ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV130 )
| ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ SV540 @ SV130 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3296]) ).
thf(3918,plain,
! [SV131: int,SV541: int] :
( ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV541 ) )
= $true )
| ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV131 )
| ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ SV541 @ SV131 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3297]) ).
thf(3919,plain,
! [SV132: nat,SV542: int] :
( ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV542 ) )
= $true )
| ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ SV542 @ SV132 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3298]) ).
thf(3920,plain,
! [SV828: int,SV543: int,SV133: int] :
( ( ~ ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ SV133 @ SV543 ) @ SV828 ) )
| ~ ( ord_less_int @ SV828 @ SV133 )
| ~ ( ord_less_int @ zero_zero_int @ SV133 )
| ( ord_less_eq_int @ zero_zero_int @ SV543 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3299]) ).
thf(3921,plain,
! [SV829: int,SV544: int,SV134: int] :
( ( ~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ SV134 @ SV544 ) @ SV829 ) @ zero_zero_int )
| ~ ( ord_less_eq_int @ zero_zero_int @ SV829 )
| ~ ( ord_less_int @ zero_zero_int @ SV134 )
| ( ord_less_eq_int @ SV544 @ zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3300]) ).
thf(3922,plain,
! [SV830: int,SV545: int,SV135: int] :
( ( ! [SY2329: int,SY2330: int] :
( ~ ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SV135 @ SV545 ) @ SV830 ) @ ( plus_plus_int @ ( times_times_int @ SV135 @ SY2329 ) @ SY2330 ) )
| ~ ( ord_less_eq_int @ zero_zero_int @ SV830 )
| ~ ( ord_less_int @ SV830 @ SV135 )
| ~ ( ord_less_int @ SY2330 @ SV135 )
| ( ord_less_eq_int @ SV545 @ SY2329 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3301]) ).
thf(3923,plain,
! [SV831: int,SV546: int,SV136: int] :
( ( ! [SY2331: int,SY2332: int,SY2333: int] :
( ( ( plus_plus_int @ ( times_times_int @ SV136 @ SV546 ) @ SV831 )
!= ( plus_plus_int @ ( times_times_int @ SY2331 @ SY2332 ) @ SY2333 ) )
| ~ ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ SY2331 @ SY2332 ) @ SY2333 ) )
| ~ ( ord_less_int @ SY2333 @ SY2331 )
| ~ ( ord_less_eq_int @ zero_zero_int @ SV831 )
| ~ ( ord_less_int @ zero_zero_int @ SY2331 )
| ~ ( ord_less_eq_int @ SY2331 @ SV136 )
| ( ord_less_eq_int @ SV546 @ SY2332 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3302]) ).
thf(3924,plain,
! [SV832: int,SV547: int,SV137: int] :
( ( ! [SY2334: int,SY2335: int] :
( ~ ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SV137 @ SV547 ) @ SV832 ) @ ( plus_plus_int @ ( times_times_int @ SV137 @ SY2334 ) @ SY2335 ) )
| ~ ( ord_less_eq_int @ SY2335 @ zero_zero_int )
| ~ ( ord_less_int @ SV137 @ SY2335 )
| ~ ( ord_less_int @ SV137 @ SV832 )
| ( ord_less_eq_int @ SY2334 @ SV547 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3303]) ).
thf(3925,plain,
! [SV833: int,SV548: int,SV138: int] :
( ( ! [SY2336: int,SY2337: int,SY2338: int] :
( ( ( plus_plus_int @ ( times_times_int @ SV138 @ SV548 ) @ SV833 )
!= ( plus_plus_int @ ( times_times_int @ SY2336 @ SY2337 ) @ SY2338 ) )
| ~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ SY2336 @ SY2337 ) @ SY2338 ) @ zero_zero_int )
| ~ ( ord_less_int @ SV833 @ SV138 )
| ~ ( ord_less_eq_int @ zero_zero_int @ SY2338 )
| ~ ( ord_less_int @ zero_zero_int @ SY2336 )
| ~ ( ord_less_eq_int @ SY2336 @ SV138 )
| ( ord_less_eq_int @ SY2337 @ SV548 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3304]) ).
thf(3926,plain,
! [SV143: int,SV834: int,SV549: int] :
( ( ( zcong @ SV549 @ zero_zero_int @ SV834 )
| ~ ( zcong @ ( power_power_int @ SV143 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SV549 @ SV834 )
| ~ ( dvd_dvd_int @ SV834 @ SV143 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3305]) ).
thf(3927,plain,
! [SV550: int,SV146: int] :
( ( ( ~ ( ord_less_eq_int @ SV146 @ SV550 ) )
= $true )
| ( ( ( SV146 = SV550 )
| ( ord_less_int @ SV146 @ SV550 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3308]) ).
thf(3928,plain,
! [SV147: int,SV835: int,SV551: int] :
( ( ~ ( ord_less_int @ SV551 @ SV835 )
| ~ ( ord_less_int @ SV147 @ SV835 )
| ( ord_less_eq_int @ SV551 @ SV147 )
| ( ord_less_eq_int @ SV147 @ SV551 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3309]) ).
thf(3929,plain,
! [SV553: int,SV149: int,SV836: int] :
( ( ! [SY2339: int,SY2340: int] :
( ~ ( zcong @ SV836 @ SY2339 @ SY2340 )
| ~ ( zcong @ SV149 @ SV553 @ SY2340 )
| ( zcong @ ( plus_plus_int @ SV836 @ SV149 ) @ ( plus_plus_int @ SY2339 @ SV553 ) @ SY2340 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3311]) ).
thf(3930,plain,
! [SV150: int,SV554: int,SV837: int] :
( ( ~ ( ord_less_int @ zero_zero_int @ SV837 )
| ~ ( ord_less_int @ SV837 @ SV554 )
| ~ ( ord_less_int @ zero_zero_int @ SV150 )
| ~ ( ord_less_int @ SV150 @ SV837 )
| ~ ( zcong @ SV837 @ SV150 @ SV554 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3312]) ).
thf(3931,plain,
! [SV151: int,SV555: int] :
( ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV555 ) )
= $true )
| ( ( ~ ( ord_less_int @ SV555 @ SV151 )
| ~ ( zcong @ SV555 @ zero_zero_int @ SV151 )
| ( SV555 = zero_zero_int ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3313]) ).
thf(3932,plain,
! [SV152: int,SV556: int,SV838: int] :
( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV838 )
| ~ ( ord_less_int @ SV838 @ SV556 )
| ~ ( ord_less_eq_int @ zero_zero_int @ SV152 )
| ~ ( ord_less_int @ SV152 @ SV556 )
| ~ ( zcong @ SV838 @ SV152 @ SV556 )
| ( SV838 = SV152 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3314]) ).
thf(3933,plain,
! [SV153: nat,SV839: nat,SV557: int] :
( ( ! [SY2341: int] :
( ~ ( zcong @ ( power_power_int @ SV557 @ SV839 ) @ one_one_int @ SY2341 )
| ( zcong @ ( power_power_int @ SV557 @ ( times_times_nat @ SV839 @ SV153 ) ) @ one_one_int @ SY2341 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3315]) ).
thf(3934,plain,
! [SV840: int,SV559: int,SV156: int] :
( ( ( ( minus_minus_int @ SV156 @ SV559 )
!= SV840 )
| ( SV156
= ( plus_plus_int @ SV840 @ SV559 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3317]) ).
thf(3935,plain,
! [SV841: int,SV562: int,SV160: int] :
( ( ! [SY2342: int,SY2343: int,SY2344: int,SY2345: int] :
( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ SV160 @ ( times_times_int @ SV562 @ SV841 ) ) @ SY2342 ) @ ( times_times_int @ ( minus_minus_int @ SY2343 @ ( times_times_int @ SV562 @ SY2344 ) ) @ SY2345 ) )
= ( minus_minus_int @ ( plus_plus_int @ ( times_times_int @ SV160 @ SY2342 ) @ ( times_times_int @ SY2343 @ SY2345 ) ) @ ( times_times_int @ SV562 @ ( plus_plus_int @ ( times_times_int @ SV841 @ SY2342 ) @ ( times_times_int @ SY2344 @ SY2345 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3320]) ).
thf(3936,plain,
! [SV842: int,SV563: int,SV161: int] :
( ( ( plus_plus_int @ ( number_number_of_int @ SV161 ) @ ( minus_minus_int @ ( number_number_of_int @ SV563 ) @ SV842 ) )
= ( minus_minus_int @ ( number_number_of_int @ ( plus_plus_int @ SV161 @ SV563 ) ) @ SV842 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3321]) ).
thf(3937,plain,
! [SV162: int,SV564: int] :
( ( ( ~ ( ord_less_int @ zero_zero_int @ SV564 ) )
= $true )
| ( ( ~ ( ord_less_int @ SV564 @ SV162 )
| ( SV564
= ( minus_minus_int @ SV162 @ one_one_int ) )
| ( ord_less_int @ SV564 @ ( minus_minus_int @ SV162 @ one_one_int ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3322]) ).
thf(3938,plain,
! [SV168: int,SV843: int,SV566: int] :
( ( ! [SY2346: int] :
( ~ ( zcong @ SV566 @ SV843 @ SY2346 )
| ( zcong @ ( plus_plus_int @ SV566 @ SV168 ) @ ( plus_plus_int @ SV843 @ SV168 ) @ SY2346 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3324]) ).
thf(3939,plain,
! [SV169: nat,SV844: int,SV567: int] :
( ( ! [SY2347: int] :
( ~ ( zcong @ SV567 @ SV844 @ SY2347 )
| ( zcong @ ( power_power_int @ SV567 @ SV169 ) @ ( power_power_int @ SV844 @ SV169 ) @ SY2347 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3325]) ).
thf(3940,plain,
! [SV170: int,SV568: int,SV845: int] :
( ( ~ ( ord_less_int @ zero_zero_int @ SV845 )
| ~ ( ord_less_int @ zero_zero_int @ SV568 )
| ~ ( ord_less_int @ zero_zero_int @ SV170 )
| ~ ( zcong @ SV845 @ SV568 @ SV170 )
| ~ ( ord_less_int @ SV845 @ SV170 )
| ~ ( ord_less_int @ SV568 @ SV170 )
| ( SV845 = SV568 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3326]) ).
thf(3941,plain,
! [SV171: int,SV569: int] :
( ( ( ~ ( ord_less_int @ zero_zero_int @ SV569 ) )
= $true )
| ( ( ~ ( ord_less_int @ SV569 @ SV171 )
| ~ ( zcong @ SV569 @ zero_zero_int @ SV171 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3327]) ).
thf(3942,plain,
! [SV570: int,SV172: int] :
( ( ( ~ ( dvd_dvd_int @ SV172 @ SV570 ) )
= $true )
| ( ( ( ord_less_eq_int @ SV570 @ zero_zero_int )
| ( ord_less_eq_int @ SV172 @ SV570 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3328]) ).
thf(3943,plain,
! [SV173: int,SV571: int] :
( ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV571 ) )
= $true )
| ( ( ~ ( ord_less_int @ SV571 @ SV173 )
| ~ ( zcong @ SV571 @ zero_zero_int @ SV173 )
| ( SV571 = zero_zero_int ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3329]) ).
thf(3944,plain,
! [SV846: int,SV572: int,SV175: int] :
( ( ! [SY2348: int] :
( ( minus_minus_int @ ( plus_plus_int @ SV175 @ SV572 ) @ ( plus_plus_int @ SV846 @ SY2348 ) )
= ( plus_plus_int @ ( minus_minus_int @ SV175 @ SV846 ) @ ( minus_minus_int @ SV572 @ SY2348 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3331]) ).
thf(3945,plain,
! [SV847: int,SV573: int,SV176: int] :
( ( ! [SY2349: int] :
( ( minus_minus_int @ ( times_times_int @ SV176 @ SV573 ) @ ( times_times_int @ SV847 @ SY2349 ) )
= ( plus_plus_int @ ( times_times_int @ SV176 @ ( minus_minus_int @ SV573 @ SY2349 ) ) @ ( times_times_int @ ( minus_minus_int @ SV176 @ SV847 ) @ SY2349 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3332]) ).
thf(3946,plain,
! [SV178: nat,SV574: int] :
( ( ( SV574 = zero_zero_int )
= $true )
| ( ( ( power_power_int @ SV574 @ SV178 )
!= zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3333]) ).
thf(3947,plain,
! [SV848: nat,SV575: int,SV179: int] :
( ( ( power_power_int @ ( times_times_int @ SV179 @ SV575 ) @ SV848 )
= ( times_times_int @ ( power_power_int @ SV179 @ SV848 ) @ ( power_power_int @ SV575 @ SV848 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3334]) ).
thf(3948,plain,
! [SV182: nat,SV849: int,SV577: int] :
( ( ~ ( dvd_dvd_int @ SV577 @ SV849 )
| ( dvd_dvd_int @ ( power_power_int @ SV577 @ SV182 ) @ ( power_power_int @ SV849 @ SV182 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3336]) ).
thf(3949,plain,
! [SV850: nat,SV578: nat,SV183: int] :
( ( ( power_power_int @ SV183 @ ( times_times_nat @ SV578 @ SV850 ) )
= ( power_power_int @ ( power_power_int @ SV183 @ SV578 ) @ SV850 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3337]) ).
thf(3950,plain,
! [SV185: nat,SV851: int,SV579: int] :
( ( ~ ( ord_less_eq_int @ SV579 @ SV851 )
| ~ ( ord_less_eq_int @ zero_zero_int @ SV579 )
| ( ord_less_eq_int @ ( power_power_int @ SV579 @ SV185 ) @ ( power_power_int @ SV851 @ SV185 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3338]) ).
thf(3951,plain,
! [SV186: nat,SV580: int] :
( ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV580 ) )
= $true )
| ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ SV580 @ SV186 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3339]) ).
thf(3952,plain,
! [SV187: nat,SV581: int] :
( ( ( ~ ( ord_less_int @ zero_zero_int @ SV581 ) )
= $true )
| ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ SV581 @ SV187 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3340]) ).
thf(3953,plain,
! [SV188: nat,SV582: int] :
( ( ( ~ ( ord_less_eq_int @ one_one_int @ SV582 ) )
= $true )
| ( ( ord_less_eq_int @ one_one_int @ ( power_power_int @ SV582 @ SV188 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3341]) ).
thf(3954,plain,
! [SV852: nat,SV583: nat,SV190: int] :
( ( ( power_power_int @ SV190 @ ( plus_plus_nat @ SV583 @ SV852 ) )
= ( times_times_int @ ( power_power_int @ SV190 @ SV583 ) @ ( power_power_int @ SV190 @ SV852 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3342]) ).
thf(3955,plain,
! [SV191: nat,SV853: nat,SV584: int] :
( ( ! [SY2350: int] :
( ~ ( dvd_dvd_int @ ( power_power_int @ SV584 @ SV853 ) @ SY2350 )
| ~ ( ord_less_eq_nat @ SV191 @ SV853 )
| ( dvd_dvd_int @ ( power_power_int @ SV584 @ SV191 ) @ SY2350 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3343]) ).
thf(3956,plain,
! [SV585: nat,SV192: nat,SV854: int] :
( ( ! [SY2351: int] :
( ~ ( dvd_dvd_int @ SV854 @ SY2351 )
| ~ ( ord_less_eq_nat @ SV192 @ SV585 )
| ( dvd_dvd_int @ ( power_power_int @ SV854 @ SV192 ) @ ( power_power_int @ SY2351 @ SV585 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3344]) ).
thf(3957,plain,
! [SV193: int,SV855: nat,SV586: nat] :
( ( ~ ( ord_less_eq_nat @ SV586 @ SV855 )
| ( dvd_dvd_int @ ( power_power_int @ SV193 @ SV586 ) @ ( power_power_int @ SV193 @ SV855 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3345]) ).
thf(3958,plain,
! [SV856: int,SV587: nat,SV194: int] :
( ( ~ ( ord_less_int @ ( power_power_int @ SV194 @ SV587 ) @ ( power_power_int @ SV856 @ SV587 ) )
| ~ ( ord_less_eq_int @ zero_zero_int @ SV856 )
| ( ord_less_int @ SV194 @ SV856 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3346]) ).
thf(3959,plain,
! [SV195: nat,SV588: int] :
( ( ( ~ ( ord_less_int @ one_one_int @ SV588 ) )
= $true )
| ( ( ord_less_int @ ( power_power_int @ SV588 @ SV195 ) @ ( times_times_int @ SV588 @ ( power_power_int @ SV588 @ SV195 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3347]) ).
thf(3960,plain,
! [SV196: nat,SV589: int] :
( ( ( ~ ( ord_less_int @ one_one_int @ SV589 ) )
= $true )
| ( ( ord_less_int @ one_one_int @ ( times_times_int @ SV589 @ ( power_power_int @ SV589 @ SV196 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3348]) ).
thf(3961,plain,
! [SV197: int,SV857: nat,SV590: nat] :
( ( ~ ( ord_less_nat @ SV590 @ SV857 )
| ~ ( ord_less_int @ one_one_int @ SV197 )
| ( ord_less_int @ ( power_power_int @ SV197 @ SV590 ) @ ( power_power_int @ SV197 @ SV857 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3349]) ).
thf(3962,plain,
! [SV591: nat,SV198: nat,SV858: int] :
( ( ~ ( ord_less_int @ one_one_int @ SV858 )
| ~ ( ord_less_int @ ( power_power_int @ SV858 @ SV198 ) @ ( power_power_int @ SV858 @ SV591 ) )
| ( ord_less_nat @ SV198 @ SV591 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3350]) ).
thf(3963,plain,
! [SV199: int,SV859: nat,SV592: nat] :
( ( ~ ( ord_less_eq_nat @ SV592 @ SV859 )
| ~ ( ord_less_eq_int @ one_one_int @ SV199 )
| ( ord_less_eq_int @ ( power_power_int @ SV199 @ SV592 ) @ ( power_power_int @ SV199 @ SV859 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3351]) ).
thf(3964,plain,
! [SV200: nat,SV593: int] :
( ( ( ~ ( ord_less_int @ zero_zero_int @ SV593 ) )
= $true )
| ( ( ~ ( ord_less_int @ SV593 @ one_one_int )
| ( ord_less_int @ ( times_times_int @ SV593 @ ( power_power_int @ SV593 @ SV200 ) ) @ ( power_power_int @ SV593 @ SV200 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3352]) ).
thf(3965,plain,
! [SV201: int,SV860: nat,SV594: nat] :
( ( ~ ( ord_less_nat @ SV594 @ SV860 )
| ~ ( ord_less_int @ zero_zero_int @ SV201 )
| ~ ( ord_less_int @ SV201 @ one_one_int )
| ( ord_less_int @ ( power_power_int @ SV201 @ SV860 ) @ ( power_power_int @ SV201 @ SV594 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3353]) ).
thf(3966,plain,
! [SV595: real,SV202: real] :
( ( ord_less_real @ ( plus_plus_real @ ( power_power_real @ SV202 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SV595 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_real )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3354]) ).
thf(3967,plain,
! [SV597: int,SV209: int] :
( ( ( ord_less_eq_int @ SV209 @ SV597 )
= $true )
| ( ( ord_less_eq_int @ SV597 @ SV209 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3357]) ).
thf(3968,plain,
! [SV861: int,SV599: int,SV211: int] :
( ( ( times_times_int @ ( times_times_int @ SV211 @ SV599 ) @ SV861 )
= ( times_times_int @ SV211 @ ( times_times_int @ SV599 @ SV861 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3359]) ).
thf(3969,plain,
! [SV212: int,SV862: int,SV600: int] :
( ( ~ ( ord_less_eq_int @ SV600 @ SV862 )
| ~ ( ord_less_eq_int @ SV862 @ SV212 )
| ( ord_less_eq_int @ SV600 @ SV212 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3360]) ).
thf(3970,plain,
! [SV601: int,SV213: int] :
( ( ( ~ ( ord_less_eq_int @ SV213 @ SV601 ) )
= $true )
| ( ( ~ ( ord_less_eq_int @ SV601 @ SV213 )
| ( SV213 = SV601 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3361]) ).
thf(3971,plain,
! [SV214: int,SV602: int] :
( ( ( ~ ( ord_less_eq_int @ pls @ SV602 ) )
= $true )
| ( ( ~ ( ord_less_eq_int @ pls @ SV214 )
| ( ( times_times_real @ ( number267125858f_real @ SV602 ) @ ( number267125858f_real @ SV214 ) )
= ( number267125858f_real @ ( times_times_int @ SV602 @ SV214 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3362]) ).
thf(3972,plain,
! [SV215: int,SV603: int] :
( ( ( ~ ( ord_less_eq_int @ pls @ SV603 ) )
= $true )
| ( ( ~ ( ord_less_eq_int @ pls @ SV215 )
| ( ( times_times_nat @ ( number_number_of_nat @ SV603 ) @ ( number_number_of_nat @ SV215 ) )
= ( number_number_of_nat @ ( times_times_int @ SV603 @ SV215 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3363]) ).
thf(3973,plain,
! [SV216: int,SV604: int] :
( ( ( ~ ( ord_less_eq_int @ pls @ SV604 ) )
= $true )
| ( ( ~ ( ord_less_eq_int @ pls @ SV216 )
| ( ( times_times_int @ ( number_number_of_int @ SV604 ) @ ( number_number_of_int @ SV216 ) )
= ( number_number_of_int @ ( times_times_int @ SV604 @ SV216 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3364]) ).
thf(3974,plain,
! [SV863: real,SV605: int,SV217: int] :
( ( ( times_times_real @ ( number267125858f_real @ SV217 ) @ ( times_times_real @ ( number267125858f_real @ SV605 ) @ SV863 ) )
= ( times_times_real @ ( number267125858f_real @ ( times_times_int @ SV217 @ SV605 ) ) @ SV863 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3365]) ).
thf(3975,plain,
! [SV864: int,SV606: int,SV218: int] :
( ( ( times_times_int @ ( number_number_of_int @ SV218 ) @ ( times_times_int @ ( number_number_of_int @ SV606 ) @ SV864 ) )
= ( times_times_int @ ( number_number_of_int @ ( times_times_int @ SV218 @ SV606 ) ) @ SV864 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3366]) ).
thf(3976,plain,
! [SV224: int,SV612: int] :
( ( ( ~ ( ord_less_eq_int @ pls @ SV612 ) )
= $true )
| ( ( ~ ( ord_less_eq_int @ pls @ SV224 )
| ( ( plus_plus_real @ ( number267125858f_real @ SV612 ) @ ( number267125858f_real @ SV224 ) )
= ( number267125858f_real @ ( plus_plus_int @ SV612 @ SV224 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3372]) ).
thf(3977,plain,
! [SV865: int,SV613: real,SV225: real] :
( ( ( times_times_real @ ( plus_plus_real @ SV225 @ SV613 ) @ ( number267125858f_real @ SV865 ) )
= ( plus_plus_real @ ( times_times_real @ SV225 @ ( number267125858f_real @ SV865 ) ) @ ( times_times_real @ SV613 @ ( number267125858f_real @ SV865 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3373]) ).
thf(3978,plain,
! [SV866: real,SV614: real,SV226: int] :
( ( ( times_times_real @ ( number267125858f_real @ SV226 ) @ ( plus_plus_real @ SV614 @ SV866 ) )
= ( plus_plus_real @ ( times_times_real @ ( number267125858f_real @ SV226 ) @ SV614 ) @ ( times_times_real @ ( number267125858f_real @ SV226 ) @ SV866 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3374]) ).
thf(3979,plain,
! [SV615: real,SV227: real] :
( ( ( ( power_power_real @ SV227 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= ( power_power_real @ SV615 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $true )
| ( ( ~ ( ord_less_eq_real @ zero_zero_real @ SV227 )
| ~ ( ord_less_eq_real @ zero_zero_real @ SV615 )
| ( SV227 = SV615 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3375]) ).
thf(3980,plain,
! [SV616: nat,SV228: nat] :
( ( ( ( power_power_nat @ SV228 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= ( power_power_nat @ SV616 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV228 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV616 )
| ( SV228 = SV616 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3376]) ).
thf(3981,plain,
! [SV617: real,SV229: real] :
( ( ( ~ ( ord_less_eq_real @ ( power_power_real @ SV229 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SV617 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true )
| ( ( ~ ( ord_less_eq_real @ zero_zero_real @ SV617 )
| ( ord_less_eq_real @ SV229 @ SV617 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3377]) ).
thf(3982,plain,
! [SV618: nat,SV230: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( power_power_nat @ SV230 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_nat @ SV618 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV618 )
| ( ord_less_eq_nat @ SV230 @ SV618 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3378]) ).
thf(3983,plain,
! [SV619: real,SV232: real] :
( ( ( ~ ( ord_less_real @ ( power_power_real @ SV232 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SV619 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true )
| ( ( ~ ( ord_less_eq_real @ zero_zero_real @ SV619 )
| ( ord_less_real @ SV232 @ SV619 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3379]) ).
thf(3984,plain,
! [SV620: nat,SV233: nat] :
( ( ( ~ ( ord_less_nat @ ( power_power_nat @ SV233 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_nat @ SV620 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV620 )
| ( ord_less_nat @ SV233 @ SV620 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3380]) ).
thf(3985,plain,
! [SV622: real,SV235: real] :
( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ SV235 @ SV235 ) @ ( times_times_real @ SV622 @ SV622 ) ) @ zero_zero_real )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3382]) ).
thf(3986,plain,
! [SV867: nat,SV626: nat,SV247: real] :
( ( ( power_power_real @ ( power_power_real @ SV247 @ SV626 ) @ SV867 )
= ( power_power_real @ SV247 @ ( times_times_nat @ SV626 @ SV867 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3386]) ).
thf(3987,plain,
! [SV868: nat,SV627: nat,SV248: nat] :
( ( ( power_power_nat @ ( power_power_nat @ SV248 @ SV627 ) @ SV868 )
= ( power_power_nat @ SV248 @ ( times_times_nat @ SV627 @ SV868 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3387]) ).
thf(3988,plain,
! [SV628: int,SV249: nat,SV869: int] :
( ( ! [SY2352: int] :
( ~ ( zprime @ SY2352 )
| ( dvd_dvd_int @ SY2352 @ SV869 )
| ~ ( dvd_dvd_int @ ( power_power_int @ SY2352 @ SV249 ) @ ( times_times_int @ SV628 @ SV869 ) )
| ( dvd_dvd_int @ ( power_power_int @ SY2352 @ SV249 ) @ SV628 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3388]) ).
thf(3989,plain,
! [SV629: int,SV250: nat,SV870: int] :
( ( ! [SY2353: int] :
( ~ ( zprime @ SY2353 )
| ( dvd_dvd_int @ SY2353 @ SV870 )
| ~ ( dvd_dvd_int @ ( power_power_int @ SY2353 @ SV250 ) @ ( times_times_int @ SV870 @ SV629 ) )
| ( dvd_dvd_int @ ( power_power_int @ SY2353 @ SV250 ) @ SV629 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3389]) ).
thf(3990,plain,
! [SV251: int,SV630: int] :
( ( ( ~ ( twoSqu362149276sum2sq @ SV630 ) )
= $true )
| ( ( ~ ( twoSqu362149276sum2sq @ SV251 )
| ( twoSqu362149276sum2sq @ ( times_times_int @ SV630 @ SV251 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3390]) ).
thf(3991,plain,
! [SV871: real,SV631: real,SV252: real] :
( ( ! [SY2354: real] :
( ( times_times_real @ ( times_times_real @ SV252 @ SV631 ) @ ( times_times_real @ SV871 @ SY2354 ) )
= ( times_times_real @ ( times_times_real @ SV252 @ SV871 ) @ ( times_times_real @ SV631 @ SY2354 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3391]) ).
thf(3992,plain,
! [SV872: nat,SV632: nat,SV253: nat] :
( ( ! [SY2355: nat] :
( ( times_times_nat @ ( times_times_nat @ SV253 @ SV632 ) @ ( times_times_nat @ SV872 @ SY2355 ) )
= ( times_times_nat @ ( times_times_nat @ SV253 @ SV872 ) @ ( times_times_nat @ SV632 @ SY2355 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3392]) ).
thf(3993,plain,
! [SV873: int,SV633: int,SV254: int] :
( ( ! [SY2356: int] :
( ( times_times_int @ ( times_times_int @ SV254 @ SV633 ) @ ( times_times_int @ SV873 @ SY2356 ) )
= ( times_times_int @ ( times_times_int @ SV254 @ SV873 ) @ ( times_times_int @ SV633 @ SY2356 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3393]) ).
thf(3994,plain,
! [SV874: real,SV634: real,SV255: real] :
( ( ! [SY2357: real] :
( ( times_times_real @ ( times_times_real @ SV255 @ SV634 ) @ ( times_times_real @ SV874 @ SY2357 ) )
= ( times_times_real @ SV874 @ ( times_times_real @ ( times_times_real @ SV255 @ SV634 ) @ SY2357 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3394]) ).
thf(3995,plain,
! [SV875: nat,SV635: nat,SV256: nat] :
( ( ! [SY2358: nat] :
( ( times_times_nat @ ( times_times_nat @ SV256 @ SV635 ) @ ( times_times_nat @ SV875 @ SY2358 ) )
= ( times_times_nat @ SV875 @ ( times_times_nat @ ( times_times_nat @ SV256 @ SV635 ) @ SY2358 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3395]) ).
thf(3996,plain,
! [SV876: int,SV636: int,SV257: int] :
( ( ! [SY2359: int] :
( ( times_times_int @ ( times_times_int @ SV257 @ SV636 ) @ ( times_times_int @ SV876 @ SY2359 ) )
= ( times_times_int @ SV876 @ ( times_times_int @ ( times_times_int @ SV257 @ SV636 ) @ SY2359 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3396]) ).
thf(3997,plain,
! [SV877: real,SV637: real,SV258: real] :
( ( ! [SY2360: real] :
( ( times_times_real @ ( times_times_real @ SV258 @ SV637 ) @ ( times_times_real @ SV877 @ SY2360 ) )
= ( times_times_real @ SV258 @ ( times_times_real @ SV637 @ ( times_times_real @ SV877 @ SY2360 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3397]) ).
thf(3998,plain,
! [SV878: nat,SV638: nat,SV259: nat] :
( ( ! [SY2361: nat] :
( ( times_times_nat @ ( times_times_nat @ SV259 @ SV638 ) @ ( times_times_nat @ SV878 @ SY2361 ) )
= ( times_times_nat @ SV259 @ ( times_times_nat @ SV638 @ ( times_times_nat @ SV878 @ SY2361 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3398]) ).
thf(3999,plain,
! [SV879: int,SV639: int,SV260: int] :
( ( ! [SY2362: int] :
( ( times_times_int @ ( times_times_int @ SV260 @ SV639 ) @ ( times_times_int @ SV879 @ SY2362 ) )
= ( times_times_int @ SV260 @ ( times_times_int @ SV639 @ ( times_times_int @ SV879 @ SY2362 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3399]) ).
thf(4000,plain,
! [SV880: real,SV640: real,SV261: real] :
( ( ( times_times_real @ ( times_times_real @ SV261 @ SV640 ) @ SV880 )
= ( times_times_real @ ( times_times_real @ SV261 @ SV880 ) @ SV640 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3400]) ).
thf(4001,plain,
! [SV881: nat,SV641: nat,SV262: nat] :
( ( ( times_times_nat @ ( times_times_nat @ SV262 @ SV641 ) @ SV881 )
= ( times_times_nat @ ( times_times_nat @ SV262 @ SV881 ) @ SV641 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3401]) ).
thf(4002,plain,
! [SV882: int,SV642: int,SV263: int] :
( ( ( times_times_int @ ( times_times_int @ SV263 @ SV642 ) @ SV882 )
= ( times_times_int @ ( times_times_int @ SV263 @ SV882 ) @ SV642 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3402]) ).
thf(4003,plain,
! [SV883: real,SV643: real,SV264: real] :
( ( ( times_times_real @ ( times_times_real @ SV264 @ SV643 ) @ SV883 )
= ( times_times_real @ SV264 @ ( times_times_real @ SV643 @ SV883 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3403]) ).
thf(4004,plain,
! [SV884: nat,SV644: nat,SV265: nat] :
( ( ( times_times_nat @ ( times_times_nat @ SV265 @ SV644 ) @ SV884 )
= ( times_times_nat @ SV265 @ ( times_times_nat @ SV644 @ SV884 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3404]) ).
thf(4005,plain,
! [SV885: int,SV645: int,SV266: int] :
( ( ( times_times_int @ ( times_times_int @ SV266 @ SV645 ) @ SV885 )
= ( times_times_int @ SV266 @ ( times_times_int @ SV645 @ SV885 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3405]) ).
thf(4006,plain,
! [SV886: real,SV646: real,SV267: real] :
( ( ( times_times_real @ SV267 @ ( times_times_real @ SV646 @ SV886 ) )
= ( times_times_real @ ( times_times_real @ SV267 @ SV646 ) @ SV886 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3406]) ).
thf(4007,plain,
! [SV887: nat,SV647: nat,SV268: nat] :
( ( ( times_times_nat @ SV268 @ ( times_times_nat @ SV647 @ SV887 ) )
= ( times_times_nat @ ( times_times_nat @ SV268 @ SV647 ) @ SV887 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3407]) ).
thf(4008,plain,
! [SV888: int,SV648: int,SV269: int] :
( ( ( times_times_int @ SV269 @ ( times_times_int @ SV648 @ SV888 ) )
= ( times_times_int @ ( times_times_int @ SV269 @ SV648 ) @ SV888 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3408]) ).
thf(4009,plain,
! [SV889: real,SV649: real,SV270: real] :
( ( ( times_times_real @ SV270 @ ( times_times_real @ SV649 @ SV889 ) )
= ( times_times_real @ SV649 @ ( times_times_real @ SV270 @ SV889 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3409]) ).
thf(4010,plain,
! [SV890: nat,SV650: nat,SV271: nat] :
( ( ( times_times_nat @ SV271 @ ( times_times_nat @ SV650 @ SV890 ) )
= ( times_times_nat @ SV650 @ ( times_times_nat @ SV271 @ SV890 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3410]) ).
thf(4011,plain,
! [SV891: int,SV651: int,SV272: int] :
( ( ( times_times_int @ SV272 @ ( times_times_int @ SV651 @ SV891 ) )
= ( times_times_int @ SV651 @ ( times_times_int @ SV272 @ SV891 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3411]) ).
thf(4012,plain,
! [SV892: real,SV657: real,SV278: real] :
( ( ( plus_plus_real @ SV278 @ ( plus_plus_real @ SV657 @ SV892 ) )
= ( plus_plus_real @ SV657 @ ( plus_plus_real @ SV278 @ SV892 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3417]) ).
thf(4013,plain,
! [SV893: nat,SV658: nat,SV279: nat] :
( ( ( plus_plus_nat @ SV279 @ ( plus_plus_nat @ SV658 @ SV893 ) )
= ( plus_plus_nat @ SV658 @ ( plus_plus_nat @ SV279 @ SV893 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3418]) ).
thf(4014,plain,
! [SV894: real,SV659: real,SV280: real] :
( ( ( plus_plus_real @ SV280 @ ( plus_plus_real @ SV659 @ SV894 ) )
= ( plus_plus_real @ ( plus_plus_real @ SV280 @ SV659 ) @ SV894 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3419]) ).
thf(4015,plain,
! [SV895: nat,SV660: nat,SV281: nat] :
( ( ( plus_plus_nat @ SV281 @ ( plus_plus_nat @ SV660 @ SV895 ) )
= ( plus_plus_nat @ ( plus_plus_nat @ SV281 @ SV660 ) @ SV895 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3420]) ).
thf(4016,plain,
! [SV896: real,SV661: real,SV282: real] :
( ( ( plus_plus_real @ ( plus_plus_real @ SV282 @ SV661 ) @ SV896 )
= ( plus_plus_real @ SV282 @ ( plus_plus_real @ SV661 @ SV896 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3421]) ).
thf(4017,plain,
! [SV897: nat,SV662: nat,SV283: nat] :
( ( ( plus_plus_nat @ ( plus_plus_nat @ SV283 @ SV662 ) @ SV897 )
= ( plus_plus_nat @ SV283 @ ( plus_plus_nat @ SV662 @ SV897 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3422]) ).
thf(4018,plain,
! [SV898: real,SV663: real,SV284: real] :
( ( ( plus_plus_real @ ( plus_plus_real @ SV284 @ SV663 ) @ SV898 )
= ( plus_plus_real @ ( plus_plus_real @ SV284 @ SV898 ) @ SV663 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3423]) ).
thf(4019,plain,
! [SV899: nat,SV664: nat,SV285: nat] :
( ( ( plus_plus_nat @ ( plus_plus_nat @ SV285 @ SV664 ) @ SV899 )
= ( plus_plus_nat @ ( plus_plus_nat @ SV285 @ SV899 ) @ SV664 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3424]) ).
thf(4020,plain,
! [SV900: real,SV665: real,SV286: real] :
( ( ! [SY2363: real] :
( ( plus_plus_real @ ( plus_plus_real @ SV286 @ SV665 ) @ ( plus_plus_real @ SV900 @ SY2363 ) )
= ( plus_plus_real @ ( plus_plus_real @ SV286 @ SV900 ) @ ( plus_plus_real @ SV665 @ SY2363 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3425]) ).
thf(4021,plain,
! [SV901: nat,SV666: nat,SV287: nat] :
( ( ! [SY2364: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ SV287 @ SV666 ) @ ( plus_plus_nat @ SV901 @ SY2364 ) )
= ( plus_plus_nat @ ( plus_plus_nat @ SV287 @ SV901 ) @ ( plus_plus_nat @ SV666 @ SY2364 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3426]) ).
thf(4022,plain,
! [SV902: nat,SV290: real] :
( ( ( ~ ( ord_less_eq_real @ ( power_power_real @ SV290 @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV902 ) ) @ zero_zero_real ) )
= $true )
| ( ( SV290 = zero_zero_real )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3427]) ).
thf(4023,plain,
! [SV903: real,SV667: real,SV299: real] :
( ( ( times_times_real @ SV299 @ ( plus_plus_real @ SV667 @ SV903 ) )
= ( plus_plus_real @ ( times_times_real @ SV299 @ SV667 ) @ ( times_times_real @ SV299 @ SV903 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3428]) ).
thf(4024,plain,
! [SV904: nat,SV668: nat,SV300: nat] :
( ( ( times_times_nat @ SV300 @ ( plus_plus_nat @ SV668 @ SV904 ) )
= ( plus_plus_nat @ ( times_times_nat @ SV300 @ SV668 ) @ ( times_times_nat @ SV300 @ SV904 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3429]) ).
thf(4025,plain,
! [SV905: real,SV669: real,SV301: real] :
( ( ( times_times_real @ ( plus_plus_real @ SV301 @ SV669 ) @ SV905 )
= ( plus_plus_real @ ( times_times_real @ SV301 @ SV905 ) @ ( times_times_real @ SV669 @ SV905 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3430]) ).
thf(4026,plain,
! [SV906: nat,SV670: nat,SV302: nat] :
( ( ( times_times_nat @ ( plus_plus_nat @ SV302 @ SV670 ) @ SV906 )
= ( plus_plus_nat @ ( times_times_nat @ SV302 @ SV906 ) @ ( times_times_nat @ SV670 @ SV906 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3431]) ).
thf(4027,plain,
! [SV907: real,SV671: real,SV303: real] :
( ( ( plus_plus_real @ ( times_times_real @ SV303 @ SV671 ) @ ( times_times_real @ SV907 @ SV671 ) )
= ( times_times_real @ ( plus_plus_real @ SV303 @ SV907 ) @ SV671 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3432]) ).
thf(4028,plain,
! [SV908: nat,SV672: nat,SV304: nat] :
( ( ( plus_plus_nat @ ( times_times_nat @ SV304 @ SV672 ) @ ( times_times_nat @ SV908 @ SV672 ) )
= ( times_times_nat @ ( plus_plus_nat @ SV304 @ SV908 ) @ SV672 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3433]) ).
thf(4029,plain,
! [SV909: nat,SV673: real,SV309: real] :
( ( ( power_power_real @ ( times_times_real @ SV309 @ SV673 ) @ SV909 )
= ( times_times_real @ ( power_power_real @ SV309 @ SV909 ) @ ( power_power_real @ SV673 @ SV909 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3434]) ).
thf(4030,plain,
! [SV910: nat,SV674: nat,SV310: nat] :
( ( ( power_power_nat @ ( times_times_nat @ SV310 @ SV674 ) @ SV910 )
= ( times_times_nat @ ( power_power_nat @ SV310 @ SV910 ) @ ( power_power_nat @ SV674 @ SV910 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3435]) ).
thf(4031,plain,
! [SV911: nat,SV675: nat,SV311: real] :
( ( ( times_times_real @ ( power_power_real @ SV311 @ SV675 ) @ ( power_power_real @ SV311 @ SV911 ) )
= ( power_power_real @ SV311 @ ( plus_plus_nat @ SV675 @ SV911 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3436]) ).
thf(4032,plain,
! [SV912: nat,SV676: nat,SV312: nat] :
( ( ( times_times_nat @ ( power_power_nat @ SV312 @ SV676 ) @ ( power_power_nat @ SV312 @ SV912 ) )
= ( power_power_nat @ SV312 @ ( plus_plus_nat @ SV676 @ SV912 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3437]) ).
thf(4033,plain,
! [SV913: real,SV678: real,SV316: real] :
( ( ! [SY2365: real,SY2366: real] :
( ( SY2366 = zero_zero_real )
| ( SV316 = SV678 )
| ( SV913 != SY2365 )
| ( ( plus_plus_real @ SV913 @ ( times_times_real @ SY2366 @ SV316 ) )
!= ( plus_plus_real @ SY2365 @ ( times_times_real @ SY2366 @ SV678 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3439]) ).
thf(4034,plain,
! [SV914: nat,SV679: nat,SV317: nat] :
( ( ! [SY2367: nat,SY2368: nat] :
( ( SY2368 = zero_zero_nat )
| ( SV317 = SV679 )
| ( SV914 != SY2367 )
| ( ( plus_plus_nat @ SV914 @ ( times_times_nat @ SY2368 @ SV317 ) )
!= ( plus_plus_nat @ SY2367 @ ( times_times_nat @ SY2368 @ SV679 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3440]) ).
thf(4035,plain,
! [SV324: int] :
( ( ( zprime @ SV324 )
= $false )
| ( ( ( SV324
= ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
| ( SV324
= ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) )
| ( ord_less_eq_int @ ( number_number_of_int @ ( bit1 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SV324 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3445]) ).
thf(4036,plain,
! [SV915: int,SV325: int] :
( ( ( ( times_times_int @ SV325 @ SV915 )
!= one_one_int )
= $true )
| ( ( ( SV325 = one_one_int )
| ( SV325
= ( number_number_of_int @ min ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3446]) ).
thf(4037,plain,
! [SV327: int,SV916: int,SV685: int] :
( ( ! [SY2369: int] :
( ~ ( zcong @ SV685 @ SV916 @ SY2369 )
| ~ ( zcong @ SV916 @ SV327 @ SY2369 )
| ( zcong @ SV685 @ SV327 @ SY2369 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3448]) ).
thf(4038,plain,
! [SV686: real,SV328: real] :
( ( ( ~ ( ord_less_eq_real @ SV328 @ SV686 ) )
= $true )
| ( ( ( SV328 = SV686 )
| ( ord_less_real @ SV328 @ SV686 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3449]) ).
thf(4039,plain,
! [SV687: nat,SV329: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV329 @ SV687 ) )
= $true )
| ( ( ( SV329 = SV687 )
| ( ord_less_nat @ SV329 @ SV687 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3450]) ).
thf(4040,plain,
! [SV917: int,SV688: int,SV330: int] :
( ( zcong @ ( times_times_int @ SV330 @ SV688 ) @ ( times_times_int @ SV917 @ SV688 ) @ SV688 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3451]) ).
thf(4041,plain,
! [SV331: int,SV918: int,SV689: int] :
( ( ! [SY2370: int] :
( ~ ( zcong @ SV689 @ SV918 @ SY2370 )
| ( zcong @ ( times_times_int @ SV689 @ SV331 ) @ ( times_times_int @ SV918 @ SV331 ) @ SY2370 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3452]) ).
thf(4042,plain,
! [SV332: int,SV919: int,SV690: int] :
( ( ! [SY2371: int] :
( ~ ( zcong @ SV690 @ SV919 @ SY2371 )
| ( zcong @ ( times_times_int @ SV332 @ SV690 ) @ ( times_times_int @ SV332 @ SV919 ) @ SY2371 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3453]) ).
thf(4043,plain,
! [SV691: int,SV333: int,SV920: int] :
( ( ! [SY2372: int,SY2373: int] :
( ~ ( zcong @ SV920 @ SY2372 @ SY2373 )
| ~ ( zcong @ SV333 @ SV691 @ SY2373 )
| ( zcong @ ( times_times_int @ SV920 @ SV333 ) @ ( times_times_int @ SY2372 @ SV691 ) @ SY2373 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3454]) ).
thf(4044,plain,
! [SV337: int,SV692: int,SV921: int] :
( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV921 )
| ~ ( zprime @ SV692 )
| ~ ( dvd_dvd_int @ SV692 @ ( times_times_int @ SV921 @ SV337 ) )
| ( dvd_dvd_int @ SV692 @ SV921 )
| ( dvd_dvd_int @ SV692 @ SV337 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3455]) ).
thf(4045,plain,
! [SV693: nat,SV338: nat,SV922: int] :
( ( ~ ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV922 )
| ~ ( zcong @ ( power_power_int @ ( number_number_of_int @ min ) @ SV338 ) @ ( power_power_int @ ( number_number_of_int @ min ) @ SV693 ) @ SV922 )
| ( ( power_power_int @ ( number_number_of_int @ min ) @ SV338 )
= ( power_power_int @ ( number_number_of_int @ min ) @ SV693 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3456]) ).
thf(4046,plain,
! [SV339: int,SV694: int] :
( ( ( ~ ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV694 ) )
= $true )
| ( ( ~ ( zcong @ SV339 @ ( number_number_of_int @ min ) @ SV694 )
| ~ ( zcong @ SV339 @ one_one_int @ SV694 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3457]) ).
thf(4047,plain,
! [SV695: int,SV340: int,SV923: int] :
( ( ! [SY2374: int,SY2375: int] :
( ~ ( zcong @ SV923 @ SY2374 @ SY2375 )
| ~ ( zcong @ SV340 @ SV695 @ SY2375 )
| ( zcong @ ( minus_minus_int @ SV923 @ SV340 ) @ ( minus_minus_int @ SY2374 @ SV695 ) @ SY2375 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3458]) ).
thf(4048,plain,
! [SV924: int,SV696: int,SV341: int] :
( ( ~ ( dvd_dvd_int @ SV341 @ ( minus_minus_int @ SV696 @ SV924 ) )
| ~ ( dvd_dvd_int @ SV341 @ SV924 )
| ( dvd_dvd_int @ SV341 @ SV696 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3459]) ).
thf(4049,plain,
! [SV925: int,SV697: int,SV342: int] :
( ( ( times_times_int @ SV342 @ ( minus_minus_int @ SV697 @ SV925 ) )
= ( minus_minus_int @ ( times_times_int @ SV342 @ SV697 ) @ ( times_times_int @ SV342 @ SV925 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3460]) ).
thf(4050,plain,
! [SV926: int,SV698: int,SV343: int] :
( ( ( times_times_int @ ( minus_minus_int @ SV343 @ SV698 ) @ SV926 )
= ( minus_minus_int @ ( times_times_int @ SV343 @ SV926 ) @ ( times_times_int @ SV698 @ SV926 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3461]) ).
thf(4051,plain,
! [SV927: real,SV701: real,SV346: int] :
( ( ( times_times_real @ ( number267125858f_real @ SV346 ) @ ( minus_minus_real @ SV701 @ SV927 ) )
= ( minus_minus_real @ ( times_times_real @ ( number267125858f_real @ SV346 ) @ SV701 ) @ ( times_times_real @ ( number267125858f_real @ SV346 ) @ SV927 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3464]) ).
thf(4052,plain,
! [SV928: int,SV702: int,SV347: int] :
( ( ( times_times_int @ ( number_number_of_int @ SV347 ) @ ( minus_minus_int @ SV702 @ SV928 ) )
= ( minus_minus_int @ ( times_times_int @ ( number_number_of_int @ SV347 ) @ SV702 ) @ ( times_times_int @ ( number_number_of_int @ SV347 ) @ SV928 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3465]) ).
thf(4053,plain,
! [SV929: int,SV703: real,SV348: real] :
( ( ( times_times_real @ ( minus_minus_real @ SV348 @ SV703 ) @ ( number267125858f_real @ SV929 ) )
= ( minus_minus_real @ ( times_times_real @ SV348 @ ( number267125858f_real @ SV929 ) ) @ ( times_times_real @ SV703 @ ( number267125858f_real @ SV929 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3466]) ).
thf(4054,plain,
! [SV930: int,SV704: int,SV349: int] :
( ( ( times_times_int @ ( minus_minus_int @ SV349 @ SV704 ) @ ( number_number_of_int @ SV930 ) )
= ( minus_minus_int @ ( times_times_int @ SV349 @ ( number_number_of_int @ SV930 ) ) @ ( times_times_int @ SV704 @ ( number_number_of_int @ SV930 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3467]) ).
thf(4055,plain,
! [SV931: real,SV705: int,SV350: int] :
( ( ( plus_plus_real @ ( number267125858f_real @ SV350 ) @ ( minus_minus_real @ ( number267125858f_real @ SV705 ) @ SV931 ) )
= ( minus_minus_real @ ( number267125858f_real @ ( plus_plus_int @ SV350 @ SV705 ) ) @ SV931 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3468]) ).
thf(4056,plain,
! [SV351: int,SV706: int,SV932: int] :
( ( ! [SY2376: int,SY2377: int] :
( ~ ( zcong @ SV932 @ SY2376 @ SY2377 )
| ( SY2376 != SV706 )
| ~ ( zcong @ SV706 @ SV351 @ SY2377 )
| ( zcong @ SV932 @ SV351 @ SY2377 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3469]) ).
thf(4057,plain,
! [SV352: int,SV707: int] :
( ( ( ~ ( zprime @ SV707 ) )
= $true )
| ( ( ~ ( ord_less_int @ zero_zero_int @ SV352 )
| ~ ( ord_less_int @ SV352 @ SV707 )
| ~ ( zcong @ ( times_times_int @ SV352 @ SV352 ) @ one_one_int @ SV707 )
| ( SV352 = one_one_int )
| ( SV352
= ( minus_minus_int @ SV707 @ one_one_int ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3470]) ).
thf(4058,plain,
! [SV353: int,SV708: int] :
( ( ( ~ ( zprime @ SV708 ) )
= $true )
| ( ( ~ ( ord_less_int @ zero_zero_int @ SV353 )
| ~ ( zcong @ ( times_times_int @ SV353 @ SV353 ) @ one_one_int @ SV708 )
| ( zcong @ SV353 @ one_one_int @ SV708 )
| ( zcong @ SV353 @ ( minus_minus_int @ SV708 @ one_one_int ) @ SV708 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3471]) ).
thf(4059,plain,
! [SV713: int,SV358: int,SV933: int] :
( ( ~ ( zprime @ SV933 )
| ~ ( dvd_dvd_int @ SV933 @ ( times_times_int @ SV358 @ SV713 ) )
| ( dvd_dvd_int @ SV933 @ SV358 )
| ( dvd_dvd_int @ SV933 @ SV713 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3476]) ).
thf(4060,plain,
! [SV714: int,SV359: int,SV934: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ SV934 )
| ~ ( dvd_dvd_int @ SV359 @ SV714 )
| ( dvd_dvd_int @ SV359 @ ( power_power_int @ SV714 @ SV934 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3477]) ).
thf(4061,plain,
! [SV360: int,SV715: int,SV935: int] :
( ( ~ ( zprime @ SV935 )
| ( zcong @ SV715 @ zero_zero_int @ SV935 )
| ( zcong @ SV360 @ zero_zero_int @ SV935 )
| ~ ( zcong @ ( times_times_int @ SV715 @ SV360 ) @ zero_zero_int @ SV935 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3478]) ).
thf(4062,plain,
! [SV361: int,SV716: int,SV936: int] :
( ( ~ ( zprime @ SV936 )
| ~ ( ord_less_int @ zero_zero_int @ SV716 )
| ( zcong @ SV716 @ zero_zero_int @ SV936 )
| ( zcong @ SV361 @ zero_zero_int @ SV936 )
| ~ ( zcong @ ( times_times_int @ SV716 @ SV361 ) @ zero_zero_int @ SV936 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3479]) ).
thf(4063,plain,
! [SV362: int,SV717: int,SV937: int] :
( ( ~ ( zprime @ SV937 )
| ~ ( ord_less_int @ zero_zero_int @ SV717 )
| ~ ( zcong @ ( times_times_int @ SV717 @ SV362 ) @ zero_zero_int @ SV937 )
| ( zcong @ SV717 @ zero_zero_int @ SV937 )
| ( zcong @ SV362 @ zero_zero_int @ SV937 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3480]) ).
thf(4064,plain,
! [SV718: nat,SV363: int,SV938: int] :
( ( ~ ( zprime @ SV938 )
| ~ ( dvd_dvd_int @ SV938 @ ( power_power_int @ SV363 @ SV718 ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV718 )
| ( dvd_dvd_int @ SV938 @ SV363 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3481]) ).
thf(4065,plain,
! [SV364: int] :
( ( ( zprime @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SV364 ) @ one_one_int ) )
= $false )
| ( ( ( legendre @ ( number_number_of_int @ min ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SV364 ) @ one_one_int ) )
= one_one_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3482]) ).
thf(4066,plain,
! [SV365: int] :
( ( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV365 )
= $false )
| ( ( ~ ( zcong @ one_one_int @ ( number_number_of_int @ min ) @ SV365 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3483]) ).
thf(4067,plain,
! [SV939: real,SV721: real,SV368: real] :
( ( ( times_times_real @ ( times_times_real @ SV368 @ SV721 ) @ SV939 )
= ( times_times_real @ SV368 @ ( times_times_real @ SV721 @ SV939 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3486]) ).
thf(4068,plain,
! [SV371: real,SV940: real,SV723: real] :
( ( ~ ( ord_less_eq_real @ SV723 @ SV940 )
| ( ord_less_eq_real @ ( plus_plus_real @ SV371 @ SV723 ) @ ( plus_plus_real @ SV371 @ SV940 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3488]) ).
thf(4069,plain,
! [SV941: real,SV724: real,SV372: real] :
( ( ! [SY2378: real] :
( ( minus_minus_real @ ( plus_plus_real @ SV372 @ SV724 ) @ ( plus_plus_real @ SV941 @ SY2378 ) )
= ( plus_plus_real @ ( minus_minus_real @ SV372 @ SV941 ) @ ( minus_minus_real @ SV724 @ SY2378 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3489]) ).
thf(4070,plain,
! [SV942: real,SV725: real,SV373: real] :
( ( ( times_times_real @ ( plus_plus_real @ SV373 @ SV725 ) @ SV942 )
= ( plus_plus_real @ ( times_times_real @ SV373 @ SV942 ) @ ( times_times_real @ SV725 @ SV942 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3490]) ).
thf(4071,plain,
! [SV943: real,SV726: real,SV374: real] :
( ( ! [SY2379: real] :
( ( minus_minus_real @ ( times_times_real @ SV374 @ SV726 ) @ ( times_times_real @ SV943 @ SY2379 ) )
= ( plus_plus_real @ ( times_times_real @ SV374 @ ( minus_minus_real @ SV726 @ SY2379 ) ) @ ( times_times_real @ ( minus_minus_real @ SV374 @ SV943 ) @ SY2379 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3491]) ).
thf(4072,plain,
! [SV727: real,SV375: real,SV944: real] :
( ( ~ ( ord_less_real @ zero_zero_real @ SV944 )
| ~ ( ord_less_real @ SV375 @ SV727 )
| ( ord_less_real @ ( times_times_real @ SV944 @ SV375 ) @ ( times_times_real @ SV944 @ SV727 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3492]) ).
thf(4073,plain,
! [SV376: real,SV728: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV728 ) )
= $true )
| ( ( ~ ( ord_less_real @ zero_zero_real @ SV376 )
| ( ord_less_real @ zero_zero_real @ ( times_times_real @ SV728 @ SV376 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3493]) ).
thf(4074,plain,
! [SV378: real,SV729: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV729 ) )
= $true )
| ( ( ( times_times_real @ ( power_power_real @ SV378 @ ( minus_minus_nat @ SV729 @ one_one_nat ) ) @ SV378 )
= ( power_power_real @ SV378 @ SV729 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3494]) ).
thf(4075,plain,
! [SV379: nat,SV730: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV730 ) )
= $true )
| ( ( ( times_times_nat @ ( power_power_nat @ SV379 @ ( minus_minus_nat @ SV730 @ one_one_nat ) ) @ SV379 )
= ( power_power_nat @ SV379 @ SV730 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3495]) ).
thf(4076,plain,
! [SV380: int,SV731: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV731 ) )
= $true )
| ( ( ( times_times_int @ ( power_power_int @ SV380 @ ( minus_minus_nat @ SV731 @ one_one_nat ) ) @ SV380 )
= ( power_power_int @ SV380 @ SV731 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3496]) ).
thf(4077,plain,
! [SV382: nat,SV945: real,SV732: real] :
( ( ~ ( ord_less_real @ SV732 @ SV945 )
| ~ ( ord_less_eq_real @ zero_zero_real @ SV732 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV382 )
| ( ord_less_real @ ( power_power_real @ SV732 @ SV382 ) @ ( power_power_real @ SV945 @ SV382 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3497]) ).
thf(4078,plain,
! [SV383: nat,SV946: nat,SV733: nat] :
( ( ~ ( ord_less_nat @ SV733 @ SV946 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV733 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV383 )
| ( ord_less_nat @ ( power_power_nat @ SV733 @ SV383 ) @ ( power_power_nat @ SV946 @ SV383 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3498]) ).
thf(4079,plain,
! [SV384: nat,SV947: int,SV734: int] :
( ( ~ ( ord_less_int @ SV734 @ SV947 )
| ~ ( ord_less_eq_int @ zero_zero_int @ SV734 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV384 )
| ( ord_less_int @ ( power_power_int @ SV734 @ SV384 ) @ ( power_power_int @ SV947 @ SV384 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3499]) ).
thf(4080,plain,
! [SV385: nat,SV735: real] :
( ( ( SV735 = zero_zero_real )
= $true )
| ( ( ( power_power_real @ SV735 @ SV385 )
!= zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3500]) ).
thf(4081,plain,
! [SV948: nat,SV736: real,SV386: real] :
( ( ( power_power_real @ ( times_times_real @ SV386 @ SV736 ) @ SV948 )
= ( times_times_real @ ( power_power_real @ SV386 @ SV948 ) @ ( power_power_real @ SV736 @ SV948 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3501]) ).
thf(4082,plain,
! [SV949: nat,SV737: nat,SV387: nat] :
( ( ( power_power_nat @ ( times_times_nat @ SV387 @ SV737 ) @ SV949 )
= ( times_times_nat @ ( power_power_nat @ SV387 @ SV949 ) @ ( power_power_nat @ SV737 @ SV949 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3502]) ).
thf(4083,plain,
! [SV392: nat,SV950: nat,SV740: nat] :
( ( ~ ( dvd_dvd_nat @ SV740 @ SV950 )
| ( dvd_dvd_nat @ ( power_power_nat @ SV740 @ SV392 ) @ ( power_power_nat @ SV950 @ SV392 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3505]) ).
thf(4084,plain,
! [SV393: nat,SV951: real,SV741: real] :
( ( ~ ( dvd_dvd_real @ SV741 @ SV951 )
| ( dvd_dvd_real @ ( power_power_real @ SV741 @ SV393 ) @ ( power_power_real @ SV951 @ SV393 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3506]) ).
thf(4085,plain,
! [SV952: nat,SV742: nat,SV394: real] :
( ( ( power_power_real @ SV394 @ ( times_times_nat @ SV742 @ SV952 ) )
= ( power_power_real @ ( power_power_real @ SV394 @ SV742 ) @ SV952 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3507]) ).
thf(4086,plain,
! [SV953: nat,SV743: nat,SV395: nat] :
( ( ( power_power_nat @ SV395 @ ( times_times_nat @ SV743 @ SV953 ) )
= ( power_power_nat @ ( power_power_nat @ SV395 @ SV743 ) @ SV953 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3508]) ).
thf(4087,plain,
! [SV398: nat,SV954: real,SV744: real] :
( ( ~ ( ord_less_eq_real @ SV744 @ SV954 )
| ~ ( ord_less_eq_real @ zero_zero_real @ SV744 )
| ( ord_less_eq_real @ ( power_power_real @ SV744 @ SV398 ) @ ( power_power_real @ SV954 @ SV398 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3509]) ).
thf(4088,plain,
! [SV399: nat,SV955: nat,SV745: nat] :
( ( ~ ( ord_less_eq_nat @ SV745 @ SV955 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV745 )
| ( ord_less_eq_nat @ ( power_power_nat @ SV745 @ SV399 ) @ ( power_power_nat @ SV955 @ SV399 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3510]) ).
thf(4089,plain,
! [SV400: nat,SV746: real] :
( ( ( ~ ( ord_less_eq_real @ zero_zero_real @ SV746 ) )
= $true )
| ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ SV746 @ SV400 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3511]) ).
thf(4090,plain,
! [SV401: nat,SV747: nat] :
( ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV747 ) )
= $true )
| ( ( ord_less_eq_nat @ zero_zero_nat @ ( power_power_nat @ SV747 @ SV401 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3512]) ).
thf(4091,plain,
! [SV402: nat,SV748: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV748 ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ SV748 @ SV402 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3513]) ).
thf(4092,plain,
! [SV403: nat,SV749: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV749 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV749 @ SV403 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3514]) ).
thf(4093,plain,
! [SV404: nat,SV750: real] :
( ( ( ~ ( ord_less_eq_real @ one_one_real @ SV750 ) )
= $true )
| ( ( ord_less_eq_real @ one_one_real @ ( power_power_real @ SV750 @ SV404 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3515]) ).
thf(4094,plain,
! [SV405: nat,SV751: nat] :
( ( ( ~ ( ord_less_eq_nat @ one_one_nat @ SV751 ) )
= $true )
| ( ( ord_less_eq_nat @ one_one_nat @ ( power_power_nat @ SV751 @ SV405 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3516]) ).
thf(4095,plain,
! [SV956: nat,SV752: nat,SV408: real] :
( ( ( power_power_real @ SV408 @ ( plus_plus_nat @ SV752 @ SV956 ) )
= ( times_times_real @ ( power_power_real @ SV408 @ SV752 ) @ ( power_power_real @ SV408 @ SV956 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3517]) ).
thf(4096,plain,
! [SV957: nat,SV753: nat,SV409: nat] :
( ( ( power_power_nat @ SV409 @ ( plus_plus_nat @ SV753 @ SV957 ) )
= ( times_times_nat @ ( power_power_nat @ SV409 @ SV753 ) @ ( power_power_nat @ SV409 @ SV957 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3518]) ).
thf(4097,plain,
! [SV410: nat,SV958: nat,SV754: nat] :
( ( ! [SY2380: nat] :
( ~ ( dvd_dvd_nat @ ( power_power_nat @ SV754 @ SV958 ) @ SY2380 )
| ~ ( ord_less_eq_nat @ SV410 @ SV958 )
| ( dvd_dvd_nat @ ( power_power_nat @ SV754 @ SV410 ) @ SY2380 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3519]) ).
thf(4098,plain,
! [SV411: nat,SV959: nat,SV755: real] :
( ( ! [SY2381: real] :
( ~ ( dvd_dvd_real @ ( power_power_real @ SV755 @ SV959 ) @ SY2381 )
| ~ ( ord_less_eq_nat @ SV411 @ SV959 )
| ( dvd_dvd_real @ ( power_power_real @ SV755 @ SV411 ) @ SY2381 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3520]) ).
thf(4099,plain,
! [SV756: nat,SV412: nat,SV960: nat] :
( ( ! [SY2382: nat] :
( ~ ( dvd_dvd_nat @ SV960 @ SY2382 )
| ~ ( ord_less_eq_nat @ SV412 @ SV756 )
| ( dvd_dvd_nat @ ( power_power_nat @ SV960 @ SV412 ) @ ( power_power_nat @ SY2382 @ SV756 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3521]) ).
thf(4100,plain,
! [SV757: nat,SV413: nat,SV961: real] :
( ( ! [SY2383: real] :
( ~ ( dvd_dvd_real @ SV961 @ SY2383 )
| ~ ( ord_less_eq_nat @ SV413 @ SV757 )
| ( dvd_dvd_real @ ( power_power_real @ SV961 @ SV413 ) @ ( power_power_real @ SY2383 @ SV757 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3522]) ).
thf(4101,plain,
! [SV414: nat,SV962: nat,SV758: nat] :
( ( ~ ( ord_less_eq_nat @ SV758 @ SV962 )
| ( dvd_dvd_nat @ ( power_power_nat @ SV414 @ SV758 ) @ ( power_power_nat @ SV414 @ SV962 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3523]) ).
thf(4102,plain,
! [SV415: real,SV963: nat,SV759: nat] :
( ( ~ ( ord_less_eq_nat @ SV759 @ SV963 )
| ( dvd_dvd_real @ ( power_power_real @ SV415 @ SV759 ) @ ( power_power_real @ SV415 @ SV963 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3524]) ).
thf(4103,plain,
! [SV760: nat,SV416: nat,SV964: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ SV964 )
| ~ ( ord_less_nat @ ( power_power_nat @ SV964 @ SV416 ) @ ( power_power_nat @ SV964 @ SV760 ) )
| ( ord_less_nat @ SV416 @ SV760 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3525]) ).
thf(4104,plain,
! [SV965: real,SV761: nat,SV417: real] :
( ( ~ ( ord_less_real @ ( power_power_real @ SV417 @ SV761 ) @ ( power_power_real @ SV965 @ SV761 ) )
| ~ ( ord_less_eq_real @ zero_zero_real @ SV965 )
| ( ord_less_real @ SV417 @ SV965 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3526]) ).
thf(4105,plain,
! [SV966: nat,SV762: nat,SV418: nat] :
( ( ~ ( ord_less_nat @ ( power_power_nat @ SV418 @ SV762 ) @ ( power_power_nat @ SV966 @ SV762 ) )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV966 )
| ( ord_less_nat @ SV418 @ SV966 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3527]) ).
thf(4106,plain,
! [SV419: nat,SV763: real] :
( ( ( ~ ( ord_less_real @ one_one_real @ SV763 ) )
= $true )
| ( ( ord_less_real @ ( power_power_real @ SV763 @ SV419 ) @ ( times_times_real @ SV763 @ ( power_power_real @ SV763 @ SV419 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3528]) ).
thf(4107,plain,
! [SV420: nat,SV764: nat] :
( ( ( ~ ( ord_less_nat @ one_one_nat @ SV764 ) )
= $true )
| ( ( ord_less_nat @ ( power_power_nat @ SV764 @ SV420 ) @ ( times_times_nat @ SV764 @ ( power_power_nat @ SV764 @ SV420 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3529]) ).
thf(4108,plain,
! [SV421: nat,SV765: real] :
( ( ( ~ ( ord_less_real @ one_one_real @ SV765 ) )
= $true )
| ( ( ord_less_real @ one_one_real @ ( times_times_real @ SV765 @ ( power_power_real @ SV765 @ SV421 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3530]) ).
thf(4109,plain,
! [SV422: nat,SV766: nat] :
( ( ( ~ ( ord_less_nat @ one_one_nat @ SV766 ) )
= $true )
| ( ( ord_less_nat @ one_one_nat @ ( times_times_nat @ SV766 @ ( power_power_nat @ SV766 @ SV422 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3531]) ).
thf(4110,plain,
! [SV423: real,SV967: nat,SV767: nat] :
( ( ~ ( ord_less_nat @ SV767 @ SV967 )
| ~ ( ord_less_real @ one_one_real @ SV423 )
| ( ord_less_real @ ( power_power_real @ SV423 @ SV767 ) @ ( power_power_real @ SV423 @ SV967 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3532]) ).
thf(4111,plain,
! [SV424: nat,SV968: nat,SV768: nat] :
( ( ~ ( ord_less_nat @ SV768 @ SV968 )
| ~ ( ord_less_nat @ one_one_nat @ SV424 )
| ( ord_less_nat @ ( power_power_nat @ SV424 @ SV768 ) @ ( power_power_nat @ SV424 @ SV968 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3533]) ).
thf(4112,plain,
! [SV769: nat,SV425: nat,SV969: real] :
( ( ~ ( ord_less_real @ one_one_real @ SV969 )
| ~ ( ord_less_real @ ( power_power_real @ SV969 @ SV425 ) @ ( power_power_real @ SV969 @ SV769 ) )
| ( ord_less_nat @ SV425 @ SV769 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3534]) ).
thf(4113,plain,
! [SV770: nat,SV426: nat,SV970: nat] :
( ( ~ ( ord_less_nat @ one_one_nat @ SV970 )
| ~ ( ord_less_nat @ ( power_power_nat @ SV970 @ SV426 ) @ ( power_power_nat @ SV970 @ SV770 ) )
| ( ord_less_nat @ SV426 @ SV770 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3535]) ).
thf(4114,plain,
! [SV427: real,SV971: nat,SV771: nat] :
( ( ~ ( ord_less_eq_nat @ SV771 @ SV971 )
| ~ ( ord_less_eq_real @ one_one_real @ SV427 )
| ( ord_less_eq_real @ ( power_power_real @ SV427 @ SV771 ) @ ( power_power_real @ SV427 @ SV971 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3536]) ).
thf(4115,plain,
! [SV428: nat,SV972: nat,SV772: nat] :
( ( ~ ( ord_less_eq_nat @ SV772 @ SV972 )
| ~ ( ord_less_eq_nat @ one_one_nat @ SV428 )
| ( ord_less_eq_nat @ ( power_power_nat @ SV428 @ SV772 ) @ ( power_power_nat @ SV428 @ SV972 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3537]) ).
thf(4116,plain,
! [SV429: nat,SV773: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV773 ) )
= $true )
| ( ( ~ ( ord_less_real @ SV773 @ one_one_real )
| ( ord_less_real @ ( times_times_real @ SV773 @ ( power_power_real @ SV773 @ SV429 ) ) @ ( power_power_real @ SV773 @ SV429 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3538]) ).
thf(4117,plain,
! [SV430: nat,SV774: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV774 ) )
= $true )
| ( ( ~ ( ord_less_nat @ SV774 @ one_one_nat )
| ( ord_less_nat @ ( times_times_nat @ SV774 @ ( power_power_nat @ SV774 @ SV430 ) ) @ ( power_power_nat @ SV774 @ SV430 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3539]) ).
thf(4118,plain,
! [SV775: nat,SV431: nat] :
( ( ( ~ ( dvd_dvd_nat @ SV431 @ SV775 ) )
= $true )
| ( ( ( SV775 = zero_zero_nat )
| ( ord_less_eq_nat @ SV431 @ SV775 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3540]) ).
thf(4119,plain,
! [SV432: nat,SV973: nat,SV776: nat] :
( ( ~ ( dvd_dvd_nat @ SV776 @ SV973 )
| ( dvd_dvd_nat @ ( power_power_nat @ SV776 @ SV432 ) @ ( power_power_nat @ SV973 @ SV432 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3541]) ).
thf(4120,plain,
! [SV433: nat,SV974: nat,SV777: nat] :
( ( ~ ( dvd_dvd_nat @ SV777 @ SV974 )
| ( dvd_dvd_nat @ ( times_times_nat @ SV433 @ SV777 ) @ ( times_times_nat @ SV433 @ SV974 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3542]) ).
thf(4121,plain,
! [SV434: nat,SV975: nat,SV778: nat] :
( ( ~ ( dvd_dvd_nat @ SV778 @ SV975 )
| ( dvd_dvd_nat @ ( times_times_nat @ SV778 @ SV434 ) @ ( times_times_nat @ SV975 @ SV434 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3543]) ).
thf(4122,plain,
! [SV435: nat,SV976: nat,SV779: nat] :
( ( ~ ( dvd_dvd_nat @ SV779 @ SV976 )
| ~ ( dvd_dvd_nat @ SV779 @ ( plus_plus_nat @ SV976 @ SV435 ) )
| ( dvd_dvd_nat @ SV779 @ SV435 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3544]) ).
thf(4123,plain,
! [SV977: nat,SV780: nat,SV436: nat] :
( ( ~ ( dvd_dvd_nat @ ( power_power_nat @ SV436 @ SV780 ) @ ( power_power_nat @ SV977 @ SV780 ) )
| ( SV780 = zero_zero_nat )
| ( dvd_dvd_nat @ SV436 @ SV977 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3545]) ).
thf(4124,plain,
! [SV781: nat,SV437: nat,SV978: nat] :
( ( ( SV978 = zero_zero_nat )
| ~ ( dvd_dvd_nat @ ( power_power_nat @ SV437 @ SV978 ) @ SV781 )
| ( dvd_dvd_nat @ SV437 @ SV781 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3546]) ).
thf(4125,plain,
! [SV979: nat,SV782: nat,SV438: nat] :
( ( ! [SY2384: nat] :
( ( SV438
!= ( plus_plus_nat @ ( times_times_nat @ SV782 @ SV979 ) @ SY2384 ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SY2384 )
| ~ ( ord_less_nat @ SY2384 @ SV979 )
| ~ ( dvd_dvd_nat @ SV979 @ SV438 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3547]) ).
thf(4126,plain,
! [SV980: nat,SV783: nat,SV439: nat] :
( ( ~ ( dvd_dvd_nat @ ( power_power_nat @ SV439 @ SV783 ) @ ( power_power_nat @ SV439 @ SV980 ) )
| ~ ( ord_less_nat @ one_one_nat @ SV439 )
| ( ord_less_eq_nat @ SV783 @ SV980 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3548]) ).
thf(4127,plain,
! [SV784: nat,SV440: nat] :
( ( ( ~ ( dvd_dvd_nat @ SV440 @ SV784 ) )
= $true )
| ( ( ( ord_less_eq_nat @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV440 ) @ SV784 )
| ( SV784 = zero_zero_nat )
| ( SV784 = SV440 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3549]) ).
thf(4128,plain,
( ( ! [SX0: real] :
( ( ( power_power_real @ SX0 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= zero_zero_real )
| ( SX0 = zero_zero_real ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3550]) ).
thf(4129,plain,
( ( ! [SX0: real] :
( ( SX0 != zero_zero_real )
| ( ( power_power_real @ SX0 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_real ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3551]) ).
thf(4130,plain,
( ( ! [SX0: nat,SX1: nat] :
( ( SX1 = zero_zero_nat )
| ( SX0 != zero_zero_nat )
| ( ( power_power_nat @ SX0 @ SX1 )
= zero_zero_nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3552]) ).
thf(4131,plain,
( ( ~ ( ~ ! [SX0: nat,SX1: nat] :
( ( ( power_power_nat @ SX0 @ SX1 )
!= zero_zero_nat )
| ( SX1 != zero_zero_nat ) )
| ~ ! [SX0: nat] :
( ! [SX1: nat] :
( ( power_power_nat @ SX0 @ SX1 )
!= zero_zero_nat )
| ( SX0 = zero_zero_nat ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3553]) ).
thf(4132,plain,
( ( ! [SX0: nat,SX1: int] :
( ( ( number_number_of_nat @ SX1 )
= zero_zero_nat )
| ( SX0 != zero_zero_nat )
| ( ( power_power_nat @ SX0 @ ( number_number_of_nat @ SX1 ) )
= zero_zero_nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3554]) ).
thf(4133,plain,
( ( ~ ( ~ ! [SX0: nat,SX1: int] :
( ( ( power_power_nat @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_nat )
| ( ( number_number_of_nat @ SX1 )
!= zero_zero_nat ) )
| ~ ! [SX0: nat] :
( ! [SX1: int] :
( ( power_power_nat @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_nat )
| ( SX0 = zero_zero_nat ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3555]) ).
thf(4134,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_eq_int @ min @ ( bit0 @ SX0 ) )
| ( ord_less_int @ min @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3556]) ).
thf(4135,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_int @ min @ SX0 )
| ( ord_less_eq_int @ min @ ( bit0 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3557]) ).
thf(4136,plain,
( ( ! [SX0: real,SX1: real] :
( ~ ( ord_less_real @ 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 ) ) ) ) ) )
| ( SX0 != zero_zero_real )
| ( SX1 != zero_zero_real ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3558]) ).
thf(4137,plain,
( ( ~ ( ~ ! [SX0: real] :
( ( SX0 = zero_zero_real )
| ! [SX1: real] : ( ord_less_real @ 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 ) ) ) ) ) ) )
| ~ ! [SX0: real,SX1: real] :
( ( SX1 = zero_zero_real )
| ( ord_less_real @ 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 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3559]) ).
thf(4138,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_eq_int @ pls @ SX0 )
| ( ord_less_eq_real @ zero_zero_real @ ( number267125858f_real @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3560]) ).
thf(4139,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_eq_real @ zero_zero_real @ ( number267125858f_real @ SX0 ) )
| ( ord_less_eq_int @ pls @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3561]) ).
thf(4140,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_eq_int @ pls @ SX0 )
| ( ord_less_int @ pls @ ( bit1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3562]) ).
thf(4141,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_int @ pls @ ( bit1 @ SX0 ) )
| ( ord_less_eq_int @ pls @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3563]) ).
thf(4142,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3564]) ).
thf(4143,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3565]) ).
thf(4144,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_int @ min @ ( bit1 @ SX0 ) )
| ( ord_less_int @ min @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3566]) ).
thf(4145,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_int @ min @ SX0 )
| ( ord_less_int @ min @ ( bit1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3567]) ).
thf(4146,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3568]) ).
thf(4147,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3569]) ).
thf(4148,plain,
( ( ! [SX0: nat,SX1: nat] :
( ( ( power_power_nat @ SX0 @ SX1 )
!= one_one_nat )
| ( SX0 = one_one_nat )
| ( SX1 = zero_zero_nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3570]) ).
thf(4149,plain,
( ( ~ ( ~ ! [SX0: nat] :
( ( SX0 != one_one_nat )
| ! [SX1: nat] :
( ( power_power_nat @ SX0 @ SX1 )
= one_one_nat ) )
| ~ ! [SX0: nat,SX1: nat] :
( ( SX1 != zero_zero_nat )
| ( ( power_power_nat @ SX0 @ SX1 )
= one_one_nat ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3571]) ).
thf(4150,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_eq_real @ ( number267125858f_real @ SX0 ) @ ( number267125858f_real @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3572]) ).
thf(4151,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_real @ ( number267125858f_real @ SX0 ) @ ( number267125858f_real @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3573]) ).
thf(4152,plain,
( ( ! [SX0: nat] :
( ( SX0 != zero_zero_nat )
| ( ( power_power_real @ zero_zero_real @ SX0 )
= one_one_real ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3574]) ).
thf(4153,plain,
( ( ! [SX0: nat] :
( ( SX0 = zero_zero_nat )
| ( ( power_power_real @ zero_zero_real @ SX0 )
= zero_zero_real ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3575]) ).
thf(4154,plain,
( ( ! [SX0: int,SX1: int] :
( ( ( bit1 @ SX0 )
!= ( bit1 @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3576]) ).
thf(4155,plain,
( ( ! [SX0: int,SX1: int] :
( ( SX0 != SX1 )
| ( ( bit1 @ SX0 )
= ( bit1 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3577]) ).
thf(4156,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ ( number_number_of_int @ SX0 ) @ ( number_number_of_int @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3578]) ).
thf(4157,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ ( number_number_of_int @ SX0 ) @ ( number_number_of_int @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3579]) ).
thf(4158,plain,
( ( ! [SX0: real,SX1: real] :
( ( SX0 != zero_zero_real )
| ( SX1 != zero_zero_real )
| ( ord_less_eq_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(extcnf_not_neg,[status(thm)],[3580]) ).
thf(4159,plain,
( ( ~ ( ~ ! [SX0: real] :
( ! [SX1: real] :
~ ( ord_less_eq_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 )
| ( SX0 = zero_zero_real ) )
| ~ ! [SX0: real,SX1: real] :
( ~ ( ord_less_eq_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 )
| ( SX1 = zero_zero_real ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3581]) ).
thf(4160,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ ( plus_plus_int @ SX1 @ one_one_int ) )
| ( SX0 = SX1 )
| ( ord_less_int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3582]) ).
thf(4161,plain,
( ( ~ ( ~ ! [SX0: int,SX1: int] :
( ( SX0 != SX1 )
| ( ord_less_int @ SX0 @ ( plus_plus_int @ SX1 @ one_one_int ) ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ SX0 @ ( plus_plus_int @ SX1 @ one_one_int ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3583]) ).
thf(4162,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_eq_int @ min @ ( bit1 @ SX0 ) )
| ( ord_less_eq_int @ min @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3584]) ).
thf(4163,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_eq_int @ min @ SX0 )
| ( ord_less_eq_int @ min @ ( bit1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3585]) ).
thf(4164,plain,
( ( ! [SX0: int] :
( ( ( number_number_of_nat @ SX0 )
!= zero_zero_nat )
| ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ SX0 ) )
= one_one_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3586]) ).
thf(4165,plain,
( ( ! [SX0: int] :
( ( ( number_number_of_nat @ SX0 )
= zero_zero_nat )
| ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ SX0 ) )
= zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3587]) ).
thf(4166,plain,
! [SV785: nat,SV441: nat] :
( ( ~ ~ ( ~ ! [SY2273: nat,SY2274: nat] :
( ( ( plus_plus_nat @ ( times_times_nat @ SY2273 @ SV441 ) @ ( times_times_nat @ SY2274 @ SV785 ) )
= ( plus_plus_nat @ ( times_times_nat @ SY2273 @ SV785 ) @ ( times_times_nat @ SY2274 @ SV441 ) ) )
| ( SY2273 != SY2274 ) )
| ~ ( ! [SY2275: nat,SY2276: nat] :
( ( plus_plus_nat @ ( times_times_nat @ SY2275 @ SV441 ) @ ( times_times_nat @ SY2276 @ SV785 ) )
= ( plus_plus_nat @ ( times_times_nat @ SY2275 @ SV785 ) @ ( times_times_nat @ SY2276 @ SV441 ) ) )
| ( SV441 != SV785 ) ) )
| ~ ! [SY2277: nat,SY2278: nat] :
( ( SY2277 = SY2278 )
| ( SV441 = SV785 )
| ( ( plus_plus_nat @ ( times_times_nat @ SY2277 @ SV441 ) @ ( times_times_nat @ SY2278 @ SV785 ) )
!= ( plus_plus_nat @ ( times_times_nat @ SY2277 @ SV785 ) @ ( times_times_nat @ SY2278 @ SV441 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3588]) ).
thf(4167,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3589]) ).
thf(4168,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3590]) ).
thf(4169,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3591]) ).
thf(4170,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3592]) ).
thf(4171,plain,
( ( ! [SX0: real,SX1: int] :
( ( ( number_number_of_nat @ SX1 )
= zero_zero_nat )
| ( SX0 != zero_zero_real )
| ( ( power_power_real @ SX0 @ ( number_number_of_nat @ SX1 ) )
= zero_zero_real ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3593]) ).
thf(4172,plain,
( ( ~ ( ~ ! [SX0: real,SX1: int] :
( ( ( power_power_real @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_real )
| ( ( number_number_of_nat @ SX1 )
!= zero_zero_nat ) )
| ~ ! [SX0: real] :
( ! [SX1: int] :
( ( power_power_real @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_real )
| ( SX0 = zero_zero_real ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3594]) ).
thf(4173,plain,
( ( ! [SX0: real,SX1: real] :
( ~ ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ SX0 @ SX0 ) @ ( times_times_real @ SX1 @ SX1 ) ) )
| ( SX0 != zero_zero_real )
| ( SX1 != zero_zero_real ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3595]) ).
thf(4174,plain,
( ( ~ ( ~ ! [SX0: real] :
( ( SX0 = zero_zero_real )
| ! [SX1: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ SX0 @ SX0 ) @ ( times_times_real @ SX1 @ SX1 ) ) ) )
| ~ ! [SX0: real,SX1: real] :
( ( SX1 = zero_zero_real )
| ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ SX0 @ SX0 ) @ ( times_times_real @ SX1 @ SX1 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3596]) ).
thf(4175,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SX0 @ SX1 ) )
| ( SX1 = zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3597]) ).
thf(4176,plain,
( ( ~ ( ~ ! [SX0: nat,SX1: nat] :
( ( SX1 != zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SX0 @ SX1 ) ) )
| ~ ! [SX0: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SX0 )
| ! [SX1: nat] : ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3598]) ).
thf(4177,plain,
! [SV786: real,SV442: real] :
( ( ~ ~ ( ~ ! [SY2279: real,SY2280: real] :
( ( ( plus_plus_real @ ( times_times_real @ SY2279 @ SV442 ) @ ( times_times_real @ SY2280 @ SV786 ) )
= ( plus_plus_real @ ( times_times_real @ SY2279 @ SV786 ) @ ( times_times_real @ SY2280 @ SV442 ) ) )
| ( SY2279 != SY2280 ) )
| ~ ( ! [SY2281: real,SY2282: real] :
( ( plus_plus_real @ ( times_times_real @ SY2281 @ SV442 ) @ ( times_times_real @ SY2282 @ SV786 ) )
= ( plus_plus_real @ ( times_times_real @ SY2281 @ SV786 ) @ ( times_times_real @ SY2282 @ SV442 ) ) )
| ( SV442 != SV786 ) ) )
| ~ ! [SY2283: real,SY2284: real] :
( ( SY2283 = SY2284 )
| ( SV442 = SV786 )
| ( ( plus_plus_real @ ( times_times_real @ SY2283 @ SV442 ) @ ( times_times_real @ SY2284 @ SV786 ) )
!= ( plus_plus_real @ ( times_times_real @ SY2283 @ SV786 ) @ ( times_times_real @ SY2284 @ SV442 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3599]) ).
thf(4178,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_eq_int @ ( bit0 @ SX0 ) @ pls )
| ( ord_less_eq_int @ SX0 @ pls ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3600]) ).
thf(4179,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_eq_int @ SX0 @ pls )
| ( ord_less_eq_int @ ( bit0 @ SX0 ) @ pls ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3601]) ).
thf(4180,plain,
( ( ! [SX0: int] :
( ( ( bit1 @ SX0 )
!= min )
| ( SX0 = min ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3602]) ).
thf(4181,plain,
( ( ! [SX0: int] :
( ( SX0 != min )
| ( ( bit1 @ SX0 )
= min ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3603]) ).
thf(4182,plain,
( ( ! [SX0: real,SX1: real] :
( ~ ( ord_less_eq_real @ SX0 @ SX1 )
| ( SX0 = SX1 )
| ( ord_less_real @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3604]) ).
thf(4183,plain,
( ( ~ ( ~ ! [SX0: real,SX1: real] :
( ( SX0 != SX1 )
| ( ord_less_eq_real @ SX0 @ SX1 ) )
| ~ ! [SX0: real,SX1: real] :
( ~ ( ord_less_real @ SX0 @ SX1 )
| ( ord_less_eq_real @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3605]) ).
thf(4184,plain,
( ( ! [SX0: real] :
( ( ( plus_plus_real @ SX0 @ SX0 )
!= zero_zero_real )
| ( SX0 = zero_zero_real ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3606]) ).
thf(4185,plain,
( ( ! [SX0: real] :
( ( SX0 != zero_zero_real )
| ( ( plus_plus_real @ SX0 @ SX0 )
= zero_zero_real ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3607]) ).
thf(4186,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ zero_zero_int @ ( 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 ) ) ) ) ) )
| ( SX0 != zero_zero_int )
| ( SX1 != zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3608]) ).
thf(4187,plain,
( ( ~ ( ~ ! [SX0: int] :
( ( SX0 = zero_zero_int )
| ! [SX1: int] : ( ord_less_int @ zero_zero_int @ ( 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 ) ) ) ) ) ) )
| ~ ! [SX0: int,SX1: int] :
( ( SX1 = zero_zero_int )
| ( ord_less_int @ zero_zero_int @ ( 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 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3609]) ).
thf(4188,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_int @ pls @ SX0 )
| ( ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3610]) ).
thf(4189,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ SX0 ) )
| ( ord_less_int @ pls @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3611]) ).
thf(4190,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ ( number_number_of_int @ SX0 ) @ ( number_number_of_int @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3612]) ).
thf(4191,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( number_number_of_int @ SX0 ) @ ( number_number_of_int @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3613]) ).
thf(4192,plain,
( ( ! [SX0: real,SX1: 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(extcnf_not_neg,[status(thm)],[3614]) ).
thf(4193,plain,
( ( ~ ( ~ ! [SX0: real] :
( ! [SX1: 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 )
| ( SX0 = zero_zero_real ) )
| ~ ! [SX0: real,SX1: 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 )
| ( SX1 = zero_zero_real ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3615]) ).
thf(4194,plain,
( ( ! [SX0: int,SX1: nat] :
( ( SX1 != zero_zero_nat )
| ( ( power_power_int @ SX0 @ SX1 )
= one_one_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3616]) ).
thf(4195,plain,
( ( ! [SX0: int,SX1: nat] :
( ( SX1 = zero_zero_nat )
| ( ( power_power_int @ SX0 @ SX1 )
= ( times_times_int @ SX0 @ ( power_power_int @ SX0 @ ( minus_minus_nat @ SX1 @ one_one_nat ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3617]) ).
thf(4196,plain,
( ( ! [SX0: int] :
( ( ( number_number_of_nat @ SX0 )
!= zero_zero_nat )
| ( ord_less_eq_int @ SX0 @ pls ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3618]) ).
thf(4197,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_eq_int @ SX0 @ pls )
| ( ( number_number_of_nat @ SX0 )
= zero_zero_nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3619]) ).
thf(4198,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( dvd_dvd_int @ SX1 @ SX0 )
| ( zcong @ SX0 @ zero_zero_int @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3620]) ).
thf(4199,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( zcong @ SX0 @ zero_zero_int @ SX1 )
| ( dvd_dvd_int @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3621]) ).
thf(4200,plain,
( ( ! [SX0: nat,SX1: nat] :
( ( SX1 != zero_zero_nat )
| ( ( power_power_nat @ SX0 @ SX1 )
= one_one_nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3622]) ).
thf(4201,plain,
( ( ! [SX0: nat,SX1: 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(extcnf_not_neg,[status(thm)],[3623]) ).
thf(4202,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_int @ ( bit1 @ SX0 ) @ min )
| ( ord_less_int @ SX0 @ min ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3624]) ).
thf(4203,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_int @ SX0 @ min )
| ( ord_less_int @ ( bit1 @ SX0 ) @ min ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3625]) ).
thf(4204,plain,
! [SV443: nat] :
( ( ~ ! [SY1911: nat,SY1912: int] :
( ~ ( ord_less_int @ one_one_int @ SY1912 )
| ~ ( ord_less_int @ ( power_power_int @ SY1912 @ SV443 ) @ ( power_power_int @ SY1912 @ SY1911 ) )
| ( ord_less_nat @ SV443 @ SY1911 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3626]) ).
thf(4205,plain,
! [SV443: nat] :
( ( ~ ! [SY1913: nat,SY1914: int] :
( ~ ( ord_less_int @ one_one_int @ SY1914 )
| ~ ( ord_less_nat @ SV443 @ SY1913 )
| ( ord_less_int @ ( power_power_int @ SY1914 @ SV443 ) @ ( power_power_int @ SY1914 @ SY1913 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3626]) ).
thf(4206,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_int @ ( bit1 @ SX0 ) @ zero_zero_int )
| ( ord_less_int @ SX0 @ zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3627]) ).
thf(4207,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_int @ SX0 @ zero_zero_int )
| ( ord_less_int @ ( bit1 @ SX0 ) @ zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3628]) ).
thf(4208,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_eq_int @ SX0 @ pls )
| ( ord_less_eq_real @ ( number267125858f_real @ SX0 ) @ zero_zero_real ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3629]) ).
thf(4209,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_eq_real @ ( number267125858f_real @ SX0 ) @ zero_zero_real )
| ( ord_less_eq_int @ SX0 @ pls ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3630]) ).
thf(4210,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_int @ min @ ( bit0 @ SX0 ) )
| ( ord_less_int @ min @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3631]) ).
thf(4211,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_int @ min @ SX0 )
| ( ord_less_int @ min @ ( bit0 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3632]) ).
thf(4212,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ ( number_number_of_int @ SX0 ) @ ( number_number_of_int @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3633]) ).
thf(4213,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( number_number_of_int @ SX0 ) @ ( number_number_of_int @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3634]) ).
thf(4214,plain,
! [SV444: int] :
( ( ~ ! [SY1915: int] :
( ! [SY1916: int] :
~ ( dvd_dvd_int @ SV444 @ ( plus_plus_int @ SY1915 @ ( times_times_int @ SV444 @ SY1916 ) ) )
| ( dvd_dvd_int @ SV444 @ SY1915 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3635]) ).
thf(4215,plain,
! [SV444: int] :
( ( ~ ! [SY1917: int] :
( ~ ( dvd_dvd_int @ SV444 @ SY1917 )
| ! [SY1918: int] : ( dvd_dvd_int @ SV444 @ ( plus_plus_int @ SY1917 @ ( times_times_int @ SV444 @ SY1918 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3635]) ).
thf(4216,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ SX0 @ ( minus_minus_int @ SX1 @ one_one_int ) )
| ( ord_less_int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3636]) ).
thf(4217,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ SX0 @ ( minus_minus_int @ SX1 @ one_one_int ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3637]) ).
thf(4218,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3638]) ).
thf(4219,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3639]) ).
thf(4220,plain,
( ( ! [SX0: int,SX1: int] :
( ( ( number_number_of_nat @ SX1 )
= zero_zero_nat )
| ( SX0 != zero_zero_int )
| ( ( power_power_int @ SX0 @ ( number_number_of_nat @ SX1 ) )
= zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3640]) ).
thf(4221,plain,
( ( ~ ( ~ ! [SX0: int,SX1: int] :
( ( ( power_power_int @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_int )
| ( ( number_number_of_nat @ SX1 )
!= zero_zero_nat ) )
| ~ ! [SX0: int] :
( ! [SX1: int] :
( ( power_power_int @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3641]) ).
thf(4222,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_real @ ( number267125858f_real @ SX0 ) @ ( number267125858f_real @ SX1 ) )
| ~ ( ord_less_real @ ( number267125858f_real @ SX1 ) @ ( number267125858f_real @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3642]) ).
thf(4223,plain,
( ( ! [SX0: int,SX1: int] :
( ( ord_less_real @ ( number267125858f_real @ SX1 ) @ ( number267125858f_real @ SX0 ) )
| ( ord_less_eq_real @ ( number267125858f_real @ SX0 ) @ ( number267125858f_real @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3643]) ).
thf(4224,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ ( minus_minus_int @ SX0 @ SX1 ) @ zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3644]) ).
thf(4225,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ ( minus_minus_int @ SX0 @ SX1 ) @ zero_zero_int )
| ( ord_less_int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3645]) ).
thf(4226,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( 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 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3646]) ).
thf(4227,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( 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(extcnf_not_neg,[status(thm)],[3647]) ).
thf(4228,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_int @ ( bit0 @ SX0 ) @ pls )
| ( ord_less_int @ SX0 @ pls ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3648]) ).
thf(4229,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_int @ SX0 @ pls )
| ( ord_less_int @ ( bit0 @ SX0 ) @ pls ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3649]) ).
thf(4230,plain,
( ( ! [SX0: nat,SX1: nat] :
( ( SX1 != zero_zero_nat )
| ( ( times_times_nat @ SX1 @ SX0 )
= zero_zero_nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3650]) ).
thf(4231,plain,
( ( ! [SX0: nat,SX1: 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(extcnf_not_neg,[status(thm)],[3651]) ).
thf(4232,plain,
( ( ! [SX0: real,SX1: 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(extcnf_not_neg,[status(thm)],[3652]) ).
thf(4233,plain,
( ( ~ ( ~ ! [SX0: real] :
( ! [SX1: 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 )
| ( SX0 = zero_zero_real ) )
| ~ ! [SX0: real,SX1: 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 )
| ( SX1 = zero_zero_real ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3653]) ).
thf(4234,plain,
( ( ! [SX0: int,SX1: int] :
( ( SX0 != zero_zero_int )
| ( SX1 != zero_zero_int )
| ( ( 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 ) ) ) ) )
= zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3654]) ).
thf(4235,plain,
( ( ~ ( ~ ! [SX0: int] :
( ! [SX1: int] :
( ( 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 ) ) ) ) )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) )
| ~ ! [SX0: int,SX1: int] :
( ( ( 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 ) ) ) ) )
!= zero_zero_int )
| ( SX1 = zero_zero_int ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3655]) ).
thf(4236,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( dvd_dvd_int @ SX1 @ SX0 )
| ( zcong @ SX0 @ zero_zero_int @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3656]) ).
thf(4237,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( zcong @ SX0 @ zero_zero_int @ SX1 )
| ( dvd_dvd_int @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3657]) ).
thf(4238,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3658]) ).
thf(4239,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3659]) ).
thf(4240,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_int @ ( plus_plus_int @ SX0 @ SX0 ) @ zero_zero_int )
| ( ord_less_int @ SX0 @ zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3660]) ).
thf(4241,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_int @ SX0 @ zero_zero_int )
| ( ord_less_int @ ( plus_plus_int @ SX0 @ SX0 ) @ zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3661]) ).
thf(4242,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_eq_int @ one_one_int @ SX0 )
| ( ord_less_int @ zero_zero_int @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3662]) ).
thf(4243,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_int @ zero_zero_int @ SX0 )
| ( ord_less_eq_int @ one_one_int @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3663]) ).
thf(4244,plain,
! [SV445: real] :
( ( ~ ! [SY1919: real,SY1920: real] :
( ~ ( ord_less_real @ zero_zero_real @ SY1920 )
| ~ ( ord_less_eq_real @ ( times_times_real @ SV445 @ SY1920 ) @ ( times_times_real @ SY1919 @ SY1920 ) )
| ( ord_less_eq_real @ SV445 @ SY1919 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3664]) ).
thf(4245,plain,
! [SV445: real] :
( ( ~ ! [SY1921: real,SY1922: real] :
( ~ ( ord_less_real @ zero_zero_real @ SY1922 )
| ~ ( ord_less_eq_real @ SV445 @ SY1921 )
| ( ord_less_eq_real @ ( times_times_real @ SV445 @ SY1922 ) @ ( times_times_real @ SY1921 @ SY1922 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3664]) ).
thf(4246,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_int @ pls @ SX0 )
| ( ord_less_real @ zero_zero_real @ ( number267125858f_real @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3665]) ).
thf(4247,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_real @ zero_zero_real @ ( number267125858f_real @ SX0 ) )
| ( ord_less_int @ pls @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3666]) ).
thf(4248,plain,
( ( ! [SX0: real,SX1: real] :
( ( SX0 != zero_zero_real )
| ( SX1 != zero_zero_real )
| ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ SX0 @ SX0 ) @ ( times_times_real @ SX1 @ SX1 ) ) @ zero_zero_real ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3667]) ).
thf(4249,plain,
( ( ~ ( ~ ! [SX0: real] :
( ! [SX1: real] :
~ ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ SX0 @ SX0 ) @ ( times_times_real @ SX1 @ SX1 ) ) @ zero_zero_real )
| ( SX0 = zero_zero_real ) )
| ~ ! [SX0: real,SX1: real] :
( ~ ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ SX0 @ SX0 ) @ ( times_times_real @ SX1 @ SX1 ) ) @ zero_zero_real )
| ( SX1 = zero_zero_real ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3668]) ).
thf(4250,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3669]) ).
thf(4251,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3670]) ).
thf(4252,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_int @ zero_zero_int @ ( number_number_of_int @ SX0 ) )
| ( ord_less_int @ pls @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3671]) ).
thf(4253,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_int @ pls @ SX0 )
| ( ord_less_int @ zero_zero_int @ ( number_number_of_int @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3672]) ).
thf(4254,plain,
( ( ! [SX0: int,SX1: int] :
( ( SX0 != zero_zero_int )
| ( SX1 != zero_zero_int )
| ( ord_less_eq_int @ ( 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 ) ) ) ) ) @ zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3673]) ).
thf(4255,plain,
( ( ~ ( ~ ! [SX0: int] :
( ! [SX1: int] :
~ ( ord_less_eq_int @ ( 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 ) ) ) ) ) @ zero_zero_int )
| ( SX0 = zero_zero_int ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ ( 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 ) ) ) ) ) @ zero_zero_int )
| ( SX1 = zero_zero_int ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3674]) ).
thf(4256,plain,
( ( ! [SX0: int] :
( ( min
!= ( bit1 @ SX0 ) )
| ( min = SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3675]) ).
thf(4257,plain,
( ( ! [SX0: int] :
( ( min != SX0 )
| ( min
= ( bit1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3676]) ).
thf(4258,plain,
( ( ! [SX0: int,SX1: int] :
( ( SX0 != zero_zero_int )
| ( SX1 != zero_zero_int )
| ( ( plus_plus_int @ ( times_times_int @ SX0 @ SX0 ) @ ( times_times_int @ SX1 @ SX1 ) )
= zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3677]) ).
thf(4259,plain,
( ( ~ ( ~ ! [SX0: int] :
( ! [SX1: int] :
( ( plus_plus_int @ ( times_times_int @ SX0 @ SX0 ) @ ( times_times_int @ SX1 @ SX1 ) )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) )
| ~ ! [SX0: int,SX1: int] :
( ( ( plus_plus_int @ ( times_times_int @ SX0 @ SX0 ) @ ( times_times_int @ SX1 @ SX1 ) )
!= zero_zero_int )
| ( SX1 = zero_zero_int ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3678]) ).
thf(4260,plain,
( ( ! [SX0: int,SX1: int] :
( ( SX0 = SX1 )
| ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3679]) ).
thf(4261,plain,
( ( ~ ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3680]) ).
thf(4262,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_eq_int @ ( number_number_of_int @ SX0 ) @ zero_zero_int )
| ( ord_less_eq_int @ SX0 @ pls ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3681]) ).
thf(4263,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_eq_int @ SX0 @ pls )
| ( ord_less_eq_int @ ( number_number_of_int @ SX0 ) @ zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3682]) ).
thf(4264,plain,
! [SV446: nat] :
( ( ~ ! [SY1923: nat,SY1924: nat] :
( ~ ( ord_less_nat @ one_one_nat @ SY1924 )
| ~ ( ord_less_nat @ ( power_power_nat @ SY1924 @ SV446 ) @ ( power_power_nat @ SY1924 @ SY1923 ) )
| ( ord_less_nat @ SV446 @ SY1923 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3683]) ).
thf(4265,plain,
! [SV446: nat] :
( ( ~ ! [SY1925: nat,SY1926: nat] :
( ~ ( ord_less_nat @ one_one_nat @ SY1926 )
| ~ ( ord_less_nat @ SV446 @ SY1925 )
| ( ord_less_nat @ ( power_power_nat @ SY1926 @ SV446 ) @ ( power_power_nat @ SY1926 @ SY1925 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3683]) ).
thf(4266,plain,
( ( ! [SX0: nat,SX1: nat] :
( ( SX0 != one_one_nat )
| ( SX1 != one_one_nat )
| ( ( times_times_nat @ SX0 @ SX1 )
= one_one_nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3684]) ).
thf(4267,plain,
( ( ~ ( ~ ! [SX0: nat] :
( ! [SX1: nat] :
( ( times_times_nat @ SX0 @ SX1 )
!= one_one_nat )
| ( SX0 = one_one_nat ) )
| ~ ! [SX0: nat,SX1: nat] :
( ( ( times_times_nat @ SX0 @ SX1 )
!= one_one_nat )
| ( SX1 = one_one_nat ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3685]) ).
thf(4268,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: int] :
( ! [SX1: int] :
( ( times_times_int @ SX0 @ SX1 )
!= one_one_int )
| ( SX0 = one_one_int )
| ( SX0
= ( number_number_of_int @ min ) ) )
| ~ ! [SX0: int,SX1: int] :
( ( ( times_times_int @ SX0 @ SX1 )
!= one_one_int )
| ( SX0 = one_one_int )
| ( SX1
= ( number_number_of_int @ min ) ) ) )
| ~ ~ ( ~ ! [SX0: int,SX1: int] :
( ( ( times_times_int @ SX0 @ SX1 )
!= one_one_int )
| ( SX1 = one_one_int )
| ( SX0
= ( number_number_of_int @ min ) ) )
| ~ ! [SX0: int,SX1: int] :
( ( ( times_times_int @ SX0 @ SX1 )
!= one_one_int )
| ( SX1 = one_one_int )
| ( SX1
= ( number_number_of_int @ min ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3686]) ).
thf(4269,plain,
( ( ~ ( ~ ! [SX0: int,SX1: int] :
( ( SX0 != one_one_int )
| ( SX1 != one_one_int )
| ( ( times_times_int @ SX0 @ SX1 )
= one_one_int ) )
| ~ ! [SX0: int,SX1: int] :
( ( SX0
!= ( number_number_of_int @ min ) )
| ( SX1
!= ( number_number_of_int @ min ) )
| ( ( times_times_int @ SX0 @ SX1 )
= one_one_int ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3687]) ).
thf(4270,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_int @ SX0 @ ( bit1 @ pls ) )
| ( ord_less_real @ ( number267125858f_real @ SX0 ) @ one_one_real ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3688]) ).
thf(4271,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_real @ ( number267125858f_real @ SX0 ) @ one_one_real )
| ( ord_less_int @ SX0 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3689]) ).
thf(4272,plain,
( ( ! [SX0: int,SX1: int] :
( ( ( number_number_of_int @ SX0 )
!= SX1 )
| ( SX1
= ( number_number_of_int @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3690]) ).
thf(4273,plain,
( ( ! [SX0: int,SX1: int] :
( ( SX1
!= ( number_number_of_int @ SX0 ) )
| ( ( number_number_of_int @ SX0 )
= SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3691]) ).
thf(4274,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_int @ SX0 @ ( plus_plus_int @ SX1 @ one_one_int ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3692]) ).
thf(4275,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ ( plus_plus_int @ SX1 @ one_one_int ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3693]) ).
thf(4276,plain,
( ( ! [SX0: real,SX1: 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(extcnf_not_neg,[status(thm)],[3694]) ).
thf(4277,plain,
( ( ~ ( ~ ! [SX0: real] :
( ! [SX1: real] :
( ( plus_plus_real @ ( times_times_real @ SX0 @ SX0 ) @ ( times_times_real @ SX1 @ SX1 ) )
!= zero_zero_real )
| ( SX0 = zero_zero_real ) )
| ~ ! [SX0: real,SX1: real] :
( ( ( plus_plus_real @ ( times_times_real @ SX0 @ SX0 ) @ ( times_times_real @ SX1 @ SX1 ) )
!= zero_zero_real )
| ( SX1 = zero_zero_real ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3695]) ).
thf(4278,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_eq_int @ ( bit1 @ SX0 ) @ pls )
| ( ord_less_int @ SX0 @ pls ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3696]) ).
thf(4279,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_int @ SX0 @ pls )
| ( ord_less_eq_int @ ( bit1 @ SX0 ) @ pls ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3697]) ).
thf(4280,plain,
! [SV447: nat] :
( ( ~ ! [SY1927: nat,SY1928: real] :
( ~ ( ord_less_real @ one_one_real @ SY1928 )
| ~ ( ord_less_nat @ SV447 @ SY1927 )
| ( ord_less_real @ ( power_power_real @ SY1928 @ SV447 ) @ ( power_power_real @ SY1928 @ SY1927 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3698]) ).
thf(4281,plain,
! [SV447: nat] :
( ( ~ ! [SY1929: nat,SY1930: real] :
( ~ ( ord_less_real @ one_one_real @ SY1930 )
| ~ ( ord_less_real @ ( power_power_real @ SY1930 @ SV447 ) @ ( power_power_real @ SY1930 @ SY1929 ) )
| ( ord_less_nat @ SV447 @ SY1929 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3698]) ).
thf(4282,plain,
( ( ! [SX0: int] :
( ( ( bit0 @ SX0 )
!= pls )
| ( SX0 = pls ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3699]) ).
thf(4283,plain,
( ( ! [SX0: int] :
( ( SX0 != pls )
| ( ( bit0 @ SX0 )
= pls ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3700]) ).
thf(4284,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ SX0 @ SX0 ) @ ( times_times_int @ SX1 @ SX1 ) ) )
| ( SX0 != zero_zero_int )
| ( SX1 != zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3701]) ).
thf(4285,plain,
( ( ~ ( ~ ! [SX0: int] :
( ( SX0 = zero_zero_int )
| ! [SX1: int] : ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ SX0 @ SX0 ) @ ( times_times_int @ SX1 @ SX1 ) ) ) )
| ~ ! [SX0: int,SX1: int] :
( ( SX1 = zero_zero_int )
| ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ SX0 @ SX0 ) @ ( times_times_int @ SX1 @ SX1 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3702]) ).
thf(4286,plain,
( ( ! [SX0: int,SX1: nat] :
( ( ( number_number_of_nat @ SX0 )
!= SX1 )
| ( SX1
= ( number_number_of_nat @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3703]) ).
thf(4287,plain,
( ( ! [SX0: int,SX1: nat] :
( ( SX1
!= ( number_number_of_nat @ SX0 ) )
| ( ( number_number_of_nat @ SX0 )
= SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3704]) ).
thf(4288,plain,
( ( ! [SX0: real] :
( ( SX0 != zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ ( times_times_real @ SX0 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3705]) ).
thf(4289,plain,
( ( ! [SX0: real] :
( ( ord_less_real @ zero_zero_real @ ( times_times_real @ SX0 @ SX0 ) )
| ( SX0 = zero_zero_real ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3706]) ).
thf(4290,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_int @ ( number_number_of_int @ SX0 ) @ one_one_int )
| ( ord_less_int @ SX0 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3707]) ).
thf(4291,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_int @ SX0 @ ( bit1 @ pls ) )
| ( ord_less_int @ ( number_number_of_int @ SX0 ) @ one_one_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3708]) ).
thf(4292,plain,
! [SV448: real] :
( ( ~ ! [SY1931: real,SY1932: real] :
( ( SY1932 = zero_zero_real )
| ( ( times_times_real @ SY1932 @ SV448 )
!= ( times_times_real @ SY1932 @ SY1931 ) )
| ( SV448 = SY1931 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3709]) ).
thf(4293,plain,
! [SV448: real] :
( ( ~ ! [SY1933: real,SY1934: real] :
( ( SY1934 = zero_zero_real )
| ( SV448 != SY1933 )
| ( ( times_times_real @ SY1934 @ SV448 )
= ( times_times_real @ SY1934 @ SY1933 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3709]) ).
thf(4294,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3710]) ).
thf(4295,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3711]) ).
thf(4296,plain,
( ( ! [SX0: int] :
( ( pls
!= ( bit0 @ SX0 ) )
| ( pls = SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3712]) ).
thf(4297,plain,
( ( ! [SX0: int] :
( ( pls != SX0 )
| ( pls
= ( bit0 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3713]) ).
thf(4298,plain,
( ( ~ ( ~ ! [SX0: int,SX1: int] :
( ( ord_less_int @ SX0 @ SX1 )
| ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_nat @ ( number_number_of_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( 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(extcnf_not_neg,[status(thm)],[3714]) ).
thf(4299,plain,
( ( ~ ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_nat @ ( number_number_of_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) )
| ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ pls @ SX1 ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_nat @ ( number_number_of_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3715]) ).
thf(4300,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3716]) ).
thf(4301,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3717]) ).
thf(4302,plain,
! [SV787: int,SV449: int,SV981: int] :
( ( ~ ( ~ ! [SY2385: int,SY2386: int] :
( ~ ( zcong @ SV981 @ SY2385 @ SY2386 )
| ~ ( zcong @ SV449 @ ( times_times_int @ SV981 @ SV787 ) @ SY2386 )
| ( zcong @ SV449 @ ( times_times_int @ SY2385 @ SV787 ) @ SY2386 ) )
| ~ ! [SY2387: int,SY2388: int] :
( ~ ( zcong @ SV981 @ SY2387 @ SY2388 )
| ~ ( zcong @ SV449 @ ( times_times_int @ SY2387 @ SV787 ) @ SY2388 )
| ( zcong @ SV449 @ ( times_times_int @ SV981 @ SV787 ) @ SY2388 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3718]) ).
thf(4303,plain,
( ( ! [SX0: real,SX1: nat] :
( ( SX1 != zero_zero_nat )
| ( ( power_power_real @ SX0 @ SX1 )
= one_one_real ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3719]) ).
thf(4304,plain,
( ( ! [SX0: real,SX1: nat] :
( ( SX1 = zero_zero_nat )
| ( ( power_power_real @ SX0 @ SX1 )
= ( times_times_real @ SX0 @ ( power_power_real @ SX0 @ ( minus_minus_nat @ SX1 @ one_one_nat ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3720]) ).
thf(4305,plain,
! [SV788: int,SV450: int] :
( ( ~ ~ ( ~ ! [SY2290: int,SY2291: int] :
( ( ( plus_plus_int @ ( times_times_int @ SY2290 @ SV450 ) @ ( times_times_int @ SY2291 @ SV788 ) )
= ( plus_plus_int @ ( times_times_int @ SY2290 @ SV788 ) @ ( times_times_int @ SY2291 @ SV450 ) ) )
| ( SY2290 != SY2291 ) )
| ~ ( ! [SY2292: int,SY2293: int] :
( ( plus_plus_int @ ( times_times_int @ SY2292 @ SV450 ) @ ( times_times_int @ SY2293 @ SV788 ) )
= ( plus_plus_int @ ( times_times_int @ SY2292 @ SV788 ) @ ( times_times_int @ SY2293 @ SV450 ) ) )
| ( SV450 != SV788 ) ) )
| ~ ! [SY2294: int,SY2295: int] :
( ( SY2294 = SY2295 )
| ( SV450 = SV788 )
| ( ( plus_plus_int @ ( times_times_int @ SY2294 @ SV450 ) @ ( times_times_int @ SY2295 @ SV788 ) )
!= ( plus_plus_int @ ( times_times_int @ SY2294 @ SV788 ) @ ( times_times_int @ SY2295 @ SV450 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3721]) ).
thf(4306,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3722]) ).
thf(4307,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3723]) ).
thf(4308,plain,
( ( ! [SX0: int] :
( ( SX0 = zero_zero_int )
| ( ord_less_int @ zero_zero_int @ ( power_power_int @ SX0 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3724]) ).
thf(4309,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_int @ zero_zero_int @ ( power_power_int @ SX0 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ( SX0 != zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3725]) ).
thf(4310,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_int @ SX0 @ pls )
| ( ord_less_real @ ( number267125858f_real @ SX0 ) @ zero_zero_real ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3726]) ).
thf(4311,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_real @ ( number267125858f_real @ SX0 ) @ zero_zero_real )
| ( ord_less_int @ SX0 @ pls ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3727]) ).
thf(4312,plain,
( ( ! [SX0: real,SX1: 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(extcnf_not_neg,[status(thm)],[3728]) ).
thf(4313,plain,
( ( ~ ( ~ ! [SX0: real] :
( ! [SX1: real] :
( ( plus_plus_real @ ( times_times_real @ SX0 @ SX0 ) @ ( times_times_real @ SX1 @ SX1 ) )
!= zero_zero_real )
| ( SX0 = zero_zero_real ) )
| ~ ! [SX0: real,SX1: real] :
( ( ( plus_plus_real @ ( times_times_real @ SX0 @ SX0 ) @ ( times_times_real @ SX1 @ SX1 ) )
!= zero_zero_real )
| ( SX1 = zero_zero_real ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3729]) ).
thf(4314,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_eq_int @ ( bit1 @ pls ) @ SX0 )
| ( ord_less_eq_real @ one_one_real @ ( number267125858f_real @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3730]) ).
thf(4315,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_eq_real @ one_one_real @ ( number267125858f_real @ SX0 ) )
| ( ord_less_eq_int @ ( bit1 @ pls ) @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3731]) ).
thf(4316,plain,
! [SV789: int,SV451: int,SV982: int] :
( ( ~ ( ~ ! [SY2389: int,SY2390: int] :
( ~ ( zcong @ SV982 @ SY2389 @ SY2390 )
| ~ ( zcong @ SV451 @ ( times_times_int @ SV789 @ SV982 ) @ SY2390 )
| ( zcong @ SV451 @ ( times_times_int @ SV789 @ SY2389 ) @ SY2390 ) )
| ~ ! [SY2391: int,SY2392: int] :
( ~ ( zcong @ SV982 @ SY2391 @ SY2392 )
| ~ ( zcong @ SV451 @ ( times_times_int @ SV789 @ SY2391 ) @ SY2392 )
| ( zcong @ SV451 @ ( times_times_int @ SV789 @ SV982 ) @ SY2392 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3732]) ).
thf(4317,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_eq_int @ ( bit1 @ SX0 ) @ min )
| ( ord_less_eq_int @ SX0 @ min ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3733]) ).
thf(4318,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_eq_int @ SX0 @ min )
| ( ord_less_eq_int @ ( bit1 @ SX0 ) @ min ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3734]) ).
thf(4319,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3735]) ).
thf(4320,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3736]) ).
thf(4321,plain,
( ( ! [SX0: int,SX1: int] :
( ( SX0 != SX1 )
| ( zcong @ SX0 @ SX1 @ zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3737]) ).
thf(4322,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( zcong @ SX0 @ SX1 @ zero_zero_int )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3738]) ).
thf(4323,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3739]) ).
thf(4324,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3740]) ).
thf(4325,plain,
! [SV790: nat,SV452: nat] :
( ( ~ ! [SY2301: nat,SY2302: nat] :
( ( ( plus_plus_nat @ ( times_times_nat @ SV452 @ SV790 ) @ ( times_times_nat @ SY2301 @ SY2302 ) )
!= ( plus_plus_nat @ ( times_times_nat @ SV452 @ SY2302 ) @ ( times_times_nat @ SY2301 @ SV790 ) ) )
| ( SV452 = SY2301 )
| ( SV790 = SY2302 ) )
| ~ ~ ( ~ ! [SY2303: nat] :
( ( SV452 != SY2303 )
| ! [SY2304: nat] :
( ( plus_plus_nat @ ( times_times_nat @ SV452 @ SV790 ) @ ( times_times_nat @ SY2303 @ SY2304 ) )
= ( plus_plus_nat @ ( times_times_nat @ SV452 @ SY2304 ) @ ( times_times_nat @ SY2303 @ SV790 ) ) ) )
| ~ ! [SY2305: nat,SY2306: nat] :
( ( SV790 != SY2306 )
| ( ( plus_plus_nat @ ( times_times_nat @ SV452 @ SV790 ) @ ( times_times_nat @ SY2305 @ SY2306 ) )
= ( plus_plus_nat @ ( times_times_nat @ SV452 @ SY2306 ) @ ( times_times_nat @ SY2305 @ SV790 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3741]) ).
thf(4326,plain,
( ( ! [SX0: real,SX1: nat] :
( ( SX1 = zero_zero_nat )
| ( SX0 != zero_zero_real )
| ( ( power_power_real @ SX0 @ SX1 )
= zero_zero_real ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3742]) ).
thf(4327,plain,
( ( ~ ( ~ ! [SX0: real,SX1: nat] :
( ( ( power_power_real @ SX0 @ SX1 )
!= zero_zero_real )
| ( SX1 != zero_zero_nat ) )
| ~ ! [SX0: real] :
( ! [SX1: nat] :
( ( power_power_real @ SX0 @ SX1 )
!= zero_zero_real )
| ( SX0 = zero_zero_real ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3743]) ).
thf(4328,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SX0 @ SX1 ) )
| ( SX1 = zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3744]) ).
thf(4329,plain,
( ( ~ ( ~ ! [SX0: nat,SX1: nat] :
( ( SX1 != zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SX0 @ SX1 ) ) )
| ~ ! [SX0: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SX0 )
| ! [SX1: nat] : ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3745]) ).
thf(4330,plain,
! [SV791: int,SV453: int] :
( ( ~ ! [SY2307: int,SY2308: int] :
( ( ( plus_plus_int @ ( times_times_int @ SV453 @ SV791 ) @ ( times_times_int @ SY2307 @ SY2308 ) )
!= ( plus_plus_int @ ( times_times_int @ SV453 @ SY2308 ) @ ( times_times_int @ SY2307 @ SV791 ) ) )
| ( SV453 = SY2307 )
| ( SV791 = SY2308 ) )
| ~ ~ ( ~ ! [SY2309: int] :
( ( SV453 != SY2309 )
| ! [SY2310: int] :
( ( plus_plus_int @ ( times_times_int @ SV453 @ SV791 ) @ ( times_times_int @ SY2309 @ SY2310 ) )
= ( plus_plus_int @ ( times_times_int @ SV453 @ SY2310 ) @ ( times_times_int @ SY2309 @ SV791 ) ) ) )
| ~ ! [SY2311: int,SY2312: int] :
( ( SV791 != SY2312 )
| ( ( plus_plus_int @ ( times_times_int @ SV453 @ SV791 ) @ ( times_times_int @ SY2311 @ SY2312 ) )
= ( plus_plus_int @ ( times_times_int @ SV453 @ SY2312 ) @ ( times_times_int @ SY2311 @ SV791 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3746]) ).
thf(4331,plain,
( ( ! [SX0: nat,SX1: nat] :
( ( SX1 != zero_zero_nat )
| ( ( power_power_nat @ SX0 @ SX1 )
= one_one_nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3747]) ).
thf(4332,plain,
( ( ! [SX0: nat,SX1: 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(extcnf_not_neg,[status(thm)],[3748]) ).
thf(4333,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ zero_zero_int @ SX1 )
| ( SX1 != one_one_int )
| ( SX0 != one_one_int )
| ( ( times_times_int @ SX1 @ SX0 )
= one_one_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3749]) ).
thf(4334,plain,
( ( ~ ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ zero_zero_int @ SX1 )
| ( ( times_times_int @ SX1 @ SX0 )
!= one_one_int )
| ( SX1 = one_one_int ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ zero_zero_int @ SX1 )
| ( ( times_times_int @ SX1 @ SX0 )
!= one_one_int )
| ( SX0 = one_one_int ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3750]) ).
thf(4335,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ ( plus_plus_int @ SX0 @ one_one_int ) @ SX1 )
| ( ord_less_int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3751]) ).
thf(4336,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( plus_plus_int @ SX0 @ one_one_int ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3752]) ).
thf(4337,plain,
( ( ! [SX0: int] :
( ( ( number_number_of_nat @ SX0 )
!= zero_zero_nat )
| ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ SX0 ) )
= one_one_nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3753]) ).
thf(4338,plain,
( ( ! [SX0: int] :
( ( ( number_number_of_nat @ SX0 )
= zero_zero_nat )
| ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ SX0 ) )
= zero_zero_nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3754]) ).
thf(4339,plain,
( ( ! [SX0: real,SX1: real] :
( ( SX0 = SX1 )
| ~ ( ord_less_eq_real @ SX0 @ SX1 )
| ( ord_less_real @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3755]) ).
thf(4340,plain,
( ( ~ ( ~ ! [SX0: real,SX1: real] :
( ~ ( ord_less_real @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: real,SX1: real] :
( ~ ( ord_less_real @ SX0 @ SX1 )
| ( ord_less_eq_real @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3756]) ).
thf(4341,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_real @ ( number267125858f_real @ SX0 ) @ ( number267125858f_real @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3757]) ).
thf(4342,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_real @ ( number267125858f_real @ SX0 ) @ ( number267125858f_real @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3758]) ).
thf(4343,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ ( number_number_of_int @ SX0 ) @ ( number_number_of_int @ SX1 ) )
| ~ ( ord_less_int @ ( number_number_of_int @ SX1 ) @ ( number_number_of_int @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3759]) ).
thf(4344,plain,
( ( ! [SX0: int,SX1: int] :
( ( ord_less_int @ ( number_number_of_int @ SX1 ) @ ( number_number_of_int @ SX0 ) )
| ( ord_less_eq_int @ ( number_number_of_int @ SX0 ) @ ( number_number_of_int @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3760]) ).
thf(4345,plain,
( ( ! [SX0: int] :
( ( ( plus_plus_int @ SX0 @ SX0 )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3761]) ).
thf(4346,plain,
( ( ! [SX0: int] :
( ( SX0 != zero_zero_int )
| ( ( plus_plus_int @ SX0 @ SX0 )
= zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3762]) ).
thf(4347,plain,
( ( ! [SX0: nat,SX1: int] :
( ~ ( 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 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3763]) ).
thf(4348,plain,
( ( ~ ( ~ ! [SX0: nat,SX1: int] :
( ( ( number_number_of_nat @ SX1 )
!= zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SX0 @ ( number_number_of_nat @ SX1 ) ) ) )
| ~ ! [SX0: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SX0 )
| ! [SX1: int] : ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SX0 @ ( number_number_of_nat @ SX1 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3764]) ).
thf(4349,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_eq_int @ SX0 @ ( bit1 @ pls ) )
| ( ord_less_eq_real @ ( number267125858f_real @ SX0 ) @ one_one_real ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3765]) ).
thf(4350,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_eq_real @ ( number267125858f_real @ SX0 ) @ one_one_real )
| ( ord_less_eq_int @ SX0 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3766]) ).
thf(4351,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX1 @ pls )
| ( ( times_times_nat @ ( number_number_of_nat @ SX1 ) @ ( number_number_of_nat @ SX0 ) )
= zero_zero_nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3767]) ).
thf(4352,plain,
( ( ! [SX0: int,SX1: int] :
( ( 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(extcnf_not_neg,[status(thm)],[3768]) ).
thf(4353,plain,
( ( ! [SX0: real] :
( ( SX0 = zero_zero_real )
| ( ord_less_real @ zero_zero_real @ ( power_power_real @ SX0 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3769]) ).
thf(4354,plain,
( ( ! [SX0: real] :
( ~ ( ord_less_real @ zero_zero_real @ ( power_power_real @ SX0 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ( SX0 != zero_zero_real ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3770]) ).
thf(4355,plain,
( ( ! [SX0: int] :
( ~ ( ~ ~ ( ~ ( dvd_dvd_int @ ( sK3_M_9 @ SX0 ) @ SX0 )
| ~ ( ord_less_eq_int @ zero_zero_int @ ( sK3_M_9 @ SX0 ) ) )
| ~ ~ ( ~ ( ( ( sK3_M_9 @ SX0 )
!= one_one_int ) )
| ~ ( ( ( sK3_M_9 @ SX0 )
!= SX0 ) ) ) )
| ~ ( ord_less_int @ one_one_int @ SX0 )
| ( zprime @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3771]) ).
thf(4356,plain,
( ( ~ ( ~ ! [SX0: int] :
( ~ ( zprime @ SX0 )
| ! [SX1: int] :
( ~ ( dvd_dvd_int @ SX1 @ SX0 )
| ~ ( ord_less_eq_int @ zero_zero_int @ SX1 )
| ( SX1 = one_one_int )
| ( SX1 = SX0 ) ) )
| ~ ! [SX0: int] :
( ~ ( zprime @ SX0 )
| ( ord_less_int @ one_one_int @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3772]) ).
thf(4357,plain,
! [SV454: int] :
( ( ~ ! [SY1968: nat,SY1969: int] :
( ~ ( ord_less_int @ SY1969 @ pls )
| ( ( times_times_nat @ ( number_number_of_nat @ SY1969 ) @ ( times_times_nat @ ( number_number_of_nat @ SV454 ) @ SY1968 ) )
= zero_zero_nat ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3773]) ).
thf(4358,plain,
! [SV454: int] :
( ( ~ ! [SY1970: nat,SY1971: int] :
( ( ord_less_int @ SY1971 @ pls )
| ( ( times_times_nat @ ( number_number_of_nat @ SY1971 ) @ ( times_times_nat @ ( number_number_of_nat @ SV454 ) @ SY1970 ) )
= ( times_times_nat @ ( number_number_of_nat @ ( times_times_int @ SY1971 @ SV454 ) ) @ SY1970 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3773]) ).
thf(4359,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( zcong @ SX0 @ zero_zero_int @ SX1 )
| ( ( legendre @ SX0 @ SX1 )
= zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3774]) ).
thf(4360,plain,
( ( ~ ( ~ ! [SX0: int,SX1: int] :
( ( zcong @ SX0 @ zero_zero_int @ SX1 )
| ~ ( quadRes @ SX1 @ SX0 )
| ( ( legendre @ SX0 @ SX1 )
= one_one_int ) )
| ~ ! [SX0: int,SX1: int] :
( ( zcong @ SX0 @ zero_zero_int @ SX1 )
| ( quadRes @ SX1 @ SX0 )
| ( ( legendre @ SX0 @ SX1 )
= ( number_number_of_int @ min ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3775]) ).
thf(4361,plain,
( ( ! [SX0: nat] :
( ( SX0 != zero_zero_nat )
| ( ( power_power_int @ zero_zero_int @ SX0 )
= one_one_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3776]) ).
thf(4362,plain,
( ( ! [SX0: nat] :
( ( SX0 = zero_zero_nat )
| ( ( power_power_int @ zero_zero_int @ SX0 )
= zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3777]) ).
thf(4363,plain,
! [SV455: real,SV792: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV792 ) )
= $true )
| ( ( ~ ( ord_less_real @ zero_zero_real @ SV455 )
| ~ ( ~ ! [SY2313: real] :
( ( ( power_power_real @ SY2313 @ SV792 )
!= SV455 )
| ~ ( ord_less_real @ zero_zero_real @ SY2313 )
| ( SY2313
= ( sK1_X_1 @ SV792 @ SV455 ) ) )
| ~ ~ ( ( ( power_power_real @ ( sK1_X_1 @ SV792 @ SV455 ) @ SV792 )
!= SV455 )
| ~ ( ord_less_real @ zero_zero_real @ ( sK1_X_1 @ SV792 @ SV455 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3778]) ).
thf(4364,plain,
( ( ! [SX0: int] :
( ( zero_zero_nat
!= ( number_number_of_nat @ SX0 ) )
| ( ord_less_eq_int @ SX0 @ pls ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3779]) ).
thf(4365,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_eq_int @ SX0 @ pls )
| ( zero_zero_nat
= ( number_number_of_nat @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3780]) ).
thf(4366,plain,
( ( ~ ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_eq_nat @ ( number_number_of_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ SX0 @ pls )
| ! [SX1: int] : ( ord_less_eq_nat @ ( number_number_of_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3781]) ).
thf(4367,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( 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 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3782]) ).
thf(4368,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_int @ ( number_number_of_int @ SX0 ) @ zero_zero_int )
| ( ord_less_int @ SX0 @ pls ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3783]) ).
thf(4369,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_int @ SX0 @ pls )
| ( ord_less_int @ ( number_number_of_int @ SX0 ) @ zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3784]) ).
thf(4370,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_eq_int @ one_one_int @ ( number_number_of_int @ SX0 ) )
| ( ord_less_eq_int @ ( bit1 @ pls ) @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3785]) ).
thf(4371,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_eq_int @ ( bit1 @ pls ) @ SX0 )
| ( ord_less_eq_int @ one_one_int @ ( number_number_of_int @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3786]) ).
thf(4372,plain,
( ( ! [SX0: int,SX1: real] :
( ( ( number267125858f_real @ SX0 )
!= SX1 )
| ( SX1
= ( number267125858f_real @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3787]) ).
thf(4373,plain,
( ( ! [SX0: int,SX1: real] :
( ( SX1
!= ( number267125858f_real @ SX0 ) )
| ( ( number267125858f_real @ SX0 )
= SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3788]) ).
thf(4374,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ SX0 ) @ SX0 ) @ zero_zero_int )
| ( ord_less_int @ SX0 @ zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3789]) ).
thf(4375,plain,
( ( ! [SX0: 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(extcnf_not_neg,[status(thm)],[3790]) ).
thf(4376,plain,
! [SV456: int] :
( ( ~ ! [SY1974: int,SY1975: int] :
( ~ ( zcong @ SV456 @ SY1974 @ SY1975 )
| ( zcong @ SY1974 @ SV456 @ SY1975 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3791]) ).
thf(4377,plain,
! [SV456: int] :
( ( ~ ! [SY1976: int,SY1977: int] :
( ~ ( zcong @ SY1976 @ SV456 @ SY1977 )
| ( zcong @ SV456 @ SY1976 @ SY1977 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3791]) ).
thf(4378,plain,
! [SV457: int,SV983: int,SV793: int] :
( ( ~ ( ~ ! [SY2393: int,SY2394: int] :
( ~ ( dvd_dvd_int @ SY2393 @ SY2394 )
| ~ ( dvd_dvd_int @ SY2393 @ ( plus_plus_int @ SV793 @ SV983 ) )
| ( dvd_dvd_int @ SY2393 @ ( plus_plus_int @ ( plus_plus_int @ SV793 @ ( times_times_int @ SV457 @ SY2394 ) ) @ SV983 ) ) )
| ~ ! [SY2395: int,SY2396: int] :
( ~ ( dvd_dvd_int @ SY2395 @ SY2396 )
| ~ ( dvd_dvd_int @ SY2395 @ ( plus_plus_int @ ( plus_plus_int @ SV793 @ ( times_times_int @ SV457 @ SY2396 ) ) @ SV983 ) )
| ( dvd_dvd_int @ SY2395 @ ( plus_plus_int @ SV793 @ SV983 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3792]) ).
thf(4379,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_int @ ( bit1 @ pls ) @ SX0 )
| ( ord_less_real @ one_one_real @ ( number267125858f_real @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3793]) ).
thf(4380,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_real @ one_one_real @ ( number267125858f_real @ SX0 ) )
| ( ord_less_int @ ( bit1 @ pls ) @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3794]) ).
thf(4381,plain,
( ( ! [SX0: real,SX1: real] :
( ( SX0
!= ( plus_plus_real @ SX0 @ SX1 ) )
| ( SX1 = zero_zero_real ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3795]) ).
thf(4382,plain,
( ( ! [SX0: real,SX1: real] :
( ( SX1 != zero_zero_real )
| ( SX0
= ( plus_plus_real @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3796]) ).
thf(4383,plain,
! [SV458: int] :
( ( ~ ! [SY1984: int,SY1985: int] :
( ! [SY1986: int] :
( SY1984
!= ( plus_plus_int @ SV458 @ ( times_times_int @ SY1985 @ SY1986 ) ) )
| ( zcong @ SV458 @ SY1984 @ SY1985 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3797]) ).
thf(4384,plain,
! [SV458: int] :
( ( ~ ! [SY1987: int,SY1988: int] :
( ~ ( zcong @ SV458 @ SY1987 @ SY1988 )
| ( SY1987
= ( plus_plus_int @ SV458 @ ( times_times_int @ SY1988 @ ( sK6_K_1 @ SY1988 @ SY1987 @ SV458 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3797]) ).
thf(4385,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_eq_int @ pls @ ( bit0 @ SX0 ) )
| ( ord_less_eq_int @ pls @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3798]) ).
thf(4386,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_eq_int @ pls @ SX0 )
| ( ord_less_eq_int @ pls @ ( bit0 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3799]) ).
thf(4387,plain,
! [SV459: nat] :
( ( ~ ! [SY1989: nat,SY1990: nat] :
( ~ ( ord_less_nat @ one_one_nat @ SY1990 )
| ( ( power_power_nat @ SY1990 @ SV459 )
!= ( power_power_nat @ SY1990 @ SY1989 ) )
| ( SV459 = SY1989 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3800]) ).
thf(4388,plain,
! [SV459: nat] :
( ( ~ ! [SY1991: nat,SY1992: nat] :
( ~ ( ord_less_nat @ one_one_nat @ SY1992 )
| ( SV459 != SY1991 )
| ( ( power_power_nat @ SY1992 @ SV459 )
= ( power_power_nat @ SY1992 @ SY1991 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3800]) ).
thf(4389,plain,
! [SV794: real,SV460: real] :
( ( ~ ! [SY2319: real,SY2320: real] :
( ( ( plus_plus_real @ ( times_times_real @ SV460 @ SV794 ) @ ( times_times_real @ SY2319 @ SY2320 ) )
!= ( plus_plus_real @ ( times_times_real @ SV460 @ SY2320 ) @ ( times_times_real @ SY2319 @ SV794 ) ) )
| ( SV460 = SY2319 )
| ( SV794 = SY2320 ) )
| ~ ~ ( ~ ! [SY2321: real] :
( ( SV460 != SY2321 )
| ! [SY2322: real] :
( ( plus_plus_real @ ( times_times_real @ SV460 @ SV794 ) @ ( times_times_real @ SY2321 @ SY2322 ) )
= ( plus_plus_real @ ( times_times_real @ SV460 @ SY2322 ) @ ( times_times_real @ SY2321 @ SV794 ) ) ) )
| ~ ! [SY2323: real,SY2324: real] :
( ( SV794 != SY2324 )
| ( ( plus_plus_real @ ( times_times_real @ SV460 @ SV794 ) @ ( times_times_real @ SY2323 @ SY2324 ) )
= ( plus_plus_real @ ( times_times_real @ SV460 @ SY2324 ) @ ( times_times_real @ SY2323 @ SV794 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3801]) ).
thf(4390,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_int @ ( bit1 @ SX0 ) @ pls )
| ( ord_less_int @ SX0 @ pls ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3802]) ).
thf(4391,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_int @ SX0 @ pls )
| ( ord_less_int @ ( bit1 @ SX0 ) @ pls ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3803]) ).
thf(4392,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ SX0 ) )
| ( ord_less_eq_int @ pls @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3804]) ).
thf(4393,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_eq_int @ pls @ SX0 )
| ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3805]) ).
thf(4394,plain,
! [SV461: nat] :
( ( ~ ! [SY2000: nat,SY2001: nat] :
( ~ ( dvd_dvd_nat @ ( times_times_nat @ SV461 @ SY2000 ) @ ( times_times_nat @ SY2001 @ SY2000 ) )
| ( SY2000 = zero_zero_nat )
| ( dvd_dvd_nat @ SV461 @ SY2001 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3806]) ).
thf(4395,plain,
! [SV461: nat] :
( ( ~ ~ ( ~ ! [SY2002: nat] :
( ( SY2002 != zero_zero_nat )
| ! [SY2003: nat] : ( dvd_dvd_nat @ ( times_times_nat @ SV461 @ SY2002 ) @ ( times_times_nat @ SY2003 @ SY2002 ) ) )
| ~ ! [SY2004: nat,SY2005: nat] :
( ~ ( dvd_dvd_nat @ SV461 @ SY2005 )
| ( dvd_dvd_nat @ ( times_times_nat @ SV461 @ SY2004 ) @ ( times_times_nat @ SY2005 @ SY2004 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3806]) ).
thf(4396,plain,
( ( ! [SX0: int,SX1: int] :
( ( ( number267125858f_real @ SX0 )
!= ( number267125858f_real @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3807]) ).
thf(4397,plain,
( ( ! [SX0: int,SX1: int] :
( ( SX0 != SX1 )
| ( ( number267125858f_real @ SX0 )
= ( number267125858f_real @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3808]) ).
thf(4398,plain,
( ( ! [SX0: nat] :
( ( SX0 != zero_zero_nat )
| ( ( power_power_nat @ zero_zero_nat @ SX0 )
= one_one_nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3809]) ).
thf(4399,plain,
( ( ! [SX0: nat] :
( ( SX0 = zero_zero_nat )
| ( ( power_power_nat @ zero_zero_nat @ SX0 )
= zero_zero_nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3810]) ).
thf(4400,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_eq_int @ ( bit0 @ SX0 ) @ min )
| ( ord_less_eq_int @ SX0 @ min ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3811]) ).
thf(4401,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_eq_int @ SX0 @ min )
| ( ord_less_eq_int @ ( bit0 @ SX0 ) @ min ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3812]) ).
thf(4402,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3813]) ).
thf(4403,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3814]) ).
thf(4404,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3815]) ).
thf(4405,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3816]) ).
thf(4406,plain,
( ( ! [SX0: nat,SX1: nat] :
( ( SX0
!= ( plus_plus_nat @ SX0 @ SX1 ) )
| ( SX1 = zero_zero_nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3817]) ).
thf(4407,plain,
( ( ! [SX0: nat,SX1: nat] :
( ( SX1 != zero_zero_nat )
| ( SX0
= ( plus_plus_nat @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3818]) ).
thf(4408,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3819]) ).
thf(4409,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3820]) ).
thf(4410,plain,
( ( ! [SX0: nat,SX1: nat] :
( ( SX1 = zero_zero_nat )
| ( SX0 != zero_zero_nat )
| ( ( power_power_nat @ SX0 @ SX1 )
= zero_zero_nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3821]) ).
thf(4411,plain,
( ( ~ ( ~ ! [SX0: nat,SX1: nat] :
( ( ( power_power_nat @ SX0 @ SX1 )
!= zero_zero_nat )
| ( SX1 != zero_zero_nat ) )
| ~ ! [SX0: nat] :
( ! [SX1: nat] :
( ( power_power_nat @ SX0 @ SX1 )
!= zero_zero_nat )
| ( SX0 = zero_zero_nat ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3822]) ).
thf(4412,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3823]) ).
thf(4413,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3824]) ).
thf(4414,plain,
( ( ! [SX0: int,SX1: int] :
( ( SX0
!= ( plus_plus_int @ SX0 @ SX1 ) )
| ( SX1 = zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3825]) ).
thf(4415,plain,
( ( ! [SX0: int,SX1: int] :
( ( SX1 != zero_zero_int )
| ( SX0
= ( plus_plus_int @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3826]) ).
thf(4416,plain,
( ( ! [SX0: int,SX1: int] :
( ! [SX2: int] :
~ ( zcong @ ( power_power_int @ SX2 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SX1 @ SX0 )
| ( quadRes @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3827]) ).
thf(4417,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( quadRes @ SX0 @ SX1 )
| ( zcong @ ( power_power_int @ ( sK5_Y_1 @ SX1 @ SX0 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3828]) ).
thf(4418,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_int @ one_one_int @ ( number_number_of_int @ SX0 ) )
| ( ord_less_int @ ( bit1 @ pls ) @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3829]) ).
thf(4419,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_int @ ( bit1 @ pls ) @ SX0 )
| ( ord_less_int @ one_one_int @ ( number_number_of_int @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3830]) ).
thf(4420,plain,
! [SV462: nat] :
( ( ~ ! [SY2006: nat,SY2007: real] :
( ~ ( ord_less_real @ one_one_real @ SY2007 )
| ( ( power_power_real @ SY2007 @ SV462 )
!= ( power_power_real @ SY2007 @ SY2006 ) )
| ( SV462 = SY2006 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3831]) ).
thf(4421,plain,
! [SV462: nat] :
( ( ~ ! [SY2008: nat,SY2009: real] :
( ~ ( ord_less_real @ one_one_real @ SY2009 )
| ( SV462 != SY2008 )
| ( ( power_power_real @ SY2009 @ SV462 )
= ( power_power_real @ SY2009 @ SY2008 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3831]) ).
thf(4422,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX1 @ pls )
| ( ( plus_plus_nat @ ( number_number_of_nat @ SX1 ) @ ( number_number_of_nat @ SX0 ) )
= ( number_number_of_nat @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3832]) ).
thf(4423,plain,
( ( ~ ( ~ ! [SX0: int,SX1: int] :
( ( 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 ) ) )
| ~ ! [SX0: int,SX1: int] :
( ( 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 @ ( plus_plus_int @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3833]) ).
thf(4424,plain,
! [SV463: real] :
( ( ~ ! [SY2010: real,SY2011: real] :
( ( SY2011 = zero_zero_real )
| ( ( times_times_real @ SV463 @ SY2011 )
!= ( times_times_real @ SY2010 @ SY2011 ) )
| ( SV463 = SY2010 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3834]) ).
thf(4425,plain,
! [SV463: real] :
( ( ~ ! [SY2012: real,SY2013: real] :
( ( SY2013 = zero_zero_real )
| ( SV463 != SY2012 )
| ( ( times_times_real @ SV463 @ SY2013 )
= ( times_times_real @ SY2012 @ SY2013 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3834]) ).
thf(4426,plain,
! [SV464: real] :
( ( ~ ! [SY2014: real,SY2015: real] :
( ~ ( ord_less_real @ zero_zero_real @ SY2015 )
| ~ ( ord_less_real @ ( times_times_real @ SV464 @ SY2015 ) @ ( times_times_real @ SY2014 @ SY2015 ) )
| ( ord_less_real @ SV464 @ SY2014 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3835]) ).
thf(4427,plain,
! [SV464: real] :
( ( ~ ! [SY2016: real,SY2017: real] :
( ~ ( ord_less_real @ zero_zero_real @ SY2017 )
| ~ ( ord_less_real @ SV464 @ SY2016 )
| ( ord_less_real @ ( times_times_real @ SV464 @ SY2017 ) @ ( times_times_real @ SY2016 @ SY2017 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3835]) ).
thf(4428,plain,
! [SV465: real] :
( ( ~ ! [SY2018: real,SY2019: real] :
( ~ ( ord_less_real @ zero_zero_real @ SY2019 )
| ~ ( ord_less_eq_real @ ( times_times_real @ SY2019 @ SV465 ) @ ( times_times_real @ SY2019 @ SY2018 ) )
| ( ord_less_eq_real @ SV465 @ SY2018 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3836]) ).
thf(4429,plain,
! [SV465: real] :
( ( ~ ! [SY2020: real,SY2021: real] :
( ~ ( ord_less_real @ zero_zero_real @ SY2021 )
| ~ ( ord_less_eq_real @ SV465 @ SY2020 )
| ( ord_less_eq_real @ ( times_times_real @ SY2021 @ SV465 ) @ ( times_times_real @ SY2021 @ SY2020 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3836]) ).
thf(4430,plain,
( ( ! [SX0: int,SX1: int] :
( ( ( bit0 @ SX0 )
!= ( bit0 @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3837]) ).
thf(4431,plain,
( ( ! [SX0: int,SX1: int] :
( ( SX0 != SX1 )
| ( ( bit0 @ SX0 )
= ( bit0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3838]) ).
thf(4432,plain,
( ( ! [SX0: int] :
( ( ( power_power_int @ SX0 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3839]) ).
thf(4433,plain,
( ( ! [SX0: int] :
( ( SX0 != zero_zero_int )
| ( ( power_power_int @ SX0 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3840]) ).
thf(4434,plain,
( ( ! [SX0: int,SX1: int] :
( ( SX0 != zero_zero_int )
| ( SX1 != zero_zero_int )
| ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SX0 @ SX0 ) @ ( times_times_int @ SX1 @ SX1 ) ) @ zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3841]) ).
thf(4435,plain,
( ( ~ ( ~ ! [SX0: int] :
( ! [SX1: int] :
~ ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SX0 @ SX0 ) @ ( times_times_int @ SX1 @ SX1 ) ) @ zero_zero_int )
| ( SX0 = zero_zero_int ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SX0 @ SX0 ) @ ( times_times_int @ SX1 @ SX1 ) ) @ zero_zero_int )
| ( SX1 = zero_zero_int ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3842]) ).
thf(4436,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_int @ pls @ ( bit0 @ SX0 ) )
| ( ord_less_int @ pls @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3843]) ).
thf(4437,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_int @ pls @ SX0 )
| ( ord_less_int @ pls @ ( bit0 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3844]) ).
thf(4438,plain,
( ( ! [SX0: real] :
( ~ ( ord_less_real @ ( plus_plus_real @ SX0 @ SX0 ) @ zero_zero_real )
| ( ord_less_real @ SX0 @ zero_zero_real ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3845]) ).
thf(4439,plain,
( ( ! [SX0: real] :
( ~ ( ord_less_real @ SX0 @ zero_zero_real )
| ( ord_less_real @ ( plus_plus_real @ SX0 @ SX0 ) @ zero_zero_real ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3846]) ).
thf(4440,plain,
( ( ! [SX0: int,SX1: nat] :
( ( SX1 = zero_zero_nat )
| ( SX0 != zero_zero_int )
| ( ( power_power_int @ SX0 @ SX1 )
= zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3847]) ).
thf(4441,plain,
( ( ~ ( ~ ! [SX0: int,SX1: nat] :
( ( ( power_power_int @ SX0 @ SX1 )
!= zero_zero_int )
| ( SX1 != zero_zero_nat ) )
| ~ ! [SX0: int] :
( ! [SX1: nat] :
( ( power_power_int @ SX0 @ SX1 )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3848]) ).
thf(4442,plain,
( ( ! [SX0: int,SX1: int] :
( ( ( number_number_of_int @ SX0 )
!= ( number_number_of_int @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3849]) ).
thf(4443,plain,
( ( ! [SX0: int,SX1: int] :
( ( SX0 != SX1 )
| ( ( number_number_of_int @ SX0 )
= ( number_number_of_int @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3850]) ).
thf(4444,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_eq_int @ SX0 @ min )
| ( ord_less_int @ ( bit0 @ SX0 ) @ min ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3851]) ).
thf(4445,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_int @ ( bit0 @ SX0 ) @ min )
| ( ord_less_eq_int @ SX0 @ min ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3852]) ).
thf(4446,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_nat @ ( number_number_of_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) )
| ~ ( ord_less_nat @ ( number_number_of_nat @ SX1 ) @ ( number_number_of_nat @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3853]) ).
thf(4447,plain,
( ( ! [SX0: int,SX1: int] :
( ( ord_less_nat @ ( number_number_of_nat @ SX1 ) @ ( number_number_of_nat @ SX0 ) )
| ( ord_less_eq_nat @ ( number_number_of_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3854]) ).
thf(4448,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_eq_int @ ( number_number_of_int @ SX0 ) @ one_one_int )
| ( ord_less_eq_int @ SX0 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3855]) ).
thf(4449,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_eq_int @ SX0 @ ( bit1 @ pls ) )
| ( ord_less_eq_int @ ( number_number_of_int @ SX0 ) @ one_one_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3856]) ).
thf(4450,plain,
! [SV466: int] :
( ( ~ ! [SY2022: int,SY2023: int] :
( ~ ( dvd_dvd_int @ SY2023 @ ( minus_minus_int @ SV466 @ SY2022 ) )
| ( zcong @ SV466 @ SY2022 @ SY2023 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3857]) ).
thf(4451,plain,
! [SV466: int] :
( ( ~ ! [SY2024: int,SY2025: int] :
( ~ ( zcong @ SV466 @ SY2024 @ SY2025 )
| ( dvd_dvd_int @ SY2025 @ ( minus_minus_int @ SV466 @ SY2024 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3857]) ).
thf(4452,plain,
( ( ! [SX0: int] :
( ( ( number_number_of_nat @ SX0 )
!= zero_zero_nat )
| ( ( power_power_real @ zero_zero_real @ ( number_number_of_nat @ SX0 ) )
= one_one_real ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3858]) ).
thf(4453,plain,
( ( ! [SX0: int] :
( ( ( number_number_of_nat @ SX0 )
= zero_zero_nat )
| ( ( power_power_real @ zero_zero_real @ ( number_number_of_nat @ SX0 ) )
= zero_zero_real ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3859]) ).
thf(4454,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_int @ ( bit0 @ SX0 ) @ zero_zero_int )
| ( ord_less_int @ SX0 @ zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3860]) ).
thf(4455,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_int @ SX0 @ zero_zero_int )
| ( ord_less_int @ ( bit0 @ SX0 ) @ zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3861]) ).
thf(4456,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_eq_int @ pls @ ( bit1 @ SX0 ) )
| ( ord_less_eq_int @ pls @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3862]) ).
thf(4457,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_eq_int @ pls @ SX0 )
| ( ord_less_eq_int @ pls @ ( bit1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3863]) ).
thf(4458,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ ( number_number_of_int @ SX0 ) @ ( number_number_of_int @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3864]) ).
thf(4459,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ ( number_number_of_int @ SX0 ) @ ( number_number_of_int @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3865]) ).
thf(4460,plain,
! [SV467: nat] :
( ( ~ ! [SY2026: nat,SY2027: int] :
( ~ ( ord_less_int @ one_one_int @ SY2027 )
| ( ( power_power_int @ SY2027 @ SV467 )
!= ( power_power_int @ SY2027 @ SY2026 ) )
| ( SV467 = SY2026 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3866]) ).
thf(4461,plain,
! [SV467: nat] :
( ( ~ ! [SY2028: nat,SY2029: int] :
( ~ ( ord_less_int @ one_one_int @ SY2029 )
| ( SV467 != SY2028 )
| ( ( power_power_int @ SY2029 @ SV467 )
= ( power_power_int @ SY2029 @ SY2028 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3866]) ).
thf(4462,plain,
! [SV6: int,SV796: int,SV470: int] :
( ( ( ~ ( ord_less_eq_int @ SV470 @ SV796 ) )
= $true )
| ( ( ord_less_eq_int @ ( plus_plus_int @ SV6 @ SV470 ) @ ( plus_plus_int @ SV6 @ SV796 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3869]) ).
thf(4463,plain,
! [SV472: int,SV8: int,SV984: int,SV797: int] :
( ( ~ ( ord_less_int @ SV797 @ SV984 )
| ~ ( ord_less_eq_int @ SV8 @ SV472 )
| ( ord_less_int @ ( plus_plus_int @ SV797 @ SV8 ) @ ( plus_plus_int @ SV984 @ SV472 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3870]) ).
thf(4464,plain,
! [SV477: int,SV16: int] :
( ( ( ord_less_int @ SV16 @ SV477 )
= $false )
| ( ( ord_less_eq_int @ ( plus_plus_int @ SV16 @ one_one_int ) @ SV477 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3873]) ).
thf(4465,plain,
! [SV17: int,SV478: int] :
( ( ( ord_less_eq_int @ pls @ SV478 )
= $false )
| ( ( ~ ( ord_less_eq_int @ pls @ SV17 )
| ( ( plus_plus_nat @ ( number_number_of_nat @ SV478 ) @ ( number_number_of_nat @ SV17 ) )
= ( number_number_of_nat @ ( plus_plus_int @ SV478 @ SV17 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3874]) ).
thf(4466,plain,
! [SV18: int,SV479: int] :
( ( ( ord_less_eq_int @ pls @ SV479 )
= $false )
| ( ( ~ ( ord_less_eq_int @ pls @ SV18 )
| ( ( plus_plus_int @ ( number_number_of_int @ SV479 ) @ ( number_number_of_int @ SV18 ) )
= ( number_number_of_int @ ( plus_plus_int @ SV479 @ SV18 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3875]) ).
thf(4467,plain,
! [SV480: int,SV20: int] :
( ( ( SV20 = SV480 )
= $true )
| ( ( ord_less_int @ SV20 @ SV480 )
= $true )
| ( ( ord_less_int @ SV480 @ SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3877]) ).
thf(4468,plain,
! [SV28: int,SV806: int,SV488: int] :
( ( ( ~ ( ord_less_int @ SV488 @ SV806 ) )
= $true )
| ( ( ~ ( ord_less_int @ zero_zero_int @ SV28 )
| ( ord_less_int @ ( times_times_int @ SV28 @ SV488 ) @ ( times_times_int @ SV28 @ SV806 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3884]) ).
thf(4469,plain,
! [SV489: int,SV29: int] :
( ( ( ( power_power_int @ SV29 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power_int @ SV489 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $false )
| ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV29 )
| ~ ( ord_less_eq_int @ zero_zero_int @ SV489 )
| ( SV29 = SV489 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3885]) ).
thf(4470,plain,
! [SV490: int,SV30: int] :
( ( ( ord_less_eq_int @ ( power_power_int @ SV30 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV490 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $false )
| ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV490 )
| ( ord_less_eq_int @ SV30 @ SV490 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3886]) ).
thf(4471,plain,
! [SV491: int,SV32: int] :
( ( ( ord_less_int @ ( power_power_int @ SV32 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV491 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $false )
| ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV491 )
| ( ord_less_int @ SV32 @ SV491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3887]) ).
thf(4472,plain,
! [SV50: int,SV807: int,SV498: int] :
( ( ( ~ ( ord_less_int @ SV498 @ SV807 ) )
= $true )
| ( ( ord_less_int @ ( plus_plus_int @ SV498 @ SV50 ) @ ( plus_plus_int @ SV807 @ SV50 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3891]) ).
thf(4473,plain,
! [SV85: int] :
( ( ( ~ ( ord_less_int @ SV85 @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $true )
| ( ( ( SV85 = zero_zero_int )
| ( SV85 = one_one_int ) )
= $true )
| ( ( ord_less_eq_int @ zero_zero_int @ SV85 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3894]) ).
thf(4474,plain,
! [SV510: int,SV88: int,SV810: int] :
( ( ( ~ ( ord_less_int @ zero_zero_int @ SV810 ) )
= $true )
| ( ( ( SV810
!= ( plus_plus_int @ SV88 @ ( times_times_int @ SV810 @ SV510 ) ) )
| ~ ( ord_less_int @ SV88 @ SV810 )
| ( ord_less_eq_int @ one_one_int @ SV510 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3895]) ).
thf(4475,plain,
! [SV511: int,SV89: int,SV811: int] :
( ( ( ~ ( ord_less_int @ zero_zero_int @ SV811 ) )
= $true )
| ( ( ( SV811
!= ( plus_plus_int @ SV89 @ ( times_times_int @ SV811 @ SV511 ) ) )
| ~ ( ord_less_eq_int @ zero_zero_int @ SV89 )
| ( ord_less_eq_int @ SV511 @ one_one_int ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3896]) ).
thf(4476,plain,
! [SV514: nat,SV92: int,SV812: int] :
( ( ( ~ ( zprime @ SV812 ) )
= $true )
| ( ( ~ ( dvd_dvd_int @ SV812 @ ( power_power_int @ SV92 @ SV514 ) )
| ( dvd_dvd_int @ SV812 @ SV92 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3897]) ).
thf(4477,plain,
! [SV95: int,SV517: int] :
( ( ( ord_less_int @ zero_zero_int @ SV517 )
= $false )
| ( ( ~ ( ord_less_int @ SV517 @ SV95 )
| ~ ( dvd_dvd_int @ SV95 @ SV517 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3900]) ).
thf(4478,plain,
! [SV96: int,SV518: int] :
( ( ( ord_less_eq_int @ zero_zero_int @ SV518 )
= $false )
| ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV96 )
| ~ ( dvd_dvd_int @ SV518 @ SV96 )
| ~ ( dvd_dvd_int @ SV96 @ SV518 )
| ( SV518 = SV96 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3901]) ).
thf(4479,plain,
! [SV815: int,SV519: int,SV97: int] :
( ( ( ~ ( dvd_dvd_int @ ( times_times_int @ SV97 @ SV519 ) @ ( times_times_int @ SV97 @ SV815 ) ) )
= $true )
| ( ( ( SV97 = zero_zero_int )
| ( dvd_dvd_int @ SV519 @ SV815 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3902]) ).
thf(4480,plain,
! [SV520: int,SV98: int] :
( ( ( dvd_dvd_int @ SV98 @ SV520 )
= $false )
| ( ( ~ ( ord_less_int @ zero_zero_int @ SV520 )
| ( ord_less_eq_int @ SV98 @ SV520 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3903]) ).
thf(4481,plain,
! [SV985: int,SV820: int,SV526: int,SV104: int] :
( ( ( plus_plus_int @ ( plus_plus_int @ SV104 @ SV526 ) @ ( plus_plus_int @ SV820 @ SV985 ) )
= ( plus_plus_int @ ( plus_plus_int @ SV104 @ SV820 ) @ ( plus_plus_int @ SV526 @ SV985 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3908]) ).
thf(4482,plain,
! [SV821: nat,SV111: int] :
( ( ( ord_less_eq_int @ ( power_power_int @ SV111 @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV821 ) ) @ zero_zero_int )
= $false )
| ( ( SV111 = zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3909]) ).
thf(4483,plain,
! [SV986: int,SV827: int,SV536: int,SV125: int] :
( ( ! [SY2397: int] :
( ( SY2397 = zero_zero_int )
| ( SV125 = SV536 )
| ( SV827 != SV986 )
| ( ( plus_plus_int @ SV827 @ ( times_times_int @ SY2397 @ SV125 ) )
!= ( plus_plus_int @ SV986 @ ( times_times_int @ SY2397 @ SV536 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3915]) ).
thf(4484,plain,
! [SV129: int,SV539: int] :
( ( ( ord_less_int @ zero_zero_int @ SV539 )
= $false )
| ( ( ~ ( ord_less_int @ zero_zero_int @ ( times_times_int @ SV539 @ SV129 ) )
| ( ord_less_int @ zero_zero_int @ SV129 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3916]) ).
thf(4485,plain,
! [SV130: int,SV540: int] :
( ( ( ord_less_eq_int @ zero_zero_int @ SV540 )
= $false )
| ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV130 )
| ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ SV540 @ SV130 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3917]) ).
thf(4486,plain,
! [SV131: int,SV541: int] :
( ( ( ord_less_eq_int @ zero_zero_int @ SV541 )
= $false )
| ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV131 )
| ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ SV541 @ SV131 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3918]) ).
thf(4487,plain,
! [SV132: nat,SV542: int] :
( ( ( ord_less_eq_int @ zero_zero_int @ SV542 )
= $false )
| ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ SV542 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3919]) ).
thf(4488,plain,
! [SV828: int,SV543: int,SV133: int] :
( ( ( ~ ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ SV133 @ SV543 ) @ SV828 ) ) )
= $true )
| ( ( ~ ( ord_less_int @ SV828 @ SV133 )
| ~ ( ord_less_int @ zero_zero_int @ SV133 )
| ( ord_less_eq_int @ zero_zero_int @ SV543 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3920]) ).
thf(4489,plain,
! [SV829: int,SV544: int,SV134: int] :
( ( ( ~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ SV134 @ SV544 ) @ SV829 ) @ zero_zero_int ) )
= $true )
| ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV829 )
| ~ ( ord_less_int @ zero_zero_int @ SV134 )
| ( ord_less_eq_int @ SV544 @ zero_zero_int ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3921]) ).
thf(4490,plain,
! [SV987: int,SV830: int,SV545: int,SV135: int] :
( ( ! [SY2398: int] :
( ~ ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SV135 @ SV545 ) @ SV830 ) @ ( plus_plus_int @ ( times_times_int @ SV135 @ SV987 ) @ SY2398 ) )
| ~ ( ord_less_eq_int @ zero_zero_int @ SV830 )
| ~ ( ord_less_int @ SV830 @ SV135 )
| ~ ( ord_less_int @ SY2398 @ SV135 )
| ( ord_less_eq_int @ SV545 @ SV987 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3922]) ).
thf(4491,plain,
! [SV988: int,SV831: int,SV546: int,SV136: int] :
( ( ! [SY2399: int,SY2400: int] :
( ( ( plus_plus_int @ ( times_times_int @ SV136 @ SV546 ) @ SV831 )
!= ( plus_plus_int @ ( times_times_int @ SV988 @ SY2399 ) @ SY2400 ) )
| ~ ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ SV988 @ SY2399 ) @ SY2400 ) )
| ~ ( ord_less_int @ SY2400 @ SV988 )
| ~ ( ord_less_eq_int @ zero_zero_int @ SV831 )
| ~ ( ord_less_int @ zero_zero_int @ SV988 )
| ~ ( ord_less_eq_int @ SV988 @ SV136 )
| ( ord_less_eq_int @ SV546 @ SY2399 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3923]) ).
thf(4492,plain,
! [SV989: int,SV832: int,SV547: int,SV137: int] :
( ( ! [SY2401: int] :
( ~ ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SV137 @ SV547 ) @ SV832 ) @ ( plus_plus_int @ ( times_times_int @ SV137 @ SV989 ) @ SY2401 ) )
| ~ ( ord_less_eq_int @ SY2401 @ zero_zero_int )
| ~ ( ord_less_int @ SV137 @ SY2401 )
| ~ ( ord_less_int @ SV137 @ SV832 )
| ( ord_less_eq_int @ SV989 @ SV547 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3924]) ).
thf(4493,plain,
! [SV990: int,SV833: int,SV548: int,SV138: int] :
( ( ! [SY2402: int,SY2403: int] :
( ( ( plus_plus_int @ ( times_times_int @ SV138 @ SV548 ) @ SV833 )
!= ( plus_plus_int @ ( times_times_int @ SV990 @ SY2402 ) @ SY2403 ) )
| ~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ SV990 @ SY2402 ) @ SY2403 ) @ zero_zero_int )
| ~ ( ord_less_int @ SV833 @ SV138 )
| ~ ( ord_less_eq_int @ zero_zero_int @ SY2403 )
| ~ ( ord_less_int @ zero_zero_int @ SV990 )
| ~ ( ord_less_eq_int @ SV990 @ SV138 )
| ( ord_less_eq_int @ SY2402 @ SV548 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3925]) ).
thf(4494,plain,
! [SV143: int,SV834: int,SV549: int] :
( ( ( zcong @ SV549 @ zero_zero_int @ SV834 )
= $true )
| ( ( ~ ( zcong @ ( power_power_int @ SV143 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SV549 @ SV834 )
| ~ ( dvd_dvd_int @ SV834 @ SV143 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3926]) ).
thf(4495,plain,
! [SV550: int,SV146: int] :
( ( ( ord_less_eq_int @ SV146 @ SV550 )
= $false )
| ( ( ( SV146 = SV550 )
| ( ord_less_int @ SV146 @ SV550 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3927]) ).
thf(4496,plain,
! [SV147: int,SV835: int,SV551: int] :
( ( ( ~ ( ord_less_int @ SV551 @ SV835 ) )
= $true )
| ( ( ~ ( ord_less_int @ SV147 @ SV835 )
| ( ord_less_eq_int @ SV551 @ SV147 )
| ( ord_less_eq_int @ SV147 @ SV551 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3928]) ).
thf(4497,plain,
! [SV553: int,SV149: int,SV991: int,SV836: int] :
( ( ! [SY2404: int] :
( ~ ( zcong @ SV836 @ SV991 @ SY2404 )
| ~ ( zcong @ SV149 @ SV553 @ SY2404 )
| ( zcong @ ( plus_plus_int @ SV836 @ SV149 ) @ ( plus_plus_int @ SV991 @ SV553 ) @ SY2404 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3929]) ).
thf(4498,plain,
! [SV150: int,SV554: int,SV837: int] :
( ( ( ~ ( ord_less_int @ zero_zero_int @ SV837 ) )
= $true )
| ( ( ~ ( ord_less_int @ SV837 @ SV554 )
| ~ ( ord_less_int @ zero_zero_int @ SV150 )
| ~ ( ord_less_int @ SV150 @ SV837 )
| ~ ( zcong @ SV837 @ SV150 @ SV554 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3930]) ).
thf(4499,plain,
! [SV151: int,SV555: int] :
( ( ( ord_less_eq_int @ zero_zero_int @ SV555 )
= $false )
| ( ( ~ ( ord_less_int @ SV555 @ SV151 )
| ~ ( zcong @ SV555 @ zero_zero_int @ SV151 )
| ( SV555 = zero_zero_int ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3931]) ).
thf(4500,plain,
! [SV152: int,SV556: int,SV838: int] :
( ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV838 ) )
= $true )
| ( ( ~ ( ord_less_int @ SV838 @ SV556 )
| ~ ( ord_less_eq_int @ zero_zero_int @ SV152 )
| ~ ( ord_less_int @ SV152 @ SV556 )
| ~ ( zcong @ SV838 @ SV152 @ SV556 )
| ( SV838 = SV152 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3932]) ).
thf(4501,plain,
! [SV153: nat,SV992: int,SV839: nat,SV557: int] :
( ( ~ ( zcong @ ( power_power_int @ SV557 @ SV839 ) @ one_one_int @ SV992 )
| ( zcong @ ( power_power_int @ SV557 @ ( times_times_nat @ SV839 @ SV153 ) ) @ one_one_int @ SV992 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3933]) ).
thf(4502,plain,
! [SV840: int,SV559: int,SV156: int] :
( ( ( ( minus_minus_int @ SV156 @ SV559 )
!= SV840 )
= $true )
| ( ( SV156
= ( plus_plus_int @ SV840 @ SV559 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3934]) ).
thf(4503,plain,
! [SV993: int,SV841: int,SV562: int,SV160: int] :
( ( ! [SY2405: int,SY2406: int,SY2407: int] :
( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ SV160 @ ( times_times_int @ SV562 @ SV841 ) ) @ SV993 ) @ ( times_times_int @ ( minus_minus_int @ SY2405 @ ( times_times_int @ SV562 @ SY2406 ) ) @ SY2407 ) )
= ( minus_minus_int @ ( plus_plus_int @ ( times_times_int @ SV160 @ SV993 ) @ ( times_times_int @ SY2405 @ SY2407 ) ) @ ( times_times_int @ SV562 @ ( plus_plus_int @ ( times_times_int @ SV841 @ SV993 ) @ ( times_times_int @ SY2406 @ SY2407 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3935]) ).
thf(4504,plain,
! [SV162: int,SV564: int] :
( ( ( ord_less_int @ zero_zero_int @ SV564 )
= $false )
| ( ( ~ ( ord_less_int @ SV564 @ SV162 )
| ( SV564
= ( minus_minus_int @ SV162 @ one_one_int ) )
| ( ord_less_int @ SV564 @ ( minus_minus_int @ SV162 @ one_one_int ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3937]) ).
thf(4505,plain,
! [SV168: int,SV994: int,SV843: int,SV566: int] :
( ( ~ ( zcong @ SV566 @ SV843 @ SV994 )
| ( zcong @ ( plus_plus_int @ SV566 @ SV168 ) @ ( plus_plus_int @ SV843 @ SV168 ) @ SV994 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3938]) ).
thf(4506,plain,
! [SV169: nat,SV995: int,SV844: int,SV567: int] :
( ( ~ ( zcong @ SV567 @ SV844 @ SV995 )
| ( zcong @ ( power_power_int @ SV567 @ SV169 ) @ ( power_power_int @ SV844 @ SV169 ) @ SV995 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3939]) ).
thf(4507,plain,
! [SV170: int,SV568: int,SV845: int] :
( ( ( ~ ( ord_less_int @ zero_zero_int @ SV845 ) )
= $true )
| ( ( ~ ( ord_less_int @ zero_zero_int @ SV568 )
| ~ ( ord_less_int @ zero_zero_int @ SV170 )
| ~ ( zcong @ SV845 @ SV568 @ SV170 )
| ~ ( ord_less_int @ SV845 @ SV170 )
| ~ ( ord_less_int @ SV568 @ SV170 )
| ( SV845 = SV568 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3940]) ).
thf(4508,plain,
! [SV171: int,SV569: int] :
( ( ( ord_less_int @ zero_zero_int @ SV569 )
= $false )
| ( ( ~ ( ord_less_int @ SV569 @ SV171 )
| ~ ( zcong @ SV569 @ zero_zero_int @ SV171 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3941]) ).
thf(4509,plain,
! [SV570: int,SV172: int] :
( ( ( dvd_dvd_int @ SV172 @ SV570 )
= $false )
| ( ( ( ord_less_eq_int @ SV570 @ zero_zero_int )
| ( ord_less_eq_int @ SV172 @ SV570 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3942]) ).
thf(4510,plain,
! [SV173: int,SV571: int] :
( ( ( ord_less_eq_int @ zero_zero_int @ SV571 )
= $false )
| ( ( ~ ( ord_less_int @ SV571 @ SV173 )
| ~ ( zcong @ SV571 @ zero_zero_int @ SV173 )
| ( SV571 = zero_zero_int ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3943]) ).
thf(4511,plain,
! [SV996: int,SV846: int,SV572: int,SV175: int] :
( ( ( minus_minus_int @ ( plus_plus_int @ SV175 @ SV572 ) @ ( plus_plus_int @ SV846 @ SV996 ) )
= ( plus_plus_int @ ( minus_minus_int @ SV175 @ SV846 ) @ ( minus_minus_int @ SV572 @ SV996 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3944]) ).
thf(4512,plain,
! [SV997: int,SV847: int,SV573: int,SV176: int] :
( ( ( minus_minus_int @ ( times_times_int @ SV176 @ SV573 ) @ ( times_times_int @ SV847 @ SV997 ) )
= ( plus_plus_int @ ( times_times_int @ SV176 @ ( minus_minus_int @ SV573 @ SV997 ) ) @ ( times_times_int @ ( minus_minus_int @ SV176 @ SV847 ) @ SV997 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3945]) ).
thf(4513,plain,
! [SV178: nat,SV574: int] :
( ( ( ( power_power_int @ SV574 @ SV178 )
= zero_zero_int )
= $false )
| ( ( SV574 = zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3946]) ).
thf(4514,plain,
! [SV182: nat,SV849: int,SV577: int] :
( ( ( ~ ( dvd_dvd_int @ SV577 @ SV849 ) )
= $true )
| ( ( dvd_dvd_int @ ( power_power_int @ SV577 @ SV182 ) @ ( power_power_int @ SV849 @ SV182 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3948]) ).
thf(4515,plain,
! [SV185: nat,SV851: int,SV579: int] :
( ( ( ~ ( ord_less_eq_int @ SV579 @ SV851 ) )
= $true )
| ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV579 )
| ( ord_less_eq_int @ ( power_power_int @ SV579 @ SV185 ) @ ( power_power_int @ SV851 @ SV185 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3950]) ).
thf(4516,plain,
! [SV186: nat,SV580: int] :
( ( ( ord_less_eq_int @ zero_zero_int @ SV580 )
= $false )
| ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ SV580 @ SV186 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3951]) ).
thf(4517,plain,
! [SV187: nat,SV581: int] :
( ( ( ord_less_int @ zero_zero_int @ SV581 )
= $false )
| ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ SV581 @ SV187 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3952]) ).
thf(4518,plain,
! [SV188: nat,SV582: int] :
( ( ( ord_less_eq_int @ one_one_int @ SV582 )
= $false )
| ( ( ord_less_eq_int @ one_one_int @ ( power_power_int @ SV582 @ SV188 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3953]) ).
thf(4519,plain,
! [SV191: nat,SV998: int,SV853: nat,SV584: int] :
( ( ~ ( dvd_dvd_int @ ( power_power_int @ SV584 @ SV853 ) @ SV998 )
| ~ ( ord_less_eq_nat @ SV191 @ SV853 )
| ( dvd_dvd_int @ ( power_power_int @ SV584 @ SV191 ) @ SV998 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3955]) ).
thf(4520,plain,
! [SV585: nat,SV192: nat,SV999: int,SV854: int] :
( ( ~ ( dvd_dvd_int @ SV854 @ SV999 )
| ~ ( ord_less_eq_nat @ SV192 @ SV585 )
| ( dvd_dvd_int @ ( power_power_int @ SV854 @ SV192 ) @ ( power_power_int @ SV999 @ SV585 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3956]) ).
thf(4521,plain,
! [SV193: int,SV855: nat,SV586: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV586 @ SV855 ) )
= $true )
| ( ( dvd_dvd_int @ ( power_power_int @ SV193 @ SV586 ) @ ( power_power_int @ SV193 @ SV855 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3957]) ).
thf(4522,plain,
! [SV856: int,SV587: nat,SV194: int] :
( ( ( ~ ( ord_less_int @ ( power_power_int @ SV194 @ SV587 ) @ ( power_power_int @ SV856 @ SV587 ) ) )
= $true )
| ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV856 )
| ( ord_less_int @ SV194 @ SV856 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3958]) ).
thf(4523,plain,
! [SV195: nat,SV588: int] :
( ( ( ord_less_int @ one_one_int @ SV588 )
= $false )
| ( ( ord_less_int @ ( power_power_int @ SV588 @ SV195 ) @ ( times_times_int @ SV588 @ ( power_power_int @ SV588 @ SV195 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3959]) ).
thf(4524,plain,
! [SV196: nat,SV589: int] :
( ( ( ord_less_int @ one_one_int @ SV589 )
= $false )
| ( ( ord_less_int @ one_one_int @ ( times_times_int @ SV589 @ ( power_power_int @ SV589 @ SV196 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3960]) ).
thf(4525,plain,
! [SV197: int,SV857: nat,SV590: nat] :
( ( ( ~ ( ord_less_nat @ SV590 @ SV857 ) )
= $true )
| ( ( ~ ( ord_less_int @ one_one_int @ SV197 )
| ( ord_less_int @ ( power_power_int @ SV197 @ SV590 ) @ ( power_power_int @ SV197 @ SV857 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3961]) ).
thf(4526,plain,
! [SV591: nat,SV198: nat,SV858: int] :
( ( ( ~ ( ord_less_int @ one_one_int @ SV858 ) )
= $true )
| ( ( ~ ( ord_less_int @ ( power_power_int @ SV858 @ SV198 ) @ ( power_power_int @ SV858 @ SV591 ) )
| ( ord_less_nat @ SV198 @ SV591 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3962]) ).
thf(4527,plain,
! [SV199: int,SV859: nat,SV592: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV592 @ SV859 ) )
= $true )
| ( ( ~ ( ord_less_eq_int @ one_one_int @ SV199 )
| ( ord_less_eq_int @ ( power_power_int @ SV199 @ SV592 ) @ ( power_power_int @ SV199 @ SV859 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3963]) ).
thf(4528,plain,
! [SV200: nat,SV593: int] :
( ( ( ord_less_int @ zero_zero_int @ SV593 )
= $false )
| ( ( ~ ( ord_less_int @ SV593 @ one_one_int )
| ( ord_less_int @ ( times_times_int @ SV593 @ ( power_power_int @ SV593 @ SV200 ) ) @ ( power_power_int @ SV593 @ SV200 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3964]) ).
thf(4529,plain,
! [SV201: int,SV860: nat,SV594: nat] :
( ( ( ~ ( ord_less_nat @ SV594 @ SV860 ) )
= $true )
| ( ( ~ ( ord_less_int @ zero_zero_int @ SV201 )
| ~ ( ord_less_int @ SV201 @ one_one_int )
| ( ord_less_int @ ( power_power_int @ SV201 @ SV860 ) @ ( power_power_int @ SV201 @ SV594 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3965]) ).
thf(4530,plain,
! [SV212: int,SV862: int,SV600: int] :
( ( ( ~ ( ord_less_eq_int @ SV600 @ SV862 ) )
= $true )
| ( ( ~ ( ord_less_eq_int @ SV862 @ SV212 )
| ( ord_less_eq_int @ SV600 @ SV212 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3969]) ).
thf(4531,plain,
! [SV601: int,SV213: int] :
( ( ( ord_less_eq_int @ SV213 @ SV601 )
= $false )
| ( ( ~ ( ord_less_eq_int @ SV601 @ SV213 )
| ( SV213 = SV601 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3970]) ).
thf(4532,plain,
! [SV214: int,SV602: int] :
( ( ( ord_less_eq_int @ pls @ SV602 )
= $false )
| ( ( ~ ( ord_less_eq_int @ pls @ SV214 )
| ( ( times_times_real @ ( number267125858f_real @ SV602 ) @ ( number267125858f_real @ SV214 ) )
= ( number267125858f_real @ ( times_times_int @ SV602 @ SV214 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3971]) ).
thf(4533,plain,
! [SV215: int,SV603: int] :
( ( ( ord_less_eq_int @ pls @ SV603 )
= $false )
| ( ( ~ ( ord_less_eq_int @ pls @ SV215 )
| ( ( times_times_nat @ ( number_number_of_nat @ SV603 ) @ ( number_number_of_nat @ SV215 ) )
= ( number_number_of_nat @ ( times_times_int @ SV603 @ SV215 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3972]) ).
thf(4534,plain,
! [SV216: int,SV604: int] :
( ( ( ord_less_eq_int @ pls @ SV604 )
= $false )
| ( ( ~ ( ord_less_eq_int @ pls @ SV216 )
| ( ( times_times_int @ ( number_number_of_int @ SV604 ) @ ( number_number_of_int @ SV216 ) )
= ( number_number_of_int @ ( times_times_int @ SV604 @ SV216 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3973]) ).
thf(4535,plain,
! [SV224: int,SV612: int] :
( ( ( ord_less_eq_int @ pls @ SV612 )
= $false )
| ( ( ~ ( ord_less_eq_int @ pls @ SV224 )
| ( ( plus_plus_real @ ( number267125858f_real @ SV612 ) @ ( number267125858f_real @ SV224 ) )
= ( number267125858f_real @ ( plus_plus_int @ SV612 @ SV224 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3976]) ).
thf(4536,plain,
! [SV615: real,SV227: real] :
( ( ( ( power_power_real @ SV227 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power_real @ SV615 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $false )
| ( ( ~ ( ord_less_eq_real @ zero_zero_real @ SV227 )
| ~ ( ord_less_eq_real @ zero_zero_real @ SV615 )
| ( SV227 = SV615 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3979]) ).
thf(4537,plain,
! [SV616: nat,SV228: nat] :
( ( ( ( power_power_nat @ SV228 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power_nat @ SV616 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $false )
| ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV228 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV616 )
| ( SV228 = SV616 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3980]) ).
thf(4538,plain,
! [SV617: real,SV229: real] :
( ( ( ord_less_eq_real @ ( power_power_real @ SV229 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SV617 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $false )
| ( ( ~ ( ord_less_eq_real @ zero_zero_real @ SV617 )
| ( ord_less_eq_real @ SV229 @ SV617 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3981]) ).
thf(4539,plain,
! [SV618: nat,SV230: nat] :
( ( ( ord_less_eq_nat @ ( power_power_nat @ SV230 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_nat @ SV618 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $false )
| ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV618 )
| ( ord_less_eq_nat @ SV230 @ SV618 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3982]) ).
thf(4540,plain,
! [SV619: real,SV232: real] :
( ( ( ord_less_real @ ( power_power_real @ SV232 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SV619 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $false )
| ( ( ~ ( ord_less_eq_real @ zero_zero_real @ SV619 )
| ( ord_less_real @ SV232 @ SV619 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3983]) ).
thf(4541,plain,
! [SV620: nat,SV233: nat] :
( ( ( ord_less_nat @ ( power_power_nat @ SV233 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_nat @ SV620 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $false )
| ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV620 )
| ( ord_less_nat @ SV233 @ SV620 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3984]) ).
thf(4542,plain,
! [SV628: int,SV249: nat,SV869: int,SV1000: int] :
( ( ~ ( zprime @ SV1000 )
| ( dvd_dvd_int @ SV1000 @ SV869 )
| ~ ( dvd_dvd_int @ ( power_power_int @ SV1000 @ SV249 ) @ ( times_times_int @ SV628 @ SV869 ) )
| ( dvd_dvd_int @ ( power_power_int @ SV1000 @ SV249 ) @ SV628 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3988]) ).
thf(4543,plain,
! [SV629: int,SV250: nat,SV870: int,SV1001: int] :
( ( ~ ( zprime @ SV1001 )
| ( dvd_dvd_int @ SV1001 @ SV870 )
| ~ ( dvd_dvd_int @ ( power_power_int @ SV1001 @ SV250 ) @ ( times_times_int @ SV870 @ SV629 ) )
| ( dvd_dvd_int @ ( power_power_int @ SV1001 @ SV250 ) @ SV629 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3989]) ).
thf(4544,plain,
! [SV251: int,SV630: int] :
( ( ( twoSqu362149276sum2sq @ SV630 )
= $false )
| ( ( ~ ( twoSqu362149276sum2sq @ SV251 )
| ( twoSqu362149276sum2sq @ ( times_times_int @ SV630 @ SV251 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3990]) ).
thf(4545,plain,
! [SV1002: real,SV871: real,SV631: real,SV252: real] :
( ( ( times_times_real @ ( times_times_real @ SV252 @ SV631 ) @ ( times_times_real @ SV871 @ SV1002 ) )
= ( times_times_real @ ( times_times_real @ SV252 @ SV871 ) @ ( times_times_real @ SV631 @ SV1002 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3991]) ).
thf(4546,plain,
! [SV1003: nat,SV872: nat,SV632: nat,SV253: nat] :
( ( ( times_times_nat @ ( times_times_nat @ SV253 @ SV632 ) @ ( times_times_nat @ SV872 @ SV1003 ) )
= ( times_times_nat @ ( times_times_nat @ SV253 @ SV872 ) @ ( times_times_nat @ SV632 @ SV1003 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3992]) ).
thf(4547,plain,
! [SV1004: int,SV873: int,SV633: int,SV254: int] :
( ( ( times_times_int @ ( times_times_int @ SV254 @ SV633 ) @ ( times_times_int @ SV873 @ SV1004 ) )
= ( times_times_int @ ( times_times_int @ SV254 @ SV873 ) @ ( times_times_int @ SV633 @ SV1004 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3993]) ).
thf(4548,plain,
! [SV1005: real,SV874: real,SV634: real,SV255: real] :
( ( ( times_times_real @ ( times_times_real @ SV255 @ SV634 ) @ ( times_times_real @ SV874 @ SV1005 ) )
= ( times_times_real @ SV874 @ ( times_times_real @ ( times_times_real @ SV255 @ SV634 ) @ SV1005 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3994]) ).
thf(4549,plain,
! [SV1006: nat,SV875: nat,SV635: nat,SV256: nat] :
( ( ( times_times_nat @ ( times_times_nat @ SV256 @ SV635 ) @ ( times_times_nat @ SV875 @ SV1006 ) )
= ( times_times_nat @ SV875 @ ( times_times_nat @ ( times_times_nat @ SV256 @ SV635 ) @ SV1006 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3995]) ).
thf(4550,plain,
! [SV1007: int,SV876: int,SV636: int,SV257: int] :
( ( ( times_times_int @ ( times_times_int @ SV257 @ SV636 ) @ ( times_times_int @ SV876 @ SV1007 ) )
= ( times_times_int @ SV876 @ ( times_times_int @ ( times_times_int @ SV257 @ SV636 ) @ SV1007 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3996]) ).
thf(4551,plain,
! [SV1008: real,SV877: real,SV637: real,SV258: real] :
( ( ( times_times_real @ ( times_times_real @ SV258 @ SV637 ) @ ( times_times_real @ SV877 @ SV1008 ) )
= ( times_times_real @ SV258 @ ( times_times_real @ SV637 @ ( times_times_real @ SV877 @ SV1008 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3997]) ).
thf(4552,plain,
! [SV1009: nat,SV878: nat,SV638: nat,SV259: nat] :
( ( ( times_times_nat @ ( times_times_nat @ SV259 @ SV638 ) @ ( times_times_nat @ SV878 @ SV1009 ) )
= ( times_times_nat @ SV259 @ ( times_times_nat @ SV638 @ ( times_times_nat @ SV878 @ SV1009 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3998]) ).
thf(4553,plain,
! [SV1010: int,SV879: int,SV639: int,SV260: int] :
( ( ( times_times_int @ ( times_times_int @ SV260 @ SV639 ) @ ( times_times_int @ SV879 @ SV1010 ) )
= ( times_times_int @ SV260 @ ( times_times_int @ SV639 @ ( times_times_int @ SV879 @ SV1010 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3999]) ).
thf(4554,plain,
! [SV1011: real,SV900: real,SV665: real,SV286: real] :
( ( ( plus_plus_real @ ( plus_plus_real @ SV286 @ SV665 ) @ ( plus_plus_real @ SV900 @ SV1011 ) )
= ( plus_plus_real @ ( plus_plus_real @ SV286 @ SV900 ) @ ( plus_plus_real @ SV665 @ SV1011 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4020]) ).
thf(4555,plain,
! [SV1012: nat,SV901: nat,SV666: nat,SV287: nat] :
( ( ( plus_plus_nat @ ( plus_plus_nat @ SV287 @ SV666 ) @ ( plus_plus_nat @ SV901 @ SV1012 ) )
= ( plus_plus_nat @ ( plus_plus_nat @ SV287 @ SV901 ) @ ( plus_plus_nat @ SV666 @ SV1012 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4021]) ).
thf(4556,plain,
! [SV902: nat,SV290: real] :
( ( ( ord_less_eq_real @ ( power_power_real @ SV290 @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV902 ) ) @ zero_zero_real )
= $false )
| ( ( SV290 = zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4022]) ).
thf(4557,plain,
! [SV1013: real,SV913: real,SV678: real,SV316: real] :
( ( ! [SY2408: real] :
( ( SY2408 = zero_zero_real )
| ( SV316 = SV678 )
| ( SV913 != SV1013 )
| ( ( plus_plus_real @ SV913 @ ( times_times_real @ SY2408 @ SV316 ) )
!= ( plus_plus_real @ SV1013 @ ( times_times_real @ SY2408 @ SV678 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4033]) ).
thf(4558,plain,
! [SV1014: nat,SV914: nat,SV679: nat,SV317: nat] :
( ( ! [SY2409: nat] :
( ( SY2409 = zero_zero_nat )
| ( SV317 = SV679 )
| ( SV914 != SV1014 )
| ( ( plus_plus_nat @ SV914 @ ( times_times_nat @ SY2409 @ SV317 ) )
!= ( plus_plus_nat @ SV1014 @ ( times_times_nat @ SY2409 @ SV679 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4034]) ).
thf(4559,plain,
! [SV324: int] :
( ( ( SV324
= ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true )
| ( ( ( SV324
= ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) )
| ( ord_less_eq_int @ ( number_number_of_int @ ( bit1 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SV324 ) )
= $true )
| ( ( zprime @ SV324 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4035]) ).
thf(4560,plain,
! [SV915: int,SV325: int] :
( ( ( ( times_times_int @ SV325 @ SV915 )
= one_one_int )
= $false )
| ( ( ( SV325 = one_one_int )
| ( SV325
= ( number_number_of_int @ min ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4036]) ).
thf(4561,plain,
! [SV327: int,SV1015: int,SV916: int,SV685: int] :
( ( ~ ( zcong @ SV685 @ SV916 @ SV1015 )
| ~ ( zcong @ SV916 @ SV327 @ SV1015 )
| ( zcong @ SV685 @ SV327 @ SV1015 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4037]) ).
thf(4562,plain,
! [SV686: real,SV328: real] :
( ( ( ord_less_eq_real @ SV328 @ SV686 )
= $false )
| ( ( ( SV328 = SV686 )
| ( ord_less_real @ SV328 @ SV686 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4038]) ).
thf(4563,plain,
! [SV687: nat,SV329: nat] :
( ( ( ord_less_eq_nat @ SV329 @ SV687 )
= $false )
| ( ( ( SV329 = SV687 )
| ( ord_less_nat @ SV329 @ SV687 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4039]) ).
thf(4564,plain,
! [SV331: int,SV1016: int,SV918: int,SV689: int] :
( ( ~ ( zcong @ SV689 @ SV918 @ SV1016 )
| ( zcong @ ( times_times_int @ SV689 @ SV331 ) @ ( times_times_int @ SV918 @ SV331 ) @ SV1016 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4041]) ).
thf(4565,plain,
! [SV332: int,SV1017: int,SV919: int,SV690: int] :
( ( ~ ( zcong @ SV690 @ SV919 @ SV1017 )
| ( zcong @ ( times_times_int @ SV332 @ SV690 ) @ ( times_times_int @ SV332 @ SV919 ) @ SV1017 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4042]) ).
thf(4566,plain,
! [SV691: int,SV333: int,SV1018: int,SV920: int] :
( ( ! [SY2410: int] :
( ~ ( zcong @ SV920 @ SV1018 @ SY2410 )
| ~ ( zcong @ SV333 @ SV691 @ SY2410 )
| ( zcong @ ( times_times_int @ SV920 @ SV333 ) @ ( times_times_int @ SV1018 @ SV691 ) @ SY2410 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4043]) ).
thf(4567,plain,
! [SV337: int,SV692: int,SV921: int] :
( ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV921 ) )
= $true )
| ( ( ~ ( zprime @ SV692 )
| ~ ( dvd_dvd_int @ SV692 @ ( times_times_int @ SV921 @ SV337 ) )
| ( dvd_dvd_int @ SV692 @ SV921 )
| ( dvd_dvd_int @ SV692 @ SV337 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4044]) ).
thf(4568,plain,
! [SV693: nat,SV338: nat,SV922: int] :
( ( ( ~ ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV922 ) )
= $true )
| ( ( ~ ( zcong @ ( power_power_int @ ( number_number_of_int @ min ) @ SV338 ) @ ( power_power_int @ ( number_number_of_int @ min ) @ SV693 ) @ SV922 )
| ( ( power_power_int @ ( number_number_of_int @ min ) @ SV338 )
= ( power_power_int @ ( number_number_of_int @ min ) @ SV693 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4045]) ).
thf(4569,plain,
! [SV339: int,SV694: int] :
( ( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV694 )
= $false )
| ( ( ~ ( zcong @ SV339 @ ( number_number_of_int @ min ) @ SV694 )
| ~ ( zcong @ SV339 @ one_one_int @ SV694 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4046]) ).
thf(4570,plain,
! [SV695: int,SV340: int,SV1019: int,SV923: int] :
( ( ! [SY2411: int] :
( ~ ( zcong @ SV923 @ SV1019 @ SY2411 )
| ~ ( zcong @ SV340 @ SV695 @ SY2411 )
| ( zcong @ ( minus_minus_int @ SV923 @ SV340 ) @ ( minus_minus_int @ SV1019 @ SV695 ) @ SY2411 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4047]) ).
thf(4571,plain,
! [SV924: int,SV696: int,SV341: int] :
( ( ( ~ ( dvd_dvd_int @ SV341 @ ( minus_minus_int @ SV696 @ SV924 ) ) )
= $true )
| ( ( ~ ( dvd_dvd_int @ SV341 @ SV924 )
| ( dvd_dvd_int @ SV341 @ SV696 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4048]) ).
thf(4572,plain,
! [SV351: int,SV706: int,SV1020: int,SV932: int] :
( ( ! [SY2412: int] :
( ~ ( zcong @ SV932 @ SV1020 @ SY2412 )
| ( SV1020 != SV706 )
| ~ ( zcong @ SV706 @ SV351 @ SY2412 )
| ( zcong @ SV932 @ SV351 @ SY2412 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4056]) ).
thf(4573,plain,
! [SV352: int,SV707: int] :
( ( ( zprime @ SV707 )
= $false )
| ( ( ~ ( ord_less_int @ zero_zero_int @ SV352 )
| ~ ( ord_less_int @ SV352 @ SV707 )
| ~ ( zcong @ ( times_times_int @ SV352 @ SV352 ) @ one_one_int @ SV707 )
| ( SV352 = one_one_int )
| ( SV352
= ( minus_minus_int @ SV707 @ one_one_int ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4057]) ).
thf(4574,plain,
! [SV353: int,SV708: int] :
( ( ( zprime @ SV708 )
= $false )
| ( ( ~ ( ord_less_int @ zero_zero_int @ SV353 )
| ~ ( zcong @ ( times_times_int @ SV353 @ SV353 ) @ one_one_int @ SV708 )
| ( zcong @ SV353 @ one_one_int @ SV708 )
| ( zcong @ SV353 @ ( minus_minus_int @ SV708 @ one_one_int ) @ SV708 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4058]) ).
thf(4575,plain,
! [SV713: int,SV358: int,SV933: int] :
( ( ( ~ ( zprime @ SV933 ) )
= $true )
| ( ( ~ ( dvd_dvd_int @ SV933 @ ( times_times_int @ SV358 @ SV713 ) )
| ( dvd_dvd_int @ SV933 @ SV358 )
| ( dvd_dvd_int @ SV933 @ SV713 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4059]) ).
thf(4576,plain,
! [SV714: int,SV359: int,SV934: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV934 ) )
= $true )
| ( ( ~ ( dvd_dvd_int @ SV359 @ SV714 )
| ( dvd_dvd_int @ SV359 @ ( power_power_int @ SV714 @ SV934 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4060]) ).
thf(4577,plain,
! [SV360: int,SV715: int,SV935: int] :
( ( ( ~ ( zprime @ SV935 ) )
= $true )
| ( ( ( zcong @ SV715 @ zero_zero_int @ SV935 )
| ( zcong @ SV360 @ zero_zero_int @ SV935 )
| ~ ( zcong @ ( times_times_int @ SV715 @ SV360 ) @ zero_zero_int @ SV935 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4061]) ).
thf(4578,plain,
! [SV361: int,SV716: int,SV936: int] :
( ( ( ~ ( zprime @ SV936 ) )
= $true )
| ( ( ~ ( ord_less_int @ zero_zero_int @ SV716 )
| ( zcong @ SV716 @ zero_zero_int @ SV936 )
| ( zcong @ SV361 @ zero_zero_int @ SV936 )
| ~ ( zcong @ ( times_times_int @ SV716 @ SV361 ) @ zero_zero_int @ SV936 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4062]) ).
thf(4579,plain,
! [SV362: int,SV717: int,SV937: int] :
( ( ( ~ ( zprime @ SV937 ) )
= $true )
| ( ( ~ ( ord_less_int @ zero_zero_int @ SV717 )
| ~ ( zcong @ ( times_times_int @ SV717 @ SV362 ) @ zero_zero_int @ SV937 )
| ( zcong @ SV717 @ zero_zero_int @ SV937 )
| ( zcong @ SV362 @ zero_zero_int @ SV937 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4063]) ).
thf(4580,plain,
! [SV718: nat,SV363: int,SV938: int] :
( ( ( ~ ( zprime @ SV938 ) )
= $true )
| ( ( ~ ( dvd_dvd_int @ SV938 @ ( power_power_int @ SV363 @ SV718 ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV718 )
| ( dvd_dvd_int @ SV938 @ SV363 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4064]) ).
thf(4581,plain,
! [SV365: int] :
( ( ( zcong @ one_one_int @ ( number_number_of_int @ min ) @ SV365 )
= $false )
| ( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV365 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4066]) ).
thf(4582,plain,
! [SV371: real,SV940: real,SV723: real] :
( ( ( ~ ( ord_less_eq_real @ SV723 @ SV940 ) )
= $true )
| ( ( ord_less_eq_real @ ( plus_plus_real @ SV371 @ SV723 ) @ ( plus_plus_real @ SV371 @ SV940 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4068]) ).
thf(4583,plain,
! [SV1021: real,SV941: real,SV724: real,SV372: real] :
( ( ( minus_minus_real @ ( plus_plus_real @ SV372 @ SV724 ) @ ( plus_plus_real @ SV941 @ SV1021 ) )
= ( plus_plus_real @ ( minus_minus_real @ SV372 @ SV941 ) @ ( minus_minus_real @ SV724 @ SV1021 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4069]) ).
thf(4584,plain,
! [SV1022: real,SV943: real,SV726: real,SV374: real] :
( ( ( minus_minus_real @ ( times_times_real @ SV374 @ SV726 ) @ ( times_times_real @ SV943 @ SV1022 ) )
= ( plus_plus_real @ ( times_times_real @ SV374 @ ( minus_minus_real @ SV726 @ SV1022 ) ) @ ( times_times_real @ ( minus_minus_real @ SV374 @ SV943 ) @ SV1022 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4071]) ).
thf(4585,plain,
! [SV727: real,SV375: real,SV944: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV944 ) )
= $true )
| ( ( ~ ( ord_less_real @ SV375 @ SV727 )
| ( ord_less_real @ ( times_times_real @ SV944 @ SV375 ) @ ( times_times_real @ SV944 @ SV727 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4072]) ).
thf(4586,plain,
! [SV376: real,SV728: real] :
( ( ( ord_less_real @ zero_zero_real @ SV728 )
= $false )
| ( ( ~ ( ord_less_real @ zero_zero_real @ SV376 )
| ( ord_less_real @ zero_zero_real @ ( times_times_real @ SV728 @ SV376 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4073]) ).
thf(4587,plain,
! [SV378: real,SV729: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV729 )
= $false )
| ( ( ( times_times_real @ ( power_power_real @ SV378 @ ( minus_minus_nat @ SV729 @ one_one_nat ) ) @ SV378 )
= ( power_power_real @ SV378 @ SV729 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4074]) ).
thf(4588,plain,
! [SV379: nat,SV730: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV730 )
= $false )
| ( ( ( times_times_nat @ ( power_power_nat @ SV379 @ ( minus_minus_nat @ SV730 @ one_one_nat ) ) @ SV379 )
= ( power_power_nat @ SV379 @ SV730 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4075]) ).
thf(4589,plain,
! [SV380: int,SV731: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV731 )
= $false )
| ( ( ( times_times_int @ ( power_power_int @ SV380 @ ( minus_minus_nat @ SV731 @ one_one_nat ) ) @ SV380 )
= ( power_power_int @ SV380 @ SV731 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4076]) ).
thf(4590,plain,
! [SV382: nat,SV945: real,SV732: real] :
( ( ( ~ ( ord_less_real @ SV732 @ SV945 ) )
= $true )
| ( ( ~ ( ord_less_eq_real @ zero_zero_real @ SV732 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV382 )
| ( ord_less_real @ ( power_power_real @ SV732 @ SV382 ) @ ( power_power_real @ SV945 @ SV382 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4077]) ).
thf(4591,plain,
! [SV383: nat,SV946: nat,SV733: nat] :
( ( ( ~ ( ord_less_nat @ SV733 @ SV946 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV733 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV383 )
| ( ord_less_nat @ ( power_power_nat @ SV733 @ SV383 ) @ ( power_power_nat @ SV946 @ SV383 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4078]) ).
thf(4592,plain,
! [SV384: nat,SV947: int,SV734: int] :
( ( ( ~ ( ord_less_int @ SV734 @ SV947 ) )
= $true )
| ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV734 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV384 )
| ( ord_less_int @ ( power_power_int @ SV734 @ SV384 ) @ ( power_power_int @ SV947 @ SV384 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4079]) ).
thf(4593,plain,
! [SV385: nat,SV735: real] :
( ( ( ( power_power_real @ SV735 @ SV385 )
= zero_zero_real )
= $false )
| ( ( SV735 = zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4080]) ).
thf(4594,plain,
! [SV392: nat,SV950: nat,SV740: nat] :
( ( ( ~ ( dvd_dvd_nat @ SV740 @ SV950 ) )
= $true )
| ( ( dvd_dvd_nat @ ( power_power_nat @ SV740 @ SV392 ) @ ( power_power_nat @ SV950 @ SV392 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4083]) ).
thf(4595,plain,
! [SV393: nat,SV951: real,SV741: real] :
( ( ( ~ ( dvd_dvd_real @ SV741 @ SV951 ) )
= $true )
| ( ( dvd_dvd_real @ ( power_power_real @ SV741 @ SV393 ) @ ( power_power_real @ SV951 @ SV393 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4084]) ).
thf(4596,plain,
! [SV398: nat,SV954: real,SV744: real] :
( ( ( ~ ( ord_less_eq_real @ SV744 @ SV954 ) )
= $true )
| ( ( ~ ( ord_less_eq_real @ zero_zero_real @ SV744 )
| ( ord_less_eq_real @ ( power_power_real @ SV744 @ SV398 ) @ ( power_power_real @ SV954 @ SV398 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4087]) ).
thf(4597,plain,
! [SV399: nat,SV955: nat,SV745: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV745 @ SV955 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV745 )
| ( ord_less_eq_nat @ ( power_power_nat @ SV745 @ SV399 ) @ ( power_power_nat @ SV955 @ SV399 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4088]) ).
thf(4598,plain,
! [SV400: nat,SV746: real] :
( ( ( ord_less_eq_real @ zero_zero_real @ SV746 )
= $false )
| ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ SV746 @ SV400 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4089]) ).
thf(4599,plain,
! [SV401: nat,SV747: nat] :
( ( ( ord_less_eq_nat @ zero_zero_nat @ SV747 )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ ( power_power_nat @ SV747 @ SV401 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4090]) ).
thf(4600,plain,
! [SV402: nat,SV748: real] :
( ( ( ord_less_real @ zero_zero_real @ SV748 )
= $false )
| ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ SV748 @ SV402 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4091]) ).
thf(4601,plain,
! [SV403: nat,SV749: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV749 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV749 @ SV403 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4092]) ).
thf(4602,plain,
! [SV404: nat,SV750: real] :
( ( ( ord_less_eq_real @ one_one_real @ SV750 )
= $false )
| ( ( ord_less_eq_real @ one_one_real @ ( power_power_real @ SV750 @ SV404 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4093]) ).
thf(4603,plain,
! [SV405: nat,SV751: nat] :
( ( ( ord_less_eq_nat @ one_one_nat @ SV751 )
= $false )
| ( ( ord_less_eq_nat @ one_one_nat @ ( power_power_nat @ SV751 @ SV405 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4094]) ).
thf(4604,plain,
! [SV410: nat,SV1023: nat,SV958: nat,SV754: nat] :
( ( ~ ( dvd_dvd_nat @ ( power_power_nat @ SV754 @ SV958 ) @ SV1023 )
| ~ ( ord_less_eq_nat @ SV410 @ SV958 )
| ( dvd_dvd_nat @ ( power_power_nat @ SV754 @ SV410 ) @ SV1023 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4097]) ).
thf(4605,plain,
! [SV411: nat,SV1024: real,SV959: nat,SV755: real] :
( ( ~ ( dvd_dvd_real @ ( power_power_real @ SV755 @ SV959 ) @ SV1024 )
| ~ ( ord_less_eq_nat @ SV411 @ SV959 )
| ( dvd_dvd_real @ ( power_power_real @ SV755 @ SV411 ) @ SV1024 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4098]) ).
thf(4606,plain,
! [SV756: nat,SV412: nat,SV1025: nat,SV960: nat] :
( ( ~ ( dvd_dvd_nat @ SV960 @ SV1025 )
| ~ ( ord_less_eq_nat @ SV412 @ SV756 )
| ( dvd_dvd_nat @ ( power_power_nat @ SV960 @ SV412 ) @ ( power_power_nat @ SV1025 @ SV756 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4099]) ).
thf(4607,plain,
! [SV757: nat,SV413: nat,SV1026: real,SV961: real] :
( ( ~ ( dvd_dvd_real @ SV961 @ SV1026 )
| ~ ( ord_less_eq_nat @ SV413 @ SV757 )
| ( dvd_dvd_real @ ( power_power_real @ SV961 @ SV413 ) @ ( power_power_real @ SV1026 @ SV757 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4100]) ).
thf(4608,plain,
! [SV414: nat,SV962: nat,SV758: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV758 @ SV962 ) )
= $true )
| ( ( dvd_dvd_nat @ ( power_power_nat @ SV414 @ SV758 ) @ ( power_power_nat @ SV414 @ SV962 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4101]) ).
thf(4609,plain,
! [SV415: real,SV963: nat,SV759: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV759 @ SV963 ) )
= $true )
| ( ( dvd_dvd_real @ ( power_power_real @ SV415 @ SV759 ) @ ( power_power_real @ SV415 @ SV963 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4102]) ).
thf(4610,plain,
! [SV760: nat,SV416: nat,SV964: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV964 ) )
= $true )
| ( ( ~ ( ord_less_nat @ ( power_power_nat @ SV964 @ SV416 ) @ ( power_power_nat @ SV964 @ SV760 ) )
| ( ord_less_nat @ SV416 @ SV760 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4103]) ).
thf(4611,plain,
! [SV965: real,SV761: nat,SV417: real] :
( ( ( ~ ( ord_less_real @ ( power_power_real @ SV417 @ SV761 ) @ ( power_power_real @ SV965 @ SV761 ) ) )
= $true )
| ( ( ~ ( ord_less_eq_real @ zero_zero_real @ SV965 )
| ( ord_less_real @ SV417 @ SV965 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4104]) ).
thf(4612,plain,
! [SV966: nat,SV762: nat,SV418: nat] :
( ( ( ~ ( ord_less_nat @ ( power_power_nat @ SV418 @ SV762 ) @ ( power_power_nat @ SV966 @ SV762 ) ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV966 )
| ( ord_less_nat @ SV418 @ SV966 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4105]) ).
thf(4613,plain,
! [SV419: nat,SV763: real] :
( ( ( ord_less_real @ one_one_real @ SV763 )
= $false )
| ( ( ord_less_real @ ( power_power_real @ SV763 @ SV419 ) @ ( times_times_real @ SV763 @ ( power_power_real @ SV763 @ SV419 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4106]) ).
thf(4614,plain,
! [SV420: nat,SV764: nat] :
( ( ( ord_less_nat @ one_one_nat @ SV764 )
= $false )
| ( ( ord_less_nat @ ( power_power_nat @ SV764 @ SV420 ) @ ( times_times_nat @ SV764 @ ( power_power_nat @ SV764 @ SV420 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4107]) ).
thf(4615,plain,
! [SV421: nat,SV765: real] :
( ( ( ord_less_real @ one_one_real @ SV765 )
= $false )
| ( ( ord_less_real @ one_one_real @ ( times_times_real @ SV765 @ ( power_power_real @ SV765 @ SV421 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4108]) ).
thf(4616,plain,
! [SV422: nat,SV766: nat] :
( ( ( ord_less_nat @ one_one_nat @ SV766 )
= $false )
| ( ( ord_less_nat @ one_one_nat @ ( times_times_nat @ SV766 @ ( power_power_nat @ SV766 @ SV422 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4109]) ).
thf(4617,plain,
! [SV423: real,SV967: nat,SV767: nat] :
( ( ( ~ ( ord_less_nat @ SV767 @ SV967 ) )
= $true )
| ( ( ~ ( ord_less_real @ one_one_real @ SV423 )
| ( ord_less_real @ ( power_power_real @ SV423 @ SV767 ) @ ( power_power_real @ SV423 @ SV967 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4110]) ).
thf(4618,plain,
! [SV424: nat,SV968: nat,SV768: nat] :
( ( ( ~ ( ord_less_nat @ SV768 @ SV968 ) )
= $true )
| ( ( ~ ( ord_less_nat @ one_one_nat @ SV424 )
| ( ord_less_nat @ ( power_power_nat @ SV424 @ SV768 ) @ ( power_power_nat @ SV424 @ SV968 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4111]) ).
thf(4619,plain,
! [SV769: nat,SV425: nat,SV969: real] :
( ( ( ~ ( ord_less_real @ one_one_real @ SV969 ) )
= $true )
| ( ( ~ ( ord_less_real @ ( power_power_real @ SV969 @ SV425 ) @ ( power_power_real @ SV969 @ SV769 ) )
| ( ord_less_nat @ SV425 @ SV769 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4112]) ).
thf(4620,plain,
! [SV770: nat,SV426: nat,SV970: nat] :
( ( ( ~ ( ord_less_nat @ one_one_nat @ SV970 ) )
= $true )
| ( ( ~ ( ord_less_nat @ ( power_power_nat @ SV970 @ SV426 ) @ ( power_power_nat @ SV970 @ SV770 ) )
| ( ord_less_nat @ SV426 @ SV770 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4113]) ).
thf(4621,plain,
! [SV427: real,SV971: nat,SV771: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV771 @ SV971 ) )
= $true )
| ( ( ~ ( ord_less_eq_real @ one_one_real @ SV427 )
| ( ord_less_eq_real @ ( power_power_real @ SV427 @ SV771 ) @ ( power_power_real @ SV427 @ SV971 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4114]) ).
thf(4622,plain,
! [SV428: nat,SV972: nat,SV772: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV772 @ SV972 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ one_one_nat @ SV428 )
| ( ord_less_eq_nat @ ( power_power_nat @ SV428 @ SV772 ) @ ( power_power_nat @ SV428 @ SV972 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4115]) ).
thf(4623,plain,
! [SV429: nat,SV773: real] :
( ( ( ord_less_real @ zero_zero_real @ SV773 )
= $false )
| ( ( ~ ( ord_less_real @ SV773 @ one_one_real )
| ( ord_less_real @ ( times_times_real @ SV773 @ ( power_power_real @ SV773 @ SV429 ) ) @ ( power_power_real @ SV773 @ SV429 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4116]) ).
thf(4624,plain,
! [SV430: nat,SV774: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV774 )
= $false )
| ( ( ~ ( ord_less_nat @ SV774 @ one_one_nat )
| ( ord_less_nat @ ( times_times_nat @ SV774 @ ( power_power_nat @ SV774 @ SV430 ) ) @ ( power_power_nat @ SV774 @ SV430 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4117]) ).
thf(4625,plain,
! [SV775: nat,SV431: nat] :
( ( ( dvd_dvd_nat @ SV431 @ SV775 )
= $false )
| ( ( ( SV775 = zero_zero_nat )
| ( ord_less_eq_nat @ SV431 @ SV775 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4118]) ).
thf(4626,plain,
! [SV432: nat,SV973: nat,SV776: nat] :
( ( ( ~ ( dvd_dvd_nat @ SV776 @ SV973 ) )
= $true )
| ( ( dvd_dvd_nat @ ( power_power_nat @ SV776 @ SV432 ) @ ( power_power_nat @ SV973 @ SV432 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4119]) ).
thf(4627,plain,
! [SV433: nat,SV974: nat,SV777: nat] :
( ( ( ~ ( dvd_dvd_nat @ SV777 @ SV974 ) )
= $true )
| ( ( dvd_dvd_nat @ ( times_times_nat @ SV433 @ SV777 ) @ ( times_times_nat @ SV433 @ SV974 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4120]) ).
thf(4628,plain,
! [SV434: nat,SV975: nat,SV778: nat] :
( ( ( ~ ( dvd_dvd_nat @ SV778 @ SV975 ) )
= $true )
| ( ( dvd_dvd_nat @ ( times_times_nat @ SV778 @ SV434 ) @ ( times_times_nat @ SV975 @ SV434 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4121]) ).
thf(4629,plain,
! [SV435: nat,SV976: nat,SV779: nat] :
( ( ( ~ ( dvd_dvd_nat @ SV779 @ SV976 ) )
= $true )
| ( ( ~ ( dvd_dvd_nat @ SV779 @ ( plus_plus_nat @ SV976 @ SV435 ) )
| ( dvd_dvd_nat @ SV779 @ SV435 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4122]) ).
thf(4630,plain,
! [SV977: nat,SV780: nat,SV436: nat] :
( ( ( ~ ( dvd_dvd_nat @ ( power_power_nat @ SV436 @ SV780 ) @ ( power_power_nat @ SV977 @ SV780 ) ) )
= $true )
| ( ( ( SV780 = zero_zero_nat )
| ( dvd_dvd_nat @ SV436 @ SV977 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4123]) ).
thf(4631,plain,
! [SV781: nat,SV437: nat,SV978: nat] :
( ( ( SV978 = zero_zero_nat )
= $true )
| ( ( ~ ( dvd_dvd_nat @ ( power_power_nat @ SV437 @ SV978 ) @ SV781 )
| ( dvd_dvd_nat @ SV437 @ SV781 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4124]) ).
thf(4632,plain,
! [SV1027: nat,SV979: nat,SV782: nat,SV438: nat] :
( ( ( SV438
!= ( plus_plus_nat @ ( times_times_nat @ SV782 @ SV979 ) @ SV1027 ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV1027 )
| ~ ( ord_less_nat @ SV1027 @ SV979 )
| ~ ( dvd_dvd_nat @ SV979 @ SV438 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4125]) ).
thf(4633,plain,
! [SV980: nat,SV783: nat,SV439: nat] :
( ( ( ~ ( dvd_dvd_nat @ ( power_power_nat @ SV439 @ SV783 ) @ ( power_power_nat @ SV439 @ SV980 ) ) )
= $true )
| ( ( ~ ( ord_less_nat @ one_one_nat @ SV439 )
| ( ord_less_eq_nat @ SV783 @ SV980 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4126]) ).
thf(4634,plain,
! [SV784: nat,SV440: nat] :
( ( ( dvd_dvd_nat @ SV440 @ SV784 )
= $false )
| ( ( ( ord_less_eq_nat @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV440 ) @ SV784 )
| ( SV784 = zero_zero_nat )
| ( SV784 = SV440 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4127]) ).
thf(4635,plain,
! [SV1028: real] :
( ( ( ( power_power_real @ SV1028 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= zero_zero_real )
| ( SV1028 = zero_zero_real ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4128]) ).
thf(4636,plain,
! [SV1029: real] :
( ( ( SV1029 != zero_zero_real )
| ( ( power_power_real @ SV1029 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_real ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4129]) ).
thf(4637,plain,
! [SV1030: nat] :
( ( ! [SY2413: nat] :
( ( SY2413 = zero_zero_nat )
| ( SV1030 != zero_zero_nat )
| ( ( power_power_nat @ SV1030 @ SY2413 )
= zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4130]) ).
thf(4638,plain,
( ( ~ ! [SX0: nat,SX1: nat] :
( ( ( power_power_nat @ SX0 @ SX1 )
!= zero_zero_nat )
| ( SX1 != zero_zero_nat ) )
| ~ ! [SX0: nat] :
( ! [SX1: nat] :
( ( power_power_nat @ SX0 @ SX1 )
!= zero_zero_nat )
| ( SX0 = zero_zero_nat ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4131]) ).
thf(4639,plain,
! [SV1031: nat] :
( ( ! [SY2414: int] :
( ( ( number_number_of_nat @ SY2414 )
= zero_zero_nat )
| ( SV1031 != zero_zero_nat )
| ( ( power_power_nat @ SV1031 @ ( number_number_of_nat @ SY2414 ) )
= zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4132]) ).
thf(4640,plain,
( ( ~ ! [SX0: nat,SX1: int] :
( ( ( power_power_nat @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_nat )
| ( ( number_number_of_nat @ SX1 )
!= zero_zero_nat ) )
| ~ ! [SX0: nat] :
( ! [SX1: int] :
( ( power_power_nat @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_nat )
| ( SX0 = zero_zero_nat ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4133]) ).
thf(4641,plain,
! [SV1032: int] :
( ( ~ ( ord_less_eq_int @ min @ ( bit0 @ SV1032 ) )
| ( ord_less_int @ min @ SV1032 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4134]) ).
thf(4642,plain,
! [SV1033: int] :
( ( ~ ( ord_less_int @ min @ SV1033 )
| ( ord_less_eq_int @ min @ ( bit0 @ SV1033 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4135]) ).
thf(4643,plain,
! [SV1034: real] :
( ( ! [SY2415: real] :
( ~ ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ SV1034 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SY2415 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
| ( SV1034 != zero_zero_real )
| ( SY2415 != zero_zero_real ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4136]) ).
thf(4644,plain,
( ( ~ ! [SX0: real] :
( ( SX0 = zero_zero_real )
| ! [SX1: real] : ( ord_less_real @ 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 ) ) ) ) ) ) )
| ~ ! [SX0: real,SX1: real] :
( ( SX1 = zero_zero_real )
| ( ord_less_real @ 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 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4137]) ).
thf(4645,plain,
! [SV1035: int] :
( ( ~ ( ord_less_eq_int @ pls @ SV1035 )
| ( ord_less_eq_real @ zero_zero_real @ ( number267125858f_real @ SV1035 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4138]) ).
thf(4646,plain,
! [SV1036: int] :
( ( ~ ( ord_less_eq_real @ zero_zero_real @ ( number267125858f_real @ SV1036 ) )
| ( ord_less_eq_int @ pls @ SV1036 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4139]) ).
thf(4647,plain,
! [SV1037: int] :
( ( ~ ( ord_less_eq_int @ pls @ SV1037 )
| ( ord_less_int @ pls @ ( bit1 @ SV1037 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4140]) ).
thf(4648,plain,
! [SV1038: int] :
( ( ~ ( ord_less_int @ pls @ ( bit1 @ SV1038 ) )
| ( ord_less_eq_int @ pls @ SV1038 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4141]) ).
thf(4649,plain,
! [SV1039: int] :
( ( ! [SY2416: int] :
( ~ ( ord_less_eq_int @ SV1039 @ SY2416 )
| ( ord_less_int @ ( bit0 @ SV1039 ) @ ( bit1 @ SY2416 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4142]) ).
thf(4650,plain,
! [SV1040: int] :
( ( ! [SY2417: int] :
( ~ ( ord_less_int @ ( bit0 @ SV1040 ) @ ( bit1 @ SY2417 ) )
| ( ord_less_eq_int @ SV1040 @ SY2417 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4143]) ).
thf(4651,plain,
! [SV1041: int] :
( ( ~ ( ord_less_int @ min @ ( bit1 @ SV1041 ) )
| ( ord_less_int @ min @ SV1041 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4144]) ).
thf(4652,plain,
! [SV1042: int] :
( ( ~ ( ord_less_int @ min @ SV1042 )
| ( ord_less_int @ min @ ( bit1 @ SV1042 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4145]) ).
thf(4653,plain,
! [SV1043: int] :
( ( ! [SY2418: int] :
( ~ ( ord_less_int @ ( bit1 @ SV1043 ) @ ( bit1 @ SY2418 ) )
| ( ord_less_int @ SV1043 @ SY2418 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4146]) ).
thf(4654,plain,
! [SV1044: int] :
( ( ! [SY2419: int] :
( ~ ( ord_less_int @ SV1044 @ SY2419 )
| ( ord_less_int @ ( bit1 @ SV1044 ) @ ( bit1 @ SY2419 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4147]) ).
thf(4655,plain,
! [SV1045: nat] :
( ( ! [SY2420: nat] :
( ( ( power_power_nat @ SV1045 @ SY2420 )
!= one_one_nat )
| ( SV1045 = one_one_nat )
| ( SY2420 = zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4148]) ).
thf(4656,plain,
( ( ~ ! [SX0: nat] :
( ( SX0 != one_one_nat )
| ! [SX1: nat] :
( ( power_power_nat @ SX0 @ SX1 )
= one_one_nat ) )
| ~ ! [SX0: nat,SX1: nat] :
( ( SX1 != zero_zero_nat )
| ( ( power_power_nat @ SX0 @ SX1 )
= one_one_nat ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4149]) ).
thf(4657,plain,
! [SV1046: int] :
( ( ! [SY2421: int] :
( ~ ( ord_less_eq_int @ SV1046 @ SY2421 )
| ( ord_less_eq_real @ ( number267125858f_real @ SV1046 ) @ ( number267125858f_real @ SY2421 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4150]) ).
thf(4658,plain,
! [SV1047: int] :
( ( ! [SY2422: int] :
( ~ ( ord_less_eq_real @ ( number267125858f_real @ SV1047 ) @ ( number267125858f_real @ SY2422 ) )
| ( ord_less_eq_int @ SV1047 @ SY2422 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4151]) ).
thf(4659,plain,
! [SV1048: nat] :
( ( ( SV1048 != zero_zero_nat )
| ( ( power_power_real @ zero_zero_real @ SV1048 )
= one_one_real ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4152]) ).
thf(4660,plain,
! [SV1049: nat] :
( ( ( SV1049 = zero_zero_nat )
| ( ( power_power_real @ zero_zero_real @ SV1049 )
= zero_zero_real ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4153]) ).
thf(4661,plain,
! [SV1050: int] :
( ( ! [SY2423: int] :
( ( ( bit1 @ SV1050 )
!= ( bit1 @ SY2423 ) )
| ( SV1050 = SY2423 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4154]) ).
thf(4662,plain,
! [SV1051: int] :
( ( ! [SY2424: int] :
( ( SV1051 != SY2424 )
| ( ( bit1 @ SV1051 )
= ( bit1 @ SY2424 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4155]) ).
thf(4663,plain,
! [SV1052: int] :
( ( ! [SY2425: int] :
( ~ ( ord_less_int @ ( number_number_of_int @ SV1052 ) @ ( number_number_of_int @ SY2425 ) )
| ( ord_less_int @ SV1052 @ SY2425 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4156]) ).
thf(4664,plain,
! [SV1053: int] :
( ( ! [SY2426: int] :
( ~ ( ord_less_int @ SV1053 @ SY2426 )
| ( ord_less_int @ ( number_number_of_int @ SV1053 ) @ ( number_number_of_int @ SY2426 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4157]) ).
thf(4665,plain,
! [SV1054: real] :
( ( ! [SY2427: real] :
( ( SV1054 != zero_zero_real )
| ( SY2427 != zero_zero_real )
| ( ord_less_eq_real @ ( plus_plus_real @ ( power_power_real @ SV1054 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SY2427 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_real ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4158]) ).
thf(4666,plain,
( ( ~ ! [SX0: real] :
( ! [SX1: real] :
~ ( ord_less_eq_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 )
| ( SX0 = zero_zero_real ) )
| ~ ! [SX0: real,SX1: real] :
( ~ ( ord_less_eq_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 )
| ( SX1 = zero_zero_real ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4159]) ).
thf(4667,plain,
! [SV1055: int] :
( ( ! [SY2428: int] :
( ~ ( ord_less_int @ SV1055 @ ( plus_plus_int @ SY2428 @ one_one_int ) )
| ( SV1055 = SY2428 )
| ( ord_less_int @ SV1055 @ SY2428 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4160]) ).
thf(4668,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ( SX0 != SX1 )
| ( ord_less_int @ SX0 @ ( plus_plus_int @ SX1 @ one_one_int ) ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ SX0 @ ( plus_plus_int @ SX1 @ one_one_int ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4161]) ).
thf(4669,plain,
! [SV1056: int] :
( ( ~ ( ord_less_eq_int @ min @ ( bit1 @ SV1056 ) )
| ( ord_less_eq_int @ min @ SV1056 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4162]) ).
thf(4670,plain,
! [SV1057: int] :
( ( ~ ( ord_less_eq_int @ min @ SV1057 )
| ( ord_less_eq_int @ min @ ( bit1 @ SV1057 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4163]) ).
thf(4671,plain,
! [SV1058: int] :
( ( ( ( number_number_of_nat @ SV1058 )
!= zero_zero_nat )
| ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ SV1058 ) )
= one_one_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4164]) ).
thf(4672,plain,
! [SV1059: int] :
( ( ( ( number_number_of_nat @ SV1059 )
= zero_zero_nat )
| ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ SV1059 ) )
= zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4165]) ).
thf(4673,plain,
! [SV785: nat,SV441: nat] :
( ( ~ ~ ( ~ ! [SY2273: nat,SY2274: nat] :
( ( ( plus_plus_nat @ ( times_times_nat @ SY2273 @ SV441 ) @ ( times_times_nat @ SY2274 @ SV785 ) )
= ( plus_plus_nat @ ( times_times_nat @ SY2273 @ SV785 ) @ ( times_times_nat @ SY2274 @ SV441 ) ) )
| ( SY2273 != SY2274 ) )
| ~ ( ! [SY2275: nat,SY2276: nat] :
( ( plus_plus_nat @ ( times_times_nat @ SY2275 @ SV441 ) @ ( times_times_nat @ SY2276 @ SV785 ) )
= ( plus_plus_nat @ ( times_times_nat @ SY2275 @ SV785 ) @ ( times_times_nat @ SY2276 @ SV441 ) ) )
| ( SV441 != SV785 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4166]) ).
thf(4674,plain,
! [SV785: nat,SV441: nat] :
( ( ~ ! [SY2277: nat,SY2278: nat] :
( ( SY2277 = SY2278 )
| ( SV441 = SV785 )
| ( ( plus_plus_nat @ ( times_times_nat @ SY2277 @ SV441 ) @ ( times_times_nat @ SY2278 @ SV785 ) )
!= ( plus_plus_nat @ ( times_times_nat @ SY2277 @ SV785 ) @ ( times_times_nat @ SY2278 @ SV441 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4166]) ).
thf(4675,plain,
! [SV1060: int] :
( ( ! [SY2429: int] :
( ~ ( ord_less_eq_int @ ( bit1 @ SV1060 ) @ ( bit1 @ SY2429 ) )
| ( ord_less_eq_int @ SV1060 @ SY2429 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4167]) ).
thf(4676,plain,
! [SV1061: int] :
( ( ! [SY2430: int] :
( ~ ( ord_less_eq_int @ SV1061 @ SY2430 )
| ( ord_less_eq_int @ ( bit1 @ SV1061 ) @ ( bit1 @ SY2430 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4168]) ).
thf(4677,plain,
! [SV1062: int] :
( ( ! [SY2431: int] :
( ~ ( ord_less_int @ ( bit0 @ SV1062 ) @ ( bit0 @ SY2431 ) )
| ( ord_less_int @ SV1062 @ SY2431 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4169]) ).
thf(4678,plain,
! [SV1063: int] :
( ( ! [SY2432: int] :
( ~ ( ord_less_int @ SV1063 @ SY2432 )
| ( ord_less_int @ ( bit0 @ SV1063 ) @ ( bit0 @ SY2432 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4170]) ).
thf(4679,plain,
! [SV1064: real] :
( ( ! [SY2433: int] :
( ( ( number_number_of_nat @ SY2433 )
= zero_zero_nat )
| ( SV1064 != zero_zero_real )
| ( ( power_power_real @ SV1064 @ ( number_number_of_nat @ SY2433 ) )
= zero_zero_real ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4171]) ).
thf(4680,plain,
( ( ~ ! [SX0: real,SX1: int] :
( ( ( power_power_real @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_real )
| ( ( number_number_of_nat @ SX1 )
!= zero_zero_nat ) )
| ~ ! [SX0: real] :
( ! [SX1: int] :
( ( power_power_real @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_real )
| ( SX0 = zero_zero_real ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4172]) ).
thf(4681,plain,
! [SV1065: real] :
( ( ! [SY2434: real] :
( ~ ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ SV1065 @ SV1065 ) @ ( times_times_real @ SY2434 @ SY2434 ) ) )
| ( SV1065 != zero_zero_real )
| ( SY2434 != zero_zero_real ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4173]) ).
thf(4682,plain,
( ( ~ ! [SX0: real] :
( ( SX0 = zero_zero_real )
| ! [SX1: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ SX0 @ SX0 ) @ ( times_times_real @ SX1 @ SX1 ) ) ) )
| ~ ! [SX0: real,SX1: real] :
( ( SX1 = zero_zero_real )
| ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ SX0 @ SX0 ) @ ( times_times_real @ SX1 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4174]) ).
thf(4683,plain,
! [SV1066: nat] :
( ( ! [SY2435: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV1066 @ SY2435 ) )
| ( SY2435 = zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV1066 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4175]) ).
thf(4684,plain,
( ( ~ ! [SX0: nat,SX1: nat] :
( ( SX1 != zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SX0 @ SX1 ) ) )
| ~ ! [SX0: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SX0 )
| ! [SX1: nat] : ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4176]) ).
thf(4685,plain,
! [SV786: real,SV442: real] :
( ( ~ ~ ( ~ ! [SY2279: real,SY2280: real] :
( ( ( plus_plus_real @ ( times_times_real @ SY2279 @ SV442 ) @ ( times_times_real @ SY2280 @ SV786 ) )
= ( plus_plus_real @ ( times_times_real @ SY2279 @ SV786 ) @ ( times_times_real @ SY2280 @ SV442 ) ) )
| ( SY2279 != SY2280 ) )
| ~ ( ! [SY2281: real,SY2282: real] :
( ( plus_plus_real @ ( times_times_real @ SY2281 @ SV442 ) @ ( times_times_real @ SY2282 @ SV786 ) )
= ( plus_plus_real @ ( times_times_real @ SY2281 @ SV786 ) @ ( times_times_real @ SY2282 @ SV442 ) ) )
| ( SV442 != SV786 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4177]) ).
thf(4686,plain,
! [SV786: real,SV442: real] :
( ( ~ ! [SY2283: real,SY2284: real] :
( ( SY2283 = SY2284 )
| ( SV442 = SV786 )
| ( ( plus_plus_real @ ( times_times_real @ SY2283 @ SV442 ) @ ( times_times_real @ SY2284 @ SV786 ) )
!= ( plus_plus_real @ ( times_times_real @ SY2283 @ SV786 ) @ ( times_times_real @ SY2284 @ SV442 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4177]) ).
thf(4687,plain,
! [SV1067: int] :
( ( ~ ( ord_less_eq_int @ ( bit0 @ SV1067 ) @ pls )
| ( ord_less_eq_int @ SV1067 @ pls ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4178]) ).
thf(4688,plain,
! [SV1068: int] :
( ( ~ ( ord_less_eq_int @ SV1068 @ pls )
| ( ord_less_eq_int @ ( bit0 @ SV1068 ) @ pls ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4179]) ).
thf(4689,plain,
! [SV1069: int] :
( ( ( ( bit1 @ SV1069 )
!= min )
| ( SV1069 = min ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4180]) ).
thf(4690,plain,
! [SV1070: int] :
( ( ( SV1070 != min )
| ( ( bit1 @ SV1070 )
= min ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4181]) ).
thf(4691,plain,
! [SV1071: real] :
( ( ! [SY2436: real] :
( ~ ( ord_less_eq_real @ SV1071 @ SY2436 )
| ( SV1071 = SY2436 )
| ( ord_less_real @ SV1071 @ SY2436 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4182]) ).
thf(4692,plain,
( ( ~ ! [SX0: real,SX1: real] :
( ( SX0 != SX1 )
| ( ord_less_eq_real @ SX0 @ SX1 ) )
| ~ ! [SX0: real,SX1: real] :
( ~ ( ord_less_real @ SX0 @ SX1 )
| ( ord_less_eq_real @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4183]) ).
thf(4693,plain,
! [SV1072: real] :
( ( ( ( plus_plus_real @ SV1072 @ SV1072 )
!= zero_zero_real )
| ( SV1072 = zero_zero_real ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4184]) ).
thf(4694,plain,
! [SV1073: real] :
( ( ( SV1073 != zero_zero_real )
| ( ( plus_plus_real @ SV1073 @ SV1073 )
= zero_zero_real ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4185]) ).
thf(4695,plain,
! [SV1074: int] :
( ( ! [SY2437: int] :
( ~ ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ SV1074 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SY2437 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
| ( SV1074 != zero_zero_int )
| ( SY2437 != zero_zero_int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4186]) ).
thf(4696,plain,
( ( ~ ! [SX0: int] :
( ( SX0 = zero_zero_int )
| ! [SX1: int] : ( ord_less_int @ zero_zero_int @ ( 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 ) ) ) ) ) ) )
| ~ ! [SX0: int,SX1: int] :
( ( SX1 = zero_zero_int )
| ( ord_less_int @ zero_zero_int @ ( 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 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4187]) ).
thf(4697,plain,
! [SV1075: int] :
( ( ~ ( ord_less_int @ pls @ SV1075 )
| ( ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ SV1075 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4188]) ).
thf(4698,plain,
! [SV1076: int] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ SV1076 ) )
| ( ord_less_int @ pls @ SV1076 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4189]) ).
thf(4699,plain,
! [SV1077: int] :
( ( ! [SY2438: int] :
( ~ ( ord_less_eq_int @ ( number_number_of_int @ SV1077 ) @ ( number_number_of_int @ SY2438 ) )
| ( ord_less_eq_int @ SV1077 @ SY2438 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4190]) ).
thf(4700,plain,
! [SV1078: int] :
( ( ! [SY2439: int] :
( ~ ( ord_less_eq_int @ SV1078 @ SY2439 )
| ( ord_less_eq_int @ ( number_number_of_int @ SV1078 ) @ ( number_number_of_int @ SY2439 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4191]) ).
thf(4701,plain,
! [SV1079: real] :
( ( ! [SY2440: real] :
( ( SV1079 != zero_zero_real )
| ( SY2440 != zero_zero_real )
| ( ( plus_plus_real @ ( power_power_real @ SV1079 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SY2440 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_real ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4192]) ).
thf(4702,plain,
( ( ~ ! [SX0: real] :
( ! [SX1: 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 )
| ( SX0 = zero_zero_real ) )
| ~ ! [SX0: real,SX1: 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 )
| ( SX1 = zero_zero_real ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4193]) ).
thf(4703,plain,
! [SV1080: int] :
( ( ! [SY2441: nat] :
( ( SY2441 != zero_zero_nat )
| ( ( power_power_int @ SV1080 @ SY2441 )
= one_one_int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4194]) ).
thf(4704,plain,
! [SV1081: int] :
( ( ! [SY2442: nat] :
( ( SY2442 = zero_zero_nat )
| ( ( power_power_int @ SV1081 @ SY2442 )
= ( times_times_int @ SV1081 @ ( power_power_int @ SV1081 @ ( minus_minus_nat @ SY2442 @ one_one_nat ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4195]) ).
thf(4705,plain,
! [SV1082: int] :
( ( ( ( number_number_of_nat @ SV1082 )
!= zero_zero_nat )
| ( ord_less_eq_int @ SV1082 @ pls ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4196]) ).
thf(4706,plain,
! [SV1083: int] :
( ( ~ ( ord_less_eq_int @ SV1083 @ pls )
| ( ( number_number_of_nat @ SV1083 )
= zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4197]) ).
thf(4707,plain,
! [SV1084: int] :
( ( ! [SY2443: int] :
( ~ ( dvd_dvd_int @ SY2443 @ SV1084 )
| ( zcong @ SV1084 @ zero_zero_int @ SY2443 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4198]) ).
thf(4708,plain,
! [SV1085: int] :
( ( ! [SY2444: int] :
( ~ ( zcong @ SV1085 @ zero_zero_int @ SY2444 )
| ( dvd_dvd_int @ SY2444 @ SV1085 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4199]) ).
thf(4709,plain,
! [SV1086: nat] :
( ( ! [SY2445: nat] :
( ( SY2445 != zero_zero_nat )
| ( ( power_power_nat @ SV1086 @ SY2445 )
= one_one_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4200]) ).
thf(4710,plain,
! [SV1087: nat] :
( ( ! [SY2446: nat] :
( ( SY2446 = zero_zero_nat )
| ( ( power_power_nat @ SV1087 @ SY2446 )
= ( times_times_nat @ SV1087 @ ( power_power_nat @ SV1087 @ ( minus_minus_nat @ SY2446 @ one_one_nat ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4201]) ).
thf(4711,plain,
! [SV1088: int] :
( ( ~ ( ord_less_int @ ( bit1 @ SV1088 ) @ min )
| ( ord_less_int @ SV1088 @ min ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4202]) ).
thf(4712,plain,
! [SV1089: int] :
( ( ~ ( ord_less_int @ SV1089 @ min )
| ( ord_less_int @ ( bit1 @ SV1089 ) @ min ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4203]) ).
thf(4713,plain,
! [SV443: nat] :
( ( ! [SY1911: nat,SY1912: int] :
( ~ ( ord_less_int @ one_one_int @ SY1912 )
| ~ ( ord_less_int @ ( power_power_int @ SY1912 @ SV443 ) @ ( power_power_int @ SY1912 @ SY1911 ) )
| ( ord_less_nat @ SV443 @ SY1911 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4204]) ).
thf(4714,plain,
! [SV443: nat] :
( ( ! [SY1913: nat,SY1914: int] :
( ~ ( ord_less_int @ one_one_int @ SY1914 )
| ~ ( ord_less_nat @ SV443 @ SY1913 )
| ( ord_less_int @ ( power_power_int @ SY1914 @ SV443 ) @ ( power_power_int @ SY1914 @ SY1913 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4205]) ).
thf(4715,plain,
! [SV1090: int] :
( ( ~ ( ord_less_int @ ( bit1 @ SV1090 ) @ zero_zero_int )
| ( ord_less_int @ SV1090 @ zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4206]) ).
thf(4716,plain,
! [SV1091: int] :
( ( ~ ( ord_less_int @ SV1091 @ zero_zero_int )
| ( ord_less_int @ ( bit1 @ SV1091 ) @ zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4207]) ).
thf(4717,plain,
! [SV1092: int] :
( ( ~ ( ord_less_eq_int @ SV1092 @ pls )
| ( ord_less_eq_real @ ( number267125858f_real @ SV1092 ) @ zero_zero_real ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4208]) ).
thf(4718,plain,
! [SV1093: int] :
( ( ~ ( ord_less_eq_real @ ( number267125858f_real @ SV1093 ) @ zero_zero_real )
| ( ord_less_eq_int @ SV1093 @ pls ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4209]) ).
thf(4719,plain,
! [SV1094: int] :
( ( ~ ( ord_less_int @ min @ ( bit0 @ SV1094 ) )
| ( ord_less_int @ min @ SV1094 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4210]) ).
thf(4720,plain,
! [SV1095: int] :
( ( ~ ( ord_less_int @ min @ SV1095 )
| ( ord_less_int @ min @ ( bit0 @ SV1095 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4211]) ).
thf(4721,plain,
! [SV1096: int] :
( ( ! [SY2447: int] :
( ~ ( ord_less_eq_int @ ( number_number_of_int @ SV1096 ) @ ( number_number_of_int @ SY2447 ) )
| ( ord_less_eq_int @ SV1096 @ SY2447 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4212]) ).
thf(4722,plain,
! [SV1097: int] :
( ( ! [SY2448: int] :
( ~ ( ord_less_eq_int @ SV1097 @ SY2448 )
| ( ord_less_eq_int @ ( number_number_of_int @ SV1097 ) @ ( number_number_of_int @ SY2448 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4213]) ).
thf(4723,plain,
! [SV444: int] :
( ( ! [SY1915: int] :
( ! [SY1916: int] :
~ ( dvd_dvd_int @ SV444 @ ( plus_plus_int @ SY1915 @ ( times_times_int @ SV444 @ SY1916 ) ) )
| ( dvd_dvd_int @ SV444 @ SY1915 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4214]) ).
thf(4724,plain,
! [SV444: int] :
( ( ! [SY1917: int] :
( ~ ( dvd_dvd_int @ SV444 @ SY1917 )
| ! [SY1918: int] : ( dvd_dvd_int @ SV444 @ ( plus_plus_int @ SY1917 @ ( times_times_int @ SV444 @ SY1918 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4215]) ).
thf(4725,plain,
! [SV1098: int] :
( ( ! [SY2449: int] :
( ~ ( ord_less_eq_int @ SV1098 @ ( minus_minus_int @ SY2449 @ one_one_int ) )
| ( ord_less_int @ SV1098 @ SY2449 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4216]) ).
thf(4726,plain,
! [SV1099: int] :
( ( ! [SY2450: int] :
( ~ ( ord_less_int @ SV1099 @ SY2450 )
| ( ord_less_eq_int @ SV1099 @ ( minus_minus_int @ SY2450 @ one_one_int ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4217]) ).
thf(4727,plain,
! [SV1100: int] :
( ( ! [SY2451: int] :
( ~ ( ord_less_eq_int @ ( bit0 @ SV1100 ) @ ( bit0 @ SY2451 ) )
| ( ord_less_eq_int @ SV1100 @ SY2451 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4218]) ).
thf(4728,plain,
! [SV1101: int] :
( ( ! [SY2452: int] :
( ~ ( ord_less_eq_int @ SV1101 @ SY2452 )
| ( ord_less_eq_int @ ( bit0 @ SV1101 ) @ ( bit0 @ SY2452 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4219]) ).
thf(4729,plain,
! [SV1102: int] :
( ( ! [SY2453: int] :
( ( ( number_number_of_nat @ SY2453 )
= zero_zero_nat )
| ( SV1102 != zero_zero_int )
| ( ( power_power_int @ SV1102 @ ( number_number_of_nat @ SY2453 ) )
= zero_zero_int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4220]) ).
thf(4730,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ( ( power_power_int @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_int )
| ( ( number_number_of_nat @ SX1 )
!= zero_zero_nat ) )
| ~ ! [SX0: int] :
( ! [SX1: int] :
( ( power_power_int @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4221]) ).
thf(4731,plain,
! [SV1103: int] :
( ( ! [SY2454: int] :
( ~ ( ord_less_eq_real @ ( number267125858f_real @ SV1103 ) @ ( number267125858f_real @ SY2454 ) )
| ~ ( ord_less_real @ ( number267125858f_real @ SY2454 ) @ ( number267125858f_real @ SV1103 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4222]) ).
thf(4732,plain,
! [SV1104: int] :
( ( ! [SY2455: int] :
( ( ord_less_real @ ( number267125858f_real @ SY2455 ) @ ( number267125858f_real @ SV1104 ) )
| ( ord_less_eq_real @ ( number267125858f_real @ SV1104 ) @ ( number267125858f_real @ SY2455 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4223]) ).
thf(4733,plain,
! [SV1105: int] :
( ( ! [SY2456: int] :
( ~ ( ord_less_int @ SV1105 @ SY2456 )
| ( ord_less_int @ ( minus_minus_int @ SV1105 @ SY2456 ) @ zero_zero_int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4224]) ).
thf(4734,plain,
! [SV1106: int] :
( ( ! [SY2457: int] :
( ~ ( ord_less_int @ ( minus_minus_int @ SV1106 @ SY2457 ) @ zero_zero_int )
| ( ord_less_int @ SV1106 @ SY2457 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4225]) ).
thf(4735,plain,
! [SV1107: int] :
( ( ! [SY2458: int] :
( ~ ( zcong @ ( times_times_int @ SV1107 @ ( minus_minus_int @ SY2458 @ one_one_int ) ) @ one_one_int @ SY2458 )
| ( zcong @ SV1107 @ ( minus_minus_int @ SY2458 @ one_one_int ) @ SY2458 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4226]) ).
thf(4736,plain,
! [SV1108: int] :
( ( ! [SY2459: int] :
( ~ ( zcong @ SV1108 @ ( minus_minus_int @ SY2459 @ one_one_int ) @ SY2459 )
| ( zcong @ ( times_times_int @ SV1108 @ ( minus_minus_int @ SY2459 @ one_one_int ) ) @ one_one_int @ SY2459 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4227]) ).
thf(4737,plain,
! [SV1109: int] :
( ( ~ ( ord_less_int @ ( bit0 @ SV1109 ) @ pls )
| ( ord_less_int @ SV1109 @ pls ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4228]) ).
thf(4738,plain,
! [SV1110: int] :
( ( ~ ( ord_less_int @ SV1110 @ pls )
| ( ord_less_int @ ( bit0 @ SV1110 ) @ pls ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4229]) ).
thf(4739,plain,
! [SV1111: nat] :
( ( ! [SY2460: nat] :
( ( SY2460 != zero_zero_nat )
| ( ( times_times_nat @ SY2460 @ SV1111 )
= zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4230]) ).
thf(4740,plain,
! [SV1112: nat] :
( ( ! [SY2461: nat] :
( ( SY2461 = zero_zero_nat )
| ( ( times_times_nat @ SY2461 @ SV1112 )
= ( plus_plus_nat @ SV1112 @ ( times_times_nat @ ( minus_minus_nat @ SY2461 @ one_one_nat ) @ SV1112 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4231]) ).
thf(4741,plain,
! [SV1113: real] :
( ( ! [SY2462: real] :
( ( SV1113 != zero_zero_real )
| ( SY2462 != zero_zero_real )
| ( ( plus_plus_real @ ( power_power_real @ SV1113 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SY2462 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_real ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4232]) ).
thf(4742,plain,
( ( ~ ! [SX0: real] :
( ! [SX1: 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 )
| ( SX0 = zero_zero_real ) )
| ~ ! [SX0: real,SX1: 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 )
| ( SX1 = zero_zero_real ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4233]) ).
thf(4743,plain,
! [SV1114: int] :
( ( ! [SY2463: int] :
( ( SV1114 != zero_zero_int )
| ( SY2463 != zero_zero_int )
| ( ( plus_plus_int @ ( power_power_int @ SV1114 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SY2463 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4234]) ).
thf(4744,plain,
( ( ~ ! [SX0: int] :
( ! [SX1: int] :
( ( 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 ) ) ) ) )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) )
| ~ ! [SX0: int,SX1: int] :
( ( ( 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 ) ) ) ) )
!= zero_zero_int )
| ( SX1 = zero_zero_int ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4235]) ).
thf(4745,plain,
! [SV1115: int] :
( ( ! [SY2464: int] :
( ~ ( dvd_dvd_int @ SY2464 @ SV1115 )
| ( zcong @ SV1115 @ zero_zero_int @ SY2464 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4236]) ).
thf(4746,plain,
! [SV1116: int] :
( ( ! [SY2465: int] :
( ~ ( zcong @ SV1116 @ zero_zero_int @ SY2465 )
| ( dvd_dvd_int @ SY2465 @ SV1116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4237]) ).
thf(4747,plain,
! [SV1117: int] :
( ( ! [SY2466: int] :
( ~ ( ord_less_eq_int @ ( bit0 @ SV1117 ) @ ( bit1 @ SY2466 ) )
| ( ord_less_eq_int @ SV1117 @ SY2466 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4238]) ).
thf(4748,plain,
! [SV1118: int] :
( ( ! [SY2467: int] :
( ~ ( ord_less_eq_int @ SV1118 @ SY2467 )
| ( ord_less_eq_int @ ( bit0 @ SV1118 ) @ ( bit1 @ SY2467 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4239]) ).
thf(4749,plain,
! [SV1119: int] :
( ( ~ ( ord_less_int @ ( plus_plus_int @ SV1119 @ SV1119 ) @ zero_zero_int )
| ( ord_less_int @ SV1119 @ zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4240]) ).
thf(4750,plain,
! [SV1120: int] :
( ( ~ ( ord_less_int @ SV1120 @ zero_zero_int )
| ( ord_less_int @ ( plus_plus_int @ SV1120 @ SV1120 ) @ zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4241]) ).
thf(4751,plain,
! [SV1121: int] :
( ( ~ ( ord_less_eq_int @ one_one_int @ SV1121 )
| ( ord_less_int @ zero_zero_int @ SV1121 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4242]) ).
thf(4752,plain,
! [SV1122: int] :
( ( ~ ( ord_less_int @ zero_zero_int @ SV1122 )
| ( ord_less_eq_int @ one_one_int @ SV1122 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4243]) ).
thf(4753,plain,
! [SV445: real] :
( ( ! [SY1919: real,SY1920: real] :
( ~ ( ord_less_real @ zero_zero_real @ SY1920 )
| ~ ( ord_less_eq_real @ ( times_times_real @ SV445 @ SY1920 ) @ ( times_times_real @ SY1919 @ SY1920 ) )
| ( ord_less_eq_real @ SV445 @ SY1919 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4244]) ).
thf(4754,plain,
! [SV445: real] :
( ( ! [SY1921: real,SY1922: real] :
( ~ ( ord_less_real @ zero_zero_real @ SY1922 )
| ~ ( ord_less_eq_real @ SV445 @ SY1921 )
| ( ord_less_eq_real @ ( times_times_real @ SV445 @ SY1922 ) @ ( times_times_real @ SY1921 @ SY1922 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4245]) ).
thf(4755,plain,
! [SV1123: int] :
( ( ~ ( ord_less_int @ pls @ SV1123 )
| ( ord_less_real @ zero_zero_real @ ( number267125858f_real @ SV1123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4246]) ).
thf(4756,plain,
! [SV1124: int] :
( ( ~ ( ord_less_real @ zero_zero_real @ ( number267125858f_real @ SV1124 ) )
| ( ord_less_int @ pls @ SV1124 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4247]) ).
thf(4757,plain,
! [SV1125: real] :
( ( ! [SY2468: real] :
( ( SV1125 != zero_zero_real )
| ( SY2468 != zero_zero_real )
| ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ SV1125 @ SV1125 ) @ ( times_times_real @ SY2468 @ SY2468 ) ) @ zero_zero_real ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4248]) ).
thf(4758,plain,
( ( ~ ! [SX0: real] :
( ! [SX1: real] :
~ ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ SX0 @ SX0 ) @ ( times_times_real @ SX1 @ SX1 ) ) @ zero_zero_real )
| ( SX0 = zero_zero_real ) )
| ~ ! [SX0: real,SX1: real] :
( ~ ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ SX0 @ SX0 ) @ ( times_times_real @ SX1 @ SX1 ) ) @ zero_zero_real )
| ( SX1 = zero_zero_real ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4249]) ).
thf(4759,plain,
! [SV1126: int] :
( ( ! [SY2469: int] :
( ~ ( ord_less_eq_int @ ( bit1 @ SV1126 ) @ ( bit0 @ SY2469 ) )
| ( ord_less_int @ SV1126 @ SY2469 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4250]) ).
thf(4760,plain,
! [SV1127: int] :
( ( ! [SY2470: int] :
( ~ ( ord_less_int @ SV1127 @ SY2470 )
| ( ord_less_eq_int @ ( bit1 @ SV1127 ) @ ( bit0 @ SY2470 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4251]) ).
thf(4761,plain,
! [SV1128: int] :
( ( ~ ( ord_less_int @ zero_zero_int @ ( number_number_of_int @ SV1128 ) )
| ( ord_less_int @ pls @ SV1128 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4252]) ).
thf(4762,plain,
! [SV1129: int] :
( ( ~ ( ord_less_int @ pls @ SV1129 )
| ( ord_less_int @ zero_zero_int @ ( number_number_of_int @ SV1129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4253]) ).
thf(4763,plain,
! [SV1130: int] :
( ( ! [SY2471: int] :
( ( SV1130 != zero_zero_int )
| ( SY2471 != zero_zero_int )
| ( ord_less_eq_int @ ( plus_plus_int @ ( power_power_int @ SV1130 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SY2471 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4254]) ).
thf(4764,plain,
( ( ~ ! [SX0: int] :
( ! [SX1: int] :
~ ( ord_less_eq_int @ ( 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 ) ) ) ) ) @ zero_zero_int )
| ( SX0 = zero_zero_int ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ ( 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 ) ) ) ) ) @ zero_zero_int )
| ( SX1 = zero_zero_int ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4255]) ).
thf(4765,plain,
! [SV1131: int] :
( ( ( min
!= ( bit1 @ SV1131 ) )
| ( min = SV1131 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4256]) ).
thf(4766,plain,
! [SV1132: int] :
( ( ( min != SV1132 )
| ( min
= ( bit1 @ SV1132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4257]) ).
thf(4767,plain,
! [SV1133: int] :
( ( ! [SY2472: int] :
( ( SV1133 != zero_zero_int )
| ( SY2472 != zero_zero_int )
| ( ( plus_plus_int @ ( times_times_int @ SV1133 @ SV1133 ) @ ( times_times_int @ SY2472 @ SY2472 ) )
= zero_zero_int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4258]) ).
thf(4768,plain,
( ( ~ ! [SX0: int] :
( ! [SX1: int] :
( ( plus_plus_int @ ( times_times_int @ SX0 @ SX0 ) @ ( times_times_int @ SX1 @ SX1 ) )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) )
| ~ ! [SX0: int,SX1: int] :
( ( ( plus_plus_int @ ( times_times_int @ SX0 @ SX0 ) @ ( times_times_int @ SX1 @ SX1 ) )
!= zero_zero_int )
| ( SX1 = zero_zero_int ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4259]) ).
thf(4769,plain,
! [SV1134: int] :
( ( ! [SY2473: int] :
( ( SV1134 = SY2473 )
| ~ ( ord_less_eq_int @ SV1134 @ SY2473 )
| ( ord_less_int @ SV1134 @ SY2473 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4260]) ).
thf(4770,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4261]) ).
thf(4771,plain,
! [SV1135: int] :
( ( ~ ( ord_less_eq_int @ ( number_number_of_int @ SV1135 ) @ zero_zero_int )
| ( ord_less_eq_int @ SV1135 @ pls ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4262]) ).
thf(4772,plain,
! [SV1136: int] :
( ( ~ ( ord_less_eq_int @ SV1136 @ pls )
| ( ord_less_eq_int @ ( number_number_of_int @ SV1136 ) @ zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4263]) ).
thf(4773,plain,
! [SV446: nat] :
( ( ! [SY1923: nat,SY1924: nat] :
( ~ ( ord_less_nat @ one_one_nat @ SY1924 )
| ~ ( ord_less_nat @ ( power_power_nat @ SY1924 @ SV446 ) @ ( power_power_nat @ SY1924 @ SY1923 ) )
| ( ord_less_nat @ SV446 @ SY1923 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4264]) ).
thf(4774,plain,
! [SV446: nat] :
( ( ! [SY1925: nat,SY1926: nat] :
( ~ ( ord_less_nat @ one_one_nat @ SY1926 )
| ~ ( ord_less_nat @ SV446 @ SY1925 )
| ( ord_less_nat @ ( power_power_nat @ SY1926 @ SV446 ) @ ( power_power_nat @ SY1926 @ SY1925 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4265]) ).
thf(4775,plain,
! [SV1137: nat] :
( ( ! [SY2474: nat] :
( ( SV1137 != one_one_nat )
| ( SY2474 != one_one_nat )
| ( ( times_times_nat @ SV1137 @ SY2474 )
= one_one_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4266]) ).
thf(4776,plain,
( ( ~ ! [SX0: nat] :
( ! [SX1: nat] :
( ( times_times_nat @ SX0 @ SX1 )
!= one_one_nat )
| ( SX0 = one_one_nat ) )
| ~ ! [SX0: nat,SX1: nat] :
( ( ( times_times_nat @ SX0 @ SX1 )
!= one_one_nat )
| ( SX1 = one_one_nat ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4267]) ).
thf(4777,plain,
( ( ~ ~ ( ~ ! [SX0: int] :
( ! [SX1: int] :
( ( times_times_int @ SX0 @ SX1 )
!= one_one_int )
| ( SX0 = one_one_int )
| ( SX0
= ( number_number_of_int @ min ) ) )
| ~ ! [SX0: int,SX1: int] :
( ( ( times_times_int @ SX0 @ SX1 )
!= one_one_int )
| ( SX0 = one_one_int )
| ( SX1
= ( number_number_of_int @ min ) ) ) )
| ~ ~ ( ~ ! [SX0: int,SX1: int] :
( ( ( times_times_int @ SX0 @ SX1 )
!= one_one_int )
| ( SX1 = one_one_int )
| ( SX0
= ( number_number_of_int @ min ) ) )
| ~ ! [SX0: int,SX1: int] :
( ( ( times_times_int @ SX0 @ SX1 )
!= one_one_int )
| ( SX1 = one_one_int )
| ( SX1
= ( number_number_of_int @ min ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4268]) ).
thf(4778,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ( SX0 != one_one_int )
| ( SX1 != one_one_int )
| ( ( times_times_int @ SX0 @ SX1 )
= one_one_int ) )
| ~ ! [SX0: int,SX1: int] :
( ( SX0
!= ( number_number_of_int @ min ) )
| ( SX1
!= ( number_number_of_int @ min ) )
| ( ( times_times_int @ SX0 @ SX1 )
= one_one_int ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4269]) ).
thf(4779,plain,
! [SV1138: int] :
( ( ~ ( ord_less_int @ SV1138 @ ( bit1 @ pls ) )
| ( ord_less_real @ ( number267125858f_real @ SV1138 ) @ one_one_real ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4270]) ).
thf(4780,plain,
! [SV1139: int] :
( ( ~ ( ord_less_real @ ( number267125858f_real @ SV1139 ) @ one_one_real )
| ( ord_less_int @ SV1139 @ ( bit1 @ pls ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4271]) ).
thf(4781,plain,
! [SV1140: int] :
( ( ! [SY2475: int] :
( ( ( number_number_of_int @ SV1140 )
!= SY2475 )
| ( SY2475
= ( number_number_of_int @ SV1140 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4272]) ).
thf(4782,plain,
! [SV1141: int] :
( ( ! [SY2476: int] :
( ( SY2476
!= ( number_number_of_int @ SV1141 ) )
| ( ( number_number_of_int @ SV1141 )
= SY2476 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4273]) ).
thf(4783,plain,
! [SV1142: int] :
( ( ! [SY2477: int] :
( ~ ( ord_less_eq_int @ SV1142 @ SY2477 )
| ( ord_less_int @ SV1142 @ ( plus_plus_int @ SY2477 @ one_one_int ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4274]) ).
thf(4784,plain,
! [SV1143: int] :
( ( ! [SY2478: int] :
( ~ ( ord_less_int @ SV1143 @ ( plus_plus_int @ SY2478 @ one_one_int ) )
| ( ord_less_eq_int @ SV1143 @ SY2478 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4275]) ).
thf(4785,plain,
! [SV1144: real] :
( ( ! [SY2479: real] :
( ( SV1144 != zero_zero_real )
| ( SY2479 != zero_zero_real )
| ( ( plus_plus_real @ ( times_times_real @ SV1144 @ SV1144 ) @ ( times_times_real @ SY2479 @ SY2479 ) )
= zero_zero_real ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4276]) ).
thf(4786,plain,
( ( ~ ! [SX0: real] :
( ! [SX1: real] :
( ( plus_plus_real @ ( times_times_real @ SX0 @ SX0 ) @ ( times_times_real @ SX1 @ SX1 ) )
!= zero_zero_real )
| ( SX0 = zero_zero_real ) )
| ~ ! [SX0: real,SX1: real] :
( ( ( plus_plus_real @ ( times_times_real @ SX0 @ SX0 ) @ ( times_times_real @ SX1 @ SX1 ) )
!= zero_zero_real )
| ( SX1 = zero_zero_real ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4277]) ).
thf(4787,plain,
! [SV1145: int] :
( ( ~ ( ord_less_eq_int @ ( bit1 @ SV1145 ) @ pls )
| ( ord_less_int @ SV1145 @ pls ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4278]) ).
thf(4788,plain,
! [SV1146: int] :
( ( ~ ( ord_less_int @ SV1146 @ pls )
| ( ord_less_eq_int @ ( bit1 @ SV1146 ) @ pls ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4279]) ).
thf(4789,plain,
! [SV447: nat] :
( ( ! [SY1927: nat,SY1928: real] :
( ~ ( ord_less_real @ one_one_real @ SY1928 )
| ~ ( ord_less_nat @ SV447 @ SY1927 )
| ( ord_less_real @ ( power_power_real @ SY1928 @ SV447 ) @ ( power_power_real @ SY1928 @ SY1927 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4280]) ).
thf(4790,plain,
! [SV447: nat] :
( ( ! [SY1929: nat,SY1930: real] :
( ~ ( ord_less_real @ one_one_real @ SY1930 )
| ~ ( ord_less_real @ ( power_power_real @ SY1930 @ SV447 ) @ ( power_power_real @ SY1930 @ SY1929 ) )
| ( ord_less_nat @ SV447 @ SY1929 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4281]) ).
thf(4791,plain,
! [SV1147: int] :
( ( ( ( bit0 @ SV1147 )
!= pls )
| ( SV1147 = pls ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4282]) ).
thf(4792,plain,
! [SV1148: int] :
( ( ( SV1148 != pls )
| ( ( bit0 @ SV1148 )
= pls ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4283]) ).
thf(4793,plain,
! [SV1149: int] :
( ( ! [SY2480: int] :
( ~ ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ SV1149 @ SV1149 ) @ ( times_times_int @ SY2480 @ SY2480 ) ) )
| ( SV1149 != zero_zero_int )
| ( SY2480 != zero_zero_int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4284]) ).
thf(4794,plain,
( ( ~ ! [SX0: int] :
( ( SX0 = zero_zero_int )
| ! [SX1: int] : ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ SX0 @ SX0 ) @ ( times_times_int @ SX1 @ SX1 ) ) ) )
| ~ ! [SX0: int,SX1: int] :
( ( SX1 = zero_zero_int )
| ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ SX0 @ SX0 ) @ ( times_times_int @ SX1 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4285]) ).
thf(4795,plain,
! [SV1150: int] :
( ( ! [SY2481: nat] :
( ( ( number_number_of_nat @ SV1150 )
!= SY2481 )
| ( SY2481
= ( number_number_of_nat @ SV1150 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4286]) ).
thf(4796,plain,
! [SV1151: int] :
( ( ! [SY2482: nat] :
( ( SY2482
!= ( number_number_of_nat @ SV1151 ) )
| ( ( number_number_of_nat @ SV1151 )
= SY2482 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4287]) ).
thf(4797,plain,
! [SV1152: real] :
( ( ( SV1152 != zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ ( times_times_real @ SV1152 @ SV1152 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4288]) ).
thf(4798,plain,
! [SV1153: real] :
( ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ SV1153 @ SV1153 ) )
| ( SV1153 = zero_zero_real ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4289]) ).
thf(4799,plain,
! [SV1154: int] :
( ( ~ ( ord_less_int @ ( number_number_of_int @ SV1154 ) @ one_one_int )
| ( ord_less_int @ SV1154 @ ( bit1 @ pls ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4290]) ).
thf(4800,plain,
! [SV1155: int] :
( ( ~ ( ord_less_int @ SV1155 @ ( bit1 @ pls ) )
| ( ord_less_int @ ( number_number_of_int @ SV1155 ) @ one_one_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4291]) ).
thf(4801,plain,
! [SV448: real] :
( ( ! [SY1931: real,SY1932: real] :
( ( SY1932 = zero_zero_real )
| ( ( times_times_real @ SY1932 @ SV448 )
!= ( times_times_real @ SY1932 @ SY1931 ) )
| ( SV448 = SY1931 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4292]) ).
thf(4802,plain,
! [SV448: real] :
( ( ! [SY1933: real,SY1934: real] :
( ( SY1934 = zero_zero_real )
| ( SV448 != SY1933 )
| ( ( times_times_real @ SY1934 @ SV448 )
= ( times_times_real @ SY1934 @ SY1933 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4293]) ).
thf(4803,plain,
! [SV1156: int] :
( ( ! [SY2483: int] :
( ~ ( ord_less_eq_int @ ( bit0 @ SV1156 ) @ ( bit1 @ SY2483 ) )
| ( ord_less_eq_int @ SV1156 @ SY2483 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4294]) ).
thf(4804,plain,
! [SV1157: int] :
( ( ! [SY2484: int] :
( ~ ( ord_less_eq_int @ SV1157 @ SY2484 )
| ( ord_less_eq_int @ ( bit0 @ SV1157 ) @ ( bit1 @ SY2484 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4295]) ).
thf(4805,plain,
! [SV1158: int] :
( ( ( pls
!= ( bit0 @ SV1158 ) )
| ( pls = SV1158 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4296]) ).
thf(4806,plain,
! [SV1159: int] :
( ( ( pls != SV1159 )
| ( pls
= ( bit0 @ SV1159 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4297]) ).
thf(4807,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ( ord_less_int @ SX0 @ SX1 )
| ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_nat @ ( number_number_of_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ pls @ SX1 )
| ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_nat @ ( number_number_of_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4298]) ).
thf(4808,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_nat @ ( number_number_of_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) )
| ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ pls @ SX1 ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_nat @ ( number_number_of_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4299]) ).
thf(4809,plain,
! [SV1160: int] :
( ( ! [SY2485: int] :
( ~ ( ord_less_int @ ( bit0 @ SV1160 ) @ ( bit0 @ SY2485 ) )
| ( ord_less_int @ SV1160 @ SY2485 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4300]) ).
thf(4810,plain,
! [SV1161: int] :
( ( ! [SY2486: int] :
( ~ ( ord_less_int @ SV1161 @ SY2486 )
| ( ord_less_int @ ( bit0 @ SV1161 ) @ ( bit0 @ SY2486 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4301]) ).
thf(4811,plain,
! [SV787: int,SV449: int,SV981: int] :
( ( ~ ! [SY2385: int,SY2386: int] :
( ~ ( zcong @ SV981 @ SY2385 @ SY2386 )
| ~ ( zcong @ SV449 @ ( times_times_int @ SV981 @ SV787 ) @ SY2386 )
| ( zcong @ SV449 @ ( times_times_int @ SY2385 @ SV787 ) @ SY2386 ) )
| ~ ! [SY2387: int,SY2388: int] :
( ~ ( zcong @ SV981 @ SY2387 @ SY2388 )
| ~ ( zcong @ SV449 @ ( times_times_int @ SY2387 @ SV787 ) @ SY2388 )
| ( zcong @ SV449 @ ( times_times_int @ SV981 @ SV787 ) @ SY2388 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4302]) ).
thf(4812,plain,
! [SV1162: real] :
( ( ! [SY2487: nat] :
( ( SY2487 != zero_zero_nat )
| ( ( power_power_real @ SV1162 @ SY2487 )
= one_one_real ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4303]) ).
thf(4813,plain,
! [SV1163: real] :
( ( ! [SY2488: nat] :
( ( SY2488 = zero_zero_nat )
| ( ( power_power_real @ SV1163 @ SY2488 )
= ( times_times_real @ SV1163 @ ( power_power_real @ SV1163 @ ( minus_minus_nat @ SY2488 @ one_one_nat ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4304]) ).
thf(4814,plain,
! [SV788: int,SV450: int] :
( ( ~ ~ ( ~ ! [SY2290: int,SY2291: int] :
( ( ( plus_plus_int @ ( times_times_int @ SY2290 @ SV450 ) @ ( times_times_int @ SY2291 @ SV788 ) )
= ( plus_plus_int @ ( times_times_int @ SY2290 @ SV788 ) @ ( times_times_int @ SY2291 @ SV450 ) ) )
| ( SY2290 != SY2291 ) )
| ~ ( ! [SY2292: int,SY2293: int] :
( ( plus_plus_int @ ( times_times_int @ SY2292 @ SV450 ) @ ( times_times_int @ SY2293 @ SV788 ) )
= ( plus_plus_int @ ( times_times_int @ SY2292 @ SV788 ) @ ( times_times_int @ SY2293 @ SV450 ) ) )
| ( SV450 != SV788 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4305]) ).
thf(4815,plain,
! [SV788: int,SV450: int] :
( ( ~ ! [SY2294: int,SY2295: int] :
( ( SY2294 = SY2295 )
| ( SV450 = SV788 )
| ( ( plus_plus_int @ ( times_times_int @ SY2294 @ SV450 ) @ ( times_times_int @ SY2295 @ SV788 ) )
!= ( plus_plus_int @ ( times_times_int @ SY2294 @ SV788 ) @ ( times_times_int @ SY2295 @ SV450 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4305]) ).
thf(4816,plain,
! [SV1164: int] :
( ( ! [SY2489: int] :
( ~ ( ord_less_eq_int @ SV1164 @ SY2489 )
| ( ord_less_int @ ( bit0 @ SV1164 ) @ ( bit1 @ SY2489 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4306]) ).
thf(4817,plain,
! [SV1165: int] :
( ( ! [SY2490: int] :
( ~ ( ord_less_int @ ( bit0 @ SV1165 ) @ ( bit1 @ SY2490 ) )
| ( ord_less_eq_int @ SV1165 @ SY2490 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4307]) ).
thf(4818,plain,
! [SV1166: int] :
( ( ( SV1166 = zero_zero_int )
| ( ord_less_int @ zero_zero_int @ ( power_power_int @ SV1166 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4308]) ).
thf(4819,plain,
! [SV1167: int] :
( ( ~ ( ord_less_int @ zero_zero_int @ ( power_power_int @ SV1167 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ( SV1167 != zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4309]) ).
thf(4820,plain,
! [SV1168: int] :
( ( ~ ( ord_less_int @ SV1168 @ pls )
| ( ord_less_real @ ( number267125858f_real @ SV1168 ) @ zero_zero_real ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4310]) ).
thf(4821,plain,
! [SV1169: int] :
( ( ~ ( ord_less_real @ ( number267125858f_real @ SV1169 ) @ zero_zero_real )
| ( ord_less_int @ SV1169 @ pls ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4311]) ).
thf(4822,plain,
! [SV1170: real] :
( ( ! [SY2491: real] :
( ( SV1170 != zero_zero_real )
| ( SY2491 != zero_zero_real )
| ( ( plus_plus_real @ ( times_times_real @ SV1170 @ SV1170 ) @ ( times_times_real @ SY2491 @ SY2491 ) )
= zero_zero_real ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4312]) ).
thf(4823,plain,
( ( ~ ! [SX0: real] :
( ! [SX1: real] :
( ( plus_plus_real @ ( times_times_real @ SX0 @ SX0 ) @ ( times_times_real @ SX1 @ SX1 ) )
!= zero_zero_real )
| ( SX0 = zero_zero_real ) )
| ~ ! [SX0: real,SX1: real] :
( ( ( plus_plus_real @ ( times_times_real @ SX0 @ SX0 ) @ ( times_times_real @ SX1 @ SX1 ) )
!= zero_zero_real )
| ( SX1 = zero_zero_real ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4313]) ).
thf(4824,plain,
! [SV1171: int] :
( ( ~ ( ord_less_eq_int @ ( bit1 @ pls ) @ SV1171 )
| ( ord_less_eq_real @ one_one_real @ ( number267125858f_real @ SV1171 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4314]) ).
thf(4825,plain,
! [SV1172: int] :
( ( ~ ( ord_less_eq_real @ one_one_real @ ( number267125858f_real @ SV1172 ) )
| ( ord_less_eq_int @ ( bit1 @ pls ) @ SV1172 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4315]) ).
thf(4826,plain,
! [SV789: int,SV451: int,SV982: int] :
( ( ~ ! [SY2389: int,SY2390: int] :
( ~ ( zcong @ SV982 @ SY2389 @ SY2390 )
| ~ ( zcong @ SV451 @ ( times_times_int @ SV789 @ SV982 ) @ SY2390 )
| ( zcong @ SV451 @ ( times_times_int @ SV789 @ SY2389 ) @ SY2390 ) )
| ~ ! [SY2391: int,SY2392: int] :
( ~ ( zcong @ SV982 @ SY2391 @ SY2392 )
| ~ ( zcong @ SV451 @ ( times_times_int @ SV789 @ SY2391 ) @ SY2392 )
| ( zcong @ SV451 @ ( times_times_int @ SV789 @ SV982 ) @ SY2392 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4316]) ).
thf(4827,plain,
! [SV1173: int] :
( ( ~ ( ord_less_eq_int @ ( bit1 @ SV1173 ) @ min )
| ( ord_less_eq_int @ SV1173 @ min ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4317]) ).
thf(4828,plain,
! [SV1174: int] :
( ( ~ ( ord_less_eq_int @ SV1174 @ min )
| ( ord_less_eq_int @ ( bit1 @ SV1174 ) @ min ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4318]) ).
thf(4829,plain,
! [SV1175: int] :
( ( ! [SY2492: int] :
( ~ ( ord_less_eq_int @ ( bit1 @ SV1175 ) @ ( bit1 @ SY2492 ) )
| ( ord_less_eq_int @ SV1175 @ SY2492 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4319]) ).
thf(4830,plain,
! [SV1176: int] :
( ( ! [SY2493: int] :
( ~ ( ord_less_eq_int @ SV1176 @ SY2493 )
| ( ord_less_eq_int @ ( bit1 @ SV1176 ) @ ( bit1 @ SY2493 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4320]) ).
thf(4831,plain,
! [SV1177: int] :
( ( ! [SY2494: int] :
( ( SV1177 != SY2494 )
| ( zcong @ SV1177 @ SY2494 @ zero_zero_int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4321]) ).
thf(4832,plain,
! [SV1178: int] :
( ( ! [SY2495: int] :
( ~ ( zcong @ SV1178 @ SY2495 @ zero_zero_int )
| ( SV1178 = SY2495 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4322]) ).
thf(4833,plain,
! [SV1179: int] :
( ( ! [SY2496: int] :
( ~ ( ord_less_eq_int @ ( bit1 @ SV1179 ) @ ( bit0 @ SY2496 ) )
| ( ord_less_int @ SV1179 @ SY2496 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4323]) ).
thf(4834,plain,
! [SV1180: int] :
( ( ! [SY2497: int] :
( ~ ( ord_less_int @ SV1180 @ SY2497 )
| ( ord_less_eq_int @ ( bit1 @ SV1180 ) @ ( bit0 @ SY2497 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4324]) ).
thf(4835,plain,
! [SV790: nat,SV452: nat] :
( ( ~ ! [SY2301: nat,SY2302: nat] :
( ( ( plus_plus_nat @ ( times_times_nat @ SV452 @ SV790 ) @ ( times_times_nat @ SY2301 @ SY2302 ) )
!= ( plus_plus_nat @ ( times_times_nat @ SV452 @ SY2302 ) @ ( times_times_nat @ SY2301 @ SV790 ) ) )
| ( SV452 = SY2301 )
| ( SV790 = SY2302 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4325]) ).
thf(4836,plain,
! [SV790: nat,SV452: nat] :
( ( ~ ~ ( ~ ! [SY2303: nat] :
( ( SV452 != SY2303 )
| ! [SY2304: nat] :
( ( plus_plus_nat @ ( times_times_nat @ SV452 @ SV790 ) @ ( times_times_nat @ SY2303 @ SY2304 ) )
= ( plus_plus_nat @ ( times_times_nat @ SV452 @ SY2304 ) @ ( times_times_nat @ SY2303 @ SV790 ) ) ) )
| ~ ! [SY2305: nat,SY2306: nat] :
( ( SV790 != SY2306 )
| ( ( plus_plus_nat @ ( times_times_nat @ SV452 @ SV790 ) @ ( times_times_nat @ SY2305 @ SY2306 ) )
= ( plus_plus_nat @ ( times_times_nat @ SV452 @ SY2306 ) @ ( times_times_nat @ SY2305 @ SV790 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4325]) ).
thf(4837,plain,
! [SV1181: real] :
( ( ! [SY2498: nat] :
( ( SY2498 = zero_zero_nat )
| ( SV1181 != zero_zero_real )
| ( ( power_power_real @ SV1181 @ SY2498 )
= zero_zero_real ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4326]) ).
thf(4838,plain,
( ( ~ ! [SX0: real,SX1: nat] :
( ( ( power_power_real @ SX0 @ SX1 )
!= zero_zero_real )
| ( SX1 != zero_zero_nat ) )
| ~ ! [SX0: real] :
( ! [SX1: nat] :
( ( power_power_real @ SX0 @ SX1 )
!= zero_zero_real )
| ( SX0 = zero_zero_real ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4327]) ).
thf(4839,plain,
! [SV1182: nat] :
( ( ! [SY2499: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV1182 @ SY2499 ) )
| ( SY2499 = zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV1182 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4328]) ).
thf(4840,plain,
( ( ~ ! [SX0: nat,SX1: nat] :
( ( SX1 != zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SX0 @ SX1 ) ) )
| ~ ! [SX0: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SX0 )
| ! [SX1: nat] : ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4329]) ).
thf(4841,plain,
! [SV791: int,SV453: int] :
( ( ~ ! [SY2307: int,SY2308: int] :
( ( ( plus_plus_int @ ( times_times_int @ SV453 @ SV791 ) @ ( times_times_int @ SY2307 @ SY2308 ) )
!= ( plus_plus_int @ ( times_times_int @ SV453 @ SY2308 ) @ ( times_times_int @ SY2307 @ SV791 ) ) )
| ( SV453 = SY2307 )
| ( SV791 = SY2308 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4330]) ).
thf(4842,plain,
! [SV791: int,SV453: int] :
( ( ~ ~ ( ~ ! [SY2309: int] :
( ( SV453 != SY2309 )
| ! [SY2310: int] :
( ( plus_plus_int @ ( times_times_int @ SV453 @ SV791 ) @ ( times_times_int @ SY2309 @ SY2310 ) )
= ( plus_plus_int @ ( times_times_int @ SV453 @ SY2310 ) @ ( times_times_int @ SY2309 @ SV791 ) ) ) )
| ~ ! [SY2311: int,SY2312: int] :
( ( SV791 != SY2312 )
| ( ( plus_plus_int @ ( times_times_int @ SV453 @ SV791 ) @ ( times_times_int @ SY2311 @ SY2312 ) )
= ( plus_plus_int @ ( times_times_int @ SV453 @ SY2312 ) @ ( times_times_int @ SY2311 @ SV791 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4330]) ).
thf(4843,plain,
! [SV1183: nat] :
( ( ! [SY2500: nat] :
( ( SY2500 != zero_zero_nat )
| ( ( power_power_nat @ SV1183 @ SY2500 )
= one_one_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4331]) ).
thf(4844,plain,
! [SV1184: nat] :
( ( ! [SY2501: nat] :
( ( SY2501 = zero_zero_nat )
| ( ( power_power_nat @ SV1184 @ SY2501 )
= ( times_times_nat @ SV1184 @ ( power_power_nat @ SV1184 @ ( minus_minus_nat @ SY2501 @ one_one_nat ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4332]) ).
thf(4845,plain,
! [SV1185: int] :
( ( ! [SY2502: int] :
( ~ ( ord_less_int @ zero_zero_int @ SY2502 )
| ( SY2502 != one_one_int )
| ( SV1185 != one_one_int )
| ( ( times_times_int @ SY2502 @ SV1185 )
= one_one_int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4333]) ).
thf(4846,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ zero_zero_int @ SX1 )
| ( ( times_times_int @ SX1 @ SX0 )
!= one_one_int )
| ( SX1 = one_one_int ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ zero_zero_int @ SX1 )
| ( ( times_times_int @ SX1 @ SX0 )
!= one_one_int )
| ( SX0 = one_one_int ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4334]) ).
thf(4847,plain,
! [SV1186: int] :
( ( ! [SY2503: int] :
( ~ ( ord_less_eq_int @ ( plus_plus_int @ SV1186 @ one_one_int ) @ SY2503 )
| ( ord_less_int @ SV1186 @ SY2503 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4335]) ).
thf(4848,plain,
! [SV1187: int] :
( ( ! [SY2504: int] :
( ~ ( ord_less_int @ SV1187 @ SY2504 )
| ( ord_less_eq_int @ ( plus_plus_int @ SV1187 @ one_one_int ) @ SY2504 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4336]) ).
thf(4849,plain,
! [SV1188: int] :
( ( ( ( number_number_of_nat @ SV1188 )
!= zero_zero_nat )
| ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ SV1188 ) )
= one_one_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4337]) ).
thf(4850,plain,
! [SV1189: int] :
( ( ( ( number_number_of_nat @ SV1189 )
= zero_zero_nat )
| ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ SV1189 ) )
= zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4338]) ).
thf(4851,plain,
! [SV1190: real] :
( ( ! [SY2505: real] :
( ( SV1190 = SY2505 )
| ~ ( ord_less_eq_real @ SV1190 @ SY2505 )
| ( ord_less_real @ SV1190 @ SY2505 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4339]) ).
thf(4852,plain,
( ( ~ ! [SX0: real,SX1: real] :
( ~ ( ord_less_real @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: real,SX1: real] :
( ~ ( ord_less_real @ SX0 @ SX1 )
| ( ord_less_eq_real @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4340]) ).
thf(4853,plain,
! [SV1191: int] :
( ( ! [SY2506: int] :
( ~ ( ord_less_int @ SV1191 @ SY2506 )
| ( ord_less_real @ ( number267125858f_real @ SV1191 ) @ ( number267125858f_real @ SY2506 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4341]) ).
thf(4854,plain,
! [SV1192: int] :
( ( ! [SY2507: int] :
( ~ ( ord_less_real @ ( number267125858f_real @ SV1192 ) @ ( number267125858f_real @ SY2507 ) )
| ( ord_less_int @ SV1192 @ SY2507 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4342]) ).
thf(4855,plain,
! [SV1193: int] :
( ( ! [SY2508: int] :
( ~ ( ord_less_eq_int @ ( number_number_of_int @ SV1193 ) @ ( number_number_of_int @ SY2508 ) )
| ~ ( ord_less_int @ ( number_number_of_int @ SY2508 ) @ ( number_number_of_int @ SV1193 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4343]) ).
thf(4856,plain,
! [SV1194: int] :
( ( ! [SY2509: int] :
( ( ord_less_int @ ( number_number_of_int @ SY2509 ) @ ( number_number_of_int @ SV1194 ) )
| ( ord_less_eq_int @ ( number_number_of_int @ SV1194 ) @ ( number_number_of_int @ SY2509 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4344]) ).
thf(4857,plain,
! [SV1195: int] :
( ( ( ( plus_plus_int @ SV1195 @ SV1195 )
!= zero_zero_int )
| ( SV1195 = zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4345]) ).
thf(4858,plain,
! [SV1196: int] :
( ( ( SV1196 != zero_zero_int )
| ( ( plus_plus_int @ SV1196 @ SV1196 )
= zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4346]) ).
thf(4859,plain,
! [SV1197: nat] :
( ( ! [SY2510: int] :
( ~ ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV1197 @ ( number_number_of_nat @ SY2510 ) ) )
| ( ( number_number_of_nat @ SY2510 )
= zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV1197 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4347]) ).
thf(4860,plain,
( ( ~ ! [SX0: nat,SX1: int] :
( ( ( number_number_of_nat @ SX1 )
!= zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SX0 @ ( number_number_of_nat @ SX1 ) ) ) )
| ~ ! [SX0: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SX0 )
| ! [SX1: int] : ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SX0 @ ( number_number_of_nat @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4348]) ).
thf(4861,plain,
! [SV1198: int] :
( ( ~ ( ord_less_eq_int @ SV1198 @ ( bit1 @ pls ) )
| ( ord_less_eq_real @ ( number267125858f_real @ SV1198 ) @ one_one_real ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4349]) ).
thf(4862,plain,
! [SV1199: int] :
( ( ~ ( ord_less_eq_real @ ( number267125858f_real @ SV1199 ) @ one_one_real )
| ( ord_less_eq_int @ SV1199 @ ( bit1 @ pls ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4350]) ).
thf(4863,plain,
! [SV1200: int] :
( ( ! [SY2511: int] :
( ~ ( ord_less_int @ SY2511 @ pls )
| ( ( times_times_nat @ ( number_number_of_nat @ SY2511 ) @ ( number_number_of_nat @ SV1200 ) )
= zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4351]) ).
thf(4864,plain,
! [SV1201: int] :
( ( ! [SY2512: int] :
( ( ord_less_int @ SY2512 @ pls )
| ( ( times_times_nat @ ( number_number_of_nat @ SY2512 ) @ ( number_number_of_nat @ SV1201 ) )
= ( number_number_of_nat @ ( times_times_int @ SY2512 @ SV1201 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4352]) ).
thf(4865,plain,
! [SV1202: real] :
( ( ( SV1202 = zero_zero_real )
| ( ord_less_real @ zero_zero_real @ ( power_power_real @ SV1202 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4353]) ).
thf(4866,plain,
! [SV1203: real] :
( ( ~ ( ord_less_real @ zero_zero_real @ ( power_power_real @ SV1203 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ( SV1203 != zero_zero_real ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4354]) ).
thf(4867,plain,
! [SV1204: int] :
( ( ~ ( ~ ~ ( ~ ( dvd_dvd_int @ ( sK3_M_9 @ SV1204 ) @ SV1204 )
| ~ ( ord_less_eq_int @ zero_zero_int @ ( sK3_M_9 @ SV1204 ) ) )
| ~ ~ ( ~ ( ( ( sK3_M_9 @ SV1204 )
!= one_one_int ) )
| ~ ( ( ( sK3_M_9 @ SV1204 )
!= SV1204 ) ) ) )
| ~ ( ord_less_int @ one_one_int @ SV1204 )
| ( zprime @ SV1204 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4355]) ).
thf(4868,plain,
( ( ~ ! [SX0: int] :
( ~ ( zprime @ SX0 )
| ! [SX1: int] :
( ~ ( dvd_dvd_int @ SX1 @ SX0 )
| ~ ( ord_less_eq_int @ zero_zero_int @ SX1 )
| ( SX1 = one_one_int )
| ( SX1 = SX0 ) ) )
| ~ ! [SX0: int] :
( ~ ( zprime @ SX0 )
| ( ord_less_int @ one_one_int @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4356]) ).
thf(4869,plain,
! [SV454: int] :
( ( ! [SY1968: nat,SY1969: int] :
( ~ ( ord_less_int @ SY1969 @ pls )
| ( ( times_times_nat @ ( number_number_of_nat @ SY1969 ) @ ( times_times_nat @ ( number_number_of_nat @ SV454 ) @ SY1968 ) )
= zero_zero_nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4357]) ).
thf(4870,plain,
! [SV454: int] :
( ( ! [SY1970: nat,SY1971: int] :
( ( ord_less_int @ SY1971 @ pls )
| ( ( times_times_nat @ ( number_number_of_nat @ SY1971 ) @ ( times_times_nat @ ( number_number_of_nat @ SV454 ) @ SY1970 ) )
= ( times_times_nat @ ( number_number_of_nat @ ( times_times_int @ SY1971 @ SV454 ) ) @ SY1970 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4358]) ).
thf(4871,plain,
! [SV1205: int] :
( ( ! [SY2513: int] :
( ~ ( zcong @ SV1205 @ zero_zero_int @ SY2513 )
| ( ( legendre @ SV1205 @ SY2513 )
= zero_zero_int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4359]) ).
thf(4872,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ( zcong @ SX0 @ zero_zero_int @ SX1 )
| ~ ( quadRes @ SX1 @ SX0 )
| ( ( legendre @ SX0 @ SX1 )
= one_one_int ) )
| ~ ! [SX0: int,SX1: int] :
( ( zcong @ SX0 @ zero_zero_int @ SX1 )
| ( quadRes @ SX1 @ SX0 )
| ( ( legendre @ SX0 @ SX1 )
= ( number_number_of_int @ min ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4360]) ).
thf(4873,plain,
! [SV1206: nat] :
( ( ( SV1206 != zero_zero_nat )
| ( ( power_power_int @ zero_zero_int @ SV1206 )
= one_one_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4361]) ).
thf(4874,plain,
! [SV1207: nat] :
( ( ( SV1207 = zero_zero_nat )
| ( ( power_power_int @ zero_zero_int @ SV1207 )
= zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4362]) ).
thf(4875,plain,
! [SV455: real,SV792: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV792 )
= $false )
| ( ( ~ ( ord_less_real @ zero_zero_real @ SV455 )
| ~ ( ~ ! [SY2313: real] :
( ( ( power_power_real @ SY2313 @ SV792 )
!= SV455 )
| ~ ( ord_less_real @ zero_zero_real @ SY2313 )
| ( SY2313
= ( sK1_X_1 @ SV792 @ SV455 ) ) )
| ~ ~ ( ( ( power_power_real @ ( sK1_X_1 @ SV792 @ SV455 ) @ SV792 )
!= SV455 )
| ~ ( ord_less_real @ zero_zero_real @ ( sK1_X_1 @ SV792 @ SV455 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4363]) ).
thf(4876,plain,
! [SV1208: int] :
( ( ( zero_zero_nat
!= ( number_number_of_nat @ SV1208 ) )
| ( ord_less_eq_int @ SV1208 @ pls ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4364]) ).
thf(4877,plain,
! [SV1209: int] :
( ( ~ ( ord_less_eq_int @ SV1209 @ pls )
| ( zero_zero_nat
= ( number_number_of_nat @ SV1209 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4365]) ).
thf(4878,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_eq_nat @ ( number_number_of_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) ) )
| ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ SX0 @ pls )
| ! [SX1: int] : ( ord_less_eq_nat @ ( number_number_of_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4366]) ).
thf(4879,plain,
! [SV1210: int] :
( ( ! [SY2514: int] :
( ~ ( ord_less_eq_nat @ ( number_number_of_nat @ SV1210 ) @ ( number_number_of_nat @ SY2514 ) )
| ( ord_less_eq_int @ SV1210 @ SY2514 )
| ( ord_less_eq_int @ SV1210 @ pls ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4367]) ).
thf(4880,plain,
! [SV1211: int] :
( ( ~ ( ord_less_int @ ( number_number_of_int @ SV1211 ) @ zero_zero_int )
| ( ord_less_int @ SV1211 @ pls ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4368]) ).
thf(4881,plain,
! [SV1212: int] :
( ( ~ ( ord_less_int @ SV1212 @ pls )
| ( ord_less_int @ ( number_number_of_int @ SV1212 ) @ zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4369]) ).
thf(4882,plain,
! [SV1213: int] :
( ( ~ ( ord_less_eq_int @ one_one_int @ ( number_number_of_int @ SV1213 ) )
| ( ord_less_eq_int @ ( bit1 @ pls ) @ SV1213 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4370]) ).
thf(4883,plain,
! [SV1214: int] :
( ( ~ ( ord_less_eq_int @ ( bit1 @ pls ) @ SV1214 )
| ( ord_less_eq_int @ one_one_int @ ( number_number_of_int @ SV1214 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4371]) ).
thf(4884,plain,
! [SV1215: int] :
( ( ! [SY2515: real] :
( ( ( number267125858f_real @ SV1215 )
!= SY2515 )
| ( SY2515
= ( number267125858f_real @ SV1215 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4372]) ).
thf(4885,plain,
! [SV1216: int] :
( ( ! [SY2516: real] :
( ( SY2516
!= ( number267125858f_real @ SV1216 ) )
| ( ( number267125858f_real @ SV1216 )
= SY2516 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4373]) ).
thf(4886,plain,
! [SV1217: int] :
( ( ~ ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ SV1217 ) @ SV1217 ) @ zero_zero_int )
| ( ord_less_int @ SV1217 @ zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4374]) ).
thf(4887,plain,
! [SV1218: int] :
( ( ~ ( ord_less_int @ SV1218 @ zero_zero_int )
| ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ SV1218 ) @ SV1218 ) @ zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4375]) ).
thf(4888,plain,
! [SV456: int] :
( ( ! [SY1974: int,SY1975: int] :
( ~ ( zcong @ SV456 @ SY1974 @ SY1975 )
| ( zcong @ SY1974 @ SV456 @ SY1975 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4376]) ).
thf(4889,plain,
! [SV456: int] :
( ( ! [SY1976: int,SY1977: int] :
( ~ ( zcong @ SY1976 @ SV456 @ SY1977 )
| ( zcong @ SV456 @ SY1976 @ SY1977 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4377]) ).
thf(4890,plain,
! [SV457: int,SV983: int,SV793: int] :
( ( ~ ! [SY2393: int,SY2394: int] :
( ~ ( dvd_dvd_int @ SY2393 @ SY2394 )
| ~ ( dvd_dvd_int @ SY2393 @ ( plus_plus_int @ SV793 @ SV983 ) )
| ( dvd_dvd_int @ SY2393 @ ( plus_plus_int @ ( plus_plus_int @ SV793 @ ( times_times_int @ SV457 @ SY2394 ) ) @ SV983 ) ) )
| ~ ! [SY2395: int,SY2396: int] :
( ~ ( dvd_dvd_int @ SY2395 @ SY2396 )
| ~ ( dvd_dvd_int @ SY2395 @ ( plus_plus_int @ ( plus_plus_int @ SV793 @ ( times_times_int @ SV457 @ SY2396 ) ) @ SV983 ) )
| ( dvd_dvd_int @ SY2395 @ ( plus_plus_int @ SV793 @ SV983 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4378]) ).
thf(4891,plain,
! [SV1219: int] :
( ( ~ ( ord_less_int @ ( bit1 @ pls ) @ SV1219 )
| ( ord_less_real @ one_one_real @ ( number267125858f_real @ SV1219 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4379]) ).
thf(4892,plain,
! [SV1220: int] :
( ( ~ ( ord_less_real @ one_one_real @ ( number267125858f_real @ SV1220 ) )
| ( ord_less_int @ ( bit1 @ pls ) @ SV1220 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4380]) ).
thf(4893,plain,
! [SV1221: real] :
( ( ! [SY2517: real] :
( ( SV1221
!= ( plus_plus_real @ SV1221 @ SY2517 ) )
| ( SY2517 = zero_zero_real ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4381]) ).
thf(4894,plain,
! [SV1222: real] :
( ( ! [SY2518: real] :
( ( SY2518 != zero_zero_real )
| ( SV1222
= ( plus_plus_real @ SV1222 @ SY2518 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4382]) ).
thf(4895,plain,
! [SV458: int] :
( ( ! [SY1984: int,SY1985: int] :
( ! [SY1986: int] :
( SY1984
!= ( plus_plus_int @ SV458 @ ( times_times_int @ SY1985 @ SY1986 ) ) )
| ( zcong @ SV458 @ SY1984 @ SY1985 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4383]) ).
thf(4896,plain,
! [SV458: int] :
( ( ! [SY1987: int,SY1988: int] :
( ~ ( zcong @ SV458 @ SY1987 @ SY1988 )
| ( SY1987
= ( plus_plus_int @ SV458 @ ( times_times_int @ SY1988 @ ( sK6_K_1 @ SY1988 @ SY1987 @ SV458 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4384]) ).
thf(4897,plain,
! [SV1223: int] :
( ( ~ ( ord_less_eq_int @ pls @ ( bit0 @ SV1223 ) )
| ( ord_less_eq_int @ pls @ SV1223 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4385]) ).
thf(4898,plain,
! [SV1224: int] :
( ( ~ ( ord_less_eq_int @ pls @ SV1224 )
| ( ord_less_eq_int @ pls @ ( bit0 @ SV1224 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4386]) ).
thf(4899,plain,
! [SV459: nat] :
( ( ! [SY1989: nat,SY1990: nat] :
( ~ ( ord_less_nat @ one_one_nat @ SY1990 )
| ( ( power_power_nat @ SY1990 @ SV459 )
!= ( power_power_nat @ SY1990 @ SY1989 ) )
| ( SV459 = SY1989 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4387]) ).
thf(4900,plain,
! [SV459: nat] :
( ( ! [SY1991: nat,SY1992: nat] :
( ~ ( ord_less_nat @ one_one_nat @ SY1992 )
| ( SV459 != SY1991 )
| ( ( power_power_nat @ SY1992 @ SV459 )
= ( power_power_nat @ SY1992 @ SY1991 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4388]) ).
thf(4901,plain,
! [SV794: real,SV460: real] :
( ( ~ ! [SY2319: real,SY2320: real] :
( ( ( plus_plus_real @ ( times_times_real @ SV460 @ SV794 ) @ ( times_times_real @ SY2319 @ SY2320 ) )
!= ( plus_plus_real @ ( times_times_real @ SV460 @ SY2320 ) @ ( times_times_real @ SY2319 @ SV794 ) ) )
| ( SV460 = SY2319 )
| ( SV794 = SY2320 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4389]) ).
thf(4902,plain,
! [SV794: real,SV460: real] :
( ( ~ ~ ( ~ ! [SY2321: real] :
( ( SV460 != SY2321 )
| ! [SY2322: real] :
( ( plus_plus_real @ ( times_times_real @ SV460 @ SV794 ) @ ( times_times_real @ SY2321 @ SY2322 ) )
= ( plus_plus_real @ ( times_times_real @ SV460 @ SY2322 ) @ ( times_times_real @ SY2321 @ SV794 ) ) ) )
| ~ ! [SY2323: real,SY2324: real] :
( ( SV794 != SY2324 )
| ( ( plus_plus_real @ ( times_times_real @ SV460 @ SV794 ) @ ( times_times_real @ SY2323 @ SY2324 ) )
= ( plus_plus_real @ ( times_times_real @ SV460 @ SY2324 ) @ ( times_times_real @ SY2323 @ SV794 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4389]) ).
thf(4903,plain,
! [SV1225: int] :
( ( ~ ( ord_less_int @ ( bit1 @ SV1225 ) @ pls )
| ( ord_less_int @ SV1225 @ pls ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4390]) ).
thf(4904,plain,
! [SV1226: int] :
( ( ~ ( ord_less_int @ SV1226 @ pls )
| ( ord_less_int @ ( bit1 @ SV1226 ) @ pls ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4391]) ).
thf(4905,plain,
! [SV1227: int] :
( ( ~ ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ SV1227 ) )
| ( ord_less_eq_int @ pls @ SV1227 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4392]) ).
thf(4906,plain,
! [SV1228: int] :
( ( ~ ( ord_less_eq_int @ pls @ SV1228 )
| ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ SV1228 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4393]) ).
thf(4907,plain,
! [SV461: nat] :
( ( ! [SY2000: nat,SY2001: nat] :
( ~ ( dvd_dvd_nat @ ( times_times_nat @ SV461 @ SY2000 ) @ ( times_times_nat @ SY2001 @ SY2000 ) )
| ( SY2000 = zero_zero_nat )
| ( dvd_dvd_nat @ SV461 @ SY2001 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4394]) ).
thf(4908,plain,
! [SV461: nat] :
( ( ~ ( ~ ! [SY2002: nat] :
( ( SY2002 != zero_zero_nat )
| ! [SY2003: nat] : ( dvd_dvd_nat @ ( times_times_nat @ SV461 @ SY2002 ) @ ( times_times_nat @ SY2003 @ SY2002 ) ) )
| ~ ! [SY2004: nat,SY2005: nat] :
( ~ ( dvd_dvd_nat @ SV461 @ SY2005 )
| ( dvd_dvd_nat @ ( times_times_nat @ SV461 @ SY2004 ) @ ( times_times_nat @ SY2005 @ SY2004 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4395]) ).
thf(4909,plain,
! [SV1229: int] :
( ( ! [SY2519: int] :
( ( ( number267125858f_real @ SV1229 )
!= ( number267125858f_real @ SY2519 ) )
| ( SV1229 = SY2519 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4396]) ).
thf(4910,plain,
! [SV1230: int] :
( ( ! [SY2520: int] :
( ( SV1230 != SY2520 )
| ( ( number267125858f_real @ SV1230 )
= ( number267125858f_real @ SY2520 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4397]) ).
thf(4911,plain,
! [SV1231: nat] :
( ( ( SV1231 != zero_zero_nat )
| ( ( power_power_nat @ zero_zero_nat @ SV1231 )
= one_one_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4398]) ).
thf(4912,plain,
! [SV1232: nat] :
( ( ( SV1232 = zero_zero_nat )
| ( ( power_power_nat @ zero_zero_nat @ SV1232 )
= zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4399]) ).
thf(4913,plain,
! [SV1233: int] :
( ( ~ ( ord_less_eq_int @ ( bit0 @ SV1233 ) @ min )
| ( ord_less_eq_int @ SV1233 @ min ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4400]) ).
thf(4914,plain,
! [SV1234: int] :
( ( ~ ( ord_less_eq_int @ SV1234 @ min )
| ( ord_less_eq_int @ ( bit0 @ SV1234 ) @ min ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4401]) ).
thf(4915,plain,
! [SV1235: int] :
( ( ! [SY2521: int] :
( ~ ( ord_less_int @ ( bit1 @ SV1235 ) @ ( bit0 @ SY2521 ) )
| ( ord_less_int @ SV1235 @ SY2521 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4402]) ).
thf(4916,plain,
! [SV1236: int] :
( ( ! [SY2522: int] :
( ~ ( ord_less_int @ SV1236 @ SY2522 )
| ( ord_less_int @ ( bit1 @ SV1236 ) @ ( bit0 @ SY2522 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4403]) ).
thf(4917,plain,
! [SV1237: int] :
( ( ! [SY2523: int] :
( ~ ( ord_less_eq_int @ ( bit0 @ SV1237 ) @ ( bit0 @ SY2523 ) )
| ( ord_less_eq_int @ SV1237 @ SY2523 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4404]) ).
thf(4918,plain,
! [SV1238: int] :
( ( ! [SY2524: int] :
( ~ ( ord_less_eq_int @ SV1238 @ SY2524 )
| ( ord_less_eq_int @ ( bit0 @ SV1238 ) @ ( bit0 @ SY2524 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4405]) ).
thf(4919,plain,
! [SV1239: nat] :
( ( ! [SY2525: nat] :
( ( SV1239
!= ( plus_plus_nat @ SV1239 @ SY2525 ) )
| ( SY2525 = zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4406]) ).
thf(4920,plain,
! [SV1240: nat] :
( ( ! [SY2526: nat] :
( ( SY2526 != zero_zero_nat )
| ( SV1240
= ( plus_plus_nat @ SV1240 @ SY2526 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4407]) ).
thf(4921,plain,
! [SV1241: int] :
( ( ! [SY2527: int] :
( ~ ( ord_less_int @ ( bit1 @ SV1241 ) @ ( bit1 @ SY2527 ) )
| ( ord_less_int @ SV1241 @ SY2527 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4408]) ).
thf(4922,plain,
! [SV1242: int] :
( ( ! [SY2528: int] :
( ~ ( ord_less_int @ SV1242 @ SY2528 )
| ( ord_less_int @ ( bit1 @ SV1242 ) @ ( bit1 @ SY2528 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4409]) ).
thf(4923,plain,
! [SV1243: nat] :
( ( ! [SY2529: nat] :
( ( SY2529 = zero_zero_nat )
| ( SV1243 != zero_zero_nat )
| ( ( power_power_nat @ SV1243 @ SY2529 )
= zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4410]) ).
thf(4924,plain,
( ( ~ ! [SX0: nat,SX1: nat] :
( ( ( power_power_nat @ SX0 @ SX1 )
!= zero_zero_nat )
| ( SX1 != zero_zero_nat ) )
| ~ ! [SX0: nat] :
( ! [SX1: nat] :
( ( power_power_nat @ SX0 @ SX1 )
!= zero_zero_nat )
| ( SX0 = zero_zero_nat ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4411]) ).
thf(4925,plain,
! [SV1244: int] :
( ( ! [SY2530: int] :
( ~ ( ord_less_int @ ( bit1 @ SV1244 ) @ ( bit0 @ SY2530 ) )
| ( ord_less_int @ SV1244 @ SY2530 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4412]) ).
thf(4926,plain,
! [SV1245: int] :
( ( ! [SY2531: int] :
( ~ ( ord_less_int @ SV1245 @ SY2531 )
| ( ord_less_int @ ( bit1 @ SV1245 ) @ ( bit0 @ SY2531 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4413]) ).
thf(4927,plain,
! [SV1246: int] :
( ( ! [SY2532: int] :
( ( SV1246
!= ( plus_plus_int @ SV1246 @ SY2532 ) )
| ( SY2532 = zero_zero_int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4414]) ).
thf(4928,plain,
! [SV1247: int] :
( ( ! [SY2533: int] :
( ( SY2533 != zero_zero_int )
| ( SV1247
= ( plus_plus_int @ SV1247 @ SY2533 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4415]) ).
thf(4929,plain,
! [SV1248: int] :
( ( ! [SY2534: int] :
( ! [SY2535: int] :
~ ( zcong @ ( power_power_int @ SY2535 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SY2534 @ SV1248 )
| ( quadRes @ SV1248 @ SY2534 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4416]) ).
thf(4930,plain,
! [SV1249: int] :
( ( ! [SY2536: int] :
( ~ ( quadRes @ SV1249 @ SY2536 )
| ( zcong @ ( power_power_int @ ( sK5_Y_1 @ SY2536 @ SV1249 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SY2536 @ SV1249 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4417]) ).
thf(4931,plain,
! [SV1250: int] :
( ( ~ ( ord_less_int @ one_one_int @ ( number_number_of_int @ SV1250 ) )
| ( ord_less_int @ ( bit1 @ pls ) @ SV1250 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4418]) ).
thf(4932,plain,
! [SV1251: int] :
( ( ~ ( ord_less_int @ ( bit1 @ pls ) @ SV1251 )
| ( ord_less_int @ one_one_int @ ( number_number_of_int @ SV1251 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4419]) ).
thf(4933,plain,
! [SV462: nat] :
( ( ! [SY2006: nat,SY2007: real] :
( ~ ( ord_less_real @ one_one_real @ SY2007 )
| ( ( power_power_real @ SY2007 @ SV462 )
!= ( power_power_real @ SY2007 @ SY2006 ) )
| ( SV462 = SY2006 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4420]) ).
thf(4934,plain,
! [SV462: nat] :
( ( ! [SY2008: nat,SY2009: real] :
( ~ ( ord_less_real @ one_one_real @ SY2009 )
| ( SV462 != SY2008 )
| ( ( power_power_real @ SY2009 @ SV462 )
= ( power_power_real @ SY2009 @ SY2008 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4421]) ).
thf(4935,plain,
! [SV1252: int] :
( ( ! [SY2537: int] :
( ~ ( ord_less_int @ SY2537 @ pls )
| ( ( plus_plus_nat @ ( number_number_of_nat @ SY2537 ) @ ( number_number_of_nat @ SV1252 ) )
= ( number_number_of_nat @ SV1252 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4422]) ).
thf(4936,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ( 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 ) ) )
| ~ ! [SX0: int,SX1: int] :
( ( 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 @ ( plus_plus_int @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4423]) ).
thf(4937,plain,
! [SV463: real] :
( ( ! [SY2010: real,SY2011: real] :
( ( SY2011 = zero_zero_real )
| ( ( times_times_real @ SV463 @ SY2011 )
!= ( times_times_real @ SY2010 @ SY2011 ) )
| ( SV463 = SY2010 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4424]) ).
thf(4938,plain,
! [SV463: real] :
( ( ! [SY2012: real,SY2013: real] :
( ( SY2013 = zero_zero_real )
| ( SV463 != SY2012 )
| ( ( times_times_real @ SV463 @ SY2013 )
= ( times_times_real @ SY2012 @ SY2013 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4425]) ).
thf(4939,plain,
! [SV464: real] :
( ( ! [SY2014: real,SY2015: real] :
( ~ ( ord_less_real @ zero_zero_real @ SY2015 )
| ~ ( ord_less_real @ ( times_times_real @ SV464 @ SY2015 ) @ ( times_times_real @ SY2014 @ SY2015 ) )
| ( ord_less_real @ SV464 @ SY2014 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4426]) ).
thf(4940,plain,
! [SV464: real] :
( ( ! [SY2016: real,SY2017: real] :
( ~ ( ord_less_real @ zero_zero_real @ SY2017 )
| ~ ( ord_less_real @ SV464 @ SY2016 )
| ( ord_less_real @ ( times_times_real @ SV464 @ SY2017 ) @ ( times_times_real @ SY2016 @ SY2017 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4427]) ).
thf(4941,plain,
! [SV465: real] :
( ( ! [SY2018: real,SY2019: real] :
( ~ ( ord_less_real @ zero_zero_real @ SY2019 )
| ~ ( ord_less_eq_real @ ( times_times_real @ SY2019 @ SV465 ) @ ( times_times_real @ SY2019 @ SY2018 ) )
| ( ord_less_eq_real @ SV465 @ SY2018 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4428]) ).
thf(4942,plain,
! [SV465: real] :
( ( ! [SY2020: real,SY2021: real] :
( ~ ( ord_less_real @ zero_zero_real @ SY2021 )
| ~ ( ord_less_eq_real @ SV465 @ SY2020 )
| ( ord_less_eq_real @ ( times_times_real @ SY2021 @ SV465 ) @ ( times_times_real @ SY2021 @ SY2020 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4429]) ).
thf(4943,plain,
! [SV1253: int] :
( ( ! [SY2538: int] :
( ( ( bit0 @ SV1253 )
!= ( bit0 @ SY2538 ) )
| ( SV1253 = SY2538 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4430]) ).
thf(4944,plain,
! [SV1254: int] :
( ( ! [SY2539: int] :
( ( SV1254 != SY2539 )
| ( ( bit0 @ SV1254 )
= ( bit0 @ SY2539 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4431]) ).
thf(4945,plain,
! [SV1255: int] :
( ( ( ( power_power_int @ SV1255 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= zero_zero_int )
| ( SV1255 = zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4432]) ).
thf(4946,plain,
! [SV1256: int] :
( ( ( SV1256 != zero_zero_int )
| ( ( power_power_int @ SV1256 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4433]) ).
thf(4947,plain,
! [SV1257: int] :
( ( ! [SY2540: int] :
( ( SV1257 != zero_zero_int )
| ( SY2540 != zero_zero_int )
| ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SV1257 @ SV1257 ) @ ( times_times_int @ SY2540 @ SY2540 ) ) @ zero_zero_int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4434]) ).
thf(4948,plain,
( ( ~ ! [SX0: int] :
( ! [SX1: int] :
~ ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SX0 @ SX0 ) @ ( times_times_int @ SX1 @ SX1 ) ) @ zero_zero_int )
| ( SX0 = zero_zero_int ) )
| ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SX0 @ SX0 ) @ ( times_times_int @ SX1 @ SX1 ) ) @ zero_zero_int )
| ( SX1 = zero_zero_int ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4435]) ).
thf(4949,plain,
! [SV1258: int] :
( ( ~ ( ord_less_int @ pls @ ( bit0 @ SV1258 ) )
| ( ord_less_int @ pls @ SV1258 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4436]) ).
thf(4950,plain,
! [SV1259: int] :
( ( ~ ( ord_less_int @ pls @ SV1259 )
| ( ord_less_int @ pls @ ( bit0 @ SV1259 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4437]) ).
thf(4951,plain,
! [SV1260: real] :
( ( ~ ( ord_less_real @ ( plus_plus_real @ SV1260 @ SV1260 ) @ zero_zero_real )
| ( ord_less_real @ SV1260 @ zero_zero_real ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4438]) ).
thf(4952,plain,
! [SV1261: real] :
( ( ~ ( ord_less_real @ SV1261 @ zero_zero_real )
| ( ord_less_real @ ( plus_plus_real @ SV1261 @ SV1261 ) @ zero_zero_real ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4439]) ).
thf(4953,plain,
! [SV1262: int] :
( ( ! [SY2541: nat] :
( ( SY2541 = zero_zero_nat )
| ( SV1262 != zero_zero_int )
| ( ( power_power_int @ SV1262 @ SY2541 )
= zero_zero_int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4440]) ).
thf(4954,plain,
( ( ~ ! [SX0: int,SX1: nat] :
( ( ( power_power_int @ SX0 @ SX1 )
!= zero_zero_int )
| ( SX1 != zero_zero_nat ) )
| ~ ! [SX0: int] :
( ! [SX1: nat] :
( ( power_power_int @ SX0 @ SX1 )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4441]) ).
thf(4955,plain,
! [SV1263: int] :
( ( ! [SY2542: int] :
( ( ( number_number_of_int @ SV1263 )
!= ( number_number_of_int @ SY2542 ) )
| ( SV1263 = SY2542 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4442]) ).
thf(4956,plain,
! [SV1264: int] :
( ( ! [SY2543: int] :
( ( SV1264 != SY2543 )
| ( ( number_number_of_int @ SV1264 )
= ( number_number_of_int @ SY2543 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4443]) ).
thf(4957,plain,
! [SV1265: int] :
( ( ~ ( ord_less_eq_int @ SV1265 @ min )
| ( ord_less_int @ ( bit0 @ SV1265 ) @ min ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4444]) ).
thf(4958,plain,
! [SV1266: int] :
( ( ~ ( ord_less_int @ ( bit0 @ SV1266 ) @ min )
| ( ord_less_eq_int @ SV1266 @ min ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4445]) ).
thf(4959,plain,
! [SV1267: int] :
( ( ! [SY2544: int] :
( ~ ( ord_less_eq_nat @ ( number_number_of_nat @ SV1267 ) @ ( number_number_of_nat @ SY2544 ) )
| ~ ( ord_less_nat @ ( number_number_of_nat @ SY2544 ) @ ( number_number_of_nat @ SV1267 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4446]) ).
thf(4960,plain,
! [SV1268: int] :
( ( ! [SY2545: int] :
( ( ord_less_nat @ ( number_number_of_nat @ SY2545 ) @ ( number_number_of_nat @ SV1268 ) )
| ( ord_less_eq_nat @ ( number_number_of_nat @ SV1268 ) @ ( number_number_of_nat @ SY2545 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4447]) ).
thf(4961,plain,
! [SV1269: int] :
( ( ~ ( ord_less_eq_int @ ( number_number_of_int @ SV1269 ) @ one_one_int )
| ( ord_less_eq_int @ SV1269 @ ( bit1 @ pls ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4448]) ).
thf(4962,plain,
! [SV1270: int] :
( ( ~ ( ord_less_eq_int @ SV1270 @ ( bit1 @ pls ) )
| ( ord_less_eq_int @ ( number_number_of_int @ SV1270 ) @ one_one_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4449]) ).
thf(4963,plain,
! [SV466: int] :
( ( ! [SY2022: int,SY2023: int] :
( ~ ( dvd_dvd_int @ SY2023 @ ( minus_minus_int @ SV466 @ SY2022 ) )
| ( zcong @ SV466 @ SY2022 @ SY2023 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4450]) ).
thf(4964,plain,
! [SV466: int] :
( ( ! [SY2024: int,SY2025: int] :
( ~ ( zcong @ SV466 @ SY2024 @ SY2025 )
| ( dvd_dvd_int @ SY2025 @ ( minus_minus_int @ SV466 @ SY2024 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4451]) ).
thf(4965,plain,
! [SV1271: int] :
( ( ( ( number_number_of_nat @ SV1271 )
!= zero_zero_nat )
| ( ( power_power_real @ zero_zero_real @ ( number_number_of_nat @ SV1271 ) )
= one_one_real ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4452]) ).
thf(4966,plain,
! [SV1272: int] :
( ( ( ( number_number_of_nat @ SV1272 )
= zero_zero_nat )
| ( ( power_power_real @ zero_zero_real @ ( number_number_of_nat @ SV1272 ) )
= zero_zero_real ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4453]) ).
thf(4967,plain,
! [SV1273: int] :
( ( ~ ( ord_less_int @ ( bit0 @ SV1273 ) @ zero_zero_int )
| ( ord_less_int @ SV1273 @ zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4454]) ).
thf(4968,plain,
! [SV1274: int] :
( ( ~ ( ord_less_int @ SV1274 @ zero_zero_int )
| ( ord_less_int @ ( bit0 @ SV1274 ) @ zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4455]) ).
thf(4969,plain,
! [SV1275: int] :
( ( ~ ( ord_less_eq_int @ pls @ ( bit1 @ SV1275 ) )
| ( ord_less_eq_int @ pls @ SV1275 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4456]) ).
thf(4970,plain,
! [SV1276: int] :
( ( ~ ( ord_less_eq_int @ pls @ SV1276 )
| ( ord_less_eq_int @ pls @ ( bit1 @ SV1276 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4457]) ).
thf(4971,plain,
! [SV1277: int] :
( ( ! [SY2546: int] :
( ~ ( ord_less_int @ ( number_number_of_int @ SV1277 ) @ ( number_number_of_int @ SY2546 ) )
| ( ord_less_int @ SV1277 @ SY2546 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4458]) ).
thf(4972,plain,
! [SV1278: int] :
( ( ! [SY2547: int] :
( ~ ( ord_less_int @ SV1278 @ SY2547 )
| ( ord_less_int @ ( number_number_of_int @ SV1278 ) @ ( number_number_of_int @ SY2547 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4459]) ).
thf(4973,plain,
! [SV467: nat] :
( ( ! [SY2026: nat,SY2027: int] :
( ~ ( ord_less_int @ one_one_int @ SY2027 )
| ( ( power_power_int @ SY2027 @ SV467 )
!= ( power_power_int @ SY2027 @ SY2026 ) )
| ( SV467 = SY2026 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4460]) ).
thf(4974,plain,
! [SV467: nat] :
( ( ! [SY2028: nat,SY2029: int] :
( ~ ( ord_less_int @ one_one_int @ SY2029 )
| ( SV467 != SY2028 )
| ( ( power_power_int @ SY2029 @ SV467 )
= ( power_power_int @ SY2029 @ SY2028 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4461]) ).
thf(4975,plain,
! [SV6: int,SV796: int,SV470: int] :
( ( ( ord_less_eq_int @ SV470 @ SV796 )
= $false )
| ( ( ord_less_eq_int @ ( plus_plus_int @ SV6 @ SV470 ) @ ( plus_plus_int @ SV6 @ SV796 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4462]) ).
thf(4976,plain,
! [SV472: int,SV8: int,SV984: int,SV797: int] :
( ( ( ~ ( ord_less_int @ SV797 @ SV984 ) )
= $true )
| ( ( ~ ( ord_less_eq_int @ SV8 @ SV472 )
| ( ord_less_int @ ( plus_plus_int @ SV797 @ SV8 ) @ ( plus_plus_int @ SV984 @ SV472 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4463]) ).
thf(4977,plain,
! [SV478: int,SV17: int] :
( ( ( ~ ( ord_less_eq_int @ pls @ SV17 ) )
= $true )
| ( ( ( plus_plus_nat @ ( number_number_of_nat @ SV478 ) @ ( number_number_of_nat @ SV17 ) )
= ( number_number_of_nat @ ( plus_plus_int @ SV478 @ SV17 ) ) )
= $true )
| ( ( ord_less_eq_int @ pls @ SV478 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4465]) ).
thf(4978,plain,
! [SV479: int,SV18: int] :
( ( ( ~ ( ord_less_eq_int @ pls @ SV18 ) )
= $true )
| ( ( ( plus_plus_int @ ( number_number_of_int @ SV479 ) @ ( number_number_of_int @ SV18 ) )
= ( number_number_of_int @ ( plus_plus_int @ SV479 @ SV18 ) ) )
= $true )
| ( ( ord_less_eq_int @ pls @ SV479 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4466]) ).
thf(4979,plain,
! [SV28: int,SV806: int,SV488: int] :
( ( ( ord_less_int @ SV488 @ SV806 )
= $false )
| ( ( ~ ( ord_less_int @ zero_zero_int @ SV28 )
| ( ord_less_int @ ( times_times_int @ SV28 @ SV488 ) @ ( times_times_int @ SV28 @ SV806 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4468]) ).
thf(4980,plain,
! [SV489: int,SV29: int] :
( ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV29 ) )
= $true )
| ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV489 )
| ( SV29 = SV489 ) )
= $true )
| ( ( ( power_power_int @ SV29 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power_int @ SV489 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4469]) ).
thf(4981,plain,
! [SV30: int,SV490: int] :
( ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV490 ) )
= $true )
| ( ( ord_less_eq_int @ SV30 @ SV490 )
= $true )
| ( ( ord_less_eq_int @ ( power_power_int @ SV30 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV490 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4470]) ).
thf(4982,plain,
! [SV32: int,SV491: int] :
( ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV491 ) )
= $true )
| ( ( ord_less_int @ SV32 @ SV491 )
= $true )
| ( ( ord_less_int @ ( power_power_int @ SV32 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV491 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4471]) ).
thf(4983,plain,
! [SV50: int,SV807: int,SV498: int] :
( ( ( ord_less_int @ SV498 @ SV807 )
= $false )
| ( ( ord_less_int @ ( plus_plus_int @ SV498 @ SV50 ) @ ( plus_plus_int @ SV807 @ SV50 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4472]) ).
thf(4984,plain,
! [SV85: int] :
( ( ( ord_less_int @ SV85 @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $false )
| ( ( ( SV85 = zero_zero_int )
| ( SV85 = one_one_int ) )
= $true )
| ( ( ord_less_eq_int @ zero_zero_int @ SV85 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4473]) ).
thf(4985,plain,
! [SV510: int,SV88: int,SV810: int] :
( ( ( ord_less_int @ zero_zero_int @ SV810 )
= $false )
| ( ( ( SV810
!= ( plus_plus_int @ SV88 @ ( times_times_int @ SV810 @ SV510 ) ) )
| ~ ( ord_less_int @ SV88 @ SV810 )
| ( ord_less_eq_int @ one_one_int @ SV510 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4474]) ).
thf(4986,plain,
! [SV511: int,SV89: int,SV811: int] :
( ( ( ord_less_int @ zero_zero_int @ SV811 )
= $false )
| ( ( ( SV811
!= ( plus_plus_int @ SV89 @ ( times_times_int @ SV811 @ SV511 ) ) )
| ~ ( ord_less_eq_int @ zero_zero_int @ SV89 )
| ( ord_less_eq_int @ SV511 @ one_one_int ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4475]) ).
thf(4987,plain,
! [SV514: nat,SV92: int,SV812: int] :
( ( ( zprime @ SV812 )
= $false )
| ( ( ~ ( dvd_dvd_int @ SV812 @ ( power_power_int @ SV92 @ SV514 ) )
| ( dvd_dvd_int @ SV812 @ SV92 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4476]) ).
thf(4988,plain,
! [SV95: int,SV517: int] :
( ( ( ~ ( ord_less_int @ SV517 @ SV95 ) )
= $true )
| ( ( ~ ( dvd_dvd_int @ SV95 @ SV517 ) )
= $true )
| ( ( ord_less_int @ zero_zero_int @ SV517 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4477]) ).
thf(4989,plain,
! [SV518: int,SV96: int] :
( ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV96 ) )
= $true )
| ( ( ~ ( dvd_dvd_int @ SV518 @ SV96 )
| ~ ( dvd_dvd_int @ SV96 @ SV518 )
| ( SV518 = SV96 ) )
= $true )
| ( ( ord_less_eq_int @ zero_zero_int @ SV518 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4478]) ).
thf(4990,plain,
! [SV815: int,SV519: int,SV97: int] :
( ( ( dvd_dvd_int @ ( times_times_int @ SV97 @ SV519 ) @ ( times_times_int @ SV97 @ SV815 ) )
= $false )
| ( ( ( SV97 = zero_zero_int )
| ( dvd_dvd_int @ SV519 @ SV815 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4479]) ).
thf(4991,plain,
! [SV98: int,SV520: int] :
( ( ( ~ ( ord_less_int @ zero_zero_int @ SV520 ) )
= $true )
| ( ( ord_less_eq_int @ SV98 @ SV520 )
= $true )
| ( ( dvd_dvd_int @ SV98 @ SV520 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4480]) ).
thf(4992,plain,
! [SV986: int,SV827: int,SV536: int,SV125: int,SV1279: int] :
( ( ( SV1279 = zero_zero_int )
| ( SV125 = SV536 )
| ( SV827 != SV986 )
| ( ( plus_plus_int @ SV827 @ ( times_times_int @ SV1279 @ SV125 ) )
!= ( plus_plus_int @ SV986 @ ( times_times_int @ SV1279 @ SV536 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4483]) ).
thf(4993,plain,
! [SV129: int,SV539: int] :
( ( ( ~ ( ord_less_int @ zero_zero_int @ ( times_times_int @ SV539 @ SV129 ) ) )
= $true )
| ( ( ord_less_int @ zero_zero_int @ SV129 )
= $true )
| ( ( ord_less_int @ zero_zero_int @ SV539 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4484]) ).
thf(4994,plain,
! [SV540: int,SV130: int] :
( ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV130 ) )
= $true )
| ( ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ SV540 @ SV130 ) )
= $true )
| ( ( ord_less_eq_int @ zero_zero_int @ SV540 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4485]) ).
thf(4995,plain,
! [SV541: int,SV131: int] :
( ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV131 ) )
= $true )
| ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ SV541 @ SV131 ) )
= $true )
| ( ( ord_less_eq_int @ zero_zero_int @ SV541 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4486]) ).
thf(4996,plain,
! [SV828: int,SV543: int,SV133: int] :
( ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ SV133 @ SV543 ) @ SV828 ) )
= $false )
| ( ( ~ ( ord_less_int @ SV828 @ SV133 )
| ~ ( ord_less_int @ zero_zero_int @ SV133 )
| ( ord_less_eq_int @ zero_zero_int @ SV543 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4488]) ).
thf(4997,plain,
! [SV829: int,SV544: int,SV134: int] :
( ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ SV134 @ SV544 ) @ SV829 ) @ zero_zero_int )
= $false )
| ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV829 )
| ~ ( ord_less_int @ zero_zero_int @ SV134 )
| ( ord_less_eq_int @ SV544 @ zero_zero_int ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4489]) ).
thf(4998,plain,
! [SV1280: int,SV987: int,SV830: int,SV545: int,SV135: int] :
( ( ~ ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SV135 @ SV545 ) @ SV830 ) @ ( plus_plus_int @ ( times_times_int @ SV135 @ SV987 ) @ SV1280 ) )
| ~ ( ord_less_eq_int @ zero_zero_int @ SV830 )
| ~ ( ord_less_int @ SV830 @ SV135 )
| ~ ( ord_less_int @ SV1280 @ SV135 )
| ( ord_less_eq_int @ SV545 @ SV987 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4490]) ).
thf(4999,plain,
! [SV1281: int,SV988: int,SV831: int,SV546: int,SV136: int] :
( ( ! [SY2548: int] :
( ( ( plus_plus_int @ ( times_times_int @ SV136 @ SV546 ) @ SV831 )
!= ( plus_plus_int @ ( times_times_int @ SV988 @ SV1281 ) @ SY2548 ) )
| ~ ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ SV988 @ SV1281 ) @ SY2548 ) )
| ~ ( ord_less_int @ SY2548 @ SV988 )
| ~ ( ord_less_eq_int @ zero_zero_int @ SV831 )
| ~ ( ord_less_int @ zero_zero_int @ SV988 )
| ~ ( ord_less_eq_int @ SV988 @ SV136 )
| ( ord_less_eq_int @ SV546 @ SV1281 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4491]) ).
thf(5000,plain,
! [SV1282: int,SV989: int,SV832: int,SV547: int,SV137: int] :
( ( ~ ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SV137 @ SV547 ) @ SV832 ) @ ( plus_plus_int @ ( times_times_int @ SV137 @ SV989 ) @ SV1282 ) )
| ~ ( ord_less_eq_int @ SV1282 @ zero_zero_int )
| ~ ( ord_less_int @ SV137 @ SV1282 )
| ~ ( ord_less_int @ SV137 @ SV832 )
| ( ord_less_eq_int @ SV989 @ SV547 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4492]) ).
thf(5001,plain,
! [SV1283: int,SV990: int,SV833: int,SV548: int,SV138: int] :
( ( ! [SY2549: int] :
( ( ( plus_plus_int @ ( times_times_int @ SV138 @ SV548 ) @ SV833 )
!= ( plus_plus_int @ ( times_times_int @ SV990 @ SV1283 ) @ SY2549 ) )
| ~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ SV990 @ SV1283 ) @ SY2549 ) @ zero_zero_int )
| ~ ( ord_less_int @ SV833 @ SV138 )
| ~ ( ord_less_eq_int @ zero_zero_int @ SY2549 )
| ~ ( ord_less_int @ zero_zero_int @ SV990 )
| ~ ( ord_less_eq_int @ SV990 @ SV138 )
| ( ord_less_eq_int @ SV1283 @ SV548 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4493]) ).
thf(5002,plain,
! [SV834: int,SV549: int,SV143: int] :
( ( ( ~ ( zcong @ ( power_power_int @ SV143 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SV549 @ SV834 ) )
= $true )
| ( ( ~ ( dvd_dvd_int @ SV834 @ SV143 ) )
= $true )
| ( ( zcong @ SV549 @ zero_zero_int @ SV834 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4494]) ).
thf(5003,plain,
! [SV550: int,SV146: int] :
( ( ( SV146 = SV550 )
= $true )
| ( ( ord_less_int @ SV146 @ SV550 )
= $true )
| ( ( ord_less_eq_int @ SV146 @ SV550 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4495]) ).
thf(5004,plain,
! [SV147: int,SV835: int,SV551: int] :
( ( ( ord_less_int @ SV551 @ SV835 )
= $false )
| ( ( ~ ( ord_less_int @ SV147 @ SV835 )
| ( ord_less_eq_int @ SV551 @ SV147 )
| ( ord_less_eq_int @ SV147 @ SV551 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4496]) ).
thf(5005,plain,
! [SV553: int,SV149: int,SV1284: int,SV991: int,SV836: int] :
( ( ~ ( zcong @ SV836 @ SV991 @ SV1284 )
| ~ ( zcong @ SV149 @ SV553 @ SV1284 )
| ( zcong @ ( plus_plus_int @ SV836 @ SV149 ) @ ( plus_plus_int @ SV991 @ SV553 ) @ SV1284 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4497]) ).
thf(5006,plain,
! [SV150: int,SV554: int,SV837: int] :
( ( ( ord_less_int @ zero_zero_int @ SV837 )
= $false )
| ( ( ~ ( ord_less_int @ SV837 @ SV554 )
| ~ ( ord_less_int @ zero_zero_int @ SV150 )
| ~ ( ord_less_int @ SV150 @ SV837 )
| ~ ( zcong @ SV837 @ SV150 @ SV554 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4498]) ).
thf(5007,plain,
! [SV151: int,SV555: int] :
( ( ( ~ ( ord_less_int @ SV555 @ SV151 ) )
= $true )
| ( ( ~ ( zcong @ SV555 @ zero_zero_int @ SV151 )
| ( SV555 = zero_zero_int ) )
= $true )
| ( ( ord_less_eq_int @ zero_zero_int @ SV555 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4499]) ).
thf(5008,plain,
! [SV152: int,SV556: int,SV838: int] :
( ( ( ord_less_eq_int @ zero_zero_int @ SV838 )
= $false )
| ( ( ~ ( ord_less_int @ SV838 @ SV556 )
| ~ ( ord_less_eq_int @ zero_zero_int @ SV152 )
| ~ ( ord_less_int @ SV152 @ SV556 )
| ~ ( zcong @ SV838 @ SV152 @ SV556 )
| ( SV838 = SV152 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4500]) ).
thf(5009,plain,
! [SV153: nat,SV992: int,SV839: nat,SV557: int] :
( ( ( ~ ( zcong @ ( power_power_int @ SV557 @ SV839 ) @ one_one_int @ SV992 ) )
= $true )
| ( ( zcong @ ( power_power_int @ SV557 @ ( times_times_nat @ SV839 @ SV153 ) ) @ one_one_int @ SV992 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4501]) ).
thf(5010,plain,
! [SV840: int,SV559: int,SV156: int] :
( ( ( ( minus_minus_int @ SV156 @ SV559 )
= SV840 )
= $false )
| ( ( SV156
= ( plus_plus_int @ SV840 @ SV559 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4502]) ).
thf(5011,plain,
! [SV1285: int,SV993: int,SV841: int,SV562: int,SV160: int] :
( ( ! [SY2550: int,SY2551: int] :
( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ SV160 @ ( times_times_int @ SV562 @ SV841 ) ) @ SV993 ) @ ( times_times_int @ ( minus_minus_int @ SV1285 @ ( times_times_int @ SV562 @ SY2550 ) ) @ SY2551 ) )
= ( minus_minus_int @ ( plus_plus_int @ ( times_times_int @ SV160 @ SV993 ) @ ( times_times_int @ SV1285 @ SY2551 ) ) @ ( times_times_int @ SV562 @ ( plus_plus_int @ ( times_times_int @ SV841 @ SV993 ) @ ( times_times_int @ SY2550 @ SY2551 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4503]) ).
thf(5012,plain,
! [SV162: int,SV564: int] :
( ( ( ~ ( ord_less_int @ SV564 @ SV162 ) )
= $true )
| ( ( ( SV564
= ( minus_minus_int @ SV162 @ one_one_int ) )
| ( ord_less_int @ SV564 @ ( minus_minus_int @ SV162 @ one_one_int ) ) )
= $true )
| ( ( ord_less_int @ zero_zero_int @ SV564 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4504]) ).
thf(5013,plain,
! [SV168: int,SV994: int,SV843: int,SV566: int] :
( ( ( ~ ( zcong @ SV566 @ SV843 @ SV994 ) )
= $true )
| ( ( zcong @ ( plus_plus_int @ SV566 @ SV168 ) @ ( plus_plus_int @ SV843 @ SV168 ) @ SV994 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4505]) ).
thf(5014,plain,
! [SV169: nat,SV995: int,SV844: int,SV567: int] :
( ( ( ~ ( zcong @ SV567 @ SV844 @ SV995 ) )
= $true )
| ( ( zcong @ ( power_power_int @ SV567 @ SV169 ) @ ( power_power_int @ SV844 @ SV169 ) @ SV995 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4506]) ).
thf(5015,plain,
! [SV170: int,SV568: int,SV845: int] :
( ( ( ord_less_int @ zero_zero_int @ SV845 )
= $false )
| ( ( ~ ( ord_less_int @ zero_zero_int @ SV568 )
| ~ ( ord_less_int @ zero_zero_int @ SV170 )
| ~ ( zcong @ SV845 @ SV568 @ SV170 )
| ~ ( ord_less_int @ SV845 @ SV170 )
| ~ ( ord_less_int @ SV568 @ SV170 )
| ( SV845 = SV568 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4507]) ).
thf(5016,plain,
! [SV171: int,SV569: int] :
( ( ( ~ ( ord_less_int @ SV569 @ SV171 ) )
= $true )
| ( ( ~ ( zcong @ SV569 @ zero_zero_int @ SV171 ) )
= $true )
| ( ( ord_less_int @ zero_zero_int @ SV569 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4508]) ).
thf(5017,plain,
! [SV172: int,SV570: int] :
( ( ( ord_less_eq_int @ SV570 @ zero_zero_int )
= $true )
| ( ( ord_less_eq_int @ SV172 @ SV570 )
= $true )
| ( ( dvd_dvd_int @ SV172 @ SV570 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4509]) ).
thf(5018,plain,
! [SV173: int,SV571: int] :
( ( ( ~ ( ord_less_int @ SV571 @ SV173 ) )
= $true )
| ( ( ~ ( zcong @ SV571 @ zero_zero_int @ SV173 )
| ( SV571 = zero_zero_int ) )
= $true )
| ( ( ord_less_eq_int @ zero_zero_int @ SV571 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4510]) ).
thf(5019,plain,
! [SV182: nat,SV849: int,SV577: int] :
( ( ( dvd_dvd_int @ SV577 @ SV849 )
= $false )
| ( ( dvd_dvd_int @ ( power_power_int @ SV577 @ SV182 ) @ ( power_power_int @ SV849 @ SV182 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4514]) ).
thf(5020,plain,
! [SV185: nat,SV851: int,SV579: int] :
( ( ( ord_less_eq_int @ SV579 @ SV851 )
= $false )
| ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV579 )
| ( ord_less_eq_int @ ( power_power_int @ SV579 @ SV185 ) @ ( power_power_int @ SV851 @ SV185 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4515]) ).
thf(5021,plain,
! [SV191: nat,SV998: int,SV853: nat,SV584: int] :
( ( ( ~ ( dvd_dvd_int @ ( power_power_int @ SV584 @ SV853 ) @ SV998 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV191 @ SV853 )
| ( dvd_dvd_int @ ( power_power_int @ SV584 @ SV191 ) @ SV998 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4519]) ).
thf(5022,plain,
! [SV585: nat,SV192: nat,SV999: int,SV854: int] :
( ( ( ~ ( dvd_dvd_int @ SV854 @ SV999 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV192 @ SV585 )
| ( dvd_dvd_int @ ( power_power_int @ SV854 @ SV192 ) @ ( power_power_int @ SV999 @ SV585 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4520]) ).
thf(5023,plain,
! [SV193: int,SV855: nat,SV586: nat] :
( ( ( ord_less_eq_nat @ SV586 @ SV855 )
= $false )
| ( ( dvd_dvd_int @ ( power_power_int @ SV193 @ SV586 ) @ ( power_power_int @ SV193 @ SV855 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4521]) ).
thf(5024,plain,
! [SV856: int,SV587: nat,SV194: int] :
( ( ( ord_less_int @ ( power_power_int @ SV194 @ SV587 ) @ ( power_power_int @ SV856 @ SV587 ) )
= $false )
| ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV856 )
| ( ord_less_int @ SV194 @ SV856 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4522]) ).
thf(5025,plain,
! [SV197: int,SV857: nat,SV590: nat] :
( ( ( ord_less_nat @ SV590 @ SV857 )
= $false )
| ( ( ~ ( ord_less_int @ one_one_int @ SV197 )
| ( ord_less_int @ ( power_power_int @ SV197 @ SV590 ) @ ( power_power_int @ SV197 @ SV857 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4525]) ).
thf(5026,plain,
! [SV591: nat,SV198: nat,SV858: int] :
( ( ( ord_less_int @ one_one_int @ SV858 )
= $false )
| ( ( ~ ( ord_less_int @ ( power_power_int @ SV858 @ SV198 ) @ ( power_power_int @ SV858 @ SV591 ) )
| ( ord_less_nat @ SV198 @ SV591 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4526]) ).
thf(5027,plain,
! [SV199: int,SV859: nat,SV592: nat] :
( ( ( ord_less_eq_nat @ SV592 @ SV859 )
= $false )
| ( ( ~ ( ord_less_eq_int @ one_one_int @ SV199 )
| ( ord_less_eq_int @ ( power_power_int @ SV199 @ SV592 ) @ ( power_power_int @ SV199 @ SV859 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4527]) ).
thf(5028,plain,
! [SV200: nat,SV593: int] :
( ( ( ~ ( ord_less_int @ SV593 @ one_one_int ) )
= $true )
| ( ( ord_less_int @ ( times_times_int @ SV593 @ ( power_power_int @ SV593 @ SV200 ) ) @ ( power_power_int @ SV593 @ SV200 ) )
= $true )
| ( ( ord_less_int @ zero_zero_int @ SV593 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4528]) ).
thf(5029,plain,
! [SV201: int,SV860: nat,SV594: nat] :
( ( ( ord_less_nat @ SV594 @ SV860 )
= $false )
| ( ( ~ ( ord_less_int @ zero_zero_int @ SV201 )
| ~ ( ord_less_int @ SV201 @ one_one_int )
| ( ord_less_int @ ( power_power_int @ SV201 @ SV860 ) @ ( power_power_int @ SV201 @ SV594 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4529]) ).
thf(5030,plain,
! [SV212: int,SV862: int,SV600: int] :
( ( ( ord_less_eq_int @ SV600 @ SV862 )
= $false )
| ( ( ~ ( ord_less_eq_int @ SV862 @ SV212 )
| ( ord_less_eq_int @ SV600 @ SV212 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4530]) ).
thf(5031,plain,
! [SV213: int,SV601: int] :
( ( ( ~ ( ord_less_eq_int @ SV601 @ SV213 ) )
= $true )
| ( ( SV213 = SV601 )
= $true )
| ( ( ord_less_eq_int @ SV213 @ SV601 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4531]) ).
thf(5032,plain,
! [SV602: int,SV214: int] :
( ( ( ~ ( ord_less_eq_int @ pls @ SV214 ) )
= $true )
| ( ( ( times_times_real @ ( number267125858f_real @ SV602 ) @ ( number267125858f_real @ SV214 ) )
= ( number267125858f_real @ ( times_times_int @ SV602 @ SV214 ) ) )
= $true )
| ( ( ord_less_eq_int @ pls @ SV602 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4532]) ).
thf(5033,plain,
! [SV603: int,SV215: int] :
( ( ( ~ ( ord_less_eq_int @ pls @ SV215 ) )
= $true )
| ( ( ( times_times_nat @ ( number_number_of_nat @ SV603 ) @ ( number_number_of_nat @ SV215 ) )
= ( number_number_of_nat @ ( times_times_int @ SV603 @ SV215 ) ) )
= $true )
| ( ( ord_less_eq_int @ pls @ SV603 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4533]) ).
thf(5034,plain,
! [SV604: int,SV216: int] :
( ( ( ~ ( ord_less_eq_int @ pls @ SV216 ) )
= $true )
| ( ( ( times_times_int @ ( number_number_of_int @ SV604 ) @ ( number_number_of_int @ SV216 ) )
= ( number_number_of_int @ ( times_times_int @ SV604 @ SV216 ) ) )
= $true )
| ( ( ord_less_eq_int @ pls @ SV604 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4534]) ).
thf(5035,plain,
! [SV612: int,SV224: int] :
( ( ( ~ ( ord_less_eq_int @ pls @ SV224 ) )
= $true )
| ( ( ( plus_plus_real @ ( number267125858f_real @ SV612 ) @ ( number267125858f_real @ SV224 ) )
= ( number267125858f_real @ ( plus_plus_int @ SV612 @ SV224 ) ) )
= $true )
| ( ( ord_less_eq_int @ pls @ SV612 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4535]) ).
thf(5036,plain,
! [SV615: real,SV227: real] :
( ( ( ~ ( ord_less_eq_real @ zero_zero_real @ SV227 ) )
= $true )
| ( ( ~ ( ord_less_eq_real @ zero_zero_real @ SV615 )
| ( SV227 = SV615 ) )
= $true )
| ( ( ( power_power_real @ SV227 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power_real @ SV615 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4536]) ).
thf(5037,plain,
! [SV616: nat,SV228: nat] :
( ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV228 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV616 )
| ( SV228 = SV616 ) )
= $true )
| ( ( ( power_power_nat @ SV228 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power_nat @ SV616 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4537]) ).
thf(5038,plain,
! [SV229: real,SV617: real] :
( ( ( ~ ( ord_less_eq_real @ zero_zero_real @ SV617 ) )
= $true )
| ( ( ord_less_eq_real @ SV229 @ SV617 )
= $true )
| ( ( ord_less_eq_real @ ( power_power_real @ SV229 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SV617 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4538]) ).
thf(5039,plain,
! [SV230: nat,SV618: nat] :
( ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV618 ) )
= $true )
| ( ( ord_less_eq_nat @ SV230 @ SV618 )
= $true )
| ( ( ord_less_eq_nat @ ( power_power_nat @ SV230 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_nat @ SV618 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4539]) ).
thf(5040,plain,
! [SV232: real,SV619: real] :
( ( ( ~ ( ord_less_eq_real @ zero_zero_real @ SV619 ) )
= $true )
| ( ( ord_less_real @ SV232 @ SV619 )
= $true )
| ( ( ord_less_real @ ( power_power_real @ SV232 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SV619 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4540]) ).
thf(5041,plain,
! [SV233: nat,SV620: nat] :
( ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV620 ) )
= $true )
| ( ( ord_less_nat @ SV233 @ SV620 )
= $true )
| ( ( ord_less_nat @ ( power_power_nat @ SV233 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_nat @ SV620 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4541]) ).
thf(5042,plain,
! [SV628: int,SV249: nat,SV869: int,SV1000: int] :
( ( ( ~ ( zprime @ SV1000 ) )
= $true )
| ( ( ( dvd_dvd_int @ SV1000 @ SV869 )
| ~ ( dvd_dvd_int @ ( power_power_int @ SV1000 @ SV249 ) @ ( times_times_int @ SV628 @ SV869 ) )
| ( dvd_dvd_int @ ( power_power_int @ SV1000 @ SV249 ) @ SV628 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4542]) ).
thf(5043,plain,
! [SV629: int,SV250: nat,SV870: int,SV1001: int] :
( ( ( ~ ( zprime @ SV1001 ) )
= $true )
| ( ( ( dvd_dvd_int @ SV1001 @ SV870 )
| ~ ( dvd_dvd_int @ ( power_power_int @ SV1001 @ SV250 ) @ ( times_times_int @ SV870 @ SV629 ) )
| ( dvd_dvd_int @ ( power_power_int @ SV1001 @ SV250 ) @ SV629 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4543]) ).
thf(5044,plain,
! [SV630: int,SV251: int] :
( ( ( ~ ( twoSqu362149276sum2sq @ SV251 ) )
= $true )
| ( ( twoSqu362149276sum2sq @ ( times_times_int @ SV630 @ SV251 ) )
= $true )
| ( ( twoSqu362149276sum2sq @ SV630 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4544]) ).
thf(5045,plain,
! [SV1013: real,SV913: real,SV678: real,SV316: real,SV1286: real] :
( ( ( SV1286 = zero_zero_real )
| ( SV316 = SV678 )
| ( SV913 != SV1013 )
| ( ( plus_plus_real @ SV913 @ ( times_times_real @ SV1286 @ SV316 ) )
!= ( plus_plus_real @ SV1013 @ ( times_times_real @ SV1286 @ SV678 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4557]) ).
thf(5046,plain,
! [SV1014: nat,SV914: nat,SV679: nat,SV317: nat,SV1287: nat] :
( ( ( SV1287 = zero_zero_nat )
| ( SV317 = SV679 )
| ( SV914 != SV1014 )
| ( ( plus_plus_nat @ SV914 @ ( times_times_nat @ SV1287 @ SV317 ) )
!= ( plus_plus_nat @ SV1014 @ ( times_times_nat @ SV1287 @ SV679 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4558]) ).
thf(5047,plain,
! [SV324: int] :
( ( ( SV324
= ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) )
= $true )
| ( ( ord_less_eq_int @ ( number_number_of_int @ ( bit1 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SV324 )
= $true )
| ( ( SV324
= ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true )
| ( ( zprime @ SV324 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4559]) ).
thf(5048,plain,
! [SV915: int,SV325: int] :
( ( ( SV325 = one_one_int )
= $true )
| ( ( SV325
= ( number_number_of_int @ min ) )
= $true )
| ( ( ( times_times_int @ SV325 @ SV915 )
= one_one_int )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4560]) ).
thf(5049,plain,
! [SV327: int,SV1015: int,SV916: int,SV685: int] :
( ( ( ~ ( zcong @ SV685 @ SV916 @ SV1015 ) )
= $true )
| ( ( ~ ( zcong @ SV916 @ SV327 @ SV1015 )
| ( zcong @ SV685 @ SV327 @ SV1015 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4561]) ).
thf(5050,plain,
! [SV686: real,SV328: real] :
( ( ( SV328 = SV686 )
= $true )
| ( ( ord_less_real @ SV328 @ SV686 )
= $true )
| ( ( ord_less_eq_real @ SV328 @ SV686 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4562]) ).
thf(5051,plain,
! [SV687: nat,SV329: nat] :
( ( ( SV329 = SV687 )
= $true )
| ( ( ord_less_nat @ SV329 @ SV687 )
= $true )
| ( ( ord_less_eq_nat @ SV329 @ SV687 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4563]) ).
thf(5052,plain,
! [SV331: int,SV1016: int,SV918: int,SV689: int] :
( ( ( ~ ( zcong @ SV689 @ SV918 @ SV1016 ) )
= $true )
| ( ( zcong @ ( times_times_int @ SV689 @ SV331 ) @ ( times_times_int @ SV918 @ SV331 ) @ SV1016 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4564]) ).
thf(5053,plain,
! [SV332: int,SV1017: int,SV919: int,SV690: int] :
( ( ( ~ ( zcong @ SV690 @ SV919 @ SV1017 ) )
= $true )
| ( ( zcong @ ( times_times_int @ SV332 @ SV690 ) @ ( times_times_int @ SV332 @ SV919 ) @ SV1017 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4565]) ).
thf(5054,plain,
! [SV691: int,SV333: int,SV1288: int,SV1018: int,SV920: int] :
( ( ~ ( zcong @ SV920 @ SV1018 @ SV1288 )
| ~ ( zcong @ SV333 @ SV691 @ SV1288 )
| ( zcong @ ( times_times_int @ SV920 @ SV333 ) @ ( times_times_int @ SV1018 @ SV691 ) @ SV1288 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4566]) ).
thf(5055,plain,
! [SV337: int,SV692: int,SV921: int] :
( ( ( ord_less_eq_int @ zero_zero_int @ SV921 )
= $false )
| ( ( ~ ( zprime @ SV692 )
| ~ ( dvd_dvd_int @ SV692 @ ( times_times_int @ SV921 @ SV337 ) )
| ( dvd_dvd_int @ SV692 @ SV921 )
| ( dvd_dvd_int @ SV692 @ SV337 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4567]) ).
thf(5056,plain,
! [SV693: nat,SV338: nat,SV922: int] :
( ( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV922 )
= $false )
| ( ( ~ ( zcong @ ( power_power_int @ ( number_number_of_int @ min ) @ SV338 ) @ ( power_power_int @ ( number_number_of_int @ min ) @ SV693 ) @ SV922 )
| ( ( power_power_int @ ( number_number_of_int @ min ) @ SV338 )
= ( power_power_int @ ( number_number_of_int @ min ) @ SV693 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4568]) ).
thf(5057,plain,
! [SV694: int,SV339: int] :
( ( ( ~ ( zcong @ SV339 @ ( number_number_of_int @ min ) @ SV694 ) )
= $true )
| ( ( ~ ( zcong @ SV339 @ one_one_int @ SV694 ) )
= $true )
| ( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV694 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4569]) ).
thf(5058,plain,
! [SV695: int,SV340: int,SV1289: int,SV1019: int,SV923: int] :
( ( ~ ( zcong @ SV923 @ SV1019 @ SV1289 )
| ~ ( zcong @ SV340 @ SV695 @ SV1289 )
| ( zcong @ ( minus_minus_int @ SV923 @ SV340 ) @ ( minus_minus_int @ SV1019 @ SV695 ) @ SV1289 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4570]) ).
thf(5059,plain,
! [SV924: int,SV696: int,SV341: int] :
( ( ( dvd_dvd_int @ SV341 @ ( minus_minus_int @ SV696 @ SV924 ) )
= $false )
| ( ( ~ ( dvd_dvd_int @ SV341 @ SV924 )
| ( dvd_dvd_int @ SV341 @ SV696 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4571]) ).
thf(5060,plain,
! [SV351: int,SV706: int,SV1290: int,SV1020: int,SV932: int] :
( ( ~ ( zcong @ SV932 @ SV1020 @ SV1290 )
| ( SV1020 != SV706 )
| ~ ( zcong @ SV706 @ SV351 @ SV1290 )
| ( zcong @ SV932 @ SV351 @ SV1290 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4572]) ).
thf(5061,plain,
! [SV707: int,SV352: int] :
( ( ( ~ ( ord_less_int @ zero_zero_int @ SV352 ) )
= $true )
| ( ( ~ ( ord_less_int @ SV352 @ SV707 )
| ~ ( zcong @ ( times_times_int @ SV352 @ SV352 ) @ one_one_int @ SV707 )
| ( SV352 = one_one_int )
| ( SV352
= ( minus_minus_int @ SV707 @ one_one_int ) ) )
= $true )
| ( ( zprime @ SV707 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4573]) ).
thf(5062,plain,
! [SV708: int,SV353: int] :
( ( ( ~ ( ord_less_int @ zero_zero_int @ SV353 ) )
= $true )
| ( ( ~ ( zcong @ ( times_times_int @ SV353 @ SV353 ) @ one_one_int @ SV708 )
| ( zcong @ SV353 @ one_one_int @ SV708 )
| ( zcong @ SV353 @ ( minus_minus_int @ SV708 @ one_one_int ) @ SV708 ) )
= $true )
| ( ( zprime @ SV708 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4574]) ).
thf(5063,plain,
! [SV713: int,SV358: int,SV933: int] :
( ( ( zprime @ SV933 )
= $false )
| ( ( ~ ( dvd_dvd_int @ SV933 @ ( times_times_int @ SV358 @ SV713 ) )
| ( dvd_dvd_int @ SV933 @ SV358 )
| ( dvd_dvd_int @ SV933 @ SV713 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4575]) ).
thf(5064,plain,
! [SV714: int,SV359: int,SV934: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV934 )
= $false )
| ( ( ~ ( dvd_dvd_int @ SV359 @ SV714 )
| ( dvd_dvd_int @ SV359 @ ( power_power_int @ SV714 @ SV934 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4576]) ).
thf(5065,plain,
! [SV360: int,SV715: int,SV935: int] :
( ( ( zprime @ SV935 )
= $false )
| ( ( ( zcong @ SV715 @ zero_zero_int @ SV935 )
| ( zcong @ SV360 @ zero_zero_int @ SV935 )
| ~ ( zcong @ ( times_times_int @ SV715 @ SV360 ) @ zero_zero_int @ SV935 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4577]) ).
thf(5066,plain,
! [SV361: int,SV716: int,SV936: int] :
( ( ( zprime @ SV936 )
= $false )
| ( ( ~ ( ord_less_int @ zero_zero_int @ SV716 )
| ( zcong @ SV716 @ zero_zero_int @ SV936 )
| ( zcong @ SV361 @ zero_zero_int @ SV936 )
| ~ ( zcong @ ( times_times_int @ SV716 @ SV361 ) @ zero_zero_int @ SV936 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4578]) ).
thf(5067,plain,
! [SV362: int,SV717: int,SV937: int] :
( ( ( zprime @ SV937 )
= $false )
| ( ( ~ ( ord_less_int @ zero_zero_int @ SV717 )
| ~ ( zcong @ ( times_times_int @ SV717 @ SV362 ) @ zero_zero_int @ SV937 )
| ( zcong @ SV717 @ zero_zero_int @ SV937 )
| ( zcong @ SV362 @ zero_zero_int @ SV937 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4579]) ).
thf(5068,plain,
! [SV718: nat,SV363: int,SV938: int] :
( ( ( zprime @ SV938 )
= $false )
| ( ( ~ ( dvd_dvd_int @ SV938 @ ( power_power_int @ SV363 @ SV718 ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV718 )
| ( dvd_dvd_int @ SV938 @ SV363 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4580]) ).
thf(5069,plain,
! [SV371: real,SV940: real,SV723: real] :
( ( ( ord_less_eq_real @ SV723 @ SV940 )
= $false )
| ( ( ord_less_eq_real @ ( plus_plus_real @ SV371 @ SV723 ) @ ( plus_plus_real @ SV371 @ SV940 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4582]) ).
thf(5070,plain,
! [SV727: real,SV375: real,SV944: real] :
( ( ( ord_less_real @ zero_zero_real @ SV944 )
= $false )
| ( ( ~ ( ord_less_real @ SV375 @ SV727 )
| ( ord_less_real @ ( times_times_real @ SV944 @ SV375 ) @ ( times_times_real @ SV944 @ SV727 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4585]) ).
thf(5071,plain,
! [SV728: real,SV376: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV376 ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ SV728 @ SV376 ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV728 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4586]) ).
thf(5072,plain,
! [SV382: nat,SV945: real,SV732: real] :
( ( ( ord_less_real @ SV732 @ SV945 )
= $false )
| ( ( ~ ( ord_less_eq_real @ zero_zero_real @ SV732 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV382 )
| ( ord_less_real @ ( power_power_real @ SV732 @ SV382 ) @ ( power_power_real @ SV945 @ SV382 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4590]) ).
thf(5073,plain,
! [SV383: nat,SV946: nat,SV733: nat] :
( ( ( ord_less_nat @ SV733 @ SV946 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV733 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV383 )
| ( ord_less_nat @ ( power_power_nat @ SV733 @ SV383 ) @ ( power_power_nat @ SV946 @ SV383 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4591]) ).
thf(5074,plain,
! [SV384: nat,SV947: int,SV734: int] :
( ( ( ord_less_int @ SV734 @ SV947 )
= $false )
| ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV734 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV384 )
| ( ord_less_int @ ( power_power_int @ SV734 @ SV384 ) @ ( power_power_int @ SV947 @ SV384 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4592]) ).
thf(5075,plain,
! [SV392: nat,SV950: nat,SV740: nat] :
( ( ( dvd_dvd_nat @ SV740 @ SV950 )
= $false )
| ( ( dvd_dvd_nat @ ( power_power_nat @ SV740 @ SV392 ) @ ( power_power_nat @ SV950 @ SV392 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4594]) ).
thf(5076,plain,
! [SV393: nat,SV951: real,SV741: real] :
( ( ( dvd_dvd_real @ SV741 @ SV951 )
= $false )
| ( ( dvd_dvd_real @ ( power_power_real @ SV741 @ SV393 ) @ ( power_power_real @ SV951 @ SV393 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4595]) ).
thf(5077,plain,
! [SV398: nat,SV954: real,SV744: real] :
( ( ( ord_less_eq_real @ SV744 @ SV954 )
= $false )
| ( ( ~ ( ord_less_eq_real @ zero_zero_real @ SV744 )
| ( ord_less_eq_real @ ( power_power_real @ SV744 @ SV398 ) @ ( power_power_real @ SV954 @ SV398 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4596]) ).
thf(5078,plain,
! [SV399: nat,SV955: nat,SV745: nat] :
( ( ( ord_less_eq_nat @ SV745 @ SV955 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV745 )
| ( ord_less_eq_nat @ ( power_power_nat @ SV745 @ SV399 ) @ ( power_power_nat @ SV955 @ SV399 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4597]) ).
thf(5079,plain,
! [SV410: nat,SV1023: nat,SV958: nat,SV754: nat] :
( ( ( ~ ( dvd_dvd_nat @ ( power_power_nat @ SV754 @ SV958 ) @ SV1023 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV410 @ SV958 )
| ( dvd_dvd_nat @ ( power_power_nat @ SV754 @ SV410 ) @ SV1023 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4604]) ).
thf(5080,plain,
! [SV411: nat,SV1024: real,SV959: nat,SV755: real] :
( ( ( ~ ( dvd_dvd_real @ ( power_power_real @ SV755 @ SV959 ) @ SV1024 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV411 @ SV959 )
| ( dvd_dvd_real @ ( power_power_real @ SV755 @ SV411 ) @ SV1024 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4605]) ).
thf(5081,plain,
! [SV756: nat,SV412: nat,SV1025: nat,SV960: nat] :
( ( ( ~ ( dvd_dvd_nat @ SV960 @ SV1025 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV412 @ SV756 )
| ( dvd_dvd_nat @ ( power_power_nat @ SV960 @ SV412 ) @ ( power_power_nat @ SV1025 @ SV756 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4606]) ).
thf(5082,plain,
! [SV757: nat,SV413: nat,SV1026: real,SV961: real] :
( ( ( ~ ( dvd_dvd_real @ SV961 @ SV1026 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV413 @ SV757 )
| ( dvd_dvd_real @ ( power_power_real @ SV961 @ SV413 ) @ ( power_power_real @ SV1026 @ SV757 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4607]) ).
thf(5083,plain,
! [SV414: nat,SV962: nat,SV758: nat] :
( ( ( ord_less_eq_nat @ SV758 @ SV962 )
= $false )
| ( ( dvd_dvd_nat @ ( power_power_nat @ SV414 @ SV758 ) @ ( power_power_nat @ SV414 @ SV962 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4608]) ).
thf(5084,plain,
! [SV415: real,SV963: nat,SV759: nat] :
( ( ( ord_less_eq_nat @ SV759 @ SV963 )
= $false )
| ( ( dvd_dvd_real @ ( power_power_real @ SV415 @ SV759 ) @ ( power_power_real @ SV415 @ SV963 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4609]) ).
thf(5085,plain,
! [SV760: nat,SV416: nat,SV964: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV964 )
= $false )
| ( ( ~ ( ord_less_nat @ ( power_power_nat @ SV964 @ SV416 ) @ ( power_power_nat @ SV964 @ SV760 ) )
| ( ord_less_nat @ SV416 @ SV760 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4610]) ).
thf(5086,plain,
! [SV965: real,SV761: nat,SV417: real] :
( ( ( ord_less_real @ ( power_power_real @ SV417 @ SV761 ) @ ( power_power_real @ SV965 @ SV761 ) )
= $false )
| ( ( ~ ( ord_less_eq_real @ zero_zero_real @ SV965 )
| ( ord_less_real @ SV417 @ SV965 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4611]) ).
thf(5087,plain,
! [SV966: nat,SV762: nat,SV418: nat] :
( ( ( ord_less_nat @ ( power_power_nat @ SV418 @ SV762 ) @ ( power_power_nat @ SV966 @ SV762 ) )
= $false )
| ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV966 )
| ( ord_less_nat @ SV418 @ SV966 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4612]) ).
thf(5088,plain,
! [SV423: real,SV967: nat,SV767: nat] :
( ( ( ord_less_nat @ SV767 @ SV967 )
= $false )
| ( ( ~ ( ord_less_real @ one_one_real @ SV423 )
| ( ord_less_real @ ( power_power_real @ SV423 @ SV767 ) @ ( power_power_real @ SV423 @ SV967 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4617]) ).
thf(5089,plain,
! [SV424: nat,SV968: nat,SV768: nat] :
( ( ( ord_less_nat @ SV768 @ SV968 )
= $false )
| ( ( ~ ( ord_less_nat @ one_one_nat @ SV424 )
| ( ord_less_nat @ ( power_power_nat @ SV424 @ SV768 ) @ ( power_power_nat @ SV424 @ SV968 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4618]) ).
thf(5090,plain,
! [SV769: nat,SV425: nat,SV969: real] :
( ( ( ord_less_real @ one_one_real @ SV969 )
= $false )
| ( ( ~ ( ord_less_real @ ( power_power_real @ SV969 @ SV425 ) @ ( power_power_real @ SV969 @ SV769 ) )
| ( ord_less_nat @ SV425 @ SV769 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4619]) ).
thf(5091,plain,
! [SV770: nat,SV426: nat,SV970: nat] :
( ( ( ord_less_nat @ one_one_nat @ SV970 )
= $false )
| ( ( ~ ( ord_less_nat @ ( power_power_nat @ SV970 @ SV426 ) @ ( power_power_nat @ SV970 @ SV770 ) )
| ( ord_less_nat @ SV426 @ SV770 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4620]) ).
thf(5092,plain,
! [SV427: real,SV971: nat,SV771: nat] :
( ( ( ord_less_eq_nat @ SV771 @ SV971 )
= $false )
| ( ( ~ ( ord_less_eq_real @ one_one_real @ SV427 )
| ( ord_less_eq_real @ ( power_power_real @ SV427 @ SV771 ) @ ( power_power_real @ SV427 @ SV971 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4621]) ).
thf(5093,plain,
! [SV428: nat,SV972: nat,SV772: nat] :
( ( ( ord_less_eq_nat @ SV772 @ SV972 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ one_one_nat @ SV428 )
| ( ord_less_eq_nat @ ( power_power_nat @ SV428 @ SV772 ) @ ( power_power_nat @ SV428 @ SV972 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4622]) ).
thf(5094,plain,
! [SV429: nat,SV773: real] :
( ( ( ~ ( ord_less_real @ SV773 @ one_one_real ) )
= $true )
| ( ( ord_less_real @ ( times_times_real @ SV773 @ ( power_power_real @ SV773 @ SV429 ) ) @ ( power_power_real @ SV773 @ SV429 ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV773 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4623]) ).
thf(5095,plain,
! [SV430: nat,SV774: nat] :
( ( ( ~ ( ord_less_nat @ SV774 @ one_one_nat ) )
= $true )
| ( ( ord_less_nat @ ( times_times_nat @ SV774 @ ( power_power_nat @ SV774 @ SV430 ) ) @ ( power_power_nat @ SV774 @ SV430 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV774 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4624]) ).
thf(5096,plain,
! [SV431: nat,SV775: nat] :
( ( ( SV775 = zero_zero_nat )
= $true )
| ( ( ord_less_eq_nat @ SV431 @ SV775 )
= $true )
| ( ( dvd_dvd_nat @ SV431 @ SV775 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4625]) ).
thf(5097,plain,
! [SV432: nat,SV973: nat,SV776: nat] :
( ( ( dvd_dvd_nat @ SV776 @ SV973 )
= $false )
| ( ( dvd_dvd_nat @ ( power_power_nat @ SV776 @ SV432 ) @ ( power_power_nat @ SV973 @ SV432 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4626]) ).
thf(5098,plain,
! [SV433: nat,SV974: nat,SV777: nat] :
( ( ( dvd_dvd_nat @ SV777 @ SV974 )
= $false )
| ( ( dvd_dvd_nat @ ( times_times_nat @ SV433 @ SV777 ) @ ( times_times_nat @ SV433 @ SV974 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4627]) ).
thf(5099,plain,
! [SV434: nat,SV975: nat,SV778: nat] :
( ( ( dvd_dvd_nat @ SV778 @ SV975 )
= $false )
| ( ( dvd_dvd_nat @ ( times_times_nat @ SV778 @ SV434 ) @ ( times_times_nat @ SV975 @ SV434 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4628]) ).
thf(5100,plain,
! [SV435: nat,SV976: nat,SV779: nat] :
( ( ( dvd_dvd_nat @ SV779 @ SV976 )
= $false )
| ( ( ~ ( dvd_dvd_nat @ SV779 @ ( plus_plus_nat @ SV976 @ SV435 ) )
| ( dvd_dvd_nat @ SV779 @ SV435 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4629]) ).
thf(5101,plain,
! [SV977: nat,SV780: nat,SV436: nat] :
( ( ( dvd_dvd_nat @ ( power_power_nat @ SV436 @ SV780 ) @ ( power_power_nat @ SV977 @ SV780 ) )
= $false )
| ( ( ( SV780 = zero_zero_nat )
| ( dvd_dvd_nat @ SV436 @ SV977 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4630]) ).
thf(5102,plain,
! [SV781: nat,SV978: nat,SV437: nat] :
( ( ( ~ ( dvd_dvd_nat @ ( power_power_nat @ SV437 @ SV978 ) @ SV781 ) )
= $true )
| ( ( dvd_dvd_nat @ SV437 @ SV781 )
= $true )
| ( ( SV978 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4631]) ).
thf(5103,plain,
! [SV1027: nat,SV979: nat,SV782: nat,SV438: nat] :
( ( ( SV438
!= ( plus_plus_nat @ ( times_times_nat @ SV782 @ SV979 ) @ SV1027 ) )
= $true )
| ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV1027 )
| ~ ( ord_less_nat @ SV1027 @ SV979 )
| ~ ( dvd_dvd_nat @ SV979 @ SV438 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4632]) ).
thf(5104,plain,
! [SV980: nat,SV783: nat,SV439: nat] :
( ( ( dvd_dvd_nat @ ( power_power_nat @ SV439 @ SV783 ) @ ( power_power_nat @ SV439 @ SV980 ) )
= $false )
| ( ( ~ ( ord_less_nat @ one_one_nat @ SV439 )
| ( ord_less_eq_nat @ SV783 @ SV980 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4633]) ).
thf(5105,plain,
! [SV784: nat,SV440: nat] :
( ( ( ord_less_eq_nat @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV440 ) @ SV784 )
= $true )
| ( ( ( SV784 = zero_zero_nat )
| ( SV784 = SV440 ) )
= $true )
| ( ( dvd_dvd_nat @ SV440 @ SV784 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4634]) ).
thf(5106,plain,
! [SV1028: real] :
( ( ( ( power_power_real @ SV1028 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= zero_zero_real )
= $true )
| ( ( SV1028 = zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4635]) ).
thf(5107,plain,
! [SV1029: real] :
( ( ( SV1029 != zero_zero_real )
= $true )
| ( ( ( power_power_real @ SV1029 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4636]) ).
thf(5108,plain,
! [SV1030: nat,SV1291: nat] :
( ( ( SV1291 = zero_zero_nat )
| ( SV1030 != zero_zero_nat )
| ( ( power_power_nat @ SV1030 @ SV1291 )
= zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4637]) ).
thf(5109,plain,
( ( ~ ! [SX0: nat,SX1: nat] :
( ( ( power_power_nat @ SX0 @ SX1 )
!= zero_zero_nat )
| ( SX1 != zero_zero_nat ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4638]) ).
thf(5110,plain,
( ( ~ ! [SX0: nat] :
( ! [SX1: nat] :
( ( power_power_nat @ SX0 @ SX1 )
!= zero_zero_nat )
| ( SX0 = zero_zero_nat ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4638]) ).
thf(5111,plain,
! [SV1031: nat,SV1292: int] :
( ( ( ( number_number_of_nat @ SV1292 )
= zero_zero_nat )
| ( SV1031 != zero_zero_nat )
| ( ( power_power_nat @ SV1031 @ ( number_number_of_nat @ SV1292 ) )
= zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4639]) ).
thf(5112,plain,
( ( ~ ! [SX0: nat,SX1: int] :
( ( ( power_power_nat @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_nat )
| ( ( number_number_of_nat @ SX1 )
!= zero_zero_nat ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4640]) ).
thf(5113,plain,
( ( ~ ! [SX0: nat] :
( ! [SX1: int] :
( ( power_power_nat @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_nat )
| ( SX0 = zero_zero_nat ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4640]) ).
thf(5114,plain,
! [SV1032: int] :
( ( ( ~ ( ord_less_eq_int @ min @ ( bit0 @ SV1032 ) ) )
= $true )
| ( ( ord_less_int @ min @ SV1032 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4641]) ).
thf(5115,plain,
! [SV1033: int] :
( ( ( ~ ( ord_less_int @ min @ SV1033 ) )
= $true )
| ( ( ord_less_eq_int @ min @ ( bit0 @ SV1033 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4642]) ).
thf(5116,plain,
! [SV1293: real,SV1034: real] :
( ( ~ ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ SV1034 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SV1293 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
| ( SV1034 != zero_zero_real )
| ( SV1293 != zero_zero_real ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4643]) ).
thf(5117,plain,
( ( ~ ! [SX0: real] :
( ( SX0 = zero_zero_real )
| ! [SX1: real] : ( ord_less_real @ 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 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4644]) ).
thf(5118,plain,
( ( ~ ! [SX0: real,SX1: real] :
( ( SX1 = zero_zero_real )
| ( ord_less_real @ 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 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4644]) ).
thf(5119,plain,
! [SV1035: int] :
( ( ( ~ ( ord_less_eq_int @ pls @ SV1035 ) )
= $true )
| ( ( ord_less_eq_real @ zero_zero_real @ ( number267125858f_real @ SV1035 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4645]) ).
thf(5120,plain,
! [SV1036: int] :
( ( ( ~ ( ord_less_eq_real @ zero_zero_real @ ( number267125858f_real @ SV1036 ) ) )
= $true )
| ( ( ord_less_eq_int @ pls @ SV1036 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4646]) ).
thf(5121,plain,
! [SV1037: int] :
( ( ( ~ ( ord_less_eq_int @ pls @ SV1037 ) )
= $true )
| ( ( ord_less_int @ pls @ ( bit1 @ SV1037 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4647]) ).
thf(5122,plain,
! [SV1038: int] :
( ( ( ~ ( ord_less_int @ pls @ ( bit1 @ SV1038 ) ) )
= $true )
| ( ( ord_less_eq_int @ pls @ SV1038 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4648]) ).
thf(5123,plain,
! [SV1294: int,SV1039: int] :
( ( ~ ( ord_less_eq_int @ SV1039 @ SV1294 )
| ( ord_less_int @ ( bit0 @ SV1039 ) @ ( bit1 @ SV1294 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4649]) ).
thf(5124,plain,
! [SV1295: int,SV1040: int] :
( ( ~ ( ord_less_int @ ( bit0 @ SV1040 ) @ ( bit1 @ SV1295 ) )
| ( ord_less_eq_int @ SV1040 @ SV1295 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4650]) ).
thf(5125,plain,
! [SV1041: int] :
( ( ( ~ ( ord_less_int @ min @ ( bit1 @ SV1041 ) ) )
= $true )
| ( ( ord_less_int @ min @ SV1041 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4651]) ).
thf(5126,plain,
! [SV1042: int] :
( ( ( ~ ( ord_less_int @ min @ SV1042 ) )
= $true )
| ( ( ord_less_int @ min @ ( bit1 @ SV1042 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4652]) ).
thf(5127,plain,
! [SV1296: int,SV1043: int] :
( ( ~ ( ord_less_int @ ( bit1 @ SV1043 ) @ ( bit1 @ SV1296 ) )
| ( ord_less_int @ SV1043 @ SV1296 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4653]) ).
thf(5128,plain,
! [SV1297: int,SV1044: int] :
( ( ~ ( ord_less_int @ SV1044 @ SV1297 )
| ( ord_less_int @ ( bit1 @ SV1044 ) @ ( bit1 @ SV1297 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4654]) ).
thf(5129,plain,
! [SV1298: nat,SV1045: nat] :
( ( ( ( power_power_nat @ SV1045 @ SV1298 )
!= one_one_nat )
| ( SV1045 = one_one_nat )
| ( SV1298 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4655]) ).
thf(5130,plain,
( ( ~ ! [SX0: nat] :
( ( SX0 != one_one_nat )
| ! [SX1: nat] :
( ( power_power_nat @ SX0 @ SX1 )
= one_one_nat ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4656]) ).
thf(5131,plain,
( ( ~ ! [SX0: nat,SX1: nat] :
( ( SX1 != zero_zero_nat )
| ( ( power_power_nat @ SX0 @ SX1 )
= one_one_nat ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4656]) ).
thf(5132,plain,
! [SV1299: int,SV1046: int] :
( ( ~ ( ord_less_eq_int @ SV1046 @ SV1299 )
| ( ord_less_eq_real @ ( number267125858f_real @ SV1046 ) @ ( number267125858f_real @ SV1299 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4657]) ).
thf(5133,plain,
! [SV1300: int,SV1047: int] :
( ( ~ ( ord_less_eq_real @ ( number267125858f_real @ SV1047 ) @ ( number267125858f_real @ SV1300 ) )
| ( ord_less_eq_int @ SV1047 @ SV1300 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4658]) ).
thf(5134,plain,
! [SV1048: nat] :
( ( ( SV1048 != zero_zero_nat )
= $true )
| ( ( ( power_power_real @ zero_zero_real @ SV1048 )
= one_one_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4659]) ).
thf(5135,plain,
! [SV1049: nat] :
( ( ( SV1049 = zero_zero_nat )
= $true )
| ( ( ( power_power_real @ zero_zero_real @ SV1049 )
= zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4660]) ).
thf(5136,plain,
! [SV1301: int,SV1050: int] :
( ( ( ( bit1 @ SV1050 )
!= ( bit1 @ SV1301 ) )
| ( SV1050 = SV1301 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4661]) ).
thf(5137,plain,
! [SV1302: int,SV1051: int] :
( ( ( SV1051 != SV1302 )
| ( ( bit1 @ SV1051 )
= ( bit1 @ SV1302 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4662]) ).
thf(5138,plain,
! [SV1303: int,SV1052: int] :
( ( ~ ( ord_less_int @ ( number_number_of_int @ SV1052 ) @ ( number_number_of_int @ SV1303 ) )
| ( ord_less_int @ SV1052 @ SV1303 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4663]) ).
thf(5139,plain,
! [SV1304: int,SV1053: int] :
( ( ~ ( ord_less_int @ SV1053 @ SV1304 )
| ( ord_less_int @ ( number_number_of_int @ SV1053 ) @ ( number_number_of_int @ SV1304 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4664]) ).
thf(5140,plain,
! [SV1305: real,SV1054: real] :
( ( ( SV1054 != zero_zero_real )
| ( SV1305 != zero_zero_real )
| ( ord_less_eq_real @ ( plus_plus_real @ ( power_power_real @ SV1054 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SV1305 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_real ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4665]) ).
thf(5141,plain,
( ( ~ ! [SX0: real] :
( ! [SX1: real] :
~ ( ord_less_eq_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 )
| ( SX0 = zero_zero_real ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4666]) ).
thf(5142,plain,
( ( ~ ! [SX0: real,SX1: real] :
( ~ ( ord_less_eq_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 )
| ( SX1 = zero_zero_real ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4666]) ).
thf(5143,plain,
! [SV1306: int,SV1055: int] :
( ( ~ ( ord_less_int @ SV1055 @ ( plus_plus_int @ SV1306 @ one_one_int ) )
| ( SV1055 = SV1306 )
| ( ord_less_int @ SV1055 @ SV1306 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4667]) ).
thf(5144,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ( SX0 != SX1 )
| ( ord_less_int @ SX0 @ ( plus_plus_int @ SX1 @ one_one_int ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4668]) ).
thf(5145,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ SX0 @ ( plus_plus_int @ SX1 @ one_one_int ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4668]) ).
thf(5146,plain,
! [SV1056: int] :
( ( ( ~ ( ord_less_eq_int @ min @ ( bit1 @ SV1056 ) ) )
= $true )
| ( ( ord_less_eq_int @ min @ SV1056 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4669]) ).
thf(5147,plain,
! [SV1057: int] :
( ( ( ~ ( ord_less_eq_int @ min @ SV1057 ) )
= $true )
| ( ( ord_less_eq_int @ min @ ( bit1 @ SV1057 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4670]) ).
thf(5148,plain,
! [SV1058: int] :
( ( ( ( number_number_of_nat @ SV1058 )
!= zero_zero_nat )
= $true )
| ( ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ SV1058 ) )
= one_one_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4671]) ).
thf(5149,plain,
! [SV1059: int] :
( ( ( ( number_number_of_nat @ SV1059 )
= zero_zero_nat )
= $true )
| ( ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ SV1059 ) )
= zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4672]) ).
thf(5150,plain,
! [SV785: nat,SV441: nat] :
( ( ~ ( ~ ! [SY2273: nat,SY2274: nat] :
( ( ( plus_plus_nat @ ( times_times_nat @ SY2273 @ SV441 ) @ ( times_times_nat @ SY2274 @ SV785 ) )
= ( plus_plus_nat @ ( times_times_nat @ SY2273 @ SV785 ) @ ( times_times_nat @ SY2274 @ SV441 ) ) )
| ( SY2273 != SY2274 ) )
| ~ ( ! [SY2275: nat,SY2276: nat] :
( ( plus_plus_nat @ ( times_times_nat @ SY2275 @ SV441 ) @ ( times_times_nat @ SY2276 @ SV785 ) )
= ( plus_plus_nat @ ( times_times_nat @ SY2275 @ SV785 ) @ ( times_times_nat @ SY2276 @ SV441 ) ) )
| ( SV441 != SV785 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4673]) ).
thf(5151,plain,
! [SV785: nat,SV441: nat] :
( ( ! [SY2277: nat,SY2278: nat] :
( ( SY2277 = SY2278 )
| ( SV441 = SV785 )
| ( ( plus_plus_nat @ ( times_times_nat @ SY2277 @ SV441 ) @ ( times_times_nat @ SY2278 @ SV785 ) )
!= ( plus_plus_nat @ ( times_times_nat @ SY2277 @ SV785 ) @ ( times_times_nat @ SY2278 @ SV441 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4674]) ).
thf(5152,plain,
! [SV1307: int,SV1060: int] :
( ( ~ ( ord_less_eq_int @ ( bit1 @ SV1060 ) @ ( bit1 @ SV1307 ) )
| ( ord_less_eq_int @ SV1060 @ SV1307 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4675]) ).
thf(5153,plain,
! [SV1308: int,SV1061: int] :
( ( ~ ( ord_less_eq_int @ SV1061 @ SV1308 )
| ( ord_less_eq_int @ ( bit1 @ SV1061 ) @ ( bit1 @ SV1308 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4676]) ).
thf(5154,plain,
! [SV1309: int,SV1062: int] :
( ( ~ ( ord_less_int @ ( bit0 @ SV1062 ) @ ( bit0 @ SV1309 ) )
| ( ord_less_int @ SV1062 @ SV1309 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4677]) ).
thf(5155,plain,
! [SV1310: int,SV1063: int] :
( ( ~ ( ord_less_int @ SV1063 @ SV1310 )
| ( ord_less_int @ ( bit0 @ SV1063 ) @ ( bit0 @ SV1310 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4678]) ).
thf(5156,plain,
! [SV1064: real,SV1311: int] :
( ( ( ( number_number_of_nat @ SV1311 )
= zero_zero_nat )
| ( SV1064 != zero_zero_real )
| ( ( power_power_real @ SV1064 @ ( number_number_of_nat @ SV1311 ) )
= zero_zero_real ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4679]) ).
thf(5157,plain,
( ( ~ ! [SX0: real,SX1: int] :
( ( ( power_power_real @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_real )
| ( ( number_number_of_nat @ SX1 )
!= zero_zero_nat ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4680]) ).
thf(5158,plain,
( ( ~ ! [SX0: real] :
( ! [SX1: int] :
( ( power_power_real @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_real )
| ( SX0 = zero_zero_real ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4680]) ).
thf(5159,plain,
! [SV1312: real,SV1065: real] :
( ( ~ ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ SV1065 @ SV1065 ) @ ( times_times_real @ SV1312 @ SV1312 ) ) )
| ( SV1065 != zero_zero_real )
| ( SV1312 != zero_zero_real ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4681]) ).
thf(5160,plain,
( ( ~ ! [SX0: real] :
( ( SX0 = zero_zero_real )
| ! [SX1: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ SX0 @ SX0 ) @ ( times_times_real @ SX1 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4682]) ).
thf(5161,plain,
( ( ~ ! [SX0: real,SX1: real] :
( ( SX1 = zero_zero_real )
| ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ SX0 @ SX0 ) @ ( times_times_real @ SX1 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4682]) ).
thf(5162,plain,
! [SV1313: nat,SV1066: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV1066 @ SV1313 ) )
| ( SV1313 = zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV1066 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4683]) ).
thf(5163,plain,
( ( ~ ! [SX0: nat,SX1: nat] :
( ( SX1 != zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4684]) ).
thf(5164,plain,
( ( ~ ! [SX0: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SX0 )
| ! [SX1: nat] : ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4684]) ).
thf(5165,plain,
! [SV786: real,SV442: real] :
( ( ~ ( ~ ! [SY2279: real,SY2280: real] :
( ( ( plus_plus_real @ ( times_times_real @ SY2279 @ SV442 ) @ ( times_times_real @ SY2280 @ SV786 ) )
= ( plus_plus_real @ ( times_times_real @ SY2279 @ SV786 ) @ ( times_times_real @ SY2280 @ SV442 ) ) )
| ( SY2279 != SY2280 ) )
| ~ ( ! [SY2281: real,SY2282: real] :
( ( plus_plus_real @ ( times_times_real @ SY2281 @ SV442 ) @ ( times_times_real @ SY2282 @ SV786 ) )
= ( plus_plus_real @ ( times_times_real @ SY2281 @ SV786 ) @ ( times_times_real @ SY2282 @ SV442 ) ) )
| ( SV442 != SV786 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4685]) ).
thf(5166,plain,
! [SV786: real,SV442: real] :
( ( ! [SY2283: real,SY2284: real] :
( ( SY2283 = SY2284 )
| ( SV442 = SV786 )
| ( ( plus_plus_real @ ( times_times_real @ SY2283 @ SV442 ) @ ( times_times_real @ SY2284 @ SV786 ) )
!= ( plus_plus_real @ ( times_times_real @ SY2283 @ SV786 ) @ ( times_times_real @ SY2284 @ SV442 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4686]) ).
thf(5167,plain,
! [SV1067: int] :
( ( ( ~ ( ord_less_eq_int @ ( bit0 @ SV1067 ) @ pls ) )
= $true )
| ( ( ord_less_eq_int @ SV1067 @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4687]) ).
thf(5168,plain,
! [SV1068: int] :
( ( ( ~ ( ord_less_eq_int @ SV1068 @ pls ) )
= $true )
| ( ( ord_less_eq_int @ ( bit0 @ SV1068 ) @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4688]) ).
thf(5169,plain,
! [SV1069: int] :
( ( ( ( bit1 @ SV1069 )
!= min )
= $true )
| ( ( SV1069 = min )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4689]) ).
thf(5170,plain,
! [SV1070: int] :
( ( ( SV1070 != min )
= $true )
| ( ( ( bit1 @ SV1070 )
= min )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4690]) ).
thf(5171,plain,
! [SV1314: real,SV1071: real] :
( ( ~ ( ord_less_eq_real @ SV1071 @ SV1314 )
| ( SV1071 = SV1314 )
| ( ord_less_real @ SV1071 @ SV1314 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4691]) ).
thf(5172,plain,
( ( ~ ! [SX0: real,SX1: real] :
( ( SX0 != SX1 )
| ( ord_less_eq_real @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4692]) ).
thf(5173,plain,
( ( ~ ! [SX0: real,SX1: real] :
( ~ ( ord_less_real @ SX0 @ SX1 )
| ( ord_less_eq_real @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4692]) ).
thf(5174,plain,
! [SV1072: real] :
( ( ( ( plus_plus_real @ SV1072 @ SV1072 )
!= zero_zero_real )
= $true )
| ( ( SV1072 = zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4693]) ).
thf(5175,plain,
! [SV1073: real] :
( ( ( SV1073 != zero_zero_real )
= $true )
| ( ( ( plus_plus_real @ SV1073 @ SV1073 )
= zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4694]) ).
thf(5176,plain,
! [SV1315: int,SV1074: int] :
( ( ~ ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ SV1074 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV1315 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
| ( SV1074 != zero_zero_int )
| ( SV1315 != zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4695]) ).
thf(5177,plain,
( ( ~ ! [SX0: int] :
( ( SX0 = zero_zero_int )
| ! [SX1: int] : ( ord_less_int @ zero_zero_int @ ( 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 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4696]) ).
thf(5178,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ( SX1 = zero_zero_int )
| ( ord_less_int @ zero_zero_int @ ( 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 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4696]) ).
thf(5179,plain,
! [SV1075: int] :
( ( ( ~ ( ord_less_int @ pls @ SV1075 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ SV1075 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4697]) ).
thf(5180,plain,
! [SV1076: int] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ SV1076 ) ) )
= $true )
| ( ( ord_less_int @ pls @ SV1076 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4698]) ).
thf(5181,plain,
! [SV1316: int,SV1077: int] :
( ( ~ ( ord_less_eq_int @ ( number_number_of_int @ SV1077 ) @ ( number_number_of_int @ SV1316 ) )
| ( ord_less_eq_int @ SV1077 @ SV1316 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4699]) ).
thf(5182,plain,
! [SV1317: int,SV1078: int] :
( ( ~ ( ord_less_eq_int @ SV1078 @ SV1317 )
| ( ord_less_eq_int @ ( number_number_of_int @ SV1078 ) @ ( number_number_of_int @ SV1317 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4700]) ).
thf(5183,plain,
! [SV1318: real,SV1079: real] :
( ( ( SV1079 != zero_zero_real )
| ( SV1318 != zero_zero_real )
| ( ( plus_plus_real @ ( power_power_real @ SV1079 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SV1318 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_real ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4701]) ).
thf(5184,plain,
( ( ~ ! [SX0: real] :
( ! [SX1: 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 )
| ( SX0 = zero_zero_real ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4702]) ).
thf(5185,plain,
( ( ~ ! [SX0: real,SX1: 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 )
| ( SX1 = zero_zero_real ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4702]) ).
thf(5186,plain,
! [SV1080: int,SV1319: nat] :
( ( ( SV1319 != zero_zero_nat )
| ( ( power_power_int @ SV1080 @ SV1319 )
= one_one_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4703]) ).
thf(5187,plain,
! [SV1081: int,SV1320: nat] :
( ( ( SV1320 = zero_zero_nat )
| ( ( power_power_int @ SV1081 @ SV1320 )
= ( times_times_int @ SV1081 @ ( power_power_int @ SV1081 @ ( minus_minus_nat @ SV1320 @ one_one_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4704]) ).
thf(5188,plain,
! [SV1082: int] :
( ( ( ( number_number_of_nat @ SV1082 )
!= zero_zero_nat )
= $true )
| ( ( ord_less_eq_int @ SV1082 @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4705]) ).
thf(5189,plain,
! [SV1083: int] :
( ( ( ~ ( ord_less_eq_int @ SV1083 @ pls ) )
= $true )
| ( ( ( number_number_of_nat @ SV1083 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4706]) ).
thf(5190,plain,
! [SV1084: int,SV1321: int] :
( ( ~ ( dvd_dvd_int @ SV1321 @ SV1084 )
| ( zcong @ SV1084 @ zero_zero_int @ SV1321 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4707]) ).
thf(5191,plain,
! [SV1322: int,SV1085: int] :
( ( ~ ( zcong @ SV1085 @ zero_zero_int @ SV1322 )
| ( dvd_dvd_int @ SV1322 @ SV1085 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4708]) ).
thf(5192,plain,
! [SV1086: nat,SV1323: nat] :
( ( ( SV1323 != zero_zero_nat )
| ( ( power_power_nat @ SV1086 @ SV1323 )
= one_one_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4709]) ).
thf(5193,plain,
! [SV1087: nat,SV1324: nat] :
( ( ( SV1324 = zero_zero_nat )
| ( ( power_power_nat @ SV1087 @ SV1324 )
= ( times_times_nat @ SV1087 @ ( power_power_nat @ SV1087 @ ( minus_minus_nat @ SV1324 @ one_one_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4710]) ).
thf(5194,plain,
! [SV1088: int] :
( ( ( ~ ( ord_less_int @ ( bit1 @ SV1088 ) @ min ) )
= $true )
| ( ( ord_less_int @ SV1088 @ min )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4711]) ).
thf(5195,plain,
! [SV1089: int] :
( ( ( ~ ( ord_less_int @ SV1089 @ min ) )
= $true )
| ( ( ord_less_int @ ( bit1 @ SV1089 ) @ min )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4712]) ).
thf(5196,plain,
! [SV1325: nat,SV443: nat] :
( ( ! [SY2552: int] :
( ~ ( ord_less_int @ one_one_int @ SY2552 )
| ~ ( ord_less_int @ ( power_power_int @ SY2552 @ SV443 ) @ ( power_power_int @ SY2552 @ SV1325 ) )
| ( ord_less_nat @ SV443 @ SV1325 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4713]) ).
thf(5197,plain,
! [SV1326: nat,SV443: nat] :
( ( ! [SY2553: int] :
( ~ ( ord_less_int @ one_one_int @ SY2553 )
| ~ ( ord_less_nat @ SV443 @ SV1326 )
| ( ord_less_int @ ( power_power_int @ SY2553 @ SV443 ) @ ( power_power_int @ SY2553 @ SV1326 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4714]) ).
thf(5198,plain,
! [SV1090: int] :
( ( ( ~ ( ord_less_int @ ( bit1 @ SV1090 ) @ zero_zero_int ) )
= $true )
| ( ( ord_less_int @ SV1090 @ zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4715]) ).
thf(5199,plain,
! [SV1091: int] :
( ( ( ~ ( ord_less_int @ SV1091 @ zero_zero_int ) )
= $true )
| ( ( ord_less_int @ ( bit1 @ SV1091 ) @ zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4716]) ).
thf(5200,plain,
! [SV1092: int] :
( ( ( ~ ( ord_less_eq_int @ SV1092 @ pls ) )
= $true )
| ( ( ord_less_eq_real @ ( number267125858f_real @ SV1092 ) @ zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4717]) ).
thf(5201,plain,
! [SV1093: int] :
( ( ( ~ ( ord_less_eq_real @ ( number267125858f_real @ SV1093 ) @ zero_zero_real ) )
= $true )
| ( ( ord_less_eq_int @ SV1093 @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4718]) ).
thf(5202,plain,
! [SV1094: int] :
( ( ( ~ ( ord_less_int @ min @ ( bit0 @ SV1094 ) ) )
= $true )
| ( ( ord_less_int @ min @ SV1094 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4719]) ).
thf(5203,plain,
! [SV1095: int] :
( ( ( ~ ( ord_less_int @ min @ SV1095 ) )
= $true )
| ( ( ord_less_int @ min @ ( bit0 @ SV1095 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4720]) ).
thf(5204,plain,
! [SV1327: int,SV1096: int] :
( ( ~ ( ord_less_eq_int @ ( number_number_of_int @ SV1096 ) @ ( number_number_of_int @ SV1327 ) )
| ( ord_less_eq_int @ SV1096 @ SV1327 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4721]) ).
thf(5205,plain,
! [SV1328: int,SV1097: int] :
( ( ~ ( ord_less_eq_int @ SV1097 @ SV1328 )
| ( ord_less_eq_int @ ( number_number_of_int @ SV1097 ) @ ( number_number_of_int @ SV1328 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4722]) ).
thf(5206,plain,
! [SV1329: int,SV444: int] :
( ( ! [SY2554: int] :
~ ( dvd_dvd_int @ SV444 @ ( plus_plus_int @ SV1329 @ ( times_times_int @ SV444 @ SY2554 ) ) )
| ( dvd_dvd_int @ SV444 @ SV1329 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4723]) ).
thf(5207,plain,
! [SV1330: int,SV444: int] :
( ( ~ ( dvd_dvd_int @ SV444 @ SV1330 )
| ! [SY2555: int] : ( dvd_dvd_int @ SV444 @ ( plus_plus_int @ SV1330 @ ( times_times_int @ SV444 @ SY2555 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4724]) ).
thf(5208,plain,
! [SV1331: int,SV1098: int] :
( ( ~ ( ord_less_eq_int @ SV1098 @ ( minus_minus_int @ SV1331 @ one_one_int ) )
| ( ord_less_int @ SV1098 @ SV1331 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4725]) ).
thf(5209,plain,
! [SV1332: int,SV1099: int] :
( ( ~ ( ord_less_int @ SV1099 @ SV1332 )
| ( ord_less_eq_int @ SV1099 @ ( minus_minus_int @ SV1332 @ one_one_int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4726]) ).
thf(5210,plain,
! [SV1333: int,SV1100: int] :
( ( ~ ( ord_less_eq_int @ ( bit0 @ SV1100 ) @ ( bit0 @ SV1333 ) )
| ( ord_less_eq_int @ SV1100 @ SV1333 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4727]) ).
thf(5211,plain,
! [SV1334: int,SV1101: int] :
( ( ~ ( ord_less_eq_int @ SV1101 @ SV1334 )
| ( ord_less_eq_int @ ( bit0 @ SV1101 ) @ ( bit0 @ SV1334 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4728]) ).
thf(5212,plain,
! [SV1102: int,SV1335: int] :
( ( ( ( number_number_of_nat @ SV1335 )
= zero_zero_nat )
| ( SV1102 != zero_zero_int )
| ( ( power_power_int @ SV1102 @ ( number_number_of_nat @ SV1335 ) )
= zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4729]) ).
thf(5213,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ( ( power_power_int @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_int )
| ( ( number_number_of_nat @ SX1 )
!= zero_zero_nat ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4730]) ).
thf(5214,plain,
( ( ~ ! [SX0: int] :
( ! [SX1: int] :
( ( power_power_int @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4730]) ).
thf(5215,plain,
! [SV1336: int,SV1103: int] :
( ( ~ ( ord_less_eq_real @ ( number267125858f_real @ SV1103 ) @ ( number267125858f_real @ SV1336 ) )
| ~ ( ord_less_real @ ( number267125858f_real @ SV1336 ) @ ( number267125858f_real @ SV1103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4731]) ).
thf(5216,plain,
! [SV1104: int,SV1337: int] :
( ( ( ord_less_real @ ( number267125858f_real @ SV1337 ) @ ( number267125858f_real @ SV1104 ) )
| ( ord_less_eq_real @ ( number267125858f_real @ SV1104 ) @ ( number267125858f_real @ SV1337 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4732]) ).
thf(5217,plain,
! [SV1338: int,SV1105: int] :
( ( ~ ( ord_less_int @ SV1105 @ SV1338 )
| ( ord_less_int @ ( minus_minus_int @ SV1105 @ SV1338 ) @ zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4733]) ).
thf(5218,plain,
! [SV1339: int,SV1106: int] :
( ( ~ ( ord_less_int @ ( minus_minus_int @ SV1106 @ SV1339 ) @ zero_zero_int )
| ( ord_less_int @ SV1106 @ SV1339 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4734]) ).
thf(5219,plain,
! [SV1340: int,SV1107: int] :
( ( ~ ( zcong @ ( times_times_int @ SV1107 @ ( minus_minus_int @ SV1340 @ one_one_int ) ) @ one_one_int @ SV1340 )
| ( zcong @ SV1107 @ ( minus_minus_int @ SV1340 @ one_one_int ) @ SV1340 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4735]) ).
thf(5220,plain,
! [SV1341: int,SV1108: int] :
( ( ~ ( zcong @ SV1108 @ ( minus_minus_int @ SV1341 @ one_one_int ) @ SV1341 )
| ( zcong @ ( times_times_int @ SV1108 @ ( minus_minus_int @ SV1341 @ one_one_int ) ) @ one_one_int @ SV1341 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4736]) ).
thf(5221,plain,
! [SV1109: int] :
( ( ( ~ ( ord_less_int @ ( bit0 @ SV1109 ) @ pls ) )
= $true )
| ( ( ord_less_int @ SV1109 @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4737]) ).
thf(5222,plain,
! [SV1110: int] :
( ( ( ~ ( ord_less_int @ SV1110 @ pls ) )
= $true )
| ( ( ord_less_int @ ( bit0 @ SV1110 ) @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4738]) ).
thf(5223,plain,
! [SV1111: nat,SV1342: nat] :
( ( ( SV1342 != zero_zero_nat )
| ( ( times_times_nat @ SV1342 @ SV1111 )
= zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4739]) ).
thf(5224,plain,
! [SV1112: nat,SV1343: nat] :
( ( ( SV1343 = zero_zero_nat )
| ( ( times_times_nat @ SV1343 @ SV1112 )
= ( plus_plus_nat @ SV1112 @ ( times_times_nat @ ( minus_minus_nat @ SV1343 @ one_one_nat ) @ SV1112 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4740]) ).
thf(5225,plain,
! [SV1344: real,SV1113: real] :
( ( ( SV1113 != zero_zero_real )
| ( SV1344 != zero_zero_real )
| ( ( plus_plus_real @ ( power_power_real @ SV1113 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SV1344 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_real ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4741]) ).
thf(5226,plain,
( ( ~ ! [SX0: real] :
( ! [SX1: 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 )
| ( SX0 = zero_zero_real ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4742]) ).
thf(5227,plain,
( ( ~ ! [SX0: real,SX1: 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 )
| ( SX1 = zero_zero_real ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4742]) ).
thf(5228,plain,
! [SV1345: int,SV1114: int] :
( ( ( SV1114 != zero_zero_int )
| ( SV1345 != zero_zero_int )
| ( ( plus_plus_int @ ( power_power_int @ SV1114 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV1345 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4743]) ).
thf(5229,plain,
( ( ~ ! [SX0: int] :
( ! [SX1: int] :
( ( 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 ) ) ) ) )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4744]) ).
thf(5230,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ( ( 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 ) ) ) ) )
!= zero_zero_int )
| ( SX1 = zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4744]) ).
thf(5231,plain,
! [SV1115: int,SV1346: int] :
( ( ~ ( dvd_dvd_int @ SV1346 @ SV1115 )
| ( zcong @ SV1115 @ zero_zero_int @ SV1346 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4745]) ).
thf(5232,plain,
! [SV1347: int,SV1116: int] :
( ( ~ ( zcong @ SV1116 @ zero_zero_int @ SV1347 )
| ( dvd_dvd_int @ SV1347 @ SV1116 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4746]) ).
thf(5233,plain,
! [SV1348: int,SV1117: int] :
( ( ~ ( ord_less_eq_int @ ( bit0 @ SV1117 ) @ ( bit1 @ SV1348 ) )
| ( ord_less_eq_int @ SV1117 @ SV1348 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4747]) ).
thf(5234,plain,
! [SV1349: int,SV1118: int] :
( ( ~ ( ord_less_eq_int @ SV1118 @ SV1349 )
| ( ord_less_eq_int @ ( bit0 @ SV1118 ) @ ( bit1 @ SV1349 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4748]) ).
thf(5235,plain,
! [SV1119: int] :
( ( ( ~ ( ord_less_int @ ( plus_plus_int @ SV1119 @ SV1119 ) @ zero_zero_int ) )
= $true )
| ( ( ord_less_int @ SV1119 @ zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4749]) ).
thf(5236,plain,
! [SV1120: int] :
( ( ( ~ ( ord_less_int @ SV1120 @ zero_zero_int ) )
= $true )
| ( ( ord_less_int @ ( plus_plus_int @ SV1120 @ SV1120 ) @ zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4750]) ).
thf(5237,plain,
! [SV1121: int] :
( ( ( ~ ( ord_less_eq_int @ one_one_int @ SV1121 ) )
= $true )
| ( ( ord_less_int @ zero_zero_int @ SV1121 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4751]) ).
thf(5238,plain,
! [SV1122: int] :
( ( ( ~ ( ord_less_int @ zero_zero_int @ SV1122 ) )
= $true )
| ( ( ord_less_eq_int @ one_one_int @ SV1122 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4752]) ).
thf(5239,plain,
! [SV1350: real,SV445: real] :
( ( ! [SY2556: real] :
( ~ ( ord_less_real @ zero_zero_real @ SY2556 )
| ~ ( ord_less_eq_real @ ( times_times_real @ SV445 @ SY2556 ) @ ( times_times_real @ SV1350 @ SY2556 ) )
| ( ord_less_eq_real @ SV445 @ SV1350 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4753]) ).
thf(5240,plain,
! [SV1351: real,SV445: real] :
( ( ! [SY2557: real] :
( ~ ( ord_less_real @ zero_zero_real @ SY2557 )
| ~ ( ord_less_eq_real @ SV445 @ SV1351 )
| ( ord_less_eq_real @ ( times_times_real @ SV445 @ SY2557 ) @ ( times_times_real @ SV1351 @ SY2557 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4754]) ).
thf(5241,plain,
! [SV1123: int] :
( ( ( ~ ( ord_less_int @ pls @ SV1123 ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ ( number267125858f_real @ SV1123 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4755]) ).
thf(5242,plain,
! [SV1124: int] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ ( number267125858f_real @ SV1124 ) ) )
= $true )
| ( ( ord_less_int @ pls @ SV1124 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4756]) ).
thf(5243,plain,
! [SV1352: real,SV1125: real] :
( ( ( SV1125 != zero_zero_real )
| ( SV1352 != zero_zero_real )
| ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ SV1125 @ SV1125 ) @ ( times_times_real @ SV1352 @ SV1352 ) ) @ zero_zero_real ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4757]) ).
thf(5244,plain,
( ( ~ ! [SX0: real] :
( ! [SX1: real] :
~ ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ SX0 @ SX0 ) @ ( times_times_real @ SX1 @ SX1 ) ) @ zero_zero_real )
| ( SX0 = zero_zero_real ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4758]) ).
thf(5245,plain,
( ( ~ ! [SX0: real,SX1: real] :
( ~ ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ SX0 @ SX0 ) @ ( times_times_real @ SX1 @ SX1 ) ) @ zero_zero_real )
| ( SX1 = zero_zero_real ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4758]) ).
thf(5246,plain,
! [SV1353: int,SV1126: int] :
( ( ~ ( ord_less_eq_int @ ( bit1 @ SV1126 ) @ ( bit0 @ SV1353 ) )
| ( ord_less_int @ SV1126 @ SV1353 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4759]) ).
thf(5247,plain,
! [SV1354: int,SV1127: int] :
( ( ~ ( ord_less_int @ SV1127 @ SV1354 )
| ( ord_less_eq_int @ ( bit1 @ SV1127 ) @ ( bit0 @ SV1354 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4760]) ).
thf(5248,plain,
! [SV1128: int] :
( ( ( ~ ( ord_less_int @ zero_zero_int @ ( number_number_of_int @ SV1128 ) ) )
= $true )
| ( ( ord_less_int @ pls @ SV1128 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4761]) ).
thf(5249,plain,
! [SV1129: int] :
( ( ( ~ ( ord_less_int @ pls @ SV1129 ) )
= $true )
| ( ( ord_less_int @ zero_zero_int @ ( number_number_of_int @ SV1129 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4762]) ).
thf(5250,plain,
! [SV1355: int,SV1130: int] :
( ( ( SV1130 != zero_zero_int )
| ( SV1355 != zero_zero_int )
| ( ord_less_eq_int @ ( plus_plus_int @ ( power_power_int @ SV1130 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV1355 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4763]) ).
thf(5251,plain,
( ( ~ ! [SX0: int] :
( ! [SX1: int] :
~ ( ord_less_eq_int @ ( 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 ) ) ) ) ) @ zero_zero_int )
| ( SX0 = zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4764]) ).
thf(5252,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ ( 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 ) ) ) ) ) @ zero_zero_int )
| ( SX1 = zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4764]) ).
thf(5253,plain,
! [SV1131: int] :
( ( ( min
!= ( bit1 @ SV1131 ) )
= $true )
| ( ( min = SV1131 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4765]) ).
thf(5254,plain,
! [SV1132: int] :
( ( ( min != SV1132 )
= $true )
| ( ( min
= ( bit1 @ SV1132 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4766]) ).
thf(5255,plain,
! [SV1356: int,SV1133: int] :
( ( ( SV1133 != zero_zero_int )
| ( SV1356 != zero_zero_int )
| ( ( plus_plus_int @ ( times_times_int @ SV1133 @ SV1133 ) @ ( times_times_int @ SV1356 @ SV1356 ) )
= zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4767]) ).
thf(5256,plain,
( ( ~ ! [SX0: int] :
( ! [SX1: int] :
( ( plus_plus_int @ ( times_times_int @ SX0 @ SX0 ) @ ( times_times_int @ SX1 @ SX1 ) )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4768]) ).
thf(5257,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ( ( plus_plus_int @ ( times_times_int @ SX0 @ SX0 ) @ ( times_times_int @ SX1 @ SX1 ) )
!= zero_zero_int )
| ( SX1 = zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4768]) ).
thf(5258,plain,
! [SV1357: int,SV1134: int] :
( ( ( SV1134 = SV1357 )
| ~ ( ord_less_eq_int @ SV1134 @ SV1357 )
| ( ord_less_int @ SV1134 @ SV1357 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4769]) ).
thf(5259,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4770]) ).
thf(5260,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4770]) ).
thf(5261,plain,
! [SV1135: int] :
( ( ( ~ ( ord_less_eq_int @ ( number_number_of_int @ SV1135 ) @ zero_zero_int ) )
= $true )
| ( ( ord_less_eq_int @ SV1135 @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4771]) ).
thf(5262,plain,
! [SV1136: int] :
( ( ( ~ ( ord_less_eq_int @ SV1136 @ pls ) )
= $true )
| ( ( ord_less_eq_int @ ( number_number_of_int @ SV1136 ) @ zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4772]) ).
thf(5263,plain,
! [SV1358: nat,SV446: nat] :
( ( ! [SY2558: nat] :
( ~ ( ord_less_nat @ one_one_nat @ SY2558 )
| ~ ( ord_less_nat @ ( power_power_nat @ SY2558 @ SV446 ) @ ( power_power_nat @ SY2558 @ SV1358 ) )
| ( ord_less_nat @ SV446 @ SV1358 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4773]) ).
thf(5264,plain,
! [SV1359: nat,SV446: nat] :
( ( ! [SY2559: nat] :
( ~ ( ord_less_nat @ one_one_nat @ SY2559 )
| ~ ( ord_less_nat @ SV446 @ SV1359 )
| ( ord_less_nat @ ( power_power_nat @ SY2559 @ SV446 ) @ ( power_power_nat @ SY2559 @ SV1359 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4774]) ).
thf(5265,plain,
! [SV1360: nat,SV1137: nat] :
( ( ( SV1137 != one_one_nat )
| ( SV1360 != one_one_nat )
| ( ( times_times_nat @ SV1137 @ SV1360 )
= one_one_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4775]) ).
thf(5266,plain,
( ( ~ ! [SX0: nat] :
( ! [SX1: nat] :
( ( times_times_nat @ SX0 @ SX1 )
!= one_one_nat )
| ( SX0 = one_one_nat ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4776]) ).
thf(5267,plain,
( ( ~ ! [SX0: nat,SX1: nat] :
( ( ( times_times_nat @ SX0 @ SX1 )
!= one_one_nat )
| ( SX1 = one_one_nat ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4776]) ).
thf(5268,plain,
( ( ~ ~ ( ~ ! [SX0: int] :
( ! [SX1: int] :
( ( times_times_int @ SX0 @ SX1 )
!= one_one_int )
| ( SX0 = one_one_int )
| ( SX0
= ( number_number_of_int @ min ) ) )
| ~ ! [SX0: int,SX1: int] :
( ( ( times_times_int @ SX0 @ SX1 )
!= one_one_int )
| ( SX0 = one_one_int )
| ( SX1
= ( number_number_of_int @ min ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4777]) ).
thf(5269,plain,
( ( ~ ~ ( ~ ! [SX0: int,SX1: int] :
( ( ( times_times_int @ SX0 @ SX1 )
!= one_one_int )
| ( SX1 = one_one_int )
| ( SX0
= ( number_number_of_int @ min ) ) )
| ~ ! [SX0: int,SX1: int] :
( ( ( times_times_int @ SX0 @ SX1 )
!= one_one_int )
| ( SX1 = one_one_int )
| ( SX1
= ( number_number_of_int @ min ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4777]) ).
thf(5270,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ( SX0 != one_one_int )
| ( SX1 != one_one_int )
| ( ( times_times_int @ SX0 @ SX1 )
= one_one_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4778]) ).
thf(5271,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ( SX0
!= ( number_number_of_int @ min ) )
| ( SX1
!= ( number_number_of_int @ min ) )
| ( ( times_times_int @ SX0 @ SX1 )
= one_one_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4778]) ).
thf(5272,plain,
! [SV1138: int] :
( ( ( ~ ( ord_less_int @ SV1138 @ ( bit1 @ pls ) ) )
= $true )
| ( ( ord_less_real @ ( number267125858f_real @ SV1138 ) @ one_one_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4779]) ).
thf(5273,plain,
! [SV1139: int] :
( ( ( ~ ( ord_less_real @ ( number267125858f_real @ SV1139 ) @ one_one_real ) )
= $true )
| ( ( ord_less_int @ SV1139 @ ( bit1 @ pls ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4780]) ).
thf(5274,plain,
! [SV1361: int,SV1140: int] :
( ( ( ( number_number_of_int @ SV1140 )
!= SV1361 )
| ( SV1361
= ( number_number_of_int @ SV1140 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4781]) ).
thf(5275,plain,
! [SV1141: int,SV1362: int] :
( ( ( SV1362
!= ( number_number_of_int @ SV1141 ) )
| ( ( number_number_of_int @ SV1141 )
= SV1362 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4782]) ).
thf(5276,plain,
! [SV1363: int,SV1142: int] :
( ( ~ ( ord_less_eq_int @ SV1142 @ SV1363 )
| ( ord_less_int @ SV1142 @ ( plus_plus_int @ SV1363 @ one_one_int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4783]) ).
thf(5277,plain,
! [SV1364: int,SV1143: int] :
( ( ~ ( ord_less_int @ SV1143 @ ( plus_plus_int @ SV1364 @ one_one_int ) )
| ( ord_less_eq_int @ SV1143 @ SV1364 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4784]) ).
thf(5278,plain,
! [SV1365: real,SV1144: real] :
( ( ( SV1144 != zero_zero_real )
| ( SV1365 != zero_zero_real )
| ( ( plus_plus_real @ ( times_times_real @ SV1144 @ SV1144 ) @ ( times_times_real @ SV1365 @ SV1365 ) )
= zero_zero_real ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4785]) ).
thf(5279,plain,
( ( ~ ! [SX0: real] :
( ! [SX1: real] :
( ( plus_plus_real @ ( times_times_real @ SX0 @ SX0 ) @ ( times_times_real @ SX1 @ SX1 ) )
!= zero_zero_real )
| ( SX0 = zero_zero_real ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4786]) ).
thf(5280,plain,
( ( ~ ! [SX0: real,SX1: real] :
( ( ( plus_plus_real @ ( times_times_real @ SX0 @ SX0 ) @ ( times_times_real @ SX1 @ SX1 ) )
!= zero_zero_real )
| ( SX1 = zero_zero_real ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4786]) ).
thf(5281,plain,
! [SV1145: int] :
( ( ( ~ ( ord_less_eq_int @ ( bit1 @ SV1145 ) @ pls ) )
= $true )
| ( ( ord_less_int @ SV1145 @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4787]) ).
thf(5282,plain,
! [SV1146: int] :
( ( ( ~ ( ord_less_int @ SV1146 @ pls ) )
= $true )
| ( ( ord_less_eq_int @ ( bit1 @ SV1146 ) @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4788]) ).
thf(5283,plain,
! [SV1366: nat,SV447: nat] :
( ( ! [SY2560: real] :
( ~ ( ord_less_real @ one_one_real @ SY2560 )
| ~ ( ord_less_nat @ SV447 @ SV1366 )
| ( ord_less_real @ ( power_power_real @ SY2560 @ SV447 ) @ ( power_power_real @ SY2560 @ SV1366 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4789]) ).
thf(5284,plain,
! [SV1367: nat,SV447: nat] :
( ( ! [SY2561: real] :
( ~ ( ord_less_real @ one_one_real @ SY2561 )
| ~ ( ord_less_real @ ( power_power_real @ SY2561 @ SV447 ) @ ( power_power_real @ SY2561 @ SV1367 ) )
| ( ord_less_nat @ SV447 @ SV1367 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4790]) ).
thf(5285,plain,
! [SV1147: int] :
( ( ( ( bit0 @ SV1147 )
!= pls )
= $true )
| ( ( SV1147 = pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4791]) ).
thf(5286,plain,
! [SV1148: int] :
( ( ( SV1148 != pls )
= $true )
| ( ( ( bit0 @ SV1148 )
= pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4792]) ).
thf(5287,plain,
! [SV1368: int,SV1149: int] :
( ( ~ ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ SV1149 @ SV1149 ) @ ( times_times_int @ SV1368 @ SV1368 ) ) )
| ( SV1149 != zero_zero_int )
| ( SV1368 != zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4793]) ).
thf(5288,plain,
( ( ~ ! [SX0: int] :
( ( SX0 = zero_zero_int )
| ! [SX1: int] : ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ SX0 @ SX0 ) @ ( times_times_int @ SX1 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4794]) ).
thf(5289,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ( SX1 = zero_zero_int )
| ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ SX0 @ SX0 ) @ ( times_times_int @ SX1 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4794]) ).
thf(5290,plain,
! [SV1369: nat,SV1150: int] :
( ( ( ( number_number_of_nat @ SV1150 )
!= SV1369 )
| ( SV1369
= ( number_number_of_nat @ SV1150 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4795]) ).
thf(5291,plain,
! [SV1151: int,SV1370: nat] :
( ( ( SV1370
!= ( number_number_of_nat @ SV1151 ) )
| ( ( number_number_of_nat @ SV1151 )
= SV1370 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4796]) ).
thf(5292,plain,
! [SV1152: real] :
( ( ( SV1152 != zero_zero_real )
= $true )
| ( ( ~ ( ord_less_real @ zero_zero_real @ ( times_times_real @ SV1152 @ SV1152 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4797]) ).
thf(5293,plain,
! [SV1153: real] :
( ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ SV1153 @ SV1153 ) )
= $true )
| ( ( SV1153 = zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4798]) ).
thf(5294,plain,
! [SV1154: int] :
( ( ( ~ ( ord_less_int @ ( number_number_of_int @ SV1154 ) @ one_one_int ) )
= $true )
| ( ( ord_less_int @ SV1154 @ ( bit1 @ pls ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4799]) ).
thf(5295,plain,
! [SV1155: int] :
( ( ( ~ ( ord_less_int @ SV1155 @ ( bit1 @ pls ) ) )
= $true )
| ( ( ord_less_int @ ( number_number_of_int @ SV1155 ) @ one_one_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4800]) ).
thf(5296,plain,
! [SV1371: real,SV448: real] :
( ( ! [SY2562: real] :
( ( SY2562 = zero_zero_real )
| ( ( times_times_real @ SY2562 @ SV448 )
!= ( times_times_real @ SY2562 @ SV1371 ) )
| ( SV448 = SV1371 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4801]) ).
thf(5297,plain,
! [SV1372: real,SV448: real] :
( ( ! [SY2563: real] :
( ( SY2563 = zero_zero_real )
| ( SV448 != SV1372 )
| ( ( times_times_real @ SY2563 @ SV448 )
= ( times_times_real @ SY2563 @ SV1372 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4802]) ).
thf(5298,plain,
! [SV1373: int,SV1156: int] :
( ( ~ ( ord_less_eq_int @ ( bit0 @ SV1156 ) @ ( bit1 @ SV1373 ) )
| ( ord_less_eq_int @ SV1156 @ SV1373 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4803]) ).
thf(5299,plain,
! [SV1374: int,SV1157: int] :
( ( ~ ( ord_less_eq_int @ SV1157 @ SV1374 )
| ( ord_less_eq_int @ ( bit0 @ SV1157 ) @ ( bit1 @ SV1374 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4804]) ).
thf(5300,plain,
! [SV1158: int] :
( ( ( pls
!= ( bit0 @ SV1158 ) )
= $true )
| ( ( pls = SV1158 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4805]) ).
thf(5301,plain,
! [SV1159: int] :
( ( ( pls != SV1159 )
= $true )
| ( ( pls
= ( bit0 @ SV1159 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4806]) ).
thf(5302,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ( ord_less_int @ SX0 @ SX1 )
| ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_nat @ ( number_number_of_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4807]) ).
thf(5303,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ pls @ SX1 )
| ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_nat @ ( number_number_of_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4807]) ).
thf(5304,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_nat @ ( number_number_of_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) )
| ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ pls @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4808]) ).
thf(5305,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_nat @ ( number_number_of_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4808]) ).
thf(5306,plain,
! [SV1375: int,SV1160: int] :
( ( ~ ( ord_less_int @ ( bit0 @ SV1160 ) @ ( bit0 @ SV1375 ) )
| ( ord_less_int @ SV1160 @ SV1375 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4809]) ).
thf(5307,plain,
! [SV1376: int,SV1161: int] :
( ( ~ ( ord_less_int @ SV1161 @ SV1376 )
| ( ord_less_int @ ( bit0 @ SV1161 ) @ ( bit0 @ SV1376 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4810]) ).
thf(5308,plain,
! [SV787: int,SV449: int,SV981: int] :
( ( ~ ! [SY2385: int,SY2386: int] :
( ~ ( zcong @ SV981 @ SY2385 @ SY2386 )
| ~ ( zcong @ SV449 @ ( times_times_int @ SV981 @ SV787 ) @ SY2386 )
| ( zcong @ SV449 @ ( times_times_int @ SY2385 @ SV787 ) @ SY2386 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4811]) ).
thf(5309,plain,
! [SV787: int,SV449: int,SV981: int] :
( ( ~ ! [SY2387: int,SY2388: int] :
( ~ ( zcong @ SV981 @ SY2387 @ SY2388 )
| ~ ( zcong @ SV449 @ ( times_times_int @ SY2387 @ SV787 ) @ SY2388 )
| ( zcong @ SV449 @ ( times_times_int @ SV981 @ SV787 ) @ SY2388 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4811]) ).
thf(5310,plain,
! [SV1162: real,SV1377: nat] :
( ( ( SV1377 != zero_zero_nat )
| ( ( power_power_real @ SV1162 @ SV1377 )
= one_one_real ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4812]) ).
thf(5311,plain,
! [SV1163: real,SV1378: nat] :
( ( ( SV1378 = zero_zero_nat )
| ( ( power_power_real @ SV1163 @ SV1378 )
= ( times_times_real @ SV1163 @ ( power_power_real @ SV1163 @ ( minus_minus_nat @ SV1378 @ one_one_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4813]) ).
thf(5312,plain,
! [SV788: int,SV450: int] :
( ( ~ ( ~ ! [SY2290: int,SY2291: int] :
( ( ( plus_plus_int @ ( times_times_int @ SY2290 @ SV450 ) @ ( times_times_int @ SY2291 @ SV788 ) )
= ( plus_plus_int @ ( times_times_int @ SY2290 @ SV788 ) @ ( times_times_int @ SY2291 @ SV450 ) ) )
| ( SY2290 != SY2291 ) )
| ~ ( ! [SY2292: int,SY2293: int] :
( ( plus_plus_int @ ( times_times_int @ SY2292 @ SV450 ) @ ( times_times_int @ SY2293 @ SV788 ) )
= ( plus_plus_int @ ( times_times_int @ SY2292 @ SV788 ) @ ( times_times_int @ SY2293 @ SV450 ) ) )
| ( SV450 != SV788 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4814]) ).
thf(5313,plain,
! [SV788: int,SV450: int] :
( ( ! [SY2294: int,SY2295: int] :
( ( SY2294 = SY2295 )
| ( SV450 = SV788 )
| ( ( plus_plus_int @ ( times_times_int @ SY2294 @ SV450 ) @ ( times_times_int @ SY2295 @ SV788 ) )
!= ( plus_plus_int @ ( times_times_int @ SY2294 @ SV788 ) @ ( times_times_int @ SY2295 @ SV450 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4815]) ).
thf(5314,plain,
! [SV1379: int,SV1164: int] :
( ( ~ ( ord_less_eq_int @ SV1164 @ SV1379 )
| ( ord_less_int @ ( bit0 @ SV1164 ) @ ( bit1 @ SV1379 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4816]) ).
thf(5315,plain,
! [SV1380: int,SV1165: int] :
( ( ~ ( ord_less_int @ ( bit0 @ SV1165 ) @ ( bit1 @ SV1380 ) )
| ( ord_less_eq_int @ SV1165 @ SV1380 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4817]) ).
thf(5316,plain,
! [SV1166: int] :
( ( ( SV1166 = zero_zero_int )
= $true )
| ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ SV1166 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4818]) ).
thf(5317,plain,
! [SV1167: int] :
( ( ( ~ ( ord_less_int @ zero_zero_int @ ( power_power_int @ SV1167 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true )
| ( ( SV1167 != zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4819]) ).
thf(5318,plain,
! [SV1168: int] :
( ( ( ~ ( ord_less_int @ SV1168 @ pls ) )
= $true )
| ( ( ord_less_real @ ( number267125858f_real @ SV1168 ) @ zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4820]) ).
thf(5319,plain,
! [SV1169: int] :
( ( ( ~ ( ord_less_real @ ( number267125858f_real @ SV1169 ) @ zero_zero_real ) )
= $true )
| ( ( ord_less_int @ SV1169 @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4821]) ).
thf(5320,plain,
! [SV1381: real,SV1170: real] :
( ( ( SV1170 != zero_zero_real )
| ( SV1381 != zero_zero_real )
| ( ( plus_plus_real @ ( times_times_real @ SV1170 @ SV1170 ) @ ( times_times_real @ SV1381 @ SV1381 ) )
= zero_zero_real ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4822]) ).
thf(5321,plain,
( ( ~ ! [SX0: real] :
( ! [SX1: real] :
( ( plus_plus_real @ ( times_times_real @ SX0 @ SX0 ) @ ( times_times_real @ SX1 @ SX1 ) )
!= zero_zero_real )
| ( SX0 = zero_zero_real ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4823]) ).
thf(5322,plain,
( ( ~ ! [SX0: real,SX1: real] :
( ( ( plus_plus_real @ ( times_times_real @ SX0 @ SX0 ) @ ( times_times_real @ SX1 @ SX1 ) )
!= zero_zero_real )
| ( SX1 = zero_zero_real ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4823]) ).
thf(5323,plain,
! [SV1171: int] :
( ( ( ~ ( ord_less_eq_int @ ( bit1 @ pls ) @ SV1171 ) )
= $true )
| ( ( ord_less_eq_real @ one_one_real @ ( number267125858f_real @ SV1171 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4824]) ).
thf(5324,plain,
! [SV1172: int] :
( ( ( ~ ( ord_less_eq_real @ one_one_real @ ( number267125858f_real @ SV1172 ) ) )
= $true )
| ( ( ord_less_eq_int @ ( bit1 @ pls ) @ SV1172 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4825]) ).
thf(5325,plain,
! [SV789: int,SV451: int,SV982: int] :
( ( ~ ! [SY2389: int,SY2390: int] :
( ~ ( zcong @ SV982 @ SY2389 @ SY2390 )
| ~ ( zcong @ SV451 @ ( times_times_int @ SV789 @ SV982 ) @ SY2390 )
| ( zcong @ SV451 @ ( times_times_int @ SV789 @ SY2389 ) @ SY2390 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4826]) ).
thf(5326,plain,
! [SV789: int,SV451: int,SV982: int] :
( ( ~ ! [SY2391: int,SY2392: int] :
( ~ ( zcong @ SV982 @ SY2391 @ SY2392 )
| ~ ( zcong @ SV451 @ ( times_times_int @ SV789 @ SY2391 ) @ SY2392 )
| ( zcong @ SV451 @ ( times_times_int @ SV789 @ SV982 ) @ SY2392 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4826]) ).
thf(5327,plain,
! [SV1173: int] :
( ( ( ~ ( ord_less_eq_int @ ( bit1 @ SV1173 ) @ min ) )
= $true )
| ( ( ord_less_eq_int @ SV1173 @ min )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4827]) ).
thf(5328,plain,
! [SV1174: int] :
( ( ( ~ ( ord_less_eq_int @ SV1174 @ min ) )
= $true )
| ( ( ord_less_eq_int @ ( bit1 @ SV1174 ) @ min )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4828]) ).
thf(5329,plain,
! [SV1382: int,SV1175: int] :
( ( ~ ( ord_less_eq_int @ ( bit1 @ SV1175 ) @ ( bit1 @ SV1382 ) )
| ( ord_less_eq_int @ SV1175 @ SV1382 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4829]) ).
thf(5330,plain,
! [SV1383: int,SV1176: int] :
( ( ~ ( ord_less_eq_int @ SV1176 @ SV1383 )
| ( ord_less_eq_int @ ( bit1 @ SV1176 ) @ ( bit1 @ SV1383 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4830]) ).
thf(5331,plain,
! [SV1384: int,SV1177: int] :
( ( ( SV1177 != SV1384 )
| ( zcong @ SV1177 @ SV1384 @ zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4831]) ).
thf(5332,plain,
! [SV1385: int,SV1178: int] :
( ( ~ ( zcong @ SV1178 @ SV1385 @ zero_zero_int )
| ( SV1178 = SV1385 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4832]) ).
thf(5333,plain,
! [SV1386: int,SV1179: int] :
( ( ~ ( ord_less_eq_int @ ( bit1 @ SV1179 ) @ ( bit0 @ SV1386 ) )
| ( ord_less_int @ SV1179 @ SV1386 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4833]) ).
thf(5334,plain,
! [SV1387: int,SV1180: int] :
( ( ~ ( ord_less_int @ SV1180 @ SV1387 )
| ( ord_less_eq_int @ ( bit1 @ SV1180 ) @ ( bit0 @ SV1387 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4834]) ).
thf(5335,plain,
! [SV790: nat,SV452: nat] :
( ( ! [SY2301: nat,SY2302: nat] :
( ( ( plus_plus_nat @ ( times_times_nat @ SV452 @ SV790 ) @ ( times_times_nat @ SY2301 @ SY2302 ) )
!= ( plus_plus_nat @ ( times_times_nat @ SV452 @ SY2302 ) @ ( times_times_nat @ SY2301 @ SV790 ) ) )
| ( SV452 = SY2301 )
| ( SV790 = SY2302 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4835]) ).
thf(5336,plain,
! [SV790: nat,SV452: nat] :
( ( ~ ( ~ ! [SY2303: nat] :
( ( SV452 != SY2303 )
| ! [SY2304: nat] :
( ( plus_plus_nat @ ( times_times_nat @ SV452 @ SV790 ) @ ( times_times_nat @ SY2303 @ SY2304 ) )
= ( plus_plus_nat @ ( times_times_nat @ SV452 @ SY2304 ) @ ( times_times_nat @ SY2303 @ SV790 ) ) ) )
| ~ ! [SY2305: nat,SY2306: nat] :
( ( SV790 != SY2306 )
| ( ( plus_plus_nat @ ( times_times_nat @ SV452 @ SV790 ) @ ( times_times_nat @ SY2305 @ SY2306 ) )
= ( plus_plus_nat @ ( times_times_nat @ SV452 @ SY2306 ) @ ( times_times_nat @ SY2305 @ SV790 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4836]) ).
thf(5337,plain,
! [SV1181: real,SV1388: nat] :
( ( ( SV1388 = zero_zero_nat )
| ( SV1181 != zero_zero_real )
| ( ( power_power_real @ SV1181 @ SV1388 )
= zero_zero_real ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4837]) ).
thf(5338,plain,
( ( ~ ! [SX0: real,SX1: nat] :
( ( ( power_power_real @ SX0 @ SX1 )
!= zero_zero_real )
| ( SX1 != zero_zero_nat ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4838]) ).
thf(5339,plain,
( ( ~ ! [SX0: real] :
( ! [SX1: nat] :
( ( power_power_real @ SX0 @ SX1 )
!= zero_zero_real )
| ( SX0 = zero_zero_real ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4838]) ).
thf(5340,plain,
! [SV1389: nat,SV1182: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV1182 @ SV1389 ) )
| ( SV1389 = zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV1182 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4839]) ).
thf(5341,plain,
( ( ~ ! [SX0: nat,SX1: nat] :
( ( SX1 != zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4840]) ).
thf(5342,plain,
( ( ~ ! [SX0: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SX0 )
| ! [SX1: nat] : ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4840]) ).
thf(5343,plain,
! [SV791: int,SV453: int] :
( ( ! [SY2307: int,SY2308: int] :
( ( ( plus_plus_int @ ( times_times_int @ SV453 @ SV791 ) @ ( times_times_int @ SY2307 @ SY2308 ) )
!= ( plus_plus_int @ ( times_times_int @ SV453 @ SY2308 ) @ ( times_times_int @ SY2307 @ SV791 ) ) )
| ( SV453 = SY2307 )
| ( SV791 = SY2308 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4841]) ).
thf(5344,plain,
! [SV791: int,SV453: int] :
( ( ~ ( ~ ! [SY2309: int] :
( ( SV453 != SY2309 )
| ! [SY2310: int] :
( ( plus_plus_int @ ( times_times_int @ SV453 @ SV791 ) @ ( times_times_int @ SY2309 @ SY2310 ) )
= ( plus_plus_int @ ( times_times_int @ SV453 @ SY2310 ) @ ( times_times_int @ SY2309 @ SV791 ) ) ) )
| ~ ! [SY2311: int,SY2312: int] :
( ( SV791 != SY2312 )
| ( ( plus_plus_int @ ( times_times_int @ SV453 @ SV791 ) @ ( times_times_int @ SY2311 @ SY2312 ) )
= ( plus_plus_int @ ( times_times_int @ SV453 @ SY2312 ) @ ( times_times_int @ SY2311 @ SV791 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4842]) ).
thf(5345,plain,
! [SV1183: nat,SV1390: nat] :
( ( ( SV1390 != zero_zero_nat )
| ( ( power_power_nat @ SV1183 @ SV1390 )
= one_one_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4843]) ).
thf(5346,plain,
! [SV1184: nat,SV1391: nat] :
( ( ( SV1391 = zero_zero_nat )
| ( ( power_power_nat @ SV1184 @ SV1391 )
= ( times_times_nat @ SV1184 @ ( power_power_nat @ SV1184 @ ( minus_minus_nat @ SV1391 @ one_one_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4844]) ).
thf(5347,plain,
! [SV1185: int,SV1392: int] :
( ( ~ ( ord_less_int @ zero_zero_int @ SV1392 )
| ( SV1392 != one_one_int )
| ( SV1185 != one_one_int )
| ( ( times_times_int @ SV1392 @ SV1185 )
= one_one_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4845]) ).
thf(5348,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ zero_zero_int @ SX1 )
| ( ( times_times_int @ SX1 @ SX0 )
!= one_one_int )
| ( SX1 = one_one_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4846]) ).
thf(5349,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ zero_zero_int @ SX1 )
| ( ( times_times_int @ SX1 @ SX0 )
!= one_one_int )
| ( SX0 = one_one_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4846]) ).
thf(5350,plain,
! [SV1393: int,SV1186: int] :
( ( ~ ( ord_less_eq_int @ ( plus_plus_int @ SV1186 @ one_one_int ) @ SV1393 )
| ( ord_less_int @ SV1186 @ SV1393 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4847]) ).
thf(5351,plain,
! [SV1394: int,SV1187: int] :
( ( ~ ( ord_less_int @ SV1187 @ SV1394 )
| ( ord_less_eq_int @ ( plus_plus_int @ SV1187 @ one_one_int ) @ SV1394 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4848]) ).
thf(5352,plain,
! [SV1188: int] :
( ( ( ( number_number_of_nat @ SV1188 )
!= zero_zero_nat )
= $true )
| ( ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ SV1188 ) )
= one_one_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4849]) ).
thf(5353,plain,
! [SV1189: int] :
( ( ( ( number_number_of_nat @ SV1189 )
= zero_zero_nat )
= $true )
| ( ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ SV1189 ) )
= zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4850]) ).
thf(5354,plain,
! [SV1395: real,SV1190: real] :
( ( ( SV1190 = SV1395 )
| ~ ( ord_less_eq_real @ SV1190 @ SV1395 )
| ( ord_less_real @ SV1190 @ SV1395 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4851]) ).
thf(5355,plain,
( ( ~ ! [SX0: real,SX1: real] :
( ~ ( ord_less_real @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4852]) ).
thf(5356,plain,
( ( ~ ! [SX0: real,SX1: real] :
( ~ ( ord_less_real @ SX0 @ SX1 )
| ( ord_less_eq_real @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4852]) ).
thf(5357,plain,
! [SV1396: int,SV1191: int] :
( ( ~ ( ord_less_int @ SV1191 @ SV1396 )
| ( ord_less_real @ ( number267125858f_real @ SV1191 ) @ ( number267125858f_real @ SV1396 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4853]) ).
thf(5358,plain,
! [SV1397: int,SV1192: int] :
( ( ~ ( ord_less_real @ ( number267125858f_real @ SV1192 ) @ ( number267125858f_real @ SV1397 ) )
| ( ord_less_int @ SV1192 @ SV1397 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4854]) ).
thf(5359,plain,
! [SV1398: int,SV1193: int] :
( ( ~ ( ord_less_eq_int @ ( number_number_of_int @ SV1193 ) @ ( number_number_of_int @ SV1398 ) )
| ~ ( ord_less_int @ ( number_number_of_int @ SV1398 ) @ ( number_number_of_int @ SV1193 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4855]) ).
thf(5360,plain,
! [SV1194: int,SV1399: int] :
( ( ( ord_less_int @ ( number_number_of_int @ SV1399 ) @ ( number_number_of_int @ SV1194 ) )
| ( ord_less_eq_int @ ( number_number_of_int @ SV1194 ) @ ( number_number_of_int @ SV1399 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4856]) ).
thf(5361,plain,
! [SV1195: int] :
( ( ( ( plus_plus_int @ SV1195 @ SV1195 )
!= zero_zero_int )
= $true )
| ( ( SV1195 = zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4857]) ).
thf(5362,plain,
! [SV1196: int] :
( ( ( SV1196 != zero_zero_int )
= $true )
| ( ( ( plus_plus_int @ SV1196 @ SV1196 )
= zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4858]) ).
thf(5363,plain,
! [SV1400: int,SV1197: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV1197 @ ( number_number_of_nat @ SV1400 ) ) )
| ( ( number_number_of_nat @ SV1400 )
= zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV1197 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4859]) ).
thf(5364,plain,
( ( ~ ! [SX0: nat,SX1: int] :
( ( ( number_number_of_nat @ SX1 )
!= zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SX0 @ ( number_number_of_nat @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4860]) ).
thf(5365,plain,
( ( ~ ! [SX0: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SX0 )
| ! [SX1: int] : ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SX0 @ ( number_number_of_nat @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4860]) ).
thf(5366,plain,
! [SV1198: int] :
( ( ( ~ ( ord_less_eq_int @ SV1198 @ ( bit1 @ pls ) ) )
= $true )
| ( ( ord_less_eq_real @ ( number267125858f_real @ SV1198 ) @ one_one_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4861]) ).
thf(5367,plain,
! [SV1199: int] :
( ( ( ~ ( ord_less_eq_real @ ( number267125858f_real @ SV1199 ) @ one_one_real ) )
= $true )
| ( ( ord_less_eq_int @ SV1199 @ ( bit1 @ pls ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4862]) ).
thf(5368,plain,
! [SV1200: int,SV1401: int] :
( ( ~ ( ord_less_int @ SV1401 @ pls )
| ( ( times_times_nat @ ( number_number_of_nat @ SV1401 ) @ ( number_number_of_nat @ SV1200 ) )
= zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4863]) ).
thf(5369,plain,
! [SV1201: int,SV1402: int] :
( ( ( ord_less_int @ SV1402 @ pls )
| ( ( times_times_nat @ ( number_number_of_nat @ SV1402 ) @ ( number_number_of_nat @ SV1201 ) )
= ( number_number_of_nat @ ( times_times_int @ SV1402 @ SV1201 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4864]) ).
thf(5370,plain,
! [SV1202: real] :
( ( ( SV1202 = zero_zero_real )
= $true )
| ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ SV1202 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4865]) ).
thf(5371,plain,
! [SV1203: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ ( power_power_real @ SV1203 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true )
| ( ( SV1203 != zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4866]) ).
thf(5372,plain,
! [SV1204: int] :
( ( ( ~ ( ~ ~ ( ~ ( dvd_dvd_int @ ( sK3_M_9 @ SV1204 ) @ SV1204 )
| ~ ( ord_less_eq_int @ zero_zero_int @ ( sK3_M_9 @ SV1204 ) ) )
| ~ ~ ( ~ ( ( ( sK3_M_9 @ SV1204 )
!= one_one_int ) )
| ~ ( ( ( sK3_M_9 @ SV1204 )
!= SV1204 ) ) ) )
| ~ ( ord_less_int @ one_one_int @ SV1204 ) )
= $true )
| ( ( zprime @ SV1204 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4867]) ).
thf(5373,plain,
( ( ~ ! [SX0: int] :
( ~ ( zprime @ SX0 )
| ! [SX1: int] :
( ~ ( dvd_dvd_int @ SX1 @ SX0 )
| ~ ( ord_less_eq_int @ zero_zero_int @ SX1 )
| ( SX1 = one_one_int )
| ( SX1 = SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4868]) ).
thf(5374,plain,
( ( ~ ! [SX0: int] :
( ~ ( zprime @ SX0 )
| ( ord_less_int @ one_one_int @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4868]) ).
thf(5375,plain,
! [SV1403: nat,SV454: int] :
( ( ! [SY2564: int] :
( ~ ( ord_less_int @ SY2564 @ pls )
| ( ( times_times_nat @ ( number_number_of_nat @ SY2564 ) @ ( times_times_nat @ ( number_number_of_nat @ SV454 ) @ SV1403 ) )
= zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4869]) ).
thf(5376,plain,
! [SV1404: nat,SV454: int] :
( ( ! [SY2565: int] :
( ( ord_less_int @ SY2565 @ pls )
| ( ( times_times_nat @ ( number_number_of_nat @ SY2565 ) @ ( times_times_nat @ ( number_number_of_nat @ SV454 ) @ SV1404 ) )
= ( times_times_nat @ ( number_number_of_nat @ ( times_times_int @ SY2565 @ SV454 ) ) @ SV1404 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4870]) ).
thf(5377,plain,
! [SV1405: int,SV1205: int] :
( ( ~ ( zcong @ SV1205 @ zero_zero_int @ SV1405 )
| ( ( legendre @ SV1205 @ SV1405 )
= zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4871]) ).
thf(5378,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ( zcong @ SX0 @ zero_zero_int @ SX1 )
| ~ ( quadRes @ SX1 @ SX0 )
| ( ( legendre @ SX0 @ SX1 )
= one_one_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4872]) ).
thf(5379,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ( zcong @ SX0 @ zero_zero_int @ SX1 )
| ( quadRes @ SX1 @ SX0 )
| ( ( legendre @ SX0 @ SX1 )
= ( number_number_of_int @ min ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4872]) ).
thf(5380,plain,
! [SV1206: nat] :
( ( ( SV1206 != zero_zero_nat )
= $true )
| ( ( ( power_power_int @ zero_zero_int @ SV1206 )
= one_one_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4873]) ).
thf(5381,plain,
! [SV1207: nat] :
( ( ( SV1207 = zero_zero_nat )
= $true )
| ( ( ( power_power_int @ zero_zero_int @ SV1207 )
= zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4874]) ).
thf(5382,plain,
! [SV792: nat,SV455: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV455 ) )
= $true )
| ( ( ~ ( ~ ! [SY2313: real] :
( ( ( power_power_real @ SY2313 @ SV792 )
!= SV455 )
| ~ ( ord_less_real @ zero_zero_real @ SY2313 )
| ( SY2313
= ( sK1_X_1 @ SV792 @ SV455 ) ) )
| ~ ~ ( ( ( power_power_real @ ( sK1_X_1 @ SV792 @ SV455 ) @ SV792 )
!= SV455 )
| ~ ( ord_less_real @ zero_zero_real @ ( sK1_X_1 @ SV792 @ SV455 ) ) ) ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV792 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4875]) ).
thf(5383,plain,
! [SV1208: int] :
( ( ( zero_zero_nat
!= ( number_number_of_nat @ SV1208 ) )
= $true )
| ( ( ord_less_eq_int @ SV1208 @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4876]) ).
thf(5384,plain,
! [SV1209: int] :
( ( ( ~ ( ord_less_eq_int @ SV1209 @ pls ) )
= $true )
| ( ( zero_zero_nat
= ( number_number_of_nat @ SV1209 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4877]) ).
thf(5385,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_eq_nat @ ( number_number_of_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4878]) ).
thf(5386,plain,
( ( ~ ! [SX0: int] :
( ~ ( ord_less_eq_int @ SX0 @ pls )
| ! [SX1: int] : ( ord_less_eq_nat @ ( number_number_of_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4878]) ).
thf(5387,plain,
! [SV1406: int,SV1210: int] :
( ( ~ ( ord_less_eq_nat @ ( number_number_of_nat @ SV1210 ) @ ( number_number_of_nat @ SV1406 ) )
| ( ord_less_eq_int @ SV1210 @ SV1406 )
| ( ord_less_eq_int @ SV1210 @ pls ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4879]) ).
thf(5388,plain,
! [SV1211: int] :
( ( ( ~ ( ord_less_int @ ( number_number_of_int @ SV1211 ) @ zero_zero_int ) )
= $true )
| ( ( ord_less_int @ SV1211 @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4880]) ).
thf(5389,plain,
! [SV1212: int] :
( ( ( ~ ( ord_less_int @ SV1212 @ pls ) )
= $true )
| ( ( ord_less_int @ ( number_number_of_int @ SV1212 ) @ zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4881]) ).
thf(5390,plain,
! [SV1213: int] :
( ( ( ~ ( ord_less_eq_int @ one_one_int @ ( number_number_of_int @ SV1213 ) ) )
= $true )
| ( ( ord_less_eq_int @ ( bit1 @ pls ) @ SV1213 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4882]) ).
thf(5391,plain,
! [SV1214: int] :
( ( ( ~ ( ord_less_eq_int @ ( bit1 @ pls ) @ SV1214 ) )
= $true )
| ( ( ord_less_eq_int @ one_one_int @ ( number_number_of_int @ SV1214 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4883]) ).
thf(5392,plain,
! [SV1407: real,SV1215: int] :
( ( ( ( number267125858f_real @ SV1215 )
!= SV1407 )
| ( SV1407
= ( number267125858f_real @ SV1215 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4884]) ).
thf(5393,plain,
! [SV1216: int,SV1408: real] :
( ( ( SV1408
!= ( number267125858f_real @ SV1216 ) )
| ( ( number267125858f_real @ SV1216 )
= SV1408 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4885]) ).
thf(5394,plain,
! [SV1217: int] :
( ( ( ~ ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ SV1217 ) @ SV1217 ) @ zero_zero_int ) )
= $true )
| ( ( ord_less_int @ SV1217 @ zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4886]) ).
thf(5395,plain,
! [SV1218: int] :
( ( ( ~ ( ord_less_int @ SV1218 @ zero_zero_int ) )
= $true )
| ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ SV1218 ) @ SV1218 ) @ zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4887]) ).
thf(5396,plain,
! [SV1409: int,SV456: int] :
( ( ! [SY2566: int] :
( ~ ( zcong @ SV456 @ SV1409 @ SY2566 )
| ( zcong @ SV1409 @ SV456 @ SY2566 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4888]) ).
thf(5397,plain,
! [SV456: int,SV1410: int] :
( ( ! [SY2567: int] :
( ~ ( zcong @ SV1410 @ SV456 @ SY2567 )
| ( zcong @ SV456 @ SV1410 @ SY2567 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4889]) ).
thf(5398,plain,
! [SV457: int,SV983: int,SV793: int] :
( ( ~ ! [SY2393: int,SY2394: int] :
( ~ ( dvd_dvd_int @ SY2393 @ SY2394 )
| ~ ( dvd_dvd_int @ SY2393 @ ( plus_plus_int @ SV793 @ SV983 ) )
| ( dvd_dvd_int @ SY2393 @ ( plus_plus_int @ ( plus_plus_int @ SV793 @ ( times_times_int @ SV457 @ SY2394 ) ) @ SV983 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4890]) ).
thf(5399,plain,
! [SV983: int,SV457: int,SV793: int] :
( ( ~ ! [SY2395: int,SY2396: int] :
( ~ ( dvd_dvd_int @ SY2395 @ SY2396 )
| ~ ( dvd_dvd_int @ SY2395 @ ( plus_plus_int @ ( plus_plus_int @ SV793 @ ( times_times_int @ SV457 @ SY2396 ) ) @ SV983 ) )
| ( dvd_dvd_int @ SY2395 @ ( plus_plus_int @ SV793 @ SV983 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4890]) ).
thf(5400,plain,
! [SV1219: int] :
( ( ( ~ ( ord_less_int @ ( bit1 @ pls ) @ SV1219 ) )
= $true )
| ( ( ord_less_real @ one_one_real @ ( number267125858f_real @ SV1219 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4891]) ).
thf(5401,plain,
! [SV1220: int] :
( ( ( ~ ( ord_less_real @ one_one_real @ ( number267125858f_real @ SV1220 ) ) )
= $true )
| ( ( ord_less_int @ ( bit1 @ pls ) @ SV1220 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4892]) ).
thf(5402,plain,
! [SV1411: real,SV1221: real] :
( ( ( SV1221
!= ( plus_plus_real @ SV1221 @ SV1411 ) )
| ( SV1411 = zero_zero_real ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4893]) ).
thf(5403,plain,
! [SV1222: real,SV1412: real] :
( ( ( SV1412 != zero_zero_real )
| ( SV1222
= ( plus_plus_real @ SV1222 @ SV1412 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4894]) ).
thf(5404,plain,
! [SV458: int,SV1413: int] :
( ( ! [SY2568: int] :
( ! [SY2569: int] :
( SV1413
!= ( plus_plus_int @ SV458 @ ( times_times_int @ SY2568 @ SY2569 ) ) )
| ( zcong @ SV458 @ SV1413 @ SY2568 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4895]) ).
thf(5405,plain,
! [SV1414: int,SV458: int] :
( ( ! [SY2570: int] :
( ~ ( zcong @ SV458 @ SV1414 @ SY2570 )
| ( SV1414
= ( plus_plus_int @ SV458 @ ( times_times_int @ SY2570 @ ( sK6_K_1 @ SY2570 @ SV1414 @ SV458 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4896]) ).
thf(5406,plain,
! [SV1223: int] :
( ( ( ~ ( ord_less_eq_int @ pls @ ( bit0 @ SV1223 ) ) )
= $true )
| ( ( ord_less_eq_int @ pls @ SV1223 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4897]) ).
thf(5407,plain,
! [SV1224: int] :
( ( ( ~ ( ord_less_eq_int @ pls @ SV1224 ) )
= $true )
| ( ( ord_less_eq_int @ pls @ ( bit0 @ SV1224 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4898]) ).
thf(5408,plain,
! [SV1415: nat,SV459: nat] :
( ( ! [SY2571: nat] :
( ~ ( ord_less_nat @ one_one_nat @ SY2571 )
| ( ( power_power_nat @ SY2571 @ SV459 )
!= ( power_power_nat @ SY2571 @ SV1415 ) )
| ( SV459 = SV1415 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4899]) ).
thf(5409,plain,
! [SV1416: nat,SV459: nat] :
( ( ! [SY2572: nat] :
( ~ ( ord_less_nat @ one_one_nat @ SY2572 )
| ( SV459 != SV1416 )
| ( ( power_power_nat @ SY2572 @ SV459 )
= ( power_power_nat @ SY2572 @ SV1416 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4900]) ).
thf(5410,plain,
! [SV794: real,SV460: real] :
( ( ! [SY2319: real,SY2320: real] :
( ( ( plus_plus_real @ ( times_times_real @ SV460 @ SV794 ) @ ( times_times_real @ SY2319 @ SY2320 ) )
!= ( plus_plus_real @ ( times_times_real @ SV460 @ SY2320 ) @ ( times_times_real @ SY2319 @ SV794 ) ) )
| ( SV460 = SY2319 )
| ( SV794 = SY2320 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4901]) ).
thf(5411,plain,
! [SV794: real,SV460: real] :
( ( ~ ( ~ ! [SY2321: real] :
( ( SV460 != SY2321 )
| ! [SY2322: real] :
( ( plus_plus_real @ ( times_times_real @ SV460 @ SV794 ) @ ( times_times_real @ SY2321 @ SY2322 ) )
= ( plus_plus_real @ ( times_times_real @ SV460 @ SY2322 ) @ ( times_times_real @ SY2321 @ SV794 ) ) ) )
| ~ ! [SY2323: real,SY2324: real] :
( ( SV794 != SY2324 )
| ( ( plus_plus_real @ ( times_times_real @ SV460 @ SV794 ) @ ( times_times_real @ SY2323 @ SY2324 ) )
= ( plus_plus_real @ ( times_times_real @ SV460 @ SY2324 ) @ ( times_times_real @ SY2323 @ SV794 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4902]) ).
thf(5412,plain,
! [SV1225: int] :
( ( ( ~ ( ord_less_int @ ( bit1 @ SV1225 ) @ pls ) )
= $true )
| ( ( ord_less_int @ SV1225 @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4903]) ).
thf(5413,plain,
! [SV1226: int] :
( ( ( ~ ( ord_less_int @ SV1226 @ pls ) )
= $true )
| ( ( ord_less_int @ ( bit1 @ SV1226 ) @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4904]) ).
thf(5414,plain,
! [SV1227: int] :
( ( ( ~ ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ SV1227 ) ) )
= $true )
| ( ( ord_less_eq_int @ pls @ SV1227 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4905]) ).
thf(5415,plain,
! [SV1228: int] :
( ( ( ~ ( ord_less_eq_int @ pls @ SV1228 ) )
= $true )
| ( ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ SV1228 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4906]) ).
thf(5416,plain,
! [SV1417: nat,SV461: nat] :
( ( ! [SY2573: nat] :
( ~ ( dvd_dvd_nat @ ( times_times_nat @ SV461 @ SV1417 ) @ ( times_times_nat @ SY2573 @ SV1417 ) )
| ( SV1417 = zero_zero_nat )
| ( dvd_dvd_nat @ SV461 @ SY2573 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4907]) ).
thf(5417,plain,
! [SV461: nat] :
( ( ~ ! [SY2002: nat] :
( ( SY2002 != zero_zero_nat )
| ! [SY2003: nat] : ( dvd_dvd_nat @ ( times_times_nat @ SV461 @ SY2002 ) @ ( times_times_nat @ SY2003 @ SY2002 ) ) )
| ~ ! [SY2004: nat,SY2005: nat] :
( ~ ( dvd_dvd_nat @ SV461 @ SY2005 )
| ( dvd_dvd_nat @ ( times_times_nat @ SV461 @ SY2004 ) @ ( times_times_nat @ SY2005 @ SY2004 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4908]) ).
thf(5418,plain,
! [SV1418: int,SV1229: int] :
( ( ( ( number267125858f_real @ SV1229 )
!= ( number267125858f_real @ SV1418 ) )
| ( SV1229 = SV1418 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4909]) ).
thf(5419,plain,
! [SV1419: int,SV1230: int] :
( ( ( SV1230 != SV1419 )
| ( ( number267125858f_real @ SV1230 )
= ( number267125858f_real @ SV1419 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4910]) ).
thf(5420,plain,
! [SV1231: nat] :
( ( ( SV1231 != zero_zero_nat )
= $true )
| ( ( ( power_power_nat @ zero_zero_nat @ SV1231 )
= one_one_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4911]) ).
thf(5421,plain,
! [SV1232: nat] :
( ( ( SV1232 = zero_zero_nat )
= $true )
| ( ( ( power_power_nat @ zero_zero_nat @ SV1232 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4912]) ).
thf(5422,plain,
! [SV1233: int] :
( ( ( ~ ( ord_less_eq_int @ ( bit0 @ SV1233 ) @ min ) )
= $true )
| ( ( ord_less_eq_int @ SV1233 @ min )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4913]) ).
thf(5423,plain,
! [SV1234: int] :
( ( ( ~ ( ord_less_eq_int @ SV1234 @ min ) )
= $true )
| ( ( ord_less_eq_int @ ( bit0 @ SV1234 ) @ min )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4914]) ).
thf(5424,plain,
! [SV1420: int,SV1235: int] :
( ( ~ ( ord_less_int @ ( bit1 @ SV1235 ) @ ( bit0 @ SV1420 ) )
| ( ord_less_int @ SV1235 @ SV1420 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4915]) ).
thf(5425,plain,
! [SV1421: int,SV1236: int] :
( ( ~ ( ord_less_int @ SV1236 @ SV1421 )
| ( ord_less_int @ ( bit1 @ SV1236 ) @ ( bit0 @ SV1421 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4916]) ).
thf(5426,plain,
! [SV1422: int,SV1237: int] :
( ( ~ ( ord_less_eq_int @ ( bit0 @ SV1237 ) @ ( bit0 @ SV1422 ) )
| ( ord_less_eq_int @ SV1237 @ SV1422 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4917]) ).
thf(5427,plain,
! [SV1423: int,SV1238: int] :
( ( ~ ( ord_less_eq_int @ SV1238 @ SV1423 )
| ( ord_less_eq_int @ ( bit0 @ SV1238 ) @ ( bit0 @ SV1423 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4918]) ).
thf(5428,plain,
! [SV1424: nat,SV1239: nat] :
( ( ( SV1239
!= ( plus_plus_nat @ SV1239 @ SV1424 ) )
| ( SV1424 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4919]) ).
thf(5429,plain,
! [SV1240: nat,SV1425: nat] :
( ( ( SV1425 != zero_zero_nat )
| ( SV1240
= ( plus_plus_nat @ SV1240 @ SV1425 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4920]) ).
thf(5430,plain,
! [SV1426: int,SV1241: int] :
( ( ~ ( ord_less_int @ ( bit1 @ SV1241 ) @ ( bit1 @ SV1426 ) )
| ( ord_less_int @ SV1241 @ SV1426 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4921]) ).
thf(5431,plain,
! [SV1427: int,SV1242: int] :
( ( ~ ( ord_less_int @ SV1242 @ SV1427 )
| ( ord_less_int @ ( bit1 @ SV1242 ) @ ( bit1 @ SV1427 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4922]) ).
thf(5432,plain,
! [SV1243: nat,SV1428: nat] :
( ( ( SV1428 = zero_zero_nat )
| ( SV1243 != zero_zero_nat )
| ( ( power_power_nat @ SV1243 @ SV1428 )
= zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4923]) ).
thf(5433,plain,
( ( ~ ! [SX0: nat,SX1: nat] :
( ( ( power_power_nat @ SX0 @ SX1 )
!= zero_zero_nat )
| ( SX1 != zero_zero_nat ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4924]) ).
thf(5434,plain,
( ( ~ ! [SX0: nat] :
( ! [SX1: nat] :
( ( power_power_nat @ SX0 @ SX1 )
!= zero_zero_nat )
| ( SX0 = zero_zero_nat ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4924]) ).
thf(5435,plain,
! [SV1429: int,SV1244: int] :
( ( ~ ( ord_less_int @ ( bit1 @ SV1244 ) @ ( bit0 @ SV1429 ) )
| ( ord_less_int @ SV1244 @ SV1429 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4925]) ).
thf(5436,plain,
! [SV1430: int,SV1245: int] :
( ( ~ ( ord_less_int @ SV1245 @ SV1430 )
| ( ord_less_int @ ( bit1 @ SV1245 ) @ ( bit0 @ SV1430 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4926]) ).
thf(5437,plain,
! [SV1431: int,SV1246: int] :
( ( ( SV1246
!= ( plus_plus_int @ SV1246 @ SV1431 ) )
| ( SV1431 = zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4927]) ).
thf(5438,plain,
! [SV1247: int,SV1432: int] :
( ( ( SV1432 != zero_zero_int )
| ( SV1247
= ( plus_plus_int @ SV1247 @ SV1432 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4928]) ).
thf(5439,plain,
! [SV1248: int,SV1433: int] :
( ( ! [SY2574: int] :
~ ( zcong @ ( power_power_int @ SY2574 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SV1433 @ SV1248 )
| ( quadRes @ SV1248 @ SV1433 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4929]) ).
thf(5440,plain,
! [SV1434: int,SV1249: int] :
( ( ~ ( quadRes @ SV1249 @ SV1434 )
| ( zcong @ ( power_power_int @ ( sK5_Y_1 @ SV1434 @ SV1249 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SV1434 @ SV1249 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4930]) ).
thf(5441,plain,
! [SV1250: int] :
( ( ( ~ ( ord_less_int @ one_one_int @ ( number_number_of_int @ SV1250 ) ) )
= $true )
| ( ( ord_less_int @ ( bit1 @ pls ) @ SV1250 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4931]) ).
thf(5442,plain,
! [SV1251: int] :
( ( ( ~ ( ord_less_int @ ( bit1 @ pls ) @ SV1251 ) )
= $true )
| ( ( ord_less_int @ one_one_int @ ( number_number_of_int @ SV1251 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4932]) ).
thf(5443,plain,
! [SV1435: nat,SV462: nat] :
( ( ! [SY2575: real] :
( ~ ( ord_less_real @ one_one_real @ SY2575 )
| ( ( power_power_real @ SY2575 @ SV462 )
!= ( power_power_real @ SY2575 @ SV1435 ) )
| ( SV462 = SV1435 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4933]) ).
thf(5444,plain,
! [SV1436: nat,SV462: nat] :
( ( ! [SY2576: real] :
( ~ ( ord_less_real @ one_one_real @ SY2576 )
| ( SV462 != SV1436 )
| ( ( power_power_real @ SY2576 @ SV462 )
= ( power_power_real @ SY2576 @ SV1436 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4934]) ).
thf(5445,plain,
! [SV1252: int,SV1437: int] :
( ( ~ ( ord_less_int @ SV1437 @ pls )
| ( ( plus_plus_nat @ ( number_number_of_nat @ SV1437 ) @ ( number_number_of_nat @ SV1252 ) )
= ( number_number_of_nat @ SV1252 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4935]) ).
thf(5446,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ( 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 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4936]) ).
thf(5447,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ( 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 @ ( plus_plus_int @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4936]) ).
thf(5448,plain,
! [SV1438: real,SV463: real] :
( ( ! [SY2577: real] :
( ( SY2577 = zero_zero_real )
| ( ( times_times_real @ SV463 @ SY2577 )
!= ( times_times_real @ SV1438 @ SY2577 ) )
| ( SV463 = SV1438 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4937]) ).
thf(5449,plain,
! [SV1439: real,SV463: real] :
( ( ! [SY2578: real] :
( ( SY2578 = zero_zero_real )
| ( SV463 != SV1439 )
| ( ( times_times_real @ SV463 @ SY2578 )
= ( times_times_real @ SV1439 @ SY2578 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4938]) ).
thf(5450,plain,
! [SV1440: real,SV464: real] :
( ( ! [SY2579: real] :
( ~ ( ord_less_real @ zero_zero_real @ SY2579 )
| ~ ( ord_less_real @ ( times_times_real @ SV464 @ SY2579 ) @ ( times_times_real @ SV1440 @ SY2579 ) )
| ( ord_less_real @ SV464 @ SV1440 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4939]) ).
thf(5451,plain,
! [SV1441: real,SV464: real] :
( ( ! [SY2580: real] :
( ~ ( ord_less_real @ zero_zero_real @ SY2580 )
| ~ ( ord_less_real @ SV464 @ SV1441 )
| ( ord_less_real @ ( times_times_real @ SV464 @ SY2580 ) @ ( times_times_real @ SV1441 @ SY2580 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4940]) ).
thf(5452,plain,
! [SV1442: real,SV465: real] :
( ( ! [SY2581: real] :
( ~ ( ord_less_real @ zero_zero_real @ SY2581 )
| ~ ( ord_less_eq_real @ ( times_times_real @ SY2581 @ SV465 ) @ ( times_times_real @ SY2581 @ SV1442 ) )
| ( ord_less_eq_real @ SV465 @ SV1442 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4941]) ).
thf(5453,plain,
! [SV1443: real,SV465: real] :
( ( ! [SY2582: real] :
( ~ ( ord_less_real @ zero_zero_real @ SY2582 )
| ~ ( ord_less_eq_real @ SV465 @ SV1443 )
| ( ord_less_eq_real @ ( times_times_real @ SY2582 @ SV465 ) @ ( times_times_real @ SY2582 @ SV1443 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4942]) ).
thf(5454,plain,
! [SV1444: int,SV1253: int] :
( ( ( ( bit0 @ SV1253 )
!= ( bit0 @ SV1444 ) )
| ( SV1253 = SV1444 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4943]) ).
thf(5455,plain,
! [SV1445: int,SV1254: int] :
( ( ( SV1254 != SV1445 )
| ( ( bit0 @ SV1254 )
= ( bit0 @ SV1445 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4944]) ).
thf(5456,plain,
! [SV1255: int] :
( ( ( ( power_power_int @ SV1255 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= zero_zero_int )
= $true )
| ( ( SV1255 = zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4945]) ).
thf(5457,plain,
! [SV1256: int] :
( ( ( SV1256 != zero_zero_int )
= $true )
| ( ( ( power_power_int @ SV1256 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4946]) ).
thf(5458,plain,
! [SV1446: int,SV1257: int] :
( ( ( SV1257 != zero_zero_int )
| ( SV1446 != zero_zero_int )
| ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SV1257 @ SV1257 ) @ ( times_times_int @ SV1446 @ SV1446 ) ) @ zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4947]) ).
thf(5459,plain,
( ( ~ ! [SX0: int] :
( ! [SX1: int] :
~ ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SX0 @ SX0 ) @ ( times_times_int @ SX1 @ SX1 ) ) @ zero_zero_int )
| ( SX0 = zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4948]) ).
thf(5460,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SX0 @ SX0 ) @ ( times_times_int @ SX1 @ SX1 ) ) @ zero_zero_int )
| ( SX1 = zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4948]) ).
thf(5461,plain,
! [SV1258: int] :
( ( ( ~ ( ord_less_int @ pls @ ( bit0 @ SV1258 ) ) )
= $true )
| ( ( ord_less_int @ pls @ SV1258 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4949]) ).
thf(5462,plain,
! [SV1259: int] :
( ( ( ~ ( ord_less_int @ pls @ SV1259 ) )
= $true )
| ( ( ord_less_int @ pls @ ( bit0 @ SV1259 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4950]) ).
thf(5463,plain,
! [SV1260: real] :
( ( ( ~ ( ord_less_real @ ( plus_plus_real @ SV1260 @ SV1260 ) @ zero_zero_real ) )
= $true )
| ( ( ord_less_real @ SV1260 @ zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4951]) ).
thf(5464,plain,
! [SV1261: real] :
( ( ( ~ ( ord_less_real @ SV1261 @ zero_zero_real ) )
= $true )
| ( ( ord_less_real @ ( plus_plus_real @ SV1261 @ SV1261 ) @ zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4952]) ).
thf(5465,plain,
! [SV1262: int,SV1447: nat] :
( ( ( SV1447 = zero_zero_nat )
| ( SV1262 != zero_zero_int )
| ( ( power_power_int @ SV1262 @ SV1447 )
= zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4953]) ).
thf(5466,plain,
( ( ~ ! [SX0: int,SX1: nat] :
( ( ( power_power_int @ SX0 @ SX1 )
!= zero_zero_int )
| ( SX1 != zero_zero_nat ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4954]) ).
thf(5467,plain,
( ( ~ ! [SX0: int] :
( ! [SX1: nat] :
( ( power_power_int @ SX0 @ SX1 )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4954]) ).
thf(5468,plain,
! [SV1448: int,SV1263: int] :
( ( ( ( number_number_of_int @ SV1263 )
!= ( number_number_of_int @ SV1448 ) )
| ( SV1263 = SV1448 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4955]) ).
thf(5469,plain,
! [SV1449: int,SV1264: int] :
( ( ( SV1264 != SV1449 )
| ( ( number_number_of_int @ SV1264 )
= ( number_number_of_int @ SV1449 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4956]) ).
thf(5470,plain,
! [SV1265: int] :
( ( ( ~ ( ord_less_eq_int @ SV1265 @ min ) )
= $true )
| ( ( ord_less_int @ ( bit0 @ SV1265 ) @ min )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4957]) ).
thf(5471,plain,
! [SV1266: int] :
( ( ( ~ ( ord_less_int @ ( bit0 @ SV1266 ) @ min ) )
= $true )
| ( ( ord_less_eq_int @ SV1266 @ min )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4958]) ).
thf(5472,plain,
! [SV1450: int,SV1267: int] :
( ( ~ ( ord_less_eq_nat @ ( number_number_of_nat @ SV1267 ) @ ( number_number_of_nat @ SV1450 ) )
| ~ ( ord_less_nat @ ( number_number_of_nat @ SV1450 ) @ ( number_number_of_nat @ SV1267 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4959]) ).
thf(5473,plain,
! [SV1268: int,SV1451: int] :
( ( ( ord_less_nat @ ( number_number_of_nat @ SV1451 ) @ ( number_number_of_nat @ SV1268 ) )
| ( ord_less_eq_nat @ ( number_number_of_nat @ SV1268 ) @ ( number_number_of_nat @ SV1451 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4960]) ).
thf(5474,plain,
! [SV1269: int] :
( ( ( ~ ( ord_less_eq_int @ ( number_number_of_int @ SV1269 ) @ one_one_int ) )
= $true )
| ( ( ord_less_eq_int @ SV1269 @ ( bit1 @ pls ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4961]) ).
thf(5475,plain,
! [SV1270: int] :
( ( ( ~ ( ord_less_eq_int @ SV1270 @ ( bit1 @ pls ) ) )
= $true )
| ( ( ord_less_eq_int @ ( number_number_of_int @ SV1270 ) @ one_one_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4962]) ).
thf(5476,plain,
! [SV1452: int,SV466: int] :
( ( ! [SY2583: int] :
( ~ ( dvd_dvd_int @ SY2583 @ ( minus_minus_int @ SV466 @ SV1452 ) )
| ( zcong @ SV466 @ SV1452 @ SY2583 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4963]) ).
thf(5477,plain,
! [SV1453: int,SV466: int] :
( ( ! [SY2584: int] :
( ~ ( zcong @ SV466 @ SV1453 @ SY2584 )
| ( dvd_dvd_int @ SY2584 @ ( minus_minus_int @ SV466 @ SV1453 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4964]) ).
thf(5478,plain,
! [SV1271: int] :
( ( ( ( number_number_of_nat @ SV1271 )
!= zero_zero_nat )
= $true )
| ( ( ( power_power_real @ zero_zero_real @ ( number_number_of_nat @ SV1271 ) )
= one_one_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4965]) ).
thf(5479,plain,
! [SV1272: int] :
( ( ( ( number_number_of_nat @ SV1272 )
= zero_zero_nat )
= $true )
| ( ( ( power_power_real @ zero_zero_real @ ( number_number_of_nat @ SV1272 ) )
= zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4966]) ).
thf(5480,plain,
! [SV1273: int] :
( ( ( ~ ( ord_less_int @ ( bit0 @ SV1273 ) @ zero_zero_int ) )
= $true )
| ( ( ord_less_int @ SV1273 @ zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4967]) ).
thf(5481,plain,
! [SV1274: int] :
( ( ( ~ ( ord_less_int @ SV1274 @ zero_zero_int ) )
= $true )
| ( ( ord_less_int @ ( bit0 @ SV1274 ) @ zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4968]) ).
thf(5482,plain,
! [SV1275: int] :
( ( ( ~ ( ord_less_eq_int @ pls @ ( bit1 @ SV1275 ) ) )
= $true )
| ( ( ord_less_eq_int @ pls @ SV1275 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4969]) ).
thf(5483,plain,
! [SV1276: int] :
( ( ( ~ ( ord_less_eq_int @ pls @ SV1276 ) )
= $true )
| ( ( ord_less_eq_int @ pls @ ( bit1 @ SV1276 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4970]) ).
thf(5484,plain,
! [SV1454: int,SV1277: int] :
( ( ~ ( ord_less_int @ ( number_number_of_int @ SV1277 ) @ ( number_number_of_int @ SV1454 ) )
| ( ord_less_int @ SV1277 @ SV1454 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4971]) ).
thf(5485,plain,
! [SV1455: int,SV1278: int] :
( ( ~ ( ord_less_int @ SV1278 @ SV1455 )
| ( ord_less_int @ ( number_number_of_int @ SV1278 ) @ ( number_number_of_int @ SV1455 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4972]) ).
thf(5486,plain,
! [SV1456: nat,SV467: nat] :
( ( ! [SY2585: int] :
( ~ ( ord_less_int @ one_one_int @ SY2585 )
| ( ( power_power_int @ SY2585 @ SV467 )
!= ( power_power_int @ SY2585 @ SV1456 ) )
| ( SV467 = SV1456 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4973]) ).
thf(5487,plain,
! [SV1457: nat,SV467: nat] :
( ( ! [SY2586: int] :
( ~ ( ord_less_int @ one_one_int @ SY2586 )
| ( SV467 != SV1457 )
| ( ( power_power_int @ SY2586 @ SV467 )
= ( power_power_int @ SY2586 @ SV1457 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4974]) ).
thf(5488,plain,
! [SV472: int,SV8: int,SV984: int,SV797: int] :
( ( ( ord_less_int @ SV797 @ SV984 )
= $false )
| ( ( ~ ( ord_less_eq_int @ SV8 @ SV472 )
| ( ord_less_int @ ( plus_plus_int @ SV797 @ SV8 ) @ ( plus_plus_int @ SV984 @ SV472 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4976]) ).
thf(5489,plain,
! [SV478: int,SV17: int] :
( ( ( ord_less_eq_int @ pls @ SV17 )
= $false )
| ( ( ( plus_plus_nat @ ( number_number_of_nat @ SV478 ) @ ( number_number_of_nat @ SV17 ) )
= ( number_number_of_nat @ ( plus_plus_int @ SV478 @ SV17 ) ) )
= $true )
| ( ( ord_less_eq_int @ pls @ SV478 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4977]) ).
thf(5490,plain,
! [SV479: int,SV18: int] :
( ( ( ord_less_eq_int @ pls @ SV18 )
= $false )
| ( ( ( plus_plus_int @ ( number_number_of_int @ SV479 ) @ ( number_number_of_int @ SV18 ) )
= ( number_number_of_int @ ( plus_plus_int @ SV479 @ SV18 ) ) )
= $true )
| ( ( ord_less_eq_int @ pls @ SV479 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4978]) ).
thf(5491,plain,
! [SV806: int,SV488: int,SV28: int] :
( ( ( ~ ( ord_less_int @ zero_zero_int @ SV28 ) )
= $true )
| ( ( ord_less_int @ ( times_times_int @ SV28 @ SV488 ) @ ( times_times_int @ SV28 @ SV806 ) )
= $true )
| ( ( ord_less_int @ SV488 @ SV806 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4979]) ).
thf(5492,plain,
! [SV489: int,SV29: int] :
( ( ( ord_less_eq_int @ zero_zero_int @ SV29 )
= $false )
| ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV489 )
| ( SV29 = SV489 ) )
= $true )
| ( ( ( power_power_int @ SV29 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power_int @ SV489 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4980]) ).
thf(5493,plain,
! [SV30: int,SV490: int] :
( ( ( ord_less_eq_int @ zero_zero_int @ SV490 )
= $false )
| ( ( ord_less_eq_int @ SV30 @ SV490 )
= $true )
| ( ( ord_less_eq_int @ ( power_power_int @ SV30 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV490 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4981]) ).
thf(5494,plain,
! [SV32: int,SV491: int] :
( ( ( ord_less_eq_int @ zero_zero_int @ SV491 )
= $false )
| ( ( ord_less_int @ SV32 @ SV491 )
= $true )
| ( ( ord_less_int @ ( power_power_int @ SV32 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV491 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4982]) ).
thf(5495,plain,
! [SV85: int] :
( ( ( SV85 = zero_zero_int )
= $true )
| ( ( SV85 = one_one_int )
= $true )
| ( ( ord_less_int @ SV85 @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $false )
| ( ( ord_less_eq_int @ zero_zero_int @ SV85 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4984]) ).
thf(5496,plain,
! [SV510: int,SV88: int,SV810: int] :
( ( ( SV810
!= ( plus_plus_int @ SV88 @ ( times_times_int @ SV810 @ SV510 ) ) )
= $true )
| ( ( ~ ( ord_less_int @ SV88 @ SV810 )
| ( ord_less_eq_int @ one_one_int @ SV510 ) )
= $true )
| ( ( ord_less_int @ zero_zero_int @ SV810 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4985]) ).
thf(5497,plain,
! [SV511: int,SV89: int,SV811: int] :
( ( ( SV811
!= ( plus_plus_int @ SV89 @ ( times_times_int @ SV811 @ SV511 ) ) )
= $true )
| ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV89 )
| ( ord_less_eq_int @ SV511 @ one_one_int ) )
= $true )
| ( ( ord_less_int @ zero_zero_int @ SV811 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4986]) ).
thf(5498,plain,
! [SV514: nat,SV92: int,SV812: int] :
( ( ( ~ ( dvd_dvd_int @ SV812 @ ( power_power_int @ SV92 @ SV514 ) ) )
= $true )
| ( ( dvd_dvd_int @ SV812 @ SV92 )
= $true )
| ( ( zprime @ SV812 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4987]) ).
thf(5499,plain,
! [SV95: int,SV517: int] :
( ( ( ord_less_int @ SV517 @ SV95 )
= $false )
| ( ( ~ ( dvd_dvd_int @ SV95 @ SV517 ) )
= $true )
| ( ( ord_less_int @ zero_zero_int @ SV517 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4988]) ).
thf(5500,plain,
! [SV518: int,SV96: int] :
( ( ( ord_less_eq_int @ zero_zero_int @ SV96 )
= $false )
| ( ( ~ ( dvd_dvd_int @ SV518 @ SV96 )
| ~ ( dvd_dvd_int @ SV96 @ SV518 )
| ( SV518 = SV96 ) )
= $true )
| ( ( ord_less_eq_int @ zero_zero_int @ SV518 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4989]) ).
thf(5501,plain,
! [SV815: int,SV519: int,SV97: int] :
( ( ( SV97 = zero_zero_int )
= $true )
| ( ( dvd_dvd_int @ SV519 @ SV815 )
= $true )
| ( ( dvd_dvd_int @ ( times_times_int @ SV97 @ SV519 ) @ ( times_times_int @ SV97 @ SV815 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4990]) ).
thf(5502,plain,
! [SV98: int,SV520: int] :
( ( ( ord_less_int @ zero_zero_int @ SV520 )
= $false )
| ( ( ord_less_eq_int @ SV98 @ SV520 )
= $true )
| ( ( dvd_dvd_int @ SV98 @ SV520 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4991]) ).
thf(5503,plain,
! [SV986: int,SV827: int,SV536: int,SV125: int,SV1279: int] :
( ( ( SV1279 = zero_zero_int )
= $true )
| ( ( ( SV125 = SV536 )
| ( SV827 != SV986 )
| ( ( plus_plus_int @ SV827 @ ( times_times_int @ SV1279 @ SV125 ) )
!= ( plus_plus_int @ SV986 @ ( times_times_int @ SV1279 @ SV536 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4992]) ).
thf(5504,plain,
! [SV129: int,SV539: int] :
( ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ SV539 @ SV129 ) )
= $false )
| ( ( ord_less_int @ zero_zero_int @ SV129 )
= $true )
| ( ( ord_less_int @ zero_zero_int @ SV539 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4993]) ).
thf(5505,plain,
! [SV540: int,SV130: int] :
( ( ( ord_less_eq_int @ zero_zero_int @ SV130 )
= $false )
| ( ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ SV540 @ SV130 ) )
= $true )
| ( ( ord_less_eq_int @ zero_zero_int @ SV540 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4994]) ).
thf(5506,plain,
! [SV541: int,SV131: int] :
( ( ( ord_less_eq_int @ zero_zero_int @ SV131 )
= $false )
| ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ SV541 @ SV131 ) )
= $true )
| ( ( ord_less_eq_int @ zero_zero_int @ SV541 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4995]) ).
thf(5507,plain,
! [SV543: int,SV133: int,SV828: int] :
( ( ( ~ ( ord_less_int @ SV828 @ SV133 ) )
= $true )
| ( ( ~ ( ord_less_int @ zero_zero_int @ SV133 )
| ( ord_less_eq_int @ zero_zero_int @ SV543 ) )
= $true )
| ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ SV133 @ SV543 ) @ SV828 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4996]) ).
thf(5508,plain,
! [SV544: int,SV134: int,SV829: int] :
( ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV829 ) )
= $true )
| ( ( ~ ( ord_less_int @ zero_zero_int @ SV134 )
| ( ord_less_eq_int @ SV544 @ zero_zero_int ) )
= $true )
| ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ SV134 @ SV544 ) @ SV829 ) @ zero_zero_int )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4997]) ).
thf(5509,plain,
! [SV1280: int,SV987: int,SV830: int,SV545: int,SV135: int] :
( ( ( ~ ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SV135 @ SV545 ) @ SV830 ) @ ( plus_plus_int @ ( times_times_int @ SV135 @ SV987 ) @ SV1280 ) ) )
= $true )
| ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV830 )
| ~ ( ord_less_int @ SV830 @ SV135 )
| ~ ( ord_less_int @ SV1280 @ SV135 )
| ( ord_less_eq_int @ SV545 @ SV987 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4998]) ).
thf(5510,plain,
! [SV1458: int,SV1281: int,SV988: int,SV831: int,SV546: int,SV136: int] :
( ( ( ( plus_plus_int @ ( times_times_int @ SV136 @ SV546 ) @ SV831 )
!= ( plus_plus_int @ ( times_times_int @ SV988 @ SV1281 ) @ SV1458 ) )
| ~ ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ SV988 @ SV1281 ) @ SV1458 ) )
| ~ ( ord_less_int @ SV1458 @ SV988 )
| ~ ( ord_less_eq_int @ zero_zero_int @ SV831 )
| ~ ( ord_less_int @ zero_zero_int @ SV988 )
| ~ ( ord_less_eq_int @ SV988 @ SV136 )
| ( ord_less_eq_int @ SV546 @ SV1281 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4999]) ).
thf(5511,plain,
! [SV1282: int,SV989: int,SV832: int,SV547: int,SV137: int] :
( ( ( ~ ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SV137 @ SV547 ) @ SV832 ) @ ( plus_plus_int @ ( times_times_int @ SV137 @ SV989 ) @ SV1282 ) ) )
= $true )
| ( ( ~ ( ord_less_eq_int @ SV1282 @ zero_zero_int )
| ~ ( ord_less_int @ SV137 @ SV1282 )
| ~ ( ord_less_int @ SV137 @ SV832 )
| ( ord_less_eq_int @ SV989 @ SV547 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5000]) ).
thf(5512,plain,
! [SV1459: int,SV1283: int,SV990: int,SV833: int,SV548: int,SV138: int] :
( ( ( ( plus_plus_int @ ( times_times_int @ SV138 @ SV548 ) @ SV833 )
!= ( plus_plus_int @ ( times_times_int @ SV990 @ SV1283 ) @ SV1459 ) )
| ~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ SV990 @ SV1283 ) @ SV1459 ) @ zero_zero_int )
| ~ ( ord_less_int @ SV833 @ SV138 )
| ~ ( ord_less_eq_int @ zero_zero_int @ SV1459 )
| ~ ( ord_less_int @ zero_zero_int @ SV990 )
| ~ ( ord_less_eq_int @ SV990 @ SV138 )
| ( ord_less_eq_int @ SV1283 @ SV548 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5001]) ).
thf(5513,plain,
! [SV834: int,SV549: int,SV143: int] :
( ( ( zcong @ ( power_power_int @ SV143 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SV549 @ SV834 )
= $false )
| ( ( ~ ( dvd_dvd_int @ SV834 @ SV143 ) )
= $true )
| ( ( zcong @ SV549 @ zero_zero_int @ SV834 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5002]) ).
thf(5514,plain,
! [SV551: int,SV835: int,SV147: int] :
( ( ( ~ ( ord_less_int @ SV147 @ SV835 ) )
= $true )
| ( ( ( ord_less_eq_int @ SV551 @ SV147 )
| ( ord_less_eq_int @ SV147 @ SV551 ) )
= $true )
| ( ( ord_less_int @ SV551 @ SV835 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5004]) ).
thf(5515,plain,
! [SV553: int,SV149: int,SV1284: int,SV991: int,SV836: int] :
( ( ( ~ ( zcong @ SV836 @ SV991 @ SV1284 ) )
= $true )
| ( ( ~ ( zcong @ SV149 @ SV553 @ SV1284 )
| ( zcong @ ( plus_plus_int @ SV836 @ SV149 ) @ ( plus_plus_int @ SV991 @ SV553 ) @ SV1284 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5005]) ).
thf(5516,plain,
! [SV150: int,SV554: int,SV837: int] :
( ( ( ~ ( ord_less_int @ SV837 @ SV554 ) )
= $true )
| ( ( ~ ( ord_less_int @ zero_zero_int @ SV150 )
| ~ ( ord_less_int @ SV150 @ SV837 )
| ~ ( zcong @ SV837 @ SV150 @ SV554 ) )
= $true )
| ( ( ord_less_int @ zero_zero_int @ SV837 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5006]) ).
thf(5517,plain,
! [SV151: int,SV555: int] :
( ( ( ord_less_int @ SV555 @ SV151 )
= $false )
| ( ( ~ ( zcong @ SV555 @ zero_zero_int @ SV151 )
| ( SV555 = zero_zero_int ) )
= $true )
| ( ( ord_less_eq_int @ zero_zero_int @ SV555 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5007]) ).
thf(5518,plain,
! [SV152: int,SV556: int,SV838: int] :
( ( ( ~ ( ord_less_int @ SV838 @ SV556 ) )
= $true )
| ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV152 )
| ~ ( ord_less_int @ SV152 @ SV556 )
| ~ ( zcong @ SV838 @ SV152 @ SV556 )
| ( SV838 = SV152 ) )
= $true )
| ( ( ord_less_eq_int @ zero_zero_int @ SV838 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5008]) ).
thf(5519,plain,
! [SV153: nat,SV992: int,SV839: nat,SV557: int] :
( ( ( zcong @ ( power_power_int @ SV557 @ SV839 ) @ one_one_int @ SV992 )
= $false )
| ( ( zcong @ ( power_power_int @ SV557 @ ( times_times_nat @ SV839 @ SV153 ) ) @ one_one_int @ SV992 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5009]) ).
thf(5520,plain,
! [SV1460: int,SV1285: int,SV993: int,SV841: int,SV562: int,SV160: int] :
( ( ! [SY2587: int] :
( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ SV160 @ ( times_times_int @ SV562 @ SV841 ) ) @ SV993 ) @ ( times_times_int @ ( minus_minus_int @ SV1285 @ ( times_times_int @ SV562 @ SV1460 ) ) @ SY2587 ) )
= ( minus_minus_int @ ( plus_plus_int @ ( times_times_int @ SV160 @ SV993 ) @ ( times_times_int @ SV1285 @ SY2587 ) ) @ ( times_times_int @ SV562 @ ( plus_plus_int @ ( times_times_int @ SV841 @ SV993 ) @ ( times_times_int @ SV1460 @ SY2587 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5011]) ).
thf(5521,plain,
! [SV162: int,SV564: int] :
( ( ( ord_less_int @ SV564 @ SV162 )
= $false )
| ( ( ( SV564
= ( minus_minus_int @ SV162 @ one_one_int ) )
| ( ord_less_int @ SV564 @ ( minus_minus_int @ SV162 @ one_one_int ) ) )
= $true )
| ( ( ord_less_int @ zero_zero_int @ SV564 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5012]) ).
thf(5522,plain,
! [SV168: int,SV994: int,SV843: int,SV566: int] :
( ( ( zcong @ SV566 @ SV843 @ SV994 )
= $false )
| ( ( zcong @ ( plus_plus_int @ SV566 @ SV168 ) @ ( plus_plus_int @ SV843 @ SV168 ) @ SV994 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5013]) ).
thf(5523,plain,
! [SV169: nat,SV995: int,SV844: int,SV567: int] :
( ( ( zcong @ SV567 @ SV844 @ SV995 )
= $false )
| ( ( zcong @ ( power_power_int @ SV567 @ SV169 ) @ ( power_power_int @ SV844 @ SV169 ) @ SV995 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5014]) ).
thf(5524,plain,
! [SV845: int,SV170: int,SV568: int] :
( ( ( ~ ( ord_less_int @ zero_zero_int @ SV568 ) )
= $true )
| ( ( ~ ( ord_less_int @ zero_zero_int @ SV170 )
| ~ ( zcong @ SV845 @ SV568 @ SV170 )
| ~ ( ord_less_int @ SV845 @ SV170 )
| ~ ( ord_less_int @ SV568 @ SV170 )
| ( SV845 = SV568 ) )
= $true )
| ( ( ord_less_int @ zero_zero_int @ SV845 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5015]) ).
thf(5525,plain,
! [SV171: int,SV569: int] :
( ( ( ord_less_int @ SV569 @ SV171 )
= $false )
| ( ( ~ ( zcong @ SV569 @ zero_zero_int @ SV171 ) )
= $true )
| ( ( ord_less_int @ zero_zero_int @ SV569 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5016]) ).
thf(5526,plain,
! [SV173: int,SV571: int] :
( ( ( ord_less_int @ SV571 @ SV173 )
= $false )
| ( ( ~ ( zcong @ SV571 @ zero_zero_int @ SV173 )
| ( SV571 = zero_zero_int ) )
= $true )
| ( ( ord_less_eq_int @ zero_zero_int @ SV571 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5018]) ).
thf(5527,plain,
! [SV851: int,SV185: nat,SV579: int] :
( ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV579 ) )
= $true )
| ( ( ord_less_eq_int @ ( power_power_int @ SV579 @ SV185 ) @ ( power_power_int @ SV851 @ SV185 ) )
= $true )
| ( ( ord_less_eq_int @ SV579 @ SV851 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5020]) ).
thf(5528,plain,
! [SV191: nat,SV998: int,SV853: nat,SV584: int] :
( ( ( dvd_dvd_int @ ( power_power_int @ SV584 @ SV853 ) @ SV998 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV191 @ SV853 )
| ( dvd_dvd_int @ ( power_power_int @ SV584 @ SV191 ) @ SV998 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5021]) ).
thf(5529,plain,
! [SV585: nat,SV192: nat,SV999: int,SV854: int] :
( ( ( dvd_dvd_int @ SV854 @ SV999 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV192 @ SV585 )
| ( dvd_dvd_int @ ( power_power_int @ SV854 @ SV192 ) @ ( power_power_int @ SV999 @ SV585 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5022]) ).
thf(5530,plain,
! [SV587: nat,SV194: int,SV856: int] :
( ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV856 ) )
= $true )
| ( ( ord_less_int @ SV194 @ SV856 )
= $true )
| ( ( ord_less_int @ ( power_power_int @ SV194 @ SV587 ) @ ( power_power_int @ SV856 @ SV587 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5024]) ).
thf(5531,plain,
! [SV857: nat,SV590: nat,SV197: int] :
( ( ( ~ ( ord_less_int @ one_one_int @ SV197 ) )
= $true )
| ( ( ord_less_int @ ( power_power_int @ SV197 @ SV590 ) @ ( power_power_int @ SV197 @ SV857 ) )
= $true )
| ( ( ord_less_nat @ SV590 @ SV857 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5025]) ).
thf(5532,plain,
! [SV591: nat,SV198: nat,SV858: int] :
( ( ( ~ ( ord_less_int @ ( power_power_int @ SV858 @ SV198 ) @ ( power_power_int @ SV858 @ SV591 ) ) )
= $true )
| ( ( ord_less_nat @ SV198 @ SV591 )
= $true )
| ( ( ord_less_int @ one_one_int @ SV858 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5026]) ).
thf(5533,plain,
! [SV859: nat,SV592: nat,SV199: int] :
( ( ( ~ ( ord_less_eq_int @ one_one_int @ SV199 ) )
= $true )
| ( ( ord_less_eq_int @ ( power_power_int @ SV199 @ SV592 ) @ ( power_power_int @ SV199 @ SV859 ) )
= $true )
| ( ( ord_less_eq_nat @ SV592 @ SV859 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5027]) ).
thf(5534,plain,
! [SV200: nat,SV593: int] :
( ( ( ord_less_int @ SV593 @ one_one_int )
= $false )
| ( ( ord_less_int @ ( times_times_int @ SV593 @ ( power_power_int @ SV593 @ SV200 ) ) @ ( power_power_int @ SV593 @ SV200 ) )
= $true )
| ( ( ord_less_int @ zero_zero_int @ SV593 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5028]) ).
thf(5535,plain,
! [SV594: nat,SV860: nat,SV201: int] :
( ( ( ~ ( ord_less_int @ zero_zero_int @ SV201 ) )
= $true )
| ( ( ~ ( ord_less_int @ SV201 @ one_one_int )
| ( ord_less_int @ ( power_power_int @ SV201 @ SV860 ) @ ( power_power_int @ SV201 @ SV594 ) ) )
= $true )
| ( ( ord_less_nat @ SV594 @ SV860 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5029]) ).
thf(5536,plain,
! [SV600: int,SV212: int,SV862: int] :
( ( ( ~ ( ord_less_eq_int @ SV862 @ SV212 ) )
= $true )
| ( ( ord_less_eq_int @ SV600 @ SV212 )
= $true )
| ( ( ord_less_eq_int @ SV600 @ SV862 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5030]) ).
thf(5537,plain,
! [SV213: int,SV601: int] :
( ( ( ord_less_eq_int @ SV601 @ SV213 )
= $false )
| ( ( SV213 = SV601 )
= $true )
| ( ( ord_less_eq_int @ SV213 @ SV601 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5031]) ).
thf(5538,plain,
! [SV602: int,SV214: int] :
( ( ( ord_less_eq_int @ pls @ SV214 )
= $false )
| ( ( ( times_times_real @ ( number267125858f_real @ SV602 ) @ ( number267125858f_real @ SV214 ) )
= ( number267125858f_real @ ( times_times_int @ SV602 @ SV214 ) ) )
= $true )
| ( ( ord_less_eq_int @ pls @ SV602 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5032]) ).
thf(5539,plain,
! [SV603: int,SV215: int] :
( ( ( ord_less_eq_int @ pls @ SV215 )
= $false )
| ( ( ( times_times_nat @ ( number_number_of_nat @ SV603 ) @ ( number_number_of_nat @ SV215 ) )
= ( number_number_of_nat @ ( times_times_int @ SV603 @ SV215 ) ) )
= $true )
| ( ( ord_less_eq_int @ pls @ SV603 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5033]) ).
thf(5540,plain,
! [SV604: int,SV216: int] :
( ( ( ord_less_eq_int @ pls @ SV216 )
= $false )
| ( ( ( times_times_int @ ( number_number_of_int @ SV604 ) @ ( number_number_of_int @ SV216 ) )
= ( number_number_of_int @ ( times_times_int @ SV604 @ SV216 ) ) )
= $true )
| ( ( ord_less_eq_int @ pls @ SV604 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5034]) ).
thf(5541,plain,
! [SV612: int,SV224: int] :
( ( ( ord_less_eq_int @ pls @ SV224 )
= $false )
| ( ( ( plus_plus_real @ ( number267125858f_real @ SV612 ) @ ( number267125858f_real @ SV224 ) )
= ( number267125858f_real @ ( plus_plus_int @ SV612 @ SV224 ) ) )
= $true )
| ( ( ord_less_eq_int @ pls @ SV612 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5035]) ).
thf(5542,plain,
! [SV615: real,SV227: real] :
( ( ( ord_less_eq_real @ zero_zero_real @ SV227 )
= $false )
| ( ( ~ ( ord_less_eq_real @ zero_zero_real @ SV615 )
| ( SV227 = SV615 ) )
= $true )
| ( ( ( power_power_real @ SV227 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power_real @ SV615 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5036]) ).
thf(5543,plain,
! [SV616: nat,SV228: nat] :
( ( ( ord_less_eq_nat @ zero_zero_nat @ SV228 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV616 )
| ( SV228 = SV616 ) )
= $true )
| ( ( ( power_power_nat @ SV228 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power_nat @ SV616 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5037]) ).
thf(5544,plain,
! [SV229: real,SV617: real] :
( ( ( ord_less_eq_real @ zero_zero_real @ SV617 )
= $false )
| ( ( ord_less_eq_real @ SV229 @ SV617 )
= $true )
| ( ( ord_less_eq_real @ ( power_power_real @ SV229 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SV617 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5038]) ).
thf(5545,plain,
! [SV230: nat,SV618: nat] :
( ( ( ord_less_eq_nat @ zero_zero_nat @ SV618 )
= $false )
| ( ( ord_less_eq_nat @ SV230 @ SV618 )
= $true )
| ( ( ord_less_eq_nat @ ( power_power_nat @ SV230 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_nat @ SV618 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5039]) ).
thf(5546,plain,
! [SV232: real,SV619: real] :
( ( ( ord_less_eq_real @ zero_zero_real @ SV619 )
= $false )
| ( ( ord_less_real @ SV232 @ SV619 )
= $true )
| ( ( ord_less_real @ ( power_power_real @ SV232 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SV619 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5040]) ).
thf(5547,plain,
! [SV233: nat,SV620: nat] :
( ( ( ord_less_eq_nat @ zero_zero_nat @ SV620 )
= $false )
| ( ( ord_less_nat @ SV233 @ SV620 )
= $true )
| ( ( ord_less_nat @ ( power_power_nat @ SV233 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_nat @ SV620 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5041]) ).
thf(5548,plain,
! [SV628: int,SV249: nat,SV869: int,SV1000: int] :
( ( ( zprime @ SV1000 )
= $false )
| ( ( ( dvd_dvd_int @ SV1000 @ SV869 )
| ~ ( dvd_dvd_int @ ( power_power_int @ SV1000 @ SV249 ) @ ( times_times_int @ SV628 @ SV869 ) )
| ( dvd_dvd_int @ ( power_power_int @ SV1000 @ SV249 ) @ SV628 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5042]) ).
thf(5549,plain,
! [SV629: int,SV250: nat,SV870: int,SV1001: int] :
( ( ( zprime @ SV1001 )
= $false )
| ( ( ( dvd_dvd_int @ SV1001 @ SV870 )
| ~ ( dvd_dvd_int @ ( power_power_int @ SV1001 @ SV250 ) @ ( times_times_int @ SV870 @ SV629 ) )
| ( dvd_dvd_int @ ( power_power_int @ SV1001 @ SV250 ) @ SV629 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5043]) ).
thf(5550,plain,
! [SV630: int,SV251: int] :
( ( ( twoSqu362149276sum2sq @ SV251 )
= $false )
| ( ( twoSqu362149276sum2sq @ ( times_times_int @ SV630 @ SV251 ) )
= $true )
| ( ( twoSqu362149276sum2sq @ SV630 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5044]) ).
thf(5551,plain,
! [SV1013: real,SV913: real,SV678: real,SV316: real,SV1286: real] :
( ( ( SV1286 = zero_zero_real )
= $true )
| ( ( ( SV316 = SV678 )
| ( SV913 != SV1013 )
| ( ( plus_plus_real @ SV913 @ ( times_times_real @ SV1286 @ SV316 ) )
!= ( plus_plus_real @ SV1013 @ ( times_times_real @ SV1286 @ SV678 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5045]) ).
thf(5552,plain,
! [SV1014: nat,SV914: nat,SV679: nat,SV317: nat,SV1287: nat] :
( ( ( SV1287 = zero_zero_nat )
= $true )
| ( ( ( SV317 = SV679 )
| ( SV914 != SV1014 )
| ( ( plus_plus_nat @ SV914 @ ( times_times_nat @ SV1287 @ SV317 ) )
!= ( plus_plus_nat @ SV1014 @ ( times_times_nat @ SV1287 @ SV679 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5046]) ).
thf(5553,plain,
! [SV327: int,SV1015: int,SV916: int,SV685: int] :
( ( ( zcong @ SV685 @ SV916 @ SV1015 )
= $false )
| ( ( ~ ( zcong @ SV916 @ SV327 @ SV1015 )
| ( zcong @ SV685 @ SV327 @ SV1015 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5049]) ).
thf(5554,plain,
! [SV331: int,SV1016: int,SV918: int,SV689: int] :
( ( ( zcong @ SV689 @ SV918 @ SV1016 )
= $false )
| ( ( zcong @ ( times_times_int @ SV689 @ SV331 ) @ ( times_times_int @ SV918 @ SV331 ) @ SV1016 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5052]) ).
thf(5555,plain,
! [SV332: int,SV1017: int,SV919: int,SV690: int] :
( ( ( zcong @ SV690 @ SV919 @ SV1017 )
= $false )
| ( ( zcong @ ( times_times_int @ SV332 @ SV690 ) @ ( times_times_int @ SV332 @ SV919 ) @ SV1017 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5053]) ).
thf(5556,plain,
! [SV691: int,SV333: int,SV1288: int,SV1018: int,SV920: int] :
( ( ( ~ ( zcong @ SV920 @ SV1018 @ SV1288 ) )
= $true )
| ( ( ~ ( zcong @ SV333 @ SV691 @ SV1288 )
| ( zcong @ ( times_times_int @ SV920 @ SV333 ) @ ( times_times_int @ SV1018 @ SV691 ) @ SV1288 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5054]) ).
thf(5557,plain,
! [SV337: int,SV921: int,SV692: int] :
( ( ( ~ ( zprime @ SV692 ) )
= $true )
| ( ( ~ ( dvd_dvd_int @ SV692 @ ( times_times_int @ SV921 @ SV337 ) )
| ( dvd_dvd_int @ SV692 @ SV921 )
| ( dvd_dvd_int @ SV692 @ SV337 ) )
= $true )
| ( ( ord_less_eq_int @ zero_zero_int @ SV921 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5055]) ).
thf(5558,plain,
! [SV922: int,SV693: nat,SV338: nat] :
( ( ( ~ ( zcong @ ( power_power_int @ ( number_number_of_int @ min ) @ SV338 ) @ ( power_power_int @ ( number_number_of_int @ min ) @ SV693 ) @ SV922 ) )
= $true )
| ( ( ( power_power_int @ ( number_number_of_int @ min ) @ SV338 )
= ( power_power_int @ ( number_number_of_int @ min ) @ SV693 ) )
= $true )
| ( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV922 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5056]) ).
thf(5559,plain,
! [SV694: int,SV339: int] :
( ( ( zcong @ SV339 @ ( number_number_of_int @ min ) @ SV694 )
= $false )
| ( ( ~ ( zcong @ SV339 @ one_one_int @ SV694 ) )
= $true )
| ( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV694 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5057]) ).
thf(5560,plain,
! [SV695: int,SV340: int,SV1289: int,SV1019: int,SV923: int] :
( ( ( ~ ( zcong @ SV923 @ SV1019 @ SV1289 ) )
= $true )
| ( ( ~ ( zcong @ SV340 @ SV695 @ SV1289 )
| ( zcong @ ( minus_minus_int @ SV923 @ SV340 ) @ ( minus_minus_int @ SV1019 @ SV695 ) @ SV1289 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5058]) ).
thf(5561,plain,
! [SV696: int,SV924: int,SV341: int] :
( ( ( ~ ( dvd_dvd_int @ SV341 @ SV924 ) )
= $true )
| ( ( dvd_dvd_int @ SV341 @ SV696 )
= $true )
| ( ( dvd_dvd_int @ SV341 @ ( minus_minus_int @ SV696 @ SV924 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5059]) ).
thf(5562,plain,
! [SV351: int,SV706: int,SV1290: int,SV1020: int,SV932: int] :
( ( ( ~ ( zcong @ SV932 @ SV1020 @ SV1290 ) )
= $true )
| ( ( ( SV1020 != SV706 )
| ~ ( zcong @ SV706 @ SV351 @ SV1290 )
| ( zcong @ SV932 @ SV351 @ SV1290 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5060]) ).
thf(5563,plain,
! [SV707: int,SV352: int] :
( ( ( ord_less_int @ zero_zero_int @ SV352 )
= $false )
| ( ( ~ ( ord_less_int @ SV352 @ SV707 )
| ~ ( zcong @ ( times_times_int @ SV352 @ SV352 ) @ one_one_int @ SV707 )
| ( SV352 = one_one_int )
| ( SV352
= ( minus_minus_int @ SV707 @ one_one_int ) ) )
= $true )
| ( ( zprime @ SV707 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5061]) ).
thf(5564,plain,
! [SV708: int,SV353: int] :
( ( ( ord_less_int @ zero_zero_int @ SV353 )
= $false )
| ( ( ~ ( zcong @ ( times_times_int @ SV353 @ SV353 ) @ one_one_int @ SV708 )
| ( zcong @ SV353 @ one_one_int @ SV708 )
| ( zcong @ SV353 @ ( minus_minus_int @ SV708 @ one_one_int ) @ SV708 ) )
= $true )
| ( ( zprime @ SV708 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5062]) ).
thf(5565,plain,
! [SV713: int,SV358: int,SV933: int] :
( ( ( ~ ( dvd_dvd_int @ SV933 @ ( times_times_int @ SV358 @ SV713 ) ) )
= $true )
| ( ( ( dvd_dvd_int @ SV933 @ SV358 )
| ( dvd_dvd_int @ SV933 @ SV713 ) )
= $true )
| ( ( zprime @ SV933 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5063]) ).
thf(5566,plain,
! [SV934: nat,SV714: int,SV359: int] :
( ( ( ~ ( dvd_dvd_int @ SV359 @ SV714 ) )
= $true )
| ( ( dvd_dvd_int @ SV359 @ ( power_power_int @ SV714 @ SV934 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV934 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5064]) ).
thf(5567,plain,
! [SV360: int,SV935: int,SV715: int] :
( ( ( zcong @ SV715 @ zero_zero_int @ SV935 )
= $true )
| ( ( ( zcong @ SV360 @ zero_zero_int @ SV935 )
| ~ ( zcong @ ( times_times_int @ SV715 @ SV360 ) @ zero_zero_int @ SV935 ) )
= $true )
| ( ( zprime @ SV935 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5065]) ).
thf(5568,plain,
! [SV361: int,SV936: int,SV716: int] :
( ( ( ~ ( ord_less_int @ zero_zero_int @ SV716 ) )
= $true )
| ( ( ( zcong @ SV716 @ zero_zero_int @ SV936 )
| ( zcong @ SV361 @ zero_zero_int @ SV936 )
| ~ ( zcong @ ( times_times_int @ SV716 @ SV361 ) @ zero_zero_int @ SV936 ) )
= $true )
| ( ( zprime @ SV936 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5066]) ).
thf(5569,plain,
! [SV937: int,SV362: int,SV717: int] :
( ( ( ~ ( ord_less_int @ zero_zero_int @ SV717 ) )
= $true )
| ( ( ~ ( zcong @ ( times_times_int @ SV717 @ SV362 ) @ zero_zero_int @ SV937 )
| ( zcong @ SV717 @ zero_zero_int @ SV937 )
| ( zcong @ SV362 @ zero_zero_int @ SV937 ) )
= $true )
| ( ( zprime @ SV937 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5067]) ).
thf(5570,plain,
! [SV718: nat,SV363: int,SV938: int] :
( ( ( ~ ( dvd_dvd_int @ SV938 @ ( power_power_int @ SV363 @ SV718 ) ) )
= $true )
| ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV718 )
| ( dvd_dvd_int @ SV938 @ SV363 ) )
= $true )
| ( ( zprime @ SV938 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5068]) ).
thf(5571,plain,
! [SV944: real,SV727: real,SV375: real] :
( ( ( ~ ( ord_less_real @ SV375 @ SV727 ) )
= $true )
| ( ( ord_less_real @ ( times_times_real @ SV944 @ SV375 ) @ ( times_times_real @ SV944 @ SV727 ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV944 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5070]) ).
thf(5572,plain,
! [SV728: real,SV376: real] :
( ( ( ord_less_real @ zero_zero_real @ SV376 )
= $false )
| ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ SV728 @ SV376 ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV728 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5071]) ).
thf(5573,plain,
! [SV945: real,SV382: nat,SV732: real] :
( ( ( ~ ( ord_less_eq_real @ zero_zero_real @ SV732 ) )
= $true )
| ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV382 )
| ( ord_less_real @ ( power_power_real @ SV732 @ SV382 ) @ ( power_power_real @ SV945 @ SV382 ) ) )
= $true )
| ( ( ord_less_real @ SV732 @ SV945 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5072]) ).
thf(5574,plain,
! [SV946: nat,SV383: nat,SV733: nat] :
( ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV733 ) )
= $true )
| ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV383 )
| ( ord_less_nat @ ( power_power_nat @ SV733 @ SV383 ) @ ( power_power_nat @ SV946 @ SV383 ) ) )
= $true )
| ( ( ord_less_nat @ SV733 @ SV946 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5073]) ).
thf(5575,plain,
! [SV947: int,SV384: nat,SV734: int] :
( ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV734 ) )
= $true )
| ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV384 )
| ( ord_less_int @ ( power_power_int @ SV734 @ SV384 ) @ ( power_power_int @ SV947 @ SV384 ) ) )
= $true )
| ( ( ord_less_int @ SV734 @ SV947 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5074]) ).
thf(5576,plain,
! [SV954: real,SV398: nat,SV744: real] :
( ( ( ~ ( ord_less_eq_real @ zero_zero_real @ SV744 ) )
= $true )
| ( ( ord_less_eq_real @ ( power_power_real @ SV744 @ SV398 ) @ ( power_power_real @ SV954 @ SV398 ) )
= $true )
| ( ( ord_less_eq_real @ SV744 @ SV954 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5077]) ).
thf(5577,plain,
! [SV955: nat,SV399: nat,SV745: nat] :
( ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV745 ) )
= $true )
| ( ( ord_less_eq_nat @ ( power_power_nat @ SV745 @ SV399 ) @ ( power_power_nat @ SV955 @ SV399 ) )
= $true )
| ( ( ord_less_eq_nat @ SV745 @ SV955 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5078]) ).
thf(5578,plain,
! [SV410: nat,SV1023: nat,SV958: nat,SV754: nat] :
( ( ( dvd_dvd_nat @ ( power_power_nat @ SV754 @ SV958 ) @ SV1023 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV410 @ SV958 )
| ( dvd_dvd_nat @ ( power_power_nat @ SV754 @ SV410 ) @ SV1023 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5079]) ).
thf(5579,plain,
! [SV411: nat,SV1024: real,SV959: nat,SV755: real] :
( ( ( dvd_dvd_real @ ( power_power_real @ SV755 @ SV959 ) @ SV1024 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV411 @ SV959 )
| ( dvd_dvd_real @ ( power_power_real @ SV755 @ SV411 ) @ SV1024 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5080]) ).
thf(5580,plain,
! [SV756: nat,SV412: nat,SV1025: nat,SV960: nat] :
( ( ( dvd_dvd_nat @ SV960 @ SV1025 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV412 @ SV756 )
| ( dvd_dvd_nat @ ( power_power_nat @ SV960 @ SV412 ) @ ( power_power_nat @ SV1025 @ SV756 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5081]) ).
thf(5581,plain,
! [SV757: nat,SV413: nat,SV1026: real,SV961: real] :
( ( ( dvd_dvd_real @ SV961 @ SV1026 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV413 @ SV757 )
| ( dvd_dvd_real @ ( power_power_real @ SV961 @ SV413 ) @ ( power_power_real @ SV1026 @ SV757 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5082]) ).
thf(5582,plain,
! [SV760: nat,SV416: nat,SV964: nat] :
( ( ( ~ ( ord_less_nat @ ( power_power_nat @ SV964 @ SV416 ) @ ( power_power_nat @ SV964 @ SV760 ) ) )
= $true )
| ( ( ord_less_nat @ SV416 @ SV760 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV964 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5085]) ).
thf(5583,plain,
! [SV761: nat,SV417: real,SV965: real] :
( ( ( ~ ( ord_less_eq_real @ zero_zero_real @ SV965 ) )
= $true )
| ( ( ord_less_real @ SV417 @ SV965 )
= $true )
| ( ( ord_less_real @ ( power_power_real @ SV417 @ SV761 ) @ ( power_power_real @ SV965 @ SV761 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5086]) ).
thf(5584,plain,
! [SV762: nat,SV418: nat,SV966: nat] :
( ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV966 ) )
= $true )
| ( ( ord_less_nat @ SV418 @ SV966 )
= $true )
| ( ( ord_less_nat @ ( power_power_nat @ SV418 @ SV762 ) @ ( power_power_nat @ SV966 @ SV762 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5087]) ).
thf(5585,plain,
! [SV967: nat,SV767: nat,SV423: real] :
( ( ( ~ ( ord_less_real @ one_one_real @ SV423 ) )
= $true )
| ( ( ord_less_real @ ( power_power_real @ SV423 @ SV767 ) @ ( power_power_real @ SV423 @ SV967 ) )
= $true )
| ( ( ord_less_nat @ SV767 @ SV967 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5088]) ).
thf(5586,plain,
! [SV968: nat,SV768: nat,SV424: nat] :
( ( ( ~ ( ord_less_nat @ one_one_nat @ SV424 ) )
= $true )
| ( ( ord_less_nat @ ( power_power_nat @ SV424 @ SV768 ) @ ( power_power_nat @ SV424 @ SV968 ) )
= $true )
| ( ( ord_less_nat @ SV768 @ SV968 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5089]) ).
thf(5587,plain,
! [SV769: nat,SV425: nat,SV969: real] :
( ( ( ~ ( ord_less_real @ ( power_power_real @ SV969 @ SV425 ) @ ( power_power_real @ SV969 @ SV769 ) ) )
= $true )
| ( ( ord_less_nat @ SV425 @ SV769 )
= $true )
| ( ( ord_less_real @ one_one_real @ SV969 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5090]) ).
thf(5588,plain,
! [SV770: nat,SV426: nat,SV970: nat] :
( ( ( ~ ( ord_less_nat @ ( power_power_nat @ SV970 @ SV426 ) @ ( power_power_nat @ SV970 @ SV770 ) ) )
= $true )
| ( ( ord_less_nat @ SV426 @ SV770 )
= $true )
| ( ( ord_less_nat @ one_one_nat @ SV970 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5091]) ).
thf(5589,plain,
! [SV971: nat,SV771: nat,SV427: real] :
( ( ( ~ ( ord_less_eq_real @ one_one_real @ SV427 ) )
= $true )
| ( ( ord_less_eq_real @ ( power_power_real @ SV427 @ SV771 ) @ ( power_power_real @ SV427 @ SV971 ) )
= $true )
| ( ( ord_less_eq_nat @ SV771 @ SV971 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5092]) ).
thf(5590,plain,
! [SV972: nat,SV772: nat,SV428: nat] :
( ( ( ~ ( ord_less_eq_nat @ one_one_nat @ SV428 ) )
= $true )
| ( ( ord_less_eq_nat @ ( power_power_nat @ SV428 @ SV772 ) @ ( power_power_nat @ SV428 @ SV972 ) )
= $true )
| ( ( ord_less_eq_nat @ SV772 @ SV972 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5093]) ).
thf(5591,plain,
! [SV429: nat,SV773: real] :
( ( ( ord_less_real @ SV773 @ one_one_real )
= $false )
| ( ( ord_less_real @ ( times_times_real @ SV773 @ ( power_power_real @ SV773 @ SV429 ) ) @ ( power_power_real @ SV773 @ SV429 ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV773 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5094]) ).
thf(5592,plain,
! [SV430: nat,SV774: nat] :
( ( ( ord_less_nat @ SV774 @ one_one_nat )
= $false )
| ( ( ord_less_nat @ ( times_times_nat @ SV774 @ ( power_power_nat @ SV774 @ SV430 ) ) @ ( power_power_nat @ SV774 @ SV430 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV774 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5095]) ).
thf(5593,plain,
! [SV435: nat,SV976: nat,SV779: nat] :
( ( ( ~ ( dvd_dvd_nat @ SV779 @ ( plus_plus_nat @ SV976 @ SV435 ) ) )
= $true )
| ( ( dvd_dvd_nat @ SV779 @ SV435 )
= $true )
| ( ( dvd_dvd_nat @ SV779 @ SV976 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5100]) ).
thf(5594,plain,
! [SV977: nat,SV436: nat,SV780: nat] :
( ( ( SV780 = zero_zero_nat )
= $true )
| ( ( dvd_dvd_nat @ SV436 @ SV977 )
= $true )
| ( ( dvd_dvd_nat @ ( power_power_nat @ SV436 @ SV780 ) @ ( power_power_nat @ SV977 @ SV780 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5101]) ).
thf(5595,plain,
! [SV781: nat,SV978: nat,SV437: nat] :
( ( ( dvd_dvd_nat @ ( power_power_nat @ SV437 @ SV978 ) @ SV781 )
= $false )
| ( ( dvd_dvd_nat @ SV437 @ SV781 )
= $true )
| ( ( SV978 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5102]) ).
thf(5596,plain,
! [SV1027: nat,SV979: nat,SV782: nat,SV438: nat] :
( ( ( SV438
= ( plus_plus_nat @ ( times_times_nat @ SV782 @ SV979 ) @ SV1027 ) )
= $false )
| ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV1027 )
| ~ ( ord_less_nat @ SV1027 @ SV979 )
| ~ ( dvd_dvd_nat @ SV979 @ SV438 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5103]) ).
thf(5597,plain,
! [SV980: nat,SV783: nat,SV439: nat] :
( ( ( ~ ( ord_less_nat @ one_one_nat @ SV439 ) )
= $true )
| ( ( ord_less_eq_nat @ SV783 @ SV980 )
= $true )
| ( ( dvd_dvd_nat @ ( power_power_nat @ SV439 @ SV783 ) @ ( power_power_nat @ SV439 @ SV980 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5104]) ).
thf(5598,plain,
! [SV440: nat,SV784: nat] :
( ( ( SV784 = zero_zero_nat )
= $true )
| ( ( SV784 = SV440 )
= $true )
| ( ( ord_less_eq_nat @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV440 ) @ SV784 )
= $true )
| ( ( dvd_dvd_nat @ SV440 @ SV784 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5105]) ).
thf(5599,plain,
! [SV1028: real] :
( ( ( ( power_power_real @ SV1028 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_real )
= $false )
| ( ( SV1028 = zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5106]) ).
thf(5600,plain,
! [SV1029: real] :
( ( ( SV1029 = zero_zero_real )
= $false )
| ( ( ( power_power_real @ SV1029 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5107]) ).
thf(5601,plain,
! [SV1030: nat,SV1291: nat] :
( ( ( ( SV1291 = zero_zero_nat )
| ( SV1030 != zero_zero_nat ) )
= $true )
| ( ( ( power_power_nat @ SV1030 @ SV1291 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5108]) ).
thf(5602,plain,
( ( ! [SX0: nat,SX1: nat] :
( ( ( power_power_nat @ SX0 @ SX1 )
!= zero_zero_nat )
| ( SX1 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5109]) ).
thf(5603,plain,
( ( ! [SX0: nat] :
( ! [SX1: nat] :
( ( power_power_nat @ SX0 @ SX1 )
!= zero_zero_nat )
| ( SX0 = zero_zero_nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5110]) ).
thf(5604,plain,
! [SV1031: nat,SV1292: int] :
( ( ( ( ( number_number_of_nat @ SV1292 )
= zero_zero_nat )
| ( SV1031 != zero_zero_nat ) )
= $true )
| ( ( ( power_power_nat @ SV1031 @ ( number_number_of_nat @ SV1292 ) )
= zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5111]) ).
thf(5605,plain,
( ( ! [SX0: nat,SX1: int] :
( ( ( power_power_nat @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_nat )
| ( ( number_number_of_nat @ SX1 )
!= zero_zero_nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5112]) ).
thf(5606,plain,
( ( ! [SX0: nat] :
( ! [SX1: int] :
( ( power_power_nat @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_nat )
| ( SX0 = zero_zero_nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5113]) ).
thf(5607,plain,
! [SV1032: int] :
( ( ( ord_less_eq_int @ min @ ( bit0 @ SV1032 ) )
= $false )
| ( ( ord_less_int @ min @ SV1032 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5114]) ).
thf(5608,plain,
! [SV1033: int] :
( ( ( ord_less_int @ min @ SV1033 )
= $false )
| ( ( ord_less_eq_int @ min @ ( bit0 @ SV1033 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5115]) ).
thf(5609,plain,
! [SV1293: real,SV1034: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ SV1034 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SV1293 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true )
| ( ( ( SV1034 != zero_zero_real )
| ( SV1293 != zero_zero_real ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5116]) ).
thf(5610,plain,
( ( ! [SX0: real] :
( ( SX0 = zero_zero_real )
| ! [SX1: real] : ( ord_less_real @ 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 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5117]) ).
thf(5611,plain,
( ( ! [SX0: real,SX1: real] :
( ( SX1 = zero_zero_real )
| ( ord_less_real @ 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 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5118]) ).
thf(5612,plain,
! [SV1035: int] :
( ( ( ord_less_eq_int @ pls @ SV1035 )
= $false )
| ( ( ord_less_eq_real @ zero_zero_real @ ( number267125858f_real @ SV1035 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5119]) ).
thf(5613,plain,
! [SV1036: int] :
( ( ( ord_less_eq_real @ zero_zero_real @ ( number267125858f_real @ SV1036 ) )
= $false )
| ( ( ord_less_eq_int @ pls @ SV1036 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5120]) ).
thf(5614,plain,
! [SV1037: int] :
( ( ( ord_less_eq_int @ pls @ SV1037 )
= $false )
| ( ( ord_less_int @ pls @ ( bit1 @ SV1037 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5121]) ).
thf(5615,plain,
! [SV1038: int] :
( ( ( ord_less_int @ pls @ ( bit1 @ SV1038 ) )
= $false )
| ( ( ord_less_eq_int @ pls @ SV1038 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5122]) ).
thf(5616,plain,
! [SV1294: int,SV1039: int] :
( ( ( ~ ( ord_less_eq_int @ SV1039 @ SV1294 ) )
= $true )
| ( ( ord_less_int @ ( bit0 @ SV1039 ) @ ( bit1 @ SV1294 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5123]) ).
thf(5617,plain,
! [SV1295: int,SV1040: int] :
( ( ( ~ ( ord_less_int @ ( bit0 @ SV1040 ) @ ( bit1 @ SV1295 ) ) )
= $true )
| ( ( ord_less_eq_int @ SV1040 @ SV1295 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5124]) ).
thf(5618,plain,
! [SV1041: int] :
( ( ( ord_less_int @ min @ ( bit1 @ SV1041 ) )
= $false )
| ( ( ord_less_int @ min @ SV1041 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5125]) ).
thf(5619,plain,
! [SV1042: int] :
( ( ( ord_less_int @ min @ SV1042 )
= $false )
| ( ( ord_less_int @ min @ ( bit1 @ SV1042 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5126]) ).
thf(5620,plain,
! [SV1296: int,SV1043: int] :
( ( ( ~ ( ord_less_int @ ( bit1 @ SV1043 ) @ ( bit1 @ SV1296 ) ) )
= $true )
| ( ( ord_less_int @ SV1043 @ SV1296 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5127]) ).
thf(5621,plain,
! [SV1297: int,SV1044: int] :
( ( ( ~ ( ord_less_int @ SV1044 @ SV1297 ) )
= $true )
| ( ( ord_less_int @ ( bit1 @ SV1044 ) @ ( bit1 @ SV1297 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5128]) ).
thf(5622,plain,
! [SV1298: nat,SV1045: nat] :
( ( ( ( power_power_nat @ SV1045 @ SV1298 )
!= one_one_nat )
= $true )
| ( ( ( SV1045 = one_one_nat )
| ( SV1298 = zero_zero_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5129]) ).
thf(5623,plain,
( ( ! [SX0: nat] :
( ( SX0 != one_one_nat )
| ! [SX1: nat] :
( ( power_power_nat @ SX0 @ SX1 )
= one_one_nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5130]) ).
thf(5624,plain,
( ( ! [SX0: nat,SX1: nat] :
( ( SX1 != zero_zero_nat )
| ( ( power_power_nat @ SX0 @ SX1 )
= one_one_nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5131]) ).
thf(5625,plain,
! [SV1299: int,SV1046: int] :
( ( ( ~ ( ord_less_eq_int @ SV1046 @ SV1299 ) )
= $true )
| ( ( ord_less_eq_real @ ( number267125858f_real @ SV1046 ) @ ( number267125858f_real @ SV1299 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5132]) ).
thf(5626,plain,
! [SV1300: int,SV1047: int] :
( ( ( ~ ( ord_less_eq_real @ ( number267125858f_real @ SV1047 ) @ ( number267125858f_real @ SV1300 ) ) )
= $true )
| ( ( ord_less_eq_int @ SV1047 @ SV1300 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5133]) ).
thf(5627,plain,
! [SV1048: nat] :
( ( ( SV1048 = zero_zero_nat )
= $false )
| ( ( ( power_power_real @ zero_zero_real @ SV1048 )
= one_one_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5134]) ).
thf(5628,plain,
! [SV1301: int,SV1050: int] :
( ( ( ( bit1 @ SV1050 )
!= ( bit1 @ SV1301 ) )
= $true )
| ( ( SV1050 = SV1301 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5136]) ).
thf(5629,plain,
! [SV1302: int,SV1051: int] :
( ( ( SV1051 != SV1302 )
= $true )
| ( ( ( bit1 @ SV1051 )
= ( bit1 @ SV1302 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5137]) ).
thf(5630,plain,
! [SV1303: int,SV1052: int] :
( ( ( ~ ( ord_less_int @ ( number_number_of_int @ SV1052 ) @ ( number_number_of_int @ SV1303 ) ) )
= $true )
| ( ( ord_less_int @ SV1052 @ SV1303 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5138]) ).
thf(5631,plain,
! [SV1304: int,SV1053: int] :
( ( ( ~ ( ord_less_int @ SV1053 @ SV1304 ) )
= $true )
| ( ( ord_less_int @ ( number_number_of_int @ SV1053 ) @ ( number_number_of_int @ SV1304 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5139]) ).
thf(5632,plain,
! [SV1305: real,SV1054: real] :
( ( ( ( SV1054 != zero_zero_real )
| ( SV1305 != zero_zero_real ) )
= $true )
| ( ( ord_less_eq_real @ ( plus_plus_real @ ( power_power_real @ SV1054 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SV1305 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5140]) ).
thf(5633,plain,
( ( ! [SX0: real] :
( ! [SX1: real] :
~ ( ord_less_eq_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 )
| ( SX0 = zero_zero_real ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5141]) ).
thf(5634,plain,
( ( ! [SX0: real,SX1: real] :
( ~ ( ord_less_eq_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 )
| ( SX1 = zero_zero_real ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5142]) ).
thf(5635,plain,
! [SV1306: int,SV1055: int] :
( ( ( ~ ( ord_less_int @ SV1055 @ ( plus_plus_int @ SV1306 @ one_one_int ) ) )
= $true )
| ( ( ( SV1055 = SV1306 )
| ( ord_less_int @ SV1055 @ SV1306 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5143]) ).
thf(5636,plain,
( ( ! [SX0: int,SX1: int] :
( ( SX0 != SX1 )
| ( ord_less_int @ SX0 @ ( plus_plus_int @ SX1 @ one_one_int ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5144]) ).
thf(5637,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ SX0 @ ( plus_plus_int @ SX1 @ one_one_int ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5145]) ).
thf(5638,plain,
! [SV1056: int] :
( ( ( ord_less_eq_int @ min @ ( bit1 @ SV1056 ) )
= $false )
| ( ( ord_less_eq_int @ min @ SV1056 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5146]) ).
thf(5639,plain,
! [SV1057: int] :
( ( ( ord_less_eq_int @ min @ SV1057 )
= $false )
| ( ( ord_less_eq_int @ min @ ( bit1 @ SV1057 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5147]) ).
thf(5640,plain,
! [SV1058: int] :
( ( ( ( number_number_of_nat @ SV1058 )
= zero_zero_nat )
= $false )
| ( ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ SV1058 ) )
= one_one_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5148]) ).
thf(5641,plain,
! [SV785: nat,SV441: nat] :
( ( ~ ! [SY2273: nat,SY2274: nat] :
( ( ( plus_plus_nat @ ( times_times_nat @ SY2273 @ SV441 ) @ ( times_times_nat @ SY2274 @ SV785 ) )
= ( plus_plus_nat @ ( times_times_nat @ SY2273 @ SV785 ) @ ( times_times_nat @ SY2274 @ SV441 ) ) )
| ( SY2273 != SY2274 ) )
| ~ ( ! [SY2275: nat,SY2276: nat] :
( ( plus_plus_nat @ ( times_times_nat @ SY2275 @ SV441 ) @ ( times_times_nat @ SY2276 @ SV785 ) )
= ( plus_plus_nat @ ( times_times_nat @ SY2275 @ SV785 ) @ ( times_times_nat @ SY2276 @ SV441 ) ) )
| ( SV441 != SV785 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5150]) ).
thf(5642,plain,
! [SV785: nat,SV441: nat,SV1461: nat] :
( ( ! [SY2588: nat] :
( ( SV1461 = SY2588 )
| ( SV441 = SV785 )
| ( ( plus_plus_nat @ ( times_times_nat @ SV1461 @ SV441 ) @ ( times_times_nat @ SY2588 @ SV785 ) )
!= ( plus_plus_nat @ ( times_times_nat @ SV1461 @ SV785 ) @ ( times_times_nat @ SY2588 @ SV441 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5151]) ).
thf(5643,plain,
! [SV1307: int,SV1060: int] :
( ( ( ~ ( ord_less_eq_int @ ( bit1 @ SV1060 ) @ ( bit1 @ SV1307 ) ) )
= $true )
| ( ( ord_less_eq_int @ SV1060 @ SV1307 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5152]) ).
thf(5644,plain,
! [SV1308: int,SV1061: int] :
( ( ( ~ ( ord_less_eq_int @ SV1061 @ SV1308 ) )
= $true )
| ( ( ord_less_eq_int @ ( bit1 @ SV1061 ) @ ( bit1 @ SV1308 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5153]) ).
thf(5645,plain,
! [SV1309: int,SV1062: int] :
( ( ( ~ ( ord_less_int @ ( bit0 @ SV1062 ) @ ( bit0 @ SV1309 ) ) )
= $true )
| ( ( ord_less_int @ SV1062 @ SV1309 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5154]) ).
thf(5646,plain,
! [SV1310: int,SV1063: int] :
( ( ( ~ ( ord_less_int @ SV1063 @ SV1310 ) )
= $true )
| ( ( ord_less_int @ ( bit0 @ SV1063 ) @ ( bit0 @ SV1310 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5155]) ).
thf(5647,plain,
! [SV1064: real,SV1311: int] :
( ( ( ( ( number_number_of_nat @ SV1311 )
= zero_zero_nat )
| ( SV1064 != zero_zero_real ) )
= $true )
| ( ( ( power_power_real @ SV1064 @ ( number_number_of_nat @ SV1311 ) )
= zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5156]) ).
thf(5648,plain,
( ( ! [SX0: real,SX1: int] :
( ( ( power_power_real @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_real )
| ( ( number_number_of_nat @ SX1 )
!= zero_zero_nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5157]) ).
thf(5649,plain,
( ( ! [SX0: real] :
( ! [SX1: int] :
( ( power_power_real @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_real )
| ( SX0 = zero_zero_real ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5158]) ).
thf(5650,plain,
! [SV1312: real,SV1065: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ SV1065 @ SV1065 ) @ ( times_times_real @ SV1312 @ SV1312 ) ) ) )
= $true )
| ( ( ( SV1065 != zero_zero_real )
| ( SV1312 != zero_zero_real ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5159]) ).
thf(5651,plain,
( ( ! [SX0: real] :
( ( SX0 = zero_zero_real )
| ! [SX1: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ SX0 @ SX0 ) @ ( times_times_real @ SX1 @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5160]) ).
thf(5652,plain,
( ( ! [SX0: real,SX1: real] :
( ( SX1 = zero_zero_real )
| ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ SX0 @ SX0 ) @ ( times_times_real @ SX1 @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5161]) ).
thf(5653,plain,
! [SV1313: nat,SV1066: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV1066 @ SV1313 ) ) )
= $true )
| ( ( ( SV1313 = zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV1066 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5162]) ).
thf(5654,plain,
( ( ! [SX0: nat,SX1: nat] :
( ( SX1 != zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5163]) ).
thf(5655,plain,
( ( ! [SX0: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SX0 )
| ! [SX1: nat] : ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5164]) ).
thf(5656,plain,
! [SV786: real,SV442: real] :
( ( ~ ! [SY2279: real,SY2280: real] :
( ( ( plus_plus_real @ ( times_times_real @ SY2279 @ SV442 ) @ ( times_times_real @ SY2280 @ SV786 ) )
= ( plus_plus_real @ ( times_times_real @ SY2279 @ SV786 ) @ ( times_times_real @ SY2280 @ SV442 ) ) )
| ( SY2279 != SY2280 ) )
| ~ ( ! [SY2281: real,SY2282: real] :
( ( plus_plus_real @ ( times_times_real @ SY2281 @ SV442 ) @ ( times_times_real @ SY2282 @ SV786 ) )
= ( plus_plus_real @ ( times_times_real @ SY2281 @ SV786 ) @ ( times_times_real @ SY2282 @ SV442 ) ) )
| ( SV442 != SV786 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5165]) ).
thf(5657,plain,
! [SV786: real,SV442: real,SV1462: real] :
( ( ! [SY2589: real] :
( ( SV1462 = SY2589 )
| ( SV442 = SV786 )
| ( ( plus_plus_real @ ( times_times_real @ SV1462 @ SV442 ) @ ( times_times_real @ SY2589 @ SV786 ) )
!= ( plus_plus_real @ ( times_times_real @ SV1462 @ SV786 ) @ ( times_times_real @ SY2589 @ SV442 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5166]) ).
thf(5658,plain,
! [SV1067: int] :
( ( ( ord_less_eq_int @ ( bit0 @ SV1067 ) @ pls )
= $false )
| ( ( ord_less_eq_int @ SV1067 @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5167]) ).
thf(5659,plain,
! [SV1068: int] :
( ( ( ord_less_eq_int @ SV1068 @ pls )
= $false )
| ( ( ord_less_eq_int @ ( bit0 @ SV1068 ) @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5168]) ).
thf(5660,plain,
! [SV1069: int] :
( ( ( ( bit1 @ SV1069 )
= min )
= $false )
| ( ( SV1069 = min )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5169]) ).
thf(5661,plain,
! [SV1070: int] :
( ( ( SV1070 = min )
= $false )
| ( ( ( bit1 @ SV1070 )
= min )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5170]) ).
thf(5662,plain,
! [SV1314: real,SV1071: real] :
( ( ( ~ ( ord_less_eq_real @ SV1071 @ SV1314 ) )
= $true )
| ( ( ( SV1071 = SV1314 )
| ( ord_less_real @ SV1071 @ SV1314 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5171]) ).
thf(5663,plain,
( ( ! [SX0: real,SX1: real] :
( ( SX0 != SX1 )
| ( ord_less_eq_real @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5172]) ).
thf(5664,plain,
( ( ! [SX0: real,SX1: real] :
( ~ ( ord_less_real @ SX0 @ SX1 )
| ( ord_less_eq_real @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5173]) ).
thf(5665,plain,
! [SV1072: real] :
( ( ( ( plus_plus_real @ SV1072 @ SV1072 )
= zero_zero_real )
= $false )
| ( ( SV1072 = zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5174]) ).
thf(5666,plain,
! [SV1073: real] :
( ( ( SV1073 = zero_zero_real )
= $false )
| ( ( ( plus_plus_real @ SV1073 @ SV1073 )
= zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5175]) ).
thf(5667,plain,
! [SV1315: int,SV1074: int] :
( ( ( ~ ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ SV1074 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV1315 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true )
| ( ( ( SV1074 != zero_zero_int )
| ( SV1315 != zero_zero_int ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5176]) ).
thf(5668,plain,
( ( ! [SX0: int] :
( ( SX0 = zero_zero_int )
| ! [SX1: int] : ( ord_less_int @ zero_zero_int @ ( 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 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5177]) ).
thf(5669,plain,
( ( ! [SX0: int,SX1: int] :
( ( SX1 = zero_zero_int )
| ( ord_less_int @ zero_zero_int @ ( 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 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5178]) ).
thf(5670,plain,
! [SV1075: int] :
( ( ( ord_less_int @ pls @ SV1075 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ SV1075 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5179]) ).
thf(5671,plain,
! [SV1076: int] :
( ( ( ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ SV1076 ) )
= $false )
| ( ( ord_less_int @ pls @ SV1076 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5180]) ).
thf(5672,plain,
! [SV1316: int,SV1077: int] :
( ( ( ~ ( ord_less_eq_int @ ( number_number_of_int @ SV1077 ) @ ( number_number_of_int @ SV1316 ) ) )
= $true )
| ( ( ord_less_eq_int @ SV1077 @ SV1316 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5181]) ).
thf(5673,plain,
! [SV1317: int,SV1078: int] :
( ( ( ~ ( ord_less_eq_int @ SV1078 @ SV1317 ) )
= $true )
| ( ( ord_less_eq_int @ ( number_number_of_int @ SV1078 ) @ ( number_number_of_int @ SV1317 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5182]) ).
thf(5674,plain,
! [SV1318: real,SV1079: real] :
( ( ( ( SV1079 != zero_zero_real )
| ( SV1318 != zero_zero_real ) )
= $true )
| ( ( ( plus_plus_real @ ( power_power_real @ SV1079 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SV1318 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5183]) ).
thf(5675,plain,
( ( ! [SX0: real] :
( ! [SX1: 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 )
| ( SX0 = zero_zero_real ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5184]) ).
thf(5676,plain,
( ( ! [SX0: real,SX1: 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 )
| ( SX1 = zero_zero_real ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5185]) ).
thf(5677,plain,
! [SV1080: int,SV1319: nat] :
( ( ( SV1319 != zero_zero_nat )
= $true )
| ( ( ( power_power_int @ SV1080 @ SV1319 )
= one_one_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5186]) ).
thf(5678,plain,
! [SV1081: int,SV1320: nat] :
( ( ( SV1320 = zero_zero_nat )
= $true )
| ( ( ( power_power_int @ SV1081 @ SV1320 )
= ( times_times_int @ SV1081 @ ( power_power_int @ SV1081 @ ( minus_minus_nat @ SV1320 @ one_one_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5187]) ).
thf(5679,plain,
! [SV1082: int] :
( ( ( ( number_number_of_nat @ SV1082 )
= zero_zero_nat )
= $false )
| ( ( ord_less_eq_int @ SV1082 @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5188]) ).
thf(5680,plain,
! [SV1083: int] :
( ( ( ord_less_eq_int @ SV1083 @ pls )
= $false )
| ( ( ( number_number_of_nat @ SV1083 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5189]) ).
thf(5681,plain,
! [SV1084: int,SV1321: int] :
( ( ( ~ ( dvd_dvd_int @ SV1321 @ SV1084 ) )
= $true )
| ( ( zcong @ SV1084 @ zero_zero_int @ SV1321 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5190]) ).
thf(5682,plain,
! [SV1322: int,SV1085: int] :
( ( ( ~ ( zcong @ SV1085 @ zero_zero_int @ SV1322 ) )
= $true )
| ( ( dvd_dvd_int @ SV1322 @ SV1085 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5191]) ).
thf(5683,plain,
! [SV1086: nat,SV1323: nat] :
( ( ( SV1323 != zero_zero_nat )
= $true )
| ( ( ( power_power_nat @ SV1086 @ SV1323 )
= one_one_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5192]) ).
thf(5684,plain,
! [SV1087: nat,SV1324: nat] :
( ( ( SV1324 = zero_zero_nat )
= $true )
| ( ( ( power_power_nat @ SV1087 @ SV1324 )
= ( times_times_nat @ SV1087 @ ( power_power_nat @ SV1087 @ ( minus_minus_nat @ SV1324 @ one_one_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5193]) ).
thf(5685,plain,
! [SV1088: int] :
( ( ( ord_less_int @ ( bit1 @ SV1088 ) @ min )
= $false )
| ( ( ord_less_int @ SV1088 @ min )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5194]) ).
thf(5686,plain,
! [SV1089: int] :
( ( ( ord_less_int @ SV1089 @ min )
= $false )
| ( ( ord_less_int @ ( bit1 @ SV1089 ) @ min )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5195]) ).
thf(5687,plain,
! [SV1325: nat,SV443: nat,SV1463: int] :
( ( ~ ( ord_less_int @ one_one_int @ SV1463 )
| ~ ( ord_less_int @ ( power_power_int @ SV1463 @ SV443 ) @ ( power_power_int @ SV1463 @ SV1325 ) )
| ( ord_less_nat @ SV443 @ SV1325 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5196]) ).
thf(5688,plain,
! [SV1326: nat,SV443: nat,SV1464: int] :
( ( ~ ( ord_less_int @ one_one_int @ SV1464 )
| ~ ( ord_less_nat @ SV443 @ SV1326 )
| ( ord_less_int @ ( power_power_int @ SV1464 @ SV443 ) @ ( power_power_int @ SV1464 @ SV1326 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5197]) ).
thf(5689,plain,
! [SV1090: int] :
( ( ( ord_less_int @ ( bit1 @ SV1090 ) @ zero_zero_int )
= $false )
| ( ( ord_less_int @ SV1090 @ zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5198]) ).
thf(5690,plain,
! [SV1091: int] :
( ( ( ord_less_int @ SV1091 @ zero_zero_int )
= $false )
| ( ( ord_less_int @ ( bit1 @ SV1091 ) @ zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5199]) ).
thf(5691,plain,
! [SV1092: int] :
( ( ( ord_less_eq_int @ SV1092 @ pls )
= $false )
| ( ( ord_less_eq_real @ ( number267125858f_real @ SV1092 ) @ zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5200]) ).
thf(5692,plain,
! [SV1093: int] :
( ( ( ord_less_eq_real @ ( number267125858f_real @ SV1093 ) @ zero_zero_real )
= $false )
| ( ( ord_less_eq_int @ SV1093 @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5201]) ).
thf(5693,plain,
! [SV1094: int] :
( ( ( ord_less_int @ min @ ( bit0 @ SV1094 ) )
= $false )
| ( ( ord_less_int @ min @ SV1094 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5202]) ).
thf(5694,plain,
! [SV1095: int] :
( ( ( ord_less_int @ min @ SV1095 )
= $false )
| ( ( ord_less_int @ min @ ( bit0 @ SV1095 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5203]) ).
thf(5695,plain,
! [SV1327: int,SV1096: int] :
( ( ( ~ ( ord_less_eq_int @ ( number_number_of_int @ SV1096 ) @ ( number_number_of_int @ SV1327 ) ) )
= $true )
| ( ( ord_less_eq_int @ SV1096 @ SV1327 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5204]) ).
thf(5696,plain,
! [SV1328: int,SV1097: int] :
( ( ( ~ ( ord_less_eq_int @ SV1097 @ SV1328 ) )
= $true )
| ( ( ord_less_eq_int @ ( number_number_of_int @ SV1097 ) @ ( number_number_of_int @ SV1328 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5205]) ).
thf(5697,plain,
! [SV1329: int,SV444: int] :
( ( ( ! [SY2554: int] :
~ ( dvd_dvd_int @ SV444 @ ( plus_plus_int @ SV1329 @ ( times_times_int @ SV444 @ SY2554 ) ) ) )
= $true )
| ( ( dvd_dvd_int @ SV444 @ SV1329 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5206]) ).
thf(5698,plain,
! [SV1330: int,SV444: int] :
( ( ( ~ ( dvd_dvd_int @ SV444 @ SV1330 ) )
= $true )
| ( ( ! [SY2555: int] : ( dvd_dvd_int @ SV444 @ ( plus_plus_int @ SV1330 @ ( times_times_int @ SV444 @ SY2555 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5207]) ).
thf(5699,plain,
! [SV1331: int,SV1098: int] :
( ( ( ~ ( ord_less_eq_int @ SV1098 @ ( minus_minus_int @ SV1331 @ one_one_int ) ) )
= $true )
| ( ( ord_less_int @ SV1098 @ SV1331 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5208]) ).
thf(5700,plain,
! [SV1332: int,SV1099: int] :
( ( ( ~ ( ord_less_int @ SV1099 @ SV1332 ) )
= $true )
| ( ( ord_less_eq_int @ SV1099 @ ( minus_minus_int @ SV1332 @ one_one_int ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5209]) ).
thf(5701,plain,
! [SV1333: int,SV1100: int] :
( ( ( ~ ( ord_less_eq_int @ ( bit0 @ SV1100 ) @ ( bit0 @ SV1333 ) ) )
= $true )
| ( ( ord_less_eq_int @ SV1100 @ SV1333 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5210]) ).
thf(5702,plain,
! [SV1334: int,SV1101: int] :
( ( ( ~ ( ord_less_eq_int @ SV1101 @ SV1334 ) )
= $true )
| ( ( ord_less_eq_int @ ( bit0 @ SV1101 ) @ ( bit0 @ SV1334 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5211]) ).
thf(5703,plain,
! [SV1102: int,SV1335: int] :
( ( ( ( ( number_number_of_nat @ SV1335 )
= zero_zero_nat )
| ( SV1102 != zero_zero_int ) )
= $true )
| ( ( ( power_power_int @ SV1102 @ ( number_number_of_nat @ SV1335 ) )
= zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5212]) ).
thf(5704,plain,
( ( ! [SX0: int,SX1: int] :
( ( ( power_power_int @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_int )
| ( ( number_number_of_nat @ SX1 )
!= zero_zero_nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5213]) ).
thf(5705,plain,
( ( ! [SX0: int] :
( ! [SX1: int] :
( ( power_power_int @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5214]) ).
thf(5706,plain,
! [SV1336: int,SV1103: int] :
( ( ( ~ ( ord_less_eq_real @ ( number267125858f_real @ SV1103 ) @ ( number267125858f_real @ SV1336 ) ) )
= $true )
| ( ( ~ ( ord_less_real @ ( number267125858f_real @ SV1336 ) @ ( number267125858f_real @ SV1103 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5215]) ).
thf(5707,plain,
! [SV1104: int,SV1337: int] :
( ( ( ord_less_real @ ( number267125858f_real @ SV1337 ) @ ( number267125858f_real @ SV1104 ) )
= $true )
| ( ( ord_less_eq_real @ ( number267125858f_real @ SV1104 ) @ ( number267125858f_real @ SV1337 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5216]) ).
thf(5708,plain,
! [SV1338: int,SV1105: int] :
( ( ( ~ ( ord_less_int @ SV1105 @ SV1338 ) )
= $true )
| ( ( ord_less_int @ ( minus_minus_int @ SV1105 @ SV1338 ) @ zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5217]) ).
thf(5709,plain,
! [SV1339: int,SV1106: int] :
( ( ( ~ ( ord_less_int @ ( minus_minus_int @ SV1106 @ SV1339 ) @ zero_zero_int ) )
= $true )
| ( ( ord_less_int @ SV1106 @ SV1339 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5218]) ).
thf(5710,plain,
! [SV1340: int,SV1107: int] :
( ( ( ~ ( zcong @ ( times_times_int @ SV1107 @ ( minus_minus_int @ SV1340 @ one_one_int ) ) @ one_one_int @ SV1340 ) )
= $true )
| ( ( zcong @ SV1107 @ ( minus_minus_int @ SV1340 @ one_one_int ) @ SV1340 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5219]) ).
thf(5711,plain,
! [SV1341: int,SV1108: int] :
( ( ( ~ ( zcong @ SV1108 @ ( minus_minus_int @ SV1341 @ one_one_int ) @ SV1341 ) )
= $true )
| ( ( zcong @ ( times_times_int @ SV1108 @ ( minus_minus_int @ SV1341 @ one_one_int ) ) @ one_one_int @ SV1341 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5220]) ).
thf(5712,plain,
! [SV1109: int] :
( ( ( ord_less_int @ ( bit0 @ SV1109 ) @ pls )
= $false )
| ( ( ord_less_int @ SV1109 @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5221]) ).
thf(5713,plain,
! [SV1110: int] :
( ( ( ord_less_int @ SV1110 @ pls )
= $false )
| ( ( ord_less_int @ ( bit0 @ SV1110 ) @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5222]) ).
thf(5714,plain,
! [SV1111: nat,SV1342: nat] :
( ( ( SV1342 != zero_zero_nat )
= $true )
| ( ( ( times_times_nat @ SV1342 @ SV1111 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5223]) ).
thf(5715,plain,
! [SV1112: nat,SV1343: nat] :
( ( ( SV1343 = zero_zero_nat )
= $true )
| ( ( ( times_times_nat @ SV1343 @ SV1112 )
= ( plus_plus_nat @ SV1112 @ ( times_times_nat @ ( minus_minus_nat @ SV1343 @ one_one_nat ) @ SV1112 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5224]) ).
thf(5716,plain,
! [SV1344: real,SV1113: real] :
( ( ( ( SV1113 != zero_zero_real )
| ( SV1344 != zero_zero_real ) )
= $true )
| ( ( ( plus_plus_real @ ( power_power_real @ SV1113 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SV1344 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5225]) ).
thf(5717,plain,
( ( ! [SX0: real] :
( ! [SX1: 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 )
| ( SX0 = zero_zero_real ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5226]) ).
thf(5718,plain,
( ( ! [SX0: real,SX1: 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 )
| ( SX1 = zero_zero_real ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5227]) ).
thf(5719,plain,
! [SV1345: int,SV1114: int] :
( ( ( ( SV1114 != zero_zero_int )
| ( SV1345 != zero_zero_int ) )
= $true )
| ( ( ( plus_plus_int @ ( power_power_int @ SV1114 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV1345 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5228]) ).
thf(5720,plain,
( ( ! [SX0: int] :
( ! [SX1: int] :
( ( 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 ) ) ) ) )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5229]) ).
thf(5721,plain,
( ( ! [SX0: int,SX1: int] :
( ( ( 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 ) ) ) ) )
!= zero_zero_int )
| ( SX1 = zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5230]) ).
thf(5722,plain,
! [SV1115: int,SV1346: int] :
( ( ( ~ ( dvd_dvd_int @ SV1346 @ SV1115 ) )
= $true )
| ( ( zcong @ SV1115 @ zero_zero_int @ SV1346 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5231]) ).
thf(5723,plain,
! [SV1347: int,SV1116: int] :
( ( ( ~ ( zcong @ SV1116 @ zero_zero_int @ SV1347 ) )
= $true )
| ( ( dvd_dvd_int @ SV1347 @ SV1116 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5232]) ).
thf(5724,plain,
! [SV1348: int,SV1117: int] :
( ( ( ~ ( ord_less_eq_int @ ( bit0 @ SV1117 ) @ ( bit1 @ SV1348 ) ) )
= $true )
| ( ( ord_less_eq_int @ SV1117 @ SV1348 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5233]) ).
thf(5725,plain,
! [SV1349: int,SV1118: int] :
( ( ( ~ ( ord_less_eq_int @ SV1118 @ SV1349 ) )
= $true )
| ( ( ord_less_eq_int @ ( bit0 @ SV1118 ) @ ( bit1 @ SV1349 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5234]) ).
thf(5726,plain,
! [SV1119: int] :
( ( ( ord_less_int @ ( plus_plus_int @ SV1119 @ SV1119 ) @ zero_zero_int )
= $false )
| ( ( ord_less_int @ SV1119 @ zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5235]) ).
thf(5727,plain,
! [SV1120: int] :
( ( ( ord_less_int @ SV1120 @ zero_zero_int )
= $false )
| ( ( ord_less_int @ ( plus_plus_int @ SV1120 @ SV1120 ) @ zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5236]) ).
thf(5728,plain,
! [SV1121: int] :
( ( ( ord_less_eq_int @ one_one_int @ SV1121 )
= $false )
| ( ( ord_less_int @ zero_zero_int @ SV1121 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5237]) ).
thf(5729,plain,
! [SV1122: int] :
( ( ( ord_less_int @ zero_zero_int @ SV1122 )
= $false )
| ( ( ord_less_eq_int @ one_one_int @ SV1122 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5238]) ).
thf(5730,plain,
! [SV1350: real,SV445: real,SV1465: real] :
( ( ~ ( ord_less_real @ zero_zero_real @ SV1465 )
| ~ ( ord_less_eq_real @ ( times_times_real @ SV445 @ SV1465 ) @ ( times_times_real @ SV1350 @ SV1465 ) )
| ( ord_less_eq_real @ SV445 @ SV1350 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5239]) ).
thf(5731,plain,
! [SV1351: real,SV445: real,SV1466: real] :
( ( ~ ( ord_less_real @ zero_zero_real @ SV1466 )
| ~ ( ord_less_eq_real @ SV445 @ SV1351 )
| ( ord_less_eq_real @ ( times_times_real @ SV445 @ SV1466 ) @ ( times_times_real @ SV1351 @ SV1466 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5240]) ).
thf(5732,plain,
! [SV1123: int] :
( ( ( ord_less_int @ pls @ SV1123 )
= $false )
| ( ( ord_less_real @ zero_zero_real @ ( number267125858f_real @ SV1123 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5241]) ).
thf(5733,plain,
! [SV1124: int] :
( ( ( ord_less_real @ zero_zero_real @ ( number267125858f_real @ SV1124 ) )
= $false )
| ( ( ord_less_int @ pls @ SV1124 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5242]) ).
thf(5734,plain,
! [SV1352: real,SV1125: real] :
( ( ( ( SV1125 != zero_zero_real )
| ( SV1352 != zero_zero_real ) )
= $true )
| ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ SV1125 @ SV1125 ) @ ( times_times_real @ SV1352 @ SV1352 ) ) @ zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5243]) ).
thf(5735,plain,
( ( ! [SX0: real] :
( ! [SX1: real] :
~ ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ SX0 @ SX0 ) @ ( times_times_real @ SX1 @ SX1 ) ) @ zero_zero_real )
| ( SX0 = zero_zero_real ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5244]) ).
thf(5736,plain,
( ( ! [SX0: real,SX1: real] :
( ~ ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ SX0 @ SX0 ) @ ( times_times_real @ SX1 @ SX1 ) ) @ zero_zero_real )
| ( SX1 = zero_zero_real ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5245]) ).
thf(5737,plain,
! [SV1353: int,SV1126: int] :
( ( ( ~ ( ord_less_eq_int @ ( bit1 @ SV1126 ) @ ( bit0 @ SV1353 ) ) )
= $true )
| ( ( ord_less_int @ SV1126 @ SV1353 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5246]) ).
thf(5738,plain,
! [SV1354: int,SV1127: int] :
( ( ( ~ ( ord_less_int @ SV1127 @ SV1354 ) )
= $true )
| ( ( ord_less_eq_int @ ( bit1 @ SV1127 ) @ ( bit0 @ SV1354 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5247]) ).
thf(5739,plain,
! [SV1128: int] :
( ( ( ord_less_int @ zero_zero_int @ ( number_number_of_int @ SV1128 ) )
= $false )
| ( ( ord_less_int @ pls @ SV1128 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5248]) ).
thf(5740,plain,
! [SV1129: int] :
( ( ( ord_less_int @ pls @ SV1129 )
= $false )
| ( ( ord_less_int @ zero_zero_int @ ( number_number_of_int @ SV1129 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5249]) ).
thf(5741,plain,
! [SV1355: int,SV1130: int] :
( ( ( ( SV1130 != zero_zero_int )
| ( SV1355 != zero_zero_int ) )
= $true )
| ( ( ord_less_eq_int @ ( plus_plus_int @ ( power_power_int @ SV1130 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV1355 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5250]) ).
thf(5742,plain,
( ( ! [SX0: int] :
( ! [SX1: int] :
~ ( ord_less_eq_int @ ( 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 ) ) ) ) ) @ zero_zero_int )
| ( SX0 = zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5251]) ).
thf(5743,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ ( 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 ) ) ) ) ) @ zero_zero_int )
| ( SX1 = zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5252]) ).
thf(5744,plain,
! [SV1131: int] :
( ( ( min
= ( bit1 @ SV1131 ) )
= $false )
| ( ( min = SV1131 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5253]) ).
thf(5745,plain,
! [SV1132: int] :
( ( ( min = SV1132 )
= $false )
| ( ( min
= ( bit1 @ SV1132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5254]) ).
thf(5746,plain,
! [SV1356: int,SV1133: int] :
( ( ( ( SV1133 != zero_zero_int )
| ( SV1356 != zero_zero_int ) )
= $true )
| ( ( ( plus_plus_int @ ( times_times_int @ SV1133 @ SV1133 ) @ ( times_times_int @ SV1356 @ SV1356 ) )
= zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5255]) ).
thf(5747,plain,
( ( ! [SX0: int] :
( ! [SX1: int] :
( ( plus_plus_int @ ( times_times_int @ SX0 @ SX0 ) @ ( times_times_int @ SX1 @ SX1 ) )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5256]) ).
thf(5748,plain,
( ( ! [SX0: int,SX1: int] :
( ( ( plus_plus_int @ ( times_times_int @ SX0 @ SX0 ) @ ( times_times_int @ SX1 @ SX1 ) )
!= zero_zero_int )
| ( SX1 = zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5257]) ).
thf(5749,plain,
! [SV1357: int,SV1134: int] :
( ( ( ( SV1134 = SV1357 )
| ~ ( ord_less_eq_int @ SV1134 @ SV1357 ) )
= $true )
| ( ( ord_less_int @ SV1134 @ SV1357 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5258]) ).
thf(5750,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5259]) ).
thf(5751,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5260]) ).
thf(5752,plain,
! [SV1135: int] :
( ( ( ord_less_eq_int @ ( number_number_of_int @ SV1135 ) @ zero_zero_int )
= $false )
| ( ( ord_less_eq_int @ SV1135 @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5261]) ).
thf(5753,plain,
! [SV1136: int] :
( ( ( ord_less_eq_int @ SV1136 @ pls )
= $false )
| ( ( ord_less_eq_int @ ( number_number_of_int @ SV1136 ) @ zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5262]) ).
thf(5754,plain,
! [SV1358: nat,SV446: nat,SV1467: nat] :
( ( ~ ( ord_less_nat @ one_one_nat @ SV1467 )
| ~ ( ord_less_nat @ ( power_power_nat @ SV1467 @ SV446 ) @ ( power_power_nat @ SV1467 @ SV1358 ) )
| ( ord_less_nat @ SV446 @ SV1358 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5263]) ).
thf(5755,plain,
! [SV1359: nat,SV446: nat,SV1468: nat] :
( ( ~ ( ord_less_nat @ one_one_nat @ SV1468 )
| ~ ( ord_less_nat @ SV446 @ SV1359 )
| ( ord_less_nat @ ( power_power_nat @ SV1468 @ SV446 ) @ ( power_power_nat @ SV1468 @ SV1359 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5264]) ).
thf(5756,plain,
! [SV1360: nat,SV1137: nat] :
( ( ( ( SV1137 != one_one_nat )
| ( SV1360 != one_one_nat ) )
= $true )
| ( ( ( times_times_nat @ SV1137 @ SV1360 )
= one_one_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5265]) ).
thf(5757,plain,
( ( ! [SX0: nat] :
( ! [SX1: nat] :
( ( times_times_nat @ SX0 @ SX1 )
!= one_one_nat )
| ( SX0 = one_one_nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5266]) ).
thf(5758,plain,
( ( ! [SX0: nat,SX1: nat] :
( ( ( times_times_nat @ SX0 @ SX1 )
!= one_one_nat )
| ( SX1 = one_one_nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5267]) ).
thf(5759,plain,
( ( ~ ( ~ ! [SX0: int] :
( ! [SX1: int] :
( ( times_times_int @ SX0 @ SX1 )
!= one_one_int )
| ( SX0 = one_one_int )
| ( SX0
= ( number_number_of_int @ min ) ) )
| ~ ! [SX0: int,SX1: int] :
( ( ( times_times_int @ SX0 @ SX1 )
!= one_one_int )
| ( SX0 = one_one_int )
| ( SX1
= ( number_number_of_int @ min ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5268]) ).
thf(5760,plain,
( ( ~ ( ~ ! [SX0: int,SX1: int] :
( ( ( times_times_int @ SX0 @ SX1 )
!= one_one_int )
| ( SX1 = one_one_int )
| ( SX0
= ( number_number_of_int @ min ) ) )
| ~ ! [SX0: int,SX1: int] :
( ( ( times_times_int @ SX0 @ SX1 )
!= one_one_int )
| ( SX1 = one_one_int )
| ( SX1
= ( number_number_of_int @ min ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5269]) ).
thf(5761,plain,
( ( ! [SX0: int,SX1: int] :
( ( SX0 != one_one_int )
| ( SX1 != one_one_int )
| ( ( times_times_int @ SX0 @ SX1 )
= one_one_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5270]) ).
thf(5762,plain,
( ( ! [SX0: int,SX1: int] :
( ( SX0
!= ( number_number_of_int @ min ) )
| ( SX1
!= ( number_number_of_int @ min ) )
| ( ( times_times_int @ SX0 @ SX1 )
= one_one_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5271]) ).
thf(5763,plain,
! [SV1138: int] :
( ( ( ord_less_int @ SV1138 @ ( bit1 @ pls ) )
= $false )
| ( ( ord_less_real @ ( number267125858f_real @ SV1138 ) @ one_one_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5272]) ).
thf(5764,plain,
! [SV1139: int] :
( ( ( ord_less_real @ ( number267125858f_real @ SV1139 ) @ one_one_real )
= $false )
| ( ( ord_less_int @ SV1139 @ ( bit1 @ pls ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5273]) ).
thf(5765,plain,
! [SV1361: int,SV1140: int] :
( ( ( ( number_number_of_int @ SV1140 )
!= SV1361 )
= $true )
| ( ( SV1361
= ( number_number_of_int @ SV1140 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5274]) ).
thf(5766,plain,
! [SV1141: int,SV1362: int] :
( ( ( SV1362
!= ( number_number_of_int @ SV1141 ) )
= $true )
| ( ( ( number_number_of_int @ SV1141 )
= SV1362 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5275]) ).
thf(5767,plain,
! [SV1363: int,SV1142: int] :
( ( ( ~ ( ord_less_eq_int @ SV1142 @ SV1363 ) )
= $true )
| ( ( ord_less_int @ SV1142 @ ( plus_plus_int @ SV1363 @ one_one_int ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5276]) ).
thf(5768,plain,
! [SV1364: int,SV1143: int] :
( ( ( ~ ( ord_less_int @ SV1143 @ ( plus_plus_int @ SV1364 @ one_one_int ) ) )
= $true )
| ( ( ord_less_eq_int @ SV1143 @ SV1364 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5277]) ).
thf(5769,plain,
! [SV1365: real,SV1144: real] :
( ( ( ( SV1144 != zero_zero_real )
| ( SV1365 != zero_zero_real ) )
= $true )
| ( ( ( plus_plus_real @ ( times_times_real @ SV1144 @ SV1144 ) @ ( times_times_real @ SV1365 @ SV1365 ) )
= zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5278]) ).
thf(5770,plain,
( ( ! [SX0: real] :
( ! [SX1: real] :
( ( plus_plus_real @ ( times_times_real @ SX0 @ SX0 ) @ ( times_times_real @ SX1 @ SX1 ) )
!= zero_zero_real )
| ( SX0 = zero_zero_real ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5279]) ).
thf(5771,plain,
( ( ! [SX0: real,SX1: real] :
( ( ( plus_plus_real @ ( times_times_real @ SX0 @ SX0 ) @ ( times_times_real @ SX1 @ SX1 ) )
!= zero_zero_real )
| ( SX1 = zero_zero_real ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5280]) ).
thf(5772,plain,
! [SV1145: int] :
( ( ( ord_less_eq_int @ ( bit1 @ SV1145 ) @ pls )
= $false )
| ( ( ord_less_int @ SV1145 @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5281]) ).
thf(5773,plain,
! [SV1146: int] :
( ( ( ord_less_int @ SV1146 @ pls )
= $false )
| ( ( ord_less_eq_int @ ( bit1 @ SV1146 ) @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5282]) ).
thf(5774,plain,
! [SV1366: nat,SV447: nat,SV1469: real] :
( ( ~ ( ord_less_real @ one_one_real @ SV1469 )
| ~ ( ord_less_nat @ SV447 @ SV1366 )
| ( ord_less_real @ ( power_power_real @ SV1469 @ SV447 ) @ ( power_power_real @ SV1469 @ SV1366 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5283]) ).
thf(5775,plain,
! [SV1367: nat,SV447: nat,SV1470: real] :
( ( ~ ( ord_less_real @ one_one_real @ SV1470 )
| ~ ( ord_less_real @ ( power_power_real @ SV1470 @ SV447 ) @ ( power_power_real @ SV1470 @ SV1367 ) )
| ( ord_less_nat @ SV447 @ SV1367 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5284]) ).
thf(5776,plain,
! [SV1147: int] :
( ( ( ( bit0 @ SV1147 )
= pls )
= $false )
| ( ( SV1147 = pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5285]) ).
thf(5777,plain,
! [SV1148: int] :
( ( ( SV1148 = pls )
= $false )
| ( ( ( bit0 @ SV1148 )
= pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5286]) ).
thf(5778,plain,
! [SV1368: int,SV1149: int] :
( ( ( ~ ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ SV1149 @ SV1149 ) @ ( times_times_int @ SV1368 @ SV1368 ) ) ) )
= $true )
| ( ( ( SV1149 != zero_zero_int )
| ( SV1368 != zero_zero_int ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5287]) ).
thf(5779,plain,
( ( ! [SX0: int] :
( ( SX0 = zero_zero_int )
| ! [SX1: int] : ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ SX0 @ SX0 ) @ ( times_times_int @ SX1 @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5288]) ).
thf(5780,plain,
( ( ! [SX0: int,SX1: int] :
( ( SX1 = zero_zero_int )
| ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ SX0 @ SX0 ) @ ( times_times_int @ SX1 @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5289]) ).
thf(5781,plain,
! [SV1369: nat,SV1150: int] :
( ( ( ( number_number_of_nat @ SV1150 )
!= SV1369 )
= $true )
| ( ( SV1369
= ( number_number_of_nat @ SV1150 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5290]) ).
thf(5782,plain,
! [SV1151: int,SV1370: nat] :
( ( ( SV1370
!= ( number_number_of_nat @ SV1151 ) )
= $true )
| ( ( ( number_number_of_nat @ SV1151 )
= SV1370 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5291]) ).
thf(5783,plain,
! [SV1152: real] :
( ( ( SV1152 = zero_zero_real )
= $false )
| ( ( ~ ( ord_less_real @ zero_zero_real @ ( times_times_real @ SV1152 @ SV1152 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5292]) ).
thf(5784,plain,
! [SV1154: int] :
( ( ( ord_less_int @ ( number_number_of_int @ SV1154 ) @ one_one_int )
= $false )
| ( ( ord_less_int @ SV1154 @ ( bit1 @ pls ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5294]) ).
thf(5785,plain,
! [SV1155: int] :
( ( ( ord_less_int @ SV1155 @ ( bit1 @ pls ) )
= $false )
| ( ( ord_less_int @ ( number_number_of_int @ SV1155 ) @ one_one_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5295]) ).
thf(5786,plain,
! [SV1371: real,SV448: real,SV1471: real] :
( ( ( SV1471 = zero_zero_real )
| ( ( times_times_real @ SV1471 @ SV448 )
!= ( times_times_real @ SV1471 @ SV1371 ) )
| ( SV448 = SV1371 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5296]) ).
thf(5787,plain,
! [SV1372: real,SV448: real,SV1472: real] :
( ( ( SV1472 = zero_zero_real )
| ( SV448 != SV1372 )
| ( ( times_times_real @ SV1472 @ SV448 )
= ( times_times_real @ SV1472 @ SV1372 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5297]) ).
thf(5788,plain,
! [SV1373: int,SV1156: int] :
( ( ( ~ ( ord_less_eq_int @ ( bit0 @ SV1156 ) @ ( bit1 @ SV1373 ) ) )
= $true )
| ( ( ord_less_eq_int @ SV1156 @ SV1373 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5298]) ).
thf(5789,plain,
! [SV1374: int,SV1157: int] :
( ( ( ~ ( ord_less_eq_int @ SV1157 @ SV1374 ) )
= $true )
| ( ( ord_less_eq_int @ ( bit0 @ SV1157 ) @ ( bit1 @ SV1374 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5299]) ).
thf(5790,plain,
! [SV1158: int] :
( ( ( pls
= ( bit0 @ SV1158 ) )
= $false )
| ( ( pls = SV1158 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5300]) ).
thf(5791,plain,
! [SV1159: int] :
( ( ( pls = SV1159 )
= $false )
| ( ( pls
= ( bit0 @ SV1159 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5301]) ).
thf(5792,plain,
( ( ! [SX0: int,SX1: int] :
( ( ord_less_int @ SX0 @ SX1 )
| ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_nat @ ( number_number_of_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5302]) ).
thf(5793,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( 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(extcnf_not_neg,[status(thm)],[5303]) ).
thf(5794,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_nat @ ( number_number_of_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) )
| ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ pls @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5304]) ).
thf(5795,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_nat @ ( number_number_of_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5305]) ).
thf(5796,plain,
! [SV1375: int,SV1160: int] :
( ( ( ~ ( ord_less_int @ ( bit0 @ SV1160 ) @ ( bit0 @ SV1375 ) ) )
= $true )
| ( ( ord_less_int @ SV1160 @ SV1375 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5306]) ).
thf(5797,plain,
! [SV1376: int,SV1161: int] :
( ( ( ~ ( ord_less_int @ SV1161 @ SV1376 ) )
= $true )
| ( ( ord_less_int @ ( bit0 @ SV1161 ) @ ( bit0 @ SV1376 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5307]) ).
thf(5798,plain,
! [SV787: int,SV449: int,SV981: int] :
( ( ! [SY2385: int,SY2386: int] :
( ~ ( zcong @ SV981 @ SY2385 @ SY2386 )
| ~ ( zcong @ SV449 @ ( times_times_int @ SV981 @ SV787 ) @ SY2386 )
| ( zcong @ SV449 @ ( times_times_int @ SY2385 @ SV787 ) @ SY2386 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5308]) ).
thf(5799,plain,
! [SV787: int,SV449: int,SV981: int] :
( ( ! [SY2387: int,SY2388: int] :
( ~ ( zcong @ SV981 @ SY2387 @ SY2388 )
| ~ ( zcong @ SV449 @ ( times_times_int @ SY2387 @ SV787 ) @ SY2388 )
| ( zcong @ SV449 @ ( times_times_int @ SV981 @ SV787 ) @ SY2388 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5309]) ).
thf(5800,plain,
! [SV1162: real,SV1377: nat] :
( ( ( SV1377 != zero_zero_nat )
= $true )
| ( ( ( power_power_real @ SV1162 @ SV1377 )
= one_one_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5310]) ).
thf(5801,plain,
! [SV1163: real,SV1378: nat] :
( ( ( SV1378 = zero_zero_nat )
= $true )
| ( ( ( power_power_real @ SV1163 @ SV1378 )
= ( times_times_real @ SV1163 @ ( power_power_real @ SV1163 @ ( minus_minus_nat @ SV1378 @ one_one_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5311]) ).
thf(5802,plain,
! [SV788: int,SV450: int] :
( ( ~ ! [SY2290: int,SY2291: int] :
( ( ( plus_plus_int @ ( times_times_int @ SY2290 @ SV450 ) @ ( times_times_int @ SY2291 @ SV788 ) )
= ( plus_plus_int @ ( times_times_int @ SY2290 @ SV788 ) @ ( times_times_int @ SY2291 @ SV450 ) ) )
| ( SY2290 != SY2291 ) )
| ~ ( ! [SY2292: int,SY2293: int] :
( ( plus_plus_int @ ( times_times_int @ SY2292 @ SV450 ) @ ( times_times_int @ SY2293 @ SV788 ) )
= ( plus_plus_int @ ( times_times_int @ SY2292 @ SV788 ) @ ( times_times_int @ SY2293 @ SV450 ) ) )
| ( SV450 != SV788 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5312]) ).
thf(5803,plain,
! [SV788: int,SV450: int,SV1473: int] :
( ( ! [SY2590: int] :
( ( SV1473 = SY2590 )
| ( SV450 = SV788 )
| ( ( plus_plus_int @ ( times_times_int @ SV1473 @ SV450 ) @ ( times_times_int @ SY2590 @ SV788 ) )
!= ( plus_plus_int @ ( times_times_int @ SV1473 @ SV788 ) @ ( times_times_int @ SY2590 @ SV450 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5313]) ).
thf(5804,plain,
! [SV1379: int,SV1164: int] :
( ( ( ~ ( ord_less_eq_int @ SV1164 @ SV1379 ) )
= $true )
| ( ( ord_less_int @ ( bit0 @ SV1164 ) @ ( bit1 @ SV1379 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5314]) ).
thf(5805,plain,
! [SV1380: int,SV1165: int] :
( ( ( ~ ( ord_less_int @ ( bit0 @ SV1165 ) @ ( bit1 @ SV1380 ) ) )
= $true )
| ( ( ord_less_eq_int @ SV1165 @ SV1380 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5315]) ).
thf(5806,plain,
! [SV1167: int] :
( ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ SV1167 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $false )
| ( ( SV1167 != zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5317]) ).
thf(5807,plain,
! [SV1168: int] :
( ( ( ord_less_int @ SV1168 @ pls )
= $false )
| ( ( ord_less_real @ ( number267125858f_real @ SV1168 ) @ zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5318]) ).
thf(5808,plain,
! [SV1169: int] :
( ( ( ord_less_real @ ( number267125858f_real @ SV1169 ) @ zero_zero_real )
= $false )
| ( ( ord_less_int @ SV1169 @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5319]) ).
thf(5809,plain,
! [SV1381: real,SV1170: real] :
( ( ( ( SV1170 != zero_zero_real )
| ( SV1381 != zero_zero_real ) )
= $true )
| ( ( ( plus_plus_real @ ( times_times_real @ SV1170 @ SV1170 ) @ ( times_times_real @ SV1381 @ SV1381 ) )
= zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5320]) ).
thf(5810,plain,
( ( ! [SX0: real] :
( ! [SX1: real] :
( ( plus_plus_real @ ( times_times_real @ SX0 @ SX0 ) @ ( times_times_real @ SX1 @ SX1 ) )
!= zero_zero_real )
| ( SX0 = zero_zero_real ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5321]) ).
thf(5811,plain,
( ( ! [SX0: real,SX1: real] :
( ( ( plus_plus_real @ ( times_times_real @ SX0 @ SX0 ) @ ( times_times_real @ SX1 @ SX1 ) )
!= zero_zero_real )
| ( SX1 = zero_zero_real ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5322]) ).
thf(5812,plain,
! [SV1171: int] :
( ( ( ord_less_eq_int @ ( bit1 @ pls ) @ SV1171 )
= $false )
| ( ( ord_less_eq_real @ one_one_real @ ( number267125858f_real @ SV1171 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5323]) ).
thf(5813,plain,
! [SV1172: int] :
( ( ( ord_less_eq_real @ one_one_real @ ( number267125858f_real @ SV1172 ) )
= $false )
| ( ( ord_less_eq_int @ ( bit1 @ pls ) @ SV1172 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5324]) ).
thf(5814,plain,
! [SV789: int,SV451: int,SV982: int] :
( ( ! [SY2389: int,SY2390: int] :
( ~ ( zcong @ SV982 @ SY2389 @ SY2390 )
| ~ ( zcong @ SV451 @ ( times_times_int @ SV789 @ SV982 ) @ SY2390 )
| ( zcong @ SV451 @ ( times_times_int @ SV789 @ SY2389 ) @ SY2390 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5325]) ).
thf(5815,plain,
! [SV789: int,SV451: int,SV982: int] :
( ( ! [SY2391: int,SY2392: int] :
( ~ ( zcong @ SV982 @ SY2391 @ SY2392 )
| ~ ( zcong @ SV451 @ ( times_times_int @ SV789 @ SY2391 ) @ SY2392 )
| ( zcong @ SV451 @ ( times_times_int @ SV789 @ SV982 ) @ SY2392 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5326]) ).
thf(5816,plain,
! [SV1173: int] :
( ( ( ord_less_eq_int @ ( bit1 @ SV1173 ) @ min )
= $false )
| ( ( ord_less_eq_int @ SV1173 @ min )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5327]) ).
thf(5817,plain,
! [SV1174: int] :
( ( ( ord_less_eq_int @ SV1174 @ min )
= $false )
| ( ( ord_less_eq_int @ ( bit1 @ SV1174 ) @ min )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5328]) ).
thf(5818,plain,
! [SV1382: int,SV1175: int] :
( ( ( ~ ( ord_less_eq_int @ ( bit1 @ SV1175 ) @ ( bit1 @ SV1382 ) ) )
= $true )
| ( ( ord_less_eq_int @ SV1175 @ SV1382 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5329]) ).
thf(5819,plain,
! [SV1383: int,SV1176: int] :
( ( ( ~ ( ord_less_eq_int @ SV1176 @ SV1383 ) )
= $true )
| ( ( ord_less_eq_int @ ( bit1 @ SV1176 ) @ ( bit1 @ SV1383 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5330]) ).
thf(5820,plain,
! [SV1384: int,SV1177: int] :
( ( ( SV1177 != SV1384 )
= $true )
| ( ( zcong @ SV1177 @ SV1384 @ zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5331]) ).
thf(5821,plain,
! [SV1385: int,SV1178: int] :
( ( ( ~ ( zcong @ SV1178 @ SV1385 @ zero_zero_int ) )
= $true )
| ( ( SV1178 = SV1385 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5332]) ).
thf(5822,plain,
! [SV1386: int,SV1179: int] :
( ( ( ~ ( ord_less_eq_int @ ( bit1 @ SV1179 ) @ ( bit0 @ SV1386 ) ) )
= $true )
| ( ( ord_less_int @ SV1179 @ SV1386 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5333]) ).
thf(5823,plain,
! [SV1387: int,SV1180: int] :
( ( ( ~ ( ord_less_int @ SV1180 @ SV1387 ) )
= $true )
| ( ( ord_less_eq_int @ ( bit1 @ SV1180 ) @ ( bit0 @ SV1387 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5334]) ).
thf(5824,plain,
! [SV1474: nat,SV790: nat,SV452: nat] :
( ( ! [SY2591: nat] :
( ( ( plus_plus_nat @ ( times_times_nat @ SV452 @ SV790 ) @ ( times_times_nat @ SV1474 @ SY2591 ) )
!= ( plus_plus_nat @ ( times_times_nat @ SV452 @ SY2591 ) @ ( times_times_nat @ SV1474 @ SV790 ) ) )
| ( SV452 = SV1474 )
| ( SV790 = SY2591 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5335]) ).
thf(5825,plain,
! [SV790: nat,SV452: nat] :
( ( ~ ! [SY2303: nat] :
( ( SV452 != SY2303 )
| ! [SY2304: nat] :
( ( plus_plus_nat @ ( times_times_nat @ SV452 @ SV790 ) @ ( times_times_nat @ SY2303 @ SY2304 ) )
= ( plus_plus_nat @ ( times_times_nat @ SV452 @ SY2304 ) @ ( times_times_nat @ SY2303 @ SV790 ) ) ) )
| ~ ! [SY2305: nat,SY2306: nat] :
( ( SV790 != SY2306 )
| ( ( plus_plus_nat @ ( times_times_nat @ SV452 @ SV790 ) @ ( times_times_nat @ SY2305 @ SY2306 ) )
= ( plus_plus_nat @ ( times_times_nat @ SV452 @ SY2306 ) @ ( times_times_nat @ SY2305 @ SV790 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5336]) ).
thf(5826,plain,
! [SV1181: real,SV1388: nat] :
( ( ( ( SV1388 = zero_zero_nat )
| ( SV1181 != zero_zero_real ) )
= $true )
| ( ( ( power_power_real @ SV1181 @ SV1388 )
= zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5337]) ).
thf(5827,plain,
( ( ! [SX0: real,SX1: nat] :
( ( ( power_power_real @ SX0 @ SX1 )
!= zero_zero_real )
| ( SX1 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5338]) ).
thf(5828,plain,
( ( ! [SX0: real] :
( ! [SX1: nat] :
( ( power_power_real @ SX0 @ SX1 )
!= zero_zero_real )
| ( SX0 = zero_zero_real ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5339]) ).
thf(5829,plain,
! [SV1389: nat,SV1182: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV1182 @ SV1389 ) ) )
= $true )
| ( ( ( SV1389 = zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV1182 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5340]) ).
thf(5830,plain,
( ( ! [SX0: nat,SX1: nat] :
( ( SX1 != zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5341]) ).
thf(5831,plain,
( ( ! [SX0: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SX0 )
| ! [SX1: nat] : ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5342]) ).
thf(5832,plain,
! [SV1475: int,SV791: int,SV453: int] :
( ( ! [SY2592: int] :
( ( ( plus_plus_int @ ( times_times_int @ SV453 @ SV791 ) @ ( times_times_int @ SV1475 @ SY2592 ) )
!= ( plus_plus_int @ ( times_times_int @ SV453 @ SY2592 ) @ ( times_times_int @ SV1475 @ SV791 ) ) )
| ( SV453 = SV1475 )
| ( SV791 = SY2592 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5343]) ).
thf(5833,plain,
! [SV791: int,SV453: int] :
( ( ~ ! [SY2309: int] :
( ( SV453 != SY2309 )
| ! [SY2310: int] :
( ( plus_plus_int @ ( times_times_int @ SV453 @ SV791 ) @ ( times_times_int @ SY2309 @ SY2310 ) )
= ( plus_plus_int @ ( times_times_int @ SV453 @ SY2310 ) @ ( times_times_int @ SY2309 @ SV791 ) ) ) )
| ~ ! [SY2311: int,SY2312: int] :
( ( SV791 != SY2312 )
| ( ( plus_plus_int @ ( times_times_int @ SV453 @ SV791 ) @ ( times_times_int @ SY2311 @ SY2312 ) )
= ( plus_plus_int @ ( times_times_int @ SV453 @ SY2312 ) @ ( times_times_int @ SY2311 @ SV791 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5344]) ).
thf(5834,plain,
! [SV1183: nat,SV1390: nat] :
( ( ( SV1390 != zero_zero_nat )
= $true )
| ( ( ( power_power_nat @ SV1183 @ SV1390 )
= one_one_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5345]) ).
thf(5835,plain,
! [SV1184: nat,SV1391: nat] :
( ( ( SV1391 = zero_zero_nat )
= $true )
| ( ( ( power_power_nat @ SV1184 @ SV1391 )
= ( times_times_nat @ SV1184 @ ( power_power_nat @ SV1184 @ ( minus_minus_nat @ SV1391 @ one_one_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5346]) ).
thf(5836,plain,
! [SV1185: int,SV1392: int] :
( ( ( ~ ( ord_less_int @ zero_zero_int @ SV1392 ) )
= $true )
| ( ( ( SV1392 != one_one_int )
| ( SV1185 != one_one_int )
| ( ( times_times_int @ SV1392 @ SV1185 )
= one_one_int ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5347]) ).
thf(5837,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ zero_zero_int @ SX1 )
| ( ( times_times_int @ SX1 @ SX0 )
!= one_one_int )
| ( SX1 = one_one_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5348]) ).
thf(5838,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_int @ zero_zero_int @ SX1 )
| ( ( times_times_int @ SX1 @ SX0 )
!= one_one_int )
| ( SX0 = one_one_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5349]) ).
thf(5839,plain,
! [SV1393: int,SV1186: int] :
( ( ( ~ ( ord_less_eq_int @ ( plus_plus_int @ SV1186 @ one_one_int ) @ SV1393 ) )
= $true )
| ( ( ord_less_int @ SV1186 @ SV1393 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5350]) ).
thf(5840,plain,
! [SV1394: int,SV1187: int] :
( ( ( ~ ( ord_less_int @ SV1187 @ SV1394 ) )
= $true )
| ( ( ord_less_eq_int @ ( plus_plus_int @ SV1187 @ one_one_int ) @ SV1394 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5351]) ).
thf(5841,plain,
! [SV1188: int] :
( ( ( ( number_number_of_nat @ SV1188 )
= zero_zero_nat )
= $false )
| ( ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ SV1188 ) )
= one_one_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5352]) ).
thf(5842,plain,
! [SV1395: real,SV1190: real] :
( ( ( ( SV1190 = SV1395 )
| ~ ( ord_less_eq_real @ SV1190 @ SV1395 ) )
= $true )
| ( ( ord_less_real @ SV1190 @ SV1395 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5354]) ).
thf(5843,plain,
( ( ! [SX0: real,SX1: real] :
( ~ ( ord_less_real @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5355]) ).
thf(5844,plain,
( ( ! [SX0: real,SX1: real] :
( ~ ( ord_less_real @ SX0 @ SX1 )
| ( ord_less_eq_real @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5356]) ).
thf(5845,plain,
! [SV1396: int,SV1191: int] :
( ( ( ~ ( ord_less_int @ SV1191 @ SV1396 ) )
= $true )
| ( ( ord_less_real @ ( number267125858f_real @ SV1191 ) @ ( number267125858f_real @ SV1396 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5357]) ).
thf(5846,plain,
! [SV1397: int,SV1192: int] :
( ( ( ~ ( ord_less_real @ ( number267125858f_real @ SV1192 ) @ ( number267125858f_real @ SV1397 ) ) )
= $true )
| ( ( ord_less_int @ SV1192 @ SV1397 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5358]) ).
thf(5847,plain,
! [SV1398: int,SV1193: int] :
( ( ( ~ ( ord_less_eq_int @ ( number_number_of_int @ SV1193 ) @ ( number_number_of_int @ SV1398 ) ) )
= $true )
| ( ( ~ ( ord_less_int @ ( number_number_of_int @ SV1398 ) @ ( number_number_of_int @ SV1193 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5359]) ).
thf(5848,plain,
! [SV1194: int,SV1399: int] :
( ( ( ord_less_int @ ( number_number_of_int @ SV1399 ) @ ( number_number_of_int @ SV1194 ) )
= $true )
| ( ( ord_less_eq_int @ ( number_number_of_int @ SV1194 ) @ ( number_number_of_int @ SV1399 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5360]) ).
thf(5849,plain,
! [SV1195: int] :
( ( ( ( plus_plus_int @ SV1195 @ SV1195 )
= zero_zero_int )
= $false )
| ( ( SV1195 = zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5361]) ).
thf(5850,plain,
! [SV1196: int] :
( ( ( SV1196 = zero_zero_int )
= $false )
| ( ( ( plus_plus_int @ SV1196 @ SV1196 )
= zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5362]) ).
thf(5851,plain,
! [SV1400: int,SV1197: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV1197 @ ( number_number_of_nat @ SV1400 ) ) ) )
= $true )
| ( ( ( ( number_number_of_nat @ SV1400 )
= zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV1197 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5363]) ).
thf(5852,plain,
( ( ! [SX0: nat,SX1: int] :
( ( ( number_number_of_nat @ SX1 )
!= zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SX0 @ ( number_number_of_nat @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5364]) ).
thf(5853,plain,
( ( ! [SX0: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SX0 )
| ! [SX1: int] : ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SX0 @ ( number_number_of_nat @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5365]) ).
thf(5854,plain,
! [SV1198: int] :
( ( ( ord_less_eq_int @ SV1198 @ ( bit1 @ pls ) )
= $false )
| ( ( ord_less_eq_real @ ( number267125858f_real @ SV1198 ) @ one_one_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5366]) ).
thf(5855,plain,
! [SV1199: int] :
( ( ( ord_less_eq_real @ ( number267125858f_real @ SV1199 ) @ one_one_real )
= $false )
| ( ( ord_less_eq_int @ SV1199 @ ( bit1 @ pls ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5367]) ).
thf(5856,plain,
! [SV1200: int,SV1401: int] :
( ( ( ~ ( ord_less_int @ SV1401 @ pls ) )
= $true )
| ( ( ( times_times_nat @ ( number_number_of_nat @ SV1401 ) @ ( number_number_of_nat @ SV1200 ) )
= zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5368]) ).
thf(5857,plain,
! [SV1201: int,SV1402: int] :
( ( ( ord_less_int @ SV1402 @ pls )
= $true )
| ( ( ( times_times_nat @ ( number_number_of_nat @ SV1402 ) @ ( number_number_of_nat @ SV1201 ) )
= ( number_number_of_nat @ ( times_times_int @ SV1402 @ SV1201 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5369]) ).
thf(5858,plain,
! [SV1203: real] :
( ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ SV1203 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $false )
| ( ( SV1203 != zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5371]) ).
thf(5859,plain,
! [SV1204: int] :
( ( ( ~ ( ~ ~ ( ~ ( dvd_dvd_int @ ( sK3_M_9 @ SV1204 ) @ SV1204 )
| ~ ( ord_less_eq_int @ zero_zero_int @ ( sK3_M_9 @ SV1204 ) ) )
| ~ ~ ( ~ ( ( ( sK3_M_9 @ SV1204 )
!= one_one_int ) )
| ~ ( ( ( sK3_M_9 @ SV1204 )
!= SV1204 ) ) ) ) )
= $true )
| ( ( ~ ( ord_less_int @ one_one_int @ SV1204 ) )
= $true )
| ( ( zprime @ SV1204 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5372]) ).
thf(5860,plain,
( ( ! [SX0: int] :
( ~ ( zprime @ SX0 )
| ! [SX1: int] :
( ~ ( dvd_dvd_int @ SX1 @ SX0 )
| ~ ( ord_less_eq_int @ zero_zero_int @ SX1 )
| ( SX1 = one_one_int )
| ( SX1 = SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5373]) ).
thf(5861,plain,
( ( ! [SX0: int] :
( ~ ( zprime @ SX0 )
| ( ord_less_int @ one_one_int @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5374]) ).
thf(5862,plain,
! [SV1403: nat,SV454: int,SV1476: int] :
( ( ~ ( ord_less_int @ SV1476 @ pls )
| ( ( times_times_nat @ ( number_number_of_nat @ SV1476 ) @ ( times_times_nat @ ( number_number_of_nat @ SV454 ) @ SV1403 ) )
= zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5375]) ).
thf(5863,plain,
! [SV1404: nat,SV454: int,SV1477: int] :
( ( ( ord_less_int @ SV1477 @ pls )
| ( ( times_times_nat @ ( number_number_of_nat @ SV1477 ) @ ( times_times_nat @ ( number_number_of_nat @ SV454 ) @ SV1404 ) )
= ( times_times_nat @ ( number_number_of_nat @ ( times_times_int @ SV1477 @ SV454 ) ) @ SV1404 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5376]) ).
thf(5864,plain,
! [SV1405: int,SV1205: int] :
( ( ( ~ ( zcong @ SV1205 @ zero_zero_int @ SV1405 ) )
= $true )
| ( ( ( legendre @ SV1205 @ SV1405 )
= zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5377]) ).
thf(5865,plain,
( ( ! [SX0: int,SX1: int] :
( ( zcong @ SX0 @ zero_zero_int @ SX1 )
| ~ ( quadRes @ SX1 @ SX0 )
| ( ( legendre @ SX0 @ SX1 )
= one_one_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5378]) ).
thf(5866,plain,
( ( ! [SX0: int,SX1: int] :
( ( zcong @ SX0 @ zero_zero_int @ SX1 )
| ( quadRes @ SX1 @ SX0 )
| ( ( legendre @ SX0 @ SX1 )
= ( number_number_of_int @ min ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5379]) ).
thf(5867,plain,
! [SV1206: nat] :
( ( ( SV1206 = zero_zero_nat )
= $false )
| ( ( ( power_power_int @ zero_zero_int @ SV1206 )
= one_one_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5380]) ).
thf(5868,plain,
! [SV792: nat,SV455: real] :
( ( ( ord_less_real @ zero_zero_real @ SV455 )
= $false )
| ( ( ~ ( ~ ! [SY2313: real] :
( ( ( power_power_real @ SY2313 @ SV792 )
!= SV455 )
| ~ ( ord_less_real @ zero_zero_real @ SY2313 )
| ( SY2313
= ( sK1_X_1 @ SV792 @ SV455 ) ) )
| ~ ~ ( ( ( power_power_real @ ( sK1_X_1 @ SV792 @ SV455 ) @ SV792 )
!= SV455 )
| ~ ( ord_less_real @ zero_zero_real @ ( sK1_X_1 @ SV792 @ SV455 ) ) ) ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV792 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5382]) ).
thf(5869,plain,
! [SV1208: int] :
( ( ( zero_zero_nat
= ( number_number_of_nat @ SV1208 ) )
= $false )
| ( ( ord_less_eq_int @ SV1208 @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5383]) ).
thf(5870,plain,
! [SV1209: int] :
( ( ( ord_less_eq_int @ SV1209 @ pls )
= $false )
| ( ( zero_zero_nat
= ( number_number_of_nat @ SV1209 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5384]) ).
thf(5871,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_eq_nat @ ( number_number_of_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5385]) ).
thf(5872,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_eq_int @ SX0 @ pls )
| ! [SX1: int] : ( ord_less_eq_nat @ ( number_number_of_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5386]) ).
thf(5873,plain,
! [SV1406: int,SV1210: int] :
( ( ( ~ ( ord_less_eq_nat @ ( number_number_of_nat @ SV1210 ) @ ( number_number_of_nat @ SV1406 ) ) )
= $true )
| ( ( ( ord_less_eq_int @ SV1210 @ SV1406 )
| ( ord_less_eq_int @ SV1210 @ pls ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5387]) ).
thf(5874,plain,
! [SV1211: int] :
( ( ( ord_less_int @ ( number_number_of_int @ SV1211 ) @ zero_zero_int )
= $false )
| ( ( ord_less_int @ SV1211 @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5388]) ).
thf(5875,plain,
! [SV1212: int] :
( ( ( ord_less_int @ SV1212 @ pls )
= $false )
| ( ( ord_less_int @ ( number_number_of_int @ SV1212 ) @ zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5389]) ).
thf(5876,plain,
! [SV1213: int] :
( ( ( ord_less_eq_int @ one_one_int @ ( number_number_of_int @ SV1213 ) )
= $false )
| ( ( ord_less_eq_int @ ( bit1 @ pls ) @ SV1213 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5390]) ).
thf(5877,plain,
! [SV1214: int] :
( ( ( ord_less_eq_int @ ( bit1 @ pls ) @ SV1214 )
= $false )
| ( ( ord_less_eq_int @ one_one_int @ ( number_number_of_int @ SV1214 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5391]) ).
thf(5878,plain,
! [SV1407: real,SV1215: int] :
( ( ( ( number267125858f_real @ SV1215 )
!= SV1407 )
= $true )
| ( ( SV1407
= ( number267125858f_real @ SV1215 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5392]) ).
thf(5879,plain,
! [SV1216: int,SV1408: real] :
( ( ( SV1408
!= ( number267125858f_real @ SV1216 ) )
= $true )
| ( ( ( number267125858f_real @ SV1216 )
= SV1408 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5393]) ).
thf(5880,plain,
! [SV1217: int] :
( ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ SV1217 ) @ SV1217 ) @ zero_zero_int )
= $false )
| ( ( ord_less_int @ SV1217 @ zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5394]) ).
thf(5881,plain,
! [SV1218: int] :
( ( ( ord_less_int @ SV1218 @ zero_zero_int )
= $false )
| ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ SV1218 ) @ SV1218 ) @ zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5395]) ).
thf(5882,plain,
! [SV1478: int,SV1409: int,SV456: int] :
( ( ~ ( zcong @ SV456 @ SV1409 @ SV1478 )
| ( zcong @ SV1409 @ SV456 @ SV1478 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5396]) ).
thf(5883,plain,
! [SV1479: int,SV456: int,SV1410: int] :
( ( ~ ( zcong @ SV1410 @ SV456 @ SV1479 )
| ( zcong @ SV456 @ SV1410 @ SV1479 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5397]) ).
thf(5884,plain,
! [SV457: int,SV983: int,SV793: int] :
( ( ! [SY2393: int,SY2394: int] :
( ~ ( dvd_dvd_int @ SY2393 @ SY2394 )
| ~ ( dvd_dvd_int @ SY2393 @ ( plus_plus_int @ SV793 @ SV983 ) )
| ( dvd_dvd_int @ SY2393 @ ( plus_plus_int @ ( plus_plus_int @ SV793 @ ( times_times_int @ SV457 @ SY2394 ) ) @ SV983 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5398]) ).
thf(5885,plain,
! [SV983: int,SV457: int,SV793: int] :
( ( ! [SY2395: int,SY2396: int] :
( ~ ( dvd_dvd_int @ SY2395 @ SY2396 )
| ~ ( dvd_dvd_int @ SY2395 @ ( plus_plus_int @ ( plus_plus_int @ SV793 @ ( times_times_int @ SV457 @ SY2396 ) ) @ SV983 ) )
| ( dvd_dvd_int @ SY2395 @ ( plus_plus_int @ SV793 @ SV983 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5399]) ).
thf(5886,plain,
! [SV1219: int] :
( ( ( ord_less_int @ ( bit1 @ pls ) @ SV1219 )
= $false )
| ( ( ord_less_real @ one_one_real @ ( number267125858f_real @ SV1219 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5400]) ).
thf(5887,plain,
! [SV1220: int] :
( ( ( ord_less_real @ one_one_real @ ( number267125858f_real @ SV1220 ) )
= $false )
| ( ( ord_less_int @ ( bit1 @ pls ) @ SV1220 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5401]) ).
thf(5888,plain,
! [SV1411: real,SV1221: real] :
( ( ( SV1221
!= ( plus_plus_real @ SV1221 @ SV1411 ) )
= $true )
| ( ( SV1411 = zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5402]) ).
thf(5889,plain,
! [SV1222: real,SV1412: real] :
( ( ( SV1412 != zero_zero_real )
= $true )
| ( ( SV1222
= ( plus_plus_real @ SV1222 @ SV1412 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5403]) ).
thf(5890,plain,
! [SV1480: int,SV458: int,SV1413: int] :
( ( ! [SY2593: int] :
( SV1413
!= ( plus_plus_int @ SV458 @ ( times_times_int @ SV1480 @ SY2593 ) ) )
| ( zcong @ SV458 @ SV1413 @ SV1480 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5404]) ).
thf(5891,plain,
! [SV1481: int,SV1414: int,SV458: int] :
( ( ~ ( zcong @ SV458 @ SV1414 @ SV1481 )
| ( SV1414
= ( plus_plus_int @ SV458 @ ( times_times_int @ SV1481 @ ( sK6_K_1 @ SV1481 @ SV1414 @ SV458 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5405]) ).
thf(5892,plain,
! [SV1223: int] :
( ( ( ord_less_eq_int @ pls @ ( bit0 @ SV1223 ) )
= $false )
| ( ( ord_less_eq_int @ pls @ SV1223 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5406]) ).
thf(5893,plain,
! [SV1224: int] :
( ( ( ord_less_eq_int @ pls @ SV1224 )
= $false )
| ( ( ord_less_eq_int @ pls @ ( bit0 @ SV1224 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5407]) ).
thf(5894,plain,
! [SV1415: nat,SV459: nat,SV1482: nat] :
( ( ~ ( ord_less_nat @ one_one_nat @ SV1482 )
| ( ( power_power_nat @ SV1482 @ SV459 )
!= ( power_power_nat @ SV1482 @ SV1415 ) )
| ( SV459 = SV1415 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5408]) ).
thf(5895,plain,
! [SV1416: nat,SV459: nat,SV1483: nat] :
( ( ~ ( ord_less_nat @ one_one_nat @ SV1483 )
| ( SV459 != SV1416 )
| ( ( power_power_nat @ SV1483 @ SV459 )
= ( power_power_nat @ SV1483 @ SV1416 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5409]) ).
thf(5896,plain,
! [SV1484: real,SV794: real,SV460: real] :
( ( ! [SY2594: real] :
( ( ( plus_plus_real @ ( times_times_real @ SV460 @ SV794 ) @ ( times_times_real @ SV1484 @ SY2594 ) )
!= ( plus_plus_real @ ( times_times_real @ SV460 @ SY2594 ) @ ( times_times_real @ SV1484 @ SV794 ) ) )
| ( SV460 = SV1484 )
| ( SV794 = SY2594 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5410]) ).
thf(5897,plain,
! [SV794: real,SV460: real] :
( ( ~ ! [SY2321: real] :
( ( SV460 != SY2321 )
| ! [SY2322: real] :
( ( plus_plus_real @ ( times_times_real @ SV460 @ SV794 ) @ ( times_times_real @ SY2321 @ SY2322 ) )
= ( plus_plus_real @ ( times_times_real @ SV460 @ SY2322 ) @ ( times_times_real @ SY2321 @ SV794 ) ) ) )
| ~ ! [SY2323: real,SY2324: real] :
( ( SV794 != SY2324 )
| ( ( plus_plus_real @ ( times_times_real @ SV460 @ SV794 ) @ ( times_times_real @ SY2323 @ SY2324 ) )
= ( plus_plus_real @ ( times_times_real @ SV460 @ SY2324 ) @ ( times_times_real @ SY2323 @ SV794 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5411]) ).
thf(5898,plain,
! [SV1225: int] :
( ( ( ord_less_int @ ( bit1 @ SV1225 ) @ pls )
= $false )
| ( ( ord_less_int @ SV1225 @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5412]) ).
thf(5899,plain,
! [SV1226: int] :
( ( ( ord_less_int @ SV1226 @ pls )
= $false )
| ( ( ord_less_int @ ( bit1 @ SV1226 ) @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5413]) ).
thf(5900,plain,
! [SV1227: int] :
( ( ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ SV1227 ) )
= $false )
| ( ( ord_less_eq_int @ pls @ SV1227 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5414]) ).
thf(5901,plain,
! [SV1228: int] :
( ( ( ord_less_eq_int @ pls @ SV1228 )
= $false )
| ( ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ SV1228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5415]) ).
thf(5902,plain,
! [SV1485: nat,SV1417: nat,SV461: nat] :
( ( ~ ( dvd_dvd_nat @ ( times_times_nat @ SV461 @ SV1417 ) @ ( times_times_nat @ SV1485 @ SV1417 ) )
| ( SV1417 = zero_zero_nat )
| ( dvd_dvd_nat @ SV461 @ SV1485 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5416]) ).
thf(5903,plain,
! [SV461: nat] :
( ( ~ ! [SY2002: nat] :
( ( SY2002 != zero_zero_nat )
| ! [SY2003: nat] : ( dvd_dvd_nat @ ( times_times_nat @ SV461 @ SY2002 ) @ ( times_times_nat @ SY2003 @ SY2002 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5417]) ).
thf(5904,plain,
! [SV461: nat] :
( ( ~ ! [SY2004: nat,SY2005: nat] :
( ~ ( dvd_dvd_nat @ SV461 @ SY2005 )
| ( dvd_dvd_nat @ ( times_times_nat @ SV461 @ SY2004 ) @ ( times_times_nat @ SY2005 @ SY2004 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5417]) ).
thf(5905,plain,
! [SV1418: int,SV1229: int] :
( ( ( ( number267125858f_real @ SV1229 )
!= ( number267125858f_real @ SV1418 ) )
= $true )
| ( ( SV1229 = SV1418 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5418]) ).
thf(5906,plain,
! [SV1419: int,SV1230: int] :
( ( ( SV1230 != SV1419 )
= $true )
| ( ( ( number267125858f_real @ SV1230 )
= ( number267125858f_real @ SV1419 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5419]) ).
thf(5907,plain,
! [SV1231: nat] :
( ( ( SV1231 = zero_zero_nat )
= $false )
| ( ( ( power_power_nat @ zero_zero_nat @ SV1231 )
= one_one_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5420]) ).
thf(5908,plain,
! [SV1233: int] :
( ( ( ord_less_eq_int @ ( bit0 @ SV1233 ) @ min )
= $false )
| ( ( ord_less_eq_int @ SV1233 @ min )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5422]) ).
thf(5909,plain,
! [SV1234: int] :
( ( ( ord_less_eq_int @ SV1234 @ min )
= $false )
| ( ( ord_less_eq_int @ ( bit0 @ SV1234 ) @ min )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5423]) ).
thf(5910,plain,
! [SV1420: int,SV1235: int] :
( ( ( ~ ( ord_less_int @ ( bit1 @ SV1235 ) @ ( bit0 @ SV1420 ) ) )
= $true )
| ( ( ord_less_int @ SV1235 @ SV1420 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5424]) ).
thf(5911,plain,
! [SV1421: int,SV1236: int] :
( ( ( ~ ( ord_less_int @ SV1236 @ SV1421 ) )
= $true )
| ( ( ord_less_int @ ( bit1 @ SV1236 ) @ ( bit0 @ SV1421 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5425]) ).
thf(5912,plain,
! [SV1422: int,SV1237: int] :
( ( ( ~ ( ord_less_eq_int @ ( bit0 @ SV1237 ) @ ( bit0 @ SV1422 ) ) )
= $true )
| ( ( ord_less_eq_int @ SV1237 @ SV1422 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5426]) ).
thf(5913,plain,
! [SV1423: int,SV1238: int] :
( ( ( ~ ( ord_less_eq_int @ SV1238 @ SV1423 ) )
= $true )
| ( ( ord_less_eq_int @ ( bit0 @ SV1238 ) @ ( bit0 @ SV1423 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5427]) ).
thf(5914,plain,
! [SV1424: nat,SV1239: nat] :
( ( ( SV1239
!= ( plus_plus_nat @ SV1239 @ SV1424 ) )
= $true )
| ( ( SV1424 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5428]) ).
thf(5915,plain,
! [SV1240: nat,SV1425: nat] :
( ( ( SV1425 != zero_zero_nat )
= $true )
| ( ( SV1240
= ( plus_plus_nat @ SV1240 @ SV1425 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5429]) ).
thf(5916,plain,
! [SV1426: int,SV1241: int] :
( ( ( ~ ( ord_less_int @ ( bit1 @ SV1241 ) @ ( bit1 @ SV1426 ) ) )
= $true )
| ( ( ord_less_int @ SV1241 @ SV1426 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5430]) ).
thf(5917,plain,
! [SV1427: int,SV1242: int] :
( ( ( ~ ( ord_less_int @ SV1242 @ SV1427 ) )
= $true )
| ( ( ord_less_int @ ( bit1 @ SV1242 ) @ ( bit1 @ SV1427 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5431]) ).
thf(5918,plain,
! [SV1243: nat,SV1428: nat] :
( ( ( ( SV1428 = zero_zero_nat )
| ( SV1243 != zero_zero_nat ) )
= $true )
| ( ( ( power_power_nat @ SV1243 @ SV1428 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5432]) ).
thf(5919,plain,
( ( ! [SX0: nat,SX1: nat] :
( ( ( power_power_nat @ SX0 @ SX1 )
!= zero_zero_nat )
| ( SX1 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5433]) ).
thf(5920,plain,
( ( ! [SX0: nat] :
( ! [SX1: nat] :
( ( power_power_nat @ SX0 @ SX1 )
!= zero_zero_nat )
| ( SX0 = zero_zero_nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5434]) ).
thf(5921,plain,
! [SV1429: int,SV1244: int] :
( ( ( ~ ( ord_less_int @ ( bit1 @ SV1244 ) @ ( bit0 @ SV1429 ) ) )
= $true )
| ( ( ord_less_int @ SV1244 @ SV1429 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5435]) ).
thf(5922,plain,
! [SV1430: int,SV1245: int] :
( ( ( ~ ( ord_less_int @ SV1245 @ SV1430 ) )
= $true )
| ( ( ord_less_int @ ( bit1 @ SV1245 ) @ ( bit0 @ SV1430 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5436]) ).
thf(5923,plain,
! [SV1431: int,SV1246: int] :
( ( ( SV1246
!= ( plus_plus_int @ SV1246 @ SV1431 ) )
= $true )
| ( ( SV1431 = zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5437]) ).
thf(5924,plain,
! [SV1247: int,SV1432: int] :
( ( ( SV1432 != zero_zero_int )
= $true )
| ( ( SV1247
= ( plus_plus_int @ SV1247 @ SV1432 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5438]) ).
thf(5925,plain,
! [SV1248: int,SV1433: int] :
( ( ( ! [SY2574: int] :
~ ( zcong @ ( power_power_int @ SY2574 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SV1433 @ SV1248 ) )
= $true )
| ( ( quadRes @ SV1248 @ SV1433 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5439]) ).
thf(5926,plain,
! [SV1434: int,SV1249: int] :
( ( ( ~ ( quadRes @ SV1249 @ SV1434 ) )
= $true )
| ( ( zcong @ ( power_power_int @ ( sK5_Y_1 @ SV1434 @ SV1249 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SV1434 @ SV1249 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5440]) ).
thf(5927,plain,
! [SV1250: int] :
( ( ( ord_less_int @ one_one_int @ ( number_number_of_int @ SV1250 ) )
= $false )
| ( ( ord_less_int @ ( bit1 @ pls ) @ SV1250 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5441]) ).
thf(5928,plain,
! [SV1251: int] :
( ( ( ord_less_int @ ( bit1 @ pls ) @ SV1251 )
= $false )
| ( ( ord_less_int @ one_one_int @ ( number_number_of_int @ SV1251 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5442]) ).
thf(5929,plain,
! [SV1435: nat,SV462: nat,SV1486: real] :
( ( ~ ( ord_less_real @ one_one_real @ SV1486 )
| ( ( power_power_real @ SV1486 @ SV462 )
!= ( power_power_real @ SV1486 @ SV1435 ) )
| ( SV462 = SV1435 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5443]) ).
thf(5930,plain,
! [SV1436: nat,SV462: nat,SV1487: real] :
( ( ~ ( ord_less_real @ one_one_real @ SV1487 )
| ( SV462 != SV1436 )
| ( ( power_power_real @ SV1487 @ SV462 )
= ( power_power_real @ SV1487 @ SV1436 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5444]) ).
thf(5931,plain,
! [SV1252: int,SV1437: int] :
( ( ( ~ ( ord_less_int @ SV1437 @ pls ) )
= $true )
| ( ( ( plus_plus_nat @ ( number_number_of_nat @ SV1437 ) @ ( number_number_of_nat @ SV1252 ) )
= ( number_number_of_nat @ SV1252 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5445]) ).
thf(5932,plain,
( ( ! [SX0: int,SX1: int] :
( ( 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 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5446]) ).
thf(5933,plain,
( ( ! [SX0: int,SX1: int] :
( ( 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 @ ( plus_plus_int @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5447]) ).
thf(5934,plain,
! [SV1438: real,SV463: real,SV1488: real] :
( ( ( SV1488 = zero_zero_real )
| ( ( times_times_real @ SV463 @ SV1488 )
!= ( times_times_real @ SV1438 @ SV1488 ) )
| ( SV463 = SV1438 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5448]) ).
thf(5935,plain,
! [SV1439: real,SV463: real,SV1489: real] :
( ( ( SV1489 = zero_zero_real )
| ( SV463 != SV1439 )
| ( ( times_times_real @ SV463 @ SV1489 )
= ( times_times_real @ SV1439 @ SV1489 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5449]) ).
thf(5936,plain,
! [SV1440: real,SV464: real,SV1490: real] :
( ( ~ ( ord_less_real @ zero_zero_real @ SV1490 )
| ~ ( ord_less_real @ ( times_times_real @ SV464 @ SV1490 ) @ ( times_times_real @ SV1440 @ SV1490 ) )
| ( ord_less_real @ SV464 @ SV1440 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5450]) ).
thf(5937,plain,
! [SV1441: real,SV464: real,SV1491: real] :
( ( ~ ( ord_less_real @ zero_zero_real @ SV1491 )
| ~ ( ord_less_real @ SV464 @ SV1441 )
| ( ord_less_real @ ( times_times_real @ SV464 @ SV1491 ) @ ( times_times_real @ SV1441 @ SV1491 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5451]) ).
thf(5938,plain,
! [SV1442: real,SV465: real,SV1492: real] :
( ( ~ ( ord_less_real @ zero_zero_real @ SV1492 )
| ~ ( ord_less_eq_real @ ( times_times_real @ SV1492 @ SV465 ) @ ( times_times_real @ SV1492 @ SV1442 ) )
| ( ord_less_eq_real @ SV465 @ SV1442 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5452]) ).
thf(5939,plain,
! [SV1443: real,SV465: real,SV1493: real] :
( ( ~ ( ord_less_real @ zero_zero_real @ SV1493 )
| ~ ( ord_less_eq_real @ SV465 @ SV1443 )
| ( ord_less_eq_real @ ( times_times_real @ SV1493 @ SV465 ) @ ( times_times_real @ SV1493 @ SV1443 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5453]) ).
thf(5940,plain,
! [SV1444: int,SV1253: int] :
( ( ( ( bit0 @ SV1253 )
!= ( bit0 @ SV1444 ) )
= $true )
| ( ( SV1253 = SV1444 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5454]) ).
thf(5941,plain,
! [SV1445: int,SV1254: int] :
( ( ( SV1254 != SV1445 )
= $true )
| ( ( ( bit0 @ SV1254 )
= ( bit0 @ SV1445 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5455]) ).
thf(5942,plain,
! [SV1255: int] :
( ( ( ( power_power_int @ SV1255 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int )
= $false )
| ( ( SV1255 = zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5456]) ).
thf(5943,plain,
! [SV1256: int] :
( ( ( SV1256 = zero_zero_int )
= $false )
| ( ( ( power_power_int @ SV1256 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5457]) ).
thf(5944,plain,
! [SV1446: int,SV1257: int] :
( ( ( ( SV1257 != zero_zero_int )
| ( SV1446 != zero_zero_int ) )
= $true )
| ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SV1257 @ SV1257 ) @ ( times_times_int @ SV1446 @ SV1446 ) ) @ zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5458]) ).
thf(5945,plain,
( ( ! [SX0: int] :
( ! [SX1: int] :
~ ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SX0 @ SX0 ) @ ( times_times_int @ SX1 @ SX1 ) ) @ zero_zero_int )
| ( SX0 = zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5459]) ).
thf(5946,plain,
( ( ! [SX0: int,SX1: int] :
( ~ ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SX0 @ SX0 ) @ ( times_times_int @ SX1 @ SX1 ) ) @ zero_zero_int )
| ( SX1 = zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5460]) ).
thf(5947,plain,
! [SV1258: int] :
( ( ( ord_less_int @ pls @ ( bit0 @ SV1258 ) )
= $false )
| ( ( ord_less_int @ pls @ SV1258 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5461]) ).
thf(5948,plain,
! [SV1259: int] :
( ( ( ord_less_int @ pls @ SV1259 )
= $false )
| ( ( ord_less_int @ pls @ ( bit0 @ SV1259 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5462]) ).
thf(5949,plain,
! [SV1260: real] :
( ( ( ord_less_real @ ( plus_plus_real @ SV1260 @ SV1260 ) @ zero_zero_real )
= $false )
| ( ( ord_less_real @ SV1260 @ zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5463]) ).
thf(5950,plain,
! [SV1261: real] :
( ( ( ord_less_real @ SV1261 @ zero_zero_real )
= $false )
| ( ( ord_less_real @ ( plus_plus_real @ SV1261 @ SV1261 ) @ zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5464]) ).
thf(5951,plain,
! [SV1262: int,SV1447: nat] :
( ( ( ( SV1447 = zero_zero_nat )
| ( SV1262 != zero_zero_int ) )
= $true )
| ( ( ( power_power_int @ SV1262 @ SV1447 )
= zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5465]) ).
thf(5952,plain,
( ( ! [SX0: int,SX1: nat] :
( ( ( power_power_int @ SX0 @ SX1 )
!= zero_zero_int )
| ( SX1 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5466]) ).
thf(5953,plain,
( ( ! [SX0: int] :
( ! [SX1: nat] :
( ( power_power_int @ SX0 @ SX1 )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5467]) ).
thf(5954,plain,
! [SV1448: int,SV1263: int] :
( ( ( ( number_number_of_int @ SV1263 )
!= ( number_number_of_int @ SV1448 ) )
= $true )
| ( ( SV1263 = SV1448 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5468]) ).
thf(5955,plain,
! [SV1449: int,SV1264: int] :
( ( ( SV1264 != SV1449 )
= $true )
| ( ( ( number_number_of_int @ SV1264 )
= ( number_number_of_int @ SV1449 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5469]) ).
thf(5956,plain,
! [SV1265: int] :
( ( ( ord_less_eq_int @ SV1265 @ min )
= $false )
| ( ( ord_less_int @ ( bit0 @ SV1265 ) @ min )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5470]) ).
thf(5957,plain,
! [SV1266: int] :
( ( ( ord_less_int @ ( bit0 @ SV1266 ) @ min )
= $false )
| ( ( ord_less_eq_int @ SV1266 @ min )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5471]) ).
thf(5958,plain,
! [SV1450: int,SV1267: int] :
( ( ( ~ ( ord_less_eq_nat @ ( number_number_of_nat @ SV1267 ) @ ( number_number_of_nat @ SV1450 ) ) )
= $true )
| ( ( ~ ( ord_less_nat @ ( number_number_of_nat @ SV1450 ) @ ( number_number_of_nat @ SV1267 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5472]) ).
thf(5959,plain,
! [SV1268: int,SV1451: int] :
( ( ( ord_less_nat @ ( number_number_of_nat @ SV1451 ) @ ( number_number_of_nat @ SV1268 ) )
= $true )
| ( ( ord_less_eq_nat @ ( number_number_of_nat @ SV1268 ) @ ( number_number_of_nat @ SV1451 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5473]) ).
thf(5960,plain,
! [SV1269: int] :
( ( ( ord_less_eq_int @ ( number_number_of_int @ SV1269 ) @ one_one_int )
= $false )
| ( ( ord_less_eq_int @ SV1269 @ ( bit1 @ pls ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5474]) ).
thf(5961,plain,
! [SV1270: int] :
( ( ( ord_less_eq_int @ SV1270 @ ( bit1 @ pls ) )
= $false )
| ( ( ord_less_eq_int @ ( number_number_of_int @ SV1270 ) @ one_one_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5475]) ).
thf(5962,plain,
! [SV1452: int,SV466: int,SV1494: int] :
( ( ~ ( dvd_dvd_int @ SV1494 @ ( minus_minus_int @ SV466 @ SV1452 ) )
| ( zcong @ SV466 @ SV1452 @ SV1494 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5476]) ).
thf(5963,plain,
! [SV1495: int,SV1453: int,SV466: int] :
( ( ~ ( zcong @ SV466 @ SV1453 @ SV1495 )
| ( dvd_dvd_int @ SV1495 @ ( minus_minus_int @ SV466 @ SV1453 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5477]) ).
thf(5964,plain,
! [SV1271: int] :
( ( ( ( number_number_of_nat @ SV1271 )
= zero_zero_nat )
= $false )
| ( ( ( power_power_real @ zero_zero_real @ ( number_number_of_nat @ SV1271 ) )
= one_one_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5478]) ).
thf(5965,plain,
! [SV1273: int] :
( ( ( ord_less_int @ ( bit0 @ SV1273 ) @ zero_zero_int )
= $false )
| ( ( ord_less_int @ SV1273 @ zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5480]) ).
thf(5966,plain,
! [SV1274: int] :
( ( ( ord_less_int @ SV1274 @ zero_zero_int )
= $false )
| ( ( ord_less_int @ ( bit0 @ SV1274 ) @ zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5481]) ).
thf(5967,plain,
! [SV1275: int] :
( ( ( ord_less_eq_int @ pls @ ( bit1 @ SV1275 ) )
= $false )
| ( ( ord_less_eq_int @ pls @ SV1275 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5482]) ).
thf(5968,plain,
! [SV1276: int] :
( ( ( ord_less_eq_int @ pls @ SV1276 )
= $false )
| ( ( ord_less_eq_int @ pls @ ( bit1 @ SV1276 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5483]) ).
thf(5969,plain,
! [SV1454: int,SV1277: int] :
( ( ( ~ ( ord_less_int @ ( number_number_of_int @ SV1277 ) @ ( number_number_of_int @ SV1454 ) ) )
= $true )
| ( ( ord_less_int @ SV1277 @ SV1454 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5484]) ).
thf(5970,plain,
! [SV1455: int,SV1278: int] :
( ( ( ~ ( ord_less_int @ SV1278 @ SV1455 ) )
= $true )
| ( ( ord_less_int @ ( number_number_of_int @ SV1278 ) @ ( number_number_of_int @ SV1455 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5485]) ).
thf(5971,plain,
! [SV1456: nat,SV467: nat,SV1496: int] :
( ( ~ ( ord_less_int @ one_one_int @ SV1496 )
| ( ( power_power_int @ SV1496 @ SV467 )
!= ( power_power_int @ SV1496 @ SV1456 ) )
| ( SV467 = SV1456 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5486]) ).
thf(5972,plain,
! [SV1457: nat,SV467: nat,SV1497: int] :
( ( ~ ( ord_less_int @ one_one_int @ SV1497 )
| ( SV467 != SV1457 )
| ( ( power_power_int @ SV1497 @ SV467 )
= ( power_power_int @ SV1497 @ SV1457 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5487]) ).
thf(5973,plain,
! [SV984: int,SV797: int,SV472: int,SV8: int] :
( ( ( ~ ( ord_less_eq_int @ SV8 @ SV472 ) )
= $true )
| ( ( ord_less_int @ ( plus_plus_int @ SV797 @ SV8 ) @ ( plus_plus_int @ SV984 @ SV472 ) )
= $true )
| ( ( ord_less_int @ SV797 @ SV984 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5488]) ).
thf(5974,plain,
! [SV806: int,SV488: int,SV28: int] :
( ( ( ord_less_int @ zero_zero_int @ SV28 )
= $false )
| ( ( ord_less_int @ ( times_times_int @ SV28 @ SV488 ) @ ( times_times_int @ SV28 @ SV806 ) )
= $true )
| ( ( ord_less_int @ SV488 @ SV806 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5491]) ).
thf(5975,plain,
! [SV29: int,SV489: int] :
( ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV489 ) )
= $true )
| ( ( SV29 = SV489 )
= $true )
| ( ( ord_less_eq_int @ zero_zero_int @ SV29 )
= $false )
| ( ( ( power_power_int @ SV29 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power_int @ SV489 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5492]) ).
thf(5976,plain,
! [SV510: int,SV88: int,SV810: int] :
( ( ( SV810
= ( plus_plus_int @ SV88 @ ( times_times_int @ SV810 @ SV510 ) ) )
= $false )
| ( ( ~ ( ord_less_int @ SV88 @ SV810 )
| ( ord_less_eq_int @ one_one_int @ SV510 ) )
= $true )
| ( ( ord_less_int @ zero_zero_int @ SV810 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5496]) ).
thf(5977,plain,
! [SV511: int,SV89: int,SV811: int] :
( ( ( SV811
= ( plus_plus_int @ SV89 @ ( times_times_int @ SV811 @ SV511 ) ) )
= $false )
| ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV89 )
| ( ord_less_eq_int @ SV511 @ one_one_int ) )
= $true )
| ( ( ord_less_int @ zero_zero_int @ SV811 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5497]) ).
thf(5978,plain,
! [SV514: nat,SV92: int,SV812: int] :
( ( ( dvd_dvd_int @ SV812 @ ( power_power_int @ SV92 @ SV514 ) )
= $false )
| ( ( dvd_dvd_int @ SV812 @ SV92 )
= $true )
| ( ( zprime @ SV812 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5498]) ).
thf(5979,plain,
! [SV517: int,SV95: int] :
( ( ( dvd_dvd_int @ SV95 @ SV517 )
= $false )
| ( ( ord_less_int @ SV517 @ SV95 )
= $false )
| ( ( ord_less_int @ zero_zero_int @ SV517 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5499]) ).
thf(5980,plain,
! [SV96: int,SV518: int] :
( ( ( ~ ( dvd_dvd_int @ SV518 @ SV96 ) )
= $true )
| ( ( ~ ( dvd_dvd_int @ SV96 @ SV518 )
| ( SV518 = SV96 ) )
= $true )
| ( ( ord_less_eq_int @ zero_zero_int @ SV96 )
= $false )
| ( ( ord_less_eq_int @ zero_zero_int @ SV518 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5500]) ).
thf(5981,plain,
! [SV1279: int,SV986: int,SV827: int,SV536: int,SV125: int] :
( ( ( ( SV125 = SV536 )
| ( SV827 != SV986 ) )
= $true )
| ( ( ( plus_plus_int @ SV827 @ ( times_times_int @ SV1279 @ SV125 ) )
!= ( plus_plus_int @ SV986 @ ( times_times_int @ SV1279 @ SV536 ) ) )
= $true )
| ( ( SV1279 = zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5503]) ).
thf(5982,plain,
! [SV543: int,SV133: int,SV828: int] :
( ( ( ord_less_int @ SV828 @ SV133 )
= $false )
| ( ( ~ ( ord_less_int @ zero_zero_int @ SV133 )
| ( ord_less_eq_int @ zero_zero_int @ SV543 ) )
= $true )
| ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ SV133 @ SV543 ) @ SV828 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5507]) ).
thf(5983,plain,
! [SV544: int,SV134: int,SV829: int] :
( ( ( ord_less_eq_int @ zero_zero_int @ SV829 )
= $false )
| ( ( ~ ( ord_less_int @ zero_zero_int @ SV134 )
| ( ord_less_eq_int @ SV544 @ zero_zero_int ) )
= $true )
| ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ SV134 @ SV544 ) @ SV829 ) @ zero_zero_int )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5508]) ).
thf(5984,plain,
! [SV1280: int,SV987: int,SV830: int,SV545: int,SV135: int] :
( ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SV135 @ SV545 ) @ SV830 ) @ ( plus_plus_int @ ( times_times_int @ SV135 @ SV987 ) @ SV1280 ) )
= $false )
| ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV830 )
| ~ ( ord_less_int @ SV830 @ SV135 )
| ~ ( ord_less_int @ SV1280 @ SV135 )
| ( ord_less_eq_int @ SV545 @ SV987 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5509]) ).
thf(5985,plain,
! [SV1458: int,SV1281: int,SV988: int,SV831: int,SV546: int,SV136: int] :
( ( ( ( plus_plus_int @ ( times_times_int @ SV136 @ SV546 ) @ SV831 )
!= ( plus_plus_int @ ( times_times_int @ SV988 @ SV1281 ) @ SV1458 ) )
= $true )
| ( ( ~ ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ SV988 @ SV1281 ) @ SV1458 ) )
| ~ ( ord_less_int @ SV1458 @ SV988 )
| ~ ( ord_less_eq_int @ zero_zero_int @ SV831 )
| ~ ( ord_less_int @ zero_zero_int @ SV988 )
| ~ ( ord_less_eq_int @ SV988 @ SV136 )
| ( ord_less_eq_int @ SV546 @ SV1281 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5510]) ).
thf(5986,plain,
! [SV1282: int,SV989: int,SV832: int,SV547: int,SV137: int] :
( ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SV137 @ SV547 ) @ SV832 ) @ ( plus_plus_int @ ( times_times_int @ SV137 @ SV989 ) @ SV1282 ) )
= $false )
| ( ( ~ ( ord_less_eq_int @ SV1282 @ zero_zero_int )
| ~ ( ord_less_int @ SV137 @ SV1282 )
| ~ ( ord_less_int @ SV137 @ SV832 )
| ( ord_less_eq_int @ SV989 @ SV547 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5511]) ).
thf(5987,plain,
! [SV1459: int,SV1283: int,SV990: int,SV833: int,SV548: int,SV138: int] :
( ( ( ( plus_plus_int @ ( times_times_int @ SV138 @ SV548 ) @ SV833 )
!= ( plus_plus_int @ ( times_times_int @ SV990 @ SV1283 ) @ SV1459 ) )
= $true )
| ( ( ~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ SV990 @ SV1283 ) @ SV1459 ) @ zero_zero_int )
| ~ ( ord_less_int @ SV833 @ SV138 )
| ~ ( ord_less_eq_int @ zero_zero_int @ SV1459 )
| ~ ( ord_less_int @ zero_zero_int @ SV990 )
| ~ ( ord_less_eq_int @ SV990 @ SV138 )
| ( ord_less_eq_int @ SV1283 @ SV548 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5512]) ).
thf(5988,plain,
! [SV549: int,SV143: int,SV834: int] :
( ( ( dvd_dvd_int @ SV834 @ SV143 )
= $false )
| ( ( zcong @ ( power_power_int @ SV143 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SV549 @ SV834 )
= $false )
| ( ( zcong @ SV549 @ zero_zero_int @ SV834 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5513]) ).
thf(5989,plain,
! [SV551: int,SV835: int,SV147: int] :
( ( ( ord_less_int @ SV147 @ SV835 )
= $false )
| ( ( ( ord_less_eq_int @ SV551 @ SV147 )
| ( ord_less_eq_int @ SV147 @ SV551 ) )
= $true )
| ( ( ord_less_int @ SV551 @ SV835 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5514]) ).
thf(5990,plain,
! [SV553: int,SV149: int,SV1284: int,SV991: int,SV836: int] :
( ( ( zcong @ SV836 @ SV991 @ SV1284 )
= $false )
| ( ( ~ ( zcong @ SV149 @ SV553 @ SV1284 )
| ( zcong @ ( plus_plus_int @ SV836 @ SV149 ) @ ( plus_plus_int @ SV991 @ SV553 ) @ SV1284 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5515]) ).
thf(5991,plain,
! [SV150: int,SV554: int,SV837: int] :
( ( ( ord_less_int @ SV837 @ SV554 )
= $false )
| ( ( ~ ( ord_less_int @ zero_zero_int @ SV150 )
| ~ ( ord_less_int @ SV150 @ SV837 )
| ~ ( zcong @ SV837 @ SV150 @ SV554 ) )
= $true )
| ( ( ord_less_int @ zero_zero_int @ SV837 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5516]) ).
thf(5992,plain,
! [SV151: int,SV555: int] :
( ( ( ~ ( zcong @ SV555 @ zero_zero_int @ SV151 ) )
= $true )
| ( ( SV555 = zero_zero_int )
= $true )
| ( ( ord_less_int @ SV555 @ SV151 )
= $false )
| ( ( ord_less_eq_int @ zero_zero_int @ SV555 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5517]) ).
thf(5993,plain,
! [SV152: int,SV556: int,SV838: int] :
( ( ( ord_less_int @ SV838 @ SV556 )
= $false )
| ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV152 )
| ~ ( ord_less_int @ SV152 @ SV556 )
| ~ ( zcong @ SV838 @ SV152 @ SV556 )
| ( SV838 = SV152 ) )
= $true )
| ( ( ord_less_eq_int @ zero_zero_int @ SV838 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5518]) ).
thf(5994,plain,
! [SV1498: int,SV1460: int,SV1285: int,SV993: int,SV841: int,SV562: int,SV160: int] :
( ( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ SV160 @ ( times_times_int @ SV562 @ SV841 ) ) @ SV993 ) @ ( times_times_int @ ( minus_minus_int @ SV1285 @ ( times_times_int @ SV562 @ SV1460 ) ) @ SV1498 ) )
= ( minus_minus_int @ ( plus_plus_int @ ( times_times_int @ SV160 @ SV993 ) @ ( times_times_int @ SV1285 @ SV1498 ) ) @ ( times_times_int @ SV562 @ ( plus_plus_int @ ( times_times_int @ SV841 @ SV993 ) @ ( times_times_int @ SV1460 @ SV1498 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5520]) ).
thf(5995,plain,
! [SV162: int,SV564: int] :
( ( ( SV564
= ( minus_minus_int @ SV162 @ one_one_int ) )
= $true )
| ( ( ord_less_int @ SV564 @ ( minus_minus_int @ SV162 @ one_one_int ) )
= $true )
| ( ( ord_less_int @ SV564 @ SV162 )
= $false )
| ( ( ord_less_int @ zero_zero_int @ SV564 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5521]) ).
thf(5996,plain,
! [SV845: int,SV170: int,SV568: int] :
( ( ( ord_less_int @ zero_zero_int @ SV568 )
= $false )
| ( ( ~ ( ord_less_int @ zero_zero_int @ SV170 )
| ~ ( zcong @ SV845 @ SV568 @ SV170 )
| ~ ( ord_less_int @ SV845 @ SV170 )
| ~ ( ord_less_int @ SV568 @ SV170 )
| ( SV845 = SV568 ) )
= $true )
| ( ( ord_less_int @ zero_zero_int @ SV845 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5524]) ).
thf(5997,plain,
! [SV171: int,SV569: int] :
( ( ( zcong @ SV569 @ zero_zero_int @ SV171 )
= $false )
| ( ( ord_less_int @ SV569 @ SV171 )
= $false )
| ( ( ord_less_int @ zero_zero_int @ SV569 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5525]) ).
thf(5998,plain,
! [SV173: int,SV571: int] :
( ( ( ~ ( zcong @ SV571 @ zero_zero_int @ SV173 ) )
= $true )
| ( ( SV571 = zero_zero_int )
= $true )
| ( ( ord_less_int @ SV571 @ SV173 )
= $false )
| ( ( ord_less_eq_int @ zero_zero_int @ SV571 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5526]) ).
thf(5999,plain,
! [SV851: int,SV185: nat,SV579: int] :
( ( ( ord_less_eq_int @ zero_zero_int @ SV579 )
= $false )
| ( ( ord_less_eq_int @ ( power_power_int @ SV579 @ SV185 ) @ ( power_power_int @ SV851 @ SV185 ) )
= $true )
| ( ( ord_less_eq_int @ SV579 @ SV851 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5527]) ).
thf(6000,plain,
! [SV998: int,SV584: int,SV853: nat,SV191: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV191 @ SV853 ) )
= $true )
| ( ( dvd_dvd_int @ ( power_power_int @ SV584 @ SV191 ) @ SV998 )
= $true )
| ( ( dvd_dvd_int @ ( power_power_int @ SV584 @ SV853 ) @ SV998 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5528]) ).
thf(6001,plain,
! [SV999: int,SV854: int,SV585: nat,SV192: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV192 @ SV585 ) )
= $true )
| ( ( dvd_dvd_int @ ( power_power_int @ SV854 @ SV192 ) @ ( power_power_int @ SV999 @ SV585 ) )
= $true )
| ( ( dvd_dvd_int @ SV854 @ SV999 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5529]) ).
thf(6002,plain,
! [SV587: nat,SV194: int,SV856: int] :
( ( ( ord_less_eq_int @ zero_zero_int @ SV856 )
= $false )
| ( ( ord_less_int @ SV194 @ SV856 )
= $true )
| ( ( ord_less_int @ ( power_power_int @ SV194 @ SV587 ) @ ( power_power_int @ SV856 @ SV587 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5530]) ).
thf(6003,plain,
! [SV857: nat,SV590: nat,SV197: int] :
( ( ( ord_less_int @ one_one_int @ SV197 )
= $false )
| ( ( ord_less_int @ ( power_power_int @ SV197 @ SV590 ) @ ( power_power_int @ SV197 @ SV857 ) )
= $true )
| ( ( ord_less_nat @ SV590 @ SV857 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5531]) ).
thf(6004,plain,
! [SV591: nat,SV198: nat,SV858: int] :
( ( ( ord_less_int @ ( power_power_int @ SV858 @ SV198 ) @ ( power_power_int @ SV858 @ SV591 ) )
= $false )
| ( ( ord_less_nat @ SV198 @ SV591 )
= $true )
| ( ( ord_less_int @ one_one_int @ SV858 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5532]) ).
thf(6005,plain,
! [SV859: nat,SV592: nat,SV199: int] :
( ( ( ord_less_eq_int @ one_one_int @ SV199 )
= $false )
| ( ( ord_less_eq_int @ ( power_power_int @ SV199 @ SV592 ) @ ( power_power_int @ SV199 @ SV859 ) )
= $true )
| ( ( ord_less_eq_nat @ SV592 @ SV859 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5533]) ).
thf(6006,plain,
! [SV594: nat,SV860: nat,SV201: int] :
( ( ( ord_less_int @ zero_zero_int @ SV201 )
= $false )
| ( ( ~ ( ord_less_int @ SV201 @ one_one_int )
| ( ord_less_int @ ( power_power_int @ SV201 @ SV860 ) @ ( power_power_int @ SV201 @ SV594 ) ) )
= $true )
| ( ( ord_less_nat @ SV594 @ SV860 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5535]) ).
thf(6007,plain,
! [SV600: int,SV212: int,SV862: int] :
( ( ( ord_less_eq_int @ SV862 @ SV212 )
= $false )
| ( ( ord_less_eq_int @ SV600 @ SV212 )
= $true )
| ( ( ord_less_eq_int @ SV600 @ SV862 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5536]) ).
thf(6008,plain,
! [SV227: real,SV615: real] :
( ( ( ~ ( ord_less_eq_real @ zero_zero_real @ SV615 ) )
= $true )
| ( ( SV227 = SV615 )
= $true )
| ( ( ord_less_eq_real @ zero_zero_real @ SV227 )
= $false )
| ( ( ( power_power_real @ SV227 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power_real @ SV615 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5542]) ).
thf(6009,plain,
! [SV228: nat,SV616: nat] :
( ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV616 ) )
= $true )
| ( ( SV228 = SV616 )
= $true )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV228 )
= $false )
| ( ( ( power_power_nat @ SV228 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power_nat @ SV616 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5543]) ).
thf(6010,plain,
! [SV628: int,SV249: nat,SV869: int,SV1000: int] :
( ( ( dvd_dvd_int @ SV1000 @ SV869 )
= $true )
| ( ( ~ ( dvd_dvd_int @ ( power_power_int @ SV1000 @ SV249 ) @ ( times_times_int @ SV628 @ SV869 ) )
| ( dvd_dvd_int @ ( power_power_int @ SV1000 @ SV249 ) @ SV628 ) )
= $true )
| ( ( zprime @ SV1000 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5548]) ).
thf(6011,plain,
! [SV629: int,SV250: nat,SV870: int,SV1001: int] :
( ( ( dvd_dvd_int @ SV1001 @ SV870 )
= $true )
| ( ( ~ ( dvd_dvd_int @ ( power_power_int @ SV1001 @ SV250 ) @ ( times_times_int @ SV870 @ SV629 ) )
| ( dvd_dvd_int @ ( power_power_int @ SV1001 @ SV250 ) @ SV629 ) )
= $true )
| ( ( zprime @ SV1001 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5549]) ).
thf(6012,plain,
! [SV1286: real,SV1013: real,SV913: real,SV678: real,SV316: real] :
( ( ( ( SV316 = SV678 )
| ( SV913 != SV1013 ) )
= $true )
| ( ( ( plus_plus_real @ SV913 @ ( times_times_real @ SV1286 @ SV316 ) )
!= ( plus_plus_real @ SV1013 @ ( times_times_real @ SV1286 @ SV678 ) ) )
= $true )
| ( ( SV1286 = zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5551]) ).
thf(6013,plain,
! [SV1287: nat,SV1014: nat,SV914: nat,SV679: nat,SV317: nat] :
( ( ( ( SV317 = SV679 )
| ( SV914 != SV1014 ) )
= $true )
| ( ( ( plus_plus_nat @ SV914 @ ( times_times_nat @ SV1287 @ SV317 ) )
!= ( plus_plus_nat @ SV1014 @ ( times_times_nat @ SV1287 @ SV679 ) ) )
= $true )
| ( ( SV1287 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5552]) ).
thf(6014,plain,
! [SV685: int,SV1015: int,SV327: int,SV916: int] :
( ( ( ~ ( zcong @ SV916 @ SV327 @ SV1015 ) )
= $true )
| ( ( zcong @ SV685 @ SV327 @ SV1015 )
= $true )
| ( ( zcong @ SV685 @ SV916 @ SV1015 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5553]) ).
thf(6015,plain,
! [SV691: int,SV333: int,SV1288: int,SV1018: int,SV920: int] :
( ( ( zcong @ SV920 @ SV1018 @ SV1288 )
= $false )
| ( ( ~ ( zcong @ SV333 @ SV691 @ SV1288 )
| ( zcong @ ( times_times_int @ SV920 @ SV333 ) @ ( times_times_int @ SV1018 @ SV691 ) @ SV1288 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5556]) ).
thf(6016,plain,
! [SV337: int,SV921: int,SV692: int] :
( ( ( zprime @ SV692 )
= $false )
| ( ( ~ ( dvd_dvd_int @ SV692 @ ( times_times_int @ SV921 @ SV337 ) )
| ( dvd_dvd_int @ SV692 @ SV921 )
| ( dvd_dvd_int @ SV692 @ SV337 ) )
= $true )
| ( ( ord_less_eq_int @ zero_zero_int @ SV921 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5557]) ).
thf(6017,plain,
! [SV922: int,SV693: nat,SV338: nat] :
( ( ( zcong @ ( power_power_int @ ( number_number_of_int @ min ) @ SV338 ) @ ( power_power_int @ ( number_number_of_int @ min ) @ SV693 ) @ SV922 )
= $false )
| ( ( ( power_power_int @ ( number_number_of_int @ min ) @ SV338 )
= ( power_power_int @ ( number_number_of_int @ min ) @ SV693 ) )
= $true )
| ( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV922 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5558]) ).
thf(6018,plain,
! [SV694: int,SV339: int] :
( ( ( zcong @ SV339 @ one_one_int @ SV694 )
= $false )
| ( ( zcong @ SV339 @ ( number_number_of_int @ min ) @ SV694 )
= $false )
| ( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV694 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5559]) ).
thf(6019,plain,
! [SV695: int,SV340: int,SV1289: int,SV1019: int,SV923: int] :
( ( ( zcong @ SV923 @ SV1019 @ SV1289 )
= $false )
| ( ( ~ ( zcong @ SV340 @ SV695 @ SV1289 )
| ( zcong @ ( minus_minus_int @ SV923 @ SV340 ) @ ( minus_minus_int @ SV1019 @ SV695 ) @ SV1289 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5560]) ).
thf(6020,plain,
! [SV696: int,SV924: int,SV341: int] :
( ( ( dvd_dvd_int @ SV341 @ SV924 )
= $false )
| ( ( dvd_dvd_int @ SV341 @ SV696 )
= $true )
| ( ( dvd_dvd_int @ SV341 @ ( minus_minus_int @ SV696 @ SV924 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5561]) ).
thf(6021,plain,
! [SV351: int,SV706: int,SV1290: int,SV1020: int,SV932: int] :
( ( ( zcong @ SV932 @ SV1020 @ SV1290 )
= $false )
| ( ( ( SV1020 != SV706 )
| ~ ( zcong @ SV706 @ SV351 @ SV1290 )
| ( zcong @ SV932 @ SV351 @ SV1290 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5562]) ).
thf(6022,plain,
! [SV707: int,SV352: int] :
( ( ( ~ ( ord_less_int @ SV352 @ SV707 ) )
= $true )
| ( ( ~ ( zcong @ ( times_times_int @ SV352 @ SV352 ) @ one_one_int @ SV707 )
| ( SV352 = one_one_int )
| ( SV352
= ( minus_minus_int @ SV707 @ one_one_int ) ) )
= $true )
| ( ( ord_less_int @ zero_zero_int @ SV352 )
= $false )
| ( ( zprime @ SV707 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5563]) ).
thf(6023,plain,
! [SV708: int,SV353: int] :
( ( ( ~ ( zcong @ ( times_times_int @ SV353 @ SV353 ) @ one_one_int @ SV708 ) )
= $true )
| ( ( ( zcong @ SV353 @ one_one_int @ SV708 )
| ( zcong @ SV353 @ ( minus_minus_int @ SV708 @ one_one_int ) @ SV708 ) )
= $true )
| ( ( ord_less_int @ zero_zero_int @ SV353 )
= $false )
| ( ( zprime @ SV708 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5564]) ).
thf(6024,plain,
! [SV713: int,SV358: int,SV933: int] :
( ( ( dvd_dvd_int @ SV933 @ ( times_times_int @ SV358 @ SV713 ) )
= $false )
| ( ( ( dvd_dvd_int @ SV933 @ SV358 )
| ( dvd_dvd_int @ SV933 @ SV713 ) )
= $true )
| ( ( zprime @ SV933 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5565]) ).
thf(6025,plain,
! [SV934: nat,SV714: int,SV359: int] :
( ( ( dvd_dvd_int @ SV359 @ SV714 )
= $false )
| ( ( dvd_dvd_int @ SV359 @ ( power_power_int @ SV714 @ SV934 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV934 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5566]) ).
thf(6026,plain,
! [SV715: int,SV935: int,SV360: int] :
( ( ( zcong @ SV360 @ zero_zero_int @ SV935 )
= $true )
| ( ( ~ ( zcong @ ( times_times_int @ SV715 @ SV360 ) @ zero_zero_int @ SV935 ) )
= $true )
| ( ( zcong @ SV715 @ zero_zero_int @ SV935 )
= $true )
| ( ( zprime @ SV935 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5567]) ).
thf(6027,plain,
! [SV361: int,SV936: int,SV716: int] :
( ( ( ord_less_int @ zero_zero_int @ SV716 )
= $false )
| ( ( ( zcong @ SV716 @ zero_zero_int @ SV936 )
| ( zcong @ SV361 @ zero_zero_int @ SV936 )
| ~ ( zcong @ ( times_times_int @ SV716 @ SV361 ) @ zero_zero_int @ SV936 ) )
= $true )
| ( ( zprime @ SV936 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5568]) ).
thf(6028,plain,
! [SV937: int,SV362: int,SV717: int] :
( ( ( ord_less_int @ zero_zero_int @ SV717 )
= $false )
| ( ( ~ ( zcong @ ( times_times_int @ SV717 @ SV362 ) @ zero_zero_int @ SV937 )
| ( zcong @ SV717 @ zero_zero_int @ SV937 )
| ( zcong @ SV362 @ zero_zero_int @ SV937 ) )
= $true )
| ( ( zprime @ SV937 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5569]) ).
thf(6029,plain,
! [SV718: nat,SV363: int,SV938: int] :
( ( ( dvd_dvd_int @ SV938 @ ( power_power_int @ SV363 @ SV718 ) )
= $false )
| ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV718 )
| ( dvd_dvd_int @ SV938 @ SV363 ) )
= $true )
| ( ( zprime @ SV938 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5570]) ).
thf(6030,plain,
! [SV944: real,SV727: real,SV375: real] :
( ( ( ord_less_real @ SV375 @ SV727 )
= $false )
| ( ( ord_less_real @ ( times_times_real @ SV944 @ SV375 ) @ ( times_times_real @ SV944 @ SV727 ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV944 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5571]) ).
thf(6031,plain,
! [SV945: real,SV382: nat,SV732: real] :
( ( ( ord_less_eq_real @ zero_zero_real @ SV732 )
= $false )
| ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV382 )
| ( ord_less_real @ ( power_power_real @ SV732 @ SV382 ) @ ( power_power_real @ SV945 @ SV382 ) ) )
= $true )
| ( ( ord_less_real @ SV732 @ SV945 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5573]) ).
thf(6032,plain,
! [SV946: nat,SV383: nat,SV733: nat] :
( ( ( ord_less_eq_nat @ zero_zero_nat @ SV733 )
= $false )
| ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV383 )
| ( ord_less_nat @ ( power_power_nat @ SV733 @ SV383 ) @ ( power_power_nat @ SV946 @ SV383 ) ) )
= $true )
| ( ( ord_less_nat @ SV733 @ SV946 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5574]) ).
thf(6033,plain,
! [SV947: int,SV384: nat,SV734: int] :
( ( ( ord_less_eq_int @ zero_zero_int @ SV734 )
= $false )
| ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV384 )
| ( ord_less_int @ ( power_power_int @ SV734 @ SV384 ) @ ( power_power_int @ SV947 @ SV384 ) ) )
= $true )
| ( ( ord_less_int @ SV734 @ SV947 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5575]) ).
thf(6034,plain,
! [SV954: real,SV398: nat,SV744: real] :
( ( ( ord_less_eq_real @ zero_zero_real @ SV744 )
= $false )
| ( ( ord_less_eq_real @ ( power_power_real @ SV744 @ SV398 ) @ ( power_power_real @ SV954 @ SV398 ) )
= $true )
| ( ( ord_less_eq_real @ SV744 @ SV954 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5576]) ).
thf(6035,plain,
! [SV955: nat,SV399: nat,SV745: nat] :
( ( ( ord_less_eq_nat @ zero_zero_nat @ SV745 )
= $false )
| ( ( ord_less_eq_nat @ ( power_power_nat @ SV745 @ SV399 ) @ ( power_power_nat @ SV955 @ SV399 ) )
= $true )
| ( ( ord_less_eq_nat @ SV745 @ SV955 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5577]) ).
thf(6036,plain,
! [SV1023: nat,SV754: nat,SV958: nat,SV410: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV410 @ SV958 ) )
= $true )
| ( ( dvd_dvd_nat @ ( power_power_nat @ SV754 @ SV410 ) @ SV1023 )
= $true )
| ( ( dvd_dvd_nat @ ( power_power_nat @ SV754 @ SV958 ) @ SV1023 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5578]) ).
thf(6037,plain,
! [SV1024: real,SV755: real,SV959: nat,SV411: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV411 @ SV959 ) )
= $true )
| ( ( dvd_dvd_real @ ( power_power_real @ SV755 @ SV411 ) @ SV1024 )
= $true )
| ( ( dvd_dvd_real @ ( power_power_real @ SV755 @ SV959 ) @ SV1024 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5579]) ).
thf(6038,plain,
! [SV1025: nat,SV960: nat,SV756: nat,SV412: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV412 @ SV756 ) )
= $true )
| ( ( dvd_dvd_nat @ ( power_power_nat @ SV960 @ SV412 ) @ ( power_power_nat @ SV1025 @ SV756 ) )
= $true )
| ( ( dvd_dvd_nat @ SV960 @ SV1025 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5580]) ).
thf(6039,plain,
! [SV1026: real,SV961: real,SV757: nat,SV413: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV413 @ SV757 ) )
= $true )
| ( ( dvd_dvd_real @ ( power_power_real @ SV961 @ SV413 ) @ ( power_power_real @ SV1026 @ SV757 ) )
= $true )
| ( ( dvd_dvd_real @ SV961 @ SV1026 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5581]) ).
thf(6040,plain,
! [SV760: nat,SV416: nat,SV964: nat] :
( ( ( ord_less_nat @ ( power_power_nat @ SV964 @ SV416 ) @ ( power_power_nat @ SV964 @ SV760 ) )
= $false )
| ( ( ord_less_nat @ SV416 @ SV760 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV964 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5582]) ).
thf(6041,plain,
! [SV761: nat,SV417: real,SV965: real] :
( ( ( ord_less_eq_real @ zero_zero_real @ SV965 )
= $false )
| ( ( ord_less_real @ SV417 @ SV965 )
= $true )
| ( ( ord_less_real @ ( power_power_real @ SV417 @ SV761 ) @ ( power_power_real @ SV965 @ SV761 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5583]) ).
thf(6042,plain,
! [SV762: nat,SV418: nat,SV966: nat] :
( ( ( ord_less_eq_nat @ zero_zero_nat @ SV966 )
= $false )
| ( ( ord_less_nat @ SV418 @ SV966 )
= $true )
| ( ( ord_less_nat @ ( power_power_nat @ SV418 @ SV762 ) @ ( power_power_nat @ SV966 @ SV762 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5584]) ).
thf(6043,plain,
! [SV967: nat,SV767: nat,SV423: real] :
( ( ( ord_less_real @ one_one_real @ SV423 )
= $false )
| ( ( ord_less_real @ ( power_power_real @ SV423 @ SV767 ) @ ( power_power_real @ SV423 @ SV967 ) )
= $true )
| ( ( ord_less_nat @ SV767 @ SV967 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5585]) ).
thf(6044,plain,
! [SV968: nat,SV768: nat,SV424: nat] :
( ( ( ord_less_nat @ one_one_nat @ SV424 )
= $false )
| ( ( ord_less_nat @ ( power_power_nat @ SV424 @ SV768 ) @ ( power_power_nat @ SV424 @ SV968 ) )
= $true )
| ( ( ord_less_nat @ SV768 @ SV968 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5586]) ).
thf(6045,plain,
! [SV769: nat,SV425: nat,SV969: real] :
( ( ( ord_less_real @ ( power_power_real @ SV969 @ SV425 ) @ ( power_power_real @ SV969 @ SV769 ) )
= $false )
| ( ( ord_less_nat @ SV425 @ SV769 )
= $true )
| ( ( ord_less_real @ one_one_real @ SV969 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5587]) ).
thf(6046,plain,
! [SV770: nat,SV426: nat,SV970: nat] :
( ( ( ord_less_nat @ ( power_power_nat @ SV970 @ SV426 ) @ ( power_power_nat @ SV970 @ SV770 ) )
= $false )
| ( ( ord_less_nat @ SV426 @ SV770 )
= $true )
| ( ( ord_less_nat @ one_one_nat @ SV970 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5588]) ).
thf(6047,plain,
! [SV971: nat,SV771: nat,SV427: real] :
( ( ( ord_less_eq_real @ one_one_real @ SV427 )
= $false )
| ( ( ord_less_eq_real @ ( power_power_real @ SV427 @ SV771 ) @ ( power_power_real @ SV427 @ SV971 ) )
= $true )
| ( ( ord_less_eq_nat @ SV771 @ SV971 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5589]) ).
thf(6048,plain,
! [SV972: nat,SV772: nat,SV428: nat] :
( ( ( ord_less_eq_nat @ one_one_nat @ SV428 )
= $false )
| ( ( ord_less_eq_nat @ ( power_power_nat @ SV428 @ SV772 ) @ ( power_power_nat @ SV428 @ SV972 ) )
= $true )
| ( ( ord_less_eq_nat @ SV772 @ SV972 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5590]) ).
thf(6049,plain,
! [SV435: nat,SV976: nat,SV779: nat] :
( ( ( dvd_dvd_nat @ SV779 @ ( plus_plus_nat @ SV976 @ SV435 ) )
= $false )
| ( ( dvd_dvd_nat @ SV779 @ SV435 )
= $true )
| ( ( dvd_dvd_nat @ SV779 @ SV976 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5593]) ).
thf(6050,plain,
! [SV782: nat,SV438: nat,SV979: nat,SV1027: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV1027 ) )
= $true )
| ( ( ~ ( ord_less_nat @ SV1027 @ SV979 )
| ~ ( dvd_dvd_nat @ SV979 @ SV438 ) )
= $true )
| ( ( SV438
= ( plus_plus_nat @ ( times_times_nat @ SV782 @ SV979 ) @ SV1027 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5596]) ).
thf(6051,plain,
! [SV980: nat,SV783: nat,SV439: nat] :
( ( ( ord_less_nat @ one_one_nat @ SV439 )
= $false )
| ( ( ord_less_eq_nat @ SV783 @ SV980 )
= $true )
| ( ( dvd_dvd_nat @ ( power_power_nat @ SV439 @ SV783 ) @ ( power_power_nat @ SV439 @ SV980 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5597]) ).
thf(6052,plain,
! [SV1030: nat,SV1291: nat] :
( ( ( SV1291 = zero_zero_nat )
= $true )
| ( ( SV1030 != zero_zero_nat )
= $true )
| ( ( ( power_power_nat @ SV1030 @ SV1291 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5601]) ).
thf(6053,plain,
! [SV1499: nat] :
( ( ! [SY2595: nat] :
( ( ( power_power_nat @ SV1499 @ SY2595 )
!= zero_zero_nat )
| ( SY2595 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5602]) ).
thf(6054,plain,
! [SV1500: nat] :
( ( ! [SY2596: nat] :
( ( power_power_nat @ SV1500 @ SY2596 )
!= zero_zero_nat )
| ( SV1500 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5603]) ).
thf(6055,plain,
! [SV1031: nat,SV1292: int] :
( ( ( ( number_number_of_nat @ SV1292 )
= zero_zero_nat )
= $true )
| ( ( SV1031 != zero_zero_nat )
= $true )
| ( ( ( power_power_nat @ SV1031 @ ( number_number_of_nat @ SV1292 ) )
= zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5604]) ).
thf(6056,plain,
! [SV1501: nat] :
( ( ! [SY2597: int] :
( ( ( power_power_nat @ SV1501 @ ( number_number_of_nat @ SY2597 ) )
!= zero_zero_nat )
| ( ( number_number_of_nat @ SY2597 )
!= zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5605]) ).
thf(6057,plain,
! [SV1502: nat] :
( ( ! [SY2598: int] :
( ( power_power_nat @ SV1502 @ ( number_number_of_nat @ SY2598 ) )
!= zero_zero_nat )
| ( SV1502 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5606]) ).
thf(6058,plain,
! [SV1293: real,SV1034: real] :
( ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ SV1034 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SV1293 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $false )
| ( ( ( SV1034 != zero_zero_real )
| ( SV1293 != zero_zero_real ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5609]) ).
thf(6059,plain,
! [SV1503: real] :
( ( ( SV1503 = zero_zero_real )
| ! [SY2599: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ SV1503 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SY2599 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5610]) ).
thf(6060,plain,
! [SV1504: real] :
( ( ! [SY2600: real] :
( ( SY2600 = zero_zero_real )
| ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ SV1504 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SY2600 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5611]) ).
thf(6061,plain,
! [SV1294: int,SV1039: int] :
( ( ( ord_less_eq_int @ SV1039 @ SV1294 )
= $false )
| ( ( ord_less_int @ ( bit0 @ SV1039 ) @ ( bit1 @ SV1294 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5616]) ).
thf(6062,plain,
! [SV1295: int,SV1040: int] :
( ( ( ord_less_int @ ( bit0 @ SV1040 ) @ ( bit1 @ SV1295 ) )
= $false )
| ( ( ord_less_eq_int @ SV1040 @ SV1295 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5617]) ).
thf(6063,plain,
! [SV1296: int,SV1043: int] :
( ( ( ord_less_int @ ( bit1 @ SV1043 ) @ ( bit1 @ SV1296 ) )
= $false )
| ( ( ord_less_int @ SV1043 @ SV1296 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5620]) ).
thf(6064,plain,
! [SV1297: int,SV1044: int] :
( ( ( ord_less_int @ SV1044 @ SV1297 )
= $false )
| ( ( ord_less_int @ ( bit1 @ SV1044 ) @ ( bit1 @ SV1297 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5621]) ).
thf(6065,plain,
! [SV1298: nat,SV1045: nat] :
( ( ( ( power_power_nat @ SV1045 @ SV1298 )
= one_one_nat )
= $false )
| ( ( ( SV1045 = one_one_nat )
| ( SV1298 = zero_zero_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5622]) ).
thf(6066,plain,
! [SV1505: nat] :
( ( ( SV1505 != one_one_nat )
| ! [SY2601: nat] :
( ( power_power_nat @ SV1505 @ SY2601 )
= one_one_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5623]) ).
thf(6067,plain,
! [SV1506: nat] :
( ( ! [SY2602: nat] :
( ( SY2602 != zero_zero_nat )
| ( ( power_power_nat @ SV1506 @ SY2602 )
= one_one_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5624]) ).
thf(6068,plain,
! [SV1299: int,SV1046: int] :
( ( ( ord_less_eq_int @ SV1046 @ SV1299 )
= $false )
| ( ( ord_less_eq_real @ ( number267125858f_real @ SV1046 ) @ ( number267125858f_real @ SV1299 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5625]) ).
thf(6069,plain,
! [SV1300: int,SV1047: int] :
( ( ( ord_less_eq_real @ ( number267125858f_real @ SV1047 ) @ ( number267125858f_real @ SV1300 ) )
= $false )
| ( ( ord_less_eq_int @ SV1047 @ SV1300 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5626]) ).
thf(6070,plain,
! [SV1301: int,SV1050: int] :
( ( ( ( bit1 @ SV1050 )
= ( bit1 @ SV1301 ) )
= $false )
| ( ( SV1050 = SV1301 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5628]) ).
thf(6071,plain,
! [SV1302: int,SV1051: int] :
( ( ( SV1051 = SV1302 )
= $false )
| ( ( ( bit1 @ SV1051 )
= ( bit1 @ SV1302 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5629]) ).
thf(6072,plain,
! [SV1303: int,SV1052: int] :
( ( ( ord_less_int @ ( number_number_of_int @ SV1052 ) @ ( number_number_of_int @ SV1303 ) )
= $false )
| ( ( ord_less_int @ SV1052 @ SV1303 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5630]) ).
thf(6073,plain,
! [SV1304: int,SV1053: int] :
( ( ( ord_less_int @ SV1053 @ SV1304 )
= $false )
| ( ( ord_less_int @ ( number_number_of_int @ SV1053 ) @ ( number_number_of_int @ SV1304 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5631]) ).
thf(6074,plain,
! [SV1305: real,SV1054: real] :
( ( ( SV1054 != zero_zero_real )
= $true )
| ( ( SV1305 != zero_zero_real )
= $true )
| ( ( ord_less_eq_real @ ( plus_plus_real @ ( power_power_real @ SV1054 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SV1305 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5632]) ).
thf(6075,plain,
! [SV1507: real] :
( ( ! [SY2603: real] :
~ ( ord_less_eq_real @ ( plus_plus_real @ ( power_power_real @ SV1507 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SY2603 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_real )
| ( SV1507 = zero_zero_real ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5633]) ).
thf(6076,plain,
! [SV1508: real] :
( ( ! [SY2604: real] :
( ~ ( ord_less_eq_real @ ( plus_plus_real @ ( power_power_real @ SV1508 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SY2604 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_real )
| ( SY2604 = zero_zero_real ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5634]) ).
thf(6077,plain,
! [SV1306: int,SV1055: int] :
( ( ( ord_less_int @ SV1055 @ ( plus_plus_int @ SV1306 @ one_one_int ) )
= $false )
| ( ( ( SV1055 = SV1306 )
| ( ord_less_int @ SV1055 @ SV1306 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5635]) ).
thf(6078,plain,
! [SV1509: int] :
( ( ! [SY2605: int] :
( ( SV1509 != SY2605 )
| ( ord_less_int @ SV1509 @ ( plus_plus_int @ SY2605 @ one_one_int ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5636]) ).
thf(6079,plain,
! [SV1510: int] :
( ( ! [SY2606: int] :
( ~ ( ord_less_int @ SV1510 @ SY2606 )
| ( ord_less_int @ SV1510 @ ( plus_plus_int @ SY2606 @ one_one_int ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5637]) ).
thf(6080,plain,
! [SV785: nat,SV441: nat] :
( ( ~ ! [SY2273: nat,SY2274: nat] :
( ( ( plus_plus_nat @ ( times_times_nat @ SY2273 @ SV441 ) @ ( times_times_nat @ SY2274 @ SV785 ) )
= ( plus_plus_nat @ ( times_times_nat @ SY2273 @ SV785 ) @ ( times_times_nat @ SY2274 @ SV441 ) ) )
| ( SY2273 != SY2274 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5641]) ).
thf(6081,plain,
! [SV785: nat,SV441: nat] :
( ( ~ ( ! [SY2275: nat,SY2276: nat] :
( ( plus_plus_nat @ ( times_times_nat @ SY2275 @ SV441 ) @ ( times_times_nat @ SY2276 @ SV785 ) )
= ( plus_plus_nat @ ( times_times_nat @ SY2275 @ SV785 ) @ ( times_times_nat @ SY2276 @ SV441 ) ) )
| ( SV441 != SV785 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5641]) ).
thf(6082,plain,
! [SV785: nat,SV441: nat,SV1511: nat,SV1461: nat] :
( ( ( SV1461 = SV1511 )
| ( SV441 = SV785 )
| ( ( plus_plus_nat @ ( times_times_nat @ SV1461 @ SV441 ) @ ( times_times_nat @ SV1511 @ SV785 ) )
!= ( plus_plus_nat @ ( times_times_nat @ SV1461 @ SV785 ) @ ( times_times_nat @ SV1511 @ SV441 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5642]) ).
thf(6083,plain,
! [SV1307: int,SV1060: int] :
( ( ( ord_less_eq_int @ ( bit1 @ SV1060 ) @ ( bit1 @ SV1307 ) )
= $false )
| ( ( ord_less_eq_int @ SV1060 @ SV1307 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5643]) ).
thf(6084,plain,
! [SV1308: int,SV1061: int] :
( ( ( ord_less_eq_int @ SV1061 @ SV1308 )
= $false )
| ( ( ord_less_eq_int @ ( bit1 @ SV1061 ) @ ( bit1 @ SV1308 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5644]) ).
thf(6085,plain,
! [SV1309: int,SV1062: int] :
( ( ( ord_less_int @ ( bit0 @ SV1062 ) @ ( bit0 @ SV1309 ) )
= $false )
| ( ( ord_less_int @ SV1062 @ SV1309 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5645]) ).
thf(6086,plain,
! [SV1310: int,SV1063: int] :
( ( ( ord_less_int @ SV1063 @ SV1310 )
= $false )
| ( ( ord_less_int @ ( bit0 @ SV1063 ) @ ( bit0 @ SV1310 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5646]) ).
thf(6087,plain,
! [SV1064: real,SV1311: int] :
( ( ( ( number_number_of_nat @ SV1311 )
= zero_zero_nat )
= $true )
| ( ( SV1064 != zero_zero_real )
= $true )
| ( ( ( power_power_real @ SV1064 @ ( number_number_of_nat @ SV1311 ) )
= zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5647]) ).
thf(6088,plain,
! [SV1512: real] :
( ( ! [SY2607: int] :
( ( ( power_power_real @ SV1512 @ ( number_number_of_nat @ SY2607 ) )
!= zero_zero_real )
| ( ( number_number_of_nat @ SY2607 )
!= zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5648]) ).
thf(6089,plain,
! [SV1513: real] :
( ( ! [SY2608: int] :
( ( power_power_real @ SV1513 @ ( number_number_of_nat @ SY2608 ) )
!= zero_zero_real )
| ( SV1513 = zero_zero_real ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5649]) ).
thf(6090,plain,
! [SV1312: real,SV1065: real] :
( ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ SV1065 @ SV1065 ) @ ( times_times_real @ SV1312 @ SV1312 ) ) )
= $false )
| ( ( ( SV1065 != zero_zero_real )
| ( SV1312 != zero_zero_real ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5650]) ).
thf(6091,plain,
! [SV1514: real] :
( ( ( SV1514 = zero_zero_real )
| ! [SY2609: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ SV1514 @ SV1514 ) @ ( times_times_real @ SY2609 @ SY2609 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5651]) ).
thf(6092,plain,
! [SV1515: real] :
( ( ! [SY2610: real] :
( ( SY2610 = zero_zero_real )
| ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ SV1515 @ SV1515 ) @ ( times_times_real @ SY2610 @ SY2610 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5652]) ).
thf(6093,plain,
! [SV1313: nat,SV1066: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV1066 @ SV1313 ) )
= $false )
| ( ( ( SV1313 = zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV1066 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5653]) ).
thf(6094,plain,
! [SV1516: nat] :
( ( ! [SY2611: nat] :
( ( SY2611 != zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV1516 @ SY2611 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5654]) ).
thf(6095,plain,
! [SV1517: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ SV1517 )
| ! [SY2612: nat] : ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV1517 @ SY2612 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5655]) ).
thf(6096,plain,
! [SV786: real,SV442: real] :
( ( ~ ! [SY2279: real,SY2280: real] :
( ( ( plus_plus_real @ ( times_times_real @ SY2279 @ SV442 ) @ ( times_times_real @ SY2280 @ SV786 ) )
= ( plus_plus_real @ ( times_times_real @ SY2279 @ SV786 ) @ ( times_times_real @ SY2280 @ SV442 ) ) )
| ( SY2279 != SY2280 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5656]) ).
thf(6097,plain,
! [SV786: real,SV442: real] :
( ( ~ ( ! [SY2281: real,SY2282: real] :
( ( plus_plus_real @ ( times_times_real @ SY2281 @ SV442 ) @ ( times_times_real @ SY2282 @ SV786 ) )
= ( plus_plus_real @ ( times_times_real @ SY2281 @ SV786 ) @ ( times_times_real @ SY2282 @ SV442 ) ) )
| ( SV442 != SV786 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5656]) ).
thf(6098,plain,
! [SV786: real,SV442: real,SV1518: real,SV1462: real] :
( ( ( SV1462 = SV1518 )
| ( SV442 = SV786 )
| ( ( plus_plus_real @ ( times_times_real @ SV1462 @ SV442 ) @ ( times_times_real @ SV1518 @ SV786 ) )
!= ( plus_plus_real @ ( times_times_real @ SV1462 @ SV786 ) @ ( times_times_real @ SV1518 @ SV442 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5657]) ).
thf(6099,plain,
! [SV1314: real,SV1071: real] :
( ( ( ord_less_eq_real @ SV1071 @ SV1314 )
= $false )
| ( ( ( SV1071 = SV1314 )
| ( ord_less_real @ SV1071 @ SV1314 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5662]) ).
thf(6100,plain,
! [SV1519: real] :
( ( ! [SY2613: real] :
( ( SV1519 != SY2613 )
| ( ord_less_eq_real @ SV1519 @ SY2613 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5663]) ).
thf(6101,plain,
! [SV1520: real] :
( ( ! [SY2614: real] :
( ~ ( ord_less_real @ SV1520 @ SY2614 )
| ( ord_less_eq_real @ SV1520 @ SY2614 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5664]) ).
thf(6102,plain,
! [SV1315: int,SV1074: int] :
( ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ SV1074 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV1315 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $false )
| ( ( ( SV1074 != zero_zero_int )
| ( SV1315 != zero_zero_int ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5667]) ).
thf(6103,plain,
! [SV1521: int] :
( ( ( SV1521 = zero_zero_int )
| ! [SY2615: int] : ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ SV1521 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SY2615 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5668]) ).
thf(6104,plain,
! [SV1522: int] :
( ( ! [SY2616: int] :
( ( SY2616 = zero_zero_int )
| ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ SV1522 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SY2616 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5669]) ).
thf(6105,plain,
! [SV1316: int,SV1077: int] :
( ( ( ord_less_eq_int @ ( number_number_of_int @ SV1077 ) @ ( number_number_of_int @ SV1316 ) )
= $false )
| ( ( ord_less_eq_int @ SV1077 @ SV1316 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5672]) ).
thf(6106,plain,
! [SV1317: int,SV1078: int] :
( ( ( ord_less_eq_int @ SV1078 @ SV1317 )
= $false )
| ( ( ord_less_eq_int @ ( number_number_of_int @ SV1078 ) @ ( number_number_of_int @ SV1317 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5673]) ).
thf(6107,plain,
! [SV1318: real,SV1079: real] :
( ( ( SV1079 != zero_zero_real )
= $true )
| ( ( SV1318 != zero_zero_real )
= $true )
| ( ( ( plus_plus_real @ ( power_power_real @ SV1079 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SV1318 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5674]) ).
thf(6108,plain,
! [SV1523: real] :
( ( ! [SY2617: real] :
( ( plus_plus_real @ ( power_power_real @ SV1523 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SY2617 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_real )
| ( SV1523 = zero_zero_real ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5675]) ).
thf(6109,plain,
! [SV1524: real] :
( ( ! [SY2618: real] :
( ( ( plus_plus_real @ ( power_power_real @ SV1524 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SY2618 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_real )
| ( SY2618 = zero_zero_real ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5676]) ).
thf(6110,plain,
! [SV1080: int,SV1319: nat] :
( ( ( SV1319 = zero_zero_nat )
= $false )
| ( ( ( power_power_int @ SV1080 @ SV1319 )
= one_one_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5677]) ).
thf(6111,plain,
! [SV1084: int,SV1321: int] :
( ( ( dvd_dvd_int @ SV1321 @ SV1084 )
= $false )
| ( ( zcong @ SV1084 @ zero_zero_int @ SV1321 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5681]) ).
thf(6112,plain,
! [SV1322: int,SV1085: int] :
( ( ( zcong @ SV1085 @ zero_zero_int @ SV1322 )
= $false )
| ( ( dvd_dvd_int @ SV1322 @ SV1085 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5682]) ).
thf(6113,plain,
! [SV1086: nat,SV1323: nat] :
( ( ( SV1323 = zero_zero_nat )
= $false )
| ( ( ( power_power_nat @ SV1086 @ SV1323 )
= one_one_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5683]) ).
thf(6114,plain,
! [SV1325: nat,SV443: nat,SV1463: int] :
( ( ( ~ ( ord_less_int @ one_one_int @ SV1463 ) )
= $true )
| ( ( ~ ( ord_less_int @ ( power_power_int @ SV1463 @ SV443 ) @ ( power_power_int @ SV1463 @ SV1325 ) )
| ( ord_less_nat @ SV443 @ SV1325 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5687]) ).
thf(6115,plain,
! [SV1326: nat,SV443: nat,SV1464: int] :
( ( ( ~ ( ord_less_int @ one_one_int @ SV1464 ) )
= $true )
| ( ( ~ ( ord_less_nat @ SV443 @ SV1326 )
| ( ord_less_int @ ( power_power_int @ SV1464 @ SV443 ) @ ( power_power_int @ SV1464 @ SV1326 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5688]) ).
thf(6116,plain,
! [SV1327: int,SV1096: int] :
( ( ( ord_less_eq_int @ ( number_number_of_int @ SV1096 ) @ ( number_number_of_int @ SV1327 ) )
= $false )
| ( ( ord_less_eq_int @ SV1096 @ SV1327 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5695]) ).
thf(6117,plain,
! [SV1328: int,SV1097: int] :
( ( ( ord_less_eq_int @ SV1097 @ SV1328 )
= $false )
| ( ( ord_less_eq_int @ ( number_number_of_int @ SV1097 ) @ ( number_number_of_int @ SV1328 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5696]) ).
thf(6118,plain,
! [SV1525: int,SV1329: int,SV444: int] :
( ( ( ~ ( dvd_dvd_int @ SV444 @ ( plus_plus_int @ SV1329 @ ( times_times_int @ SV444 @ SV1525 ) ) ) )
= $true )
| ( ( dvd_dvd_int @ SV444 @ SV1329 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5697]) ).
thf(6119,plain,
! [SV1330: int,SV444: int] :
( ( ( dvd_dvd_int @ SV444 @ SV1330 )
= $false )
| ( ( ! [SY2555: int] : ( dvd_dvd_int @ SV444 @ ( plus_plus_int @ SV1330 @ ( times_times_int @ SV444 @ SY2555 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5698]) ).
thf(6120,plain,
! [SV1331: int,SV1098: int] :
( ( ( ord_less_eq_int @ SV1098 @ ( minus_minus_int @ SV1331 @ one_one_int ) )
= $false )
| ( ( ord_less_int @ SV1098 @ SV1331 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5699]) ).
thf(6121,plain,
! [SV1332: int,SV1099: int] :
( ( ( ord_less_int @ SV1099 @ SV1332 )
= $false )
| ( ( ord_less_eq_int @ SV1099 @ ( minus_minus_int @ SV1332 @ one_one_int ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5700]) ).
thf(6122,plain,
! [SV1333: int,SV1100: int] :
( ( ( ord_less_eq_int @ ( bit0 @ SV1100 ) @ ( bit0 @ SV1333 ) )
= $false )
| ( ( ord_less_eq_int @ SV1100 @ SV1333 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5701]) ).
thf(6123,plain,
! [SV1334: int,SV1101: int] :
( ( ( ord_less_eq_int @ SV1101 @ SV1334 )
= $false )
| ( ( ord_less_eq_int @ ( bit0 @ SV1101 ) @ ( bit0 @ SV1334 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5702]) ).
thf(6124,plain,
! [SV1102: int,SV1335: int] :
( ( ( ( number_number_of_nat @ SV1335 )
= zero_zero_nat )
= $true )
| ( ( SV1102 != zero_zero_int )
= $true )
| ( ( ( power_power_int @ SV1102 @ ( number_number_of_nat @ SV1335 ) )
= zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5703]) ).
thf(6125,plain,
! [SV1526: int] :
( ( ! [SY2619: int] :
( ( ( power_power_int @ SV1526 @ ( number_number_of_nat @ SY2619 ) )
!= zero_zero_int )
| ( ( number_number_of_nat @ SY2619 )
!= zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5704]) ).
thf(6126,plain,
! [SV1527: int] :
( ( ! [SY2620: int] :
( ( power_power_int @ SV1527 @ ( number_number_of_nat @ SY2620 ) )
!= zero_zero_int )
| ( SV1527 = zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5705]) ).
thf(6127,plain,
! [SV1336: int,SV1103: int] :
( ( ( ord_less_eq_real @ ( number267125858f_real @ SV1103 ) @ ( number267125858f_real @ SV1336 ) )
= $false )
| ( ( ~ ( ord_less_real @ ( number267125858f_real @ SV1336 ) @ ( number267125858f_real @ SV1103 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5706]) ).
thf(6128,plain,
! [SV1338: int,SV1105: int] :
( ( ( ord_less_int @ SV1105 @ SV1338 )
= $false )
| ( ( ord_less_int @ ( minus_minus_int @ SV1105 @ SV1338 ) @ zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5708]) ).
thf(6129,plain,
! [SV1339: int,SV1106: int] :
( ( ( ord_less_int @ ( minus_minus_int @ SV1106 @ SV1339 ) @ zero_zero_int )
= $false )
| ( ( ord_less_int @ SV1106 @ SV1339 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5709]) ).
thf(6130,plain,
! [SV1340: int,SV1107: int] :
( ( ( zcong @ ( times_times_int @ SV1107 @ ( minus_minus_int @ SV1340 @ one_one_int ) ) @ one_one_int @ SV1340 )
= $false )
| ( ( zcong @ SV1107 @ ( minus_minus_int @ SV1340 @ one_one_int ) @ SV1340 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5710]) ).
thf(6131,plain,
! [SV1341: int,SV1108: int] :
( ( ( zcong @ SV1108 @ ( minus_minus_int @ SV1341 @ one_one_int ) @ SV1341 )
= $false )
| ( ( zcong @ ( times_times_int @ SV1108 @ ( minus_minus_int @ SV1341 @ one_one_int ) ) @ one_one_int @ SV1341 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5711]) ).
thf(6132,plain,
! [SV1111: nat,SV1342: nat] :
( ( ( SV1342 = zero_zero_nat )
= $false )
| ( ( ( times_times_nat @ SV1342 @ SV1111 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5714]) ).
thf(6133,plain,
! [SV1344: real,SV1113: real] :
( ( ( SV1113 != zero_zero_real )
= $true )
| ( ( SV1344 != zero_zero_real )
= $true )
| ( ( ( plus_plus_real @ ( power_power_real @ SV1113 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SV1344 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5716]) ).
thf(6134,plain,
! [SV1528: real] :
( ( ! [SY2621: real] :
( ( plus_plus_real @ ( power_power_real @ SV1528 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SY2621 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_real )
| ( SV1528 = zero_zero_real ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5717]) ).
thf(6135,plain,
! [SV1529: real] :
( ( ! [SY2622: real] :
( ( ( plus_plus_real @ ( power_power_real @ SV1529 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SY2622 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_real )
| ( SY2622 = zero_zero_real ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5718]) ).
thf(6136,plain,
! [SV1345: int,SV1114: int] :
( ( ( SV1114 != zero_zero_int )
= $true )
| ( ( SV1345 != zero_zero_int )
= $true )
| ( ( ( plus_plus_int @ ( power_power_int @ SV1114 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV1345 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5719]) ).
thf(6137,plain,
! [SV1530: int] :
( ( ! [SY2623: int] :
( ( plus_plus_int @ ( power_power_int @ SV1530 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SY2623 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_int )
| ( SV1530 = zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5720]) ).
thf(6138,plain,
! [SV1531: int] :
( ( ! [SY2624: int] :
( ( ( plus_plus_int @ ( power_power_int @ SV1531 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SY2624 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_int )
| ( SY2624 = zero_zero_int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5721]) ).
thf(6139,plain,
! [SV1115: int,SV1346: int] :
( ( ( dvd_dvd_int @ SV1346 @ SV1115 )
= $false )
| ( ( zcong @ SV1115 @ zero_zero_int @ SV1346 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5722]) ).
thf(6140,plain,
! [SV1347: int,SV1116: int] :
( ( ( zcong @ SV1116 @ zero_zero_int @ SV1347 )
= $false )
| ( ( dvd_dvd_int @ SV1347 @ SV1116 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5723]) ).
thf(6141,plain,
! [SV1348: int,SV1117: int] :
( ( ( ord_less_eq_int @ ( bit0 @ SV1117 ) @ ( bit1 @ SV1348 ) )
= $false )
| ( ( ord_less_eq_int @ SV1117 @ SV1348 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5724]) ).
thf(6142,plain,
! [SV1349: int,SV1118: int] :
( ( ( ord_less_eq_int @ SV1118 @ SV1349 )
= $false )
| ( ( ord_less_eq_int @ ( bit0 @ SV1118 ) @ ( bit1 @ SV1349 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5725]) ).
thf(6143,plain,
! [SV1350: real,SV445: real,SV1465: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV1465 ) )
= $true )
| ( ( ~ ( ord_less_eq_real @ ( times_times_real @ SV445 @ SV1465 ) @ ( times_times_real @ SV1350 @ SV1465 ) )
| ( ord_less_eq_real @ SV445 @ SV1350 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5730]) ).
thf(6144,plain,
! [SV1351: real,SV445: real,SV1466: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV1466 ) )
= $true )
| ( ( ~ ( ord_less_eq_real @ SV445 @ SV1351 )
| ( ord_less_eq_real @ ( times_times_real @ SV445 @ SV1466 ) @ ( times_times_real @ SV1351 @ SV1466 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5731]) ).
thf(6145,plain,
! [SV1352: real,SV1125: real] :
( ( ( SV1125 != zero_zero_real )
= $true )
| ( ( SV1352 != zero_zero_real )
= $true )
| ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ SV1125 @ SV1125 ) @ ( times_times_real @ SV1352 @ SV1352 ) ) @ zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5734]) ).
thf(6146,plain,
! [SV1532: real] :
( ( ! [SY2625: real] :
~ ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ SV1532 @ SV1532 ) @ ( times_times_real @ SY2625 @ SY2625 ) ) @ zero_zero_real )
| ( SV1532 = zero_zero_real ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5735]) ).
thf(6147,plain,
! [SV1533: real] :
( ( ! [SY2626: real] :
( ~ ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ SV1533 @ SV1533 ) @ ( times_times_real @ SY2626 @ SY2626 ) ) @ zero_zero_real )
| ( SY2626 = zero_zero_real ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5736]) ).
thf(6148,plain,
! [SV1353: int,SV1126: int] :
( ( ( ord_less_eq_int @ ( bit1 @ SV1126 ) @ ( bit0 @ SV1353 ) )
= $false )
| ( ( ord_less_int @ SV1126 @ SV1353 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5737]) ).
thf(6149,plain,
! [SV1354: int,SV1127: int] :
( ( ( ord_less_int @ SV1127 @ SV1354 )
= $false )
| ( ( ord_less_eq_int @ ( bit1 @ SV1127 ) @ ( bit0 @ SV1354 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5738]) ).
thf(6150,plain,
! [SV1355: int,SV1130: int] :
( ( ( SV1130 != zero_zero_int )
= $true )
| ( ( SV1355 != zero_zero_int )
= $true )
| ( ( ord_less_eq_int @ ( plus_plus_int @ ( power_power_int @ SV1130 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV1355 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5741]) ).
thf(6151,plain,
! [SV1534: int] :
( ( ! [SY2627: int] :
~ ( ord_less_eq_int @ ( plus_plus_int @ ( power_power_int @ SV1534 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SY2627 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_int )
| ( SV1534 = zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5742]) ).
thf(6152,plain,
! [SV1535: int] :
( ( ! [SY2628: int] :
( ~ ( ord_less_eq_int @ ( plus_plus_int @ ( power_power_int @ SV1535 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SY2628 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_int )
| ( SY2628 = zero_zero_int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5743]) ).
thf(6153,plain,
! [SV1356: int,SV1133: int] :
( ( ( SV1133 != zero_zero_int )
= $true )
| ( ( SV1356 != zero_zero_int )
= $true )
| ( ( ( plus_plus_int @ ( times_times_int @ SV1133 @ SV1133 ) @ ( times_times_int @ SV1356 @ SV1356 ) )
= zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5746]) ).
thf(6154,plain,
! [SV1536: int] :
( ( ! [SY2629: int] :
( ( plus_plus_int @ ( times_times_int @ SV1536 @ SV1536 ) @ ( times_times_int @ SY2629 @ SY2629 ) )
!= zero_zero_int )
| ( SV1536 = zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5747]) ).
thf(6155,plain,
! [SV1537: int] :
( ( ! [SY2630: int] :
( ( ( plus_plus_int @ ( times_times_int @ SV1537 @ SV1537 ) @ ( times_times_int @ SY2630 @ SY2630 ) )
!= zero_zero_int )
| ( SY2630 = zero_zero_int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5748]) ).
thf(6156,plain,
! [SV1357: int,SV1134: int] :
( ( ( SV1134 = SV1357 )
= $true )
| ( ( ~ ( ord_less_eq_int @ SV1134 @ SV1357 ) )
= $true )
| ( ( ord_less_int @ SV1134 @ SV1357 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5749]) ).
thf(6157,plain,
! [SV1538: int] :
( ( ! [SY2631: int] :
( ~ ( ord_less_int @ SV1538 @ SY2631 )
| ( SV1538 != SY2631 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5750]) ).
thf(6158,plain,
! [SV1539: int] :
( ( ! [SY2632: int] :
( ~ ( ord_less_int @ SV1539 @ SY2632 )
| ( ord_less_eq_int @ SV1539 @ SY2632 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5751]) ).
thf(6159,plain,
! [SV1358: nat,SV446: nat,SV1467: nat] :
( ( ( ~ ( ord_less_nat @ one_one_nat @ SV1467 ) )
= $true )
| ( ( ~ ( ord_less_nat @ ( power_power_nat @ SV1467 @ SV446 ) @ ( power_power_nat @ SV1467 @ SV1358 ) )
| ( ord_less_nat @ SV446 @ SV1358 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5754]) ).
thf(6160,plain,
! [SV1359: nat,SV446: nat,SV1468: nat] :
( ( ( ~ ( ord_less_nat @ one_one_nat @ SV1468 ) )
= $true )
| ( ( ~ ( ord_less_nat @ SV446 @ SV1359 )
| ( ord_less_nat @ ( power_power_nat @ SV1468 @ SV446 ) @ ( power_power_nat @ SV1468 @ SV1359 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5755]) ).
thf(6161,plain,
! [SV1360: nat,SV1137: nat] :
( ( ( SV1137 != one_one_nat )
= $true )
| ( ( SV1360 != one_one_nat )
= $true )
| ( ( ( times_times_nat @ SV1137 @ SV1360 )
= one_one_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5756]) ).
thf(6162,plain,
! [SV1540: nat] :
( ( ! [SY2633: nat] :
( ( times_times_nat @ SV1540 @ SY2633 )
!= one_one_nat )
| ( SV1540 = one_one_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5757]) ).
thf(6163,plain,
! [SV1541: nat] :
( ( ! [SY2634: nat] :
( ( ( times_times_nat @ SV1541 @ SY2634 )
!= one_one_nat )
| ( SY2634 = one_one_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5758]) ).
thf(6164,plain,
( ( ~ ! [SX0: int] :
( ! [SX1: int] :
( ( times_times_int @ SX0 @ SX1 )
!= one_one_int )
| ( SX0 = one_one_int )
| ( SX0
= ( number_number_of_int @ min ) ) )
| ~ ! [SX0: int,SX1: int] :
( ( ( times_times_int @ SX0 @ SX1 )
!= one_one_int )
| ( SX0 = one_one_int )
| ( SX1
= ( number_number_of_int @ min ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5759]) ).
thf(6165,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ( ( times_times_int @ SX0 @ SX1 )
!= one_one_int )
| ( SX1 = one_one_int )
| ( SX0
= ( number_number_of_int @ min ) ) )
| ~ ! [SX0: int,SX1: int] :
( ( ( times_times_int @ SX0 @ SX1 )
!= one_one_int )
| ( SX1 = one_one_int )
| ( SX1
= ( number_number_of_int @ min ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5760]) ).
thf(6166,plain,
! [SV1542: int] :
( ( ! [SY2635: int] :
( ( SV1542 != one_one_int )
| ( SY2635 != one_one_int )
| ( ( times_times_int @ SV1542 @ SY2635 )
= one_one_int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5761]) ).
thf(6167,plain,
! [SV1543: int] :
( ( ! [SY2636: int] :
( ( SV1543
!= ( number_number_of_int @ min ) )
| ( SY2636
!= ( number_number_of_int @ min ) )
| ( ( times_times_int @ SV1543 @ SY2636 )
= one_one_int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5762]) ).
thf(6168,plain,
! [SV1361: int,SV1140: int] :
( ( ( ( number_number_of_int @ SV1140 )
= SV1361 )
= $false )
| ( ( SV1361
= ( number_number_of_int @ SV1140 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5765]) ).
thf(6169,plain,
! [SV1141: int,SV1362: int] :
( ( ( SV1362
= ( number_number_of_int @ SV1141 ) )
= $false )
| ( ( ( number_number_of_int @ SV1141 )
= SV1362 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5766]) ).
thf(6170,plain,
! [SV1363: int,SV1142: int] :
( ( ( ord_less_eq_int @ SV1142 @ SV1363 )
= $false )
| ( ( ord_less_int @ SV1142 @ ( plus_plus_int @ SV1363 @ one_one_int ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5767]) ).
thf(6171,plain,
! [SV1364: int,SV1143: int] :
( ( ( ord_less_int @ SV1143 @ ( plus_plus_int @ SV1364 @ one_one_int ) )
= $false )
| ( ( ord_less_eq_int @ SV1143 @ SV1364 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5768]) ).
thf(6172,plain,
! [SV1365: real,SV1144: real] :
( ( ( SV1144 != zero_zero_real )
= $true )
| ( ( SV1365 != zero_zero_real )
= $true )
| ( ( ( plus_plus_real @ ( times_times_real @ SV1144 @ SV1144 ) @ ( times_times_real @ SV1365 @ SV1365 ) )
= zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5769]) ).
thf(6173,plain,
! [SV1544: real] :
( ( ! [SY2637: real] :
( ( plus_plus_real @ ( times_times_real @ SV1544 @ SV1544 ) @ ( times_times_real @ SY2637 @ SY2637 ) )
!= zero_zero_real )
| ( SV1544 = zero_zero_real ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5770]) ).
thf(6174,plain,
! [SV1545: real] :
( ( ! [SY2638: real] :
( ( ( plus_plus_real @ ( times_times_real @ SV1545 @ SV1545 ) @ ( times_times_real @ SY2638 @ SY2638 ) )
!= zero_zero_real )
| ( SY2638 = zero_zero_real ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5771]) ).
thf(6175,plain,
! [SV1366: nat,SV447: nat,SV1469: real] :
( ( ( ~ ( ord_less_real @ one_one_real @ SV1469 ) )
= $true )
| ( ( ~ ( ord_less_nat @ SV447 @ SV1366 )
| ( ord_less_real @ ( power_power_real @ SV1469 @ SV447 ) @ ( power_power_real @ SV1469 @ SV1366 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5774]) ).
thf(6176,plain,
! [SV1367: nat,SV447: nat,SV1470: real] :
( ( ( ~ ( ord_less_real @ one_one_real @ SV1470 ) )
= $true )
| ( ( ~ ( ord_less_real @ ( power_power_real @ SV1470 @ SV447 ) @ ( power_power_real @ SV1470 @ SV1367 ) )
| ( ord_less_nat @ SV447 @ SV1367 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5775]) ).
thf(6177,plain,
! [SV1368: int,SV1149: int] :
( ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ SV1149 @ SV1149 ) @ ( times_times_int @ SV1368 @ SV1368 ) ) )
= $false )
| ( ( ( SV1149 != zero_zero_int )
| ( SV1368 != zero_zero_int ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5778]) ).
thf(6178,plain,
! [SV1546: int] :
( ( ( SV1546 = zero_zero_int )
| ! [SY2639: int] : ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ SV1546 @ SV1546 ) @ ( times_times_int @ SY2639 @ SY2639 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5779]) ).
thf(6179,plain,
! [SV1547: int] :
( ( ! [SY2640: int] :
( ( SY2640 = zero_zero_int )
| ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ SV1547 @ SV1547 ) @ ( times_times_int @ SY2640 @ SY2640 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5780]) ).
thf(6180,plain,
! [SV1369: nat,SV1150: int] :
( ( ( ( number_number_of_nat @ SV1150 )
= SV1369 )
= $false )
| ( ( SV1369
= ( number_number_of_nat @ SV1150 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5781]) ).
thf(6181,plain,
! [SV1151: int,SV1370: nat] :
( ( ( SV1370
= ( number_number_of_nat @ SV1151 ) )
= $false )
| ( ( ( number_number_of_nat @ SV1151 )
= SV1370 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5782]) ).
thf(6182,plain,
! [SV1152: real] :
( ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ SV1152 @ SV1152 ) )
= $false )
| ( ( SV1152 = zero_zero_real )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5783]) ).
thf(6183,plain,
! [SV1371: real,SV448: real,SV1471: real] :
( ( ( SV1471 = zero_zero_real )
= $true )
| ( ( ( ( times_times_real @ SV1471 @ SV448 )
!= ( times_times_real @ SV1471 @ SV1371 ) )
| ( SV448 = SV1371 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5786]) ).
thf(6184,plain,
! [SV1372: real,SV448: real,SV1472: real] :
( ( ( SV1472 = zero_zero_real )
= $true )
| ( ( ( SV448 != SV1372 )
| ( ( times_times_real @ SV1472 @ SV448 )
= ( times_times_real @ SV1472 @ SV1372 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5787]) ).
thf(6185,plain,
! [SV1373: int,SV1156: int] :
( ( ( ord_less_eq_int @ ( bit0 @ SV1156 ) @ ( bit1 @ SV1373 ) )
= $false )
| ( ( ord_less_eq_int @ SV1156 @ SV1373 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5788]) ).
thf(6186,plain,
! [SV1374: int,SV1157: int] :
( ( ( ord_less_eq_int @ SV1157 @ SV1374 )
= $false )
| ( ( ord_less_eq_int @ ( bit0 @ SV1157 ) @ ( bit1 @ SV1374 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5789]) ).
thf(6187,plain,
! [SV1548: int] :
( ( ! [SY2641: int] :
( ( ord_less_int @ SV1548 @ SY2641 )
| ~ ( ord_less_int @ SV1548 @ SY2641 )
| ( ord_less_nat @ ( number_number_of_nat @ SV1548 ) @ ( number_number_of_nat @ SY2641 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5792]) ).
thf(6188,plain,
! [SV1549: int] :
( ( ! [SY2642: int] :
( ~ ( ord_less_int @ pls @ SY2642 )
| ~ ( ord_less_int @ SV1549 @ SY2642 )
| ( ord_less_nat @ ( number_number_of_nat @ SV1549 ) @ ( number_number_of_nat @ SY2642 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5793]) ).
thf(6189,plain,
! [SV1550: int] :
( ( ! [SY2643: int] :
( ~ ( ord_less_nat @ ( number_number_of_nat @ SV1550 ) @ ( number_number_of_nat @ SY2643 ) )
| ~ ( ord_less_int @ SV1550 @ SY2643 )
| ( ord_less_int @ pls @ SY2643 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5794]) ).
thf(6190,plain,
! [SV1551: int] :
( ( ! [SY2644: int] :
( ~ ( ord_less_nat @ ( number_number_of_nat @ SV1551 ) @ ( number_number_of_nat @ SY2644 ) )
| ( ord_less_int @ SV1551 @ SY2644 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5795]) ).
thf(6191,plain,
! [SV1375: int,SV1160: int] :
( ( ( ord_less_int @ ( bit0 @ SV1160 ) @ ( bit0 @ SV1375 ) )
= $false )
| ( ( ord_less_int @ SV1160 @ SV1375 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5796]) ).
thf(6192,plain,
! [SV1376: int,SV1161: int] :
( ( ( ord_less_int @ SV1161 @ SV1376 )
= $false )
| ( ( ord_less_int @ ( bit0 @ SV1161 ) @ ( bit0 @ SV1376 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5797]) ).
thf(6193,plain,
! [SV787: int,SV449: int,SV1552: int,SV981: int] :
( ( ! [SY2645: int] :
( ~ ( zcong @ SV981 @ SV1552 @ SY2645 )
| ~ ( zcong @ SV449 @ ( times_times_int @ SV981 @ SV787 ) @ SY2645 )
| ( zcong @ SV449 @ ( times_times_int @ SV1552 @ SV787 ) @ SY2645 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5798]) ).
thf(6194,plain,
! [SV787: int,SV449: int,SV1553: int,SV981: int] :
( ( ! [SY2646: int] :
( ~ ( zcong @ SV981 @ SV1553 @ SY2646 )
| ~ ( zcong @ SV449 @ ( times_times_int @ SV1553 @ SV787 ) @ SY2646 )
| ( zcong @ SV449 @ ( times_times_int @ SV981 @ SV787 ) @ SY2646 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5799]) ).
thf(6195,plain,
! [SV1162: real,SV1377: nat] :
( ( ( SV1377 = zero_zero_nat )
= $false )
| ( ( ( power_power_real @ SV1162 @ SV1377 )
= one_one_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5800]) ).
thf(6196,plain,
! [SV788: int,SV450: int] :
( ( ~ ! [SY2290: int,SY2291: int] :
( ( ( plus_plus_int @ ( times_times_int @ SY2290 @ SV450 ) @ ( times_times_int @ SY2291 @ SV788 ) )
= ( plus_plus_int @ ( times_times_int @ SY2290 @ SV788 ) @ ( times_times_int @ SY2291 @ SV450 ) ) )
| ( SY2290 != SY2291 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5802]) ).
thf(6197,plain,
! [SV788: int,SV450: int] :
( ( ~ ( ! [SY2292: int,SY2293: int] :
( ( plus_plus_int @ ( times_times_int @ SY2292 @ SV450 ) @ ( times_times_int @ SY2293 @ SV788 ) )
= ( plus_plus_int @ ( times_times_int @ SY2292 @ SV788 ) @ ( times_times_int @ SY2293 @ SV450 ) ) )
| ( SV450 != SV788 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5802]) ).
thf(6198,plain,
! [SV788: int,SV450: int,SV1554: int,SV1473: int] :
( ( ( SV1473 = SV1554 )
| ( SV450 = SV788 )
| ( ( plus_plus_int @ ( times_times_int @ SV1473 @ SV450 ) @ ( times_times_int @ SV1554 @ SV788 ) )
!= ( plus_plus_int @ ( times_times_int @ SV1473 @ SV788 ) @ ( times_times_int @ SV1554 @ SV450 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5803]) ).
thf(6199,plain,
! [SV1379: int,SV1164: int] :
( ( ( ord_less_eq_int @ SV1164 @ SV1379 )
= $false )
| ( ( ord_less_int @ ( bit0 @ SV1164 ) @ ( bit1 @ SV1379 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5804]) ).
thf(6200,plain,
! [SV1380: int,SV1165: int] :
( ( ( ord_less_int @ ( bit0 @ SV1165 ) @ ( bit1 @ SV1380 ) )
= $false )
| ( ( ord_less_eq_int @ SV1165 @ SV1380 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5805]) ).
thf(6201,plain,
! [SV1167: int] :
( ( ( SV1167 = zero_zero_int )
= $false )
| ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ SV1167 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5806]) ).
thf(6202,plain,
! [SV1381: real,SV1170: real] :
( ( ( SV1170 != zero_zero_real )
= $true )
| ( ( SV1381 != zero_zero_real )
= $true )
| ( ( ( plus_plus_real @ ( times_times_real @ SV1170 @ SV1170 ) @ ( times_times_real @ SV1381 @ SV1381 ) )
= zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5809]) ).
thf(6203,plain,
! [SV1555: real] :
( ( ! [SY2647: real] :
( ( plus_plus_real @ ( times_times_real @ SV1555 @ SV1555 ) @ ( times_times_real @ SY2647 @ SY2647 ) )
!= zero_zero_real )
| ( SV1555 = zero_zero_real ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5810]) ).
thf(6204,plain,
! [SV1556: real] :
( ( ! [SY2648: real] :
( ( ( plus_plus_real @ ( times_times_real @ SV1556 @ SV1556 ) @ ( times_times_real @ SY2648 @ SY2648 ) )
!= zero_zero_real )
| ( SY2648 = zero_zero_real ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5811]) ).
thf(6205,plain,
! [SV789: int,SV451: int,SV1557: int,SV982: int] :
( ( ! [SY2649: int] :
( ~ ( zcong @ SV982 @ SV1557 @ SY2649 )
| ~ ( zcong @ SV451 @ ( times_times_int @ SV789 @ SV982 ) @ SY2649 )
| ( zcong @ SV451 @ ( times_times_int @ SV789 @ SV1557 ) @ SY2649 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5814]) ).
thf(6206,plain,
! [SV789: int,SV451: int,SV1558: int,SV982: int] :
( ( ! [SY2650: int] :
( ~ ( zcong @ SV982 @ SV1558 @ SY2650 )
| ~ ( zcong @ SV451 @ ( times_times_int @ SV789 @ SV1558 ) @ SY2650 )
| ( zcong @ SV451 @ ( times_times_int @ SV789 @ SV982 ) @ SY2650 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5815]) ).
thf(6207,plain,
! [SV1382: int,SV1175: int] :
( ( ( ord_less_eq_int @ ( bit1 @ SV1175 ) @ ( bit1 @ SV1382 ) )
= $false )
| ( ( ord_less_eq_int @ SV1175 @ SV1382 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5818]) ).
thf(6208,plain,
! [SV1383: int,SV1176: int] :
( ( ( ord_less_eq_int @ SV1176 @ SV1383 )
= $false )
| ( ( ord_less_eq_int @ ( bit1 @ SV1176 ) @ ( bit1 @ SV1383 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5819]) ).
thf(6209,plain,
! [SV1384: int,SV1177: int] :
( ( ( SV1177 = SV1384 )
= $false )
| ( ( zcong @ SV1177 @ SV1384 @ zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5820]) ).
thf(6210,plain,
! [SV1385: int,SV1178: int] :
( ( ( zcong @ SV1178 @ SV1385 @ zero_zero_int )
= $false )
| ( ( SV1178 = SV1385 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5821]) ).
thf(6211,plain,
! [SV1386: int,SV1179: int] :
( ( ( ord_less_eq_int @ ( bit1 @ SV1179 ) @ ( bit0 @ SV1386 ) )
= $false )
| ( ( ord_less_int @ SV1179 @ SV1386 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5822]) ).
thf(6212,plain,
! [SV1387: int,SV1180: int] :
( ( ( ord_less_int @ SV1180 @ SV1387 )
= $false )
| ( ( ord_less_eq_int @ ( bit1 @ SV1180 ) @ ( bit0 @ SV1387 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5823]) ).
thf(6213,plain,
! [SV1559: nat,SV1474: nat,SV790: nat,SV452: nat] :
( ( ( ( plus_plus_nat @ ( times_times_nat @ SV452 @ SV790 ) @ ( times_times_nat @ SV1474 @ SV1559 ) )
!= ( plus_plus_nat @ ( times_times_nat @ SV452 @ SV1559 ) @ ( times_times_nat @ SV1474 @ SV790 ) ) )
| ( SV452 = SV1474 )
| ( SV790 = SV1559 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5824]) ).
thf(6214,plain,
! [SV790: nat,SV452: nat] :
( ( ~ ! [SY2303: nat] :
( ( SV452 != SY2303 )
| ! [SY2304: nat] :
( ( plus_plus_nat @ ( times_times_nat @ SV452 @ SV790 ) @ ( times_times_nat @ SY2303 @ SY2304 ) )
= ( plus_plus_nat @ ( times_times_nat @ SV452 @ SY2304 ) @ ( times_times_nat @ SY2303 @ SV790 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5825]) ).
thf(6215,plain,
! [SV452: nat,SV790: nat] :
( ( ~ ! [SY2305: nat,SY2306: nat] :
( ( SV790 != SY2306 )
| ( ( plus_plus_nat @ ( times_times_nat @ SV452 @ SV790 ) @ ( times_times_nat @ SY2305 @ SY2306 ) )
= ( plus_plus_nat @ ( times_times_nat @ SV452 @ SY2306 ) @ ( times_times_nat @ SY2305 @ SV790 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5825]) ).
thf(6216,plain,
! [SV1181: real,SV1388: nat] :
( ( ( SV1388 = zero_zero_nat )
= $true )
| ( ( SV1181 != zero_zero_real )
= $true )
| ( ( ( power_power_real @ SV1181 @ SV1388 )
= zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5826]) ).
thf(6217,plain,
! [SV1560: real] :
( ( ! [SY2651: nat] :
( ( ( power_power_real @ SV1560 @ SY2651 )
!= zero_zero_real )
| ( SY2651 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5827]) ).
thf(6218,plain,
! [SV1561: real] :
( ( ! [SY2652: nat] :
( ( power_power_real @ SV1561 @ SY2652 )
!= zero_zero_real )
| ( SV1561 = zero_zero_real ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5828]) ).
thf(6219,plain,
! [SV1389: nat,SV1182: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV1182 @ SV1389 ) )
= $false )
| ( ( ( SV1389 = zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV1182 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5829]) ).
thf(6220,plain,
! [SV1562: nat] :
( ( ! [SY2653: nat] :
( ( SY2653 != zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV1562 @ SY2653 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5830]) ).
thf(6221,plain,
! [SV1563: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ SV1563 )
| ! [SY2654: nat] : ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV1563 @ SY2654 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5831]) ).
thf(6222,plain,
! [SV1564: int,SV1475: int,SV791: int,SV453: int] :
( ( ( ( plus_plus_int @ ( times_times_int @ SV453 @ SV791 ) @ ( times_times_int @ SV1475 @ SV1564 ) )
!= ( plus_plus_int @ ( times_times_int @ SV453 @ SV1564 ) @ ( times_times_int @ SV1475 @ SV791 ) ) )
| ( SV453 = SV1475 )
| ( SV791 = SV1564 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5832]) ).
thf(6223,plain,
! [SV791: int,SV453: int] :
( ( ~ ! [SY2309: int] :
( ( SV453 != SY2309 )
| ! [SY2310: int] :
( ( plus_plus_int @ ( times_times_int @ SV453 @ SV791 ) @ ( times_times_int @ SY2309 @ SY2310 ) )
= ( plus_plus_int @ ( times_times_int @ SV453 @ SY2310 ) @ ( times_times_int @ SY2309 @ SV791 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5833]) ).
thf(6224,plain,
! [SV453: int,SV791: int] :
( ( ~ ! [SY2311: int,SY2312: int] :
( ( SV791 != SY2312 )
| ( ( plus_plus_int @ ( times_times_int @ SV453 @ SV791 ) @ ( times_times_int @ SY2311 @ SY2312 ) )
= ( plus_plus_int @ ( times_times_int @ SV453 @ SY2312 ) @ ( times_times_int @ SY2311 @ SV791 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5833]) ).
thf(6225,plain,
! [SV1183: nat,SV1390: nat] :
( ( ( SV1390 = zero_zero_nat )
= $false )
| ( ( ( power_power_nat @ SV1183 @ SV1390 )
= one_one_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5834]) ).
thf(6226,plain,
! [SV1185: int,SV1392: int] :
( ( ( ord_less_int @ zero_zero_int @ SV1392 )
= $false )
| ( ( ( SV1392 != one_one_int )
| ( SV1185 != one_one_int )
| ( ( times_times_int @ SV1392 @ SV1185 )
= one_one_int ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5836]) ).
thf(6227,plain,
! [SV1565: int] :
( ( ! [SY2655: int] :
( ~ ( ord_less_int @ zero_zero_int @ SY2655 )
| ( ( times_times_int @ SY2655 @ SV1565 )
!= one_one_int )
| ( SY2655 = one_one_int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5837]) ).
thf(6228,plain,
! [SV1566: int] :
( ( ! [SY2656: int] :
( ~ ( ord_less_int @ zero_zero_int @ SY2656 )
| ( ( times_times_int @ SY2656 @ SV1566 )
!= one_one_int )
| ( SV1566 = one_one_int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5838]) ).
thf(6229,plain,
! [SV1393: int,SV1186: int] :
( ( ( ord_less_eq_int @ ( plus_plus_int @ SV1186 @ one_one_int ) @ SV1393 )
= $false )
| ( ( ord_less_int @ SV1186 @ SV1393 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5839]) ).
thf(6230,plain,
! [SV1394: int,SV1187: int] :
( ( ( ord_less_int @ SV1187 @ SV1394 )
= $false )
| ( ( ord_less_eq_int @ ( plus_plus_int @ SV1187 @ one_one_int ) @ SV1394 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5840]) ).
thf(6231,plain,
! [SV1395: real,SV1190: real] :
( ( ( SV1190 = SV1395 )
= $true )
| ( ( ~ ( ord_less_eq_real @ SV1190 @ SV1395 ) )
= $true )
| ( ( ord_less_real @ SV1190 @ SV1395 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5842]) ).
thf(6232,plain,
! [SV1567: real] :
( ( ! [SY2657: real] :
( ~ ( ord_less_real @ SV1567 @ SY2657 )
| ( SV1567 != SY2657 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5843]) ).
thf(6233,plain,
! [SV1568: real] :
( ( ! [SY2658: real] :
( ~ ( ord_less_real @ SV1568 @ SY2658 )
| ( ord_less_eq_real @ SV1568 @ SY2658 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5844]) ).
thf(6234,plain,
! [SV1396: int,SV1191: int] :
( ( ( ord_less_int @ SV1191 @ SV1396 )
= $false )
| ( ( ord_less_real @ ( number267125858f_real @ SV1191 ) @ ( number267125858f_real @ SV1396 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5845]) ).
thf(6235,plain,
! [SV1397: int,SV1192: int] :
( ( ( ord_less_real @ ( number267125858f_real @ SV1192 ) @ ( number267125858f_real @ SV1397 ) )
= $false )
| ( ( ord_less_int @ SV1192 @ SV1397 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5846]) ).
thf(6236,plain,
! [SV1398: int,SV1193: int] :
( ( ( ord_less_eq_int @ ( number_number_of_int @ SV1193 ) @ ( number_number_of_int @ SV1398 ) )
= $false )
| ( ( ~ ( ord_less_int @ ( number_number_of_int @ SV1398 ) @ ( number_number_of_int @ SV1193 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5847]) ).
thf(6237,plain,
! [SV1400: int,SV1197: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV1197 @ ( number_number_of_nat @ SV1400 ) ) )
= $false )
| ( ( ( ( number_number_of_nat @ SV1400 )
= zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV1197 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5851]) ).
thf(6238,plain,
! [SV1569: nat] :
( ( ! [SY2659: int] :
( ( ( number_number_of_nat @ SY2659 )
!= zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV1569 @ ( number_number_of_nat @ SY2659 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5852]) ).
thf(6239,plain,
! [SV1570: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ SV1570 )
| ! [SY2660: int] : ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV1570 @ ( number_number_of_nat @ SY2660 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5853]) ).
thf(6240,plain,
! [SV1200: int,SV1401: int] :
( ( ( ord_less_int @ SV1401 @ pls )
= $false )
| ( ( ( times_times_nat @ ( number_number_of_nat @ SV1401 ) @ ( number_number_of_nat @ SV1200 ) )
= zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5856]) ).
thf(6241,plain,
! [SV1203: real] :
( ( ( SV1203 = zero_zero_real )
= $false )
| ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ SV1203 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5858]) ).
thf(6242,plain,
! [SV1204: int] :
( ( ( ~ ~ ( ~ ( dvd_dvd_int @ ( sK3_M_9 @ SV1204 ) @ SV1204 )
| ~ ( ord_less_eq_int @ zero_zero_int @ ( sK3_M_9 @ SV1204 ) ) )
| ~ ~ ( ~ ( ( ( sK3_M_9 @ SV1204 )
!= one_one_int ) )
| ~ ( ( ( sK3_M_9 @ SV1204 )
!= SV1204 ) ) ) )
= $false )
| ( ( ~ ( ord_less_int @ one_one_int @ SV1204 ) )
= $true )
| ( ( zprime @ SV1204 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5859]) ).
thf(6243,plain,
! [SV1571: int] :
( ( ~ ( zprime @ SV1571 )
| ! [SY2661: int] :
( ~ ( dvd_dvd_int @ SY2661 @ SV1571 )
| ~ ( ord_less_eq_int @ zero_zero_int @ SY2661 )
| ( SY2661 = one_one_int )
| ( SY2661 = SV1571 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5860]) ).
thf(6244,plain,
! [SV1572: int] :
( ( ~ ( zprime @ SV1572 )
| ( ord_less_int @ one_one_int @ SV1572 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5861]) ).
thf(6245,plain,
! [SV1403: nat,SV454: int,SV1476: int] :
( ( ( ~ ( ord_less_int @ SV1476 @ pls ) )
= $true )
| ( ( ( times_times_nat @ ( number_number_of_nat @ SV1476 ) @ ( times_times_nat @ ( number_number_of_nat @ SV454 ) @ SV1403 ) )
= zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5862]) ).
thf(6246,plain,
! [SV1404: nat,SV454: int,SV1477: int] :
( ( ( ord_less_int @ SV1477 @ pls )
= $true )
| ( ( ( times_times_nat @ ( number_number_of_nat @ SV1477 ) @ ( times_times_nat @ ( number_number_of_nat @ SV454 ) @ SV1404 ) )
= ( times_times_nat @ ( number_number_of_nat @ ( times_times_int @ SV1477 @ SV454 ) ) @ SV1404 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5863]) ).
thf(6247,plain,
! [SV1405: int,SV1205: int] :
( ( ( zcong @ SV1205 @ zero_zero_int @ SV1405 )
= $false )
| ( ( ( legendre @ SV1205 @ SV1405 )
= zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5864]) ).
thf(6248,plain,
! [SV1573: int] :
( ( ! [SY2662: int] :
( ( zcong @ SV1573 @ zero_zero_int @ SY2662 )
| ~ ( quadRes @ SY2662 @ SV1573 )
| ( ( legendre @ SV1573 @ SY2662 )
= one_one_int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5865]) ).
thf(6249,plain,
! [SV1574: int] :
( ( ! [SY2663: int] :
( ( zcong @ SV1574 @ zero_zero_int @ SY2663 )
| ( quadRes @ SY2663 @ SV1574 )
| ( ( legendre @ SV1574 @ SY2663 )
= ( number_number_of_int @ min ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5866]) ).
thf(6250,plain,
! [SV455: real,SV792: nat] :
( ( ( ~ ! [SY2313: real] :
( ( ( power_power_real @ SY2313 @ SV792 )
!= SV455 )
| ~ ( ord_less_real @ zero_zero_real @ SY2313 )
| ( SY2313
= ( sK1_X_1 @ SV792 @ SV455 ) ) )
| ~ ~ ( ( ( power_power_real @ ( sK1_X_1 @ SV792 @ SV455 ) @ SV792 )
!= SV455 )
| ~ ( ord_less_real @ zero_zero_real @ ( sK1_X_1 @ SV792 @ SV455 ) ) ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV455 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV792 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5868]) ).
thf(6251,plain,
! [SV1575: int] :
( ( ! [SY2664: int] :
( ~ ( ord_less_eq_int @ SV1575 @ SY2664 )
| ( ord_less_eq_nat @ ( number_number_of_nat @ SV1575 ) @ ( number_number_of_nat @ SY2664 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5871]) ).
thf(6252,plain,
! [SV1576: int] :
( ( ~ ( ord_less_eq_int @ SV1576 @ pls )
| ! [SY2665: int] : ( ord_less_eq_nat @ ( number_number_of_nat @ SV1576 ) @ ( number_number_of_nat @ SY2665 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5872]) ).
thf(6253,plain,
! [SV1406: int,SV1210: int] :
( ( ( ord_less_eq_nat @ ( number_number_of_nat @ SV1210 ) @ ( number_number_of_nat @ SV1406 ) )
= $false )
| ( ( ( ord_less_eq_int @ SV1210 @ SV1406 )
| ( ord_less_eq_int @ SV1210 @ pls ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5873]) ).
thf(6254,plain,
! [SV1407: real,SV1215: int] :
( ( ( ( number267125858f_real @ SV1215 )
= SV1407 )
= $false )
| ( ( SV1407
= ( number267125858f_real @ SV1215 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5878]) ).
thf(6255,plain,
! [SV1216: int,SV1408: real] :
( ( ( SV1408
= ( number267125858f_real @ SV1216 ) )
= $false )
| ( ( ( number267125858f_real @ SV1216 )
= SV1408 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5879]) ).
thf(6256,plain,
! [SV1478: int,SV1409: int,SV456: int] :
( ( ( ~ ( zcong @ SV456 @ SV1409 @ SV1478 ) )
= $true )
| ( ( zcong @ SV1409 @ SV456 @ SV1478 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5882]) ).
thf(6257,plain,
! [SV1479: int,SV456: int,SV1410: int] :
( ( ( ~ ( zcong @ SV1410 @ SV456 @ SV1479 ) )
= $true )
| ( ( zcong @ SV456 @ SV1410 @ SV1479 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5883]) ).
thf(6258,plain,
! [SV457: int,SV983: int,SV793: int,SV1577: int] :
( ( ! [SY2666: int] :
( ~ ( dvd_dvd_int @ SV1577 @ SY2666 )
| ~ ( dvd_dvd_int @ SV1577 @ ( plus_plus_int @ SV793 @ SV983 ) )
| ( dvd_dvd_int @ SV1577 @ ( plus_plus_int @ ( plus_plus_int @ SV793 @ ( times_times_int @ SV457 @ SY2666 ) ) @ SV983 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5884]) ).
thf(6259,plain,
! [SV983: int,SV457: int,SV793: int,SV1578: int] :
( ( ! [SY2667: int] :
( ~ ( dvd_dvd_int @ SV1578 @ SY2667 )
| ~ ( dvd_dvd_int @ SV1578 @ ( plus_plus_int @ ( plus_plus_int @ SV793 @ ( times_times_int @ SV457 @ SY2667 ) ) @ SV983 ) )
| ( dvd_dvd_int @ SV1578 @ ( plus_plus_int @ SV793 @ SV983 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5885]) ).
thf(6260,plain,
! [SV1411: real,SV1221: real] :
( ( ( SV1221
= ( plus_plus_real @ SV1221 @ SV1411 ) )
= $false )
| ( ( SV1411 = zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5888]) ).
thf(6261,plain,
! [SV1222: real,SV1412: real] :
( ( ( SV1412 = zero_zero_real )
= $false )
| ( ( SV1222
= ( plus_plus_real @ SV1222 @ SV1412 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5889]) ).
thf(6262,plain,
! [SV1480: int,SV458: int,SV1413: int] :
( ( ( ! [SY2593: int] :
( SV1413
!= ( plus_plus_int @ SV458 @ ( times_times_int @ SV1480 @ SY2593 ) ) ) )
= $true )
| ( ( zcong @ SV458 @ SV1413 @ SV1480 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5890]) ).
thf(6263,plain,
! [SV1481: int,SV1414: int,SV458: int] :
( ( ( ~ ( zcong @ SV458 @ SV1414 @ SV1481 ) )
= $true )
| ( ( SV1414
= ( plus_plus_int @ SV458 @ ( times_times_int @ SV1481 @ ( sK6_K_1 @ SV1481 @ SV1414 @ SV458 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5891]) ).
thf(6264,plain,
! [SV1415: nat,SV459: nat,SV1482: nat] :
( ( ( ~ ( ord_less_nat @ one_one_nat @ SV1482 ) )
= $true )
| ( ( ( ( power_power_nat @ SV1482 @ SV459 )
!= ( power_power_nat @ SV1482 @ SV1415 ) )
| ( SV459 = SV1415 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5894]) ).
thf(6265,plain,
! [SV1416: nat,SV459: nat,SV1483: nat] :
( ( ( ~ ( ord_less_nat @ one_one_nat @ SV1483 ) )
= $true )
| ( ( ( SV459 != SV1416 )
| ( ( power_power_nat @ SV1483 @ SV459 )
= ( power_power_nat @ SV1483 @ SV1416 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5895]) ).
thf(6266,plain,
! [SV1579: real,SV1484: real,SV794: real,SV460: real] :
( ( ( ( plus_plus_real @ ( times_times_real @ SV460 @ SV794 ) @ ( times_times_real @ SV1484 @ SV1579 ) )
!= ( plus_plus_real @ ( times_times_real @ SV460 @ SV1579 ) @ ( times_times_real @ SV1484 @ SV794 ) ) )
| ( SV460 = SV1484 )
| ( SV794 = SV1579 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5896]) ).
thf(6267,plain,
! [SV794: real,SV460: real] :
( ( ~ ! [SY2321: real] :
( ( SV460 != SY2321 )
| ! [SY2322: real] :
( ( plus_plus_real @ ( times_times_real @ SV460 @ SV794 ) @ ( times_times_real @ SY2321 @ SY2322 ) )
= ( plus_plus_real @ ( times_times_real @ SV460 @ SY2322 ) @ ( times_times_real @ SY2321 @ SV794 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5897]) ).
thf(6268,plain,
! [SV460: real,SV794: real] :
( ( ~ ! [SY2323: real,SY2324: real] :
( ( SV794 != SY2324 )
| ( ( plus_plus_real @ ( times_times_real @ SV460 @ SV794 ) @ ( times_times_real @ SY2323 @ SY2324 ) )
= ( plus_plus_real @ ( times_times_real @ SV460 @ SY2324 ) @ ( times_times_real @ SY2323 @ SV794 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5897]) ).
thf(6269,plain,
! [SV1485: nat,SV1417: nat,SV461: nat] :
( ( ( ~ ( dvd_dvd_nat @ ( times_times_nat @ SV461 @ SV1417 ) @ ( times_times_nat @ SV1485 @ SV1417 ) ) )
= $true )
| ( ( ( SV1417 = zero_zero_nat )
| ( dvd_dvd_nat @ SV461 @ SV1485 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5902]) ).
thf(6270,plain,
! [SV461: nat] :
( ( ! [SY2002: nat] :
( ( SY2002 != zero_zero_nat )
| ! [SY2003: nat] : ( dvd_dvd_nat @ ( times_times_nat @ SV461 @ SY2002 ) @ ( times_times_nat @ SY2003 @ SY2002 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5903]) ).
thf(6271,plain,
! [SV461: nat] :
( ( ! [SY2004: nat,SY2005: nat] :
( ~ ( dvd_dvd_nat @ SV461 @ SY2005 )
| ( dvd_dvd_nat @ ( times_times_nat @ SV461 @ SY2004 ) @ ( times_times_nat @ SY2005 @ SY2004 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5904]) ).
thf(6272,plain,
! [SV1418: int,SV1229: int] :
( ( ( ( number267125858f_real @ SV1229 )
= ( number267125858f_real @ SV1418 ) )
= $false )
| ( ( SV1229 = SV1418 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5905]) ).
thf(6273,plain,
! [SV1419: int,SV1230: int] :
( ( ( SV1230 = SV1419 )
= $false )
| ( ( ( number267125858f_real @ SV1230 )
= ( number267125858f_real @ SV1419 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5906]) ).
thf(6274,plain,
! [SV1420: int,SV1235: int] :
( ( ( ord_less_int @ ( bit1 @ SV1235 ) @ ( bit0 @ SV1420 ) )
= $false )
| ( ( ord_less_int @ SV1235 @ SV1420 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5910]) ).
thf(6275,plain,
! [SV1421: int,SV1236: int] :
( ( ( ord_less_int @ SV1236 @ SV1421 )
= $false )
| ( ( ord_less_int @ ( bit1 @ SV1236 ) @ ( bit0 @ SV1421 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5911]) ).
thf(6276,plain,
! [SV1422: int,SV1237: int] :
( ( ( ord_less_eq_int @ ( bit0 @ SV1237 ) @ ( bit0 @ SV1422 ) )
= $false )
| ( ( ord_less_eq_int @ SV1237 @ SV1422 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5912]) ).
thf(6277,plain,
! [SV1423: int,SV1238: int] :
( ( ( ord_less_eq_int @ SV1238 @ SV1423 )
= $false )
| ( ( ord_less_eq_int @ ( bit0 @ SV1238 ) @ ( bit0 @ SV1423 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5913]) ).
thf(6278,plain,
! [SV1424: nat,SV1239: nat] :
( ( ( SV1239
= ( plus_plus_nat @ SV1239 @ SV1424 ) )
= $false )
| ( ( SV1424 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5914]) ).
thf(6279,plain,
! [SV1240: nat,SV1425: nat] :
( ( ( SV1425 = zero_zero_nat )
= $false )
| ( ( SV1240
= ( plus_plus_nat @ SV1240 @ SV1425 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5915]) ).
thf(6280,plain,
! [SV1426: int,SV1241: int] :
( ( ( ord_less_int @ ( bit1 @ SV1241 ) @ ( bit1 @ SV1426 ) )
= $false )
| ( ( ord_less_int @ SV1241 @ SV1426 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5916]) ).
thf(6281,plain,
! [SV1427: int,SV1242: int] :
( ( ( ord_less_int @ SV1242 @ SV1427 )
= $false )
| ( ( ord_less_int @ ( bit1 @ SV1242 ) @ ( bit1 @ SV1427 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5917]) ).
thf(6282,plain,
! [SV1243: nat,SV1428: nat] :
( ( ( SV1428 = zero_zero_nat )
= $true )
| ( ( SV1243 != zero_zero_nat )
= $true )
| ( ( ( power_power_nat @ SV1243 @ SV1428 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5918]) ).
thf(6283,plain,
! [SV1580: nat] :
( ( ! [SY2668: nat] :
( ( ( power_power_nat @ SV1580 @ SY2668 )
!= zero_zero_nat )
| ( SY2668 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5919]) ).
thf(6284,plain,
! [SV1581: nat] :
( ( ! [SY2669: nat] :
( ( power_power_nat @ SV1581 @ SY2669 )
!= zero_zero_nat )
| ( SV1581 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5920]) ).
thf(6285,plain,
! [SV1429: int,SV1244: int] :
( ( ( ord_less_int @ ( bit1 @ SV1244 ) @ ( bit0 @ SV1429 ) )
= $false )
| ( ( ord_less_int @ SV1244 @ SV1429 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5921]) ).
thf(6286,plain,
! [SV1430: int,SV1245: int] :
( ( ( ord_less_int @ SV1245 @ SV1430 )
= $false )
| ( ( ord_less_int @ ( bit1 @ SV1245 ) @ ( bit0 @ SV1430 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5922]) ).
thf(6287,plain,
! [SV1431: int,SV1246: int] :
( ( ( SV1246
= ( plus_plus_int @ SV1246 @ SV1431 ) )
= $false )
| ( ( SV1431 = zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5923]) ).
thf(6288,plain,
! [SV1247: int,SV1432: int] :
( ( ( SV1432 = zero_zero_int )
= $false )
| ( ( SV1247
= ( plus_plus_int @ SV1247 @ SV1432 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5924]) ).
thf(6289,plain,
! [SV1248: int,SV1433: int,SV1582: int] :
( ( ( ~ ( zcong @ ( power_power_int @ SV1582 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SV1433 @ SV1248 ) )
= $true )
| ( ( quadRes @ SV1248 @ SV1433 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5925]) ).
thf(6290,plain,
! [SV1434: int,SV1249: int] :
( ( ( quadRes @ SV1249 @ SV1434 )
= $false )
| ( ( zcong @ ( power_power_int @ ( sK5_Y_1 @ SV1434 @ SV1249 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SV1434 @ SV1249 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5926]) ).
thf(6291,plain,
! [SV1435: nat,SV462: nat,SV1486: real] :
( ( ( ~ ( ord_less_real @ one_one_real @ SV1486 ) )
= $true )
| ( ( ( ( power_power_real @ SV1486 @ SV462 )
!= ( power_power_real @ SV1486 @ SV1435 ) )
| ( SV462 = SV1435 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5929]) ).
thf(6292,plain,
! [SV1436: nat,SV462: nat,SV1487: real] :
( ( ( ~ ( ord_less_real @ one_one_real @ SV1487 ) )
= $true )
| ( ( ( SV462 != SV1436 )
| ( ( power_power_real @ SV1487 @ SV462 )
= ( power_power_real @ SV1487 @ SV1436 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5930]) ).
thf(6293,plain,
! [SV1252: int,SV1437: int] :
( ( ( ord_less_int @ SV1437 @ pls )
= $false )
| ( ( ( plus_plus_nat @ ( number_number_of_nat @ SV1437 ) @ ( number_number_of_nat @ SV1252 ) )
= ( number_number_of_nat @ SV1252 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5931]) ).
thf(6294,plain,
! [SV1583: int] :
( ( ! [SY2670: int] :
( ( ord_less_int @ SY2670 @ pls )
| ~ ( ord_less_int @ SV1583 @ pls )
| ( ( plus_plus_nat @ ( number_number_of_nat @ SY2670 ) @ ( number_number_of_nat @ SV1583 ) )
= ( number_number_of_nat @ SY2670 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5932]) ).
thf(6295,plain,
! [SV1584: int] :
( ( ! [SY2671: int] :
( ( ord_less_int @ SY2671 @ pls )
| ( ord_less_int @ SV1584 @ pls )
| ( ( plus_plus_nat @ ( number_number_of_nat @ SY2671 ) @ ( number_number_of_nat @ SV1584 ) )
= ( number_number_of_nat @ ( plus_plus_int @ SY2671 @ SV1584 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5933]) ).
thf(6296,plain,
! [SV1438: real,SV463: real,SV1488: real] :
( ( ( SV1488 = zero_zero_real )
= $true )
| ( ( ( ( times_times_real @ SV463 @ SV1488 )
!= ( times_times_real @ SV1438 @ SV1488 ) )
| ( SV463 = SV1438 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5934]) ).
thf(6297,plain,
! [SV1439: real,SV463: real,SV1489: real] :
( ( ( SV1489 = zero_zero_real )
= $true )
| ( ( ( SV463 != SV1439 )
| ( ( times_times_real @ SV463 @ SV1489 )
= ( times_times_real @ SV1439 @ SV1489 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5935]) ).
thf(6298,plain,
! [SV1440: real,SV464: real,SV1490: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV1490 ) )
= $true )
| ( ( ~ ( ord_less_real @ ( times_times_real @ SV464 @ SV1490 ) @ ( times_times_real @ SV1440 @ SV1490 ) )
| ( ord_less_real @ SV464 @ SV1440 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5936]) ).
thf(6299,plain,
! [SV1441: real,SV464: real,SV1491: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV1491 ) )
= $true )
| ( ( ~ ( ord_less_real @ SV464 @ SV1441 )
| ( ord_less_real @ ( times_times_real @ SV464 @ SV1491 ) @ ( times_times_real @ SV1441 @ SV1491 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5937]) ).
thf(6300,plain,
! [SV1442: real,SV465: real,SV1492: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV1492 ) )
= $true )
| ( ( ~ ( ord_less_eq_real @ ( times_times_real @ SV1492 @ SV465 ) @ ( times_times_real @ SV1492 @ SV1442 ) )
| ( ord_less_eq_real @ SV465 @ SV1442 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5938]) ).
thf(6301,plain,
! [SV1443: real,SV465: real,SV1493: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV1493 ) )
= $true )
| ( ( ~ ( ord_less_eq_real @ SV465 @ SV1443 )
| ( ord_less_eq_real @ ( times_times_real @ SV1493 @ SV465 ) @ ( times_times_real @ SV1493 @ SV1443 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5939]) ).
thf(6302,plain,
! [SV1444: int,SV1253: int] :
( ( ( ( bit0 @ SV1253 )
= ( bit0 @ SV1444 ) )
= $false )
| ( ( SV1253 = SV1444 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5940]) ).
thf(6303,plain,
! [SV1445: int,SV1254: int] :
( ( ( SV1254 = SV1445 )
= $false )
| ( ( ( bit0 @ SV1254 )
= ( bit0 @ SV1445 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5941]) ).
thf(6304,plain,
! [SV1446: int,SV1257: int] :
( ( ( SV1257 != zero_zero_int )
= $true )
| ( ( SV1446 != zero_zero_int )
= $true )
| ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SV1257 @ SV1257 ) @ ( times_times_int @ SV1446 @ SV1446 ) ) @ zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5944]) ).
thf(6305,plain,
! [SV1585: int] :
( ( ! [SY2672: int] :
~ ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SV1585 @ SV1585 ) @ ( times_times_int @ SY2672 @ SY2672 ) ) @ zero_zero_int )
| ( SV1585 = zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5945]) ).
thf(6306,plain,
! [SV1586: int] :
( ( ! [SY2673: int] :
( ~ ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SV1586 @ SV1586 ) @ ( times_times_int @ SY2673 @ SY2673 ) ) @ zero_zero_int )
| ( SY2673 = zero_zero_int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5946]) ).
thf(6307,plain,
! [SV1262: int,SV1447: nat] :
( ( ( SV1447 = zero_zero_nat )
= $true )
| ( ( SV1262 != zero_zero_int )
= $true )
| ( ( ( power_power_int @ SV1262 @ SV1447 )
= zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5951]) ).
thf(6308,plain,
! [SV1587: int] :
( ( ! [SY2674: nat] :
( ( ( power_power_int @ SV1587 @ SY2674 )
!= zero_zero_int )
| ( SY2674 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5952]) ).
thf(6309,plain,
! [SV1588: int] :
( ( ! [SY2675: nat] :
( ( power_power_int @ SV1588 @ SY2675 )
!= zero_zero_int )
| ( SV1588 = zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5953]) ).
thf(6310,plain,
! [SV1448: int,SV1263: int] :
( ( ( ( number_number_of_int @ SV1263 )
= ( number_number_of_int @ SV1448 ) )
= $false )
| ( ( SV1263 = SV1448 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5954]) ).
thf(6311,plain,
! [SV1449: int,SV1264: int] :
( ( ( SV1264 = SV1449 )
= $false )
| ( ( ( number_number_of_int @ SV1264 )
= ( number_number_of_int @ SV1449 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5955]) ).
thf(6312,plain,
! [SV1450: int,SV1267: int] :
( ( ( ord_less_eq_nat @ ( number_number_of_nat @ SV1267 ) @ ( number_number_of_nat @ SV1450 ) )
= $false )
| ( ( ~ ( ord_less_nat @ ( number_number_of_nat @ SV1450 ) @ ( number_number_of_nat @ SV1267 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5958]) ).
thf(6313,plain,
! [SV1452: int,SV466: int,SV1494: int] :
( ( ( ~ ( dvd_dvd_int @ SV1494 @ ( minus_minus_int @ SV466 @ SV1452 ) ) )
= $true )
| ( ( zcong @ SV466 @ SV1452 @ SV1494 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5962]) ).
thf(6314,plain,
! [SV1495: int,SV1453: int,SV466: int] :
( ( ( ~ ( zcong @ SV466 @ SV1453 @ SV1495 ) )
= $true )
| ( ( dvd_dvd_int @ SV1495 @ ( minus_minus_int @ SV466 @ SV1453 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5963]) ).
thf(6315,plain,
! [SV1454: int,SV1277: int] :
( ( ( ord_less_int @ ( number_number_of_int @ SV1277 ) @ ( number_number_of_int @ SV1454 ) )
= $false )
| ( ( ord_less_int @ SV1277 @ SV1454 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5969]) ).
thf(6316,plain,
! [SV1455: int,SV1278: int] :
( ( ( ord_less_int @ SV1278 @ SV1455 )
= $false )
| ( ( ord_less_int @ ( number_number_of_int @ SV1278 ) @ ( number_number_of_int @ SV1455 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5970]) ).
thf(6317,plain,
! [SV1456: nat,SV467: nat,SV1496: int] :
( ( ( ~ ( ord_less_int @ one_one_int @ SV1496 ) )
= $true )
| ( ( ( ( power_power_int @ SV1496 @ SV467 )
!= ( power_power_int @ SV1496 @ SV1456 ) )
| ( SV467 = SV1456 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5971]) ).
thf(6318,plain,
! [SV1457: nat,SV467: nat,SV1497: int] :
( ( ( ~ ( ord_less_int @ one_one_int @ SV1497 ) )
= $true )
| ( ( ( SV467 != SV1457 )
| ( ( power_power_int @ SV1497 @ SV467 )
= ( power_power_int @ SV1497 @ SV1457 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5972]) ).
thf(6319,plain,
! [SV984: int,SV797: int,SV472: int,SV8: int] :
( ( ( ord_less_eq_int @ SV8 @ SV472 )
= $false )
| ( ( ord_less_int @ ( plus_plus_int @ SV797 @ SV8 ) @ ( plus_plus_int @ SV984 @ SV472 ) )
= $true )
| ( ( ord_less_int @ SV797 @ SV984 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5973]) ).
thf(6320,plain,
! [SV29: int,SV489: int] :
( ( ( ord_less_eq_int @ zero_zero_int @ SV489 )
= $false )
| ( ( SV29 = SV489 )
= $true )
| ( ( ord_less_eq_int @ zero_zero_int @ SV29 )
= $false )
| ( ( ( power_power_int @ SV29 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power_int @ SV489 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5975]) ).
thf(6321,plain,
! [SV510: int,SV810: int,SV88: int] :
( ( ( ~ ( ord_less_int @ SV88 @ SV810 ) )
= $true )
| ( ( ord_less_eq_int @ one_one_int @ SV510 )
= $true )
| ( ( SV810
= ( plus_plus_int @ SV88 @ ( times_times_int @ SV810 @ SV510 ) ) )
= $false )
| ( ( ord_less_int @ zero_zero_int @ SV810 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5976]) ).
thf(6322,plain,
! [SV811: int,SV511: int,SV89: int] :
( ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV89 ) )
= $true )
| ( ( ord_less_eq_int @ SV511 @ one_one_int )
= $true )
| ( ( SV811
= ( plus_plus_int @ SV89 @ ( times_times_int @ SV811 @ SV511 ) ) )
= $false )
| ( ( ord_less_int @ zero_zero_int @ SV811 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5977]) ).
thf(6323,plain,
! [SV96: int,SV518: int] :
( ( ( dvd_dvd_int @ SV518 @ SV96 )
= $false )
| ( ( ~ ( dvd_dvd_int @ SV96 @ SV518 )
| ( SV518 = SV96 ) )
= $true )
| ( ( ord_less_eq_int @ zero_zero_int @ SV96 )
= $false )
| ( ( ord_less_eq_int @ zero_zero_int @ SV518 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5980]) ).
thf(6324,plain,
! [SV1279: int,SV986: int,SV827: int,SV536: int,SV125: int] :
( ( ( SV125 = SV536 )
= $true )
| ( ( SV827 != SV986 )
= $true )
| ( ( ( plus_plus_int @ SV827 @ ( times_times_int @ SV1279 @ SV125 ) )
!= ( plus_plus_int @ SV986 @ ( times_times_int @ SV1279 @ SV536 ) ) )
= $true )
| ( ( SV1279 = zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5981]) ).
thf(6325,plain,
! [SV828: int,SV543: int,SV133: int] :
( ( ( ~ ( ord_less_int @ zero_zero_int @ SV133 ) )
= $true )
| ( ( ord_less_eq_int @ zero_zero_int @ SV543 )
= $true )
| ( ( ord_less_int @ SV828 @ SV133 )
= $false )
| ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ SV133 @ SV543 ) @ SV828 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5982]) ).
thf(6326,plain,
! [SV829: int,SV544: int,SV134: int] :
( ( ( ~ ( ord_less_int @ zero_zero_int @ SV134 ) )
= $true )
| ( ( ord_less_eq_int @ SV544 @ zero_zero_int )
= $true )
| ( ( ord_less_eq_int @ zero_zero_int @ SV829 )
= $false )
| ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ SV134 @ SV544 ) @ SV829 ) @ zero_zero_int )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5983]) ).
thf(6327,plain,
! [SV987: int,SV545: int,SV1280: int,SV135: int,SV830: int] :
( ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV830 ) )
= $true )
| ( ( ~ ( ord_less_int @ SV830 @ SV135 )
| ~ ( ord_less_int @ SV1280 @ SV135 )
| ( ord_less_eq_int @ SV545 @ SV987 ) )
= $true )
| ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SV135 @ SV545 ) @ SV830 ) @ ( plus_plus_int @ ( times_times_int @ SV135 @ SV987 ) @ SV1280 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5984]) ).
thf(6328,plain,
! [SV1458: int,SV1281: int,SV988: int,SV831: int,SV546: int,SV136: int] :
( ( ( ( plus_plus_int @ ( times_times_int @ SV136 @ SV546 ) @ SV831 )
= ( plus_plus_int @ ( times_times_int @ SV988 @ SV1281 ) @ SV1458 ) )
= $false )
| ( ( ~ ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ SV988 @ SV1281 ) @ SV1458 ) )
| ~ ( ord_less_int @ SV1458 @ SV988 )
| ~ ( ord_less_eq_int @ zero_zero_int @ SV831 )
| ~ ( ord_less_int @ zero_zero_int @ SV988 )
| ~ ( ord_less_eq_int @ SV988 @ SV136 )
| ( ord_less_eq_int @ SV546 @ SV1281 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5985]) ).
thf(6329,plain,
! [SV547: int,SV989: int,SV832: int,SV137: int,SV1282: int] :
( ( ( ~ ( ord_less_eq_int @ SV1282 @ zero_zero_int ) )
= $true )
| ( ( ~ ( ord_less_int @ SV137 @ SV1282 )
| ~ ( ord_less_int @ SV137 @ SV832 )
| ( ord_less_eq_int @ SV989 @ SV547 ) )
= $true )
| ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SV137 @ SV547 ) @ SV832 ) @ ( plus_plus_int @ ( times_times_int @ SV137 @ SV989 ) @ SV1282 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5986]) ).
thf(6330,plain,
! [SV1459: int,SV1283: int,SV990: int,SV833: int,SV548: int,SV138: int] :
( ( ( ( plus_plus_int @ ( times_times_int @ SV138 @ SV548 ) @ SV833 )
= ( plus_plus_int @ ( times_times_int @ SV990 @ SV1283 ) @ SV1459 ) )
= $false )
| ( ( ~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ SV990 @ SV1283 ) @ SV1459 ) @ zero_zero_int )
| ~ ( ord_less_int @ SV833 @ SV138 )
| ~ ( ord_less_eq_int @ zero_zero_int @ SV1459 )
| ~ ( ord_less_int @ zero_zero_int @ SV990 )
| ~ ( ord_less_eq_int @ SV990 @ SV138 )
| ( ord_less_eq_int @ SV1283 @ SV548 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5987]) ).
thf(6331,plain,
! [SV835: int,SV147: int,SV551: int] :
( ( ( ord_less_eq_int @ SV551 @ SV147 )
= $true )
| ( ( ord_less_eq_int @ SV147 @ SV551 )
= $true )
| ( ( ord_less_int @ SV147 @ SV835 )
= $false )
| ( ( ord_less_int @ SV551 @ SV835 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5989]) ).
thf(6332,plain,
! [SV991: int,SV836: int,SV1284: int,SV553: int,SV149: int] :
( ( ( ~ ( zcong @ SV149 @ SV553 @ SV1284 ) )
= $true )
| ( ( zcong @ ( plus_plus_int @ SV836 @ SV149 ) @ ( plus_plus_int @ SV991 @ SV553 ) @ SV1284 )
= $true )
| ( ( zcong @ SV836 @ SV991 @ SV1284 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5990]) ).
thf(6333,plain,
! [SV554: int,SV837: int,SV150: int] :
( ( ( ~ ( ord_less_int @ zero_zero_int @ SV150 ) )
= $true )
| ( ( ~ ( ord_less_int @ SV150 @ SV837 )
| ~ ( zcong @ SV837 @ SV150 @ SV554 ) )
= $true )
| ( ( ord_less_int @ SV837 @ SV554 )
= $false )
| ( ( ord_less_int @ zero_zero_int @ SV837 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5991]) ).
thf(6334,plain,
! [SV151: int,SV555: int] :
( ( ( zcong @ SV555 @ zero_zero_int @ SV151 )
= $false )
| ( ( SV555 = zero_zero_int )
= $true )
| ( ( ord_less_int @ SV555 @ SV151 )
= $false )
| ( ( ord_less_eq_int @ zero_zero_int @ SV555 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5992]) ).
thf(6335,plain,
! [SV838: int,SV556: int,SV152: int] :
( ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV152 ) )
= $true )
| ( ( ~ ( ord_less_int @ SV152 @ SV556 )
| ~ ( zcong @ SV838 @ SV152 @ SV556 )
| ( SV838 = SV152 ) )
= $true )
| ( ( ord_less_int @ SV838 @ SV556 )
= $false )
| ( ( ord_less_eq_int @ zero_zero_int @ SV838 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5993]) ).
thf(6336,plain,
! [SV568: int,SV845: int,SV170: int] :
( ( ( ~ ( ord_less_int @ zero_zero_int @ SV170 ) )
= $true )
| ( ( ~ ( zcong @ SV845 @ SV568 @ SV170 )
| ~ ( ord_less_int @ SV845 @ SV170 )
| ~ ( ord_less_int @ SV568 @ SV170 )
| ( SV845 = SV568 ) )
= $true )
| ( ( ord_less_int @ zero_zero_int @ SV568 )
= $false )
| ( ( ord_less_int @ zero_zero_int @ SV845 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5996]) ).
thf(6337,plain,
! [SV173: int,SV571: int] :
( ( ( zcong @ SV571 @ zero_zero_int @ SV173 )
= $false )
| ( ( SV571 = zero_zero_int )
= $true )
| ( ( ord_less_int @ SV571 @ SV173 )
= $false )
| ( ( ord_less_eq_int @ zero_zero_int @ SV571 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5998]) ).
thf(6338,plain,
! [SV998: int,SV584: int,SV853: nat,SV191: nat] :
( ( ( ord_less_eq_nat @ SV191 @ SV853 )
= $false )
| ( ( dvd_dvd_int @ ( power_power_int @ SV584 @ SV191 ) @ SV998 )
= $true )
| ( ( dvd_dvd_int @ ( power_power_int @ SV584 @ SV853 ) @ SV998 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6000]) ).
thf(6339,plain,
! [SV999: int,SV854: int,SV585: nat,SV192: nat] :
( ( ( ord_less_eq_nat @ SV192 @ SV585 )
= $false )
| ( ( dvd_dvd_int @ ( power_power_int @ SV854 @ SV192 ) @ ( power_power_int @ SV999 @ SV585 ) )
= $true )
| ( ( dvd_dvd_int @ SV854 @ SV999 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6001]) ).
thf(6340,plain,
! [SV594: nat,SV860: nat,SV201: int] :
( ( ( ~ ( ord_less_int @ SV201 @ one_one_int ) )
= $true )
| ( ( ord_less_int @ ( power_power_int @ SV201 @ SV860 ) @ ( power_power_int @ SV201 @ SV594 ) )
= $true )
| ( ( ord_less_int @ zero_zero_int @ SV201 )
= $false )
| ( ( ord_less_nat @ SV594 @ SV860 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6006]) ).
thf(6341,plain,
! [SV227: real,SV615: real] :
( ( ( ord_less_eq_real @ zero_zero_real @ SV615 )
= $false )
| ( ( SV227 = SV615 )
= $true )
| ( ( ord_less_eq_real @ zero_zero_real @ SV227 )
= $false )
| ( ( ( power_power_real @ SV227 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power_real @ SV615 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6008]) ).
thf(6342,plain,
! [SV228: nat,SV616: nat] :
( ( ( ord_less_eq_nat @ zero_zero_nat @ SV616 )
= $false )
| ( ( SV228 = SV616 )
= $true )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV228 )
= $false )
| ( ( ( power_power_nat @ SV228 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power_nat @ SV616 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6009]) ).
thf(6343,plain,
! [SV869: int,SV628: int,SV249: nat,SV1000: int] :
( ( ( ~ ( dvd_dvd_int @ ( power_power_int @ SV1000 @ SV249 ) @ ( times_times_int @ SV628 @ SV869 ) ) )
= $true )
| ( ( dvd_dvd_int @ ( power_power_int @ SV1000 @ SV249 ) @ SV628 )
= $true )
| ( ( dvd_dvd_int @ SV1000 @ SV869 )
= $true )
| ( ( zprime @ SV1000 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6010]) ).
thf(6344,plain,
! [SV629: int,SV870: int,SV250: nat,SV1001: int] :
( ( ( ~ ( dvd_dvd_int @ ( power_power_int @ SV1001 @ SV250 ) @ ( times_times_int @ SV870 @ SV629 ) ) )
= $true )
| ( ( dvd_dvd_int @ ( power_power_int @ SV1001 @ SV250 ) @ SV629 )
= $true )
| ( ( dvd_dvd_int @ SV1001 @ SV870 )
= $true )
| ( ( zprime @ SV1001 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6011]) ).
thf(6345,plain,
! [SV1286: real,SV1013: real,SV913: real,SV678: real,SV316: real] :
( ( ( SV316 = SV678 )
= $true )
| ( ( SV913 != SV1013 )
= $true )
| ( ( ( plus_plus_real @ SV913 @ ( times_times_real @ SV1286 @ SV316 ) )
!= ( plus_plus_real @ SV1013 @ ( times_times_real @ SV1286 @ SV678 ) ) )
= $true )
| ( ( SV1286 = zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6012]) ).
thf(6346,plain,
! [SV1287: nat,SV1014: nat,SV914: nat,SV679: nat,SV317: nat] :
( ( ( SV317 = SV679 )
= $true )
| ( ( SV914 != SV1014 )
= $true )
| ( ( ( plus_plus_nat @ SV914 @ ( times_times_nat @ SV1287 @ SV317 ) )
!= ( plus_plus_nat @ SV1014 @ ( times_times_nat @ SV1287 @ SV679 ) ) )
= $true )
| ( ( SV1287 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6013]) ).
thf(6347,plain,
! [SV685: int,SV1015: int,SV327: int,SV916: int] :
( ( ( zcong @ SV916 @ SV327 @ SV1015 )
= $false )
| ( ( zcong @ SV685 @ SV327 @ SV1015 )
= $true )
| ( ( zcong @ SV685 @ SV916 @ SV1015 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6014]) ).
thf(6348,plain,
! [SV1018: int,SV920: int,SV1288: int,SV691: int,SV333: int] :
( ( ( ~ ( zcong @ SV333 @ SV691 @ SV1288 ) )
= $true )
| ( ( zcong @ ( times_times_int @ SV920 @ SV333 ) @ ( times_times_int @ SV1018 @ SV691 ) @ SV1288 )
= $true )
| ( ( zcong @ SV920 @ SV1018 @ SV1288 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6015]) ).
thf(6349,plain,
! [SV337: int,SV921: int,SV692: int] :
( ( ( ~ ( dvd_dvd_int @ SV692 @ ( times_times_int @ SV921 @ SV337 ) ) )
= $true )
| ( ( ( dvd_dvd_int @ SV692 @ SV921 )
| ( dvd_dvd_int @ SV692 @ SV337 ) )
= $true )
| ( ( zprime @ SV692 )
= $false )
| ( ( ord_less_eq_int @ zero_zero_int @ SV921 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6016]) ).
thf(6350,plain,
! [SV1019: int,SV923: int,SV1289: int,SV695: int,SV340: int] :
( ( ( ~ ( zcong @ SV340 @ SV695 @ SV1289 ) )
= $true )
| ( ( zcong @ ( minus_minus_int @ SV923 @ SV340 ) @ ( minus_minus_int @ SV1019 @ SV695 ) @ SV1289 )
= $true )
| ( ( zcong @ SV923 @ SV1019 @ SV1289 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6019]) ).
thf(6351,plain,
! [SV932: int,SV1290: int,SV351: int,SV706: int,SV1020: int] :
( ( ( SV1020 != SV706 )
= $true )
| ( ( ~ ( zcong @ SV706 @ SV351 @ SV1290 )
| ( zcong @ SV932 @ SV351 @ SV1290 ) )
= $true )
| ( ( zcong @ SV932 @ SV1020 @ SV1290 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6021]) ).
thf(6352,plain,
! [SV707: int,SV352: int] :
( ( ( ord_less_int @ SV352 @ SV707 )
= $false )
| ( ( ~ ( zcong @ ( times_times_int @ SV352 @ SV352 ) @ one_one_int @ SV707 )
| ( SV352 = one_one_int )
| ( SV352
= ( minus_minus_int @ SV707 @ one_one_int ) ) )
= $true )
| ( ( ord_less_int @ zero_zero_int @ SV352 )
= $false )
| ( ( zprime @ SV707 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6022]) ).
thf(6353,plain,
! [SV708: int,SV353: int] :
( ( ( zcong @ ( times_times_int @ SV353 @ SV353 ) @ one_one_int @ SV708 )
= $false )
| ( ( ( zcong @ SV353 @ one_one_int @ SV708 )
| ( zcong @ SV353 @ ( minus_minus_int @ SV708 @ one_one_int ) @ SV708 ) )
= $true )
| ( ( ord_less_int @ zero_zero_int @ SV353 )
= $false )
| ( ( zprime @ SV708 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6023]) ).
thf(6354,plain,
! [SV713: int,SV358: int,SV933: int] :
( ( ( dvd_dvd_int @ SV933 @ SV358 )
= $true )
| ( ( dvd_dvd_int @ SV933 @ SV713 )
= $true )
| ( ( dvd_dvd_int @ SV933 @ ( times_times_int @ SV358 @ SV713 ) )
= $false )
| ( ( zprime @ SV933 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6024]) ).
thf(6355,plain,
! [SV935: int,SV360: int,SV715: int] :
( ( ( zcong @ ( times_times_int @ SV715 @ SV360 ) @ zero_zero_int @ SV935 )
= $false )
| ( ( zcong @ SV360 @ zero_zero_int @ SV935 )
= $true )
| ( ( zcong @ SV715 @ zero_zero_int @ SV935 )
= $true )
| ( ( zprime @ SV935 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6026]) ).
thf(6356,plain,
! [SV361: int,SV936: int,SV716: int] :
( ( ( ( zcong @ SV716 @ zero_zero_int @ SV936 )
| ( zcong @ SV361 @ zero_zero_int @ SV936 ) )
= $true )
| ( ( ~ ( zcong @ ( times_times_int @ SV716 @ SV361 ) @ zero_zero_int @ SV936 ) )
= $true )
| ( ( ord_less_int @ zero_zero_int @ SV716 )
= $false )
| ( ( zprime @ SV936 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6027]) ).
thf(6357,plain,
! [SV937: int,SV362: int,SV717: int] :
( ( ( ~ ( zcong @ ( times_times_int @ SV717 @ SV362 ) @ zero_zero_int @ SV937 ) )
= $true )
| ( ( ( zcong @ SV717 @ zero_zero_int @ SV937 )
| ( zcong @ SV362 @ zero_zero_int @ SV937 ) )
= $true )
| ( ( ord_less_int @ zero_zero_int @ SV717 )
= $false )
| ( ( zprime @ SV937 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6028]) ).
thf(6358,plain,
! [SV363: int,SV938: int,SV718: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV718 ) )
= $true )
| ( ( dvd_dvd_int @ SV938 @ SV363 )
= $true )
| ( ( dvd_dvd_int @ SV938 @ ( power_power_int @ SV363 @ SV718 ) )
= $false )
| ( ( zprime @ SV938 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6029]) ).
thf(6359,plain,
! [SV945: real,SV732: real,SV382: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV382 ) )
= $true )
| ( ( ord_less_real @ ( power_power_real @ SV732 @ SV382 ) @ ( power_power_real @ SV945 @ SV382 ) )
= $true )
| ( ( ord_less_eq_real @ zero_zero_real @ SV732 )
= $false )
| ( ( ord_less_real @ SV732 @ SV945 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6031]) ).
thf(6360,plain,
! [SV946: nat,SV733: nat,SV383: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV383 ) )
= $true )
| ( ( ord_less_nat @ ( power_power_nat @ SV733 @ SV383 ) @ ( power_power_nat @ SV946 @ SV383 ) )
= $true )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV733 )
= $false )
| ( ( ord_less_nat @ SV733 @ SV946 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6032]) ).
thf(6361,plain,
! [SV947: int,SV734: int,SV384: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV384 ) )
= $true )
| ( ( ord_less_int @ ( power_power_int @ SV734 @ SV384 ) @ ( power_power_int @ SV947 @ SV384 ) )
= $true )
| ( ( ord_less_eq_int @ zero_zero_int @ SV734 )
= $false )
| ( ( ord_less_int @ SV734 @ SV947 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6033]) ).
thf(6362,plain,
! [SV1023: nat,SV754: nat,SV958: nat,SV410: nat] :
( ( ( ord_less_eq_nat @ SV410 @ SV958 )
= $false )
| ( ( dvd_dvd_nat @ ( power_power_nat @ SV754 @ SV410 ) @ SV1023 )
= $true )
| ( ( dvd_dvd_nat @ ( power_power_nat @ SV754 @ SV958 ) @ SV1023 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6036]) ).
thf(6363,plain,
! [SV1024: real,SV755: real,SV959: nat,SV411: nat] :
( ( ( ord_less_eq_nat @ SV411 @ SV959 )
= $false )
| ( ( dvd_dvd_real @ ( power_power_real @ SV755 @ SV411 ) @ SV1024 )
= $true )
| ( ( dvd_dvd_real @ ( power_power_real @ SV755 @ SV959 ) @ SV1024 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6037]) ).
thf(6364,plain,
! [SV1025: nat,SV960: nat,SV756: nat,SV412: nat] :
( ( ( ord_less_eq_nat @ SV412 @ SV756 )
= $false )
| ( ( dvd_dvd_nat @ ( power_power_nat @ SV960 @ SV412 ) @ ( power_power_nat @ SV1025 @ SV756 ) )
= $true )
| ( ( dvd_dvd_nat @ SV960 @ SV1025 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6038]) ).
thf(6365,plain,
! [SV1026: real,SV961: real,SV757: nat,SV413: nat] :
( ( ( ord_less_eq_nat @ SV413 @ SV757 )
= $false )
| ( ( dvd_dvd_real @ ( power_power_real @ SV961 @ SV413 ) @ ( power_power_real @ SV1026 @ SV757 ) )
= $true )
| ( ( dvd_dvd_real @ SV961 @ SV1026 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6039]) ).
thf(6366,plain,
! [SV782: nat,SV438: nat,SV979: nat,SV1027: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV1027 )
= $false )
| ( ( ~ ( ord_less_nat @ SV1027 @ SV979 )
| ~ ( dvd_dvd_nat @ SV979 @ SV438 ) )
= $true )
| ( ( SV438
= ( plus_plus_nat @ ( times_times_nat @ SV782 @ SV979 ) @ SV1027 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6050]) ).
thf(6367,plain,
! [SV1291: nat,SV1030: nat] :
( ( ( SV1030 = zero_zero_nat )
= $false )
| ( ( SV1291 = zero_zero_nat )
= $true )
| ( ( ( power_power_nat @ SV1030 @ SV1291 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6052]) ).
thf(6368,plain,
! [SV1589: nat,SV1499: nat] :
( ( ( ( power_power_nat @ SV1499 @ SV1589 )
!= zero_zero_nat )
| ( SV1589 != zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6053]) ).
thf(6369,plain,
! [SV1500: nat] :
( ( ( ! [SY2596: nat] :
( ( power_power_nat @ SV1500 @ SY2596 )
!= zero_zero_nat ) )
= $true )
| ( ( SV1500 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6054]) ).
thf(6370,plain,
! [SV1292: int,SV1031: nat] :
( ( ( SV1031 = zero_zero_nat )
= $false )
| ( ( ( number_number_of_nat @ SV1292 )
= zero_zero_nat )
= $true )
| ( ( ( power_power_nat @ SV1031 @ ( number_number_of_nat @ SV1292 ) )
= zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6055]) ).
thf(6371,plain,
! [SV1590: int,SV1501: nat] :
( ( ( ( power_power_nat @ SV1501 @ ( number_number_of_nat @ SV1590 ) )
!= zero_zero_nat )
| ( ( number_number_of_nat @ SV1590 )
!= zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6056]) ).
thf(6372,plain,
! [SV1502: nat] :
( ( ( ! [SY2598: int] :
( ( power_power_nat @ SV1502 @ ( number_number_of_nat @ SY2598 ) )
!= zero_zero_nat ) )
= $true )
| ( ( SV1502 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6057]) ).
thf(6373,plain,
! [SV1293: real,SV1034: real] :
( ( ( SV1034 != zero_zero_real )
= $true )
| ( ( SV1293 != zero_zero_real )
= $true )
| ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ SV1034 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SV1293 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6058]) ).
thf(6374,plain,
! [SV1503: real] :
( ( ( SV1503 = zero_zero_real )
= $true )
| ( ( ! [SY2599: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ SV1503 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SY2599 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6059]) ).
thf(6375,plain,
! [SV1504: real,SV1591: real] :
( ( ( SV1591 = zero_zero_real )
| ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ SV1504 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SV1591 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6060]) ).
thf(6376,plain,
! [SV1298: nat,SV1045: nat] :
( ( ( SV1045 = one_one_nat )
= $true )
| ( ( SV1298 = zero_zero_nat )
= $true )
| ( ( ( power_power_nat @ SV1045 @ SV1298 )
= one_one_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6065]) ).
thf(6377,plain,
! [SV1505: nat] :
( ( ( SV1505 != one_one_nat )
= $true )
| ( ( ! [SY2601: nat] :
( ( power_power_nat @ SV1505 @ SY2601 )
= one_one_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6066]) ).
thf(6378,plain,
! [SV1506: nat,SV1592: nat] :
( ( ( SV1592 != zero_zero_nat )
| ( ( power_power_nat @ SV1506 @ SV1592 )
= one_one_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6067]) ).
thf(6379,plain,
! [SV1305: real,SV1054: real] :
( ( ( SV1054 = zero_zero_real )
= $false )
| ( ( SV1305 != zero_zero_real )
= $true )
| ( ( ord_less_eq_real @ ( plus_plus_real @ ( power_power_real @ SV1054 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SV1305 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6074]) ).
thf(6380,plain,
! [SV1507: real] :
( ( ( ! [SY2603: real] :
~ ( ord_less_eq_real @ ( plus_plus_real @ ( power_power_real @ SV1507 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SY2603 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_real ) )
= $true )
| ( ( SV1507 = zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6075]) ).
thf(6381,plain,
! [SV1593: real,SV1508: real] :
( ( ~ ( ord_less_eq_real @ ( plus_plus_real @ ( power_power_real @ SV1508 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SV1593 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_real )
| ( SV1593 = zero_zero_real ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6076]) ).
thf(6382,plain,
! [SV1306: int,SV1055: int] :
( ( ( SV1055 = SV1306 )
= $true )
| ( ( ord_less_int @ SV1055 @ SV1306 )
= $true )
| ( ( ord_less_int @ SV1055 @ ( plus_plus_int @ SV1306 @ one_one_int ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6077]) ).
thf(6383,plain,
! [SV1594: int,SV1509: int] :
( ( ( SV1509 != SV1594 )
| ( ord_less_int @ SV1509 @ ( plus_plus_int @ SV1594 @ one_one_int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6078]) ).
thf(6384,plain,
! [SV1595: int,SV1510: int] :
( ( ~ ( ord_less_int @ SV1510 @ SV1595 )
| ( ord_less_int @ SV1510 @ ( plus_plus_int @ SV1595 @ one_one_int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6079]) ).
thf(6385,plain,
! [SV785: nat,SV441: nat] :
( ( ! [SY2273: nat,SY2274: nat] :
( ( ( plus_plus_nat @ ( times_times_nat @ SY2273 @ SV441 ) @ ( times_times_nat @ SY2274 @ SV785 ) )
= ( plus_plus_nat @ ( times_times_nat @ SY2273 @ SV785 ) @ ( times_times_nat @ SY2274 @ SV441 ) ) )
| ( SY2273 != SY2274 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6080]) ).
thf(6386,plain,
! [SV785: nat,SV441: nat] :
( ( ! [SY2275: nat,SY2276: nat] :
( ( plus_plus_nat @ ( times_times_nat @ SY2275 @ SV441 ) @ ( times_times_nat @ SY2276 @ SV785 ) )
= ( plus_plus_nat @ ( times_times_nat @ SY2275 @ SV785 ) @ ( times_times_nat @ SY2276 @ SV441 ) ) )
| ( SV441 != SV785 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6081]) ).
thf(6387,plain,
! [SV785: nat,SV441: nat,SV1511: nat,SV1461: nat] :
( ( ( ( SV1461 = SV1511 )
| ( SV441 = SV785 ) )
= $true )
| ( ( ( plus_plus_nat @ ( times_times_nat @ SV1461 @ SV441 ) @ ( times_times_nat @ SV1511 @ SV785 ) )
!= ( plus_plus_nat @ ( times_times_nat @ SV1461 @ SV785 ) @ ( times_times_nat @ SV1511 @ SV441 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6082]) ).
thf(6388,plain,
! [SV1311: int,SV1064: real] :
( ( ( SV1064 = zero_zero_real )
= $false )
| ( ( ( number_number_of_nat @ SV1311 )
= zero_zero_nat )
= $true )
| ( ( ( power_power_real @ SV1064 @ ( number_number_of_nat @ SV1311 ) )
= zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6087]) ).
thf(6389,plain,
! [SV1596: int,SV1512: real] :
( ( ( ( power_power_real @ SV1512 @ ( number_number_of_nat @ SV1596 ) )
!= zero_zero_real )
| ( ( number_number_of_nat @ SV1596 )
!= zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6088]) ).
thf(6390,plain,
! [SV1513: real] :
( ( ( ! [SY2608: int] :
( ( power_power_real @ SV1513 @ ( number_number_of_nat @ SY2608 ) )
!= zero_zero_real ) )
= $true )
| ( ( SV1513 = zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6089]) ).
thf(6391,plain,
! [SV1312: real,SV1065: real] :
( ( ( SV1065 != zero_zero_real )
= $true )
| ( ( SV1312 != zero_zero_real )
= $true )
| ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ SV1065 @ SV1065 ) @ ( times_times_real @ SV1312 @ SV1312 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6090]) ).
thf(6392,plain,
! [SV1514: real] :
( ( ( SV1514 = zero_zero_real )
= $true )
| ( ( ! [SY2609: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ SV1514 @ SV1514 ) @ ( times_times_real @ SY2609 @ SY2609 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6091]) ).
thf(6393,plain,
! [SV1515: real,SV1597: real] :
( ( ( SV1597 = zero_zero_real )
| ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ SV1515 @ SV1515 ) @ ( times_times_real @ SV1597 @ SV1597 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6092]) ).
thf(6394,plain,
! [SV1066: nat,SV1313: nat] :
( ( ( SV1313 = zero_zero_nat )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV1066 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV1066 @ SV1313 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6093]) ).
thf(6395,plain,
! [SV1516: nat,SV1598: nat] :
( ( ( SV1598 != zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV1516 @ SV1598 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6094]) ).
thf(6396,plain,
! [SV1517: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV1517 ) )
= $true )
| ( ( ! [SY2612: nat] : ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV1517 @ SY2612 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6095]) ).
thf(6397,plain,
! [SV786: real,SV442: real] :
( ( ! [SY2279: real,SY2280: real] :
( ( ( plus_plus_real @ ( times_times_real @ SY2279 @ SV442 ) @ ( times_times_real @ SY2280 @ SV786 ) )
= ( plus_plus_real @ ( times_times_real @ SY2279 @ SV786 ) @ ( times_times_real @ SY2280 @ SV442 ) ) )
| ( SY2279 != SY2280 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6096]) ).
thf(6398,plain,
! [SV786: real,SV442: real] :
( ( ! [SY2281: real,SY2282: real] :
( ( plus_plus_real @ ( times_times_real @ SY2281 @ SV442 ) @ ( times_times_real @ SY2282 @ SV786 ) )
= ( plus_plus_real @ ( times_times_real @ SY2281 @ SV786 ) @ ( times_times_real @ SY2282 @ SV442 ) ) )
| ( SV442 != SV786 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6097]) ).
thf(6399,plain,
! [SV786: real,SV442: real,SV1518: real,SV1462: real] :
( ( ( ( SV1462 = SV1518 )
| ( SV442 = SV786 ) )
= $true )
| ( ( ( plus_plus_real @ ( times_times_real @ SV1462 @ SV442 ) @ ( times_times_real @ SV1518 @ SV786 ) )
!= ( plus_plus_real @ ( times_times_real @ SV1462 @ SV786 ) @ ( times_times_real @ SV1518 @ SV442 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6098]) ).
thf(6400,plain,
! [SV1314: real,SV1071: real] :
( ( ( SV1071 = SV1314 )
= $true )
| ( ( ord_less_real @ SV1071 @ SV1314 )
= $true )
| ( ( ord_less_eq_real @ SV1071 @ SV1314 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6099]) ).
thf(6401,plain,
! [SV1599: real,SV1519: real] :
( ( ( SV1519 != SV1599 )
| ( ord_less_eq_real @ SV1519 @ SV1599 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6100]) ).
thf(6402,plain,
! [SV1600: real,SV1520: real] :
( ( ~ ( ord_less_real @ SV1520 @ SV1600 )
| ( ord_less_eq_real @ SV1520 @ SV1600 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6101]) ).
thf(6403,plain,
! [SV1315: int,SV1074: int] :
( ( ( SV1074 != zero_zero_int )
= $true )
| ( ( SV1315 != zero_zero_int )
= $true )
| ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ SV1074 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV1315 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6102]) ).
thf(6404,plain,
! [SV1521: int] :
( ( ( SV1521 = zero_zero_int )
= $true )
| ( ( ! [SY2615: int] : ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ SV1521 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SY2615 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6103]) ).
thf(6405,plain,
! [SV1522: int,SV1601: int] :
( ( ( SV1601 = zero_zero_int )
| ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ SV1522 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV1601 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6104]) ).
thf(6406,plain,
! [SV1318: real,SV1079: real] :
( ( ( SV1079 = zero_zero_real )
= $false )
| ( ( SV1318 != zero_zero_real )
= $true )
| ( ( ( plus_plus_real @ ( power_power_real @ SV1079 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SV1318 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6107]) ).
thf(6407,plain,
! [SV1523: real] :
( ( ( ! [SY2617: real] :
( ( plus_plus_real @ ( power_power_real @ SV1523 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SY2617 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_real ) )
= $true )
| ( ( SV1523 = zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6108]) ).
thf(6408,plain,
! [SV1602: real,SV1524: real] :
( ( ( ( plus_plus_real @ ( power_power_real @ SV1524 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SV1602 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_real )
| ( SV1602 = zero_zero_real ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6109]) ).
thf(6409,plain,
! [SV1325: nat,SV443: nat,SV1463: int] :
( ( ( ord_less_int @ one_one_int @ SV1463 )
= $false )
| ( ( ~ ( ord_less_int @ ( power_power_int @ SV1463 @ SV443 ) @ ( power_power_int @ SV1463 @ SV1325 ) )
| ( ord_less_nat @ SV443 @ SV1325 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6114]) ).
thf(6410,plain,
! [SV1326: nat,SV443: nat,SV1464: int] :
( ( ( ord_less_int @ one_one_int @ SV1464 )
= $false )
| ( ( ~ ( ord_less_nat @ SV443 @ SV1326 )
| ( ord_less_int @ ( power_power_int @ SV1464 @ SV443 ) @ ( power_power_int @ SV1464 @ SV1326 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6115]) ).
thf(6411,plain,
! [SV1525: int,SV1329: int,SV444: int] :
( ( ( dvd_dvd_int @ SV444 @ ( plus_plus_int @ SV1329 @ ( times_times_int @ SV444 @ SV1525 ) ) )
= $false )
| ( ( dvd_dvd_int @ SV444 @ SV1329 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6118]) ).
thf(6412,plain,
! [SV1603: int,SV1330: int,SV444: int] :
( ( ( dvd_dvd_int @ SV444 @ ( plus_plus_int @ SV1330 @ ( times_times_int @ SV444 @ SV1603 ) ) )
= $true )
| ( ( dvd_dvd_int @ SV444 @ SV1330 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6119]) ).
thf(6413,plain,
! [SV1335: int,SV1102: int] :
( ( ( SV1102 = zero_zero_int )
= $false )
| ( ( ( number_number_of_nat @ SV1335 )
= zero_zero_nat )
= $true )
| ( ( ( power_power_int @ SV1102 @ ( number_number_of_nat @ SV1335 ) )
= zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6124]) ).
thf(6414,plain,
! [SV1604: int,SV1526: int] :
( ( ( ( power_power_int @ SV1526 @ ( number_number_of_nat @ SV1604 ) )
!= zero_zero_int )
| ( ( number_number_of_nat @ SV1604 )
!= zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6125]) ).
thf(6415,plain,
! [SV1527: int] :
( ( ( ! [SY2620: int] :
( ( power_power_int @ SV1527 @ ( number_number_of_nat @ SY2620 ) )
!= zero_zero_int ) )
= $true )
| ( ( SV1527 = zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6126]) ).
thf(6416,plain,
! [SV1103: int,SV1336: int] :
( ( ( ord_less_real @ ( number267125858f_real @ SV1336 ) @ ( number267125858f_real @ SV1103 ) )
= $false )
| ( ( ord_less_eq_real @ ( number267125858f_real @ SV1103 ) @ ( number267125858f_real @ SV1336 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6127]) ).
thf(6417,plain,
! [SV1344: real,SV1113: real] :
( ( ( SV1113 = zero_zero_real )
= $false )
| ( ( SV1344 != zero_zero_real )
= $true )
| ( ( ( plus_plus_real @ ( power_power_real @ SV1113 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SV1344 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6133]) ).
thf(6418,plain,
! [SV1528: real] :
( ( ( ! [SY2621: real] :
( ( plus_plus_real @ ( power_power_real @ SV1528 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SY2621 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_real ) )
= $true )
| ( ( SV1528 = zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6134]) ).
thf(6419,plain,
! [SV1605: real,SV1529: real] :
( ( ( ( plus_plus_real @ ( power_power_real @ SV1529 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SV1605 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_real )
| ( SV1605 = zero_zero_real ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6135]) ).
thf(6420,plain,
! [SV1345: int,SV1114: int] :
( ( ( SV1114 = zero_zero_int )
= $false )
| ( ( SV1345 != zero_zero_int )
= $true )
| ( ( ( plus_plus_int @ ( power_power_int @ SV1114 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV1345 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6136]) ).
thf(6421,plain,
! [SV1530: int] :
( ( ( ! [SY2623: int] :
( ( plus_plus_int @ ( power_power_int @ SV1530 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SY2623 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_int ) )
= $true )
| ( ( SV1530 = zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6137]) ).
thf(6422,plain,
! [SV1606: int,SV1531: int] :
( ( ( ( plus_plus_int @ ( power_power_int @ SV1531 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV1606 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_int )
| ( SV1606 = zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6138]) ).
thf(6423,plain,
! [SV1350: real,SV445: real,SV1465: real] :
( ( ( ord_less_real @ zero_zero_real @ SV1465 )
= $false )
| ( ( ~ ( ord_less_eq_real @ ( times_times_real @ SV445 @ SV1465 ) @ ( times_times_real @ SV1350 @ SV1465 ) )
| ( ord_less_eq_real @ SV445 @ SV1350 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6143]) ).
thf(6424,plain,
! [SV1351: real,SV445: real,SV1466: real] :
( ( ( ord_less_real @ zero_zero_real @ SV1466 )
= $false )
| ( ( ~ ( ord_less_eq_real @ SV445 @ SV1351 )
| ( ord_less_eq_real @ ( times_times_real @ SV445 @ SV1466 ) @ ( times_times_real @ SV1351 @ SV1466 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6144]) ).
thf(6425,plain,
! [SV1352: real,SV1125: real] :
( ( ( SV1125 = zero_zero_real )
= $false )
| ( ( SV1352 != zero_zero_real )
= $true )
| ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ SV1125 @ SV1125 ) @ ( times_times_real @ SV1352 @ SV1352 ) ) @ zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6145]) ).
thf(6426,plain,
! [SV1532: real] :
( ( ( ! [SY2625: real] :
~ ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ SV1532 @ SV1532 ) @ ( times_times_real @ SY2625 @ SY2625 ) ) @ zero_zero_real ) )
= $true )
| ( ( SV1532 = zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6146]) ).
thf(6427,plain,
! [SV1607: real,SV1533: real] :
( ( ~ ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ SV1533 @ SV1533 ) @ ( times_times_real @ SV1607 @ SV1607 ) ) @ zero_zero_real )
| ( SV1607 = zero_zero_real ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6147]) ).
thf(6428,plain,
! [SV1355: int,SV1130: int] :
( ( ( SV1130 = zero_zero_int )
= $false )
| ( ( SV1355 != zero_zero_int )
= $true )
| ( ( ord_less_eq_int @ ( plus_plus_int @ ( power_power_int @ SV1130 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV1355 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6150]) ).
thf(6429,plain,
! [SV1534: int] :
( ( ( ! [SY2627: int] :
~ ( ord_less_eq_int @ ( plus_plus_int @ ( power_power_int @ SV1534 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SY2627 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_int ) )
= $true )
| ( ( SV1534 = zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6151]) ).
thf(6430,plain,
! [SV1608: int,SV1535: int] :
( ( ~ ( ord_less_eq_int @ ( plus_plus_int @ ( power_power_int @ SV1535 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV1608 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_int )
| ( SV1608 = zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6152]) ).
thf(6431,plain,
! [SV1356: int,SV1133: int] :
( ( ( SV1133 = zero_zero_int )
= $false )
| ( ( SV1356 != zero_zero_int )
= $true )
| ( ( ( plus_plus_int @ ( times_times_int @ SV1133 @ SV1133 ) @ ( times_times_int @ SV1356 @ SV1356 ) )
= zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6153]) ).
thf(6432,plain,
! [SV1536: int] :
( ( ( ! [SY2629: int] :
( ( plus_plus_int @ ( times_times_int @ SV1536 @ SV1536 ) @ ( times_times_int @ SY2629 @ SY2629 ) )
!= zero_zero_int ) )
= $true )
| ( ( SV1536 = zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6154]) ).
thf(6433,plain,
! [SV1609: int,SV1537: int] :
( ( ( ( plus_plus_int @ ( times_times_int @ SV1537 @ SV1537 ) @ ( times_times_int @ SV1609 @ SV1609 ) )
!= zero_zero_int )
| ( SV1609 = zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6155]) ).
thf(6434,plain,
! [SV1357: int,SV1134: int] :
( ( ( ord_less_eq_int @ SV1134 @ SV1357 )
= $false )
| ( ( SV1134 = SV1357 )
= $true )
| ( ( ord_less_int @ SV1134 @ SV1357 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6156]) ).
thf(6435,plain,
! [SV1610: int,SV1538: int] :
( ( ~ ( ord_less_int @ SV1538 @ SV1610 )
| ( SV1538 != SV1610 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6157]) ).
thf(6436,plain,
! [SV1611: int,SV1539: int] :
( ( ~ ( ord_less_int @ SV1539 @ SV1611 )
| ( ord_less_eq_int @ SV1539 @ SV1611 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6158]) ).
thf(6437,plain,
! [SV1358: nat,SV446: nat,SV1467: nat] :
( ( ( ord_less_nat @ one_one_nat @ SV1467 )
= $false )
| ( ( ~ ( ord_less_nat @ ( power_power_nat @ SV1467 @ SV446 ) @ ( power_power_nat @ SV1467 @ SV1358 ) )
| ( ord_less_nat @ SV446 @ SV1358 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6159]) ).
thf(6438,plain,
! [SV1359: nat,SV446: nat,SV1468: nat] :
( ( ( ord_less_nat @ one_one_nat @ SV1468 )
= $false )
| ( ( ~ ( ord_less_nat @ SV446 @ SV1359 )
| ( ord_less_nat @ ( power_power_nat @ SV1468 @ SV446 ) @ ( power_power_nat @ SV1468 @ SV1359 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6160]) ).
thf(6439,plain,
! [SV1360: nat,SV1137: nat] :
( ( ( SV1137 = one_one_nat )
= $false )
| ( ( SV1360 != one_one_nat )
= $true )
| ( ( ( times_times_nat @ SV1137 @ SV1360 )
= one_one_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6161]) ).
thf(6440,plain,
! [SV1540: nat] :
( ( ( ! [SY2633: nat] :
( ( times_times_nat @ SV1540 @ SY2633 )
!= one_one_nat ) )
= $true )
| ( ( SV1540 = one_one_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6162]) ).
thf(6441,plain,
! [SV1612: nat,SV1541: nat] :
( ( ( ( times_times_nat @ SV1541 @ SV1612 )
!= one_one_nat )
| ( SV1612 = one_one_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6163]) ).
thf(6442,plain,
( ( ~ ! [SX0: int] :
( ! [SX1: int] :
( ( times_times_int @ SX0 @ SX1 )
!= one_one_int )
| ( SX0 = one_one_int )
| ( SX0
= ( number_number_of_int @ min ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6164]) ).
thf(6443,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ( ( times_times_int @ SX0 @ SX1 )
!= one_one_int )
| ( SX0 = one_one_int )
| ( SX1
= ( number_number_of_int @ min ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6164]) ).
thf(6444,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ( ( times_times_int @ SX0 @ SX1 )
!= one_one_int )
| ( SX1 = one_one_int )
| ( SX0
= ( number_number_of_int @ min ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6165]) ).
thf(6445,plain,
( ( ~ ! [SX0: int,SX1: int] :
( ( ( times_times_int @ SX0 @ SX1 )
!= one_one_int )
| ( SX1 = one_one_int )
| ( SX1
= ( number_number_of_int @ min ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6165]) ).
thf(6446,plain,
! [SV1613: int,SV1542: int] :
( ( ( SV1542 != one_one_int )
| ( SV1613 != one_one_int )
| ( ( times_times_int @ SV1542 @ SV1613 )
= one_one_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6166]) ).
thf(6447,plain,
! [SV1614: int,SV1543: int] :
( ( ( SV1543
!= ( number_number_of_int @ min ) )
| ( SV1614
!= ( number_number_of_int @ min ) )
| ( ( times_times_int @ SV1543 @ SV1614 )
= one_one_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6167]) ).
thf(6448,plain,
! [SV1365: real,SV1144: real] :
( ( ( SV1144 = zero_zero_real )
= $false )
| ( ( SV1365 != zero_zero_real )
= $true )
| ( ( ( plus_plus_real @ ( times_times_real @ SV1144 @ SV1144 ) @ ( times_times_real @ SV1365 @ SV1365 ) )
= zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6172]) ).
thf(6449,plain,
! [SV1544: real] :
( ( ( ! [SY2637: real] :
( ( plus_plus_real @ ( times_times_real @ SV1544 @ SV1544 ) @ ( times_times_real @ SY2637 @ SY2637 ) )
!= zero_zero_real ) )
= $true )
| ( ( SV1544 = zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6173]) ).
thf(6450,plain,
! [SV1615: real,SV1545: real] :
( ( ( ( plus_plus_real @ ( times_times_real @ SV1545 @ SV1545 ) @ ( times_times_real @ SV1615 @ SV1615 ) )
!= zero_zero_real )
| ( SV1615 = zero_zero_real ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6174]) ).
thf(6451,plain,
! [SV1366: nat,SV447: nat,SV1469: real] :
( ( ( ord_less_real @ one_one_real @ SV1469 )
= $false )
| ( ( ~ ( ord_less_nat @ SV447 @ SV1366 )
| ( ord_less_real @ ( power_power_real @ SV1469 @ SV447 ) @ ( power_power_real @ SV1469 @ SV1366 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6175]) ).
thf(6452,plain,
! [SV1367: nat,SV447: nat,SV1470: real] :
( ( ( ord_less_real @ one_one_real @ SV1470 )
= $false )
| ( ( ~ ( ord_less_real @ ( power_power_real @ SV1470 @ SV447 ) @ ( power_power_real @ SV1470 @ SV1367 ) )
| ( ord_less_nat @ SV447 @ SV1367 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6176]) ).
thf(6453,plain,
! [SV1368: int,SV1149: int] :
( ( ( SV1149 != zero_zero_int )
= $true )
| ( ( SV1368 != zero_zero_int )
= $true )
| ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ SV1149 @ SV1149 ) @ ( times_times_int @ SV1368 @ SV1368 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6177]) ).
thf(6454,plain,
! [SV1546: int] :
( ( ( SV1546 = zero_zero_int )
= $true )
| ( ( ! [SY2639: int] : ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ SV1546 @ SV1546 ) @ ( times_times_int @ SY2639 @ SY2639 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6178]) ).
thf(6455,plain,
! [SV1547: int,SV1616: int] :
( ( ( SV1616 = zero_zero_int )
| ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ SV1547 @ SV1547 ) @ ( times_times_int @ SV1616 @ SV1616 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6179]) ).
thf(6456,plain,
! [SV1371: real,SV448: real,SV1471: real] :
( ( ( ( times_times_real @ SV1471 @ SV448 )
!= ( times_times_real @ SV1471 @ SV1371 ) )
= $true )
| ( ( SV448 = SV1371 )
= $true )
| ( ( SV1471 = zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6183]) ).
thf(6457,plain,
! [SV1472: real,SV1372: real,SV448: real] :
( ( ( SV448 != SV1372 )
= $true )
| ( ( ( times_times_real @ SV1472 @ SV448 )
= ( times_times_real @ SV1472 @ SV1372 ) )
= $true )
| ( ( SV1472 = zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6184]) ).
thf(6458,plain,
! [SV1617: int,SV1548: int] :
( ( ( ord_less_int @ SV1548 @ SV1617 )
| ~ ( ord_less_int @ SV1548 @ SV1617 )
| ( ord_less_nat @ ( number_number_of_nat @ SV1548 ) @ ( number_number_of_nat @ SV1617 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6187]) ).
thf(6459,plain,
! [SV1549: int,SV1618: int] :
( ( ~ ( ord_less_int @ pls @ SV1618 )
| ~ ( ord_less_int @ SV1549 @ SV1618 )
| ( ord_less_nat @ ( number_number_of_nat @ SV1549 ) @ ( number_number_of_nat @ SV1618 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6188]) ).
thf(6460,plain,
! [SV1619: int,SV1550: int] :
( ( ~ ( ord_less_nat @ ( number_number_of_nat @ SV1550 ) @ ( number_number_of_nat @ SV1619 ) )
| ~ ( ord_less_int @ SV1550 @ SV1619 )
| ( ord_less_int @ pls @ SV1619 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6189]) ).
thf(6461,plain,
! [SV1620: int,SV1551: int] :
( ( ~ ( ord_less_nat @ ( number_number_of_nat @ SV1551 ) @ ( number_number_of_nat @ SV1620 ) )
| ( ord_less_int @ SV1551 @ SV1620 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6190]) ).
thf(6462,plain,
! [SV787: int,SV449: int,SV1621: int,SV1552: int,SV981: int] :
( ( ~ ( zcong @ SV981 @ SV1552 @ SV1621 )
| ~ ( zcong @ SV449 @ ( times_times_int @ SV981 @ SV787 ) @ SV1621 )
| ( zcong @ SV449 @ ( times_times_int @ SV1552 @ SV787 ) @ SV1621 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6193]) ).
thf(6463,plain,
! [SV787: int,SV449: int,SV1622: int,SV1553: int,SV981: int] :
( ( ~ ( zcong @ SV981 @ SV1553 @ SV1622 )
| ~ ( zcong @ SV449 @ ( times_times_int @ SV1553 @ SV787 ) @ SV1622 )
| ( zcong @ SV449 @ ( times_times_int @ SV981 @ SV787 ) @ SV1622 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6194]) ).
thf(6464,plain,
! [SV788: int,SV450: int] :
( ( ! [SY2290: int,SY2291: int] :
( ( ( plus_plus_int @ ( times_times_int @ SY2290 @ SV450 ) @ ( times_times_int @ SY2291 @ SV788 ) )
= ( plus_plus_int @ ( times_times_int @ SY2290 @ SV788 ) @ ( times_times_int @ SY2291 @ SV450 ) ) )
| ( SY2290 != SY2291 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6196]) ).
thf(6465,plain,
! [SV788: int,SV450: int] :
( ( ! [SY2292: int,SY2293: int] :
( ( plus_plus_int @ ( times_times_int @ SY2292 @ SV450 ) @ ( times_times_int @ SY2293 @ SV788 ) )
= ( plus_plus_int @ ( times_times_int @ SY2292 @ SV788 ) @ ( times_times_int @ SY2293 @ SV450 ) ) )
| ( SV450 != SV788 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6197]) ).
thf(6466,plain,
! [SV788: int,SV450: int,SV1554: int,SV1473: int] :
( ( ( ( SV1473 = SV1554 )
| ( SV450 = SV788 ) )
= $true )
| ( ( ( plus_plus_int @ ( times_times_int @ SV1473 @ SV450 ) @ ( times_times_int @ SV1554 @ SV788 ) )
!= ( plus_plus_int @ ( times_times_int @ SV1473 @ SV788 ) @ ( times_times_int @ SV1554 @ SV450 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6198]) ).
thf(6467,plain,
! [SV1381: real,SV1170: real] :
( ( ( SV1170 = zero_zero_real )
= $false )
| ( ( SV1381 != zero_zero_real )
= $true )
| ( ( ( plus_plus_real @ ( times_times_real @ SV1170 @ SV1170 ) @ ( times_times_real @ SV1381 @ SV1381 ) )
= zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6202]) ).
thf(6468,plain,
! [SV1555: real] :
( ( ( ! [SY2647: real] :
( ( plus_plus_real @ ( times_times_real @ SV1555 @ SV1555 ) @ ( times_times_real @ SY2647 @ SY2647 ) )
!= zero_zero_real ) )
= $true )
| ( ( SV1555 = zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6203]) ).
thf(6469,plain,
! [SV1623: real,SV1556: real] :
( ( ( ( plus_plus_real @ ( times_times_real @ SV1556 @ SV1556 ) @ ( times_times_real @ SV1623 @ SV1623 ) )
!= zero_zero_real )
| ( SV1623 = zero_zero_real ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6204]) ).
thf(6470,plain,
! [SV789: int,SV451: int,SV1624: int,SV1557: int,SV982: int] :
( ( ~ ( zcong @ SV982 @ SV1557 @ SV1624 )
| ~ ( zcong @ SV451 @ ( times_times_int @ SV789 @ SV982 ) @ SV1624 )
| ( zcong @ SV451 @ ( times_times_int @ SV789 @ SV1557 ) @ SV1624 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6205]) ).
thf(6471,plain,
! [SV789: int,SV451: int,SV1625: int,SV1558: int,SV982: int] :
( ( ~ ( zcong @ SV982 @ SV1558 @ SV1625 )
| ~ ( zcong @ SV451 @ ( times_times_int @ SV789 @ SV1558 ) @ SV1625 )
| ( zcong @ SV451 @ ( times_times_int @ SV789 @ SV982 ) @ SV1625 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6206]) ).
thf(6472,plain,
! [SV1559: nat,SV1474: nat,SV790: nat,SV452: nat] :
( ( ( ( plus_plus_nat @ ( times_times_nat @ SV452 @ SV790 ) @ ( times_times_nat @ SV1474 @ SV1559 ) )
!= ( plus_plus_nat @ ( times_times_nat @ SV452 @ SV1559 ) @ ( times_times_nat @ SV1474 @ SV790 ) ) )
= $true )
| ( ( ( SV452 = SV1474 )
| ( SV790 = SV1559 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6213]) ).
thf(6473,plain,
! [SV790: nat,SV452: nat] :
( ( ! [SY2303: nat] :
( ( SV452 != SY2303 )
| ! [SY2304: nat] :
( ( plus_plus_nat @ ( times_times_nat @ SV452 @ SV790 ) @ ( times_times_nat @ SY2303 @ SY2304 ) )
= ( plus_plus_nat @ ( times_times_nat @ SV452 @ SY2304 ) @ ( times_times_nat @ SY2303 @ SV790 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6214]) ).
thf(6474,plain,
! [SV452: nat,SV790: nat] :
( ( ! [SY2305: nat,SY2306: nat] :
( ( SV790 != SY2306 )
| ( ( plus_plus_nat @ ( times_times_nat @ SV452 @ SV790 ) @ ( times_times_nat @ SY2305 @ SY2306 ) )
= ( plus_plus_nat @ ( times_times_nat @ SV452 @ SY2306 ) @ ( times_times_nat @ SY2305 @ SV790 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6215]) ).
thf(6475,plain,
! [SV1388: nat,SV1181: real] :
( ( ( SV1181 = zero_zero_real )
= $false )
| ( ( SV1388 = zero_zero_nat )
= $true )
| ( ( ( power_power_real @ SV1181 @ SV1388 )
= zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6216]) ).
thf(6476,plain,
! [SV1626: nat,SV1560: real] :
( ( ( ( power_power_real @ SV1560 @ SV1626 )
!= zero_zero_real )
| ( SV1626 != zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6217]) ).
thf(6477,plain,
! [SV1561: real] :
( ( ( ! [SY2652: nat] :
( ( power_power_real @ SV1561 @ SY2652 )
!= zero_zero_real ) )
= $true )
| ( ( SV1561 = zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6218]) ).
thf(6478,plain,
! [SV1182: nat,SV1389: nat] :
( ( ( SV1389 = zero_zero_nat )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV1182 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV1182 @ SV1389 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6219]) ).
thf(6479,plain,
! [SV1562: nat,SV1627: nat] :
( ( ( SV1627 != zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV1562 @ SV1627 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6220]) ).
thf(6480,plain,
! [SV1563: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV1563 ) )
= $true )
| ( ( ! [SY2654: nat] : ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV1563 @ SY2654 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6221]) ).
thf(6481,plain,
! [SV1564: int,SV1475: int,SV791: int,SV453: int] :
( ( ( ( plus_plus_int @ ( times_times_int @ SV453 @ SV791 ) @ ( times_times_int @ SV1475 @ SV1564 ) )
!= ( plus_plus_int @ ( times_times_int @ SV453 @ SV1564 ) @ ( times_times_int @ SV1475 @ SV791 ) ) )
= $true )
| ( ( ( SV453 = SV1475 )
| ( SV791 = SV1564 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6222]) ).
thf(6482,plain,
! [SV791: int,SV453: int] :
( ( ! [SY2309: int] :
( ( SV453 != SY2309 )
| ! [SY2310: int] :
( ( plus_plus_int @ ( times_times_int @ SV453 @ SV791 ) @ ( times_times_int @ SY2309 @ SY2310 ) )
= ( plus_plus_int @ ( times_times_int @ SV453 @ SY2310 ) @ ( times_times_int @ SY2309 @ SV791 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6223]) ).
thf(6483,plain,
! [SV453: int,SV791: int] :
( ( ! [SY2311: int,SY2312: int] :
( ( SV791 != SY2312 )
| ( ( plus_plus_int @ ( times_times_int @ SV453 @ SV791 ) @ ( times_times_int @ SY2311 @ SY2312 ) )
= ( plus_plus_int @ ( times_times_int @ SV453 @ SY2312 ) @ ( times_times_int @ SY2311 @ SV791 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6224]) ).
thf(6484,plain,
! [SV1185: int,SV1392: int] :
( ( ( ( SV1392 != one_one_int )
| ( SV1185 != one_one_int ) )
= $true )
| ( ( ( times_times_int @ SV1392 @ SV1185 )
= one_one_int )
= $true )
| ( ( ord_less_int @ zero_zero_int @ SV1392 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6226]) ).
thf(6485,plain,
! [SV1565: int,SV1628: int] :
( ( ~ ( ord_less_int @ zero_zero_int @ SV1628 )
| ( ( times_times_int @ SV1628 @ SV1565 )
!= one_one_int )
| ( SV1628 = one_one_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6227]) ).
thf(6486,plain,
! [SV1566: int,SV1629: int] :
( ( ~ ( ord_less_int @ zero_zero_int @ SV1629 )
| ( ( times_times_int @ SV1629 @ SV1566 )
!= one_one_int )
| ( SV1566 = one_one_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6228]) ).
thf(6487,plain,
! [SV1395: real,SV1190: real] :
( ( ( ord_less_eq_real @ SV1190 @ SV1395 )
= $false )
| ( ( SV1190 = SV1395 )
= $true )
| ( ( ord_less_real @ SV1190 @ SV1395 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6231]) ).
thf(6488,plain,
! [SV1630: real,SV1567: real] :
( ( ~ ( ord_less_real @ SV1567 @ SV1630 )
| ( SV1567 != SV1630 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6232]) ).
thf(6489,plain,
! [SV1631: real,SV1568: real] :
( ( ~ ( ord_less_real @ SV1568 @ SV1631 )
| ( ord_less_eq_real @ SV1568 @ SV1631 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6233]) ).
thf(6490,plain,
! [SV1193: int,SV1398: int] :
( ( ( ord_less_int @ ( number_number_of_int @ SV1398 ) @ ( number_number_of_int @ SV1193 ) )
= $false )
| ( ( ord_less_eq_int @ ( number_number_of_int @ SV1193 ) @ ( number_number_of_int @ SV1398 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6236]) ).
thf(6491,plain,
! [SV1197: nat,SV1400: int] :
( ( ( ( number_number_of_nat @ SV1400 )
= zero_zero_nat )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV1197 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV1197 @ ( number_number_of_nat @ SV1400 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6237]) ).
thf(6492,plain,
! [SV1569: nat,SV1632: int] :
( ( ( ( number_number_of_nat @ SV1632 )
!= zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV1569 @ ( number_number_of_nat @ SV1632 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6238]) ).
thf(6493,plain,
! [SV1570: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV1570 ) )
= $true )
| ( ( ! [SY2660: int] : ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV1570 @ ( number_number_of_nat @ SY2660 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6239]) ).
thf(6494,plain,
! [SV1204: int] :
( ( ( ~ ~ ( ~ ( dvd_dvd_int @ ( sK3_M_9 @ SV1204 ) @ SV1204 )
| ~ ( ord_less_eq_int @ zero_zero_int @ ( sK3_M_9 @ SV1204 ) ) ) )
= $false )
| ( ( ~ ( ord_less_int @ one_one_int @ SV1204 ) )
= $true )
| ( ( zprime @ SV1204 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[6242]) ).
thf(6495,plain,
! [SV1204: int] :
( ( ( ~ ~ ( ~ ( ( ( sK3_M_9 @ SV1204 )
!= one_one_int ) )
| ~ ( ( ( sK3_M_9 @ SV1204 )
!= SV1204 ) ) ) )
= $false )
| ( ( ~ ( ord_less_int @ one_one_int @ SV1204 ) )
= $true )
| ( ( zprime @ SV1204 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[6242]) ).
thf(6496,plain,
! [SV1571: int] :
( ( ( ~ ( zprime @ SV1571 ) )
= $true )
| ( ( ! [SY2661: int] :
( ~ ( dvd_dvd_int @ SY2661 @ SV1571 )
| ~ ( ord_less_eq_int @ zero_zero_int @ SY2661 )
| ( SY2661 = one_one_int )
| ( SY2661 = SV1571 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6243]) ).
thf(6497,plain,
! [SV1572: int] :
( ( ( ~ ( zprime @ SV1572 ) )
= $true )
| ( ( ord_less_int @ one_one_int @ SV1572 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6244]) ).
thf(6498,plain,
! [SV1403: nat,SV454: int,SV1476: int] :
( ( ( ord_less_int @ SV1476 @ pls )
= $false )
| ( ( ( times_times_nat @ ( number_number_of_nat @ SV1476 ) @ ( times_times_nat @ ( number_number_of_nat @ SV454 ) @ SV1403 ) )
= zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6245]) ).
thf(6499,plain,
! [SV1633: int,SV1573: int] :
( ( ( zcong @ SV1573 @ zero_zero_int @ SV1633 )
| ~ ( quadRes @ SV1633 @ SV1573 )
| ( ( legendre @ SV1573 @ SV1633 )
= one_one_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6248]) ).
thf(6500,plain,
! [SV1634: int,SV1574: int] :
( ( ( zcong @ SV1574 @ zero_zero_int @ SV1634 )
| ( quadRes @ SV1634 @ SV1574 )
| ( ( legendre @ SV1574 @ SV1634 )
= ( number_number_of_int @ min ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6249]) ).
thf(6501,plain,
! [SV455: real,SV792: nat] :
( ( ( ~ ! [SY2313: real] :
( ( ( power_power_real @ SY2313 @ SV792 )
!= SV455 )
| ~ ( ord_less_real @ zero_zero_real @ SY2313 )
| ( SY2313
= ( sK1_X_1 @ SV792 @ SV455 ) ) ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV455 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV792 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6250]) ).
thf(6502,plain,
! [SV455: real,SV792: nat] :
( ( ( ~ ~ ( ( ( power_power_real @ ( sK1_X_1 @ SV792 @ SV455 ) @ SV792 )
!= SV455 )
| ~ ( ord_less_real @ zero_zero_real @ ( sK1_X_1 @ SV792 @ SV455 ) ) ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV455 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV792 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6250]) ).
thf(6503,plain,
! [SV1635: int,SV1575: int] :
( ( ~ ( ord_less_eq_int @ SV1575 @ SV1635 )
| ( ord_less_eq_nat @ ( number_number_of_nat @ SV1575 ) @ ( number_number_of_nat @ SV1635 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6251]) ).
thf(6504,plain,
! [SV1576: int] :
( ( ( ~ ( ord_less_eq_int @ SV1576 @ pls ) )
= $true )
| ( ( ! [SY2665: int] : ( ord_less_eq_nat @ ( number_number_of_nat @ SV1576 ) @ ( number_number_of_nat @ SY2665 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6252]) ).
thf(6505,plain,
! [SV1406: int,SV1210: int] :
( ( ( ord_less_eq_int @ SV1210 @ SV1406 )
= $true )
| ( ( ord_less_eq_int @ SV1210 @ pls )
= $true )
| ( ( ord_less_eq_nat @ ( number_number_of_nat @ SV1210 ) @ ( number_number_of_nat @ SV1406 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6253]) ).
thf(6506,plain,
! [SV1478: int,SV1409: int,SV456: int] :
( ( ( zcong @ SV456 @ SV1409 @ SV1478 )
= $false )
| ( ( zcong @ SV1409 @ SV456 @ SV1478 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6256]) ).
thf(6507,plain,
! [SV1479: int,SV456: int,SV1410: int] :
( ( ( zcong @ SV1410 @ SV456 @ SV1479 )
= $false )
| ( ( zcong @ SV456 @ SV1410 @ SV1479 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6257]) ).
thf(6508,plain,
! [SV457: int,SV983: int,SV793: int,SV1636: int,SV1577: int] :
( ( ~ ( dvd_dvd_int @ SV1577 @ SV1636 )
| ~ ( dvd_dvd_int @ SV1577 @ ( plus_plus_int @ SV793 @ SV983 ) )
| ( dvd_dvd_int @ SV1577 @ ( plus_plus_int @ ( plus_plus_int @ SV793 @ ( times_times_int @ SV457 @ SV1636 ) ) @ SV983 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6258]) ).
thf(6509,plain,
! [SV983: int,SV457: int,SV793: int,SV1637: int,SV1578: int] :
( ( ~ ( dvd_dvd_int @ SV1578 @ SV1637 )
| ~ ( dvd_dvd_int @ SV1578 @ ( plus_plus_int @ ( plus_plus_int @ SV793 @ ( times_times_int @ SV457 @ SV1637 ) ) @ SV983 ) )
| ( dvd_dvd_int @ SV1578 @ ( plus_plus_int @ SV793 @ SV983 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6259]) ).
thf(6510,plain,
! [SV1638: int,SV1480: int,SV458: int,SV1413: int] :
( ( ( SV1413
!= ( plus_plus_int @ SV458 @ ( times_times_int @ SV1480 @ SV1638 ) ) )
= $true )
| ( ( zcong @ SV458 @ SV1413 @ SV1480 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6262]) ).
thf(6511,plain,
! [SV1481: int,SV1414: int,SV458: int] :
( ( ( zcong @ SV458 @ SV1414 @ SV1481 )
= $false )
| ( ( SV1414
= ( plus_plus_int @ SV458 @ ( times_times_int @ SV1481 @ ( sK6_K_1 @ SV1481 @ SV1414 @ SV458 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6263]) ).
thf(6512,plain,
! [SV1415: nat,SV459: nat,SV1482: nat] :
( ( ( ord_less_nat @ one_one_nat @ SV1482 )
= $false )
| ( ( ( ( power_power_nat @ SV1482 @ SV459 )
!= ( power_power_nat @ SV1482 @ SV1415 ) )
| ( SV459 = SV1415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6264]) ).
thf(6513,plain,
! [SV1416: nat,SV459: nat,SV1483: nat] :
( ( ( ord_less_nat @ one_one_nat @ SV1483 )
= $false )
| ( ( ( SV459 != SV1416 )
| ( ( power_power_nat @ SV1483 @ SV459 )
= ( power_power_nat @ SV1483 @ SV1416 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6265]) ).
thf(6514,plain,
! [SV1579: real,SV1484: real,SV794: real,SV460: real] :
( ( ( ( plus_plus_real @ ( times_times_real @ SV460 @ SV794 ) @ ( times_times_real @ SV1484 @ SV1579 ) )
!= ( plus_plus_real @ ( times_times_real @ SV460 @ SV1579 ) @ ( times_times_real @ SV1484 @ SV794 ) ) )
= $true )
| ( ( ( SV460 = SV1484 )
| ( SV794 = SV1579 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6266]) ).
thf(6515,plain,
! [SV794: real,SV460: real] :
( ( ! [SY2321: real] :
( ( SV460 != SY2321 )
| ! [SY2322: real] :
( ( plus_plus_real @ ( times_times_real @ SV460 @ SV794 ) @ ( times_times_real @ SY2321 @ SY2322 ) )
= ( plus_plus_real @ ( times_times_real @ SV460 @ SY2322 ) @ ( times_times_real @ SY2321 @ SV794 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6267]) ).
thf(6516,plain,
! [SV460: real,SV794: real] :
( ( ! [SY2323: real,SY2324: real] :
( ( SV794 != SY2324 )
| ( ( plus_plus_real @ ( times_times_real @ SV460 @ SV794 ) @ ( times_times_real @ SY2323 @ SY2324 ) )
= ( plus_plus_real @ ( times_times_real @ SV460 @ SY2324 ) @ ( times_times_real @ SY2323 @ SV794 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6268]) ).
thf(6517,plain,
! [SV1485: nat,SV1417: nat,SV461: nat] :
( ( ( dvd_dvd_nat @ ( times_times_nat @ SV461 @ SV1417 ) @ ( times_times_nat @ SV1485 @ SV1417 ) )
= $false )
| ( ( ( SV1417 = zero_zero_nat )
| ( dvd_dvd_nat @ SV461 @ SV1485 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6269]) ).
thf(6518,plain,
! [SV461: nat,SV1639: nat] :
( ( ( SV1639 != zero_zero_nat )
| ! [SY2676: nat] : ( dvd_dvd_nat @ ( times_times_nat @ SV461 @ SV1639 ) @ ( times_times_nat @ SY2676 @ SV1639 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6270]) ).
thf(6519,plain,
! [SV1640: nat,SV461: nat] :
( ( ! [SY2677: nat] :
( ~ ( dvd_dvd_nat @ SV461 @ SY2677 )
| ( dvd_dvd_nat @ ( times_times_nat @ SV461 @ SV1640 ) @ ( times_times_nat @ SY2677 @ SV1640 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6271]) ).
thf(6520,plain,
! [SV1428: nat,SV1243: nat] :
( ( ( SV1243 = zero_zero_nat )
= $false )
| ( ( SV1428 = zero_zero_nat )
= $true )
| ( ( ( power_power_nat @ SV1243 @ SV1428 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6282]) ).
thf(6521,plain,
! [SV1641: nat,SV1580: nat] :
( ( ( ( power_power_nat @ SV1580 @ SV1641 )
!= zero_zero_nat )
| ( SV1641 != zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6283]) ).
thf(6522,plain,
! [SV1581: nat] :
( ( ( ! [SY2669: nat] :
( ( power_power_nat @ SV1581 @ SY2669 )
!= zero_zero_nat ) )
= $true )
| ( ( SV1581 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6284]) ).
thf(6523,plain,
! [SV1248: int,SV1433: int,SV1582: int] :
( ( ( zcong @ ( power_power_int @ SV1582 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ SV1433 @ SV1248 )
= $false )
| ( ( quadRes @ SV1248 @ SV1433 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6289]) ).
thf(6524,plain,
! [SV1435: nat,SV462: nat,SV1486: real] :
( ( ( ord_less_real @ one_one_real @ SV1486 )
= $false )
| ( ( ( ( power_power_real @ SV1486 @ SV462 )
!= ( power_power_real @ SV1486 @ SV1435 ) )
| ( SV462 = SV1435 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6291]) ).
thf(6525,plain,
! [SV1436: nat,SV462: nat,SV1487: real] :
( ( ( ord_less_real @ one_one_real @ SV1487 )
= $false )
| ( ( ( SV462 != SV1436 )
| ( ( power_power_real @ SV1487 @ SV462 )
= ( power_power_real @ SV1487 @ SV1436 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6292]) ).
thf(6526,plain,
! [SV1583: int,SV1642: int] :
( ( ( ord_less_int @ SV1642 @ pls )
| ~ ( ord_less_int @ SV1583 @ pls )
| ( ( plus_plus_nat @ ( number_number_of_nat @ SV1642 ) @ ( number_number_of_nat @ SV1583 ) )
= ( number_number_of_nat @ SV1642 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6294]) ).
thf(6527,plain,
! [SV1584: int,SV1643: int] :
( ( ( ord_less_int @ SV1643 @ pls )
| ( ord_less_int @ SV1584 @ pls )
| ( ( plus_plus_nat @ ( number_number_of_nat @ SV1643 ) @ ( number_number_of_nat @ SV1584 ) )
= ( number_number_of_nat @ ( plus_plus_int @ SV1643 @ SV1584 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6295]) ).
thf(6528,plain,
! [SV1438: real,SV1488: real,SV463: real] :
( ( ( ( times_times_real @ SV463 @ SV1488 )
!= ( times_times_real @ SV1438 @ SV1488 ) )
= $true )
| ( ( SV463 = SV1438 )
= $true )
| ( ( SV1488 = zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6296]) ).
thf(6529,plain,
! [SV1489: real,SV1439: real,SV463: real] :
( ( ( SV463 != SV1439 )
= $true )
| ( ( ( times_times_real @ SV463 @ SV1489 )
= ( times_times_real @ SV1439 @ SV1489 ) )
= $true )
| ( ( SV1489 = zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6297]) ).
thf(6530,plain,
! [SV1440: real,SV464: real,SV1490: real] :
( ( ( ord_less_real @ zero_zero_real @ SV1490 )
= $false )
| ( ( ~ ( ord_less_real @ ( times_times_real @ SV464 @ SV1490 ) @ ( times_times_real @ SV1440 @ SV1490 ) )
| ( ord_less_real @ SV464 @ SV1440 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6298]) ).
thf(6531,plain,
! [SV1441: real,SV464: real,SV1491: real] :
( ( ( ord_less_real @ zero_zero_real @ SV1491 )
= $false )
| ( ( ~ ( ord_less_real @ SV464 @ SV1441 )
| ( ord_less_real @ ( times_times_real @ SV464 @ SV1491 ) @ ( times_times_real @ SV1441 @ SV1491 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6299]) ).
thf(6532,plain,
! [SV1442: real,SV465: real,SV1492: real] :
( ( ( ord_less_real @ zero_zero_real @ SV1492 )
= $false )
| ( ( ~ ( ord_less_eq_real @ ( times_times_real @ SV1492 @ SV465 ) @ ( times_times_real @ SV1492 @ SV1442 ) )
| ( ord_less_eq_real @ SV465 @ SV1442 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6300]) ).
thf(6533,plain,
! [SV1443: real,SV465: real,SV1493: real] :
( ( ( ord_less_real @ zero_zero_real @ SV1493 )
= $false )
| ( ( ~ ( ord_less_eq_real @ SV465 @ SV1443 )
| ( ord_less_eq_real @ ( times_times_real @ SV1493 @ SV465 ) @ ( times_times_real @ SV1493 @ SV1443 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6301]) ).
thf(6534,plain,
! [SV1446: int,SV1257: int] :
( ( ( SV1257 = zero_zero_int )
= $false )
| ( ( SV1446 != zero_zero_int )
= $true )
| ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SV1257 @ SV1257 ) @ ( times_times_int @ SV1446 @ SV1446 ) ) @ zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6304]) ).
thf(6535,plain,
! [SV1585: int] :
( ( ( ! [SY2672: int] :
~ ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SV1585 @ SV1585 ) @ ( times_times_int @ SY2672 @ SY2672 ) ) @ zero_zero_int ) )
= $true )
| ( ( SV1585 = zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6305]) ).
thf(6536,plain,
! [SV1644: int,SV1586: int] :
( ( ~ ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SV1586 @ SV1586 ) @ ( times_times_int @ SV1644 @ SV1644 ) ) @ zero_zero_int )
| ( SV1644 = zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6306]) ).
thf(6537,plain,
! [SV1447: nat,SV1262: int] :
( ( ( SV1262 = zero_zero_int )
= $false )
| ( ( SV1447 = zero_zero_nat )
= $true )
| ( ( ( power_power_int @ SV1262 @ SV1447 )
= zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6307]) ).
thf(6538,plain,
! [SV1645: nat,SV1587: int] :
( ( ( ( power_power_int @ SV1587 @ SV1645 )
!= zero_zero_int )
| ( SV1645 != zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6308]) ).
thf(6539,plain,
! [SV1588: int] :
( ( ( ! [SY2675: nat] :
( ( power_power_int @ SV1588 @ SY2675 )
!= zero_zero_int ) )
= $true )
| ( ( SV1588 = zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6309]) ).
thf(6540,plain,
! [SV1267: int,SV1450: int] :
( ( ( ord_less_nat @ ( number_number_of_nat @ SV1450 ) @ ( number_number_of_nat @ SV1267 ) )
= $false )
| ( ( ord_less_eq_nat @ ( number_number_of_nat @ SV1267 ) @ ( number_number_of_nat @ SV1450 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6312]) ).
thf(6541,plain,
! [SV1452: int,SV466: int,SV1494: int] :
( ( ( dvd_dvd_int @ SV1494 @ ( minus_minus_int @ SV466 @ SV1452 ) )
= $false )
| ( ( zcong @ SV466 @ SV1452 @ SV1494 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6313]) ).
thf(6542,plain,
! [SV1495: int,SV1453: int,SV466: int] :
( ( ( zcong @ SV466 @ SV1453 @ SV1495 )
= $false )
| ( ( dvd_dvd_int @ SV1495 @ ( minus_minus_int @ SV466 @ SV1453 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6314]) ).
thf(6543,plain,
! [SV1456: nat,SV467: nat,SV1496: int] :
( ( ( ord_less_int @ one_one_int @ SV1496 )
= $false )
| ( ( ( ( power_power_int @ SV1496 @ SV467 )
!= ( power_power_int @ SV1496 @ SV1456 ) )
| ( SV467 = SV1456 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6317]) ).
thf(6544,plain,
! [SV1457: nat,SV467: nat,SV1497: int] :
( ( ( ord_less_int @ one_one_int @ SV1497 )
= $false )
| ( ( ( SV467 != SV1457 )
| ( ( power_power_int @ SV1497 @ SV467 )
= ( power_power_int @ SV1497 @ SV1457 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6318]) ).
thf(6545,plain,
! [SV510: int,SV810: int,SV88: int] :
( ( ( ord_less_int @ SV88 @ SV810 )
= $false )
| ( ( ord_less_eq_int @ one_one_int @ SV510 )
= $true )
| ( ( SV810
= ( plus_plus_int @ SV88 @ ( times_times_int @ SV810 @ SV510 ) ) )
= $false )
| ( ( ord_less_int @ zero_zero_int @ SV810 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6321]) ).
thf(6546,plain,
! [SV811: int,SV511: int,SV89: int] :
( ( ( ord_less_eq_int @ zero_zero_int @ SV89 )
= $false )
| ( ( ord_less_eq_int @ SV511 @ one_one_int )
= $true )
| ( ( SV811
= ( plus_plus_int @ SV89 @ ( times_times_int @ SV811 @ SV511 ) ) )
= $false )
| ( ( ord_less_int @ zero_zero_int @ SV811 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6322]) ).
thf(6547,plain,
! [SV518: int,SV96: int] :
( ( ( ~ ( dvd_dvd_int @ SV96 @ SV518 ) )
= $true )
| ( ( SV518 = SV96 )
= $true )
| ( ( dvd_dvd_int @ SV518 @ SV96 )
= $false )
| ( ( ord_less_eq_int @ zero_zero_int @ SV96 )
= $false )
| ( ( ord_less_eq_int @ zero_zero_int @ SV518 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6323]) ).
thf(6548,plain,
! [SV1279: int,SV536: int,SV125: int,SV986: int,SV827: int] :
( ( ( SV827 = SV986 )
= $false )
| ( ( SV125 = SV536 )
= $true )
| ( ( ( plus_plus_int @ SV827 @ ( times_times_int @ SV1279 @ SV125 ) )
!= ( plus_plus_int @ SV986 @ ( times_times_int @ SV1279 @ SV536 ) ) )
= $true )
| ( ( SV1279 = zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6324]) ).
thf(6549,plain,
! [SV828: int,SV543: int,SV133: int] :
( ( ( ord_less_int @ zero_zero_int @ SV133 )
= $false )
| ( ( ord_less_eq_int @ zero_zero_int @ SV543 )
= $true )
| ( ( ord_less_int @ SV828 @ SV133 )
= $false )
| ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ SV133 @ SV543 ) @ SV828 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6325]) ).
thf(6550,plain,
! [SV829: int,SV544: int,SV134: int] :
( ( ( ord_less_int @ zero_zero_int @ SV134 )
= $false )
| ( ( ord_less_eq_int @ SV544 @ zero_zero_int )
= $true )
| ( ( ord_less_eq_int @ zero_zero_int @ SV829 )
= $false )
| ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ SV134 @ SV544 ) @ SV829 ) @ zero_zero_int )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6326]) ).
thf(6551,plain,
! [SV987: int,SV545: int,SV1280: int,SV135: int,SV830: int] :
( ( ( ord_less_eq_int @ zero_zero_int @ SV830 )
= $false )
| ( ( ~ ( ord_less_int @ SV830 @ SV135 )
| ~ ( ord_less_int @ SV1280 @ SV135 )
| ( ord_less_eq_int @ SV545 @ SV987 ) )
= $true )
| ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SV135 @ SV545 ) @ SV830 ) @ ( plus_plus_int @ ( times_times_int @ SV135 @ SV987 ) @ SV1280 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6327]) ).
thf(6552,plain,
! [SV546: int,SV136: int,SV831: int,SV1458: int,SV1281: int,SV988: int] :
( ( ( ~ ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ SV988 @ SV1281 ) @ SV1458 ) ) )
= $true )
| ( ( ~ ( ord_less_int @ SV1458 @ SV988 )
| ~ ( ord_less_eq_int @ zero_zero_int @ SV831 )
| ~ ( ord_less_int @ zero_zero_int @ SV988 )
| ~ ( ord_less_eq_int @ SV988 @ SV136 )
| ( ord_less_eq_int @ SV546 @ SV1281 ) )
= $true )
| ( ( ( plus_plus_int @ ( times_times_int @ SV136 @ SV546 ) @ SV831 )
= ( plus_plus_int @ ( times_times_int @ SV988 @ SV1281 ) @ SV1458 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6328]) ).
thf(6553,plain,
! [SV547: int,SV989: int,SV832: int,SV137: int,SV1282: int] :
( ( ( ord_less_eq_int @ SV1282 @ zero_zero_int )
= $false )
| ( ( ~ ( ord_less_int @ SV137 @ SV1282 )
| ~ ( ord_less_int @ SV137 @ SV832 )
| ( ord_less_eq_int @ SV989 @ SV547 ) )
= $true )
| ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SV137 @ SV547 ) @ SV832 ) @ ( plus_plus_int @ ( times_times_int @ SV137 @ SV989 ) @ SV1282 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6329]) ).
thf(6554,plain,
! [SV548: int,SV138: int,SV833: int,SV1459: int,SV1283: int,SV990: int] :
( ( ( ~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ SV990 @ SV1283 ) @ SV1459 ) @ zero_zero_int ) )
= $true )
| ( ( ~ ( ord_less_int @ SV833 @ SV138 )
| ~ ( ord_less_eq_int @ zero_zero_int @ SV1459 )
| ~ ( ord_less_int @ zero_zero_int @ SV990 )
| ~ ( ord_less_eq_int @ SV990 @ SV138 )
| ( ord_less_eq_int @ SV1283 @ SV548 ) )
= $true )
| ( ( ( plus_plus_int @ ( times_times_int @ SV138 @ SV548 ) @ SV833 )
= ( plus_plus_int @ ( times_times_int @ SV990 @ SV1283 ) @ SV1459 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6330]) ).
thf(6555,plain,
! [SV991: int,SV836: int,SV1284: int,SV553: int,SV149: int] :
( ( ( zcong @ SV149 @ SV553 @ SV1284 )
= $false )
| ( ( zcong @ ( plus_plus_int @ SV836 @ SV149 ) @ ( plus_plus_int @ SV991 @ SV553 ) @ SV1284 )
= $true )
| ( ( zcong @ SV836 @ SV991 @ SV1284 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6332]) ).
thf(6556,plain,
! [SV554: int,SV837: int,SV150: int] :
( ( ( ord_less_int @ zero_zero_int @ SV150 )
= $false )
| ( ( ~ ( ord_less_int @ SV150 @ SV837 )
| ~ ( zcong @ SV837 @ SV150 @ SV554 ) )
= $true )
| ( ( ord_less_int @ SV837 @ SV554 )
= $false )
| ( ( ord_less_int @ zero_zero_int @ SV837 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6333]) ).
thf(6557,plain,
! [SV838: int,SV556: int,SV152: int] :
( ( ( ord_less_eq_int @ zero_zero_int @ SV152 )
= $false )
| ( ( ~ ( ord_less_int @ SV152 @ SV556 )
| ~ ( zcong @ SV838 @ SV152 @ SV556 )
| ( SV838 = SV152 ) )
= $true )
| ( ( ord_less_int @ SV838 @ SV556 )
= $false )
| ( ( ord_less_eq_int @ zero_zero_int @ SV838 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6335]) ).
thf(6558,plain,
! [SV568: int,SV845: int,SV170: int] :
( ( ( ord_less_int @ zero_zero_int @ SV170 )
= $false )
| ( ( ~ ( zcong @ SV845 @ SV568 @ SV170 )
| ~ ( ord_less_int @ SV845 @ SV170 )
| ~ ( ord_less_int @ SV568 @ SV170 )
| ( SV845 = SV568 ) )
= $true )
| ( ( ord_less_int @ zero_zero_int @ SV568 )
= $false )
| ( ( ord_less_int @ zero_zero_int @ SV845 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6336]) ).
thf(6559,plain,
! [SV594: nat,SV860: nat,SV201: int] :
( ( ( ord_less_int @ SV201 @ one_one_int )
= $false )
| ( ( ord_less_int @ ( power_power_int @ SV201 @ SV860 ) @ ( power_power_int @ SV201 @ SV594 ) )
= $true )
| ( ( ord_less_int @ zero_zero_int @ SV201 )
= $false )
| ( ( ord_less_nat @ SV594 @ SV860 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6340]) ).
thf(6560,plain,
! [SV869: int,SV628: int,SV249: nat,SV1000: int] :
( ( ( dvd_dvd_int @ ( power_power_int @ SV1000 @ SV249 ) @ ( times_times_int @ SV628 @ SV869 ) )
= $false )
| ( ( dvd_dvd_int @ ( power_power_int @ SV1000 @ SV249 ) @ SV628 )
= $true )
| ( ( dvd_dvd_int @ SV1000 @ SV869 )
= $true )
| ( ( zprime @ SV1000 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6343]) ).
thf(6561,plain,
! [SV629: int,SV870: int,SV250: nat,SV1001: int] :
( ( ( dvd_dvd_int @ ( power_power_int @ SV1001 @ SV250 ) @ ( times_times_int @ SV870 @ SV629 ) )
= $false )
| ( ( dvd_dvd_int @ ( power_power_int @ SV1001 @ SV250 ) @ SV629 )
= $true )
| ( ( dvd_dvd_int @ SV1001 @ SV870 )
= $true )
| ( ( zprime @ SV1001 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6344]) ).
thf(6562,plain,
! [SV1286: real,SV678: real,SV316: real,SV1013: real,SV913: real] :
( ( ( SV913 = SV1013 )
= $false )
| ( ( SV316 = SV678 )
= $true )
| ( ( ( plus_plus_real @ SV913 @ ( times_times_real @ SV1286 @ SV316 ) )
!= ( plus_plus_real @ SV1013 @ ( times_times_real @ SV1286 @ SV678 ) ) )
= $true )
| ( ( SV1286 = zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6345]) ).
thf(6563,plain,
! [SV1287: nat,SV679: nat,SV317: nat,SV1014: nat,SV914: nat] :
( ( ( SV914 = SV1014 )
= $false )
| ( ( SV317 = SV679 )
= $true )
| ( ( ( plus_plus_nat @ SV914 @ ( times_times_nat @ SV1287 @ SV317 ) )
!= ( plus_plus_nat @ SV1014 @ ( times_times_nat @ SV1287 @ SV679 ) ) )
= $true )
| ( ( SV1287 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6346]) ).
thf(6564,plain,
! [SV1018: int,SV920: int,SV1288: int,SV691: int,SV333: int] :
( ( ( zcong @ SV333 @ SV691 @ SV1288 )
= $false )
| ( ( zcong @ ( times_times_int @ SV920 @ SV333 ) @ ( times_times_int @ SV1018 @ SV691 ) @ SV1288 )
= $true )
| ( ( zcong @ SV920 @ SV1018 @ SV1288 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6348]) ).
thf(6565,plain,
! [SV337: int,SV921: int,SV692: int] :
( ( ( dvd_dvd_int @ SV692 @ ( times_times_int @ SV921 @ SV337 ) )
= $false )
| ( ( ( dvd_dvd_int @ SV692 @ SV921 )
| ( dvd_dvd_int @ SV692 @ SV337 ) )
= $true )
| ( ( zprime @ SV692 )
= $false )
| ( ( ord_less_eq_int @ zero_zero_int @ SV921 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6349]) ).
thf(6566,plain,
! [SV1019: int,SV923: int,SV1289: int,SV695: int,SV340: int] :
( ( ( zcong @ SV340 @ SV695 @ SV1289 )
= $false )
| ( ( zcong @ ( minus_minus_int @ SV923 @ SV340 ) @ ( minus_minus_int @ SV1019 @ SV695 ) @ SV1289 )
= $true )
| ( ( zcong @ SV923 @ SV1019 @ SV1289 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6350]) ).
thf(6567,plain,
! [SV932: int,SV1290: int,SV351: int,SV706: int,SV1020: int] :
( ( ( SV1020 = SV706 )
= $false )
| ( ( ~ ( zcong @ SV706 @ SV351 @ SV1290 )
| ( zcong @ SV932 @ SV351 @ SV1290 ) )
= $true )
| ( ( zcong @ SV932 @ SV1020 @ SV1290 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6351]) ).
thf(6568,plain,
! [SV707: int,SV352: int] :
( ( ( ~ ( zcong @ ( times_times_int @ SV352 @ SV352 ) @ one_one_int @ SV707 ) )
= $true )
| ( ( ( SV352 = one_one_int )
| ( SV352
= ( minus_minus_int @ SV707 @ one_one_int ) ) )
= $true )
| ( ( ord_less_int @ SV352 @ SV707 )
= $false )
| ( ( ord_less_int @ zero_zero_int @ SV352 )
= $false )
| ( ( zprime @ SV707 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6352]) ).
thf(6569,plain,
! [SV708: int,SV353: int] :
( ( ( zcong @ SV353 @ one_one_int @ SV708 )
= $true )
| ( ( zcong @ SV353 @ ( minus_minus_int @ SV708 @ one_one_int ) @ SV708 )
= $true )
| ( ( zcong @ ( times_times_int @ SV353 @ SV353 ) @ one_one_int @ SV708 )
= $false )
| ( ( ord_less_int @ zero_zero_int @ SV353 )
= $false )
| ( ( zprime @ SV708 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6353]) ).
thf(6570,plain,
! [SV361: int,SV936: int,SV716: int] :
( ( ( zcong @ SV716 @ zero_zero_int @ SV936 )
= $true )
| ( ( zcong @ SV361 @ zero_zero_int @ SV936 )
= $true )
| ( ( ~ ( zcong @ ( times_times_int @ SV716 @ SV361 ) @ zero_zero_int @ SV936 ) )
= $true )
| ( ( ord_less_int @ zero_zero_int @ SV716 )
= $false )
| ( ( zprime @ SV936 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6356]) ).
thf(6571,plain,
! [SV937: int,SV362: int,SV717: int] :
( ( ( zcong @ ( times_times_int @ SV717 @ SV362 ) @ zero_zero_int @ SV937 )
= $false )
| ( ( ( zcong @ SV717 @ zero_zero_int @ SV937 )
| ( zcong @ SV362 @ zero_zero_int @ SV937 ) )
= $true )
| ( ( ord_less_int @ zero_zero_int @ SV717 )
= $false )
| ( ( zprime @ SV937 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6357]) ).
thf(6572,plain,
! [SV363: int,SV938: int,SV718: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV718 )
= $false )
| ( ( dvd_dvd_int @ SV938 @ SV363 )
= $true )
| ( ( dvd_dvd_int @ SV938 @ ( power_power_int @ SV363 @ SV718 ) )
= $false )
| ( ( zprime @ SV938 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6358]) ).
thf(6573,plain,
! [SV945: real,SV732: real,SV382: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV382 )
= $false )
| ( ( ord_less_real @ ( power_power_real @ SV732 @ SV382 ) @ ( power_power_real @ SV945 @ SV382 ) )
= $true )
| ( ( ord_less_eq_real @ zero_zero_real @ SV732 )
= $false )
| ( ( ord_less_real @ SV732 @ SV945 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6359]) ).
thf(6574,plain,
! [SV946: nat,SV733: nat,SV383: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV383 )
= $false )
| ( ( ord_less_nat @ ( power_power_nat @ SV733 @ SV383 ) @ ( power_power_nat @ SV946 @ SV383 ) )
= $true )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV733 )
= $false )
| ( ( ord_less_nat @ SV733 @ SV946 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6360]) ).
thf(6575,plain,
! [SV947: int,SV734: int,SV384: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV384 )
= $false )
| ( ( ord_less_int @ ( power_power_int @ SV734 @ SV384 ) @ ( power_power_int @ SV947 @ SV384 ) )
= $true )
| ( ( ord_less_eq_int @ zero_zero_int @ SV734 )
= $false )
| ( ( ord_less_int @ SV734 @ SV947 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6361]) ).
thf(6576,plain,
! [SV782: nat,SV438: nat,SV979: nat,SV1027: nat] :
( ( ( ~ ( ord_less_nat @ SV1027 @ SV979 ) )
= $true )
| ( ( ~ ( dvd_dvd_nat @ SV979 @ SV438 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV1027 )
= $false )
| ( ( SV438
= ( plus_plus_nat @ ( times_times_nat @ SV782 @ SV979 ) @ SV1027 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6366]) ).
thf(6577,plain,
! [SV1589: nat,SV1499: nat] :
( ( ( ( power_power_nat @ SV1499 @ SV1589 )
!= zero_zero_nat )
= $true )
| ( ( SV1589 != zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6368]) ).
thf(6578,plain,
! [SV1646: nat,SV1500: nat] :
( ( ( ( power_power_nat @ SV1500 @ SV1646 )
!= zero_zero_nat )
= $true )
| ( ( SV1500 = zero_zero_nat )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6369]) ).
thf(6579,plain,
! [SV1590: int,SV1501: nat] :
( ( ( ( power_power_nat @ SV1501 @ ( number_number_of_nat @ SV1590 ) )
!= zero_zero_nat )
= $true )
| ( ( ( number_number_of_nat @ SV1590 )
!= zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6371]) ).
thf(6580,plain,
! [SV1647: int,SV1502: nat] :
( ( ( ( power_power_nat @ SV1502 @ ( number_number_of_nat @ SV1647 ) )
!= zero_zero_nat )
= $true )
| ( ( SV1502 = zero_zero_nat )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6372]) ).
thf(6581,plain,
! [SV1293: real,SV1034: real] :
( ( ( SV1034 = zero_zero_real )
= $false )
| ( ( SV1293 != zero_zero_real )
= $true )
| ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ SV1034 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SV1293 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6373]) ).
thf(6582,plain,
! [SV1648: real,SV1503: real] :
( ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ SV1503 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SV1648 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true )
| ( ( SV1503 = zero_zero_real )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6374]) ).
thf(6583,plain,
! [SV1504: real,SV1591: real] :
( ( ( SV1591 = zero_zero_real )
= $true )
| ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ SV1504 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SV1591 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6375]) ).
thf(6584,plain,
! [SV1505: nat] :
( ( ( SV1505 = one_one_nat )
= $false )
| ( ( ! [SY2601: nat] :
( ( power_power_nat @ SV1505 @ SY2601 )
= one_one_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6377]) ).
thf(6585,plain,
! [SV1506: nat,SV1592: nat] :
( ( ( SV1592 != zero_zero_nat )
= $true )
| ( ( ( power_power_nat @ SV1506 @ SV1592 )
= one_one_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6378]) ).
thf(6586,plain,
! [SV1054: real,SV1305: real] :
( ( ( SV1305 = zero_zero_real )
= $false )
| ( ( SV1054 = zero_zero_real )
= $false )
| ( ( ord_less_eq_real @ ( plus_plus_real @ ( power_power_real @ SV1054 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SV1305 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6379]) ).
thf(6587,plain,
! [SV1649: real,SV1507: real] :
( ( ( ~ ( ord_less_eq_real @ ( plus_plus_real @ ( power_power_real @ SV1507 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SV1649 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_real ) )
= $true )
| ( ( SV1507 = zero_zero_real )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6380]) ).
thf(6588,plain,
! [SV1593: real,SV1508: real] :
( ( ( ~ ( ord_less_eq_real @ ( plus_plus_real @ ( power_power_real @ SV1508 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SV1593 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_real ) )
= $true )
| ( ( SV1593 = zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6381]) ).
thf(6589,plain,
! [SV1594: int,SV1509: int] :
( ( ( SV1509 != SV1594 )
= $true )
| ( ( ord_less_int @ SV1509 @ ( plus_plus_int @ SV1594 @ one_one_int ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6383]) ).
thf(6590,plain,
! [SV1595: int,SV1510: int] :
( ( ( ~ ( ord_less_int @ SV1510 @ SV1595 ) )
= $true )
| ( ( ord_less_int @ SV1510 @ ( plus_plus_int @ SV1595 @ one_one_int ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6384]) ).
thf(6591,plain,
! [SV785: nat,SV441: nat,SV1650: nat] :
( ( ! [SY2678: nat] :
( ( ( plus_plus_nat @ ( times_times_nat @ SV1650 @ SV441 ) @ ( times_times_nat @ SY2678 @ SV785 ) )
= ( plus_plus_nat @ ( times_times_nat @ SV1650 @ SV785 ) @ ( times_times_nat @ SY2678 @ SV441 ) ) )
| ( SV1650 != SY2678 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6385]) ).
thf(6592,plain,
! [SV785: nat,SV441: nat] :
( ( ( ! [SY2275: nat,SY2276: nat] :
( ( plus_plus_nat @ ( times_times_nat @ SY2275 @ SV441 ) @ ( times_times_nat @ SY2276 @ SV785 ) )
= ( plus_plus_nat @ ( times_times_nat @ SY2275 @ SV785 ) @ ( times_times_nat @ SY2276 @ SV441 ) ) ) )
= $true )
| ( ( SV441 != SV785 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6386]) ).
thf(6593,plain,
! [SV785: nat,SV441: nat,SV1511: nat,SV1461: nat] :
( ( ( SV1461 = SV1511 )
= $true )
| ( ( SV441 = SV785 )
= $true )
| ( ( ( plus_plus_nat @ ( times_times_nat @ SV1461 @ SV441 ) @ ( times_times_nat @ SV1511 @ SV785 ) )
!= ( plus_plus_nat @ ( times_times_nat @ SV1461 @ SV785 ) @ ( times_times_nat @ SV1511 @ SV441 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6387]) ).
thf(6594,plain,
! [SV1596: int,SV1512: real] :
( ( ( ( power_power_real @ SV1512 @ ( number_number_of_nat @ SV1596 ) )
!= zero_zero_real )
= $true )
| ( ( ( number_number_of_nat @ SV1596 )
!= zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6389]) ).
thf(6595,plain,
! [SV1651: int,SV1513: real] :
( ( ( ( power_power_real @ SV1513 @ ( number_number_of_nat @ SV1651 ) )
!= zero_zero_real )
= $true )
| ( ( SV1513 = zero_zero_real )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6390]) ).
thf(6596,plain,
! [SV1312: real,SV1065: real] :
( ( ( SV1065 = zero_zero_real )
= $false )
| ( ( SV1312 != zero_zero_real )
= $true )
| ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ SV1065 @ SV1065 ) @ ( times_times_real @ SV1312 @ SV1312 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6391]) ).
thf(6597,plain,
! [SV1652: real,SV1514: real] :
( ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ SV1514 @ SV1514 ) @ ( times_times_real @ SV1652 @ SV1652 ) ) )
= $true )
| ( ( SV1514 = zero_zero_real )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6392]) ).
thf(6598,plain,
! [SV1515: real,SV1597: real] :
( ( ( SV1597 = zero_zero_real )
= $true )
| ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ SV1515 @ SV1515 ) @ ( times_times_real @ SV1597 @ SV1597 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6393]) ).
thf(6599,plain,
! [SV1516: nat,SV1598: nat] :
( ( ( SV1598 != zero_zero_nat )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV1516 @ SV1598 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6395]) ).
thf(6600,plain,
! [SV1517: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV1517 )
= $false )
| ( ( ! [SY2612: nat] : ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV1517 @ SY2612 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6396]) ).
thf(6601,plain,
! [SV786: real,SV442: real,SV1653: real] :
( ( ! [SY2679: real] :
( ( ( plus_plus_real @ ( times_times_real @ SV1653 @ SV442 ) @ ( times_times_real @ SY2679 @ SV786 ) )
= ( plus_plus_real @ ( times_times_real @ SV1653 @ SV786 ) @ ( times_times_real @ SY2679 @ SV442 ) ) )
| ( SV1653 != SY2679 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6397]) ).
thf(6602,plain,
! [SV786: real,SV442: real] :
( ( ( ! [SY2281: real,SY2282: real] :
( ( plus_plus_real @ ( times_times_real @ SY2281 @ SV442 ) @ ( times_times_real @ SY2282 @ SV786 ) )
= ( plus_plus_real @ ( times_times_real @ SY2281 @ SV786 ) @ ( times_times_real @ SY2282 @ SV442 ) ) ) )
= $true )
| ( ( SV442 != SV786 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6398]) ).
thf(6603,plain,
! [SV786: real,SV442: real,SV1518: real,SV1462: real] :
( ( ( SV1462 = SV1518 )
= $true )
| ( ( SV442 = SV786 )
= $true )
| ( ( ( plus_plus_real @ ( times_times_real @ SV1462 @ SV442 ) @ ( times_times_real @ SV1518 @ SV786 ) )
!= ( plus_plus_real @ ( times_times_real @ SV1462 @ SV786 ) @ ( times_times_real @ SV1518 @ SV442 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6399]) ).
thf(6604,plain,
! [SV1599: real,SV1519: real] :
( ( ( SV1519 != SV1599 )
= $true )
| ( ( ord_less_eq_real @ SV1519 @ SV1599 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6401]) ).
thf(6605,plain,
! [SV1600: real,SV1520: real] :
( ( ( ~ ( ord_less_real @ SV1520 @ SV1600 ) )
= $true )
| ( ( ord_less_eq_real @ SV1520 @ SV1600 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6402]) ).
thf(6606,plain,
! [SV1315: int,SV1074: int] :
( ( ( SV1074 = zero_zero_int )
= $false )
| ( ( SV1315 != zero_zero_int )
= $true )
| ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ SV1074 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV1315 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6403]) ).
thf(6607,plain,
! [SV1654: int,SV1521: int] :
( ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ SV1521 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV1654 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true )
| ( ( SV1521 = zero_zero_int )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6404]) ).
thf(6608,plain,
! [SV1522: int,SV1601: int] :
( ( ( SV1601 = zero_zero_int )
= $true )
| ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ SV1522 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV1601 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6405]) ).
thf(6609,plain,
! [SV1079: real,SV1318: real] :
( ( ( SV1318 = zero_zero_real )
= $false )
| ( ( SV1079 = zero_zero_real )
= $false )
| ( ( ( plus_plus_real @ ( power_power_real @ SV1079 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SV1318 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6406]) ).
thf(6610,plain,
! [SV1655: real,SV1523: real] :
( ( ( ( plus_plus_real @ ( power_power_real @ SV1523 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SV1655 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_real )
= $true )
| ( ( SV1523 = zero_zero_real )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6407]) ).
thf(6611,plain,
! [SV1602: real,SV1524: real] :
( ( ( ( plus_plus_real @ ( power_power_real @ SV1524 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SV1602 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_real )
= $true )
| ( ( SV1602 = zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6408]) ).
thf(6612,plain,
! [SV1325: nat,SV443: nat,SV1463: int] :
( ( ( ~ ( ord_less_int @ ( power_power_int @ SV1463 @ SV443 ) @ ( power_power_int @ SV1463 @ SV1325 ) ) )
= $true )
| ( ( ord_less_nat @ SV443 @ SV1325 )
= $true )
| ( ( ord_less_int @ one_one_int @ SV1463 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6409]) ).
thf(6613,plain,
! [SV1464: int,SV1326: nat,SV443: nat] :
( ( ( ~ ( ord_less_nat @ SV443 @ SV1326 ) )
= $true )
| ( ( ord_less_int @ ( power_power_int @ SV1464 @ SV443 ) @ ( power_power_int @ SV1464 @ SV1326 ) )
= $true )
| ( ( ord_less_int @ one_one_int @ SV1464 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6410]) ).
thf(6614,plain,
! [SV1604: int,SV1526: int] :
( ( ( ( power_power_int @ SV1526 @ ( number_number_of_nat @ SV1604 ) )
!= zero_zero_int )
= $true )
| ( ( ( number_number_of_nat @ SV1604 )
!= zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6414]) ).
thf(6615,plain,
! [SV1656: int,SV1527: int] :
( ( ( ( power_power_int @ SV1527 @ ( number_number_of_nat @ SV1656 ) )
!= zero_zero_int )
= $true )
| ( ( SV1527 = zero_zero_int )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6415]) ).
thf(6616,plain,
! [SV1113: real,SV1344: real] :
( ( ( SV1344 = zero_zero_real )
= $false )
| ( ( SV1113 = zero_zero_real )
= $false )
| ( ( ( plus_plus_real @ ( power_power_real @ SV1113 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SV1344 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6417]) ).
thf(6617,plain,
! [SV1657: real,SV1528: real] :
( ( ( ( plus_plus_real @ ( power_power_real @ SV1528 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SV1657 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_real )
= $true )
| ( ( SV1528 = zero_zero_real )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6418]) ).
thf(6618,plain,
! [SV1605: real,SV1529: real] :
( ( ( ( plus_plus_real @ ( power_power_real @ SV1529 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SV1605 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_real )
= $true )
| ( ( SV1605 = zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6419]) ).
thf(6619,plain,
! [SV1114: int,SV1345: int] :
( ( ( SV1345 = zero_zero_int )
= $false )
| ( ( SV1114 = zero_zero_int )
= $false )
| ( ( ( plus_plus_int @ ( power_power_int @ SV1114 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV1345 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6420]) ).
thf(6620,plain,
! [SV1658: int,SV1530: int] :
( ( ( ( plus_plus_int @ ( power_power_int @ SV1530 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV1658 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_int )
= $true )
| ( ( SV1530 = zero_zero_int )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6421]) ).
thf(6621,plain,
! [SV1606: int,SV1531: int] :
( ( ( ( plus_plus_int @ ( power_power_int @ SV1531 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV1606 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_int )
= $true )
| ( ( SV1606 = zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6422]) ).
thf(6622,plain,
! [SV1350: real,SV1465: real,SV445: real] :
( ( ( ~ ( ord_less_eq_real @ ( times_times_real @ SV445 @ SV1465 ) @ ( times_times_real @ SV1350 @ SV1465 ) ) )
= $true )
| ( ( ord_less_eq_real @ SV445 @ SV1350 )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV1465 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6423]) ).
thf(6623,plain,
! [SV1466: real,SV1351: real,SV445: real] :
( ( ( ~ ( ord_less_eq_real @ SV445 @ SV1351 ) )
= $true )
| ( ( ord_less_eq_real @ ( times_times_real @ SV445 @ SV1466 ) @ ( times_times_real @ SV1351 @ SV1466 ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV1466 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6424]) ).
thf(6624,plain,
! [SV1125: real,SV1352: real] :
( ( ( SV1352 = zero_zero_real )
= $false )
| ( ( SV1125 = zero_zero_real )
= $false )
| ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ SV1125 @ SV1125 ) @ ( times_times_real @ SV1352 @ SV1352 ) ) @ zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6425]) ).
thf(6625,plain,
! [SV1659: real,SV1532: real] :
( ( ( ~ ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ SV1532 @ SV1532 ) @ ( times_times_real @ SV1659 @ SV1659 ) ) @ zero_zero_real ) )
= $true )
| ( ( SV1532 = zero_zero_real )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6426]) ).
thf(6626,plain,
! [SV1607: real,SV1533: real] :
( ( ( ~ ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ SV1533 @ SV1533 ) @ ( times_times_real @ SV1607 @ SV1607 ) ) @ zero_zero_real ) )
= $true )
| ( ( SV1607 = zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6427]) ).
thf(6627,plain,
! [SV1130: int,SV1355: int] :
( ( ( SV1355 = zero_zero_int )
= $false )
| ( ( SV1130 = zero_zero_int )
= $false )
| ( ( ord_less_eq_int @ ( plus_plus_int @ ( power_power_int @ SV1130 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV1355 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6428]) ).
thf(6628,plain,
! [SV1660: int,SV1534: int] :
( ( ( ~ ( ord_less_eq_int @ ( plus_plus_int @ ( power_power_int @ SV1534 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV1660 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_int ) )
= $true )
| ( ( SV1534 = zero_zero_int )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6429]) ).
thf(6629,plain,
! [SV1608: int,SV1535: int] :
( ( ( ~ ( ord_less_eq_int @ ( plus_plus_int @ ( power_power_int @ SV1535 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV1608 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_int ) )
= $true )
| ( ( SV1608 = zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6430]) ).
thf(6630,plain,
! [SV1133: int,SV1356: int] :
( ( ( SV1356 = zero_zero_int )
= $false )
| ( ( SV1133 = zero_zero_int )
= $false )
| ( ( ( plus_plus_int @ ( times_times_int @ SV1133 @ SV1133 ) @ ( times_times_int @ SV1356 @ SV1356 ) )
= zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6431]) ).
thf(6631,plain,
! [SV1661: int,SV1536: int] :
( ( ( ( plus_plus_int @ ( times_times_int @ SV1536 @ SV1536 ) @ ( times_times_int @ SV1661 @ SV1661 ) )
!= zero_zero_int )
= $true )
| ( ( SV1536 = zero_zero_int )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6432]) ).
thf(6632,plain,
! [SV1609: int,SV1537: int] :
( ( ( ( plus_plus_int @ ( times_times_int @ SV1537 @ SV1537 ) @ ( times_times_int @ SV1609 @ SV1609 ) )
!= zero_zero_int )
= $true )
| ( ( SV1609 = zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6433]) ).
thf(6633,plain,
! [SV1610: int,SV1538: int] :
( ( ( ~ ( ord_less_int @ SV1538 @ SV1610 ) )
= $true )
| ( ( SV1538 != SV1610 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6435]) ).
thf(6634,plain,
! [SV1611: int,SV1539: int] :
( ( ( ~ ( ord_less_int @ SV1539 @ SV1611 ) )
= $true )
| ( ( ord_less_eq_int @ SV1539 @ SV1611 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6436]) ).
thf(6635,plain,
! [SV1358: nat,SV446: nat,SV1467: nat] :
( ( ( ~ ( ord_less_nat @ ( power_power_nat @ SV1467 @ SV446 ) @ ( power_power_nat @ SV1467 @ SV1358 ) ) )
= $true )
| ( ( ord_less_nat @ SV446 @ SV1358 )
= $true )
| ( ( ord_less_nat @ one_one_nat @ SV1467 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6437]) ).
thf(6636,plain,
! [SV1468: nat,SV1359: nat,SV446: nat] :
( ( ( ~ ( ord_less_nat @ SV446 @ SV1359 ) )
= $true )
| ( ( ord_less_nat @ ( power_power_nat @ SV1468 @ SV446 ) @ ( power_power_nat @ SV1468 @ SV1359 ) )
= $true )
| ( ( ord_less_nat @ one_one_nat @ SV1468 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6438]) ).
thf(6637,plain,
! [SV1137: nat,SV1360: nat] :
( ( ( SV1360 = one_one_nat )
= $false )
| ( ( SV1137 = one_one_nat )
= $false )
| ( ( ( times_times_nat @ SV1137 @ SV1360 )
= one_one_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6439]) ).
thf(6638,plain,
! [SV1662: nat,SV1540: nat] :
( ( ( ( times_times_nat @ SV1540 @ SV1662 )
!= one_one_nat )
= $true )
| ( ( SV1540 = one_one_nat )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6440]) ).
thf(6639,plain,
! [SV1612: nat,SV1541: nat] :
( ( ( ( times_times_nat @ SV1541 @ SV1612 )
!= one_one_nat )
= $true )
| ( ( SV1612 = one_one_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6441]) ).
thf(6640,plain,
( ( ! [SX0: int] :
( ! [SX1: int] :
( ( times_times_int @ SX0 @ SX1 )
!= one_one_int )
| ( SX0 = one_one_int )
| ( SX0
= ( number_number_of_int @ min ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6442]) ).
thf(6641,plain,
( ( ! [SX0: int,SX1: int] :
( ( ( times_times_int @ SX0 @ SX1 )
!= one_one_int )
| ( SX0 = one_one_int )
| ( SX1
= ( number_number_of_int @ min ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6443]) ).
thf(6642,plain,
( ( ! [SX0: int,SX1: int] :
( ( ( times_times_int @ SX0 @ SX1 )
!= one_one_int )
| ( SX1 = one_one_int )
| ( SX0
= ( number_number_of_int @ min ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6444]) ).
thf(6643,plain,
( ( ! [SX0: int,SX1: int] :
( ( ( times_times_int @ SX0 @ SX1 )
!= one_one_int )
| ( SX1 = one_one_int )
| ( SX1
= ( number_number_of_int @ min ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6445]) ).
thf(6644,plain,
! [SV1613: int,SV1542: int] :
( ( ( ( SV1542 != one_one_int )
| ( SV1613 != one_one_int ) )
= $true )
| ( ( ( times_times_int @ SV1542 @ SV1613 )
= one_one_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6446]) ).
thf(6645,plain,
! [SV1614: int,SV1543: int] :
( ( ( ( SV1543
!= ( number_number_of_int @ min ) )
| ( SV1614
!= ( number_number_of_int @ min ) ) )
= $true )
| ( ( ( times_times_int @ SV1543 @ SV1614 )
= one_one_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6447]) ).
thf(6646,plain,
! [SV1144: real,SV1365: real] :
( ( ( SV1365 = zero_zero_real )
= $false )
| ( ( SV1144 = zero_zero_real )
= $false )
| ( ( ( plus_plus_real @ ( times_times_real @ SV1144 @ SV1144 ) @ ( times_times_real @ SV1365 @ SV1365 ) )
= zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6448]) ).
thf(6647,plain,
! [SV1663: real,SV1544: real] :
( ( ( ( plus_plus_real @ ( times_times_real @ SV1544 @ SV1544 ) @ ( times_times_real @ SV1663 @ SV1663 ) )
!= zero_zero_real )
= $true )
| ( ( SV1544 = zero_zero_real )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6449]) ).
thf(6648,plain,
! [SV1615: real,SV1545: real] :
( ( ( ( plus_plus_real @ ( times_times_real @ SV1545 @ SV1545 ) @ ( times_times_real @ SV1615 @ SV1615 ) )
!= zero_zero_real )
= $true )
| ( ( SV1615 = zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6450]) ).
thf(6649,plain,
! [SV1469: real,SV1366: nat,SV447: nat] :
( ( ( ~ ( ord_less_nat @ SV447 @ SV1366 ) )
= $true )
| ( ( ord_less_real @ ( power_power_real @ SV1469 @ SV447 ) @ ( power_power_real @ SV1469 @ SV1366 ) )
= $true )
| ( ( ord_less_real @ one_one_real @ SV1469 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6451]) ).
thf(6650,plain,
! [SV1367: nat,SV447: nat,SV1470: real] :
( ( ( ~ ( ord_less_real @ ( power_power_real @ SV1470 @ SV447 ) @ ( power_power_real @ SV1470 @ SV1367 ) ) )
= $true )
| ( ( ord_less_nat @ SV447 @ SV1367 )
= $true )
| ( ( ord_less_real @ one_one_real @ SV1470 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6452]) ).
thf(6651,plain,
! [SV1368: int,SV1149: int] :
( ( ( SV1149 = zero_zero_int )
= $false )
| ( ( SV1368 != zero_zero_int )
= $true )
| ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ SV1149 @ SV1149 ) @ ( times_times_int @ SV1368 @ SV1368 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6453]) ).
thf(6652,plain,
! [SV1664: int,SV1546: int] :
( ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ SV1546 @ SV1546 ) @ ( times_times_int @ SV1664 @ SV1664 ) ) )
= $true )
| ( ( SV1546 = zero_zero_int )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6454]) ).
thf(6653,plain,
! [SV1547: int,SV1616: int] :
( ( ( SV1616 = zero_zero_int )
= $true )
| ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ SV1547 @ SV1547 ) @ ( times_times_int @ SV1616 @ SV1616 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6455]) ).
thf(6654,plain,
! [SV1371: real,SV448: real,SV1471: real] :
( ( ( ( times_times_real @ SV1471 @ SV448 )
= ( times_times_real @ SV1471 @ SV1371 ) )
= $false )
| ( ( SV448 = SV1371 )
= $true )
| ( ( SV1471 = zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6456]) ).
thf(6655,plain,
! [SV1472: real,SV1372: real,SV448: real] :
( ( ( SV448 = SV1372 )
= $false )
| ( ( ( times_times_real @ SV1472 @ SV448 )
= ( times_times_real @ SV1472 @ SV1372 ) )
= $true )
| ( ( SV1472 = zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6457]) ).
thf(6656,plain,
! [SV1617: int,SV1548: int] :
( ( ( ( ord_less_int @ SV1548 @ SV1617 )
| ~ ( ord_less_int @ SV1548 @ SV1617 ) )
= $true )
| ( ( ord_less_nat @ ( number_number_of_nat @ SV1548 ) @ ( number_number_of_nat @ SV1617 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6458]) ).
thf(6657,plain,
! [SV1549: int,SV1618: int] :
( ( ( ~ ( ord_less_int @ pls @ SV1618 )
| ~ ( ord_less_int @ SV1549 @ SV1618 ) )
= $true )
| ( ( ord_less_nat @ ( number_number_of_nat @ SV1549 ) @ ( number_number_of_nat @ SV1618 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6459]) ).
thf(6658,plain,
! [SV1619: int,SV1550: int] :
( ( ( ~ ( ord_less_nat @ ( number_number_of_nat @ SV1550 ) @ ( number_number_of_nat @ SV1619 ) ) )
= $true )
| ( ( ~ ( ord_less_int @ SV1550 @ SV1619 )
| ( ord_less_int @ pls @ SV1619 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6460]) ).
thf(6659,plain,
! [SV1620: int,SV1551: int] :
( ( ( ~ ( ord_less_nat @ ( number_number_of_nat @ SV1551 ) @ ( number_number_of_nat @ SV1620 ) ) )
= $true )
| ( ( ord_less_int @ SV1551 @ SV1620 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6461]) ).
thf(6660,plain,
! [SV787: int,SV449: int,SV1621: int,SV1552: int,SV981: int] :
( ( ( ~ ( zcong @ SV981 @ SV1552 @ SV1621 ) )
= $true )
| ( ( ~ ( zcong @ SV449 @ ( times_times_int @ SV981 @ SV787 ) @ SV1621 )
| ( zcong @ SV449 @ ( times_times_int @ SV1552 @ SV787 ) @ SV1621 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6462]) ).
thf(6661,plain,
! [SV787: int,SV449: int,SV1622: int,SV1553: int,SV981: int] :
( ( ( ~ ( zcong @ SV981 @ SV1553 @ SV1622 ) )
= $true )
| ( ( ~ ( zcong @ SV449 @ ( times_times_int @ SV1553 @ SV787 ) @ SV1622 )
| ( zcong @ SV449 @ ( times_times_int @ SV981 @ SV787 ) @ SV1622 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6463]) ).
thf(6662,plain,
! [SV788: int,SV450: int,SV1665: int] :
( ( ! [SY2680: int] :
( ( ( plus_plus_int @ ( times_times_int @ SV1665 @ SV450 ) @ ( times_times_int @ SY2680 @ SV788 ) )
= ( plus_plus_int @ ( times_times_int @ SV1665 @ SV788 ) @ ( times_times_int @ SY2680 @ SV450 ) ) )
| ( SV1665 != SY2680 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6464]) ).
thf(6663,plain,
! [SV788: int,SV450: int] :
( ( ( ! [SY2292: int,SY2293: int] :
( ( plus_plus_int @ ( times_times_int @ SY2292 @ SV450 ) @ ( times_times_int @ SY2293 @ SV788 ) )
= ( plus_plus_int @ ( times_times_int @ SY2292 @ SV788 ) @ ( times_times_int @ SY2293 @ SV450 ) ) ) )
= $true )
| ( ( SV450 != SV788 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6465]) ).
thf(6664,plain,
! [SV788: int,SV450: int,SV1554: int,SV1473: int] :
( ( ( SV1473 = SV1554 )
= $true )
| ( ( SV450 = SV788 )
= $true )
| ( ( ( plus_plus_int @ ( times_times_int @ SV1473 @ SV450 ) @ ( times_times_int @ SV1554 @ SV788 ) )
!= ( plus_plus_int @ ( times_times_int @ SV1473 @ SV788 ) @ ( times_times_int @ SV1554 @ SV450 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6466]) ).
thf(6665,plain,
! [SV1170: real,SV1381: real] :
( ( ( SV1381 = zero_zero_real )
= $false )
| ( ( SV1170 = zero_zero_real )
= $false )
| ( ( ( plus_plus_real @ ( times_times_real @ SV1170 @ SV1170 ) @ ( times_times_real @ SV1381 @ SV1381 ) )
= zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6467]) ).
thf(6666,plain,
! [SV1666: real,SV1555: real] :
( ( ( ( plus_plus_real @ ( times_times_real @ SV1555 @ SV1555 ) @ ( times_times_real @ SV1666 @ SV1666 ) )
!= zero_zero_real )
= $true )
| ( ( SV1555 = zero_zero_real )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6468]) ).
thf(6667,plain,
! [SV1623: real,SV1556: real] :
( ( ( ( plus_plus_real @ ( times_times_real @ SV1556 @ SV1556 ) @ ( times_times_real @ SV1623 @ SV1623 ) )
!= zero_zero_real )
= $true )
| ( ( SV1623 = zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6469]) ).
thf(6668,plain,
! [SV789: int,SV451: int,SV1624: int,SV1557: int,SV982: int] :
( ( ( ~ ( zcong @ SV982 @ SV1557 @ SV1624 ) )
= $true )
| ( ( ~ ( zcong @ SV451 @ ( times_times_int @ SV789 @ SV982 ) @ SV1624 )
| ( zcong @ SV451 @ ( times_times_int @ SV789 @ SV1557 ) @ SV1624 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6470]) ).
thf(6669,plain,
! [SV789: int,SV451: int,SV1625: int,SV1558: int,SV982: int] :
( ( ( ~ ( zcong @ SV982 @ SV1558 @ SV1625 ) )
= $true )
| ( ( ~ ( zcong @ SV451 @ ( times_times_int @ SV789 @ SV1558 ) @ SV1625 )
| ( zcong @ SV451 @ ( times_times_int @ SV789 @ SV982 ) @ SV1625 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6471]) ).
thf(6670,plain,
! [SV1559: nat,SV1474: nat,SV790: nat,SV452: nat] :
( ( ( ( plus_plus_nat @ ( times_times_nat @ SV452 @ SV790 ) @ ( times_times_nat @ SV1474 @ SV1559 ) )
= ( plus_plus_nat @ ( times_times_nat @ SV452 @ SV1559 ) @ ( times_times_nat @ SV1474 @ SV790 ) ) )
= $false )
| ( ( ( SV452 = SV1474 )
| ( SV790 = SV1559 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6472]) ).
thf(6671,plain,
! [SV790: nat,SV1667: nat,SV452: nat] :
( ( ( SV452 != SV1667 )
| ! [SY2681: nat] :
( ( plus_plus_nat @ ( times_times_nat @ SV452 @ SV790 ) @ ( times_times_nat @ SV1667 @ SY2681 ) )
= ( plus_plus_nat @ ( times_times_nat @ SV452 @ SY2681 ) @ ( times_times_nat @ SV1667 @ SV790 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6473]) ).
thf(6672,plain,
! [SV1668: nat,SV452: nat,SV790: nat] :
( ( ! [SY2682: nat] :
( ( SV790 != SY2682 )
| ( ( plus_plus_nat @ ( times_times_nat @ SV452 @ SV790 ) @ ( times_times_nat @ SV1668 @ SY2682 ) )
= ( plus_plus_nat @ ( times_times_nat @ SV452 @ SY2682 ) @ ( times_times_nat @ SV1668 @ SV790 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6474]) ).
thf(6673,plain,
! [SV1626: nat,SV1560: real] :
( ( ( ( power_power_real @ SV1560 @ SV1626 )
!= zero_zero_real )
= $true )
| ( ( SV1626 != zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6476]) ).
thf(6674,plain,
! [SV1669: nat,SV1561: real] :
( ( ( ( power_power_real @ SV1561 @ SV1669 )
!= zero_zero_real )
= $true )
| ( ( SV1561 = zero_zero_real )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6477]) ).
thf(6675,plain,
! [SV1562: nat,SV1627: nat] :
( ( ( SV1627 != zero_zero_nat )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV1562 @ SV1627 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6479]) ).
thf(6676,plain,
! [SV1563: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV1563 )
= $false )
| ( ( ! [SY2654: nat] : ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV1563 @ SY2654 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6480]) ).
thf(6677,plain,
! [SV1564: int,SV1475: int,SV791: int,SV453: int] :
( ( ( ( plus_plus_int @ ( times_times_int @ SV453 @ SV791 ) @ ( times_times_int @ SV1475 @ SV1564 ) )
= ( plus_plus_int @ ( times_times_int @ SV453 @ SV1564 ) @ ( times_times_int @ SV1475 @ SV791 ) ) )
= $false )
| ( ( ( SV453 = SV1475 )
| ( SV791 = SV1564 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6481]) ).
thf(6678,plain,
! [SV791: int,SV1670: int,SV453: int] :
( ( ( SV453 != SV1670 )
| ! [SY2683: int] :
( ( plus_plus_int @ ( times_times_int @ SV453 @ SV791 ) @ ( times_times_int @ SV1670 @ SY2683 ) )
= ( plus_plus_int @ ( times_times_int @ SV453 @ SY2683 ) @ ( times_times_int @ SV1670 @ SV791 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6482]) ).
thf(6679,plain,
! [SV1671: int,SV453: int,SV791: int] :
( ( ! [SY2684: int] :
( ( SV791 != SY2684 )
| ( ( plus_plus_int @ ( times_times_int @ SV453 @ SV791 ) @ ( times_times_int @ SV1671 @ SY2684 ) )
= ( plus_plus_int @ ( times_times_int @ SV453 @ SY2684 ) @ ( times_times_int @ SV1671 @ SV791 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6483]) ).
thf(6680,plain,
! [SV1185: int,SV1392: int] :
( ( ( SV1392 != one_one_int )
= $true )
| ( ( SV1185 != one_one_int )
= $true )
| ( ( ( times_times_int @ SV1392 @ SV1185 )
= one_one_int )
= $true )
| ( ( ord_less_int @ zero_zero_int @ SV1392 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6484]) ).
thf(6681,plain,
! [SV1565: int,SV1628: int] :
( ( ( ~ ( ord_less_int @ zero_zero_int @ SV1628 ) )
= $true )
| ( ( ( ( times_times_int @ SV1628 @ SV1565 )
!= one_one_int )
| ( SV1628 = one_one_int ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6485]) ).
thf(6682,plain,
! [SV1566: int,SV1629: int] :
( ( ( ~ ( ord_less_int @ zero_zero_int @ SV1629 ) )
= $true )
| ( ( ( ( times_times_int @ SV1629 @ SV1566 )
!= one_one_int )
| ( SV1566 = one_one_int ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6486]) ).
thf(6683,plain,
! [SV1630: real,SV1567: real] :
( ( ( ~ ( ord_less_real @ SV1567 @ SV1630 ) )
= $true )
| ( ( SV1567 != SV1630 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6488]) ).
thf(6684,plain,
! [SV1631: real,SV1568: real] :
( ( ( ~ ( ord_less_real @ SV1568 @ SV1631 ) )
= $true )
| ( ( ord_less_eq_real @ SV1568 @ SV1631 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6489]) ).
thf(6685,plain,
! [SV1569: nat,SV1632: int] :
( ( ( ( number_number_of_nat @ SV1632 )
!= zero_zero_nat )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV1569 @ ( number_number_of_nat @ SV1632 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6492]) ).
thf(6686,plain,
! [SV1570: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV1570 )
= $false )
| ( ( ! [SY2660: int] : ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV1570 @ ( number_number_of_nat @ SY2660 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6493]) ).
thf(6687,plain,
! [SV1204: int] :
( ( ( ~ ( ~ ( dvd_dvd_int @ ( sK3_M_9 @ SV1204 ) @ SV1204 )
| ~ ( ord_less_eq_int @ zero_zero_int @ ( sK3_M_9 @ SV1204 ) ) ) )
= $true )
| ( ( ~ ( ord_less_int @ one_one_int @ SV1204 ) )
= $true )
| ( ( zprime @ SV1204 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6494]) ).
thf(6688,plain,
! [SV1204: int] :
( ( ( ~ ( ~ ( ( ( sK3_M_9 @ SV1204 )
!= one_one_int ) )
| ~ ( ( ( sK3_M_9 @ SV1204 )
!= SV1204 ) ) ) )
= $true )
| ( ( ~ ( ord_less_int @ one_one_int @ SV1204 ) )
= $true )
| ( ( zprime @ SV1204 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6495]) ).
thf(6689,plain,
! [SV1571: int] :
( ( ( zprime @ SV1571 )
= $false )
| ( ( ! [SY2661: int] :
( ~ ( dvd_dvd_int @ SY2661 @ SV1571 )
| ~ ( ord_less_eq_int @ zero_zero_int @ SY2661 )
| ( SY2661 = one_one_int )
| ( SY2661 = SV1571 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6496]) ).
thf(6690,plain,
! [SV1572: int] :
( ( ( zprime @ SV1572 )
= $false )
| ( ( ord_less_int @ one_one_int @ SV1572 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6497]) ).
thf(6691,plain,
! [SV1633: int,SV1573: int] :
( ( ( zcong @ SV1573 @ zero_zero_int @ SV1633 )
= $true )
| ( ( ~ ( quadRes @ SV1633 @ SV1573 )
| ( ( legendre @ SV1573 @ SV1633 )
= one_one_int ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6499]) ).
thf(6692,plain,
! [SV1634: int,SV1574: int] :
( ( ( zcong @ SV1574 @ zero_zero_int @ SV1634 )
= $true )
| ( ( ( quadRes @ SV1634 @ SV1574 )
| ( ( legendre @ SV1574 @ SV1634 )
= ( number_number_of_int @ min ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6500]) ).
thf(6693,plain,
! [SV455: real,SV792: nat] :
( ( ( ! [SY2313: real] :
( ( ( power_power_real @ SY2313 @ SV792 )
!= SV455 )
| ~ ( ord_less_real @ zero_zero_real @ SY2313 )
| ( SY2313
= ( sK1_X_1 @ SV792 @ SV455 ) ) ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV455 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV792 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6501]) ).
thf(6694,plain,
! [SV455: real,SV792: nat] :
( ( ( ~ ( ( ( power_power_real @ ( sK1_X_1 @ SV792 @ SV455 ) @ SV792 )
!= SV455 )
| ~ ( ord_less_real @ zero_zero_real @ ( sK1_X_1 @ SV792 @ SV455 ) ) ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV455 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV792 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6502]) ).
thf(6695,plain,
! [SV1635: int,SV1575: int] :
( ( ( ~ ( ord_less_eq_int @ SV1575 @ SV1635 ) )
= $true )
| ( ( ord_less_eq_nat @ ( number_number_of_nat @ SV1575 ) @ ( number_number_of_nat @ SV1635 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6503]) ).
thf(6696,plain,
! [SV1576: int] :
( ( ( ord_less_eq_int @ SV1576 @ pls )
= $false )
| ( ( ! [SY2665: int] : ( ord_less_eq_nat @ ( number_number_of_nat @ SV1576 ) @ ( number_number_of_nat @ SY2665 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6504]) ).
thf(6697,plain,
! [SV457: int,SV983: int,SV793: int,SV1636: int,SV1577: int] :
( ( ( ~ ( dvd_dvd_int @ SV1577 @ SV1636 ) )
= $true )
| ( ( ~ ( dvd_dvd_int @ SV1577 @ ( plus_plus_int @ SV793 @ SV983 ) )
| ( dvd_dvd_int @ SV1577 @ ( plus_plus_int @ ( plus_plus_int @ SV793 @ ( times_times_int @ SV457 @ SV1636 ) ) @ SV983 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6508]) ).
thf(6698,plain,
! [SV983: int,SV457: int,SV793: int,SV1637: int,SV1578: int] :
( ( ( ~ ( dvd_dvd_int @ SV1578 @ SV1637 ) )
= $true )
| ( ( ~ ( dvd_dvd_int @ SV1578 @ ( plus_plus_int @ ( plus_plus_int @ SV793 @ ( times_times_int @ SV457 @ SV1637 ) ) @ SV983 ) )
| ( dvd_dvd_int @ SV1578 @ ( plus_plus_int @ SV793 @ SV983 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6509]) ).
thf(6699,plain,
! [SV1638: int,SV1480: int,SV458: int,SV1413: int] :
( ( ( SV1413
= ( plus_plus_int @ SV458 @ ( times_times_int @ SV1480 @ SV1638 ) ) )
= $false )
| ( ( zcong @ SV458 @ SV1413 @ SV1480 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6510]) ).
thf(6700,plain,
! [SV1415: nat,SV459: nat,SV1482: nat] :
( ( ( ( power_power_nat @ SV1482 @ SV459 )
!= ( power_power_nat @ SV1482 @ SV1415 ) )
= $true )
| ( ( SV459 = SV1415 )
= $true )
| ( ( ord_less_nat @ one_one_nat @ SV1482 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6512]) ).
thf(6701,plain,
! [SV1483: nat,SV1416: nat,SV459: nat] :
( ( ( SV459 != SV1416 )
= $true )
| ( ( ( power_power_nat @ SV1483 @ SV459 )
= ( power_power_nat @ SV1483 @ SV1416 ) )
= $true )
| ( ( ord_less_nat @ one_one_nat @ SV1483 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6513]) ).
thf(6702,plain,
! [SV1579: real,SV1484: real,SV794: real,SV460: real] :
( ( ( ( plus_plus_real @ ( times_times_real @ SV460 @ SV794 ) @ ( times_times_real @ SV1484 @ SV1579 ) )
= ( plus_plus_real @ ( times_times_real @ SV460 @ SV1579 ) @ ( times_times_real @ SV1484 @ SV794 ) ) )
= $false )
| ( ( ( SV460 = SV1484 )
| ( SV794 = SV1579 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6514]) ).
thf(6703,plain,
! [SV794: real,SV1672: real,SV460: real] :
( ( ( SV460 != SV1672 )
| ! [SY2685: real] :
( ( plus_plus_real @ ( times_times_real @ SV460 @ SV794 ) @ ( times_times_real @ SV1672 @ SY2685 ) )
= ( plus_plus_real @ ( times_times_real @ SV460 @ SY2685 ) @ ( times_times_real @ SV1672 @ SV794 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6515]) ).
thf(6704,plain,
! [SV1673: real,SV460: real,SV794: real] :
( ( ! [SY2686: real] :
( ( SV794 != SY2686 )
| ( ( plus_plus_real @ ( times_times_real @ SV460 @ SV794 ) @ ( times_times_real @ SV1673 @ SY2686 ) )
= ( plus_plus_real @ ( times_times_real @ SV460 @ SY2686 ) @ ( times_times_real @ SV1673 @ SV794 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6516]) ).
thf(6705,plain,
! [SV1485: nat,SV461: nat,SV1417: nat] :
( ( ( SV1417 = zero_zero_nat )
= $true )
| ( ( dvd_dvd_nat @ SV461 @ SV1485 )
= $true )
| ( ( dvd_dvd_nat @ ( times_times_nat @ SV461 @ SV1417 ) @ ( times_times_nat @ SV1485 @ SV1417 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6517]) ).
thf(6706,plain,
! [SV461: nat,SV1639: nat] :
( ( ( SV1639 != zero_zero_nat )
= $true )
| ( ( ! [SY2676: nat] : ( dvd_dvd_nat @ ( times_times_nat @ SV461 @ SV1639 ) @ ( times_times_nat @ SY2676 @ SV1639 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6518]) ).
thf(6707,plain,
! [SV1640: nat,SV1674: nat,SV461: nat] :
( ( ~ ( dvd_dvd_nat @ SV461 @ SV1674 )
| ( dvd_dvd_nat @ ( times_times_nat @ SV461 @ SV1640 ) @ ( times_times_nat @ SV1674 @ SV1640 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6519]) ).
thf(6708,plain,
! [SV1641: nat,SV1580: nat] :
( ( ( ( power_power_nat @ SV1580 @ SV1641 )
!= zero_zero_nat )
= $true )
| ( ( SV1641 != zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6521]) ).
thf(6709,plain,
! [SV1675: nat,SV1581: nat] :
( ( ( ( power_power_nat @ SV1581 @ SV1675 )
!= zero_zero_nat )
= $true )
| ( ( SV1581 = zero_zero_nat )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6522]) ).
thf(6710,plain,
! [SV1435: nat,SV462: nat,SV1486: real] :
( ( ( ( power_power_real @ SV1486 @ SV462 )
!= ( power_power_real @ SV1486 @ SV1435 ) )
= $true )
| ( ( SV462 = SV1435 )
= $true )
| ( ( ord_less_real @ one_one_real @ SV1486 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6524]) ).
thf(6711,plain,
! [SV1487: real,SV1436: nat,SV462: nat] :
( ( ( SV462 != SV1436 )
= $true )
| ( ( ( power_power_real @ SV1487 @ SV462 )
= ( power_power_real @ SV1487 @ SV1436 ) )
= $true )
| ( ( ord_less_real @ one_one_real @ SV1487 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6525]) ).
thf(6712,plain,
! [SV1583: int,SV1642: int] :
( ( ( ord_less_int @ SV1642 @ pls )
= $true )
| ( ( ~ ( ord_less_int @ SV1583 @ pls )
| ( ( plus_plus_nat @ ( number_number_of_nat @ SV1642 ) @ ( number_number_of_nat @ SV1583 ) )
= ( number_number_of_nat @ SV1642 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6526]) ).
thf(6713,plain,
! [SV1584: int,SV1643: int] :
( ( ( ord_less_int @ SV1643 @ pls )
= $true )
| ( ( ( ord_less_int @ SV1584 @ pls )
| ( ( plus_plus_nat @ ( number_number_of_nat @ SV1643 ) @ ( number_number_of_nat @ SV1584 ) )
= ( number_number_of_nat @ ( plus_plus_int @ SV1643 @ SV1584 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6527]) ).
thf(6714,plain,
! [SV1438: real,SV1488: real,SV463: real] :
( ( ( ( times_times_real @ SV463 @ SV1488 )
= ( times_times_real @ SV1438 @ SV1488 ) )
= $false )
| ( ( SV463 = SV1438 )
= $true )
| ( ( SV1488 = zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6528]) ).
thf(6715,plain,
! [SV1489: real,SV1439: real,SV463: real] :
( ( ( SV463 = SV1439 )
= $false )
| ( ( ( times_times_real @ SV463 @ SV1489 )
= ( times_times_real @ SV1439 @ SV1489 ) )
= $true )
| ( ( SV1489 = zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6529]) ).
thf(6716,plain,
! [SV1440: real,SV1490: real,SV464: real] :
( ( ( ~ ( ord_less_real @ ( times_times_real @ SV464 @ SV1490 ) @ ( times_times_real @ SV1440 @ SV1490 ) ) )
= $true )
| ( ( ord_less_real @ SV464 @ SV1440 )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV1490 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6530]) ).
thf(6717,plain,
! [SV1491: real,SV1441: real,SV464: real] :
( ( ( ~ ( ord_less_real @ SV464 @ SV1441 ) )
= $true )
| ( ( ord_less_real @ ( times_times_real @ SV464 @ SV1491 ) @ ( times_times_real @ SV1441 @ SV1491 ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV1491 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6531]) ).
thf(6718,plain,
! [SV1442: real,SV465: real,SV1492: real] :
( ( ( ~ ( ord_less_eq_real @ ( times_times_real @ SV1492 @ SV465 ) @ ( times_times_real @ SV1492 @ SV1442 ) ) )
= $true )
| ( ( ord_less_eq_real @ SV465 @ SV1442 )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV1492 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6532]) ).
thf(6719,plain,
! [SV1493: real,SV1443: real,SV465: real] :
( ( ( ~ ( ord_less_eq_real @ SV465 @ SV1443 ) )
= $true )
| ( ( ord_less_eq_real @ ( times_times_real @ SV1493 @ SV465 ) @ ( times_times_real @ SV1493 @ SV1443 ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV1493 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6533]) ).
thf(6720,plain,
! [SV1257: int,SV1446: int] :
( ( ( SV1446 = zero_zero_int )
= $false )
| ( ( SV1257 = zero_zero_int )
= $false )
| ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SV1257 @ SV1257 ) @ ( times_times_int @ SV1446 @ SV1446 ) ) @ zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6534]) ).
thf(6721,plain,
! [SV1676: int,SV1585: int] :
( ( ( ~ ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SV1585 @ SV1585 ) @ ( times_times_int @ SV1676 @ SV1676 ) ) @ zero_zero_int ) )
= $true )
| ( ( SV1585 = zero_zero_int )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6535]) ).
thf(6722,plain,
! [SV1644: int,SV1586: int] :
( ( ( ~ ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SV1586 @ SV1586 ) @ ( times_times_int @ SV1644 @ SV1644 ) ) @ zero_zero_int ) )
= $true )
| ( ( SV1644 = zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6536]) ).
thf(6723,plain,
! [SV1645: nat,SV1587: int] :
( ( ( ( power_power_int @ SV1587 @ SV1645 )
!= zero_zero_int )
= $true )
| ( ( SV1645 != zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6538]) ).
thf(6724,plain,
! [SV1677: nat,SV1588: int] :
( ( ( ( power_power_int @ SV1588 @ SV1677 )
!= zero_zero_int )
= $true )
| ( ( SV1588 = zero_zero_int )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6539]) ).
thf(6725,plain,
! [SV1456: nat,SV467: nat,SV1496: int] :
( ( ( ( power_power_int @ SV1496 @ SV467 )
!= ( power_power_int @ SV1496 @ SV1456 ) )
= $true )
| ( ( SV467 = SV1456 )
= $true )
| ( ( ord_less_int @ one_one_int @ SV1496 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6543]) ).
thf(6726,plain,
! [SV1497: int,SV1457: nat,SV467: nat] :
( ( ( SV467 != SV1457 )
= $true )
| ( ( ( power_power_int @ SV1497 @ SV467 )
= ( power_power_int @ SV1497 @ SV1457 ) )
= $true )
| ( ( ord_less_int @ one_one_int @ SV1497 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6544]) ).
thf(6727,plain,
! [SV518: int,SV96: int] :
( ( ( dvd_dvd_int @ SV96 @ SV518 )
= $false )
| ( ( SV518 = SV96 )
= $true )
| ( ( dvd_dvd_int @ SV518 @ SV96 )
= $false )
| ( ( ord_less_eq_int @ zero_zero_int @ SV96 )
= $false )
| ( ( ord_less_eq_int @ zero_zero_int @ SV518 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6547]) ).
thf(6728,plain,
! [SV536: int,SV986: int,SV125: int,SV1279: int,SV827: int] :
( ( ( ( plus_plus_int @ SV827 @ ( times_times_int @ SV1279 @ SV125 ) )
= ( plus_plus_int @ SV986 @ ( times_times_int @ SV1279 @ SV536 ) ) )
= $false )
| ( ( SV125 = SV536 )
= $true )
| ( ( SV827 = SV986 )
= $false )
| ( ( SV1279 = zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6548]) ).
thf(6729,plain,
! [SV987: int,SV545: int,SV1280: int,SV135: int,SV830: int] :
( ( ( ~ ( ord_less_int @ SV830 @ SV135 ) )
= $true )
| ( ( ~ ( ord_less_int @ SV1280 @ SV135 )
| ( ord_less_eq_int @ SV545 @ SV987 ) )
= $true )
| ( ( ord_less_eq_int @ zero_zero_int @ SV830 )
= $false )
| ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SV135 @ SV545 ) @ SV830 ) @ ( plus_plus_int @ ( times_times_int @ SV135 @ SV987 ) @ SV1280 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6551]) ).
thf(6730,plain,
! [SV546: int,SV136: int,SV831: int,SV1458: int,SV1281: int,SV988: int] :
( ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ SV988 @ SV1281 ) @ SV1458 ) )
= $false )
| ( ( ~ ( ord_less_int @ SV1458 @ SV988 )
| ~ ( ord_less_eq_int @ zero_zero_int @ SV831 )
| ~ ( ord_less_int @ zero_zero_int @ SV988 )
| ~ ( ord_less_eq_int @ SV988 @ SV136 )
| ( ord_less_eq_int @ SV546 @ SV1281 ) )
= $true )
| ( ( ( plus_plus_int @ ( times_times_int @ SV136 @ SV546 ) @ SV831 )
= ( plus_plus_int @ ( times_times_int @ SV988 @ SV1281 ) @ SV1458 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6552]) ).
thf(6731,plain,
! [SV547: int,SV989: int,SV832: int,SV1282: int,SV137: int] :
( ( ( ~ ( ord_less_int @ SV137 @ SV1282 ) )
= $true )
| ( ( ~ ( ord_less_int @ SV137 @ SV832 )
| ( ord_less_eq_int @ SV989 @ SV547 ) )
= $true )
| ( ( ord_less_eq_int @ SV1282 @ zero_zero_int )
= $false )
| ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SV137 @ SV547 ) @ SV832 ) @ ( plus_plus_int @ ( times_times_int @ SV137 @ SV989 ) @ SV1282 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6553]) ).
thf(6732,plain,
! [SV548: int,SV138: int,SV833: int,SV1459: int,SV1283: int,SV990: int] :
( ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ SV990 @ SV1283 ) @ SV1459 ) @ zero_zero_int )
= $false )
| ( ( ~ ( ord_less_int @ SV833 @ SV138 )
| ~ ( ord_less_eq_int @ zero_zero_int @ SV1459 )
| ~ ( ord_less_int @ zero_zero_int @ SV990 )
| ~ ( ord_less_eq_int @ SV990 @ SV138 )
| ( ord_less_eq_int @ SV1283 @ SV548 ) )
= $true )
| ( ( ( plus_plus_int @ ( times_times_int @ SV138 @ SV548 ) @ SV833 )
= ( plus_plus_int @ ( times_times_int @ SV990 @ SV1283 ) @ SV1459 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6554]) ).
thf(6733,plain,
! [SV554: int,SV837: int,SV150: int] :
( ( ( ~ ( ord_less_int @ SV150 @ SV837 ) )
= $true )
| ( ( ~ ( zcong @ SV837 @ SV150 @ SV554 ) )
= $true )
| ( ( ord_less_int @ zero_zero_int @ SV150 )
= $false )
| ( ( ord_less_int @ SV837 @ SV554 )
= $false )
| ( ( ord_less_int @ zero_zero_int @ SV837 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6556]) ).
thf(6734,plain,
! [SV838: int,SV556: int,SV152: int] :
( ( ( ~ ( ord_less_int @ SV152 @ SV556 ) )
= $true )
| ( ( ~ ( zcong @ SV838 @ SV152 @ SV556 )
| ( SV838 = SV152 ) )
= $true )
| ( ( ord_less_eq_int @ zero_zero_int @ SV152 )
= $false )
| ( ( ord_less_int @ SV838 @ SV556 )
= $false )
| ( ( ord_less_eq_int @ zero_zero_int @ SV838 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6557]) ).
thf(6735,plain,
! [SV170: int,SV568: int,SV845: int] :
( ( ( ~ ( zcong @ SV845 @ SV568 @ SV170 ) )
= $true )
| ( ( ~ ( ord_less_int @ SV845 @ SV170 )
| ~ ( ord_less_int @ SV568 @ SV170 )
| ( SV845 = SV568 ) )
= $true )
| ( ( ord_less_int @ zero_zero_int @ SV170 )
= $false )
| ( ( ord_less_int @ zero_zero_int @ SV568 )
= $false )
| ( ( ord_less_int @ zero_zero_int @ SV845 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6558]) ).
thf(6736,plain,
! [SV678: real,SV1013: real,SV316: real,SV1286: real,SV913: real] :
( ( ( ( plus_plus_real @ SV913 @ ( times_times_real @ SV1286 @ SV316 ) )
= ( plus_plus_real @ SV1013 @ ( times_times_real @ SV1286 @ SV678 ) ) )
= $false )
| ( ( SV316 = SV678 )
= $true )
| ( ( SV913 = SV1013 )
= $false )
| ( ( SV1286 = zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6562]) ).
thf(6737,plain,
! [SV679: nat,SV1014: nat,SV317: nat,SV1287: nat,SV914: nat] :
( ( ( ( plus_plus_nat @ SV914 @ ( times_times_nat @ SV1287 @ SV317 ) )
= ( plus_plus_nat @ SV1014 @ ( times_times_nat @ SV1287 @ SV679 ) ) )
= $false )
| ( ( SV317 = SV679 )
= $true )
| ( ( SV914 = SV1014 )
= $false )
| ( ( SV1287 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6563]) ).
thf(6738,plain,
! [SV337: int,SV921: int,SV692: int] :
( ( ( dvd_dvd_int @ SV692 @ SV921 )
= $true )
| ( ( dvd_dvd_int @ SV692 @ SV337 )
= $true )
| ( ( dvd_dvd_int @ SV692 @ ( times_times_int @ SV921 @ SV337 ) )
= $false )
| ( ( zprime @ SV692 )
= $false )
| ( ( ord_less_eq_int @ zero_zero_int @ SV921 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6565]) ).
thf(6739,plain,
! [SV1020: int,SV932: int,SV1290: int,SV351: int,SV706: int] :
( ( ( ~ ( zcong @ SV706 @ SV351 @ SV1290 ) )
= $true )
| ( ( zcong @ SV932 @ SV351 @ SV1290 )
= $true )
| ( ( SV1020 = SV706 )
= $false )
| ( ( zcong @ SV932 @ SV1020 @ SV1290 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6567]) ).
thf(6740,plain,
! [SV707: int,SV352: int] :
( ( ( zcong @ ( times_times_int @ SV352 @ SV352 ) @ one_one_int @ SV707 )
= $false )
| ( ( ( SV352 = one_one_int )
| ( SV352
= ( minus_minus_int @ SV707 @ one_one_int ) ) )
= $true )
| ( ( ord_less_int @ SV352 @ SV707 )
= $false )
| ( ( ord_less_int @ zero_zero_int @ SV352 )
= $false )
| ( ( zprime @ SV707 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6568]) ).
thf(6741,plain,
! [SV936: int,SV361: int,SV716: int] :
( ( ( zcong @ ( times_times_int @ SV716 @ SV361 ) @ zero_zero_int @ SV936 )
= $false )
| ( ( zcong @ SV361 @ zero_zero_int @ SV936 )
= $true )
| ( ( zcong @ SV716 @ zero_zero_int @ SV936 )
= $true )
| ( ( ord_less_int @ zero_zero_int @ SV716 )
= $false )
| ( ( zprime @ SV936 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6570]) ).
thf(6742,plain,
! [SV362: int,SV937: int,SV717: int] :
( ( ( zcong @ SV717 @ zero_zero_int @ SV937 )
= $true )
| ( ( zcong @ SV362 @ zero_zero_int @ SV937 )
= $true )
| ( ( zcong @ ( times_times_int @ SV717 @ SV362 ) @ zero_zero_int @ SV937 )
= $false )
| ( ( ord_less_int @ zero_zero_int @ SV717 )
= $false )
| ( ( zprime @ SV937 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6571]) ).
thf(6743,plain,
! [SV782: nat,SV438: nat,SV979: nat,SV1027: nat] :
( ( ( ord_less_nat @ SV1027 @ SV979 )
= $false )
| ( ( ~ ( dvd_dvd_nat @ SV979 @ SV438 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV1027 )
= $false )
| ( ( SV438
= ( plus_plus_nat @ ( times_times_nat @ SV782 @ SV979 ) @ SV1027 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6576]) ).
thf(6744,plain,
! [SV1589: nat,SV1499: nat] :
( ( ( ( power_power_nat @ SV1499 @ SV1589 )
= zero_zero_nat )
= $false )
| ( ( SV1589 != zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6577]) ).
thf(6745,plain,
! [SV1646: nat,SV1500: nat] :
( ( ( ( power_power_nat @ SV1500 @ SV1646 )
= zero_zero_nat )
= $false )
| ( ( SV1500 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6578]) ).
thf(6746,plain,
! [SV1590: int,SV1501: nat] :
( ( ( ( power_power_nat @ SV1501 @ ( number_number_of_nat @ SV1590 ) )
= zero_zero_nat )
= $false )
| ( ( ( number_number_of_nat @ SV1590 )
!= zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6579]) ).
thf(6747,plain,
! [SV1647: int,SV1502: nat] :
( ( ( ( power_power_nat @ SV1502 @ ( number_number_of_nat @ SV1647 ) )
= zero_zero_nat )
= $false )
| ( ( SV1502 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6580]) ).
thf(6748,plain,
! [SV1034: real,SV1293: real] :
( ( ( SV1293 = zero_zero_real )
= $false )
| ( ( SV1034 = zero_zero_real )
= $false )
| ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ SV1034 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SV1293 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6581]) ).
thf(6749,plain,
! [SV1678: nat,SV1505: nat] :
( ( ( ( power_power_nat @ SV1505 @ SV1678 )
= one_one_nat )
= $true )
| ( ( SV1505 = one_one_nat )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6584]) ).
thf(6750,plain,
! [SV1506: nat,SV1592: nat] :
( ( ( SV1592 = zero_zero_nat )
= $false )
| ( ( ( power_power_nat @ SV1506 @ SV1592 )
= one_one_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6585]) ).
thf(6751,plain,
! [SV1649: real,SV1507: real] :
( ( ( ord_less_eq_real @ ( plus_plus_real @ ( power_power_real @ SV1507 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SV1649 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_real )
= $false )
| ( ( SV1507 = zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6587]) ).
thf(6752,plain,
! [SV1593: real,SV1508: real] :
( ( ( ord_less_eq_real @ ( plus_plus_real @ ( power_power_real @ SV1508 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SV1593 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_real )
= $false )
| ( ( SV1593 = zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6588]) ).
thf(6753,plain,
! [SV1594: int,SV1509: int] :
( ( ( SV1509 = SV1594 )
= $false )
| ( ( ord_less_int @ SV1509 @ ( plus_plus_int @ SV1594 @ one_one_int ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6589]) ).
thf(6754,plain,
! [SV1595: int,SV1510: int] :
( ( ( ord_less_int @ SV1510 @ SV1595 )
= $false )
| ( ( ord_less_int @ SV1510 @ ( plus_plus_int @ SV1595 @ one_one_int ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6590]) ).
thf(6755,plain,
! [SV785: nat,SV1679: nat,SV441: nat,SV1650: nat] :
( ( ( ( plus_plus_nat @ ( times_times_nat @ SV1650 @ SV441 ) @ ( times_times_nat @ SV1679 @ SV785 ) )
= ( plus_plus_nat @ ( times_times_nat @ SV1650 @ SV785 ) @ ( times_times_nat @ SV1679 @ SV441 ) ) )
| ( SV1650 != SV1679 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6591]) ).
thf(6756,plain,
! [SV785: nat,SV441: nat,SV1680: nat] :
( ( ( ! [SY2687: nat] :
( ( plus_plus_nat @ ( times_times_nat @ SV1680 @ SV441 ) @ ( times_times_nat @ SY2687 @ SV785 ) )
= ( plus_plus_nat @ ( times_times_nat @ SV1680 @ SV785 ) @ ( times_times_nat @ SY2687 @ SV441 ) ) ) )
= $true )
| ( ( SV441 != SV785 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6592]) ).
thf(6757,plain,
! [SV785: nat,SV1511: nat,SV441: nat,SV1461: nat] :
( ( ( ( plus_plus_nat @ ( times_times_nat @ SV1461 @ SV441 ) @ ( times_times_nat @ SV1511 @ SV785 ) )
= ( plus_plus_nat @ ( times_times_nat @ SV1461 @ SV785 ) @ ( times_times_nat @ SV1511 @ SV441 ) ) )
= $false )
| ( ( SV441 = SV785 )
= $true )
| ( ( SV1461 = SV1511 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6593]) ).
thf(6758,plain,
! [SV1596: int,SV1512: real] :
( ( ( ( power_power_real @ SV1512 @ ( number_number_of_nat @ SV1596 ) )
= zero_zero_real )
= $false )
| ( ( ( number_number_of_nat @ SV1596 )
!= zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6594]) ).
thf(6759,plain,
! [SV1651: int,SV1513: real] :
( ( ( ( power_power_real @ SV1513 @ ( number_number_of_nat @ SV1651 ) )
= zero_zero_real )
= $false )
| ( ( SV1513 = zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6595]) ).
thf(6760,plain,
! [SV1065: real,SV1312: real] :
( ( ( SV1312 = zero_zero_real )
= $false )
| ( ( SV1065 = zero_zero_real )
= $false )
| ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ SV1065 @ SV1065 ) @ ( times_times_real @ SV1312 @ SV1312 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6596]) ).
thf(6761,plain,
! [SV1516: nat,SV1598: nat] :
( ( ( SV1598 = zero_zero_nat )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV1516 @ SV1598 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6599]) ).
thf(6762,plain,
! [SV1681: nat,SV1517: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV1517 @ SV1681 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV1517 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6600]) ).
thf(6763,plain,
! [SV786: real,SV1682: real,SV442: real,SV1653: real] :
( ( ( ( plus_plus_real @ ( times_times_real @ SV1653 @ SV442 ) @ ( times_times_real @ SV1682 @ SV786 ) )
= ( plus_plus_real @ ( times_times_real @ SV1653 @ SV786 ) @ ( times_times_real @ SV1682 @ SV442 ) ) )
| ( SV1653 != SV1682 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6601]) ).
thf(6764,plain,
! [SV786: real,SV442: real,SV1683: real] :
( ( ( ! [SY2688: real] :
( ( plus_plus_real @ ( times_times_real @ SV1683 @ SV442 ) @ ( times_times_real @ SY2688 @ SV786 ) )
= ( plus_plus_real @ ( times_times_real @ SV1683 @ SV786 ) @ ( times_times_real @ SY2688 @ SV442 ) ) ) )
= $true )
| ( ( SV442 != SV786 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6602]) ).
thf(6765,plain,
! [SV786: real,SV1518: real,SV442: real,SV1462: real] :
( ( ( ( plus_plus_real @ ( times_times_real @ SV1462 @ SV442 ) @ ( times_times_real @ SV1518 @ SV786 ) )
= ( plus_plus_real @ ( times_times_real @ SV1462 @ SV786 ) @ ( times_times_real @ SV1518 @ SV442 ) ) )
= $false )
| ( ( SV442 = SV786 )
= $true )
| ( ( SV1462 = SV1518 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6603]) ).
thf(6766,plain,
! [SV1599: real,SV1519: real] :
( ( ( SV1519 = SV1599 )
= $false )
| ( ( ord_less_eq_real @ SV1519 @ SV1599 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6604]) ).
thf(6767,plain,
! [SV1600: real,SV1520: real] :
( ( ( ord_less_real @ SV1520 @ SV1600 )
= $false )
| ( ( ord_less_eq_real @ SV1520 @ SV1600 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6605]) ).
thf(6768,plain,
! [SV1074: int,SV1315: int] :
( ( ( SV1315 = zero_zero_int )
= $false )
| ( ( SV1074 = zero_zero_int )
= $false )
| ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ SV1074 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV1315 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6606]) ).
thf(6769,plain,
! [SV1655: real,SV1523: real] :
( ( ( ( plus_plus_real @ ( power_power_real @ SV1523 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SV1655 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_real )
= $false )
| ( ( SV1523 = zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6610]) ).
thf(6770,plain,
! [SV1602: real,SV1524: real] :
( ( ( ( plus_plus_real @ ( power_power_real @ SV1524 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SV1602 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_real )
= $false )
| ( ( SV1602 = zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6611]) ).
thf(6771,plain,
! [SV1325: nat,SV443: nat,SV1463: int] :
( ( ( ord_less_int @ ( power_power_int @ SV1463 @ SV443 ) @ ( power_power_int @ SV1463 @ SV1325 ) )
= $false )
| ( ( ord_less_nat @ SV443 @ SV1325 )
= $true )
| ( ( ord_less_int @ one_one_int @ SV1463 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6612]) ).
thf(6772,plain,
! [SV1464: int,SV1326: nat,SV443: nat] :
( ( ( ord_less_nat @ SV443 @ SV1326 )
= $false )
| ( ( ord_less_int @ ( power_power_int @ SV1464 @ SV443 ) @ ( power_power_int @ SV1464 @ SV1326 ) )
= $true )
| ( ( ord_less_int @ one_one_int @ SV1464 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6613]) ).
thf(6773,plain,
! [SV1604: int,SV1526: int] :
( ( ( ( power_power_int @ SV1526 @ ( number_number_of_nat @ SV1604 ) )
= zero_zero_int )
= $false )
| ( ( ( number_number_of_nat @ SV1604 )
!= zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6614]) ).
thf(6774,plain,
! [SV1656: int,SV1527: int] :
( ( ( ( power_power_int @ SV1527 @ ( number_number_of_nat @ SV1656 ) )
= zero_zero_int )
= $false )
| ( ( SV1527 = zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6615]) ).
thf(6775,plain,
! [SV1657: real,SV1528: real] :
( ( ( ( plus_plus_real @ ( power_power_real @ SV1528 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SV1657 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_real )
= $false )
| ( ( SV1528 = zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6617]) ).
thf(6776,plain,
! [SV1605: real,SV1529: real] :
( ( ( ( plus_plus_real @ ( power_power_real @ SV1529 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ SV1605 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_real )
= $false )
| ( ( SV1605 = zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6618]) ).
thf(6777,plain,
! [SV1658: int,SV1530: int] :
( ( ( ( plus_plus_int @ ( power_power_int @ SV1530 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV1658 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_int )
= $false )
| ( ( SV1530 = zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6620]) ).
thf(6778,plain,
! [SV1606: int,SV1531: int] :
( ( ( ( plus_plus_int @ ( power_power_int @ SV1531 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV1606 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_int )
= $false )
| ( ( SV1606 = zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6621]) ).
thf(6779,plain,
! [SV1350: real,SV1465: real,SV445: real] :
( ( ( ord_less_eq_real @ ( times_times_real @ SV445 @ SV1465 ) @ ( times_times_real @ SV1350 @ SV1465 ) )
= $false )
| ( ( ord_less_eq_real @ SV445 @ SV1350 )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV1465 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6622]) ).
thf(6780,plain,
! [SV1466: real,SV1351: real,SV445: real] :
( ( ( ord_less_eq_real @ SV445 @ SV1351 )
= $false )
| ( ( ord_less_eq_real @ ( times_times_real @ SV445 @ SV1466 ) @ ( times_times_real @ SV1351 @ SV1466 ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV1466 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6623]) ).
thf(6781,plain,
! [SV1659: real,SV1532: real] :
( ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ SV1532 @ SV1532 ) @ ( times_times_real @ SV1659 @ SV1659 ) ) @ zero_zero_real )
= $false )
| ( ( SV1532 = zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6625]) ).
thf(6782,plain,
! [SV1607: real,SV1533: real] :
( ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ SV1533 @ SV1533 ) @ ( times_times_real @ SV1607 @ SV1607 ) ) @ zero_zero_real )
= $false )
| ( ( SV1607 = zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6626]) ).
thf(6783,plain,
! [SV1660: int,SV1534: int] :
( ( ( ord_less_eq_int @ ( plus_plus_int @ ( power_power_int @ SV1534 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV1660 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_int )
= $false )
| ( ( SV1534 = zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6628]) ).
thf(6784,plain,
! [SV1608: int,SV1535: int] :
( ( ( ord_less_eq_int @ ( plus_plus_int @ ( power_power_int @ SV1535 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV1608 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_int )
= $false )
| ( ( SV1608 = zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6629]) ).
thf(6785,plain,
! [SV1661: int,SV1536: int] :
( ( ( ( plus_plus_int @ ( times_times_int @ SV1536 @ SV1536 ) @ ( times_times_int @ SV1661 @ SV1661 ) )
= zero_zero_int )
= $false )
| ( ( SV1536 = zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6631]) ).
thf(6786,plain,
! [SV1609: int,SV1537: int] :
( ( ( ( plus_plus_int @ ( times_times_int @ SV1537 @ SV1537 ) @ ( times_times_int @ SV1609 @ SV1609 ) )
= zero_zero_int )
= $false )
| ( ( SV1609 = zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6632]) ).
thf(6787,plain,
! [SV1610: int,SV1538: int] :
( ( ( ord_less_int @ SV1538 @ SV1610 )
= $false )
| ( ( SV1538 != SV1610 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6633]) ).
thf(6788,plain,
! [SV1611: int,SV1539: int] :
( ( ( ord_less_int @ SV1539 @ SV1611 )
= $false )
| ( ( ord_less_eq_int @ SV1539 @ SV1611 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6634]) ).
thf(6789,plain,
! [SV1358: nat,SV446: nat,SV1467: nat] :
( ( ( ord_less_nat @ ( power_power_nat @ SV1467 @ SV446 ) @ ( power_power_nat @ SV1467 @ SV1358 ) )
= $false )
| ( ( ord_less_nat @ SV446 @ SV1358 )
= $true )
| ( ( ord_less_nat @ one_one_nat @ SV1467 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6635]) ).
thf(6790,plain,
! [SV1468: nat,SV1359: nat,SV446: nat] :
( ( ( ord_less_nat @ SV446 @ SV1359 )
= $false )
| ( ( ord_less_nat @ ( power_power_nat @ SV1468 @ SV446 ) @ ( power_power_nat @ SV1468 @ SV1359 ) )
= $true )
| ( ( ord_less_nat @ one_one_nat @ SV1468 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6636]) ).
thf(6791,plain,
! [SV1662: nat,SV1540: nat] :
( ( ( ( times_times_nat @ SV1540 @ SV1662 )
= one_one_nat )
= $false )
| ( ( SV1540 = one_one_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6638]) ).
thf(6792,plain,
! [SV1612: nat,SV1541: nat] :
( ( ( ( times_times_nat @ SV1541 @ SV1612 )
= one_one_nat )
= $false )
| ( ( SV1612 = one_one_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6639]) ).
thf(6793,plain,
! [SV1684: int] :
( ( ! [SY2689: int] :
( ( times_times_int @ SV1684 @ SY2689 )
!= one_one_int )
| ( SV1684 = one_one_int )
| ( SV1684
= ( number_number_of_int @ min ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6640]) ).
thf(6794,plain,
! [SV1685: int] :
( ( ! [SY2690: int] :
( ( ( times_times_int @ SV1685 @ SY2690 )
!= one_one_int )
| ( SV1685 = one_one_int )
| ( SY2690
= ( number_number_of_int @ min ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6641]) ).
thf(6795,plain,
! [SV1686: int] :
( ( ! [SY2691: int] :
( ( ( times_times_int @ SV1686 @ SY2691 )
!= one_one_int )
| ( SY2691 = one_one_int )
| ( SV1686
= ( number_number_of_int @ min ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6642]) ).
thf(6796,plain,
! [SV1687: int] :
( ( ! [SY2692: int] :
( ( ( times_times_int @ SV1687 @ SY2692 )
!= one_one_int )
| ( SY2692 = one_one_int )
| ( SY2692
= ( number_number_of_int @ min ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6643]) ).
thf(6797,plain,
! [SV1613: int,SV1542: int] :
( ( ( SV1542 != one_one_int )
= $true )
| ( ( SV1613 != one_one_int )
= $true )
| ( ( ( times_times_int @ SV1542 @ SV1613 )
= one_one_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6644]) ).
thf(6798,plain,
! [SV1614: int,SV1543: int] :
( ( ( SV1543
!= ( number_number_of_int @ min ) )
= $true )
| ( ( SV1614
!= ( number_number_of_int @ min ) )
= $true )
| ( ( ( times_times_int @ SV1543 @ SV1614 )
= one_one_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6645]) ).
thf(6799,plain,
! [SV1663: real,SV1544: real] :
( ( ( ( plus_plus_real @ ( times_times_real @ SV1544 @ SV1544 ) @ ( times_times_real @ SV1663 @ SV1663 ) )
= zero_zero_real )
= $false )
| ( ( SV1544 = zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6647]) ).
thf(6800,plain,
! [SV1615: real,SV1545: real] :
( ( ( ( plus_plus_real @ ( times_times_real @ SV1545 @ SV1545 ) @ ( times_times_real @ SV1615 @ SV1615 ) )
= zero_zero_real )
= $false )
| ( ( SV1615 = zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6648]) ).
thf(6801,plain,
! [SV1469: real,SV1366: nat,SV447: nat] :
( ( ( ord_less_nat @ SV447 @ SV1366 )
= $false )
| ( ( ord_less_real @ ( power_power_real @ SV1469 @ SV447 ) @ ( power_power_real @ SV1469 @ SV1366 ) )
= $true )
| ( ( ord_less_real @ one_one_real @ SV1469 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6649]) ).
thf(6802,plain,
! [SV1367: nat,SV447: nat,SV1470: real] :
( ( ( ord_less_real @ ( power_power_real @ SV1470 @ SV447 ) @ ( power_power_real @ SV1470 @ SV1367 ) )
= $false )
| ( ( ord_less_nat @ SV447 @ SV1367 )
= $true )
| ( ( ord_less_real @ one_one_real @ SV1470 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6650]) ).
thf(6803,plain,
! [SV1149: int,SV1368: int] :
( ( ( SV1368 = zero_zero_int )
= $false )
| ( ( SV1149 = zero_zero_int )
= $false )
| ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ SV1149 @ SV1149 ) @ ( times_times_int @ SV1368 @ SV1368 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6651]) ).
thf(6804,plain,
! [SV1617: int,SV1548: int] :
( ( ( ord_less_int @ SV1548 @ SV1617 )
= $true )
| ( ( ~ ( ord_less_int @ SV1548 @ SV1617 ) )
= $true )
| ( ( ord_less_nat @ ( number_number_of_nat @ SV1548 ) @ ( number_number_of_nat @ SV1617 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6656]) ).
thf(6805,plain,
! [SV1549: int,SV1618: int] :
( ( ( ~ ( ord_less_int @ pls @ SV1618 ) )
= $true )
| ( ( ~ ( ord_less_int @ SV1549 @ SV1618 ) )
= $true )
| ( ( ord_less_nat @ ( number_number_of_nat @ SV1549 ) @ ( number_number_of_nat @ SV1618 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6657]) ).
thf(6806,plain,
! [SV1619: int,SV1550: int] :
( ( ( ord_less_nat @ ( number_number_of_nat @ SV1550 ) @ ( number_number_of_nat @ SV1619 ) )
= $false )
| ( ( ~ ( ord_less_int @ SV1550 @ SV1619 )
| ( ord_less_int @ pls @ SV1619 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6658]) ).
thf(6807,plain,
! [SV1620: int,SV1551: int] :
( ( ( ord_less_nat @ ( number_number_of_nat @ SV1551 ) @ ( number_number_of_nat @ SV1620 ) )
= $false )
| ( ( ord_less_int @ SV1551 @ SV1620 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6659]) ).
thf(6808,plain,
! [SV787: int,SV449: int,SV1621: int,SV1552: int,SV981: int] :
( ( ( zcong @ SV981 @ SV1552 @ SV1621 )
= $false )
| ( ( ~ ( zcong @ SV449 @ ( times_times_int @ SV981 @ SV787 ) @ SV1621 )
| ( zcong @ SV449 @ ( times_times_int @ SV1552 @ SV787 ) @ SV1621 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6660]) ).
thf(6809,plain,
! [SV787: int,SV449: int,SV1622: int,SV1553: int,SV981: int] :
( ( ( zcong @ SV981 @ SV1553 @ SV1622 )
= $false )
| ( ( ~ ( zcong @ SV449 @ ( times_times_int @ SV1553 @ SV787 ) @ SV1622 )
| ( zcong @ SV449 @ ( times_times_int @ SV981 @ SV787 ) @ SV1622 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6661]) ).
thf(6810,plain,
! [SV788: int,SV1688: int,SV450: int,SV1665: int] :
( ( ( ( plus_plus_int @ ( times_times_int @ SV1665 @ SV450 ) @ ( times_times_int @ SV1688 @ SV788 ) )
= ( plus_plus_int @ ( times_times_int @ SV1665 @ SV788 ) @ ( times_times_int @ SV1688 @ SV450 ) ) )
| ( SV1665 != SV1688 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6662]) ).
thf(6811,plain,
! [SV788: int,SV450: int,SV1689: int] :
( ( ( ! [SY2693: int] :
( ( plus_plus_int @ ( times_times_int @ SV1689 @ SV450 ) @ ( times_times_int @ SY2693 @ SV788 ) )
= ( plus_plus_int @ ( times_times_int @ SV1689 @ SV788 ) @ ( times_times_int @ SY2693 @ SV450 ) ) ) )
= $true )
| ( ( SV450 != SV788 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6663]) ).
thf(6812,plain,
! [SV788: int,SV1554: int,SV450: int,SV1473: int] :
( ( ( ( plus_plus_int @ ( times_times_int @ SV1473 @ SV450 ) @ ( times_times_int @ SV1554 @ SV788 ) )
= ( plus_plus_int @ ( times_times_int @ SV1473 @ SV788 ) @ ( times_times_int @ SV1554 @ SV450 ) ) )
= $false )
| ( ( SV450 = SV788 )
= $true )
| ( ( SV1473 = SV1554 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6664]) ).
thf(6813,plain,
! [SV1666: real,SV1555: real] :
( ( ( ( plus_plus_real @ ( times_times_real @ SV1555 @ SV1555 ) @ ( times_times_real @ SV1666 @ SV1666 ) )
= zero_zero_real )
= $false )
| ( ( SV1555 = zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6666]) ).
thf(6814,plain,
! [SV1623: real,SV1556: real] :
( ( ( ( plus_plus_real @ ( times_times_real @ SV1556 @ SV1556 ) @ ( times_times_real @ SV1623 @ SV1623 ) )
= zero_zero_real )
= $false )
| ( ( SV1623 = zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6667]) ).
thf(6815,plain,
! [SV789: int,SV451: int,SV1624: int,SV1557: int,SV982: int] :
( ( ( zcong @ SV982 @ SV1557 @ SV1624 )
= $false )
| ( ( ~ ( zcong @ SV451 @ ( times_times_int @ SV789 @ SV982 ) @ SV1624 )
| ( zcong @ SV451 @ ( times_times_int @ SV789 @ SV1557 ) @ SV1624 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6668]) ).
thf(6816,plain,
! [SV789: int,SV451: int,SV1625: int,SV1558: int,SV982: int] :
( ( ( zcong @ SV982 @ SV1558 @ SV1625 )
= $false )
| ( ( ~ ( zcong @ SV451 @ ( times_times_int @ SV789 @ SV1558 ) @ SV1625 )
| ( zcong @ SV451 @ ( times_times_int @ SV789 @ SV982 ) @ SV1625 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6669]) ).
thf(6817,plain,
! [SV1559: nat,SV790: nat,SV1474: nat,SV452: nat] :
( ( ( SV452 = SV1474 )
= $true )
| ( ( SV790 = SV1559 )
= $true )
| ( ( ( plus_plus_nat @ ( times_times_nat @ SV452 @ SV790 ) @ ( times_times_nat @ SV1474 @ SV1559 ) )
= ( plus_plus_nat @ ( times_times_nat @ SV452 @ SV1559 ) @ ( times_times_nat @ SV1474 @ SV790 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6670]) ).
thf(6818,plain,
! [SV790: nat,SV1667: nat,SV452: nat] :
( ( ( SV452 != SV1667 )
= $true )
| ( ( ! [SY2681: nat] :
( ( plus_plus_nat @ ( times_times_nat @ SV452 @ SV790 ) @ ( times_times_nat @ SV1667 @ SY2681 ) )
= ( plus_plus_nat @ ( times_times_nat @ SV452 @ SY2681 ) @ ( times_times_nat @ SV1667 @ SV790 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6671]) ).
thf(6819,plain,
! [SV1668: nat,SV452: nat,SV1690: nat,SV790: nat] :
( ( ( SV790 != SV1690 )
| ( ( plus_plus_nat @ ( times_times_nat @ SV452 @ SV790 ) @ ( times_times_nat @ SV1668 @ SV1690 ) )
= ( plus_plus_nat @ ( times_times_nat @ SV452 @ SV1690 ) @ ( times_times_nat @ SV1668 @ SV790 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6672]) ).
thf(6820,plain,
! [SV1626: nat,SV1560: real] :
( ( ( ( power_power_real @ SV1560 @ SV1626 )
= zero_zero_real )
= $false )
| ( ( SV1626 != zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6673]) ).
thf(6821,plain,
! [SV1669: nat,SV1561: real] :
( ( ( ( power_power_real @ SV1561 @ SV1669 )
= zero_zero_real )
= $false )
| ( ( SV1561 = zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6674]) ).
thf(6822,plain,
! [SV1562: nat,SV1627: nat] :
( ( ( SV1627 = zero_zero_nat )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV1562 @ SV1627 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6675]) ).
thf(6823,plain,
! [SV1691: nat,SV1563: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV1563 @ SV1691 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV1563 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6676]) ).
thf(6824,plain,
! [SV1564: int,SV791: int,SV1475: int,SV453: int] :
( ( ( SV453 = SV1475 )
= $true )
| ( ( SV791 = SV1564 )
= $true )
| ( ( ( plus_plus_int @ ( times_times_int @ SV453 @ SV791 ) @ ( times_times_int @ SV1475 @ SV1564 ) )
= ( plus_plus_int @ ( times_times_int @ SV453 @ SV1564 ) @ ( times_times_int @ SV1475 @ SV791 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6677]) ).
thf(6825,plain,
! [SV791: int,SV1670: int,SV453: int] :
( ( ( SV453 != SV1670 )
= $true )
| ( ( ! [SY2683: int] :
( ( plus_plus_int @ ( times_times_int @ SV453 @ SV791 ) @ ( times_times_int @ SV1670 @ SY2683 ) )
= ( plus_plus_int @ ( times_times_int @ SV453 @ SY2683 ) @ ( times_times_int @ SV1670 @ SV791 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6678]) ).
thf(6826,plain,
! [SV1671: int,SV453: int,SV1692: int,SV791: int] :
( ( ( SV791 != SV1692 )
| ( ( plus_plus_int @ ( times_times_int @ SV453 @ SV791 ) @ ( times_times_int @ SV1671 @ SV1692 ) )
= ( plus_plus_int @ ( times_times_int @ SV453 @ SV1692 ) @ ( times_times_int @ SV1671 @ SV791 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6679]) ).
thf(6827,plain,
! [SV1185: int,SV1392: int] :
( ( ( SV1392 = one_one_int )
= $false )
| ( ( SV1185 != one_one_int )
= $true )
| ( ( ( times_times_int @ SV1392 @ SV1185 )
= one_one_int )
= $true )
| ( ( ord_less_int @ zero_zero_int @ SV1392 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6680]) ).
thf(6828,plain,
! [SV1565: int,SV1628: int] :
( ( ( ord_less_int @ zero_zero_int @ SV1628 )
= $false )
| ( ( ( ( times_times_int @ SV1628 @ SV1565 )
!= one_one_int )
| ( SV1628 = one_one_int ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6681]) ).
thf(6829,plain,
! [SV1566: int,SV1629: int] :
( ( ( ord_less_int @ zero_zero_int @ SV1629 )
= $false )
| ( ( ( ( times_times_int @ SV1629 @ SV1566 )
!= one_one_int )
| ( SV1566 = one_one_int ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6682]) ).
thf(6830,plain,
! [SV1630: real,SV1567: real] :
( ( ( ord_less_real @ SV1567 @ SV1630 )
= $false )
| ( ( SV1567 != SV1630 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6683]) ).
thf(6831,plain,
! [SV1631: real,SV1568: real] :
( ( ( ord_less_real @ SV1568 @ SV1631 )
= $false )
| ( ( ord_less_eq_real @ SV1568 @ SV1631 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6684]) ).
thf(6832,plain,
! [SV1569: nat,SV1632: int] :
( ( ( ( number_number_of_nat @ SV1632 )
= zero_zero_nat )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV1569 @ ( number_number_of_nat @ SV1632 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6685]) ).
thf(6833,plain,
! [SV1693: int,SV1570: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV1570 @ ( number_number_of_nat @ SV1693 ) ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV1570 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6686]) ).
thf(6834,plain,
! [SV1204: int] :
( ( ( ~ ( dvd_dvd_int @ ( sK3_M_9 @ SV1204 ) @ SV1204 )
| ~ ( ord_less_eq_int @ zero_zero_int @ ( sK3_M_9 @ SV1204 ) ) )
= $false )
| ( ( ~ ( ord_less_int @ one_one_int @ SV1204 ) )
= $true )
| ( ( zprime @ SV1204 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6687]) ).
thf(6835,plain,
! [SV1204: int] :
( ( ( ~ ( ( ( sK3_M_9 @ SV1204 )
!= one_one_int ) )
| ~ ( ( ( sK3_M_9 @ SV1204 )
!= SV1204 ) ) )
= $false )
| ( ( ~ ( ord_less_int @ one_one_int @ SV1204 ) )
= $true )
| ( ( zprime @ SV1204 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6688]) ).
thf(6836,plain,
! [SV1571: int,SV1694: int] :
( ( ( ~ ( dvd_dvd_int @ SV1694 @ SV1571 )
| ~ ( ord_less_eq_int @ zero_zero_int @ SV1694 )
| ( SV1694 = one_one_int )
| ( SV1694 = SV1571 ) )
= $true )
| ( ( zprime @ SV1571 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6689]) ).
thf(6837,plain,
! [SV1573: int,SV1633: int] :
( ( ( ~ ( quadRes @ SV1633 @ SV1573 ) )
= $true )
| ( ( ( legendre @ SV1573 @ SV1633 )
= one_one_int )
= $true )
| ( ( zcong @ SV1573 @ zero_zero_int @ SV1633 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6691]) ).
thf(6838,plain,
! [SV1574: int,SV1634: int] :
( ( ( quadRes @ SV1634 @ SV1574 )
= $true )
| ( ( ( legendre @ SV1574 @ SV1634 )
= ( number_number_of_int @ min ) )
= $true )
| ( ( zcong @ SV1574 @ zero_zero_int @ SV1634 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6692]) ).
thf(6839,plain,
! [SV455: real,SV792: nat,SV1695: real] :
( ( ( ( ( power_power_real @ SV1695 @ SV792 )
!= SV455 )
| ~ ( ord_less_real @ zero_zero_real @ SV1695 )
| ( SV1695
= ( sK1_X_1 @ SV792 @ SV455 ) ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV455 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV792 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6693]) ).
thf(6840,plain,
! [SV455: real,SV792: nat] :
( ( ( ( ( power_power_real @ ( sK1_X_1 @ SV792 @ SV455 ) @ SV792 )
!= SV455 )
| ~ ( ord_less_real @ zero_zero_real @ ( sK1_X_1 @ SV792 @ SV455 ) ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV455 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV792 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6694]) ).
thf(6841,plain,
! [SV1635: int,SV1575: int] :
( ( ( ord_less_eq_int @ SV1575 @ SV1635 )
= $false )
| ( ( ord_less_eq_nat @ ( number_number_of_nat @ SV1575 ) @ ( number_number_of_nat @ SV1635 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6695]) ).
thf(6842,plain,
! [SV1696: int,SV1576: int] :
( ( ( ord_less_eq_nat @ ( number_number_of_nat @ SV1576 ) @ ( number_number_of_nat @ SV1696 ) )
= $true )
| ( ( ord_less_eq_int @ SV1576 @ pls )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6696]) ).
thf(6843,plain,
! [SV457: int,SV983: int,SV793: int,SV1636: int,SV1577: int] :
( ( ( dvd_dvd_int @ SV1577 @ SV1636 )
= $false )
| ( ( ~ ( dvd_dvd_int @ SV1577 @ ( plus_plus_int @ SV793 @ SV983 ) )
| ( dvd_dvd_int @ SV1577 @ ( plus_plus_int @ ( plus_plus_int @ SV793 @ ( times_times_int @ SV457 @ SV1636 ) ) @ SV983 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6697]) ).
thf(6844,plain,
! [SV983: int,SV457: int,SV793: int,SV1637: int,SV1578: int] :
( ( ( dvd_dvd_int @ SV1578 @ SV1637 )
= $false )
| ( ( ~ ( dvd_dvd_int @ SV1578 @ ( plus_plus_int @ ( plus_plus_int @ SV793 @ ( times_times_int @ SV457 @ SV1637 ) ) @ SV983 ) )
| ( dvd_dvd_int @ SV1578 @ ( plus_plus_int @ SV793 @ SV983 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6698]) ).
thf(6845,plain,
! [SV1415: nat,SV459: nat,SV1482: nat] :
( ( ( ( power_power_nat @ SV1482 @ SV459 )
= ( power_power_nat @ SV1482 @ SV1415 ) )
= $false )
| ( ( SV459 = SV1415 )
= $true )
| ( ( ord_less_nat @ one_one_nat @ SV1482 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6700]) ).
thf(6846,plain,
! [SV1483: nat,SV1416: nat,SV459: nat] :
( ( ( SV459 = SV1416 )
= $false )
| ( ( ( power_power_nat @ SV1483 @ SV459 )
= ( power_power_nat @ SV1483 @ SV1416 ) )
= $true )
| ( ( ord_less_nat @ one_one_nat @ SV1483 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6701]) ).
thf(6847,plain,
! [SV1579: real,SV794: real,SV1484: real,SV460: real] :
( ( ( SV460 = SV1484 )
= $true )
| ( ( SV794 = SV1579 )
= $true )
| ( ( ( plus_plus_real @ ( times_times_real @ SV460 @ SV794 ) @ ( times_times_real @ SV1484 @ SV1579 ) )
= ( plus_plus_real @ ( times_times_real @ SV460 @ SV1579 ) @ ( times_times_real @ SV1484 @ SV794 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6702]) ).
thf(6848,plain,
! [SV794: real,SV1672: real,SV460: real] :
( ( ( SV460 != SV1672 )
= $true )
| ( ( ! [SY2685: real] :
( ( plus_plus_real @ ( times_times_real @ SV460 @ SV794 ) @ ( times_times_real @ SV1672 @ SY2685 ) )
= ( plus_plus_real @ ( times_times_real @ SV460 @ SY2685 ) @ ( times_times_real @ SV1672 @ SV794 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6703]) ).
thf(6849,plain,
! [SV1673: real,SV460: real,SV1697: real,SV794: real] :
( ( ( SV794 != SV1697 )
| ( ( plus_plus_real @ ( times_times_real @ SV460 @ SV794 ) @ ( times_times_real @ SV1673 @ SV1697 ) )
= ( plus_plus_real @ ( times_times_real @ SV460 @ SV1697 ) @ ( times_times_real @ SV1673 @ SV794 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6704]) ).
thf(6850,plain,
! [SV461: nat,SV1639: nat] :
( ( ( SV1639 = zero_zero_nat )
= $false )
| ( ( ! [SY2676: nat] : ( dvd_dvd_nat @ ( times_times_nat @ SV461 @ SV1639 ) @ ( times_times_nat @ SY2676 @ SV1639 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6706]) ).
thf(6851,plain,
! [SV1640: nat,SV1674: nat,SV461: nat] :
( ( ( ~ ( dvd_dvd_nat @ SV461 @ SV1674 ) )
= $true )
| ( ( dvd_dvd_nat @ ( times_times_nat @ SV461 @ SV1640 ) @ ( times_times_nat @ SV1674 @ SV1640 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6707]) ).
thf(6852,plain,
! [SV1641: nat,SV1580: nat] :
( ( ( ( power_power_nat @ SV1580 @ SV1641 )
= zero_zero_nat )
= $false )
| ( ( SV1641 != zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6708]) ).
thf(6853,plain,
! [SV1675: nat,SV1581: nat] :
( ( ( ( power_power_nat @ SV1581 @ SV1675 )
= zero_zero_nat )
= $false )
| ( ( SV1581 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6709]) ).
thf(6854,plain,
! [SV1435: nat,SV462: nat,SV1486: real] :
( ( ( ( power_power_real @ SV1486 @ SV462 )
= ( power_power_real @ SV1486 @ SV1435 ) )
= $false )
| ( ( SV462 = SV1435 )
= $true )
| ( ( ord_less_real @ one_one_real @ SV1486 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6710]) ).
thf(6855,plain,
! [SV1487: real,SV1436: nat,SV462: nat] :
( ( ( SV462 = SV1436 )
= $false )
| ( ( ( power_power_real @ SV1487 @ SV462 )
= ( power_power_real @ SV1487 @ SV1436 ) )
= $true )
| ( ( ord_less_real @ one_one_real @ SV1487 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6711]) ).
thf(6856,plain,
! [SV1642: int,SV1583: int] :
( ( ( ~ ( ord_less_int @ SV1583 @ pls ) )
= $true )
| ( ( ( plus_plus_nat @ ( number_number_of_nat @ SV1642 ) @ ( number_number_of_nat @ SV1583 ) )
= ( number_number_of_nat @ SV1642 ) )
= $true )
| ( ( ord_less_int @ SV1642 @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6712]) ).
thf(6857,plain,
! [SV1643: int,SV1584: int] :
( ( ( ord_less_int @ SV1584 @ pls )
= $true )
| ( ( ( plus_plus_nat @ ( number_number_of_nat @ SV1643 ) @ ( number_number_of_nat @ SV1584 ) )
= ( number_number_of_nat @ ( plus_plus_int @ SV1643 @ SV1584 ) ) )
= $true )
| ( ( ord_less_int @ SV1643 @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6713]) ).
thf(6858,plain,
! [SV1440: real,SV1490: real,SV464: real] :
( ( ( ord_less_real @ ( times_times_real @ SV464 @ SV1490 ) @ ( times_times_real @ SV1440 @ SV1490 ) )
= $false )
| ( ( ord_less_real @ SV464 @ SV1440 )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV1490 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6716]) ).
thf(6859,plain,
! [SV1491: real,SV1441: real,SV464: real] :
( ( ( ord_less_real @ SV464 @ SV1441 )
= $false )
| ( ( ord_less_real @ ( times_times_real @ SV464 @ SV1491 ) @ ( times_times_real @ SV1441 @ SV1491 ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV1491 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6717]) ).
thf(6860,plain,
! [SV1442: real,SV465: real,SV1492: real] :
( ( ( ord_less_eq_real @ ( times_times_real @ SV1492 @ SV465 ) @ ( times_times_real @ SV1492 @ SV1442 ) )
= $false )
| ( ( ord_less_eq_real @ SV465 @ SV1442 )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV1492 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6718]) ).
thf(6861,plain,
! [SV1493: real,SV1443: real,SV465: real] :
( ( ( ord_less_eq_real @ SV465 @ SV1443 )
= $false )
| ( ( ord_less_eq_real @ ( times_times_real @ SV1493 @ SV465 ) @ ( times_times_real @ SV1493 @ SV1443 ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV1493 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6719]) ).
thf(6862,plain,
! [SV1676: int,SV1585: int] :
( ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SV1585 @ SV1585 ) @ ( times_times_int @ SV1676 @ SV1676 ) ) @ zero_zero_int )
= $false )
| ( ( SV1585 = zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6721]) ).
thf(6863,plain,
! [SV1644: int,SV1586: int] :
( ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SV1586 @ SV1586 ) @ ( times_times_int @ SV1644 @ SV1644 ) ) @ zero_zero_int )
= $false )
| ( ( SV1644 = zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6722]) ).
thf(6864,plain,
! [SV1645: nat,SV1587: int] :
( ( ( ( power_power_int @ SV1587 @ SV1645 )
= zero_zero_int )
= $false )
| ( ( SV1645 != zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6723]) ).
thf(6865,plain,
! [SV1677: nat,SV1588: int] :
( ( ( ( power_power_int @ SV1588 @ SV1677 )
= zero_zero_int )
= $false )
| ( ( SV1588 = zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6724]) ).
thf(6866,plain,
! [SV1456: nat,SV467: nat,SV1496: int] :
( ( ( ( power_power_int @ SV1496 @ SV467 )
= ( power_power_int @ SV1496 @ SV1456 ) )
= $false )
| ( ( SV467 = SV1456 )
= $true )
| ( ( ord_less_int @ one_one_int @ SV1496 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6725]) ).
thf(6867,plain,
! [SV1497: int,SV1457: nat,SV467: nat] :
( ( ( SV467 = SV1457 )
= $false )
| ( ( ( power_power_int @ SV1497 @ SV467 )
= ( power_power_int @ SV1497 @ SV1457 ) )
= $true )
| ( ( ord_less_int @ one_one_int @ SV1497 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6726]) ).
thf(6868,plain,
! [SV987: int,SV545: int,SV1280: int,SV135: int,SV830: int] :
( ( ( ord_less_int @ SV830 @ SV135 )
= $false )
| ( ( ~ ( ord_less_int @ SV1280 @ SV135 )
| ( ord_less_eq_int @ SV545 @ SV987 ) )
= $true )
| ( ( ord_less_eq_int @ zero_zero_int @ SV830 )
= $false )
| ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SV135 @ SV545 ) @ SV830 ) @ ( plus_plus_int @ ( times_times_int @ SV135 @ SV987 ) @ SV1280 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6729]) ).
thf(6869,plain,
! [SV1281: int,SV546: int,SV136: int,SV831: int,SV988: int,SV1458: int] :
( ( ( ~ ( ord_less_int @ SV1458 @ SV988 ) )
= $true )
| ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV831 )
| ~ ( ord_less_int @ zero_zero_int @ SV988 )
| ~ ( ord_less_eq_int @ SV988 @ SV136 )
| ( ord_less_eq_int @ SV546 @ SV1281 ) )
= $true )
| ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ SV988 @ SV1281 ) @ SV1458 ) )
= $false )
| ( ( ( plus_plus_int @ ( times_times_int @ SV136 @ SV546 ) @ SV831 )
= ( plus_plus_int @ ( times_times_int @ SV988 @ SV1281 ) @ SV1458 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6730]) ).
thf(6870,plain,
! [SV547: int,SV989: int,SV832: int,SV1282: int,SV137: int] :
( ( ( ord_less_int @ SV137 @ SV1282 )
= $false )
| ( ( ~ ( ord_less_int @ SV137 @ SV832 )
| ( ord_less_eq_int @ SV989 @ SV547 ) )
= $true )
| ( ( ord_less_eq_int @ SV1282 @ zero_zero_int )
= $false )
| ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SV137 @ SV547 ) @ SV832 ) @ ( plus_plus_int @ ( times_times_int @ SV137 @ SV989 ) @ SV1282 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6731]) ).
thf(6871,plain,
! [SV548: int,SV1283: int,SV990: int,SV1459: int,SV138: int,SV833: int] :
( ( ( ~ ( ord_less_int @ SV833 @ SV138 ) )
= $true )
| ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV1459 )
| ~ ( ord_less_int @ zero_zero_int @ SV990 )
| ~ ( ord_less_eq_int @ SV990 @ SV138 )
| ( ord_less_eq_int @ SV1283 @ SV548 ) )
= $true )
| ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ SV990 @ SV1283 ) @ SV1459 ) @ zero_zero_int )
= $false )
| ( ( ( plus_plus_int @ ( times_times_int @ SV138 @ SV548 ) @ SV833 )
= ( plus_plus_int @ ( times_times_int @ SV990 @ SV1283 ) @ SV1459 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6732]) ).
thf(6872,plain,
! [SV554: int,SV837: int,SV150: int] :
( ( ( ord_less_int @ SV150 @ SV837 )
= $false )
| ( ( ~ ( zcong @ SV837 @ SV150 @ SV554 ) )
= $true )
| ( ( ord_less_int @ zero_zero_int @ SV150 )
= $false )
| ( ( ord_less_int @ SV837 @ SV554 )
= $false )
| ( ( ord_less_int @ zero_zero_int @ SV837 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6733]) ).
thf(6873,plain,
! [SV838: int,SV556: int,SV152: int] :
( ( ( ord_less_int @ SV152 @ SV556 )
= $false )
| ( ( ~ ( zcong @ SV838 @ SV152 @ SV556 )
| ( SV838 = SV152 ) )
= $true )
| ( ( ord_less_eq_int @ zero_zero_int @ SV152 )
= $false )
| ( ( ord_less_int @ SV838 @ SV556 )
= $false )
| ( ( ord_less_eq_int @ zero_zero_int @ SV838 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6734]) ).
thf(6874,plain,
! [SV170: int,SV568: int,SV845: int] :
( ( ( zcong @ SV845 @ SV568 @ SV170 )
= $false )
| ( ( ~ ( ord_less_int @ SV845 @ SV170 )
| ~ ( ord_less_int @ SV568 @ SV170 )
| ( SV845 = SV568 ) )
= $true )
| ( ( ord_less_int @ zero_zero_int @ SV170 )
= $false )
| ( ( ord_less_int @ zero_zero_int @ SV568 )
= $false )
| ( ( ord_less_int @ zero_zero_int @ SV845 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6735]) ).
thf(6875,plain,
! [SV1020: int,SV932: int,SV1290: int,SV351: int,SV706: int] :
( ( ( zcong @ SV706 @ SV351 @ SV1290 )
= $false )
| ( ( zcong @ SV932 @ SV351 @ SV1290 )
= $true )
| ( ( SV1020 = SV706 )
= $false )
| ( ( zcong @ SV932 @ SV1020 @ SV1290 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6739]) ).
thf(6876,plain,
! [SV707: int,SV352: int] :
( ( ( SV352 = one_one_int )
= $true )
| ( ( SV352
= ( minus_minus_int @ SV707 @ one_one_int ) )
= $true )
| ( ( zcong @ ( times_times_int @ SV352 @ SV352 ) @ one_one_int @ SV707 )
= $false )
| ( ( ord_less_int @ SV352 @ SV707 )
= $false )
| ( ( ord_less_int @ zero_zero_int @ SV352 )
= $false )
| ( ( zprime @ SV707 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6740]) ).
thf(6877,plain,
! [SV782: nat,SV1027: nat,SV438: nat,SV979: nat] :
( ( ( dvd_dvd_nat @ SV979 @ SV438 )
= $false )
| ( ( ord_less_nat @ SV1027 @ SV979 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV1027 )
= $false )
| ( ( SV438
= ( plus_plus_nat @ ( times_times_nat @ SV782 @ SV979 ) @ SV1027 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6743]) ).
thf(6878,plain,
! [SV1499: nat,SV1589: nat] :
( ( ( SV1589 = zero_zero_nat )
= $false )
| ( ( ( power_power_nat @ SV1499 @ SV1589 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6744]) ).
thf(6879,plain,
! [SV1501: nat,SV1590: int] :
( ( ( ( number_number_of_nat @ SV1590 )
= zero_zero_nat )
= $false )
| ( ( ( power_power_nat @ SV1501 @ ( number_number_of_nat @ SV1590 ) )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6746]) ).
thf(6880,plain,
! [SV785: nat,SV1679: nat,SV441: nat,SV1650: nat] :
( ( ( ( plus_plus_nat @ ( times_times_nat @ SV1650 @ SV441 ) @ ( times_times_nat @ SV1679 @ SV785 ) )
= ( plus_plus_nat @ ( times_times_nat @ SV1650 @ SV785 ) @ ( times_times_nat @ SV1679 @ SV441 ) ) )
= $true )
| ( ( SV1650 != SV1679 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6755]) ).
thf(6881,plain,
! [SV785: nat,SV1698: nat,SV441: nat,SV1680: nat] :
( ( ( ( plus_plus_nat @ ( times_times_nat @ SV1680 @ SV441 ) @ ( times_times_nat @ SV1698 @ SV785 ) )
= ( plus_plus_nat @ ( times_times_nat @ SV1680 @ SV785 ) @ ( times_times_nat @ SV1698 @ SV441 ) ) )
= $true )
| ( ( SV441 != SV785 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6756]) ).
thf(6882,plain,
! [SV1512: real,SV1596: int] :
( ( ( ( number_number_of_nat @ SV1596 )
= zero_zero_nat )
= $false )
| ( ( ( power_power_real @ SV1512 @ ( number_number_of_nat @ SV1596 ) )
= zero_zero_real )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6758]) ).
thf(6883,plain,
! [SV786: real,SV1682: real,SV442: real,SV1653: real] :
( ( ( ( plus_plus_real @ ( times_times_real @ SV1653 @ SV442 ) @ ( times_times_real @ SV1682 @ SV786 ) )
= ( plus_plus_real @ ( times_times_real @ SV1653 @ SV786 ) @ ( times_times_real @ SV1682 @ SV442 ) ) )
= $true )
| ( ( SV1653 != SV1682 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6763]) ).
thf(6884,plain,
! [SV786: real,SV1699: real,SV442: real,SV1683: real] :
( ( ( ( plus_plus_real @ ( times_times_real @ SV1683 @ SV442 ) @ ( times_times_real @ SV1699 @ SV786 ) )
= ( plus_plus_real @ ( times_times_real @ SV1683 @ SV786 ) @ ( times_times_real @ SV1699 @ SV442 ) ) )
= $true )
| ( ( SV442 != SV786 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6764]) ).
thf(6885,plain,
! [SV1526: int,SV1604: int] :
( ( ( ( number_number_of_nat @ SV1604 )
= zero_zero_nat )
= $false )
| ( ( ( power_power_int @ SV1526 @ ( number_number_of_nat @ SV1604 ) )
= zero_zero_int )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6773]) ).
thf(6886,plain,
! [SV1610: int,SV1538: int] :
( ( ( SV1538 = SV1610 )
= $false )
| ( ( ord_less_int @ SV1538 @ SV1610 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6787]) ).
thf(6887,plain,
! [SV1684: int] :
( ( ( ! [SY2689: int] :
( ( times_times_int @ SV1684 @ SY2689 )
!= one_one_int ) )
= $true )
| ( ( ( SV1684 = one_one_int )
| ( SV1684
= ( number_number_of_int @ min ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6793]) ).
thf(6888,plain,
! [SV1700: int,SV1685: int] :
( ( ( ( times_times_int @ SV1685 @ SV1700 )
!= one_one_int )
| ( SV1685 = one_one_int )
| ( SV1700
= ( number_number_of_int @ min ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6794]) ).
thf(6889,plain,
! [SV1701: int,SV1686: int] :
( ( ( ( times_times_int @ SV1686 @ SV1701 )
!= one_one_int )
| ( SV1701 = one_one_int )
| ( SV1686
= ( number_number_of_int @ min ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6795]) ).
thf(6890,plain,
! [SV1702: int,SV1687: int] :
( ( ( ( times_times_int @ SV1687 @ SV1702 )
!= one_one_int )
| ( SV1702 = one_one_int )
| ( SV1702
= ( number_number_of_int @ min ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6796]) ).
thf(6891,plain,
! [SV1613: int,SV1542: int] :
( ( ( SV1542 = one_one_int )
= $false )
| ( ( SV1613 != one_one_int )
= $true )
| ( ( ( times_times_int @ SV1542 @ SV1613 )
= one_one_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6797]) ).
thf(6892,plain,
! [SV1614: int,SV1543: int] :
( ( ( SV1543
= ( number_number_of_int @ min ) )
= $false )
| ( ( SV1614
!= ( number_number_of_int @ min ) )
= $true )
| ( ( ( times_times_int @ SV1543 @ SV1614 )
= one_one_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6798]) ).
thf(6893,plain,
! [SV1617: int,SV1548: int] :
( ( ( ord_less_int @ SV1548 @ SV1617 )
= $false )
| ( ( ord_less_int @ SV1548 @ SV1617 )
= $true )
| ( ( ord_less_nat @ ( number_number_of_nat @ SV1548 ) @ ( number_number_of_nat @ SV1617 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6804]) ).
thf(6894,plain,
! [SV1549: int,SV1618: int] :
( ( ( ord_less_int @ pls @ SV1618 )
= $false )
| ( ( ~ ( ord_less_int @ SV1549 @ SV1618 ) )
= $true )
| ( ( ord_less_nat @ ( number_number_of_nat @ SV1549 ) @ ( number_number_of_nat @ SV1618 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6805]) ).
thf(6895,plain,
! [SV1619: int,SV1550: int] :
( ( ( ~ ( ord_less_int @ SV1550 @ SV1619 ) )
= $true )
| ( ( ord_less_int @ pls @ SV1619 )
= $true )
| ( ( ord_less_nat @ ( number_number_of_nat @ SV1550 ) @ ( number_number_of_nat @ SV1619 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6806]) ).
thf(6896,plain,
! [SV1552: int,SV1621: int,SV787: int,SV981: int,SV449: int] :
( ( ( ~ ( zcong @ SV449 @ ( times_times_int @ SV981 @ SV787 ) @ SV1621 ) )
= $true )
| ( ( zcong @ SV449 @ ( times_times_int @ SV1552 @ SV787 ) @ SV1621 )
= $true )
| ( ( zcong @ SV981 @ SV1552 @ SV1621 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6808]) ).
thf(6897,plain,
! [SV981: int,SV1622: int,SV787: int,SV1553: int,SV449: int] :
( ( ( ~ ( zcong @ SV449 @ ( times_times_int @ SV1553 @ SV787 ) @ SV1622 ) )
= $true )
| ( ( zcong @ SV449 @ ( times_times_int @ SV981 @ SV787 ) @ SV1622 )
= $true )
| ( ( zcong @ SV981 @ SV1553 @ SV1622 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6809]) ).
thf(6898,plain,
! [SV788: int,SV1688: int,SV450: int,SV1665: int] :
( ( ( ( plus_plus_int @ ( times_times_int @ SV1665 @ SV450 ) @ ( times_times_int @ SV1688 @ SV788 ) )
= ( plus_plus_int @ ( times_times_int @ SV1665 @ SV788 ) @ ( times_times_int @ SV1688 @ SV450 ) ) )
= $true )
| ( ( SV1665 != SV1688 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6810]) ).
thf(6899,plain,
! [SV788: int,SV1703: int,SV450: int,SV1689: int] :
( ( ( ( plus_plus_int @ ( times_times_int @ SV1689 @ SV450 ) @ ( times_times_int @ SV1703 @ SV788 ) )
= ( plus_plus_int @ ( times_times_int @ SV1689 @ SV788 ) @ ( times_times_int @ SV1703 @ SV450 ) ) )
= $true )
| ( ( SV450 != SV788 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6811]) ).
thf(6900,plain,
! [SV1557: int,SV1624: int,SV982: int,SV789: int,SV451: int] :
( ( ( ~ ( zcong @ SV451 @ ( times_times_int @ SV789 @ SV982 ) @ SV1624 ) )
= $true )
| ( ( zcong @ SV451 @ ( times_times_int @ SV789 @ SV1557 ) @ SV1624 )
= $true )
| ( ( zcong @ SV982 @ SV1557 @ SV1624 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6815]) ).
thf(6901,plain,
! [SV982: int,SV1625: int,SV1558: int,SV789: int,SV451: int] :
( ( ( ~ ( zcong @ SV451 @ ( times_times_int @ SV789 @ SV1558 ) @ SV1625 ) )
= $true )
| ( ( zcong @ SV451 @ ( times_times_int @ SV789 @ SV982 ) @ SV1625 )
= $true )
| ( ( zcong @ SV982 @ SV1558 @ SV1625 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6816]) ).
thf(6902,plain,
! [SV790: nat,SV1667: nat,SV452: nat] :
( ( ( SV452 = SV1667 )
= $false )
| ( ( ! [SY2681: nat] :
( ( plus_plus_nat @ ( times_times_nat @ SV452 @ SV790 ) @ ( times_times_nat @ SV1667 @ SY2681 ) )
= ( plus_plus_nat @ ( times_times_nat @ SV452 @ SY2681 ) @ ( times_times_nat @ SV1667 @ SV790 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6818]) ).
thf(6903,plain,
! [SV1668: nat,SV452: nat,SV1690: nat,SV790: nat] :
( ( ( SV790 != SV1690 )
= $true )
| ( ( ( plus_plus_nat @ ( times_times_nat @ SV452 @ SV790 ) @ ( times_times_nat @ SV1668 @ SV1690 ) )
= ( plus_plus_nat @ ( times_times_nat @ SV452 @ SV1690 ) @ ( times_times_nat @ SV1668 @ SV790 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6819]) ).
thf(6904,plain,
! [SV1560: real,SV1626: nat] :
( ( ( SV1626 = zero_zero_nat )
= $false )
| ( ( ( power_power_real @ SV1560 @ SV1626 )
= zero_zero_real )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6820]) ).
thf(6905,plain,
! [SV791: int,SV1670: int,SV453: int] :
( ( ( SV453 = SV1670 )
= $false )
| ( ( ! [SY2683: int] :
( ( plus_plus_int @ ( times_times_int @ SV453 @ SV791 ) @ ( times_times_int @ SV1670 @ SY2683 ) )
= ( plus_plus_int @ ( times_times_int @ SV453 @ SY2683 ) @ ( times_times_int @ SV1670 @ SV791 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6825]) ).
thf(6906,plain,
! [SV1671: int,SV453: int,SV1692: int,SV791: int] :
( ( ( SV791 != SV1692 )
= $true )
| ( ( ( plus_plus_int @ ( times_times_int @ SV453 @ SV791 ) @ ( times_times_int @ SV1671 @ SV1692 ) )
= ( plus_plus_int @ ( times_times_int @ SV453 @ SV1692 ) @ ( times_times_int @ SV1671 @ SV791 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6826]) ).
thf(6907,plain,
! [SV1392: int,SV1185: int] :
( ( ( SV1185 = one_one_int )
= $false )
| ( ( SV1392 = one_one_int )
= $false )
| ( ( ( times_times_int @ SV1392 @ SV1185 )
= one_one_int )
= $true )
| ( ( ord_less_int @ zero_zero_int @ SV1392 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6827]) ).
thf(6908,plain,
! [SV1565: int,SV1628: int] :
( ( ( ( times_times_int @ SV1628 @ SV1565 )
!= one_one_int )
= $true )
| ( ( SV1628 = one_one_int )
= $true )
| ( ( ord_less_int @ zero_zero_int @ SV1628 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6828]) ).
thf(6909,plain,
! [SV1566: int,SV1629: int] :
( ( ( ( times_times_int @ SV1629 @ SV1566 )
!= one_one_int )
= $true )
| ( ( SV1566 = one_one_int )
= $true )
| ( ( ord_less_int @ zero_zero_int @ SV1629 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6829]) ).
thf(6910,plain,
! [SV1630: real,SV1567: real] :
( ( ( SV1567 = SV1630 )
= $false )
| ( ( ord_less_real @ SV1567 @ SV1630 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6830]) ).
thf(6911,plain,
! [SV1204: int] :
( ( ( ~ ( dvd_dvd_int @ ( sK3_M_9 @ SV1204 ) @ SV1204 ) )
= $false )
| ( ( ~ ( ord_less_int @ one_one_int @ SV1204 ) )
= $true )
| ( ( zprime @ SV1204 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[6834]) ).
thf(6912,plain,
! [SV1204: int] :
( ( ( ~ ( ord_less_eq_int @ zero_zero_int @ ( sK3_M_9 @ SV1204 ) ) )
= $false )
| ( ( ~ ( ord_less_int @ one_one_int @ SV1204 ) )
= $true )
| ( ( zprime @ SV1204 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[6834]) ).
thf(6913,plain,
! [SV1204: int] :
( ( ( ~ ( ( ( sK3_M_9 @ SV1204 )
!= one_one_int ) ) )
= $false )
| ( ( ~ ( ord_less_int @ one_one_int @ SV1204 ) )
= $true )
| ( ( zprime @ SV1204 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[6835]) ).
thf(6914,plain,
! [SV1204: int] :
( ( ( ~ ( ( ( sK3_M_9 @ SV1204 )
!= SV1204 ) ) )
= $false )
| ( ( ~ ( ord_less_int @ one_one_int @ SV1204 ) )
= $true )
| ( ( zprime @ SV1204 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[6835]) ).
thf(6915,plain,
! [SV1571: int,SV1694: int] :
( ( ( ~ ( dvd_dvd_int @ SV1694 @ SV1571 )
| ~ ( ord_less_eq_int @ zero_zero_int @ SV1694 ) )
= $true )
| ( ( ( SV1694 = one_one_int )
| ( SV1694 = SV1571 ) )
= $true )
| ( ( zprime @ SV1571 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6836]) ).
thf(6916,plain,
! [SV1573: int,SV1633: int] :
( ( ( quadRes @ SV1633 @ SV1573 )
= $false )
| ( ( ( legendre @ SV1573 @ SV1633 )
= one_one_int )
= $true )
| ( ( zcong @ SV1573 @ zero_zero_int @ SV1633 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6837]) ).
thf(6917,plain,
! [SV455: real,SV792: nat,SV1695: real] :
( ( ( ( ( power_power_real @ SV1695 @ SV792 )
!= SV455 )
| ~ ( ord_less_real @ zero_zero_real @ SV1695 ) )
= $true )
| ( ( SV1695
= ( sK1_X_1 @ SV792 @ SV455 ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV455 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV792 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6839]) ).
thf(6918,plain,
! [SV455: real,SV792: nat] :
( ( ( ( power_power_real @ ( sK1_X_1 @ SV792 @ SV455 ) @ SV792 )
!= SV455 )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV455 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV792 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6840]) ).
thf(6919,plain,
! [SV455: real,SV792: nat] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ ( sK1_X_1 @ SV792 @ SV455 ) ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV455 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV792 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6840]) ).
thf(6920,plain,
! [SV1636: int,SV457: int,SV983: int,SV793: int,SV1577: int] :
( ( ( ~ ( dvd_dvd_int @ SV1577 @ ( plus_plus_int @ SV793 @ SV983 ) ) )
= $true )
| ( ( dvd_dvd_int @ SV1577 @ ( plus_plus_int @ ( plus_plus_int @ SV793 @ ( times_times_int @ SV457 @ SV1636 ) ) @ SV983 ) )
= $true )
| ( ( dvd_dvd_int @ SV1577 @ SV1636 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6843]) ).
thf(6921,plain,
! [SV983: int,SV1637: int,SV457: int,SV793: int,SV1578: int] :
( ( ( ~ ( dvd_dvd_int @ SV1578 @ ( plus_plus_int @ ( plus_plus_int @ SV793 @ ( times_times_int @ SV457 @ SV1637 ) ) @ SV983 ) ) )
= $true )
| ( ( dvd_dvd_int @ SV1578 @ ( plus_plus_int @ SV793 @ SV983 ) )
= $true )
| ( ( dvd_dvd_int @ SV1578 @ SV1637 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6844]) ).
thf(6922,plain,
! [SV794: real,SV1672: real,SV460: real] :
( ( ( SV460 = SV1672 )
= $false )
| ( ( ! [SY2685: real] :
( ( plus_plus_real @ ( times_times_real @ SV460 @ SV794 ) @ ( times_times_real @ SV1672 @ SY2685 ) )
= ( plus_plus_real @ ( times_times_real @ SV460 @ SY2685 ) @ ( times_times_real @ SV1672 @ SV794 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6848]) ).
thf(6923,plain,
! [SV1673: real,SV460: real,SV1697: real,SV794: real] :
( ( ( SV794 != SV1697 )
= $true )
| ( ( ( plus_plus_real @ ( times_times_real @ SV460 @ SV794 ) @ ( times_times_real @ SV1673 @ SV1697 ) )
= ( plus_plus_real @ ( times_times_real @ SV460 @ SV1697 ) @ ( times_times_real @ SV1673 @ SV794 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6849]) ).
thf(6924,plain,
! [SV1704: nat,SV1639: nat,SV461: nat] :
( ( ( dvd_dvd_nat @ ( times_times_nat @ SV461 @ SV1639 ) @ ( times_times_nat @ SV1704 @ SV1639 ) )
= $true )
| ( ( SV1639 = zero_zero_nat )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6850]) ).
thf(6925,plain,
! [SV1640: nat,SV1674: nat,SV461: nat] :
( ( ( dvd_dvd_nat @ SV461 @ SV1674 )
= $false )
| ( ( dvd_dvd_nat @ ( times_times_nat @ SV461 @ SV1640 ) @ ( times_times_nat @ SV1674 @ SV1640 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6851]) ).
thf(6926,plain,
! [SV1580: nat,SV1641: nat] :
( ( ( SV1641 = zero_zero_nat )
= $false )
| ( ( ( power_power_nat @ SV1580 @ SV1641 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6852]) ).
thf(6927,plain,
! [SV1642: int,SV1583: int] :
( ( ( ord_less_int @ SV1583 @ pls )
= $false )
| ( ( ( plus_plus_nat @ ( number_number_of_nat @ SV1642 ) @ ( number_number_of_nat @ SV1583 ) )
= ( number_number_of_nat @ SV1642 ) )
= $true )
| ( ( ord_less_int @ SV1642 @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6856]) ).
thf(6928,plain,
! [SV1587: int,SV1645: nat] :
( ( ( SV1645 = zero_zero_nat )
= $false )
| ( ( ( power_power_int @ SV1587 @ SV1645 )
= zero_zero_int )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6864]) ).
thf(6929,plain,
! [SV830: int,SV987: int,SV545: int,SV135: int,SV1280: int] :
( ( ( ~ ( ord_less_int @ SV1280 @ SV135 ) )
= $true )
| ( ( ord_less_eq_int @ SV545 @ SV987 )
= $true )
| ( ( ord_less_int @ SV830 @ SV135 )
= $false )
| ( ( ord_less_eq_int @ zero_zero_int @ SV830 )
= $false )
| ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SV135 @ SV545 ) @ SV830 ) @ ( plus_plus_int @ ( times_times_int @ SV135 @ SV987 ) @ SV1280 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6868]) ).
thf(6930,plain,
! [SV1281: int,SV546: int,SV136: int,SV831: int,SV988: int,SV1458: int] :
( ( ( ord_less_int @ SV1458 @ SV988 )
= $false )
| ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV831 )
| ~ ( ord_less_int @ zero_zero_int @ SV988 )
| ~ ( ord_less_eq_int @ SV988 @ SV136 )
| ( ord_less_eq_int @ SV546 @ SV1281 ) )
= $true )
| ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ SV988 @ SV1281 ) @ SV1458 ) )
= $false )
| ( ( ( plus_plus_int @ ( times_times_int @ SV136 @ SV546 ) @ SV831 )
= ( plus_plus_int @ ( times_times_int @ SV988 @ SV1281 ) @ SV1458 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6869]) ).
thf(6931,plain,
! [SV1282: int,SV547: int,SV989: int,SV832: int,SV137: int] :
( ( ( ~ ( ord_less_int @ SV137 @ SV832 ) )
= $true )
| ( ( ord_less_eq_int @ SV989 @ SV547 )
= $true )
| ( ( ord_less_int @ SV137 @ SV1282 )
= $false )
| ( ( ord_less_eq_int @ SV1282 @ zero_zero_int )
= $false )
| ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SV137 @ SV547 ) @ SV832 ) @ ( plus_plus_int @ ( times_times_int @ SV137 @ SV989 ) @ SV1282 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6870]) ).
thf(6932,plain,
! [SV548: int,SV1283: int,SV990: int,SV1459: int,SV138: int,SV833: int] :
( ( ( ord_less_int @ SV833 @ SV138 )
= $false )
| ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV1459 )
| ~ ( ord_less_int @ zero_zero_int @ SV990 )
| ~ ( ord_less_eq_int @ SV990 @ SV138 )
| ( ord_less_eq_int @ SV1283 @ SV548 ) )
= $true )
| ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ SV990 @ SV1283 ) @ SV1459 ) @ zero_zero_int )
= $false )
| ( ( ( plus_plus_int @ ( times_times_int @ SV138 @ SV548 ) @ SV833 )
= ( plus_plus_int @ ( times_times_int @ SV990 @ SV1283 ) @ SV1459 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6871]) ).
thf(6933,plain,
! [SV554: int,SV150: int,SV837: int] :
( ( ( zcong @ SV837 @ SV150 @ SV554 )
= $false )
| ( ( ord_less_int @ SV150 @ SV837 )
= $false )
| ( ( ord_less_int @ zero_zero_int @ SV150 )
= $false )
| ( ( ord_less_int @ SV837 @ SV554 )
= $false )
| ( ( ord_less_int @ zero_zero_int @ SV837 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6872]) ).
thf(6934,plain,
! [SV556: int,SV152: int,SV838: int] :
( ( ( ~ ( zcong @ SV838 @ SV152 @ SV556 ) )
= $true )
| ( ( SV838 = SV152 )
= $true )
| ( ( ord_less_int @ SV152 @ SV556 )
= $false )
| ( ( ord_less_eq_int @ zero_zero_int @ SV152 )
= $false )
| ( ( ord_less_int @ SV838 @ SV556 )
= $false )
| ( ( ord_less_eq_int @ zero_zero_int @ SV838 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6873]) ).
thf(6935,plain,
! [SV568: int,SV170: int,SV845: int] :
( ( ( ~ ( ord_less_int @ SV845 @ SV170 ) )
= $true )
| ( ( ~ ( ord_less_int @ SV568 @ SV170 )
| ( SV845 = SV568 ) )
= $true )
| ( ( zcong @ SV845 @ SV568 @ SV170 )
= $false )
| ( ( ord_less_int @ zero_zero_int @ SV170 )
= $false )
| ( ( ord_less_int @ zero_zero_int @ SV568 )
= $false )
| ( ( ord_less_int @ zero_zero_int @ SV845 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6874]) ).
thf(6936,plain,
! [SV785: nat,SV441: nat,SV1679: nat,SV1650: nat] :
( ( ( SV1650 = SV1679 )
= $false )
| ( ( ( plus_plus_nat @ ( times_times_nat @ SV1650 @ SV441 ) @ ( times_times_nat @ SV1679 @ SV785 ) )
= ( plus_plus_nat @ ( times_times_nat @ SV1650 @ SV785 ) @ ( times_times_nat @ SV1679 @ SV441 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6880]) ).
thf(6937,plain,
! [SV1698: nat,SV1680: nat,SV785: nat,SV441: nat] :
( ( ( SV441 = SV785 )
= $false )
| ( ( ( plus_plus_nat @ ( times_times_nat @ SV1680 @ SV441 ) @ ( times_times_nat @ SV1698 @ SV785 ) )
= ( plus_plus_nat @ ( times_times_nat @ SV1680 @ SV785 ) @ ( times_times_nat @ SV1698 @ SV441 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6881]) ).
thf(6938,plain,
! [SV786: real,SV442: real,SV1682: real,SV1653: real] :
( ( ( SV1653 = SV1682 )
= $false )
| ( ( ( plus_plus_real @ ( times_times_real @ SV1653 @ SV442 ) @ ( times_times_real @ SV1682 @ SV786 ) )
= ( plus_plus_real @ ( times_times_real @ SV1653 @ SV786 ) @ ( times_times_real @ SV1682 @ SV442 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6883]) ).
thf(6939,plain,
! [SV1699: real,SV1683: real,SV786: real,SV442: real] :
( ( ( SV442 = SV786 )
= $false )
| ( ( ( plus_plus_real @ ( times_times_real @ SV1683 @ SV442 ) @ ( times_times_real @ SV1699 @ SV786 ) )
= ( plus_plus_real @ ( times_times_real @ SV1683 @ SV786 ) @ ( times_times_real @ SV1699 @ SV442 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6884]) ).
thf(6940,plain,
! [SV1705: int,SV1684: int] :
( ( ( ( times_times_int @ SV1684 @ SV1705 )
!= one_one_int )
= $true )
| ( ( ( SV1684 = one_one_int )
| ( SV1684
= ( number_number_of_int @ min ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6887]) ).
thf(6941,plain,
! [SV1700: int,SV1685: int] :
( ( ( ( times_times_int @ SV1685 @ SV1700 )
!= one_one_int )
= $true )
| ( ( ( SV1685 = one_one_int )
| ( SV1700
= ( number_number_of_int @ min ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6888]) ).
thf(6942,plain,
! [SV1701: int,SV1686: int] :
( ( ( ( times_times_int @ SV1686 @ SV1701 )
!= one_one_int )
= $true )
| ( ( ( SV1701 = one_one_int )
| ( SV1686
= ( number_number_of_int @ min ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6889]) ).
thf(6943,plain,
! [SV1702: int,SV1687: int] :
( ( ( ( times_times_int @ SV1687 @ SV1702 )
!= one_one_int )
= $true )
| ( ( ( SV1702 = one_one_int )
| ( SV1702
= ( number_number_of_int @ min ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6890]) ).
thf(6944,plain,
! [SV1542: int,SV1613: int] :
( ( ( SV1613 = one_one_int )
= $false )
| ( ( SV1542 = one_one_int )
= $false )
| ( ( ( times_times_int @ SV1542 @ SV1613 )
= one_one_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6891]) ).
thf(6945,plain,
! [SV1543: int,SV1614: int] :
( ( ( SV1614
= ( number_number_of_int @ min ) )
= $false )
| ( ( SV1543
= ( number_number_of_int @ min ) )
= $false )
| ( ( ( times_times_int @ SV1543 @ SV1614 )
= one_one_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6892]) ).
thf(6946,plain,
! [SV1618: int,SV1549: int] :
( ( ( ord_less_int @ SV1549 @ SV1618 )
= $false )
| ( ( ord_less_int @ pls @ SV1618 )
= $false )
| ( ( ord_less_nat @ ( number_number_of_nat @ SV1549 ) @ ( number_number_of_nat @ SV1618 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6894]) ).
thf(6947,plain,
! [SV1619: int,SV1550: int] :
( ( ( ord_less_int @ SV1550 @ SV1619 )
= $false )
| ( ( ord_less_int @ pls @ SV1619 )
= $true )
| ( ( ord_less_nat @ ( number_number_of_nat @ SV1550 ) @ ( number_number_of_nat @ SV1619 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6895]) ).
thf(6948,plain,
! [SV1552: int,SV1621: int,SV787: int,SV981: int,SV449: int] :
( ( ( zcong @ SV449 @ ( times_times_int @ SV981 @ SV787 ) @ SV1621 )
= $false )
| ( ( zcong @ SV449 @ ( times_times_int @ SV1552 @ SV787 ) @ SV1621 )
= $true )
| ( ( zcong @ SV981 @ SV1552 @ SV1621 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6896]) ).
thf(6949,plain,
! [SV981: int,SV1622: int,SV787: int,SV1553: int,SV449: int] :
( ( ( zcong @ SV449 @ ( times_times_int @ SV1553 @ SV787 ) @ SV1622 )
= $false )
| ( ( zcong @ SV449 @ ( times_times_int @ SV981 @ SV787 ) @ SV1622 )
= $true )
| ( ( zcong @ SV981 @ SV1553 @ SV1622 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6897]) ).
thf(6950,plain,
! [SV788: int,SV450: int,SV1688: int,SV1665: int] :
( ( ( SV1665 = SV1688 )
= $false )
| ( ( ( plus_plus_int @ ( times_times_int @ SV1665 @ SV450 ) @ ( times_times_int @ SV1688 @ SV788 ) )
= ( plus_plus_int @ ( times_times_int @ SV1665 @ SV788 ) @ ( times_times_int @ SV1688 @ SV450 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6898]) ).
thf(6951,plain,
! [SV1703: int,SV1689: int,SV788: int,SV450: int] :
( ( ( SV450 = SV788 )
= $false )
| ( ( ( plus_plus_int @ ( times_times_int @ SV1689 @ SV450 ) @ ( times_times_int @ SV1703 @ SV788 ) )
= ( plus_plus_int @ ( times_times_int @ SV1689 @ SV788 ) @ ( times_times_int @ SV1703 @ SV450 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6899]) ).
thf(6952,plain,
! [SV1557: int,SV1624: int,SV982: int,SV789: int,SV451: int] :
( ( ( zcong @ SV451 @ ( times_times_int @ SV789 @ SV982 ) @ SV1624 )
= $false )
| ( ( zcong @ SV451 @ ( times_times_int @ SV789 @ SV1557 ) @ SV1624 )
= $true )
| ( ( zcong @ SV982 @ SV1557 @ SV1624 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6900]) ).
thf(6953,plain,
! [SV982: int,SV1625: int,SV1558: int,SV789: int,SV451: int] :
( ( ( zcong @ SV451 @ ( times_times_int @ SV789 @ SV1558 ) @ SV1625 )
= $false )
| ( ( zcong @ SV451 @ ( times_times_int @ SV789 @ SV982 ) @ SV1625 )
= $true )
| ( ( zcong @ SV982 @ SV1558 @ SV1625 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6901]) ).
thf(6954,plain,
! [SV1706: nat,SV1667: nat,SV790: nat,SV452: nat] :
( ( ( ( plus_plus_nat @ ( times_times_nat @ SV452 @ SV790 ) @ ( times_times_nat @ SV1667 @ SV1706 ) )
= ( plus_plus_nat @ ( times_times_nat @ SV452 @ SV1706 ) @ ( times_times_nat @ SV1667 @ SV790 ) ) )
= $true )
| ( ( SV452 = SV1667 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6902]) ).
thf(6955,plain,
! [SV1668: nat,SV452: nat,SV1690: nat,SV790: nat] :
( ( ( SV790 = SV1690 )
= $false )
| ( ( ( plus_plus_nat @ ( times_times_nat @ SV452 @ SV790 ) @ ( times_times_nat @ SV1668 @ SV1690 ) )
= ( plus_plus_nat @ ( times_times_nat @ SV452 @ SV1690 ) @ ( times_times_nat @ SV1668 @ SV790 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6903]) ).
thf(6956,plain,
! [SV1707: int,SV1670: int,SV791: int,SV453: int] :
( ( ( ( plus_plus_int @ ( times_times_int @ SV453 @ SV791 ) @ ( times_times_int @ SV1670 @ SV1707 ) )
= ( plus_plus_int @ ( times_times_int @ SV453 @ SV1707 ) @ ( times_times_int @ SV1670 @ SV791 ) ) )
= $true )
| ( ( SV453 = SV1670 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6905]) ).
thf(6957,plain,
! [SV1671: int,SV453: int,SV1692: int,SV791: int] :
( ( ( SV791 = SV1692 )
= $false )
| ( ( ( plus_plus_int @ ( times_times_int @ SV453 @ SV791 ) @ ( times_times_int @ SV1671 @ SV1692 ) )
= ( plus_plus_int @ ( times_times_int @ SV453 @ SV1692 ) @ ( times_times_int @ SV1671 @ SV791 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6906]) ).
thf(6958,plain,
! [SV1565: int,SV1628: int] :
( ( ( ( times_times_int @ SV1628 @ SV1565 )
= one_one_int )
= $false )
| ( ( SV1628 = one_one_int )
= $true )
| ( ( ord_less_int @ zero_zero_int @ SV1628 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6908]) ).
thf(6959,plain,
! [SV1566: int,SV1629: int] :
( ( ( ( times_times_int @ SV1629 @ SV1566 )
= one_one_int )
= $false )
| ( ( SV1566 = one_one_int )
= $true )
| ( ( ord_less_int @ zero_zero_int @ SV1629 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6909]) ).
thf(6960,plain,
! [SV1204: int] :
( ( ( dvd_dvd_int @ ( sK3_M_9 @ SV1204 ) @ SV1204 )
= $true )
| ( ( ~ ( ord_less_int @ one_one_int @ SV1204 ) )
= $true )
| ( ( zprime @ SV1204 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6911]) ).
thf(6961,plain,
! [SV1204: int] :
( ( ( ord_less_eq_int @ zero_zero_int @ ( sK3_M_9 @ SV1204 ) )
= $true )
| ( ( ~ ( ord_less_int @ one_one_int @ SV1204 ) )
= $true )
| ( ( zprime @ SV1204 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6912]) ).
thf(6962,plain,
! [SV1204: int] :
( ( ( ( sK3_M_9 @ SV1204 )
!= one_one_int )
= $true )
| ( ( ~ ( ord_less_int @ one_one_int @ SV1204 ) )
= $true )
| ( ( zprime @ SV1204 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6913]) ).
thf(6963,plain,
! [SV1204: int] :
( ( ( ( sK3_M_9 @ SV1204 )
!= SV1204 )
= $true )
| ( ( ~ ( ord_less_int @ one_one_int @ SV1204 ) )
= $true )
| ( ( zprime @ SV1204 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6914]) ).
thf(6964,plain,
! [SV1571: int,SV1694: int] :
( ( ( ~ ( dvd_dvd_int @ SV1694 @ SV1571 ) )
= $true )
| ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV1694 ) )
= $true )
| ( ( ( SV1694 = one_one_int )
| ( SV1694 = SV1571 ) )
= $true )
| ( ( zprime @ SV1571 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6915]) ).
thf(6965,plain,
! [SV455: real,SV792: nat,SV1695: real] :
( ( ( ( power_power_real @ SV1695 @ SV792 )
!= SV455 )
= $true )
| ( ( ~ ( ord_less_real @ zero_zero_real @ SV1695 ) )
= $true )
| ( ( SV1695
= ( sK1_X_1 @ SV792 @ SV455 ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV455 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV792 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6917]) ).
thf(6966,plain,
! [SV455: real,SV792: nat] :
( ( ( ( power_power_real @ ( sK1_X_1 @ SV792 @ SV455 ) @ SV792 )
= SV455 )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV455 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV792 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6918]) ).
thf(6967,plain,
! [SV455: real,SV792: nat] :
( ( ( ord_less_real @ zero_zero_real @ ( sK1_X_1 @ SV792 @ SV455 ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV455 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV792 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6919]) ).
thf(6968,plain,
! [SV1636: int,SV457: int,SV983: int,SV793: int,SV1577: int] :
( ( ( dvd_dvd_int @ SV1577 @ ( plus_plus_int @ SV793 @ SV983 ) )
= $false )
| ( ( dvd_dvd_int @ SV1577 @ ( plus_plus_int @ ( plus_plus_int @ SV793 @ ( times_times_int @ SV457 @ SV1636 ) ) @ SV983 ) )
= $true )
| ( ( dvd_dvd_int @ SV1577 @ SV1636 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6920]) ).
thf(6969,plain,
! [SV983: int,SV1637: int,SV457: int,SV793: int,SV1578: int] :
( ( ( dvd_dvd_int @ SV1578 @ ( plus_plus_int @ ( plus_plus_int @ SV793 @ ( times_times_int @ SV457 @ SV1637 ) ) @ SV983 ) )
= $false )
| ( ( dvd_dvd_int @ SV1578 @ ( plus_plus_int @ SV793 @ SV983 ) )
= $true )
| ( ( dvd_dvd_int @ SV1578 @ SV1637 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6921]) ).
thf(6970,plain,
! [SV1708: real,SV1672: real,SV794: real,SV460: real] :
( ( ( ( plus_plus_real @ ( times_times_real @ SV460 @ SV794 ) @ ( times_times_real @ SV1672 @ SV1708 ) )
= ( plus_plus_real @ ( times_times_real @ SV460 @ SV1708 ) @ ( times_times_real @ SV1672 @ SV794 ) ) )
= $true )
| ( ( SV460 = SV1672 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6922]) ).
thf(6971,plain,
! [SV1673: real,SV460: real,SV1697: real,SV794: real] :
( ( ( SV794 = SV1697 )
= $false )
| ( ( ( plus_plus_real @ ( times_times_real @ SV460 @ SV794 ) @ ( times_times_real @ SV1673 @ SV1697 ) )
= ( plus_plus_real @ ( times_times_real @ SV460 @ SV1697 ) @ ( times_times_real @ SV1673 @ SV794 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6923]) ).
thf(6972,plain,
! [SV830: int,SV987: int,SV545: int,SV135: int,SV1280: int] :
( ( ( ord_less_int @ SV1280 @ SV135 )
= $false )
| ( ( ord_less_eq_int @ SV545 @ SV987 )
= $true )
| ( ( ord_less_int @ SV830 @ SV135 )
= $false )
| ( ( ord_less_eq_int @ zero_zero_int @ SV830 )
= $false )
| ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SV135 @ SV545 ) @ SV830 ) @ ( plus_plus_int @ ( times_times_int @ SV135 @ SV987 ) @ SV1280 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6929]) ).
thf(6973,plain,
! [SV1458: int,SV1281: int,SV546: int,SV136: int,SV988: int,SV831: int] :
( ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV831 ) )
= $true )
| ( ( ~ ( ord_less_int @ zero_zero_int @ SV988 )
| ~ ( ord_less_eq_int @ SV988 @ SV136 )
| ( ord_less_eq_int @ SV546 @ SV1281 ) )
= $true )
| ( ( ord_less_int @ SV1458 @ SV988 )
= $false )
| ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ SV988 @ SV1281 ) @ SV1458 ) )
= $false )
| ( ( ( plus_plus_int @ ( times_times_int @ SV136 @ SV546 ) @ SV831 )
= ( plus_plus_int @ ( times_times_int @ SV988 @ SV1281 ) @ SV1458 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6930]) ).
thf(6974,plain,
! [SV1282: int,SV547: int,SV989: int,SV832: int,SV137: int] :
( ( ( ord_less_int @ SV137 @ SV832 )
= $false )
| ( ( ord_less_eq_int @ SV989 @ SV547 )
= $true )
| ( ( ord_less_int @ SV137 @ SV1282 )
= $false )
| ( ( ord_less_eq_int @ SV1282 @ zero_zero_int )
= $false )
| ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SV137 @ SV547 ) @ SV832 ) @ ( plus_plus_int @ ( times_times_int @ SV137 @ SV989 ) @ SV1282 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6931]) ).
thf(6975,plain,
! [SV833: int,SV548: int,SV1283: int,SV138: int,SV990: int,SV1459: int] :
( ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV1459 ) )
= $true )
| ( ( ~ ( ord_less_int @ zero_zero_int @ SV990 )
| ~ ( ord_less_eq_int @ SV990 @ SV138 )
| ( ord_less_eq_int @ SV1283 @ SV548 ) )
= $true )
| ( ( ord_less_int @ SV833 @ SV138 )
= $false )
| ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ SV990 @ SV1283 ) @ SV1459 ) @ zero_zero_int )
= $false )
| ( ( ( plus_plus_int @ ( times_times_int @ SV138 @ SV548 ) @ SV833 )
= ( plus_plus_int @ ( times_times_int @ SV990 @ SV1283 ) @ SV1459 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6932]) ).
thf(6976,plain,
! [SV556: int,SV152: int,SV838: int] :
( ( ( zcong @ SV838 @ SV152 @ SV556 )
= $false )
| ( ( SV838 = SV152 )
= $true )
| ( ( ord_less_int @ SV152 @ SV556 )
= $false )
| ( ( ord_less_eq_int @ zero_zero_int @ SV152 )
= $false )
| ( ( ord_less_int @ SV838 @ SV556 )
= $false )
| ( ( ord_less_eq_int @ zero_zero_int @ SV838 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6934]) ).
thf(6977,plain,
! [SV568: int,SV170: int,SV845: int] :
( ( ( ord_less_int @ SV845 @ SV170 )
= $false )
| ( ( ~ ( ord_less_int @ SV568 @ SV170 )
| ( SV845 = SV568 ) )
= $true )
| ( ( zcong @ SV845 @ SV568 @ SV170 )
= $false )
| ( ( ord_less_int @ zero_zero_int @ SV170 )
= $false )
| ( ( ord_less_int @ zero_zero_int @ SV568 )
= $false )
| ( ( ord_less_int @ zero_zero_int @ SV845 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6935]) ).
thf(6978,plain,
! [SV1705: int,SV1684: int] :
( ( ( ( times_times_int @ SV1684 @ SV1705 )
= one_one_int )
= $false )
| ( ( ( SV1684 = one_one_int )
| ( SV1684
= ( number_number_of_int @ min ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6940]) ).
thf(6979,plain,
! [SV1700: int,SV1685: int] :
( ( ( ( times_times_int @ SV1685 @ SV1700 )
= one_one_int )
= $false )
| ( ( ( SV1685 = one_one_int )
| ( SV1700
= ( number_number_of_int @ min ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6941]) ).
thf(6980,plain,
! [SV1701: int,SV1686: int] :
( ( ( ( times_times_int @ SV1686 @ SV1701 )
= one_one_int )
= $false )
| ( ( ( SV1701 = one_one_int )
| ( SV1686
= ( number_number_of_int @ min ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6942]) ).
thf(6981,plain,
! [SV1702: int,SV1687: int] :
( ( ( ( times_times_int @ SV1687 @ SV1702 )
= one_one_int )
= $false )
| ( ( ( SV1702 = one_one_int )
| ( SV1702
= ( number_number_of_int @ min ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6943]) ).
thf(6982,plain,
! [SV1204: int] :
( ( ( ord_less_int @ one_one_int @ SV1204 )
= $false )
| ( ( dvd_dvd_int @ ( sK3_M_9 @ SV1204 ) @ SV1204 )
= $true )
| ( ( zprime @ SV1204 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6960]) ).
thf(6983,plain,
! [SV1204: int] :
( ( ( ord_less_int @ one_one_int @ SV1204 )
= $false )
| ( ( ord_less_eq_int @ zero_zero_int @ ( sK3_M_9 @ SV1204 ) )
= $true )
| ( ( zprime @ SV1204 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6961]) ).
thf(6984,plain,
! [SV1204: int] :
( ( ( ( sK3_M_9 @ SV1204 )
= one_one_int )
= $false )
| ( ( ~ ( ord_less_int @ one_one_int @ SV1204 ) )
= $true )
| ( ( zprime @ SV1204 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6962]) ).
thf(6985,plain,
! [SV1204: int] :
( ( ( ( sK3_M_9 @ SV1204 )
= SV1204 )
= $false )
| ( ( ~ ( ord_less_int @ one_one_int @ SV1204 ) )
= $true )
| ( ( zprime @ SV1204 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6963]) ).
thf(6986,plain,
! [SV1571: int,SV1694: int] :
( ( ( dvd_dvd_int @ SV1694 @ SV1571 )
= $false )
| ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV1694 ) )
= $true )
| ( ( ( SV1694 = one_one_int )
| ( SV1694 = SV1571 ) )
= $true )
| ( ( zprime @ SV1571 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6964]) ).
thf(6987,plain,
! [SV455: real,SV792: nat,SV1695: real] :
( ( ( ( power_power_real @ SV1695 @ SV792 )
= SV455 )
= $false )
| ( ( ~ ( ord_less_real @ zero_zero_real @ SV1695 ) )
= $true )
| ( ( SV1695
= ( sK1_X_1 @ SV792 @ SV455 ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV455 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV792 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6965]) ).
thf(6988,plain,
! [SV1458: int,SV1281: int,SV546: int,SV136: int,SV988: int,SV831: int] :
( ( ( ord_less_eq_int @ zero_zero_int @ SV831 )
= $false )
| ( ( ~ ( ord_less_int @ zero_zero_int @ SV988 )
| ~ ( ord_less_eq_int @ SV988 @ SV136 )
| ( ord_less_eq_int @ SV546 @ SV1281 ) )
= $true )
| ( ( ord_less_int @ SV1458 @ SV988 )
= $false )
| ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ SV988 @ SV1281 ) @ SV1458 ) )
= $false )
| ( ( ( plus_plus_int @ ( times_times_int @ SV136 @ SV546 ) @ SV831 )
= ( plus_plus_int @ ( times_times_int @ SV988 @ SV1281 ) @ SV1458 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6973]) ).
thf(6989,plain,
! [SV833: int,SV548: int,SV1283: int,SV138: int,SV990: int,SV1459: int] :
( ( ( ord_less_eq_int @ zero_zero_int @ SV1459 )
= $false )
| ( ( ~ ( ord_less_int @ zero_zero_int @ SV990 )
| ~ ( ord_less_eq_int @ SV990 @ SV138 )
| ( ord_less_eq_int @ SV1283 @ SV548 ) )
= $true )
| ( ( ord_less_int @ SV833 @ SV138 )
= $false )
| ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ SV990 @ SV1283 ) @ SV1459 ) @ zero_zero_int )
= $false )
| ( ( ( plus_plus_int @ ( times_times_int @ SV138 @ SV548 ) @ SV833 )
= ( plus_plus_int @ ( times_times_int @ SV990 @ SV1283 ) @ SV1459 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6975]) ).
thf(6990,plain,
! [SV845: int,SV170: int,SV568: int] :
( ( ( ~ ( ord_less_int @ SV568 @ SV170 ) )
= $true )
| ( ( SV845 = SV568 )
= $true )
| ( ( ord_less_int @ SV845 @ SV170 )
= $false )
| ( ( zcong @ SV845 @ SV568 @ SV170 )
= $false )
| ( ( ord_less_int @ zero_zero_int @ SV170 )
= $false )
| ( ( ord_less_int @ zero_zero_int @ SV568 )
= $false )
| ( ( ord_less_int @ zero_zero_int @ SV845 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6977]) ).
thf(6991,plain,
! [SV1705: int,SV1684: int] :
( ( ( SV1684 = one_one_int )
= $true )
| ( ( SV1684
= ( number_number_of_int @ min ) )
= $true )
| ( ( ( times_times_int @ SV1684 @ SV1705 )
= one_one_int )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6978]) ).
thf(6992,plain,
! [SV1700: int,SV1685: int] :
( ( ( SV1685 = one_one_int )
= $true )
| ( ( SV1700
= ( number_number_of_int @ min ) )
= $true )
| ( ( ( times_times_int @ SV1685 @ SV1700 )
= one_one_int )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6979]) ).
thf(6993,plain,
! [SV1686: int,SV1701: int] :
( ( ( SV1701 = one_one_int )
= $true )
| ( ( SV1686
= ( number_number_of_int @ min ) )
= $true )
| ( ( ( times_times_int @ SV1686 @ SV1701 )
= one_one_int )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6980]) ).
thf(6994,plain,
! [SV1687: int,SV1702: int] :
( ( ( SV1702 = one_one_int )
= $true )
| ( ( SV1702
= ( number_number_of_int @ min ) )
= $true )
| ( ( ( times_times_int @ SV1687 @ SV1702 )
= one_one_int )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6981]) ).
thf(6995,plain,
! [SV1204: int] :
( ( ( ord_less_int @ one_one_int @ SV1204 )
= $false )
| ( ( ( sK3_M_9 @ SV1204 )
= one_one_int )
= $false )
| ( ( zprime @ SV1204 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6984]) ).
thf(6996,plain,
! [SV1204: int] :
( ( ( ord_less_int @ one_one_int @ SV1204 )
= $false )
| ( ( ( sK3_M_9 @ SV1204 )
= SV1204 )
= $false )
| ( ( zprime @ SV1204 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6985]) ).
thf(6997,plain,
! [SV1571: int,SV1694: int] :
( ( ( ord_less_eq_int @ zero_zero_int @ SV1694 )
= $false )
| ( ( dvd_dvd_int @ SV1694 @ SV1571 )
= $false )
| ( ( ( SV1694 = one_one_int )
| ( SV1694 = SV1571 ) )
= $true )
| ( ( zprime @ SV1571 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6986]) ).
thf(6998,plain,
! [SV455: real,SV792: nat,SV1695: real] :
( ( ( ord_less_real @ zero_zero_real @ SV1695 )
= $false )
| ( ( ( power_power_real @ SV1695 @ SV792 )
= SV455 )
= $false )
| ( ( SV1695
= ( sK1_X_1 @ SV792 @ SV455 ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV455 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV792 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6987]) ).
thf(6999,plain,
! [SV1458: int,SV831: int,SV1281: int,SV546: int,SV136: int,SV988: int] :
( ( ( ~ ( ord_less_int @ zero_zero_int @ SV988 ) )
= $true )
| ( ( ~ ( ord_less_eq_int @ SV988 @ SV136 )
| ( ord_less_eq_int @ SV546 @ SV1281 ) )
= $true )
| ( ( ord_less_eq_int @ zero_zero_int @ SV831 )
= $false )
| ( ( ord_less_int @ SV1458 @ SV988 )
= $false )
| ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ SV988 @ SV1281 ) @ SV1458 ) )
= $false )
| ( ( ( plus_plus_int @ ( times_times_int @ SV136 @ SV546 ) @ SV831 )
= ( plus_plus_int @ ( times_times_int @ SV988 @ SV1281 ) @ SV1458 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6988]) ).
thf(7000,plain,
! [SV833: int,SV1459: int,SV548: int,SV1283: int,SV138: int,SV990: int] :
( ( ( ~ ( ord_less_int @ zero_zero_int @ SV990 ) )
= $true )
| ( ( ~ ( ord_less_eq_int @ SV990 @ SV138 )
| ( ord_less_eq_int @ SV1283 @ SV548 ) )
= $true )
| ( ( ord_less_eq_int @ zero_zero_int @ SV1459 )
= $false )
| ( ( ord_less_int @ SV833 @ SV138 )
= $false )
| ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ SV990 @ SV1283 ) @ SV1459 ) @ zero_zero_int )
= $false )
| ( ( ( plus_plus_int @ ( times_times_int @ SV138 @ SV548 ) @ SV833 )
= ( plus_plus_int @ ( times_times_int @ SV990 @ SV1283 ) @ SV1459 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6989]) ).
thf(7001,plain,
! [SV845: int,SV170: int,SV568: int] :
( ( ( ord_less_int @ SV568 @ SV170 )
= $false )
| ( ( SV845 = SV568 )
= $true )
| ( ( ord_less_int @ SV845 @ SV170 )
= $false )
| ( ( zcong @ SV845 @ SV568 @ SV170 )
= $false )
| ( ( ord_less_int @ zero_zero_int @ SV170 )
= $false )
| ( ( ord_less_int @ zero_zero_int @ SV568 )
= $false )
| ( ( ord_less_int @ zero_zero_int @ SV845 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6990]) ).
thf(7002,plain,
! [SV1571: int,SV1694: int] :
( ( ( SV1694 = one_one_int )
= $true )
| ( ( SV1694 = SV1571 )
= $true )
| ( ( dvd_dvd_int @ SV1694 @ SV1571 )
= $false )
| ( ( ord_less_eq_int @ zero_zero_int @ SV1694 )
= $false )
| ( ( zprime @ SV1571 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6997]) ).
thf(7003,plain,
! [SV1458: int,SV831: int,SV1281: int,SV546: int,SV136: int,SV988: int] :
( ( ( ord_less_int @ zero_zero_int @ SV988 )
= $false )
| ( ( ~ ( ord_less_eq_int @ SV988 @ SV136 )
| ( ord_less_eq_int @ SV546 @ SV1281 ) )
= $true )
| ( ( ord_less_eq_int @ zero_zero_int @ SV831 )
= $false )
| ( ( ord_less_int @ SV1458 @ SV988 )
= $false )
| ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ SV988 @ SV1281 ) @ SV1458 ) )
= $false )
| ( ( ( plus_plus_int @ ( times_times_int @ SV136 @ SV546 ) @ SV831 )
= ( plus_plus_int @ ( times_times_int @ SV988 @ SV1281 ) @ SV1458 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6999]) ).
thf(7004,plain,
! [SV833: int,SV1459: int,SV548: int,SV1283: int,SV138: int,SV990: int] :
( ( ( ord_less_int @ zero_zero_int @ SV990 )
= $false )
| ( ( ~ ( ord_less_eq_int @ SV990 @ SV138 )
| ( ord_less_eq_int @ SV1283 @ SV548 ) )
= $true )
| ( ( ord_less_eq_int @ zero_zero_int @ SV1459 )
= $false )
| ( ( ord_less_int @ SV833 @ SV138 )
= $false )
| ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ SV990 @ SV1283 ) @ SV1459 ) @ zero_zero_int )
= $false )
| ( ( ( plus_plus_int @ ( times_times_int @ SV138 @ SV548 ) @ SV833 )
= ( plus_plus_int @ ( times_times_int @ SV990 @ SV1283 ) @ SV1459 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7000]) ).
thf(7005,plain,
! [SV1458: int,SV831: int,SV1281: int,SV546: int,SV136: int,SV988: int] :
( ( ( ~ ( ord_less_eq_int @ SV988 @ SV136 ) )
= $true )
| ( ( ord_less_eq_int @ SV546 @ SV1281 )
= $true )
| ( ( ord_less_int @ zero_zero_int @ SV988 )
= $false )
| ( ( ord_less_eq_int @ zero_zero_int @ SV831 )
= $false )
| ( ( ord_less_int @ SV1458 @ SV988 )
= $false )
| ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ SV988 @ SV1281 ) @ SV1458 ) )
= $false )
| ( ( ( plus_plus_int @ ( times_times_int @ SV136 @ SV546 ) @ SV831 )
= ( plus_plus_int @ ( times_times_int @ SV988 @ SV1281 ) @ SV1458 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7003]) ).
thf(7006,plain,
! [SV833: int,SV1459: int,SV548: int,SV1283: int,SV138: int,SV990: int] :
( ( ( ~ ( ord_less_eq_int @ SV990 @ SV138 ) )
= $true )
| ( ( ord_less_eq_int @ SV1283 @ SV548 )
= $true )
| ( ( ord_less_int @ zero_zero_int @ SV990 )
= $false )
| ( ( ord_less_eq_int @ zero_zero_int @ SV1459 )
= $false )
| ( ( ord_less_int @ SV833 @ SV138 )
= $false )
| ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ SV990 @ SV1283 ) @ SV1459 ) @ zero_zero_int )
= $false )
| ( ( ( plus_plus_int @ ( times_times_int @ SV138 @ SV548 ) @ SV833 )
= ( plus_plus_int @ ( times_times_int @ SV990 @ SV1283 ) @ SV1459 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7004]) ).
thf(7007,plain,
! [SV1458: int,SV831: int,SV1281: int,SV546: int,SV136: int,SV988: int] :
( ( ( ord_less_eq_int @ SV988 @ SV136 )
= $false )
| ( ( ord_less_eq_int @ SV546 @ SV1281 )
= $true )
| ( ( ord_less_int @ zero_zero_int @ SV988 )
= $false )
| ( ( ord_less_eq_int @ zero_zero_int @ SV831 )
= $false )
| ( ( ord_less_int @ SV1458 @ SV988 )
= $false )
| ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ SV988 @ SV1281 ) @ SV1458 ) )
= $false )
| ( ( ( plus_plus_int @ ( times_times_int @ SV136 @ SV546 ) @ SV831 )
= ( plus_plus_int @ ( times_times_int @ SV988 @ SV1281 ) @ SV1458 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7005]) ).
thf(7008,plain,
! [SV833: int,SV1459: int,SV548: int,SV1283: int,SV138: int,SV990: int] :
( ( ( ord_less_eq_int @ SV990 @ SV138 )
= $false )
| ( ( ord_less_eq_int @ SV1283 @ SV548 )
= $true )
| ( ( ord_less_int @ zero_zero_int @ SV990 )
= $false )
| ( ( ord_less_eq_int @ zero_zero_int @ SV1459 )
= $false )
| ( ( ord_less_int @ SV833 @ SV138 )
= $false )
| ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ SV990 @ SV1283 ) @ SV1459 ) @ zero_zero_int )
= $false )
| ( ( ( plus_plus_int @ ( times_times_int @ SV138 @ SV548 ) @ SV833 )
= ( plus_plus_int @ ( times_times_int @ SV990 @ SV1283 ) @ SV1459 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7006]) ).
thf(7009,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[1733,7008,7007,7002,7001,6998,6996,6995,6994,6993,6992,6991,6983,6982,6976,6974,6972,6971,6970,6969,6968,6967,6966,6959,6958,6957,6956,6955,6954,6953,6952,6951,6950,6949,6948,6947,6946,6945,6944,6939,6938,6937,6936,6933,6928,6927,6926,6925,6924,6916,6910,6907,6904,6893,6886,6885,6882,6879,6878,6877,6876,6875,6867,6866,6865,6863,6862,6861,6860,6859,6858,6857,6855,6854,6853,6847,6846,6845,6842,6841,6838,6833,6832,6831,6824,6823,6822,6821,6817,6814,6813,6812,6807,6803,6802,6801,6800,6799,6792,6791,6790,6789,6788,6786,6785,6784,6783,6782,6781,6780,6779,6778,6777,6776,6775,6774,6772,6771,6770,6769,6768,6767,6766,6765,6762,6761,6760,6759,6757,6754,6753,6752,6751,6750,6749,6748,6747,6745,6742,6741,6738,6737,6736,6728,6727,6720,6715,6714,6705,6699,6690,6665,6655,6654,6653,6652,6646,6637,6630,6627,6624,6619,6616,6609,6608,6607,6598,6597,6586,6583,6582,6575,6574,6573,6572,6569,6566,6564,6561,6560,6559,6555,6550,6549,6546,6545,6542,6541,6540,6537,6523,6520,6511,6507,6506,6505,6498,6491,6490,6487,6478,6475,6434,6416,6413,6412,6411,6400,6394,6388,6382,6376,6370,6367,6365,6364,6363,6362,6355,6354,6347,6342,6341,6339,6338,6337,6334,6331,6320,6319,6316,6315,6311,6310,6303,6302,6293,6290,6288,6287,6286,6285,6281,6280,6279,6278,6277,6276,6275,6274,6273,6272,6261,6260,6255,6254,6247,6246,6241,6240,6235,6234,6230,6229,6225,6212,6211,6210,6209,6208,6207,6201,6200,6199,6195,6192,6191,6186,6185,6182,6181,6180,6171,6170,6169,6168,6149,6148,6142,6141,6140,6139,6132,6131,6130,6129,6128,6123,6122,6121,6120,6117,6116,6113,6112,6111,6110,6106,6105,6086,6085,6084,6083,6073,6072,6071,6070,6069,6068,6064,6063,6062,6061,6051,6049,6048,6047,6046,6045,6044,6043,6042,6041,6040,6035,6034,6030,6025,6020,6018,6017,6007,6005,6004,6003,6002,5999,5997,5995,5994,5988,5979,5978,5974,5968,5967,5966,5965,5964,5961,5960,5959,5957,5956,5950,5949,5948,5947,5943,5942,5928,5927,5909,5908,5907,5901,5900,5899,5898,5893,5892,5887,5886,5881,5880,5877,5876,5875,5874,5870,5869,5867,5857,5855,5854,5850,5849,5848,5841,5835,5817,5816,5813,5812,5808,5807,5801,5791,5790,5785,5784,5777,5776,5773,5772,5764,5763,5753,5752,5745,5744,5740,5739,5733,5732,5729,5728,5727,5726,5715,5713,5712,5707,5694,5693,5692,5691,5690,5689,5686,5685,5684,5680,5679,5678,5671,5670,5666,5665,5661,5660,5659,5658,5640,5639,5638,5627,5619,5618,5615,5614,5613,5612,5608,5607,5600,5599,5598,5595,5594,5592,5591,5572,5555,5554,5550,5547,5546,5545,5544,5541,5540,5539,5538,5537,5534,5523,5522,5519,5506,5505,5504,5502,5501,5495,5494,5493,5490,5489,5479,5421,5381,5370,5353,5316,5293,5149,5135,5099,5098,5097,5096,5084,5083,5076,5075,5069,5051,5050,5048,5047,5023,5019,5017,5010,5003,4983,4975,4616,4615,4614,4613,4603,4602,4601,4600,4599,4598,4593,4589,4588,4587,4584,4583,4581,4556,4555,4554,4553,4552,4551,4550,4549,4548,4547,4546,4545,4524,4523,4518,4517,4516,4513,4512,4511,4487,4482,4481,4467,4464,4096,4095,4086,4085,4082,4081,4070,4067,4065,4055,4054,4053,4052,4051,4050,4049,4040,4032,4031,4030,4029,4028,4027,4026,4025,4024,4023,4019,4018,4017,4016,4015,4014,4013,4012,4011,4010,4009,4008,4007,4006,4005,4004,4003,4002,4001,4000,3987,3986,3985,3978,3977,3975,3974,3968,3967,3966,3954,3949,3947,3936,3914,3913,3912,3911,3910,3907,3906,3905,3904,3899,3898,3893,3892,3890,3889,3888,3883,3882,3881,3880,3879,3878,3876,3872,3871,3868,3867,3504,3503,3487,3485,3484,3475,3474,3473,3472,3463,3462,3447,3444,3443,3442,3441,3438,3416,3415,3414,3413,3412,3385,3384,3383,3381,3371,3370,3369,3368,3367,3358,3356,3355,3335,3330,3323,3319,3318,3316,3310,3307,3306,3294,3293,3291,3284,3283,3282,3276,3268,3267,3263,3262,3261,3260,3259,3258,3257,3256,3255,3254,3250,3247,3246,3245,3243,3238,3224,3223,3221,3218,3216,3043,3009,3008,2999,2998,2993,2992,2983,2979,2972,2969,2937,2936,2935,2920,2919,2915,2914,2909,2908,2907,2906,2899,2898,2897,2896,2895,2894,2893,2892,2890,2889,2846,2845,2842,2841,2840,2839,2838,2837,2832,2808,2807,2806,2805,2790,2785,2782,2778,2768,2766,2765,2764,2760,2756,2746,2745,2744,2743,2740,2739,2737,2736,2735,2734,2721,2718,2715,2714,2710,2709,2708,2707,2702,2701,2700,2682,2681,2677,2676,2674,2673,2671,2668,2661,2660,2659,2658,2657,2656,2655,2654,2653,2652,2651,2650,2649,2648,2647,2646,2645,2643,2642,2641,2639,2638,2637,2636,2630,2629,2628,2627,2623,2604,2603,2601,2596,2595,2592,2281,2278,2277,2261,2260,2257,2165,2162,2161,2100,2099,2098,2090,2089,2088,2015,2012,2010,1999,1998,1986,1981,1972,1941,1930,1920,1919,1918,1914,1913,1912,1911,1910,1909,1908,1899,1876,1875,1874,1873,1872,1871,1870,1842,1841,1831,1817,1797,1796,1779,1776,1775,1755,1747,1746,1745,1744,1743,1742,1734]) ).
thf(7010,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[7009]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM924^2 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.21 % Computer : n005.cluster.edu
% 0.06/0.21 % Model : x86_64 x86_64
% 0.06/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.21 % Memory : 8046.5625MB
% 0.06/0.21 % OS : Linux 6.8.0-71-generic
% 0.06/0.21 % CPULimit : 300
% 0.06/0.21 % WCLimit : 300
% 0.06/0.21 % DateTime : Tue Oct 6 13:44:09 UTC 2026
% 0.06/0.22 % CPUTime :
% 0.06/0.22 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 174.32/29.38 .....
% 174.32/29.38
% 174.32/29.38 No.of.Axioms: 698
% 174.32/29.38
% 174.32/29.38 Length.of.Defs: 0
% 174.32/29.38
% 174.32/29.38 Contains.Choice.Funs: false
% 174.32/29.38 ........................................................................................................................................................................................................................................................................
% 174.32/29.38
% 174.32/29.38 ********************************
% 174.32/29.38 * All subproblems solved! *
% 174.32/29.38 ********************************
% 174.32/29.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:2,axioms:685,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:7009,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 174.32/29.38
% 174.32/29.38 %**** Beginning of derivation protocol ****
% 174.32/29.38 % SZS output start CNFRefutation
% See solution above
% 29.29/29.44
% 29.29/29.44 %**** End of derivation protocol ****
% 29.29/29.44 %**** no. of clauses in derivation: 6997 ****
% 29.29/29.44 %**** clause counter: 7009 ****
% 29.29/29.44
% 29.29/29.44 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:2,axioms:685,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:7009,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------