TSTP Solution File: NUM925+2 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : NUM925+2 : 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 : n021.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 11:57:48 EDT 2022
% Result : Theorem 2.27s 2.51s
% Output : CNFRefutation 2.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 240
% Syntax : Number of formulae : 1550 (1226 unt; 50 typ; 0 def)
% Number of atoms : 6089 (4538 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 11096 (1514 ~;1257 |; 124 &;8091 @)
% ( 78 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 41 ( 41 >; 0 *; 0 +; 0 <<)
% Number of symbols : 53 ( 50 usr; 24 con; 0-2 aty)
% Number of variables : 2908 ( 0 ^2908 !; 0 ?;2908 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_bit0,type,
bit0: $i > $i ).
thf(tp_bit1,type,
bit1: $i > $i ).
thf(tp_fFalse,type,
fFalse: $i ).
thf(tp_fTrue,type,
fTrue: $i ).
thf(tp_hAPP_i1948725293t_bool,type,
hAPP_i1948725293t_bool: $i > $i > $i ).
thf(tp_hAPP_int_bool,type,
hAPP_int_bool: $i > $i > $i ).
thf(tp_hAPP_int_int,type,
hAPP_int_int: $i > $i > $i ).
thf(tp_hAPP_n1699378549t_bool,type,
hAPP_n1699378549t_bool: $i > $i > $i ).
thf(tp_hAPP_nat_bool,type,
hAPP_nat_bool: $i > $i > $i ).
thf(tp_hAPP_nat_int,type,
hAPP_nat_int: $i > $i > $i ).
thf(tp_hAPP_nat_nat,type,
hAPP_nat_nat: $i > $i > $i ).
thf(tp_hAPP_nat_real,type,
hAPP_nat_real: $i > $i > $i ).
thf(tp_hAPP_r1134773055l_bool,type,
hAPP_r1134773055l_bool: $i > $i > $i ).
thf(tp_hAPP_real_bool,type,
hAPP_real_bool: $i > $i > $i ).
thf(tp_hAPP_real_real,type,
hAPP_real_real: $i > $i > $i ).
thf(tp_hBOOL,type,
hBOOL: $i > $o ).
thf(tp_if_nat,type,
if_nat: $i > $i > $i ).
thf(tp_is_bool,type,
is_bool: $i > $o ).
thf(tp_m1,type,
m1: $i ).
thf(tp_n,type,
n: $i ).
thf(tp_number267125858f_real,type,
number267125858f_real: $i > $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_one_one_real,type,
one_one_real: $i ).
thf(tp_ord_less_eq_int,type,
ord_less_eq_int: $i ).
thf(tp_ord_less_eq_nat,type,
ord_less_eq_nat: $i ).
thf(tp_ord_less_eq_real,type,
ord_less_eq_real: $i ).
thf(tp_ord_less_int,type,
ord_less_int: $i ).
thf(tp_ord_less_nat,type,
ord_less_nat: $i ).
thf(tp_ord_less_real,type,
ord_less_real: $i ).
thf(tp_pls,type,
pls: $i ).
thf(tp_plus_plus_int,type,
plus_plus_int: $i > $i ).
thf(tp_plus_plus_nat,type,
plus_plus_nat: $i > $i ).
thf(tp_plus_plus_real,type,
plus_plus_real: $i > $i ).
thf(tp_power_power_int,type,
power_power_int: $i > $i ).
thf(tp_power_power_nat,type,
power_power_nat: $i > $i ).
thf(tp_power_power_real,type,
power_power_real: $i > $i ).
thf(tp_semiri132038758t_real,type,
semiri132038758t_real: $i ).
thf(tp_semiri1621563631at_int,type,
semiri1621563631at_int: $i ).
thf(tp_semiri984289939at_nat,type,
semiri984289939at_nat: $i ).
thf(tp_sqrt,type,
sqrt: $i > $i ).
thf(tp_succ,type,
succ: $i > $i ).
thf(tp_t,type,
t: $i ).
thf(tp_times_times_int,type,
times_times_int: $i > $i > $i ).
thf(tp_tn,type,
tn: $i ).
thf(tp_zero_zero_int,type,
zero_zero_int: $i ).
thf(tp_zero_zero_nat,type,
zero_zero_nat: $i ).
thf(tp_zero_zero_real,type,
zero_zero_real: $i ).
thf(10,axiom,
! [K: $i,L: $i] :
( ( times_times_int @ ( bit1 @ K ) @ L )
= ( hAPP_int_int @ ( plus_plus_int @ ( bit0 @ ( times_times_int @ K @ L ) ) ) @ L ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_692_mult__Bit1) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( hAPP_nat_int @ ( power_power_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_691_zadd__power2) ).
thf(118,axiom,
! [K: $i,L: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( bit1 @ K ) ) @ ( bit1 @ L ) )
= ( bit0 @ ( hAPP_int_int @ ( plus_plus_int @ K ) @ ( succ @ L ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_584_add__Bit1__Bit1) ).
thf(119,axiom,
! [K_3: $i] :
( ( number_number_of_int @ ( succ @ K_3 ) )
= ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ ( number_number_of_int @ K_3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_583_number__of__succ) ).
thf(129,axiom,
! [K: $i] :
( ( succ @ K )
= ( hAPP_int_int @ ( plus_plus_int @ K ) @ one_one_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_573_succ__def) ).
thf(133,axiom,
! [K: $i] :
( ( succ @ ( bit1 @ K ) )
= ( bit0 @ ( succ @ K ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_569_succ__Bit1) ).
thf(134,axiom,
! [K: $i] :
( ( succ @ ( bit0 @ K ) )
= ( bit1 @ K ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_568_succ__Bit0) ).
thf(135,axiom,
( ( succ @ pls )
= ( bit1 @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_567_succ__Pls) ).
thf(306,axiom,
! [Ma: $i,Na: $i] :
( ( ( hAPP_nat_nat @ ( power_power_nat @ Ma ) @ Na )
= zero_zero_nat )
<=> ( ( Na != zero_zero_nat )
& ( Ma = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_396_nat__power__eq__0__iff) ).
thf(307,axiom,
! [X_13: $i] :
( ( hAPP_nat_int @ ( power_power_int @ X_13 ) @ one_one_nat )
= X_13 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_395_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
thf(308,axiom,
! [X_13: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ X_13 ) @ one_one_nat )
= X_13 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_394_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
thf(331,axiom,
! [A_40: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ zero_zero_int ) @ A_40 )
= A_40 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_371_add__0__left) ).
thf(332,axiom,
! [A_40: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ zero_zero_nat ) @ A_40 )
= A_40 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_370_add__0__left) ).
thf(334,axiom,
! [A_41: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ zero_zero_int ) @ A_41 )
= A_41 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_368_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
thf(335,axiom,
! [A_41: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ zero_zero_nat ) @ A_41 )
= A_41 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_367_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
thf(337,axiom,
! [A_42: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ zero_zero_int ) @ A_42 )
= A_42 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_365_add__0) ).
thf(338,axiom,
! [A_42: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ zero_zero_nat ) @ A_42 )
= A_42 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_364_add__0) ).
thf(340,axiom,
! [A_24: $i] :
( ( zero_zero_int
= ( hAPP_int_int @ ( plus_plus_int @ A_24 ) @ A_24 ) )
<=> ( A_24 = zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_362_double__zero__sym) ).
thf(342,axiom,
! [A_43: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ A_43 ) @ zero_zero_int )
= A_43 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_360_add__0__right) ).
thf(343,axiom,
! [A_43: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ A_43 ) @ zero_zero_nat )
= A_43 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_359_add__0__right) ).
thf(345,axiom,
! [A_44: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ A_44 ) @ zero_zero_int )
= A_44 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_357_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
thf(346,axiom,
! [A_44: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ A_44 ) @ zero_zero_nat )
= A_44 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_356_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
thf(348,axiom,
! [A_45: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ A_45 ) @ zero_zero_int )
= A_45 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_354_add_Ocomm__neutral) ).
thf(349,axiom,
! [A_45: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ A_45 ) @ zero_zero_nat )
= A_45 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_353_add_Ocomm__neutral) ).
thf(351,axiom,
! [B_21: $i,A_24: $i] :
( ( B_21
= ( hAPP_int_int @ ( plus_plus_int @ B_21 ) @ A_24 ) )
<=> ( A_24 = zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_351_add__0__iff) ).
thf(352,axiom,
! [B_21: $i,A_24: $i] :
( ( B_21
= ( hAPP_nat_nat @ ( plus_plus_nat @ B_21 ) @ A_24 ) )
<=> ( A_24 = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_350_add__0__iff) ).
thf(354,axiom,
! [Xa: $i] :
( ( one_one_int = Xa )
<=> ( Xa = one_one_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_348_one__reorient) ).
thf(355,axiom,
! [Xa: $i] :
( ( one_one_nat = Xa )
<=> ( Xa = one_one_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_347_one__reorient) ).
thf(356,axiom,
! [Xa: $i] :
( ( one_one_real = Xa )
<=> ( Xa = one_one_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_346_one__reorient) ).
thf(357,axiom,
! [A_46: $i,C_21: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ A_46 ) @ C_21 )
= ( hAPP_int_int @ ( plus_plus_int @ C_21 ) @ A_46 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_345_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(358,axiom,
! [A_46: $i,C_21: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ A_46 ) @ C_21 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ C_21 ) @ A_46 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_344_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(360,axiom,
! [A_47: $i,C_22: $i,D_4: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ A_47 ) @ ( hAPP_int_int @ ( plus_plus_int @ C_22 ) @ D_4 ) )
= ( hAPP_int_int @ ( plus_plus_int @ C_22 ) @ ( hAPP_int_int @ ( plus_plus_int @ A_47 ) @ D_4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_342_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(361,axiom,
! [A_47: $i,C_22: $i,D_4: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ A_47 ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C_22 ) @ D_4 ) )
= ( hAPP_nat_nat @ ( plus_plus_nat @ C_22 ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A_47 ) @ D_4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_341_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(363,axiom,
! [A_48: $i,C_23: $i,D_5: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ A_48 ) @ ( hAPP_int_int @ ( plus_plus_int @ C_23 ) @ D_5 ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ A_48 ) @ C_23 ) ) @ D_5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_339_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(364,axiom,
! [A_48: $i,C_23: $i,D_5: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ A_48 ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C_23 ) @ D_5 ) )
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A_48 ) @ C_23 ) ) @ D_5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_338_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(366,axiom,
! [A_49: $i,B_34: $i,C_24: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ A_49 ) @ B_34 ) ) @ C_24 )
= ( hAPP_int_int @ ( plus_plus_int @ A_49 ) @ ( hAPP_int_int @ ( plus_plus_int @ B_34 ) @ C_24 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_336_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(367,axiom,
! [A_49: $i,B_34: $i,C_24: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A_49 ) @ B_34 ) ) @ C_24 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ A_49 ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B_34 ) @ C_24 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_335_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(369,axiom,
! [A_50: $i,B_35: $i,C_25: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ A_50 ) @ B_35 ) ) @ C_25 )
= ( hAPP_int_int @ ( plus_plus_int @ A_50 ) @ ( hAPP_int_int @ ( plus_plus_int @ B_35 ) @ C_25 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_333_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(370,axiom,
! [A_50: $i,B_35: $i,C_25: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A_50 ) @ B_35 ) ) @ C_25 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ A_50 ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B_35 ) @ C_25 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_332_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(372,axiom,
! [A_51: $i,B_36: $i,C_26: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ A_51 ) @ B_36 ) ) @ C_26 )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ A_51 ) @ C_26 ) ) @ B_36 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_330_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(373,axiom,
! [A_51: $i,B_36: $i,C_26: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A_51 ) @ B_36 ) ) @ C_26 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A_51 ) @ C_26 ) ) @ B_36 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_329_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(375,axiom,
! [A_24: $i,B_21: $i,C_15: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ A_24 ) @ B_21 )
= ( hAPP_int_int @ ( plus_plus_int @ A_24 ) @ C_15 ) )
<=> ( B_21 = C_15 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_327_add__left__cancel) ).
thf(376,axiom,
! [A_24: $i,B_21: $i,C_15: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ A_24 ) @ B_21 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ A_24 ) @ C_15 ) )
<=> ( B_21 = C_15 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_326_add__left__cancel) ).
thf(378,axiom,
! [B_21: $i,A_24: $i,C_15: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ B_21 ) @ A_24 )
= ( hAPP_int_int @ ( plus_plus_int @ C_15 ) @ A_24 ) )
<=> ( B_21 = C_15 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_324_add__right__cancel) ).
thf(379,axiom,
! [B_21: $i,A_24: $i,C_15: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ B_21 ) @ A_24 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ C_15 ) @ A_24 ) )
<=> ( B_21 = C_15 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_323_add__right__cancel) ).
thf(381,axiom,
! [A_52: $i,B_37: $i,C_27: $i,D_6: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ A_52 ) @ B_37 ) ) @ ( hAPP_int_int @ ( plus_plus_int @ C_27 ) @ D_6 ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ A_52 ) @ C_27 ) ) @ ( hAPP_int_int @ ( plus_plus_int @ B_37 ) @ D_6 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_321_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(382,axiom,
! [A_52: $i,B_37: $i,C_27: $i,D_6: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A_52 ) @ B_37 ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C_27 ) @ D_6 ) )
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A_52 ) @ C_27 ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B_37 ) @ D_6 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_320_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(384,axiom,
! [A_53: $i,B_38: $i,C_28: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ A_53 ) @ B_38 )
= ( hAPP_int_int @ ( plus_plus_int @ A_53 ) @ C_28 ) )
=> ( B_38 = C_28 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_318_add__left__imp__eq) ).
thf(385,axiom,
! [A_53: $i,B_38: $i,C_28: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ A_53 ) @ B_38 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ A_53 ) @ C_28 ) )
=> ( B_38 = C_28 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_317_add__left__imp__eq) ).
thf(387,axiom,
! [A_54: $i,B_39: $i,C_29: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ A_54 ) @ B_39 )
= ( hAPP_int_int @ ( plus_plus_int @ A_54 ) @ C_29 ) )
=> ( B_39 = C_29 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_315_add__imp__eq) ).
thf(388,axiom,
! [A_54: $i,B_39: $i,C_29: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ A_54 ) @ B_39 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ A_54 ) @ C_29 ) )
=> ( B_39 = C_29 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_314_add__imp__eq) ).
thf(390,axiom,
! [B_40: $i,A_55: $i,C_30: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ B_40 ) @ A_55 )
= ( hAPP_int_int @ ( plus_plus_int @ C_30 ) @ A_55 ) )
=> ( B_40 = C_30 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_312_add__right__imp__eq) ).
thf(391,axiom,
! [B_40: $i,A_55: $i,C_30: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ B_40 ) @ A_55 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ C_30 ) @ A_55 ) )
=> ( B_40 = C_30 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_311_add__right__imp__eq) ).
thf(393,axiom,
! [Xa: $i] :
( ( zero_zero_int = Xa )
<=> ( Xa = zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_309_zero__reorient) ).
thf(394,axiom,
! [Xa: $i] :
( ( zero_zero_nat = Xa )
<=> ( Xa = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_308_zero__reorient) ).
thf(395,axiom,
! [Xa: $i] :
( ( zero_zero_real = Xa )
<=> ( Xa = zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_307_zero__reorient) ).
thf(400,axiom,
! [X_14: $i] :
( ( hAPP_nat_int @ ( power_power_int @ X_14 ) @ zero_zero_nat )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_302_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
thf(401,axiom,
! [X_14: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ X_14 ) @ zero_zero_nat )
= one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_301_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
thf(403,axiom,
! [Xa: $i,Na: $i] :
( ( ( hAPP_nat_nat @ ( power_power_nat @ Xa ) @ Na )
= one_one_nat )
<=> ( ( Xa = one_one_nat )
| ( Na = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_299_exp__eq__1) ).
thf(407,axiom,
( zero_zero_int
= ( hAPP_nat_int @ semiri1621563631at_int @ zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_295_transfer__int__nat__numerals_I1_J) ).
thf(408,axiom,
( ( hAPP_nat_int @ semiri1621563631at_int @ zero_zero_nat )
= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_of__nat__0) ).
thf(409,axiom,
( ( hAPP_nat_nat @ semiri984289939at_nat @ zero_zero_nat )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_293_of__nat__0) ).
thf(411,axiom,
! [A_56: $i] :
( ( hAPP_nat_int @ ( power_power_int @ A_56 ) @ zero_zero_nat )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_291_power__0) ).
thf(412,axiom,
! [A_56: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ A_56 ) @ zero_zero_nat )
= one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_290_power__0) ).
thf(417,axiom,
! [A_24: $i,Na: $i] :
( ( ( hAPP_nat_int @ ( power_power_int @ A_24 ) @ Na )
= zero_zero_int )
<=> ( ( A_24 = zero_zero_int )
& ( Na != zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_285_power__eq__0__iff) ).
thf(418,axiom,
! [A_24: $i,Na: $i] :
( ( ( hAPP_nat_nat @ ( power_power_nat @ A_24 ) @ Na )
= zero_zero_nat )
<=> ( ( A_24 = zero_zero_nat )
& ( Na != zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_power__eq__0__iff) ).
thf(447,axiom,
! [X: $i,N_1: $i] :
( ( hAPP_nat_int @ ( power_power_int @ ( hAPP_nat_int @ semiri1621563631at_int @ X ) ) @ N_1 )
= ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( power_power_nat @ X ) @ N_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_Nat__Transfer_Otransfer__int__nat__functions_I4_J) ).
thf(448,axiom,
! [X: $i,Y: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ X ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ Y ) )
= ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( plus_plus_nat @ X ) @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_Nat__Transfer_Otransfer__int__nat__functions_I1_J) ).
thf(449,axiom,
( one_one_int
= ( hAPP_nat_int @ semiri1621563631at_int @ one_one_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_transfer__int__nat__numerals_I2_J) ).
thf(450,axiom,
! [M_6: $i,N_18: $i] :
( ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( power_power_nat @ M_6 ) @ N_18 ) )
= ( hAPP_nat_int @ ( power_power_int @ ( hAPP_nat_int @ semiri1621563631at_int @ M_6 ) ) @ N_18 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_of__nat__power) ).
thf(451,axiom,
! [M_6: $i,N_18: $i] :
( ( hAPP_nat_nat @ semiri984289939at_nat @ ( hAPP_nat_nat @ ( power_power_nat @ M_6 ) @ N_18 ) )
= ( hAPP_nat_nat @ ( power_power_nat @ ( hAPP_nat_nat @ semiri984289939at_nat @ M_6 ) ) @ N_18 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_of__nat__power) ).
thf(453,axiom,
( ( hAPP_nat_int @ semiri1621563631at_int @ one_one_nat )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_of__nat__1) ).
thf(454,axiom,
( ( hAPP_nat_nat @ semiri984289939at_nat @ one_one_nat )
= one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_of__nat__1) ).
thf(456,axiom,
! [M_7: $i,N_19: $i] :
( ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( plus_plus_nat @ M_7 ) @ N_19 ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ M_7 ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ N_19 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_of__nat__add) ).
thf(457,axiom,
! [M_7: $i,N_19: $i] :
( ( hAPP_nat_nat @ semiri984289939at_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ M_7 ) @ N_19 ) )
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ semiri984289939at_nat @ M_7 ) ) @ ( hAPP_nat_nat @ semiri984289939at_nat @ N_19 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_of__nat__add) ).
thf(468,axiom,
! [N_22: $i] :
( ( hAPP_nat_int @ ( power_power_int @ one_one_int ) @ N_22 )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_power__one) ).
thf(469,axiom,
! [N_22: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ one_one_nat ) @ N_22 )
= one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_power__one) ).
thf(471,axiom,
! [N_23: $i,A_62: $i] :
( ( A_62 != zero_zero_int )
=> ( ( hAPP_nat_int @ ( power_power_int @ A_62 ) @ N_23 )
!= zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_field__power__not__zero) ).
thf(473,axiom,
zero_zero_int != one_one_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_zero__neq__one) ).
thf(474,axiom,
zero_zero_nat != one_one_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_zero__neq__one) ).
thf(475,axiom,
zero_zero_real != one_one_real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_zero__neq__one) ).
thf(476,axiom,
one_one_int != zero_zero_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_one__neq__zero) ).
thf(477,axiom,
one_one_nat != zero_zero_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_one__neq__zero) ).
thf(478,axiom,
one_one_real != zero_zero_real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_one__neq__zero) ).
thf(482,axiom,
! [Xa: $i,Ya: $i] :
( ( ( hAPP_nat_int @ semiri1621563631at_int @ Xa )
= ( hAPP_nat_int @ semiri1621563631at_int @ Ya ) )
<=> ( Xa = Ya ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_Nat__Transfer_Otransfer__int__nat__relations_I1_J) ).
thf(483,axiom,
! [Ma: $i,Na: $i] :
( ( ( hAPP_nat_int @ semiri1621563631at_int @ Ma )
= ( hAPP_nat_int @ semiri1621563631at_int @ Na ) )
<=> ( Ma = Na ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_of__nat__eq__iff) ).
thf(484,axiom,
! [Ma: $i,Na: $i] :
( ( ( hAPP_nat_nat @ semiri984289939at_nat @ Ma )
= ( hAPP_nat_nat @ semiri984289939at_nat @ Na ) )
<=> ( Ma = Na ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_of__nat__eq__iff) ).
thf(486,axiom,
! [A_63: $i] :
( ( hAPP_nat_int @ ( power_power_int @ A_63 ) @ one_one_nat )
= A_63 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_power__one__right) ).
thf(487,axiom,
! [A_63: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ A_63 ) @ one_one_nat )
= A_63 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_power__one__right) ).
thf(489,axiom,
! [N_1: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ zero_zero_nat ) @ N_1 )
= N_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_plus__nat_Oadd__0) ).
thf(490,axiom,
! [M_1: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ M_1 ) @ zero_zero_nat )
= M_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_Nat_Oadd__0__right) ).
thf(491,axiom,
! [Ma: $i,Na: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ Ma ) @ Na )
= zero_zero_nat )
<=> ( ( Ma = zero_zero_nat )
& ( Na = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_add__is__0) ).
thf(492,axiom,
! [M_1: $i,N_1: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ M_1 ) @ N_1 )
= M_1 )
=> ( N_1 = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_add__eq__self__zero) ).
thf(520,axiom,
! [Ma: $i,K_2: $i,Na: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ Ma ) @ K_2 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ Na ) @ K_2 ) )
<=> ( Ma = Na ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_nat__add__right__cancel) ).
thf(521,axiom,
! [K_2: $i,Ma: $i,Na: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ K_2 ) @ Ma )
= ( hAPP_nat_nat @ ( plus_plus_nat @ K_2 ) @ Na ) )
<=> ( Ma = Na ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_nat__add__left__cancel) ).
thf(522,axiom,
! [M_1: $i,N_1: $i,K: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ M_1 ) @ N_1 ) ) @ K )
= ( hAPP_nat_nat @ ( plus_plus_nat @ M_1 ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ N_1 ) @ K ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_nat__add__assoc) ).
thf(523,axiom,
! [X: $i,Y: $i,Z_2: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ X ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ Y ) @ Z_2 ) )
= ( hAPP_nat_nat @ ( plus_plus_nat @ Y ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ X ) @ Z_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_nat__add__left__commute) ).
thf(524,axiom,
! [M_1: $i,N_1: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ M_1 ) @ N_1 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ N_1 ) @ M_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_nat__add__commute) ).
thf(526,axiom,
! [K: $i] :
( ( number_number_of_int @ K )
= K ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_number__of__is__id) ).
thf(530,axiom,
zero_zero_real != one_one_real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_real__zero__not__eq__one) ).
thf(541,axiom,
! [N_26: $i] :
( ( ( N_26 = zero_zero_nat )
=> ( ( hAPP_nat_nat @ ( power_power_nat @ zero_zero_nat ) @ N_26 )
= one_one_nat ) )
& ( ( N_26 != zero_zero_nat )
=> ( ( hAPP_nat_nat @ ( power_power_nat @ zero_zero_nat ) @ N_26 )
= zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_power__0__left) ).
thf(542,axiom,
! [N_26: $i] :
( ( ( N_26 = zero_zero_nat )
=> ( ( hAPP_nat_int @ ( power_power_int @ zero_zero_int ) @ N_26 )
= one_one_int ) )
& ( ( N_26 != zero_zero_nat )
=> ( ( hAPP_nat_int @ ( power_power_int @ zero_zero_int ) @ N_26 )
= zero_zero_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_power__0__left) ).
thf(550,axiom,
( ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) )
= ( hAPP_nat_int @ semiri1621563631at_int @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_transfer__int__nat__numerals_I4_J) ).
thf(551,axiom,
( ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) )
= ( hAPP_nat_int @ semiri1621563631at_int @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_transfer__int__nat__numerals_I3_J) ).
thf(555,axiom,
( ( number267125858f_real @ ( bit1 @ pls ) )
= one_one_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_semiring__numeral__1__eq__1) ).
thf(556,axiom,
( ( number_number_of_nat @ ( bit1 @ pls ) )
= one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_semiring__numeral__1__eq__1) ).
thf(557,axiom,
( ( number_number_of_int @ ( bit1 @ pls ) )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_semiring__numeral__1__eq__1) ).
thf(559,axiom,
! [W_2: $i] :
( ( number_number_of_int @ ( bit1 @ W_2 ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ ( number_number_of_int @ W_2 ) ) ) @ ( number_number_of_int @ W_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_number__of__Bit1) ).
thf(561,axiom,
! [W_3: $i] :
( ( number_number_of_int @ ( bit0 @ W_3 ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ zero_zero_int ) @ ( number_number_of_int @ W_3 ) ) ) @ ( number_number_of_int @ W_3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_number__of__Bit0) ).
thf(571,axiom,
! [N_29: $i] :
( ( number_number_of_int @ ( hAPP_nat_int @ semiri1621563631at_int @ N_29 ) )
= ( hAPP_nat_int @ semiri1621563631at_int @ N_29 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_number__of__int) ).
thf(572,axiom,
! [N_29: $i] :
( ( number_number_of_nat @ ( hAPP_nat_int @ semiri1621563631at_int @ N_29 ) )
= ( hAPP_nat_nat @ semiri984289939at_nat @ N_29 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_number__of__int) ).
thf(573,axiom,
! [Z_2: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ Z_2 ) ) @ Z_2 )
!= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_odd__nonzero) ).
thf(574,axiom,
! [K: $i] :
( ( bit1 @ K )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ K ) ) @ K ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_Bit1__def) ).
thf(575,axiom,
! [K: $i,L: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( bit0 @ K ) ) @ ( bit1 @ L ) )
= ( bit1 @ ( hAPP_int_int @ ( plus_plus_int @ K ) @ L ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_add__Bit0__Bit1) ).
thf(576,axiom,
! [K: $i,L: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( bit1 @ K ) ) @ ( bit0 @ L ) )
= ( bit1 @ ( hAPP_int_int @ ( plus_plus_int @ K ) @ L ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_add__Bit1__Bit0) ).
thf(578,axiom,
! [V_7: $i,W_4: $i] :
( ( number_number_of_int @ ( hAPP_int_int @ ( plus_plus_int @ V_7 ) @ W_4 ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( number_number_of_int @ V_7 ) ) @ ( number_number_of_int @ W_4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_number__of__add) ).
thf(580,axiom,
! [V_8: $i,W_5: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( number_number_of_int @ V_8 ) ) @ ( number_number_of_int @ W_5 ) )
= ( number_number_of_int @ ( hAPP_int_int @ ( plus_plus_int @ V_8 ) @ W_5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_add__number__of__eq) ).
thf(582,axiom,
! [V_9: $i,W_6: $i,Z_5: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( number_number_of_int @ V_9 ) ) @ ( hAPP_int_int @ ( plus_plus_int @ ( number_number_of_int @ W_6 ) ) @ Z_5 ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( number_number_of_int @ ( hAPP_int_int @ ( plus_plus_int @ V_9 ) @ W_6 ) ) ) @ Z_5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_add__number__of__left) ).
thf(584,axiom,
! [A_24: $i,Wa: $i] :
( ( ( hAPP_nat_nat @ ( power_power_nat @ A_24 ) @ ( number_number_of_nat @ Wa ) )
= zero_zero_nat )
<=> ( ( A_24 = zero_zero_nat )
& ( ( number_number_of_nat @ Wa )
!= zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_power__eq__0__iff__number__of) ).
thf(585,axiom,
! [A_24: $i,Wa: $i] :
( ( ( hAPP_nat_int @ ( power_power_int @ A_24 ) @ ( number_number_of_nat @ Wa ) )
= zero_zero_int )
<=> ( ( A_24 = zero_zero_int )
& ( ( number_number_of_nat @ Wa )
!= zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_power__eq__0__iff__number__of) ).
thf(587,axiom,
! [A_67: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ A_67 ) @ ( number_number_of_int @ pls ) )
= A_67 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_add__numeral__0__right) ).
thf(589,axiom,
! [A_68: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( number_number_of_int @ pls ) ) @ A_68 )
= A_68 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_add__numeral__0) ).
thf(590,axiom,
( zero_zero_real
= ( number267125858f_real @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_semiring__norm_I112_J) ).
thf(591,axiom,
( zero_zero_int
= ( number_number_of_int @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_semiring__norm_I112_J) ).
thf(592,axiom,
( ( number267125858f_real @ pls )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_number__of__Pls) ).
thf(593,axiom,
( ( number_number_of_int @ pls )
= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_number__of__Pls) ).
thf(594,axiom,
( ( number267125858f_real @ pls )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_semiring__numeral__0__eq__0) ).
thf(595,axiom,
( ( number_number_of_nat @ pls )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_semiring__numeral__0__eq__0) ).
thf(596,axiom,
( ( number_number_of_int @ pls )
= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_semiring__numeral__0__eq__0) ).
thf(597,axiom,
! [Z_2: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ zero_zero_int ) @ Z_2 )
= Z_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_zadd__0) ).
thf(598,axiom,
! [Z_2: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ Z_2 ) @ zero_zero_int )
= Z_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_zadd__0__right) ).
thf(599,axiom,
! [K: $i] :
( ( bit0 @ K )
= ( hAPP_int_int @ ( plus_plus_int @ K ) @ K ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_Bit0__def) ).
thf(600,axiom,
! [K: $i,L: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( bit0 @ K ) ) @ ( bit0 @ L ) )
= ( bit0 @ ( hAPP_int_int @ ( plus_plus_int @ K ) @ L ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_add__Bit0__Bit0) ).
thf(601,axiom,
! [K: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ pls ) @ K )
= K ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_add__Pls) ).
thf(602,axiom,
! [K: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ K ) @ pls )
= K ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_add__Pls__right) ).
thf(603,axiom,
zero_zero_int != one_one_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_int__0__neq__1) ).
thf(604,axiom,
pls = zero_zero_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_Pls__def) ).
thf(605,axiom,
( ( bit0 @ pls )
= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_Bit0__Pls) ).
thf(606,axiom,
! [L_1: $i] :
( ( pls
= ( bit0 @ L_1 ) )
<=> ( pls = L_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_rel__simps_I38_J) ).
thf(607,axiom,
! [K_2: $i] :
( ( ( bit0 @ K_2 )
= pls )
<=> ( K_2 = pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_rel__simps_I44_J) ).
thf(608,axiom,
! [K: $i,L: $i] :
( ( bit0 @ K )
!= ( bit1 @ L ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_rel__simps_I49_J) ).
thf(609,axiom,
! [K: $i,L: $i] :
( ( bit1 @ K )
!= ( bit0 @ L ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_rel__simps_I50_J) ).
thf(610,axiom,
! [L: $i] :
( pls
!= ( bit1 @ L ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_rel__simps_I39_J) ).
thf(611,axiom,
! [K: $i] :
( ( bit1 @ K )
!= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_rel__simps_I46_J) ).
thf(613,axiom,
! [A_24: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ A_24 ) @ A_24 )
= zero_zero_int )
<=> ( A_24 = zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_double__eq__0__iff) ).
thf(634,axiom,
! [Ma: $i,Na: $i] :
( ( ( hAPP_nat_int @ semiri1621563631at_int @ Ma )
= ( hAPP_nat_int @ semiri1621563631at_int @ Na ) )
<=> ( Ma = Na ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_int__int__eq) ).
thf(635,axiom,
! [Z_2: $i,W: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ Z_2 ) @ W )
= ( hAPP_int_int @ ( plus_plus_int @ W ) @ Z_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_zadd__commute) ).
thf(636,axiom,
! [X: $i,Y: $i,Z_2: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ X ) @ ( hAPP_int_int @ ( plus_plus_int @ Y ) @ Z_2 ) )
= ( hAPP_int_int @ ( plus_plus_int @ Y ) @ ( hAPP_int_int @ ( plus_plus_int @ X ) @ Z_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_zadd__left__commute) ).
thf(637,axiom,
! [Z1: $i,Z2: $i,Z3: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ Z1 ) @ Z2 ) ) @ Z3 )
= ( hAPP_int_int @ ( plus_plus_int @ Z1 ) @ ( hAPP_int_int @ ( plus_plus_int @ Z2 ) @ Z3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_zadd__assoc) ).
thf(640,axiom,
! [K_2: $i,L_1: $i] :
( ( ( bit0 @ K_2 )
= ( bit0 @ L_1 ) )
<=> ( K_2 = L_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_rel__simps_I48_J) ).
thf(641,axiom,
! [K_2: $i,L_1: $i] :
( ( ( bit1 @ K_2 )
= ( bit1 @ L_1 ) )
<=> ( K_2 = L_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_rel__simps_I51_J) ).
thf(642,axiom,
! [Wa: $i,Xa: $i] :
( ( ( number267125858f_real @ Wa )
= Xa )
<=> ( Xa
= ( number267125858f_real @ Wa ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_number__of__reorient) ).
thf(643,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_59_number__of__reorient) ).
thf(644,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_58_number__of__reorient) ).
thf(645,axiom,
! [Xa: $i,Ya: $i] :
( ( ( number267125858f_real @ Xa )
= ( number267125858f_real @ Ya ) )
<=> ( Xa = Ya ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_eq__number__of) ).
thf(646,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_56_eq__number__of) ).
thf(647,axiom,
( one_one_nat
= ( number_number_of_nat @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_Numeral1__eq1__nat) ).
thf(648,axiom,
( ( number_number_of_nat @ ( bit1 @ pls ) )
= one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_nat__numeral__1__eq__1) ).
thf(649,axiom,
( one_one_int
= ( number_number_of_int @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_one__is__num__one) ).
thf(657,axiom,
( ( hAPP_nat_nat @ ( plus_plus_nat @ one_one_nat ) @ one_one_nat )
= ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_nat__1__add__1) ).
thf(658,axiom,
( ( hAPP_nat_int @ semiri1621563631at_int @ zero_zero_nat )
= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_int__0) ).
thf(659,axiom,
! [Na: $i] :
( ( ( hAPP_nat_int @ semiri1621563631at_int @ Na )
= zero_zero_int )
<=> ( Na = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_int__eq__0__conv) ).
thf(660,axiom,
( zero_zero_nat
= ( number_number_of_nat @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_semiring__norm_I113_J) ).
thf(661,axiom,
( ( number_number_of_nat @ pls )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_nat__number__of__Pls) ).
thf(662,axiom,
( ( hAPP_nat_int @ semiri1621563631at_int @ one_one_nat )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_int__1) ).
thf(663,axiom,
! [M_1: $i,N_1: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ M_1 ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ N_1 ) )
= ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( plus_plus_nat @ M_1 ) @ N_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_zadd__int) ).
thf(664,axiom,
! [M_1: $i,N_1: $i,Z_2: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ M_1 ) ) @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ N_1 ) ) @ Z_2 ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( plus_plus_nat @ M_1 ) @ N_1 ) ) ) @ Z_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_zadd__int__left) ).
thf(665,axiom,
! [M_1: $i,N_1: $i] :
( ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( power_power_nat @ M_1 ) @ N_1 ) )
= ( hAPP_nat_int @ ( power_power_int @ ( hAPP_nat_int @ semiri1621563631at_int @ M_1 ) ) @ N_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_int__power) ).
thf(666,axiom,
! [M_1: $i,N_1: $i] :
( ( hAPP_nat_int @ ( power_power_int @ ( hAPP_nat_int @ semiri1621563631at_int @ M_1 ) ) @ N_1 )
= ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( power_power_nat @ M_1 ) @ N_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_zpower__int) ).
thf(667,axiom,
( zero_zero_int
= ( number_number_of_int @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_zero__is__num__zero) ).
thf(670,axiom,
! [V_6: $i,W: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( number_number_of_int @ V_6 ) ) @ ( number_number_of_int @ W ) )
= ( number_number_of_int @ ( hAPP_int_int @ ( plus_plus_int @ V_6 ) @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_plus__numeral__code_I9_J) ).
thf(674,axiom,
( ( number267125858f_real @ ( bit1 @ pls ) )
= one_one_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_numeral__1__eq__1) ).
thf(675,axiom,
( ( number_number_of_int @ ( bit1 @ pls ) )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_numeral__1__eq__1) ).
thf(676,axiom,
( one_one_real
= ( number267125858f_real @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_semiring__norm_I110_J) ).
thf(677,axiom,
( one_one_int
= ( number_number_of_int @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_semiring__norm_I110_J) ).
thf(679,axiom,
! [W_7: $i] :
( ( ( ( number_number_of_nat @ W_7 )
= zero_zero_nat )
=> ( ( hAPP_nat_nat @ ( power_power_nat @ zero_zero_nat ) @ ( number_number_of_nat @ W_7 ) )
= one_one_nat ) )
& ( ( ( number_number_of_nat @ W_7 )
!= zero_zero_nat )
=> ( ( hAPP_nat_nat @ ( power_power_nat @ zero_zero_nat ) @ ( number_number_of_nat @ W_7 ) )
= zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_power__0__left__number__of) ).
thf(680,axiom,
! [W_7: $i] :
( ( ( ( number_number_of_nat @ W_7 )
= zero_zero_nat )
=> ( ( hAPP_nat_int @ ( power_power_int @ zero_zero_int ) @ ( number_number_of_nat @ W_7 ) )
= one_one_int ) )
& ( ( ( number_number_of_nat @ W_7 )
!= zero_zero_nat )
=> ( ( hAPP_nat_int @ ( power_power_int @ zero_zero_int ) @ ( number_number_of_nat @ W_7 ) )
= zero_zero_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_power__0__left__number__of) ).
thf(681,axiom,
! [X: $i] :
( ( hAPP_nat_int @ ( power_power_int @ ( hAPP_nat_int @ ( power_power_int @ X ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( hAPP_nat_int @ ( power_power_int @ X ) @ ( number_number_of_nat @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_quartic__square__square) ).
thf(683,axiom,
( ( hAPP_nat_nat @ ( plus_plus_nat @ one_one_nat ) @ one_one_nat )
= ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_semiring__one__add__one__is__two) ).
thf(684,axiom,
( ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ one_one_int )
= ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_semiring__one__add__one__is__two) ).
thf(686,axiom,
( ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ one_one_int )
= ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_one__add__one__is__two) ).
thf(688,axiom,
! [V_11: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( number_number_of_int @ V_11 ) ) @ one_one_int )
= ( number_number_of_int @ ( hAPP_int_int @ ( plus_plus_int @ V_11 ) @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_add__special_I3_J) ).
thf(690,axiom,
! [W_8: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ ( number_number_of_int @ W_8 ) )
= ( number_number_of_int @ ( hAPP_int_int @ ( plus_plus_int @ ( bit1 @ pls ) ) @ W_8 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_add__special_I2_J) ).
thf(692,axiom,
! [A_24: $i] :
( ( ( hAPP_nat_int @ ( power_power_int @ A_24 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int )
<=> ( A_24 = zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_zero__eq__power2) ).
thf(694,axiom,
( ( hAPP_nat_nat @ ( power_power_nat @ zero_zero_nat ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_zero__power2) ).
thf(695,axiom,
( ( hAPP_nat_int @ ( power_power_int @ zero_zero_int ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_zero__power2) ).
thf(697,axiom,
( ( hAPP_nat_nat @ ( power_power_nat @ one_one_nat ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_one__power2) ).
thf(698,axiom,
( ( hAPP_nat_int @ ( power_power_int @ one_one_int ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_one__power2) ).
thf(700,axiom,
! [Xa: $i,Ya: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ Xa ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( 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(708,conjecture,
( hAPP_nat_int @ ( power_power_int @ ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ ( hAPP_nat_int @ semiri1621563631at_int @ n ) ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= zero_zero_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(709,negated_conjecture,
( ( ( ( hAPP_nat_int @ ( power_power_int @ ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ ( hAPP_nat_int @ semiri1621563631at_int @ n ) ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= zero_zero_int ) )
= $false ),
inference(negate_conjecture,[status(cth)],[708]) ).
thf(710,plain,
( ( ( ( hAPP_nat_int @ ( power_power_int @ ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ ( hAPP_nat_int @ semiri1621563631at_int @ n ) ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= zero_zero_int ) )
= $false ),
inference(unfold_def,[status(thm)],[709]) ).
thf(711,plain,
( ( ! [Ma: $i,Na: $i] :
( ( ( hAPP_nat_nat @ ( power_power_nat @ Ma ) @ Na )
= zero_zero_nat )
<=> ( ( Na != zero_zero_nat )
& ( Ma = zero_zero_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[306]) ).
thf(712,plain,
( ( ! [X_13: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ X_13 ) @ one_one_nat )
= X_13 ) )
= $true ),
inference(unfold_def,[status(thm)],[308]) ).
thf(713,plain,
( ( ! [A_40: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ zero_zero_nat ) @ A_40 )
= A_40 ) )
= $true ),
inference(unfold_def,[status(thm)],[332]) ).
thf(714,plain,
( ( ! [A_41: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ zero_zero_nat ) @ A_41 )
= A_41 ) )
= $true ),
inference(unfold_def,[status(thm)],[335]) ).
thf(715,plain,
( ( ! [A_42: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ zero_zero_nat ) @ A_42 )
= A_42 ) )
= $true ),
inference(unfold_def,[status(thm)],[338]) ).
thf(716,plain,
( ( ! [A_43: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ A_43 ) @ zero_zero_nat )
= A_43 ) )
= $true ),
inference(unfold_def,[status(thm)],[343]) ).
thf(717,plain,
( ( ! [A_44: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ A_44 ) @ zero_zero_nat )
= A_44 ) )
= $true ),
inference(unfold_def,[status(thm)],[346]) ).
thf(718,plain,
( ( ! [A_45: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ A_45 ) @ zero_zero_nat )
= A_45 ) )
= $true ),
inference(unfold_def,[status(thm)],[349]) ).
thf(719,plain,
( ( ! [B_21: $i,A_24: $i] :
( ( B_21
= ( hAPP_nat_nat @ ( plus_plus_nat @ B_21 ) @ A_24 ) )
<=> ( A_24 = zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[352]) ).
thf(720,plain,
( ( ! [Xa: $i] :
( ( one_one_nat = Xa )
<=> ( Xa = one_one_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[355]) ).
thf(721,plain,
( ( ! [Xa: $i] :
( ( one_one_real = Xa )
<=> ( Xa = one_one_real ) ) )
= $true ),
inference(unfold_def,[status(thm)],[356]) ).
thf(722,plain,
( ( ! [A_46: $i,C_21: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ A_46 ) @ C_21 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ C_21 ) @ A_46 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[358]) ).
thf(723,plain,
( ( ! [A_47: $i,C_22: $i,D_4: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ A_47 ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C_22 ) @ D_4 ) )
= ( hAPP_nat_nat @ ( plus_plus_nat @ C_22 ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A_47 ) @ D_4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[361]) ).
thf(724,plain,
( ( ! [A_48: $i,C_23: $i,D_5: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ A_48 ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C_23 ) @ D_5 ) )
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A_48 ) @ C_23 ) ) @ D_5 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[364]) ).
thf(725,plain,
( ( ! [A_49: $i,B_34: $i,C_24: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A_49 ) @ B_34 ) ) @ C_24 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ A_49 ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B_34 ) @ C_24 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[367]) ).
thf(726,plain,
( ( ! [A_50: $i,B_35: $i,C_25: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A_50 ) @ B_35 ) ) @ C_25 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ A_50 ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B_35 ) @ C_25 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[370]) ).
thf(727,plain,
( ( ! [A_51: $i,B_36: $i,C_26: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A_51 ) @ B_36 ) ) @ C_26 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A_51 ) @ C_26 ) ) @ B_36 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[373]) ).
thf(728,plain,
( ( ! [A_24: $i,B_21: $i,C_15: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ A_24 ) @ B_21 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ A_24 ) @ C_15 ) )
<=> ( B_21 = C_15 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[376]) ).
thf(729,plain,
( ( ! [B_21: $i,A_24: $i,C_15: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ B_21 ) @ A_24 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ C_15 ) @ A_24 ) )
<=> ( B_21 = C_15 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[379]) ).
thf(730,plain,
( ( ! [A_52: $i,B_37: $i,C_27: $i,D_6: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A_52 ) @ B_37 ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C_27 ) @ D_6 ) )
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A_52 ) @ C_27 ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B_37 ) @ D_6 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[382]) ).
thf(731,plain,
( ( ! [A_53: $i,B_38: $i,C_28: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ A_53 ) @ B_38 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ A_53 ) @ C_28 ) )
=> ( B_38 = C_28 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[385]) ).
thf(732,plain,
( ( ! [A_54: $i,B_39: $i,C_29: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ A_54 ) @ B_39 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ A_54 ) @ C_29 ) )
=> ( B_39 = C_29 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[388]) ).
thf(733,plain,
( ( ! [B_40: $i,A_55: $i,C_30: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ B_40 ) @ A_55 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ C_30 ) @ A_55 ) )
=> ( B_40 = C_30 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[391]) ).
thf(734,plain,
( ( ! [Xa: $i] :
( ( zero_zero_nat = Xa )
<=> ( Xa = zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[394]) ).
thf(735,plain,
( ( ! [Xa: $i] :
( ( zero_zero_real = Xa )
<=> ( Xa = zero_zero_real ) ) )
= $true ),
inference(unfold_def,[status(thm)],[395]) ).
thf(736,plain,
( ( ! [X_14: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ X_14 ) @ zero_zero_nat )
= one_one_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[401]) ).
thf(737,plain,
( ( ! [Xa: $i,Na: $i] :
( ( ( hAPP_nat_nat @ ( power_power_nat @ Xa ) @ Na )
= one_one_nat )
<=> ( ( Xa = one_one_nat )
| ( Na = zero_zero_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[403]) ).
thf(738,plain,
( ( ( hAPP_nat_nat @ semiri984289939at_nat @ zero_zero_nat )
= zero_zero_nat )
= $true ),
inference(unfold_def,[status(thm)],[409]) ).
thf(739,plain,
( ( ! [A_56: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ A_56 ) @ zero_zero_nat )
= one_one_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[412]) ).
thf(740,plain,
( ( ! [A_24: $i,Na: $i] :
( ( ( hAPP_nat_nat @ ( power_power_nat @ A_24 ) @ Na )
= zero_zero_nat )
<=> ( ( A_24 = zero_zero_nat )
& ( Na != zero_zero_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[418]) ).
thf(741,plain,
( ( ! [M_6: $i,N_18: $i] :
( ( hAPP_nat_nat @ semiri984289939at_nat @ ( hAPP_nat_nat @ ( power_power_nat @ M_6 ) @ N_18 ) )
= ( hAPP_nat_nat @ ( power_power_nat @ ( hAPP_nat_nat @ semiri984289939at_nat @ M_6 ) ) @ N_18 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[451]) ).
thf(742,plain,
( ( ( hAPP_nat_nat @ semiri984289939at_nat @ one_one_nat )
= one_one_nat )
= $true ),
inference(unfold_def,[status(thm)],[454]) ).
thf(743,plain,
( ( ! [M_7: $i,N_19: $i] :
( ( hAPP_nat_nat @ semiri984289939at_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ M_7 ) @ N_19 ) )
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ semiri984289939at_nat @ M_7 ) ) @ ( hAPP_nat_nat @ semiri984289939at_nat @ N_19 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[457]) ).
thf(744,plain,
( ( ! [N_22: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ one_one_nat ) @ N_22 )
= one_one_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[469]) ).
thf(745,plain,
( ( ( zero_zero_nat != one_one_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[474]) ).
thf(746,plain,
( ( ( zero_zero_real != one_one_real ) )
= $true ),
inference(unfold_def,[status(thm)],[475]) ).
thf(747,plain,
( ( ( one_one_nat != zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[477]) ).
thf(748,plain,
( ( ( one_one_real != zero_zero_real ) )
= $true ),
inference(unfold_def,[status(thm)],[478]) ).
thf(749,plain,
( ( ! [Ma: $i,Na: $i] :
( ( ( hAPP_nat_nat @ semiri984289939at_nat @ Ma )
= ( hAPP_nat_nat @ semiri984289939at_nat @ Na ) )
<=> ( Ma = Na ) ) )
= $true ),
inference(unfold_def,[status(thm)],[484]) ).
thf(750,plain,
( ( ! [A_63: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ A_63 ) @ one_one_nat )
= A_63 ) )
= $true ),
inference(unfold_def,[status(thm)],[487]) ).
thf(751,plain,
( ( ! [N_1: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ zero_zero_nat ) @ N_1 )
= N_1 ) )
= $true ),
inference(unfold_def,[status(thm)],[489]) ).
thf(752,plain,
( ( ! [M_1: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ M_1 ) @ zero_zero_nat )
= M_1 ) )
= $true ),
inference(unfold_def,[status(thm)],[490]) ).
thf(753,plain,
( ( ! [Ma: $i,Na: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ Ma ) @ Na )
= zero_zero_nat )
<=> ( ( Ma = zero_zero_nat )
& ( Na = zero_zero_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[491]) ).
thf(754,plain,
( ( ! [M_1: $i,N_1: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ M_1 ) @ N_1 )
= M_1 )
=> ( N_1 = zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[492]) ).
thf(755,plain,
( ( ! [Ma: $i,K_2: $i,Na: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ Ma ) @ K_2 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ Na ) @ K_2 ) )
<=> ( Ma = Na ) ) )
= $true ),
inference(unfold_def,[status(thm)],[520]) ).
thf(756,plain,
( ( ! [K_2: $i,Ma: $i,Na: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ K_2 ) @ Ma )
= ( hAPP_nat_nat @ ( plus_plus_nat @ K_2 ) @ Na ) )
<=> ( Ma = Na ) ) )
= $true ),
inference(unfold_def,[status(thm)],[521]) ).
thf(757,plain,
( ( ! [M_1: $i,N_1: $i,K: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ M_1 ) @ N_1 ) ) @ K )
= ( hAPP_nat_nat @ ( plus_plus_nat @ M_1 ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ N_1 ) @ K ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[522]) ).
thf(758,plain,
( ( ! [X: $i,Y: $i,Z_2: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ X ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ Y ) @ Z_2 ) )
= ( hAPP_nat_nat @ ( plus_plus_nat @ Y ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ X ) @ Z_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[523]) ).
thf(759,plain,
( ( ! [M_1: $i,N_1: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ M_1 ) @ N_1 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ N_1 ) @ M_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[524]) ).
thf(760,plain,
( ( ! [K: $i] :
( ( number_number_of_int @ K )
= K ) )
= $true ),
inference(unfold_def,[status(thm)],[526]) ).
thf(761,plain,
( ( ( zero_zero_real != one_one_real ) )
= $true ),
inference(unfold_def,[status(thm)],[530]) ).
thf(762,plain,
( ( ! [N_26: $i] :
( ( ( N_26 = zero_zero_nat )
=> ( ( hAPP_nat_nat @ ( power_power_nat @ zero_zero_nat ) @ N_26 )
= one_one_nat ) )
& ( ( N_26 != zero_zero_nat )
=> ( ( hAPP_nat_nat @ ( power_power_nat @ zero_zero_nat ) @ N_26 )
= zero_zero_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[541]) ).
thf(763,plain,
( ( ! [A_24: $i,Wa: $i] :
( ( ( hAPP_nat_nat @ ( power_power_nat @ A_24 ) @ ( number_number_of_nat @ Wa ) )
= zero_zero_nat )
<=> ( ( A_24 = zero_zero_nat )
& ( ( number_number_of_nat @ Wa )
!= zero_zero_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[584]) ).
thf(764,plain,
( ( ! [Wa: $i,Xa: $i] :
( ( ( number267125858f_real @ Wa )
= Xa )
<=> ( Xa
= ( number267125858f_real @ Wa ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[642]) ).
thf(765,plain,
( ( ! [Wa: $i,Xa: $i] :
( ( ( number_number_of_int @ Wa )
= Xa )
<=> ( Xa
= ( number_number_of_int @ Wa ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[643]) ).
thf(766,plain,
( ( ! [Xa: $i,Ya: $i] :
( ( ( number267125858f_real @ Xa )
= ( number267125858f_real @ Ya ) )
<=> ( Xa = Ya ) ) )
= $true ),
inference(unfold_def,[status(thm)],[645]) ).
thf(767,plain,
( ( ! [Xa: $i,Ya: $i] :
( ( ( number_number_of_int @ Xa )
= ( number_number_of_int @ Ya ) )
<=> ( Xa = Ya ) ) )
= $true ),
inference(unfold_def,[status(thm)],[646]) ).
thf(768,plain,
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ one_one_nat ) @ one_one_nat )
= ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[657]) ).
thf(769,plain,
( ( ! [W_7: $i] :
( ( ( ( number_number_of_nat @ W_7 )
= zero_zero_nat )
=> ( ( hAPP_nat_nat @ ( power_power_nat @ zero_zero_nat ) @ ( number_number_of_nat @ W_7 ) )
= one_one_nat ) )
& ( ( ( number_number_of_nat @ W_7 )
!= zero_zero_nat )
=> ( ( hAPP_nat_nat @ ( power_power_nat @ zero_zero_nat ) @ ( number_number_of_nat @ W_7 ) )
= zero_zero_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[679]) ).
thf(770,plain,
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ one_one_nat ) @ one_one_nat )
= ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[683]) ).
thf(771,plain,
( ( ( hAPP_nat_nat @ ( power_power_nat @ zero_zero_nat ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_nat )
= $true ),
inference(unfold_def,[status(thm)],[694]) ).
thf(772,plain,
( ( ( hAPP_nat_nat @ ( power_power_nat @ one_one_nat ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_nat )
= $true ),
inference(unfold_def,[status(thm)],[697]) ).
thf(773,plain,
( ( ! [K: $i,L: $i] :
( ( times_times_int @ ( bit1 @ K ) @ L )
= ( hAPP_int_int @ ( plus_plus_int @ ( bit0 @ ( times_times_int @ K @ L ) ) ) @ L ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(774,plain,
( ( ! [A: $i,B: $i] :
( ( hAPP_nat_int @ ( power_power_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(775,plain,
( ( ! [K: $i,L: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( bit1 @ K ) ) @ ( bit1 @ L ) )
= ( bit0 @ ( hAPP_int_int @ ( plus_plus_int @ K ) @ ( succ @ L ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[118]) ).
thf(776,plain,
( ( ! [K_3: $i] :
( ( number_number_of_int @ ( succ @ K_3 ) )
= ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ ( number_number_of_int @ K_3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[119]) ).
thf(777,plain,
( ( ! [K: $i] :
( ( succ @ K )
= ( hAPP_int_int @ ( plus_plus_int @ K ) @ one_one_int ) ) )
= $true ),
inference(unfold_def,[status(thm)],[129]) ).
thf(778,plain,
( ( ! [K: $i] :
( ( succ @ ( bit1 @ K ) )
= ( bit0 @ ( succ @ K ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[133]) ).
thf(779,plain,
( ( ! [K: $i] :
( ( succ @ ( bit0 @ K ) )
= ( bit1 @ K ) ) )
= $true ),
inference(unfold_def,[status(thm)],[134]) ).
thf(780,plain,
( ( ( succ @ pls )
= ( bit1 @ pls ) )
= $true ),
inference(unfold_def,[status(thm)],[135]) ).
thf(781,plain,
( ( ! [X_13: $i] :
( ( hAPP_nat_int @ ( power_power_int @ X_13 ) @ one_one_nat )
= X_13 ) )
= $true ),
inference(unfold_def,[status(thm)],[307]) ).
thf(782,plain,
( ( ! [A_40: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ zero_zero_int ) @ A_40 )
= A_40 ) )
= $true ),
inference(unfold_def,[status(thm)],[331]) ).
thf(783,plain,
( ( ! [A_41: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ zero_zero_int ) @ A_41 )
= A_41 ) )
= $true ),
inference(unfold_def,[status(thm)],[334]) ).
thf(784,plain,
( ( ! [A_42: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ zero_zero_int ) @ A_42 )
= A_42 ) )
= $true ),
inference(unfold_def,[status(thm)],[337]) ).
thf(785,plain,
( ( ! [A_24: $i] :
( ( zero_zero_int
= ( hAPP_int_int @ ( plus_plus_int @ A_24 ) @ A_24 ) )
<=> ( A_24 = zero_zero_int ) ) )
= $true ),
inference(unfold_def,[status(thm)],[340]) ).
thf(786,plain,
( ( ! [A_43: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ A_43 ) @ zero_zero_int )
= A_43 ) )
= $true ),
inference(unfold_def,[status(thm)],[342]) ).
thf(787,plain,
( ( ! [A_44: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ A_44 ) @ zero_zero_int )
= A_44 ) )
= $true ),
inference(unfold_def,[status(thm)],[345]) ).
thf(788,plain,
( ( ! [A_45: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ A_45 ) @ zero_zero_int )
= A_45 ) )
= $true ),
inference(unfold_def,[status(thm)],[348]) ).
thf(789,plain,
( ( ! [B_21: $i,A_24: $i] :
( ( B_21
= ( hAPP_int_int @ ( plus_plus_int @ B_21 ) @ A_24 ) )
<=> ( A_24 = zero_zero_int ) ) )
= $true ),
inference(unfold_def,[status(thm)],[351]) ).
thf(790,plain,
( ( ! [Xa: $i] :
( ( one_one_int = Xa )
<=> ( Xa = one_one_int ) ) )
= $true ),
inference(unfold_def,[status(thm)],[354]) ).
thf(791,plain,
( ( ! [A_46: $i,C_21: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ A_46 ) @ C_21 )
= ( hAPP_int_int @ ( plus_plus_int @ C_21 ) @ A_46 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[357]) ).
thf(792,plain,
( ( ! [A_47: $i,C_22: $i,D_4: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ A_47 ) @ ( hAPP_int_int @ ( plus_plus_int @ C_22 ) @ D_4 ) )
= ( hAPP_int_int @ ( plus_plus_int @ C_22 ) @ ( hAPP_int_int @ ( plus_plus_int @ A_47 ) @ D_4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[360]) ).
thf(793,plain,
( ( ! [A_48: $i,C_23: $i,D_5: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ A_48 ) @ ( hAPP_int_int @ ( plus_plus_int @ C_23 ) @ D_5 ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ A_48 ) @ C_23 ) ) @ D_5 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[363]) ).
thf(794,plain,
( ( ! [A_49: $i,B_34: $i,C_24: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ A_49 ) @ B_34 ) ) @ C_24 )
= ( hAPP_int_int @ ( plus_plus_int @ A_49 ) @ ( hAPP_int_int @ ( plus_plus_int @ B_34 ) @ C_24 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[366]) ).
thf(795,plain,
( ( ! [A_50: $i,B_35: $i,C_25: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ A_50 ) @ B_35 ) ) @ C_25 )
= ( hAPP_int_int @ ( plus_plus_int @ A_50 ) @ ( hAPP_int_int @ ( plus_plus_int @ B_35 ) @ C_25 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[369]) ).
thf(796,plain,
( ( ! [A_51: $i,B_36: $i,C_26: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ A_51 ) @ B_36 ) ) @ C_26 )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ A_51 ) @ C_26 ) ) @ B_36 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[372]) ).
thf(797,plain,
( ( ! [A_24: $i,B_21: $i,C_15: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ A_24 ) @ B_21 )
= ( hAPP_int_int @ ( plus_plus_int @ A_24 ) @ C_15 ) )
<=> ( B_21 = C_15 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[375]) ).
thf(798,plain,
( ( ! [B_21: $i,A_24: $i,C_15: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ B_21 ) @ A_24 )
= ( hAPP_int_int @ ( plus_plus_int @ C_15 ) @ A_24 ) )
<=> ( B_21 = C_15 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[378]) ).
thf(799,plain,
( ( ! [A_52: $i,B_37: $i,C_27: $i,D_6: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ A_52 ) @ B_37 ) ) @ ( hAPP_int_int @ ( plus_plus_int @ C_27 ) @ D_6 ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ A_52 ) @ C_27 ) ) @ ( hAPP_int_int @ ( plus_plus_int @ B_37 ) @ D_6 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[381]) ).
thf(800,plain,
( ( ! [A_53: $i,B_38: $i,C_28: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ A_53 ) @ B_38 )
= ( hAPP_int_int @ ( plus_plus_int @ A_53 ) @ C_28 ) )
=> ( B_38 = C_28 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[384]) ).
thf(801,plain,
( ( ! [A_54: $i,B_39: $i,C_29: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ A_54 ) @ B_39 )
= ( hAPP_int_int @ ( plus_plus_int @ A_54 ) @ C_29 ) )
=> ( B_39 = C_29 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[387]) ).
thf(802,plain,
( ( ! [B_40: $i,A_55: $i,C_30: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ B_40 ) @ A_55 )
= ( hAPP_int_int @ ( plus_plus_int @ C_30 ) @ A_55 ) )
=> ( B_40 = C_30 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[390]) ).
thf(803,plain,
( ( ! [Xa: $i] :
( ( zero_zero_int = Xa )
<=> ( Xa = zero_zero_int ) ) )
= $true ),
inference(unfold_def,[status(thm)],[393]) ).
thf(804,plain,
( ( ! [X_14: $i] :
( ( hAPP_nat_int @ ( power_power_int @ X_14 ) @ zero_zero_nat )
= one_one_int ) )
= $true ),
inference(unfold_def,[status(thm)],[400]) ).
thf(805,plain,
( ( zero_zero_int
= ( hAPP_nat_int @ semiri1621563631at_int @ zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[407]) ).
thf(806,plain,
( ( ( hAPP_nat_int @ semiri1621563631at_int @ zero_zero_nat )
= zero_zero_int )
= $true ),
inference(unfold_def,[status(thm)],[408]) ).
thf(807,plain,
( ( ! [A_56: $i] :
( ( hAPP_nat_int @ ( power_power_int @ A_56 ) @ zero_zero_nat )
= one_one_int ) )
= $true ),
inference(unfold_def,[status(thm)],[411]) ).
thf(808,plain,
( ( ! [A_24: $i,Na: $i] :
( ( ( hAPP_nat_int @ ( power_power_int @ A_24 ) @ Na )
= zero_zero_int )
<=> ( ( A_24 = zero_zero_int )
& ( Na != zero_zero_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[417]) ).
thf(809,plain,
( ( ! [X: $i,N_1: $i] :
( ( hAPP_nat_int @ ( power_power_int @ ( hAPP_nat_int @ semiri1621563631at_int @ X ) ) @ N_1 )
= ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( power_power_nat @ X ) @ N_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[447]) ).
thf(810,plain,
( ( ! [X: $i,Y: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ X ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ Y ) )
= ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( plus_plus_nat @ X ) @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[448]) ).
thf(811,plain,
( ( one_one_int
= ( hAPP_nat_int @ semiri1621563631at_int @ one_one_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[449]) ).
thf(812,plain,
( ( ! [M_6: $i,N_18: $i] :
( ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( power_power_nat @ M_6 ) @ N_18 ) )
= ( hAPP_nat_int @ ( power_power_int @ ( hAPP_nat_int @ semiri1621563631at_int @ M_6 ) ) @ N_18 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[450]) ).
thf(813,plain,
( ( ( hAPP_nat_int @ semiri1621563631at_int @ one_one_nat )
= one_one_int )
= $true ),
inference(unfold_def,[status(thm)],[453]) ).
thf(814,plain,
( ( ! [M_7: $i,N_19: $i] :
( ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( plus_plus_nat @ M_7 ) @ N_19 ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ M_7 ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ N_19 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[456]) ).
thf(815,plain,
( ( ! [N_22: $i] :
( ( hAPP_nat_int @ ( power_power_int @ one_one_int ) @ N_22 )
= one_one_int ) )
= $true ),
inference(unfold_def,[status(thm)],[468]) ).
thf(816,plain,
( ( ! [N_23: $i,A_62: $i] :
( ( A_62 != zero_zero_int )
=> ( ( hAPP_nat_int @ ( power_power_int @ A_62 ) @ N_23 )
!= zero_zero_int ) ) )
= $true ),
inference(unfold_def,[status(thm)],[471]) ).
thf(817,plain,
( ( ( zero_zero_int != one_one_int ) )
= $true ),
inference(unfold_def,[status(thm)],[473]) ).
thf(818,plain,
( ( ( one_one_int != zero_zero_int ) )
= $true ),
inference(unfold_def,[status(thm)],[476]) ).
thf(819,plain,
( ( ! [Xa: $i,Ya: $i] :
( ( ( hAPP_nat_int @ semiri1621563631at_int @ Xa )
= ( hAPP_nat_int @ semiri1621563631at_int @ Ya ) )
<=> ( Xa = Ya ) ) )
= $true ),
inference(unfold_def,[status(thm)],[482]) ).
thf(820,plain,
( ( ! [Ma: $i,Na: $i] :
( ( ( hAPP_nat_int @ semiri1621563631at_int @ Ma )
= ( hAPP_nat_int @ semiri1621563631at_int @ Na ) )
<=> ( Ma = Na ) ) )
= $true ),
inference(unfold_def,[status(thm)],[483]) ).
thf(821,plain,
( ( ! [A_63: $i] :
( ( hAPP_nat_int @ ( power_power_int @ A_63 ) @ one_one_nat )
= A_63 ) )
= $true ),
inference(unfold_def,[status(thm)],[486]) ).
thf(822,plain,
( ( ! [N_26: $i] :
( ( ( N_26 = zero_zero_nat )
=> ( ( hAPP_nat_int @ ( power_power_int @ zero_zero_int ) @ N_26 )
= one_one_int ) )
& ( ( N_26 != zero_zero_nat )
=> ( ( hAPP_nat_int @ ( power_power_int @ zero_zero_int ) @ N_26 )
= zero_zero_int ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[542]) ).
thf(823,plain,
( ( ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) )
= ( hAPP_nat_int @ semiri1621563631at_int @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[550]) ).
thf(824,plain,
( ( ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) )
= ( hAPP_nat_int @ semiri1621563631at_int @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[551]) ).
thf(825,plain,
( ( ( number267125858f_real @ ( bit1 @ pls ) )
= one_one_real )
= $true ),
inference(unfold_def,[status(thm)],[555]) ).
thf(826,plain,
( ( ( number_number_of_nat @ ( bit1 @ pls ) )
= one_one_nat )
= $true ),
inference(unfold_def,[status(thm)],[556]) ).
thf(827,plain,
( ( ( number_number_of_int @ ( bit1 @ pls ) )
= one_one_int )
= $true ),
inference(unfold_def,[status(thm)],[557]) ).
thf(828,plain,
( ( ! [W_2: $i] :
( ( number_number_of_int @ ( bit1 @ W_2 ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ ( number_number_of_int @ W_2 ) ) ) @ ( number_number_of_int @ W_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[559]) ).
thf(829,plain,
( ( ! [W_3: $i] :
( ( number_number_of_int @ ( bit0 @ W_3 ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ zero_zero_int ) @ ( number_number_of_int @ W_3 ) ) ) @ ( number_number_of_int @ W_3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[561]) ).
thf(830,plain,
( ( ! [N_29: $i] :
( ( number_number_of_int @ ( hAPP_nat_int @ semiri1621563631at_int @ N_29 ) )
= ( hAPP_nat_int @ semiri1621563631at_int @ N_29 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[571]) ).
thf(831,plain,
( ( ! [N_29: $i] :
( ( number_number_of_nat @ ( hAPP_nat_int @ semiri1621563631at_int @ N_29 ) )
= ( hAPP_nat_nat @ semiri984289939at_nat @ N_29 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[572]) ).
thf(832,plain,
( ( ! [Z_2: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ Z_2 ) ) @ Z_2 )
!= zero_zero_int ) )
= $true ),
inference(unfold_def,[status(thm)],[573]) ).
thf(833,plain,
( ( ! [K: $i] :
( ( bit1 @ K )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ K ) ) @ K ) ) )
= $true ),
inference(unfold_def,[status(thm)],[574]) ).
thf(834,plain,
( ( ! [K: $i,L: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( bit0 @ K ) ) @ ( bit1 @ L ) )
= ( bit1 @ ( hAPP_int_int @ ( plus_plus_int @ K ) @ L ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[575]) ).
thf(835,plain,
( ( ! [K: $i,L: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( bit1 @ K ) ) @ ( bit0 @ L ) )
= ( bit1 @ ( hAPP_int_int @ ( plus_plus_int @ K ) @ L ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[576]) ).
thf(836,plain,
( ( ! [V_7: $i,W_4: $i] :
( ( number_number_of_int @ ( hAPP_int_int @ ( plus_plus_int @ V_7 ) @ W_4 ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( number_number_of_int @ V_7 ) ) @ ( number_number_of_int @ W_4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[578]) ).
thf(837,plain,
( ( ! [V_8: $i,W_5: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( number_number_of_int @ V_8 ) ) @ ( number_number_of_int @ W_5 ) )
= ( number_number_of_int @ ( hAPP_int_int @ ( plus_plus_int @ V_8 ) @ W_5 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[580]) ).
thf(838,plain,
( ( ! [V_9: $i,W_6: $i,Z_5: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( number_number_of_int @ V_9 ) ) @ ( hAPP_int_int @ ( plus_plus_int @ ( number_number_of_int @ W_6 ) ) @ Z_5 ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( number_number_of_int @ ( hAPP_int_int @ ( plus_plus_int @ V_9 ) @ W_6 ) ) ) @ Z_5 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[582]) ).
thf(839,plain,
( ( ! [A_24: $i,Wa: $i] :
( ( ( hAPP_nat_int @ ( power_power_int @ A_24 ) @ ( number_number_of_nat @ Wa ) )
= zero_zero_int )
<=> ( ( A_24 = zero_zero_int )
& ( ( number_number_of_nat @ Wa )
!= zero_zero_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[585]) ).
thf(840,plain,
( ( ! [A_67: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ A_67 ) @ ( number_number_of_int @ pls ) )
= A_67 ) )
= $true ),
inference(unfold_def,[status(thm)],[587]) ).
thf(841,plain,
( ( ! [A_68: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( number_number_of_int @ pls ) ) @ A_68 )
= A_68 ) )
= $true ),
inference(unfold_def,[status(thm)],[589]) ).
thf(842,plain,
( ( zero_zero_real
= ( number267125858f_real @ pls ) )
= $true ),
inference(unfold_def,[status(thm)],[590]) ).
thf(843,plain,
( ( zero_zero_int
= ( number_number_of_int @ pls ) )
= $true ),
inference(unfold_def,[status(thm)],[591]) ).
thf(844,plain,
( ( ( number267125858f_real @ pls )
= zero_zero_real )
= $true ),
inference(unfold_def,[status(thm)],[592]) ).
thf(845,plain,
( ( ( number_number_of_int @ pls )
= zero_zero_int )
= $true ),
inference(unfold_def,[status(thm)],[593]) ).
thf(846,plain,
( ( ( number267125858f_real @ pls )
= zero_zero_real )
= $true ),
inference(unfold_def,[status(thm)],[594]) ).
thf(847,plain,
( ( ( number_number_of_nat @ pls )
= zero_zero_nat )
= $true ),
inference(unfold_def,[status(thm)],[595]) ).
thf(848,plain,
( ( ( number_number_of_int @ pls )
= zero_zero_int )
= $true ),
inference(unfold_def,[status(thm)],[596]) ).
thf(849,plain,
( ( ! [Z_2: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ zero_zero_int ) @ Z_2 )
= Z_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[597]) ).
thf(850,plain,
( ( ! [Z_2: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ Z_2 ) @ zero_zero_int )
= Z_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[598]) ).
thf(851,plain,
( ( ! [K: $i] :
( ( bit0 @ K )
= ( hAPP_int_int @ ( plus_plus_int @ K ) @ K ) ) )
= $true ),
inference(unfold_def,[status(thm)],[599]) ).
thf(852,plain,
( ( ! [K: $i,L: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( bit0 @ K ) ) @ ( bit0 @ L ) )
= ( bit0 @ ( hAPP_int_int @ ( plus_plus_int @ K ) @ L ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[600]) ).
thf(853,plain,
( ( ! [K: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ pls ) @ K )
= K ) )
= $true ),
inference(unfold_def,[status(thm)],[601]) ).
thf(854,plain,
( ( ! [K: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ K ) @ pls )
= K ) )
= $true ),
inference(unfold_def,[status(thm)],[602]) ).
thf(855,plain,
( ( ( zero_zero_int != one_one_int ) )
= $true ),
inference(unfold_def,[status(thm)],[603]) ).
thf(856,plain,
( ( pls = zero_zero_int )
= $true ),
inference(unfold_def,[status(thm)],[604]) ).
thf(857,plain,
( ( ( bit0 @ pls )
= pls )
= $true ),
inference(unfold_def,[status(thm)],[605]) ).
thf(858,plain,
( ( ! [L_1: $i] :
( ( pls
= ( bit0 @ L_1 ) )
<=> ( pls = L_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[606]) ).
thf(859,plain,
( ( ! [K_2: $i] :
( ( ( bit0 @ K_2 )
= pls )
<=> ( K_2 = pls ) ) )
= $true ),
inference(unfold_def,[status(thm)],[607]) ).
thf(860,plain,
( ( ! [K: $i,L: $i] :
( ( bit0 @ K )
!= ( bit1 @ L ) ) )
= $true ),
inference(unfold_def,[status(thm)],[608]) ).
thf(861,plain,
( ( ! [K: $i,L: $i] :
( ( bit1 @ K )
!= ( bit0 @ L ) ) )
= $true ),
inference(unfold_def,[status(thm)],[609]) ).
thf(862,plain,
( ( ! [L: $i] :
( pls
!= ( bit1 @ L ) ) )
= $true ),
inference(unfold_def,[status(thm)],[610]) ).
thf(863,plain,
( ( ! [K: $i] :
( ( bit1 @ K )
!= pls ) )
= $true ),
inference(unfold_def,[status(thm)],[611]) ).
thf(864,plain,
( ( ! [A_24: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ A_24 ) @ A_24 )
= zero_zero_int )
<=> ( A_24 = zero_zero_int ) ) )
= $true ),
inference(unfold_def,[status(thm)],[613]) ).
thf(865,plain,
( ( ! [Ma: $i,Na: $i] :
( ( ( hAPP_nat_int @ semiri1621563631at_int @ Ma )
= ( hAPP_nat_int @ semiri1621563631at_int @ Na ) )
<=> ( Ma = Na ) ) )
= $true ),
inference(unfold_def,[status(thm)],[634]) ).
thf(866,plain,
( ( ! [Z_2: $i,W: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ Z_2 ) @ W )
= ( hAPP_int_int @ ( plus_plus_int @ W ) @ Z_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[635]) ).
thf(867,plain,
( ( ! [X: $i,Y: $i,Z_2: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ X ) @ ( hAPP_int_int @ ( plus_plus_int @ Y ) @ Z_2 ) )
= ( hAPP_int_int @ ( plus_plus_int @ Y ) @ ( hAPP_int_int @ ( plus_plus_int @ X ) @ Z_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[636]) ).
thf(868,plain,
( ( ! [Z1: $i,Z2: $i,Z3: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ Z1 ) @ Z2 ) ) @ Z3 )
= ( hAPP_int_int @ ( plus_plus_int @ Z1 ) @ ( hAPP_int_int @ ( plus_plus_int @ Z2 ) @ Z3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[637]) ).
thf(869,plain,
( ( ! [K_2: $i,L_1: $i] :
( ( ( bit0 @ K_2 )
= ( bit0 @ L_1 ) )
<=> ( K_2 = L_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[640]) ).
thf(870,plain,
( ( ! [K_2: $i,L_1: $i] :
( ( ( bit1 @ K_2 )
= ( bit1 @ L_1 ) )
<=> ( K_2 = L_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[641]) ).
thf(871,plain,
( ( ! [Wa: $i,Xa: $i] :
( ( ( number_number_of_nat @ Wa )
= Xa )
<=> ( Xa
= ( number_number_of_nat @ Wa ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[644]) ).
thf(872,plain,
( ( one_one_nat
= ( number_number_of_nat @ ( bit1 @ pls ) ) )
= $true ),
inference(unfold_def,[status(thm)],[647]) ).
thf(873,plain,
( ( ( number_number_of_nat @ ( bit1 @ pls ) )
= one_one_nat )
= $true ),
inference(unfold_def,[status(thm)],[648]) ).
thf(874,plain,
( ( one_one_int
= ( number_number_of_int @ ( bit1 @ pls ) ) )
= $true ),
inference(unfold_def,[status(thm)],[649]) ).
thf(875,plain,
( ( ( hAPP_nat_int @ semiri1621563631at_int @ zero_zero_nat )
= zero_zero_int )
= $true ),
inference(unfold_def,[status(thm)],[658]) ).
thf(876,plain,
( ( ! [Na: $i] :
( ( ( hAPP_nat_int @ semiri1621563631at_int @ Na )
= zero_zero_int )
<=> ( Na = zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[659]) ).
thf(877,plain,
( ( zero_zero_nat
= ( number_number_of_nat @ pls ) )
= $true ),
inference(unfold_def,[status(thm)],[660]) ).
thf(878,plain,
( ( ( number_number_of_nat @ pls )
= zero_zero_nat )
= $true ),
inference(unfold_def,[status(thm)],[661]) ).
thf(879,plain,
( ( ( hAPP_nat_int @ semiri1621563631at_int @ one_one_nat )
= one_one_int )
= $true ),
inference(unfold_def,[status(thm)],[662]) ).
thf(880,plain,
( ( ! [M_1: $i,N_1: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ M_1 ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ N_1 ) )
= ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( plus_plus_nat @ M_1 ) @ N_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[663]) ).
thf(881,plain,
( ( ! [M_1: $i,N_1: $i,Z_2: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ M_1 ) ) @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ N_1 ) ) @ Z_2 ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( plus_plus_nat @ M_1 ) @ N_1 ) ) ) @ Z_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[664]) ).
thf(882,plain,
( ( ! [M_1: $i,N_1: $i] :
( ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( power_power_nat @ M_1 ) @ N_1 ) )
= ( hAPP_nat_int @ ( power_power_int @ ( hAPP_nat_int @ semiri1621563631at_int @ M_1 ) ) @ N_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[665]) ).
thf(883,plain,
( ( ! [M_1: $i,N_1: $i] :
( ( hAPP_nat_int @ ( power_power_int @ ( hAPP_nat_int @ semiri1621563631at_int @ M_1 ) ) @ N_1 )
= ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( power_power_nat @ M_1 ) @ N_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[666]) ).
thf(884,plain,
( ( zero_zero_int
= ( number_number_of_int @ pls ) )
= $true ),
inference(unfold_def,[status(thm)],[667]) ).
thf(885,plain,
( ( ! [V_6: $i,W: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( number_number_of_int @ V_6 ) ) @ ( number_number_of_int @ W ) )
= ( number_number_of_int @ ( hAPP_int_int @ ( plus_plus_int @ V_6 ) @ W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[670]) ).
thf(886,plain,
( ( ( number267125858f_real @ ( bit1 @ pls ) )
= one_one_real )
= $true ),
inference(unfold_def,[status(thm)],[674]) ).
thf(887,plain,
( ( ( number_number_of_int @ ( bit1 @ pls ) )
= one_one_int )
= $true ),
inference(unfold_def,[status(thm)],[675]) ).
thf(888,plain,
( ( one_one_real
= ( number267125858f_real @ ( bit1 @ pls ) ) )
= $true ),
inference(unfold_def,[status(thm)],[676]) ).
thf(889,plain,
( ( one_one_int
= ( number_number_of_int @ ( bit1 @ pls ) ) )
= $true ),
inference(unfold_def,[status(thm)],[677]) ).
thf(890,plain,
( ( ! [W_7: $i] :
( ( ( ( number_number_of_nat @ W_7 )
= zero_zero_nat )
=> ( ( hAPP_nat_int @ ( power_power_int @ zero_zero_int ) @ ( number_number_of_nat @ W_7 ) )
= one_one_int ) )
& ( ( ( number_number_of_nat @ W_7 )
!= zero_zero_nat )
=> ( ( hAPP_nat_int @ ( power_power_int @ zero_zero_int ) @ ( number_number_of_nat @ W_7 ) )
= zero_zero_int ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[680]) ).
thf(891,plain,
( ( ! [X: $i] :
( ( hAPP_nat_int @ ( power_power_int @ ( hAPP_nat_int @ ( power_power_int @ X ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( hAPP_nat_int @ ( power_power_int @ X ) @ ( number_number_of_nat @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[681]) ).
thf(892,plain,
( ( ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ one_one_int )
= ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[684]) ).
thf(893,plain,
( ( ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ one_one_int )
= ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[686]) ).
thf(894,plain,
( ( ! [V_11: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( number_number_of_int @ V_11 ) ) @ one_one_int )
= ( number_number_of_int @ ( hAPP_int_int @ ( plus_plus_int @ V_11 ) @ ( bit1 @ pls ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[688]) ).
thf(895,plain,
( ( ! [W_8: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ ( number_number_of_int @ W_8 ) )
= ( number_number_of_int @ ( hAPP_int_int @ ( plus_plus_int @ ( bit1 @ pls ) ) @ W_8 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[690]) ).
thf(896,plain,
( ( ! [A_24: $i] :
( ( ( hAPP_nat_int @ ( power_power_int @ A_24 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int )
<=> ( A_24 = zero_zero_int ) ) )
= $true ),
inference(unfold_def,[status(thm)],[692]) ).
thf(897,plain,
( ( ( hAPP_nat_int @ ( power_power_int @ zero_zero_int ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int )
= $true ),
inference(unfold_def,[status(thm)],[695]) ).
thf(898,plain,
( ( ( hAPP_nat_int @ ( power_power_int @ one_one_int ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_int )
= $true ),
inference(unfold_def,[status(thm)],[698]) ).
thf(899,plain,
( ( ! [Xa: $i,Ya: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ Xa ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( 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)],[700]) ).
thf(900,plain,
( ( ~ ( ( ( hAPP_nat_int @ ( power_power_int @ ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ ( hAPP_nat_int @ semiri1621563631at_int @ n ) ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= zero_zero_int ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[710]) ).
thf(901,plain,
( ( ( hAPP_nat_int @ ( power_power_int @ ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ ( hAPP_nat_int @ semiri1621563631at_int @ n ) ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int )
= $true ),
inference(extcnf_combined,[status(esa)],[900]) ).
thf(902,plain,
( ( ! [Ma: $i,Na: $i] :
( ( Na = zero_zero_nat )
| ( Ma != zero_zero_nat )
| ( ( hAPP_nat_nat @ ( power_power_nat @ Ma ) @ Na )
= zero_zero_nat ) )
& ! [Ma: $i,Na: $i] :
( ( ( hAPP_nat_nat @ ( power_power_nat @ Ma ) @ Na )
!= zero_zero_nat )
| ( Na != zero_zero_nat ) )
& ! [Ma: $i] :
( ! [Na: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ Ma ) @ Na )
!= zero_zero_nat )
| ( Ma = zero_zero_nat ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[711]) ).
thf(903,plain,
( ( ! [B_21: $i,A_24: $i] :
( ( B_21
!= ( hAPP_nat_nat @ ( plus_plus_nat @ B_21 ) @ A_24 ) )
| ( A_24 = zero_zero_nat ) )
& ! [B_21: $i,A_24: $i] :
( ( A_24 != zero_zero_nat )
| ( B_21
= ( hAPP_nat_nat @ ( plus_plus_nat @ B_21 ) @ A_24 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[719]) ).
thf(904,plain,
( ( ! [Xa: $i] :
( ( one_one_nat != Xa )
| ( Xa = one_one_nat ) )
& ! [Xa: $i] :
( ( Xa != one_one_nat )
| ( one_one_nat = Xa ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[720]) ).
thf(905,plain,
( ( ! [Xa: $i] :
( ( one_one_real != Xa )
| ( Xa = one_one_real ) )
& ! [Xa: $i] :
( ( Xa != one_one_real )
| ( one_one_real = Xa ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[721]) ).
thf(906,plain,
( ( ! [A_24: $i] :
( ! [B_21: $i,C_15: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ A_24 ) @ B_21 )
!= ( hAPP_nat_nat @ ( plus_plus_nat @ A_24 ) @ C_15 ) )
| ( B_21 = C_15 ) )
& ! [B_21: $i,C_15: $i] :
( ( B_21 != C_15 )
| ( ( hAPP_nat_nat @ ( plus_plus_nat @ A_24 ) @ B_21 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ A_24 ) @ C_15 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[728]) ).
thf(907,plain,
( ( ! [B_21: $i] :
( ! [A_24: $i,C_15: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ B_21 ) @ A_24 )
!= ( hAPP_nat_nat @ ( plus_plus_nat @ C_15 ) @ A_24 ) )
| ( B_21 = C_15 ) )
& ! [A_24: $i,C_15: $i] :
( ( B_21 != C_15 )
| ( ( hAPP_nat_nat @ ( plus_plus_nat @ B_21 ) @ A_24 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ C_15 ) @ A_24 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[729]) ).
thf(908,plain,
( ( ! [A_53: $i,B_38: $i,C_28: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ A_53 ) @ B_38 )
!= ( hAPP_nat_nat @ ( plus_plus_nat @ A_53 ) @ C_28 ) )
| ( B_38 = C_28 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[731]) ).
thf(909,plain,
( ( ! [A_54: $i,B_39: $i,C_29: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ A_54 ) @ B_39 )
!= ( hAPP_nat_nat @ ( plus_plus_nat @ A_54 ) @ C_29 ) )
| ( B_39 = C_29 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[732]) ).
thf(910,plain,
( ( ! [B_40: $i,A_55: $i,C_30: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ B_40 ) @ A_55 )
!= ( hAPP_nat_nat @ ( plus_plus_nat @ C_30 ) @ A_55 ) )
| ( B_40 = C_30 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[733]) ).
thf(911,plain,
( ( ! [Xa: $i] :
( ( zero_zero_nat != Xa )
| ( Xa = zero_zero_nat ) )
& ! [Xa: $i] :
( ( Xa != zero_zero_nat )
| ( zero_zero_nat = Xa ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[734]) ).
thf(912,plain,
( ( ! [Xa: $i] :
( ( zero_zero_real != Xa )
| ( Xa = zero_zero_real ) )
& ! [Xa: $i] :
( ( Xa != zero_zero_real )
| ( zero_zero_real = Xa ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[735]) ).
thf(913,plain,
( ( ! [Xa: $i,Na: $i] :
( ( ( hAPP_nat_nat @ ( power_power_nat @ Xa ) @ Na )
!= one_one_nat )
| ( Xa = one_one_nat )
| ( Na = zero_zero_nat ) )
& ! [Xa: $i] :
( ( Xa != one_one_nat )
| ! [Na: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ Xa ) @ Na )
= one_one_nat ) )
& ! [Xa: $i,Na: $i] :
( ( Na != zero_zero_nat )
| ( ( hAPP_nat_nat @ ( power_power_nat @ Xa ) @ Na )
= one_one_nat ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[737]) ).
thf(914,plain,
( ( ! [A_24: $i,Na: $i] :
( ( Na = zero_zero_nat )
| ( A_24 != zero_zero_nat )
| ( ( hAPP_nat_nat @ ( power_power_nat @ A_24 ) @ Na )
= zero_zero_nat ) )
& ! [A_24: $i,Na: $i] :
( ( ( hAPP_nat_nat @ ( power_power_nat @ A_24 ) @ Na )
!= zero_zero_nat )
| ( Na != zero_zero_nat ) )
& ! [A_24: $i] :
( ! [Na: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ A_24 ) @ Na )
!= zero_zero_nat )
| ( A_24 = zero_zero_nat ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[740]) ).
thf(915,plain,
( ( ( zero_zero_nat != one_one_nat ) )
= $true ),
inference(extcnf_combined,[status(esa)],[745]) ).
thf(916,plain,
( ( ( zero_zero_real != one_one_real ) )
= $true ),
inference(extcnf_combined,[status(esa)],[746]) ).
thf(917,plain,
( ( ( one_one_nat != zero_zero_nat ) )
= $true ),
inference(extcnf_combined,[status(esa)],[747]) ).
thf(918,plain,
( ( ( one_one_real != zero_zero_real ) )
= $true ),
inference(extcnf_combined,[status(esa)],[748]) ).
thf(919,plain,
( ( ! [Ma: $i,Na: $i] :
( ( ( hAPP_nat_nat @ semiri984289939at_nat @ Ma )
!= ( hAPP_nat_nat @ semiri984289939at_nat @ Na ) )
| ( Ma = Na ) )
& ! [Ma: $i,Na: $i] :
( ( Ma != Na )
| ( ( hAPP_nat_nat @ semiri984289939at_nat @ Ma )
= ( hAPP_nat_nat @ semiri984289939at_nat @ Na ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[749]) ).
thf(920,plain,
( ( ! [Ma: $i,Na: $i] :
( ( Ma != zero_zero_nat )
| ( Na != zero_zero_nat )
| ( ( hAPP_nat_nat @ ( plus_plus_nat @ Ma ) @ Na )
= zero_zero_nat ) )
& ! [Ma: $i] :
( ! [Na: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ Ma ) @ Na )
!= zero_zero_nat )
| ( Ma = zero_zero_nat ) )
& ! [Ma: $i,Na: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ Ma ) @ Na )
!= zero_zero_nat )
| ( Na = zero_zero_nat ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[753]) ).
thf(921,plain,
( ( ! [M_1: $i,N_1: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ M_1 ) @ N_1 )
!= M_1 )
| ( N_1 = zero_zero_nat ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[754]) ).
thf(922,plain,
( ( ! [Ma: $i] :
( ! [K_2: $i,Na: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ Ma ) @ K_2 )
!= ( hAPP_nat_nat @ ( plus_plus_nat @ Na ) @ K_2 ) )
| ( Ma = Na ) )
& ! [K_2: $i,Na: $i] :
( ( Ma != Na )
| ( ( hAPP_nat_nat @ ( plus_plus_nat @ Ma ) @ K_2 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ Na ) @ K_2 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[755]) ).
thf(923,plain,
( ( ! [K_2: $i] :
( ! [Ma: $i,Na: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ K_2 ) @ Ma )
!= ( hAPP_nat_nat @ ( plus_plus_nat @ K_2 ) @ Na ) )
| ( Ma = Na ) )
& ! [Ma: $i,Na: $i] :
( ( Ma != Na )
| ( ( hAPP_nat_nat @ ( plus_plus_nat @ K_2 ) @ Ma )
= ( hAPP_nat_nat @ ( plus_plus_nat @ K_2 ) @ Na ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[756]) ).
thf(924,plain,
( ( ( zero_zero_real != one_one_real ) )
= $true ),
inference(extcnf_combined,[status(esa)],[761]) ).
thf(925,plain,
( ( ! [N_26: $i] :
( ( N_26 != zero_zero_nat )
| ( ( hAPP_nat_nat @ ( power_power_nat @ zero_zero_nat ) @ N_26 )
= one_one_nat ) )
& ! [N_26: $i] :
( ( N_26 = zero_zero_nat )
| ( ( hAPP_nat_nat @ ( power_power_nat @ zero_zero_nat ) @ N_26 )
= zero_zero_nat ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[762]) ).
thf(926,plain,
( ( ! [A_24: $i,Wa: $i] :
( ( ( number_number_of_nat @ Wa )
= zero_zero_nat )
| ( A_24 != zero_zero_nat )
| ( ( hAPP_nat_nat @ ( power_power_nat @ A_24 ) @ ( number_number_of_nat @ Wa ) )
= zero_zero_nat ) )
& ! [A_24: $i,Wa: $i] :
( ( ( hAPP_nat_nat @ ( power_power_nat @ A_24 ) @ ( number_number_of_nat @ Wa ) )
!= zero_zero_nat )
| ( ( number_number_of_nat @ Wa )
!= zero_zero_nat ) )
& ! [A_24: $i] :
( ! [Wa: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ A_24 ) @ ( number_number_of_nat @ Wa ) )
!= zero_zero_nat )
| ( A_24 = zero_zero_nat ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[763]) ).
thf(927,plain,
( ( ! [Wa: $i,Xa: $i] :
( ( ( number267125858f_real @ Wa )
!= Xa )
| ( Xa
= ( number267125858f_real @ Wa ) ) )
& ! [Wa: $i,Xa: $i] :
( ( Xa
!= ( number267125858f_real @ Wa ) )
| ( ( number267125858f_real @ Wa )
= Xa ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[764]) ).
thf(928,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)],[765]) ).
thf(929,plain,
( ( ! [Xa: $i,Ya: $i] :
( ( ( number267125858f_real @ Xa )
!= ( number267125858f_real @ Ya ) )
| ( Xa = Ya ) )
& ! [Xa: $i,Ya: $i] :
( ( Xa != Ya )
| ( ( number267125858f_real @ Xa )
= ( number267125858f_real @ Ya ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[766]) ).
thf(930,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)],[767]) ).
thf(931,plain,
( ( ! [W_7: $i] :
( ( ( number_number_of_nat @ W_7 )
!= zero_zero_nat )
| ( ( hAPP_nat_nat @ ( power_power_nat @ zero_zero_nat ) @ ( number_number_of_nat @ W_7 ) )
= one_one_nat ) )
& ! [W_7: $i] :
( ( ( number_number_of_nat @ W_7 )
= zero_zero_nat )
| ( ( hAPP_nat_nat @ ( power_power_nat @ zero_zero_nat ) @ ( number_number_of_nat @ W_7 ) )
= zero_zero_nat ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[769]) ).
thf(932,plain,
( ( ! [A_24: $i] :
( ( zero_zero_int
!= ( hAPP_int_int @ ( plus_plus_int @ A_24 ) @ A_24 ) )
| ( A_24 = zero_zero_int ) )
& ! [A_24: $i] :
( ( A_24 != zero_zero_int )
| ( zero_zero_int
= ( hAPP_int_int @ ( plus_plus_int @ A_24 ) @ A_24 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[785]) ).
thf(933,plain,
( ( ! [B_21: $i,A_24: $i] :
( ( B_21
!= ( hAPP_int_int @ ( plus_plus_int @ B_21 ) @ A_24 ) )
| ( A_24 = zero_zero_int ) )
& ! [B_21: $i,A_24: $i] :
( ( A_24 != zero_zero_int )
| ( B_21
= ( hAPP_int_int @ ( plus_plus_int @ B_21 ) @ A_24 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[789]) ).
thf(934,plain,
( ( ! [Xa: $i] :
( ( one_one_int != Xa )
| ( Xa = one_one_int ) )
& ! [Xa: $i] :
( ( Xa != one_one_int )
| ( one_one_int = Xa ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[790]) ).
thf(935,plain,
( ( ! [A_24: $i] :
( ! [B_21: $i,C_15: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ A_24 ) @ B_21 )
!= ( hAPP_int_int @ ( plus_plus_int @ A_24 ) @ C_15 ) )
| ( B_21 = C_15 ) )
& ! [B_21: $i,C_15: $i] :
( ( B_21 != C_15 )
| ( ( hAPP_int_int @ ( plus_plus_int @ A_24 ) @ B_21 )
= ( hAPP_int_int @ ( plus_plus_int @ A_24 ) @ C_15 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[797]) ).
thf(936,plain,
( ( ! [B_21: $i] :
( ! [A_24: $i,C_15: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ B_21 ) @ A_24 )
!= ( hAPP_int_int @ ( plus_plus_int @ C_15 ) @ A_24 ) )
| ( B_21 = C_15 ) )
& ! [A_24: $i,C_15: $i] :
( ( B_21 != C_15 )
| ( ( hAPP_int_int @ ( plus_plus_int @ B_21 ) @ A_24 )
= ( hAPP_int_int @ ( plus_plus_int @ C_15 ) @ A_24 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[798]) ).
thf(937,plain,
( ( ! [A_53: $i,B_38: $i,C_28: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ A_53 ) @ B_38 )
!= ( hAPP_int_int @ ( plus_plus_int @ A_53 ) @ C_28 ) )
| ( B_38 = C_28 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[800]) ).
thf(938,plain,
( ( ! [A_54: $i,B_39: $i,C_29: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ A_54 ) @ B_39 )
!= ( hAPP_int_int @ ( plus_plus_int @ A_54 ) @ C_29 ) )
| ( B_39 = C_29 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[801]) ).
thf(939,plain,
( ( ! [B_40: $i,A_55: $i,C_30: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ B_40 ) @ A_55 )
!= ( hAPP_int_int @ ( plus_plus_int @ C_30 ) @ A_55 ) )
| ( B_40 = C_30 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[802]) ).
thf(940,plain,
( ( ! [Xa: $i] :
( ( zero_zero_int != Xa )
| ( Xa = zero_zero_int ) )
& ! [Xa: $i] :
( ( Xa != zero_zero_int )
| ( zero_zero_int = Xa ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[803]) ).
thf(941,plain,
( ( ! [A_24: $i,Na: $i] :
( ( Na = zero_zero_nat )
| ( A_24 != zero_zero_int )
| ( ( hAPP_nat_int @ ( power_power_int @ A_24 ) @ Na )
= zero_zero_int ) )
& ! [A_24: $i,Na: $i] :
( ( ( hAPP_nat_int @ ( power_power_int @ A_24 ) @ Na )
!= zero_zero_int )
| ( Na != zero_zero_nat ) )
& ! [A_24: $i] :
( ! [Na: $i] :
( ( hAPP_nat_int @ ( power_power_int @ A_24 ) @ Na )
!= zero_zero_int )
| ( A_24 = zero_zero_int ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[808]) ).
thf(942,plain,
( ( ! [N_23: $i,A_62: $i] :
( ( A_62 = zero_zero_int )
| ( ( hAPP_nat_int @ ( power_power_int @ A_62 ) @ N_23 )
!= zero_zero_int ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[816]) ).
thf(943,plain,
( ( ( zero_zero_int != one_one_int ) )
= $true ),
inference(extcnf_combined,[status(esa)],[817]) ).
thf(944,plain,
( ( ( one_one_int != zero_zero_int ) )
= $true ),
inference(extcnf_combined,[status(esa)],[818]) ).
thf(945,plain,
( ( ! [Xa: $i,Ya: $i] :
( ( ( hAPP_nat_int @ semiri1621563631at_int @ Xa )
!= ( hAPP_nat_int @ semiri1621563631at_int @ Ya ) )
| ( Xa = Ya ) )
& ! [Xa: $i,Ya: $i] :
( ( Xa != Ya )
| ( ( hAPP_nat_int @ semiri1621563631at_int @ Xa )
= ( hAPP_nat_int @ semiri1621563631at_int @ Ya ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[819]) ).
thf(946,plain,
( ( ! [Ma: $i,Na: $i] :
( ( ( hAPP_nat_int @ semiri1621563631at_int @ Ma )
!= ( hAPP_nat_int @ semiri1621563631at_int @ Na ) )
| ( Ma = Na ) )
& ! [Ma: $i,Na: $i] :
( ( Ma != Na )
| ( ( hAPP_nat_int @ semiri1621563631at_int @ Ma )
= ( hAPP_nat_int @ semiri1621563631at_int @ Na ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[820]) ).
thf(947,plain,
( ( ! [N_26: $i] :
( ( N_26 != zero_zero_nat )
| ( ( hAPP_nat_int @ ( power_power_int @ zero_zero_int ) @ N_26 )
= one_one_int ) )
& ! [N_26: $i] :
( ( N_26 = zero_zero_nat )
| ( ( hAPP_nat_int @ ( power_power_int @ zero_zero_int ) @ N_26 )
= zero_zero_int ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[822]) ).
thf(948,plain,
( ( ! [Z_2: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ Z_2 ) ) @ Z_2 )
!= zero_zero_int ) )
= $true ),
inference(extcnf_combined,[status(esa)],[832]) ).
thf(949,plain,
( ( ! [A_24: $i,Wa: $i] :
( ( ( number_number_of_nat @ Wa )
= zero_zero_nat )
| ( A_24 != zero_zero_int )
| ( ( hAPP_nat_int @ ( power_power_int @ A_24 ) @ ( number_number_of_nat @ Wa ) )
= zero_zero_int ) )
& ! [A_24: $i,Wa: $i] :
( ( ( hAPP_nat_int @ ( power_power_int @ A_24 ) @ ( number_number_of_nat @ Wa ) )
!= zero_zero_int )
| ( ( number_number_of_nat @ Wa )
!= zero_zero_nat ) )
& ! [A_24: $i] :
( ! [Wa: $i] :
( ( hAPP_nat_int @ ( power_power_int @ A_24 ) @ ( number_number_of_nat @ Wa ) )
!= zero_zero_int )
| ( A_24 = zero_zero_int ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[839]) ).
thf(950,plain,
( ( ( zero_zero_int != one_one_int ) )
= $true ),
inference(extcnf_combined,[status(esa)],[855]) ).
thf(951,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)],[858]) ).
thf(952,plain,
( ( ! [K_2: $i] :
( ( ( bit0 @ K_2 )
!= pls )
| ( K_2 = pls ) )
& ! [K_2: $i] :
( ( K_2 != pls )
| ( ( bit0 @ K_2 )
= pls ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[859]) ).
thf(953,plain,
( ( ! [K: $i,L: $i] :
( ( bit0 @ K )
!= ( bit1 @ L ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[860]) ).
thf(954,plain,
( ( ! [K: $i,L: $i] :
( ( bit1 @ K )
!= ( bit0 @ L ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[861]) ).
thf(955,plain,
( ( ! [L: $i] :
( pls
!= ( bit1 @ L ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[862]) ).
thf(956,plain,
( ( ! [K: $i] :
( ( bit1 @ K )
!= pls ) )
= $true ),
inference(extcnf_combined,[status(esa)],[863]) ).
thf(957,plain,
( ( ! [A_24: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ A_24 ) @ A_24 )
!= zero_zero_int )
| ( A_24 = zero_zero_int ) )
& ! [A_24: $i] :
( ( A_24 != zero_zero_int )
| ( ( hAPP_int_int @ ( plus_plus_int @ A_24 ) @ A_24 )
= zero_zero_int ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[864]) ).
thf(958,plain,
( ( ! [Ma: $i,Na: $i] :
( ( ( hAPP_nat_int @ semiri1621563631at_int @ Ma )
!= ( hAPP_nat_int @ semiri1621563631at_int @ Na ) )
| ( Ma = Na ) )
& ! [Ma: $i,Na: $i] :
( ( Ma != Na )
| ( ( hAPP_nat_int @ semiri1621563631at_int @ Ma )
= ( hAPP_nat_int @ semiri1621563631at_int @ Na ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[865]) ).
thf(959,plain,
( ( ! [K_2: $i,L_1: $i] :
( ( ( bit0 @ K_2 )
!= ( bit0 @ L_1 ) )
| ( K_2 = L_1 ) )
& ! [K_2: $i,L_1: $i] :
( ( K_2 != L_1 )
| ( ( bit0 @ K_2 )
= ( bit0 @ L_1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[869]) ).
thf(960,plain,
( ( ! [K_2: $i,L_1: $i] :
( ( ( bit1 @ K_2 )
!= ( bit1 @ L_1 ) )
| ( K_2 = L_1 ) )
& ! [K_2: $i,L_1: $i] :
( ( K_2 != L_1 )
| ( ( bit1 @ K_2 )
= ( bit1 @ L_1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[870]) ).
thf(961,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)],[871]) ).
thf(962,plain,
( ( ! [Na: $i] :
( ( ( hAPP_nat_int @ semiri1621563631at_int @ Na )
!= zero_zero_int )
| ( Na = zero_zero_nat ) )
& ! [Na: $i] :
( ( Na != zero_zero_nat )
| ( ( hAPP_nat_int @ semiri1621563631at_int @ Na )
= zero_zero_int ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[876]) ).
thf(963,plain,
( ( ! [W_7: $i] :
( ( ( number_number_of_nat @ W_7 )
!= zero_zero_nat )
| ( ( hAPP_nat_int @ ( power_power_int @ zero_zero_int ) @ ( number_number_of_nat @ W_7 ) )
= one_one_int ) )
& ! [W_7: $i] :
( ( ( number_number_of_nat @ W_7 )
= zero_zero_nat )
| ( ( hAPP_nat_int @ ( power_power_int @ zero_zero_int ) @ ( number_number_of_nat @ W_7 ) )
= zero_zero_int ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[890]) ).
thf(964,plain,
( ( ! [A_24: $i] :
( ( ( hAPP_nat_int @ ( power_power_int @ A_24 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= zero_zero_int )
| ( A_24 = zero_zero_int ) )
& ! [A_24: $i] :
( ( A_24 != zero_zero_int )
| ( ( hAPP_nat_int @ ( power_power_int @ A_24 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[896]) ).
thf(965,plain,
( ( ! [Xa: $i,Ya: $i] :
( ( Xa != zero_zero_int )
| ( Ya != zero_zero_int )
| ( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ Xa ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ Ya ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_int ) )
& ! [Xa: $i] :
( ! [Ya: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ Xa ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ Ya ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_int )
| ( Xa = zero_zero_int ) )
& ! [Xa: $i,Ya: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ Xa ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ Ya ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_int )
| ( Ya = zero_zero_int ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[899]) ).
thf(966,plain,
( ( ! [Xa: $i,Ya: $i] :
( ( Xa != zero_zero_int )
| ( Ya != zero_zero_int )
| ( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ Xa ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ Ya ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_int ) )
& ! [Xa: $i] :
( ! [Ya: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ Xa ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ Ya ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_int )
| ( Xa = zero_zero_int ) )
& ! [Xa: $i,Ya: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ Xa ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ Ya ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_int )
| ( Ya = zero_zero_int ) ) )
= $true ),
inference(copy,[status(thm)],[965]) ).
thf(967,plain,
( ( ( hAPP_nat_int @ ( power_power_int @ one_one_int ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_int )
= $true ),
inference(copy,[status(thm)],[898]) ).
thf(968,plain,
( ( ( hAPP_nat_int @ ( power_power_int @ zero_zero_int ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int )
= $true ),
inference(copy,[status(thm)],[897]) ).
thf(969,plain,
( ( ! [A_24: $i] :
( ( ( hAPP_nat_int @ ( power_power_int @ A_24 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= zero_zero_int )
| ( A_24 = zero_zero_int ) )
& ! [A_24: $i] :
( ( A_24 != zero_zero_int )
| ( ( hAPP_nat_int @ ( power_power_int @ A_24 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int ) ) )
= $true ),
inference(copy,[status(thm)],[964]) ).
thf(970,plain,
( ( ! [W_8: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ ( number_number_of_int @ W_8 ) )
= ( number_number_of_int @ ( hAPP_int_int @ ( plus_plus_int @ ( bit1 @ pls ) ) @ W_8 ) ) ) )
= $true ),
inference(copy,[status(thm)],[895]) ).
thf(971,plain,
( ( ! [V_11: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( number_number_of_int @ V_11 ) ) @ one_one_int )
= ( number_number_of_int @ ( hAPP_int_int @ ( plus_plus_int @ V_11 ) @ ( bit1 @ pls ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[894]) ).
thf(972,plain,
( ( ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ one_one_int )
= ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(copy,[status(thm)],[893]) ).
thf(973,plain,
( ( ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ one_one_int )
= ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(copy,[status(thm)],[892]) ).
thf(974,plain,
( ( ! [X: $i] :
( ( hAPP_nat_int @ ( power_power_int @ ( hAPP_nat_int @ ( power_power_int @ X ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( hAPP_nat_int @ ( power_power_int @ X ) @ ( number_number_of_nat @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[891]) ).
thf(975,plain,
( ( ! [W_7: $i] :
( ( ( number_number_of_nat @ W_7 )
!= zero_zero_nat )
| ( ( hAPP_nat_int @ ( power_power_int @ zero_zero_int ) @ ( number_number_of_nat @ W_7 ) )
= one_one_int ) )
& ! [W_7: $i] :
( ( ( number_number_of_nat @ W_7 )
= zero_zero_nat )
| ( ( hAPP_nat_int @ ( power_power_int @ zero_zero_int ) @ ( number_number_of_nat @ W_7 ) )
= zero_zero_int ) ) )
= $true ),
inference(copy,[status(thm)],[963]) ).
thf(976,plain,
( ( one_one_int
= ( number_number_of_int @ ( bit1 @ pls ) ) )
= $true ),
inference(copy,[status(thm)],[889]) ).
thf(977,plain,
( ( one_one_real
= ( number267125858f_real @ ( bit1 @ pls ) ) )
= $true ),
inference(copy,[status(thm)],[888]) ).
thf(978,plain,
( ( ( number_number_of_int @ ( bit1 @ pls ) )
= one_one_int )
= $true ),
inference(copy,[status(thm)],[887]) ).
thf(979,plain,
( ( ( number267125858f_real @ ( bit1 @ pls ) )
= one_one_real )
= $true ),
inference(copy,[status(thm)],[886]) ).
thf(980,plain,
( ( ! [V_6: $i,W: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( number_number_of_int @ V_6 ) ) @ ( number_number_of_int @ W ) )
= ( number_number_of_int @ ( hAPP_int_int @ ( plus_plus_int @ V_6 ) @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[885]) ).
thf(981,plain,
( ( zero_zero_int
= ( number_number_of_int @ pls ) )
= $true ),
inference(copy,[status(thm)],[884]) ).
thf(982,plain,
( ( ! [M_1: $i,N_1: $i] :
( ( hAPP_nat_int @ ( power_power_int @ ( hAPP_nat_int @ semiri1621563631at_int @ M_1 ) ) @ N_1 )
= ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( power_power_nat @ M_1 ) @ N_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[883]) ).
thf(983,plain,
( ( ! [M_1: $i,N_1: $i] :
( ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( power_power_nat @ M_1 ) @ N_1 ) )
= ( hAPP_nat_int @ ( power_power_int @ ( hAPP_nat_int @ semiri1621563631at_int @ M_1 ) ) @ N_1 ) ) )
= $true ),
inference(copy,[status(thm)],[882]) ).
thf(984,plain,
( ( ! [M_1: $i,N_1: $i,Z_2: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ M_1 ) ) @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ N_1 ) ) @ Z_2 ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( plus_plus_nat @ M_1 ) @ N_1 ) ) ) @ Z_2 ) ) )
= $true ),
inference(copy,[status(thm)],[881]) ).
thf(985,plain,
( ( ! [M_1: $i,N_1: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ M_1 ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ N_1 ) )
= ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( plus_plus_nat @ M_1 ) @ N_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[880]) ).
thf(986,plain,
( ( ( hAPP_nat_int @ semiri1621563631at_int @ one_one_nat )
= one_one_int )
= $true ),
inference(copy,[status(thm)],[879]) ).
thf(987,plain,
( ( ( number_number_of_nat @ pls )
= zero_zero_nat )
= $true ),
inference(copy,[status(thm)],[878]) ).
thf(988,plain,
( ( zero_zero_nat
= ( number_number_of_nat @ pls ) )
= $true ),
inference(copy,[status(thm)],[877]) ).
thf(989,plain,
( ( ! [Na: $i] :
( ( ( hAPP_nat_int @ semiri1621563631at_int @ Na )
!= zero_zero_int )
| ( Na = zero_zero_nat ) )
& ! [Na: $i] :
( ( Na != zero_zero_nat )
| ( ( hAPP_nat_int @ semiri1621563631at_int @ Na )
= zero_zero_int ) ) )
= $true ),
inference(copy,[status(thm)],[962]) ).
thf(990,plain,
( ( ( hAPP_nat_int @ semiri1621563631at_int @ zero_zero_nat )
= zero_zero_int )
= $true ),
inference(copy,[status(thm)],[875]) ).
thf(991,plain,
( ( one_one_int
= ( number_number_of_int @ ( bit1 @ pls ) ) )
= $true ),
inference(copy,[status(thm)],[874]) ).
thf(992,plain,
( ( ( number_number_of_nat @ ( bit1 @ pls ) )
= one_one_nat )
= $true ),
inference(copy,[status(thm)],[873]) ).
thf(993,plain,
( ( one_one_nat
= ( number_number_of_nat @ ( bit1 @ pls ) ) )
= $true ),
inference(copy,[status(thm)],[872]) ).
thf(994,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)],[961]) ).
thf(995,plain,
( ( ! [K_2: $i,L_1: $i] :
( ( ( bit1 @ K_2 )
!= ( bit1 @ L_1 ) )
| ( K_2 = L_1 ) )
& ! [K_2: $i,L_1: $i] :
( ( K_2 != L_1 )
| ( ( bit1 @ K_2 )
= ( bit1 @ L_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[960]) ).
thf(996,plain,
( ( ! [K_2: $i,L_1: $i] :
( ( ( bit0 @ K_2 )
!= ( bit0 @ L_1 ) )
| ( K_2 = L_1 ) )
& ! [K_2: $i,L_1: $i] :
( ( K_2 != L_1 )
| ( ( bit0 @ K_2 )
= ( bit0 @ L_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[959]) ).
thf(997,plain,
( ( ! [Z1: $i,Z2: $i,Z3: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ Z1 ) @ Z2 ) ) @ Z3 )
= ( hAPP_int_int @ ( plus_plus_int @ Z1 ) @ ( hAPP_int_int @ ( plus_plus_int @ Z2 ) @ Z3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[868]) ).
thf(998,plain,
( ( ! [X: $i,Y: $i,Z_2: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ X ) @ ( hAPP_int_int @ ( plus_plus_int @ Y ) @ Z_2 ) )
= ( hAPP_int_int @ ( plus_plus_int @ Y ) @ ( hAPP_int_int @ ( plus_plus_int @ X ) @ Z_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[867]) ).
thf(999,plain,
( ( ! [Z_2: $i,W: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ Z_2 ) @ W )
= ( hAPP_int_int @ ( plus_plus_int @ W ) @ Z_2 ) ) )
= $true ),
inference(copy,[status(thm)],[866]) ).
thf(1000,plain,
( ( ! [Ma: $i,Na: $i] :
( ( ( hAPP_nat_int @ semiri1621563631at_int @ Ma )
!= ( hAPP_nat_int @ semiri1621563631at_int @ Na ) )
| ( Ma = Na ) )
& ! [Ma: $i,Na: $i] :
( ( Ma != Na )
| ( ( hAPP_nat_int @ semiri1621563631at_int @ Ma )
= ( hAPP_nat_int @ semiri1621563631at_int @ Na ) ) ) )
= $true ),
inference(copy,[status(thm)],[958]) ).
thf(1001,plain,
( ( ! [A_24: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ A_24 ) @ A_24 )
!= zero_zero_int )
| ( A_24 = zero_zero_int ) )
& ! [A_24: $i] :
( ( A_24 != zero_zero_int )
| ( ( hAPP_int_int @ ( plus_plus_int @ A_24 ) @ A_24 )
= zero_zero_int ) ) )
= $true ),
inference(copy,[status(thm)],[957]) ).
thf(1002,plain,
( ( ! [K: $i] :
( ( bit1 @ K )
!= pls ) )
= $true ),
inference(copy,[status(thm)],[956]) ).
thf(1003,plain,
( ( ! [L: $i] :
( pls
!= ( bit1 @ L ) ) )
= $true ),
inference(copy,[status(thm)],[955]) ).
thf(1004,plain,
( ( ! [K: $i,L: $i] :
( ( bit1 @ K )
!= ( bit0 @ L ) ) )
= $true ),
inference(copy,[status(thm)],[954]) ).
thf(1005,plain,
( ( ! [K: $i,L: $i] :
( ( bit0 @ K )
!= ( bit1 @ L ) ) )
= $true ),
inference(copy,[status(thm)],[953]) ).
thf(1006,plain,
( ( ! [K_2: $i] :
( ( ( bit0 @ K_2 )
!= pls )
| ( K_2 = pls ) )
& ! [K_2: $i] :
( ( K_2 != pls )
| ( ( bit0 @ K_2 )
= pls ) ) )
= $true ),
inference(copy,[status(thm)],[952]) ).
thf(1007,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)],[951]) ).
thf(1008,plain,
( ( ( bit0 @ pls )
= pls )
= $true ),
inference(copy,[status(thm)],[857]) ).
thf(1009,plain,
( ( pls = zero_zero_int )
= $true ),
inference(copy,[status(thm)],[856]) ).
thf(1010,plain,
( ( ( zero_zero_int != one_one_int ) )
= $true ),
inference(copy,[status(thm)],[950]) ).
thf(1011,plain,
( ( ! [K: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ K ) @ pls )
= K ) )
= $true ),
inference(copy,[status(thm)],[854]) ).
thf(1012,plain,
( ( ! [K: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ pls ) @ K )
= K ) )
= $true ),
inference(copy,[status(thm)],[853]) ).
thf(1013,plain,
( ( ! [K: $i,L: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( bit0 @ K ) ) @ ( bit0 @ L ) )
= ( bit0 @ ( hAPP_int_int @ ( plus_plus_int @ K ) @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[852]) ).
thf(1014,plain,
( ( ! [K: $i] :
( ( bit0 @ K )
= ( hAPP_int_int @ ( plus_plus_int @ K ) @ K ) ) )
= $true ),
inference(copy,[status(thm)],[851]) ).
thf(1015,plain,
( ( ! [Z_2: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ Z_2 ) @ zero_zero_int )
= Z_2 ) )
= $true ),
inference(copy,[status(thm)],[850]) ).
thf(1016,plain,
( ( ! [Z_2: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ zero_zero_int ) @ Z_2 )
= Z_2 ) )
= $true ),
inference(copy,[status(thm)],[849]) ).
thf(1017,plain,
( ( ( number_number_of_int @ pls )
= zero_zero_int )
= $true ),
inference(copy,[status(thm)],[848]) ).
thf(1018,plain,
( ( ( number_number_of_nat @ pls )
= zero_zero_nat )
= $true ),
inference(copy,[status(thm)],[847]) ).
thf(1019,plain,
( ( ( number267125858f_real @ pls )
= zero_zero_real )
= $true ),
inference(copy,[status(thm)],[846]) ).
thf(1020,plain,
( ( ( number_number_of_int @ pls )
= zero_zero_int )
= $true ),
inference(copy,[status(thm)],[845]) ).
thf(1021,plain,
( ( ( number267125858f_real @ pls )
= zero_zero_real )
= $true ),
inference(copy,[status(thm)],[844]) ).
thf(1022,plain,
( ( zero_zero_int
= ( number_number_of_int @ pls ) )
= $true ),
inference(copy,[status(thm)],[843]) ).
thf(1023,plain,
( ( zero_zero_real
= ( number267125858f_real @ pls ) )
= $true ),
inference(copy,[status(thm)],[842]) ).
thf(1024,plain,
( ( ! [A_68: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( number_number_of_int @ pls ) ) @ A_68 )
= A_68 ) )
= $true ),
inference(copy,[status(thm)],[841]) ).
thf(1025,plain,
( ( ! [A_67: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ A_67 ) @ ( number_number_of_int @ pls ) )
= A_67 ) )
= $true ),
inference(copy,[status(thm)],[840]) ).
thf(1026,plain,
( ( ! [A_24: $i,Wa: $i] :
( ( ( number_number_of_nat @ Wa )
= zero_zero_nat )
| ( A_24 != zero_zero_int )
| ( ( hAPP_nat_int @ ( power_power_int @ A_24 ) @ ( number_number_of_nat @ Wa ) )
= zero_zero_int ) )
& ! [A_24: $i,Wa: $i] :
( ( ( hAPP_nat_int @ ( power_power_int @ A_24 ) @ ( number_number_of_nat @ Wa ) )
!= zero_zero_int )
| ( ( number_number_of_nat @ Wa )
!= zero_zero_nat ) )
& ! [A_24: $i] :
( ! [Wa: $i] :
( ( hAPP_nat_int @ ( power_power_int @ A_24 ) @ ( number_number_of_nat @ Wa ) )
!= zero_zero_int )
| ( A_24 = zero_zero_int ) ) )
= $true ),
inference(copy,[status(thm)],[949]) ).
thf(1027,plain,
( ( ! [V_9: $i,W_6: $i,Z_5: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( number_number_of_int @ V_9 ) ) @ ( hAPP_int_int @ ( plus_plus_int @ ( number_number_of_int @ W_6 ) ) @ Z_5 ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( number_number_of_int @ ( hAPP_int_int @ ( plus_plus_int @ V_9 ) @ W_6 ) ) ) @ Z_5 ) ) )
= $true ),
inference(copy,[status(thm)],[838]) ).
thf(1028,plain,
( ( ! [V_8: $i,W_5: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( number_number_of_int @ V_8 ) ) @ ( number_number_of_int @ W_5 ) )
= ( number_number_of_int @ ( hAPP_int_int @ ( plus_plus_int @ V_8 ) @ W_5 ) ) ) )
= $true ),
inference(copy,[status(thm)],[837]) ).
thf(1029,plain,
( ( ! [V_7: $i,W_4: $i] :
( ( number_number_of_int @ ( hAPP_int_int @ ( plus_plus_int @ V_7 ) @ W_4 ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( number_number_of_int @ V_7 ) ) @ ( number_number_of_int @ W_4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[836]) ).
thf(1030,plain,
( ( ! [K: $i,L: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( bit1 @ K ) ) @ ( bit0 @ L ) )
= ( bit1 @ ( hAPP_int_int @ ( plus_plus_int @ K ) @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[835]) ).
thf(1031,plain,
( ( ! [K: $i,L: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( bit0 @ K ) ) @ ( bit1 @ L ) )
= ( bit1 @ ( hAPP_int_int @ ( plus_plus_int @ K ) @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[834]) ).
thf(1032,plain,
( ( ! [K: $i] :
( ( bit1 @ K )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ K ) ) @ K ) ) )
= $true ),
inference(copy,[status(thm)],[833]) ).
thf(1033,plain,
( ( ! [Z_2: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ Z_2 ) ) @ Z_2 )
!= zero_zero_int ) )
= $true ),
inference(copy,[status(thm)],[948]) ).
thf(1034,plain,
( ( ! [N_29: $i] :
( ( number_number_of_nat @ ( hAPP_nat_int @ semiri1621563631at_int @ N_29 ) )
= ( hAPP_nat_nat @ semiri984289939at_nat @ N_29 ) ) )
= $true ),
inference(copy,[status(thm)],[831]) ).
thf(1035,plain,
( ( ! [N_29: $i] :
( ( number_number_of_int @ ( hAPP_nat_int @ semiri1621563631at_int @ N_29 ) )
= ( hAPP_nat_int @ semiri1621563631at_int @ N_29 ) ) )
= $true ),
inference(copy,[status(thm)],[830]) ).
thf(1036,plain,
( ( ! [W_3: $i] :
( ( number_number_of_int @ ( bit0 @ W_3 ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ zero_zero_int ) @ ( number_number_of_int @ W_3 ) ) ) @ ( number_number_of_int @ W_3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[829]) ).
thf(1037,plain,
( ( ! [W_2: $i] :
( ( number_number_of_int @ ( bit1 @ W_2 ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ ( number_number_of_int @ W_2 ) ) ) @ ( number_number_of_int @ W_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[828]) ).
thf(1038,plain,
( ( ( number_number_of_int @ ( bit1 @ pls ) )
= one_one_int )
= $true ),
inference(copy,[status(thm)],[827]) ).
thf(1039,plain,
( ( ( number_number_of_nat @ ( bit1 @ pls ) )
= one_one_nat )
= $true ),
inference(copy,[status(thm)],[826]) ).
thf(1040,plain,
( ( ( number267125858f_real @ ( bit1 @ pls ) )
= one_one_real )
= $true ),
inference(copy,[status(thm)],[825]) ).
thf(1041,plain,
( ( ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) )
= ( hAPP_nat_int @ semiri1621563631at_int @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[824]) ).
thf(1042,plain,
( ( ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) )
= ( hAPP_nat_int @ semiri1621563631at_int @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[823]) ).
thf(1043,plain,
( ( ! [N_26: $i] :
( ( N_26 != zero_zero_nat )
| ( ( hAPP_nat_int @ ( power_power_int @ zero_zero_int ) @ N_26 )
= one_one_int ) )
& ! [N_26: $i] :
( ( N_26 = zero_zero_nat )
| ( ( hAPP_nat_int @ ( power_power_int @ zero_zero_int ) @ N_26 )
= zero_zero_int ) ) )
= $true ),
inference(copy,[status(thm)],[947]) ).
thf(1044,plain,
( ( ! [A_63: $i] :
( ( hAPP_nat_int @ ( power_power_int @ A_63 ) @ one_one_nat )
= A_63 ) )
= $true ),
inference(copy,[status(thm)],[821]) ).
thf(1045,plain,
( ( ! [Ma: $i,Na: $i] :
( ( ( hAPP_nat_int @ semiri1621563631at_int @ Ma )
!= ( hAPP_nat_int @ semiri1621563631at_int @ Na ) )
| ( Ma = Na ) )
& ! [Ma: $i,Na: $i] :
( ( Ma != Na )
| ( ( hAPP_nat_int @ semiri1621563631at_int @ Ma )
= ( hAPP_nat_int @ semiri1621563631at_int @ Na ) ) ) )
= $true ),
inference(copy,[status(thm)],[946]) ).
thf(1046,plain,
( ( ! [Xa: $i,Ya: $i] :
( ( ( hAPP_nat_int @ semiri1621563631at_int @ Xa )
!= ( hAPP_nat_int @ semiri1621563631at_int @ Ya ) )
| ( Xa = Ya ) )
& ! [Xa: $i,Ya: $i] :
( ( Xa != Ya )
| ( ( hAPP_nat_int @ semiri1621563631at_int @ Xa )
= ( hAPP_nat_int @ semiri1621563631at_int @ Ya ) ) ) )
= $true ),
inference(copy,[status(thm)],[945]) ).
thf(1047,plain,
( ( ( one_one_int != zero_zero_int ) )
= $true ),
inference(copy,[status(thm)],[944]) ).
thf(1048,plain,
( ( ( zero_zero_int != one_one_int ) )
= $true ),
inference(copy,[status(thm)],[943]) ).
thf(1049,plain,
( ( ! [N_23: $i,A_62: $i] :
( ( A_62 = zero_zero_int )
| ( ( hAPP_nat_int @ ( power_power_int @ A_62 ) @ N_23 )
!= zero_zero_int ) ) )
= $true ),
inference(copy,[status(thm)],[942]) ).
thf(1050,plain,
( ( ! [N_22: $i] :
( ( hAPP_nat_int @ ( power_power_int @ one_one_int ) @ N_22 )
= one_one_int ) )
= $true ),
inference(copy,[status(thm)],[815]) ).
thf(1051,plain,
( ( ! [M_7: $i,N_19: $i] :
( ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( plus_plus_nat @ M_7 ) @ N_19 ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ M_7 ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ N_19 ) ) ) )
= $true ),
inference(copy,[status(thm)],[814]) ).
thf(1052,plain,
( ( ( hAPP_nat_int @ semiri1621563631at_int @ one_one_nat )
= one_one_int )
= $true ),
inference(copy,[status(thm)],[813]) ).
thf(1053,plain,
( ( ! [M_6: $i,N_18: $i] :
( ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( power_power_nat @ M_6 ) @ N_18 ) )
= ( hAPP_nat_int @ ( power_power_int @ ( hAPP_nat_int @ semiri1621563631at_int @ M_6 ) ) @ N_18 ) ) )
= $true ),
inference(copy,[status(thm)],[812]) ).
thf(1054,plain,
( ( one_one_int
= ( hAPP_nat_int @ semiri1621563631at_int @ one_one_nat ) )
= $true ),
inference(copy,[status(thm)],[811]) ).
thf(1055,plain,
( ( ! [X: $i,Y: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ X ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ Y ) )
= ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( plus_plus_nat @ X ) @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[810]) ).
thf(1056,plain,
( ( ! [X: $i,N_1: $i] :
( ( hAPP_nat_int @ ( power_power_int @ ( hAPP_nat_int @ semiri1621563631at_int @ X ) ) @ N_1 )
= ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( power_power_nat @ X ) @ N_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[809]) ).
thf(1057,plain,
( ( ! [A_24: $i,Na: $i] :
( ( Na = zero_zero_nat )
| ( A_24 != zero_zero_int )
| ( ( hAPP_nat_int @ ( power_power_int @ A_24 ) @ Na )
= zero_zero_int ) )
& ! [A_24: $i,Na: $i] :
( ( ( hAPP_nat_int @ ( power_power_int @ A_24 ) @ Na )
!= zero_zero_int )
| ( Na != zero_zero_nat ) )
& ! [A_24: $i] :
( ! [Na: $i] :
( ( hAPP_nat_int @ ( power_power_int @ A_24 ) @ Na )
!= zero_zero_int )
| ( A_24 = zero_zero_int ) ) )
= $true ),
inference(copy,[status(thm)],[941]) ).
thf(1058,plain,
( ( ! [A_56: $i] :
( ( hAPP_nat_int @ ( power_power_int @ A_56 ) @ zero_zero_nat )
= one_one_int ) )
= $true ),
inference(copy,[status(thm)],[807]) ).
thf(1059,plain,
( ( ( hAPP_nat_int @ semiri1621563631at_int @ zero_zero_nat )
= zero_zero_int )
= $true ),
inference(copy,[status(thm)],[806]) ).
thf(1060,plain,
( ( zero_zero_int
= ( hAPP_nat_int @ semiri1621563631at_int @ zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[805]) ).
thf(1061,plain,
( ( ! [X_14: $i] :
( ( hAPP_nat_int @ ( power_power_int @ X_14 ) @ zero_zero_nat )
= one_one_int ) )
= $true ),
inference(copy,[status(thm)],[804]) ).
thf(1062,plain,
( ( ! [Xa: $i] :
( ( zero_zero_int != Xa )
| ( Xa = zero_zero_int ) )
& ! [Xa: $i] :
( ( Xa != zero_zero_int )
| ( zero_zero_int = Xa ) ) )
= $true ),
inference(copy,[status(thm)],[940]) ).
thf(1063,plain,
( ( ! [B_40: $i,A_55: $i,C_30: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ B_40 ) @ A_55 )
!= ( hAPP_int_int @ ( plus_plus_int @ C_30 ) @ A_55 ) )
| ( B_40 = C_30 ) ) )
= $true ),
inference(copy,[status(thm)],[939]) ).
thf(1064,plain,
( ( ! [A_54: $i,B_39: $i,C_29: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ A_54 ) @ B_39 )
!= ( hAPP_int_int @ ( plus_plus_int @ A_54 ) @ C_29 ) )
| ( B_39 = C_29 ) ) )
= $true ),
inference(copy,[status(thm)],[938]) ).
thf(1065,plain,
( ( ! [A_53: $i,B_38: $i,C_28: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ A_53 ) @ B_38 )
!= ( hAPP_int_int @ ( plus_plus_int @ A_53 ) @ C_28 ) )
| ( B_38 = C_28 ) ) )
= $true ),
inference(copy,[status(thm)],[937]) ).
thf(1066,plain,
( ( ! [A_52: $i,B_37: $i,C_27: $i,D_6: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ A_52 ) @ B_37 ) ) @ ( hAPP_int_int @ ( plus_plus_int @ C_27 ) @ D_6 ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ A_52 ) @ C_27 ) ) @ ( hAPP_int_int @ ( plus_plus_int @ B_37 ) @ D_6 ) ) ) )
= $true ),
inference(copy,[status(thm)],[799]) ).
thf(1067,plain,
( ( ! [B_21: $i] :
( ! [A_24: $i,C_15: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ B_21 ) @ A_24 )
!= ( hAPP_int_int @ ( plus_plus_int @ C_15 ) @ A_24 ) )
| ( B_21 = C_15 ) )
& ! [A_24: $i,C_15: $i] :
( ( B_21 != C_15 )
| ( ( hAPP_int_int @ ( plus_plus_int @ B_21 ) @ A_24 )
= ( hAPP_int_int @ ( plus_plus_int @ C_15 ) @ A_24 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[936]) ).
thf(1068,plain,
( ( ! [A_24: $i] :
( ! [B_21: $i,C_15: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ A_24 ) @ B_21 )
!= ( hAPP_int_int @ ( plus_plus_int @ A_24 ) @ C_15 ) )
| ( B_21 = C_15 ) )
& ! [B_21: $i,C_15: $i] :
( ( B_21 != C_15 )
| ( ( hAPP_int_int @ ( plus_plus_int @ A_24 ) @ B_21 )
= ( hAPP_int_int @ ( plus_plus_int @ A_24 ) @ C_15 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[935]) ).
thf(1069,plain,
( ( ! [A_51: $i,B_36: $i,C_26: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ A_51 ) @ B_36 ) ) @ C_26 )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ A_51 ) @ C_26 ) ) @ B_36 ) ) )
= $true ),
inference(copy,[status(thm)],[796]) ).
thf(1070,plain,
( ( ! [A_50: $i,B_35: $i,C_25: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ A_50 ) @ B_35 ) ) @ C_25 )
= ( hAPP_int_int @ ( plus_plus_int @ A_50 ) @ ( hAPP_int_int @ ( plus_plus_int @ B_35 ) @ C_25 ) ) ) )
= $true ),
inference(copy,[status(thm)],[795]) ).
thf(1071,plain,
( ( ! [A_49: $i,B_34: $i,C_24: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ A_49 ) @ B_34 ) ) @ C_24 )
= ( hAPP_int_int @ ( plus_plus_int @ A_49 ) @ ( hAPP_int_int @ ( plus_plus_int @ B_34 ) @ C_24 ) ) ) )
= $true ),
inference(copy,[status(thm)],[794]) ).
thf(1072,plain,
( ( ! [A_48: $i,C_23: $i,D_5: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ A_48 ) @ ( hAPP_int_int @ ( plus_plus_int @ C_23 ) @ D_5 ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ A_48 ) @ C_23 ) ) @ D_5 ) ) )
= $true ),
inference(copy,[status(thm)],[793]) ).
thf(1073,plain,
( ( ! [A_47: $i,C_22: $i,D_4: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ A_47 ) @ ( hAPP_int_int @ ( plus_plus_int @ C_22 ) @ D_4 ) )
= ( hAPP_int_int @ ( plus_plus_int @ C_22 ) @ ( hAPP_int_int @ ( plus_plus_int @ A_47 ) @ D_4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[792]) ).
thf(1074,plain,
( ( ! [A_46: $i,C_21: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ A_46 ) @ C_21 )
= ( hAPP_int_int @ ( plus_plus_int @ C_21 ) @ A_46 ) ) )
= $true ),
inference(copy,[status(thm)],[791]) ).
thf(1075,plain,
( ( ! [Xa: $i] :
( ( one_one_int != Xa )
| ( Xa = one_one_int ) )
& ! [Xa: $i] :
( ( Xa != one_one_int )
| ( one_one_int = Xa ) ) )
= $true ),
inference(copy,[status(thm)],[934]) ).
thf(1076,plain,
( ( ! [B_21: $i,A_24: $i] :
( ( B_21
!= ( hAPP_int_int @ ( plus_plus_int @ B_21 ) @ A_24 ) )
| ( A_24 = zero_zero_int ) )
& ! [B_21: $i,A_24: $i] :
( ( A_24 != zero_zero_int )
| ( B_21
= ( hAPP_int_int @ ( plus_plus_int @ B_21 ) @ A_24 ) ) ) )
= $true ),
inference(copy,[status(thm)],[933]) ).
thf(1077,plain,
( ( ! [A_45: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ A_45 ) @ zero_zero_int )
= A_45 ) )
= $true ),
inference(copy,[status(thm)],[788]) ).
thf(1078,plain,
( ( ! [A_44: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ A_44 ) @ zero_zero_int )
= A_44 ) )
= $true ),
inference(copy,[status(thm)],[787]) ).
thf(1079,plain,
( ( ! [A_43: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ A_43 ) @ zero_zero_int )
= A_43 ) )
= $true ),
inference(copy,[status(thm)],[786]) ).
thf(1080,plain,
( ( ! [A_24: $i] :
( ( zero_zero_int
!= ( hAPP_int_int @ ( plus_plus_int @ A_24 ) @ A_24 ) )
| ( A_24 = zero_zero_int ) )
& ! [A_24: $i] :
( ( A_24 != zero_zero_int )
| ( zero_zero_int
= ( hAPP_int_int @ ( plus_plus_int @ A_24 ) @ A_24 ) ) ) )
= $true ),
inference(copy,[status(thm)],[932]) ).
thf(1081,plain,
( ( ! [A_42: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ zero_zero_int ) @ A_42 )
= A_42 ) )
= $true ),
inference(copy,[status(thm)],[784]) ).
thf(1082,plain,
( ( ! [A_41: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ zero_zero_int ) @ A_41 )
= A_41 ) )
= $true ),
inference(copy,[status(thm)],[783]) ).
thf(1083,plain,
( ( ! [A_40: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ zero_zero_int ) @ A_40 )
= A_40 ) )
= $true ),
inference(copy,[status(thm)],[782]) ).
thf(1084,plain,
( ( ! [X_13: $i] :
( ( hAPP_nat_int @ ( power_power_int @ X_13 ) @ one_one_nat )
= X_13 ) )
= $true ),
inference(copy,[status(thm)],[781]) ).
thf(1085,plain,
( ( ( succ @ pls )
= ( bit1 @ pls ) )
= $true ),
inference(copy,[status(thm)],[780]) ).
thf(1086,plain,
( ( ! [K: $i] :
( ( succ @ ( bit0 @ K ) )
= ( bit1 @ K ) ) )
= $true ),
inference(copy,[status(thm)],[779]) ).
thf(1087,plain,
( ( ! [K: $i] :
( ( succ @ ( bit1 @ K ) )
= ( bit0 @ ( succ @ K ) ) ) )
= $true ),
inference(copy,[status(thm)],[778]) ).
thf(1088,plain,
( ( ! [K: $i] :
( ( succ @ K )
= ( hAPP_int_int @ ( plus_plus_int @ K ) @ one_one_int ) ) )
= $true ),
inference(copy,[status(thm)],[777]) ).
thf(1089,plain,
( ( ! [K_3: $i] :
( ( number_number_of_int @ ( succ @ K_3 ) )
= ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ ( number_number_of_int @ K_3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[776]) ).
thf(1090,plain,
( ( ! [K: $i,L: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( bit1 @ K ) ) @ ( bit1 @ L ) )
= ( bit0 @ ( hAPP_int_int @ ( plus_plus_int @ K ) @ ( succ @ L ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[775]) ).
thf(1091,plain,
( ( ! [A: $i,B: $i] :
( ( hAPP_nat_int @ ( power_power_int @ ( hAPP_int_int @ ( plus_plus_int @ A ) @ B ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[774]) ).
thf(1092,plain,
( ( ! [K: $i,L: $i] :
( ( times_times_int @ ( bit1 @ K ) @ L )
= ( hAPP_int_int @ ( plus_plus_int @ ( bit0 @ ( times_times_int @ K @ L ) ) ) @ L ) ) )
= $true ),
inference(copy,[status(thm)],[773]) ).
thf(1093,plain,
( ( ( hAPP_nat_nat @ ( power_power_nat @ one_one_nat ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_nat )
= $true ),
inference(copy,[status(thm)],[772]) ).
thf(1094,plain,
( ( ( hAPP_nat_nat @ ( power_power_nat @ zero_zero_nat ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_nat )
= $true ),
inference(copy,[status(thm)],[771]) ).
thf(1095,plain,
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ one_one_nat ) @ one_one_nat )
= ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(copy,[status(thm)],[770]) ).
thf(1096,plain,
( ( ! [W_7: $i] :
( ( ( number_number_of_nat @ W_7 )
!= zero_zero_nat )
| ( ( hAPP_nat_nat @ ( power_power_nat @ zero_zero_nat ) @ ( number_number_of_nat @ W_7 ) )
= one_one_nat ) )
& ! [W_7: $i] :
( ( ( number_number_of_nat @ W_7 )
= zero_zero_nat )
| ( ( hAPP_nat_nat @ ( power_power_nat @ zero_zero_nat ) @ ( number_number_of_nat @ W_7 ) )
= zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[931]) ).
thf(1097,plain,
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ one_one_nat ) @ one_one_nat )
= ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(copy,[status(thm)],[768]) ).
thf(1098,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)],[930]) ).
thf(1099,plain,
( ( ! [Xa: $i,Ya: $i] :
( ( ( number267125858f_real @ Xa )
!= ( number267125858f_real @ Ya ) )
| ( Xa = Ya ) )
& ! [Xa: $i,Ya: $i] :
( ( Xa != Ya )
| ( ( number267125858f_real @ Xa )
= ( number267125858f_real @ Ya ) ) ) )
= $true ),
inference(copy,[status(thm)],[929]) ).
thf(1100,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)],[928]) ).
thf(1101,plain,
( ( ! [Wa: $i,Xa: $i] :
( ( ( number267125858f_real @ Wa )
!= Xa )
| ( Xa
= ( number267125858f_real @ Wa ) ) )
& ! [Wa: $i,Xa: $i] :
( ( Xa
!= ( number267125858f_real @ Wa ) )
| ( ( number267125858f_real @ Wa )
= Xa ) ) )
= $true ),
inference(copy,[status(thm)],[927]) ).
thf(1102,plain,
( ( ! [A_24: $i,Wa: $i] :
( ( ( number_number_of_nat @ Wa )
= zero_zero_nat )
| ( A_24 != zero_zero_nat )
| ( ( hAPP_nat_nat @ ( power_power_nat @ A_24 ) @ ( number_number_of_nat @ Wa ) )
= zero_zero_nat ) )
& ! [A_24: $i,Wa: $i] :
( ( ( hAPP_nat_nat @ ( power_power_nat @ A_24 ) @ ( number_number_of_nat @ Wa ) )
!= zero_zero_nat )
| ( ( number_number_of_nat @ Wa )
!= zero_zero_nat ) )
& ! [A_24: $i] :
( ! [Wa: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ A_24 ) @ ( number_number_of_nat @ Wa ) )
!= zero_zero_nat )
| ( A_24 = zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[926]) ).
thf(1103,plain,
( ( ! [N_26: $i] :
( ( N_26 != zero_zero_nat )
| ( ( hAPP_nat_nat @ ( power_power_nat @ zero_zero_nat ) @ N_26 )
= one_one_nat ) )
& ! [N_26: $i] :
( ( N_26 = zero_zero_nat )
| ( ( hAPP_nat_nat @ ( power_power_nat @ zero_zero_nat ) @ N_26 )
= zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[925]) ).
thf(1104,plain,
( ( ( zero_zero_real != one_one_real ) )
= $true ),
inference(copy,[status(thm)],[924]) ).
thf(1105,plain,
( ( ! [K: $i] :
( ( number_number_of_int @ K )
= K ) )
= $true ),
inference(copy,[status(thm)],[760]) ).
thf(1106,plain,
( ( ! [M_1: $i,N_1: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ M_1 ) @ N_1 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ N_1 ) @ M_1 ) ) )
= $true ),
inference(copy,[status(thm)],[759]) ).
thf(1107,plain,
( ( ! [X: $i,Y: $i,Z_2: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ X ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ Y ) @ Z_2 ) )
= ( hAPP_nat_nat @ ( plus_plus_nat @ Y ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ X ) @ Z_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[758]) ).
thf(1108,plain,
( ( ! [M_1: $i,N_1: $i,K: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ M_1 ) @ N_1 ) ) @ K )
= ( hAPP_nat_nat @ ( plus_plus_nat @ M_1 ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ N_1 ) @ K ) ) ) )
= $true ),
inference(copy,[status(thm)],[757]) ).
thf(1109,plain,
( ( ! [K_2: $i] :
( ! [Ma: $i,Na: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ K_2 ) @ Ma )
!= ( hAPP_nat_nat @ ( plus_plus_nat @ K_2 ) @ Na ) )
| ( Ma = Na ) )
& ! [Ma: $i,Na: $i] :
( ( Ma != Na )
| ( ( hAPP_nat_nat @ ( plus_plus_nat @ K_2 ) @ Ma )
= ( hAPP_nat_nat @ ( plus_plus_nat @ K_2 ) @ Na ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[923]) ).
thf(1110,plain,
( ( ! [Ma: $i] :
( ! [K_2: $i,Na: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ Ma ) @ K_2 )
!= ( hAPP_nat_nat @ ( plus_plus_nat @ Na ) @ K_2 ) )
| ( Ma = Na ) )
& ! [K_2: $i,Na: $i] :
( ( Ma != Na )
| ( ( hAPP_nat_nat @ ( plus_plus_nat @ Ma ) @ K_2 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ Na ) @ K_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[922]) ).
thf(1111,plain,
( ( ! [M_1: $i,N_1: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ M_1 ) @ N_1 )
!= M_1 )
| ( N_1 = zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[921]) ).
thf(1112,plain,
( ( ! [Ma: $i,Na: $i] :
( ( Ma != zero_zero_nat )
| ( Na != zero_zero_nat )
| ( ( hAPP_nat_nat @ ( plus_plus_nat @ Ma ) @ Na )
= zero_zero_nat ) )
& ! [Ma: $i] :
( ! [Na: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ Ma ) @ Na )
!= zero_zero_nat )
| ( Ma = zero_zero_nat ) )
& ! [Ma: $i,Na: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ Ma ) @ Na )
!= zero_zero_nat )
| ( Na = zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[920]) ).
thf(1113,plain,
( ( ! [M_1: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ M_1 ) @ zero_zero_nat )
= M_1 ) )
= $true ),
inference(copy,[status(thm)],[752]) ).
thf(1114,plain,
( ( ! [N_1: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ zero_zero_nat ) @ N_1 )
= N_1 ) )
= $true ),
inference(copy,[status(thm)],[751]) ).
thf(1115,plain,
( ( ! [A_63: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ A_63 ) @ one_one_nat )
= A_63 ) )
= $true ),
inference(copy,[status(thm)],[750]) ).
thf(1116,plain,
( ( ! [Ma: $i,Na: $i] :
( ( ( hAPP_nat_nat @ semiri984289939at_nat @ Ma )
!= ( hAPP_nat_nat @ semiri984289939at_nat @ Na ) )
| ( Ma = Na ) )
& ! [Ma: $i,Na: $i] :
( ( Ma != Na )
| ( ( hAPP_nat_nat @ semiri984289939at_nat @ Ma )
= ( hAPP_nat_nat @ semiri984289939at_nat @ Na ) ) ) )
= $true ),
inference(copy,[status(thm)],[919]) ).
thf(1117,plain,
( ( ( one_one_real != zero_zero_real ) )
= $true ),
inference(copy,[status(thm)],[918]) ).
thf(1118,plain,
( ( ( one_one_nat != zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[917]) ).
thf(1119,plain,
( ( ( zero_zero_real != one_one_real ) )
= $true ),
inference(copy,[status(thm)],[916]) ).
thf(1120,plain,
( ( ( zero_zero_nat != one_one_nat ) )
= $true ),
inference(copy,[status(thm)],[915]) ).
thf(1121,plain,
( ( ! [N_22: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ one_one_nat ) @ N_22 )
= one_one_nat ) )
= $true ),
inference(copy,[status(thm)],[744]) ).
thf(1122,plain,
( ( ! [M_7: $i,N_19: $i] :
( ( hAPP_nat_nat @ semiri984289939at_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ M_7 ) @ N_19 ) )
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ semiri984289939at_nat @ M_7 ) ) @ ( hAPP_nat_nat @ semiri984289939at_nat @ N_19 ) ) ) )
= $true ),
inference(copy,[status(thm)],[743]) ).
thf(1123,plain,
( ( ( hAPP_nat_nat @ semiri984289939at_nat @ one_one_nat )
= one_one_nat )
= $true ),
inference(copy,[status(thm)],[742]) ).
thf(1124,plain,
( ( ! [M_6: $i,N_18: $i] :
( ( hAPP_nat_nat @ semiri984289939at_nat @ ( hAPP_nat_nat @ ( power_power_nat @ M_6 ) @ N_18 ) )
= ( hAPP_nat_nat @ ( power_power_nat @ ( hAPP_nat_nat @ semiri984289939at_nat @ M_6 ) ) @ N_18 ) ) )
= $true ),
inference(copy,[status(thm)],[741]) ).
thf(1125,plain,
( ( ! [A_24: $i,Na: $i] :
( ( Na = zero_zero_nat )
| ( A_24 != zero_zero_nat )
| ( ( hAPP_nat_nat @ ( power_power_nat @ A_24 ) @ Na )
= zero_zero_nat ) )
& ! [A_24: $i,Na: $i] :
( ( ( hAPP_nat_nat @ ( power_power_nat @ A_24 ) @ Na )
!= zero_zero_nat )
| ( Na != zero_zero_nat ) )
& ! [A_24: $i] :
( ! [Na: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ A_24 ) @ Na )
!= zero_zero_nat )
| ( A_24 = zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[914]) ).
thf(1126,plain,
( ( ! [A_56: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ A_56 ) @ zero_zero_nat )
= one_one_nat ) )
= $true ),
inference(copy,[status(thm)],[739]) ).
thf(1127,plain,
( ( ( hAPP_nat_nat @ semiri984289939at_nat @ zero_zero_nat )
= zero_zero_nat )
= $true ),
inference(copy,[status(thm)],[738]) ).
thf(1128,plain,
( ( ! [Xa: $i,Na: $i] :
( ( ( hAPP_nat_nat @ ( power_power_nat @ Xa ) @ Na )
!= one_one_nat )
| ( Xa = one_one_nat )
| ( Na = zero_zero_nat ) )
& ! [Xa: $i] :
( ( Xa != one_one_nat )
| ! [Na: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ Xa ) @ Na )
= one_one_nat ) )
& ! [Xa: $i,Na: $i] :
( ( Na != zero_zero_nat )
| ( ( hAPP_nat_nat @ ( power_power_nat @ Xa ) @ Na )
= one_one_nat ) ) )
= $true ),
inference(copy,[status(thm)],[913]) ).
thf(1129,plain,
( ( ! [X_14: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ X_14 ) @ zero_zero_nat )
= one_one_nat ) )
= $true ),
inference(copy,[status(thm)],[736]) ).
thf(1130,plain,
( ( ! [Xa: $i] :
( ( zero_zero_real != Xa )
| ( Xa = zero_zero_real ) )
& ! [Xa: $i] :
( ( Xa != zero_zero_real )
| ( zero_zero_real = Xa ) ) )
= $true ),
inference(copy,[status(thm)],[912]) ).
thf(1131,plain,
( ( ! [Xa: $i] :
( ( zero_zero_nat != Xa )
| ( Xa = zero_zero_nat ) )
& ! [Xa: $i] :
( ( Xa != zero_zero_nat )
| ( zero_zero_nat = Xa ) ) )
= $true ),
inference(copy,[status(thm)],[911]) ).
thf(1132,plain,
( ( ! [B_40: $i,A_55: $i,C_30: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ B_40 ) @ A_55 )
!= ( hAPP_nat_nat @ ( plus_plus_nat @ C_30 ) @ A_55 ) )
| ( B_40 = C_30 ) ) )
= $true ),
inference(copy,[status(thm)],[910]) ).
thf(1133,plain,
( ( ! [A_54: $i,B_39: $i,C_29: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ A_54 ) @ B_39 )
!= ( hAPP_nat_nat @ ( plus_plus_nat @ A_54 ) @ C_29 ) )
| ( B_39 = C_29 ) ) )
= $true ),
inference(copy,[status(thm)],[909]) ).
thf(1134,plain,
( ( ! [A_53: $i,B_38: $i,C_28: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ A_53 ) @ B_38 )
!= ( hAPP_nat_nat @ ( plus_plus_nat @ A_53 ) @ C_28 ) )
| ( B_38 = C_28 ) ) )
= $true ),
inference(copy,[status(thm)],[908]) ).
thf(1135,plain,
( ( ! [A_52: $i,B_37: $i,C_27: $i,D_6: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A_52 ) @ B_37 ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C_27 ) @ D_6 ) )
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A_52 ) @ C_27 ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B_37 ) @ D_6 ) ) ) )
= $true ),
inference(copy,[status(thm)],[730]) ).
thf(1136,plain,
( ( ! [B_21: $i] :
( ! [A_24: $i,C_15: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ B_21 ) @ A_24 )
!= ( hAPP_nat_nat @ ( plus_plus_nat @ C_15 ) @ A_24 ) )
| ( B_21 = C_15 ) )
& ! [A_24: $i,C_15: $i] :
( ( B_21 != C_15 )
| ( ( hAPP_nat_nat @ ( plus_plus_nat @ B_21 ) @ A_24 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ C_15 ) @ A_24 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[907]) ).
thf(1137,plain,
( ( ! [A_24: $i] :
( ! [B_21: $i,C_15: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ A_24 ) @ B_21 )
!= ( hAPP_nat_nat @ ( plus_plus_nat @ A_24 ) @ C_15 ) )
| ( B_21 = C_15 ) )
& ! [B_21: $i,C_15: $i] :
( ( B_21 != C_15 )
| ( ( hAPP_nat_nat @ ( plus_plus_nat @ A_24 ) @ B_21 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ A_24 ) @ C_15 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[906]) ).
thf(1138,plain,
( ( ! [A_51: $i,B_36: $i,C_26: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A_51 ) @ B_36 ) ) @ C_26 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A_51 ) @ C_26 ) ) @ B_36 ) ) )
= $true ),
inference(copy,[status(thm)],[727]) ).
thf(1139,plain,
( ( ! [A_50: $i,B_35: $i,C_25: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A_50 ) @ B_35 ) ) @ C_25 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ A_50 ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B_35 ) @ C_25 ) ) ) )
= $true ),
inference(copy,[status(thm)],[726]) ).
thf(1140,plain,
( ( ! [A_49: $i,B_34: $i,C_24: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A_49 ) @ B_34 ) ) @ C_24 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ A_49 ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B_34 ) @ C_24 ) ) ) )
= $true ),
inference(copy,[status(thm)],[725]) ).
thf(1141,plain,
( ( ! [A_48: $i,C_23: $i,D_5: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ A_48 ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C_23 ) @ D_5 ) )
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A_48 ) @ C_23 ) ) @ D_5 ) ) )
= $true ),
inference(copy,[status(thm)],[724]) ).
thf(1142,plain,
( ( ! [A_47: $i,C_22: $i,D_4: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ A_47 ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C_22 ) @ D_4 ) )
= ( hAPP_nat_nat @ ( plus_plus_nat @ C_22 ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A_47 ) @ D_4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[723]) ).
thf(1143,plain,
( ( ! [A_46: $i,C_21: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ A_46 ) @ C_21 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ C_21 ) @ A_46 ) ) )
= $true ),
inference(copy,[status(thm)],[722]) ).
thf(1144,plain,
( ( ! [Xa: $i] :
( ( one_one_real != Xa )
| ( Xa = one_one_real ) )
& ! [Xa: $i] :
( ( Xa != one_one_real )
| ( one_one_real = Xa ) ) )
= $true ),
inference(copy,[status(thm)],[905]) ).
thf(1145,plain,
( ( ! [Xa: $i] :
( ( one_one_nat != Xa )
| ( Xa = one_one_nat ) )
& ! [Xa: $i] :
( ( Xa != one_one_nat )
| ( one_one_nat = Xa ) ) )
= $true ),
inference(copy,[status(thm)],[904]) ).
thf(1146,plain,
( ( ! [B_21: $i,A_24: $i] :
( ( B_21
!= ( hAPP_nat_nat @ ( plus_plus_nat @ B_21 ) @ A_24 ) )
| ( A_24 = zero_zero_nat ) )
& ! [B_21: $i,A_24: $i] :
( ( A_24 != zero_zero_nat )
| ( B_21
= ( hAPP_nat_nat @ ( plus_plus_nat @ B_21 ) @ A_24 ) ) ) )
= $true ),
inference(copy,[status(thm)],[903]) ).
thf(1147,plain,
( ( ! [A_45: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ A_45 ) @ zero_zero_nat )
= A_45 ) )
= $true ),
inference(copy,[status(thm)],[718]) ).
thf(1148,plain,
( ( ! [A_44: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ A_44 ) @ zero_zero_nat )
= A_44 ) )
= $true ),
inference(copy,[status(thm)],[717]) ).
thf(1149,plain,
( ( ! [A_43: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ A_43 ) @ zero_zero_nat )
= A_43 ) )
= $true ),
inference(copy,[status(thm)],[716]) ).
thf(1150,plain,
( ( ! [A_42: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ zero_zero_nat ) @ A_42 )
= A_42 ) )
= $true ),
inference(copy,[status(thm)],[715]) ).
thf(1151,plain,
( ( ! [A_41: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ zero_zero_nat ) @ A_41 )
= A_41 ) )
= $true ),
inference(copy,[status(thm)],[714]) ).
thf(1152,plain,
( ( ! [A_40: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ zero_zero_nat ) @ A_40 )
= A_40 ) )
= $true ),
inference(copy,[status(thm)],[713]) ).
thf(1153,plain,
( ( ! [X_13: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ X_13 ) @ one_one_nat )
= X_13 ) )
= $true ),
inference(copy,[status(thm)],[712]) ).
thf(1154,plain,
( ( ! [Ma: $i,Na: $i] :
( ( Na = zero_zero_nat )
| ( Ma != zero_zero_nat )
| ( ( hAPP_nat_nat @ ( power_power_nat @ Ma ) @ Na )
= zero_zero_nat ) )
& ! [Ma: $i,Na: $i] :
( ( ( hAPP_nat_nat @ ( power_power_nat @ Ma ) @ Na )
!= zero_zero_nat )
| ( Na != zero_zero_nat ) )
& ! [Ma: $i] :
( ! [Na: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ Ma ) @ Na )
!= zero_zero_nat )
| ( Ma = zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[902]) ).
thf(1155,plain,
( ( ( hAPP_nat_int @ ( power_power_int @ ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ ( hAPP_nat_int @ semiri1621563631at_int @ n ) ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int )
= $true ),
inference(copy,[status(thm)],[901]) ).
thf(1156,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( SX0 != zero_zero_nat )
| ( ( hAPP_nat_nat @ ( power_power_nat @ zero_zero_nat ) @ SX0 )
= one_one_nat ) )
| ~ ! [SX0: $i] :
( ( SX0 = zero_zero_nat )
| ( ( hAPP_nat_nat @ ( power_power_nat @ zero_zero_nat ) @ SX0 )
= zero_zero_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1103]) ).
thf(1157,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( number_number_of_nat @ SX1 )
= zero_zero_nat )
| ( SX0 != zero_zero_nat )
| ( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) )
= zero_zero_nat ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_nat )
| ( ( number_number_of_nat @ SX1 )
!= zero_zero_nat ) )
| ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_nat )
| ( SX0 = zero_zero_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1102]) ).
thf(1158,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( hAPP_nat_int @ semiri1621563631at_int @ SX0 )
!= ( hAPP_nat_int @ semiri1621563631at_int @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( hAPP_nat_int @ semiri1621563631at_int @ SX0 )
= ( hAPP_nat_int @ semiri1621563631at_int @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1000]) ).
thf(1159,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SX0 ) @ SX1 )
!= ( hAPP_nat_nat @ ( plus_plus_nat @ SX0 ) @ SX2 ) )
| ( SX1 = SX2 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX1 != SX2 )
| ( ( hAPP_nat_nat @ ( plus_plus_nat @ SX0 ) @ SX1 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ SX0 ) @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1137]) ).
thf(1160,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( hAPP_nat_int @ semiri1621563631at_int @ SX0 )
!= ( hAPP_nat_int @ semiri1621563631at_int @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( hAPP_nat_int @ semiri1621563631at_int @ SX0 )
= ( hAPP_nat_int @ semiri1621563631at_int @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1045]) ).
thf(1161,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( ( number_number_of_nat @ SX0 )
!= zero_zero_nat )
| ( ( hAPP_nat_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 )
| ( ( hAPP_nat_nat @ ( power_power_nat @ zero_zero_nat ) @ ( number_number_of_nat @ SX0 ) )
= zero_zero_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1096]) ).
thf(1162,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SX0 ) @ SX1 )
!= ( hAPP_nat_nat @ ( plus_plus_nat @ SX0 ) @ SX2 ) )
| ( SX1 = SX2 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX1 != SX2 )
| ( ( hAPP_nat_nat @ ( plus_plus_nat @ SX0 ) @ SX1 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ SX0 ) @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1109]) ).
thf(1163,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)],[996]) ).
thf(1164,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( zero_zero_int
!= ( hAPP_int_int @ ( plus_plus_int @ SX0 ) @ SX0 ) )
| ( SX0 = zero_zero_int ) )
| ~ ! [SX0: $i] :
( ( SX0 != zero_zero_int )
| ( zero_zero_int
= ( hAPP_int_int @ ( plus_plus_int @ SX0 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1080]) ).
thf(1165,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( number267125858f_real @ SX0 )
!= ( number267125858f_real @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( number267125858f_real @ SX0 )
= ( number267125858f_real @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1099]) ).
thf(1166,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( hAPP_nat_nat @ ( plus_plus_nat @ SX0 ) @ SX1 ) )
| ( SX1 = zero_zero_nat ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1 != zero_zero_nat )
| ( SX0
= ( hAPP_nat_nat @ ( plus_plus_nat @ SX0 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1146]) ).
thf(1167,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( ( number_number_of_nat @ SX0 )
!= zero_zero_nat )
| ( ( hAPP_nat_int @ ( power_power_int @ zero_zero_int ) @ ( number_number_of_nat @ SX0 ) )
= one_one_int ) )
| ~ ! [SX0: $i] :
( ( ( number_number_of_nat @ SX0 )
= zero_zero_nat )
| ( ( hAPP_nat_int @ ( power_power_int @ zero_zero_int ) @ ( number_number_of_nat @ SX0 ) )
= zero_zero_int ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[975]) ).
thf(1168,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)],[1098]) ).
thf(1169,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( zero_zero_real != SX0 )
| ( SX0 = zero_zero_real ) )
| ~ ! [SX0: $i] :
( ( SX0 != zero_zero_real )
| ( zero_zero_real = SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1130]) ).
thf(1170,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)],[995]) ).
thf(1171,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ SX1 )
!= one_one_nat )
| ( SX0 = one_one_nat )
| ( SX1 = zero_zero_nat ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != one_one_nat )
| ! [SX1: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ SX1 )
= one_one_nat ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1 != zero_zero_nat )
| ( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ SX1 )
= one_one_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1128]) ).
thf(1172,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( ( hAPP_nat_int @ ( power_power_int @ SX0 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) )
| ~ ! [SX0: $i] :
( ( SX0 != zero_zero_int )
| ( ( hAPP_nat_int @ ( power_power_int @ SX0 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[969]) ).
thf(1173,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( hAPP_nat_nat @ semiri984289939at_nat @ SX0 )
!= ( hAPP_nat_nat @ semiri984289939at_nat @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( hAPP_nat_nat @ semiri984289939at_nat @ SX0 )
= ( hAPP_nat_nat @ semiri984289939at_nat @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1116]) ).
thf(1174,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( SX0 != zero_zero_nat )
| ( ( hAPP_nat_int @ ( power_power_int @ zero_zero_int ) @ SX0 )
= one_one_int ) )
| ~ ! [SX0: $i] :
( ( SX0 = zero_zero_nat )
| ( ( hAPP_nat_int @ ( power_power_int @ zero_zero_int ) @ SX0 )
= zero_zero_int ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1043]) ).
thf(1175,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( hAPP_nat_int @ semiri1621563631at_int @ SX0 )
!= ( hAPP_nat_int @ semiri1621563631at_int @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( hAPP_nat_int @ semiri1621563631at_int @ SX0 )
= ( hAPP_nat_int @ semiri1621563631at_int @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1046]) ).
thf(1176,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1 = zero_zero_nat )
| ( SX0 != zero_zero_nat )
| ( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ SX1 )
= zero_zero_nat ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ SX1 )
!= zero_zero_nat )
| ( SX1 != zero_zero_nat ) )
| ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ SX1 )
!= zero_zero_nat )
| ( SX0 = zero_zero_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1125]) ).
thf(1177,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( number_number_of_nat @ SX1 )
= zero_zero_nat )
| ( SX0 != zero_zero_int )
| ( ( hAPP_nat_int @ ( power_power_int @ SX0 ) @ ( number_number_of_nat @ SX1 ) )
= zero_zero_int ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( hAPP_nat_int @ ( power_power_int @ SX0 ) @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_int )
| ( ( number_number_of_nat @ SX1 )
!= zero_zero_nat ) )
| ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( hAPP_nat_int @ ( power_power_int @ SX0 ) @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1026]) ).
thf(1178,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SX0 ) @ SX1 )
!= ( hAPP_nat_nat @ ( plus_plus_nat @ SX2 ) @ SX1 ) )
| ( SX0 = SX2 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX0 != SX2 )
| ( ( hAPP_nat_nat @ ( plus_plus_nat @ SX0 ) @ SX1 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ SX2 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1110]) ).
thf(1179,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ SX0 ) @ SX1 )
!= ( hAPP_int_int @ ( plus_plus_int @ SX2 ) @ SX1 ) )
| ( SX0 = SX2 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX0 != SX2 )
| ( ( hAPP_int_int @ ( plus_plus_int @ SX0 ) @ SX1 )
= ( hAPP_int_int @ ( plus_plus_int @ SX2 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1067]) ).
thf(1180,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( ( bit0 @ SX0 )
!= pls )
| ( SX0 = pls ) )
| ~ ! [SX0: $i] :
( ( SX0 != pls )
| ( ( bit0 @ SX0 )
= pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1006]) ).
thf(1181,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( number267125858f_real @ SX0 )
!= SX1 )
| ( SX1
= ( number267125858f_real @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( number267125858f_real @ SX0 ) )
| ( ( number267125858f_real @ SX0 )
= SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1101]) ).
thf(1182,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( one_one_nat != SX0 )
| ( SX0 = one_one_nat ) )
| ~ ! [SX0: $i] :
( ( SX0 != one_one_nat )
| ( one_one_nat = SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1145]) ).
thf(1183,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)],[994]) ).
thf(1184,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ SX0 ) @ SX0 )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) )
| ~ ! [SX0: $i] :
( ( SX0 != zero_zero_int )
| ( ( hAPP_int_int @ ( plus_plus_int @ SX0 ) @ SX0 )
= zero_zero_int ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1001]) ).
thf(1185,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( one_one_real != SX0 )
| ( SX0 = one_one_real ) )
| ~ ! [SX0: $i] :
( ( SX0 != one_one_real )
| ( one_one_real = SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1144]) ).
thf(1186,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1 = zero_zero_nat )
| ( SX0 != zero_zero_int )
| ( ( hAPP_nat_int @ ( power_power_int @ SX0 ) @ SX1 )
= zero_zero_int ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( hAPP_nat_int @ ( power_power_int @ SX0 ) @ SX1 )
!= zero_zero_int )
| ( SX1 != zero_zero_nat ) )
| ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( hAPP_nat_int @ ( power_power_int @ SX0 ) @ SX1 )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1057]) ).
thf(1187,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( zero_zero_int != SX0 )
| ( SX0 = zero_zero_int ) )
| ~ ! [SX0: $i] :
( ( SX0 != zero_zero_int )
| ( zero_zero_int = SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1062]) ).
thf(1188,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != zero_zero_nat )
| ( SX1 != zero_zero_nat )
| ( ( hAPP_nat_nat @ ( plus_plus_nat @ SX0 ) @ SX1 )
= zero_zero_nat ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ SX0 ) @ SX1 )
!= zero_zero_nat )
| ( SX0 = zero_zero_nat ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SX0 ) @ SX1 )
!= zero_zero_nat )
| ( SX1 = zero_zero_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1112]) ).
thf(1189,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)],[1100]) ).
thf(1190,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != zero_zero_int )
| ( SX1 != zero_zero_int )
| ( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ SX0 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ SX1 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_int ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ SX0 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ SX1 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ SX0 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ SX1 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_int )
| ( SX1 = zero_zero_int ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[966]) ).
thf(1191,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( ( hAPP_nat_int @ semiri1621563631at_int @ SX0 )
!= zero_zero_int )
| ( SX0 = zero_zero_nat ) )
| ~ ! [SX0: $i] :
( ( SX0 != zero_zero_nat )
| ( ( hAPP_nat_int @ semiri1621563631at_int @ SX0 )
= zero_zero_int ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[989]) ).
thf(1192,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SX0 ) @ SX1 )
!= ( hAPP_nat_nat @ ( plus_plus_nat @ SX2 ) @ SX1 ) )
| ( SX0 = SX2 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX0 != SX2 )
| ( ( hAPP_nat_nat @ ( plus_plus_nat @ SX0 ) @ SX1 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ SX2 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1136]) ).
thf(1193,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( one_one_int != SX0 )
| ( SX0 = one_one_int ) )
| ~ ! [SX0: $i] :
( ( SX0 != one_one_int )
| ( one_one_int = SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1075]) ).
thf(1194,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1 = zero_zero_nat )
| ( SX0 != zero_zero_nat )
| ( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ SX1 )
= zero_zero_nat ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ SX1 )
!= zero_zero_nat )
| ( SX1 != zero_zero_nat ) )
| ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ SX1 )
!= zero_zero_nat )
| ( SX0 = zero_zero_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1154]) ).
thf(1195,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( zero_zero_nat != SX0 )
| ( SX0 = zero_zero_nat ) )
| ~ ! [SX0: $i] :
( ( SX0 != zero_zero_nat )
| ( zero_zero_nat = SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1131]) ).
thf(1196,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ SX0 ) @ SX1 )
!= ( hAPP_int_int @ ( plus_plus_int @ SX0 ) @ SX2 ) )
| ( SX1 = SX2 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX1 != SX2 )
| ( ( hAPP_int_int @ ( plus_plus_int @ SX0 ) @ SX1 )
= ( hAPP_int_int @ ( plus_plus_int @ SX0 ) @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1068]) ).
thf(1197,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( pls
!= ( bit0 @ SX0 ) )
| ( pls = SX0 ) )
| ~ ! [SX0: $i] :
( ( pls != SX0 )
| ( pls
= ( bit0 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1007]) ).
thf(1198,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( hAPP_int_int @ ( plus_plus_int @ SX0 ) @ SX1 ) )
| ( SX1 = zero_zero_int ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1 != zero_zero_int )
| ( SX0
= ( hAPP_int_int @ ( plus_plus_int @ SX0 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1076]) ).
thf(1199,plain,
! [SV1: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ ( number_number_of_int @ SV1 ) )
= ( number_number_of_int @ ( hAPP_int_int @ ( plus_plus_int @ ( bit1 @ pls ) ) @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[970]) ).
thf(1200,plain,
! [SV2: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ ( number_number_of_int @ SV2 ) ) @ one_one_int )
= ( number_number_of_int @ ( hAPP_int_int @ ( plus_plus_int @ SV2 ) @ ( bit1 @ pls ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[971]) ).
thf(1201,plain,
! [SV3: $i] :
( ( ( hAPP_nat_int @ ( power_power_int @ ( hAPP_nat_int @ ( power_power_int @ SV3 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( hAPP_nat_int @ ( power_power_int @ SV3 ) @ ( number_number_of_nat @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[974]) ).
thf(1202,plain,
! [SV4: $i] :
( ( ! [SY249: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( number_number_of_int @ SV4 ) ) @ ( number_number_of_int @ SY249 ) )
= ( number_number_of_int @ ( hAPP_int_int @ ( plus_plus_int @ SV4 ) @ SY249 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[980]) ).
thf(1203,plain,
! [SV5: $i] :
( ( ! [SY250: $i] :
( ( hAPP_nat_int @ ( power_power_int @ ( hAPP_nat_int @ semiri1621563631at_int @ SV5 ) ) @ SY250 )
= ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( power_power_nat @ SV5 ) @ SY250 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[982]) ).
thf(1204,plain,
! [SV6: $i] :
( ( ! [SY251: $i] :
( ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( power_power_nat @ SV6 ) @ SY251 ) )
= ( hAPP_nat_int @ ( power_power_int @ ( hAPP_nat_int @ semiri1621563631at_int @ SV6 ) ) @ SY251 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[983]) ).
thf(1205,plain,
! [SV7: $i] :
( ( ! [SY252: $i,SY253: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ SV7 ) ) @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ SY252 ) ) @ SY253 ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( plus_plus_nat @ SV7 ) @ SY252 ) ) ) @ SY253 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[984]) ).
thf(1206,plain,
! [SV8: $i] :
( ( ! [SY254: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ SV8 ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ SY254 ) )
= ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( plus_plus_nat @ SV8 ) @ SY254 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[985]) ).
thf(1207,plain,
! [SV9: $i] :
( ( ! [SY255: $i,SY256: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ SV9 ) @ SY255 ) ) @ SY256 )
= ( hAPP_int_int @ ( plus_plus_int @ SV9 ) @ ( hAPP_int_int @ ( plus_plus_int @ SY255 ) @ SY256 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[997]) ).
thf(1208,plain,
! [SV10: $i] :
( ( ! [SY257: $i,SY258: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ SV10 ) @ ( hAPP_int_int @ ( plus_plus_int @ SY257 ) @ SY258 ) )
= ( hAPP_int_int @ ( plus_plus_int @ SY257 ) @ ( hAPP_int_int @ ( plus_plus_int @ SV10 ) @ SY258 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[998]) ).
thf(1209,plain,
! [SV11: $i] :
( ( ! [SY259: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ SV11 ) @ SY259 )
= ( hAPP_int_int @ ( plus_plus_int @ SY259 ) @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[999]) ).
thf(1210,plain,
! [SV12: $i] :
( ( ( ( bit1 @ SV12 )
!= pls ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1002]) ).
thf(1211,plain,
! [SV13: $i] :
( ( ( pls
!= ( bit1 @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1003]) ).
thf(1212,plain,
! [SV14: $i] :
( ( ! [SY260: $i] :
( ( bit1 @ SV14 )
!= ( bit0 @ SY260 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1004]) ).
thf(1213,plain,
! [SV15: $i] :
( ( ! [SY261: $i] :
( ( bit0 @ SV15 )
!= ( bit1 @ SY261 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1005]) ).
thf(1214,plain,
( ( zero_zero_int = one_one_int )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1010]) ).
thf(1215,plain,
! [SV16: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ SV16 ) @ pls )
= SV16 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1011]) ).
thf(1216,plain,
! [SV17: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ pls ) @ SV17 )
= SV17 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1012]) ).
thf(1217,plain,
! [SV18: $i] :
( ( ! [SY262: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( bit0 @ SV18 ) ) @ ( bit0 @ SY262 ) )
= ( bit0 @ ( hAPP_int_int @ ( plus_plus_int @ SV18 ) @ SY262 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1013]) ).
thf(1218,plain,
! [SV19: $i] :
( ( ( bit0 @ SV19 )
= ( hAPP_int_int @ ( plus_plus_int @ SV19 ) @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1014]) ).
thf(1219,plain,
! [SV20: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ SV20 ) @ zero_zero_int )
= SV20 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1015]) ).
thf(1220,plain,
! [SV21: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ zero_zero_int ) @ SV21 )
= SV21 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1016]) ).
thf(1221,plain,
! [SV22: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ ( number_number_of_int @ pls ) ) @ SV22 )
= SV22 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1024]) ).
thf(1222,plain,
! [SV23: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ SV23 ) @ ( number_number_of_int @ pls ) )
= SV23 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1025]) ).
thf(1223,plain,
! [SV24: $i] :
( ( ! [SY263: $i,SY264: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( number_number_of_int @ SV24 ) ) @ ( hAPP_int_int @ ( plus_plus_int @ ( number_number_of_int @ SY263 ) ) @ SY264 ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( number_number_of_int @ ( hAPP_int_int @ ( plus_plus_int @ SV24 ) @ SY263 ) ) ) @ SY264 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1027]) ).
thf(1224,plain,
! [SV25: $i] :
( ( ! [SY265: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( number_number_of_int @ SV25 ) ) @ ( number_number_of_int @ SY265 ) )
= ( number_number_of_int @ ( hAPP_int_int @ ( plus_plus_int @ SV25 ) @ SY265 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1028]) ).
thf(1225,plain,
! [SV26: $i] :
( ( ! [SY266: $i] :
( ( number_number_of_int @ ( hAPP_int_int @ ( plus_plus_int @ SV26 ) @ SY266 ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( number_number_of_int @ SV26 ) ) @ ( number_number_of_int @ SY266 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1029]) ).
thf(1226,plain,
! [SV27: $i] :
( ( ! [SY267: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( bit1 @ SV27 ) ) @ ( bit0 @ SY267 ) )
= ( bit1 @ ( hAPP_int_int @ ( plus_plus_int @ SV27 ) @ SY267 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1030]) ).
thf(1227,plain,
! [SV28: $i] :
( ( ! [SY268: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( bit0 @ SV28 ) ) @ ( bit1 @ SY268 ) )
= ( bit1 @ ( hAPP_int_int @ ( plus_plus_int @ SV28 ) @ SY268 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1031]) ).
thf(1228,plain,
! [SV29: $i] :
( ( ( bit1 @ SV29 )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ SV29 ) ) @ SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1032]) ).
thf(1229,plain,
! [SV30: $i] :
( ( ( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ SV30 ) ) @ SV30 )
!= zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1033]) ).
thf(1230,plain,
! [SV31: $i] :
( ( ( number_number_of_nat @ ( hAPP_nat_int @ semiri1621563631at_int @ SV31 ) )
= ( hAPP_nat_nat @ semiri984289939at_nat @ SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1034]) ).
thf(1231,plain,
! [SV32: $i] :
( ( ( number_number_of_int @ ( hAPP_nat_int @ semiri1621563631at_int @ SV32 ) )
= ( hAPP_nat_int @ semiri1621563631at_int @ SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1035]) ).
thf(1232,plain,
! [SV33: $i] :
( ( ( number_number_of_int @ ( bit0 @ SV33 ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ zero_zero_int ) @ ( number_number_of_int @ SV33 ) ) ) @ ( number_number_of_int @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1036]) ).
thf(1233,plain,
! [SV34: $i] :
( ( ( number_number_of_int @ ( bit1 @ SV34 ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ ( number_number_of_int @ SV34 ) ) ) @ ( number_number_of_int @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1037]) ).
thf(1234,plain,
! [SV35: $i] :
( ( ( hAPP_nat_int @ ( power_power_int @ SV35 ) @ one_one_nat )
= SV35 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1044]) ).
thf(1235,plain,
( ( one_one_int = zero_zero_int )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1047]) ).
thf(1236,plain,
( ( zero_zero_int = one_one_int )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1048]) ).
thf(1237,plain,
! [SV36: $i] :
( ( ! [SY269: $i] :
( ( SY269 = zero_zero_int )
| ( ( hAPP_nat_int @ ( power_power_int @ SY269 ) @ SV36 )
!= zero_zero_int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1049]) ).
thf(1238,plain,
! [SV37: $i] :
( ( ( hAPP_nat_int @ ( power_power_int @ one_one_int ) @ SV37 )
= one_one_int )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1050]) ).
thf(1239,plain,
! [SV38: $i] :
( ( ! [SY270: $i] :
( ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( plus_plus_nat @ SV38 ) @ SY270 ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ SV38 ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ SY270 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1051]) ).
thf(1240,plain,
! [SV39: $i] :
( ( ! [SY271: $i] :
( ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( power_power_nat @ SV39 ) @ SY271 ) )
= ( hAPP_nat_int @ ( power_power_int @ ( hAPP_nat_int @ semiri1621563631at_int @ SV39 ) ) @ SY271 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1053]) ).
thf(1241,plain,
! [SV40: $i] :
( ( ! [SY272: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ SV40 ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ SY272 ) )
= ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( plus_plus_nat @ SV40 ) @ SY272 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1055]) ).
thf(1242,plain,
! [SV41: $i] :
( ( ! [SY273: $i] :
( ( hAPP_nat_int @ ( power_power_int @ ( hAPP_nat_int @ semiri1621563631at_int @ SV41 ) ) @ SY273 )
= ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( power_power_nat @ SV41 ) @ SY273 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1056]) ).
thf(1243,plain,
! [SV42: $i] :
( ( ( hAPP_nat_int @ ( power_power_int @ SV42 ) @ zero_zero_nat )
= one_one_int )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1058]) ).
thf(1244,plain,
! [SV43: $i] :
( ( ( hAPP_nat_int @ ( power_power_int @ SV43 ) @ zero_zero_nat )
= one_one_int )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1061]) ).
thf(1245,plain,
! [SV44: $i] :
( ( ! [SY274: $i,SY275: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ SV44 ) @ SY274 )
!= ( hAPP_int_int @ ( plus_plus_int @ SY275 ) @ SY274 ) )
| ( SV44 = SY275 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1063]) ).
thf(1246,plain,
! [SV45: $i] :
( ( ! [SY276: $i,SY277: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ SV45 ) @ SY276 )
!= ( hAPP_int_int @ ( plus_plus_int @ SV45 ) @ SY277 ) )
| ( SY276 = SY277 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1064]) ).
thf(1247,plain,
! [SV46: $i] :
( ( ! [SY278: $i,SY279: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ SV46 ) @ SY278 )
!= ( hAPP_int_int @ ( plus_plus_int @ SV46 ) @ SY279 ) )
| ( SY278 = SY279 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1065]) ).
thf(1248,plain,
! [SV47: $i] :
( ( ! [SY280: $i,SY281: $i,SY282: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ SV47 ) @ SY280 ) ) @ ( hAPP_int_int @ ( plus_plus_int @ SY281 ) @ SY282 ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ SV47 ) @ SY281 ) ) @ ( hAPP_int_int @ ( plus_plus_int @ SY280 ) @ SY282 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1066]) ).
thf(1249,plain,
! [SV48: $i] :
( ( ! [SY283: $i,SY284: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ SV48 ) @ SY283 ) ) @ SY284 )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ SV48 ) @ SY284 ) ) @ SY283 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1069]) ).
thf(1250,plain,
! [SV49: $i] :
( ( ! [SY285: $i,SY286: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ SV49 ) @ SY285 ) ) @ SY286 )
= ( hAPP_int_int @ ( plus_plus_int @ SV49 ) @ ( hAPP_int_int @ ( plus_plus_int @ SY285 ) @ SY286 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1070]) ).
thf(1251,plain,
! [SV50: $i] :
( ( ! [SY287: $i,SY288: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ SV50 ) @ SY287 ) ) @ SY288 )
= ( hAPP_int_int @ ( plus_plus_int @ SV50 ) @ ( hAPP_int_int @ ( plus_plus_int @ SY287 ) @ SY288 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1071]) ).
thf(1252,plain,
! [SV51: $i] :
( ( ! [SY289: $i,SY290: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ SV51 ) @ ( hAPP_int_int @ ( plus_plus_int @ SY289 ) @ SY290 ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ SV51 ) @ SY289 ) ) @ SY290 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1072]) ).
thf(1253,plain,
! [SV52: $i] :
( ( ! [SY291: $i,SY292: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ SV52 ) @ ( hAPP_int_int @ ( plus_plus_int @ SY291 ) @ SY292 ) )
= ( hAPP_int_int @ ( plus_plus_int @ SY291 ) @ ( hAPP_int_int @ ( plus_plus_int @ SV52 ) @ SY292 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1073]) ).
thf(1254,plain,
! [SV53: $i] :
( ( ! [SY293: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ SV53 ) @ SY293 )
= ( hAPP_int_int @ ( plus_plus_int @ SY293 ) @ SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1074]) ).
thf(1255,plain,
! [SV54: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ SV54 ) @ zero_zero_int )
= SV54 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1077]) ).
thf(1256,plain,
! [SV55: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ SV55 ) @ zero_zero_int )
= SV55 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1078]) ).
thf(1257,plain,
! [SV56: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ SV56 ) @ zero_zero_int )
= SV56 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1079]) ).
thf(1258,plain,
! [SV57: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ zero_zero_int ) @ SV57 )
= SV57 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1081]) ).
thf(1259,plain,
! [SV58: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ zero_zero_int ) @ SV58 )
= SV58 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1082]) ).
thf(1260,plain,
! [SV59: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ zero_zero_int ) @ SV59 )
= SV59 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1083]) ).
thf(1261,plain,
! [SV60: $i] :
( ( ( hAPP_nat_int @ ( power_power_int @ SV60 ) @ one_one_nat )
= SV60 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1084]) ).
thf(1262,plain,
! [SV61: $i] :
( ( ( succ @ ( bit0 @ SV61 ) )
= ( bit1 @ SV61 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1086]) ).
thf(1263,plain,
! [SV62: $i] :
( ( ( succ @ ( bit1 @ SV62 ) )
= ( bit0 @ ( succ @ SV62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1087]) ).
thf(1264,plain,
! [SV63: $i] :
( ( ( succ @ SV63 )
= ( hAPP_int_int @ ( plus_plus_int @ SV63 ) @ one_one_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1088]) ).
thf(1265,plain,
! [SV64: $i] :
( ( ( number_number_of_int @ ( succ @ SV64 ) )
= ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ ( number_number_of_int @ SV64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1089]) ).
thf(1266,plain,
! [SV65: $i] :
( ( ! [SY294: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( bit1 @ SV65 ) ) @ ( bit1 @ SY294 ) )
= ( bit0 @ ( hAPP_int_int @ ( plus_plus_int @ SV65 ) @ ( succ @ SY294 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1090]) ).
thf(1267,plain,
! [SV66: $i] :
( ( ! [SY295: $i] :
( ( hAPP_nat_int @ ( power_power_int @ ( hAPP_int_int @ ( plus_plus_int @ SV66 ) @ SY295 ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ SV66 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV66 ) @ SY295 ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ SY295 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1091]) ).
thf(1268,plain,
! [SV67: $i] :
( ( ! [SY296: $i] :
( ( times_times_int @ ( bit1 @ SV67 ) @ SY296 )
= ( hAPP_int_int @ ( plus_plus_int @ ( bit0 @ ( times_times_int @ SV67 @ SY296 ) ) ) @ SY296 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1092]) ).
thf(1269,plain,
( ( zero_zero_real = one_one_real )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1104]) ).
thf(1270,plain,
! [SV68: $i] :
( ( ( number_number_of_int @ SV68 )
= SV68 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1105]) ).
thf(1271,plain,
! [SV69: $i] :
( ( ! [SY297: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ SV69 ) @ SY297 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ SY297 ) @ SV69 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1106]) ).
thf(1272,plain,
! [SV70: $i] :
( ( ! [SY298: $i,SY299: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ SV70 ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ SY298 ) @ SY299 ) )
= ( hAPP_nat_nat @ ( plus_plus_nat @ SY298 ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ SV70 ) @ SY299 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1107]) ).
thf(1273,plain,
! [SV71: $i] :
( ( ! [SY300: $i,SY301: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ SV71 ) @ SY300 ) ) @ SY301 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ SV71 ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ SY300 ) @ SY301 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1108]) ).
thf(1274,plain,
! [SV72: $i] :
( ( ! [SY302: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV72 ) @ SY302 )
!= SV72 )
| ( SY302 = zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1111]) ).
thf(1275,plain,
! [SV73: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV73 ) @ zero_zero_nat )
= SV73 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1113]) ).
thf(1276,plain,
! [SV74: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ zero_zero_nat ) @ SV74 )
= SV74 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1114]) ).
thf(1277,plain,
! [SV75: $i] :
( ( ( hAPP_nat_nat @ ( power_power_nat @ SV75 ) @ one_one_nat )
= SV75 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1115]) ).
thf(1278,plain,
( ( one_one_real = zero_zero_real )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1117]) ).
thf(1279,plain,
( ( one_one_nat = zero_zero_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1118]) ).
thf(1280,plain,
( ( zero_zero_real = one_one_real )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1119]) ).
thf(1281,plain,
( ( zero_zero_nat = one_one_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1120]) ).
thf(1282,plain,
! [SV76: $i] :
( ( ( hAPP_nat_nat @ ( power_power_nat @ one_one_nat ) @ SV76 )
= one_one_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1121]) ).
thf(1283,plain,
! [SV77: $i] :
( ( ! [SY303: $i] :
( ( hAPP_nat_nat @ semiri984289939at_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ SV77 ) @ SY303 ) )
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ semiri984289939at_nat @ SV77 ) ) @ ( hAPP_nat_nat @ semiri984289939at_nat @ SY303 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1122]) ).
thf(1284,plain,
! [SV78: $i] :
( ( ! [SY304: $i] :
( ( hAPP_nat_nat @ semiri984289939at_nat @ ( hAPP_nat_nat @ ( power_power_nat @ SV78 ) @ SY304 ) )
= ( hAPP_nat_nat @ ( power_power_nat @ ( hAPP_nat_nat @ semiri984289939at_nat @ SV78 ) ) @ SY304 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1124]) ).
thf(1285,plain,
! [SV79: $i] :
( ( ( hAPP_nat_nat @ ( power_power_nat @ SV79 ) @ zero_zero_nat )
= one_one_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1126]) ).
thf(1286,plain,
! [SV80: $i] :
( ( ( hAPP_nat_nat @ ( power_power_nat @ SV80 ) @ zero_zero_nat )
= one_one_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1129]) ).
thf(1287,plain,
! [SV81: $i] :
( ( ! [SY305: $i,SY306: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV81 ) @ SY305 )
!= ( hAPP_nat_nat @ ( plus_plus_nat @ SY306 ) @ SY305 ) )
| ( SV81 = SY306 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1132]) ).
thf(1288,plain,
! [SV82: $i] :
( ( ! [SY307: $i,SY308: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV82 ) @ SY307 )
!= ( hAPP_nat_nat @ ( plus_plus_nat @ SV82 ) @ SY308 ) )
| ( SY307 = SY308 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1133]) ).
thf(1289,plain,
! [SV83: $i] :
( ( ! [SY309: $i,SY310: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV83 ) @ SY309 )
!= ( hAPP_nat_nat @ ( plus_plus_nat @ SV83 ) @ SY310 ) )
| ( SY309 = SY310 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1134]) ).
thf(1290,plain,
! [SV84: $i] :
( ( ! [SY311: $i,SY312: $i,SY313: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ SV84 ) @ SY311 ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ SY312 ) @ SY313 ) )
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ SV84 ) @ SY312 ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ SY311 ) @ SY313 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1135]) ).
thf(1291,plain,
! [SV85: $i] :
( ( ! [SY314: $i,SY315: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ SV85 ) @ SY314 ) ) @ SY315 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ SV85 ) @ SY315 ) ) @ SY314 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1138]) ).
thf(1292,plain,
! [SV86: $i] :
( ( ! [SY316: $i,SY317: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ SV86 ) @ SY316 ) ) @ SY317 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ SV86 ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ SY316 ) @ SY317 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1139]) ).
thf(1293,plain,
! [SV87: $i] :
( ( ! [SY318: $i,SY319: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ SV87 ) @ SY318 ) ) @ SY319 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ SV87 ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ SY318 ) @ SY319 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1140]) ).
thf(1294,plain,
! [SV88: $i] :
( ( ! [SY320: $i,SY321: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ SV88 ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ SY320 ) @ SY321 ) )
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ SV88 ) @ SY320 ) ) @ SY321 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1141]) ).
thf(1295,plain,
! [SV89: $i] :
( ( ! [SY322: $i,SY323: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ SV89 ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ SY322 ) @ SY323 ) )
= ( hAPP_nat_nat @ ( plus_plus_nat @ SY322 ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ SV89 ) @ SY323 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1142]) ).
thf(1296,plain,
! [SV90: $i] :
( ( ! [SY324: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ SV90 ) @ SY324 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ SY324 ) @ SV90 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1143]) ).
thf(1297,plain,
! [SV91: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV91 ) @ zero_zero_nat )
= SV91 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1147]) ).
thf(1298,plain,
! [SV92: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV92 ) @ zero_zero_nat )
= SV92 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1148]) ).
thf(1299,plain,
! [SV93: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV93 ) @ zero_zero_nat )
= SV93 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1149]) ).
thf(1300,plain,
! [SV94: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ zero_zero_nat ) @ SV94 )
= SV94 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1150]) ).
thf(1301,plain,
! [SV95: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ zero_zero_nat ) @ SV95 )
= SV95 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1151]) ).
thf(1302,plain,
! [SV96: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ zero_zero_nat ) @ SV96 )
= SV96 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1152]) ).
thf(1303,plain,
! [SV97: $i] :
( ( ( hAPP_nat_nat @ ( power_power_nat @ SV97 ) @ one_one_nat )
= SV97 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1153]) ).
thf(1304,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != zero_zero_nat )
| ( ( hAPP_nat_nat @ ( power_power_nat @ zero_zero_nat ) @ SX0 )
= one_one_nat ) )
| ~ ! [SX0: $i] :
( ( SX0 = zero_zero_nat )
| ( ( hAPP_nat_nat @ ( power_power_nat @ zero_zero_nat ) @ SX0 )
= zero_zero_nat ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1156]) ).
thf(1305,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( number_number_of_nat @ SX1 )
= zero_zero_nat )
| ( SX0 != zero_zero_nat )
| ( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) )
= zero_zero_nat ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_nat )
| ( ( number_number_of_nat @ SX1 )
!= zero_zero_nat ) )
| ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_nat )
| ( SX0 = zero_zero_nat ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1157]) ).
thf(1306,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( hAPP_nat_int @ semiri1621563631at_int @ SX0 )
!= ( hAPP_nat_int @ semiri1621563631at_int @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( hAPP_nat_int @ semiri1621563631at_int @ SX0 )
= ( hAPP_nat_int @ semiri1621563631at_int @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1158]) ).
thf(1307,plain,
! [SV98: $i] :
( ( ~ ( ~ ! [SY325: $i,SY326: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV98 ) @ SY325 )
!= ( hAPP_nat_nat @ ( plus_plus_nat @ SV98 ) @ SY326 ) )
| ( SY325 = SY326 ) )
| ~ ! [SY327: $i,SY328: $i] :
( ( SY327 != SY328 )
| ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV98 ) @ SY327 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ SV98 ) @ SY328 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1159]) ).
thf(1308,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( hAPP_nat_int @ semiri1621563631at_int @ SX0 )
!= ( hAPP_nat_int @ semiri1621563631at_int @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( hAPP_nat_int @ semiri1621563631at_int @ SX0 )
= ( hAPP_nat_int @ semiri1621563631at_int @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1160]) ).
thf(1309,plain,
( ( ~ ! [SX0: $i] :
( ( ( number_number_of_nat @ SX0 )
!= zero_zero_nat )
| ( ( hAPP_nat_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 )
| ( ( hAPP_nat_nat @ ( power_power_nat @ zero_zero_nat ) @ ( number_number_of_nat @ SX0 ) )
= zero_zero_nat ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1161]) ).
thf(1310,plain,
! [SV99: $i] :
( ( ~ ( ~ ! [SY329: $i,SY330: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV99 ) @ SY329 )
!= ( hAPP_nat_nat @ ( plus_plus_nat @ SV99 ) @ SY330 ) )
| ( SY329 = SY330 ) )
| ~ ! [SY331: $i,SY332: $i] :
( ( SY331 != SY332 )
| ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV99 ) @ SY331 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ SV99 ) @ SY332 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1162]) ).
thf(1311,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)],[1163]) ).
thf(1312,plain,
( ( ~ ! [SX0: $i] :
( ( zero_zero_int
!= ( hAPP_int_int @ ( plus_plus_int @ SX0 ) @ SX0 ) )
| ( SX0 = zero_zero_int ) )
| ~ ! [SX0: $i] :
( ( SX0 != zero_zero_int )
| ( zero_zero_int
= ( hAPP_int_int @ ( plus_plus_int @ SX0 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1164]) ).
thf(1313,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( number267125858f_real @ SX0 )
!= ( number267125858f_real @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( number267125858f_real @ SX0 )
= ( number267125858f_real @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1165]) ).
thf(1314,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( hAPP_nat_nat @ ( plus_plus_nat @ SX0 ) @ SX1 ) )
| ( SX1 = zero_zero_nat ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1 != zero_zero_nat )
| ( SX0
= ( hAPP_nat_nat @ ( plus_plus_nat @ SX0 ) @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1166]) ).
thf(1315,plain,
( ( ~ ! [SX0: $i] :
( ( ( number_number_of_nat @ SX0 )
!= zero_zero_nat )
| ( ( hAPP_nat_int @ ( power_power_int @ zero_zero_int ) @ ( number_number_of_nat @ SX0 ) )
= one_one_int ) )
| ~ ! [SX0: $i] :
( ( ( number_number_of_nat @ SX0 )
= zero_zero_nat )
| ( ( hAPP_nat_int @ ( power_power_int @ zero_zero_int ) @ ( number_number_of_nat @ SX0 ) )
= zero_zero_int ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1167]) ).
thf(1316,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)],[1168]) ).
thf(1317,plain,
( ( ~ ! [SX0: $i] :
( ( zero_zero_real != SX0 )
| ( SX0 = zero_zero_real ) )
| ~ ! [SX0: $i] :
( ( SX0 != zero_zero_real )
| ( zero_zero_real = SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1169]) ).
thf(1318,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)],[1170]) ).
thf(1319,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ SX1 )
!= one_one_nat )
| ( SX0 = one_one_nat )
| ( SX1 = zero_zero_nat ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != one_one_nat )
| ! [SX1: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ SX1 )
= one_one_nat ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1 != zero_zero_nat )
| ( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ SX1 )
= one_one_nat ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1171]) ).
thf(1320,plain,
( ( ~ ! [SX0: $i] :
( ( ( hAPP_nat_int @ ( power_power_int @ SX0 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) )
| ~ ! [SX0: $i] :
( ( SX0 != zero_zero_int )
| ( ( hAPP_nat_int @ ( power_power_int @ SX0 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1172]) ).
thf(1321,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( hAPP_nat_nat @ semiri984289939at_nat @ SX0 )
!= ( hAPP_nat_nat @ semiri984289939at_nat @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( hAPP_nat_nat @ semiri984289939at_nat @ SX0 )
= ( hAPP_nat_nat @ semiri984289939at_nat @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1173]) ).
thf(1322,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != zero_zero_nat )
| ( ( hAPP_nat_int @ ( power_power_int @ zero_zero_int ) @ SX0 )
= one_one_int ) )
| ~ ! [SX0: $i] :
( ( SX0 = zero_zero_nat )
| ( ( hAPP_nat_int @ ( power_power_int @ zero_zero_int ) @ SX0 )
= zero_zero_int ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1174]) ).
thf(1323,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( hAPP_nat_int @ semiri1621563631at_int @ SX0 )
!= ( hAPP_nat_int @ semiri1621563631at_int @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( hAPP_nat_int @ semiri1621563631at_int @ SX0 )
= ( hAPP_nat_int @ semiri1621563631at_int @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1175]) ).
thf(1324,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1 = zero_zero_nat )
| ( SX0 != zero_zero_nat )
| ( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ SX1 )
= zero_zero_nat ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ SX1 )
!= zero_zero_nat )
| ( SX1 != zero_zero_nat ) )
| ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ SX1 )
!= zero_zero_nat )
| ( SX0 = zero_zero_nat ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1176]) ).
thf(1325,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( number_number_of_nat @ SX1 )
= zero_zero_nat )
| ( SX0 != zero_zero_int )
| ( ( hAPP_nat_int @ ( power_power_int @ SX0 ) @ ( number_number_of_nat @ SX1 ) )
= zero_zero_int ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( hAPP_nat_int @ ( power_power_int @ SX0 ) @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_int )
| ( ( number_number_of_nat @ SX1 )
!= zero_zero_nat ) )
| ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( hAPP_nat_int @ ( power_power_int @ SX0 ) @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1177]) ).
thf(1326,plain,
! [SV100: $i] :
( ( ~ ( ~ ! [SY333: $i,SY334: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV100 ) @ SY333 )
!= ( hAPP_nat_nat @ ( plus_plus_nat @ SY334 ) @ SY333 ) )
| ( SV100 = SY334 ) )
| ~ ! [SY335: $i,SY336: $i] :
( ( SV100 != SY336 )
| ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV100 ) @ SY335 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ SY336 ) @ SY335 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1178]) ).
thf(1327,plain,
! [SV101: $i] :
( ( ~ ( ~ ! [SY337: $i,SY338: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ SV101 ) @ SY337 )
!= ( hAPP_int_int @ ( plus_plus_int @ SY338 ) @ SY337 ) )
| ( SV101 = SY338 ) )
| ~ ! [SY339: $i,SY340: $i] :
( ( SV101 != SY340 )
| ( ( hAPP_int_int @ ( plus_plus_int @ SV101 ) @ SY339 )
= ( hAPP_int_int @ ( plus_plus_int @ SY340 ) @ SY339 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1179]) ).
thf(1328,plain,
( ( ~ ! [SX0: $i] :
( ( ( bit0 @ SX0 )
!= pls )
| ( SX0 = pls ) )
| ~ ! [SX0: $i] :
( ( SX0 != pls )
| ( ( bit0 @ SX0 )
= pls ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1180]) ).
thf(1329,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( number267125858f_real @ SX0 )
!= SX1 )
| ( SX1
= ( number267125858f_real @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( number267125858f_real @ SX0 ) )
| ( ( number267125858f_real @ SX0 )
= SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1181]) ).
thf(1330,plain,
( ( ~ ! [SX0: $i] :
( ( one_one_nat != SX0 )
| ( SX0 = one_one_nat ) )
| ~ ! [SX0: $i] :
( ( SX0 != one_one_nat )
| ( one_one_nat = SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1182]) ).
thf(1331,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)],[1183]) ).
thf(1332,plain,
( ( ~ ! [SX0: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ SX0 ) @ SX0 )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) )
| ~ ! [SX0: $i] :
( ( SX0 != zero_zero_int )
| ( ( hAPP_int_int @ ( plus_plus_int @ SX0 ) @ SX0 )
= zero_zero_int ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1184]) ).
thf(1333,plain,
( ( ~ ! [SX0: $i] :
( ( one_one_real != SX0 )
| ( SX0 = one_one_real ) )
| ~ ! [SX0: $i] :
( ( SX0 != one_one_real )
| ( one_one_real = SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1185]) ).
thf(1334,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1 = zero_zero_nat )
| ( SX0 != zero_zero_int )
| ( ( hAPP_nat_int @ ( power_power_int @ SX0 ) @ SX1 )
= zero_zero_int ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( hAPP_nat_int @ ( power_power_int @ SX0 ) @ SX1 )
!= zero_zero_int )
| ( SX1 != zero_zero_nat ) )
| ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( hAPP_nat_int @ ( power_power_int @ SX0 ) @ SX1 )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1186]) ).
thf(1335,plain,
( ( ~ ! [SX0: $i] :
( ( zero_zero_int != SX0 )
| ( SX0 = zero_zero_int ) )
| ~ ! [SX0: $i] :
( ( SX0 != zero_zero_int )
| ( zero_zero_int = SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1187]) ).
thf(1336,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != zero_zero_nat )
| ( SX1 != zero_zero_nat )
| ( ( hAPP_nat_nat @ ( plus_plus_nat @ SX0 ) @ SX1 )
= zero_zero_nat ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ SX0 ) @ SX1 )
!= zero_zero_nat )
| ( SX0 = zero_zero_nat ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SX0 ) @ SX1 )
!= zero_zero_nat )
| ( SX1 = zero_zero_nat ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1188]) ).
thf(1337,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)],[1189]) ).
thf(1338,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != zero_zero_int )
| ( SX1 != zero_zero_int )
| ( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ SX0 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ SX1 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_int ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ SX0 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ SX1 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ SX0 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( 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)],[1190]) ).
thf(1339,plain,
( ( ~ ! [SX0: $i] :
( ( ( hAPP_nat_int @ semiri1621563631at_int @ SX0 )
!= zero_zero_int )
| ( SX0 = zero_zero_nat ) )
| ~ ! [SX0: $i] :
( ( SX0 != zero_zero_nat )
| ( ( hAPP_nat_int @ semiri1621563631at_int @ SX0 )
= zero_zero_int ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1191]) ).
thf(1340,plain,
! [SV102: $i] :
( ( ~ ( ~ ! [SY341: $i,SY342: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV102 ) @ SY341 )
!= ( hAPP_nat_nat @ ( plus_plus_nat @ SY342 ) @ SY341 ) )
| ( SV102 = SY342 ) )
| ~ ! [SY343: $i,SY344: $i] :
( ( SV102 != SY344 )
| ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV102 ) @ SY343 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ SY344 ) @ SY343 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1192]) ).
thf(1341,plain,
( ( ~ ! [SX0: $i] :
( ( one_one_int != SX0 )
| ( SX0 = one_one_int ) )
| ~ ! [SX0: $i] :
( ( SX0 != one_one_int )
| ( one_one_int = SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1193]) ).
thf(1342,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1 = zero_zero_nat )
| ( SX0 != zero_zero_nat )
| ( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ SX1 )
= zero_zero_nat ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ SX1 )
!= zero_zero_nat )
| ( SX1 != zero_zero_nat ) )
| ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ SX1 )
!= zero_zero_nat )
| ( SX0 = zero_zero_nat ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1194]) ).
thf(1343,plain,
( ( ~ ! [SX0: $i] :
( ( zero_zero_nat != SX0 )
| ( SX0 = zero_zero_nat ) )
| ~ ! [SX0: $i] :
( ( SX0 != zero_zero_nat )
| ( zero_zero_nat = SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1195]) ).
thf(1344,plain,
! [SV103: $i] :
( ( ~ ( ~ ! [SY345: $i,SY346: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ SV103 ) @ SY345 )
!= ( hAPP_int_int @ ( plus_plus_int @ SV103 ) @ SY346 ) )
| ( SY345 = SY346 ) )
| ~ ! [SY347: $i,SY348: $i] :
( ( SY347 != SY348 )
| ( ( hAPP_int_int @ ( plus_plus_int @ SV103 ) @ SY347 )
= ( hAPP_int_int @ ( plus_plus_int @ SV103 ) @ SY348 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1196]) ).
thf(1345,plain,
( ( ~ ! [SX0: $i] :
( ( pls
!= ( bit0 @ SX0 ) )
| ( pls = SX0 ) )
| ~ ! [SX0: $i] :
( ( pls != SX0 )
| ( pls
= ( bit0 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1197]) ).
thf(1346,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( hAPP_int_int @ ( plus_plus_int @ SX0 ) @ SX1 ) )
| ( SX1 = zero_zero_int ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1 != zero_zero_int )
| ( SX0
= ( hAPP_int_int @ ( plus_plus_int @ SX0 ) @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1198]) ).
thf(1347,plain,
! [SV104: $i,SV4: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ ( number_number_of_int @ SV4 ) ) @ ( number_number_of_int @ SV104 ) )
= ( number_number_of_int @ ( hAPP_int_int @ ( plus_plus_int @ SV4 ) @ SV104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1202]) ).
thf(1348,plain,
! [SV105: $i,SV5: $i] :
( ( ( hAPP_nat_int @ ( power_power_int @ ( hAPP_nat_int @ semiri1621563631at_int @ SV5 ) ) @ SV105 )
= ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( power_power_nat @ SV5 ) @ SV105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1203]) ).
thf(1349,plain,
! [SV106: $i,SV6: $i] :
( ( ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( power_power_nat @ SV6 ) @ SV106 ) )
= ( hAPP_nat_int @ ( power_power_int @ ( hAPP_nat_int @ semiri1621563631at_int @ SV6 ) ) @ SV106 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1204]) ).
thf(1350,plain,
! [SV107: $i,SV7: $i] :
( ( ! [SY349: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ SV7 ) ) @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ SV107 ) ) @ SY349 ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( plus_plus_nat @ SV7 ) @ SV107 ) ) ) @ SY349 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1205]) ).
thf(1351,plain,
! [SV108: $i,SV8: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ SV8 ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ SV108 ) )
= ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( plus_plus_nat @ SV8 ) @ SV108 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1206]) ).
thf(1352,plain,
! [SV109: $i,SV9: $i] :
( ( ! [SY350: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ SV9 ) @ SV109 ) ) @ SY350 )
= ( hAPP_int_int @ ( plus_plus_int @ SV9 ) @ ( hAPP_int_int @ ( plus_plus_int @ SV109 ) @ SY350 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1207]) ).
thf(1353,plain,
! [SV110: $i,SV10: $i] :
( ( ! [SY351: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ SV10 ) @ ( hAPP_int_int @ ( plus_plus_int @ SV110 ) @ SY351 ) )
= ( hAPP_int_int @ ( plus_plus_int @ SV110 ) @ ( hAPP_int_int @ ( plus_plus_int @ SV10 ) @ SY351 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1208]) ).
thf(1354,plain,
! [SV111: $i,SV11: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ SV11 ) @ SV111 )
= ( hAPP_int_int @ ( plus_plus_int @ SV111 ) @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1209]) ).
thf(1355,plain,
! [SV12: $i] :
( ( ( bit1 @ SV12 )
= pls )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1210]) ).
thf(1356,plain,
! [SV13: $i] :
( ( pls
= ( bit1 @ SV13 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1211]) ).
thf(1357,plain,
! [SV112: $i,SV14: $i] :
( ( ( ( bit1 @ SV14 )
!= ( bit0 @ SV112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1212]) ).
thf(1358,plain,
! [SV113: $i,SV15: $i] :
( ( ( ( bit0 @ SV15 )
!= ( bit1 @ SV113 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1213]) ).
thf(1359,plain,
! [SV114: $i,SV18: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ ( bit0 @ SV18 ) ) @ ( bit0 @ SV114 ) )
= ( bit0 @ ( hAPP_int_int @ ( plus_plus_int @ SV18 ) @ SV114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1217]) ).
thf(1360,plain,
! [SV115: $i,SV24: $i] :
( ( ! [SY352: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( number_number_of_int @ SV24 ) ) @ ( hAPP_int_int @ ( plus_plus_int @ ( number_number_of_int @ SV115 ) ) @ SY352 ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( number_number_of_int @ ( hAPP_int_int @ ( plus_plus_int @ SV24 ) @ SV115 ) ) ) @ SY352 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1223]) ).
thf(1361,plain,
! [SV116: $i,SV25: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ ( number_number_of_int @ SV25 ) ) @ ( number_number_of_int @ SV116 ) )
= ( number_number_of_int @ ( hAPP_int_int @ ( plus_plus_int @ SV25 ) @ SV116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1224]) ).
thf(1362,plain,
! [SV117: $i,SV26: $i] :
( ( ( number_number_of_int @ ( hAPP_int_int @ ( plus_plus_int @ SV26 ) @ SV117 ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( number_number_of_int @ SV26 ) ) @ ( number_number_of_int @ SV117 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1225]) ).
thf(1363,plain,
! [SV118: $i,SV27: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ ( bit1 @ SV27 ) ) @ ( bit0 @ SV118 ) )
= ( bit1 @ ( hAPP_int_int @ ( plus_plus_int @ SV27 ) @ SV118 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1226]) ).
thf(1364,plain,
! [SV119: $i,SV28: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ ( bit0 @ SV28 ) ) @ ( bit1 @ SV119 ) )
= ( bit1 @ ( hAPP_int_int @ ( plus_plus_int @ SV28 ) @ SV119 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1227]) ).
thf(1365,plain,
! [SV30: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ one_one_int ) @ SV30 ) ) @ SV30 )
= zero_zero_int )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1229]) ).
thf(1366,plain,
! [SV36: $i,SV120: $i] :
( ( ( SV120 = zero_zero_int )
| ( ( hAPP_nat_int @ ( power_power_int @ SV120 ) @ SV36 )
!= zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1237]) ).
thf(1367,plain,
! [SV121: $i,SV38: $i] :
( ( ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( plus_plus_nat @ SV38 ) @ SV121 ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ SV38 ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ SV121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1239]) ).
thf(1368,plain,
! [SV122: $i,SV39: $i] :
( ( ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( power_power_nat @ SV39 ) @ SV122 ) )
= ( hAPP_nat_int @ ( power_power_int @ ( hAPP_nat_int @ semiri1621563631at_int @ SV39 ) ) @ SV122 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1240]) ).
thf(1369,plain,
! [SV123: $i,SV40: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ SV40 ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ SV123 ) )
= ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( plus_plus_nat @ SV40 ) @ SV123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1241]) ).
thf(1370,plain,
! [SV124: $i,SV41: $i] :
( ( ( hAPP_nat_int @ ( power_power_int @ ( hAPP_nat_int @ semiri1621563631at_int @ SV41 ) ) @ SV124 )
= ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( power_power_nat @ SV41 ) @ SV124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1242]) ).
thf(1371,plain,
! [SV125: $i,SV44: $i] :
( ( ! [SY353: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ SV44 ) @ SV125 )
!= ( hAPP_int_int @ ( plus_plus_int @ SY353 ) @ SV125 ) )
| ( SV44 = SY353 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1245]) ).
thf(1372,plain,
! [SV126: $i,SV45: $i] :
( ( ! [SY354: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ SV45 ) @ SV126 )
!= ( hAPP_int_int @ ( plus_plus_int @ SV45 ) @ SY354 ) )
| ( SV126 = SY354 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1246]) ).
thf(1373,plain,
! [SV127: $i,SV46: $i] :
( ( ! [SY355: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ SV46 ) @ SV127 )
!= ( hAPP_int_int @ ( plus_plus_int @ SV46 ) @ SY355 ) )
| ( SV127 = SY355 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1247]) ).
thf(1374,plain,
! [SV128: $i,SV47: $i] :
( ( ! [SY356: $i,SY357: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ SV47 ) @ SV128 ) ) @ ( hAPP_int_int @ ( plus_plus_int @ SY356 ) @ SY357 ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ SV47 ) @ SY356 ) ) @ ( hAPP_int_int @ ( plus_plus_int @ SV128 ) @ SY357 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1248]) ).
thf(1375,plain,
! [SV129: $i,SV48: $i] :
( ( ! [SY358: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ SV48 ) @ SV129 ) ) @ SY358 )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ SV48 ) @ SY358 ) ) @ SV129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1249]) ).
thf(1376,plain,
! [SV130: $i,SV49: $i] :
( ( ! [SY359: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ SV49 ) @ SV130 ) ) @ SY359 )
= ( hAPP_int_int @ ( plus_plus_int @ SV49 ) @ ( hAPP_int_int @ ( plus_plus_int @ SV130 ) @ SY359 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1250]) ).
thf(1377,plain,
! [SV131: $i,SV50: $i] :
( ( ! [SY360: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ SV50 ) @ SV131 ) ) @ SY360 )
= ( hAPP_int_int @ ( plus_plus_int @ SV50 ) @ ( hAPP_int_int @ ( plus_plus_int @ SV131 ) @ SY360 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1251]) ).
thf(1378,plain,
! [SV132: $i,SV51: $i] :
( ( ! [SY361: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ SV51 ) @ ( hAPP_int_int @ ( plus_plus_int @ SV132 ) @ SY361 ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ SV51 ) @ SV132 ) ) @ SY361 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1252]) ).
thf(1379,plain,
! [SV133: $i,SV52: $i] :
( ( ! [SY362: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ SV52 ) @ ( hAPP_int_int @ ( plus_plus_int @ SV133 ) @ SY362 ) )
= ( hAPP_int_int @ ( plus_plus_int @ SV133 ) @ ( hAPP_int_int @ ( plus_plus_int @ SV52 ) @ SY362 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1253]) ).
thf(1380,plain,
! [SV134: $i,SV53: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ SV53 ) @ SV134 )
= ( hAPP_int_int @ ( plus_plus_int @ SV134 ) @ SV53 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1254]) ).
thf(1381,plain,
! [SV135: $i,SV65: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ ( bit1 @ SV65 ) ) @ ( bit1 @ SV135 ) )
= ( bit0 @ ( hAPP_int_int @ ( plus_plus_int @ SV65 ) @ ( succ @ SV135 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1266]) ).
thf(1382,plain,
! [SV136: $i,SV66: $i] :
( ( ( hAPP_nat_int @ ( power_power_int @ ( hAPP_int_int @ ( plus_plus_int @ SV66 ) @ SV136 ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ SV66 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV66 ) @ SV136 ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ SV136 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1267]) ).
thf(1383,plain,
! [SV137: $i,SV67: $i] :
( ( ( times_times_int @ ( bit1 @ SV67 ) @ SV137 )
= ( hAPP_int_int @ ( plus_plus_int @ ( bit0 @ ( times_times_int @ SV67 @ SV137 ) ) ) @ SV137 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1268]) ).
thf(1384,plain,
! [SV138: $i,SV69: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV69 ) @ SV138 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ SV138 ) @ SV69 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1271]) ).
thf(1385,plain,
! [SV139: $i,SV70: $i] :
( ( ! [SY363: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ SV70 ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ SV139 ) @ SY363 ) )
= ( hAPP_nat_nat @ ( plus_plus_nat @ SV139 ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ SV70 ) @ SY363 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1272]) ).
thf(1386,plain,
! [SV140: $i,SV71: $i] :
( ( ! [SY364: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ SV71 ) @ SV140 ) ) @ SY364 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ SV71 ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ SV140 ) @ SY364 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1273]) ).
thf(1387,plain,
! [SV141: $i,SV72: $i] :
( ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV72 ) @ SV141 )
!= SV72 )
| ( SV141 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1274]) ).
thf(1388,plain,
! [SV142: $i,SV77: $i] :
( ( ( hAPP_nat_nat @ semiri984289939at_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ SV77 ) @ SV142 ) )
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ semiri984289939at_nat @ SV77 ) ) @ ( hAPP_nat_nat @ semiri984289939at_nat @ SV142 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1283]) ).
thf(1389,plain,
! [SV143: $i,SV78: $i] :
( ( ( hAPP_nat_nat @ semiri984289939at_nat @ ( hAPP_nat_nat @ ( power_power_nat @ SV78 ) @ SV143 ) )
= ( hAPP_nat_nat @ ( power_power_nat @ ( hAPP_nat_nat @ semiri984289939at_nat @ SV78 ) ) @ SV143 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1284]) ).
thf(1390,plain,
! [SV144: $i,SV81: $i] :
( ( ! [SY365: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV81 ) @ SV144 )
!= ( hAPP_nat_nat @ ( plus_plus_nat @ SY365 ) @ SV144 ) )
| ( SV81 = SY365 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1287]) ).
thf(1391,plain,
! [SV145: $i,SV82: $i] :
( ( ! [SY366: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV82 ) @ SV145 )
!= ( hAPP_nat_nat @ ( plus_plus_nat @ SV82 ) @ SY366 ) )
| ( SV145 = SY366 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1288]) ).
thf(1392,plain,
! [SV146: $i,SV83: $i] :
( ( ! [SY367: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV83 ) @ SV146 )
!= ( hAPP_nat_nat @ ( plus_plus_nat @ SV83 ) @ SY367 ) )
| ( SV146 = SY367 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1289]) ).
thf(1393,plain,
! [SV147: $i,SV84: $i] :
( ( ! [SY368: $i,SY369: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ SV84 ) @ SV147 ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ SY368 ) @ SY369 ) )
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ SV84 ) @ SY368 ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ SV147 ) @ SY369 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1290]) ).
thf(1394,plain,
! [SV148: $i,SV85: $i] :
( ( ! [SY370: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ SV85 ) @ SV148 ) ) @ SY370 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ SV85 ) @ SY370 ) ) @ SV148 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1291]) ).
thf(1395,plain,
! [SV149: $i,SV86: $i] :
( ( ! [SY371: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ SV86 ) @ SV149 ) ) @ SY371 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ SV86 ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ SV149 ) @ SY371 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1292]) ).
thf(1396,plain,
! [SV150: $i,SV87: $i] :
( ( ! [SY372: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ SV87 ) @ SV150 ) ) @ SY372 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ SV87 ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ SV150 ) @ SY372 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1293]) ).
thf(1397,plain,
! [SV151: $i,SV88: $i] :
( ( ! [SY373: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ SV88 ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ SV151 ) @ SY373 ) )
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ SV88 ) @ SV151 ) ) @ SY373 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1294]) ).
thf(1398,plain,
! [SV152: $i,SV89: $i] :
( ( ! [SY374: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ SV89 ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ SV152 ) @ SY374 ) )
= ( hAPP_nat_nat @ ( plus_plus_nat @ SV152 ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ SV89 ) @ SY374 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1295]) ).
thf(1399,plain,
! [SV153: $i,SV90: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV90 ) @ SV153 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ SV153 ) @ SV90 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1296]) ).
thf(1400,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != zero_zero_nat )
| ( ( hAPP_nat_nat @ ( power_power_nat @ zero_zero_nat ) @ SX0 )
= one_one_nat ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1304]) ).
thf(1401,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 = zero_zero_nat )
| ( ( hAPP_nat_nat @ ( power_power_nat @ zero_zero_nat ) @ SX0 )
= zero_zero_nat ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1304]) ).
thf(1402,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( number_number_of_nat @ SX1 )
= zero_zero_nat )
| ( SX0 != zero_zero_nat )
| ( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) )
= zero_zero_nat ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1305]) ).
thf(1403,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_nat )
| ( ( number_number_of_nat @ SX1 )
!= zero_zero_nat ) )
| ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_nat )
| ( SX0 = zero_zero_nat ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1305]) ).
thf(1404,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( hAPP_nat_int @ semiri1621563631at_int @ SX0 )
!= ( hAPP_nat_int @ semiri1621563631at_int @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1306]) ).
thf(1405,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( hAPP_nat_int @ semiri1621563631at_int @ SX0 )
= ( hAPP_nat_int @ semiri1621563631at_int @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1306]) ).
thf(1406,plain,
! [SV98: $i] :
( ( ~ ! [SY325: $i,SY326: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV98 ) @ SY325 )
!= ( hAPP_nat_nat @ ( plus_plus_nat @ SV98 ) @ SY326 ) )
| ( SY325 = SY326 ) )
| ~ ! [SY327: $i,SY328: $i] :
( ( SY327 != SY328 )
| ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV98 ) @ SY327 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ SV98 ) @ SY328 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1307]) ).
thf(1407,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( hAPP_nat_int @ semiri1621563631at_int @ SX0 )
!= ( hAPP_nat_int @ semiri1621563631at_int @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1308]) ).
thf(1408,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( hAPP_nat_int @ semiri1621563631at_int @ SX0 )
= ( hAPP_nat_int @ semiri1621563631at_int @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1308]) ).
thf(1409,plain,
( ( ~ ! [SX0: $i] :
( ( ( number_number_of_nat @ SX0 )
!= zero_zero_nat )
| ( ( hAPP_nat_nat @ ( power_power_nat @ zero_zero_nat ) @ ( number_number_of_nat @ SX0 ) )
= one_one_nat ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1309]) ).
thf(1410,plain,
( ( ~ ! [SX0: $i] :
( ( ( number_number_of_nat @ SX0 )
= zero_zero_nat )
| ( ( hAPP_nat_nat @ ( power_power_nat @ zero_zero_nat ) @ ( number_number_of_nat @ SX0 ) )
= zero_zero_nat ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1309]) ).
thf(1411,plain,
! [SV99: $i] :
( ( ~ ! [SY329: $i,SY330: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV99 ) @ SY329 )
!= ( hAPP_nat_nat @ ( plus_plus_nat @ SV99 ) @ SY330 ) )
| ( SY329 = SY330 ) )
| ~ ! [SY331: $i,SY332: $i] :
( ( SY331 != SY332 )
| ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV99 ) @ SY331 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ SV99 ) @ SY332 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1310]) ).
thf(1412,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( bit0 @ SX0 )
!= ( bit0 @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1311]) ).
thf(1413,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( bit0 @ SX0 )
= ( bit0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1311]) ).
thf(1414,plain,
( ( ~ ! [SX0: $i] :
( ( zero_zero_int
!= ( hAPP_int_int @ ( plus_plus_int @ SX0 ) @ SX0 ) )
| ( SX0 = zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1312]) ).
thf(1415,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != zero_zero_int )
| ( zero_zero_int
= ( hAPP_int_int @ ( plus_plus_int @ SX0 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1312]) ).
thf(1416,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( number267125858f_real @ SX0 )
!= ( number267125858f_real @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1313]) ).
thf(1417,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( number267125858f_real @ SX0 )
= ( number267125858f_real @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1313]) ).
thf(1418,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( hAPP_nat_nat @ ( plus_plus_nat @ SX0 ) @ SX1 ) )
| ( SX1 = zero_zero_nat ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1314]) ).
thf(1419,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1 != zero_zero_nat )
| ( SX0
= ( hAPP_nat_nat @ ( plus_plus_nat @ SX0 ) @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1314]) ).
thf(1420,plain,
( ( ~ ! [SX0: $i] :
( ( ( number_number_of_nat @ SX0 )
!= zero_zero_nat )
| ( ( hAPP_nat_int @ ( power_power_int @ zero_zero_int ) @ ( number_number_of_nat @ SX0 ) )
= one_one_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1315]) ).
thf(1421,plain,
( ( ~ ! [SX0: $i] :
( ( ( number_number_of_nat @ SX0 )
= zero_zero_nat )
| ( ( hAPP_nat_int @ ( power_power_int @ zero_zero_int ) @ ( number_number_of_nat @ SX0 ) )
= zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1315]) ).
thf(1422,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( number_number_of_int @ SX0 )
!= ( number_number_of_int @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1316]) ).
thf(1423,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( number_number_of_int @ SX0 )
= ( number_number_of_int @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1316]) ).
thf(1424,plain,
( ( ~ ! [SX0: $i] :
( ( zero_zero_real != SX0 )
| ( SX0 = zero_zero_real ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1317]) ).
thf(1425,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != zero_zero_real )
| ( zero_zero_real = SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1317]) ).
thf(1426,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( bit1 @ SX0 )
!= ( bit1 @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1318]) ).
thf(1427,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( bit1 @ SX0 )
= ( bit1 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1318]) ).
thf(1428,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ SX1 )
!= one_one_nat )
| ( SX0 = one_one_nat )
| ( SX1 = zero_zero_nat ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1319]) ).
thf(1429,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != one_one_nat )
| ! [SX1: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ SX1 )
= one_one_nat ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1 != zero_zero_nat )
| ( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ SX1 )
= one_one_nat ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1319]) ).
thf(1430,plain,
( ( ~ ! [SX0: $i] :
( ( ( hAPP_nat_int @ ( power_power_int @ SX0 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1320]) ).
thf(1431,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != zero_zero_int )
| ( ( hAPP_nat_int @ ( power_power_int @ SX0 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1320]) ).
thf(1432,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( hAPP_nat_nat @ semiri984289939at_nat @ SX0 )
!= ( hAPP_nat_nat @ semiri984289939at_nat @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1321]) ).
thf(1433,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( hAPP_nat_nat @ semiri984289939at_nat @ SX0 )
= ( hAPP_nat_nat @ semiri984289939at_nat @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1321]) ).
thf(1434,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != zero_zero_nat )
| ( ( hAPP_nat_int @ ( power_power_int @ zero_zero_int ) @ SX0 )
= one_one_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1322]) ).
thf(1435,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 = zero_zero_nat )
| ( ( hAPP_nat_int @ ( power_power_int @ zero_zero_int ) @ SX0 )
= zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1322]) ).
thf(1436,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( hAPP_nat_int @ semiri1621563631at_int @ SX0 )
!= ( hAPP_nat_int @ semiri1621563631at_int @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1323]) ).
thf(1437,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( hAPP_nat_int @ semiri1621563631at_int @ SX0 )
= ( hAPP_nat_int @ semiri1621563631at_int @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1323]) ).
thf(1438,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1 = zero_zero_nat )
| ( SX0 != zero_zero_nat )
| ( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ SX1 )
= zero_zero_nat ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1324]) ).
thf(1439,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ SX1 )
!= zero_zero_nat )
| ( SX1 != zero_zero_nat ) )
| ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ SX1 )
!= zero_zero_nat )
| ( SX0 = zero_zero_nat ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1324]) ).
thf(1440,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( number_number_of_nat @ SX1 )
= zero_zero_nat )
| ( SX0 != zero_zero_int )
| ( ( hAPP_nat_int @ ( power_power_int @ SX0 ) @ ( number_number_of_nat @ SX1 ) )
= zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1325]) ).
thf(1441,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( hAPP_nat_int @ ( power_power_int @ SX0 ) @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_int )
| ( ( number_number_of_nat @ SX1 )
!= zero_zero_nat ) )
| ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( hAPP_nat_int @ ( power_power_int @ SX0 ) @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1325]) ).
thf(1442,plain,
! [SV100: $i] :
( ( ~ ! [SY333: $i,SY334: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV100 ) @ SY333 )
!= ( hAPP_nat_nat @ ( plus_plus_nat @ SY334 ) @ SY333 ) )
| ( SV100 = SY334 ) )
| ~ ! [SY335: $i,SY336: $i] :
( ( SV100 != SY336 )
| ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV100 ) @ SY335 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ SY336 ) @ SY335 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1326]) ).
thf(1443,plain,
! [SV101: $i] :
( ( ~ ! [SY337: $i,SY338: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ SV101 ) @ SY337 )
!= ( hAPP_int_int @ ( plus_plus_int @ SY338 ) @ SY337 ) )
| ( SV101 = SY338 ) )
| ~ ! [SY339: $i,SY340: $i] :
( ( SV101 != SY340 )
| ( ( hAPP_int_int @ ( plus_plus_int @ SV101 ) @ SY339 )
= ( hAPP_int_int @ ( plus_plus_int @ SY340 ) @ SY339 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1327]) ).
thf(1444,plain,
( ( ~ ! [SX0: $i] :
( ( ( bit0 @ SX0 )
!= pls )
| ( SX0 = pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1328]) ).
thf(1445,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != pls )
| ( ( bit0 @ SX0 )
= pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1328]) ).
thf(1446,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( number267125858f_real @ SX0 )
!= SX1 )
| ( SX1
= ( number267125858f_real @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1329]) ).
thf(1447,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( number267125858f_real @ SX0 ) )
| ( ( number267125858f_real @ SX0 )
= SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1329]) ).
thf(1448,plain,
( ( ~ ! [SX0: $i] :
( ( one_one_nat != SX0 )
| ( SX0 = one_one_nat ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1330]) ).
thf(1449,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != one_one_nat )
| ( one_one_nat = SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1330]) ).
thf(1450,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( number_number_of_nat @ SX0 )
!= SX1 )
| ( SX1
= ( number_number_of_nat @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1331]) ).
thf(1451,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( number_number_of_nat @ SX0 ) )
| ( ( number_number_of_nat @ SX0 )
= SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1331]) ).
thf(1452,plain,
( ( ~ ! [SX0: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ SX0 ) @ SX0 )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1332]) ).
thf(1453,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != zero_zero_int )
| ( ( hAPP_int_int @ ( plus_plus_int @ SX0 ) @ SX0 )
= zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1332]) ).
thf(1454,plain,
( ( ~ ! [SX0: $i] :
( ( one_one_real != SX0 )
| ( SX0 = one_one_real ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1333]) ).
thf(1455,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != one_one_real )
| ( one_one_real = SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1333]) ).
thf(1456,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1 = zero_zero_nat )
| ( SX0 != zero_zero_int )
| ( ( hAPP_nat_int @ ( power_power_int @ SX0 ) @ SX1 )
= zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1334]) ).
thf(1457,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( hAPP_nat_int @ ( power_power_int @ SX0 ) @ SX1 )
!= zero_zero_int )
| ( SX1 != zero_zero_nat ) )
| ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( hAPP_nat_int @ ( power_power_int @ SX0 ) @ SX1 )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1334]) ).
thf(1458,plain,
( ( ~ ! [SX0: $i] :
( ( zero_zero_int != SX0 )
| ( SX0 = zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1335]) ).
thf(1459,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != zero_zero_int )
| ( zero_zero_int = SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1335]) ).
thf(1460,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != zero_zero_nat )
| ( SX1 != zero_zero_nat )
| ( ( hAPP_nat_nat @ ( plus_plus_nat @ SX0 ) @ SX1 )
= zero_zero_nat ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1336]) ).
thf(1461,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ SX0 ) @ SX1 )
!= zero_zero_nat )
| ( SX0 = zero_zero_nat ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SX0 ) @ SX1 )
!= zero_zero_nat )
| ( SX1 = zero_zero_nat ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1336]) ).
thf(1462,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( number_number_of_int @ SX0 )
!= SX1 )
| ( SX1
= ( number_number_of_int @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1337]) ).
thf(1463,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( number_number_of_int @ SX0 ) )
| ( ( number_number_of_int @ SX0 )
= SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1337]) ).
thf(1464,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != zero_zero_int )
| ( SX1 != zero_zero_int )
| ( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ SX0 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ SX1 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1338]) ).
thf(1465,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ SX0 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ SX1 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ SX0 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( 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)],[1338]) ).
thf(1466,plain,
( ( ~ ! [SX0: $i] :
( ( ( hAPP_nat_int @ semiri1621563631at_int @ SX0 )
!= zero_zero_int )
| ( SX0 = zero_zero_nat ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1339]) ).
thf(1467,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != zero_zero_nat )
| ( ( hAPP_nat_int @ semiri1621563631at_int @ SX0 )
= zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1339]) ).
thf(1468,plain,
! [SV102: $i] :
( ( ~ ! [SY341: $i,SY342: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV102 ) @ SY341 )
!= ( hAPP_nat_nat @ ( plus_plus_nat @ SY342 ) @ SY341 ) )
| ( SV102 = SY342 ) )
| ~ ! [SY343: $i,SY344: $i] :
( ( SV102 != SY344 )
| ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV102 ) @ SY343 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ SY344 ) @ SY343 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1340]) ).
thf(1469,plain,
( ( ~ ! [SX0: $i] :
( ( one_one_int != SX0 )
| ( SX0 = one_one_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1341]) ).
thf(1470,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != one_one_int )
| ( one_one_int = SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1341]) ).
thf(1471,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1 = zero_zero_nat )
| ( SX0 != zero_zero_nat )
| ( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ SX1 )
= zero_zero_nat ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1342]) ).
thf(1472,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ SX1 )
!= zero_zero_nat )
| ( SX1 != zero_zero_nat ) )
| ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ SX1 )
!= zero_zero_nat )
| ( SX0 = zero_zero_nat ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1342]) ).
thf(1473,plain,
( ( ~ ! [SX0: $i] :
( ( zero_zero_nat != SX0 )
| ( SX0 = zero_zero_nat ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1343]) ).
thf(1474,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != zero_zero_nat )
| ( zero_zero_nat = SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1343]) ).
thf(1475,plain,
! [SV103: $i] :
( ( ~ ! [SY345: $i,SY346: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ SV103 ) @ SY345 )
!= ( hAPP_int_int @ ( plus_plus_int @ SV103 ) @ SY346 ) )
| ( SY345 = SY346 ) )
| ~ ! [SY347: $i,SY348: $i] :
( ( SY347 != SY348 )
| ( ( hAPP_int_int @ ( plus_plus_int @ SV103 ) @ SY347 )
= ( hAPP_int_int @ ( plus_plus_int @ SV103 ) @ SY348 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1344]) ).
thf(1476,plain,
( ( ~ ! [SX0: $i] :
( ( pls
!= ( bit0 @ SX0 ) )
| ( pls = SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1345]) ).
thf(1477,plain,
( ( ~ ! [SX0: $i] :
( ( pls != SX0 )
| ( pls
= ( bit0 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1345]) ).
thf(1478,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( hAPP_int_int @ ( plus_plus_int @ SX0 ) @ SX1 ) )
| ( SX1 = zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1346]) ).
thf(1479,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1 != zero_zero_int )
| ( SX0
= ( hAPP_int_int @ ( plus_plus_int @ SX0 ) @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1346]) ).
thf(1480,plain,
! [SV154: $i,SV107: $i,SV7: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ SV7 ) ) @ ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ SV107 ) ) @ SV154 ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( plus_plus_nat @ SV7 ) @ SV107 ) ) ) @ SV154 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1350]) ).
thf(1481,plain,
! [SV155: $i,SV109: $i,SV9: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ SV9 ) @ SV109 ) ) @ SV155 )
= ( hAPP_int_int @ ( plus_plus_int @ SV9 ) @ ( hAPP_int_int @ ( plus_plus_int @ SV109 ) @ SV155 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1352]) ).
thf(1482,plain,
! [SV156: $i,SV110: $i,SV10: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ SV10 ) @ ( hAPP_int_int @ ( plus_plus_int @ SV110 ) @ SV156 ) )
= ( hAPP_int_int @ ( plus_plus_int @ SV110 ) @ ( hAPP_int_int @ ( plus_plus_int @ SV10 ) @ SV156 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1353]) ).
thf(1483,plain,
! [SV112: $i,SV14: $i] :
( ( ( bit1 @ SV14 )
= ( bit0 @ SV112 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1357]) ).
thf(1484,plain,
! [SV113: $i,SV15: $i] :
( ( ( bit0 @ SV15 )
= ( bit1 @ SV113 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1358]) ).
thf(1485,plain,
! [SV157: $i,SV115: $i,SV24: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ ( number_number_of_int @ SV24 ) ) @ ( hAPP_int_int @ ( plus_plus_int @ ( number_number_of_int @ SV115 ) ) @ SV157 ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( number_number_of_int @ ( hAPP_int_int @ ( plus_plus_int @ SV24 ) @ SV115 ) ) ) @ SV157 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1360]) ).
thf(1486,plain,
! [SV36: $i,SV120: $i] :
( ( ( SV120 = zero_zero_int )
= $true )
| ( ( ( ( hAPP_nat_int @ ( power_power_int @ SV120 ) @ SV36 )
!= zero_zero_int ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1366]) ).
thf(1487,plain,
! [SV158: $i,SV125: $i,SV44: $i] :
( ( ( ( hAPP_int_int @ ( plus_plus_int @ SV44 ) @ SV125 )
!= ( hAPP_int_int @ ( plus_plus_int @ SV158 ) @ SV125 ) )
| ( SV44 = SV158 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1371]) ).
thf(1488,plain,
! [SV159: $i,SV126: $i,SV45: $i] :
( ( ( ( hAPP_int_int @ ( plus_plus_int @ SV45 ) @ SV126 )
!= ( hAPP_int_int @ ( plus_plus_int @ SV45 ) @ SV159 ) )
| ( SV126 = SV159 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1372]) ).
thf(1489,plain,
! [SV160: $i,SV127: $i,SV46: $i] :
( ( ( ( hAPP_int_int @ ( plus_plus_int @ SV46 ) @ SV127 )
!= ( hAPP_int_int @ ( plus_plus_int @ SV46 ) @ SV160 ) )
| ( SV127 = SV160 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1373]) ).
thf(1490,plain,
! [SV161: $i,SV128: $i,SV47: $i] :
( ( ! [SY375: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ SV47 ) @ SV128 ) ) @ ( hAPP_int_int @ ( plus_plus_int @ SV161 ) @ SY375 ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ SV47 ) @ SV161 ) ) @ ( hAPP_int_int @ ( plus_plus_int @ SV128 ) @ SY375 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1374]) ).
thf(1491,plain,
! [SV162: $i,SV129: $i,SV48: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ SV48 ) @ SV129 ) ) @ SV162 )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ SV48 ) @ SV162 ) ) @ SV129 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1375]) ).
thf(1492,plain,
! [SV163: $i,SV130: $i,SV49: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ SV49 ) @ SV130 ) ) @ SV163 )
= ( hAPP_int_int @ ( plus_plus_int @ SV49 ) @ ( hAPP_int_int @ ( plus_plus_int @ SV130 ) @ SV163 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1376]) ).
thf(1493,plain,
! [SV164: $i,SV131: $i,SV50: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ SV50 ) @ SV131 ) ) @ SV164 )
= ( hAPP_int_int @ ( plus_plus_int @ SV50 ) @ ( hAPP_int_int @ ( plus_plus_int @ SV131 ) @ SV164 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1377]) ).
thf(1494,plain,
! [SV165: $i,SV132: $i,SV51: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ SV51 ) @ ( hAPP_int_int @ ( plus_plus_int @ SV132 ) @ SV165 ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ SV51 ) @ SV132 ) ) @ SV165 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1378]) ).
thf(1495,plain,
! [SV166: $i,SV133: $i,SV52: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ SV52 ) @ ( hAPP_int_int @ ( plus_plus_int @ SV133 ) @ SV166 ) )
= ( hAPP_int_int @ ( plus_plus_int @ SV133 ) @ ( hAPP_int_int @ ( plus_plus_int @ SV52 ) @ SV166 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1379]) ).
thf(1496,plain,
! [SV167: $i,SV139: $i,SV70: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV70 ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ SV139 ) @ SV167 ) )
= ( hAPP_nat_nat @ ( plus_plus_nat @ SV139 ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ SV70 ) @ SV167 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1385]) ).
thf(1497,plain,
! [SV168: $i,SV140: $i,SV71: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ SV71 ) @ SV140 ) ) @ SV168 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ SV71 ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ SV140 ) @ SV168 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1386]) ).
thf(1498,plain,
! [SV141: $i,SV72: $i] :
( ( ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV72 ) @ SV141 )
!= SV72 ) )
= $true )
| ( ( SV141 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1387]) ).
thf(1499,plain,
! [SV169: $i,SV144: $i,SV81: $i] :
( ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV81 ) @ SV144 )
!= ( hAPP_nat_nat @ ( plus_plus_nat @ SV169 ) @ SV144 ) )
| ( SV81 = SV169 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1390]) ).
thf(1500,plain,
! [SV170: $i,SV145: $i,SV82: $i] :
( ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV82 ) @ SV145 )
!= ( hAPP_nat_nat @ ( plus_plus_nat @ SV82 ) @ SV170 ) )
| ( SV145 = SV170 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1391]) ).
thf(1501,plain,
! [SV171: $i,SV146: $i,SV83: $i] :
( ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV83 ) @ SV146 )
!= ( hAPP_nat_nat @ ( plus_plus_nat @ SV83 ) @ SV171 ) )
| ( SV146 = SV171 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1392]) ).
thf(1502,plain,
! [SV172: $i,SV147: $i,SV84: $i] :
( ( ! [SY376: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ SV84 ) @ SV147 ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ SV172 ) @ SY376 ) )
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ SV84 ) @ SV172 ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ SV147 ) @ SY376 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1393]) ).
thf(1503,plain,
! [SV173: $i,SV148: $i,SV85: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ SV85 ) @ SV148 ) ) @ SV173 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ SV85 ) @ SV173 ) ) @ SV148 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1394]) ).
thf(1504,plain,
! [SV174: $i,SV149: $i,SV86: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ SV86 ) @ SV149 ) ) @ SV174 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ SV86 ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ SV149 ) @ SV174 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1395]) ).
thf(1505,plain,
! [SV175: $i,SV150: $i,SV87: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ SV87 ) @ SV150 ) ) @ SV175 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ SV87 ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ SV150 ) @ SV175 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1396]) ).
thf(1506,plain,
! [SV176: $i,SV151: $i,SV88: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV88 ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ SV151 ) @ SV176 ) )
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ SV88 ) @ SV151 ) ) @ SV176 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1397]) ).
thf(1507,plain,
! [SV177: $i,SV152: $i,SV89: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV89 ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ SV152 ) @ SV177 ) )
= ( hAPP_nat_nat @ ( plus_plus_nat @ SV152 ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ SV89 ) @ SV177 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1398]) ).
thf(1508,plain,
( ( ! [SX0: $i] :
( ( SX0 != zero_zero_nat )
| ( ( hAPP_nat_nat @ ( power_power_nat @ zero_zero_nat ) @ SX0 )
= one_one_nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1400]) ).
thf(1509,plain,
( ( ! [SX0: $i] :
( ( SX0 = zero_zero_nat )
| ( ( hAPP_nat_nat @ ( power_power_nat @ zero_zero_nat ) @ SX0 )
= zero_zero_nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1401]) ).
thf(1510,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( number_number_of_nat @ SX1 )
= zero_zero_nat )
| ( SX0 != zero_zero_nat )
| ( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) )
= zero_zero_nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1402]) ).
thf(1511,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_nat )
| ( ( number_number_of_nat @ SX1 )
!= zero_zero_nat ) )
| ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_nat )
| ( SX0 = zero_zero_nat ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1403]) ).
thf(1512,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( hAPP_nat_int @ semiri1621563631at_int @ SX0 )
!= ( hAPP_nat_int @ semiri1621563631at_int @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1404]) ).
thf(1513,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( hAPP_nat_int @ semiri1621563631at_int @ SX0 )
= ( hAPP_nat_int @ semiri1621563631at_int @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1405]) ).
thf(1514,plain,
! [SV98: $i] :
( ( ~ ! [SY325: $i,SY326: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV98 ) @ SY325 )
!= ( hAPP_nat_nat @ ( plus_plus_nat @ SV98 ) @ SY326 ) )
| ( SY325 = SY326 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1406]) ).
thf(1515,plain,
! [SV98: $i] :
( ( ~ ! [SY327: $i,SY328: $i] :
( ( SY327 != SY328 )
| ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV98 ) @ SY327 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ SV98 ) @ SY328 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1406]) ).
thf(1516,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( hAPP_nat_int @ semiri1621563631at_int @ SX0 )
!= ( hAPP_nat_int @ semiri1621563631at_int @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1407]) ).
thf(1517,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( hAPP_nat_int @ semiri1621563631at_int @ SX0 )
= ( hAPP_nat_int @ semiri1621563631at_int @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1408]) ).
thf(1518,plain,
( ( ! [SX0: $i] :
( ( ( number_number_of_nat @ SX0 )
!= zero_zero_nat )
| ( ( hAPP_nat_nat @ ( power_power_nat @ zero_zero_nat ) @ ( number_number_of_nat @ SX0 ) )
= one_one_nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1409]) ).
thf(1519,plain,
( ( ! [SX0: $i] :
( ( ( number_number_of_nat @ SX0 )
= zero_zero_nat )
| ( ( hAPP_nat_nat @ ( power_power_nat @ zero_zero_nat ) @ ( number_number_of_nat @ SX0 ) )
= zero_zero_nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1410]) ).
thf(1520,plain,
! [SV99: $i] :
( ( ~ ! [SY329: $i,SY330: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV99 ) @ SY329 )
!= ( hAPP_nat_nat @ ( plus_plus_nat @ SV99 ) @ SY330 ) )
| ( SY329 = SY330 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1411]) ).
thf(1521,plain,
! [SV99: $i] :
( ( ~ ! [SY331: $i,SY332: $i] :
( ( SY331 != SY332 )
| ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV99 ) @ SY331 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ SV99 ) @ SY332 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1411]) ).
thf(1522,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( bit0 @ SX0 )
!= ( bit0 @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1412]) ).
thf(1523,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( bit0 @ SX0 )
= ( bit0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1413]) ).
thf(1524,plain,
( ( ! [SX0: $i] :
( ( zero_zero_int
!= ( hAPP_int_int @ ( plus_plus_int @ SX0 ) @ SX0 ) )
| ( SX0 = zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1414]) ).
thf(1525,plain,
( ( ! [SX0: $i] :
( ( SX0 != zero_zero_int )
| ( zero_zero_int
= ( hAPP_int_int @ ( plus_plus_int @ SX0 ) @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1415]) ).
thf(1526,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( number267125858f_real @ SX0 )
!= ( number267125858f_real @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1416]) ).
thf(1527,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( number267125858f_real @ SX0 )
= ( number267125858f_real @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1417]) ).
thf(1528,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( hAPP_nat_nat @ ( plus_plus_nat @ SX0 ) @ SX1 ) )
| ( SX1 = zero_zero_nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1418]) ).
thf(1529,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1 != zero_zero_nat )
| ( SX0
= ( hAPP_nat_nat @ ( plus_plus_nat @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1419]) ).
thf(1530,plain,
( ( ! [SX0: $i] :
( ( ( number_number_of_nat @ SX0 )
!= zero_zero_nat )
| ( ( hAPP_nat_int @ ( power_power_int @ zero_zero_int ) @ ( number_number_of_nat @ SX0 ) )
= one_one_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1420]) ).
thf(1531,plain,
( ( ! [SX0: $i] :
( ( ( number_number_of_nat @ SX0 )
= zero_zero_nat )
| ( ( hAPP_nat_int @ ( power_power_int @ zero_zero_int ) @ ( number_number_of_nat @ SX0 ) )
= zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1421]) ).
thf(1532,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( number_number_of_int @ SX0 )
!= ( number_number_of_int @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1422]) ).
thf(1533,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( number_number_of_int @ SX0 )
= ( number_number_of_int @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1423]) ).
thf(1534,plain,
( ( ! [SX0: $i] :
( ( zero_zero_real != SX0 )
| ( SX0 = zero_zero_real ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1424]) ).
thf(1535,plain,
( ( ! [SX0: $i] :
( ( SX0 != zero_zero_real )
| ( zero_zero_real = SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1425]) ).
thf(1536,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( bit1 @ SX0 )
!= ( bit1 @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1426]) ).
thf(1537,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( bit1 @ SX0 )
= ( bit1 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1427]) ).
thf(1538,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ SX1 )
!= one_one_nat )
| ( SX0 = one_one_nat )
| ( SX1 = zero_zero_nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1428]) ).
thf(1539,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( SX0 != one_one_nat )
| ! [SX1: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ SX1 )
= one_one_nat ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1 != zero_zero_nat )
| ( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ SX1 )
= one_one_nat ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1429]) ).
thf(1540,plain,
( ( ! [SX0: $i] :
( ( ( hAPP_nat_int @ ( power_power_int @ SX0 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1430]) ).
thf(1541,plain,
( ( ! [SX0: $i] :
( ( SX0 != zero_zero_int )
| ( ( hAPP_nat_int @ ( power_power_int @ SX0 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1431]) ).
thf(1542,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( hAPP_nat_nat @ semiri984289939at_nat @ SX0 )
!= ( hAPP_nat_nat @ semiri984289939at_nat @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1432]) ).
thf(1543,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( hAPP_nat_nat @ semiri984289939at_nat @ SX0 )
= ( hAPP_nat_nat @ semiri984289939at_nat @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1433]) ).
thf(1544,plain,
( ( ! [SX0: $i] :
( ( SX0 != zero_zero_nat )
| ( ( hAPP_nat_int @ ( power_power_int @ zero_zero_int ) @ SX0 )
= one_one_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1434]) ).
thf(1545,plain,
( ( ! [SX0: $i] :
( ( SX0 = zero_zero_nat )
| ( ( hAPP_nat_int @ ( power_power_int @ zero_zero_int ) @ SX0 )
= zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1435]) ).
thf(1546,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( hAPP_nat_int @ semiri1621563631at_int @ SX0 )
!= ( hAPP_nat_int @ semiri1621563631at_int @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1436]) ).
thf(1547,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( hAPP_nat_int @ semiri1621563631at_int @ SX0 )
= ( hAPP_nat_int @ semiri1621563631at_int @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1437]) ).
thf(1548,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1 = zero_zero_nat )
| ( SX0 != zero_zero_nat )
| ( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ SX1 )
= zero_zero_nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1438]) ).
thf(1549,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ SX1 )
!= zero_zero_nat )
| ( SX1 != zero_zero_nat ) )
| ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ SX1 )
!= zero_zero_nat )
| ( SX0 = zero_zero_nat ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1439]) ).
thf(1550,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( number_number_of_nat @ SX1 )
= zero_zero_nat )
| ( SX0 != zero_zero_int )
| ( ( hAPP_nat_int @ ( power_power_int @ SX0 ) @ ( number_number_of_nat @ SX1 ) )
= zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1440]) ).
thf(1551,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( hAPP_nat_int @ ( power_power_int @ SX0 ) @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_int )
| ( ( number_number_of_nat @ SX1 )
!= zero_zero_nat ) )
| ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( hAPP_nat_int @ ( power_power_int @ SX0 ) @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1441]) ).
thf(1552,plain,
! [SV100: $i] :
( ( ~ ! [SY333: $i,SY334: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV100 ) @ SY333 )
!= ( hAPP_nat_nat @ ( plus_plus_nat @ SY334 ) @ SY333 ) )
| ( SV100 = SY334 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1442]) ).
thf(1553,plain,
! [SV100: $i] :
( ( ~ ! [SY335: $i,SY336: $i] :
( ( SV100 != SY336 )
| ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV100 ) @ SY335 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ SY336 ) @ SY335 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1442]) ).
thf(1554,plain,
! [SV101: $i] :
( ( ~ ! [SY337: $i,SY338: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ SV101 ) @ SY337 )
!= ( hAPP_int_int @ ( plus_plus_int @ SY338 ) @ SY337 ) )
| ( SV101 = SY338 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1443]) ).
thf(1555,plain,
! [SV101: $i] :
( ( ~ ! [SY339: $i,SY340: $i] :
( ( SV101 != SY340 )
| ( ( hAPP_int_int @ ( plus_plus_int @ SV101 ) @ SY339 )
= ( hAPP_int_int @ ( plus_plus_int @ SY340 ) @ SY339 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1443]) ).
thf(1556,plain,
( ( ! [SX0: $i] :
( ( ( bit0 @ SX0 )
!= pls )
| ( SX0 = pls ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1444]) ).
thf(1557,plain,
( ( ! [SX0: $i] :
( ( SX0 != pls )
| ( ( bit0 @ SX0 )
= pls ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1445]) ).
thf(1558,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( number267125858f_real @ SX0 )
!= SX1 )
| ( SX1
= ( number267125858f_real @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1446]) ).
thf(1559,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( number267125858f_real @ SX0 ) )
| ( ( number267125858f_real @ SX0 )
= SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1447]) ).
thf(1560,plain,
( ( ! [SX0: $i] :
( ( one_one_nat != SX0 )
| ( SX0 = one_one_nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1448]) ).
thf(1561,plain,
( ( ! [SX0: $i] :
( ( SX0 != one_one_nat )
| ( one_one_nat = SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1449]) ).
thf(1562,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( number_number_of_nat @ SX0 )
!= SX1 )
| ( SX1
= ( number_number_of_nat @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1450]) ).
thf(1563,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( number_number_of_nat @ SX0 ) )
| ( ( number_number_of_nat @ SX0 )
= SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1451]) ).
thf(1564,plain,
( ( ! [SX0: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ SX0 ) @ SX0 )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1452]) ).
thf(1565,plain,
( ( ! [SX0: $i] :
( ( SX0 != zero_zero_int )
| ( ( hAPP_int_int @ ( plus_plus_int @ SX0 ) @ SX0 )
= zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1453]) ).
thf(1566,plain,
( ( ! [SX0: $i] :
( ( one_one_real != SX0 )
| ( SX0 = one_one_real ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1454]) ).
thf(1567,plain,
( ( ! [SX0: $i] :
( ( SX0 != one_one_real )
| ( one_one_real = SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1455]) ).
thf(1568,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1 = zero_zero_nat )
| ( SX0 != zero_zero_int )
| ( ( hAPP_nat_int @ ( power_power_int @ SX0 ) @ SX1 )
= zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1456]) ).
thf(1569,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( hAPP_nat_int @ ( power_power_int @ SX0 ) @ SX1 )
!= zero_zero_int )
| ( SX1 != zero_zero_nat ) )
| ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( hAPP_nat_int @ ( power_power_int @ SX0 ) @ SX1 )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1457]) ).
thf(1570,plain,
( ( ! [SX0: $i] :
( ( zero_zero_int != SX0 )
| ( SX0 = zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1458]) ).
thf(1571,plain,
( ( ! [SX0: $i] :
( ( SX0 != zero_zero_int )
| ( zero_zero_int = SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1459]) ).
thf(1572,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != zero_zero_nat )
| ( SX1 != zero_zero_nat )
| ( ( hAPP_nat_nat @ ( plus_plus_nat @ SX0 ) @ SX1 )
= zero_zero_nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1460]) ).
thf(1573,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ SX0 ) @ SX1 )
!= zero_zero_nat )
| ( SX0 = zero_zero_nat ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SX0 ) @ SX1 )
!= zero_zero_nat )
| ( SX1 = zero_zero_nat ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1461]) ).
thf(1574,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( number_number_of_int @ SX0 )
!= SX1 )
| ( SX1
= ( number_number_of_int @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1462]) ).
thf(1575,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( number_number_of_int @ SX0 ) )
| ( ( number_number_of_int @ SX0 )
= SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1463]) ).
thf(1576,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != zero_zero_int )
| ( SX1 != zero_zero_int )
| ( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ SX0 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ SX1 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1464]) ).
thf(1577,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ SX0 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ SX1 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ SX0 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( 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)],[1465]) ).
thf(1578,plain,
( ( ! [SX0: $i] :
( ( ( hAPP_nat_int @ semiri1621563631at_int @ SX0 )
!= zero_zero_int )
| ( SX0 = zero_zero_nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1466]) ).
thf(1579,plain,
( ( ! [SX0: $i] :
( ( SX0 != zero_zero_nat )
| ( ( hAPP_nat_int @ semiri1621563631at_int @ SX0 )
= zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1467]) ).
thf(1580,plain,
! [SV102: $i] :
( ( ~ ! [SY341: $i,SY342: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV102 ) @ SY341 )
!= ( hAPP_nat_nat @ ( plus_plus_nat @ SY342 ) @ SY341 ) )
| ( SV102 = SY342 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1468]) ).
thf(1581,plain,
! [SV102: $i] :
( ( ~ ! [SY343: $i,SY344: $i] :
( ( SV102 != SY344 )
| ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV102 ) @ SY343 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ SY344 ) @ SY343 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1468]) ).
thf(1582,plain,
( ( ! [SX0: $i] :
( ( one_one_int != SX0 )
| ( SX0 = one_one_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1469]) ).
thf(1583,plain,
( ( ! [SX0: $i] :
( ( SX0 != one_one_int )
| ( one_one_int = SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1470]) ).
thf(1584,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1 = zero_zero_nat )
| ( SX0 != zero_zero_nat )
| ( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ SX1 )
= zero_zero_nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1471]) ).
thf(1585,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ SX1 )
!= zero_zero_nat )
| ( SX1 != zero_zero_nat ) )
| ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ SX1 )
!= zero_zero_nat )
| ( SX0 = zero_zero_nat ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1472]) ).
thf(1586,plain,
( ( ! [SX0: $i] :
( ( zero_zero_nat != SX0 )
| ( SX0 = zero_zero_nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1473]) ).
thf(1587,plain,
( ( ! [SX0: $i] :
( ( SX0 != zero_zero_nat )
| ( zero_zero_nat = SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1474]) ).
thf(1588,plain,
! [SV103: $i] :
( ( ~ ! [SY345: $i,SY346: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ SV103 ) @ SY345 )
!= ( hAPP_int_int @ ( plus_plus_int @ SV103 ) @ SY346 ) )
| ( SY345 = SY346 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1475]) ).
thf(1589,plain,
! [SV103: $i] :
( ( ~ ! [SY347: $i,SY348: $i] :
( ( SY347 != SY348 )
| ( ( hAPP_int_int @ ( plus_plus_int @ SV103 ) @ SY347 )
= ( hAPP_int_int @ ( plus_plus_int @ SV103 ) @ SY348 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1475]) ).
thf(1590,plain,
( ( ! [SX0: $i] :
( ( pls
!= ( bit0 @ SX0 ) )
| ( pls = SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1476]) ).
thf(1591,plain,
( ( ! [SX0: $i] :
( ( pls != SX0 )
| ( pls
= ( bit0 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1477]) ).
thf(1592,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( hAPP_int_int @ ( plus_plus_int @ SX0 ) @ SX1 ) )
| ( SX1 = zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1478]) ).
thf(1593,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1 != zero_zero_int )
| ( SX0
= ( hAPP_int_int @ ( plus_plus_int @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1479]) ).
thf(1594,plain,
! [SV36: $i,SV120: $i] :
( ( ( ( hAPP_nat_int @ ( power_power_int @ SV120 ) @ SV36 )
= zero_zero_int )
= $false )
| ( ( SV120 = zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1486]) ).
thf(1595,plain,
! [SV158: $i,SV125: $i,SV44: $i] :
( ( ( ( ( hAPP_int_int @ ( plus_plus_int @ SV44 ) @ SV125 )
!= ( hAPP_int_int @ ( plus_plus_int @ SV158 ) @ SV125 ) ) )
= $true )
| ( ( SV44 = SV158 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1487]) ).
thf(1596,plain,
! [SV159: $i,SV126: $i,SV45: $i] :
( ( ( ( ( hAPP_int_int @ ( plus_plus_int @ SV45 ) @ SV126 )
!= ( hAPP_int_int @ ( plus_plus_int @ SV45 ) @ SV159 ) ) )
= $true )
| ( ( SV126 = SV159 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1488]) ).
thf(1597,plain,
! [SV160: $i,SV127: $i,SV46: $i] :
( ( ( ( ( hAPP_int_int @ ( plus_plus_int @ SV46 ) @ SV127 )
!= ( hAPP_int_int @ ( plus_plus_int @ SV46 ) @ SV160 ) ) )
= $true )
| ( ( SV127 = SV160 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1489]) ).
thf(1598,plain,
! [SV178: $i,SV161: $i,SV128: $i,SV47: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ SV47 ) @ SV128 ) ) @ ( hAPP_int_int @ ( plus_plus_int @ SV161 ) @ SV178 ) )
= ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_int_int @ ( plus_plus_int @ SV47 ) @ SV161 ) ) @ ( hAPP_int_int @ ( plus_plus_int @ SV128 ) @ SV178 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1490]) ).
thf(1599,plain,
! [SV141: $i,SV72: $i] :
( ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV72 ) @ SV141 )
= SV72 )
= $false )
| ( ( SV141 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1498]) ).
thf(1600,plain,
! [SV169: $i,SV144: $i,SV81: $i] :
( ( ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV81 ) @ SV144 )
!= ( hAPP_nat_nat @ ( plus_plus_nat @ SV169 ) @ SV144 ) ) )
= $true )
| ( ( SV81 = SV169 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1499]) ).
thf(1601,plain,
! [SV170: $i,SV145: $i,SV82: $i] :
( ( ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV82 ) @ SV145 )
!= ( hAPP_nat_nat @ ( plus_plus_nat @ SV82 ) @ SV170 ) ) )
= $true )
| ( ( SV145 = SV170 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1500]) ).
thf(1602,plain,
! [SV171: $i,SV146: $i,SV83: $i] :
( ( ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV83 ) @ SV146 )
!= ( hAPP_nat_nat @ ( plus_plus_nat @ SV83 ) @ SV171 ) ) )
= $true )
| ( ( SV146 = SV171 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1501]) ).
thf(1603,plain,
! [SV179: $i,SV172: $i,SV147: $i,SV84: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ SV84 ) @ SV147 ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ SV172 ) @ SV179 ) )
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ SV84 ) @ SV172 ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ SV147 ) @ SV179 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1502]) ).
thf(1604,plain,
! [SV180: $i] :
( ( ( SV180 != zero_zero_nat )
| ( ( hAPP_nat_nat @ ( power_power_nat @ zero_zero_nat ) @ SV180 )
= one_one_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1508]) ).
thf(1605,plain,
! [SV181: $i] :
( ( ( SV181 = zero_zero_nat )
| ( ( hAPP_nat_nat @ ( power_power_nat @ zero_zero_nat ) @ SV181 )
= zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1509]) ).
thf(1606,plain,
! [SV182: $i] :
( ( ! [SY377: $i] :
( ( ( number_number_of_nat @ SY377 )
= zero_zero_nat )
| ( SV182 != zero_zero_nat )
| ( ( hAPP_nat_nat @ ( power_power_nat @ SV182 ) @ ( number_number_of_nat @ SY377 ) )
= zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1510]) ).
thf(1607,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_nat )
| ( ( number_number_of_nat @ SX1 )
!= zero_zero_nat ) )
| ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_nat )
| ( SX0 = zero_zero_nat ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1511]) ).
thf(1608,plain,
! [SV183: $i] :
( ( ! [SY378: $i] :
( ( ( hAPP_nat_int @ semiri1621563631at_int @ SV183 )
!= ( hAPP_nat_int @ semiri1621563631at_int @ SY378 ) )
| ( SV183 = SY378 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1512]) ).
thf(1609,plain,
! [SV184: $i] :
( ( ! [SY379: $i] :
( ( SV184 != SY379 )
| ( ( hAPP_nat_int @ semiri1621563631at_int @ SV184 )
= ( hAPP_nat_int @ semiri1621563631at_int @ SY379 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1513]) ).
thf(1610,plain,
! [SV98: $i] :
( ( ! [SY325: $i,SY326: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV98 ) @ SY325 )
!= ( hAPP_nat_nat @ ( plus_plus_nat @ SV98 ) @ SY326 ) )
| ( SY325 = SY326 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1514]) ).
thf(1611,plain,
! [SV98: $i] :
( ( ! [SY327: $i,SY328: $i] :
( ( SY327 != SY328 )
| ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV98 ) @ SY327 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ SV98 ) @ SY328 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1515]) ).
thf(1612,plain,
! [SV185: $i] :
( ( ! [SY380: $i] :
( ( ( hAPP_nat_int @ semiri1621563631at_int @ SV185 )
!= ( hAPP_nat_int @ semiri1621563631at_int @ SY380 ) )
| ( SV185 = SY380 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1516]) ).
thf(1613,plain,
! [SV186: $i] :
( ( ! [SY381: $i] :
( ( SV186 != SY381 )
| ( ( hAPP_nat_int @ semiri1621563631at_int @ SV186 )
= ( hAPP_nat_int @ semiri1621563631at_int @ SY381 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1517]) ).
thf(1614,plain,
! [SV187: $i] :
( ( ( ( number_number_of_nat @ SV187 )
!= zero_zero_nat )
| ( ( hAPP_nat_nat @ ( power_power_nat @ zero_zero_nat ) @ ( number_number_of_nat @ SV187 ) )
= one_one_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1518]) ).
thf(1615,plain,
! [SV188: $i] :
( ( ( ( number_number_of_nat @ SV188 )
= zero_zero_nat )
| ( ( hAPP_nat_nat @ ( power_power_nat @ zero_zero_nat ) @ ( number_number_of_nat @ SV188 ) )
= zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1519]) ).
thf(1616,plain,
! [SV99: $i] :
( ( ! [SY329: $i,SY330: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV99 ) @ SY329 )
!= ( hAPP_nat_nat @ ( plus_plus_nat @ SV99 ) @ SY330 ) )
| ( SY329 = SY330 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1520]) ).
thf(1617,plain,
! [SV99: $i] :
( ( ! [SY331: $i,SY332: $i] :
( ( SY331 != SY332 )
| ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV99 ) @ SY331 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ SV99 ) @ SY332 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1521]) ).
thf(1618,plain,
! [SV189: $i] :
( ( ! [SY382: $i] :
( ( ( bit0 @ SV189 )
!= ( bit0 @ SY382 ) )
| ( SV189 = SY382 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1522]) ).
thf(1619,plain,
! [SV190: $i] :
( ( ! [SY383: $i] :
( ( SV190 != SY383 )
| ( ( bit0 @ SV190 )
= ( bit0 @ SY383 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1523]) ).
thf(1620,plain,
! [SV191: $i] :
( ( ( zero_zero_int
!= ( hAPP_int_int @ ( plus_plus_int @ SV191 ) @ SV191 ) )
| ( SV191 = zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1524]) ).
thf(1621,plain,
! [SV192: $i] :
( ( ( SV192 != zero_zero_int )
| ( zero_zero_int
= ( hAPP_int_int @ ( plus_plus_int @ SV192 ) @ SV192 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1525]) ).
thf(1622,plain,
! [SV193: $i] :
( ( ! [SY384: $i] :
( ( ( number267125858f_real @ SV193 )
!= ( number267125858f_real @ SY384 ) )
| ( SV193 = SY384 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1526]) ).
thf(1623,plain,
! [SV194: $i] :
( ( ! [SY385: $i] :
( ( SV194 != SY385 )
| ( ( number267125858f_real @ SV194 )
= ( number267125858f_real @ SY385 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1527]) ).
thf(1624,plain,
! [SV195: $i] :
( ( ! [SY386: $i] :
( ( SV195
!= ( hAPP_nat_nat @ ( plus_plus_nat @ SV195 ) @ SY386 ) )
| ( SY386 = zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1528]) ).
thf(1625,plain,
! [SV196: $i] :
( ( ! [SY387: $i] :
( ( SY387 != zero_zero_nat )
| ( SV196
= ( hAPP_nat_nat @ ( plus_plus_nat @ SV196 ) @ SY387 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1529]) ).
thf(1626,plain,
! [SV197: $i] :
( ( ( ( number_number_of_nat @ SV197 )
!= zero_zero_nat )
| ( ( hAPP_nat_int @ ( power_power_int @ zero_zero_int ) @ ( number_number_of_nat @ SV197 ) )
= one_one_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1530]) ).
thf(1627,plain,
! [SV198: $i] :
( ( ( ( number_number_of_nat @ SV198 )
= zero_zero_nat )
| ( ( hAPP_nat_int @ ( power_power_int @ zero_zero_int ) @ ( number_number_of_nat @ SV198 ) )
= zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1531]) ).
thf(1628,plain,
! [SV199: $i] :
( ( ! [SY388: $i] :
( ( ( number_number_of_int @ SV199 )
!= ( number_number_of_int @ SY388 ) )
| ( SV199 = SY388 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1532]) ).
thf(1629,plain,
! [SV200: $i] :
( ( ! [SY389: $i] :
( ( SV200 != SY389 )
| ( ( number_number_of_int @ SV200 )
= ( number_number_of_int @ SY389 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1533]) ).
thf(1630,plain,
! [SV201: $i] :
( ( ( zero_zero_real != SV201 )
| ( SV201 = zero_zero_real ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1534]) ).
thf(1631,plain,
! [SV202: $i] :
( ( ( SV202 != zero_zero_real )
| ( zero_zero_real = SV202 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1535]) ).
thf(1632,plain,
! [SV203: $i] :
( ( ! [SY390: $i] :
( ( ( bit1 @ SV203 )
!= ( bit1 @ SY390 ) )
| ( SV203 = SY390 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1536]) ).
thf(1633,plain,
! [SV204: $i] :
( ( ! [SY391: $i] :
( ( SV204 != SY391 )
| ( ( bit1 @ SV204 )
= ( bit1 @ SY391 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1537]) ).
thf(1634,plain,
! [SV205: $i] :
( ( ! [SY392: $i] :
( ( ( hAPP_nat_nat @ ( power_power_nat @ SV205 ) @ SY392 )
!= one_one_nat )
| ( SV205 = one_one_nat )
| ( SY392 = zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1538]) ).
thf(1635,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != one_one_nat )
| ! [SX1: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ SX1 )
= one_one_nat ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1 != zero_zero_nat )
| ( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ SX1 )
= one_one_nat ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1539]) ).
thf(1636,plain,
! [SV206: $i] :
( ( ( ( hAPP_nat_int @ ( power_power_int @ SV206 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= zero_zero_int )
| ( SV206 = zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1540]) ).
thf(1637,plain,
! [SV207: $i] :
( ( ( SV207 != zero_zero_int )
| ( ( hAPP_nat_int @ ( power_power_int @ SV207 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1541]) ).
thf(1638,plain,
! [SV208: $i] :
( ( ! [SY393: $i] :
( ( ( hAPP_nat_nat @ semiri984289939at_nat @ SV208 )
!= ( hAPP_nat_nat @ semiri984289939at_nat @ SY393 ) )
| ( SV208 = SY393 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1542]) ).
thf(1639,plain,
! [SV209: $i] :
( ( ! [SY394: $i] :
( ( SV209 != SY394 )
| ( ( hAPP_nat_nat @ semiri984289939at_nat @ SV209 )
= ( hAPP_nat_nat @ semiri984289939at_nat @ SY394 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1543]) ).
thf(1640,plain,
! [SV210: $i] :
( ( ( SV210 != zero_zero_nat )
| ( ( hAPP_nat_int @ ( power_power_int @ zero_zero_int ) @ SV210 )
= one_one_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1544]) ).
thf(1641,plain,
! [SV211: $i] :
( ( ( SV211 = zero_zero_nat )
| ( ( hAPP_nat_int @ ( power_power_int @ zero_zero_int ) @ SV211 )
= zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1545]) ).
thf(1642,plain,
! [SV212: $i] :
( ( ! [SY395: $i] :
( ( ( hAPP_nat_int @ semiri1621563631at_int @ SV212 )
!= ( hAPP_nat_int @ semiri1621563631at_int @ SY395 ) )
| ( SV212 = SY395 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1546]) ).
thf(1643,plain,
! [SV213: $i] :
( ( ! [SY396: $i] :
( ( SV213 != SY396 )
| ( ( hAPP_nat_int @ semiri1621563631at_int @ SV213 )
= ( hAPP_nat_int @ semiri1621563631at_int @ SY396 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1547]) ).
thf(1644,plain,
! [SV214: $i] :
( ( ! [SY397: $i] :
( ( SY397 = zero_zero_nat )
| ( SV214 != zero_zero_nat )
| ( ( hAPP_nat_nat @ ( power_power_nat @ SV214 ) @ SY397 )
= zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1548]) ).
thf(1645,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ SX1 )
!= zero_zero_nat )
| ( SX1 != zero_zero_nat ) )
| ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ SX1 )
!= zero_zero_nat )
| ( SX0 = zero_zero_nat ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1549]) ).
thf(1646,plain,
! [SV215: $i] :
( ( ! [SY398: $i] :
( ( ( number_number_of_nat @ SY398 )
= zero_zero_nat )
| ( SV215 != zero_zero_int )
| ( ( hAPP_nat_int @ ( power_power_int @ SV215 ) @ ( number_number_of_nat @ SY398 ) )
= zero_zero_int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1550]) ).
thf(1647,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( hAPP_nat_int @ ( power_power_int @ SX0 ) @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_int )
| ( ( number_number_of_nat @ SX1 )
!= zero_zero_nat ) )
| ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( hAPP_nat_int @ ( power_power_int @ SX0 ) @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1551]) ).
thf(1648,plain,
! [SV100: $i] :
( ( ! [SY333: $i,SY334: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV100 ) @ SY333 )
!= ( hAPP_nat_nat @ ( plus_plus_nat @ SY334 ) @ SY333 ) )
| ( SV100 = SY334 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1552]) ).
thf(1649,plain,
! [SV100: $i] :
( ( ! [SY335: $i,SY336: $i] :
( ( SV100 != SY336 )
| ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV100 ) @ SY335 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ SY336 ) @ SY335 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1553]) ).
thf(1650,plain,
! [SV101: $i] :
( ( ! [SY337: $i,SY338: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ SV101 ) @ SY337 )
!= ( hAPP_int_int @ ( plus_plus_int @ SY338 ) @ SY337 ) )
| ( SV101 = SY338 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1554]) ).
thf(1651,plain,
! [SV101: $i] :
( ( ! [SY339: $i,SY340: $i] :
( ( SV101 != SY340 )
| ( ( hAPP_int_int @ ( plus_plus_int @ SV101 ) @ SY339 )
= ( hAPP_int_int @ ( plus_plus_int @ SY340 ) @ SY339 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1555]) ).
thf(1652,plain,
! [SV216: $i] :
( ( ( ( bit0 @ SV216 )
!= pls )
| ( SV216 = pls ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1556]) ).
thf(1653,plain,
! [SV217: $i] :
( ( ( SV217 != pls )
| ( ( bit0 @ SV217 )
= pls ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1557]) ).
thf(1654,plain,
! [SV218: $i] :
( ( ! [SY399: $i] :
( ( ( number267125858f_real @ SV218 )
!= SY399 )
| ( SY399
= ( number267125858f_real @ SV218 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1558]) ).
thf(1655,plain,
! [SV219: $i] :
( ( ! [SY400: $i] :
( ( SY400
!= ( number267125858f_real @ SV219 ) )
| ( ( number267125858f_real @ SV219 )
= SY400 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1559]) ).
thf(1656,plain,
! [SV220: $i] :
( ( ( one_one_nat != SV220 )
| ( SV220 = one_one_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1560]) ).
thf(1657,plain,
! [SV221: $i] :
( ( ( SV221 != one_one_nat )
| ( one_one_nat = SV221 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1561]) ).
thf(1658,plain,
! [SV222: $i] :
( ( ! [SY401: $i] :
( ( ( number_number_of_nat @ SV222 )
!= SY401 )
| ( SY401
= ( number_number_of_nat @ SV222 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1562]) ).
thf(1659,plain,
! [SV223: $i] :
( ( ! [SY402: $i] :
( ( SY402
!= ( number_number_of_nat @ SV223 ) )
| ( ( number_number_of_nat @ SV223 )
= SY402 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1563]) ).
thf(1660,plain,
! [SV224: $i] :
( ( ( ( hAPP_int_int @ ( plus_plus_int @ SV224 ) @ SV224 )
!= zero_zero_int )
| ( SV224 = zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1564]) ).
thf(1661,plain,
! [SV225: $i] :
( ( ( SV225 != zero_zero_int )
| ( ( hAPP_int_int @ ( plus_plus_int @ SV225 ) @ SV225 )
= zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1565]) ).
thf(1662,plain,
! [SV226: $i] :
( ( ( one_one_real != SV226 )
| ( SV226 = one_one_real ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1566]) ).
thf(1663,plain,
! [SV227: $i] :
( ( ( SV227 != one_one_real )
| ( one_one_real = SV227 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1567]) ).
thf(1664,plain,
! [SV228: $i] :
( ( ! [SY403: $i] :
( ( SY403 = zero_zero_nat )
| ( SV228 != zero_zero_int )
| ( ( hAPP_nat_int @ ( power_power_int @ SV228 ) @ SY403 )
= zero_zero_int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1568]) ).
thf(1665,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( hAPP_nat_int @ ( power_power_int @ SX0 ) @ SX1 )
!= zero_zero_int )
| ( SX1 != zero_zero_nat ) )
| ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( hAPP_nat_int @ ( power_power_int @ SX0 ) @ SX1 )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1569]) ).
thf(1666,plain,
! [SV229: $i] :
( ( ( zero_zero_int != SV229 )
| ( SV229 = zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1570]) ).
thf(1667,plain,
! [SV230: $i] :
( ( ( SV230 != zero_zero_int )
| ( zero_zero_int = SV230 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1571]) ).
thf(1668,plain,
! [SV231: $i] :
( ( ! [SY404: $i] :
( ( SV231 != zero_zero_nat )
| ( SY404 != zero_zero_nat )
| ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV231 ) @ SY404 )
= zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1572]) ).
thf(1669,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ SX0 ) @ SX1 )
!= zero_zero_nat )
| ( SX0 = zero_zero_nat ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SX0 ) @ SX1 )
!= zero_zero_nat )
| ( SX1 = zero_zero_nat ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1573]) ).
thf(1670,plain,
! [SV232: $i] :
( ( ! [SY405: $i] :
( ( ( number_number_of_int @ SV232 )
!= SY405 )
| ( SY405
= ( number_number_of_int @ SV232 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1574]) ).
thf(1671,plain,
! [SV233: $i] :
( ( ! [SY406: $i] :
( ( SY406
!= ( number_number_of_int @ SV233 ) )
| ( ( number_number_of_int @ SV233 )
= SY406 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1575]) ).
thf(1672,plain,
! [SV234: $i] :
( ( ! [SY407: $i] :
( ( SV234 != zero_zero_int )
| ( SY407 != zero_zero_int )
| ( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ SV234 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ SY407 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1576]) ).
thf(1673,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ SX0 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ SX1 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ SX0 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( 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)],[1577]) ).
thf(1674,plain,
! [SV235: $i] :
( ( ( ( hAPP_nat_int @ semiri1621563631at_int @ SV235 )
!= zero_zero_int )
| ( SV235 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1578]) ).
thf(1675,plain,
! [SV236: $i] :
( ( ( SV236 != zero_zero_nat )
| ( ( hAPP_nat_int @ semiri1621563631at_int @ SV236 )
= zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1579]) ).
thf(1676,plain,
! [SV102: $i] :
( ( ! [SY341: $i,SY342: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV102 ) @ SY341 )
!= ( hAPP_nat_nat @ ( plus_plus_nat @ SY342 ) @ SY341 ) )
| ( SV102 = SY342 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1580]) ).
thf(1677,plain,
! [SV102: $i] :
( ( ! [SY343: $i,SY344: $i] :
( ( SV102 != SY344 )
| ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV102 ) @ SY343 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ SY344 ) @ SY343 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1581]) ).
thf(1678,plain,
! [SV237: $i] :
( ( ( one_one_int != SV237 )
| ( SV237 = one_one_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1582]) ).
thf(1679,plain,
! [SV238: $i] :
( ( ( SV238 != one_one_int )
| ( one_one_int = SV238 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1583]) ).
thf(1680,plain,
! [SV239: $i] :
( ( ! [SY408: $i] :
( ( SY408 = zero_zero_nat )
| ( SV239 != zero_zero_nat )
| ( ( hAPP_nat_nat @ ( power_power_nat @ SV239 ) @ SY408 )
= zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1584]) ).
thf(1681,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ SX1 )
!= zero_zero_nat )
| ( SX1 != zero_zero_nat ) )
| ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ SX1 )
!= zero_zero_nat )
| ( SX0 = zero_zero_nat ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1585]) ).
thf(1682,plain,
! [SV240: $i] :
( ( ( zero_zero_nat != SV240 )
| ( SV240 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1586]) ).
thf(1683,plain,
! [SV241: $i] :
( ( ( SV241 != zero_zero_nat )
| ( zero_zero_nat = SV241 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1587]) ).
thf(1684,plain,
! [SV103: $i] :
( ( ! [SY345: $i,SY346: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ SV103 ) @ SY345 )
!= ( hAPP_int_int @ ( plus_plus_int @ SV103 ) @ SY346 ) )
| ( SY345 = SY346 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1588]) ).
thf(1685,plain,
! [SV103: $i] :
( ( ! [SY347: $i,SY348: $i] :
( ( SY347 != SY348 )
| ( ( hAPP_int_int @ ( plus_plus_int @ SV103 ) @ SY347 )
= ( hAPP_int_int @ ( plus_plus_int @ SV103 ) @ SY348 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1589]) ).
thf(1686,plain,
! [SV242: $i] :
( ( ( pls
!= ( bit0 @ SV242 ) )
| ( pls = SV242 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1590]) ).
thf(1687,plain,
! [SV243: $i] :
( ( ( pls != SV243 )
| ( pls
= ( bit0 @ SV243 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1591]) ).
thf(1688,plain,
! [SV244: $i] :
( ( ! [SY409: $i] :
( ( SV244
!= ( hAPP_int_int @ ( plus_plus_int @ SV244 ) @ SY409 ) )
| ( SY409 = zero_zero_int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1592]) ).
thf(1689,plain,
! [SV245: $i] :
( ( ! [SY410: $i] :
( ( SY410 != zero_zero_int )
| ( SV245
= ( hAPP_int_int @ ( plus_plus_int @ SV245 ) @ SY410 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1593]) ).
thf(1690,plain,
! [SV158: $i,SV125: $i,SV44: $i] :
( ( ( ( hAPP_int_int @ ( plus_plus_int @ SV44 ) @ SV125 )
= ( hAPP_int_int @ ( plus_plus_int @ SV158 ) @ SV125 ) )
= $false )
| ( ( SV44 = SV158 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1595]) ).
thf(1691,plain,
! [SV159: $i,SV126: $i,SV45: $i] :
( ( ( ( hAPP_int_int @ ( plus_plus_int @ SV45 ) @ SV126 )
= ( hAPP_int_int @ ( plus_plus_int @ SV45 ) @ SV159 ) )
= $false )
| ( ( SV126 = SV159 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1596]) ).
thf(1692,plain,
! [SV160: $i,SV127: $i,SV46: $i] :
( ( ( ( hAPP_int_int @ ( plus_plus_int @ SV46 ) @ SV127 )
= ( hAPP_int_int @ ( plus_plus_int @ SV46 ) @ SV160 ) )
= $false )
| ( ( SV127 = SV160 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1597]) ).
thf(1693,plain,
! [SV169: $i,SV144: $i,SV81: $i] :
( ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV81 ) @ SV144 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ SV169 ) @ SV144 ) )
= $false )
| ( ( SV81 = SV169 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1600]) ).
thf(1694,plain,
! [SV170: $i,SV145: $i,SV82: $i] :
( ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV82 ) @ SV145 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ SV82 ) @ SV170 ) )
= $false )
| ( ( SV145 = SV170 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1601]) ).
thf(1695,plain,
! [SV171: $i,SV146: $i,SV83: $i] :
( ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV83 ) @ SV146 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ SV83 ) @ SV171 ) )
= $false )
| ( ( SV146 = SV171 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1602]) ).
thf(1696,plain,
! [SV180: $i] :
( ( ( ( SV180 != zero_zero_nat ) )
= $true )
| ( ( ( hAPP_nat_nat @ ( power_power_nat @ zero_zero_nat ) @ SV180 )
= one_one_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1604]) ).
thf(1697,plain,
! [SV181: $i] :
( ( ( SV181 = zero_zero_nat )
= $true )
| ( ( ( hAPP_nat_nat @ ( power_power_nat @ zero_zero_nat ) @ SV181 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1605]) ).
thf(1698,plain,
! [SV182: $i,SV246: $i] :
( ( ( ( number_number_of_nat @ SV246 )
= zero_zero_nat )
| ( SV182 != zero_zero_nat )
| ( ( hAPP_nat_nat @ ( power_power_nat @ SV182 ) @ ( number_number_of_nat @ SV246 ) )
= zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1606]) ).
thf(1699,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( hAPP_nat_nat @ ( 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)],[1607]) ).
thf(1700,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_nat )
| ( SX0 = zero_zero_nat ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1607]) ).
thf(1701,plain,
! [SV247: $i,SV183: $i] :
( ( ( ( hAPP_nat_int @ semiri1621563631at_int @ SV183 )
!= ( hAPP_nat_int @ semiri1621563631at_int @ SV247 ) )
| ( SV183 = SV247 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1608]) ).
thf(1702,plain,
! [SV248: $i,SV184: $i] :
( ( ( SV184 != SV248 )
| ( ( hAPP_nat_int @ semiri1621563631at_int @ SV184 )
= ( hAPP_nat_int @ semiri1621563631at_int @ SV248 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1609]) ).
thf(1703,plain,
! [SV249: $i,SV98: $i] :
( ( ! [SY411: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV98 ) @ SV249 )
!= ( hAPP_nat_nat @ ( plus_plus_nat @ SV98 ) @ SY411 ) )
| ( SV249 = SY411 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1610]) ).
thf(1704,plain,
! [SV98: $i,SV250: $i] :
( ( ! [SY412: $i] :
( ( SV250 != SY412 )
| ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV98 ) @ SV250 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ SV98 ) @ SY412 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1611]) ).
thf(1705,plain,
! [SV251: $i,SV185: $i] :
( ( ( ( hAPP_nat_int @ semiri1621563631at_int @ SV185 )
!= ( hAPP_nat_int @ semiri1621563631at_int @ SV251 ) )
| ( SV185 = SV251 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1612]) ).
thf(1706,plain,
! [SV252: $i,SV186: $i] :
( ( ( SV186 != SV252 )
| ( ( hAPP_nat_int @ semiri1621563631at_int @ SV186 )
= ( hAPP_nat_int @ semiri1621563631at_int @ SV252 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1613]) ).
thf(1707,plain,
! [SV187: $i] :
( ( ( ( ( number_number_of_nat @ SV187 )
!= zero_zero_nat ) )
= $true )
| ( ( ( hAPP_nat_nat @ ( power_power_nat @ zero_zero_nat ) @ ( number_number_of_nat @ SV187 ) )
= one_one_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1614]) ).
thf(1708,plain,
! [SV188: $i] :
( ( ( ( number_number_of_nat @ SV188 )
= zero_zero_nat )
= $true )
| ( ( ( hAPP_nat_nat @ ( power_power_nat @ zero_zero_nat ) @ ( number_number_of_nat @ SV188 ) )
= zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1615]) ).
thf(1709,plain,
! [SV253: $i,SV99: $i] :
( ( ! [SY413: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV99 ) @ SV253 )
!= ( hAPP_nat_nat @ ( plus_plus_nat @ SV99 ) @ SY413 ) )
| ( SV253 = SY413 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1616]) ).
thf(1710,plain,
! [SV99: $i,SV254: $i] :
( ( ! [SY414: $i] :
( ( SV254 != SY414 )
| ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV99 ) @ SV254 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ SV99 ) @ SY414 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1617]) ).
thf(1711,plain,
! [SV255: $i,SV189: $i] :
( ( ( ( bit0 @ SV189 )
!= ( bit0 @ SV255 ) )
| ( SV189 = SV255 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1618]) ).
thf(1712,plain,
! [SV256: $i,SV190: $i] :
( ( ( SV190 != SV256 )
| ( ( bit0 @ SV190 )
= ( bit0 @ SV256 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1619]) ).
thf(1713,plain,
! [SV191: $i] :
( ( ( ( zero_zero_int
!= ( hAPP_int_int @ ( plus_plus_int @ SV191 ) @ SV191 ) ) )
= $true )
| ( ( SV191 = zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1620]) ).
thf(1714,plain,
! [SV192: $i] :
( ( ( ( SV192 != zero_zero_int ) )
= $true )
| ( ( zero_zero_int
= ( hAPP_int_int @ ( plus_plus_int @ SV192 ) @ SV192 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1621]) ).
thf(1715,plain,
! [SV257: $i,SV193: $i] :
( ( ( ( number267125858f_real @ SV193 )
!= ( number267125858f_real @ SV257 ) )
| ( SV193 = SV257 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1622]) ).
thf(1716,plain,
! [SV258: $i,SV194: $i] :
( ( ( SV194 != SV258 )
| ( ( number267125858f_real @ SV194 )
= ( number267125858f_real @ SV258 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1623]) ).
thf(1717,plain,
! [SV259: $i,SV195: $i] :
( ( ( SV195
!= ( hAPP_nat_nat @ ( plus_plus_nat @ SV195 ) @ SV259 ) )
| ( SV259 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1624]) ).
thf(1718,plain,
! [SV196: $i,SV260: $i] :
( ( ( SV260 != zero_zero_nat )
| ( SV196
= ( hAPP_nat_nat @ ( plus_plus_nat @ SV196 ) @ SV260 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1625]) ).
thf(1719,plain,
! [SV197: $i] :
( ( ( ( ( number_number_of_nat @ SV197 )
!= zero_zero_nat ) )
= $true )
| ( ( ( hAPP_nat_int @ ( power_power_int @ zero_zero_int ) @ ( number_number_of_nat @ SV197 ) )
= one_one_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1626]) ).
thf(1720,plain,
! [SV198: $i] :
( ( ( ( number_number_of_nat @ SV198 )
= zero_zero_nat )
= $true )
| ( ( ( hAPP_nat_int @ ( power_power_int @ zero_zero_int ) @ ( number_number_of_nat @ SV198 ) )
= zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1627]) ).
thf(1721,plain,
! [SV261: $i,SV199: $i] :
( ( ( ( number_number_of_int @ SV199 )
!= ( number_number_of_int @ SV261 ) )
| ( SV199 = SV261 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1628]) ).
thf(1722,plain,
! [SV262: $i,SV200: $i] :
( ( ( SV200 != SV262 )
| ( ( number_number_of_int @ SV200 )
= ( number_number_of_int @ SV262 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1629]) ).
thf(1723,plain,
! [SV201: $i] :
( ( ( ( zero_zero_real != SV201 ) )
= $true )
| ( ( SV201 = zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1630]) ).
thf(1724,plain,
! [SV202: $i] :
( ( ( ( SV202 != zero_zero_real ) )
= $true )
| ( ( zero_zero_real = SV202 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1631]) ).
thf(1725,plain,
! [SV263: $i,SV203: $i] :
( ( ( ( bit1 @ SV203 )
!= ( bit1 @ SV263 ) )
| ( SV203 = SV263 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1632]) ).
thf(1726,plain,
! [SV264: $i,SV204: $i] :
( ( ( SV204 != SV264 )
| ( ( bit1 @ SV204 )
= ( bit1 @ SV264 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1633]) ).
thf(1727,plain,
! [SV265: $i,SV205: $i] :
( ( ( ( hAPP_nat_nat @ ( power_power_nat @ SV205 ) @ SV265 )
!= one_one_nat )
| ( SV205 = one_one_nat )
| ( SV265 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1634]) ).
thf(1728,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != one_one_nat )
| ! [SX1: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ SX1 )
= one_one_nat ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1635]) ).
thf(1729,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1 != zero_zero_nat )
| ( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ SX1 )
= one_one_nat ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1635]) ).
thf(1730,plain,
! [SV206: $i] :
( ( ( ( ( hAPP_nat_int @ ( power_power_int @ SV206 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= zero_zero_int ) )
= $true )
| ( ( SV206 = zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1636]) ).
thf(1731,plain,
! [SV207: $i] :
( ( ( ( SV207 != zero_zero_int ) )
= $true )
| ( ( ( hAPP_nat_int @ ( power_power_int @ SV207 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1637]) ).
thf(1732,plain,
! [SV266: $i,SV208: $i] :
( ( ( ( hAPP_nat_nat @ semiri984289939at_nat @ SV208 )
!= ( hAPP_nat_nat @ semiri984289939at_nat @ SV266 ) )
| ( SV208 = SV266 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1638]) ).
thf(1733,plain,
! [SV267: $i,SV209: $i] :
( ( ( SV209 != SV267 )
| ( ( hAPP_nat_nat @ semiri984289939at_nat @ SV209 )
= ( hAPP_nat_nat @ semiri984289939at_nat @ SV267 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1639]) ).
thf(1734,plain,
! [SV210: $i] :
( ( ( ( SV210 != zero_zero_nat ) )
= $true )
| ( ( ( hAPP_nat_int @ ( power_power_int @ zero_zero_int ) @ SV210 )
= one_one_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1640]) ).
thf(1735,plain,
! [SV211: $i] :
( ( ( SV211 = zero_zero_nat )
= $true )
| ( ( ( hAPP_nat_int @ ( power_power_int @ zero_zero_int ) @ SV211 )
= zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1641]) ).
thf(1736,plain,
! [SV268: $i,SV212: $i] :
( ( ( ( hAPP_nat_int @ semiri1621563631at_int @ SV212 )
!= ( hAPP_nat_int @ semiri1621563631at_int @ SV268 ) )
| ( SV212 = SV268 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1642]) ).
thf(1737,plain,
! [SV269: $i,SV213: $i] :
( ( ( SV213 != SV269 )
| ( ( hAPP_nat_int @ semiri1621563631at_int @ SV213 )
= ( hAPP_nat_int @ semiri1621563631at_int @ SV269 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1643]) ).
thf(1738,plain,
! [SV214: $i,SV270: $i] :
( ( ( SV270 = zero_zero_nat )
| ( SV214 != zero_zero_nat )
| ( ( hAPP_nat_nat @ ( power_power_nat @ SV214 ) @ SV270 )
= zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1644]) ).
thf(1739,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ SX1 )
!= zero_zero_nat )
| ( SX1 != zero_zero_nat ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1645]) ).
thf(1740,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ SX1 )
!= zero_zero_nat )
| ( SX0 = zero_zero_nat ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1645]) ).
thf(1741,plain,
! [SV215: $i,SV271: $i] :
( ( ( ( number_number_of_nat @ SV271 )
= zero_zero_nat )
| ( SV215 != zero_zero_int )
| ( ( hAPP_nat_int @ ( power_power_int @ SV215 ) @ ( number_number_of_nat @ SV271 ) )
= zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1646]) ).
thf(1742,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( hAPP_nat_int @ ( power_power_int @ SX0 ) @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_int )
| ( ( number_number_of_nat @ SX1 )
!= zero_zero_nat ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1647]) ).
thf(1743,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( hAPP_nat_int @ ( power_power_int @ SX0 ) @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1647]) ).
thf(1744,plain,
! [SV272: $i,SV100: $i] :
( ( ! [SY415: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV100 ) @ SV272 )
!= ( hAPP_nat_nat @ ( plus_plus_nat @ SY415 ) @ SV272 ) )
| ( SV100 = SY415 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1648]) ).
thf(1745,plain,
! [SV273: $i,SV100: $i] :
( ( ! [SY416: $i] :
( ( SV100 != SY416 )
| ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV100 ) @ SV273 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ SY416 ) @ SV273 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1649]) ).
thf(1746,plain,
! [SV274: $i,SV101: $i] :
( ( ! [SY417: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ SV101 ) @ SV274 )
!= ( hAPP_int_int @ ( plus_plus_int @ SY417 ) @ SV274 ) )
| ( SV101 = SY417 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1650]) ).
thf(1747,plain,
! [SV275: $i,SV101: $i] :
( ( ! [SY418: $i] :
( ( SV101 != SY418 )
| ( ( hAPP_int_int @ ( plus_plus_int @ SV101 ) @ SV275 )
= ( hAPP_int_int @ ( plus_plus_int @ SY418 ) @ SV275 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1651]) ).
thf(1748,plain,
! [SV216: $i] :
( ( ( ( ( bit0 @ SV216 )
!= pls ) )
= $true )
| ( ( SV216 = pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1652]) ).
thf(1749,plain,
! [SV217: $i] :
( ( ( ( SV217 != pls ) )
= $true )
| ( ( ( bit0 @ SV217 )
= pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1653]) ).
thf(1750,plain,
! [SV276: $i,SV218: $i] :
( ( ( ( number267125858f_real @ SV218 )
!= SV276 )
| ( SV276
= ( number267125858f_real @ SV218 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1654]) ).
thf(1751,plain,
! [SV219: $i,SV277: $i] :
( ( ( SV277
!= ( number267125858f_real @ SV219 ) )
| ( ( number267125858f_real @ SV219 )
= SV277 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1655]) ).
thf(1752,plain,
! [SV220: $i] :
( ( ( ( one_one_nat != SV220 ) )
= $true )
| ( ( SV220 = one_one_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1656]) ).
thf(1753,plain,
! [SV221: $i] :
( ( ( ( SV221 != one_one_nat ) )
= $true )
| ( ( one_one_nat = SV221 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1657]) ).
thf(1754,plain,
! [SV278: $i,SV222: $i] :
( ( ( ( number_number_of_nat @ SV222 )
!= SV278 )
| ( SV278
= ( number_number_of_nat @ SV222 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1658]) ).
thf(1755,plain,
! [SV223: $i,SV279: $i] :
( ( ( SV279
!= ( number_number_of_nat @ SV223 ) )
| ( ( number_number_of_nat @ SV223 )
= SV279 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1659]) ).
thf(1756,plain,
! [SV224: $i] :
( ( ( ( ( hAPP_int_int @ ( plus_plus_int @ SV224 ) @ SV224 )
!= zero_zero_int ) )
= $true )
| ( ( SV224 = zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1660]) ).
thf(1757,plain,
! [SV225: $i] :
( ( ( ( SV225 != zero_zero_int ) )
= $true )
| ( ( ( hAPP_int_int @ ( plus_plus_int @ SV225 ) @ SV225 )
= zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1661]) ).
thf(1758,plain,
! [SV226: $i] :
( ( ( ( one_one_real != SV226 ) )
= $true )
| ( ( SV226 = one_one_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1662]) ).
thf(1759,plain,
! [SV227: $i] :
( ( ( ( SV227 != one_one_real ) )
= $true )
| ( ( one_one_real = SV227 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1663]) ).
thf(1760,plain,
! [SV228: $i,SV280: $i] :
( ( ( SV280 = zero_zero_nat )
| ( SV228 != zero_zero_int )
| ( ( hAPP_nat_int @ ( power_power_int @ SV228 ) @ SV280 )
= zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1664]) ).
thf(1761,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( hAPP_nat_int @ ( power_power_int @ SX0 ) @ SX1 )
!= zero_zero_int )
| ( SX1 != zero_zero_nat ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1665]) ).
thf(1762,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( hAPP_nat_int @ ( power_power_int @ SX0 ) @ SX1 )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1665]) ).
thf(1763,plain,
! [SV229: $i] :
( ( ( ( zero_zero_int != SV229 ) )
= $true )
| ( ( SV229 = zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1666]) ).
thf(1764,plain,
! [SV230: $i] :
( ( ( ( SV230 != zero_zero_int ) )
= $true )
| ( ( zero_zero_int = SV230 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1667]) ).
thf(1765,plain,
! [SV281: $i,SV231: $i] :
( ( ( SV231 != zero_zero_nat )
| ( SV281 != zero_zero_nat )
| ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV231 ) @ SV281 )
= zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1668]) ).
thf(1766,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ SX0 ) @ SX1 )
!= zero_zero_nat )
| ( SX0 = zero_zero_nat ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1669]) ).
thf(1767,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SX0 ) @ SX1 )
!= zero_zero_nat )
| ( SX1 = zero_zero_nat ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1669]) ).
thf(1768,plain,
! [SV282: $i,SV232: $i] :
( ( ( ( number_number_of_int @ SV232 )
!= SV282 )
| ( SV282
= ( number_number_of_int @ SV232 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1670]) ).
thf(1769,plain,
! [SV233: $i,SV283: $i] :
( ( ( SV283
!= ( number_number_of_int @ SV233 ) )
| ( ( number_number_of_int @ SV233 )
= SV283 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1671]) ).
thf(1770,plain,
! [SV284: $i,SV234: $i] :
( ( ( SV234 != zero_zero_int )
| ( SV284 != zero_zero_int )
| ( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ SV234 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ SV284 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1672]) ).
thf(1771,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ SX0 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( 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)],[1673]) ).
thf(1772,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ SX0 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( 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)],[1673]) ).
thf(1773,plain,
! [SV235: $i] :
( ( ( ( ( hAPP_nat_int @ semiri1621563631at_int @ SV235 )
!= zero_zero_int ) )
= $true )
| ( ( SV235 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1674]) ).
thf(1774,plain,
! [SV236: $i] :
( ( ( ( SV236 != zero_zero_nat ) )
= $true )
| ( ( ( hAPP_nat_int @ semiri1621563631at_int @ SV236 )
= zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1675]) ).
thf(1775,plain,
! [SV285: $i,SV102: $i] :
( ( ! [SY419: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV102 ) @ SV285 )
!= ( hAPP_nat_nat @ ( plus_plus_nat @ SY419 ) @ SV285 ) )
| ( SV102 = SY419 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1676]) ).
thf(1776,plain,
! [SV286: $i,SV102: $i] :
( ( ! [SY420: $i] :
( ( SV102 != SY420 )
| ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV102 ) @ SV286 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ SY420 ) @ SV286 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1677]) ).
thf(1777,plain,
! [SV237: $i] :
( ( ( ( one_one_int != SV237 ) )
= $true )
| ( ( SV237 = one_one_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1678]) ).
thf(1778,plain,
! [SV238: $i] :
( ( ( ( SV238 != one_one_int ) )
= $true )
| ( ( one_one_int = SV238 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1679]) ).
thf(1779,plain,
! [SV239: $i,SV287: $i] :
( ( ( SV287 = zero_zero_nat )
| ( SV239 != zero_zero_nat )
| ( ( hAPP_nat_nat @ ( power_power_nat @ SV239 ) @ SV287 )
= zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1680]) ).
thf(1780,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ SX1 )
!= zero_zero_nat )
| ( SX1 != zero_zero_nat ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1681]) ).
thf(1781,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ SX1 )
!= zero_zero_nat )
| ( SX0 = zero_zero_nat ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1681]) ).
thf(1782,plain,
! [SV240: $i] :
( ( ( ( zero_zero_nat != SV240 ) )
= $true )
| ( ( SV240 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1682]) ).
thf(1783,plain,
! [SV241: $i] :
( ( ( ( SV241 != zero_zero_nat ) )
= $true )
| ( ( zero_zero_nat = SV241 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1683]) ).
thf(1784,plain,
! [SV288: $i,SV103: $i] :
( ( ! [SY421: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ SV103 ) @ SV288 )
!= ( hAPP_int_int @ ( plus_plus_int @ SV103 ) @ SY421 ) )
| ( SV288 = SY421 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1684]) ).
thf(1785,plain,
! [SV103: $i,SV289: $i] :
( ( ! [SY422: $i] :
( ( SV289 != SY422 )
| ( ( hAPP_int_int @ ( plus_plus_int @ SV103 ) @ SV289 )
= ( hAPP_int_int @ ( plus_plus_int @ SV103 ) @ SY422 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1685]) ).
thf(1786,plain,
! [SV242: $i] :
( ( ( ( pls
!= ( bit0 @ SV242 ) ) )
= $true )
| ( ( pls = SV242 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1686]) ).
thf(1787,plain,
! [SV243: $i] :
( ( ( ( pls != SV243 ) )
= $true )
| ( ( pls
= ( bit0 @ SV243 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1687]) ).
thf(1788,plain,
! [SV290: $i,SV244: $i] :
( ( ( SV244
!= ( hAPP_int_int @ ( plus_plus_int @ SV244 ) @ SV290 ) )
| ( SV290 = zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1688]) ).
thf(1789,plain,
! [SV245: $i,SV291: $i] :
( ( ( SV291 != zero_zero_int )
| ( SV245
= ( hAPP_int_int @ ( plus_plus_int @ SV245 ) @ SV291 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1689]) ).
thf(1790,plain,
! [SV180: $i] :
( ( ( SV180 = zero_zero_nat )
= $false )
| ( ( ( hAPP_nat_nat @ ( power_power_nat @ zero_zero_nat ) @ SV180 )
= one_one_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1696]) ).
thf(1791,plain,
! [SV182: $i,SV246: $i] :
( ( ( ( ( number_number_of_nat @ SV246 )
= zero_zero_nat )
| ( SV182 != zero_zero_nat ) )
= $true )
| ( ( ( hAPP_nat_nat @ ( power_power_nat @ SV182 ) @ ( number_number_of_nat @ SV246 ) )
= zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1698]) ).
thf(1792,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( hAPP_nat_nat @ ( 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)],[1699]) ).
thf(1793,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_nat )
| ( SX0 = zero_zero_nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1700]) ).
thf(1794,plain,
! [SV247: $i,SV183: $i] :
( ( ( ( ( hAPP_nat_int @ semiri1621563631at_int @ SV183 )
!= ( hAPP_nat_int @ semiri1621563631at_int @ SV247 ) ) )
= $true )
| ( ( SV183 = SV247 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1701]) ).
thf(1795,plain,
! [SV248: $i,SV184: $i] :
( ( ( ( SV184 != SV248 ) )
= $true )
| ( ( ( hAPP_nat_int @ semiri1621563631at_int @ SV184 )
= ( hAPP_nat_int @ semiri1621563631at_int @ SV248 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1702]) ).
thf(1796,plain,
! [SV292: $i,SV249: $i,SV98: $i] :
( ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV98 ) @ SV249 )
!= ( hAPP_nat_nat @ ( plus_plus_nat @ SV98 ) @ SV292 ) )
| ( SV249 = SV292 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1703]) ).
thf(1797,plain,
! [SV98: $i,SV293: $i,SV250: $i] :
( ( ( SV250 != SV293 )
| ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV98 ) @ SV250 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ SV98 ) @ SV293 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1704]) ).
thf(1798,plain,
! [SV251: $i,SV185: $i] :
( ( ( ( ( hAPP_nat_int @ semiri1621563631at_int @ SV185 )
!= ( hAPP_nat_int @ semiri1621563631at_int @ SV251 ) ) )
= $true )
| ( ( SV185 = SV251 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1705]) ).
thf(1799,plain,
! [SV252: $i,SV186: $i] :
( ( ( ( SV186 != SV252 ) )
= $true )
| ( ( ( hAPP_nat_int @ semiri1621563631at_int @ SV186 )
= ( hAPP_nat_int @ semiri1621563631at_int @ SV252 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1706]) ).
thf(1800,plain,
! [SV187: $i] :
( ( ( ( number_number_of_nat @ SV187 )
= zero_zero_nat )
= $false )
| ( ( ( hAPP_nat_nat @ ( power_power_nat @ zero_zero_nat ) @ ( number_number_of_nat @ SV187 ) )
= one_one_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1707]) ).
thf(1801,plain,
! [SV294: $i,SV253: $i,SV99: $i] :
( ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV99 ) @ SV253 )
!= ( hAPP_nat_nat @ ( plus_plus_nat @ SV99 ) @ SV294 ) )
| ( SV253 = SV294 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1709]) ).
thf(1802,plain,
! [SV99: $i,SV295: $i,SV254: $i] :
( ( ( SV254 != SV295 )
| ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV99 ) @ SV254 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ SV99 ) @ SV295 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1710]) ).
thf(1803,plain,
! [SV255: $i,SV189: $i] :
( ( ( ( ( bit0 @ SV189 )
!= ( bit0 @ SV255 ) ) )
= $true )
| ( ( SV189 = SV255 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1711]) ).
thf(1804,plain,
! [SV256: $i,SV190: $i] :
( ( ( ( SV190 != SV256 ) )
= $true )
| ( ( ( bit0 @ SV190 )
= ( bit0 @ SV256 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1712]) ).
thf(1805,plain,
! [SV191: $i] :
( ( ( zero_zero_int
= ( hAPP_int_int @ ( plus_plus_int @ SV191 ) @ SV191 ) )
= $false )
| ( ( SV191 = zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1713]) ).
thf(1806,plain,
! [SV192: $i] :
( ( ( SV192 = zero_zero_int )
= $false )
| ( ( zero_zero_int
= ( hAPP_int_int @ ( plus_plus_int @ SV192 ) @ SV192 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1714]) ).
thf(1807,plain,
! [SV257: $i,SV193: $i] :
( ( ( ( ( number267125858f_real @ SV193 )
!= ( number267125858f_real @ SV257 ) ) )
= $true )
| ( ( SV193 = SV257 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1715]) ).
thf(1808,plain,
! [SV258: $i,SV194: $i] :
( ( ( ( SV194 != SV258 ) )
= $true )
| ( ( ( number267125858f_real @ SV194 )
= ( number267125858f_real @ SV258 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1716]) ).
thf(1809,plain,
! [SV259: $i,SV195: $i] :
( ( ( ( SV195
!= ( hAPP_nat_nat @ ( plus_plus_nat @ SV195 ) @ SV259 ) ) )
= $true )
| ( ( SV259 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1717]) ).
thf(1810,plain,
! [SV196: $i,SV260: $i] :
( ( ( ( SV260 != zero_zero_nat ) )
= $true )
| ( ( SV196
= ( hAPP_nat_nat @ ( plus_plus_nat @ SV196 ) @ SV260 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1718]) ).
thf(1811,plain,
! [SV197: $i] :
( ( ( ( number_number_of_nat @ SV197 )
= zero_zero_nat )
= $false )
| ( ( ( hAPP_nat_int @ ( power_power_int @ zero_zero_int ) @ ( number_number_of_nat @ SV197 ) )
= one_one_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1719]) ).
thf(1812,plain,
! [SV261: $i,SV199: $i] :
( ( ( ( ( number_number_of_int @ SV199 )
!= ( number_number_of_int @ SV261 ) ) )
= $true )
| ( ( SV199 = SV261 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1721]) ).
thf(1813,plain,
! [SV262: $i,SV200: $i] :
( ( ( ( SV200 != SV262 ) )
= $true )
| ( ( ( number_number_of_int @ SV200 )
= ( number_number_of_int @ SV262 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1722]) ).
thf(1814,plain,
! [SV201: $i] :
( ( ( zero_zero_real = SV201 )
= $false )
| ( ( SV201 = zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1723]) ).
thf(1815,plain,
! [SV202: $i] :
( ( ( SV202 = zero_zero_real )
= $false )
| ( ( zero_zero_real = SV202 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1724]) ).
thf(1816,plain,
! [SV263: $i,SV203: $i] :
( ( ( ( ( bit1 @ SV203 )
!= ( bit1 @ SV263 ) ) )
= $true )
| ( ( SV203 = SV263 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1725]) ).
thf(1817,plain,
! [SV264: $i,SV204: $i] :
( ( ( ( SV204 != SV264 ) )
= $true )
| ( ( ( bit1 @ SV204 )
= ( bit1 @ SV264 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1726]) ).
thf(1818,plain,
! [SV265: $i,SV205: $i] :
( ( ( ( ( hAPP_nat_nat @ ( power_power_nat @ SV205 ) @ SV265 )
!= one_one_nat ) )
= $true )
| ( ( ( SV205 = one_one_nat )
| ( SV265 = zero_zero_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1727]) ).
thf(1819,plain,
( ( ! [SX0: $i] :
( ( SX0 != one_one_nat )
| ! [SX1: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ SX1 )
= one_one_nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1728]) ).
thf(1820,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1 != zero_zero_nat )
| ( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ SX1 )
= one_one_nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1729]) ).
thf(1821,plain,
! [SV206: $i] :
( ( ( ( hAPP_nat_int @ ( power_power_int @ SV206 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int )
= $false )
| ( ( SV206 = zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1730]) ).
thf(1822,plain,
! [SV207: $i] :
( ( ( SV207 = zero_zero_int )
= $false )
| ( ( ( hAPP_nat_int @ ( power_power_int @ SV207 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1731]) ).
thf(1823,plain,
! [SV266: $i,SV208: $i] :
( ( ( ( ( hAPP_nat_nat @ semiri984289939at_nat @ SV208 )
!= ( hAPP_nat_nat @ semiri984289939at_nat @ SV266 ) ) )
= $true )
| ( ( SV208 = SV266 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1732]) ).
thf(1824,plain,
! [SV267: $i,SV209: $i] :
( ( ( ( SV209 != SV267 ) )
= $true )
| ( ( ( hAPP_nat_nat @ semiri984289939at_nat @ SV209 )
= ( hAPP_nat_nat @ semiri984289939at_nat @ SV267 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1733]) ).
thf(1825,plain,
! [SV210: $i] :
( ( ( SV210 = zero_zero_nat )
= $false )
| ( ( ( hAPP_nat_int @ ( power_power_int @ zero_zero_int ) @ SV210 )
= one_one_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1734]) ).
thf(1826,plain,
! [SV268: $i,SV212: $i] :
( ( ( ( ( hAPP_nat_int @ semiri1621563631at_int @ SV212 )
!= ( hAPP_nat_int @ semiri1621563631at_int @ SV268 ) ) )
= $true )
| ( ( SV212 = SV268 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1736]) ).
thf(1827,plain,
! [SV269: $i,SV213: $i] :
( ( ( ( SV213 != SV269 ) )
= $true )
| ( ( ( hAPP_nat_int @ semiri1621563631at_int @ SV213 )
= ( hAPP_nat_int @ semiri1621563631at_int @ SV269 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1737]) ).
thf(1828,plain,
! [SV214: $i,SV270: $i] :
( ( ( ( SV270 = zero_zero_nat )
| ( SV214 != zero_zero_nat ) )
= $true )
| ( ( ( hAPP_nat_nat @ ( power_power_nat @ SV214 ) @ SV270 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1738]) ).
thf(1829,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ SX1 )
!= zero_zero_nat )
| ( SX1 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1739]) ).
thf(1830,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ SX1 )
!= zero_zero_nat )
| ( SX0 = zero_zero_nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1740]) ).
thf(1831,plain,
! [SV215: $i,SV271: $i] :
( ( ( ( ( number_number_of_nat @ SV271 )
= zero_zero_nat )
| ( SV215 != zero_zero_int ) )
= $true )
| ( ( ( hAPP_nat_int @ ( power_power_int @ SV215 ) @ ( number_number_of_nat @ SV271 ) )
= zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1741]) ).
thf(1832,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( hAPP_nat_int @ ( power_power_int @ SX0 ) @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_int )
| ( ( number_number_of_nat @ SX1 )
!= zero_zero_nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1742]) ).
thf(1833,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
( ( hAPP_nat_int @ ( power_power_int @ SX0 ) @ ( number_number_of_nat @ SX1 ) )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1743]) ).
thf(1834,plain,
! [SV296: $i,SV272: $i,SV100: $i] :
( ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV100 ) @ SV272 )
!= ( hAPP_nat_nat @ ( plus_plus_nat @ SV296 ) @ SV272 ) )
| ( SV100 = SV296 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1744]) ).
thf(1835,plain,
! [SV273: $i,SV297: $i,SV100: $i] :
( ( ( SV100 != SV297 )
| ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV100 ) @ SV273 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ SV297 ) @ SV273 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1745]) ).
thf(1836,plain,
! [SV298: $i,SV274: $i,SV101: $i] :
( ( ( ( hAPP_int_int @ ( plus_plus_int @ SV101 ) @ SV274 )
!= ( hAPP_int_int @ ( plus_plus_int @ SV298 ) @ SV274 ) )
| ( SV101 = SV298 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1746]) ).
thf(1837,plain,
! [SV275: $i,SV299: $i,SV101: $i] :
( ( ( SV101 != SV299 )
| ( ( hAPP_int_int @ ( plus_plus_int @ SV101 ) @ SV275 )
= ( hAPP_int_int @ ( plus_plus_int @ SV299 ) @ SV275 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1747]) ).
thf(1838,plain,
! [SV216: $i] :
( ( ( ( bit0 @ SV216 )
= pls )
= $false )
| ( ( SV216 = pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1748]) ).
thf(1839,plain,
! [SV217: $i] :
( ( ( SV217 = pls )
= $false )
| ( ( ( bit0 @ SV217 )
= pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1749]) ).
thf(1840,plain,
! [SV276: $i,SV218: $i] :
( ( ( ( ( number267125858f_real @ SV218 )
!= SV276 ) )
= $true )
| ( ( SV276
= ( number267125858f_real @ SV218 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1750]) ).
thf(1841,plain,
! [SV219: $i,SV277: $i] :
( ( ( ( SV277
!= ( number267125858f_real @ SV219 ) ) )
= $true )
| ( ( ( number267125858f_real @ SV219 )
= SV277 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1751]) ).
thf(1842,plain,
! [SV220: $i] :
( ( ( one_one_nat = SV220 )
= $false )
| ( ( SV220 = one_one_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1752]) ).
thf(1843,plain,
! [SV221: $i] :
( ( ( SV221 = one_one_nat )
= $false )
| ( ( one_one_nat = SV221 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1753]) ).
thf(1844,plain,
! [SV278: $i,SV222: $i] :
( ( ( ( ( number_number_of_nat @ SV222 )
!= SV278 ) )
= $true )
| ( ( SV278
= ( number_number_of_nat @ SV222 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1754]) ).
thf(1845,plain,
! [SV223: $i,SV279: $i] :
( ( ( ( SV279
!= ( number_number_of_nat @ SV223 ) ) )
= $true )
| ( ( ( number_number_of_nat @ SV223 )
= SV279 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1755]) ).
thf(1846,plain,
! [SV224: $i] :
( ( ( ( hAPP_int_int @ ( plus_plus_int @ SV224 ) @ SV224 )
= zero_zero_int )
= $false )
| ( ( SV224 = zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1756]) ).
thf(1847,plain,
! [SV225: $i] :
( ( ( SV225 = zero_zero_int )
= $false )
| ( ( ( hAPP_int_int @ ( plus_plus_int @ SV225 ) @ SV225 )
= zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1757]) ).
thf(1848,plain,
! [SV226: $i] :
( ( ( one_one_real = SV226 )
= $false )
| ( ( SV226 = one_one_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1758]) ).
thf(1849,plain,
! [SV227: $i] :
( ( ( SV227 = one_one_real )
= $false )
| ( ( one_one_real = SV227 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1759]) ).
thf(1850,plain,
! [SV228: $i,SV280: $i] :
( ( ( ( SV280 = zero_zero_nat )
| ( SV228 != zero_zero_int ) )
= $true )
| ( ( ( hAPP_nat_int @ ( power_power_int @ SV228 ) @ SV280 )
= zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1760]) ).
thf(1851,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( hAPP_nat_int @ ( power_power_int @ SX0 ) @ SX1 )
!= zero_zero_int )
| ( SX1 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1761]) ).
thf(1852,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
( ( hAPP_nat_int @ ( power_power_int @ SX0 ) @ SX1 )
!= zero_zero_int )
| ( SX0 = zero_zero_int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1762]) ).
thf(1853,plain,
! [SV229: $i] :
( ( ( zero_zero_int = SV229 )
= $false )
| ( ( SV229 = zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1763]) ).
thf(1854,plain,
! [SV230: $i] :
( ( ( SV230 = zero_zero_int )
= $false )
| ( ( zero_zero_int = SV230 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1764]) ).
thf(1855,plain,
! [SV281: $i,SV231: $i] :
( ( ( ( SV231 != zero_zero_nat )
| ( SV281 != zero_zero_nat ) )
= $true )
| ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV231 ) @ SV281 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1765]) ).
thf(1856,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ SX0 ) @ SX1 )
!= zero_zero_nat )
| ( SX0 = zero_zero_nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1766]) ).
thf(1857,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SX0 ) @ SX1 )
!= zero_zero_nat )
| ( SX1 = zero_zero_nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1767]) ).
thf(1858,plain,
! [SV282: $i,SV232: $i] :
( ( ( ( ( number_number_of_int @ SV232 )
!= SV282 ) )
= $true )
| ( ( SV282
= ( number_number_of_int @ SV232 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1768]) ).
thf(1859,plain,
! [SV233: $i,SV283: $i] :
( ( ( ( SV283
!= ( number_number_of_int @ SV233 ) ) )
= $true )
| ( ( ( number_number_of_int @ SV233 )
= SV283 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1769]) ).
thf(1860,plain,
! [SV284: $i,SV234: $i] :
( ( ( ( SV234 != zero_zero_int )
| ( SV284 != zero_zero_int ) )
= $true )
| ( ( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ SV234 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ SV284 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1770]) ).
thf(1861,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ SX0 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( 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)],[1771]) ).
thf(1862,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ SX0 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( 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)],[1772]) ).
thf(1863,plain,
! [SV235: $i] :
( ( ( ( hAPP_nat_int @ semiri1621563631at_int @ SV235 )
= zero_zero_int )
= $false )
| ( ( SV235 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1773]) ).
thf(1864,plain,
! [SV236: $i] :
( ( ( SV236 = zero_zero_nat )
= $false )
| ( ( ( hAPP_nat_int @ semiri1621563631at_int @ SV236 )
= zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1774]) ).
thf(1865,plain,
! [SV300: $i,SV285: $i,SV102: $i] :
( ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV102 ) @ SV285 )
!= ( hAPP_nat_nat @ ( plus_plus_nat @ SV300 ) @ SV285 ) )
| ( SV102 = SV300 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1775]) ).
thf(1866,plain,
! [SV286: $i,SV301: $i,SV102: $i] :
( ( ( SV102 != SV301 )
| ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV102 ) @ SV286 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ SV301 ) @ SV286 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1776]) ).
thf(1867,plain,
! [SV237: $i] :
( ( ( one_one_int = SV237 )
= $false )
| ( ( SV237 = one_one_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1777]) ).
thf(1868,plain,
! [SV238: $i] :
( ( ( SV238 = one_one_int )
= $false )
| ( ( one_one_int = SV238 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1778]) ).
thf(1869,plain,
! [SV239: $i,SV287: $i] :
( ( ( ( SV287 = zero_zero_nat )
| ( SV239 != zero_zero_nat ) )
= $true )
| ( ( ( hAPP_nat_nat @ ( power_power_nat @ SV239 ) @ SV287 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1779]) ).
thf(1870,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ SX1 )
!= zero_zero_nat )
| ( SX1 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1780]) ).
thf(1871,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ SX0 ) @ SX1 )
!= zero_zero_nat )
| ( SX0 = zero_zero_nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1781]) ).
thf(1872,plain,
! [SV240: $i] :
( ( ( zero_zero_nat = SV240 )
= $false )
| ( ( SV240 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1782]) ).
thf(1873,plain,
! [SV241: $i] :
( ( ( SV241 = zero_zero_nat )
= $false )
| ( ( zero_zero_nat = SV241 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1783]) ).
thf(1874,plain,
! [SV302: $i,SV288: $i,SV103: $i] :
( ( ( ( hAPP_int_int @ ( plus_plus_int @ SV103 ) @ SV288 )
!= ( hAPP_int_int @ ( plus_plus_int @ SV103 ) @ SV302 ) )
| ( SV288 = SV302 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1784]) ).
thf(1875,plain,
! [SV103: $i,SV303: $i,SV289: $i] :
( ( ( SV289 != SV303 )
| ( ( hAPP_int_int @ ( plus_plus_int @ SV103 ) @ SV289 )
= ( hAPP_int_int @ ( plus_plus_int @ SV103 ) @ SV303 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1785]) ).
thf(1876,plain,
! [SV242: $i] :
( ( ( pls
= ( bit0 @ SV242 ) )
= $false )
| ( ( pls = SV242 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1786]) ).
thf(1877,plain,
! [SV243: $i] :
( ( ( pls = SV243 )
= $false )
| ( ( pls
= ( bit0 @ SV243 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1787]) ).
thf(1878,plain,
! [SV290: $i,SV244: $i] :
( ( ( ( SV244
!= ( hAPP_int_int @ ( plus_plus_int @ SV244 ) @ SV290 ) ) )
= $true )
| ( ( SV290 = zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1788]) ).
thf(1879,plain,
! [SV245: $i,SV291: $i] :
( ( ( ( SV291 != zero_zero_int ) )
= $true )
| ( ( SV245
= ( hAPP_int_int @ ( plus_plus_int @ SV245 ) @ SV291 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1789]) ).
thf(1880,plain,
! [SV182: $i,SV246: $i] :
( ( ( ( number_number_of_nat @ SV246 )
= zero_zero_nat )
= $true )
| ( ( ( SV182 != zero_zero_nat ) )
= $true )
| ( ( ( hAPP_nat_nat @ ( power_power_nat @ SV182 ) @ ( number_number_of_nat @ SV246 ) )
= zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1791]) ).
thf(1881,plain,
! [SV304: $i] :
( ( ! [SY423: $i] :
( ( ( hAPP_nat_nat @ ( power_power_nat @ SV304 ) @ ( number_number_of_nat @ SY423 ) )
!= zero_zero_nat )
| ( ( number_number_of_nat @ SY423 )
!= zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1792]) ).
thf(1882,plain,
! [SV305: $i] :
( ( ! [SY424: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ SV305 ) @ ( number_number_of_nat @ SY424 ) )
!= zero_zero_nat )
| ( SV305 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1793]) ).
thf(1883,plain,
! [SV247: $i,SV183: $i] :
( ( ( ( hAPP_nat_int @ semiri1621563631at_int @ SV183 )
= ( hAPP_nat_int @ semiri1621563631at_int @ SV247 ) )
= $false )
| ( ( SV183 = SV247 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1794]) ).
thf(1884,plain,
! [SV248: $i,SV184: $i] :
( ( ( SV184 = SV248 )
= $false )
| ( ( ( hAPP_nat_int @ semiri1621563631at_int @ SV184 )
= ( hAPP_nat_int @ semiri1621563631at_int @ SV248 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1795]) ).
thf(1885,plain,
! [SV292: $i,SV249: $i,SV98: $i] :
( ( ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV98 ) @ SV249 )
!= ( hAPP_nat_nat @ ( plus_plus_nat @ SV98 ) @ SV292 ) ) )
= $true )
| ( ( SV249 = SV292 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1796]) ).
thf(1886,plain,
! [SV98: $i,SV293: $i,SV250: $i] :
( ( ( ( SV250 != SV293 ) )
= $true )
| ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV98 ) @ SV250 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ SV98 ) @ SV293 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1797]) ).
thf(1887,plain,
! [SV251: $i,SV185: $i] :
( ( ( ( hAPP_nat_int @ semiri1621563631at_int @ SV185 )
= ( hAPP_nat_int @ semiri1621563631at_int @ SV251 ) )
= $false )
| ( ( SV185 = SV251 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1798]) ).
thf(1888,plain,
! [SV252: $i,SV186: $i] :
( ( ( SV186 = SV252 )
= $false )
| ( ( ( hAPP_nat_int @ semiri1621563631at_int @ SV186 )
= ( hAPP_nat_int @ semiri1621563631at_int @ SV252 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1799]) ).
thf(1889,plain,
! [SV294: $i,SV253: $i,SV99: $i] :
( ( ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV99 ) @ SV253 )
!= ( hAPP_nat_nat @ ( plus_plus_nat @ SV99 ) @ SV294 ) ) )
= $true )
| ( ( SV253 = SV294 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1801]) ).
thf(1890,plain,
! [SV99: $i,SV295: $i,SV254: $i] :
( ( ( ( SV254 != SV295 ) )
= $true )
| ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV99 ) @ SV254 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ SV99 ) @ SV295 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1802]) ).
thf(1891,plain,
! [SV255: $i,SV189: $i] :
( ( ( ( bit0 @ SV189 )
= ( bit0 @ SV255 ) )
= $false )
| ( ( SV189 = SV255 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1803]) ).
thf(1892,plain,
! [SV256: $i,SV190: $i] :
( ( ( SV190 = SV256 )
= $false )
| ( ( ( bit0 @ SV190 )
= ( bit0 @ SV256 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1804]) ).
thf(1893,plain,
! [SV257: $i,SV193: $i] :
( ( ( ( number267125858f_real @ SV193 )
= ( number267125858f_real @ SV257 ) )
= $false )
| ( ( SV193 = SV257 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1807]) ).
thf(1894,plain,
! [SV258: $i,SV194: $i] :
( ( ( SV194 = SV258 )
= $false )
| ( ( ( number267125858f_real @ SV194 )
= ( number267125858f_real @ SV258 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1808]) ).
thf(1895,plain,
! [SV259: $i,SV195: $i] :
( ( ( SV195
= ( hAPP_nat_nat @ ( plus_plus_nat @ SV195 ) @ SV259 ) )
= $false )
| ( ( SV259 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1809]) ).
thf(1896,plain,
! [SV196: $i,SV260: $i] :
( ( ( SV260 = zero_zero_nat )
= $false )
| ( ( SV196
= ( hAPP_nat_nat @ ( plus_plus_nat @ SV196 ) @ SV260 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1810]) ).
thf(1897,plain,
! [SV261: $i,SV199: $i] :
( ( ( ( number_number_of_int @ SV199 )
= ( number_number_of_int @ SV261 ) )
= $false )
| ( ( SV199 = SV261 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1812]) ).
thf(1898,plain,
! [SV262: $i,SV200: $i] :
( ( ( SV200 = SV262 )
= $false )
| ( ( ( number_number_of_int @ SV200 )
= ( number_number_of_int @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1813]) ).
thf(1899,plain,
! [SV263: $i,SV203: $i] :
( ( ( ( bit1 @ SV203 )
= ( bit1 @ SV263 ) )
= $false )
| ( ( SV203 = SV263 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1816]) ).
thf(1900,plain,
! [SV264: $i,SV204: $i] :
( ( ( SV204 = SV264 )
= $false )
| ( ( ( bit1 @ SV204 )
= ( bit1 @ SV264 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1817]) ).
thf(1901,plain,
! [SV265: $i,SV205: $i] :
( ( ( ( hAPP_nat_nat @ ( power_power_nat @ SV205 ) @ SV265 )
= one_one_nat )
= $false )
| ( ( ( SV205 = one_one_nat )
| ( SV265 = zero_zero_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1818]) ).
thf(1902,plain,
! [SV306: $i] :
( ( ( SV306 != one_one_nat )
| ! [SY425: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ SV306 ) @ SY425 )
= one_one_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1819]) ).
thf(1903,plain,
! [SV307: $i] :
( ( ! [SY426: $i] :
( ( SY426 != zero_zero_nat )
| ( ( hAPP_nat_nat @ ( power_power_nat @ SV307 ) @ SY426 )
= one_one_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1820]) ).
thf(1904,plain,
! [SV266: $i,SV208: $i] :
( ( ( ( hAPP_nat_nat @ semiri984289939at_nat @ SV208 )
= ( hAPP_nat_nat @ semiri984289939at_nat @ SV266 ) )
= $false )
| ( ( SV208 = SV266 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1823]) ).
thf(1905,plain,
! [SV267: $i,SV209: $i] :
( ( ( SV209 = SV267 )
= $false )
| ( ( ( hAPP_nat_nat @ semiri984289939at_nat @ SV209 )
= ( hAPP_nat_nat @ semiri984289939at_nat @ SV267 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1824]) ).
thf(1906,plain,
! [SV268: $i,SV212: $i] :
( ( ( ( hAPP_nat_int @ semiri1621563631at_int @ SV212 )
= ( hAPP_nat_int @ semiri1621563631at_int @ SV268 ) )
= $false )
| ( ( SV212 = SV268 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1826]) ).
thf(1907,plain,
! [SV269: $i,SV213: $i] :
( ( ( SV213 = SV269 )
= $false )
| ( ( ( hAPP_nat_int @ semiri1621563631at_int @ SV213 )
= ( hAPP_nat_int @ semiri1621563631at_int @ SV269 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1827]) ).
thf(1908,plain,
! [SV214: $i,SV270: $i] :
( ( ( SV270 = zero_zero_nat )
= $true )
| ( ( ( SV214 != zero_zero_nat ) )
= $true )
| ( ( ( hAPP_nat_nat @ ( power_power_nat @ SV214 ) @ SV270 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1828]) ).
thf(1909,plain,
! [SV308: $i] :
( ( ! [SY427: $i] :
( ( ( hAPP_nat_nat @ ( power_power_nat @ SV308 ) @ SY427 )
!= zero_zero_nat )
| ( SY427 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1829]) ).
thf(1910,plain,
! [SV309: $i] :
( ( ! [SY428: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ SV309 ) @ SY428 )
!= zero_zero_nat )
| ( SV309 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1830]) ).
thf(1911,plain,
! [SV215: $i,SV271: $i] :
( ( ( ( number_number_of_nat @ SV271 )
= zero_zero_nat )
= $true )
| ( ( ( SV215 != zero_zero_int ) )
= $true )
| ( ( ( hAPP_nat_int @ ( power_power_int @ SV215 ) @ ( number_number_of_nat @ SV271 ) )
= zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1831]) ).
thf(1912,plain,
! [SV310: $i] :
( ( ! [SY429: $i] :
( ( ( hAPP_nat_int @ ( power_power_int @ SV310 ) @ ( number_number_of_nat @ SY429 ) )
!= zero_zero_int )
| ( ( number_number_of_nat @ SY429 )
!= zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1832]) ).
thf(1913,plain,
! [SV311: $i] :
( ( ! [SY430: $i] :
( ( hAPP_nat_int @ ( power_power_int @ SV311 ) @ ( number_number_of_nat @ SY430 ) )
!= zero_zero_int )
| ( SV311 = zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1833]) ).
thf(1914,plain,
! [SV296: $i,SV272: $i,SV100: $i] :
( ( ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV100 ) @ SV272 )
!= ( hAPP_nat_nat @ ( plus_plus_nat @ SV296 ) @ SV272 ) ) )
= $true )
| ( ( SV100 = SV296 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1834]) ).
thf(1915,plain,
! [SV273: $i,SV297: $i,SV100: $i] :
( ( ( ( SV100 != SV297 ) )
= $true )
| ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV100 ) @ SV273 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ SV297 ) @ SV273 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1835]) ).
thf(1916,plain,
! [SV298: $i,SV274: $i,SV101: $i] :
( ( ( ( ( hAPP_int_int @ ( plus_plus_int @ SV101 ) @ SV274 )
!= ( hAPP_int_int @ ( plus_plus_int @ SV298 ) @ SV274 ) ) )
= $true )
| ( ( SV101 = SV298 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1836]) ).
thf(1917,plain,
! [SV275: $i,SV299: $i,SV101: $i] :
( ( ( ( SV101 != SV299 ) )
= $true )
| ( ( ( hAPP_int_int @ ( plus_plus_int @ SV101 ) @ SV275 )
= ( hAPP_int_int @ ( plus_plus_int @ SV299 ) @ SV275 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1837]) ).
thf(1918,plain,
! [SV276: $i,SV218: $i] :
( ( ( ( number267125858f_real @ SV218 )
= SV276 )
= $false )
| ( ( SV276
= ( number267125858f_real @ SV218 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1840]) ).
thf(1919,plain,
! [SV219: $i,SV277: $i] :
( ( ( SV277
= ( number267125858f_real @ SV219 ) )
= $false )
| ( ( ( number267125858f_real @ SV219 )
= SV277 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1841]) ).
thf(1920,plain,
! [SV278: $i,SV222: $i] :
( ( ( ( number_number_of_nat @ SV222 )
= SV278 )
= $false )
| ( ( SV278
= ( number_number_of_nat @ SV222 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1844]) ).
thf(1921,plain,
! [SV223: $i,SV279: $i] :
( ( ( SV279
= ( number_number_of_nat @ SV223 ) )
= $false )
| ( ( ( number_number_of_nat @ SV223 )
= SV279 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1845]) ).
thf(1922,plain,
! [SV228: $i,SV280: $i] :
( ( ( SV280 = zero_zero_nat )
= $true )
| ( ( ( SV228 != zero_zero_int ) )
= $true )
| ( ( ( hAPP_nat_int @ ( power_power_int @ SV228 ) @ SV280 )
= zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1850]) ).
thf(1923,plain,
! [SV312: $i] :
( ( ! [SY431: $i] :
( ( ( hAPP_nat_int @ ( power_power_int @ SV312 ) @ SY431 )
!= zero_zero_int )
| ( SY431 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1851]) ).
thf(1924,plain,
! [SV313: $i] :
( ( ! [SY432: $i] :
( ( hAPP_nat_int @ ( power_power_int @ SV313 ) @ SY432 )
!= zero_zero_int )
| ( SV313 = zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1852]) ).
thf(1925,plain,
! [SV281: $i,SV231: $i] :
( ( ( ( SV231 != zero_zero_nat ) )
= $true )
| ( ( ( SV281 != zero_zero_nat ) )
= $true )
| ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV231 ) @ SV281 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1855]) ).
thf(1926,plain,
! [SV314: $i] :
( ( ! [SY433: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ SV314 ) @ SY433 )
!= zero_zero_nat )
| ( SV314 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1856]) ).
thf(1927,plain,
! [SV315: $i] :
( ( ! [SY434: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV315 ) @ SY434 )
!= zero_zero_nat )
| ( SY434 = zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1857]) ).
thf(1928,plain,
! [SV282: $i,SV232: $i] :
( ( ( ( number_number_of_int @ SV232 )
= SV282 )
= $false )
| ( ( SV282
= ( number_number_of_int @ SV232 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1858]) ).
thf(1929,plain,
! [SV233: $i,SV283: $i] :
( ( ( SV283
= ( number_number_of_int @ SV233 ) )
= $false )
| ( ( ( number_number_of_int @ SV233 )
= SV283 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1859]) ).
thf(1930,plain,
! [SV284: $i,SV234: $i] :
( ( ( ( SV234 != zero_zero_int ) )
= $true )
| ( ( ( SV284 != zero_zero_int ) )
= $true )
| ( ( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ SV234 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ SV284 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1860]) ).
thf(1931,plain,
! [SV316: $i] :
( ( ! [SY435: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ SV316 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ SY435 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_int )
| ( SV316 = zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1861]) ).
thf(1932,plain,
! [SV317: $i] :
( ( ! [SY436: $i] :
( ( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ SV317 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ SY436 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_int )
| ( SY436 = zero_zero_int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1862]) ).
thf(1933,plain,
! [SV300: $i,SV285: $i,SV102: $i] :
( ( ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV102 ) @ SV285 )
!= ( hAPP_nat_nat @ ( plus_plus_nat @ SV300 ) @ SV285 ) ) )
= $true )
| ( ( SV102 = SV300 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1865]) ).
thf(1934,plain,
! [SV286: $i,SV301: $i,SV102: $i] :
( ( ( ( SV102 != SV301 ) )
= $true )
| ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV102 ) @ SV286 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ SV301 ) @ SV286 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1866]) ).
thf(1935,plain,
! [SV239: $i,SV287: $i] :
( ( ( SV287 = zero_zero_nat )
= $true )
| ( ( ( SV239 != zero_zero_nat ) )
= $true )
| ( ( ( hAPP_nat_nat @ ( power_power_nat @ SV239 ) @ SV287 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1869]) ).
thf(1936,plain,
! [SV318: $i] :
( ( ! [SY437: $i] :
( ( ( hAPP_nat_nat @ ( power_power_nat @ SV318 ) @ SY437 )
!= zero_zero_nat )
| ( SY437 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1870]) ).
thf(1937,plain,
! [SV319: $i] :
( ( ! [SY438: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ SV319 ) @ SY438 )
!= zero_zero_nat )
| ( SV319 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1871]) ).
thf(1938,plain,
! [SV302: $i,SV288: $i,SV103: $i] :
( ( ( ( ( hAPP_int_int @ ( plus_plus_int @ SV103 ) @ SV288 )
!= ( hAPP_int_int @ ( plus_plus_int @ SV103 ) @ SV302 ) ) )
= $true )
| ( ( SV288 = SV302 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1874]) ).
thf(1939,plain,
! [SV103: $i,SV303: $i,SV289: $i] :
( ( ( ( SV289 != SV303 ) )
= $true )
| ( ( ( hAPP_int_int @ ( plus_plus_int @ SV103 ) @ SV289 )
= ( hAPP_int_int @ ( plus_plus_int @ SV103 ) @ SV303 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1875]) ).
thf(1940,plain,
! [SV290: $i,SV244: $i] :
( ( ( SV244
= ( hAPP_int_int @ ( plus_plus_int @ SV244 ) @ SV290 ) )
= $false )
| ( ( SV290 = zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1878]) ).
thf(1941,plain,
! [SV245: $i,SV291: $i] :
( ( ( SV291 = zero_zero_int )
= $false )
| ( ( SV245
= ( hAPP_int_int @ ( plus_plus_int @ SV245 ) @ SV291 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1879]) ).
thf(1942,plain,
! [SV246: $i,SV182: $i] :
( ( ( SV182 = zero_zero_nat )
= $false )
| ( ( ( number_number_of_nat @ SV246 )
= zero_zero_nat )
= $true )
| ( ( ( hAPP_nat_nat @ ( power_power_nat @ SV182 ) @ ( number_number_of_nat @ SV246 ) )
= zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1880]) ).
thf(1943,plain,
! [SV320: $i,SV304: $i] :
( ( ( ( hAPP_nat_nat @ ( power_power_nat @ SV304 ) @ ( number_number_of_nat @ SV320 ) )
!= zero_zero_nat )
| ( ( number_number_of_nat @ SV320 )
!= zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1881]) ).
thf(1944,plain,
! [SV305: $i] :
( ( ( ! [SY424: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ SV305 ) @ ( number_number_of_nat @ SY424 ) )
!= zero_zero_nat ) )
= $true )
| ( ( SV305 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1882]) ).
thf(1945,plain,
! [SV292: $i,SV249: $i,SV98: $i] :
( ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV98 ) @ SV249 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ SV98 ) @ SV292 ) )
= $false )
| ( ( SV249 = SV292 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1885]) ).
thf(1946,plain,
! [SV98: $i,SV293: $i,SV250: $i] :
( ( ( SV250 = SV293 )
= $false )
| ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV98 ) @ SV250 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ SV98 ) @ SV293 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1886]) ).
thf(1947,plain,
! [SV294: $i,SV253: $i,SV99: $i] :
( ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV99 ) @ SV253 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ SV99 ) @ SV294 ) )
= $false )
| ( ( SV253 = SV294 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1889]) ).
thf(1948,plain,
! [SV99: $i,SV295: $i,SV254: $i] :
( ( ( SV254 = SV295 )
= $false )
| ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV99 ) @ SV254 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ SV99 ) @ SV295 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1890]) ).
thf(1949,plain,
! [SV265: $i,SV205: $i] :
( ( ( SV205 = one_one_nat )
= $true )
| ( ( SV265 = zero_zero_nat )
= $true )
| ( ( ( hAPP_nat_nat @ ( power_power_nat @ SV205 ) @ SV265 )
= one_one_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1901]) ).
thf(1950,plain,
! [SV306: $i] :
( ( ( ( SV306 != one_one_nat ) )
= $true )
| ( ( ! [SY425: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ SV306 ) @ SY425 )
= one_one_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1902]) ).
thf(1951,plain,
! [SV307: $i,SV321: $i] :
( ( ( SV321 != zero_zero_nat )
| ( ( hAPP_nat_nat @ ( power_power_nat @ SV307 ) @ SV321 )
= one_one_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1903]) ).
thf(1952,plain,
! [SV270: $i,SV214: $i] :
( ( ( SV214 = zero_zero_nat )
= $false )
| ( ( SV270 = zero_zero_nat )
= $true )
| ( ( ( hAPP_nat_nat @ ( power_power_nat @ SV214 ) @ SV270 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1908]) ).
thf(1953,plain,
! [SV322: $i,SV308: $i] :
( ( ( ( hAPP_nat_nat @ ( power_power_nat @ SV308 ) @ SV322 )
!= zero_zero_nat )
| ( SV322 != zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1909]) ).
thf(1954,plain,
! [SV309: $i] :
( ( ( ! [SY428: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ SV309 ) @ SY428 )
!= zero_zero_nat ) )
= $true )
| ( ( SV309 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1910]) ).
thf(1955,plain,
! [SV271: $i,SV215: $i] :
( ( ( SV215 = zero_zero_int )
= $false )
| ( ( ( number_number_of_nat @ SV271 )
= zero_zero_nat )
= $true )
| ( ( ( hAPP_nat_int @ ( power_power_int @ SV215 ) @ ( number_number_of_nat @ SV271 ) )
= zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1911]) ).
thf(1956,plain,
! [SV323: $i,SV310: $i] :
( ( ( ( hAPP_nat_int @ ( power_power_int @ SV310 ) @ ( number_number_of_nat @ SV323 ) )
!= zero_zero_int )
| ( ( number_number_of_nat @ SV323 )
!= zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1912]) ).
thf(1957,plain,
! [SV311: $i] :
( ( ( ! [SY430: $i] :
( ( hAPP_nat_int @ ( power_power_int @ SV311 ) @ ( number_number_of_nat @ SY430 ) )
!= zero_zero_int ) )
= $true )
| ( ( SV311 = zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1913]) ).
thf(1958,plain,
! [SV296: $i,SV272: $i,SV100: $i] :
( ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV100 ) @ SV272 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ SV296 ) @ SV272 ) )
= $false )
| ( ( SV100 = SV296 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1914]) ).
thf(1959,plain,
! [SV273: $i,SV297: $i,SV100: $i] :
( ( ( SV100 = SV297 )
= $false )
| ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV100 ) @ SV273 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ SV297 ) @ SV273 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1915]) ).
thf(1960,plain,
! [SV298: $i,SV274: $i,SV101: $i] :
( ( ( ( hAPP_int_int @ ( plus_plus_int @ SV101 ) @ SV274 )
= ( hAPP_int_int @ ( plus_plus_int @ SV298 ) @ SV274 ) )
= $false )
| ( ( SV101 = SV298 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1916]) ).
thf(1961,plain,
! [SV275: $i,SV299: $i,SV101: $i] :
( ( ( SV101 = SV299 )
= $false )
| ( ( ( hAPP_int_int @ ( plus_plus_int @ SV101 ) @ SV275 )
= ( hAPP_int_int @ ( plus_plus_int @ SV299 ) @ SV275 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1917]) ).
thf(1962,plain,
! [SV280: $i,SV228: $i] :
( ( ( SV228 = zero_zero_int )
= $false )
| ( ( SV280 = zero_zero_nat )
= $true )
| ( ( ( hAPP_nat_int @ ( power_power_int @ SV228 ) @ SV280 )
= zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1922]) ).
thf(1963,plain,
! [SV324: $i,SV312: $i] :
( ( ( ( hAPP_nat_int @ ( power_power_int @ SV312 ) @ SV324 )
!= zero_zero_int )
| ( SV324 != zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1923]) ).
thf(1964,plain,
! [SV313: $i] :
( ( ( ! [SY432: $i] :
( ( hAPP_nat_int @ ( power_power_int @ SV313 ) @ SY432 )
!= zero_zero_int ) )
= $true )
| ( ( SV313 = zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1924]) ).
thf(1965,plain,
! [SV281: $i,SV231: $i] :
( ( ( SV231 = zero_zero_nat )
= $false )
| ( ( ( SV281 != zero_zero_nat ) )
= $true )
| ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV231 ) @ SV281 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1925]) ).
thf(1966,plain,
! [SV314: $i] :
( ( ( ! [SY433: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ SV314 ) @ SY433 )
!= zero_zero_nat ) )
= $true )
| ( ( SV314 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1926]) ).
thf(1967,plain,
! [SV325: $i,SV315: $i] :
( ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV315 ) @ SV325 )
!= zero_zero_nat )
| ( SV325 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1927]) ).
thf(1968,plain,
! [SV284: $i,SV234: $i] :
( ( ( SV234 = zero_zero_int )
= $false )
| ( ( ( SV284 != zero_zero_int ) )
= $true )
| ( ( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ SV234 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ SV284 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1930]) ).
thf(1969,plain,
! [SV316: $i] :
( ( ( ! [SY435: $i] :
( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ SV316 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ SY435 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_int ) )
= $true )
| ( ( SV316 = zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1931]) ).
thf(1970,plain,
! [SV326: $i,SV317: $i] :
( ( ( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ SV317 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ SV326 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_int )
| ( SV326 = zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1932]) ).
thf(1971,plain,
! [SV300: $i,SV285: $i,SV102: $i] :
( ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV102 ) @ SV285 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ SV300 ) @ SV285 ) )
= $false )
| ( ( SV102 = SV300 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1933]) ).
thf(1972,plain,
! [SV286: $i,SV301: $i,SV102: $i] :
( ( ( SV102 = SV301 )
= $false )
| ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV102 ) @ SV286 )
= ( hAPP_nat_nat @ ( plus_plus_nat @ SV301 ) @ SV286 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1934]) ).
thf(1973,plain,
! [SV287: $i,SV239: $i] :
( ( ( SV239 = zero_zero_nat )
= $false )
| ( ( SV287 = zero_zero_nat )
= $true )
| ( ( ( hAPP_nat_nat @ ( power_power_nat @ SV239 ) @ SV287 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1935]) ).
thf(1974,plain,
! [SV327: $i,SV318: $i] :
( ( ( ( hAPP_nat_nat @ ( power_power_nat @ SV318 ) @ SV327 )
!= zero_zero_nat )
| ( SV327 != zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1936]) ).
thf(1975,plain,
! [SV319: $i] :
( ( ( ! [SY438: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ SV319 ) @ SY438 )
!= zero_zero_nat ) )
= $true )
| ( ( SV319 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1937]) ).
thf(1976,plain,
! [SV302: $i,SV288: $i,SV103: $i] :
( ( ( ( hAPP_int_int @ ( plus_plus_int @ SV103 ) @ SV288 )
= ( hAPP_int_int @ ( plus_plus_int @ SV103 ) @ SV302 ) )
= $false )
| ( ( SV288 = SV302 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1938]) ).
thf(1977,plain,
! [SV103: $i,SV303: $i,SV289: $i] :
( ( ( SV289 = SV303 )
= $false )
| ( ( ( hAPP_int_int @ ( plus_plus_int @ SV103 ) @ SV289 )
= ( hAPP_int_int @ ( plus_plus_int @ SV103 ) @ SV303 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1939]) ).
thf(1978,plain,
! [SV320: $i,SV304: $i] :
( ( ( ( ( hAPP_nat_nat @ ( power_power_nat @ SV304 ) @ ( number_number_of_nat @ SV320 ) )
!= zero_zero_nat ) )
= $true )
| ( ( ( ( number_number_of_nat @ SV320 )
!= zero_zero_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1943]) ).
thf(1979,plain,
! [SV328: $i,SV305: $i] :
( ( ( ( ( hAPP_nat_nat @ ( power_power_nat @ SV305 ) @ ( number_number_of_nat @ SV328 ) )
!= zero_zero_nat ) )
= $true )
| ( ( SV305 = zero_zero_nat )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1944]) ).
thf(1980,plain,
! [SV306: $i] :
( ( ( SV306 = one_one_nat )
= $false )
| ( ( ! [SY425: $i] :
( ( hAPP_nat_nat @ ( power_power_nat @ SV306 ) @ SY425 )
= one_one_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1950]) ).
thf(1981,plain,
! [SV307: $i,SV321: $i] :
( ( ( ( SV321 != zero_zero_nat ) )
= $true )
| ( ( ( hAPP_nat_nat @ ( power_power_nat @ SV307 ) @ SV321 )
= one_one_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1951]) ).
thf(1982,plain,
! [SV322: $i,SV308: $i] :
( ( ( ( ( hAPP_nat_nat @ ( power_power_nat @ SV308 ) @ SV322 )
!= zero_zero_nat ) )
= $true )
| ( ( ( SV322 != zero_zero_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1953]) ).
thf(1983,plain,
! [SV329: $i,SV309: $i] :
( ( ( ( ( hAPP_nat_nat @ ( power_power_nat @ SV309 ) @ SV329 )
!= zero_zero_nat ) )
= $true )
| ( ( SV309 = zero_zero_nat )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1954]) ).
thf(1984,plain,
! [SV323: $i,SV310: $i] :
( ( ( ( ( hAPP_nat_int @ ( power_power_int @ SV310 ) @ ( number_number_of_nat @ SV323 ) )
!= zero_zero_int ) )
= $true )
| ( ( ( ( number_number_of_nat @ SV323 )
!= zero_zero_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1956]) ).
thf(1985,plain,
! [SV330: $i,SV311: $i] :
( ( ( ( ( hAPP_nat_int @ ( power_power_int @ SV311 ) @ ( number_number_of_nat @ SV330 ) )
!= zero_zero_int ) )
= $true )
| ( ( SV311 = zero_zero_int )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1957]) ).
thf(1986,plain,
! [SV324: $i,SV312: $i] :
( ( ( ( ( hAPP_nat_int @ ( power_power_int @ SV312 ) @ SV324 )
!= zero_zero_int ) )
= $true )
| ( ( ( SV324 != zero_zero_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1963]) ).
thf(1987,plain,
! [SV331: $i,SV313: $i] :
( ( ( ( ( hAPP_nat_int @ ( power_power_int @ SV313 ) @ SV331 )
!= zero_zero_int ) )
= $true )
| ( ( SV313 = zero_zero_int )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1964]) ).
thf(1988,plain,
! [SV231: $i,SV281: $i] :
( ( ( SV281 = zero_zero_nat )
= $false )
| ( ( SV231 = zero_zero_nat )
= $false )
| ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV231 ) @ SV281 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1965]) ).
thf(1989,plain,
! [SV332: $i,SV314: $i] :
( ( ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV314 ) @ SV332 )
!= zero_zero_nat ) )
= $true )
| ( ( SV314 = zero_zero_nat )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1966]) ).
thf(1990,plain,
! [SV325: $i,SV315: $i] :
( ( ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV315 ) @ SV325 )
!= zero_zero_nat ) )
= $true )
| ( ( SV325 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1967]) ).
thf(1991,plain,
! [SV234: $i,SV284: $i] :
( ( ( SV284 = zero_zero_int )
= $false )
| ( ( SV234 = zero_zero_int )
= $false )
| ( ( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ SV234 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ SV284 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1968]) ).
thf(1992,plain,
! [SV333: $i,SV316: $i] :
( ( ( ( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ SV316 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ SV333 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_int ) )
= $true )
| ( ( SV316 = zero_zero_int )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1969]) ).
thf(1993,plain,
! [SV326: $i,SV317: $i] :
( ( ( ( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ SV317 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ SV326 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= zero_zero_int ) )
= $true )
| ( ( SV326 = zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1970]) ).
thf(1994,plain,
! [SV327: $i,SV318: $i] :
( ( ( ( ( hAPP_nat_nat @ ( power_power_nat @ SV318 ) @ SV327 )
!= zero_zero_nat ) )
= $true )
| ( ( ( SV327 != zero_zero_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1974]) ).
thf(1995,plain,
! [SV334: $i,SV319: $i] :
( ( ( ( ( hAPP_nat_nat @ ( power_power_nat @ SV319 ) @ SV334 )
!= zero_zero_nat ) )
= $true )
| ( ( SV319 = zero_zero_nat )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1975]) ).
thf(1996,plain,
! [SV320: $i,SV304: $i] :
( ( ( ( hAPP_nat_nat @ ( power_power_nat @ SV304 ) @ ( number_number_of_nat @ SV320 ) )
= zero_zero_nat )
= $false )
| ( ( ( ( number_number_of_nat @ SV320 )
!= zero_zero_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1978]) ).
thf(1997,plain,
! [SV328: $i,SV305: $i] :
( ( ( ( hAPP_nat_nat @ ( power_power_nat @ SV305 ) @ ( number_number_of_nat @ SV328 ) )
= zero_zero_nat )
= $false )
| ( ( SV305 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1979]) ).
thf(1998,plain,
! [SV335: $i,SV306: $i] :
( ( ( ( hAPP_nat_nat @ ( power_power_nat @ SV306 ) @ SV335 )
= one_one_nat )
= $true )
| ( ( SV306 = one_one_nat )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1980]) ).
thf(1999,plain,
! [SV307: $i,SV321: $i] :
( ( ( SV321 = zero_zero_nat )
= $false )
| ( ( ( hAPP_nat_nat @ ( power_power_nat @ SV307 ) @ SV321 )
= one_one_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1981]) ).
thf(2000,plain,
! [SV322: $i,SV308: $i] :
( ( ( ( hAPP_nat_nat @ ( power_power_nat @ SV308 ) @ SV322 )
= zero_zero_nat )
= $false )
| ( ( ( SV322 != zero_zero_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1982]) ).
thf(2001,plain,
! [SV329: $i,SV309: $i] :
( ( ( ( hAPP_nat_nat @ ( power_power_nat @ SV309 ) @ SV329 )
= zero_zero_nat )
= $false )
| ( ( SV309 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1983]) ).
thf(2002,plain,
! [SV323: $i,SV310: $i] :
( ( ( ( hAPP_nat_int @ ( power_power_int @ SV310 ) @ ( number_number_of_nat @ SV323 ) )
= zero_zero_int )
= $false )
| ( ( ( ( number_number_of_nat @ SV323 )
!= zero_zero_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1984]) ).
thf(2003,plain,
! [SV330: $i,SV311: $i] :
( ( ( ( hAPP_nat_int @ ( power_power_int @ SV311 ) @ ( number_number_of_nat @ SV330 ) )
= zero_zero_int )
= $false )
| ( ( SV311 = zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1985]) ).
thf(2004,plain,
! [SV324: $i,SV312: $i] :
( ( ( ( hAPP_nat_int @ ( power_power_int @ SV312 ) @ SV324 )
= zero_zero_int )
= $false )
| ( ( ( SV324 != zero_zero_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1986]) ).
thf(2005,plain,
! [SV331: $i,SV313: $i] :
( ( ( ( hAPP_nat_int @ ( power_power_int @ SV313 ) @ SV331 )
= zero_zero_int )
= $false )
| ( ( SV313 = zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1987]) ).
thf(2006,plain,
! [SV332: $i,SV314: $i] :
( ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV314 ) @ SV332 )
= zero_zero_nat )
= $false )
| ( ( SV314 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1989]) ).
thf(2007,plain,
! [SV325: $i,SV315: $i] :
( ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ SV315 ) @ SV325 )
= zero_zero_nat )
= $false )
| ( ( SV325 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1990]) ).
thf(2008,plain,
! [SV333: $i,SV316: $i] :
( ( ( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ SV316 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ SV333 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_int )
= $false )
| ( ( SV316 = zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1992]) ).
thf(2009,plain,
! [SV326: $i,SV317: $i] :
( ( ( ( hAPP_int_int @ ( plus_plus_int @ ( hAPP_nat_int @ ( power_power_int @ SV317 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( power_power_int @ SV326 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_int )
= $false )
| ( ( SV326 = zero_zero_int )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1993]) ).
thf(2010,plain,
! [SV327: $i,SV318: $i] :
( ( ( ( hAPP_nat_nat @ ( power_power_nat @ SV318 ) @ SV327 )
= zero_zero_nat )
= $false )
| ( ( ( SV327 != zero_zero_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1994]) ).
thf(2011,plain,
! [SV334: $i,SV319: $i] :
( ( ( ( hAPP_nat_nat @ ( power_power_nat @ SV319 ) @ SV334 )
= zero_zero_nat )
= $false )
| ( ( SV319 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1995]) ).
thf(2012,plain,
! [SV304: $i,SV320: $i] :
( ( ( ( number_number_of_nat @ SV320 )
= zero_zero_nat )
= $false )
| ( ( ( hAPP_nat_nat @ ( power_power_nat @ SV304 ) @ ( number_number_of_nat @ SV320 ) )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1996]) ).
thf(2013,plain,
! [SV308: $i,SV322: $i] :
( ( ( SV322 = zero_zero_nat )
= $false )
| ( ( ( hAPP_nat_nat @ ( power_power_nat @ SV308 ) @ SV322 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2000]) ).
thf(2014,plain,
! [SV310: $i,SV323: $i] :
( ( ( ( number_number_of_nat @ SV323 )
= zero_zero_nat )
= $false )
| ( ( ( hAPP_nat_int @ ( power_power_int @ SV310 ) @ ( number_number_of_nat @ SV323 ) )
= zero_zero_int )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2002]) ).
thf(2015,plain,
! [SV312: $i,SV324: $i] :
( ( ( SV324 = zero_zero_nat )
= $false )
| ( ( ( hAPP_nat_int @ ( power_power_int @ SV312 ) @ SV324 )
= zero_zero_int )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2004]) ).
thf(2016,plain,
! [SV318: $i,SV327: $i] :
( ( ( SV327 = zero_zero_nat )
= $false )
| ( ( ( hAPP_nat_nat @ ( power_power_nat @ SV318 ) @ SV327 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2010]) ).
thf(2017,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[967,2016,2015,2014,2013,2012,2011,2009,2008,2007,2006,2005,2003,2001,1999,1998,1997,1991,1988,1977,1976,1973,1972,1971,1962,1961,1960,1959,1958,1955,1952,1949,1948,1947,1946,1945,1942,1941,1940,1929,1928,1921,1920,1919,1918,1907,1906,1905,1904,1900,1899,1898,1897,1896,1895,1894,1893,1892,1891,1888,1887,1884,1883,1877,1876,1873,1872,1868,1867,1864,1863,1854,1853,1849,1848,1847,1846,1843,1842,1839,1838,1825,1822,1821,1815,1814,1811,1806,1805,1800,1790,1735,1720,1708,1697,1695,1694,1693,1692,1691,1690,1603,1599,1598,1594,1507,1506,1505,1504,1503,1497,1496,1495,1494,1493,1492,1491,1485,1484,1483,1482,1481,1480,1399,1389,1388,1384,1383,1382,1381,1380,1370,1369,1368,1367,1365,1364,1363,1362,1361,1359,1356,1355,1354,1351,1349,1348,1347,1303,1302,1301,1300,1299,1298,1297,1286,1285,1282,1281,1280,1279,1278,1277,1276,1275,1270,1269,1265,1264,1263,1262,1261,1260,1259,1258,1257,1256,1255,1244,1243,1238,1236,1235,1234,1233,1232,1231,1230,1228,1222,1221,1220,1219,1218,1216,1215,1214,1201,1200,1199,1155,1127,1123,1097,1095,1094,1093,1085,1060,1059,1054,1052,1042,1041,1040,1039,1038,1023,1022,1021,1020,1019,1018,1017,1009,1008,993,992,991,990,988,987,986,981,979,978,977,976,973,972,968]) ).
thf(2018,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[2017]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM925+2 : TPTP v8.1.0. Released v5.3.0.
% 0.07/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n021.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jul 6 19:13:49 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.53 ...............
% 0.82/0.99
% 0.82/0.99 No.of.Axioms: 707
% 0.82/0.99
% 0.82/0.99 Length.of.Defs: 0
% 0.82/0.99
% 0.82/0.99 Contains.Choice.Funs: false
% 0.92/1.13 ..................................
% 1.06/1.26 (rf:2,axioms:189,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:709,loop_count:0,foatp_calls:0,translation:fof_full).........................................................................................
% 2.27/2.51
% 2.27/2.51 ********************************
% 2.27/2.51 * All subproblems solved! *
% 2.27/2.51 ********************************
% 2.27/2.51 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:2,axioms:189,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:2017,loop_count:0,foatp_calls:1,translation:fof_full)
% 2.88/3.11
% 2.88/3.11 %**** Beginning of derivation protocol ****
% 2.88/3.11 % SZS output start CNFRefutation
% See solution above
% 2.88/3.12
% 2.88/3.12 %**** End of derivation protocol ****
% 2.88/3.12 %**** no. of clauses in derivation: 1500 ****
% 2.88/3.12 %**** clause counter: 2017 ****
% 2.88/3.12
% 2.88/3.12 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:2,axioms:189,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:2017,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------