TSTP Solution File: NUM925+1 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : NUM925+1 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 11:57:47 EDT 2022
% Result : Theorem 1.75s 1.98s
% Output : CNFRefutation 2.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 126
% Syntax : Number of formulae : 1034 ( 791 unt; 19 typ; 0 def)
% Number of atoms : 4484 (2325 equ; 0 cnn)
% Maximal formula atoms : 7 ( 4 avg)
% Number of connectives : 8714 (1210 ~;1065 |; 104 &;6245 @)
% ( 72 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 19 usr; 9 con; 0-2 aty)
% Number of variables : 1791 ( 0 ^1791 !; 0 ?;1791 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_bit0,type,
bit0: $i > $i ).
thf(tp_bit1,type,
bit1: $i > $i ).
thf(tp_n,type,
n: $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_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_semiri1621563631at_int,type,
semiri1621563631at_int: $i > $i ).
thf(tp_semiri984289939at_nat,type,
semiri984289939at_nat: $i > $i ).
thf(tp_t,type,
t: $i ).
thf(tp_zero_zero_int,type,
zero_zero_int: $i ).
thf(tp_zero_zero_nat,type,
zero_zero_nat: $i ).
thf(1,axiom,
! [Xa: $i,Ya: $i] :
( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ Xa @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Ya @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
<=> ( ( Xa != zero_zero_int )
| ( Ya != zero_zero_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_sum__power2__gt__zero__iff) ).
thf(2,axiom,
! [A: $i] :
~ ( ord_less_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_power2__less__0) ).
thf(3,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/sandbox/benchmark/theBenchmark.p',fact_103_zero__less__power2) ).
thf(4,axiom,
! [N: $i] :
( ( number_number_of_int @ ( semiri1621563631at_int @ N ) )
= ( semiri1621563631at_int @ N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_number__of__int) ).
thf(5,axiom,
! [N: $i] :
( ( number_number_of_nat @ ( semiri1621563631at_int @ N ) )
= ( semiri984289939at_nat @ N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_number__of__int) ).
thf(6,axiom,
! [Z: $i] :
( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z )
!= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_odd__nonzero) ).
thf(7,axiom,
! [K: $i] :
( ( bit1 @ K )
= ( plus_plus_int @ ( plus_plus_int @ one_one_int @ K ) @ K ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_Bit1__def) ).
thf(8,axiom,
! [K: $i,L: $i] :
( ( plus_plus_int @ ( bit0 @ K ) @ ( bit1 @ L ) )
= ( bit1 @ ( plus_plus_int @ K @ L ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_add__Bit0__Bit1) ).
thf(9,axiom,
! [K: $i,L: $i] :
( ( plus_plus_int @ ( bit1 @ K ) @ ( bit0 @ L ) )
= ( bit1 @ ( plus_plus_int @ K @ L ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_add__Bit1__Bit0) ).
thf(10,axiom,
! [V: $i,W: $i] :
( ( number_number_of_int @ ( plus_plus_int @ V @ W ) )
= ( plus_plus_int @ ( number_number_of_int @ V ) @ ( number_number_of_int @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_number__of__add) ).
thf(11,axiom,
! [V_1: $i,W_1: $i] :
( ( plus_plus_int @ ( number_number_of_int @ V_1 ) @ ( number_number_of_int @ W_1 ) )
= ( number_number_of_int @ ( plus_plus_int @ V_1 @ W_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_add__number__of__eq) ).
thf(12,axiom,
! [V_2: $i,W_2: $i,Z_1: $i] :
( ( plus_plus_int @ ( number_number_of_int @ V_2 ) @ ( plus_plus_int @ ( number_number_of_int @ W_2 ) @ Z_1 ) )
= ( plus_plus_int @ ( number_number_of_int @ ( plus_plus_int @ V_2 @ W_2 ) ) @ Z_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_add__number__of__left) ).
thf(13,axiom,
! [A_1: $i,Wa: $i] :
( ( ( power_power_nat @ A_1 @ ( number_number_of_nat @ Wa ) )
= zero_zero_nat )
<=> ( ( A_1 = zero_zero_nat )
& ( ( number_number_of_nat @ Wa )
!= zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_power__eq__0__iff__number__of) ).
thf(14,axiom,
! [A_1: $i,Wa: $i] :
( ( ( power_power_int @ A_1 @ ( number_number_of_nat @ Wa ) )
= zero_zero_int )
<=> ( ( A_1 = zero_zero_int )
& ( ( number_number_of_nat @ Wa )
!= zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_power__eq__0__iff__number__of) ).
thf(15,axiom,
! [A_2: $i] :
( ( plus_plus_int @ A_2 @ ( number_number_of_int @ pls ) )
= A_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_add__numeral__0__right) ).
thf(16,axiom,
! [A_3: $i] :
( ( plus_plus_int @ ( number_number_of_int @ pls ) @ A_3 )
= A_3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_add__numeral__0) ).
thf(17,axiom,
( zero_zero_int
= ( number_number_of_int @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_semiring__norm_I112_J) ).
thf(18,axiom,
( ( number_number_of_int @ pls )
= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_number__of__Pls) ).
thf(19,axiom,
( ( number_number_of_nat @ pls )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_semiring__numeral__0__eq__0) ).
thf(20,axiom,
( ( number_number_of_int @ pls )
= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_semiring__numeral__0__eq__0) ).
thf(21,axiom,
! [Z: $i] :
( ( plus_plus_int @ zero_zero_int @ Z )
= Z ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_zadd__0) ).
thf(22,axiom,
! [Z: $i] :
( ( plus_plus_int @ Z @ zero_zero_int )
= Z ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_zadd__0__right) ).
thf(23,axiom,
! [K: $i] :
( ( bit0 @ K )
= ( plus_plus_int @ K @ K ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_Bit0__def) ).
thf(24,axiom,
! [K: $i,L: $i] :
( ( plus_plus_int @ ( bit0 @ K ) @ ( bit0 @ L ) )
= ( bit0 @ ( plus_plus_int @ K @ L ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_add__Bit0__Bit0) ).
thf(25,axiom,
! [K: $i] :
( ( plus_plus_int @ pls @ K )
= K ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_add__Pls) ).
thf(26,axiom,
! [K: $i] :
( ( plus_plus_int @ K @ pls )
= K ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_add__Pls__right) ).
thf(27,axiom,
zero_zero_int != one_one_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_int__0__neq__1) ).
thf(28,axiom,
pls = zero_zero_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_Pls__def) ).
thf(29,axiom,
( ( bit0 @ pls )
= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_Bit0__Pls) ).
thf(30,axiom,
! [L_1: $i] :
( ( pls
= ( bit0 @ L_1 ) )
<=> ( pls = L_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_rel__simps_I38_J) ).
thf(31,axiom,
! [K_1: $i] :
( ( ( bit0 @ K_1 )
= pls )
<=> ( K_1 = pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_rel__simps_I44_J) ).
thf(32,axiom,
! [K: $i,L: $i] :
( ( bit0 @ K )
!= ( bit1 @ L ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_rel__simps_I49_J) ).
thf(33,axiom,
! [K: $i,L: $i] :
( ( bit1 @ K )
!= ( bit0 @ L ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_rel__simps_I50_J) ).
thf(34,axiom,
! [L: $i] :
( pls
!= ( bit1 @ L ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_rel__simps_I39_J) ).
thf(35,axiom,
! [K: $i] :
( ( bit1 @ K )
!= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_rel__simps_I46_J) ).
thf(36,axiom,
! [A_1: $i] :
( ( ( plus_plus_int @ A_1 @ A_1 )
= zero_zero_int )
<=> ( A_1 = zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_double__eq__0__iff) ).
thf(37,axiom,
! [Z_2: $i] :
( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z_2 ) @ Z_2 ) @ zero_zero_int )
<=> ( ord_less_int @ Z_2 @ zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_odd__less__0) ).
thf(38,axiom,
! [Ya: $i] :
( ( ord_less_int @ one_one_int @ ( number_number_of_int @ Ya ) )
<=> ( ord_less_int @ ( bit1 @ pls ) @ Ya ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_less__special_I2_J) ).
thf(39,axiom,
! [Xa: $i] :
( ( ord_less_int @ ( number_number_of_int @ Xa ) @ one_one_int )
<=> ( ord_less_int @ Xa @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_less__special_I4_J) ).
thf(40,axiom,
! [K: $i] :
~ ( ord_less_int @ ( semiri1621563631at_int @ K ) @ zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_int__less__0__conv) ).
thf(41,axiom,
! [Wa: $i,Z_2: $i] :
( ( ord_less_int @ Wa @ ( plus_plus_int @ Z_2 @ one_one_int ) )
<=> ( ( ord_less_int @ Wa @ Z_2 )
| ( Wa = Z_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_zless__add1__eq) ).
thf(42,axiom,
ord_less_int @ zero_zero_int @ one_one_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_int__0__less__1) ).
thf(43,axiom,
! [Wa: $i] :
( ( ord_less_int @ ( bit0 @ Wa ) @ zero_zero_int )
<=> ( ord_less_int @ Wa @ zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_bin__less__0__simps_I3_J) ).
thf(44,axiom,
~ ( ord_less_int @ pls @ zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_bin__less__0__simps_I1_J) ).
thf(45,axiom,
! [Wa: $i] :
( ( ord_less_int @ ( bit1 @ Wa ) @ zero_zero_int )
<=> ( ord_less_int @ Wa @ zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_bin__less__0__simps_I4_J) ).
thf(46,axiom,
! [K_1: $i] :
( ( ord_less_int @ pls @ ( bit0 @ K_1 ) )
<=> ( ord_less_int @ pls @ K_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_rel__simps_I4_J) ).
thf(47,axiom,
! [K_1: $i] :
( ( ord_less_int @ ( bit0 @ K_1 ) @ pls )
<=> ( ord_less_int @ K_1 @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_rel__simps_I10_J) ).
thf(48,axiom,
! [K_1: $i,L_1: $i] :
( ( ord_less_int @ ( bit1 @ K_1 ) @ ( bit0 @ L_1 ) )
<=> ( ord_less_int @ K_1 @ L_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_rel__simps_I16_J) ).
thf(49,axiom,
! [K1: $i,K2: $i] :
( ( ord_less_int @ ( bit1 @ K1 ) @ ( bit0 @ K2 ) )
<=> ( ord_less_int @ K1 @ K2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_less__int__code_I15_J) ).
thf(50,axiom,
! [K_1: $i] :
( ( ord_less_int @ ( bit1 @ K_1 ) @ pls )
<=> ( ord_less_int @ K_1 @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_rel__simps_I12_J) ).
thf(51,axiom,
! [Ya: $i] :
( ( ord_less_int @ zero_zero_int @ ( number_number_of_int @ Ya ) )
<=> ( ord_less_int @ pls @ Ya ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_less__special_I1_J) ).
thf(52,axiom,
! [Xa: $i] :
( ( ord_less_int @ ( number_number_of_int @ Xa ) @ zero_zero_int )
<=> ( ord_less_int @ Xa @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_less__special_I3_J) ).
thf(53,axiom,
! [Ma: $i,Na: $i] :
( ( ( semiri1621563631at_int @ Ma )
= ( semiri1621563631at_int @ Na ) )
<=> ( Ma = Na ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_int__int__eq) ).
thf(54,axiom,
! [Z: $i,W_3: $i] :
( ( plus_plus_int @ Z @ W_3 )
= ( plus_plus_int @ W_3 @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_zadd__commute) ).
thf(55,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/sandbox/benchmark/theBenchmark.p',fact_51_zadd__left__commute) ).
thf(56,axiom,
! [Z1: $i,Z2: $i,Z3: $i] :
( ( plus_plus_int @ ( plus_plus_int @ Z1 @ Z2 ) @ Z3 )
= ( plus_plus_int @ Z1 @ ( plus_plus_int @ Z2 @ Z3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_zadd__assoc) ).
thf(57,axiom,
! [A_1: $i] :
( ( ord_less_int @ ( plus_plus_int @ A_1 @ A_1 ) @ zero_zero_int )
<=> ( ord_less_int @ A_1 @ zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_even__less__0__iff) ).
thf(58,axiom,
! [K_1: $i,L_1: $i] :
( ( ( bit0 @ K_1 )
= ( bit0 @ L_1 ) )
<=> ( K_1 = L_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_rel__simps_I48_J) ).
thf(59,axiom,
! [K_1: $i,L_1: $i] :
( ( ( bit1 @ K_1 )
= ( bit1 @ L_1 ) )
<=> ( K_1 = L_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_rel__simps_I51_J) ).
thf(60,axiom,
! [Wa: $i,Xa: $i] :
( ( ( number_number_of_int @ Wa )
= Xa )
<=> ( Xa
= ( number_number_of_int @ Wa ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_number__of__reorient) ).
thf(61,axiom,
! [Wa: $i,Xa: $i] :
( ( ( number_number_of_nat @ Wa )
= Xa )
<=> ( Xa
= ( number_number_of_nat @ Wa ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_number__of__reorient) ).
thf(62,axiom,
! [Xa: $i,Ya: $i] :
( ( ( number_number_of_int @ Xa )
= ( number_number_of_int @ Ya ) )
<=> ( Xa = Ya ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_eq__number__of) ).
thf(63,axiom,
( one_one_nat
= ( number_number_of_nat @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_Numeral1__eq1__nat) ).
thf(64,axiom,
( ( number_number_of_nat @ ( bit1 @ pls ) )
= one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_nat__numeral__1__eq__1) ).
thf(65,axiom,
( one_one_int
= ( number_number_of_int @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_one__is__num__one) ).
thf(66,axiom,
! [V_4: $i,V_3: $i] :
( ( ( ord_less_int @ V_3 @ pls )
=> ( ( plus_plus_nat @ ( number_number_of_nat @ V_3 ) @ ( number_number_of_nat @ V_4 ) )
= ( number_number_of_nat @ V_4 ) ) )
& ( ~ ( ord_less_int @ V_3 @ pls )
=> ( ( ( ord_less_int @ V_4 @ pls )
=> ( ( plus_plus_nat @ ( number_number_of_nat @ V_3 ) @ ( number_number_of_nat @ V_4 ) )
= ( number_number_of_nat @ V_3 ) ) )
& ( ~ ( ord_less_int @ V_4 @ pls )
=> ( ( plus_plus_nat @ ( number_number_of_nat @ V_3 ) @ ( number_number_of_nat @ V_4 ) )
= ( number_number_of_nat @ ( plus_plus_int @ V_3 @ V_4 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_add__nat__number__of) ).
thf(67,axiom,
! [K: $i,I: $i,J: $i] :
( ( ord_less_int @ I @ J )
=> ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ K ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_zadd__strict__right__mono) ).
thf(68,axiom,
! [K_1: $i,L_1: $i] :
( ( ord_less_int @ ( bit0 @ K_1 ) @ ( bit0 @ L_1 ) )
<=> ( ord_less_int @ K_1 @ L_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_rel__simps_I14_J) ).
thf(69,axiom,
! [K1: $i,K2: $i] :
( ( ord_less_int @ ( bit0 @ K1 ) @ ( bit0 @ K2 ) )
<=> ( ord_less_int @ K1 @ K2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_less__int__code_I13_J) ).
thf(70,axiom,
~ ( ord_less_int @ pls @ pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_rel__simps_I2_J) ).
thf(71,axiom,
! [K_1: $i,L_1: $i] :
( ( ord_less_int @ ( bit1 @ K_1 ) @ ( bit1 @ L_1 ) )
<=> ( ord_less_int @ K_1 @ L_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_rel__simps_I17_J) ).
thf(72,axiom,
! [K1: $i,K2: $i] :
( ( ord_less_int @ ( bit1 @ K1 ) @ ( bit1 @ K2 ) )
<=> ( ord_less_int @ K1 @ K2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_less__int__code_I16_J) ).
thf(73,axiom,
( ( plus_plus_nat @ one_one_nat @ one_one_nat )
= ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_nat__1__add__1) ).
thf(74,axiom,
( ( semiri1621563631at_int @ zero_zero_nat )
= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_int__0) ).
thf(75,axiom,
! [Na: $i] :
( ( ( semiri1621563631at_int @ Na )
= zero_zero_int )
<=> ( Na = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_int__eq__0__conv) ).
thf(76,axiom,
( zero_zero_nat
= ( number_number_of_nat @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_semiring__norm_I113_J) ).
thf(77,axiom,
( ( number_number_of_nat @ pls )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_nat__number__of__Pls) ).
thf(78,axiom,
( ( semiri1621563631at_int @ one_one_nat )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_int__1) ).
thf(79,axiom,
! [M: $i,N_1: $i] :
( ( plus_plus_int @ ( semiri1621563631at_int @ M ) @ ( semiri1621563631at_int @ N_1 ) )
= ( semiri1621563631at_int @ ( plus_plus_nat @ M @ N_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_zadd__int) ).
thf(80,axiom,
! [M: $i,N_1: $i,Z: $i] :
( ( plus_plus_int @ ( semiri1621563631at_int @ M ) @ ( plus_plus_int @ ( semiri1621563631at_int @ N_1 ) @ Z ) )
= ( plus_plus_int @ ( semiri1621563631at_int @ ( plus_plus_nat @ M @ N_1 ) ) @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_zadd__int__left) ).
thf(81,axiom,
! [M: $i,N_1: $i] :
( ( semiri1621563631at_int @ ( power_power_nat @ M @ N_1 ) )
= ( power_power_int @ ( semiri1621563631at_int @ M ) @ N_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_int__power) ).
thf(82,axiom,
! [M: $i,N_1: $i] :
( ( power_power_int @ ( semiri1621563631at_int @ M ) @ N_1 )
= ( semiri1621563631at_int @ ( power_power_nat @ M @ N_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_zpower__int) ).
thf(83,axiom,
( zero_zero_int
= ( number_number_of_int @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_zero__is__num__zero) ).
thf(84,axiom,
! [Xa: $i,Ya: $i] :
( ( ord_less_int @ ( number_number_of_int @ Xa ) @ ( number_number_of_int @ Ya ) )
<=> ( ord_less_int @ Xa @ Ya ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_less__number__of) ).
thf(85,axiom,
! [V_3: $i,W_3: $i] :
( ( plus_plus_int @ ( number_number_of_int @ V_3 ) @ ( number_number_of_int @ W_3 ) )
= ( number_number_of_int @ ( plus_plus_int @ V_3 @ W_3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_plus__numeral__code_I9_J) ).
thf(86,axiom,
! [K_1: $i,L_1: $i] :
( ( ord_less_int @ ( number_number_of_int @ K_1 ) @ ( number_number_of_int @ L_1 ) )
<=> ( ord_less_int @ K_1 @ L_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_less__number__of__int__code) ).
thf(87,axiom,
! [X: $i,Y: $i] :
( ( ord_less_int @ X @ Y )
| ( X = Y )
| ( ord_less_int @ Y @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_zless__linear) ).
thf(88,axiom,
ord_less_nat @ zero_zero_nat @ n,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_n0) ).
thf(89,axiom,
( ( number_number_of_int @ ( bit1 @ pls ) )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_numeral__1__eq__1) ).
thf(90,axiom,
( one_one_int
= ( number_number_of_int @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_semiring__norm_I110_J) ).
thf(91,axiom,
! [W_4: $i] :
( ( ( ( number_number_of_nat @ W_4 )
= zero_zero_nat )
=> ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ W_4 ) )
= one_one_nat ) )
& ( ( ( number_number_of_nat @ W_4 )
!= zero_zero_nat )
=> ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ W_4 ) )
= zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_power__0__left__number__of) ).
thf(92,axiom,
! [W_4: $i] :
( ( ( ( number_number_of_nat @ W_4 )
= zero_zero_nat )
=> ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ W_4 ) )
= one_one_int ) )
& ( ( ( number_number_of_nat @ W_4 )
!= zero_zero_nat )
=> ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ W_4 ) )
= zero_zero_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_power__0__left__number__of) ).
thf(93,axiom,
! [X: $i] :
( ( power_power_int @ ( power_power_int @ X @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power_int @ X @ ( number_number_of_nat @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_quartic__square__square) ).
thf(94,axiom,
( ( plus_plus_nat @ one_one_nat @ one_one_nat )
= ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_semiring__one__add__one__is__two) ).
thf(95,axiom,
( ( plus_plus_int @ one_one_int @ one_one_int )
= ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_semiring__one__add__one__is__two) ).
thf(96,axiom,
( ( plus_plus_int @ one_one_int @ one_one_int )
= ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_one__add__one__is__two) ).
thf(97,axiom,
! [V_5: $i] :
( ( plus_plus_int @ ( number_number_of_int @ V_5 ) @ one_one_int )
= ( number_number_of_int @ ( plus_plus_int @ V_5 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_add__special_I3_J) ).
thf(98,axiom,
! [W_5: $i] :
( ( plus_plus_int @ one_one_int @ ( number_number_of_int @ W_5 ) )
= ( number_number_of_int @ ( plus_plus_int @ ( bit1 @ pls ) @ W_5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_add__special_I2_J) ).
thf(99,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/sandbox/benchmark/theBenchmark.p',fact_7_zero__eq__power2) ).
thf(100,axiom,
( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_zero__power2) ).
thf(101,axiom,
( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_zero__power2) ).
thf(102,axiom,
( ( power_power_nat @ one_one_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_one__power2) ).
thf(103,axiom,
( ( power_power_int @ one_one_int @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_one__power2) ).
thf(104,axiom,
! [Xa: $i,Ya: $i] :
( ( ( plus_plus_int @ ( power_power_int @ Xa @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Ya @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_int )
<=> ( ( Xa = zero_zero_int )
& ( Ya = zero_zero_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_sum__power2__eq__zero__iff) ).
thf(105,axiom,
ord_less_int @ one_one_int @ t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_t1) ).
thf(106,axiom,
ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_n1pos) ).
thf(107,conjecture,
( power_power_int @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= zero_zero_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(108,negated_conjecture,
( ( ( ( power_power_int @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= zero_zero_int ) )
= $false ),
inference(negate_conjecture,[status(cth)],[107]) ).
thf(109,plain,
( ( ( ( power_power_int @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= zero_zero_int ) )
= $false ),
inference(unfold_def,[status(thm)],[108]) ).
thf(110,plain,
( ( ! [Wa: $i,Xa: $i] :
( ( ( number_number_of_int @ Wa )
= Xa )
<=> ( Xa
= ( number_number_of_int @ Wa ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(111,plain,
( ( ! [Xa: $i,Ya: $i] :
( ( ( number_number_of_int @ Xa )
= ( number_number_of_int @ Ya ) )
<=> ( Xa = Ya ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(112,plain,
( ( ! [Xa: $i,Ya: $i] :
( ( ord_less_int @ ( number_number_of_int @ Xa ) @ ( number_number_of_int @ Ya ) )
<=> ( ord_less_int @ Xa @ Ya ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(113,plain,
( ( ! [K_1: $i,L_1: $i] :
( ( ord_less_int @ ( number_number_of_int @ K_1 ) @ ( number_number_of_int @ L_1 ) )
<=> ( ord_less_int @ K_1 @ L_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(114,plain,
( ( ! [X: $i,Y: $i] :
( ( ord_less_int @ X @ Y )
| ( X = Y )
| ( ord_less_int @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(115,plain,
( ( ! [W_4: $i] :
( ( ( ( number_number_of_nat @ W_4 )
= zero_zero_nat )
=> ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ W_4 ) )
= one_one_nat ) )
& ( ( ( number_number_of_nat @ W_4 )
!= zero_zero_nat )
=> ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ W_4 ) )
= zero_zero_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(116,plain,
( ( ! [Xa: $i,Ya: $i] :
( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ Xa @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Ya @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
<=> ( ( Xa != zero_zero_int )
| ( Ya != zero_zero_int ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(117,plain,
( ( ! [A: $i] :
~ ( ord_less_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ zero_zero_int ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(118,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)],[3]) ).
thf(119,plain,
( ( ! [N: $i] :
( ( number_number_of_int @ ( semiri1621563631at_int @ N ) )
= ( semiri1621563631at_int @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(120,plain,
( ( ! [N: $i] :
( ( number_number_of_nat @ ( semiri1621563631at_int @ N ) )
= ( semiri984289939at_nat @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(121,plain,
( ( ! [Z: $i] :
( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z )
!= zero_zero_int ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(122,plain,
( ( ! [K: $i] :
( ( bit1 @ K )
= ( plus_plus_int @ ( plus_plus_int @ one_one_int @ K ) @ K ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(123,plain,
( ( ! [K: $i,L: $i] :
( ( plus_plus_int @ ( bit0 @ K ) @ ( bit1 @ L ) )
= ( bit1 @ ( plus_plus_int @ K @ L ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(124,plain,
( ( ! [K: $i,L: $i] :
( ( plus_plus_int @ ( bit1 @ K ) @ ( bit0 @ L ) )
= ( bit1 @ ( plus_plus_int @ K @ L ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(125,plain,
( ( ! [V: $i,W: $i] :
( ( number_number_of_int @ ( plus_plus_int @ V @ W ) )
= ( plus_plus_int @ ( number_number_of_int @ V ) @ ( number_number_of_int @ W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(126,plain,
( ( ! [V_1: $i,W_1: $i] :
( ( plus_plus_int @ ( number_number_of_int @ V_1 ) @ ( number_number_of_int @ W_1 ) )
= ( number_number_of_int @ ( plus_plus_int @ V_1 @ W_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(127,plain,
( ( ! [V_2: $i,W_2: $i,Z_1: $i] :
( ( plus_plus_int @ ( number_number_of_int @ V_2 ) @ ( plus_plus_int @ ( number_number_of_int @ W_2 ) @ Z_1 ) )
= ( plus_plus_int @ ( number_number_of_int @ ( plus_plus_int @ V_2 @ W_2 ) ) @ Z_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(128,plain,
( ( ! [A_1: $i,Wa: $i] :
( ( ( power_power_nat @ A_1 @ ( number_number_of_nat @ Wa ) )
= zero_zero_nat )
<=> ( ( A_1 = zero_zero_nat )
& ( ( number_number_of_nat @ Wa )
!= zero_zero_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(129,plain,
( ( ! [A_1: $i,Wa: $i] :
( ( ( power_power_int @ A_1 @ ( number_number_of_nat @ Wa ) )
= zero_zero_int )
<=> ( ( A_1 = zero_zero_int )
& ( ( number_number_of_nat @ Wa )
!= zero_zero_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(130,plain,
( ( ! [A_2: $i] :
( ( plus_plus_int @ A_2 @ ( number_number_of_int @ pls ) )
= A_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(131,plain,
( ( ! [A_3: $i] :
( ( plus_plus_int @ ( number_number_of_int @ pls ) @ A_3 )
= A_3 ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(132,plain,
( ( zero_zero_int
= ( number_number_of_int @ pls ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(133,plain,
( ( ( number_number_of_int @ pls )
= zero_zero_int )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(134,plain,
( ( ( number_number_of_nat @ pls )
= zero_zero_nat )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(135,plain,
( ( ( number_number_of_int @ pls )
= zero_zero_int )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(136,plain,
( ( ! [Z: $i] :
( ( plus_plus_int @ zero_zero_int @ Z )
= Z ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(137,plain,
( ( ! [Z: $i] :
( ( plus_plus_int @ Z @ zero_zero_int )
= Z ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(138,plain,
( ( ! [K: $i] :
( ( bit0 @ K )
= ( plus_plus_int @ K @ K ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(139,plain,
( ( ! [K: $i,L: $i] :
( ( plus_plus_int @ ( bit0 @ K ) @ ( bit0 @ L ) )
= ( bit0 @ ( plus_plus_int @ K @ L ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(140,plain,
( ( ! [K: $i] :
( ( plus_plus_int @ pls @ K )
= K ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(141,plain,
( ( ! [K: $i] :
( ( plus_plus_int @ K @ pls )
= K ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(142,plain,
( ( ( zero_zero_int != one_one_int ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(143,plain,
( ( pls = zero_zero_int )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(144,plain,
( ( ( bit0 @ pls )
= pls )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(145,plain,
( ( ! [L_1: $i] :
( ( pls
= ( bit0 @ L_1 ) )
<=> ( pls = L_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(146,plain,
( ( ! [K_1: $i] :
( ( ( bit0 @ K_1 )
= pls )
<=> ( K_1 = pls ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(147,plain,
( ( ! [K: $i,L: $i] :
( ( bit0 @ K )
!= ( bit1 @ L ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(148,plain,
( ( ! [K: $i,L: $i] :
( ( bit1 @ K )
!= ( bit0 @ L ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(149,plain,
( ( ! [L: $i] :
( pls
!= ( bit1 @ L ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(150,plain,
( ( ! [K: $i] :
( ( bit1 @ K )
!= pls ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(151,plain,
( ( ! [A_1: $i] :
( ( ( plus_plus_int @ A_1 @ A_1 )
= zero_zero_int )
<=> ( A_1 = zero_zero_int ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(152,plain,
( ( ! [Z_2: $i] :
( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z_2 ) @ Z_2 ) @ zero_zero_int )
<=> ( ord_less_int @ Z_2 @ zero_zero_int ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(153,plain,
( ( ! [Ya: $i] :
( ( ord_less_int @ one_one_int @ ( number_number_of_int @ Ya ) )
<=> ( ord_less_int @ ( bit1 @ pls ) @ Ya ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(154,plain,
( ( ! [Xa: $i] :
( ( ord_less_int @ ( number_number_of_int @ Xa ) @ one_one_int )
<=> ( ord_less_int @ Xa @ ( bit1 @ pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(155,plain,
( ( ! [K: $i] :
~ ( ord_less_int @ ( semiri1621563631at_int @ K ) @ zero_zero_int ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(156,plain,
( ( ! [Wa: $i,Z_2: $i] :
( ( ord_less_int @ Wa @ ( plus_plus_int @ Z_2 @ one_one_int ) )
<=> ( ( ord_less_int @ Wa @ Z_2 )
| ( Wa = Z_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(157,plain,
( ( ord_less_int @ zero_zero_int @ one_one_int )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(158,plain,
( ( ! [Wa: $i] :
( ( ord_less_int @ ( bit0 @ Wa ) @ zero_zero_int )
<=> ( ord_less_int @ Wa @ zero_zero_int ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(159,plain,
( ( ~ ( ord_less_int @ pls @ zero_zero_int ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(160,plain,
( ( ! [Wa: $i] :
( ( ord_less_int @ ( bit1 @ Wa ) @ zero_zero_int )
<=> ( ord_less_int @ Wa @ zero_zero_int ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(161,plain,
( ( ! [K_1: $i] :
( ( ord_less_int @ pls @ ( bit0 @ K_1 ) )
<=> ( ord_less_int @ pls @ K_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(162,plain,
( ( ! [K_1: $i] :
( ( ord_less_int @ ( bit0 @ K_1 ) @ pls )
<=> ( ord_less_int @ K_1 @ pls ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(163,plain,
( ( ! [K_1: $i,L_1: $i] :
( ( ord_less_int @ ( bit1 @ K_1 ) @ ( bit0 @ L_1 ) )
<=> ( ord_less_int @ K_1 @ L_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(164,plain,
( ( ! [K1: $i,K2: $i] :
( ( ord_less_int @ ( bit1 @ K1 ) @ ( bit0 @ K2 ) )
<=> ( ord_less_int @ K1 @ K2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(165,plain,
( ( ! [K_1: $i] :
( ( ord_less_int @ ( bit1 @ K_1 ) @ pls )
<=> ( ord_less_int @ K_1 @ pls ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(166,plain,
( ( ! [Ya: $i] :
( ( ord_less_int @ zero_zero_int @ ( number_number_of_int @ Ya ) )
<=> ( ord_less_int @ pls @ Ya ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(167,plain,
( ( ! [Xa: $i] :
( ( ord_less_int @ ( number_number_of_int @ Xa ) @ zero_zero_int )
<=> ( ord_less_int @ Xa @ pls ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(168,plain,
( ( ! [Ma: $i,Na: $i] :
( ( ( semiri1621563631at_int @ Ma )
= ( semiri1621563631at_int @ Na ) )
<=> ( Ma = Na ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(169,plain,
( ( ! [Z: $i,W_3: $i] :
( ( plus_plus_int @ Z @ W_3 )
= ( plus_plus_int @ W_3 @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(170,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)],[55]) ).
thf(171,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)],[56]) ).
thf(172,plain,
( ( ! [A_1: $i] :
( ( ord_less_int @ ( plus_plus_int @ A_1 @ A_1 ) @ zero_zero_int )
<=> ( ord_less_int @ A_1 @ zero_zero_int ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(173,plain,
( ( ! [K_1: $i,L_1: $i] :
( ( ( bit0 @ K_1 )
= ( bit0 @ L_1 ) )
<=> ( K_1 = L_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(174,plain,
( ( ! [K_1: $i,L_1: $i] :
( ( ( bit1 @ K_1 )
= ( bit1 @ L_1 ) )
<=> ( K_1 = L_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(175,plain,
( ( ! [Wa: $i,Xa: $i] :
( ( ( number_number_of_nat @ Wa )
= Xa )
<=> ( Xa
= ( number_number_of_nat @ Wa ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(176,plain,
( ( one_one_nat
= ( number_number_of_nat @ ( bit1 @ pls ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(177,plain,
( ( ( number_number_of_nat @ ( bit1 @ pls ) )
= one_one_nat )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(178,plain,
( ( one_one_int
= ( number_number_of_int @ ( bit1 @ pls ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(179,plain,
( ( ! [V_4: $i,V_3: $i] :
( ( ( ord_less_int @ V_3 @ pls )
=> ( ( plus_plus_nat @ ( number_number_of_nat @ V_3 ) @ ( number_number_of_nat @ V_4 ) )
= ( number_number_of_nat @ V_4 ) ) )
& ( ~ ( ord_less_int @ V_3 @ pls )
=> ( ( ( ord_less_int @ V_4 @ pls )
=> ( ( plus_plus_nat @ ( number_number_of_nat @ V_3 ) @ ( number_number_of_nat @ V_4 ) )
= ( number_number_of_nat @ V_3 ) ) )
& ( ~ ( ord_less_int @ V_4 @ pls )
=> ( ( plus_plus_nat @ ( number_number_of_nat @ V_3 ) @ ( number_number_of_nat @ V_4 ) )
= ( number_number_of_nat @ ( plus_plus_int @ V_3 @ V_4 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(180,plain,
( ( ! [K: $i,I: $i,J: $i] :
( ( ord_less_int @ I @ J )
=> ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ K ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(181,plain,
( ( ! [K_1: $i,L_1: $i] :
( ( ord_less_int @ ( bit0 @ K_1 ) @ ( bit0 @ L_1 ) )
<=> ( ord_less_int @ K_1 @ L_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(182,plain,
( ( ! [K1: $i,K2: $i] :
( ( ord_less_int @ ( bit0 @ K1 ) @ ( bit0 @ K2 ) )
<=> ( ord_less_int @ K1 @ K2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(183,plain,
( ( ~ ( ord_less_int @ pls @ pls ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(184,plain,
( ( ! [K_1: $i,L_1: $i] :
( ( ord_less_int @ ( bit1 @ K_1 ) @ ( bit1 @ L_1 ) )
<=> ( ord_less_int @ K_1 @ L_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(185,plain,
( ( ! [K1: $i,K2: $i] :
( ( ord_less_int @ ( bit1 @ K1 ) @ ( bit1 @ K2 ) )
<=> ( ord_less_int @ K1 @ K2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(186,plain,
( ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
= ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(187,plain,
( ( ( semiri1621563631at_int @ zero_zero_nat )
= zero_zero_int )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(188,plain,
( ( ! [Na: $i] :
( ( ( semiri1621563631at_int @ Na )
= zero_zero_int )
<=> ( Na = zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(189,plain,
( ( zero_zero_nat
= ( number_number_of_nat @ pls ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(190,plain,
( ( ( number_number_of_nat @ pls )
= zero_zero_nat )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(191,plain,
( ( ( semiri1621563631at_int @ one_one_nat )
= one_one_int )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(192,plain,
( ( ! [M: $i,N_1: $i] :
( ( plus_plus_int @ ( semiri1621563631at_int @ M ) @ ( semiri1621563631at_int @ N_1 ) )
= ( semiri1621563631at_int @ ( plus_plus_nat @ M @ N_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(193,plain,
( ( ! [M: $i,N_1: $i,Z: $i] :
( ( plus_plus_int @ ( semiri1621563631at_int @ M ) @ ( plus_plus_int @ ( semiri1621563631at_int @ N_1 ) @ Z ) )
= ( plus_plus_int @ ( semiri1621563631at_int @ ( plus_plus_nat @ M @ N_1 ) ) @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(194,plain,
( ( ! [M: $i,N_1: $i] :
( ( semiri1621563631at_int @ ( power_power_nat @ M @ N_1 ) )
= ( power_power_int @ ( semiri1621563631at_int @ M ) @ N_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(195,plain,
( ( ! [M: $i,N_1: $i] :
( ( power_power_int @ ( semiri1621563631at_int @ M ) @ N_1 )
= ( semiri1621563631at_int @ ( power_power_nat @ M @ N_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(196,plain,
( ( zero_zero_int
= ( number_number_of_int @ pls ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(197,plain,
( ( ! [V_3: $i,W_3: $i] :
( ( plus_plus_int @ ( number_number_of_int @ V_3 ) @ ( number_number_of_int @ W_3 ) )
= ( number_number_of_int @ ( plus_plus_int @ V_3 @ W_3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(198,plain,
( ( ord_less_nat @ zero_zero_nat @ n )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(199,plain,
( ( ( number_number_of_int @ ( bit1 @ pls ) )
= one_one_int )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(200,plain,
( ( one_one_int
= ( number_number_of_int @ ( bit1 @ pls ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(201,plain,
( ( ! [W_4: $i] :
( ( ( ( number_number_of_nat @ W_4 )
= zero_zero_nat )
=> ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ W_4 ) )
= one_one_int ) )
& ( ( ( number_number_of_nat @ W_4 )
!= zero_zero_nat )
=> ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ W_4 ) )
= zero_zero_int ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(202,plain,
( ( ! [X: $i] :
( ( power_power_int @ ( power_power_int @ X @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power_int @ X @ ( number_number_of_nat @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(203,plain,
( ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
= ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(204,plain,
( ( ( plus_plus_int @ one_one_int @ one_one_int )
= ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(205,plain,
( ( ( plus_plus_int @ one_one_int @ one_one_int )
= ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(206,plain,
( ( ! [V_5: $i] :
( ( plus_plus_int @ ( number_number_of_int @ V_5 ) @ one_one_int )
= ( number_number_of_int @ ( plus_plus_int @ V_5 @ ( bit1 @ pls ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(207,plain,
( ( ! [W_5: $i] :
( ( plus_plus_int @ one_one_int @ ( number_number_of_int @ W_5 ) )
= ( number_number_of_int @ ( plus_plus_int @ ( bit1 @ pls ) @ W_5 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(208,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)],[99]) ).
thf(209,plain,
( ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_nat )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(210,plain,
( ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(211,plain,
( ( ( power_power_nat @ one_one_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_nat )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(212,plain,
( ( ( power_power_int @ one_one_int @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_int )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(213,plain,
( ( ! [Xa: $i,Ya: $i] :
( ( ( plus_plus_int @ ( power_power_int @ Xa @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Ya @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_int )
<=> ( ( Xa = zero_zero_int )
& ( Ya = zero_zero_int ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(214,plain,
( ( ord_less_int @ one_one_int @ t )
= $true ),
inference(unfold_def,[status(thm)],[105]) ).
thf(215,plain,
( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(216,plain,
( ( ~ ( ( ( power_power_int @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= zero_zero_int ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[109]) ).
thf(217,plain,
( ( ( power_power_int @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int )
= $true ),
inference(extcnf_combined,[status(esa)],[216]) ).
thf(218,plain,
( ( ! [Wa: $i,Xa: $i] :
( ( ( number_number_of_int @ Wa )
!= Xa )
| ( Xa
= ( number_number_of_int @ Wa ) ) )
& ! [Wa: $i,Xa: $i] :
( ( Xa
!= ( number_number_of_int @ Wa ) )
| ( ( number_number_of_int @ Wa )
= Xa ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[110]) ).
thf(219,plain,
( ( ! [Xa: $i,Ya: $i] :
( ( ( number_number_of_int @ Xa )
!= ( number_number_of_int @ Ya ) )
| ( Xa = Ya ) )
& ! [Xa: $i,Ya: $i] :
( ( Xa != Ya )
| ( ( number_number_of_int @ Xa )
= ( number_number_of_int @ Ya ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[111]) ).
thf(220,plain,
( ( ! [Xa: $i,Ya: $i] :
( ~ ( ord_less_int @ ( number_number_of_int @ Xa ) @ ( number_number_of_int @ Ya ) )
| ( ord_less_int @ Xa @ Ya ) )
& ! [Xa: $i,Ya: $i] :
( ~ ( ord_less_int @ Xa @ Ya )
| ( ord_less_int @ ( number_number_of_int @ Xa ) @ ( number_number_of_int @ Ya ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[112]) ).
thf(221,plain,
( ( ! [K_1: $i,L_1: $i] :
( ~ ( ord_less_int @ ( number_number_of_int @ K_1 ) @ ( number_number_of_int @ L_1 ) )
| ( ord_less_int @ K_1 @ L_1 ) )
& ! [K_1: $i,L_1: $i] :
( ~ ( ord_less_int @ K_1 @ L_1 )
| ( ord_less_int @ ( number_number_of_int @ K_1 ) @ ( number_number_of_int @ L_1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[113]) ).
thf(222,plain,
( ( ! [X: $i,Y: $i] :
( ( ord_less_int @ Y @ X )
| ( X = Y )
| ( ord_less_int @ X @ Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[114]) ).
thf(223,plain,
( ( ! [W_4: $i] :
( ( ( number_number_of_nat @ W_4 )
!= zero_zero_nat )
| ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ W_4 ) )
= one_one_nat ) )
& ! [W_4: $i] :
( ( ( number_number_of_nat @ W_4 )
= zero_zero_nat )
| ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ W_4 ) )
= zero_zero_nat ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[115]) ).
thf(224,plain,
( ( ! [Xa: $i,Ya: $i] :
( ~ ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ Xa @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Ya @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
| ( Xa != zero_zero_int )
| ( Ya != zero_zero_int ) )
& ! [Xa: $i] :
( ( Xa = zero_zero_int )
| ! [Ya: $i] : ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ Xa @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Ya @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
& ! [Xa: $i,Ya: $i] :
( ( Ya = zero_zero_int )
| ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ Xa @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Ya @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[116]) ).
thf(225,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)],[118]) ).
thf(226,plain,
( ( ! [Z: $i] :
( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z )
!= zero_zero_int ) )
= $true ),
inference(extcnf_combined,[status(esa)],[121]) ).
thf(227,plain,
( ( ! [A_1: $i,Wa: $i] :
( ( ( number_number_of_nat @ Wa )
= zero_zero_nat )
| ( A_1 != zero_zero_nat )
| ( ( power_power_nat @ A_1 @ ( number_number_of_nat @ Wa ) )
= zero_zero_nat ) )
& ! [A_1: $i,Wa: $i] :
( ( ( power_power_nat @ A_1 @ ( number_number_of_nat @ Wa ) )
!= zero_zero_nat )
| ( ( number_number_of_nat @ Wa )
!= zero_zero_nat ) )
& ! [A_1: $i] :
( ! [Wa: $i] :
( ( power_power_nat @ A_1 @ ( number_number_of_nat @ Wa ) )
!= zero_zero_nat )
| ( A_1 = zero_zero_nat ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[128]) ).
thf(228,plain,
( ( ! [A_1: $i,Wa: $i] :
( ( ( number_number_of_nat @ Wa )
= zero_zero_nat )
| ( A_1 != zero_zero_int )
| ( ( power_power_int @ A_1 @ ( number_number_of_nat @ Wa ) )
= zero_zero_int ) )
& ! [A_1: $i,Wa: $i] :
( ( ( power_power_int @ A_1 @ ( number_number_of_nat @ Wa ) )
!= zero_zero_int )
| ( ( number_number_of_nat @ Wa )
!= zero_zero_nat ) )
& ! [A_1: $i] :
( ! [Wa: $i] :
( ( power_power_int @ A_1 @ ( number_number_of_nat @ Wa ) )
!= zero_zero_int )
| ( A_1 = zero_zero_int ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[129]) ).
thf(229,plain,
( ( ( zero_zero_int != one_one_int ) )
= $true ),
inference(extcnf_combined,[status(esa)],[142]) ).
thf(230,plain,
( ( ! [L_1: $i] :
( ( pls
!= ( bit0 @ L_1 ) )
| ( pls = L_1 ) )
& ! [L_1: $i] :
( ( pls != L_1 )
| ( pls
= ( bit0 @ L_1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[145]) ).
thf(231,plain,
( ( ! [K_1: $i] :
( ( ( bit0 @ K_1 )
!= pls )
| ( K_1 = pls ) )
& ! [K_1: $i] :
( ( K_1 != pls )
| ( ( bit0 @ K_1 )
= pls ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[146]) ).
thf(232,plain,
( ( ! [K: $i,L: $i] :
( ( bit0 @ K )
!= ( bit1 @ L ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[147]) ).
thf(233,plain,
( ( ! [K: $i,L: $i] :
( ( bit1 @ K )
!= ( bit0 @ L ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[148]) ).
thf(234,plain,
( ( ! [L: $i] :
( pls
!= ( bit1 @ L ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[149]) ).
thf(235,plain,
( ( ! [K: $i] :
( ( bit1 @ K )
!= pls ) )
= $true ),
inference(extcnf_combined,[status(esa)],[150]) ).
thf(236,plain,
( ( ! [A_1: $i] :
( ( ( plus_plus_int @ A_1 @ A_1 )
!= zero_zero_int )
| ( A_1 = zero_zero_int ) )
& ! [A_1: $i] :
( ( A_1 != zero_zero_int )
| ( ( plus_plus_int @ A_1 @ A_1 )
= zero_zero_int ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[151]) ).
thf(237,plain,
( ( ! [Z_2: $i] :
( ~ ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z_2 ) @ Z_2 ) @ zero_zero_int )
| ( ord_less_int @ Z_2 @ zero_zero_int ) )
& ! [Z_2: $i] :
( ~ ( ord_less_int @ Z_2 @ zero_zero_int )
| ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z_2 ) @ Z_2 ) @ zero_zero_int ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[152]) ).
thf(238,plain,
( ( ! [Ya: $i] :
( ~ ( ord_less_int @ one_one_int @ ( number_number_of_int @ Ya ) )
| ( ord_less_int @ ( bit1 @ pls ) @ Ya ) )
& ! [Ya: $i] :
( ~ ( ord_less_int @ ( bit1 @ pls ) @ Ya )
| ( ord_less_int @ one_one_int @ ( number_number_of_int @ Ya ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[153]) ).
thf(239,plain,
( ( ! [Xa: $i] :
( ~ ( ord_less_int @ ( number_number_of_int @ Xa ) @ one_one_int )
| ( ord_less_int @ Xa @ ( bit1 @ pls ) ) )
& ! [Xa: $i] :
( ~ ( ord_less_int @ Xa @ ( bit1 @ pls ) )
| ( ord_less_int @ ( number_number_of_int @ Xa ) @ one_one_int ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[154]) ).
thf(240,plain,
( ( ! [Wa: $i,Z_2: $i] :
( ~ ( ord_less_int @ Wa @ ( plus_plus_int @ Z_2 @ one_one_int ) )
| ( Wa = Z_2 )
| ( ord_less_int @ Wa @ Z_2 ) )
& ! [Wa: $i,Z_2: $i] :
( ( Wa != Z_2 )
| ( ord_less_int @ Wa @ ( plus_plus_int @ Z_2 @ one_one_int ) ) )
& ! [Wa: $i,Z_2: $i] :
( ~ ( ord_less_int @ Wa @ Z_2 )
| ( ord_less_int @ Wa @ ( plus_plus_int @ Z_2 @ one_one_int ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[156]) ).
thf(241,plain,
( ( ! [Wa: $i] :
( ~ ( ord_less_int @ ( bit0 @ Wa ) @ zero_zero_int )
| ( ord_less_int @ Wa @ zero_zero_int ) )
& ! [Wa: $i] :
( ~ ( ord_less_int @ Wa @ zero_zero_int )
| ( ord_less_int @ ( bit0 @ Wa ) @ zero_zero_int ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[158]) ).
thf(242,plain,
( ( ! [Wa: $i] :
( ~ ( ord_less_int @ ( bit1 @ Wa ) @ zero_zero_int )
| ( ord_less_int @ Wa @ zero_zero_int ) )
& ! [Wa: $i] :
( ~ ( ord_less_int @ Wa @ zero_zero_int )
| ( ord_less_int @ ( bit1 @ Wa ) @ zero_zero_int ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[160]) ).
thf(243,plain,
( ( ! [K_1: $i] :
( ~ ( ord_less_int @ pls @ ( bit0 @ K_1 ) )
| ( ord_less_int @ pls @ K_1 ) )
& ! [K_1: $i] :
( ~ ( ord_less_int @ pls @ K_1 )
| ( ord_less_int @ pls @ ( bit0 @ K_1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[161]) ).
thf(244,plain,
( ( ! [K_1: $i] :
( ~ ( ord_less_int @ ( bit0 @ K_1 ) @ pls )
| ( ord_less_int @ K_1 @ pls ) )
& ! [K_1: $i] :
( ~ ( ord_less_int @ K_1 @ pls )
| ( ord_less_int @ ( bit0 @ K_1 ) @ pls ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[162]) ).
thf(245,plain,
( ( ! [K_1: $i,L_1: $i] :
( ~ ( ord_less_int @ ( bit1 @ K_1 ) @ ( bit0 @ L_1 ) )
| ( ord_less_int @ K_1 @ L_1 ) )
& ! [K_1: $i,L_1: $i] :
( ~ ( ord_less_int @ K_1 @ L_1 )
| ( ord_less_int @ ( bit1 @ K_1 ) @ ( bit0 @ L_1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[163]) ).
thf(246,plain,
( ( ! [K1: $i,K2: $i] :
( ~ ( ord_less_int @ ( bit1 @ K1 ) @ ( bit0 @ K2 ) )
| ( ord_less_int @ K1 @ K2 ) )
& ! [K1: $i,K2: $i] :
( ~ ( ord_less_int @ K1 @ K2 )
| ( ord_less_int @ ( bit1 @ K1 ) @ ( bit0 @ K2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[164]) ).
thf(247,plain,
( ( ! [K_1: $i] :
( ~ ( ord_less_int @ ( bit1 @ K_1 ) @ pls )
| ( ord_less_int @ K_1 @ pls ) )
& ! [K_1: $i] :
( ~ ( ord_less_int @ K_1 @ pls )
| ( ord_less_int @ ( bit1 @ K_1 ) @ pls ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[165]) ).
thf(248,plain,
( ( ! [Ya: $i] :
( ~ ( ord_less_int @ zero_zero_int @ ( number_number_of_int @ Ya ) )
| ( ord_less_int @ pls @ Ya ) )
& ! [Ya: $i] :
( ~ ( ord_less_int @ pls @ Ya )
| ( ord_less_int @ zero_zero_int @ ( number_number_of_int @ Ya ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[166]) ).
thf(249,plain,
( ( ! [Xa: $i] :
( ~ ( ord_less_int @ ( number_number_of_int @ Xa ) @ zero_zero_int )
| ( ord_less_int @ Xa @ pls ) )
& ! [Xa: $i] :
( ~ ( ord_less_int @ Xa @ pls )
| ( ord_less_int @ ( number_number_of_int @ Xa ) @ zero_zero_int ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[167]) ).
thf(250,plain,
( ( ! [Ma: $i,Na: $i] :
( ( ( semiri1621563631at_int @ Ma )
!= ( semiri1621563631at_int @ Na ) )
| ( Ma = Na ) )
& ! [Ma: $i,Na: $i] :
( ( Ma != Na )
| ( ( semiri1621563631at_int @ Ma )
= ( semiri1621563631at_int @ Na ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[168]) ).
thf(251,plain,
( ( ! [A_1: $i] :
( ~ ( ord_less_int @ ( plus_plus_int @ A_1 @ A_1 ) @ zero_zero_int )
| ( ord_less_int @ A_1 @ zero_zero_int ) )
& ! [A_1: $i] :
( ~ ( ord_less_int @ A_1 @ zero_zero_int )
| ( ord_less_int @ ( plus_plus_int @ A_1 @ A_1 ) @ zero_zero_int ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[172]) ).
thf(252,plain,
( ( ! [K_1: $i,L_1: $i] :
( ( ( bit0 @ K_1 )
!= ( bit0 @ L_1 ) )
| ( K_1 = L_1 ) )
& ! [K_1: $i,L_1: $i] :
( ( K_1 != L_1 )
| ( ( bit0 @ K_1 )
= ( bit0 @ L_1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[173]) ).
thf(253,plain,
( ( ! [K_1: $i,L_1: $i] :
( ( ( bit1 @ K_1 )
!= ( bit1 @ L_1 ) )
| ( K_1 = L_1 ) )
& ! [K_1: $i,L_1: $i] :
( ( K_1 != L_1 )
| ( ( bit1 @ K_1 )
= ( bit1 @ L_1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[174]) ).
thf(254,plain,
( ( ! [Wa: $i,Xa: $i] :
( ( ( number_number_of_nat @ Wa )
!= Xa )
| ( Xa
= ( number_number_of_nat @ Wa ) ) )
& ! [Wa: $i,Xa: $i] :
( ( Xa
!= ( number_number_of_nat @ Wa ) )
| ( ( number_number_of_nat @ Wa )
= Xa ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[175]) ).
thf(255,plain,
( ( ! [V_4: $i,V_3: $i] :
( ~ ( ord_less_int @ V_3 @ pls )
| ( ( plus_plus_nat @ ( number_number_of_nat @ V_3 ) @ ( number_number_of_nat @ V_4 ) )
= ( number_number_of_nat @ V_4 ) ) )
& ! [V_4: $i,V_3: $i] :
( ( ord_less_int @ V_3 @ pls )
| ~ ( ord_less_int @ V_4 @ pls )
| ( ( plus_plus_nat @ ( number_number_of_nat @ V_3 ) @ ( number_number_of_nat @ V_4 ) )
= ( number_number_of_nat @ V_3 ) ) )
& ! [V_4: $i,V_3: $i] :
( ( ord_less_int @ V_3 @ pls )
| ( ord_less_int @ V_4 @ pls )
| ( ( plus_plus_nat @ ( number_number_of_nat @ V_3 ) @ ( number_number_of_nat @ V_4 ) )
= ( number_number_of_nat @ ( plus_plus_int @ V_3 @ V_4 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[179]) ).
thf(256,plain,
( ( ! [K: $i,I: $i,J: $i] :
( ~ ( ord_less_int @ I @ J )
| ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ K ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[180]) ).
thf(257,plain,
( ( ! [K_1: $i,L_1: $i] :
( ~ ( ord_less_int @ ( bit0 @ K_1 ) @ ( bit0 @ L_1 ) )
| ( ord_less_int @ K_1 @ L_1 ) )
& ! [K_1: $i,L_1: $i] :
( ~ ( ord_less_int @ K_1 @ L_1 )
| ( ord_less_int @ ( bit0 @ K_1 ) @ ( bit0 @ L_1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[181]) ).
thf(258,plain,
( ( ! [K1: $i,K2: $i] :
( ~ ( ord_less_int @ ( bit0 @ K1 ) @ ( bit0 @ K2 ) )
| ( ord_less_int @ K1 @ K2 ) )
& ! [K1: $i,K2: $i] :
( ~ ( ord_less_int @ K1 @ K2 )
| ( ord_less_int @ ( bit0 @ K1 ) @ ( bit0 @ K2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[182]) ).
thf(259,plain,
( ( ! [K_1: $i,L_1: $i] :
( ~ ( ord_less_int @ ( bit1 @ K_1 ) @ ( bit1 @ L_1 ) )
| ( ord_less_int @ K_1 @ L_1 ) )
& ! [K_1: $i,L_1: $i] :
( ~ ( ord_less_int @ K_1 @ L_1 )
| ( ord_less_int @ ( bit1 @ K_1 ) @ ( bit1 @ L_1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[184]) ).
thf(260,plain,
( ( ! [K1: $i,K2: $i] :
( ~ ( ord_less_int @ ( bit1 @ K1 ) @ ( bit1 @ K2 ) )
| ( ord_less_int @ K1 @ K2 ) )
& ! [K1: $i,K2: $i] :
( ~ ( ord_less_int @ K1 @ K2 )
| ( ord_less_int @ ( bit1 @ K1 ) @ ( bit1 @ K2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[185]) ).
thf(261,plain,
( ( ! [Na: $i] :
( ( ( semiri1621563631at_int @ Na )
!= zero_zero_int )
| ( Na = zero_zero_nat ) )
& ! [Na: $i] :
( ( Na != zero_zero_nat )
| ( ( semiri1621563631at_int @ Na )
= zero_zero_int ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[188]) ).
thf(262,plain,
( ( ! [W_4: $i] :
( ( ( number_number_of_nat @ W_4 )
!= zero_zero_nat )
| ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ W_4 ) )
= one_one_int ) )
& ! [W_4: $i] :
( ( ( number_number_of_nat @ W_4 )
= zero_zero_nat )
| ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ W_4 ) )
= zero_zero_int ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[201]) ).
thf(263,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)],[208]) ).
thf(264,plain,
( ( ! [Xa: $i,Ya: $i] :
( ( Xa != zero_zero_int )
| ( Ya != zero_zero_int )
| ( ( plus_plus_int @ ( power_power_int @ Xa @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Ya @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_int ) )
& ! [Xa: $i] :
( ! [Ya: $i] :
( ( plus_plus_int @ ( power_power_int @ Xa @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Ya @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_int )
| ( Xa = zero_zero_int ) )
& ! [Xa: $i,Ya: $i] :
( ( ( plus_plus_int @ ( power_power_int @ Xa @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Ya @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_int )
| ( Ya = zero_zero_int ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[213]) ).
thf(265,plain,
( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) )
= $true ),
inference(copy,[status(thm)],[215]) ).
thf(266,plain,
( ( ord_less_int @ one_one_int @ t )
= $true ),
inference(copy,[status(thm)],[214]) ).
thf(267,plain,
( ( ! [Xa: $i,Ya: $i] :
( ( Xa != zero_zero_int )
| ( Ya != zero_zero_int )
| ( ( plus_plus_int @ ( power_power_int @ Xa @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Ya @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_int ) )
& ! [Xa: $i] :
( ! [Ya: $i] :
( ( plus_plus_int @ ( power_power_int @ Xa @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Ya @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_int )
| ( Xa = zero_zero_int ) )
& ! [Xa: $i,Ya: $i] :
( ( ( plus_plus_int @ ( power_power_int @ Xa @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Ya @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_int )
| ( Ya = zero_zero_int ) ) )
= $true ),
inference(copy,[status(thm)],[264]) ).
thf(268,plain,
( ( ( power_power_int @ one_one_int @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_int )
= $true ),
inference(copy,[status(thm)],[212]) ).
thf(269,plain,
( ( ( power_power_nat @ one_one_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_nat )
= $true ),
inference(copy,[status(thm)],[211]) ).
thf(270,plain,
( ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int )
= $true ),
inference(copy,[status(thm)],[210]) ).
thf(271,plain,
( ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_nat )
= $true ),
inference(copy,[status(thm)],[209]) ).
thf(272,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)],[263]) ).
thf(273,plain,
( ( ! [W_5: $i] :
( ( plus_plus_int @ one_one_int @ ( number_number_of_int @ W_5 ) )
= ( number_number_of_int @ ( plus_plus_int @ ( bit1 @ pls ) @ W_5 ) ) ) )
= $true ),
inference(copy,[status(thm)],[207]) ).
thf(274,plain,
( ( ! [V_5: $i] :
( ( plus_plus_int @ ( number_number_of_int @ V_5 ) @ one_one_int )
= ( number_number_of_int @ ( plus_plus_int @ V_5 @ ( bit1 @ pls ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[206]) ).
thf(275,plain,
( ( ( plus_plus_int @ one_one_int @ one_one_int )
= ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(copy,[status(thm)],[205]) ).
thf(276,plain,
( ( ( plus_plus_int @ one_one_int @ one_one_int )
= ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(copy,[status(thm)],[204]) ).
thf(277,plain,
( ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
= ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(copy,[status(thm)],[203]) ).
thf(278,plain,
( ( ! [X: $i] :
( ( power_power_int @ ( power_power_int @ X @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power_int @ X @ ( number_number_of_nat @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[202]) ).
thf(279,plain,
( ( ! [W_4: $i] :
( ( ( number_number_of_nat @ W_4 )
!= zero_zero_nat )
| ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ W_4 ) )
= one_one_int ) )
& ! [W_4: $i] :
( ( ( number_number_of_nat @ W_4 )
= zero_zero_nat )
| ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ W_4 ) )
= zero_zero_int ) ) )
= $true ),
inference(copy,[status(thm)],[262]) ).
thf(280,plain,
( ( one_one_int
= ( number_number_of_int @ ( bit1 @ pls ) ) )
= $true ),
inference(copy,[status(thm)],[200]) ).
thf(281,plain,
( ( ( number_number_of_int @ ( bit1 @ pls ) )
= one_one_int )
= $true ),
inference(copy,[status(thm)],[199]) ).
thf(282,plain,
( ( ord_less_nat @ zero_zero_nat @ n )
= $true ),
inference(copy,[status(thm)],[198]) ).
thf(283,plain,
( ( ! [V_3: $i,W_3: $i] :
( ( plus_plus_int @ ( number_number_of_int @ V_3 ) @ ( number_number_of_int @ W_3 ) )
= ( number_number_of_int @ ( plus_plus_int @ V_3 @ W_3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[197]) ).
thf(284,plain,
( ( zero_zero_int
= ( number_number_of_int @ pls ) )
= $true ),
inference(copy,[status(thm)],[196]) ).
thf(285,plain,
( ( ! [M: $i,N_1: $i] :
( ( power_power_int @ ( semiri1621563631at_int @ M ) @ N_1 )
= ( semiri1621563631at_int @ ( power_power_nat @ M @ N_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[195]) ).
thf(286,plain,
( ( ! [M: $i,N_1: $i] :
( ( semiri1621563631at_int @ ( power_power_nat @ M @ N_1 ) )
= ( power_power_int @ ( semiri1621563631at_int @ M ) @ N_1 ) ) )
= $true ),
inference(copy,[status(thm)],[194]) ).
thf(287,plain,
( ( ! [M: $i,N_1: $i,Z: $i] :
( ( plus_plus_int @ ( semiri1621563631at_int @ M ) @ ( plus_plus_int @ ( semiri1621563631at_int @ N_1 ) @ Z ) )
= ( plus_plus_int @ ( semiri1621563631at_int @ ( plus_plus_nat @ M @ N_1 ) ) @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[193]) ).
thf(288,plain,
( ( ! [M: $i,N_1: $i] :
( ( plus_plus_int @ ( semiri1621563631at_int @ M ) @ ( semiri1621563631at_int @ N_1 ) )
= ( semiri1621563631at_int @ ( plus_plus_nat @ M @ N_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[192]) ).
thf(289,plain,
( ( ( semiri1621563631at_int @ one_one_nat )
= one_one_int )
= $true ),
inference(copy,[status(thm)],[191]) ).
thf(290,plain,
( ( ( number_number_of_nat @ pls )
= zero_zero_nat )
= $true ),
inference(copy,[status(thm)],[190]) ).
thf(291,plain,
( ( zero_zero_nat
= ( number_number_of_nat @ pls ) )
= $true ),
inference(copy,[status(thm)],[189]) ).
thf(292,plain,
( ( ! [Na: $i] :
( ( ( semiri1621563631at_int @ Na )
!= zero_zero_int )
| ( Na = zero_zero_nat ) )
& ! [Na: $i] :
( ( Na != zero_zero_nat )
| ( ( semiri1621563631at_int @ Na )
= zero_zero_int ) ) )
= $true ),
inference(copy,[status(thm)],[261]) ).
thf(293,plain,
( ( ( semiri1621563631at_int @ zero_zero_nat )
= zero_zero_int )
= $true ),
inference(copy,[status(thm)],[187]) ).
thf(294,plain,
( ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
= ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(copy,[status(thm)],[186]) ).
thf(295,plain,
( ( ! [K1: $i,K2: $i] :
( ~ ( ord_less_int @ ( bit1 @ K1 ) @ ( bit1 @ K2 ) )
| ( ord_less_int @ K1 @ K2 ) )
& ! [K1: $i,K2: $i] :
( ~ ( ord_less_int @ K1 @ K2 )
| ( ord_less_int @ ( bit1 @ K1 ) @ ( bit1 @ K2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[260]) ).
thf(296,plain,
( ( ! [K_1: $i,L_1: $i] :
( ~ ( ord_less_int @ ( bit1 @ K_1 ) @ ( bit1 @ L_1 ) )
| ( ord_less_int @ K_1 @ L_1 ) )
& ! [K_1: $i,L_1: $i] :
( ~ ( ord_less_int @ K_1 @ L_1 )
| ( ord_less_int @ ( bit1 @ K_1 ) @ ( bit1 @ L_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[259]) ).
thf(297,plain,
( ( ~ ( ord_less_int @ pls @ pls ) )
= $true ),
inference(copy,[status(thm)],[183]) ).
thf(298,plain,
( ( ! [K1: $i,K2: $i] :
( ~ ( ord_less_int @ ( bit0 @ K1 ) @ ( bit0 @ K2 ) )
| ( ord_less_int @ K1 @ K2 ) )
& ! [K1: $i,K2: $i] :
( ~ ( ord_less_int @ K1 @ K2 )
| ( ord_less_int @ ( bit0 @ K1 ) @ ( bit0 @ K2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[258]) ).
thf(299,plain,
( ( ! [K_1: $i,L_1: $i] :
( ~ ( ord_less_int @ ( bit0 @ K_1 ) @ ( bit0 @ L_1 ) )
| ( ord_less_int @ K_1 @ L_1 ) )
& ! [K_1: $i,L_1: $i] :
( ~ ( ord_less_int @ K_1 @ L_1 )
| ( ord_less_int @ ( bit0 @ K_1 ) @ ( bit0 @ L_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[257]) ).
thf(300,plain,
( ( ! [K: $i,I: $i,J: $i] :
( ~ ( ord_less_int @ I @ J )
| ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ K ) ) ) )
= $true ),
inference(copy,[status(thm)],[256]) ).
thf(301,plain,
( ( ! [V_4: $i,V_3: $i] :
( ~ ( ord_less_int @ V_3 @ pls )
| ( ( plus_plus_nat @ ( number_number_of_nat @ V_3 ) @ ( number_number_of_nat @ V_4 ) )
= ( number_number_of_nat @ V_4 ) ) )
& ! [V_4: $i,V_3: $i] :
( ( ord_less_int @ V_3 @ pls )
| ~ ( ord_less_int @ V_4 @ pls )
| ( ( plus_plus_nat @ ( number_number_of_nat @ V_3 ) @ ( number_number_of_nat @ V_4 ) )
= ( number_number_of_nat @ V_3 ) ) )
& ! [V_4: $i,V_3: $i] :
( ( ord_less_int @ V_3 @ pls )
| ( ord_less_int @ V_4 @ pls )
| ( ( plus_plus_nat @ ( number_number_of_nat @ V_3 ) @ ( number_number_of_nat @ V_4 ) )
= ( number_number_of_nat @ ( plus_plus_int @ V_3 @ V_4 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[255]) ).
thf(302,plain,
( ( one_one_int
= ( number_number_of_int @ ( bit1 @ pls ) ) )
= $true ),
inference(copy,[status(thm)],[178]) ).
thf(303,plain,
( ( ( number_number_of_nat @ ( bit1 @ pls ) )
= one_one_nat )
= $true ),
inference(copy,[status(thm)],[177]) ).
thf(304,plain,
( ( one_one_nat
= ( number_number_of_nat @ ( bit1 @ pls ) ) )
= $true ),
inference(copy,[status(thm)],[176]) ).
thf(305,plain,
( ( ! [Wa: $i,Xa: $i] :
( ( ( number_number_of_nat @ Wa )
!= Xa )
| ( Xa
= ( number_number_of_nat @ Wa ) ) )
& ! [Wa: $i,Xa: $i] :
( ( Xa
!= ( number_number_of_nat @ Wa ) )
| ( ( number_number_of_nat @ Wa )
= Xa ) ) )
= $true ),
inference(copy,[status(thm)],[254]) ).
thf(306,plain,
( ( ! [K_1: $i,L_1: $i] :
( ( ( bit1 @ K_1 )
!= ( bit1 @ L_1 ) )
| ( K_1 = L_1 ) )
& ! [K_1: $i,L_1: $i] :
( ( K_1 != L_1 )
| ( ( bit1 @ K_1 )
= ( bit1 @ L_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[253]) ).
thf(307,plain,
( ( ! [K_1: $i,L_1: $i] :
( ( ( bit0 @ K_1 )
!= ( bit0 @ L_1 ) )
| ( K_1 = L_1 ) )
& ! [K_1: $i,L_1: $i] :
( ( K_1 != L_1 )
| ( ( bit0 @ K_1 )
= ( bit0 @ L_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[252]) ).
thf(308,plain,
( ( ! [A_1: $i] :
( ~ ( ord_less_int @ ( plus_plus_int @ A_1 @ A_1 ) @ zero_zero_int )
| ( ord_less_int @ A_1 @ zero_zero_int ) )
& ! [A_1: $i] :
( ~ ( ord_less_int @ A_1 @ zero_zero_int )
| ( ord_less_int @ ( plus_plus_int @ A_1 @ A_1 ) @ zero_zero_int ) ) )
= $true ),
inference(copy,[status(thm)],[251]) ).
thf(309,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)],[171]) ).
thf(310,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)],[170]) ).
thf(311,plain,
( ( ! [Z: $i,W_3: $i] :
( ( plus_plus_int @ Z @ W_3 )
= ( plus_plus_int @ W_3 @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[169]) ).
thf(312,plain,
( ( ! [Ma: $i,Na: $i] :
( ( ( semiri1621563631at_int @ Ma )
!= ( semiri1621563631at_int @ Na ) )
| ( Ma = Na ) )
& ! [Ma: $i,Na: $i] :
( ( Ma != Na )
| ( ( semiri1621563631at_int @ Ma )
= ( semiri1621563631at_int @ Na ) ) ) )
= $true ),
inference(copy,[status(thm)],[250]) ).
thf(313,plain,
( ( ! [Xa: $i] :
( ~ ( ord_less_int @ ( number_number_of_int @ Xa ) @ zero_zero_int )
| ( ord_less_int @ Xa @ pls ) )
& ! [Xa: $i] :
( ~ ( ord_less_int @ Xa @ pls )
| ( ord_less_int @ ( number_number_of_int @ Xa ) @ zero_zero_int ) ) )
= $true ),
inference(copy,[status(thm)],[249]) ).
thf(314,plain,
( ( ! [Ya: $i] :
( ~ ( ord_less_int @ zero_zero_int @ ( number_number_of_int @ Ya ) )
| ( ord_less_int @ pls @ Ya ) )
& ! [Ya: $i] :
( ~ ( ord_less_int @ pls @ Ya )
| ( ord_less_int @ zero_zero_int @ ( number_number_of_int @ Ya ) ) ) )
= $true ),
inference(copy,[status(thm)],[248]) ).
thf(315,plain,
( ( ! [K_1: $i] :
( ~ ( ord_less_int @ ( bit1 @ K_1 ) @ pls )
| ( ord_less_int @ K_1 @ pls ) )
& ! [K_1: $i] :
( ~ ( ord_less_int @ K_1 @ pls )
| ( ord_less_int @ ( bit1 @ K_1 ) @ pls ) ) )
= $true ),
inference(copy,[status(thm)],[247]) ).
thf(316,plain,
( ( ! [K1: $i,K2: $i] :
( ~ ( ord_less_int @ ( bit1 @ K1 ) @ ( bit0 @ K2 ) )
| ( ord_less_int @ K1 @ K2 ) )
& ! [K1: $i,K2: $i] :
( ~ ( ord_less_int @ K1 @ K2 )
| ( ord_less_int @ ( bit1 @ K1 ) @ ( bit0 @ K2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[246]) ).
thf(317,plain,
( ( ! [K_1: $i,L_1: $i] :
( ~ ( ord_less_int @ ( bit1 @ K_1 ) @ ( bit0 @ L_1 ) )
| ( ord_less_int @ K_1 @ L_1 ) )
& ! [K_1: $i,L_1: $i] :
( ~ ( ord_less_int @ K_1 @ L_1 )
| ( ord_less_int @ ( bit1 @ K_1 ) @ ( bit0 @ L_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[245]) ).
thf(318,plain,
( ( ! [K_1: $i] :
( ~ ( ord_less_int @ ( bit0 @ K_1 ) @ pls )
| ( ord_less_int @ K_1 @ pls ) )
& ! [K_1: $i] :
( ~ ( ord_less_int @ K_1 @ pls )
| ( ord_less_int @ ( bit0 @ K_1 ) @ pls ) ) )
= $true ),
inference(copy,[status(thm)],[244]) ).
thf(319,plain,
( ( ! [K_1: $i] :
( ~ ( ord_less_int @ pls @ ( bit0 @ K_1 ) )
| ( ord_less_int @ pls @ K_1 ) )
& ! [K_1: $i] :
( ~ ( ord_less_int @ pls @ K_1 )
| ( ord_less_int @ pls @ ( bit0 @ K_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[243]) ).
thf(320,plain,
( ( ! [Wa: $i] :
( ~ ( ord_less_int @ ( bit1 @ Wa ) @ zero_zero_int )
| ( ord_less_int @ Wa @ zero_zero_int ) )
& ! [Wa: $i] :
( ~ ( ord_less_int @ Wa @ zero_zero_int )
| ( ord_less_int @ ( bit1 @ Wa ) @ zero_zero_int ) ) )
= $true ),
inference(copy,[status(thm)],[242]) ).
thf(321,plain,
( ( ~ ( ord_less_int @ pls @ zero_zero_int ) )
= $true ),
inference(copy,[status(thm)],[159]) ).
thf(322,plain,
( ( ! [Wa: $i] :
( ~ ( ord_less_int @ ( bit0 @ Wa ) @ zero_zero_int )
| ( ord_less_int @ Wa @ zero_zero_int ) )
& ! [Wa: $i] :
( ~ ( ord_less_int @ Wa @ zero_zero_int )
| ( ord_less_int @ ( bit0 @ Wa ) @ zero_zero_int ) ) )
= $true ),
inference(copy,[status(thm)],[241]) ).
thf(323,plain,
( ( ord_less_int @ zero_zero_int @ one_one_int )
= $true ),
inference(copy,[status(thm)],[157]) ).
thf(324,plain,
( ( ! [Wa: $i,Z_2: $i] :
( ~ ( ord_less_int @ Wa @ ( plus_plus_int @ Z_2 @ one_one_int ) )
| ( Wa = Z_2 )
| ( ord_less_int @ Wa @ Z_2 ) )
& ! [Wa: $i,Z_2: $i] :
( ( Wa != Z_2 )
| ( ord_less_int @ Wa @ ( plus_plus_int @ Z_2 @ one_one_int ) ) )
& ! [Wa: $i,Z_2: $i] :
( ~ ( ord_less_int @ Wa @ Z_2 )
| ( ord_less_int @ Wa @ ( plus_plus_int @ Z_2 @ one_one_int ) ) ) )
= $true ),
inference(copy,[status(thm)],[240]) ).
thf(325,plain,
( ( ! [K: $i] :
~ ( ord_less_int @ ( semiri1621563631at_int @ K ) @ zero_zero_int ) )
= $true ),
inference(copy,[status(thm)],[155]) ).
thf(326,plain,
( ( ! [Xa: $i] :
( ~ ( ord_less_int @ ( number_number_of_int @ Xa ) @ one_one_int )
| ( ord_less_int @ Xa @ ( bit1 @ pls ) ) )
& ! [Xa: $i] :
( ~ ( ord_less_int @ Xa @ ( bit1 @ pls ) )
| ( ord_less_int @ ( number_number_of_int @ Xa ) @ one_one_int ) ) )
= $true ),
inference(copy,[status(thm)],[239]) ).
thf(327,plain,
( ( ! [Ya: $i] :
( ~ ( ord_less_int @ one_one_int @ ( number_number_of_int @ Ya ) )
| ( ord_less_int @ ( bit1 @ pls ) @ Ya ) )
& ! [Ya: $i] :
( ~ ( ord_less_int @ ( bit1 @ pls ) @ Ya )
| ( ord_less_int @ one_one_int @ ( number_number_of_int @ Ya ) ) ) )
= $true ),
inference(copy,[status(thm)],[238]) ).
thf(328,plain,
( ( ! [Z_2: $i] :
( ~ ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z_2 ) @ Z_2 ) @ zero_zero_int )
| ( ord_less_int @ Z_2 @ zero_zero_int ) )
& ! [Z_2: $i] :
( ~ ( ord_less_int @ Z_2 @ zero_zero_int )
| ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z_2 ) @ Z_2 ) @ zero_zero_int ) ) )
= $true ),
inference(copy,[status(thm)],[237]) ).
thf(329,plain,
( ( ! [A_1: $i] :
( ( ( plus_plus_int @ A_1 @ A_1 )
!= zero_zero_int )
| ( A_1 = zero_zero_int ) )
& ! [A_1: $i] :
( ( A_1 != zero_zero_int )
| ( ( plus_plus_int @ A_1 @ A_1 )
= zero_zero_int ) ) )
= $true ),
inference(copy,[status(thm)],[236]) ).
thf(330,plain,
( ( ! [K: $i] :
( ( bit1 @ K )
!= pls ) )
= $true ),
inference(copy,[status(thm)],[235]) ).
thf(331,plain,
( ( ! [L: $i] :
( pls
!= ( bit1 @ L ) ) )
= $true ),
inference(copy,[status(thm)],[234]) ).
thf(332,plain,
( ( ! [K: $i,L: $i] :
( ( bit1 @ K )
!= ( bit0 @ L ) ) )
= $true ),
inference(copy,[status(thm)],[233]) ).
thf(333,plain,
( ( ! [K: $i,L: $i] :
( ( bit0 @ K )
!= ( bit1 @ L ) ) )
= $true ),
inference(copy,[status(thm)],[232]) ).
thf(334,plain,
( ( ! [K_1: $i] :
( ( ( bit0 @ K_1 )
!= pls )
| ( K_1 = pls ) )
& ! [K_1: $i] :
( ( K_1 != pls )
| ( ( bit0 @ K_1 )
= pls ) ) )
= $true ),
inference(copy,[status(thm)],[231]) ).
thf(335,plain,
( ( ! [L_1: $i] :
( ( pls
!= ( bit0 @ L_1 ) )
| ( pls = L_1 ) )
& ! [L_1: $i] :
( ( pls != L_1 )
| ( pls
= ( bit0 @ L_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[230]) ).
thf(336,plain,
( ( ( bit0 @ pls )
= pls )
= $true ),
inference(copy,[status(thm)],[144]) ).
thf(337,plain,
( ( pls = zero_zero_int )
= $true ),
inference(copy,[status(thm)],[143]) ).
thf(338,plain,
( ( ( zero_zero_int != one_one_int ) )
= $true ),
inference(copy,[status(thm)],[229]) ).
thf(339,plain,
( ( ! [K: $i] :
( ( plus_plus_int @ K @ pls )
= K ) )
= $true ),
inference(copy,[status(thm)],[141]) ).
thf(340,plain,
( ( ! [K: $i] :
( ( plus_plus_int @ pls @ K )
= K ) )
= $true ),
inference(copy,[status(thm)],[140]) ).
thf(341,plain,
( ( ! [K: $i,L: $i] :
( ( plus_plus_int @ ( bit0 @ K ) @ ( bit0 @ L ) )
= ( bit0 @ ( plus_plus_int @ K @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[139]) ).
thf(342,plain,
( ( ! [K: $i] :
( ( bit0 @ K )
= ( plus_plus_int @ K @ K ) ) )
= $true ),
inference(copy,[status(thm)],[138]) ).
thf(343,plain,
( ( ! [Z: $i] :
( ( plus_plus_int @ Z @ zero_zero_int )
= Z ) )
= $true ),
inference(copy,[status(thm)],[137]) ).
thf(344,plain,
( ( ! [Z: $i] :
( ( plus_plus_int @ zero_zero_int @ Z )
= Z ) )
= $true ),
inference(copy,[status(thm)],[136]) ).
thf(345,plain,
( ( ( number_number_of_int @ pls )
= zero_zero_int )
= $true ),
inference(copy,[status(thm)],[135]) ).
thf(346,plain,
( ( ( number_number_of_nat @ pls )
= zero_zero_nat )
= $true ),
inference(copy,[status(thm)],[134]) ).
thf(347,plain,
( ( ( number_number_of_int @ pls )
= zero_zero_int )
= $true ),
inference(copy,[status(thm)],[133]) ).
thf(348,plain,
( ( zero_zero_int
= ( number_number_of_int @ pls ) )
= $true ),
inference(copy,[status(thm)],[132]) ).
thf(349,plain,
( ( ! [A_3: $i] :
( ( plus_plus_int @ ( number_number_of_int @ pls ) @ A_3 )
= A_3 ) )
= $true ),
inference(copy,[status(thm)],[131]) ).
thf(350,plain,
( ( ! [A_2: $i] :
( ( plus_plus_int @ A_2 @ ( number_number_of_int @ pls ) )
= A_2 ) )
= $true ),
inference(copy,[status(thm)],[130]) ).
thf(351,plain,
( ( ! [A_1: $i,Wa: $i] :
( ( ( number_number_of_nat @ Wa )
= zero_zero_nat )
| ( A_1 != zero_zero_int )
| ( ( power_power_int @ A_1 @ ( number_number_of_nat @ Wa ) )
= zero_zero_int ) )
& ! [A_1: $i,Wa: $i] :
( ( ( power_power_int @ A_1 @ ( number_number_of_nat @ Wa ) )
!= zero_zero_int )
| ( ( number_number_of_nat @ Wa )
!= zero_zero_nat ) )
& ! [A_1: $i] :
( ! [Wa: $i] :
( ( power_power_int @ A_1 @ ( number_number_of_nat @ Wa ) )
!= zero_zero_int )
| ( A_1 = zero_zero_int ) ) )
= $true ),
inference(copy,[status(thm)],[228]) ).
thf(352,plain,
( ( ! [A_1: $i,Wa: $i] :
( ( ( number_number_of_nat @ Wa )
= zero_zero_nat )
| ( A_1 != zero_zero_nat )
| ( ( power_power_nat @ A_1 @ ( number_number_of_nat @ Wa ) )
= zero_zero_nat ) )
& ! [A_1: $i,Wa: $i] :
( ( ( power_power_nat @ A_1 @ ( number_number_of_nat @ Wa ) )
!= zero_zero_nat )
| ( ( number_number_of_nat @ Wa )
!= zero_zero_nat ) )
& ! [A_1: $i] :
( ! [Wa: $i] :
( ( power_power_nat @ A_1 @ ( number_number_of_nat @ Wa ) )
!= zero_zero_nat )
| ( A_1 = zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[227]) ).
thf(353,plain,
( ( ! [V_2: $i,W_2: $i,Z_1: $i] :
( ( plus_plus_int @ ( number_number_of_int @ V_2 ) @ ( plus_plus_int @ ( number_number_of_int @ W_2 ) @ Z_1 ) )
= ( plus_plus_int @ ( number_number_of_int @ ( plus_plus_int @ V_2 @ W_2 ) ) @ Z_1 ) ) )
= $true ),
inference(copy,[status(thm)],[127]) ).
thf(354,plain,
( ( ! [V_1: $i,W_1: $i] :
( ( plus_plus_int @ ( number_number_of_int @ V_1 ) @ ( number_number_of_int @ W_1 ) )
= ( number_number_of_int @ ( plus_plus_int @ V_1 @ W_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[126]) ).
thf(355,plain,
( ( ! [V: $i,W: $i] :
( ( number_number_of_int @ ( plus_plus_int @ V @ W ) )
= ( plus_plus_int @ ( number_number_of_int @ V ) @ ( number_number_of_int @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[125]) ).
thf(356,plain,
( ( ! [K: $i,L: $i] :
( ( plus_plus_int @ ( bit1 @ K ) @ ( bit0 @ L ) )
= ( bit1 @ ( plus_plus_int @ K @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[124]) ).
thf(357,plain,
( ( ! [K: $i,L: $i] :
( ( plus_plus_int @ ( bit0 @ K ) @ ( bit1 @ L ) )
= ( bit1 @ ( plus_plus_int @ K @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[123]) ).
thf(358,plain,
( ( ! [K: $i] :
( ( bit1 @ K )
= ( plus_plus_int @ ( plus_plus_int @ one_one_int @ K ) @ K ) ) )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(359,plain,
( ( ! [Z: $i] :
( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z )
!= zero_zero_int ) )
= $true ),
inference(copy,[status(thm)],[226]) ).
thf(360,plain,
( ( ! [N: $i] :
( ( number_number_of_nat @ ( semiri1621563631at_int @ N ) )
= ( semiri984289939at_nat @ N ) ) )
= $true ),
inference(copy,[status(thm)],[120]) ).
thf(361,plain,
( ( ! [N: $i] :
( ( number_number_of_int @ ( semiri1621563631at_int @ N ) )
= ( semiri1621563631at_int @ N ) ) )
= $true ),
inference(copy,[status(thm)],[119]) ).
thf(362,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)],[225]) ).
thf(363,plain,
( ( ! [A: $i] :
~ ( ord_less_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ zero_zero_int ) )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(364,plain,
( ( ! [Xa: $i,Ya: $i] :
( ~ ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ Xa @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Ya @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
| ( Xa != zero_zero_int )
| ( Ya != zero_zero_int ) )
& ! [Xa: $i] :
( ( Xa = zero_zero_int )
| ! [Ya: $i] : ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ Xa @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Ya @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
& ! [Xa: $i,Ya: $i] :
( ( Ya = zero_zero_int )
| ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ Xa @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Ya @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[224]) ).
thf(365,plain,
( ( ! [W_4: $i] :
( ( ( number_number_of_nat @ W_4 )
!= zero_zero_nat )
| ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ W_4 ) )
= one_one_nat ) )
& ! [W_4: $i] :
( ( ( number_number_of_nat @ W_4 )
= zero_zero_nat )
| ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ W_4 ) )
= zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[223]) ).
thf(366,plain,
( ( ! [X: $i,Y: $i] :
( ( ord_less_int @ Y @ X )
| ( X = Y )
| ( ord_less_int @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[222]) ).
thf(367,plain,
( ( ! [K_1: $i,L_1: $i] :
( ~ ( ord_less_int @ ( number_number_of_int @ K_1 ) @ ( number_number_of_int @ L_1 ) )
| ( ord_less_int @ K_1 @ L_1 ) )
& ! [K_1: $i,L_1: $i] :
( ~ ( ord_less_int @ K_1 @ L_1 )
| ( ord_less_int @ ( number_number_of_int @ K_1 ) @ ( number_number_of_int @ L_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[221]) ).
thf(368,plain,
( ( ! [Xa: $i,Ya: $i] :
( ~ ( ord_less_int @ ( number_number_of_int @ Xa ) @ ( number_number_of_int @ Ya ) )
| ( ord_less_int @ Xa @ Ya ) )
& ! [Xa: $i,Ya: $i] :
( ~ ( ord_less_int @ Xa @ Ya )
| ( ord_less_int @ ( number_number_of_int @ Xa ) @ ( number_number_of_int @ Ya ) ) ) )
= $true ),
inference(copy,[status(thm)],[220]) ).
thf(369,plain,
( ( ! [Xa: $i,Ya: $i] :
( ( ( number_number_of_int @ Xa )
!= ( number_number_of_int @ Ya ) )
| ( Xa = Ya ) )
& ! [Xa: $i,Ya: $i] :
( ( Xa != Ya )
| ( ( number_number_of_int @ Xa )
= ( number_number_of_int @ Ya ) ) ) )
= $true ),
inference(copy,[status(thm)],[219]) ).
thf(370,plain,
( ( ! [Wa: $i,Xa: $i] :
( ( ( number_number_of_int @ Wa )
!= Xa )
| ( Xa
= ( number_number_of_int @ Wa ) ) )
& ! [Wa: $i,Xa: $i] :
( ( Xa
!= ( number_number_of_int @ Wa ) )
| ( ( number_number_of_int @ Wa )
= Xa ) ) )
= $true ),
inference(copy,[status(thm)],[218]) ).
thf(371,plain,
( ( ( power_power_int @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int )
= $true ),
inference(copy,[status(thm)],[217]) ).
thf(372,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ord_less_int @ one_one_int @ ( number_number_of_int @ SX0 ) )
| ( ord_less_int @ ( bit1 @ pls ) @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less_int @ ( bit1 @ pls ) @ SX0 )
| ( ord_less_int @ one_one_int @ ( number_number_of_int @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[327]) ).
thf(373,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)],[267]) ).
thf(374,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ord_less_int @ ( bit0 @ SX0 ) @ zero_zero_int )
| ( ord_less_int @ SX0 @ zero_zero_int ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less_int @ SX0 @ zero_zero_int )
| ( ord_less_int @ ( bit0 @ SX0 ) @ zero_zero_int ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[322]) ).
thf(375,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[316]) ).
thf(376,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( semiri1621563631at_int @ SX0 )
!= ( semiri1621563631at_int @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( semiri1621563631at_int @ SX0 )
= ( semiri1621563631at_int @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[312]) ).
thf(377,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[299]) ).
thf(378,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( number_number_of_nat @ SX1 )
= zero_zero_nat )
| ( SX0 != zero_zero_int )
| ( ( power_power_int @ SX0 @ ( number_number_of_nat @ SX1 ) )
= zero_zero_int ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( power_power_int @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_int )
| ( ( number_number_of_nat @ SX1 )
!= zero_zero_nat ) )
| ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( power_power_int @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[351]) ).
thf(379,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)],[369]) ).
thf(380,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( number_number_of_nat @ SX1 )
= zero_zero_nat )
| ( SX0 != zero_zero_nat )
| ( ( power_power_nat @ SX0 @ ( number_number_of_nat @ SX1 ) )
= zero_zero_nat ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( power_power_nat @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_nat )
| ( ( number_number_of_nat @ SX1 )
!= zero_zero_nat ) )
| ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( power_power_nat @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_nat )
| ( SX0 = zero_zero_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[352]) ).
thf(381,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( ( plus_plus_int @ SX0 @ SX0 )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) )
| ~ ! [SX0: $i] :
( ( SX0 != zero_zero_int )
| ( ( plus_plus_int @ SX0 @ SX0 )
= zero_zero_int ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[329]) ).
thf(382,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)],[367]) ).
thf(383,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[298]) ).
thf(384,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ord_less_int @ pls @ ( bit0 @ SX0 ) )
| ( ord_less_int @ pls @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less_int @ pls @ SX0 )
| ( ord_less_int @ pls @ ( bit0 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[319]) ).
thf(385,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ord_less_int @ ( bit1 @ SX0 ) @ zero_zero_int )
| ( ord_less_int @ SX0 @ zero_zero_int ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less_int @ SX0 @ zero_zero_int )
| ( ord_less_int @ ( bit1 @ SX0 ) @ zero_zero_int ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[320]) ).
thf(386,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)],[307]) ).
thf(387,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[296]) ).
thf(388,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)],[306]) ).
thf(389,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)],[370]) ).
thf(390,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( pls
!= ( bit0 @ SX0 ) )
| ( pls = SX0 ) )
| ~ ! [SX0: $i] :
( ( pls != SX0 )
| ( pls
= ( bit0 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[335]) ).
thf(391,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)],[301]) ).
thf(392,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ord_less_int @ ( bit0 @ SX0 ) @ pls )
| ( ord_less_int @ SX0 @ pls ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less_int @ SX0 @ pls )
| ( ord_less_int @ ( bit0 @ SX0 ) @ pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[318]) ).
thf(393,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX0 @ ( plus_plus_int @ SX1 @ one_one_int ) )
| ( SX0 = SX1 )
| ( ord_less_int @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ord_less_int @ SX0 @ ( plus_plus_int @ SX1 @ one_one_int ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ SX0 @ ( plus_plus_int @ SX1 @ one_one_int ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[324]) ).
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)],[368]) ).
thf(395,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)],[362]) ).
thf(396,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ord_less_int @ ( plus_plus_int @ SX0 @ SX0 ) @ zero_zero_int )
| ( ord_less_int @ SX0 @ zero_zero_int ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less_int @ SX0 @ zero_zero_int )
| ( ord_less_int @ ( plus_plus_int @ SX0 @ SX0 ) @ zero_zero_int ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[308]) ).
thf(397,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ord_less_int @ zero_zero_int @ ( number_number_of_int @ SX0 ) )
| ( ord_less_int @ pls @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less_int @ pls @ SX0 )
| ( ord_less_int @ zero_zero_int @ ( number_number_of_int @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[314]) ).
thf(398,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ord_less_int @ ( bit1 @ SX0 ) @ pls )
| ( ord_less_int @ SX0 @ pls ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less_int @ SX0 @ pls )
| ( ord_less_int @ ( bit1 @ SX0 ) @ pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[315]) ).
thf(399,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( ( semiri1621563631at_int @ SX0 )
!= zero_zero_int )
| ( SX0 = zero_zero_nat ) )
| ~ ! [SX0: $i] :
( ( SX0 != zero_zero_nat )
| ( ( semiri1621563631at_int @ SX0 )
= zero_zero_int ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[292]) ).
thf(400,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( ( number_number_of_nat @ SX0 )
!= zero_zero_nat )
| ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ SX0 ) )
= one_one_nat ) )
| ~ ! [SX0: $i] :
( ( ( number_number_of_nat @ SX0 )
= zero_zero_nat )
| ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ SX0 ) )
= zero_zero_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[365]) ).
thf(401,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[317]) ).
thf(402,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)],[364]) ).
thf(403,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( ( bit0 @ SX0 )
!= pls )
| ( SX0 = pls ) )
| ~ ! [SX0: $i] :
( ( SX0 != pls )
| ( ( bit0 @ SX0 )
= pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[334]) ).
thf(404,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ SX0 ) @ SX0 ) @ zero_zero_int )
| ( ord_less_int @ SX0 @ zero_zero_int ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less_int @ SX0 @ zero_zero_int )
| ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ SX0 ) @ SX0 ) @ zero_zero_int ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[328]) ).
thf(405,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[295]) ).
thf(406,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ord_less_int @ ( number_number_of_int @ SX0 ) @ zero_zero_int )
| ( ord_less_int @ SX0 @ pls ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less_int @ SX0 @ pls )
| ( ord_less_int @ ( number_number_of_int @ SX0 ) @ zero_zero_int ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[313]) ).
thf(407,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ord_less_int @ ( number_number_of_int @ SX0 ) @ one_one_int )
| ( ord_less_int @ SX0 @ ( bit1 @ pls ) ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less_int @ SX0 @ ( bit1 @ pls ) )
| ( ord_less_int @ ( number_number_of_int @ SX0 ) @ one_one_int ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[326]) ).
thf(408,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( ( number_number_of_nat @ SX0 )
!= zero_zero_nat )
| ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ SX0 ) )
= one_one_int ) )
| ~ ! [SX0: $i] :
( ( ( number_number_of_nat @ SX0 )
= zero_zero_nat )
| ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ SX0 ) )
= zero_zero_int ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[279]) ).
thf(409,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)],[305]) ).
thf(410,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)],[272]) ).
thf(411,plain,
! [SV1: $i] :
( ( ( plus_plus_int @ one_one_int @ ( number_number_of_int @ SV1 ) )
= ( number_number_of_int @ ( plus_plus_int @ ( bit1 @ pls ) @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[273]) ).
thf(412,plain,
! [SV2: $i] :
( ( ( plus_plus_int @ ( number_number_of_int @ SV2 ) @ one_one_int )
= ( number_number_of_int @ ( plus_plus_int @ SV2 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[274]) ).
thf(413,plain,
! [SV3: $i] :
( ( ( power_power_int @ ( power_power_int @ SV3 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power_int @ SV3 @ ( number_number_of_nat @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[278]) ).
thf(414,plain,
! [SV4: $i] :
( ( ! [SY118: $i] :
( ( plus_plus_int @ ( number_number_of_int @ SV4 ) @ ( number_number_of_int @ SY118 ) )
= ( number_number_of_int @ ( plus_plus_int @ SV4 @ SY118 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[283]) ).
thf(415,plain,
! [SV5: $i] :
( ( ! [SY119: $i] :
( ( power_power_int @ ( semiri1621563631at_int @ SV5 ) @ SY119 )
= ( semiri1621563631at_int @ ( power_power_nat @ SV5 @ SY119 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[285]) ).
thf(416,plain,
! [SV6: $i] :
( ( ! [SY120: $i] :
( ( semiri1621563631at_int @ ( power_power_nat @ SV6 @ SY120 ) )
= ( power_power_int @ ( semiri1621563631at_int @ SV6 ) @ SY120 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[286]) ).
thf(417,plain,
! [SV7: $i] :
( ( ! [SY121: $i,SY122: $i] :
( ( plus_plus_int @ ( semiri1621563631at_int @ SV7 ) @ ( plus_plus_int @ ( semiri1621563631at_int @ SY121 ) @ SY122 ) )
= ( plus_plus_int @ ( semiri1621563631at_int @ ( plus_plus_nat @ SV7 @ SY121 ) ) @ SY122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[287]) ).
thf(418,plain,
! [SV8: $i] :
( ( ! [SY123: $i] :
( ( plus_plus_int @ ( semiri1621563631at_int @ SV8 ) @ ( semiri1621563631at_int @ SY123 ) )
= ( semiri1621563631at_int @ ( plus_plus_nat @ SV8 @ SY123 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[288]) ).
thf(419,plain,
( ( ord_less_int @ pls @ pls )
= $false ),
inference(extcnf_not_pos,[status(thm)],[297]) ).
thf(420,plain,
! [SV9: $i] :
( ( ! [SY124: $i,SY125: $i] :
( ~ ( ord_less_int @ SY124 @ SY125 )
| ( ord_less_int @ ( plus_plus_int @ SY124 @ SV9 ) @ ( plus_plus_int @ SY125 @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[300]) ).
thf(421,plain,
! [SV10: $i] :
( ( ! [SY126: $i,SY127: $i] :
( ( plus_plus_int @ ( plus_plus_int @ SV10 @ SY126 ) @ SY127 )
= ( plus_plus_int @ SV10 @ ( plus_plus_int @ SY126 @ SY127 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[309]) ).
thf(422,plain,
! [SV11: $i] :
( ( ! [SY128: $i,SY129: $i] :
( ( plus_plus_int @ SV11 @ ( plus_plus_int @ SY128 @ SY129 ) )
= ( plus_plus_int @ SY128 @ ( plus_plus_int @ SV11 @ SY129 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[310]) ).
thf(423,plain,
! [SV12: $i] :
( ( ! [SY130: $i] :
( ( plus_plus_int @ SV12 @ SY130 )
= ( plus_plus_int @ SY130 @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[311]) ).
thf(424,plain,
( ( ord_less_int @ pls @ zero_zero_int )
= $false ),
inference(extcnf_not_pos,[status(thm)],[321]) ).
thf(425,plain,
! [SV13: $i] :
( ( ~ ( ord_less_int @ ( semiri1621563631at_int @ SV13 ) @ zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[325]) ).
thf(426,plain,
! [SV14: $i] :
( ( ( ( bit1 @ SV14 )
!= pls ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[330]) ).
thf(427,plain,
! [SV15: $i] :
( ( ( pls
!= ( bit1 @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[331]) ).
thf(428,plain,
! [SV16: $i] :
( ( ! [SY131: $i] :
( ( bit1 @ SV16 )
!= ( bit0 @ SY131 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[332]) ).
thf(429,plain,
! [SV17: $i] :
( ( ! [SY132: $i] :
( ( bit0 @ SV17 )
!= ( bit1 @ SY132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[333]) ).
thf(430,plain,
( ( zero_zero_int = one_one_int )
= $false ),
inference(extcnf_not_pos,[status(thm)],[338]) ).
thf(431,plain,
! [SV18: $i] :
( ( ( plus_plus_int @ SV18 @ pls )
= SV18 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[339]) ).
thf(432,plain,
! [SV19: $i] :
( ( ( plus_plus_int @ pls @ SV19 )
= SV19 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[340]) ).
thf(433,plain,
! [SV20: $i] :
( ( ! [SY133: $i] :
( ( plus_plus_int @ ( bit0 @ SV20 ) @ ( bit0 @ SY133 ) )
= ( bit0 @ ( plus_plus_int @ SV20 @ SY133 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[341]) ).
thf(434,plain,
! [SV21: $i] :
( ( ( bit0 @ SV21 )
= ( plus_plus_int @ SV21 @ SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[342]) ).
thf(435,plain,
! [SV22: $i] :
( ( ( plus_plus_int @ SV22 @ zero_zero_int )
= SV22 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[343]) ).
thf(436,plain,
! [SV23: $i] :
( ( ( plus_plus_int @ zero_zero_int @ SV23 )
= SV23 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[344]) ).
thf(437,plain,
! [SV24: $i] :
( ( ( plus_plus_int @ ( number_number_of_int @ pls ) @ SV24 )
= SV24 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[349]) ).
thf(438,plain,
! [SV25: $i] :
( ( ( plus_plus_int @ SV25 @ ( number_number_of_int @ pls ) )
= SV25 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[350]) ).
thf(439,plain,
! [SV26: $i] :
( ( ! [SY134: $i,SY135: $i] :
( ( plus_plus_int @ ( number_number_of_int @ SV26 ) @ ( plus_plus_int @ ( number_number_of_int @ SY134 ) @ SY135 ) )
= ( plus_plus_int @ ( number_number_of_int @ ( plus_plus_int @ SV26 @ SY134 ) ) @ SY135 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[353]) ).
thf(440,plain,
! [SV27: $i] :
( ( ! [SY136: $i] :
( ( plus_plus_int @ ( number_number_of_int @ SV27 ) @ ( number_number_of_int @ SY136 ) )
= ( number_number_of_int @ ( plus_plus_int @ SV27 @ SY136 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[354]) ).
thf(441,plain,
! [SV28: $i] :
( ( ! [SY137: $i] :
( ( number_number_of_int @ ( plus_plus_int @ SV28 @ SY137 ) )
= ( plus_plus_int @ ( number_number_of_int @ SV28 ) @ ( number_number_of_int @ SY137 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[355]) ).
thf(442,plain,
! [SV29: $i] :
( ( ! [SY138: $i] :
( ( plus_plus_int @ ( bit1 @ SV29 ) @ ( bit0 @ SY138 ) )
= ( bit1 @ ( plus_plus_int @ SV29 @ SY138 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[356]) ).
thf(443,plain,
! [SV30: $i] :
( ( ! [SY139: $i] :
( ( plus_plus_int @ ( bit0 @ SV30 ) @ ( bit1 @ SY139 ) )
= ( bit1 @ ( plus_plus_int @ SV30 @ SY139 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[357]) ).
thf(444,plain,
! [SV31: $i] :
( ( ( bit1 @ SV31 )
= ( plus_plus_int @ ( plus_plus_int @ one_one_int @ SV31 ) @ SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[358]) ).
thf(445,plain,
! [SV32: $i] :
( ( ( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ SV32 ) @ SV32 )
!= zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[359]) ).
thf(446,plain,
! [SV33: $i] :
( ( ( number_number_of_nat @ ( semiri1621563631at_int @ SV33 ) )
= ( semiri984289939at_nat @ SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[360]) ).
thf(447,plain,
! [SV34: $i] :
( ( ( number_number_of_int @ ( semiri1621563631at_int @ SV34 ) )
= ( semiri1621563631at_int @ SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[361]) ).
thf(448,plain,
! [SV35: $i] :
( ( ~ ( ord_less_int @ ( power_power_int @ SV35 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[363]) ).
thf(449,plain,
! [SV36: $i] :
( ( ! [SY140: $i] :
( ( ord_less_int @ SY140 @ SV36 )
| ( SV36 = SY140 )
| ( ord_less_int @ SV36 @ SY140 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[366]) ).
thf(450,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_int @ one_one_int @ ( number_number_of_int @ SX0 ) )
| ( ord_less_int @ ( bit1 @ pls ) @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less_int @ ( bit1 @ pls ) @ SX0 )
| ( ord_less_int @ one_one_int @ ( number_number_of_int @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[372]) ).
thf(451,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)],[373]) ).
thf(452,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_int @ ( bit0 @ SX0 ) @ zero_zero_int )
| ( ord_less_int @ SX0 @ zero_zero_int ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less_int @ SX0 @ zero_zero_int )
| ( ord_less_int @ ( bit0 @ SX0 ) @ zero_zero_int ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[374]) ).
thf(453,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[375]) ).
thf(454,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( semiri1621563631at_int @ SX0 )
!= ( semiri1621563631at_int @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( semiri1621563631at_int @ SX0 )
= ( semiri1621563631at_int @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[376]) ).
thf(455,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[377]) ).
thf(456,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( number_number_of_nat @ SX1 )
= zero_zero_nat )
| ( SX0 != zero_zero_int )
| ( ( power_power_int @ SX0 @ ( number_number_of_nat @ SX1 ) )
= zero_zero_int ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( power_power_int @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_int )
| ( ( number_number_of_nat @ SX1 )
!= zero_zero_nat ) )
| ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( power_power_int @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[378]) ).
thf(457,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)],[379]) ).
thf(458,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( number_number_of_nat @ SX1 )
= zero_zero_nat )
| ( SX0 != zero_zero_nat )
| ( ( power_power_nat @ SX0 @ ( number_number_of_nat @ SX1 ) )
= zero_zero_nat ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( power_power_nat @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_nat )
| ( ( number_number_of_nat @ SX1 )
!= zero_zero_nat ) )
| ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( power_power_nat @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_nat )
| ( SX0 = zero_zero_nat ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[380]) ).
thf(459,plain,
( ( ~ ! [SX0: $i] :
( ( ( plus_plus_int @ SX0 @ SX0 )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) )
| ~ ! [SX0: $i] :
( ( SX0 != zero_zero_int )
| ( ( plus_plus_int @ SX0 @ SX0 )
= zero_zero_int ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[381]) ).
thf(460,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)],[382]) ).
thf(461,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[383]) ).
thf(462,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_int @ pls @ ( bit0 @ SX0 ) )
| ( ord_less_int @ pls @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less_int @ pls @ SX0 )
| ( ord_less_int @ pls @ ( bit0 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[384]) ).
thf(463,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_int @ ( bit1 @ SX0 ) @ zero_zero_int )
| ( ord_less_int @ SX0 @ zero_zero_int ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less_int @ SX0 @ zero_zero_int )
| ( ord_less_int @ ( bit1 @ SX0 ) @ zero_zero_int ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[385]) ).
thf(464,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)],[386]) ).
thf(465,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[387]) ).
thf(466,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)],[388]) ).
thf(467,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)],[389]) ).
thf(468,plain,
( ( ~ ! [SX0: $i] :
( ( pls
!= ( bit0 @ SX0 ) )
| ( pls = SX0 ) )
| ~ ! [SX0: $i] :
( ( pls != SX0 )
| ( pls
= ( bit0 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[390]) ).
thf(469,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)],[391]) ).
thf(470,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_int @ ( bit0 @ SX0 ) @ pls )
| ( ord_less_int @ SX0 @ pls ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less_int @ SX0 @ pls )
| ( ord_less_int @ ( bit0 @ SX0 ) @ pls ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[392]) ).
thf(471,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX0 @ ( plus_plus_int @ SX1 @ one_one_int ) )
| ( SX0 = SX1 )
| ( ord_less_int @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ord_less_int @ SX0 @ ( plus_plus_int @ SX1 @ one_one_int ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ SX0 @ ( plus_plus_int @ SX1 @ one_one_int ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[393]) ).
thf(472,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(473,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)],[395]) ).
thf(474,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_int @ ( plus_plus_int @ SX0 @ SX0 ) @ zero_zero_int )
| ( ord_less_int @ SX0 @ zero_zero_int ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less_int @ SX0 @ zero_zero_int )
| ( ord_less_int @ ( plus_plus_int @ SX0 @ SX0 ) @ zero_zero_int ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[396]) ).
thf(475,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_int @ zero_zero_int @ ( number_number_of_int @ SX0 ) )
| ( ord_less_int @ pls @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less_int @ pls @ SX0 )
| ( ord_less_int @ zero_zero_int @ ( number_number_of_int @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[397]) ).
thf(476,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_int @ ( bit1 @ SX0 ) @ pls )
| ( ord_less_int @ SX0 @ pls ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less_int @ SX0 @ pls )
| ( ord_less_int @ ( bit1 @ SX0 ) @ pls ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[398]) ).
thf(477,plain,
( ( ~ ! [SX0: $i] :
( ( ( semiri1621563631at_int @ SX0 )
!= zero_zero_int )
| ( SX0 = zero_zero_nat ) )
| ~ ! [SX0: $i] :
( ( SX0 != zero_zero_nat )
| ( ( semiri1621563631at_int @ SX0 )
= zero_zero_int ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[399]) ).
thf(478,plain,
( ( ~ ! [SX0: $i] :
( ( ( number_number_of_nat @ SX0 )
!= zero_zero_nat )
| ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ SX0 ) )
= one_one_nat ) )
| ~ ! [SX0: $i] :
( ( ( number_number_of_nat @ SX0 )
= zero_zero_nat )
| ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ SX0 ) )
= zero_zero_nat ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[400]) ).
thf(479,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[401]) ).
thf(480,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)],[402]) ).
thf(481,plain,
( ( ~ ! [SX0: $i] :
( ( ( bit0 @ SX0 )
!= pls )
| ( SX0 = pls ) )
| ~ ! [SX0: $i] :
( ( SX0 != pls )
| ( ( bit0 @ SX0 )
= pls ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[403]) ).
thf(482,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ SX0 ) @ SX0 ) @ zero_zero_int )
| ( ord_less_int @ SX0 @ zero_zero_int ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less_int @ SX0 @ zero_zero_int )
| ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ SX0 ) @ SX0 ) @ zero_zero_int ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[404]) ).
thf(483,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[405]) ).
thf(484,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_int @ ( number_number_of_int @ SX0 ) @ zero_zero_int )
| ( ord_less_int @ SX0 @ pls ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less_int @ SX0 @ pls )
| ( ord_less_int @ ( number_number_of_int @ SX0 ) @ zero_zero_int ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[406]) ).
thf(485,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_int @ ( number_number_of_int @ SX0 ) @ one_one_int )
| ( ord_less_int @ SX0 @ ( bit1 @ pls ) ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less_int @ SX0 @ ( bit1 @ pls ) )
| ( ord_less_int @ ( number_number_of_int @ SX0 ) @ one_one_int ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[407]) ).
thf(486,plain,
( ( ~ ! [SX0: $i] :
( ( ( number_number_of_nat @ SX0 )
!= zero_zero_nat )
| ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ SX0 ) )
= one_one_int ) )
| ~ ! [SX0: $i] :
( ( ( number_number_of_nat @ SX0 )
= zero_zero_nat )
| ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ SX0 ) )
= zero_zero_int ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[408]) ).
thf(487,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)],[409]) ).
thf(488,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)],[410]) ).
thf(489,plain,
! [SV37: $i,SV4: $i] :
( ( ( plus_plus_int @ ( number_number_of_int @ SV4 ) @ ( number_number_of_int @ SV37 ) )
= ( number_number_of_int @ ( plus_plus_int @ SV4 @ SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[414]) ).
thf(490,plain,
! [SV38: $i,SV5: $i] :
( ( ( power_power_int @ ( semiri1621563631at_int @ SV5 ) @ SV38 )
= ( semiri1621563631at_int @ ( power_power_nat @ SV5 @ SV38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[415]) ).
thf(491,plain,
! [SV39: $i,SV6: $i] :
( ( ( semiri1621563631at_int @ ( power_power_nat @ SV6 @ SV39 ) )
= ( power_power_int @ ( semiri1621563631at_int @ SV6 ) @ SV39 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[416]) ).
thf(492,plain,
! [SV40: $i,SV7: $i] :
( ( ! [SY141: $i] :
( ( plus_plus_int @ ( semiri1621563631at_int @ SV7 ) @ ( plus_plus_int @ ( semiri1621563631at_int @ SV40 ) @ SY141 ) )
= ( plus_plus_int @ ( semiri1621563631at_int @ ( plus_plus_nat @ SV7 @ SV40 ) ) @ SY141 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[417]) ).
thf(493,plain,
! [SV41: $i,SV8: $i] :
( ( ( plus_plus_int @ ( semiri1621563631at_int @ SV8 ) @ ( semiri1621563631at_int @ SV41 ) )
= ( semiri1621563631at_int @ ( plus_plus_nat @ SV8 @ SV41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[418]) ).
thf(494,plain,
! [SV9: $i,SV42: $i] :
( ( ! [SY142: $i] :
( ~ ( ord_less_int @ SV42 @ SY142 )
| ( ord_less_int @ ( plus_plus_int @ SV42 @ SV9 ) @ ( plus_plus_int @ SY142 @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[420]) ).
thf(495,plain,
! [SV43: $i,SV10: $i] :
( ( ! [SY143: $i] :
( ( plus_plus_int @ ( plus_plus_int @ SV10 @ SV43 ) @ SY143 )
= ( plus_plus_int @ SV10 @ ( plus_plus_int @ SV43 @ SY143 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[421]) ).
thf(496,plain,
! [SV44: $i,SV11: $i] :
( ( ! [SY144: $i] :
( ( plus_plus_int @ SV11 @ ( plus_plus_int @ SV44 @ SY144 ) )
= ( plus_plus_int @ SV44 @ ( plus_plus_int @ SV11 @ SY144 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[422]) ).
thf(497,plain,
! [SV45: $i,SV12: $i] :
( ( ( plus_plus_int @ SV12 @ SV45 )
= ( plus_plus_int @ SV45 @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[423]) ).
thf(498,plain,
! [SV13: $i] :
( ( ord_less_int @ ( semiri1621563631at_int @ SV13 ) @ zero_zero_int )
= $false ),
inference(extcnf_not_pos,[status(thm)],[425]) ).
thf(499,plain,
! [SV14: $i] :
( ( ( bit1 @ SV14 )
= pls )
= $false ),
inference(extcnf_not_pos,[status(thm)],[426]) ).
thf(500,plain,
! [SV15: $i] :
( ( pls
= ( bit1 @ SV15 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[427]) ).
thf(501,plain,
! [SV46: $i,SV16: $i] :
( ( ( ( bit1 @ SV16 )
!= ( bit0 @ SV46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[428]) ).
thf(502,plain,
! [SV47: $i,SV17: $i] :
( ( ( ( bit0 @ SV17 )
!= ( bit1 @ SV47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[429]) ).
thf(503,plain,
! [SV48: $i,SV20: $i] :
( ( ( plus_plus_int @ ( bit0 @ SV20 ) @ ( bit0 @ SV48 ) )
= ( bit0 @ ( plus_plus_int @ SV20 @ SV48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[433]) ).
thf(504,plain,
! [SV49: $i,SV26: $i] :
( ( ! [SY145: $i] :
( ( plus_plus_int @ ( number_number_of_int @ SV26 ) @ ( plus_plus_int @ ( number_number_of_int @ SV49 ) @ SY145 ) )
= ( plus_plus_int @ ( number_number_of_int @ ( plus_plus_int @ SV26 @ SV49 ) ) @ SY145 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[439]) ).
thf(505,plain,
! [SV50: $i,SV27: $i] :
( ( ( plus_plus_int @ ( number_number_of_int @ SV27 ) @ ( number_number_of_int @ SV50 ) )
= ( number_number_of_int @ ( plus_plus_int @ SV27 @ SV50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[440]) ).
thf(506,plain,
! [SV51: $i,SV28: $i] :
( ( ( number_number_of_int @ ( plus_plus_int @ SV28 @ SV51 ) )
= ( plus_plus_int @ ( number_number_of_int @ SV28 ) @ ( number_number_of_int @ SV51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[441]) ).
thf(507,plain,
! [SV52: $i,SV29: $i] :
( ( ( plus_plus_int @ ( bit1 @ SV29 ) @ ( bit0 @ SV52 ) )
= ( bit1 @ ( plus_plus_int @ SV29 @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[442]) ).
thf(508,plain,
! [SV53: $i,SV30: $i] :
( ( ( plus_plus_int @ ( bit0 @ SV30 ) @ ( bit1 @ SV53 ) )
= ( bit1 @ ( plus_plus_int @ SV30 @ SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[443]) ).
thf(509,plain,
! [SV32: $i] :
( ( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ SV32 ) @ SV32 )
= zero_zero_int )
= $false ),
inference(extcnf_not_pos,[status(thm)],[445]) ).
thf(510,plain,
! [SV35: $i] :
( ( ord_less_int @ ( power_power_int @ SV35 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ zero_zero_int )
= $false ),
inference(extcnf_not_pos,[status(thm)],[448]) ).
thf(511,plain,
! [SV36: $i,SV54: $i] :
( ( ( ord_less_int @ SV54 @ SV36 )
| ( SV36 = SV54 )
| ( ord_less_int @ SV36 @ SV54 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[449]) ).
thf(512,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_int @ one_one_int @ ( number_number_of_int @ SX0 ) )
| ( ord_less_int @ ( bit1 @ pls ) @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[450]) ).
thf(513,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_int @ ( bit1 @ pls ) @ SX0 )
| ( ord_less_int @ one_one_int @ ( number_number_of_int @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[450]) ).
thf(514,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)],[451]) ).
thf(515,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)],[451]) ).
thf(516,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_int @ ( bit0 @ SX0 ) @ zero_zero_int )
| ( ord_less_int @ SX0 @ zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[452]) ).
thf(517,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_int @ SX0 @ zero_zero_int )
| ( ord_less_int @ ( bit0 @ SX0 ) @ zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[452]) ).
thf(518,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[453]) ).
thf(519,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[453]) ).
thf(520,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( semiri1621563631at_int @ SX0 )
!= ( semiri1621563631at_int @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[454]) ).
thf(521,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( semiri1621563631at_int @ SX0 )
= ( semiri1621563631at_int @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[454]) ).
thf(522,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[455]) ).
thf(523,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[455]) ).
thf(524,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( number_number_of_nat @ SX1 )
= zero_zero_nat )
| ( SX0 != zero_zero_int )
| ( ( power_power_int @ SX0 @ ( number_number_of_nat @ SX1 ) )
= zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[456]) ).
thf(525,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( power_power_int @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_int )
| ( ( number_number_of_nat @ SX1 )
!= zero_zero_nat ) )
| ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( power_power_int @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[456]) ).
thf(526,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( number_number_of_int @ SX0 )
!= ( number_number_of_int @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[457]) ).
thf(527,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( number_number_of_int @ SX0 )
= ( number_number_of_int @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[457]) ).
thf(528,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( number_number_of_nat @ SX1 )
= zero_zero_nat )
| ( SX0 != zero_zero_nat )
| ( ( power_power_nat @ SX0 @ ( number_number_of_nat @ SX1 ) )
= zero_zero_nat ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[458]) ).
thf(529,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( power_power_nat @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_nat )
| ( ( number_number_of_nat @ SX1 )
!= zero_zero_nat ) )
| ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( power_power_nat @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_nat )
| ( SX0 = zero_zero_nat ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[458]) ).
thf(530,plain,
( ( ~ ! [SX0: $i] :
( ( ( plus_plus_int @ SX0 @ SX0 )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[459]) ).
thf(531,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != zero_zero_int )
| ( ( plus_plus_int @ SX0 @ SX0 )
= zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[459]) ).
thf(532,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)],[460]) ).
thf(533,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)],[460]) ).
thf(534,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[461]) ).
thf(535,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[461]) ).
thf(536,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_int @ pls @ ( bit0 @ SX0 ) )
| ( ord_less_int @ pls @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[462]) ).
thf(537,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_int @ pls @ SX0 )
| ( ord_less_int @ pls @ ( bit0 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[462]) ).
thf(538,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_int @ ( bit1 @ SX0 ) @ zero_zero_int )
| ( ord_less_int @ SX0 @ zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[463]) ).
thf(539,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_int @ SX0 @ zero_zero_int )
| ( ord_less_int @ ( bit1 @ SX0 ) @ zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[463]) ).
thf(540,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( bit0 @ SX0 )
!= ( bit0 @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[464]) ).
thf(541,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( bit0 @ SX0 )
= ( bit0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[464]) ).
thf(542,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[465]) ).
thf(543,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[465]) ).
thf(544,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( bit1 @ SX0 )
!= ( bit1 @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[466]) ).
thf(545,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( bit1 @ SX0 )
= ( bit1 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[466]) ).
thf(546,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( number_number_of_int @ SX0 )
!= SX1 )
| ( SX1
= ( number_number_of_int @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[467]) ).
thf(547,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( number_number_of_int @ SX0 ) )
| ( ( number_number_of_int @ SX0 )
= SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[467]) ).
thf(548,plain,
( ( ~ ! [SX0: $i] :
( ( pls
!= ( bit0 @ SX0 ) )
| ( pls = SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[468]) ).
thf(549,plain,
( ( ~ ! [SX0: $i] :
( ( pls != SX0 )
| ( pls
= ( bit0 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[468]) ).
thf(550,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)],[469]) ).
thf(551,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)],[469]) ).
thf(552,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_int @ ( bit0 @ SX0 ) @ pls )
| ( ord_less_int @ SX0 @ pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[470]) ).
thf(553,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_int @ SX0 @ pls )
| ( ord_less_int @ ( bit0 @ SX0 ) @ pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[470]) ).
thf(554,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX0 @ ( plus_plus_int @ SX1 @ one_one_int ) )
| ( SX0 = SX1 )
| ( ord_less_int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[471]) ).
thf(555,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ord_less_int @ SX0 @ ( plus_plus_int @ SX1 @ one_one_int ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ SX0 @ ( plus_plus_int @ SX1 @ one_one_int ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[471]) ).
thf(556,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)],[472]) ).
thf(557,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)],[472]) ).
thf(558,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)],[473]) ).
thf(559,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)],[473]) ).
thf(560,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_int @ ( plus_plus_int @ SX0 @ SX0 ) @ zero_zero_int )
| ( ord_less_int @ SX0 @ zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[474]) ).
thf(561,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_int @ SX0 @ zero_zero_int )
| ( ord_less_int @ ( plus_plus_int @ SX0 @ SX0 ) @ zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[474]) ).
thf(562,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_int @ zero_zero_int @ ( number_number_of_int @ SX0 ) )
| ( ord_less_int @ pls @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[475]) ).
thf(563,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_int @ pls @ SX0 )
| ( ord_less_int @ zero_zero_int @ ( number_number_of_int @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[475]) ).
thf(564,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_int @ ( bit1 @ SX0 ) @ pls )
| ( ord_less_int @ SX0 @ pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[476]) ).
thf(565,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_int @ SX0 @ pls )
| ( ord_less_int @ ( bit1 @ SX0 ) @ pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[476]) ).
thf(566,plain,
( ( ~ ! [SX0: $i] :
( ( ( semiri1621563631at_int @ SX0 )
!= zero_zero_int )
| ( SX0 = zero_zero_nat ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[477]) ).
thf(567,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != zero_zero_nat )
| ( ( semiri1621563631at_int @ SX0 )
= zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[477]) ).
thf(568,plain,
( ( ~ ! [SX0: $i] :
( ( ( number_number_of_nat @ SX0 )
!= zero_zero_nat )
| ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ SX0 ) )
= one_one_nat ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[478]) ).
thf(569,plain,
( ( ~ ! [SX0: $i] :
( ( ( number_number_of_nat @ SX0 )
= zero_zero_nat )
| ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ SX0 ) )
= zero_zero_nat ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[478]) ).
thf(570,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[479]) ).
thf(571,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[479]) ).
thf(572,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)],[480]) ).
thf(573,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)],[480]) ).
thf(574,plain,
( ( ~ ! [SX0: $i] :
( ( ( bit0 @ SX0 )
!= pls )
| ( SX0 = pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[481]) ).
thf(575,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != pls )
| ( ( bit0 @ SX0 )
= pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[481]) ).
thf(576,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ SX0 ) @ SX0 ) @ zero_zero_int )
| ( ord_less_int @ SX0 @ zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[482]) ).
thf(577,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_int @ SX0 @ zero_zero_int )
| ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ SX0 ) @ SX0 ) @ zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[482]) ).
thf(578,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[483]) ).
thf(579,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[483]) ).
thf(580,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_int @ ( number_number_of_int @ SX0 ) @ zero_zero_int )
| ( ord_less_int @ SX0 @ pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[484]) ).
thf(581,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_int @ SX0 @ pls )
| ( ord_less_int @ ( number_number_of_int @ SX0 ) @ zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[484]) ).
thf(582,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_int @ ( number_number_of_int @ SX0 ) @ one_one_int )
| ( ord_less_int @ SX0 @ ( bit1 @ pls ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[485]) ).
thf(583,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_int @ SX0 @ ( bit1 @ pls ) )
| ( ord_less_int @ ( number_number_of_int @ SX0 ) @ one_one_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[485]) ).
thf(584,plain,
( ( ~ ! [SX0: $i] :
( ( ( number_number_of_nat @ SX0 )
!= zero_zero_nat )
| ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ SX0 ) )
= one_one_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[486]) ).
thf(585,plain,
( ( ~ ! [SX0: $i] :
( ( ( number_number_of_nat @ SX0 )
= zero_zero_nat )
| ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ SX0 ) )
= zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[486]) ).
thf(586,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( number_number_of_nat @ SX0 )
!= SX1 )
| ( SX1
= ( number_number_of_nat @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[487]) ).
thf(587,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( number_number_of_nat @ SX0 ) )
| ( ( number_number_of_nat @ SX0 )
= SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[487]) ).
thf(588,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)],[488]) ).
thf(589,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)],[488]) ).
thf(590,plain,
! [SV55: $i,SV40: $i,SV7: $i] :
( ( ( plus_plus_int @ ( semiri1621563631at_int @ SV7 ) @ ( plus_plus_int @ ( semiri1621563631at_int @ SV40 ) @ SV55 ) )
= ( plus_plus_int @ ( semiri1621563631at_int @ ( plus_plus_nat @ SV7 @ SV40 ) ) @ SV55 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[492]) ).
thf(591,plain,
! [SV9: $i,SV56: $i,SV42: $i] :
( ( ~ ( ord_less_int @ SV42 @ SV56 )
| ( ord_less_int @ ( plus_plus_int @ SV42 @ SV9 ) @ ( plus_plus_int @ SV56 @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[494]) ).
thf(592,plain,
! [SV57: $i,SV43: $i,SV10: $i] :
( ( ( plus_plus_int @ ( plus_plus_int @ SV10 @ SV43 ) @ SV57 )
= ( plus_plus_int @ SV10 @ ( plus_plus_int @ SV43 @ SV57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[495]) ).
thf(593,plain,
! [SV58: $i,SV44: $i,SV11: $i] :
( ( ( plus_plus_int @ SV11 @ ( plus_plus_int @ SV44 @ SV58 ) )
= ( plus_plus_int @ SV44 @ ( plus_plus_int @ SV11 @ SV58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[496]) ).
thf(594,plain,
! [SV46: $i,SV16: $i] :
( ( ( bit1 @ SV16 )
= ( bit0 @ SV46 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[501]) ).
thf(595,plain,
! [SV47: $i,SV17: $i] :
( ( ( bit0 @ SV17 )
= ( bit1 @ SV47 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[502]) ).
thf(596,plain,
! [SV59: $i,SV49: $i,SV26: $i] :
( ( ( plus_plus_int @ ( number_number_of_int @ SV26 ) @ ( plus_plus_int @ ( number_number_of_int @ SV49 ) @ SV59 ) )
= ( plus_plus_int @ ( number_number_of_int @ ( plus_plus_int @ SV26 @ SV49 ) ) @ SV59 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[504]) ).
thf(597,plain,
! [SV36: $i,SV54: $i] :
( ( ( ord_less_int @ SV54 @ SV36 )
= $true )
| ( ( ( SV36 = SV54 )
| ( ord_less_int @ SV36 @ SV54 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[511]) ).
thf(598,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less_int @ one_one_int @ ( number_number_of_int @ SX0 ) )
| ( ord_less_int @ ( bit1 @ pls ) @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[512]) ).
thf(599,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less_int @ ( bit1 @ pls ) @ SX0 )
| ( ord_less_int @ one_one_int @ ( number_number_of_int @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[513]) ).
thf(600,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)],[514]) ).
thf(601,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)],[515]) ).
thf(602,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less_int @ ( bit0 @ SX0 ) @ zero_zero_int )
| ( ord_less_int @ SX0 @ zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[516]) ).
thf(603,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less_int @ SX0 @ zero_zero_int )
| ( ord_less_int @ ( bit0 @ SX0 ) @ zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[517]) ).
thf(604,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[518]) ).
thf(605,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[519]) ).
thf(606,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( semiri1621563631at_int @ SX0 )
!= ( semiri1621563631at_int @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[520]) ).
thf(607,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( semiri1621563631at_int @ SX0 )
= ( semiri1621563631at_int @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[521]) ).
thf(608,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[522]) ).
thf(609,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[523]) ).
thf(610,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( number_number_of_nat @ SX1 )
= zero_zero_nat )
| ( SX0 != zero_zero_int )
| ( ( power_power_int @ SX0 @ ( number_number_of_nat @ SX1 ) )
= zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[524]) ).
thf(611,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( power_power_int @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_int )
| ( ( number_number_of_nat @ SX1 )
!= zero_zero_nat ) )
| ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( power_power_int @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[525]) ).
thf(612,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( number_number_of_int @ SX0 )
!= ( number_number_of_int @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[526]) ).
thf(613,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( number_number_of_int @ SX0 )
= ( number_number_of_int @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[527]) ).
thf(614,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( number_number_of_nat @ SX1 )
= zero_zero_nat )
| ( SX0 != zero_zero_nat )
| ( ( power_power_nat @ SX0 @ ( number_number_of_nat @ SX1 ) )
= zero_zero_nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[528]) ).
thf(615,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( power_power_nat @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_nat )
| ( ( number_number_of_nat @ SX1 )
!= zero_zero_nat ) )
| ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( power_power_nat @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_nat )
| ( SX0 = zero_zero_nat ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[529]) ).
thf(616,plain,
( ( ! [SX0: $i] :
( ( ( plus_plus_int @ SX0 @ SX0 )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[530]) ).
thf(617,plain,
( ( ! [SX0: $i] :
( ( SX0 != zero_zero_int )
| ( ( plus_plus_int @ SX0 @ SX0 )
= zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[531]) ).
thf(618,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)],[532]) ).
thf(619,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)],[533]) ).
thf(620,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[534]) ).
thf(621,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[535]) ).
thf(622,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less_int @ pls @ ( bit0 @ SX0 ) )
| ( ord_less_int @ pls @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[536]) ).
thf(623,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less_int @ pls @ SX0 )
| ( ord_less_int @ pls @ ( bit0 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[537]) ).
thf(624,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less_int @ ( bit1 @ SX0 ) @ zero_zero_int )
| ( ord_less_int @ SX0 @ zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[538]) ).
thf(625,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less_int @ SX0 @ zero_zero_int )
| ( ord_less_int @ ( bit1 @ SX0 ) @ zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[539]) ).
thf(626,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( bit0 @ SX0 )
!= ( bit0 @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[540]) ).
thf(627,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( bit0 @ SX0 )
= ( bit0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[541]) ).
thf(628,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[542]) ).
thf(629,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[543]) ).
thf(630,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( bit1 @ SX0 )
!= ( bit1 @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[544]) ).
thf(631,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( bit1 @ SX0 )
= ( bit1 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[545]) ).
thf(632,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( number_number_of_int @ SX0 )
!= SX1 )
| ( SX1
= ( number_number_of_int @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[546]) ).
thf(633,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( number_number_of_int @ SX0 ) )
| ( ( number_number_of_int @ SX0 )
= SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[547]) ).
thf(634,plain,
( ( ! [SX0: $i] :
( ( pls
!= ( bit0 @ SX0 ) )
| ( pls = SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[548]) ).
thf(635,plain,
( ( ! [SX0: $i] :
( ( pls != SX0 )
| ( pls
= ( bit0 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[549]) ).
thf(636,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)],[550]) ).
thf(637,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)],[551]) ).
thf(638,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less_int @ ( bit0 @ SX0 ) @ pls )
| ( ord_less_int @ SX0 @ pls ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[552]) ).
thf(639,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less_int @ SX0 @ pls )
| ( ord_less_int @ ( bit0 @ SX0 ) @ pls ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[553]) ).
thf(640,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX0 @ ( plus_plus_int @ SX1 @ one_one_int ) )
| ( SX0 = SX1 )
| ( ord_less_int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[554]) ).
thf(641,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ord_less_int @ SX0 @ ( plus_plus_int @ SX1 @ one_one_int ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ SX0 @ ( plus_plus_int @ SX1 @ one_one_int ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[555]) ).
thf(642,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)],[556]) ).
thf(643,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)],[557]) ).
thf(644,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)],[558]) ).
thf(645,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)],[559]) ).
thf(646,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less_int @ ( plus_plus_int @ SX0 @ SX0 ) @ zero_zero_int )
| ( ord_less_int @ SX0 @ zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[560]) ).
thf(647,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less_int @ SX0 @ zero_zero_int )
| ( ord_less_int @ ( plus_plus_int @ SX0 @ SX0 ) @ zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[561]) ).
thf(648,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less_int @ zero_zero_int @ ( number_number_of_int @ SX0 ) )
| ( ord_less_int @ pls @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[562]) ).
thf(649,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less_int @ pls @ SX0 )
| ( ord_less_int @ zero_zero_int @ ( number_number_of_int @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[563]) ).
thf(650,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less_int @ ( bit1 @ SX0 ) @ pls )
| ( ord_less_int @ SX0 @ pls ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[564]) ).
thf(651,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less_int @ SX0 @ pls )
| ( ord_less_int @ ( bit1 @ SX0 ) @ pls ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[565]) ).
thf(652,plain,
( ( ! [SX0: $i] :
( ( ( semiri1621563631at_int @ SX0 )
!= zero_zero_int )
| ( SX0 = zero_zero_nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[566]) ).
thf(653,plain,
( ( ! [SX0: $i] :
( ( SX0 != zero_zero_nat )
| ( ( semiri1621563631at_int @ SX0 )
= zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[567]) ).
thf(654,plain,
( ( ! [SX0: $i] :
( ( ( number_number_of_nat @ SX0 )
!= zero_zero_nat )
| ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ SX0 ) )
= one_one_nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[568]) ).
thf(655,plain,
( ( ! [SX0: $i] :
( ( ( number_number_of_nat @ SX0 )
= zero_zero_nat )
| ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ SX0 ) )
= zero_zero_nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[569]) ).
thf(656,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[570]) ).
thf(657,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[571]) ).
thf(658,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)],[572]) ).
thf(659,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)],[573]) ).
thf(660,plain,
( ( ! [SX0: $i] :
( ( ( bit0 @ SX0 )
!= pls )
| ( SX0 = pls ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[574]) ).
thf(661,plain,
( ( ! [SX0: $i] :
( ( SX0 != pls )
| ( ( bit0 @ SX0 )
= pls ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[575]) ).
thf(662,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ SX0 ) @ SX0 ) @ zero_zero_int )
| ( ord_less_int @ SX0 @ zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[576]) ).
thf(663,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less_int @ SX0 @ zero_zero_int )
| ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ SX0 ) @ SX0 ) @ zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[577]) ).
thf(664,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[578]) ).
thf(665,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[579]) ).
thf(666,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less_int @ ( number_number_of_int @ SX0 ) @ zero_zero_int )
| ( ord_less_int @ SX0 @ pls ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[580]) ).
thf(667,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less_int @ SX0 @ pls )
| ( ord_less_int @ ( number_number_of_int @ SX0 ) @ zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[581]) ).
thf(668,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less_int @ ( number_number_of_int @ SX0 ) @ one_one_int )
| ( ord_less_int @ SX0 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[582]) ).
thf(669,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less_int @ SX0 @ ( bit1 @ pls ) )
| ( ord_less_int @ ( number_number_of_int @ SX0 ) @ one_one_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[583]) ).
thf(670,plain,
( ( ! [SX0: $i] :
( ( ( number_number_of_nat @ SX0 )
!= zero_zero_nat )
| ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ SX0 ) )
= one_one_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[584]) ).
thf(671,plain,
( ( ! [SX0: $i] :
( ( ( number_number_of_nat @ SX0 )
= zero_zero_nat )
| ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ SX0 ) )
= zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[585]) ).
thf(672,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( number_number_of_nat @ SX0 )
!= SX1 )
| ( SX1
= ( number_number_of_nat @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[586]) ).
thf(673,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( number_number_of_nat @ SX0 ) )
| ( ( number_number_of_nat @ SX0 )
= SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[587]) ).
thf(674,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)],[588]) ).
thf(675,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)],[589]) ).
thf(676,plain,
! [SV9: $i,SV56: $i,SV42: $i] :
( ( ( ~ ( ord_less_int @ SV42 @ SV56 ) )
= $true )
| ( ( ord_less_int @ ( plus_plus_int @ SV42 @ SV9 ) @ ( plus_plus_int @ SV56 @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[591]) ).
thf(677,plain,
! [SV54: $i,SV36: $i] :
( ( ( SV36 = SV54 )
= $true )
| ( ( ord_less_int @ SV36 @ SV54 )
= $true )
| ( ( ord_less_int @ SV54 @ SV36 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[597]) ).
thf(678,plain,
! [SV60: $i] :
( ( ~ ( ord_less_int @ one_one_int @ ( number_number_of_int @ SV60 ) )
| ( ord_less_int @ ( bit1 @ pls ) @ SV60 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[598]) ).
thf(679,plain,
! [SV61: $i] :
( ( ~ ( ord_less_int @ ( bit1 @ pls ) @ SV61 )
| ( ord_less_int @ one_one_int @ ( number_number_of_int @ SV61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[599]) ).
thf(680,plain,
! [SV62: $i] :
( ( ! [SY146: $i] :
( ( SV62 != zero_zero_int )
| ( SY146 != zero_zero_int )
| ( ( plus_plus_int @ ( power_power_int @ SV62 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SY146 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[600]) ).
thf(681,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)],[601]) ).
thf(682,plain,
! [SV63: $i] :
( ( ~ ( ord_less_int @ ( bit0 @ SV63 ) @ zero_zero_int )
| ( ord_less_int @ SV63 @ zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[602]) ).
thf(683,plain,
! [SV64: $i] :
( ( ~ ( ord_less_int @ SV64 @ zero_zero_int )
| ( ord_less_int @ ( bit0 @ SV64 ) @ zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[603]) ).
thf(684,plain,
! [SV65: $i] :
( ( ! [SY147: $i] :
( ~ ( ord_less_int @ ( bit1 @ SV65 ) @ ( bit0 @ SY147 ) )
| ( ord_less_int @ SV65 @ SY147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[604]) ).
thf(685,plain,
! [SV66: $i] :
( ( ! [SY148: $i] :
( ~ ( ord_less_int @ SV66 @ SY148 )
| ( ord_less_int @ ( bit1 @ SV66 ) @ ( bit0 @ SY148 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[605]) ).
thf(686,plain,
! [SV67: $i] :
( ( ! [SY149: $i] :
( ( ( semiri1621563631at_int @ SV67 )
!= ( semiri1621563631at_int @ SY149 ) )
| ( SV67 = SY149 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[606]) ).
thf(687,plain,
! [SV68: $i] :
( ( ! [SY150: $i] :
( ( SV68 != SY150 )
| ( ( semiri1621563631at_int @ SV68 )
= ( semiri1621563631at_int @ SY150 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[607]) ).
thf(688,plain,
! [SV69: $i] :
( ( ! [SY151: $i] :
( ~ ( ord_less_int @ ( bit0 @ SV69 ) @ ( bit0 @ SY151 ) )
| ( ord_less_int @ SV69 @ SY151 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[608]) ).
thf(689,plain,
! [SV70: $i] :
( ( ! [SY152: $i] :
( ~ ( ord_less_int @ SV70 @ SY152 )
| ( ord_less_int @ ( bit0 @ SV70 ) @ ( bit0 @ SY152 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[609]) ).
thf(690,plain,
! [SV71: $i] :
( ( ! [SY153: $i] :
( ( ( number_number_of_nat @ SY153 )
= zero_zero_nat )
| ( SV71 != zero_zero_int )
| ( ( power_power_int @ SV71 @ ( number_number_of_nat @ SY153 ) )
= zero_zero_int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[610]) ).
thf(691,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( power_power_int @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_int )
| ( ( number_number_of_nat @ SX1 )
!= zero_zero_nat ) )
| ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( power_power_int @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[611]) ).
thf(692,plain,
! [SV72: $i] :
( ( ! [SY154: $i] :
( ( ( number_number_of_int @ SV72 )
!= ( number_number_of_int @ SY154 ) )
| ( SV72 = SY154 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[612]) ).
thf(693,plain,
! [SV73: $i] :
( ( ! [SY155: $i] :
( ( SV73 != SY155 )
| ( ( number_number_of_int @ SV73 )
= ( number_number_of_int @ SY155 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[613]) ).
thf(694,plain,
! [SV74: $i] :
( ( ! [SY156: $i] :
( ( ( number_number_of_nat @ SY156 )
= zero_zero_nat )
| ( SV74 != zero_zero_nat )
| ( ( power_power_nat @ SV74 @ ( number_number_of_nat @ SY156 ) )
= zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[614]) ).
thf(695,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( power_power_nat @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_nat )
| ( ( number_number_of_nat @ SX1 )
!= zero_zero_nat ) )
| ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( power_power_nat @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_nat )
| ( SX0 = zero_zero_nat ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[615]) ).
thf(696,plain,
! [SV75: $i] :
( ( ( ( plus_plus_int @ SV75 @ SV75 )
!= zero_zero_int )
| ( SV75 = zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[616]) ).
thf(697,plain,
! [SV76: $i] :
( ( ( SV76 != zero_zero_int )
| ( ( plus_plus_int @ SV76 @ SV76 )
= zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[617]) ).
thf(698,plain,
! [SV77: $i] :
( ( ! [SY157: $i] :
( ~ ( ord_less_int @ ( number_number_of_int @ SV77 ) @ ( number_number_of_int @ SY157 ) )
| ( ord_less_int @ SV77 @ SY157 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[618]) ).
thf(699,plain,
! [SV78: $i] :
( ( ! [SY158: $i] :
( ~ ( ord_less_int @ SV78 @ SY158 )
| ( ord_less_int @ ( number_number_of_int @ SV78 ) @ ( number_number_of_int @ SY158 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[619]) ).
thf(700,plain,
! [SV79: $i] :
( ( ! [SY159: $i] :
( ~ ( ord_less_int @ ( bit0 @ SV79 ) @ ( bit0 @ SY159 ) )
| ( ord_less_int @ SV79 @ SY159 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[620]) ).
thf(701,plain,
! [SV80: $i] :
( ( ! [SY160: $i] :
( ~ ( ord_less_int @ SV80 @ SY160 )
| ( ord_less_int @ ( bit0 @ SV80 ) @ ( bit0 @ SY160 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[621]) ).
thf(702,plain,
! [SV81: $i] :
( ( ~ ( ord_less_int @ pls @ ( bit0 @ SV81 ) )
| ( ord_less_int @ pls @ SV81 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[622]) ).
thf(703,plain,
! [SV82: $i] :
( ( ~ ( ord_less_int @ pls @ SV82 )
| ( ord_less_int @ pls @ ( bit0 @ SV82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[623]) ).
thf(704,plain,
! [SV83: $i] :
( ( ~ ( ord_less_int @ ( bit1 @ SV83 ) @ zero_zero_int )
| ( ord_less_int @ SV83 @ zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[624]) ).
thf(705,plain,
! [SV84: $i] :
( ( ~ ( ord_less_int @ SV84 @ zero_zero_int )
| ( ord_less_int @ ( bit1 @ SV84 ) @ zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[625]) ).
thf(706,plain,
! [SV85: $i] :
( ( ! [SY161: $i] :
( ( ( bit0 @ SV85 )
!= ( bit0 @ SY161 ) )
| ( SV85 = SY161 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[626]) ).
thf(707,plain,
! [SV86: $i] :
( ( ! [SY162: $i] :
( ( SV86 != SY162 )
| ( ( bit0 @ SV86 )
= ( bit0 @ SY162 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[627]) ).
thf(708,plain,
! [SV87: $i] :
( ( ! [SY163: $i] :
( ~ ( ord_less_int @ ( bit1 @ SV87 ) @ ( bit1 @ SY163 ) )
| ( ord_less_int @ SV87 @ SY163 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[628]) ).
thf(709,plain,
! [SV88: $i] :
( ( ! [SY164: $i] :
( ~ ( ord_less_int @ SV88 @ SY164 )
| ( ord_less_int @ ( bit1 @ SV88 ) @ ( bit1 @ SY164 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[629]) ).
thf(710,plain,
! [SV89: $i] :
( ( ! [SY165: $i] :
( ( ( bit1 @ SV89 )
!= ( bit1 @ SY165 ) )
| ( SV89 = SY165 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[630]) ).
thf(711,plain,
! [SV90: $i] :
( ( ! [SY166: $i] :
( ( SV90 != SY166 )
| ( ( bit1 @ SV90 )
= ( bit1 @ SY166 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[631]) ).
thf(712,plain,
! [SV91: $i] :
( ( ! [SY167: $i] :
( ( ( number_number_of_int @ SV91 )
!= SY167 )
| ( SY167
= ( number_number_of_int @ SV91 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[632]) ).
thf(713,plain,
! [SV92: $i] :
( ( ! [SY168: $i] :
( ( SY168
!= ( number_number_of_int @ SV92 ) )
| ( ( number_number_of_int @ SV92 )
= SY168 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[633]) ).
thf(714,plain,
! [SV93: $i] :
( ( ( pls
!= ( bit0 @ SV93 ) )
| ( pls = SV93 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[634]) ).
thf(715,plain,
! [SV94: $i] :
( ( ( pls != SV94 )
| ( pls
= ( bit0 @ SV94 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[635]) ).
thf(716,plain,
! [SV95: $i] :
( ( ! [SY169: $i] :
( ~ ( ord_less_int @ SY169 @ pls )
| ( ( plus_plus_nat @ ( number_number_of_nat @ SY169 ) @ ( number_number_of_nat @ SV95 ) )
= ( number_number_of_nat @ SV95 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[636]) ).
thf(717,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)],[637]) ).
thf(718,plain,
! [SV96: $i] :
( ( ~ ( ord_less_int @ ( bit0 @ SV96 ) @ pls )
| ( ord_less_int @ SV96 @ pls ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[638]) ).
thf(719,plain,
! [SV97: $i] :
( ( ~ ( ord_less_int @ SV97 @ pls )
| ( ord_less_int @ ( bit0 @ SV97 ) @ pls ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[639]) ).
thf(720,plain,
! [SV98: $i] :
( ( ! [SY170: $i] :
( ~ ( ord_less_int @ SV98 @ ( plus_plus_int @ SY170 @ one_one_int ) )
| ( SV98 = SY170 )
| ( ord_less_int @ SV98 @ SY170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[640]) ).
thf(721,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ord_less_int @ SX0 @ ( plus_plus_int @ SX1 @ one_one_int ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ SX0 @ ( plus_plus_int @ SX1 @ one_one_int ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[641]) ).
thf(722,plain,
! [SV99: $i] :
( ( ! [SY171: $i] :
( ~ ( ord_less_int @ ( number_number_of_int @ SV99 ) @ ( number_number_of_int @ SY171 ) )
| ( ord_less_int @ SV99 @ SY171 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[642]) ).
thf(723,plain,
! [SV100: $i] :
( ( ! [SY172: $i] :
( ~ ( ord_less_int @ SV100 @ SY172 )
| ( ord_less_int @ ( number_number_of_int @ SV100 ) @ ( number_number_of_int @ SY172 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[643]) ).
thf(724,plain,
! [SV101: $i] :
( ( ( SV101 = zero_zero_int )
| ( ord_less_int @ zero_zero_int @ ( power_power_int @ SV101 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[644]) ).
thf(725,plain,
! [SV102: $i] :
( ( ~ ( ord_less_int @ zero_zero_int @ ( power_power_int @ SV102 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ( SV102 != zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[645]) ).
thf(726,plain,
! [SV103: $i] :
( ( ~ ( ord_less_int @ ( plus_plus_int @ SV103 @ SV103 ) @ zero_zero_int )
| ( ord_less_int @ SV103 @ zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[646]) ).
thf(727,plain,
! [SV104: $i] :
( ( ~ ( ord_less_int @ SV104 @ zero_zero_int )
| ( ord_less_int @ ( plus_plus_int @ SV104 @ SV104 ) @ zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[647]) ).
thf(728,plain,
! [SV105: $i] :
( ( ~ ( ord_less_int @ zero_zero_int @ ( number_number_of_int @ SV105 ) )
| ( ord_less_int @ pls @ SV105 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[648]) ).
thf(729,plain,
! [SV106: $i] :
( ( ~ ( ord_less_int @ pls @ SV106 )
| ( ord_less_int @ zero_zero_int @ ( number_number_of_int @ SV106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[649]) ).
thf(730,plain,
! [SV107: $i] :
( ( ~ ( ord_less_int @ ( bit1 @ SV107 ) @ pls )
| ( ord_less_int @ SV107 @ pls ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[650]) ).
thf(731,plain,
! [SV108: $i] :
( ( ~ ( ord_less_int @ SV108 @ pls )
| ( ord_less_int @ ( bit1 @ SV108 ) @ pls ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[651]) ).
thf(732,plain,
! [SV109: $i] :
( ( ( ( semiri1621563631at_int @ SV109 )
!= zero_zero_int )
| ( SV109 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[652]) ).
thf(733,plain,
! [SV110: $i] :
( ( ( SV110 != zero_zero_nat )
| ( ( semiri1621563631at_int @ SV110 )
= zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[653]) ).
thf(734,plain,
! [SV111: $i] :
( ( ( ( number_number_of_nat @ SV111 )
!= zero_zero_nat )
| ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ SV111 ) )
= one_one_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[654]) ).
thf(735,plain,
! [SV112: $i] :
( ( ( ( number_number_of_nat @ SV112 )
= zero_zero_nat )
| ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ SV112 ) )
= zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[655]) ).
thf(736,plain,
! [SV113: $i] :
( ( ! [SY173: $i] :
( ~ ( ord_less_int @ ( bit1 @ SV113 ) @ ( bit0 @ SY173 ) )
| ( ord_less_int @ SV113 @ SY173 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[656]) ).
thf(737,plain,
! [SV114: $i] :
( ( ! [SY174: $i] :
( ~ ( ord_less_int @ SV114 @ SY174 )
| ( ord_less_int @ ( bit1 @ SV114 ) @ ( bit0 @ SY174 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[657]) ).
thf(738,plain,
! [SV115: $i] :
( ( ! [SY175: $i] :
( ~ ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ SV115 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SY175 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
| ( SV115 != zero_zero_int )
| ( SY175 != zero_zero_int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[658]) ).
thf(739,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)],[659]) ).
thf(740,plain,
! [SV116: $i] :
( ( ( ( bit0 @ SV116 )
!= pls )
| ( SV116 = pls ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[660]) ).
thf(741,plain,
! [SV117: $i] :
( ( ( SV117 != pls )
| ( ( bit0 @ SV117 )
= pls ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[661]) ).
thf(742,plain,
! [SV118: $i] :
( ( ~ ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ SV118 ) @ SV118 ) @ zero_zero_int )
| ( ord_less_int @ SV118 @ zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[662]) ).
thf(743,plain,
! [SV119: $i] :
( ( ~ ( ord_less_int @ SV119 @ zero_zero_int )
| ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ SV119 ) @ SV119 ) @ zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[663]) ).
thf(744,plain,
! [SV120: $i] :
( ( ! [SY176: $i] :
( ~ ( ord_less_int @ ( bit1 @ SV120 ) @ ( bit1 @ SY176 ) )
| ( ord_less_int @ SV120 @ SY176 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[664]) ).
thf(745,plain,
! [SV121: $i] :
( ( ! [SY177: $i] :
( ~ ( ord_less_int @ SV121 @ SY177 )
| ( ord_less_int @ ( bit1 @ SV121 ) @ ( bit1 @ SY177 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[665]) ).
thf(746,plain,
! [SV122: $i] :
( ( ~ ( ord_less_int @ ( number_number_of_int @ SV122 ) @ zero_zero_int )
| ( ord_less_int @ SV122 @ pls ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[666]) ).
thf(747,plain,
! [SV123: $i] :
( ( ~ ( ord_less_int @ SV123 @ pls )
| ( ord_less_int @ ( number_number_of_int @ SV123 ) @ zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[667]) ).
thf(748,plain,
! [SV124: $i] :
( ( ~ ( ord_less_int @ ( number_number_of_int @ SV124 ) @ one_one_int )
| ( ord_less_int @ SV124 @ ( bit1 @ pls ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[668]) ).
thf(749,plain,
! [SV125: $i] :
( ( ~ ( ord_less_int @ SV125 @ ( bit1 @ pls ) )
| ( ord_less_int @ ( number_number_of_int @ SV125 ) @ one_one_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[669]) ).
thf(750,plain,
! [SV126: $i] :
( ( ( ( number_number_of_nat @ SV126 )
!= zero_zero_nat )
| ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ SV126 ) )
= one_one_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[670]) ).
thf(751,plain,
! [SV127: $i] :
( ( ( ( number_number_of_nat @ SV127 )
= zero_zero_nat )
| ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ SV127 ) )
= zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[671]) ).
thf(752,plain,
! [SV128: $i] :
( ( ! [SY178: $i] :
( ( ( number_number_of_nat @ SV128 )
!= SY178 )
| ( SY178
= ( number_number_of_nat @ SV128 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[672]) ).
thf(753,plain,
! [SV129: $i] :
( ( ! [SY179: $i] :
( ( SY179
!= ( number_number_of_nat @ SV129 ) )
| ( ( number_number_of_nat @ SV129 )
= SY179 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[673]) ).
thf(754,plain,
! [SV130: $i] :
( ( ( ( power_power_int @ SV130 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= zero_zero_int )
| ( SV130 = zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[674]) ).
thf(755,plain,
! [SV131: $i] :
( ( ( SV131 != zero_zero_int )
| ( ( power_power_int @ SV131 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[675]) ).
thf(756,plain,
! [SV9: $i,SV56: $i,SV42: $i] :
( ( ( ord_less_int @ SV42 @ SV56 )
= $false )
| ( ( ord_less_int @ ( plus_plus_int @ SV42 @ SV9 ) @ ( plus_plus_int @ SV56 @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[676]) ).
thf(757,plain,
! [SV60: $i] :
( ( ( ~ ( ord_less_int @ one_one_int @ ( number_number_of_int @ SV60 ) ) )
= $true )
| ( ( ord_less_int @ ( bit1 @ pls ) @ SV60 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[678]) ).
thf(758,plain,
! [SV61: $i] :
( ( ( ~ ( ord_less_int @ ( bit1 @ pls ) @ SV61 ) )
= $true )
| ( ( ord_less_int @ one_one_int @ ( number_number_of_int @ SV61 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[679]) ).
thf(759,plain,
! [SV132: $i,SV62: $i] :
( ( ( SV62 != zero_zero_int )
| ( SV132 != zero_zero_int )
| ( ( plus_plus_int @ ( power_power_int @ SV62 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV132 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[680]) ).
thf(760,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)],[681]) ).
thf(761,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)],[681]) ).
thf(762,plain,
! [SV63: $i] :
( ( ( ~ ( ord_less_int @ ( bit0 @ SV63 ) @ zero_zero_int ) )
= $true )
| ( ( ord_less_int @ SV63 @ zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[682]) ).
thf(763,plain,
! [SV64: $i] :
( ( ( ~ ( ord_less_int @ SV64 @ zero_zero_int ) )
= $true )
| ( ( ord_less_int @ ( bit0 @ SV64 ) @ zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[683]) ).
thf(764,plain,
! [SV133: $i,SV65: $i] :
( ( ~ ( ord_less_int @ ( bit1 @ SV65 ) @ ( bit0 @ SV133 ) )
| ( ord_less_int @ SV65 @ SV133 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[684]) ).
thf(765,plain,
! [SV134: $i,SV66: $i] :
( ( ~ ( ord_less_int @ SV66 @ SV134 )
| ( ord_less_int @ ( bit1 @ SV66 ) @ ( bit0 @ SV134 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[685]) ).
thf(766,plain,
! [SV135: $i,SV67: $i] :
( ( ( ( semiri1621563631at_int @ SV67 )
!= ( semiri1621563631at_int @ SV135 ) )
| ( SV67 = SV135 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[686]) ).
thf(767,plain,
! [SV136: $i,SV68: $i] :
( ( ( SV68 != SV136 )
| ( ( semiri1621563631at_int @ SV68 )
= ( semiri1621563631at_int @ SV136 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[687]) ).
thf(768,plain,
! [SV137: $i,SV69: $i] :
( ( ~ ( ord_less_int @ ( bit0 @ SV69 ) @ ( bit0 @ SV137 ) )
| ( ord_less_int @ SV69 @ SV137 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[688]) ).
thf(769,plain,
! [SV138: $i,SV70: $i] :
( ( ~ ( ord_less_int @ SV70 @ SV138 )
| ( ord_less_int @ ( bit0 @ SV70 ) @ ( bit0 @ SV138 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[689]) ).
thf(770,plain,
! [SV71: $i,SV139: $i] :
( ( ( ( number_number_of_nat @ SV139 )
= zero_zero_nat )
| ( SV71 != zero_zero_int )
| ( ( power_power_int @ SV71 @ ( number_number_of_nat @ SV139 ) )
= zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[690]) ).
thf(771,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( power_power_int @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_int )
| ( ( number_number_of_nat @ SX1 )
!= zero_zero_nat ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[691]) ).
thf(772,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( power_power_int @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[691]) ).
thf(773,plain,
! [SV140: $i,SV72: $i] :
( ( ( ( number_number_of_int @ SV72 )
!= ( number_number_of_int @ SV140 ) )
| ( SV72 = SV140 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[692]) ).
thf(774,plain,
! [SV141: $i,SV73: $i] :
( ( ( SV73 != SV141 )
| ( ( number_number_of_int @ SV73 )
= ( number_number_of_int @ SV141 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[693]) ).
thf(775,plain,
! [SV74: $i,SV142: $i] :
( ( ( ( number_number_of_nat @ SV142 )
= zero_zero_nat )
| ( SV74 != zero_zero_nat )
| ( ( power_power_nat @ SV74 @ ( number_number_of_nat @ SV142 ) )
= zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[694]) ).
thf(776,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( power_power_nat @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_nat )
| ( ( number_number_of_nat @ SX1 )
!= zero_zero_nat ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[695]) ).
thf(777,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( power_power_nat @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_nat )
| ( SX0 = zero_zero_nat ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[695]) ).
thf(778,plain,
! [SV75: $i] :
( ( ( ( ( plus_plus_int @ SV75 @ SV75 )
!= zero_zero_int ) )
= $true )
| ( ( SV75 = zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[696]) ).
thf(779,plain,
! [SV76: $i] :
( ( ( ( SV76 != zero_zero_int ) )
= $true )
| ( ( ( plus_plus_int @ SV76 @ SV76 )
= zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[697]) ).
thf(780,plain,
! [SV143: $i,SV77: $i] :
( ( ~ ( ord_less_int @ ( number_number_of_int @ SV77 ) @ ( number_number_of_int @ SV143 ) )
| ( ord_less_int @ SV77 @ SV143 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[698]) ).
thf(781,plain,
! [SV144: $i,SV78: $i] :
( ( ~ ( ord_less_int @ SV78 @ SV144 )
| ( ord_less_int @ ( number_number_of_int @ SV78 ) @ ( number_number_of_int @ SV144 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[699]) ).
thf(782,plain,
! [SV145: $i,SV79: $i] :
( ( ~ ( ord_less_int @ ( bit0 @ SV79 ) @ ( bit0 @ SV145 ) )
| ( ord_less_int @ SV79 @ SV145 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[700]) ).
thf(783,plain,
! [SV146: $i,SV80: $i] :
( ( ~ ( ord_less_int @ SV80 @ SV146 )
| ( ord_less_int @ ( bit0 @ SV80 ) @ ( bit0 @ SV146 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[701]) ).
thf(784,plain,
! [SV81: $i] :
( ( ( ~ ( ord_less_int @ pls @ ( bit0 @ SV81 ) ) )
= $true )
| ( ( ord_less_int @ pls @ SV81 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[702]) ).
thf(785,plain,
! [SV82: $i] :
( ( ( ~ ( ord_less_int @ pls @ SV82 ) )
= $true )
| ( ( ord_less_int @ pls @ ( bit0 @ SV82 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[703]) ).
thf(786,plain,
! [SV83: $i] :
( ( ( ~ ( ord_less_int @ ( bit1 @ SV83 ) @ zero_zero_int ) )
= $true )
| ( ( ord_less_int @ SV83 @ zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[704]) ).
thf(787,plain,
! [SV84: $i] :
( ( ( ~ ( ord_less_int @ SV84 @ zero_zero_int ) )
= $true )
| ( ( ord_less_int @ ( bit1 @ SV84 ) @ zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[705]) ).
thf(788,plain,
! [SV147: $i,SV85: $i] :
( ( ( ( bit0 @ SV85 )
!= ( bit0 @ SV147 ) )
| ( SV85 = SV147 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[706]) ).
thf(789,plain,
! [SV148: $i,SV86: $i] :
( ( ( SV86 != SV148 )
| ( ( bit0 @ SV86 )
= ( bit0 @ SV148 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[707]) ).
thf(790,plain,
! [SV149: $i,SV87: $i] :
( ( ~ ( ord_less_int @ ( bit1 @ SV87 ) @ ( bit1 @ SV149 ) )
| ( ord_less_int @ SV87 @ SV149 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[708]) ).
thf(791,plain,
! [SV150: $i,SV88: $i] :
( ( ~ ( ord_less_int @ SV88 @ SV150 )
| ( ord_less_int @ ( bit1 @ SV88 ) @ ( bit1 @ SV150 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[709]) ).
thf(792,plain,
! [SV151: $i,SV89: $i] :
( ( ( ( bit1 @ SV89 )
!= ( bit1 @ SV151 ) )
| ( SV89 = SV151 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[710]) ).
thf(793,plain,
! [SV152: $i,SV90: $i] :
( ( ( SV90 != SV152 )
| ( ( bit1 @ SV90 )
= ( bit1 @ SV152 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[711]) ).
thf(794,plain,
! [SV153: $i,SV91: $i] :
( ( ( ( number_number_of_int @ SV91 )
!= SV153 )
| ( SV153
= ( number_number_of_int @ SV91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[712]) ).
thf(795,plain,
! [SV92: $i,SV154: $i] :
( ( ( SV154
!= ( number_number_of_int @ SV92 ) )
| ( ( number_number_of_int @ SV92 )
= SV154 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[713]) ).
thf(796,plain,
! [SV93: $i] :
( ( ( ( pls
!= ( bit0 @ SV93 ) ) )
= $true )
| ( ( pls = SV93 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[714]) ).
thf(797,plain,
! [SV94: $i] :
( ( ( ( pls != SV94 ) )
= $true )
| ( ( pls
= ( bit0 @ SV94 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[715]) ).
thf(798,plain,
! [SV95: $i,SV155: $i] :
( ( ~ ( ord_less_int @ SV155 @ pls )
| ( ( plus_plus_nat @ ( number_number_of_nat @ SV155 ) @ ( number_number_of_nat @ SV95 ) )
= ( number_number_of_nat @ SV95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[716]) ).
thf(799,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)],[717]) ).
thf(800,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)],[717]) ).
thf(801,plain,
! [SV96: $i] :
( ( ( ~ ( ord_less_int @ ( bit0 @ SV96 ) @ pls ) )
= $true )
| ( ( ord_less_int @ SV96 @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[718]) ).
thf(802,plain,
! [SV97: $i] :
( ( ( ~ ( ord_less_int @ SV97 @ pls ) )
= $true )
| ( ( ord_less_int @ ( bit0 @ SV97 ) @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[719]) ).
thf(803,plain,
! [SV156: $i,SV98: $i] :
( ( ~ ( ord_less_int @ SV98 @ ( plus_plus_int @ SV156 @ one_one_int ) )
| ( SV98 = SV156 )
| ( ord_less_int @ SV98 @ SV156 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[720]) ).
thf(804,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ord_less_int @ SX0 @ ( plus_plus_int @ SX1 @ one_one_int ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[721]) ).
thf(805,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ SX0 @ ( plus_plus_int @ SX1 @ one_one_int ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[721]) ).
thf(806,plain,
! [SV157: $i,SV99: $i] :
( ( ~ ( ord_less_int @ ( number_number_of_int @ SV99 ) @ ( number_number_of_int @ SV157 ) )
| ( ord_less_int @ SV99 @ SV157 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[722]) ).
thf(807,plain,
! [SV158: $i,SV100: $i] :
( ( ~ ( ord_less_int @ SV100 @ SV158 )
| ( ord_less_int @ ( number_number_of_int @ SV100 ) @ ( number_number_of_int @ SV158 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[723]) ).
thf(808,plain,
! [SV101: $i] :
( ( ( SV101 = zero_zero_int )
= $true )
| ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ SV101 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[724]) ).
thf(809,plain,
! [SV102: $i] :
( ( ( ~ ( ord_less_int @ zero_zero_int @ ( power_power_int @ SV102 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true )
| ( ( ( SV102 != zero_zero_int ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[725]) ).
thf(810,plain,
! [SV103: $i] :
( ( ( ~ ( ord_less_int @ ( plus_plus_int @ SV103 @ SV103 ) @ zero_zero_int ) )
= $true )
| ( ( ord_less_int @ SV103 @ zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[726]) ).
thf(811,plain,
! [SV104: $i] :
( ( ( ~ ( ord_less_int @ SV104 @ zero_zero_int ) )
= $true )
| ( ( ord_less_int @ ( plus_plus_int @ SV104 @ SV104 ) @ zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[727]) ).
thf(812,plain,
! [SV105: $i] :
( ( ( ~ ( ord_less_int @ zero_zero_int @ ( number_number_of_int @ SV105 ) ) )
= $true )
| ( ( ord_less_int @ pls @ SV105 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[728]) ).
thf(813,plain,
! [SV106: $i] :
( ( ( ~ ( ord_less_int @ pls @ SV106 ) )
= $true )
| ( ( ord_less_int @ zero_zero_int @ ( number_number_of_int @ SV106 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[729]) ).
thf(814,plain,
! [SV107: $i] :
( ( ( ~ ( ord_less_int @ ( bit1 @ SV107 ) @ pls ) )
= $true )
| ( ( ord_less_int @ SV107 @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[730]) ).
thf(815,plain,
! [SV108: $i] :
( ( ( ~ ( ord_less_int @ SV108 @ pls ) )
= $true )
| ( ( ord_less_int @ ( bit1 @ SV108 ) @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[731]) ).
thf(816,plain,
! [SV109: $i] :
( ( ( ( ( semiri1621563631at_int @ SV109 )
!= zero_zero_int ) )
= $true )
| ( ( SV109 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[732]) ).
thf(817,plain,
! [SV110: $i] :
( ( ( ( SV110 != zero_zero_nat ) )
= $true )
| ( ( ( semiri1621563631at_int @ SV110 )
= zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[733]) ).
thf(818,plain,
! [SV111: $i] :
( ( ( ( ( number_number_of_nat @ SV111 )
!= zero_zero_nat ) )
= $true )
| ( ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ SV111 ) )
= one_one_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[734]) ).
thf(819,plain,
! [SV112: $i] :
( ( ( ( number_number_of_nat @ SV112 )
= zero_zero_nat )
= $true )
| ( ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ SV112 ) )
= zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[735]) ).
thf(820,plain,
! [SV159: $i,SV113: $i] :
( ( ~ ( ord_less_int @ ( bit1 @ SV113 ) @ ( bit0 @ SV159 ) )
| ( ord_less_int @ SV113 @ SV159 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[736]) ).
thf(821,plain,
! [SV160: $i,SV114: $i] :
( ( ~ ( ord_less_int @ SV114 @ SV160 )
| ( ord_less_int @ ( bit1 @ SV114 ) @ ( bit0 @ SV160 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[737]) ).
thf(822,plain,
! [SV161: $i,SV115: $i] :
( ( ~ ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ SV115 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV161 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
| ( SV115 != zero_zero_int )
| ( SV161 != zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[738]) ).
thf(823,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)],[739]) ).
thf(824,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)],[739]) ).
thf(825,plain,
! [SV116: $i] :
( ( ( ( ( bit0 @ SV116 )
!= pls ) )
= $true )
| ( ( SV116 = pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[740]) ).
thf(826,plain,
! [SV117: $i] :
( ( ( ( SV117 != pls ) )
= $true )
| ( ( ( bit0 @ SV117 )
= pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[741]) ).
thf(827,plain,
! [SV118: $i] :
( ( ( ~ ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ SV118 ) @ SV118 ) @ zero_zero_int ) )
= $true )
| ( ( ord_less_int @ SV118 @ zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[742]) ).
thf(828,plain,
! [SV119: $i] :
( ( ( ~ ( ord_less_int @ SV119 @ zero_zero_int ) )
= $true )
| ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ SV119 ) @ SV119 ) @ zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[743]) ).
thf(829,plain,
! [SV162: $i,SV120: $i] :
( ( ~ ( ord_less_int @ ( bit1 @ SV120 ) @ ( bit1 @ SV162 ) )
| ( ord_less_int @ SV120 @ SV162 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[744]) ).
thf(830,plain,
! [SV163: $i,SV121: $i] :
( ( ~ ( ord_less_int @ SV121 @ SV163 )
| ( ord_less_int @ ( bit1 @ SV121 ) @ ( bit1 @ SV163 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[745]) ).
thf(831,plain,
! [SV122: $i] :
( ( ( ~ ( ord_less_int @ ( number_number_of_int @ SV122 ) @ zero_zero_int ) )
= $true )
| ( ( ord_less_int @ SV122 @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[746]) ).
thf(832,plain,
! [SV123: $i] :
( ( ( ~ ( ord_less_int @ SV123 @ pls ) )
= $true )
| ( ( ord_less_int @ ( number_number_of_int @ SV123 ) @ zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[747]) ).
thf(833,plain,
! [SV124: $i] :
( ( ( ~ ( ord_less_int @ ( number_number_of_int @ SV124 ) @ one_one_int ) )
= $true )
| ( ( ord_less_int @ SV124 @ ( bit1 @ pls ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[748]) ).
thf(834,plain,
! [SV125: $i] :
( ( ( ~ ( ord_less_int @ SV125 @ ( bit1 @ pls ) ) )
= $true )
| ( ( ord_less_int @ ( number_number_of_int @ SV125 ) @ one_one_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[749]) ).
thf(835,plain,
! [SV126: $i] :
( ( ( ( ( number_number_of_nat @ SV126 )
!= zero_zero_nat ) )
= $true )
| ( ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ SV126 ) )
= one_one_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[750]) ).
thf(836,plain,
! [SV127: $i] :
( ( ( ( number_number_of_nat @ SV127 )
= zero_zero_nat )
= $true )
| ( ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ SV127 ) )
= zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[751]) ).
thf(837,plain,
! [SV164: $i,SV128: $i] :
( ( ( ( number_number_of_nat @ SV128 )
!= SV164 )
| ( SV164
= ( number_number_of_nat @ SV128 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[752]) ).
thf(838,plain,
! [SV129: $i,SV165: $i] :
( ( ( SV165
!= ( number_number_of_nat @ SV129 ) )
| ( ( number_number_of_nat @ SV129 )
= SV165 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[753]) ).
thf(839,plain,
! [SV130: $i] :
( ( ( ( ( power_power_int @ SV130 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= zero_zero_int ) )
= $true )
| ( ( SV130 = zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[754]) ).
thf(840,plain,
! [SV131: $i] :
( ( ( ( SV131 != zero_zero_int ) )
= $true )
| ( ( ( power_power_int @ SV131 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[755]) ).
thf(841,plain,
! [SV60: $i] :
( ( ( ord_less_int @ one_one_int @ ( number_number_of_int @ SV60 ) )
= $false )
| ( ( ord_less_int @ ( bit1 @ pls ) @ SV60 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[757]) ).
thf(842,plain,
! [SV61: $i] :
( ( ( ord_less_int @ ( bit1 @ pls ) @ SV61 )
= $false )
| ( ( ord_less_int @ one_one_int @ ( number_number_of_int @ SV61 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[758]) ).
thf(843,plain,
! [SV132: $i,SV62: $i] :
( ( ( ( SV62 != zero_zero_int )
| ( SV132 != zero_zero_int ) )
= $true )
| ( ( ( plus_plus_int @ ( power_power_int @ SV62 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV132 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[759]) ).
thf(844,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)],[760]) ).
thf(845,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)],[761]) ).
thf(846,plain,
! [SV63: $i] :
( ( ( ord_less_int @ ( bit0 @ SV63 ) @ zero_zero_int )
= $false )
| ( ( ord_less_int @ SV63 @ zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[762]) ).
thf(847,plain,
! [SV64: $i] :
( ( ( ord_less_int @ SV64 @ zero_zero_int )
= $false )
| ( ( ord_less_int @ ( bit0 @ SV64 ) @ zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[763]) ).
thf(848,plain,
! [SV133: $i,SV65: $i] :
( ( ( ~ ( ord_less_int @ ( bit1 @ SV65 ) @ ( bit0 @ SV133 ) ) )
= $true )
| ( ( ord_less_int @ SV65 @ SV133 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[764]) ).
thf(849,plain,
! [SV134: $i,SV66: $i] :
( ( ( ~ ( ord_less_int @ SV66 @ SV134 ) )
= $true )
| ( ( ord_less_int @ ( bit1 @ SV66 ) @ ( bit0 @ SV134 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[765]) ).
thf(850,plain,
! [SV135: $i,SV67: $i] :
( ( ( ( ( semiri1621563631at_int @ SV67 )
!= ( semiri1621563631at_int @ SV135 ) ) )
= $true )
| ( ( SV67 = SV135 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[766]) ).
thf(851,plain,
! [SV136: $i,SV68: $i] :
( ( ( ( SV68 != SV136 ) )
= $true )
| ( ( ( semiri1621563631at_int @ SV68 )
= ( semiri1621563631at_int @ SV136 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[767]) ).
thf(852,plain,
! [SV137: $i,SV69: $i] :
( ( ( ~ ( ord_less_int @ ( bit0 @ SV69 ) @ ( bit0 @ SV137 ) ) )
= $true )
| ( ( ord_less_int @ SV69 @ SV137 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[768]) ).
thf(853,plain,
! [SV138: $i,SV70: $i] :
( ( ( ~ ( ord_less_int @ SV70 @ SV138 ) )
= $true )
| ( ( ord_less_int @ ( bit0 @ SV70 ) @ ( bit0 @ SV138 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[769]) ).
thf(854,plain,
! [SV71: $i,SV139: $i] :
( ( ( ( ( number_number_of_nat @ SV139 )
= zero_zero_nat )
| ( SV71 != zero_zero_int ) )
= $true )
| ( ( ( power_power_int @ SV71 @ ( number_number_of_nat @ SV139 ) )
= zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[770]) ).
thf(855,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( power_power_int @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_int )
| ( ( number_number_of_nat @ SX1 )
!= zero_zero_nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[771]) ).
thf(856,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
( ( power_power_int @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[772]) ).
thf(857,plain,
! [SV140: $i,SV72: $i] :
( ( ( ( ( number_number_of_int @ SV72 )
!= ( number_number_of_int @ SV140 ) ) )
= $true )
| ( ( SV72 = SV140 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[773]) ).
thf(858,plain,
! [SV141: $i,SV73: $i] :
( ( ( ( SV73 != SV141 ) )
= $true )
| ( ( ( number_number_of_int @ SV73 )
= ( number_number_of_int @ SV141 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[774]) ).
thf(859,plain,
! [SV74: $i,SV142: $i] :
( ( ( ( ( number_number_of_nat @ SV142 )
= zero_zero_nat )
| ( SV74 != zero_zero_nat ) )
= $true )
| ( ( ( power_power_nat @ SV74 @ ( number_number_of_nat @ SV142 ) )
= zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[775]) ).
thf(860,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( power_power_nat @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_nat )
| ( ( number_number_of_nat @ SX1 )
!= zero_zero_nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[776]) ).
thf(861,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
( ( power_power_nat @ SX0 @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_nat )
| ( SX0 = zero_zero_nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[777]) ).
thf(862,plain,
! [SV75: $i] :
( ( ( ( plus_plus_int @ SV75 @ SV75 )
= zero_zero_int )
= $false )
| ( ( SV75 = zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[778]) ).
thf(863,plain,
! [SV76: $i] :
( ( ( SV76 = zero_zero_int )
= $false )
| ( ( ( plus_plus_int @ SV76 @ SV76 )
= zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[779]) ).
thf(864,plain,
! [SV143: $i,SV77: $i] :
( ( ( ~ ( ord_less_int @ ( number_number_of_int @ SV77 ) @ ( number_number_of_int @ SV143 ) ) )
= $true )
| ( ( ord_less_int @ SV77 @ SV143 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[780]) ).
thf(865,plain,
! [SV144: $i,SV78: $i] :
( ( ( ~ ( ord_less_int @ SV78 @ SV144 ) )
= $true )
| ( ( ord_less_int @ ( number_number_of_int @ SV78 ) @ ( number_number_of_int @ SV144 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[781]) ).
thf(866,plain,
! [SV145: $i,SV79: $i] :
( ( ( ~ ( ord_less_int @ ( bit0 @ SV79 ) @ ( bit0 @ SV145 ) ) )
= $true )
| ( ( ord_less_int @ SV79 @ SV145 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[782]) ).
thf(867,plain,
! [SV146: $i,SV80: $i] :
( ( ( ~ ( ord_less_int @ SV80 @ SV146 ) )
= $true )
| ( ( ord_less_int @ ( bit0 @ SV80 ) @ ( bit0 @ SV146 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[783]) ).
thf(868,plain,
! [SV81: $i] :
( ( ( ord_less_int @ pls @ ( bit0 @ SV81 ) )
= $false )
| ( ( ord_less_int @ pls @ SV81 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[784]) ).
thf(869,plain,
! [SV82: $i] :
( ( ( ord_less_int @ pls @ SV82 )
= $false )
| ( ( ord_less_int @ pls @ ( bit0 @ SV82 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[785]) ).
thf(870,plain,
! [SV83: $i] :
( ( ( ord_less_int @ ( bit1 @ SV83 ) @ zero_zero_int )
= $false )
| ( ( ord_less_int @ SV83 @ zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[786]) ).
thf(871,plain,
! [SV84: $i] :
( ( ( ord_less_int @ SV84 @ zero_zero_int )
= $false )
| ( ( ord_less_int @ ( bit1 @ SV84 ) @ zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[787]) ).
thf(872,plain,
! [SV147: $i,SV85: $i] :
( ( ( ( ( bit0 @ SV85 )
!= ( bit0 @ SV147 ) ) )
= $true )
| ( ( SV85 = SV147 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[788]) ).
thf(873,plain,
! [SV148: $i,SV86: $i] :
( ( ( ( SV86 != SV148 ) )
= $true )
| ( ( ( bit0 @ SV86 )
= ( bit0 @ SV148 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[789]) ).
thf(874,plain,
! [SV149: $i,SV87: $i] :
( ( ( ~ ( ord_less_int @ ( bit1 @ SV87 ) @ ( bit1 @ SV149 ) ) )
= $true )
| ( ( ord_less_int @ SV87 @ SV149 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[790]) ).
thf(875,plain,
! [SV150: $i,SV88: $i] :
( ( ( ~ ( ord_less_int @ SV88 @ SV150 ) )
= $true )
| ( ( ord_less_int @ ( bit1 @ SV88 ) @ ( bit1 @ SV150 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[791]) ).
thf(876,plain,
! [SV151: $i,SV89: $i] :
( ( ( ( ( bit1 @ SV89 )
!= ( bit1 @ SV151 ) ) )
= $true )
| ( ( SV89 = SV151 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[792]) ).
thf(877,plain,
! [SV152: $i,SV90: $i] :
( ( ( ( SV90 != SV152 ) )
= $true )
| ( ( ( bit1 @ SV90 )
= ( bit1 @ SV152 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[793]) ).
thf(878,plain,
! [SV153: $i,SV91: $i] :
( ( ( ( ( number_number_of_int @ SV91 )
!= SV153 ) )
= $true )
| ( ( SV153
= ( number_number_of_int @ SV91 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[794]) ).
thf(879,plain,
! [SV92: $i,SV154: $i] :
( ( ( ( SV154
!= ( number_number_of_int @ SV92 ) ) )
= $true )
| ( ( ( number_number_of_int @ SV92 )
= SV154 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[795]) ).
thf(880,plain,
! [SV93: $i] :
( ( ( pls
= ( bit0 @ SV93 ) )
= $false )
| ( ( pls = SV93 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[796]) ).
thf(881,plain,
! [SV94: $i] :
( ( ( pls = SV94 )
= $false )
| ( ( pls
= ( bit0 @ SV94 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[797]) ).
thf(882,plain,
! [SV95: $i,SV155: $i] :
( ( ( ~ ( ord_less_int @ SV155 @ pls ) )
= $true )
| ( ( ( plus_plus_nat @ ( number_number_of_nat @ SV155 ) @ ( number_number_of_nat @ SV95 ) )
= ( number_number_of_nat @ SV95 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[798]) ).
thf(883,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)],[799]) ).
thf(884,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)],[800]) ).
thf(885,plain,
! [SV96: $i] :
( ( ( ord_less_int @ ( bit0 @ SV96 ) @ pls )
= $false )
| ( ( ord_less_int @ SV96 @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[801]) ).
thf(886,plain,
! [SV97: $i] :
( ( ( ord_less_int @ SV97 @ pls )
= $false )
| ( ( ord_less_int @ ( bit0 @ SV97 ) @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[802]) ).
thf(887,plain,
! [SV156: $i,SV98: $i] :
( ( ( ~ ( ord_less_int @ SV98 @ ( plus_plus_int @ SV156 @ one_one_int ) ) )
= $true )
| ( ( ( SV98 = SV156 )
| ( ord_less_int @ SV98 @ SV156 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[803]) ).
thf(888,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ord_less_int @ SX0 @ ( plus_plus_int @ SX1 @ one_one_int ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[804]) ).
thf(889,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_int @ SX0 @ SX1 )
| ( ord_less_int @ SX0 @ ( plus_plus_int @ SX1 @ one_one_int ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[805]) ).
thf(890,plain,
! [SV157: $i,SV99: $i] :
( ( ( ~ ( ord_less_int @ ( number_number_of_int @ SV99 ) @ ( number_number_of_int @ SV157 ) ) )
= $true )
| ( ( ord_less_int @ SV99 @ SV157 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[806]) ).
thf(891,plain,
! [SV158: $i,SV100: $i] :
( ( ( ~ ( ord_less_int @ SV100 @ SV158 ) )
= $true )
| ( ( ord_less_int @ ( number_number_of_int @ SV100 ) @ ( number_number_of_int @ SV158 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[807]) ).
thf(892,plain,
! [SV102: $i] :
( ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ SV102 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $false )
| ( ( ( SV102 != zero_zero_int ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[809]) ).
thf(893,plain,
! [SV103: $i] :
( ( ( ord_less_int @ ( plus_plus_int @ SV103 @ SV103 ) @ zero_zero_int )
= $false )
| ( ( ord_less_int @ SV103 @ zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[810]) ).
thf(894,plain,
! [SV104: $i] :
( ( ( ord_less_int @ SV104 @ zero_zero_int )
= $false )
| ( ( ord_less_int @ ( plus_plus_int @ SV104 @ SV104 ) @ zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[811]) ).
thf(895,plain,
! [SV105: $i] :
( ( ( ord_less_int @ zero_zero_int @ ( number_number_of_int @ SV105 ) )
= $false )
| ( ( ord_less_int @ pls @ SV105 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[812]) ).
thf(896,plain,
! [SV106: $i] :
( ( ( ord_less_int @ pls @ SV106 )
= $false )
| ( ( ord_less_int @ zero_zero_int @ ( number_number_of_int @ SV106 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[813]) ).
thf(897,plain,
! [SV107: $i] :
( ( ( ord_less_int @ ( bit1 @ SV107 ) @ pls )
= $false )
| ( ( ord_less_int @ SV107 @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[814]) ).
thf(898,plain,
! [SV108: $i] :
( ( ( ord_less_int @ SV108 @ pls )
= $false )
| ( ( ord_less_int @ ( bit1 @ SV108 ) @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[815]) ).
thf(899,plain,
! [SV109: $i] :
( ( ( ( semiri1621563631at_int @ SV109 )
= zero_zero_int )
= $false )
| ( ( SV109 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[816]) ).
thf(900,plain,
! [SV110: $i] :
( ( ( SV110 = zero_zero_nat )
= $false )
| ( ( ( semiri1621563631at_int @ SV110 )
= zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[817]) ).
thf(901,plain,
! [SV111: $i] :
( ( ( ( number_number_of_nat @ SV111 )
= zero_zero_nat )
= $false )
| ( ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ SV111 ) )
= one_one_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[818]) ).
thf(902,plain,
! [SV159: $i,SV113: $i] :
( ( ( ~ ( ord_less_int @ ( bit1 @ SV113 ) @ ( bit0 @ SV159 ) ) )
= $true )
| ( ( ord_less_int @ SV113 @ SV159 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[820]) ).
thf(903,plain,
! [SV160: $i,SV114: $i] :
( ( ( ~ ( ord_less_int @ SV114 @ SV160 ) )
= $true )
| ( ( ord_less_int @ ( bit1 @ SV114 ) @ ( bit0 @ SV160 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[821]) ).
thf(904,plain,
! [SV161: $i,SV115: $i] :
( ( ( ~ ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ SV115 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV161 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true )
| ( ( ( SV115 != zero_zero_int )
| ( SV161 != zero_zero_int ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[822]) ).
thf(905,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)],[823]) ).
thf(906,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)],[824]) ).
thf(907,plain,
! [SV116: $i] :
( ( ( ( bit0 @ SV116 )
= pls )
= $false )
| ( ( SV116 = pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[825]) ).
thf(908,plain,
! [SV117: $i] :
( ( ( SV117 = pls )
= $false )
| ( ( ( bit0 @ SV117 )
= pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[826]) ).
thf(909,plain,
! [SV118: $i] :
( ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ SV118 ) @ SV118 ) @ zero_zero_int )
= $false )
| ( ( ord_less_int @ SV118 @ zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[827]) ).
thf(910,plain,
! [SV119: $i] :
( ( ( ord_less_int @ SV119 @ zero_zero_int )
= $false )
| ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ SV119 ) @ SV119 ) @ zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[828]) ).
thf(911,plain,
! [SV162: $i,SV120: $i] :
( ( ( ~ ( ord_less_int @ ( bit1 @ SV120 ) @ ( bit1 @ SV162 ) ) )
= $true )
| ( ( ord_less_int @ SV120 @ SV162 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[829]) ).
thf(912,plain,
! [SV163: $i,SV121: $i] :
( ( ( ~ ( ord_less_int @ SV121 @ SV163 ) )
= $true )
| ( ( ord_less_int @ ( bit1 @ SV121 ) @ ( bit1 @ SV163 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[830]) ).
thf(913,plain,
! [SV122: $i] :
( ( ( ord_less_int @ ( number_number_of_int @ SV122 ) @ zero_zero_int )
= $false )
| ( ( ord_less_int @ SV122 @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[831]) ).
thf(914,plain,
! [SV123: $i] :
( ( ( ord_less_int @ SV123 @ pls )
= $false )
| ( ( ord_less_int @ ( number_number_of_int @ SV123 ) @ zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[832]) ).
thf(915,plain,
! [SV124: $i] :
( ( ( ord_less_int @ ( number_number_of_int @ SV124 ) @ one_one_int )
= $false )
| ( ( ord_less_int @ SV124 @ ( bit1 @ pls ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[833]) ).
thf(916,plain,
! [SV125: $i] :
( ( ( ord_less_int @ SV125 @ ( bit1 @ pls ) )
= $false )
| ( ( ord_less_int @ ( number_number_of_int @ SV125 ) @ one_one_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[834]) ).
thf(917,plain,
! [SV126: $i] :
( ( ( ( number_number_of_nat @ SV126 )
= zero_zero_nat )
= $false )
| ( ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ SV126 ) )
= one_one_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[835]) ).
thf(918,plain,
! [SV164: $i,SV128: $i] :
( ( ( ( ( number_number_of_nat @ SV128 )
!= SV164 ) )
= $true )
| ( ( SV164
= ( number_number_of_nat @ SV128 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[837]) ).
thf(919,plain,
! [SV129: $i,SV165: $i] :
( ( ( ( SV165
!= ( number_number_of_nat @ SV129 ) ) )
= $true )
| ( ( ( number_number_of_nat @ SV129 )
= SV165 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[838]) ).
thf(920,plain,
! [SV130: $i] :
( ( ( ( power_power_int @ SV130 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int )
= $false )
| ( ( SV130 = zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[839]) ).
thf(921,plain,
! [SV131: $i] :
( ( ( SV131 = zero_zero_int )
= $false )
| ( ( ( power_power_int @ SV131 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[840]) ).
thf(922,plain,
! [SV132: $i,SV62: $i] :
( ( ( ( SV62 != zero_zero_int ) )
= $true )
| ( ( ( SV132 != zero_zero_int ) )
= $true )
| ( ( ( plus_plus_int @ ( power_power_int @ SV62 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV132 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[843]) ).
thf(923,plain,
! [SV166: $i] :
( ( ! [SY180: $i] :
( ( plus_plus_int @ ( power_power_int @ SV166 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SY180 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_int )
| ( SV166 = zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[844]) ).
thf(924,plain,
! [SV167: $i] :
( ( ! [SY181: $i] :
( ( ( plus_plus_int @ ( power_power_int @ SV167 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SY181 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_int )
| ( SY181 = zero_zero_int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[845]) ).
thf(925,plain,
! [SV133: $i,SV65: $i] :
( ( ( ord_less_int @ ( bit1 @ SV65 ) @ ( bit0 @ SV133 ) )
= $false )
| ( ( ord_less_int @ SV65 @ SV133 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[848]) ).
thf(926,plain,
! [SV134: $i,SV66: $i] :
( ( ( ord_less_int @ SV66 @ SV134 )
= $false )
| ( ( ord_less_int @ ( bit1 @ SV66 ) @ ( bit0 @ SV134 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[849]) ).
thf(927,plain,
! [SV135: $i,SV67: $i] :
( ( ( ( semiri1621563631at_int @ SV67 )
= ( semiri1621563631at_int @ SV135 ) )
= $false )
| ( ( SV67 = SV135 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[850]) ).
thf(928,plain,
! [SV136: $i,SV68: $i] :
( ( ( SV68 = SV136 )
= $false )
| ( ( ( semiri1621563631at_int @ SV68 )
= ( semiri1621563631at_int @ SV136 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[851]) ).
thf(929,plain,
! [SV137: $i,SV69: $i] :
( ( ( ord_less_int @ ( bit0 @ SV69 ) @ ( bit0 @ SV137 ) )
= $false )
| ( ( ord_less_int @ SV69 @ SV137 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[852]) ).
thf(930,plain,
! [SV138: $i,SV70: $i] :
( ( ( ord_less_int @ SV70 @ SV138 )
= $false )
| ( ( ord_less_int @ ( bit0 @ SV70 ) @ ( bit0 @ SV138 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[853]) ).
thf(931,plain,
! [SV71: $i,SV139: $i] :
( ( ( ( number_number_of_nat @ SV139 )
= zero_zero_nat )
= $true )
| ( ( ( SV71 != zero_zero_int ) )
= $true )
| ( ( ( power_power_int @ SV71 @ ( number_number_of_nat @ SV139 ) )
= zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[854]) ).
thf(932,plain,
! [SV168: $i] :
( ( ! [SY182: $i] :
( ( ( power_power_int @ SV168 @ ( number_number_of_nat @ SY182 ) )
!= zero_zero_int )
| ( ( number_number_of_nat @ SY182 )
!= zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[855]) ).
thf(933,plain,
! [SV169: $i] :
( ( ! [SY183: $i] :
( ( power_power_int @ SV169 @ ( number_number_of_nat @ SY183 ) )
!= zero_zero_int )
| ( SV169 = zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[856]) ).
thf(934,plain,
! [SV140: $i,SV72: $i] :
( ( ( ( number_number_of_int @ SV72 )
= ( number_number_of_int @ SV140 ) )
= $false )
| ( ( SV72 = SV140 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[857]) ).
thf(935,plain,
! [SV141: $i,SV73: $i] :
( ( ( SV73 = SV141 )
= $false )
| ( ( ( number_number_of_int @ SV73 )
= ( number_number_of_int @ SV141 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[858]) ).
thf(936,plain,
! [SV74: $i,SV142: $i] :
( ( ( ( number_number_of_nat @ SV142 )
= zero_zero_nat )
= $true )
| ( ( ( SV74 != zero_zero_nat ) )
= $true )
| ( ( ( power_power_nat @ SV74 @ ( number_number_of_nat @ SV142 ) )
= zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[859]) ).
thf(937,plain,
! [SV170: $i] :
( ( ! [SY184: $i] :
( ( ( power_power_nat @ SV170 @ ( number_number_of_nat @ SY184 ) )
!= zero_zero_nat )
| ( ( number_number_of_nat @ SY184 )
!= zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[860]) ).
thf(938,plain,
! [SV171: $i] :
( ( ! [SY185: $i] :
( ( power_power_nat @ SV171 @ ( number_number_of_nat @ SY185 ) )
!= zero_zero_nat )
| ( SV171 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[861]) ).
thf(939,plain,
! [SV143: $i,SV77: $i] :
( ( ( ord_less_int @ ( number_number_of_int @ SV77 ) @ ( number_number_of_int @ SV143 ) )
= $false )
| ( ( ord_less_int @ SV77 @ SV143 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[864]) ).
thf(940,plain,
! [SV144: $i,SV78: $i] :
( ( ( ord_less_int @ SV78 @ SV144 )
= $false )
| ( ( ord_less_int @ ( number_number_of_int @ SV78 ) @ ( number_number_of_int @ SV144 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[865]) ).
thf(941,plain,
! [SV145: $i,SV79: $i] :
( ( ( ord_less_int @ ( bit0 @ SV79 ) @ ( bit0 @ SV145 ) )
= $false )
| ( ( ord_less_int @ SV79 @ SV145 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[866]) ).
thf(942,plain,
! [SV146: $i,SV80: $i] :
( ( ( ord_less_int @ SV80 @ SV146 )
= $false )
| ( ( ord_less_int @ ( bit0 @ SV80 ) @ ( bit0 @ SV146 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[867]) ).
thf(943,plain,
! [SV147: $i,SV85: $i] :
( ( ( ( bit0 @ SV85 )
= ( bit0 @ SV147 ) )
= $false )
| ( ( SV85 = SV147 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[872]) ).
thf(944,plain,
! [SV148: $i,SV86: $i] :
( ( ( SV86 = SV148 )
= $false )
| ( ( ( bit0 @ SV86 )
= ( bit0 @ SV148 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[873]) ).
thf(945,plain,
! [SV149: $i,SV87: $i] :
( ( ( ord_less_int @ ( bit1 @ SV87 ) @ ( bit1 @ SV149 ) )
= $false )
| ( ( ord_less_int @ SV87 @ SV149 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[874]) ).
thf(946,plain,
! [SV150: $i,SV88: $i] :
( ( ( ord_less_int @ SV88 @ SV150 )
= $false )
| ( ( ord_less_int @ ( bit1 @ SV88 ) @ ( bit1 @ SV150 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[875]) ).
thf(947,plain,
! [SV151: $i,SV89: $i] :
( ( ( ( bit1 @ SV89 )
= ( bit1 @ SV151 ) )
= $false )
| ( ( SV89 = SV151 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[876]) ).
thf(948,plain,
! [SV152: $i,SV90: $i] :
( ( ( SV90 = SV152 )
= $false )
| ( ( ( bit1 @ SV90 )
= ( bit1 @ SV152 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[877]) ).
thf(949,plain,
! [SV153: $i,SV91: $i] :
( ( ( ( number_number_of_int @ SV91 )
= SV153 )
= $false )
| ( ( SV153
= ( number_number_of_int @ SV91 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[878]) ).
thf(950,plain,
! [SV92: $i,SV154: $i] :
( ( ( SV154
= ( number_number_of_int @ SV92 ) )
= $false )
| ( ( ( number_number_of_int @ SV92 )
= SV154 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[879]) ).
thf(951,plain,
! [SV95: $i,SV155: $i] :
( ( ( ord_less_int @ SV155 @ pls )
= $false )
| ( ( ( plus_plus_nat @ ( number_number_of_nat @ SV155 ) @ ( number_number_of_nat @ SV95 ) )
= ( number_number_of_nat @ SV95 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[882]) ).
thf(952,plain,
! [SV172: $i] :
( ( ! [SY186: $i] :
( ( ord_less_int @ SY186 @ pls )
| ~ ( ord_less_int @ SV172 @ pls )
| ( ( plus_plus_nat @ ( number_number_of_nat @ SY186 ) @ ( number_number_of_nat @ SV172 ) )
= ( number_number_of_nat @ SY186 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[883]) ).
thf(953,plain,
! [SV173: $i] :
( ( ! [SY187: $i] :
( ( ord_less_int @ SY187 @ pls )
| ( ord_less_int @ SV173 @ pls )
| ( ( plus_plus_nat @ ( number_number_of_nat @ SY187 ) @ ( number_number_of_nat @ SV173 ) )
= ( number_number_of_nat @ ( plus_plus_int @ SY187 @ SV173 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[884]) ).
thf(954,plain,
! [SV156: $i,SV98: $i] :
( ( ( ord_less_int @ SV98 @ ( plus_plus_int @ SV156 @ one_one_int ) )
= $false )
| ( ( ( SV98 = SV156 )
| ( ord_less_int @ SV98 @ SV156 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[887]) ).
thf(955,plain,
! [SV174: $i] :
( ( ! [SY188: $i] :
( ( SV174 != SY188 )
| ( ord_less_int @ SV174 @ ( plus_plus_int @ SY188 @ one_one_int ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[888]) ).
thf(956,plain,
! [SV175: $i] :
( ( ! [SY189: $i] :
( ~ ( ord_less_int @ SV175 @ SY189 )
| ( ord_less_int @ SV175 @ ( plus_plus_int @ SY189 @ one_one_int ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[889]) ).
thf(957,plain,
! [SV157: $i,SV99: $i] :
( ( ( ord_less_int @ ( number_number_of_int @ SV99 ) @ ( number_number_of_int @ SV157 ) )
= $false )
| ( ( ord_less_int @ SV99 @ SV157 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[890]) ).
thf(958,plain,
! [SV158: $i,SV100: $i] :
( ( ( ord_less_int @ SV100 @ SV158 )
= $false )
| ( ( ord_less_int @ ( number_number_of_int @ SV100 ) @ ( number_number_of_int @ SV158 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[891]) ).
thf(959,plain,
! [SV102: $i] :
( ( ( SV102 = zero_zero_int )
= $false )
| ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ SV102 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[892]) ).
thf(960,plain,
! [SV159: $i,SV113: $i] :
( ( ( ord_less_int @ ( bit1 @ SV113 ) @ ( bit0 @ SV159 ) )
= $false )
| ( ( ord_less_int @ SV113 @ SV159 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[902]) ).
thf(961,plain,
! [SV160: $i,SV114: $i] :
( ( ( ord_less_int @ SV114 @ SV160 )
= $false )
| ( ( ord_less_int @ ( bit1 @ SV114 ) @ ( bit0 @ SV160 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[903]) ).
thf(962,plain,
! [SV161: $i,SV115: $i] :
( ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ SV115 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV161 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $false )
| ( ( ( SV115 != zero_zero_int )
| ( SV161 != zero_zero_int ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[904]) ).
thf(963,plain,
! [SV176: $i] :
( ( ( SV176 = zero_zero_int )
| ! [SY190: $i] : ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ SV176 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SY190 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[905]) ).
thf(964,plain,
! [SV177: $i] :
( ( ! [SY191: $i] :
( ( SY191 = zero_zero_int )
| ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ SV177 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SY191 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[906]) ).
thf(965,plain,
! [SV162: $i,SV120: $i] :
( ( ( ord_less_int @ ( bit1 @ SV120 ) @ ( bit1 @ SV162 ) )
= $false )
| ( ( ord_less_int @ SV120 @ SV162 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[911]) ).
thf(966,plain,
! [SV163: $i,SV121: $i] :
( ( ( ord_less_int @ SV121 @ SV163 )
= $false )
| ( ( ord_less_int @ ( bit1 @ SV121 ) @ ( bit1 @ SV163 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[912]) ).
thf(967,plain,
! [SV164: $i,SV128: $i] :
( ( ( ( number_number_of_nat @ SV128 )
= SV164 )
= $false )
| ( ( SV164
= ( number_number_of_nat @ SV128 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[918]) ).
thf(968,plain,
! [SV129: $i,SV165: $i] :
( ( ( SV165
= ( number_number_of_nat @ SV129 ) )
= $false )
| ( ( ( number_number_of_nat @ SV129 )
= SV165 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[919]) ).
thf(969,plain,
! [SV132: $i,SV62: $i] :
( ( ( SV62 = zero_zero_int )
= $false )
| ( ( ( SV132 != zero_zero_int ) )
= $true )
| ( ( ( plus_plus_int @ ( power_power_int @ SV62 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV132 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[922]) ).
thf(970,plain,
! [SV166: $i] :
( ( ( ! [SY180: $i] :
( ( plus_plus_int @ ( power_power_int @ SV166 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SY180 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_int ) )
= $true )
| ( ( SV166 = zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[923]) ).
thf(971,plain,
! [SV178: $i,SV167: $i] :
( ( ( ( plus_plus_int @ ( power_power_int @ SV167 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV178 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_int )
| ( SV178 = zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[924]) ).
thf(972,plain,
! [SV139: $i,SV71: $i] :
( ( ( SV71 = zero_zero_int )
= $false )
| ( ( ( number_number_of_nat @ SV139 )
= zero_zero_nat )
= $true )
| ( ( ( power_power_int @ SV71 @ ( number_number_of_nat @ SV139 ) )
= zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[931]) ).
thf(973,plain,
! [SV179: $i,SV168: $i] :
( ( ( ( power_power_int @ SV168 @ ( number_number_of_nat @ SV179 ) )
!= zero_zero_int )
| ( ( number_number_of_nat @ SV179 )
!= zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[932]) ).
thf(974,plain,
! [SV169: $i] :
( ( ( ! [SY183: $i] :
( ( power_power_int @ SV169 @ ( number_number_of_nat @ SY183 ) )
!= zero_zero_int ) )
= $true )
| ( ( SV169 = zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[933]) ).
thf(975,plain,
! [SV142: $i,SV74: $i] :
( ( ( SV74 = zero_zero_nat )
= $false )
| ( ( ( number_number_of_nat @ SV142 )
= zero_zero_nat )
= $true )
| ( ( ( power_power_nat @ SV74 @ ( number_number_of_nat @ SV142 ) )
= zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[936]) ).
thf(976,plain,
! [SV180: $i,SV170: $i] :
( ( ( ( power_power_nat @ SV170 @ ( number_number_of_nat @ SV180 ) )
!= zero_zero_nat )
| ( ( number_number_of_nat @ SV180 )
!= zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[937]) ).
thf(977,plain,
! [SV171: $i] :
( ( ( ! [SY185: $i] :
( ( power_power_nat @ SV171 @ ( number_number_of_nat @ SY185 ) )
!= zero_zero_nat ) )
= $true )
| ( ( SV171 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[938]) ).
thf(978,plain,
! [SV172: $i,SV181: $i] :
( ( ( ord_less_int @ SV181 @ pls )
| ~ ( ord_less_int @ SV172 @ pls )
| ( ( plus_plus_nat @ ( number_number_of_nat @ SV181 ) @ ( number_number_of_nat @ SV172 ) )
= ( number_number_of_nat @ SV181 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[952]) ).
thf(979,plain,
! [SV173: $i,SV182: $i] :
( ( ( ord_less_int @ SV182 @ pls )
| ( ord_less_int @ SV173 @ pls )
| ( ( plus_plus_nat @ ( number_number_of_nat @ SV182 ) @ ( number_number_of_nat @ SV173 ) )
= ( number_number_of_nat @ ( plus_plus_int @ SV182 @ SV173 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[953]) ).
thf(980,plain,
! [SV156: $i,SV98: $i] :
( ( ( SV98 = SV156 )
= $true )
| ( ( ord_less_int @ SV98 @ SV156 )
= $true )
| ( ( ord_less_int @ SV98 @ ( plus_plus_int @ SV156 @ one_one_int ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[954]) ).
thf(981,plain,
! [SV183: $i,SV174: $i] :
( ( ( SV174 != SV183 )
| ( ord_less_int @ SV174 @ ( plus_plus_int @ SV183 @ one_one_int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[955]) ).
thf(982,plain,
! [SV184: $i,SV175: $i] :
( ( ~ ( ord_less_int @ SV175 @ SV184 )
| ( ord_less_int @ SV175 @ ( plus_plus_int @ SV184 @ one_one_int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[956]) ).
thf(983,plain,
! [SV161: $i,SV115: $i] :
( ( ( ( SV115 != zero_zero_int ) )
= $true )
| ( ( ( SV161 != zero_zero_int ) )
= $true )
| ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ SV115 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV161 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[962]) ).
thf(984,plain,
! [SV176: $i] :
( ( ( SV176 = zero_zero_int )
= $true )
| ( ( ! [SY190: $i] : ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ SV176 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SY190 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[963]) ).
thf(985,plain,
! [SV177: $i,SV185: $i] :
( ( ( SV185 = zero_zero_int )
| ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ SV177 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV185 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[964]) ).
thf(986,plain,
! [SV62: $i,SV132: $i] :
( ( ( SV132 = zero_zero_int )
= $false )
| ( ( SV62 = zero_zero_int )
= $false )
| ( ( ( plus_plus_int @ ( power_power_int @ SV62 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV132 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[969]) ).
thf(987,plain,
! [SV186: $i,SV166: $i] :
( ( ( ( ( plus_plus_int @ ( power_power_int @ SV166 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV186 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_int ) )
= $true )
| ( ( SV166 = zero_zero_int )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[970]) ).
thf(988,plain,
! [SV178: $i,SV167: $i] :
( ( ( ( ( plus_plus_int @ ( power_power_int @ SV167 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV178 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_int ) )
= $true )
| ( ( SV178 = zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[971]) ).
thf(989,plain,
! [SV179: $i,SV168: $i] :
( ( ( ( ( power_power_int @ SV168 @ ( number_number_of_nat @ SV179 ) )
!= zero_zero_int ) )
= $true )
| ( ( ( ( number_number_of_nat @ SV179 )
!= zero_zero_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[973]) ).
thf(990,plain,
! [SV187: $i,SV169: $i] :
( ( ( ( ( power_power_int @ SV169 @ ( number_number_of_nat @ SV187 ) )
!= zero_zero_int ) )
= $true )
| ( ( SV169 = zero_zero_int )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[974]) ).
thf(991,plain,
! [SV180: $i,SV170: $i] :
( ( ( ( ( power_power_nat @ SV170 @ ( number_number_of_nat @ SV180 ) )
!= zero_zero_nat ) )
= $true )
| ( ( ( ( number_number_of_nat @ SV180 )
!= zero_zero_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[976]) ).
thf(992,plain,
! [SV188: $i,SV171: $i] :
( ( ( ( ( power_power_nat @ SV171 @ ( number_number_of_nat @ SV188 ) )
!= zero_zero_nat ) )
= $true )
| ( ( SV171 = zero_zero_nat )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[977]) ).
thf(993,plain,
! [SV172: $i,SV181: $i] :
( ( ( ord_less_int @ SV181 @ pls )
= $true )
| ( ( ~ ( ord_less_int @ SV172 @ pls )
| ( ( plus_plus_nat @ ( number_number_of_nat @ SV181 ) @ ( number_number_of_nat @ SV172 ) )
= ( number_number_of_nat @ SV181 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[978]) ).
thf(994,plain,
! [SV173: $i,SV182: $i] :
( ( ( ord_less_int @ SV182 @ pls )
= $true )
| ( ( ( ord_less_int @ SV173 @ pls )
| ( ( plus_plus_nat @ ( number_number_of_nat @ SV182 ) @ ( number_number_of_nat @ SV173 ) )
= ( number_number_of_nat @ ( plus_plus_int @ SV182 @ SV173 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[979]) ).
thf(995,plain,
! [SV183: $i,SV174: $i] :
( ( ( ( SV174 != SV183 ) )
= $true )
| ( ( ord_less_int @ SV174 @ ( plus_plus_int @ SV183 @ one_one_int ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[981]) ).
thf(996,plain,
! [SV184: $i,SV175: $i] :
( ( ( ~ ( ord_less_int @ SV175 @ SV184 ) )
= $true )
| ( ( ord_less_int @ SV175 @ ( plus_plus_int @ SV184 @ one_one_int ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[982]) ).
thf(997,plain,
! [SV161: $i,SV115: $i] :
( ( ( SV115 = zero_zero_int )
= $false )
| ( ( ( SV161 != zero_zero_int ) )
= $true )
| ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ SV115 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV161 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[983]) ).
thf(998,plain,
! [SV189: $i,SV176: $i] :
( ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ SV176 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV189 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true )
| ( ( SV176 = zero_zero_int )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[984]) ).
thf(999,plain,
! [SV177: $i,SV185: $i] :
( ( ( SV185 = zero_zero_int )
= $true )
| ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ SV177 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV185 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[985]) ).
thf(1000,plain,
! [SV186: $i,SV166: $i] :
( ( ( ( plus_plus_int @ ( power_power_int @ SV166 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV186 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_int )
= $false )
| ( ( SV166 = zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[987]) ).
thf(1001,plain,
! [SV178: $i,SV167: $i] :
( ( ( ( plus_plus_int @ ( power_power_int @ SV167 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV178 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_int )
= $false )
| ( ( SV178 = zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[988]) ).
thf(1002,plain,
! [SV179: $i,SV168: $i] :
( ( ( ( power_power_int @ SV168 @ ( number_number_of_nat @ SV179 ) )
= zero_zero_int )
= $false )
| ( ( ( ( number_number_of_nat @ SV179 )
!= zero_zero_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[989]) ).
thf(1003,plain,
! [SV187: $i,SV169: $i] :
( ( ( ( power_power_int @ SV169 @ ( number_number_of_nat @ SV187 ) )
= zero_zero_int )
= $false )
| ( ( SV169 = zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[990]) ).
thf(1004,plain,
! [SV180: $i,SV170: $i] :
( ( ( ( power_power_nat @ SV170 @ ( number_number_of_nat @ SV180 ) )
= zero_zero_nat )
= $false )
| ( ( ( ( number_number_of_nat @ SV180 )
!= zero_zero_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[991]) ).
thf(1005,plain,
! [SV188: $i,SV171: $i] :
( ( ( ( power_power_nat @ SV171 @ ( number_number_of_nat @ SV188 ) )
= zero_zero_nat )
= $false )
| ( ( SV171 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[992]) ).
thf(1006,plain,
! [SV181: $i,SV172: $i] :
( ( ( ~ ( ord_less_int @ SV172 @ pls ) )
= $true )
| ( ( ( plus_plus_nat @ ( number_number_of_nat @ SV181 ) @ ( number_number_of_nat @ SV172 ) )
= ( number_number_of_nat @ SV181 ) )
= $true )
| ( ( ord_less_int @ SV181 @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[993]) ).
thf(1007,plain,
! [SV182: $i,SV173: $i] :
( ( ( ord_less_int @ SV173 @ pls )
= $true )
| ( ( ( plus_plus_nat @ ( number_number_of_nat @ SV182 ) @ ( number_number_of_nat @ SV173 ) )
= ( number_number_of_nat @ ( plus_plus_int @ SV182 @ SV173 ) ) )
= $true )
| ( ( ord_less_int @ SV182 @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[994]) ).
thf(1008,plain,
! [SV183: $i,SV174: $i] :
( ( ( SV174 = SV183 )
= $false )
| ( ( ord_less_int @ SV174 @ ( plus_plus_int @ SV183 @ one_one_int ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[995]) ).
thf(1009,plain,
! [SV184: $i,SV175: $i] :
( ( ( ord_less_int @ SV175 @ SV184 )
= $false )
| ( ( ord_less_int @ SV175 @ ( plus_plus_int @ SV184 @ one_one_int ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[996]) ).
thf(1010,plain,
! [SV115: $i,SV161: $i] :
( ( ( SV161 = zero_zero_int )
= $false )
| ( ( SV115 = zero_zero_int )
= $false )
| ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ SV115 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ SV161 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[997]) ).
thf(1011,plain,
! [SV168: $i,SV179: $i] :
( ( ( ( number_number_of_nat @ SV179 )
= zero_zero_nat )
= $false )
| ( ( ( power_power_int @ SV168 @ ( number_number_of_nat @ SV179 ) )
= zero_zero_int )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1002]) ).
thf(1012,plain,
! [SV170: $i,SV180: $i] :
( ( ( ( number_number_of_nat @ SV180 )
= zero_zero_nat )
= $false )
| ( ( ( power_power_nat @ SV170 @ ( number_number_of_nat @ SV180 ) )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1004]) ).
thf(1013,plain,
! [SV181: $i,SV172: $i] :
( ( ( ord_less_int @ SV172 @ pls )
= $false )
| ( ( ( plus_plus_nat @ ( number_number_of_nat @ SV181 ) @ ( number_number_of_nat @ SV172 ) )
= ( number_number_of_nat @ SV181 ) )
= $true )
| ( ( ord_less_int @ SV181 @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1006]) ).
thf(1014,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[265,1013,1012,1011,1010,1009,1008,1007,1005,1003,1001,1000,999,998,986,980,975,972,968,967,966,965,961,960,959,958,957,951,950,949,948,947,946,945,944,943,942,941,940,939,935,934,930,929,928,927,926,925,921,920,917,916,915,914,913,910,909,908,907,901,900,899,898,897,896,895,894,893,886,885,881,880,871,870,869,868,863,862,847,846,842,841,836,819,808,756,677,596,595,594,593,592,590,510,509,508,507,506,505,503,500,499,498,497,493,491,490,489,447,446,444,438,437,436,435,434,432,431,430,424,419,413,412,411,371,348,347,346,345,337,336,323,304,303,302,294,293,291,290,289,284,282,281,280,277,276,275,271,270,269,268,266]) ).
thf(1015,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[1014]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM925+1 : TPTP v8.1.0. Released v5.3.0.
% 0.03/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n003.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jul 5 06:48:40 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.18/0.37 .
% 0.18/0.38
% 0.18/0.38 No.of.Axioms: 106
% 0.18/0.38
% 0.18/0.38 Length.of.Defs: 0
% 0.18/0.38
% 0.18/0.38 Contains.Choice.Funs: false
% 0.18/0.41 ......
% 0.18/0.44 (rf:2,axioms:106,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:108,loop_count:0,foatp_calls:0,translation:fof_full).........................................................
% 1.75/1.98
% 1.75/1.98 ********************************
% 1.75/1.98 * All subproblems solved! *
% 1.75/1.98 ********************************
% 1.75/1.98 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:2,axioms:106,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:1014,loop_count:0,foatp_calls:1,translation:fof_full)
% 2.12/2.32
% 2.12/2.32 %**** Beginning of derivation protocol ****
% 2.12/2.32 % SZS output start CNFRefutation
% See solution above
% 2.12/2.33
% 2.12/2.33 %**** End of derivation protocol ****
% 2.12/2.33 %**** no. of clauses in derivation: 1015 ****
% 2.12/2.33 %**** clause counter: 1014 ****
% 2.12/2.33
% 2.12/2.33 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:2,axioms:106,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:1014,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------