TSTP Solution File: NUM925+5 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : NUM925+5 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 11:58:04 EDT 2022
% Result : Theorem 45.29s 45.54s
% Output : CNFRefutation 45.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 182
% Syntax : Number of formulae : 1484 ( 875 unt; 29 typ; 0 def)
% Number of atoms : 8536 (3680 equ; 0 cnn)
% Maximal formula atoms : 7 ( 5 avg)
% Number of connectives : 21012 (2173 ~;2381 |; 154 &;16104 @)
% ( 76 <=>; 124 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 33 ( 33 >; 0 *; 0 +; 0 <<)
% Number of symbols : 32 ( 29 usr; 7 con; 0-3 aty)
% Number of variables : 3174 ( 0 ^3174 !; 0 ?;3174 :)
% 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(1,axiom,
! [T: $i,A: $i] :
( ( ti @ T @ ( ti @ T @ A ) )
= ( ti @ T @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_ti_idem) ).
thf(2,axiom,
number @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber) ).
thf(3,axiom,
power @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Power_Opower) ).
thf(4,axiom,
mult_zero @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Omult__zero) ).
thf(5,axiom,
semiring_0 @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__0) ).
thf(6,axiom,
semiring_1 @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__1) ).
thf(7,axiom,
zero_neq_one @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ozero__neq__one) ).
thf(8,axiom,
number_semiring @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber__semiring) ).
thf(9,axiom,
no_zero_divisors @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ono__zero__divisors) ).
thf(10,axiom,
number @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber) ).
thf(11,axiom,
power @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Power_Opower) ).
thf(12,axiom,
number_ring @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
thf(13,axiom,
ring_char_0 @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Oring__char__0) ).
thf(14,axiom,
mult_zero @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Omult__zero) ).
thf(15,axiom,
semiring_0 @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring__0) ).
thf(16,axiom,
semiring_1 @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring__1) ).
thf(17,axiom,
zero_neq_one @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ozero__neq__one) ).
thf(18,axiom,
number_semiring @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__semiring) ).
thf(19,axiom,
linordered_idom @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__idom) ).
thf(20,axiom,
no_zero_divisors @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ono__zero__divisors) ).
thf(21,axiom,
ring_11004092258visors @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring__1__no__zero__divisors) ).
thf(22,axiom,
linord219039673up_add @ int,
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_87_add__number__of__left) ).
thf(34,axiom,
! [X_a: $i] :
( ( ( power @ X_a )
& ( mult_zero @ X_a )
& ( no_zero_divisors @ X_a )
& ( zero_neq_one @ X_a ) )
=> ! [A_2: $i,Wa: $i] :
( ( ( power_power @ X_a @ A_2 @ ( number_number_of @ nat @ Wa ) )
= ( zero_zero @ X_a ) )
<=> ( ( ( ti @ X_a @ A_2 )
= ( zero_zero @ X_a ) )
& ( ( number_number_of @ nat @ Wa )
!= ( zero_zero @ nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_power__eq__0__iff__number__of) ).
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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_80_zadd__0) ).
thf(41,axiom,
! [Z: $i] :
( ( plus_plus @ int @ Z @ ( zero_zero @ int ) )
= Z ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_zadd__0__right) ).
thf(42,axiom,
! [K: $i] :
( ( bit0 @ K )
= ( plus_plus @ int @ K @ K ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_77_add__Bit0__Bit0) ).
thf(44,axiom,
! [K: $i] :
( ( plus_plus @ int @ pls @ K )
= K ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_add__Pls) ).
thf(45,axiom,
! [K: $i] :
( ( plus_plus @ int @ K @ pls )
= K ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_add__Pls__right) ).
thf(46,axiom,
( zero_zero @ int )
!= ( one_one @ int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_int__0__neq__1) ).
thf(47,axiom,
( pls
= ( zero_zero @ int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_Pls__def) ).
thf(48,axiom,
( ( bit0 @ pls )
= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_Bit0__Pls) ).
thf(49,axiom,
! [L_1: $i] :
( ( pls
= ( bit0 @ L_1 ) )
<=> ( pls = L_1 ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_70_rel__simps_I44_J) ).
thf(51,axiom,
! [K: $i,L: $i] :
( ( bit0 @ K )
!= ( bit1 @ L ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_rel__simps_I49_J) ).
thf(52,axiom,
! [K: $i,L: $i] :
( ( bit1 @ K )
!= ( bit0 @ L ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_rel__simps_I50_J) ).
thf(53,axiom,
! [L: $i] :
( pls
!= ( bit1 @ L ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_rel__simps_I39_J) ).
thf(54,axiom,
! [K: $i] :
( ( bit1 @ K )
!= pls ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_60_zless__add1__eq) ).
thf(61,axiom,
ord_less @ int @ ( zero_zero @ int ) @ ( one_one @ int ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_58_bin__less__0__simps_I3_J) ).
thf(63,axiom,
~ ( ord_less @ int @ pls @ ( zero_zero @ int ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_40_eq__number__of) ).
thf(81,axiom,
( ( one_one @ nat )
= ( number_number_of @ nat @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_Numeral1__eq1__nat) ).
thf(82,axiom,
( ( number_number_of @ nat @ ( bit1 @ pls ) )
= ( one_one @ nat ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_33_less__int__code_I13_J) ).
thf(88,axiom,
~ ( ord_less @ int @ pls @ pls ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_27_int__eq__0__conv) ).
thf(94,axiom,
( ( zero_zero @ nat )
= ( number_number_of @ nat @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_semiring__norm_I113_J) ).
thf(95,axiom,
( ( number_number_of @ nat @ pls )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_20_zpower__int) ).
thf(101,axiom,
( ( zero_zero @ int )
= ( number_number_of @ int @ pls ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_15_zless__linear) ).
thf(106,axiom,
ord_less @ nat @ ( zero_zero @ nat ) @ n,
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_2_sum__power2__eq__zero__iff) ).
thf(119,axiom,
ord_less @ int @ ( one_one @ int ) @ t,
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_0_n1pos) ).
thf(121,axiom,
( ( ti @ int @ t )
= t ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',tsy_c_Power_Opower__class_Opower_1_arg1) ).
thf(125,axiom,
! [B_1: $i,B_2: $i,X_a: $i] :
( ( ( power @ X_a )
& ( mult_zero @ X_a )
& ( no_zero_divisors @ X_a )
& ( zero_neq_one @ X_a ) )
=> ( ( ti @ X_a @ ( power_power @ X_a @ B_1 @ B_2 ) )
= ( power_power @ X_a @ B_1 @ B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Power_Opower__class_Opower_0_res) ).
thf(126,axiom,
! [B_1: $i,B_2: $i,X_a: $i] :
( ( ( power @ X_a )
& ( mult_zero @ X_a )
& ( no_zero_divisors @ X_a )
& ( zero_neq_one @ X_a ) )
=> ( ( power_power @ X_a @ B_1 @ ( ti @ nat @ B_2 ) )
= ( power_power @ X_a @ B_1 @ B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Power_Opower__class_Opower_0_arg2) ).
thf(127,axiom,
! [B_1: $i,B_2: $i,X_a: $i] :
( ( ( power @ X_a )
& ( mult_zero @ X_a )
& ( no_zero_divisors @ X_a )
& ( zero_neq_one @ X_a ) )
=> ( ( power_power @ X_a @ ( ti @ X_a @ B_1 ) @ B_2 )
= ( power_power @ X_a @ B_1 @ B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Power_Opower__class_Opower_0_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/sandbox/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/sandbox/benchmark/theBenchmark.p',tsy_c_Orderings_Oord__class_Oless_1_arg1) ).
thf(130,axiom,
! [B_1: $i,B_2: $i,X_a: $i] :
( ( linordered_idom @ X_a )
=> ( ( ord_less @ X_a @ B_1 @ ( ti @ X_a @ B_2 ) )
<=> ( ord_less @ X_a @ B_1 @ B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Orderings_Oord__class_Oless_0_arg2) ).
thf(131,axiom,
! [B_1: $i,B_2: $i,X_a: $i] :
( ( linordered_idom @ X_a )
=> ( ( ord_less @ X_a @ ( ti @ X_a @ B_1 ) @ B_2 )
<=> ( ord_less @ X_a @ B_1 @ B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Orderings_Oord__class_Oless_0_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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',tsy_c_Int_Onumber__class_Onumber__of_arg1) ).
thf(136,axiom,
! [X_a: $i] :
( ( ti @ X_a @ ( undefined @ X_a ) )
= ( undefined @ X_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_HOL_Oundefined_res) ).
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/sandbox/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/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Ozero__class_Ozero_1_res) ).
thf(139,axiom,
! [X_a: $i] :
( ( ( power @ X_a )
& ( mult_zero @ X_a )
& ( no_zero_divisors @ X_a )
& ( zero_neq_one @ X_a ) )
=> ( ( ti @ X_a @ ( zero_zero @ X_a ) )
= ( zero_zero @ X_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Ozero__class_Ozero_0_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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Oone__class_Oone_res) ).
thf(147,axiom,
( ( ti @ nat @ n )
= n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_n_____res) ).
thf(148,axiom,
( ( ti @ int @ pls )
= pls ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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,
( ( ! [T: $i,A: $i] :
( ( ti @ T @ ( ti @ T @ A ) )
= ( ti @ T @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(157,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(158,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(159,plain,
( ( ! [X_a: $i] :
( ( ( power @ X_a )
& ( mult_zero @ X_a )
& ( no_zero_divisors @ X_a )
& ( zero_neq_one @ X_a ) )
=> ! [A_2: $i,Wa: $i] :
( ( ( power_power @ X_a @ A_2 @ ( number_number_of @ nat @ Wa ) )
= ( zero_zero @ X_a ) )
<=> ( ( ( ti @ X_a @ A_2 )
= ( zero_zero @ X_a ) )
& ( ( number_number_of @ nat @ Wa )
!= ( zero_zero @ nat ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(160,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(161,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(162,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(163,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(164,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(165,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(166,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(167,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(168,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ( ( power @ X_a )
& ( mult_zero @ X_a )
& ( no_zero_divisors @ X_a )
& ( zero_neq_one @ 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)],[125]) ).
thf(169,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ( ( power @ X_a )
& ( mult_zero @ X_a )
& ( no_zero_divisors @ X_a )
& ( zero_neq_one @ 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)],[126]) ).
thf(170,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ( ( power @ X_a )
& ( mult_zero @ X_a )
& ( no_zero_divisors @ X_a )
& ( zero_neq_one @ 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)],[127]) ).
thf(171,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ( linordered_idom @ X_a )
=> ( ( ord_less @ X_a @ B_1 @ ( ti @ X_a @ B_2 ) )
<=> ( ord_less @ X_a @ B_1 @ B_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[130]) ).
thf(172,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ( linordered_idom @ X_a )
=> ( ( ord_less @ X_a @ ( ti @ X_a @ B_1 ) @ B_2 )
<=> ( ord_less @ X_a @ B_1 @ B_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[131]) ).
thf(173,plain,
( ( ! [X_a: $i] :
( ( ti @ X_a @ ( undefined @ X_a ) )
= ( undefined @ X_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[136]) ).
thf(174,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(175,plain,
( ( ! [X_a: $i] :
( ( ( power @ X_a )
& ( mult_zero @ X_a )
& ( no_zero_divisors @ X_a )
& ( zero_neq_one @ X_a ) )
=> ( ( ti @ X_a @ ( zero_zero @ X_a ) )
= ( zero_zero @ X_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[139]) ).
thf(176,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(177,plain,
( ( number @ nat )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(178,plain,
( ( power @ nat )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(179,plain,
( ( mult_zero @ nat )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(180,plain,
( ( semiring_0 @ nat )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(181,plain,
( ( semiring_1 @ nat )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(182,plain,
( ( zero_neq_one @ nat )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(183,plain,
( ( number_semiring @ nat )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(184,plain,
( ( no_zero_divisors @ nat )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(185,plain,
( ( number @ int )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(186,plain,
( ( power @ int )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(187,plain,
( ( number_ring @ int )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(188,plain,
( ( ring_char_0 @ int )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(189,plain,
( ( mult_zero @ int )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(190,plain,
( ( semiring_0 @ int )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(191,plain,
( ( semiring_1 @ int )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(192,plain,
( ( zero_neq_one @ int )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(193,plain,
( ( number_semiring @ int )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(194,plain,
( ( linordered_idom @ int )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(195,plain,
( ( no_zero_divisors @ int )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(196,plain,
( ( ring_11004092258visors @ int )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(197,plain,
( ( linord219039673up_add @ int )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(198,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(199,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(200,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(201,plain,
( ( ! [K: $i] :
( ( bit1 @ K )
= ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ K ) @ K ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(202,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(203,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(204,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(205,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(206,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(207,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(208,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(209,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(210,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(211,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(212,plain,
( ( ! [Z: $i] :
( ( plus_plus @ int @ ( zero_zero @ int ) @ Z )
= Z ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(213,plain,
( ( ! [Z: $i] :
( ( plus_plus @ int @ Z @ ( zero_zero @ int ) )
= Z ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(214,plain,
( ( ! [K: $i] :
( ( bit0 @ K )
= ( plus_plus @ int @ K @ K ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(215,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(216,plain,
( ( ! [K: $i] :
( ( plus_plus @ int @ pls @ K )
= K ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(217,plain,
( ( ! [K: $i] :
( ( plus_plus @ int @ K @ pls )
= K ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(218,plain,
( ( ( ( zero_zero @ int )
!= ( one_one @ int ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(219,plain,
( ( pls
= ( zero_zero @ int ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(220,plain,
( ( ( bit0 @ pls )
= pls )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(221,plain,
( ( ! [L_1: $i] :
( ( pls
= ( bit0 @ L_1 ) )
<=> ( pls = L_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(222,plain,
( ( ! [K_1: $i] :
( ( ( bit0 @ K_1 )
= pls )
<=> ( K_1 = pls ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(223,plain,
( ( ! [K: $i,L: $i] :
( ( bit0 @ K )
!= ( bit1 @ L ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(224,plain,
( ( ! [K: $i,L: $i] :
( ( bit1 @ K )
!= ( bit0 @ L ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(225,plain,
( ( ! [L: $i] :
( pls
!= ( bit1 @ L ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(226,plain,
( ( ! [K: $i] :
( ( bit1 @ K )
!= pls ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(227,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(228,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(229,plain,
( ( ! [K: $i] :
~ ( ord_less @ int @ ( semiring_1_of_nat @ int @ K ) @ ( zero_zero @ int ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(230,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(231,plain,
( ( ord_less @ int @ ( zero_zero @ int ) @ ( one_one @ int ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(232,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(233,plain,
( ( ~ ( ord_less @ int @ pls @ ( zero_zero @ int ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(234,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(235,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(236,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(237,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(238,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(239,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(240,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(241,plain,
( ( ! [Z: $i,W: $i] :
( ( plus_plus @ int @ Z @ W )
= ( plus_plus @ int @ W @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(242,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(243,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(244,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(245,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(246,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(247,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(248,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(249,plain,
( ( ( one_one @ nat )
= ( number_number_of @ nat @ ( bit1 @ pls ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(250,plain,
( ( ( number_number_of @ nat @ ( bit1 @ pls ) )
= ( one_one @ nat ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(251,plain,
( ( ( one_one @ int )
= ( number_number_of @ int @ ( bit1 @ pls ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(252,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(253,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(254,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(255,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(256,plain,
( ( ~ ( ord_less @ int @ pls @ pls ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(257,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(258,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(259,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(260,plain,
( ( ( semiring_1_of_nat @ int @ ( zero_zero @ nat ) )
= ( zero_zero @ int ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(261,plain,
( ( ! [Na: $i] :
( ( ( semiring_1_of_nat @ int @ Na )
= ( zero_zero @ int ) )
<=> ( Na
= ( zero_zero @ nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(262,plain,
( ( ( zero_zero @ nat )
= ( number_number_of @ nat @ pls ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(263,plain,
( ( ( number_number_of @ nat @ pls )
= ( zero_zero @ nat ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(264,plain,
( ( ( semiring_1_of_nat @ int @ ( one_one @ nat ) )
= ( one_one @ int ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(265,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(266,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(267,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(268,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(269,plain,
( ( ( zero_zero @ int )
= ( number_number_of @ int @ pls ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(270,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(271,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(272,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(273,plain,
( ( ord_less @ nat @ ( zero_zero @ nat ) @ n )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(274,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(275,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(276,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(277,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(278,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(279,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(280,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(281,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(282,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(283,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(284,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(285,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(286,plain,
( ( ord_less @ int @ ( one_one @ int ) @ t )
= $true ),
inference(unfold_def,[status(thm)],[119]) ).
thf(287,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(288,plain,
( ( ( ti @ int @ t )
= t )
= $true ),
inference(unfold_def,[status(thm)],[121]) ).
thf(289,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(290,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(291,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(292,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(293,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(294,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(295,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(296,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(297,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(298,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(299,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(300,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(301,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(302,plain,
( ( ( ti @ nat @ n )
= n )
= $true ),
inference(unfold_def,[status(thm)],[147]) ).
thf(303,plain,
( ( ( ti @ int @ pls )
= pls )
= $true ),
inference(unfold_def,[status(thm)],[148]) ).
thf(304,plain,
( ( ! [B_1: $i] :
( ( ti @ int @ ( bit1 @ B_1 ) )
= ( bit1 @ B_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[149]) ).
thf(305,plain,
( ( ! [B_1: $i] :
( ( bit1 @ ( ti @ int @ B_1 ) )
= ( bit1 @ B_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[150]) ).
thf(306,plain,
( ( ! [B_1: $i] :
( ( ti @ int @ ( bit0 @ B_1 ) )
= ( bit0 @ B_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[151]) ).
thf(307,plain,
( ( ! [B_1: $i] :
( ( bit0 @ ( ti @ int @ B_1 ) )
= ( bit0 @ B_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[152]) ).
thf(308,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(309,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_combined,[status(esa)],[308]) ).
thf(310,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 ) ) )
& ! [Xa: $i] :
( ( ( ti @ X_a @ Xa )
= ( zero_zero @ X_a ) )
| ! [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 ) ) ) ) ) ) )
& ! [Xa: $i,Ya: $i] :
( ( ( ti @ X_a @ Ya )
= ( zero_zero @ X_a ) )
| ( 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 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[157]) ).
thf(311,plain,
( ( ! [X_a: $i] :
( ~ ( linordered_idom @ X_a )
| ( ! [A_2: $i] :
( ( ( ti @ X_a @ A_2 )
= ( zero_zero @ X_a ) )
| ( ord_less @ X_a @ ( zero_zero @ X_a ) @ ( power_power @ X_a @ A_2 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
& ! [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(extcnf_combined,[status(esa)],[158]) ).
thf(312,plain,
( ( ! [X_a: $i] :
( ~ ( mult_zero @ X_a )
| ~ ( power @ X_a )
| ~ ( no_zero_divisors @ X_a )
| ~ ( zero_neq_one @ X_a )
| ( ! [A_2: $i,Wa: $i] :
( ( ( number_number_of @ nat @ Wa )
= ( zero_zero @ nat ) )
| ( ( ti @ X_a @ A_2 )
!= ( zero_zero @ X_a ) )
| ( ( power_power @ X_a @ A_2 @ ( number_number_of @ nat @ Wa ) )
= ( zero_zero @ X_a ) ) )
& ! [A_2: $i,Wa: $i] :
( ( ( power_power @ X_a @ A_2 @ ( number_number_of @ nat @ Wa ) )
!= ( zero_zero @ X_a ) )
| ( ( number_number_of @ nat @ Wa )
!= ( zero_zero @ nat ) ) )
& ! [A_2: $i] :
( ! [Wa: $i] :
( ( power_power @ X_a @ A_2 @ ( number_number_of @ nat @ Wa ) )
!= ( zero_zero @ X_a ) )
| ( ( ti @ X_a @ A_2 )
= ( zero_zero @ X_a ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[159]) ).
thf(313,plain,
( ( ! [X_a: $i] :
( ~ ( linordered_idom @ X_a )
| ~ ( number_ring @ X_a )
| ( ! [Ya: $i] :
( ~ ( ord_less @ X_a @ ( one_one @ X_a ) @ ( number_number_of @ X_a @ Ya ) )
| ( ord_less @ int @ ( bit1 @ pls ) @ Ya ) )
& ! [Ya: $i] :
( ~ ( ord_less @ int @ ( bit1 @ pls ) @ Ya )
| ( ord_less @ X_a @ ( one_one @ X_a ) @ ( number_number_of @ X_a @ Ya ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[160]) ).
thf(314,plain,
( ( ! [X_a: $i] :
( ~ ( linordered_idom @ X_a )
| ~ ( number_ring @ X_a )
| ( ! [Xa: $i] :
( ~ ( ord_less @ X_a @ ( number_number_of @ X_a @ Xa ) @ ( one_one @ X_a ) )
| ( ord_less @ int @ Xa @ ( bit1 @ pls ) ) )
& ! [Xa: $i] :
( ~ ( ord_less @ int @ Xa @ ( bit1 @ pls ) )
| ( ord_less @ X_a @ ( number_number_of @ X_a @ Xa ) @ ( one_one @ X_a ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[161]) ).
thf(315,plain,
( ( ! [X_a: $i] :
( ~ ( linordered_idom @ X_a )
| ~ ( number_ring @ X_a )
| ( ! [Ya: $i] :
( ~ ( ord_less @ X_a @ ( zero_zero @ X_a ) @ ( number_number_of @ X_a @ Ya ) )
| ( ord_less @ int @ pls @ Ya ) )
& ! [Ya: $i] :
( ~ ( ord_less @ int @ pls @ Ya )
| ( ord_less @ X_a @ ( zero_zero @ X_a ) @ ( number_number_of @ X_a @ Ya ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[162]) ).
thf(316,plain,
( ( ! [X_a: $i] :
( ~ ( linordered_idom @ X_a )
| ~ ( number_ring @ X_a )
| ( ! [Xa: $i] :
( ~ ( ord_less @ X_a @ ( number_number_of @ X_a @ Xa ) @ ( zero_zero @ X_a ) )
| ( ord_less @ int @ Xa @ pls ) )
& ! [Xa: $i] :
( ~ ( ord_less @ int @ Xa @ pls )
| ( ord_less @ X_a @ ( number_number_of @ X_a @ Xa ) @ ( zero_zero @ X_a ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[163]) ).
thf(317,plain,
( ( ! [X_a: $i] :
( ~ ( linordered_idom @ X_a )
| ~ ( number_ring @ 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 ) )
& ! [Xa: $i,Ya: $i] :
( ~ ( ord_less @ int @ Xa @ Ya )
| ( ord_less @ X_a @ ( number_number_of @ X_a @ Xa ) @ ( number_number_of @ X_a @ Ya ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[164]) ).
thf(318,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(extcnf_combined,[status(esa)],[165]) ).
thf(319,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(extcnf_combined,[status(esa)],[166]) ).
thf(320,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(extcnf_combined,[status(esa)],[167]) ).
thf(321,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ~ ( mult_zero @ X_a )
| ~ ( power @ X_a )
| ~ ( no_zero_divisors @ X_a )
| ~ ( zero_neq_one @ X_a )
| ( ( ti @ X_a @ ( power_power @ X_a @ B_1 @ B_2 ) )
= ( power_power @ X_a @ B_1 @ B_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[168]) ).
thf(322,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ~ ( mult_zero @ X_a )
| ~ ( power @ X_a )
| ~ ( no_zero_divisors @ X_a )
| ~ ( zero_neq_one @ X_a )
| ( ( power_power @ X_a @ B_1 @ ( ti @ nat @ B_2 ) )
= ( power_power @ X_a @ B_1 @ B_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[169]) ).
thf(323,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ~ ( mult_zero @ X_a )
| ~ ( power @ X_a )
| ~ ( no_zero_divisors @ X_a )
| ~ ( zero_neq_one @ X_a )
| ( ( power_power @ X_a @ ( ti @ X_a @ B_1 ) @ B_2 )
= ( power_power @ X_a @ B_1 @ B_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[170]) ).
thf(324,plain,
( ( ! [B_1: $i] :
( ! [B_2: $i,X_a: $i] :
( ~ ( linordered_idom @ X_a )
| ~ ( ord_less @ X_a @ B_1 @ ( ti @ X_a @ B_2 ) )
| ( ord_less @ X_a @ B_1 @ B_2 ) )
& ! [B_2: $i,X_a: $i] :
( ~ ( linordered_idom @ X_a )
| ~ ( ord_less @ X_a @ B_1 @ B_2 )
| ( ord_less @ X_a @ B_1 @ ( ti @ X_a @ B_2 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[171]) ).
thf(325,plain,
( ( ! [B_1: $i] :
( ! [B_2: $i,X_a: $i] :
( ~ ( linordered_idom @ X_a )
| ~ ( ord_less @ X_a @ ( ti @ X_a @ B_1 ) @ B_2 )
| ( ord_less @ X_a @ B_1 @ B_2 ) )
& ! [B_2: $i,X_a: $i] :
( ~ ( linordered_idom @ X_a )
| ~ ( ord_less @ X_a @ B_1 @ B_2 )
| ( ord_less @ X_a @ ( ti @ X_a @ B_1 ) @ B_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[172]) ).
thf(326,plain,
( ( ! [X_a: $i] :
( ~ ( power @ X_a )
| ~ ( semiring_0 @ X_a )
| ( ( ti @ X_a @ ( zero_zero @ X_a ) )
= ( zero_zero @ X_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[174]) ).
thf(327,plain,
( ( ! [X_a: $i] :
( ~ ( mult_zero @ X_a )
| ~ ( power @ X_a )
| ~ ( no_zero_divisors @ X_a )
| ~ ( zero_neq_one @ X_a )
| ( ( ti @ X_a @ ( zero_zero @ X_a ) )
= ( zero_zero @ X_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[175]) ).
thf(328,plain,
( ( ! [X_a: $i] :
( ~ ( power @ X_a )
| ~ ( semiring_0 @ X_a )
| ( ( ti @ X_a @ ( one_one @ X_a ) )
= ( one_one @ X_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[176]) ).
thf(329,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(extcnf_combined,[status(esa)],[198]) ).
thf(330,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(extcnf_combined,[status(esa)],[199]) ).
thf(331,plain,
( ( ! [Z: $i] :
( ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ Z ) @ Z )
!= ( zero_zero @ int ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[200]) ).
thf(332,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(extcnf_combined,[status(esa)],[204]) ).
thf(333,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(extcnf_combined,[status(esa)],[205]) ).
thf(334,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(extcnf_combined,[status(esa)],[206]) ).
thf(335,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(extcnf_combined,[status(esa)],[207]) ).
thf(336,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(extcnf_combined,[status(esa)],[208]) ).
thf(337,plain,
( ( ! [X_a: $i] :
( ~ ( number_ring @ X_a )
| ( ( zero_zero @ X_a )
= ( number_number_of @ X_a @ pls ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[209]) ).
thf(338,plain,
( ( ! [X_a: $i] :
( ~ ( number_ring @ X_a )
| ( ( number_number_of @ X_a @ pls )
= ( zero_zero @ X_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[210]) ).
thf(339,plain,
( ( ! [X_a: $i] :
( ~ ( number_semiring @ X_a )
| ( ( number_number_of @ X_a @ pls )
= ( zero_zero @ X_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[211]) ).
thf(340,plain,
( ( ( ( zero_zero @ int )
!= ( one_one @ int ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[218]) ).
thf(341,plain,
( ( ! [L_1: $i] :
( ( pls
!= ( bit0 @ L_1 ) )
| ( pls = L_1 ) )
& ! [L_1: $i] :
( ( pls != L_1 )
| ( pls
= ( bit0 @ L_1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[221]) ).
thf(342,plain,
( ( ! [K_1: $i] :
( ( ( bit0 @ K_1 )
!= pls )
| ( K_1 = pls ) )
& ! [K_1: $i] :
( ( K_1 != pls )
| ( ( bit0 @ K_1 )
= pls ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[222]) ).
thf(343,plain,
( ( ! [K: $i,L: $i] :
( ( bit0 @ K )
!= ( bit1 @ L ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[223]) ).
thf(344,plain,
( ( ! [K: $i,L: $i] :
( ( bit1 @ K )
!= ( bit0 @ L ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[224]) ).
thf(345,plain,
( ( ! [L: $i] :
( pls
!= ( bit1 @ L ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[225]) ).
thf(346,plain,
( ( ! [K: $i] :
( ( bit1 @ K )
!= pls ) )
= $true ),
inference(extcnf_combined,[status(esa)],[226]) ).
thf(347,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 ) ) )
& ! [A_2: $i] :
( ( ( ti @ X_a @ A_2 )
!= ( zero_zero @ X_a ) )
| ( ( plus_plus @ X_a @ A_2 @ A_2 )
= ( zero_zero @ X_a ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[227]) ).
thf(348,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 ) ) )
& ! [Z_1: $i] :
( ~ ( ord_less @ int @ Z_1 @ ( zero_zero @ int ) )
| ( ord_less @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ Z_1 ) @ Z_1 ) @ ( zero_zero @ int ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[228]) ).
thf(349,plain,
( ( ! [Wa: $i,Z_1: $i] :
( ~ ( ord_less @ int @ Wa @ ( plus_plus @ int @ Z_1 @ ( one_one @ int ) ) )
| ( Wa = Z_1 )
| ( ord_less @ int @ Wa @ Z_1 ) )
& ! [Wa: $i,Z_1: $i] :
( ( Wa != Z_1 )
| ( ord_less @ int @ Wa @ ( plus_plus @ int @ Z_1 @ ( one_one @ int ) ) ) )
& ! [Wa: $i,Z_1: $i] :
( ~ ( ord_less @ int @ Wa @ Z_1 )
| ( ord_less @ int @ Wa @ ( plus_plus @ int @ Z_1 @ ( one_one @ int ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[230]) ).
thf(350,plain,
( ( ! [Wa: $i] :
( ~ ( ord_less @ int @ ( bit0 @ Wa ) @ ( zero_zero @ int ) )
| ( ord_less @ int @ Wa @ ( zero_zero @ int ) ) )
& ! [Wa: $i] :
( ~ ( ord_less @ int @ Wa @ ( zero_zero @ int ) )
| ( ord_less @ int @ ( bit0 @ Wa ) @ ( zero_zero @ int ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[232]) ).
thf(351,plain,
( ( ! [Wa: $i] :
( ~ ( ord_less @ int @ ( bit1 @ Wa ) @ ( zero_zero @ int ) )
| ( ord_less @ int @ Wa @ ( zero_zero @ int ) ) )
& ! [Wa: $i] :
( ~ ( ord_less @ int @ Wa @ ( zero_zero @ int ) )
| ( ord_less @ int @ ( bit1 @ Wa ) @ ( zero_zero @ int ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[234]) ).
thf(352,plain,
( ( ! [K_1: $i] :
( ~ ( ord_less @ int @ pls @ ( bit0 @ K_1 ) )
| ( ord_less @ int @ pls @ K_1 ) )
& ! [K_1: $i] :
( ~ ( ord_less @ int @ pls @ K_1 )
| ( ord_less @ int @ pls @ ( bit0 @ K_1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[235]) ).
thf(353,plain,
( ( ! [K_1: $i] :
( ~ ( ord_less @ int @ ( bit0 @ K_1 ) @ pls )
| ( ord_less @ int @ K_1 @ pls ) )
& ! [K_1: $i] :
( ~ ( ord_less @ int @ K_1 @ pls )
| ( ord_less @ int @ ( bit0 @ K_1 ) @ pls ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[236]) ).
thf(354,plain,
( ( ! [K_1: $i,L_1: $i] :
( ~ ( ord_less @ int @ ( bit1 @ K_1 ) @ ( bit0 @ L_1 ) )
| ( ord_less @ int @ K_1 @ L_1 ) )
& ! [K_1: $i,L_1: $i] :
( ~ ( ord_less @ int @ K_1 @ L_1 )
| ( ord_less @ int @ ( bit1 @ K_1 ) @ ( bit0 @ L_1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[237]) ).
thf(355,plain,
( ( ! [K1: $i,K2: $i] :
( ~ ( ord_less @ int @ ( bit1 @ K1 ) @ ( bit0 @ K2 ) )
| ( ord_less @ int @ K1 @ K2 ) )
& ! [K1: $i,K2: $i] :
( ~ ( ord_less @ int @ K1 @ K2 )
| ( ord_less @ int @ ( bit1 @ K1 ) @ ( bit0 @ K2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[238]) ).
thf(356,plain,
( ( ! [K_1: $i] :
( ~ ( ord_less @ int @ ( bit1 @ K_1 ) @ pls )
| ( ord_less @ int @ K_1 @ pls ) )
& ! [K_1: $i] :
( ~ ( ord_less @ int @ K_1 @ pls )
| ( ord_less @ int @ ( bit1 @ K_1 ) @ pls ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[239]) ).
thf(357,plain,
( ( ! [Ma: $i,Na: $i] :
( ( ( semiring_1_of_nat @ int @ Ma )
!= ( semiring_1_of_nat @ int @ Na ) )
| ( Ma = Na ) )
& ! [Ma: $i,Na: $i] :
( ( Ma != Na )
| ( ( semiring_1_of_nat @ int @ Ma )
= ( semiring_1_of_nat @ int @ Na ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[240]) ).
thf(358,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 ) ) )
& ! [A_2: $i] :
( ~ ( ord_less @ X_a @ A_2 @ ( zero_zero @ X_a ) )
| ( ord_less @ X_a @ ( plus_plus @ X_a @ A_2 @ A_2 ) @ ( zero_zero @ X_a ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[244]) ).
thf(359,plain,
( ( ! [K_1: $i,L_1: $i] :
( ( ( bit0 @ K_1 )
!= ( bit0 @ L_1 ) )
| ( K_1 = L_1 ) )
& ! [K_1: $i,L_1: $i] :
( ( K_1 != L_1 )
| ( ( bit0 @ K_1 )
= ( bit0 @ L_1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[245]) ).
thf(360,plain,
( ( ! [K_1: $i,L_1: $i] :
( ( ( bit1 @ K_1 )
!= ( bit1 @ L_1 ) )
| ( K_1 = L_1 ) )
& ! [K_1: $i,L_1: $i] :
( ( K_1 != L_1 )
| ( ( bit1 @ K_1 )
= ( bit1 @ L_1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[246]) ).
thf(361,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 ) ) )
& ! [Wa: $i,Xa: $i] :
( ( ( ti @ X_a @ Xa )
!= ( number_number_of @ X_a @ Wa ) )
| ( ( number_number_of @ X_a @ Wa )
= ( ti @ X_a @ Xa ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[247]) ).
thf(362,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 ) )
& ! [Xa: $i,Ya: $i] :
( ( Xa != Ya )
| ( ( number_number_of @ X_a @ Xa )
= ( number_number_of @ X_a @ Ya ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[248]) ).
thf(363,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 ) ) )
& ! [V_1: $i,V: $i] :
( ( 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 ) ) )
& ! [V_1: $i,V: $i] :
( ( 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 @ ( plus_plus @ int @ V @ V_1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[252]) ).
thf(364,plain,
( ( ! [K: $i,I: $i,J: $i] :
( ~ ( ord_less @ int @ I @ J )
| ( ord_less @ int @ ( plus_plus @ int @ I @ K ) @ ( plus_plus @ int @ J @ K ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[253]) ).
thf(365,plain,
( ( ! [K_1: $i,L_1: $i] :
( ~ ( ord_less @ int @ ( bit0 @ K_1 ) @ ( bit0 @ L_1 ) )
| ( ord_less @ int @ K_1 @ L_1 ) )
& ! [K_1: $i,L_1: $i] :
( ~ ( ord_less @ int @ K_1 @ L_1 )
| ( ord_less @ int @ ( bit0 @ K_1 ) @ ( bit0 @ L_1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[254]) ).
thf(366,plain,
( ( ! [K1: $i,K2: $i] :
( ~ ( ord_less @ int @ ( bit0 @ K1 ) @ ( bit0 @ K2 ) )
| ( ord_less @ int @ K1 @ K2 ) )
& ! [K1: $i,K2: $i] :
( ~ ( ord_less @ int @ K1 @ K2 )
| ( ord_less @ int @ ( bit0 @ K1 ) @ ( bit0 @ K2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[255]) ).
thf(367,plain,
( ( ! [K_1: $i,L_1: $i] :
( ~ ( ord_less @ int @ ( bit1 @ K_1 ) @ ( bit1 @ L_1 ) )
| ( ord_less @ int @ K_1 @ L_1 ) )
& ! [K_1: $i,L_1: $i] :
( ~ ( ord_less @ int @ K_1 @ L_1 )
| ( ord_less @ int @ ( bit1 @ K_1 ) @ ( bit1 @ L_1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[257]) ).
thf(368,plain,
( ( ! [K1: $i,K2: $i] :
( ~ ( ord_less @ int @ ( bit1 @ K1 ) @ ( bit1 @ K2 ) )
| ( ord_less @ int @ K1 @ K2 ) )
& ! [K1: $i,K2: $i] :
( ~ ( ord_less @ int @ K1 @ K2 )
| ( ord_less @ int @ ( bit1 @ K1 ) @ ( bit1 @ K2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[258]) ).
thf(369,plain,
( ( ! [Na: $i] :
( ( ( semiring_1_of_nat @ int @ Na )
!= ( zero_zero @ int ) )
| ( Na
= ( zero_zero @ nat ) ) )
& ! [Na: $i] :
( ( Na
!= ( zero_zero @ nat ) )
| ( ( semiring_1_of_nat @ int @ Na )
= ( zero_zero @ int ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[261]) ).
thf(370,plain,
( ( ! [K_1: $i,L_1: $i] :
( ~ ( ord_less @ int @ ( number_number_of @ int @ K_1 ) @ ( number_number_of @ int @ L_1 ) )
| ( ord_less @ int @ K_1 @ L_1 ) )
& ! [K_1: $i,L_1: $i] :
( ~ ( ord_less @ int @ K_1 @ L_1 )
| ( ord_less @ int @ ( number_number_of @ int @ K_1 ) @ ( number_number_of @ int @ L_1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[271]) ).
thf(371,plain,
( ( ! [X: $i,Y: $i] :
( ( ord_less @ int @ Y @ X )
| ( X = Y )
| ( ord_less @ int @ X @ Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[272]) ).
thf(372,plain,
( ( ! [X_a: $i] :
( ~ ( number_ring @ X_a )
| ( ( number_number_of @ X_a @ ( bit1 @ pls ) )
= ( one_one @ X_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[274]) ).
thf(373,plain,
( ( ! [X_a: $i] :
( ~ ( number_ring @ X_a )
| ( ( one_one @ X_a )
= ( number_number_of @ X_a @ ( bit1 @ pls ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[275]) ).
thf(374,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 ) ) )
& ! [W: $i] :
( ( ( 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(extcnf_combined,[status(esa)],[276]) ).
thf(375,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(extcnf_combined,[status(esa)],[278]) ).
thf(376,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(extcnf_combined,[status(esa)],[279]) ).
thf(377,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(extcnf_combined,[status(esa)],[280]) ).
thf(378,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(extcnf_combined,[status(esa)],[281]) ).
thf(379,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 ) ) )
& ! [A_2: $i] :
( ( ( ti @ X_a @ A_2 )
!= ( zero_zero @ X_a ) )
| ( ( power_power @ X_a @ A_2 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ X_a ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[282]) ).
thf(380,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(extcnf_combined,[status(esa)],[283]) ).
thf(381,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(extcnf_combined,[status(esa)],[284]) ).
thf(382,plain,
( ( ! [X_a: $i] :
( ~ ( linordered_idom @ X_a )
| ( ! [Xa: $i,Ya: $i] :
( ( ( ti @ X_a @ Xa )
!= ( zero_zero @ X_a ) )
| ( ( ti @ X_a @ Ya )
!= ( 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 ) ) ) ) )
= ( zero_zero @ 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 ) ) )
& ! [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 @ Ya )
= ( zero_zero @ X_a ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[285]) ).
thf(383,plain,
( ( ! [B_1: $i,B_2: $i] :
( ~ ( ord_less @ nat @ B_1 @ ( ti @ nat @ B_2 ) )
| ( ord_less @ nat @ B_1 @ B_2 ) )
& ! [B_1: $i,B_2: $i] :
( ~ ( ord_less @ nat @ B_1 @ B_2 )
| ( ord_less @ nat @ B_1 @ ( ti @ nat @ B_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[289]) ).
thf(384,plain,
( ( ! [B_1: $i,B_2: $i] :
( ~ ( ord_less @ nat @ ( ti @ nat @ B_1 ) @ B_2 )
| ( ord_less @ nat @ B_1 @ B_2 ) )
& ! [B_1: $i,B_2: $i] :
( ~ ( ord_less @ nat @ B_1 @ B_2 )
| ( ord_less @ nat @ ( ti @ nat @ B_1 ) @ B_2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[290]) ).
thf(385,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(extcnf_combined,[status(esa)],[291]) ).
thf(386,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(extcnf_combined,[status(esa)],[292]) ).
thf(387,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(extcnf_combined,[status(esa)],[293]) ).
thf(388,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(extcnf_combined,[status(esa)],[294]) ).
thf(389,plain,
( ( ! [X_a: $i] :
( ~ ( linord219039673up_add @ X_a )
| ( ( ti @ X_a @ ( zero_zero @ X_a ) )
= ( zero_zero @ X_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[295]) ).
thf(390,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(extcnf_combined,[status(esa)],[296]) ).
thf(391,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(extcnf_combined,[status(esa)],[297]) ).
thf(392,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(extcnf_combined,[status(esa)],[298]) ).
thf(393,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(extcnf_combined,[status(esa)],[299]) ).
thf(394,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(extcnf_combined,[status(esa)],[300]) ).
thf(395,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(extcnf_combined,[status(esa)],[301]) ).
thf(396,plain,
( ( ! [B_1: $i] :
( ( bit0 @ ( ti @ int @ B_1 ) )
= ( bit0 @ B_1 ) ) )
= $true ),
inference(copy,[status(thm)],[307]) ).
thf(397,plain,
( ( ! [B_1: $i] :
( ( ti @ int @ ( bit0 @ B_1 ) )
= ( bit0 @ B_1 ) ) )
= $true ),
inference(copy,[status(thm)],[306]) ).
thf(398,plain,
( ( ! [B_1: $i] :
( ( bit1 @ ( ti @ int @ B_1 ) )
= ( bit1 @ B_1 ) ) )
= $true ),
inference(copy,[status(thm)],[305]) ).
thf(399,plain,
( ( ! [B_1: $i] :
( ( ti @ int @ ( bit1 @ B_1 ) )
= ( bit1 @ B_1 ) ) )
= $true ),
inference(copy,[status(thm)],[304]) ).
thf(400,plain,
( ( ( ti @ int @ pls )
= pls )
= $true ),
inference(copy,[status(thm)],[303]) ).
thf(401,plain,
( ( ( ti @ nat @ n )
= n )
= $true ),
inference(copy,[status(thm)],[302]) ).
thf(402,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)],[395]) ).
thf(403,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)],[394]) ).
thf(404,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)],[393]) ).
thf(405,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)],[392]) ).
thf(406,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)],[391]) ).
thf(407,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)],[390]) ).
thf(408,plain,
( ( ! [X_a: $i] :
( ~ ( linord219039673up_add @ X_a )
| ( ( ti @ X_a @ ( zero_zero @ X_a ) )
= ( zero_zero @ X_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[389]) ).
thf(409,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)],[388]) ).
thf(410,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)],[387]) ).
thf(411,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)],[386]) ).
thf(412,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)],[385]) ).
thf(413,plain,
( ( ! [B_1: $i,B_2: $i] :
( ~ ( ord_less @ nat @ ( ti @ nat @ B_1 ) @ B_2 )
| ( ord_less @ nat @ B_1 @ B_2 ) )
& ! [B_1: $i,B_2: $i] :
( ~ ( ord_less @ nat @ B_1 @ B_2 )
| ( ord_less @ nat @ ( ti @ nat @ B_1 ) @ B_2 ) ) )
= $true ),
inference(copy,[status(thm)],[384]) ).
thf(414,plain,
( ( ! [B_1: $i,B_2: $i] :
( ~ ( ord_less @ nat @ B_1 @ ( ti @ nat @ B_2 ) )
| ( ord_less @ nat @ B_1 @ B_2 ) )
& ! [B_1: $i,B_2: $i] :
( ~ ( ord_less @ nat @ B_1 @ B_2 )
| ( ord_less @ nat @ B_1 @ ( ti @ nat @ B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[383]) ).
thf(415,plain,
( ( ( ti @ int @ t )
= t )
= $true ),
inference(copy,[status(thm)],[288]) ).
thf(416,plain,
( ( ord_less @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( one_one @ int ) @ ( semiring_1_of_nat @ int @ n ) ) )
= $true ),
inference(copy,[status(thm)],[287]) ).
thf(417,plain,
( ( ord_less @ int @ ( one_one @ int ) @ t )
= $true ),
inference(copy,[status(thm)],[286]) ).
thf(418,plain,
( ( ! [X_a: $i] :
( ~ ( linordered_idom @ X_a )
| ( ! [Xa: $i,Ya: $i] :
( ( ( ti @ X_a @ Xa )
!= ( zero_zero @ X_a ) )
| ( ( ti @ X_a @ Ya )
!= ( 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 ) ) ) ) )
= ( zero_zero @ 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 ) ) )
& ! [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 @ Ya )
= ( zero_zero @ X_a ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[382]) ).
thf(419,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)],[381]) ).
thf(420,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)],[380]) ).
thf(421,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 ) ) )
& ! [A_2: $i] :
( ( ( ti @ X_a @ A_2 )
!= ( zero_zero @ X_a ) )
| ( ( power_power @ X_a @ A_2 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ X_a ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[379]) ).
thf(422,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)],[378]) ).
thf(423,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)],[377]) ).
thf(424,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)],[376]) ).
thf(425,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)],[375]) ).
thf(426,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)],[277]) ).
thf(427,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 ) ) )
& ! [W: $i] :
( ( ( 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)],[374]) ).
thf(428,plain,
( ( ! [X_a: $i] :
( ~ ( number_ring @ X_a )
| ( ( one_one @ X_a )
= ( number_number_of @ X_a @ ( bit1 @ pls ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[373]) ).
thf(429,plain,
( ( ! [X_a: $i] :
( ~ ( number_ring @ X_a )
| ( ( number_number_of @ X_a @ ( bit1 @ pls ) )
= ( one_one @ X_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[372]) ).
thf(430,plain,
( ( ord_less @ nat @ ( zero_zero @ nat ) @ n )
= $true ),
inference(copy,[status(thm)],[273]) ).
thf(431,plain,
( ( ! [X: $i,Y: $i] :
( ( ord_less @ int @ Y @ X )
| ( X = Y )
| ( ord_less @ int @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[371]) ).
thf(432,plain,
( ( ! [K_1: $i,L_1: $i] :
( ~ ( ord_less @ int @ ( number_number_of @ int @ K_1 ) @ ( number_number_of @ int @ L_1 ) )
| ( ord_less @ int @ K_1 @ L_1 ) )
& ! [K_1: $i,L_1: $i] :
( ~ ( ord_less @ int @ K_1 @ L_1 )
| ( ord_less @ int @ ( number_number_of @ int @ K_1 ) @ ( number_number_of @ int @ L_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[370]) ).
thf(433,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)],[270]) ).
thf(434,plain,
( ( ( zero_zero @ int )
= ( number_number_of @ int @ pls ) )
= $true ),
inference(copy,[status(thm)],[269]) ).
thf(435,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)],[268]) ).
thf(436,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)],[267]) ).
thf(437,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)],[266]) ).
thf(438,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)],[265]) ).
thf(439,plain,
( ( ( semiring_1_of_nat @ int @ ( one_one @ nat ) )
= ( one_one @ int ) )
= $true ),
inference(copy,[status(thm)],[264]) ).
thf(440,plain,
( ( ( number_number_of @ nat @ pls )
= ( zero_zero @ nat ) )
= $true ),
inference(copy,[status(thm)],[263]) ).
thf(441,plain,
( ( ( zero_zero @ nat )
= ( number_number_of @ nat @ pls ) )
= $true ),
inference(copy,[status(thm)],[262]) ).
thf(442,plain,
( ( ! [Na: $i] :
( ( ( semiring_1_of_nat @ int @ Na )
!= ( zero_zero @ int ) )
| ( Na
= ( zero_zero @ nat ) ) )
& ! [Na: $i] :
( ( Na
!= ( zero_zero @ nat ) )
| ( ( semiring_1_of_nat @ int @ Na )
= ( zero_zero @ int ) ) ) )
= $true ),
inference(copy,[status(thm)],[369]) ).
thf(443,plain,
( ( ( semiring_1_of_nat @ int @ ( zero_zero @ nat ) )
= ( zero_zero @ int ) )
= $true ),
inference(copy,[status(thm)],[260]) ).
thf(444,plain,
( ( ( plus_plus @ nat @ ( one_one @ nat ) @ ( one_one @ nat ) )
= ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(copy,[status(thm)],[259]) ).
thf(445,plain,
( ( ! [K1: $i,K2: $i] :
( ~ ( ord_less @ int @ ( bit1 @ K1 ) @ ( bit1 @ K2 ) )
| ( ord_less @ int @ K1 @ K2 ) )
& ! [K1: $i,K2: $i] :
( ~ ( ord_less @ int @ K1 @ K2 )
| ( ord_less @ int @ ( bit1 @ K1 ) @ ( bit1 @ K2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[368]) ).
thf(446,plain,
( ( ! [K_1: $i,L_1: $i] :
( ~ ( ord_less @ int @ ( bit1 @ K_1 ) @ ( bit1 @ L_1 ) )
| ( ord_less @ int @ K_1 @ L_1 ) )
& ! [K_1: $i,L_1: $i] :
( ~ ( ord_less @ int @ K_1 @ L_1 )
| ( ord_less @ int @ ( bit1 @ K_1 ) @ ( bit1 @ L_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[367]) ).
thf(447,plain,
( ( ~ ( ord_less @ int @ pls @ pls ) )
= $true ),
inference(copy,[status(thm)],[256]) ).
thf(448,plain,
( ( ! [K1: $i,K2: $i] :
( ~ ( ord_less @ int @ ( bit0 @ K1 ) @ ( bit0 @ K2 ) )
| ( ord_less @ int @ K1 @ K2 ) )
& ! [K1: $i,K2: $i] :
( ~ ( ord_less @ int @ K1 @ K2 )
| ( ord_less @ int @ ( bit0 @ K1 ) @ ( bit0 @ K2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[366]) ).
thf(449,plain,
( ( ! [K_1: $i,L_1: $i] :
( ~ ( ord_less @ int @ ( bit0 @ K_1 ) @ ( bit0 @ L_1 ) )
| ( ord_less @ int @ K_1 @ L_1 ) )
& ! [K_1: $i,L_1: $i] :
( ~ ( ord_less @ int @ K_1 @ L_1 )
| ( ord_less @ int @ ( bit0 @ K_1 ) @ ( bit0 @ L_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[365]) ).
thf(450,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)],[364]) ).
thf(451,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 ) ) )
& ! [V_1: $i,V: $i] :
( ( 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 ) ) )
& ! [V_1: $i,V: $i] :
( ( 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 @ ( plus_plus @ int @ V @ V_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[363]) ).
thf(452,plain,
( ( ( one_one @ int )
= ( number_number_of @ int @ ( bit1 @ pls ) ) )
= $true ),
inference(copy,[status(thm)],[251]) ).
thf(453,plain,
( ( ( number_number_of @ nat @ ( bit1 @ pls ) )
= ( one_one @ nat ) )
= $true ),
inference(copy,[status(thm)],[250]) ).
thf(454,plain,
( ( ( one_one @ nat )
= ( number_number_of @ nat @ ( bit1 @ pls ) ) )
= $true ),
inference(copy,[status(thm)],[249]) ).
thf(455,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 ) )
& ! [Xa: $i,Ya: $i] :
( ( Xa != Ya )
| ( ( number_number_of @ X_a @ Xa )
= ( number_number_of @ X_a @ Ya ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[362]) ).
thf(456,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 ) ) )
& ! [Wa: $i,Xa: $i] :
( ( ( ti @ X_a @ Xa )
!= ( number_number_of @ X_a @ Wa ) )
| ( ( number_number_of @ X_a @ Wa )
= ( ti @ X_a @ Xa ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[361]) ).
thf(457,plain,
( ( ! [K_1: $i,L_1: $i] :
( ( ( bit1 @ K_1 )
!= ( bit1 @ L_1 ) )
| ( K_1 = L_1 ) )
& ! [K_1: $i,L_1: $i] :
( ( K_1 != L_1 )
| ( ( bit1 @ K_1 )
= ( bit1 @ L_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[360]) ).
thf(458,plain,
( ( ! [K_1: $i,L_1: $i] :
( ( ( bit0 @ K_1 )
!= ( bit0 @ L_1 ) )
| ( K_1 = L_1 ) )
& ! [K_1: $i,L_1: $i] :
( ( K_1 != L_1 )
| ( ( bit0 @ K_1 )
= ( bit0 @ L_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[359]) ).
thf(459,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 ) ) )
& ! [A_2: $i] :
( ~ ( ord_less @ X_a @ A_2 @ ( zero_zero @ X_a ) )
| ( ord_less @ X_a @ ( plus_plus @ X_a @ A_2 @ A_2 ) @ ( zero_zero @ X_a ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[358]) ).
thf(460,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)],[243]) ).
thf(461,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)],[242]) ).
thf(462,plain,
( ( ! [Z: $i,W: $i] :
( ( plus_plus @ int @ Z @ W )
= ( plus_plus @ int @ W @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[241]) ).
thf(463,plain,
( ( ! [Ma: $i,Na: $i] :
( ( ( semiring_1_of_nat @ int @ Ma )
!= ( semiring_1_of_nat @ int @ Na ) )
| ( Ma = Na ) )
& ! [Ma: $i,Na: $i] :
( ( Ma != Na )
| ( ( semiring_1_of_nat @ int @ Ma )
= ( semiring_1_of_nat @ int @ Na ) ) ) )
= $true ),
inference(copy,[status(thm)],[357]) ).
thf(464,plain,
( ( ! [K_1: $i] :
( ~ ( ord_less @ int @ ( bit1 @ K_1 ) @ pls )
| ( ord_less @ int @ K_1 @ pls ) )
& ! [K_1: $i] :
( ~ ( ord_less @ int @ K_1 @ pls )
| ( ord_less @ int @ ( bit1 @ K_1 ) @ pls ) ) )
= $true ),
inference(copy,[status(thm)],[356]) ).
thf(465,plain,
( ( ! [K1: $i,K2: $i] :
( ~ ( ord_less @ int @ ( bit1 @ K1 ) @ ( bit0 @ K2 ) )
| ( ord_less @ int @ K1 @ K2 ) )
& ! [K1: $i,K2: $i] :
( ~ ( ord_less @ int @ K1 @ K2 )
| ( ord_less @ int @ ( bit1 @ K1 ) @ ( bit0 @ K2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[355]) ).
thf(466,plain,
( ( ! [K_1: $i,L_1: $i] :
( ~ ( ord_less @ int @ ( bit1 @ K_1 ) @ ( bit0 @ L_1 ) )
| ( ord_less @ int @ K_1 @ L_1 ) )
& ! [K_1: $i,L_1: $i] :
( ~ ( ord_less @ int @ K_1 @ L_1 )
| ( ord_less @ int @ ( bit1 @ K_1 ) @ ( bit0 @ L_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[354]) ).
thf(467,plain,
( ( ! [K_1: $i] :
( ~ ( ord_less @ int @ ( bit0 @ K_1 ) @ pls )
| ( ord_less @ int @ K_1 @ pls ) )
& ! [K_1: $i] :
( ~ ( ord_less @ int @ K_1 @ pls )
| ( ord_less @ int @ ( bit0 @ K_1 ) @ pls ) ) )
= $true ),
inference(copy,[status(thm)],[353]) ).
thf(468,plain,
( ( ! [K_1: $i] :
( ~ ( ord_less @ int @ pls @ ( bit0 @ K_1 ) )
| ( ord_less @ int @ pls @ K_1 ) )
& ! [K_1: $i] :
( ~ ( ord_less @ int @ pls @ K_1 )
| ( ord_less @ int @ pls @ ( bit0 @ K_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[352]) ).
thf(469,plain,
( ( ! [Wa: $i] :
( ~ ( ord_less @ int @ ( bit1 @ Wa ) @ ( zero_zero @ int ) )
| ( ord_less @ int @ Wa @ ( zero_zero @ int ) ) )
& ! [Wa: $i] :
( ~ ( ord_less @ int @ Wa @ ( zero_zero @ int ) )
| ( ord_less @ int @ ( bit1 @ Wa ) @ ( zero_zero @ int ) ) ) )
= $true ),
inference(copy,[status(thm)],[351]) ).
thf(470,plain,
( ( ~ ( ord_less @ int @ pls @ ( zero_zero @ int ) ) )
= $true ),
inference(copy,[status(thm)],[233]) ).
thf(471,plain,
( ( ! [Wa: $i] :
( ~ ( ord_less @ int @ ( bit0 @ Wa ) @ ( zero_zero @ int ) )
| ( ord_less @ int @ Wa @ ( zero_zero @ int ) ) )
& ! [Wa: $i] :
( ~ ( ord_less @ int @ Wa @ ( zero_zero @ int ) )
| ( ord_less @ int @ ( bit0 @ Wa ) @ ( zero_zero @ int ) ) ) )
= $true ),
inference(copy,[status(thm)],[350]) ).
thf(472,plain,
( ( ord_less @ int @ ( zero_zero @ int ) @ ( one_one @ int ) )
= $true ),
inference(copy,[status(thm)],[231]) ).
thf(473,plain,
( ( ! [Wa: $i,Z_1: $i] :
( ~ ( ord_less @ int @ Wa @ ( plus_plus @ int @ Z_1 @ ( one_one @ int ) ) )
| ( Wa = Z_1 )
| ( ord_less @ int @ Wa @ Z_1 ) )
& ! [Wa: $i,Z_1: $i] :
( ( Wa != Z_1 )
| ( ord_less @ int @ Wa @ ( plus_plus @ int @ Z_1 @ ( one_one @ int ) ) ) )
& ! [Wa: $i,Z_1: $i] :
( ~ ( ord_less @ int @ Wa @ Z_1 )
| ( ord_less @ int @ Wa @ ( plus_plus @ int @ Z_1 @ ( one_one @ int ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[349]) ).
thf(474,plain,
( ( ! [K: $i] :
~ ( ord_less @ int @ ( semiring_1_of_nat @ int @ K ) @ ( zero_zero @ int ) ) )
= $true ),
inference(copy,[status(thm)],[229]) ).
thf(475,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 ) ) )
& ! [Z_1: $i] :
( ~ ( ord_less @ int @ Z_1 @ ( zero_zero @ int ) )
| ( ord_less @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ Z_1 ) @ Z_1 ) @ ( zero_zero @ int ) ) ) )
= $true ),
inference(copy,[status(thm)],[348]) ).
thf(476,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 ) ) )
& ! [A_2: $i] :
( ( ( ti @ X_a @ A_2 )
!= ( zero_zero @ X_a ) )
| ( ( plus_plus @ X_a @ A_2 @ A_2 )
= ( zero_zero @ X_a ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[347]) ).
thf(477,plain,
( ( ! [K: $i] :
( ( bit1 @ K )
!= pls ) )
= $true ),
inference(copy,[status(thm)],[346]) ).
thf(478,plain,
( ( ! [L: $i] :
( pls
!= ( bit1 @ L ) ) )
= $true ),
inference(copy,[status(thm)],[345]) ).
thf(479,plain,
( ( ! [K: $i,L: $i] :
( ( bit1 @ K )
!= ( bit0 @ L ) ) )
= $true ),
inference(copy,[status(thm)],[344]) ).
thf(480,plain,
( ( ! [K: $i,L: $i] :
( ( bit0 @ K )
!= ( bit1 @ L ) ) )
= $true ),
inference(copy,[status(thm)],[343]) ).
thf(481,plain,
( ( ! [K_1: $i] :
( ( ( bit0 @ K_1 )
!= pls )
| ( K_1 = pls ) )
& ! [K_1: $i] :
( ( K_1 != pls )
| ( ( bit0 @ K_1 )
= pls ) ) )
= $true ),
inference(copy,[status(thm)],[342]) ).
thf(482,plain,
( ( ! [L_1: $i] :
( ( pls
!= ( bit0 @ L_1 ) )
| ( pls = L_1 ) )
& ! [L_1: $i] :
( ( pls != L_1 )
| ( pls
= ( bit0 @ L_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[341]) ).
thf(483,plain,
( ( ( bit0 @ pls )
= pls )
= $true ),
inference(copy,[status(thm)],[220]) ).
thf(484,plain,
( ( pls
= ( zero_zero @ int ) )
= $true ),
inference(copy,[status(thm)],[219]) ).
thf(485,plain,
( ( ( ( zero_zero @ int )
!= ( one_one @ int ) ) )
= $true ),
inference(copy,[status(thm)],[340]) ).
thf(486,plain,
( ( ! [K: $i] :
( ( plus_plus @ int @ K @ pls )
= K ) )
= $true ),
inference(copy,[status(thm)],[217]) ).
thf(487,plain,
( ( ! [K: $i] :
( ( plus_plus @ int @ pls @ K )
= K ) )
= $true ),
inference(copy,[status(thm)],[216]) ).
thf(488,plain,
( ( ! [K: $i,L: $i] :
( ( plus_plus @ int @ ( bit0 @ K ) @ ( bit0 @ L ) )
= ( bit0 @ ( plus_plus @ int @ K @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[215]) ).
thf(489,plain,
( ( ! [K: $i] :
( ( bit0 @ K )
= ( plus_plus @ int @ K @ K ) ) )
= $true ),
inference(copy,[status(thm)],[214]) ).
thf(490,plain,
( ( ! [Z: $i] :
( ( plus_plus @ int @ Z @ ( zero_zero @ int ) )
= Z ) )
= $true ),
inference(copy,[status(thm)],[213]) ).
thf(491,plain,
( ( ! [Z: $i] :
( ( plus_plus @ int @ ( zero_zero @ int ) @ Z )
= Z ) )
= $true ),
inference(copy,[status(thm)],[212]) ).
thf(492,plain,
( ( ! [X_a: $i] :
( ~ ( number_semiring @ X_a )
| ( ( number_number_of @ X_a @ pls )
= ( zero_zero @ X_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[339]) ).
thf(493,plain,
( ( ! [X_a: $i] :
( ~ ( number_ring @ X_a )
| ( ( number_number_of @ X_a @ pls )
= ( zero_zero @ X_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[338]) ).
thf(494,plain,
( ( ! [X_a: $i] :
( ~ ( number_ring @ X_a )
| ( ( zero_zero @ X_a )
= ( number_number_of @ X_a @ pls ) ) ) )
= $true ),
inference(copy,[status(thm)],[337]) ).
thf(495,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)],[336]) ).
thf(496,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)],[335]) ).
thf(497,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)],[334]) ).
thf(498,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)],[333]) ).
thf(499,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)],[332]) ).
thf(500,plain,
( ( ! [K: $i,L: $i] :
( ( plus_plus @ int @ ( bit1 @ K ) @ ( bit0 @ L ) )
= ( bit1 @ ( plus_plus @ int @ K @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[203]) ).
thf(501,plain,
( ( ! [K: $i,L: $i] :
( ( plus_plus @ int @ ( bit0 @ K ) @ ( bit1 @ L ) )
= ( bit1 @ ( plus_plus @ int @ K @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[202]) ).
thf(502,plain,
( ( ! [K: $i] :
( ( bit1 @ K )
= ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ K ) @ K ) ) )
= $true ),
inference(copy,[status(thm)],[201]) ).
thf(503,plain,
( ( ! [Z: $i] :
( ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ Z ) @ Z )
!= ( zero_zero @ int ) ) )
= $true ),
inference(copy,[status(thm)],[331]) ).
thf(504,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)],[330]) ).
thf(505,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)],[329]) ).
thf(506,plain,
( ( linord219039673up_add @ int )
= $true ),
inference(copy,[status(thm)],[197]) ).
thf(507,plain,
( ( ring_11004092258visors @ int )
= $true ),
inference(copy,[status(thm)],[196]) ).
thf(508,plain,
( ( no_zero_divisors @ int )
= $true ),
inference(copy,[status(thm)],[195]) ).
thf(509,plain,
( ( linordered_idom @ int )
= $true ),
inference(copy,[status(thm)],[194]) ).
thf(510,plain,
( ( number_semiring @ int )
= $true ),
inference(copy,[status(thm)],[193]) ).
thf(511,plain,
( ( zero_neq_one @ int )
= $true ),
inference(copy,[status(thm)],[192]) ).
thf(512,plain,
( ( semiring_1 @ int )
= $true ),
inference(copy,[status(thm)],[191]) ).
thf(513,plain,
( ( semiring_0 @ int )
= $true ),
inference(copy,[status(thm)],[190]) ).
thf(514,plain,
( ( mult_zero @ int )
= $true ),
inference(copy,[status(thm)],[189]) ).
thf(515,plain,
( ( ring_char_0 @ int )
= $true ),
inference(copy,[status(thm)],[188]) ).
thf(516,plain,
( ( number_ring @ int )
= $true ),
inference(copy,[status(thm)],[187]) ).
thf(517,plain,
( ( power @ int )
= $true ),
inference(copy,[status(thm)],[186]) ).
thf(518,plain,
( ( number @ int )
= $true ),
inference(copy,[status(thm)],[185]) ).
thf(519,plain,
( ( no_zero_divisors @ nat )
= $true ),
inference(copy,[status(thm)],[184]) ).
thf(520,plain,
( ( number_semiring @ nat )
= $true ),
inference(copy,[status(thm)],[183]) ).
thf(521,plain,
( ( zero_neq_one @ nat )
= $true ),
inference(copy,[status(thm)],[182]) ).
thf(522,plain,
( ( semiring_1 @ nat )
= $true ),
inference(copy,[status(thm)],[181]) ).
thf(523,plain,
( ( semiring_0 @ nat )
= $true ),
inference(copy,[status(thm)],[180]) ).
thf(524,plain,
( ( mult_zero @ nat )
= $true ),
inference(copy,[status(thm)],[179]) ).
thf(525,plain,
( ( power @ nat )
= $true ),
inference(copy,[status(thm)],[178]) ).
thf(526,plain,
( ( number @ nat )
= $true ),
inference(copy,[status(thm)],[177]) ).
thf(527,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)],[328]) ).
thf(528,plain,
( ( ! [X_a: $i] :
( ~ ( mult_zero @ X_a )
| ~ ( power @ X_a )
| ~ ( no_zero_divisors @ X_a )
| ~ ( zero_neq_one @ X_a )
| ( ( ti @ X_a @ ( zero_zero @ X_a ) )
= ( zero_zero @ X_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[327]) ).
thf(529,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)],[326]) ).
thf(530,plain,
( ( ! [X_a: $i] :
( ( ti @ X_a @ ( undefined @ X_a ) )
= ( undefined @ X_a ) ) )
= $true ),
inference(copy,[status(thm)],[173]) ).
thf(531,plain,
( ( ! [B_1: $i] :
( ! [B_2: $i,X_a: $i] :
( ~ ( linordered_idom @ X_a )
| ~ ( ord_less @ X_a @ ( ti @ X_a @ B_1 ) @ B_2 )
| ( ord_less @ X_a @ B_1 @ B_2 ) )
& ! [B_2: $i,X_a: $i] :
( ~ ( linordered_idom @ X_a )
| ~ ( ord_less @ X_a @ B_1 @ B_2 )
| ( ord_less @ X_a @ ( ti @ X_a @ B_1 ) @ B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[325]) ).
thf(532,plain,
( ( ! [B_1: $i] :
( ! [B_2: $i,X_a: $i] :
( ~ ( linordered_idom @ X_a )
| ~ ( ord_less @ X_a @ B_1 @ ( ti @ X_a @ B_2 ) )
| ( ord_less @ X_a @ B_1 @ B_2 ) )
& ! [B_2: $i,X_a: $i] :
( ~ ( linordered_idom @ X_a )
| ~ ( ord_less @ X_a @ B_1 @ B_2 )
| ( ord_less @ X_a @ B_1 @ ( ti @ X_a @ B_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[324]) ).
thf(533,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ~ ( mult_zero @ X_a )
| ~ ( power @ X_a )
| ~ ( no_zero_divisors @ X_a )
| ~ ( zero_neq_one @ 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)],[323]) ).
thf(534,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ~ ( mult_zero @ X_a )
| ~ ( power @ X_a )
| ~ ( no_zero_divisors @ X_a )
| ~ ( zero_neq_one @ 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)],[322]) ).
thf(535,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ~ ( mult_zero @ X_a )
| ~ ( power @ X_a )
| ~ ( no_zero_divisors @ X_a )
| ~ ( zero_neq_one @ 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)],[321]) ).
thf(536,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)],[320]) ).
thf(537,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)],[319]) ).
thf(538,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)],[318]) ).
thf(539,plain,
( ( ! [X_a: $i] :
( ~ ( linordered_idom @ X_a )
| ~ ( number_ring @ 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 ) )
& ! [Xa: $i,Ya: $i] :
( ~ ( ord_less @ int @ Xa @ Ya )
| ( ord_less @ X_a @ ( number_number_of @ X_a @ Xa ) @ ( number_number_of @ X_a @ Ya ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[317]) ).
thf(540,plain,
( ( ! [X_a: $i] :
( ~ ( linordered_idom @ X_a )
| ~ ( number_ring @ X_a )
| ( ! [Xa: $i] :
( ~ ( ord_less @ X_a @ ( number_number_of @ X_a @ Xa ) @ ( zero_zero @ X_a ) )
| ( ord_less @ int @ Xa @ pls ) )
& ! [Xa: $i] :
( ~ ( ord_less @ int @ Xa @ pls )
| ( ord_less @ X_a @ ( number_number_of @ X_a @ Xa ) @ ( zero_zero @ X_a ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[316]) ).
thf(541,plain,
( ( ! [X_a: $i] :
( ~ ( linordered_idom @ X_a )
| ~ ( number_ring @ X_a )
| ( ! [Ya: $i] :
( ~ ( ord_less @ X_a @ ( zero_zero @ X_a ) @ ( number_number_of @ X_a @ Ya ) )
| ( ord_less @ int @ pls @ Ya ) )
& ! [Ya: $i] :
( ~ ( ord_less @ int @ pls @ Ya )
| ( ord_less @ X_a @ ( zero_zero @ X_a ) @ ( number_number_of @ X_a @ Ya ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[315]) ).
thf(542,plain,
( ( ! [X_a: $i] :
( ~ ( linordered_idom @ X_a )
| ~ ( number_ring @ X_a )
| ( ! [Xa: $i] :
( ~ ( ord_less @ X_a @ ( number_number_of @ X_a @ Xa ) @ ( one_one @ X_a ) )
| ( ord_less @ int @ Xa @ ( bit1 @ pls ) ) )
& ! [Xa: $i] :
( ~ ( ord_less @ int @ Xa @ ( bit1 @ pls ) )
| ( ord_less @ X_a @ ( number_number_of @ X_a @ Xa ) @ ( one_one @ X_a ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[314]) ).
thf(543,plain,
( ( ! [X_a: $i] :
( ~ ( linordered_idom @ X_a )
| ~ ( number_ring @ X_a )
| ( ! [Ya: $i] :
( ~ ( ord_less @ X_a @ ( one_one @ X_a ) @ ( number_number_of @ X_a @ Ya ) )
| ( ord_less @ int @ ( bit1 @ pls ) @ Ya ) )
& ! [Ya: $i] :
( ~ ( ord_less @ int @ ( bit1 @ pls ) @ Ya )
| ( ord_less @ X_a @ ( one_one @ X_a ) @ ( number_number_of @ X_a @ Ya ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[313]) ).
thf(544,plain,
( ( ! [X_a: $i] :
( ~ ( mult_zero @ X_a )
| ~ ( power @ X_a )
| ~ ( no_zero_divisors @ X_a )
| ~ ( zero_neq_one @ X_a )
| ( ! [A_2: $i,Wa: $i] :
( ( ( number_number_of @ nat @ Wa )
= ( zero_zero @ nat ) )
| ( ( ti @ X_a @ A_2 )
!= ( zero_zero @ X_a ) )
| ( ( power_power @ X_a @ A_2 @ ( number_number_of @ nat @ Wa ) )
= ( zero_zero @ X_a ) ) )
& ! [A_2: $i,Wa: $i] :
( ( ( power_power @ X_a @ A_2 @ ( number_number_of @ nat @ Wa ) )
!= ( zero_zero @ X_a ) )
| ( ( number_number_of @ nat @ Wa )
!= ( zero_zero @ nat ) ) )
& ! [A_2: $i] :
( ! [Wa: $i] :
( ( power_power @ X_a @ A_2 @ ( number_number_of @ nat @ Wa ) )
!= ( zero_zero @ X_a ) )
| ( ( ti @ X_a @ A_2 )
= ( zero_zero @ X_a ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[312]) ).
thf(545,plain,
( ( ! [X_a: $i] :
( ~ ( linordered_idom @ X_a )
| ( ! [A_2: $i] :
( ( ( ti @ X_a @ A_2 )
= ( zero_zero @ X_a ) )
| ( ord_less @ X_a @ ( zero_zero @ X_a ) @ ( power_power @ X_a @ A_2 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
& ! [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)],[311]) ).
thf(546,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 ) ) )
& ! [Xa: $i] :
( ( ( ti @ X_a @ Xa )
= ( zero_zero @ X_a ) )
| ! [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 ) ) ) ) ) ) )
& ! [Xa: $i,Ya: $i] :
( ( ( ti @ X_a @ Ya )
= ( zero_zero @ X_a ) )
| ( 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 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[310]) ).
thf(547,plain,
( ( ! [T: $i,A: $i] :
( ( ti @ T @ ( ti @ T @ A ) )
= ( ti @ T @ A ) ) )
= $true ),
inference(copy,[status(thm)],[156]) ).
thf(548,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)],[309]) ).
thf(549,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ord_less @ int @ ( bit1 @ SX0 ) @ ( zero_zero @ int ) )
| ( ord_less @ int @ SX0 @ ( zero_zero @ int ) ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less @ int @ SX0 @ ( zero_zero @ int ) )
| ( ord_less @ int @ ( bit1 @ SX0 ) @ ( zero_zero @ int ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[469]) ).
thf(550,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: $i,SX2: $i] :
( ( SX1 != SX2 )
| ( ( number_number_of @ SX0 @ SX1 )
= ( number_number_of @ SX0 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[455]) ).
thf(551,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( linordered_idom @ SX2 )
| ~ ( ord_less @ SX2 @ ( ti @ SX2 @ SX0 ) @ SX1 )
| ( ord_less @ SX2 @ SX0 @ SX1 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( linordered_idom @ SX2 )
| ~ ( ord_less @ SX2 @ SX0 @ SX1 )
| ( ord_less @ SX2 @ ( ti @ SX2 @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[531]) ).
thf(552,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ord_less @ int @ ( bit0 @ SX0 ) @ ( zero_zero @ int ) )
| ( ord_less @ int @ SX0 @ ( zero_zero @ int ) ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less @ int @ SX0 @ ( zero_zero @ int ) )
| ( ord_less @ int @ ( bit0 @ SX0 ) @ ( zero_zero @ int ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[471]) ).
thf(553,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ord_less @ int @ ( bit0 @ SX0 ) @ pls )
| ( ord_less @ int @ SX0 @ pls ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less @ int @ SX0 @ pls )
| ( ord_less @ int @ ( bit0 @ SX0 ) @ pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[467]) ).
thf(554,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ ( plus_plus @ int @ SX1 @ ( one_one @ int ) ) )
| ( SX0 = SX1 )
| ( ord_less @ int @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ord_less @ int @ SX0 @ ( plus_plus @ int @ SX1 @ ( one_one @ int ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ int @ SX0 @ ( plus_plus @ int @ SX1 @ ( one_one @ int ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[473]) ).
thf(555,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ nat @ ( ti @ nat @ SX0 ) @ SX1 )
| ( ord_less @ nat @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ nat @ SX0 @ SX1 )
| ( ord_less @ nat @ ( ti @ nat @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[413]) ).
thf(556,plain,
( ( ! [SX0: $i] :
( ~ ( linordered_idom @ SX0 )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( ( 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 ) ) )
| ~ ~ ( ~ ! [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 ) ) )
| ~ ! [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 @ SX2 )
= ( zero_zero @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[418]) ).
thf(557,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 ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ( ( ti @ SX0 @ SX1 )
= ( zero_zero @ SX0 ) )
| ! [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 ) ) ) ) ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( ( 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)],[546]) ).
thf(558,plain,
( ( ! [SX0: $i] :
( ~ ( linordered_idom @ SX0 )
| ~ ( number_ring @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ord_less @ SX0 @ ( number_number_of @ SX0 @ SX1 ) @ ( one_one @ SX0 ) )
| ( ord_less @ int @ SX1 @ ( bit1 @ pls ) ) )
| ~ ! [SX1: $i] :
( ~ ( ord_less @ int @ SX1 @ ( bit1 @ pls ) )
| ( ord_less @ SX0 @ ( number_number_of @ SX0 @ SX1 ) @ ( one_one @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[542]) ).
thf(559,plain,
( ( ! [SX0: $i] :
( ~ ( linordered_idom @ SX0 )
| ~ ( number_ring @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ord_less @ SX0 @ ( zero_zero @ SX0 ) @ ( number_number_of @ SX0 @ SX1 ) )
| ( ord_less @ int @ pls @ SX1 ) )
| ~ ! [SX1: $i] :
( ~ ( ord_less @ int @ pls @ SX1 )
| ( ord_less @ SX0 @ ( zero_zero @ SX0 ) @ ( number_number_of @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[541]) ).
thf(560,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less @ int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[448]) ).
thf(561,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ord_less @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ SX0 ) @ SX0 ) @ ( zero_zero @ int ) )
| ( ord_less @ int @ SX0 @ ( zero_zero @ int ) ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less @ int @ SX0 @ ( zero_zero @ int ) )
| ( ord_less @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ SX0 ) @ SX0 ) @ ( zero_zero @ int ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[475]) ).
thf(562,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ nat @ SX0 @ ( ti @ nat @ SX1 ) )
| ( ord_less @ nat @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ nat @ SX0 @ SX1 )
| ( ord_less @ nat @ SX0 @ ( ti @ nat @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[414]) ).
thf(563,plain,
( ( ! [SX0: $i] :
( ~ ( mult_zero @ SX0 )
| ~ ( power @ SX0 )
| ~ ( no_zero_divisors @ SX0 )
| ~ ( zero_neq_one @ SX0 )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( ( number_number_of @ nat @ SX2 )
= ( zero_zero @ nat ) )
| ( ( ti @ SX0 @ SX1 )
!= ( zero_zero @ SX0 ) )
| ( ( power_power @ SX0 @ SX1 @ ( number_number_of @ nat @ SX2 ) )
= ( zero_zero @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( ( power_power @ SX0 @ SX1 @ ( number_number_of @ nat @ SX2 ) )
!= ( zero_zero @ SX0 ) )
| ( ( number_number_of @ nat @ SX2 )
!= ( zero_zero @ nat ) ) )
| ~ ! [SX1: $i] :
( ! [SX2: $i] :
( ( power_power @ SX0 @ SX1 @ ( number_number_of @ nat @ SX2 ) )
!= ( zero_zero @ SX0 ) )
| ( ( ti @ SX0 @ SX1 )
= ( zero_zero @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[544]) ).
thf(564,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( linordered_idom @ SX2 )
| ~ ( ord_less @ SX2 @ SX0 @ ( ti @ SX2 @ SX1 ) )
| ( ord_less @ SX2 @ SX0 @ SX1 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( linordered_idom @ SX2 )
| ~ ( ord_less @ SX2 @ SX0 @ SX1 )
| ( ord_less @ SX2 @ SX0 @ ( ti @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[532]) ).
thf(565,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ord_less @ int @ ( bit1 @ SX0 ) @ pls )
| ( ord_less @ int @ SX0 @ pls ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less @ int @ SX0 @ pls )
| ( ord_less @ int @ ( bit1 @ SX0 ) @ pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[464]) ).
thf(566,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( bit1 @ SX0 )
!= ( bit1 @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( bit1 @ SX0 )
= ( bit1 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[457]) ).
thf(567,plain,
( ( ! [SX0: $i] :
( ~ ( linord219039673up_add @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ( ( plus_plus @ SX0 @ SX1 @ SX1 )
!= ( zero_zero @ SX0 ) )
| ( ( ti @ SX0 @ SX1 )
= ( zero_zero @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ( ( ti @ SX0 @ SX1 )
!= ( zero_zero @ SX0 ) )
| ( ( plus_plus @ SX0 @ SX1 @ SX1 )
= ( zero_zero @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[476]) ).
thf(568,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less @ int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[446]) ).
thf(569,plain,
( ( ! [SX0: $i] :
( ~ ( linordered_idom @ SX0 )
| ~ ( number_ring @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ord_less @ SX0 @ ( number_number_of @ SX0 @ SX1 ) @ ( zero_zero @ SX0 ) )
| ( ord_less @ int @ SX1 @ pls ) )
| ~ ! [SX1: $i] :
( ~ ( ord_less @ int @ SX1 @ pls )
| ( ord_less @ SX0 @ ( number_number_of @ SX0 @ SX1 ) @ ( zero_zero @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[540]) ).
thf(570,plain,
( ( ! [SX0: $i] :
( ~ ( linordered_idom @ SX0 )
| ~ ( number_ring @ SX0 )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ord_less @ SX0 @ ( number_number_of @ SX0 @ SX1 ) @ ( number_number_of @ SX0 @ SX2 ) )
| ( ord_less @ int @ SX1 @ SX2 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( ord_less @ int @ SX1 @ SX2 )
| ( ord_less @ SX0 @ ( number_number_of @ SX0 @ SX1 ) @ ( number_number_of @ SX0 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[539]) ).
thf(571,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( bit0 @ SX0 )
!= ( bit0 @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( bit0 @ SX0 )
= ( bit0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[458]) ).
thf(572,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less @ int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[449]) ).
thf(573,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 ) ) )
| ~ ! [SX1: $i] :
( ~ ( ord_less @ SX0 @ SX1 @ ( zero_zero @ SX0 ) )
| ( ord_less @ SX0 @ ( plus_plus @ SX0 @ SX1 @ SX1 ) @ ( zero_zero @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[459]) ).
thf(574,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 ) ) )
| ~ ! [SX1: $i] :
( ( ( 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)],[427]) ).
thf(575,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX1 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SX1 ) @ ( number_number_of @ nat @ SX0 ) )
= ( number_number_of @ nat @ SX0 ) ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ord_less @ int @ SX1 @ pls )
| ~ ( ord_less @ int @ SX0 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SX1 ) @ ( number_number_of @ nat @ SX0 ) )
= ( number_number_of @ nat @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( ord_less @ int @ SX1 @ pls )
| ( ord_less @ int @ SX0 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SX1 ) @ ( number_number_of @ nat @ SX0 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SX1 @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[451]) ).
thf(576,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( ( semiring_1_of_nat @ int @ SX0 )
!= ( zero_zero @ int ) )
| ( SX0
= ( zero_zero @ nat ) ) )
| ~ ! [SX0: $i] :
( ( SX0
!= ( zero_zero @ nat ) )
| ( ( semiring_1_of_nat @ int @ SX0 )
= ( zero_zero @ int ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[442]) ).
thf(577,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ord_less @ int @ pls @ ( bit0 @ SX0 ) )
| ( ord_less @ int @ pls @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less @ int @ pls @ SX0 )
| ( ord_less @ int @ pls @ ( bit0 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[468]) ).
thf(578,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less @ int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[466]) ).
thf(579,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less @ int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[445]) ).
thf(580,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 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( ( ti @ SX0 @ SX2 )
!= ( number_number_of @ SX0 @ SX1 ) )
| ( ( number_number_of @ SX0 @ SX1 )
= ( ti @ SX0 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[456]) ).
thf(581,plain,
( ( ! [SX0: $i] :
( ~ ( linordered_idom @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ( ( ti @ SX0 @ SX1 )
= ( zero_zero @ SX0 ) )
| ( ord_less @ SX0 @ ( zero_zero @ SX0 ) @ ( power_power @ SX0 @ SX1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
| ~ ! [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 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[545]) ).
thf(582,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( semiring_1_of_nat @ int @ SX0 )
!= ( semiring_1_of_nat @ int @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( semiring_1_of_nat @ int @ SX0 )
= ( semiring_1_of_nat @ int @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[463]) ).
thf(583,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( ( bit0 @ SX0 )
!= pls )
| ( SX0 = pls ) )
| ~ ! [SX0: $i] :
( ( SX0 != pls )
| ( ( bit0 @ SX0 )
= pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[481]) ).
thf(584,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 ) ) )
| ~ ! [SX1: $i] :
( ( ( 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)],[421]) ).
thf(585,plain,
( ( ! [SX0: $i] :
( ~ ( linordered_idom @ SX0 )
| ~ ( number_ring @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ord_less @ SX0 @ ( one_one @ SX0 ) @ ( number_number_of @ SX0 @ SX1 ) )
| ( ord_less @ int @ ( bit1 @ pls ) @ SX1 ) )
| ~ ! [SX1: $i] :
( ~ ( ord_less @ int @ ( bit1 @ pls ) @ SX1 )
| ( ord_less @ SX0 @ ( one_one @ SX0 ) @ ( number_number_of @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[543]) ).
thf(586,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( pls
!= ( bit0 @ SX0 ) )
| ( pls = SX0 ) )
| ~ ! [SX0: $i] :
( ( pls != SX0 )
| ( pls
= ( bit0 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[482]) ).
thf(587,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ ( number_number_of @ int @ SX0 ) @ ( number_number_of @ int @ SX1 ) )
| ( ord_less @ int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ int @ ( number_number_of @ int @ SX0 ) @ ( number_number_of @ int @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[432]) ).
thf(588,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less @ int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[465]) ).
thf(589,plain,
! [SV1: $i] :
( ( ( bit0 @ ( ti @ int @ SV1 ) )
= ( bit0 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[396]) ).
thf(590,plain,
! [SV2: $i] :
( ( ( ti @ int @ ( bit0 @ SV2 ) )
= ( bit0 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[397]) ).
thf(591,plain,
! [SV3: $i] :
( ( ( bit1 @ ( ti @ int @ SV3 ) )
= ( bit1 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[398]) ).
thf(592,plain,
! [SV4: $i] :
( ( ( ti @ int @ ( bit1 @ SV4 ) )
= ( bit1 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[399]) ).
thf(593,plain,
! [SV5: $i] :
( ( ! [SY210: $i,SY211: $i] :
( ~ ( linord219039673up_add @ SY211 )
| ( ( plus_plus @ SY211 @ ( ti @ SY211 @ SV5 ) @ SY210 )
= ( plus_plus @ SY211 @ SV5 @ SY210 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[402]) ).
thf(594,plain,
! [SV6: $i] :
( ( ! [SY212: $i,SY213: $i] :
( ~ ( linord219039673up_add @ SY213 )
| ( ( plus_plus @ SY213 @ SV6 @ ( ti @ SY213 @ SY212 ) )
= ( plus_plus @ SY213 @ SV6 @ SY212 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[403]) ).
thf(595,plain,
! [SV7: $i] :
( ( ! [SY214: $i,SY215: $i] :
( ~ ( linord219039673up_add @ SY215 )
| ( ( ti @ SY215 @ ( plus_plus @ SY215 @ SV7 @ SY214 ) )
= ( plus_plus @ SY215 @ SV7 @ SY214 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[404]) ).
thf(596,plain,
! [SV8: $i] :
( ( ! [SY216: $i,SY217: $i] :
( ~ ( number_semiring @ SY217 )
| ( ( plus_plus @ SY217 @ ( ti @ SY217 @ SV8 ) @ SY216 )
= ( plus_plus @ SY217 @ SV8 @ SY216 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[405]) ).
thf(597,plain,
! [SV9: $i] :
( ( ! [SY218: $i,SY219: $i] :
( ~ ( number_semiring @ SY219 )
| ( ( plus_plus @ SY219 @ SV9 @ ( ti @ SY219 @ SY218 ) )
= ( plus_plus @ SY219 @ SV9 @ SY218 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[406]) ).
thf(598,plain,
! [SV10: $i] :
( ( ! [SY220: $i,SY221: $i] :
( ~ ( number_semiring @ SY221 )
| ( ( ti @ SY221 @ ( plus_plus @ SY221 @ SV10 @ SY220 ) )
= ( plus_plus @ SY221 @ SV10 @ SY220 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[407]) ).
thf(599,plain,
! [SV11: $i] :
( ( ~ ( linord219039673up_add @ SV11 )
| ( ( ti @ SV11 @ ( zero_zero @ SV11 ) )
= ( zero_zero @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[408]) ).
thf(600,plain,
! [SV12: $i] :
( ( ! [SY222: $i] :
( ~ ( number @ SY222 )
| ( ( number_number_of @ SY222 @ ( ti @ int @ SV12 ) )
= ( number_number_of @ SY222 @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[409]) ).
thf(601,plain,
! [SV13: $i] :
( ( ! [SY223: $i] :
( ~ ( number @ SY223 )
| ( ( ti @ SY223 @ ( number_number_of @ SY223 @ SV13 ) )
= ( number_number_of @ SY223 @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[410]) ).
thf(602,plain,
! [SV14: $i] :
( ( ! [SY224: $i] :
( ~ ( number_semiring @ SY224 )
| ( ( semiring_1_of_nat @ SY224 @ ( ti @ nat @ SV14 ) )
= ( semiring_1_of_nat @ SY224 @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[411]) ).
thf(603,plain,
! [SV15: $i] :
( ( ! [SY225: $i] :
( ~ ( number_semiring @ SY225 )
| ( ( ti @ SY225 @ ( semiring_1_of_nat @ SY225 @ SV15 ) )
= ( semiring_1_of_nat @ SY225 @ SV15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[412]) ).
thf(604,plain,
! [SV16: $i] :
( ( ~ ( semiring_1 @ SV16 )
| ( ( power_power @ SV16 @ ( one_one @ SV16 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( one_one @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[419]) ).
thf(605,plain,
! [SV17: $i] :
( ( ~ ( semiring_1 @ SV17 )
| ( ( power_power @ SV17 @ ( zero_zero @ SV17 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[420]) ).
thf(606,plain,
! [SV18: $i] :
( ( ~ ( number_ring @ SV18 )
| ! [SY226: $i] :
( ( plus_plus @ SV18 @ ( one_one @ SV18 ) @ ( number_number_of @ SV18 @ SY226 ) )
= ( number_number_of @ SV18 @ ( plus_plus @ int @ ( bit1 @ pls ) @ SY226 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[422]) ).
thf(607,plain,
! [SV19: $i] :
( ( ~ ( number_ring @ SV19 )
| ! [SY227: $i] :
( ( plus_plus @ SV19 @ ( number_number_of @ SV19 @ SY227 ) @ ( one_one @ SV19 ) )
= ( number_number_of @ SV19 @ ( plus_plus @ int @ SY227 @ ( bit1 @ pls ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[423]) ).
thf(608,plain,
! [SV20: $i] :
( ( ~ ( number_ring @ SV20 )
| ( ( plus_plus @ SV20 @ ( one_one @ SV20 ) @ ( one_one @ SV20 ) )
= ( number_number_of @ SV20 @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[424]) ).
thf(609,plain,
! [SV21: $i] :
( ( ~ ( number_semiring @ SV21 )
| ( ( plus_plus @ SV21 @ ( one_one @ SV21 ) @ ( one_one @ SV21 ) )
= ( number_number_of @ SV21 @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[425]) ).
thf(610,plain,
! [SV22: $i] :
( ( ( power_power @ int @ ( power_power @ int @ SV22 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power @ int @ SV22 @ ( number_number_of @ nat @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[426]) ).
thf(611,plain,
! [SV23: $i] :
( ( ~ ( number_ring @ SV23 )
| ( ( one_one @ SV23 )
= ( number_number_of @ SV23 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[428]) ).
thf(612,plain,
! [SV24: $i] :
( ( ~ ( number_ring @ SV24 )
| ( ( number_number_of @ SV24 @ ( bit1 @ pls ) )
= ( one_one @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[429]) ).
thf(613,plain,
! [SV25: $i] :
( ( ! [SY228: $i] :
( ( ord_less @ int @ SY228 @ SV25 )
| ( SV25 = SY228 )
| ( ord_less @ int @ SV25 @ SY228 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[431]) ).
thf(614,plain,
! [SV26: $i] :
( ( ! [SY229: $i] :
( ( plus_plus @ int @ ( number_number_of @ int @ SV26 ) @ ( number_number_of @ int @ SY229 ) )
= ( number_number_of @ int @ ( plus_plus @ int @ SV26 @ SY229 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[433]) ).
thf(615,plain,
! [SV27: $i] :
( ( ! [SY230: $i] :
( ( power_power @ int @ ( semiring_1_of_nat @ int @ SV27 ) @ SY230 )
= ( semiring_1_of_nat @ int @ ( power_power @ nat @ SV27 @ SY230 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[435]) ).
thf(616,plain,
! [SV28: $i] :
( ( ! [SY231: $i] :
( ( semiring_1_of_nat @ int @ ( power_power @ nat @ SV28 @ SY231 ) )
= ( power_power @ int @ ( semiring_1_of_nat @ int @ SV28 ) @ SY231 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[436]) ).
thf(617,plain,
! [SV29: $i] :
( ( ! [SY232: $i,SY233: $i] :
( ( plus_plus @ int @ ( semiring_1_of_nat @ int @ SV29 ) @ ( plus_plus @ int @ ( semiring_1_of_nat @ int @ SY232 ) @ SY233 ) )
= ( plus_plus @ int @ ( semiring_1_of_nat @ int @ ( plus_plus @ nat @ SV29 @ SY232 ) ) @ SY233 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[437]) ).
thf(618,plain,
! [SV30: $i] :
( ( ! [SY234: $i] :
( ( plus_plus @ int @ ( semiring_1_of_nat @ int @ SV30 ) @ ( semiring_1_of_nat @ int @ SY234 ) )
= ( semiring_1_of_nat @ int @ ( plus_plus @ nat @ SV30 @ SY234 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[438]) ).
thf(619,plain,
( ( ord_less @ int @ pls @ pls )
= $false ),
inference(extcnf_not_pos,[status(thm)],[447]) ).
thf(620,plain,
! [SV31: $i] :
( ( ! [SY235: $i,SY236: $i] :
( ~ ( ord_less @ int @ SY235 @ SY236 )
| ( ord_less @ int @ ( plus_plus @ int @ SY235 @ SV31 ) @ ( plus_plus @ int @ SY236 @ SV31 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[450]) ).
thf(621,plain,
! [SV32: $i] :
( ( ! [SY237: $i,SY238: $i] :
( ( plus_plus @ int @ ( plus_plus @ int @ SV32 @ SY237 ) @ SY238 )
= ( plus_plus @ int @ SV32 @ ( plus_plus @ int @ SY237 @ SY238 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[460]) ).
thf(622,plain,
! [SV33: $i] :
( ( ! [SY239: $i,SY240: $i] :
( ( plus_plus @ int @ SV33 @ ( plus_plus @ int @ SY239 @ SY240 ) )
= ( plus_plus @ int @ SY239 @ ( plus_plus @ int @ SV33 @ SY240 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[461]) ).
thf(623,plain,
! [SV34: $i] :
( ( ! [SY241: $i] :
( ( plus_plus @ int @ SV34 @ SY241 )
= ( plus_plus @ int @ SY241 @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[462]) ).
thf(624,plain,
( ( ord_less @ int @ pls @ ( zero_zero @ int ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[470]) ).
thf(625,plain,
! [SV35: $i] :
( ( ~ ( ord_less @ int @ ( semiring_1_of_nat @ int @ SV35 ) @ ( zero_zero @ int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[474]) ).
thf(626,plain,
! [SV36: $i] :
( ( ( ( bit1 @ SV36 )
!= pls ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[477]) ).
thf(627,plain,
! [SV37: $i] :
( ( ( pls
!= ( bit1 @ SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[478]) ).
thf(628,plain,
! [SV38: $i] :
( ( ! [SY242: $i] :
( ( bit1 @ SV38 )
!= ( bit0 @ SY242 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[479]) ).
thf(629,plain,
! [SV39: $i] :
( ( ! [SY243: $i] :
( ( bit0 @ SV39 )
!= ( bit1 @ SY243 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[480]) ).
thf(630,plain,
( ( ( zero_zero @ int )
= ( one_one @ int ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[485]) ).
thf(631,plain,
! [SV40: $i] :
( ( ( plus_plus @ int @ SV40 @ pls )
= SV40 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[486]) ).
thf(632,plain,
! [SV41: $i] :
( ( ( plus_plus @ int @ pls @ SV41 )
= SV41 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[487]) ).
thf(633,plain,
! [SV42: $i] :
( ( ! [SY244: $i] :
( ( plus_plus @ int @ ( bit0 @ SV42 ) @ ( bit0 @ SY244 ) )
= ( bit0 @ ( plus_plus @ int @ SV42 @ SY244 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[488]) ).
thf(634,plain,
! [SV43: $i] :
( ( ( bit0 @ SV43 )
= ( plus_plus @ int @ SV43 @ SV43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[489]) ).
thf(635,plain,
! [SV44: $i] :
( ( ( plus_plus @ int @ SV44 @ ( zero_zero @ int ) )
= SV44 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[490]) ).
thf(636,plain,
! [SV45: $i] :
( ( ( plus_plus @ int @ ( zero_zero @ int ) @ SV45 )
= SV45 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[491]) ).
thf(637,plain,
! [SV46: $i] :
( ( ~ ( number_semiring @ SV46 )
| ( ( number_number_of @ SV46 @ pls )
= ( zero_zero @ SV46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[492]) ).
thf(638,plain,
! [SV47: $i] :
( ( ~ ( number_ring @ SV47 )
| ( ( number_number_of @ SV47 @ pls )
= ( zero_zero @ SV47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[493]) ).
thf(639,plain,
! [SV48: $i] :
( ( ~ ( number_ring @ SV48 )
| ( ( zero_zero @ SV48 )
= ( number_number_of @ SV48 @ pls ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[494]) ).
thf(640,plain,
! [SV49: $i] :
( ( ~ ( number_ring @ SV49 )
| ! [SY245: $i] :
( ( plus_plus @ SV49 @ ( number_number_of @ SV49 @ pls ) @ SY245 )
= ( ti @ SV49 @ SY245 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[495]) ).
thf(641,plain,
! [SV50: $i] :
( ( ~ ( number_ring @ SV50 )
| ! [SY246: $i] :
( ( plus_plus @ SV50 @ SY246 @ ( number_number_of @ SV50 @ pls ) )
= ( ti @ SV50 @ SY246 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[496]) ).
thf(642,plain,
! [SV51: $i] :
( ( ~ ( number_ring @ SV51 )
| ! [SY247: $i,SY248: $i,SY249: $i] :
( ( plus_plus @ SV51 @ ( number_number_of @ SV51 @ SY247 ) @ ( plus_plus @ SV51 @ ( number_number_of @ SV51 @ SY248 ) @ SY249 ) )
= ( plus_plus @ SV51 @ ( number_number_of @ SV51 @ ( plus_plus @ int @ SY247 @ SY248 ) ) @ SY249 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[497]) ).
thf(643,plain,
! [SV52: $i] :
( ( ~ ( number_ring @ SV52 )
| ! [SY250: $i,SY251: $i] :
( ( plus_plus @ SV52 @ ( number_number_of @ SV52 @ SY250 ) @ ( number_number_of @ SV52 @ SY251 ) )
= ( number_number_of @ SV52 @ ( plus_plus @ int @ SY250 @ SY251 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[498]) ).
thf(644,plain,
! [SV53: $i] :
( ( ~ ( number_ring @ SV53 )
| ! [SY252: $i,SY253: $i] :
( ( number_number_of @ SV53 @ ( plus_plus @ int @ SY252 @ SY253 ) )
= ( plus_plus @ SV53 @ ( number_number_of @ SV53 @ SY252 ) @ ( number_number_of @ SV53 @ SY253 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[499]) ).
thf(645,plain,
! [SV54: $i] :
( ( ! [SY254: $i] :
( ( plus_plus @ int @ ( bit1 @ SV54 ) @ ( bit0 @ SY254 ) )
= ( bit1 @ ( plus_plus @ int @ SV54 @ SY254 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[500]) ).
thf(646,plain,
! [SV55: $i] :
( ( ! [SY255: $i] :
( ( plus_plus @ int @ ( bit0 @ SV55 ) @ ( bit1 @ SY255 ) )
= ( bit1 @ ( plus_plus @ int @ SV55 @ SY255 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[501]) ).
thf(647,plain,
! [SV56: $i] :
( ( ( bit1 @ SV56 )
= ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ SV56 ) @ SV56 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[502]) ).
thf(648,plain,
! [SV57: $i] :
( ( ( ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ SV57 ) @ SV57 )
!= ( zero_zero @ int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[503]) ).
thf(649,plain,
! [SV58: $i] :
( ( ~ ( number_semiring @ SV58 )
| ! [SY256: $i] :
( ( number_number_of @ SV58 @ ( semiring_1_of_nat @ int @ SY256 ) )
= ( semiring_1_of_nat @ SV58 @ SY256 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[504]) ).
thf(650,plain,
! [SV59: $i] :
( ( ~ ( linordered_idom @ SV59 )
| ! [SY257: $i] :
~ ( ord_less @ SV59 @ ( power_power @ SV59 @ SY257 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( zero_zero @ SV59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[505]) ).
thf(651,plain,
! [SV60: $i] :
( ( ~ ( power @ SV60 )
| ~ ( semiring_0 @ SV60 )
| ( ( ti @ SV60 @ ( one_one @ SV60 ) )
= ( one_one @ SV60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[527]) ).
thf(652,plain,
! [SV61: $i] :
( ( ~ ( mult_zero @ SV61 )
| ~ ( power @ SV61 )
| ~ ( no_zero_divisors @ SV61 )
| ~ ( zero_neq_one @ SV61 )
| ( ( ti @ SV61 @ ( zero_zero @ SV61 ) )
= ( zero_zero @ SV61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[528]) ).
thf(653,plain,
! [SV62: $i] :
( ( ~ ( power @ SV62 )
| ~ ( semiring_0 @ SV62 )
| ( ( ti @ SV62 @ ( zero_zero @ SV62 ) )
= ( zero_zero @ SV62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[529]) ).
thf(654,plain,
! [SV63: $i] :
( ( ( ti @ SV63 @ ( undefined @ SV63 ) )
= ( undefined @ SV63 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[530]) ).
thf(655,plain,
! [SV64: $i] :
( ( ! [SY258: $i,SY259: $i] :
( ~ ( mult_zero @ SY259 )
| ~ ( power @ SY259 )
| ~ ( no_zero_divisors @ SY259 )
| ~ ( zero_neq_one @ SY259 )
| ( ( power_power @ SY259 @ ( ti @ SY259 @ SV64 ) @ SY258 )
= ( power_power @ SY259 @ SV64 @ SY258 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[533]) ).
thf(656,plain,
! [SV65: $i] :
( ( ! [SY260: $i,SY261: $i] :
( ~ ( mult_zero @ SY261 )
| ~ ( power @ SY261 )
| ~ ( no_zero_divisors @ SY261 )
| ~ ( zero_neq_one @ SY261 )
| ( ( power_power @ SY261 @ SV65 @ ( ti @ nat @ SY260 ) )
= ( power_power @ SY261 @ SV65 @ SY260 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[534]) ).
thf(657,plain,
! [SV66: $i] :
( ( ! [SY262: $i,SY263: $i] :
( ~ ( mult_zero @ SY263 )
| ~ ( power @ SY263 )
| ~ ( no_zero_divisors @ SY263 )
| ~ ( zero_neq_one @ SY263 )
| ( ( ti @ SY263 @ ( power_power @ SY263 @ SV66 @ SY262 ) )
= ( power_power @ SY263 @ SV66 @ SY262 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[535]) ).
thf(658,plain,
! [SV67: $i] :
( ( ! [SY264: $i,SY265: $i] :
( ~ ( power @ SY265 )
| ~ ( semiring_0 @ SY265 )
| ( ( power_power @ SY265 @ ( ti @ SY265 @ SV67 ) @ SY264 )
= ( power_power @ SY265 @ SV67 @ SY264 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[536]) ).
thf(659,plain,
! [SV68: $i] :
( ( ! [SY266: $i,SY267: $i] :
( ~ ( power @ SY267 )
| ~ ( semiring_0 @ SY267 )
| ( ( power_power @ SY267 @ SV68 @ ( ti @ nat @ SY266 ) )
= ( power_power @ SY267 @ SV68 @ SY266 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[537]) ).
thf(660,plain,
! [SV69: $i] :
( ( ! [SY268: $i,SY269: $i] :
( ~ ( power @ SY269 )
| ~ ( semiring_0 @ SY269 )
| ( ( ti @ SY269 @ ( power_power @ SY269 @ SV69 @ SY268 ) )
= ( power_power @ SY269 @ SV69 @ SY268 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[538]) ).
thf(661,plain,
! [SV70: $i] :
( ( ! [SY270: $i] :
( ( ti @ SV70 @ ( ti @ SV70 @ SY270 ) )
= ( ti @ SV70 @ SY270 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[547]) ).
thf(662,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less @ int @ ( bit1 @ SX0 ) @ ( zero_zero @ int ) )
| ( ord_less @ int @ SX0 @ ( zero_zero @ int ) ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less @ int @ SX0 @ ( zero_zero @ int ) )
| ( ord_less @ int @ ( bit1 @ SX0 ) @ ( zero_zero @ int ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[549]) ).
thf(663,plain,
! [SV71: $i] :
( ( ~ ( number_ring @ SV71 )
| ~ ( ring_char_0 @ SV71 )
| ~ ( ~ ! [SY271: $i,SY272: $i] :
( ( ( number_number_of @ SV71 @ SY271 )
!= ( number_number_of @ SV71 @ SY272 ) )
| ( SY271 = SY272 ) )
| ~ ! [SY273: $i,SY274: $i] :
( ( SY273 != SY274 )
| ( ( number_number_of @ SV71 @ SY273 )
= ( number_number_of @ SV71 @ SY274 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[550]) ).
thf(664,plain,
! [SV72: $i] :
( ( ~ ( ~ ! [SY275: $i,SY276: $i] :
( ~ ( linordered_idom @ SY276 )
| ~ ( ord_less @ SY276 @ ( ti @ SY276 @ SV72 ) @ SY275 )
| ( ord_less @ SY276 @ SV72 @ SY275 ) )
| ~ ! [SY277: $i,SY278: $i] :
( ~ ( linordered_idom @ SY278 )
| ~ ( ord_less @ SY278 @ SV72 @ SY277 )
| ( ord_less @ SY278 @ ( ti @ SY278 @ SV72 ) @ SY277 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[551]) ).
thf(665,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less @ int @ ( bit0 @ SX0 ) @ ( zero_zero @ int ) )
| ( ord_less @ int @ SX0 @ ( zero_zero @ int ) ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less @ int @ SX0 @ ( zero_zero @ int ) )
| ( ord_less @ int @ ( bit0 @ SX0 ) @ ( zero_zero @ int ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[552]) ).
thf(666,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less @ int @ ( bit0 @ SX0 ) @ pls )
| ( ord_less @ int @ SX0 @ pls ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less @ int @ SX0 @ pls )
| ( ord_less @ int @ ( bit0 @ SX0 ) @ pls ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[553]) ).
thf(667,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ ( plus_plus @ int @ SX1 @ ( one_one @ int ) ) )
| ( SX0 = SX1 )
| ( ord_less @ int @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ord_less @ int @ SX0 @ ( plus_plus @ int @ SX1 @ ( one_one @ int ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ int @ SX0 @ ( plus_plus @ int @ SX1 @ ( one_one @ int ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[554]) ).
thf(668,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ nat @ ( ti @ nat @ SX0 ) @ SX1 )
| ( ord_less @ nat @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ nat @ SX0 @ SX1 )
| ( ord_less @ nat @ ( ti @ nat @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[555]) ).
thf(669,plain,
! [SV73: $i] :
( ( ~ ( linordered_idom @ SV73 )
| ~ ( ~ ! [SY279: $i,SY280: $i] :
( ( ( ti @ SV73 @ SY279 )
!= ( zero_zero @ SV73 ) )
| ( ( ti @ SV73 @ SY280 )
!= ( zero_zero @ SV73 ) )
| ( ( plus_plus @ SV73 @ ( power_power @ SV73 @ SY279 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV73 @ SY280 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV73 ) ) )
| ~ ~ ( ~ ! [SY281: $i] :
( ! [SY282: $i] :
( ( plus_plus @ SV73 @ ( power_power @ SV73 @ SY281 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV73 @ SY282 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV73 ) )
| ( ( ti @ SV73 @ SY281 )
= ( zero_zero @ SV73 ) ) )
| ~ ! [SY283: $i,SY284: $i] :
( ( ( plus_plus @ SV73 @ ( power_power @ SV73 @ SY283 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV73 @ SY284 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV73 ) )
| ( ( ti @ SV73 @ SY284 )
= ( zero_zero @ SV73 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[556]) ).
thf(670,plain,
! [SV74: $i] :
( ( ~ ( linordered_idom @ SV74 )
| ~ ( ~ ! [SY285: $i,SY286: $i] :
( ~ ( ord_less @ SV74 @ ( zero_zero @ SV74 ) @ ( plus_plus @ SV74 @ ( power_power @ SV74 @ SY285 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV74 @ SY286 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
| ( ( ti @ SV74 @ SY285 )
!= ( zero_zero @ SV74 ) )
| ( ( ti @ SV74 @ SY286 )
!= ( zero_zero @ SV74 ) ) )
| ~ ~ ( ~ ! [SY287: $i] :
( ( ( ti @ SV74 @ SY287 )
= ( zero_zero @ SV74 ) )
| ! [SY288: $i] : ( ord_less @ SV74 @ ( zero_zero @ SV74 ) @ ( plus_plus @ SV74 @ ( power_power @ SV74 @ SY287 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV74 @ SY288 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
| ~ ! [SY289: $i,SY290: $i] :
( ( ( ti @ SV74 @ SY290 )
= ( zero_zero @ SV74 ) )
| ( ord_less @ SV74 @ ( zero_zero @ SV74 ) @ ( plus_plus @ SV74 @ ( power_power @ SV74 @ SY289 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV74 @ SY290 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[557]) ).
thf(671,plain,
! [SV75: $i] :
( ( ~ ( linordered_idom @ SV75 )
| ~ ( number_ring @ SV75 )
| ~ ( ~ ! [SY291: $i] :
( ~ ( ord_less @ SV75 @ ( number_number_of @ SV75 @ SY291 ) @ ( one_one @ SV75 ) )
| ( ord_less @ int @ SY291 @ ( bit1 @ pls ) ) )
| ~ ! [SY292: $i] :
( ~ ( ord_less @ int @ SY292 @ ( bit1 @ pls ) )
| ( ord_less @ SV75 @ ( number_number_of @ SV75 @ SY292 ) @ ( one_one @ SV75 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[558]) ).
thf(672,plain,
! [SV76: $i] :
( ( ~ ( linordered_idom @ SV76 )
| ~ ( number_ring @ SV76 )
| ~ ( ~ ! [SY293: $i] :
( ~ ( ord_less @ SV76 @ ( zero_zero @ SV76 ) @ ( number_number_of @ SV76 @ SY293 ) )
| ( ord_less @ int @ pls @ SY293 ) )
| ~ ! [SY294: $i] :
( ~ ( ord_less @ int @ pls @ SY294 )
| ( ord_less @ SV76 @ ( zero_zero @ SV76 ) @ ( number_number_of @ SV76 @ SY294 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[559]) ).
thf(673,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less @ int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[560]) ).
thf(674,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ SX0 ) @ SX0 ) @ ( zero_zero @ int ) )
| ( ord_less @ int @ SX0 @ ( zero_zero @ int ) ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less @ int @ SX0 @ ( zero_zero @ int ) )
| ( ord_less @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ SX0 ) @ SX0 ) @ ( zero_zero @ int ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[561]) ).
thf(675,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ nat @ SX0 @ ( ti @ nat @ SX1 ) )
| ( ord_less @ nat @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ nat @ SX0 @ SX1 )
| ( ord_less @ nat @ SX0 @ ( ti @ nat @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[562]) ).
thf(676,plain,
! [SV77: $i] :
( ( ~ ( mult_zero @ SV77 )
| ~ ( power @ SV77 )
| ~ ( no_zero_divisors @ SV77 )
| ~ ( zero_neq_one @ SV77 )
| ~ ( ~ ! [SY295: $i,SY296: $i] :
( ( ( number_number_of @ nat @ SY296 )
= ( zero_zero @ nat ) )
| ( ( ti @ SV77 @ SY295 )
!= ( zero_zero @ SV77 ) )
| ( ( power_power @ SV77 @ SY295 @ ( number_number_of @ nat @ SY296 ) )
= ( zero_zero @ SV77 ) ) )
| ~ ~ ( ~ ! [SY297: $i,SY298: $i] :
( ( ( power_power @ SV77 @ SY297 @ ( number_number_of @ nat @ SY298 ) )
!= ( zero_zero @ SV77 ) )
| ( ( number_number_of @ nat @ SY298 )
!= ( zero_zero @ nat ) ) )
| ~ ! [SY299: $i] :
( ! [SY300: $i] :
( ( power_power @ SV77 @ SY299 @ ( number_number_of @ nat @ SY300 ) )
!= ( zero_zero @ SV77 ) )
| ( ( ti @ SV77 @ SY299 )
= ( zero_zero @ SV77 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[563]) ).
thf(677,plain,
! [SV78: $i] :
( ( ~ ( ~ ! [SY301: $i,SY302: $i] :
( ~ ( linordered_idom @ SY302 )
| ~ ( ord_less @ SY302 @ SV78 @ ( ti @ SY302 @ SY301 ) )
| ( ord_less @ SY302 @ SV78 @ SY301 ) )
| ~ ! [SY303: $i,SY304: $i] :
( ~ ( linordered_idom @ SY304 )
| ~ ( ord_less @ SY304 @ SV78 @ SY303 )
| ( ord_less @ SY304 @ SV78 @ ( ti @ SY304 @ SY303 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[564]) ).
thf(678,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less @ int @ ( bit1 @ SX0 ) @ pls )
| ( ord_less @ int @ SX0 @ pls ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less @ int @ SX0 @ pls )
| ( ord_less @ int @ ( bit1 @ SX0 ) @ pls ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[565]) ).
thf(679,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( bit1 @ SX0 )
!= ( bit1 @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( bit1 @ SX0 )
= ( bit1 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[566]) ).
thf(680,plain,
! [SV79: $i] :
( ( ~ ( linord219039673up_add @ SV79 )
| ~ ( ~ ! [SY305: $i] :
( ( ( plus_plus @ SV79 @ SY305 @ SY305 )
!= ( zero_zero @ SV79 ) )
| ( ( ti @ SV79 @ SY305 )
= ( zero_zero @ SV79 ) ) )
| ~ ! [SY306: $i] :
( ( ( ti @ SV79 @ SY306 )
!= ( zero_zero @ SV79 ) )
| ( ( plus_plus @ SV79 @ SY306 @ SY306 )
= ( zero_zero @ SV79 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[567]) ).
thf(681,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less @ int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[568]) ).
thf(682,plain,
! [SV80: $i] :
( ( ~ ( linordered_idom @ SV80 )
| ~ ( number_ring @ SV80 )
| ~ ( ~ ! [SY307: $i] :
( ~ ( ord_less @ SV80 @ ( number_number_of @ SV80 @ SY307 ) @ ( zero_zero @ SV80 ) )
| ( ord_less @ int @ SY307 @ pls ) )
| ~ ! [SY308: $i] :
( ~ ( ord_less @ int @ SY308 @ pls )
| ( ord_less @ SV80 @ ( number_number_of @ SV80 @ SY308 ) @ ( zero_zero @ SV80 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[569]) ).
thf(683,plain,
! [SV81: $i] :
( ( ~ ( linordered_idom @ SV81 )
| ~ ( number_ring @ SV81 )
| ~ ( ~ ! [SY309: $i,SY310: $i] :
( ~ ( ord_less @ SV81 @ ( number_number_of @ SV81 @ SY309 ) @ ( number_number_of @ SV81 @ SY310 ) )
| ( ord_less @ int @ SY309 @ SY310 ) )
| ~ ! [SY311: $i,SY312: $i] :
( ~ ( ord_less @ int @ SY311 @ SY312 )
| ( ord_less @ SV81 @ ( number_number_of @ SV81 @ SY311 ) @ ( number_number_of @ SV81 @ SY312 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[570]) ).
thf(684,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( bit0 @ SX0 )
!= ( bit0 @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( bit0 @ SX0 )
= ( bit0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[571]) ).
thf(685,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less @ int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[572]) ).
thf(686,plain,
! [SV82: $i] :
( ( ~ ( linordered_idom @ SV82 )
| ~ ( ~ ! [SY313: $i] :
( ~ ( ord_less @ SV82 @ ( plus_plus @ SV82 @ SY313 @ SY313 ) @ ( zero_zero @ SV82 ) )
| ( ord_less @ SV82 @ SY313 @ ( zero_zero @ SV82 ) ) )
| ~ ! [SY314: $i] :
( ~ ( ord_less @ SV82 @ SY314 @ ( zero_zero @ SV82 ) )
| ( ord_less @ SV82 @ ( plus_plus @ SV82 @ SY314 @ SY314 ) @ ( zero_zero @ SV82 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[573]) ).
thf(687,plain,
! [SV83: $i] :
( ( ~ ( power @ SV83 )
| ~ ( semiring_0 @ SV83 )
| ~ ( ~ ! [SY315: $i] :
( ( ( number_number_of @ nat @ SY315 )
!= ( zero_zero @ nat ) )
| ( ( power_power @ SV83 @ ( zero_zero @ SV83 ) @ ( number_number_of @ nat @ SY315 ) )
= ( one_one @ SV83 ) ) )
| ~ ! [SY316: $i] :
( ( ( number_number_of @ nat @ SY316 )
= ( zero_zero @ nat ) )
| ( ( power_power @ SV83 @ ( zero_zero @ SV83 ) @ ( number_number_of @ nat @ SY316 ) )
= ( zero_zero @ SV83 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[574]) ).
thf(688,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX1 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SX1 ) @ ( number_number_of @ nat @ SX0 ) )
= ( number_number_of @ nat @ SX0 ) ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ord_less @ int @ SX1 @ pls )
| ~ ( ord_less @ int @ SX0 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SX1 ) @ ( number_number_of @ nat @ SX0 ) )
= ( number_number_of @ nat @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( ord_less @ int @ SX1 @ pls )
| ( ord_less @ int @ SX0 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SX1 ) @ ( number_number_of @ nat @ SX0 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SX1 @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[575]) ).
thf(689,plain,
( ( ~ ! [SX0: $i] :
( ( ( semiring_1_of_nat @ int @ SX0 )
!= ( zero_zero @ int ) )
| ( SX0
= ( zero_zero @ nat ) ) )
| ~ ! [SX0: $i] :
( ( SX0
!= ( zero_zero @ nat ) )
| ( ( semiring_1_of_nat @ int @ SX0 )
= ( zero_zero @ int ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[576]) ).
thf(690,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less @ int @ pls @ ( bit0 @ SX0 ) )
| ( ord_less @ int @ pls @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less @ int @ pls @ SX0 )
| ( ord_less @ int @ pls @ ( bit0 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[577]) ).
thf(691,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less @ int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[578]) ).
thf(692,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less @ int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[579]) ).
thf(693,plain,
! [SV84: $i] :
( ( ~ ( number @ SV84 )
| ~ ( ~ ! [SY317: $i,SY318: $i] :
( ( ( number_number_of @ SV84 @ SY317 )
!= ( ti @ SV84 @ SY318 ) )
| ( ( ti @ SV84 @ SY318 )
= ( number_number_of @ SV84 @ SY317 ) ) )
| ~ ! [SY319: $i,SY320: $i] :
( ( ( ti @ SV84 @ SY320 )
!= ( number_number_of @ SV84 @ SY319 ) )
| ( ( number_number_of @ SV84 @ SY319 )
= ( ti @ SV84 @ SY320 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[580]) ).
thf(694,plain,
! [SV85: $i] :
( ( ~ ( linordered_idom @ SV85 )
| ~ ( ~ ! [SY321: $i] :
( ( ( ti @ SV85 @ SY321 )
= ( zero_zero @ SV85 ) )
| ( ord_less @ SV85 @ ( zero_zero @ SV85 ) @ ( power_power @ SV85 @ SY321 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
| ~ ! [SY322: $i] :
( ~ ( ord_less @ SV85 @ ( zero_zero @ SV85 ) @ ( power_power @ SV85 @ SY322 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ( ( ti @ SV85 @ SY322 )
!= ( zero_zero @ SV85 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[581]) ).
thf(695,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( semiring_1_of_nat @ int @ SX0 )
!= ( semiring_1_of_nat @ int @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( semiring_1_of_nat @ int @ SX0 )
= ( semiring_1_of_nat @ int @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[582]) ).
thf(696,plain,
( ( ~ ! [SX0: $i] :
( ( ( bit0 @ SX0 )
!= pls )
| ( SX0 = pls ) )
| ~ ! [SX0: $i] :
( ( SX0 != pls )
| ( ( bit0 @ SX0 )
= pls ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[583]) ).
thf(697,plain,
! [SV86: $i] :
( ( ~ ( ring_11004092258visors @ SV86 )
| ~ ( ~ ! [SY323: $i] :
( ( ( power_power @ SV86 @ SY323 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= ( zero_zero @ SV86 ) )
| ( ( ti @ SV86 @ SY323 )
= ( zero_zero @ SV86 ) ) )
| ~ ! [SY324: $i] :
( ( ( ti @ SV86 @ SY324 )
!= ( zero_zero @ SV86 ) )
| ( ( power_power @ SV86 @ SY324 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SV86 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[584]) ).
thf(698,plain,
! [SV87: $i] :
( ( ~ ( linordered_idom @ SV87 )
| ~ ( number_ring @ SV87 )
| ~ ( ~ ! [SY325: $i] :
( ~ ( ord_less @ SV87 @ ( one_one @ SV87 ) @ ( number_number_of @ SV87 @ SY325 ) )
| ( ord_less @ int @ ( bit1 @ pls ) @ SY325 ) )
| ~ ! [SY326: $i] :
( ~ ( ord_less @ int @ ( bit1 @ pls ) @ SY326 )
| ( ord_less @ SV87 @ ( one_one @ SV87 ) @ ( number_number_of @ SV87 @ SY326 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[585]) ).
thf(699,plain,
( ( ~ ! [SX0: $i] :
( ( pls
!= ( bit0 @ SX0 ) )
| ( pls = SX0 ) )
| ~ ! [SX0: $i] :
( ( pls != SX0 )
| ( pls
= ( bit0 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[586]) ).
thf(700,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ ( number_number_of @ int @ SX0 ) @ ( number_number_of @ int @ SX1 ) )
| ( ord_less @ int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ int @ ( number_number_of @ int @ SX0 ) @ ( number_number_of @ int @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[587]) ).
thf(701,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less @ int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[588]) ).
thf(702,plain,
! [SV88: $i,SV5: $i] :
( ( ! [SY327: $i] :
( ~ ( linord219039673up_add @ SY327 )
| ( ( plus_plus @ SY327 @ ( ti @ SY327 @ SV5 ) @ SV88 )
= ( plus_plus @ SY327 @ SV5 @ SV88 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[593]) ).
thf(703,plain,
! [SV89: $i,SV6: $i] :
( ( ! [SY328: $i] :
( ~ ( linord219039673up_add @ SY328 )
| ( ( plus_plus @ SY328 @ SV6 @ ( ti @ SY328 @ SV89 ) )
= ( plus_plus @ SY328 @ SV6 @ SV89 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[594]) ).
thf(704,plain,
! [SV90: $i,SV7: $i] :
( ( ! [SY329: $i] :
( ~ ( linord219039673up_add @ SY329 )
| ( ( ti @ SY329 @ ( plus_plus @ SY329 @ SV7 @ SV90 ) )
= ( plus_plus @ SY329 @ SV7 @ SV90 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[595]) ).
thf(705,plain,
! [SV91: $i,SV8: $i] :
( ( ! [SY330: $i] :
( ~ ( number_semiring @ SY330 )
| ( ( plus_plus @ SY330 @ ( ti @ SY330 @ SV8 ) @ SV91 )
= ( plus_plus @ SY330 @ SV8 @ SV91 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[596]) ).
thf(706,plain,
! [SV92: $i,SV9: $i] :
( ( ! [SY331: $i] :
( ~ ( number_semiring @ SY331 )
| ( ( plus_plus @ SY331 @ SV9 @ ( ti @ SY331 @ SV92 ) )
= ( plus_plus @ SY331 @ SV9 @ SV92 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[597]) ).
thf(707,plain,
! [SV93: $i,SV10: $i] :
( ( ! [SY332: $i] :
( ~ ( number_semiring @ SY332 )
| ( ( ti @ SY332 @ ( plus_plus @ SY332 @ SV10 @ SV93 ) )
= ( plus_plus @ SY332 @ SV10 @ SV93 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[598]) ).
thf(708,plain,
! [SV11: $i] :
( ( ( ~ ( linord219039673up_add @ SV11 ) )
= $true )
| ( ( ( ti @ SV11 @ ( zero_zero @ SV11 ) )
= ( zero_zero @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[599]) ).
thf(709,plain,
! [SV12: $i,SV94: $i] :
( ( ~ ( number @ SV94 )
| ( ( number_number_of @ SV94 @ ( ti @ int @ SV12 ) )
= ( number_number_of @ SV94 @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[600]) ).
thf(710,plain,
! [SV13: $i,SV95: $i] :
( ( ~ ( number @ SV95 )
| ( ( ti @ SV95 @ ( number_number_of @ SV95 @ SV13 ) )
= ( number_number_of @ SV95 @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[601]) ).
thf(711,plain,
! [SV14: $i,SV96: $i] :
( ( ~ ( number_semiring @ SV96 )
| ( ( semiring_1_of_nat @ SV96 @ ( ti @ nat @ SV14 ) )
= ( semiring_1_of_nat @ SV96 @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[602]) ).
thf(712,plain,
! [SV15: $i,SV97: $i] :
( ( ~ ( number_semiring @ SV97 )
| ( ( ti @ SV97 @ ( semiring_1_of_nat @ SV97 @ SV15 ) )
= ( semiring_1_of_nat @ SV97 @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[603]) ).
thf(713,plain,
! [SV16: $i] :
( ( ( ~ ( semiring_1 @ SV16 ) )
= $true )
| ( ( ( power_power @ SV16 @ ( one_one @ SV16 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( one_one @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[604]) ).
thf(714,plain,
! [SV17: $i] :
( ( ( ~ ( semiring_1 @ SV17 ) )
= $true )
| ( ( ( power_power @ SV17 @ ( zero_zero @ SV17 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[605]) ).
thf(715,plain,
! [SV18: $i] :
( ( ( ~ ( number_ring @ SV18 ) )
= $true )
| ( ( ! [SY226: $i] :
( ( plus_plus @ SV18 @ ( one_one @ SV18 ) @ ( number_number_of @ SV18 @ SY226 ) )
= ( number_number_of @ SV18 @ ( plus_plus @ int @ ( bit1 @ pls ) @ SY226 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[606]) ).
thf(716,plain,
! [SV19: $i] :
( ( ( ~ ( number_ring @ SV19 ) )
= $true )
| ( ( ! [SY227: $i] :
( ( plus_plus @ SV19 @ ( number_number_of @ SV19 @ SY227 ) @ ( one_one @ SV19 ) )
= ( number_number_of @ SV19 @ ( plus_plus @ int @ SY227 @ ( bit1 @ pls ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[607]) ).
thf(717,plain,
! [SV20: $i] :
( ( ( ~ ( number_ring @ SV20 ) )
= $true )
| ( ( ( plus_plus @ SV20 @ ( one_one @ SV20 ) @ ( one_one @ SV20 ) )
= ( number_number_of @ SV20 @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[608]) ).
thf(718,plain,
! [SV21: $i] :
( ( ( ~ ( number_semiring @ SV21 ) )
= $true )
| ( ( ( plus_plus @ SV21 @ ( one_one @ SV21 ) @ ( one_one @ SV21 ) )
= ( number_number_of @ SV21 @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[609]) ).
thf(719,plain,
! [SV23: $i] :
( ( ( ~ ( number_ring @ SV23 ) )
= $true )
| ( ( ( one_one @ SV23 )
= ( number_number_of @ SV23 @ ( bit1 @ pls ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[611]) ).
thf(720,plain,
! [SV24: $i] :
( ( ( ~ ( number_ring @ SV24 ) )
= $true )
| ( ( ( number_number_of @ SV24 @ ( bit1 @ pls ) )
= ( one_one @ SV24 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[612]) ).
thf(721,plain,
! [SV25: $i,SV98: $i] :
( ( ( ord_less @ int @ SV98 @ SV25 )
| ( SV25 = SV98 )
| ( ord_less @ int @ SV25 @ SV98 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[613]) ).
thf(722,plain,
! [SV99: $i,SV26: $i] :
( ( ( plus_plus @ int @ ( number_number_of @ int @ SV26 ) @ ( number_number_of @ int @ SV99 ) )
= ( number_number_of @ int @ ( plus_plus @ int @ SV26 @ SV99 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[614]) ).
thf(723,plain,
! [SV100: $i,SV27: $i] :
( ( ( power_power @ int @ ( semiring_1_of_nat @ int @ SV27 ) @ SV100 )
= ( semiring_1_of_nat @ int @ ( power_power @ nat @ SV27 @ SV100 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[615]) ).
thf(724,plain,
! [SV101: $i,SV28: $i] :
( ( ( semiring_1_of_nat @ int @ ( power_power @ nat @ SV28 @ SV101 ) )
= ( power_power @ int @ ( semiring_1_of_nat @ int @ SV28 ) @ SV101 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[616]) ).
thf(725,plain,
! [SV102: $i,SV29: $i] :
( ( ! [SY333: $i] :
( ( plus_plus @ int @ ( semiring_1_of_nat @ int @ SV29 ) @ ( plus_plus @ int @ ( semiring_1_of_nat @ int @ SV102 ) @ SY333 ) )
= ( plus_plus @ int @ ( semiring_1_of_nat @ int @ ( plus_plus @ nat @ SV29 @ SV102 ) ) @ SY333 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[617]) ).
thf(726,plain,
! [SV103: $i,SV30: $i] :
( ( ( plus_plus @ int @ ( semiring_1_of_nat @ int @ SV30 ) @ ( semiring_1_of_nat @ int @ SV103 ) )
= ( semiring_1_of_nat @ int @ ( plus_plus @ nat @ SV30 @ SV103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[618]) ).
thf(727,plain,
! [SV31: $i,SV104: $i] :
( ( ! [SY334: $i] :
( ~ ( ord_less @ int @ SV104 @ SY334 )
| ( ord_less @ int @ ( plus_plus @ int @ SV104 @ SV31 ) @ ( plus_plus @ int @ SY334 @ SV31 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[620]) ).
thf(728,plain,
! [SV105: $i,SV32: $i] :
( ( ! [SY335: $i] :
( ( plus_plus @ int @ ( plus_plus @ int @ SV32 @ SV105 ) @ SY335 )
= ( plus_plus @ int @ SV32 @ ( plus_plus @ int @ SV105 @ SY335 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[621]) ).
thf(729,plain,
! [SV106: $i,SV33: $i] :
( ( ! [SY336: $i] :
( ( plus_plus @ int @ SV33 @ ( plus_plus @ int @ SV106 @ SY336 ) )
= ( plus_plus @ int @ SV106 @ ( plus_plus @ int @ SV33 @ SY336 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[622]) ).
thf(730,plain,
! [SV107: $i,SV34: $i] :
( ( ( plus_plus @ int @ SV34 @ SV107 )
= ( plus_plus @ int @ SV107 @ SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[623]) ).
thf(731,plain,
! [SV35: $i] :
( ( ord_less @ int @ ( semiring_1_of_nat @ int @ SV35 ) @ ( zero_zero @ int ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[625]) ).
thf(732,plain,
! [SV36: $i] :
( ( ( bit1 @ SV36 )
= pls )
= $false ),
inference(extcnf_not_pos,[status(thm)],[626]) ).
thf(733,plain,
! [SV37: $i] :
( ( pls
= ( bit1 @ SV37 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[627]) ).
thf(734,plain,
! [SV108: $i,SV38: $i] :
( ( ( ( bit1 @ SV38 )
!= ( bit0 @ SV108 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[628]) ).
thf(735,plain,
! [SV109: $i,SV39: $i] :
( ( ( ( bit0 @ SV39 )
!= ( bit1 @ SV109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[629]) ).
thf(736,plain,
! [SV110: $i,SV42: $i] :
( ( ( plus_plus @ int @ ( bit0 @ SV42 ) @ ( bit0 @ SV110 ) )
= ( bit0 @ ( plus_plus @ int @ SV42 @ SV110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[633]) ).
thf(737,plain,
! [SV46: $i] :
( ( ( ~ ( number_semiring @ SV46 ) )
= $true )
| ( ( ( number_number_of @ SV46 @ pls )
= ( zero_zero @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[637]) ).
thf(738,plain,
! [SV47: $i] :
( ( ( ~ ( number_ring @ SV47 ) )
= $true )
| ( ( ( number_number_of @ SV47 @ pls )
= ( zero_zero @ SV47 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[638]) ).
thf(739,plain,
! [SV48: $i] :
( ( ( ~ ( number_ring @ SV48 ) )
= $true )
| ( ( ( zero_zero @ SV48 )
= ( number_number_of @ SV48 @ pls ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[639]) ).
thf(740,plain,
! [SV49: $i] :
( ( ( ~ ( number_ring @ SV49 ) )
= $true )
| ( ( ! [SY245: $i] :
( ( plus_plus @ SV49 @ ( number_number_of @ SV49 @ pls ) @ SY245 )
= ( ti @ SV49 @ SY245 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[640]) ).
thf(741,plain,
! [SV50: $i] :
( ( ( ~ ( number_ring @ SV50 ) )
= $true )
| ( ( ! [SY246: $i] :
( ( plus_plus @ SV50 @ SY246 @ ( number_number_of @ SV50 @ pls ) )
= ( ti @ SV50 @ SY246 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[641]) ).
thf(742,plain,
! [SV51: $i] :
( ( ( ~ ( number_ring @ SV51 ) )
= $true )
| ( ( ! [SY247: $i,SY248: $i,SY249: $i] :
( ( plus_plus @ SV51 @ ( number_number_of @ SV51 @ SY247 ) @ ( plus_plus @ SV51 @ ( number_number_of @ SV51 @ SY248 ) @ SY249 ) )
= ( plus_plus @ SV51 @ ( number_number_of @ SV51 @ ( plus_plus @ int @ SY247 @ SY248 ) ) @ SY249 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[642]) ).
thf(743,plain,
! [SV52: $i] :
( ( ( ~ ( number_ring @ SV52 ) )
= $true )
| ( ( ! [SY250: $i,SY251: $i] :
( ( plus_plus @ SV52 @ ( number_number_of @ SV52 @ SY250 ) @ ( number_number_of @ SV52 @ SY251 ) )
= ( number_number_of @ SV52 @ ( plus_plus @ int @ SY250 @ SY251 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[643]) ).
thf(744,plain,
! [SV53: $i] :
( ( ( ~ ( number_ring @ SV53 ) )
= $true )
| ( ( ! [SY252: $i,SY253: $i] :
( ( number_number_of @ SV53 @ ( plus_plus @ int @ SY252 @ SY253 ) )
= ( plus_plus @ SV53 @ ( number_number_of @ SV53 @ SY252 ) @ ( number_number_of @ SV53 @ SY253 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[644]) ).
thf(745,plain,
! [SV111: $i,SV54: $i] :
( ( ( plus_plus @ int @ ( bit1 @ SV54 ) @ ( bit0 @ SV111 ) )
= ( bit1 @ ( plus_plus @ int @ SV54 @ SV111 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[645]) ).
thf(746,plain,
! [SV112: $i,SV55: $i] :
( ( ( plus_plus @ int @ ( bit0 @ SV55 ) @ ( bit1 @ SV112 ) )
= ( bit1 @ ( plus_plus @ int @ SV55 @ SV112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[646]) ).
thf(747,plain,
! [SV57: $i] :
( ( ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ SV57 ) @ SV57 )
= ( zero_zero @ int ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[648]) ).
thf(748,plain,
! [SV58: $i] :
( ( ( ~ ( number_semiring @ SV58 ) )
= $true )
| ( ( ! [SY256: $i] :
( ( number_number_of @ SV58 @ ( semiring_1_of_nat @ int @ SY256 ) )
= ( semiring_1_of_nat @ SV58 @ SY256 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[649]) ).
thf(749,plain,
! [SV59: $i] :
( ( ( ~ ( linordered_idom @ SV59 ) )
= $true )
| ( ( ! [SY257: $i] :
~ ( ord_less @ SV59 @ ( power_power @ SV59 @ SY257 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( zero_zero @ SV59 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[650]) ).
thf(750,plain,
! [SV60: $i] :
( ( ( ~ ( power @ SV60 )
| ~ ( semiring_0 @ SV60 ) )
= $true )
| ( ( ( ti @ SV60 @ ( one_one @ SV60 ) )
= ( one_one @ SV60 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[651]) ).
thf(751,plain,
! [SV61: $i] :
( ( ( ~ ( mult_zero @ SV61 )
| ~ ( power @ SV61 )
| ~ ( no_zero_divisors @ SV61 )
| ~ ( zero_neq_one @ SV61 ) )
= $true )
| ( ( ( ti @ SV61 @ ( zero_zero @ SV61 ) )
= ( zero_zero @ SV61 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[652]) ).
thf(752,plain,
! [SV62: $i] :
( ( ( ~ ( power @ SV62 )
| ~ ( semiring_0 @ SV62 ) )
= $true )
| ( ( ( ti @ SV62 @ ( zero_zero @ SV62 ) )
= ( zero_zero @ SV62 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[653]) ).
thf(753,plain,
! [SV113: $i,SV64: $i] :
( ( ! [SY337: $i] :
( ~ ( mult_zero @ SY337 )
| ~ ( power @ SY337 )
| ~ ( no_zero_divisors @ SY337 )
| ~ ( zero_neq_one @ SY337 )
| ( ( power_power @ SY337 @ ( ti @ SY337 @ SV64 ) @ SV113 )
= ( power_power @ SY337 @ SV64 @ SV113 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[655]) ).
thf(754,plain,
! [SV114: $i,SV65: $i] :
( ( ! [SY338: $i] :
( ~ ( mult_zero @ SY338 )
| ~ ( power @ SY338 )
| ~ ( no_zero_divisors @ SY338 )
| ~ ( zero_neq_one @ SY338 )
| ( ( power_power @ SY338 @ SV65 @ ( ti @ nat @ SV114 ) )
= ( power_power @ SY338 @ SV65 @ SV114 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[656]) ).
thf(755,plain,
! [SV115: $i,SV66: $i] :
( ( ! [SY339: $i] :
( ~ ( mult_zero @ SY339 )
| ~ ( power @ SY339 )
| ~ ( no_zero_divisors @ SY339 )
| ~ ( zero_neq_one @ SY339 )
| ( ( ti @ SY339 @ ( power_power @ SY339 @ SV66 @ SV115 ) )
= ( power_power @ SY339 @ SV66 @ SV115 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[657]) ).
thf(756,plain,
! [SV116: $i,SV67: $i] :
( ( ! [SY340: $i] :
( ~ ( power @ SY340 )
| ~ ( semiring_0 @ SY340 )
| ( ( power_power @ SY340 @ ( ti @ SY340 @ SV67 ) @ SV116 )
= ( power_power @ SY340 @ SV67 @ SV116 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[658]) ).
thf(757,plain,
! [SV117: $i,SV68: $i] :
( ( ! [SY341: $i] :
( ~ ( power @ SY341 )
| ~ ( semiring_0 @ SY341 )
| ( ( power_power @ SY341 @ SV68 @ ( ti @ nat @ SV117 ) )
= ( power_power @ SY341 @ SV68 @ SV117 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[659]) ).
thf(758,plain,
! [SV118: $i,SV69: $i] :
( ( ! [SY342: $i] :
( ~ ( power @ SY342 )
| ~ ( semiring_0 @ SY342 )
| ( ( ti @ SY342 @ ( power_power @ SY342 @ SV69 @ SV118 ) )
= ( power_power @ SY342 @ SV69 @ SV118 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[660]) ).
thf(759,plain,
! [SV119: $i,SV70: $i] :
( ( ( ti @ SV70 @ ( ti @ SV70 @ SV119 ) )
= ( ti @ SV70 @ SV119 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[661]) ).
thf(760,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less @ int @ ( bit1 @ SX0 ) @ ( zero_zero @ int ) )
| ( ord_less @ int @ SX0 @ ( zero_zero @ int ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[662]) ).
thf(761,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less @ int @ SX0 @ ( zero_zero @ int ) )
| ( ord_less @ int @ ( bit1 @ SX0 ) @ ( zero_zero @ int ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[662]) ).
thf(762,plain,
! [SV71: $i] :
( ( ( ~ ( number_ring @ SV71 )
| ~ ( ring_char_0 @ SV71 ) )
= $true )
| ( ( ~ ( ~ ! [SY271: $i,SY272: $i] :
( ( ( number_number_of @ SV71 @ SY271 )
!= ( number_number_of @ SV71 @ SY272 ) )
| ( SY271 = SY272 ) )
| ~ ! [SY273: $i,SY274: $i] :
( ( SY273 != SY274 )
| ( ( number_number_of @ SV71 @ SY273 )
= ( number_number_of @ SV71 @ SY274 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[663]) ).
thf(763,plain,
! [SV72: $i] :
( ( ~ ! [SY275: $i,SY276: $i] :
( ~ ( linordered_idom @ SY276 )
| ~ ( ord_less @ SY276 @ ( ti @ SY276 @ SV72 ) @ SY275 )
| ( ord_less @ SY276 @ SV72 @ SY275 ) )
| ~ ! [SY277: $i,SY278: $i] :
( ~ ( linordered_idom @ SY278 )
| ~ ( ord_less @ SY278 @ SV72 @ SY277 )
| ( ord_less @ SY278 @ ( ti @ SY278 @ SV72 ) @ SY277 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[664]) ).
thf(764,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less @ int @ ( bit0 @ SX0 ) @ ( zero_zero @ int ) )
| ( ord_less @ int @ SX0 @ ( zero_zero @ int ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[665]) ).
thf(765,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less @ int @ SX0 @ ( zero_zero @ int ) )
| ( ord_less @ int @ ( bit0 @ SX0 ) @ ( zero_zero @ int ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[665]) ).
thf(766,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less @ int @ ( bit0 @ SX0 ) @ pls )
| ( ord_less @ int @ SX0 @ pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[666]) ).
thf(767,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less @ int @ SX0 @ pls )
| ( ord_less @ int @ ( bit0 @ SX0 ) @ pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[666]) ).
thf(768,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ ( plus_plus @ int @ SX1 @ ( one_one @ int ) ) )
| ( SX0 = SX1 )
| ( ord_less @ int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[667]) ).
thf(769,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ord_less @ int @ SX0 @ ( plus_plus @ int @ SX1 @ ( one_one @ int ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ int @ SX0 @ ( plus_plus @ int @ SX1 @ ( one_one @ int ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[667]) ).
thf(770,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ nat @ ( ti @ nat @ SX0 ) @ SX1 )
| ( ord_less @ nat @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[668]) ).
thf(771,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ nat @ SX0 @ SX1 )
| ( ord_less @ nat @ ( ti @ nat @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[668]) ).
thf(772,plain,
! [SV73: $i] :
( ( ( ~ ( linordered_idom @ SV73 ) )
= $true )
| ( ( ~ ( ~ ! [SY279: $i,SY280: $i] :
( ( ( ti @ SV73 @ SY279 )
!= ( zero_zero @ SV73 ) )
| ( ( ti @ SV73 @ SY280 )
!= ( zero_zero @ SV73 ) )
| ( ( plus_plus @ SV73 @ ( power_power @ SV73 @ SY279 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV73 @ SY280 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV73 ) ) )
| ~ ~ ( ~ ! [SY281: $i] :
( ! [SY282: $i] :
( ( plus_plus @ SV73 @ ( power_power @ SV73 @ SY281 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV73 @ SY282 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV73 ) )
| ( ( ti @ SV73 @ SY281 )
= ( zero_zero @ SV73 ) ) )
| ~ ! [SY283: $i,SY284: $i] :
( ( ( plus_plus @ SV73 @ ( power_power @ SV73 @ SY283 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV73 @ SY284 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV73 ) )
| ( ( ti @ SV73 @ SY284 )
= ( zero_zero @ SV73 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[669]) ).
thf(773,plain,
! [SV74: $i] :
( ( ( ~ ( linordered_idom @ SV74 ) )
= $true )
| ( ( ~ ( ~ ! [SY285: $i,SY286: $i] :
( ~ ( ord_less @ SV74 @ ( zero_zero @ SV74 ) @ ( plus_plus @ SV74 @ ( power_power @ SV74 @ SY285 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV74 @ SY286 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
| ( ( ti @ SV74 @ SY285 )
!= ( zero_zero @ SV74 ) )
| ( ( ti @ SV74 @ SY286 )
!= ( zero_zero @ SV74 ) ) )
| ~ ~ ( ~ ! [SY287: $i] :
( ( ( ti @ SV74 @ SY287 )
= ( zero_zero @ SV74 ) )
| ! [SY288: $i] : ( ord_less @ SV74 @ ( zero_zero @ SV74 ) @ ( plus_plus @ SV74 @ ( power_power @ SV74 @ SY287 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV74 @ SY288 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
| ~ ! [SY289: $i,SY290: $i] :
( ( ( ti @ SV74 @ SY290 )
= ( zero_zero @ SV74 ) )
| ( ord_less @ SV74 @ ( zero_zero @ SV74 ) @ ( plus_plus @ SV74 @ ( power_power @ SV74 @ SY289 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV74 @ SY290 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[670]) ).
thf(774,plain,
! [SV75: $i] :
( ( ( ~ ( linordered_idom @ SV75 )
| ~ ( number_ring @ SV75 ) )
= $true )
| ( ( ~ ( ~ ! [SY291: $i] :
( ~ ( ord_less @ SV75 @ ( number_number_of @ SV75 @ SY291 ) @ ( one_one @ SV75 ) )
| ( ord_less @ int @ SY291 @ ( bit1 @ pls ) ) )
| ~ ! [SY292: $i] :
( ~ ( ord_less @ int @ SY292 @ ( bit1 @ pls ) )
| ( ord_less @ SV75 @ ( number_number_of @ SV75 @ SY292 ) @ ( one_one @ SV75 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[671]) ).
thf(775,plain,
! [SV76: $i] :
( ( ( ~ ( linordered_idom @ SV76 )
| ~ ( number_ring @ SV76 ) )
= $true )
| ( ( ~ ( ~ ! [SY293: $i] :
( ~ ( ord_less @ SV76 @ ( zero_zero @ SV76 ) @ ( number_number_of @ SV76 @ SY293 ) )
| ( ord_less @ int @ pls @ SY293 ) )
| ~ ! [SY294: $i] :
( ~ ( ord_less @ int @ pls @ SY294 )
| ( ord_less @ SV76 @ ( zero_zero @ SV76 ) @ ( number_number_of @ SV76 @ SY294 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[672]) ).
thf(776,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less @ int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[673]) ).
thf(777,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[673]) ).
thf(778,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ SX0 ) @ SX0 ) @ ( zero_zero @ int ) )
| ( ord_less @ int @ SX0 @ ( zero_zero @ int ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[674]) ).
thf(779,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less @ int @ SX0 @ ( zero_zero @ int ) )
| ( ord_less @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ SX0 ) @ SX0 ) @ ( zero_zero @ int ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[674]) ).
thf(780,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ nat @ SX0 @ ( ti @ nat @ SX1 ) )
| ( ord_less @ nat @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[675]) ).
thf(781,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ nat @ SX0 @ SX1 )
| ( ord_less @ nat @ SX0 @ ( ti @ nat @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[675]) ).
thf(782,plain,
! [SV77: $i] :
( ( ( ~ ( mult_zero @ SV77 )
| ~ ( power @ SV77 )
| ~ ( no_zero_divisors @ SV77 )
| ~ ( zero_neq_one @ SV77 ) )
= $true )
| ( ( ~ ( ~ ! [SY295: $i,SY296: $i] :
( ( ( number_number_of @ nat @ SY296 )
= ( zero_zero @ nat ) )
| ( ( ti @ SV77 @ SY295 )
!= ( zero_zero @ SV77 ) )
| ( ( power_power @ SV77 @ SY295 @ ( number_number_of @ nat @ SY296 ) )
= ( zero_zero @ SV77 ) ) )
| ~ ~ ( ~ ! [SY297: $i,SY298: $i] :
( ( ( power_power @ SV77 @ SY297 @ ( number_number_of @ nat @ SY298 ) )
!= ( zero_zero @ SV77 ) )
| ( ( number_number_of @ nat @ SY298 )
!= ( zero_zero @ nat ) ) )
| ~ ! [SY299: $i] :
( ! [SY300: $i] :
( ( power_power @ SV77 @ SY299 @ ( number_number_of @ nat @ SY300 ) )
!= ( zero_zero @ SV77 ) )
| ( ( ti @ SV77 @ SY299 )
= ( zero_zero @ SV77 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[676]) ).
thf(783,plain,
! [SV78: $i] :
( ( ~ ! [SY301: $i,SY302: $i] :
( ~ ( linordered_idom @ SY302 )
| ~ ( ord_less @ SY302 @ SV78 @ ( ti @ SY302 @ SY301 ) )
| ( ord_less @ SY302 @ SV78 @ SY301 ) )
| ~ ! [SY303: $i,SY304: $i] :
( ~ ( linordered_idom @ SY304 )
| ~ ( ord_less @ SY304 @ SV78 @ SY303 )
| ( ord_less @ SY304 @ SV78 @ ( ti @ SY304 @ SY303 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[677]) ).
thf(784,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less @ int @ ( bit1 @ SX0 ) @ pls )
| ( ord_less @ int @ SX0 @ pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[678]) ).
thf(785,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less @ int @ SX0 @ pls )
| ( ord_less @ int @ ( bit1 @ SX0 ) @ pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[678]) ).
thf(786,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( bit1 @ SX0 )
!= ( bit1 @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[679]) ).
thf(787,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( bit1 @ SX0 )
= ( bit1 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[679]) ).
thf(788,plain,
! [SV79: $i] :
( ( ( ~ ( linord219039673up_add @ SV79 ) )
= $true )
| ( ( ~ ( ~ ! [SY305: $i] :
( ( ( plus_plus @ SV79 @ SY305 @ SY305 )
!= ( zero_zero @ SV79 ) )
| ( ( ti @ SV79 @ SY305 )
= ( zero_zero @ SV79 ) ) )
| ~ ! [SY306: $i] :
( ( ( ti @ SV79 @ SY306 )
!= ( zero_zero @ SV79 ) )
| ( ( plus_plus @ SV79 @ SY306 @ SY306 )
= ( zero_zero @ SV79 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[680]) ).
thf(789,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less @ int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[681]) ).
thf(790,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[681]) ).
thf(791,plain,
! [SV80: $i] :
( ( ( ~ ( linordered_idom @ SV80 )
| ~ ( number_ring @ SV80 ) )
= $true )
| ( ( ~ ( ~ ! [SY307: $i] :
( ~ ( ord_less @ SV80 @ ( number_number_of @ SV80 @ SY307 ) @ ( zero_zero @ SV80 ) )
| ( ord_less @ int @ SY307 @ pls ) )
| ~ ! [SY308: $i] :
( ~ ( ord_less @ int @ SY308 @ pls )
| ( ord_less @ SV80 @ ( number_number_of @ SV80 @ SY308 ) @ ( zero_zero @ SV80 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[682]) ).
thf(792,plain,
! [SV81: $i] :
( ( ( ~ ( linordered_idom @ SV81 )
| ~ ( number_ring @ SV81 ) )
= $true )
| ( ( ~ ( ~ ! [SY309: $i,SY310: $i] :
( ~ ( ord_less @ SV81 @ ( number_number_of @ SV81 @ SY309 ) @ ( number_number_of @ SV81 @ SY310 ) )
| ( ord_less @ int @ SY309 @ SY310 ) )
| ~ ! [SY311: $i,SY312: $i] :
( ~ ( ord_less @ int @ SY311 @ SY312 )
| ( ord_less @ SV81 @ ( number_number_of @ SV81 @ SY311 ) @ ( number_number_of @ SV81 @ SY312 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[683]) ).
thf(793,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( bit0 @ SX0 )
!= ( bit0 @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[684]) ).
thf(794,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( bit0 @ SX0 )
= ( bit0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[684]) ).
thf(795,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less @ int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[685]) ).
thf(796,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[685]) ).
thf(797,plain,
! [SV82: $i] :
( ( ( ~ ( linordered_idom @ SV82 ) )
= $true )
| ( ( ~ ( ~ ! [SY313: $i] :
( ~ ( ord_less @ SV82 @ ( plus_plus @ SV82 @ SY313 @ SY313 ) @ ( zero_zero @ SV82 ) )
| ( ord_less @ SV82 @ SY313 @ ( zero_zero @ SV82 ) ) )
| ~ ! [SY314: $i] :
( ~ ( ord_less @ SV82 @ SY314 @ ( zero_zero @ SV82 ) )
| ( ord_less @ SV82 @ ( plus_plus @ SV82 @ SY314 @ SY314 ) @ ( zero_zero @ SV82 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[686]) ).
thf(798,plain,
! [SV83: $i] :
( ( ( ~ ( power @ SV83 )
| ~ ( semiring_0 @ SV83 ) )
= $true )
| ( ( ~ ( ~ ! [SY315: $i] :
( ( ( number_number_of @ nat @ SY315 )
!= ( zero_zero @ nat ) )
| ( ( power_power @ SV83 @ ( zero_zero @ SV83 ) @ ( number_number_of @ nat @ SY315 ) )
= ( one_one @ SV83 ) ) )
| ~ ! [SY316: $i] :
( ( ( number_number_of @ nat @ SY316 )
= ( zero_zero @ nat ) )
| ( ( power_power @ SV83 @ ( zero_zero @ SV83 ) @ ( number_number_of @ nat @ SY316 ) )
= ( zero_zero @ SV83 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[687]) ).
thf(799,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX1 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SX1 ) @ ( number_number_of @ nat @ SX0 ) )
= ( number_number_of @ nat @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[688]) ).
thf(800,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ord_less @ int @ SX1 @ pls )
| ~ ( ord_less @ int @ SX0 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SX1 ) @ ( number_number_of @ nat @ SX0 ) )
= ( number_number_of @ nat @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( ord_less @ int @ SX1 @ pls )
| ( ord_less @ int @ SX0 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SX1 ) @ ( number_number_of @ nat @ SX0 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SX1 @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[688]) ).
thf(801,plain,
( ( ~ ! [SX0: $i] :
( ( ( semiring_1_of_nat @ int @ SX0 )
!= ( zero_zero @ int ) )
| ( SX0
= ( zero_zero @ nat ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[689]) ).
thf(802,plain,
( ( ~ ! [SX0: $i] :
( ( SX0
!= ( zero_zero @ nat ) )
| ( ( semiring_1_of_nat @ int @ SX0 )
= ( zero_zero @ int ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[689]) ).
thf(803,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less @ int @ pls @ ( bit0 @ SX0 ) )
| ( ord_less @ int @ pls @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[690]) ).
thf(804,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less @ int @ pls @ SX0 )
| ( ord_less @ int @ pls @ ( bit0 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[690]) ).
thf(805,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less @ int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[691]) ).
thf(806,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[691]) ).
thf(807,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less @ int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[692]) ).
thf(808,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[692]) ).
thf(809,plain,
! [SV84: $i] :
( ( ( ~ ( number @ SV84 ) )
= $true )
| ( ( ~ ( ~ ! [SY317: $i,SY318: $i] :
( ( ( number_number_of @ SV84 @ SY317 )
!= ( ti @ SV84 @ SY318 ) )
| ( ( ti @ SV84 @ SY318 )
= ( number_number_of @ SV84 @ SY317 ) ) )
| ~ ! [SY319: $i,SY320: $i] :
( ( ( ti @ SV84 @ SY320 )
!= ( number_number_of @ SV84 @ SY319 ) )
| ( ( number_number_of @ SV84 @ SY319 )
= ( ti @ SV84 @ SY320 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[693]) ).
thf(810,plain,
! [SV85: $i] :
( ( ( ~ ( linordered_idom @ SV85 ) )
= $true )
| ( ( ~ ( ~ ! [SY321: $i] :
( ( ( ti @ SV85 @ SY321 )
= ( zero_zero @ SV85 ) )
| ( ord_less @ SV85 @ ( zero_zero @ SV85 ) @ ( power_power @ SV85 @ SY321 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
| ~ ! [SY322: $i] :
( ~ ( ord_less @ SV85 @ ( zero_zero @ SV85 ) @ ( power_power @ SV85 @ SY322 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ( ( ti @ SV85 @ SY322 )
!= ( zero_zero @ SV85 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[694]) ).
thf(811,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( semiring_1_of_nat @ int @ SX0 )
!= ( semiring_1_of_nat @ int @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[695]) ).
thf(812,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( semiring_1_of_nat @ int @ SX0 )
= ( semiring_1_of_nat @ int @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[695]) ).
thf(813,plain,
( ( ~ ! [SX0: $i] :
( ( ( bit0 @ SX0 )
!= pls )
| ( SX0 = pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[696]) ).
thf(814,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != pls )
| ( ( bit0 @ SX0 )
= pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[696]) ).
thf(815,plain,
! [SV86: $i] :
( ( ( ~ ( ring_11004092258visors @ SV86 ) )
= $true )
| ( ( ~ ( ~ ! [SY323: $i] :
( ( ( power_power @ SV86 @ SY323 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= ( zero_zero @ SV86 ) )
| ( ( ti @ SV86 @ SY323 )
= ( zero_zero @ SV86 ) ) )
| ~ ! [SY324: $i] :
( ( ( ti @ SV86 @ SY324 )
!= ( zero_zero @ SV86 ) )
| ( ( power_power @ SV86 @ SY324 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SV86 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[697]) ).
thf(816,plain,
! [SV87: $i] :
( ( ( ~ ( linordered_idom @ SV87 )
| ~ ( number_ring @ SV87 ) )
= $true )
| ( ( ~ ( ~ ! [SY325: $i] :
( ~ ( ord_less @ SV87 @ ( one_one @ SV87 ) @ ( number_number_of @ SV87 @ SY325 ) )
| ( ord_less @ int @ ( bit1 @ pls ) @ SY325 ) )
| ~ ! [SY326: $i] :
( ~ ( ord_less @ int @ ( bit1 @ pls ) @ SY326 )
| ( ord_less @ SV87 @ ( one_one @ SV87 ) @ ( number_number_of @ SV87 @ SY326 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[698]) ).
thf(817,plain,
( ( ~ ! [SX0: $i] :
( ( pls
!= ( bit0 @ SX0 ) )
| ( pls = SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[699]) ).
thf(818,plain,
( ( ~ ! [SX0: $i] :
( ( pls != SX0 )
| ( pls
= ( bit0 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[699]) ).
thf(819,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ ( number_number_of @ int @ SX0 ) @ ( number_number_of @ int @ SX1 ) )
| ( ord_less @ int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[700]) ).
thf(820,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ int @ ( number_number_of @ int @ SX0 ) @ ( number_number_of @ int @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[700]) ).
thf(821,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less @ int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[701]) ).
thf(822,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[701]) ).
thf(823,plain,
! [SV88: $i,SV5: $i,SV120: $i] :
( ( ~ ( linord219039673up_add @ SV120 )
| ( ( plus_plus @ SV120 @ ( ti @ SV120 @ SV5 ) @ SV88 )
= ( plus_plus @ SV120 @ SV5 @ SV88 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[702]) ).
thf(824,plain,
! [SV89: $i,SV6: $i,SV121: $i] :
( ( ~ ( linord219039673up_add @ SV121 )
| ( ( plus_plus @ SV121 @ SV6 @ ( ti @ SV121 @ SV89 ) )
= ( plus_plus @ SV121 @ SV6 @ SV89 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[703]) ).
thf(825,plain,
! [SV90: $i,SV7: $i,SV122: $i] :
( ( ~ ( linord219039673up_add @ SV122 )
| ( ( ti @ SV122 @ ( plus_plus @ SV122 @ SV7 @ SV90 ) )
= ( plus_plus @ SV122 @ SV7 @ SV90 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[704]) ).
thf(826,plain,
! [SV91: $i,SV8: $i,SV123: $i] :
( ( ~ ( number_semiring @ SV123 )
| ( ( plus_plus @ SV123 @ ( ti @ SV123 @ SV8 ) @ SV91 )
= ( plus_plus @ SV123 @ SV8 @ SV91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[705]) ).
thf(827,plain,
! [SV92: $i,SV9: $i,SV124: $i] :
( ( ~ ( number_semiring @ SV124 )
| ( ( plus_plus @ SV124 @ SV9 @ ( ti @ SV124 @ SV92 ) )
= ( plus_plus @ SV124 @ SV9 @ SV92 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[706]) ).
thf(828,plain,
! [SV93: $i,SV10: $i,SV125: $i] :
( ( ~ ( number_semiring @ SV125 )
| ( ( ti @ SV125 @ ( plus_plus @ SV125 @ SV10 @ SV93 ) )
= ( plus_plus @ SV125 @ SV10 @ SV93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[707]) ).
thf(829,plain,
! [SV11: $i] :
( ( ( linord219039673up_add @ SV11 )
= $false )
| ( ( ( ti @ SV11 @ ( zero_zero @ SV11 ) )
= ( zero_zero @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[708]) ).
thf(830,plain,
! [SV12: $i,SV94: $i] :
( ( ( ~ ( number @ SV94 ) )
= $true )
| ( ( ( number_number_of @ SV94 @ ( ti @ int @ SV12 ) )
= ( number_number_of @ SV94 @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[709]) ).
thf(831,plain,
! [SV13: $i,SV95: $i] :
( ( ( ~ ( number @ SV95 ) )
= $true )
| ( ( ( ti @ SV95 @ ( number_number_of @ SV95 @ SV13 ) )
= ( number_number_of @ SV95 @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[710]) ).
thf(832,plain,
! [SV14: $i,SV96: $i] :
( ( ( ~ ( number_semiring @ SV96 ) )
= $true )
| ( ( ( semiring_1_of_nat @ SV96 @ ( ti @ nat @ SV14 ) )
= ( semiring_1_of_nat @ SV96 @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[711]) ).
thf(833,plain,
! [SV15: $i,SV97: $i] :
( ( ( ~ ( number_semiring @ SV97 ) )
= $true )
| ( ( ( ti @ SV97 @ ( semiring_1_of_nat @ SV97 @ SV15 ) )
= ( semiring_1_of_nat @ SV97 @ SV15 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[712]) ).
thf(834,plain,
! [SV16: $i] :
( ( ( semiring_1 @ SV16 )
= $false )
| ( ( ( power_power @ SV16 @ ( one_one @ SV16 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( one_one @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[713]) ).
thf(835,plain,
! [SV17: $i] :
( ( ( semiring_1 @ SV17 )
= $false )
| ( ( ( power_power @ SV17 @ ( zero_zero @ SV17 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[714]) ).
thf(836,plain,
! [SV18: $i] :
( ( ( number_ring @ SV18 )
= $false )
| ( ( ! [SY226: $i] :
( ( plus_plus @ SV18 @ ( one_one @ SV18 ) @ ( number_number_of @ SV18 @ SY226 ) )
= ( number_number_of @ SV18 @ ( plus_plus @ int @ ( bit1 @ pls ) @ SY226 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[715]) ).
thf(837,plain,
! [SV19: $i] :
( ( ( number_ring @ SV19 )
= $false )
| ( ( ! [SY227: $i] :
( ( plus_plus @ SV19 @ ( number_number_of @ SV19 @ SY227 ) @ ( one_one @ SV19 ) )
= ( number_number_of @ SV19 @ ( plus_plus @ int @ SY227 @ ( bit1 @ pls ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[716]) ).
thf(838,plain,
! [SV20: $i] :
( ( ( number_ring @ SV20 )
= $false )
| ( ( ( plus_plus @ SV20 @ ( one_one @ SV20 ) @ ( one_one @ SV20 ) )
= ( number_number_of @ SV20 @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[717]) ).
thf(839,plain,
! [SV21: $i] :
( ( ( number_semiring @ SV21 )
= $false )
| ( ( ( plus_plus @ SV21 @ ( one_one @ SV21 ) @ ( one_one @ SV21 ) )
= ( number_number_of @ SV21 @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[718]) ).
thf(840,plain,
! [SV23: $i] :
( ( ( number_ring @ SV23 )
= $false )
| ( ( ( one_one @ SV23 )
= ( number_number_of @ SV23 @ ( bit1 @ pls ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[719]) ).
thf(841,plain,
! [SV24: $i] :
( ( ( number_ring @ SV24 )
= $false )
| ( ( ( number_number_of @ SV24 @ ( bit1 @ pls ) )
= ( one_one @ SV24 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[720]) ).
thf(842,plain,
! [SV25: $i,SV98: $i] :
( ( ( ord_less @ int @ SV98 @ SV25 )
= $true )
| ( ( ( SV25 = SV98 )
| ( ord_less @ int @ SV25 @ SV98 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[721]) ).
thf(843,plain,
! [SV126: $i,SV102: $i,SV29: $i] :
( ( ( plus_plus @ int @ ( semiring_1_of_nat @ int @ SV29 ) @ ( plus_plus @ int @ ( semiring_1_of_nat @ int @ SV102 ) @ SV126 ) )
= ( plus_plus @ int @ ( semiring_1_of_nat @ int @ ( plus_plus @ nat @ SV29 @ SV102 ) ) @ SV126 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[725]) ).
thf(844,plain,
! [SV31: $i,SV127: $i,SV104: $i] :
( ( ~ ( ord_less @ int @ SV104 @ SV127 )
| ( ord_less @ int @ ( plus_plus @ int @ SV104 @ SV31 ) @ ( plus_plus @ int @ SV127 @ SV31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[727]) ).
thf(845,plain,
! [SV128: $i,SV105: $i,SV32: $i] :
( ( ( plus_plus @ int @ ( plus_plus @ int @ SV32 @ SV105 ) @ SV128 )
= ( plus_plus @ int @ SV32 @ ( plus_plus @ int @ SV105 @ SV128 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[728]) ).
thf(846,plain,
! [SV129: $i,SV106: $i,SV33: $i] :
( ( ( plus_plus @ int @ SV33 @ ( plus_plus @ int @ SV106 @ SV129 ) )
= ( plus_plus @ int @ SV106 @ ( plus_plus @ int @ SV33 @ SV129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[729]) ).
thf(847,plain,
! [SV108: $i,SV38: $i] :
( ( ( bit1 @ SV38 )
= ( bit0 @ SV108 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[734]) ).
thf(848,plain,
! [SV109: $i,SV39: $i] :
( ( ( bit0 @ SV39 )
= ( bit1 @ SV109 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[735]) ).
thf(849,plain,
! [SV46: $i] :
( ( ( number_semiring @ SV46 )
= $false )
| ( ( ( number_number_of @ SV46 @ pls )
= ( zero_zero @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[737]) ).
thf(850,plain,
! [SV47: $i] :
( ( ( number_ring @ SV47 )
= $false )
| ( ( ( number_number_of @ SV47 @ pls )
= ( zero_zero @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[738]) ).
thf(851,plain,
! [SV48: $i] :
( ( ( number_ring @ SV48 )
= $false )
| ( ( ( zero_zero @ SV48 )
= ( number_number_of @ SV48 @ pls ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[739]) ).
thf(852,plain,
! [SV49: $i] :
( ( ( number_ring @ SV49 )
= $false )
| ( ( ! [SY245: $i] :
( ( plus_plus @ SV49 @ ( number_number_of @ SV49 @ pls ) @ SY245 )
= ( ti @ SV49 @ SY245 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[740]) ).
thf(853,plain,
! [SV50: $i] :
( ( ( number_ring @ SV50 )
= $false )
| ( ( ! [SY246: $i] :
( ( plus_plus @ SV50 @ SY246 @ ( number_number_of @ SV50 @ pls ) )
= ( ti @ SV50 @ SY246 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[741]) ).
thf(854,plain,
! [SV51: $i] :
( ( ( number_ring @ SV51 )
= $false )
| ( ( ! [SY247: $i,SY248: $i,SY249: $i] :
( ( plus_plus @ SV51 @ ( number_number_of @ SV51 @ SY247 ) @ ( plus_plus @ SV51 @ ( number_number_of @ SV51 @ SY248 ) @ SY249 ) )
= ( plus_plus @ SV51 @ ( number_number_of @ SV51 @ ( plus_plus @ int @ SY247 @ SY248 ) ) @ SY249 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[742]) ).
thf(855,plain,
! [SV52: $i] :
( ( ( number_ring @ SV52 )
= $false )
| ( ( ! [SY250: $i,SY251: $i] :
( ( plus_plus @ SV52 @ ( number_number_of @ SV52 @ SY250 ) @ ( number_number_of @ SV52 @ SY251 ) )
= ( number_number_of @ SV52 @ ( plus_plus @ int @ SY250 @ SY251 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[743]) ).
thf(856,plain,
! [SV53: $i] :
( ( ( number_ring @ SV53 )
= $false )
| ( ( ! [SY252: $i,SY253: $i] :
( ( number_number_of @ SV53 @ ( plus_plus @ int @ SY252 @ SY253 ) )
= ( plus_plus @ SV53 @ ( number_number_of @ SV53 @ SY252 ) @ ( number_number_of @ SV53 @ SY253 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[744]) ).
thf(857,plain,
! [SV58: $i] :
( ( ( number_semiring @ SV58 )
= $false )
| ( ( ! [SY256: $i] :
( ( number_number_of @ SV58 @ ( semiring_1_of_nat @ int @ SY256 ) )
= ( semiring_1_of_nat @ SV58 @ SY256 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[748]) ).
thf(858,plain,
! [SV59: $i] :
( ( ( linordered_idom @ SV59 )
= $false )
| ( ( ! [SY257: $i] :
~ ( ord_less @ SV59 @ ( power_power @ SV59 @ SY257 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( zero_zero @ SV59 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[749]) ).
thf(859,plain,
! [SV60: $i] :
( ( ( ~ ( power @ SV60 ) )
= $true )
| ( ( ~ ( semiring_0 @ SV60 ) )
= $true )
| ( ( ( ti @ SV60 @ ( one_one @ SV60 ) )
= ( one_one @ SV60 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[750]) ).
thf(860,plain,
! [SV61: $i] :
( ( ( ~ ( mult_zero @ SV61 )
| ~ ( power @ SV61 )
| ~ ( no_zero_divisors @ SV61 ) )
= $true )
| ( ( ~ ( zero_neq_one @ SV61 ) )
= $true )
| ( ( ( ti @ SV61 @ ( zero_zero @ SV61 ) )
= ( zero_zero @ SV61 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[751]) ).
thf(861,plain,
! [SV62: $i] :
( ( ( ~ ( power @ SV62 ) )
= $true )
| ( ( ~ ( semiring_0 @ SV62 ) )
= $true )
| ( ( ( ti @ SV62 @ ( zero_zero @ SV62 ) )
= ( zero_zero @ SV62 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[752]) ).
thf(862,plain,
! [SV113: $i,SV64: $i,SV130: $i] :
( ( ~ ( mult_zero @ SV130 )
| ~ ( power @ SV130 )
| ~ ( no_zero_divisors @ SV130 )
| ~ ( zero_neq_one @ SV130 )
| ( ( power_power @ SV130 @ ( ti @ SV130 @ SV64 ) @ SV113 )
= ( power_power @ SV130 @ SV64 @ SV113 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[753]) ).
thf(863,plain,
! [SV114: $i,SV65: $i,SV131: $i] :
( ( ~ ( mult_zero @ SV131 )
| ~ ( power @ SV131 )
| ~ ( no_zero_divisors @ SV131 )
| ~ ( zero_neq_one @ SV131 )
| ( ( power_power @ SV131 @ SV65 @ ( ti @ nat @ SV114 ) )
= ( power_power @ SV131 @ SV65 @ SV114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[754]) ).
thf(864,plain,
! [SV115: $i,SV66: $i,SV132: $i] :
( ( ~ ( mult_zero @ SV132 )
| ~ ( power @ SV132 )
| ~ ( no_zero_divisors @ SV132 )
| ~ ( zero_neq_one @ SV132 )
| ( ( ti @ SV132 @ ( power_power @ SV132 @ SV66 @ SV115 ) )
= ( power_power @ SV132 @ SV66 @ SV115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[755]) ).
thf(865,plain,
! [SV116: $i,SV67: $i,SV133: $i] :
( ( ~ ( power @ SV133 )
| ~ ( semiring_0 @ SV133 )
| ( ( power_power @ SV133 @ ( ti @ SV133 @ SV67 ) @ SV116 )
= ( power_power @ SV133 @ SV67 @ SV116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[756]) ).
thf(866,plain,
! [SV117: $i,SV68: $i,SV134: $i] :
( ( ~ ( power @ SV134 )
| ~ ( semiring_0 @ SV134 )
| ( ( power_power @ SV134 @ SV68 @ ( ti @ nat @ SV117 ) )
= ( power_power @ SV134 @ SV68 @ SV117 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[757]) ).
thf(867,plain,
! [SV118: $i,SV69: $i,SV135: $i] :
( ( ~ ( power @ SV135 )
| ~ ( semiring_0 @ SV135 )
| ( ( ti @ SV135 @ ( power_power @ SV135 @ SV69 @ SV118 ) )
= ( power_power @ SV135 @ SV69 @ SV118 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[758]) ).
thf(868,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less @ int @ ( bit1 @ SX0 ) @ ( zero_zero @ int ) )
| ( ord_less @ int @ SX0 @ ( zero_zero @ int ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[760]) ).
thf(869,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less @ int @ SX0 @ ( zero_zero @ int ) )
| ( ord_less @ int @ ( bit1 @ SX0 ) @ ( zero_zero @ int ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[761]) ).
thf(870,plain,
! [SV71: $i] :
( ( ( ~ ( number_ring @ SV71 ) )
= $true )
| ( ( ~ ( ring_char_0 @ SV71 ) )
= $true )
| ( ( ~ ( ~ ! [SY271: $i,SY272: $i] :
( ( ( number_number_of @ SV71 @ SY271 )
!= ( number_number_of @ SV71 @ SY272 ) )
| ( SY271 = SY272 ) )
| ~ ! [SY273: $i,SY274: $i] :
( ( SY273 != SY274 )
| ( ( number_number_of @ SV71 @ SY273 )
= ( number_number_of @ SV71 @ SY274 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[762]) ).
thf(871,plain,
! [SV72: $i] :
( ( ~ ! [SY275: $i,SY276: $i] :
( ~ ( linordered_idom @ SY276 )
| ~ ( ord_less @ SY276 @ ( ti @ SY276 @ SV72 ) @ SY275 )
| ( ord_less @ SY276 @ SV72 @ SY275 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[763]) ).
thf(872,plain,
! [SV72: $i] :
( ( ~ ! [SY277: $i,SY278: $i] :
( ~ ( linordered_idom @ SY278 )
| ~ ( ord_less @ SY278 @ SV72 @ SY277 )
| ( ord_less @ SY278 @ ( ti @ SY278 @ SV72 ) @ SY277 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[763]) ).
thf(873,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less @ int @ ( bit0 @ SX0 ) @ ( zero_zero @ int ) )
| ( ord_less @ int @ SX0 @ ( zero_zero @ int ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[764]) ).
thf(874,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less @ int @ SX0 @ ( zero_zero @ int ) )
| ( ord_less @ int @ ( bit0 @ SX0 ) @ ( zero_zero @ int ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[765]) ).
thf(875,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less @ int @ ( bit0 @ SX0 ) @ pls )
| ( ord_less @ int @ SX0 @ pls ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[766]) ).
thf(876,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less @ int @ SX0 @ pls )
| ( ord_less @ int @ ( bit0 @ SX0 ) @ pls ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[767]) ).
thf(877,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ ( plus_plus @ int @ SX1 @ ( one_one @ int ) ) )
| ( SX0 = SX1 )
| ( ord_less @ int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[768]) ).
thf(878,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ord_less @ int @ SX0 @ ( plus_plus @ int @ SX1 @ ( one_one @ int ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ int @ SX0 @ ( plus_plus @ int @ SX1 @ ( one_one @ int ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[769]) ).
thf(879,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ nat @ ( ti @ nat @ SX0 ) @ SX1 )
| ( ord_less @ nat @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[770]) ).
thf(880,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ nat @ SX0 @ SX1 )
| ( ord_less @ nat @ ( ti @ nat @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[771]) ).
thf(881,plain,
! [SV73: $i] :
( ( ( linordered_idom @ SV73 )
= $false )
| ( ( ~ ( ~ ! [SY279: $i,SY280: $i] :
( ( ( ti @ SV73 @ SY279 )
!= ( zero_zero @ SV73 ) )
| ( ( ti @ SV73 @ SY280 )
!= ( zero_zero @ SV73 ) )
| ( ( plus_plus @ SV73 @ ( power_power @ SV73 @ SY279 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV73 @ SY280 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV73 ) ) )
| ~ ~ ( ~ ! [SY281: $i] :
( ! [SY282: $i] :
( ( plus_plus @ SV73 @ ( power_power @ SV73 @ SY281 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV73 @ SY282 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV73 ) )
| ( ( ti @ SV73 @ SY281 )
= ( zero_zero @ SV73 ) ) )
| ~ ! [SY283: $i,SY284: $i] :
( ( ( plus_plus @ SV73 @ ( power_power @ SV73 @ SY283 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV73 @ SY284 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV73 ) )
| ( ( ti @ SV73 @ SY284 )
= ( zero_zero @ SV73 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[772]) ).
thf(882,plain,
! [SV74: $i] :
( ( ( linordered_idom @ SV74 )
= $false )
| ( ( ~ ( ~ ! [SY285: $i,SY286: $i] :
( ~ ( ord_less @ SV74 @ ( zero_zero @ SV74 ) @ ( plus_plus @ SV74 @ ( power_power @ SV74 @ SY285 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV74 @ SY286 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
| ( ( ti @ SV74 @ SY285 )
!= ( zero_zero @ SV74 ) )
| ( ( ti @ SV74 @ SY286 )
!= ( zero_zero @ SV74 ) ) )
| ~ ~ ( ~ ! [SY287: $i] :
( ( ( ti @ SV74 @ SY287 )
= ( zero_zero @ SV74 ) )
| ! [SY288: $i] : ( ord_less @ SV74 @ ( zero_zero @ SV74 ) @ ( plus_plus @ SV74 @ ( power_power @ SV74 @ SY287 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV74 @ SY288 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
| ~ ! [SY289: $i,SY290: $i] :
( ( ( ti @ SV74 @ SY290 )
= ( zero_zero @ SV74 ) )
| ( ord_less @ SV74 @ ( zero_zero @ SV74 ) @ ( plus_plus @ SV74 @ ( power_power @ SV74 @ SY289 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV74 @ SY290 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[773]) ).
thf(883,plain,
! [SV75: $i] :
( ( ( ~ ( linordered_idom @ SV75 ) )
= $true )
| ( ( ~ ( number_ring @ SV75 ) )
= $true )
| ( ( ~ ( ~ ! [SY291: $i] :
( ~ ( ord_less @ SV75 @ ( number_number_of @ SV75 @ SY291 ) @ ( one_one @ SV75 ) )
| ( ord_less @ int @ SY291 @ ( bit1 @ pls ) ) )
| ~ ! [SY292: $i] :
( ~ ( ord_less @ int @ SY292 @ ( bit1 @ pls ) )
| ( ord_less @ SV75 @ ( number_number_of @ SV75 @ SY292 ) @ ( one_one @ SV75 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[774]) ).
thf(884,plain,
! [SV76: $i] :
( ( ( ~ ( linordered_idom @ SV76 ) )
= $true )
| ( ( ~ ( number_ring @ SV76 ) )
= $true )
| ( ( ~ ( ~ ! [SY293: $i] :
( ~ ( ord_less @ SV76 @ ( zero_zero @ SV76 ) @ ( number_number_of @ SV76 @ SY293 ) )
| ( ord_less @ int @ pls @ SY293 ) )
| ~ ! [SY294: $i] :
( ~ ( ord_less @ int @ pls @ SY294 )
| ( ord_less @ SV76 @ ( zero_zero @ SV76 ) @ ( number_number_of @ SV76 @ SY294 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[775]) ).
thf(885,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less @ int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[776]) ).
thf(886,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[777]) ).
thf(887,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ SX0 ) @ SX0 ) @ ( zero_zero @ int ) )
| ( ord_less @ int @ SX0 @ ( zero_zero @ int ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[778]) ).
thf(888,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less @ int @ SX0 @ ( zero_zero @ int ) )
| ( ord_less @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ SX0 ) @ SX0 ) @ ( zero_zero @ int ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[779]) ).
thf(889,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ nat @ SX0 @ ( ti @ nat @ SX1 ) )
| ( ord_less @ nat @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[780]) ).
thf(890,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ nat @ SX0 @ SX1 )
| ( ord_less @ nat @ SX0 @ ( ti @ nat @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[781]) ).
thf(891,plain,
! [SV77: $i] :
( ( ( ~ ( mult_zero @ SV77 )
| ~ ( power @ SV77 )
| ~ ( no_zero_divisors @ SV77 ) )
= $true )
| ( ( ~ ( zero_neq_one @ SV77 ) )
= $true )
| ( ( ~ ( ~ ! [SY295: $i,SY296: $i] :
( ( ( number_number_of @ nat @ SY296 )
= ( zero_zero @ nat ) )
| ( ( ti @ SV77 @ SY295 )
!= ( zero_zero @ SV77 ) )
| ( ( power_power @ SV77 @ SY295 @ ( number_number_of @ nat @ SY296 ) )
= ( zero_zero @ SV77 ) ) )
| ~ ~ ( ~ ! [SY297: $i,SY298: $i] :
( ( ( power_power @ SV77 @ SY297 @ ( number_number_of @ nat @ SY298 ) )
!= ( zero_zero @ SV77 ) )
| ( ( number_number_of @ nat @ SY298 )
!= ( zero_zero @ nat ) ) )
| ~ ! [SY299: $i] :
( ! [SY300: $i] :
( ( power_power @ SV77 @ SY299 @ ( number_number_of @ nat @ SY300 ) )
!= ( zero_zero @ SV77 ) )
| ( ( ti @ SV77 @ SY299 )
= ( zero_zero @ SV77 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[782]) ).
thf(892,plain,
! [SV78: $i] :
( ( ~ ! [SY301: $i,SY302: $i] :
( ~ ( linordered_idom @ SY302 )
| ~ ( ord_less @ SY302 @ SV78 @ ( ti @ SY302 @ SY301 ) )
| ( ord_less @ SY302 @ SV78 @ SY301 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[783]) ).
thf(893,plain,
! [SV78: $i] :
( ( ~ ! [SY303: $i,SY304: $i] :
( ~ ( linordered_idom @ SY304 )
| ~ ( ord_less @ SY304 @ SV78 @ SY303 )
| ( ord_less @ SY304 @ SV78 @ ( ti @ SY304 @ SY303 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[783]) ).
thf(894,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less @ int @ ( bit1 @ SX0 ) @ pls )
| ( ord_less @ int @ SX0 @ pls ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[784]) ).
thf(895,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less @ int @ SX0 @ pls )
| ( ord_less @ int @ ( bit1 @ SX0 ) @ pls ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[785]) ).
thf(896,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( bit1 @ SX0 )
!= ( bit1 @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[786]) ).
thf(897,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( bit1 @ SX0 )
= ( bit1 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[787]) ).
thf(898,plain,
! [SV79: $i] :
( ( ( linord219039673up_add @ SV79 )
= $false )
| ( ( ~ ( ~ ! [SY305: $i] :
( ( ( plus_plus @ SV79 @ SY305 @ SY305 )
!= ( zero_zero @ SV79 ) )
| ( ( ti @ SV79 @ SY305 )
= ( zero_zero @ SV79 ) ) )
| ~ ! [SY306: $i] :
( ( ( ti @ SV79 @ SY306 )
!= ( zero_zero @ SV79 ) )
| ( ( plus_plus @ SV79 @ SY306 @ SY306 )
= ( zero_zero @ SV79 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[788]) ).
thf(899,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less @ int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[789]) ).
thf(900,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[790]) ).
thf(901,plain,
! [SV80: $i] :
( ( ( ~ ( linordered_idom @ SV80 ) )
= $true )
| ( ( ~ ( number_ring @ SV80 ) )
= $true )
| ( ( ~ ( ~ ! [SY307: $i] :
( ~ ( ord_less @ SV80 @ ( number_number_of @ SV80 @ SY307 ) @ ( zero_zero @ SV80 ) )
| ( ord_less @ int @ SY307 @ pls ) )
| ~ ! [SY308: $i] :
( ~ ( ord_less @ int @ SY308 @ pls )
| ( ord_less @ SV80 @ ( number_number_of @ SV80 @ SY308 ) @ ( zero_zero @ SV80 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[791]) ).
thf(902,plain,
! [SV81: $i] :
( ( ( ~ ( linordered_idom @ SV81 ) )
= $true )
| ( ( ~ ( number_ring @ SV81 ) )
= $true )
| ( ( ~ ( ~ ! [SY309: $i,SY310: $i] :
( ~ ( ord_less @ SV81 @ ( number_number_of @ SV81 @ SY309 ) @ ( number_number_of @ SV81 @ SY310 ) )
| ( ord_less @ int @ SY309 @ SY310 ) )
| ~ ! [SY311: $i,SY312: $i] :
( ~ ( ord_less @ int @ SY311 @ SY312 )
| ( ord_less @ SV81 @ ( number_number_of @ SV81 @ SY311 ) @ ( number_number_of @ SV81 @ SY312 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[792]) ).
thf(903,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( bit0 @ SX0 )
!= ( bit0 @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[793]) ).
thf(904,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( bit0 @ SX0 )
= ( bit0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[794]) ).
thf(905,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less @ int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[795]) ).
thf(906,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[796]) ).
thf(907,plain,
! [SV82: $i] :
( ( ( linordered_idom @ SV82 )
= $false )
| ( ( ~ ( ~ ! [SY313: $i] :
( ~ ( ord_less @ SV82 @ ( plus_plus @ SV82 @ SY313 @ SY313 ) @ ( zero_zero @ SV82 ) )
| ( ord_less @ SV82 @ SY313 @ ( zero_zero @ SV82 ) ) )
| ~ ! [SY314: $i] :
( ~ ( ord_less @ SV82 @ SY314 @ ( zero_zero @ SV82 ) )
| ( ord_less @ SV82 @ ( plus_plus @ SV82 @ SY314 @ SY314 ) @ ( zero_zero @ SV82 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[797]) ).
thf(908,plain,
! [SV83: $i] :
( ( ( ~ ( power @ SV83 ) )
= $true )
| ( ( ~ ( semiring_0 @ SV83 ) )
= $true )
| ( ( ~ ( ~ ! [SY315: $i] :
( ( ( number_number_of @ nat @ SY315 )
!= ( zero_zero @ nat ) )
| ( ( power_power @ SV83 @ ( zero_zero @ SV83 ) @ ( number_number_of @ nat @ SY315 ) )
= ( one_one @ SV83 ) ) )
| ~ ! [SY316: $i] :
( ( ( number_number_of @ nat @ SY316 )
= ( zero_zero @ nat ) )
| ( ( power_power @ SV83 @ ( zero_zero @ SV83 ) @ ( number_number_of @ nat @ SY316 ) )
= ( zero_zero @ SV83 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[798]) ).
thf(909,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX1 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SX1 ) @ ( number_number_of @ nat @ SX0 ) )
= ( number_number_of @ nat @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[799]) ).
thf(910,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ord_less @ int @ SX1 @ pls )
| ~ ( ord_less @ int @ SX0 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SX1 ) @ ( number_number_of @ nat @ SX0 ) )
= ( number_number_of @ nat @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( ord_less @ int @ SX1 @ pls )
| ( ord_less @ int @ SX0 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SX1 ) @ ( number_number_of @ nat @ SX0 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[800]) ).
thf(911,plain,
( ( ! [SX0: $i] :
( ( ( semiring_1_of_nat @ int @ SX0 )
!= ( zero_zero @ int ) )
| ( SX0
= ( zero_zero @ nat ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[801]) ).
thf(912,plain,
( ( ! [SX0: $i] :
( ( SX0
!= ( zero_zero @ nat ) )
| ( ( semiring_1_of_nat @ int @ SX0 )
= ( zero_zero @ int ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[802]) ).
thf(913,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less @ int @ pls @ ( bit0 @ SX0 ) )
| ( ord_less @ int @ pls @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[803]) ).
thf(914,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less @ int @ pls @ SX0 )
| ( ord_less @ int @ pls @ ( bit0 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[804]) ).
thf(915,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less @ int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[805]) ).
thf(916,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[806]) ).
thf(917,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less @ int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[807]) ).
thf(918,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[808]) ).
thf(919,plain,
! [SV84: $i] :
( ( ( number @ SV84 )
= $false )
| ( ( ~ ( ~ ! [SY317: $i,SY318: $i] :
( ( ( number_number_of @ SV84 @ SY317 )
!= ( ti @ SV84 @ SY318 ) )
| ( ( ti @ SV84 @ SY318 )
= ( number_number_of @ SV84 @ SY317 ) ) )
| ~ ! [SY319: $i,SY320: $i] :
( ( ( ti @ SV84 @ SY320 )
!= ( number_number_of @ SV84 @ SY319 ) )
| ( ( number_number_of @ SV84 @ SY319 )
= ( ti @ SV84 @ SY320 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[809]) ).
thf(920,plain,
! [SV85: $i] :
( ( ( linordered_idom @ SV85 )
= $false )
| ( ( ~ ( ~ ! [SY321: $i] :
( ( ( ti @ SV85 @ SY321 )
= ( zero_zero @ SV85 ) )
| ( ord_less @ SV85 @ ( zero_zero @ SV85 ) @ ( power_power @ SV85 @ SY321 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
| ~ ! [SY322: $i] :
( ~ ( ord_less @ SV85 @ ( zero_zero @ SV85 ) @ ( power_power @ SV85 @ SY322 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ( ( ti @ SV85 @ SY322 )
!= ( zero_zero @ SV85 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[810]) ).
thf(921,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( semiring_1_of_nat @ int @ SX0 )
!= ( semiring_1_of_nat @ int @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[811]) ).
thf(922,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( semiring_1_of_nat @ int @ SX0 )
= ( semiring_1_of_nat @ int @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[812]) ).
thf(923,plain,
( ( ! [SX0: $i] :
( ( ( bit0 @ SX0 )
!= pls )
| ( SX0 = pls ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[813]) ).
thf(924,plain,
( ( ! [SX0: $i] :
( ( SX0 != pls )
| ( ( bit0 @ SX0 )
= pls ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[814]) ).
thf(925,plain,
! [SV86: $i] :
( ( ( ring_11004092258visors @ SV86 )
= $false )
| ( ( ~ ( ~ ! [SY323: $i] :
( ( ( power_power @ SV86 @ SY323 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= ( zero_zero @ SV86 ) )
| ( ( ti @ SV86 @ SY323 )
= ( zero_zero @ SV86 ) ) )
| ~ ! [SY324: $i] :
( ( ( ti @ SV86 @ SY324 )
!= ( zero_zero @ SV86 ) )
| ( ( power_power @ SV86 @ SY324 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SV86 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[815]) ).
thf(926,plain,
! [SV87: $i] :
( ( ( ~ ( linordered_idom @ SV87 ) )
= $true )
| ( ( ~ ( number_ring @ SV87 ) )
= $true )
| ( ( ~ ( ~ ! [SY325: $i] :
( ~ ( ord_less @ SV87 @ ( one_one @ SV87 ) @ ( number_number_of @ SV87 @ SY325 ) )
| ( ord_less @ int @ ( bit1 @ pls ) @ SY325 ) )
| ~ ! [SY326: $i] :
( ~ ( ord_less @ int @ ( bit1 @ pls ) @ SY326 )
| ( ord_less @ SV87 @ ( one_one @ SV87 ) @ ( number_number_of @ SV87 @ SY326 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[816]) ).
thf(927,plain,
( ( ! [SX0: $i] :
( ( pls
!= ( bit0 @ SX0 ) )
| ( pls = SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[817]) ).
thf(928,plain,
( ( ! [SX0: $i] :
( ( pls != SX0 )
| ( pls
= ( bit0 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[818]) ).
thf(929,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ ( number_number_of @ int @ SX0 ) @ ( number_number_of @ int @ SX1 ) )
| ( ord_less @ int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[819]) ).
thf(930,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ int @ ( number_number_of @ int @ SX0 ) @ ( number_number_of @ int @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[820]) ).
thf(931,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less @ int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[821]) ).
thf(932,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[822]) ).
thf(933,plain,
! [SV88: $i,SV5: $i,SV120: $i] :
( ( ( ~ ( linord219039673up_add @ SV120 ) )
= $true )
| ( ( ( plus_plus @ SV120 @ ( ti @ SV120 @ SV5 ) @ SV88 )
= ( plus_plus @ SV120 @ SV5 @ SV88 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[823]) ).
thf(934,plain,
! [SV89: $i,SV6: $i,SV121: $i] :
( ( ( ~ ( linord219039673up_add @ SV121 ) )
= $true )
| ( ( ( plus_plus @ SV121 @ SV6 @ ( ti @ SV121 @ SV89 ) )
= ( plus_plus @ SV121 @ SV6 @ SV89 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[824]) ).
thf(935,plain,
! [SV90: $i,SV7: $i,SV122: $i] :
( ( ( ~ ( linord219039673up_add @ SV122 ) )
= $true )
| ( ( ( ti @ SV122 @ ( plus_plus @ SV122 @ SV7 @ SV90 ) )
= ( plus_plus @ SV122 @ SV7 @ SV90 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[825]) ).
thf(936,plain,
! [SV91: $i,SV8: $i,SV123: $i] :
( ( ( ~ ( number_semiring @ SV123 ) )
= $true )
| ( ( ( plus_plus @ SV123 @ ( ti @ SV123 @ SV8 ) @ SV91 )
= ( plus_plus @ SV123 @ SV8 @ SV91 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[826]) ).
thf(937,plain,
! [SV92: $i,SV9: $i,SV124: $i] :
( ( ( ~ ( number_semiring @ SV124 ) )
= $true )
| ( ( ( plus_plus @ SV124 @ SV9 @ ( ti @ SV124 @ SV92 ) )
= ( plus_plus @ SV124 @ SV9 @ SV92 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[827]) ).
thf(938,plain,
! [SV93: $i,SV10: $i,SV125: $i] :
( ( ( ~ ( number_semiring @ SV125 ) )
= $true )
| ( ( ( ti @ SV125 @ ( plus_plus @ SV125 @ SV10 @ SV93 ) )
= ( plus_plus @ SV125 @ SV10 @ SV93 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[828]) ).
thf(939,plain,
! [SV12: $i,SV94: $i] :
( ( ( number @ SV94 )
= $false )
| ( ( ( number_number_of @ SV94 @ ( ti @ int @ SV12 ) )
= ( number_number_of @ SV94 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[830]) ).
thf(940,plain,
! [SV13: $i,SV95: $i] :
( ( ( number @ SV95 )
= $false )
| ( ( ( ti @ SV95 @ ( number_number_of @ SV95 @ SV13 ) )
= ( number_number_of @ SV95 @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[831]) ).
thf(941,plain,
! [SV14: $i,SV96: $i] :
( ( ( number_semiring @ SV96 )
= $false )
| ( ( ( semiring_1_of_nat @ SV96 @ ( ti @ nat @ SV14 ) )
= ( semiring_1_of_nat @ SV96 @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[832]) ).
thf(942,plain,
! [SV15: $i,SV97: $i] :
( ( ( number_semiring @ SV97 )
= $false )
| ( ( ( ti @ SV97 @ ( semiring_1_of_nat @ SV97 @ SV15 ) )
= ( semiring_1_of_nat @ SV97 @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[833]) ).
thf(943,plain,
! [SV136: $i,SV18: $i] :
( ( ( ( plus_plus @ SV18 @ ( one_one @ SV18 ) @ ( number_number_of @ SV18 @ SV136 ) )
= ( number_number_of @ SV18 @ ( plus_plus @ int @ ( bit1 @ pls ) @ SV136 ) ) )
= $true )
| ( ( number_ring @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[836]) ).
thf(944,plain,
! [SV137: $i,SV19: $i] :
( ( ( ( plus_plus @ SV19 @ ( number_number_of @ SV19 @ SV137 ) @ ( one_one @ SV19 ) )
= ( number_number_of @ SV19 @ ( plus_plus @ int @ SV137 @ ( bit1 @ pls ) ) ) )
= $true )
| ( ( number_ring @ SV19 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[837]) ).
thf(945,plain,
! [SV98: $i,SV25: $i] :
( ( ( SV25 = SV98 )
= $true )
| ( ( ord_less @ int @ SV25 @ SV98 )
= $true )
| ( ( ord_less @ int @ SV98 @ SV25 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[842]) ).
thf(946,plain,
! [SV31: $i,SV127: $i,SV104: $i] :
( ( ( ~ ( ord_less @ int @ SV104 @ SV127 ) )
= $true )
| ( ( ord_less @ int @ ( plus_plus @ int @ SV104 @ SV31 ) @ ( plus_plus @ int @ SV127 @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[844]) ).
thf(947,plain,
! [SV138: $i,SV49: $i] :
( ( ( ( plus_plus @ SV49 @ ( number_number_of @ SV49 @ pls ) @ SV138 )
= ( ti @ SV49 @ SV138 ) )
= $true )
| ( ( number_ring @ SV49 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[852]) ).
thf(948,plain,
! [SV139: $i,SV50: $i] :
( ( ( ( plus_plus @ SV50 @ SV139 @ ( number_number_of @ SV50 @ pls ) )
= ( ti @ SV50 @ SV139 ) )
= $true )
| ( ( number_ring @ SV50 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[853]) ).
thf(949,plain,
! [SV140: $i,SV51: $i] :
( ( ( ! [SY343: $i,SY344: $i] :
( ( plus_plus @ SV51 @ ( number_number_of @ SV51 @ SV140 ) @ ( plus_plus @ SV51 @ ( number_number_of @ SV51 @ SY343 ) @ SY344 ) )
= ( plus_plus @ SV51 @ ( number_number_of @ SV51 @ ( plus_plus @ int @ SV140 @ SY343 ) ) @ SY344 ) ) )
= $true )
| ( ( number_ring @ SV51 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[854]) ).
thf(950,plain,
! [SV141: $i,SV52: $i] :
( ( ( ! [SY345: $i] :
( ( plus_plus @ SV52 @ ( number_number_of @ SV52 @ SV141 ) @ ( number_number_of @ SV52 @ SY345 ) )
= ( number_number_of @ SV52 @ ( plus_plus @ int @ SV141 @ SY345 ) ) ) )
= $true )
| ( ( number_ring @ SV52 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[855]) ).
thf(951,plain,
! [SV142: $i,SV53: $i] :
( ( ( ! [SY346: $i] :
( ( number_number_of @ SV53 @ ( plus_plus @ int @ SV142 @ SY346 ) )
= ( plus_plus @ SV53 @ ( number_number_of @ SV53 @ SV142 ) @ ( number_number_of @ SV53 @ SY346 ) ) ) )
= $true )
| ( ( number_ring @ SV53 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[856]) ).
thf(952,plain,
! [SV143: $i,SV58: $i] :
( ( ( ( number_number_of @ SV58 @ ( semiring_1_of_nat @ int @ SV143 ) )
= ( semiring_1_of_nat @ SV58 @ SV143 ) )
= $true )
| ( ( number_semiring @ SV58 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[857]) ).
thf(953,plain,
! [SV144: $i,SV59: $i] :
( ( ( ~ ( ord_less @ SV59 @ ( power_power @ SV59 @ SV144 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( zero_zero @ SV59 ) ) )
= $true )
| ( ( linordered_idom @ SV59 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[858]) ).
thf(954,plain,
! [SV60: $i] :
( ( ( power @ SV60 )
= $false )
| ( ( ~ ( semiring_0 @ SV60 ) )
= $true )
| ( ( ( ti @ SV60 @ ( one_one @ SV60 ) )
= ( one_one @ SV60 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[859]) ).
thf(955,plain,
! [SV61: $i] :
( ( ( ~ ( mult_zero @ SV61 )
| ~ ( power @ SV61 ) )
= $true )
| ( ( ~ ( no_zero_divisors @ SV61 ) )
= $true )
| ( ( ~ ( zero_neq_one @ SV61 ) )
= $true )
| ( ( ( ti @ SV61 @ ( zero_zero @ SV61 ) )
= ( zero_zero @ SV61 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[860]) ).
thf(956,plain,
! [SV62: $i] :
( ( ( power @ SV62 )
= $false )
| ( ( ~ ( semiring_0 @ SV62 ) )
= $true )
| ( ( ( ti @ SV62 @ ( zero_zero @ SV62 ) )
= ( zero_zero @ SV62 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[861]) ).
thf(957,plain,
! [SV113: $i,SV64: $i,SV130: $i] :
( ( ( ~ ( mult_zero @ SV130 )
| ~ ( power @ SV130 )
| ~ ( no_zero_divisors @ SV130 )
| ~ ( zero_neq_one @ SV130 ) )
= $true )
| ( ( ( power_power @ SV130 @ ( ti @ SV130 @ SV64 ) @ SV113 )
= ( power_power @ SV130 @ SV64 @ SV113 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[862]) ).
thf(958,plain,
! [SV114: $i,SV65: $i,SV131: $i] :
( ( ( ~ ( mult_zero @ SV131 )
| ~ ( power @ SV131 )
| ~ ( no_zero_divisors @ SV131 )
| ~ ( zero_neq_one @ SV131 ) )
= $true )
| ( ( ( power_power @ SV131 @ SV65 @ ( ti @ nat @ SV114 ) )
= ( power_power @ SV131 @ SV65 @ SV114 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[863]) ).
thf(959,plain,
! [SV115: $i,SV66: $i,SV132: $i] :
( ( ( ~ ( mult_zero @ SV132 )
| ~ ( power @ SV132 )
| ~ ( no_zero_divisors @ SV132 )
| ~ ( zero_neq_one @ SV132 ) )
= $true )
| ( ( ( ti @ SV132 @ ( power_power @ SV132 @ SV66 @ SV115 ) )
= ( power_power @ SV132 @ SV66 @ SV115 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[864]) ).
thf(960,plain,
! [SV116: $i,SV67: $i,SV133: $i] :
( ( ( ~ ( power @ SV133 )
| ~ ( semiring_0 @ SV133 ) )
= $true )
| ( ( ( power_power @ SV133 @ ( ti @ SV133 @ SV67 ) @ SV116 )
= ( power_power @ SV133 @ SV67 @ SV116 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[865]) ).
thf(961,plain,
! [SV117: $i,SV68: $i,SV134: $i] :
( ( ( ~ ( power @ SV134 )
| ~ ( semiring_0 @ SV134 ) )
= $true )
| ( ( ( power_power @ SV134 @ SV68 @ ( ti @ nat @ SV117 ) )
= ( power_power @ SV134 @ SV68 @ SV117 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[866]) ).
thf(962,plain,
! [SV118: $i,SV69: $i,SV135: $i] :
( ( ( ~ ( power @ SV135 )
| ~ ( semiring_0 @ SV135 ) )
= $true )
| ( ( ( ti @ SV135 @ ( power_power @ SV135 @ SV69 @ SV118 ) )
= ( power_power @ SV135 @ SV69 @ SV118 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[867]) ).
thf(963,plain,
! [SV145: $i] :
( ( ~ ( ord_less @ int @ ( bit1 @ SV145 ) @ ( zero_zero @ int ) )
| ( ord_less @ int @ SV145 @ ( zero_zero @ int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[868]) ).
thf(964,plain,
! [SV146: $i] :
( ( ~ ( ord_less @ int @ SV146 @ ( zero_zero @ int ) )
| ( ord_less @ int @ ( bit1 @ SV146 ) @ ( zero_zero @ int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[869]) ).
thf(965,plain,
! [SV71: $i] :
( ( ( number_ring @ SV71 )
= $false )
| ( ( ~ ( ring_char_0 @ SV71 ) )
= $true )
| ( ( ~ ( ~ ! [SY271: $i,SY272: $i] :
( ( ( number_number_of @ SV71 @ SY271 )
!= ( number_number_of @ SV71 @ SY272 ) )
| ( SY271 = SY272 ) )
| ~ ! [SY273: $i,SY274: $i] :
( ( SY273 != SY274 )
| ( ( number_number_of @ SV71 @ SY273 )
= ( number_number_of @ SV71 @ SY274 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[870]) ).
thf(966,plain,
! [SV72: $i] :
( ( ! [SY275: $i,SY276: $i] :
( ~ ( linordered_idom @ SY276 )
| ~ ( ord_less @ SY276 @ ( ti @ SY276 @ SV72 ) @ SY275 )
| ( ord_less @ SY276 @ SV72 @ SY275 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[871]) ).
thf(967,plain,
! [SV72: $i] :
( ( ! [SY277: $i,SY278: $i] :
( ~ ( linordered_idom @ SY278 )
| ~ ( ord_less @ SY278 @ SV72 @ SY277 )
| ( ord_less @ SY278 @ ( ti @ SY278 @ SV72 ) @ SY277 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[872]) ).
thf(968,plain,
! [SV147: $i] :
( ( ~ ( ord_less @ int @ ( bit0 @ SV147 ) @ ( zero_zero @ int ) )
| ( ord_less @ int @ SV147 @ ( zero_zero @ int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[873]) ).
thf(969,plain,
! [SV148: $i] :
( ( ~ ( ord_less @ int @ SV148 @ ( zero_zero @ int ) )
| ( ord_less @ int @ ( bit0 @ SV148 ) @ ( zero_zero @ int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[874]) ).
thf(970,plain,
! [SV149: $i] :
( ( ~ ( ord_less @ int @ ( bit0 @ SV149 ) @ pls )
| ( ord_less @ int @ SV149 @ pls ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[875]) ).
thf(971,plain,
! [SV150: $i] :
( ( ~ ( ord_less @ int @ SV150 @ pls )
| ( ord_less @ int @ ( bit0 @ SV150 ) @ pls ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[876]) ).
thf(972,plain,
! [SV151: $i] :
( ( ! [SY347: $i] :
( ~ ( ord_less @ int @ SV151 @ ( plus_plus @ int @ SY347 @ ( one_one @ int ) ) )
| ( SV151 = SY347 )
| ( ord_less @ int @ SV151 @ SY347 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[877]) ).
thf(973,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ord_less @ int @ SX0 @ ( plus_plus @ int @ SX1 @ ( one_one @ int ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ int @ SX0 @ ( plus_plus @ int @ SX1 @ ( one_one @ int ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[878]) ).
thf(974,plain,
! [SV152: $i] :
( ( ! [SY348: $i] :
( ~ ( ord_less @ nat @ ( ti @ nat @ SV152 ) @ SY348 )
| ( ord_less @ nat @ SV152 @ SY348 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[879]) ).
thf(975,plain,
! [SV153: $i] :
( ( ! [SY349: $i] :
( ~ ( ord_less @ nat @ SV153 @ SY349 )
| ( ord_less @ nat @ ( ti @ nat @ SV153 ) @ SY349 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[880]) ).
thf(976,plain,
! [SV73: $i] :
( ( ( ~ ! [SY279: $i,SY280: $i] :
( ( ( ti @ SV73 @ SY279 )
!= ( zero_zero @ SV73 ) )
| ( ( ti @ SV73 @ SY280 )
!= ( zero_zero @ SV73 ) )
| ( ( plus_plus @ SV73 @ ( power_power @ SV73 @ SY279 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV73 @ SY280 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV73 ) ) )
| ~ ~ ( ~ ! [SY281: $i] :
( ! [SY282: $i] :
( ( plus_plus @ SV73 @ ( power_power @ SV73 @ SY281 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV73 @ SY282 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV73 ) )
| ( ( ti @ SV73 @ SY281 )
= ( zero_zero @ SV73 ) ) )
| ~ ! [SY283: $i,SY284: $i] :
( ( ( plus_plus @ SV73 @ ( power_power @ SV73 @ SY283 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV73 @ SY284 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV73 ) )
| ( ( ti @ SV73 @ SY284 )
= ( zero_zero @ SV73 ) ) ) ) )
= $false )
| ( ( linordered_idom @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[881]) ).
thf(977,plain,
! [SV74: $i] :
( ( ( ~ ! [SY285: $i,SY286: $i] :
( ~ ( ord_less @ SV74 @ ( zero_zero @ SV74 ) @ ( plus_plus @ SV74 @ ( power_power @ SV74 @ SY285 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV74 @ SY286 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
| ( ( ti @ SV74 @ SY285 )
!= ( zero_zero @ SV74 ) )
| ( ( ti @ SV74 @ SY286 )
!= ( zero_zero @ SV74 ) ) )
| ~ ~ ( ~ ! [SY287: $i] :
( ( ( ti @ SV74 @ SY287 )
= ( zero_zero @ SV74 ) )
| ! [SY288: $i] : ( ord_less @ SV74 @ ( zero_zero @ SV74 ) @ ( plus_plus @ SV74 @ ( power_power @ SV74 @ SY287 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV74 @ SY288 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
| ~ ! [SY289: $i,SY290: $i] :
( ( ( ti @ SV74 @ SY290 )
= ( zero_zero @ SV74 ) )
| ( ord_less @ SV74 @ ( zero_zero @ SV74 ) @ ( plus_plus @ SV74 @ ( power_power @ SV74 @ SY289 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV74 @ SY290 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) ) )
= $false )
| ( ( linordered_idom @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[882]) ).
thf(978,plain,
! [SV75: $i] :
( ( ( linordered_idom @ SV75 )
= $false )
| ( ( ~ ( number_ring @ SV75 ) )
= $true )
| ( ( ~ ( ~ ! [SY291: $i] :
( ~ ( ord_less @ SV75 @ ( number_number_of @ SV75 @ SY291 ) @ ( one_one @ SV75 ) )
| ( ord_less @ int @ SY291 @ ( bit1 @ pls ) ) )
| ~ ! [SY292: $i] :
( ~ ( ord_less @ int @ SY292 @ ( bit1 @ pls ) )
| ( ord_less @ SV75 @ ( number_number_of @ SV75 @ SY292 ) @ ( one_one @ SV75 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[883]) ).
thf(979,plain,
! [SV76: $i] :
( ( ( linordered_idom @ SV76 )
= $false )
| ( ( ~ ( number_ring @ SV76 ) )
= $true )
| ( ( ~ ( ~ ! [SY293: $i] :
( ~ ( ord_less @ SV76 @ ( zero_zero @ SV76 ) @ ( number_number_of @ SV76 @ SY293 ) )
| ( ord_less @ int @ pls @ SY293 ) )
| ~ ! [SY294: $i] :
( ~ ( ord_less @ int @ pls @ SY294 )
| ( ord_less @ SV76 @ ( zero_zero @ SV76 ) @ ( number_number_of @ SV76 @ SY294 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[884]) ).
thf(980,plain,
! [SV154: $i] :
( ( ! [SY350: $i] :
( ~ ( ord_less @ int @ ( bit0 @ SV154 ) @ ( bit0 @ SY350 ) )
| ( ord_less @ int @ SV154 @ SY350 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[885]) ).
thf(981,plain,
! [SV155: $i] :
( ( ! [SY351: $i] :
( ~ ( ord_less @ int @ SV155 @ SY351 )
| ( ord_less @ int @ ( bit0 @ SV155 ) @ ( bit0 @ SY351 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[886]) ).
thf(982,plain,
! [SV156: $i] :
( ( ~ ( ord_less @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ SV156 ) @ SV156 ) @ ( zero_zero @ int ) )
| ( ord_less @ int @ SV156 @ ( zero_zero @ int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[887]) ).
thf(983,plain,
! [SV157: $i] :
( ( ~ ( ord_less @ int @ SV157 @ ( zero_zero @ int ) )
| ( ord_less @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ SV157 ) @ SV157 ) @ ( zero_zero @ int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[888]) ).
thf(984,plain,
! [SV158: $i] :
( ( ! [SY352: $i] :
( ~ ( ord_less @ nat @ SV158 @ ( ti @ nat @ SY352 ) )
| ( ord_less @ nat @ SV158 @ SY352 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[889]) ).
thf(985,plain,
! [SV159: $i] :
( ( ! [SY353: $i] :
( ~ ( ord_less @ nat @ SV159 @ SY353 )
| ( ord_less @ nat @ SV159 @ ( ti @ nat @ SY353 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[890]) ).
thf(986,plain,
! [SV77: $i] :
( ( ( ~ ( mult_zero @ SV77 )
| ~ ( power @ SV77 ) )
= $true )
| ( ( ~ ( no_zero_divisors @ SV77 ) )
= $true )
| ( ( ~ ( zero_neq_one @ SV77 ) )
= $true )
| ( ( ~ ( ~ ! [SY295: $i,SY296: $i] :
( ( ( number_number_of @ nat @ SY296 )
= ( zero_zero @ nat ) )
| ( ( ti @ SV77 @ SY295 )
!= ( zero_zero @ SV77 ) )
| ( ( power_power @ SV77 @ SY295 @ ( number_number_of @ nat @ SY296 ) )
= ( zero_zero @ SV77 ) ) )
| ~ ~ ( ~ ! [SY297: $i,SY298: $i] :
( ( ( power_power @ SV77 @ SY297 @ ( number_number_of @ nat @ SY298 ) )
!= ( zero_zero @ SV77 ) )
| ( ( number_number_of @ nat @ SY298 )
!= ( zero_zero @ nat ) ) )
| ~ ! [SY299: $i] :
( ! [SY300: $i] :
( ( power_power @ SV77 @ SY299 @ ( number_number_of @ nat @ SY300 ) )
!= ( zero_zero @ SV77 ) )
| ( ( ti @ SV77 @ SY299 )
= ( zero_zero @ SV77 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[891]) ).
thf(987,plain,
! [SV78: $i] :
( ( ! [SY301: $i,SY302: $i] :
( ~ ( linordered_idom @ SY302 )
| ~ ( ord_less @ SY302 @ SV78 @ ( ti @ SY302 @ SY301 ) )
| ( ord_less @ SY302 @ SV78 @ SY301 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[892]) ).
thf(988,plain,
! [SV78: $i] :
( ( ! [SY303: $i,SY304: $i] :
( ~ ( linordered_idom @ SY304 )
| ~ ( ord_less @ SY304 @ SV78 @ SY303 )
| ( ord_less @ SY304 @ SV78 @ ( ti @ SY304 @ SY303 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[893]) ).
thf(989,plain,
! [SV160: $i] :
( ( ~ ( ord_less @ int @ ( bit1 @ SV160 ) @ pls )
| ( ord_less @ int @ SV160 @ pls ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[894]) ).
thf(990,plain,
! [SV161: $i] :
( ( ~ ( ord_less @ int @ SV161 @ pls )
| ( ord_less @ int @ ( bit1 @ SV161 ) @ pls ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[895]) ).
thf(991,plain,
! [SV162: $i] :
( ( ! [SY354: $i] :
( ( ( bit1 @ SV162 )
!= ( bit1 @ SY354 ) )
| ( SV162 = SY354 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[896]) ).
thf(992,plain,
! [SV163: $i] :
( ( ! [SY355: $i] :
( ( SV163 != SY355 )
| ( ( bit1 @ SV163 )
= ( bit1 @ SY355 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[897]) ).
thf(993,plain,
! [SV79: $i] :
( ( ( ~ ! [SY305: $i] :
( ( ( plus_plus @ SV79 @ SY305 @ SY305 )
!= ( zero_zero @ SV79 ) )
| ( ( ti @ SV79 @ SY305 )
= ( zero_zero @ SV79 ) ) )
| ~ ! [SY306: $i] :
( ( ( ti @ SV79 @ SY306 )
!= ( zero_zero @ SV79 ) )
| ( ( plus_plus @ SV79 @ SY306 @ SY306 )
= ( zero_zero @ SV79 ) ) ) )
= $false )
| ( ( linord219039673up_add @ SV79 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[898]) ).
thf(994,plain,
! [SV164: $i] :
( ( ! [SY356: $i] :
( ~ ( ord_less @ int @ ( bit1 @ SV164 ) @ ( bit1 @ SY356 ) )
| ( ord_less @ int @ SV164 @ SY356 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[899]) ).
thf(995,plain,
! [SV165: $i] :
( ( ! [SY357: $i] :
( ~ ( ord_less @ int @ SV165 @ SY357 )
| ( ord_less @ int @ ( bit1 @ SV165 ) @ ( bit1 @ SY357 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[900]) ).
thf(996,plain,
! [SV80: $i] :
( ( ( linordered_idom @ SV80 )
= $false )
| ( ( ~ ( number_ring @ SV80 ) )
= $true )
| ( ( ~ ( ~ ! [SY307: $i] :
( ~ ( ord_less @ SV80 @ ( number_number_of @ SV80 @ SY307 ) @ ( zero_zero @ SV80 ) )
| ( ord_less @ int @ SY307 @ pls ) )
| ~ ! [SY308: $i] :
( ~ ( ord_less @ int @ SY308 @ pls )
| ( ord_less @ SV80 @ ( number_number_of @ SV80 @ SY308 ) @ ( zero_zero @ SV80 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[901]) ).
thf(997,plain,
! [SV81: $i] :
( ( ( linordered_idom @ SV81 )
= $false )
| ( ( ~ ( number_ring @ SV81 ) )
= $true )
| ( ( ~ ( ~ ! [SY309: $i,SY310: $i] :
( ~ ( ord_less @ SV81 @ ( number_number_of @ SV81 @ SY309 ) @ ( number_number_of @ SV81 @ SY310 ) )
| ( ord_less @ int @ SY309 @ SY310 ) )
| ~ ! [SY311: $i,SY312: $i] :
( ~ ( ord_less @ int @ SY311 @ SY312 )
| ( ord_less @ SV81 @ ( number_number_of @ SV81 @ SY311 ) @ ( number_number_of @ SV81 @ SY312 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[902]) ).
thf(998,plain,
! [SV166: $i] :
( ( ! [SY358: $i] :
( ( ( bit0 @ SV166 )
!= ( bit0 @ SY358 ) )
| ( SV166 = SY358 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[903]) ).
thf(999,plain,
! [SV167: $i] :
( ( ! [SY359: $i] :
( ( SV167 != SY359 )
| ( ( bit0 @ SV167 )
= ( bit0 @ SY359 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[904]) ).
thf(1000,plain,
! [SV168: $i] :
( ( ! [SY360: $i] :
( ~ ( ord_less @ int @ ( bit0 @ SV168 ) @ ( bit0 @ SY360 ) )
| ( ord_less @ int @ SV168 @ SY360 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[905]) ).
thf(1001,plain,
! [SV169: $i] :
( ( ! [SY361: $i] :
( ~ ( ord_less @ int @ SV169 @ SY361 )
| ( ord_less @ int @ ( bit0 @ SV169 ) @ ( bit0 @ SY361 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[906]) ).
thf(1002,plain,
! [SV82: $i] :
( ( ( ~ ! [SY313: $i] :
( ~ ( ord_less @ SV82 @ ( plus_plus @ SV82 @ SY313 @ SY313 ) @ ( zero_zero @ SV82 ) )
| ( ord_less @ SV82 @ SY313 @ ( zero_zero @ SV82 ) ) )
| ~ ! [SY314: $i] :
( ~ ( ord_less @ SV82 @ SY314 @ ( zero_zero @ SV82 ) )
| ( ord_less @ SV82 @ ( plus_plus @ SV82 @ SY314 @ SY314 ) @ ( zero_zero @ SV82 ) ) ) )
= $false )
| ( ( linordered_idom @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[907]) ).
thf(1003,plain,
! [SV83: $i] :
( ( ( power @ SV83 )
= $false )
| ( ( ~ ( semiring_0 @ SV83 ) )
= $true )
| ( ( ~ ( ~ ! [SY315: $i] :
( ( ( number_number_of @ nat @ SY315 )
!= ( zero_zero @ nat ) )
| ( ( power_power @ SV83 @ ( zero_zero @ SV83 ) @ ( number_number_of @ nat @ SY315 ) )
= ( one_one @ SV83 ) ) )
| ~ ! [SY316: $i] :
( ( ( number_number_of @ nat @ SY316 )
= ( zero_zero @ nat ) )
| ( ( power_power @ SV83 @ ( zero_zero @ SV83 ) @ ( number_number_of @ nat @ SY316 ) )
= ( zero_zero @ SV83 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[908]) ).
thf(1004,plain,
! [SV170: $i] :
( ( ! [SY362: $i] :
( ~ ( ord_less @ int @ SY362 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SY362 ) @ ( number_number_of @ nat @ SV170 ) )
= ( number_number_of @ nat @ SV170 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[909]) ).
thf(1005,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ord_less @ int @ SX1 @ pls )
| ~ ( ord_less @ int @ SX0 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SX1 ) @ ( number_number_of @ nat @ SX0 ) )
= ( number_number_of @ nat @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( ord_less @ int @ SX1 @ pls )
| ( ord_less @ int @ SX0 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SX1 ) @ ( number_number_of @ nat @ SX0 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[910]) ).
thf(1006,plain,
! [SV171: $i] :
( ( ( ( semiring_1_of_nat @ int @ SV171 )
!= ( zero_zero @ int ) )
| ( SV171
= ( zero_zero @ nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[911]) ).
thf(1007,plain,
! [SV172: $i] :
( ( ( SV172
!= ( zero_zero @ nat ) )
| ( ( semiring_1_of_nat @ int @ SV172 )
= ( zero_zero @ int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[912]) ).
thf(1008,plain,
! [SV173: $i] :
( ( ~ ( ord_less @ int @ pls @ ( bit0 @ SV173 ) )
| ( ord_less @ int @ pls @ SV173 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[913]) ).
thf(1009,plain,
! [SV174: $i] :
( ( ~ ( ord_less @ int @ pls @ SV174 )
| ( ord_less @ int @ pls @ ( bit0 @ SV174 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[914]) ).
thf(1010,plain,
! [SV175: $i] :
( ( ! [SY363: $i] :
( ~ ( ord_less @ int @ ( bit1 @ SV175 ) @ ( bit0 @ SY363 ) )
| ( ord_less @ int @ SV175 @ SY363 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[915]) ).
thf(1011,plain,
! [SV176: $i] :
( ( ! [SY364: $i] :
( ~ ( ord_less @ int @ SV176 @ SY364 )
| ( ord_less @ int @ ( bit1 @ SV176 ) @ ( bit0 @ SY364 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[916]) ).
thf(1012,plain,
! [SV177: $i] :
( ( ! [SY365: $i] :
( ~ ( ord_less @ int @ ( bit1 @ SV177 ) @ ( bit1 @ SY365 ) )
| ( ord_less @ int @ SV177 @ SY365 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[917]) ).
thf(1013,plain,
! [SV178: $i] :
( ( ! [SY366: $i] :
( ~ ( ord_less @ int @ SV178 @ SY366 )
| ( ord_less @ int @ ( bit1 @ SV178 ) @ ( bit1 @ SY366 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[918]) ).
thf(1014,plain,
! [SV84: $i] :
( ( ( ~ ! [SY317: $i,SY318: $i] :
( ( ( number_number_of @ SV84 @ SY317 )
!= ( ti @ SV84 @ SY318 ) )
| ( ( ti @ SV84 @ SY318 )
= ( number_number_of @ SV84 @ SY317 ) ) )
| ~ ! [SY319: $i,SY320: $i] :
( ( ( ti @ SV84 @ SY320 )
!= ( number_number_of @ SV84 @ SY319 ) )
| ( ( number_number_of @ SV84 @ SY319 )
= ( ti @ SV84 @ SY320 ) ) ) )
= $false )
| ( ( number @ SV84 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[919]) ).
thf(1015,plain,
! [SV85: $i] :
( ( ( ~ ! [SY321: $i] :
( ( ( ti @ SV85 @ SY321 )
= ( zero_zero @ SV85 ) )
| ( ord_less @ SV85 @ ( zero_zero @ SV85 ) @ ( power_power @ SV85 @ SY321 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
| ~ ! [SY322: $i] :
( ~ ( ord_less @ SV85 @ ( zero_zero @ SV85 ) @ ( power_power @ SV85 @ SY322 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ( ( ti @ SV85 @ SY322 )
!= ( zero_zero @ SV85 ) ) ) )
= $false )
| ( ( linordered_idom @ SV85 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[920]) ).
thf(1016,plain,
! [SV179: $i] :
( ( ! [SY367: $i] :
( ( ( semiring_1_of_nat @ int @ SV179 )
!= ( semiring_1_of_nat @ int @ SY367 ) )
| ( SV179 = SY367 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[921]) ).
thf(1017,plain,
! [SV180: $i] :
( ( ! [SY368: $i] :
( ( SV180 != SY368 )
| ( ( semiring_1_of_nat @ int @ SV180 )
= ( semiring_1_of_nat @ int @ SY368 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[922]) ).
thf(1018,plain,
! [SV181: $i] :
( ( ( ( bit0 @ SV181 )
!= pls )
| ( SV181 = pls ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[923]) ).
thf(1019,plain,
! [SV182: $i] :
( ( ( SV182 != pls )
| ( ( bit0 @ SV182 )
= pls ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[924]) ).
thf(1020,plain,
! [SV86: $i] :
( ( ( ~ ! [SY323: $i] :
( ( ( power_power @ SV86 @ SY323 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= ( zero_zero @ SV86 ) )
| ( ( ti @ SV86 @ SY323 )
= ( zero_zero @ SV86 ) ) )
| ~ ! [SY324: $i] :
( ( ( ti @ SV86 @ SY324 )
!= ( zero_zero @ SV86 ) )
| ( ( power_power @ SV86 @ SY324 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SV86 ) ) ) )
= $false )
| ( ( ring_11004092258visors @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[925]) ).
thf(1021,plain,
! [SV87: $i] :
( ( ( linordered_idom @ SV87 )
= $false )
| ( ( ~ ( number_ring @ SV87 ) )
= $true )
| ( ( ~ ( ~ ! [SY325: $i] :
( ~ ( ord_less @ SV87 @ ( one_one @ SV87 ) @ ( number_number_of @ SV87 @ SY325 ) )
| ( ord_less @ int @ ( bit1 @ pls ) @ SY325 ) )
| ~ ! [SY326: $i] :
( ~ ( ord_less @ int @ ( bit1 @ pls ) @ SY326 )
| ( ord_less @ SV87 @ ( one_one @ SV87 ) @ ( number_number_of @ SV87 @ SY326 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[926]) ).
thf(1022,plain,
! [SV183: $i] :
( ( ( pls
!= ( bit0 @ SV183 ) )
| ( pls = SV183 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[927]) ).
thf(1023,plain,
! [SV184: $i] :
( ( ( pls != SV184 )
| ( pls
= ( bit0 @ SV184 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[928]) ).
thf(1024,plain,
! [SV185: $i] :
( ( ! [SY369: $i] :
( ~ ( ord_less @ int @ ( number_number_of @ int @ SV185 ) @ ( number_number_of @ int @ SY369 ) )
| ( ord_less @ int @ SV185 @ SY369 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[929]) ).
thf(1025,plain,
! [SV186: $i] :
( ( ! [SY370: $i] :
( ~ ( ord_less @ int @ SV186 @ SY370 )
| ( ord_less @ int @ ( number_number_of @ int @ SV186 ) @ ( number_number_of @ int @ SY370 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[930]) ).
thf(1026,plain,
! [SV187: $i] :
( ( ! [SY371: $i] :
( ~ ( ord_less @ int @ ( bit1 @ SV187 ) @ ( bit0 @ SY371 ) )
| ( ord_less @ int @ SV187 @ SY371 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[931]) ).
thf(1027,plain,
! [SV188: $i] :
( ( ! [SY372: $i] :
( ~ ( ord_less @ int @ SV188 @ SY372 )
| ( ord_less @ int @ ( bit1 @ SV188 ) @ ( bit0 @ SY372 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[932]) ).
thf(1028,plain,
! [SV88: $i,SV5: $i,SV120: $i] :
( ( ( linord219039673up_add @ SV120 )
= $false )
| ( ( ( plus_plus @ SV120 @ ( ti @ SV120 @ SV5 ) @ SV88 )
= ( plus_plus @ SV120 @ SV5 @ SV88 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[933]) ).
thf(1029,plain,
! [SV89: $i,SV6: $i,SV121: $i] :
( ( ( linord219039673up_add @ SV121 )
= $false )
| ( ( ( plus_plus @ SV121 @ SV6 @ ( ti @ SV121 @ SV89 ) )
= ( plus_plus @ SV121 @ SV6 @ SV89 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[934]) ).
thf(1030,plain,
! [SV90: $i,SV7: $i,SV122: $i] :
( ( ( linord219039673up_add @ SV122 )
= $false )
| ( ( ( ti @ SV122 @ ( plus_plus @ SV122 @ SV7 @ SV90 ) )
= ( plus_plus @ SV122 @ SV7 @ SV90 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[935]) ).
thf(1031,plain,
! [SV91: $i,SV8: $i,SV123: $i] :
( ( ( number_semiring @ SV123 )
= $false )
| ( ( ( plus_plus @ SV123 @ ( ti @ SV123 @ SV8 ) @ SV91 )
= ( plus_plus @ SV123 @ SV8 @ SV91 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[936]) ).
thf(1032,plain,
! [SV92: $i,SV9: $i,SV124: $i] :
( ( ( number_semiring @ SV124 )
= $false )
| ( ( ( plus_plus @ SV124 @ SV9 @ ( ti @ SV124 @ SV92 ) )
= ( plus_plus @ SV124 @ SV9 @ SV92 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[937]) ).
thf(1033,plain,
! [SV93: $i,SV10: $i,SV125: $i] :
( ( ( number_semiring @ SV125 )
= $false )
| ( ( ( ti @ SV125 @ ( plus_plus @ SV125 @ SV10 @ SV93 ) )
= ( plus_plus @ SV125 @ SV10 @ SV93 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[938]) ).
thf(1034,plain,
! [SV31: $i,SV127: $i,SV104: $i] :
( ( ( ord_less @ int @ SV104 @ SV127 )
= $false )
| ( ( ord_less @ int @ ( plus_plus @ int @ SV104 @ SV31 ) @ ( plus_plus @ int @ SV127 @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[946]) ).
thf(1035,plain,
! [SV189: $i,SV140: $i,SV51: $i] :
( ( ( ! [SY373: $i] :
( ( plus_plus @ SV51 @ ( number_number_of @ SV51 @ SV140 ) @ ( plus_plus @ SV51 @ ( number_number_of @ SV51 @ SV189 ) @ SY373 ) )
= ( plus_plus @ SV51 @ ( number_number_of @ SV51 @ ( plus_plus @ int @ SV140 @ SV189 ) ) @ SY373 ) ) )
= $true )
| ( ( number_ring @ SV51 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[949]) ).
thf(1036,plain,
! [SV190: $i,SV141: $i,SV52: $i] :
( ( ( ( plus_plus @ SV52 @ ( number_number_of @ SV52 @ SV141 ) @ ( number_number_of @ SV52 @ SV190 ) )
= ( number_number_of @ SV52 @ ( plus_plus @ int @ SV141 @ SV190 ) ) )
= $true )
| ( ( number_ring @ SV52 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[950]) ).
thf(1037,plain,
! [SV191: $i,SV142: $i,SV53: $i] :
( ( ( ( number_number_of @ SV53 @ ( plus_plus @ int @ SV142 @ SV191 ) )
= ( plus_plus @ SV53 @ ( number_number_of @ SV53 @ SV142 ) @ ( number_number_of @ SV53 @ SV191 ) ) )
= $true )
| ( ( number_ring @ SV53 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[951]) ).
thf(1038,plain,
! [SV144: $i,SV59: $i] :
( ( ( ord_less @ SV59 @ ( power_power @ SV59 @ SV144 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( zero_zero @ SV59 ) )
= $false )
| ( ( linordered_idom @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[953]) ).
thf(1039,plain,
! [SV60: $i] :
( ( ( semiring_0 @ SV60 )
= $false )
| ( ( power @ SV60 )
= $false )
| ( ( ( ti @ SV60 @ ( one_one @ SV60 ) )
= ( one_one @ SV60 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[954]) ).
thf(1040,plain,
! [SV61: $i] :
( ( ( ~ ( mult_zero @ SV61 ) )
= $true )
| ( ( ~ ( power @ SV61 ) )
= $true )
| ( ( ~ ( no_zero_divisors @ SV61 ) )
= $true )
| ( ( ~ ( zero_neq_one @ SV61 ) )
= $true )
| ( ( ( ti @ SV61 @ ( zero_zero @ SV61 ) )
= ( zero_zero @ SV61 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[955]) ).
thf(1041,plain,
! [SV62: $i] :
( ( ( semiring_0 @ SV62 )
= $false )
| ( ( power @ SV62 )
= $false )
| ( ( ( ti @ SV62 @ ( zero_zero @ SV62 ) )
= ( zero_zero @ SV62 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[956]) ).
thf(1042,plain,
! [SV113: $i,SV64: $i,SV130: $i] :
( ( ( ~ ( mult_zero @ SV130 )
| ~ ( power @ SV130 )
| ~ ( no_zero_divisors @ SV130 ) )
= $true )
| ( ( ~ ( zero_neq_one @ SV130 ) )
= $true )
| ( ( ( power_power @ SV130 @ ( ti @ SV130 @ SV64 ) @ SV113 )
= ( power_power @ SV130 @ SV64 @ SV113 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[957]) ).
thf(1043,plain,
! [SV114: $i,SV65: $i,SV131: $i] :
( ( ( ~ ( mult_zero @ SV131 )
| ~ ( power @ SV131 )
| ~ ( no_zero_divisors @ SV131 ) )
= $true )
| ( ( ~ ( zero_neq_one @ SV131 ) )
= $true )
| ( ( ( power_power @ SV131 @ SV65 @ ( ti @ nat @ SV114 ) )
= ( power_power @ SV131 @ SV65 @ SV114 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[958]) ).
thf(1044,plain,
! [SV115: $i,SV66: $i,SV132: $i] :
( ( ( ~ ( mult_zero @ SV132 )
| ~ ( power @ SV132 )
| ~ ( no_zero_divisors @ SV132 ) )
= $true )
| ( ( ~ ( zero_neq_one @ SV132 ) )
= $true )
| ( ( ( ti @ SV132 @ ( power_power @ SV132 @ SV66 @ SV115 ) )
= ( power_power @ SV132 @ SV66 @ SV115 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[959]) ).
thf(1045,plain,
! [SV116: $i,SV67: $i,SV133: $i] :
( ( ( ~ ( power @ SV133 ) )
= $true )
| ( ( ~ ( semiring_0 @ SV133 ) )
= $true )
| ( ( ( power_power @ SV133 @ ( ti @ SV133 @ SV67 ) @ SV116 )
= ( power_power @ SV133 @ SV67 @ SV116 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[960]) ).
thf(1046,plain,
! [SV117: $i,SV68: $i,SV134: $i] :
( ( ( ~ ( power @ SV134 ) )
= $true )
| ( ( ~ ( semiring_0 @ SV134 ) )
= $true )
| ( ( ( power_power @ SV134 @ SV68 @ ( ti @ nat @ SV117 ) )
= ( power_power @ SV134 @ SV68 @ SV117 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[961]) ).
thf(1047,plain,
! [SV118: $i,SV69: $i,SV135: $i] :
( ( ( ~ ( power @ SV135 ) )
= $true )
| ( ( ~ ( semiring_0 @ SV135 ) )
= $true )
| ( ( ( ti @ SV135 @ ( power_power @ SV135 @ SV69 @ SV118 ) )
= ( power_power @ SV135 @ SV69 @ SV118 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[962]) ).
thf(1048,plain,
! [SV145: $i] :
( ( ( ~ ( ord_less @ int @ ( bit1 @ SV145 ) @ ( zero_zero @ int ) ) )
= $true )
| ( ( ord_less @ int @ SV145 @ ( zero_zero @ int ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[963]) ).
thf(1049,plain,
! [SV146: $i] :
( ( ( ~ ( ord_less @ int @ SV146 @ ( zero_zero @ int ) ) )
= $true )
| ( ( ord_less @ int @ ( bit1 @ SV146 ) @ ( zero_zero @ int ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[964]) ).
thf(1050,plain,
! [SV71: $i] :
( ( ( ring_char_0 @ SV71 )
= $false )
| ( ( number_ring @ SV71 )
= $false )
| ( ( ~ ( ~ ! [SY271: $i,SY272: $i] :
( ( ( number_number_of @ SV71 @ SY271 )
!= ( number_number_of @ SV71 @ SY272 ) )
| ( SY271 = SY272 ) )
| ~ ! [SY273: $i,SY274: $i] :
( ( SY273 != SY274 )
| ( ( number_number_of @ SV71 @ SY273 )
= ( number_number_of @ SV71 @ SY274 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[965]) ).
thf(1051,plain,
! [SV192: $i,SV72: $i] :
( ( ! [SY374: $i] :
( ~ ( linordered_idom @ SY374 )
| ~ ( ord_less @ SY374 @ ( ti @ SY374 @ SV72 ) @ SV192 )
| ( ord_less @ SY374 @ SV72 @ SV192 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[966]) ).
thf(1052,plain,
! [SV193: $i,SV72: $i] :
( ( ! [SY375: $i] :
( ~ ( linordered_idom @ SY375 )
| ~ ( ord_less @ SY375 @ SV72 @ SV193 )
| ( ord_less @ SY375 @ ( ti @ SY375 @ SV72 ) @ SV193 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[967]) ).
thf(1053,plain,
! [SV147: $i] :
( ( ( ~ ( ord_less @ int @ ( bit0 @ SV147 ) @ ( zero_zero @ int ) ) )
= $true )
| ( ( ord_less @ int @ SV147 @ ( zero_zero @ int ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[968]) ).
thf(1054,plain,
! [SV148: $i] :
( ( ( ~ ( ord_less @ int @ SV148 @ ( zero_zero @ int ) ) )
= $true )
| ( ( ord_less @ int @ ( bit0 @ SV148 ) @ ( zero_zero @ int ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[969]) ).
thf(1055,plain,
! [SV149: $i] :
( ( ( ~ ( ord_less @ int @ ( bit0 @ SV149 ) @ pls ) )
= $true )
| ( ( ord_less @ int @ SV149 @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[970]) ).
thf(1056,plain,
! [SV150: $i] :
( ( ( ~ ( ord_less @ int @ SV150 @ pls ) )
= $true )
| ( ( ord_less @ int @ ( bit0 @ SV150 ) @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[971]) ).
thf(1057,plain,
! [SV194: $i,SV151: $i] :
( ( ~ ( ord_less @ int @ SV151 @ ( plus_plus @ int @ SV194 @ ( one_one @ int ) ) )
| ( SV151 = SV194 )
| ( ord_less @ int @ SV151 @ SV194 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[972]) ).
thf(1058,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ord_less @ int @ SX0 @ ( plus_plus @ int @ SX1 @ ( one_one @ int ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[973]) ).
thf(1059,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ int @ SX0 @ ( plus_plus @ int @ SX1 @ ( one_one @ int ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[973]) ).
thf(1060,plain,
! [SV195: $i,SV152: $i] :
( ( ~ ( ord_less @ nat @ ( ti @ nat @ SV152 ) @ SV195 )
| ( ord_less @ nat @ SV152 @ SV195 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[974]) ).
thf(1061,plain,
! [SV196: $i,SV153: $i] :
( ( ~ ( ord_less @ nat @ SV153 @ SV196 )
| ( ord_less @ nat @ ( ti @ nat @ SV153 ) @ SV196 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[975]) ).
thf(1062,plain,
! [SV73: $i] :
( ( ( ~ ! [SY279: $i,SY280: $i] :
( ( ( ti @ SV73 @ SY279 )
!= ( zero_zero @ SV73 ) )
| ( ( ti @ SV73 @ SY280 )
!= ( zero_zero @ SV73 ) )
| ( ( plus_plus @ SV73 @ ( power_power @ SV73 @ SY279 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV73 @ SY280 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV73 ) ) ) )
= $false )
| ( ( linordered_idom @ SV73 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[976]) ).
thf(1063,plain,
! [SV73: $i] :
( ( ( ~ ~ ( ~ ! [SY281: $i] :
( ! [SY282: $i] :
( ( plus_plus @ SV73 @ ( power_power @ SV73 @ SY281 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV73 @ SY282 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV73 ) )
| ( ( ti @ SV73 @ SY281 )
= ( zero_zero @ SV73 ) ) )
| ~ ! [SY283: $i,SY284: $i] :
( ( ( plus_plus @ SV73 @ ( power_power @ SV73 @ SY283 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV73 @ SY284 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV73 ) )
| ( ( ti @ SV73 @ SY284 )
= ( zero_zero @ SV73 ) ) ) ) )
= $false )
| ( ( linordered_idom @ SV73 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[976]) ).
thf(1064,plain,
! [SV74: $i] :
( ( ( ~ ! [SY285: $i,SY286: $i] :
( ~ ( ord_less @ SV74 @ ( zero_zero @ SV74 ) @ ( plus_plus @ SV74 @ ( power_power @ SV74 @ SY285 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV74 @ SY286 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
| ( ( ti @ SV74 @ SY285 )
!= ( zero_zero @ SV74 ) )
| ( ( ti @ SV74 @ SY286 )
!= ( zero_zero @ SV74 ) ) ) )
= $false )
| ( ( linordered_idom @ SV74 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[977]) ).
thf(1065,plain,
! [SV74: $i] :
( ( ( ~ ~ ( ~ ! [SY287: $i] :
( ( ( ti @ SV74 @ SY287 )
= ( zero_zero @ SV74 ) )
| ! [SY288: $i] : ( ord_less @ SV74 @ ( zero_zero @ SV74 ) @ ( plus_plus @ SV74 @ ( power_power @ SV74 @ SY287 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV74 @ SY288 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
| ~ ! [SY289: $i,SY290: $i] :
( ( ( ti @ SV74 @ SY290 )
= ( zero_zero @ SV74 ) )
| ( ord_less @ SV74 @ ( zero_zero @ SV74 ) @ ( plus_plus @ SV74 @ ( power_power @ SV74 @ SY289 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV74 @ SY290 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) ) )
= $false )
| ( ( linordered_idom @ SV74 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[977]) ).
thf(1066,plain,
! [SV75: $i] :
( ( ( number_ring @ SV75 )
= $false )
| ( ( linordered_idom @ SV75 )
= $false )
| ( ( ~ ( ~ ! [SY291: $i] :
( ~ ( ord_less @ SV75 @ ( number_number_of @ SV75 @ SY291 ) @ ( one_one @ SV75 ) )
| ( ord_less @ int @ SY291 @ ( bit1 @ pls ) ) )
| ~ ! [SY292: $i] :
( ~ ( ord_less @ int @ SY292 @ ( bit1 @ pls ) )
| ( ord_less @ SV75 @ ( number_number_of @ SV75 @ SY292 ) @ ( one_one @ SV75 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[978]) ).
thf(1067,plain,
! [SV76: $i] :
( ( ( number_ring @ SV76 )
= $false )
| ( ( linordered_idom @ SV76 )
= $false )
| ( ( ~ ( ~ ! [SY293: $i] :
( ~ ( ord_less @ SV76 @ ( zero_zero @ SV76 ) @ ( number_number_of @ SV76 @ SY293 ) )
| ( ord_less @ int @ pls @ SY293 ) )
| ~ ! [SY294: $i] :
( ~ ( ord_less @ int @ pls @ SY294 )
| ( ord_less @ SV76 @ ( zero_zero @ SV76 ) @ ( number_number_of @ SV76 @ SY294 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[979]) ).
thf(1068,plain,
! [SV197: $i,SV154: $i] :
( ( ~ ( ord_less @ int @ ( bit0 @ SV154 ) @ ( bit0 @ SV197 ) )
| ( ord_less @ int @ SV154 @ SV197 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[980]) ).
thf(1069,plain,
! [SV198: $i,SV155: $i] :
( ( ~ ( ord_less @ int @ SV155 @ SV198 )
| ( ord_less @ int @ ( bit0 @ SV155 ) @ ( bit0 @ SV198 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[981]) ).
thf(1070,plain,
! [SV156: $i] :
( ( ( ~ ( ord_less @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ SV156 ) @ SV156 ) @ ( zero_zero @ int ) ) )
= $true )
| ( ( ord_less @ int @ SV156 @ ( zero_zero @ int ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[982]) ).
thf(1071,plain,
! [SV157: $i] :
( ( ( ~ ( ord_less @ int @ SV157 @ ( zero_zero @ int ) ) )
= $true )
| ( ( ord_less @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ SV157 ) @ SV157 ) @ ( zero_zero @ int ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[983]) ).
thf(1072,plain,
! [SV199: $i,SV158: $i] :
( ( ~ ( ord_less @ nat @ SV158 @ ( ti @ nat @ SV199 ) )
| ( ord_less @ nat @ SV158 @ SV199 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[984]) ).
thf(1073,plain,
! [SV200: $i,SV159: $i] :
( ( ~ ( ord_less @ nat @ SV159 @ SV200 )
| ( ord_less @ nat @ SV159 @ ( ti @ nat @ SV200 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[985]) ).
thf(1074,plain,
! [SV77: $i] :
( ( ( ~ ( mult_zero @ SV77 ) )
= $true )
| ( ( ~ ( power @ SV77 ) )
= $true )
| ( ( ~ ( no_zero_divisors @ SV77 ) )
= $true )
| ( ( ~ ( zero_neq_one @ SV77 ) )
= $true )
| ( ( ~ ( ~ ! [SY295: $i,SY296: $i] :
( ( ( number_number_of @ nat @ SY296 )
= ( zero_zero @ nat ) )
| ( ( ti @ SV77 @ SY295 )
!= ( zero_zero @ SV77 ) )
| ( ( power_power @ SV77 @ SY295 @ ( number_number_of @ nat @ SY296 ) )
= ( zero_zero @ SV77 ) ) )
| ~ ~ ( ~ ! [SY297: $i,SY298: $i] :
( ( ( power_power @ SV77 @ SY297 @ ( number_number_of @ nat @ SY298 ) )
!= ( zero_zero @ SV77 ) )
| ( ( number_number_of @ nat @ SY298 )
!= ( zero_zero @ nat ) ) )
| ~ ! [SY299: $i] :
( ! [SY300: $i] :
( ( power_power @ SV77 @ SY299 @ ( number_number_of @ nat @ SY300 ) )
!= ( zero_zero @ SV77 ) )
| ( ( ti @ SV77 @ SY299 )
= ( zero_zero @ SV77 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[986]) ).
thf(1075,plain,
! [SV201: $i,SV78: $i] :
( ( ! [SY376: $i] :
( ~ ( linordered_idom @ SY376 )
| ~ ( ord_less @ SY376 @ SV78 @ ( ti @ SY376 @ SV201 ) )
| ( ord_less @ SY376 @ SV78 @ SV201 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[987]) ).
thf(1076,plain,
! [SV202: $i,SV78: $i] :
( ( ! [SY377: $i] :
( ~ ( linordered_idom @ SY377 )
| ~ ( ord_less @ SY377 @ SV78 @ SV202 )
| ( ord_less @ SY377 @ SV78 @ ( ti @ SY377 @ SV202 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[988]) ).
thf(1077,plain,
! [SV160: $i] :
( ( ( ~ ( ord_less @ int @ ( bit1 @ SV160 ) @ pls ) )
= $true )
| ( ( ord_less @ int @ SV160 @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[989]) ).
thf(1078,plain,
! [SV161: $i] :
( ( ( ~ ( ord_less @ int @ SV161 @ pls ) )
= $true )
| ( ( ord_less @ int @ ( bit1 @ SV161 ) @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[990]) ).
thf(1079,plain,
! [SV203: $i,SV162: $i] :
( ( ( ( bit1 @ SV162 )
!= ( bit1 @ SV203 ) )
| ( SV162 = SV203 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[991]) ).
thf(1080,plain,
! [SV204: $i,SV163: $i] :
( ( ( SV163 != SV204 )
| ( ( bit1 @ SV163 )
= ( bit1 @ SV204 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[992]) ).
thf(1081,plain,
! [SV79: $i] :
( ( ( ~ ! [SY305: $i] :
( ( ( plus_plus @ SV79 @ SY305 @ SY305 )
!= ( zero_zero @ SV79 ) )
| ( ( ti @ SV79 @ SY305 )
= ( zero_zero @ SV79 ) ) ) )
= $false )
| ( ( linord219039673up_add @ SV79 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[993]) ).
thf(1082,plain,
! [SV79: $i] :
( ( ( ~ ! [SY306: $i] :
( ( ( ti @ SV79 @ SY306 )
!= ( zero_zero @ SV79 ) )
| ( ( plus_plus @ SV79 @ SY306 @ SY306 )
= ( zero_zero @ SV79 ) ) ) )
= $false )
| ( ( linord219039673up_add @ SV79 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[993]) ).
thf(1083,plain,
! [SV205: $i,SV164: $i] :
( ( ~ ( ord_less @ int @ ( bit1 @ SV164 ) @ ( bit1 @ SV205 ) )
| ( ord_less @ int @ SV164 @ SV205 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[994]) ).
thf(1084,plain,
! [SV206: $i,SV165: $i] :
( ( ~ ( ord_less @ int @ SV165 @ SV206 )
| ( ord_less @ int @ ( bit1 @ SV165 ) @ ( bit1 @ SV206 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[995]) ).
thf(1085,plain,
! [SV80: $i] :
( ( ( number_ring @ SV80 )
= $false )
| ( ( linordered_idom @ SV80 )
= $false )
| ( ( ~ ( ~ ! [SY307: $i] :
( ~ ( ord_less @ SV80 @ ( number_number_of @ SV80 @ SY307 ) @ ( zero_zero @ SV80 ) )
| ( ord_less @ int @ SY307 @ pls ) )
| ~ ! [SY308: $i] :
( ~ ( ord_less @ int @ SY308 @ pls )
| ( ord_less @ SV80 @ ( number_number_of @ SV80 @ SY308 ) @ ( zero_zero @ SV80 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[996]) ).
thf(1086,plain,
! [SV81: $i] :
( ( ( number_ring @ SV81 )
= $false )
| ( ( linordered_idom @ SV81 )
= $false )
| ( ( ~ ( ~ ! [SY309: $i,SY310: $i] :
( ~ ( ord_less @ SV81 @ ( number_number_of @ SV81 @ SY309 ) @ ( number_number_of @ SV81 @ SY310 ) )
| ( ord_less @ int @ SY309 @ SY310 ) )
| ~ ! [SY311: $i,SY312: $i] :
( ~ ( ord_less @ int @ SY311 @ SY312 )
| ( ord_less @ SV81 @ ( number_number_of @ SV81 @ SY311 ) @ ( number_number_of @ SV81 @ SY312 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[997]) ).
thf(1087,plain,
! [SV207: $i,SV166: $i] :
( ( ( ( bit0 @ SV166 )
!= ( bit0 @ SV207 ) )
| ( SV166 = SV207 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[998]) ).
thf(1088,plain,
! [SV208: $i,SV167: $i] :
( ( ( SV167 != SV208 )
| ( ( bit0 @ SV167 )
= ( bit0 @ SV208 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[999]) ).
thf(1089,plain,
! [SV209: $i,SV168: $i] :
( ( ~ ( ord_less @ int @ ( bit0 @ SV168 ) @ ( bit0 @ SV209 ) )
| ( ord_less @ int @ SV168 @ SV209 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1000]) ).
thf(1090,plain,
! [SV210: $i,SV169: $i] :
( ( ~ ( ord_less @ int @ SV169 @ SV210 )
| ( ord_less @ int @ ( bit0 @ SV169 ) @ ( bit0 @ SV210 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1001]) ).
thf(1091,plain,
! [SV82: $i] :
( ( ( ~ ! [SY313: $i] :
( ~ ( ord_less @ SV82 @ ( plus_plus @ SV82 @ SY313 @ SY313 ) @ ( zero_zero @ SV82 ) )
| ( ord_less @ SV82 @ SY313 @ ( zero_zero @ SV82 ) ) ) )
= $false )
| ( ( linordered_idom @ SV82 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1002]) ).
thf(1092,plain,
! [SV82: $i] :
( ( ( ~ ! [SY314: $i] :
( ~ ( ord_less @ SV82 @ SY314 @ ( zero_zero @ SV82 ) )
| ( ord_less @ SV82 @ ( plus_plus @ SV82 @ SY314 @ SY314 ) @ ( zero_zero @ SV82 ) ) ) )
= $false )
| ( ( linordered_idom @ SV82 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1002]) ).
thf(1093,plain,
! [SV83: $i] :
( ( ( semiring_0 @ SV83 )
= $false )
| ( ( power @ SV83 )
= $false )
| ( ( ~ ( ~ ! [SY315: $i] :
( ( ( number_number_of @ nat @ SY315 )
!= ( zero_zero @ nat ) )
| ( ( power_power @ SV83 @ ( zero_zero @ SV83 ) @ ( number_number_of @ nat @ SY315 ) )
= ( one_one @ SV83 ) ) )
| ~ ! [SY316: $i] :
( ( ( number_number_of @ nat @ SY316 )
= ( zero_zero @ nat ) )
| ( ( power_power @ SV83 @ ( zero_zero @ SV83 ) @ ( number_number_of @ nat @ SY316 ) )
= ( zero_zero @ SV83 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1003]) ).
thf(1094,plain,
! [SV170: $i,SV211: $i] :
( ( ~ ( ord_less @ int @ SV211 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV211 ) @ ( number_number_of @ nat @ SV170 ) )
= ( number_number_of @ nat @ SV170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1004]) ).
thf(1095,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ord_less @ int @ SX1 @ pls )
| ~ ( ord_less @ int @ SX0 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SX1 ) @ ( number_number_of @ nat @ SX0 ) )
= ( number_number_of @ nat @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1005]) ).
thf(1096,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ord_less @ int @ SX1 @ pls )
| ( ord_less @ int @ SX0 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SX1 ) @ ( number_number_of @ nat @ SX0 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1005]) ).
thf(1097,plain,
! [SV171: $i] :
( ( ( ( ( semiring_1_of_nat @ int @ SV171 )
!= ( zero_zero @ int ) ) )
= $true )
| ( ( SV171
= ( zero_zero @ nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1006]) ).
thf(1098,plain,
! [SV172: $i] :
( ( ( ( SV172
!= ( zero_zero @ nat ) ) )
= $true )
| ( ( ( semiring_1_of_nat @ int @ SV172 )
= ( zero_zero @ int ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1007]) ).
thf(1099,plain,
! [SV173: $i] :
( ( ( ~ ( ord_less @ int @ pls @ ( bit0 @ SV173 ) ) )
= $true )
| ( ( ord_less @ int @ pls @ SV173 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1008]) ).
thf(1100,plain,
! [SV174: $i] :
( ( ( ~ ( ord_less @ int @ pls @ SV174 ) )
= $true )
| ( ( ord_less @ int @ pls @ ( bit0 @ SV174 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1009]) ).
thf(1101,plain,
! [SV212: $i,SV175: $i] :
( ( ~ ( ord_less @ int @ ( bit1 @ SV175 ) @ ( bit0 @ SV212 ) )
| ( ord_less @ int @ SV175 @ SV212 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1010]) ).
thf(1102,plain,
! [SV213: $i,SV176: $i] :
( ( ~ ( ord_less @ int @ SV176 @ SV213 )
| ( ord_less @ int @ ( bit1 @ SV176 ) @ ( bit0 @ SV213 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1011]) ).
thf(1103,plain,
! [SV214: $i,SV177: $i] :
( ( ~ ( ord_less @ int @ ( bit1 @ SV177 ) @ ( bit1 @ SV214 ) )
| ( ord_less @ int @ SV177 @ SV214 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1012]) ).
thf(1104,plain,
! [SV215: $i,SV178: $i] :
( ( ~ ( ord_less @ int @ SV178 @ SV215 )
| ( ord_less @ int @ ( bit1 @ SV178 ) @ ( bit1 @ SV215 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1013]) ).
thf(1105,plain,
! [SV84: $i] :
( ( ( ~ ! [SY317: $i,SY318: $i] :
( ( ( number_number_of @ SV84 @ SY317 )
!= ( ti @ SV84 @ SY318 ) )
| ( ( ti @ SV84 @ SY318 )
= ( number_number_of @ SV84 @ SY317 ) ) ) )
= $false )
| ( ( number @ SV84 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1014]) ).
thf(1106,plain,
! [SV84: $i] :
( ( ( ~ ! [SY319: $i,SY320: $i] :
( ( ( ti @ SV84 @ SY320 )
!= ( number_number_of @ SV84 @ SY319 ) )
| ( ( number_number_of @ SV84 @ SY319 )
= ( ti @ SV84 @ SY320 ) ) ) )
= $false )
| ( ( number @ SV84 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1014]) ).
thf(1107,plain,
! [SV85: $i] :
( ( ( ~ ! [SY321: $i] :
( ( ( ti @ SV85 @ SY321 )
= ( zero_zero @ SV85 ) )
| ( ord_less @ SV85 @ ( zero_zero @ SV85 ) @ ( power_power @ SV85 @ SY321 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $false )
| ( ( linordered_idom @ SV85 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1015]) ).
thf(1108,plain,
! [SV85: $i] :
( ( ( ~ ! [SY322: $i] :
( ~ ( ord_less @ SV85 @ ( zero_zero @ SV85 ) @ ( power_power @ SV85 @ SY322 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ( ( ti @ SV85 @ SY322 )
!= ( zero_zero @ SV85 ) ) ) )
= $false )
| ( ( linordered_idom @ SV85 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1015]) ).
thf(1109,plain,
! [SV216: $i,SV179: $i] :
( ( ( ( semiring_1_of_nat @ int @ SV179 )
!= ( semiring_1_of_nat @ int @ SV216 ) )
| ( SV179 = SV216 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1016]) ).
thf(1110,plain,
! [SV217: $i,SV180: $i] :
( ( ( SV180 != SV217 )
| ( ( semiring_1_of_nat @ int @ SV180 )
= ( semiring_1_of_nat @ int @ SV217 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1017]) ).
thf(1111,plain,
! [SV181: $i] :
( ( ( ( ( bit0 @ SV181 )
!= pls ) )
= $true )
| ( ( SV181 = pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1018]) ).
thf(1112,plain,
! [SV182: $i] :
( ( ( ( SV182 != pls ) )
= $true )
| ( ( ( bit0 @ SV182 )
= pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1019]) ).
thf(1113,plain,
! [SV86: $i] :
( ( ( ~ ! [SY323: $i] :
( ( ( power_power @ SV86 @ SY323 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= ( zero_zero @ SV86 ) )
| ( ( ti @ SV86 @ SY323 )
= ( zero_zero @ SV86 ) ) ) )
= $false )
| ( ( ring_11004092258visors @ SV86 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1020]) ).
thf(1114,plain,
! [SV86: $i] :
( ( ( ~ ! [SY324: $i] :
( ( ( ti @ SV86 @ SY324 )
!= ( zero_zero @ SV86 ) )
| ( ( power_power @ SV86 @ SY324 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SV86 ) ) ) )
= $false )
| ( ( ring_11004092258visors @ SV86 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1020]) ).
thf(1115,plain,
! [SV87: $i] :
( ( ( number_ring @ SV87 )
= $false )
| ( ( linordered_idom @ SV87 )
= $false )
| ( ( ~ ( ~ ! [SY325: $i] :
( ~ ( ord_less @ SV87 @ ( one_one @ SV87 ) @ ( number_number_of @ SV87 @ SY325 ) )
| ( ord_less @ int @ ( bit1 @ pls ) @ SY325 ) )
| ~ ! [SY326: $i] :
( ~ ( ord_less @ int @ ( bit1 @ pls ) @ SY326 )
| ( ord_less @ SV87 @ ( one_one @ SV87 ) @ ( number_number_of @ SV87 @ SY326 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1021]) ).
thf(1116,plain,
! [SV183: $i] :
( ( ( ( pls
!= ( bit0 @ SV183 ) ) )
= $true )
| ( ( pls = SV183 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1022]) ).
thf(1117,plain,
! [SV184: $i] :
( ( ( ( pls != SV184 ) )
= $true )
| ( ( pls
= ( bit0 @ SV184 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1023]) ).
thf(1118,plain,
! [SV218: $i,SV185: $i] :
( ( ~ ( ord_less @ int @ ( number_number_of @ int @ SV185 ) @ ( number_number_of @ int @ SV218 ) )
| ( ord_less @ int @ SV185 @ SV218 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1024]) ).
thf(1119,plain,
! [SV219: $i,SV186: $i] :
( ( ~ ( ord_less @ int @ SV186 @ SV219 )
| ( ord_less @ int @ ( number_number_of @ int @ SV186 ) @ ( number_number_of @ int @ SV219 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1025]) ).
thf(1120,plain,
! [SV220: $i,SV187: $i] :
( ( ~ ( ord_less @ int @ ( bit1 @ SV187 ) @ ( bit0 @ SV220 ) )
| ( ord_less @ int @ SV187 @ SV220 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1026]) ).
thf(1121,plain,
! [SV221: $i,SV188: $i] :
( ( ~ ( ord_less @ int @ SV188 @ SV221 )
| ( ord_less @ int @ ( bit1 @ SV188 ) @ ( bit0 @ SV221 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1027]) ).
thf(1122,plain,
! [SV222: $i,SV189: $i,SV140: $i,SV51: $i] :
( ( ( ( plus_plus @ SV51 @ ( number_number_of @ SV51 @ SV140 ) @ ( plus_plus @ SV51 @ ( number_number_of @ SV51 @ SV189 ) @ SV222 ) )
= ( plus_plus @ SV51 @ ( number_number_of @ SV51 @ ( plus_plus @ int @ SV140 @ SV189 ) ) @ SV222 ) )
= $true )
| ( ( number_ring @ SV51 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1035]) ).
thf(1123,plain,
! [SV61: $i] :
( ( ( mult_zero @ SV61 )
= $false )
| ( ( ~ ( power @ SV61 ) )
= $true )
| ( ( ~ ( no_zero_divisors @ SV61 ) )
= $true )
| ( ( ~ ( zero_neq_one @ SV61 ) )
= $true )
| ( ( ( ti @ SV61 @ ( zero_zero @ SV61 ) )
= ( zero_zero @ SV61 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1040]) ).
thf(1124,plain,
! [SV113: $i,SV64: $i,SV130: $i] :
( ( ( ~ ( mult_zero @ SV130 )
| ~ ( power @ SV130 ) )
= $true )
| ( ( ~ ( no_zero_divisors @ SV130 ) )
= $true )
| ( ( ~ ( zero_neq_one @ SV130 ) )
= $true )
| ( ( ( power_power @ SV130 @ ( ti @ SV130 @ SV64 ) @ SV113 )
= ( power_power @ SV130 @ SV64 @ SV113 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1042]) ).
thf(1125,plain,
! [SV114: $i,SV65: $i,SV131: $i] :
( ( ( ~ ( mult_zero @ SV131 )
| ~ ( power @ SV131 ) )
= $true )
| ( ( ~ ( no_zero_divisors @ SV131 ) )
= $true )
| ( ( ~ ( zero_neq_one @ SV131 ) )
= $true )
| ( ( ( power_power @ SV131 @ SV65 @ ( ti @ nat @ SV114 ) )
= ( power_power @ SV131 @ SV65 @ SV114 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1043]) ).
thf(1126,plain,
! [SV115: $i,SV66: $i,SV132: $i] :
( ( ( ~ ( mult_zero @ SV132 )
| ~ ( power @ SV132 ) )
= $true )
| ( ( ~ ( no_zero_divisors @ SV132 ) )
= $true )
| ( ( ~ ( zero_neq_one @ SV132 ) )
= $true )
| ( ( ( ti @ SV132 @ ( power_power @ SV132 @ SV66 @ SV115 ) )
= ( power_power @ SV132 @ SV66 @ SV115 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1044]) ).
thf(1127,plain,
! [SV116: $i,SV67: $i,SV133: $i] :
( ( ( power @ SV133 )
= $false )
| ( ( ~ ( semiring_0 @ SV133 ) )
= $true )
| ( ( ( power_power @ SV133 @ ( ti @ SV133 @ SV67 ) @ SV116 )
= ( power_power @ SV133 @ SV67 @ SV116 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1045]) ).
thf(1128,plain,
! [SV117: $i,SV68: $i,SV134: $i] :
( ( ( power @ SV134 )
= $false )
| ( ( ~ ( semiring_0 @ SV134 ) )
= $true )
| ( ( ( power_power @ SV134 @ SV68 @ ( ti @ nat @ SV117 ) )
= ( power_power @ SV134 @ SV68 @ SV117 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1046]) ).
thf(1129,plain,
! [SV118: $i,SV69: $i,SV135: $i] :
( ( ( power @ SV135 )
= $false )
| ( ( ~ ( semiring_0 @ SV135 ) )
= $true )
| ( ( ( ti @ SV135 @ ( power_power @ SV135 @ SV69 @ SV118 ) )
= ( power_power @ SV135 @ SV69 @ SV118 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1047]) ).
thf(1130,plain,
! [SV145: $i] :
( ( ( ord_less @ int @ ( bit1 @ SV145 ) @ ( zero_zero @ int ) )
= $false )
| ( ( ord_less @ int @ SV145 @ ( zero_zero @ int ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1048]) ).
thf(1131,plain,
! [SV146: $i] :
( ( ( ord_less @ int @ SV146 @ ( zero_zero @ int ) )
= $false )
| ( ( ord_less @ int @ ( bit1 @ SV146 ) @ ( zero_zero @ int ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1049]) ).
thf(1132,plain,
! [SV71: $i] :
( ( ( ~ ! [SY271: $i,SY272: $i] :
( ( ( number_number_of @ SV71 @ SY271 )
!= ( number_number_of @ SV71 @ SY272 ) )
| ( SY271 = SY272 ) )
| ~ ! [SY273: $i,SY274: $i] :
( ( SY273 != SY274 )
| ( ( number_number_of @ SV71 @ SY273 )
= ( number_number_of @ SV71 @ SY274 ) ) ) )
= $false )
| ( ( number_ring @ SV71 )
= $false )
| ( ( ring_char_0 @ SV71 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1050]) ).
thf(1133,plain,
! [SV192: $i,SV72: $i,SV223: $i] :
( ( ~ ( linordered_idom @ SV223 )
| ~ ( ord_less @ SV223 @ ( ti @ SV223 @ SV72 ) @ SV192 )
| ( ord_less @ SV223 @ SV72 @ SV192 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1051]) ).
thf(1134,plain,
! [SV193: $i,SV72: $i,SV224: $i] :
( ( ~ ( linordered_idom @ SV224 )
| ~ ( ord_less @ SV224 @ SV72 @ SV193 )
| ( ord_less @ SV224 @ ( ti @ SV224 @ SV72 ) @ SV193 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1052]) ).
thf(1135,plain,
! [SV147: $i] :
( ( ( ord_less @ int @ ( bit0 @ SV147 ) @ ( zero_zero @ int ) )
= $false )
| ( ( ord_less @ int @ SV147 @ ( zero_zero @ int ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1053]) ).
thf(1136,plain,
! [SV148: $i] :
( ( ( ord_less @ int @ SV148 @ ( zero_zero @ int ) )
= $false )
| ( ( ord_less @ int @ ( bit0 @ SV148 ) @ ( zero_zero @ int ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1054]) ).
thf(1137,plain,
! [SV149: $i] :
( ( ( ord_less @ int @ ( bit0 @ SV149 ) @ pls )
= $false )
| ( ( ord_less @ int @ SV149 @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1055]) ).
thf(1138,plain,
! [SV150: $i] :
( ( ( ord_less @ int @ SV150 @ pls )
= $false )
| ( ( ord_less @ int @ ( bit0 @ SV150 ) @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1056]) ).
thf(1139,plain,
! [SV194: $i,SV151: $i] :
( ( ( ~ ( ord_less @ int @ SV151 @ ( plus_plus @ int @ SV194 @ ( one_one @ int ) ) ) )
= $true )
| ( ( ( SV151 = SV194 )
| ( ord_less @ int @ SV151 @ SV194 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1057]) ).
thf(1140,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ord_less @ int @ SX0 @ ( plus_plus @ int @ SX1 @ ( one_one @ int ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1058]) ).
thf(1141,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ int @ SX0 @ ( plus_plus @ int @ SX1 @ ( one_one @ int ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1059]) ).
thf(1142,plain,
! [SV195: $i,SV152: $i] :
( ( ( ~ ( ord_less @ nat @ ( ti @ nat @ SV152 ) @ SV195 ) )
= $true )
| ( ( ord_less @ nat @ SV152 @ SV195 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1060]) ).
thf(1143,plain,
! [SV196: $i,SV153: $i] :
( ( ( ~ ( ord_less @ nat @ SV153 @ SV196 ) )
= $true )
| ( ( ord_less @ nat @ ( ti @ nat @ SV153 ) @ SV196 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1061]) ).
thf(1144,plain,
! [SV73: $i] :
( ( ( ! [SY279: $i,SY280: $i] :
( ( ( ti @ SV73 @ SY279 )
!= ( zero_zero @ SV73 ) )
| ( ( ti @ SV73 @ SY280 )
!= ( zero_zero @ SV73 ) )
| ( ( plus_plus @ SV73 @ ( power_power @ SV73 @ SY279 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV73 @ SY280 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV73 ) ) ) )
= $true )
| ( ( linordered_idom @ SV73 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1062]) ).
thf(1145,plain,
! [SV73: $i] :
( ( ( ~ ( ~ ! [SY281: $i] :
( ! [SY282: $i] :
( ( plus_plus @ SV73 @ ( power_power @ SV73 @ SY281 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV73 @ SY282 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV73 ) )
| ( ( ti @ SV73 @ SY281 )
= ( zero_zero @ SV73 ) ) )
| ~ ! [SY283: $i,SY284: $i] :
( ( ( plus_plus @ SV73 @ ( power_power @ SV73 @ SY283 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV73 @ SY284 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV73 ) )
| ( ( ti @ SV73 @ SY284 )
= ( zero_zero @ SV73 ) ) ) ) )
= $true )
| ( ( linordered_idom @ SV73 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1063]) ).
thf(1146,plain,
! [SV74: $i] :
( ( ( ! [SY285: $i,SY286: $i] :
( ~ ( ord_less @ SV74 @ ( zero_zero @ SV74 ) @ ( plus_plus @ SV74 @ ( power_power @ SV74 @ SY285 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV74 @ SY286 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
| ( ( ti @ SV74 @ SY285 )
!= ( zero_zero @ SV74 ) )
| ( ( ti @ SV74 @ SY286 )
!= ( zero_zero @ SV74 ) ) ) )
= $true )
| ( ( linordered_idom @ SV74 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1064]) ).
thf(1147,plain,
! [SV74: $i] :
( ( ( ~ ( ~ ! [SY287: $i] :
( ( ( ti @ SV74 @ SY287 )
= ( zero_zero @ SV74 ) )
| ! [SY288: $i] : ( ord_less @ SV74 @ ( zero_zero @ SV74 ) @ ( plus_plus @ SV74 @ ( power_power @ SV74 @ SY287 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV74 @ SY288 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
| ~ ! [SY289: $i,SY290: $i] :
( ( ( ti @ SV74 @ SY290 )
= ( zero_zero @ SV74 ) )
| ( ord_less @ SV74 @ ( zero_zero @ SV74 ) @ ( plus_plus @ SV74 @ ( power_power @ SV74 @ SY289 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV74 @ SY290 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) ) )
= $true )
| ( ( linordered_idom @ SV74 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1065]) ).
thf(1148,plain,
! [SV75: $i] :
( ( ( ~ ! [SY291: $i] :
( ~ ( ord_less @ SV75 @ ( number_number_of @ SV75 @ SY291 ) @ ( one_one @ SV75 ) )
| ( ord_less @ int @ SY291 @ ( bit1 @ pls ) ) )
| ~ ! [SY292: $i] :
( ~ ( ord_less @ int @ SY292 @ ( bit1 @ pls ) )
| ( ord_less @ SV75 @ ( number_number_of @ SV75 @ SY292 ) @ ( one_one @ SV75 ) ) ) )
= $false )
| ( ( linordered_idom @ SV75 )
= $false )
| ( ( number_ring @ SV75 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1066]) ).
thf(1149,plain,
! [SV76: $i] :
( ( ( ~ ! [SY293: $i] :
( ~ ( ord_less @ SV76 @ ( zero_zero @ SV76 ) @ ( number_number_of @ SV76 @ SY293 ) )
| ( ord_less @ int @ pls @ SY293 ) )
| ~ ! [SY294: $i] :
( ~ ( ord_less @ int @ pls @ SY294 )
| ( ord_less @ SV76 @ ( zero_zero @ SV76 ) @ ( number_number_of @ SV76 @ SY294 ) ) ) )
= $false )
| ( ( linordered_idom @ SV76 )
= $false )
| ( ( number_ring @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1067]) ).
thf(1150,plain,
! [SV197: $i,SV154: $i] :
( ( ( ~ ( ord_less @ int @ ( bit0 @ SV154 ) @ ( bit0 @ SV197 ) ) )
= $true )
| ( ( ord_less @ int @ SV154 @ SV197 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1068]) ).
thf(1151,plain,
! [SV198: $i,SV155: $i] :
( ( ( ~ ( ord_less @ int @ SV155 @ SV198 ) )
= $true )
| ( ( ord_less @ int @ ( bit0 @ SV155 ) @ ( bit0 @ SV198 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1069]) ).
thf(1152,plain,
! [SV156: $i] :
( ( ( ord_less @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ SV156 ) @ SV156 ) @ ( zero_zero @ int ) )
= $false )
| ( ( ord_less @ int @ SV156 @ ( zero_zero @ int ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1070]) ).
thf(1153,plain,
! [SV157: $i] :
( ( ( ord_less @ int @ SV157 @ ( zero_zero @ int ) )
= $false )
| ( ( ord_less @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ SV157 ) @ SV157 ) @ ( zero_zero @ int ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1071]) ).
thf(1154,plain,
! [SV199: $i,SV158: $i] :
( ( ( ~ ( ord_less @ nat @ SV158 @ ( ti @ nat @ SV199 ) ) )
= $true )
| ( ( ord_less @ nat @ SV158 @ SV199 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1072]) ).
thf(1155,plain,
! [SV200: $i,SV159: $i] :
( ( ( ~ ( ord_less @ nat @ SV159 @ SV200 ) )
= $true )
| ( ( ord_less @ nat @ SV159 @ ( ti @ nat @ SV200 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1073]) ).
thf(1156,plain,
! [SV77: $i] :
( ( ( mult_zero @ SV77 )
= $false )
| ( ( ~ ( power @ SV77 ) )
= $true )
| ( ( ~ ( no_zero_divisors @ SV77 ) )
= $true )
| ( ( ~ ( zero_neq_one @ SV77 ) )
= $true )
| ( ( ~ ( ~ ! [SY295: $i,SY296: $i] :
( ( ( number_number_of @ nat @ SY296 )
= ( zero_zero @ nat ) )
| ( ( ti @ SV77 @ SY295 )
!= ( zero_zero @ SV77 ) )
| ( ( power_power @ SV77 @ SY295 @ ( number_number_of @ nat @ SY296 ) )
= ( zero_zero @ SV77 ) ) )
| ~ ~ ( ~ ! [SY297: $i,SY298: $i] :
( ( ( power_power @ SV77 @ SY297 @ ( number_number_of @ nat @ SY298 ) )
!= ( zero_zero @ SV77 ) )
| ( ( number_number_of @ nat @ SY298 )
!= ( zero_zero @ nat ) ) )
| ~ ! [SY299: $i] :
( ! [SY300: $i] :
( ( power_power @ SV77 @ SY299 @ ( number_number_of @ nat @ SY300 ) )
!= ( zero_zero @ SV77 ) )
| ( ( ti @ SV77 @ SY299 )
= ( zero_zero @ SV77 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1074]) ).
thf(1157,plain,
! [SV201: $i,SV78: $i,SV225: $i] :
( ( ~ ( linordered_idom @ SV225 )
| ~ ( ord_less @ SV225 @ SV78 @ ( ti @ SV225 @ SV201 ) )
| ( ord_less @ SV225 @ SV78 @ SV201 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1075]) ).
thf(1158,plain,
! [SV202: $i,SV78: $i,SV226: $i] :
( ( ~ ( linordered_idom @ SV226 )
| ~ ( ord_less @ SV226 @ SV78 @ SV202 )
| ( ord_less @ SV226 @ SV78 @ ( ti @ SV226 @ SV202 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1076]) ).
thf(1159,plain,
! [SV160: $i] :
( ( ( ord_less @ int @ ( bit1 @ SV160 ) @ pls )
= $false )
| ( ( ord_less @ int @ SV160 @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1077]) ).
thf(1160,plain,
! [SV161: $i] :
( ( ( ord_less @ int @ SV161 @ pls )
= $false )
| ( ( ord_less @ int @ ( bit1 @ SV161 ) @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1078]) ).
thf(1161,plain,
! [SV203: $i,SV162: $i] :
( ( ( ( ( bit1 @ SV162 )
!= ( bit1 @ SV203 ) ) )
= $true )
| ( ( SV162 = SV203 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1079]) ).
thf(1162,plain,
! [SV204: $i,SV163: $i] :
( ( ( ( SV163 != SV204 ) )
= $true )
| ( ( ( bit1 @ SV163 )
= ( bit1 @ SV204 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1080]) ).
thf(1163,plain,
! [SV79: $i] :
( ( ( ! [SY305: $i] :
( ( ( plus_plus @ SV79 @ SY305 @ SY305 )
!= ( zero_zero @ SV79 ) )
| ( ( ti @ SV79 @ SY305 )
= ( zero_zero @ SV79 ) ) ) )
= $true )
| ( ( linord219039673up_add @ SV79 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1081]) ).
thf(1164,plain,
! [SV79: $i] :
( ( ( ! [SY306: $i] :
( ( ( ti @ SV79 @ SY306 )
!= ( zero_zero @ SV79 ) )
| ( ( plus_plus @ SV79 @ SY306 @ SY306 )
= ( zero_zero @ SV79 ) ) ) )
= $true )
| ( ( linord219039673up_add @ SV79 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1082]) ).
thf(1165,plain,
! [SV205: $i,SV164: $i] :
( ( ( ~ ( ord_less @ int @ ( bit1 @ SV164 ) @ ( bit1 @ SV205 ) ) )
= $true )
| ( ( ord_less @ int @ SV164 @ SV205 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1083]) ).
thf(1166,plain,
! [SV206: $i,SV165: $i] :
( ( ( ~ ( ord_less @ int @ SV165 @ SV206 ) )
= $true )
| ( ( ord_less @ int @ ( bit1 @ SV165 ) @ ( bit1 @ SV206 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1084]) ).
thf(1167,plain,
! [SV80: $i] :
( ( ( ~ ! [SY307: $i] :
( ~ ( ord_less @ SV80 @ ( number_number_of @ SV80 @ SY307 ) @ ( zero_zero @ SV80 ) )
| ( ord_less @ int @ SY307 @ pls ) )
| ~ ! [SY308: $i] :
( ~ ( ord_less @ int @ SY308 @ pls )
| ( ord_less @ SV80 @ ( number_number_of @ SV80 @ SY308 ) @ ( zero_zero @ SV80 ) ) ) )
= $false )
| ( ( linordered_idom @ SV80 )
= $false )
| ( ( number_ring @ SV80 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1085]) ).
thf(1168,plain,
! [SV81: $i] :
( ( ( ~ ! [SY309: $i,SY310: $i] :
( ~ ( ord_less @ SV81 @ ( number_number_of @ SV81 @ SY309 ) @ ( number_number_of @ SV81 @ SY310 ) )
| ( ord_less @ int @ SY309 @ SY310 ) )
| ~ ! [SY311: $i,SY312: $i] :
( ~ ( ord_less @ int @ SY311 @ SY312 )
| ( ord_less @ SV81 @ ( number_number_of @ SV81 @ SY311 ) @ ( number_number_of @ SV81 @ SY312 ) ) ) )
= $false )
| ( ( linordered_idom @ SV81 )
= $false )
| ( ( number_ring @ SV81 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1086]) ).
thf(1169,plain,
! [SV207: $i,SV166: $i] :
( ( ( ( ( bit0 @ SV166 )
!= ( bit0 @ SV207 ) ) )
= $true )
| ( ( SV166 = SV207 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1087]) ).
thf(1170,plain,
! [SV208: $i,SV167: $i] :
( ( ( ( SV167 != SV208 ) )
= $true )
| ( ( ( bit0 @ SV167 )
= ( bit0 @ SV208 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1088]) ).
thf(1171,plain,
! [SV209: $i,SV168: $i] :
( ( ( ~ ( ord_less @ int @ ( bit0 @ SV168 ) @ ( bit0 @ SV209 ) ) )
= $true )
| ( ( ord_less @ int @ SV168 @ SV209 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1089]) ).
thf(1172,plain,
! [SV210: $i,SV169: $i] :
( ( ( ~ ( ord_less @ int @ SV169 @ SV210 ) )
= $true )
| ( ( ord_less @ int @ ( bit0 @ SV169 ) @ ( bit0 @ SV210 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1090]) ).
thf(1173,plain,
! [SV82: $i] :
( ( ( ! [SY313: $i] :
( ~ ( ord_less @ SV82 @ ( plus_plus @ SV82 @ SY313 @ SY313 ) @ ( zero_zero @ SV82 ) )
| ( ord_less @ SV82 @ SY313 @ ( zero_zero @ SV82 ) ) ) )
= $true )
| ( ( linordered_idom @ SV82 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1091]) ).
thf(1174,plain,
! [SV82: $i] :
( ( ( ! [SY314: $i] :
( ~ ( ord_less @ SV82 @ SY314 @ ( zero_zero @ SV82 ) )
| ( ord_less @ SV82 @ ( plus_plus @ SV82 @ SY314 @ SY314 ) @ ( zero_zero @ SV82 ) ) ) )
= $true )
| ( ( linordered_idom @ SV82 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1092]) ).
thf(1175,plain,
! [SV83: $i] :
( ( ( ~ ! [SY315: $i] :
( ( ( number_number_of @ nat @ SY315 )
!= ( zero_zero @ nat ) )
| ( ( power_power @ SV83 @ ( zero_zero @ SV83 ) @ ( number_number_of @ nat @ SY315 ) )
= ( one_one @ SV83 ) ) )
| ~ ! [SY316: $i] :
( ( ( number_number_of @ nat @ SY316 )
= ( zero_zero @ nat ) )
| ( ( power_power @ SV83 @ ( zero_zero @ SV83 ) @ ( number_number_of @ nat @ SY316 ) )
= ( zero_zero @ SV83 ) ) ) )
= $false )
| ( ( power @ SV83 )
= $false )
| ( ( semiring_0 @ SV83 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1093]) ).
thf(1176,plain,
! [SV170: $i,SV211: $i] :
( ( ( ~ ( ord_less @ int @ SV211 @ pls ) )
= $true )
| ( ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV211 ) @ ( number_number_of @ nat @ SV170 ) )
= ( number_number_of @ nat @ SV170 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1094]) ).
thf(1177,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ord_less @ int @ SX1 @ pls )
| ~ ( ord_less @ int @ SX0 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SX1 ) @ ( number_number_of @ nat @ SX0 ) )
= ( number_number_of @ nat @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1095]) ).
thf(1178,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ord_less @ int @ SX1 @ pls )
| ( ord_less @ int @ SX0 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SX1 ) @ ( number_number_of @ nat @ SX0 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1096]) ).
thf(1179,plain,
! [SV171: $i] :
( ( ( ( semiring_1_of_nat @ int @ SV171 )
= ( zero_zero @ int ) )
= $false )
| ( ( SV171
= ( zero_zero @ nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1097]) ).
thf(1180,plain,
! [SV172: $i] :
( ( ( SV172
= ( zero_zero @ nat ) )
= $false )
| ( ( ( semiring_1_of_nat @ int @ SV172 )
= ( zero_zero @ int ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1098]) ).
thf(1181,plain,
! [SV173: $i] :
( ( ( ord_less @ int @ pls @ ( bit0 @ SV173 ) )
= $false )
| ( ( ord_less @ int @ pls @ SV173 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1099]) ).
thf(1182,plain,
! [SV174: $i] :
( ( ( ord_less @ int @ pls @ SV174 )
= $false )
| ( ( ord_less @ int @ pls @ ( bit0 @ SV174 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1100]) ).
thf(1183,plain,
! [SV212: $i,SV175: $i] :
( ( ( ~ ( ord_less @ int @ ( bit1 @ SV175 ) @ ( bit0 @ SV212 ) ) )
= $true )
| ( ( ord_less @ int @ SV175 @ SV212 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1101]) ).
thf(1184,plain,
! [SV213: $i,SV176: $i] :
( ( ( ~ ( ord_less @ int @ SV176 @ SV213 ) )
= $true )
| ( ( ord_less @ int @ ( bit1 @ SV176 ) @ ( bit0 @ SV213 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1102]) ).
thf(1185,plain,
! [SV214: $i,SV177: $i] :
( ( ( ~ ( ord_less @ int @ ( bit1 @ SV177 ) @ ( bit1 @ SV214 ) ) )
= $true )
| ( ( ord_less @ int @ SV177 @ SV214 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1103]) ).
thf(1186,plain,
! [SV215: $i,SV178: $i] :
( ( ( ~ ( ord_less @ int @ SV178 @ SV215 ) )
= $true )
| ( ( ord_less @ int @ ( bit1 @ SV178 ) @ ( bit1 @ SV215 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1104]) ).
thf(1187,plain,
! [SV84: $i] :
( ( ( ! [SY317: $i,SY318: $i] :
( ( ( number_number_of @ SV84 @ SY317 )
!= ( ti @ SV84 @ SY318 ) )
| ( ( ti @ SV84 @ SY318 )
= ( number_number_of @ SV84 @ SY317 ) ) ) )
= $true )
| ( ( number @ SV84 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1105]) ).
thf(1188,plain,
! [SV84: $i] :
( ( ( ! [SY319: $i,SY320: $i] :
( ( ( ti @ SV84 @ SY320 )
!= ( number_number_of @ SV84 @ SY319 ) )
| ( ( number_number_of @ SV84 @ SY319 )
= ( ti @ SV84 @ SY320 ) ) ) )
= $true )
| ( ( number @ SV84 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1106]) ).
thf(1189,plain,
! [SV85: $i] :
( ( ( ! [SY321: $i] :
( ( ( ti @ SV85 @ SY321 )
= ( zero_zero @ SV85 ) )
| ( ord_less @ SV85 @ ( zero_zero @ SV85 ) @ ( power_power @ SV85 @ SY321 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true )
| ( ( linordered_idom @ SV85 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1107]) ).
thf(1190,plain,
! [SV85: $i] :
( ( ( ! [SY322: $i] :
( ~ ( ord_less @ SV85 @ ( zero_zero @ SV85 ) @ ( power_power @ SV85 @ SY322 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ( ( ti @ SV85 @ SY322 )
!= ( zero_zero @ SV85 ) ) ) )
= $true )
| ( ( linordered_idom @ SV85 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1108]) ).
thf(1191,plain,
! [SV216: $i,SV179: $i] :
( ( ( ( ( semiring_1_of_nat @ int @ SV179 )
!= ( semiring_1_of_nat @ int @ SV216 ) ) )
= $true )
| ( ( SV179 = SV216 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1109]) ).
thf(1192,plain,
! [SV217: $i,SV180: $i] :
( ( ( ( SV180 != SV217 ) )
= $true )
| ( ( ( semiring_1_of_nat @ int @ SV180 )
= ( semiring_1_of_nat @ int @ SV217 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1110]) ).
thf(1193,plain,
! [SV181: $i] :
( ( ( ( bit0 @ SV181 )
= pls )
= $false )
| ( ( SV181 = pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1111]) ).
thf(1194,plain,
! [SV182: $i] :
( ( ( SV182 = pls )
= $false )
| ( ( ( bit0 @ SV182 )
= pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1112]) ).
thf(1195,plain,
! [SV86: $i] :
( ( ( ! [SY323: $i] :
( ( ( power_power @ SV86 @ SY323 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= ( zero_zero @ SV86 ) )
| ( ( ti @ SV86 @ SY323 )
= ( zero_zero @ SV86 ) ) ) )
= $true )
| ( ( ring_11004092258visors @ SV86 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1113]) ).
thf(1196,plain,
! [SV86: $i] :
( ( ( ! [SY324: $i] :
( ( ( ti @ SV86 @ SY324 )
!= ( zero_zero @ SV86 ) )
| ( ( power_power @ SV86 @ SY324 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SV86 ) ) ) )
= $true )
| ( ( ring_11004092258visors @ SV86 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1114]) ).
thf(1197,plain,
! [SV87: $i] :
( ( ( ~ ! [SY325: $i] :
( ~ ( ord_less @ SV87 @ ( one_one @ SV87 ) @ ( number_number_of @ SV87 @ SY325 ) )
| ( ord_less @ int @ ( bit1 @ pls ) @ SY325 ) )
| ~ ! [SY326: $i] :
( ~ ( ord_less @ int @ ( bit1 @ pls ) @ SY326 )
| ( ord_less @ SV87 @ ( one_one @ SV87 ) @ ( number_number_of @ SV87 @ SY326 ) ) ) )
= $false )
| ( ( linordered_idom @ SV87 )
= $false )
| ( ( number_ring @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1115]) ).
thf(1198,plain,
! [SV183: $i] :
( ( ( pls
= ( bit0 @ SV183 ) )
= $false )
| ( ( pls = SV183 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1116]) ).
thf(1199,plain,
! [SV184: $i] :
( ( ( pls = SV184 )
= $false )
| ( ( pls
= ( bit0 @ SV184 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1117]) ).
thf(1200,plain,
! [SV218: $i,SV185: $i] :
( ( ( ~ ( ord_less @ int @ ( number_number_of @ int @ SV185 ) @ ( number_number_of @ int @ SV218 ) ) )
= $true )
| ( ( ord_less @ int @ SV185 @ SV218 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1118]) ).
thf(1201,plain,
! [SV219: $i,SV186: $i] :
( ( ( ~ ( ord_less @ int @ SV186 @ SV219 ) )
= $true )
| ( ( ord_less @ int @ ( number_number_of @ int @ SV186 ) @ ( number_number_of @ int @ SV219 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1119]) ).
thf(1202,plain,
! [SV220: $i,SV187: $i] :
( ( ( ~ ( ord_less @ int @ ( bit1 @ SV187 ) @ ( bit0 @ SV220 ) ) )
= $true )
| ( ( ord_less @ int @ SV187 @ SV220 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1120]) ).
thf(1203,plain,
! [SV221: $i,SV188: $i] :
( ( ( ~ ( ord_less @ int @ SV188 @ SV221 ) )
= $true )
| ( ( ord_less @ int @ ( bit1 @ SV188 ) @ ( bit0 @ SV221 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1121]) ).
thf(1204,plain,
! [SV61: $i] :
( ( ( power @ SV61 )
= $false )
| ( ( mult_zero @ SV61 )
= $false )
| ( ( ~ ( no_zero_divisors @ SV61 ) )
= $true )
| ( ( ~ ( zero_neq_one @ SV61 ) )
= $true )
| ( ( ( ti @ SV61 @ ( zero_zero @ SV61 ) )
= ( zero_zero @ SV61 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1123]) ).
thf(1205,plain,
! [SV113: $i,SV64: $i,SV130: $i] :
( ( ( ~ ( mult_zero @ SV130 ) )
= $true )
| ( ( ~ ( power @ SV130 ) )
= $true )
| ( ( ~ ( no_zero_divisors @ SV130 ) )
= $true )
| ( ( ~ ( zero_neq_one @ SV130 ) )
= $true )
| ( ( ( power_power @ SV130 @ ( ti @ SV130 @ SV64 ) @ SV113 )
= ( power_power @ SV130 @ SV64 @ SV113 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1124]) ).
thf(1206,plain,
! [SV114: $i,SV65: $i,SV131: $i] :
( ( ( ~ ( mult_zero @ SV131 ) )
= $true )
| ( ( ~ ( power @ SV131 ) )
= $true )
| ( ( ~ ( no_zero_divisors @ SV131 ) )
= $true )
| ( ( ~ ( zero_neq_one @ SV131 ) )
= $true )
| ( ( ( power_power @ SV131 @ SV65 @ ( ti @ nat @ SV114 ) )
= ( power_power @ SV131 @ SV65 @ SV114 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1125]) ).
thf(1207,plain,
! [SV115: $i,SV66: $i,SV132: $i] :
( ( ( ~ ( mult_zero @ SV132 ) )
= $true )
| ( ( ~ ( power @ SV132 ) )
= $true )
| ( ( ~ ( no_zero_divisors @ SV132 ) )
= $true )
| ( ( ~ ( zero_neq_one @ SV132 ) )
= $true )
| ( ( ( ti @ SV132 @ ( power_power @ SV132 @ SV66 @ SV115 ) )
= ( power_power @ SV132 @ SV66 @ SV115 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1126]) ).
thf(1208,plain,
! [SV116: $i,SV67: $i,SV133: $i] :
( ( ( semiring_0 @ SV133 )
= $false )
| ( ( power @ SV133 )
= $false )
| ( ( ( power_power @ SV133 @ ( ti @ SV133 @ SV67 ) @ SV116 )
= ( power_power @ SV133 @ SV67 @ SV116 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1127]) ).
thf(1209,plain,
! [SV117: $i,SV68: $i,SV134: $i] :
( ( ( semiring_0 @ SV134 )
= $false )
| ( ( power @ SV134 )
= $false )
| ( ( ( power_power @ SV134 @ SV68 @ ( ti @ nat @ SV117 ) )
= ( power_power @ SV134 @ SV68 @ SV117 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1128]) ).
thf(1210,plain,
! [SV118: $i,SV69: $i,SV135: $i] :
( ( ( semiring_0 @ SV135 )
= $false )
| ( ( power @ SV135 )
= $false )
| ( ( ( ti @ SV135 @ ( power_power @ SV135 @ SV69 @ SV118 ) )
= ( power_power @ SV135 @ SV69 @ SV118 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1129]) ).
thf(1211,plain,
! [SV71: $i] :
( ( ( ~ ! [SY271: $i,SY272: $i] :
( ( ( number_number_of @ SV71 @ SY271 )
!= ( number_number_of @ SV71 @ SY272 ) )
| ( SY271 = SY272 ) ) )
= $false )
| ( ( number_ring @ SV71 )
= $false )
| ( ( ring_char_0 @ SV71 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1132]) ).
thf(1212,plain,
! [SV71: $i] :
( ( ( ~ ! [SY273: $i,SY274: $i] :
( ( SY273 != SY274 )
| ( ( number_number_of @ SV71 @ SY273 )
= ( number_number_of @ SV71 @ SY274 ) ) ) )
= $false )
| ( ( number_ring @ SV71 )
= $false )
| ( ( ring_char_0 @ SV71 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1132]) ).
thf(1213,plain,
! [SV192: $i,SV72: $i,SV223: $i] :
( ( ( ~ ( linordered_idom @ SV223 ) )
= $true )
| ( ( ~ ( ord_less @ SV223 @ ( ti @ SV223 @ SV72 ) @ SV192 )
| ( ord_less @ SV223 @ SV72 @ SV192 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1133]) ).
thf(1214,plain,
! [SV193: $i,SV72: $i,SV224: $i] :
( ( ( ~ ( linordered_idom @ SV224 ) )
= $true )
| ( ( ~ ( ord_less @ SV224 @ SV72 @ SV193 )
| ( ord_less @ SV224 @ ( ti @ SV224 @ SV72 ) @ SV193 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1134]) ).
thf(1215,plain,
! [SV194: $i,SV151: $i] :
( ( ( ord_less @ int @ SV151 @ ( plus_plus @ int @ SV194 @ ( one_one @ int ) ) )
= $false )
| ( ( ( SV151 = SV194 )
| ( ord_less @ int @ SV151 @ SV194 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1139]) ).
thf(1216,plain,
! [SV227: $i] :
( ( ! [SY378: $i] :
( ( SV227 != SY378 )
| ( ord_less @ int @ SV227 @ ( plus_plus @ int @ SY378 @ ( one_one @ int ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1140]) ).
thf(1217,plain,
! [SV228: $i] :
( ( ! [SY379: $i] :
( ~ ( ord_less @ int @ SV228 @ SY379 )
| ( ord_less @ int @ SV228 @ ( plus_plus @ int @ SY379 @ ( one_one @ int ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1141]) ).
thf(1218,plain,
! [SV195: $i,SV152: $i] :
( ( ( ord_less @ nat @ ( ti @ nat @ SV152 ) @ SV195 )
= $false )
| ( ( ord_less @ nat @ SV152 @ SV195 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1142]) ).
thf(1219,plain,
! [SV196: $i,SV153: $i] :
( ( ( ord_less @ nat @ SV153 @ SV196 )
= $false )
| ( ( ord_less @ nat @ ( ti @ nat @ SV153 ) @ SV196 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1143]) ).
thf(1220,plain,
! [SV229: $i,SV73: $i] :
( ( ( ! [SY380: $i] :
( ( ( ti @ SV73 @ SV229 )
!= ( zero_zero @ SV73 ) )
| ( ( ti @ SV73 @ SY380 )
!= ( zero_zero @ SV73 ) )
| ( ( plus_plus @ SV73 @ ( power_power @ SV73 @ SV229 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV73 @ SY380 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV73 ) ) ) )
= $true )
| ( ( linordered_idom @ SV73 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1144]) ).
thf(1221,plain,
! [SV73: $i] :
( ( ( ~ ! [SY281: $i] :
( ! [SY282: $i] :
( ( plus_plus @ SV73 @ ( power_power @ SV73 @ SY281 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV73 @ SY282 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV73 ) )
| ( ( ti @ SV73 @ SY281 )
= ( zero_zero @ SV73 ) ) )
| ~ ! [SY283: $i,SY284: $i] :
( ( ( plus_plus @ SV73 @ ( power_power @ SV73 @ SY283 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV73 @ SY284 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV73 ) )
| ( ( ti @ SV73 @ SY284 )
= ( zero_zero @ SV73 ) ) ) )
= $false )
| ( ( linordered_idom @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1145]) ).
thf(1222,plain,
! [SV230: $i,SV74: $i] :
( ( ( ! [SY381: $i] :
( ~ ( ord_less @ SV74 @ ( zero_zero @ SV74 ) @ ( plus_plus @ SV74 @ ( power_power @ SV74 @ SV230 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV74 @ SY381 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
| ( ( ti @ SV74 @ SV230 )
!= ( zero_zero @ SV74 ) )
| ( ( ti @ SV74 @ SY381 )
!= ( zero_zero @ SV74 ) ) ) )
= $true )
| ( ( linordered_idom @ SV74 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1146]) ).
thf(1223,plain,
! [SV74: $i] :
( ( ( ~ ! [SY287: $i] :
( ( ( ti @ SV74 @ SY287 )
= ( zero_zero @ SV74 ) )
| ! [SY288: $i] : ( ord_less @ SV74 @ ( zero_zero @ SV74 ) @ ( plus_plus @ SV74 @ ( power_power @ SV74 @ SY287 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV74 @ SY288 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
| ~ ! [SY289: $i,SY290: $i] :
( ( ( ti @ SV74 @ SY290 )
= ( zero_zero @ SV74 ) )
| ( ord_less @ SV74 @ ( zero_zero @ SV74 ) @ ( plus_plus @ SV74 @ ( power_power @ SV74 @ SY289 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV74 @ SY290 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) )
= $false )
| ( ( linordered_idom @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1147]) ).
thf(1224,plain,
! [SV75: $i] :
( ( ( ~ ! [SY291: $i] :
( ~ ( ord_less @ SV75 @ ( number_number_of @ SV75 @ SY291 ) @ ( one_one @ SV75 ) )
| ( ord_less @ int @ SY291 @ ( bit1 @ pls ) ) ) )
= $false )
| ( ( linordered_idom @ SV75 )
= $false )
| ( ( number_ring @ SV75 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1148]) ).
thf(1225,plain,
! [SV75: $i] :
( ( ( ~ ! [SY292: $i] :
( ~ ( ord_less @ int @ SY292 @ ( bit1 @ pls ) )
| ( ord_less @ SV75 @ ( number_number_of @ SV75 @ SY292 ) @ ( one_one @ SV75 ) ) ) )
= $false )
| ( ( linordered_idom @ SV75 )
= $false )
| ( ( number_ring @ SV75 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1148]) ).
thf(1226,plain,
! [SV76: $i] :
( ( ( ~ ! [SY293: $i] :
( ~ ( ord_less @ SV76 @ ( zero_zero @ SV76 ) @ ( number_number_of @ SV76 @ SY293 ) )
| ( ord_less @ int @ pls @ SY293 ) ) )
= $false )
| ( ( linordered_idom @ SV76 )
= $false )
| ( ( number_ring @ SV76 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1149]) ).
thf(1227,plain,
! [SV76: $i] :
( ( ( ~ ! [SY294: $i] :
( ~ ( ord_less @ int @ pls @ SY294 )
| ( ord_less @ SV76 @ ( zero_zero @ SV76 ) @ ( number_number_of @ SV76 @ SY294 ) ) ) )
= $false )
| ( ( linordered_idom @ SV76 )
= $false )
| ( ( number_ring @ SV76 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1149]) ).
thf(1228,plain,
! [SV197: $i,SV154: $i] :
( ( ( ord_less @ int @ ( bit0 @ SV154 ) @ ( bit0 @ SV197 ) )
= $false )
| ( ( ord_less @ int @ SV154 @ SV197 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1150]) ).
thf(1229,plain,
! [SV198: $i,SV155: $i] :
( ( ( ord_less @ int @ SV155 @ SV198 )
= $false )
| ( ( ord_less @ int @ ( bit0 @ SV155 ) @ ( bit0 @ SV198 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1151]) ).
thf(1230,plain,
! [SV199: $i,SV158: $i] :
( ( ( ord_less @ nat @ SV158 @ ( ti @ nat @ SV199 ) )
= $false )
| ( ( ord_less @ nat @ SV158 @ SV199 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1154]) ).
thf(1231,plain,
! [SV200: $i,SV159: $i] :
( ( ( ord_less @ nat @ SV159 @ SV200 )
= $false )
| ( ( ord_less @ nat @ SV159 @ ( ti @ nat @ SV200 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1155]) ).
thf(1232,plain,
! [SV77: $i] :
( ( ( power @ SV77 )
= $false )
| ( ( mult_zero @ SV77 )
= $false )
| ( ( ~ ( no_zero_divisors @ SV77 ) )
= $true )
| ( ( ~ ( zero_neq_one @ SV77 ) )
= $true )
| ( ( ~ ( ~ ! [SY295: $i,SY296: $i] :
( ( ( number_number_of @ nat @ SY296 )
= ( zero_zero @ nat ) )
| ( ( ti @ SV77 @ SY295 )
!= ( zero_zero @ SV77 ) )
| ( ( power_power @ SV77 @ SY295 @ ( number_number_of @ nat @ SY296 ) )
= ( zero_zero @ SV77 ) ) )
| ~ ~ ( ~ ! [SY297: $i,SY298: $i] :
( ( ( power_power @ SV77 @ SY297 @ ( number_number_of @ nat @ SY298 ) )
!= ( zero_zero @ SV77 ) )
| ( ( number_number_of @ nat @ SY298 )
!= ( zero_zero @ nat ) ) )
| ~ ! [SY299: $i] :
( ! [SY300: $i] :
( ( power_power @ SV77 @ SY299 @ ( number_number_of @ nat @ SY300 ) )
!= ( zero_zero @ SV77 ) )
| ( ( ti @ SV77 @ SY299 )
= ( zero_zero @ SV77 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1156]) ).
thf(1233,plain,
! [SV201: $i,SV78: $i,SV225: $i] :
( ( ( ~ ( linordered_idom @ SV225 ) )
= $true )
| ( ( ~ ( ord_less @ SV225 @ SV78 @ ( ti @ SV225 @ SV201 ) )
| ( ord_less @ SV225 @ SV78 @ SV201 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1157]) ).
thf(1234,plain,
! [SV202: $i,SV78: $i,SV226: $i] :
( ( ( ~ ( linordered_idom @ SV226 ) )
= $true )
| ( ( ~ ( ord_less @ SV226 @ SV78 @ SV202 )
| ( ord_less @ SV226 @ SV78 @ ( ti @ SV226 @ SV202 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1158]) ).
thf(1235,plain,
! [SV203: $i,SV162: $i] :
( ( ( ( bit1 @ SV162 )
= ( bit1 @ SV203 ) )
= $false )
| ( ( SV162 = SV203 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1161]) ).
thf(1236,plain,
! [SV204: $i,SV163: $i] :
( ( ( SV163 = SV204 )
= $false )
| ( ( ( bit1 @ SV163 )
= ( bit1 @ SV204 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1162]) ).
thf(1237,plain,
! [SV231: $i,SV79: $i] :
( ( ( ( ( plus_plus @ SV79 @ SV231 @ SV231 )
!= ( zero_zero @ SV79 ) )
| ( ( ti @ SV79 @ SV231 )
= ( zero_zero @ SV79 ) ) )
= $true )
| ( ( linord219039673up_add @ SV79 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1163]) ).
thf(1238,plain,
! [SV232: $i,SV79: $i] :
( ( ( ( ( ti @ SV79 @ SV232 )
!= ( zero_zero @ SV79 ) )
| ( ( plus_plus @ SV79 @ SV232 @ SV232 )
= ( zero_zero @ SV79 ) ) )
= $true )
| ( ( linord219039673up_add @ SV79 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1164]) ).
thf(1239,plain,
! [SV205: $i,SV164: $i] :
( ( ( ord_less @ int @ ( bit1 @ SV164 ) @ ( bit1 @ SV205 ) )
= $false )
| ( ( ord_less @ int @ SV164 @ SV205 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1165]) ).
thf(1240,plain,
! [SV206: $i,SV165: $i] :
( ( ( ord_less @ int @ SV165 @ SV206 )
= $false )
| ( ( ord_less @ int @ ( bit1 @ SV165 ) @ ( bit1 @ SV206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1166]) ).
thf(1241,plain,
! [SV80: $i] :
( ( ( ~ ! [SY307: $i] :
( ~ ( ord_less @ SV80 @ ( number_number_of @ SV80 @ SY307 ) @ ( zero_zero @ SV80 ) )
| ( ord_less @ int @ SY307 @ pls ) ) )
= $false )
| ( ( linordered_idom @ SV80 )
= $false )
| ( ( number_ring @ SV80 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1167]) ).
thf(1242,plain,
! [SV80: $i] :
( ( ( ~ ! [SY308: $i] :
( ~ ( ord_less @ int @ SY308 @ pls )
| ( ord_less @ SV80 @ ( number_number_of @ SV80 @ SY308 ) @ ( zero_zero @ SV80 ) ) ) )
= $false )
| ( ( linordered_idom @ SV80 )
= $false )
| ( ( number_ring @ SV80 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1167]) ).
thf(1243,plain,
! [SV81: $i] :
( ( ( ~ ! [SY309: $i,SY310: $i] :
( ~ ( ord_less @ SV81 @ ( number_number_of @ SV81 @ SY309 ) @ ( number_number_of @ SV81 @ SY310 ) )
| ( ord_less @ int @ SY309 @ SY310 ) ) )
= $false )
| ( ( linordered_idom @ SV81 )
= $false )
| ( ( number_ring @ SV81 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1168]) ).
thf(1244,plain,
! [SV81: $i] :
( ( ( ~ ! [SY311: $i,SY312: $i] :
( ~ ( ord_less @ int @ SY311 @ SY312 )
| ( ord_less @ SV81 @ ( number_number_of @ SV81 @ SY311 ) @ ( number_number_of @ SV81 @ SY312 ) ) ) )
= $false )
| ( ( linordered_idom @ SV81 )
= $false )
| ( ( number_ring @ SV81 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1168]) ).
thf(1245,plain,
! [SV207: $i,SV166: $i] :
( ( ( ( bit0 @ SV166 )
= ( bit0 @ SV207 ) )
= $false )
| ( ( SV166 = SV207 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1169]) ).
thf(1246,plain,
! [SV208: $i,SV167: $i] :
( ( ( SV167 = SV208 )
= $false )
| ( ( ( bit0 @ SV167 )
= ( bit0 @ SV208 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1170]) ).
thf(1247,plain,
! [SV209: $i,SV168: $i] :
( ( ( ord_less @ int @ ( bit0 @ SV168 ) @ ( bit0 @ SV209 ) )
= $false )
| ( ( ord_less @ int @ SV168 @ SV209 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1171]) ).
thf(1248,plain,
! [SV210: $i,SV169: $i] :
( ( ( ord_less @ int @ SV169 @ SV210 )
= $false )
| ( ( ord_less @ int @ ( bit0 @ SV169 ) @ ( bit0 @ SV210 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1172]) ).
thf(1249,plain,
! [SV233: $i,SV82: $i] :
( ( ( ~ ( ord_less @ SV82 @ ( plus_plus @ SV82 @ SV233 @ SV233 ) @ ( zero_zero @ SV82 ) )
| ( ord_less @ SV82 @ SV233 @ ( zero_zero @ SV82 ) ) )
= $true )
| ( ( linordered_idom @ SV82 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1173]) ).
thf(1250,plain,
! [SV234: $i,SV82: $i] :
( ( ( ~ ( ord_less @ SV82 @ SV234 @ ( zero_zero @ SV82 ) )
| ( ord_less @ SV82 @ ( plus_plus @ SV82 @ SV234 @ SV234 ) @ ( zero_zero @ SV82 ) ) )
= $true )
| ( ( linordered_idom @ SV82 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1174]) ).
thf(1251,plain,
! [SV83: $i] :
( ( ( ~ ! [SY315: $i] :
( ( ( number_number_of @ nat @ SY315 )
!= ( zero_zero @ nat ) )
| ( ( power_power @ SV83 @ ( zero_zero @ SV83 ) @ ( number_number_of @ nat @ SY315 ) )
= ( one_one @ SV83 ) ) ) )
= $false )
| ( ( power @ SV83 )
= $false )
| ( ( semiring_0 @ SV83 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1175]) ).
thf(1252,plain,
! [SV83: $i] :
( ( ( ~ ! [SY316: $i] :
( ( ( number_number_of @ nat @ SY316 )
= ( zero_zero @ nat ) )
| ( ( power_power @ SV83 @ ( zero_zero @ SV83 ) @ ( number_number_of @ nat @ SY316 ) )
= ( zero_zero @ SV83 ) ) ) )
= $false )
| ( ( power @ SV83 )
= $false )
| ( ( semiring_0 @ SV83 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1175]) ).
thf(1253,plain,
! [SV170: $i,SV211: $i] :
( ( ( ord_less @ int @ SV211 @ pls )
= $false )
| ( ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV211 ) @ ( number_number_of @ nat @ SV170 ) )
= ( number_number_of @ nat @ SV170 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1176]) ).
thf(1254,plain,
! [SV235: $i] :
( ( ! [SY382: $i] :
( ( ord_less @ int @ SY382 @ pls )
| ~ ( ord_less @ int @ SV235 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SY382 ) @ ( number_number_of @ nat @ SV235 ) )
= ( number_number_of @ nat @ SY382 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1177]) ).
thf(1255,plain,
! [SV236: $i] :
( ( ! [SY383: $i] :
( ( ord_less @ int @ SY383 @ pls )
| ( ord_less @ int @ SV236 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SY383 ) @ ( number_number_of @ nat @ SV236 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SY383 @ SV236 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1178]) ).
thf(1256,plain,
! [SV212: $i,SV175: $i] :
( ( ( ord_less @ int @ ( bit1 @ SV175 ) @ ( bit0 @ SV212 ) )
= $false )
| ( ( ord_less @ int @ SV175 @ SV212 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1183]) ).
thf(1257,plain,
! [SV213: $i,SV176: $i] :
( ( ( ord_less @ int @ SV176 @ SV213 )
= $false )
| ( ( ord_less @ int @ ( bit1 @ SV176 ) @ ( bit0 @ SV213 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1184]) ).
thf(1258,plain,
! [SV214: $i,SV177: $i] :
( ( ( ord_less @ int @ ( bit1 @ SV177 ) @ ( bit1 @ SV214 ) )
= $false )
| ( ( ord_less @ int @ SV177 @ SV214 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1185]) ).
thf(1259,plain,
! [SV215: $i,SV178: $i] :
( ( ( ord_less @ int @ SV178 @ SV215 )
= $false )
| ( ( ord_less @ int @ ( bit1 @ SV178 ) @ ( bit1 @ SV215 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1186]) ).
thf(1260,plain,
! [SV237: $i,SV84: $i] :
( ( ( ! [SY384: $i] :
( ( ( number_number_of @ SV84 @ SV237 )
!= ( ti @ SV84 @ SY384 ) )
| ( ( ti @ SV84 @ SY384 )
= ( number_number_of @ SV84 @ SV237 ) ) ) )
= $true )
| ( ( number @ SV84 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1187]) ).
thf(1261,plain,
! [SV238: $i,SV84: $i] :
( ( ( ! [SY385: $i] :
( ( ( ti @ SV84 @ SY385 )
!= ( number_number_of @ SV84 @ SV238 ) )
| ( ( number_number_of @ SV84 @ SV238 )
= ( ti @ SV84 @ SY385 ) ) ) )
= $true )
| ( ( number @ SV84 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1188]) ).
thf(1262,plain,
! [SV239: $i,SV85: $i] :
( ( ( ( ( ti @ SV85 @ SV239 )
= ( zero_zero @ SV85 ) )
| ( ord_less @ SV85 @ ( zero_zero @ SV85 ) @ ( power_power @ SV85 @ SV239 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true )
| ( ( linordered_idom @ SV85 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1189]) ).
thf(1263,plain,
! [SV240: $i,SV85: $i] :
( ( ( ~ ( ord_less @ SV85 @ ( zero_zero @ SV85 ) @ ( power_power @ SV85 @ SV240 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ( ( ti @ SV85 @ SV240 )
!= ( zero_zero @ SV85 ) ) )
= $true )
| ( ( linordered_idom @ SV85 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1190]) ).
thf(1264,plain,
! [SV216: $i,SV179: $i] :
( ( ( ( semiring_1_of_nat @ int @ SV179 )
= ( semiring_1_of_nat @ int @ SV216 ) )
= $false )
| ( ( SV179 = SV216 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1191]) ).
thf(1265,plain,
! [SV217: $i,SV180: $i] :
( ( ( SV180 = SV217 )
= $false )
| ( ( ( semiring_1_of_nat @ int @ SV180 )
= ( semiring_1_of_nat @ int @ SV217 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1192]) ).
thf(1266,plain,
! [SV241: $i,SV86: $i] :
( ( ( ( ( power_power @ SV86 @ SV241 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= ( zero_zero @ SV86 ) )
| ( ( ti @ SV86 @ SV241 )
= ( zero_zero @ SV86 ) ) )
= $true )
| ( ( ring_11004092258visors @ SV86 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1195]) ).
thf(1267,plain,
! [SV242: $i,SV86: $i] :
( ( ( ( ( ti @ SV86 @ SV242 )
!= ( zero_zero @ SV86 ) )
| ( ( power_power @ SV86 @ SV242 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SV86 ) ) )
= $true )
| ( ( ring_11004092258visors @ SV86 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1196]) ).
thf(1268,plain,
! [SV87: $i] :
( ( ( ~ ! [SY325: $i] :
( ~ ( ord_less @ SV87 @ ( one_one @ SV87 ) @ ( number_number_of @ SV87 @ SY325 ) )
| ( ord_less @ int @ ( bit1 @ pls ) @ SY325 ) ) )
= $false )
| ( ( linordered_idom @ SV87 )
= $false )
| ( ( number_ring @ SV87 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1197]) ).
thf(1269,plain,
! [SV87: $i] :
( ( ( ~ ! [SY326: $i] :
( ~ ( ord_less @ int @ ( bit1 @ pls ) @ SY326 )
| ( ord_less @ SV87 @ ( one_one @ SV87 ) @ ( number_number_of @ SV87 @ SY326 ) ) ) )
= $false )
| ( ( linordered_idom @ SV87 )
= $false )
| ( ( number_ring @ SV87 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1197]) ).
thf(1270,plain,
! [SV218: $i,SV185: $i] :
( ( ( ord_less @ int @ ( number_number_of @ int @ SV185 ) @ ( number_number_of @ int @ SV218 ) )
= $false )
| ( ( ord_less @ int @ SV185 @ SV218 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1200]) ).
thf(1271,plain,
! [SV219: $i,SV186: $i] :
( ( ( ord_less @ int @ SV186 @ SV219 )
= $false )
| ( ( ord_less @ int @ ( number_number_of @ int @ SV186 ) @ ( number_number_of @ int @ SV219 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1201]) ).
thf(1272,plain,
! [SV220: $i,SV187: $i] :
( ( ( ord_less @ int @ ( bit1 @ SV187 ) @ ( bit0 @ SV220 ) )
= $false )
| ( ( ord_less @ int @ SV187 @ SV220 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1202]) ).
thf(1273,plain,
! [SV221: $i,SV188: $i] :
( ( ( ord_less @ int @ SV188 @ SV221 )
= $false )
| ( ( ord_less @ int @ ( bit1 @ SV188 ) @ ( bit0 @ SV221 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1203]) ).
thf(1274,plain,
! [SV61: $i] :
( ( ( no_zero_divisors @ SV61 )
= $false )
| ( ( mult_zero @ SV61 )
= $false )
| ( ( power @ SV61 )
= $false )
| ( ( ~ ( zero_neq_one @ SV61 ) )
= $true )
| ( ( ( ti @ SV61 @ ( zero_zero @ SV61 ) )
= ( zero_zero @ SV61 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1204]) ).
thf(1275,plain,
! [SV113: $i,SV64: $i,SV130: $i] :
( ( ( mult_zero @ SV130 )
= $false )
| ( ( ~ ( power @ SV130 ) )
= $true )
| ( ( ~ ( no_zero_divisors @ SV130 ) )
= $true )
| ( ( ~ ( zero_neq_one @ SV130 ) )
= $true )
| ( ( ( power_power @ SV130 @ ( ti @ SV130 @ SV64 ) @ SV113 )
= ( power_power @ SV130 @ SV64 @ SV113 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1205]) ).
thf(1276,plain,
! [SV114: $i,SV65: $i,SV131: $i] :
( ( ( mult_zero @ SV131 )
= $false )
| ( ( ~ ( power @ SV131 ) )
= $true )
| ( ( ~ ( no_zero_divisors @ SV131 ) )
= $true )
| ( ( ~ ( zero_neq_one @ SV131 ) )
= $true )
| ( ( ( power_power @ SV131 @ SV65 @ ( ti @ nat @ SV114 ) )
= ( power_power @ SV131 @ SV65 @ SV114 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1206]) ).
thf(1277,plain,
! [SV115: $i,SV66: $i,SV132: $i] :
( ( ( mult_zero @ SV132 )
= $false )
| ( ( ~ ( power @ SV132 ) )
= $true )
| ( ( ~ ( no_zero_divisors @ SV132 ) )
= $true )
| ( ( ~ ( zero_neq_one @ SV132 ) )
= $true )
| ( ( ( ti @ SV132 @ ( power_power @ SV132 @ SV66 @ SV115 ) )
= ( power_power @ SV132 @ SV66 @ SV115 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1207]) ).
thf(1278,plain,
! [SV71: $i] :
( ( ( ! [SY271: $i,SY272: $i] :
( ( ( number_number_of @ SV71 @ SY271 )
!= ( number_number_of @ SV71 @ SY272 ) )
| ( SY271 = SY272 ) ) )
= $true )
| ( ( number_ring @ SV71 )
= $false )
| ( ( ring_char_0 @ SV71 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1211]) ).
thf(1279,plain,
! [SV71: $i] :
( ( ( ! [SY273: $i,SY274: $i] :
( ( SY273 != SY274 )
| ( ( number_number_of @ SV71 @ SY273 )
= ( number_number_of @ SV71 @ SY274 ) ) ) )
= $true )
| ( ( number_ring @ SV71 )
= $false )
| ( ( ring_char_0 @ SV71 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1212]) ).
thf(1280,plain,
! [SV192: $i,SV72: $i,SV223: $i] :
( ( ( linordered_idom @ SV223 )
= $false )
| ( ( ~ ( ord_less @ SV223 @ ( ti @ SV223 @ SV72 ) @ SV192 )
| ( ord_less @ SV223 @ SV72 @ SV192 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1213]) ).
thf(1281,plain,
! [SV193: $i,SV72: $i,SV224: $i] :
( ( ( linordered_idom @ SV224 )
= $false )
| ( ( ~ ( ord_less @ SV224 @ SV72 @ SV193 )
| ( ord_less @ SV224 @ ( ti @ SV224 @ SV72 ) @ SV193 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1214]) ).
thf(1282,plain,
! [SV194: $i,SV151: $i] :
( ( ( SV151 = SV194 )
= $true )
| ( ( ord_less @ int @ SV151 @ SV194 )
= $true )
| ( ( ord_less @ int @ SV151 @ ( plus_plus @ int @ SV194 @ ( one_one @ int ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1215]) ).
thf(1283,plain,
! [SV243: $i,SV227: $i] :
( ( ( SV227 != SV243 )
| ( ord_less @ int @ SV227 @ ( plus_plus @ int @ SV243 @ ( one_one @ int ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1216]) ).
thf(1284,plain,
! [SV244: $i,SV228: $i] :
( ( ~ ( ord_less @ int @ SV228 @ SV244 )
| ( ord_less @ int @ SV228 @ ( plus_plus @ int @ SV244 @ ( one_one @ int ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1217]) ).
thf(1285,plain,
! [SV245: $i,SV229: $i,SV73: $i] :
( ( ( ( ( ti @ SV73 @ SV229 )
!= ( zero_zero @ SV73 ) )
| ( ( ti @ SV73 @ SV245 )
!= ( zero_zero @ SV73 ) )
| ( ( plus_plus @ SV73 @ ( power_power @ SV73 @ SV229 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV73 @ SV245 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV73 ) ) )
= $true )
| ( ( linordered_idom @ SV73 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1220]) ).
thf(1286,plain,
! [SV73: $i] :
( ( ( ~ ! [SY281: $i] :
( ! [SY282: $i] :
( ( plus_plus @ SV73 @ ( power_power @ SV73 @ SY281 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV73 @ SY282 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV73 ) )
| ( ( ti @ SV73 @ SY281 )
= ( zero_zero @ SV73 ) ) ) )
= $false )
| ( ( linordered_idom @ SV73 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1221]) ).
thf(1287,plain,
! [SV73: $i] :
( ( ( ~ ! [SY283: $i,SY284: $i] :
( ( ( plus_plus @ SV73 @ ( power_power @ SV73 @ SY283 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV73 @ SY284 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV73 ) )
| ( ( ti @ SV73 @ SY284 )
= ( zero_zero @ SV73 ) ) ) )
= $false )
| ( ( linordered_idom @ SV73 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1221]) ).
thf(1288,plain,
! [SV246: $i,SV230: $i,SV74: $i] :
( ( ( ~ ( ord_less @ SV74 @ ( zero_zero @ SV74 ) @ ( plus_plus @ SV74 @ ( power_power @ SV74 @ SV230 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV74 @ SV246 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
| ( ( ti @ SV74 @ SV230 )
!= ( zero_zero @ SV74 ) )
| ( ( ti @ SV74 @ SV246 )
!= ( zero_zero @ SV74 ) ) )
= $true )
| ( ( linordered_idom @ SV74 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1222]) ).
thf(1289,plain,
! [SV74: $i] :
( ( ( ~ ! [SY287: $i] :
( ( ( ti @ SV74 @ SY287 )
= ( zero_zero @ SV74 ) )
| ! [SY288: $i] : ( ord_less @ SV74 @ ( zero_zero @ SV74 ) @ ( plus_plus @ SV74 @ ( power_power @ SV74 @ SY287 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV74 @ SY288 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) )
= $false )
| ( ( linordered_idom @ SV74 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1223]) ).
thf(1290,plain,
! [SV74: $i] :
( ( ( ~ ! [SY289: $i,SY290: $i] :
( ( ( ti @ SV74 @ SY290 )
= ( zero_zero @ SV74 ) )
| ( ord_less @ SV74 @ ( zero_zero @ SV74 ) @ ( plus_plus @ SV74 @ ( power_power @ SV74 @ SY289 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV74 @ SY290 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) )
= $false )
| ( ( linordered_idom @ SV74 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1223]) ).
thf(1291,plain,
! [SV75: $i] :
( ( ( ! [SY291: $i] :
( ~ ( ord_less @ SV75 @ ( number_number_of @ SV75 @ SY291 ) @ ( one_one @ SV75 ) )
| ( ord_less @ int @ SY291 @ ( bit1 @ pls ) ) ) )
= $true )
| ( ( linordered_idom @ SV75 )
= $false )
| ( ( number_ring @ SV75 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1224]) ).
thf(1292,plain,
! [SV75: $i] :
( ( ( ! [SY292: $i] :
( ~ ( ord_less @ int @ SY292 @ ( bit1 @ pls ) )
| ( ord_less @ SV75 @ ( number_number_of @ SV75 @ SY292 ) @ ( one_one @ SV75 ) ) ) )
= $true )
| ( ( linordered_idom @ SV75 )
= $false )
| ( ( number_ring @ SV75 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1225]) ).
thf(1293,plain,
! [SV76: $i] :
( ( ( ! [SY293: $i] :
( ~ ( ord_less @ SV76 @ ( zero_zero @ SV76 ) @ ( number_number_of @ SV76 @ SY293 ) )
| ( ord_less @ int @ pls @ SY293 ) ) )
= $true )
| ( ( linordered_idom @ SV76 )
= $false )
| ( ( number_ring @ SV76 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1226]) ).
thf(1294,plain,
! [SV76: $i] :
( ( ( ! [SY294: $i] :
( ~ ( ord_less @ int @ pls @ SY294 )
| ( ord_less @ SV76 @ ( zero_zero @ SV76 ) @ ( number_number_of @ SV76 @ SY294 ) ) ) )
= $true )
| ( ( linordered_idom @ SV76 )
= $false )
| ( ( number_ring @ SV76 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1227]) ).
thf(1295,plain,
! [SV77: $i] :
( ( ( no_zero_divisors @ SV77 )
= $false )
| ( ( mult_zero @ SV77 )
= $false )
| ( ( power @ SV77 )
= $false )
| ( ( ~ ( zero_neq_one @ SV77 ) )
= $true )
| ( ( ~ ( ~ ! [SY295: $i,SY296: $i] :
( ( ( number_number_of @ nat @ SY296 )
= ( zero_zero @ nat ) )
| ( ( ti @ SV77 @ SY295 )
!= ( zero_zero @ SV77 ) )
| ( ( power_power @ SV77 @ SY295 @ ( number_number_of @ nat @ SY296 ) )
= ( zero_zero @ SV77 ) ) )
| ~ ~ ( ~ ! [SY297: $i,SY298: $i] :
( ( ( power_power @ SV77 @ SY297 @ ( number_number_of @ nat @ SY298 ) )
!= ( zero_zero @ SV77 ) )
| ( ( number_number_of @ nat @ SY298 )
!= ( zero_zero @ nat ) ) )
| ~ ! [SY299: $i] :
( ! [SY300: $i] :
( ( power_power @ SV77 @ SY299 @ ( number_number_of @ nat @ SY300 ) )
!= ( zero_zero @ SV77 ) )
| ( ( ti @ SV77 @ SY299 )
= ( zero_zero @ SV77 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1232]) ).
thf(1296,plain,
! [SV201: $i,SV78: $i,SV225: $i] :
( ( ( linordered_idom @ SV225 )
= $false )
| ( ( ~ ( ord_less @ SV225 @ SV78 @ ( ti @ SV225 @ SV201 ) )
| ( ord_less @ SV225 @ SV78 @ SV201 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1233]) ).
thf(1297,plain,
! [SV202: $i,SV78: $i,SV226: $i] :
( ( ( linordered_idom @ SV226 )
= $false )
| ( ( ~ ( ord_less @ SV226 @ SV78 @ SV202 )
| ( ord_less @ SV226 @ SV78 @ ( ti @ SV226 @ SV202 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1234]) ).
thf(1298,plain,
! [SV231: $i,SV79: $i] :
( ( ( ( ( plus_plus @ SV79 @ SV231 @ SV231 )
!= ( zero_zero @ SV79 ) ) )
= $true )
| ( ( ( ti @ SV79 @ SV231 )
= ( zero_zero @ SV79 ) )
= $true )
| ( ( linord219039673up_add @ SV79 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1237]) ).
thf(1299,plain,
! [SV232: $i,SV79: $i] :
( ( ( ( ( ti @ SV79 @ SV232 )
!= ( zero_zero @ SV79 ) ) )
= $true )
| ( ( ( plus_plus @ SV79 @ SV232 @ SV232 )
= ( zero_zero @ SV79 ) )
= $true )
| ( ( linord219039673up_add @ SV79 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1238]) ).
thf(1300,plain,
! [SV80: $i] :
( ( ( ! [SY307: $i] :
( ~ ( ord_less @ SV80 @ ( number_number_of @ SV80 @ SY307 ) @ ( zero_zero @ SV80 ) )
| ( ord_less @ int @ SY307 @ pls ) ) )
= $true )
| ( ( linordered_idom @ SV80 )
= $false )
| ( ( number_ring @ SV80 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1241]) ).
thf(1301,plain,
! [SV80: $i] :
( ( ( ! [SY308: $i] :
( ~ ( ord_less @ int @ SY308 @ pls )
| ( ord_less @ SV80 @ ( number_number_of @ SV80 @ SY308 ) @ ( zero_zero @ SV80 ) ) ) )
= $true )
| ( ( linordered_idom @ SV80 )
= $false )
| ( ( number_ring @ SV80 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1242]) ).
thf(1302,plain,
! [SV81: $i] :
( ( ( ! [SY309: $i,SY310: $i] :
( ~ ( ord_less @ SV81 @ ( number_number_of @ SV81 @ SY309 ) @ ( number_number_of @ SV81 @ SY310 ) )
| ( ord_less @ int @ SY309 @ SY310 ) ) )
= $true )
| ( ( linordered_idom @ SV81 )
= $false )
| ( ( number_ring @ SV81 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1243]) ).
thf(1303,plain,
! [SV81: $i] :
( ( ( ! [SY311: $i,SY312: $i] :
( ~ ( ord_less @ int @ SY311 @ SY312 )
| ( ord_less @ SV81 @ ( number_number_of @ SV81 @ SY311 ) @ ( number_number_of @ SV81 @ SY312 ) ) ) )
= $true )
| ( ( linordered_idom @ SV81 )
= $false )
| ( ( number_ring @ SV81 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1244]) ).
thf(1304,plain,
! [SV233: $i,SV82: $i] :
( ( ( ~ ( ord_less @ SV82 @ ( plus_plus @ SV82 @ SV233 @ SV233 ) @ ( zero_zero @ SV82 ) ) )
= $true )
| ( ( ord_less @ SV82 @ SV233 @ ( zero_zero @ SV82 ) )
= $true )
| ( ( linordered_idom @ SV82 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1249]) ).
thf(1305,plain,
! [SV234: $i,SV82: $i] :
( ( ( ~ ( ord_less @ SV82 @ SV234 @ ( zero_zero @ SV82 ) ) )
= $true )
| ( ( ord_less @ SV82 @ ( plus_plus @ SV82 @ SV234 @ SV234 ) @ ( zero_zero @ SV82 ) )
= $true )
| ( ( linordered_idom @ SV82 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1250]) ).
thf(1306,plain,
! [SV83: $i] :
( ( ( ! [SY315: $i] :
( ( ( number_number_of @ nat @ SY315 )
!= ( zero_zero @ nat ) )
| ( ( power_power @ SV83 @ ( zero_zero @ SV83 ) @ ( number_number_of @ nat @ SY315 ) )
= ( one_one @ SV83 ) ) ) )
= $true )
| ( ( power @ SV83 )
= $false )
| ( ( semiring_0 @ SV83 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1251]) ).
thf(1307,plain,
! [SV83: $i] :
( ( ( ! [SY316: $i] :
( ( ( number_number_of @ nat @ SY316 )
= ( zero_zero @ nat ) )
| ( ( power_power @ SV83 @ ( zero_zero @ SV83 ) @ ( number_number_of @ nat @ SY316 ) )
= ( zero_zero @ SV83 ) ) ) )
= $true )
| ( ( power @ SV83 )
= $false )
| ( ( semiring_0 @ SV83 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1252]) ).
thf(1308,plain,
! [SV235: $i,SV247: $i] :
( ( ( ord_less @ int @ SV247 @ pls )
| ~ ( ord_less @ int @ SV235 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV247 ) @ ( number_number_of @ nat @ SV235 ) )
= ( number_number_of @ nat @ SV247 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1254]) ).
thf(1309,plain,
! [SV236: $i,SV248: $i] :
( ( ( ord_less @ int @ SV248 @ pls )
| ( ord_less @ int @ SV236 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV248 ) @ ( number_number_of @ nat @ SV236 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SV248 @ SV236 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1255]) ).
thf(1310,plain,
! [SV249: $i,SV237: $i,SV84: $i] :
( ( ( ( ( number_number_of @ SV84 @ SV237 )
!= ( ti @ SV84 @ SV249 ) )
| ( ( ti @ SV84 @ SV249 )
= ( number_number_of @ SV84 @ SV237 ) ) )
= $true )
| ( ( number @ SV84 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1260]) ).
thf(1311,plain,
! [SV238: $i,SV250: $i,SV84: $i] :
( ( ( ( ( ti @ SV84 @ SV250 )
!= ( number_number_of @ SV84 @ SV238 ) )
| ( ( number_number_of @ SV84 @ SV238 )
= ( ti @ SV84 @ SV250 ) ) )
= $true )
| ( ( number @ SV84 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1261]) ).
thf(1312,plain,
! [SV239: $i,SV85: $i] :
( ( ( ( ti @ SV85 @ SV239 )
= ( zero_zero @ SV85 ) )
= $true )
| ( ( ord_less @ SV85 @ ( zero_zero @ SV85 ) @ ( power_power @ SV85 @ SV239 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $true )
| ( ( linordered_idom @ SV85 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1262]) ).
thf(1313,plain,
! [SV240: $i,SV85: $i] :
( ( ( ~ ( ord_less @ SV85 @ ( zero_zero @ SV85 ) @ ( power_power @ SV85 @ SV240 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true )
| ( ( ( ( ti @ SV85 @ SV240 )
!= ( zero_zero @ SV85 ) ) )
= $true )
| ( ( linordered_idom @ SV85 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1263]) ).
thf(1314,plain,
! [SV241: $i,SV86: $i] :
( ( ( ( ( power_power @ SV86 @ SV241 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= ( zero_zero @ SV86 ) ) )
= $true )
| ( ( ( ti @ SV86 @ SV241 )
= ( zero_zero @ SV86 ) )
= $true )
| ( ( ring_11004092258visors @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1266]) ).
thf(1315,plain,
! [SV242: $i,SV86: $i] :
( ( ( ( ( ti @ SV86 @ SV242 )
!= ( zero_zero @ SV86 ) ) )
= $true )
| ( ( ( power_power @ SV86 @ SV242 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SV86 ) )
= $true )
| ( ( ring_11004092258visors @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1267]) ).
thf(1316,plain,
! [SV87: $i] :
( ( ( ! [SY325: $i] :
( ~ ( ord_less @ SV87 @ ( one_one @ SV87 ) @ ( number_number_of @ SV87 @ SY325 ) )
| ( ord_less @ int @ ( bit1 @ pls ) @ SY325 ) ) )
= $true )
| ( ( linordered_idom @ SV87 )
= $false )
| ( ( number_ring @ SV87 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1268]) ).
thf(1317,plain,
! [SV87: $i] :
( ( ( ! [SY326: $i] :
( ~ ( ord_less @ int @ ( bit1 @ pls ) @ SY326 )
| ( ord_less @ SV87 @ ( one_one @ SV87 ) @ ( number_number_of @ SV87 @ SY326 ) ) ) )
= $true )
| ( ( linordered_idom @ SV87 )
= $false )
| ( ( number_ring @ SV87 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1269]) ).
thf(1318,plain,
! [SV61: $i] :
( ( ( zero_neq_one @ SV61 )
= $false )
| ( ( power @ SV61 )
= $false )
| ( ( mult_zero @ SV61 )
= $false )
| ( ( no_zero_divisors @ SV61 )
= $false )
| ( ( ( ti @ SV61 @ ( zero_zero @ SV61 ) )
= ( zero_zero @ SV61 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1274]) ).
thf(1319,plain,
! [SV113: $i,SV64: $i,SV130: $i] :
( ( ( power @ SV130 )
= $false )
| ( ( mult_zero @ SV130 )
= $false )
| ( ( ~ ( no_zero_divisors @ SV130 ) )
= $true )
| ( ( ~ ( zero_neq_one @ SV130 ) )
= $true )
| ( ( ( power_power @ SV130 @ ( ti @ SV130 @ SV64 ) @ SV113 )
= ( power_power @ SV130 @ SV64 @ SV113 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1275]) ).
thf(1320,plain,
! [SV114: $i,SV65: $i,SV131: $i] :
( ( ( power @ SV131 )
= $false )
| ( ( mult_zero @ SV131 )
= $false )
| ( ( ~ ( no_zero_divisors @ SV131 ) )
= $true )
| ( ( ~ ( zero_neq_one @ SV131 ) )
= $true )
| ( ( ( power_power @ SV131 @ SV65 @ ( ti @ nat @ SV114 ) )
= ( power_power @ SV131 @ SV65 @ SV114 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1276]) ).
thf(1321,plain,
! [SV115: $i,SV66: $i,SV132: $i] :
( ( ( power @ SV132 )
= $false )
| ( ( mult_zero @ SV132 )
= $false )
| ( ( ~ ( no_zero_divisors @ SV132 ) )
= $true )
| ( ( ~ ( zero_neq_one @ SV132 ) )
= $true )
| ( ( ( ti @ SV132 @ ( power_power @ SV132 @ SV66 @ SV115 ) )
= ( power_power @ SV132 @ SV66 @ SV115 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1277]) ).
thf(1322,plain,
! [SV251: $i,SV71: $i] :
( ( ( ! [SY386: $i] :
( ( ( number_number_of @ SV71 @ SV251 )
!= ( number_number_of @ SV71 @ SY386 ) )
| ( SV251 = SY386 ) ) )
= $true )
| ( ( number_ring @ SV71 )
= $false )
| ( ( ring_char_0 @ SV71 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1278]) ).
thf(1323,plain,
! [SV71: $i,SV252: $i] :
( ( ( ! [SY387: $i] :
( ( SV252 != SY387 )
| ( ( number_number_of @ SV71 @ SV252 )
= ( number_number_of @ SV71 @ SY387 ) ) ) )
= $true )
| ( ( number_ring @ SV71 )
= $false )
| ( ( ring_char_0 @ SV71 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1279]) ).
thf(1324,plain,
! [SV192: $i,SV72: $i,SV223: $i] :
( ( ( ~ ( ord_less @ SV223 @ ( ti @ SV223 @ SV72 ) @ SV192 ) )
= $true )
| ( ( ord_less @ SV223 @ SV72 @ SV192 )
= $true )
| ( ( linordered_idom @ SV223 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1280]) ).
thf(1325,plain,
! [SV193: $i,SV72: $i,SV224: $i] :
( ( ( ~ ( ord_less @ SV224 @ SV72 @ SV193 ) )
= $true )
| ( ( ord_less @ SV224 @ ( ti @ SV224 @ SV72 ) @ SV193 )
= $true )
| ( ( linordered_idom @ SV224 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1281]) ).
thf(1326,plain,
! [SV243: $i,SV227: $i] :
( ( ( ( SV227 != SV243 ) )
= $true )
| ( ( ord_less @ int @ SV227 @ ( plus_plus @ int @ SV243 @ ( one_one @ int ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1283]) ).
thf(1327,plain,
! [SV244: $i,SV228: $i] :
( ( ( ~ ( ord_less @ int @ SV228 @ SV244 ) )
= $true )
| ( ( ord_less @ int @ SV228 @ ( plus_plus @ int @ SV244 @ ( one_one @ int ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1284]) ).
thf(1328,plain,
! [SV245: $i,SV229: $i,SV73: $i] :
( ( ( ( ( ti @ SV73 @ SV229 )
!= ( zero_zero @ SV73 ) )
| ( ( ti @ SV73 @ SV245 )
!= ( zero_zero @ SV73 ) ) )
= $true )
| ( ( ( plus_plus @ SV73 @ ( power_power @ SV73 @ SV229 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV73 @ SV245 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV73 ) )
= $true )
| ( ( linordered_idom @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1285]) ).
thf(1329,plain,
! [SV73: $i] :
( ( ( ! [SY281: $i] :
( ! [SY282: $i] :
( ( plus_plus @ SV73 @ ( power_power @ SV73 @ SY281 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV73 @ SY282 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV73 ) )
| ( ( ti @ SV73 @ SY281 )
= ( zero_zero @ SV73 ) ) ) )
= $true )
| ( ( linordered_idom @ SV73 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1286]) ).
thf(1330,plain,
! [SV73: $i] :
( ( ( ! [SY283: $i,SY284: $i] :
( ( ( plus_plus @ SV73 @ ( power_power @ SV73 @ SY283 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV73 @ SY284 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV73 ) )
| ( ( ti @ SV73 @ SY284 )
= ( zero_zero @ SV73 ) ) ) )
= $true )
| ( ( linordered_idom @ SV73 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1287]) ).
thf(1331,plain,
! [SV246: $i,SV230: $i,SV74: $i] :
( ( ( ~ ( ord_less @ SV74 @ ( zero_zero @ SV74 ) @ ( plus_plus @ SV74 @ ( power_power @ SV74 @ SV230 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV74 @ SV246 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true )
| ( ( ( ( ti @ SV74 @ SV230 )
!= ( zero_zero @ SV74 ) )
| ( ( ti @ SV74 @ SV246 )
!= ( zero_zero @ SV74 ) ) )
= $true )
| ( ( linordered_idom @ SV74 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1288]) ).
thf(1332,plain,
! [SV74: $i] :
( ( ( ! [SY287: $i] :
( ( ( ti @ SV74 @ SY287 )
= ( zero_zero @ SV74 ) )
| ! [SY288: $i] : ( ord_less @ SV74 @ ( zero_zero @ SV74 ) @ ( plus_plus @ SV74 @ ( power_power @ SV74 @ SY287 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV74 @ SY288 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) )
= $true )
| ( ( linordered_idom @ SV74 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1289]) ).
thf(1333,plain,
! [SV74: $i] :
( ( ( ! [SY289: $i,SY290: $i] :
( ( ( ti @ SV74 @ SY290 )
= ( zero_zero @ SV74 ) )
| ( ord_less @ SV74 @ ( zero_zero @ SV74 ) @ ( plus_plus @ SV74 @ ( power_power @ SV74 @ SY289 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV74 @ SY290 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) )
= $true )
| ( ( linordered_idom @ SV74 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1290]) ).
thf(1334,plain,
! [SV253: $i,SV75: $i] :
( ( ( ~ ( ord_less @ SV75 @ ( number_number_of @ SV75 @ SV253 ) @ ( one_one @ SV75 ) )
| ( ord_less @ int @ SV253 @ ( bit1 @ pls ) ) )
= $true )
| ( ( linordered_idom @ SV75 )
= $false )
| ( ( number_ring @ SV75 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1291]) ).
thf(1335,plain,
! [SV75: $i,SV254: $i] :
( ( ( ~ ( ord_less @ int @ SV254 @ ( bit1 @ pls ) )
| ( ord_less @ SV75 @ ( number_number_of @ SV75 @ SV254 ) @ ( one_one @ SV75 ) ) )
= $true )
| ( ( linordered_idom @ SV75 )
= $false )
| ( ( number_ring @ SV75 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1292]) ).
thf(1336,plain,
! [SV255: $i,SV76: $i] :
( ( ( ~ ( ord_less @ SV76 @ ( zero_zero @ SV76 ) @ ( number_number_of @ SV76 @ SV255 ) )
| ( ord_less @ int @ pls @ SV255 ) )
= $true )
| ( ( linordered_idom @ SV76 )
= $false )
| ( ( number_ring @ SV76 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1293]) ).
thf(1337,plain,
! [SV76: $i,SV256: $i] :
( ( ( ~ ( ord_less @ int @ pls @ SV256 )
| ( ord_less @ SV76 @ ( zero_zero @ SV76 ) @ ( number_number_of @ SV76 @ SV256 ) ) )
= $true )
| ( ( linordered_idom @ SV76 )
= $false )
| ( ( number_ring @ SV76 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1294]) ).
thf(1338,plain,
! [SV77: $i] :
( ( ( zero_neq_one @ SV77 )
= $false )
| ( ( power @ SV77 )
= $false )
| ( ( mult_zero @ SV77 )
= $false )
| ( ( no_zero_divisors @ SV77 )
= $false )
| ( ( ~ ( ~ ! [SY295: $i,SY296: $i] :
( ( ( number_number_of @ nat @ SY296 )
= ( zero_zero @ nat ) )
| ( ( ti @ SV77 @ SY295 )
!= ( zero_zero @ SV77 ) )
| ( ( power_power @ SV77 @ SY295 @ ( number_number_of @ nat @ SY296 ) )
= ( zero_zero @ SV77 ) ) )
| ~ ~ ( ~ ! [SY297: $i,SY298: $i] :
( ( ( power_power @ SV77 @ SY297 @ ( number_number_of @ nat @ SY298 ) )
!= ( zero_zero @ SV77 ) )
| ( ( number_number_of @ nat @ SY298 )
!= ( zero_zero @ nat ) ) )
| ~ ! [SY299: $i] :
( ! [SY300: $i] :
( ( power_power @ SV77 @ SY299 @ ( number_number_of @ nat @ SY300 ) )
!= ( zero_zero @ SV77 ) )
| ( ( ti @ SV77 @ SY299 )
= ( zero_zero @ SV77 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1295]) ).
thf(1339,plain,
! [SV201: $i,SV78: $i,SV225: $i] :
( ( ( ~ ( ord_less @ SV225 @ SV78 @ ( ti @ SV225 @ SV201 ) ) )
= $true )
| ( ( ord_less @ SV225 @ SV78 @ SV201 )
= $true )
| ( ( linordered_idom @ SV225 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1296]) ).
thf(1340,plain,
! [SV202: $i,SV78: $i,SV226: $i] :
( ( ( ~ ( ord_less @ SV226 @ SV78 @ SV202 ) )
= $true )
| ( ( ord_less @ SV226 @ SV78 @ ( ti @ SV226 @ SV202 ) )
= $true )
| ( ( linordered_idom @ SV226 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1297]) ).
thf(1341,plain,
! [SV231: $i,SV79: $i] :
( ( ( ( plus_plus @ SV79 @ SV231 @ SV231 )
= ( zero_zero @ SV79 ) )
= $false )
| ( ( ( ti @ SV79 @ SV231 )
= ( zero_zero @ SV79 ) )
= $true )
| ( ( linord219039673up_add @ SV79 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1298]) ).
thf(1342,plain,
! [SV232: $i,SV79: $i] :
( ( ( ( ti @ SV79 @ SV232 )
= ( zero_zero @ SV79 ) )
= $false )
| ( ( ( plus_plus @ SV79 @ SV232 @ SV232 )
= ( zero_zero @ SV79 ) )
= $true )
| ( ( linord219039673up_add @ SV79 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1299]) ).
thf(1343,plain,
! [SV257: $i,SV80: $i] :
( ( ( ~ ( ord_less @ SV80 @ ( number_number_of @ SV80 @ SV257 ) @ ( zero_zero @ SV80 ) )
| ( ord_less @ int @ SV257 @ pls ) )
= $true )
| ( ( linordered_idom @ SV80 )
= $false )
| ( ( number_ring @ SV80 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1300]) ).
thf(1344,plain,
! [SV80: $i,SV258: $i] :
( ( ( ~ ( ord_less @ int @ SV258 @ pls )
| ( ord_less @ SV80 @ ( number_number_of @ SV80 @ SV258 ) @ ( zero_zero @ SV80 ) ) )
= $true )
| ( ( linordered_idom @ SV80 )
= $false )
| ( ( number_ring @ SV80 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1301]) ).
thf(1345,plain,
! [SV259: $i,SV81: $i] :
( ( ( ! [SY388: $i] :
( ~ ( ord_less @ SV81 @ ( number_number_of @ SV81 @ SV259 ) @ ( number_number_of @ SV81 @ SY388 ) )
| ( ord_less @ int @ SV259 @ SY388 ) ) )
= $true )
| ( ( linordered_idom @ SV81 )
= $false )
| ( ( number_ring @ SV81 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1302]) ).
thf(1346,plain,
! [SV81: $i,SV260: $i] :
( ( ( ! [SY389: $i] :
( ~ ( ord_less @ int @ SV260 @ SY389 )
| ( ord_less @ SV81 @ ( number_number_of @ SV81 @ SV260 ) @ ( number_number_of @ SV81 @ SY389 ) ) ) )
= $true )
| ( ( linordered_idom @ SV81 )
= $false )
| ( ( number_ring @ SV81 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1303]) ).
thf(1347,plain,
! [SV233: $i,SV82: $i] :
( ( ( ord_less @ SV82 @ ( plus_plus @ SV82 @ SV233 @ SV233 ) @ ( zero_zero @ SV82 ) )
= $false )
| ( ( ord_less @ SV82 @ SV233 @ ( zero_zero @ SV82 ) )
= $true )
| ( ( linordered_idom @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1304]) ).
thf(1348,plain,
! [SV234: $i,SV82: $i] :
( ( ( ord_less @ SV82 @ SV234 @ ( zero_zero @ SV82 ) )
= $false )
| ( ( ord_less @ SV82 @ ( plus_plus @ SV82 @ SV234 @ SV234 ) @ ( zero_zero @ SV82 ) )
= $true )
| ( ( linordered_idom @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1305]) ).
thf(1349,plain,
! [SV83: $i,SV261: $i] :
( ( ( ( ( number_number_of @ nat @ SV261 )
!= ( zero_zero @ nat ) )
| ( ( power_power @ SV83 @ ( zero_zero @ SV83 ) @ ( number_number_of @ nat @ SV261 ) )
= ( one_one @ SV83 ) ) )
= $true )
| ( ( power @ SV83 )
= $false )
| ( ( semiring_0 @ SV83 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1306]) ).
thf(1350,plain,
! [SV83: $i,SV262: $i] :
( ( ( ( ( number_number_of @ nat @ SV262 )
= ( zero_zero @ nat ) )
| ( ( power_power @ SV83 @ ( zero_zero @ SV83 ) @ ( number_number_of @ nat @ SV262 ) )
= ( zero_zero @ SV83 ) ) )
= $true )
| ( ( power @ SV83 )
= $false )
| ( ( semiring_0 @ SV83 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1307]) ).
thf(1351,plain,
! [SV235: $i,SV247: $i] :
( ( ( ord_less @ int @ SV247 @ pls )
= $true )
| ( ( ~ ( ord_less @ int @ SV235 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV247 ) @ ( number_number_of @ nat @ SV235 ) )
= ( number_number_of @ nat @ SV247 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1308]) ).
thf(1352,plain,
! [SV236: $i,SV248: $i] :
( ( ( ord_less @ int @ SV248 @ pls )
= $true )
| ( ( ( ord_less @ int @ SV236 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV248 ) @ ( number_number_of @ nat @ SV236 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SV248 @ SV236 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1309]) ).
thf(1353,plain,
! [SV249: $i,SV237: $i,SV84: $i] :
( ( ( ( ( number_number_of @ SV84 @ SV237 )
!= ( ti @ SV84 @ SV249 ) ) )
= $true )
| ( ( ( ti @ SV84 @ SV249 )
= ( number_number_of @ SV84 @ SV237 ) )
= $true )
| ( ( number @ SV84 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1310]) ).
thf(1354,plain,
! [SV238: $i,SV250: $i,SV84: $i] :
( ( ( ( ( ti @ SV84 @ SV250 )
!= ( number_number_of @ SV84 @ SV238 ) ) )
= $true )
| ( ( ( number_number_of @ SV84 @ SV238 )
= ( ti @ SV84 @ SV250 ) )
= $true )
| ( ( number @ SV84 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1311]) ).
thf(1355,plain,
! [SV240: $i,SV85: $i] :
( ( ( ord_less @ SV85 @ ( zero_zero @ SV85 ) @ ( power_power @ SV85 @ SV240 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $false )
| ( ( ( ( ti @ SV85 @ SV240 )
!= ( zero_zero @ SV85 ) ) )
= $true )
| ( ( linordered_idom @ SV85 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1313]) ).
thf(1356,plain,
! [SV241: $i,SV86: $i] :
( ( ( ( power_power @ SV86 @ SV241 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SV86 ) )
= $false )
| ( ( ( ti @ SV86 @ SV241 )
= ( zero_zero @ SV86 ) )
= $true )
| ( ( ring_11004092258visors @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1314]) ).
thf(1357,plain,
! [SV242: $i,SV86: $i] :
( ( ( ( ti @ SV86 @ SV242 )
= ( zero_zero @ SV86 ) )
= $false )
| ( ( ( power_power @ SV86 @ SV242 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SV86 ) )
= $true )
| ( ( ring_11004092258visors @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1315]) ).
thf(1358,plain,
! [SV263: $i,SV87: $i] :
( ( ( ~ ( ord_less @ SV87 @ ( one_one @ SV87 ) @ ( number_number_of @ SV87 @ SV263 ) )
| ( ord_less @ int @ ( bit1 @ pls ) @ SV263 ) )
= $true )
| ( ( linordered_idom @ SV87 )
= $false )
| ( ( number_ring @ SV87 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1316]) ).
thf(1359,plain,
! [SV87: $i,SV264: $i] :
( ( ( ~ ( ord_less @ int @ ( bit1 @ pls ) @ SV264 )
| ( ord_less @ SV87 @ ( one_one @ SV87 ) @ ( number_number_of @ SV87 @ SV264 ) ) )
= $true )
| ( ( linordered_idom @ SV87 )
= $false )
| ( ( number_ring @ SV87 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1317]) ).
thf(1360,plain,
! [SV113: $i,SV64: $i,SV130: $i] :
( ( ( no_zero_divisors @ SV130 )
= $false )
| ( ( mult_zero @ SV130 )
= $false )
| ( ( power @ SV130 )
= $false )
| ( ( ~ ( zero_neq_one @ SV130 ) )
= $true )
| ( ( ( power_power @ SV130 @ ( ti @ SV130 @ SV64 ) @ SV113 )
= ( power_power @ SV130 @ SV64 @ SV113 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1319]) ).
thf(1361,plain,
! [SV114: $i,SV65: $i,SV131: $i] :
( ( ( no_zero_divisors @ SV131 )
= $false )
| ( ( mult_zero @ SV131 )
= $false )
| ( ( power @ SV131 )
= $false )
| ( ( ~ ( zero_neq_one @ SV131 ) )
= $true )
| ( ( ( power_power @ SV131 @ SV65 @ ( ti @ nat @ SV114 ) )
= ( power_power @ SV131 @ SV65 @ SV114 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1320]) ).
thf(1362,plain,
! [SV115: $i,SV66: $i,SV132: $i] :
( ( ( no_zero_divisors @ SV132 )
= $false )
| ( ( mult_zero @ SV132 )
= $false )
| ( ( power @ SV132 )
= $false )
| ( ( ~ ( zero_neq_one @ SV132 ) )
= $true )
| ( ( ( ti @ SV132 @ ( power_power @ SV132 @ SV66 @ SV115 ) )
= ( power_power @ SV132 @ SV66 @ SV115 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1321]) ).
thf(1363,plain,
! [SV265: $i,SV251: $i,SV71: $i] :
( ( ( ( ( number_number_of @ SV71 @ SV251 )
!= ( number_number_of @ SV71 @ SV265 ) )
| ( SV251 = SV265 ) )
= $true )
| ( ( number_ring @ SV71 )
= $false )
| ( ( ring_char_0 @ SV71 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1322]) ).
thf(1364,plain,
! [SV71: $i,SV266: $i,SV252: $i] :
( ( ( ( SV252 != SV266 )
| ( ( number_number_of @ SV71 @ SV252 )
= ( number_number_of @ SV71 @ SV266 ) ) )
= $true )
| ( ( number_ring @ SV71 )
= $false )
| ( ( ring_char_0 @ SV71 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1323]) ).
thf(1365,plain,
! [SV192: $i,SV72: $i,SV223: $i] :
( ( ( ord_less @ SV223 @ ( ti @ SV223 @ SV72 ) @ SV192 )
= $false )
| ( ( ord_less @ SV223 @ SV72 @ SV192 )
= $true )
| ( ( linordered_idom @ SV223 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1324]) ).
thf(1366,plain,
! [SV193: $i,SV72: $i,SV224: $i] :
( ( ( ord_less @ SV224 @ SV72 @ SV193 )
= $false )
| ( ( ord_less @ SV224 @ ( ti @ SV224 @ SV72 ) @ SV193 )
= $true )
| ( ( linordered_idom @ SV224 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1325]) ).
thf(1367,plain,
! [SV243: $i,SV227: $i] :
( ( ( SV227 = SV243 )
= $false )
| ( ( ord_less @ int @ SV227 @ ( plus_plus @ int @ SV243 @ ( one_one @ int ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1326]) ).
thf(1368,plain,
! [SV244: $i,SV228: $i] :
( ( ( ord_less @ int @ SV228 @ SV244 )
= $false )
| ( ( ord_less @ int @ SV228 @ ( plus_plus @ int @ SV244 @ ( one_one @ int ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1327]) ).
thf(1369,plain,
! [SV245: $i,SV229: $i,SV73: $i] :
( ( ( ( ( ti @ SV73 @ SV229 )
!= ( zero_zero @ SV73 ) ) )
= $true )
| ( ( ( ( ti @ SV73 @ SV245 )
!= ( zero_zero @ SV73 ) ) )
= $true )
| ( ( ( plus_plus @ SV73 @ ( power_power @ SV73 @ SV229 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV73 @ SV245 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV73 ) )
= $true )
| ( ( linordered_idom @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1328]) ).
thf(1370,plain,
! [SV267: $i,SV73: $i] :
( ( ( ! [SY390: $i] :
( ( plus_plus @ SV73 @ ( power_power @ SV73 @ SV267 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV73 @ SY390 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV73 ) )
| ( ( ti @ SV73 @ SV267 )
= ( zero_zero @ SV73 ) ) )
= $true )
| ( ( linordered_idom @ SV73 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1329]) ).
thf(1371,plain,
! [SV268: $i,SV73: $i] :
( ( ( ! [SY391: $i] :
( ( ( plus_plus @ SV73 @ ( power_power @ SV73 @ SV268 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV73 @ SY391 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV73 ) )
| ( ( ti @ SV73 @ SY391 )
= ( zero_zero @ SV73 ) ) ) )
= $true )
| ( ( linordered_idom @ SV73 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1330]) ).
thf(1372,plain,
! [SV246: $i,SV230: $i,SV74: $i] :
( ( ( ord_less @ SV74 @ ( zero_zero @ SV74 ) @ ( plus_plus @ SV74 @ ( power_power @ SV74 @ SV230 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV74 @ SV246 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $false )
| ( ( ( ( ti @ SV74 @ SV230 )
!= ( zero_zero @ SV74 ) )
| ( ( ti @ SV74 @ SV246 )
!= ( zero_zero @ SV74 ) ) )
= $true )
| ( ( linordered_idom @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1331]) ).
thf(1373,plain,
! [SV269: $i,SV74: $i] :
( ( ( ( ( ti @ SV74 @ SV269 )
= ( zero_zero @ SV74 ) )
| ! [SY392: $i] : ( ord_less @ SV74 @ ( zero_zero @ SV74 ) @ ( plus_plus @ SV74 @ ( power_power @ SV74 @ SV269 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV74 @ SY392 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true )
| ( ( linordered_idom @ SV74 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1332]) ).
thf(1374,plain,
! [SV270: $i,SV74: $i] :
( ( ( ! [SY393: $i] :
( ( ( ti @ SV74 @ SY393 )
= ( zero_zero @ SV74 ) )
| ( ord_less @ SV74 @ ( zero_zero @ SV74 ) @ ( plus_plus @ SV74 @ ( power_power @ SV74 @ SV270 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV74 @ SY393 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) )
= $true )
| ( ( linordered_idom @ SV74 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1333]) ).
thf(1375,plain,
! [SV253: $i,SV75: $i] :
( ( ( ~ ( ord_less @ SV75 @ ( number_number_of @ SV75 @ SV253 ) @ ( one_one @ SV75 ) ) )
= $true )
| ( ( ord_less @ int @ SV253 @ ( bit1 @ pls ) )
= $true )
| ( ( linordered_idom @ SV75 )
= $false )
| ( ( number_ring @ SV75 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1334]) ).
thf(1376,plain,
! [SV75: $i,SV254: $i] :
( ( ( ~ ( ord_less @ int @ SV254 @ ( bit1 @ pls ) ) )
= $true )
| ( ( ord_less @ SV75 @ ( number_number_of @ SV75 @ SV254 ) @ ( one_one @ SV75 ) )
= $true )
| ( ( linordered_idom @ SV75 )
= $false )
| ( ( number_ring @ SV75 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1335]) ).
thf(1377,plain,
! [SV255: $i,SV76: $i] :
( ( ( ~ ( ord_less @ SV76 @ ( zero_zero @ SV76 ) @ ( number_number_of @ SV76 @ SV255 ) ) )
= $true )
| ( ( ord_less @ int @ pls @ SV255 )
= $true )
| ( ( linordered_idom @ SV76 )
= $false )
| ( ( number_ring @ SV76 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1336]) ).
thf(1378,plain,
! [SV76: $i,SV256: $i] :
( ( ( ~ ( ord_less @ int @ pls @ SV256 ) )
= $true )
| ( ( ord_less @ SV76 @ ( zero_zero @ SV76 ) @ ( number_number_of @ SV76 @ SV256 ) )
= $true )
| ( ( linordered_idom @ SV76 )
= $false )
| ( ( number_ring @ SV76 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1337]) ).
thf(1379,plain,
! [SV77: $i] :
( ( ( ~ ! [SY295: $i,SY296: $i] :
( ( ( number_number_of @ nat @ SY296 )
= ( zero_zero @ nat ) )
| ( ( ti @ SV77 @ SY295 )
!= ( zero_zero @ SV77 ) )
| ( ( power_power @ SV77 @ SY295 @ ( number_number_of @ nat @ SY296 ) )
= ( zero_zero @ SV77 ) ) )
| ~ ~ ( ~ ! [SY297: $i,SY298: $i] :
( ( ( power_power @ SV77 @ SY297 @ ( number_number_of @ nat @ SY298 ) )
!= ( zero_zero @ SV77 ) )
| ( ( number_number_of @ nat @ SY298 )
!= ( zero_zero @ nat ) ) )
| ~ ! [SY299: $i] :
( ! [SY300: $i] :
( ( power_power @ SV77 @ SY299 @ ( number_number_of @ nat @ SY300 ) )
!= ( zero_zero @ SV77 ) )
| ( ( ti @ SV77 @ SY299 )
= ( zero_zero @ SV77 ) ) ) ) )
= $false )
| ( ( no_zero_divisors @ SV77 )
= $false )
| ( ( mult_zero @ SV77 )
= $false )
| ( ( power @ SV77 )
= $false )
| ( ( zero_neq_one @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1338]) ).
thf(1380,plain,
! [SV201: $i,SV78: $i,SV225: $i] :
( ( ( ord_less @ SV225 @ SV78 @ ( ti @ SV225 @ SV201 ) )
= $false )
| ( ( ord_less @ SV225 @ SV78 @ SV201 )
= $true )
| ( ( linordered_idom @ SV225 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1339]) ).
thf(1381,plain,
! [SV202: $i,SV78: $i,SV226: $i] :
( ( ( ord_less @ SV226 @ SV78 @ SV202 )
= $false )
| ( ( ord_less @ SV226 @ SV78 @ ( ti @ SV226 @ SV202 ) )
= $true )
| ( ( linordered_idom @ SV226 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1340]) ).
thf(1382,plain,
! [SV257: $i,SV80: $i] :
( ( ( ~ ( ord_less @ SV80 @ ( number_number_of @ SV80 @ SV257 ) @ ( zero_zero @ SV80 ) ) )
= $true )
| ( ( ord_less @ int @ SV257 @ pls )
= $true )
| ( ( linordered_idom @ SV80 )
= $false )
| ( ( number_ring @ SV80 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1343]) ).
thf(1383,plain,
! [SV80: $i,SV258: $i] :
( ( ( ~ ( ord_less @ int @ SV258 @ pls ) )
= $true )
| ( ( ord_less @ SV80 @ ( number_number_of @ SV80 @ SV258 ) @ ( zero_zero @ SV80 ) )
= $true )
| ( ( linordered_idom @ SV80 )
= $false )
| ( ( number_ring @ SV80 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1344]) ).
thf(1384,plain,
! [SV271: $i,SV259: $i,SV81: $i] :
( ( ( ~ ( ord_less @ SV81 @ ( number_number_of @ SV81 @ SV259 ) @ ( number_number_of @ SV81 @ SV271 ) )
| ( ord_less @ int @ SV259 @ SV271 ) )
= $true )
| ( ( linordered_idom @ SV81 )
= $false )
| ( ( number_ring @ SV81 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1345]) ).
thf(1385,plain,
! [SV81: $i,SV272: $i,SV260: $i] :
( ( ( ~ ( ord_less @ int @ SV260 @ SV272 )
| ( ord_less @ SV81 @ ( number_number_of @ SV81 @ SV260 ) @ ( number_number_of @ SV81 @ SV272 ) ) )
= $true )
| ( ( linordered_idom @ SV81 )
= $false )
| ( ( number_ring @ SV81 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1346]) ).
thf(1386,plain,
! [SV83: $i,SV261: $i] :
( ( ( ( ( number_number_of @ nat @ SV261 )
!= ( zero_zero @ nat ) ) )
= $true )
| ( ( ( power_power @ SV83 @ ( zero_zero @ SV83 ) @ ( number_number_of @ nat @ SV261 ) )
= ( one_one @ SV83 ) )
= $true )
| ( ( power @ SV83 )
= $false )
| ( ( semiring_0 @ SV83 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1349]) ).
thf(1387,plain,
! [SV83: $i,SV262: $i] :
( ( ( ( number_number_of @ nat @ SV262 )
= ( zero_zero @ nat ) )
= $true )
| ( ( ( power_power @ SV83 @ ( zero_zero @ SV83 ) @ ( number_number_of @ nat @ SV262 ) )
= ( zero_zero @ SV83 ) )
= $true )
| ( ( power @ SV83 )
= $false )
| ( ( semiring_0 @ SV83 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1350]) ).
thf(1388,plain,
! [SV247: $i,SV235: $i] :
( ( ( ~ ( ord_less @ int @ SV235 @ pls ) )
= $true )
| ( ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV247 ) @ ( number_number_of @ nat @ SV235 ) )
= ( number_number_of @ nat @ SV247 ) )
= $true )
| ( ( ord_less @ int @ SV247 @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1351]) ).
thf(1389,plain,
! [SV248: $i,SV236: $i] :
( ( ( ord_less @ int @ SV236 @ pls )
= $true )
| ( ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV248 ) @ ( number_number_of @ nat @ SV236 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SV248 @ SV236 ) ) )
= $true )
| ( ( ord_less @ int @ SV248 @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1352]) ).
thf(1390,plain,
! [SV249: $i,SV237: $i,SV84: $i] :
( ( ( ( number_number_of @ SV84 @ SV237 )
= ( ti @ SV84 @ SV249 ) )
= $false )
| ( ( ( ti @ SV84 @ SV249 )
= ( number_number_of @ SV84 @ SV237 ) )
= $true )
| ( ( number @ SV84 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1353]) ).
thf(1391,plain,
! [SV238: $i,SV250: $i,SV84: $i] :
( ( ( ( ti @ SV84 @ SV250 )
= ( number_number_of @ SV84 @ SV238 ) )
= $false )
| ( ( ( number_number_of @ SV84 @ SV238 )
= ( ti @ SV84 @ SV250 ) )
= $true )
| ( ( number @ SV84 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1354]) ).
thf(1392,plain,
! [SV240: $i,SV85: $i] :
( ( ( ( ti @ SV85 @ SV240 )
= ( zero_zero @ SV85 ) )
= $false )
| ( ( ord_less @ SV85 @ ( zero_zero @ SV85 ) @ ( power_power @ SV85 @ SV240 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $false )
| ( ( linordered_idom @ SV85 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1355]) ).
thf(1393,plain,
! [SV263: $i,SV87: $i] :
( ( ( ~ ( ord_less @ SV87 @ ( one_one @ SV87 ) @ ( number_number_of @ SV87 @ SV263 ) ) )
= $true )
| ( ( ord_less @ int @ ( bit1 @ pls ) @ SV263 )
= $true )
| ( ( linordered_idom @ SV87 )
= $false )
| ( ( number_ring @ SV87 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1358]) ).
thf(1394,plain,
! [SV87: $i,SV264: $i] :
( ( ( ~ ( ord_less @ int @ ( bit1 @ pls ) @ SV264 ) )
= $true )
| ( ( ord_less @ SV87 @ ( one_one @ SV87 ) @ ( number_number_of @ SV87 @ SV264 ) )
= $true )
| ( ( linordered_idom @ SV87 )
= $false )
| ( ( number_ring @ SV87 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1359]) ).
thf(1395,plain,
! [SV113: $i,SV64: $i,SV130: $i] :
( ( ( zero_neq_one @ SV130 )
= $false )
| ( ( power @ SV130 )
= $false )
| ( ( mult_zero @ SV130 )
= $false )
| ( ( no_zero_divisors @ SV130 )
= $false )
| ( ( ( power_power @ SV130 @ ( ti @ SV130 @ SV64 ) @ SV113 )
= ( power_power @ SV130 @ SV64 @ SV113 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1360]) ).
thf(1396,plain,
! [SV114: $i,SV65: $i,SV131: $i] :
( ( ( zero_neq_one @ SV131 )
= $false )
| ( ( power @ SV131 )
= $false )
| ( ( mult_zero @ SV131 )
= $false )
| ( ( no_zero_divisors @ SV131 )
= $false )
| ( ( ( power_power @ SV131 @ SV65 @ ( ti @ nat @ SV114 ) )
= ( power_power @ SV131 @ SV65 @ SV114 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1361]) ).
thf(1397,plain,
! [SV115: $i,SV66: $i,SV132: $i] :
( ( ( zero_neq_one @ SV132 )
= $false )
| ( ( power @ SV132 )
= $false )
| ( ( mult_zero @ SV132 )
= $false )
| ( ( no_zero_divisors @ SV132 )
= $false )
| ( ( ( ti @ SV132 @ ( power_power @ SV132 @ SV66 @ SV115 ) )
= ( power_power @ SV132 @ SV66 @ SV115 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1362]) ).
thf(1398,plain,
! [SV265: $i,SV251: $i,SV71: $i] :
( ( ( ( ( number_number_of @ SV71 @ SV251 )
!= ( number_number_of @ SV71 @ SV265 ) ) )
= $true )
| ( ( SV251 = SV265 )
= $true )
| ( ( number_ring @ SV71 )
= $false )
| ( ( ring_char_0 @ SV71 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1363]) ).
thf(1399,plain,
! [SV71: $i,SV266: $i,SV252: $i] :
( ( ( ( SV252 != SV266 ) )
= $true )
| ( ( ( number_number_of @ SV71 @ SV252 )
= ( number_number_of @ SV71 @ SV266 ) )
= $true )
| ( ( number_ring @ SV71 )
= $false )
| ( ( ring_char_0 @ SV71 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1364]) ).
thf(1400,plain,
! [SV245: $i,SV229: $i,SV73: $i] :
( ( ( ( ti @ SV73 @ SV229 )
= ( zero_zero @ SV73 ) )
= $false )
| ( ( ( ( ti @ SV73 @ SV245 )
!= ( zero_zero @ SV73 ) ) )
= $true )
| ( ( ( plus_plus @ SV73 @ ( power_power @ SV73 @ SV229 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV73 @ SV245 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV73 ) )
= $true )
| ( ( linordered_idom @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1369]) ).
thf(1401,plain,
! [SV267: $i,SV73: $i] :
( ( ( ! [SY390: $i] :
( ( plus_plus @ SV73 @ ( power_power @ SV73 @ SV267 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV73 @ SY390 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV73 ) ) )
= $true )
| ( ( ( ti @ SV73 @ SV267 )
= ( zero_zero @ SV73 ) )
= $true )
| ( ( linordered_idom @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1370]) ).
thf(1402,plain,
! [SV273: $i,SV268: $i,SV73: $i] :
( ( ( ( ( plus_plus @ SV73 @ ( power_power @ SV73 @ SV268 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV73 @ SV273 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV73 ) )
| ( ( ti @ SV73 @ SV273 )
= ( zero_zero @ SV73 ) ) )
= $true )
| ( ( linordered_idom @ SV73 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1371]) ).
thf(1403,plain,
! [SV246: $i,SV230: $i,SV74: $i] :
( ( ( ( ( ti @ SV74 @ SV230 )
!= ( zero_zero @ SV74 ) ) )
= $true )
| ( ( ( ( ti @ SV74 @ SV246 )
!= ( zero_zero @ SV74 ) ) )
= $true )
| ( ( ord_less @ SV74 @ ( zero_zero @ SV74 ) @ ( plus_plus @ SV74 @ ( power_power @ SV74 @ SV230 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV74 @ SV246 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $false )
| ( ( linordered_idom @ SV74 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1372]) ).
thf(1404,plain,
! [SV269: $i,SV74: $i] :
( ( ( ( ti @ SV74 @ SV269 )
= ( zero_zero @ SV74 ) )
= $true )
| ( ( ! [SY392: $i] : ( ord_less @ SV74 @ ( zero_zero @ SV74 ) @ ( plus_plus @ SV74 @ ( power_power @ SV74 @ SV269 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV74 @ SY392 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true )
| ( ( linordered_idom @ SV74 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1373]) ).
thf(1405,plain,
! [SV270: $i,SV274: $i,SV74: $i] :
( ( ( ( ( ti @ SV74 @ SV274 )
= ( zero_zero @ SV74 ) )
| ( ord_less @ SV74 @ ( zero_zero @ SV74 ) @ ( plus_plus @ SV74 @ ( power_power @ SV74 @ SV270 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV74 @ SV274 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true )
| ( ( linordered_idom @ SV74 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1374]) ).
thf(1406,plain,
! [SV253: $i,SV75: $i] :
( ( ( ord_less @ SV75 @ ( number_number_of @ SV75 @ SV253 ) @ ( one_one @ SV75 ) )
= $false )
| ( ( ord_less @ int @ SV253 @ ( bit1 @ pls ) )
= $true )
| ( ( linordered_idom @ SV75 )
= $false )
| ( ( number_ring @ SV75 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1375]) ).
thf(1407,plain,
! [SV75: $i,SV254: $i] :
( ( ( ord_less @ int @ SV254 @ ( bit1 @ pls ) )
= $false )
| ( ( ord_less @ SV75 @ ( number_number_of @ SV75 @ SV254 ) @ ( one_one @ SV75 ) )
= $true )
| ( ( linordered_idom @ SV75 )
= $false )
| ( ( number_ring @ SV75 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1376]) ).
thf(1408,plain,
! [SV255: $i,SV76: $i] :
( ( ( ord_less @ SV76 @ ( zero_zero @ SV76 ) @ ( number_number_of @ SV76 @ SV255 ) )
= $false )
| ( ( ord_less @ int @ pls @ SV255 )
= $true )
| ( ( linordered_idom @ SV76 )
= $false )
| ( ( number_ring @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1377]) ).
thf(1409,plain,
! [SV76: $i,SV256: $i] :
( ( ( ord_less @ int @ pls @ SV256 )
= $false )
| ( ( ord_less @ SV76 @ ( zero_zero @ SV76 ) @ ( number_number_of @ SV76 @ SV256 ) )
= $true )
| ( ( linordered_idom @ SV76 )
= $false )
| ( ( number_ring @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1378]) ).
thf(1410,plain,
! [SV77: $i] :
( ( ( ~ ! [SY295: $i,SY296: $i] :
( ( ( number_number_of @ nat @ SY296 )
= ( zero_zero @ nat ) )
| ( ( ti @ SV77 @ SY295 )
!= ( zero_zero @ SV77 ) )
| ( ( power_power @ SV77 @ SY295 @ ( number_number_of @ nat @ SY296 ) )
= ( zero_zero @ SV77 ) ) ) )
= $false )
| ( ( no_zero_divisors @ SV77 )
= $false )
| ( ( mult_zero @ SV77 )
= $false )
| ( ( power @ SV77 )
= $false )
| ( ( zero_neq_one @ SV77 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1379]) ).
thf(1411,plain,
! [SV77: $i] :
( ( ( ~ ~ ( ~ ! [SY297: $i,SY298: $i] :
( ( ( power_power @ SV77 @ SY297 @ ( number_number_of @ nat @ SY298 ) )
!= ( zero_zero @ SV77 ) )
| ( ( number_number_of @ nat @ SY298 )
!= ( zero_zero @ nat ) ) )
| ~ ! [SY299: $i] :
( ! [SY300: $i] :
( ( power_power @ SV77 @ SY299 @ ( number_number_of @ nat @ SY300 ) )
!= ( zero_zero @ SV77 ) )
| ( ( ti @ SV77 @ SY299 )
= ( zero_zero @ SV77 ) ) ) ) )
= $false )
| ( ( no_zero_divisors @ SV77 )
= $false )
| ( ( mult_zero @ SV77 )
= $false )
| ( ( power @ SV77 )
= $false )
| ( ( zero_neq_one @ SV77 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1379]) ).
thf(1412,plain,
! [SV257: $i,SV80: $i] :
( ( ( ord_less @ SV80 @ ( number_number_of @ SV80 @ SV257 ) @ ( zero_zero @ SV80 ) )
= $false )
| ( ( ord_less @ int @ SV257 @ pls )
= $true )
| ( ( linordered_idom @ SV80 )
= $false )
| ( ( number_ring @ SV80 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1382]) ).
thf(1413,plain,
! [SV80: $i,SV258: $i] :
( ( ( ord_less @ int @ SV258 @ pls )
= $false )
| ( ( ord_less @ SV80 @ ( number_number_of @ SV80 @ SV258 ) @ ( zero_zero @ SV80 ) )
= $true )
| ( ( linordered_idom @ SV80 )
= $false )
| ( ( number_ring @ SV80 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1383]) ).
thf(1414,plain,
! [SV271: $i,SV259: $i,SV81: $i] :
( ( ( ~ ( ord_less @ SV81 @ ( number_number_of @ SV81 @ SV259 ) @ ( number_number_of @ SV81 @ SV271 ) ) )
= $true )
| ( ( ord_less @ int @ SV259 @ SV271 )
= $true )
| ( ( linordered_idom @ SV81 )
= $false )
| ( ( number_ring @ SV81 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1384]) ).
thf(1415,plain,
! [SV81: $i,SV272: $i,SV260: $i] :
( ( ( ~ ( ord_less @ int @ SV260 @ SV272 ) )
= $true )
| ( ( ord_less @ SV81 @ ( number_number_of @ SV81 @ SV260 ) @ ( number_number_of @ SV81 @ SV272 ) )
= $true )
| ( ( linordered_idom @ SV81 )
= $false )
| ( ( number_ring @ SV81 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1385]) ).
thf(1416,plain,
! [SV83: $i,SV261: $i] :
( ( ( ( number_number_of @ nat @ SV261 )
= ( zero_zero @ nat ) )
= $false )
| ( ( ( power_power @ SV83 @ ( zero_zero @ SV83 ) @ ( number_number_of @ nat @ SV261 ) )
= ( one_one @ SV83 ) )
= $true )
| ( ( power @ SV83 )
= $false )
| ( ( semiring_0 @ SV83 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1386]) ).
thf(1417,plain,
! [SV247: $i,SV235: $i] :
( ( ( ord_less @ int @ SV235 @ pls )
= $false )
| ( ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV247 ) @ ( number_number_of @ nat @ SV235 ) )
= ( number_number_of @ nat @ SV247 ) )
= $true )
| ( ( ord_less @ int @ SV247 @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1388]) ).
thf(1418,plain,
! [SV263: $i,SV87: $i] :
( ( ( ord_less @ SV87 @ ( one_one @ SV87 ) @ ( number_number_of @ SV87 @ SV263 ) )
= $false )
| ( ( ord_less @ int @ ( bit1 @ pls ) @ SV263 )
= $true )
| ( ( linordered_idom @ SV87 )
= $false )
| ( ( number_ring @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1393]) ).
thf(1419,plain,
! [SV87: $i,SV264: $i] :
( ( ( ord_less @ int @ ( bit1 @ pls ) @ SV264 )
= $false )
| ( ( ord_less @ SV87 @ ( one_one @ SV87 ) @ ( number_number_of @ SV87 @ SV264 ) )
= $true )
| ( ( linordered_idom @ SV87 )
= $false )
| ( ( number_ring @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1394]) ).
thf(1420,plain,
! [SV265: $i,SV251: $i,SV71: $i] :
( ( ( ( number_number_of @ SV71 @ SV251 )
= ( number_number_of @ SV71 @ SV265 ) )
= $false )
| ( ( SV251 = SV265 )
= $true )
| ( ( number_ring @ SV71 )
= $false )
| ( ( ring_char_0 @ SV71 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1398]) ).
thf(1421,plain,
! [SV71: $i,SV266: $i,SV252: $i] :
( ( ( SV252 = SV266 )
= $false )
| ( ( ( number_number_of @ SV71 @ SV252 )
= ( number_number_of @ SV71 @ SV266 ) )
= $true )
| ( ( number_ring @ SV71 )
= $false )
| ( ( ring_char_0 @ SV71 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1399]) ).
thf(1422,plain,
! [SV229: $i,SV245: $i,SV73: $i] :
( ( ( ( ti @ SV73 @ SV245 )
= ( zero_zero @ SV73 ) )
= $false )
| ( ( ( ti @ SV73 @ SV229 )
= ( zero_zero @ SV73 ) )
= $false )
| ( ( ( plus_plus @ SV73 @ ( power_power @ SV73 @ SV229 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV73 @ SV245 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV73 ) )
= $true )
| ( ( linordered_idom @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1400]) ).
thf(1423,plain,
! [SV275: $i,SV267: $i,SV73: $i] :
( ( ( ( ( plus_plus @ SV73 @ ( power_power @ SV73 @ SV267 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV73 @ SV275 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV73 ) ) )
= $true )
| ( ( ( ti @ SV73 @ SV267 )
= ( zero_zero @ SV73 ) )
= $true )
| ( ( linordered_idom @ SV73 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1401]) ).
thf(1424,plain,
! [SV273: $i,SV268: $i,SV73: $i] :
( ( ( ( ( plus_plus @ SV73 @ ( power_power @ SV73 @ SV268 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV73 @ SV273 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV73 ) ) )
= $true )
| ( ( ( ti @ SV73 @ SV273 )
= ( zero_zero @ SV73 ) )
= $true )
| ( ( linordered_idom @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1402]) ).
thf(1425,plain,
! [SV246: $i,SV230: $i,SV74: $i] :
( ( ( ( ti @ SV74 @ SV230 )
= ( zero_zero @ SV74 ) )
= $false )
| ( ( ( ( ti @ SV74 @ SV246 )
!= ( zero_zero @ SV74 ) ) )
= $true )
| ( ( ord_less @ SV74 @ ( zero_zero @ SV74 ) @ ( plus_plus @ SV74 @ ( power_power @ SV74 @ SV230 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV74 @ SV246 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $false )
| ( ( linordered_idom @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1403]) ).
thf(1426,plain,
! [SV276: $i,SV269: $i,SV74: $i] :
( ( ( ord_less @ SV74 @ ( zero_zero @ SV74 ) @ ( plus_plus @ SV74 @ ( power_power @ SV74 @ SV269 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV74 @ SV276 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true )
| ( ( ( ti @ SV74 @ SV269 )
= ( zero_zero @ SV74 ) )
= $true )
| ( ( linordered_idom @ SV74 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1404]) ).
thf(1427,plain,
! [SV270: $i,SV274: $i,SV74: $i] :
( ( ( ( ti @ SV74 @ SV274 )
= ( zero_zero @ SV74 ) )
= $true )
| ( ( ord_less @ SV74 @ ( zero_zero @ SV74 ) @ ( plus_plus @ SV74 @ ( power_power @ SV74 @ SV270 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV74 @ SV274 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true )
| ( ( linordered_idom @ SV74 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1405]) ).
thf(1428,plain,
! [SV77: $i] :
( ( ( ! [SY295: $i,SY296: $i] :
( ( ( number_number_of @ nat @ SY296 )
= ( zero_zero @ nat ) )
| ( ( ti @ SV77 @ SY295 )
!= ( zero_zero @ SV77 ) )
| ( ( power_power @ SV77 @ SY295 @ ( number_number_of @ nat @ SY296 ) )
= ( zero_zero @ SV77 ) ) ) )
= $true )
| ( ( no_zero_divisors @ SV77 )
= $false )
| ( ( mult_zero @ SV77 )
= $false )
| ( ( power @ SV77 )
= $false )
| ( ( zero_neq_one @ SV77 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1410]) ).
thf(1429,plain,
! [SV77: $i] :
( ( ( ~ ( ~ ! [SY297: $i,SY298: $i] :
( ( ( power_power @ SV77 @ SY297 @ ( number_number_of @ nat @ SY298 ) )
!= ( zero_zero @ SV77 ) )
| ( ( number_number_of @ nat @ SY298 )
!= ( zero_zero @ nat ) ) )
| ~ ! [SY299: $i] :
( ! [SY300: $i] :
( ( power_power @ SV77 @ SY299 @ ( number_number_of @ nat @ SY300 ) )
!= ( zero_zero @ SV77 ) )
| ( ( ti @ SV77 @ SY299 )
= ( zero_zero @ SV77 ) ) ) ) )
= $true )
| ( ( no_zero_divisors @ SV77 )
= $false )
| ( ( mult_zero @ SV77 )
= $false )
| ( ( power @ SV77 )
= $false )
| ( ( zero_neq_one @ SV77 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1411]) ).
thf(1430,plain,
! [SV271: $i,SV259: $i,SV81: $i] :
( ( ( ord_less @ SV81 @ ( number_number_of @ SV81 @ SV259 ) @ ( number_number_of @ SV81 @ SV271 ) )
= $false )
| ( ( ord_less @ int @ SV259 @ SV271 )
= $true )
| ( ( linordered_idom @ SV81 )
= $false )
| ( ( number_ring @ SV81 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1414]) ).
thf(1431,plain,
! [SV81: $i,SV272: $i,SV260: $i] :
( ( ( ord_less @ int @ SV260 @ SV272 )
= $false )
| ( ( ord_less @ SV81 @ ( number_number_of @ SV81 @ SV260 ) @ ( number_number_of @ SV81 @ SV272 ) )
= $true )
| ( ( linordered_idom @ SV81 )
= $false )
| ( ( number_ring @ SV81 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1415]) ).
thf(1432,plain,
! [SV275: $i,SV267: $i,SV73: $i] :
( ( ( ( plus_plus @ SV73 @ ( power_power @ SV73 @ SV267 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV73 @ SV275 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV73 ) )
= $false )
| ( ( ( ti @ SV73 @ SV267 )
= ( zero_zero @ SV73 ) )
= $true )
| ( ( linordered_idom @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1423]) ).
thf(1433,plain,
! [SV273: $i,SV268: $i,SV73: $i] :
( ( ( ( plus_plus @ SV73 @ ( power_power @ SV73 @ SV268 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV73 @ SV273 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV73 ) )
= $false )
| ( ( ( ti @ SV73 @ SV273 )
= ( zero_zero @ SV73 ) )
= $true )
| ( ( linordered_idom @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1424]) ).
thf(1434,plain,
! [SV230: $i,SV246: $i,SV74: $i] :
( ( ( ( ti @ SV74 @ SV246 )
= ( zero_zero @ SV74 ) )
= $false )
| ( ( ( ti @ SV74 @ SV230 )
= ( zero_zero @ SV74 ) )
= $false )
| ( ( ord_less @ SV74 @ ( zero_zero @ SV74 ) @ ( plus_plus @ SV74 @ ( power_power @ SV74 @ SV230 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV74 @ SV246 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $false )
| ( ( linordered_idom @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1425]) ).
thf(1435,plain,
! [SV277: $i,SV77: $i] :
( ( ( ! [SY394: $i] :
( ( ( number_number_of @ nat @ SY394 )
= ( zero_zero @ nat ) )
| ( ( ti @ SV77 @ SV277 )
!= ( zero_zero @ SV77 ) )
| ( ( power_power @ SV77 @ SV277 @ ( number_number_of @ nat @ SY394 ) )
= ( zero_zero @ SV77 ) ) ) )
= $true )
| ( ( no_zero_divisors @ SV77 )
= $false )
| ( ( mult_zero @ SV77 )
= $false )
| ( ( power @ SV77 )
= $false )
| ( ( zero_neq_one @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1428]) ).
thf(1436,plain,
! [SV77: $i] :
( ( ( ~ ! [SY297: $i,SY298: $i] :
( ( ( power_power @ SV77 @ SY297 @ ( number_number_of @ nat @ SY298 ) )
!= ( zero_zero @ SV77 ) )
| ( ( number_number_of @ nat @ SY298 )
!= ( zero_zero @ nat ) ) )
| ~ ! [SY299: $i] :
( ! [SY300: $i] :
( ( power_power @ SV77 @ SY299 @ ( number_number_of @ nat @ SY300 ) )
!= ( zero_zero @ SV77 ) )
| ( ( ti @ SV77 @ SY299 )
= ( zero_zero @ SV77 ) ) ) )
= $false )
| ( ( no_zero_divisors @ SV77 )
= $false )
| ( ( mult_zero @ SV77 )
= $false )
| ( ( power @ SV77 )
= $false )
| ( ( zero_neq_one @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1429]) ).
thf(1437,plain,
! [SV277: $i,SV77: $i,SV278: $i] :
( ( ( ( ( number_number_of @ nat @ SV278 )
= ( zero_zero @ nat ) )
| ( ( ti @ SV77 @ SV277 )
!= ( zero_zero @ SV77 ) )
| ( ( power_power @ SV77 @ SV277 @ ( number_number_of @ nat @ SV278 ) )
= ( zero_zero @ SV77 ) ) )
= $true )
| ( ( no_zero_divisors @ SV77 )
= $false )
| ( ( mult_zero @ SV77 )
= $false )
| ( ( power @ SV77 )
= $false )
| ( ( zero_neq_one @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1435]) ).
thf(1438,plain,
! [SV77: $i] :
( ( ( ~ ! [SY297: $i,SY298: $i] :
( ( ( power_power @ SV77 @ SY297 @ ( number_number_of @ nat @ SY298 ) )
!= ( zero_zero @ SV77 ) )
| ( ( number_number_of @ nat @ SY298 )
!= ( zero_zero @ nat ) ) ) )
= $false )
| ( ( no_zero_divisors @ SV77 )
= $false )
| ( ( mult_zero @ SV77 )
= $false )
| ( ( power @ SV77 )
= $false )
| ( ( zero_neq_one @ SV77 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1436]) ).
thf(1439,plain,
! [SV77: $i] :
( ( ( ~ ! [SY299: $i] :
( ! [SY300: $i] :
( ( power_power @ SV77 @ SY299 @ ( number_number_of @ nat @ SY300 ) )
!= ( zero_zero @ SV77 ) )
| ( ( ti @ SV77 @ SY299 )
= ( zero_zero @ SV77 ) ) ) )
= $false )
| ( ( no_zero_divisors @ SV77 )
= $false )
| ( ( mult_zero @ SV77 )
= $false )
| ( ( power @ SV77 )
= $false )
| ( ( zero_neq_one @ SV77 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1436]) ).
thf(1440,plain,
! [SV277: $i,SV77: $i,SV278: $i] :
( ( ( ( ( number_number_of @ nat @ SV278 )
= ( zero_zero @ nat ) )
| ( ( ti @ SV77 @ SV277 )
!= ( zero_zero @ SV77 ) ) )
= $true )
| ( ( ( power_power @ SV77 @ SV277 @ ( number_number_of @ nat @ SV278 ) )
= ( zero_zero @ SV77 ) )
= $true )
| ( ( no_zero_divisors @ SV77 )
= $false )
| ( ( mult_zero @ SV77 )
= $false )
| ( ( power @ SV77 )
= $false )
| ( ( zero_neq_one @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1437]) ).
thf(1441,plain,
! [SV77: $i] :
( ( ( ! [SY297: $i,SY298: $i] :
( ( ( power_power @ SV77 @ SY297 @ ( number_number_of @ nat @ SY298 ) )
!= ( zero_zero @ SV77 ) )
| ( ( number_number_of @ nat @ SY298 )
!= ( zero_zero @ nat ) ) ) )
= $true )
| ( ( no_zero_divisors @ SV77 )
= $false )
| ( ( mult_zero @ SV77 )
= $false )
| ( ( power @ SV77 )
= $false )
| ( ( zero_neq_one @ SV77 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1438]) ).
thf(1442,plain,
! [SV77: $i] :
( ( ( ! [SY299: $i] :
( ! [SY300: $i] :
( ( power_power @ SV77 @ SY299 @ ( number_number_of @ nat @ SY300 ) )
!= ( zero_zero @ SV77 ) )
| ( ( ti @ SV77 @ SY299 )
= ( zero_zero @ SV77 ) ) ) )
= $true )
| ( ( no_zero_divisors @ SV77 )
= $false )
| ( ( mult_zero @ SV77 )
= $false )
| ( ( power @ SV77 )
= $false )
| ( ( zero_neq_one @ SV77 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1439]) ).
thf(1443,plain,
! [SV277: $i,SV77: $i,SV278: $i] :
( ( ( ( number_number_of @ nat @ SV278 )
= ( zero_zero @ nat ) )
= $true )
| ( ( ( ( ti @ SV77 @ SV277 )
!= ( zero_zero @ SV77 ) ) )
= $true )
| ( ( ( power_power @ SV77 @ SV277 @ ( number_number_of @ nat @ SV278 ) )
= ( zero_zero @ SV77 ) )
= $true )
| ( ( no_zero_divisors @ SV77 )
= $false )
| ( ( mult_zero @ SV77 )
= $false )
| ( ( power @ SV77 )
= $false )
| ( ( zero_neq_one @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1440]) ).
thf(1444,plain,
! [SV279: $i,SV77: $i] :
( ( ( ! [SY395: $i] :
( ( ( power_power @ SV77 @ SV279 @ ( number_number_of @ nat @ SY395 ) )
!= ( zero_zero @ SV77 ) )
| ( ( number_number_of @ nat @ SY395 )
!= ( zero_zero @ nat ) ) ) )
= $true )
| ( ( no_zero_divisors @ SV77 )
= $false )
| ( ( mult_zero @ SV77 )
= $false )
| ( ( power @ SV77 )
= $false )
| ( ( zero_neq_one @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1441]) ).
thf(1445,plain,
! [SV280: $i,SV77: $i] :
( ( ( ! [SY396: $i] :
( ( power_power @ SV77 @ SV280 @ ( number_number_of @ nat @ SY396 ) )
!= ( zero_zero @ SV77 ) )
| ( ( ti @ SV77 @ SV280 )
= ( zero_zero @ SV77 ) ) )
= $true )
| ( ( no_zero_divisors @ SV77 )
= $false )
| ( ( mult_zero @ SV77 )
= $false )
| ( ( power @ SV77 )
= $false )
| ( ( zero_neq_one @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1442]) ).
thf(1446,plain,
! [SV278: $i,SV277: $i,SV77: $i] :
( ( ( ( ti @ SV77 @ SV277 )
= ( zero_zero @ SV77 ) )
= $false )
| ( ( ( number_number_of @ nat @ SV278 )
= ( zero_zero @ nat ) )
= $true )
| ( ( ( power_power @ SV77 @ SV277 @ ( number_number_of @ nat @ SV278 ) )
= ( zero_zero @ SV77 ) )
= $true )
| ( ( no_zero_divisors @ SV77 )
= $false )
| ( ( mult_zero @ SV77 )
= $false )
| ( ( power @ SV77 )
= $false )
| ( ( zero_neq_one @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1443]) ).
thf(1447,plain,
! [SV281: $i,SV279: $i,SV77: $i] :
( ( ( ( ( power_power @ SV77 @ SV279 @ ( number_number_of @ nat @ SV281 ) )
!= ( zero_zero @ SV77 ) )
| ( ( number_number_of @ nat @ SV281 )
!= ( zero_zero @ nat ) ) )
= $true )
| ( ( no_zero_divisors @ SV77 )
= $false )
| ( ( mult_zero @ SV77 )
= $false )
| ( ( power @ SV77 )
= $false )
| ( ( zero_neq_one @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1444]) ).
thf(1448,plain,
! [SV280: $i,SV77: $i] :
( ( ( ! [SY396: $i] :
( ( power_power @ SV77 @ SV280 @ ( number_number_of @ nat @ SY396 ) )
!= ( zero_zero @ SV77 ) ) )
= $true )
| ( ( ( ti @ SV77 @ SV280 )
= ( zero_zero @ SV77 ) )
= $true )
| ( ( no_zero_divisors @ SV77 )
= $false )
| ( ( mult_zero @ SV77 )
= $false )
| ( ( power @ SV77 )
= $false )
| ( ( zero_neq_one @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1445]) ).
thf(1449,plain,
! [SV281: $i,SV279: $i,SV77: $i] :
( ( ( ( ( power_power @ SV77 @ SV279 @ ( number_number_of @ nat @ SV281 ) )
!= ( zero_zero @ SV77 ) ) )
= $true )
| ( ( ( ( number_number_of @ nat @ SV281 )
!= ( zero_zero @ nat ) ) )
= $true )
| ( ( no_zero_divisors @ SV77 )
= $false )
| ( ( mult_zero @ SV77 )
= $false )
| ( ( power @ SV77 )
= $false )
| ( ( zero_neq_one @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1447]) ).
thf(1450,plain,
! [SV282: $i,SV280: $i,SV77: $i] :
( ( ( ( ( power_power @ SV77 @ SV280 @ ( number_number_of @ nat @ SV282 ) )
!= ( zero_zero @ SV77 ) ) )
= $true )
| ( ( ( ti @ SV77 @ SV280 )
= ( zero_zero @ SV77 ) )
= $true )
| ( ( no_zero_divisors @ SV77 )
= $false )
| ( ( mult_zero @ SV77 )
= $false )
| ( ( power @ SV77 )
= $false )
| ( ( zero_neq_one @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1448]) ).
thf(1451,plain,
! [SV281: $i,SV279: $i,SV77: $i] :
( ( ( ( power_power @ SV77 @ SV279 @ ( number_number_of @ nat @ SV281 ) )
= ( zero_zero @ SV77 ) )
= $false )
| ( ( ( ( number_number_of @ nat @ SV281 )
!= ( zero_zero @ nat ) ) )
= $true )
| ( ( no_zero_divisors @ SV77 )
= $false )
| ( ( mult_zero @ SV77 )
= $false )
| ( ( power @ SV77 )
= $false )
| ( ( zero_neq_one @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1449]) ).
thf(1452,plain,
! [SV282: $i,SV280: $i,SV77: $i] :
( ( ( ( power_power @ SV77 @ SV280 @ ( number_number_of @ nat @ SV282 ) )
= ( zero_zero @ SV77 ) )
= $false )
| ( ( ( ti @ SV77 @ SV280 )
= ( zero_zero @ SV77 ) )
= $true )
| ( ( no_zero_divisors @ SV77 )
= $false )
| ( ( mult_zero @ SV77 )
= $false )
| ( ( power @ SV77 )
= $false )
| ( ( zero_neq_one @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1450]) ).
thf(1453,plain,
! [SV279: $i,SV77: $i,SV281: $i] :
( ( ( ( number_number_of @ nat @ SV281 )
= ( zero_zero @ nat ) )
= $false )
| ( ( ( power_power @ SV77 @ SV279 @ ( number_number_of @ nat @ SV281 ) )
= ( zero_zero @ SV77 ) )
= $false )
| ( ( no_zero_divisors @ SV77 )
= $false )
| ( ( mult_zero @ SV77 )
= $false )
| ( ( power @ SV77 )
= $false )
| ( ( zero_neq_one @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1451]) ).
thf(1454,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[400,1453,1452,1446,1434,1433,1432,1431,1430,1427,1426,1422,1421,1420,1419,1418,1417,1416,1413,1412,1409,1408,1407,1406,1397,1396,1395,1392,1391,1390,1389,1387,1381,1380,1368,1367,1366,1365,1357,1356,1348,1347,1342,1341,1318,1312,1282,1273,1272,1271,1270,1265,1264,1259,1258,1257,1256,1253,1248,1247,1246,1245,1240,1239,1236,1235,1231,1230,1229,1228,1219,1218,1210,1209,1208,1199,1198,1194,1193,1182,1181,1180,1179,1160,1159,1153,1152,1138,1137,1136,1135,1131,1130,1122,1041,1039,1038,1037,1036,1034,1033,1032,1031,1030,1029,1028,952,948,947,945,944,943,942,941,940,939,851,850,849,848,847,846,845,843,841,840,839,838,835,834,829,759,747,746,745,736,733,732,731,730,726,724,723,722,654,647,636,635,634,632,631,630,624,619,610,592,591,590,589,548,526,525,524,523,522,521,520,519,518,517,516,515,514,513,512,511,510,509,508,507,506,484,483,472,454,453,452,444,443,441,440,439,434,430,417,416,415,401]) ).
thf(1455,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[1454]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM925+5 : TPTP v8.1.0. Released v5.3.0.
% 0.11/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33 % Computer : n027.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Wed Jul 6 17:29:13 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.39 ...
% 0.18/0.45
% 0.18/0.45 No.of.Axioms: 152
% 0.18/0.45
% 0.18/0.45 Length.of.Defs: 0
% 0.18/0.45
% 0.18/0.45 Contains.Choice.Funs: false
% 0.18/0.49 .........
% 0.18/0.54 (rf:2,axioms:152,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:154,loop_count:0,foatp_calls:0,translation:fof_full)...............................................................................................
% 45.29/45.54
% 45.29/45.54 ********************************
% 45.29/45.54 * All subproblems solved! *
% 45.29/45.54 ********************************
% 45.29/45.54 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:2,axioms:152,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:1454,loop_count:0,foatp_calls:1,translation:fof_full)
% 45.90/46.11
% 45.90/46.11 %**** Beginning of derivation protocol ****
% 45.90/46.11 % SZS output start CNFRefutation
% See solution above
% 45.90/46.11
% 45.90/46.11 %**** End of derivation protocol ****
% 45.90/46.11 %**** no. of clauses in derivation: 1455 ****
% 45.90/46.11 %**** clause counter: 1454 ****
% 45.90/46.11
% 45.90/46.11 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:2,axioms:152,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:1454,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------