%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM925+5 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:35:45 AM UTC 2026
% Result : Theorem 8.42s 1.67s
% Output : CNFRefutation 8.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 144
% Syntax : Number of formulae : 1229 ( 724 unt; 0 typ; 0 def)
% Number of atoms : 6651 (2938 equ; 0 cnn)
% Maximal formula atoms : 7 ( 5 avg)
% Number of connectives : 16938 (1966 ~;1678 |; 48 &;12976 @)
% ( 105 <=>; 165 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 32 ( 29 usr; 7 con; 0-3 aty)
% Number of variables : 2165 ( 0 ^;2165 !; 0 ?;2165 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_bit0,type,
bit0: $i > $i ).
thf(tp_bit1,type,
bit1: $i > $i ).
thf(tp_int,type,
int: $i ).
thf(tp_linord219039673up_add,type,
linord219039673up_add: $i > $o ).
thf(tp_linordered_idom,type,
linordered_idom: $i > $o ).
thf(tp_mult_zero,type,
mult_zero: $i > $o ).
thf(tp_n,type,
n: $i ).
thf(tp_nat,type,
nat: $i ).
thf(tp_no_zero_divisors,type,
no_zero_divisors: $i > $o ).
thf(tp_number,type,
number: $i > $o ).
thf(tp_number_number_of,type,
number_number_of: $i > $i > $i ).
thf(tp_number_ring,type,
number_ring: $i > $o ).
thf(tp_number_semiring,type,
number_semiring: $i > $o ).
thf(tp_one_one,type,
one_one: $i > $i ).
thf(tp_ord_less,type,
ord_less: $i > $i > $i > $o ).
thf(tp_pls,type,
pls: $i ).
thf(tp_plus_plus,type,
plus_plus: $i > $i > $i > $i ).
thf(tp_power,type,
power: $i > $o ).
thf(tp_power_power,type,
power_power: $i > $i > $i > $i ).
thf(tp_ring_11004092258visors,type,
ring_11004092258visors: $i > $o ).
thf(tp_ring_char_0,type,
ring_char_0: $i > $o ).
thf(tp_semiring_0,type,
semiring_0: $i > $o ).
thf(tp_semiring_1,type,
semiring_1: $i > $o ).
thf(tp_semiring_1_of_nat,type,
semiring_1_of_nat: $i > $i > $i ).
thf(tp_t,type,
t: $i ).
thf(tp_ti,type,
ti: $i > $i > $i ).
thf(tp_undefined,type,
undefined: $i > $i ).
thf(tp_zero_neq_one,type,
zero_neq_one: $i > $o ).
thf(tp_zero_zero,type,
zero_zero: $i > $i ).
thf(2,axiom,
number @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber) ).
thf(3,axiom,
power @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Power_Opower) ).
thf(4,axiom,
mult_zero @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Omult__zero) ).
thf(5,axiom,
semiring_0 @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__0) ).
thf(6,axiom,
semiring_1 @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__1) ).
thf(7,axiom,
zero_neq_one @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ozero__neq__one) ).
thf(8,axiom,
number_semiring @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber__semiring) ).
thf(9,axiom,
no_zero_divisors @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ono__zero__divisors) ).
thf(10,axiom,
number @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber) ).
thf(11,axiom,
power @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Power_Opower) ).
thf(12,axiom,
number_ring @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
thf(13,axiom,
ring_char_0 @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Oring__char__0) ).
thf(14,axiom,
mult_zero @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Omult__zero) ).
thf(15,axiom,
semiring_0 @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring__0) ).
thf(16,axiom,
semiring_1 @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring__1) ).
thf(17,axiom,
zero_neq_one @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ozero__neq__one) ).
thf(18,axiom,
number_semiring @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__semiring) ).
thf(19,axiom,
linordered_idom @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__idom) ).
thf(20,axiom,
no_zero_divisors @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ono__zero__divisors) ).
thf(21,axiom,
ring_11004092258visors @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring__1__no__zero__divisors) ).
thf(22,axiom,
linord219039673up_add @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Olinordered__ab__group__add) ).
thf(23,axiom,
! [X_a: $i] :
( ( linordered_idom @ X_a )
=> ! [Xa: $i,Ya: $i] :
( ( ord_less @ X_a @ ( zero_zero @ X_a ) @ ( plus_plus @ X_a @ ( power_power @ X_a @ Xa @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ X_a @ Ya @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
<=> ( ( ( ti @ X_a @ Xa )
!= ( zero_zero @ X_a ) )
| ( ( ti @ X_a @ Ya )
!= ( zero_zero @ X_a ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_sum__power2__gt__zero__iff) ).
thf(24,axiom,
! [X_a: $i] :
( ( linordered_idom @ X_a )
=> ! [A_1: $i] :
~ ( ord_less @ X_a @ ( power_power @ X_a @ A_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( zero_zero @ X_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_power2__less__0) ).
thf(25,axiom,
! [X_a: $i] :
( ( linordered_idom @ X_a )
=> ! [A_2: $i] :
( ( ord_less @ X_a @ ( zero_zero @ X_a ) @ ( power_power @ X_a @ A_2 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
<=> ( ( ti @ X_a @ A_2 )
!= ( zero_zero @ X_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_zero__less__power2) ).
thf(26,axiom,
! [X_a: $i] :
( ( number_semiring @ X_a )
=> ! [N: $i] :
( ( number_number_of @ X_a @ ( semiring_1_of_nat @ int @ N ) )
= ( semiring_1_of_nat @ X_a @ N ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_number__of__int) ).
thf(27,axiom,
! [Z: $i] :
( ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ Z ) @ Z )
!= ( zero_zero @ int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_odd__nonzero) ).
thf(28,axiom,
! [K: $i] :
( ( bit1 @ K )
= ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ K ) @ K ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_Bit1__def) ).
thf(29,axiom,
! [K: $i,L: $i] :
( ( plus_plus @ int @ ( bit0 @ K ) @ ( bit1 @ L ) )
= ( bit1 @ ( plus_plus @ int @ K @ L ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_add__Bit0__Bit1) ).
thf(30,axiom,
! [K: $i,L: $i] :
( ( plus_plus @ int @ ( bit1 @ K ) @ ( bit0 @ L ) )
= ( bit1 @ ( plus_plus @ int @ K @ L ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_add__Bit1__Bit0) ).
thf(31,axiom,
! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [V: $i,W: $i] :
( ( number_number_of @ X_a @ ( plus_plus @ int @ V @ W ) )
= ( plus_plus @ X_a @ ( number_number_of @ X_a @ V ) @ ( number_number_of @ X_a @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_number__of__add) ).
thf(32,axiom,
! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [V: $i,W: $i] :
( ( plus_plus @ X_a @ ( number_number_of @ X_a @ V ) @ ( number_number_of @ X_a @ W ) )
= ( number_number_of @ X_a @ ( plus_plus @ int @ V @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_add__number__of__eq) ).
thf(33,axiom,
! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [V: $i,W: $i,Z: $i] :
( ( plus_plus @ X_a @ ( number_number_of @ X_a @ V ) @ ( plus_plus @ X_a @ ( number_number_of @ X_a @ W ) @ Z ) )
= ( plus_plus @ X_a @ ( number_number_of @ X_a @ ( plus_plus @ int @ V @ W ) ) @ Z ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_add__number__of__left) ).
thf(35,axiom,
! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [A_1: $i] :
( ( plus_plus @ X_a @ A_1 @ ( number_number_of @ X_a @ pls ) )
= ( ti @ X_a @ A_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_add__numeral__0__right) ).
thf(36,axiom,
! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [A_1: $i] :
( ( plus_plus @ X_a @ ( number_number_of @ X_a @ pls ) @ A_1 )
= ( ti @ X_a @ A_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_add__numeral__0) ).
thf(37,axiom,
! [X_a: $i] :
( ( number_ring @ X_a )
=> ( ( zero_zero @ X_a )
= ( number_number_of @ X_a @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_semiring__norm_I112_J) ).
thf(38,axiom,
! [X_a: $i] :
( ( number_ring @ X_a )
=> ( ( number_number_of @ X_a @ pls )
= ( zero_zero @ X_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_number__of__Pls) ).
thf(39,axiom,
! [X_a: $i] :
( ( number_semiring @ X_a )
=> ( ( number_number_of @ X_a @ pls )
= ( zero_zero @ X_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_semiring__numeral__0__eq__0) ).
thf(40,axiom,
! [Z: $i] :
( ( plus_plus @ int @ ( zero_zero @ int ) @ Z )
= Z ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_zadd__0) ).
thf(41,axiom,
! [Z: $i] :
( ( plus_plus @ int @ Z @ ( zero_zero @ int ) )
= Z ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_zadd__0__right) ).
thf(42,axiom,
! [K: $i] :
( ( bit0 @ K )
= ( plus_plus @ int @ K @ K ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_Bit0__def) ).
thf(43,axiom,
! [K: $i,L: $i] :
( ( plus_plus @ int @ ( bit0 @ K ) @ ( bit0 @ L ) )
= ( bit0 @ ( plus_plus @ int @ K @ L ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_add__Bit0__Bit0) ).
thf(44,axiom,
! [K: $i] :
( ( plus_plus @ int @ pls @ K )
= K ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_add__Pls) ).
thf(45,axiom,
! [K: $i] :
( ( plus_plus @ int @ K @ pls )
= K ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_add__Pls__right) ).
thf(46,axiom,
( ( zero_zero @ int )
!= ( one_one @ int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_int__0__neq__1) ).
thf(47,axiom,
( pls
= ( zero_zero @ int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_Pls__def) ).
thf(48,axiom,
( ( bit0 @ pls )
= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_Bit0__Pls) ).
thf(49,axiom,
! [L_1: $i] :
( ( pls
= ( bit0 @ L_1 ) )
<=> ( pls = L_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_rel__simps_I38_J) ).
thf(50,axiom,
! [K_1: $i] :
( ( ( bit0 @ K_1 )
= pls )
<=> ( K_1 = pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_rel__simps_I44_J) ).
thf(51,axiom,
! [K: $i,L: $i] :
( ( bit0 @ K )
!= ( bit1 @ L ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_rel__simps_I49_J) ).
thf(52,axiom,
! [K: $i,L: $i] :
( ( bit1 @ K )
!= ( bit0 @ L ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_rel__simps_I50_J) ).
thf(53,axiom,
! [L: $i] :
( pls
!= ( bit1 @ L ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_rel__simps_I39_J) ).
thf(54,axiom,
! [K: $i] :
( ( bit1 @ K )
!= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_rel__simps_I46_J) ).
thf(55,axiom,
! [X_a: $i] :
( ( linord219039673up_add @ X_a )
=> ! [A_2: $i] :
( ( ( plus_plus @ X_a @ A_2 @ A_2 )
= ( zero_zero @ X_a ) )
<=> ( ( ti @ X_a @ A_2 )
= ( zero_zero @ X_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_double__eq__0__iff) ).
thf(56,axiom,
! [Z_1: $i] :
( ( ord_less @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ Z_1 ) @ Z_1 ) @ ( zero_zero @ int ) )
<=> ( ord_less @ int @ Z_1 @ ( zero_zero @ int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_odd__less__0) ).
thf(57,axiom,
! [X_a: $i] :
( ( ( number_ring @ X_a )
& ( linordered_idom @ X_a ) )
=> ! [Ya: $i] :
( ( ord_less @ X_a @ ( one_one @ X_a ) @ ( number_number_of @ X_a @ Ya ) )
<=> ( ord_less @ int @ ( bit1 @ pls ) @ Ya ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_less__special_I2_J) ).
thf(58,axiom,
! [X_a: $i] :
( ( ( number_ring @ X_a )
& ( linordered_idom @ X_a ) )
=> ! [Xa: $i] :
( ( ord_less @ X_a @ ( number_number_of @ X_a @ Xa ) @ ( one_one @ X_a ) )
<=> ( ord_less @ int @ Xa @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_less__special_I4_J) ).
thf(59,axiom,
! [K: $i] :
~ ( ord_less @ int @ ( semiring_1_of_nat @ int @ K ) @ ( zero_zero @ int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_int__less__0__conv) ).
thf(60,axiom,
! [Wa: $i,Z_1: $i] :
( ( ord_less @ int @ Wa @ ( plus_plus @ int @ Z_1 @ ( one_one @ int ) ) )
<=> ( ( ord_less @ int @ Wa @ Z_1 )
| ( Wa = Z_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_zless__add1__eq) ).
thf(61,axiom,
ord_less @ int @ ( zero_zero @ int ) @ ( one_one @ int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_int__0__less__1) ).
thf(62,axiom,
! [Wa: $i] :
( ( ord_less @ int @ ( bit0 @ Wa ) @ ( zero_zero @ int ) )
<=> ( ord_less @ int @ Wa @ ( zero_zero @ int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_bin__less__0__simps_I3_J) ).
thf(63,axiom,
~ ( ord_less @ int @ pls @ ( zero_zero @ int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_bin__less__0__simps_I1_J) ).
thf(64,axiom,
! [Wa: $i] :
( ( ord_less @ int @ ( bit1 @ Wa ) @ ( zero_zero @ int ) )
<=> ( ord_less @ int @ Wa @ ( zero_zero @ int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_bin__less__0__simps_I4_J) ).
thf(65,axiom,
! [K_1: $i] :
( ( ord_less @ int @ pls @ ( bit0 @ K_1 ) )
<=> ( ord_less @ int @ pls @ K_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_rel__simps_I4_J) ).
thf(66,axiom,
! [K_1: $i] :
( ( ord_less @ int @ ( bit0 @ K_1 ) @ pls )
<=> ( ord_less @ int @ K_1 @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_rel__simps_I10_J) ).
thf(67,axiom,
! [K_1: $i,L_1: $i] :
( ( ord_less @ int @ ( bit1 @ K_1 ) @ ( bit0 @ L_1 ) )
<=> ( ord_less @ int @ K_1 @ L_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_rel__simps_I16_J) ).
thf(68,axiom,
! [K1: $i,K2: $i] :
( ( ord_less @ int @ ( bit1 @ K1 ) @ ( bit0 @ K2 ) )
<=> ( ord_less @ int @ K1 @ K2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_less__int__code_I15_J) ).
thf(69,axiom,
! [K_1: $i] :
( ( ord_less @ int @ ( bit1 @ K_1 ) @ pls )
<=> ( ord_less @ int @ K_1 @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_rel__simps_I12_J) ).
thf(70,axiom,
! [X_a: $i] :
( ( ( number_ring @ X_a )
& ( linordered_idom @ X_a ) )
=> ! [Ya: $i] :
( ( ord_less @ X_a @ ( zero_zero @ X_a ) @ ( number_number_of @ X_a @ Ya ) )
<=> ( ord_less @ int @ pls @ Ya ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_less__special_I1_J) ).
thf(71,axiom,
! [X_a: $i] :
( ( ( number_ring @ X_a )
& ( linordered_idom @ X_a ) )
=> ! [Xa: $i] :
( ( ord_less @ X_a @ ( number_number_of @ X_a @ Xa ) @ ( zero_zero @ X_a ) )
<=> ( ord_less @ int @ Xa @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_less__special_I3_J) ).
thf(72,axiom,
! [Ma: $i,Na: $i] :
( ( ( semiring_1_of_nat @ int @ Ma )
= ( semiring_1_of_nat @ int @ Na ) )
<=> ( Ma = Na ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_int__int__eq) ).
thf(73,axiom,
! [Z: $i,W: $i] :
( ( plus_plus @ int @ Z @ W )
= ( plus_plus @ int @ W @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_zadd__commute) ).
thf(74,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( plus_plus @ int @ X @ ( plus_plus @ int @ Y @ Z ) )
= ( plus_plus @ int @ Y @ ( plus_plus @ int @ X @ Z ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_zadd__left__commute) ).
thf(75,axiom,
! [Z1: $i,Z2: $i,Z3: $i] :
( ( plus_plus @ int @ ( plus_plus @ int @ Z1 @ Z2 ) @ Z3 )
= ( plus_plus @ int @ Z1 @ ( plus_plus @ int @ Z2 @ Z3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_zadd__assoc) ).
thf(76,axiom,
! [X_a: $i] :
( ( linordered_idom @ X_a )
=> ! [A_2: $i] :
( ( ord_less @ X_a @ ( plus_plus @ X_a @ A_2 @ A_2 ) @ ( zero_zero @ X_a ) )
<=> ( ord_less @ X_a @ A_2 @ ( zero_zero @ X_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_even__less__0__iff) ).
thf(77,axiom,
! [K_1: $i,L_1: $i] :
( ( ( bit0 @ K_1 )
= ( bit0 @ L_1 ) )
<=> ( K_1 = L_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_rel__simps_I48_J) ).
thf(78,axiom,
! [K_1: $i,L_1: $i] :
( ( ( bit1 @ K_1 )
= ( bit1 @ L_1 ) )
<=> ( K_1 = L_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_rel__simps_I51_J) ).
thf(79,axiom,
! [X_a: $i] :
( ( number @ X_a )
=> ! [Wa: $i,Xa: $i] :
( ( ( number_number_of @ X_a @ Wa )
= ( ti @ X_a @ Xa ) )
<=> ( ( ti @ X_a @ Xa )
= ( number_number_of @ X_a @ Wa ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_number__of__reorient) ).
thf(80,axiom,
! [X_a: $i] :
( ( ( number_ring @ X_a )
& ( ring_char_0 @ X_a ) )
=> ! [Xa: $i,Ya: $i] :
( ( ( number_number_of @ X_a @ Xa )
= ( number_number_of @ X_a @ Ya ) )
<=> ( Xa = Ya ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_eq__number__of) ).
thf(81,axiom,
( ( one_one @ nat )
= ( number_number_of @ nat @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_Numeral1__eq1__nat) ).
thf(82,axiom,
( ( number_number_of @ nat @ ( bit1 @ pls ) )
= ( one_one @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_nat__numeral__1__eq__1) ).
thf(83,axiom,
( ( one_one @ int )
= ( number_number_of @ int @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_one__is__num__one) ).
thf(84,axiom,
! [V_1: $i,V: $i] :
( ( ( ord_less @ int @ V @ pls )
=> ( ( plus_plus @ nat @ ( number_number_of @ nat @ V ) @ ( number_number_of @ nat @ V_1 ) )
= ( number_number_of @ nat @ V_1 ) ) )
& ( ~ ( ord_less @ int @ V @ pls )
=> ( ( ( ord_less @ int @ V_1 @ pls )
=> ( ( plus_plus @ nat @ ( number_number_of @ nat @ V ) @ ( number_number_of @ nat @ V_1 ) )
= ( number_number_of @ nat @ V ) ) )
& ( ~ ( ord_less @ int @ V_1 @ pls )
=> ( ( plus_plus @ nat @ ( number_number_of @ nat @ V ) @ ( number_number_of @ nat @ V_1 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ V @ V_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_add__nat__number__of) ).
thf(85,axiom,
! [K: $i,I: $i,J: $i] :
( ( ord_less @ int @ I @ J )
=> ( ord_less @ int @ ( plus_plus @ int @ I @ K ) @ ( plus_plus @ int @ J @ K ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_zadd__strict__right__mono) ).
thf(86,axiom,
! [K_1: $i,L_1: $i] :
( ( ord_less @ int @ ( bit0 @ K_1 ) @ ( bit0 @ L_1 ) )
<=> ( ord_less @ int @ K_1 @ L_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_rel__simps_I14_J) ).
thf(87,axiom,
! [K1: $i,K2: $i] :
( ( ord_less @ int @ ( bit0 @ K1 ) @ ( bit0 @ K2 ) )
<=> ( ord_less @ int @ K1 @ K2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_less__int__code_I13_J) ).
thf(88,axiom,
~ ( ord_less @ int @ pls @ pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_rel__simps_I2_J) ).
thf(89,axiom,
! [K_1: $i,L_1: $i] :
( ( ord_less @ int @ ( bit1 @ K_1 ) @ ( bit1 @ L_1 ) )
<=> ( ord_less @ int @ K_1 @ L_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_rel__simps_I17_J) ).
thf(90,axiom,
! [K1: $i,K2: $i] :
( ( ord_less @ int @ ( bit1 @ K1 ) @ ( bit1 @ K2 ) )
<=> ( ord_less @ int @ K1 @ K2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_less__int__code_I16_J) ).
thf(91,axiom,
( ( plus_plus @ nat @ ( one_one @ nat ) @ ( one_one @ nat ) )
= ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_nat__1__add__1) ).
thf(92,axiom,
( ( semiring_1_of_nat @ int @ ( zero_zero @ nat ) )
= ( zero_zero @ int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_int__0) ).
thf(93,axiom,
! [Na: $i] :
( ( ( semiring_1_of_nat @ int @ Na )
= ( zero_zero @ int ) )
<=> ( Na
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_int__eq__0__conv) ).
thf(94,axiom,
( ( zero_zero @ nat )
= ( number_number_of @ nat @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_semiring__norm_I113_J) ).
thf(95,axiom,
( ( number_number_of @ nat @ pls )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_nat__number__of__Pls) ).
thf(96,axiom,
( ( semiring_1_of_nat @ int @ ( one_one @ nat ) )
= ( one_one @ int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_int__1) ).
thf(97,axiom,
! [M: $i,N: $i] :
( ( plus_plus @ int @ ( semiring_1_of_nat @ int @ M ) @ ( semiring_1_of_nat @ int @ N ) )
= ( semiring_1_of_nat @ int @ ( plus_plus @ nat @ M @ N ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_zadd__int) ).
thf(98,axiom,
! [M: $i,N: $i,Z: $i] :
( ( plus_plus @ int @ ( semiring_1_of_nat @ int @ M ) @ ( plus_plus @ int @ ( semiring_1_of_nat @ int @ N ) @ Z ) )
= ( plus_plus @ int @ ( semiring_1_of_nat @ int @ ( plus_plus @ nat @ M @ N ) ) @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_zadd__int__left) ).
thf(99,axiom,
! [M: $i,N: $i] :
( ( semiring_1_of_nat @ int @ ( power_power @ nat @ M @ N ) )
= ( power_power @ int @ ( semiring_1_of_nat @ int @ M ) @ N ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_int__power) ).
thf(100,axiom,
! [M: $i,N: $i] :
( ( power_power @ int @ ( semiring_1_of_nat @ int @ M ) @ N )
= ( semiring_1_of_nat @ int @ ( power_power @ nat @ M @ N ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_zpower__int) ).
thf(101,axiom,
( ( zero_zero @ int )
= ( number_number_of @ int @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_zero__is__num__zero) ).
thf(102,axiom,
! [X_a: $i] :
( ( ( number_ring @ X_a )
& ( linordered_idom @ X_a ) )
=> ! [Xa: $i,Ya: $i] :
( ( ord_less @ X_a @ ( number_number_of @ X_a @ Xa ) @ ( number_number_of @ X_a @ Ya ) )
<=> ( ord_less @ int @ Xa @ Ya ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_less__number__of) ).
thf(103,axiom,
! [V: $i,W: $i] :
( ( plus_plus @ int @ ( number_number_of @ int @ V ) @ ( number_number_of @ int @ W ) )
= ( number_number_of @ int @ ( plus_plus @ int @ V @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_plus__numeral__code_I9_J) ).
thf(104,axiom,
! [K_1: $i,L_1: $i] :
( ( ord_less @ int @ ( number_number_of @ int @ K_1 ) @ ( number_number_of @ int @ L_1 ) )
<=> ( ord_less @ int @ K_1 @ L_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_less__number__of__int__code) ).
thf(105,axiom,
! [X: $i,Y: $i] :
( ( ord_less @ int @ X @ Y )
| ( X = Y )
| ( ord_less @ int @ Y @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_zless__linear) ).
thf(106,axiom,
ord_less @ nat @ ( zero_zero @ nat ) @ n,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_n0) ).
thf(107,axiom,
! [X_a: $i] :
( ( number_ring @ X_a )
=> ( ( number_number_of @ X_a @ ( bit1 @ pls ) )
= ( one_one @ X_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_numeral__1__eq__1) ).
thf(108,axiom,
! [X_a: $i] :
( ( number_ring @ X_a )
=> ( ( one_one @ X_a )
= ( number_number_of @ X_a @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_semiring__norm_I110_J) ).
thf(109,axiom,
! [X_a: $i] :
( ( ( power @ X_a )
& ( semiring_0 @ X_a ) )
=> ! [W: $i] :
( ( ( ( number_number_of @ nat @ W )
= ( zero_zero @ nat ) )
=> ( ( power_power @ X_a @ ( zero_zero @ X_a ) @ ( number_number_of @ nat @ W ) )
= ( one_one @ X_a ) ) )
& ( ( ( number_number_of @ nat @ W )
!= ( zero_zero @ nat ) )
=> ( ( power_power @ X_a @ ( zero_zero @ X_a ) @ ( number_number_of @ nat @ W ) )
= ( zero_zero @ X_a ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_power__0__left__number__of) ).
thf(110,axiom,
! [X: $i] :
( ( power_power @ int @ ( power_power @ int @ X @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power @ int @ X @ ( number_number_of @ nat @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_quartic__square__square) ).
thf(111,axiom,
! [X_a: $i] :
( ( number_semiring @ X_a )
=> ( ( plus_plus @ X_a @ ( one_one @ X_a ) @ ( one_one @ X_a ) )
= ( number_number_of @ X_a @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_semiring__one__add__one__is__two) ).
thf(112,axiom,
! [X_a: $i] :
( ( number_ring @ X_a )
=> ( ( plus_plus @ X_a @ ( one_one @ X_a ) @ ( one_one @ X_a ) )
= ( number_number_of @ X_a @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_one__add__one__is__two) ).
thf(113,axiom,
! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [V: $i] :
( ( plus_plus @ X_a @ ( number_number_of @ X_a @ V ) @ ( one_one @ X_a ) )
= ( number_number_of @ X_a @ ( plus_plus @ int @ V @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_add__special_I3_J) ).
thf(114,axiom,
! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [W: $i] :
( ( plus_plus @ X_a @ ( one_one @ X_a ) @ ( number_number_of @ X_a @ W ) )
= ( number_number_of @ X_a @ ( plus_plus @ int @ ( bit1 @ pls ) @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_add__special_I2_J) ).
thf(115,axiom,
! [X_a: $i] :
( ( ring_11004092258visors @ X_a )
=> ! [A_2: $i] :
( ( ( power_power @ X_a @ A_2 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ X_a ) )
<=> ( ( ti @ X_a @ A_2 )
= ( zero_zero @ X_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_zero__eq__power2) ).
thf(116,axiom,
! [X_a: $i] :
( ( semiring_1 @ X_a )
=> ( ( power_power @ X_a @ ( zero_zero @ X_a ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ X_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_zero__power2) ).
thf(117,axiom,
! [X_a: $i] :
( ( semiring_1 @ X_a )
=> ( ( power_power @ X_a @ ( one_one @ X_a ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( one_one @ X_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_one__power2) ).
thf(118,axiom,
! [X_a: $i] :
( ( linordered_idom @ X_a )
=> ! [Xa: $i,Ya: $i] :
( ( ( plus_plus @ X_a @ ( power_power @ X_a @ Xa @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ X_a @ Ya @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ X_a ) )
<=> ( ( ( ti @ X_a @ Xa )
= ( zero_zero @ X_a ) )
& ( ( ti @ X_a @ Ya )
= ( zero_zero @ X_a ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_sum__power2__eq__zero__iff) ).
thf(119,axiom,
ord_less @ int @ ( one_one @ int ) @ t,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_t1) ).
thf(120,axiom,
ord_less @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( one_one @ int ) @ ( semiring_1_of_nat @ int @ n ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_n1pos) ).
thf(121,axiom,
( ( ti @ int @ t )
= t ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_t_____res) ).
thf(122,axiom,
! [B_1: $i,B_2: $i,X_a: $i] :
( ( ( power @ X_a )
& ( semiring_0 @ X_a ) )
=> ( ( ti @ X_a @ ( power_power @ X_a @ B_1 @ B_2 ) )
= ( power_power @ X_a @ B_1 @ B_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Power_Opower__class_Opower_1_res) ).
thf(123,axiom,
! [B_1: $i,B_2: $i,X_a: $i] :
( ( ( power @ X_a )
& ( semiring_0 @ X_a ) )
=> ( ( power_power @ X_a @ B_1 @ ( ti @ nat @ B_2 ) )
= ( power_power @ X_a @ B_1 @ B_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Power_Opower__class_Opower_1_arg2) ).
thf(124,axiom,
! [B_1: $i,B_2: $i,X_a: $i] :
( ( ( power @ X_a )
& ( semiring_0 @ X_a ) )
=> ( ( power_power @ X_a @ ( ti @ X_a @ B_1 ) @ B_2 )
= ( power_power @ X_a @ B_1 @ B_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Power_Opower__class_Opower_1_arg1) ).
thf(128,axiom,
! [B_1: $i,B_2: $i] :
( ( ord_less @ nat @ B_1 @ ( ti @ nat @ B_2 ) )
<=> ( ord_less @ nat @ B_1 @ B_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Orderings_Oord__class_Oless_1_arg2) ).
thf(129,axiom,
! [B_1: $i,B_2: $i] :
( ( ord_less @ nat @ ( ti @ nat @ B_1 ) @ B_2 )
<=> ( ord_less @ nat @ B_1 @ B_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Orderings_Oord__class_Oless_1_arg1) ).
thf(132,axiom,
! [B_1: $i,X_a: $i] :
( ( number_semiring @ X_a )
=> ( ( ti @ X_a @ ( semiring_1_of_nat @ X_a @ B_1 ) )
= ( semiring_1_of_nat @ X_a @ B_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Nat_Osemiring__1__class_Oof__nat_res) ).
thf(133,axiom,
! [B_1: $i,X_a: $i] :
( ( number_semiring @ X_a )
=> ( ( semiring_1_of_nat @ X_a @ ( ti @ nat @ B_1 ) )
= ( semiring_1_of_nat @ X_a @ B_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Nat_Osemiring__1__class_Oof__nat_arg1) ).
thf(134,axiom,
! [B_1: $i,X_a: $i] :
( ( number @ X_a )
=> ( ( ti @ X_a @ ( number_number_of @ X_a @ B_1 ) )
= ( number_number_of @ X_a @ B_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Int_Onumber__class_Onumber__of_res) ).
thf(135,axiom,
! [B_1: $i,X_a: $i] :
( ( number @ X_a )
=> ( ( number_number_of @ X_a @ ( ti @ int @ B_1 ) )
= ( number_number_of @ X_a @ B_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Int_Onumber__class_Onumber__of_arg1) ).
thf(137,axiom,
! [X_a: $i] :
( ( ( power @ X_a )
& ( semiring_0 @ X_a ) )
=> ( ( ti @ X_a @ ( zero_zero @ X_a ) )
= ( zero_zero @ X_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Ozero__class_Ozero_2_res) ).
thf(138,axiom,
! [X_a: $i] :
( ( linord219039673up_add @ X_a )
=> ( ( ti @ X_a @ ( zero_zero @ X_a ) )
= ( zero_zero @ X_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Ozero__class_Ozero_1_res) ).
thf(140,axiom,
! [B_1: $i,B_2: $i,X_a: $i] :
( ( number_semiring @ X_a )
=> ( ( ti @ X_a @ ( plus_plus @ X_a @ B_1 @ B_2 ) )
= ( plus_plus @ X_a @ B_1 @ B_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_1_res) ).
thf(141,axiom,
! [B_1: $i,B_2: $i,X_a: $i] :
( ( number_semiring @ X_a )
=> ( ( plus_plus @ X_a @ B_1 @ ( ti @ X_a @ B_2 ) )
= ( plus_plus @ X_a @ B_1 @ B_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_1_arg2) ).
thf(142,axiom,
! [B_1: $i,B_2: $i,X_a: $i] :
( ( number_semiring @ X_a )
=> ( ( plus_plus @ X_a @ ( ti @ X_a @ B_1 ) @ B_2 )
= ( plus_plus @ X_a @ B_1 @ B_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_1_arg1) ).
thf(143,axiom,
! [B_1: $i,B_2: $i,X_a: $i] :
( ( linord219039673up_add @ X_a )
=> ( ( ti @ X_a @ ( plus_plus @ X_a @ B_1 @ B_2 ) )
= ( plus_plus @ X_a @ B_1 @ B_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_0_res) ).
thf(144,axiom,
! [B_1: $i,B_2: $i,X_a: $i] :
( ( linord219039673up_add @ X_a )
=> ( ( plus_plus @ X_a @ B_1 @ ( ti @ X_a @ B_2 ) )
= ( plus_plus @ X_a @ B_1 @ B_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_0_arg2) ).
thf(145,axiom,
! [B_1: $i,B_2: $i,X_a: $i] :
( ( linord219039673up_add @ X_a )
=> ( ( plus_plus @ X_a @ ( ti @ X_a @ B_1 ) @ B_2 )
= ( plus_plus @ X_a @ B_1 @ B_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_0_arg1) ).
thf(146,axiom,
! [X_a: $i] :
( ( ( power @ X_a )
& ( semiring_0 @ X_a ) )
=> ( ( ti @ X_a @ ( one_one @ X_a ) )
= ( one_one @ X_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Oone__class_Oone_res) ).
thf(147,axiom,
( ( ti @ nat @ n )
= n ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_n_____res) ).
thf(148,axiom,
( ( ti @ int @ pls )
= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Int_OPls_res) ).
thf(149,axiom,
! [B_1: $i] :
( ( ti @ int @ ( bit1 @ B_1 ) )
= ( bit1 @ B_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Int_OBit1_res) ).
thf(150,axiom,
! [B_1: $i] :
( ( bit1 @ ( ti @ int @ B_1 ) )
= ( bit1 @ B_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Int_OBit1_arg1) ).
thf(151,axiom,
! [B_1: $i] :
( ( ti @ int @ ( bit0 @ B_1 ) )
= ( bit0 @ B_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Int_OBit0_res) ).
thf(152,axiom,
! [B_1: $i] :
( ( bit0 @ ( ti @ int @ B_1 ) )
= ( bit0 @ B_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Int_OBit0_arg1) ).
thf(153,conjecture,
( ( power_power @ int @ ( plus_plus @ int @ ( one_one @ int ) @ ( semiring_1_of_nat @ int @ n ) ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= ( zero_zero @ int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(154,negated_conjecture,
( ( ( power_power @ int @ ( plus_plus @ int @ ( one_one @ int ) @ ( semiring_1_of_nat @ int @ n ) ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= ( zero_zero @ int ) )
= $false ),
inference(negate_conjecture,[status(cth)],[153]) ).
thf(155,plain,
( ( ( power_power @ int @ ( plus_plus @ int @ ( one_one @ int ) @ ( semiring_1_of_nat @ int @ n ) ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= ( zero_zero @ int ) )
= $false ),
inference(unfold_def,[status(thm)],[154]) ).
thf(156,plain,
( ( number @ nat )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(157,plain,
( ( power @ nat )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(158,plain,
( ( mult_zero @ nat )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(159,plain,
( ( semiring_0 @ nat )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(160,plain,
( ( semiring_1 @ nat )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(161,plain,
( ( zero_neq_one @ nat )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(162,plain,
( ( number_semiring @ nat )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(163,plain,
( ( no_zero_divisors @ nat )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(164,plain,
( ( number @ int )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(165,plain,
( ( power @ int )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(166,plain,
( ( number_ring @ int )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(167,plain,
( ( ring_char_0 @ int )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(168,plain,
( ( mult_zero @ int )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(169,plain,
( ( semiring_0 @ int )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(170,plain,
( ( semiring_1 @ int )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(171,plain,
( ( zero_neq_one @ int )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(172,plain,
( ( number_semiring @ int )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(173,plain,
( ( linordered_idom @ int )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(174,plain,
( ( no_zero_divisors @ int )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(175,plain,
( ( ring_11004092258visors @ int )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(176,plain,
( ( linord219039673up_add @ int )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(177,plain,
( ( ! [X_a: $i] :
( ( linordered_idom @ X_a )
=> ! [Xa: $i,Ya: $i] :
( ( ord_less @ X_a @ ( zero_zero @ X_a ) @ ( plus_plus @ X_a @ ( power_power @ X_a @ Xa @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ X_a @ Ya @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
<=> ( ( ( ti @ X_a @ Xa )
!= ( zero_zero @ X_a ) )
| ( ( ti @ X_a @ Ya )
!= ( zero_zero @ X_a ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(178,plain,
( ( ! [X_a: $i] :
( ( linordered_idom @ X_a )
=> ! [A_1: $i] :
~ ( ord_less @ X_a @ ( power_power @ X_a @ A_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( zero_zero @ X_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(179,plain,
( ( ! [X_a: $i] :
( ( linordered_idom @ X_a )
=> ! [A_2: $i] :
( ( ord_less @ X_a @ ( zero_zero @ X_a ) @ ( power_power @ X_a @ A_2 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
<=> ( ( ti @ X_a @ A_2 )
!= ( zero_zero @ X_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(180,plain,
( ( ! [X_a: $i] :
( ( number_semiring @ X_a )
=> ! [N: $i] :
( ( number_number_of @ X_a @ ( semiring_1_of_nat @ int @ N ) )
= ( semiring_1_of_nat @ X_a @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(181,plain,
( ( ! [Z: $i] :
( ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ Z ) @ Z )
!= ( zero_zero @ int ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(182,plain,
( ( ! [K: $i] :
( ( bit1 @ K )
= ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ K ) @ K ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(183,plain,
( ( ! [K: $i,L: $i] :
( ( plus_plus @ int @ ( bit0 @ K ) @ ( bit1 @ L ) )
= ( bit1 @ ( plus_plus @ int @ K @ L ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(184,plain,
( ( ! [K: $i,L: $i] :
( ( plus_plus @ int @ ( bit1 @ K ) @ ( bit0 @ L ) )
= ( bit1 @ ( plus_plus @ int @ K @ L ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(185,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [V: $i,W: $i] :
( ( number_number_of @ X_a @ ( plus_plus @ int @ V @ W ) )
= ( plus_plus @ X_a @ ( number_number_of @ X_a @ V ) @ ( number_number_of @ X_a @ W ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(186,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [V: $i,W: $i] :
( ( plus_plus @ X_a @ ( number_number_of @ X_a @ V ) @ ( number_number_of @ X_a @ W ) )
= ( number_number_of @ X_a @ ( plus_plus @ int @ V @ W ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(187,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [V: $i,W: $i,Z: $i] :
( ( plus_plus @ X_a @ ( number_number_of @ X_a @ V ) @ ( plus_plus @ X_a @ ( number_number_of @ X_a @ W ) @ Z ) )
= ( plus_plus @ X_a @ ( number_number_of @ X_a @ ( plus_plus @ int @ V @ W ) ) @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(188,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [A_1: $i] :
( ( plus_plus @ X_a @ A_1 @ ( number_number_of @ X_a @ pls ) )
= ( ti @ X_a @ A_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(189,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [A_1: $i] :
( ( plus_plus @ X_a @ ( number_number_of @ X_a @ pls ) @ A_1 )
= ( ti @ X_a @ A_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(190,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ( ( zero_zero @ X_a )
= ( number_number_of @ X_a @ pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(191,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ( ( number_number_of @ X_a @ pls )
= ( zero_zero @ X_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(192,plain,
( ( ! [X_a: $i] :
( ( number_semiring @ X_a )
=> ( ( number_number_of @ X_a @ pls )
= ( zero_zero @ X_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(193,plain,
( ( ! [Z: $i] :
( ( plus_plus @ int @ ( zero_zero @ int ) @ Z )
= Z ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(194,plain,
( ( ! [Z: $i] :
( ( plus_plus @ int @ Z @ ( zero_zero @ int ) )
= Z ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(195,plain,
( ( ! [K: $i] :
( ( bit0 @ K )
= ( plus_plus @ int @ K @ K ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(196,plain,
( ( ! [K: $i,L: $i] :
( ( plus_plus @ int @ ( bit0 @ K ) @ ( bit0 @ L ) )
= ( bit0 @ ( plus_plus @ int @ K @ L ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(197,plain,
( ( ! [K: $i] :
( ( plus_plus @ int @ pls @ K )
= K ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(198,plain,
( ( ! [K: $i] :
( ( plus_plus @ int @ K @ pls )
= K ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(199,plain,
( ( ( zero_zero @ int )
!= ( one_one @ int ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(200,plain,
( ( pls
= ( zero_zero @ int ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(201,plain,
( ( ( bit0 @ pls )
= pls )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(202,plain,
( ( ! [L_1: $i] :
( ( pls
= ( bit0 @ L_1 ) )
<=> ( pls = L_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(203,plain,
( ( ! [K_1: $i] :
( ( ( bit0 @ K_1 )
= pls )
<=> ( K_1 = pls ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(204,plain,
( ( ! [K: $i,L: $i] :
( ( bit0 @ K )
!= ( bit1 @ L ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(205,plain,
( ( ! [K: $i,L: $i] :
( ( bit1 @ K )
!= ( bit0 @ L ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(206,plain,
( ( ! [L: $i] :
( pls
!= ( bit1 @ L ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(207,plain,
( ( ! [K: $i] :
( ( bit1 @ K )
!= pls ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(208,plain,
( ( ! [X_a: $i] :
( ( linord219039673up_add @ X_a )
=> ! [A_2: $i] :
( ( ( plus_plus @ X_a @ A_2 @ A_2 )
= ( zero_zero @ X_a ) )
<=> ( ( ti @ X_a @ A_2 )
= ( zero_zero @ X_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(209,plain,
( ( ! [Z_1: $i] :
( ( ord_less @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ Z_1 ) @ Z_1 ) @ ( zero_zero @ int ) )
<=> ( ord_less @ int @ Z_1 @ ( zero_zero @ int ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(210,plain,
( ( ! [X_a: $i] :
( ( ( number_ring @ X_a )
& ( linordered_idom @ X_a ) )
=> ! [Ya: $i] :
( ( ord_less @ X_a @ ( one_one @ X_a ) @ ( number_number_of @ X_a @ Ya ) )
<=> ( ord_less @ int @ ( bit1 @ pls ) @ Ya ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(211,plain,
( ( ! [X_a: $i] :
( ( ( number_ring @ X_a )
& ( linordered_idom @ X_a ) )
=> ! [Xa: $i] :
( ( ord_less @ X_a @ ( number_number_of @ X_a @ Xa ) @ ( one_one @ X_a ) )
<=> ( ord_less @ int @ Xa @ ( bit1 @ pls ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(212,plain,
( ( ! [K: $i] :
~ ( ord_less @ int @ ( semiring_1_of_nat @ int @ K ) @ ( zero_zero @ int ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(213,plain,
( ( ! [Wa: $i,Z_1: $i] :
( ( ord_less @ int @ Wa @ ( plus_plus @ int @ Z_1 @ ( one_one @ int ) ) )
<=> ( ( ord_less @ int @ Wa @ Z_1 )
| ( Wa = Z_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(214,plain,
( ( ord_less @ int @ ( zero_zero @ int ) @ ( one_one @ int ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(215,plain,
( ( ! [Wa: $i] :
( ( ord_less @ int @ ( bit0 @ Wa ) @ ( zero_zero @ int ) )
<=> ( ord_less @ int @ Wa @ ( zero_zero @ int ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(216,plain,
( ( ~ ( ord_less @ int @ pls @ ( zero_zero @ int ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(217,plain,
( ( ! [Wa: $i] :
( ( ord_less @ int @ ( bit1 @ Wa ) @ ( zero_zero @ int ) )
<=> ( ord_less @ int @ Wa @ ( zero_zero @ int ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(218,plain,
( ( ! [K_1: $i] :
( ( ord_less @ int @ pls @ ( bit0 @ K_1 ) )
<=> ( ord_less @ int @ pls @ K_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(219,plain,
( ( ! [K_1: $i] :
( ( ord_less @ int @ ( bit0 @ K_1 ) @ pls )
<=> ( ord_less @ int @ K_1 @ pls ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(220,plain,
( ( ! [K_1: $i,L_1: $i] :
( ( ord_less @ int @ ( bit1 @ K_1 ) @ ( bit0 @ L_1 ) )
<=> ( ord_less @ int @ K_1 @ L_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(221,plain,
( ( ! [K1: $i,K2: $i] :
( ( ord_less @ int @ ( bit1 @ K1 ) @ ( bit0 @ K2 ) )
<=> ( ord_less @ int @ K1 @ K2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(222,plain,
( ( ! [K_1: $i] :
( ( ord_less @ int @ ( bit1 @ K_1 ) @ pls )
<=> ( ord_less @ int @ K_1 @ pls ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(223,plain,
( ( ! [X_a: $i] :
( ( ( number_ring @ X_a )
& ( linordered_idom @ X_a ) )
=> ! [Ya: $i] :
( ( ord_less @ X_a @ ( zero_zero @ X_a ) @ ( number_number_of @ X_a @ Ya ) )
<=> ( ord_less @ int @ pls @ Ya ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(224,plain,
( ( ! [X_a: $i] :
( ( ( number_ring @ X_a )
& ( linordered_idom @ X_a ) )
=> ! [Xa: $i] :
( ( ord_less @ X_a @ ( number_number_of @ X_a @ Xa ) @ ( zero_zero @ X_a ) )
<=> ( ord_less @ int @ Xa @ pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(225,plain,
( ( ! [Ma: $i,Na: $i] :
( ( ( semiring_1_of_nat @ int @ Ma )
= ( semiring_1_of_nat @ int @ Na ) )
<=> ( Ma = Na ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(226,plain,
( ( ! [Z: $i,W: $i] :
( ( plus_plus @ int @ Z @ W )
= ( plus_plus @ int @ W @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(227,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( plus_plus @ int @ X @ ( plus_plus @ int @ Y @ Z ) )
= ( plus_plus @ int @ Y @ ( plus_plus @ int @ X @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(228,plain,
( ( ! [Z1: $i,Z2: $i,Z3: $i] :
( ( plus_plus @ int @ ( plus_plus @ int @ Z1 @ Z2 ) @ Z3 )
= ( plus_plus @ int @ Z1 @ ( plus_plus @ int @ Z2 @ Z3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(229,plain,
( ( ! [X_a: $i] :
( ( linordered_idom @ X_a )
=> ! [A_2: $i] :
( ( ord_less @ X_a @ ( plus_plus @ X_a @ A_2 @ A_2 ) @ ( zero_zero @ X_a ) )
<=> ( ord_less @ X_a @ A_2 @ ( zero_zero @ X_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(230,plain,
( ( ! [K_1: $i,L_1: $i] :
( ( ( bit0 @ K_1 )
= ( bit0 @ L_1 ) )
<=> ( K_1 = L_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(231,plain,
( ( ! [K_1: $i,L_1: $i] :
( ( ( bit1 @ K_1 )
= ( bit1 @ L_1 ) )
<=> ( K_1 = L_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(232,plain,
( ( ! [X_a: $i] :
( ( number @ X_a )
=> ! [Wa: $i,Xa: $i] :
( ( ( number_number_of @ X_a @ Wa )
= ( ti @ X_a @ Xa ) )
<=> ( ( ti @ X_a @ Xa )
= ( number_number_of @ X_a @ Wa ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(233,plain,
( ( ! [X_a: $i] :
( ( ( number_ring @ X_a )
& ( ring_char_0 @ X_a ) )
=> ! [Xa: $i,Ya: $i] :
( ( ( number_number_of @ X_a @ Xa )
= ( number_number_of @ X_a @ Ya ) )
<=> ( Xa = Ya ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(234,plain,
( ( ( one_one @ nat )
= ( number_number_of @ nat @ ( bit1 @ pls ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(235,plain,
( ( ( number_number_of @ nat @ ( bit1 @ pls ) )
= ( one_one @ nat ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(236,plain,
( ( ( one_one @ int )
= ( number_number_of @ int @ ( bit1 @ pls ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(237,plain,
( ( ! [V_1: $i,V: $i] :
( ( ( ord_less @ int @ V @ pls )
=> ( ( plus_plus @ nat @ ( number_number_of @ nat @ V ) @ ( number_number_of @ nat @ V_1 ) )
= ( number_number_of @ nat @ V_1 ) ) )
& ( ~ ( ord_less @ int @ V @ pls )
=> ( ( ( ord_less @ int @ V_1 @ pls )
=> ( ( plus_plus @ nat @ ( number_number_of @ nat @ V ) @ ( number_number_of @ nat @ V_1 ) )
= ( number_number_of @ nat @ V ) ) )
& ( ~ ( ord_less @ int @ V_1 @ pls )
=> ( ( plus_plus @ nat @ ( number_number_of @ nat @ V ) @ ( number_number_of @ nat @ V_1 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ V @ V_1 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(238,plain,
( ( ! [K: $i,I: $i,J: $i] :
( ( ord_less @ int @ I @ J )
=> ( ord_less @ int @ ( plus_plus @ int @ I @ K ) @ ( plus_plus @ int @ J @ K ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(239,plain,
( ( ! [K_1: $i,L_1: $i] :
( ( ord_less @ int @ ( bit0 @ K_1 ) @ ( bit0 @ L_1 ) )
<=> ( ord_less @ int @ K_1 @ L_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(240,plain,
( ( ! [K1: $i,K2: $i] :
( ( ord_less @ int @ ( bit0 @ K1 ) @ ( bit0 @ K2 ) )
<=> ( ord_less @ int @ K1 @ K2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(241,plain,
( ( ~ ( ord_less @ int @ pls @ pls ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(242,plain,
( ( ! [K_1: $i,L_1: $i] :
( ( ord_less @ int @ ( bit1 @ K_1 ) @ ( bit1 @ L_1 ) )
<=> ( ord_less @ int @ K_1 @ L_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(243,plain,
( ( ! [K1: $i,K2: $i] :
( ( ord_less @ int @ ( bit1 @ K1 ) @ ( bit1 @ K2 ) )
<=> ( ord_less @ int @ K1 @ K2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(244,plain,
( ( ( plus_plus @ nat @ ( one_one @ nat ) @ ( one_one @ nat ) )
= ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(245,plain,
( ( ( semiring_1_of_nat @ int @ ( zero_zero @ nat ) )
= ( zero_zero @ int ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(246,plain,
( ( ! [Na: $i] :
( ( ( semiring_1_of_nat @ int @ Na )
= ( zero_zero @ int ) )
<=> ( Na
= ( zero_zero @ nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(247,plain,
( ( ( zero_zero @ nat )
= ( number_number_of @ nat @ pls ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(248,plain,
( ( ( number_number_of @ nat @ pls )
= ( zero_zero @ nat ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(249,plain,
( ( ( semiring_1_of_nat @ int @ ( one_one @ nat ) )
= ( one_one @ int ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(250,plain,
( ( ! [M: $i,N: $i] :
( ( plus_plus @ int @ ( semiring_1_of_nat @ int @ M ) @ ( semiring_1_of_nat @ int @ N ) )
= ( semiring_1_of_nat @ int @ ( plus_plus @ nat @ M @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(251,plain,
( ( ! [M: $i,N: $i,Z: $i] :
( ( plus_plus @ int @ ( semiring_1_of_nat @ int @ M ) @ ( plus_plus @ int @ ( semiring_1_of_nat @ int @ N ) @ Z ) )
= ( plus_plus @ int @ ( semiring_1_of_nat @ int @ ( plus_plus @ nat @ M @ N ) ) @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(252,plain,
( ( ! [M: $i,N: $i] :
( ( semiring_1_of_nat @ int @ ( power_power @ nat @ M @ N ) )
= ( power_power @ int @ ( semiring_1_of_nat @ int @ M ) @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(253,plain,
( ( ! [M: $i,N: $i] :
( ( power_power @ int @ ( semiring_1_of_nat @ int @ M ) @ N )
= ( semiring_1_of_nat @ int @ ( power_power @ nat @ M @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(254,plain,
( ( ( zero_zero @ int )
= ( number_number_of @ int @ pls ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(255,plain,
( ( ! [X_a: $i] :
( ( ( number_ring @ X_a )
& ( linordered_idom @ X_a ) )
=> ! [Xa: $i,Ya: $i] :
( ( ord_less @ X_a @ ( number_number_of @ X_a @ Xa ) @ ( number_number_of @ X_a @ Ya ) )
<=> ( ord_less @ int @ Xa @ Ya ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(256,plain,
( ( ! [V: $i,W: $i] :
( ( plus_plus @ int @ ( number_number_of @ int @ V ) @ ( number_number_of @ int @ W ) )
= ( number_number_of @ int @ ( plus_plus @ int @ V @ W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(257,plain,
( ( ! [K_1: $i,L_1: $i] :
( ( ord_less @ int @ ( number_number_of @ int @ K_1 ) @ ( number_number_of @ int @ L_1 ) )
<=> ( ord_less @ int @ K_1 @ L_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(258,plain,
( ( ! [X: $i,Y: $i] :
( ( ord_less @ int @ X @ Y )
| ( X = Y )
| ( ord_less @ int @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[105]) ).
thf(259,plain,
( ( ord_less @ nat @ ( zero_zero @ nat ) @ n )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(260,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ( ( number_number_of @ X_a @ ( bit1 @ pls ) )
= ( one_one @ X_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(261,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ( ( one_one @ X_a )
= ( number_number_of @ X_a @ ( bit1 @ pls ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[108]) ).
thf(262,plain,
( ( ! [X_a: $i] :
( ( ( power @ X_a )
& ( semiring_0 @ X_a ) )
=> ! [W: $i] :
( ( ( ( number_number_of @ nat @ W )
= ( zero_zero @ nat ) )
=> ( ( power_power @ X_a @ ( zero_zero @ X_a ) @ ( number_number_of @ nat @ W ) )
= ( one_one @ X_a ) ) )
& ( ( ( number_number_of @ nat @ W )
!= ( zero_zero @ nat ) )
=> ( ( power_power @ X_a @ ( zero_zero @ X_a ) @ ( number_number_of @ nat @ W ) )
= ( zero_zero @ X_a ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(263,plain,
( ( ! [X: $i] :
( ( power_power @ int @ ( power_power @ int @ X @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power @ int @ X @ ( number_number_of @ nat @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[110]) ).
thf(264,plain,
( ( ! [X_a: $i] :
( ( number_semiring @ X_a )
=> ( ( plus_plus @ X_a @ ( one_one @ X_a ) @ ( one_one @ X_a ) )
= ( number_number_of @ X_a @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[111]) ).
thf(265,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ( ( plus_plus @ X_a @ ( one_one @ X_a ) @ ( one_one @ X_a ) )
= ( number_number_of @ X_a @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[112]) ).
thf(266,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [V: $i] :
( ( plus_plus @ X_a @ ( number_number_of @ X_a @ V ) @ ( one_one @ X_a ) )
= ( number_number_of @ X_a @ ( plus_plus @ int @ V @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[113]) ).
thf(267,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [W: $i] :
( ( plus_plus @ X_a @ ( one_one @ X_a ) @ ( number_number_of @ X_a @ W ) )
= ( number_number_of @ X_a @ ( plus_plus @ int @ ( bit1 @ pls ) @ W ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[114]) ).
thf(268,plain,
( ( ! [X_a: $i] :
( ( ring_11004092258visors @ X_a )
=> ! [A_2: $i] :
( ( ( power_power @ X_a @ A_2 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ X_a ) )
<=> ( ( ti @ X_a @ A_2 )
= ( zero_zero @ X_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[115]) ).
thf(269,plain,
( ( ! [X_a: $i] :
( ( semiring_1 @ X_a )
=> ( ( power_power @ X_a @ ( zero_zero @ X_a ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ X_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[116]) ).
thf(270,plain,
( ( ! [X_a: $i] :
( ( semiring_1 @ X_a )
=> ( ( power_power @ X_a @ ( one_one @ X_a ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( one_one @ X_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[117]) ).
thf(271,plain,
( ( ! [X_a: $i] :
( ( linordered_idom @ X_a )
=> ! [Xa: $i,Ya: $i] :
( ( ( plus_plus @ X_a @ ( power_power @ X_a @ Xa @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ X_a @ Ya @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ X_a ) )
<=> ( ( ( ti @ X_a @ Xa )
= ( zero_zero @ X_a ) )
& ( ( ti @ X_a @ Ya )
= ( zero_zero @ X_a ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[118]) ).
thf(272,plain,
( ( ord_less @ int @ ( one_one @ int ) @ t )
= $true ),
inference(unfold_def,[status(thm)],[119]) ).
thf(273,plain,
( ( ord_less @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( one_one @ int ) @ ( semiring_1_of_nat @ int @ n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[120]) ).
thf(274,plain,
( ( ( ti @ int @ t )
= t )
= $true ),
inference(unfold_def,[status(thm)],[121]) ).
thf(275,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ( ( power @ X_a )
& ( semiring_0 @ X_a ) )
=> ( ( ti @ X_a @ ( power_power @ X_a @ B_1 @ B_2 ) )
= ( power_power @ X_a @ B_1 @ B_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[122]) ).
thf(276,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ( ( power @ X_a )
& ( semiring_0 @ X_a ) )
=> ( ( power_power @ X_a @ B_1 @ ( ti @ nat @ B_2 ) )
= ( power_power @ X_a @ B_1 @ B_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[123]) ).
thf(277,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ( ( power @ X_a )
& ( semiring_0 @ X_a ) )
=> ( ( power_power @ X_a @ ( ti @ X_a @ B_1 ) @ B_2 )
= ( power_power @ X_a @ B_1 @ B_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[124]) ).
thf(278,plain,
( ( ! [B_1: $i,B_2: $i] :
( ( ord_less @ nat @ B_1 @ ( ti @ nat @ B_2 ) )
<=> ( ord_less @ nat @ B_1 @ B_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[128]) ).
thf(279,plain,
( ( ! [B_1: $i,B_2: $i] :
( ( ord_less @ nat @ ( ti @ nat @ B_1 ) @ B_2 )
<=> ( ord_less @ nat @ B_1 @ B_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[129]) ).
thf(280,plain,
( ( ! [B_1: $i,X_a: $i] :
( ( number_semiring @ X_a )
=> ( ( ti @ X_a @ ( semiring_1_of_nat @ X_a @ B_1 ) )
= ( semiring_1_of_nat @ X_a @ B_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[132]) ).
thf(281,plain,
( ( ! [B_1: $i,X_a: $i] :
( ( number_semiring @ X_a )
=> ( ( semiring_1_of_nat @ X_a @ ( ti @ nat @ B_1 ) )
= ( semiring_1_of_nat @ X_a @ B_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[133]) ).
thf(282,plain,
( ( ! [B_1: $i,X_a: $i] :
( ( number @ X_a )
=> ( ( ti @ X_a @ ( number_number_of @ X_a @ B_1 ) )
= ( number_number_of @ X_a @ B_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[134]) ).
thf(283,plain,
( ( ! [B_1: $i,X_a: $i] :
( ( number @ X_a )
=> ( ( number_number_of @ X_a @ ( ti @ int @ B_1 ) )
= ( number_number_of @ X_a @ B_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[135]) ).
thf(284,plain,
( ( ! [X_a: $i] :
( ( ( power @ X_a )
& ( semiring_0 @ X_a ) )
=> ( ( ti @ X_a @ ( zero_zero @ X_a ) )
= ( zero_zero @ X_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[137]) ).
thf(285,plain,
( ( ! [X_a: $i] :
( ( linord219039673up_add @ X_a )
=> ( ( ti @ X_a @ ( zero_zero @ X_a ) )
= ( zero_zero @ X_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[138]) ).
thf(286,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ( number_semiring @ X_a )
=> ( ( ti @ X_a @ ( plus_plus @ X_a @ B_1 @ B_2 ) )
= ( plus_plus @ X_a @ B_1 @ B_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[140]) ).
thf(287,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ( number_semiring @ X_a )
=> ( ( plus_plus @ X_a @ B_1 @ ( ti @ X_a @ B_2 ) )
= ( plus_plus @ X_a @ B_1 @ B_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[141]) ).
thf(288,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ( number_semiring @ X_a )
=> ( ( plus_plus @ X_a @ ( ti @ X_a @ B_1 ) @ B_2 )
= ( plus_plus @ X_a @ B_1 @ B_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[142]) ).
thf(289,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ( linord219039673up_add @ X_a )
=> ( ( ti @ X_a @ ( plus_plus @ X_a @ B_1 @ B_2 ) )
= ( plus_plus @ X_a @ B_1 @ B_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[143]) ).
thf(290,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ( linord219039673up_add @ X_a )
=> ( ( plus_plus @ X_a @ B_1 @ ( ti @ X_a @ B_2 ) )
= ( plus_plus @ X_a @ B_1 @ B_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[144]) ).
thf(291,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ( linord219039673up_add @ X_a )
=> ( ( plus_plus @ X_a @ ( ti @ X_a @ B_1 ) @ B_2 )
= ( plus_plus @ X_a @ B_1 @ B_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[145]) ).
thf(292,plain,
( ( ! [X_a: $i] :
( ( ( power @ X_a )
& ( semiring_0 @ X_a ) )
=> ( ( ti @ X_a @ ( one_one @ X_a ) )
= ( one_one @ X_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[146]) ).
thf(293,plain,
( ( ( ti @ nat @ n )
= n )
= $true ),
inference(unfold_def,[status(thm)],[147]) ).
thf(294,plain,
( ( ( ti @ int @ pls )
= pls )
= $true ),
inference(unfold_def,[status(thm)],[148]) ).
thf(295,plain,
( ( ! [B_1: $i] :
( ( ti @ int @ ( bit1 @ B_1 ) )
= ( bit1 @ B_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[149]) ).
thf(296,plain,
( ( ! [B_1: $i] :
( ( bit1 @ ( ti @ int @ B_1 ) )
= ( bit1 @ B_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[150]) ).
thf(297,plain,
( ( ! [B_1: $i] :
( ( ti @ int @ ( bit0 @ B_1 ) )
= ( bit0 @ B_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[151]) ).
thf(298,plain,
( ( ! [B_1: $i] :
( ( bit0 @ ( ti @ int @ B_1 ) )
= ( bit0 @ B_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[152]) ).
thf(299,plain,
( ( ~ ( ( ( power_power @ int @ ( plus_plus @ int @ ( one_one @ int ) @ ( semiring_1_of_nat @ int @ n ) ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= ( zero_zero @ int ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[155]) ).
thf(300,plain,
( ( ! [B_1: $i] :
( ( bit0 @ ( ti @ int @ B_1 ) )
= ( bit0 @ B_1 ) ) )
= $true ),
inference(copy,[status(thm)],[298]) ).
thf(301,plain,
( ( ! [B_1: $i] :
( ( ti @ int @ ( bit0 @ B_1 ) )
= ( bit0 @ B_1 ) ) )
= $true ),
inference(copy,[status(thm)],[297]) ).
thf(302,plain,
( ( ! [B_1: $i] :
( ( bit1 @ ( ti @ int @ B_1 ) )
= ( bit1 @ B_1 ) ) )
= $true ),
inference(copy,[status(thm)],[296]) ).
thf(303,plain,
( ( ! [B_1: $i] :
( ( ti @ int @ ( bit1 @ B_1 ) )
= ( bit1 @ B_1 ) ) )
= $true ),
inference(copy,[status(thm)],[295]) ).
thf(304,plain,
( ( ( ti @ int @ pls )
= pls )
= $true ),
inference(copy,[status(thm)],[294]) ).
thf(305,plain,
( ( ( ti @ nat @ n )
= n )
= $true ),
inference(copy,[status(thm)],[293]) ).
thf(306,plain,
( ( ! [X_a: $i] :
( ( ( power @ X_a )
& ( semiring_0 @ X_a ) )
=> ( ( ti @ X_a @ ( one_one @ X_a ) )
= ( one_one @ X_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[292]) ).
thf(307,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ( linord219039673up_add @ X_a )
=> ( ( plus_plus @ X_a @ ( ti @ X_a @ B_1 ) @ B_2 )
= ( plus_plus @ X_a @ B_1 @ B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[291]) ).
thf(308,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ( linord219039673up_add @ X_a )
=> ( ( plus_plus @ X_a @ B_1 @ ( ti @ X_a @ B_2 ) )
= ( plus_plus @ X_a @ B_1 @ B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[290]) ).
thf(309,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ( linord219039673up_add @ X_a )
=> ( ( ti @ X_a @ ( plus_plus @ X_a @ B_1 @ B_2 ) )
= ( plus_plus @ X_a @ B_1 @ B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[289]) ).
thf(310,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ( number_semiring @ X_a )
=> ( ( plus_plus @ X_a @ ( ti @ X_a @ B_1 ) @ B_2 )
= ( plus_plus @ X_a @ B_1 @ B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[288]) ).
thf(311,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ( number_semiring @ X_a )
=> ( ( plus_plus @ X_a @ B_1 @ ( ti @ X_a @ B_2 ) )
= ( plus_plus @ X_a @ B_1 @ B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[287]) ).
thf(312,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ( number_semiring @ X_a )
=> ( ( ti @ X_a @ ( plus_plus @ X_a @ B_1 @ B_2 ) )
= ( plus_plus @ X_a @ B_1 @ B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[286]) ).
thf(313,plain,
( ( ! [X_a: $i] :
( ( linord219039673up_add @ X_a )
=> ( ( ti @ X_a @ ( zero_zero @ X_a ) )
= ( zero_zero @ X_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[285]) ).
thf(314,plain,
( ( ! [X_a: $i] :
( ( ( power @ X_a )
& ( semiring_0 @ X_a ) )
=> ( ( ti @ X_a @ ( zero_zero @ X_a ) )
= ( zero_zero @ X_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[284]) ).
thf(315,plain,
( ( ! [B_1: $i,X_a: $i] :
( ( number @ X_a )
=> ( ( number_number_of @ X_a @ ( ti @ int @ B_1 ) )
= ( number_number_of @ X_a @ B_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[283]) ).
thf(316,plain,
( ( ! [B_1: $i,X_a: $i] :
( ( number @ X_a )
=> ( ( ti @ X_a @ ( number_number_of @ X_a @ B_1 ) )
= ( number_number_of @ X_a @ B_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[282]) ).
thf(317,plain,
( ( ! [B_1: $i,X_a: $i] :
( ( number_semiring @ X_a )
=> ( ( semiring_1_of_nat @ X_a @ ( ti @ nat @ B_1 ) )
= ( semiring_1_of_nat @ X_a @ B_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[281]) ).
thf(318,plain,
( ( ! [B_1: $i,X_a: $i] :
( ( number_semiring @ X_a )
=> ( ( ti @ X_a @ ( semiring_1_of_nat @ X_a @ B_1 ) )
= ( semiring_1_of_nat @ X_a @ B_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[280]) ).
thf(319,plain,
( ( ! [B_1: $i,B_2: $i] :
( ( ord_less @ nat @ ( ti @ nat @ B_1 ) @ B_2 )
<=> ( ord_less @ nat @ B_1 @ B_2 ) ) )
= $true ),
inference(copy,[status(thm)],[279]) ).
thf(320,plain,
( ( ! [B_1: $i,B_2: $i] :
( ( ord_less @ nat @ B_1 @ ( ti @ nat @ B_2 ) )
<=> ( ord_less @ nat @ B_1 @ B_2 ) ) )
= $true ),
inference(copy,[status(thm)],[278]) ).
thf(321,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ( ( power @ X_a )
& ( semiring_0 @ X_a ) )
=> ( ( power_power @ X_a @ ( ti @ X_a @ B_1 ) @ B_2 )
= ( power_power @ X_a @ B_1 @ B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[277]) ).
thf(322,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ( ( power @ X_a )
& ( semiring_0 @ X_a ) )
=> ( ( power_power @ X_a @ B_1 @ ( ti @ nat @ B_2 ) )
= ( power_power @ X_a @ B_1 @ B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[276]) ).
thf(323,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ( ( power @ X_a )
& ( semiring_0 @ X_a ) )
=> ( ( ti @ X_a @ ( power_power @ X_a @ B_1 @ B_2 ) )
= ( power_power @ X_a @ B_1 @ B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[275]) ).
thf(324,plain,
( ( ( ti @ int @ t )
= t )
= $true ),
inference(copy,[status(thm)],[274]) ).
thf(325,plain,
( ( ord_less @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( one_one @ int ) @ ( semiring_1_of_nat @ int @ n ) ) )
= $true ),
inference(copy,[status(thm)],[273]) ).
thf(326,plain,
( ( ord_less @ int @ ( one_one @ int ) @ t )
= $true ),
inference(copy,[status(thm)],[272]) ).
thf(327,plain,
( ( ! [X_a: $i] :
( ( linordered_idom @ X_a )
=> ! [Xa: $i,Ya: $i] :
( ( ( plus_plus @ X_a @ ( power_power @ X_a @ Xa @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ X_a @ Ya @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ X_a ) )
<=> ( ( ( ti @ X_a @ Xa )
= ( zero_zero @ X_a ) )
& ( ( ti @ X_a @ Ya )
= ( zero_zero @ X_a ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[271]) ).
thf(328,plain,
( ( ! [X_a: $i] :
( ( semiring_1 @ X_a )
=> ( ( power_power @ X_a @ ( one_one @ X_a ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( one_one @ X_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[270]) ).
thf(329,plain,
( ( ! [X_a: $i] :
( ( semiring_1 @ X_a )
=> ( ( power_power @ X_a @ ( zero_zero @ X_a ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ X_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[269]) ).
thf(330,plain,
( ( ! [X_a: $i] :
( ( ring_11004092258visors @ X_a )
=> ! [A_2: $i] :
( ( ( power_power @ X_a @ A_2 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ X_a ) )
<=> ( ( ti @ X_a @ A_2 )
= ( zero_zero @ X_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[268]) ).
thf(331,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [W: $i] :
( ( plus_plus @ X_a @ ( one_one @ X_a ) @ ( number_number_of @ X_a @ W ) )
= ( number_number_of @ X_a @ ( plus_plus @ int @ ( bit1 @ pls ) @ W ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[267]) ).
thf(332,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [V: $i] :
( ( plus_plus @ X_a @ ( number_number_of @ X_a @ V ) @ ( one_one @ X_a ) )
= ( number_number_of @ X_a @ ( plus_plus @ int @ V @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[266]) ).
thf(333,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ( ( plus_plus @ X_a @ ( one_one @ X_a ) @ ( one_one @ X_a ) )
= ( number_number_of @ X_a @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[265]) ).
thf(334,plain,
( ( ! [X_a: $i] :
( ( number_semiring @ X_a )
=> ( ( plus_plus @ X_a @ ( one_one @ X_a ) @ ( one_one @ X_a ) )
= ( number_number_of @ X_a @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[264]) ).
thf(335,plain,
( ( ! [X: $i] :
( ( power_power @ int @ ( power_power @ int @ X @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power @ int @ X @ ( number_number_of @ nat @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[263]) ).
thf(336,plain,
( ( ! [X_a: $i] :
( ( ( power @ X_a )
& ( semiring_0 @ X_a ) )
=> ! [W: $i] :
( ( ( ( number_number_of @ nat @ W )
= ( zero_zero @ nat ) )
=> ( ( power_power @ X_a @ ( zero_zero @ X_a ) @ ( number_number_of @ nat @ W ) )
= ( one_one @ X_a ) ) )
& ( ( ( number_number_of @ nat @ W )
!= ( zero_zero @ nat ) )
=> ( ( power_power @ X_a @ ( zero_zero @ X_a ) @ ( number_number_of @ nat @ W ) )
= ( zero_zero @ X_a ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[262]) ).
thf(337,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ( ( one_one @ X_a )
= ( number_number_of @ X_a @ ( bit1 @ pls ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[261]) ).
thf(338,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ( ( number_number_of @ X_a @ ( bit1 @ pls ) )
= ( one_one @ X_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[260]) ).
thf(339,plain,
( ( ord_less @ nat @ ( zero_zero @ nat ) @ n )
= $true ),
inference(copy,[status(thm)],[259]) ).
thf(340,plain,
( ( ! [X: $i,Y: $i] :
( ( ord_less @ int @ X @ Y )
| ( X = Y )
| ( ord_less @ int @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[258]) ).
thf(341,plain,
( ( ! [K_1: $i,L_1: $i] :
( ( ord_less @ int @ ( number_number_of @ int @ K_1 ) @ ( number_number_of @ int @ L_1 ) )
<=> ( ord_less @ int @ K_1 @ L_1 ) ) )
= $true ),
inference(copy,[status(thm)],[257]) ).
thf(342,plain,
( ( ! [V: $i,W: $i] :
( ( plus_plus @ int @ ( number_number_of @ int @ V ) @ ( number_number_of @ int @ W ) )
= ( number_number_of @ int @ ( plus_plus @ int @ V @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[256]) ).
thf(343,plain,
( ( ! [X_a: $i] :
( ( ( number_ring @ X_a )
& ( linordered_idom @ X_a ) )
=> ! [Xa: $i,Ya: $i] :
( ( ord_less @ X_a @ ( number_number_of @ X_a @ Xa ) @ ( number_number_of @ X_a @ Ya ) )
<=> ( ord_less @ int @ Xa @ Ya ) ) ) )
= $true ),
inference(copy,[status(thm)],[255]) ).
thf(344,plain,
( ( ( zero_zero @ int )
= ( number_number_of @ int @ pls ) )
= $true ),
inference(copy,[status(thm)],[254]) ).
thf(345,plain,
( ( ! [M: $i,N: $i] :
( ( power_power @ int @ ( semiring_1_of_nat @ int @ M ) @ N )
= ( semiring_1_of_nat @ int @ ( power_power @ nat @ M @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[253]) ).
thf(346,plain,
( ( ! [M: $i,N: $i] :
( ( semiring_1_of_nat @ int @ ( power_power @ nat @ M @ N ) )
= ( power_power @ int @ ( semiring_1_of_nat @ int @ M ) @ N ) ) )
= $true ),
inference(copy,[status(thm)],[252]) ).
thf(347,plain,
( ( ! [M: $i,N: $i,Z: $i] :
( ( plus_plus @ int @ ( semiring_1_of_nat @ int @ M ) @ ( plus_plus @ int @ ( semiring_1_of_nat @ int @ N ) @ Z ) )
= ( plus_plus @ int @ ( semiring_1_of_nat @ int @ ( plus_plus @ nat @ M @ N ) ) @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[251]) ).
thf(348,plain,
( ( ! [M: $i,N: $i] :
( ( plus_plus @ int @ ( semiring_1_of_nat @ int @ M ) @ ( semiring_1_of_nat @ int @ N ) )
= ( semiring_1_of_nat @ int @ ( plus_plus @ nat @ M @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[250]) ).
thf(349,plain,
( ( ( semiring_1_of_nat @ int @ ( one_one @ nat ) )
= ( one_one @ int ) )
= $true ),
inference(copy,[status(thm)],[249]) ).
thf(350,plain,
( ( ( number_number_of @ nat @ pls )
= ( zero_zero @ nat ) )
= $true ),
inference(copy,[status(thm)],[248]) ).
thf(351,plain,
( ( ( zero_zero @ nat )
= ( number_number_of @ nat @ pls ) )
= $true ),
inference(copy,[status(thm)],[247]) ).
thf(352,plain,
( ( ! [Na: $i] :
( ( ( semiring_1_of_nat @ int @ Na )
= ( zero_zero @ int ) )
<=> ( Na
= ( zero_zero @ nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[246]) ).
thf(353,plain,
( ( ( semiring_1_of_nat @ int @ ( zero_zero @ nat ) )
= ( zero_zero @ int ) )
= $true ),
inference(copy,[status(thm)],[245]) ).
thf(354,plain,
( ( ( plus_plus @ nat @ ( one_one @ nat ) @ ( one_one @ nat ) )
= ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(copy,[status(thm)],[244]) ).
thf(355,plain,
( ( ! [K1: $i,K2: $i] :
( ( ord_less @ int @ ( bit1 @ K1 ) @ ( bit1 @ K2 ) )
<=> ( ord_less @ int @ K1 @ K2 ) ) )
= $true ),
inference(copy,[status(thm)],[243]) ).
thf(356,plain,
( ( ! [K_1: $i,L_1: $i] :
( ( ord_less @ int @ ( bit1 @ K_1 ) @ ( bit1 @ L_1 ) )
<=> ( ord_less @ int @ K_1 @ L_1 ) ) )
= $true ),
inference(copy,[status(thm)],[242]) ).
thf(357,plain,
( ( ~ ( ord_less @ int @ pls @ pls ) )
= $true ),
inference(copy,[status(thm)],[241]) ).
thf(358,plain,
( ( ! [K1: $i,K2: $i] :
( ( ord_less @ int @ ( bit0 @ K1 ) @ ( bit0 @ K2 ) )
<=> ( ord_less @ int @ K1 @ K2 ) ) )
= $true ),
inference(copy,[status(thm)],[240]) ).
thf(359,plain,
( ( ! [K_1: $i,L_1: $i] :
( ( ord_less @ int @ ( bit0 @ K_1 ) @ ( bit0 @ L_1 ) )
<=> ( ord_less @ int @ K_1 @ L_1 ) ) )
= $true ),
inference(copy,[status(thm)],[239]) ).
thf(360,plain,
( ( ! [K: $i,I: $i,J: $i] :
( ( ord_less @ int @ I @ J )
=> ( ord_less @ int @ ( plus_plus @ int @ I @ K ) @ ( plus_plus @ int @ J @ K ) ) ) )
= $true ),
inference(copy,[status(thm)],[238]) ).
thf(361,plain,
( ( ! [V_1: $i,V: $i] :
( ( ( ord_less @ int @ V @ pls )
=> ( ( plus_plus @ nat @ ( number_number_of @ nat @ V ) @ ( number_number_of @ nat @ V_1 ) )
= ( number_number_of @ nat @ V_1 ) ) )
& ( ~ ( ord_less @ int @ V @ pls )
=> ( ( ( ord_less @ int @ V_1 @ pls )
=> ( ( plus_plus @ nat @ ( number_number_of @ nat @ V ) @ ( number_number_of @ nat @ V_1 ) )
= ( number_number_of @ nat @ V ) ) )
& ( ~ ( ord_less @ int @ V_1 @ pls )
=> ( ( plus_plus @ nat @ ( number_number_of @ nat @ V ) @ ( number_number_of @ nat @ V_1 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ V @ V_1 ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[237]) ).
thf(362,plain,
( ( ( one_one @ int )
= ( number_number_of @ int @ ( bit1 @ pls ) ) )
= $true ),
inference(copy,[status(thm)],[236]) ).
thf(363,plain,
( ( ( number_number_of @ nat @ ( bit1 @ pls ) )
= ( one_one @ nat ) )
= $true ),
inference(copy,[status(thm)],[235]) ).
thf(364,plain,
( ( ( one_one @ nat )
= ( number_number_of @ nat @ ( bit1 @ pls ) ) )
= $true ),
inference(copy,[status(thm)],[234]) ).
thf(365,plain,
( ( ! [X_a: $i] :
( ( ( number_ring @ X_a )
& ( ring_char_0 @ X_a ) )
=> ! [Xa: $i,Ya: $i] :
( ( ( number_number_of @ X_a @ Xa )
= ( number_number_of @ X_a @ Ya ) )
<=> ( Xa = Ya ) ) ) )
= $true ),
inference(copy,[status(thm)],[233]) ).
thf(366,plain,
( ( ! [X_a: $i] :
( ( number @ X_a )
=> ! [Wa: $i,Xa: $i] :
( ( ( number_number_of @ X_a @ Wa )
= ( ti @ X_a @ Xa ) )
<=> ( ( ti @ X_a @ Xa )
= ( number_number_of @ X_a @ Wa ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[232]) ).
thf(367,plain,
( ( ! [K_1: $i,L_1: $i] :
( ( ( bit1 @ K_1 )
= ( bit1 @ L_1 ) )
<=> ( K_1 = L_1 ) ) )
= $true ),
inference(copy,[status(thm)],[231]) ).
thf(368,plain,
( ( ! [K_1: $i,L_1: $i] :
( ( ( bit0 @ K_1 )
= ( bit0 @ L_1 ) )
<=> ( K_1 = L_1 ) ) )
= $true ),
inference(copy,[status(thm)],[230]) ).
thf(369,plain,
( ( ! [X_a: $i] :
( ( linordered_idom @ X_a )
=> ! [A_2: $i] :
( ( ord_less @ X_a @ ( plus_plus @ X_a @ A_2 @ A_2 ) @ ( zero_zero @ X_a ) )
<=> ( ord_less @ X_a @ A_2 @ ( zero_zero @ X_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[229]) ).
thf(370,plain,
( ( ! [Z1: $i,Z2: $i,Z3: $i] :
( ( plus_plus @ int @ ( plus_plus @ int @ Z1 @ Z2 ) @ Z3 )
= ( plus_plus @ int @ Z1 @ ( plus_plus @ int @ Z2 @ Z3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[228]) ).
thf(371,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( plus_plus @ int @ X @ ( plus_plus @ int @ Y @ Z ) )
= ( plus_plus @ int @ Y @ ( plus_plus @ int @ X @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[227]) ).
thf(372,plain,
( ( ! [Z: $i,W: $i] :
( ( plus_plus @ int @ Z @ W )
= ( plus_plus @ int @ W @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[226]) ).
thf(373,plain,
( ( ! [Ma: $i,Na: $i] :
( ( ( semiring_1_of_nat @ int @ Ma )
= ( semiring_1_of_nat @ int @ Na ) )
<=> ( Ma = Na ) ) )
= $true ),
inference(copy,[status(thm)],[225]) ).
thf(374,plain,
( ( ! [X_a: $i] :
( ( ( number_ring @ X_a )
& ( linordered_idom @ X_a ) )
=> ! [Xa: $i] :
( ( ord_less @ X_a @ ( number_number_of @ X_a @ Xa ) @ ( zero_zero @ X_a ) )
<=> ( ord_less @ int @ Xa @ pls ) ) ) )
= $true ),
inference(copy,[status(thm)],[224]) ).
thf(375,plain,
( ( ! [X_a: $i] :
( ( ( number_ring @ X_a )
& ( linordered_idom @ X_a ) )
=> ! [Ya: $i] :
( ( ord_less @ X_a @ ( zero_zero @ X_a ) @ ( number_number_of @ X_a @ Ya ) )
<=> ( ord_less @ int @ pls @ Ya ) ) ) )
= $true ),
inference(copy,[status(thm)],[223]) ).
thf(376,plain,
( ( ! [K_1: $i] :
( ( ord_less @ int @ ( bit1 @ K_1 ) @ pls )
<=> ( ord_less @ int @ K_1 @ pls ) ) )
= $true ),
inference(copy,[status(thm)],[222]) ).
thf(377,plain,
( ( ! [K1: $i,K2: $i] :
( ( ord_less @ int @ ( bit1 @ K1 ) @ ( bit0 @ K2 ) )
<=> ( ord_less @ int @ K1 @ K2 ) ) )
= $true ),
inference(copy,[status(thm)],[221]) ).
thf(378,plain,
( ( ! [K_1: $i,L_1: $i] :
( ( ord_less @ int @ ( bit1 @ K_1 ) @ ( bit0 @ L_1 ) )
<=> ( ord_less @ int @ K_1 @ L_1 ) ) )
= $true ),
inference(copy,[status(thm)],[220]) ).
thf(379,plain,
( ( ! [K_1: $i] :
( ( ord_less @ int @ ( bit0 @ K_1 ) @ pls )
<=> ( ord_less @ int @ K_1 @ pls ) ) )
= $true ),
inference(copy,[status(thm)],[219]) ).
thf(380,plain,
( ( ! [K_1: $i] :
( ( ord_less @ int @ pls @ ( bit0 @ K_1 ) )
<=> ( ord_less @ int @ pls @ K_1 ) ) )
= $true ),
inference(copy,[status(thm)],[218]) ).
thf(381,plain,
( ( ! [Wa: $i] :
( ( ord_less @ int @ ( bit1 @ Wa ) @ ( zero_zero @ int ) )
<=> ( ord_less @ int @ Wa @ ( zero_zero @ int ) ) ) )
= $true ),
inference(copy,[status(thm)],[217]) ).
thf(382,plain,
( ( ~ ( ord_less @ int @ pls @ ( zero_zero @ int ) ) )
= $true ),
inference(copy,[status(thm)],[216]) ).
thf(383,plain,
( ( ! [Wa: $i] :
( ( ord_less @ int @ ( bit0 @ Wa ) @ ( zero_zero @ int ) )
<=> ( ord_less @ int @ Wa @ ( zero_zero @ int ) ) ) )
= $true ),
inference(copy,[status(thm)],[215]) ).
thf(384,plain,
( ( ord_less @ int @ ( zero_zero @ int ) @ ( one_one @ int ) )
= $true ),
inference(copy,[status(thm)],[214]) ).
thf(385,plain,
( ( ! [Wa: $i,Z_1: $i] :
( ( ord_less @ int @ Wa @ ( plus_plus @ int @ Z_1 @ ( one_one @ int ) ) )
<=> ( ( ord_less @ int @ Wa @ Z_1 )
| ( Wa = Z_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[213]) ).
thf(386,plain,
( ( ! [K: $i] :
~ ( ord_less @ int @ ( semiring_1_of_nat @ int @ K ) @ ( zero_zero @ int ) ) )
= $true ),
inference(copy,[status(thm)],[212]) ).
thf(387,plain,
( ( ! [X_a: $i] :
( ( ( number_ring @ X_a )
& ( linordered_idom @ X_a ) )
=> ! [Xa: $i] :
( ( ord_less @ X_a @ ( number_number_of @ X_a @ Xa ) @ ( one_one @ X_a ) )
<=> ( ord_less @ int @ Xa @ ( bit1 @ pls ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[211]) ).
thf(388,plain,
( ( ! [X_a: $i] :
( ( ( number_ring @ X_a )
& ( linordered_idom @ X_a ) )
=> ! [Ya: $i] :
( ( ord_less @ X_a @ ( one_one @ X_a ) @ ( number_number_of @ X_a @ Ya ) )
<=> ( ord_less @ int @ ( bit1 @ pls ) @ Ya ) ) ) )
= $true ),
inference(copy,[status(thm)],[210]) ).
thf(389,plain,
( ( ! [Z_1: $i] :
( ( ord_less @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ Z_1 ) @ Z_1 ) @ ( zero_zero @ int ) )
<=> ( ord_less @ int @ Z_1 @ ( zero_zero @ int ) ) ) )
= $true ),
inference(copy,[status(thm)],[209]) ).
thf(390,plain,
( ( ! [X_a: $i] :
( ( linord219039673up_add @ X_a )
=> ! [A_2: $i] :
( ( ( plus_plus @ X_a @ A_2 @ A_2 )
= ( zero_zero @ X_a ) )
<=> ( ( ti @ X_a @ A_2 )
= ( zero_zero @ X_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[208]) ).
thf(391,plain,
( ( ! [K: $i] :
( ( bit1 @ K )
!= pls ) )
= $true ),
inference(copy,[status(thm)],[207]) ).
thf(392,plain,
( ( ! [L: $i] :
( pls
!= ( bit1 @ L ) ) )
= $true ),
inference(copy,[status(thm)],[206]) ).
thf(393,plain,
( ( ! [K: $i,L: $i] :
( ( bit1 @ K )
!= ( bit0 @ L ) ) )
= $true ),
inference(copy,[status(thm)],[205]) ).
thf(394,plain,
( ( ! [K: $i,L: $i] :
( ( bit0 @ K )
!= ( bit1 @ L ) ) )
= $true ),
inference(copy,[status(thm)],[204]) ).
thf(395,plain,
( ( ! [K_1: $i] :
( ( ( bit0 @ K_1 )
= pls )
<=> ( K_1 = pls ) ) )
= $true ),
inference(copy,[status(thm)],[203]) ).
thf(396,plain,
( ( ! [L_1: $i] :
( ( pls
= ( bit0 @ L_1 ) )
<=> ( pls = L_1 ) ) )
= $true ),
inference(copy,[status(thm)],[202]) ).
thf(397,plain,
( ( ( bit0 @ pls )
= pls )
= $true ),
inference(copy,[status(thm)],[201]) ).
thf(398,plain,
( ( pls
= ( zero_zero @ int ) )
= $true ),
inference(copy,[status(thm)],[200]) ).
thf(399,plain,
( ( ( zero_zero @ int )
!= ( one_one @ int ) )
= $true ),
inference(copy,[status(thm)],[199]) ).
thf(400,plain,
( ( ! [K: $i] :
( ( plus_plus @ int @ K @ pls )
= K ) )
= $true ),
inference(copy,[status(thm)],[198]) ).
thf(401,plain,
( ( ! [K: $i] :
( ( plus_plus @ int @ pls @ K )
= K ) )
= $true ),
inference(copy,[status(thm)],[197]) ).
thf(402,plain,
( ( ! [K: $i,L: $i] :
( ( plus_plus @ int @ ( bit0 @ K ) @ ( bit0 @ L ) )
= ( bit0 @ ( plus_plus @ int @ K @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[196]) ).
thf(403,plain,
( ( ! [K: $i] :
( ( bit0 @ K )
= ( plus_plus @ int @ K @ K ) ) )
= $true ),
inference(copy,[status(thm)],[195]) ).
thf(404,plain,
( ( ! [Z: $i] :
( ( plus_plus @ int @ Z @ ( zero_zero @ int ) )
= Z ) )
= $true ),
inference(copy,[status(thm)],[194]) ).
thf(405,plain,
( ( ! [Z: $i] :
( ( plus_plus @ int @ ( zero_zero @ int ) @ Z )
= Z ) )
= $true ),
inference(copy,[status(thm)],[193]) ).
thf(406,plain,
( ( ! [X_a: $i] :
( ( number_semiring @ X_a )
=> ( ( number_number_of @ X_a @ pls )
= ( zero_zero @ X_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[192]) ).
thf(407,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ( ( number_number_of @ X_a @ pls )
= ( zero_zero @ X_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[191]) ).
thf(408,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ( ( zero_zero @ X_a )
= ( number_number_of @ X_a @ pls ) ) ) )
= $true ),
inference(copy,[status(thm)],[190]) ).
thf(409,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [A_1: $i] :
( ( plus_plus @ X_a @ ( number_number_of @ X_a @ pls ) @ A_1 )
= ( ti @ X_a @ A_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[189]) ).
thf(410,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [A_1: $i] :
( ( plus_plus @ X_a @ A_1 @ ( number_number_of @ X_a @ pls ) )
= ( ti @ X_a @ A_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[188]) ).
thf(411,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [V: $i,W: $i,Z: $i] :
( ( plus_plus @ X_a @ ( number_number_of @ X_a @ V ) @ ( plus_plus @ X_a @ ( number_number_of @ X_a @ W ) @ Z ) )
= ( plus_plus @ X_a @ ( number_number_of @ X_a @ ( plus_plus @ int @ V @ W ) ) @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[187]) ).
thf(412,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [V: $i,W: $i] :
( ( plus_plus @ X_a @ ( number_number_of @ X_a @ V ) @ ( number_number_of @ X_a @ W ) )
= ( number_number_of @ X_a @ ( plus_plus @ int @ V @ W ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[186]) ).
thf(413,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [V: $i,W: $i] :
( ( number_number_of @ X_a @ ( plus_plus @ int @ V @ W ) )
= ( plus_plus @ X_a @ ( number_number_of @ X_a @ V ) @ ( number_number_of @ X_a @ W ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[185]) ).
thf(414,plain,
( ( ! [K: $i,L: $i] :
( ( plus_plus @ int @ ( bit1 @ K ) @ ( bit0 @ L ) )
= ( bit1 @ ( plus_plus @ int @ K @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[184]) ).
thf(415,plain,
( ( ! [K: $i,L: $i] :
( ( plus_plus @ int @ ( bit0 @ K ) @ ( bit1 @ L ) )
= ( bit1 @ ( plus_plus @ int @ K @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[183]) ).
thf(416,plain,
( ( ! [K: $i] :
( ( bit1 @ K )
= ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ K ) @ K ) ) )
= $true ),
inference(copy,[status(thm)],[182]) ).
thf(417,plain,
( ( ! [Z: $i] :
( ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ Z ) @ Z )
!= ( zero_zero @ int ) ) )
= $true ),
inference(copy,[status(thm)],[181]) ).
thf(418,plain,
( ( ! [X_a: $i] :
( ( number_semiring @ X_a )
=> ! [N: $i] :
( ( number_number_of @ X_a @ ( semiring_1_of_nat @ int @ N ) )
= ( semiring_1_of_nat @ X_a @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[180]) ).
thf(419,plain,
( ( ! [X_a: $i] :
( ( linordered_idom @ X_a )
=> ! [A_2: $i] :
( ( ord_less @ X_a @ ( zero_zero @ X_a ) @ ( power_power @ X_a @ A_2 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
<=> ( ( ti @ X_a @ A_2 )
!= ( zero_zero @ X_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[179]) ).
thf(420,plain,
( ( ! [X_a: $i] :
( ( linordered_idom @ X_a )
=> ! [A_1: $i] :
~ ( ord_less @ X_a @ ( power_power @ X_a @ A_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( zero_zero @ X_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[178]) ).
thf(421,plain,
( ( ! [X_a: $i] :
( ( linordered_idom @ X_a )
=> ! [Xa: $i,Ya: $i] :
( ( ord_less @ X_a @ ( zero_zero @ X_a ) @ ( plus_plus @ X_a @ ( power_power @ X_a @ Xa @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ X_a @ Ya @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
<=> ( ( ( ti @ X_a @ Xa )
!= ( zero_zero @ X_a ) )
| ( ( ti @ X_a @ Ya )
!= ( zero_zero @ X_a ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[177]) ).
thf(422,plain,
( ( linord219039673up_add @ int )
= $true ),
inference(copy,[status(thm)],[176]) ).
thf(423,plain,
( ( ring_11004092258visors @ int )
= $true ),
inference(copy,[status(thm)],[175]) ).
thf(424,plain,
( ( no_zero_divisors @ int )
= $true ),
inference(copy,[status(thm)],[174]) ).
thf(425,plain,
( ( linordered_idom @ int )
= $true ),
inference(copy,[status(thm)],[173]) ).
thf(426,plain,
( ( number_semiring @ int )
= $true ),
inference(copy,[status(thm)],[172]) ).
thf(427,plain,
( ( zero_neq_one @ int )
= $true ),
inference(copy,[status(thm)],[171]) ).
thf(428,plain,
( ( semiring_1 @ int )
= $true ),
inference(copy,[status(thm)],[170]) ).
thf(429,plain,
( ( semiring_0 @ int )
= $true ),
inference(copy,[status(thm)],[169]) ).
thf(430,plain,
( ( mult_zero @ int )
= $true ),
inference(copy,[status(thm)],[168]) ).
thf(431,plain,
( ( ring_char_0 @ int )
= $true ),
inference(copy,[status(thm)],[167]) ).
thf(432,plain,
( ( number_ring @ int )
= $true ),
inference(copy,[status(thm)],[166]) ).
thf(433,plain,
( ( power @ int )
= $true ),
inference(copy,[status(thm)],[165]) ).
thf(434,plain,
( ( number @ int )
= $true ),
inference(copy,[status(thm)],[164]) ).
thf(435,plain,
( ( no_zero_divisors @ nat )
= $true ),
inference(copy,[status(thm)],[163]) ).
thf(436,plain,
( ( number_semiring @ nat )
= $true ),
inference(copy,[status(thm)],[162]) ).
thf(437,plain,
( ( zero_neq_one @ nat )
= $true ),
inference(copy,[status(thm)],[161]) ).
thf(438,plain,
( ( semiring_1 @ nat )
= $true ),
inference(copy,[status(thm)],[160]) ).
thf(439,plain,
( ( semiring_0 @ nat )
= $true ),
inference(copy,[status(thm)],[159]) ).
thf(440,plain,
( ( mult_zero @ nat )
= $true ),
inference(copy,[status(thm)],[158]) ).
thf(441,plain,
( ( power @ nat )
= $true ),
inference(copy,[status(thm)],[157]) ).
thf(442,plain,
( ( number @ nat )
= $true ),
inference(copy,[status(thm)],[156]) ).
thf(443,plain,
( ( ~ ( ( ( power_power @ int @ ( plus_plus @ int @ ( one_one @ int ) @ ( semiring_1_of_nat @ int @ n ) ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= ( zero_zero @ int ) ) ) )
= $true ),
inference(copy,[status(thm)],[299]) ).
thf(444,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( power @ SX0 )
| ~ ( semiring_0 @ SX0 ) )
| ! [SX1: $i] :
~ ( ~ ( ( ( number_number_of @ nat @ SX1 )
!= ( zero_zero @ nat ) )
| ( ( power_power @ SX0 @ ( zero_zero @ SX0 ) @ ( number_number_of @ nat @ SX1 ) )
= ( one_one @ SX0 ) ) )
| ~ ( ~ ( ( ( number_number_of @ nat @ SX1 )
!= ( zero_zero @ nat ) ) )
| ( ( power_power @ SX0 @ ( zero_zero @ SX0 ) @ ( number_number_of @ nat @ SX1 ) )
= ( zero_zero @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[336]) ).
thf(445,plain,
( ( ! [SX0: $i] :
( ~ ( linordered_idom @ SX0 )
| ! [SX1: $i,SX2: $i] :
~ ( ~ ( ( ( plus_plus @ SX0 @ ( power_power @ SX0 @ SX1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SX0 @ SX2 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SX0 ) )
| ~ ( ( ( ti @ SX0 @ SX1 )
!= ( zero_zero @ SX0 ) )
| ( ( ti @ SX0 @ SX2 )
!= ( zero_zero @ SX0 ) ) ) )
| ~ ( ~ ~ ( ( ( ti @ SX0 @ SX1 )
!= ( zero_zero @ SX0 ) )
| ( ( ti @ SX0 @ SX2 )
!= ( zero_zero @ SX0 ) ) )
| ( ( plus_plus @ SX0 @ ( power_power @ SX0 @ SX1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SX0 @ SX2 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[327]) ).
thf(446,plain,
( ( ! [SX0: $i] :
( ~ ( number_ring @ SX0 )
| ( ( zero_zero @ SX0 )
= ( number_number_of @ SX0 @ pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[408]) ).
thf(447,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( number_semiring @ SX2 )
| ( ( plus_plus @ SX2 @ SX0 @ ( ti @ SX2 @ SX1 ) )
= ( plus_plus @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[311]) ).
thf(448,plain,
( ( ! [SX0: $i] :
( ~ ( number_semiring @ SX0 )
| ( ( number_number_of @ SX0 @ pls )
= ( zero_zero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[406]) ).
thf(449,plain,
( ( ! [SX0: $i] :
( ~ ( number_ring @ SX0 )
| ! [SX1: $i] :
( ( plus_plus @ SX0 @ SX1 @ ( number_number_of @ SX0 @ pls ) )
= ( ti @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[410]) ).
thf(450,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SX0 ) @ ( zero_zero @ int ) )
| ( ord_less @ int @ SX0 @ ( zero_zero @ int ) ) )
| ~ ( ~ ( ord_less @ int @ SX0 @ ( zero_zero @ int ) )
| ( ord_less @ int @ ( bit0 @ SX0 ) @ ( zero_zero @ int ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[383]) ).
thf(451,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( power @ SX2 )
| ~ ( semiring_0 @ SX2 ) )
| ( ( power_power @ SX2 @ SX0 @ ( ti @ nat @ SX1 ) )
= ( power_power @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[322]) ).
thf(452,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( number @ SX1 )
| ( ( ti @ SX1 @ ( number_number_of @ SX1 @ SX0 ) )
= ( number_number_of @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[316]) ).
thf(453,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( number_semiring @ SX2 )
| ( ( ti @ SX2 @ ( plus_plus @ SX2 @ SX0 @ SX1 ) )
= ( plus_plus @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[312]) ).
thf(454,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( ord_less @ int @ SX1 @ SX2 )
| ( ord_less @ int @ ( plus_plus @ int @ SX1 @ SX0 ) @ ( plus_plus @ int @ SX2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[360]) ).
thf(455,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( bit1 @ SX0 )
!= ( bit0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[393]) ).
thf(456,plain,
( ( ! [SX0: $i] :
( ~ ( number_ring @ SX0 )
| ( ( one_one @ SX0 )
= ( number_number_of @ SX0 @ ( bit1 @ pls ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[337]) ).
thf(457,plain,
( ( ! [SX0: $i] :
( ~ ( number_ring @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ( plus_plus @ SX0 @ ( number_number_of @ SX0 @ SX1 ) @ ( plus_plus @ SX0 @ ( number_number_of @ SX0 @ SX2 ) @ SX3 ) )
= ( plus_plus @ SX0 @ ( number_number_of @ SX0 @ ( plus_plus @ int @ SX1 @ SX2 ) ) @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[411]) ).
thf(458,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ( pls
!= ( bit0 @ SX0 ) )
| ( pls = SX0 ) )
| ~ ( ( pls != SX0 )
| ( pls
= ( bit0 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[396]) ).
thf(459,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ord_less @ int @ ( number_number_of @ int @ SX0 ) @ ( number_number_of @ int @ SX1 ) )
| ( ord_less @ int @ SX0 @ SX1 ) )
| ~ ( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ int @ ( number_number_of @ int @ SX0 ) @ ( number_number_of @ int @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[341]) ).
thf(460,plain,
( ( ~ ( ( ( power_power @ int @ ( plus_plus @ int @ ( one_one @ int ) @ ( semiring_1_of_nat @ int @ n ) ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= ( zero_zero @ int ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[443]) ).
thf(461,plain,
( ( ! [SX0: $i] :
( ~ ( linordered_idom @ SX0 )
| ! [SX1: $i] :
~ ( ~ ( ~ ( ord_less @ SX0 @ ( plus_plus @ SX0 @ SX1 @ SX1 ) @ ( zero_zero @ SX0 ) )
| ( ord_less @ SX0 @ SX1 @ ( zero_zero @ SX0 ) ) )
| ~ ( ~ ( ord_less @ SX0 @ SX1 @ ( zero_zero @ SX0 ) )
| ( ord_less @ SX0 @ ( plus_plus @ SX0 @ SX1 @ SX1 ) @ ( zero_zero @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[369]) ).
thf(462,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SX0 ) @ pls )
| ( ord_less @ int @ SX0 @ pls ) )
| ~ ( ~ ( ord_less @ int @ SX0 @ pls )
| ( ord_less @ int @ ( bit1 @ SX0 ) @ pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[376]) ).
thf(463,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less @ int @ SX0 @ SX1 ) )
| ~ ( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[358]) ).
thf(464,plain,
( ( ! [SX0: $i] :
( ~ ( number_ring @ SX0 )
| ! [SX1: $i] :
( ( plus_plus @ SX0 @ ( number_number_of @ SX0 @ pls ) @ SX1 )
= ( ti @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[409]) ).
thf(465,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ( ( semiring_1_of_nat @ int @ SX0 )
!= ( zero_zero @ int ) )
| ( SX0
= ( zero_zero @ nat ) ) )
| ~ ( ( SX0
!= ( zero_zero @ nat ) )
| ( ( semiring_1_of_nat @ int @ SX0 )
= ( zero_zero @ int ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[352]) ).
thf(466,plain,
( ( ! [SX0: $i] :
( ~ ( semiring_1 @ SX0 )
| ( ( power_power @ SX0 @ ( zero_zero @ SX0 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[329]) ).
thf(467,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( ( bit1 @ SX0 )
!= ( bit1 @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ( ( SX0 != SX1 )
| ( ( bit1 @ SX0 )
= ( bit1 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[367]) ).
thf(468,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ord_less @ int @ SX1 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SX1 ) @ ( number_number_of @ nat @ SX0 ) )
= ( number_number_of @ nat @ SX0 ) ) )
| ~ ( ~ ~ ( ord_less @ int @ SX1 @ pls )
| ~ ( ~ ( ~ ( ord_less @ int @ SX0 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SX1 ) @ ( number_number_of @ nat @ SX0 ) )
= ( number_number_of @ nat @ SX1 ) ) )
| ~ ( ~ ~ ( ord_less @ int @ SX0 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SX1 ) @ ( number_number_of @ nat @ SX0 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SX1 @ SX0 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[361]) ).
thf(469,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( linord219039673up_add @ SX2 )
| ( ( ti @ SX2 @ ( plus_plus @ SX2 @ SX0 @ SX1 ) )
= ( plus_plus @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[309]) ).
thf(470,plain,
( ( ! [SX0: $i] :
( ~ ( number_ring @ SX0 )
| ( ( number_number_of @ SX0 @ ( bit1 @ pls ) )
= ( one_one @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[338]) ).
thf(471,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( bit0 @ SX0 )
!= ( bit1 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[394]) ).
thf(472,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SX0 ) @ pls )
| ( ord_less @ int @ SX0 @ pls ) )
| ~ ( ~ ( ord_less @ int @ SX0 @ pls )
| ( ord_less @ int @ ( bit0 @ SX0 ) @ pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[379]) ).
thf(473,plain,
( ( ! [SX0: $i] :
( ~ ( number_ring @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ( number_number_of @ SX0 @ ( plus_plus @ int @ SX1 @ SX2 ) )
= ( plus_plus @ SX0 @ ( number_number_of @ SX0 @ SX1 ) @ ( number_number_of @ SX0 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[413]) ).
thf(474,plain,
( ( ! [SX0: $i] :
( ~ ( number_semiring @ SX0 )
| ! [SX1: $i] :
( ( number_number_of @ SX0 @ ( semiring_1_of_nat @ int @ SX1 ) )
= ( semiring_1_of_nat @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[418]) ).
thf(475,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ord_less @ nat @ ( ti @ nat @ SX0 ) @ SX1 )
| ( ord_less @ nat @ SX0 @ SX1 ) )
| ~ ( ~ ( ord_less @ nat @ SX0 @ SX1 )
| ( ord_less @ nat @ ( ti @ nat @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[319]) ).
thf(476,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ord_less @ nat @ SX0 @ ( ti @ nat @ SX1 ) )
| ( ord_less @ nat @ SX0 @ SX1 ) )
| ~ ( ~ ( ord_less @ nat @ SX0 @ SX1 )
| ( ord_less @ nat @ SX0 @ ( ti @ nat @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[320]) ).
thf(477,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( linord219039673up_add @ SX2 )
| ( ( plus_plus @ SX2 @ ( ti @ SX2 @ SX0 ) @ SX1 )
= ( plus_plus @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[307]) ).
thf(478,plain,
( ( ! [SX0: $i] :
( ~ ( number_ring @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ( plus_plus @ SX0 @ ( number_number_of @ SX0 @ SX1 ) @ ( number_number_of @ SX0 @ SX2 ) )
= ( number_number_of @ SX0 @ ( plus_plus @ int @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[412]) ).
thf(479,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( power @ SX0 )
| ~ ( semiring_0 @ SX0 ) )
| ( ( ti @ SX0 @ ( one_one @ SX0 ) )
= ( one_one @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[306]) ).
thf(480,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( power @ SX2 )
| ~ ( semiring_0 @ SX2 ) )
| ( ( ti @ SX2 @ ( power_power @ SX2 @ SX0 @ SX1 ) )
= ( power_power @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[323]) ).
thf(481,plain,
( ( ! [SX0: $i] :
( ~ ( linordered_idom @ SX0 )
| ! [SX1: $i] :
~ ( ~ ( ~ ( ord_less @ SX0 @ ( zero_zero @ SX0 ) @ ( power_power @ SX0 @ SX1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ( ( ti @ SX0 @ SX1 )
!= ( zero_zero @ SX0 ) ) )
| ~ ( ~ ( ( ( ti @ SX0 @ SX1 )
!= ( zero_zero @ SX0 ) ) )
| ( ord_less @ SX0 @ ( zero_zero @ SX0 ) @ ( power_power @ SX0 @ SX1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[419]) ).
thf(482,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( number_ring @ SX0 )
| ~ ( linordered_idom @ SX0 ) )
| ! [SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( ord_less @ SX0 @ ( number_number_of @ SX0 @ SX1 ) @ ( number_number_of @ SX0 @ SX2 ) )
| ( ord_less @ int @ SX1 @ SX2 ) )
| ~ ( ~ ( ord_less @ int @ SX1 @ SX2 )
| ( ord_less @ SX0 @ ( number_number_of @ SX0 @ SX1 ) @ ( number_number_of @ SX0 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[343]) ).
thf(483,plain,
( ( ! [SX0: $i] :
( ~ ( number_ring @ SX0 )
| ! [SX1: $i] :
( ( plus_plus @ SX0 @ ( number_number_of @ SX0 @ SX1 ) @ ( one_one @ SX0 ) )
= ( number_number_of @ SX0 @ ( plus_plus @ int @ SX1 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[332]) ).
thf(484,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less @ int @ SX0 @ SX1 ) )
| ~ ( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[378]) ).
thf(485,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( number_semiring @ SX1 )
| ( ( ti @ SX1 @ ( semiring_1_of_nat @ SX1 @ SX0 ) )
= ( semiring_1_of_nat @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[318]) ).
thf(486,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( ( bit0 @ SX0 )
!= ( bit0 @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ( ( SX0 != SX1 )
| ( ( bit0 @ SX0 )
= ( bit0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[368]) ).
thf(487,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( ( semiring_1_of_nat @ int @ SX0 )
!= ( semiring_1_of_nat @ int @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ( ( SX0 != SX1 )
| ( ( semiring_1_of_nat @ int @ SX0 )
= ( semiring_1_of_nat @ int @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[373]) ).
thf(488,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( ord_less @ int @ pls @ ( bit0 @ SX0 ) )
| ( ord_less @ int @ pls @ SX0 ) )
| ~ ( ~ ( ord_less @ int @ pls @ SX0 )
| ( ord_less @ int @ pls @ ( bit0 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[380]) ).
thf(489,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( number_ring @ SX0 )
| ~ ( linordered_idom @ SX0 ) )
| ! [SX1: $i] :
~ ( ~ ( ~ ( ord_less @ SX0 @ ( number_number_of @ SX0 @ SX1 ) @ ( zero_zero @ SX0 ) )
| ( ord_less @ int @ SX1 @ pls ) )
| ~ ( ~ ( ord_less @ int @ SX1 @ pls )
| ( ord_less @ SX0 @ ( number_number_of @ SX0 @ SX1 ) @ ( zero_zero @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[374]) ).
thf(490,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( linord219039673up_add @ SX2 )
| ( ( plus_plus @ SX2 @ SX0 @ ( ti @ SX2 @ SX1 ) )
= ( plus_plus @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[308]) ).
thf(491,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( power @ SX0 )
| ~ ( semiring_0 @ SX0 ) )
| ( ( ti @ SX0 @ ( zero_zero @ SX0 ) )
= ( zero_zero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[314]) ).
thf(492,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( power @ SX2 )
| ~ ( semiring_0 @ SX2 ) )
| ( ( power_power @ SX2 @ ( ti @ SX2 @ SX0 ) @ SX1 )
= ( power_power @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[321]) ).
thf(493,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( number_ring @ SX0 )
| ~ ( linordered_idom @ SX0 ) )
| ! [SX1: $i] :
~ ( ~ ( ~ ( ord_less @ SX0 @ ( one_one @ SX0 ) @ ( number_number_of @ SX0 @ SX1 ) )
| ( ord_less @ int @ ( bit1 @ pls ) @ SX1 ) )
| ~ ( ~ ( ord_less @ int @ ( bit1 @ pls ) @ SX1 )
| ( ord_less @ SX0 @ ( one_one @ SX0 ) @ ( number_number_of @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[388]) ).
thf(494,plain,
( ( ! [SX0: $i] :
( ~ ( number_ring @ SX0 )
| ! [SX1: $i] :
( ( plus_plus @ SX0 @ ( one_one @ SX0 ) @ ( number_number_of @ SX0 @ SX1 ) )
= ( number_number_of @ SX0 @ ( plus_plus @ int @ ( bit1 @ pls ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[331]) ).
thf(495,plain,
( ( ! [SX0: $i] :
( ~ ( linord219039673up_add @ SX0 )
| ! [SX1: $i] :
~ ( ~ ( ( ( plus_plus @ SX0 @ SX1 @ SX1 )
!= ( zero_zero @ SX0 ) )
| ( ( ti @ SX0 @ SX1 )
= ( zero_zero @ SX0 ) ) )
| ~ ( ( ( ti @ SX0 @ SX1 )
!= ( zero_zero @ SX0 ) )
| ( ( plus_plus @ SX0 @ SX1 @ SX1 )
= ( zero_zero @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[390]) ).
thf(496,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( number_ring @ SX0 )
| ~ ( linordered_idom @ SX0 ) )
| ! [SX1: $i] :
~ ( ~ ( ~ ( ord_less @ SX0 @ ( zero_zero @ SX0 ) @ ( number_number_of @ SX0 @ SX1 ) )
| ( ord_less @ int @ pls @ SX1 ) )
| ~ ( ~ ( ord_less @ int @ pls @ SX1 )
| ( ord_less @ SX0 @ ( zero_zero @ SX0 ) @ ( number_number_of @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[375]) ).
thf(497,plain,
( ( ! [SX0: $i] :
( ~ ( linordered_idom @ SX0 )
| ! [SX1: $i] :
~ ( ord_less @ SX0 @ ( power_power @ SX0 @ SX1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( zero_zero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[420]) ).
thf(498,plain,
( ( ! [SX0: $i] :
( ~ ( linordered_idom @ SX0 )
| ! [SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( ord_less @ SX0 @ ( zero_zero @ SX0 ) @ ( plus_plus @ SX0 @ ( power_power @ SX0 @ SX1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SX0 @ SX2 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
| ( ( ti @ SX0 @ SX1 )
!= ( zero_zero @ SX0 ) )
| ( ( ti @ SX0 @ SX2 )
!= ( zero_zero @ SX0 ) ) )
| ~ ( ~ ( ( ( ti @ SX0 @ SX1 )
!= ( zero_zero @ SX0 ) )
| ( ( ti @ SX0 @ SX2 )
!= ( zero_zero @ SX0 ) ) )
| ( ord_less @ SX0 @ ( zero_zero @ SX0 ) @ ( plus_plus @ SX0 @ ( power_power @ SX0 @ SX1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SX0 @ SX2 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[421]) ).
thf(499,plain,
( ( ! [SX0: $i] :
( ~ ( number_ring @ SX0 )
| ( ( number_number_of @ SX0 @ pls )
= ( zero_zero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[407]) ).
thf(500,plain,
( ( ( zero_zero @ int )
!= ( one_one @ int ) )
= $true ),
inference(unfold_def,[status(thm)],[399]) ).
thf(501,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less @ int @ SX0 @ SX1 ) )
| ~ ( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[356]) ).
thf(502,plain,
( ( ! [SX0: $i] :
( ~ ( number @ SX0 )
| ! [SX1: $i,SX2: $i] :
~ ( ~ ( ( ( number_number_of @ SX0 @ SX1 )
!= ( ti @ SX0 @ SX2 ) )
| ( ( ti @ SX0 @ SX2 )
= ( number_number_of @ SX0 @ SX1 ) ) )
| ~ ( ( ( ti @ SX0 @ SX2 )
!= ( number_number_of @ SX0 @ SX1 ) )
| ( ( number_number_of @ SX0 @ SX1 )
= ( ti @ SX0 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[366]) ).
thf(503,plain,
( ( ! [SX0: $i] :
( ~ ( number_ring @ SX0 )
| ( ( plus_plus @ SX0 @ ( one_one @ SX0 ) @ ( one_one @ SX0 ) )
= ( number_number_of @ SX0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[333]) ).
thf(504,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( number_semiring @ SX2 )
| ( ( plus_plus @ SX2 @ ( ti @ SX2 @ SX0 ) @ SX1 )
= ( plus_plus @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[310]) ).
thf(505,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( number @ SX1 )
| ( ( number_number_of @ SX1 @ ( ti @ int @ SX0 ) )
= ( number_number_of @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[315]) ).
thf(506,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( number_ring @ SX0 )
| ~ ( linordered_idom @ SX0 ) )
| ! [SX1: $i] :
~ ( ~ ( ~ ( ord_less @ SX0 @ ( number_number_of @ SX0 @ SX1 ) @ ( one_one @ SX0 ) )
| ( ord_less @ int @ SX1 @ ( bit1 @ pls ) ) )
| ~ ( ~ ( ord_less @ int @ SX1 @ ( bit1 @ pls ) )
| ( ord_less @ SX0 @ ( number_number_of @ SX0 @ SX1 ) @ ( one_one @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[387]) ).
thf(507,plain,
( ( ! [SX0: $i] :
( ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ SX0 ) @ SX0 )
!= ( zero_zero @ int ) ) )
= $true ),
inference(unfold_def,[status(thm)],[417]) ).
thf(508,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( number_ring @ SX0 )
| ~ ( ring_char_0 @ SX0 ) )
| ! [SX1: $i,SX2: $i] :
~ ( ~ ( ( ( number_number_of @ SX0 @ SX1 )
!= ( number_number_of @ SX0 @ SX2 ) )
| ( SX1 = SX2 ) )
| ~ ( ( SX1 != SX2 )
| ( ( number_number_of @ SX0 @ SX1 )
= ( number_number_of @ SX0 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[365]) ).
thf(509,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less @ int @ SX0 @ SX1 ) )
| ~ ( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[355]) ).
thf(510,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( number_semiring @ SX1 )
| ( ( semiring_1_of_nat @ SX1 @ ( ti @ nat @ SX0 ) )
= ( semiring_1_of_nat @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[317]) ).
thf(511,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less @ int @ SX0 @ SX1 ) )
| ~ ( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[359]) ).
thf(512,plain,
( ( ! [SX0: $i] :
( ~ ( ring_11004092258visors @ SX0 )
| ! [SX1: $i] :
~ ( ~ ( ( ( power_power @ SX0 @ SX1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= ( zero_zero @ SX0 ) )
| ( ( ti @ SX0 @ SX1 )
= ( zero_zero @ SX0 ) ) )
| ~ ( ( ( ti @ SX0 @ SX1 )
!= ( zero_zero @ SX0 ) )
| ( ( power_power @ SX0 @ SX1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[330]) ).
thf(513,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ( ( bit0 @ SX0 )
!= pls )
| ( SX0 = pls ) )
| ~ ( ( SX0 != pls )
| ( ( bit0 @ SX0 )
= pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[395]) ).
thf(514,plain,
( ( ! [SX0: $i] :
( ~ ( number_semiring @ SX0 )
| ( ( plus_plus @ SX0 @ ( one_one @ SX0 ) @ ( one_one @ SX0 ) )
= ( number_number_of @ SX0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[334]) ).
thf(515,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( ord_less @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ SX0 ) @ SX0 ) @ ( zero_zero @ int ) )
| ( ord_less @ int @ SX0 @ ( zero_zero @ int ) ) )
| ~ ( ~ ( ord_less @ int @ SX0 @ ( zero_zero @ int ) )
| ( ord_less @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ SX0 ) @ SX0 ) @ ( zero_zero @ int ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[389]) ).
thf(516,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SX0 ) @ ( zero_zero @ int ) )
| ( ord_less @ int @ SX0 @ ( zero_zero @ int ) ) )
| ~ ( ~ ( ord_less @ int @ SX0 @ ( zero_zero @ int ) )
| ( ord_less @ int @ ( bit1 @ SX0 ) @ ( zero_zero @ int ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[381]) ).
thf(517,plain,
( ( ! [SX0: $i] :
( ~ ( semiring_1 @ SX0 )
| ( ( power_power @ SX0 @ ( one_one @ SX0 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( one_one @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[328]) ).
thf(518,plain,
( ( ! [SX0: $i] :
( ~ ( linord219039673up_add @ SX0 )
| ( ( ti @ SX0 @ ( zero_zero @ SX0 ) )
= ( zero_zero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[313]) ).
thf(519,plain,
( ( ! [SX0: $i] :
( ( bit1 @ SX0 )
!= pls ) )
= $true ),
inference(unfold_def,[status(thm)],[391]) ).
thf(520,plain,
( ( ! [SX0: $i] :
( pls
!= ( bit1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[392]) ).
thf(521,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less @ int @ SX0 @ SX1 ) )
| ~ ( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[377]) ).
thf(522,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ord_less @ int @ SX0 @ ( plus_plus @ int @ SX1 @ ( one_one @ int ) ) )
| ( ord_less @ int @ SX0 @ SX1 )
| ( SX0 = SX1 ) )
| ~ ( ~ ( ( ord_less @ int @ SX0 @ SX1 )
| ( SX0 = SX1 ) )
| ( ord_less @ int @ SX0 @ ( plus_plus @ int @ SX1 @ ( one_one @ int ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[385]) ).
thf(523,plain,
! [SV1: $i] :
( ( ( bit0 @ ( ti @ int @ SV1 ) )
= ( bit0 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[300]) ).
thf(524,plain,
! [SV2: $i] :
( ( ( ti @ int @ ( bit0 @ SV2 ) )
= ( bit0 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[301]) ).
thf(525,plain,
! [SV3: $i] :
( ( ( bit1 @ ( ti @ int @ SV3 ) )
= ( bit1 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[302]) ).
thf(526,plain,
! [SV4: $i] :
( ( ( ti @ int @ ( bit1 @ SV4 ) )
= ( bit1 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[303]) ).
thf(527,plain,
! [SV5: $i] :
( ( ( power_power @ int @ ( power_power @ int @ SV5 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power @ int @ SV5 @ ( number_number_of @ nat @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[335]) ).
thf(528,plain,
! [SV6: $i] :
( ( ! [SY188: $i] :
( ( ord_less @ int @ SV6 @ SY188 )
| ( SV6 = SY188 )
| ( ord_less @ int @ SY188 @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[340]) ).
thf(529,plain,
! [SV7: $i] :
( ( ! [SY189: $i] :
( ( plus_plus @ int @ ( number_number_of @ int @ SV7 ) @ ( number_number_of @ int @ SY189 ) )
= ( number_number_of @ int @ ( plus_plus @ int @ SV7 @ SY189 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[342]) ).
thf(530,plain,
! [SV8: $i] :
( ( ! [SY190: $i] :
( ( power_power @ int @ ( semiring_1_of_nat @ int @ SV8 ) @ SY190 )
= ( semiring_1_of_nat @ int @ ( power_power @ nat @ SV8 @ SY190 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[345]) ).
thf(531,plain,
! [SV9: $i] :
( ( ! [SY191: $i] :
( ( semiring_1_of_nat @ int @ ( power_power @ nat @ SV9 @ SY191 ) )
= ( power_power @ int @ ( semiring_1_of_nat @ int @ SV9 ) @ SY191 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[346]) ).
thf(532,plain,
! [SV10: $i] :
( ( ! [SY192: $i,SY193: $i] :
( ( plus_plus @ int @ ( semiring_1_of_nat @ int @ SV10 ) @ ( plus_plus @ int @ ( semiring_1_of_nat @ int @ SY192 ) @ SY193 ) )
= ( plus_plus @ int @ ( semiring_1_of_nat @ int @ ( plus_plus @ nat @ SV10 @ SY192 ) ) @ SY193 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[347]) ).
thf(533,plain,
! [SV11: $i] :
( ( ! [SY194: $i] :
( ( plus_plus @ int @ ( semiring_1_of_nat @ int @ SV11 ) @ ( semiring_1_of_nat @ int @ SY194 ) )
= ( semiring_1_of_nat @ int @ ( plus_plus @ nat @ SV11 @ SY194 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[348]) ).
thf(534,plain,
( ( ord_less @ int @ pls @ pls )
= $false ),
inference(extcnf_not_pos,[status(thm)],[357]) ).
thf(535,plain,
! [SV12: $i] :
( ( ! [SY195: $i,SY196: $i] :
( ( plus_plus @ int @ ( plus_plus @ int @ SV12 @ SY195 ) @ SY196 )
= ( plus_plus @ int @ SV12 @ ( plus_plus @ int @ SY195 @ SY196 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[370]) ).
thf(536,plain,
! [SV13: $i] :
( ( ! [SY197: $i,SY198: $i] :
( ( plus_plus @ int @ SV13 @ ( plus_plus @ int @ SY197 @ SY198 ) )
= ( plus_plus @ int @ SY197 @ ( plus_plus @ int @ SV13 @ SY198 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[371]) ).
thf(537,plain,
! [SV14: $i] :
( ( ! [SY199: $i] :
( ( plus_plus @ int @ SV14 @ SY199 )
= ( plus_plus @ int @ SY199 @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[372]) ).
thf(538,plain,
( ( ord_less @ int @ pls @ ( zero_zero @ int ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[382]) ).
thf(539,plain,
! [SV15: $i] :
( ( ~ ( ord_less @ int @ ( semiring_1_of_nat @ int @ SV15 ) @ ( zero_zero @ int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[386]) ).
thf(540,plain,
! [SV16: $i] :
( ( ( plus_plus @ int @ SV16 @ pls )
= SV16 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[400]) ).
thf(541,plain,
! [SV17: $i] :
( ( ( plus_plus @ int @ pls @ SV17 )
= SV17 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[401]) ).
thf(542,plain,
! [SV18: $i] :
( ( ! [SY200: $i] :
( ( plus_plus @ int @ ( bit0 @ SV18 ) @ ( bit0 @ SY200 ) )
= ( bit0 @ ( plus_plus @ int @ SV18 @ SY200 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[402]) ).
thf(543,plain,
! [SV19: $i] :
( ( ( bit0 @ SV19 )
= ( plus_plus @ int @ SV19 @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[403]) ).
thf(544,plain,
! [SV20: $i] :
( ( ( plus_plus @ int @ SV20 @ ( zero_zero @ int ) )
= SV20 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[404]) ).
thf(545,plain,
! [SV21: $i] :
( ( ( plus_plus @ int @ ( zero_zero @ int ) @ SV21 )
= SV21 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[405]) ).
thf(546,plain,
! [SV22: $i] :
( ( ! [SY201: $i] :
( ( plus_plus @ int @ ( bit1 @ SV22 ) @ ( bit0 @ SY201 ) )
= ( bit1 @ ( plus_plus @ int @ SV22 @ SY201 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[414]) ).
thf(547,plain,
! [SV23: $i] :
( ( ! [SY202: $i] :
( ( plus_plus @ int @ ( bit0 @ SV23 ) @ ( bit1 @ SY202 ) )
= ( bit1 @ ( plus_plus @ int @ SV23 @ SY202 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[415]) ).
thf(548,plain,
! [SV24: $i] :
( ( ( bit1 @ SV24 )
= ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ SV24 ) @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[416]) ).
thf(549,plain,
! [SV25: $i] :
( ( ~ ~ ( ~ ( power @ SV25 )
| ~ ( semiring_0 @ SV25 ) )
| ! [SY203: $i] :
~ ( ~ ( ( ( number_number_of @ nat @ SY203 )
!= ( zero_zero @ nat ) )
| ( ( power_power @ SV25 @ ( zero_zero @ SV25 ) @ ( number_number_of @ nat @ SY203 ) )
= ( one_one @ SV25 ) ) )
| ~ ( ~ ( ( ( number_number_of @ nat @ SY203 )
!= ( zero_zero @ nat ) ) )
| ( ( power_power @ SV25 @ ( zero_zero @ SV25 ) @ ( number_number_of @ nat @ SY203 ) )
= ( zero_zero @ SV25 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[444]) ).
thf(550,plain,
! [SV26: $i] :
( ( ~ ( linordered_idom @ SV26 )
| ! [SY204: $i,SY205: $i] :
~ ( ~ ( ( ( plus_plus @ SV26 @ ( power_power @ SV26 @ SY204 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV26 @ SY205 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV26 ) )
| ~ ( ( ( ti @ SV26 @ SY204 )
!= ( zero_zero @ SV26 ) )
| ( ( ti @ SV26 @ SY205 )
!= ( zero_zero @ SV26 ) ) ) )
| ~ ( ~ ~ ( ( ( ti @ SV26 @ SY204 )
!= ( zero_zero @ SV26 ) )
| ( ( ti @ SV26 @ SY205 )
!= ( zero_zero @ SV26 ) ) )
| ( ( plus_plus @ SV26 @ ( power_power @ SV26 @ SY204 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV26 @ SY205 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV26 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[445]) ).
thf(551,plain,
! [SV27: $i] :
( ( ~ ( number_ring @ SV27 )
| ( ( zero_zero @ SV27 )
= ( number_number_of @ SV27 @ pls ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[446]) ).
thf(552,plain,
! [SV28: $i] :
( ( ! [SY206: $i,SY207: $i] :
( ~ ( number_semiring @ SY207 )
| ( ( plus_plus @ SY207 @ SV28 @ ( ti @ SY207 @ SY206 ) )
= ( plus_plus @ SY207 @ SV28 @ SY206 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[447]) ).
thf(553,plain,
! [SV29: $i] :
( ( ~ ( number_semiring @ SV29 )
| ( ( number_number_of @ SV29 @ pls )
= ( zero_zero @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[448]) ).
thf(554,plain,
! [SV30: $i] :
( ( ~ ( number_ring @ SV30 )
| ! [SY208: $i] :
( ( plus_plus @ SV30 @ SY208 @ ( number_number_of @ SV30 @ pls ) )
= ( ti @ SV30 @ SY208 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[449]) ).
thf(555,plain,
! [SV31: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SV31 ) @ ( zero_zero @ int ) )
| ( ord_less @ int @ SV31 @ ( zero_zero @ int ) ) )
| ~ ( ~ ( ord_less @ int @ SV31 @ ( zero_zero @ int ) )
| ( ord_less @ int @ ( bit0 @ SV31 ) @ ( zero_zero @ int ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[450]) ).
thf(556,plain,
! [SV32: $i] :
( ( ! [SY209: $i,SY210: $i] :
( ~ ~ ( ~ ( power @ SY210 )
| ~ ( semiring_0 @ SY210 ) )
| ( ( power_power @ SY210 @ SV32 @ ( ti @ nat @ SY209 ) )
= ( power_power @ SY210 @ SV32 @ SY209 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[451]) ).
thf(557,plain,
! [SV33: $i] :
( ( ! [SY211: $i] :
( ~ ( number @ SY211 )
| ( ( ti @ SY211 @ ( number_number_of @ SY211 @ SV33 ) )
= ( number_number_of @ SY211 @ SV33 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[452]) ).
thf(558,plain,
! [SV34: $i] :
( ( ! [SY212: $i,SY213: $i] :
( ~ ( number_semiring @ SY213 )
| ( ( ti @ SY213 @ ( plus_plus @ SY213 @ SV34 @ SY212 ) )
= ( plus_plus @ SY213 @ SV34 @ SY212 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[453]) ).
thf(559,plain,
! [SV35: $i] :
( ( ! [SY214: $i,SY215: $i] :
( ~ ( ord_less @ int @ SY214 @ SY215 )
| ( ord_less @ int @ ( plus_plus @ int @ SY214 @ SV35 ) @ ( plus_plus @ int @ SY215 @ SV35 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[454]) ).
thf(560,plain,
! [SV36: $i] :
( ( ! [SY216: $i] :
( ( bit1 @ SV36 )
!= ( bit0 @ SY216 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[455]) ).
thf(561,plain,
! [SV37: $i] :
( ( ~ ( number_ring @ SV37 )
| ( ( one_one @ SV37 )
= ( number_number_of @ SV37 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[456]) ).
thf(562,plain,
! [SV38: $i] :
( ( ~ ( number_ring @ SV38 )
| ! [SY217: $i,SY218: $i,SY219: $i] :
( ( plus_plus @ SV38 @ ( number_number_of @ SV38 @ SY217 ) @ ( plus_plus @ SV38 @ ( number_number_of @ SV38 @ SY218 ) @ SY219 ) )
= ( plus_plus @ SV38 @ ( number_number_of @ SV38 @ ( plus_plus @ int @ SY217 @ SY218 ) ) @ SY219 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[457]) ).
thf(563,plain,
! [SV39: $i] :
( ( ~ ( ~ ( ( pls
!= ( bit0 @ SV39 ) )
| ( pls = SV39 ) )
| ~ ( ( pls != SV39 )
| ( pls
= ( bit0 @ SV39 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[458]) ).
thf(564,plain,
! [SV40: $i] :
( ( ! [SY220: $i] :
~ ( ~ ( ~ ( ord_less @ int @ ( number_number_of @ int @ SV40 ) @ ( number_number_of @ int @ SY220 ) )
| ( ord_less @ int @ SV40 @ SY220 ) )
| ~ ( ~ ( ord_less @ int @ SV40 @ SY220 )
| ( ord_less @ int @ ( number_number_of @ int @ SV40 ) @ ( number_number_of @ int @ SY220 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[459]) ).
thf(565,plain,
( ( ( power_power @ int @ ( plus_plus @ int @ ( one_one @ int ) @ ( semiring_1_of_nat @ int @ n ) ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= ( zero_zero @ int ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[460]) ).
thf(566,plain,
! [SV41: $i] :
( ( ~ ( linordered_idom @ SV41 )
| ! [SY221: $i] :
~ ( ~ ( ~ ( ord_less @ SV41 @ ( plus_plus @ SV41 @ SY221 @ SY221 ) @ ( zero_zero @ SV41 ) )
| ( ord_less @ SV41 @ SY221 @ ( zero_zero @ SV41 ) ) )
| ~ ( ~ ( ord_less @ SV41 @ SY221 @ ( zero_zero @ SV41 ) )
| ( ord_less @ SV41 @ ( plus_plus @ SV41 @ SY221 @ SY221 ) @ ( zero_zero @ SV41 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[461]) ).
thf(567,plain,
! [SV42: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SV42 ) @ pls )
| ( ord_less @ int @ SV42 @ pls ) )
| ~ ( ~ ( ord_less @ int @ SV42 @ pls )
| ( ord_less @ int @ ( bit1 @ SV42 ) @ pls ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[462]) ).
thf(568,plain,
! [SV43: $i] :
( ( ! [SY222: $i] :
~ ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SV43 ) @ ( bit0 @ SY222 ) )
| ( ord_less @ int @ SV43 @ SY222 ) )
| ~ ( ~ ( ord_less @ int @ SV43 @ SY222 )
| ( ord_less @ int @ ( bit0 @ SV43 ) @ ( bit0 @ SY222 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[463]) ).
thf(569,plain,
! [SV44: $i] :
( ( ~ ( number_ring @ SV44 )
| ! [SY223: $i] :
( ( plus_plus @ SV44 @ ( number_number_of @ SV44 @ pls ) @ SY223 )
= ( ti @ SV44 @ SY223 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[464]) ).
thf(570,plain,
! [SV45: $i] :
( ( ~ ( ~ ( ( ( semiring_1_of_nat @ int @ SV45 )
!= ( zero_zero @ int ) )
| ( SV45
= ( zero_zero @ nat ) ) )
| ~ ( ( SV45
!= ( zero_zero @ nat ) )
| ( ( semiring_1_of_nat @ int @ SV45 )
= ( zero_zero @ int ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[465]) ).
thf(571,plain,
! [SV46: $i] :
( ( ~ ( semiring_1 @ SV46 )
| ( ( power_power @ SV46 @ ( zero_zero @ SV46 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SV46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[466]) ).
thf(572,plain,
! [SV47: $i] :
( ( ! [SY224: $i] :
~ ( ~ ( ( ( bit1 @ SV47 )
!= ( bit1 @ SY224 ) )
| ( SV47 = SY224 ) )
| ~ ( ( SV47 != SY224 )
| ( ( bit1 @ SV47 )
= ( bit1 @ SY224 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[467]) ).
thf(573,plain,
! [SV48: $i] :
( ( ! [SY225: $i] :
~ ( ~ ( ~ ( ord_less @ int @ SY225 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SY225 ) @ ( number_number_of @ nat @ SV48 ) )
= ( number_number_of @ nat @ SV48 ) ) )
| ~ ( ~ ~ ( ord_less @ int @ SY225 @ pls )
| ~ ( ~ ( ~ ( ord_less @ int @ SV48 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SY225 ) @ ( number_number_of @ nat @ SV48 ) )
= ( number_number_of @ nat @ SY225 ) ) )
| ~ ( ~ ~ ( ord_less @ int @ SV48 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SY225 ) @ ( number_number_of @ nat @ SV48 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SY225 @ SV48 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[468]) ).
thf(574,plain,
! [SV49: $i] :
( ( ! [SY226: $i,SY227: $i] :
( ~ ( linord219039673up_add @ SY227 )
| ( ( ti @ SY227 @ ( plus_plus @ SY227 @ SV49 @ SY226 ) )
= ( plus_plus @ SY227 @ SV49 @ SY226 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[469]) ).
thf(575,plain,
! [SV50: $i] :
( ( ~ ( number_ring @ SV50 )
| ( ( number_number_of @ SV50 @ ( bit1 @ pls ) )
= ( one_one @ SV50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[470]) ).
thf(576,plain,
! [SV51: $i] :
( ( ! [SY228: $i] :
( ( bit0 @ SV51 )
!= ( bit1 @ SY228 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[471]) ).
thf(577,plain,
! [SV52: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SV52 ) @ pls )
| ( ord_less @ int @ SV52 @ pls ) )
| ~ ( ~ ( ord_less @ int @ SV52 @ pls )
| ( ord_less @ int @ ( bit0 @ SV52 ) @ pls ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[472]) ).
thf(578,plain,
! [SV53: $i] :
( ( ~ ( number_ring @ SV53 )
| ! [SY229: $i,SY230: $i] :
( ( number_number_of @ SV53 @ ( plus_plus @ int @ SY229 @ SY230 ) )
= ( plus_plus @ SV53 @ ( number_number_of @ SV53 @ SY229 ) @ ( number_number_of @ SV53 @ SY230 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[473]) ).
thf(579,plain,
! [SV54: $i] :
( ( ~ ( number_semiring @ SV54 )
| ! [SY231: $i] :
( ( number_number_of @ SV54 @ ( semiring_1_of_nat @ int @ SY231 ) )
= ( semiring_1_of_nat @ SV54 @ SY231 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[474]) ).
thf(580,plain,
! [SV55: $i] :
( ( ! [SY232: $i] :
~ ( ~ ( ~ ( ord_less @ nat @ ( ti @ nat @ SV55 ) @ SY232 )
| ( ord_less @ nat @ SV55 @ SY232 ) )
| ~ ( ~ ( ord_less @ nat @ SV55 @ SY232 )
| ( ord_less @ nat @ ( ti @ nat @ SV55 ) @ SY232 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[475]) ).
thf(581,plain,
! [SV56: $i] :
( ( ! [SY233: $i] :
~ ( ~ ( ~ ( ord_less @ nat @ SV56 @ ( ti @ nat @ SY233 ) )
| ( ord_less @ nat @ SV56 @ SY233 ) )
| ~ ( ~ ( ord_less @ nat @ SV56 @ SY233 )
| ( ord_less @ nat @ SV56 @ ( ti @ nat @ SY233 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[476]) ).
thf(582,plain,
! [SV57: $i] :
( ( ! [SY234: $i,SY235: $i] :
( ~ ( linord219039673up_add @ SY235 )
| ( ( plus_plus @ SY235 @ ( ti @ SY235 @ SV57 ) @ SY234 )
= ( plus_plus @ SY235 @ SV57 @ SY234 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[477]) ).
thf(583,plain,
! [SV58: $i] :
( ( ~ ( number_ring @ SV58 )
| ! [SY236: $i,SY237: $i] :
( ( plus_plus @ SV58 @ ( number_number_of @ SV58 @ SY236 ) @ ( number_number_of @ SV58 @ SY237 ) )
= ( number_number_of @ SV58 @ ( plus_plus @ int @ SY236 @ SY237 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[478]) ).
thf(584,plain,
! [SV59: $i] :
( ( ~ ~ ( ~ ( power @ SV59 )
| ~ ( semiring_0 @ SV59 ) )
| ( ( ti @ SV59 @ ( one_one @ SV59 ) )
= ( one_one @ SV59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[479]) ).
thf(585,plain,
! [SV60: $i] :
( ( ! [SY238: $i,SY239: $i] :
( ~ ~ ( ~ ( power @ SY239 )
| ~ ( semiring_0 @ SY239 ) )
| ( ( ti @ SY239 @ ( power_power @ SY239 @ SV60 @ SY238 ) )
= ( power_power @ SY239 @ SV60 @ SY238 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[480]) ).
thf(586,plain,
! [SV61: $i] :
( ( ~ ( linordered_idom @ SV61 )
| ! [SY240: $i] :
~ ( ~ ( ~ ( ord_less @ SV61 @ ( zero_zero @ SV61 ) @ ( power_power @ SV61 @ SY240 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ( ( ti @ SV61 @ SY240 )
!= ( zero_zero @ SV61 ) ) )
| ~ ( ~ ( ( ( ti @ SV61 @ SY240 )
!= ( zero_zero @ SV61 ) ) )
| ( ord_less @ SV61 @ ( zero_zero @ SV61 ) @ ( power_power @ SV61 @ SY240 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[481]) ).
thf(587,plain,
! [SV62: $i] :
( ( ~ ~ ( ~ ( number_ring @ SV62 )
| ~ ( linordered_idom @ SV62 ) )
| ! [SY241: $i,SY242: $i] :
~ ( ~ ( ~ ( ord_less @ SV62 @ ( number_number_of @ SV62 @ SY241 ) @ ( number_number_of @ SV62 @ SY242 ) )
| ( ord_less @ int @ SY241 @ SY242 ) )
| ~ ( ~ ( ord_less @ int @ SY241 @ SY242 )
| ( ord_less @ SV62 @ ( number_number_of @ SV62 @ SY241 ) @ ( number_number_of @ SV62 @ SY242 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[482]) ).
thf(588,plain,
! [SV63: $i] :
( ( ~ ( number_ring @ SV63 )
| ! [SY243: $i] :
( ( plus_plus @ SV63 @ ( number_number_of @ SV63 @ SY243 ) @ ( one_one @ SV63 ) )
= ( number_number_of @ SV63 @ ( plus_plus @ int @ SY243 @ ( bit1 @ pls ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[483]) ).
thf(589,plain,
! [SV64: $i] :
( ( ! [SY244: $i] :
~ ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SV64 ) @ ( bit0 @ SY244 ) )
| ( ord_less @ int @ SV64 @ SY244 ) )
| ~ ( ~ ( ord_less @ int @ SV64 @ SY244 )
| ( ord_less @ int @ ( bit1 @ SV64 ) @ ( bit0 @ SY244 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[484]) ).
thf(590,plain,
! [SV65: $i] :
( ( ! [SY245: $i] :
( ~ ( number_semiring @ SY245 )
| ( ( ti @ SY245 @ ( semiring_1_of_nat @ SY245 @ SV65 ) )
= ( semiring_1_of_nat @ SY245 @ SV65 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[485]) ).
thf(591,plain,
! [SV66: $i] :
( ( ! [SY246: $i] :
~ ( ~ ( ( ( bit0 @ SV66 )
!= ( bit0 @ SY246 ) )
| ( SV66 = SY246 ) )
| ~ ( ( SV66 != SY246 )
| ( ( bit0 @ SV66 )
= ( bit0 @ SY246 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[486]) ).
thf(592,plain,
! [SV67: $i] :
( ( ! [SY247: $i] :
~ ( ~ ( ( ( semiring_1_of_nat @ int @ SV67 )
!= ( semiring_1_of_nat @ int @ SY247 ) )
| ( SV67 = SY247 ) )
| ~ ( ( SV67 != SY247 )
| ( ( semiring_1_of_nat @ int @ SV67 )
= ( semiring_1_of_nat @ int @ SY247 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[487]) ).
thf(593,plain,
! [SV68: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ int @ pls @ ( bit0 @ SV68 ) )
| ( ord_less @ int @ pls @ SV68 ) )
| ~ ( ~ ( ord_less @ int @ pls @ SV68 )
| ( ord_less @ int @ pls @ ( bit0 @ SV68 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[488]) ).
thf(594,plain,
! [SV69: $i] :
( ( ~ ~ ( ~ ( number_ring @ SV69 )
| ~ ( linordered_idom @ SV69 ) )
| ! [SY248: $i] :
~ ( ~ ( ~ ( ord_less @ SV69 @ ( number_number_of @ SV69 @ SY248 ) @ ( zero_zero @ SV69 ) )
| ( ord_less @ int @ SY248 @ pls ) )
| ~ ( ~ ( ord_less @ int @ SY248 @ pls )
| ( ord_less @ SV69 @ ( number_number_of @ SV69 @ SY248 ) @ ( zero_zero @ SV69 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[489]) ).
thf(595,plain,
! [SV70: $i] :
( ( ! [SY249: $i,SY250: $i] :
( ~ ( linord219039673up_add @ SY250 )
| ( ( plus_plus @ SY250 @ SV70 @ ( ti @ SY250 @ SY249 ) )
= ( plus_plus @ SY250 @ SV70 @ SY249 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[490]) ).
thf(596,plain,
! [SV71: $i] :
( ( ~ ~ ( ~ ( power @ SV71 )
| ~ ( semiring_0 @ SV71 ) )
| ( ( ti @ SV71 @ ( zero_zero @ SV71 ) )
= ( zero_zero @ SV71 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[491]) ).
thf(597,plain,
! [SV72: $i] :
( ( ! [SY251: $i,SY252: $i] :
( ~ ~ ( ~ ( power @ SY252 )
| ~ ( semiring_0 @ SY252 ) )
| ( ( power_power @ SY252 @ ( ti @ SY252 @ SV72 ) @ SY251 )
= ( power_power @ SY252 @ SV72 @ SY251 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[492]) ).
thf(598,plain,
! [SV73: $i] :
( ( ~ ~ ( ~ ( number_ring @ SV73 )
| ~ ( linordered_idom @ SV73 ) )
| ! [SY253: $i] :
~ ( ~ ( ~ ( ord_less @ SV73 @ ( one_one @ SV73 ) @ ( number_number_of @ SV73 @ SY253 ) )
| ( ord_less @ int @ ( bit1 @ pls ) @ SY253 ) )
| ~ ( ~ ( ord_less @ int @ ( bit1 @ pls ) @ SY253 )
| ( ord_less @ SV73 @ ( one_one @ SV73 ) @ ( number_number_of @ SV73 @ SY253 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[493]) ).
thf(599,plain,
! [SV74: $i] :
( ( ~ ( number_ring @ SV74 )
| ! [SY254: $i] :
( ( plus_plus @ SV74 @ ( one_one @ SV74 ) @ ( number_number_of @ SV74 @ SY254 ) )
= ( number_number_of @ SV74 @ ( plus_plus @ int @ ( bit1 @ pls ) @ SY254 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[494]) ).
thf(600,plain,
! [SV75: $i] :
( ( ~ ( linord219039673up_add @ SV75 )
| ! [SY255: $i] :
~ ( ~ ( ( ( plus_plus @ SV75 @ SY255 @ SY255 )
!= ( zero_zero @ SV75 ) )
| ( ( ti @ SV75 @ SY255 )
= ( zero_zero @ SV75 ) ) )
| ~ ( ( ( ti @ SV75 @ SY255 )
!= ( zero_zero @ SV75 ) )
| ( ( plus_plus @ SV75 @ SY255 @ SY255 )
= ( zero_zero @ SV75 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[495]) ).
thf(601,plain,
! [SV76: $i] :
( ( ~ ~ ( ~ ( number_ring @ SV76 )
| ~ ( linordered_idom @ SV76 ) )
| ! [SY256: $i] :
~ ( ~ ( ~ ( ord_less @ SV76 @ ( zero_zero @ SV76 ) @ ( number_number_of @ SV76 @ SY256 ) )
| ( ord_less @ int @ pls @ SY256 ) )
| ~ ( ~ ( ord_less @ int @ pls @ SY256 )
| ( ord_less @ SV76 @ ( zero_zero @ SV76 ) @ ( number_number_of @ SV76 @ SY256 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[496]) ).
thf(602,plain,
! [SV77: $i] :
( ( ~ ( linordered_idom @ SV77 )
| ! [SY257: $i] :
~ ( ord_less @ SV77 @ ( power_power @ SV77 @ SY257 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( zero_zero @ SV77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[497]) ).
thf(603,plain,
! [SV78: $i] :
( ( ~ ( linordered_idom @ SV78 )
| ! [SY258: $i,SY259: $i] :
~ ( ~ ( ~ ( ord_less @ SV78 @ ( zero_zero @ SV78 ) @ ( plus_plus @ SV78 @ ( power_power @ SV78 @ SY258 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV78 @ SY259 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
| ( ( ti @ SV78 @ SY258 )
!= ( zero_zero @ SV78 ) )
| ( ( ti @ SV78 @ SY259 )
!= ( zero_zero @ SV78 ) ) )
| ~ ( ~ ( ( ( ti @ SV78 @ SY258 )
!= ( zero_zero @ SV78 ) )
| ( ( ti @ SV78 @ SY259 )
!= ( zero_zero @ SV78 ) ) )
| ( ord_less @ SV78 @ ( zero_zero @ SV78 ) @ ( plus_plus @ SV78 @ ( power_power @ SV78 @ SY258 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV78 @ SY259 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[498]) ).
thf(604,plain,
! [SV79: $i] :
( ( ~ ( number_ring @ SV79 )
| ( ( number_number_of @ SV79 @ pls )
= ( zero_zero @ SV79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[499]) ).
thf(605,plain,
( ( ( zero_zero @ int )
= ( one_one @ int ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[500]) ).
thf(606,plain,
! [SV80: $i] :
( ( ! [SY260: $i] :
~ ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SV80 ) @ ( bit1 @ SY260 ) )
| ( ord_less @ int @ SV80 @ SY260 ) )
| ~ ( ~ ( ord_less @ int @ SV80 @ SY260 )
| ( ord_less @ int @ ( bit1 @ SV80 ) @ ( bit1 @ SY260 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[501]) ).
thf(607,plain,
! [SV81: $i] :
( ( ~ ( number @ SV81 )
| ! [SY261: $i,SY262: $i] :
~ ( ~ ( ( ( number_number_of @ SV81 @ SY261 )
!= ( ti @ SV81 @ SY262 ) )
| ( ( ti @ SV81 @ SY262 )
= ( number_number_of @ SV81 @ SY261 ) ) )
| ~ ( ( ( ti @ SV81 @ SY262 )
!= ( number_number_of @ SV81 @ SY261 ) )
| ( ( number_number_of @ SV81 @ SY261 )
= ( ti @ SV81 @ SY262 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[502]) ).
thf(608,plain,
! [SV82: $i] :
( ( ~ ( number_ring @ SV82 )
| ( ( plus_plus @ SV82 @ ( one_one @ SV82 ) @ ( one_one @ SV82 ) )
= ( number_number_of @ SV82 @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[503]) ).
thf(609,plain,
! [SV83: $i] :
( ( ! [SY263: $i,SY264: $i] :
( ~ ( number_semiring @ SY264 )
| ( ( plus_plus @ SY264 @ ( ti @ SY264 @ SV83 ) @ SY263 )
= ( plus_plus @ SY264 @ SV83 @ SY263 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[504]) ).
thf(610,plain,
! [SV84: $i] :
( ( ! [SY265: $i] :
( ~ ( number @ SY265 )
| ( ( number_number_of @ SY265 @ ( ti @ int @ SV84 ) )
= ( number_number_of @ SY265 @ SV84 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[505]) ).
thf(611,plain,
! [SV85: $i] :
( ( ~ ~ ( ~ ( number_ring @ SV85 )
| ~ ( linordered_idom @ SV85 ) )
| ! [SY266: $i] :
~ ( ~ ( ~ ( ord_less @ SV85 @ ( number_number_of @ SV85 @ SY266 ) @ ( one_one @ SV85 ) )
| ( ord_less @ int @ SY266 @ ( bit1 @ pls ) ) )
| ~ ( ~ ( ord_less @ int @ SY266 @ ( bit1 @ pls ) )
| ( ord_less @ SV85 @ ( number_number_of @ SV85 @ SY266 ) @ ( one_one @ SV85 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[506]) ).
thf(612,plain,
! [SV86: $i] :
( ( ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ SV86 ) @ SV86 )
!= ( zero_zero @ int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[507]) ).
thf(613,plain,
! [SV87: $i] :
( ( ~ ~ ( ~ ( number_ring @ SV87 )
| ~ ( ring_char_0 @ SV87 ) )
| ! [SY267: $i,SY268: $i] :
~ ( ~ ( ( ( number_number_of @ SV87 @ SY267 )
!= ( number_number_of @ SV87 @ SY268 ) )
| ( SY267 = SY268 ) )
| ~ ( ( SY267 != SY268 )
| ( ( number_number_of @ SV87 @ SY267 )
= ( number_number_of @ SV87 @ SY268 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[508]) ).
thf(614,plain,
! [SV88: $i] :
( ( ! [SY269: $i] :
~ ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SV88 ) @ ( bit1 @ SY269 ) )
| ( ord_less @ int @ SV88 @ SY269 ) )
| ~ ( ~ ( ord_less @ int @ SV88 @ SY269 )
| ( ord_less @ int @ ( bit1 @ SV88 ) @ ( bit1 @ SY269 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[509]) ).
thf(615,plain,
! [SV89: $i] :
( ( ! [SY270: $i] :
( ~ ( number_semiring @ SY270 )
| ( ( semiring_1_of_nat @ SY270 @ ( ti @ nat @ SV89 ) )
= ( semiring_1_of_nat @ SY270 @ SV89 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[510]) ).
thf(616,plain,
! [SV90: $i] :
( ( ! [SY271: $i] :
~ ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SV90 ) @ ( bit0 @ SY271 ) )
| ( ord_less @ int @ SV90 @ SY271 ) )
| ~ ( ~ ( ord_less @ int @ SV90 @ SY271 )
| ( ord_less @ int @ ( bit0 @ SV90 ) @ ( bit0 @ SY271 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[511]) ).
thf(617,plain,
! [SV91: $i] :
( ( ~ ( ring_11004092258visors @ SV91 )
| ! [SY272: $i] :
~ ( ~ ( ( ( power_power @ SV91 @ SY272 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= ( zero_zero @ SV91 ) )
| ( ( ti @ SV91 @ SY272 )
= ( zero_zero @ SV91 ) ) )
| ~ ( ( ( ti @ SV91 @ SY272 )
!= ( zero_zero @ SV91 ) )
| ( ( power_power @ SV91 @ SY272 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SV91 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[512]) ).
thf(618,plain,
! [SV92: $i] :
( ( ~ ( ~ ( ( ( bit0 @ SV92 )
!= pls )
| ( SV92 = pls ) )
| ~ ( ( SV92 != pls )
| ( ( bit0 @ SV92 )
= pls ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[513]) ).
thf(619,plain,
! [SV93: $i] :
( ( ~ ( number_semiring @ SV93 )
| ( ( plus_plus @ SV93 @ ( one_one @ SV93 ) @ ( one_one @ SV93 ) )
= ( number_number_of @ SV93 @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[514]) ).
thf(620,plain,
! [SV94: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ SV94 ) @ SV94 ) @ ( zero_zero @ int ) )
| ( ord_less @ int @ SV94 @ ( zero_zero @ int ) ) )
| ~ ( ~ ( ord_less @ int @ SV94 @ ( zero_zero @ int ) )
| ( ord_less @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ SV94 ) @ SV94 ) @ ( zero_zero @ int ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[515]) ).
thf(621,plain,
! [SV95: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SV95 ) @ ( zero_zero @ int ) )
| ( ord_less @ int @ SV95 @ ( zero_zero @ int ) ) )
| ~ ( ~ ( ord_less @ int @ SV95 @ ( zero_zero @ int ) )
| ( ord_less @ int @ ( bit1 @ SV95 ) @ ( zero_zero @ int ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[516]) ).
thf(622,plain,
! [SV96: $i] :
( ( ~ ( semiring_1 @ SV96 )
| ( ( power_power @ SV96 @ ( one_one @ SV96 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( one_one @ SV96 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[517]) ).
thf(623,plain,
! [SV97: $i] :
( ( ~ ( linord219039673up_add @ SV97 )
| ( ( ti @ SV97 @ ( zero_zero @ SV97 ) )
= ( zero_zero @ SV97 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[518]) ).
thf(624,plain,
! [SV98: $i] :
( ( ( bit1 @ SV98 )
!= pls )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[519]) ).
thf(625,plain,
! [SV99: $i] :
( ( pls
!= ( bit1 @ SV99 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[520]) ).
thf(626,plain,
! [SV100: $i] :
( ( ! [SY273: $i] :
~ ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SV100 ) @ ( bit0 @ SY273 ) )
| ( ord_less @ int @ SV100 @ SY273 ) )
| ~ ( ~ ( ord_less @ int @ SV100 @ SY273 )
| ( ord_less @ int @ ( bit1 @ SV100 ) @ ( bit0 @ SY273 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[521]) ).
thf(627,plain,
! [SV101: $i] :
( ( ! [SY274: $i] :
~ ( ~ ( ~ ( ord_less @ int @ SV101 @ ( plus_plus @ int @ SY274 @ ( one_one @ int ) ) )
| ( ord_less @ int @ SV101 @ SY274 )
| ( SV101 = SY274 ) )
| ~ ( ~ ( ( ord_less @ int @ SV101 @ SY274 )
| ( SV101 = SY274 ) )
| ( ord_less @ int @ SV101 @ ( plus_plus @ int @ SY274 @ ( one_one @ int ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[522]) ).
thf(628,plain,
! [SV102: $i,SV6: $i] :
( ( ( ord_less @ int @ SV6 @ SV102 )
| ( SV6 = SV102 )
| ( ord_less @ int @ SV102 @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[528]) ).
thf(629,plain,
! [SV103: $i,SV7: $i] :
( ( ( plus_plus @ int @ ( number_number_of @ int @ SV7 ) @ ( number_number_of @ int @ SV103 ) )
= ( number_number_of @ int @ ( plus_plus @ int @ SV7 @ SV103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[529]) ).
thf(630,plain,
! [SV104: $i,SV8: $i] :
( ( ( power_power @ int @ ( semiring_1_of_nat @ int @ SV8 ) @ SV104 )
= ( semiring_1_of_nat @ int @ ( power_power @ nat @ SV8 @ SV104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[530]) ).
thf(631,plain,
! [SV105: $i,SV9: $i] :
( ( ( semiring_1_of_nat @ int @ ( power_power @ nat @ SV9 @ SV105 ) )
= ( power_power @ int @ ( semiring_1_of_nat @ int @ SV9 ) @ SV105 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[531]) ).
thf(632,plain,
! [SV106: $i,SV10: $i] :
( ( ! [SY275: $i] :
( ( plus_plus @ int @ ( semiring_1_of_nat @ int @ SV10 ) @ ( plus_plus @ int @ ( semiring_1_of_nat @ int @ SV106 ) @ SY275 ) )
= ( plus_plus @ int @ ( semiring_1_of_nat @ int @ ( plus_plus @ nat @ SV10 @ SV106 ) ) @ SY275 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[532]) ).
thf(633,plain,
! [SV107: $i,SV11: $i] :
( ( ( plus_plus @ int @ ( semiring_1_of_nat @ int @ SV11 ) @ ( semiring_1_of_nat @ int @ SV107 ) )
= ( semiring_1_of_nat @ int @ ( plus_plus @ nat @ SV11 @ SV107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[533]) ).
thf(634,plain,
! [SV108: $i,SV12: $i] :
( ( ! [SY276: $i] :
( ( plus_plus @ int @ ( plus_plus @ int @ SV12 @ SV108 ) @ SY276 )
= ( plus_plus @ int @ SV12 @ ( plus_plus @ int @ SV108 @ SY276 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[535]) ).
thf(635,plain,
! [SV109: $i,SV13: $i] :
( ( ! [SY277: $i] :
( ( plus_plus @ int @ SV13 @ ( plus_plus @ int @ SV109 @ SY277 ) )
= ( plus_plus @ int @ SV109 @ ( plus_plus @ int @ SV13 @ SY277 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[536]) ).
thf(636,plain,
! [SV110: $i,SV14: $i] :
( ( ( plus_plus @ int @ SV14 @ SV110 )
= ( plus_plus @ int @ SV110 @ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[537]) ).
thf(637,plain,
! [SV15: $i] :
( ( ord_less @ int @ ( semiring_1_of_nat @ int @ SV15 ) @ ( zero_zero @ int ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[539]) ).
thf(638,plain,
! [SV111: $i,SV18: $i] :
( ( ( plus_plus @ int @ ( bit0 @ SV18 ) @ ( bit0 @ SV111 ) )
= ( bit0 @ ( plus_plus @ int @ SV18 @ SV111 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[542]) ).
thf(639,plain,
! [SV112: $i,SV22: $i] :
( ( ( plus_plus @ int @ ( bit1 @ SV22 ) @ ( bit0 @ SV112 ) )
= ( bit1 @ ( plus_plus @ int @ SV22 @ SV112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[546]) ).
thf(640,plain,
! [SV113: $i,SV23: $i] :
( ( ( plus_plus @ int @ ( bit0 @ SV23 ) @ ( bit1 @ SV113 ) )
= ( bit1 @ ( plus_plus @ int @ SV23 @ SV113 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[547]) ).
thf(641,plain,
! [SV25: $i] :
( ( ( ~ ~ ( ~ ( power @ SV25 )
| ~ ( semiring_0 @ SV25 ) ) )
= $true )
| ( ( ! [SY203: $i] :
~ ( ~ ( ( ( number_number_of @ nat @ SY203 )
!= ( zero_zero @ nat ) )
| ( ( power_power @ SV25 @ ( zero_zero @ SV25 ) @ ( number_number_of @ nat @ SY203 ) )
= ( one_one @ SV25 ) ) )
| ~ ( ~ ( ( ( number_number_of @ nat @ SY203 )
!= ( zero_zero @ nat ) ) )
| ( ( power_power @ SV25 @ ( zero_zero @ SV25 ) @ ( number_number_of @ nat @ SY203 ) )
= ( zero_zero @ SV25 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[549]) ).
thf(642,plain,
! [SV26: $i] :
( ( ( ~ ( linordered_idom @ SV26 ) )
= $true )
| ( ( ! [SY204: $i,SY205: $i] :
~ ( ~ ( ( ( plus_plus @ SV26 @ ( power_power @ SV26 @ SY204 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV26 @ SY205 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV26 ) )
| ~ ( ( ( ti @ SV26 @ SY204 )
!= ( zero_zero @ SV26 ) )
| ( ( ti @ SV26 @ SY205 )
!= ( zero_zero @ SV26 ) ) ) )
| ~ ( ~ ~ ( ( ( ti @ SV26 @ SY204 )
!= ( zero_zero @ SV26 ) )
| ( ( ti @ SV26 @ SY205 )
!= ( zero_zero @ SV26 ) ) )
| ( ( plus_plus @ SV26 @ ( power_power @ SV26 @ SY204 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV26 @ SY205 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV26 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[550]) ).
thf(643,plain,
! [SV27: $i] :
( ( ( ~ ( number_ring @ SV27 ) )
= $true )
| ( ( ( zero_zero @ SV27 )
= ( number_number_of @ SV27 @ pls ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[551]) ).
thf(644,plain,
! [SV114: $i,SV28: $i] :
( ( ! [SY278: $i] :
( ~ ( number_semiring @ SY278 )
| ( ( plus_plus @ SY278 @ SV28 @ ( ti @ SY278 @ SV114 ) )
= ( plus_plus @ SY278 @ SV28 @ SV114 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[552]) ).
thf(645,plain,
! [SV29: $i] :
( ( ( ~ ( number_semiring @ SV29 ) )
= $true )
| ( ( ( number_number_of @ SV29 @ pls )
= ( zero_zero @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[553]) ).
thf(646,plain,
! [SV30: $i] :
( ( ( ~ ( number_ring @ SV30 ) )
= $true )
| ( ( ! [SY208: $i] :
( ( plus_plus @ SV30 @ SY208 @ ( number_number_of @ SV30 @ pls ) )
= ( ti @ SV30 @ SY208 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[554]) ).
thf(647,plain,
! [SV31: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SV31 ) @ ( zero_zero @ int ) )
| ( ord_less @ int @ SV31 @ ( zero_zero @ int ) ) )
| ~ ( ~ ( ord_less @ int @ SV31 @ ( zero_zero @ int ) )
| ( ord_less @ int @ ( bit0 @ SV31 ) @ ( zero_zero @ int ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[555]) ).
thf(648,plain,
! [SV115: $i,SV32: $i] :
( ( ! [SY279: $i] :
( ~ ~ ( ~ ( power @ SY279 )
| ~ ( semiring_0 @ SY279 ) )
| ( ( power_power @ SY279 @ SV32 @ ( ti @ nat @ SV115 ) )
= ( power_power @ SY279 @ SV32 @ SV115 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[556]) ).
thf(649,plain,
! [SV33: $i,SV116: $i] :
( ( ~ ( number @ SV116 )
| ( ( ti @ SV116 @ ( number_number_of @ SV116 @ SV33 ) )
= ( number_number_of @ SV116 @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[557]) ).
thf(650,plain,
! [SV117: $i,SV34: $i] :
( ( ! [SY280: $i] :
( ~ ( number_semiring @ SY280 )
| ( ( ti @ SY280 @ ( plus_plus @ SY280 @ SV34 @ SV117 ) )
= ( plus_plus @ SY280 @ SV34 @ SV117 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[558]) ).
thf(651,plain,
! [SV35: $i,SV118: $i] :
( ( ! [SY281: $i] :
( ~ ( ord_less @ int @ SV118 @ SY281 )
| ( ord_less @ int @ ( plus_plus @ int @ SV118 @ SV35 ) @ ( plus_plus @ int @ SY281 @ SV35 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[559]) ).
thf(652,plain,
! [SV119: $i,SV36: $i] :
( ( ( bit1 @ SV36 )
!= ( bit0 @ SV119 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[560]) ).
thf(653,plain,
! [SV37: $i] :
( ( ( ~ ( number_ring @ SV37 ) )
= $true )
| ( ( ( one_one @ SV37 )
= ( number_number_of @ SV37 @ ( bit1 @ pls ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[561]) ).
thf(654,plain,
! [SV38: $i] :
( ( ( ~ ( number_ring @ SV38 ) )
= $true )
| ( ( ! [SY217: $i,SY218: $i,SY219: $i] :
( ( plus_plus @ SV38 @ ( number_number_of @ SV38 @ SY217 ) @ ( plus_plus @ SV38 @ ( number_number_of @ SV38 @ SY218 ) @ SY219 ) )
= ( plus_plus @ SV38 @ ( number_number_of @ SV38 @ ( plus_plus @ int @ SY217 @ SY218 ) ) @ SY219 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[562]) ).
thf(655,plain,
! [SV39: $i] :
( ( ~ ( ( pls
!= ( bit0 @ SV39 ) )
| ( pls = SV39 ) )
| ~ ( ( pls != SV39 )
| ( pls
= ( bit0 @ SV39 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[563]) ).
thf(656,plain,
! [SV120: $i,SV40: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ int @ ( number_number_of @ int @ SV40 ) @ ( number_number_of @ int @ SV120 ) )
| ( ord_less @ int @ SV40 @ SV120 ) )
| ~ ( ~ ( ord_less @ int @ SV40 @ SV120 )
| ( ord_less @ int @ ( number_number_of @ int @ SV40 ) @ ( number_number_of @ int @ SV120 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[564]) ).
thf(657,plain,
( ( ( power_power @ int @ ( plus_plus @ int @ ( one_one @ int ) @ ( semiring_1_of_nat @ int @ n ) ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ int ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[565]) ).
thf(658,plain,
! [SV41: $i] :
( ( ( ~ ( linordered_idom @ SV41 ) )
= $true )
| ( ( ! [SY221: $i] :
~ ( ~ ( ~ ( ord_less @ SV41 @ ( plus_plus @ SV41 @ SY221 @ SY221 ) @ ( zero_zero @ SV41 ) )
| ( ord_less @ SV41 @ SY221 @ ( zero_zero @ SV41 ) ) )
| ~ ( ~ ( ord_less @ SV41 @ SY221 @ ( zero_zero @ SV41 ) )
| ( ord_less @ SV41 @ ( plus_plus @ SV41 @ SY221 @ SY221 ) @ ( zero_zero @ SV41 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[566]) ).
thf(659,plain,
! [SV42: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SV42 ) @ pls )
| ( ord_less @ int @ SV42 @ pls ) )
| ~ ( ~ ( ord_less @ int @ SV42 @ pls )
| ( ord_less @ int @ ( bit1 @ SV42 ) @ pls ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[567]) ).
thf(660,plain,
! [SV121: $i,SV43: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SV43 ) @ ( bit0 @ SV121 ) )
| ( ord_less @ int @ SV43 @ SV121 ) )
| ~ ( ~ ( ord_less @ int @ SV43 @ SV121 )
| ( ord_less @ int @ ( bit0 @ SV43 ) @ ( bit0 @ SV121 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[568]) ).
thf(661,plain,
! [SV44: $i] :
( ( ( ~ ( number_ring @ SV44 ) )
= $true )
| ( ( ! [SY223: $i] :
( ( plus_plus @ SV44 @ ( number_number_of @ SV44 @ pls ) @ SY223 )
= ( ti @ SV44 @ SY223 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[569]) ).
thf(662,plain,
! [SV45: $i] :
( ( ~ ( ( ( semiring_1_of_nat @ int @ SV45 )
!= ( zero_zero @ int ) )
| ( SV45
= ( zero_zero @ nat ) ) )
| ~ ( ( SV45
!= ( zero_zero @ nat ) )
| ( ( semiring_1_of_nat @ int @ SV45 )
= ( zero_zero @ int ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[570]) ).
thf(663,plain,
! [SV46: $i] :
( ( ( ~ ( semiring_1 @ SV46 ) )
= $true )
| ( ( ( power_power @ SV46 @ ( zero_zero @ SV46 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[571]) ).
thf(664,plain,
! [SV122: $i,SV47: $i] :
( ( ~ ( ~ ( ( ( bit1 @ SV47 )
!= ( bit1 @ SV122 ) )
| ( SV47 = SV122 ) )
| ~ ( ( SV47 != SV122 )
| ( ( bit1 @ SV47 )
= ( bit1 @ SV122 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[572]) ).
thf(665,plain,
! [SV48: $i,SV123: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ int @ SV123 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV123 ) @ ( number_number_of @ nat @ SV48 ) )
= ( number_number_of @ nat @ SV48 ) ) )
| ~ ( ~ ~ ( ord_less @ int @ SV123 @ pls )
| ~ ( ~ ( ~ ( ord_less @ int @ SV48 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV123 ) @ ( number_number_of @ nat @ SV48 ) )
= ( number_number_of @ nat @ SV123 ) ) )
| ~ ( ~ ~ ( ord_less @ int @ SV48 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV123 ) @ ( number_number_of @ nat @ SV48 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SV123 @ SV48 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[573]) ).
thf(666,plain,
! [SV124: $i,SV49: $i] :
( ( ! [SY282: $i] :
( ~ ( linord219039673up_add @ SY282 )
| ( ( ti @ SY282 @ ( plus_plus @ SY282 @ SV49 @ SV124 ) )
= ( plus_plus @ SY282 @ SV49 @ SV124 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[574]) ).
thf(667,plain,
! [SV50: $i] :
( ( ( ~ ( number_ring @ SV50 ) )
= $true )
| ( ( ( number_number_of @ SV50 @ ( bit1 @ pls ) )
= ( one_one @ SV50 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[575]) ).
thf(668,plain,
! [SV125: $i,SV51: $i] :
( ( ( bit0 @ SV51 )
!= ( bit1 @ SV125 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[576]) ).
thf(669,plain,
! [SV52: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SV52 ) @ pls )
| ( ord_less @ int @ SV52 @ pls ) )
| ~ ( ~ ( ord_less @ int @ SV52 @ pls )
| ( ord_less @ int @ ( bit0 @ SV52 ) @ pls ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[577]) ).
thf(670,plain,
! [SV53: $i] :
( ( ( ~ ( number_ring @ SV53 ) )
= $true )
| ( ( ! [SY229: $i,SY230: $i] :
( ( number_number_of @ SV53 @ ( plus_plus @ int @ SY229 @ SY230 ) )
= ( plus_plus @ SV53 @ ( number_number_of @ SV53 @ SY229 ) @ ( number_number_of @ SV53 @ SY230 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[578]) ).
thf(671,plain,
! [SV54: $i] :
( ( ( ~ ( number_semiring @ SV54 ) )
= $true )
| ( ( ! [SY231: $i] :
( ( number_number_of @ SV54 @ ( semiring_1_of_nat @ int @ SY231 ) )
= ( semiring_1_of_nat @ SV54 @ SY231 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[579]) ).
thf(672,plain,
! [SV126: $i,SV55: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ nat @ ( ti @ nat @ SV55 ) @ SV126 )
| ( ord_less @ nat @ SV55 @ SV126 ) )
| ~ ( ~ ( ord_less @ nat @ SV55 @ SV126 )
| ( ord_less @ nat @ ( ti @ nat @ SV55 ) @ SV126 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[580]) ).
thf(673,plain,
! [SV127: $i,SV56: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ nat @ SV56 @ ( ti @ nat @ SV127 ) )
| ( ord_less @ nat @ SV56 @ SV127 ) )
| ~ ( ~ ( ord_less @ nat @ SV56 @ SV127 )
| ( ord_less @ nat @ SV56 @ ( ti @ nat @ SV127 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[581]) ).
thf(674,plain,
! [SV128: $i,SV57: $i] :
( ( ! [SY283: $i] :
( ~ ( linord219039673up_add @ SY283 )
| ( ( plus_plus @ SY283 @ ( ti @ SY283 @ SV57 ) @ SV128 )
= ( plus_plus @ SY283 @ SV57 @ SV128 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[582]) ).
thf(675,plain,
! [SV58: $i] :
( ( ( ~ ( number_ring @ SV58 ) )
= $true )
| ( ( ! [SY236: $i,SY237: $i] :
( ( plus_plus @ SV58 @ ( number_number_of @ SV58 @ SY236 ) @ ( number_number_of @ SV58 @ SY237 ) )
= ( number_number_of @ SV58 @ ( plus_plus @ int @ SY236 @ SY237 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[583]) ).
thf(676,plain,
! [SV59: $i] :
( ( ( ~ ~ ( ~ ( power @ SV59 )
| ~ ( semiring_0 @ SV59 ) ) )
= $true )
| ( ( ( ti @ SV59 @ ( one_one @ SV59 ) )
= ( one_one @ SV59 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[584]) ).
thf(677,plain,
! [SV129: $i,SV60: $i] :
( ( ! [SY284: $i] :
( ~ ~ ( ~ ( power @ SY284 )
| ~ ( semiring_0 @ SY284 ) )
| ( ( ti @ SY284 @ ( power_power @ SY284 @ SV60 @ SV129 ) )
= ( power_power @ SY284 @ SV60 @ SV129 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[585]) ).
thf(678,plain,
! [SV61: $i] :
( ( ( ~ ( linordered_idom @ SV61 ) )
= $true )
| ( ( ! [SY240: $i] :
~ ( ~ ( ~ ( ord_less @ SV61 @ ( zero_zero @ SV61 ) @ ( power_power @ SV61 @ SY240 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ( ( ti @ SV61 @ SY240 )
!= ( zero_zero @ SV61 ) ) )
| ~ ( ~ ( ( ( ti @ SV61 @ SY240 )
!= ( zero_zero @ SV61 ) ) )
| ( ord_less @ SV61 @ ( zero_zero @ SV61 ) @ ( power_power @ SV61 @ SY240 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[586]) ).
thf(679,plain,
! [SV62: $i] :
( ( ( ~ ~ ( ~ ( number_ring @ SV62 )
| ~ ( linordered_idom @ SV62 ) ) )
= $true )
| ( ( ! [SY241: $i,SY242: $i] :
~ ( ~ ( ~ ( ord_less @ SV62 @ ( number_number_of @ SV62 @ SY241 ) @ ( number_number_of @ SV62 @ SY242 ) )
| ( ord_less @ int @ SY241 @ SY242 ) )
| ~ ( ~ ( ord_less @ int @ SY241 @ SY242 )
| ( ord_less @ SV62 @ ( number_number_of @ SV62 @ SY241 ) @ ( number_number_of @ SV62 @ SY242 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[587]) ).
thf(680,plain,
! [SV63: $i] :
( ( ( ~ ( number_ring @ SV63 ) )
= $true )
| ( ( ! [SY243: $i] :
( ( plus_plus @ SV63 @ ( number_number_of @ SV63 @ SY243 ) @ ( one_one @ SV63 ) )
= ( number_number_of @ SV63 @ ( plus_plus @ int @ SY243 @ ( bit1 @ pls ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[588]) ).
thf(681,plain,
! [SV130: $i,SV64: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SV64 ) @ ( bit0 @ SV130 ) )
| ( ord_less @ int @ SV64 @ SV130 ) )
| ~ ( ~ ( ord_less @ int @ SV64 @ SV130 )
| ( ord_less @ int @ ( bit1 @ SV64 ) @ ( bit0 @ SV130 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[589]) ).
thf(682,plain,
! [SV65: $i,SV131: $i] :
( ( ~ ( number_semiring @ SV131 )
| ( ( ti @ SV131 @ ( semiring_1_of_nat @ SV131 @ SV65 ) )
= ( semiring_1_of_nat @ SV131 @ SV65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[590]) ).
thf(683,plain,
! [SV132: $i,SV66: $i] :
( ( ~ ( ~ ( ( ( bit0 @ SV66 )
!= ( bit0 @ SV132 ) )
| ( SV66 = SV132 ) )
| ~ ( ( SV66 != SV132 )
| ( ( bit0 @ SV66 )
= ( bit0 @ SV132 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[591]) ).
thf(684,plain,
! [SV133: $i,SV67: $i] :
( ( ~ ( ~ ( ( ( semiring_1_of_nat @ int @ SV67 )
!= ( semiring_1_of_nat @ int @ SV133 ) )
| ( SV67 = SV133 ) )
| ~ ( ( SV67 != SV133 )
| ( ( semiring_1_of_nat @ int @ SV67 )
= ( semiring_1_of_nat @ int @ SV133 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[592]) ).
thf(685,plain,
! [SV68: $i] :
( ( ~ ( ~ ( ord_less @ int @ pls @ ( bit0 @ SV68 ) )
| ( ord_less @ int @ pls @ SV68 ) )
| ~ ( ~ ( ord_less @ int @ pls @ SV68 )
| ( ord_less @ int @ pls @ ( bit0 @ SV68 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[593]) ).
thf(686,plain,
! [SV69: $i] :
( ( ( ~ ~ ( ~ ( number_ring @ SV69 )
| ~ ( linordered_idom @ SV69 ) ) )
= $true )
| ( ( ! [SY248: $i] :
~ ( ~ ( ~ ( ord_less @ SV69 @ ( number_number_of @ SV69 @ SY248 ) @ ( zero_zero @ SV69 ) )
| ( ord_less @ int @ SY248 @ pls ) )
| ~ ( ~ ( ord_less @ int @ SY248 @ pls )
| ( ord_less @ SV69 @ ( number_number_of @ SV69 @ SY248 ) @ ( zero_zero @ SV69 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[594]) ).
thf(687,plain,
! [SV134: $i,SV70: $i] :
( ( ! [SY285: $i] :
( ~ ( linord219039673up_add @ SY285 )
| ( ( plus_plus @ SY285 @ SV70 @ ( ti @ SY285 @ SV134 ) )
= ( plus_plus @ SY285 @ SV70 @ SV134 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[595]) ).
thf(688,plain,
! [SV71: $i] :
( ( ( ~ ~ ( ~ ( power @ SV71 )
| ~ ( semiring_0 @ SV71 ) ) )
= $true )
| ( ( ( ti @ SV71 @ ( zero_zero @ SV71 ) )
= ( zero_zero @ SV71 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[596]) ).
thf(689,plain,
! [SV135: $i,SV72: $i] :
( ( ! [SY286: $i] :
( ~ ~ ( ~ ( power @ SY286 )
| ~ ( semiring_0 @ SY286 ) )
| ( ( power_power @ SY286 @ ( ti @ SY286 @ SV72 ) @ SV135 )
= ( power_power @ SY286 @ SV72 @ SV135 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[597]) ).
thf(690,plain,
! [SV73: $i] :
( ( ( ~ ~ ( ~ ( number_ring @ SV73 )
| ~ ( linordered_idom @ SV73 ) ) )
= $true )
| ( ( ! [SY253: $i] :
~ ( ~ ( ~ ( ord_less @ SV73 @ ( one_one @ SV73 ) @ ( number_number_of @ SV73 @ SY253 ) )
| ( ord_less @ int @ ( bit1 @ pls ) @ SY253 ) )
| ~ ( ~ ( ord_less @ int @ ( bit1 @ pls ) @ SY253 )
| ( ord_less @ SV73 @ ( one_one @ SV73 ) @ ( number_number_of @ SV73 @ SY253 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[598]) ).
thf(691,plain,
! [SV74: $i] :
( ( ( ~ ( number_ring @ SV74 ) )
= $true )
| ( ( ! [SY254: $i] :
( ( plus_plus @ SV74 @ ( one_one @ SV74 ) @ ( number_number_of @ SV74 @ SY254 ) )
= ( number_number_of @ SV74 @ ( plus_plus @ int @ ( bit1 @ pls ) @ SY254 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[599]) ).
thf(692,plain,
! [SV75: $i] :
( ( ( ~ ( linord219039673up_add @ SV75 ) )
= $true )
| ( ( ! [SY255: $i] :
~ ( ~ ( ( ( plus_plus @ SV75 @ SY255 @ SY255 )
!= ( zero_zero @ SV75 ) )
| ( ( ti @ SV75 @ SY255 )
= ( zero_zero @ SV75 ) ) )
| ~ ( ( ( ti @ SV75 @ SY255 )
!= ( zero_zero @ SV75 ) )
| ( ( plus_plus @ SV75 @ SY255 @ SY255 )
= ( zero_zero @ SV75 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[600]) ).
thf(693,plain,
! [SV76: $i] :
( ( ( ~ ~ ( ~ ( number_ring @ SV76 )
| ~ ( linordered_idom @ SV76 ) ) )
= $true )
| ( ( ! [SY256: $i] :
~ ( ~ ( ~ ( ord_less @ SV76 @ ( zero_zero @ SV76 ) @ ( number_number_of @ SV76 @ SY256 ) )
| ( ord_less @ int @ pls @ SY256 ) )
| ~ ( ~ ( ord_less @ int @ pls @ SY256 )
| ( ord_less @ SV76 @ ( zero_zero @ SV76 ) @ ( number_number_of @ SV76 @ SY256 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[601]) ).
thf(694,plain,
! [SV77: $i] :
( ( ( ~ ( linordered_idom @ SV77 ) )
= $true )
| ( ( ! [SY257: $i] :
~ ( ord_less @ SV77 @ ( power_power @ SV77 @ SY257 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( zero_zero @ SV77 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[602]) ).
thf(695,plain,
! [SV78: $i] :
( ( ( ~ ( linordered_idom @ SV78 ) )
= $true )
| ( ( ! [SY258: $i,SY259: $i] :
~ ( ~ ( ~ ( ord_less @ SV78 @ ( zero_zero @ SV78 ) @ ( plus_plus @ SV78 @ ( power_power @ SV78 @ SY258 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV78 @ SY259 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
| ( ( ti @ SV78 @ SY258 )
!= ( zero_zero @ SV78 ) )
| ( ( ti @ SV78 @ SY259 )
!= ( zero_zero @ SV78 ) ) )
| ~ ( ~ ( ( ( ti @ SV78 @ SY258 )
!= ( zero_zero @ SV78 ) )
| ( ( ti @ SV78 @ SY259 )
!= ( zero_zero @ SV78 ) ) )
| ( ord_less @ SV78 @ ( zero_zero @ SV78 ) @ ( plus_plus @ SV78 @ ( power_power @ SV78 @ SY258 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV78 @ SY259 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[603]) ).
thf(696,plain,
! [SV79: $i] :
( ( ( ~ ( number_ring @ SV79 ) )
= $true )
| ( ( ( number_number_of @ SV79 @ pls )
= ( zero_zero @ SV79 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[604]) ).
thf(697,plain,
! [SV136: $i,SV80: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SV80 ) @ ( bit1 @ SV136 ) )
| ( ord_less @ int @ SV80 @ SV136 ) )
| ~ ( ~ ( ord_less @ int @ SV80 @ SV136 )
| ( ord_less @ int @ ( bit1 @ SV80 ) @ ( bit1 @ SV136 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[606]) ).
thf(698,plain,
! [SV81: $i] :
( ( ( ~ ( number @ SV81 ) )
= $true )
| ( ( ! [SY261: $i,SY262: $i] :
~ ( ~ ( ( ( number_number_of @ SV81 @ SY261 )
!= ( ti @ SV81 @ SY262 ) )
| ( ( ti @ SV81 @ SY262 )
= ( number_number_of @ SV81 @ SY261 ) ) )
| ~ ( ( ( ti @ SV81 @ SY262 )
!= ( number_number_of @ SV81 @ SY261 ) )
| ( ( number_number_of @ SV81 @ SY261 )
= ( ti @ SV81 @ SY262 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[607]) ).
thf(699,plain,
! [SV82: $i] :
( ( ( ~ ( number_ring @ SV82 ) )
= $true )
| ( ( ( plus_plus @ SV82 @ ( one_one @ SV82 ) @ ( one_one @ SV82 ) )
= ( number_number_of @ SV82 @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[608]) ).
thf(700,plain,
! [SV137: $i,SV83: $i] :
( ( ! [SY287: $i] :
( ~ ( number_semiring @ SY287 )
| ( ( plus_plus @ SY287 @ ( ti @ SY287 @ SV83 ) @ SV137 )
= ( plus_plus @ SY287 @ SV83 @ SV137 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[609]) ).
thf(701,plain,
! [SV84: $i,SV138: $i] :
( ( ~ ( number @ SV138 )
| ( ( number_number_of @ SV138 @ ( ti @ int @ SV84 ) )
= ( number_number_of @ SV138 @ SV84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[610]) ).
thf(702,plain,
! [SV85: $i] :
( ( ( ~ ~ ( ~ ( number_ring @ SV85 )
| ~ ( linordered_idom @ SV85 ) ) )
= $true )
| ( ( ! [SY266: $i] :
~ ( ~ ( ~ ( ord_less @ SV85 @ ( number_number_of @ SV85 @ SY266 ) @ ( one_one @ SV85 ) )
| ( ord_less @ int @ SY266 @ ( bit1 @ pls ) ) )
| ~ ( ~ ( ord_less @ int @ SY266 @ ( bit1 @ pls ) )
| ( ord_less @ SV85 @ ( number_number_of @ SV85 @ SY266 ) @ ( one_one @ SV85 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[611]) ).
thf(703,plain,
! [SV86: $i] :
( ( ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ SV86 ) @ SV86 )
= ( zero_zero @ int ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[612]) ).
thf(704,plain,
! [SV87: $i] :
( ( ( ~ ~ ( ~ ( number_ring @ SV87 )
| ~ ( ring_char_0 @ SV87 ) ) )
= $true )
| ( ( ! [SY267: $i,SY268: $i] :
~ ( ~ ( ( ( number_number_of @ SV87 @ SY267 )
!= ( number_number_of @ SV87 @ SY268 ) )
| ( SY267 = SY268 ) )
| ~ ( ( SY267 != SY268 )
| ( ( number_number_of @ SV87 @ SY267 )
= ( number_number_of @ SV87 @ SY268 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[613]) ).
thf(705,plain,
! [SV139: $i,SV88: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SV88 ) @ ( bit1 @ SV139 ) )
| ( ord_less @ int @ SV88 @ SV139 ) )
| ~ ( ~ ( ord_less @ int @ SV88 @ SV139 )
| ( ord_less @ int @ ( bit1 @ SV88 ) @ ( bit1 @ SV139 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[614]) ).
thf(706,plain,
! [SV89: $i,SV140: $i] :
( ( ~ ( number_semiring @ SV140 )
| ( ( semiring_1_of_nat @ SV140 @ ( ti @ nat @ SV89 ) )
= ( semiring_1_of_nat @ SV140 @ SV89 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[615]) ).
thf(707,plain,
! [SV141: $i,SV90: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SV90 ) @ ( bit0 @ SV141 ) )
| ( ord_less @ int @ SV90 @ SV141 ) )
| ~ ( ~ ( ord_less @ int @ SV90 @ SV141 )
| ( ord_less @ int @ ( bit0 @ SV90 ) @ ( bit0 @ SV141 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[616]) ).
thf(708,plain,
! [SV91: $i] :
( ( ( ~ ( ring_11004092258visors @ SV91 ) )
= $true )
| ( ( ! [SY272: $i] :
~ ( ~ ( ( ( power_power @ SV91 @ SY272 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= ( zero_zero @ SV91 ) )
| ( ( ti @ SV91 @ SY272 )
= ( zero_zero @ SV91 ) ) )
| ~ ( ( ( ti @ SV91 @ SY272 )
!= ( zero_zero @ SV91 ) )
| ( ( power_power @ SV91 @ SY272 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SV91 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[617]) ).
thf(709,plain,
! [SV92: $i] :
( ( ~ ( ( ( bit0 @ SV92 )
!= pls )
| ( SV92 = pls ) )
| ~ ( ( SV92 != pls )
| ( ( bit0 @ SV92 )
= pls ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[618]) ).
thf(710,plain,
! [SV93: $i] :
( ( ( ~ ( number_semiring @ SV93 ) )
= $true )
| ( ( ( plus_plus @ SV93 @ ( one_one @ SV93 ) @ ( one_one @ SV93 ) )
= ( number_number_of @ SV93 @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[619]) ).
thf(711,plain,
! [SV94: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ SV94 ) @ SV94 ) @ ( zero_zero @ int ) )
| ( ord_less @ int @ SV94 @ ( zero_zero @ int ) ) )
| ~ ( ~ ( ord_less @ int @ SV94 @ ( zero_zero @ int ) )
| ( ord_less @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ SV94 ) @ SV94 ) @ ( zero_zero @ int ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[620]) ).
thf(712,plain,
! [SV95: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SV95 ) @ ( zero_zero @ int ) )
| ( ord_less @ int @ SV95 @ ( zero_zero @ int ) ) )
| ~ ( ~ ( ord_less @ int @ SV95 @ ( zero_zero @ int ) )
| ( ord_less @ int @ ( bit1 @ SV95 ) @ ( zero_zero @ int ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[621]) ).
thf(713,plain,
! [SV96: $i] :
( ( ( ~ ( semiring_1 @ SV96 ) )
= $true )
| ( ( ( power_power @ SV96 @ ( one_one @ SV96 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( one_one @ SV96 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[622]) ).
thf(714,plain,
! [SV97: $i] :
( ( ( ~ ( linord219039673up_add @ SV97 ) )
= $true )
| ( ( ( ti @ SV97 @ ( zero_zero @ SV97 ) )
= ( zero_zero @ SV97 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[623]) ).
thf(715,plain,
! [SV98: $i] :
( ( ( bit1 @ SV98 )
= pls )
= $false ),
inference(extcnf_not_pos,[status(thm)],[624]) ).
thf(716,plain,
! [SV99: $i] :
( ( pls
= ( bit1 @ SV99 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[625]) ).
thf(717,plain,
! [SV142: $i,SV100: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SV100 ) @ ( bit0 @ SV142 ) )
| ( ord_less @ int @ SV100 @ SV142 ) )
| ~ ( ~ ( ord_less @ int @ SV100 @ SV142 )
| ( ord_less @ int @ ( bit1 @ SV100 ) @ ( bit0 @ SV142 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[626]) ).
thf(718,plain,
! [SV143: $i,SV101: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ int @ SV101 @ ( plus_plus @ int @ SV143 @ ( one_one @ int ) ) )
| ( ord_less @ int @ SV101 @ SV143 )
| ( SV101 = SV143 ) )
| ~ ( ~ ( ( ord_less @ int @ SV101 @ SV143 )
| ( SV101 = SV143 ) )
| ( ord_less @ int @ SV101 @ ( plus_plus @ int @ SV143 @ ( one_one @ int ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[627]) ).
thf(719,plain,
! [SV102: $i,SV6: $i] :
( ( ( ( ord_less @ int @ SV6 @ SV102 )
| ( SV6 = SV102 ) )
= $true )
| ( ( ord_less @ int @ SV102 @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[628]) ).
thf(720,plain,
! [SV144: $i,SV106: $i,SV10: $i] :
( ( ( plus_plus @ int @ ( semiring_1_of_nat @ int @ SV10 ) @ ( plus_plus @ int @ ( semiring_1_of_nat @ int @ SV106 ) @ SV144 ) )
= ( plus_plus @ int @ ( semiring_1_of_nat @ int @ ( plus_plus @ nat @ SV10 @ SV106 ) ) @ SV144 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[632]) ).
thf(721,plain,
! [SV145: $i,SV108: $i,SV12: $i] :
( ( ( plus_plus @ int @ ( plus_plus @ int @ SV12 @ SV108 ) @ SV145 )
= ( plus_plus @ int @ SV12 @ ( plus_plus @ int @ SV108 @ SV145 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[634]) ).
thf(722,plain,
! [SV146: $i,SV109: $i,SV13: $i] :
( ( ( plus_plus @ int @ SV13 @ ( plus_plus @ int @ SV109 @ SV146 ) )
= ( plus_plus @ int @ SV109 @ ( plus_plus @ int @ SV13 @ SV146 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[635]) ).
thf(723,plain,
! [SV25: $i] :
( ( ( ~ ( ~ ( power @ SV25 )
| ~ ( semiring_0 @ SV25 ) ) )
= $false )
| ( ( ! [SY203: $i] :
~ ( ~ ( ( ( number_number_of @ nat @ SY203 )
!= ( zero_zero @ nat ) )
| ( ( power_power @ SV25 @ ( zero_zero @ SV25 ) @ ( number_number_of @ nat @ SY203 ) )
= ( one_one @ SV25 ) ) )
| ~ ( ~ ( ( ( number_number_of @ nat @ SY203 )
!= ( zero_zero @ nat ) ) )
| ( ( power_power @ SV25 @ ( zero_zero @ SV25 ) @ ( number_number_of @ nat @ SY203 ) )
= ( zero_zero @ SV25 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[641]) ).
thf(724,plain,
! [SV26: $i] :
( ( ( linordered_idom @ SV26 )
= $false )
| ( ( ! [SY204: $i,SY205: $i] :
~ ( ~ ( ( ( plus_plus @ SV26 @ ( power_power @ SV26 @ SY204 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV26 @ SY205 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV26 ) )
| ~ ( ( ( ti @ SV26 @ SY204 )
!= ( zero_zero @ SV26 ) )
| ( ( ti @ SV26 @ SY205 )
!= ( zero_zero @ SV26 ) ) ) )
| ~ ( ~ ~ ( ( ( ti @ SV26 @ SY204 )
!= ( zero_zero @ SV26 ) )
| ( ( ti @ SV26 @ SY205 )
!= ( zero_zero @ SV26 ) ) )
| ( ( plus_plus @ SV26 @ ( power_power @ SV26 @ SY204 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV26 @ SY205 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV26 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[642]) ).
thf(725,plain,
! [SV27: $i] :
( ( ( number_ring @ SV27 )
= $false )
| ( ( ( zero_zero @ SV27 )
= ( number_number_of @ SV27 @ pls ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[643]) ).
thf(726,plain,
! [SV114: $i,SV28: $i,SV147: $i] :
( ( ~ ( number_semiring @ SV147 )
| ( ( plus_plus @ SV147 @ SV28 @ ( ti @ SV147 @ SV114 ) )
= ( plus_plus @ SV147 @ SV28 @ SV114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[644]) ).
thf(727,plain,
! [SV29: $i] :
( ( ( number_semiring @ SV29 )
= $false )
| ( ( ( number_number_of @ SV29 @ pls )
= ( zero_zero @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[645]) ).
thf(728,plain,
! [SV30: $i] :
( ( ( number_ring @ SV30 )
= $false )
| ( ( ! [SY208: $i] :
( ( plus_plus @ SV30 @ SY208 @ ( number_number_of @ SV30 @ pls ) )
= ( ti @ SV30 @ SY208 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[646]) ).
thf(729,plain,
! [SV31: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SV31 ) @ ( zero_zero @ int ) )
| ( ord_less @ int @ SV31 @ ( zero_zero @ int ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[647]) ).
thf(730,plain,
! [SV31: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV31 @ ( zero_zero @ int ) )
| ( ord_less @ int @ ( bit0 @ SV31 ) @ ( zero_zero @ int ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[647]) ).
thf(731,plain,
! [SV115: $i,SV32: $i,SV148: $i] :
( ( ~ ~ ( ~ ( power @ SV148 )
| ~ ( semiring_0 @ SV148 ) )
| ( ( power_power @ SV148 @ SV32 @ ( ti @ nat @ SV115 ) )
= ( power_power @ SV148 @ SV32 @ SV115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[648]) ).
thf(732,plain,
! [SV33: $i,SV116: $i] :
( ( ( ~ ( number @ SV116 ) )
= $true )
| ( ( ( ti @ SV116 @ ( number_number_of @ SV116 @ SV33 ) )
= ( number_number_of @ SV116 @ SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[649]) ).
thf(733,plain,
! [SV117: $i,SV34: $i,SV149: $i] :
( ( ~ ( number_semiring @ SV149 )
| ( ( ti @ SV149 @ ( plus_plus @ SV149 @ SV34 @ SV117 ) )
= ( plus_plus @ SV149 @ SV34 @ SV117 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[650]) ).
thf(734,plain,
! [SV35: $i,SV150: $i,SV118: $i] :
( ( ~ ( ord_less @ int @ SV118 @ SV150 )
| ( ord_less @ int @ ( plus_plus @ int @ SV118 @ SV35 ) @ ( plus_plus @ int @ SV150 @ SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[651]) ).
thf(735,plain,
! [SV119: $i,SV36: $i] :
( ( ( bit1 @ SV36 )
= ( bit0 @ SV119 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[652]) ).
thf(736,plain,
! [SV37: $i] :
( ( ( number_ring @ SV37 )
= $false )
| ( ( ( one_one @ SV37 )
= ( number_number_of @ SV37 @ ( bit1 @ pls ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[653]) ).
thf(737,plain,
! [SV38: $i] :
( ( ( number_ring @ SV38 )
= $false )
| ( ( ! [SY217: $i,SY218: $i,SY219: $i] :
( ( plus_plus @ SV38 @ ( number_number_of @ SV38 @ SY217 ) @ ( plus_plus @ SV38 @ ( number_number_of @ SV38 @ SY218 ) @ SY219 ) )
= ( plus_plus @ SV38 @ ( number_number_of @ SV38 @ ( plus_plus @ int @ SY217 @ SY218 ) ) @ SY219 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[654]) ).
thf(738,plain,
! [SV39: $i] :
( ( ~ ( ( pls
!= ( bit0 @ SV39 ) )
| ( pls = SV39 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[655]) ).
thf(739,plain,
! [SV39: $i] :
( ( ~ ( ( pls != SV39 )
| ( pls
= ( bit0 @ SV39 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[655]) ).
thf(740,plain,
! [SV120: $i,SV40: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( number_number_of @ int @ SV40 ) @ ( number_number_of @ int @ SV120 ) )
| ( ord_less @ int @ SV40 @ SV120 ) )
| ~ ( ~ ( ord_less @ int @ SV40 @ SV120 )
| ( ord_less @ int @ ( number_number_of @ int @ SV40 ) @ ( number_number_of @ int @ SV120 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[656]) ).
thf(741,plain,
! [SV41: $i] :
( ( ( linordered_idom @ SV41 )
= $false )
| ( ( ! [SY221: $i] :
~ ( ~ ( ~ ( ord_less @ SV41 @ ( plus_plus @ SV41 @ SY221 @ SY221 ) @ ( zero_zero @ SV41 ) )
| ( ord_less @ SV41 @ SY221 @ ( zero_zero @ SV41 ) ) )
| ~ ( ~ ( ord_less @ SV41 @ SY221 @ ( zero_zero @ SV41 ) )
| ( ord_less @ SV41 @ ( plus_plus @ SV41 @ SY221 @ SY221 ) @ ( zero_zero @ SV41 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[658]) ).
thf(742,plain,
! [SV42: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SV42 ) @ pls )
| ( ord_less @ int @ SV42 @ pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[659]) ).
thf(743,plain,
! [SV42: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV42 @ pls )
| ( ord_less @ int @ ( bit1 @ SV42 ) @ pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[659]) ).
thf(744,plain,
! [SV121: $i,SV43: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SV43 ) @ ( bit0 @ SV121 ) )
| ( ord_less @ int @ SV43 @ SV121 ) )
| ~ ( ~ ( ord_less @ int @ SV43 @ SV121 )
| ( ord_less @ int @ ( bit0 @ SV43 ) @ ( bit0 @ SV121 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[660]) ).
thf(745,plain,
! [SV44: $i] :
( ( ( number_ring @ SV44 )
= $false )
| ( ( ! [SY223: $i] :
( ( plus_plus @ SV44 @ ( number_number_of @ SV44 @ pls ) @ SY223 )
= ( ti @ SV44 @ SY223 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[661]) ).
thf(746,plain,
! [SV45: $i] :
( ( ~ ( ( ( semiring_1_of_nat @ int @ SV45 )
!= ( zero_zero @ int ) )
| ( SV45
= ( zero_zero @ nat ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[662]) ).
thf(747,plain,
! [SV45: $i] :
( ( ~ ( ( SV45
!= ( zero_zero @ nat ) )
| ( ( semiring_1_of_nat @ int @ SV45 )
= ( zero_zero @ int ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[662]) ).
thf(748,plain,
! [SV46: $i] :
( ( ( semiring_1 @ SV46 )
= $false )
| ( ( ( power_power @ SV46 @ ( zero_zero @ SV46 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[663]) ).
thf(749,plain,
! [SV122: $i,SV47: $i] :
( ( ~ ( ( ( bit1 @ SV47 )
!= ( bit1 @ SV122 ) )
| ( SV47 = SV122 ) )
| ~ ( ( SV47 != SV122 )
| ( ( bit1 @ SV47 )
= ( bit1 @ SV122 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[664]) ).
thf(750,plain,
! [SV48: $i,SV123: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV123 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV123 ) @ ( number_number_of @ nat @ SV48 ) )
= ( number_number_of @ nat @ SV48 ) ) )
| ~ ( ~ ~ ( ord_less @ int @ SV123 @ pls )
| ~ ( ~ ( ~ ( ord_less @ int @ SV48 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV123 ) @ ( number_number_of @ nat @ SV48 ) )
= ( number_number_of @ nat @ SV123 ) ) )
| ~ ( ~ ~ ( ord_less @ int @ SV48 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV123 ) @ ( number_number_of @ nat @ SV48 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SV123 @ SV48 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[665]) ).
thf(751,plain,
! [SV124: $i,SV49: $i,SV151: $i] :
( ( ~ ( linord219039673up_add @ SV151 )
| ( ( ti @ SV151 @ ( plus_plus @ SV151 @ SV49 @ SV124 ) )
= ( plus_plus @ SV151 @ SV49 @ SV124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[666]) ).
thf(752,plain,
! [SV50: $i] :
( ( ( number_ring @ SV50 )
= $false )
| ( ( ( number_number_of @ SV50 @ ( bit1 @ pls ) )
= ( one_one @ SV50 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[667]) ).
thf(753,plain,
! [SV125: $i,SV51: $i] :
( ( ( bit0 @ SV51 )
= ( bit1 @ SV125 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[668]) ).
thf(754,plain,
! [SV52: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SV52 ) @ pls )
| ( ord_less @ int @ SV52 @ pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[669]) ).
thf(755,plain,
! [SV52: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV52 @ pls )
| ( ord_less @ int @ ( bit0 @ SV52 ) @ pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[669]) ).
thf(756,plain,
! [SV53: $i] :
( ( ( number_ring @ SV53 )
= $false )
| ( ( ! [SY229: $i,SY230: $i] :
( ( number_number_of @ SV53 @ ( plus_plus @ int @ SY229 @ SY230 ) )
= ( plus_plus @ SV53 @ ( number_number_of @ SV53 @ SY229 ) @ ( number_number_of @ SV53 @ SY230 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[670]) ).
thf(757,plain,
! [SV54: $i] :
( ( ( number_semiring @ SV54 )
= $false )
| ( ( ! [SY231: $i] :
( ( number_number_of @ SV54 @ ( semiring_1_of_nat @ int @ SY231 ) )
= ( semiring_1_of_nat @ SV54 @ SY231 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[671]) ).
thf(758,plain,
! [SV126: $i,SV55: $i] :
( ( ~ ( ~ ( ord_less @ nat @ ( ti @ nat @ SV55 ) @ SV126 )
| ( ord_less @ nat @ SV55 @ SV126 ) )
| ~ ( ~ ( ord_less @ nat @ SV55 @ SV126 )
| ( ord_less @ nat @ ( ti @ nat @ SV55 ) @ SV126 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[672]) ).
thf(759,plain,
! [SV127: $i,SV56: $i] :
( ( ~ ( ~ ( ord_less @ nat @ SV56 @ ( ti @ nat @ SV127 ) )
| ( ord_less @ nat @ SV56 @ SV127 ) )
| ~ ( ~ ( ord_less @ nat @ SV56 @ SV127 )
| ( ord_less @ nat @ SV56 @ ( ti @ nat @ SV127 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[673]) ).
thf(760,plain,
! [SV128: $i,SV57: $i,SV152: $i] :
( ( ~ ( linord219039673up_add @ SV152 )
| ( ( plus_plus @ SV152 @ ( ti @ SV152 @ SV57 ) @ SV128 )
= ( plus_plus @ SV152 @ SV57 @ SV128 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[674]) ).
thf(761,plain,
! [SV58: $i] :
( ( ( number_ring @ SV58 )
= $false )
| ( ( ! [SY236: $i,SY237: $i] :
( ( plus_plus @ SV58 @ ( number_number_of @ SV58 @ SY236 ) @ ( number_number_of @ SV58 @ SY237 ) )
= ( number_number_of @ SV58 @ ( plus_plus @ int @ SY236 @ SY237 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[675]) ).
thf(762,plain,
! [SV59: $i] :
( ( ( ~ ( ~ ( power @ SV59 )
| ~ ( semiring_0 @ SV59 ) ) )
= $false )
| ( ( ( ti @ SV59 @ ( one_one @ SV59 ) )
= ( one_one @ SV59 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[676]) ).
thf(763,plain,
! [SV129: $i,SV60: $i,SV153: $i] :
( ( ~ ~ ( ~ ( power @ SV153 )
| ~ ( semiring_0 @ SV153 ) )
| ( ( ti @ SV153 @ ( power_power @ SV153 @ SV60 @ SV129 ) )
= ( power_power @ SV153 @ SV60 @ SV129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[677]) ).
thf(764,plain,
! [SV61: $i] :
( ( ( linordered_idom @ SV61 )
= $false )
| ( ( ! [SY240: $i] :
~ ( ~ ( ~ ( ord_less @ SV61 @ ( zero_zero @ SV61 ) @ ( power_power @ SV61 @ SY240 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ( ( ti @ SV61 @ SY240 )
!= ( zero_zero @ SV61 ) ) )
| ~ ( ~ ( ( ( ti @ SV61 @ SY240 )
!= ( zero_zero @ SV61 ) ) )
| ( ord_less @ SV61 @ ( zero_zero @ SV61 ) @ ( power_power @ SV61 @ SY240 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[678]) ).
thf(765,plain,
! [SV62: $i] :
( ( ( ~ ( ~ ( number_ring @ SV62 )
| ~ ( linordered_idom @ SV62 ) ) )
= $false )
| ( ( ! [SY241: $i,SY242: $i] :
~ ( ~ ( ~ ( ord_less @ SV62 @ ( number_number_of @ SV62 @ SY241 ) @ ( number_number_of @ SV62 @ SY242 ) )
| ( ord_less @ int @ SY241 @ SY242 ) )
| ~ ( ~ ( ord_less @ int @ SY241 @ SY242 )
| ( ord_less @ SV62 @ ( number_number_of @ SV62 @ SY241 ) @ ( number_number_of @ SV62 @ SY242 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[679]) ).
thf(766,plain,
! [SV63: $i] :
( ( ( number_ring @ SV63 )
= $false )
| ( ( ! [SY243: $i] :
( ( plus_plus @ SV63 @ ( number_number_of @ SV63 @ SY243 ) @ ( one_one @ SV63 ) )
= ( number_number_of @ SV63 @ ( plus_plus @ int @ SY243 @ ( bit1 @ pls ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[680]) ).
thf(767,plain,
! [SV130: $i,SV64: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SV64 ) @ ( bit0 @ SV130 ) )
| ( ord_less @ int @ SV64 @ SV130 ) )
| ~ ( ~ ( ord_less @ int @ SV64 @ SV130 )
| ( ord_less @ int @ ( bit1 @ SV64 ) @ ( bit0 @ SV130 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[681]) ).
thf(768,plain,
! [SV65: $i,SV131: $i] :
( ( ( ~ ( number_semiring @ SV131 ) )
= $true )
| ( ( ( ti @ SV131 @ ( semiring_1_of_nat @ SV131 @ SV65 ) )
= ( semiring_1_of_nat @ SV131 @ SV65 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[682]) ).
thf(769,plain,
! [SV132: $i,SV66: $i] :
( ( ~ ( ( ( bit0 @ SV66 )
!= ( bit0 @ SV132 ) )
| ( SV66 = SV132 ) )
| ~ ( ( SV66 != SV132 )
| ( ( bit0 @ SV66 )
= ( bit0 @ SV132 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[683]) ).
thf(770,plain,
! [SV133: $i,SV67: $i] :
( ( ~ ( ( ( semiring_1_of_nat @ int @ SV67 )
!= ( semiring_1_of_nat @ int @ SV133 ) )
| ( SV67 = SV133 ) )
| ~ ( ( SV67 != SV133 )
| ( ( semiring_1_of_nat @ int @ SV67 )
= ( semiring_1_of_nat @ int @ SV133 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[684]) ).
thf(771,plain,
! [SV68: $i] :
( ( ~ ( ~ ( ord_less @ int @ pls @ ( bit0 @ SV68 ) )
| ( ord_less @ int @ pls @ SV68 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[685]) ).
thf(772,plain,
! [SV68: $i] :
( ( ~ ( ~ ( ord_less @ int @ pls @ SV68 )
| ( ord_less @ int @ pls @ ( bit0 @ SV68 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[685]) ).
thf(773,plain,
! [SV69: $i] :
( ( ( ~ ( ~ ( number_ring @ SV69 )
| ~ ( linordered_idom @ SV69 ) ) )
= $false )
| ( ( ! [SY248: $i] :
~ ( ~ ( ~ ( ord_less @ SV69 @ ( number_number_of @ SV69 @ SY248 ) @ ( zero_zero @ SV69 ) )
| ( ord_less @ int @ SY248 @ pls ) )
| ~ ( ~ ( ord_less @ int @ SY248 @ pls )
| ( ord_less @ SV69 @ ( number_number_of @ SV69 @ SY248 ) @ ( zero_zero @ SV69 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[686]) ).
thf(774,plain,
! [SV134: $i,SV70: $i,SV154: $i] :
( ( ~ ( linord219039673up_add @ SV154 )
| ( ( plus_plus @ SV154 @ SV70 @ ( ti @ SV154 @ SV134 ) )
= ( plus_plus @ SV154 @ SV70 @ SV134 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[687]) ).
thf(775,plain,
! [SV71: $i] :
( ( ( ~ ( ~ ( power @ SV71 )
| ~ ( semiring_0 @ SV71 ) ) )
= $false )
| ( ( ( ti @ SV71 @ ( zero_zero @ SV71 ) )
= ( zero_zero @ SV71 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[688]) ).
thf(776,plain,
! [SV135: $i,SV72: $i,SV155: $i] :
( ( ~ ~ ( ~ ( power @ SV155 )
| ~ ( semiring_0 @ SV155 ) )
| ( ( power_power @ SV155 @ ( ti @ SV155 @ SV72 ) @ SV135 )
= ( power_power @ SV155 @ SV72 @ SV135 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[689]) ).
thf(777,plain,
! [SV73: $i] :
( ( ( ~ ( ~ ( number_ring @ SV73 )
| ~ ( linordered_idom @ SV73 ) ) )
= $false )
| ( ( ! [SY253: $i] :
~ ( ~ ( ~ ( ord_less @ SV73 @ ( one_one @ SV73 ) @ ( number_number_of @ SV73 @ SY253 ) )
| ( ord_less @ int @ ( bit1 @ pls ) @ SY253 ) )
| ~ ( ~ ( ord_less @ int @ ( bit1 @ pls ) @ SY253 )
| ( ord_less @ SV73 @ ( one_one @ SV73 ) @ ( number_number_of @ SV73 @ SY253 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[690]) ).
thf(778,plain,
! [SV74: $i] :
( ( ( number_ring @ SV74 )
= $false )
| ( ( ! [SY254: $i] :
( ( plus_plus @ SV74 @ ( one_one @ SV74 ) @ ( number_number_of @ SV74 @ SY254 ) )
= ( number_number_of @ SV74 @ ( plus_plus @ int @ ( bit1 @ pls ) @ SY254 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[691]) ).
thf(779,plain,
! [SV75: $i] :
( ( ( linord219039673up_add @ SV75 )
= $false )
| ( ( ! [SY255: $i] :
~ ( ~ ( ( ( plus_plus @ SV75 @ SY255 @ SY255 )
!= ( zero_zero @ SV75 ) )
| ( ( ti @ SV75 @ SY255 )
= ( zero_zero @ SV75 ) ) )
| ~ ( ( ( ti @ SV75 @ SY255 )
!= ( zero_zero @ SV75 ) )
| ( ( plus_plus @ SV75 @ SY255 @ SY255 )
= ( zero_zero @ SV75 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[692]) ).
thf(780,plain,
! [SV76: $i] :
( ( ( ~ ( ~ ( number_ring @ SV76 )
| ~ ( linordered_idom @ SV76 ) ) )
= $false )
| ( ( ! [SY256: $i] :
~ ( ~ ( ~ ( ord_less @ SV76 @ ( zero_zero @ SV76 ) @ ( number_number_of @ SV76 @ SY256 ) )
| ( ord_less @ int @ pls @ SY256 ) )
| ~ ( ~ ( ord_less @ int @ pls @ SY256 )
| ( ord_less @ SV76 @ ( zero_zero @ SV76 ) @ ( number_number_of @ SV76 @ SY256 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[693]) ).
thf(781,plain,
! [SV77: $i] :
( ( ( linordered_idom @ SV77 )
= $false )
| ( ( ! [SY257: $i] :
~ ( ord_less @ SV77 @ ( power_power @ SV77 @ SY257 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( zero_zero @ SV77 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[694]) ).
thf(782,plain,
! [SV78: $i] :
( ( ( linordered_idom @ SV78 )
= $false )
| ( ( ! [SY258: $i,SY259: $i] :
~ ( ~ ( ~ ( ord_less @ SV78 @ ( zero_zero @ SV78 ) @ ( plus_plus @ SV78 @ ( power_power @ SV78 @ SY258 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV78 @ SY259 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
| ( ( ti @ SV78 @ SY258 )
!= ( zero_zero @ SV78 ) )
| ( ( ti @ SV78 @ SY259 )
!= ( zero_zero @ SV78 ) ) )
| ~ ( ~ ( ( ( ti @ SV78 @ SY258 )
!= ( zero_zero @ SV78 ) )
| ( ( ti @ SV78 @ SY259 )
!= ( zero_zero @ SV78 ) ) )
| ( ord_less @ SV78 @ ( zero_zero @ SV78 ) @ ( plus_plus @ SV78 @ ( power_power @ SV78 @ SY258 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV78 @ SY259 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[695]) ).
thf(783,plain,
! [SV79: $i] :
( ( ( number_ring @ SV79 )
= $false )
| ( ( ( number_number_of @ SV79 @ pls )
= ( zero_zero @ SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[696]) ).
thf(784,plain,
! [SV136: $i,SV80: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SV80 ) @ ( bit1 @ SV136 ) )
| ( ord_less @ int @ SV80 @ SV136 ) )
| ~ ( ~ ( ord_less @ int @ SV80 @ SV136 )
| ( ord_less @ int @ ( bit1 @ SV80 ) @ ( bit1 @ SV136 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[697]) ).
thf(785,plain,
! [SV81: $i] :
( ( ( number @ SV81 )
= $false )
| ( ( ! [SY261: $i,SY262: $i] :
~ ( ~ ( ( ( number_number_of @ SV81 @ SY261 )
!= ( ti @ SV81 @ SY262 ) )
| ( ( ti @ SV81 @ SY262 )
= ( number_number_of @ SV81 @ SY261 ) ) )
| ~ ( ( ( ti @ SV81 @ SY262 )
!= ( number_number_of @ SV81 @ SY261 ) )
| ( ( number_number_of @ SV81 @ SY261 )
= ( ti @ SV81 @ SY262 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[698]) ).
thf(786,plain,
! [SV82: $i] :
( ( ( number_ring @ SV82 )
= $false )
| ( ( ( plus_plus @ SV82 @ ( one_one @ SV82 ) @ ( one_one @ SV82 ) )
= ( number_number_of @ SV82 @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[699]) ).
thf(787,plain,
! [SV137: $i,SV83: $i,SV156: $i] :
( ( ~ ( number_semiring @ SV156 )
| ( ( plus_plus @ SV156 @ ( ti @ SV156 @ SV83 ) @ SV137 )
= ( plus_plus @ SV156 @ SV83 @ SV137 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[700]) ).
thf(788,plain,
! [SV84: $i,SV138: $i] :
( ( ( ~ ( number @ SV138 ) )
= $true )
| ( ( ( number_number_of @ SV138 @ ( ti @ int @ SV84 ) )
= ( number_number_of @ SV138 @ SV84 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[701]) ).
thf(789,plain,
! [SV85: $i] :
( ( ( ~ ( ~ ( number_ring @ SV85 )
| ~ ( linordered_idom @ SV85 ) ) )
= $false )
| ( ( ! [SY266: $i] :
~ ( ~ ( ~ ( ord_less @ SV85 @ ( number_number_of @ SV85 @ SY266 ) @ ( one_one @ SV85 ) )
| ( ord_less @ int @ SY266 @ ( bit1 @ pls ) ) )
| ~ ( ~ ( ord_less @ int @ SY266 @ ( bit1 @ pls ) )
| ( ord_less @ SV85 @ ( number_number_of @ SV85 @ SY266 ) @ ( one_one @ SV85 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[702]) ).
thf(790,plain,
! [SV87: $i] :
( ( ( ~ ( ~ ( number_ring @ SV87 )
| ~ ( ring_char_0 @ SV87 ) ) )
= $false )
| ( ( ! [SY267: $i,SY268: $i] :
~ ( ~ ( ( ( number_number_of @ SV87 @ SY267 )
!= ( number_number_of @ SV87 @ SY268 ) )
| ( SY267 = SY268 ) )
| ~ ( ( SY267 != SY268 )
| ( ( number_number_of @ SV87 @ SY267 )
= ( number_number_of @ SV87 @ SY268 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[704]) ).
thf(791,plain,
! [SV139: $i,SV88: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SV88 ) @ ( bit1 @ SV139 ) )
| ( ord_less @ int @ SV88 @ SV139 ) )
| ~ ( ~ ( ord_less @ int @ SV88 @ SV139 )
| ( ord_less @ int @ ( bit1 @ SV88 ) @ ( bit1 @ SV139 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[705]) ).
thf(792,plain,
! [SV89: $i,SV140: $i] :
( ( ( ~ ( number_semiring @ SV140 ) )
= $true )
| ( ( ( semiring_1_of_nat @ SV140 @ ( ti @ nat @ SV89 ) )
= ( semiring_1_of_nat @ SV140 @ SV89 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[706]) ).
thf(793,plain,
! [SV141: $i,SV90: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SV90 ) @ ( bit0 @ SV141 ) )
| ( ord_less @ int @ SV90 @ SV141 ) )
| ~ ( ~ ( ord_less @ int @ SV90 @ SV141 )
| ( ord_less @ int @ ( bit0 @ SV90 ) @ ( bit0 @ SV141 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[707]) ).
thf(794,plain,
! [SV91: $i] :
( ( ( ring_11004092258visors @ SV91 )
= $false )
| ( ( ! [SY272: $i] :
~ ( ~ ( ( ( power_power @ SV91 @ SY272 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= ( zero_zero @ SV91 ) )
| ( ( ti @ SV91 @ SY272 )
= ( zero_zero @ SV91 ) ) )
| ~ ( ( ( ti @ SV91 @ SY272 )
!= ( zero_zero @ SV91 ) )
| ( ( power_power @ SV91 @ SY272 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SV91 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[708]) ).
thf(795,plain,
! [SV92: $i] :
( ( ~ ( ( ( bit0 @ SV92 )
!= pls )
| ( SV92 = pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[709]) ).
thf(796,plain,
! [SV92: $i] :
( ( ~ ( ( SV92 != pls )
| ( ( bit0 @ SV92 )
= pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[709]) ).
thf(797,plain,
! [SV93: $i] :
( ( ( number_semiring @ SV93 )
= $false )
| ( ( ( plus_plus @ SV93 @ ( one_one @ SV93 ) @ ( one_one @ SV93 ) )
= ( number_number_of @ SV93 @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[710]) ).
thf(798,plain,
! [SV94: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ SV94 ) @ SV94 ) @ ( zero_zero @ int ) )
| ( ord_less @ int @ SV94 @ ( zero_zero @ int ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[711]) ).
thf(799,plain,
! [SV94: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV94 @ ( zero_zero @ int ) )
| ( ord_less @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ SV94 ) @ SV94 ) @ ( zero_zero @ int ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[711]) ).
thf(800,plain,
! [SV95: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SV95 ) @ ( zero_zero @ int ) )
| ( ord_less @ int @ SV95 @ ( zero_zero @ int ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[712]) ).
thf(801,plain,
! [SV95: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV95 @ ( zero_zero @ int ) )
| ( ord_less @ int @ ( bit1 @ SV95 ) @ ( zero_zero @ int ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[712]) ).
thf(802,plain,
! [SV96: $i] :
( ( ( semiring_1 @ SV96 )
= $false )
| ( ( ( power_power @ SV96 @ ( one_one @ SV96 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( one_one @ SV96 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[713]) ).
thf(803,plain,
! [SV97: $i] :
( ( ( linord219039673up_add @ SV97 )
= $false )
| ( ( ( ti @ SV97 @ ( zero_zero @ SV97 ) )
= ( zero_zero @ SV97 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[714]) ).
thf(804,plain,
! [SV142: $i,SV100: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SV100 ) @ ( bit0 @ SV142 ) )
| ( ord_less @ int @ SV100 @ SV142 ) )
| ~ ( ~ ( ord_less @ int @ SV100 @ SV142 )
| ( ord_less @ int @ ( bit1 @ SV100 ) @ ( bit0 @ SV142 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[717]) ).
thf(805,plain,
! [SV143: $i,SV101: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV101 @ ( plus_plus @ int @ SV143 @ ( one_one @ int ) ) )
| ( ord_less @ int @ SV101 @ SV143 )
| ( SV101 = SV143 ) )
| ~ ( ~ ( ( ord_less @ int @ SV101 @ SV143 )
| ( SV101 = SV143 ) )
| ( ord_less @ int @ SV101 @ ( plus_plus @ int @ SV143 @ ( one_one @ int ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[718]) ).
thf(806,plain,
! [SV102: $i,SV6: $i] :
( ( ( ord_less @ int @ SV6 @ SV102 )
= $true )
| ( ( SV6 = SV102 )
= $true )
| ( ( ord_less @ int @ SV102 @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[719]) ).
thf(807,plain,
! [SV25: $i] :
( ( ( ~ ( power @ SV25 )
| ~ ( semiring_0 @ SV25 ) )
= $true )
| ( ( ! [SY203: $i] :
~ ( ~ ( ( ( number_number_of @ nat @ SY203 )
!= ( zero_zero @ nat ) )
| ( ( power_power @ SV25 @ ( zero_zero @ SV25 ) @ ( number_number_of @ nat @ SY203 ) )
= ( one_one @ SV25 ) ) )
| ~ ( ~ ( ( ( number_number_of @ nat @ SY203 )
!= ( zero_zero @ nat ) ) )
| ( ( power_power @ SV25 @ ( zero_zero @ SV25 ) @ ( number_number_of @ nat @ SY203 ) )
= ( zero_zero @ SV25 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[723]) ).
thf(808,plain,
! [SV157: $i,SV26: $i] :
( ( ( ! [SY288: $i] :
~ ( ~ ( ( ( plus_plus @ SV26 @ ( power_power @ SV26 @ SV157 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV26 @ SY288 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV26 ) )
| ~ ( ( ( ti @ SV26 @ SV157 )
!= ( zero_zero @ SV26 ) )
| ( ( ti @ SV26 @ SY288 )
!= ( zero_zero @ SV26 ) ) ) )
| ~ ( ~ ~ ( ( ( ti @ SV26 @ SV157 )
!= ( zero_zero @ SV26 ) )
| ( ( ti @ SV26 @ SY288 )
!= ( zero_zero @ SV26 ) ) )
| ( ( plus_plus @ SV26 @ ( power_power @ SV26 @ SV157 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV26 @ SY288 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV26 ) ) ) ) )
= $true )
| ( ( linordered_idom @ SV26 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[724]) ).
thf(809,plain,
! [SV114: $i,SV28: $i,SV147: $i] :
( ( ( ~ ( number_semiring @ SV147 ) )
= $true )
| ( ( ( plus_plus @ SV147 @ SV28 @ ( ti @ SV147 @ SV114 ) )
= ( plus_plus @ SV147 @ SV28 @ SV114 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[726]) ).
thf(810,plain,
! [SV158: $i,SV30: $i] :
( ( ( ( plus_plus @ SV30 @ SV158 @ ( number_number_of @ SV30 @ pls ) )
= ( ti @ SV30 @ SV158 ) )
= $true )
| ( ( number_ring @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[728]) ).
thf(811,plain,
! [SV31: $i] :
( ( ~ ( ord_less @ int @ ( bit0 @ SV31 ) @ ( zero_zero @ int ) )
| ( ord_less @ int @ SV31 @ ( zero_zero @ int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[729]) ).
thf(812,plain,
! [SV31: $i] :
( ( ~ ( ord_less @ int @ SV31 @ ( zero_zero @ int ) )
| ( ord_less @ int @ ( bit0 @ SV31 ) @ ( zero_zero @ int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[730]) ).
thf(813,plain,
! [SV115: $i,SV32: $i,SV148: $i] :
( ( ( ~ ~ ( ~ ( power @ SV148 )
| ~ ( semiring_0 @ SV148 ) ) )
= $true )
| ( ( ( power_power @ SV148 @ SV32 @ ( ti @ nat @ SV115 ) )
= ( power_power @ SV148 @ SV32 @ SV115 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[731]) ).
thf(814,plain,
! [SV33: $i,SV116: $i] :
( ( ( number @ SV116 )
= $false )
| ( ( ( ti @ SV116 @ ( number_number_of @ SV116 @ SV33 ) )
= ( number_number_of @ SV116 @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[732]) ).
thf(815,plain,
! [SV117: $i,SV34: $i,SV149: $i] :
( ( ( ~ ( number_semiring @ SV149 ) )
= $true )
| ( ( ( ti @ SV149 @ ( plus_plus @ SV149 @ SV34 @ SV117 ) )
= ( plus_plus @ SV149 @ SV34 @ SV117 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[733]) ).
thf(816,plain,
! [SV35: $i,SV150: $i,SV118: $i] :
( ( ( ~ ( ord_less @ int @ SV118 @ SV150 ) )
= $true )
| ( ( ord_less @ int @ ( plus_plus @ int @ SV118 @ SV35 ) @ ( plus_plus @ int @ SV150 @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[734]) ).
thf(817,plain,
! [SV159: $i,SV38: $i] :
( ( ( ! [SY289: $i,SY290: $i] :
( ( plus_plus @ SV38 @ ( number_number_of @ SV38 @ SV159 ) @ ( plus_plus @ SV38 @ ( number_number_of @ SV38 @ SY289 ) @ SY290 ) )
= ( plus_plus @ SV38 @ ( number_number_of @ SV38 @ ( plus_plus @ int @ SV159 @ SY289 ) ) @ SY290 ) ) )
= $true )
| ( ( number_ring @ SV38 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[737]) ).
thf(818,plain,
! [SV39: $i] :
( ( ( pls
!= ( bit0 @ SV39 ) )
| ( pls = SV39 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[738]) ).
thf(819,plain,
! [SV39: $i] :
( ( ( pls != SV39 )
| ( pls
= ( bit0 @ SV39 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[739]) ).
thf(820,plain,
! [SV120: $i,SV40: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( number_number_of @ int @ SV40 ) @ ( number_number_of @ int @ SV120 ) )
| ( ord_less @ int @ SV40 @ SV120 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[740]) ).
thf(821,plain,
! [SV120: $i,SV40: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV40 @ SV120 )
| ( ord_less @ int @ ( number_number_of @ int @ SV40 ) @ ( number_number_of @ int @ SV120 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[740]) ).
thf(822,plain,
! [SV160: $i,SV41: $i] :
( ( ( ~ ( ~ ( ~ ( ord_less @ SV41 @ ( plus_plus @ SV41 @ SV160 @ SV160 ) @ ( zero_zero @ SV41 ) )
| ( ord_less @ SV41 @ SV160 @ ( zero_zero @ SV41 ) ) )
| ~ ( ~ ( ord_less @ SV41 @ SV160 @ ( zero_zero @ SV41 ) )
| ( ord_less @ SV41 @ ( plus_plus @ SV41 @ SV160 @ SV160 ) @ ( zero_zero @ SV41 ) ) ) ) )
= $true )
| ( ( linordered_idom @ SV41 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[741]) ).
thf(823,plain,
! [SV42: $i] :
( ( ~ ( ord_less @ int @ ( bit1 @ SV42 ) @ pls )
| ( ord_less @ int @ SV42 @ pls ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[742]) ).
thf(824,plain,
! [SV42: $i] :
( ( ~ ( ord_less @ int @ SV42 @ pls )
| ( ord_less @ int @ ( bit1 @ SV42 ) @ pls ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[743]) ).
thf(825,plain,
! [SV121: $i,SV43: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SV43 ) @ ( bit0 @ SV121 ) )
| ( ord_less @ int @ SV43 @ SV121 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[744]) ).
thf(826,plain,
! [SV121: $i,SV43: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV43 @ SV121 )
| ( ord_less @ int @ ( bit0 @ SV43 ) @ ( bit0 @ SV121 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[744]) ).
thf(827,plain,
! [SV161: $i,SV44: $i] :
( ( ( ( plus_plus @ SV44 @ ( number_number_of @ SV44 @ pls ) @ SV161 )
= ( ti @ SV44 @ SV161 ) )
= $true )
| ( ( number_ring @ SV44 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[745]) ).
thf(828,plain,
! [SV45: $i] :
( ( ( ( semiring_1_of_nat @ int @ SV45 )
!= ( zero_zero @ int ) )
| ( SV45
= ( zero_zero @ nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[746]) ).
thf(829,plain,
! [SV45: $i] :
( ( ( SV45
!= ( zero_zero @ nat ) )
| ( ( semiring_1_of_nat @ int @ SV45 )
= ( zero_zero @ int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[747]) ).
thf(830,plain,
! [SV122: $i,SV47: $i] :
( ( ~ ( ( ( bit1 @ SV47 )
!= ( bit1 @ SV122 ) )
| ( SV47 = SV122 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[749]) ).
thf(831,plain,
! [SV122: $i,SV47: $i] :
( ( ~ ( ( SV47 != SV122 )
| ( ( bit1 @ SV47 )
= ( bit1 @ SV122 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[749]) ).
thf(832,plain,
! [SV48: $i,SV123: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV123 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV123 ) @ ( number_number_of @ nat @ SV48 ) )
= ( number_number_of @ nat @ SV48 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[750]) ).
thf(833,plain,
! [SV48: $i,SV123: $i] :
( ( ~ ( ~ ~ ( ord_less @ int @ SV123 @ pls )
| ~ ( ~ ( ~ ( ord_less @ int @ SV48 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV123 ) @ ( number_number_of @ nat @ SV48 ) )
= ( number_number_of @ nat @ SV123 ) ) )
| ~ ( ~ ~ ( ord_less @ int @ SV48 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV123 ) @ ( number_number_of @ nat @ SV48 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SV123 @ SV48 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[750]) ).
thf(834,plain,
! [SV124: $i,SV49: $i,SV151: $i] :
( ( ( ~ ( linord219039673up_add @ SV151 ) )
= $true )
| ( ( ( ti @ SV151 @ ( plus_plus @ SV151 @ SV49 @ SV124 ) )
= ( plus_plus @ SV151 @ SV49 @ SV124 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[751]) ).
thf(835,plain,
! [SV52: $i] :
( ( ~ ( ord_less @ int @ ( bit0 @ SV52 ) @ pls )
| ( ord_less @ int @ SV52 @ pls ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[754]) ).
thf(836,plain,
! [SV52: $i] :
( ( ~ ( ord_less @ int @ SV52 @ pls )
| ( ord_less @ int @ ( bit0 @ SV52 ) @ pls ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[755]) ).
thf(837,plain,
! [SV162: $i,SV53: $i] :
( ( ( ! [SY291: $i] :
( ( number_number_of @ SV53 @ ( plus_plus @ int @ SV162 @ SY291 ) )
= ( plus_plus @ SV53 @ ( number_number_of @ SV53 @ SV162 ) @ ( number_number_of @ SV53 @ SY291 ) ) ) )
= $true )
| ( ( number_ring @ SV53 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[756]) ).
thf(838,plain,
! [SV163: $i,SV54: $i] :
( ( ( ( number_number_of @ SV54 @ ( semiring_1_of_nat @ int @ SV163 ) )
= ( semiring_1_of_nat @ SV54 @ SV163 ) )
= $true )
| ( ( number_semiring @ SV54 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[757]) ).
thf(839,plain,
! [SV126: $i,SV55: $i] :
( ( ~ ( ~ ( ord_less @ nat @ ( ti @ nat @ SV55 ) @ SV126 )
| ( ord_less @ nat @ SV55 @ SV126 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[758]) ).
thf(840,plain,
! [SV126: $i,SV55: $i] :
( ( ~ ( ~ ( ord_less @ nat @ SV55 @ SV126 )
| ( ord_less @ nat @ ( ti @ nat @ SV55 ) @ SV126 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[758]) ).
thf(841,plain,
! [SV127: $i,SV56: $i] :
( ( ~ ( ~ ( ord_less @ nat @ SV56 @ ( ti @ nat @ SV127 ) )
| ( ord_less @ nat @ SV56 @ SV127 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[759]) ).
thf(842,plain,
! [SV127: $i,SV56: $i] :
( ( ~ ( ~ ( ord_less @ nat @ SV56 @ SV127 )
| ( ord_less @ nat @ SV56 @ ( ti @ nat @ SV127 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[759]) ).
thf(843,plain,
! [SV128: $i,SV57: $i,SV152: $i] :
( ( ( ~ ( linord219039673up_add @ SV152 ) )
= $true )
| ( ( ( plus_plus @ SV152 @ ( ti @ SV152 @ SV57 ) @ SV128 )
= ( plus_plus @ SV152 @ SV57 @ SV128 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[760]) ).
thf(844,plain,
! [SV164: $i,SV58: $i] :
( ( ( ! [SY292: $i] :
( ( plus_plus @ SV58 @ ( number_number_of @ SV58 @ SV164 ) @ ( number_number_of @ SV58 @ SY292 ) )
= ( number_number_of @ SV58 @ ( plus_plus @ int @ SV164 @ SY292 ) ) ) )
= $true )
| ( ( number_ring @ SV58 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[761]) ).
thf(845,plain,
! [SV59: $i] :
( ( ( ~ ( power @ SV59 )
| ~ ( semiring_0 @ SV59 ) )
= $true )
| ( ( ( ti @ SV59 @ ( one_one @ SV59 ) )
= ( one_one @ SV59 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[762]) ).
thf(846,plain,
! [SV129: $i,SV60: $i,SV153: $i] :
( ( ( ~ ~ ( ~ ( power @ SV153 )
| ~ ( semiring_0 @ SV153 ) ) )
= $true )
| ( ( ( ti @ SV153 @ ( power_power @ SV153 @ SV60 @ SV129 ) )
= ( power_power @ SV153 @ SV60 @ SV129 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[763]) ).
thf(847,plain,
! [SV165: $i,SV61: $i] :
( ( ( ~ ( ~ ( ~ ( ord_less @ SV61 @ ( zero_zero @ SV61 ) @ ( power_power @ SV61 @ SV165 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ( ( ti @ SV61 @ SV165 )
!= ( zero_zero @ SV61 ) ) )
| ~ ( ~ ( ( ( ti @ SV61 @ SV165 )
!= ( zero_zero @ SV61 ) ) )
| ( ord_less @ SV61 @ ( zero_zero @ SV61 ) @ ( power_power @ SV61 @ SV165 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) )
= $true )
| ( ( linordered_idom @ SV61 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[764]) ).
thf(848,plain,
! [SV62: $i] :
( ( ( ~ ( number_ring @ SV62 )
| ~ ( linordered_idom @ SV62 ) )
= $true )
| ( ( ! [SY241: $i,SY242: $i] :
~ ( ~ ( ~ ( ord_less @ SV62 @ ( number_number_of @ SV62 @ SY241 ) @ ( number_number_of @ SV62 @ SY242 ) )
| ( ord_less @ int @ SY241 @ SY242 ) )
| ~ ( ~ ( ord_less @ int @ SY241 @ SY242 )
| ( ord_less @ SV62 @ ( number_number_of @ SV62 @ SY241 ) @ ( number_number_of @ SV62 @ SY242 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[765]) ).
thf(849,plain,
! [SV166: $i,SV63: $i] :
( ( ( ( plus_plus @ SV63 @ ( number_number_of @ SV63 @ SV166 ) @ ( one_one @ SV63 ) )
= ( number_number_of @ SV63 @ ( plus_plus @ int @ SV166 @ ( bit1 @ pls ) ) ) )
= $true )
| ( ( number_ring @ SV63 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[766]) ).
thf(850,plain,
! [SV130: $i,SV64: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SV64 ) @ ( bit0 @ SV130 ) )
| ( ord_less @ int @ SV64 @ SV130 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[767]) ).
thf(851,plain,
! [SV130: $i,SV64: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV64 @ SV130 )
| ( ord_less @ int @ ( bit1 @ SV64 ) @ ( bit0 @ SV130 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[767]) ).
thf(852,plain,
! [SV65: $i,SV131: $i] :
( ( ( number_semiring @ SV131 )
= $false )
| ( ( ( ti @ SV131 @ ( semiring_1_of_nat @ SV131 @ SV65 ) )
= ( semiring_1_of_nat @ SV131 @ SV65 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[768]) ).
thf(853,plain,
! [SV132: $i,SV66: $i] :
( ( ~ ( ( ( bit0 @ SV66 )
!= ( bit0 @ SV132 ) )
| ( SV66 = SV132 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[769]) ).
thf(854,plain,
! [SV132: $i,SV66: $i] :
( ( ~ ( ( SV66 != SV132 )
| ( ( bit0 @ SV66 )
= ( bit0 @ SV132 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[769]) ).
thf(855,plain,
! [SV133: $i,SV67: $i] :
( ( ~ ( ( ( semiring_1_of_nat @ int @ SV67 )
!= ( semiring_1_of_nat @ int @ SV133 ) )
| ( SV67 = SV133 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[770]) ).
thf(856,plain,
! [SV133: $i,SV67: $i] :
( ( ~ ( ( SV67 != SV133 )
| ( ( semiring_1_of_nat @ int @ SV67 )
= ( semiring_1_of_nat @ int @ SV133 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[770]) ).
thf(857,plain,
! [SV68: $i] :
( ( ~ ( ord_less @ int @ pls @ ( bit0 @ SV68 ) )
| ( ord_less @ int @ pls @ SV68 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[771]) ).
thf(858,plain,
! [SV68: $i] :
( ( ~ ( ord_less @ int @ pls @ SV68 )
| ( ord_less @ int @ pls @ ( bit0 @ SV68 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[772]) ).
thf(859,plain,
! [SV69: $i] :
( ( ( ~ ( number_ring @ SV69 )
| ~ ( linordered_idom @ SV69 ) )
= $true )
| ( ( ! [SY248: $i] :
~ ( ~ ( ~ ( ord_less @ SV69 @ ( number_number_of @ SV69 @ SY248 ) @ ( zero_zero @ SV69 ) )
| ( ord_less @ int @ SY248 @ pls ) )
| ~ ( ~ ( ord_less @ int @ SY248 @ pls )
| ( ord_less @ SV69 @ ( number_number_of @ SV69 @ SY248 ) @ ( zero_zero @ SV69 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[773]) ).
thf(860,plain,
! [SV134: $i,SV70: $i,SV154: $i] :
( ( ( ~ ( linord219039673up_add @ SV154 ) )
= $true )
| ( ( ( plus_plus @ SV154 @ SV70 @ ( ti @ SV154 @ SV134 ) )
= ( plus_plus @ SV154 @ SV70 @ SV134 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[774]) ).
thf(861,plain,
! [SV71: $i] :
( ( ( ~ ( power @ SV71 )
| ~ ( semiring_0 @ SV71 ) )
= $true )
| ( ( ( ti @ SV71 @ ( zero_zero @ SV71 ) )
= ( zero_zero @ SV71 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[775]) ).
thf(862,plain,
! [SV135: $i,SV72: $i,SV155: $i] :
( ( ( ~ ~ ( ~ ( power @ SV155 )
| ~ ( semiring_0 @ SV155 ) ) )
= $true )
| ( ( ( power_power @ SV155 @ ( ti @ SV155 @ SV72 ) @ SV135 )
= ( power_power @ SV155 @ SV72 @ SV135 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[776]) ).
thf(863,plain,
! [SV73: $i] :
( ( ( ~ ( number_ring @ SV73 )
| ~ ( linordered_idom @ SV73 ) )
= $true )
| ( ( ! [SY253: $i] :
~ ( ~ ( ~ ( ord_less @ SV73 @ ( one_one @ SV73 ) @ ( number_number_of @ SV73 @ SY253 ) )
| ( ord_less @ int @ ( bit1 @ pls ) @ SY253 ) )
| ~ ( ~ ( ord_less @ int @ ( bit1 @ pls ) @ SY253 )
| ( ord_less @ SV73 @ ( one_one @ SV73 ) @ ( number_number_of @ SV73 @ SY253 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[777]) ).
thf(864,plain,
! [SV167: $i,SV74: $i] :
( ( ( ( plus_plus @ SV74 @ ( one_one @ SV74 ) @ ( number_number_of @ SV74 @ SV167 ) )
= ( number_number_of @ SV74 @ ( plus_plus @ int @ ( bit1 @ pls ) @ SV167 ) ) )
= $true )
| ( ( number_ring @ SV74 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[778]) ).
thf(865,plain,
! [SV168: $i,SV75: $i] :
( ( ( ~ ( ~ ( ( ( plus_plus @ SV75 @ SV168 @ SV168 )
!= ( zero_zero @ SV75 ) )
| ( ( ti @ SV75 @ SV168 )
= ( zero_zero @ SV75 ) ) )
| ~ ( ( ( ti @ SV75 @ SV168 )
!= ( zero_zero @ SV75 ) )
| ( ( plus_plus @ SV75 @ SV168 @ SV168 )
= ( zero_zero @ SV75 ) ) ) ) )
= $true )
| ( ( linord219039673up_add @ SV75 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[779]) ).
thf(866,plain,
! [SV76: $i] :
( ( ( ~ ( number_ring @ SV76 )
| ~ ( linordered_idom @ SV76 ) )
= $true )
| ( ( ! [SY256: $i] :
~ ( ~ ( ~ ( ord_less @ SV76 @ ( zero_zero @ SV76 ) @ ( number_number_of @ SV76 @ SY256 ) )
| ( ord_less @ int @ pls @ SY256 ) )
| ~ ( ~ ( ord_less @ int @ pls @ SY256 )
| ( ord_less @ SV76 @ ( zero_zero @ SV76 ) @ ( number_number_of @ SV76 @ SY256 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[780]) ).
thf(867,plain,
! [SV169: $i,SV77: $i] :
( ( ( ~ ( ord_less @ SV77 @ ( power_power @ SV77 @ SV169 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( zero_zero @ SV77 ) ) )
= $true )
| ( ( linordered_idom @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[781]) ).
thf(868,plain,
! [SV170: $i,SV78: $i] :
( ( ( ! [SY293: $i] :
~ ( ~ ( ~ ( ord_less @ SV78 @ ( zero_zero @ SV78 ) @ ( plus_plus @ SV78 @ ( power_power @ SV78 @ SV170 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV78 @ SY293 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
| ( ( ti @ SV78 @ SV170 )
!= ( zero_zero @ SV78 ) )
| ( ( ti @ SV78 @ SY293 )
!= ( zero_zero @ SV78 ) ) )
| ~ ( ~ ( ( ( ti @ SV78 @ SV170 )
!= ( zero_zero @ SV78 ) )
| ( ( ti @ SV78 @ SY293 )
!= ( zero_zero @ SV78 ) ) )
| ( ord_less @ SV78 @ ( zero_zero @ SV78 ) @ ( plus_plus @ SV78 @ ( power_power @ SV78 @ SV170 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV78 @ SY293 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) ) )
= $true )
| ( ( linordered_idom @ SV78 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[782]) ).
thf(869,plain,
! [SV136: $i,SV80: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SV80 ) @ ( bit1 @ SV136 ) )
| ( ord_less @ int @ SV80 @ SV136 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[784]) ).
thf(870,plain,
! [SV136: $i,SV80: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV80 @ SV136 )
| ( ord_less @ int @ ( bit1 @ SV80 ) @ ( bit1 @ SV136 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[784]) ).
thf(871,plain,
! [SV171: $i,SV81: $i] :
( ( ( ! [SY294: $i] :
~ ( ~ ( ( ( number_number_of @ SV81 @ SV171 )
!= ( ti @ SV81 @ SY294 ) )
| ( ( ti @ SV81 @ SY294 )
= ( number_number_of @ SV81 @ SV171 ) ) )
| ~ ( ( ( ti @ SV81 @ SY294 )
!= ( number_number_of @ SV81 @ SV171 ) )
| ( ( number_number_of @ SV81 @ SV171 )
= ( ti @ SV81 @ SY294 ) ) ) ) )
= $true )
| ( ( number @ SV81 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[785]) ).
thf(872,plain,
! [SV137: $i,SV83: $i,SV156: $i] :
( ( ( ~ ( number_semiring @ SV156 ) )
= $true )
| ( ( ( plus_plus @ SV156 @ ( ti @ SV156 @ SV83 ) @ SV137 )
= ( plus_plus @ SV156 @ SV83 @ SV137 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[787]) ).
thf(873,plain,
! [SV84: $i,SV138: $i] :
( ( ( number @ SV138 )
= $false )
| ( ( ( number_number_of @ SV138 @ ( ti @ int @ SV84 ) )
= ( number_number_of @ SV138 @ SV84 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[788]) ).
thf(874,plain,
! [SV85: $i] :
( ( ( ~ ( number_ring @ SV85 )
| ~ ( linordered_idom @ SV85 ) )
= $true )
| ( ( ! [SY266: $i] :
~ ( ~ ( ~ ( ord_less @ SV85 @ ( number_number_of @ SV85 @ SY266 ) @ ( one_one @ SV85 ) )
| ( ord_less @ int @ SY266 @ ( bit1 @ pls ) ) )
| ~ ( ~ ( ord_less @ int @ SY266 @ ( bit1 @ pls ) )
| ( ord_less @ SV85 @ ( number_number_of @ SV85 @ SY266 ) @ ( one_one @ SV85 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[789]) ).
thf(875,plain,
! [SV87: $i] :
( ( ( ~ ( number_ring @ SV87 )
| ~ ( ring_char_0 @ SV87 ) )
= $true )
| ( ( ! [SY267: $i,SY268: $i] :
~ ( ~ ( ( ( number_number_of @ SV87 @ SY267 )
!= ( number_number_of @ SV87 @ SY268 ) )
| ( SY267 = SY268 ) )
| ~ ( ( SY267 != SY268 )
| ( ( number_number_of @ SV87 @ SY267 )
= ( number_number_of @ SV87 @ SY268 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[790]) ).
thf(876,plain,
! [SV139: $i,SV88: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SV88 ) @ ( bit1 @ SV139 ) )
| ( ord_less @ int @ SV88 @ SV139 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[791]) ).
thf(877,plain,
! [SV139: $i,SV88: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV88 @ SV139 )
| ( ord_less @ int @ ( bit1 @ SV88 ) @ ( bit1 @ SV139 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[791]) ).
thf(878,plain,
! [SV89: $i,SV140: $i] :
( ( ( number_semiring @ SV140 )
= $false )
| ( ( ( semiring_1_of_nat @ SV140 @ ( ti @ nat @ SV89 ) )
= ( semiring_1_of_nat @ SV140 @ SV89 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[792]) ).
thf(879,plain,
! [SV141: $i,SV90: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SV90 ) @ ( bit0 @ SV141 ) )
| ( ord_less @ int @ SV90 @ SV141 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[793]) ).
thf(880,plain,
! [SV141: $i,SV90: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV90 @ SV141 )
| ( ord_less @ int @ ( bit0 @ SV90 ) @ ( bit0 @ SV141 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[793]) ).
thf(881,plain,
! [SV172: $i,SV91: $i] :
( ( ( ~ ( ~ ( ( ( power_power @ SV91 @ SV172 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= ( zero_zero @ SV91 ) )
| ( ( ti @ SV91 @ SV172 )
= ( zero_zero @ SV91 ) ) )
| ~ ( ( ( ti @ SV91 @ SV172 )
!= ( zero_zero @ SV91 ) )
| ( ( power_power @ SV91 @ SV172 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SV91 ) ) ) ) )
= $true )
| ( ( ring_11004092258visors @ SV91 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[794]) ).
thf(882,plain,
! [SV92: $i] :
( ( ( ( bit0 @ SV92 )
!= pls )
| ( SV92 = pls ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[795]) ).
thf(883,plain,
! [SV92: $i] :
( ( ( SV92 != pls )
| ( ( bit0 @ SV92 )
= pls ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[796]) ).
thf(884,plain,
! [SV94: $i] :
( ( ~ ( ord_less @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ SV94 ) @ SV94 ) @ ( zero_zero @ int ) )
| ( ord_less @ int @ SV94 @ ( zero_zero @ int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[798]) ).
thf(885,plain,
! [SV94: $i] :
( ( ~ ( ord_less @ int @ SV94 @ ( zero_zero @ int ) )
| ( ord_less @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ SV94 ) @ SV94 ) @ ( zero_zero @ int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[799]) ).
thf(886,plain,
! [SV95: $i] :
( ( ~ ( ord_less @ int @ ( bit1 @ SV95 ) @ ( zero_zero @ int ) )
| ( ord_less @ int @ SV95 @ ( zero_zero @ int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[800]) ).
thf(887,plain,
! [SV95: $i] :
( ( ~ ( ord_less @ int @ SV95 @ ( zero_zero @ int ) )
| ( ord_less @ int @ ( bit1 @ SV95 ) @ ( zero_zero @ int ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[801]) ).
thf(888,plain,
! [SV142: $i,SV100: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SV100 ) @ ( bit0 @ SV142 ) )
| ( ord_less @ int @ SV100 @ SV142 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[804]) ).
thf(889,plain,
! [SV142: $i,SV100: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV100 @ SV142 )
| ( ord_less @ int @ ( bit1 @ SV100 ) @ ( bit0 @ SV142 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[804]) ).
thf(890,plain,
! [SV143: $i,SV101: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV101 @ ( plus_plus @ int @ SV143 @ ( one_one @ int ) ) )
| ( ord_less @ int @ SV101 @ SV143 )
| ( SV101 = SV143 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[805]) ).
thf(891,plain,
! [SV143: $i,SV101: $i] :
( ( ~ ( ~ ( ( ord_less @ int @ SV101 @ SV143 )
| ( SV101 = SV143 ) )
| ( ord_less @ int @ SV101 @ ( plus_plus @ int @ SV143 @ ( one_one @ int ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[805]) ).
thf(892,plain,
! [SV25: $i] :
( ( ( ~ ( power @ SV25 ) )
= $true )
| ( ( ~ ( semiring_0 @ SV25 ) )
= $true )
| ( ( ! [SY203: $i] :
~ ( ~ ( ( ( number_number_of @ nat @ SY203 )
!= ( zero_zero @ nat ) )
| ( ( power_power @ SV25 @ ( zero_zero @ SV25 ) @ ( number_number_of @ nat @ SY203 ) )
= ( one_one @ SV25 ) ) )
| ~ ( ~ ( ( ( number_number_of @ nat @ SY203 )
!= ( zero_zero @ nat ) ) )
| ( ( power_power @ SV25 @ ( zero_zero @ SV25 ) @ ( number_number_of @ nat @ SY203 ) )
= ( zero_zero @ SV25 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[807]) ).
thf(893,plain,
! [SV173: $i,SV157: $i,SV26: $i] :
( ( ( ~ ( ~ ( ( ( plus_plus @ SV26 @ ( power_power @ SV26 @ SV157 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV26 @ SV173 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV26 ) )
| ~ ( ( ( ti @ SV26 @ SV157 )
!= ( zero_zero @ SV26 ) )
| ( ( ti @ SV26 @ SV173 )
!= ( zero_zero @ SV26 ) ) ) )
| ~ ( ~ ~ ( ( ( ti @ SV26 @ SV157 )
!= ( zero_zero @ SV26 ) )
| ( ( ti @ SV26 @ SV173 )
!= ( zero_zero @ SV26 ) ) )
| ( ( plus_plus @ SV26 @ ( power_power @ SV26 @ SV157 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV26 @ SV173 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV26 ) ) ) ) )
= $true )
| ( ( linordered_idom @ SV26 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[808]) ).
thf(894,plain,
! [SV114: $i,SV28: $i,SV147: $i] :
( ( ( number_semiring @ SV147 )
= $false )
| ( ( ( plus_plus @ SV147 @ SV28 @ ( ti @ SV147 @ SV114 ) )
= ( plus_plus @ SV147 @ SV28 @ SV114 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[809]) ).
thf(895,plain,
! [SV31: $i] :
( ( ( ~ ( ord_less @ int @ ( bit0 @ SV31 ) @ ( zero_zero @ int ) ) )
= $true )
| ( ( ord_less @ int @ SV31 @ ( zero_zero @ int ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[811]) ).
thf(896,plain,
! [SV31: $i] :
( ( ( ~ ( ord_less @ int @ SV31 @ ( zero_zero @ int ) ) )
= $true )
| ( ( ord_less @ int @ ( bit0 @ SV31 ) @ ( zero_zero @ int ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[812]) ).
thf(897,plain,
! [SV115: $i,SV32: $i,SV148: $i] :
( ( ( ~ ( ~ ( power @ SV148 )
| ~ ( semiring_0 @ SV148 ) ) )
= $false )
| ( ( ( power_power @ SV148 @ SV32 @ ( ti @ nat @ SV115 ) )
= ( power_power @ SV148 @ SV32 @ SV115 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[813]) ).
thf(898,plain,
! [SV117: $i,SV34: $i,SV149: $i] :
( ( ( number_semiring @ SV149 )
= $false )
| ( ( ( ti @ SV149 @ ( plus_plus @ SV149 @ SV34 @ SV117 ) )
= ( plus_plus @ SV149 @ SV34 @ SV117 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[815]) ).
thf(899,plain,
! [SV35: $i,SV150: $i,SV118: $i] :
( ( ( ord_less @ int @ SV118 @ SV150 )
= $false )
| ( ( ord_less @ int @ ( plus_plus @ int @ SV118 @ SV35 ) @ ( plus_plus @ int @ SV150 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[816]) ).
thf(900,plain,
! [SV174: $i,SV159: $i,SV38: $i] :
( ( ( ! [SY295: $i] :
( ( plus_plus @ SV38 @ ( number_number_of @ SV38 @ SV159 ) @ ( plus_plus @ SV38 @ ( number_number_of @ SV38 @ SV174 ) @ SY295 ) )
= ( plus_plus @ SV38 @ ( number_number_of @ SV38 @ ( plus_plus @ int @ SV159 @ SV174 ) ) @ SY295 ) ) )
= $true )
| ( ( number_ring @ SV38 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[817]) ).
thf(901,plain,
! [SV39: $i] :
( ( ( pls
!= ( bit0 @ SV39 ) )
= $true )
| ( ( pls = SV39 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[818]) ).
thf(902,plain,
! [SV39: $i] :
( ( ( pls != SV39 )
= $true )
| ( ( pls
= ( bit0 @ SV39 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[819]) ).
thf(903,plain,
! [SV120: $i,SV40: $i] :
( ( ~ ( ord_less @ int @ ( number_number_of @ int @ SV40 ) @ ( number_number_of @ int @ SV120 ) )
| ( ord_less @ int @ SV40 @ SV120 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[820]) ).
thf(904,plain,
! [SV120: $i,SV40: $i] :
( ( ~ ( ord_less @ int @ SV40 @ SV120 )
| ( ord_less @ int @ ( number_number_of @ int @ SV40 ) @ ( number_number_of @ int @ SV120 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[821]) ).
thf(905,plain,
! [SV160: $i,SV41: $i] :
( ( ( ~ ( ~ ( ord_less @ SV41 @ ( plus_plus @ SV41 @ SV160 @ SV160 ) @ ( zero_zero @ SV41 ) )
| ( ord_less @ SV41 @ SV160 @ ( zero_zero @ SV41 ) ) )
| ~ ( ~ ( ord_less @ SV41 @ SV160 @ ( zero_zero @ SV41 ) )
| ( ord_less @ SV41 @ ( plus_plus @ SV41 @ SV160 @ SV160 ) @ ( zero_zero @ SV41 ) ) ) )
= $false )
| ( ( linordered_idom @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[822]) ).
thf(906,plain,
! [SV42: $i] :
( ( ( ~ ( ord_less @ int @ ( bit1 @ SV42 ) @ pls ) )
= $true )
| ( ( ord_less @ int @ SV42 @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[823]) ).
thf(907,plain,
! [SV42: $i] :
( ( ( ~ ( ord_less @ int @ SV42 @ pls ) )
= $true )
| ( ( ord_less @ int @ ( bit1 @ SV42 ) @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[824]) ).
thf(908,plain,
! [SV121: $i,SV43: $i] :
( ( ~ ( ord_less @ int @ ( bit0 @ SV43 ) @ ( bit0 @ SV121 ) )
| ( ord_less @ int @ SV43 @ SV121 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[825]) ).
thf(909,plain,
! [SV121: $i,SV43: $i] :
( ( ~ ( ord_less @ int @ SV43 @ SV121 )
| ( ord_less @ int @ ( bit0 @ SV43 ) @ ( bit0 @ SV121 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[826]) ).
thf(910,plain,
! [SV45: $i] :
( ( ( ( semiring_1_of_nat @ int @ SV45 )
!= ( zero_zero @ int ) )
= $true )
| ( ( SV45
= ( zero_zero @ nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[828]) ).
thf(911,plain,
! [SV45: $i] :
( ( ( SV45
!= ( zero_zero @ nat ) )
= $true )
| ( ( ( semiring_1_of_nat @ int @ SV45 )
= ( zero_zero @ int ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[829]) ).
thf(912,plain,
! [SV122: $i,SV47: $i] :
( ( ( ( bit1 @ SV47 )
!= ( bit1 @ SV122 ) )
| ( SV47 = SV122 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[830]) ).
thf(913,plain,
! [SV122: $i,SV47: $i] :
( ( ( SV47 != SV122 )
| ( ( bit1 @ SV47 )
= ( bit1 @ SV122 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[831]) ).
thf(914,plain,
! [SV48: $i,SV123: $i] :
( ( ~ ( ord_less @ int @ SV123 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV123 ) @ ( number_number_of @ nat @ SV48 ) )
= ( number_number_of @ nat @ SV48 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[832]) ).
thf(915,plain,
! [SV48: $i,SV123: $i] :
( ( ~ ~ ( ord_less @ int @ SV123 @ pls )
| ~ ( ~ ( ~ ( ord_less @ int @ SV48 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV123 ) @ ( number_number_of @ nat @ SV48 ) )
= ( number_number_of @ nat @ SV123 ) ) )
| ~ ( ~ ~ ( ord_less @ int @ SV48 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV123 ) @ ( number_number_of @ nat @ SV48 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SV123 @ SV48 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[833]) ).
thf(916,plain,
! [SV124: $i,SV49: $i,SV151: $i] :
( ( ( linord219039673up_add @ SV151 )
= $false )
| ( ( ( ti @ SV151 @ ( plus_plus @ SV151 @ SV49 @ SV124 ) )
= ( plus_plus @ SV151 @ SV49 @ SV124 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[834]) ).
thf(917,plain,
! [SV52: $i] :
( ( ( ~ ( ord_less @ int @ ( bit0 @ SV52 ) @ pls ) )
= $true )
| ( ( ord_less @ int @ SV52 @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[835]) ).
thf(918,plain,
! [SV52: $i] :
( ( ( ~ ( ord_less @ int @ SV52 @ pls ) )
= $true )
| ( ( ord_less @ int @ ( bit0 @ SV52 ) @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[836]) ).
thf(919,plain,
! [SV175: $i,SV162: $i,SV53: $i] :
( ( ( ( number_number_of @ SV53 @ ( plus_plus @ int @ SV162 @ SV175 ) )
= ( plus_plus @ SV53 @ ( number_number_of @ SV53 @ SV162 ) @ ( number_number_of @ SV53 @ SV175 ) ) )
= $true )
| ( ( number_ring @ SV53 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[837]) ).
thf(920,plain,
! [SV126: $i,SV55: $i] :
( ( ~ ( ord_less @ nat @ ( ti @ nat @ SV55 ) @ SV126 )
| ( ord_less @ nat @ SV55 @ SV126 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[839]) ).
thf(921,plain,
! [SV126: $i,SV55: $i] :
( ( ~ ( ord_less @ nat @ SV55 @ SV126 )
| ( ord_less @ nat @ ( ti @ nat @ SV55 ) @ SV126 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[840]) ).
thf(922,plain,
! [SV127: $i,SV56: $i] :
( ( ~ ( ord_less @ nat @ SV56 @ ( ti @ nat @ SV127 ) )
| ( ord_less @ nat @ SV56 @ SV127 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[841]) ).
thf(923,plain,
! [SV127: $i,SV56: $i] :
( ( ~ ( ord_less @ nat @ SV56 @ SV127 )
| ( ord_less @ nat @ SV56 @ ( ti @ nat @ SV127 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[842]) ).
thf(924,plain,
! [SV128: $i,SV57: $i,SV152: $i] :
( ( ( linord219039673up_add @ SV152 )
= $false )
| ( ( ( plus_plus @ SV152 @ ( ti @ SV152 @ SV57 ) @ SV128 )
= ( plus_plus @ SV152 @ SV57 @ SV128 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[843]) ).
thf(925,plain,
! [SV176: $i,SV164: $i,SV58: $i] :
( ( ( ( plus_plus @ SV58 @ ( number_number_of @ SV58 @ SV164 ) @ ( number_number_of @ SV58 @ SV176 ) )
= ( number_number_of @ SV58 @ ( plus_plus @ int @ SV164 @ SV176 ) ) )
= $true )
| ( ( number_ring @ SV58 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[844]) ).
thf(926,plain,
! [SV59: $i] :
( ( ( ~ ( power @ SV59 ) )
= $true )
| ( ( ~ ( semiring_0 @ SV59 ) )
= $true )
| ( ( ( ti @ SV59 @ ( one_one @ SV59 ) )
= ( one_one @ SV59 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[845]) ).
thf(927,plain,
! [SV129: $i,SV60: $i,SV153: $i] :
( ( ( ~ ( ~ ( power @ SV153 )
| ~ ( semiring_0 @ SV153 ) ) )
= $false )
| ( ( ( ti @ SV153 @ ( power_power @ SV153 @ SV60 @ SV129 ) )
= ( power_power @ SV153 @ SV60 @ SV129 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[846]) ).
thf(928,plain,
! [SV165: $i,SV61: $i] :
( ( ( ~ ( ~ ( ord_less @ SV61 @ ( zero_zero @ SV61 ) @ ( power_power @ SV61 @ SV165 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ( ( ti @ SV61 @ SV165 )
!= ( zero_zero @ SV61 ) ) )
| ~ ( ~ ( ( ( ti @ SV61 @ SV165 )
!= ( zero_zero @ SV61 ) ) )
| ( ord_less @ SV61 @ ( zero_zero @ SV61 ) @ ( power_power @ SV61 @ SV165 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $false )
| ( ( linordered_idom @ SV61 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[847]) ).
thf(929,plain,
! [SV62: $i] :
( ( ( ~ ( number_ring @ SV62 ) )
= $true )
| ( ( ~ ( linordered_idom @ SV62 ) )
= $true )
| ( ( ! [SY241: $i,SY242: $i] :
~ ( ~ ( ~ ( ord_less @ SV62 @ ( number_number_of @ SV62 @ SY241 ) @ ( number_number_of @ SV62 @ SY242 ) )
| ( ord_less @ int @ SY241 @ SY242 ) )
| ~ ( ~ ( ord_less @ int @ SY241 @ SY242 )
| ( ord_less @ SV62 @ ( number_number_of @ SV62 @ SY241 ) @ ( number_number_of @ SV62 @ SY242 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[848]) ).
thf(930,plain,
! [SV130: $i,SV64: $i] :
( ( ~ ( ord_less @ int @ ( bit1 @ SV64 ) @ ( bit0 @ SV130 ) )
| ( ord_less @ int @ SV64 @ SV130 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[850]) ).
thf(931,plain,
! [SV130: $i,SV64: $i] :
( ( ~ ( ord_less @ int @ SV64 @ SV130 )
| ( ord_less @ int @ ( bit1 @ SV64 ) @ ( bit0 @ SV130 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[851]) ).
thf(932,plain,
! [SV132: $i,SV66: $i] :
( ( ( ( bit0 @ SV66 )
!= ( bit0 @ SV132 ) )
| ( SV66 = SV132 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[853]) ).
thf(933,plain,
! [SV132: $i,SV66: $i] :
( ( ( SV66 != SV132 )
| ( ( bit0 @ SV66 )
= ( bit0 @ SV132 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[854]) ).
thf(934,plain,
! [SV133: $i,SV67: $i] :
( ( ( ( semiring_1_of_nat @ int @ SV67 )
!= ( semiring_1_of_nat @ int @ SV133 ) )
| ( SV67 = SV133 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[855]) ).
thf(935,plain,
! [SV133: $i,SV67: $i] :
( ( ( SV67 != SV133 )
| ( ( semiring_1_of_nat @ int @ SV67 )
= ( semiring_1_of_nat @ int @ SV133 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[856]) ).
thf(936,plain,
! [SV68: $i] :
( ( ( ~ ( ord_less @ int @ pls @ ( bit0 @ SV68 ) ) )
= $true )
| ( ( ord_less @ int @ pls @ SV68 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[857]) ).
thf(937,plain,
! [SV68: $i] :
( ( ( ~ ( ord_less @ int @ pls @ SV68 ) )
= $true )
| ( ( ord_less @ int @ pls @ ( bit0 @ SV68 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[858]) ).
thf(938,plain,
! [SV69: $i] :
( ( ( ~ ( number_ring @ SV69 ) )
= $true )
| ( ( ~ ( linordered_idom @ SV69 ) )
= $true )
| ( ( ! [SY248: $i] :
~ ( ~ ( ~ ( ord_less @ SV69 @ ( number_number_of @ SV69 @ SY248 ) @ ( zero_zero @ SV69 ) )
| ( ord_less @ int @ SY248 @ pls ) )
| ~ ( ~ ( ord_less @ int @ SY248 @ pls )
| ( ord_less @ SV69 @ ( number_number_of @ SV69 @ SY248 ) @ ( zero_zero @ SV69 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[859]) ).
thf(939,plain,
! [SV134: $i,SV70: $i,SV154: $i] :
( ( ( linord219039673up_add @ SV154 )
= $false )
| ( ( ( plus_plus @ SV154 @ SV70 @ ( ti @ SV154 @ SV134 ) )
= ( plus_plus @ SV154 @ SV70 @ SV134 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[860]) ).
thf(940,plain,
! [SV71: $i] :
( ( ( ~ ( power @ SV71 ) )
= $true )
| ( ( ~ ( semiring_0 @ SV71 ) )
= $true )
| ( ( ( ti @ SV71 @ ( zero_zero @ SV71 ) )
= ( zero_zero @ SV71 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[861]) ).
thf(941,plain,
! [SV135: $i,SV72: $i,SV155: $i] :
( ( ( ~ ( ~ ( power @ SV155 )
| ~ ( semiring_0 @ SV155 ) ) )
= $false )
| ( ( ( power_power @ SV155 @ ( ti @ SV155 @ SV72 ) @ SV135 )
= ( power_power @ SV155 @ SV72 @ SV135 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[862]) ).
thf(942,plain,
! [SV73: $i] :
( ( ( ~ ( number_ring @ SV73 ) )
= $true )
| ( ( ~ ( linordered_idom @ SV73 ) )
= $true )
| ( ( ! [SY253: $i] :
~ ( ~ ( ~ ( ord_less @ SV73 @ ( one_one @ SV73 ) @ ( number_number_of @ SV73 @ SY253 ) )
| ( ord_less @ int @ ( bit1 @ pls ) @ SY253 ) )
| ~ ( ~ ( ord_less @ int @ ( bit1 @ pls ) @ SY253 )
| ( ord_less @ SV73 @ ( one_one @ SV73 ) @ ( number_number_of @ SV73 @ SY253 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[863]) ).
thf(943,plain,
! [SV168: $i,SV75: $i] :
( ( ( ~ ( ( ( plus_plus @ SV75 @ SV168 @ SV168 )
!= ( zero_zero @ SV75 ) )
| ( ( ti @ SV75 @ SV168 )
= ( zero_zero @ SV75 ) ) )
| ~ ( ( ( ti @ SV75 @ SV168 )
!= ( zero_zero @ SV75 ) )
| ( ( plus_plus @ SV75 @ SV168 @ SV168 )
= ( zero_zero @ SV75 ) ) ) )
= $false )
| ( ( linord219039673up_add @ SV75 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[865]) ).
thf(944,plain,
! [SV76: $i] :
( ( ( ~ ( number_ring @ SV76 ) )
= $true )
| ( ( ~ ( linordered_idom @ SV76 ) )
= $true )
| ( ( ! [SY256: $i] :
~ ( ~ ( ~ ( ord_less @ SV76 @ ( zero_zero @ SV76 ) @ ( number_number_of @ SV76 @ SY256 ) )
| ( ord_less @ int @ pls @ SY256 ) )
| ~ ( ~ ( ord_less @ int @ pls @ SY256 )
| ( ord_less @ SV76 @ ( zero_zero @ SV76 ) @ ( number_number_of @ SV76 @ SY256 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[866]) ).
thf(945,plain,
! [SV169: $i,SV77: $i] :
( ( ( ord_less @ SV77 @ ( power_power @ SV77 @ SV169 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( zero_zero @ SV77 ) )
= $false )
| ( ( linordered_idom @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[867]) ).
thf(946,plain,
! [SV177: $i,SV170: $i,SV78: $i] :
( ( ( ~ ( ~ ( ~ ( ord_less @ SV78 @ ( zero_zero @ SV78 ) @ ( plus_plus @ SV78 @ ( power_power @ SV78 @ SV170 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV78 @ SV177 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
| ( ( ti @ SV78 @ SV170 )
!= ( zero_zero @ SV78 ) )
| ( ( ti @ SV78 @ SV177 )
!= ( zero_zero @ SV78 ) ) )
| ~ ( ~ ( ( ( ti @ SV78 @ SV170 )
!= ( zero_zero @ SV78 ) )
| ( ( ti @ SV78 @ SV177 )
!= ( zero_zero @ SV78 ) ) )
| ( ord_less @ SV78 @ ( zero_zero @ SV78 ) @ ( plus_plus @ SV78 @ ( power_power @ SV78 @ SV170 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV78 @ SV177 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) ) )
= $true )
| ( ( linordered_idom @ SV78 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[868]) ).
thf(947,plain,
! [SV136: $i,SV80: $i] :
( ( ~ ( ord_less @ int @ ( bit1 @ SV80 ) @ ( bit1 @ SV136 ) )
| ( ord_less @ int @ SV80 @ SV136 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[869]) ).
thf(948,plain,
! [SV136: $i,SV80: $i] :
( ( ~ ( ord_less @ int @ SV80 @ SV136 )
| ( ord_less @ int @ ( bit1 @ SV80 ) @ ( bit1 @ SV136 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[870]) ).
thf(949,plain,
! [SV178: $i,SV171: $i,SV81: $i] :
( ( ( ~ ( ~ ( ( ( number_number_of @ SV81 @ SV171 )
!= ( ti @ SV81 @ SV178 ) )
| ( ( ti @ SV81 @ SV178 )
= ( number_number_of @ SV81 @ SV171 ) ) )
| ~ ( ( ( ti @ SV81 @ SV178 )
!= ( number_number_of @ SV81 @ SV171 ) )
| ( ( number_number_of @ SV81 @ SV171 )
= ( ti @ SV81 @ SV178 ) ) ) ) )
= $true )
| ( ( number @ SV81 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[871]) ).
thf(950,plain,
! [SV137: $i,SV83: $i,SV156: $i] :
( ( ( number_semiring @ SV156 )
= $false )
| ( ( ( plus_plus @ SV156 @ ( ti @ SV156 @ SV83 ) @ SV137 )
= ( plus_plus @ SV156 @ SV83 @ SV137 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[872]) ).
thf(951,plain,
! [SV85: $i] :
( ( ( ~ ( number_ring @ SV85 ) )
= $true )
| ( ( ~ ( linordered_idom @ SV85 ) )
= $true )
| ( ( ! [SY266: $i] :
~ ( ~ ( ~ ( ord_less @ SV85 @ ( number_number_of @ SV85 @ SY266 ) @ ( one_one @ SV85 ) )
| ( ord_less @ int @ SY266 @ ( bit1 @ pls ) ) )
| ~ ( ~ ( ord_less @ int @ SY266 @ ( bit1 @ pls ) )
| ( ord_less @ SV85 @ ( number_number_of @ SV85 @ SY266 ) @ ( one_one @ SV85 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[874]) ).
thf(952,plain,
! [SV87: $i] :
( ( ( ~ ( number_ring @ SV87 ) )
= $true )
| ( ( ~ ( ring_char_0 @ SV87 ) )
= $true )
| ( ( ! [SY267: $i,SY268: $i] :
~ ( ~ ( ( ( number_number_of @ SV87 @ SY267 )
!= ( number_number_of @ SV87 @ SY268 ) )
| ( SY267 = SY268 ) )
| ~ ( ( SY267 != SY268 )
| ( ( number_number_of @ SV87 @ SY267 )
= ( number_number_of @ SV87 @ SY268 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[875]) ).
thf(953,plain,
! [SV139: $i,SV88: $i] :
( ( ~ ( ord_less @ int @ ( bit1 @ SV88 ) @ ( bit1 @ SV139 ) )
| ( ord_less @ int @ SV88 @ SV139 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[876]) ).
thf(954,plain,
! [SV139: $i,SV88: $i] :
( ( ~ ( ord_less @ int @ SV88 @ SV139 )
| ( ord_less @ int @ ( bit1 @ SV88 ) @ ( bit1 @ SV139 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[877]) ).
thf(955,plain,
! [SV141: $i,SV90: $i] :
( ( ~ ( ord_less @ int @ ( bit0 @ SV90 ) @ ( bit0 @ SV141 ) )
| ( ord_less @ int @ SV90 @ SV141 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[879]) ).
thf(956,plain,
! [SV141: $i,SV90: $i] :
( ( ~ ( ord_less @ int @ SV90 @ SV141 )
| ( ord_less @ int @ ( bit0 @ SV90 ) @ ( bit0 @ SV141 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[880]) ).
thf(957,plain,
! [SV172: $i,SV91: $i] :
( ( ( ~ ( ( ( power_power @ SV91 @ SV172 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= ( zero_zero @ SV91 ) )
| ( ( ti @ SV91 @ SV172 )
= ( zero_zero @ SV91 ) ) )
| ~ ( ( ( ti @ SV91 @ SV172 )
!= ( zero_zero @ SV91 ) )
| ( ( power_power @ SV91 @ SV172 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SV91 ) ) ) )
= $false )
| ( ( ring_11004092258visors @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[881]) ).
thf(958,plain,
! [SV92: $i] :
( ( ( ( bit0 @ SV92 )
!= pls )
= $true )
| ( ( SV92 = pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[882]) ).
thf(959,plain,
! [SV92: $i] :
( ( ( SV92 != pls )
= $true )
| ( ( ( bit0 @ SV92 )
= pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[883]) ).
thf(960,plain,
! [SV94: $i] :
( ( ( ~ ( ord_less @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ SV94 ) @ SV94 ) @ ( zero_zero @ int ) ) )
= $true )
| ( ( ord_less @ int @ SV94 @ ( zero_zero @ int ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[884]) ).
thf(961,plain,
! [SV94: $i] :
( ( ( ~ ( ord_less @ int @ SV94 @ ( zero_zero @ int ) ) )
= $true )
| ( ( ord_less @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ SV94 ) @ SV94 ) @ ( zero_zero @ int ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[885]) ).
thf(962,plain,
! [SV95: $i] :
( ( ( ~ ( ord_less @ int @ ( bit1 @ SV95 ) @ ( zero_zero @ int ) ) )
= $true )
| ( ( ord_less @ int @ SV95 @ ( zero_zero @ int ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[886]) ).
thf(963,plain,
! [SV95: $i] :
( ( ( ~ ( ord_less @ int @ SV95 @ ( zero_zero @ int ) ) )
= $true )
| ( ( ord_less @ int @ ( bit1 @ SV95 ) @ ( zero_zero @ int ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[887]) ).
thf(964,plain,
! [SV142: $i,SV100: $i] :
( ( ~ ( ord_less @ int @ ( bit1 @ SV100 ) @ ( bit0 @ SV142 ) )
| ( ord_less @ int @ SV100 @ SV142 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[888]) ).
thf(965,plain,
! [SV142: $i,SV100: $i] :
( ( ~ ( ord_less @ int @ SV100 @ SV142 )
| ( ord_less @ int @ ( bit1 @ SV100 ) @ ( bit0 @ SV142 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[889]) ).
thf(966,plain,
! [SV143: $i,SV101: $i] :
( ( ~ ( ord_less @ int @ SV101 @ ( plus_plus @ int @ SV143 @ ( one_one @ int ) ) )
| ( ord_less @ int @ SV101 @ SV143 )
| ( SV101 = SV143 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[890]) ).
thf(967,plain,
! [SV143: $i,SV101: $i] :
( ( ~ ( ( ord_less @ int @ SV101 @ SV143 )
| ( SV101 = SV143 ) )
| ( ord_less @ int @ SV101 @ ( plus_plus @ int @ SV143 @ ( one_one @ int ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[891]) ).
thf(968,plain,
! [SV25: $i] :
( ( ( power @ SV25 )
= $false )
| ( ( ~ ( semiring_0 @ SV25 ) )
= $true )
| ( ( ! [SY203: $i] :
~ ( ~ ( ( ( number_number_of @ nat @ SY203 )
!= ( zero_zero @ nat ) )
| ( ( power_power @ SV25 @ ( zero_zero @ SV25 ) @ ( number_number_of @ nat @ SY203 ) )
= ( one_one @ SV25 ) ) )
| ~ ( ~ ( ( ( number_number_of @ nat @ SY203 )
!= ( zero_zero @ nat ) ) )
| ( ( power_power @ SV25 @ ( zero_zero @ SV25 ) @ ( number_number_of @ nat @ SY203 ) )
= ( zero_zero @ SV25 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[892]) ).
thf(969,plain,
! [SV173: $i,SV157: $i,SV26: $i] :
( ( ( ~ ( ( ( plus_plus @ SV26 @ ( power_power @ SV26 @ SV157 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV26 @ SV173 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV26 ) )
| ~ ( ( ( ti @ SV26 @ SV157 )
!= ( zero_zero @ SV26 ) )
| ( ( ti @ SV26 @ SV173 )
!= ( zero_zero @ SV26 ) ) ) )
| ~ ( ~ ~ ( ( ( ti @ SV26 @ SV157 )
!= ( zero_zero @ SV26 ) )
| ( ( ti @ SV26 @ SV173 )
!= ( zero_zero @ SV26 ) ) )
| ( ( plus_plus @ SV26 @ ( power_power @ SV26 @ SV157 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV26 @ SV173 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV26 ) ) ) )
= $false )
| ( ( linordered_idom @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[893]) ).
thf(970,plain,
! [SV31: $i] :
( ( ( ord_less @ int @ ( bit0 @ SV31 ) @ ( zero_zero @ int ) )
= $false )
| ( ( ord_less @ int @ SV31 @ ( zero_zero @ int ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[895]) ).
thf(971,plain,
! [SV31: $i] :
( ( ( ord_less @ int @ SV31 @ ( zero_zero @ int ) )
= $false )
| ( ( ord_less @ int @ ( bit0 @ SV31 ) @ ( zero_zero @ int ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[896]) ).
thf(972,plain,
! [SV115: $i,SV32: $i,SV148: $i] :
( ( ( ~ ( power @ SV148 )
| ~ ( semiring_0 @ SV148 ) )
= $true )
| ( ( ( power_power @ SV148 @ SV32 @ ( ti @ nat @ SV115 ) )
= ( power_power @ SV148 @ SV32 @ SV115 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[897]) ).
thf(973,plain,
! [SV179: $i,SV174: $i,SV159: $i,SV38: $i] :
( ( ( ( plus_plus @ SV38 @ ( number_number_of @ SV38 @ SV159 ) @ ( plus_plus @ SV38 @ ( number_number_of @ SV38 @ SV174 ) @ SV179 ) )
= ( plus_plus @ SV38 @ ( number_number_of @ SV38 @ ( plus_plus @ int @ SV159 @ SV174 ) ) @ SV179 ) )
= $true )
| ( ( number_ring @ SV38 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[900]) ).
thf(974,plain,
! [SV39: $i] :
( ( ( pls
= ( bit0 @ SV39 ) )
= $false )
| ( ( pls = SV39 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[901]) ).
thf(975,plain,
! [SV39: $i] :
( ( ( pls = SV39 )
= $false )
| ( ( pls
= ( bit0 @ SV39 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[902]) ).
thf(976,plain,
! [SV120: $i,SV40: $i] :
( ( ( ~ ( ord_less @ int @ ( number_number_of @ int @ SV40 ) @ ( number_number_of @ int @ SV120 ) ) )
= $true )
| ( ( ord_less @ int @ SV40 @ SV120 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[903]) ).
thf(977,plain,
! [SV120: $i,SV40: $i] :
( ( ( ~ ( ord_less @ int @ SV40 @ SV120 ) )
= $true )
| ( ( ord_less @ int @ ( number_number_of @ int @ SV40 ) @ ( number_number_of @ int @ SV120 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[904]) ).
thf(978,plain,
! [SV160: $i,SV41: $i] :
( ( ( ~ ( ~ ( ord_less @ SV41 @ ( plus_plus @ SV41 @ SV160 @ SV160 ) @ ( zero_zero @ SV41 ) )
| ( ord_less @ SV41 @ SV160 @ ( zero_zero @ SV41 ) ) ) )
= $false )
| ( ( linordered_idom @ SV41 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[905]) ).
thf(979,plain,
! [SV160: $i,SV41: $i] :
( ( ( ~ ( ~ ( ord_less @ SV41 @ SV160 @ ( zero_zero @ SV41 ) )
| ( ord_less @ SV41 @ ( plus_plus @ SV41 @ SV160 @ SV160 ) @ ( zero_zero @ SV41 ) ) ) )
= $false )
| ( ( linordered_idom @ SV41 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[905]) ).
thf(980,plain,
! [SV42: $i] :
( ( ( ord_less @ int @ ( bit1 @ SV42 ) @ pls )
= $false )
| ( ( ord_less @ int @ SV42 @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[906]) ).
thf(981,plain,
! [SV42: $i] :
( ( ( ord_less @ int @ SV42 @ pls )
= $false )
| ( ( ord_less @ int @ ( bit1 @ SV42 ) @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[907]) ).
thf(982,plain,
! [SV121: $i,SV43: $i] :
( ( ( ~ ( ord_less @ int @ ( bit0 @ SV43 ) @ ( bit0 @ SV121 ) ) )
= $true )
| ( ( ord_less @ int @ SV43 @ SV121 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[908]) ).
thf(983,plain,
! [SV121: $i,SV43: $i] :
( ( ( ~ ( ord_less @ int @ SV43 @ SV121 ) )
= $true )
| ( ( ord_less @ int @ ( bit0 @ SV43 ) @ ( bit0 @ SV121 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[909]) ).
thf(984,plain,
! [SV45: $i] :
( ( ( ( semiring_1_of_nat @ int @ SV45 )
= ( zero_zero @ int ) )
= $false )
| ( ( SV45
= ( zero_zero @ nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[910]) ).
thf(985,plain,
! [SV45: $i] :
( ( ( SV45
= ( zero_zero @ nat ) )
= $false )
| ( ( ( semiring_1_of_nat @ int @ SV45 )
= ( zero_zero @ int ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[911]) ).
thf(986,plain,
! [SV122: $i,SV47: $i] :
( ( ( ( bit1 @ SV47 )
!= ( bit1 @ SV122 ) )
= $true )
| ( ( SV47 = SV122 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[912]) ).
thf(987,plain,
! [SV122: $i,SV47: $i] :
( ( ( SV47 != SV122 )
= $true )
| ( ( ( bit1 @ SV47 )
= ( bit1 @ SV122 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[913]) ).
thf(988,plain,
! [SV48: $i,SV123: $i] :
( ( ( ~ ( ord_less @ int @ SV123 @ pls ) )
= $true )
| ( ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV123 ) @ ( number_number_of @ nat @ SV48 ) )
= ( number_number_of @ nat @ SV48 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[914]) ).
thf(989,plain,
! [SV48: $i,SV123: $i] :
( ( ( ~ ~ ( ord_less @ int @ SV123 @ pls ) )
= $true )
| ( ( ~ ( ~ ( ~ ( ord_less @ int @ SV48 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV123 ) @ ( number_number_of @ nat @ SV48 ) )
= ( number_number_of @ nat @ SV123 ) ) )
| ~ ( ~ ~ ( ord_less @ int @ SV48 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV123 ) @ ( number_number_of @ nat @ SV48 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SV123 @ SV48 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[915]) ).
thf(990,plain,
! [SV52: $i] :
( ( ( ord_less @ int @ ( bit0 @ SV52 ) @ pls )
= $false )
| ( ( ord_less @ int @ SV52 @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[917]) ).
thf(991,plain,
! [SV52: $i] :
( ( ( ord_less @ int @ SV52 @ pls )
= $false )
| ( ( ord_less @ int @ ( bit0 @ SV52 ) @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[918]) ).
thf(992,plain,
! [SV126: $i,SV55: $i] :
( ( ( ~ ( ord_less @ nat @ ( ti @ nat @ SV55 ) @ SV126 ) )
= $true )
| ( ( ord_less @ nat @ SV55 @ SV126 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[920]) ).
thf(993,plain,
! [SV126: $i,SV55: $i] :
( ( ( ~ ( ord_less @ nat @ SV55 @ SV126 ) )
= $true )
| ( ( ord_less @ nat @ ( ti @ nat @ SV55 ) @ SV126 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[921]) ).
thf(994,plain,
! [SV127: $i,SV56: $i] :
( ( ( ~ ( ord_less @ nat @ SV56 @ ( ti @ nat @ SV127 ) ) )
= $true )
| ( ( ord_less @ nat @ SV56 @ SV127 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[922]) ).
thf(995,plain,
! [SV127: $i,SV56: $i] :
( ( ( ~ ( ord_less @ nat @ SV56 @ SV127 ) )
= $true )
| ( ( ord_less @ nat @ SV56 @ ( ti @ nat @ SV127 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[923]) ).
thf(996,plain,
! [SV59: $i] :
( ( ( power @ SV59 )
= $false )
| ( ( ~ ( semiring_0 @ SV59 ) )
= $true )
| ( ( ( ti @ SV59 @ ( one_one @ SV59 ) )
= ( one_one @ SV59 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[926]) ).
thf(997,plain,
! [SV129: $i,SV60: $i,SV153: $i] :
( ( ( ~ ( power @ SV153 )
| ~ ( semiring_0 @ SV153 ) )
= $true )
| ( ( ( ti @ SV153 @ ( power_power @ SV153 @ SV60 @ SV129 ) )
= ( power_power @ SV153 @ SV60 @ SV129 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[927]) ).
thf(998,plain,
! [SV165: $i,SV61: $i] :
( ( ( ~ ( ~ ( ord_less @ SV61 @ ( zero_zero @ SV61 ) @ ( power_power @ SV61 @ SV165 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ( ( ti @ SV61 @ SV165 )
!= ( zero_zero @ SV61 ) ) ) )
= $false )
| ( ( linordered_idom @ SV61 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[928]) ).
thf(999,plain,
! [SV165: $i,SV61: $i] :
( ( ( ~ ( ~ ( ( ( ti @ SV61 @ SV165 )
!= ( zero_zero @ SV61 ) ) )
| ( ord_less @ SV61 @ ( zero_zero @ SV61 ) @ ( power_power @ SV61 @ SV165 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $false )
| ( ( linordered_idom @ SV61 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[928]) ).
thf(1000,plain,
! [SV62: $i] :
( ( ( number_ring @ SV62 )
= $false )
| ( ( ~ ( linordered_idom @ SV62 ) )
= $true )
| ( ( ! [SY241: $i,SY242: $i] :
~ ( ~ ( ~ ( ord_less @ SV62 @ ( number_number_of @ SV62 @ SY241 ) @ ( number_number_of @ SV62 @ SY242 ) )
| ( ord_less @ int @ SY241 @ SY242 ) )
| ~ ( ~ ( ord_less @ int @ SY241 @ SY242 )
| ( ord_less @ SV62 @ ( number_number_of @ SV62 @ SY241 ) @ ( number_number_of @ SV62 @ SY242 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[929]) ).
thf(1001,plain,
! [SV130: $i,SV64: $i] :
( ( ( ~ ( ord_less @ int @ ( bit1 @ SV64 ) @ ( bit0 @ SV130 ) ) )
= $true )
| ( ( ord_less @ int @ SV64 @ SV130 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[930]) ).
thf(1002,plain,
! [SV130: $i,SV64: $i] :
( ( ( ~ ( ord_less @ int @ SV64 @ SV130 ) )
= $true )
| ( ( ord_less @ int @ ( bit1 @ SV64 ) @ ( bit0 @ SV130 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[931]) ).
thf(1003,plain,
! [SV132: $i,SV66: $i] :
( ( ( ( bit0 @ SV66 )
!= ( bit0 @ SV132 ) )
= $true )
| ( ( SV66 = SV132 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[932]) ).
thf(1004,plain,
! [SV132: $i,SV66: $i] :
( ( ( SV66 != SV132 )
= $true )
| ( ( ( bit0 @ SV66 )
= ( bit0 @ SV132 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[933]) ).
thf(1005,plain,
! [SV133: $i,SV67: $i] :
( ( ( ( semiring_1_of_nat @ int @ SV67 )
!= ( semiring_1_of_nat @ int @ SV133 ) )
= $true )
| ( ( SV67 = SV133 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[934]) ).
thf(1006,plain,
! [SV133: $i,SV67: $i] :
( ( ( SV67 != SV133 )
= $true )
| ( ( ( semiring_1_of_nat @ int @ SV67 )
= ( semiring_1_of_nat @ int @ SV133 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[935]) ).
thf(1007,plain,
! [SV68: $i] :
( ( ( ord_less @ int @ pls @ ( bit0 @ SV68 ) )
= $false )
| ( ( ord_less @ int @ pls @ SV68 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[936]) ).
thf(1008,plain,
! [SV68: $i] :
( ( ( ord_less @ int @ pls @ SV68 )
= $false )
| ( ( ord_less @ int @ pls @ ( bit0 @ SV68 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[937]) ).
thf(1009,plain,
! [SV69: $i] :
( ( ( number_ring @ SV69 )
= $false )
| ( ( ~ ( linordered_idom @ SV69 ) )
= $true )
| ( ( ! [SY248: $i] :
~ ( ~ ( ~ ( ord_less @ SV69 @ ( number_number_of @ SV69 @ SY248 ) @ ( zero_zero @ SV69 ) )
| ( ord_less @ int @ SY248 @ pls ) )
| ~ ( ~ ( ord_less @ int @ SY248 @ pls )
| ( ord_less @ SV69 @ ( number_number_of @ SV69 @ SY248 ) @ ( zero_zero @ SV69 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[938]) ).
thf(1010,plain,
! [SV71: $i] :
( ( ( power @ SV71 )
= $false )
| ( ( ~ ( semiring_0 @ SV71 ) )
= $true )
| ( ( ( ti @ SV71 @ ( zero_zero @ SV71 ) )
= ( zero_zero @ SV71 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[940]) ).
thf(1011,plain,
! [SV135: $i,SV72: $i,SV155: $i] :
( ( ( ~ ( power @ SV155 )
| ~ ( semiring_0 @ SV155 ) )
= $true )
| ( ( ( power_power @ SV155 @ ( ti @ SV155 @ SV72 ) @ SV135 )
= ( power_power @ SV155 @ SV72 @ SV135 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[941]) ).
thf(1012,plain,
! [SV73: $i] :
( ( ( number_ring @ SV73 )
= $false )
| ( ( ~ ( linordered_idom @ SV73 ) )
= $true )
| ( ( ! [SY253: $i] :
~ ( ~ ( ~ ( ord_less @ SV73 @ ( one_one @ SV73 ) @ ( number_number_of @ SV73 @ SY253 ) )
| ( ord_less @ int @ ( bit1 @ pls ) @ SY253 ) )
| ~ ( ~ ( ord_less @ int @ ( bit1 @ pls ) @ SY253 )
| ( ord_less @ SV73 @ ( one_one @ SV73 ) @ ( number_number_of @ SV73 @ SY253 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[942]) ).
thf(1013,plain,
! [SV168: $i,SV75: $i] :
( ( ( ~ ( ( ( plus_plus @ SV75 @ SV168 @ SV168 )
!= ( zero_zero @ SV75 ) )
| ( ( ti @ SV75 @ SV168 )
= ( zero_zero @ SV75 ) ) ) )
= $false )
| ( ( linord219039673up_add @ SV75 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[943]) ).
thf(1014,plain,
! [SV168: $i,SV75: $i] :
( ( ( ~ ( ( ( ti @ SV75 @ SV168 )
!= ( zero_zero @ SV75 ) )
| ( ( plus_plus @ SV75 @ SV168 @ SV168 )
= ( zero_zero @ SV75 ) ) ) )
= $false )
| ( ( linord219039673up_add @ SV75 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[943]) ).
thf(1015,plain,
! [SV76: $i] :
( ( ( number_ring @ SV76 )
= $false )
| ( ( ~ ( linordered_idom @ SV76 ) )
= $true )
| ( ( ! [SY256: $i] :
~ ( ~ ( ~ ( ord_less @ SV76 @ ( zero_zero @ SV76 ) @ ( number_number_of @ SV76 @ SY256 ) )
| ( ord_less @ int @ pls @ SY256 ) )
| ~ ( ~ ( ord_less @ int @ pls @ SY256 )
| ( ord_less @ SV76 @ ( zero_zero @ SV76 ) @ ( number_number_of @ SV76 @ SY256 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[944]) ).
thf(1016,plain,
! [SV177: $i,SV170: $i,SV78: $i] :
( ( ( ~ ( ~ ( ord_less @ SV78 @ ( zero_zero @ SV78 ) @ ( plus_plus @ SV78 @ ( power_power @ SV78 @ SV170 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV78 @ SV177 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
| ( ( ti @ SV78 @ SV170 )
!= ( zero_zero @ SV78 ) )
| ( ( ti @ SV78 @ SV177 )
!= ( zero_zero @ SV78 ) ) )
| ~ ( ~ ( ( ( ti @ SV78 @ SV170 )
!= ( zero_zero @ SV78 ) )
| ( ( ti @ SV78 @ SV177 )
!= ( zero_zero @ SV78 ) ) )
| ( ord_less @ SV78 @ ( zero_zero @ SV78 ) @ ( plus_plus @ SV78 @ ( power_power @ SV78 @ SV170 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV78 @ SV177 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) )
= $false )
| ( ( linordered_idom @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[946]) ).
thf(1017,plain,
! [SV136: $i,SV80: $i] :
( ( ( ~ ( ord_less @ int @ ( bit1 @ SV80 ) @ ( bit1 @ SV136 ) ) )
= $true )
| ( ( ord_less @ int @ SV80 @ SV136 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[947]) ).
thf(1018,plain,
! [SV136: $i,SV80: $i] :
( ( ( ~ ( ord_less @ int @ SV80 @ SV136 ) )
= $true )
| ( ( ord_less @ int @ ( bit1 @ SV80 ) @ ( bit1 @ SV136 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[948]) ).
thf(1019,plain,
! [SV178: $i,SV171: $i,SV81: $i] :
( ( ( ~ ( ( ( number_number_of @ SV81 @ SV171 )
!= ( ti @ SV81 @ SV178 ) )
| ( ( ti @ SV81 @ SV178 )
= ( number_number_of @ SV81 @ SV171 ) ) )
| ~ ( ( ( ti @ SV81 @ SV178 )
!= ( number_number_of @ SV81 @ SV171 ) )
| ( ( number_number_of @ SV81 @ SV171 )
= ( ti @ SV81 @ SV178 ) ) ) )
= $false )
| ( ( number @ SV81 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[949]) ).
thf(1020,plain,
! [SV85: $i] :
( ( ( number_ring @ SV85 )
= $false )
| ( ( ~ ( linordered_idom @ SV85 ) )
= $true )
| ( ( ! [SY266: $i] :
~ ( ~ ( ~ ( ord_less @ SV85 @ ( number_number_of @ SV85 @ SY266 ) @ ( one_one @ SV85 ) )
| ( ord_less @ int @ SY266 @ ( bit1 @ pls ) ) )
| ~ ( ~ ( ord_less @ int @ SY266 @ ( bit1 @ pls ) )
| ( ord_less @ SV85 @ ( number_number_of @ SV85 @ SY266 ) @ ( one_one @ SV85 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[951]) ).
thf(1021,plain,
! [SV87: $i] :
( ( ( number_ring @ SV87 )
= $false )
| ( ( ~ ( ring_char_0 @ SV87 ) )
= $true )
| ( ( ! [SY267: $i,SY268: $i] :
~ ( ~ ( ( ( number_number_of @ SV87 @ SY267 )
!= ( number_number_of @ SV87 @ SY268 ) )
| ( SY267 = SY268 ) )
| ~ ( ( SY267 != SY268 )
| ( ( number_number_of @ SV87 @ SY267 )
= ( number_number_of @ SV87 @ SY268 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[952]) ).
thf(1022,plain,
! [SV139: $i,SV88: $i] :
( ( ( ~ ( ord_less @ int @ ( bit1 @ SV88 ) @ ( bit1 @ SV139 ) ) )
= $true )
| ( ( ord_less @ int @ SV88 @ SV139 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[953]) ).
thf(1023,plain,
! [SV139: $i,SV88: $i] :
( ( ( ~ ( ord_less @ int @ SV88 @ SV139 ) )
= $true )
| ( ( ord_less @ int @ ( bit1 @ SV88 ) @ ( bit1 @ SV139 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[954]) ).
thf(1024,plain,
! [SV141: $i,SV90: $i] :
( ( ( ~ ( ord_less @ int @ ( bit0 @ SV90 ) @ ( bit0 @ SV141 ) ) )
= $true )
| ( ( ord_less @ int @ SV90 @ SV141 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[955]) ).
thf(1025,plain,
! [SV141: $i,SV90: $i] :
( ( ( ~ ( ord_less @ int @ SV90 @ SV141 ) )
= $true )
| ( ( ord_less @ int @ ( bit0 @ SV90 ) @ ( bit0 @ SV141 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[956]) ).
thf(1026,plain,
! [SV172: $i,SV91: $i] :
( ( ( ~ ( ( ( power_power @ SV91 @ SV172 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= ( zero_zero @ SV91 ) )
| ( ( ti @ SV91 @ SV172 )
= ( zero_zero @ SV91 ) ) ) )
= $false )
| ( ( ring_11004092258visors @ SV91 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[957]) ).
thf(1027,plain,
! [SV172: $i,SV91: $i] :
( ( ( ~ ( ( ( ti @ SV91 @ SV172 )
!= ( zero_zero @ SV91 ) )
| ( ( power_power @ SV91 @ SV172 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SV91 ) ) ) )
= $false )
| ( ( ring_11004092258visors @ SV91 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[957]) ).
thf(1028,plain,
! [SV92: $i] :
( ( ( ( bit0 @ SV92 )
= pls )
= $false )
| ( ( SV92 = pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[958]) ).
thf(1029,plain,
! [SV92: $i] :
( ( ( SV92 = pls )
= $false )
| ( ( ( bit0 @ SV92 )
= pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[959]) ).
thf(1030,plain,
! [SV94: $i] :
( ( ( ord_less @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ SV94 ) @ SV94 ) @ ( zero_zero @ int ) )
= $false )
| ( ( ord_less @ int @ SV94 @ ( zero_zero @ int ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[960]) ).
thf(1031,plain,
! [SV94: $i] :
( ( ( ord_less @ int @ SV94 @ ( zero_zero @ int ) )
= $false )
| ( ( ord_less @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ SV94 ) @ SV94 ) @ ( zero_zero @ int ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[961]) ).
thf(1032,plain,
! [SV95: $i] :
( ( ( ord_less @ int @ ( bit1 @ SV95 ) @ ( zero_zero @ int ) )
= $false )
| ( ( ord_less @ int @ SV95 @ ( zero_zero @ int ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[962]) ).
thf(1033,plain,
! [SV95: $i] :
( ( ( ord_less @ int @ SV95 @ ( zero_zero @ int ) )
= $false )
| ( ( ord_less @ int @ ( bit1 @ SV95 ) @ ( zero_zero @ int ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[963]) ).
thf(1034,plain,
! [SV142: $i,SV100: $i] :
( ( ( ~ ( ord_less @ int @ ( bit1 @ SV100 ) @ ( bit0 @ SV142 ) ) )
= $true )
| ( ( ord_less @ int @ SV100 @ SV142 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[964]) ).
thf(1035,plain,
! [SV142: $i,SV100: $i] :
( ( ( ~ ( ord_less @ int @ SV100 @ SV142 ) )
= $true )
| ( ( ord_less @ int @ ( bit1 @ SV100 ) @ ( bit0 @ SV142 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[965]) ).
thf(1036,plain,
! [SV143: $i,SV101: $i] :
( ( ( ~ ( ord_less @ int @ SV101 @ ( plus_plus @ int @ SV143 @ ( one_one @ int ) ) ) )
= $true )
| ( ( ( ord_less @ int @ SV101 @ SV143 )
| ( SV101 = SV143 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[966]) ).
thf(1037,plain,
! [SV143: $i,SV101: $i] :
( ( ( ~ ( ( ord_less @ int @ SV101 @ SV143 )
| ( SV101 = SV143 ) ) )
= $true )
| ( ( ord_less @ int @ SV101 @ ( plus_plus @ int @ SV143 @ ( one_one @ int ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[967]) ).
thf(1038,plain,
! [SV25: $i] :
( ( ( semiring_0 @ SV25 )
= $false )
| ( ( power @ SV25 )
= $false )
| ( ( ! [SY203: $i] :
~ ( ~ ( ( ( number_number_of @ nat @ SY203 )
!= ( zero_zero @ nat ) )
| ( ( power_power @ SV25 @ ( zero_zero @ SV25 ) @ ( number_number_of @ nat @ SY203 ) )
= ( one_one @ SV25 ) ) )
| ~ ( ~ ( ( ( number_number_of @ nat @ SY203 )
!= ( zero_zero @ nat ) ) )
| ( ( power_power @ SV25 @ ( zero_zero @ SV25 ) @ ( number_number_of @ nat @ SY203 ) )
= ( zero_zero @ SV25 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[968]) ).
thf(1039,plain,
! [SV173: $i,SV157: $i,SV26: $i] :
( ( ( ~ ( ( ( plus_plus @ SV26 @ ( power_power @ SV26 @ SV157 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV26 @ SV173 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV26 ) )
| ~ ( ( ( ti @ SV26 @ SV157 )
!= ( zero_zero @ SV26 ) )
| ( ( ti @ SV26 @ SV173 )
!= ( zero_zero @ SV26 ) ) ) ) )
= $false )
| ( ( linordered_idom @ SV26 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[969]) ).
thf(1040,plain,
! [SV173: $i,SV157: $i,SV26: $i] :
( ( ( ~ ( ~ ~ ( ( ( ti @ SV26 @ SV157 )
!= ( zero_zero @ SV26 ) )
| ( ( ti @ SV26 @ SV173 )
!= ( zero_zero @ SV26 ) ) )
| ( ( plus_plus @ SV26 @ ( power_power @ SV26 @ SV157 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV26 @ SV173 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV26 ) ) ) )
= $false )
| ( ( linordered_idom @ SV26 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[969]) ).
thf(1041,plain,
! [SV115: $i,SV32: $i,SV148: $i] :
( ( ( ~ ( power @ SV148 ) )
= $true )
| ( ( ~ ( semiring_0 @ SV148 ) )
= $true )
| ( ( ( power_power @ SV148 @ SV32 @ ( ti @ nat @ SV115 ) )
= ( power_power @ SV148 @ SV32 @ SV115 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[972]) ).
thf(1042,plain,
! [SV120: $i,SV40: $i] :
( ( ( ord_less @ int @ ( number_number_of @ int @ SV40 ) @ ( number_number_of @ int @ SV120 ) )
= $false )
| ( ( ord_less @ int @ SV40 @ SV120 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[976]) ).
thf(1043,plain,
! [SV120: $i,SV40: $i] :
( ( ( ord_less @ int @ SV40 @ SV120 )
= $false )
| ( ( ord_less @ int @ ( number_number_of @ int @ SV40 ) @ ( number_number_of @ int @ SV120 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[977]) ).
thf(1044,plain,
! [SV160: $i,SV41: $i] :
( ( ( ~ ( ord_less @ SV41 @ ( plus_plus @ SV41 @ SV160 @ SV160 ) @ ( zero_zero @ SV41 ) )
| ( ord_less @ SV41 @ SV160 @ ( zero_zero @ SV41 ) ) )
= $true )
| ( ( linordered_idom @ SV41 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[978]) ).
thf(1045,plain,
! [SV160: $i,SV41: $i] :
( ( ( ~ ( ord_less @ SV41 @ SV160 @ ( zero_zero @ SV41 ) )
| ( ord_less @ SV41 @ ( plus_plus @ SV41 @ SV160 @ SV160 ) @ ( zero_zero @ SV41 ) ) )
= $true )
| ( ( linordered_idom @ SV41 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[979]) ).
thf(1046,plain,
! [SV121: $i,SV43: $i] :
( ( ( ord_less @ int @ ( bit0 @ SV43 ) @ ( bit0 @ SV121 ) )
= $false )
| ( ( ord_less @ int @ SV43 @ SV121 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[982]) ).
thf(1047,plain,
! [SV121: $i,SV43: $i] :
( ( ( ord_less @ int @ SV43 @ SV121 )
= $false )
| ( ( ord_less @ int @ ( bit0 @ SV43 ) @ ( bit0 @ SV121 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[983]) ).
thf(1048,plain,
! [SV122: $i,SV47: $i] :
( ( ( ( bit1 @ SV47 )
= ( bit1 @ SV122 ) )
= $false )
| ( ( SV47 = SV122 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[986]) ).
thf(1049,plain,
! [SV122: $i,SV47: $i] :
( ( ( SV47 = SV122 )
= $false )
| ( ( ( bit1 @ SV47 )
= ( bit1 @ SV122 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[987]) ).
thf(1050,plain,
! [SV48: $i,SV123: $i] :
( ( ( ord_less @ int @ SV123 @ pls )
= $false )
| ( ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV123 ) @ ( number_number_of @ nat @ SV48 ) )
= ( number_number_of @ nat @ SV48 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[988]) ).
thf(1051,plain,
! [SV48: $i,SV123: $i] :
( ( ( ~ ( ord_less @ int @ SV123 @ pls ) )
= $false )
| ( ( ~ ( ~ ( ~ ( ord_less @ int @ SV48 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV123 ) @ ( number_number_of @ nat @ SV48 ) )
= ( number_number_of @ nat @ SV123 ) ) )
| ~ ( ~ ~ ( ord_less @ int @ SV48 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV123 ) @ ( number_number_of @ nat @ SV48 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SV123 @ SV48 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[989]) ).
thf(1052,plain,
! [SV126: $i,SV55: $i] :
( ( ( ord_less @ nat @ ( ti @ nat @ SV55 ) @ SV126 )
= $false )
| ( ( ord_less @ nat @ SV55 @ SV126 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[992]) ).
thf(1053,plain,
! [SV126: $i,SV55: $i] :
( ( ( ord_less @ nat @ SV55 @ SV126 )
= $false )
| ( ( ord_less @ nat @ ( ti @ nat @ SV55 ) @ SV126 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[993]) ).
thf(1054,plain,
! [SV127: $i,SV56: $i] :
( ( ( ord_less @ nat @ SV56 @ ( ti @ nat @ SV127 ) )
= $false )
| ( ( ord_less @ nat @ SV56 @ SV127 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[994]) ).
thf(1055,plain,
! [SV127: $i,SV56: $i] :
( ( ( ord_less @ nat @ SV56 @ SV127 )
= $false )
| ( ( ord_less @ nat @ SV56 @ ( ti @ nat @ SV127 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[995]) ).
thf(1056,plain,
! [SV59: $i] :
( ( ( semiring_0 @ SV59 )
= $false )
| ( ( power @ SV59 )
= $false )
| ( ( ( ti @ SV59 @ ( one_one @ SV59 ) )
= ( one_one @ SV59 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[996]) ).
thf(1057,plain,
! [SV129: $i,SV60: $i,SV153: $i] :
( ( ( ~ ( power @ SV153 ) )
= $true )
| ( ( ~ ( semiring_0 @ SV153 ) )
= $true )
| ( ( ( ti @ SV153 @ ( power_power @ SV153 @ SV60 @ SV129 ) )
= ( power_power @ SV153 @ SV60 @ SV129 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[997]) ).
thf(1058,plain,
! [SV165: $i,SV61: $i] :
( ( ( ~ ( ord_less @ SV61 @ ( zero_zero @ SV61 ) @ ( power_power @ SV61 @ SV165 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ( ( ti @ SV61 @ SV165 )
!= ( zero_zero @ SV61 ) ) )
= $true )
| ( ( linordered_idom @ SV61 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[998]) ).
thf(1059,plain,
! [SV165: $i,SV61: $i] :
( ( ( ~ ( ( ( ti @ SV61 @ SV165 )
!= ( zero_zero @ SV61 ) ) )
| ( ord_less @ SV61 @ ( zero_zero @ SV61 ) @ ( power_power @ SV61 @ SV165 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true )
| ( ( linordered_idom @ SV61 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[999]) ).
thf(1060,plain,
! [SV62: $i] :
( ( ( linordered_idom @ SV62 )
= $false )
| ( ( number_ring @ SV62 )
= $false )
| ( ( ! [SY241: $i,SY242: $i] :
~ ( ~ ( ~ ( ord_less @ SV62 @ ( number_number_of @ SV62 @ SY241 ) @ ( number_number_of @ SV62 @ SY242 ) )
| ( ord_less @ int @ SY241 @ SY242 ) )
| ~ ( ~ ( ord_less @ int @ SY241 @ SY242 )
| ( ord_less @ SV62 @ ( number_number_of @ SV62 @ SY241 ) @ ( number_number_of @ SV62 @ SY242 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1000]) ).
thf(1061,plain,
! [SV130: $i,SV64: $i] :
( ( ( ord_less @ int @ ( bit1 @ SV64 ) @ ( bit0 @ SV130 ) )
= $false )
| ( ( ord_less @ int @ SV64 @ SV130 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1001]) ).
thf(1062,plain,
! [SV130: $i,SV64: $i] :
( ( ( ord_less @ int @ SV64 @ SV130 )
= $false )
| ( ( ord_less @ int @ ( bit1 @ SV64 ) @ ( bit0 @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1002]) ).
thf(1063,plain,
! [SV132: $i,SV66: $i] :
( ( ( ( bit0 @ SV66 )
= ( bit0 @ SV132 ) )
= $false )
| ( ( SV66 = SV132 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1003]) ).
thf(1064,plain,
! [SV132: $i,SV66: $i] :
( ( ( SV66 = SV132 )
= $false )
| ( ( ( bit0 @ SV66 )
= ( bit0 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1004]) ).
thf(1065,plain,
! [SV133: $i,SV67: $i] :
( ( ( ( semiring_1_of_nat @ int @ SV67 )
= ( semiring_1_of_nat @ int @ SV133 ) )
= $false )
| ( ( SV67 = SV133 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1005]) ).
thf(1066,plain,
! [SV133: $i,SV67: $i] :
( ( ( SV67 = SV133 )
= $false )
| ( ( ( semiring_1_of_nat @ int @ SV67 )
= ( semiring_1_of_nat @ int @ SV133 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1006]) ).
thf(1067,plain,
! [SV69: $i] :
( ( ( linordered_idom @ SV69 )
= $false )
| ( ( number_ring @ SV69 )
= $false )
| ( ( ! [SY248: $i] :
~ ( ~ ( ~ ( ord_less @ SV69 @ ( number_number_of @ SV69 @ SY248 ) @ ( zero_zero @ SV69 ) )
| ( ord_less @ int @ SY248 @ pls ) )
| ~ ( ~ ( ord_less @ int @ SY248 @ pls )
| ( ord_less @ SV69 @ ( number_number_of @ SV69 @ SY248 ) @ ( zero_zero @ SV69 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1009]) ).
thf(1068,plain,
! [SV71: $i] :
( ( ( semiring_0 @ SV71 )
= $false )
| ( ( power @ SV71 )
= $false )
| ( ( ( ti @ SV71 @ ( zero_zero @ SV71 ) )
= ( zero_zero @ SV71 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1010]) ).
thf(1069,plain,
! [SV135: $i,SV72: $i,SV155: $i] :
( ( ( ~ ( power @ SV155 ) )
= $true )
| ( ( ~ ( semiring_0 @ SV155 ) )
= $true )
| ( ( ( power_power @ SV155 @ ( ti @ SV155 @ SV72 ) @ SV135 )
= ( power_power @ SV155 @ SV72 @ SV135 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1011]) ).
thf(1070,plain,
! [SV73: $i] :
( ( ( linordered_idom @ SV73 )
= $false )
| ( ( number_ring @ SV73 )
= $false )
| ( ( ! [SY253: $i] :
~ ( ~ ( ~ ( ord_less @ SV73 @ ( one_one @ SV73 ) @ ( number_number_of @ SV73 @ SY253 ) )
| ( ord_less @ int @ ( bit1 @ pls ) @ SY253 ) )
| ~ ( ~ ( ord_less @ int @ ( bit1 @ pls ) @ SY253 )
| ( ord_less @ SV73 @ ( one_one @ SV73 ) @ ( number_number_of @ SV73 @ SY253 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1012]) ).
thf(1071,plain,
! [SV168: $i,SV75: $i] :
( ( ( ( ( plus_plus @ SV75 @ SV168 @ SV168 )
!= ( zero_zero @ SV75 ) )
| ( ( ti @ SV75 @ SV168 )
= ( zero_zero @ SV75 ) ) )
= $true )
| ( ( linord219039673up_add @ SV75 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1013]) ).
thf(1072,plain,
! [SV168: $i,SV75: $i] :
( ( ( ( ( ti @ SV75 @ SV168 )
!= ( zero_zero @ SV75 ) )
| ( ( plus_plus @ SV75 @ SV168 @ SV168 )
= ( zero_zero @ SV75 ) ) )
= $true )
| ( ( linord219039673up_add @ SV75 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1014]) ).
thf(1073,plain,
! [SV76: $i] :
( ( ( linordered_idom @ SV76 )
= $false )
| ( ( number_ring @ SV76 )
= $false )
| ( ( ! [SY256: $i] :
~ ( ~ ( ~ ( ord_less @ SV76 @ ( zero_zero @ SV76 ) @ ( number_number_of @ SV76 @ SY256 ) )
| ( ord_less @ int @ pls @ SY256 ) )
| ~ ( ~ ( ord_less @ int @ pls @ SY256 )
| ( ord_less @ SV76 @ ( zero_zero @ SV76 ) @ ( number_number_of @ SV76 @ SY256 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1015]) ).
thf(1074,plain,
! [SV177: $i,SV170: $i,SV78: $i] :
( ( ( ~ ( ~ ( ord_less @ SV78 @ ( zero_zero @ SV78 ) @ ( plus_plus @ SV78 @ ( power_power @ SV78 @ SV170 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV78 @ SV177 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
| ( ( ti @ SV78 @ SV170 )
!= ( zero_zero @ SV78 ) )
| ( ( ti @ SV78 @ SV177 )
!= ( zero_zero @ SV78 ) ) ) )
= $false )
| ( ( linordered_idom @ SV78 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1016]) ).
thf(1075,plain,
! [SV177: $i,SV170: $i,SV78: $i] :
( ( ( ~ ( ~ ( ( ( ti @ SV78 @ SV170 )
!= ( zero_zero @ SV78 ) )
| ( ( ti @ SV78 @ SV177 )
!= ( zero_zero @ SV78 ) ) )
| ( ord_less @ SV78 @ ( zero_zero @ SV78 ) @ ( plus_plus @ SV78 @ ( power_power @ SV78 @ SV170 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV78 @ SV177 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) )
= $false )
| ( ( linordered_idom @ SV78 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1016]) ).
thf(1076,plain,
! [SV136: $i,SV80: $i] :
( ( ( ord_less @ int @ ( bit1 @ SV80 ) @ ( bit1 @ SV136 ) )
= $false )
| ( ( ord_less @ int @ SV80 @ SV136 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1017]) ).
thf(1077,plain,
! [SV136: $i,SV80: $i] :
( ( ( ord_less @ int @ SV80 @ SV136 )
= $false )
| ( ( ord_less @ int @ ( bit1 @ SV80 ) @ ( bit1 @ SV136 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1018]) ).
thf(1078,plain,
! [SV178: $i,SV171: $i,SV81: $i] :
( ( ( ~ ( ( ( number_number_of @ SV81 @ SV171 )
!= ( ti @ SV81 @ SV178 ) )
| ( ( ti @ SV81 @ SV178 )
= ( number_number_of @ SV81 @ SV171 ) ) ) )
= $false )
| ( ( number @ SV81 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1019]) ).
thf(1079,plain,
! [SV171: $i,SV178: $i,SV81: $i] :
( ( ( ~ ( ( ( ti @ SV81 @ SV178 )
!= ( number_number_of @ SV81 @ SV171 ) )
| ( ( number_number_of @ SV81 @ SV171 )
= ( ti @ SV81 @ SV178 ) ) ) )
= $false )
| ( ( number @ SV81 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1019]) ).
thf(1080,plain,
! [SV85: $i] :
( ( ( linordered_idom @ SV85 )
= $false )
| ( ( number_ring @ SV85 )
= $false )
| ( ( ! [SY266: $i] :
~ ( ~ ( ~ ( ord_less @ SV85 @ ( number_number_of @ SV85 @ SY266 ) @ ( one_one @ SV85 ) )
| ( ord_less @ int @ SY266 @ ( bit1 @ pls ) ) )
| ~ ( ~ ( ord_less @ int @ SY266 @ ( bit1 @ pls ) )
| ( ord_less @ SV85 @ ( number_number_of @ SV85 @ SY266 ) @ ( one_one @ SV85 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1020]) ).
thf(1081,plain,
! [SV87: $i] :
( ( ( ring_char_0 @ SV87 )
= $false )
| ( ( number_ring @ SV87 )
= $false )
| ( ( ! [SY267: $i,SY268: $i] :
~ ( ~ ( ( ( number_number_of @ SV87 @ SY267 )
!= ( number_number_of @ SV87 @ SY268 ) )
| ( SY267 = SY268 ) )
| ~ ( ( SY267 != SY268 )
| ( ( number_number_of @ SV87 @ SY267 )
= ( number_number_of @ SV87 @ SY268 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1021]) ).
thf(1082,plain,
! [SV139: $i,SV88: $i] :
( ( ( ord_less @ int @ ( bit1 @ SV88 ) @ ( bit1 @ SV139 ) )
= $false )
| ( ( ord_less @ int @ SV88 @ SV139 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1022]) ).
thf(1083,plain,
! [SV139: $i,SV88: $i] :
( ( ( ord_less @ int @ SV88 @ SV139 )
= $false )
| ( ( ord_less @ int @ ( bit1 @ SV88 ) @ ( bit1 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1023]) ).
thf(1084,plain,
! [SV141: $i,SV90: $i] :
( ( ( ord_less @ int @ ( bit0 @ SV90 ) @ ( bit0 @ SV141 ) )
= $false )
| ( ( ord_less @ int @ SV90 @ SV141 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1024]) ).
thf(1085,plain,
! [SV141: $i,SV90: $i] :
( ( ( ord_less @ int @ SV90 @ SV141 )
= $false )
| ( ( ord_less @ int @ ( bit0 @ SV90 ) @ ( bit0 @ SV141 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1025]) ).
thf(1086,plain,
! [SV172: $i,SV91: $i] :
( ( ( ( ( power_power @ SV91 @ SV172 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= ( zero_zero @ SV91 ) )
| ( ( ti @ SV91 @ SV172 )
= ( zero_zero @ SV91 ) ) )
= $true )
| ( ( ring_11004092258visors @ SV91 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1026]) ).
thf(1087,plain,
! [SV172: $i,SV91: $i] :
( ( ( ( ( ti @ SV91 @ SV172 )
!= ( zero_zero @ SV91 ) )
| ( ( power_power @ SV91 @ SV172 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SV91 ) ) )
= $true )
| ( ( ring_11004092258visors @ SV91 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1027]) ).
thf(1088,plain,
! [SV142: $i,SV100: $i] :
( ( ( ord_less @ int @ ( bit1 @ SV100 ) @ ( bit0 @ SV142 ) )
= $false )
| ( ( ord_less @ int @ SV100 @ SV142 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1034]) ).
thf(1089,plain,
! [SV142: $i,SV100: $i] :
( ( ( ord_less @ int @ SV100 @ SV142 )
= $false )
| ( ( ord_less @ int @ ( bit1 @ SV100 ) @ ( bit0 @ SV142 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1035]) ).
thf(1090,plain,
! [SV143: $i,SV101: $i] :
( ( ( ord_less @ int @ SV101 @ ( plus_plus @ int @ SV143 @ ( one_one @ int ) ) )
= $false )
| ( ( ( ord_less @ int @ SV101 @ SV143 )
| ( SV101 = SV143 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1036]) ).
thf(1091,plain,
! [SV143: $i,SV101: $i] :
( ( ( ( ord_less @ int @ SV101 @ SV143 )
| ( SV101 = SV143 ) )
= $false )
| ( ( ord_less @ int @ SV101 @ ( plus_plus @ int @ SV143 @ ( one_one @ int ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1037]) ).
thf(1092,plain,
! [SV25: $i,SV180: $i] :
( ( ( ~ ( ~ ( ( ( number_number_of @ nat @ SV180 )
!= ( zero_zero @ nat ) )
| ( ( power_power @ SV25 @ ( zero_zero @ SV25 ) @ ( number_number_of @ nat @ SV180 ) )
= ( one_one @ SV25 ) ) )
| ~ ( ~ ( ( ( number_number_of @ nat @ SV180 )
!= ( zero_zero @ nat ) ) )
| ( ( power_power @ SV25 @ ( zero_zero @ SV25 ) @ ( number_number_of @ nat @ SV180 ) )
= ( zero_zero @ SV25 ) ) ) ) )
= $true )
| ( ( power @ SV25 )
= $false )
| ( ( semiring_0 @ SV25 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1038]) ).
thf(1093,plain,
! [SV173: $i,SV157: $i,SV26: $i] :
( ( ( ( ( plus_plus @ SV26 @ ( power_power @ SV26 @ SV157 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV26 @ SV173 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV26 ) )
| ~ ( ( ( ti @ SV26 @ SV157 )
!= ( zero_zero @ SV26 ) )
| ( ( ti @ SV26 @ SV173 )
!= ( zero_zero @ SV26 ) ) ) )
= $true )
| ( ( linordered_idom @ SV26 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1039]) ).
thf(1094,plain,
! [SV173: $i,SV157: $i,SV26: $i] :
( ( ( ~ ~ ( ( ( ti @ SV26 @ SV157 )
!= ( zero_zero @ SV26 ) )
| ( ( ti @ SV26 @ SV173 )
!= ( zero_zero @ SV26 ) ) )
| ( ( plus_plus @ SV26 @ ( power_power @ SV26 @ SV157 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV26 @ SV173 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV26 ) ) )
= $true )
| ( ( linordered_idom @ SV26 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1040]) ).
thf(1095,plain,
! [SV115: $i,SV32: $i,SV148: $i] :
( ( ( power @ SV148 )
= $false )
| ( ( ~ ( semiring_0 @ SV148 ) )
= $true )
| ( ( ( power_power @ SV148 @ SV32 @ ( ti @ nat @ SV115 ) )
= ( power_power @ SV148 @ SV32 @ SV115 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1041]) ).
thf(1096,plain,
! [SV160: $i,SV41: $i] :
( ( ( ~ ( ord_less @ SV41 @ ( plus_plus @ SV41 @ SV160 @ SV160 ) @ ( zero_zero @ SV41 ) ) )
= $true )
| ( ( ord_less @ SV41 @ SV160 @ ( zero_zero @ SV41 ) )
= $true )
| ( ( linordered_idom @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1044]) ).
thf(1097,plain,
! [SV160: $i,SV41: $i] :
( ( ( ~ ( ord_less @ SV41 @ SV160 @ ( zero_zero @ SV41 ) ) )
= $true )
| ( ( ord_less @ SV41 @ ( plus_plus @ SV41 @ SV160 @ SV160 ) @ ( zero_zero @ SV41 ) )
= $true )
| ( ( linordered_idom @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1045]) ).
thf(1098,plain,
! [SV48: $i,SV123: $i] :
( ( ( ord_less @ int @ SV123 @ pls )
= $true )
| ( ( ~ ( ~ ( ~ ( ord_less @ int @ SV48 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV123 ) @ ( number_number_of @ nat @ SV48 ) )
= ( number_number_of @ nat @ SV123 ) ) )
| ~ ( ~ ~ ( ord_less @ int @ SV48 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV123 ) @ ( number_number_of @ nat @ SV48 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SV123 @ SV48 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1051]) ).
thf(1099,plain,
! [SV129: $i,SV60: $i,SV153: $i] :
( ( ( power @ SV153 )
= $false )
| ( ( ~ ( semiring_0 @ SV153 ) )
= $true )
| ( ( ( ti @ SV153 @ ( power_power @ SV153 @ SV60 @ SV129 ) )
= ( power_power @ SV153 @ SV60 @ SV129 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1057]) ).
thf(1100,plain,
! [SV165: $i,SV61: $i] :
( ( ( ~ ( ord_less @ SV61 @ ( zero_zero @ SV61 ) @ ( power_power @ SV61 @ SV165 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true )
| ( ( ( ti @ SV61 @ SV165 )
!= ( zero_zero @ SV61 ) )
= $true )
| ( ( linordered_idom @ SV61 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1058]) ).
thf(1101,plain,
! [SV165: $i,SV61: $i] :
( ( ( ~ ( ( ( ti @ SV61 @ SV165 )
!= ( zero_zero @ SV61 ) ) ) )
= $true )
| ( ( ord_less @ SV61 @ ( zero_zero @ SV61 ) @ ( power_power @ SV61 @ SV165 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $true )
| ( ( linordered_idom @ SV61 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1059]) ).
thf(1102,plain,
! [SV181: $i,SV62: $i] :
( ( ( ! [SY296: $i] :
~ ( ~ ( ~ ( ord_less @ SV62 @ ( number_number_of @ SV62 @ SV181 ) @ ( number_number_of @ SV62 @ SY296 ) )
| ( ord_less @ int @ SV181 @ SY296 ) )
| ~ ( ~ ( ord_less @ int @ SV181 @ SY296 )
| ( ord_less @ SV62 @ ( number_number_of @ SV62 @ SV181 ) @ ( number_number_of @ SV62 @ SY296 ) ) ) ) )
= $true )
| ( ( number_ring @ SV62 )
= $false )
| ( ( linordered_idom @ SV62 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1060]) ).
thf(1103,plain,
! [SV182: $i,SV69: $i] :
( ( ( ~ ( ~ ( ~ ( ord_less @ SV69 @ ( number_number_of @ SV69 @ SV182 ) @ ( zero_zero @ SV69 ) )
| ( ord_less @ int @ SV182 @ pls ) )
| ~ ( ~ ( ord_less @ int @ SV182 @ pls )
| ( ord_less @ SV69 @ ( number_number_of @ SV69 @ SV182 ) @ ( zero_zero @ SV69 ) ) ) ) )
= $true )
| ( ( number_ring @ SV69 )
= $false )
| ( ( linordered_idom @ SV69 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1067]) ).
thf(1104,plain,
! [SV135: $i,SV72: $i,SV155: $i] :
( ( ( power @ SV155 )
= $false )
| ( ( ~ ( semiring_0 @ SV155 ) )
= $true )
| ( ( ( power_power @ SV155 @ ( ti @ SV155 @ SV72 ) @ SV135 )
= ( power_power @ SV155 @ SV72 @ SV135 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1069]) ).
thf(1105,plain,
! [SV183: $i,SV73: $i] :
( ( ( ~ ( ~ ( ~ ( ord_less @ SV73 @ ( one_one @ SV73 ) @ ( number_number_of @ SV73 @ SV183 ) )
| ( ord_less @ int @ ( bit1 @ pls ) @ SV183 ) )
| ~ ( ~ ( ord_less @ int @ ( bit1 @ pls ) @ SV183 )
| ( ord_less @ SV73 @ ( one_one @ SV73 ) @ ( number_number_of @ SV73 @ SV183 ) ) ) ) )
= $true )
| ( ( number_ring @ SV73 )
= $false )
| ( ( linordered_idom @ SV73 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1070]) ).
thf(1106,plain,
! [SV168: $i,SV75: $i] :
( ( ( ( plus_plus @ SV75 @ SV168 @ SV168 )
!= ( zero_zero @ SV75 ) )
= $true )
| ( ( ( ti @ SV75 @ SV168 )
= ( zero_zero @ SV75 ) )
= $true )
| ( ( linord219039673up_add @ SV75 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1071]) ).
thf(1107,plain,
! [SV168: $i,SV75: $i] :
( ( ( ( ti @ SV75 @ SV168 )
!= ( zero_zero @ SV75 ) )
= $true )
| ( ( ( plus_plus @ SV75 @ SV168 @ SV168 )
= ( zero_zero @ SV75 ) )
= $true )
| ( ( linord219039673up_add @ SV75 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1072]) ).
thf(1108,plain,
! [SV184: $i,SV76: $i] :
( ( ( ~ ( ~ ( ~ ( ord_less @ SV76 @ ( zero_zero @ SV76 ) @ ( number_number_of @ SV76 @ SV184 ) )
| ( ord_less @ int @ pls @ SV184 ) )
| ~ ( ~ ( ord_less @ int @ pls @ SV184 )
| ( ord_less @ SV76 @ ( zero_zero @ SV76 ) @ ( number_number_of @ SV76 @ SV184 ) ) ) ) )
= $true )
| ( ( number_ring @ SV76 )
= $false )
| ( ( linordered_idom @ SV76 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1073]) ).
thf(1109,plain,
! [SV177: $i,SV170: $i,SV78: $i] :
( ( ( ~ ( ord_less @ SV78 @ ( zero_zero @ SV78 ) @ ( plus_plus @ SV78 @ ( power_power @ SV78 @ SV170 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV78 @ SV177 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
| ( ( ti @ SV78 @ SV170 )
!= ( zero_zero @ SV78 ) )
| ( ( ti @ SV78 @ SV177 )
!= ( zero_zero @ SV78 ) ) )
= $true )
| ( ( linordered_idom @ SV78 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1074]) ).
thf(1110,plain,
! [SV177: $i,SV170: $i,SV78: $i] :
( ( ( ~ ( ( ( ti @ SV78 @ SV170 )
!= ( zero_zero @ SV78 ) )
| ( ( ti @ SV78 @ SV177 )
!= ( zero_zero @ SV78 ) ) )
| ( ord_less @ SV78 @ ( zero_zero @ SV78 ) @ ( plus_plus @ SV78 @ ( power_power @ SV78 @ SV170 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV78 @ SV177 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true )
| ( ( linordered_idom @ SV78 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1075]) ).
thf(1111,plain,
! [SV178: $i,SV171: $i,SV81: $i] :
( ( ( ( ( number_number_of @ SV81 @ SV171 )
!= ( ti @ SV81 @ SV178 ) )
| ( ( ti @ SV81 @ SV178 )
= ( number_number_of @ SV81 @ SV171 ) ) )
= $true )
| ( ( number @ SV81 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1078]) ).
thf(1112,plain,
! [SV171: $i,SV178: $i,SV81: $i] :
( ( ( ( ( ti @ SV81 @ SV178 )
!= ( number_number_of @ SV81 @ SV171 ) )
| ( ( number_number_of @ SV81 @ SV171 )
= ( ti @ SV81 @ SV178 ) ) )
= $true )
| ( ( number @ SV81 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1079]) ).
thf(1113,plain,
! [SV185: $i,SV85: $i] :
( ( ( ~ ( ~ ( ~ ( ord_less @ SV85 @ ( number_number_of @ SV85 @ SV185 ) @ ( one_one @ SV85 ) )
| ( ord_less @ int @ SV185 @ ( bit1 @ pls ) ) )
| ~ ( ~ ( ord_less @ int @ SV185 @ ( bit1 @ pls ) )
| ( ord_less @ SV85 @ ( number_number_of @ SV85 @ SV185 ) @ ( one_one @ SV85 ) ) ) ) )
= $true )
| ( ( number_ring @ SV85 )
= $false )
| ( ( linordered_idom @ SV85 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1080]) ).
thf(1114,plain,
! [SV186: $i,SV87: $i] :
( ( ( ! [SY297: $i] :
~ ( ~ ( ( ( number_number_of @ SV87 @ SV186 )
!= ( number_number_of @ SV87 @ SY297 ) )
| ( SV186 = SY297 ) )
| ~ ( ( SV186 != SY297 )
| ( ( number_number_of @ SV87 @ SV186 )
= ( number_number_of @ SV87 @ SY297 ) ) ) ) )
= $true )
| ( ( number_ring @ SV87 )
= $false )
| ( ( ring_char_0 @ SV87 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1081]) ).
thf(1115,plain,
! [SV172: $i,SV91: $i] :
( ( ( ( power_power @ SV91 @ SV172 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= ( zero_zero @ SV91 ) )
= $true )
| ( ( ( ti @ SV91 @ SV172 )
= ( zero_zero @ SV91 ) )
= $true )
| ( ( ring_11004092258visors @ SV91 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1086]) ).
thf(1116,plain,
! [SV172: $i,SV91: $i] :
( ( ( ( ti @ SV91 @ SV172 )
!= ( zero_zero @ SV91 ) )
= $true )
| ( ( ( power_power @ SV91 @ SV172 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SV91 ) )
= $true )
| ( ( ring_11004092258visors @ SV91 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1087]) ).
thf(1117,plain,
! [SV143: $i,SV101: $i] :
( ( ( ord_less @ int @ SV101 @ SV143 )
= $true )
| ( ( SV101 = SV143 )
= $true )
| ( ( ord_less @ int @ SV101 @ ( plus_plus @ int @ SV143 @ ( one_one @ int ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1090]) ).
thf(1118,plain,
! [SV143: $i,SV101: $i] :
( ( ( ord_less @ int @ SV101 @ SV143 )
= $false )
| ( ( ord_less @ int @ SV101 @ ( plus_plus @ int @ SV143 @ ( one_one @ int ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1091]) ).
thf(1119,plain,
! [SV143: $i,SV101: $i] :
( ( ( SV101 = SV143 )
= $false )
| ( ( ord_less @ int @ SV101 @ ( plus_plus @ int @ SV143 @ ( one_one @ int ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1091]) ).
thf(1120,plain,
! [SV25: $i,SV180: $i] :
( ( ( ~ ( ( ( number_number_of @ nat @ SV180 )
!= ( zero_zero @ nat ) )
| ( ( power_power @ SV25 @ ( zero_zero @ SV25 ) @ ( number_number_of @ nat @ SV180 ) )
= ( one_one @ SV25 ) ) )
| ~ ( ~ ( ( ( number_number_of @ nat @ SV180 )
!= ( zero_zero @ nat ) ) )
| ( ( power_power @ SV25 @ ( zero_zero @ SV25 ) @ ( number_number_of @ nat @ SV180 ) )
= ( zero_zero @ SV25 ) ) ) )
= $false )
| ( ( power @ SV25 )
= $false )
| ( ( semiring_0 @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1092]) ).
thf(1121,plain,
! [SV173: $i,SV157: $i,SV26: $i] :
( ( ( ( plus_plus @ SV26 @ ( power_power @ SV26 @ SV157 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV26 @ SV173 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV26 ) )
= $true )
| ( ( ~ ( ( ( ti @ SV26 @ SV157 )
!= ( zero_zero @ SV26 ) )
| ( ( ti @ SV26 @ SV173 )
!= ( zero_zero @ SV26 ) ) ) )
= $true )
| ( ( linordered_idom @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1093]) ).
thf(1122,plain,
! [SV173: $i,SV157: $i,SV26: $i] :
( ( ( ~ ~ ( ( ( ti @ SV26 @ SV157 )
!= ( zero_zero @ SV26 ) )
| ( ( ti @ SV26 @ SV173 )
!= ( zero_zero @ SV26 ) ) ) )
= $true )
| ( ( ( plus_plus @ SV26 @ ( power_power @ SV26 @ SV157 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV26 @ SV173 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV26 ) )
= $true )
| ( ( linordered_idom @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1094]) ).
thf(1123,plain,
! [SV115: $i,SV32: $i,SV148: $i] :
( ( ( semiring_0 @ SV148 )
= $false )
| ( ( power @ SV148 )
= $false )
| ( ( ( power_power @ SV148 @ SV32 @ ( ti @ nat @ SV115 ) )
= ( power_power @ SV148 @ SV32 @ SV115 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1095]) ).
thf(1124,plain,
! [SV160: $i,SV41: $i] :
( ( ( ord_less @ SV41 @ ( plus_plus @ SV41 @ SV160 @ SV160 ) @ ( zero_zero @ SV41 ) )
= $false )
| ( ( ord_less @ SV41 @ SV160 @ ( zero_zero @ SV41 ) )
= $true )
| ( ( linordered_idom @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1096]) ).
thf(1125,plain,
! [SV160: $i,SV41: $i] :
( ( ( ord_less @ SV41 @ SV160 @ ( zero_zero @ SV41 ) )
= $false )
| ( ( ord_less @ SV41 @ ( plus_plus @ SV41 @ SV160 @ SV160 ) @ ( zero_zero @ SV41 ) )
= $true )
| ( ( linordered_idom @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1097]) ).
thf(1126,plain,
! [SV123: $i,SV48: $i] :
( ( ( ~ ( ~ ( ord_less @ int @ SV48 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV123 ) @ ( number_number_of @ nat @ SV48 ) )
= ( number_number_of @ nat @ SV123 ) ) )
| ~ ( ~ ~ ( ord_less @ int @ SV48 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV123 ) @ ( number_number_of @ nat @ SV48 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SV123 @ SV48 ) ) ) ) )
= $false )
| ( ( ord_less @ int @ SV123 @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1098]) ).
thf(1127,plain,
! [SV129: $i,SV60: $i,SV153: $i] :
( ( ( semiring_0 @ SV153 )
= $false )
| ( ( power @ SV153 )
= $false )
| ( ( ( ti @ SV153 @ ( power_power @ SV153 @ SV60 @ SV129 ) )
= ( power_power @ SV153 @ SV60 @ SV129 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1099]) ).
thf(1128,plain,
! [SV165: $i,SV61: $i] :
( ( ( ord_less @ SV61 @ ( zero_zero @ SV61 ) @ ( power_power @ SV61 @ SV165 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $false )
| ( ( ( ti @ SV61 @ SV165 )
!= ( zero_zero @ SV61 ) )
= $true )
| ( ( linordered_idom @ SV61 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1100]) ).
thf(1129,plain,
! [SV165: $i,SV61: $i] :
( ( ( ( ti @ SV61 @ SV165 )
!= ( zero_zero @ SV61 ) )
= $false )
| ( ( ord_less @ SV61 @ ( zero_zero @ SV61 ) @ ( power_power @ SV61 @ SV165 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $true )
| ( ( linordered_idom @ SV61 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1101]) ).
thf(1130,plain,
! [SV187: $i,SV181: $i,SV62: $i] :
( ( ( ~ ( ~ ( ~ ( ord_less @ SV62 @ ( number_number_of @ SV62 @ SV181 ) @ ( number_number_of @ SV62 @ SV187 ) )
| ( ord_less @ int @ SV181 @ SV187 ) )
| ~ ( ~ ( ord_less @ int @ SV181 @ SV187 )
| ( ord_less @ SV62 @ ( number_number_of @ SV62 @ SV181 ) @ ( number_number_of @ SV62 @ SV187 ) ) ) ) )
= $true )
| ( ( number_ring @ SV62 )
= $false )
| ( ( linordered_idom @ SV62 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1102]) ).
thf(1131,plain,
! [SV182: $i,SV69: $i] :
( ( ( ~ ( ~ ( ord_less @ SV69 @ ( number_number_of @ SV69 @ SV182 ) @ ( zero_zero @ SV69 ) )
| ( ord_less @ int @ SV182 @ pls ) )
| ~ ( ~ ( ord_less @ int @ SV182 @ pls )
| ( ord_less @ SV69 @ ( number_number_of @ SV69 @ SV182 ) @ ( zero_zero @ SV69 ) ) ) )
= $false )
| ( ( number_ring @ SV69 )
= $false )
| ( ( linordered_idom @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1103]) ).
thf(1132,plain,
! [SV135: $i,SV72: $i,SV155: $i] :
( ( ( semiring_0 @ SV155 )
= $false )
| ( ( power @ SV155 )
= $false )
| ( ( ( power_power @ SV155 @ ( ti @ SV155 @ SV72 ) @ SV135 )
= ( power_power @ SV155 @ SV72 @ SV135 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1104]) ).
thf(1133,plain,
! [SV183: $i,SV73: $i] :
( ( ( ~ ( ~ ( ord_less @ SV73 @ ( one_one @ SV73 ) @ ( number_number_of @ SV73 @ SV183 ) )
| ( ord_less @ int @ ( bit1 @ pls ) @ SV183 ) )
| ~ ( ~ ( ord_less @ int @ ( bit1 @ pls ) @ SV183 )
| ( ord_less @ SV73 @ ( one_one @ SV73 ) @ ( number_number_of @ SV73 @ SV183 ) ) ) )
= $false )
| ( ( number_ring @ SV73 )
= $false )
| ( ( linordered_idom @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1105]) ).
thf(1134,plain,
! [SV168: $i,SV75: $i] :
( ( ( ( plus_plus @ SV75 @ SV168 @ SV168 )
= ( zero_zero @ SV75 ) )
= $false )
| ( ( ( ti @ SV75 @ SV168 )
= ( zero_zero @ SV75 ) )
= $true )
| ( ( linord219039673up_add @ SV75 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1106]) ).
thf(1135,plain,
! [SV168: $i,SV75: $i] :
( ( ( ( ti @ SV75 @ SV168 )
= ( zero_zero @ SV75 ) )
= $false )
| ( ( ( plus_plus @ SV75 @ SV168 @ SV168 )
= ( zero_zero @ SV75 ) )
= $true )
| ( ( linord219039673up_add @ SV75 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1107]) ).
thf(1136,plain,
! [SV184: $i,SV76: $i] :
( ( ( ~ ( ~ ( ord_less @ SV76 @ ( zero_zero @ SV76 ) @ ( number_number_of @ SV76 @ SV184 ) )
| ( ord_less @ int @ pls @ SV184 ) )
| ~ ( ~ ( ord_less @ int @ pls @ SV184 )
| ( ord_less @ SV76 @ ( zero_zero @ SV76 ) @ ( number_number_of @ SV76 @ SV184 ) ) ) )
= $false )
| ( ( number_ring @ SV76 )
= $false )
| ( ( linordered_idom @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1108]) ).
thf(1137,plain,
! [SV177: $i,SV170: $i,SV78: $i] :
( ( ( ~ ( ord_less @ SV78 @ ( zero_zero @ SV78 ) @ ( plus_plus @ SV78 @ ( power_power @ SV78 @ SV170 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV78 @ SV177 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true )
| ( ( ( ( ti @ SV78 @ SV170 )
!= ( zero_zero @ SV78 ) )
| ( ( ti @ SV78 @ SV177 )
!= ( zero_zero @ SV78 ) ) )
= $true )
| ( ( linordered_idom @ SV78 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1109]) ).
thf(1138,plain,
! [SV177: $i,SV170: $i,SV78: $i] :
( ( ( ~ ( ( ( ti @ SV78 @ SV170 )
!= ( zero_zero @ SV78 ) )
| ( ( ti @ SV78 @ SV177 )
!= ( zero_zero @ SV78 ) ) ) )
= $true )
| ( ( ord_less @ SV78 @ ( zero_zero @ SV78 ) @ ( plus_plus @ SV78 @ ( power_power @ SV78 @ SV170 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV78 @ SV177 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true )
| ( ( linordered_idom @ SV78 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1110]) ).
thf(1139,plain,
! [SV178: $i,SV171: $i,SV81: $i] :
( ( ( ( number_number_of @ SV81 @ SV171 )
!= ( ti @ SV81 @ SV178 ) )
= $true )
| ( ( ( ti @ SV81 @ SV178 )
= ( number_number_of @ SV81 @ SV171 ) )
= $true )
| ( ( number @ SV81 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1111]) ).
thf(1140,plain,
! [SV171: $i,SV178: $i,SV81: $i] :
( ( ( ( ti @ SV81 @ SV178 )
!= ( number_number_of @ SV81 @ SV171 ) )
= $true )
| ( ( ( number_number_of @ SV81 @ SV171 )
= ( ti @ SV81 @ SV178 ) )
= $true )
| ( ( number @ SV81 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1112]) ).
thf(1141,plain,
! [SV185: $i,SV85: $i] :
( ( ( ~ ( ~ ( ord_less @ SV85 @ ( number_number_of @ SV85 @ SV185 ) @ ( one_one @ SV85 ) )
| ( ord_less @ int @ SV185 @ ( bit1 @ pls ) ) )
| ~ ( ~ ( ord_less @ int @ SV185 @ ( bit1 @ pls ) )
| ( ord_less @ SV85 @ ( number_number_of @ SV85 @ SV185 ) @ ( one_one @ SV85 ) ) ) )
= $false )
| ( ( number_ring @ SV85 )
= $false )
| ( ( linordered_idom @ SV85 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1113]) ).
thf(1142,plain,
! [SV188: $i,SV186: $i,SV87: $i] :
( ( ( ~ ( ~ ( ( ( number_number_of @ SV87 @ SV186 )
!= ( number_number_of @ SV87 @ SV188 ) )
| ( SV186 = SV188 ) )
| ~ ( ( SV186 != SV188 )
| ( ( number_number_of @ SV87 @ SV186 )
= ( number_number_of @ SV87 @ SV188 ) ) ) ) )
= $true )
| ( ( number_ring @ SV87 )
= $false )
| ( ( ring_char_0 @ SV87 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1114]) ).
thf(1143,plain,
! [SV172: $i,SV91: $i] :
( ( ( ( power_power @ SV91 @ SV172 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SV91 ) )
= $false )
| ( ( ( ti @ SV91 @ SV172 )
= ( zero_zero @ SV91 ) )
= $true )
| ( ( ring_11004092258visors @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1115]) ).
thf(1144,plain,
! [SV172: $i,SV91: $i] :
( ( ( ( ti @ SV91 @ SV172 )
= ( zero_zero @ SV91 ) )
= $false )
| ( ( ( power_power @ SV91 @ SV172 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SV91 ) )
= $true )
| ( ( ring_11004092258visors @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1116]) ).
thf(1145,plain,
! [SV25: $i,SV180: $i] :
( ( ( ~ ( ( ( number_number_of @ nat @ SV180 )
!= ( zero_zero @ nat ) )
| ( ( power_power @ SV25 @ ( zero_zero @ SV25 ) @ ( number_number_of @ nat @ SV180 ) )
= ( one_one @ SV25 ) ) ) )
= $false )
| ( ( power @ SV25 )
= $false )
| ( ( semiring_0 @ SV25 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1120]) ).
thf(1146,plain,
! [SV25: $i,SV180: $i] :
( ( ( ~ ( ~ ( ( ( number_number_of @ nat @ SV180 )
!= ( zero_zero @ nat ) ) )
| ( ( power_power @ SV25 @ ( zero_zero @ SV25 ) @ ( number_number_of @ nat @ SV180 ) )
= ( zero_zero @ SV25 ) ) ) )
= $false )
| ( ( power @ SV25 )
= $false )
| ( ( semiring_0 @ SV25 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1120]) ).
thf(1147,plain,
! [SV173: $i,SV157: $i,SV26: $i] :
( ( ( ( plus_plus @ SV26 @ ( power_power @ SV26 @ SV157 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV26 @ SV173 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV26 ) )
= $false )
| ( ( ~ ( ( ( ti @ SV26 @ SV157 )
!= ( zero_zero @ SV26 ) )
| ( ( ti @ SV26 @ SV173 )
!= ( zero_zero @ SV26 ) ) ) )
= $true )
| ( ( linordered_idom @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1121]) ).
thf(1148,plain,
! [SV173: $i,SV157: $i,SV26: $i] :
( ( ( ~ ( ( ( ti @ SV26 @ SV157 )
!= ( zero_zero @ SV26 ) )
| ( ( ti @ SV26 @ SV173 )
!= ( zero_zero @ SV26 ) ) ) )
= $false )
| ( ( ( plus_plus @ SV26 @ ( power_power @ SV26 @ SV157 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV26 @ SV173 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV26 ) )
= $true )
| ( ( linordered_idom @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1122]) ).
thf(1149,plain,
! [SV123: $i,SV48: $i] :
( ( ( ~ ( ~ ( ord_less @ int @ SV48 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV123 ) @ ( number_number_of @ nat @ SV48 ) )
= ( number_number_of @ nat @ SV123 ) ) ) )
= $false )
| ( ( ord_less @ int @ SV123 @ pls )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1126]) ).
thf(1150,plain,
! [SV123: $i,SV48: $i] :
( ( ( ~ ( ~ ~ ( ord_less @ int @ SV48 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV123 ) @ ( number_number_of @ nat @ SV48 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SV123 @ SV48 ) ) ) ) )
= $false )
| ( ( ord_less @ int @ SV123 @ pls )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1126]) ).
thf(1151,plain,
! [SV165: $i,SV61: $i] :
( ( ( ( ti @ SV61 @ SV165 )
= ( zero_zero @ SV61 ) )
= $false )
| ( ( ord_less @ SV61 @ ( zero_zero @ SV61 ) @ ( power_power @ SV61 @ SV165 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $false )
| ( ( linordered_idom @ SV61 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1128]) ).
thf(1152,plain,
! [SV165: $i,SV61: $i] :
( ( ( ( ti @ SV61 @ SV165 )
= ( zero_zero @ SV61 ) )
= $true )
| ( ( ord_less @ SV61 @ ( zero_zero @ SV61 ) @ ( power_power @ SV61 @ SV165 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $true )
| ( ( linordered_idom @ SV61 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1129]) ).
thf(1153,plain,
! [SV187: $i,SV181: $i,SV62: $i] :
( ( ( ~ ( ~ ( ord_less @ SV62 @ ( number_number_of @ SV62 @ SV181 ) @ ( number_number_of @ SV62 @ SV187 ) )
| ( ord_less @ int @ SV181 @ SV187 ) )
| ~ ( ~ ( ord_less @ int @ SV181 @ SV187 )
| ( ord_less @ SV62 @ ( number_number_of @ SV62 @ SV181 ) @ ( number_number_of @ SV62 @ SV187 ) ) ) )
= $false )
| ( ( number_ring @ SV62 )
= $false )
| ( ( linordered_idom @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1130]) ).
thf(1154,plain,
! [SV182: $i,SV69: $i] :
( ( ( ~ ( ~ ( ord_less @ SV69 @ ( number_number_of @ SV69 @ SV182 ) @ ( zero_zero @ SV69 ) )
| ( ord_less @ int @ SV182 @ pls ) ) )
= $false )
| ( ( number_ring @ SV69 )
= $false )
| ( ( linordered_idom @ SV69 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1131]) ).
thf(1155,plain,
! [SV69: $i,SV182: $i] :
( ( ( ~ ( ~ ( ord_less @ int @ SV182 @ pls )
| ( ord_less @ SV69 @ ( number_number_of @ SV69 @ SV182 ) @ ( zero_zero @ SV69 ) ) ) )
= $false )
| ( ( number_ring @ SV69 )
= $false )
| ( ( linordered_idom @ SV69 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1131]) ).
thf(1156,plain,
! [SV183: $i,SV73: $i] :
( ( ( ~ ( ~ ( ord_less @ SV73 @ ( one_one @ SV73 ) @ ( number_number_of @ SV73 @ SV183 ) )
| ( ord_less @ int @ ( bit1 @ pls ) @ SV183 ) ) )
= $false )
| ( ( number_ring @ SV73 )
= $false )
| ( ( linordered_idom @ SV73 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1133]) ).
thf(1157,plain,
! [SV73: $i,SV183: $i] :
( ( ( ~ ( ~ ( ord_less @ int @ ( bit1 @ pls ) @ SV183 )
| ( ord_less @ SV73 @ ( one_one @ SV73 ) @ ( number_number_of @ SV73 @ SV183 ) ) ) )
= $false )
| ( ( number_ring @ SV73 )
= $false )
| ( ( linordered_idom @ SV73 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1133]) ).
thf(1158,plain,
! [SV184: $i,SV76: $i] :
( ( ( ~ ( ~ ( ord_less @ SV76 @ ( zero_zero @ SV76 ) @ ( number_number_of @ SV76 @ SV184 ) )
| ( ord_less @ int @ pls @ SV184 ) ) )
= $false )
| ( ( number_ring @ SV76 )
= $false )
| ( ( linordered_idom @ SV76 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1136]) ).
thf(1159,plain,
! [SV76: $i,SV184: $i] :
( ( ( ~ ( ~ ( ord_less @ int @ pls @ SV184 )
| ( ord_less @ SV76 @ ( zero_zero @ SV76 ) @ ( number_number_of @ SV76 @ SV184 ) ) ) )
= $false )
| ( ( number_ring @ SV76 )
= $false )
| ( ( linordered_idom @ SV76 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1136]) ).
thf(1160,plain,
! [SV177: $i,SV170: $i,SV78: $i] :
( ( ( ord_less @ SV78 @ ( zero_zero @ SV78 ) @ ( plus_plus @ SV78 @ ( power_power @ SV78 @ SV170 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV78 @ SV177 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $false )
| ( ( ( ( ti @ SV78 @ SV170 )
!= ( zero_zero @ SV78 ) )
| ( ( ti @ SV78 @ SV177 )
!= ( zero_zero @ SV78 ) ) )
= $true )
| ( ( linordered_idom @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1137]) ).
thf(1161,plain,
! [SV177: $i,SV170: $i,SV78: $i] :
( ( ( ( ( ti @ SV78 @ SV170 )
!= ( zero_zero @ SV78 ) )
| ( ( ti @ SV78 @ SV177 )
!= ( zero_zero @ SV78 ) ) )
= $false )
| ( ( ord_less @ SV78 @ ( zero_zero @ SV78 ) @ ( plus_plus @ SV78 @ ( power_power @ SV78 @ SV170 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV78 @ SV177 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true )
| ( ( linordered_idom @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1138]) ).
thf(1162,plain,
! [SV178: $i,SV171: $i,SV81: $i] :
( ( ( ( number_number_of @ SV81 @ SV171 )
= ( ti @ SV81 @ SV178 ) )
= $false )
| ( ( ( ti @ SV81 @ SV178 )
= ( number_number_of @ SV81 @ SV171 ) )
= $true )
| ( ( number @ SV81 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1139]) ).
thf(1163,plain,
! [SV171: $i,SV178: $i,SV81: $i] :
( ( ( ( ti @ SV81 @ SV178 )
= ( number_number_of @ SV81 @ SV171 ) )
= $false )
| ( ( ( number_number_of @ SV81 @ SV171 )
= ( ti @ SV81 @ SV178 ) )
= $true )
| ( ( number @ SV81 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1140]) ).
thf(1164,plain,
! [SV185: $i,SV85: $i] :
( ( ( ~ ( ~ ( ord_less @ SV85 @ ( number_number_of @ SV85 @ SV185 ) @ ( one_one @ SV85 ) )
| ( ord_less @ int @ SV185 @ ( bit1 @ pls ) ) ) )
= $false )
| ( ( number_ring @ SV85 )
= $false )
| ( ( linordered_idom @ SV85 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1141]) ).
thf(1165,plain,
! [SV85: $i,SV185: $i] :
( ( ( ~ ( ~ ( ord_less @ int @ SV185 @ ( bit1 @ pls ) )
| ( ord_less @ SV85 @ ( number_number_of @ SV85 @ SV185 ) @ ( one_one @ SV85 ) ) ) )
= $false )
| ( ( number_ring @ SV85 )
= $false )
| ( ( linordered_idom @ SV85 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1141]) ).
thf(1166,plain,
! [SV188: $i,SV186: $i,SV87: $i] :
( ( ( ~ ( ( ( number_number_of @ SV87 @ SV186 )
!= ( number_number_of @ SV87 @ SV188 ) )
| ( SV186 = SV188 ) )
| ~ ( ( SV186 != SV188 )
| ( ( number_number_of @ SV87 @ SV186 )
= ( number_number_of @ SV87 @ SV188 ) ) ) )
= $false )
| ( ( number_ring @ SV87 )
= $false )
| ( ( ring_char_0 @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1142]) ).
thf(1167,plain,
! [SV25: $i,SV180: $i] :
( ( ( ( ( number_number_of @ nat @ SV180 )
!= ( zero_zero @ nat ) )
| ( ( power_power @ SV25 @ ( zero_zero @ SV25 ) @ ( number_number_of @ nat @ SV180 ) )
= ( one_one @ SV25 ) ) )
= $true )
| ( ( power @ SV25 )
= $false )
| ( ( semiring_0 @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1145]) ).
thf(1168,plain,
! [SV25: $i,SV180: $i] :
( ( ( ~ ( ( ( number_number_of @ nat @ SV180 )
!= ( zero_zero @ nat ) ) )
| ( ( power_power @ SV25 @ ( zero_zero @ SV25 ) @ ( number_number_of @ nat @ SV180 ) )
= ( zero_zero @ SV25 ) ) )
= $true )
| ( ( power @ SV25 )
= $false )
| ( ( semiring_0 @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1146]) ).
thf(1169,plain,
! [SV173: $i,SV157: $i,SV26: $i] :
( ( ( ( ( ti @ SV26 @ SV157 )
!= ( zero_zero @ SV26 ) )
| ( ( ti @ SV26 @ SV173 )
!= ( zero_zero @ SV26 ) ) )
= $false )
| ( ( ( plus_plus @ SV26 @ ( power_power @ SV26 @ SV157 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV26 @ SV173 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV26 ) )
= $false )
| ( ( linordered_idom @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1147]) ).
thf(1170,plain,
! [SV173: $i,SV157: $i,SV26: $i] :
( ( ( ( ( ti @ SV26 @ SV157 )
!= ( zero_zero @ SV26 ) )
| ( ( ti @ SV26 @ SV173 )
!= ( zero_zero @ SV26 ) ) )
= $true )
| ( ( ( plus_plus @ SV26 @ ( power_power @ SV26 @ SV157 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV26 @ SV173 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV26 ) )
= $true )
| ( ( linordered_idom @ SV26 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1148]) ).
thf(1171,plain,
! [SV123: $i,SV48: $i] :
( ( ( ~ ( ord_less @ int @ SV48 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV123 ) @ ( number_number_of @ nat @ SV48 ) )
= ( number_number_of @ nat @ SV123 ) ) )
= $true )
| ( ( ord_less @ int @ SV123 @ pls )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1149]) ).
thf(1172,plain,
! [SV123: $i,SV48: $i] :
( ( ( ~ ~ ( ord_less @ int @ SV48 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV123 ) @ ( number_number_of @ nat @ SV48 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SV123 @ SV48 ) ) ) )
= $true )
| ( ( ord_less @ int @ SV123 @ pls )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1150]) ).
thf(1173,plain,
! [SV187: $i,SV181: $i,SV62: $i] :
( ( ( ~ ( ~ ( ord_less @ SV62 @ ( number_number_of @ SV62 @ SV181 ) @ ( number_number_of @ SV62 @ SV187 ) )
| ( ord_less @ int @ SV181 @ SV187 ) ) )
= $false )
| ( ( number_ring @ SV62 )
= $false )
| ( ( linordered_idom @ SV62 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1153]) ).
thf(1174,plain,
! [SV62: $i,SV187: $i,SV181: $i] :
( ( ( ~ ( ~ ( ord_less @ int @ SV181 @ SV187 )
| ( ord_less @ SV62 @ ( number_number_of @ SV62 @ SV181 ) @ ( number_number_of @ SV62 @ SV187 ) ) ) )
= $false )
| ( ( number_ring @ SV62 )
= $false )
| ( ( linordered_idom @ SV62 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1153]) ).
thf(1175,plain,
! [SV182: $i,SV69: $i] :
( ( ( ~ ( ord_less @ SV69 @ ( number_number_of @ SV69 @ SV182 ) @ ( zero_zero @ SV69 ) )
| ( ord_less @ int @ SV182 @ pls ) )
= $true )
| ( ( number_ring @ SV69 )
= $false )
| ( ( linordered_idom @ SV69 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1154]) ).
thf(1176,plain,
! [SV69: $i,SV182: $i] :
( ( ( ~ ( ord_less @ int @ SV182 @ pls )
| ( ord_less @ SV69 @ ( number_number_of @ SV69 @ SV182 ) @ ( zero_zero @ SV69 ) ) )
= $true )
| ( ( number_ring @ SV69 )
= $false )
| ( ( linordered_idom @ SV69 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1155]) ).
thf(1177,plain,
! [SV183: $i,SV73: $i] :
( ( ( ~ ( ord_less @ SV73 @ ( one_one @ SV73 ) @ ( number_number_of @ SV73 @ SV183 ) )
| ( ord_less @ int @ ( bit1 @ pls ) @ SV183 ) )
= $true )
| ( ( number_ring @ SV73 )
= $false )
| ( ( linordered_idom @ SV73 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1156]) ).
thf(1178,plain,
! [SV73: $i,SV183: $i] :
( ( ( ~ ( ord_less @ int @ ( bit1 @ pls ) @ SV183 )
| ( ord_less @ SV73 @ ( one_one @ SV73 ) @ ( number_number_of @ SV73 @ SV183 ) ) )
= $true )
| ( ( number_ring @ SV73 )
= $false )
| ( ( linordered_idom @ SV73 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1157]) ).
thf(1179,plain,
! [SV184: $i,SV76: $i] :
( ( ( ~ ( ord_less @ SV76 @ ( zero_zero @ SV76 ) @ ( number_number_of @ SV76 @ SV184 ) )
| ( ord_less @ int @ pls @ SV184 ) )
= $true )
| ( ( number_ring @ SV76 )
= $false )
| ( ( linordered_idom @ SV76 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1158]) ).
thf(1180,plain,
! [SV76: $i,SV184: $i] :
( ( ( ~ ( ord_less @ int @ pls @ SV184 )
| ( ord_less @ SV76 @ ( zero_zero @ SV76 ) @ ( number_number_of @ SV76 @ SV184 ) ) )
= $true )
| ( ( number_ring @ SV76 )
= $false )
| ( ( linordered_idom @ SV76 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1159]) ).
thf(1181,plain,
! [SV177: $i,SV170: $i,SV78: $i] :
( ( ( ( ti @ SV78 @ SV170 )
!= ( zero_zero @ SV78 ) )
= $true )
| ( ( ( ti @ SV78 @ SV177 )
!= ( zero_zero @ SV78 ) )
= $true )
| ( ( ord_less @ SV78 @ ( zero_zero @ SV78 ) @ ( plus_plus @ SV78 @ ( power_power @ SV78 @ SV170 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV78 @ SV177 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $false )
| ( ( linordered_idom @ SV78 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1160]) ).
thf(1182,plain,
! [SV177: $i,SV170: $i,SV78: $i] :
( ( ( ( ti @ SV78 @ SV170 )
!= ( zero_zero @ SV78 ) )
= $false )
| ( ( ord_less @ SV78 @ ( zero_zero @ SV78 ) @ ( plus_plus @ SV78 @ ( power_power @ SV78 @ SV170 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV78 @ SV177 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true )
| ( ( linordered_idom @ SV78 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1161]) ).
thf(1183,plain,
! [SV170: $i,SV177: $i,SV78: $i] :
( ( ( ( ti @ SV78 @ SV177 )
!= ( zero_zero @ SV78 ) )
= $false )
| ( ( ord_less @ SV78 @ ( zero_zero @ SV78 ) @ ( plus_plus @ SV78 @ ( power_power @ SV78 @ SV170 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV78 @ SV177 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true )
| ( ( linordered_idom @ SV78 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1161]) ).
thf(1184,plain,
! [SV185: $i,SV85: $i] :
( ( ( ~ ( ord_less @ SV85 @ ( number_number_of @ SV85 @ SV185 ) @ ( one_one @ SV85 ) )
| ( ord_less @ int @ SV185 @ ( bit1 @ pls ) ) )
= $true )
| ( ( number_ring @ SV85 )
= $false )
| ( ( linordered_idom @ SV85 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1164]) ).
thf(1185,plain,
! [SV85: $i,SV185: $i] :
( ( ( ~ ( ord_less @ int @ SV185 @ ( bit1 @ pls ) )
| ( ord_less @ SV85 @ ( number_number_of @ SV85 @ SV185 ) @ ( one_one @ SV85 ) ) )
= $true )
| ( ( number_ring @ SV85 )
= $false )
| ( ( linordered_idom @ SV85 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1165]) ).
thf(1186,plain,
! [SV188: $i,SV186: $i,SV87: $i] :
( ( ( ~ ( ( ( number_number_of @ SV87 @ SV186 )
!= ( number_number_of @ SV87 @ SV188 ) )
| ( SV186 = SV188 ) ) )
= $false )
| ( ( number_ring @ SV87 )
= $false )
| ( ( ring_char_0 @ SV87 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1166]) ).
thf(1187,plain,
! [SV87: $i,SV188: $i,SV186: $i] :
( ( ( ~ ( ( SV186 != SV188 )
| ( ( number_number_of @ SV87 @ SV186 )
= ( number_number_of @ SV87 @ SV188 ) ) ) )
= $false )
| ( ( number_ring @ SV87 )
= $false )
| ( ( ring_char_0 @ SV87 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1166]) ).
thf(1188,plain,
! [SV25: $i,SV180: $i] :
( ( ( ( number_number_of @ nat @ SV180 )
!= ( zero_zero @ nat ) )
= $true )
| ( ( ( power_power @ SV25 @ ( zero_zero @ SV25 ) @ ( number_number_of @ nat @ SV180 ) )
= ( one_one @ SV25 ) )
= $true )
| ( ( power @ SV25 )
= $false )
| ( ( semiring_0 @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1167]) ).
thf(1189,plain,
! [SV25: $i,SV180: $i] :
( ( ( ~ ( ( ( number_number_of @ nat @ SV180 )
!= ( zero_zero @ nat ) ) ) )
= $true )
| ( ( ( power_power @ SV25 @ ( zero_zero @ SV25 ) @ ( number_number_of @ nat @ SV180 ) )
= ( zero_zero @ SV25 ) )
= $true )
| ( ( power @ SV25 )
= $false )
| ( ( semiring_0 @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1168]) ).
thf(1190,plain,
! [SV173: $i,SV157: $i,SV26: $i] :
( ( ( ( ti @ SV26 @ SV157 )
!= ( zero_zero @ SV26 ) )
= $false )
| ( ( ( plus_plus @ SV26 @ ( power_power @ SV26 @ SV157 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV26 @ SV173 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV26 ) )
= $false )
| ( ( linordered_idom @ SV26 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1169]) ).
thf(1191,plain,
! [SV157: $i,SV173: $i,SV26: $i] :
( ( ( ( ti @ SV26 @ SV173 )
!= ( zero_zero @ SV26 ) )
= $false )
| ( ( ( plus_plus @ SV26 @ ( power_power @ SV26 @ SV157 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV26 @ SV173 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV26 ) )
= $false )
| ( ( linordered_idom @ SV26 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1169]) ).
thf(1192,plain,
! [SV173: $i,SV157: $i,SV26: $i] :
( ( ( ( ti @ SV26 @ SV157 )
!= ( zero_zero @ SV26 ) )
= $true )
| ( ( ( ti @ SV26 @ SV173 )
!= ( zero_zero @ SV26 ) )
= $true )
| ( ( ( plus_plus @ SV26 @ ( power_power @ SV26 @ SV157 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV26 @ SV173 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV26 ) )
= $true )
| ( ( linordered_idom @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1170]) ).
thf(1193,plain,
! [SV123: $i,SV48: $i] :
( ( ( ~ ( ord_less @ int @ SV48 @ pls ) )
= $true )
| ( ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV123 ) @ ( number_number_of @ nat @ SV48 ) )
= ( number_number_of @ nat @ SV123 ) )
= $true )
| ( ( ord_less @ int @ SV123 @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1171]) ).
thf(1194,plain,
! [SV123: $i,SV48: $i] :
( ( ( ~ ~ ( ord_less @ int @ SV48 @ pls ) )
= $true )
| ( ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV123 ) @ ( number_number_of @ nat @ SV48 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SV123 @ SV48 ) ) )
= $true )
| ( ( ord_less @ int @ SV123 @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1172]) ).
thf(1195,plain,
! [SV187: $i,SV181: $i,SV62: $i] :
( ( ( ~ ( ord_less @ SV62 @ ( number_number_of @ SV62 @ SV181 ) @ ( number_number_of @ SV62 @ SV187 ) )
| ( ord_less @ int @ SV181 @ SV187 ) )
= $true )
| ( ( number_ring @ SV62 )
= $false )
| ( ( linordered_idom @ SV62 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1173]) ).
thf(1196,plain,
! [SV62: $i,SV187: $i,SV181: $i] :
( ( ( ~ ( ord_less @ int @ SV181 @ SV187 )
| ( ord_less @ SV62 @ ( number_number_of @ SV62 @ SV181 ) @ ( number_number_of @ SV62 @ SV187 ) ) )
= $true )
| ( ( number_ring @ SV62 )
= $false )
| ( ( linordered_idom @ SV62 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1174]) ).
thf(1197,plain,
! [SV182: $i,SV69: $i] :
( ( ( ~ ( ord_less @ SV69 @ ( number_number_of @ SV69 @ SV182 ) @ ( zero_zero @ SV69 ) ) )
= $true )
| ( ( ord_less @ int @ SV182 @ pls )
= $true )
| ( ( number_ring @ SV69 )
= $false )
| ( ( linordered_idom @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1175]) ).
thf(1198,plain,
! [SV69: $i,SV182: $i] :
( ( ( ~ ( ord_less @ int @ SV182 @ pls ) )
= $true )
| ( ( ord_less @ SV69 @ ( number_number_of @ SV69 @ SV182 ) @ ( zero_zero @ SV69 ) )
= $true )
| ( ( number_ring @ SV69 )
= $false )
| ( ( linordered_idom @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1176]) ).
thf(1199,plain,
! [SV183: $i,SV73: $i] :
( ( ( ~ ( ord_less @ SV73 @ ( one_one @ SV73 ) @ ( number_number_of @ SV73 @ SV183 ) ) )
= $true )
| ( ( ord_less @ int @ ( bit1 @ pls ) @ SV183 )
= $true )
| ( ( number_ring @ SV73 )
= $false )
| ( ( linordered_idom @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1177]) ).
thf(1200,plain,
! [SV73: $i,SV183: $i] :
( ( ( ~ ( ord_less @ int @ ( bit1 @ pls ) @ SV183 ) )
= $true )
| ( ( ord_less @ SV73 @ ( one_one @ SV73 ) @ ( number_number_of @ SV73 @ SV183 ) )
= $true )
| ( ( number_ring @ SV73 )
= $false )
| ( ( linordered_idom @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1178]) ).
thf(1201,plain,
! [SV184: $i,SV76: $i] :
( ( ( ~ ( ord_less @ SV76 @ ( zero_zero @ SV76 ) @ ( number_number_of @ SV76 @ SV184 ) ) )
= $true )
| ( ( ord_less @ int @ pls @ SV184 )
= $true )
| ( ( number_ring @ SV76 )
= $false )
| ( ( linordered_idom @ SV76 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1179]) ).
thf(1202,plain,
! [SV76: $i,SV184: $i] :
( ( ( ~ ( ord_less @ int @ pls @ SV184 ) )
= $true )
| ( ( ord_less @ SV76 @ ( zero_zero @ SV76 ) @ ( number_number_of @ SV76 @ SV184 ) )
= $true )
| ( ( number_ring @ SV76 )
= $false )
| ( ( linordered_idom @ SV76 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1180]) ).
thf(1203,plain,
! [SV177: $i,SV170: $i,SV78: $i] :
( ( ( ( ti @ SV78 @ SV170 )
= ( zero_zero @ SV78 ) )
= $false )
| ( ( ( ti @ SV78 @ SV177 )
!= ( zero_zero @ SV78 ) )
= $true )
| ( ( ord_less @ SV78 @ ( zero_zero @ SV78 ) @ ( plus_plus @ SV78 @ ( power_power @ SV78 @ SV170 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV78 @ SV177 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $false )
| ( ( linordered_idom @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1181]) ).
thf(1204,plain,
! [SV177: $i,SV170: $i,SV78: $i] :
( ( ( ( ti @ SV78 @ SV170 )
= ( zero_zero @ SV78 ) )
= $true )
| ( ( ord_less @ SV78 @ ( zero_zero @ SV78 ) @ ( plus_plus @ SV78 @ ( power_power @ SV78 @ SV170 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV78 @ SV177 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true )
| ( ( linordered_idom @ SV78 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1182]) ).
thf(1205,plain,
! [SV170: $i,SV177: $i,SV78: $i] :
( ( ( ( ti @ SV78 @ SV177 )
= ( zero_zero @ SV78 ) )
= $true )
| ( ( ord_less @ SV78 @ ( zero_zero @ SV78 ) @ ( plus_plus @ SV78 @ ( power_power @ SV78 @ SV170 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV78 @ SV177 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true )
| ( ( linordered_idom @ SV78 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1183]) ).
thf(1206,plain,
! [SV185: $i,SV85: $i] :
( ( ( ~ ( ord_less @ SV85 @ ( number_number_of @ SV85 @ SV185 ) @ ( one_one @ SV85 ) ) )
= $true )
| ( ( ord_less @ int @ SV185 @ ( bit1 @ pls ) )
= $true )
| ( ( number_ring @ SV85 )
= $false )
| ( ( linordered_idom @ SV85 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1184]) ).
thf(1207,plain,
! [SV85: $i,SV185: $i] :
( ( ( ~ ( ord_less @ int @ SV185 @ ( bit1 @ pls ) ) )
= $true )
| ( ( ord_less @ SV85 @ ( number_number_of @ SV85 @ SV185 ) @ ( one_one @ SV85 ) )
= $true )
| ( ( number_ring @ SV85 )
= $false )
| ( ( linordered_idom @ SV85 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1185]) ).
thf(1208,plain,
! [SV188: $i,SV186: $i,SV87: $i] :
( ( ( ( ( number_number_of @ SV87 @ SV186 )
!= ( number_number_of @ SV87 @ SV188 ) )
| ( SV186 = SV188 ) )
= $true )
| ( ( number_ring @ SV87 )
= $false )
| ( ( ring_char_0 @ SV87 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1186]) ).
thf(1209,plain,
! [SV87: $i,SV188: $i,SV186: $i] :
( ( ( ( SV186 != SV188 )
| ( ( number_number_of @ SV87 @ SV186 )
= ( number_number_of @ SV87 @ SV188 ) ) )
= $true )
| ( ( number_ring @ SV87 )
= $false )
| ( ( ring_char_0 @ SV87 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1187]) ).
thf(1210,plain,
! [SV25: $i,SV180: $i] :
( ( ( ( number_number_of @ nat @ SV180 )
= ( zero_zero @ nat ) )
= $false )
| ( ( ( power_power @ SV25 @ ( zero_zero @ SV25 ) @ ( number_number_of @ nat @ SV180 ) )
= ( one_one @ SV25 ) )
= $true )
| ( ( power @ SV25 )
= $false )
| ( ( semiring_0 @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1188]) ).
thf(1211,plain,
! [SV25: $i,SV180: $i] :
( ( ( ( number_number_of @ nat @ SV180 )
!= ( zero_zero @ nat ) )
= $false )
| ( ( ( power_power @ SV25 @ ( zero_zero @ SV25 ) @ ( number_number_of @ nat @ SV180 ) )
= ( zero_zero @ SV25 ) )
= $true )
| ( ( power @ SV25 )
= $false )
| ( ( semiring_0 @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1189]) ).
thf(1212,plain,
! [SV173: $i,SV157: $i,SV26: $i] :
( ( ( ( ti @ SV26 @ SV157 )
= ( zero_zero @ SV26 ) )
= $true )
| ( ( ( plus_plus @ SV26 @ ( power_power @ SV26 @ SV157 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV26 @ SV173 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV26 ) )
= $false )
| ( ( linordered_idom @ SV26 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1190]) ).
thf(1213,plain,
! [SV157: $i,SV173: $i,SV26: $i] :
( ( ( ( ti @ SV26 @ SV173 )
= ( zero_zero @ SV26 ) )
= $true )
| ( ( ( plus_plus @ SV26 @ ( power_power @ SV26 @ SV157 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV26 @ SV173 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV26 ) )
= $false )
| ( ( linordered_idom @ SV26 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1191]) ).
thf(1214,plain,
! [SV173: $i,SV157: $i,SV26: $i] :
( ( ( ( ti @ SV26 @ SV157 )
= ( zero_zero @ SV26 ) )
= $false )
| ( ( ( ti @ SV26 @ SV173 )
!= ( zero_zero @ SV26 ) )
= $true )
| ( ( ( plus_plus @ SV26 @ ( power_power @ SV26 @ SV157 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV26 @ SV173 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV26 ) )
= $true )
| ( ( linordered_idom @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1192]) ).
thf(1215,plain,
! [SV123: $i,SV48: $i] :
( ( ( ord_less @ int @ SV48 @ pls )
= $false )
| ( ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV123 ) @ ( number_number_of @ nat @ SV48 ) )
= ( number_number_of @ nat @ SV123 ) )
= $true )
| ( ( ord_less @ int @ SV123 @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1193]) ).
thf(1216,plain,
! [SV123: $i,SV48: $i] :
( ( ( ~ ( ord_less @ int @ SV48 @ pls ) )
= $false )
| ( ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV123 ) @ ( number_number_of @ nat @ SV48 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SV123 @ SV48 ) ) )
= $true )
| ( ( ord_less @ int @ SV123 @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1194]) ).
thf(1217,plain,
! [SV187: $i,SV181: $i,SV62: $i] :
( ( ( ~ ( ord_less @ SV62 @ ( number_number_of @ SV62 @ SV181 ) @ ( number_number_of @ SV62 @ SV187 ) ) )
= $true )
| ( ( ord_less @ int @ SV181 @ SV187 )
= $true )
| ( ( number_ring @ SV62 )
= $false )
| ( ( linordered_idom @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1195]) ).
thf(1218,plain,
! [SV62: $i,SV187: $i,SV181: $i] :
( ( ( ~ ( ord_less @ int @ SV181 @ SV187 ) )
= $true )
| ( ( ord_less @ SV62 @ ( number_number_of @ SV62 @ SV181 ) @ ( number_number_of @ SV62 @ SV187 ) )
= $true )
| ( ( number_ring @ SV62 )
= $false )
| ( ( linordered_idom @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1196]) ).
thf(1219,plain,
! [SV182: $i,SV69: $i] :
( ( ( ord_less @ SV69 @ ( number_number_of @ SV69 @ SV182 ) @ ( zero_zero @ SV69 ) )
= $false )
| ( ( ord_less @ int @ SV182 @ pls )
= $true )
| ( ( number_ring @ SV69 )
= $false )
| ( ( linordered_idom @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1197]) ).
thf(1220,plain,
! [SV69: $i,SV182: $i] :
( ( ( ord_less @ int @ SV182 @ pls )
= $false )
| ( ( ord_less @ SV69 @ ( number_number_of @ SV69 @ SV182 ) @ ( zero_zero @ SV69 ) )
= $true )
| ( ( number_ring @ SV69 )
= $false )
| ( ( linordered_idom @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1198]) ).
thf(1221,plain,
! [SV183: $i,SV73: $i] :
( ( ( ord_less @ SV73 @ ( one_one @ SV73 ) @ ( number_number_of @ SV73 @ SV183 ) )
= $false )
| ( ( ord_less @ int @ ( bit1 @ pls ) @ SV183 )
= $true )
| ( ( number_ring @ SV73 )
= $false )
| ( ( linordered_idom @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1199]) ).
thf(1222,plain,
! [SV73: $i,SV183: $i] :
( ( ( ord_less @ int @ ( bit1 @ pls ) @ SV183 )
= $false )
| ( ( ord_less @ SV73 @ ( one_one @ SV73 ) @ ( number_number_of @ SV73 @ SV183 ) )
= $true )
| ( ( number_ring @ SV73 )
= $false )
| ( ( linordered_idom @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1200]) ).
thf(1223,plain,
! [SV184: $i,SV76: $i] :
( ( ( ord_less @ SV76 @ ( zero_zero @ SV76 ) @ ( number_number_of @ SV76 @ SV184 ) )
= $false )
| ( ( ord_less @ int @ pls @ SV184 )
= $true )
| ( ( number_ring @ SV76 )
= $false )
| ( ( linordered_idom @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1201]) ).
thf(1224,plain,
! [SV76: $i,SV184: $i] :
( ( ( ord_less @ int @ pls @ SV184 )
= $false )
| ( ( ord_less @ SV76 @ ( zero_zero @ SV76 ) @ ( number_number_of @ SV76 @ SV184 ) )
= $true )
| ( ( number_ring @ SV76 )
= $false )
| ( ( linordered_idom @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1202]) ).
thf(1225,plain,
! [SV170: $i,SV177: $i,SV78: $i] :
( ( ( ( ti @ SV78 @ SV177 )
= ( zero_zero @ SV78 ) )
= $false )
| ( ( ( ti @ SV78 @ SV170 )
= ( zero_zero @ SV78 ) )
= $false )
| ( ( ord_less @ SV78 @ ( zero_zero @ SV78 ) @ ( plus_plus @ SV78 @ ( power_power @ SV78 @ SV170 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV78 @ SV177 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $false )
| ( ( linordered_idom @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1203]) ).
thf(1226,plain,
! [SV185: $i,SV85: $i] :
( ( ( ord_less @ SV85 @ ( number_number_of @ SV85 @ SV185 ) @ ( one_one @ SV85 ) )
= $false )
| ( ( ord_less @ int @ SV185 @ ( bit1 @ pls ) )
= $true )
| ( ( number_ring @ SV85 )
= $false )
| ( ( linordered_idom @ SV85 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1206]) ).
thf(1227,plain,
! [SV85: $i,SV185: $i] :
( ( ( ord_less @ int @ SV185 @ ( bit1 @ pls ) )
= $false )
| ( ( ord_less @ SV85 @ ( number_number_of @ SV85 @ SV185 ) @ ( one_one @ SV85 ) )
= $true )
| ( ( number_ring @ SV85 )
= $false )
| ( ( linordered_idom @ SV85 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1207]) ).
thf(1228,plain,
! [SV188: $i,SV186: $i,SV87: $i] :
( ( ( ( number_number_of @ SV87 @ SV186 )
!= ( number_number_of @ SV87 @ SV188 ) )
= $true )
| ( ( SV186 = SV188 )
= $true )
| ( ( number_ring @ SV87 )
= $false )
| ( ( ring_char_0 @ SV87 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1208]) ).
thf(1229,plain,
! [SV87: $i,SV188: $i,SV186: $i] :
( ( ( SV186 != SV188 )
= $true )
| ( ( ( number_number_of @ SV87 @ SV186 )
= ( number_number_of @ SV87 @ SV188 ) )
= $true )
| ( ( number_ring @ SV87 )
= $false )
| ( ( ring_char_0 @ SV87 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1209]) ).
thf(1230,plain,
! [SV25: $i,SV180: $i] :
( ( ( ( number_number_of @ nat @ SV180 )
= ( zero_zero @ nat ) )
= $true )
| ( ( ( power_power @ SV25 @ ( zero_zero @ SV25 ) @ ( number_number_of @ nat @ SV180 ) )
= ( zero_zero @ SV25 ) )
= $true )
| ( ( power @ SV25 )
= $false )
| ( ( semiring_0 @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1211]) ).
thf(1231,plain,
! [SV157: $i,SV173: $i,SV26: $i] :
( ( ( ( ti @ SV26 @ SV173 )
= ( zero_zero @ SV26 ) )
= $false )
| ( ( ( ti @ SV26 @ SV157 )
= ( zero_zero @ SV26 ) )
= $false )
| ( ( ( plus_plus @ SV26 @ ( power_power @ SV26 @ SV157 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV26 @ SV173 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV26 ) )
= $true )
| ( ( linordered_idom @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1214]) ).
thf(1232,plain,
! [SV123: $i,SV48: $i] :
( ( ( ord_less @ int @ SV48 @ pls )
= $true )
| ( ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV123 ) @ ( number_number_of @ nat @ SV48 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SV123 @ SV48 ) ) )
= $true )
| ( ( ord_less @ int @ SV123 @ pls )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1216]) ).
thf(1233,plain,
! [SV187: $i,SV181: $i,SV62: $i] :
( ( ( ord_less @ SV62 @ ( number_number_of @ SV62 @ SV181 ) @ ( number_number_of @ SV62 @ SV187 ) )
= $false )
| ( ( ord_less @ int @ SV181 @ SV187 )
= $true )
| ( ( number_ring @ SV62 )
= $false )
| ( ( linordered_idom @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1217]) ).
thf(1234,plain,
! [SV62: $i,SV187: $i,SV181: $i] :
( ( ( ord_less @ int @ SV181 @ SV187 )
= $false )
| ( ( ord_less @ SV62 @ ( number_number_of @ SV62 @ SV181 ) @ ( number_number_of @ SV62 @ SV187 ) )
= $true )
| ( ( number_ring @ SV62 )
= $false )
| ( ( linordered_idom @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1218]) ).
thf(1235,plain,
! [SV188: $i,SV186: $i,SV87: $i] :
( ( ( ( number_number_of @ SV87 @ SV186 )
= ( number_number_of @ SV87 @ SV188 ) )
= $false )
| ( ( SV186 = SV188 )
= $true )
| ( ( number_ring @ SV87 )
= $false )
| ( ( ring_char_0 @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1228]) ).
thf(1236,plain,
! [SV87: $i,SV188: $i,SV186: $i] :
( ( ( SV186 = SV188 )
= $false )
| ( ( ( number_number_of @ SV87 @ SV186 )
= ( number_number_of @ SV87 @ SV188 ) )
= $true )
| ( ( number_ring @ SV87 )
= $false )
| ( ( ring_char_0 @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1229]) ).
thf(1237,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[304,1236,1235,1234,1233,1232,1231,1230,1227,1226,1225,1224,1223,1222,1221,1220,1219,1215,1213,1212,1210,1205,1204,1163,1162,1152,1151,1144,1143,1135,1134,1132,1127,1125,1124,1123,1119,1118,1117,1089,1088,1085,1084,1083,1082,1077,1076,1068,1066,1065,1064,1063,1062,1061,1056,1055,1054,1053,1052,1050,1049,1048,1047,1046,1043,1042,1033,1032,1031,1030,1029,1028,1008,1007,991,990,985,984,981,980,975,974,973,971,970,950,945,939,925,924,919,916,899,898,894,878,873,864,852,849,838,827,814,810,806,803,802,797,786,783,753,752,748,736,735,727,725,722,721,720,716,715,703,657,640,639,638,637,636,633,631,630,629,605,548,545,544,543,541,540,538,534,527,526,525,524,523,442,441,440,439,438,437,436,435,434,433,432,431,430,429,428,427,426,425,424,423,422,398,397,384,364,363,362,354,353,351,350,349,344,339,326,325,324,305]) ).
thf(1238,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[1237]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM925+5 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.05 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.19 % Computer : n007.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Oct 6 13:42:46 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.42/1.67 .
% 8.42/1.67
% 8.42/1.67 No.of.Axioms: 143
% 8.42/1.67
% 8.42/1.67 Length.of.Defs: 0
% 8.42/1.67
% 8.42/1.67 Contains.Choice.Funs: false
% 8.42/1.67 .......................................
% 8.42/1.67
% 8.42/1.67 ********************************
% 8.42/1.67 * All subproblems solved! *
% 8.42/1.67 ********************************
% 8.42/1.67 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:143,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:1237,loop_count:0,foatp_calls:1,translation:fof_full)
% 8.42/1.67
% 8.42/1.67 %**** Beginning of derivation protocol ****
% 8.42/1.67 % SZS output start CNFRefutation
% See solution above
% 8.42/1.68
% 8.42/1.68 %**** End of derivation protocol ****
% 8.42/1.68 %**** no. of clauses in derivation: 1229 ****
% 8.42/1.68 %**** clause counter: 1237 ****
% 8.42/1.68
% 8.42/1.68 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:143,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:1237,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------