%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM924+1 : 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 : n017.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 10:35:31 AM UTC 2026
% Result : Theorem 5.98s 1.22s
% Output : CNFRefutation 5.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 105
% Syntax : Number of formulae : 1178 ( 871 unt; 0 typ; 0 def)
% Number of atoms : 5566 (2279 equ; 0 cnn)
% Maximal formula atoms : 7 ( 4 avg)
% Number of connectives : 12296 (1531 ~;1416 |; 118 &;9099 @)
% ( 86 <=>; 46 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 25 usr; 11 con; 0-2 aty)
% Number of variables : 2446 ( 0 ^;2446 !; 0 ?;2446 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_bit0,type,
bit0: $i > $i ).
thf(tp_bit1,type,
bit1: $i > $i ).
thf(tp_m,type,
m: $i ).
thf(tp_number_number_of_int,type,
number_number_of_int: $i > $i ).
thf(tp_number_number_of_nat,type,
number_number_of_nat: $i > $i ).
thf(tp_one_one_int,type,
one_one_int: $i ).
thf(tp_one_one_nat,type,
one_one_nat: $i ).
thf(tp_ord_less_eq_int,type,
ord_less_eq_int: $i > $i > $o ).
thf(tp_ord_less_eq_nat,type,
ord_less_eq_nat: $i > $i > $o ).
thf(tp_ord_less_int,type,
ord_less_int: $i > $i > $o ).
thf(tp_ord_less_nat,type,
ord_less_nat: $i > $i > $o ).
thf(tp_pls,type,
pls: $i ).
thf(tp_plus_plus_int,type,
plus_plus_int: $i > $i > $i ).
thf(tp_plus_plus_nat,type,
plus_plus_nat: $i > $i > $i ).
thf(tp_power_power_int,type,
power_power_int: $i > $i > $i ).
thf(tp_power_power_nat,type,
power_power_nat: $i > $i > $i ).
thf(tp_s,type,
s: $i ).
thf(tp_sK1_T,type,
sK1_T: $i ).
thf(tp_t,type,
t: $i ).
thf(tp_times_times_int,type,
times_times_int: $i > $i > $i ).
thf(tp_times_times_nat,type,
times_times_nat: $i > $i > $i ).
thf(tp_twoSqu526106917sum2sq,type,
twoSqu526106917sum2sq: $i > $o ).
thf(tp_zero_zero_int,type,
zero_zero_int: $i ).
thf(tp_zero_zero_nat,type,
zero_zero_nat: $i ).
thf(tp_zprime,type,
zprime: $i > $o ).
thf(1,axiom,
( zero_zero_int
= ( number_number_of_int @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_zero__is__num__zero) ).
thf(2,axiom,
! [Z: $i,W: $i] :
( ( plus_plus_int @ Z @ W )
= ( plus_plus_int @ W @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_zadd__commute) ).
thf(3,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( 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_103_zadd__left__commute) ).
thf(4,axiom,
! [Z1: $i,Z2: $i,Z3: $i] :
( ( plus_plus_int @ ( plus_plus_int @ Z1 @ Z2 ) @ Z3 )
= ( plus_plus_int @ Z1 @ ( plus_plus_int @ Z2 @ Z3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_zadd__assoc) ).
thf(5,axiom,
! [V: $i,B: $i,C: $i] :
( ( times_times_nat @ ( number_number_of_nat @ V ) @ ( plus_plus_nat @ B @ C ) )
= ( plus_plus_nat @ ( times_times_nat @ ( number_number_of_nat @ V ) @ B ) @ ( times_times_nat @ ( number_number_of_nat @ V ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_right__distrib__number__of) ).
thf(6,axiom,
! [V: $i,B: $i,C: $i] :
( ( times_times_int @ ( number_number_of_int @ V ) @ ( plus_plus_int @ B @ C ) )
= ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ V ) @ B ) @ ( times_times_int @ ( number_number_of_int @ V ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_right__distrib__number__of) ).
thf(7,axiom,
! [A: $i,B_1: $i,V_1: $i] :
( ( times_times_nat @ ( plus_plus_nat @ A @ B_1 ) @ ( number_number_of_nat @ V_1 ) )
= ( plus_plus_nat @ ( times_times_nat @ A @ ( number_number_of_nat @ V_1 ) ) @ ( times_times_nat @ B_1 @ ( number_number_of_nat @ V_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_left__distrib__number__of) ).
thf(8,axiom,
! [A: $i,B_1: $i,V_1: $i] :
( ( times_times_int @ ( plus_plus_int @ A @ B_1 ) @ ( number_number_of_int @ V_1 ) )
= ( plus_plus_int @ ( times_times_int @ A @ ( number_number_of_int @ V_1 ) ) @ ( times_times_int @ B_1 @ ( number_number_of_int @ V_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_left__distrib__number__of) ).
thf(9,axiom,
! [X_1: $i,Y_1: $i] :
( ( ( plus_plus_int @ ( times_times_int @ X_1 @ X_1 ) @ ( times_times_int @ Y_1 @ Y_1 ) )
= zero_zero_int )
<=> ( ( X_1 = zero_zero_int )
& ( Y_1 = zero_zero_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_sum__squares__eq__zero__iff) ).
thf(10,axiom,
! [X: $i,Y: $i] :
( ( ord_less_int @ X @ Y )
| ( X = Y )
| ( ord_less_int @ Y @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_zless__linear) ).
thf(11,axiom,
! [K: $i,L: $i] :
( ( ( bit0 @ K )
= ( bit0 @ L ) )
<=> ( K = L ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_rel__simps_I48_J) ).
thf(12,axiom,
! [K: $i,L: $i] :
( ( ( bit1 @ K )
= ( bit1 @ L ) )
<=> ( K = L ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_rel__simps_I51_J) ).
thf(13,axiom,
! [W_1: $i,X_1: $i] :
( ( ( number_number_of_int @ W_1 )
= X_1 )
<=> ( X_1
= ( number_number_of_int @ W_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_number__of__reorient) ).
thf(14,axiom,
! [W_1: $i,X_1: $i] :
( ( ( number_number_of_nat @ W_1 )
= X_1 )
<=> ( X_1
= ( number_number_of_nat @ W_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_number__of__reorient) ).
thf(15,axiom,
! [X_1: $i,Y_1: $i] :
( ( ( number_number_of_int @ X_1 )
= ( number_number_of_int @ Y_1 ) )
<=> ( X_1 = Y_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_eq__number__of) ).
thf(16,axiom,
! [Z: $i] :
( ( ord_less_eq_int @ zero_zero_int @ Z )
=> ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ Z ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_le__imp__0__less) ).
thf(17,axiom,
! [V_3: $i,V_2: $i] :
( ( ( ord_less_int @ V_2 @ pls )
=> ( ( plus_plus_nat @ ( number_number_of_nat @ V_2 ) @ ( number_number_of_nat @ V_3 ) )
= ( number_number_of_nat @ V_3 ) ) )
& ( ~ ( ord_less_int @ V_2 @ pls )
=> ( ( ( ord_less_int @ V_3 @ pls )
=> ( ( plus_plus_nat @ ( number_number_of_nat @ V_2 ) @ ( number_number_of_nat @ V_3 ) )
= ( number_number_of_nat @ V_2 ) ) )
& ( ~ ( ord_less_int @ V_3 @ pls )
=> ( ( plus_plus_nat @ ( number_number_of_nat @ V_2 ) @ ( number_number_of_nat @ V_3 ) )
= ( number_number_of_nat @ ( plus_plus_int @ V_2 @ V_3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_add__nat__number__of) ).
thf(18,axiom,
! [V_5: $i,V_4: $i] :
( ( ord_less_eq_int @ pls @ V_4 )
=> ( ( ord_less_eq_int @ pls @ V_5 )
=> ( ( 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_88_semiring__add__number__of) ).
thf(19,axiom,
! [V_5: $i,V_4: $i] :
( ( ord_less_eq_int @ pls @ V_4 )
=> ( ( ord_less_eq_int @ pls @ V_5 )
=> ( ( plus_plus_int @ ( number_number_of_int @ V_4 ) @ ( number_number_of_int @ V_5 ) )
= ( number_number_of_int @ ( plus_plus_int @ V_4 @ V_5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_semiring__add__number__of) ).
thf(20,axiom,
! [W_1: $i,Z_1: $i] :
( ( ord_less_int @ W_1 @ ( plus_plus_int @ Z_1 @ one_one_int ) )
<=> ( ord_less_eq_int @ W_1 @ Z_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_zle__add1__eq__le) ).
thf(21,axiom,
! [W_1: $i,Z_1: $i] :
( ( ord_less_eq_int @ ( plus_plus_int @ W_1 @ one_one_int ) @ Z_1 )
<=> ( ord_less_int @ W_1 @ Z_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_add1__zle__eq) ).
thf(22,axiom,
! [W: $i,Z: $i] :
( ( ord_less_int @ W @ Z )
=> ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_zless__imp__add1__zle) ).
thf(23,axiom,
( one_one_nat
= ( number_number_of_nat @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_Numeral1__eq1__nat) ).
thf(24,axiom,
( ( number_number_of_nat @ ( bit1 @ pls ) )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_nat__numeral__1__eq__1) ).
thf(25,axiom,
! [Z_1: $i] :
( ( ord_less_eq_int @ one_one_int @ Z_1 )
<=> ( ord_less_int @ zero_zero_int @ Z_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_int__one__le__iff__zero__less) ).
thf(26,axiom,
! [V_7: $i,V_6: $i] :
( ( ord_less_nat @ ( number_number_of_nat @ V_7 ) @ ( number_number_of_nat @ V_6 ) )
<=> ( ( ( ord_less_int @ V_7 @ V_6 )
=> ( ord_less_int @ pls @ V_6 ) )
& ( ord_less_int @ V_7 @ V_6 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_less__nat__number__of) ).
thf(27,axiom,
! [K: $i,L: $i] :
( ( ord_less_int @ ( bit0 @ K ) @ ( bit1 @ L ) )
<=> ( ord_less_eq_int @ K @ L ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_rel__simps_I15_J) ).
thf(28,axiom,
! [K1: $i,K2: $i] :
( ( ord_less_int @ ( bit0 @ K1 ) @ ( bit1 @ K2 ) )
<=> ( ord_less_eq_int @ K1 @ K2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_less__int__code_I14_J) ).
thf(29,axiom,
! [K: $i,L: $i] :
( ( ord_less_eq_int @ ( bit1 @ K ) @ ( bit0 @ L ) )
<=> ( ord_less_int @ K @ L ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_rel__simps_I33_J) ).
thf(30,axiom,
! [K1: $i,K2: $i] :
( ( ord_less_eq_int @ ( bit1 @ K1 ) @ ( bit0 @ K2 ) )
<=> ( ord_less_int @ K1 @ K2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_less__eq__int__code_I15_J) ).
thf(31,axiom,
! [K: $i] :
( ( ord_less_int @ pls @ ( bit1 @ K ) )
<=> ( ord_less_eq_int @ pls @ K ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_rel__simps_I5_J) ).
thf(32,axiom,
! [K: $i] :
( ( ord_less_eq_int @ ( bit1 @ K ) @ pls )
<=> ( ord_less_int @ K @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_rel__simps_I29_J) ).
thf(33,axiom,
! [W: $i,Z1: $i,Z2: $i] :
( ( times_times_int @ W @ ( plus_plus_int @ Z1 @ Z2 ) )
= ( plus_plus_int @ ( times_times_int @ W @ Z1 ) @ ( times_times_int @ W @ Z2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_zadd__zmult__distrib2) ).
thf(34,axiom,
! [Z1: $i,Z2: $i,W: $i] :
( ( times_times_int @ ( plus_plus_int @ Z1 @ Z2 ) @ W )
= ( plus_plus_int @ ( times_times_int @ Z1 @ W ) @ ( times_times_int @ Z2 @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_zadd__zmult__distrib) ).
thf(35,axiom,
! [V_2: $i,W: $i] :
( ( plus_plus_int @ ( number_number_of_int @ V_2 ) @ ( number_number_of_int @ W ) )
= ( number_number_of_int @ ( plus_plus_int @ V_2 @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_plus__numeral__code_I9_J) ).
thf(36,axiom,
! [Z: $i] :
( ( times_times_int @ one_one_int @ Z )
= Z ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_zmult__1) ).
thf(37,axiom,
! [Z: $i] :
( ( times_times_int @ Z @ one_one_int )
= Z ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_zmult__1__right) ).
thf(38,axiom,
! [K: $i,L: $i] :
( ( 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_68_less__number__of__int__code) ).
thf(39,axiom,
! [K_1: $i,L_1: $i] :
( ( times_times_int @ ( bit0 @ K_1 ) @ L_1 )
= ( bit0 @ ( times_times_int @ K_1 @ L_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_mult__Bit0) ).
thf(40,axiom,
! [W: $i] :
( ( times_times_int @ pls @ W )
= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_mult__Pls) ).
thf(41,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_65_nat__1__add__1) ).
thf(42,axiom,
! [Y_1: $i] :
( ( ord_less_eq_int @ one_one_int @ ( number_number_of_int @ Y_1 ) )
<=> ( ord_less_eq_int @ ( bit1 @ pls ) @ Y_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_le__special_I2_J) ).
thf(43,axiom,
! [X_1: $i] :
( ( ord_less_eq_int @ ( number_number_of_int @ X_1 ) @ one_one_int )
<=> ( ord_less_eq_int @ X_1 @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_le__special_I4_J) ).
thf(44,axiom,
( zero_zero_nat
= ( number_number_of_nat @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_semiring__norm_I113_J) ).
thf(45,axiom,
( ( number_number_of_nat @ pls )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_nat__number__of__Pls) ).
thf(46,axiom,
! [Z_2: $i,Z: $i,W_2: $i,W: $i] :
( ( ord_less_int @ W_2 @ W )
=> ( ( ord_less_eq_int @ Z_2 @ Z )
=> ( ord_less_int @ ( plus_plus_int @ W_2 @ Z_2 ) @ ( plus_plus_int @ W @ Z ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_zadd__zless__mono) ).
thf(47,axiom,
! [K: $i] :
( ( ord_less_eq_int @ pls @ ( bit0 @ K ) )
<=> ( ord_less_eq_int @ pls @ K ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_rel__simps_I21_J) ).
thf(48,axiom,
! [K: $i] :
( ( ord_less_eq_int @ ( bit0 @ K ) @ pls )
<=> ( ord_less_eq_int @ K @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_rel__simps_I27_J) ).
thf(49,axiom,
! [K: $i,L: $i] :
( ( ord_less_eq_int @ ( bit0 @ K ) @ ( bit1 @ L ) )
<=> ( ord_less_eq_int @ K @ L ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_rel__simps_I32_J) ).
thf(50,axiom,
! [K1: $i,K2: $i] :
( ( ord_less_eq_int @ ( bit0 @ K1 ) @ ( bit1 @ K2 ) )
<=> ( ord_less_eq_int @ K1 @ K2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_less__eq__int__code_I14_J) ).
thf(51,axiom,
! [K: $i] :
( ( ord_less_eq_int @ pls @ ( bit1 @ K ) )
<=> ( ord_less_eq_int @ pls @ K ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_rel__simps_I22_J) ).
thf(52,axiom,
! [V_7: $i,W_1: $i] :
( ( ord_less_eq_nat @ ( number_number_of_nat @ V_7 ) @ ( number_number_of_nat @ W_1 ) )
<=> ~ ( ord_less_nat @ ( number_number_of_nat @ W_1 ) @ ( number_number_of_nat @ V_7 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_le__number__of__eq__not__less) ).
thf(53,axiom,
! [V_7: $i,W_1: $i] :
( ( ord_less_eq_int @ ( number_number_of_int @ V_7 ) @ ( number_number_of_int @ W_1 ) )
<=> ~ ( ord_less_int @ ( number_number_of_int @ W_1 ) @ ( number_number_of_int @ V_7 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_le__number__of__eq__not__less) ).
thf(54,axiom,
! [V_7: $i] :
( ( ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ V_7 ) )
<=> ( ord_less_int @ pls @ V_7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_less__0__number__of) ).
thf(55,axiom,
! [Y_1: $i] :
( ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ Y_1 ) )
<=> ( ord_less_eq_int @ pls @ Y_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_le__special_I1_J) ).
thf(56,axiom,
! [X_1: $i] :
( ( ord_less_eq_int @ ( number_number_of_int @ X_1 ) @ zero_zero_int )
<=> ( ord_less_eq_int @ X_1 @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_le__special_I3_J) ).
thf(57,axiom,
! [X_2: $i,Y_2: $i] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X_2 @ X_2 ) @ ( times_times_int @ Y_2 @ Y_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_sum__squares__ge__zero) ).
thf(58,axiom,
! [X_1: $i,Y_1: $i] :
( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ X_1 @ X_1 ) @ ( times_times_int @ Y_1 @ Y_1 ) ) @ zero_zero_int )
<=> ( ( X_1 = zero_zero_int )
& ( Y_1 = zero_zero_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_sum__squares__le__zero__iff) ).
thf(59,axiom,
! [V_8: $i,W_3: $i] :
( ( number_number_of_int @ ( times_times_int @ V_8 @ W_3 ) )
= ( times_times_int @ ( number_number_of_int @ V_8 ) @ ( number_number_of_int @ W_3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_number__of__mult) ).
thf(60,axiom,
! [V_9: $i,W_4: $i] :
( ( times_times_int @ ( number_number_of_int @ V_9 ) @ ( number_number_of_int @ W_4 ) )
= ( number_number_of_int @ ( times_times_int @ V_9 @ W_4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_arith__simps_I32_J) ).
thf(61,axiom,
! [V_10: $i,W_5: $i,Z_3: $i] :
( ( times_times_int @ ( number_number_of_int @ V_10 ) @ ( times_times_int @ ( number_number_of_int @ W_5 ) @ Z_3 ) )
= ( times_times_int @ ( number_number_of_int @ ( times_times_int @ V_10 @ W_5 ) ) @ Z_3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_mult__number__of__left) ).
thf(62,axiom,
! [V_12: $i,V_11: $i] :
( ( ord_less_eq_int @ pls @ V_11 )
=> ( ( ord_less_eq_int @ pls @ V_12 )
=> ( ( times_times_int @ ( number_number_of_int @ V_11 ) @ ( number_number_of_int @ V_12 ) )
= ( number_number_of_int @ ( times_times_int @ V_11 @ V_12 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_semiring__mult__number__of) ).
thf(63,axiom,
! [V_12: $i,V_11: $i] :
( ( ord_less_eq_int @ pls @ V_11 )
=> ( ( ord_less_eq_int @ pls @ V_12 )
=> ( ( times_times_nat @ ( number_number_of_nat @ V_11 ) @ ( number_number_of_nat @ V_12 ) )
= ( number_number_of_nat @ ( times_times_int @ V_11 @ V_12 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_semiring__mult__number__of) ).
thf(64,axiom,
! [V_7: $i] :
( ( zero_zero_nat
= ( number_number_of_nat @ V_7 ) )
<=> ( ord_less_eq_int @ V_7 @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_eq__0__number__of) ).
thf(65,axiom,
! [V_7: $i] :
( ( ( number_number_of_nat @ V_7 )
= zero_zero_nat )
<=> ( ord_less_eq_int @ V_7 @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_eq__number__of__0) ).
thf(66,axiom,
! [K_1: $i,I: $i,J: $i] :
( ( ord_less_eq_int @ I @ J )
=> ( ord_less_eq_int @ ( plus_plus_int @ K_1 @ I ) @ ( plus_plus_int @ K_1 @ J ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_zadd__left__mono) ).
thf(67,axiom,
! [Z_1: $i,W_1: $i] :
( ( ord_less_int @ Z_1 @ W_1 )
<=> ( ( ord_less_eq_int @ Z_1 @ W_1 )
& ( Z_1 != W_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_zless__le) ).
thf(68,axiom,
! [K: $i,L: $i] :
( ( ord_less_eq_int @ ( bit0 @ K ) @ ( bit0 @ L ) )
<=> ( ord_less_eq_int @ K @ L ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_rel__simps_I31_J) ).
thf(69,axiom,
! [K1: $i,K2: $i] :
( ( ord_less_eq_int @ ( bit0 @ K1 ) @ ( bit0 @ K2 ) )
<=> ( ord_less_eq_int @ K1 @ K2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_less__eq__int__code_I13_J) ).
thf(70,axiom,
ord_less_eq_int @ pls @ pls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_rel__simps_I19_J) ).
thf(71,axiom,
! [K: $i,L: $i] :
( ( ord_less_eq_int @ ( bit1 @ K ) @ ( bit1 @ L ) )
<=> ( ord_less_eq_int @ K @ L ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_rel__simps_I34_J) ).
thf(72,axiom,
! [K1: $i,K2: $i] :
( ( ord_less_eq_int @ ( bit1 @ K1 ) @ ( bit1 @ K2 ) )
<=> ( ord_less_eq_int @ K1 @ K2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_less__eq__int__code_I16_J) ).
thf(73,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( 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_33_zpower__zadd__distrib) ).
thf(74,axiom,
! [Z: $i,W: $i] :
( ( ord_less_eq_int @ Z @ W )
=> ( ( ord_less_eq_int @ W @ Z )
=> ( Z = W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_zle__antisym) ).
thf(75,axiom,
! [K_1: $i,I: $i,J: $i] :
( ( ord_less_eq_int @ I @ J )
=> ( ( ord_less_eq_int @ J @ K_1 )
=> ( ord_less_eq_int @ I @ K_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_zle__trans) ).
thf(76,axiom,
! [Z1: $i,Z2: $i,Z3: $i] :
( ( times_times_int @ ( times_times_int @ Z1 @ Z2 ) @ Z3 )
= ( times_times_int @ Z1 @ ( times_times_int @ Z2 @ Z3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_zmult__assoc) ).
thf(77,axiom,
! [X_1: $i,Y_1: $i] :
( ( ord_less_eq_int @ ( number_number_of_int @ X_1 ) @ ( number_number_of_int @ Y_1 ) )
<=> ( ord_less_eq_int @ X_1 @ Y_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_le__number__of) ).
thf(78,axiom,
! [K: $i,L: $i] :
( ( 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_28_less__eq__number__of__int__code) ).
thf(79,axiom,
! [V_2: $i,W: $i] :
( ( times_times_int @ ( number_number_of_int @ V_2 ) @ ( number_number_of_int @ W ) )
= ( number_number_of_int @ ( times_times_int @ V_2 @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_times__numeral__code_I5_J) ).
thf(80,axiom,
! [Z: $i,W: $i] :
( ( ord_less_eq_int @ Z @ W )
| ( ord_less_eq_int @ W @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_zle__linear) ).
thf(81,axiom,
! [Z: $i,W: $i] :
( ( times_times_int @ Z @ W )
= ( times_times_int @ W @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_zmult__commute) ).
thf(82,axiom,
! [K_1: $i] :
( ( number_number_of_int @ K_1 )
= K_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_number__of__is__id) ).
thf(83,axiom,
! [W: $i] : ( ord_less_eq_int @ W @ W ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_zle__refl) ).
thf(86,axiom,
~ ! [T: $i] :
( ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int )
!= ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ T ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20__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(87,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_19_t__l__p) ).
thf(88,axiom,
! [V_13: $i] :
( ( plus_plus_int @ ( number_number_of_int @ V_13 ) @ one_one_int )
= ( number_number_of_int @ ( plus_plus_int @ V_13 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_add__special_I3_J) ).
thf(89,axiom,
! [W_6: $i] :
( ( plus_plus_int @ one_one_int @ ( number_number_of_int @ W_6 ) )
= ( number_number_of_int @ ( plus_plus_int @ ( bit1 @ pls ) @ W_6 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_add__special_I2_J) ).
thf(90,axiom,
! [A_1: $i] :
( ( ( power_power_int @ A_1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int )
<=> ( A_1 = zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_zero__eq__power2) ).
thf(91,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_15_zero__power2) ).
thf(92,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_14_zero__power2) ).
thf(93,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_13_one__power2) ).
thf(94,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_12_one__power2) ).
thf(95,axiom,
! [A_1: $i] :
( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A_1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
<=> ( A_1 != zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_zero__less__power2) ).
thf(96,axiom,
! [A_2: $i] :
~ ( ord_less_int @ ( power_power_int @ A_2 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_power2__less__0) ).
thf(97,axiom,
! [X_1: $i,Y_1: $i] :
( ( ( plus_plus_int @ ( power_power_int @ X_1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_int )
<=> ( ( X_1 = zero_zero_int )
& ( Y_1 = zero_zero_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_sum__power2__eq__zero__iff) ).
thf(98,axiom,
! [X_1: $i,Y_1: $i] :
( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X_1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
<=> ( ( X_1 != zero_zero_int )
| ( Y_1 != zero_zero_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_sum__power2__gt__zero__iff) ).
thf(99,axiom,
! [X: $i,Y: $i] :
~ ( 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_7_not__sum__power2__lt__zero) ).
thf(100,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(101,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(102,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(103,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(104,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(105,axiom,
ord_less_int @ t @ one_one_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_calculation_I1_J) ).
thf(106,axiom,
ord_less_int @ t @ zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__096t_A_060_A0_096) ).
thf(107,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(108,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)],[107]) ).
thf(109,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)],[108]) ).
thf(110,plain,
( ( ! [W_1: $i,X_1: $i] :
( ( ( number_number_of_int @ W_1 )
= X_1 )
<=> ( X_1
= ( number_number_of_int @ W_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(111,plain,
( ( ! [X_1: $i,Y_1: $i] :
( ( ( number_number_of_int @ X_1 )
= ( number_number_of_int @ Y_1 ) )
<=> ( X_1 = Y_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(112,plain,
( ( ! [V_8: $i,W_3: $i] :
( ( number_number_of_int @ ( times_times_int @ V_8 @ W_3 ) )
= ( times_times_int @ ( number_number_of_int @ V_8 ) @ ( number_number_of_int @ W_3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(113,plain,
( ( ! [V_9: $i,W_4: $i] :
( ( times_times_int @ ( number_number_of_int @ V_9 ) @ ( number_number_of_int @ W_4 ) )
= ( number_number_of_int @ ( times_times_int @ V_9 @ W_4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(114,plain,
( ( ! [V_10: $i,W_5: $i,Z_3: $i] :
( ( times_times_int @ ( number_number_of_int @ V_10 ) @ ( times_times_int @ ( number_number_of_int @ W_5 ) @ Z_3 ) )
= ( times_times_int @ ( number_number_of_int @ ( times_times_int @ V_10 @ W_5 ) ) @ Z_3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(115,plain,
( ( ! [V_12: $i,V_11: $i] :
( ( ord_less_eq_int @ pls @ V_11 )
=> ( ( ord_less_eq_int @ pls @ V_12 )
=> ( ( times_times_int @ ( number_number_of_int @ V_11 ) @ ( number_number_of_int @ V_12 ) )
= ( number_number_of_int @ ( times_times_int @ V_11 @ V_12 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(116,plain,
( ( ! [V_12: $i,V_11: $i] :
( ( ord_less_eq_int @ pls @ V_11 )
=> ( ( ord_less_eq_int @ pls @ V_12 )
=> ( ( times_times_nat @ ( number_number_of_nat @ V_11 ) @ ( number_number_of_nat @ V_12 ) )
= ( number_number_of_nat @ ( times_times_int @ V_11 @ V_12 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(117,plain,
( ( ! [Z: $i,W: $i] :
( ( ord_less_eq_int @ Z @ W )
=> ( ( ord_less_eq_int @ W @ Z )
=> ( Z = W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(118,plain,
( ( ! [K_1: $i,I: $i,J: $i] :
( ( ord_less_eq_int @ I @ J )
=> ( ( ord_less_eq_int @ J @ K_1 )
=> ( ord_less_eq_int @ I @ K_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(119,plain,
( ( ! [Z1: $i,Z2: $i,Z3: $i] :
( ( times_times_int @ ( times_times_int @ Z1 @ Z2 ) @ Z3 )
= ( times_times_int @ Z1 @ ( times_times_int @ Z2 @ Z3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(120,plain,
( ( ! [X_1: $i,Y_1: $i] :
( ( ord_less_eq_int @ ( number_number_of_int @ X_1 ) @ ( number_number_of_int @ Y_1 ) )
<=> ( ord_less_eq_int @ X_1 @ Y_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(121,plain,
( ( ! [K: $i,L: $i] :
( ( 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)],[78]) ).
thf(122,plain,
( ( ! [V_2: $i,W: $i] :
( ( times_times_int @ ( number_number_of_int @ V_2 ) @ ( number_number_of_int @ W ) )
= ( number_number_of_int @ ( times_times_int @ V_2 @ W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(123,plain,
( ( ! [Z: $i,W: $i] :
( ( ord_less_eq_int @ Z @ W )
| ( ord_less_eq_int @ W @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(124,plain,
( ( ! [Z: $i,W: $i] :
( ( times_times_int @ Z @ W )
= ( times_times_int @ W @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(125,plain,
( ( ! [K_1: $i] :
( ( number_number_of_int @ K_1 )
= K_1 ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(126,plain,
( ( ! [W: $i] : ( ord_less_eq_int @ W @ W ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(127,plain,
( ( ~ ! [T: $i] :
( ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int )
!= ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(128,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)],[87]) ).
thf(129,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)],[100]) ).
thf(130,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)],[103]) ).
thf(131,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)],[104]) ).
thf(132,plain,
( ( zero_zero_int
= ( number_number_of_int @ pls ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(133,plain,
( ( ! [Z: $i,W: $i] :
( ( plus_plus_int @ Z @ W )
= ( plus_plus_int @ W @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(134,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( plus_plus_int @ X @ ( plus_plus_int @ Y @ Z ) )
= ( plus_plus_int @ Y @ ( plus_plus_int @ X @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(135,plain,
( ( ! [Z1: $i,Z2: $i,Z3: $i] :
( ( plus_plus_int @ ( plus_plus_int @ Z1 @ Z2 ) @ Z3 )
= ( plus_plus_int @ Z1 @ ( plus_plus_int @ Z2 @ Z3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(136,plain,
( ( ! [V: $i,B: $i,C: $i] :
( ( times_times_nat @ ( number_number_of_nat @ V ) @ ( plus_plus_nat @ B @ C ) )
= ( plus_plus_nat @ ( times_times_nat @ ( number_number_of_nat @ V ) @ B ) @ ( times_times_nat @ ( number_number_of_nat @ V ) @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(137,plain,
( ( ! [V: $i,B: $i,C: $i] :
( ( times_times_int @ ( number_number_of_int @ V ) @ ( plus_plus_int @ B @ C ) )
= ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ V ) @ B ) @ ( times_times_int @ ( number_number_of_int @ V ) @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(138,plain,
( ( ! [A: $i,B_1: $i,V_1: $i] :
( ( times_times_nat @ ( plus_plus_nat @ A @ B_1 ) @ ( number_number_of_nat @ V_1 ) )
= ( plus_plus_nat @ ( times_times_nat @ A @ ( number_number_of_nat @ V_1 ) ) @ ( times_times_nat @ B_1 @ ( number_number_of_nat @ V_1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(139,plain,
( ( ! [A: $i,B_1: $i,V_1: $i] :
( ( times_times_int @ ( plus_plus_int @ A @ B_1 ) @ ( number_number_of_int @ V_1 ) )
= ( plus_plus_int @ ( times_times_int @ A @ ( number_number_of_int @ V_1 ) ) @ ( times_times_int @ B_1 @ ( number_number_of_int @ V_1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(140,plain,
( ( ! [X_1: $i,Y_1: $i] :
( ( ( plus_plus_int @ ( times_times_int @ X_1 @ X_1 ) @ ( times_times_int @ Y_1 @ Y_1 ) )
= zero_zero_int )
<=> ( ( X_1 = zero_zero_int )
& ( Y_1 = zero_zero_int ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(141,plain,
( ( ! [X: $i,Y: $i] :
( ( ord_less_int @ X @ Y )
| ( X = Y )
| ( ord_less_int @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(142,plain,
( ( ! [K: $i,L: $i] :
( ( ( bit0 @ K )
= ( bit0 @ L ) )
<=> ( K = L ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(143,plain,
( ( ! [K: $i,L: $i] :
( ( ( bit1 @ K )
= ( bit1 @ L ) )
<=> ( K = L ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(144,plain,
( ( ! [W_1: $i,X_1: $i] :
( ( ( number_number_of_nat @ W_1 )
= X_1 )
<=> ( X_1
= ( number_number_of_nat @ W_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(145,plain,
( ( ! [Z: $i] :
( ( ord_less_eq_int @ zero_zero_int @ Z )
=> ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(146,plain,
( ( ! [V_3: $i,V_2: $i] :
( ( ( ord_less_int @ V_2 @ pls )
=> ( ( plus_plus_nat @ ( number_number_of_nat @ V_2 ) @ ( number_number_of_nat @ V_3 ) )
= ( number_number_of_nat @ V_3 ) ) )
& ( ~ ( ord_less_int @ V_2 @ pls )
=> ( ( ( ord_less_int @ V_3 @ pls )
=> ( ( plus_plus_nat @ ( number_number_of_nat @ V_2 ) @ ( number_number_of_nat @ V_3 ) )
= ( number_number_of_nat @ V_2 ) ) )
& ( ~ ( ord_less_int @ V_3 @ pls )
=> ( ( plus_plus_nat @ ( number_number_of_nat @ V_2 ) @ ( number_number_of_nat @ V_3 ) )
= ( number_number_of_nat @ ( plus_plus_int @ V_2 @ V_3 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(147,plain,
( ( ! [V_5: $i,V_4: $i] :
( ( ord_less_eq_int @ pls @ V_4 )
=> ( ( ord_less_eq_int @ pls @ V_5 )
=> ( ( 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)],[18]) ).
thf(148,plain,
( ( ! [V_5: $i,V_4: $i] :
( ( ord_less_eq_int @ pls @ V_4 )
=> ( ( ord_less_eq_int @ pls @ V_5 )
=> ( ( plus_plus_int @ ( number_number_of_int @ V_4 ) @ ( number_number_of_int @ V_5 ) )
= ( number_number_of_int @ ( plus_plus_int @ V_4 @ V_5 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(149,plain,
( ( ! [W_1: $i,Z_1: $i] :
( ( ord_less_int @ W_1 @ ( plus_plus_int @ Z_1 @ one_one_int ) )
<=> ( ord_less_eq_int @ W_1 @ Z_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(150,plain,
( ( ! [W_1: $i,Z_1: $i] :
( ( ord_less_eq_int @ ( plus_plus_int @ W_1 @ one_one_int ) @ Z_1 )
<=> ( ord_less_int @ W_1 @ Z_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(151,plain,
( ( ! [W: $i,Z: $i] :
( ( ord_less_int @ W @ Z )
=> ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(152,plain,
( ( one_one_nat
= ( number_number_of_nat @ ( bit1 @ pls ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(153,plain,
( ( ( number_number_of_nat @ ( bit1 @ pls ) )
= one_one_nat )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(154,plain,
( ( ! [Z_1: $i] :
( ( ord_less_eq_int @ one_one_int @ Z_1 )
<=> ( ord_less_int @ zero_zero_int @ Z_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(155,plain,
( ( ! [V_7: $i,V_6: $i] :
( ( ord_less_nat @ ( number_number_of_nat @ V_7 ) @ ( number_number_of_nat @ V_6 ) )
<=> ( ( ( ord_less_int @ V_7 @ V_6 )
=> ( ord_less_int @ pls @ V_6 ) )
& ( ord_less_int @ V_7 @ V_6 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(156,plain,
( ( ! [K: $i,L: $i] :
( ( ord_less_int @ ( bit0 @ K ) @ ( bit1 @ L ) )
<=> ( ord_less_eq_int @ K @ L ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(157,plain,
( ( ! [K1: $i,K2: $i] :
( ( ord_less_int @ ( bit0 @ K1 ) @ ( bit1 @ K2 ) )
<=> ( ord_less_eq_int @ K1 @ K2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(158,plain,
( ( ! [K: $i,L: $i] :
( ( ord_less_eq_int @ ( bit1 @ K ) @ ( bit0 @ L ) )
<=> ( ord_less_int @ K @ L ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(159,plain,
( ( ! [K1: $i,K2: $i] :
( ( ord_less_eq_int @ ( bit1 @ K1 ) @ ( bit0 @ K2 ) )
<=> ( ord_less_int @ K1 @ K2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(160,plain,
( ( ! [K: $i] :
( ( ord_less_int @ pls @ ( bit1 @ K ) )
<=> ( ord_less_eq_int @ pls @ K ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(161,plain,
( ( ! [K: $i] :
( ( ord_less_eq_int @ ( bit1 @ K ) @ pls )
<=> ( ord_less_int @ K @ pls ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(162,plain,
( ( ! [W: $i,Z1: $i,Z2: $i] :
( ( times_times_int @ W @ ( plus_plus_int @ Z1 @ Z2 ) )
= ( plus_plus_int @ ( times_times_int @ W @ Z1 ) @ ( times_times_int @ W @ Z2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(163,plain,
( ( ! [Z1: $i,Z2: $i,W: $i] :
( ( times_times_int @ ( plus_plus_int @ Z1 @ Z2 ) @ W )
= ( plus_plus_int @ ( times_times_int @ Z1 @ W ) @ ( times_times_int @ Z2 @ W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(164,plain,
( ( ! [V_2: $i,W: $i] :
( ( plus_plus_int @ ( number_number_of_int @ V_2 ) @ ( number_number_of_int @ W ) )
= ( number_number_of_int @ ( plus_plus_int @ V_2 @ W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(165,plain,
( ( ! [Z: $i] :
( ( times_times_int @ one_one_int @ Z )
= Z ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(166,plain,
( ( ! [Z: $i] :
( ( times_times_int @ Z @ one_one_int )
= Z ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(167,plain,
( ( ! [K: $i,L: $i] :
( ( ord_less_int @ ( number_number_of_int @ K ) @ ( number_number_of_int @ L ) )
<=> ( ord_less_int @ K @ L ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(168,plain,
( ( ! [K_1: $i,L_1: $i] :
( ( times_times_int @ ( bit0 @ K_1 ) @ L_1 )
= ( bit0 @ ( times_times_int @ K_1 @ L_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(169,plain,
( ( ! [W: $i] :
( ( times_times_int @ pls @ W )
= pls ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(170,plain,
( ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
= ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(171,plain,
( ( ! [Y_1: $i] :
( ( ord_less_eq_int @ one_one_int @ ( number_number_of_int @ Y_1 ) )
<=> ( ord_less_eq_int @ ( bit1 @ pls ) @ Y_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(172,plain,
( ( ! [X_1: $i] :
( ( ord_less_eq_int @ ( number_number_of_int @ X_1 ) @ one_one_int )
<=> ( ord_less_eq_int @ X_1 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(173,plain,
( ( zero_zero_nat
= ( number_number_of_nat @ pls ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(174,plain,
( ( ( number_number_of_nat @ pls )
= zero_zero_nat )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(175,plain,
( ( ! [Z_2: $i,Z: $i,W_2: $i,W: $i] :
( ( ord_less_int @ W_2 @ W )
=> ( ( ord_less_eq_int @ Z_2 @ Z )
=> ( ord_less_int @ ( plus_plus_int @ W_2 @ Z_2 ) @ ( plus_plus_int @ W @ Z ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(176,plain,
( ( ! [K: $i] :
( ( ord_less_eq_int @ pls @ ( bit0 @ K ) )
<=> ( ord_less_eq_int @ pls @ K ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(177,plain,
( ( ! [K: $i] :
( ( ord_less_eq_int @ ( bit0 @ K ) @ pls )
<=> ( ord_less_eq_int @ K @ pls ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(178,plain,
( ( ! [K: $i,L: $i] :
( ( ord_less_eq_int @ ( bit0 @ K ) @ ( bit1 @ L ) )
<=> ( ord_less_eq_int @ K @ L ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(179,plain,
( ( ! [K1: $i,K2: $i] :
( ( ord_less_eq_int @ ( bit0 @ K1 ) @ ( bit1 @ K2 ) )
<=> ( ord_less_eq_int @ K1 @ K2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(180,plain,
( ( ! [K: $i] :
( ( ord_less_eq_int @ pls @ ( bit1 @ K ) )
<=> ( ord_less_eq_int @ pls @ K ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(181,plain,
( ( ! [V_7: $i,W_1: $i] :
( ( ord_less_eq_nat @ ( number_number_of_nat @ V_7 ) @ ( number_number_of_nat @ W_1 ) )
<=> ~ ( ord_less_nat @ ( number_number_of_nat @ W_1 ) @ ( number_number_of_nat @ V_7 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(182,plain,
( ( ! [V_7: $i,W_1: $i] :
( ( ord_less_eq_int @ ( number_number_of_int @ V_7 ) @ ( number_number_of_int @ W_1 ) )
<=> ~ ( ord_less_int @ ( number_number_of_int @ W_1 ) @ ( number_number_of_int @ V_7 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(183,plain,
( ( ! [V_7: $i] :
( ( ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ V_7 ) )
<=> ( ord_less_int @ pls @ V_7 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(184,plain,
( ( ! [Y_1: $i] :
( ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ Y_1 ) )
<=> ( ord_less_eq_int @ pls @ Y_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(185,plain,
( ( ! [X_1: $i] :
( ( ord_less_eq_int @ ( number_number_of_int @ X_1 ) @ zero_zero_int )
<=> ( ord_less_eq_int @ X_1 @ pls ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(186,plain,
( ( ! [X_2: $i,Y_2: $i] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X_2 @ X_2 ) @ ( times_times_int @ Y_2 @ Y_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(187,plain,
( ( ! [X_1: $i,Y_1: $i] :
( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ X_1 @ X_1 ) @ ( times_times_int @ Y_1 @ Y_1 ) ) @ zero_zero_int )
<=> ( ( X_1 = zero_zero_int )
& ( Y_1 = zero_zero_int ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(188,plain,
( ( ! [V_7: $i] :
( ( zero_zero_nat
= ( number_number_of_nat @ V_7 ) )
<=> ( ord_less_eq_int @ V_7 @ pls ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(189,plain,
( ( ! [V_7: $i] :
( ( ( number_number_of_nat @ V_7 )
= zero_zero_nat )
<=> ( ord_less_eq_int @ V_7 @ pls ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(190,plain,
( ( ! [K_1: $i,I: $i,J: $i] :
( ( ord_less_eq_int @ I @ J )
=> ( ord_less_eq_int @ ( plus_plus_int @ K_1 @ I ) @ ( plus_plus_int @ K_1 @ J ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(191,plain,
( ( ! [Z_1: $i,W_1: $i] :
( ( ord_less_int @ Z_1 @ W_1 )
<=> ( ( ord_less_eq_int @ Z_1 @ W_1 )
& ( Z_1 != W_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(192,plain,
( ( ! [K: $i,L: $i] :
( ( ord_less_eq_int @ ( bit0 @ K ) @ ( bit0 @ L ) )
<=> ( ord_less_eq_int @ K @ L ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(193,plain,
( ( ! [K1: $i,K2: $i] :
( ( ord_less_eq_int @ ( bit0 @ K1 ) @ ( bit0 @ K2 ) )
<=> ( ord_less_eq_int @ K1 @ K2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(194,plain,
( ( ord_less_eq_int @ pls @ pls )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(195,plain,
( ( ! [K: $i,L: $i] :
( ( ord_less_eq_int @ ( bit1 @ K ) @ ( bit1 @ L ) )
<=> ( ord_less_eq_int @ K @ L ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(196,plain,
( ( ! [K1: $i,K2: $i] :
( ( ord_less_eq_int @ ( bit1 @ K1 ) @ ( bit1 @ K2 ) )
<=> ( ord_less_eq_int @ K1 @ K2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(197,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( 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)],[73]) ).
thf(198,plain,
( ( ! [V_13: $i] :
( ( plus_plus_int @ ( number_number_of_int @ V_13 ) @ one_one_int )
= ( number_number_of_int @ ( plus_plus_int @ V_13 @ ( bit1 @ pls ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(199,plain,
( ( ! [W_6: $i] :
( ( plus_plus_int @ one_one_int @ ( number_number_of_int @ W_6 ) )
= ( number_number_of_int @ ( plus_plus_int @ ( bit1 @ pls ) @ W_6 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(200,plain,
( ( ! [A_1: $i] :
( ( ( power_power_int @ A_1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int )
<=> ( A_1 = zero_zero_int ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(201,plain,
( ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(202,plain,
( ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_nat )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(203,plain,
( ( ( power_power_int @ one_one_int @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_int )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(204,plain,
( ( ( power_power_nat @ one_one_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_nat )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(205,plain,
( ( ! [A_1: $i] :
( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A_1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
<=> ( A_1 != zero_zero_int ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(206,plain,
( ( ! [A_2: $i] :
~ ( ord_less_int @ ( power_power_int @ A_2 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ zero_zero_int ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(207,plain,
( ( ! [X_1: $i,Y_1: $i] :
( ( ( plus_plus_int @ ( power_power_int @ X_1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_int )
<=> ( ( X_1 = zero_zero_int )
& ( Y_1 = zero_zero_int ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(208,plain,
( ( ! [X_1: $i,Y_1: $i] :
( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X_1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
<=> ( ( X_1 != zero_zero_int )
| ( Y_1 != zero_zero_int ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(209,plain,
( ( ! [X: $i,Y: $i] :
~ ( 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)],[99]) ).
thf(210,plain,
( ( ~ ( ord_less_eq_int @ one_one_int @ t ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(211,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)],[102]) ).
thf(212,plain,
( ( ord_less_int @ t @ one_one_int )
= $true ),
inference(unfold_def,[status(thm)],[105]) ).
thf(213,plain,
( ( ord_less_int @ t @ zero_zero_int )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(214,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)],[109]) ).
thf(215,plain,
( ( ! [W_1: $i,X_1: $i] :
( ( ( number_number_of_int @ W_1 )
!= X_1 )
| ( X_1
= ( number_number_of_int @ W_1 ) ) )
& ! [W_1: $i,X_1: $i] :
( ( X_1
!= ( number_number_of_int @ W_1 ) )
| ( ( number_number_of_int @ W_1 )
= X_1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[110]) ).
thf(216,plain,
( ( ! [X_1: $i,Y_1: $i] :
( ( ( number_number_of_int @ X_1 )
!= ( number_number_of_int @ Y_1 ) )
| ( X_1 = Y_1 ) )
& ! [X_1: $i,Y_1: $i] :
( ( X_1 != Y_1 )
| ( ( number_number_of_int @ X_1 )
= ( number_number_of_int @ Y_1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[111]) ).
thf(217,plain,
( ( ! [V_12: $i,V_11: $i] :
( ~ ( ord_less_eq_int @ pls @ V_11 )
| ~ ( ord_less_eq_int @ pls @ V_12 )
| ( ( times_times_int @ ( number_number_of_int @ V_11 ) @ ( number_number_of_int @ V_12 ) )
= ( number_number_of_int @ ( times_times_int @ V_11 @ V_12 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[115]) ).
thf(218,plain,
( ( ! [V_12: $i,V_11: $i] :
( ~ ( ord_less_eq_int @ pls @ V_11 )
| ~ ( ord_less_eq_int @ pls @ V_12 )
| ( ( times_times_nat @ ( number_number_of_nat @ V_11 ) @ ( number_number_of_nat @ V_12 ) )
= ( number_number_of_nat @ ( times_times_int @ V_11 @ V_12 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[116]) ).
thf(219,plain,
( ( ! [Z: $i,W: $i] :
( ~ ( ord_less_eq_int @ Z @ W )
| ~ ( ord_less_eq_int @ W @ Z )
| ( Z = W ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[117]) ).
thf(220,plain,
( ( ! [K_1: $i,I: $i,J: $i] :
( ~ ( ord_less_eq_int @ I @ J )
| ~ ( ord_less_eq_int @ J @ K_1 )
| ( ord_less_eq_int @ I @ K_1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[118]) ).
thf(221,plain,
( ( ! [X_1: $i,Y_1: $i] :
( ~ ( ord_less_eq_int @ ( number_number_of_int @ X_1 ) @ ( number_number_of_int @ Y_1 ) )
| ( ord_less_eq_int @ X_1 @ Y_1 ) )
& ! [X_1: $i,Y_1: $i] :
( ~ ( ord_less_eq_int @ X_1 @ Y_1 )
| ( ord_less_eq_int @ ( number_number_of_int @ X_1 ) @ ( number_number_of_int @ Y_1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[120]) ).
thf(222,plain,
( ( ! [K: $i,L: $i] :
( ~ ( ord_less_eq_int @ ( number_number_of_int @ K ) @ ( number_number_of_int @ L ) )
| ( ord_less_eq_int @ K @ L ) )
& ! [K: $i,L: $i] :
( ~ ( 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)],[121]) ).
thf(223,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 ) @ sK1_T ) )
= $true ),
inference(extcnf_combined,[status(esa)],[127]) ).
thf(224,plain,
( ( ! [X_1: $i,Y_1: $i] :
( ( X_1 != zero_zero_int )
| ( Y_1 != zero_zero_int )
| ( ( plus_plus_int @ ( times_times_int @ X_1 @ X_1 ) @ ( times_times_int @ Y_1 @ Y_1 ) )
= zero_zero_int ) )
& ! [X_1: $i] :
( ! [Y_1: $i] :
( ( plus_plus_int @ ( times_times_int @ X_1 @ X_1 ) @ ( times_times_int @ Y_1 @ Y_1 ) )
!= zero_zero_int )
| ( X_1 = zero_zero_int ) )
& ! [X_1: $i,Y_1: $i] :
( ( ( plus_plus_int @ ( times_times_int @ X_1 @ X_1 ) @ ( times_times_int @ Y_1 @ Y_1 ) )
!= zero_zero_int )
| ( Y_1 = zero_zero_int ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[140]) ).
thf(225,plain,
( ( ! [X: $i,Y: $i] :
( ( ord_less_int @ Y @ X )
| ( X = Y )
| ( ord_less_int @ X @ Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[141]) ).
thf(226,plain,
( ( ! [K: $i,L: $i] :
( ( ( bit0 @ K )
!= ( bit0 @ L ) )
| ( K = L ) )
& ! [K: $i,L: $i] :
( ( K != L )
| ( ( bit0 @ K )
= ( bit0 @ L ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[142]) ).
thf(227,plain,
( ( ! [K: $i,L: $i] :
( ( ( bit1 @ K )
!= ( bit1 @ L ) )
| ( K = L ) )
& ! [K: $i,L: $i] :
( ( K != L )
| ( ( bit1 @ K )
= ( bit1 @ L ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[143]) ).
thf(228,plain,
( ( ! [W_1: $i,X_1: $i] :
( ( ( number_number_of_nat @ W_1 )
!= X_1 )
| ( X_1
= ( number_number_of_nat @ W_1 ) ) )
& ! [W_1: $i,X_1: $i] :
( ( X_1
!= ( number_number_of_nat @ W_1 ) )
| ( ( number_number_of_nat @ W_1 )
= X_1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[144]) ).
thf(229,plain,
( ( ! [Z: $i] :
( ~ ( ord_less_eq_int @ zero_zero_int @ Z )
| ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[145]) ).
thf(230,plain,
( ( ! [V_3: $i,V_2: $i] :
( ~ ( ord_less_int @ V_2 @ pls )
| ( ( plus_plus_nat @ ( number_number_of_nat @ V_2 ) @ ( number_number_of_nat @ V_3 ) )
= ( number_number_of_nat @ V_3 ) ) )
& ! [V_3: $i,V_2: $i] :
( ( ord_less_int @ V_2 @ pls )
| ~ ( ord_less_int @ V_3 @ pls )
| ( ( plus_plus_nat @ ( number_number_of_nat @ V_2 ) @ ( number_number_of_nat @ V_3 ) )
= ( number_number_of_nat @ V_2 ) ) )
& ! [V_3: $i,V_2: $i] :
( ( ord_less_int @ V_2 @ pls )
| ( ord_less_int @ V_3 @ pls )
| ( ( plus_plus_nat @ ( number_number_of_nat @ V_2 ) @ ( number_number_of_nat @ V_3 ) )
= ( number_number_of_nat @ ( plus_plus_int @ V_2 @ V_3 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[146]) ).
thf(231,plain,
( ( ! [V_5: $i,V_4: $i] :
( ~ ( ord_less_eq_int @ pls @ V_4 )
| ~ ( ord_less_eq_int @ pls @ V_5 )
| ( ( 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)],[147]) ).
thf(232,plain,
( ( ! [V_5: $i,V_4: $i] :
( ~ ( ord_less_eq_int @ pls @ V_4 )
| ~ ( ord_less_eq_int @ pls @ V_5 )
| ( ( plus_plus_int @ ( number_number_of_int @ V_4 ) @ ( number_number_of_int @ V_5 ) )
= ( number_number_of_int @ ( plus_plus_int @ V_4 @ V_5 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[148]) ).
thf(233,plain,
( ( ! [W_1: $i,Z_1: $i] :
( ~ ( ord_less_eq_int @ W_1 @ Z_1 )
| ( ord_less_int @ W_1 @ ( plus_plus_int @ Z_1 @ one_one_int ) ) )
& ! [W_1: $i,Z_1: $i] :
( ~ ( ord_less_int @ W_1 @ ( plus_plus_int @ Z_1 @ one_one_int ) )
| ( ord_less_eq_int @ W_1 @ Z_1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[149]) ).
thf(234,plain,
( ( ! [W_1: $i,Z_1: $i] :
( ~ ( ord_less_eq_int @ ( plus_plus_int @ W_1 @ one_one_int ) @ Z_1 )
| ( ord_less_int @ W_1 @ Z_1 ) )
& ! [W_1: $i,Z_1: $i] :
( ~ ( ord_less_int @ W_1 @ Z_1 )
| ( ord_less_eq_int @ ( plus_plus_int @ W_1 @ one_one_int ) @ Z_1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[150]) ).
thf(235,plain,
( ( ! [W: $i,Z: $i] :
( ~ ( ord_less_int @ W @ Z )
| ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[151]) ).
thf(236,plain,
( ( ! [Z_1: $i] :
( ~ ( ord_less_eq_int @ one_one_int @ Z_1 )
| ( ord_less_int @ zero_zero_int @ Z_1 ) )
& ! [Z_1: $i] :
( ~ ( ord_less_int @ zero_zero_int @ Z_1 )
| ( ord_less_eq_int @ one_one_int @ Z_1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[154]) ).
thf(237,plain,
( ( ! [V_7: $i,V_6: $i] :
( ( ord_less_int @ V_7 @ V_6 )
| ~ ( ord_less_int @ V_7 @ V_6 )
| ( ord_less_nat @ ( number_number_of_nat @ V_7 ) @ ( number_number_of_nat @ V_6 ) ) )
& ! [V_7: $i,V_6: $i] :
( ~ ( ord_less_int @ pls @ V_6 )
| ~ ( ord_less_int @ V_7 @ V_6 )
| ( ord_less_nat @ ( number_number_of_nat @ V_7 ) @ ( number_number_of_nat @ V_6 ) ) )
& ! [V_7: $i,V_6: $i] :
( ~ ( ord_less_nat @ ( number_number_of_nat @ V_7 ) @ ( number_number_of_nat @ V_6 ) )
| ~ ( ord_less_int @ V_7 @ V_6 )
| ( ord_less_int @ pls @ V_6 ) )
& ! [V_7: $i,V_6: $i] :
( ~ ( ord_less_nat @ ( number_number_of_nat @ V_7 ) @ ( number_number_of_nat @ V_6 ) )
| ( ord_less_int @ V_7 @ V_6 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[155]) ).
thf(238,plain,
( ( ! [K: $i,L: $i] :
( ~ ( ord_less_eq_int @ K @ L )
| ( ord_less_int @ ( bit0 @ K ) @ ( bit1 @ L ) ) )
& ! [K: $i,L: $i] :
( ~ ( ord_less_int @ ( bit0 @ K ) @ ( bit1 @ L ) )
| ( ord_less_eq_int @ K @ L ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[156]) ).
thf(239,plain,
( ( ! [K1: $i,K2: $i] :
( ~ ( ord_less_eq_int @ K1 @ K2 )
| ( ord_less_int @ ( bit0 @ K1 ) @ ( bit1 @ K2 ) ) )
& ! [K1: $i,K2: $i] :
( ~ ( ord_less_int @ ( bit0 @ K1 ) @ ( bit1 @ K2 ) )
| ( ord_less_eq_int @ K1 @ K2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[157]) ).
thf(240,plain,
( ( ! [K: $i,L: $i] :
( ~ ( ord_less_eq_int @ ( bit1 @ K ) @ ( bit0 @ L ) )
| ( ord_less_int @ K @ L ) )
& ! [K: $i,L: $i] :
( ~ ( ord_less_int @ K @ L )
| ( ord_less_eq_int @ ( bit1 @ K ) @ ( bit0 @ L ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[158]) ).
thf(241,plain,
( ( ! [K1: $i,K2: $i] :
( ~ ( ord_less_eq_int @ ( bit1 @ K1 ) @ ( bit0 @ K2 ) )
| ( ord_less_int @ K1 @ K2 ) )
& ! [K1: $i,K2: $i] :
( ~ ( ord_less_int @ K1 @ K2 )
| ( ord_less_eq_int @ ( bit1 @ K1 ) @ ( bit0 @ K2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[159]) ).
thf(242,plain,
( ( ! [K: $i] :
( ~ ( ord_less_eq_int @ pls @ K )
| ( ord_less_int @ pls @ ( bit1 @ K ) ) )
& ! [K: $i] :
( ~ ( ord_less_int @ pls @ ( bit1 @ K ) )
| ( ord_less_eq_int @ pls @ K ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[160]) ).
thf(243,plain,
( ( ! [K: $i] :
( ~ ( ord_less_eq_int @ ( bit1 @ K ) @ pls )
| ( ord_less_int @ K @ pls ) )
& ! [K: $i] :
( ~ ( ord_less_int @ K @ pls )
| ( ord_less_eq_int @ ( bit1 @ K ) @ pls ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[161]) ).
thf(244,plain,
( ( ! [K: $i,L: $i] :
( ~ ( ord_less_int @ ( number_number_of_int @ K ) @ ( number_number_of_int @ L ) )
| ( ord_less_int @ K @ L ) )
& ! [K: $i,L: $i] :
( ~ ( ord_less_int @ K @ L )
| ( ord_less_int @ ( number_number_of_int @ K ) @ ( number_number_of_int @ L ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[167]) ).
thf(245,plain,
( ( ! [Y_1: $i] :
( ~ ( ord_less_eq_int @ one_one_int @ ( number_number_of_int @ Y_1 ) )
| ( ord_less_eq_int @ ( bit1 @ pls ) @ Y_1 ) )
& ! [Y_1: $i] :
( ~ ( ord_less_eq_int @ ( bit1 @ pls ) @ Y_1 )
| ( ord_less_eq_int @ one_one_int @ ( number_number_of_int @ Y_1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[171]) ).
thf(246,plain,
( ( ! [X_1: $i] :
( ~ ( ord_less_eq_int @ ( number_number_of_int @ X_1 ) @ one_one_int )
| ( ord_less_eq_int @ X_1 @ ( bit1 @ pls ) ) )
& ! [X_1: $i] :
( ~ ( ord_less_eq_int @ X_1 @ ( bit1 @ pls ) )
| ( ord_less_eq_int @ ( number_number_of_int @ X_1 ) @ one_one_int ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[172]) ).
thf(247,plain,
( ( ! [Z_2: $i,Z: $i,W_2: $i,W: $i] :
( ~ ( ord_less_int @ W_2 @ W )
| ~ ( ord_less_eq_int @ Z_2 @ Z )
| ( ord_less_int @ ( plus_plus_int @ W_2 @ Z_2 ) @ ( plus_plus_int @ W @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[175]) ).
thf(248,plain,
( ( ! [K: $i] :
( ~ ( ord_less_eq_int @ pls @ ( bit0 @ K ) )
| ( ord_less_eq_int @ pls @ K ) )
& ! [K: $i] :
( ~ ( ord_less_eq_int @ pls @ K )
| ( ord_less_eq_int @ pls @ ( bit0 @ K ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[176]) ).
thf(249,plain,
( ( ! [K: $i] :
( ~ ( ord_less_eq_int @ ( bit0 @ K ) @ pls )
| ( ord_less_eq_int @ K @ pls ) )
& ! [K: $i] :
( ~ ( ord_less_eq_int @ K @ pls )
| ( ord_less_eq_int @ ( bit0 @ K ) @ pls ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[177]) ).
thf(250,plain,
( ( ! [K: $i,L: $i] :
( ~ ( ord_less_eq_int @ ( bit0 @ K ) @ ( bit1 @ L ) )
| ( ord_less_eq_int @ K @ L ) )
& ! [K: $i,L: $i] :
( ~ ( ord_less_eq_int @ K @ L )
| ( ord_less_eq_int @ ( bit0 @ K ) @ ( bit1 @ L ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[178]) ).
thf(251,plain,
( ( ! [K1: $i,K2: $i] :
( ~ ( ord_less_eq_int @ ( bit0 @ K1 ) @ ( bit1 @ K2 ) )
| ( ord_less_eq_int @ K1 @ K2 ) )
& ! [K1: $i,K2: $i] :
( ~ ( ord_less_eq_int @ K1 @ K2 )
| ( ord_less_eq_int @ ( bit0 @ K1 ) @ ( bit1 @ K2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[179]) ).
thf(252,plain,
( ( ! [K: $i] :
( ~ ( ord_less_eq_int @ pls @ ( bit1 @ K ) )
| ( ord_less_eq_int @ pls @ K ) )
& ! [K: $i] :
( ~ ( ord_less_eq_int @ pls @ K )
| ( ord_less_eq_int @ pls @ ( bit1 @ K ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[180]) ).
thf(253,plain,
( ( ! [V_7: $i,W_1: $i] :
( ~ ( ord_less_eq_nat @ ( number_number_of_nat @ V_7 ) @ ( number_number_of_nat @ W_1 ) )
| ~ ( ord_less_nat @ ( number_number_of_nat @ W_1 ) @ ( number_number_of_nat @ V_7 ) ) )
& ! [V_7: $i,W_1: $i] :
( ( ord_less_nat @ ( number_number_of_nat @ W_1 ) @ ( number_number_of_nat @ V_7 ) )
| ( ord_less_eq_nat @ ( number_number_of_nat @ V_7 ) @ ( number_number_of_nat @ W_1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[181]) ).
thf(254,plain,
( ( ! [V_7: $i,W_1: $i] :
( ~ ( ord_less_eq_int @ ( number_number_of_int @ V_7 ) @ ( number_number_of_int @ W_1 ) )
| ~ ( ord_less_int @ ( number_number_of_int @ W_1 ) @ ( number_number_of_int @ V_7 ) ) )
& ! [V_7: $i,W_1: $i] :
( ( ord_less_int @ ( number_number_of_int @ W_1 ) @ ( number_number_of_int @ V_7 ) )
| ( ord_less_eq_int @ ( number_number_of_int @ V_7 ) @ ( number_number_of_int @ W_1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[182]) ).
thf(255,plain,
( ( ! [V_7: $i] :
( ~ ( ord_less_int @ pls @ V_7 )
| ( ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ V_7 ) ) )
& ! [V_7: $i] :
( ~ ( ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ V_7 ) )
| ( ord_less_int @ pls @ V_7 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[183]) ).
thf(256,plain,
( ( ! [Y_1: $i] :
( ~ ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ Y_1 ) )
| ( ord_less_eq_int @ pls @ Y_1 ) )
& ! [Y_1: $i] :
( ~ ( ord_less_eq_int @ pls @ Y_1 )
| ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ Y_1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[184]) ).
thf(257,plain,
( ( ! [X_1: $i] :
( ~ ( ord_less_eq_int @ ( number_number_of_int @ X_1 ) @ zero_zero_int )
| ( ord_less_eq_int @ X_1 @ pls ) )
& ! [X_1: $i] :
( ~ ( ord_less_eq_int @ X_1 @ pls )
| ( ord_less_eq_int @ ( number_number_of_int @ X_1 ) @ zero_zero_int ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[185]) ).
thf(258,plain,
( ( ! [X_1: $i,Y_1: $i] :
( ( X_1 != zero_zero_int )
| ( Y_1 != zero_zero_int )
| ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ X_1 @ X_1 ) @ ( times_times_int @ Y_1 @ Y_1 ) ) @ zero_zero_int ) )
& ! [X_1: $i] :
( ! [Y_1: $i] :
~ ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ X_1 @ X_1 ) @ ( times_times_int @ Y_1 @ Y_1 ) ) @ zero_zero_int )
| ( X_1 = zero_zero_int ) )
& ! [X_1: $i,Y_1: $i] :
( ~ ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ X_1 @ X_1 ) @ ( times_times_int @ Y_1 @ Y_1 ) ) @ zero_zero_int )
| ( Y_1 = zero_zero_int ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[187]) ).
thf(259,plain,
( ( ! [V_7: $i] :
( ( zero_zero_nat
!= ( number_number_of_nat @ V_7 ) )
| ( ord_less_eq_int @ V_7 @ pls ) )
& ! [V_7: $i] :
( ~ ( ord_less_eq_int @ V_7 @ pls )
| ( zero_zero_nat
= ( number_number_of_nat @ V_7 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[188]) ).
thf(260,plain,
( ( ! [V_7: $i] :
( ( ( number_number_of_nat @ V_7 )
!= zero_zero_nat )
| ( ord_less_eq_int @ V_7 @ pls ) )
& ! [V_7: $i] :
( ~ ( ord_less_eq_int @ V_7 @ pls )
| ( ( number_number_of_nat @ V_7 )
= zero_zero_nat ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[189]) ).
thf(261,plain,
( ( ! [K_1: $i,I: $i,J: $i] :
( ~ ( ord_less_eq_int @ I @ J )
| ( ord_less_eq_int @ ( plus_plus_int @ K_1 @ I ) @ ( plus_plus_int @ K_1 @ J ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[190]) ).
thf(262,plain,
( ( ! [Z_1: $i,W_1: $i] :
( ( Z_1 = W_1 )
| ~ ( ord_less_eq_int @ Z_1 @ W_1 )
| ( ord_less_int @ Z_1 @ W_1 ) )
& ! [Z_1: $i,W_1: $i] :
( ~ ( ord_less_int @ Z_1 @ W_1 )
| ( Z_1 != W_1 ) )
& ! [Z_1: $i,W_1: $i] :
( ~ ( ord_less_int @ Z_1 @ W_1 )
| ( ord_less_eq_int @ Z_1 @ W_1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[191]) ).
thf(263,plain,
( ( ! [K: $i,L: $i] :
( ~ ( ord_less_eq_int @ ( bit0 @ K ) @ ( bit0 @ L ) )
| ( ord_less_eq_int @ K @ L ) )
& ! [K: $i,L: $i] :
( ~ ( ord_less_eq_int @ K @ L )
| ( ord_less_eq_int @ ( bit0 @ K ) @ ( bit0 @ L ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[192]) ).
thf(264,plain,
( ( ! [K1: $i,K2: $i] :
( ~ ( ord_less_eq_int @ ( bit0 @ K1 ) @ ( bit0 @ K2 ) )
| ( ord_less_eq_int @ K1 @ K2 ) )
& ! [K1: $i,K2: $i] :
( ~ ( ord_less_eq_int @ K1 @ K2 )
| ( ord_less_eq_int @ ( bit0 @ K1 ) @ ( bit0 @ K2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[193]) ).
thf(265,plain,
( ( ! [K: $i,L: $i] :
( ~ ( ord_less_eq_int @ ( bit1 @ K ) @ ( bit1 @ L ) )
| ( ord_less_eq_int @ K @ L ) )
& ! [K: $i,L: $i] :
( ~ ( ord_less_eq_int @ K @ L )
| ( ord_less_eq_int @ ( bit1 @ K ) @ ( bit1 @ L ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[195]) ).
thf(266,plain,
( ( ! [K1: $i,K2: $i] :
( ~ ( ord_less_eq_int @ ( bit1 @ K1 ) @ ( bit1 @ K2 ) )
| ( ord_less_eq_int @ K1 @ K2 ) )
& ! [K1: $i,K2: $i] :
( ~ ( ord_less_eq_int @ K1 @ K2 )
| ( ord_less_eq_int @ ( bit1 @ K1 ) @ ( bit1 @ K2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[196]) ).
thf(267,plain,
( ( ! [A_1: $i] :
( ( ( power_power_int @ A_1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= zero_zero_int )
| ( A_1 = zero_zero_int ) )
& ! [A_1: $i] :
( ( A_1 != zero_zero_int )
| ( ( power_power_int @ A_1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[200]) ).
thf(268,plain,
( ( ! [A_1: $i] :
( ( A_1 = zero_zero_int )
| ( ord_less_int @ zero_zero_int @ ( power_power_int @ A_1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
& ! [A_1: $i] :
( ~ ( ord_less_int @ zero_zero_int @ ( power_power_int @ A_1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ( A_1 != zero_zero_int ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[205]) ).
thf(269,plain,
( ( ! [X_1: $i,Y_1: $i] :
( ( X_1 != zero_zero_int )
| ( Y_1 != zero_zero_int )
| ( ( plus_plus_int @ ( power_power_int @ X_1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_int ) )
& ! [X_1: $i] :
( ! [Y_1: $i] :
( ( plus_plus_int @ ( power_power_int @ X_1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_int )
| ( X_1 = zero_zero_int ) )
& ! [X_1: $i,Y_1: $i] :
( ( ( plus_plus_int @ ( power_power_int @ X_1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_int )
| ( Y_1 = zero_zero_int ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[207]) ).
thf(270,plain,
( ( ! [X_1: $i,Y_1: $i] :
( ~ ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X_1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
| ( X_1 != zero_zero_int )
| ( Y_1 != zero_zero_int ) )
& ! [X_1: $i] :
( ( X_1 = zero_zero_int )
| ! [Y_1: $i] : ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X_1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
& ! [X_1: $i,Y_1: $i] :
( ( Y_1 = zero_zero_int )
| ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X_1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[208]) ).
thf(271,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)],[211]) ).
thf(272,plain,
( ( ord_less_int @ t @ zero_zero_int )
= $true ),
inference(copy,[status(thm)],[213]) ).
thf(273,plain,
( ( ord_less_int @ t @ one_one_int )
= $true ),
inference(copy,[status(thm)],[212]) ).
thf(274,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)],[271]) ).
thf(275,plain,
( ( ~ ( ord_less_eq_int @ one_one_int @ t ) )
= $true ),
inference(copy,[status(thm)],[210]) ).
thf(276,plain,
( ( ! [X: $i,Y: $i] :
~ ( 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)],[209]) ).
thf(277,plain,
( ( ! [X_1: $i,Y_1: $i] :
( ~ ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X_1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
| ( X_1 != zero_zero_int )
| ( Y_1 != zero_zero_int ) )
& ! [X_1: $i] :
( ( X_1 = zero_zero_int )
| ! [Y_1: $i] : ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X_1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
& ! [X_1: $i,Y_1: $i] :
( ( Y_1 = zero_zero_int )
| ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X_1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[270]) ).
thf(278,plain,
( ( ! [X_1: $i,Y_1: $i] :
( ( X_1 != zero_zero_int )
| ( Y_1 != zero_zero_int )
| ( ( plus_plus_int @ ( power_power_int @ X_1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_int ) )
& ! [X_1: $i] :
( ! [Y_1: $i] :
( ( plus_plus_int @ ( power_power_int @ X_1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_int )
| ( X_1 = zero_zero_int ) )
& ! [X_1: $i,Y_1: $i] :
( ( ( plus_plus_int @ ( power_power_int @ X_1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_int )
| ( Y_1 = zero_zero_int ) ) )
= $true ),
inference(copy,[status(thm)],[269]) ).
thf(279,plain,
( ( ! [A_2: $i] :
~ ( ord_less_int @ ( power_power_int @ A_2 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ zero_zero_int ) )
= $true ),
inference(copy,[status(thm)],[206]) ).
thf(280,plain,
( ( ! [A_1: $i] :
( ( A_1 = zero_zero_int )
| ( ord_less_int @ zero_zero_int @ ( power_power_int @ A_1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
& ! [A_1: $i] :
( ~ ( ord_less_int @ zero_zero_int @ ( power_power_int @ A_1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ( A_1 != zero_zero_int ) ) )
= $true ),
inference(copy,[status(thm)],[268]) ).
thf(281,plain,
( ( ( power_power_nat @ one_one_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_nat )
= $true ),
inference(copy,[status(thm)],[204]) ).
thf(282,plain,
( ( ( power_power_int @ one_one_int @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_int )
= $true ),
inference(copy,[status(thm)],[203]) ).
thf(283,plain,
( ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_nat )
= $true ),
inference(copy,[status(thm)],[202]) ).
thf(284,plain,
( ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int )
= $true ),
inference(copy,[status(thm)],[201]) ).
thf(285,plain,
( ( ! [A_1: $i] :
( ( ( power_power_int @ A_1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= zero_zero_int )
| ( A_1 = zero_zero_int ) )
& ! [A_1: $i] :
( ( A_1 != zero_zero_int )
| ( ( power_power_int @ A_1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int ) ) )
= $true ),
inference(copy,[status(thm)],[267]) ).
thf(286,plain,
( ( ! [W_6: $i] :
( ( plus_plus_int @ one_one_int @ ( number_number_of_int @ W_6 ) )
= ( number_number_of_int @ ( plus_plus_int @ ( bit1 @ pls ) @ W_6 ) ) ) )
= $true ),
inference(copy,[status(thm)],[199]) ).
thf(287,plain,
( ( ! [V_13: $i] :
( ( plus_plus_int @ ( number_number_of_int @ V_13 ) @ one_one_int )
= ( number_number_of_int @ ( plus_plus_int @ V_13 @ ( bit1 @ pls ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[198]) ).
thf(288,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( 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)],[197]) ).
thf(289,plain,
( ( ! [K1: $i,K2: $i] :
( ~ ( ord_less_eq_int @ ( bit1 @ K1 ) @ ( bit1 @ K2 ) )
| ( ord_less_eq_int @ K1 @ K2 ) )
& ! [K1: $i,K2: $i] :
( ~ ( ord_less_eq_int @ K1 @ K2 )
| ( ord_less_eq_int @ ( bit1 @ K1 ) @ ( bit1 @ K2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[266]) ).
thf(290,plain,
( ( ! [K: $i,L: $i] :
( ~ ( ord_less_eq_int @ ( bit1 @ K ) @ ( bit1 @ L ) )
| ( ord_less_eq_int @ K @ L ) )
& ! [K: $i,L: $i] :
( ~ ( ord_less_eq_int @ K @ L )
| ( ord_less_eq_int @ ( bit1 @ K ) @ ( bit1 @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[265]) ).
thf(291,plain,
( ( ord_less_eq_int @ pls @ pls )
= $true ),
inference(copy,[status(thm)],[194]) ).
thf(292,plain,
( ( ! [K1: $i,K2: $i] :
( ~ ( ord_less_eq_int @ ( bit0 @ K1 ) @ ( bit0 @ K2 ) )
| ( ord_less_eq_int @ K1 @ K2 ) )
& ! [K1: $i,K2: $i] :
( ~ ( ord_less_eq_int @ K1 @ K2 )
| ( ord_less_eq_int @ ( bit0 @ K1 ) @ ( bit0 @ K2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[264]) ).
thf(293,plain,
( ( ! [K: $i,L: $i] :
( ~ ( ord_less_eq_int @ ( bit0 @ K ) @ ( bit0 @ L ) )
| ( ord_less_eq_int @ K @ L ) )
& ! [K: $i,L: $i] :
( ~ ( ord_less_eq_int @ K @ L )
| ( ord_less_eq_int @ ( bit0 @ K ) @ ( bit0 @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[263]) ).
thf(294,plain,
( ( ! [Z_1: $i,W_1: $i] :
( ( Z_1 = W_1 )
| ~ ( ord_less_eq_int @ Z_1 @ W_1 )
| ( ord_less_int @ Z_1 @ W_1 ) )
& ! [Z_1: $i,W_1: $i] :
( ~ ( ord_less_int @ Z_1 @ W_1 )
| ( Z_1 != W_1 ) )
& ! [Z_1: $i,W_1: $i] :
( ~ ( ord_less_int @ Z_1 @ W_1 )
| ( ord_less_eq_int @ Z_1 @ W_1 ) ) )
= $true ),
inference(copy,[status(thm)],[262]) ).
thf(295,plain,
( ( ! [K_1: $i,I: $i,J: $i] :
( ~ ( ord_less_eq_int @ I @ J )
| ( ord_less_eq_int @ ( plus_plus_int @ K_1 @ I ) @ ( plus_plus_int @ K_1 @ J ) ) ) )
= $true ),
inference(copy,[status(thm)],[261]) ).
thf(296,plain,
( ( ! [V_7: $i] :
( ( ( number_number_of_nat @ V_7 )
!= zero_zero_nat )
| ( ord_less_eq_int @ V_7 @ pls ) )
& ! [V_7: $i] :
( ~ ( ord_less_eq_int @ V_7 @ pls )
| ( ( number_number_of_nat @ V_7 )
= zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[260]) ).
thf(297,plain,
( ( ! [V_7: $i] :
( ( zero_zero_nat
!= ( number_number_of_nat @ V_7 ) )
| ( ord_less_eq_int @ V_7 @ pls ) )
& ! [V_7: $i] :
( ~ ( ord_less_eq_int @ V_7 @ pls )
| ( zero_zero_nat
= ( number_number_of_nat @ V_7 ) ) ) )
= $true ),
inference(copy,[status(thm)],[259]) ).
thf(298,plain,
( ( ! [X_1: $i,Y_1: $i] :
( ( X_1 != zero_zero_int )
| ( Y_1 != zero_zero_int )
| ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ X_1 @ X_1 ) @ ( times_times_int @ Y_1 @ Y_1 ) ) @ zero_zero_int ) )
& ! [X_1: $i] :
( ! [Y_1: $i] :
~ ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ X_1 @ X_1 ) @ ( times_times_int @ Y_1 @ Y_1 ) ) @ zero_zero_int )
| ( X_1 = zero_zero_int ) )
& ! [X_1: $i,Y_1: $i] :
( ~ ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ X_1 @ X_1 ) @ ( times_times_int @ Y_1 @ Y_1 ) ) @ zero_zero_int )
| ( Y_1 = zero_zero_int ) ) )
= $true ),
inference(copy,[status(thm)],[258]) ).
thf(299,plain,
( ( ! [X_2: $i,Y_2: $i] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X_2 @ X_2 ) @ ( times_times_int @ Y_2 @ Y_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[186]) ).
thf(300,plain,
( ( ! [X_1: $i] :
( ~ ( ord_less_eq_int @ ( number_number_of_int @ X_1 ) @ zero_zero_int )
| ( ord_less_eq_int @ X_1 @ pls ) )
& ! [X_1: $i] :
( ~ ( ord_less_eq_int @ X_1 @ pls )
| ( ord_less_eq_int @ ( number_number_of_int @ X_1 ) @ zero_zero_int ) ) )
= $true ),
inference(copy,[status(thm)],[257]) ).
thf(301,plain,
( ( ! [Y_1: $i] :
( ~ ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ Y_1 ) )
| ( ord_less_eq_int @ pls @ Y_1 ) )
& ! [Y_1: $i] :
( ~ ( ord_less_eq_int @ pls @ Y_1 )
| ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ Y_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[256]) ).
thf(302,plain,
( ( ! [V_7: $i] :
( ~ ( ord_less_int @ pls @ V_7 )
| ( ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ V_7 ) ) )
& ! [V_7: $i] :
( ~ ( ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ V_7 ) )
| ( ord_less_int @ pls @ V_7 ) ) )
= $true ),
inference(copy,[status(thm)],[255]) ).
thf(303,plain,
( ( ! [V_7: $i,W_1: $i] :
( ~ ( ord_less_eq_int @ ( number_number_of_int @ V_7 ) @ ( number_number_of_int @ W_1 ) )
| ~ ( ord_less_int @ ( number_number_of_int @ W_1 ) @ ( number_number_of_int @ V_7 ) ) )
& ! [V_7: $i,W_1: $i] :
( ( ord_less_int @ ( number_number_of_int @ W_1 ) @ ( number_number_of_int @ V_7 ) )
| ( ord_less_eq_int @ ( number_number_of_int @ V_7 ) @ ( number_number_of_int @ W_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[254]) ).
thf(304,plain,
( ( ! [V_7: $i,W_1: $i] :
( ~ ( ord_less_eq_nat @ ( number_number_of_nat @ V_7 ) @ ( number_number_of_nat @ W_1 ) )
| ~ ( ord_less_nat @ ( number_number_of_nat @ W_1 ) @ ( number_number_of_nat @ V_7 ) ) )
& ! [V_7: $i,W_1: $i] :
( ( ord_less_nat @ ( number_number_of_nat @ W_1 ) @ ( number_number_of_nat @ V_7 ) )
| ( ord_less_eq_nat @ ( number_number_of_nat @ V_7 ) @ ( number_number_of_nat @ W_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[253]) ).
thf(305,plain,
( ( ! [K: $i] :
( ~ ( ord_less_eq_int @ pls @ ( bit1 @ K ) )
| ( ord_less_eq_int @ pls @ K ) )
& ! [K: $i] :
( ~ ( ord_less_eq_int @ pls @ K )
| ( ord_less_eq_int @ pls @ ( bit1 @ K ) ) ) )
= $true ),
inference(copy,[status(thm)],[252]) ).
thf(306,plain,
( ( ! [K1: $i,K2: $i] :
( ~ ( ord_less_eq_int @ ( bit0 @ K1 ) @ ( bit1 @ K2 ) )
| ( ord_less_eq_int @ K1 @ K2 ) )
& ! [K1: $i,K2: $i] :
( ~ ( ord_less_eq_int @ K1 @ K2 )
| ( ord_less_eq_int @ ( bit0 @ K1 ) @ ( bit1 @ K2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[251]) ).
thf(307,plain,
( ( ! [K: $i,L: $i] :
( ~ ( ord_less_eq_int @ ( bit0 @ K ) @ ( bit1 @ L ) )
| ( ord_less_eq_int @ K @ L ) )
& ! [K: $i,L: $i] :
( ~ ( ord_less_eq_int @ K @ L )
| ( ord_less_eq_int @ ( bit0 @ K ) @ ( bit1 @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[250]) ).
thf(308,plain,
( ( ! [K: $i] :
( ~ ( ord_less_eq_int @ ( bit0 @ K ) @ pls )
| ( ord_less_eq_int @ K @ pls ) )
& ! [K: $i] :
( ~ ( ord_less_eq_int @ K @ pls )
| ( ord_less_eq_int @ ( bit0 @ K ) @ pls ) ) )
= $true ),
inference(copy,[status(thm)],[249]) ).
thf(309,plain,
( ( ! [K: $i] :
( ~ ( ord_less_eq_int @ pls @ ( bit0 @ K ) )
| ( ord_less_eq_int @ pls @ K ) )
& ! [K: $i] :
( ~ ( ord_less_eq_int @ pls @ K )
| ( ord_less_eq_int @ pls @ ( bit0 @ K ) ) ) )
= $true ),
inference(copy,[status(thm)],[248]) ).
thf(310,plain,
( ( ! [Z_2: $i,Z: $i,W_2: $i,W: $i] :
( ~ ( ord_less_int @ W_2 @ W )
| ~ ( ord_less_eq_int @ Z_2 @ Z )
| ( ord_less_int @ ( plus_plus_int @ W_2 @ Z_2 ) @ ( plus_plus_int @ W @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[247]) ).
thf(311,plain,
( ( ( number_number_of_nat @ pls )
= zero_zero_nat )
= $true ),
inference(copy,[status(thm)],[174]) ).
thf(312,plain,
( ( zero_zero_nat
= ( number_number_of_nat @ pls ) )
= $true ),
inference(copy,[status(thm)],[173]) ).
thf(313,plain,
( ( ! [X_1: $i] :
( ~ ( ord_less_eq_int @ ( number_number_of_int @ X_1 ) @ one_one_int )
| ( ord_less_eq_int @ X_1 @ ( bit1 @ pls ) ) )
& ! [X_1: $i] :
( ~ ( ord_less_eq_int @ X_1 @ ( bit1 @ pls ) )
| ( ord_less_eq_int @ ( number_number_of_int @ X_1 ) @ one_one_int ) ) )
= $true ),
inference(copy,[status(thm)],[246]) ).
thf(314,plain,
( ( ! [Y_1: $i] :
( ~ ( ord_less_eq_int @ one_one_int @ ( number_number_of_int @ Y_1 ) )
| ( ord_less_eq_int @ ( bit1 @ pls ) @ Y_1 ) )
& ! [Y_1: $i] :
( ~ ( ord_less_eq_int @ ( bit1 @ pls ) @ Y_1 )
| ( ord_less_eq_int @ one_one_int @ ( number_number_of_int @ Y_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[245]) ).
thf(315,plain,
( ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
= ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(copy,[status(thm)],[170]) ).
thf(316,plain,
( ( ! [W: $i] :
( ( times_times_int @ pls @ W )
= pls ) )
= $true ),
inference(copy,[status(thm)],[169]) ).
thf(317,plain,
( ( ! [K_1: $i,L_1: $i] :
( ( times_times_int @ ( bit0 @ K_1 ) @ L_1 )
= ( bit0 @ ( times_times_int @ K_1 @ L_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[168]) ).
thf(318,plain,
( ( ! [K: $i,L: $i] :
( ~ ( ord_less_int @ ( number_number_of_int @ K ) @ ( number_number_of_int @ L ) )
| ( ord_less_int @ K @ L ) )
& ! [K: $i,L: $i] :
( ~ ( ord_less_int @ K @ L )
| ( ord_less_int @ ( number_number_of_int @ K ) @ ( number_number_of_int @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[244]) ).
thf(319,plain,
( ( ! [Z: $i] :
( ( times_times_int @ Z @ one_one_int )
= Z ) )
= $true ),
inference(copy,[status(thm)],[166]) ).
thf(320,plain,
( ( ! [Z: $i] :
( ( times_times_int @ one_one_int @ Z )
= Z ) )
= $true ),
inference(copy,[status(thm)],[165]) ).
thf(321,plain,
( ( ! [V_2: $i,W: $i] :
( ( plus_plus_int @ ( number_number_of_int @ V_2 ) @ ( number_number_of_int @ W ) )
= ( number_number_of_int @ ( plus_plus_int @ V_2 @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[164]) ).
thf(322,plain,
( ( ! [Z1: $i,Z2: $i,W: $i] :
( ( times_times_int @ ( plus_plus_int @ Z1 @ Z2 ) @ W )
= ( plus_plus_int @ ( times_times_int @ Z1 @ W ) @ ( times_times_int @ Z2 @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[163]) ).
thf(323,plain,
( ( ! [W: $i,Z1: $i,Z2: $i] :
( ( times_times_int @ W @ ( plus_plus_int @ Z1 @ Z2 ) )
= ( plus_plus_int @ ( times_times_int @ W @ Z1 ) @ ( times_times_int @ W @ Z2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[162]) ).
thf(324,plain,
( ( ! [K: $i] :
( ~ ( ord_less_eq_int @ ( bit1 @ K ) @ pls )
| ( ord_less_int @ K @ pls ) )
& ! [K: $i] :
( ~ ( ord_less_int @ K @ pls )
| ( ord_less_eq_int @ ( bit1 @ K ) @ pls ) ) )
= $true ),
inference(copy,[status(thm)],[243]) ).
thf(325,plain,
( ( ! [K: $i] :
( ~ ( ord_less_eq_int @ pls @ K )
| ( ord_less_int @ pls @ ( bit1 @ K ) ) )
& ! [K: $i] :
( ~ ( ord_less_int @ pls @ ( bit1 @ K ) )
| ( ord_less_eq_int @ pls @ K ) ) )
= $true ),
inference(copy,[status(thm)],[242]) ).
thf(326,plain,
( ( ! [K1: $i,K2: $i] :
( ~ ( ord_less_eq_int @ ( bit1 @ K1 ) @ ( bit0 @ K2 ) )
| ( ord_less_int @ K1 @ K2 ) )
& ! [K1: $i,K2: $i] :
( ~ ( ord_less_int @ K1 @ K2 )
| ( ord_less_eq_int @ ( bit1 @ K1 ) @ ( bit0 @ K2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[241]) ).
thf(327,plain,
( ( ! [K: $i,L: $i] :
( ~ ( ord_less_eq_int @ ( bit1 @ K ) @ ( bit0 @ L ) )
| ( ord_less_int @ K @ L ) )
& ! [K: $i,L: $i] :
( ~ ( ord_less_int @ K @ L )
| ( ord_less_eq_int @ ( bit1 @ K ) @ ( bit0 @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[240]) ).
thf(328,plain,
( ( ! [K1: $i,K2: $i] :
( ~ ( ord_less_eq_int @ K1 @ K2 )
| ( ord_less_int @ ( bit0 @ K1 ) @ ( bit1 @ K2 ) ) )
& ! [K1: $i,K2: $i] :
( ~ ( ord_less_int @ ( bit0 @ K1 ) @ ( bit1 @ K2 ) )
| ( ord_less_eq_int @ K1 @ K2 ) ) )
= $true ),
inference(copy,[status(thm)],[239]) ).
thf(329,plain,
( ( ! [K: $i,L: $i] :
( ~ ( ord_less_eq_int @ K @ L )
| ( ord_less_int @ ( bit0 @ K ) @ ( bit1 @ L ) ) )
& ! [K: $i,L: $i] :
( ~ ( ord_less_int @ ( bit0 @ K ) @ ( bit1 @ L ) )
| ( ord_less_eq_int @ K @ L ) ) )
= $true ),
inference(copy,[status(thm)],[238]) ).
thf(330,plain,
( ( ! [V_7: $i,V_6: $i] :
( ( ord_less_int @ V_7 @ V_6 )
| ~ ( ord_less_int @ V_7 @ V_6 )
| ( ord_less_nat @ ( number_number_of_nat @ V_7 ) @ ( number_number_of_nat @ V_6 ) ) )
& ! [V_7: $i,V_6: $i] :
( ~ ( ord_less_int @ pls @ V_6 )
| ~ ( ord_less_int @ V_7 @ V_6 )
| ( ord_less_nat @ ( number_number_of_nat @ V_7 ) @ ( number_number_of_nat @ V_6 ) ) )
& ! [V_7: $i,V_6: $i] :
( ~ ( ord_less_nat @ ( number_number_of_nat @ V_7 ) @ ( number_number_of_nat @ V_6 ) )
| ~ ( ord_less_int @ V_7 @ V_6 )
| ( ord_less_int @ pls @ V_6 ) )
& ! [V_7: $i,V_6: $i] :
( ~ ( ord_less_nat @ ( number_number_of_nat @ V_7 ) @ ( number_number_of_nat @ V_6 ) )
| ( ord_less_int @ V_7 @ V_6 ) ) )
= $true ),
inference(copy,[status(thm)],[237]) ).
thf(331,plain,
( ( ! [Z_1: $i] :
( ~ ( ord_less_eq_int @ one_one_int @ Z_1 )
| ( ord_less_int @ zero_zero_int @ Z_1 ) )
& ! [Z_1: $i] :
( ~ ( ord_less_int @ zero_zero_int @ Z_1 )
| ( ord_less_eq_int @ one_one_int @ Z_1 ) ) )
= $true ),
inference(copy,[status(thm)],[236]) ).
thf(332,plain,
( ( ( number_number_of_nat @ ( bit1 @ pls ) )
= one_one_nat )
= $true ),
inference(copy,[status(thm)],[153]) ).
thf(333,plain,
( ( one_one_nat
= ( number_number_of_nat @ ( bit1 @ pls ) ) )
= $true ),
inference(copy,[status(thm)],[152]) ).
thf(334,plain,
( ( ! [W: $i,Z: $i] :
( ~ ( ord_less_int @ W @ Z )
| ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[235]) ).
thf(335,plain,
( ( ! [W_1: $i,Z_1: $i] :
( ~ ( ord_less_eq_int @ ( plus_plus_int @ W_1 @ one_one_int ) @ Z_1 )
| ( ord_less_int @ W_1 @ Z_1 ) )
& ! [W_1: $i,Z_1: $i] :
( ~ ( ord_less_int @ W_1 @ Z_1 )
| ( ord_less_eq_int @ ( plus_plus_int @ W_1 @ one_one_int ) @ Z_1 ) ) )
= $true ),
inference(copy,[status(thm)],[234]) ).
thf(336,plain,
( ( ! [W_1: $i,Z_1: $i] :
( ~ ( ord_less_eq_int @ W_1 @ Z_1 )
| ( ord_less_int @ W_1 @ ( plus_plus_int @ Z_1 @ one_one_int ) ) )
& ! [W_1: $i,Z_1: $i] :
( ~ ( ord_less_int @ W_1 @ ( plus_plus_int @ Z_1 @ one_one_int ) )
| ( ord_less_eq_int @ W_1 @ Z_1 ) ) )
= $true ),
inference(copy,[status(thm)],[233]) ).
thf(337,plain,
( ( ! [V_5: $i,V_4: $i] :
( ~ ( ord_less_eq_int @ pls @ V_4 )
| ~ ( ord_less_eq_int @ pls @ V_5 )
| ( ( plus_plus_int @ ( number_number_of_int @ V_4 ) @ ( number_number_of_int @ V_5 ) )
= ( number_number_of_int @ ( plus_plus_int @ V_4 @ V_5 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[232]) ).
thf(338,plain,
( ( ! [V_5: $i,V_4: $i] :
( ~ ( ord_less_eq_int @ pls @ V_4 )
| ~ ( ord_less_eq_int @ pls @ V_5 )
| ( ( 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)],[231]) ).
thf(339,plain,
( ( ! [V_3: $i,V_2: $i] :
( ~ ( ord_less_int @ V_2 @ pls )
| ( ( plus_plus_nat @ ( number_number_of_nat @ V_2 ) @ ( number_number_of_nat @ V_3 ) )
= ( number_number_of_nat @ V_3 ) ) )
& ! [V_3: $i,V_2: $i] :
( ( ord_less_int @ V_2 @ pls )
| ~ ( ord_less_int @ V_3 @ pls )
| ( ( plus_plus_nat @ ( number_number_of_nat @ V_2 ) @ ( number_number_of_nat @ V_3 ) )
= ( number_number_of_nat @ V_2 ) ) )
& ! [V_3: $i,V_2: $i] :
( ( ord_less_int @ V_2 @ pls )
| ( ord_less_int @ V_3 @ pls )
| ( ( plus_plus_nat @ ( number_number_of_nat @ V_2 ) @ ( number_number_of_nat @ V_3 ) )
= ( number_number_of_nat @ ( plus_plus_int @ V_2 @ V_3 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[230]) ).
thf(340,plain,
( ( ! [Z: $i] :
( ~ ( ord_less_eq_int @ zero_zero_int @ Z )
| ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[229]) ).
thf(341,plain,
( ( ! [W_1: $i,X_1: $i] :
( ( ( number_number_of_nat @ W_1 )
!= X_1 )
| ( X_1
= ( number_number_of_nat @ W_1 ) ) )
& ! [W_1: $i,X_1: $i] :
( ( X_1
!= ( number_number_of_nat @ W_1 ) )
| ( ( number_number_of_nat @ W_1 )
= X_1 ) ) )
= $true ),
inference(copy,[status(thm)],[228]) ).
thf(342,plain,
( ( ! [K: $i,L: $i] :
( ( ( bit1 @ K )
!= ( bit1 @ L ) )
| ( K = L ) )
& ! [K: $i,L: $i] :
( ( K != L )
| ( ( bit1 @ K )
= ( bit1 @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[227]) ).
thf(343,plain,
( ( ! [K: $i,L: $i] :
( ( ( bit0 @ K )
!= ( bit0 @ L ) )
| ( K = L ) )
& ! [K: $i,L: $i] :
( ( K != L )
| ( ( bit0 @ K )
= ( bit0 @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[226]) ).
thf(344,plain,
( ( ! [X: $i,Y: $i] :
( ( ord_less_int @ Y @ X )
| ( X = Y )
| ( ord_less_int @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[225]) ).
thf(345,plain,
( ( ! [X_1: $i,Y_1: $i] :
( ( X_1 != zero_zero_int )
| ( Y_1 != zero_zero_int )
| ( ( plus_plus_int @ ( times_times_int @ X_1 @ X_1 ) @ ( times_times_int @ Y_1 @ Y_1 ) )
= zero_zero_int ) )
& ! [X_1: $i] :
( ! [Y_1: $i] :
( ( plus_plus_int @ ( times_times_int @ X_1 @ X_1 ) @ ( times_times_int @ Y_1 @ Y_1 ) )
!= zero_zero_int )
| ( X_1 = zero_zero_int ) )
& ! [X_1: $i,Y_1: $i] :
( ( ( plus_plus_int @ ( times_times_int @ X_1 @ X_1 ) @ ( times_times_int @ Y_1 @ Y_1 ) )
!= zero_zero_int )
| ( Y_1 = zero_zero_int ) ) )
= $true ),
inference(copy,[status(thm)],[224]) ).
thf(346,plain,
( ( ! [A: $i,B_1: $i,V_1: $i] :
( ( times_times_int @ ( plus_plus_int @ A @ B_1 ) @ ( number_number_of_int @ V_1 ) )
= ( plus_plus_int @ ( times_times_int @ A @ ( number_number_of_int @ V_1 ) ) @ ( times_times_int @ B_1 @ ( number_number_of_int @ V_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[139]) ).
thf(347,plain,
( ( ! [A: $i,B_1: $i,V_1: $i] :
( ( times_times_nat @ ( plus_plus_nat @ A @ B_1 ) @ ( number_number_of_nat @ V_1 ) )
= ( plus_plus_nat @ ( times_times_nat @ A @ ( number_number_of_nat @ V_1 ) ) @ ( times_times_nat @ B_1 @ ( number_number_of_nat @ V_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[138]) ).
thf(348,plain,
( ( ! [V: $i,B: $i,C: $i] :
( ( times_times_int @ ( number_number_of_int @ V ) @ ( plus_plus_int @ B @ C ) )
= ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ V ) @ B ) @ ( times_times_int @ ( number_number_of_int @ V ) @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[137]) ).
thf(349,plain,
( ( ! [V: $i,B: $i,C: $i] :
( ( times_times_nat @ ( number_number_of_nat @ V ) @ ( plus_plus_nat @ B @ C ) )
= ( plus_plus_nat @ ( times_times_nat @ ( number_number_of_nat @ V ) @ B ) @ ( times_times_nat @ ( number_number_of_nat @ V ) @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[136]) ).
thf(350,plain,
( ( ! [Z1: $i,Z2: $i,Z3: $i] :
( ( plus_plus_int @ ( plus_plus_int @ Z1 @ Z2 ) @ Z3 )
= ( plus_plus_int @ Z1 @ ( plus_plus_int @ Z2 @ Z3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[135]) ).
thf(351,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( plus_plus_int @ X @ ( plus_plus_int @ Y @ Z ) )
= ( plus_plus_int @ Y @ ( plus_plus_int @ X @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[134]) ).
thf(352,plain,
( ( ! [Z: $i,W: $i] :
( ( plus_plus_int @ Z @ W )
= ( plus_plus_int @ W @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[133]) ).
thf(353,plain,
( ( zero_zero_int
= ( number_number_of_int @ pls ) )
= $true ),
inference(copy,[status(thm)],[132]) ).
thf(354,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)],[131]) ).
thf(355,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)],[130]) ).
thf(356,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)],[129]) ).
thf(357,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)],[128]) ).
thf(358,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 ) @ sK1_T ) )
= $true ),
inference(copy,[status(thm)],[223]) ).
thf(359,plain,
( ( ! [W: $i] : ( ord_less_eq_int @ W @ W ) )
= $true ),
inference(copy,[status(thm)],[126]) ).
thf(360,plain,
( ( ! [K_1: $i] :
( ( number_number_of_int @ K_1 )
= K_1 ) )
= $true ),
inference(copy,[status(thm)],[125]) ).
thf(361,plain,
( ( ! [Z: $i,W: $i] :
( ( times_times_int @ Z @ W )
= ( times_times_int @ W @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[124]) ).
thf(362,plain,
( ( ! [Z: $i,W: $i] :
( ( ord_less_eq_int @ Z @ W )
| ( ord_less_eq_int @ W @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[123]) ).
thf(363,plain,
( ( ! [V_2: $i,W: $i] :
( ( times_times_int @ ( number_number_of_int @ V_2 ) @ ( number_number_of_int @ W ) )
= ( number_number_of_int @ ( times_times_int @ V_2 @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(364,plain,
( ( ! [K: $i,L: $i] :
( ~ ( ord_less_eq_int @ ( number_number_of_int @ K ) @ ( number_number_of_int @ L ) )
| ( ord_less_eq_int @ K @ L ) )
& ! [K: $i,L: $i] :
( ~ ( 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)],[222]) ).
thf(365,plain,
( ( ! [X_1: $i,Y_1: $i] :
( ~ ( ord_less_eq_int @ ( number_number_of_int @ X_1 ) @ ( number_number_of_int @ Y_1 ) )
| ( ord_less_eq_int @ X_1 @ Y_1 ) )
& ! [X_1: $i,Y_1: $i] :
( ~ ( ord_less_eq_int @ X_1 @ Y_1 )
| ( ord_less_eq_int @ ( number_number_of_int @ X_1 ) @ ( number_number_of_int @ Y_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[221]) ).
thf(366,plain,
( ( ! [Z1: $i,Z2: $i,Z3: $i] :
( ( times_times_int @ ( times_times_int @ Z1 @ Z2 ) @ Z3 )
= ( times_times_int @ Z1 @ ( times_times_int @ Z2 @ Z3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[119]) ).
thf(367,plain,
( ( ! [K_1: $i,I: $i,J: $i] :
( ~ ( ord_less_eq_int @ I @ J )
| ~ ( ord_less_eq_int @ J @ K_1 )
| ( ord_less_eq_int @ I @ K_1 ) ) )
= $true ),
inference(copy,[status(thm)],[220]) ).
thf(368,plain,
( ( ! [Z: $i,W: $i] :
( ~ ( ord_less_eq_int @ Z @ W )
| ~ ( ord_less_eq_int @ W @ Z )
| ( Z = W ) ) )
= $true ),
inference(copy,[status(thm)],[219]) ).
thf(369,plain,
( ( ! [V_12: $i,V_11: $i] :
( ~ ( ord_less_eq_int @ pls @ V_11 )
| ~ ( ord_less_eq_int @ pls @ V_12 )
| ( ( times_times_nat @ ( number_number_of_nat @ V_11 ) @ ( number_number_of_nat @ V_12 ) )
= ( number_number_of_nat @ ( times_times_int @ V_11 @ V_12 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[218]) ).
thf(370,plain,
( ( ! [V_12: $i,V_11: $i] :
( ~ ( ord_less_eq_int @ pls @ V_11 )
| ~ ( ord_less_eq_int @ pls @ V_12 )
| ( ( times_times_int @ ( number_number_of_int @ V_11 ) @ ( number_number_of_int @ V_12 ) )
= ( number_number_of_int @ ( times_times_int @ V_11 @ V_12 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[217]) ).
thf(371,plain,
( ( ! [V_10: $i,W_5: $i,Z_3: $i] :
( ( times_times_int @ ( number_number_of_int @ V_10 ) @ ( times_times_int @ ( number_number_of_int @ W_5 ) @ Z_3 ) )
= ( times_times_int @ ( number_number_of_int @ ( times_times_int @ V_10 @ W_5 ) ) @ Z_3 ) ) )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(372,plain,
( ( ! [V_9: $i,W_4: $i] :
( ( times_times_int @ ( number_number_of_int @ V_9 ) @ ( number_number_of_int @ W_4 ) )
= ( number_number_of_int @ ( times_times_int @ V_9 @ W_4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(373,plain,
( ( ! [V_8: $i,W_3: $i] :
( ( number_number_of_int @ ( times_times_int @ V_8 @ W_3 ) )
= ( times_times_int @ ( number_number_of_int @ V_8 ) @ ( number_number_of_int @ W_3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(374,plain,
( ( ! [X_1: $i,Y_1: $i] :
( ( ( number_number_of_int @ X_1 )
!= ( number_number_of_int @ Y_1 ) )
| ( X_1 = Y_1 ) )
& ! [X_1: $i,Y_1: $i] :
( ( X_1 != Y_1 )
| ( ( number_number_of_int @ X_1 )
= ( number_number_of_int @ Y_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[216]) ).
thf(375,plain,
( ( ! [W_1: $i,X_1: $i] :
( ( ( number_number_of_int @ W_1 )
!= X_1 )
| ( X_1
= ( number_number_of_int @ W_1 ) ) )
& ! [W_1: $i,X_1: $i] :
( ( X_1
!= ( number_number_of_int @ W_1 ) )
| ( ( number_number_of_int @ W_1 )
= X_1 ) ) )
= $true ),
inference(copy,[status(thm)],[215]) ).
thf(376,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)],[214]) ).
thf(377,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_int @ SX0 @ ( plus_plus_int @ SX1 @ one_one_int ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX0 @ ( plus_plus_int @ SX1 @ one_one_int ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[336]) ).
thf(378,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[290]) ).
thf(379,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[327]) ).
thf(380,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( 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: $i] :
( ! [SX1: $i] :
( ( plus_plus_int @ ( power_power_int @ SX0 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SX1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( ( plus_plus_int @ ( power_power_int @ SX0 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SX1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_int )
| ( SX1 = zero_zero_int ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[278]) ).
thf(381,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ord_less_eq_int @ ( number_number_of_int @ SX0 ) @ zero_zero_int )
| ( ord_less_eq_int @ SX0 @ pls ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less_eq_int @ SX0 @ pls )
| ( ord_less_eq_int @ ( number_number_of_int @ SX0 ) @ zero_zero_int ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[300]) ).
thf(382,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( 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: $i,SX1: $i] :
( ( 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)],[304]) ).
thf(383,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( number_number_of_nat @ SX0 )
!= SX1 )
| ( SX1
= ( number_number_of_nat @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( number_number_of_nat @ SX0 ) )
| ( ( number_number_of_nat @ SX0 )
= SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[341]) ).
thf(384,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[329]) ).
thf(385,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ord_less_eq_int @ pls @ ( bit0 @ SX0 ) )
| ( ord_less_eq_int @ pls @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less_eq_int @ pls @ SX0 )
| ( ord_less_eq_int @ pls @ ( bit0 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[309]) ).
thf(386,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ord_less_eq_int @ pls @ SX0 )
| ( ord_less_int @ pls @ ( bit1 @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less_int @ pls @ ( bit1 @ SX0 ) )
| ( ord_less_eq_int @ pls @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[325]) ).
thf(387,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( 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: $i] :
( ! [SX1: $i] :
~ ( 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: $i,SX1: $i] :
( ~ ( 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)],[298]) ).
thf(388,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[307]) ).
thf(389,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( ( number_number_of_nat @ SX0 )
!= zero_zero_nat )
| ( ord_less_eq_int @ SX0 @ pls ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less_eq_int @ SX0 @ pls )
| ( ( number_number_of_nat @ SX0 )
= zero_zero_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[296]) ).
thf(390,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[306]) ).
thf(391,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( bit0 @ SX0 )
!= ( bit0 @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( bit0 @ SX0 )
= ( bit0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[343]) ).
thf(392,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ ( plus_plus_int @ SX0 @ one_one_int ) @ SX1 )
| ( ord_less_int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( plus_plus_int @ SX0 @ one_one_int ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[335]) ).
thf(393,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ SX0 ) )
| ( ord_less_eq_int @ pls @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less_eq_int @ pls @ SX0 )
| ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[301]) ).
thf(394,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ ( number_number_of_int @ SX0 ) @ ( number_number_of_int @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ ( number_number_of_int @ SX0 ) @ ( number_number_of_int @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[318]) ).
thf(395,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ord_less_eq_int @ ( bit1 @ SX0 ) @ pls )
| ( ord_less_int @ SX0 @ pls ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less_int @ SX0 @ pls )
| ( ord_less_eq_int @ ( bit1 @ SX0 ) @ pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[324]) ).
thf(396,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[293]) ).
thf(397,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( number_number_of_int @ SX0 )
!= ( number_number_of_int @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( number_number_of_int @ SX0 )
= ( number_number_of_int @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[374]) ).
thf(398,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( bit1 @ SX0 )
!= ( bit1 @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( bit1 @ SX0 )
= ( bit1 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[342]) ).
thf(399,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ord_less_eq_int @ ( bit0 @ SX0 ) @ pls )
| ( ord_less_eq_int @ SX0 @ pls ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less_eq_int @ SX0 @ pls )
| ( ord_less_eq_int @ ( bit0 @ SX0 ) @ pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[308]) ).
thf(400,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ord_less_eq_int @ one_one_int @ ( number_number_of_int @ SX0 ) )
| ( ord_less_eq_int @ ( bit1 @ pls ) @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( 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)],[314]) ).
thf(401,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( 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: $i] :
( ! [SX1: $i] :
( ( plus_plus_int @ ( times_times_int @ SX0 @ SX0 ) @ ( times_times_int @ SX1 @ SX1 ) )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( ( 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)],[345]) ).
thf(402,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX1 @ pls )
| ( ( plus_plus_nat @ ( number_number_of_nat @ SX1 ) @ ( number_number_of_nat @ SX0 ) )
= ( number_number_of_nat @ SX0 ) ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( 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: $i,SX1: $i] :
( ( 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)],[339]) ).
thf(403,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ord_less_eq_int @ one_one_int @ SX0 )
| ( ord_less_int @ zero_zero_int @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less_int @ zero_zero_int @ SX0 )
| ( ord_less_eq_int @ one_one_int @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[331]) ).
thf(404,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( number_number_of_int @ SX0 )
!= SX1 )
| ( SX1
= ( number_number_of_int @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( number_number_of_int @ SX0 ) )
| ( ( number_number_of_int @ SX0 )
= SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[375]) ).
thf(405,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( ( power_power_int @ SX0 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) )
| ~ ! [SX0: $i] :
( ( SX0 != zero_zero_int )
| ( ( power_power_int @ SX0 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[285]) ).
thf(406,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( 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: $i,SX1: $i] :
( ( 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)],[303]) ).
thf(407,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( 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: $i] :
( ( SX0 = zero_zero_int )
| ! [SX1: $i] : ( 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: $i,SX1: $i] :
( ( 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)],[277]) ).
thf(408,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_int @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[294]) ).
thf(409,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[292]) ).
thf(410,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ ( number_number_of_int @ SX0 ) @ ( number_number_of_int @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[365]) ).
thf(411,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( SX0 = zero_zero_int )
| ( ord_less_int @ zero_zero_int @ ( power_power_int @ SX0 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( 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)],[280]) ).
thf(412,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ord_less_int @ SX0 @ SX1 )
| ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_nat @ ( number_number_of_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ pls @ SX1 )
| ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_nat @ ( number_number_of_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) ) ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_nat @ ( number_number_of_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) )
| ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ pls @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_nat @ ( number_number_of_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[330]) ).
thf(413,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ ( number_number_of_int @ SX0 ) @ ( number_number_of_int @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[364]) ).
thf(414,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[289]) ).
thf(415,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[328]) ).
thf(416,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ord_less_eq_int @ ( number_number_of_int @ SX0 ) @ one_one_int )
| ( ord_less_eq_int @ SX0 @ ( bit1 @ pls ) ) )
| ~ ! [SX0: $i] :
( ~ ( 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)],[313]) ).
thf(417,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[326]) ).
thf(418,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( zero_zero_nat
!= ( number_number_of_nat @ SX0 ) )
| ( ord_less_eq_int @ SX0 @ pls ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less_eq_int @ SX0 @ pls )
| ( zero_zero_nat
= ( number_number_of_nat @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[297]) ).
thf(419,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ord_less_eq_int @ pls @ ( bit1 @ SX0 ) )
| ( ord_less_eq_int @ pls @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less_eq_int @ pls @ SX0 )
| ( ord_less_eq_int @ pls @ ( bit1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[305]) ).
thf(420,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ord_less_int @ pls @ SX0 )
| ( ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ SX0 ) )
| ( ord_less_int @ pls @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[302]) ).
thf(421,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)],[274]) ).
thf(422,plain,
( ( ord_less_eq_int @ one_one_int @ t )
= $false ),
inference(extcnf_not_pos,[status(thm)],[275]) ).
thf(423,plain,
! [SV1: $i] :
( ( ! [SY160: $i] :
~ ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ SV1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SY160 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[276]) ).
thf(424,plain,
! [SV2: $i] :
( ( ~ ( ord_less_int @ ( power_power_int @ SV2 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[279]) ).
thf(425,plain,
! [SV3: $i] :
( ( ( 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)],[286]) ).
thf(426,plain,
! [SV4: $i] :
( ( ( 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)],[287]) ).
thf(427,plain,
! [SV5: $i] :
( ( ! [SY161: $i,SY162: $i] :
( ( power_power_int @ SV5 @ ( plus_plus_nat @ SY161 @ SY162 ) )
= ( times_times_int @ ( power_power_int @ SV5 @ SY161 ) @ ( power_power_int @ SV5 @ SY162 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[288]) ).
thf(428,plain,
! [SV6: $i] :
( ( ! [SY163: $i,SY164: $i] :
( ~ ( ord_less_eq_int @ SY163 @ SY164 )
| ( ord_less_eq_int @ ( plus_plus_int @ SV6 @ SY163 ) @ ( plus_plus_int @ SV6 @ SY164 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[295]) ).
thf(429,plain,
! [SV7: $i] :
( ( ! [SY165: $i] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ SV7 @ SV7 ) @ ( times_times_int @ SY165 @ SY165 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[299]) ).
thf(430,plain,
! [SV8: $i] :
( ( ! [SY166: $i,SY167: $i,SY168: $i] :
( ~ ( ord_less_int @ SY167 @ SY168 )
| ~ ( ord_less_eq_int @ SV8 @ SY166 )
| ( ord_less_int @ ( plus_plus_int @ SY167 @ SV8 ) @ ( plus_plus_int @ SY168 @ SY166 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[310]) ).
thf(431,plain,
! [SV9: $i] :
( ( ( times_times_int @ pls @ SV9 )
= pls )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[316]) ).
thf(432,plain,
! [SV10: $i] :
( ( ! [SY169: $i] :
( ( times_times_int @ ( bit0 @ SV10 ) @ SY169 )
= ( bit0 @ ( times_times_int @ SV10 @ SY169 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[317]) ).
thf(433,plain,
! [SV11: $i] :
( ( ( times_times_int @ SV11 @ one_one_int )
= SV11 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[319]) ).
thf(434,plain,
! [SV12: $i] :
( ( ( times_times_int @ one_one_int @ SV12 )
= SV12 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[320]) ).
thf(435,plain,
! [SV13: $i] :
( ( ! [SY170: $i] :
( ( plus_plus_int @ ( number_number_of_int @ SV13 ) @ ( number_number_of_int @ SY170 ) )
= ( number_number_of_int @ ( plus_plus_int @ SV13 @ SY170 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[321]) ).
thf(436,plain,
! [SV14: $i] :
( ( ! [SY171: $i,SY172: $i] :
( ( times_times_int @ ( plus_plus_int @ SV14 @ SY171 ) @ SY172 )
= ( plus_plus_int @ ( times_times_int @ SV14 @ SY172 ) @ ( times_times_int @ SY171 @ SY172 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[322]) ).
thf(437,plain,
! [SV15: $i] :
( ( ! [SY173: $i,SY174: $i] :
( ( times_times_int @ SV15 @ ( plus_plus_int @ SY173 @ SY174 ) )
= ( plus_plus_int @ ( times_times_int @ SV15 @ SY173 ) @ ( times_times_int @ SV15 @ SY174 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[323]) ).
thf(438,plain,
! [SV16: $i] :
( ( ! [SY175: $i] :
( ~ ( ord_less_int @ SV16 @ SY175 )
| ( ord_less_eq_int @ ( plus_plus_int @ SV16 @ one_one_int ) @ SY175 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[334]) ).
thf(439,plain,
! [SV17: $i] :
( ( ! [SY176: $i] :
( ~ ( ord_less_eq_int @ pls @ SY176 )
| ~ ( ord_less_eq_int @ pls @ SV17 )
| ( ( plus_plus_int @ ( number_number_of_int @ SY176 ) @ ( number_number_of_int @ SV17 ) )
= ( number_number_of_int @ ( plus_plus_int @ SY176 @ SV17 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[337]) ).
thf(440,plain,
! [SV18: $i] :
( ( ! [SY177: $i] :
( ~ ( ord_less_eq_int @ pls @ SY177 )
| ~ ( ord_less_eq_int @ pls @ SV18 )
| ( ( plus_plus_nat @ ( number_number_of_nat @ SY177 ) @ ( number_number_of_nat @ SV18 ) )
= ( number_number_of_nat @ ( plus_plus_int @ SY177 @ SV18 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[338]) ).
thf(441,plain,
! [SV19: $i] :
( ( ~ ( 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)],[340]) ).
thf(442,plain,
! [SV20: $i] :
( ( ! [SY178: $i] :
( ( ord_less_int @ SY178 @ SV20 )
| ( SV20 = SY178 )
| ( ord_less_int @ SV20 @ SY178 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[344]) ).
thf(443,plain,
! [SV21: $i] :
( ( ! [SY179: $i,SY180: $i] :
( ( times_times_int @ ( plus_plus_int @ SV21 @ SY179 ) @ ( number_number_of_int @ SY180 ) )
= ( plus_plus_int @ ( times_times_int @ SV21 @ ( number_number_of_int @ SY180 ) ) @ ( times_times_int @ SY179 @ ( number_number_of_int @ SY180 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[346]) ).
thf(444,plain,
! [SV22: $i] :
( ( ! [SY181: $i,SY182: $i] :
( ( times_times_nat @ ( plus_plus_nat @ SV22 @ SY181 ) @ ( number_number_of_nat @ SY182 ) )
= ( plus_plus_nat @ ( times_times_nat @ SV22 @ ( number_number_of_nat @ SY182 ) ) @ ( times_times_nat @ SY181 @ ( number_number_of_nat @ SY182 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[347]) ).
thf(445,plain,
! [SV23: $i] :
( ( ! [SY183: $i,SY184: $i] :
( ( times_times_int @ ( number_number_of_int @ SV23 ) @ ( plus_plus_int @ SY183 @ SY184 ) )
= ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ SV23 ) @ SY183 ) @ ( times_times_int @ ( number_number_of_int @ SV23 ) @ SY184 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[348]) ).
thf(446,plain,
! [SV24: $i] :
( ( ! [SY185: $i,SY186: $i] :
( ( times_times_nat @ ( number_number_of_nat @ SV24 ) @ ( plus_plus_nat @ SY185 @ SY186 ) )
= ( plus_plus_nat @ ( times_times_nat @ ( number_number_of_nat @ SV24 ) @ SY185 ) @ ( times_times_nat @ ( number_number_of_nat @ SV24 ) @ SY186 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[349]) ).
thf(447,plain,
! [SV25: $i] :
( ( ! [SY187: $i,SY188: $i] :
( ( plus_plus_int @ ( plus_plus_int @ SV25 @ SY187 ) @ SY188 )
= ( plus_plus_int @ SV25 @ ( plus_plus_int @ SY187 @ SY188 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[350]) ).
thf(448,plain,
! [SV26: $i] :
( ( ! [SY189: $i,SY190: $i] :
( ( plus_plus_int @ SV26 @ ( plus_plus_int @ SY189 @ SY190 ) )
= ( plus_plus_int @ SY189 @ ( plus_plus_int @ SV26 @ SY190 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[351]) ).
thf(449,plain,
! [SV27: $i] :
( ( ! [SY191: $i] :
( ( plus_plus_int @ SV27 @ SY191 )
= ( plus_plus_int @ SY191 @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[352]) ).
thf(450,plain,
! [SV28: $i] :
( ( ord_less_eq_int @ SV28 @ SV28 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[359]) ).
thf(451,plain,
! [SV29: $i] :
( ( ( number_number_of_int @ SV29 )
= SV29 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[360]) ).
thf(452,plain,
! [SV30: $i] :
( ( ! [SY192: $i] :
( ( times_times_int @ SV30 @ SY192 )
= ( times_times_int @ SY192 @ SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[361]) ).
thf(453,plain,
! [SV31: $i] :
( ( ! [SY193: $i] :
( ( ord_less_eq_int @ SV31 @ SY193 )
| ( ord_less_eq_int @ SY193 @ SV31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[362]) ).
thf(454,plain,
! [SV32: $i] :
( ( ! [SY194: $i] :
( ( times_times_int @ ( number_number_of_int @ SV32 ) @ ( number_number_of_int @ SY194 ) )
= ( number_number_of_int @ ( times_times_int @ SV32 @ SY194 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[363]) ).
thf(455,plain,
! [SV33: $i] :
( ( ! [SY195: $i,SY196: $i] :
( ( times_times_int @ ( times_times_int @ SV33 @ SY195 ) @ SY196 )
= ( times_times_int @ SV33 @ ( times_times_int @ SY195 @ SY196 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[366]) ).
thf(456,plain,
! [SV34: $i] :
( ( ! [SY197: $i,SY198: $i] :
( ~ ( ord_less_eq_int @ SY197 @ SY198 )
| ~ ( ord_less_eq_int @ SY198 @ SV34 )
| ( ord_less_eq_int @ SY197 @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[367]) ).
thf(457,plain,
! [SV35: $i] :
( ( ! [SY199: $i] :
( ~ ( ord_less_eq_int @ SV35 @ SY199 )
| ~ ( ord_less_eq_int @ SY199 @ SV35 )
| ( SV35 = SY199 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[368]) ).
thf(458,plain,
! [SV36: $i] :
( ( ! [SY200: $i] :
( ~ ( ord_less_eq_int @ pls @ SY200 )
| ~ ( ord_less_eq_int @ pls @ SV36 )
| ( ( times_times_nat @ ( number_number_of_nat @ SY200 ) @ ( number_number_of_nat @ SV36 ) )
= ( number_number_of_nat @ ( times_times_int @ SY200 @ SV36 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[369]) ).
thf(459,plain,
! [SV37: $i] :
( ( ! [SY201: $i] :
( ~ ( ord_less_eq_int @ pls @ SY201 )
| ~ ( ord_less_eq_int @ pls @ SV37 )
| ( ( times_times_int @ ( number_number_of_int @ SY201 ) @ ( number_number_of_int @ SV37 ) )
= ( number_number_of_int @ ( times_times_int @ SY201 @ SV37 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[370]) ).
thf(460,plain,
! [SV38: $i] :
( ( ! [SY202: $i,SY203: $i] :
( ( times_times_int @ ( number_number_of_int @ SV38 ) @ ( times_times_int @ ( number_number_of_int @ SY202 ) @ SY203 ) )
= ( times_times_int @ ( number_number_of_int @ ( times_times_int @ SV38 @ SY202 ) ) @ SY203 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[371]) ).
thf(461,plain,
! [SV39: $i] :
( ( ! [SY204: $i] :
( ( times_times_int @ ( number_number_of_int @ SV39 ) @ ( number_number_of_int @ SY204 ) )
= ( number_number_of_int @ ( times_times_int @ SV39 @ SY204 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[372]) ).
thf(462,plain,
! [SV40: $i] :
( ( ! [SY205: $i] :
( ( number_number_of_int @ ( times_times_int @ SV40 @ SY205 ) )
= ( times_times_int @ ( number_number_of_int @ SV40 ) @ ( number_number_of_int @ SY205 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[373]) ).
thf(463,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)],[376]) ).
thf(464,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_int @ SX0 @ ( plus_plus_int @ SX1 @ one_one_int ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX0 @ ( plus_plus_int @ SX1 @ one_one_int ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[377]) ).
thf(465,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[378]) ).
thf(466,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[379]) ).
thf(467,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( 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: $i] :
( ! [SX1: $i] :
( ( plus_plus_int @ ( power_power_int @ SX0 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SX1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( ( plus_plus_int @ ( power_power_int @ SX0 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SX1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_int )
| ( SX1 = zero_zero_int ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[380]) ).
thf(468,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_eq_int @ ( number_number_of_int @ SX0 ) @ zero_zero_int )
| ( ord_less_eq_int @ SX0 @ pls ) )
| ~ ! [SX0: $i] :
( ~ ( 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)],[381]) ).
thf(469,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( 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: $i,SX1: $i] :
( ( 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)],[382]) ).
thf(470,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( number_number_of_nat @ SX0 )
!= SX1 )
| ( SX1
= ( number_number_of_nat @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( number_number_of_nat @ SX0 ) )
| ( ( number_number_of_nat @ SX0 )
= SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[383]) ).
thf(471,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[384]) ).
thf(472,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_eq_int @ pls @ ( bit0 @ SX0 ) )
| ( ord_less_eq_int @ pls @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less_eq_int @ pls @ SX0 )
| ( ord_less_eq_int @ pls @ ( bit0 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[385]) ).
thf(473,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_eq_int @ pls @ SX0 )
| ( ord_less_int @ pls @ ( bit1 @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less_int @ pls @ ( bit1 @ SX0 ) )
| ( ord_less_eq_int @ pls @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[386]) ).
thf(474,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( 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: $i] :
( ! [SX1: $i] :
~ ( 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: $i,SX1: $i] :
( ~ ( 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)],[387]) ).
thf(475,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[388]) ).
thf(476,plain,
( ( ~ ! [SX0: $i] :
( ( ( number_number_of_nat @ SX0 )
!= zero_zero_nat )
| ( ord_less_eq_int @ SX0 @ pls ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less_eq_int @ SX0 @ pls )
| ( ( number_number_of_nat @ SX0 )
= zero_zero_nat ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[389]) ).
thf(477,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[390]) ).
thf(478,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( bit0 @ SX0 )
!= ( bit0 @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( bit0 @ SX0 )
= ( bit0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[391]) ).
thf(479,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ ( plus_plus_int @ SX0 @ one_one_int ) @ SX1 )
| ( ord_less_int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( plus_plus_int @ SX0 @ one_one_int ) @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[392]) ).
thf(480,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ SX0 ) )
| ( ord_less_eq_int @ pls @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( 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)],[393]) ).
thf(481,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ ( number_number_of_int @ SX0 ) @ ( number_number_of_int @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[394]) ).
thf(482,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_eq_int @ ( bit1 @ SX0 ) @ pls )
| ( ord_less_int @ SX0 @ pls ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less_int @ SX0 @ pls )
| ( ord_less_eq_int @ ( bit1 @ SX0 ) @ pls ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[395]) ).
thf(483,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[396]) ).
thf(484,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( number_number_of_int @ SX0 )
!= ( number_number_of_int @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( number_number_of_int @ SX0 )
= ( number_number_of_int @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[397]) ).
thf(485,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( bit1 @ SX0 )
!= ( bit1 @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( bit1 @ SX0 )
= ( bit1 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[398]) ).
thf(486,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_eq_int @ ( bit0 @ SX0 ) @ pls )
| ( ord_less_eq_int @ SX0 @ pls ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less_eq_int @ SX0 @ pls )
| ( ord_less_eq_int @ ( bit0 @ SX0 ) @ pls ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[399]) ).
thf(487,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_eq_int @ one_one_int @ ( number_number_of_int @ SX0 ) )
| ( ord_less_eq_int @ ( bit1 @ pls ) @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( 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)],[400]) ).
thf(488,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( 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: $i] :
( ! [SX1: $i] :
( ( plus_plus_int @ ( times_times_int @ SX0 @ SX0 ) @ ( times_times_int @ SX1 @ SX1 ) )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( ( 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)],[401]) ).
thf(489,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX1 @ pls )
| ( ( plus_plus_nat @ ( number_number_of_nat @ SX1 ) @ ( number_number_of_nat @ SX0 ) )
= ( number_number_of_nat @ SX0 ) ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( 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: $i,SX1: $i] :
( ( 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)],[402]) ).
thf(490,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_eq_int @ one_one_int @ SX0 )
| ( ord_less_int @ zero_zero_int @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less_int @ zero_zero_int @ SX0 )
| ( ord_less_eq_int @ one_one_int @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[403]) ).
thf(491,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( number_number_of_int @ SX0 )
!= SX1 )
| ( SX1
= ( number_number_of_int @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( number_number_of_int @ SX0 ) )
| ( ( number_number_of_int @ SX0 )
= SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[404]) ).
thf(492,plain,
( ( ~ ! [SX0: $i] :
( ( ( power_power_int @ SX0 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) )
| ~ ! [SX0: $i] :
( ( 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)],[405]) ).
thf(493,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( 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: $i,SX1: $i] :
( ( 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)],[406]) ).
thf(494,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( 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: $i] :
( ( SX0 = zero_zero_int )
| ! [SX1: $i] : ( 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: $i,SX1: $i] :
( ( 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)],[407]) ).
thf(495,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_int @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[408]) ).
thf(496,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[409]) ).
thf(497,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ ( number_number_of_int @ SX0 ) @ ( number_number_of_int @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[410]) ).
thf(498,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 = zero_zero_int )
| ( ord_less_int @ zero_zero_int @ ( power_power_int @ SX0 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( 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)],[411]) ).
thf(499,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ord_less_int @ SX0 @ SX1 )
| ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_nat @ ( number_number_of_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ pls @ SX1 )
| ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_nat @ ( number_number_of_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) ) ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_nat @ ( number_number_of_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) )
| ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ pls @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[412]) ).
thf(500,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ ( number_number_of_int @ SX0 ) @ ( number_number_of_int @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[413]) ).
thf(501,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[414]) ).
thf(502,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[415]) ).
thf(503,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_eq_int @ ( number_number_of_int @ SX0 ) @ one_one_int )
| ( ord_less_eq_int @ SX0 @ ( bit1 @ pls ) ) )
| ~ ! [SX0: $i] :
( ~ ( 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)],[416]) ).
thf(504,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[417]) ).
thf(505,plain,
( ( ~ ! [SX0: $i] :
( ( zero_zero_nat
!= ( number_number_of_nat @ SX0 ) )
| ( ord_less_eq_int @ SX0 @ pls ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less_eq_int @ SX0 @ pls )
| ( zero_zero_nat
= ( number_number_of_nat @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[418]) ).
thf(506,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_eq_int @ pls @ ( bit1 @ SX0 ) )
| ( ord_less_eq_int @ pls @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less_eq_int @ pls @ SX0 )
| ( ord_less_eq_int @ pls @ ( bit1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[419]) ).
thf(507,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_int @ pls @ SX0 )
| ( ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ SX0 ) )
| ( ord_less_int @ pls @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[420]) ).
thf(508,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)],[421]) ).
thf(509,plain,
! [SV41: $i,SV1: $i] :
( ( ~ ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ SV1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV41 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[423]) ).
thf(510,plain,
! [SV2: $i] :
( ( ord_less_int @ ( power_power_int @ SV2 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ zero_zero_int )
= $false ),
inference(extcnf_not_pos,[status(thm)],[424]) ).
thf(511,plain,
! [SV42: $i,SV5: $i] :
( ( ! [SY206: $i] :
( ( power_power_int @ SV5 @ ( plus_plus_nat @ SV42 @ SY206 ) )
= ( times_times_int @ ( power_power_int @ SV5 @ SV42 ) @ ( power_power_int @ SV5 @ SY206 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[427]) ).
thf(512,plain,
! [SV6: $i,SV43: $i] :
( ( ! [SY207: $i] :
( ~ ( ord_less_eq_int @ SV43 @ SY207 )
| ( ord_less_eq_int @ ( plus_plus_int @ SV6 @ SV43 ) @ ( plus_plus_int @ SV6 @ SY207 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[428]) ).
thf(513,plain,
! [SV44: $i,SV7: $i] :
( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ SV7 @ SV7 ) @ ( times_times_int @ SV44 @ SV44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[429]) ).
thf(514,plain,
! [SV45: $i,SV8: $i] :
( ( ! [SY208: $i,SY209: $i] :
( ~ ( ord_less_int @ SY208 @ SY209 )
| ~ ( ord_less_eq_int @ SV8 @ SV45 )
| ( ord_less_int @ ( plus_plus_int @ SY208 @ SV8 ) @ ( plus_plus_int @ SY209 @ SV45 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[430]) ).
thf(515,plain,
! [SV46: $i,SV10: $i] :
( ( ( times_times_int @ ( bit0 @ SV10 ) @ SV46 )
= ( bit0 @ ( times_times_int @ SV10 @ SV46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[432]) ).
thf(516,plain,
! [SV47: $i,SV13: $i] :
( ( ( plus_plus_int @ ( number_number_of_int @ SV13 ) @ ( number_number_of_int @ SV47 ) )
= ( number_number_of_int @ ( plus_plus_int @ SV13 @ SV47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[435]) ).
thf(517,plain,
! [SV48: $i,SV14: $i] :
( ( ! [SY210: $i] :
( ( times_times_int @ ( plus_plus_int @ SV14 @ SV48 ) @ SY210 )
= ( plus_plus_int @ ( times_times_int @ SV14 @ SY210 ) @ ( times_times_int @ SV48 @ SY210 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[436]) ).
thf(518,plain,
! [SV49: $i,SV15: $i] :
( ( ! [SY211: $i] :
( ( times_times_int @ SV15 @ ( plus_plus_int @ SV49 @ SY211 ) )
= ( plus_plus_int @ ( times_times_int @ SV15 @ SV49 ) @ ( times_times_int @ SV15 @ SY211 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[437]) ).
thf(519,plain,
! [SV50: $i,SV16: $i] :
( ( ~ ( ord_less_int @ SV16 @ SV50 )
| ( ord_less_eq_int @ ( plus_plus_int @ SV16 @ one_one_int ) @ SV50 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[438]) ).
thf(520,plain,
! [SV17: $i,SV51: $i] :
( ( ~ ( ord_less_eq_int @ pls @ SV51 )
| ~ ( ord_less_eq_int @ pls @ SV17 )
| ( ( plus_plus_int @ ( number_number_of_int @ SV51 ) @ ( number_number_of_int @ SV17 ) )
= ( number_number_of_int @ ( plus_plus_int @ SV51 @ SV17 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[439]) ).
thf(521,plain,
! [SV18: $i,SV52: $i] :
( ( ~ ( ord_less_eq_int @ pls @ SV52 )
| ~ ( ord_less_eq_int @ pls @ SV18 )
| ( ( plus_plus_nat @ ( number_number_of_nat @ SV52 ) @ ( number_number_of_nat @ SV18 ) )
= ( number_number_of_nat @ ( plus_plus_int @ SV52 @ SV18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[440]) ).
thf(522,plain,
! [SV19: $i] :
( ( ( ~ ( 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)],[441]) ).
thf(523,plain,
! [SV20: $i,SV53: $i] :
( ( ( ord_less_int @ SV53 @ SV20 )
| ( SV20 = SV53 )
| ( ord_less_int @ SV20 @ SV53 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[442]) ).
thf(524,plain,
! [SV54: $i,SV21: $i] :
( ( ! [SY212: $i] :
( ( times_times_int @ ( plus_plus_int @ SV21 @ SV54 ) @ ( number_number_of_int @ SY212 ) )
= ( plus_plus_int @ ( times_times_int @ SV21 @ ( number_number_of_int @ SY212 ) ) @ ( times_times_int @ SV54 @ ( number_number_of_int @ SY212 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[443]) ).
thf(525,plain,
! [SV55: $i,SV22: $i] :
( ( ! [SY213: $i] :
( ( times_times_nat @ ( plus_plus_nat @ SV22 @ SV55 ) @ ( number_number_of_nat @ SY213 ) )
= ( plus_plus_nat @ ( times_times_nat @ SV22 @ ( number_number_of_nat @ SY213 ) ) @ ( times_times_nat @ SV55 @ ( number_number_of_nat @ SY213 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[444]) ).
thf(526,plain,
! [SV56: $i,SV23: $i] :
( ( ! [SY214: $i] :
( ( times_times_int @ ( number_number_of_int @ SV23 ) @ ( plus_plus_int @ SV56 @ SY214 ) )
= ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ SV23 ) @ SV56 ) @ ( times_times_int @ ( number_number_of_int @ SV23 ) @ SY214 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[445]) ).
thf(527,plain,
! [SV57: $i,SV24: $i] :
( ( ! [SY215: $i] :
( ( times_times_nat @ ( number_number_of_nat @ SV24 ) @ ( plus_plus_nat @ SV57 @ SY215 ) )
= ( plus_plus_nat @ ( times_times_nat @ ( number_number_of_nat @ SV24 ) @ SV57 ) @ ( times_times_nat @ ( number_number_of_nat @ SV24 ) @ SY215 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[446]) ).
thf(528,plain,
! [SV58: $i,SV25: $i] :
( ( ! [SY216: $i] :
( ( plus_plus_int @ ( plus_plus_int @ SV25 @ SV58 ) @ SY216 )
= ( plus_plus_int @ SV25 @ ( plus_plus_int @ SV58 @ SY216 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[447]) ).
thf(529,plain,
! [SV59: $i,SV26: $i] :
( ( ! [SY217: $i] :
( ( plus_plus_int @ SV26 @ ( plus_plus_int @ SV59 @ SY217 ) )
= ( plus_plus_int @ SV59 @ ( plus_plus_int @ SV26 @ SY217 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[448]) ).
thf(530,plain,
! [SV60: $i,SV27: $i] :
( ( ( plus_plus_int @ SV27 @ SV60 )
= ( plus_plus_int @ SV60 @ SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[449]) ).
thf(531,plain,
! [SV61: $i,SV30: $i] :
( ( ( times_times_int @ SV30 @ SV61 )
= ( times_times_int @ SV61 @ SV30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[452]) ).
thf(532,plain,
! [SV62: $i,SV31: $i] :
( ( ( ord_less_eq_int @ SV31 @ SV62 )
| ( ord_less_eq_int @ SV62 @ SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[453]) ).
thf(533,plain,
! [SV63: $i,SV32: $i] :
( ( ( times_times_int @ ( number_number_of_int @ SV32 ) @ ( number_number_of_int @ SV63 ) )
= ( number_number_of_int @ ( times_times_int @ SV32 @ SV63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[454]) ).
thf(534,plain,
! [SV64: $i,SV33: $i] :
( ( ! [SY218: $i] :
( ( times_times_int @ ( times_times_int @ SV33 @ SV64 ) @ SY218 )
= ( times_times_int @ SV33 @ ( times_times_int @ SV64 @ SY218 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[455]) ).
thf(535,plain,
! [SV34: $i,SV65: $i] :
( ( ! [SY219: $i] :
( ~ ( ord_less_eq_int @ SV65 @ SY219 )
| ~ ( ord_less_eq_int @ SY219 @ SV34 )
| ( ord_less_eq_int @ SV65 @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[456]) ).
thf(536,plain,
! [SV66: $i,SV35: $i] :
( ( ~ ( ord_less_eq_int @ SV35 @ SV66 )
| ~ ( ord_less_eq_int @ SV66 @ SV35 )
| ( SV35 = SV66 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[457]) ).
thf(537,plain,
! [SV36: $i,SV67: $i] :
( ( ~ ( ord_less_eq_int @ pls @ SV67 )
| ~ ( ord_less_eq_int @ pls @ SV36 )
| ( ( times_times_nat @ ( number_number_of_nat @ SV67 ) @ ( number_number_of_nat @ SV36 ) )
= ( number_number_of_nat @ ( times_times_int @ SV67 @ SV36 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[458]) ).
thf(538,plain,
! [SV37: $i,SV68: $i] :
( ( ~ ( ord_less_eq_int @ pls @ SV68 )
| ~ ( ord_less_eq_int @ pls @ SV37 )
| ( ( times_times_int @ ( number_number_of_int @ SV68 ) @ ( number_number_of_int @ SV37 ) )
= ( number_number_of_int @ ( times_times_int @ SV68 @ SV37 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[459]) ).
thf(539,plain,
! [SV69: $i,SV38: $i] :
( ( ! [SY220: $i] :
( ( times_times_int @ ( number_number_of_int @ SV38 ) @ ( times_times_int @ ( number_number_of_int @ SV69 ) @ SY220 ) )
= ( times_times_int @ ( number_number_of_int @ ( times_times_int @ SV38 @ SV69 ) ) @ SY220 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[460]) ).
thf(540,plain,
! [SV70: $i,SV39: $i] :
( ( ( times_times_int @ ( number_number_of_int @ SV39 ) @ ( number_number_of_int @ SV70 ) )
= ( number_number_of_int @ ( times_times_int @ SV39 @ SV70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[461]) ).
thf(541,plain,
! [SV71: $i,SV40: $i] :
( ( ( number_number_of_int @ ( times_times_int @ SV40 @ SV71 ) )
= ( times_times_int @ ( number_number_of_int @ SV40 ) @ ( number_number_of_int @ SV71 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[462]) ).
thf(542,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_int @ SX0 @ ( plus_plus_int @ SX1 @ one_one_int ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[464]) ).
thf(543,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX0 @ ( plus_plus_int @ SX1 @ one_one_int ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[464]) ).
thf(544,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[465]) ).
thf(545,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[465]) ).
thf(546,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[466]) ).
thf(547,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[466]) ).
thf(548,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( 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)],[467]) ).
thf(549,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( plus_plus_int @ ( power_power_int @ SX0 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SX1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( ( plus_plus_int @ ( power_power_int @ SX0 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SX1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_int )
| ( SX1 = zero_zero_int ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[467]) ).
thf(550,plain,
( ( ~ ! [SX0: $i] :
( ~ ( 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)],[468]) ).
thf(551,plain,
( ( ~ ! [SX0: $i] :
( ~ ( 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)],[468]) ).
thf(552,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[469]) ).
thf(553,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( 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)],[469]) ).
thf(554,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( number_number_of_nat @ SX0 )
!= SX1 )
| ( SX1
= ( number_number_of_nat @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[470]) ).
thf(555,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( number_number_of_nat @ SX0 ) )
| ( ( number_number_of_nat @ SX0 )
= SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[470]) ).
thf(556,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[471]) ).
thf(557,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[471]) ).
thf(558,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_eq_int @ pls @ ( bit0 @ SX0 ) )
| ( ord_less_eq_int @ pls @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[472]) ).
thf(559,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_eq_int @ pls @ SX0 )
| ( ord_less_eq_int @ pls @ ( bit0 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[472]) ).
thf(560,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_eq_int @ pls @ SX0 )
| ( ord_less_int @ pls @ ( bit1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[473]) ).
thf(561,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_int @ pls @ ( bit1 @ SX0 ) )
| ( ord_less_eq_int @ pls @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[473]) ).
thf(562,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( 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)],[474]) ).
thf(563,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( 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: $i,SX1: $i] :
( ~ ( 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)],[474]) ).
thf(564,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[475]) ).
thf(565,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[475]) ).
thf(566,plain,
( ( ~ ! [SX0: $i] :
( ( ( number_number_of_nat @ SX0 )
!= zero_zero_nat )
| ( ord_less_eq_int @ SX0 @ pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[476]) ).
thf(567,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_eq_int @ SX0 @ pls )
| ( ( number_number_of_nat @ SX0 )
= zero_zero_nat ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[476]) ).
thf(568,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[477]) ).
thf(569,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[477]) ).
thf(570,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( bit0 @ SX0 )
!= ( bit0 @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[478]) ).
thf(571,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( bit0 @ SX0 )
= ( bit0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[478]) ).
thf(572,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ ( plus_plus_int @ SX0 @ one_one_int ) @ SX1 )
| ( ord_less_int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[479]) ).
thf(573,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( plus_plus_int @ SX0 @ one_one_int ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[479]) ).
thf(574,plain,
( ( ~ ! [SX0: $i] :
( ~ ( 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)],[480]) ).
thf(575,plain,
( ( ~ ! [SX0: $i] :
( ~ ( 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)],[480]) ).
thf(576,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[481]) ).
thf(577,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[481]) ).
thf(578,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_eq_int @ ( bit1 @ SX0 ) @ pls )
| ( ord_less_int @ SX0 @ pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[482]) ).
thf(579,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_int @ SX0 @ pls )
| ( ord_less_eq_int @ ( bit1 @ SX0 ) @ pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[482]) ).
thf(580,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[483]) ).
thf(581,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[483]) ).
thf(582,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( number_number_of_int @ SX0 )
!= ( number_number_of_int @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[484]) ).
thf(583,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( number_number_of_int @ SX0 )
= ( number_number_of_int @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[484]) ).
thf(584,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( bit1 @ SX0 )
!= ( bit1 @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[485]) ).
thf(585,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( bit1 @ SX0 )
= ( bit1 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[485]) ).
thf(586,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_eq_int @ ( bit0 @ SX0 ) @ pls )
| ( ord_less_eq_int @ SX0 @ pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[486]) ).
thf(587,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_eq_int @ SX0 @ pls )
| ( ord_less_eq_int @ ( bit0 @ SX0 ) @ pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[486]) ).
thf(588,plain,
( ( ~ ! [SX0: $i] :
( ~ ( 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)],[487]) ).
thf(589,plain,
( ( ~ ! [SX0: $i] :
( ~ ( 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)],[487]) ).
thf(590,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( 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)],[488]) ).
thf(591,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( plus_plus_int @ ( times_times_int @ SX0 @ SX0 ) @ ( times_times_int @ SX1 @ SX1 ) )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( ( 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)],[488]) ).
thf(592,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX1 @ pls )
| ( ( plus_plus_nat @ ( number_number_of_nat @ SX1 ) @ ( number_number_of_nat @ SX0 ) )
= ( number_number_of_nat @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[489]) ).
thf(593,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( 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: $i,SX1: $i] :
( ( 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)],[489]) ).
thf(594,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_eq_int @ one_one_int @ SX0 )
| ( ord_less_int @ zero_zero_int @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[490]) ).
thf(595,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_int @ zero_zero_int @ SX0 )
| ( ord_less_eq_int @ one_one_int @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[490]) ).
thf(596,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( number_number_of_int @ SX0 )
!= SX1 )
| ( SX1
= ( number_number_of_int @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[491]) ).
thf(597,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( number_number_of_int @ SX0 ) )
| ( ( number_number_of_int @ SX0 )
= SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[491]) ).
thf(598,plain,
( ( ~ ! [SX0: $i] :
( ( ( 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)],[492]) ).
thf(599,plain,
( ( ~ ! [SX0: $i] :
( ( 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)],[492]) ).
thf(600,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[493]) ).
thf(601,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( 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)],[493]) ).
thf(602,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[494]) ).
thf(603,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 = zero_zero_int )
| ! [SX1: $i] : ( 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: $i,SX1: $i] :
( ( 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)],[494]) ).
thf(604,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[495]) ).
thf(605,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[495]) ).
thf(606,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[496]) ).
thf(607,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[496]) ).
thf(608,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ ( number_number_of_int @ SX0 ) @ ( number_number_of_int @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[497]) ).
thf(609,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[497]) ).
thf(610,plain,
( ( ~ ! [SX0: $i] :
( ( 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)],[498]) ).
thf(611,plain,
( ( ~ ! [SX0: $i] :
( ~ ( 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)],[498]) ).
thf(612,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ord_less_int @ SX0 @ SX1 )
| ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_nat @ ( number_number_of_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[499]) ).
thf(613,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_nat @ ( number_number_of_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) )
| ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ pls @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[499]) ).
thf(614,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ ( number_number_of_int @ SX0 ) @ ( number_number_of_int @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[500]) ).
thf(615,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[500]) ).
thf(616,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[501]) ).
thf(617,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[501]) ).
thf(618,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[502]) ).
thf(619,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[502]) ).
thf(620,plain,
( ( ~ ! [SX0: $i] :
( ~ ( 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)],[503]) ).
thf(621,plain,
( ( ~ ! [SX0: $i] :
( ~ ( 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)],[503]) ).
thf(622,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[504]) ).
thf(623,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[504]) ).
thf(624,plain,
( ( ~ ! [SX0: $i] :
( ( zero_zero_nat
!= ( number_number_of_nat @ SX0 ) )
| ( ord_less_eq_int @ SX0 @ pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[505]) ).
thf(625,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_eq_int @ SX0 @ pls )
| ( zero_zero_nat
= ( number_number_of_nat @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[505]) ).
thf(626,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_eq_int @ pls @ ( bit1 @ SX0 ) )
| ( ord_less_eq_int @ pls @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[506]) ).
thf(627,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_eq_int @ pls @ SX0 )
| ( ord_less_eq_int @ pls @ ( bit1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[506]) ).
thf(628,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_int @ pls @ SX0 )
| ( ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[507]) ).
thf(629,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ SX0 ) )
| ( ord_less_int @ pls @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[507]) ).
thf(630,plain,
! [SV41: $i,SV1: $i] :
( ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ SV1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV41 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_int )
= $false ),
inference(extcnf_not_pos,[status(thm)],[509]) ).
thf(631,plain,
! [SV72: $i,SV42: $i,SV5: $i] :
( ( ( power_power_int @ SV5 @ ( plus_plus_nat @ SV42 @ SV72 ) )
= ( times_times_int @ ( power_power_int @ SV5 @ SV42 ) @ ( power_power_int @ SV5 @ SV72 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[511]) ).
thf(632,plain,
! [SV6: $i,SV73: $i,SV43: $i] :
( ( ~ ( ord_less_eq_int @ SV43 @ SV73 )
| ( ord_less_eq_int @ ( plus_plus_int @ SV6 @ SV43 ) @ ( plus_plus_int @ SV6 @ SV73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[512]) ).
thf(633,plain,
! [SV45: $i,SV8: $i,SV74: $i] :
( ( ! [SY221: $i] :
( ~ ( ord_less_int @ SV74 @ SY221 )
| ~ ( ord_less_eq_int @ SV8 @ SV45 )
| ( ord_less_int @ ( plus_plus_int @ SV74 @ SV8 ) @ ( plus_plus_int @ SY221 @ SV45 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[514]) ).
thf(634,plain,
! [SV75: $i,SV48: $i,SV14: $i] :
( ( ( times_times_int @ ( plus_plus_int @ SV14 @ SV48 ) @ SV75 )
= ( plus_plus_int @ ( times_times_int @ SV14 @ SV75 ) @ ( times_times_int @ SV48 @ SV75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[517]) ).
thf(635,plain,
! [SV76: $i,SV49: $i,SV15: $i] :
( ( ( times_times_int @ SV15 @ ( plus_plus_int @ SV49 @ SV76 ) )
= ( plus_plus_int @ ( times_times_int @ SV15 @ SV49 ) @ ( times_times_int @ SV15 @ SV76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[518]) ).
thf(636,plain,
! [SV50: $i,SV16: $i] :
( ( ( ~ ( ord_less_int @ SV16 @ SV50 ) )
= $true )
| ( ( ord_less_eq_int @ ( plus_plus_int @ SV16 @ one_one_int ) @ SV50 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[519]) ).
thf(637,plain,
! [SV17: $i,SV51: $i] :
( ( ( ~ ( ord_less_eq_int @ pls @ SV51 ) )
= $true )
| ( ( ~ ( ord_less_eq_int @ pls @ SV17 )
| ( ( plus_plus_int @ ( number_number_of_int @ SV51 ) @ ( number_number_of_int @ SV17 ) )
= ( number_number_of_int @ ( plus_plus_int @ SV51 @ SV17 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[520]) ).
thf(638,plain,
! [SV18: $i,SV52: $i] :
( ( ( ~ ( ord_less_eq_int @ pls @ SV52 ) )
= $true )
| ( ( ~ ( ord_less_eq_int @ pls @ SV18 )
| ( ( plus_plus_nat @ ( number_number_of_nat @ SV52 ) @ ( number_number_of_nat @ SV18 ) )
= ( number_number_of_nat @ ( plus_plus_int @ SV52 @ SV18 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[521]) ).
thf(639,plain,
! [SV19: $i] :
( ( ( 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)],[522]) ).
thf(640,plain,
! [SV20: $i,SV53: $i] :
( ( ( ord_less_int @ SV53 @ SV20 )
= $true )
| ( ( ( SV20 = SV53 )
| ( ord_less_int @ SV20 @ SV53 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[523]) ).
thf(641,plain,
! [SV77: $i,SV54: $i,SV21: $i] :
( ( ( times_times_int @ ( plus_plus_int @ SV21 @ SV54 ) @ ( number_number_of_int @ SV77 ) )
= ( plus_plus_int @ ( times_times_int @ SV21 @ ( number_number_of_int @ SV77 ) ) @ ( times_times_int @ SV54 @ ( number_number_of_int @ SV77 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[524]) ).
thf(642,plain,
! [SV78: $i,SV55: $i,SV22: $i] :
( ( ( times_times_nat @ ( plus_plus_nat @ SV22 @ SV55 ) @ ( number_number_of_nat @ SV78 ) )
= ( plus_plus_nat @ ( times_times_nat @ SV22 @ ( number_number_of_nat @ SV78 ) ) @ ( times_times_nat @ SV55 @ ( number_number_of_nat @ SV78 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[525]) ).
thf(643,plain,
! [SV79: $i,SV56: $i,SV23: $i] :
( ( ( times_times_int @ ( number_number_of_int @ SV23 ) @ ( plus_plus_int @ SV56 @ SV79 ) )
= ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ SV23 ) @ SV56 ) @ ( times_times_int @ ( number_number_of_int @ SV23 ) @ SV79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[526]) ).
thf(644,plain,
! [SV80: $i,SV57: $i,SV24: $i] :
( ( ( times_times_nat @ ( number_number_of_nat @ SV24 ) @ ( plus_plus_nat @ SV57 @ SV80 ) )
= ( plus_plus_nat @ ( times_times_nat @ ( number_number_of_nat @ SV24 ) @ SV57 ) @ ( times_times_nat @ ( number_number_of_nat @ SV24 ) @ SV80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[527]) ).
thf(645,plain,
! [SV81: $i,SV58: $i,SV25: $i] :
( ( ( plus_plus_int @ ( plus_plus_int @ SV25 @ SV58 ) @ SV81 )
= ( plus_plus_int @ SV25 @ ( plus_plus_int @ SV58 @ SV81 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[528]) ).
thf(646,plain,
! [SV82: $i,SV59: $i,SV26: $i] :
( ( ( plus_plus_int @ SV26 @ ( plus_plus_int @ SV59 @ SV82 ) )
= ( plus_plus_int @ SV59 @ ( plus_plus_int @ SV26 @ SV82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[529]) ).
thf(647,plain,
! [SV62: $i,SV31: $i] :
( ( ( ord_less_eq_int @ SV31 @ SV62 )
= $true )
| ( ( ord_less_eq_int @ SV62 @ SV31 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[532]) ).
thf(648,plain,
! [SV83: $i,SV64: $i,SV33: $i] :
( ( ( times_times_int @ ( times_times_int @ SV33 @ SV64 ) @ SV83 )
= ( times_times_int @ SV33 @ ( times_times_int @ SV64 @ SV83 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[534]) ).
thf(649,plain,
! [SV34: $i,SV84: $i,SV65: $i] :
( ( ~ ( ord_less_eq_int @ SV65 @ SV84 )
| ~ ( ord_less_eq_int @ SV84 @ SV34 )
| ( ord_less_eq_int @ SV65 @ SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[535]) ).
thf(650,plain,
! [SV66: $i,SV35: $i] :
( ( ( ~ ( ord_less_eq_int @ SV35 @ SV66 ) )
= $true )
| ( ( ~ ( ord_less_eq_int @ SV66 @ SV35 )
| ( SV35 = SV66 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[536]) ).
thf(651,plain,
! [SV36: $i,SV67: $i] :
( ( ( ~ ( ord_less_eq_int @ pls @ SV67 ) )
= $true )
| ( ( ~ ( ord_less_eq_int @ pls @ SV36 )
| ( ( times_times_nat @ ( number_number_of_nat @ SV67 ) @ ( number_number_of_nat @ SV36 ) )
= ( number_number_of_nat @ ( times_times_int @ SV67 @ SV36 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[537]) ).
thf(652,plain,
! [SV37: $i,SV68: $i] :
( ( ( ~ ( ord_less_eq_int @ pls @ SV68 ) )
= $true )
| ( ( ~ ( ord_less_eq_int @ pls @ SV37 )
| ( ( times_times_int @ ( number_number_of_int @ SV68 ) @ ( number_number_of_int @ SV37 ) )
= ( number_number_of_int @ ( times_times_int @ SV68 @ SV37 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[538]) ).
thf(653,plain,
! [SV85: $i,SV69: $i,SV38: $i] :
( ( ( times_times_int @ ( number_number_of_int @ SV38 ) @ ( times_times_int @ ( number_number_of_int @ SV69 ) @ SV85 ) )
= ( times_times_int @ ( number_number_of_int @ ( times_times_int @ SV38 @ SV69 ) ) @ SV85 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[539]) ).
thf(654,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_int @ SX0 @ ( plus_plus_int @ SX1 @ one_one_int ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[542]) ).
thf(655,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX0 @ ( plus_plus_int @ SX1 @ one_one_int ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[543]) ).
thf(656,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[544]) ).
thf(657,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[545]) ).
thf(658,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[546]) ).
thf(659,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[547]) ).
thf(660,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( 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)],[548]) ).
thf(661,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( plus_plus_int @ ( power_power_int @ SX0 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SX1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( ( plus_plus_int @ ( power_power_int @ SX0 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SX1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_int )
| ( SX1 = zero_zero_int ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[549]) ).
thf(662,plain,
( ( ! [SX0: $i] :
( ~ ( 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)],[550]) ).
thf(663,plain,
( ( ! [SX0: $i] :
( ~ ( 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)],[551]) ).
thf(664,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[552]) ).
thf(665,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( 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)],[553]) ).
thf(666,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( number_number_of_nat @ SX0 )
!= SX1 )
| ( SX1
= ( number_number_of_nat @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[554]) ).
thf(667,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( number_number_of_nat @ SX0 ) )
| ( ( number_number_of_nat @ SX0 )
= SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[555]) ).
thf(668,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[556]) ).
thf(669,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[557]) ).
thf(670,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less_eq_int @ pls @ ( bit0 @ SX0 ) )
| ( ord_less_eq_int @ pls @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[558]) ).
thf(671,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less_eq_int @ pls @ SX0 )
| ( ord_less_eq_int @ pls @ ( bit0 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[559]) ).
thf(672,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less_eq_int @ pls @ SX0 )
| ( ord_less_int @ pls @ ( bit1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[560]) ).
thf(673,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less_int @ pls @ ( bit1 @ SX0 ) )
| ( ord_less_eq_int @ pls @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[561]) ).
thf(674,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( 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)],[562]) ).
thf(675,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( 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: $i,SX1: $i] :
( ~ ( 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)],[563]) ).
thf(676,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[564]) ).
thf(677,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[565]) ).
thf(678,plain,
( ( ! [SX0: $i] :
( ( ( number_number_of_nat @ SX0 )
!= zero_zero_nat )
| ( ord_less_eq_int @ SX0 @ pls ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[566]) ).
thf(679,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less_eq_int @ SX0 @ pls )
| ( ( number_number_of_nat @ SX0 )
= zero_zero_nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[567]) ).
thf(680,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[568]) ).
thf(681,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[569]) ).
thf(682,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( bit0 @ SX0 )
!= ( bit0 @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[570]) ).
thf(683,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( bit0 @ SX0 )
= ( bit0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[571]) ).
thf(684,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ ( plus_plus_int @ SX0 @ one_one_int ) @ SX1 )
| ( ord_less_int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[572]) ).
thf(685,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( plus_plus_int @ SX0 @ one_one_int ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[573]) ).
thf(686,plain,
( ( ! [SX0: $i] :
( ~ ( 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)],[574]) ).
thf(687,plain,
( ( ! [SX0: $i] :
( ~ ( 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)],[575]) ).
thf(688,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[576]) ).
thf(689,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[577]) ).
thf(690,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less_eq_int @ ( bit1 @ SX0 ) @ pls )
| ( ord_less_int @ SX0 @ pls ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[578]) ).
thf(691,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less_int @ SX0 @ pls )
| ( ord_less_eq_int @ ( bit1 @ SX0 ) @ pls ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[579]) ).
thf(692,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[580]) ).
thf(693,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[581]) ).
thf(694,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( number_number_of_int @ SX0 )
!= ( number_number_of_int @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[582]) ).
thf(695,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( number_number_of_int @ SX0 )
= ( number_number_of_int @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[583]) ).
thf(696,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( bit1 @ SX0 )
!= ( bit1 @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[584]) ).
thf(697,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( bit1 @ SX0 )
= ( bit1 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[585]) ).
thf(698,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less_eq_int @ ( bit0 @ SX0 ) @ pls )
| ( ord_less_eq_int @ SX0 @ pls ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[586]) ).
thf(699,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less_eq_int @ SX0 @ pls )
| ( ord_less_eq_int @ ( bit0 @ SX0 ) @ pls ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[587]) ).
thf(700,plain,
( ( ! [SX0: $i] :
( ~ ( 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)],[588]) ).
thf(701,plain,
( ( ! [SX0: $i] :
( ~ ( 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)],[589]) ).
thf(702,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( 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)],[590]) ).
thf(703,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( plus_plus_int @ ( times_times_int @ SX0 @ SX0 ) @ ( times_times_int @ SX1 @ SX1 ) )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( ( 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)],[591]) ).
thf(704,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX1 @ pls )
| ( ( plus_plus_nat @ ( number_number_of_nat @ SX1 ) @ ( number_number_of_nat @ SX0 ) )
= ( number_number_of_nat @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[592]) ).
thf(705,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( 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: $i,SX1: $i] :
( ( 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)],[593]) ).
thf(706,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less_eq_int @ one_one_int @ SX0 )
| ( ord_less_int @ zero_zero_int @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[594]) ).
thf(707,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less_int @ zero_zero_int @ SX0 )
| ( ord_less_eq_int @ one_one_int @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[595]) ).
thf(708,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( number_number_of_int @ SX0 )
!= SX1 )
| ( SX1
= ( number_number_of_int @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[596]) ).
thf(709,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( number_number_of_int @ SX0 ) )
| ( ( number_number_of_int @ SX0 )
= SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[597]) ).
thf(710,plain,
( ( ! [SX0: $i] :
( ( ( 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)],[598]) ).
thf(711,plain,
( ( ! [SX0: $i] :
( ( 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)],[599]) ).
thf(712,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[600]) ).
thf(713,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( 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)],[601]) ).
thf(714,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[602]) ).
thf(715,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( SX0 = zero_zero_int )
| ! [SX1: $i] : ( 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: $i,SX1: $i] :
( ( 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)],[603]) ).
thf(716,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[604]) ).
thf(717,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[605]) ).
thf(718,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[606]) ).
thf(719,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[607]) ).
thf(720,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ ( number_number_of_int @ SX0 ) @ ( number_number_of_int @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[608]) ).
thf(721,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[609]) ).
thf(722,plain,
( ( ! [SX0: $i] :
( ( 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)],[610]) ).
thf(723,plain,
( ( ! [SX0: $i] :
( ~ ( 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)],[611]) ).
thf(724,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ord_less_int @ SX0 @ SX1 )
| ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_nat @ ( number_number_of_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[612]) ).
thf(725,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_nat @ ( number_number_of_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) )
| ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ pls @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[613]) ).
thf(726,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ ( number_number_of_int @ SX0 ) @ ( number_number_of_int @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[614]) ).
thf(727,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[615]) ).
thf(728,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[616]) ).
thf(729,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[617]) ).
thf(730,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ SX0 @ SX1 )
| ( ord_less_int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[618]) ).
thf(731,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[619]) ).
thf(732,plain,
( ( ! [SX0: $i] :
( ~ ( 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)],[620]) ).
thf(733,plain,
( ( ! [SX0: $i] :
( ~ ( 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)],[621]) ).
thf(734,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq_int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[622]) ).
thf(735,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[623]) ).
thf(736,plain,
( ( ! [SX0: $i] :
( ( zero_zero_nat
!= ( number_number_of_nat @ SX0 ) )
| ( ord_less_eq_int @ SX0 @ pls ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[624]) ).
thf(737,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less_eq_int @ SX0 @ pls )
| ( zero_zero_nat
= ( number_number_of_nat @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[625]) ).
thf(738,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less_eq_int @ pls @ ( bit1 @ SX0 ) )
| ( ord_less_eq_int @ pls @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[626]) ).
thf(739,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less_eq_int @ pls @ SX0 )
| ( ord_less_eq_int @ pls @ ( bit1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[627]) ).
thf(740,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less_int @ pls @ SX0 )
| ( ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[628]) ).
thf(741,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ SX0 ) )
| ( ord_less_int @ pls @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[629]) ).
thf(742,plain,
! [SV6: $i,SV73: $i,SV43: $i] :
( ( ( ~ ( ord_less_eq_int @ SV43 @ SV73 ) )
= $true )
| ( ( ord_less_eq_int @ ( plus_plus_int @ SV6 @ SV43 ) @ ( plus_plus_int @ SV6 @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[632]) ).
thf(743,plain,
! [SV45: $i,SV8: $i,SV86: $i,SV74: $i] :
( ( ~ ( ord_less_int @ SV74 @ SV86 )
| ~ ( ord_less_eq_int @ SV8 @ SV45 )
| ( ord_less_int @ ( plus_plus_int @ SV74 @ SV8 ) @ ( plus_plus_int @ SV86 @ SV45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[633]) ).
thf(744,plain,
! [SV50: $i,SV16: $i] :
( ( ( ord_less_int @ SV16 @ SV50 )
= $false )
| ( ( ord_less_eq_int @ ( plus_plus_int @ SV16 @ one_one_int ) @ SV50 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[636]) ).
thf(745,plain,
! [SV17: $i,SV51: $i] :
( ( ( ord_less_eq_int @ pls @ SV51 )
= $false )
| ( ( ~ ( ord_less_eq_int @ pls @ SV17 )
| ( ( plus_plus_int @ ( number_number_of_int @ SV51 ) @ ( number_number_of_int @ SV17 ) )
= ( number_number_of_int @ ( plus_plus_int @ SV51 @ SV17 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[637]) ).
thf(746,plain,
! [SV18: $i,SV52: $i] :
( ( ( ord_less_eq_int @ pls @ SV52 )
= $false )
| ( ( ~ ( ord_less_eq_int @ pls @ SV18 )
| ( ( plus_plus_nat @ ( number_number_of_nat @ SV52 ) @ ( number_number_of_nat @ SV18 ) )
= ( number_number_of_nat @ ( plus_plus_int @ SV52 @ SV18 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[638]) ).
thf(747,plain,
! [SV53: $i,SV20: $i] :
( ( ( SV20 = SV53 )
= $true )
| ( ( ord_less_int @ SV20 @ SV53 )
= $true )
| ( ( ord_less_int @ SV53 @ SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[640]) ).
thf(748,plain,
! [SV34: $i,SV84: $i,SV65: $i] :
( ( ( ~ ( ord_less_eq_int @ SV65 @ SV84 ) )
= $true )
| ( ( ~ ( ord_less_eq_int @ SV84 @ SV34 )
| ( ord_less_eq_int @ SV65 @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[649]) ).
thf(749,plain,
! [SV66: $i,SV35: $i] :
( ( ( ord_less_eq_int @ SV35 @ SV66 )
= $false )
| ( ( ~ ( ord_less_eq_int @ SV66 @ SV35 )
| ( SV35 = SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[650]) ).
thf(750,plain,
! [SV36: $i,SV67: $i] :
( ( ( ord_less_eq_int @ pls @ SV67 )
= $false )
| ( ( ~ ( ord_less_eq_int @ pls @ SV36 )
| ( ( times_times_nat @ ( number_number_of_nat @ SV67 ) @ ( number_number_of_nat @ SV36 ) )
= ( number_number_of_nat @ ( times_times_int @ SV67 @ SV36 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[651]) ).
thf(751,plain,
! [SV37: $i,SV68: $i] :
( ( ( ord_less_eq_int @ pls @ SV68 )
= $false )
| ( ( ~ ( ord_less_eq_int @ pls @ SV37 )
| ( ( times_times_int @ ( number_number_of_int @ SV68 ) @ ( number_number_of_int @ SV37 ) )
= ( number_number_of_int @ ( times_times_int @ SV68 @ SV37 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[652]) ).
thf(752,plain,
! [SV87: $i] :
( ( ! [SY222: $i] :
( ~ ( ord_less_eq_int @ SV87 @ SY222 )
| ( ord_less_int @ SV87 @ ( plus_plus_int @ SY222 @ one_one_int ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[654]) ).
thf(753,plain,
! [SV88: $i] :
( ( ! [SY223: $i] :
( ~ ( ord_less_int @ SV88 @ ( plus_plus_int @ SY223 @ one_one_int ) )
| ( ord_less_eq_int @ SV88 @ SY223 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[655]) ).
thf(754,plain,
! [SV89: $i] :
( ( ! [SY224: $i] :
( ~ ( ord_less_eq_int @ ( bit1 @ SV89 ) @ ( bit1 @ SY224 ) )
| ( ord_less_eq_int @ SV89 @ SY224 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[656]) ).
thf(755,plain,
! [SV90: $i] :
( ( ! [SY225: $i] :
( ~ ( ord_less_eq_int @ SV90 @ SY225 )
| ( ord_less_eq_int @ ( bit1 @ SV90 ) @ ( bit1 @ SY225 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[657]) ).
thf(756,plain,
! [SV91: $i] :
( ( ! [SY226: $i] :
( ~ ( ord_less_eq_int @ ( bit1 @ SV91 ) @ ( bit0 @ SY226 ) )
| ( ord_less_int @ SV91 @ SY226 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[658]) ).
thf(757,plain,
! [SV92: $i] :
( ( ! [SY227: $i] :
( ~ ( ord_less_int @ SV92 @ SY227 )
| ( ord_less_eq_int @ ( bit1 @ SV92 ) @ ( bit0 @ SY227 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[659]) ).
thf(758,plain,
! [SV93: $i] :
( ( ! [SY228: $i] :
( ( SV93 != zero_zero_int )
| ( SY228 != zero_zero_int )
| ( ( plus_plus_int @ ( power_power_int @ SV93 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SY228 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[660]) ).
thf(759,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( plus_plus_int @ ( power_power_int @ SX0 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SX1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( ( plus_plus_int @ ( power_power_int @ SX0 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SX1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_int )
| ( SX1 = zero_zero_int ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[661]) ).
thf(760,plain,
! [SV94: $i] :
( ( ~ ( ord_less_eq_int @ ( number_number_of_int @ SV94 ) @ zero_zero_int )
| ( ord_less_eq_int @ SV94 @ pls ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[662]) ).
thf(761,plain,
! [SV95: $i] :
( ( ~ ( ord_less_eq_int @ SV95 @ pls )
| ( ord_less_eq_int @ ( number_number_of_int @ SV95 ) @ zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[663]) ).
thf(762,plain,
! [SV96: $i] :
( ( ! [SY229: $i] :
( ~ ( ord_less_eq_nat @ ( number_number_of_nat @ SV96 ) @ ( number_number_of_nat @ SY229 ) )
| ~ ( ord_less_nat @ ( number_number_of_nat @ SY229 ) @ ( number_number_of_nat @ SV96 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[664]) ).
thf(763,plain,
! [SV97: $i] :
( ( ! [SY230: $i] :
( ( ord_less_nat @ ( number_number_of_nat @ SY230 ) @ ( number_number_of_nat @ SV97 ) )
| ( ord_less_eq_nat @ ( number_number_of_nat @ SV97 ) @ ( number_number_of_nat @ SY230 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[665]) ).
thf(764,plain,
! [SV98: $i] :
( ( ! [SY231: $i] :
( ( ( number_number_of_nat @ SV98 )
!= SY231 )
| ( SY231
= ( number_number_of_nat @ SV98 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[666]) ).
thf(765,plain,
! [SV99: $i] :
( ( ! [SY232: $i] :
( ( SY232
!= ( number_number_of_nat @ SV99 ) )
| ( ( number_number_of_nat @ SV99 )
= SY232 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[667]) ).
thf(766,plain,
! [SV100: $i] :
( ( ! [SY233: $i] :
( ~ ( ord_less_eq_int @ SV100 @ SY233 )
| ( ord_less_int @ ( bit0 @ SV100 ) @ ( bit1 @ SY233 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[668]) ).
thf(767,plain,
! [SV101: $i] :
( ( ! [SY234: $i] :
( ~ ( ord_less_int @ ( bit0 @ SV101 ) @ ( bit1 @ SY234 ) )
| ( ord_less_eq_int @ SV101 @ SY234 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[669]) ).
thf(768,plain,
! [SV102: $i] :
( ( ~ ( ord_less_eq_int @ pls @ ( bit0 @ SV102 ) )
| ( ord_less_eq_int @ pls @ SV102 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[670]) ).
thf(769,plain,
! [SV103: $i] :
( ( ~ ( ord_less_eq_int @ pls @ SV103 )
| ( ord_less_eq_int @ pls @ ( bit0 @ SV103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[671]) ).
thf(770,plain,
! [SV104: $i] :
( ( ~ ( ord_less_eq_int @ pls @ SV104 )
| ( ord_less_int @ pls @ ( bit1 @ SV104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[672]) ).
thf(771,plain,
! [SV105: $i] :
( ( ~ ( ord_less_int @ pls @ ( bit1 @ SV105 ) )
| ( ord_less_eq_int @ pls @ SV105 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[673]) ).
thf(772,plain,
! [SV106: $i] :
( ( ! [SY235: $i] :
( ( SV106 != zero_zero_int )
| ( SY235 != zero_zero_int )
| ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SV106 @ SV106 ) @ ( times_times_int @ SY235 @ SY235 ) ) @ zero_zero_int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[674]) ).
thf(773,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( 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: $i,SX1: $i] :
( ~ ( 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)],[675]) ).
thf(774,plain,
! [SV107: $i] :
( ( ! [SY236: $i] :
( ~ ( ord_less_eq_int @ ( bit0 @ SV107 ) @ ( bit1 @ SY236 ) )
| ( ord_less_eq_int @ SV107 @ SY236 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[676]) ).
thf(775,plain,
! [SV108: $i] :
( ( ! [SY237: $i] :
( ~ ( ord_less_eq_int @ SV108 @ SY237 )
| ( ord_less_eq_int @ ( bit0 @ SV108 ) @ ( bit1 @ SY237 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[677]) ).
thf(776,plain,
! [SV109: $i] :
( ( ( ( number_number_of_nat @ SV109 )
!= zero_zero_nat )
| ( ord_less_eq_int @ SV109 @ pls ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[678]) ).
thf(777,plain,
! [SV110: $i] :
( ( ~ ( ord_less_eq_int @ SV110 @ pls )
| ( ( number_number_of_nat @ SV110 )
= zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[679]) ).
thf(778,plain,
! [SV111: $i] :
( ( ! [SY238: $i] :
( ~ ( ord_less_eq_int @ ( bit0 @ SV111 ) @ ( bit1 @ SY238 ) )
| ( ord_less_eq_int @ SV111 @ SY238 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[680]) ).
thf(779,plain,
! [SV112: $i] :
( ( ! [SY239: $i] :
( ~ ( ord_less_eq_int @ SV112 @ SY239 )
| ( ord_less_eq_int @ ( bit0 @ SV112 ) @ ( bit1 @ SY239 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[681]) ).
thf(780,plain,
! [SV113: $i] :
( ( ! [SY240: $i] :
( ( ( bit0 @ SV113 )
!= ( bit0 @ SY240 ) )
| ( SV113 = SY240 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[682]) ).
thf(781,plain,
! [SV114: $i] :
( ( ! [SY241: $i] :
( ( SV114 != SY241 )
| ( ( bit0 @ SV114 )
= ( bit0 @ SY241 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[683]) ).
thf(782,plain,
! [SV115: $i] :
( ( ! [SY242: $i] :
( ~ ( ord_less_eq_int @ ( plus_plus_int @ SV115 @ one_one_int ) @ SY242 )
| ( ord_less_int @ SV115 @ SY242 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[684]) ).
thf(783,plain,
! [SV116: $i] :
( ( ! [SY243: $i] :
( ~ ( ord_less_int @ SV116 @ SY243 )
| ( ord_less_eq_int @ ( plus_plus_int @ SV116 @ one_one_int ) @ SY243 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[685]) ).
thf(784,plain,
! [SV117: $i] :
( ( ~ ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ SV117 ) )
| ( ord_less_eq_int @ pls @ SV117 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[686]) ).
thf(785,plain,
! [SV118: $i] :
( ( ~ ( ord_less_eq_int @ pls @ SV118 )
| ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ SV118 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[687]) ).
thf(786,plain,
! [SV119: $i] :
( ( ! [SY244: $i] :
( ~ ( ord_less_int @ ( number_number_of_int @ SV119 ) @ ( number_number_of_int @ SY244 ) )
| ( ord_less_int @ SV119 @ SY244 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[688]) ).
thf(787,plain,
! [SV120: $i] :
( ( ! [SY245: $i] :
( ~ ( ord_less_int @ SV120 @ SY245 )
| ( ord_less_int @ ( number_number_of_int @ SV120 ) @ ( number_number_of_int @ SY245 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[689]) ).
thf(788,plain,
! [SV121: $i] :
( ( ~ ( ord_less_eq_int @ ( bit1 @ SV121 ) @ pls )
| ( ord_less_int @ SV121 @ pls ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[690]) ).
thf(789,plain,
! [SV122: $i] :
( ( ~ ( ord_less_int @ SV122 @ pls )
| ( ord_less_eq_int @ ( bit1 @ SV122 ) @ pls ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[691]) ).
thf(790,plain,
! [SV123: $i] :
( ( ! [SY246: $i] :
( ~ ( ord_less_eq_int @ ( bit0 @ SV123 ) @ ( bit0 @ SY246 ) )
| ( ord_less_eq_int @ SV123 @ SY246 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[692]) ).
thf(791,plain,
! [SV124: $i] :
( ( ! [SY247: $i] :
( ~ ( ord_less_eq_int @ SV124 @ SY247 )
| ( ord_less_eq_int @ ( bit0 @ SV124 ) @ ( bit0 @ SY247 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[693]) ).
thf(792,plain,
! [SV125: $i] :
( ( ! [SY248: $i] :
( ( ( number_number_of_int @ SV125 )
!= ( number_number_of_int @ SY248 ) )
| ( SV125 = SY248 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[694]) ).
thf(793,plain,
! [SV126: $i] :
( ( ! [SY249: $i] :
( ( SV126 != SY249 )
| ( ( number_number_of_int @ SV126 )
= ( number_number_of_int @ SY249 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[695]) ).
thf(794,plain,
! [SV127: $i] :
( ( ! [SY250: $i] :
( ( ( bit1 @ SV127 )
!= ( bit1 @ SY250 ) )
| ( SV127 = SY250 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[696]) ).
thf(795,plain,
! [SV128: $i] :
( ( ! [SY251: $i] :
( ( SV128 != SY251 )
| ( ( bit1 @ SV128 )
= ( bit1 @ SY251 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[697]) ).
thf(796,plain,
! [SV129: $i] :
( ( ~ ( ord_less_eq_int @ ( bit0 @ SV129 ) @ pls )
| ( ord_less_eq_int @ SV129 @ pls ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[698]) ).
thf(797,plain,
! [SV130: $i] :
( ( ~ ( ord_less_eq_int @ SV130 @ pls )
| ( ord_less_eq_int @ ( bit0 @ SV130 ) @ pls ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[699]) ).
thf(798,plain,
! [SV131: $i] :
( ( ~ ( ord_less_eq_int @ one_one_int @ ( number_number_of_int @ SV131 ) )
| ( ord_less_eq_int @ ( bit1 @ pls ) @ SV131 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[700]) ).
thf(799,plain,
! [SV132: $i] :
( ( ~ ( ord_less_eq_int @ ( bit1 @ pls ) @ SV132 )
| ( ord_less_eq_int @ one_one_int @ ( number_number_of_int @ SV132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[701]) ).
thf(800,plain,
! [SV133: $i] :
( ( ! [SY252: $i] :
( ( SV133 != zero_zero_int )
| ( SY252 != zero_zero_int )
| ( ( plus_plus_int @ ( times_times_int @ SV133 @ SV133 ) @ ( times_times_int @ SY252 @ SY252 ) )
= zero_zero_int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[702]) ).
thf(801,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( plus_plus_int @ ( times_times_int @ SX0 @ SX0 ) @ ( times_times_int @ SX1 @ SX1 ) )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( ( 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)],[703]) ).
thf(802,plain,
! [SV134: $i] :
( ( ! [SY253: $i] :
( ~ ( ord_less_int @ SY253 @ pls )
| ( ( plus_plus_nat @ ( number_number_of_nat @ SY253 ) @ ( number_number_of_nat @ SV134 ) )
= ( number_number_of_nat @ SV134 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[704]) ).
thf(803,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( 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: $i,SX1: $i] :
( ( 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)],[705]) ).
thf(804,plain,
! [SV135: $i] :
( ( ~ ( ord_less_eq_int @ one_one_int @ SV135 )
| ( ord_less_int @ zero_zero_int @ SV135 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[706]) ).
thf(805,plain,
! [SV136: $i] :
( ( ~ ( ord_less_int @ zero_zero_int @ SV136 )
| ( ord_less_eq_int @ one_one_int @ SV136 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[707]) ).
thf(806,plain,
! [SV137: $i] :
( ( ! [SY254: $i] :
( ( ( number_number_of_int @ SV137 )
!= SY254 )
| ( SY254
= ( number_number_of_int @ SV137 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[708]) ).
thf(807,plain,
! [SV138: $i] :
( ( ! [SY255: $i] :
( ( SY255
!= ( number_number_of_int @ SV138 ) )
| ( ( number_number_of_int @ SV138 )
= SY255 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[709]) ).
thf(808,plain,
! [SV139: $i] :
( ( ( ( power_power_int @ SV139 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= zero_zero_int )
| ( SV139 = zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[710]) ).
thf(809,plain,
! [SV140: $i] :
( ( ( SV140 != zero_zero_int )
| ( ( power_power_int @ SV140 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[711]) ).
thf(810,plain,
! [SV141: $i] :
( ( ! [SY256: $i] :
( ~ ( ord_less_eq_int @ ( number_number_of_int @ SV141 ) @ ( number_number_of_int @ SY256 ) )
| ~ ( ord_less_int @ ( number_number_of_int @ SY256 ) @ ( number_number_of_int @ SV141 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[712]) ).
thf(811,plain,
! [SV142: $i] :
( ( ! [SY257: $i] :
( ( ord_less_int @ ( number_number_of_int @ SY257 ) @ ( number_number_of_int @ SV142 ) )
| ( ord_less_eq_int @ ( number_number_of_int @ SV142 ) @ ( number_number_of_int @ SY257 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[713]) ).
thf(812,plain,
! [SV143: $i] :
( ( ! [SY258: $i] :
( ~ ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ SV143 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SY258 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
| ( SV143 != zero_zero_int )
| ( SY258 != zero_zero_int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[714]) ).
thf(813,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 = zero_zero_int )
| ! [SX1: $i] : ( 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: $i,SX1: $i] :
( ( 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)],[715]) ).
thf(814,plain,
! [SV144: $i] :
( ( ! [SY259: $i] :
( ( SV144 = SY259 )
| ~ ( ord_less_eq_int @ SV144 @ SY259 )
| ( ord_less_int @ SV144 @ SY259 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[716]) ).
thf(815,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[717]) ).
thf(816,plain,
! [SV145: $i] :
( ( ! [SY260: $i] :
( ~ ( ord_less_eq_int @ ( bit0 @ SV145 ) @ ( bit0 @ SY260 ) )
| ( ord_less_eq_int @ SV145 @ SY260 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[718]) ).
thf(817,plain,
! [SV146: $i] :
( ( ! [SY261: $i] :
( ~ ( ord_less_eq_int @ SV146 @ SY261 )
| ( ord_less_eq_int @ ( bit0 @ SV146 ) @ ( bit0 @ SY261 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[719]) ).
thf(818,plain,
! [SV147: $i] :
( ( ! [SY262: $i] :
( ~ ( ord_less_eq_int @ ( number_number_of_int @ SV147 ) @ ( number_number_of_int @ SY262 ) )
| ( ord_less_eq_int @ SV147 @ SY262 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[720]) ).
thf(819,plain,
! [SV148: $i] :
( ( ! [SY263: $i] :
( ~ ( ord_less_eq_int @ SV148 @ SY263 )
| ( ord_less_eq_int @ ( number_number_of_int @ SV148 ) @ ( number_number_of_int @ SY263 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[721]) ).
thf(820,plain,
! [SV149: $i] :
( ( ( SV149 = zero_zero_int )
| ( ord_less_int @ zero_zero_int @ ( power_power_int @ SV149 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[722]) ).
thf(821,plain,
! [SV150: $i] :
( ( ~ ( ord_less_int @ zero_zero_int @ ( power_power_int @ SV150 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ( SV150 != zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[723]) ).
thf(822,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ord_less_int @ SX0 @ SX1 )
| ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_nat @ ( number_number_of_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[724]) ).
thf(823,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_nat @ ( number_number_of_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) )
| ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ pls @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[725]) ).
thf(824,plain,
! [SV151: $i] :
( ( ! [SY264: $i] :
( ~ ( ord_less_eq_int @ ( number_number_of_int @ SV151 ) @ ( number_number_of_int @ SY264 ) )
| ( ord_less_eq_int @ SV151 @ SY264 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[726]) ).
thf(825,plain,
! [SV152: $i] :
( ( ! [SY265: $i] :
( ~ ( ord_less_eq_int @ SV152 @ SY265 )
| ( ord_less_eq_int @ ( number_number_of_int @ SV152 ) @ ( number_number_of_int @ SY265 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[727]) ).
thf(826,plain,
! [SV153: $i] :
( ( ! [SY266: $i] :
( ~ ( ord_less_eq_int @ ( bit1 @ SV153 ) @ ( bit1 @ SY266 ) )
| ( ord_less_eq_int @ SV153 @ SY266 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[728]) ).
thf(827,plain,
! [SV154: $i] :
( ( ! [SY267: $i] :
( ~ ( ord_less_eq_int @ SV154 @ SY267 )
| ( ord_less_eq_int @ ( bit1 @ SV154 ) @ ( bit1 @ SY267 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[729]) ).
thf(828,plain,
! [SV155: $i] :
( ( ! [SY268: $i] :
( ~ ( ord_less_eq_int @ SV155 @ SY268 )
| ( ord_less_int @ ( bit0 @ SV155 ) @ ( bit1 @ SY268 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[730]) ).
thf(829,plain,
! [SV156: $i] :
( ( ! [SY269: $i] :
( ~ ( ord_less_int @ ( bit0 @ SV156 ) @ ( bit1 @ SY269 ) )
| ( ord_less_eq_int @ SV156 @ SY269 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[731]) ).
thf(830,plain,
! [SV157: $i] :
( ( ~ ( ord_less_eq_int @ ( number_number_of_int @ SV157 ) @ one_one_int )
| ( ord_less_eq_int @ SV157 @ ( bit1 @ pls ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[732]) ).
thf(831,plain,
! [SV158: $i] :
( ( ~ ( ord_less_eq_int @ SV158 @ ( bit1 @ pls ) )
| ( ord_less_eq_int @ ( number_number_of_int @ SV158 ) @ one_one_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[733]) ).
thf(832,plain,
! [SV159: $i] :
( ( ! [SY270: $i] :
( ~ ( ord_less_eq_int @ ( bit1 @ SV159 ) @ ( bit0 @ SY270 ) )
| ( ord_less_int @ SV159 @ SY270 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[734]) ).
thf(833,plain,
! [SV160: $i] :
( ( ! [SY271: $i] :
( ~ ( ord_less_int @ SV160 @ SY271 )
| ( ord_less_eq_int @ ( bit1 @ SV160 ) @ ( bit0 @ SY271 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[735]) ).
thf(834,plain,
! [SV161: $i] :
( ( ( zero_zero_nat
!= ( number_number_of_nat @ SV161 ) )
| ( ord_less_eq_int @ SV161 @ pls ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[736]) ).
thf(835,plain,
! [SV162: $i] :
( ( ~ ( ord_less_eq_int @ SV162 @ pls )
| ( zero_zero_nat
= ( number_number_of_nat @ SV162 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[737]) ).
thf(836,plain,
! [SV163: $i] :
( ( ~ ( ord_less_eq_int @ pls @ ( bit1 @ SV163 ) )
| ( ord_less_eq_int @ pls @ SV163 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[738]) ).
thf(837,plain,
! [SV164: $i] :
( ( ~ ( ord_less_eq_int @ pls @ SV164 )
| ( ord_less_eq_int @ pls @ ( bit1 @ SV164 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[739]) ).
thf(838,plain,
! [SV165: $i] :
( ( ~ ( ord_less_int @ pls @ SV165 )
| ( ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ SV165 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[740]) ).
thf(839,plain,
! [SV166: $i] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ SV166 ) )
| ( ord_less_int @ pls @ SV166 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[741]) ).
thf(840,plain,
! [SV6: $i,SV73: $i,SV43: $i] :
( ( ( ord_less_eq_int @ SV43 @ SV73 )
= $false )
| ( ( ord_less_eq_int @ ( plus_plus_int @ SV6 @ SV43 ) @ ( plus_plus_int @ SV6 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[742]) ).
thf(841,plain,
! [SV45: $i,SV8: $i,SV86: $i,SV74: $i] :
( ( ( ~ ( ord_less_int @ SV74 @ SV86 ) )
= $true )
| ( ( ~ ( ord_less_eq_int @ SV8 @ SV45 )
| ( ord_less_int @ ( plus_plus_int @ SV74 @ SV8 ) @ ( plus_plus_int @ SV86 @ SV45 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[743]) ).
thf(842,plain,
! [SV51: $i,SV17: $i] :
( ( ( ~ ( ord_less_eq_int @ pls @ SV17 ) )
= $true )
| ( ( ( plus_plus_int @ ( number_number_of_int @ SV51 ) @ ( number_number_of_int @ SV17 ) )
= ( number_number_of_int @ ( plus_plus_int @ SV51 @ SV17 ) ) )
= $true )
| ( ( ord_less_eq_int @ pls @ SV51 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[745]) ).
thf(843,plain,
! [SV52: $i,SV18: $i] :
( ( ( ~ ( ord_less_eq_int @ pls @ SV18 ) )
= $true )
| ( ( ( plus_plus_nat @ ( number_number_of_nat @ SV52 ) @ ( number_number_of_nat @ SV18 ) )
= ( number_number_of_nat @ ( plus_plus_int @ SV52 @ SV18 ) ) )
= $true )
| ( ( ord_less_eq_int @ pls @ SV52 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[746]) ).
thf(844,plain,
! [SV34: $i,SV84: $i,SV65: $i] :
( ( ( ord_less_eq_int @ SV65 @ SV84 )
= $false )
| ( ( ~ ( ord_less_eq_int @ SV84 @ SV34 )
| ( ord_less_eq_int @ SV65 @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[748]) ).
thf(845,plain,
! [SV35: $i,SV66: $i] :
( ( ( ~ ( ord_less_eq_int @ SV66 @ SV35 ) )
= $true )
| ( ( SV35 = SV66 )
= $true )
| ( ( ord_less_eq_int @ SV35 @ SV66 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[749]) ).
thf(846,plain,
! [SV67: $i,SV36: $i] :
( ( ( ~ ( ord_less_eq_int @ pls @ SV36 ) )
= $true )
| ( ( ( times_times_nat @ ( number_number_of_nat @ SV67 ) @ ( number_number_of_nat @ SV36 ) )
= ( number_number_of_nat @ ( times_times_int @ SV67 @ SV36 ) ) )
= $true )
| ( ( ord_less_eq_int @ pls @ SV67 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[750]) ).
thf(847,plain,
! [SV68: $i,SV37: $i] :
( ( ( ~ ( ord_less_eq_int @ pls @ SV37 ) )
= $true )
| ( ( ( times_times_int @ ( number_number_of_int @ SV68 ) @ ( number_number_of_int @ SV37 ) )
= ( number_number_of_int @ ( times_times_int @ SV68 @ SV37 ) ) )
= $true )
| ( ( ord_less_eq_int @ pls @ SV68 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[751]) ).
thf(848,plain,
! [SV167: $i,SV87: $i] :
( ( ~ ( ord_less_eq_int @ SV87 @ SV167 )
| ( ord_less_int @ SV87 @ ( plus_plus_int @ SV167 @ one_one_int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[752]) ).
thf(849,plain,
! [SV168: $i,SV88: $i] :
( ( ~ ( ord_less_int @ SV88 @ ( plus_plus_int @ SV168 @ one_one_int ) )
| ( ord_less_eq_int @ SV88 @ SV168 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[753]) ).
thf(850,plain,
! [SV169: $i,SV89: $i] :
( ( ~ ( ord_less_eq_int @ ( bit1 @ SV89 ) @ ( bit1 @ SV169 ) )
| ( ord_less_eq_int @ SV89 @ SV169 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[754]) ).
thf(851,plain,
! [SV170: $i,SV90: $i] :
( ( ~ ( ord_less_eq_int @ SV90 @ SV170 )
| ( ord_less_eq_int @ ( bit1 @ SV90 ) @ ( bit1 @ SV170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[755]) ).
thf(852,plain,
! [SV171: $i,SV91: $i] :
( ( ~ ( ord_less_eq_int @ ( bit1 @ SV91 ) @ ( bit0 @ SV171 ) )
| ( ord_less_int @ SV91 @ SV171 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[756]) ).
thf(853,plain,
! [SV172: $i,SV92: $i] :
( ( ~ ( ord_less_int @ SV92 @ SV172 )
| ( ord_less_eq_int @ ( bit1 @ SV92 ) @ ( bit0 @ SV172 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[757]) ).
thf(854,plain,
! [SV173: $i,SV93: $i] :
( ( ( SV93 != zero_zero_int )
| ( SV173 != zero_zero_int )
| ( ( plus_plus_int @ ( power_power_int @ SV93 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV173 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[758]) ).
thf(855,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( plus_plus_int @ ( power_power_int @ SX0 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SX1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[759]) ).
thf(856,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( plus_plus_int @ ( power_power_int @ SX0 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SX1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_int )
| ( SX1 = zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[759]) ).
thf(857,plain,
! [SV94: $i] :
( ( ( ~ ( ord_less_eq_int @ ( number_number_of_int @ SV94 ) @ zero_zero_int ) )
= $true )
| ( ( ord_less_eq_int @ SV94 @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[760]) ).
thf(858,plain,
! [SV95: $i] :
( ( ( ~ ( ord_less_eq_int @ SV95 @ pls ) )
= $true )
| ( ( ord_less_eq_int @ ( number_number_of_int @ SV95 ) @ zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[761]) ).
thf(859,plain,
! [SV174: $i,SV96: $i] :
( ( ~ ( ord_less_eq_nat @ ( number_number_of_nat @ SV96 ) @ ( number_number_of_nat @ SV174 ) )
| ~ ( ord_less_nat @ ( number_number_of_nat @ SV174 ) @ ( number_number_of_nat @ SV96 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[762]) ).
thf(860,plain,
! [SV97: $i,SV175: $i] :
( ( ( ord_less_nat @ ( number_number_of_nat @ SV175 ) @ ( number_number_of_nat @ SV97 ) )
| ( ord_less_eq_nat @ ( number_number_of_nat @ SV97 ) @ ( number_number_of_nat @ SV175 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[763]) ).
thf(861,plain,
! [SV176: $i,SV98: $i] :
( ( ( ( number_number_of_nat @ SV98 )
!= SV176 )
| ( SV176
= ( number_number_of_nat @ SV98 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[764]) ).
thf(862,plain,
! [SV99: $i,SV177: $i] :
( ( ( SV177
!= ( number_number_of_nat @ SV99 ) )
| ( ( number_number_of_nat @ SV99 )
= SV177 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[765]) ).
thf(863,plain,
! [SV178: $i,SV100: $i] :
( ( ~ ( ord_less_eq_int @ SV100 @ SV178 )
| ( ord_less_int @ ( bit0 @ SV100 ) @ ( bit1 @ SV178 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[766]) ).
thf(864,plain,
! [SV179: $i,SV101: $i] :
( ( ~ ( ord_less_int @ ( bit0 @ SV101 ) @ ( bit1 @ SV179 ) )
| ( ord_less_eq_int @ SV101 @ SV179 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[767]) ).
thf(865,plain,
! [SV102: $i] :
( ( ( ~ ( ord_less_eq_int @ pls @ ( bit0 @ SV102 ) ) )
= $true )
| ( ( ord_less_eq_int @ pls @ SV102 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[768]) ).
thf(866,plain,
! [SV103: $i] :
( ( ( ~ ( ord_less_eq_int @ pls @ SV103 ) )
= $true )
| ( ( ord_less_eq_int @ pls @ ( bit0 @ SV103 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[769]) ).
thf(867,plain,
! [SV104: $i] :
( ( ( ~ ( ord_less_eq_int @ pls @ SV104 ) )
= $true )
| ( ( ord_less_int @ pls @ ( bit1 @ SV104 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[770]) ).
thf(868,plain,
! [SV105: $i] :
( ( ( ~ ( ord_less_int @ pls @ ( bit1 @ SV105 ) ) )
= $true )
| ( ( ord_less_eq_int @ pls @ SV105 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[771]) ).
thf(869,plain,
! [SV180: $i,SV106: $i] :
( ( ( SV106 != zero_zero_int )
| ( SV180 != zero_zero_int )
| ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SV106 @ SV106 ) @ ( times_times_int @ SV180 @ SV180 ) ) @ zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[772]) ).
thf(870,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( 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)],[773]) ).
thf(871,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[773]) ).
thf(872,plain,
! [SV181: $i,SV107: $i] :
( ( ~ ( ord_less_eq_int @ ( bit0 @ SV107 ) @ ( bit1 @ SV181 ) )
| ( ord_less_eq_int @ SV107 @ SV181 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[774]) ).
thf(873,plain,
! [SV182: $i,SV108: $i] :
( ( ~ ( ord_less_eq_int @ SV108 @ SV182 )
| ( ord_less_eq_int @ ( bit0 @ SV108 ) @ ( bit1 @ SV182 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[775]) ).
thf(874,plain,
! [SV109: $i] :
( ( ( ( number_number_of_nat @ SV109 )
!= zero_zero_nat )
= $true )
| ( ( ord_less_eq_int @ SV109 @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[776]) ).
thf(875,plain,
! [SV110: $i] :
( ( ( ~ ( ord_less_eq_int @ SV110 @ pls ) )
= $true )
| ( ( ( number_number_of_nat @ SV110 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[777]) ).
thf(876,plain,
! [SV183: $i,SV111: $i] :
( ( ~ ( ord_less_eq_int @ ( bit0 @ SV111 ) @ ( bit1 @ SV183 ) )
| ( ord_less_eq_int @ SV111 @ SV183 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[778]) ).
thf(877,plain,
! [SV184: $i,SV112: $i] :
( ( ~ ( ord_less_eq_int @ SV112 @ SV184 )
| ( ord_less_eq_int @ ( bit0 @ SV112 ) @ ( bit1 @ SV184 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[779]) ).
thf(878,plain,
! [SV185: $i,SV113: $i] :
( ( ( ( bit0 @ SV113 )
!= ( bit0 @ SV185 ) )
| ( SV113 = SV185 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[780]) ).
thf(879,plain,
! [SV186: $i,SV114: $i] :
( ( ( SV114 != SV186 )
| ( ( bit0 @ SV114 )
= ( bit0 @ SV186 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[781]) ).
thf(880,plain,
! [SV187: $i,SV115: $i] :
( ( ~ ( ord_less_eq_int @ ( plus_plus_int @ SV115 @ one_one_int ) @ SV187 )
| ( ord_less_int @ SV115 @ SV187 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[782]) ).
thf(881,plain,
! [SV188: $i,SV116: $i] :
( ( ~ ( ord_less_int @ SV116 @ SV188 )
| ( ord_less_eq_int @ ( plus_plus_int @ SV116 @ one_one_int ) @ SV188 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[783]) ).
thf(882,plain,
! [SV117: $i] :
( ( ( ~ ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ SV117 ) ) )
= $true )
| ( ( ord_less_eq_int @ pls @ SV117 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[784]) ).
thf(883,plain,
! [SV118: $i] :
( ( ( ~ ( ord_less_eq_int @ pls @ SV118 ) )
= $true )
| ( ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ SV118 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[785]) ).
thf(884,plain,
! [SV189: $i,SV119: $i] :
( ( ~ ( ord_less_int @ ( number_number_of_int @ SV119 ) @ ( number_number_of_int @ SV189 ) )
| ( ord_less_int @ SV119 @ SV189 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[786]) ).
thf(885,plain,
! [SV190: $i,SV120: $i] :
( ( ~ ( ord_less_int @ SV120 @ SV190 )
| ( ord_less_int @ ( number_number_of_int @ SV120 ) @ ( number_number_of_int @ SV190 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[787]) ).
thf(886,plain,
! [SV121: $i] :
( ( ( ~ ( ord_less_eq_int @ ( bit1 @ SV121 ) @ pls ) )
= $true )
| ( ( ord_less_int @ SV121 @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[788]) ).
thf(887,plain,
! [SV122: $i] :
( ( ( ~ ( ord_less_int @ SV122 @ pls ) )
= $true )
| ( ( ord_less_eq_int @ ( bit1 @ SV122 ) @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[789]) ).
thf(888,plain,
! [SV191: $i,SV123: $i] :
( ( ~ ( ord_less_eq_int @ ( bit0 @ SV123 ) @ ( bit0 @ SV191 ) )
| ( ord_less_eq_int @ SV123 @ SV191 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[790]) ).
thf(889,plain,
! [SV192: $i,SV124: $i] :
( ( ~ ( ord_less_eq_int @ SV124 @ SV192 )
| ( ord_less_eq_int @ ( bit0 @ SV124 ) @ ( bit0 @ SV192 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[791]) ).
thf(890,plain,
! [SV193: $i,SV125: $i] :
( ( ( ( number_number_of_int @ SV125 )
!= ( number_number_of_int @ SV193 ) )
| ( SV125 = SV193 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[792]) ).
thf(891,plain,
! [SV194: $i,SV126: $i] :
( ( ( SV126 != SV194 )
| ( ( number_number_of_int @ SV126 )
= ( number_number_of_int @ SV194 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[793]) ).
thf(892,plain,
! [SV195: $i,SV127: $i] :
( ( ( ( bit1 @ SV127 )
!= ( bit1 @ SV195 ) )
| ( SV127 = SV195 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[794]) ).
thf(893,plain,
! [SV196: $i,SV128: $i] :
( ( ( SV128 != SV196 )
| ( ( bit1 @ SV128 )
= ( bit1 @ SV196 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[795]) ).
thf(894,plain,
! [SV129: $i] :
( ( ( ~ ( ord_less_eq_int @ ( bit0 @ SV129 ) @ pls ) )
= $true )
| ( ( ord_less_eq_int @ SV129 @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[796]) ).
thf(895,plain,
! [SV130: $i] :
( ( ( ~ ( ord_less_eq_int @ SV130 @ pls ) )
= $true )
| ( ( ord_less_eq_int @ ( bit0 @ SV130 ) @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[797]) ).
thf(896,plain,
! [SV131: $i] :
( ( ( ~ ( ord_less_eq_int @ one_one_int @ ( number_number_of_int @ SV131 ) ) )
= $true )
| ( ( ord_less_eq_int @ ( bit1 @ pls ) @ SV131 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[798]) ).
thf(897,plain,
! [SV132: $i] :
( ( ( ~ ( ord_less_eq_int @ ( bit1 @ pls ) @ SV132 ) )
= $true )
| ( ( ord_less_eq_int @ one_one_int @ ( number_number_of_int @ SV132 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[799]) ).
thf(898,plain,
! [SV197: $i,SV133: $i] :
( ( ( SV133 != zero_zero_int )
| ( SV197 != zero_zero_int )
| ( ( plus_plus_int @ ( times_times_int @ SV133 @ SV133 ) @ ( times_times_int @ SV197 @ SV197 ) )
= zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[800]) ).
thf(899,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( 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)],[801]) ).
thf(900,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( 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)],[801]) ).
thf(901,plain,
! [SV134: $i,SV198: $i] :
( ( ~ ( ord_less_int @ SV198 @ pls )
| ( ( plus_plus_nat @ ( number_number_of_nat @ SV198 ) @ ( number_number_of_nat @ SV134 ) )
= ( number_number_of_nat @ SV134 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[802]) ).
thf(902,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( 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)],[803]) ).
thf(903,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( 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)],[803]) ).
thf(904,plain,
! [SV135: $i] :
( ( ( ~ ( ord_less_eq_int @ one_one_int @ SV135 ) )
= $true )
| ( ( ord_less_int @ zero_zero_int @ SV135 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[804]) ).
thf(905,plain,
! [SV136: $i] :
( ( ( ~ ( ord_less_int @ zero_zero_int @ SV136 ) )
= $true )
| ( ( ord_less_eq_int @ one_one_int @ SV136 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[805]) ).
thf(906,plain,
! [SV199: $i,SV137: $i] :
( ( ( ( number_number_of_int @ SV137 )
!= SV199 )
| ( SV199
= ( number_number_of_int @ SV137 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[806]) ).
thf(907,plain,
! [SV138: $i,SV200: $i] :
( ( ( SV200
!= ( number_number_of_int @ SV138 ) )
| ( ( number_number_of_int @ SV138 )
= SV200 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[807]) ).
thf(908,plain,
! [SV139: $i] :
( ( ( ( power_power_int @ SV139 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= zero_zero_int )
= $true )
| ( ( SV139 = zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[808]) ).
thf(909,plain,
! [SV140: $i] :
( ( ( SV140 != zero_zero_int )
= $true )
| ( ( ( power_power_int @ SV140 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[809]) ).
thf(910,plain,
! [SV201: $i,SV141: $i] :
( ( ~ ( ord_less_eq_int @ ( number_number_of_int @ SV141 ) @ ( number_number_of_int @ SV201 ) )
| ~ ( ord_less_int @ ( number_number_of_int @ SV201 ) @ ( number_number_of_int @ SV141 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[810]) ).
thf(911,plain,
! [SV142: $i,SV202: $i] :
( ( ( ord_less_int @ ( number_number_of_int @ SV202 ) @ ( number_number_of_int @ SV142 ) )
| ( ord_less_eq_int @ ( number_number_of_int @ SV142 ) @ ( number_number_of_int @ SV202 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[811]) ).
thf(912,plain,
! [SV203: $i,SV143: $i] :
( ( ~ ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ SV143 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV203 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
| ( SV143 != zero_zero_int )
| ( SV203 != zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[812]) ).
thf(913,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 = zero_zero_int )
| ! [SX1: $i] : ( 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)],[813]) ).
thf(914,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( 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)],[813]) ).
thf(915,plain,
! [SV204: $i,SV144: $i] :
( ( ( SV144 = SV204 )
| ~ ( ord_less_eq_int @ SV144 @ SV204 )
| ( ord_less_int @ SV144 @ SV204 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[814]) ).
thf(916,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[815]) ).
thf(917,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[815]) ).
thf(918,plain,
! [SV205: $i,SV145: $i] :
( ( ~ ( ord_less_eq_int @ ( bit0 @ SV145 ) @ ( bit0 @ SV205 ) )
| ( ord_less_eq_int @ SV145 @ SV205 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[816]) ).
thf(919,plain,
! [SV206: $i,SV146: $i] :
( ( ~ ( ord_less_eq_int @ SV146 @ SV206 )
| ( ord_less_eq_int @ ( bit0 @ SV146 ) @ ( bit0 @ SV206 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[817]) ).
thf(920,plain,
! [SV207: $i,SV147: $i] :
( ( ~ ( ord_less_eq_int @ ( number_number_of_int @ SV147 ) @ ( number_number_of_int @ SV207 ) )
| ( ord_less_eq_int @ SV147 @ SV207 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[818]) ).
thf(921,plain,
! [SV208: $i,SV148: $i] :
( ( ~ ( ord_less_eq_int @ SV148 @ SV208 )
| ( ord_less_eq_int @ ( number_number_of_int @ SV148 ) @ ( number_number_of_int @ SV208 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[819]) ).
thf(922,plain,
! [SV149: $i] :
( ( ( SV149 = zero_zero_int )
= $true )
| ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ SV149 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[820]) ).
thf(923,plain,
! [SV150: $i] :
( ( ( ~ ( ord_less_int @ zero_zero_int @ ( power_power_int @ SV150 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true )
| ( ( SV150 != zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[821]) ).
thf(924,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( 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)],[822]) ).
thf(925,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[822]) ).
thf(926,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_nat @ ( number_number_of_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) )
| ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ pls @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[823]) ).
thf(927,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[823]) ).
thf(928,plain,
! [SV209: $i,SV151: $i] :
( ( ~ ( ord_less_eq_int @ ( number_number_of_int @ SV151 ) @ ( number_number_of_int @ SV209 ) )
| ( ord_less_eq_int @ SV151 @ SV209 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[824]) ).
thf(929,plain,
! [SV210: $i,SV152: $i] :
( ( ~ ( ord_less_eq_int @ SV152 @ SV210 )
| ( ord_less_eq_int @ ( number_number_of_int @ SV152 ) @ ( number_number_of_int @ SV210 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[825]) ).
thf(930,plain,
! [SV211: $i,SV153: $i] :
( ( ~ ( ord_less_eq_int @ ( bit1 @ SV153 ) @ ( bit1 @ SV211 ) )
| ( ord_less_eq_int @ SV153 @ SV211 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[826]) ).
thf(931,plain,
! [SV212: $i,SV154: $i] :
( ( ~ ( ord_less_eq_int @ SV154 @ SV212 )
| ( ord_less_eq_int @ ( bit1 @ SV154 ) @ ( bit1 @ SV212 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[827]) ).
thf(932,plain,
! [SV213: $i,SV155: $i] :
( ( ~ ( ord_less_eq_int @ SV155 @ SV213 )
| ( ord_less_int @ ( bit0 @ SV155 ) @ ( bit1 @ SV213 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[828]) ).
thf(933,plain,
! [SV214: $i,SV156: $i] :
( ( ~ ( ord_less_int @ ( bit0 @ SV156 ) @ ( bit1 @ SV214 ) )
| ( ord_less_eq_int @ SV156 @ SV214 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[829]) ).
thf(934,plain,
! [SV157: $i] :
( ( ( ~ ( ord_less_eq_int @ ( number_number_of_int @ SV157 ) @ one_one_int ) )
= $true )
| ( ( ord_less_eq_int @ SV157 @ ( bit1 @ pls ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[830]) ).
thf(935,plain,
! [SV158: $i] :
( ( ( ~ ( ord_less_eq_int @ SV158 @ ( bit1 @ pls ) ) )
= $true )
| ( ( ord_less_eq_int @ ( number_number_of_int @ SV158 ) @ one_one_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[831]) ).
thf(936,plain,
! [SV215: $i,SV159: $i] :
( ( ~ ( ord_less_eq_int @ ( bit1 @ SV159 ) @ ( bit0 @ SV215 ) )
| ( ord_less_int @ SV159 @ SV215 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[832]) ).
thf(937,plain,
! [SV216: $i,SV160: $i] :
( ( ~ ( ord_less_int @ SV160 @ SV216 )
| ( ord_less_eq_int @ ( bit1 @ SV160 ) @ ( bit0 @ SV216 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[833]) ).
thf(938,plain,
! [SV161: $i] :
( ( ( zero_zero_nat
!= ( number_number_of_nat @ SV161 ) )
= $true )
| ( ( ord_less_eq_int @ SV161 @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[834]) ).
thf(939,plain,
! [SV162: $i] :
( ( ( ~ ( ord_less_eq_int @ SV162 @ pls ) )
= $true )
| ( ( zero_zero_nat
= ( number_number_of_nat @ SV162 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[835]) ).
thf(940,plain,
! [SV163: $i] :
( ( ( ~ ( ord_less_eq_int @ pls @ ( bit1 @ SV163 ) ) )
= $true )
| ( ( ord_less_eq_int @ pls @ SV163 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[836]) ).
thf(941,plain,
! [SV164: $i] :
( ( ( ~ ( ord_less_eq_int @ pls @ SV164 ) )
= $true )
| ( ( ord_less_eq_int @ pls @ ( bit1 @ SV164 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[837]) ).
thf(942,plain,
! [SV165: $i] :
( ( ( ~ ( ord_less_int @ pls @ SV165 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ SV165 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[838]) ).
thf(943,plain,
! [SV166: $i] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ SV166 ) ) )
= $true )
| ( ( ord_less_int @ pls @ SV166 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[839]) ).
thf(944,plain,
! [SV45: $i,SV8: $i,SV86: $i,SV74: $i] :
( ( ( ord_less_int @ SV74 @ SV86 )
= $false )
| ( ( ~ ( ord_less_eq_int @ SV8 @ SV45 )
| ( ord_less_int @ ( plus_plus_int @ SV74 @ SV8 ) @ ( plus_plus_int @ SV86 @ SV45 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[841]) ).
thf(945,plain,
! [SV51: $i,SV17: $i] :
( ( ( ord_less_eq_int @ pls @ SV17 )
= $false )
| ( ( ( plus_plus_int @ ( number_number_of_int @ SV51 ) @ ( number_number_of_int @ SV17 ) )
= ( number_number_of_int @ ( plus_plus_int @ SV51 @ SV17 ) ) )
= $true )
| ( ( ord_less_eq_int @ pls @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[842]) ).
thf(946,plain,
! [SV52: $i,SV18: $i] :
( ( ( ord_less_eq_int @ pls @ SV18 )
= $false )
| ( ( ( plus_plus_nat @ ( number_number_of_nat @ SV52 ) @ ( number_number_of_nat @ SV18 ) )
= ( number_number_of_nat @ ( plus_plus_int @ SV52 @ SV18 ) ) )
= $true )
| ( ( ord_less_eq_int @ pls @ SV52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[843]) ).
thf(947,plain,
! [SV65: $i,SV34: $i,SV84: $i] :
( ( ( ~ ( ord_less_eq_int @ SV84 @ SV34 ) )
= $true )
| ( ( ord_less_eq_int @ SV65 @ SV34 )
= $true )
| ( ( ord_less_eq_int @ SV65 @ SV84 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[844]) ).
thf(948,plain,
! [SV35: $i,SV66: $i] :
( ( ( ord_less_eq_int @ SV66 @ SV35 )
= $false )
| ( ( SV35 = SV66 )
= $true )
| ( ( ord_less_eq_int @ SV35 @ SV66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[845]) ).
thf(949,plain,
! [SV67: $i,SV36: $i] :
( ( ( ord_less_eq_int @ pls @ SV36 )
= $false )
| ( ( ( times_times_nat @ ( number_number_of_nat @ SV67 ) @ ( number_number_of_nat @ SV36 ) )
= ( number_number_of_nat @ ( times_times_int @ SV67 @ SV36 ) ) )
= $true )
| ( ( ord_less_eq_int @ pls @ SV67 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[846]) ).
thf(950,plain,
! [SV68: $i,SV37: $i] :
( ( ( ord_less_eq_int @ pls @ SV37 )
= $false )
| ( ( ( times_times_int @ ( number_number_of_int @ SV68 ) @ ( number_number_of_int @ SV37 ) )
= ( number_number_of_int @ ( times_times_int @ SV68 @ SV37 ) ) )
= $true )
| ( ( ord_less_eq_int @ pls @ SV68 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[847]) ).
thf(951,plain,
! [SV167: $i,SV87: $i] :
( ( ( ~ ( ord_less_eq_int @ SV87 @ SV167 ) )
= $true )
| ( ( ord_less_int @ SV87 @ ( plus_plus_int @ SV167 @ one_one_int ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[848]) ).
thf(952,plain,
! [SV168: $i,SV88: $i] :
( ( ( ~ ( ord_less_int @ SV88 @ ( plus_plus_int @ SV168 @ one_one_int ) ) )
= $true )
| ( ( ord_less_eq_int @ SV88 @ SV168 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[849]) ).
thf(953,plain,
! [SV169: $i,SV89: $i] :
( ( ( ~ ( ord_less_eq_int @ ( bit1 @ SV89 ) @ ( bit1 @ SV169 ) ) )
= $true )
| ( ( ord_less_eq_int @ SV89 @ SV169 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[850]) ).
thf(954,plain,
! [SV170: $i,SV90: $i] :
( ( ( ~ ( ord_less_eq_int @ SV90 @ SV170 ) )
= $true )
| ( ( ord_less_eq_int @ ( bit1 @ SV90 ) @ ( bit1 @ SV170 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[851]) ).
thf(955,plain,
! [SV171: $i,SV91: $i] :
( ( ( ~ ( ord_less_eq_int @ ( bit1 @ SV91 ) @ ( bit0 @ SV171 ) ) )
= $true )
| ( ( ord_less_int @ SV91 @ SV171 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[852]) ).
thf(956,plain,
! [SV172: $i,SV92: $i] :
( ( ( ~ ( ord_less_int @ SV92 @ SV172 ) )
= $true )
| ( ( ord_less_eq_int @ ( bit1 @ SV92 ) @ ( bit0 @ SV172 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[853]) ).
thf(957,plain,
! [SV173: $i,SV93: $i] :
( ( ( ( SV93 != zero_zero_int )
| ( SV173 != zero_zero_int ) )
= $true )
| ( ( ( plus_plus_int @ ( power_power_int @ SV93 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV173 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[854]) ).
thf(958,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
( ( plus_plus_int @ ( power_power_int @ SX0 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SX1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[855]) ).
thf(959,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( plus_plus_int @ ( power_power_int @ SX0 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SX1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_int )
| ( SX1 = zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[856]) ).
thf(960,plain,
! [SV94: $i] :
( ( ( ord_less_eq_int @ ( number_number_of_int @ SV94 ) @ zero_zero_int )
= $false )
| ( ( ord_less_eq_int @ SV94 @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[857]) ).
thf(961,plain,
! [SV95: $i] :
( ( ( ord_less_eq_int @ SV95 @ pls )
= $false )
| ( ( ord_less_eq_int @ ( number_number_of_int @ SV95 ) @ zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[858]) ).
thf(962,plain,
! [SV174: $i,SV96: $i] :
( ( ( ~ ( ord_less_eq_nat @ ( number_number_of_nat @ SV96 ) @ ( number_number_of_nat @ SV174 ) ) )
= $true )
| ( ( ~ ( ord_less_nat @ ( number_number_of_nat @ SV174 ) @ ( number_number_of_nat @ SV96 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[859]) ).
thf(963,plain,
! [SV97: $i,SV175: $i] :
( ( ( ord_less_nat @ ( number_number_of_nat @ SV175 ) @ ( number_number_of_nat @ SV97 ) )
= $true )
| ( ( ord_less_eq_nat @ ( number_number_of_nat @ SV97 ) @ ( number_number_of_nat @ SV175 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[860]) ).
thf(964,plain,
! [SV176: $i,SV98: $i] :
( ( ( ( number_number_of_nat @ SV98 )
!= SV176 )
= $true )
| ( ( SV176
= ( number_number_of_nat @ SV98 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[861]) ).
thf(965,plain,
! [SV99: $i,SV177: $i] :
( ( ( SV177
!= ( number_number_of_nat @ SV99 ) )
= $true )
| ( ( ( number_number_of_nat @ SV99 )
= SV177 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[862]) ).
thf(966,plain,
! [SV178: $i,SV100: $i] :
( ( ( ~ ( ord_less_eq_int @ SV100 @ SV178 ) )
= $true )
| ( ( ord_less_int @ ( bit0 @ SV100 ) @ ( bit1 @ SV178 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[863]) ).
thf(967,plain,
! [SV179: $i,SV101: $i] :
( ( ( ~ ( ord_less_int @ ( bit0 @ SV101 ) @ ( bit1 @ SV179 ) ) )
= $true )
| ( ( ord_less_eq_int @ SV101 @ SV179 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[864]) ).
thf(968,plain,
! [SV102: $i] :
( ( ( ord_less_eq_int @ pls @ ( bit0 @ SV102 ) )
= $false )
| ( ( ord_less_eq_int @ pls @ SV102 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[865]) ).
thf(969,plain,
! [SV103: $i] :
( ( ( ord_less_eq_int @ pls @ SV103 )
= $false )
| ( ( ord_less_eq_int @ pls @ ( bit0 @ SV103 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[866]) ).
thf(970,plain,
! [SV104: $i] :
( ( ( ord_less_eq_int @ pls @ SV104 )
= $false )
| ( ( ord_less_int @ pls @ ( bit1 @ SV104 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[867]) ).
thf(971,plain,
! [SV105: $i] :
( ( ( ord_less_int @ pls @ ( bit1 @ SV105 ) )
= $false )
| ( ( ord_less_eq_int @ pls @ SV105 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[868]) ).
thf(972,plain,
! [SV180: $i,SV106: $i] :
( ( ( ( SV106 != zero_zero_int )
| ( SV180 != zero_zero_int ) )
= $true )
| ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SV106 @ SV106 ) @ ( times_times_int @ SV180 @ SV180 ) ) @ zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[869]) ).
thf(973,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
~ ( 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)],[870]) ).
thf(974,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[871]) ).
thf(975,plain,
! [SV181: $i,SV107: $i] :
( ( ( ~ ( ord_less_eq_int @ ( bit0 @ SV107 ) @ ( bit1 @ SV181 ) ) )
= $true )
| ( ( ord_less_eq_int @ SV107 @ SV181 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[872]) ).
thf(976,plain,
! [SV182: $i,SV108: $i] :
( ( ( ~ ( ord_less_eq_int @ SV108 @ SV182 ) )
= $true )
| ( ( ord_less_eq_int @ ( bit0 @ SV108 ) @ ( bit1 @ SV182 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[873]) ).
thf(977,plain,
! [SV109: $i] :
( ( ( ( number_number_of_nat @ SV109 )
= zero_zero_nat )
= $false )
| ( ( ord_less_eq_int @ SV109 @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[874]) ).
thf(978,plain,
! [SV110: $i] :
( ( ( ord_less_eq_int @ SV110 @ pls )
= $false )
| ( ( ( number_number_of_nat @ SV110 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[875]) ).
thf(979,plain,
! [SV183: $i,SV111: $i] :
( ( ( ~ ( ord_less_eq_int @ ( bit0 @ SV111 ) @ ( bit1 @ SV183 ) ) )
= $true )
| ( ( ord_less_eq_int @ SV111 @ SV183 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[876]) ).
thf(980,plain,
! [SV184: $i,SV112: $i] :
( ( ( ~ ( ord_less_eq_int @ SV112 @ SV184 ) )
= $true )
| ( ( ord_less_eq_int @ ( bit0 @ SV112 ) @ ( bit1 @ SV184 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[877]) ).
thf(981,plain,
! [SV185: $i,SV113: $i] :
( ( ( ( bit0 @ SV113 )
!= ( bit0 @ SV185 ) )
= $true )
| ( ( SV113 = SV185 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[878]) ).
thf(982,plain,
! [SV186: $i,SV114: $i] :
( ( ( SV114 != SV186 )
= $true )
| ( ( ( bit0 @ SV114 )
= ( bit0 @ SV186 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[879]) ).
thf(983,plain,
! [SV187: $i,SV115: $i] :
( ( ( ~ ( ord_less_eq_int @ ( plus_plus_int @ SV115 @ one_one_int ) @ SV187 ) )
= $true )
| ( ( ord_less_int @ SV115 @ SV187 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[880]) ).
thf(984,plain,
! [SV188: $i,SV116: $i] :
( ( ( ~ ( ord_less_int @ SV116 @ SV188 ) )
= $true )
| ( ( ord_less_eq_int @ ( plus_plus_int @ SV116 @ one_one_int ) @ SV188 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[881]) ).
thf(985,plain,
! [SV117: $i] :
( ( ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ SV117 ) )
= $false )
| ( ( ord_less_eq_int @ pls @ SV117 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[882]) ).
thf(986,plain,
! [SV118: $i] :
( ( ( ord_less_eq_int @ pls @ SV118 )
= $false )
| ( ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ SV118 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[883]) ).
thf(987,plain,
! [SV189: $i,SV119: $i] :
( ( ( ~ ( ord_less_int @ ( number_number_of_int @ SV119 ) @ ( number_number_of_int @ SV189 ) ) )
= $true )
| ( ( ord_less_int @ SV119 @ SV189 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[884]) ).
thf(988,plain,
! [SV190: $i,SV120: $i] :
( ( ( ~ ( ord_less_int @ SV120 @ SV190 ) )
= $true )
| ( ( ord_less_int @ ( number_number_of_int @ SV120 ) @ ( number_number_of_int @ SV190 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[885]) ).
thf(989,plain,
! [SV121: $i] :
( ( ( ord_less_eq_int @ ( bit1 @ SV121 ) @ pls )
= $false )
| ( ( ord_less_int @ SV121 @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[886]) ).
thf(990,plain,
! [SV122: $i] :
( ( ( ord_less_int @ SV122 @ pls )
= $false )
| ( ( ord_less_eq_int @ ( bit1 @ SV122 ) @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[887]) ).
thf(991,plain,
! [SV191: $i,SV123: $i] :
( ( ( ~ ( ord_less_eq_int @ ( bit0 @ SV123 ) @ ( bit0 @ SV191 ) ) )
= $true )
| ( ( ord_less_eq_int @ SV123 @ SV191 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[888]) ).
thf(992,plain,
! [SV192: $i,SV124: $i] :
( ( ( ~ ( ord_less_eq_int @ SV124 @ SV192 ) )
= $true )
| ( ( ord_less_eq_int @ ( bit0 @ SV124 ) @ ( bit0 @ SV192 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[889]) ).
thf(993,plain,
! [SV193: $i,SV125: $i] :
( ( ( ( number_number_of_int @ SV125 )
!= ( number_number_of_int @ SV193 ) )
= $true )
| ( ( SV125 = SV193 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[890]) ).
thf(994,plain,
! [SV194: $i,SV126: $i] :
( ( ( SV126 != SV194 )
= $true )
| ( ( ( number_number_of_int @ SV126 )
= ( number_number_of_int @ SV194 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[891]) ).
thf(995,plain,
! [SV195: $i,SV127: $i] :
( ( ( ( bit1 @ SV127 )
!= ( bit1 @ SV195 ) )
= $true )
| ( ( SV127 = SV195 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[892]) ).
thf(996,plain,
! [SV196: $i,SV128: $i] :
( ( ( SV128 != SV196 )
= $true )
| ( ( ( bit1 @ SV128 )
= ( bit1 @ SV196 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[893]) ).
thf(997,plain,
! [SV129: $i] :
( ( ( ord_less_eq_int @ ( bit0 @ SV129 ) @ pls )
= $false )
| ( ( ord_less_eq_int @ SV129 @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[894]) ).
thf(998,plain,
! [SV130: $i] :
( ( ( ord_less_eq_int @ SV130 @ pls )
= $false )
| ( ( ord_less_eq_int @ ( bit0 @ SV130 ) @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[895]) ).
thf(999,plain,
! [SV131: $i] :
( ( ( ord_less_eq_int @ one_one_int @ ( number_number_of_int @ SV131 ) )
= $false )
| ( ( ord_less_eq_int @ ( bit1 @ pls ) @ SV131 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[896]) ).
thf(1000,plain,
! [SV132: $i] :
( ( ( ord_less_eq_int @ ( bit1 @ pls ) @ SV132 )
= $false )
| ( ( ord_less_eq_int @ one_one_int @ ( number_number_of_int @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[897]) ).
thf(1001,plain,
! [SV197: $i,SV133: $i] :
( ( ( ( SV133 != zero_zero_int )
| ( SV197 != zero_zero_int ) )
= $true )
| ( ( ( plus_plus_int @ ( times_times_int @ SV133 @ SV133 ) @ ( times_times_int @ SV197 @ SV197 ) )
= zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[898]) ).
thf(1002,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
( ( 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)],[899]) ).
thf(1003,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( 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)],[900]) ).
thf(1004,plain,
! [SV134: $i,SV198: $i] :
( ( ( ~ ( ord_less_int @ SV198 @ pls ) )
= $true )
| ( ( ( plus_plus_nat @ ( number_number_of_nat @ SV198 ) @ ( number_number_of_nat @ SV134 ) )
= ( number_number_of_nat @ SV134 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[901]) ).
thf(1005,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( 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)],[902]) ).
thf(1006,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( 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)],[903]) ).
thf(1007,plain,
! [SV135: $i] :
( ( ( ord_less_eq_int @ one_one_int @ SV135 )
= $false )
| ( ( ord_less_int @ zero_zero_int @ SV135 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[904]) ).
thf(1008,plain,
! [SV136: $i] :
( ( ( ord_less_int @ zero_zero_int @ SV136 )
= $false )
| ( ( ord_less_eq_int @ one_one_int @ SV136 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[905]) ).
thf(1009,plain,
! [SV199: $i,SV137: $i] :
( ( ( ( number_number_of_int @ SV137 )
!= SV199 )
= $true )
| ( ( SV199
= ( number_number_of_int @ SV137 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[906]) ).
thf(1010,plain,
! [SV138: $i,SV200: $i] :
( ( ( SV200
!= ( number_number_of_int @ SV138 ) )
= $true )
| ( ( ( number_number_of_int @ SV138 )
= SV200 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[907]) ).
thf(1011,plain,
! [SV139: $i] :
( ( ( ( power_power_int @ SV139 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int )
= $false )
| ( ( SV139 = zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[908]) ).
thf(1012,plain,
! [SV140: $i] :
( ( ( SV140 = zero_zero_int )
= $false )
| ( ( ( power_power_int @ SV140 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[909]) ).
thf(1013,plain,
! [SV201: $i,SV141: $i] :
( ( ( ~ ( ord_less_eq_int @ ( number_number_of_int @ SV141 ) @ ( number_number_of_int @ SV201 ) ) )
= $true )
| ( ( ~ ( ord_less_int @ ( number_number_of_int @ SV201 ) @ ( number_number_of_int @ SV141 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[910]) ).
thf(1014,plain,
! [SV142: $i,SV202: $i] :
( ( ( ord_less_int @ ( number_number_of_int @ SV202 ) @ ( number_number_of_int @ SV142 ) )
= $true )
| ( ( ord_less_eq_int @ ( number_number_of_int @ SV142 ) @ ( number_number_of_int @ SV202 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[911]) ).
thf(1015,plain,
! [SV203: $i,SV143: $i] :
( ( ( ~ ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ SV143 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV203 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true )
| ( ( ( SV143 != zero_zero_int )
| ( SV203 != zero_zero_int ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[912]) ).
thf(1016,plain,
( ( ! [SX0: $i] :
( ( SX0 = zero_zero_int )
| ! [SX1: $i] : ( 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)],[913]) ).
thf(1017,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( 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)],[914]) ).
thf(1018,plain,
! [SV204: $i,SV144: $i] :
( ( ( ( SV144 = SV204 )
| ~ ( ord_less_eq_int @ SV144 @ SV204 ) )
= $true )
| ( ( ord_less_int @ SV144 @ SV204 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[915]) ).
thf(1019,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[916]) ).
thf(1020,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_eq_int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[917]) ).
thf(1021,plain,
! [SV205: $i,SV145: $i] :
( ( ( ~ ( ord_less_eq_int @ ( bit0 @ SV145 ) @ ( bit0 @ SV205 ) ) )
= $true )
| ( ( ord_less_eq_int @ SV145 @ SV205 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[918]) ).
thf(1022,plain,
! [SV206: $i,SV146: $i] :
( ( ( ~ ( ord_less_eq_int @ SV146 @ SV206 ) )
= $true )
| ( ( ord_less_eq_int @ ( bit0 @ SV146 ) @ ( bit0 @ SV206 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[919]) ).
thf(1023,plain,
! [SV207: $i,SV147: $i] :
( ( ( ~ ( ord_less_eq_int @ ( number_number_of_int @ SV147 ) @ ( number_number_of_int @ SV207 ) ) )
= $true )
| ( ( ord_less_eq_int @ SV147 @ SV207 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[920]) ).
thf(1024,plain,
! [SV208: $i,SV148: $i] :
( ( ( ~ ( ord_less_eq_int @ SV148 @ SV208 ) )
= $true )
| ( ( ord_less_eq_int @ ( number_number_of_int @ SV148 ) @ ( number_number_of_int @ SV208 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[921]) ).
thf(1025,plain,
! [SV150: $i] :
( ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ SV150 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $false )
| ( ( SV150 != zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[923]) ).
thf(1026,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( 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)],[924]) ).
thf(1027,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[925]) ).
thf(1028,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_nat @ ( number_number_of_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) )
| ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ pls @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[926]) ).
thf(1029,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[927]) ).
thf(1030,plain,
! [SV209: $i,SV151: $i] :
( ( ( ~ ( ord_less_eq_int @ ( number_number_of_int @ SV151 ) @ ( number_number_of_int @ SV209 ) ) )
= $true )
| ( ( ord_less_eq_int @ SV151 @ SV209 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[928]) ).
thf(1031,plain,
! [SV210: $i,SV152: $i] :
( ( ( ~ ( ord_less_eq_int @ SV152 @ SV210 ) )
= $true )
| ( ( ord_less_eq_int @ ( number_number_of_int @ SV152 ) @ ( number_number_of_int @ SV210 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[929]) ).
thf(1032,plain,
! [SV211: $i,SV153: $i] :
( ( ( ~ ( ord_less_eq_int @ ( bit1 @ SV153 ) @ ( bit1 @ SV211 ) ) )
= $true )
| ( ( ord_less_eq_int @ SV153 @ SV211 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[930]) ).
thf(1033,plain,
! [SV212: $i,SV154: $i] :
( ( ( ~ ( ord_less_eq_int @ SV154 @ SV212 ) )
= $true )
| ( ( ord_less_eq_int @ ( bit1 @ SV154 ) @ ( bit1 @ SV212 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[931]) ).
thf(1034,plain,
! [SV213: $i,SV155: $i] :
( ( ( ~ ( ord_less_eq_int @ SV155 @ SV213 ) )
= $true )
| ( ( ord_less_int @ ( bit0 @ SV155 ) @ ( bit1 @ SV213 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[932]) ).
thf(1035,plain,
! [SV214: $i,SV156: $i] :
( ( ( ~ ( ord_less_int @ ( bit0 @ SV156 ) @ ( bit1 @ SV214 ) ) )
= $true )
| ( ( ord_less_eq_int @ SV156 @ SV214 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[933]) ).
thf(1036,plain,
! [SV157: $i] :
( ( ( ord_less_eq_int @ ( number_number_of_int @ SV157 ) @ one_one_int )
= $false )
| ( ( ord_less_eq_int @ SV157 @ ( bit1 @ pls ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[934]) ).
thf(1037,plain,
! [SV158: $i] :
( ( ( ord_less_eq_int @ SV158 @ ( bit1 @ pls ) )
= $false )
| ( ( ord_less_eq_int @ ( number_number_of_int @ SV158 ) @ one_one_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[935]) ).
thf(1038,plain,
! [SV215: $i,SV159: $i] :
( ( ( ~ ( ord_less_eq_int @ ( bit1 @ SV159 ) @ ( bit0 @ SV215 ) ) )
= $true )
| ( ( ord_less_int @ SV159 @ SV215 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[936]) ).
thf(1039,plain,
! [SV216: $i,SV160: $i] :
( ( ( ~ ( ord_less_int @ SV160 @ SV216 ) )
= $true )
| ( ( ord_less_eq_int @ ( bit1 @ SV160 ) @ ( bit0 @ SV216 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[937]) ).
thf(1040,plain,
! [SV161: $i] :
( ( ( zero_zero_nat
= ( number_number_of_nat @ SV161 ) )
= $false )
| ( ( ord_less_eq_int @ SV161 @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[938]) ).
thf(1041,plain,
! [SV162: $i] :
( ( ( ord_less_eq_int @ SV162 @ pls )
= $false )
| ( ( zero_zero_nat
= ( number_number_of_nat @ SV162 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[939]) ).
thf(1042,plain,
! [SV163: $i] :
( ( ( ord_less_eq_int @ pls @ ( bit1 @ SV163 ) )
= $false )
| ( ( ord_less_eq_int @ pls @ SV163 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[940]) ).
thf(1043,plain,
! [SV164: $i] :
( ( ( ord_less_eq_int @ pls @ SV164 )
= $false )
| ( ( ord_less_eq_int @ pls @ ( bit1 @ SV164 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[941]) ).
thf(1044,plain,
! [SV165: $i] :
( ( ( ord_less_int @ pls @ SV165 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ SV165 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[942]) ).
thf(1045,plain,
! [SV166: $i] :
( ( ( ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ SV166 ) )
= $false )
| ( ( ord_less_int @ pls @ SV166 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[943]) ).
thf(1046,plain,
! [SV86: $i,SV74: $i,SV45: $i,SV8: $i] :
( ( ( ~ ( ord_less_eq_int @ SV8 @ SV45 ) )
= $true )
| ( ( ord_less_int @ ( plus_plus_int @ SV74 @ SV8 ) @ ( plus_plus_int @ SV86 @ SV45 ) )
= $true )
| ( ( ord_less_int @ SV74 @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[944]) ).
thf(1047,plain,
! [SV65: $i,SV34: $i,SV84: $i] :
( ( ( ord_less_eq_int @ SV84 @ SV34 )
= $false )
| ( ( ord_less_eq_int @ SV65 @ SV34 )
= $true )
| ( ( ord_less_eq_int @ SV65 @ SV84 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[947]) ).
thf(1048,plain,
! [SV167: $i,SV87: $i] :
( ( ( ord_less_eq_int @ SV87 @ SV167 )
= $false )
| ( ( ord_less_int @ SV87 @ ( plus_plus_int @ SV167 @ one_one_int ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[951]) ).
thf(1049,plain,
! [SV168: $i,SV88: $i] :
( ( ( ord_less_int @ SV88 @ ( plus_plus_int @ SV168 @ one_one_int ) )
= $false )
| ( ( ord_less_eq_int @ SV88 @ SV168 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[952]) ).
thf(1050,plain,
! [SV169: $i,SV89: $i] :
( ( ( ord_less_eq_int @ ( bit1 @ SV89 ) @ ( bit1 @ SV169 ) )
= $false )
| ( ( ord_less_eq_int @ SV89 @ SV169 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[953]) ).
thf(1051,plain,
! [SV170: $i,SV90: $i] :
( ( ( ord_less_eq_int @ SV90 @ SV170 )
= $false )
| ( ( ord_less_eq_int @ ( bit1 @ SV90 ) @ ( bit1 @ SV170 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[954]) ).
thf(1052,plain,
! [SV171: $i,SV91: $i] :
( ( ( ord_less_eq_int @ ( bit1 @ SV91 ) @ ( bit0 @ SV171 ) )
= $false )
| ( ( ord_less_int @ SV91 @ SV171 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[955]) ).
thf(1053,plain,
! [SV172: $i,SV92: $i] :
( ( ( ord_less_int @ SV92 @ SV172 )
= $false )
| ( ( ord_less_eq_int @ ( bit1 @ SV92 ) @ ( bit0 @ SV172 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[956]) ).
thf(1054,plain,
! [SV173: $i,SV93: $i] :
( ( ( SV93 != zero_zero_int )
= $true )
| ( ( SV173 != zero_zero_int )
= $true )
| ( ( ( plus_plus_int @ ( power_power_int @ SV93 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV173 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[957]) ).
thf(1055,plain,
! [SV217: $i] :
( ( ! [SY272: $i] :
( ( plus_plus_int @ ( power_power_int @ SV217 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SY272 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_int )
| ( SV217 = zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[958]) ).
thf(1056,plain,
! [SV218: $i] :
( ( ! [SY273: $i] :
( ( ( plus_plus_int @ ( power_power_int @ SV218 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SY273 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_int )
| ( SY273 = zero_zero_int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[959]) ).
thf(1057,plain,
! [SV174: $i,SV96: $i] :
( ( ( ord_less_eq_nat @ ( number_number_of_nat @ SV96 ) @ ( number_number_of_nat @ SV174 ) )
= $false )
| ( ( ~ ( ord_less_nat @ ( number_number_of_nat @ SV174 ) @ ( number_number_of_nat @ SV96 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[962]) ).
thf(1058,plain,
! [SV176: $i,SV98: $i] :
( ( ( ( number_number_of_nat @ SV98 )
= SV176 )
= $false )
| ( ( SV176
= ( number_number_of_nat @ SV98 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[964]) ).
thf(1059,plain,
! [SV99: $i,SV177: $i] :
( ( ( SV177
= ( number_number_of_nat @ SV99 ) )
= $false )
| ( ( ( number_number_of_nat @ SV99 )
= SV177 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[965]) ).
thf(1060,plain,
! [SV178: $i,SV100: $i] :
( ( ( ord_less_eq_int @ SV100 @ SV178 )
= $false )
| ( ( ord_less_int @ ( bit0 @ SV100 ) @ ( bit1 @ SV178 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[966]) ).
thf(1061,plain,
! [SV179: $i,SV101: $i] :
( ( ( ord_less_int @ ( bit0 @ SV101 ) @ ( bit1 @ SV179 ) )
= $false )
| ( ( ord_less_eq_int @ SV101 @ SV179 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[967]) ).
thf(1062,plain,
! [SV180: $i,SV106: $i] :
( ( ( SV106 != zero_zero_int )
= $true )
| ( ( SV180 != zero_zero_int )
= $true )
| ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SV106 @ SV106 ) @ ( times_times_int @ SV180 @ SV180 ) ) @ zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[972]) ).
thf(1063,plain,
! [SV219: $i] :
( ( ! [SY274: $i] :
~ ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SV219 @ SV219 ) @ ( times_times_int @ SY274 @ SY274 ) ) @ zero_zero_int )
| ( SV219 = zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[973]) ).
thf(1064,plain,
! [SV220: $i] :
( ( ! [SY275: $i] :
( ~ ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SV220 @ SV220 ) @ ( times_times_int @ SY275 @ SY275 ) ) @ zero_zero_int )
| ( SY275 = zero_zero_int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[974]) ).
thf(1065,plain,
! [SV181: $i,SV107: $i] :
( ( ( ord_less_eq_int @ ( bit0 @ SV107 ) @ ( bit1 @ SV181 ) )
= $false )
| ( ( ord_less_eq_int @ SV107 @ SV181 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[975]) ).
thf(1066,plain,
! [SV182: $i,SV108: $i] :
( ( ( ord_less_eq_int @ SV108 @ SV182 )
= $false )
| ( ( ord_less_eq_int @ ( bit0 @ SV108 ) @ ( bit1 @ SV182 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[976]) ).
thf(1067,plain,
! [SV183: $i,SV111: $i] :
( ( ( ord_less_eq_int @ ( bit0 @ SV111 ) @ ( bit1 @ SV183 ) )
= $false )
| ( ( ord_less_eq_int @ SV111 @ SV183 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[979]) ).
thf(1068,plain,
! [SV184: $i,SV112: $i] :
( ( ( ord_less_eq_int @ SV112 @ SV184 )
= $false )
| ( ( ord_less_eq_int @ ( bit0 @ SV112 ) @ ( bit1 @ SV184 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[980]) ).
thf(1069,plain,
! [SV185: $i,SV113: $i] :
( ( ( ( bit0 @ SV113 )
= ( bit0 @ SV185 ) )
= $false )
| ( ( SV113 = SV185 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[981]) ).
thf(1070,plain,
! [SV186: $i,SV114: $i] :
( ( ( SV114 = SV186 )
= $false )
| ( ( ( bit0 @ SV114 )
= ( bit0 @ SV186 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[982]) ).
thf(1071,plain,
! [SV187: $i,SV115: $i] :
( ( ( ord_less_eq_int @ ( plus_plus_int @ SV115 @ one_one_int ) @ SV187 )
= $false )
| ( ( ord_less_int @ SV115 @ SV187 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[983]) ).
thf(1072,plain,
! [SV188: $i,SV116: $i] :
( ( ( ord_less_int @ SV116 @ SV188 )
= $false )
| ( ( ord_less_eq_int @ ( plus_plus_int @ SV116 @ one_one_int ) @ SV188 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[984]) ).
thf(1073,plain,
! [SV189: $i,SV119: $i] :
( ( ( ord_less_int @ ( number_number_of_int @ SV119 ) @ ( number_number_of_int @ SV189 ) )
= $false )
| ( ( ord_less_int @ SV119 @ SV189 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[987]) ).
thf(1074,plain,
! [SV190: $i,SV120: $i] :
( ( ( ord_less_int @ SV120 @ SV190 )
= $false )
| ( ( ord_less_int @ ( number_number_of_int @ SV120 ) @ ( number_number_of_int @ SV190 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[988]) ).
thf(1075,plain,
! [SV191: $i,SV123: $i] :
( ( ( ord_less_eq_int @ ( bit0 @ SV123 ) @ ( bit0 @ SV191 ) )
= $false )
| ( ( ord_less_eq_int @ SV123 @ SV191 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[991]) ).
thf(1076,plain,
! [SV192: $i,SV124: $i] :
( ( ( ord_less_eq_int @ SV124 @ SV192 )
= $false )
| ( ( ord_less_eq_int @ ( bit0 @ SV124 ) @ ( bit0 @ SV192 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[992]) ).
thf(1077,plain,
! [SV193: $i,SV125: $i] :
( ( ( ( number_number_of_int @ SV125 )
= ( number_number_of_int @ SV193 ) )
= $false )
| ( ( SV125 = SV193 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[993]) ).
thf(1078,plain,
! [SV194: $i,SV126: $i] :
( ( ( SV126 = SV194 )
= $false )
| ( ( ( number_number_of_int @ SV126 )
= ( number_number_of_int @ SV194 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[994]) ).
thf(1079,plain,
! [SV195: $i,SV127: $i] :
( ( ( ( bit1 @ SV127 )
= ( bit1 @ SV195 ) )
= $false )
| ( ( SV127 = SV195 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[995]) ).
thf(1080,plain,
! [SV196: $i,SV128: $i] :
( ( ( SV128 = SV196 )
= $false )
| ( ( ( bit1 @ SV128 )
= ( bit1 @ SV196 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[996]) ).
thf(1081,plain,
! [SV197: $i,SV133: $i] :
( ( ( SV133 != zero_zero_int )
= $true )
| ( ( SV197 != zero_zero_int )
= $true )
| ( ( ( plus_plus_int @ ( times_times_int @ SV133 @ SV133 ) @ ( times_times_int @ SV197 @ SV197 ) )
= zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1001]) ).
thf(1082,plain,
! [SV221: $i] :
( ( ! [SY276: $i] :
( ( plus_plus_int @ ( times_times_int @ SV221 @ SV221 ) @ ( times_times_int @ SY276 @ SY276 ) )
!= zero_zero_int )
| ( SV221 = zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1002]) ).
thf(1083,plain,
! [SV222: $i] :
( ( ! [SY277: $i] :
( ( ( plus_plus_int @ ( times_times_int @ SV222 @ SV222 ) @ ( times_times_int @ SY277 @ SY277 ) )
!= zero_zero_int )
| ( SY277 = zero_zero_int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1003]) ).
thf(1084,plain,
! [SV134: $i,SV198: $i] :
( ( ( ord_less_int @ SV198 @ pls )
= $false )
| ( ( ( plus_plus_nat @ ( number_number_of_nat @ SV198 ) @ ( number_number_of_nat @ SV134 ) )
= ( number_number_of_nat @ SV134 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1004]) ).
thf(1085,plain,
! [SV223: $i] :
( ( ! [SY278: $i] :
( ( ord_less_int @ SY278 @ pls )
| ~ ( ord_less_int @ SV223 @ pls )
| ( ( plus_plus_nat @ ( number_number_of_nat @ SY278 ) @ ( number_number_of_nat @ SV223 ) )
= ( number_number_of_nat @ SY278 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1005]) ).
thf(1086,plain,
! [SV224: $i] :
( ( ! [SY279: $i] :
( ( ord_less_int @ SY279 @ pls )
| ( ord_less_int @ SV224 @ pls )
| ( ( plus_plus_nat @ ( number_number_of_nat @ SY279 ) @ ( number_number_of_nat @ SV224 ) )
= ( number_number_of_nat @ ( plus_plus_int @ SY279 @ SV224 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1006]) ).
thf(1087,plain,
! [SV199: $i,SV137: $i] :
( ( ( ( number_number_of_int @ SV137 )
= SV199 )
= $false )
| ( ( SV199
= ( number_number_of_int @ SV137 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1009]) ).
thf(1088,plain,
! [SV138: $i,SV200: $i] :
( ( ( SV200
= ( number_number_of_int @ SV138 ) )
= $false )
| ( ( ( number_number_of_int @ SV138 )
= SV200 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1010]) ).
thf(1089,plain,
! [SV201: $i,SV141: $i] :
( ( ( ord_less_eq_int @ ( number_number_of_int @ SV141 ) @ ( number_number_of_int @ SV201 ) )
= $false )
| ( ( ~ ( ord_less_int @ ( number_number_of_int @ SV201 ) @ ( number_number_of_int @ SV141 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1013]) ).
thf(1090,plain,
! [SV203: $i,SV143: $i] :
( ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ SV143 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV203 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $false )
| ( ( ( SV143 != zero_zero_int )
| ( SV203 != zero_zero_int ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1015]) ).
thf(1091,plain,
! [SV225: $i] :
( ( ( SV225 = zero_zero_int )
| ! [SY280: $i] : ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ SV225 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SY280 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1016]) ).
thf(1092,plain,
! [SV226: $i] :
( ( ! [SY281: $i] :
( ( SY281 = zero_zero_int )
| ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ SV226 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SY281 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1017]) ).
thf(1093,plain,
! [SV204: $i,SV144: $i] :
( ( ( SV144 = SV204 )
= $true )
| ( ( ~ ( ord_less_eq_int @ SV144 @ SV204 ) )
= $true )
| ( ( ord_less_int @ SV144 @ SV204 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1018]) ).
thf(1094,plain,
! [SV227: $i] :
( ( ! [SY282: $i] :
( ~ ( ord_less_int @ SV227 @ SY282 )
| ( SV227 != SY282 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1019]) ).
thf(1095,plain,
! [SV228: $i] :
( ( ! [SY283: $i] :
( ~ ( ord_less_int @ SV228 @ SY283 )
| ( ord_less_eq_int @ SV228 @ SY283 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1020]) ).
thf(1096,plain,
! [SV205: $i,SV145: $i] :
( ( ( ord_less_eq_int @ ( bit0 @ SV145 ) @ ( bit0 @ SV205 ) )
= $false )
| ( ( ord_less_eq_int @ SV145 @ SV205 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1021]) ).
thf(1097,plain,
! [SV206: $i,SV146: $i] :
( ( ( ord_less_eq_int @ SV146 @ SV206 )
= $false )
| ( ( ord_less_eq_int @ ( bit0 @ SV146 ) @ ( bit0 @ SV206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1022]) ).
thf(1098,plain,
! [SV207: $i,SV147: $i] :
( ( ( ord_less_eq_int @ ( number_number_of_int @ SV147 ) @ ( number_number_of_int @ SV207 ) )
= $false )
| ( ( ord_less_eq_int @ SV147 @ SV207 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1023]) ).
thf(1099,plain,
! [SV208: $i,SV148: $i] :
( ( ( ord_less_eq_int @ SV148 @ SV208 )
= $false )
| ( ( ord_less_eq_int @ ( number_number_of_int @ SV148 ) @ ( number_number_of_int @ SV208 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1024]) ).
thf(1100,plain,
! [SV150: $i] :
( ( ( SV150 = zero_zero_int )
= $false )
| ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ SV150 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1025]) ).
thf(1101,plain,
! [SV229: $i] :
( ( ! [SY284: $i] :
( ( ord_less_int @ SV229 @ SY284 )
| ~ ( ord_less_int @ SV229 @ SY284 )
| ( ord_less_nat @ ( number_number_of_nat @ SV229 ) @ ( number_number_of_nat @ SY284 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1026]) ).
thf(1102,plain,
! [SV230: $i] :
( ( ! [SY285: $i] :
( ~ ( ord_less_int @ pls @ SY285 )
| ~ ( ord_less_int @ SV230 @ SY285 )
| ( ord_less_nat @ ( number_number_of_nat @ SV230 ) @ ( number_number_of_nat @ SY285 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1027]) ).
thf(1103,plain,
! [SV231: $i] :
( ( ! [SY286: $i] :
( ~ ( ord_less_nat @ ( number_number_of_nat @ SV231 ) @ ( number_number_of_nat @ SY286 ) )
| ~ ( ord_less_int @ SV231 @ SY286 )
| ( ord_less_int @ pls @ SY286 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1028]) ).
thf(1104,plain,
! [SV232: $i] :
( ( ! [SY287: $i] :
( ~ ( ord_less_nat @ ( number_number_of_nat @ SV232 ) @ ( number_number_of_nat @ SY287 ) )
| ( ord_less_int @ SV232 @ SY287 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1029]) ).
thf(1105,plain,
! [SV209: $i,SV151: $i] :
( ( ( ord_less_eq_int @ ( number_number_of_int @ SV151 ) @ ( number_number_of_int @ SV209 ) )
= $false )
| ( ( ord_less_eq_int @ SV151 @ SV209 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1030]) ).
thf(1106,plain,
! [SV210: $i,SV152: $i] :
( ( ( ord_less_eq_int @ SV152 @ SV210 )
= $false )
| ( ( ord_less_eq_int @ ( number_number_of_int @ SV152 ) @ ( number_number_of_int @ SV210 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1031]) ).
thf(1107,plain,
! [SV211: $i,SV153: $i] :
( ( ( ord_less_eq_int @ ( bit1 @ SV153 ) @ ( bit1 @ SV211 ) )
= $false )
| ( ( ord_less_eq_int @ SV153 @ SV211 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1032]) ).
thf(1108,plain,
! [SV212: $i,SV154: $i] :
( ( ( ord_less_eq_int @ SV154 @ SV212 )
= $false )
| ( ( ord_less_eq_int @ ( bit1 @ SV154 ) @ ( bit1 @ SV212 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1033]) ).
thf(1109,plain,
! [SV213: $i,SV155: $i] :
( ( ( ord_less_eq_int @ SV155 @ SV213 )
= $false )
| ( ( ord_less_int @ ( bit0 @ SV155 ) @ ( bit1 @ SV213 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1034]) ).
thf(1110,plain,
! [SV214: $i,SV156: $i] :
( ( ( ord_less_int @ ( bit0 @ SV156 ) @ ( bit1 @ SV214 ) )
= $false )
| ( ( ord_less_eq_int @ SV156 @ SV214 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1035]) ).
thf(1111,plain,
! [SV215: $i,SV159: $i] :
( ( ( ord_less_eq_int @ ( bit1 @ SV159 ) @ ( bit0 @ SV215 ) )
= $false )
| ( ( ord_less_int @ SV159 @ SV215 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1038]) ).
thf(1112,plain,
! [SV216: $i,SV160: $i] :
( ( ( ord_less_int @ SV160 @ SV216 )
= $false )
| ( ( ord_less_eq_int @ ( bit1 @ SV160 ) @ ( bit0 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1039]) ).
thf(1113,plain,
! [SV86: $i,SV74: $i,SV45: $i,SV8: $i] :
( ( ( ord_less_eq_int @ SV8 @ SV45 )
= $false )
| ( ( ord_less_int @ ( plus_plus_int @ SV74 @ SV8 ) @ ( plus_plus_int @ SV86 @ SV45 ) )
= $true )
| ( ( ord_less_int @ SV74 @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1046]) ).
thf(1114,plain,
! [SV173: $i,SV93: $i] :
( ( ( SV93 = zero_zero_int )
= $false )
| ( ( SV173 != zero_zero_int )
= $true )
| ( ( ( plus_plus_int @ ( power_power_int @ SV93 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV173 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1054]) ).
thf(1115,plain,
! [SV217: $i] :
( ( ( ! [SY272: $i] :
( ( plus_plus_int @ ( power_power_int @ SV217 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SY272 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_int ) )
= $true )
| ( ( SV217 = zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1055]) ).
thf(1116,plain,
! [SV233: $i,SV218: $i] :
( ( ( ( plus_plus_int @ ( power_power_int @ SV218 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV233 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_int )
| ( SV233 = zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1056]) ).
thf(1117,plain,
! [SV96: $i,SV174: $i] :
( ( ( ord_less_nat @ ( number_number_of_nat @ SV174 ) @ ( number_number_of_nat @ SV96 ) )
= $false )
| ( ( ord_less_eq_nat @ ( number_number_of_nat @ SV96 ) @ ( number_number_of_nat @ SV174 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1057]) ).
thf(1118,plain,
! [SV180: $i,SV106: $i] :
( ( ( SV106 = zero_zero_int )
= $false )
| ( ( SV180 != zero_zero_int )
= $true )
| ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SV106 @ SV106 ) @ ( times_times_int @ SV180 @ SV180 ) ) @ zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1062]) ).
thf(1119,plain,
! [SV219: $i] :
( ( ( ! [SY274: $i] :
~ ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SV219 @ SV219 ) @ ( times_times_int @ SY274 @ SY274 ) ) @ zero_zero_int ) )
= $true )
| ( ( SV219 = zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1063]) ).
thf(1120,plain,
! [SV234: $i,SV220: $i] :
( ( ~ ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SV220 @ SV220 ) @ ( times_times_int @ SV234 @ SV234 ) ) @ zero_zero_int )
| ( SV234 = zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1064]) ).
thf(1121,plain,
! [SV197: $i,SV133: $i] :
( ( ( SV133 = zero_zero_int )
= $false )
| ( ( SV197 != zero_zero_int )
= $true )
| ( ( ( plus_plus_int @ ( times_times_int @ SV133 @ SV133 ) @ ( times_times_int @ SV197 @ SV197 ) )
= zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1081]) ).
thf(1122,plain,
! [SV221: $i] :
( ( ( ! [SY276: $i] :
( ( plus_plus_int @ ( times_times_int @ SV221 @ SV221 ) @ ( times_times_int @ SY276 @ SY276 ) )
!= zero_zero_int ) )
= $true )
| ( ( SV221 = zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1082]) ).
thf(1123,plain,
! [SV235: $i,SV222: $i] :
( ( ( ( plus_plus_int @ ( times_times_int @ SV222 @ SV222 ) @ ( times_times_int @ SV235 @ SV235 ) )
!= zero_zero_int )
| ( SV235 = zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1083]) ).
thf(1124,plain,
! [SV223: $i,SV236: $i] :
( ( ( ord_less_int @ SV236 @ pls )
| ~ ( ord_less_int @ SV223 @ pls )
| ( ( plus_plus_nat @ ( number_number_of_nat @ SV236 ) @ ( number_number_of_nat @ SV223 ) )
= ( number_number_of_nat @ SV236 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1085]) ).
thf(1125,plain,
! [SV224: $i,SV237: $i] :
( ( ( ord_less_int @ SV237 @ pls )
| ( ord_less_int @ SV224 @ pls )
| ( ( plus_plus_nat @ ( number_number_of_nat @ SV237 ) @ ( number_number_of_nat @ SV224 ) )
= ( number_number_of_nat @ ( plus_plus_int @ SV237 @ SV224 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1086]) ).
thf(1126,plain,
! [SV141: $i,SV201: $i] :
( ( ( ord_less_int @ ( number_number_of_int @ SV201 ) @ ( number_number_of_int @ SV141 ) )
= $false )
| ( ( ord_less_eq_int @ ( number_number_of_int @ SV141 ) @ ( number_number_of_int @ SV201 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1089]) ).
thf(1127,plain,
! [SV203: $i,SV143: $i] :
( ( ( SV143 != zero_zero_int )
= $true )
| ( ( SV203 != zero_zero_int )
= $true )
| ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ SV143 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV203 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1090]) ).
thf(1128,plain,
! [SV225: $i] :
( ( ( SV225 = zero_zero_int )
= $true )
| ( ( ! [SY280: $i] : ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ SV225 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SY280 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1091]) ).
thf(1129,plain,
! [SV226: $i,SV238: $i] :
( ( ( SV238 = zero_zero_int )
| ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ SV226 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV238 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1092]) ).
thf(1130,plain,
! [SV204: $i,SV144: $i] :
( ( ( ord_less_eq_int @ SV144 @ SV204 )
= $false )
| ( ( SV144 = SV204 )
= $true )
| ( ( ord_less_int @ SV144 @ SV204 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1093]) ).
thf(1131,plain,
! [SV239: $i,SV227: $i] :
( ( ~ ( ord_less_int @ SV227 @ SV239 )
| ( SV227 != SV239 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1094]) ).
thf(1132,plain,
! [SV240: $i,SV228: $i] :
( ( ~ ( ord_less_int @ SV228 @ SV240 )
| ( ord_less_eq_int @ SV228 @ SV240 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1095]) ).
thf(1133,plain,
! [SV241: $i,SV229: $i] :
( ( ( ord_less_int @ SV229 @ SV241 )
| ~ ( ord_less_int @ SV229 @ SV241 )
| ( ord_less_nat @ ( number_number_of_nat @ SV229 ) @ ( number_number_of_nat @ SV241 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1101]) ).
thf(1134,plain,
! [SV230: $i,SV242: $i] :
( ( ~ ( ord_less_int @ pls @ SV242 )
| ~ ( ord_less_int @ SV230 @ SV242 )
| ( ord_less_nat @ ( number_number_of_nat @ SV230 ) @ ( number_number_of_nat @ SV242 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1102]) ).
thf(1135,plain,
! [SV243: $i,SV231: $i] :
( ( ~ ( ord_less_nat @ ( number_number_of_nat @ SV231 ) @ ( number_number_of_nat @ SV243 ) )
| ~ ( ord_less_int @ SV231 @ SV243 )
| ( ord_less_int @ pls @ SV243 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1103]) ).
thf(1136,plain,
! [SV244: $i,SV232: $i] :
( ( ~ ( ord_less_nat @ ( number_number_of_nat @ SV232 ) @ ( number_number_of_nat @ SV244 ) )
| ( ord_less_int @ SV232 @ SV244 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1104]) ).
thf(1137,plain,
! [SV93: $i,SV173: $i] :
( ( ( SV173 = zero_zero_int )
= $false )
| ( ( SV93 = zero_zero_int )
= $false )
| ( ( ( plus_plus_int @ ( power_power_int @ SV93 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV173 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1114]) ).
thf(1138,plain,
! [SV245: $i,SV217: $i] :
( ( ( ( plus_plus_int @ ( power_power_int @ SV217 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV245 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_int )
= $true )
| ( ( SV217 = zero_zero_int )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1115]) ).
thf(1139,plain,
! [SV233: $i,SV218: $i] :
( ( ( ( plus_plus_int @ ( power_power_int @ SV218 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV233 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_int )
= $true )
| ( ( SV233 = zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1116]) ).
thf(1140,plain,
! [SV106: $i,SV180: $i] :
( ( ( SV180 = zero_zero_int )
= $false )
| ( ( SV106 = zero_zero_int )
= $false )
| ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SV106 @ SV106 ) @ ( times_times_int @ SV180 @ SV180 ) ) @ zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1118]) ).
thf(1141,plain,
! [SV246: $i,SV219: $i] :
( ( ( ~ ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SV219 @ SV219 ) @ ( times_times_int @ SV246 @ SV246 ) ) @ zero_zero_int ) )
= $true )
| ( ( SV219 = zero_zero_int )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1119]) ).
thf(1142,plain,
! [SV234: $i,SV220: $i] :
( ( ( ~ ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SV220 @ SV220 ) @ ( times_times_int @ SV234 @ SV234 ) ) @ zero_zero_int ) )
= $true )
| ( ( SV234 = zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1120]) ).
thf(1143,plain,
! [SV133: $i,SV197: $i] :
( ( ( SV197 = zero_zero_int )
= $false )
| ( ( SV133 = zero_zero_int )
= $false )
| ( ( ( plus_plus_int @ ( times_times_int @ SV133 @ SV133 ) @ ( times_times_int @ SV197 @ SV197 ) )
= zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1121]) ).
thf(1144,plain,
! [SV247: $i,SV221: $i] :
( ( ( ( plus_plus_int @ ( times_times_int @ SV221 @ SV221 ) @ ( times_times_int @ SV247 @ SV247 ) )
!= zero_zero_int )
= $true )
| ( ( SV221 = zero_zero_int )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1122]) ).
thf(1145,plain,
! [SV235: $i,SV222: $i] :
( ( ( ( plus_plus_int @ ( times_times_int @ SV222 @ SV222 ) @ ( times_times_int @ SV235 @ SV235 ) )
!= zero_zero_int )
= $true )
| ( ( SV235 = zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1123]) ).
thf(1146,plain,
! [SV223: $i,SV236: $i] :
( ( ( ord_less_int @ SV236 @ pls )
= $true )
| ( ( ~ ( ord_less_int @ SV223 @ pls )
| ( ( plus_plus_nat @ ( number_number_of_nat @ SV236 ) @ ( number_number_of_nat @ SV223 ) )
= ( number_number_of_nat @ SV236 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1124]) ).
thf(1147,plain,
! [SV224: $i,SV237: $i] :
( ( ( ord_less_int @ SV237 @ pls )
= $true )
| ( ( ( ord_less_int @ SV224 @ pls )
| ( ( plus_plus_nat @ ( number_number_of_nat @ SV237 ) @ ( number_number_of_nat @ SV224 ) )
= ( number_number_of_nat @ ( plus_plus_int @ SV237 @ SV224 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1125]) ).
thf(1148,plain,
! [SV203: $i,SV143: $i] :
( ( ( SV143 = zero_zero_int )
= $false )
| ( ( SV203 != zero_zero_int )
= $true )
| ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ SV143 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV203 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1127]) ).
thf(1149,plain,
! [SV248: $i,SV225: $i] :
( ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ SV225 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV248 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true )
| ( ( SV225 = zero_zero_int )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1128]) ).
thf(1150,plain,
! [SV226: $i,SV238: $i] :
( ( ( SV238 = zero_zero_int )
= $true )
| ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ SV226 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV238 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1129]) ).
thf(1151,plain,
! [SV239: $i,SV227: $i] :
( ( ( ~ ( ord_less_int @ SV227 @ SV239 ) )
= $true )
| ( ( SV227 != SV239 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1131]) ).
thf(1152,plain,
! [SV240: $i,SV228: $i] :
( ( ( ~ ( ord_less_int @ SV228 @ SV240 ) )
= $true )
| ( ( ord_less_eq_int @ SV228 @ SV240 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1132]) ).
thf(1153,plain,
! [SV241: $i,SV229: $i] :
( ( ( ( ord_less_int @ SV229 @ SV241 )
| ~ ( ord_less_int @ SV229 @ SV241 ) )
= $true )
| ( ( ord_less_nat @ ( number_number_of_nat @ SV229 ) @ ( number_number_of_nat @ SV241 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1133]) ).
thf(1154,plain,
! [SV230: $i,SV242: $i] :
( ( ( ~ ( ord_less_int @ pls @ SV242 )
| ~ ( ord_less_int @ SV230 @ SV242 ) )
= $true )
| ( ( ord_less_nat @ ( number_number_of_nat @ SV230 ) @ ( number_number_of_nat @ SV242 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1134]) ).
thf(1155,plain,
! [SV243: $i,SV231: $i] :
( ( ( ~ ( ord_less_nat @ ( number_number_of_nat @ SV231 ) @ ( number_number_of_nat @ SV243 ) ) )
= $true )
| ( ( ~ ( ord_less_int @ SV231 @ SV243 )
| ( ord_less_int @ pls @ SV243 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1135]) ).
thf(1156,plain,
! [SV244: $i,SV232: $i] :
( ( ( ~ ( ord_less_nat @ ( number_number_of_nat @ SV232 ) @ ( number_number_of_nat @ SV244 ) ) )
= $true )
| ( ( ord_less_int @ SV232 @ SV244 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1136]) ).
thf(1157,plain,
! [SV245: $i,SV217: $i] :
( ( ( ( plus_plus_int @ ( power_power_int @ SV217 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV245 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_int )
= $false )
| ( ( SV217 = zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1138]) ).
thf(1158,plain,
! [SV233: $i,SV218: $i] :
( ( ( ( plus_plus_int @ ( power_power_int @ SV218 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV233 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_int )
= $false )
| ( ( SV233 = zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1139]) ).
thf(1159,plain,
! [SV246: $i,SV219: $i] :
( ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SV219 @ SV219 ) @ ( times_times_int @ SV246 @ SV246 ) ) @ zero_zero_int )
= $false )
| ( ( SV219 = zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1141]) ).
thf(1160,plain,
! [SV234: $i,SV220: $i] :
( ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ SV220 @ SV220 ) @ ( times_times_int @ SV234 @ SV234 ) ) @ zero_zero_int )
= $false )
| ( ( SV234 = zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1142]) ).
thf(1161,plain,
! [SV247: $i,SV221: $i] :
( ( ( ( plus_plus_int @ ( times_times_int @ SV221 @ SV221 ) @ ( times_times_int @ SV247 @ SV247 ) )
= zero_zero_int )
= $false )
| ( ( SV221 = zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1144]) ).
thf(1162,plain,
! [SV235: $i,SV222: $i] :
( ( ( ( plus_plus_int @ ( times_times_int @ SV222 @ SV222 ) @ ( times_times_int @ SV235 @ SV235 ) )
= zero_zero_int )
= $false )
| ( ( SV235 = zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1145]) ).
thf(1163,plain,
! [SV236: $i,SV223: $i] :
( ( ( ~ ( ord_less_int @ SV223 @ pls ) )
= $true )
| ( ( ( plus_plus_nat @ ( number_number_of_nat @ SV236 ) @ ( number_number_of_nat @ SV223 ) )
= ( number_number_of_nat @ SV236 ) )
= $true )
| ( ( ord_less_int @ SV236 @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1146]) ).
thf(1164,plain,
! [SV237: $i,SV224: $i] :
( ( ( ord_less_int @ SV224 @ pls )
= $true )
| ( ( ( plus_plus_nat @ ( number_number_of_nat @ SV237 ) @ ( number_number_of_nat @ SV224 ) )
= ( number_number_of_nat @ ( plus_plus_int @ SV237 @ SV224 ) ) )
= $true )
| ( ( ord_less_int @ SV237 @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1147]) ).
thf(1165,plain,
! [SV143: $i,SV203: $i] :
( ( ( SV203 = zero_zero_int )
= $false )
| ( ( SV143 = zero_zero_int )
= $false )
| ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ SV143 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV203 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1148]) ).
thf(1166,plain,
! [SV239: $i,SV227: $i] :
( ( ( ord_less_int @ SV227 @ SV239 )
= $false )
| ( ( SV227 != SV239 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1151]) ).
thf(1167,plain,
! [SV240: $i,SV228: $i] :
( ( ( ord_less_int @ SV228 @ SV240 )
= $false )
| ( ( ord_less_eq_int @ SV228 @ SV240 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1152]) ).
thf(1168,plain,
! [SV241: $i,SV229: $i] :
( ( ( ord_less_int @ SV229 @ SV241 )
= $true )
| ( ( ~ ( ord_less_int @ SV229 @ SV241 ) )
= $true )
| ( ( ord_less_nat @ ( number_number_of_nat @ SV229 ) @ ( number_number_of_nat @ SV241 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1153]) ).
thf(1169,plain,
! [SV230: $i,SV242: $i] :
( ( ( ~ ( ord_less_int @ pls @ SV242 ) )
= $true )
| ( ( ~ ( ord_less_int @ SV230 @ SV242 ) )
= $true )
| ( ( ord_less_nat @ ( number_number_of_nat @ SV230 ) @ ( number_number_of_nat @ SV242 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1154]) ).
thf(1170,plain,
! [SV243: $i,SV231: $i] :
( ( ( ord_less_nat @ ( number_number_of_nat @ SV231 ) @ ( number_number_of_nat @ SV243 ) )
= $false )
| ( ( ~ ( ord_less_int @ SV231 @ SV243 )
| ( ord_less_int @ pls @ SV243 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1155]) ).
thf(1171,plain,
! [SV244: $i,SV232: $i] :
( ( ( ord_less_nat @ ( number_number_of_nat @ SV232 ) @ ( number_number_of_nat @ SV244 ) )
= $false )
| ( ( ord_less_int @ SV232 @ SV244 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1156]) ).
thf(1172,plain,
! [SV236: $i,SV223: $i] :
( ( ( ord_less_int @ SV223 @ pls )
= $false )
| ( ( ( plus_plus_nat @ ( number_number_of_nat @ SV236 ) @ ( number_number_of_nat @ SV223 ) )
= ( number_number_of_nat @ SV236 ) )
= $true )
| ( ( ord_less_int @ SV236 @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1163]) ).
thf(1173,plain,
! [SV239: $i,SV227: $i] :
( ( ( SV227 = SV239 )
= $false )
| ( ( ord_less_int @ SV227 @ SV239 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1166]) ).
thf(1174,plain,
! [SV241: $i,SV229: $i] :
( ( ( ord_less_int @ SV229 @ SV241 )
= $false )
| ( ( ord_less_int @ SV229 @ SV241 )
= $true )
| ( ( ord_less_nat @ ( number_number_of_nat @ SV229 ) @ ( number_number_of_nat @ SV241 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1168]) ).
thf(1175,plain,
! [SV230: $i,SV242: $i] :
( ( ( ord_less_int @ pls @ SV242 )
= $false )
| ( ( ~ ( ord_less_int @ SV230 @ SV242 ) )
= $true )
| ( ( ord_less_nat @ ( number_number_of_nat @ SV230 ) @ ( number_number_of_nat @ SV242 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1169]) ).
thf(1176,plain,
! [SV243: $i,SV231: $i] :
( ( ( ~ ( ord_less_int @ SV231 @ SV243 ) )
= $true )
| ( ( ord_less_int @ pls @ SV243 )
= $true )
| ( ( ord_less_nat @ ( number_number_of_nat @ SV231 ) @ ( number_number_of_nat @ SV243 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1170]) ).
thf(1177,plain,
! [SV242: $i,SV230: $i] :
( ( ( ord_less_int @ SV230 @ SV242 )
= $false )
| ( ( ord_less_int @ pls @ SV242 )
= $false )
| ( ( ord_less_nat @ ( number_number_of_nat @ SV230 ) @ ( number_number_of_nat @ SV242 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1175]) ).
thf(1178,plain,
! [SV243: $i,SV231: $i] :
( ( ( ord_less_int @ SV231 @ SV243 )
= $false )
| ( ( ord_less_int @ pls @ SV243 )
= $true )
| ( ( ord_less_nat @ ( number_number_of_nat @ SV231 ) @ ( number_number_of_nat @ SV243 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1176]) ).
thf(1179,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[272,1178,1177,1174,1173,1172,1171,1167,1165,1164,1162,1161,1160,1159,1158,1157,1150,1149,1143,1140,1137,1130,1126,1117,1113,1112,1111,1110,1109,1108,1107,1106,1105,1100,1099,1098,1097,1096,1088,1087,1084,1080,1079,1078,1077,1076,1075,1074,1073,1072,1071,1070,1069,1068,1067,1066,1065,1061,1060,1059,1058,1053,1052,1051,1050,1049,1048,1047,1045,1044,1043,1042,1041,1040,1037,1036,1014,1012,1011,1008,1007,1000,999,998,997,990,989,986,985,978,977,971,970,969,968,963,961,960,950,949,948,946,945,922,840,747,744,653,648,647,646,645,644,643,642,641,639,635,634,631,630,541,540,533,531,530,516,515,513,510,508,463,451,450,434,433,431,426,425,422,358,357,356,355,354,353,333,332,315,312,311,291,284,283,282,281,273]) ).
thf(1180,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[1179]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM924+1 : 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
% 0.07/0.19 % Computer : n017.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Oct 6 13:39:55 UTC 2026
% 0.07/0.20 % CPUTime :
% 0.07/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.98/1.22
% 5.98/1.22 No.of.Axioms: 106
% 5.98/1.22
% 5.98/1.22 Length.of.Defs: 0
% 5.98/1.22
% 5.98/1.22 Contains.Choice.Funs: false
% 5.98/1.22 ........................................
% 5.98/1.22
% 5.98/1.22 ********************************
% 5.98/1.22 * All subproblems solved! *
% 5.98/1.22 ********************************
% 5.98/1.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:2,axioms:104,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:1179,loop_count:0,foatp_calls:1,translation:fof_full)
% 5.98/1.22
% 5.98/1.22 %**** Beginning of derivation protocol ****
% 5.98/1.22 % SZS output start CNFRefutation
% See solution above
% 5.98/1.23
% 5.98/1.23 %**** End of derivation protocol ****
% 5.98/1.23 %**** no. of clauses in derivation: 1178 ****
% 5.98/1.23 %**** clause counter: 1179 ****
% 5.98/1.23
% 5.98/1.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:2,axioms:104,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:1179,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------