TSTP Solution File: NUM924+5 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : NUM924+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 : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 11:57:23 EDT 2022
% Result : Theorem 0.91s 1.15s
% Output : CNFRefutation 1.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 187
% Syntax : Number of formulae : 1757 (1018 unt; 32 typ; 0 def)
% Number of atoms : 10123 (3724 equ; 0 cnn)
% Maximal formula atoms : 7 ( 5 avg)
% Number of connectives : 27690 (2771 ~;2964 |; 172 &;21531 @)
% ( 102 <=>; 150 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 37 ( 37 >; 0 *; 0 +; 0 <<)
% Number of symbols : 35 ( 32 usr; 9 con; 0-3 aty)
% Number of variables : 4301 ( 0 ^4301 !; 0 ?;4301 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_bit0,type,
bit0: $i > $i ).
thf(tp_bit1,type,
bit1: $i > $i ).
thf(tp_int,type,
int: $i ).
thf(tp_linord581940658strict,type,
linord581940658strict: $i > $o ).
thf(tp_linorder,type,
linorder: $i > $o ).
thf(tp_linordered_idom,type,
linordered_idom: $i > $o ).
thf(tp_linordered_ring,type,
linordered_ring: $i > $o ).
thf(tp_m,type,
m: $i ).
thf(tp_nat,type,
nat: $i ).
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_ord_less_eq,type,
ord_less_eq: $i > $i > $i > $o ).
thf(tp_pls,type,
pls: $i ).
thf(tp_plus_plus,type,
plus_plus: $i > $i > $i > $i ).
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_s,type,
s: $i ).
thf(tp_sK1_T_1,type,
sK1_T_1: $i ).
thf(tp_semiring,type,
semiring: $i > $o ).
thf(tp_semiring_1,type,
semiring_1: $i > $o ).
thf(tp_t,type,
t: $i ).
thf(tp_ti,type,
ti: $i > $i > $i ).
thf(tp_times_times,type,
times_times: $i > $i > $i > $i ).
thf(tp_twoSqu33214720sum2sq,type,
twoSqu33214720sum2sq: $i > $o ).
thf(tp_undefined,type,
undefined: $i > $i ).
thf(tp_zero_zero,type,
zero_zero: $i > $i ).
thf(tp_zprime,type,
zprime: $i > $o ).
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,
semiring @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring) ).
thf(4,axiom,
semiring_1 @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__1) ).
thf(5,axiom,
linorder @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Olinorder) ).
thf(6,axiom,
number_semiring @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber__semiring) ).
thf(7,axiom,
number @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber) ).
thf(8,axiom,
semiring @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring) ).
thf(9,axiom,
number_ring @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
thf(10,axiom,
ring_char_0 @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Oring__char__0) ).
thf(11,axiom,
semiring_1 @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring__1) ).
thf(12,axiom,
linorder @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Olinorder) ).
thf(13,axiom,
number_semiring @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__semiring) ).
thf(14,axiom,
linordered_idom @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__idom) ).
thf(15,axiom,
linordered_ring @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__ring) ).
thf(16,axiom,
linord581940658strict @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__ring__strict) ).
thf(17,axiom,
ring_11004092258visors @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring__1__no__zero__divisors) ).
thf(18,axiom,
( ( zero_zero @ int )
= ( number_number_of @ int @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_zero__is__num__zero) ).
thf(19,axiom,
! [Z: $i,W: $i] :
( ( plus_plus @ int @ Z @ W )
= ( plus_plus @ int @ W @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_zadd__commute) ).
thf(20,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_95_zadd__left__commute) ).
thf(21,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_94_zadd__assoc) ).
thf(22,axiom,
! [X_b: $i] :
( ( ( number @ X_b )
& ( semiring @ X_b ) )
=> ! [V: $i,B: $i,C: $i] :
( ( times_times @ X_b @ ( number_number_of @ X_b @ V ) @ ( plus_plus @ X_b @ B @ C ) )
= ( plus_plus @ X_b @ ( times_times @ X_b @ ( number_number_of @ X_b @ V ) @ B ) @ ( times_times @ X_b @ ( number_number_of @ X_b @ V ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_right__distrib__number__of) ).
thf(23,axiom,
! [X_b: $i] :
( ( ( number @ X_b )
& ( semiring @ X_b ) )
=> ! [A_1: $i,B: $i,V: $i] :
( ( times_times @ X_b @ ( plus_plus @ X_b @ A_1 @ B ) @ ( number_number_of @ X_b @ V ) )
= ( plus_plus @ X_b @ ( times_times @ X_b @ A_1 @ ( number_number_of @ X_b @ V ) ) @ ( times_times @ X_b @ B @ ( number_number_of @ X_b @ V ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_left__distrib__number__of) ).
thf(24,axiom,
! [X_a: $i] :
( ( linord581940658strict @ X_a )
=> ! [X_1: $i,Y_1: $i] :
( ( ( plus_plus @ X_a @ ( times_times @ X_a @ X_1 @ X_1 ) @ ( times_times @ X_a @ Y_1 @ Y_1 ) )
= ( zero_zero @ X_a ) )
<=> ( ( ( ti @ X_a @ X_1 )
= ( zero_zero @ X_a ) )
& ( ( ti @ X_a @ Y_1 )
= ( zero_zero @ X_a ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_sum__squares__eq__zero__iff) ).
thf(25,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_90_zless__linear) ).
thf(26,axiom,
! [K: $i,L: $i] :
( ( ( bit0 @ K )
= ( bit0 @ L ) )
<=> ( K = L ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_rel__simps_I48_J) ).
thf(27,axiom,
! [K: $i,L: $i] :
( ( ( bit1 @ K )
= ( bit1 @ L ) )
<=> ( K = L ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_rel__simps_I51_J) ).
thf(28,axiom,
! [X_a: $i] :
( ( number @ X_a )
=> ! [W_1: $i,X_1: $i] :
( ( ( number_number_of @ X_a @ W_1 )
= ( ti @ X_a @ X_1 ) )
<=> ( ( ti @ X_a @ X_1 )
= ( number_number_of @ X_a @ W_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_number__of__reorient) ).
thf(29,axiom,
! [X_a: $i] :
( ( ( number_ring @ X_a )
& ( ring_char_0 @ X_a ) )
=> ! [X_1: $i,Y_1: $i] :
( ( ( number_number_of @ X_a @ X_1 )
= ( number_number_of @ X_a @ Y_1 ) )
<=> ( X_1 = Y_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_eq__number__of) ).
thf(30,axiom,
! [Z: $i] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ Z )
=> ( ord_less @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( one_one @ int ) @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_le__imp__0__less) ).
thf(31,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_84_add__nat__number__of) ).
thf(32,axiom,
! [X_a: $i] :
( ( number_semiring @ X_a )
=> ! [V_1: $i,V: $i] :
( ( ord_less_eq @ int @ pls @ V )
=> ( ( ord_less_eq @ int @ pls @ V_1 )
=> ( ( plus_plus @ X_a @ ( number_number_of @ X_a @ V ) @ ( number_number_of @ X_a @ V_1 ) )
= ( number_number_of @ X_a @ ( plus_plus @ int @ V @ V_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_semiring__add__number__of) ).
thf(33,axiom,
! [W_1: $i,Z_1: $i] :
( ( ord_less @ int @ W_1 @ ( plus_plus @ int @ Z_1 @ ( one_one @ int ) ) )
<=> ( ord_less_eq @ int @ W_1 @ Z_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_zle__add1__eq__le) ).
thf(34,axiom,
! [W_1: $i,Z_1: $i] :
( ( ord_less_eq @ int @ ( plus_plus @ int @ W_1 @ ( one_one @ int ) ) @ Z_1 )
<=> ( ord_less @ int @ W_1 @ Z_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_add1__zle__eq) ).
thf(35,axiom,
! [W: $i,Z: $i] :
( ( ord_less @ int @ W @ Z )
=> ( ord_less_eq @ int @ ( plus_plus @ int @ W @ ( one_one @ int ) ) @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_zless__imp__add1__zle) ).
thf(36,axiom,
( ( one_one @ nat )
= ( number_number_of @ nat @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_Numeral1__eq1__nat) ).
thf(37,axiom,
( ( number_number_of @ nat @ ( bit1 @ pls ) )
= ( one_one @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_nat__numeral__1__eq__1) ).
thf(38,axiom,
! [Z_1: $i] :
( ( ord_less_eq @ int @ ( one_one @ int ) @ Z_1 )
<=> ( ord_less @ int @ ( zero_zero @ int ) @ Z_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_int__one__le__iff__zero__less) ).
thf(39,axiom,
! [V_3: $i,V_2: $i] :
( ( ord_less @ nat @ ( number_number_of @ nat @ V_3 ) @ ( number_number_of @ nat @ V_2 ) )
<=> ( ( ( ord_less @ int @ V_3 @ V_2 )
=> ( ord_less @ int @ pls @ V_2 ) )
& ( ord_less @ int @ V_3 @ V_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_less__nat__number__of) ).
thf(40,axiom,
! [K: $i,L: $i] :
( ( ord_less @ int @ ( bit0 @ K ) @ ( bit1 @ L ) )
<=> ( ord_less_eq @ int @ K @ L ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_rel__simps_I15_J) ).
thf(41,axiom,
! [K1: $i,K2: $i] :
( ( ord_less @ int @ ( bit0 @ K1 ) @ ( bit1 @ K2 ) )
<=> ( ord_less_eq @ int @ K1 @ K2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_less__int__code_I14_J) ).
thf(42,axiom,
! [K: $i,L: $i] :
( ( ord_less_eq @ int @ ( bit1 @ K ) @ ( bit0 @ L ) )
<=> ( ord_less @ int @ K @ L ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_rel__simps_I33_J) ).
thf(43,axiom,
! [K1: $i,K2: $i] :
( ( ord_less_eq @ int @ ( bit1 @ K1 ) @ ( bit0 @ K2 ) )
<=> ( ord_less @ int @ K1 @ K2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_less__eq__int__code_I15_J) ).
thf(44,axiom,
! [K: $i] :
( ( ord_less @ int @ pls @ ( bit1 @ K ) )
<=> ( ord_less_eq @ int @ pls @ K ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_rel__simps_I5_J) ).
thf(45,axiom,
! [K: $i] :
( ( ord_less_eq @ int @ ( bit1 @ K ) @ pls )
<=> ( ord_less @ int @ K @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_rel__simps_I29_J) ).
thf(46,axiom,
! [W: $i,Z1: $i,Z2: $i] :
( ( times_times @ int @ W @ ( plus_plus @ int @ Z1 @ Z2 ) )
= ( plus_plus @ int @ ( times_times @ int @ W @ Z1 ) @ ( times_times @ int @ W @ Z2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_zadd__zmult__distrib2) ).
thf(47,axiom,
! [Z1: $i,Z2: $i,W: $i] :
( ( times_times @ int @ ( plus_plus @ int @ Z1 @ Z2 ) @ W )
= ( plus_plus @ int @ ( times_times @ int @ Z1 @ W ) @ ( times_times @ int @ Z2 @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_zadd__zmult__distrib) ).
thf(48,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_67_plus__numeral__code_I9_J) ).
thf(49,axiom,
! [Z: $i] :
( ( times_times @ int @ ( one_one @ int ) @ Z )
= Z ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_zmult__1) ).
thf(50,axiom,
! [Z: $i] :
( ( times_times @ int @ Z @ ( one_one @ int ) )
= Z ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_zmult__1__right) ).
thf(51,axiom,
! [K: $i,L: $i] :
( ( ord_less @ int @ ( number_number_of @ int @ K ) @ ( number_number_of @ int @ L ) )
<=> ( ord_less @ int @ K @ L ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_less__number__of__int__code) ).
thf(52,axiom,
! [K_1: $i,L_1: $i] :
( ( times_times @ int @ ( bit0 @ K_1 ) @ L_1 )
= ( bit0 @ ( times_times @ int @ K_1 @ L_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_mult__Bit0) ).
thf(53,axiom,
! [W: $i] :
( ( times_times @ int @ pls @ W )
= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_mult__Pls) ).
thf(54,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_61_nat__1__add__1) ).
thf(55,axiom,
! [X_a: $i] :
( ( ( number_ring @ X_a )
& ( linordered_idom @ X_a ) )
=> ! [Y_1: $i] :
( ( ord_less_eq @ X_a @ ( one_one @ X_a ) @ ( number_number_of @ X_a @ Y_1 ) )
<=> ( ord_less_eq @ int @ ( bit1 @ pls ) @ Y_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_le__special_I2_J) ).
thf(56,axiom,
! [X_a: $i] :
( ( ( number_ring @ X_a )
& ( linordered_idom @ X_a ) )
=> ! [X_1: $i] :
( ( ord_less_eq @ X_a @ ( number_number_of @ X_a @ X_1 ) @ ( one_one @ X_a ) )
<=> ( ord_less_eq @ int @ X_1 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_le__special_I4_J) ).
thf(57,axiom,
( ( zero_zero @ nat )
= ( number_number_of @ nat @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_semiring__norm_I113_J) ).
thf(58,axiom,
( ( number_number_of @ nat @ pls )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_nat__number__of__Pls) ).
thf(59,axiom,
! [Z_2: $i,Z: $i,W_2: $i,W: $i] :
( ( ord_less @ int @ W_2 @ W )
=> ( ( ord_less_eq @ int @ Z_2 @ Z )
=> ( ord_less @ int @ ( plus_plus @ int @ W_2 @ Z_2 ) @ ( plus_plus @ int @ W @ Z ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_zadd__zless__mono) ).
thf(60,axiom,
! [K: $i] :
( ( ord_less_eq @ int @ pls @ ( bit0 @ K ) )
<=> ( ord_less_eq @ int @ pls @ K ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_rel__simps_I21_J) ).
thf(61,axiom,
! [K: $i] :
( ( ord_less_eq @ int @ ( bit0 @ K ) @ pls )
<=> ( ord_less_eq @ int @ K @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_rel__simps_I27_J) ).
thf(62,axiom,
! [K: $i,L: $i] :
( ( ord_less_eq @ int @ ( bit0 @ K ) @ ( bit1 @ L ) )
<=> ( ord_less_eq @ int @ K @ L ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_rel__simps_I32_J) ).
thf(63,axiom,
! [K1: $i,K2: $i] :
( ( ord_less_eq @ int @ ( bit0 @ K1 ) @ ( bit1 @ K2 ) )
<=> ( ord_less_eq @ int @ K1 @ K2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_less__eq__int__code_I14_J) ).
thf(64,axiom,
! [K: $i] :
( ( ord_less_eq @ int @ pls @ ( bit1 @ K ) )
<=> ( ord_less_eq @ int @ pls @ K ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_rel__simps_I22_J) ).
thf(65,axiom,
! [X_a: $i] :
( ( ( number @ X_a )
& ( linorder @ X_a ) )
=> ! [V_3: $i,W_1: $i] :
( ( ord_less_eq @ X_a @ ( number_number_of @ X_a @ V_3 ) @ ( number_number_of @ X_a @ W_1 ) )
<=> ~ ( ord_less @ X_a @ ( number_number_of @ X_a @ W_1 ) @ ( number_number_of @ X_a @ V_3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_le__number__of__eq__not__less) ).
thf(66,axiom,
! [V_3: $i] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( number_number_of @ nat @ V_3 ) )
<=> ( ord_less @ int @ pls @ V_3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_less__0__number__of) ).
thf(67,axiom,
! [X_a: $i] :
( ( ( number_ring @ X_a )
& ( linordered_idom @ X_a ) )
=> ! [Y_1: $i] :
( ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ ( number_number_of @ X_a @ Y_1 ) )
<=> ( ord_less_eq @ int @ pls @ Y_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_le__special_I1_J) ).
thf(68,axiom,
! [X_a: $i] :
( ( ( number_ring @ X_a )
& ( linordered_idom @ X_a ) )
=> ! [X_1: $i] :
( ( ord_less_eq @ X_a @ ( number_number_of @ X_a @ X_1 ) @ ( zero_zero @ X_a ) )
<=> ( ord_less_eq @ int @ X_1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_le__special_I3_J) ).
thf(69,axiom,
! [X_a: $i] :
( ( linordered_ring @ X_a )
=> ! [X: $i,Y: $i] : ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ ( plus_plus @ X_a @ ( times_times @ X_a @ X @ X ) @ ( times_times @ X_a @ Y @ Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_sum__squares__ge__zero) ).
thf(70,axiom,
! [X_a: $i] :
( ( linord581940658strict @ X_a )
=> ! [X_1: $i,Y_1: $i] :
( ( ord_less_eq @ X_a @ ( plus_plus @ X_a @ ( times_times @ X_a @ X_1 @ X_1 ) @ ( times_times @ X_a @ Y_1 @ Y_1 ) ) @ ( zero_zero @ X_a ) )
<=> ( ( ( ti @ X_a @ X_1 )
= ( zero_zero @ X_a ) )
& ( ( ti @ X_a @ Y_1 )
= ( zero_zero @ X_a ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_sum__squares__le__zero__iff) ).
thf(71,axiom,
! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [V: $i,W: $i] :
( ( number_number_of @ X_a @ ( times_times @ int @ V @ W ) )
= ( times_times @ X_a @ ( number_number_of @ X_a @ V ) @ ( number_number_of @ X_a @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_number__of__mult) ).
thf(72,axiom,
! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [V: $i,W: $i] :
( ( times_times @ X_a @ ( number_number_of @ X_a @ V ) @ ( number_number_of @ X_a @ W ) )
= ( number_number_of @ X_a @ ( times_times @ int @ V @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_arith__simps_I32_J) ).
thf(73,axiom,
! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [V: $i,W: $i,Z: $i] :
( ( times_times @ X_a @ ( number_number_of @ X_a @ V ) @ ( times_times @ X_a @ ( number_number_of @ X_a @ W ) @ Z ) )
= ( times_times @ X_a @ ( number_number_of @ X_a @ ( times_times @ int @ V @ W ) ) @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_mult__number__of__left) ).
thf(74,axiom,
! [X_a: $i] :
( ( number_semiring @ X_a )
=> ! [V_1: $i,V: $i] :
( ( ord_less_eq @ int @ pls @ V )
=> ( ( ord_less_eq @ int @ pls @ V_1 )
=> ( ( times_times @ X_a @ ( number_number_of @ X_a @ V ) @ ( number_number_of @ X_a @ V_1 ) )
= ( number_number_of @ X_a @ ( times_times @ int @ V @ V_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_semiring__mult__number__of) ).
thf(75,axiom,
! [V_3: $i] :
( ( ( zero_zero @ nat )
= ( number_number_of @ nat @ V_3 ) )
<=> ( ord_less_eq @ int @ V_3 @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_eq__0__number__of) ).
thf(76,axiom,
! [V_3: $i] :
( ( ( number_number_of @ nat @ V_3 )
= ( zero_zero @ nat ) )
<=> ( ord_less_eq @ int @ V_3 @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_eq__number__of__0) ).
thf(77,axiom,
! [K_1: $i,I: $i,J: $i] :
( ( ord_less_eq @ int @ I @ J )
=> ( ord_less_eq @ int @ ( plus_plus @ int @ K_1 @ I ) @ ( plus_plus @ int @ K_1 @ J ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_zadd__left__mono) ).
thf(78,axiom,
! [Z_1: $i,W_1: $i] :
( ( ord_less @ int @ Z_1 @ W_1 )
<=> ( ( ord_less_eq @ int @ Z_1 @ W_1 )
& ( Z_1 != W_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_zless__le) ).
thf(79,axiom,
! [K: $i,L: $i] :
( ( ord_less_eq @ int @ ( bit0 @ K ) @ ( bit0 @ L ) )
<=> ( ord_less_eq @ int @ K @ L ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_rel__simps_I31_J) ).
thf(80,axiom,
! [K1: $i,K2: $i] :
( ( ord_less_eq @ int @ ( bit0 @ K1 ) @ ( bit0 @ K2 ) )
<=> ( ord_less_eq @ int @ K1 @ K2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_less__eq__int__code_I13_J) ).
thf(81,axiom,
ord_less_eq @ int @ pls @ pls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_rel__simps_I19_J) ).
thf(82,axiom,
! [K: $i,L: $i] :
( ( ord_less_eq @ int @ ( bit1 @ K ) @ ( bit1 @ L ) )
<=> ( ord_less_eq @ int @ K @ L ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_rel__simps_I34_J) ).
thf(83,axiom,
! [K1: $i,K2: $i] :
( ( ord_less_eq @ int @ ( bit1 @ K1 ) @ ( bit1 @ K2 ) )
<=> ( ord_less_eq @ int @ K1 @ K2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_less__eq__int__code_I16_J) ).
thf(84,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( power_power @ int @ X @ ( plus_plus @ nat @ Y @ Z ) )
= ( times_times @ int @ ( power_power @ int @ X @ Y ) @ ( power_power @ int @ X @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_zpower__zadd__distrib) ).
thf(85,axiom,
! [Z: $i,W: $i] :
( ( ord_less_eq @ int @ Z @ W )
=> ( ( ord_less_eq @ int @ W @ Z )
=> ( Z = W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_zle__antisym) ).
thf(86,axiom,
! [K_1: $i,I: $i,J: $i] :
( ( ord_less_eq @ int @ I @ J )
=> ( ( ord_less_eq @ int @ J @ K_1 )
=> ( ord_less_eq @ int @ I @ K_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_zle__trans) ).
thf(87,axiom,
! [Z1: $i,Z2: $i,Z3: $i] :
( ( times_times @ int @ ( times_times @ int @ Z1 @ Z2 ) @ Z3 )
= ( times_times @ int @ Z1 @ ( times_times @ int @ Z2 @ Z3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_zmult__assoc) ).
thf(88,axiom,
! [X_a: $i] :
( ( ( number_ring @ X_a )
& ( linordered_idom @ X_a ) )
=> ! [X_1: $i,Y_1: $i] :
( ( ord_less_eq @ X_a @ ( number_number_of @ X_a @ X_1 ) @ ( number_number_of @ X_a @ Y_1 ) )
<=> ( ord_less_eq @ int @ X_1 @ Y_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_le__number__of) ).
thf(89,axiom,
! [K: $i,L: $i] :
( ( ord_less_eq @ int @ ( number_number_of @ int @ K ) @ ( number_number_of @ int @ L ) )
<=> ( ord_less_eq @ int @ K @ L ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_less__eq__number__of__int__code) ).
thf(90,axiom,
! [V: $i,W: $i] :
( ( times_times @ int @ ( number_number_of @ int @ V ) @ ( number_number_of @ int @ W ) )
= ( number_number_of @ int @ ( times_times @ int @ V @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_times__numeral__code_I5_J) ).
thf(91,axiom,
! [Z: $i,W: $i] :
( ( ord_less_eq @ int @ Z @ W )
| ( ord_less_eq @ int @ W @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_zle__linear) ).
thf(92,axiom,
! [Z: $i,W: $i] :
( ( times_times @ int @ Z @ W )
= ( times_times @ int @ W @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_zmult__commute) ).
thf(93,axiom,
! [K_1: $i] :
( ( number_number_of @ int @ K_1 )
= K_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_number__of__is__id) ).
thf(94,axiom,
! [W: $i] : ( ord_less_eq @ int @ W @ W ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_zle__refl) ).
thf(95,axiom,
twoSqu33214720sum2sq @ ( times_times @ int @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) @ t ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_qf1pt) ).
thf(96,axiom,
zprime @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_p) ).
thf(97,axiom,
~ ! [T_1: $i] :
( ( plus_plus @ int @ ( power_power @ int @ s @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( one_one @ int ) )
!= ( times_times @ int @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18__096_B_Bthesis_O_A_I_B_Bt_O_As_A_094_A2_A_L_A1_A_061_A_I4_A_K_Am_A_L_A1_) ).
thf(98,axiom,
ord_less @ int @ t @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_t__l__p) ).
thf(99,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_16_add__special_I3_J) ).
thf(100,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_15_add__special_I2_J) ).
thf(101,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_14_zero__eq__power2) ).
thf(102,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_13_zero__power2) ).
thf(103,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_12_one__power2) ).
thf(104,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_11_zero__less__power2) ).
thf(105,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_10_power2__less__0) ).
thf(106,axiom,
! [X_a: $i] :
( ( linordered_idom @ X_a )
=> ! [X_1: $i,Y_1: $i] :
( ( ( plus_plus @ X_a @ ( power_power @ X_a @ X_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ X_a @ Y_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ X_a ) )
<=> ( ( ( ti @ X_a @ X_1 )
= ( zero_zero @ X_a ) )
& ( ( ti @ X_a @ Y_1 )
= ( zero_zero @ X_a ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_sum__power2__eq__zero__iff) ).
thf(107,axiom,
! [X_a: $i] :
( ( linordered_idom @ X_a )
=> ! [X_1: $i,Y_1: $i] :
( ( ord_less @ X_a @ ( zero_zero @ X_a ) @ ( plus_plus @ X_a @ ( power_power @ X_a @ X_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ X_a @ Y_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
<=> ( ( ( ti @ X_a @ X_1 )
!= ( zero_zero @ X_a ) )
| ( ( ti @ X_a @ Y_1 )
!= ( zero_zero @ X_a ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_sum__power2__gt__zero__iff) ).
thf(108,axiom,
! [X_a: $i] :
( ( linordered_idom @ X_a )
=> ! [X: $i,Y: $i] :
~ ( ord_less @ X_a @ ( plus_plus @ X_a @ ( power_power @ X_a @ X @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ X_a @ Y @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( zero_zero @ X_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_not__sum__power2__lt__zero) ).
thf(109,axiom,
ord_less @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_p0) ).
thf(110,axiom,
~ ( ord_less_eq @ int @ ( one_one @ int ) @ t ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5__096_126_A1_A_060_061_At_096) ).
thf(111,axiom,
( ( t
= ( zero_zero @ int ) )
=> ( ( plus_plus @ int @ ( power_power @ int @ s @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( one_one @ int ) )
= ( zero_zero @ int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_calculation_I2_J) ).
thf(112,axiom,
( ( plus_plus @ int @ ( power_power @ int @ s @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( one_one @ int ) )
= ( times_times @ int @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) @ t ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_t) ).
thf(113,axiom,
ord_less @ int @ ( times_times @ int @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) @ t ) @ ( times_times @ int @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) @ ( zero_zero @ int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__096_I4_A_K_Am_A_L_A1_J_A_K_At_A_060_A_I4_A_K_Am_A_L_A1_J_A_K_A0_096) ).
thf(114,axiom,
ord_less @ int @ t @ ( one_one @ int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_calculation_I1_J) ).
thf(115,axiom,
ord_less @ int @ t @ ( zero_zero @ int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__096t_A_060_A0_096) ).
thf(116,axiom,
( ( ti @ int @ t )
= t ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_t_____res) ).
thf(117,axiom,
( ( ti @ int @ m )
= m ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_m_res) ).
thf(118,axiom,
! [B_1: $i] :
( ( twoSqu33214720sum2sq @ ( ti @ int @ B_1 ) )
<=> ( twoSqu33214720sum2sq @ B_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_TwoSquares__Mirabelle__vsgmegnqdl_Ois__sum2sq_arg1) ).
thf(119,axiom,
! [B_1: $i,B_2: $i,X_a: $i] :
( ( semiring_1 @ 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_res) ).
thf(120,axiom,
! [B_1: $i,B_2: $i,X_a: $i] :
( ( semiring_1 @ 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_arg2) ).
thf(121,axiom,
! [B_1: $i,B_2: $i,X_a: $i] :
( ( semiring_1 @ 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_arg1) ).
thf(122,axiom,
! [B_1: $i,B_2: $i,X_a: $i] :
( ( linordered_ring @ X_a )
=> ( ( ord_less_eq @ X_a @ B_1 @ ( ti @ X_a @ B_2 ) )
<=> ( ord_less_eq @ X_a @ B_1 @ B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Orderings_Oord__class_Oless__eq_1_arg2) ).
thf(123,axiom,
! [B_1: $i,B_2: $i,X_a: $i] :
( ( linordered_ring @ X_a )
=> ( ( ord_less_eq @ X_a @ ( ti @ X_a @ B_1 ) @ B_2 )
<=> ( ord_less_eq @ X_a @ B_1 @ B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Orderings_Oord__class_Oless__eq_1_arg1) ).
thf(124,axiom,
! [B_1: $i,B_2: $i,X_a: $i] :
( ( ( number @ X_a )
& ( linorder @ X_a ) )
=> ( ( ord_less_eq @ X_a @ B_1 @ ( ti @ X_a @ B_2 ) )
<=> ( ord_less_eq @ X_a @ B_1 @ B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Orderings_Oord__class_Oless__eq_0_arg2) ).
thf(125,axiom,
! [B_1: $i,B_2: $i,X_a: $i] :
( ( ( number @ X_a )
& ( linorder @ X_a ) )
=> ( ( ord_less_eq @ X_a @ ( ti @ X_a @ B_1 ) @ B_2 )
<=> ( ord_less_eq @ X_a @ B_1 @ B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Orderings_Oord__class_Oless__eq_0_arg1) ).
thf(126,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_1_arg2) ).
thf(127,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_1_arg1) ).
thf(128,axiom,
! [B_1: $i,B_2: $i,X_a: $i] :
( ( ( number @ X_a )
& ( linorder @ 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(129,axiom,
! [B_1: $i,B_2: $i,X_a: $i] :
( ( ( number @ X_a )
& ( linorder @ 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(130,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(131,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(132,axiom,
! [B_1: $i] :
( ( zprime @ ( ti @ int @ B_1 ) )
<=> ( zprime @ B_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_IntPrimes_Ozprime_arg1) ).
thf(133,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(134,axiom,
! [X_a: $i] :
( ( semiring_1 @ 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(135,axiom,
! [X_a: $i] :
( ( linordered_ring @ 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(136,axiom,
! [B_1: $i,B_2: $i,X_a: $i] :
( ( linordered_ring @ X_a )
=> ( ( ti @ X_a @ ( times_times @ X_a @ B_1 @ B_2 ) )
= ( times_times @ X_a @ B_1 @ B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_1_res) ).
thf(137,axiom,
! [B_1: $i,B_2: $i,X_a: $i] :
( ( linordered_ring @ X_a )
=> ( ( times_times @ X_a @ B_1 @ ( ti @ X_a @ B_2 ) )
= ( times_times @ X_a @ B_1 @ B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_1_arg2) ).
thf(138,axiom,
! [B_1: $i,B_2: $i,X_a: $i] :
( ( linordered_ring @ X_a )
=> ( ( times_times @ X_a @ ( ti @ X_a @ B_1 ) @ B_2 )
= ( times_times @ X_a @ B_1 @ B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_1_arg1) ).
thf(139,axiom,
! [B_1: $i,B_2: $i,X_b: $i] :
( ( ( number @ X_b )
& ( semiring @ X_b ) )
=> ( ( ti @ X_b @ ( times_times @ X_b @ B_1 @ B_2 ) )
= ( times_times @ X_b @ B_1 @ B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_0_res) ).
thf(140,axiom,
! [B_1: $i,B_2: $i,X_b: $i] :
( ( ( number @ X_b )
& ( semiring @ X_b ) )
=> ( ( times_times @ X_b @ B_1 @ ( ti @ X_b @ B_2 ) )
= ( times_times @ X_b @ B_1 @ B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_0_arg2) ).
thf(141,axiom,
! [B_1: $i,B_2: $i,X_b: $i] :
( ( ( number @ X_b )
& ( semiring @ X_b ) )
=> ( ( times_times @ X_b @ ( ti @ X_b @ B_1 ) @ B_2 )
= ( times_times @ X_b @ B_1 @ B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_0_arg1) ).
thf(142,axiom,
! [B_1: $i,B_2: $i,X_a: $i] :
( ( linordered_ring @ 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(143,axiom,
! [B_1: $i,B_2: $i,X_a: $i] :
( ( linordered_ring @ 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(144,axiom,
! [B_1: $i,B_2: $i,X_a: $i] :
( ( linordered_ring @ 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(145,axiom,
! [B_1: $i,B_2: $i,X_b: $i] :
( ( ( number @ X_b )
& ( semiring @ X_b ) )
=> ( ( ti @ X_b @ ( plus_plus @ X_b @ B_1 @ B_2 ) )
= ( plus_plus @ X_b @ B_1 @ B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_0_res) ).
thf(146,axiom,
! [B_1: $i,B_2: $i,X_b: $i] :
( ( ( number @ X_b )
& ( semiring @ X_b ) )
=> ( ( plus_plus @ X_b @ B_1 @ ( ti @ X_b @ B_2 ) )
= ( plus_plus @ X_b @ B_1 @ B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_0_arg2) ).
thf(147,axiom,
! [B_1: $i,B_2: $i,X_b: $i] :
( ( ( number @ X_b )
& ( semiring @ X_b ) )
=> ( ( plus_plus @ X_b @ ( ti @ X_b @ B_1 ) @ B_2 )
= ( plus_plus @ X_b @ B_1 @ B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_0_arg1) ).
thf(148,axiom,
! [X_a: $i] :
( ( semiring_1 @ 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(149,axiom,
( ( ti @ int @ s )
= s ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_s_____res) ).
thf(150,axiom,
( ( ti @ int @ pls )
= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Int_OPls_res) ).
thf(151,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(152,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(153,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(154,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(155,conjecture,
ord_less @ int @ ( plus_plus @ int @ ( power_power @ int @ s @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( one_one @ int ) ) @ ( zero_zero @ int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(156,negated_conjecture,
( ( ord_less @ int @ ( plus_plus @ int @ ( power_power @ int @ s @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( one_one @ int ) ) @ ( zero_zero @ int ) )
= $false ),
inference(negate_conjecture,[status(cth)],[155]) ).
thf(157,plain,
( ( ord_less @ int @ ( plus_plus @ int @ ( power_power @ int @ s @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( one_one @ int ) ) @ ( zero_zero @ int ) )
= $false ),
inference(unfold_def,[status(thm)],[156]) ).
thf(158,plain,
( ( ! [T: $i,A: $i] :
( ( ti @ T @ ( ti @ T @ A ) )
= ( ti @ T @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(159,plain,
( ( ! [X_b: $i] :
( ( ( number @ X_b )
& ( semiring @ X_b ) )
=> ! [V: $i,B: $i,C: $i] :
( ( times_times @ X_b @ ( number_number_of @ X_b @ V ) @ ( plus_plus @ X_b @ B @ C ) )
= ( plus_plus @ X_b @ ( times_times @ X_b @ ( number_number_of @ X_b @ V ) @ B ) @ ( times_times @ X_b @ ( number_number_of @ X_b @ V ) @ C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(160,plain,
( ( ! [X_b: $i] :
( ( ( number @ X_b )
& ( semiring @ X_b ) )
=> ! [A_1: $i,B: $i,V: $i] :
( ( times_times @ X_b @ ( plus_plus @ X_b @ A_1 @ B ) @ ( number_number_of @ X_b @ V ) )
= ( plus_plus @ X_b @ ( times_times @ X_b @ A_1 @ ( number_number_of @ X_b @ V ) ) @ ( times_times @ X_b @ B @ ( number_number_of @ X_b @ V ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(161,plain,
( ( ! [X_a: $i] :
( ( linord581940658strict @ X_a )
=> ! [X_1: $i,Y_1: $i] :
( ( ( plus_plus @ X_a @ ( times_times @ X_a @ X_1 @ X_1 ) @ ( times_times @ X_a @ Y_1 @ Y_1 ) )
= ( zero_zero @ X_a ) )
<=> ( ( ( ti @ X_a @ X_1 )
= ( zero_zero @ X_a ) )
& ( ( ti @ X_a @ Y_1 )
= ( zero_zero @ X_a ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(162,plain,
( ( ! [X_a: $i] :
( ( ( number_ring @ X_a )
& ( linordered_idom @ X_a ) )
=> ! [Y_1: $i] :
( ( ord_less_eq @ X_a @ ( one_one @ X_a ) @ ( number_number_of @ X_a @ Y_1 ) )
<=> ( ord_less_eq @ int @ ( bit1 @ pls ) @ Y_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(163,plain,
( ( ! [X_a: $i] :
( ( ( number_ring @ X_a )
& ( linordered_idom @ X_a ) )
=> ! [X_1: $i] :
( ( ord_less_eq @ X_a @ ( number_number_of @ X_a @ X_1 ) @ ( one_one @ X_a ) )
<=> ( ord_less_eq @ int @ X_1 @ ( bit1 @ pls ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(164,plain,
( ( ! [X_a: $i] :
( ( ( number @ X_a )
& ( linorder @ X_a ) )
=> ! [V_3: $i,W_1: $i] :
( ( ord_less_eq @ X_a @ ( number_number_of @ X_a @ V_3 ) @ ( number_number_of @ X_a @ W_1 ) )
<=> ~ ( ord_less @ X_a @ ( number_number_of @ X_a @ W_1 ) @ ( number_number_of @ X_a @ V_3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(165,plain,
( ( ! [X_a: $i] :
( ( ( number_ring @ X_a )
& ( linordered_idom @ X_a ) )
=> ! [Y_1: $i] :
( ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ ( number_number_of @ X_a @ Y_1 ) )
<=> ( ord_less_eq @ int @ pls @ Y_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(166,plain,
( ( ! [X_a: $i] :
( ( ( number_ring @ X_a )
& ( linordered_idom @ X_a ) )
=> ! [X_1: $i] :
( ( ord_less_eq @ X_a @ ( number_number_of @ X_a @ X_1 ) @ ( zero_zero @ X_a ) )
<=> ( ord_less_eq @ int @ X_1 @ pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(167,plain,
( ( ! [X_a: $i] :
( ( linordered_ring @ X_a )
=> ! [X: $i,Y: $i] : ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ ( plus_plus @ X_a @ ( times_times @ X_a @ X @ X ) @ ( times_times @ X_a @ Y @ Y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(168,plain,
( ( ! [X_a: $i] :
( ( linord581940658strict @ X_a )
=> ! [X_1: $i,Y_1: $i] :
( ( ord_less_eq @ X_a @ ( plus_plus @ X_a @ ( times_times @ X_a @ X_1 @ X_1 ) @ ( times_times @ X_a @ Y_1 @ Y_1 ) ) @ ( zero_zero @ X_a ) )
<=> ( ( ( ti @ X_a @ X_1 )
= ( zero_zero @ X_a ) )
& ( ( ti @ X_a @ Y_1 )
= ( zero_zero @ X_a ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(169,plain,
( ( ! [X_a: $i] :
( ( number_semiring @ X_a )
=> ! [V_1: $i,V: $i] :
( ( ord_less_eq @ int @ pls @ V )
=> ( ( ord_less_eq @ int @ pls @ V_1 )
=> ( ( times_times @ X_a @ ( number_number_of @ X_a @ V ) @ ( number_number_of @ X_a @ V_1 ) )
= ( number_number_of @ X_a @ ( times_times @ int @ V @ V_1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(170,plain,
( ( ! [X_a: $i] :
( ( ( number_ring @ X_a )
& ( linordered_idom @ X_a ) )
=> ! [X_1: $i,Y_1: $i] :
( ( ord_less_eq @ X_a @ ( number_number_of @ X_a @ X_1 ) @ ( number_number_of @ X_a @ Y_1 ) )
<=> ( ord_less_eq @ int @ X_1 @ Y_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(171,plain,
( ( twoSqu33214720sum2sq @ ( times_times @ int @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) @ t ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(172,plain,
( ( zprime @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(173,plain,
( ( ord_less @ int @ t @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(174,plain,
( ( ( plus_plus @ int @ ( power_power @ int @ s @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( one_one @ int ) )
= ( times_times @ int @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) @ t ) )
= $true ),
inference(unfold_def,[status(thm)],[112]) ).
thf(175,plain,
( ( ord_less @ int @ ( times_times @ int @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) @ t ) @ ( times_times @ int @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) @ ( zero_zero @ int ) ) )
= $true ),
inference(unfold_def,[status(thm)],[113]) ).
thf(176,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ( linordered_ring @ X_a )
=> ( ( ord_less_eq @ X_a @ B_1 @ ( ti @ X_a @ B_2 ) )
<=> ( ord_less_eq @ X_a @ B_1 @ B_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[122]) ).
thf(177,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ( linordered_ring @ X_a )
=> ( ( ord_less_eq @ X_a @ ( ti @ X_a @ B_1 ) @ B_2 )
<=> ( ord_less_eq @ X_a @ B_1 @ B_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[123]) ).
thf(178,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ( ( number @ X_a )
& ( linorder @ X_a ) )
=> ( ( ord_less_eq @ X_a @ B_1 @ ( ti @ X_a @ B_2 ) )
<=> ( ord_less_eq @ X_a @ B_1 @ B_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[124]) ).
thf(179,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ( ( number @ X_a )
& ( linorder @ X_a ) )
=> ( ( ord_less_eq @ X_a @ ( ti @ X_a @ B_1 ) @ B_2 )
<=> ( ord_less_eq @ X_a @ B_1 @ B_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[125]) ).
thf(180,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ( ( number @ X_a )
& ( linorder @ 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)],[128]) ).
thf(181,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ( ( number @ X_a )
& ( linorder @ 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)],[129]) ).
thf(182,plain,
( ( ! [X_a: $i] :
( ( ti @ X_a @ ( undefined @ X_a ) )
= ( undefined @ X_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[133]) ).
thf(183,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ( linordered_ring @ X_a )
=> ( ( ti @ X_a @ ( times_times @ X_a @ B_1 @ B_2 ) )
= ( times_times @ X_a @ B_1 @ B_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[136]) ).
thf(184,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ( linordered_ring @ X_a )
=> ( ( times_times @ X_a @ B_1 @ ( ti @ X_a @ B_2 ) )
= ( times_times @ X_a @ B_1 @ B_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[137]) ).
thf(185,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ( linordered_ring @ X_a )
=> ( ( times_times @ X_a @ ( ti @ X_a @ B_1 ) @ B_2 )
= ( times_times @ X_a @ B_1 @ B_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[138]) ).
thf(186,plain,
( ( ! [B_1: $i,B_2: $i,X_b: $i] :
( ( ( number @ X_b )
& ( semiring @ X_b ) )
=> ( ( ti @ X_b @ ( times_times @ X_b @ B_1 @ B_2 ) )
= ( times_times @ X_b @ B_1 @ B_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[139]) ).
thf(187,plain,
( ( ! [B_1: $i,B_2: $i,X_b: $i] :
( ( ( number @ X_b )
& ( semiring @ X_b ) )
=> ( ( times_times @ X_b @ B_1 @ ( ti @ X_b @ B_2 ) )
= ( times_times @ X_b @ B_1 @ B_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[140]) ).
thf(188,plain,
( ( ! [B_1: $i,B_2: $i,X_b: $i] :
( ( ( number @ X_b )
& ( semiring @ X_b ) )
=> ( ( times_times @ X_b @ ( ti @ X_b @ B_1 ) @ B_2 )
= ( times_times @ X_b @ B_1 @ B_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[141]) ).
thf(189,plain,
( ( ! [B_1: $i,B_2: $i,X_b: $i] :
( ( ( number @ X_b )
& ( semiring @ X_b ) )
=> ( ( ti @ X_b @ ( plus_plus @ X_b @ B_1 @ B_2 ) )
= ( plus_plus @ X_b @ B_1 @ B_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[145]) ).
thf(190,plain,
( ( ! [B_1: $i,B_2: $i,X_b: $i] :
( ( ( number @ X_b )
& ( semiring @ X_b ) )
=> ( ( plus_plus @ X_b @ B_1 @ ( ti @ X_b @ B_2 ) )
= ( plus_plus @ X_b @ B_1 @ B_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[146]) ).
thf(191,plain,
( ( ! [B_1: $i,B_2: $i,X_b: $i] :
( ( ( number @ X_b )
& ( semiring @ X_b ) )
=> ( ( plus_plus @ X_b @ ( ti @ X_b @ B_1 ) @ B_2 )
= ( plus_plus @ X_b @ B_1 @ B_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[147]) ).
thf(192,plain,
( ( number @ nat )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(193,plain,
( ( semiring @ nat )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(194,plain,
( ( semiring_1 @ nat )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(195,plain,
( ( linorder @ nat )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(196,plain,
( ( number_semiring @ nat )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(197,plain,
( ( number @ int )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(198,plain,
( ( semiring @ int )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(199,plain,
( ( number_ring @ int )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(200,plain,
( ( ring_char_0 @ int )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(201,plain,
( ( semiring_1 @ int )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(202,plain,
( ( linorder @ int )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(203,plain,
( ( number_semiring @ int )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(204,plain,
( ( linordered_idom @ int )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(205,plain,
( ( linordered_ring @ int )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(206,plain,
( ( linord581940658strict @ int )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(207,plain,
( ( ring_11004092258visors @ int )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(208,plain,
( ( ( zero_zero @ int )
= ( number_number_of @ int @ pls ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(209,plain,
( ( ! [Z: $i,W: $i] :
( ( plus_plus @ int @ Z @ W )
= ( plus_plus @ int @ W @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(210,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)],[20]) ).
thf(211,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)],[21]) ).
thf(212,plain,
( ( ! [X: $i,Y: $i] :
( ( ord_less @ int @ X @ Y )
| ( X = Y )
| ( ord_less @ int @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(213,plain,
( ( ! [K: $i,L: $i] :
( ( ( bit0 @ K )
= ( bit0 @ L ) )
<=> ( K = L ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(214,plain,
( ( ! [K: $i,L: $i] :
( ( ( bit1 @ K )
= ( bit1 @ L ) )
<=> ( K = L ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(215,plain,
( ( ! [X_a: $i] :
( ( number @ X_a )
=> ! [W_1: $i,X_1: $i] :
( ( ( number_number_of @ X_a @ W_1 )
= ( ti @ X_a @ X_1 ) )
<=> ( ( ti @ X_a @ X_1 )
= ( number_number_of @ X_a @ W_1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(216,plain,
( ( ! [X_a: $i] :
( ( ( number_ring @ X_a )
& ( ring_char_0 @ X_a ) )
=> ! [X_1: $i,Y_1: $i] :
( ( ( number_number_of @ X_a @ X_1 )
= ( number_number_of @ X_a @ Y_1 ) )
<=> ( X_1 = Y_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(217,plain,
( ( ! [Z: $i] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ Z )
=> ( ord_less @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( one_one @ int ) @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(218,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)],[31]) ).
thf(219,plain,
( ( ! [X_a: $i] :
( ( number_semiring @ X_a )
=> ! [V_1: $i,V: $i] :
( ( ord_less_eq @ int @ pls @ V )
=> ( ( ord_less_eq @ int @ pls @ V_1 )
=> ( ( plus_plus @ X_a @ ( number_number_of @ X_a @ V ) @ ( number_number_of @ X_a @ V_1 ) )
= ( number_number_of @ X_a @ ( plus_plus @ int @ V @ V_1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(220,plain,
( ( ! [W_1: $i,Z_1: $i] :
( ( ord_less @ int @ W_1 @ ( plus_plus @ int @ Z_1 @ ( one_one @ int ) ) )
<=> ( ord_less_eq @ int @ W_1 @ Z_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(221,plain,
( ( ! [W_1: $i,Z_1: $i] :
( ( ord_less_eq @ int @ ( plus_plus @ int @ W_1 @ ( one_one @ int ) ) @ Z_1 )
<=> ( ord_less @ int @ W_1 @ Z_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(222,plain,
( ( ! [W: $i,Z: $i] :
( ( ord_less @ int @ W @ Z )
=> ( ord_less_eq @ int @ ( plus_plus @ int @ W @ ( one_one @ int ) ) @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(223,plain,
( ( ( one_one @ nat )
= ( number_number_of @ nat @ ( bit1 @ pls ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(224,plain,
( ( ( number_number_of @ nat @ ( bit1 @ pls ) )
= ( one_one @ nat ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(225,plain,
( ( ! [Z_1: $i] :
( ( ord_less_eq @ int @ ( one_one @ int ) @ Z_1 )
<=> ( ord_less @ int @ ( zero_zero @ int ) @ Z_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(226,plain,
( ( ! [V_3: $i,V_2: $i] :
( ( ord_less @ nat @ ( number_number_of @ nat @ V_3 ) @ ( number_number_of @ nat @ V_2 ) )
<=> ( ( ( ord_less @ int @ V_3 @ V_2 )
=> ( ord_less @ int @ pls @ V_2 ) )
& ( ord_less @ int @ V_3 @ V_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(227,plain,
( ( ! [K: $i,L: $i] :
( ( ord_less @ int @ ( bit0 @ K ) @ ( bit1 @ L ) )
<=> ( ord_less_eq @ int @ K @ L ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(228,plain,
( ( ! [K1: $i,K2: $i] :
( ( ord_less @ int @ ( bit0 @ K1 ) @ ( bit1 @ K2 ) )
<=> ( ord_less_eq @ int @ K1 @ K2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(229,plain,
( ( ! [K: $i,L: $i] :
( ( ord_less_eq @ int @ ( bit1 @ K ) @ ( bit0 @ L ) )
<=> ( ord_less @ int @ K @ L ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(230,plain,
( ( ! [K1: $i,K2: $i] :
( ( ord_less_eq @ int @ ( bit1 @ K1 ) @ ( bit0 @ K2 ) )
<=> ( ord_less @ int @ K1 @ K2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(231,plain,
( ( ! [K: $i] :
( ( ord_less @ int @ pls @ ( bit1 @ K ) )
<=> ( ord_less_eq @ int @ pls @ K ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(232,plain,
( ( ! [K: $i] :
( ( ord_less_eq @ int @ ( bit1 @ K ) @ pls )
<=> ( ord_less @ int @ K @ pls ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(233,plain,
( ( ! [W: $i,Z1: $i,Z2: $i] :
( ( times_times @ int @ W @ ( plus_plus @ int @ Z1 @ Z2 ) )
= ( plus_plus @ int @ ( times_times @ int @ W @ Z1 ) @ ( times_times @ int @ W @ Z2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(234,plain,
( ( ! [Z1: $i,Z2: $i,W: $i] :
( ( times_times @ int @ ( plus_plus @ int @ Z1 @ Z2 ) @ W )
= ( plus_plus @ int @ ( times_times @ int @ Z1 @ W ) @ ( times_times @ int @ Z2 @ W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(235,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)],[48]) ).
thf(236,plain,
( ( ! [Z: $i] :
( ( times_times @ int @ ( one_one @ int ) @ Z )
= Z ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(237,plain,
( ( ! [Z: $i] :
( ( times_times @ int @ Z @ ( one_one @ int ) )
= Z ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(238,plain,
( ( ! [K: $i,L: $i] :
( ( ord_less @ int @ ( number_number_of @ int @ K ) @ ( number_number_of @ int @ L ) )
<=> ( ord_less @ int @ K @ L ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(239,plain,
( ( ! [K_1: $i,L_1: $i] :
( ( times_times @ int @ ( bit0 @ K_1 ) @ L_1 )
= ( bit0 @ ( times_times @ int @ K_1 @ L_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(240,plain,
( ( ! [W: $i] :
( ( times_times @ int @ pls @ W )
= pls ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(241,plain,
( ( ( plus_plus @ nat @ ( one_one @ nat ) @ ( one_one @ nat ) )
= ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(242,plain,
( ( ( zero_zero @ nat )
= ( number_number_of @ nat @ pls ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(243,plain,
( ( ( number_number_of @ nat @ pls )
= ( zero_zero @ nat ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(244,plain,
( ( ! [Z_2: $i,Z: $i,W_2: $i,W: $i] :
( ( ord_less @ int @ W_2 @ W )
=> ( ( ord_less_eq @ int @ Z_2 @ Z )
=> ( ord_less @ int @ ( plus_plus @ int @ W_2 @ Z_2 ) @ ( plus_plus @ int @ W @ Z ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(245,plain,
( ( ! [K: $i] :
( ( ord_less_eq @ int @ pls @ ( bit0 @ K ) )
<=> ( ord_less_eq @ int @ pls @ K ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(246,plain,
( ( ! [K: $i] :
( ( ord_less_eq @ int @ ( bit0 @ K ) @ pls )
<=> ( ord_less_eq @ int @ K @ pls ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(247,plain,
( ( ! [K: $i,L: $i] :
( ( ord_less_eq @ int @ ( bit0 @ K ) @ ( bit1 @ L ) )
<=> ( ord_less_eq @ int @ K @ L ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(248,plain,
( ( ! [K1: $i,K2: $i] :
( ( ord_less_eq @ int @ ( bit0 @ K1 ) @ ( bit1 @ K2 ) )
<=> ( ord_less_eq @ int @ K1 @ K2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(249,plain,
( ( ! [K: $i] :
( ( ord_less_eq @ int @ pls @ ( bit1 @ K ) )
<=> ( ord_less_eq @ int @ pls @ K ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(250,plain,
( ( ! [V_3: $i] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( number_number_of @ nat @ V_3 ) )
<=> ( ord_less @ int @ pls @ V_3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(251,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [V: $i,W: $i] :
( ( number_number_of @ X_a @ ( times_times @ int @ V @ W ) )
= ( times_times @ X_a @ ( number_number_of @ X_a @ V ) @ ( number_number_of @ X_a @ W ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(252,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [V: $i,W: $i] :
( ( times_times @ X_a @ ( number_number_of @ X_a @ V ) @ ( number_number_of @ X_a @ W ) )
= ( number_number_of @ X_a @ ( times_times @ int @ V @ W ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(253,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ! [V: $i,W: $i,Z: $i] :
( ( times_times @ X_a @ ( number_number_of @ X_a @ V ) @ ( times_times @ X_a @ ( number_number_of @ X_a @ W ) @ Z ) )
= ( times_times @ X_a @ ( number_number_of @ X_a @ ( times_times @ int @ V @ W ) ) @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(254,plain,
( ( ! [V_3: $i] :
( ( ( zero_zero @ nat )
= ( number_number_of @ nat @ V_3 ) )
<=> ( ord_less_eq @ int @ V_3 @ pls ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(255,plain,
( ( ! [V_3: $i] :
( ( ( number_number_of @ nat @ V_3 )
= ( zero_zero @ nat ) )
<=> ( ord_less_eq @ int @ V_3 @ pls ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(256,plain,
( ( ! [K_1: $i,I: $i,J: $i] :
( ( ord_less_eq @ int @ I @ J )
=> ( ord_less_eq @ int @ ( plus_plus @ int @ K_1 @ I ) @ ( plus_plus @ int @ K_1 @ J ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(257,plain,
( ( ! [Z_1: $i,W_1: $i] :
( ( ord_less @ int @ Z_1 @ W_1 )
<=> ( ( ord_less_eq @ int @ Z_1 @ W_1 )
& ( Z_1 != W_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(258,plain,
( ( ! [K: $i,L: $i] :
( ( ord_less_eq @ int @ ( bit0 @ K ) @ ( bit0 @ L ) )
<=> ( ord_less_eq @ int @ K @ L ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(259,plain,
( ( ! [K1: $i,K2: $i] :
( ( ord_less_eq @ int @ ( bit0 @ K1 ) @ ( bit0 @ K2 ) )
<=> ( ord_less_eq @ int @ K1 @ K2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(260,plain,
( ( ord_less_eq @ int @ pls @ pls )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(261,plain,
( ( ! [K: $i,L: $i] :
( ( ord_less_eq @ int @ ( bit1 @ K ) @ ( bit1 @ L ) )
<=> ( ord_less_eq @ int @ K @ L ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(262,plain,
( ( ! [K1: $i,K2: $i] :
( ( ord_less_eq @ int @ ( bit1 @ K1 ) @ ( bit1 @ K2 ) )
<=> ( ord_less_eq @ int @ K1 @ K2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(263,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( power_power @ int @ X @ ( plus_plus @ nat @ Y @ Z ) )
= ( times_times @ int @ ( power_power @ int @ X @ Y ) @ ( power_power @ int @ X @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(264,plain,
( ( ! [Z: $i,W: $i] :
( ( ord_less_eq @ int @ Z @ W )
=> ( ( ord_less_eq @ int @ W @ Z )
=> ( Z = W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(265,plain,
( ( ! [K_1: $i,I: $i,J: $i] :
( ( ord_less_eq @ int @ I @ J )
=> ( ( ord_less_eq @ int @ J @ K_1 )
=> ( ord_less_eq @ int @ I @ K_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(266,plain,
( ( ! [Z1: $i,Z2: $i,Z3: $i] :
( ( times_times @ int @ ( times_times @ int @ Z1 @ Z2 ) @ Z3 )
= ( times_times @ int @ Z1 @ ( times_times @ int @ Z2 @ Z3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(267,plain,
( ( ! [K: $i,L: $i] :
( ( ord_less_eq @ int @ ( number_number_of @ int @ K ) @ ( number_number_of @ int @ L ) )
<=> ( ord_less_eq @ int @ K @ L ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(268,plain,
( ( ! [V: $i,W: $i] :
( ( times_times @ int @ ( number_number_of @ int @ V ) @ ( number_number_of @ int @ W ) )
= ( number_number_of @ int @ ( times_times @ int @ V @ W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(269,plain,
( ( ! [Z: $i,W: $i] :
( ( ord_less_eq @ int @ Z @ W )
| ( ord_less_eq @ int @ W @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(270,plain,
( ( ! [Z: $i,W: $i] :
( ( times_times @ int @ Z @ W )
= ( times_times @ int @ W @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(271,plain,
( ( ! [K_1: $i] :
( ( number_number_of @ int @ K_1 )
= K_1 ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(272,plain,
( ( ! [W: $i] : ( ord_less_eq @ int @ W @ W ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(273,plain,
( ( ~ ! [T_1: $i] :
( ( plus_plus @ int @ ( power_power @ int @ s @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( one_one @ int ) )
!= ( times_times @ int @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(274,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)],[99]) ).
thf(275,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)],[100]) ).
thf(276,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)],[101]) ).
thf(277,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)],[102]) ).
thf(278,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)],[103]) ).
thf(279,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)],[104]) ).
thf(280,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)],[105]) ).
thf(281,plain,
( ( ! [X_a: $i] :
( ( linordered_idom @ X_a )
=> ! [X_1: $i,Y_1: $i] :
( ( ( plus_plus @ X_a @ ( power_power @ X_a @ X_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ X_a @ Y_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ X_a ) )
<=> ( ( ( ti @ X_a @ X_1 )
= ( zero_zero @ X_a ) )
& ( ( ti @ X_a @ Y_1 )
= ( zero_zero @ X_a ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(282,plain,
( ( ! [X_a: $i] :
( ( linordered_idom @ X_a )
=> ! [X_1: $i,Y_1: $i] :
( ( ord_less @ X_a @ ( zero_zero @ X_a ) @ ( plus_plus @ X_a @ ( power_power @ X_a @ X_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ X_a @ Y_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
<=> ( ( ( ti @ X_a @ X_1 )
!= ( zero_zero @ X_a ) )
| ( ( ti @ X_a @ Y_1 )
!= ( zero_zero @ X_a ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(283,plain,
( ( ! [X_a: $i] :
( ( linordered_idom @ X_a )
=> ! [X: $i,Y: $i] :
~ ( ord_less @ X_a @ ( plus_plus @ X_a @ ( power_power @ X_a @ X @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ X_a @ Y @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( zero_zero @ X_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[108]) ).
thf(284,plain,
( ( ord_less @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(285,plain,
( ( ~ ( ord_less_eq @ int @ ( one_one @ int ) @ t ) )
= $true ),
inference(unfold_def,[status(thm)],[110]) ).
thf(286,plain,
( ( ( t
= ( zero_zero @ int ) )
=> ( ( plus_plus @ int @ ( power_power @ int @ s @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( one_one @ int ) )
= ( zero_zero @ int ) ) )
= $true ),
inference(unfold_def,[status(thm)],[111]) ).
thf(287,plain,
( ( ord_less @ int @ t @ ( one_one @ int ) )
= $true ),
inference(unfold_def,[status(thm)],[114]) ).
thf(288,plain,
( ( ord_less @ int @ t @ ( zero_zero @ int ) )
= $true ),
inference(unfold_def,[status(thm)],[115]) ).
thf(289,plain,
( ( ( ti @ int @ t )
= t )
= $true ),
inference(unfold_def,[status(thm)],[116]) ).
thf(290,plain,
( ( ( ti @ int @ m )
= m )
= $true ),
inference(unfold_def,[status(thm)],[117]) ).
thf(291,plain,
( ( ! [B_1: $i] :
( ( twoSqu33214720sum2sq @ ( ti @ int @ B_1 ) )
<=> ( twoSqu33214720sum2sq @ B_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[118]) ).
thf(292,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ( semiring_1 @ 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)],[119]) ).
thf(293,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ( semiring_1 @ 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)],[120]) ).
thf(294,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ( semiring_1 @ 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)],[121]) ).
thf(295,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)],[126]) ).
thf(296,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)],[127]) ).
thf(297,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)],[130]) ).
thf(298,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)],[131]) ).
thf(299,plain,
( ( ! [B_1: $i] :
( ( zprime @ ( ti @ int @ B_1 ) )
<=> ( zprime @ B_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[132]) ).
thf(300,plain,
( ( ! [X_a: $i] :
( ( semiring_1 @ X_a )
=> ( ( ti @ X_a @ ( zero_zero @ X_a ) )
= ( zero_zero @ X_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[134]) ).
thf(301,plain,
( ( ! [X_a: $i] :
( ( linordered_ring @ X_a )
=> ( ( ti @ X_a @ ( zero_zero @ X_a ) )
= ( zero_zero @ X_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[135]) ).
thf(302,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ( linordered_ring @ 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)],[142]) ).
thf(303,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ( linordered_ring @ 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)],[143]) ).
thf(304,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ( linordered_ring @ 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)],[144]) ).
thf(305,plain,
( ( ! [X_a: $i] :
( ( semiring_1 @ X_a )
=> ( ( ti @ X_a @ ( one_one @ X_a ) )
= ( one_one @ X_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[148]) ).
thf(306,plain,
( ( ( ti @ int @ s )
= s )
= $true ),
inference(unfold_def,[status(thm)],[149]) ).
thf(307,plain,
( ( ( ti @ int @ pls )
= pls )
= $true ),
inference(unfold_def,[status(thm)],[150]) ).
thf(308,plain,
( ( ! [B_1: $i] :
( ( ti @ int @ ( bit1 @ B_1 ) )
= ( bit1 @ B_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[151]) ).
thf(309,plain,
( ( ! [B_1: $i] :
( ( bit1 @ ( ti @ int @ B_1 ) )
= ( bit1 @ B_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[152]) ).
thf(310,plain,
( ( ! [B_1: $i] :
( ( ti @ int @ ( bit0 @ B_1 ) )
= ( bit0 @ B_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[153]) ).
thf(311,plain,
( ( ! [B_1: $i] :
( ( bit0 @ ( ti @ int @ B_1 ) )
= ( bit0 @ B_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[154]) ).
thf(312,plain,
( ( ~ ( ord_less @ int @ ( plus_plus @ int @ ( power_power @ int @ s @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( one_one @ int ) ) @ ( zero_zero @ int ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[157]) ).
thf(313,plain,
( ( ! [X_b: $i] :
( ~ ( number @ X_b )
| ~ ( semiring @ X_b )
| ! [V: $i,B: $i,C: $i] :
( ( times_times @ X_b @ ( number_number_of @ X_b @ V ) @ ( plus_plus @ X_b @ B @ C ) )
= ( plus_plus @ X_b @ ( times_times @ X_b @ ( number_number_of @ X_b @ V ) @ B ) @ ( times_times @ X_b @ ( number_number_of @ X_b @ V ) @ C ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[159]) ).
thf(314,plain,
( ( ! [X_b: $i] :
( ~ ( number @ X_b )
| ~ ( semiring @ X_b )
| ! [A_1: $i,B: $i,V: $i] :
( ( times_times @ X_b @ ( plus_plus @ X_b @ A_1 @ B ) @ ( number_number_of @ X_b @ V ) )
= ( plus_plus @ X_b @ ( times_times @ X_b @ A_1 @ ( number_number_of @ X_b @ V ) ) @ ( times_times @ X_b @ B @ ( number_number_of @ X_b @ V ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[160]) ).
thf(315,plain,
( ( ! [X_a: $i] :
( ~ ( linord581940658strict @ X_a )
| ( ! [X_1: $i,Y_1: $i] :
( ( ( ti @ X_a @ X_1 )
!= ( zero_zero @ X_a ) )
| ( ( ti @ X_a @ Y_1 )
!= ( zero_zero @ X_a ) )
| ( ( plus_plus @ X_a @ ( times_times @ X_a @ X_1 @ X_1 ) @ ( times_times @ X_a @ Y_1 @ Y_1 ) )
= ( zero_zero @ X_a ) ) )
& ! [X_1: $i] :
( ! [Y_1: $i] :
( ( plus_plus @ X_a @ ( times_times @ X_a @ X_1 @ X_1 ) @ ( times_times @ X_a @ Y_1 @ Y_1 ) )
!= ( zero_zero @ X_a ) )
| ( ( ti @ X_a @ X_1 )
= ( zero_zero @ X_a ) ) )
& ! [X_1: $i,Y_1: $i] :
( ( ( plus_plus @ X_a @ ( times_times @ X_a @ X_1 @ X_1 ) @ ( times_times @ X_a @ Y_1 @ Y_1 ) )
!= ( zero_zero @ X_a ) )
| ( ( ti @ X_a @ Y_1 )
= ( zero_zero @ X_a ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[161]) ).
thf(316,plain,
( ( ! [X_a: $i] :
( ~ ( linordered_idom @ X_a )
| ~ ( number_ring @ X_a )
| ( ! [Y_1: $i] :
( ~ ( ord_less_eq @ X_a @ ( one_one @ X_a ) @ ( number_number_of @ X_a @ Y_1 ) )
| ( ord_less_eq @ int @ ( bit1 @ pls ) @ Y_1 ) )
& ! [Y_1: $i] :
( ~ ( ord_less_eq @ int @ ( bit1 @ pls ) @ Y_1 )
| ( ord_less_eq @ X_a @ ( one_one @ X_a ) @ ( number_number_of @ X_a @ Y_1 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[162]) ).
thf(317,plain,
( ( ! [X_a: $i] :
( ~ ( linordered_idom @ X_a )
| ~ ( number_ring @ X_a )
| ( ! [X_1: $i] :
( ~ ( ord_less_eq @ X_a @ ( number_number_of @ X_a @ X_1 ) @ ( one_one @ X_a ) )
| ( ord_less_eq @ int @ X_1 @ ( bit1 @ pls ) ) )
& ! [X_1: $i] :
( ~ ( ord_less_eq @ int @ X_1 @ ( bit1 @ pls ) )
| ( ord_less_eq @ X_a @ ( number_number_of @ X_a @ X_1 ) @ ( one_one @ X_a ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[163]) ).
thf(318,plain,
( ( ! [X_a: $i] :
( ~ ( linorder @ X_a )
| ~ ( number @ X_a )
| ( ! [V_3: $i,W_1: $i] :
( ~ ( ord_less_eq @ X_a @ ( number_number_of @ X_a @ V_3 ) @ ( number_number_of @ X_a @ W_1 ) )
| ~ ( ord_less @ X_a @ ( number_number_of @ X_a @ W_1 ) @ ( number_number_of @ X_a @ V_3 ) ) )
& ! [V_3: $i,W_1: $i] :
( ( ord_less @ X_a @ ( number_number_of @ X_a @ W_1 ) @ ( number_number_of @ X_a @ V_3 ) )
| ( ord_less_eq @ X_a @ ( number_number_of @ X_a @ V_3 ) @ ( number_number_of @ X_a @ W_1 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[164]) ).
thf(319,plain,
( ( ! [X_a: $i] :
( ~ ( linordered_idom @ X_a )
| ~ ( number_ring @ X_a )
| ( ! [Y_1: $i] :
( ~ ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ ( number_number_of @ X_a @ Y_1 ) )
| ( ord_less_eq @ int @ pls @ Y_1 ) )
& ! [Y_1: $i] :
( ~ ( ord_less_eq @ int @ pls @ Y_1 )
| ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ ( number_number_of @ X_a @ Y_1 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[165]) ).
thf(320,plain,
( ( ! [X_a: $i] :
( ~ ( linordered_idom @ X_a )
| ~ ( number_ring @ X_a )
| ( ! [X_1: $i] :
( ~ ( ord_less_eq @ X_a @ ( number_number_of @ X_a @ X_1 ) @ ( zero_zero @ X_a ) )
| ( ord_less_eq @ int @ X_1 @ pls ) )
& ! [X_1: $i] :
( ~ ( ord_less_eq @ int @ X_1 @ pls )
| ( ord_less_eq @ X_a @ ( number_number_of @ X_a @ X_1 ) @ ( zero_zero @ X_a ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[166]) ).
thf(321,plain,
( ( ! [X_a: $i] :
( ~ ( linordered_ring @ X_a )
| ! [X: $i,Y: $i] : ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ ( plus_plus @ X_a @ ( times_times @ X_a @ X @ X ) @ ( times_times @ X_a @ Y @ Y ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[167]) ).
thf(322,plain,
( ( ! [X_a: $i] :
( ~ ( linord581940658strict @ X_a )
| ( ! [X_1: $i,Y_1: $i] :
( ( ( ti @ X_a @ X_1 )
!= ( zero_zero @ X_a ) )
| ( ( ti @ X_a @ Y_1 )
!= ( zero_zero @ X_a ) )
| ( ord_less_eq @ X_a @ ( plus_plus @ X_a @ ( times_times @ X_a @ X_1 @ X_1 ) @ ( times_times @ X_a @ Y_1 @ Y_1 ) ) @ ( zero_zero @ X_a ) ) )
& ! [X_1: $i] :
( ! [Y_1: $i] :
~ ( ord_less_eq @ X_a @ ( plus_plus @ X_a @ ( times_times @ X_a @ X_1 @ X_1 ) @ ( times_times @ X_a @ Y_1 @ Y_1 ) ) @ ( zero_zero @ X_a ) )
| ( ( ti @ X_a @ X_1 )
= ( zero_zero @ X_a ) ) )
& ! [X_1: $i,Y_1: $i] :
( ~ ( ord_less_eq @ X_a @ ( plus_plus @ X_a @ ( times_times @ X_a @ X_1 @ X_1 ) @ ( times_times @ X_a @ Y_1 @ Y_1 ) ) @ ( zero_zero @ X_a ) )
| ( ( ti @ X_a @ Y_1 )
= ( zero_zero @ X_a ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[168]) ).
thf(323,plain,
( ( ! [X_a: $i] :
( ~ ( number_semiring @ X_a )
| ! [V_1: $i,V: $i] :
( ~ ( ord_less_eq @ int @ pls @ V )
| ~ ( ord_less_eq @ int @ pls @ V_1 )
| ( ( times_times @ X_a @ ( number_number_of @ X_a @ V ) @ ( number_number_of @ X_a @ V_1 ) )
= ( number_number_of @ X_a @ ( times_times @ int @ V @ V_1 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[169]) ).
thf(324,plain,
( ( ! [X_a: $i] :
( ~ ( linordered_idom @ X_a )
| ~ ( number_ring @ X_a )
| ( ! [X_1: $i,Y_1: $i] :
( ~ ( ord_less_eq @ X_a @ ( number_number_of @ X_a @ X_1 ) @ ( number_number_of @ X_a @ Y_1 ) )
| ( ord_less_eq @ int @ X_1 @ Y_1 ) )
& ! [X_1: $i,Y_1: $i] :
( ~ ( ord_less_eq @ int @ X_1 @ Y_1 )
| ( ord_less_eq @ X_a @ ( number_number_of @ X_a @ X_1 ) @ ( number_number_of @ X_a @ Y_1 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[170]) ).
thf(325,plain,
( ( ! [B_1: $i] :
( ! [B_2: $i,X_a: $i] :
( ~ ( linordered_ring @ X_a )
| ~ ( ord_less_eq @ X_a @ B_1 @ ( ti @ X_a @ B_2 ) )
| ( ord_less_eq @ X_a @ B_1 @ B_2 ) )
& ! [B_2: $i,X_a: $i] :
( ~ ( linordered_ring @ X_a )
| ~ ( ord_less_eq @ X_a @ B_1 @ B_2 )
| ( ord_less_eq @ X_a @ B_1 @ ( ti @ X_a @ B_2 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[176]) ).
thf(326,plain,
( ( ! [B_1: $i] :
( ! [B_2: $i,X_a: $i] :
( ~ ( linordered_ring @ X_a )
| ~ ( ord_less_eq @ X_a @ ( ti @ X_a @ B_1 ) @ B_2 )
| ( ord_less_eq @ X_a @ B_1 @ B_2 ) )
& ! [B_2: $i,X_a: $i] :
( ~ ( linordered_ring @ X_a )
| ~ ( ord_less_eq @ X_a @ B_1 @ B_2 )
| ( ord_less_eq @ X_a @ ( ti @ X_a @ B_1 ) @ B_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[177]) ).
thf(327,plain,
( ( ! [B_1: $i] :
( ! [B_2: $i,X_a: $i] :
( ~ ( linorder @ X_a )
| ~ ( number @ X_a )
| ~ ( ord_less_eq @ X_a @ B_1 @ ( ti @ X_a @ B_2 ) )
| ( ord_less_eq @ X_a @ B_1 @ B_2 ) )
& ! [B_2: $i,X_a: $i] :
( ~ ( linorder @ X_a )
| ~ ( number @ X_a )
| ~ ( ord_less_eq @ X_a @ B_1 @ B_2 )
| ( ord_less_eq @ X_a @ B_1 @ ( ti @ X_a @ B_2 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[178]) ).
thf(328,plain,
( ( ! [B_1: $i] :
( ! [B_2: $i,X_a: $i] :
( ~ ( linorder @ X_a )
| ~ ( number @ X_a )
| ~ ( ord_less_eq @ X_a @ ( ti @ X_a @ B_1 ) @ B_2 )
| ( ord_less_eq @ X_a @ B_1 @ B_2 ) )
& ! [B_2: $i,X_a: $i] :
( ~ ( linorder @ X_a )
| ~ ( number @ X_a )
| ~ ( ord_less_eq @ X_a @ B_1 @ B_2 )
| ( ord_less_eq @ X_a @ ( ti @ X_a @ B_1 ) @ B_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[179]) ).
thf(329,plain,
( ( ! [B_1: $i] :
( ! [B_2: $i,X_a: $i] :
( ~ ( linorder @ X_a )
| ~ ( number @ 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] :
( ~ ( linorder @ X_a )
| ~ ( number @ 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)],[180]) ).
thf(330,plain,
( ( ! [B_1: $i] :
( ! [B_2: $i,X_a: $i] :
( ~ ( linorder @ X_a )
| ~ ( number @ 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] :
( ~ ( linorder @ X_a )
| ~ ( number @ 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)],[181]) ).
thf(331,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ~ ( linordered_ring @ X_a )
| ( ( ti @ X_a @ ( times_times @ X_a @ B_1 @ B_2 ) )
= ( times_times @ X_a @ B_1 @ B_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[183]) ).
thf(332,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ~ ( linordered_ring @ X_a )
| ( ( times_times @ X_a @ B_1 @ ( ti @ X_a @ B_2 ) )
= ( times_times @ X_a @ B_1 @ B_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[184]) ).
thf(333,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ~ ( linordered_ring @ X_a )
| ( ( times_times @ X_a @ ( ti @ X_a @ B_1 ) @ B_2 )
= ( times_times @ X_a @ B_1 @ B_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[185]) ).
thf(334,plain,
( ( ! [B_1: $i,B_2: $i,X_b: $i] :
( ~ ( number @ X_b )
| ~ ( semiring @ X_b )
| ( ( ti @ X_b @ ( times_times @ X_b @ B_1 @ B_2 ) )
= ( times_times @ X_b @ B_1 @ B_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[186]) ).
thf(335,plain,
( ( ! [B_1: $i,B_2: $i,X_b: $i] :
( ~ ( number @ X_b )
| ~ ( semiring @ X_b )
| ( ( times_times @ X_b @ B_1 @ ( ti @ X_b @ B_2 ) )
= ( times_times @ X_b @ B_1 @ B_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[187]) ).
thf(336,plain,
( ( ! [B_1: $i,B_2: $i,X_b: $i] :
( ~ ( number @ X_b )
| ~ ( semiring @ X_b )
| ( ( times_times @ X_b @ ( ti @ X_b @ B_1 ) @ B_2 )
= ( times_times @ X_b @ B_1 @ B_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[188]) ).
thf(337,plain,
( ( ! [B_1: $i,B_2: $i,X_b: $i] :
( ~ ( number @ X_b )
| ~ ( semiring @ X_b )
| ( ( ti @ X_b @ ( plus_plus @ X_b @ B_1 @ B_2 ) )
= ( plus_plus @ X_b @ B_1 @ B_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[189]) ).
thf(338,plain,
( ( ! [B_1: $i,B_2: $i,X_b: $i] :
( ~ ( number @ X_b )
| ~ ( semiring @ X_b )
| ( ( plus_plus @ X_b @ B_1 @ ( ti @ X_b @ B_2 ) )
= ( plus_plus @ X_b @ B_1 @ B_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[190]) ).
thf(339,plain,
( ( ! [B_1: $i,B_2: $i,X_b: $i] :
( ~ ( number @ X_b )
| ~ ( semiring @ X_b )
| ( ( plus_plus @ X_b @ ( ti @ X_b @ B_1 ) @ B_2 )
= ( plus_plus @ X_b @ B_1 @ B_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[191]) ).
thf(340,plain,
( ( ! [X: $i,Y: $i] :
( ( ord_less @ int @ Y @ X )
| ( X = Y )
| ( ord_less @ int @ X @ Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[212]) ).
thf(341,plain,
( ( ! [K: $i,L: $i] :
( ( ( bit0 @ K )
!= ( bit0 @ L ) )
| ( K = L ) )
& ! [K: $i,L: $i] :
( ( K != L )
| ( ( bit0 @ K )
= ( bit0 @ L ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[213]) ).
thf(342,plain,
( ( ! [K: $i,L: $i] :
( ( ( bit1 @ K )
!= ( bit1 @ L ) )
| ( K = L ) )
& ! [K: $i,L: $i] :
( ( K != L )
| ( ( bit1 @ K )
= ( bit1 @ L ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[214]) ).
thf(343,plain,
( ( ! [X_a: $i] :
( ~ ( number @ X_a )
| ( ! [W_1: $i,X_1: $i] :
( ( ( number_number_of @ X_a @ W_1 )
!= ( ti @ X_a @ X_1 ) )
| ( ( ti @ X_a @ X_1 )
= ( number_number_of @ X_a @ W_1 ) ) )
& ! [W_1: $i,X_1: $i] :
( ( ( ti @ X_a @ X_1 )
!= ( number_number_of @ X_a @ W_1 ) )
| ( ( number_number_of @ X_a @ W_1 )
= ( ti @ X_a @ X_1 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[215]) ).
thf(344,plain,
( ( ! [X_a: $i] :
( ~ ( number_ring @ X_a )
| ~ ( ring_char_0 @ X_a )
| ( ! [X_1: $i,Y_1: $i] :
( ( ( number_number_of @ X_a @ X_1 )
!= ( number_number_of @ X_a @ Y_1 ) )
| ( X_1 = Y_1 ) )
& ! [X_1: $i,Y_1: $i] :
( ( X_1 != Y_1 )
| ( ( number_number_of @ X_a @ X_1 )
= ( number_number_of @ X_a @ Y_1 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[216]) ).
thf(345,plain,
( ( ! [Z: $i] :
( ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ Z )
| ( ord_less @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( one_one @ int ) @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[217]) ).
thf(346,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)],[218]) ).
thf(347,plain,
( ( ! [X_a: $i] :
( ~ ( number_semiring @ X_a )
| ! [V_1: $i,V: $i] :
( ~ ( ord_less_eq @ int @ pls @ V )
| ~ ( ord_less_eq @ int @ pls @ V_1 )
| ( ( plus_plus @ X_a @ ( number_number_of @ X_a @ V ) @ ( number_number_of @ X_a @ V_1 ) )
= ( number_number_of @ X_a @ ( plus_plus @ int @ V @ V_1 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[219]) ).
thf(348,plain,
( ( ! [W_1: $i,Z_1: $i] :
( ~ ( ord_less @ int @ W_1 @ ( plus_plus @ int @ Z_1 @ ( one_one @ int ) ) )
| ( ord_less_eq @ int @ W_1 @ Z_1 ) )
& ! [W_1: $i,Z_1: $i] :
( ~ ( ord_less_eq @ int @ W_1 @ Z_1 )
| ( ord_less @ int @ W_1 @ ( plus_plus @ int @ Z_1 @ ( one_one @ int ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[220]) ).
thf(349,plain,
( ( ! [W_1: $i,Z_1: $i] :
( ~ ( ord_less @ int @ W_1 @ Z_1 )
| ( ord_less_eq @ int @ ( plus_plus @ int @ W_1 @ ( one_one @ int ) ) @ Z_1 ) )
& ! [W_1: $i,Z_1: $i] :
( ~ ( ord_less_eq @ int @ ( plus_plus @ int @ W_1 @ ( one_one @ int ) ) @ Z_1 )
| ( ord_less @ int @ W_1 @ Z_1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[221]) ).
thf(350,plain,
( ( ! [W: $i,Z: $i] :
( ~ ( ord_less @ int @ W @ Z )
| ( ord_less_eq @ int @ ( plus_plus @ int @ W @ ( one_one @ int ) ) @ Z ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[222]) ).
thf(351,plain,
( ( ! [Z_1: $i] :
( ~ ( ord_less @ int @ ( zero_zero @ int ) @ Z_1 )
| ( ord_less_eq @ int @ ( one_one @ int ) @ Z_1 ) )
& ! [Z_1: $i] :
( ~ ( ord_less_eq @ int @ ( one_one @ int ) @ Z_1 )
| ( ord_less @ int @ ( zero_zero @ int ) @ Z_1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[225]) ).
thf(352,plain,
( ( ! [V_3: $i,V_2: $i] :
( ( ord_less @ int @ V_3 @ V_2 )
| ~ ( ord_less @ int @ V_3 @ V_2 )
| ( ord_less @ nat @ ( number_number_of @ nat @ V_3 ) @ ( number_number_of @ nat @ V_2 ) ) )
& ! [V_3: $i,V_2: $i] :
( ~ ( ord_less @ int @ pls @ V_2 )
| ~ ( ord_less @ int @ V_3 @ V_2 )
| ( ord_less @ nat @ ( number_number_of @ nat @ V_3 ) @ ( number_number_of @ nat @ V_2 ) ) )
& ! [V_3: $i,V_2: $i] :
( ~ ( ord_less @ nat @ ( number_number_of @ nat @ V_3 ) @ ( number_number_of @ nat @ V_2 ) )
| ~ ( ord_less @ int @ V_3 @ V_2 )
| ( ord_less @ int @ pls @ V_2 ) )
& ! [V_3: $i,V_2: $i] :
( ~ ( ord_less @ nat @ ( number_number_of @ nat @ V_3 ) @ ( number_number_of @ nat @ V_2 ) )
| ( ord_less @ int @ V_3 @ V_2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[226]) ).
thf(353,plain,
( ( ! [K: $i,L: $i] :
( ~ ( ord_less @ int @ ( bit0 @ K ) @ ( bit1 @ L ) )
| ( ord_less_eq @ int @ K @ L ) )
& ! [K: $i,L: $i] :
( ~ ( ord_less_eq @ int @ K @ L )
| ( ord_less @ int @ ( bit0 @ K ) @ ( bit1 @ L ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[227]) ).
thf(354,plain,
( ( ! [K1: $i,K2: $i] :
( ~ ( ord_less @ int @ ( bit0 @ K1 ) @ ( bit1 @ K2 ) )
| ( ord_less_eq @ int @ K1 @ K2 ) )
& ! [K1: $i,K2: $i] :
( ~ ( ord_less_eq @ int @ K1 @ K2 )
| ( ord_less @ int @ ( bit0 @ K1 ) @ ( bit1 @ K2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[228]) ).
thf(355,plain,
( ( ! [K: $i,L: $i] :
( ~ ( ord_less @ int @ K @ L )
| ( ord_less_eq @ int @ ( bit1 @ K ) @ ( bit0 @ L ) ) )
& ! [K: $i,L: $i] :
( ~ ( ord_less_eq @ int @ ( bit1 @ K ) @ ( bit0 @ L ) )
| ( ord_less @ int @ K @ L ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[229]) ).
thf(356,plain,
( ( ! [K1: $i,K2: $i] :
( ~ ( ord_less @ int @ K1 @ K2 )
| ( ord_less_eq @ int @ ( bit1 @ K1 ) @ ( bit0 @ K2 ) ) )
& ! [K1: $i,K2: $i] :
( ~ ( ord_less_eq @ int @ ( bit1 @ K1 ) @ ( bit0 @ K2 ) )
| ( ord_less @ int @ K1 @ K2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[230]) ).
thf(357,plain,
( ( ! [K: $i] :
( ~ ( ord_less @ int @ pls @ ( bit1 @ K ) )
| ( ord_less_eq @ int @ pls @ K ) )
& ! [K: $i] :
( ~ ( ord_less_eq @ int @ pls @ K )
| ( ord_less @ int @ pls @ ( bit1 @ K ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[231]) ).
thf(358,plain,
( ( ! [K: $i] :
( ~ ( ord_less @ int @ K @ pls )
| ( ord_less_eq @ int @ ( bit1 @ K ) @ pls ) )
& ! [K: $i] :
( ~ ( ord_less_eq @ int @ ( bit1 @ K ) @ pls )
| ( ord_less @ int @ K @ pls ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[232]) ).
thf(359,plain,
( ( ! [K: $i,L: $i] :
( ~ ( ord_less @ int @ ( number_number_of @ int @ K ) @ ( number_number_of @ int @ L ) )
| ( ord_less @ int @ K @ L ) )
& ! [K: $i,L: $i] :
( ~ ( ord_less @ int @ K @ L )
| ( ord_less @ int @ ( number_number_of @ int @ K ) @ ( number_number_of @ int @ L ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[238]) ).
thf(360,plain,
( ( ! [Z_2: $i,Z: $i,W_2: $i,W: $i] :
( ~ ( ord_less @ int @ W_2 @ W )
| ~ ( ord_less_eq @ int @ Z_2 @ Z )
| ( ord_less @ int @ ( plus_plus @ int @ W_2 @ Z_2 ) @ ( plus_plus @ int @ W @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[244]) ).
thf(361,plain,
( ( ! [K: $i] :
( ~ ( ord_less_eq @ int @ pls @ ( bit0 @ K ) )
| ( ord_less_eq @ int @ pls @ K ) )
& ! [K: $i] :
( ~ ( ord_less_eq @ int @ pls @ K )
| ( ord_less_eq @ int @ pls @ ( bit0 @ K ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[245]) ).
thf(362,plain,
( ( ! [K: $i] :
( ~ ( ord_less_eq @ int @ ( bit0 @ K ) @ pls )
| ( ord_less_eq @ int @ K @ pls ) )
& ! [K: $i] :
( ~ ( ord_less_eq @ int @ K @ pls )
| ( ord_less_eq @ int @ ( bit0 @ K ) @ pls ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[246]) ).
thf(363,plain,
( ( ! [K: $i,L: $i] :
( ~ ( ord_less_eq @ int @ ( bit0 @ K ) @ ( bit1 @ L ) )
| ( ord_less_eq @ int @ K @ L ) )
& ! [K: $i,L: $i] :
( ~ ( ord_less_eq @ int @ K @ L )
| ( ord_less_eq @ int @ ( bit0 @ K ) @ ( bit1 @ L ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[247]) ).
thf(364,plain,
( ( ! [K1: $i,K2: $i] :
( ~ ( ord_less_eq @ int @ ( bit0 @ K1 ) @ ( bit1 @ K2 ) )
| ( ord_less_eq @ int @ K1 @ K2 ) )
& ! [K1: $i,K2: $i] :
( ~ ( ord_less_eq @ int @ K1 @ K2 )
| ( ord_less_eq @ int @ ( bit0 @ K1 ) @ ( bit1 @ K2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[248]) ).
thf(365,plain,
( ( ! [K: $i] :
( ~ ( ord_less_eq @ int @ pls @ ( bit1 @ K ) )
| ( ord_less_eq @ int @ pls @ K ) )
& ! [K: $i] :
( ~ ( ord_less_eq @ int @ pls @ K )
| ( ord_less_eq @ int @ pls @ ( bit1 @ K ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[249]) ).
thf(366,plain,
( ( ! [V_3: $i] :
( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ ( number_number_of @ nat @ V_3 ) )
| ( ord_less @ int @ pls @ V_3 ) )
& ! [V_3: $i] :
( ~ ( ord_less @ int @ pls @ V_3 )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ ( number_number_of @ nat @ V_3 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[250]) ).
thf(367,plain,
( ( ! [X_a: $i] :
( ~ ( number_ring @ X_a )
| ! [V: $i,W: $i] :
( ( number_number_of @ X_a @ ( times_times @ int @ V @ W ) )
= ( times_times @ X_a @ ( number_number_of @ X_a @ V ) @ ( number_number_of @ X_a @ W ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[251]) ).
thf(368,plain,
( ( ! [X_a: $i] :
( ~ ( number_ring @ X_a )
| ! [V: $i,W: $i] :
( ( times_times @ X_a @ ( number_number_of @ X_a @ V ) @ ( number_number_of @ X_a @ W ) )
= ( number_number_of @ X_a @ ( times_times @ int @ V @ W ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[252]) ).
thf(369,plain,
( ( ! [X_a: $i] :
( ~ ( number_ring @ X_a )
| ! [V: $i,W: $i,Z: $i] :
( ( times_times @ X_a @ ( number_number_of @ X_a @ V ) @ ( times_times @ X_a @ ( number_number_of @ X_a @ W ) @ Z ) )
= ( times_times @ X_a @ ( number_number_of @ X_a @ ( times_times @ int @ V @ W ) ) @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[253]) ).
thf(370,plain,
( ( ! [V_3: $i] :
( ( ( zero_zero @ nat )
!= ( number_number_of @ nat @ V_3 ) )
| ( ord_less_eq @ int @ V_3 @ pls ) )
& ! [V_3: $i] :
( ~ ( ord_less_eq @ int @ V_3 @ pls )
| ( ( zero_zero @ nat )
= ( number_number_of @ nat @ V_3 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[254]) ).
thf(371,plain,
( ( ! [V_3: $i] :
( ( ( number_number_of @ nat @ V_3 )
!= ( zero_zero @ nat ) )
| ( ord_less_eq @ int @ V_3 @ pls ) )
& ! [V_3: $i] :
( ~ ( ord_less_eq @ int @ V_3 @ pls )
| ( ( number_number_of @ nat @ V_3 )
= ( zero_zero @ nat ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[255]) ).
thf(372,plain,
( ( ! [K_1: $i,I: $i,J: $i] :
( ~ ( ord_less_eq @ int @ I @ J )
| ( ord_less_eq @ int @ ( plus_plus @ int @ K_1 @ I ) @ ( plus_plus @ int @ K_1 @ J ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[256]) ).
thf(373,plain,
( ( ! [Z_1: $i,W_1: $i] :
( ( Z_1 = W_1 )
| ~ ( ord_less_eq @ int @ Z_1 @ W_1 )
| ( ord_less @ int @ Z_1 @ W_1 ) )
& ! [Z_1: $i,W_1: $i] :
( ~ ( ord_less @ int @ Z_1 @ W_1 )
| ( Z_1 != W_1 ) )
& ! [Z_1: $i,W_1: $i] :
( ~ ( ord_less @ int @ Z_1 @ W_1 )
| ( ord_less_eq @ int @ Z_1 @ W_1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[257]) ).
thf(374,plain,
( ( ! [K: $i,L: $i] :
( ~ ( ord_less_eq @ int @ ( bit0 @ K ) @ ( bit0 @ L ) )
| ( ord_less_eq @ int @ K @ L ) )
& ! [K: $i,L: $i] :
( ~ ( ord_less_eq @ int @ K @ L )
| ( ord_less_eq @ int @ ( bit0 @ K ) @ ( bit0 @ L ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[258]) ).
thf(375,plain,
( ( ! [K1: $i,K2: $i] :
( ~ ( ord_less_eq @ int @ ( bit0 @ K1 ) @ ( bit0 @ K2 ) )
| ( ord_less_eq @ int @ K1 @ K2 ) )
& ! [K1: $i,K2: $i] :
( ~ ( ord_less_eq @ int @ K1 @ K2 )
| ( ord_less_eq @ int @ ( bit0 @ K1 ) @ ( bit0 @ K2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[259]) ).
thf(376,plain,
( ( ! [K: $i,L: $i] :
( ~ ( ord_less_eq @ int @ ( bit1 @ K ) @ ( bit1 @ L ) )
| ( ord_less_eq @ int @ K @ L ) )
& ! [K: $i,L: $i] :
( ~ ( ord_less_eq @ int @ K @ L )
| ( ord_less_eq @ int @ ( bit1 @ K ) @ ( bit1 @ L ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[261]) ).
thf(377,plain,
( ( ! [K1: $i,K2: $i] :
( ~ ( ord_less_eq @ int @ ( bit1 @ K1 ) @ ( bit1 @ K2 ) )
| ( ord_less_eq @ int @ K1 @ K2 ) )
& ! [K1: $i,K2: $i] :
( ~ ( ord_less_eq @ int @ K1 @ K2 )
| ( ord_less_eq @ int @ ( bit1 @ K1 ) @ ( bit1 @ K2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[262]) ).
thf(378,plain,
( ( ! [Z: $i,W: $i] :
( ~ ( ord_less_eq @ int @ Z @ W )
| ~ ( ord_less_eq @ int @ W @ Z )
| ( Z = W ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[264]) ).
thf(379,plain,
( ( ! [K_1: $i,I: $i,J: $i] :
( ~ ( ord_less_eq @ int @ I @ J )
| ~ ( ord_less_eq @ int @ J @ K_1 )
| ( ord_less_eq @ int @ I @ K_1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[265]) ).
thf(380,plain,
( ( ! [K: $i,L: $i] :
( ~ ( ord_less_eq @ int @ ( number_number_of @ int @ K ) @ ( number_number_of @ int @ L ) )
| ( ord_less_eq @ int @ K @ L ) )
& ! [K: $i,L: $i] :
( ~ ( ord_less_eq @ int @ K @ L )
| ( ord_less_eq @ int @ ( number_number_of @ int @ K ) @ ( number_number_of @ int @ L ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[267]) ).
thf(381,plain,
( ( ( plus_plus @ int @ ( power_power @ int @ s @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( one_one @ int ) )
= ( times_times @ int @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) @ sK1_T_1 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[273]) ).
thf(382,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)],[274]) ).
thf(383,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)],[275]) ).
thf(384,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)],[276]) ).
thf(385,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)],[277]) ).
thf(386,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)],[278]) ).
thf(387,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)],[279]) ).
thf(388,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)],[280]) ).
thf(389,plain,
( ( ! [X_a: $i] :
( ~ ( linordered_idom @ X_a )
| ( ! [X_1: $i,Y_1: $i] :
( ( ( ti @ X_a @ X_1 )
!= ( zero_zero @ X_a ) )
| ( ( ti @ X_a @ Y_1 )
!= ( zero_zero @ X_a ) )
| ( ( plus_plus @ X_a @ ( power_power @ X_a @ X_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ X_a @ Y_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ X_a ) ) )
& ! [X_1: $i] :
( ! [Y_1: $i] :
( ( plus_plus @ X_a @ ( power_power @ X_a @ X_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ X_a @ Y_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ X_a ) )
| ( ( ti @ X_a @ X_1 )
= ( zero_zero @ X_a ) ) )
& ! [X_1: $i,Y_1: $i] :
( ( ( plus_plus @ X_a @ ( power_power @ X_a @ X_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ X_a @ Y_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ X_a ) )
| ( ( ti @ X_a @ Y_1 )
= ( zero_zero @ X_a ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[281]) ).
thf(390,plain,
( ( ! [X_a: $i] :
( ~ ( linordered_idom @ X_a )
| ( ! [X_1: $i,Y_1: $i] :
( ~ ( ord_less @ X_a @ ( zero_zero @ X_a ) @ ( plus_plus @ X_a @ ( power_power @ X_a @ X_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ X_a @ Y_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
| ( ( ti @ X_a @ X_1 )
!= ( zero_zero @ X_a ) )
| ( ( ti @ X_a @ Y_1 )
!= ( zero_zero @ X_a ) ) )
& ! [X_1: $i] :
( ( ( ti @ X_a @ X_1 )
= ( zero_zero @ X_a ) )
| ! [Y_1: $i] : ( ord_less @ X_a @ ( zero_zero @ X_a ) @ ( plus_plus @ X_a @ ( power_power @ X_a @ X_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ X_a @ Y_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
& ! [X_1: $i,Y_1: $i] :
( ( ( ti @ X_a @ Y_1 )
= ( zero_zero @ X_a ) )
| ( ord_less @ X_a @ ( zero_zero @ X_a ) @ ( plus_plus @ X_a @ ( power_power @ X_a @ X_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ X_a @ Y_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[282]) ).
thf(391,plain,
( ( ! [X_a: $i] :
( ~ ( linordered_idom @ X_a )
| ! [X: $i,Y: $i] :
~ ( ord_less @ X_a @ ( plus_plus @ X_a @ ( power_power @ X_a @ X @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ X_a @ Y @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( zero_zero @ X_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[283]) ).
thf(392,plain,
( ( ( t
!= ( zero_zero @ int ) )
| ( ( plus_plus @ int @ ( power_power @ int @ s @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( one_one @ int ) )
= ( zero_zero @ int ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[286]) ).
thf(393,plain,
( ( ! [B_1: $i] :
( ~ ( twoSqu33214720sum2sq @ ( ti @ int @ B_1 ) )
| ( twoSqu33214720sum2sq @ B_1 ) )
& ! [B_1: $i] :
( ~ ( twoSqu33214720sum2sq @ B_1 )
| ( twoSqu33214720sum2sq @ ( ti @ int @ B_1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[291]) ).
thf(394,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ~ ( semiring_1 @ 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)],[292]) ).
thf(395,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ~ ( semiring_1 @ 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)],[293]) ).
thf(396,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ~ ( semiring_1 @ 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)],[294]) ).
thf(397,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)],[295]) ).
thf(398,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)],[296]) ).
thf(399,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)],[297]) ).
thf(400,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)],[298]) ).
thf(401,plain,
( ( ! [B_1: $i] :
( ~ ( zprime @ ( ti @ int @ B_1 ) )
| ( zprime @ B_1 ) )
& ! [B_1: $i] :
( ~ ( zprime @ B_1 )
| ( zprime @ ( ti @ int @ B_1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[299]) ).
thf(402,plain,
( ( ! [X_a: $i] :
( ~ ( semiring_1 @ X_a )
| ( ( ti @ X_a @ ( zero_zero @ X_a ) )
= ( zero_zero @ X_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[300]) ).
thf(403,plain,
( ( ! [X_a: $i] :
( ~ ( linordered_ring @ X_a )
| ( ( ti @ X_a @ ( zero_zero @ X_a ) )
= ( zero_zero @ X_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[301]) ).
thf(404,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ~ ( linordered_ring @ 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)],[302]) ).
thf(405,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ~ ( linordered_ring @ 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)],[303]) ).
thf(406,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ~ ( linordered_ring @ 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)],[304]) ).
thf(407,plain,
( ( ! [X_a: $i] :
( ~ ( semiring_1 @ X_a )
| ( ( ti @ X_a @ ( one_one @ X_a ) )
= ( one_one @ X_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[305]) ).
thf(408,plain,
( ( ! [B_1: $i] :
( ( bit0 @ ( ti @ int @ B_1 ) )
= ( bit0 @ B_1 ) ) )
= $true ),
inference(copy,[status(thm)],[311]) ).
thf(409,plain,
( ( ! [B_1: $i] :
( ( ti @ int @ ( bit0 @ B_1 ) )
= ( bit0 @ B_1 ) ) )
= $true ),
inference(copy,[status(thm)],[310]) ).
thf(410,plain,
( ( ! [B_1: $i] :
( ( bit1 @ ( ti @ int @ B_1 ) )
= ( bit1 @ B_1 ) ) )
= $true ),
inference(copy,[status(thm)],[309]) ).
thf(411,plain,
( ( ! [B_1: $i] :
( ( ti @ int @ ( bit1 @ B_1 ) )
= ( bit1 @ B_1 ) ) )
= $true ),
inference(copy,[status(thm)],[308]) ).
thf(412,plain,
( ( ( ti @ int @ pls )
= pls )
= $true ),
inference(copy,[status(thm)],[307]) ).
thf(413,plain,
( ( ( ti @ int @ s )
= s )
= $true ),
inference(copy,[status(thm)],[306]) ).
thf(414,plain,
( ( ! [X_a: $i] :
( ~ ( semiring_1 @ X_a )
| ( ( ti @ X_a @ ( one_one @ X_a ) )
= ( one_one @ X_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[407]) ).
thf(415,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ~ ( linordered_ring @ 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)],[406]) ).
thf(416,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ~ ( linordered_ring @ 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)],[405]) ).
thf(417,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ~ ( linordered_ring @ 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)],[404]) ).
thf(418,plain,
( ( ! [X_a: $i] :
( ~ ( linordered_ring @ X_a )
| ( ( ti @ X_a @ ( zero_zero @ X_a ) )
= ( zero_zero @ X_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[403]) ).
thf(419,plain,
( ( ! [X_a: $i] :
( ~ ( semiring_1 @ X_a )
| ( ( ti @ X_a @ ( zero_zero @ X_a ) )
= ( zero_zero @ X_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[402]) ).
thf(420,plain,
( ( ! [B_1: $i] :
( ~ ( zprime @ ( ti @ int @ B_1 ) )
| ( zprime @ B_1 ) )
& ! [B_1: $i] :
( ~ ( zprime @ B_1 )
| ( zprime @ ( ti @ int @ B_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[401]) ).
thf(421,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)],[400]) ).
thf(422,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)],[399]) ).
thf(423,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)],[398]) ).
thf(424,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)],[397]) ).
thf(425,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ~ ( semiring_1 @ 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)],[396]) ).
thf(426,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ~ ( semiring_1 @ 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)],[395]) ).
thf(427,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ~ ( semiring_1 @ 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)],[394]) ).
thf(428,plain,
( ( ! [B_1: $i] :
( ~ ( twoSqu33214720sum2sq @ ( ti @ int @ B_1 ) )
| ( twoSqu33214720sum2sq @ B_1 ) )
& ! [B_1: $i] :
( ~ ( twoSqu33214720sum2sq @ B_1 )
| ( twoSqu33214720sum2sq @ ( ti @ int @ B_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[393]) ).
thf(429,plain,
( ( ( ti @ int @ m )
= m )
= $true ),
inference(copy,[status(thm)],[290]) ).
thf(430,plain,
( ( ( ti @ int @ t )
= t )
= $true ),
inference(copy,[status(thm)],[289]) ).
thf(431,plain,
( ( ord_less @ int @ t @ ( zero_zero @ int ) )
= $true ),
inference(copy,[status(thm)],[288]) ).
thf(432,plain,
( ( ord_less @ int @ t @ ( one_one @ int ) )
= $true ),
inference(copy,[status(thm)],[287]) ).
thf(433,plain,
( ( ( t
!= ( zero_zero @ int ) )
| ( ( plus_plus @ int @ ( power_power @ int @ s @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( one_one @ int ) )
= ( zero_zero @ int ) ) )
= $true ),
inference(copy,[status(thm)],[392]) ).
thf(434,plain,
( ( ~ ( ord_less_eq @ int @ ( one_one @ int ) @ t ) )
= $true ),
inference(copy,[status(thm)],[285]) ).
thf(435,plain,
( ( ord_less @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) )
= $true ),
inference(copy,[status(thm)],[284]) ).
thf(436,plain,
( ( ! [X_a: $i] :
( ~ ( linordered_idom @ X_a )
| ! [X: $i,Y: $i] :
~ ( ord_less @ X_a @ ( plus_plus @ X_a @ ( power_power @ X_a @ X @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ X_a @ Y @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( zero_zero @ X_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[391]) ).
thf(437,plain,
( ( ! [X_a: $i] :
( ~ ( linordered_idom @ X_a )
| ( ! [X_1: $i,Y_1: $i] :
( ~ ( ord_less @ X_a @ ( zero_zero @ X_a ) @ ( plus_plus @ X_a @ ( power_power @ X_a @ X_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ X_a @ Y_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
| ( ( ti @ X_a @ X_1 )
!= ( zero_zero @ X_a ) )
| ( ( ti @ X_a @ Y_1 )
!= ( zero_zero @ X_a ) ) )
& ! [X_1: $i] :
( ( ( ti @ X_a @ X_1 )
= ( zero_zero @ X_a ) )
| ! [Y_1: $i] : ( ord_less @ X_a @ ( zero_zero @ X_a ) @ ( plus_plus @ X_a @ ( power_power @ X_a @ X_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ X_a @ Y_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
& ! [X_1: $i,Y_1: $i] :
( ( ( ti @ X_a @ Y_1 )
= ( zero_zero @ X_a ) )
| ( ord_less @ X_a @ ( zero_zero @ X_a ) @ ( plus_plus @ X_a @ ( power_power @ X_a @ X_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ X_a @ Y_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[390]) ).
thf(438,plain,
( ( ! [X_a: $i] :
( ~ ( linordered_idom @ X_a )
| ( ! [X_1: $i,Y_1: $i] :
( ( ( ti @ X_a @ X_1 )
!= ( zero_zero @ X_a ) )
| ( ( ti @ X_a @ Y_1 )
!= ( zero_zero @ X_a ) )
| ( ( plus_plus @ X_a @ ( power_power @ X_a @ X_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ X_a @ Y_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ X_a ) ) )
& ! [X_1: $i] :
( ! [Y_1: $i] :
( ( plus_plus @ X_a @ ( power_power @ X_a @ X_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ X_a @ Y_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ X_a ) )
| ( ( ti @ X_a @ X_1 )
= ( zero_zero @ X_a ) ) )
& ! [X_1: $i,Y_1: $i] :
( ( ( plus_plus @ X_a @ ( power_power @ X_a @ X_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ X_a @ Y_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ X_a ) )
| ( ( ti @ X_a @ Y_1 )
= ( zero_zero @ X_a ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[389]) ).
thf(439,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)],[388]) ).
thf(440,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)],[387]) ).
thf(441,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)],[386]) ).
thf(442,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)],[385]) ).
thf(443,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)],[384]) ).
thf(444,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)],[383]) ).
thf(445,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)],[382]) ).
thf(446,plain,
( ( ( plus_plus @ int @ ( power_power @ int @ s @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( one_one @ int ) )
= ( times_times @ int @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) @ sK1_T_1 ) )
= $true ),
inference(copy,[status(thm)],[381]) ).
thf(447,plain,
( ( ! [W: $i] : ( ord_less_eq @ int @ W @ W ) )
= $true ),
inference(copy,[status(thm)],[272]) ).
thf(448,plain,
( ( ! [K_1: $i] :
( ( number_number_of @ int @ K_1 )
= K_1 ) )
= $true ),
inference(copy,[status(thm)],[271]) ).
thf(449,plain,
( ( ! [Z: $i,W: $i] :
( ( times_times @ int @ Z @ W )
= ( times_times @ int @ W @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[270]) ).
thf(450,plain,
( ( ! [Z: $i,W: $i] :
( ( ord_less_eq @ int @ Z @ W )
| ( ord_less_eq @ int @ W @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[269]) ).
thf(451,plain,
( ( ! [V: $i,W: $i] :
( ( times_times @ int @ ( number_number_of @ int @ V ) @ ( number_number_of @ int @ W ) )
= ( number_number_of @ int @ ( times_times @ int @ V @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[268]) ).
thf(452,plain,
( ( ! [K: $i,L: $i] :
( ~ ( ord_less_eq @ int @ ( number_number_of @ int @ K ) @ ( number_number_of @ int @ L ) )
| ( ord_less_eq @ int @ K @ L ) )
& ! [K: $i,L: $i] :
( ~ ( ord_less_eq @ int @ K @ L )
| ( ord_less_eq @ int @ ( number_number_of @ int @ K ) @ ( number_number_of @ int @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[380]) ).
thf(453,plain,
( ( ! [Z1: $i,Z2: $i,Z3: $i] :
( ( times_times @ int @ ( times_times @ int @ Z1 @ Z2 ) @ Z3 )
= ( times_times @ int @ Z1 @ ( times_times @ int @ Z2 @ Z3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[266]) ).
thf(454,plain,
( ( ! [K_1: $i,I: $i,J: $i] :
( ~ ( ord_less_eq @ int @ I @ J )
| ~ ( ord_less_eq @ int @ J @ K_1 )
| ( ord_less_eq @ int @ I @ K_1 ) ) )
= $true ),
inference(copy,[status(thm)],[379]) ).
thf(455,plain,
( ( ! [Z: $i,W: $i] :
( ~ ( ord_less_eq @ int @ Z @ W )
| ~ ( ord_less_eq @ int @ W @ Z )
| ( Z = W ) ) )
= $true ),
inference(copy,[status(thm)],[378]) ).
thf(456,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( power_power @ int @ X @ ( plus_plus @ nat @ Y @ Z ) )
= ( times_times @ int @ ( power_power @ int @ X @ Y ) @ ( power_power @ int @ X @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[263]) ).
thf(457,plain,
( ( ! [K1: $i,K2: $i] :
( ~ ( ord_less_eq @ int @ ( bit1 @ K1 ) @ ( bit1 @ K2 ) )
| ( ord_less_eq @ int @ K1 @ K2 ) )
& ! [K1: $i,K2: $i] :
( ~ ( ord_less_eq @ int @ K1 @ K2 )
| ( ord_less_eq @ int @ ( bit1 @ K1 ) @ ( bit1 @ K2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[377]) ).
thf(458,plain,
( ( ! [K: $i,L: $i] :
( ~ ( ord_less_eq @ int @ ( bit1 @ K ) @ ( bit1 @ L ) )
| ( ord_less_eq @ int @ K @ L ) )
& ! [K: $i,L: $i] :
( ~ ( ord_less_eq @ int @ K @ L )
| ( ord_less_eq @ int @ ( bit1 @ K ) @ ( bit1 @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[376]) ).
thf(459,plain,
( ( ord_less_eq @ int @ pls @ pls )
= $true ),
inference(copy,[status(thm)],[260]) ).
thf(460,plain,
( ( ! [K1: $i,K2: $i] :
( ~ ( ord_less_eq @ int @ ( bit0 @ K1 ) @ ( bit0 @ K2 ) )
| ( ord_less_eq @ int @ K1 @ K2 ) )
& ! [K1: $i,K2: $i] :
( ~ ( ord_less_eq @ int @ K1 @ K2 )
| ( ord_less_eq @ int @ ( bit0 @ K1 ) @ ( bit0 @ K2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[375]) ).
thf(461,plain,
( ( ! [K: $i,L: $i] :
( ~ ( ord_less_eq @ int @ ( bit0 @ K ) @ ( bit0 @ L ) )
| ( ord_less_eq @ int @ K @ L ) )
& ! [K: $i,L: $i] :
( ~ ( ord_less_eq @ int @ K @ L )
| ( ord_less_eq @ int @ ( bit0 @ K ) @ ( bit0 @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[374]) ).
thf(462,plain,
( ( ! [Z_1: $i,W_1: $i] :
( ( Z_1 = W_1 )
| ~ ( ord_less_eq @ int @ Z_1 @ W_1 )
| ( ord_less @ int @ Z_1 @ W_1 ) )
& ! [Z_1: $i,W_1: $i] :
( ~ ( ord_less @ int @ Z_1 @ W_1 )
| ( Z_1 != W_1 ) )
& ! [Z_1: $i,W_1: $i] :
( ~ ( ord_less @ int @ Z_1 @ W_1 )
| ( ord_less_eq @ int @ Z_1 @ W_1 ) ) )
= $true ),
inference(copy,[status(thm)],[373]) ).
thf(463,plain,
( ( ! [K_1: $i,I: $i,J: $i] :
( ~ ( ord_less_eq @ int @ I @ J )
| ( ord_less_eq @ int @ ( plus_plus @ int @ K_1 @ I ) @ ( plus_plus @ int @ K_1 @ J ) ) ) )
= $true ),
inference(copy,[status(thm)],[372]) ).
thf(464,plain,
( ( ! [V_3: $i] :
( ( ( number_number_of @ nat @ V_3 )
!= ( zero_zero @ nat ) )
| ( ord_less_eq @ int @ V_3 @ pls ) )
& ! [V_3: $i] :
( ~ ( ord_less_eq @ int @ V_3 @ pls )
| ( ( number_number_of @ nat @ V_3 )
= ( zero_zero @ nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[371]) ).
thf(465,plain,
( ( ! [V_3: $i] :
( ( ( zero_zero @ nat )
!= ( number_number_of @ nat @ V_3 ) )
| ( ord_less_eq @ int @ V_3 @ pls ) )
& ! [V_3: $i] :
( ~ ( ord_less_eq @ int @ V_3 @ pls )
| ( ( zero_zero @ nat )
= ( number_number_of @ nat @ V_3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[370]) ).
thf(466,plain,
( ( ! [X_a: $i] :
( ~ ( number_ring @ X_a )
| ! [V: $i,W: $i,Z: $i] :
( ( times_times @ X_a @ ( number_number_of @ X_a @ V ) @ ( times_times @ X_a @ ( number_number_of @ X_a @ W ) @ Z ) )
= ( times_times @ X_a @ ( number_number_of @ X_a @ ( times_times @ int @ V @ W ) ) @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[369]) ).
thf(467,plain,
( ( ! [X_a: $i] :
( ~ ( number_ring @ X_a )
| ! [V: $i,W: $i] :
( ( times_times @ X_a @ ( number_number_of @ X_a @ V ) @ ( number_number_of @ X_a @ W ) )
= ( number_number_of @ X_a @ ( times_times @ int @ V @ W ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[368]) ).
thf(468,plain,
( ( ! [X_a: $i] :
( ~ ( number_ring @ X_a )
| ! [V: $i,W: $i] :
( ( number_number_of @ X_a @ ( times_times @ int @ V @ W ) )
= ( times_times @ X_a @ ( number_number_of @ X_a @ V ) @ ( number_number_of @ X_a @ W ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[367]) ).
thf(469,plain,
( ( ! [V_3: $i] :
( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ ( number_number_of @ nat @ V_3 ) )
| ( ord_less @ int @ pls @ V_3 ) )
& ! [V_3: $i] :
( ~ ( ord_less @ int @ pls @ V_3 )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ ( number_number_of @ nat @ V_3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[366]) ).
thf(470,plain,
( ( ! [K: $i] :
( ~ ( ord_less_eq @ int @ pls @ ( bit1 @ K ) )
| ( ord_less_eq @ int @ pls @ K ) )
& ! [K: $i] :
( ~ ( ord_less_eq @ int @ pls @ K )
| ( ord_less_eq @ int @ pls @ ( bit1 @ K ) ) ) )
= $true ),
inference(copy,[status(thm)],[365]) ).
thf(471,plain,
( ( ! [K1: $i,K2: $i] :
( ~ ( ord_less_eq @ int @ ( bit0 @ K1 ) @ ( bit1 @ K2 ) )
| ( ord_less_eq @ int @ K1 @ K2 ) )
& ! [K1: $i,K2: $i] :
( ~ ( ord_less_eq @ int @ K1 @ K2 )
| ( ord_less_eq @ int @ ( bit0 @ K1 ) @ ( bit1 @ K2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[364]) ).
thf(472,plain,
( ( ! [K: $i,L: $i] :
( ~ ( ord_less_eq @ int @ ( bit0 @ K ) @ ( bit1 @ L ) )
| ( ord_less_eq @ int @ K @ L ) )
& ! [K: $i,L: $i] :
( ~ ( ord_less_eq @ int @ K @ L )
| ( ord_less_eq @ int @ ( bit0 @ K ) @ ( bit1 @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[363]) ).
thf(473,plain,
( ( ! [K: $i] :
( ~ ( ord_less_eq @ int @ ( bit0 @ K ) @ pls )
| ( ord_less_eq @ int @ K @ pls ) )
& ! [K: $i] :
( ~ ( ord_less_eq @ int @ K @ pls )
| ( ord_less_eq @ int @ ( bit0 @ K ) @ pls ) ) )
= $true ),
inference(copy,[status(thm)],[362]) ).
thf(474,plain,
( ( ! [K: $i] :
( ~ ( ord_less_eq @ int @ pls @ ( bit0 @ K ) )
| ( ord_less_eq @ int @ pls @ K ) )
& ! [K: $i] :
( ~ ( ord_less_eq @ int @ pls @ K )
| ( ord_less_eq @ int @ pls @ ( bit0 @ K ) ) ) )
= $true ),
inference(copy,[status(thm)],[361]) ).
thf(475,plain,
( ( ! [Z_2: $i,Z: $i,W_2: $i,W: $i] :
( ~ ( ord_less @ int @ W_2 @ W )
| ~ ( ord_less_eq @ int @ Z_2 @ Z )
| ( ord_less @ int @ ( plus_plus @ int @ W_2 @ Z_2 ) @ ( plus_plus @ int @ W @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[360]) ).
thf(476,plain,
( ( ( number_number_of @ nat @ pls )
= ( zero_zero @ nat ) )
= $true ),
inference(copy,[status(thm)],[243]) ).
thf(477,plain,
( ( ( zero_zero @ nat )
= ( number_number_of @ nat @ pls ) )
= $true ),
inference(copy,[status(thm)],[242]) ).
thf(478,plain,
( ( ( plus_plus @ nat @ ( one_one @ nat ) @ ( one_one @ nat ) )
= ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(copy,[status(thm)],[241]) ).
thf(479,plain,
( ( ! [W: $i] :
( ( times_times @ int @ pls @ W )
= pls ) )
= $true ),
inference(copy,[status(thm)],[240]) ).
thf(480,plain,
( ( ! [K_1: $i,L_1: $i] :
( ( times_times @ int @ ( bit0 @ K_1 ) @ L_1 )
= ( bit0 @ ( times_times @ int @ K_1 @ L_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[239]) ).
thf(481,plain,
( ( ! [K: $i,L: $i] :
( ~ ( ord_less @ int @ ( number_number_of @ int @ K ) @ ( number_number_of @ int @ L ) )
| ( ord_less @ int @ K @ L ) )
& ! [K: $i,L: $i] :
( ~ ( ord_less @ int @ K @ L )
| ( ord_less @ int @ ( number_number_of @ int @ K ) @ ( number_number_of @ int @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[359]) ).
thf(482,plain,
( ( ! [Z: $i] :
( ( times_times @ int @ Z @ ( one_one @ int ) )
= Z ) )
= $true ),
inference(copy,[status(thm)],[237]) ).
thf(483,plain,
( ( ! [Z: $i] :
( ( times_times @ int @ ( one_one @ int ) @ Z )
= Z ) )
= $true ),
inference(copy,[status(thm)],[236]) ).
thf(484,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)],[235]) ).
thf(485,plain,
( ( ! [Z1: $i,Z2: $i,W: $i] :
( ( times_times @ int @ ( plus_plus @ int @ Z1 @ Z2 ) @ W )
= ( plus_plus @ int @ ( times_times @ int @ Z1 @ W ) @ ( times_times @ int @ Z2 @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[234]) ).
thf(486,plain,
( ( ! [W: $i,Z1: $i,Z2: $i] :
( ( times_times @ int @ W @ ( plus_plus @ int @ Z1 @ Z2 ) )
= ( plus_plus @ int @ ( times_times @ int @ W @ Z1 ) @ ( times_times @ int @ W @ Z2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[233]) ).
thf(487,plain,
( ( ! [K: $i] :
( ~ ( ord_less @ int @ K @ pls )
| ( ord_less_eq @ int @ ( bit1 @ K ) @ pls ) )
& ! [K: $i] :
( ~ ( ord_less_eq @ int @ ( bit1 @ K ) @ pls )
| ( ord_less @ int @ K @ pls ) ) )
= $true ),
inference(copy,[status(thm)],[358]) ).
thf(488,plain,
( ( ! [K: $i] :
( ~ ( ord_less @ int @ pls @ ( bit1 @ K ) )
| ( ord_less_eq @ int @ pls @ K ) )
& ! [K: $i] :
( ~ ( ord_less_eq @ int @ pls @ K )
| ( ord_less @ int @ pls @ ( bit1 @ K ) ) ) )
= $true ),
inference(copy,[status(thm)],[357]) ).
thf(489,plain,
( ( ! [K1: $i,K2: $i] :
( ~ ( ord_less @ int @ K1 @ K2 )
| ( ord_less_eq @ int @ ( bit1 @ K1 ) @ ( bit0 @ K2 ) ) )
& ! [K1: $i,K2: $i] :
( ~ ( ord_less_eq @ int @ ( bit1 @ K1 ) @ ( bit0 @ K2 ) )
| ( ord_less @ int @ K1 @ K2 ) ) )
= $true ),
inference(copy,[status(thm)],[356]) ).
thf(490,plain,
( ( ! [K: $i,L: $i] :
( ~ ( ord_less @ int @ K @ L )
| ( ord_less_eq @ int @ ( bit1 @ K ) @ ( bit0 @ L ) ) )
& ! [K: $i,L: $i] :
( ~ ( ord_less_eq @ int @ ( bit1 @ K ) @ ( bit0 @ L ) )
| ( ord_less @ int @ K @ L ) ) )
= $true ),
inference(copy,[status(thm)],[355]) ).
thf(491,plain,
( ( ! [K1: $i,K2: $i] :
( ~ ( ord_less @ int @ ( bit0 @ K1 ) @ ( bit1 @ K2 ) )
| ( ord_less_eq @ int @ K1 @ K2 ) )
& ! [K1: $i,K2: $i] :
( ~ ( ord_less_eq @ int @ K1 @ K2 )
| ( ord_less @ int @ ( bit0 @ K1 ) @ ( bit1 @ K2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[354]) ).
thf(492,plain,
( ( ! [K: $i,L: $i] :
( ~ ( ord_less @ int @ ( bit0 @ K ) @ ( bit1 @ L ) )
| ( ord_less_eq @ int @ K @ L ) )
& ! [K: $i,L: $i] :
( ~ ( ord_less_eq @ int @ K @ L )
| ( ord_less @ int @ ( bit0 @ K ) @ ( bit1 @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[353]) ).
thf(493,plain,
( ( ! [V_3: $i,V_2: $i] :
( ( ord_less @ int @ V_3 @ V_2 )
| ~ ( ord_less @ int @ V_3 @ V_2 )
| ( ord_less @ nat @ ( number_number_of @ nat @ V_3 ) @ ( number_number_of @ nat @ V_2 ) ) )
& ! [V_3: $i,V_2: $i] :
( ~ ( ord_less @ int @ pls @ V_2 )
| ~ ( ord_less @ int @ V_3 @ V_2 )
| ( ord_less @ nat @ ( number_number_of @ nat @ V_3 ) @ ( number_number_of @ nat @ V_2 ) ) )
& ! [V_3: $i,V_2: $i] :
( ~ ( ord_less @ nat @ ( number_number_of @ nat @ V_3 ) @ ( number_number_of @ nat @ V_2 ) )
| ~ ( ord_less @ int @ V_3 @ V_2 )
| ( ord_less @ int @ pls @ V_2 ) )
& ! [V_3: $i,V_2: $i] :
( ~ ( ord_less @ nat @ ( number_number_of @ nat @ V_3 ) @ ( number_number_of @ nat @ V_2 ) )
| ( ord_less @ int @ V_3 @ V_2 ) ) )
= $true ),
inference(copy,[status(thm)],[352]) ).
thf(494,plain,
( ( ! [Z_1: $i] :
( ~ ( ord_less @ int @ ( zero_zero @ int ) @ Z_1 )
| ( ord_less_eq @ int @ ( one_one @ int ) @ Z_1 ) )
& ! [Z_1: $i] :
( ~ ( ord_less_eq @ int @ ( one_one @ int ) @ Z_1 )
| ( ord_less @ int @ ( zero_zero @ int ) @ Z_1 ) ) )
= $true ),
inference(copy,[status(thm)],[351]) ).
thf(495,plain,
( ( ( number_number_of @ nat @ ( bit1 @ pls ) )
= ( one_one @ nat ) )
= $true ),
inference(copy,[status(thm)],[224]) ).
thf(496,plain,
( ( ( one_one @ nat )
= ( number_number_of @ nat @ ( bit1 @ pls ) ) )
= $true ),
inference(copy,[status(thm)],[223]) ).
thf(497,plain,
( ( ! [W: $i,Z: $i] :
( ~ ( ord_less @ int @ W @ Z )
| ( ord_less_eq @ int @ ( plus_plus @ int @ W @ ( one_one @ int ) ) @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[350]) ).
thf(498,plain,
( ( ! [W_1: $i,Z_1: $i] :
( ~ ( ord_less @ int @ W_1 @ Z_1 )
| ( ord_less_eq @ int @ ( plus_plus @ int @ W_1 @ ( one_one @ int ) ) @ Z_1 ) )
& ! [W_1: $i,Z_1: $i] :
( ~ ( ord_less_eq @ int @ ( plus_plus @ int @ W_1 @ ( one_one @ int ) ) @ Z_1 )
| ( ord_less @ int @ W_1 @ Z_1 ) ) )
= $true ),
inference(copy,[status(thm)],[349]) ).
thf(499,plain,
( ( ! [W_1: $i,Z_1: $i] :
( ~ ( ord_less @ int @ W_1 @ ( plus_plus @ int @ Z_1 @ ( one_one @ int ) ) )
| ( ord_less_eq @ int @ W_1 @ Z_1 ) )
& ! [W_1: $i,Z_1: $i] :
( ~ ( ord_less_eq @ int @ W_1 @ Z_1 )
| ( ord_less @ int @ W_1 @ ( plus_plus @ int @ Z_1 @ ( one_one @ int ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[348]) ).
thf(500,plain,
( ( ! [X_a: $i] :
( ~ ( number_semiring @ X_a )
| ! [V_1: $i,V: $i] :
( ~ ( ord_less_eq @ int @ pls @ V )
| ~ ( ord_less_eq @ int @ pls @ V_1 )
| ( ( plus_plus @ X_a @ ( number_number_of @ X_a @ V ) @ ( number_number_of @ X_a @ V_1 ) )
= ( number_number_of @ X_a @ ( plus_plus @ int @ V @ V_1 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[347]) ).
thf(501,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)],[346]) ).
thf(502,plain,
( ( ! [Z: $i] :
( ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ Z )
| ( ord_less @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( one_one @ int ) @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[345]) ).
thf(503,plain,
( ( ! [X_a: $i] :
( ~ ( number_ring @ X_a )
| ~ ( ring_char_0 @ X_a )
| ( ! [X_1: $i,Y_1: $i] :
( ( ( number_number_of @ X_a @ X_1 )
!= ( number_number_of @ X_a @ Y_1 ) )
| ( X_1 = Y_1 ) )
& ! [X_1: $i,Y_1: $i] :
( ( X_1 != Y_1 )
| ( ( number_number_of @ X_a @ X_1 )
= ( number_number_of @ X_a @ Y_1 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[344]) ).
thf(504,plain,
( ( ! [X_a: $i] :
( ~ ( number @ X_a )
| ( ! [W_1: $i,X_1: $i] :
( ( ( number_number_of @ X_a @ W_1 )
!= ( ti @ X_a @ X_1 ) )
| ( ( ti @ X_a @ X_1 )
= ( number_number_of @ X_a @ W_1 ) ) )
& ! [W_1: $i,X_1: $i] :
( ( ( ti @ X_a @ X_1 )
!= ( number_number_of @ X_a @ W_1 ) )
| ( ( number_number_of @ X_a @ W_1 )
= ( ti @ X_a @ X_1 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[343]) ).
thf(505,plain,
( ( ! [K: $i,L: $i] :
( ( ( bit1 @ K )
!= ( bit1 @ L ) )
| ( K = L ) )
& ! [K: $i,L: $i] :
( ( K != L )
| ( ( bit1 @ K )
= ( bit1 @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[342]) ).
thf(506,plain,
( ( ! [K: $i,L: $i] :
( ( ( bit0 @ K )
!= ( bit0 @ L ) )
| ( K = L ) )
& ! [K: $i,L: $i] :
( ( K != L )
| ( ( bit0 @ K )
= ( bit0 @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[341]) ).
thf(507,plain,
( ( ! [X: $i,Y: $i] :
( ( ord_less @ int @ Y @ X )
| ( X = Y )
| ( ord_less @ int @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[340]) ).
thf(508,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)],[211]) ).
thf(509,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)],[210]) ).
thf(510,plain,
( ( ! [Z: $i,W: $i] :
( ( plus_plus @ int @ Z @ W )
= ( plus_plus @ int @ W @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[209]) ).
thf(511,plain,
( ( ( zero_zero @ int )
= ( number_number_of @ int @ pls ) )
= $true ),
inference(copy,[status(thm)],[208]) ).
thf(512,plain,
( ( ring_11004092258visors @ int )
= $true ),
inference(copy,[status(thm)],[207]) ).
thf(513,plain,
( ( linord581940658strict @ int )
= $true ),
inference(copy,[status(thm)],[206]) ).
thf(514,plain,
( ( linordered_ring @ int )
= $true ),
inference(copy,[status(thm)],[205]) ).
thf(515,plain,
( ( linordered_idom @ int )
= $true ),
inference(copy,[status(thm)],[204]) ).
thf(516,plain,
( ( number_semiring @ int )
= $true ),
inference(copy,[status(thm)],[203]) ).
thf(517,plain,
( ( linorder @ int )
= $true ),
inference(copy,[status(thm)],[202]) ).
thf(518,plain,
( ( semiring_1 @ int )
= $true ),
inference(copy,[status(thm)],[201]) ).
thf(519,plain,
( ( ring_char_0 @ int )
= $true ),
inference(copy,[status(thm)],[200]) ).
thf(520,plain,
( ( number_ring @ int )
= $true ),
inference(copy,[status(thm)],[199]) ).
thf(521,plain,
( ( semiring @ int )
= $true ),
inference(copy,[status(thm)],[198]) ).
thf(522,plain,
( ( number @ int )
= $true ),
inference(copy,[status(thm)],[197]) ).
thf(523,plain,
( ( number_semiring @ nat )
= $true ),
inference(copy,[status(thm)],[196]) ).
thf(524,plain,
( ( linorder @ nat )
= $true ),
inference(copy,[status(thm)],[195]) ).
thf(525,plain,
( ( semiring_1 @ nat )
= $true ),
inference(copy,[status(thm)],[194]) ).
thf(526,plain,
( ( semiring @ nat )
= $true ),
inference(copy,[status(thm)],[193]) ).
thf(527,plain,
( ( number @ nat )
= $true ),
inference(copy,[status(thm)],[192]) ).
thf(528,plain,
( ( ! [B_1: $i,B_2: $i,X_b: $i] :
( ~ ( number @ X_b )
| ~ ( semiring @ X_b )
| ( ( plus_plus @ X_b @ ( ti @ X_b @ B_1 ) @ B_2 )
= ( plus_plus @ X_b @ B_1 @ B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[339]) ).
thf(529,plain,
( ( ! [B_1: $i,B_2: $i,X_b: $i] :
( ~ ( number @ X_b )
| ~ ( semiring @ X_b )
| ( ( plus_plus @ X_b @ B_1 @ ( ti @ X_b @ B_2 ) )
= ( plus_plus @ X_b @ B_1 @ B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[338]) ).
thf(530,plain,
( ( ! [B_1: $i,B_2: $i,X_b: $i] :
( ~ ( number @ X_b )
| ~ ( semiring @ X_b )
| ( ( ti @ X_b @ ( plus_plus @ X_b @ B_1 @ B_2 ) )
= ( plus_plus @ X_b @ B_1 @ B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[337]) ).
thf(531,plain,
( ( ! [B_1: $i,B_2: $i,X_b: $i] :
( ~ ( number @ X_b )
| ~ ( semiring @ X_b )
| ( ( times_times @ X_b @ ( ti @ X_b @ B_1 ) @ B_2 )
= ( times_times @ X_b @ B_1 @ B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[336]) ).
thf(532,plain,
( ( ! [B_1: $i,B_2: $i,X_b: $i] :
( ~ ( number @ X_b )
| ~ ( semiring @ X_b )
| ( ( times_times @ X_b @ B_1 @ ( ti @ X_b @ B_2 ) )
= ( times_times @ X_b @ B_1 @ B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[335]) ).
thf(533,plain,
( ( ! [B_1: $i,B_2: $i,X_b: $i] :
( ~ ( number @ X_b )
| ~ ( semiring @ X_b )
| ( ( ti @ X_b @ ( times_times @ X_b @ B_1 @ B_2 ) )
= ( times_times @ X_b @ B_1 @ B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[334]) ).
thf(534,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ~ ( linordered_ring @ X_a )
| ( ( times_times @ X_a @ ( ti @ X_a @ B_1 ) @ B_2 )
= ( times_times @ X_a @ B_1 @ B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[333]) ).
thf(535,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ~ ( linordered_ring @ X_a )
| ( ( times_times @ X_a @ B_1 @ ( ti @ X_a @ B_2 ) )
= ( times_times @ X_a @ B_1 @ B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[332]) ).
thf(536,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ~ ( linordered_ring @ X_a )
| ( ( ti @ X_a @ ( times_times @ X_a @ B_1 @ B_2 ) )
= ( times_times @ X_a @ B_1 @ B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[331]) ).
thf(537,plain,
( ( ! [X_a: $i] :
( ( ti @ X_a @ ( undefined @ X_a ) )
= ( undefined @ X_a ) ) )
= $true ),
inference(copy,[status(thm)],[182]) ).
thf(538,plain,
( ( ! [B_1: $i] :
( ! [B_2: $i,X_a: $i] :
( ~ ( linorder @ X_a )
| ~ ( number @ 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] :
( ~ ( linorder @ X_a )
| ~ ( number @ 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)],[330]) ).
thf(539,plain,
( ( ! [B_1: $i] :
( ! [B_2: $i,X_a: $i] :
( ~ ( linorder @ X_a )
| ~ ( number @ 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] :
( ~ ( linorder @ X_a )
| ~ ( number @ 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)],[329]) ).
thf(540,plain,
( ( ! [B_1: $i] :
( ! [B_2: $i,X_a: $i] :
( ~ ( linorder @ X_a )
| ~ ( number @ X_a )
| ~ ( ord_less_eq @ X_a @ ( ti @ X_a @ B_1 ) @ B_2 )
| ( ord_less_eq @ X_a @ B_1 @ B_2 ) )
& ! [B_2: $i,X_a: $i] :
( ~ ( linorder @ X_a )
| ~ ( number @ X_a )
| ~ ( ord_less_eq @ X_a @ B_1 @ B_2 )
| ( ord_less_eq @ X_a @ ( ti @ X_a @ B_1 ) @ B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[328]) ).
thf(541,plain,
( ( ! [B_1: $i] :
( ! [B_2: $i,X_a: $i] :
( ~ ( linorder @ X_a )
| ~ ( number @ X_a )
| ~ ( ord_less_eq @ X_a @ B_1 @ ( ti @ X_a @ B_2 ) )
| ( ord_less_eq @ X_a @ B_1 @ B_2 ) )
& ! [B_2: $i,X_a: $i] :
( ~ ( linorder @ X_a )
| ~ ( number @ X_a )
| ~ ( ord_less_eq @ X_a @ B_1 @ B_2 )
| ( ord_less_eq @ X_a @ B_1 @ ( ti @ X_a @ B_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[327]) ).
thf(542,plain,
( ( ! [B_1: $i] :
( ! [B_2: $i,X_a: $i] :
( ~ ( linordered_ring @ X_a )
| ~ ( ord_less_eq @ X_a @ ( ti @ X_a @ B_1 ) @ B_2 )
| ( ord_less_eq @ X_a @ B_1 @ B_2 ) )
& ! [B_2: $i,X_a: $i] :
( ~ ( linordered_ring @ X_a )
| ~ ( ord_less_eq @ X_a @ B_1 @ B_2 )
| ( ord_less_eq @ X_a @ ( ti @ X_a @ B_1 ) @ B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[326]) ).
thf(543,plain,
( ( ! [B_1: $i] :
( ! [B_2: $i,X_a: $i] :
( ~ ( linordered_ring @ X_a )
| ~ ( ord_less_eq @ X_a @ B_1 @ ( ti @ X_a @ B_2 ) )
| ( ord_less_eq @ X_a @ B_1 @ B_2 ) )
& ! [B_2: $i,X_a: $i] :
( ~ ( linordered_ring @ X_a )
| ~ ( ord_less_eq @ X_a @ B_1 @ B_2 )
| ( ord_less_eq @ X_a @ B_1 @ ( ti @ X_a @ B_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[325]) ).
thf(544,plain,
( ( ord_less @ int @ ( times_times @ int @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) @ t ) @ ( times_times @ int @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) @ ( zero_zero @ int ) ) )
= $true ),
inference(copy,[status(thm)],[175]) ).
thf(545,plain,
( ( ( plus_plus @ int @ ( power_power @ int @ s @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( one_one @ int ) )
= ( times_times @ int @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) @ t ) )
= $true ),
inference(copy,[status(thm)],[174]) ).
thf(546,plain,
( ( ord_less @ int @ t @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) )
= $true ),
inference(copy,[status(thm)],[173]) ).
thf(547,plain,
( ( zprime @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) )
= $true ),
inference(copy,[status(thm)],[172]) ).
thf(548,plain,
( ( twoSqu33214720sum2sq @ ( times_times @ int @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) @ t ) )
= $true ),
inference(copy,[status(thm)],[171]) ).
thf(549,plain,
( ( ! [X_a: $i] :
( ~ ( linordered_idom @ X_a )
| ~ ( number_ring @ X_a )
| ( ! [X_1: $i,Y_1: $i] :
( ~ ( ord_less_eq @ X_a @ ( number_number_of @ X_a @ X_1 ) @ ( number_number_of @ X_a @ Y_1 ) )
| ( ord_less_eq @ int @ X_1 @ Y_1 ) )
& ! [X_1: $i,Y_1: $i] :
( ~ ( ord_less_eq @ int @ X_1 @ Y_1 )
| ( ord_less_eq @ X_a @ ( number_number_of @ X_a @ X_1 ) @ ( number_number_of @ X_a @ Y_1 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[324]) ).
thf(550,plain,
( ( ! [X_a: $i] :
( ~ ( number_semiring @ X_a )
| ! [V_1: $i,V: $i] :
( ~ ( ord_less_eq @ int @ pls @ V )
| ~ ( ord_less_eq @ int @ pls @ V_1 )
| ( ( times_times @ X_a @ ( number_number_of @ X_a @ V ) @ ( number_number_of @ X_a @ V_1 ) )
= ( number_number_of @ X_a @ ( times_times @ int @ V @ V_1 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[323]) ).
thf(551,plain,
( ( ! [X_a: $i] :
( ~ ( linord581940658strict @ X_a )
| ( ! [X_1: $i,Y_1: $i] :
( ( ( ti @ X_a @ X_1 )
!= ( zero_zero @ X_a ) )
| ( ( ti @ X_a @ Y_1 )
!= ( zero_zero @ X_a ) )
| ( ord_less_eq @ X_a @ ( plus_plus @ X_a @ ( times_times @ X_a @ X_1 @ X_1 ) @ ( times_times @ X_a @ Y_1 @ Y_1 ) ) @ ( zero_zero @ X_a ) ) )
& ! [X_1: $i] :
( ! [Y_1: $i] :
~ ( ord_less_eq @ X_a @ ( plus_plus @ X_a @ ( times_times @ X_a @ X_1 @ X_1 ) @ ( times_times @ X_a @ Y_1 @ Y_1 ) ) @ ( zero_zero @ X_a ) )
| ( ( ti @ X_a @ X_1 )
= ( zero_zero @ X_a ) ) )
& ! [X_1: $i,Y_1: $i] :
( ~ ( ord_less_eq @ X_a @ ( plus_plus @ X_a @ ( times_times @ X_a @ X_1 @ X_1 ) @ ( times_times @ X_a @ Y_1 @ Y_1 ) ) @ ( zero_zero @ X_a ) )
| ( ( ti @ X_a @ Y_1 )
= ( zero_zero @ X_a ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[322]) ).
thf(552,plain,
( ( ! [X_a: $i] :
( ~ ( linordered_ring @ X_a )
| ! [X: $i,Y: $i] : ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ ( plus_plus @ X_a @ ( times_times @ X_a @ X @ X ) @ ( times_times @ X_a @ Y @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[321]) ).
thf(553,plain,
( ( ! [X_a: $i] :
( ~ ( linordered_idom @ X_a )
| ~ ( number_ring @ X_a )
| ( ! [X_1: $i] :
( ~ ( ord_less_eq @ X_a @ ( number_number_of @ X_a @ X_1 ) @ ( zero_zero @ X_a ) )
| ( ord_less_eq @ int @ X_1 @ pls ) )
& ! [X_1: $i] :
( ~ ( ord_less_eq @ int @ X_1 @ pls )
| ( ord_less_eq @ X_a @ ( number_number_of @ X_a @ X_1 ) @ ( zero_zero @ X_a ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[320]) ).
thf(554,plain,
( ( ! [X_a: $i] :
( ~ ( linordered_idom @ X_a )
| ~ ( number_ring @ X_a )
| ( ! [Y_1: $i] :
( ~ ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ ( number_number_of @ X_a @ Y_1 ) )
| ( ord_less_eq @ int @ pls @ Y_1 ) )
& ! [Y_1: $i] :
( ~ ( ord_less_eq @ int @ pls @ Y_1 )
| ( ord_less_eq @ X_a @ ( zero_zero @ X_a ) @ ( number_number_of @ X_a @ Y_1 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[319]) ).
thf(555,plain,
( ( ! [X_a: $i] :
( ~ ( linorder @ X_a )
| ~ ( number @ X_a )
| ( ! [V_3: $i,W_1: $i] :
( ~ ( ord_less_eq @ X_a @ ( number_number_of @ X_a @ V_3 ) @ ( number_number_of @ X_a @ W_1 ) )
| ~ ( ord_less @ X_a @ ( number_number_of @ X_a @ W_1 ) @ ( number_number_of @ X_a @ V_3 ) ) )
& ! [V_3: $i,W_1: $i] :
( ( ord_less @ X_a @ ( number_number_of @ X_a @ W_1 ) @ ( number_number_of @ X_a @ V_3 ) )
| ( ord_less_eq @ X_a @ ( number_number_of @ X_a @ V_3 ) @ ( number_number_of @ X_a @ W_1 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[318]) ).
thf(556,plain,
( ( ! [X_a: $i] :
( ~ ( linordered_idom @ X_a )
| ~ ( number_ring @ X_a )
| ( ! [X_1: $i] :
( ~ ( ord_less_eq @ X_a @ ( number_number_of @ X_a @ X_1 ) @ ( one_one @ X_a ) )
| ( ord_less_eq @ int @ X_1 @ ( bit1 @ pls ) ) )
& ! [X_1: $i] :
( ~ ( ord_less_eq @ int @ X_1 @ ( bit1 @ pls ) )
| ( ord_less_eq @ X_a @ ( number_number_of @ X_a @ X_1 ) @ ( one_one @ X_a ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[317]) ).
thf(557,plain,
( ( ! [X_a: $i] :
( ~ ( linordered_idom @ X_a )
| ~ ( number_ring @ X_a )
| ( ! [Y_1: $i] :
( ~ ( ord_less_eq @ X_a @ ( one_one @ X_a ) @ ( number_number_of @ X_a @ Y_1 ) )
| ( ord_less_eq @ int @ ( bit1 @ pls ) @ Y_1 ) )
& ! [Y_1: $i] :
( ~ ( ord_less_eq @ int @ ( bit1 @ pls ) @ Y_1 )
| ( ord_less_eq @ X_a @ ( one_one @ X_a ) @ ( number_number_of @ X_a @ Y_1 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[316]) ).
thf(558,plain,
( ( ! [X_a: $i] :
( ~ ( linord581940658strict @ X_a )
| ( ! [X_1: $i,Y_1: $i] :
( ( ( ti @ X_a @ X_1 )
!= ( zero_zero @ X_a ) )
| ( ( ti @ X_a @ Y_1 )
!= ( zero_zero @ X_a ) )
| ( ( plus_plus @ X_a @ ( times_times @ X_a @ X_1 @ X_1 ) @ ( times_times @ X_a @ Y_1 @ Y_1 ) )
= ( zero_zero @ X_a ) ) )
& ! [X_1: $i] :
( ! [Y_1: $i] :
( ( plus_plus @ X_a @ ( times_times @ X_a @ X_1 @ X_1 ) @ ( times_times @ X_a @ Y_1 @ Y_1 ) )
!= ( zero_zero @ X_a ) )
| ( ( ti @ X_a @ X_1 )
= ( zero_zero @ X_a ) ) )
& ! [X_1: $i,Y_1: $i] :
( ( ( plus_plus @ X_a @ ( times_times @ X_a @ X_1 @ X_1 ) @ ( times_times @ X_a @ Y_1 @ Y_1 ) )
!= ( zero_zero @ X_a ) )
| ( ( ti @ X_a @ Y_1 )
= ( zero_zero @ X_a ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[315]) ).
thf(559,plain,
( ( ! [X_b: $i] :
( ~ ( number @ X_b )
| ~ ( semiring @ X_b )
| ! [A_1: $i,B: $i,V: $i] :
( ( times_times @ X_b @ ( plus_plus @ X_b @ A_1 @ B ) @ ( number_number_of @ X_b @ V ) )
= ( plus_plus @ X_b @ ( times_times @ X_b @ A_1 @ ( number_number_of @ X_b @ V ) ) @ ( times_times @ X_b @ B @ ( number_number_of @ X_b @ V ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[314]) ).
thf(560,plain,
( ( ! [X_b: $i] :
( ~ ( number @ X_b )
| ~ ( semiring @ X_b )
| ! [V: $i,B: $i,C: $i] :
( ( times_times @ X_b @ ( number_number_of @ X_b @ V ) @ ( plus_plus @ X_b @ B @ C ) )
= ( plus_plus @ X_b @ ( times_times @ X_b @ ( number_number_of @ X_b @ V ) @ B ) @ ( times_times @ X_b @ ( number_number_of @ X_b @ V ) @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[313]) ).
thf(561,plain,
( ( ! [T: $i,A: $i] :
( ( ti @ T @ ( ti @ T @ A ) )
= ( ti @ T @ A ) ) )
= $true ),
inference(copy,[status(thm)],[158]) ).
thf(562,plain,
( ( ~ ( ord_less @ int @ ( plus_plus @ int @ ( power_power @ int @ s @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( one_one @ int ) ) @ ( zero_zero @ int ) ) )
= $true ),
inference(copy,[status(thm)],[312]) ).
thf(563,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ ( number_number_of @ nat @ SX0 ) )
| ( ord_less @ int @ pls @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less @ int @ pls @ SX0 )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ ( number_number_of @ nat @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[469]) ).
thf(564,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ( ord_less @ int @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[462]) ).
thf(565,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ord_less @ int @ ( zero_zero @ int ) @ SX0 )
| ( ord_less_eq @ int @ ( one_one @ int ) @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less_eq @ int @ ( one_one @ int ) @ SX0 )
| ( ord_less @ int @ ( zero_zero @ int ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[494]) ).
thf(566,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq @ int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[471]) ).
thf(567,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq @ int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[472]) ).
thf(568,plain,
( ( ! [SX0: $i] :
( ~ ( linordered_idom @ SX0 )
| ~ ( number_ring @ SX0 )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ord_less_eq @ SX0 @ ( number_number_of @ SX0 @ SX1 ) @ ( number_number_of @ SX0 @ SX2 ) )
| ( ord_less_eq @ int @ SX1 @ SX2 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( ord_less_eq @ int @ SX1 @ SX2 )
| ( ord_less_eq @ SX0 @ ( number_number_of @ SX0 @ SX1 ) @ ( number_number_of @ SX0 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[549]) ).
thf(569,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ord_less_eq @ int @ ( bit0 @ SX0 ) @ pls )
| ( ord_less_eq @ int @ SX0 @ pls ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less_eq @ int @ SX0 @ pls )
| ( ord_less_eq @ int @ ( bit0 @ SX0 ) @ pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[473]) ).
thf(570,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)],[501]) ).
thf(571,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)],[424]) ).
thf(572,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)],[423]) ).
thf(573,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( linordered_ring @ SX2 )
| ~ ( ord_less_eq @ SX2 @ ( ti @ SX2 @ SX0 ) @ SX1 )
| ( ord_less_eq @ SX2 @ SX0 @ SX1 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( linordered_ring @ SX2 )
| ~ ( ord_less_eq @ SX2 @ SX0 @ SX1 )
| ( ord_less_eq @ SX2 @ ( ti @ SX2 @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[542]) ).
thf(574,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)],[506]) ).
thf(575,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( linorder @ SX2 )
| ~ ( number @ SX2 )
| ~ ( ord_less_eq @ SX2 @ SX0 @ ( ti @ SX2 @ SX1 ) )
| ( ord_less_eq @ SX2 @ SX0 @ SX1 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( linorder @ SX2 )
| ~ ( number @ SX2 )
| ~ ( ord_less_eq @ SX2 @ SX0 @ SX1 )
| ( ord_less_eq @ SX2 @ SX0 @ ( ti @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[541]) ).
thf(576,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)],[504]) ).
thf(577,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less @ int @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[489]) ).
thf(578,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( twoSqu33214720sum2sq @ ( ti @ int @ SX0 ) )
| ( twoSqu33214720sum2sq @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( twoSqu33214720sum2sq @ SX0 )
| ( twoSqu33214720sum2sq @ ( ti @ int @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[428]) ).
thf(579,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ ( number_number_of @ int @ SX0 ) @ ( number_number_of @ int @ SX1 ) )
| ( ord_less_eq @ int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ ( number_number_of @ int @ SX0 ) @ ( number_number_of @ int @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[452]) ).
thf(580,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( ( number_number_of @ nat @ SX0 )
!= ( zero_zero @ nat ) )
| ( ord_less_eq @ int @ SX0 @ pls ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less_eq @ int @ SX0 @ pls )
| ( ( number_number_of @ nat @ SX0 )
= ( zero_zero @ nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[464]) ).
thf(581,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( linorder @ SX2 )
| ~ ( number @ SX2 )
| ~ ( ord_less @ SX2 @ ( ti @ SX2 @ SX0 ) @ SX1 )
| ( ord_less @ SX2 @ SX0 @ SX1 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( linorder @ SX2 )
| ~ ( number @ SX2 )
| ~ ( ord_less @ SX2 @ SX0 @ SX1 )
| ( ord_less @ SX2 @ ( ti @ SX2 @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[538]) ).
thf(582,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)],[505]) ).
thf(583,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq @ int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[457]) ).
thf(584,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( zprime @ ( ti @ int @ SX0 ) )
| ( zprime @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( zprime @ SX0 )
| ( zprime @ ( ti @ int @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[420]) ).
thf(585,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ord_less_eq @ int @ pls @ ( bit1 @ SX0 ) )
| ( ord_less_eq @ int @ pls @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less_eq @ int @ pls @ SX0 )
| ( ord_less_eq @ int @ pls @ ( bit1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[470]) ).
thf(586,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq @ int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ( ord_less @ int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[491]) ).
thf(587,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ ( plus_plus @ int @ SX0 @ ( one_one @ int ) ) @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ ( plus_plus @ int @ SX0 @ ( one_one @ int ) ) @ SX1 )
| ( ord_less @ int @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[498]) ).
thf(588,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( linorder @ SX2 )
| ~ ( number @ SX2 )
| ~ ( ord_less_eq @ SX2 @ ( ti @ SX2 @ SX0 ) @ SX1 )
| ( ord_less_eq @ SX2 @ SX0 @ SX1 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( linorder @ SX2 )
| ~ ( number @ SX2 )
| ~ ( ord_less_eq @ SX2 @ SX0 @ SX1 )
| ( ord_less_eq @ SX2 @ ( ti @ SX2 @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[540]) ).
thf(589,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( linorder @ SX2 )
| ~ ( number @ SX2 )
| ~ ( ord_less @ SX2 @ SX0 @ ( ti @ SX2 @ SX1 ) )
| ( ord_less @ SX2 @ SX0 @ SX1 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( linorder @ SX2 )
| ~ ( number @ SX2 )
| ~ ( ord_less @ SX2 @ SX0 @ SX1 )
| ( ord_less @ SX2 @ SX0 @ ( ti @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[539]) ).
thf(590,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq @ int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[458]) ).
thf(591,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less @ int @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[490]) ).
thf(592,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ ( plus_plus @ int @ SX1 @ ( one_one @ int ) ) )
| ( ord_less_eq @ int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ( ord_less @ int @ SX0 @ ( plus_plus @ int @ SX1 @ ( one_one @ int ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[499]) ).
thf(593,plain,
( ( ! [SX0: $i] :
( ~ ( linorder @ SX0 )
| ~ ( number @ SX0 )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ord_less_eq @ SX0 @ ( number_number_of @ SX0 @ SX1 ) @ ( number_number_of @ SX0 @ SX2 ) )
| ~ ( ord_less @ SX0 @ ( number_number_of @ SX0 @ SX2 ) @ ( number_number_of @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( ord_less @ SX0 @ ( number_number_of @ SX0 @ SX2 ) @ ( number_number_of @ SX0 @ SX1 ) )
| ( ord_less_eq @ SX0 @ ( number_number_of @ SX0 @ SX1 ) @ ( number_number_of @ SX0 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[555]) ).
thf(594,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)],[437]) ).
thf(595,plain,
( ( ! [SX0: $i] :
( ~ ( linordered_idom @ SX0 )
| ~ ( number_ring @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ord_less_eq @ SX0 @ ( one_one @ SX0 ) @ ( number_number_of @ SX0 @ SX1 ) )
| ( ord_less_eq @ int @ ( bit1 @ pls ) @ SX1 ) )
| ~ ! [SX1: $i] :
( ~ ( ord_less_eq @ int @ ( bit1 @ pls ) @ SX1 )
| ( ord_less_eq @ SX0 @ ( one_one @ SX0 ) @ ( number_number_of @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[557]) ).
thf(596,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)],[438]) ).
thf(597,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)],[443]) ).
thf(598,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ord_less @ int @ SX0 @ SX1 )
| ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ nat @ ( number_number_of @ nat @ SX0 ) @ ( number_number_of @ nat @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ pls @ SX1 )
| ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ nat @ ( number_number_of @ nat @ SX0 ) @ ( number_number_of @ nat @ SX1 ) ) ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ nat @ ( number_number_of @ nat @ SX0 ) @ ( number_number_of @ nat @ SX1 ) )
| ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ int @ pls @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ nat @ ( number_number_of @ nat @ SX0 ) @ ( number_number_of @ nat @ SX1 ) )
| ( ord_less @ int @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[493]) ).
thf(599,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)],[440]) ).
thf(600,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)],[503]) ).
thf(601,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ord_less_eq @ int @ pls @ ( bit0 @ SX0 ) )
| ( ord_less_eq @ int @ pls @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less_eq @ int @ pls @ SX0 )
| ( ord_less_eq @ int @ pls @ ( bit0 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[474]) ).
thf(602,plain,
( ( ! [SX0: $i] :
( ~ ( linordered_idom @ SX0 )
| ~ ( number_ring @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ord_less_eq @ SX0 @ ( number_number_of @ SX0 @ SX1 ) @ ( zero_zero @ SX0 ) )
| ( ord_less_eq @ int @ SX1 @ pls ) )
| ~ ! [SX1: $i] :
( ~ ( ord_less_eq @ int @ SX1 @ pls )
| ( ord_less_eq @ SX0 @ ( number_number_of @ SX0 @ SX1 ) @ ( zero_zero @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[553]) ).
thf(603,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)],[481]) ).
thf(604,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_eq @ int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[461]) ).
thf(605,plain,
( ( ! [SX0: $i] :
( ~ ( linord581940658strict @ SX0 )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( ( ti @ SX0 @ SX1 )
!= ( zero_zero @ SX0 ) )
| ( ( ti @ SX0 @ SX2 )
!= ( zero_zero @ SX0 ) )
| ( ( plus_plus @ SX0 @ ( times_times @ SX0 @ SX1 @ SX1 ) @ ( times_times @ SX0 @ SX2 @ SX2 ) )
= ( zero_zero @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ! [SX2: $i] :
( ( plus_plus @ SX0 @ ( times_times @ SX0 @ SX1 @ SX1 ) @ ( times_times @ SX0 @ SX2 @ SX2 ) )
!= ( zero_zero @ SX0 ) )
| ( ( ti @ SX0 @ SX1 )
= ( zero_zero @ SX0 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( ( plus_plus @ SX0 @ ( times_times @ SX0 @ SX1 @ SX1 ) @ ( times_times @ SX0 @ SX2 @ SX2 ) )
!= ( zero_zero @ SX0 ) )
| ( ( ti @ SX0 @ SX2 )
= ( zero_zero @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[558]) ).
thf(606,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( linordered_ring @ SX2 )
| ~ ( ord_less_eq @ SX2 @ SX0 @ ( ti @ SX2 @ SX1 ) )
| ( ord_less_eq @ SX2 @ SX0 @ SX1 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( linordered_ring @ SX2 )
| ~ ( ord_less_eq @ SX2 @ SX0 @ SX1 )
| ( ord_less_eq @ SX2 @ SX0 @ ( ti @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[543]) ).
thf(607,plain,
( ( ! [SX0: $i] :
( ~ ( linordered_idom @ SX0 )
| ~ ( number_ring @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ord_less_eq @ SX0 @ ( number_number_of @ SX0 @ SX1 ) @ ( one_one @ SX0 ) )
| ( ord_less_eq @ int @ SX1 @ ( bit1 @ pls ) ) )
| ~ ! [SX1: $i] :
( ~ ( ord_less_eq @ int @ SX1 @ ( bit1 @ pls ) )
| ( ord_less_eq @ SX0 @ ( number_number_of @ SX0 @ SX1 ) @ ( one_one @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[556]) ).
thf(608,plain,
( ( ! [SX0: $i] :
( ~ ( linordered_idom @ SX0 )
| ~ ( number_ring @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ord_less_eq @ SX0 @ ( zero_zero @ SX0 ) @ ( number_number_of @ SX0 @ SX1 ) )
| ( ord_less_eq @ int @ pls @ SX1 ) )
| ~ ! [SX1: $i] :
( ~ ( ord_less_eq @ int @ pls @ SX1 )
| ( ord_less_eq @ SX0 @ ( zero_zero @ SX0 ) @ ( number_number_of @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[554]) ).
thf(609,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ord_less @ int @ SX0 @ pls )
| ( ord_less_eq @ int @ ( bit1 @ SX0 ) @ pls ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less_eq @ int @ ( bit1 @ SX0 ) @ pls )
| ( ord_less @ int @ SX0 @ pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[487]) ).
thf(610,plain,
( ( ! [SX0: $i] :
( ~ ( linord581940658strict @ SX0 )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( ( ti @ SX0 @ SX1 )
!= ( zero_zero @ SX0 ) )
| ( ( ti @ SX0 @ SX2 )
!= ( zero_zero @ SX0 ) )
| ( ord_less_eq @ SX0 @ ( plus_plus @ SX0 @ ( times_times @ SX0 @ SX1 @ SX1 ) @ ( times_times @ SX0 @ SX2 @ SX2 ) ) @ ( zero_zero @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ! [SX2: $i] :
~ ( ord_less_eq @ SX0 @ ( plus_plus @ SX0 @ ( times_times @ SX0 @ SX1 @ SX1 ) @ ( times_times @ SX0 @ SX2 @ SX2 ) ) @ ( zero_zero @ SX0 ) )
| ( ( ti @ SX0 @ SX1 )
= ( zero_zero @ SX0 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( ord_less_eq @ SX0 @ ( plus_plus @ SX0 @ ( times_times @ SX0 @ SX1 @ SX1 ) @ ( times_times @ SX0 @ SX2 @ SX2 ) ) @ ( zero_zero @ SX0 ) )
| ( ( ti @ SX0 @ SX2 )
= ( zero_zero @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[551]) ).
thf(611,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq @ int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ( ord_less @ int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[492]) ).
thf(612,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_eq @ int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[460]) ).
thf(613,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( ( zero_zero @ nat )
!= ( number_number_of @ nat @ SX0 ) )
| ( ord_less_eq @ int @ SX0 @ pls ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less_eq @ int @ SX0 @ pls )
| ( ( zero_zero @ nat )
= ( number_number_of @ nat @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[465]) ).
thf(614,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ord_less @ int @ pls @ ( bit1 @ SX0 ) )
| ( ord_less_eq @ int @ pls @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less_eq @ int @ pls @ SX0 )
| ( ord_less @ int @ pls @ ( bit1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[488]) ).
thf(615,plain,
! [SV1: $i] :
( ( ( bit0 @ ( ti @ int @ SV1 ) )
= ( bit0 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[408]) ).
thf(616,plain,
! [SV2: $i] :
( ( ( ti @ int @ ( bit0 @ SV2 ) )
= ( bit0 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[409]) ).
thf(617,plain,
! [SV3: $i] :
( ( ( bit1 @ ( ti @ int @ SV3 ) )
= ( bit1 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[410]) ).
thf(618,plain,
! [SV4: $i] :
( ( ( ti @ int @ ( bit1 @ SV4 ) )
= ( bit1 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[411]) ).
thf(619,plain,
! [SV5: $i] :
( ( ~ ( semiring_1 @ SV5 )
| ( ( ti @ SV5 @ ( one_one @ SV5 ) )
= ( one_one @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[414]) ).
thf(620,plain,
! [SV6: $i] :
( ( ! [SY259: $i,SY260: $i] :
( ~ ( linordered_ring @ SY260 )
| ( ( plus_plus @ SY260 @ ( ti @ SY260 @ SV6 ) @ SY259 )
= ( plus_plus @ SY260 @ SV6 @ SY259 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[415]) ).
thf(621,plain,
! [SV7: $i] :
( ( ! [SY261: $i,SY262: $i] :
( ~ ( linordered_ring @ SY262 )
| ( ( plus_plus @ SY262 @ SV7 @ ( ti @ SY262 @ SY261 ) )
= ( plus_plus @ SY262 @ SV7 @ SY261 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[416]) ).
thf(622,plain,
! [SV8: $i] :
( ( ! [SY263: $i,SY264: $i] :
( ~ ( linordered_ring @ SY264 )
| ( ( ti @ SY264 @ ( plus_plus @ SY264 @ SV8 @ SY263 ) )
= ( plus_plus @ SY264 @ SV8 @ SY263 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[417]) ).
thf(623,plain,
! [SV9: $i] :
( ( ~ ( linordered_ring @ SV9 )
| ( ( ti @ SV9 @ ( zero_zero @ SV9 ) )
= ( zero_zero @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[418]) ).
thf(624,plain,
! [SV10: $i] :
( ( ~ ( semiring_1 @ SV10 )
| ( ( ti @ SV10 @ ( zero_zero @ SV10 ) )
= ( zero_zero @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[419]) ).
thf(625,plain,
! [SV11: $i] :
( ( ! [SY265: $i] :
( ~ ( number @ SY265 )
| ( ( number_number_of @ SY265 @ ( ti @ int @ SV11 ) )
= ( number_number_of @ SY265 @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[421]) ).
thf(626,plain,
! [SV12: $i] :
( ( ! [SY266: $i] :
( ~ ( number @ SY266 )
| ( ( ti @ SY266 @ ( number_number_of @ SY266 @ SV12 ) )
= ( number_number_of @ SY266 @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[422]) ).
thf(627,plain,
! [SV13: $i] :
( ( ! [SY267: $i,SY268: $i] :
( ~ ( semiring_1 @ SY268 )
| ( ( power_power @ SY268 @ ( ti @ SY268 @ SV13 ) @ SY267 )
= ( power_power @ SY268 @ SV13 @ SY267 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[425]) ).
thf(628,plain,
! [SV14: $i] :
( ( ! [SY269: $i,SY270: $i] :
( ~ ( semiring_1 @ SY270 )
| ( ( power_power @ SY270 @ SV14 @ ( ti @ nat @ SY269 ) )
= ( power_power @ SY270 @ SV14 @ SY269 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[426]) ).
thf(629,plain,
! [SV15: $i] :
( ( ! [SY271: $i,SY272: $i] :
( ~ ( semiring_1 @ SY272 )
| ( ( ti @ SY272 @ ( power_power @ SY272 @ SV15 @ SY271 ) )
= ( power_power @ SY272 @ SV15 @ SY271 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[427]) ).
thf(630,plain,
( ( ( ( t
!= ( zero_zero @ int ) ) )
= $true )
| ( ( ( plus_plus @ int @ ( power_power @ int @ s @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( one_one @ int ) )
= ( zero_zero @ int ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[433]) ).
thf(631,plain,
( ( ord_less_eq @ int @ ( one_one @ int ) @ t )
= $false ),
inference(extcnf_not_pos,[status(thm)],[434]) ).
thf(632,plain,
! [SV16: $i] :
( ( ~ ( linordered_idom @ SV16 )
| ! [SY273: $i,SY274: $i] :
~ ( ord_less @ SV16 @ ( plus_plus @ SV16 @ ( power_power @ SV16 @ SY273 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV16 @ SY274 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( zero_zero @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[436]) ).
thf(633,plain,
! [SV17: $i] :
( ( ~ ( linordered_idom @ SV17 )
| ! [SY275: $i] :
~ ( ord_less @ SV17 @ ( power_power @ SV17 @ SY275 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( zero_zero @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[439]) ).
thf(634,plain,
! [SV18: $i] :
( ( ~ ( semiring_1 @ SV18 )
| ( ( power_power @ SV18 @ ( one_one @ SV18 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( one_one @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[441]) ).
thf(635,plain,
! [SV19: $i] :
( ( ~ ( semiring_1 @ SV19 )
| ( ( power_power @ SV19 @ ( zero_zero @ SV19 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[442]) ).
thf(636,plain,
! [SV20: $i] :
( ( ~ ( number_ring @ SV20 )
| ! [SY276: $i] :
( ( plus_plus @ SV20 @ ( one_one @ SV20 ) @ ( number_number_of @ SV20 @ SY276 ) )
= ( number_number_of @ SV20 @ ( plus_plus @ int @ ( bit1 @ pls ) @ SY276 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[444]) ).
thf(637,plain,
! [SV21: $i] :
( ( ~ ( number_ring @ SV21 )
| ! [SY277: $i] :
( ( plus_plus @ SV21 @ ( number_number_of @ SV21 @ SY277 ) @ ( one_one @ SV21 ) )
= ( number_number_of @ SV21 @ ( plus_plus @ int @ SY277 @ ( bit1 @ pls ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[445]) ).
thf(638,plain,
! [SV22: $i] :
( ( ord_less_eq @ int @ SV22 @ SV22 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[447]) ).
thf(639,plain,
! [SV23: $i] :
( ( ( number_number_of @ int @ SV23 )
= SV23 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[448]) ).
thf(640,plain,
! [SV24: $i] :
( ( ! [SY278: $i] :
( ( times_times @ int @ SV24 @ SY278 )
= ( times_times @ int @ SY278 @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[449]) ).
thf(641,plain,
! [SV25: $i] :
( ( ! [SY279: $i] :
( ( ord_less_eq @ int @ SV25 @ SY279 )
| ( ord_less_eq @ int @ SY279 @ SV25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[450]) ).
thf(642,plain,
! [SV26: $i] :
( ( ! [SY280: $i] :
( ( times_times @ int @ ( number_number_of @ int @ SV26 ) @ ( number_number_of @ int @ SY280 ) )
= ( number_number_of @ int @ ( times_times @ int @ SV26 @ SY280 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[451]) ).
thf(643,plain,
! [SV27: $i] :
( ( ! [SY281: $i,SY282: $i] :
( ( times_times @ int @ ( times_times @ int @ SV27 @ SY281 ) @ SY282 )
= ( times_times @ int @ SV27 @ ( times_times @ int @ SY281 @ SY282 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[453]) ).
thf(644,plain,
! [SV28: $i] :
( ( ! [SY283: $i,SY284: $i] :
( ~ ( ord_less_eq @ int @ SY283 @ SY284 )
| ~ ( ord_less_eq @ int @ SY284 @ SV28 )
| ( ord_less_eq @ int @ SY283 @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[454]) ).
thf(645,plain,
! [SV29: $i] :
( ( ! [SY285: $i] :
( ~ ( ord_less_eq @ int @ SV29 @ SY285 )
| ~ ( ord_less_eq @ int @ SY285 @ SV29 )
| ( SV29 = SY285 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[455]) ).
thf(646,plain,
! [SV30: $i] :
( ( ! [SY286: $i,SY287: $i] :
( ( power_power @ int @ SV30 @ ( plus_plus @ nat @ SY286 @ SY287 ) )
= ( times_times @ int @ ( power_power @ int @ SV30 @ SY286 ) @ ( power_power @ int @ SV30 @ SY287 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[456]) ).
thf(647,plain,
! [SV31: $i] :
( ( ! [SY288: $i,SY289: $i] :
( ~ ( ord_less_eq @ int @ SY288 @ SY289 )
| ( ord_less_eq @ int @ ( plus_plus @ int @ SV31 @ SY288 ) @ ( plus_plus @ int @ SV31 @ SY289 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[463]) ).
thf(648,plain,
! [SV32: $i] :
( ( ~ ( number_ring @ SV32 )
| ! [SY290: $i,SY291: $i,SY292: $i] :
( ( times_times @ SV32 @ ( number_number_of @ SV32 @ SY290 ) @ ( times_times @ SV32 @ ( number_number_of @ SV32 @ SY291 ) @ SY292 ) )
= ( times_times @ SV32 @ ( number_number_of @ SV32 @ ( times_times @ int @ SY290 @ SY291 ) ) @ SY292 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[466]) ).
thf(649,plain,
! [SV33: $i] :
( ( ~ ( number_ring @ SV33 )
| ! [SY293: $i,SY294: $i] :
( ( times_times @ SV33 @ ( number_number_of @ SV33 @ SY293 ) @ ( number_number_of @ SV33 @ SY294 ) )
= ( number_number_of @ SV33 @ ( times_times @ int @ SY293 @ SY294 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[467]) ).
thf(650,plain,
! [SV34: $i] :
( ( ~ ( number_ring @ SV34 )
| ! [SY295: $i,SY296: $i] :
( ( number_number_of @ SV34 @ ( times_times @ int @ SY295 @ SY296 ) )
= ( times_times @ SV34 @ ( number_number_of @ SV34 @ SY295 ) @ ( number_number_of @ SV34 @ SY296 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[468]) ).
thf(651,plain,
! [SV35: $i] :
( ( ! [SY297: $i,SY298: $i,SY299: $i] :
( ~ ( ord_less @ int @ SY298 @ SY299 )
| ~ ( ord_less_eq @ int @ SV35 @ SY297 )
| ( ord_less @ int @ ( plus_plus @ int @ SY298 @ SV35 ) @ ( plus_plus @ int @ SY299 @ SY297 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[475]) ).
thf(652,plain,
! [SV36: $i] :
( ( ( times_times @ int @ pls @ SV36 )
= pls )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[479]) ).
thf(653,plain,
! [SV37: $i] :
( ( ! [SY300: $i] :
( ( times_times @ int @ ( bit0 @ SV37 ) @ SY300 )
= ( bit0 @ ( times_times @ int @ SV37 @ SY300 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[480]) ).
thf(654,plain,
! [SV38: $i] :
( ( ( times_times @ int @ SV38 @ ( one_one @ int ) )
= SV38 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[482]) ).
thf(655,plain,
! [SV39: $i] :
( ( ( times_times @ int @ ( one_one @ int ) @ SV39 )
= SV39 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[483]) ).
thf(656,plain,
! [SV40: $i] :
( ( ! [SY301: $i] :
( ( plus_plus @ int @ ( number_number_of @ int @ SV40 ) @ ( number_number_of @ int @ SY301 ) )
= ( number_number_of @ int @ ( plus_plus @ int @ SV40 @ SY301 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[484]) ).
thf(657,plain,
! [SV41: $i] :
( ( ! [SY302: $i,SY303: $i] :
( ( times_times @ int @ ( plus_plus @ int @ SV41 @ SY302 ) @ SY303 )
= ( plus_plus @ int @ ( times_times @ int @ SV41 @ SY303 ) @ ( times_times @ int @ SY302 @ SY303 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[485]) ).
thf(658,plain,
! [SV42: $i] :
( ( ! [SY304: $i,SY305: $i] :
( ( times_times @ int @ SV42 @ ( plus_plus @ int @ SY304 @ SY305 ) )
= ( plus_plus @ int @ ( times_times @ int @ SV42 @ SY304 ) @ ( times_times @ int @ SV42 @ SY305 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[486]) ).
thf(659,plain,
! [SV43: $i] :
( ( ! [SY306: $i] :
( ~ ( ord_less @ int @ SV43 @ SY306 )
| ( ord_less_eq @ int @ ( plus_plus @ int @ SV43 @ ( one_one @ int ) ) @ SY306 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[497]) ).
thf(660,plain,
! [SV44: $i] :
( ( ~ ( number_semiring @ SV44 )
| ! [SY307: $i,SY308: $i] :
( ~ ( ord_less_eq @ int @ pls @ SY308 )
| ~ ( ord_less_eq @ int @ pls @ SY307 )
| ( ( plus_plus @ SV44 @ ( number_number_of @ SV44 @ SY308 ) @ ( number_number_of @ SV44 @ SY307 ) )
= ( number_number_of @ SV44 @ ( plus_plus @ int @ SY308 @ SY307 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[500]) ).
thf(661,plain,
! [SV45: $i] :
( ( ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV45 )
| ( ord_less @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( one_one @ int ) @ SV45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[502]) ).
thf(662,plain,
! [SV46: $i] :
( ( ! [SY309: $i] :
( ( ord_less @ int @ SY309 @ SV46 )
| ( SV46 = SY309 )
| ( ord_less @ int @ SV46 @ SY309 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[507]) ).
thf(663,plain,
! [SV47: $i] :
( ( ! [SY310: $i,SY311: $i] :
( ( plus_plus @ int @ ( plus_plus @ int @ SV47 @ SY310 ) @ SY311 )
= ( plus_plus @ int @ SV47 @ ( plus_plus @ int @ SY310 @ SY311 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[508]) ).
thf(664,plain,
! [SV48: $i] :
( ( ! [SY312: $i,SY313: $i] :
( ( plus_plus @ int @ SV48 @ ( plus_plus @ int @ SY312 @ SY313 ) )
= ( plus_plus @ int @ SY312 @ ( plus_plus @ int @ SV48 @ SY313 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[509]) ).
thf(665,plain,
! [SV49: $i] :
( ( ! [SY314: $i] :
( ( plus_plus @ int @ SV49 @ SY314 )
= ( plus_plus @ int @ SY314 @ SV49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[510]) ).
thf(666,plain,
! [SV50: $i] :
( ( ! [SY315: $i,SY316: $i] :
( ~ ( number @ SY316 )
| ~ ( semiring @ SY316 )
| ( ( plus_plus @ SY316 @ ( ti @ SY316 @ SV50 ) @ SY315 )
= ( plus_plus @ SY316 @ SV50 @ SY315 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[528]) ).
thf(667,plain,
! [SV51: $i] :
( ( ! [SY317: $i,SY318: $i] :
( ~ ( number @ SY318 )
| ~ ( semiring @ SY318 )
| ( ( plus_plus @ SY318 @ SV51 @ ( ti @ SY318 @ SY317 ) )
= ( plus_plus @ SY318 @ SV51 @ SY317 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[529]) ).
thf(668,plain,
! [SV52: $i] :
( ( ! [SY319: $i,SY320: $i] :
( ~ ( number @ SY320 )
| ~ ( semiring @ SY320 )
| ( ( ti @ SY320 @ ( plus_plus @ SY320 @ SV52 @ SY319 ) )
= ( plus_plus @ SY320 @ SV52 @ SY319 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[530]) ).
thf(669,plain,
! [SV53: $i] :
( ( ! [SY321: $i,SY322: $i] :
( ~ ( number @ SY322 )
| ~ ( semiring @ SY322 )
| ( ( times_times @ SY322 @ ( ti @ SY322 @ SV53 ) @ SY321 )
= ( times_times @ SY322 @ SV53 @ SY321 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[531]) ).
thf(670,plain,
! [SV54: $i] :
( ( ! [SY323: $i,SY324: $i] :
( ~ ( number @ SY324 )
| ~ ( semiring @ SY324 )
| ( ( times_times @ SY324 @ SV54 @ ( ti @ SY324 @ SY323 ) )
= ( times_times @ SY324 @ SV54 @ SY323 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[532]) ).
thf(671,plain,
! [SV55: $i] :
( ( ! [SY325: $i,SY326: $i] :
( ~ ( number @ SY326 )
| ~ ( semiring @ SY326 )
| ( ( ti @ SY326 @ ( times_times @ SY326 @ SV55 @ SY325 ) )
= ( times_times @ SY326 @ SV55 @ SY325 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[533]) ).
thf(672,plain,
! [SV56: $i] :
( ( ! [SY327: $i,SY328: $i] :
( ~ ( linordered_ring @ SY328 )
| ( ( times_times @ SY328 @ ( ti @ SY328 @ SV56 ) @ SY327 )
= ( times_times @ SY328 @ SV56 @ SY327 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[534]) ).
thf(673,plain,
! [SV57: $i] :
( ( ! [SY329: $i,SY330: $i] :
( ~ ( linordered_ring @ SY330 )
| ( ( times_times @ SY330 @ SV57 @ ( ti @ SY330 @ SY329 ) )
= ( times_times @ SY330 @ SV57 @ SY329 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[535]) ).
thf(674,plain,
! [SV58: $i] :
( ( ! [SY331: $i,SY332: $i] :
( ~ ( linordered_ring @ SY332 )
| ( ( ti @ SY332 @ ( times_times @ SY332 @ SV58 @ SY331 ) )
= ( times_times @ SY332 @ SV58 @ SY331 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[536]) ).
thf(675,plain,
! [SV59: $i] :
( ( ( ti @ SV59 @ ( undefined @ SV59 ) )
= ( undefined @ SV59 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[537]) ).
thf(676,plain,
! [SV60: $i] :
( ( ~ ( number_semiring @ SV60 )
| ! [SY333: $i,SY334: $i] :
( ~ ( ord_less_eq @ int @ pls @ SY334 )
| ~ ( ord_less_eq @ int @ pls @ SY333 )
| ( ( times_times @ SV60 @ ( number_number_of @ SV60 @ SY334 ) @ ( number_number_of @ SV60 @ SY333 ) )
= ( number_number_of @ SV60 @ ( times_times @ int @ SY334 @ SY333 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[550]) ).
thf(677,plain,
! [SV61: $i] :
( ( ~ ( linordered_ring @ SV61 )
| ! [SY335: $i,SY336: $i] : ( ord_less_eq @ SV61 @ ( zero_zero @ SV61 ) @ ( plus_plus @ SV61 @ ( times_times @ SV61 @ SY335 @ SY335 ) @ ( times_times @ SV61 @ SY336 @ SY336 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[552]) ).
thf(678,plain,
! [SV62: $i] :
( ( ~ ( number @ SV62 )
| ~ ( semiring @ SV62 )
| ! [SY337: $i,SY338: $i,SY339: $i] :
( ( times_times @ SV62 @ ( plus_plus @ SV62 @ SY337 @ SY338 ) @ ( number_number_of @ SV62 @ SY339 ) )
= ( plus_plus @ SV62 @ ( times_times @ SV62 @ SY337 @ ( number_number_of @ SV62 @ SY339 ) ) @ ( times_times @ SV62 @ SY338 @ ( number_number_of @ SV62 @ SY339 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[559]) ).
thf(679,plain,
! [SV63: $i] :
( ( ~ ( number @ SV63 )
| ~ ( semiring @ SV63 )
| ! [SY340: $i,SY341: $i,SY342: $i] :
( ( times_times @ SV63 @ ( number_number_of @ SV63 @ SY340 ) @ ( plus_plus @ SV63 @ SY341 @ SY342 ) )
= ( plus_plus @ SV63 @ ( times_times @ SV63 @ ( number_number_of @ SV63 @ SY340 ) @ SY341 ) @ ( times_times @ SV63 @ ( number_number_of @ SV63 @ SY340 ) @ SY342 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[560]) ).
thf(680,plain,
! [SV64: $i] :
( ( ! [SY343: $i] :
( ( ti @ SV64 @ ( ti @ SV64 @ SY343 ) )
= ( ti @ SV64 @ SY343 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[561]) ).
thf(681,plain,
( ( ord_less @ int @ ( plus_plus @ int @ ( power_power @ int @ s @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( one_one @ int ) ) @ ( zero_zero @ int ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[562]) ).
thf(682,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ ( number_number_of @ nat @ SX0 ) )
| ( ord_less @ int @ pls @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less @ int @ pls @ SX0 )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ ( number_number_of @ nat @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[563]) ).
thf(683,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ( ord_less @ int @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[564]) ).
thf(684,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less @ int @ ( zero_zero @ int ) @ SX0 )
| ( ord_less_eq @ int @ ( one_one @ int ) @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less_eq @ int @ ( one_one @ int ) @ SX0 )
| ( ord_less @ int @ ( zero_zero @ int ) @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[565]) ).
thf(685,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq @ int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[566]) ).
thf(686,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq @ int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[567]) ).
thf(687,plain,
! [SV65: $i] :
( ( ~ ( linordered_idom @ SV65 )
| ~ ( number_ring @ SV65 )
| ~ ( ~ ! [SY344: $i,SY345: $i] :
( ~ ( ord_less_eq @ SV65 @ ( number_number_of @ SV65 @ SY344 ) @ ( number_number_of @ SV65 @ SY345 ) )
| ( ord_less_eq @ int @ SY344 @ SY345 ) )
| ~ ! [SY346: $i,SY347: $i] :
( ~ ( ord_less_eq @ int @ SY346 @ SY347 )
| ( ord_less_eq @ SV65 @ ( number_number_of @ SV65 @ SY346 ) @ ( number_number_of @ SV65 @ SY347 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[568]) ).
thf(688,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_eq @ int @ ( bit0 @ SX0 ) @ pls )
| ( ord_less_eq @ int @ SX0 @ pls ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less_eq @ int @ SX0 @ pls )
| ( ord_less_eq @ int @ ( bit0 @ SX0 ) @ pls ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[569]) ).
thf(689,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)],[570]) ).
thf(690,plain,
! [SV66: $i] :
( ( ~ ( ~ ! [SY348: $i,SY349: $i] :
( ~ ( linordered_idom @ SY349 )
| ~ ( ord_less @ SY349 @ SV66 @ ( ti @ SY349 @ SY348 ) )
| ( ord_less @ SY349 @ SV66 @ SY348 ) )
| ~ ! [SY350: $i,SY351: $i] :
( ~ ( linordered_idom @ SY351 )
| ~ ( ord_less @ SY351 @ SV66 @ SY350 )
| ( ord_less @ SY351 @ SV66 @ ( ti @ SY351 @ SY350 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[571]) ).
thf(691,plain,
! [SV67: $i] :
( ( ~ ( ~ ! [SY352: $i,SY353: $i] :
( ~ ( linordered_idom @ SY353 )
| ~ ( ord_less @ SY353 @ ( ti @ SY353 @ SV67 ) @ SY352 )
| ( ord_less @ SY353 @ SV67 @ SY352 ) )
| ~ ! [SY354: $i,SY355: $i] :
( ~ ( linordered_idom @ SY355 )
| ~ ( ord_less @ SY355 @ SV67 @ SY354 )
| ( ord_less @ SY355 @ ( ti @ SY355 @ SV67 ) @ SY354 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[572]) ).
thf(692,plain,
! [SV68: $i] :
( ( ~ ( ~ ! [SY356: $i,SY357: $i] :
( ~ ( linordered_ring @ SY357 )
| ~ ( ord_less_eq @ SY357 @ ( ti @ SY357 @ SV68 ) @ SY356 )
| ( ord_less_eq @ SY357 @ SV68 @ SY356 ) )
| ~ ! [SY358: $i,SY359: $i] :
( ~ ( linordered_ring @ SY359 )
| ~ ( ord_less_eq @ SY359 @ SV68 @ SY358 )
| ( ord_less_eq @ SY359 @ ( ti @ SY359 @ SV68 ) @ SY358 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[573]) ).
thf(693,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)],[574]) ).
thf(694,plain,
! [SV69: $i] :
( ( ~ ( ~ ! [SY360: $i,SY361: $i] :
( ~ ( linorder @ SY361 )
| ~ ( number @ SY361 )
| ~ ( ord_less_eq @ SY361 @ SV69 @ ( ti @ SY361 @ SY360 ) )
| ( ord_less_eq @ SY361 @ SV69 @ SY360 ) )
| ~ ! [SY362: $i,SY363: $i] :
( ~ ( linorder @ SY363 )
| ~ ( number @ SY363 )
| ~ ( ord_less_eq @ SY363 @ SV69 @ SY362 )
| ( ord_less_eq @ SY363 @ SV69 @ ( ti @ SY363 @ SY362 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[575]) ).
thf(695,plain,
! [SV70: $i] :
( ( ~ ( number @ SV70 )
| ~ ( ~ ! [SY364: $i,SY365: $i] :
( ( ( number_number_of @ SV70 @ SY364 )
!= ( ti @ SV70 @ SY365 ) )
| ( ( ti @ SV70 @ SY365 )
= ( number_number_of @ SV70 @ SY364 ) ) )
| ~ ! [SY366: $i,SY367: $i] :
( ( ( ti @ SV70 @ SY367 )
!= ( number_number_of @ SV70 @ SY366 ) )
| ( ( number_number_of @ SV70 @ SY366 )
= ( ti @ SV70 @ SY367 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[576]) ).
thf(696,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less @ int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[577]) ).
thf(697,plain,
( ( ~ ! [SX0: $i] :
( ~ ( twoSqu33214720sum2sq @ ( ti @ int @ SX0 ) )
| ( twoSqu33214720sum2sq @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( twoSqu33214720sum2sq @ SX0 )
| ( twoSqu33214720sum2sq @ ( ti @ int @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[578]) ).
thf(698,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ ( number_number_of @ int @ SX0 ) @ ( number_number_of @ int @ SX1 ) )
| ( ord_less_eq @ int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ ( number_number_of @ int @ SX0 ) @ ( number_number_of @ int @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[579]) ).
thf(699,plain,
( ( ~ ! [SX0: $i] :
( ( ( number_number_of @ nat @ SX0 )
!= ( zero_zero @ nat ) )
| ( ord_less_eq @ int @ SX0 @ pls ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less_eq @ int @ SX0 @ pls )
| ( ( number_number_of @ nat @ SX0 )
= ( zero_zero @ nat ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[580]) ).
thf(700,plain,
! [SV71: $i] :
( ( ~ ( ~ ! [SY368: $i,SY369: $i] :
( ~ ( linorder @ SY369 )
| ~ ( number @ SY369 )
| ~ ( ord_less @ SY369 @ ( ti @ SY369 @ SV71 ) @ SY368 )
| ( ord_less @ SY369 @ SV71 @ SY368 ) )
| ~ ! [SY370: $i,SY371: $i] :
( ~ ( linorder @ SY371 )
| ~ ( number @ SY371 )
| ~ ( ord_less @ SY371 @ SV71 @ SY370 )
| ( ord_less @ SY371 @ ( ti @ SY371 @ SV71 ) @ SY370 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[581]) ).
thf(701,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)],[582]) ).
thf(702,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq @ int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[583]) ).
thf(703,plain,
( ( ~ ! [SX0: $i] :
( ~ ( zprime @ ( ti @ int @ SX0 ) )
| ( zprime @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( zprime @ SX0 )
| ( zprime @ ( ti @ int @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[584]) ).
thf(704,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_eq @ int @ pls @ ( bit1 @ SX0 ) )
| ( ord_less_eq @ int @ pls @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less_eq @ int @ pls @ SX0 )
| ( ord_less_eq @ int @ pls @ ( bit1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[585]) ).
thf(705,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq @ int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ( ord_less @ int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[586]) ).
thf(706,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ ( plus_plus @ int @ SX0 @ ( one_one @ int ) ) @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ ( plus_plus @ int @ SX0 @ ( one_one @ int ) ) @ SX1 )
| ( ord_less @ int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[587]) ).
thf(707,plain,
! [SV72: $i] :
( ( ~ ( ~ ! [SY372: $i,SY373: $i] :
( ~ ( linorder @ SY373 )
| ~ ( number @ SY373 )
| ~ ( ord_less_eq @ SY373 @ ( ti @ SY373 @ SV72 ) @ SY372 )
| ( ord_less_eq @ SY373 @ SV72 @ SY372 ) )
| ~ ! [SY374: $i,SY375: $i] :
( ~ ( linorder @ SY375 )
| ~ ( number @ SY375 )
| ~ ( ord_less_eq @ SY375 @ SV72 @ SY374 )
| ( ord_less_eq @ SY375 @ ( ti @ SY375 @ SV72 ) @ SY374 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[588]) ).
thf(708,plain,
! [SV73: $i] :
( ( ~ ( ~ ! [SY376: $i,SY377: $i] :
( ~ ( linorder @ SY377 )
| ~ ( number @ SY377 )
| ~ ( ord_less @ SY377 @ SV73 @ ( ti @ SY377 @ SY376 ) )
| ( ord_less @ SY377 @ SV73 @ SY376 ) )
| ~ ! [SY378: $i,SY379: $i] :
( ~ ( linorder @ SY379 )
| ~ ( number @ SY379 )
| ~ ( ord_less @ SY379 @ SV73 @ SY378 )
| ( ord_less @ SY379 @ SV73 @ ( ti @ SY379 @ SY378 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[589]) ).
thf(709,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq @ int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[590]) ).
thf(710,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less @ int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[591]) ).
thf(711,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ ( plus_plus @ int @ SX1 @ ( one_one @ int ) ) )
| ( ord_less_eq @ int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ( ord_less @ int @ SX0 @ ( plus_plus @ int @ SX1 @ ( one_one @ int ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[592]) ).
thf(712,plain,
! [SV74: $i] :
( ( ~ ( linorder @ SV74 )
| ~ ( number @ SV74 )
| ~ ( ~ ! [SY380: $i,SY381: $i] :
( ~ ( ord_less_eq @ SV74 @ ( number_number_of @ SV74 @ SY380 ) @ ( number_number_of @ SV74 @ SY381 ) )
| ~ ( ord_less @ SV74 @ ( number_number_of @ SV74 @ SY381 ) @ ( number_number_of @ SV74 @ SY380 ) ) )
| ~ ! [SY382: $i,SY383: $i] :
( ( ord_less @ SV74 @ ( number_number_of @ SV74 @ SY383 ) @ ( number_number_of @ SV74 @ SY382 ) )
| ( ord_less_eq @ SV74 @ ( number_number_of @ SV74 @ SY382 ) @ ( number_number_of @ SV74 @ SY383 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[593]) ).
thf(713,plain,
! [SV75: $i] :
( ( ~ ( linordered_idom @ SV75 )
| ~ ( ~ ! [SY384: $i,SY385: $i] :
( ~ ( ord_less @ SV75 @ ( zero_zero @ SV75 ) @ ( plus_plus @ SV75 @ ( power_power @ SV75 @ SY384 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV75 @ SY385 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
| ( ( ti @ SV75 @ SY384 )
!= ( zero_zero @ SV75 ) )
| ( ( ti @ SV75 @ SY385 )
!= ( zero_zero @ SV75 ) ) )
| ~ ~ ( ~ ! [SY386: $i] :
( ( ( ti @ SV75 @ SY386 )
= ( zero_zero @ SV75 ) )
| ! [SY387: $i] : ( ord_less @ SV75 @ ( zero_zero @ SV75 ) @ ( plus_plus @ SV75 @ ( power_power @ SV75 @ SY386 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV75 @ SY387 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
| ~ ! [SY388: $i,SY389: $i] :
( ( ( ti @ SV75 @ SY389 )
= ( zero_zero @ SV75 ) )
| ( ord_less @ SV75 @ ( zero_zero @ SV75 ) @ ( plus_plus @ SV75 @ ( power_power @ SV75 @ SY388 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV75 @ SY389 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[594]) ).
thf(714,plain,
! [SV76: $i] :
( ( ~ ( linordered_idom @ SV76 )
| ~ ( number_ring @ SV76 )
| ~ ( ~ ! [SY390: $i] :
( ~ ( ord_less_eq @ SV76 @ ( one_one @ SV76 ) @ ( number_number_of @ SV76 @ SY390 ) )
| ( ord_less_eq @ int @ ( bit1 @ pls ) @ SY390 ) )
| ~ ! [SY391: $i] :
( ~ ( ord_less_eq @ int @ ( bit1 @ pls ) @ SY391 )
| ( ord_less_eq @ SV76 @ ( one_one @ SV76 ) @ ( number_number_of @ SV76 @ SY391 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[595]) ).
thf(715,plain,
! [SV77: $i] :
( ( ~ ( linordered_idom @ SV77 )
| ~ ( ~ ! [SY392: $i,SY393: $i] :
( ( ( ti @ SV77 @ SY392 )
!= ( zero_zero @ SV77 ) )
| ( ( ti @ SV77 @ SY393 )
!= ( zero_zero @ SV77 ) )
| ( ( plus_plus @ SV77 @ ( power_power @ SV77 @ SY392 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV77 @ SY393 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV77 ) ) )
| ~ ~ ( ~ ! [SY394: $i] :
( ! [SY395: $i] :
( ( plus_plus @ SV77 @ ( power_power @ SV77 @ SY394 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV77 @ SY395 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV77 ) )
| ( ( ti @ SV77 @ SY394 )
= ( zero_zero @ SV77 ) ) )
| ~ ! [SY396: $i,SY397: $i] :
( ( ( plus_plus @ SV77 @ ( power_power @ SV77 @ SY396 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV77 @ SY397 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV77 ) )
| ( ( ti @ SV77 @ SY397 )
= ( zero_zero @ SV77 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[596]) ).
thf(716,plain,
! [SV78: $i] :
( ( ~ ( ring_11004092258visors @ SV78 )
| ~ ( ~ ! [SY398: $i] :
( ( ( power_power @ SV78 @ SY398 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= ( zero_zero @ SV78 ) )
| ( ( ti @ SV78 @ SY398 )
= ( zero_zero @ SV78 ) ) )
| ~ ! [SY399: $i] :
( ( ( ti @ SV78 @ SY399 )
!= ( zero_zero @ SV78 ) )
| ( ( power_power @ SV78 @ SY399 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SV78 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[597]) ).
thf(717,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ord_less @ int @ SX0 @ SX1 )
| ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ nat @ ( number_number_of @ nat @ SX0 ) @ ( number_number_of @ nat @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ pls @ SX1 )
| ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ nat @ ( number_number_of @ nat @ SX0 ) @ ( number_number_of @ nat @ SX1 ) ) ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ nat @ ( number_number_of @ nat @ SX0 ) @ ( number_number_of @ nat @ SX1 ) )
| ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ int @ pls @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ nat @ ( number_number_of @ nat @ SX0 ) @ ( number_number_of @ nat @ SX1 ) )
| ( ord_less @ int @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[598]) ).
thf(718,plain,
! [SV79: $i] :
( ( ~ ( linordered_idom @ SV79 )
| ~ ( ~ ! [SY400: $i] :
( ( ( ti @ SV79 @ SY400 )
= ( zero_zero @ SV79 ) )
| ( ord_less @ SV79 @ ( zero_zero @ SV79 ) @ ( power_power @ SV79 @ SY400 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
| ~ ! [SY401: $i] :
( ~ ( ord_less @ SV79 @ ( zero_zero @ SV79 ) @ ( power_power @ SV79 @ SY401 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ( ( ti @ SV79 @ SY401 )
!= ( zero_zero @ SV79 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[599]) ).
thf(719,plain,
! [SV80: $i] :
( ( ~ ( number_ring @ SV80 )
| ~ ( ring_char_0 @ SV80 )
| ~ ( ~ ! [SY402: $i,SY403: $i] :
( ( ( number_number_of @ SV80 @ SY402 )
!= ( number_number_of @ SV80 @ SY403 ) )
| ( SY402 = SY403 ) )
| ~ ! [SY404: $i,SY405: $i] :
( ( SY404 != SY405 )
| ( ( number_number_of @ SV80 @ SY404 )
= ( number_number_of @ SV80 @ SY405 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[600]) ).
thf(720,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_eq @ int @ pls @ ( bit0 @ SX0 ) )
| ( ord_less_eq @ int @ pls @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less_eq @ int @ pls @ SX0 )
| ( ord_less_eq @ int @ pls @ ( bit0 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[601]) ).
thf(721,plain,
! [SV81: $i] :
( ( ~ ( linordered_idom @ SV81 )
| ~ ( number_ring @ SV81 )
| ~ ( ~ ! [SY406: $i] :
( ~ ( ord_less_eq @ SV81 @ ( number_number_of @ SV81 @ SY406 ) @ ( zero_zero @ SV81 ) )
| ( ord_less_eq @ int @ SY406 @ pls ) )
| ~ ! [SY407: $i] :
( ~ ( ord_less_eq @ int @ SY407 @ pls )
| ( ord_less_eq @ SV81 @ ( number_number_of @ SV81 @ SY407 ) @ ( zero_zero @ SV81 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[602]) ).
thf(722,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)],[603]) ).
thf(723,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_eq @ int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[604]) ).
thf(724,plain,
! [SV82: $i] :
( ( ~ ( linord581940658strict @ SV82 )
| ~ ( ~ ! [SY408: $i,SY409: $i] :
( ( ( ti @ SV82 @ SY408 )
!= ( zero_zero @ SV82 ) )
| ( ( ti @ SV82 @ SY409 )
!= ( zero_zero @ SV82 ) )
| ( ( plus_plus @ SV82 @ ( times_times @ SV82 @ SY408 @ SY408 ) @ ( times_times @ SV82 @ SY409 @ SY409 ) )
= ( zero_zero @ SV82 ) ) )
| ~ ~ ( ~ ! [SY410: $i] :
( ! [SY411: $i] :
( ( plus_plus @ SV82 @ ( times_times @ SV82 @ SY410 @ SY410 ) @ ( times_times @ SV82 @ SY411 @ SY411 ) )
!= ( zero_zero @ SV82 ) )
| ( ( ti @ SV82 @ SY410 )
= ( zero_zero @ SV82 ) ) )
| ~ ! [SY412: $i,SY413: $i] :
( ( ( plus_plus @ SV82 @ ( times_times @ SV82 @ SY412 @ SY412 ) @ ( times_times @ SV82 @ SY413 @ SY413 ) )
!= ( zero_zero @ SV82 ) )
| ( ( ti @ SV82 @ SY413 )
= ( zero_zero @ SV82 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[605]) ).
thf(725,plain,
! [SV83: $i] :
( ( ~ ( ~ ! [SY414: $i,SY415: $i] :
( ~ ( linordered_ring @ SY415 )
| ~ ( ord_less_eq @ SY415 @ SV83 @ ( ti @ SY415 @ SY414 ) )
| ( ord_less_eq @ SY415 @ SV83 @ SY414 ) )
| ~ ! [SY416: $i,SY417: $i] :
( ~ ( linordered_ring @ SY417 )
| ~ ( ord_less_eq @ SY417 @ SV83 @ SY416 )
| ( ord_less_eq @ SY417 @ SV83 @ ( ti @ SY417 @ SY416 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[606]) ).
thf(726,plain,
! [SV84: $i] :
( ( ~ ( linordered_idom @ SV84 )
| ~ ( number_ring @ SV84 )
| ~ ( ~ ! [SY418: $i] :
( ~ ( ord_less_eq @ SV84 @ ( number_number_of @ SV84 @ SY418 ) @ ( one_one @ SV84 ) )
| ( ord_less_eq @ int @ SY418 @ ( bit1 @ pls ) ) )
| ~ ! [SY419: $i] :
( ~ ( ord_less_eq @ int @ SY419 @ ( bit1 @ pls ) )
| ( ord_less_eq @ SV84 @ ( number_number_of @ SV84 @ SY419 ) @ ( one_one @ SV84 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[607]) ).
thf(727,plain,
! [SV85: $i] :
( ( ~ ( linordered_idom @ SV85 )
| ~ ( number_ring @ SV85 )
| ~ ( ~ ! [SY420: $i] :
( ~ ( ord_less_eq @ SV85 @ ( zero_zero @ SV85 ) @ ( number_number_of @ SV85 @ SY420 ) )
| ( ord_less_eq @ int @ pls @ SY420 ) )
| ~ ! [SY421: $i] :
( ~ ( ord_less_eq @ int @ pls @ SY421 )
| ( ord_less_eq @ SV85 @ ( zero_zero @ SV85 ) @ ( number_number_of @ SV85 @ SY421 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[608]) ).
thf(728,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less @ int @ SX0 @ pls )
| ( ord_less_eq @ int @ ( bit1 @ SX0 ) @ pls ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less_eq @ int @ ( bit1 @ SX0 ) @ pls )
| ( ord_less @ int @ SX0 @ pls ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[609]) ).
thf(729,plain,
! [SV86: $i] :
( ( ~ ( linord581940658strict @ SV86 )
| ~ ( ~ ! [SY422: $i,SY423: $i] :
( ( ( ti @ SV86 @ SY422 )
!= ( zero_zero @ SV86 ) )
| ( ( ti @ SV86 @ SY423 )
!= ( zero_zero @ SV86 ) )
| ( ord_less_eq @ SV86 @ ( plus_plus @ SV86 @ ( times_times @ SV86 @ SY422 @ SY422 ) @ ( times_times @ SV86 @ SY423 @ SY423 ) ) @ ( zero_zero @ SV86 ) ) )
| ~ ~ ( ~ ! [SY424: $i] :
( ! [SY425: $i] :
~ ( ord_less_eq @ SV86 @ ( plus_plus @ SV86 @ ( times_times @ SV86 @ SY424 @ SY424 ) @ ( times_times @ SV86 @ SY425 @ SY425 ) ) @ ( zero_zero @ SV86 ) )
| ( ( ti @ SV86 @ SY424 )
= ( zero_zero @ SV86 ) ) )
| ~ ! [SY426: $i,SY427: $i] :
( ~ ( ord_less_eq @ SV86 @ ( plus_plus @ SV86 @ ( times_times @ SV86 @ SY426 @ SY426 ) @ ( times_times @ SV86 @ SY427 @ SY427 ) ) @ ( zero_zero @ SV86 ) )
| ( ( ti @ SV86 @ SY427 )
= ( zero_zero @ SV86 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[610]) ).
thf(730,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq @ int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ( ord_less @ int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[611]) ).
thf(731,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_eq @ int @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[612]) ).
thf(732,plain,
( ( ~ ! [SX0: $i] :
( ( ( zero_zero @ nat )
!= ( number_number_of @ nat @ SX0 ) )
| ( ord_less_eq @ int @ SX0 @ pls ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less_eq @ int @ SX0 @ pls )
| ( ( zero_zero @ nat )
= ( number_number_of @ nat @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[613]) ).
thf(733,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less @ int @ pls @ ( bit1 @ SX0 ) )
| ( ord_less_eq @ int @ pls @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( ord_less_eq @ int @ pls @ SX0 )
| ( ord_less @ int @ pls @ ( bit1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[614]) ).
thf(734,plain,
! [SV5: $i] :
( ( ( ~ ( semiring_1 @ SV5 ) )
= $true )
| ( ( ( ti @ SV5 @ ( one_one @ SV5 ) )
= ( one_one @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[619]) ).
thf(735,plain,
! [SV87: $i,SV6: $i] :
( ( ! [SY428: $i] :
( ~ ( linordered_ring @ SY428 )
| ( ( plus_plus @ SY428 @ ( ti @ SY428 @ SV6 ) @ SV87 )
= ( plus_plus @ SY428 @ SV6 @ SV87 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[620]) ).
thf(736,plain,
! [SV88: $i,SV7: $i] :
( ( ! [SY429: $i] :
( ~ ( linordered_ring @ SY429 )
| ( ( plus_plus @ SY429 @ SV7 @ ( ti @ SY429 @ SV88 ) )
= ( plus_plus @ SY429 @ SV7 @ SV88 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[621]) ).
thf(737,plain,
! [SV89: $i,SV8: $i] :
( ( ! [SY430: $i] :
( ~ ( linordered_ring @ SY430 )
| ( ( ti @ SY430 @ ( plus_plus @ SY430 @ SV8 @ SV89 ) )
= ( plus_plus @ SY430 @ SV8 @ SV89 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[622]) ).
thf(738,plain,
! [SV9: $i] :
( ( ( ~ ( linordered_ring @ SV9 ) )
= $true )
| ( ( ( ti @ SV9 @ ( zero_zero @ SV9 ) )
= ( zero_zero @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[623]) ).
thf(739,plain,
! [SV10: $i] :
( ( ( ~ ( semiring_1 @ SV10 ) )
= $true )
| ( ( ( ti @ SV10 @ ( zero_zero @ SV10 ) )
= ( zero_zero @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[624]) ).
thf(740,plain,
! [SV11: $i,SV90: $i] :
( ( ~ ( number @ SV90 )
| ( ( number_number_of @ SV90 @ ( ti @ int @ SV11 ) )
= ( number_number_of @ SV90 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[625]) ).
thf(741,plain,
! [SV12: $i,SV91: $i] :
( ( ~ ( number @ SV91 )
| ( ( ti @ SV91 @ ( number_number_of @ SV91 @ SV12 ) )
= ( number_number_of @ SV91 @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[626]) ).
thf(742,plain,
! [SV92: $i,SV13: $i] :
( ( ! [SY431: $i] :
( ~ ( semiring_1 @ SY431 )
| ( ( power_power @ SY431 @ ( ti @ SY431 @ SV13 ) @ SV92 )
= ( power_power @ SY431 @ SV13 @ SV92 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[627]) ).
thf(743,plain,
! [SV93: $i,SV14: $i] :
( ( ! [SY432: $i] :
( ~ ( semiring_1 @ SY432 )
| ( ( power_power @ SY432 @ SV14 @ ( ti @ nat @ SV93 ) )
= ( power_power @ SY432 @ SV14 @ SV93 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[628]) ).
thf(744,plain,
! [SV94: $i,SV15: $i] :
( ( ! [SY433: $i] :
( ~ ( semiring_1 @ SY433 )
| ( ( ti @ SY433 @ ( power_power @ SY433 @ SV15 @ SV94 ) )
= ( power_power @ SY433 @ SV15 @ SV94 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[629]) ).
thf(745,plain,
( ( ( t
= ( zero_zero @ int ) )
= $false )
| ( ( ( plus_plus @ int @ ( power_power @ int @ s @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( one_one @ int ) )
= ( zero_zero @ int ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[630]) ).
thf(746,plain,
! [SV16: $i] :
( ( ( ~ ( linordered_idom @ SV16 ) )
= $true )
| ( ( ! [SY273: $i,SY274: $i] :
~ ( ord_less @ SV16 @ ( plus_plus @ SV16 @ ( power_power @ SV16 @ SY273 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV16 @ SY274 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( zero_zero @ SV16 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[632]) ).
thf(747,plain,
! [SV17: $i] :
( ( ( ~ ( linordered_idom @ SV17 ) )
= $true )
| ( ( ! [SY275: $i] :
~ ( ord_less @ SV17 @ ( power_power @ SV17 @ SY275 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( zero_zero @ SV17 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[633]) ).
thf(748,plain,
! [SV18: $i] :
( ( ( ~ ( semiring_1 @ SV18 ) )
= $true )
| ( ( ( power_power @ SV18 @ ( one_one @ SV18 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( one_one @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[634]) ).
thf(749,plain,
! [SV19: $i] :
( ( ( ~ ( semiring_1 @ SV19 ) )
= $true )
| ( ( ( power_power @ SV19 @ ( zero_zero @ SV19 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[635]) ).
thf(750,plain,
! [SV20: $i] :
( ( ( ~ ( number_ring @ SV20 ) )
= $true )
| ( ( ! [SY276: $i] :
( ( plus_plus @ SV20 @ ( one_one @ SV20 ) @ ( number_number_of @ SV20 @ SY276 ) )
= ( number_number_of @ SV20 @ ( plus_plus @ int @ ( bit1 @ pls ) @ SY276 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[636]) ).
thf(751,plain,
! [SV21: $i] :
( ( ( ~ ( number_ring @ SV21 ) )
= $true )
| ( ( ! [SY277: $i] :
( ( plus_plus @ SV21 @ ( number_number_of @ SV21 @ SY277 ) @ ( one_one @ SV21 ) )
= ( number_number_of @ SV21 @ ( plus_plus @ int @ SY277 @ ( bit1 @ pls ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[637]) ).
thf(752,plain,
! [SV95: $i,SV24: $i] :
( ( ( times_times @ int @ SV24 @ SV95 )
= ( times_times @ int @ SV95 @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[640]) ).
thf(753,plain,
! [SV96: $i,SV25: $i] :
( ( ( ord_less_eq @ int @ SV25 @ SV96 )
| ( ord_less_eq @ int @ SV96 @ SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[641]) ).
thf(754,plain,
! [SV97: $i,SV26: $i] :
( ( ( times_times @ int @ ( number_number_of @ int @ SV26 ) @ ( number_number_of @ int @ SV97 ) )
= ( number_number_of @ int @ ( times_times @ int @ SV26 @ SV97 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[642]) ).
thf(755,plain,
! [SV98: $i,SV27: $i] :
( ( ! [SY434: $i] :
( ( times_times @ int @ ( times_times @ int @ SV27 @ SV98 ) @ SY434 )
= ( times_times @ int @ SV27 @ ( times_times @ int @ SV98 @ SY434 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[643]) ).
thf(756,plain,
! [SV28: $i,SV99: $i] :
( ( ! [SY435: $i] :
( ~ ( ord_less_eq @ int @ SV99 @ SY435 )
| ~ ( ord_less_eq @ int @ SY435 @ SV28 )
| ( ord_less_eq @ int @ SV99 @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[644]) ).
thf(757,plain,
! [SV100: $i,SV29: $i] :
( ( ~ ( ord_less_eq @ int @ SV29 @ SV100 )
| ~ ( ord_less_eq @ int @ SV100 @ SV29 )
| ( SV29 = SV100 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[645]) ).
thf(758,plain,
! [SV101: $i,SV30: $i] :
( ( ! [SY436: $i] :
( ( power_power @ int @ SV30 @ ( plus_plus @ nat @ SV101 @ SY436 ) )
= ( times_times @ int @ ( power_power @ int @ SV30 @ SV101 ) @ ( power_power @ int @ SV30 @ SY436 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[646]) ).
thf(759,plain,
! [SV31: $i,SV102: $i] :
( ( ! [SY437: $i] :
( ~ ( ord_less_eq @ int @ SV102 @ SY437 )
| ( ord_less_eq @ int @ ( plus_plus @ int @ SV31 @ SV102 ) @ ( plus_plus @ int @ SV31 @ SY437 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[647]) ).
thf(760,plain,
! [SV32: $i] :
( ( ( ~ ( number_ring @ SV32 ) )
= $true )
| ( ( ! [SY290: $i,SY291: $i,SY292: $i] :
( ( times_times @ SV32 @ ( number_number_of @ SV32 @ SY290 ) @ ( times_times @ SV32 @ ( number_number_of @ SV32 @ SY291 ) @ SY292 ) )
= ( times_times @ SV32 @ ( number_number_of @ SV32 @ ( times_times @ int @ SY290 @ SY291 ) ) @ SY292 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[648]) ).
thf(761,plain,
! [SV33: $i] :
( ( ( ~ ( number_ring @ SV33 ) )
= $true )
| ( ( ! [SY293: $i,SY294: $i] :
( ( times_times @ SV33 @ ( number_number_of @ SV33 @ SY293 ) @ ( number_number_of @ SV33 @ SY294 ) )
= ( number_number_of @ SV33 @ ( times_times @ int @ SY293 @ SY294 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[649]) ).
thf(762,plain,
! [SV34: $i] :
( ( ( ~ ( number_ring @ SV34 ) )
= $true )
| ( ( ! [SY295: $i,SY296: $i] :
( ( number_number_of @ SV34 @ ( times_times @ int @ SY295 @ SY296 ) )
= ( times_times @ SV34 @ ( number_number_of @ SV34 @ SY295 ) @ ( number_number_of @ SV34 @ SY296 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[650]) ).
thf(763,plain,
! [SV103: $i,SV35: $i] :
( ( ! [SY438: $i,SY439: $i] :
( ~ ( ord_less @ int @ SY438 @ SY439 )
| ~ ( ord_less_eq @ int @ SV35 @ SV103 )
| ( ord_less @ int @ ( plus_plus @ int @ SY438 @ SV35 ) @ ( plus_plus @ int @ SY439 @ SV103 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[651]) ).
thf(764,plain,
! [SV104: $i,SV37: $i] :
( ( ( times_times @ int @ ( bit0 @ SV37 ) @ SV104 )
= ( bit0 @ ( times_times @ int @ SV37 @ SV104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[653]) ).
thf(765,plain,
! [SV105: $i,SV40: $i] :
( ( ( plus_plus @ int @ ( number_number_of @ int @ SV40 ) @ ( number_number_of @ int @ SV105 ) )
= ( number_number_of @ int @ ( plus_plus @ int @ SV40 @ SV105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[656]) ).
thf(766,plain,
! [SV106: $i,SV41: $i] :
( ( ! [SY440: $i] :
( ( times_times @ int @ ( plus_plus @ int @ SV41 @ SV106 ) @ SY440 )
= ( plus_plus @ int @ ( times_times @ int @ SV41 @ SY440 ) @ ( times_times @ int @ SV106 @ SY440 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[657]) ).
thf(767,plain,
! [SV107: $i,SV42: $i] :
( ( ! [SY441: $i] :
( ( times_times @ int @ SV42 @ ( plus_plus @ int @ SV107 @ SY441 ) )
= ( plus_plus @ int @ ( times_times @ int @ SV42 @ SV107 ) @ ( times_times @ int @ SV42 @ SY441 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[658]) ).
thf(768,plain,
! [SV108: $i,SV43: $i] :
( ( ~ ( ord_less @ int @ SV43 @ SV108 )
| ( ord_less_eq @ int @ ( plus_plus @ int @ SV43 @ ( one_one @ int ) ) @ SV108 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[659]) ).
thf(769,plain,
! [SV44: $i] :
( ( ( ~ ( number_semiring @ SV44 ) )
= $true )
| ( ( ! [SY307: $i,SY308: $i] :
( ~ ( ord_less_eq @ int @ pls @ SY308 )
| ~ ( ord_less_eq @ int @ pls @ SY307 )
| ( ( plus_plus @ SV44 @ ( number_number_of @ SV44 @ SY308 ) @ ( number_number_of @ SV44 @ SY307 ) )
= ( number_number_of @ SV44 @ ( plus_plus @ int @ SY308 @ SY307 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[660]) ).
thf(770,plain,
! [SV45: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV45 ) )
= $true )
| ( ( ord_less @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( one_one @ int ) @ SV45 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[661]) ).
thf(771,plain,
! [SV46: $i,SV109: $i] :
( ( ( ord_less @ int @ SV109 @ SV46 )
| ( SV46 = SV109 )
| ( ord_less @ int @ SV46 @ SV109 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[662]) ).
thf(772,plain,
! [SV110: $i,SV47: $i] :
( ( ! [SY442: $i] :
( ( plus_plus @ int @ ( plus_plus @ int @ SV47 @ SV110 ) @ SY442 )
= ( plus_plus @ int @ SV47 @ ( plus_plus @ int @ SV110 @ SY442 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[663]) ).
thf(773,plain,
! [SV111: $i,SV48: $i] :
( ( ! [SY443: $i] :
( ( plus_plus @ int @ SV48 @ ( plus_plus @ int @ SV111 @ SY443 ) )
= ( plus_plus @ int @ SV111 @ ( plus_plus @ int @ SV48 @ SY443 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[664]) ).
thf(774,plain,
! [SV112: $i,SV49: $i] :
( ( ( plus_plus @ int @ SV49 @ SV112 )
= ( plus_plus @ int @ SV112 @ SV49 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[665]) ).
thf(775,plain,
! [SV113: $i,SV50: $i] :
( ( ! [SY444: $i] :
( ~ ( number @ SY444 )
| ~ ( semiring @ SY444 )
| ( ( plus_plus @ SY444 @ ( ti @ SY444 @ SV50 ) @ SV113 )
= ( plus_plus @ SY444 @ SV50 @ SV113 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[666]) ).
thf(776,plain,
! [SV114: $i,SV51: $i] :
( ( ! [SY445: $i] :
( ~ ( number @ SY445 )
| ~ ( semiring @ SY445 )
| ( ( plus_plus @ SY445 @ SV51 @ ( ti @ SY445 @ SV114 ) )
= ( plus_plus @ SY445 @ SV51 @ SV114 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[667]) ).
thf(777,plain,
! [SV115: $i,SV52: $i] :
( ( ! [SY446: $i] :
( ~ ( number @ SY446 )
| ~ ( semiring @ SY446 )
| ( ( ti @ SY446 @ ( plus_plus @ SY446 @ SV52 @ SV115 ) )
= ( plus_plus @ SY446 @ SV52 @ SV115 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[668]) ).
thf(778,plain,
! [SV116: $i,SV53: $i] :
( ( ! [SY447: $i] :
( ~ ( number @ SY447 )
| ~ ( semiring @ SY447 )
| ( ( times_times @ SY447 @ ( ti @ SY447 @ SV53 ) @ SV116 )
= ( times_times @ SY447 @ SV53 @ SV116 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[669]) ).
thf(779,plain,
! [SV117: $i,SV54: $i] :
( ( ! [SY448: $i] :
( ~ ( number @ SY448 )
| ~ ( semiring @ SY448 )
| ( ( times_times @ SY448 @ SV54 @ ( ti @ SY448 @ SV117 ) )
= ( times_times @ SY448 @ SV54 @ SV117 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[670]) ).
thf(780,plain,
! [SV118: $i,SV55: $i] :
( ( ! [SY449: $i] :
( ~ ( number @ SY449 )
| ~ ( semiring @ SY449 )
| ( ( ti @ SY449 @ ( times_times @ SY449 @ SV55 @ SV118 ) )
= ( times_times @ SY449 @ SV55 @ SV118 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[671]) ).
thf(781,plain,
! [SV119: $i,SV56: $i] :
( ( ! [SY450: $i] :
( ~ ( linordered_ring @ SY450 )
| ( ( times_times @ SY450 @ ( ti @ SY450 @ SV56 ) @ SV119 )
= ( times_times @ SY450 @ SV56 @ SV119 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[672]) ).
thf(782,plain,
! [SV120: $i,SV57: $i] :
( ( ! [SY451: $i] :
( ~ ( linordered_ring @ SY451 )
| ( ( times_times @ SY451 @ SV57 @ ( ti @ SY451 @ SV120 ) )
= ( times_times @ SY451 @ SV57 @ SV120 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[673]) ).
thf(783,plain,
! [SV121: $i,SV58: $i] :
( ( ! [SY452: $i] :
( ~ ( linordered_ring @ SY452 )
| ( ( ti @ SY452 @ ( times_times @ SY452 @ SV58 @ SV121 ) )
= ( times_times @ SY452 @ SV58 @ SV121 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[674]) ).
thf(784,plain,
! [SV60: $i] :
( ( ( ~ ( number_semiring @ SV60 ) )
= $true )
| ( ( ! [SY333: $i,SY334: $i] :
( ~ ( ord_less_eq @ int @ pls @ SY334 )
| ~ ( ord_less_eq @ int @ pls @ SY333 )
| ( ( times_times @ SV60 @ ( number_number_of @ SV60 @ SY334 ) @ ( number_number_of @ SV60 @ SY333 ) )
= ( number_number_of @ SV60 @ ( times_times @ int @ SY334 @ SY333 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[676]) ).
thf(785,plain,
! [SV61: $i] :
( ( ( ~ ( linordered_ring @ SV61 ) )
= $true )
| ( ( ! [SY335: $i,SY336: $i] : ( ord_less_eq @ SV61 @ ( zero_zero @ SV61 ) @ ( plus_plus @ SV61 @ ( times_times @ SV61 @ SY335 @ SY335 ) @ ( times_times @ SV61 @ SY336 @ SY336 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[677]) ).
thf(786,plain,
! [SV62: $i] :
( ( ( ~ ( number @ SV62 )
| ~ ( semiring @ SV62 ) )
= $true )
| ( ( ! [SY337: $i,SY338: $i,SY339: $i] :
( ( times_times @ SV62 @ ( plus_plus @ SV62 @ SY337 @ SY338 ) @ ( number_number_of @ SV62 @ SY339 ) )
= ( plus_plus @ SV62 @ ( times_times @ SV62 @ SY337 @ ( number_number_of @ SV62 @ SY339 ) ) @ ( times_times @ SV62 @ SY338 @ ( number_number_of @ SV62 @ SY339 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[678]) ).
thf(787,plain,
! [SV63: $i] :
( ( ( ~ ( number @ SV63 )
| ~ ( semiring @ SV63 ) )
= $true )
| ( ( ! [SY340: $i,SY341: $i,SY342: $i] :
( ( times_times @ SV63 @ ( number_number_of @ SV63 @ SY340 ) @ ( plus_plus @ SV63 @ SY341 @ SY342 ) )
= ( plus_plus @ SV63 @ ( times_times @ SV63 @ ( number_number_of @ SV63 @ SY340 ) @ SY341 ) @ ( times_times @ SV63 @ ( number_number_of @ SV63 @ SY340 ) @ SY342 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[679]) ).
thf(788,plain,
! [SV122: $i,SV64: $i] :
( ( ( ti @ SV64 @ ( ti @ SV64 @ SV122 ) )
= ( ti @ SV64 @ SV122 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[680]) ).
thf(789,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ ( number_number_of @ nat @ SX0 ) )
| ( ord_less @ int @ pls @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[682]) ).
thf(790,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less @ int @ pls @ SX0 )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ ( number_number_of @ nat @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[682]) ).
thf(791,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ( ord_less @ int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[683]) ).
thf(792,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[683]) ).
thf(793,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less @ int @ ( zero_zero @ int ) @ SX0 )
| ( ord_less_eq @ int @ ( one_one @ int ) @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[684]) ).
thf(794,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_eq @ int @ ( one_one @ int ) @ SX0 )
| ( ord_less @ int @ ( zero_zero @ int ) @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[684]) ).
thf(795,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq @ int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[685]) ).
thf(796,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[685]) ).
thf(797,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq @ int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[686]) ).
thf(798,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[686]) ).
thf(799,plain,
! [SV65: $i] :
( ( ( ~ ( linordered_idom @ SV65 )
| ~ ( number_ring @ SV65 ) )
= $true )
| ( ( ~ ( ~ ! [SY344: $i,SY345: $i] :
( ~ ( ord_less_eq @ SV65 @ ( number_number_of @ SV65 @ SY344 ) @ ( number_number_of @ SV65 @ SY345 ) )
| ( ord_less_eq @ int @ SY344 @ SY345 ) )
| ~ ! [SY346: $i,SY347: $i] :
( ~ ( ord_less_eq @ int @ SY346 @ SY347 )
| ( ord_less_eq @ SV65 @ ( number_number_of @ SV65 @ SY346 ) @ ( number_number_of @ SV65 @ SY347 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[687]) ).
thf(800,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_eq @ int @ ( bit0 @ SX0 ) @ pls )
| ( ord_less_eq @ int @ SX0 @ pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[688]) ).
thf(801,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_eq @ int @ SX0 @ pls )
| ( ord_less_eq @ int @ ( bit0 @ SX0 ) @ pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[688]) ).
thf(802,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)],[689]) ).
thf(803,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ord_less @ int @ SX1 @ pls )
| ~ ( ord_less @ int @ SX0 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SX1 ) @ ( number_number_of @ nat @ SX0 ) )
= ( number_number_of @ nat @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( ord_less @ int @ SX1 @ pls )
| ( ord_less @ int @ SX0 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SX1 ) @ ( number_number_of @ nat @ SX0 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SX1 @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[689]) ).
thf(804,plain,
! [SV66: $i] :
( ( ~ ! [SY348: $i,SY349: $i] :
( ~ ( linordered_idom @ SY349 )
| ~ ( ord_less @ SY349 @ SV66 @ ( ti @ SY349 @ SY348 ) )
| ( ord_less @ SY349 @ SV66 @ SY348 ) )
| ~ ! [SY350: $i,SY351: $i] :
( ~ ( linordered_idom @ SY351 )
| ~ ( ord_less @ SY351 @ SV66 @ SY350 )
| ( ord_less @ SY351 @ SV66 @ ( ti @ SY351 @ SY350 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[690]) ).
thf(805,plain,
! [SV67: $i] :
( ( ~ ! [SY352: $i,SY353: $i] :
( ~ ( linordered_idom @ SY353 )
| ~ ( ord_less @ SY353 @ ( ti @ SY353 @ SV67 ) @ SY352 )
| ( ord_less @ SY353 @ SV67 @ SY352 ) )
| ~ ! [SY354: $i,SY355: $i] :
( ~ ( linordered_idom @ SY355 )
| ~ ( ord_less @ SY355 @ SV67 @ SY354 )
| ( ord_less @ SY355 @ ( ti @ SY355 @ SV67 ) @ SY354 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[691]) ).
thf(806,plain,
! [SV68: $i] :
( ( ~ ! [SY356: $i,SY357: $i] :
( ~ ( linordered_ring @ SY357 )
| ~ ( ord_less_eq @ SY357 @ ( ti @ SY357 @ SV68 ) @ SY356 )
| ( ord_less_eq @ SY357 @ SV68 @ SY356 ) )
| ~ ! [SY358: $i,SY359: $i] :
( ~ ( linordered_ring @ SY359 )
| ~ ( ord_less_eq @ SY359 @ SV68 @ SY358 )
| ( ord_less_eq @ SY359 @ ( ti @ SY359 @ SV68 ) @ SY358 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[692]) ).
thf(807,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( bit0 @ SX0 )
!= ( bit0 @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[693]) ).
thf(808,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( bit0 @ SX0 )
= ( bit0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[693]) ).
thf(809,plain,
! [SV69: $i] :
( ( ~ ! [SY360: $i,SY361: $i] :
( ~ ( linorder @ SY361 )
| ~ ( number @ SY361 )
| ~ ( ord_less_eq @ SY361 @ SV69 @ ( ti @ SY361 @ SY360 ) )
| ( ord_less_eq @ SY361 @ SV69 @ SY360 ) )
| ~ ! [SY362: $i,SY363: $i] :
( ~ ( linorder @ SY363 )
| ~ ( number @ SY363 )
| ~ ( ord_less_eq @ SY363 @ SV69 @ SY362 )
| ( ord_less_eq @ SY363 @ SV69 @ ( ti @ SY363 @ SY362 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[694]) ).
thf(810,plain,
! [SV70: $i] :
( ( ( ~ ( number @ SV70 ) )
= $true )
| ( ( ~ ( ~ ! [SY364: $i,SY365: $i] :
( ( ( number_number_of @ SV70 @ SY364 )
!= ( ti @ SV70 @ SY365 ) )
| ( ( ti @ SV70 @ SY365 )
= ( number_number_of @ SV70 @ SY364 ) ) )
| ~ ! [SY366: $i,SY367: $i] :
( ( ( ti @ SV70 @ SY367 )
!= ( number_number_of @ SV70 @ SY366 ) )
| ( ( number_number_of @ SV70 @ SY366 )
= ( ti @ SV70 @ SY367 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[695]) ).
thf(811,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[696]) ).
thf(812,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less @ int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[696]) ).
thf(813,plain,
( ( ~ ! [SX0: $i] :
( ~ ( twoSqu33214720sum2sq @ ( ti @ int @ SX0 ) )
| ( twoSqu33214720sum2sq @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[697]) ).
thf(814,plain,
( ( ~ ! [SX0: $i] :
( ~ ( twoSqu33214720sum2sq @ SX0 )
| ( twoSqu33214720sum2sq @ ( ti @ int @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[697]) ).
thf(815,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ ( number_number_of @ int @ SX0 ) @ ( number_number_of @ int @ SX1 ) )
| ( ord_less_eq @ int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[698]) ).
thf(816,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ ( number_number_of @ int @ SX0 ) @ ( number_number_of @ int @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[698]) ).
thf(817,plain,
( ( ~ ! [SX0: $i] :
( ( ( number_number_of @ nat @ SX0 )
!= ( zero_zero @ nat ) )
| ( ord_less_eq @ int @ SX0 @ pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[699]) ).
thf(818,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_eq @ int @ SX0 @ pls )
| ( ( number_number_of @ nat @ SX0 )
= ( zero_zero @ nat ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[699]) ).
thf(819,plain,
! [SV71: $i] :
( ( ~ ! [SY368: $i,SY369: $i] :
( ~ ( linorder @ SY369 )
| ~ ( number @ SY369 )
| ~ ( ord_less @ SY369 @ ( ti @ SY369 @ SV71 ) @ SY368 )
| ( ord_less @ SY369 @ SV71 @ SY368 ) )
| ~ ! [SY370: $i,SY371: $i] :
( ~ ( linorder @ SY371 )
| ~ ( number @ SY371 )
| ~ ( ord_less @ SY371 @ SV71 @ SY370 )
| ( ord_less @ SY371 @ ( ti @ SY371 @ SV71 ) @ SY370 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[700]) ).
thf(820,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( bit1 @ SX0 )
!= ( bit1 @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[701]) ).
thf(821,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( bit1 @ SX0 )
= ( bit1 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[701]) ).
thf(822,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq @ int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[702]) ).
thf(823,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[702]) ).
thf(824,plain,
( ( ~ ! [SX0: $i] :
( ~ ( zprime @ ( ti @ int @ SX0 ) )
| ( zprime @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[703]) ).
thf(825,plain,
( ( ~ ! [SX0: $i] :
( ~ ( zprime @ SX0 )
| ( zprime @ ( ti @ int @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[703]) ).
thf(826,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_eq @ int @ pls @ ( bit1 @ SX0 ) )
| ( ord_less_eq @ int @ pls @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[704]) ).
thf(827,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_eq @ int @ pls @ SX0 )
| ( ord_less_eq @ int @ pls @ ( bit1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[704]) ).
thf(828,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq @ int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[705]) ).
thf(829,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ( ord_less @ int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[705]) ).
thf(830,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ ( plus_plus @ int @ SX0 @ ( one_one @ int ) ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[706]) ).
thf(831,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ ( plus_plus @ int @ SX0 @ ( one_one @ int ) ) @ SX1 )
| ( ord_less @ int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[706]) ).
thf(832,plain,
! [SV72: $i] :
( ( ~ ! [SY372: $i,SY373: $i] :
( ~ ( linorder @ SY373 )
| ~ ( number @ SY373 )
| ~ ( ord_less_eq @ SY373 @ ( ti @ SY373 @ SV72 ) @ SY372 )
| ( ord_less_eq @ SY373 @ SV72 @ SY372 ) )
| ~ ! [SY374: $i,SY375: $i] :
( ~ ( linorder @ SY375 )
| ~ ( number @ SY375 )
| ~ ( ord_less_eq @ SY375 @ SV72 @ SY374 )
| ( ord_less_eq @ SY375 @ ( ti @ SY375 @ SV72 ) @ SY374 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[707]) ).
thf(833,plain,
! [SV73: $i] :
( ( ~ ! [SY376: $i,SY377: $i] :
( ~ ( linorder @ SY377 )
| ~ ( number @ SY377 )
| ~ ( ord_less @ SY377 @ SV73 @ ( ti @ SY377 @ SY376 ) )
| ( ord_less @ SY377 @ SV73 @ SY376 ) )
| ~ ! [SY378: $i,SY379: $i] :
( ~ ( linorder @ SY379 )
| ~ ( number @ SY379 )
| ~ ( ord_less @ SY379 @ SV73 @ SY378 )
| ( ord_less @ SY379 @ SV73 @ ( ti @ SY379 @ SY378 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[708]) ).
thf(834,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq @ int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[709]) ).
thf(835,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[709]) ).
thf(836,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[710]) ).
thf(837,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less @ int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[710]) ).
thf(838,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ ( plus_plus @ int @ SX1 @ ( one_one @ int ) ) )
| ( ord_less_eq @ int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[711]) ).
thf(839,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ( ord_less @ int @ SX0 @ ( plus_plus @ int @ SX1 @ ( one_one @ int ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[711]) ).
thf(840,plain,
! [SV74: $i] :
( ( ( ~ ( linorder @ SV74 )
| ~ ( number @ SV74 ) )
= $true )
| ( ( ~ ( ~ ! [SY380: $i,SY381: $i] :
( ~ ( ord_less_eq @ SV74 @ ( number_number_of @ SV74 @ SY380 ) @ ( number_number_of @ SV74 @ SY381 ) )
| ~ ( ord_less @ SV74 @ ( number_number_of @ SV74 @ SY381 ) @ ( number_number_of @ SV74 @ SY380 ) ) )
| ~ ! [SY382: $i,SY383: $i] :
( ( ord_less @ SV74 @ ( number_number_of @ SV74 @ SY383 ) @ ( number_number_of @ SV74 @ SY382 ) )
| ( ord_less_eq @ SV74 @ ( number_number_of @ SV74 @ SY382 ) @ ( number_number_of @ SV74 @ SY383 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[712]) ).
thf(841,plain,
! [SV75: $i] :
( ( ( ~ ( linordered_idom @ SV75 ) )
= $true )
| ( ( ~ ( ~ ! [SY384: $i,SY385: $i] :
( ~ ( ord_less @ SV75 @ ( zero_zero @ SV75 ) @ ( plus_plus @ SV75 @ ( power_power @ SV75 @ SY384 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV75 @ SY385 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
| ( ( ti @ SV75 @ SY384 )
!= ( zero_zero @ SV75 ) )
| ( ( ti @ SV75 @ SY385 )
!= ( zero_zero @ SV75 ) ) )
| ~ ~ ( ~ ! [SY386: $i] :
( ( ( ti @ SV75 @ SY386 )
= ( zero_zero @ SV75 ) )
| ! [SY387: $i] : ( ord_less @ SV75 @ ( zero_zero @ SV75 ) @ ( plus_plus @ SV75 @ ( power_power @ SV75 @ SY386 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV75 @ SY387 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
| ~ ! [SY388: $i,SY389: $i] :
( ( ( ti @ SV75 @ SY389 )
= ( zero_zero @ SV75 ) )
| ( ord_less @ SV75 @ ( zero_zero @ SV75 ) @ ( plus_plus @ SV75 @ ( power_power @ SV75 @ SY388 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV75 @ SY389 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[713]) ).
thf(842,plain,
! [SV76: $i] :
( ( ( ~ ( linordered_idom @ SV76 )
| ~ ( number_ring @ SV76 ) )
= $true )
| ( ( ~ ( ~ ! [SY390: $i] :
( ~ ( ord_less_eq @ SV76 @ ( one_one @ SV76 ) @ ( number_number_of @ SV76 @ SY390 ) )
| ( ord_less_eq @ int @ ( bit1 @ pls ) @ SY390 ) )
| ~ ! [SY391: $i] :
( ~ ( ord_less_eq @ int @ ( bit1 @ pls ) @ SY391 )
| ( ord_less_eq @ SV76 @ ( one_one @ SV76 ) @ ( number_number_of @ SV76 @ SY391 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[714]) ).
thf(843,plain,
! [SV77: $i] :
( ( ( ~ ( linordered_idom @ SV77 ) )
= $true )
| ( ( ~ ( ~ ! [SY392: $i,SY393: $i] :
( ( ( ti @ SV77 @ SY392 )
!= ( zero_zero @ SV77 ) )
| ( ( ti @ SV77 @ SY393 )
!= ( zero_zero @ SV77 ) )
| ( ( plus_plus @ SV77 @ ( power_power @ SV77 @ SY392 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV77 @ SY393 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV77 ) ) )
| ~ ~ ( ~ ! [SY394: $i] :
( ! [SY395: $i] :
( ( plus_plus @ SV77 @ ( power_power @ SV77 @ SY394 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV77 @ SY395 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV77 ) )
| ( ( ti @ SV77 @ SY394 )
= ( zero_zero @ SV77 ) ) )
| ~ ! [SY396: $i,SY397: $i] :
( ( ( plus_plus @ SV77 @ ( power_power @ SV77 @ SY396 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV77 @ SY397 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV77 ) )
| ( ( ti @ SV77 @ SY397 )
= ( zero_zero @ SV77 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[715]) ).
thf(844,plain,
! [SV78: $i] :
( ( ( ~ ( ring_11004092258visors @ SV78 ) )
= $true )
| ( ( ~ ( ~ ! [SY398: $i] :
( ( ( power_power @ SV78 @ SY398 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= ( zero_zero @ SV78 ) )
| ( ( ti @ SV78 @ SY398 )
= ( zero_zero @ SV78 ) ) )
| ~ ! [SY399: $i] :
( ( ( ti @ SV78 @ SY399 )
!= ( zero_zero @ SV78 ) )
| ( ( power_power @ SV78 @ SY399 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SV78 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[716]) ).
thf(845,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ord_less @ int @ SX0 @ SX1 )
| ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ nat @ ( number_number_of @ nat @ SX0 ) @ ( number_number_of @ nat @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ pls @ SX1 )
| ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ nat @ ( number_number_of @ nat @ SX0 ) @ ( number_number_of @ nat @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[717]) ).
thf(846,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ nat @ ( number_number_of @ nat @ SX0 ) @ ( number_number_of @ nat @ SX1 ) )
| ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ int @ pls @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ nat @ ( number_number_of @ nat @ SX0 ) @ ( number_number_of @ nat @ SX1 ) )
| ( ord_less @ int @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[717]) ).
thf(847,plain,
! [SV79: $i] :
( ( ( ~ ( linordered_idom @ SV79 ) )
= $true )
| ( ( ~ ( ~ ! [SY400: $i] :
( ( ( ti @ SV79 @ SY400 )
= ( zero_zero @ SV79 ) )
| ( ord_less @ SV79 @ ( zero_zero @ SV79 ) @ ( power_power @ SV79 @ SY400 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
| ~ ! [SY401: $i] :
( ~ ( ord_less @ SV79 @ ( zero_zero @ SV79 ) @ ( power_power @ SV79 @ SY401 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ( ( ti @ SV79 @ SY401 )
!= ( zero_zero @ SV79 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[718]) ).
thf(848,plain,
! [SV80: $i] :
( ( ( ~ ( number_ring @ SV80 )
| ~ ( ring_char_0 @ SV80 ) )
= $true )
| ( ( ~ ( ~ ! [SY402: $i,SY403: $i] :
( ( ( number_number_of @ SV80 @ SY402 )
!= ( number_number_of @ SV80 @ SY403 ) )
| ( SY402 = SY403 ) )
| ~ ! [SY404: $i,SY405: $i] :
( ( SY404 != SY405 )
| ( ( number_number_of @ SV80 @ SY404 )
= ( number_number_of @ SV80 @ SY405 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[719]) ).
thf(849,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_eq @ int @ pls @ ( bit0 @ SX0 ) )
| ( ord_less_eq @ int @ pls @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[720]) ).
thf(850,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_eq @ int @ pls @ SX0 )
| ( ord_less_eq @ int @ pls @ ( bit0 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[720]) ).
thf(851,plain,
! [SV81: $i] :
( ( ( ~ ( linordered_idom @ SV81 )
| ~ ( number_ring @ SV81 ) )
= $true )
| ( ( ~ ( ~ ! [SY406: $i] :
( ~ ( ord_less_eq @ SV81 @ ( number_number_of @ SV81 @ SY406 ) @ ( zero_zero @ SV81 ) )
| ( ord_less_eq @ int @ SY406 @ pls ) )
| ~ ! [SY407: $i] :
( ~ ( ord_less_eq @ int @ SY407 @ pls )
| ( ord_less_eq @ SV81 @ ( number_number_of @ SV81 @ SY407 ) @ ( zero_zero @ SV81 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[721]) ).
thf(852,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)],[722]) ).
thf(853,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)],[722]) ).
thf(854,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_eq @ int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[723]) ).
thf(855,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[723]) ).
thf(856,plain,
! [SV82: $i] :
( ( ( ~ ( linord581940658strict @ SV82 ) )
= $true )
| ( ( ~ ( ~ ! [SY408: $i,SY409: $i] :
( ( ( ti @ SV82 @ SY408 )
!= ( zero_zero @ SV82 ) )
| ( ( ti @ SV82 @ SY409 )
!= ( zero_zero @ SV82 ) )
| ( ( plus_plus @ SV82 @ ( times_times @ SV82 @ SY408 @ SY408 ) @ ( times_times @ SV82 @ SY409 @ SY409 ) )
= ( zero_zero @ SV82 ) ) )
| ~ ~ ( ~ ! [SY410: $i] :
( ! [SY411: $i] :
( ( plus_plus @ SV82 @ ( times_times @ SV82 @ SY410 @ SY410 ) @ ( times_times @ SV82 @ SY411 @ SY411 ) )
!= ( zero_zero @ SV82 ) )
| ( ( ti @ SV82 @ SY410 )
= ( zero_zero @ SV82 ) ) )
| ~ ! [SY412: $i,SY413: $i] :
( ( ( plus_plus @ SV82 @ ( times_times @ SV82 @ SY412 @ SY412 ) @ ( times_times @ SV82 @ SY413 @ SY413 ) )
!= ( zero_zero @ SV82 ) )
| ( ( ti @ SV82 @ SY413 )
= ( zero_zero @ SV82 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[724]) ).
thf(857,plain,
! [SV83: $i] :
( ( ~ ! [SY414: $i,SY415: $i] :
( ~ ( linordered_ring @ SY415 )
| ~ ( ord_less_eq @ SY415 @ SV83 @ ( ti @ SY415 @ SY414 ) )
| ( ord_less_eq @ SY415 @ SV83 @ SY414 ) )
| ~ ! [SY416: $i,SY417: $i] :
( ~ ( linordered_ring @ SY417 )
| ~ ( ord_less_eq @ SY417 @ SV83 @ SY416 )
| ( ord_less_eq @ SY417 @ SV83 @ ( ti @ SY417 @ SY416 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[725]) ).
thf(858,plain,
! [SV84: $i] :
( ( ( ~ ( linordered_idom @ SV84 )
| ~ ( number_ring @ SV84 ) )
= $true )
| ( ( ~ ( ~ ! [SY418: $i] :
( ~ ( ord_less_eq @ SV84 @ ( number_number_of @ SV84 @ SY418 ) @ ( one_one @ SV84 ) )
| ( ord_less_eq @ int @ SY418 @ ( bit1 @ pls ) ) )
| ~ ! [SY419: $i] :
( ~ ( ord_less_eq @ int @ SY419 @ ( bit1 @ pls ) )
| ( ord_less_eq @ SV84 @ ( number_number_of @ SV84 @ SY419 ) @ ( one_one @ SV84 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[726]) ).
thf(859,plain,
! [SV85: $i] :
( ( ( ~ ( linordered_idom @ SV85 )
| ~ ( number_ring @ SV85 ) )
= $true )
| ( ( ~ ( ~ ! [SY420: $i] :
( ~ ( ord_less_eq @ SV85 @ ( zero_zero @ SV85 ) @ ( number_number_of @ SV85 @ SY420 ) )
| ( ord_less_eq @ int @ pls @ SY420 ) )
| ~ ! [SY421: $i] :
( ~ ( ord_less_eq @ int @ pls @ SY421 )
| ( ord_less_eq @ SV85 @ ( zero_zero @ SV85 ) @ ( number_number_of @ SV85 @ SY421 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[727]) ).
thf(860,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less @ int @ SX0 @ pls )
| ( ord_less_eq @ int @ ( bit1 @ SX0 ) @ pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[728]) ).
thf(861,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_eq @ int @ ( bit1 @ SX0 ) @ pls )
| ( ord_less @ int @ SX0 @ pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[728]) ).
thf(862,plain,
! [SV86: $i] :
( ( ( ~ ( linord581940658strict @ SV86 ) )
= $true )
| ( ( ~ ( ~ ! [SY422: $i,SY423: $i] :
( ( ( ti @ SV86 @ SY422 )
!= ( zero_zero @ SV86 ) )
| ( ( ti @ SV86 @ SY423 )
!= ( zero_zero @ SV86 ) )
| ( ord_less_eq @ SV86 @ ( plus_plus @ SV86 @ ( times_times @ SV86 @ SY422 @ SY422 ) @ ( times_times @ SV86 @ SY423 @ SY423 ) ) @ ( zero_zero @ SV86 ) ) )
| ~ ~ ( ~ ! [SY424: $i] :
( ! [SY425: $i] :
~ ( ord_less_eq @ SV86 @ ( plus_plus @ SV86 @ ( times_times @ SV86 @ SY424 @ SY424 ) @ ( times_times @ SV86 @ SY425 @ SY425 ) ) @ ( zero_zero @ SV86 ) )
| ( ( ti @ SV86 @ SY424 )
= ( zero_zero @ SV86 ) ) )
| ~ ! [SY426: $i,SY427: $i] :
( ~ ( ord_less_eq @ SV86 @ ( plus_plus @ SV86 @ ( times_times @ SV86 @ SY426 @ SY426 ) @ ( times_times @ SV86 @ SY427 @ SY427 ) ) @ ( zero_zero @ SV86 ) )
| ( ( ti @ SV86 @ SY427 )
= ( zero_zero @ SV86 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[729]) ).
thf(863,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq @ int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[730]) ).
thf(864,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ( ord_less @ int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[730]) ).
thf(865,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_eq @ int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[731]) ).
thf(866,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[731]) ).
thf(867,plain,
( ( ~ ! [SX0: $i] :
( ( ( zero_zero @ nat )
!= ( number_number_of @ nat @ SX0 ) )
| ( ord_less_eq @ int @ SX0 @ pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[732]) ).
thf(868,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_eq @ int @ SX0 @ pls )
| ( ( zero_zero @ nat )
= ( number_number_of @ nat @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[732]) ).
thf(869,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less @ int @ pls @ ( bit1 @ SX0 ) )
| ( ord_less_eq @ int @ pls @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[733]) ).
thf(870,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ord_less_eq @ int @ pls @ SX0 )
| ( ord_less @ int @ pls @ ( bit1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[733]) ).
thf(871,plain,
! [SV5: $i] :
( ( ( semiring_1 @ SV5 )
= $false )
| ( ( ( ti @ SV5 @ ( one_one @ SV5 ) )
= ( one_one @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[734]) ).
thf(872,plain,
! [SV87: $i,SV6: $i,SV123: $i] :
( ( ~ ( linordered_ring @ SV123 )
| ( ( plus_plus @ SV123 @ ( ti @ SV123 @ SV6 ) @ SV87 )
= ( plus_plus @ SV123 @ SV6 @ SV87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[735]) ).
thf(873,plain,
! [SV88: $i,SV7: $i,SV124: $i] :
( ( ~ ( linordered_ring @ SV124 )
| ( ( plus_plus @ SV124 @ SV7 @ ( ti @ SV124 @ SV88 ) )
= ( plus_plus @ SV124 @ SV7 @ SV88 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[736]) ).
thf(874,plain,
! [SV89: $i,SV8: $i,SV125: $i] :
( ( ~ ( linordered_ring @ SV125 )
| ( ( ti @ SV125 @ ( plus_plus @ SV125 @ SV8 @ SV89 ) )
= ( plus_plus @ SV125 @ SV8 @ SV89 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[737]) ).
thf(875,plain,
! [SV9: $i] :
( ( ( linordered_ring @ SV9 )
= $false )
| ( ( ( ti @ SV9 @ ( zero_zero @ SV9 ) )
= ( zero_zero @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[738]) ).
thf(876,plain,
! [SV10: $i] :
( ( ( semiring_1 @ SV10 )
= $false )
| ( ( ( ti @ SV10 @ ( zero_zero @ SV10 ) )
= ( zero_zero @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[739]) ).
thf(877,plain,
! [SV11: $i,SV90: $i] :
( ( ( ~ ( number @ SV90 ) )
= $true )
| ( ( ( number_number_of @ SV90 @ ( ti @ int @ SV11 ) )
= ( number_number_of @ SV90 @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[740]) ).
thf(878,plain,
! [SV12: $i,SV91: $i] :
( ( ( ~ ( number @ SV91 ) )
= $true )
| ( ( ( ti @ SV91 @ ( number_number_of @ SV91 @ SV12 ) )
= ( number_number_of @ SV91 @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[741]) ).
thf(879,plain,
! [SV92: $i,SV13: $i,SV126: $i] :
( ( ~ ( semiring_1 @ SV126 )
| ( ( power_power @ SV126 @ ( ti @ SV126 @ SV13 ) @ SV92 )
= ( power_power @ SV126 @ SV13 @ SV92 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[742]) ).
thf(880,plain,
! [SV93: $i,SV14: $i,SV127: $i] :
( ( ~ ( semiring_1 @ SV127 )
| ( ( power_power @ SV127 @ SV14 @ ( ti @ nat @ SV93 ) )
= ( power_power @ SV127 @ SV14 @ SV93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[743]) ).
thf(881,plain,
! [SV94: $i,SV15: $i,SV128: $i] :
( ( ~ ( semiring_1 @ SV128 )
| ( ( ti @ SV128 @ ( power_power @ SV128 @ SV15 @ SV94 ) )
= ( power_power @ SV128 @ SV15 @ SV94 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[744]) ).
thf(882,plain,
! [SV16: $i] :
( ( ( linordered_idom @ SV16 )
= $false )
| ( ( ! [SY273: $i,SY274: $i] :
~ ( ord_less @ SV16 @ ( plus_plus @ SV16 @ ( power_power @ SV16 @ SY273 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV16 @ SY274 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( zero_zero @ SV16 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[746]) ).
thf(883,plain,
! [SV17: $i] :
( ( ( linordered_idom @ SV17 )
= $false )
| ( ( ! [SY275: $i] :
~ ( ord_less @ SV17 @ ( power_power @ SV17 @ SY275 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( zero_zero @ SV17 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[747]) ).
thf(884,plain,
! [SV18: $i] :
( ( ( semiring_1 @ SV18 )
= $false )
| ( ( ( power_power @ SV18 @ ( one_one @ SV18 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( one_one @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[748]) ).
thf(885,plain,
! [SV19: $i] :
( ( ( semiring_1 @ SV19 )
= $false )
| ( ( ( power_power @ SV19 @ ( zero_zero @ SV19 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[749]) ).
thf(886,plain,
! [SV20: $i] :
( ( ( number_ring @ SV20 )
= $false )
| ( ( ! [SY276: $i] :
( ( plus_plus @ SV20 @ ( one_one @ SV20 ) @ ( number_number_of @ SV20 @ SY276 ) )
= ( number_number_of @ SV20 @ ( plus_plus @ int @ ( bit1 @ pls ) @ SY276 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[750]) ).
thf(887,plain,
! [SV21: $i] :
( ( ( number_ring @ SV21 )
= $false )
| ( ( ! [SY277: $i] :
( ( plus_plus @ SV21 @ ( number_number_of @ SV21 @ SY277 ) @ ( one_one @ SV21 ) )
= ( number_number_of @ SV21 @ ( plus_plus @ int @ SY277 @ ( bit1 @ pls ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[751]) ).
thf(888,plain,
! [SV96: $i,SV25: $i] :
( ( ( ord_less_eq @ int @ SV25 @ SV96 )
= $true )
| ( ( ord_less_eq @ int @ SV96 @ SV25 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[753]) ).
thf(889,plain,
! [SV129: $i,SV98: $i,SV27: $i] :
( ( ( times_times @ int @ ( times_times @ int @ SV27 @ SV98 ) @ SV129 )
= ( times_times @ int @ SV27 @ ( times_times @ int @ SV98 @ SV129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[755]) ).
thf(890,plain,
! [SV28: $i,SV130: $i,SV99: $i] :
( ( ~ ( ord_less_eq @ int @ SV99 @ SV130 )
| ~ ( ord_less_eq @ int @ SV130 @ SV28 )
| ( ord_less_eq @ int @ SV99 @ SV28 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[756]) ).
thf(891,plain,
! [SV100: $i,SV29: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV29 @ SV100 ) )
= $true )
| ( ( ~ ( ord_less_eq @ int @ SV100 @ SV29 )
| ( SV29 = SV100 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[757]) ).
thf(892,plain,
! [SV131: $i,SV101: $i,SV30: $i] :
( ( ( power_power @ int @ SV30 @ ( plus_plus @ nat @ SV101 @ SV131 ) )
= ( times_times @ int @ ( power_power @ int @ SV30 @ SV101 ) @ ( power_power @ int @ SV30 @ SV131 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[758]) ).
thf(893,plain,
! [SV31: $i,SV132: $i,SV102: $i] :
( ( ~ ( ord_less_eq @ int @ SV102 @ SV132 )
| ( ord_less_eq @ int @ ( plus_plus @ int @ SV31 @ SV102 ) @ ( plus_plus @ int @ SV31 @ SV132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[759]) ).
thf(894,plain,
! [SV32: $i] :
( ( ( number_ring @ SV32 )
= $false )
| ( ( ! [SY290: $i,SY291: $i,SY292: $i] :
( ( times_times @ SV32 @ ( number_number_of @ SV32 @ SY290 ) @ ( times_times @ SV32 @ ( number_number_of @ SV32 @ SY291 ) @ SY292 ) )
= ( times_times @ SV32 @ ( number_number_of @ SV32 @ ( times_times @ int @ SY290 @ SY291 ) ) @ SY292 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[760]) ).
thf(895,plain,
! [SV33: $i] :
( ( ( number_ring @ SV33 )
= $false )
| ( ( ! [SY293: $i,SY294: $i] :
( ( times_times @ SV33 @ ( number_number_of @ SV33 @ SY293 ) @ ( number_number_of @ SV33 @ SY294 ) )
= ( number_number_of @ SV33 @ ( times_times @ int @ SY293 @ SY294 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[761]) ).
thf(896,plain,
! [SV34: $i] :
( ( ( number_ring @ SV34 )
= $false )
| ( ( ! [SY295: $i,SY296: $i] :
( ( number_number_of @ SV34 @ ( times_times @ int @ SY295 @ SY296 ) )
= ( times_times @ SV34 @ ( number_number_of @ SV34 @ SY295 ) @ ( number_number_of @ SV34 @ SY296 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[762]) ).
thf(897,plain,
! [SV103: $i,SV35: $i,SV133: $i] :
( ( ! [SY453: $i] :
( ~ ( ord_less @ int @ SV133 @ SY453 )
| ~ ( ord_less_eq @ int @ SV35 @ SV103 )
| ( ord_less @ int @ ( plus_plus @ int @ SV133 @ SV35 ) @ ( plus_plus @ int @ SY453 @ SV103 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[763]) ).
thf(898,plain,
! [SV134: $i,SV106: $i,SV41: $i] :
( ( ( times_times @ int @ ( plus_plus @ int @ SV41 @ SV106 ) @ SV134 )
= ( plus_plus @ int @ ( times_times @ int @ SV41 @ SV134 ) @ ( times_times @ int @ SV106 @ SV134 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[766]) ).
thf(899,plain,
! [SV135: $i,SV107: $i,SV42: $i] :
( ( ( times_times @ int @ SV42 @ ( plus_plus @ int @ SV107 @ SV135 ) )
= ( plus_plus @ int @ ( times_times @ int @ SV42 @ SV107 ) @ ( times_times @ int @ SV42 @ SV135 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[767]) ).
thf(900,plain,
! [SV108: $i,SV43: $i] :
( ( ( ~ ( ord_less @ int @ SV43 @ SV108 ) )
= $true )
| ( ( ord_less_eq @ int @ ( plus_plus @ int @ SV43 @ ( one_one @ int ) ) @ SV108 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[768]) ).
thf(901,plain,
! [SV44: $i] :
( ( ( number_semiring @ SV44 )
= $false )
| ( ( ! [SY307: $i,SY308: $i] :
( ~ ( ord_less_eq @ int @ pls @ SY308 )
| ~ ( ord_less_eq @ int @ pls @ SY307 )
| ( ( plus_plus @ SV44 @ ( number_number_of @ SV44 @ SY308 ) @ ( number_number_of @ SV44 @ SY307 ) )
= ( number_number_of @ SV44 @ ( plus_plus @ int @ SY308 @ SY307 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[769]) ).
thf(902,plain,
! [SV45: $i] :
( ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV45 )
= $false )
| ( ( ord_less @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( one_one @ int ) @ SV45 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[770]) ).
thf(903,plain,
! [SV46: $i,SV109: $i] :
( ( ( ord_less @ int @ SV109 @ SV46 )
= $true )
| ( ( ( SV46 = SV109 )
| ( ord_less @ int @ SV46 @ SV109 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[771]) ).
thf(904,plain,
! [SV136: $i,SV110: $i,SV47: $i] :
( ( ( plus_plus @ int @ ( plus_plus @ int @ SV47 @ SV110 ) @ SV136 )
= ( plus_plus @ int @ SV47 @ ( plus_plus @ int @ SV110 @ SV136 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[772]) ).
thf(905,plain,
! [SV137: $i,SV111: $i,SV48: $i] :
( ( ( plus_plus @ int @ SV48 @ ( plus_plus @ int @ SV111 @ SV137 ) )
= ( plus_plus @ int @ SV111 @ ( plus_plus @ int @ SV48 @ SV137 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[773]) ).
thf(906,plain,
! [SV113: $i,SV50: $i,SV138: $i] :
( ( ~ ( number @ SV138 )
| ~ ( semiring @ SV138 )
| ( ( plus_plus @ SV138 @ ( ti @ SV138 @ SV50 ) @ SV113 )
= ( plus_plus @ SV138 @ SV50 @ SV113 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[775]) ).
thf(907,plain,
! [SV114: $i,SV51: $i,SV139: $i] :
( ( ~ ( number @ SV139 )
| ~ ( semiring @ SV139 )
| ( ( plus_plus @ SV139 @ SV51 @ ( ti @ SV139 @ SV114 ) )
= ( plus_plus @ SV139 @ SV51 @ SV114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[776]) ).
thf(908,plain,
! [SV115: $i,SV52: $i,SV140: $i] :
( ( ~ ( number @ SV140 )
| ~ ( semiring @ SV140 )
| ( ( ti @ SV140 @ ( plus_plus @ SV140 @ SV52 @ SV115 ) )
= ( plus_plus @ SV140 @ SV52 @ SV115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[777]) ).
thf(909,plain,
! [SV116: $i,SV53: $i,SV141: $i] :
( ( ~ ( number @ SV141 )
| ~ ( semiring @ SV141 )
| ( ( times_times @ SV141 @ ( ti @ SV141 @ SV53 ) @ SV116 )
= ( times_times @ SV141 @ SV53 @ SV116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[778]) ).
thf(910,plain,
! [SV117: $i,SV54: $i,SV142: $i] :
( ( ~ ( number @ SV142 )
| ~ ( semiring @ SV142 )
| ( ( times_times @ SV142 @ SV54 @ ( ti @ SV142 @ SV117 ) )
= ( times_times @ SV142 @ SV54 @ SV117 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[779]) ).
thf(911,plain,
! [SV118: $i,SV55: $i,SV143: $i] :
( ( ~ ( number @ SV143 )
| ~ ( semiring @ SV143 )
| ( ( ti @ SV143 @ ( times_times @ SV143 @ SV55 @ SV118 ) )
= ( times_times @ SV143 @ SV55 @ SV118 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[780]) ).
thf(912,plain,
! [SV119: $i,SV56: $i,SV144: $i] :
( ( ~ ( linordered_ring @ SV144 )
| ( ( times_times @ SV144 @ ( ti @ SV144 @ SV56 ) @ SV119 )
= ( times_times @ SV144 @ SV56 @ SV119 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[781]) ).
thf(913,plain,
! [SV120: $i,SV57: $i,SV145: $i] :
( ( ~ ( linordered_ring @ SV145 )
| ( ( times_times @ SV145 @ SV57 @ ( ti @ SV145 @ SV120 ) )
= ( times_times @ SV145 @ SV57 @ SV120 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[782]) ).
thf(914,plain,
! [SV121: $i,SV58: $i,SV146: $i] :
( ( ~ ( linordered_ring @ SV146 )
| ( ( ti @ SV146 @ ( times_times @ SV146 @ SV58 @ SV121 ) )
= ( times_times @ SV146 @ SV58 @ SV121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[783]) ).
thf(915,plain,
! [SV60: $i] :
( ( ( number_semiring @ SV60 )
= $false )
| ( ( ! [SY333: $i,SY334: $i] :
( ~ ( ord_less_eq @ int @ pls @ SY334 )
| ~ ( ord_less_eq @ int @ pls @ SY333 )
| ( ( times_times @ SV60 @ ( number_number_of @ SV60 @ SY334 ) @ ( number_number_of @ SV60 @ SY333 ) )
= ( number_number_of @ SV60 @ ( times_times @ int @ SY334 @ SY333 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[784]) ).
thf(916,plain,
! [SV61: $i] :
( ( ( linordered_ring @ SV61 )
= $false )
| ( ( ! [SY335: $i,SY336: $i] : ( ord_less_eq @ SV61 @ ( zero_zero @ SV61 ) @ ( plus_plus @ SV61 @ ( times_times @ SV61 @ SY335 @ SY335 ) @ ( times_times @ SV61 @ SY336 @ SY336 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[785]) ).
thf(917,plain,
! [SV62: $i] :
( ( ( ~ ( number @ SV62 ) )
= $true )
| ( ( ~ ( semiring @ SV62 ) )
= $true )
| ( ( ! [SY337: $i,SY338: $i,SY339: $i] :
( ( times_times @ SV62 @ ( plus_plus @ SV62 @ SY337 @ SY338 ) @ ( number_number_of @ SV62 @ SY339 ) )
= ( plus_plus @ SV62 @ ( times_times @ SV62 @ SY337 @ ( number_number_of @ SV62 @ SY339 ) ) @ ( times_times @ SV62 @ SY338 @ ( number_number_of @ SV62 @ SY339 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[786]) ).
thf(918,plain,
! [SV63: $i] :
( ( ( ~ ( number @ SV63 ) )
= $true )
| ( ( ~ ( semiring @ SV63 ) )
= $true )
| ( ( ! [SY340: $i,SY341: $i,SY342: $i] :
( ( times_times @ SV63 @ ( number_number_of @ SV63 @ SY340 ) @ ( plus_plus @ SV63 @ SY341 @ SY342 ) )
= ( plus_plus @ SV63 @ ( times_times @ SV63 @ ( number_number_of @ SV63 @ SY340 ) @ SY341 ) @ ( times_times @ SV63 @ ( number_number_of @ SV63 @ SY340 ) @ SY342 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[787]) ).
thf(919,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ ( number_number_of @ nat @ SX0 ) )
| ( ord_less @ int @ pls @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[789]) ).
thf(920,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less @ int @ pls @ SX0 )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ ( number_number_of @ nat @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[790]) ).
thf(921,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ( ord_less @ int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[791]) ).
thf(922,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[792]) ).
thf(923,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less @ int @ ( zero_zero @ int ) @ SX0 )
| ( ord_less_eq @ int @ ( one_one @ int ) @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[793]) ).
thf(924,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less_eq @ int @ ( one_one @ int ) @ SX0 )
| ( ord_less @ int @ ( zero_zero @ int ) @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[794]) ).
thf(925,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq @ int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[795]) ).
thf(926,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[796]) ).
thf(927,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq @ int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[797]) ).
thf(928,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[798]) ).
thf(929,plain,
! [SV65: $i] :
( ( ( ~ ( linordered_idom @ SV65 ) )
= $true )
| ( ( ~ ( number_ring @ SV65 ) )
= $true )
| ( ( ~ ( ~ ! [SY344: $i,SY345: $i] :
( ~ ( ord_less_eq @ SV65 @ ( number_number_of @ SV65 @ SY344 ) @ ( number_number_of @ SV65 @ SY345 ) )
| ( ord_less_eq @ int @ SY344 @ SY345 ) )
| ~ ! [SY346: $i,SY347: $i] :
( ~ ( ord_less_eq @ int @ SY346 @ SY347 )
| ( ord_less_eq @ SV65 @ ( number_number_of @ SV65 @ SY346 ) @ ( number_number_of @ SV65 @ SY347 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[799]) ).
thf(930,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less_eq @ int @ ( bit0 @ SX0 ) @ pls )
| ( ord_less_eq @ int @ SX0 @ pls ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[800]) ).
thf(931,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less_eq @ int @ SX0 @ pls )
| ( ord_less_eq @ int @ ( bit0 @ SX0 ) @ pls ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[801]) ).
thf(932,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)],[802]) ).
thf(933,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)],[803]) ).
thf(934,plain,
! [SV66: $i] :
( ( ~ ! [SY348: $i,SY349: $i] :
( ~ ( linordered_idom @ SY349 )
| ~ ( ord_less @ SY349 @ SV66 @ ( ti @ SY349 @ SY348 ) )
| ( ord_less @ SY349 @ SV66 @ SY348 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[804]) ).
thf(935,plain,
! [SV66: $i] :
( ( ~ ! [SY350: $i,SY351: $i] :
( ~ ( linordered_idom @ SY351 )
| ~ ( ord_less @ SY351 @ SV66 @ SY350 )
| ( ord_less @ SY351 @ SV66 @ ( ti @ SY351 @ SY350 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[804]) ).
thf(936,plain,
! [SV67: $i] :
( ( ~ ! [SY352: $i,SY353: $i] :
( ~ ( linordered_idom @ SY353 )
| ~ ( ord_less @ SY353 @ ( ti @ SY353 @ SV67 ) @ SY352 )
| ( ord_less @ SY353 @ SV67 @ SY352 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[805]) ).
thf(937,plain,
! [SV67: $i] :
( ( ~ ! [SY354: $i,SY355: $i] :
( ~ ( linordered_idom @ SY355 )
| ~ ( ord_less @ SY355 @ SV67 @ SY354 )
| ( ord_less @ SY355 @ ( ti @ SY355 @ SV67 ) @ SY354 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[805]) ).
thf(938,plain,
! [SV68: $i] :
( ( ~ ! [SY356: $i,SY357: $i] :
( ~ ( linordered_ring @ SY357 )
| ~ ( ord_less_eq @ SY357 @ ( ti @ SY357 @ SV68 ) @ SY356 )
| ( ord_less_eq @ SY357 @ SV68 @ SY356 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[806]) ).
thf(939,plain,
! [SV68: $i] :
( ( ~ ! [SY358: $i,SY359: $i] :
( ~ ( linordered_ring @ SY359 )
| ~ ( ord_less_eq @ SY359 @ SV68 @ SY358 )
| ( ord_less_eq @ SY359 @ ( ti @ SY359 @ SV68 ) @ SY358 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[806]) ).
thf(940,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( bit0 @ SX0 )
!= ( bit0 @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[807]) ).
thf(941,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( bit0 @ SX0 )
= ( bit0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[808]) ).
thf(942,plain,
! [SV69: $i] :
( ( ~ ! [SY360: $i,SY361: $i] :
( ~ ( linorder @ SY361 )
| ~ ( number @ SY361 )
| ~ ( ord_less_eq @ SY361 @ SV69 @ ( ti @ SY361 @ SY360 ) )
| ( ord_less_eq @ SY361 @ SV69 @ SY360 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[809]) ).
thf(943,plain,
! [SV69: $i] :
( ( ~ ! [SY362: $i,SY363: $i] :
( ~ ( linorder @ SY363 )
| ~ ( number @ SY363 )
| ~ ( ord_less_eq @ SY363 @ SV69 @ SY362 )
| ( ord_less_eq @ SY363 @ SV69 @ ( ti @ SY363 @ SY362 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[809]) ).
thf(944,plain,
! [SV70: $i] :
( ( ( number @ SV70 )
= $false )
| ( ( ~ ( ~ ! [SY364: $i,SY365: $i] :
( ( ( number_number_of @ SV70 @ SY364 )
!= ( ti @ SV70 @ SY365 ) )
| ( ( ti @ SV70 @ SY365 )
= ( number_number_of @ SV70 @ SY364 ) ) )
| ~ ! [SY366: $i,SY367: $i] :
( ( ( ti @ SV70 @ SY367 )
!= ( number_number_of @ SV70 @ SY366 ) )
| ( ( number_number_of @ SV70 @ SY366 )
= ( ti @ SV70 @ SY367 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[810]) ).
thf(945,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[811]) ).
thf(946,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less @ int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[812]) ).
thf(947,plain,
( ( ! [SX0: $i] :
( ~ ( twoSqu33214720sum2sq @ ( ti @ int @ SX0 ) )
| ( twoSqu33214720sum2sq @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[813]) ).
thf(948,plain,
( ( ! [SX0: $i] :
( ~ ( twoSqu33214720sum2sq @ SX0 )
| ( twoSqu33214720sum2sq @ ( ti @ int @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[814]) ).
thf(949,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ ( number_number_of @ int @ SX0 ) @ ( number_number_of @ int @ SX1 ) )
| ( ord_less_eq @ int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[815]) ).
thf(950,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ ( number_number_of @ int @ SX0 ) @ ( number_number_of @ int @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[816]) ).
thf(951,plain,
( ( ! [SX0: $i] :
( ( ( number_number_of @ nat @ SX0 )
!= ( zero_zero @ nat ) )
| ( ord_less_eq @ int @ SX0 @ pls ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[817]) ).
thf(952,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less_eq @ int @ SX0 @ pls )
| ( ( number_number_of @ nat @ SX0 )
= ( zero_zero @ nat ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[818]) ).
thf(953,plain,
! [SV71: $i] :
( ( ~ ! [SY368: $i,SY369: $i] :
( ~ ( linorder @ SY369 )
| ~ ( number @ SY369 )
| ~ ( ord_less @ SY369 @ ( ti @ SY369 @ SV71 ) @ SY368 )
| ( ord_less @ SY369 @ SV71 @ SY368 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[819]) ).
thf(954,plain,
! [SV71: $i] :
( ( ~ ! [SY370: $i,SY371: $i] :
( ~ ( linorder @ SY371 )
| ~ ( number @ SY371 )
| ~ ( ord_less @ SY371 @ SV71 @ SY370 )
| ( ord_less @ SY371 @ ( ti @ SY371 @ SV71 ) @ SY370 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[819]) ).
thf(955,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( bit1 @ SX0 )
!= ( bit1 @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[820]) ).
thf(956,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( bit1 @ SX0 )
= ( bit1 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[821]) ).
thf(957,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq @ int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[822]) ).
thf(958,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[823]) ).
thf(959,plain,
( ( ! [SX0: $i] :
( ~ ( zprime @ ( ti @ int @ SX0 ) )
| ( zprime @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[824]) ).
thf(960,plain,
( ( ! [SX0: $i] :
( ~ ( zprime @ SX0 )
| ( zprime @ ( ti @ int @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[825]) ).
thf(961,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less_eq @ int @ pls @ ( bit1 @ SX0 ) )
| ( ord_less_eq @ int @ pls @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[826]) ).
thf(962,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less_eq @ int @ pls @ SX0 )
| ( ord_less_eq @ int @ pls @ ( bit1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[827]) ).
thf(963,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq @ int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[828]) ).
thf(964,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ( ord_less @ int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[829]) ).
thf(965,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ ( plus_plus @ int @ SX0 @ ( one_one @ int ) ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[830]) ).
thf(966,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ ( plus_plus @ int @ SX0 @ ( one_one @ int ) ) @ SX1 )
| ( ord_less @ int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[831]) ).
thf(967,plain,
! [SV72: $i] :
( ( ~ ! [SY372: $i,SY373: $i] :
( ~ ( linorder @ SY373 )
| ~ ( number @ SY373 )
| ~ ( ord_less_eq @ SY373 @ ( ti @ SY373 @ SV72 ) @ SY372 )
| ( ord_less_eq @ SY373 @ SV72 @ SY372 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[832]) ).
thf(968,plain,
! [SV72: $i] :
( ( ~ ! [SY374: $i,SY375: $i] :
( ~ ( linorder @ SY375 )
| ~ ( number @ SY375 )
| ~ ( ord_less_eq @ SY375 @ SV72 @ SY374 )
| ( ord_less_eq @ SY375 @ ( ti @ SY375 @ SV72 ) @ SY374 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[832]) ).
thf(969,plain,
! [SV73: $i] :
( ( ~ ! [SY376: $i,SY377: $i] :
( ~ ( linorder @ SY377 )
| ~ ( number @ SY377 )
| ~ ( ord_less @ SY377 @ SV73 @ ( ti @ SY377 @ SY376 ) )
| ( ord_less @ SY377 @ SV73 @ SY376 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[833]) ).
thf(970,plain,
! [SV73: $i] :
( ( ~ ! [SY378: $i,SY379: $i] :
( ~ ( linorder @ SY379 )
| ~ ( number @ SY379 )
| ~ ( ord_less @ SY379 @ SV73 @ SY378 )
| ( ord_less @ SY379 @ SV73 @ ( ti @ SY379 @ SY378 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[833]) ).
thf(971,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq @ int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[834]) ).
thf(972,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[835]) ).
thf(973,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[836]) ).
thf(974,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less @ int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[837]) ).
thf(975,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ ( plus_plus @ int @ SX1 @ ( one_one @ int ) ) )
| ( ord_less_eq @ int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[838]) ).
thf(976,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ( ord_less @ int @ SX0 @ ( plus_plus @ int @ SX1 @ ( one_one @ int ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[839]) ).
thf(977,plain,
! [SV74: $i] :
( ( ( ~ ( linorder @ SV74 ) )
= $true )
| ( ( ~ ( number @ SV74 ) )
= $true )
| ( ( ~ ( ~ ! [SY380: $i,SY381: $i] :
( ~ ( ord_less_eq @ SV74 @ ( number_number_of @ SV74 @ SY380 ) @ ( number_number_of @ SV74 @ SY381 ) )
| ~ ( ord_less @ SV74 @ ( number_number_of @ SV74 @ SY381 ) @ ( number_number_of @ SV74 @ SY380 ) ) )
| ~ ! [SY382: $i,SY383: $i] :
( ( ord_less @ SV74 @ ( number_number_of @ SV74 @ SY383 ) @ ( number_number_of @ SV74 @ SY382 ) )
| ( ord_less_eq @ SV74 @ ( number_number_of @ SV74 @ SY382 ) @ ( number_number_of @ SV74 @ SY383 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[840]) ).
thf(978,plain,
! [SV75: $i] :
( ( ( linordered_idom @ SV75 )
= $false )
| ( ( ~ ( ~ ! [SY384: $i,SY385: $i] :
( ~ ( ord_less @ SV75 @ ( zero_zero @ SV75 ) @ ( plus_plus @ SV75 @ ( power_power @ SV75 @ SY384 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV75 @ SY385 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
| ( ( ti @ SV75 @ SY384 )
!= ( zero_zero @ SV75 ) )
| ( ( ti @ SV75 @ SY385 )
!= ( zero_zero @ SV75 ) ) )
| ~ ~ ( ~ ! [SY386: $i] :
( ( ( ti @ SV75 @ SY386 )
= ( zero_zero @ SV75 ) )
| ! [SY387: $i] : ( ord_less @ SV75 @ ( zero_zero @ SV75 ) @ ( plus_plus @ SV75 @ ( power_power @ SV75 @ SY386 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV75 @ SY387 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
| ~ ! [SY388: $i,SY389: $i] :
( ( ( ti @ SV75 @ SY389 )
= ( zero_zero @ SV75 ) )
| ( ord_less @ SV75 @ ( zero_zero @ SV75 ) @ ( plus_plus @ SV75 @ ( power_power @ SV75 @ SY388 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV75 @ SY389 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[841]) ).
thf(979,plain,
! [SV76: $i] :
( ( ( ~ ( linordered_idom @ SV76 ) )
= $true )
| ( ( ~ ( number_ring @ SV76 ) )
= $true )
| ( ( ~ ( ~ ! [SY390: $i] :
( ~ ( ord_less_eq @ SV76 @ ( one_one @ SV76 ) @ ( number_number_of @ SV76 @ SY390 ) )
| ( ord_less_eq @ int @ ( bit1 @ pls ) @ SY390 ) )
| ~ ! [SY391: $i] :
( ~ ( ord_less_eq @ int @ ( bit1 @ pls ) @ SY391 )
| ( ord_less_eq @ SV76 @ ( one_one @ SV76 ) @ ( number_number_of @ SV76 @ SY391 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[842]) ).
thf(980,plain,
! [SV77: $i] :
( ( ( linordered_idom @ SV77 )
= $false )
| ( ( ~ ( ~ ! [SY392: $i,SY393: $i] :
( ( ( ti @ SV77 @ SY392 )
!= ( zero_zero @ SV77 ) )
| ( ( ti @ SV77 @ SY393 )
!= ( zero_zero @ SV77 ) )
| ( ( plus_plus @ SV77 @ ( power_power @ SV77 @ SY392 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV77 @ SY393 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV77 ) ) )
| ~ ~ ( ~ ! [SY394: $i] :
( ! [SY395: $i] :
( ( plus_plus @ SV77 @ ( power_power @ SV77 @ SY394 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV77 @ SY395 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV77 ) )
| ( ( ti @ SV77 @ SY394 )
= ( zero_zero @ SV77 ) ) )
| ~ ! [SY396: $i,SY397: $i] :
( ( ( plus_plus @ SV77 @ ( power_power @ SV77 @ SY396 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV77 @ SY397 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV77 ) )
| ( ( ti @ SV77 @ SY397 )
= ( zero_zero @ SV77 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[843]) ).
thf(981,plain,
! [SV78: $i] :
( ( ( ring_11004092258visors @ SV78 )
= $false )
| ( ( ~ ( ~ ! [SY398: $i] :
( ( ( power_power @ SV78 @ SY398 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= ( zero_zero @ SV78 ) )
| ( ( ti @ SV78 @ SY398 )
= ( zero_zero @ SV78 ) ) )
| ~ ! [SY399: $i] :
( ( ( ti @ SV78 @ SY399 )
!= ( zero_zero @ SV78 ) )
| ( ( power_power @ SV78 @ SY399 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SV78 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[844]) ).
thf(982,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ord_less @ int @ SX0 @ SX1 )
| ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ nat @ ( number_number_of @ nat @ SX0 ) @ ( number_number_of @ nat @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ pls @ SX1 )
| ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ nat @ ( number_number_of @ nat @ SX0 ) @ ( number_number_of @ nat @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[845]) ).
thf(983,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ nat @ ( number_number_of @ nat @ SX0 ) @ ( number_number_of @ nat @ SX1 ) )
| ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ int @ pls @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ nat @ ( number_number_of @ nat @ SX0 ) @ ( number_number_of @ nat @ SX1 ) )
| ( ord_less @ int @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[846]) ).
thf(984,plain,
! [SV79: $i] :
( ( ( linordered_idom @ SV79 )
= $false )
| ( ( ~ ( ~ ! [SY400: $i] :
( ( ( ti @ SV79 @ SY400 )
= ( zero_zero @ SV79 ) )
| ( ord_less @ SV79 @ ( zero_zero @ SV79 ) @ ( power_power @ SV79 @ SY400 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
| ~ ! [SY401: $i] :
( ~ ( ord_less @ SV79 @ ( zero_zero @ SV79 ) @ ( power_power @ SV79 @ SY401 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ( ( ti @ SV79 @ SY401 )
!= ( zero_zero @ SV79 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[847]) ).
thf(985,plain,
! [SV80: $i] :
( ( ( ~ ( number_ring @ SV80 ) )
= $true )
| ( ( ~ ( ring_char_0 @ SV80 ) )
= $true )
| ( ( ~ ( ~ ! [SY402: $i,SY403: $i] :
( ( ( number_number_of @ SV80 @ SY402 )
!= ( number_number_of @ SV80 @ SY403 ) )
| ( SY402 = SY403 ) )
| ~ ! [SY404: $i,SY405: $i] :
( ( SY404 != SY405 )
| ( ( number_number_of @ SV80 @ SY404 )
= ( number_number_of @ SV80 @ SY405 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[848]) ).
thf(986,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less_eq @ int @ pls @ ( bit0 @ SX0 ) )
| ( ord_less_eq @ int @ pls @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[849]) ).
thf(987,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less_eq @ int @ pls @ SX0 )
| ( ord_less_eq @ int @ pls @ ( bit0 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[850]) ).
thf(988,plain,
! [SV81: $i] :
( ( ( ~ ( linordered_idom @ SV81 ) )
= $true )
| ( ( ~ ( number_ring @ SV81 ) )
= $true )
| ( ( ~ ( ~ ! [SY406: $i] :
( ~ ( ord_less_eq @ SV81 @ ( number_number_of @ SV81 @ SY406 ) @ ( zero_zero @ SV81 ) )
| ( ord_less_eq @ int @ SY406 @ pls ) )
| ~ ! [SY407: $i] :
( ~ ( ord_less_eq @ int @ SY407 @ pls )
| ( ord_less_eq @ SV81 @ ( number_number_of @ SV81 @ SY407 ) @ ( zero_zero @ SV81 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[851]) ).
thf(989,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)],[852]) ).
thf(990,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)],[853]) ).
thf(991,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_eq @ int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[854]) ).
thf(992,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[855]) ).
thf(993,plain,
! [SV82: $i] :
( ( ( linord581940658strict @ SV82 )
= $false )
| ( ( ~ ( ~ ! [SY408: $i,SY409: $i] :
( ( ( ti @ SV82 @ SY408 )
!= ( zero_zero @ SV82 ) )
| ( ( ti @ SV82 @ SY409 )
!= ( zero_zero @ SV82 ) )
| ( ( plus_plus @ SV82 @ ( times_times @ SV82 @ SY408 @ SY408 ) @ ( times_times @ SV82 @ SY409 @ SY409 ) )
= ( zero_zero @ SV82 ) ) )
| ~ ~ ( ~ ! [SY410: $i] :
( ! [SY411: $i] :
( ( plus_plus @ SV82 @ ( times_times @ SV82 @ SY410 @ SY410 ) @ ( times_times @ SV82 @ SY411 @ SY411 ) )
!= ( zero_zero @ SV82 ) )
| ( ( ti @ SV82 @ SY410 )
= ( zero_zero @ SV82 ) ) )
| ~ ! [SY412: $i,SY413: $i] :
( ( ( plus_plus @ SV82 @ ( times_times @ SV82 @ SY412 @ SY412 ) @ ( times_times @ SV82 @ SY413 @ SY413 ) )
!= ( zero_zero @ SV82 ) )
| ( ( ti @ SV82 @ SY413 )
= ( zero_zero @ SV82 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[856]) ).
thf(994,plain,
! [SV83: $i] :
( ( ~ ! [SY414: $i,SY415: $i] :
( ~ ( linordered_ring @ SY415 )
| ~ ( ord_less_eq @ SY415 @ SV83 @ ( ti @ SY415 @ SY414 ) )
| ( ord_less_eq @ SY415 @ SV83 @ SY414 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[857]) ).
thf(995,plain,
! [SV83: $i] :
( ( ~ ! [SY416: $i,SY417: $i] :
( ~ ( linordered_ring @ SY417 )
| ~ ( ord_less_eq @ SY417 @ SV83 @ SY416 )
| ( ord_less_eq @ SY417 @ SV83 @ ( ti @ SY417 @ SY416 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[857]) ).
thf(996,plain,
! [SV84: $i] :
( ( ( ~ ( linordered_idom @ SV84 ) )
= $true )
| ( ( ~ ( number_ring @ SV84 ) )
= $true )
| ( ( ~ ( ~ ! [SY418: $i] :
( ~ ( ord_less_eq @ SV84 @ ( number_number_of @ SV84 @ SY418 ) @ ( one_one @ SV84 ) )
| ( ord_less_eq @ int @ SY418 @ ( bit1 @ pls ) ) )
| ~ ! [SY419: $i] :
( ~ ( ord_less_eq @ int @ SY419 @ ( bit1 @ pls ) )
| ( ord_less_eq @ SV84 @ ( number_number_of @ SV84 @ SY419 ) @ ( one_one @ SV84 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[858]) ).
thf(997,plain,
! [SV85: $i] :
( ( ( ~ ( linordered_idom @ SV85 ) )
= $true )
| ( ( ~ ( number_ring @ SV85 ) )
= $true )
| ( ( ~ ( ~ ! [SY420: $i] :
( ~ ( ord_less_eq @ SV85 @ ( zero_zero @ SV85 ) @ ( number_number_of @ SV85 @ SY420 ) )
| ( ord_less_eq @ int @ pls @ SY420 ) )
| ~ ! [SY421: $i] :
( ~ ( ord_less_eq @ int @ pls @ SY421 )
| ( ord_less_eq @ SV85 @ ( zero_zero @ SV85 ) @ ( number_number_of @ SV85 @ SY421 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[859]) ).
thf(998,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less @ int @ SX0 @ pls )
| ( ord_less_eq @ int @ ( bit1 @ SX0 ) @ pls ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[860]) ).
thf(999,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less_eq @ int @ ( bit1 @ SX0 ) @ pls )
| ( ord_less @ int @ SX0 @ pls ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[861]) ).
thf(1000,plain,
! [SV86: $i] :
( ( ( linord581940658strict @ SV86 )
= $false )
| ( ( ~ ( ~ ! [SY422: $i,SY423: $i] :
( ( ( ti @ SV86 @ SY422 )
!= ( zero_zero @ SV86 ) )
| ( ( ti @ SV86 @ SY423 )
!= ( zero_zero @ SV86 ) )
| ( ord_less_eq @ SV86 @ ( plus_plus @ SV86 @ ( times_times @ SV86 @ SY422 @ SY422 ) @ ( times_times @ SV86 @ SY423 @ SY423 ) ) @ ( zero_zero @ SV86 ) ) )
| ~ ~ ( ~ ! [SY424: $i] :
( ! [SY425: $i] :
~ ( ord_less_eq @ SV86 @ ( plus_plus @ SV86 @ ( times_times @ SV86 @ SY424 @ SY424 ) @ ( times_times @ SV86 @ SY425 @ SY425 ) ) @ ( zero_zero @ SV86 ) )
| ( ( ti @ SV86 @ SY424 )
= ( zero_zero @ SV86 ) ) )
| ~ ! [SY426: $i,SY427: $i] :
( ~ ( ord_less_eq @ SV86 @ ( plus_plus @ SV86 @ ( times_times @ SV86 @ SY426 @ SY426 ) @ ( times_times @ SV86 @ SY427 @ SY427 ) ) @ ( zero_zero @ SV86 ) )
| ( ( ti @ SV86 @ SY427 )
= ( zero_zero @ SV86 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[862]) ).
thf(1001,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq @ int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[863]) ).
thf(1002,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ( ord_less @ int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[864]) ).
thf(1003,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_eq @ int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[865]) ).
thf(1004,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[866]) ).
thf(1005,plain,
( ( ! [SX0: $i] :
( ( ( zero_zero @ nat )
!= ( number_number_of @ nat @ SX0 ) )
| ( ord_less_eq @ int @ SX0 @ pls ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[867]) ).
thf(1006,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less_eq @ int @ SX0 @ pls )
| ( ( zero_zero @ nat )
= ( number_number_of @ nat @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[868]) ).
thf(1007,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less @ int @ pls @ ( bit1 @ SX0 ) )
| ( ord_less_eq @ int @ pls @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[869]) ).
thf(1008,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less_eq @ int @ pls @ SX0 )
| ( ord_less @ int @ pls @ ( bit1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[870]) ).
thf(1009,plain,
! [SV87: $i,SV6: $i,SV123: $i] :
( ( ( ~ ( linordered_ring @ SV123 ) )
= $true )
| ( ( ( plus_plus @ SV123 @ ( ti @ SV123 @ SV6 ) @ SV87 )
= ( plus_plus @ SV123 @ SV6 @ SV87 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[872]) ).
thf(1010,plain,
! [SV88: $i,SV7: $i,SV124: $i] :
( ( ( ~ ( linordered_ring @ SV124 ) )
= $true )
| ( ( ( plus_plus @ SV124 @ SV7 @ ( ti @ SV124 @ SV88 ) )
= ( plus_plus @ SV124 @ SV7 @ SV88 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[873]) ).
thf(1011,plain,
! [SV89: $i,SV8: $i,SV125: $i] :
( ( ( ~ ( linordered_ring @ SV125 ) )
= $true )
| ( ( ( ti @ SV125 @ ( plus_plus @ SV125 @ SV8 @ SV89 ) )
= ( plus_plus @ SV125 @ SV8 @ SV89 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[874]) ).
thf(1012,plain,
! [SV11: $i,SV90: $i] :
( ( ( number @ SV90 )
= $false )
| ( ( ( number_number_of @ SV90 @ ( ti @ int @ SV11 ) )
= ( number_number_of @ SV90 @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[877]) ).
thf(1013,plain,
! [SV12: $i,SV91: $i] :
( ( ( number @ SV91 )
= $false )
| ( ( ( ti @ SV91 @ ( number_number_of @ SV91 @ SV12 ) )
= ( number_number_of @ SV91 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[878]) ).
thf(1014,plain,
! [SV92: $i,SV13: $i,SV126: $i] :
( ( ( ~ ( semiring_1 @ SV126 ) )
= $true )
| ( ( ( power_power @ SV126 @ ( ti @ SV126 @ SV13 ) @ SV92 )
= ( power_power @ SV126 @ SV13 @ SV92 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[879]) ).
thf(1015,plain,
! [SV93: $i,SV14: $i,SV127: $i] :
( ( ( ~ ( semiring_1 @ SV127 ) )
= $true )
| ( ( ( power_power @ SV127 @ SV14 @ ( ti @ nat @ SV93 ) )
= ( power_power @ SV127 @ SV14 @ SV93 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[880]) ).
thf(1016,plain,
! [SV94: $i,SV15: $i,SV128: $i] :
( ( ( ~ ( semiring_1 @ SV128 ) )
= $true )
| ( ( ( ti @ SV128 @ ( power_power @ SV128 @ SV15 @ SV94 ) )
= ( power_power @ SV128 @ SV15 @ SV94 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[881]) ).
thf(1017,plain,
! [SV147: $i,SV16: $i] :
( ( ( ! [SY454: $i] :
~ ( ord_less @ SV16 @ ( plus_plus @ SV16 @ ( power_power @ SV16 @ SV147 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV16 @ SY454 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( zero_zero @ SV16 ) ) )
= $true )
| ( ( linordered_idom @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[882]) ).
thf(1018,plain,
! [SV148: $i,SV17: $i] :
( ( ( ~ ( ord_less @ SV17 @ ( power_power @ SV17 @ SV148 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( zero_zero @ SV17 ) ) )
= $true )
| ( ( linordered_idom @ SV17 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[883]) ).
thf(1019,plain,
! [SV149: $i,SV20: $i] :
( ( ( ( plus_plus @ SV20 @ ( one_one @ SV20 ) @ ( number_number_of @ SV20 @ SV149 ) )
= ( number_number_of @ SV20 @ ( plus_plus @ int @ ( bit1 @ pls ) @ SV149 ) ) )
= $true )
| ( ( number_ring @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[886]) ).
thf(1020,plain,
! [SV150: $i,SV21: $i] :
( ( ( ( plus_plus @ SV21 @ ( number_number_of @ SV21 @ SV150 ) @ ( one_one @ SV21 ) )
= ( number_number_of @ SV21 @ ( plus_plus @ int @ SV150 @ ( bit1 @ pls ) ) ) )
= $true )
| ( ( number_ring @ SV21 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[887]) ).
thf(1021,plain,
! [SV28: $i,SV130: $i,SV99: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV99 @ SV130 ) )
= $true )
| ( ( ~ ( ord_less_eq @ int @ SV130 @ SV28 )
| ( ord_less_eq @ int @ SV99 @ SV28 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[890]) ).
thf(1022,plain,
! [SV100: $i,SV29: $i] :
( ( ( ord_less_eq @ int @ SV29 @ SV100 )
= $false )
| ( ( ~ ( ord_less_eq @ int @ SV100 @ SV29 )
| ( SV29 = SV100 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[891]) ).
thf(1023,plain,
! [SV31: $i,SV132: $i,SV102: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV102 @ SV132 ) )
= $true )
| ( ( ord_less_eq @ int @ ( plus_plus @ int @ SV31 @ SV102 ) @ ( plus_plus @ int @ SV31 @ SV132 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[893]) ).
thf(1024,plain,
! [SV151: $i,SV32: $i] :
( ( ( ! [SY455: $i,SY456: $i] :
( ( times_times @ SV32 @ ( number_number_of @ SV32 @ SV151 ) @ ( times_times @ SV32 @ ( number_number_of @ SV32 @ SY455 ) @ SY456 ) )
= ( times_times @ SV32 @ ( number_number_of @ SV32 @ ( times_times @ int @ SV151 @ SY455 ) ) @ SY456 ) ) )
= $true )
| ( ( number_ring @ SV32 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[894]) ).
thf(1025,plain,
! [SV152: $i,SV33: $i] :
( ( ( ! [SY457: $i] :
( ( times_times @ SV33 @ ( number_number_of @ SV33 @ SV152 ) @ ( number_number_of @ SV33 @ SY457 ) )
= ( number_number_of @ SV33 @ ( times_times @ int @ SV152 @ SY457 ) ) ) )
= $true )
| ( ( number_ring @ SV33 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[895]) ).
thf(1026,plain,
! [SV153: $i,SV34: $i] :
( ( ( ! [SY458: $i] :
( ( number_number_of @ SV34 @ ( times_times @ int @ SV153 @ SY458 ) )
= ( times_times @ SV34 @ ( number_number_of @ SV34 @ SV153 ) @ ( number_number_of @ SV34 @ SY458 ) ) ) )
= $true )
| ( ( number_ring @ SV34 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[896]) ).
thf(1027,plain,
! [SV103: $i,SV35: $i,SV154: $i,SV133: $i] :
( ( ~ ( ord_less @ int @ SV133 @ SV154 )
| ~ ( ord_less_eq @ int @ SV35 @ SV103 )
| ( ord_less @ int @ ( plus_plus @ int @ SV133 @ SV35 ) @ ( plus_plus @ int @ SV154 @ SV103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[897]) ).
thf(1028,plain,
! [SV108: $i,SV43: $i] :
( ( ( ord_less @ int @ SV43 @ SV108 )
= $false )
| ( ( ord_less_eq @ int @ ( plus_plus @ int @ SV43 @ ( one_one @ int ) ) @ SV108 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[900]) ).
thf(1029,plain,
! [SV44: $i,SV155: $i] :
( ( ( ! [SY459: $i] :
( ~ ( ord_less_eq @ int @ pls @ SY459 )
| ~ ( ord_less_eq @ int @ pls @ SV155 )
| ( ( plus_plus @ SV44 @ ( number_number_of @ SV44 @ SY459 ) @ ( number_number_of @ SV44 @ SV155 ) )
= ( number_number_of @ SV44 @ ( plus_plus @ int @ SY459 @ SV155 ) ) ) ) )
= $true )
| ( ( number_semiring @ SV44 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[901]) ).
thf(1030,plain,
! [SV109: $i,SV46: $i] :
( ( ( SV46 = SV109 )
= $true )
| ( ( ord_less @ int @ SV46 @ SV109 )
= $true )
| ( ( ord_less @ int @ SV109 @ SV46 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[903]) ).
thf(1031,plain,
! [SV113: $i,SV50: $i,SV138: $i] :
( ( ( ~ ( number @ SV138 )
| ~ ( semiring @ SV138 ) )
= $true )
| ( ( ( plus_plus @ SV138 @ ( ti @ SV138 @ SV50 ) @ SV113 )
= ( plus_plus @ SV138 @ SV50 @ SV113 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[906]) ).
thf(1032,plain,
! [SV114: $i,SV51: $i,SV139: $i] :
( ( ( ~ ( number @ SV139 )
| ~ ( semiring @ SV139 ) )
= $true )
| ( ( ( plus_plus @ SV139 @ SV51 @ ( ti @ SV139 @ SV114 ) )
= ( plus_plus @ SV139 @ SV51 @ SV114 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[907]) ).
thf(1033,plain,
! [SV115: $i,SV52: $i,SV140: $i] :
( ( ( ~ ( number @ SV140 )
| ~ ( semiring @ SV140 ) )
= $true )
| ( ( ( ti @ SV140 @ ( plus_plus @ SV140 @ SV52 @ SV115 ) )
= ( plus_plus @ SV140 @ SV52 @ SV115 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[908]) ).
thf(1034,plain,
! [SV116: $i,SV53: $i,SV141: $i] :
( ( ( ~ ( number @ SV141 )
| ~ ( semiring @ SV141 ) )
= $true )
| ( ( ( times_times @ SV141 @ ( ti @ SV141 @ SV53 ) @ SV116 )
= ( times_times @ SV141 @ SV53 @ SV116 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[909]) ).
thf(1035,plain,
! [SV117: $i,SV54: $i,SV142: $i] :
( ( ( ~ ( number @ SV142 )
| ~ ( semiring @ SV142 ) )
= $true )
| ( ( ( times_times @ SV142 @ SV54 @ ( ti @ SV142 @ SV117 ) )
= ( times_times @ SV142 @ SV54 @ SV117 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[910]) ).
thf(1036,plain,
! [SV118: $i,SV55: $i,SV143: $i] :
( ( ( ~ ( number @ SV143 )
| ~ ( semiring @ SV143 ) )
= $true )
| ( ( ( ti @ SV143 @ ( times_times @ SV143 @ SV55 @ SV118 ) )
= ( times_times @ SV143 @ SV55 @ SV118 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[911]) ).
thf(1037,plain,
! [SV119: $i,SV56: $i,SV144: $i] :
( ( ( ~ ( linordered_ring @ SV144 ) )
= $true )
| ( ( ( times_times @ SV144 @ ( ti @ SV144 @ SV56 ) @ SV119 )
= ( times_times @ SV144 @ SV56 @ SV119 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[912]) ).
thf(1038,plain,
! [SV120: $i,SV57: $i,SV145: $i] :
( ( ( ~ ( linordered_ring @ SV145 ) )
= $true )
| ( ( ( times_times @ SV145 @ SV57 @ ( ti @ SV145 @ SV120 ) )
= ( times_times @ SV145 @ SV57 @ SV120 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[913]) ).
thf(1039,plain,
! [SV121: $i,SV58: $i,SV146: $i] :
( ( ( ~ ( linordered_ring @ SV146 ) )
= $true )
| ( ( ( ti @ SV146 @ ( times_times @ SV146 @ SV58 @ SV121 ) )
= ( times_times @ SV146 @ SV58 @ SV121 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[914]) ).
thf(1040,plain,
! [SV60: $i,SV156: $i] :
( ( ( ! [SY460: $i] :
( ~ ( ord_less_eq @ int @ pls @ SY460 )
| ~ ( ord_less_eq @ int @ pls @ SV156 )
| ( ( times_times @ SV60 @ ( number_number_of @ SV60 @ SY460 ) @ ( number_number_of @ SV60 @ SV156 ) )
= ( number_number_of @ SV60 @ ( times_times @ int @ SY460 @ SV156 ) ) ) ) )
= $true )
| ( ( number_semiring @ SV60 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[915]) ).
thf(1041,plain,
! [SV157: $i,SV61: $i] :
( ( ( ! [SY461: $i] : ( ord_less_eq @ SV61 @ ( zero_zero @ SV61 ) @ ( plus_plus @ SV61 @ ( times_times @ SV61 @ SV157 @ SV157 ) @ ( times_times @ SV61 @ SY461 @ SY461 ) ) ) )
= $true )
| ( ( linordered_ring @ SV61 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[916]) ).
thf(1042,plain,
! [SV62: $i] :
( ( ( number @ SV62 )
= $false )
| ( ( ~ ( semiring @ SV62 ) )
= $true )
| ( ( ! [SY337: $i,SY338: $i,SY339: $i] :
( ( times_times @ SV62 @ ( plus_plus @ SV62 @ SY337 @ SY338 ) @ ( number_number_of @ SV62 @ SY339 ) )
= ( plus_plus @ SV62 @ ( times_times @ SV62 @ SY337 @ ( number_number_of @ SV62 @ SY339 ) ) @ ( times_times @ SV62 @ SY338 @ ( number_number_of @ SV62 @ SY339 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[917]) ).
thf(1043,plain,
! [SV63: $i] :
( ( ( number @ SV63 )
= $false )
| ( ( ~ ( semiring @ SV63 ) )
= $true )
| ( ( ! [SY340: $i,SY341: $i,SY342: $i] :
( ( times_times @ SV63 @ ( number_number_of @ SV63 @ SY340 ) @ ( plus_plus @ SV63 @ SY341 @ SY342 ) )
= ( plus_plus @ SV63 @ ( times_times @ SV63 @ ( number_number_of @ SV63 @ SY340 ) @ SY341 ) @ ( times_times @ SV63 @ ( number_number_of @ SV63 @ SY340 ) @ SY342 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[918]) ).
thf(1044,plain,
! [SV158: $i] :
( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ ( number_number_of @ nat @ SV158 ) )
| ( ord_less @ int @ pls @ SV158 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[919]) ).
thf(1045,plain,
! [SV159: $i] :
( ( ~ ( ord_less @ int @ pls @ SV159 )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ ( number_number_of @ nat @ SV159 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[920]) ).
thf(1046,plain,
! [SV160: $i] :
( ( ! [SY462: $i] :
( ( SV160 = SY462 )
| ~ ( ord_less_eq @ int @ SV160 @ SY462 )
| ( ord_less @ int @ SV160 @ SY462 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[921]) ).
thf(1047,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[922]) ).
thf(1048,plain,
! [SV161: $i] :
( ( ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV161 )
| ( ord_less_eq @ int @ ( one_one @ int ) @ SV161 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[923]) ).
thf(1049,plain,
! [SV162: $i] :
( ( ~ ( ord_less_eq @ int @ ( one_one @ int ) @ SV162 )
| ( ord_less @ int @ ( zero_zero @ int ) @ SV162 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[924]) ).
thf(1050,plain,
! [SV163: $i] :
( ( ! [SY463: $i] :
( ~ ( ord_less_eq @ int @ ( bit0 @ SV163 ) @ ( bit1 @ SY463 ) )
| ( ord_less_eq @ int @ SV163 @ SY463 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[925]) ).
thf(1051,plain,
! [SV164: $i] :
( ( ! [SY464: $i] :
( ~ ( ord_less_eq @ int @ SV164 @ SY464 )
| ( ord_less_eq @ int @ ( bit0 @ SV164 ) @ ( bit1 @ SY464 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[926]) ).
thf(1052,plain,
! [SV165: $i] :
( ( ! [SY465: $i] :
( ~ ( ord_less_eq @ int @ ( bit0 @ SV165 ) @ ( bit1 @ SY465 ) )
| ( ord_less_eq @ int @ SV165 @ SY465 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[927]) ).
thf(1053,plain,
! [SV166: $i] :
( ( ! [SY466: $i] :
( ~ ( ord_less_eq @ int @ SV166 @ SY466 )
| ( ord_less_eq @ int @ ( bit0 @ SV166 ) @ ( bit1 @ SY466 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[928]) ).
thf(1054,plain,
! [SV65: $i] :
( ( ( linordered_idom @ SV65 )
= $false )
| ( ( ~ ( number_ring @ SV65 ) )
= $true )
| ( ( ~ ( ~ ! [SY344: $i,SY345: $i] :
( ~ ( ord_less_eq @ SV65 @ ( number_number_of @ SV65 @ SY344 ) @ ( number_number_of @ SV65 @ SY345 ) )
| ( ord_less_eq @ int @ SY344 @ SY345 ) )
| ~ ! [SY346: $i,SY347: $i] :
( ~ ( ord_less_eq @ int @ SY346 @ SY347 )
| ( ord_less_eq @ SV65 @ ( number_number_of @ SV65 @ SY346 ) @ ( number_number_of @ SV65 @ SY347 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[929]) ).
thf(1055,plain,
! [SV167: $i] :
( ( ~ ( ord_less_eq @ int @ ( bit0 @ SV167 ) @ pls )
| ( ord_less_eq @ int @ SV167 @ pls ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[930]) ).
thf(1056,plain,
! [SV168: $i] :
( ( ~ ( ord_less_eq @ int @ SV168 @ pls )
| ( ord_less_eq @ int @ ( bit0 @ SV168 ) @ pls ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[931]) ).
thf(1057,plain,
! [SV169: $i] :
( ( ! [SY467: $i] :
( ~ ( ord_less @ int @ SY467 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SY467 ) @ ( number_number_of @ nat @ SV169 ) )
= ( number_number_of @ nat @ SV169 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[932]) ).
thf(1058,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)],[933]) ).
thf(1059,plain,
! [SV66: $i] :
( ( ! [SY348: $i,SY349: $i] :
( ~ ( linordered_idom @ SY349 )
| ~ ( ord_less @ SY349 @ SV66 @ ( ti @ SY349 @ SY348 ) )
| ( ord_less @ SY349 @ SV66 @ SY348 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[934]) ).
thf(1060,plain,
! [SV66: $i] :
( ( ! [SY350: $i,SY351: $i] :
( ~ ( linordered_idom @ SY351 )
| ~ ( ord_less @ SY351 @ SV66 @ SY350 )
| ( ord_less @ SY351 @ SV66 @ ( ti @ SY351 @ SY350 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[935]) ).
thf(1061,plain,
! [SV67: $i] :
( ( ! [SY352: $i,SY353: $i] :
( ~ ( linordered_idom @ SY353 )
| ~ ( ord_less @ SY353 @ ( ti @ SY353 @ SV67 ) @ SY352 )
| ( ord_less @ SY353 @ SV67 @ SY352 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[936]) ).
thf(1062,plain,
! [SV67: $i] :
( ( ! [SY354: $i,SY355: $i] :
( ~ ( linordered_idom @ SY355 )
| ~ ( ord_less @ SY355 @ SV67 @ SY354 )
| ( ord_less @ SY355 @ ( ti @ SY355 @ SV67 ) @ SY354 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[937]) ).
thf(1063,plain,
! [SV68: $i] :
( ( ! [SY356: $i,SY357: $i] :
( ~ ( linordered_ring @ SY357 )
| ~ ( ord_less_eq @ SY357 @ ( ti @ SY357 @ SV68 ) @ SY356 )
| ( ord_less_eq @ SY357 @ SV68 @ SY356 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[938]) ).
thf(1064,plain,
! [SV68: $i] :
( ( ! [SY358: $i,SY359: $i] :
( ~ ( linordered_ring @ SY359 )
| ~ ( ord_less_eq @ SY359 @ SV68 @ SY358 )
| ( ord_less_eq @ SY359 @ ( ti @ SY359 @ SV68 ) @ SY358 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[939]) ).
thf(1065,plain,
! [SV170: $i] :
( ( ! [SY468: $i] :
( ( ( bit0 @ SV170 )
!= ( bit0 @ SY468 ) )
| ( SV170 = SY468 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[940]) ).
thf(1066,plain,
! [SV171: $i] :
( ( ! [SY469: $i] :
( ( SV171 != SY469 )
| ( ( bit0 @ SV171 )
= ( bit0 @ SY469 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[941]) ).
thf(1067,plain,
! [SV69: $i] :
( ( ! [SY360: $i,SY361: $i] :
( ~ ( linorder @ SY361 )
| ~ ( number @ SY361 )
| ~ ( ord_less_eq @ SY361 @ SV69 @ ( ti @ SY361 @ SY360 ) )
| ( ord_less_eq @ SY361 @ SV69 @ SY360 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[942]) ).
thf(1068,plain,
! [SV69: $i] :
( ( ! [SY362: $i,SY363: $i] :
( ~ ( linorder @ SY363 )
| ~ ( number @ SY363 )
| ~ ( ord_less_eq @ SY363 @ SV69 @ SY362 )
| ( ord_less_eq @ SY363 @ SV69 @ ( ti @ SY363 @ SY362 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[943]) ).
thf(1069,plain,
! [SV70: $i] :
( ( ( ~ ! [SY364: $i,SY365: $i] :
( ( ( number_number_of @ SV70 @ SY364 )
!= ( ti @ SV70 @ SY365 ) )
| ( ( ti @ SV70 @ SY365 )
= ( number_number_of @ SV70 @ SY364 ) ) )
| ~ ! [SY366: $i,SY367: $i] :
( ( ( ti @ SV70 @ SY367 )
!= ( number_number_of @ SV70 @ SY366 ) )
| ( ( number_number_of @ SV70 @ SY366 )
= ( ti @ SV70 @ SY367 ) ) ) )
= $false )
| ( ( number @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[944]) ).
thf(1070,plain,
! [SV172: $i] :
( ( ! [SY470: $i] :
( ~ ( ord_less @ int @ SV172 @ SY470 )
| ( ord_less_eq @ int @ ( bit1 @ SV172 ) @ ( bit0 @ SY470 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[945]) ).
thf(1071,plain,
! [SV173: $i] :
( ( ! [SY471: $i] :
( ~ ( ord_less_eq @ int @ ( bit1 @ SV173 ) @ ( bit0 @ SY471 ) )
| ( ord_less @ int @ SV173 @ SY471 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[946]) ).
thf(1072,plain,
! [SV174: $i] :
( ( ~ ( twoSqu33214720sum2sq @ ( ti @ int @ SV174 ) )
| ( twoSqu33214720sum2sq @ SV174 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[947]) ).
thf(1073,plain,
! [SV175: $i] :
( ( ~ ( twoSqu33214720sum2sq @ SV175 )
| ( twoSqu33214720sum2sq @ ( ti @ int @ SV175 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[948]) ).
thf(1074,plain,
! [SV176: $i] :
( ( ! [SY472: $i] :
( ~ ( ord_less_eq @ int @ ( number_number_of @ int @ SV176 ) @ ( number_number_of @ int @ SY472 ) )
| ( ord_less_eq @ int @ SV176 @ SY472 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[949]) ).
thf(1075,plain,
! [SV177: $i] :
( ( ! [SY473: $i] :
( ~ ( ord_less_eq @ int @ SV177 @ SY473 )
| ( ord_less_eq @ int @ ( number_number_of @ int @ SV177 ) @ ( number_number_of @ int @ SY473 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[950]) ).
thf(1076,plain,
! [SV178: $i] :
( ( ( ( number_number_of @ nat @ SV178 )
!= ( zero_zero @ nat ) )
| ( ord_less_eq @ int @ SV178 @ pls ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[951]) ).
thf(1077,plain,
! [SV179: $i] :
( ( ~ ( ord_less_eq @ int @ SV179 @ pls )
| ( ( number_number_of @ nat @ SV179 )
= ( zero_zero @ nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[952]) ).
thf(1078,plain,
! [SV71: $i] :
( ( ! [SY368: $i,SY369: $i] :
( ~ ( linorder @ SY369 )
| ~ ( number @ SY369 )
| ~ ( ord_less @ SY369 @ ( ti @ SY369 @ SV71 ) @ SY368 )
| ( ord_less @ SY369 @ SV71 @ SY368 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[953]) ).
thf(1079,plain,
! [SV71: $i] :
( ( ! [SY370: $i,SY371: $i] :
( ~ ( linorder @ SY371 )
| ~ ( number @ SY371 )
| ~ ( ord_less @ SY371 @ SV71 @ SY370 )
| ( ord_less @ SY371 @ ( ti @ SY371 @ SV71 ) @ SY370 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[954]) ).
thf(1080,plain,
! [SV180: $i] :
( ( ! [SY474: $i] :
( ( ( bit1 @ SV180 )
!= ( bit1 @ SY474 ) )
| ( SV180 = SY474 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[955]) ).
thf(1081,plain,
! [SV181: $i] :
( ( ! [SY475: $i] :
( ( SV181 != SY475 )
| ( ( bit1 @ SV181 )
= ( bit1 @ SY475 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[956]) ).
thf(1082,plain,
! [SV182: $i] :
( ( ! [SY476: $i] :
( ~ ( ord_less_eq @ int @ ( bit1 @ SV182 ) @ ( bit1 @ SY476 ) )
| ( ord_less_eq @ int @ SV182 @ SY476 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[957]) ).
thf(1083,plain,
! [SV183: $i] :
( ( ! [SY477: $i] :
( ~ ( ord_less_eq @ int @ SV183 @ SY477 )
| ( ord_less_eq @ int @ ( bit1 @ SV183 ) @ ( bit1 @ SY477 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[958]) ).
thf(1084,plain,
! [SV184: $i] :
( ( ~ ( zprime @ ( ti @ int @ SV184 ) )
| ( zprime @ SV184 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[959]) ).
thf(1085,plain,
! [SV185: $i] :
( ( ~ ( zprime @ SV185 )
| ( zprime @ ( ti @ int @ SV185 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[960]) ).
thf(1086,plain,
! [SV186: $i] :
( ( ~ ( ord_less_eq @ int @ pls @ ( bit1 @ SV186 ) )
| ( ord_less_eq @ int @ pls @ SV186 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[961]) ).
thf(1087,plain,
! [SV187: $i] :
( ( ~ ( ord_less_eq @ int @ pls @ SV187 )
| ( ord_less_eq @ int @ pls @ ( bit1 @ SV187 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[962]) ).
thf(1088,plain,
! [SV188: $i] :
( ( ! [SY478: $i] :
( ~ ( ord_less @ int @ ( bit0 @ SV188 ) @ ( bit1 @ SY478 ) )
| ( ord_less_eq @ int @ SV188 @ SY478 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[963]) ).
thf(1089,plain,
! [SV189: $i] :
( ( ! [SY479: $i] :
( ~ ( ord_less_eq @ int @ SV189 @ SY479 )
| ( ord_less @ int @ ( bit0 @ SV189 ) @ ( bit1 @ SY479 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[964]) ).
thf(1090,plain,
! [SV190: $i] :
( ( ! [SY480: $i] :
( ~ ( ord_less @ int @ SV190 @ SY480 )
| ( ord_less_eq @ int @ ( plus_plus @ int @ SV190 @ ( one_one @ int ) ) @ SY480 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[965]) ).
thf(1091,plain,
! [SV191: $i] :
( ( ! [SY481: $i] :
( ~ ( ord_less_eq @ int @ ( plus_plus @ int @ SV191 @ ( one_one @ int ) ) @ SY481 )
| ( ord_less @ int @ SV191 @ SY481 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[966]) ).
thf(1092,plain,
! [SV72: $i] :
( ( ! [SY372: $i,SY373: $i] :
( ~ ( linorder @ SY373 )
| ~ ( number @ SY373 )
| ~ ( ord_less_eq @ SY373 @ ( ti @ SY373 @ SV72 ) @ SY372 )
| ( ord_less_eq @ SY373 @ SV72 @ SY372 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[967]) ).
thf(1093,plain,
! [SV72: $i] :
( ( ! [SY374: $i,SY375: $i] :
( ~ ( linorder @ SY375 )
| ~ ( number @ SY375 )
| ~ ( ord_less_eq @ SY375 @ SV72 @ SY374 )
| ( ord_less_eq @ SY375 @ ( ti @ SY375 @ SV72 ) @ SY374 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[968]) ).
thf(1094,plain,
! [SV73: $i] :
( ( ! [SY376: $i,SY377: $i] :
( ~ ( linorder @ SY377 )
| ~ ( number @ SY377 )
| ~ ( ord_less @ SY377 @ SV73 @ ( ti @ SY377 @ SY376 ) )
| ( ord_less @ SY377 @ SV73 @ SY376 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[969]) ).
thf(1095,plain,
! [SV73: $i] :
( ( ! [SY378: $i,SY379: $i] :
( ~ ( linorder @ SY379 )
| ~ ( number @ SY379 )
| ~ ( ord_less @ SY379 @ SV73 @ SY378 )
| ( ord_less @ SY379 @ SV73 @ ( ti @ SY379 @ SY378 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[970]) ).
thf(1096,plain,
! [SV192: $i] :
( ( ! [SY482: $i] :
( ~ ( ord_less_eq @ int @ ( bit1 @ SV192 ) @ ( bit1 @ SY482 ) )
| ( ord_less_eq @ int @ SV192 @ SY482 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[971]) ).
thf(1097,plain,
! [SV193: $i] :
( ( ! [SY483: $i] :
( ~ ( ord_less_eq @ int @ SV193 @ SY483 )
| ( ord_less_eq @ int @ ( bit1 @ SV193 ) @ ( bit1 @ SY483 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[972]) ).
thf(1098,plain,
! [SV194: $i] :
( ( ! [SY484: $i] :
( ~ ( ord_less @ int @ SV194 @ SY484 )
| ( ord_less_eq @ int @ ( bit1 @ SV194 ) @ ( bit0 @ SY484 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[973]) ).
thf(1099,plain,
! [SV195: $i] :
( ( ! [SY485: $i] :
( ~ ( ord_less_eq @ int @ ( bit1 @ SV195 ) @ ( bit0 @ SY485 ) )
| ( ord_less @ int @ SV195 @ SY485 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[974]) ).
thf(1100,plain,
! [SV196: $i] :
( ( ! [SY486: $i] :
( ~ ( ord_less @ int @ SV196 @ ( plus_plus @ int @ SY486 @ ( one_one @ int ) ) )
| ( ord_less_eq @ int @ SV196 @ SY486 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[975]) ).
thf(1101,plain,
! [SV197: $i] :
( ( ! [SY487: $i] :
( ~ ( ord_less_eq @ int @ SV197 @ SY487 )
| ( ord_less @ int @ SV197 @ ( plus_plus @ int @ SY487 @ ( one_one @ int ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[976]) ).
thf(1102,plain,
! [SV74: $i] :
( ( ( linorder @ SV74 )
= $false )
| ( ( ~ ( number @ SV74 ) )
= $true )
| ( ( ~ ( ~ ! [SY380: $i,SY381: $i] :
( ~ ( ord_less_eq @ SV74 @ ( number_number_of @ SV74 @ SY380 ) @ ( number_number_of @ SV74 @ SY381 ) )
| ~ ( ord_less @ SV74 @ ( number_number_of @ SV74 @ SY381 ) @ ( number_number_of @ SV74 @ SY380 ) ) )
| ~ ! [SY382: $i,SY383: $i] :
( ( ord_less @ SV74 @ ( number_number_of @ SV74 @ SY383 ) @ ( number_number_of @ SV74 @ SY382 ) )
| ( ord_less_eq @ SV74 @ ( number_number_of @ SV74 @ SY382 ) @ ( number_number_of @ SV74 @ SY383 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[977]) ).
thf(1103,plain,
! [SV75: $i] :
( ( ( ~ ! [SY384: $i,SY385: $i] :
( ~ ( ord_less @ SV75 @ ( zero_zero @ SV75 ) @ ( plus_plus @ SV75 @ ( power_power @ SV75 @ SY384 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV75 @ SY385 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
| ( ( ti @ SV75 @ SY384 )
!= ( zero_zero @ SV75 ) )
| ( ( ti @ SV75 @ SY385 )
!= ( zero_zero @ SV75 ) ) )
| ~ ~ ( ~ ! [SY386: $i] :
( ( ( ti @ SV75 @ SY386 )
= ( zero_zero @ SV75 ) )
| ! [SY387: $i] : ( ord_less @ SV75 @ ( zero_zero @ SV75 ) @ ( plus_plus @ SV75 @ ( power_power @ SV75 @ SY386 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV75 @ SY387 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
| ~ ! [SY388: $i,SY389: $i] :
( ( ( ti @ SV75 @ SY389 )
= ( zero_zero @ SV75 ) )
| ( ord_less @ SV75 @ ( zero_zero @ SV75 ) @ ( plus_plus @ SV75 @ ( power_power @ SV75 @ SY388 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV75 @ SY389 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) ) )
= $false )
| ( ( linordered_idom @ SV75 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[978]) ).
thf(1104,plain,
! [SV76: $i] :
( ( ( linordered_idom @ SV76 )
= $false )
| ( ( ~ ( number_ring @ SV76 ) )
= $true )
| ( ( ~ ( ~ ! [SY390: $i] :
( ~ ( ord_less_eq @ SV76 @ ( one_one @ SV76 ) @ ( number_number_of @ SV76 @ SY390 ) )
| ( ord_less_eq @ int @ ( bit1 @ pls ) @ SY390 ) )
| ~ ! [SY391: $i] :
( ~ ( ord_less_eq @ int @ ( bit1 @ pls ) @ SY391 )
| ( ord_less_eq @ SV76 @ ( one_one @ SV76 ) @ ( number_number_of @ SV76 @ SY391 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[979]) ).
thf(1105,plain,
! [SV77: $i] :
( ( ( ~ ! [SY392: $i,SY393: $i] :
( ( ( ti @ SV77 @ SY392 )
!= ( zero_zero @ SV77 ) )
| ( ( ti @ SV77 @ SY393 )
!= ( zero_zero @ SV77 ) )
| ( ( plus_plus @ SV77 @ ( power_power @ SV77 @ SY392 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV77 @ SY393 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV77 ) ) )
| ~ ~ ( ~ ! [SY394: $i] :
( ! [SY395: $i] :
( ( plus_plus @ SV77 @ ( power_power @ SV77 @ SY394 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV77 @ SY395 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV77 ) )
| ( ( ti @ SV77 @ SY394 )
= ( zero_zero @ SV77 ) ) )
| ~ ! [SY396: $i,SY397: $i] :
( ( ( plus_plus @ SV77 @ ( power_power @ SV77 @ SY396 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV77 @ SY397 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV77 ) )
| ( ( ti @ SV77 @ SY397 )
= ( zero_zero @ SV77 ) ) ) ) )
= $false )
| ( ( linordered_idom @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[980]) ).
thf(1106,plain,
! [SV78: $i] :
( ( ( ~ ! [SY398: $i] :
( ( ( power_power @ SV78 @ SY398 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= ( zero_zero @ SV78 ) )
| ( ( ti @ SV78 @ SY398 )
= ( zero_zero @ SV78 ) ) )
| ~ ! [SY399: $i] :
( ( ( ti @ SV78 @ SY399 )
!= ( zero_zero @ SV78 ) )
| ( ( power_power @ SV78 @ SY399 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SV78 ) ) ) )
= $false )
| ( ( ring_11004092258visors @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[981]) ).
thf(1107,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ord_less @ int @ SX0 @ SX1 )
| ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ nat @ ( number_number_of @ nat @ SX0 ) @ ( number_number_of @ nat @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ pls @ SX1 )
| ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ nat @ ( number_number_of @ nat @ SX0 ) @ ( number_number_of @ nat @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[982]) ).
thf(1108,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ nat @ ( number_number_of @ nat @ SX0 ) @ ( number_number_of @ nat @ SX1 ) )
| ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ int @ pls @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ nat @ ( number_number_of @ nat @ SX0 ) @ ( number_number_of @ nat @ SX1 ) )
| ( ord_less @ int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[983]) ).
thf(1109,plain,
! [SV79: $i] :
( ( ( ~ ! [SY400: $i] :
( ( ( ti @ SV79 @ SY400 )
= ( zero_zero @ SV79 ) )
| ( ord_less @ SV79 @ ( zero_zero @ SV79 ) @ ( power_power @ SV79 @ SY400 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
| ~ ! [SY401: $i] :
( ~ ( ord_less @ SV79 @ ( zero_zero @ SV79 ) @ ( power_power @ SV79 @ SY401 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ( ( ti @ SV79 @ SY401 )
!= ( zero_zero @ SV79 ) ) ) )
= $false )
| ( ( linordered_idom @ SV79 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[984]) ).
thf(1110,plain,
! [SV80: $i] :
( ( ( number_ring @ SV80 )
= $false )
| ( ( ~ ( ring_char_0 @ SV80 ) )
= $true )
| ( ( ~ ( ~ ! [SY402: $i,SY403: $i] :
( ( ( number_number_of @ SV80 @ SY402 )
!= ( number_number_of @ SV80 @ SY403 ) )
| ( SY402 = SY403 ) )
| ~ ! [SY404: $i,SY405: $i] :
( ( SY404 != SY405 )
| ( ( number_number_of @ SV80 @ SY404 )
= ( number_number_of @ SV80 @ SY405 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[985]) ).
thf(1111,plain,
! [SV198: $i] :
( ( ~ ( ord_less_eq @ int @ pls @ ( bit0 @ SV198 ) )
| ( ord_less_eq @ int @ pls @ SV198 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[986]) ).
thf(1112,plain,
! [SV199: $i] :
( ( ~ ( ord_less_eq @ int @ pls @ SV199 )
| ( ord_less_eq @ int @ pls @ ( bit0 @ SV199 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[987]) ).
thf(1113,plain,
! [SV81: $i] :
( ( ( linordered_idom @ SV81 )
= $false )
| ( ( ~ ( number_ring @ SV81 ) )
= $true )
| ( ( ~ ( ~ ! [SY406: $i] :
( ~ ( ord_less_eq @ SV81 @ ( number_number_of @ SV81 @ SY406 ) @ ( zero_zero @ SV81 ) )
| ( ord_less_eq @ int @ SY406 @ pls ) )
| ~ ! [SY407: $i] :
( ~ ( ord_less_eq @ int @ SY407 @ pls )
| ( ord_less_eq @ SV81 @ ( number_number_of @ SV81 @ SY407 ) @ ( zero_zero @ SV81 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[988]) ).
thf(1114,plain,
! [SV200: $i] :
( ( ! [SY488: $i] :
( ~ ( ord_less @ int @ ( number_number_of @ int @ SV200 ) @ ( number_number_of @ int @ SY488 ) )
| ( ord_less @ int @ SV200 @ SY488 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[989]) ).
thf(1115,plain,
! [SV201: $i] :
( ( ! [SY489: $i] :
( ~ ( ord_less @ int @ SV201 @ SY489 )
| ( ord_less @ int @ ( number_number_of @ int @ SV201 ) @ ( number_number_of @ int @ SY489 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[990]) ).
thf(1116,plain,
! [SV202: $i] :
( ( ! [SY490: $i] :
( ~ ( ord_less_eq @ int @ ( bit0 @ SV202 ) @ ( bit0 @ SY490 ) )
| ( ord_less_eq @ int @ SV202 @ SY490 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[991]) ).
thf(1117,plain,
! [SV203: $i] :
( ( ! [SY491: $i] :
( ~ ( ord_less_eq @ int @ SV203 @ SY491 )
| ( ord_less_eq @ int @ ( bit0 @ SV203 ) @ ( bit0 @ SY491 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[992]) ).
thf(1118,plain,
! [SV82: $i] :
( ( ( ~ ! [SY408: $i,SY409: $i] :
( ( ( ti @ SV82 @ SY408 )
!= ( zero_zero @ SV82 ) )
| ( ( ti @ SV82 @ SY409 )
!= ( zero_zero @ SV82 ) )
| ( ( plus_plus @ SV82 @ ( times_times @ SV82 @ SY408 @ SY408 ) @ ( times_times @ SV82 @ SY409 @ SY409 ) )
= ( zero_zero @ SV82 ) ) )
| ~ ~ ( ~ ! [SY410: $i] :
( ! [SY411: $i] :
( ( plus_plus @ SV82 @ ( times_times @ SV82 @ SY410 @ SY410 ) @ ( times_times @ SV82 @ SY411 @ SY411 ) )
!= ( zero_zero @ SV82 ) )
| ( ( ti @ SV82 @ SY410 )
= ( zero_zero @ SV82 ) ) )
| ~ ! [SY412: $i,SY413: $i] :
( ( ( plus_plus @ SV82 @ ( times_times @ SV82 @ SY412 @ SY412 ) @ ( times_times @ SV82 @ SY413 @ SY413 ) )
!= ( zero_zero @ SV82 ) )
| ( ( ti @ SV82 @ SY413 )
= ( zero_zero @ SV82 ) ) ) ) )
= $false )
| ( ( linord581940658strict @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[993]) ).
thf(1119,plain,
! [SV83: $i] :
( ( ! [SY414: $i,SY415: $i] :
( ~ ( linordered_ring @ SY415 )
| ~ ( ord_less_eq @ SY415 @ SV83 @ ( ti @ SY415 @ SY414 ) )
| ( ord_less_eq @ SY415 @ SV83 @ SY414 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[994]) ).
thf(1120,plain,
! [SV83: $i] :
( ( ! [SY416: $i,SY417: $i] :
( ~ ( linordered_ring @ SY417 )
| ~ ( ord_less_eq @ SY417 @ SV83 @ SY416 )
| ( ord_less_eq @ SY417 @ SV83 @ ( ti @ SY417 @ SY416 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[995]) ).
thf(1121,plain,
! [SV84: $i] :
( ( ( linordered_idom @ SV84 )
= $false )
| ( ( ~ ( number_ring @ SV84 ) )
= $true )
| ( ( ~ ( ~ ! [SY418: $i] :
( ~ ( ord_less_eq @ SV84 @ ( number_number_of @ SV84 @ SY418 ) @ ( one_one @ SV84 ) )
| ( ord_less_eq @ int @ SY418 @ ( bit1 @ pls ) ) )
| ~ ! [SY419: $i] :
( ~ ( ord_less_eq @ int @ SY419 @ ( bit1 @ pls ) )
| ( ord_less_eq @ SV84 @ ( number_number_of @ SV84 @ SY419 ) @ ( one_one @ SV84 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[996]) ).
thf(1122,plain,
! [SV85: $i] :
( ( ( linordered_idom @ SV85 )
= $false )
| ( ( ~ ( number_ring @ SV85 ) )
= $true )
| ( ( ~ ( ~ ! [SY420: $i] :
( ~ ( ord_less_eq @ SV85 @ ( zero_zero @ SV85 ) @ ( number_number_of @ SV85 @ SY420 ) )
| ( ord_less_eq @ int @ pls @ SY420 ) )
| ~ ! [SY421: $i] :
( ~ ( ord_less_eq @ int @ pls @ SY421 )
| ( ord_less_eq @ SV85 @ ( zero_zero @ SV85 ) @ ( number_number_of @ SV85 @ SY421 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[997]) ).
thf(1123,plain,
! [SV204: $i] :
( ( ~ ( ord_less @ int @ SV204 @ pls )
| ( ord_less_eq @ int @ ( bit1 @ SV204 ) @ pls ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[998]) ).
thf(1124,plain,
! [SV205: $i] :
( ( ~ ( ord_less_eq @ int @ ( bit1 @ SV205 ) @ pls )
| ( ord_less @ int @ SV205 @ pls ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[999]) ).
thf(1125,plain,
! [SV86: $i] :
( ( ( ~ ! [SY422: $i,SY423: $i] :
( ( ( ti @ SV86 @ SY422 )
!= ( zero_zero @ SV86 ) )
| ( ( ti @ SV86 @ SY423 )
!= ( zero_zero @ SV86 ) )
| ( ord_less_eq @ SV86 @ ( plus_plus @ SV86 @ ( times_times @ SV86 @ SY422 @ SY422 ) @ ( times_times @ SV86 @ SY423 @ SY423 ) ) @ ( zero_zero @ SV86 ) ) )
| ~ ~ ( ~ ! [SY424: $i] :
( ! [SY425: $i] :
~ ( ord_less_eq @ SV86 @ ( plus_plus @ SV86 @ ( times_times @ SV86 @ SY424 @ SY424 ) @ ( times_times @ SV86 @ SY425 @ SY425 ) ) @ ( zero_zero @ SV86 ) )
| ( ( ti @ SV86 @ SY424 )
= ( zero_zero @ SV86 ) ) )
| ~ ! [SY426: $i,SY427: $i] :
( ~ ( ord_less_eq @ SV86 @ ( plus_plus @ SV86 @ ( times_times @ SV86 @ SY426 @ SY426 ) @ ( times_times @ SV86 @ SY427 @ SY427 ) ) @ ( zero_zero @ SV86 ) )
| ( ( ti @ SV86 @ SY427 )
= ( zero_zero @ SV86 ) ) ) ) )
= $false )
| ( ( linord581940658strict @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1000]) ).
thf(1126,plain,
! [SV206: $i] :
( ( ! [SY492: $i] :
( ~ ( ord_less @ int @ ( bit0 @ SV206 ) @ ( bit1 @ SY492 ) )
| ( ord_less_eq @ int @ SV206 @ SY492 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1001]) ).
thf(1127,plain,
! [SV207: $i] :
( ( ! [SY493: $i] :
( ~ ( ord_less_eq @ int @ SV207 @ SY493 )
| ( ord_less @ int @ ( bit0 @ SV207 ) @ ( bit1 @ SY493 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1002]) ).
thf(1128,plain,
! [SV208: $i] :
( ( ! [SY494: $i] :
( ~ ( ord_less_eq @ int @ ( bit0 @ SV208 ) @ ( bit0 @ SY494 ) )
| ( ord_less_eq @ int @ SV208 @ SY494 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1003]) ).
thf(1129,plain,
! [SV209: $i] :
( ( ! [SY495: $i] :
( ~ ( ord_less_eq @ int @ SV209 @ SY495 )
| ( ord_less_eq @ int @ ( bit0 @ SV209 ) @ ( bit0 @ SY495 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1004]) ).
thf(1130,plain,
! [SV210: $i] :
( ( ( ( zero_zero @ nat )
!= ( number_number_of @ nat @ SV210 ) )
| ( ord_less_eq @ int @ SV210 @ pls ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1005]) ).
thf(1131,plain,
! [SV211: $i] :
( ( ~ ( ord_less_eq @ int @ SV211 @ pls )
| ( ( zero_zero @ nat )
= ( number_number_of @ nat @ SV211 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1006]) ).
thf(1132,plain,
! [SV212: $i] :
( ( ~ ( ord_less @ int @ pls @ ( bit1 @ SV212 ) )
| ( ord_less_eq @ int @ pls @ SV212 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1007]) ).
thf(1133,plain,
! [SV213: $i] :
( ( ~ ( ord_less_eq @ int @ pls @ SV213 )
| ( ord_less @ int @ pls @ ( bit1 @ SV213 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1008]) ).
thf(1134,plain,
! [SV87: $i,SV6: $i,SV123: $i] :
( ( ( linordered_ring @ SV123 )
= $false )
| ( ( ( plus_plus @ SV123 @ ( ti @ SV123 @ SV6 ) @ SV87 )
= ( plus_plus @ SV123 @ SV6 @ SV87 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1009]) ).
thf(1135,plain,
! [SV88: $i,SV7: $i,SV124: $i] :
( ( ( linordered_ring @ SV124 )
= $false )
| ( ( ( plus_plus @ SV124 @ SV7 @ ( ti @ SV124 @ SV88 ) )
= ( plus_plus @ SV124 @ SV7 @ SV88 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1010]) ).
thf(1136,plain,
! [SV89: $i,SV8: $i,SV125: $i] :
( ( ( linordered_ring @ SV125 )
= $false )
| ( ( ( ti @ SV125 @ ( plus_plus @ SV125 @ SV8 @ SV89 ) )
= ( plus_plus @ SV125 @ SV8 @ SV89 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1011]) ).
thf(1137,plain,
! [SV92: $i,SV13: $i,SV126: $i] :
( ( ( semiring_1 @ SV126 )
= $false )
| ( ( ( power_power @ SV126 @ ( ti @ SV126 @ SV13 ) @ SV92 )
= ( power_power @ SV126 @ SV13 @ SV92 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1014]) ).
thf(1138,plain,
! [SV93: $i,SV14: $i,SV127: $i] :
( ( ( semiring_1 @ SV127 )
= $false )
| ( ( ( power_power @ SV127 @ SV14 @ ( ti @ nat @ SV93 ) )
= ( power_power @ SV127 @ SV14 @ SV93 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1015]) ).
thf(1139,plain,
! [SV94: $i,SV15: $i,SV128: $i] :
( ( ( semiring_1 @ SV128 )
= $false )
| ( ( ( ti @ SV128 @ ( power_power @ SV128 @ SV15 @ SV94 ) )
= ( power_power @ SV128 @ SV15 @ SV94 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1016]) ).
thf(1140,plain,
! [SV214: $i,SV147: $i,SV16: $i] :
( ( ( ~ ( ord_less @ SV16 @ ( plus_plus @ SV16 @ ( power_power @ SV16 @ SV147 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV16 @ SV214 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( zero_zero @ SV16 ) ) )
= $true )
| ( ( linordered_idom @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1017]) ).
thf(1141,plain,
! [SV148: $i,SV17: $i] :
( ( ( ord_less @ SV17 @ ( power_power @ SV17 @ SV148 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( zero_zero @ SV17 ) )
= $false )
| ( ( linordered_idom @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1018]) ).
thf(1142,plain,
! [SV28: $i,SV130: $i,SV99: $i] :
( ( ( ord_less_eq @ int @ SV99 @ SV130 )
= $false )
| ( ( ~ ( ord_less_eq @ int @ SV130 @ SV28 )
| ( ord_less_eq @ int @ SV99 @ SV28 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1021]) ).
thf(1143,plain,
! [SV29: $i,SV100: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV100 @ SV29 ) )
= $true )
| ( ( SV29 = SV100 )
= $true )
| ( ( ord_less_eq @ int @ SV29 @ SV100 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1022]) ).
thf(1144,plain,
! [SV31: $i,SV132: $i,SV102: $i] :
( ( ( ord_less_eq @ int @ SV102 @ SV132 )
= $false )
| ( ( ord_less_eq @ int @ ( plus_plus @ int @ SV31 @ SV102 ) @ ( plus_plus @ int @ SV31 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1023]) ).
thf(1145,plain,
! [SV215: $i,SV151: $i,SV32: $i] :
( ( ( ! [SY496: $i] :
( ( times_times @ SV32 @ ( number_number_of @ SV32 @ SV151 ) @ ( times_times @ SV32 @ ( number_number_of @ SV32 @ SV215 ) @ SY496 ) )
= ( times_times @ SV32 @ ( number_number_of @ SV32 @ ( times_times @ int @ SV151 @ SV215 ) ) @ SY496 ) ) )
= $true )
| ( ( number_ring @ SV32 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1024]) ).
thf(1146,plain,
! [SV216: $i,SV152: $i,SV33: $i] :
( ( ( ( times_times @ SV33 @ ( number_number_of @ SV33 @ SV152 ) @ ( number_number_of @ SV33 @ SV216 ) )
= ( number_number_of @ SV33 @ ( times_times @ int @ SV152 @ SV216 ) ) )
= $true )
| ( ( number_ring @ SV33 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1025]) ).
thf(1147,plain,
! [SV217: $i,SV153: $i,SV34: $i] :
( ( ( ( number_number_of @ SV34 @ ( times_times @ int @ SV153 @ SV217 ) )
= ( times_times @ SV34 @ ( number_number_of @ SV34 @ SV153 ) @ ( number_number_of @ SV34 @ SV217 ) ) )
= $true )
| ( ( number_ring @ SV34 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1026]) ).
thf(1148,plain,
! [SV103: $i,SV35: $i,SV154: $i,SV133: $i] :
( ( ( ~ ( ord_less @ int @ SV133 @ SV154 ) )
= $true )
| ( ( ~ ( ord_less_eq @ int @ SV35 @ SV103 )
| ( ord_less @ int @ ( plus_plus @ int @ SV133 @ SV35 ) @ ( plus_plus @ int @ SV154 @ SV103 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1027]) ).
thf(1149,plain,
! [SV44: $i,SV155: $i,SV218: $i] :
( ( ( ~ ( ord_less_eq @ int @ pls @ SV218 )
| ~ ( ord_less_eq @ int @ pls @ SV155 )
| ( ( plus_plus @ SV44 @ ( number_number_of @ SV44 @ SV218 ) @ ( number_number_of @ SV44 @ SV155 ) )
= ( number_number_of @ SV44 @ ( plus_plus @ int @ SV218 @ SV155 ) ) ) )
= $true )
| ( ( number_semiring @ SV44 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1029]) ).
thf(1150,plain,
! [SV113: $i,SV50: $i,SV138: $i] :
( ( ( ~ ( number @ SV138 ) )
= $true )
| ( ( ~ ( semiring @ SV138 ) )
= $true )
| ( ( ( plus_plus @ SV138 @ ( ti @ SV138 @ SV50 ) @ SV113 )
= ( plus_plus @ SV138 @ SV50 @ SV113 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1031]) ).
thf(1151,plain,
! [SV114: $i,SV51: $i,SV139: $i] :
( ( ( ~ ( number @ SV139 ) )
= $true )
| ( ( ~ ( semiring @ SV139 ) )
= $true )
| ( ( ( plus_plus @ SV139 @ SV51 @ ( ti @ SV139 @ SV114 ) )
= ( plus_plus @ SV139 @ SV51 @ SV114 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1032]) ).
thf(1152,plain,
! [SV115: $i,SV52: $i,SV140: $i] :
( ( ( ~ ( number @ SV140 ) )
= $true )
| ( ( ~ ( semiring @ SV140 ) )
= $true )
| ( ( ( ti @ SV140 @ ( plus_plus @ SV140 @ SV52 @ SV115 ) )
= ( plus_plus @ SV140 @ SV52 @ SV115 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1033]) ).
thf(1153,plain,
! [SV116: $i,SV53: $i,SV141: $i] :
( ( ( ~ ( number @ SV141 ) )
= $true )
| ( ( ~ ( semiring @ SV141 ) )
= $true )
| ( ( ( times_times @ SV141 @ ( ti @ SV141 @ SV53 ) @ SV116 )
= ( times_times @ SV141 @ SV53 @ SV116 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1034]) ).
thf(1154,plain,
! [SV117: $i,SV54: $i,SV142: $i] :
( ( ( ~ ( number @ SV142 ) )
= $true )
| ( ( ~ ( semiring @ SV142 ) )
= $true )
| ( ( ( times_times @ SV142 @ SV54 @ ( ti @ SV142 @ SV117 ) )
= ( times_times @ SV142 @ SV54 @ SV117 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1035]) ).
thf(1155,plain,
! [SV118: $i,SV55: $i,SV143: $i] :
( ( ( ~ ( number @ SV143 ) )
= $true )
| ( ( ~ ( semiring @ SV143 ) )
= $true )
| ( ( ( ti @ SV143 @ ( times_times @ SV143 @ SV55 @ SV118 ) )
= ( times_times @ SV143 @ SV55 @ SV118 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1036]) ).
thf(1156,plain,
! [SV119: $i,SV56: $i,SV144: $i] :
( ( ( linordered_ring @ SV144 )
= $false )
| ( ( ( times_times @ SV144 @ ( ti @ SV144 @ SV56 ) @ SV119 )
= ( times_times @ SV144 @ SV56 @ SV119 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1037]) ).
thf(1157,plain,
! [SV120: $i,SV57: $i,SV145: $i] :
( ( ( linordered_ring @ SV145 )
= $false )
| ( ( ( times_times @ SV145 @ SV57 @ ( ti @ SV145 @ SV120 ) )
= ( times_times @ SV145 @ SV57 @ SV120 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1038]) ).
thf(1158,plain,
! [SV121: $i,SV58: $i,SV146: $i] :
( ( ( linordered_ring @ SV146 )
= $false )
| ( ( ( ti @ SV146 @ ( times_times @ SV146 @ SV58 @ SV121 ) )
= ( times_times @ SV146 @ SV58 @ SV121 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1039]) ).
thf(1159,plain,
! [SV60: $i,SV156: $i,SV219: $i] :
( ( ( ~ ( ord_less_eq @ int @ pls @ SV219 )
| ~ ( ord_less_eq @ int @ pls @ SV156 )
| ( ( times_times @ SV60 @ ( number_number_of @ SV60 @ SV219 ) @ ( number_number_of @ SV60 @ SV156 ) )
= ( number_number_of @ SV60 @ ( times_times @ int @ SV219 @ SV156 ) ) ) )
= $true )
| ( ( number_semiring @ SV60 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1040]) ).
thf(1160,plain,
! [SV220: $i,SV157: $i,SV61: $i] :
( ( ( ord_less_eq @ SV61 @ ( zero_zero @ SV61 ) @ ( plus_plus @ SV61 @ ( times_times @ SV61 @ SV157 @ SV157 ) @ ( times_times @ SV61 @ SV220 @ SV220 ) ) )
= $true )
| ( ( linordered_ring @ SV61 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1041]) ).
thf(1161,plain,
! [SV62: $i] :
( ( ( semiring @ SV62 )
= $false )
| ( ( number @ SV62 )
= $false )
| ( ( ! [SY337: $i,SY338: $i,SY339: $i] :
( ( times_times @ SV62 @ ( plus_plus @ SV62 @ SY337 @ SY338 ) @ ( number_number_of @ SV62 @ SY339 ) )
= ( plus_plus @ SV62 @ ( times_times @ SV62 @ SY337 @ ( number_number_of @ SV62 @ SY339 ) ) @ ( times_times @ SV62 @ SY338 @ ( number_number_of @ SV62 @ SY339 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1042]) ).
thf(1162,plain,
! [SV63: $i] :
( ( ( semiring @ SV63 )
= $false )
| ( ( number @ SV63 )
= $false )
| ( ( ! [SY340: $i,SY341: $i,SY342: $i] :
( ( times_times @ SV63 @ ( number_number_of @ SV63 @ SY340 ) @ ( plus_plus @ SV63 @ SY341 @ SY342 ) )
= ( plus_plus @ SV63 @ ( times_times @ SV63 @ ( number_number_of @ SV63 @ SY340 ) @ SY341 ) @ ( times_times @ SV63 @ ( number_number_of @ SV63 @ SY340 ) @ SY342 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1043]) ).
thf(1163,plain,
! [SV158: $i] :
( ( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ ( number_number_of @ nat @ SV158 ) ) )
= $true )
| ( ( ord_less @ int @ pls @ SV158 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1044]) ).
thf(1164,plain,
! [SV159: $i] :
( ( ( ~ ( ord_less @ int @ pls @ SV159 ) )
= $true )
| ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( number_number_of @ nat @ SV159 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1045]) ).
thf(1165,plain,
! [SV221: $i,SV160: $i] :
( ( ( SV160 = SV221 )
| ~ ( ord_less_eq @ int @ SV160 @ SV221 )
| ( ord_less @ int @ SV160 @ SV221 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1046]) ).
thf(1166,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1047]) ).
thf(1167,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1047]) ).
thf(1168,plain,
! [SV161: $i] :
( ( ( ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV161 ) )
= $true )
| ( ( ord_less_eq @ int @ ( one_one @ int ) @ SV161 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1048]) ).
thf(1169,plain,
! [SV162: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( one_one @ int ) @ SV162 ) )
= $true )
| ( ( ord_less @ int @ ( zero_zero @ int ) @ SV162 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1049]) ).
thf(1170,plain,
! [SV222: $i,SV163: $i] :
( ( ~ ( ord_less_eq @ int @ ( bit0 @ SV163 ) @ ( bit1 @ SV222 ) )
| ( ord_less_eq @ int @ SV163 @ SV222 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1050]) ).
thf(1171,plain,
! [SV223: $i,SV164: $i] :
( ( ~ ( ord_less_eq @ int @ SV164 @ SV223 )
| ( ord_less_eq @ int @ ( bit0 @ SV164 ) @ ( bit1 @ SV223 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1051]) ).
thf(1172,plain,
! [SV224: $i,SV165: $i] :
( ( ~ ( ord_less_eq @ int @ ( bit0 @ SV165 ) @ ( bit1 @ SV224 ) )
| ( ord_less_eq @ int @ SV165 @ SV224 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1052]) ).
thf(1173,plain,
! [SV225: $i,SV166: $i] :
( ( ~ ( ord_less_eq @ int @ SV166 @ SV225 )
| ( ord_less_eq @ int @ ( bit0 @ SV166 ) @ ( bit1 @ SV225 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1053]) ).
thf(1174,plain,
! [SV65: $i] :
( ( ( number_ring @ SV65 )
= $false )
| ( ( linordered_idom @ SV65 )
= $false )
| ( ( ~ ( ~ ! [SY344: $i,SY345: $i] :
( ~ ( ord_less_eq @ SV65 @ ( number_number_of @ SV65 @ SY344 ) @ ( number_number_of @ SV65 @ SY345 ) )
| ( ord_less_eq @ int @ SY344 @ SY345 ) )
| ~ ! [SY346: $i,SY347: $i] :
( ~ ( ord_less_eq @ int @ SY346 @ SY347 )
| ( ord_less_eq @ SV65 @ ( number_number_of @ SV65 @ SY346 ) @ ( number_number_of @ SV65 @ SY347 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1054]) ).
thf(1175,plain,
! [SV167: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( bit0 @ SV167 ) @ pls ) )
= $true )
| ( ( ord_less_eq @ int @ SV167 @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1055]) ).
thf(1176,plain,
! [SV168: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV168 @ pls ) )
= $true )
| ( ( ord_less_eq @ int @ ( bit0 @ SV168 ) @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1056]) ).
thf(1177,plain,
! [SV169: $i,SV226: $i] :
( ( ~ ( ord_less @ int @ SV226 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV226 ) @ ( number_number_of @ nat @ SV169 ) )
= ( number_number_of @ nat @ SV169 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1057]) ).
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 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1058]) ).
thf(1179,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)],[1058]) ).
thf(1180,plain,
! [SV227: $i,SV66: $i] :
( ( ! [SY497: $i] :
( ~ ( linordered_idom @ SY497 )
| ~ ( ord_less @ SY497 @ SV66 @ ( ti @ SY497 @ SV227 ) )
| ( ord_less @ SY497 @ SV66 @ SV227 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1059]) ).
thf(1181,plain,
! [SV228: $i,SV66: $i] :
( ( ! [SY498: $i] :
( ~ ( linordered_idom @ SY498 )
| ~ ( ord_less @ SY498 @ SV66 @ SV228 )
| ( ord_less @ SY498 @ SV66 @ ( ti @ SY498 @ SV228 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1060]) ).
thf(1182,plain,
! [SV229: $i,SV67: $i] :
( ( ! [SY499: $i] :
( ~ ( linordered_idom @ SY499 )
| ~ ( ord_less @ SY499 @ ( ti @ SY499 @ SV67 ) @ SV229 )
| ( ord_less @ SY499 @ SV67 @ SV229 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1061]) ).
thf(1183,plain,
! [SV230: $i,SV67: $i] :
( ( ! [SY500: $i] :
( ~ ( linordered_idom @ SY500 )
| ~ ( ord_less @ SY500 @ SV67 @ SV230 )
| ( ord_less @ SY500 @ ( ti @ SY500 @ SV67 ) @ SV230 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1062]) ).
thf(1184,plain,
! [SV231: $i,SV68: $i] :
( ( ! [SY501: $i] :
( ~ ( linordered_ring @ SY501 )
| ~ ( ord_less_eq @ SY501 @ ( ti @ SY501 @ SV68 ) @ SV231 )
| ( ord_less_eq @ SY501 @ SV68 @ SV231 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1063]) ).
thf(1185,plain,
! [SV232: $i,SV68: $i] :
( ( ! [SY502: $i] :
( ~ ( linordered_ring @ SY502 )
| ~ ( ord_less_eq @ SY502 @ SV68 @ SV232 )
| ( ord_less_eq @ SY502 @ ( ti @ SY502 @ SV68 ) @ SV232 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1064]) ).
thf(1186,plain,
! [SV233: $i,SV170: $i] :
( ( ( ( bit0 @ SV170 )
!= ( bit0 @ SV233 ) )
| ( SV170 = SV233 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1065]) ).
thf(1187,plain,
! [SV234: $i,SV171: $i] :
( ( ( SV171 != SV234 )
| ( ( bit0 @ SV171 )
= ( bit0 @ SV234 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1066]) ).
thf(1188,plain,
! [SV235: $i,SV69: $i] :
( ( ! [SY503: $i] :
( ~ ( linorder @ SY503 )
| ~ ( number @ SY503 )
| ~ ( ord_less_eq @ SY503 @ SV69 @ ( ti @ SY503 @ SV235 ) )
| ( ord_less_eq @ SY503 @ SV69 @ SV235 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1067]) ).
thf(1189,plain,
! [SV236: $i,SV69: $i] :
( ( ! [SY504: $i] :
( ~ ( linorder @ SY504 )
| ~ ( number @ SY504 )
| ~ ( ord_less_eq @ SY504 @ SV69 @ SV236 )
| ( ord_less_eq @ SY504 @ SV69 @ ( ti @ SY504 @ SV236 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1068]) ).
thf(1190,plain,
! [SV70: $i] :
( ( ( ~ ! [SY364: $i,SY365: $i] :
( ( ( number_number_of @ SV70 @ SY364 )
!= ( ti @ SV70 @ SY365 ) )
| ( ( ti @ SV70 @ SY365 )
= ( number_number_of @ SV70 @ SY364 ) ) ) )
= $false )
| ( ( number @ SV70 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1069]) ).
thf(1191,plain,
! [SV70: $i] :
( ( ( ~ ! [SY366: $i,SY367: $i] :
( ( ( ti @ SV70 @ SY367 )
!= ( number_number_of @ SV70 @ SY366 ) )
| ( ( number_number_of @ SV70 @ SY366 )
= ( ti @ SV70 @ SY367 ) ) ) )
= $false )
| ( ( number @ SV70 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1069]) ).
thf(1192,plain,
! [SV237: $i,SV172: $i] :
( ( ~ ( ord_less @ int @ SV172 @ SV237 )
| ( ord_less_eq @ int @ ( bit1 @ SV172 ) @ ( bit0 @ SV237 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1070]) ).
thf(1193,plain,
! [SV238: $i,SV173: $i] :
( ( ~ ( ord_less_eq @ int @ ( bit1 @ SV173 ) @ ( bit0 @ SV238 ) )
| ( ord_less @ int @ SV173 @ SV238 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1071]) ).
thf(1194,plain,
! [SV174: $i] :
( ( ( ~ ( twoSqu33214720sum2sq @ ( ti @ int @ SV174 ) ) )
= $true )
| ( ( twoSqu33214720sum2sq @ SV174 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1072]) ).
thf(1195,plain,
! [SV175: $i] :
( ( ( ~ ( twoSqu33214720sum2sq @ SV175 ) )
= $true )
| ( ( twoSqu33214720sum2sq @ ( ti @ int @ SV175 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1073]) ).
thf(1196,plain,
! [SV239: $i,SV176: $i] :
( ( ~ ( ord_less_eq @ int @ ( number_number_of @ int @ SV176 ) @ ( number_number_of @ int @ SV239 ) )
| ( ord_less_eq @ int @ SV176 @ SV239 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1074]) ).
thf(1197,plain,
! [SV240: $i,SV177: $i] :
( ( ~ ( ord_less_eq @ int @ SV177 @ SV240 )
| ( ord_less_eq @ int @ ( number_number_of @ int @ SV177 ) @ ( number_number_of @ int @ SV240 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1075]) ).
thf(1198,plain,
! [SV178: $i] :
( ( ( ( ( number_number_of @ nat @ SV178 )
!= ( zero_zero @ nat ) ) )
= $true )
| ( ( ord_less_eq @ int @ SV178 @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1076]) ).
thf(1199,plain,
! [SV179: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV179 @ pls ) )
= $true )
| ( ( ( number_number_of @ nat @ SV179 )
= ( zero_zero @ nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1077]) ).
thf(1200,plain,
! [SV241: $i,SV71: $i] :
( ( ! [SY505: $i] :
( ~ ( linorder @ SY505 )
| ~ ( number @ SY505 )
| ~ ( ord_less @ SY505 @ ( ti @ SY505 @ SV71 ) @ SV241 )
| ( ord_less @ SY505 @ SV71 @ SV241 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1078]) ).
thf(1201,plain,
! [SV242: $i,SV71: $i] :
( ( ! [SY506: $i] :
( ~ ( linorder @ SY506 )
| ~ ( number @ SY506 )
| ~ ( ord_less @ SY506 @ SV71 @ SV242 )
| ( ord_less @ SY506 @ ( ti @ SY506 @ SV71 ) @ SV242 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1079]) ).
thf(1202,plain,
! [SV243: $i,SV180: $i] :
( ( ( ( bit1 @ SV180 )
!= ( bit1 @ SV243 ) )
| ( SV180 = SV243 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1080]) ).
thf(1203,plain,
! [SV244: $i,SV181: $i] :
( ( ( SV181 != SV244 )
| ( ( bit1 @ SV181 )
= ( bit1 @ SV244 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1081]) ).
thf(1204,plain,
! [SV245: $i,SV182: $i] :
( ( ~ ( ord_less_eq @ int @ ( bit1 @ SV182 ) @ ( bit1 @ SV245 ) )
| ( ord_less_eq @ int @ SV182 @ SV245 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1082]) ).
thf(1205,plain,
! [SV246: $i,SV183: $i] :
( ( ~ ( ord_less_eq @ int @ SV183 @ SV246 )
| ( ord_less_eq @ int @ ( bit1 @ SV183 ) @ ( bit1 @ SV246 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1083]) ).
thf(1206,plain,
! [SV184: $i] :
( ( ( ~ ( zprime @ ( ti @ int @ SV184 ) ) )
= $true )
| ( ( zprime @ SV184 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1084]) ).
thf(1207,plain,
! [SV185: $i] :
( ( ( ~ ( zprime @ SV185 ) )
= $true )
| ( ( zprime @ ( ti @ int @ SV185 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1085]) ).
thf(1208,plain,
! [SV186: $i] :
( ( ( ~ ( ord_less_eq @ int @ pls @ ( bit1 @ SV186 ) ) )
= $true )
| ( ( ord_less_eq @ int @ pls @ SV186 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1086]) ).
thf(1209,plain,
! [SV187: $i] :
( ( ( ~ ( ord_less_eq @ int @ pls @ SV187 ) )
= $true )
| ( ( ord_less_eq @ int @ pls @ ( bit1 @ SV187 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1087]) ).
thf(1210,plain,
! [SV247: $i,SV188: $i] :
( ( ~ ( ord_less @ int @ ( bit0 @ SV188 ) @ ( bit1 @ SV247 ) )
| ( ord_less_eq @ int @ SV188 @ SV247 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1088]) ).
thf(1211,plain,
! [SV248: $i,SV189: $i] :
( ( ~ ( ord_less_eq @ int @ SV189 @ SV248 )
| ( ord_less @ int @ ( bit0 @ SV189 ) @ ( bit1 @ SV248 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1089]) ).
thf(1212,plain,
! [SV249: $i,SV190: $i] :
( ( ~ ( ord_less @ int @ SV190 @ SV249 )
| ( ord_less_eq @ int @ ( plus_plus @ int @ SV190 @ ( one_one @ int ) ) @ SV249 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1090]) ).
thf(1213,plain,
! [SV250: $i,SV191: $i] :
( ( ~ ( ord_less_eq @ int @ ( plus_plus @ int @ SV191 @ ( one_one @ int ) ) @ SV250 )
| ( ord_less @ int @ SV191 @ SV250 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1091]) ).
thf(1214,plain,
! [SV251: $i,SV72: $i] :
( ( ! [SY507: $i] :
( ~ ( linorder @ SY507 )
| ~ ( number @ SY507 )
| ~ ( ord_less_eq @ SY507 @ ( ti @ SY507 @ SV72 ) @ SV251 )
| ( ord_less_eq @ SY507 @ SV72 @ SV251 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1092]) ).
thf(1215,plain,
! [SV252: $i,SV72: $i] :
( ( ! [SY508: $i] :
( ~ ( linorder @ SY508 )
| ~ ( number @ SY508 )
| ~ ( ord_less_eq @ SY508 @ SV72 @ SV252 )
| ( ord_less_eq @ SY508 @ ( ti @ SY508 @ SV72 ) @ SV252 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1093]) ).
thf(1216,plain,
! [SV253: $i,SV73: $i] :
( ( ! [SY509: $i] :
( ~ ( linorder @ SY509 )
| ~ ( number @ SY509 )
| ~ ( ord_less @ SY509 @ SV73 @ ( ti @ SY509 @ SV253 ) )
| ( ord_less @ SY509 @ SV73 @ SV253 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1094]) ).
thf(1217,plain,
! [SV254: $i,SV73: $i] :
( ( ! [SY510: $i] :
( ~ ( linorder @ SY510 )
| ~ ( number @ SY510 )
| ~ ( ord_less @ SY510 @ SV73 @ SV254 )
| ( ord_less @ SY510 @ SV73 @ ( ti @ SY510 @ SV254 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1095]) ).
thf(1218,plain,
! [SV255: $i,SV192: $i] :
( ( ~ ( ord_less_eq @ int @ ( bit1 @ SV192 ) @ ( bit1 @ SV255 ) )
| ( ord_less_eq @ int @ SV192 @ SV255 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1096]) ).
thf(1219,plain,
! [SV256: $i,SV193: $i] :
( ( ~ ( ord_less_eq @ int @ SV193 @ SV256 )
| ( ord_less_eq @ int @ ( bit1 @ SV193 ) @ ( bit1 @ SV256 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1097]) ).
thf(1220,plain,
! [SV257: $i,SV194: $i] :
( ( ~ ( ord_less @ int @ SV194 @ SV257 )
| ( ord_less_eq @ int @ ( bit1 @ SV194 ) @ ( bit0 @ SV257 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1098]) ).
thf(1221,plain,
! [SV258: $i,SV195: $i] :
( ( ~ ( ord_less_eq @ int @ ( bit1 @ SV195 ) @ ( bit0 @ SV258 ) )
| ( ord_less @ int @ SV195 @ SV258 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1099]) ).
thf(1222,plain,
! [SV259: $i,SV196: $i] :
( ( ~ ( ord_less @ int @ SV196 @ ( plus_plus @ int @ SV259 @ ( one_one @ int ) ) )
| ( ord_less_eq @ int @ SV196 @ SV259 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1100]) ).
thf(1223,plain,
! [SV260: $i,SV197: $i] :
( ( ~ ( ord_less_eq @ int @ SV197 @ SV260 )
| ( ord_less @ int @ SV197 @ ( plus_plus @ int @ SV260 @ ( one_one @ int ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1101]) ).
thf(1224,plain,
! [SV74: $i] :
( ( ( number @ SV74 )
= $false )
| ( ( linorder @ SV74 )
= $false )
| ( ( ~ ( ~ ! [SY380: $i,SY381: $i] :
( ~ ( ord_less_eq @ SV74 @ ( number_number_of @ SV74 @ SY380 ) @ ( number_number_of @ SV74 @ SY381 ) )
| ~ ( ord_less @ SV74 @ ( number_number_of @ SV74 @ SY381 ) @ ( number_number_of @ SV74 @ SY380 ) ) )
| ~ ! [SY382: $i,SY383: $i] :
( ( ord_less @ SV74 @ ( number_number_of @ SV74 @ SY383 ) @ ( number_number_of @ SV74 @ SY382 ) )
| ( ord_less_eq @ SV74 @ ( number_number_of @ SV74 @ SY382 ) @ ( number_number_of @ SV74 @ SY383 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1102]) ).
thf(1225,plain,
! [SV75: $i] :
( ( ( ~ ! [SY384: $i,SY385: $i] :
( ~ ( ord_less @ SV75 @ ( zero_zero @ SV75 ) @ ( plus_plus @ SV75 @ ( power_power @ SV75 @ SY384 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV75 @ SY385 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
| ( ( ti @ SV75 @ SY384 )
!= ( zero_zero @ SV75 ) )
| ( ( ti @ SV75 @ SY385 )
!= ( zero_zero @ SV75 ) ) ) )
= $false )
| ( ( linordered_idom @ SV75 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1103]) ).
thf(1226,plain,
! [SV75: $i] :
( ( ( ~ ~ ( ~ ! [SY386: $i] :
( ( ( ti @ SV75 @ SY386 )
= ( zero_zero @ SV75 ) )
| ! [SY387: $i] : ( ord_less @ SV75 @ ( zero_zero @ SV75 ) @ ( plus_plus @ SV75 @ ( power_power @ SV75 @ SY386 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV75 @ SY387 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
| ~ ! [SY388: $i,SY389: $i] :
( ( ( ti @ SV75 @ SY389 )
= ( zero_zero @ SV75 ) )
| ( ord_less @ SV75 @ ( zero_zero @ SV75 ) @ ( plus_plus @ SV75 @ ( power_power @ SV75 @ SY388 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV75 @ SY389 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) ) )
= $false )
| ( ( linordered_idom @ SV75 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1103]) ).
thf(1227,plain,
! [SV76: $i] :
( ( ( number_ring @ SV76 )
= $false )
| ( ( linordered_idom @ SV76 )
= $false )
| ( ( ~ ( ~ ! [SY390: $i] :
( ~ ( ord_less_eq @ SV76 @ ( one_one @ SV76 ) @ ( number_number_of @ SV76 @ SY390 ) )
| ( ord_less_eq @ int @ ( bit1 @ pls ) @ SY390 ) )
| ~ ! [SY391: $i] :
( ~ ( ord_less_eq @ int @ ( bit1 @ pls ) @ SY391 )
| ( ord_less_eq @ SV76 @ ( one_one @ SV76 ) @ ( number_number_of @ SV76 @ SY391 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1104]) ).
thf(1228,plain,
! [SV77: $i] :
( ( ( ~ ! [SY392: $i,SY393: $i] :
( ( ( ti @ SV77 @ SY392 )
!= ( zero_zero @ SV77 ) )
| ( ( ti @ SV77 @ SY393 )
!= ( zero_zero @ SV77 ) )
| ( ( plus_plus @ SV77 @ ( power_power @ SV77 @ SY392 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV77 @ SY393 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV77 ) ) ) )
= $false )
| ( ( linordered_idom @ SV77 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1105]) ).
thf(1229,plain,
! [SV77: $i] :
( ( ( ~ ~ ( ~ ! [SY394: $i] :
( ! [SY395: $i] :
( ( plus_plus @ SV77 @ ( power_power @ SV77 @ SY394 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV77 @ SY395 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV77 ) )
| ( ( ti @ SV77 @ SY394 )
= ( zero_zero @ SV77 ) ) )
| ~ ! [SY396: $i,SY397: $i] :
( ( ( plus_plus @ SV77 @ ( power_power @ SV77 @ SY396 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV77 @ SY397 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV77 ) )
| ( ( ti @ SV77 @ SY397 )
= ( zero_zero @ SV77 ) ) ) ) )
= $false )
| ( ( linordered_idom @ SV77 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1105]) ).
thf(1230,plain,
! [SV78: $i] :
( ( ( ~ ! [SY398: $i] :
( ( ( power_power @ SV78 @ SY398 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= ( zero_zero @ SV78 ) )
| ( ( ti @ SV78 @ SY398 )
= ( zero_zero @ SV78 ) ) ) )
= $false )
| ( ( ring_11004092258visors @ SV78 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1106]) ).
thf(1231,plain,
! [SV78: $i] :
( ( ( ~ ! [SY399: $i] :
( ( ( ti @ SV78 @ SY399 )
!= ( zero_zero @ SV78 ) )
| ( ( power_power @ SV78 @ SY399 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SV78 ) ) ) )
= $false )
| ( ( ring_11004092258visors @ SV78 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1106]) ).
thf(1232,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ord_less @ int @ SX0 @ SX1 )
| ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ nat @ ( number_number_of @ nat @ SX0 ) @ ( number_number_of @ nat @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1107]) ).
thf(1233,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ pls @ SX1 )
| ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ nat @ ( number_number_of @ nat @ SX0 ) @ ( number_number_of @ nat @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1107]) ).
thf(1234,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ nat @ ( number_number_of @ nat @ SX0 ) @ ( number_number_of @ nat @ SX1 ) )
| ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ int @ pls @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1108]) ).
thf(1235,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ nat @ ( number_number_of @ nat @ SX0 ) @ ( number_number_of @ nat @ SX1 ) )
| ( ord_less @ int @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1108]) ).
thf(1236,plain,
! [SV79: $i] :
( ( ( ~ ! [SY400: $i] :
( ( ( ti @ SV79 @ SY400 )
= ( zero_zero @ SV79 ) )
| ( ord_less @ SV79 @ ( zero_zero @ SV79 ) @ ( power_power @ SV79 @ SY400 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $false )
| ( ( linordered_idom @ SV79 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1109]) ).
thf(1237,plain,
! [SV79: $i] :
( ( ( ~ ! [SY401: $i] :
( ~ ( ord_less @ SV79 @ ( zero_zero @ SV79 ) @ ( power_power @ SV79 @ SY401 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ( ( ti @ SV79 @ SY401 )
!= ( zero_zero @ SV79 ) ) ) )
= $false )
| ( ( linordered_idom @ SV79 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1109]) ).
thf(1238,plain,
! [SV80: $i] :
( ( ( ring_char_0 @ SV80 )
= $false )
| ( ( number_ring @ SV80 )
= $false )
| ( ( ~ ( ~ ! [SY402: $i,SY403: $i] :
( ( ( number_number_of @ SV80 @ SY402 )
!= ( number_number_of @ SV80 @ SY403 ) )
| ( SY402 = SY403 ) )
| ~ ! [SY404: $i,SY405: $i] :
( ( SY404 != SY405 )
| ( ( number_number_of @ SV80 @ SY404 )
= ( number_number_of @ SV80 @ SY405 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1110]) ).
thf(1239,plain,
! [SV198: $i] :
( ( ( ~ ( ord_less_eq @ int @ pls @ ( bit0 @ SV198 ) ) )
= $true )
| ( ( ord_less_eq @ int @ pls @ SV198 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1111]) ).
thf(1240,plain,
! [SV199: $i] :
( ( ( ~ ( ord_less_eq @ int @ pls @ SV199 ) )
= $true )
| ( ( ord_less_eq @ int @ pls @ ( bit0 @ SV199 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1112]) ).
thf(1241,plain,
! [SV81: $i] :
( ( ( number_ring @ SV81 )
= $false )
| ( ( linordered_idom @ SV81 )
= $false )
| ( ( ~ ( ~ ! [SY406: $i] :
( ~ ( ord_less_eq @ SV81 @ ( number_number_of @ SV81 @ SY406 ) @ ( zero_zero @ SV81 ) )
| ( ord_less_eq @ int @ SY406 @ pls ) )
| ~ ! [SY407: $i] :
( ~ ( ord_less_eq @ int @ SY407 @ pls )
| ( ord_less_eq @ SV81 @ ( number_number_of @ SV81 @ SY407 ) @ ( zero_zero @ SV81 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1113]) ).
thf(1242,plain,
! [SV261: $i,SV200: $i] :
( ( ~ ( ord_less @ int @ ( number_number_of @ int @ SV200 ) @ ( number_number_of @ int @ SV261 ) )
| ( ord_less @ int @ SV200 @ SV261 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1114]) ).
thf(1243,plain,
! [SV262: $i,SV201: $i] :
( ( ~ ( ord_less @ int @ SV201 @ SV262 )
| ( ord_less @ int @ ( number_number_of @ int @ SV201 ) @ ( number_number_of @ int @ SV262 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1115]) ).
thf(1244,plain,
! [SV263: $i,SV202: $i] :
( ( ~ ( ord_less_eq @ int @ ( bit0 @ SV202 ) @ ( bit0 @ SV263 ) )
| ( ord_less_eq @ int @ SV202 @ SV263 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1116]) ).
thf(1245,plain,
! [SV264: $i,SV203: $i] :
( ( ~ ( ord_less_eq @ int @ SV203 @ SV264 )
| ( ord_less_eq @ int @ ( bit0 @ SV203 ) @ ( bit0 @ SV264 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1117]) ).
thf(1246,plain,
! [SV82: $i] :
( ( ( ~ ! [SY408: $i,SY409: $i] :
( ( ( ti @ SV82 @ SY408 )
!= ( zero_zero @ SV82 ) )
| ( ( ti @ SV82 @ SY409 )
!= ( zero_zero @ SV82 ) )
| ( ( plus_plus @ SV82 @ ( times_times @ SV82 @ SY408 @ SY408 ) @ ( times_times @ SV82 @ SY409 @ SY409 ) )
= ( zero_zero @ SV82 ) ) ) )
= $false )
| ( ( linord581940658strict @ SV82 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1118]) ).
thf(1247,plain,
! [SV82: $i] :
( ( ( ~ ~ ( ~ ! [SY410: $i] :
( ! [SY411: $i] :
( ( plus_plus @ SV82 @ ( times_times @ SV82 @ SY410 @ SY410 ) @ ( times_times @ SV82 @ SY411 @ SY411 ) )
!= ( zero_zero @ SV82 ) )
| ( ( ti @ SV82 @ SY410 )
= ( zero_zero @ SV82 ) ) )
| ~ ! [SY412: $i,SY413: $i] :
( ( ( plus_plus @ SV82 @ ( times_times @ SV82 @ SY412 @ SY412 ) @ ( times_times @ SV82 @ SY413 @ SY413 ) )
!= ( zero_zero @ SV82 ) )
| ( ( ti @ SV82 @ SY413 )
= ( zero_zero @ SV82 ) ) ) ) )
= $false )
| ( ( linord581940658strict @ SV82 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1118]) ).
thf(1248,plain,
! [SV265: $i,SV83: $i] :
( ( ! [SY511: $i] :
( ~ ( linordered_ring @ SY511 )
| ~ ( ord_less_eq @ SY511 @ SV83 @ ( ti @ SY511 @ SV265 ) )
| ( ord_less_eq @ SY511 @ SV83 @ SV265 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1119]) ).
thf(1249,plain,
! [SV266: $i,SV83: $i] :
( ( ! [SY512: $i] :
( ~ ( linordered_ring @ SY512 )
| ~ ( ord_less_eq @ SY512 @ SV83 @ SV266 )
| ( ord_less_eq @ SY512 @ SV83 @ ( ti @ SY512 @ SV266 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1120]) ).
thf(1250,plain,
! [SV84: $i] :
( ( ( number_ring @ SV84 )
= $false )
| ( ( linordered_idom @ SV84 )
= $false )
| ( ( ~ ( ~ ! [SY418: $i] :
( ~ ( ord_less_eq @ SV84 @ ( number_number_of @ SV84 @ SY418 ) @ ( one_one @ SV84 ) )
| ( ord_less_eq @ int @ SY418 @ ( bit1 @ pls ) ) )
| ~ ! [SY419: $i] :
( ~ ( ord_less_eq @ int @ SY419 @ ( bit1 @ pls ) )
| ( ord_less_eq @ SV84 @ ( number_number_of @ SV84 @ SY419 ) @ ( one_one @ SV84 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1121]) ).
thf(1251,plain,
! [SV85: $i] :
( ( ( number_ring @ SV85 )
= $false )
| ( ( linordered_idom @ SV85 )
= $false )
| ( ( ~ ( ~ ! [SY420: $i] :
( ~ ( ord_less_eq @ SV85 @ ( zero_zero @ SV85 ) @ ( number_number_of @ SV85 @ SY420 ) )
| ( ord_less_eq @ int @ pls @ SY420 ) )
| ~ ! [SY421: $i] :
( ~ ( ord_less_eq @ int @ pls @ SY421 )
| ( ord_less_eq @ SV85 @ ( zero_zero @ SV85 ) @ ( number_number_of @ SV85 @ SY421 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1122]) ).
thf(1252,plain,
! [SV204: $i] :
( ( ( ~ ( ord_less @ int @ SV204 @ pls ) )
= $true )
| ( ( ord_less_eq @ int @ ( bit1 @ SV204 ) @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1123]) ).
thf(1253,plain,
! [SV205: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( bit1 @ SV205 ) @ pls ) )
= $true )
| ( ( ord_less @ int @ SV205 @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1124]) ).
thf(1254,plain,
! [SV86: $i] :
( ( ( ~ ! [SY422: $i,SY423: $i] :
( ( ( ti @ SV86 @ SY422 )
!= ( zero_zero @ SV86 ) )
| ( ( ti @ SV86 @ SY423 )
!= ( zero_zero @ SV86 ) )
| ( ord_less_eq @ SV86 @ ( plus_plus @ SV86 @ ( times_times @ SV86 @ SY422 @ SY422 ) @ ( times_times @ SV86 @ SY423 @ SY423 ) ) @ ( zero_zero @ SV86 ) ) ) )
= $false )
| ( ( linord581940658strict @ SV86 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1125]) ).
thf(1255,plain,
! [SV86: $i] :
( ( ( ~ ~ ( ~ ! [SY424: $i] :
( ! [SY425: $i] :
~ ( ord_less_eq @ SV86 @ ( plus_plus @ SV86 @ ( times_times @ SV86 @ SY424 @ SY424 ) @ ( times_times @ SV86 @ SY425 @ SY425 ) ) @ ( zero_zero @ SV86 ) )
| ( ( ti @ SV86 @ SY424 )
= ( zero_zero @ SV86 ) ) )
| ~ ! [SY426: $i,SY427: $i] :
( ~ ( ord_less_eq @ SV86 @ ( plus_plus @ SV86 @ ( times_times @ SV86 @ SY426 @ SY426 ) @ ( times_times @ SV86 @ SY427 @ SY427 ) ) @ ( zero_zero @ SV86 ) )
| ( ( ti @ SV86 @ SY427 )
= ( zero_zero @ SV86 ) ) ) ) )
= $false )
| ( ( linord581940658strict @ SV86 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1125]) ).
thf(1256,plain,
! [SV267: $i,SV206: $i] :
( ( ~ ( ord_less @ int @ ( bit0 @ SV206 ) @ ( bit1 @ SV267 ) )
| ( ord_less_eq @ int @ SV206 @ SV267 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1126]) ).
thf(1257,plain,
! [SV268: $i,SV207: $i] :
( ( ~ ( ord_less_eq @ int @ SV207 @ SV268 )
| ( ord_less @ int @ ( bit0 @ SV207 ) @ ( bit1 @ SV268 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1127]) ).
thf(1258,plain,
! [SV269: $i,SV208: $i] :
( ( ~ ( ord_less_eq @ int @ ( bit0 @ SV208 ) @ ( bit0 @ SV269 ) )
| ( ord_less_eq @ int @ SV208 @ SV269 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1128]) ).
thf(1259,plain,
! [SV270: $i,SV209: $i] :
( ( ~ ( ord_less_eq @ int @ SV209 @ SV270 )
| ( ord_less_eq @ int @ ( bit0 @ SV209 ) @ ( bit0 @ SV270 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1129]) ).
thf(1260,plain,
! [SV210: $i] :
( ( ( ( ( zero_zero @ nat )
!= ( number_number_of @ nat @ SV210 ) ) )
= $true )
| ( ( ord_less_eq @ int @ SV210 @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1130]) ).
thf(1261,plain,
! [SV211: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV211 @ pls ) )
= $true )
| ( ( ( zero_zero @ nat )
= ( number_number_of @ nat @ SV211 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1131]) ).
thf(1262,plain,
! [SV212: $i] :
( ( ( ~ ( ord_less @ int @ pls @ ( bit1 @ SV212 ) ) )
= $true )
| ( ( ord_less_eq @ int @ pls @ SV212 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1132]) ).
thf(1263,plain,
! [SV213: $i] :
( ( ( ~ ( ord_less_eq @ int @ pls @ SV213 ) )
= $true )
| ( ( ord_less @ int @ pls @ ( bit1 @ SV213 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1133]) ).
thf(1264,plain,
! [SV214: $i,SV147: $i,SV16: $i] :
( ( ( ord_less @ SV16 @ ( plus_plus @ SV16 @ ( power_power @ SV16 @ SV147 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV16 @ SV214 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( zero_zero @ SV16 ) )
= $false )
| ( ( linordered_idom @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1140]) ).
thf(1265,plain,
! [SV99: $i,SV28: $i,SV130: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV130 @ SV28 ) )
= $true )
| ( ( ord_less_eq @ int @ SV99 @ SV28 )
= $true )
| ( ( ord_less_eq @ int @ SV99 @ SV130 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1142]) ).
thf(1266,plain,
! [SV29: $i,SV100: $i] :
( ( ( ord_less_eq @ int @ SV100 @ SV29 )
= $false )
| ( ( SV29 = SV100 )
= $true )
| ( ( ord_less_eq @ int @ SV29 @ SV100 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1143]) ).
thf(1267,plain,
! [SV271: $i,SV215: $i,SV151: $i,SV32: $i] :
( ( ( ( times_times @ SV32 @ ( number_number_of @ SV32 @ SV151 ) @ ( times_times @ SV32 @ ( number_number_of @ SV32 @ SV215 ) @ SV271 ) )
= ( times_times @ SV32 @ ( number_number_of @ SV32 @ ( times_times @ int @ SV151 @ SV215 ) ) @ SV271 ) )
= $true )
| ( ( number_ring @ SV32 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1145]) ).
thf(1268,plain,
! [SV103: $i,SV35: $i,SV154: $i,SV133: $i] :
( ( ( ord_less @ int @ SV133 @ SV154 )
= $false )
| ( ( ~ ( ord_less_eq @ int @ SV35 @ SV103 )
| ( ord_less @ int @ ( plus_plus @ int @ SV133 @ SV35 ) @ ( plus_plus @ int @ SV154 @ SV103 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1148]) ).
thf(1269,plain,
! [SV44: $i,SV155: $i,SV218: $i] :
( ( ( ~ ( ord_less_eq @ int @ pls @ SV218 ) )
= $true )
| ( ( ~ ( ord_less_eq @ int @ pls @ SV155 )
| ( ( plus_plus @ SV44 @ ( number_number_of @ SV44 @ SV218 ) @ ( number_number_of @ SV44 @ SV155 ) )
= ( number_number_of @ SV44 @ ( plus_plus @ int @ SV218 @ SV155 ) ) ) )
= $true )
| ( ( number_semiring @ SV44 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1149]) ).
thf(1270,plain,
! [SV113: $i,SV50: $i,SV138: $i] :
( ( ( number @ SV138 )
= $false )
| ( ( ~ ( semiring @ SV138 ) )
= $true )
| ( ( ( plus_plus @ SV138 @ ( ti @ SV138 @ SV50 ) @ SV113 )
= ( plus_plus @ SV138 @ SV50 @ SV113 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1150]) ).
thf(1271,plain,
! [SV114: $i,SV51: $i,SV139: $i] :
( ( ( number @ SV139 )
= $false )
| ( ( ~ ( semiring @ SV139 ) )
= $true )
| ( ( ( plus_plus @ SV139 @ SV51 @ ( ti @ SV139 @ SV114 ) )
= ( plus_plus @ SV139 @ SV51 @ SV114 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1151]) ).
thf(1272,plain,
! [SV115: $i,SV52: $i,SV140: $i] :
( ( ( number @ SV140 )
= $false )
| ( ( ~ ( semiring @ SV140 ) )
= $true )
| ( ( ( ti @ SV140 @ ( plus_plus @ SV140 @ SV52 @ SV115 ) )
= ( plus_plus @ SV140 @ SV52 @ SV115 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1152]) ).
thf(1273,plain,
! [SV116: $i,SV53: $i,SV141: $i] :
( ( ( number @ SV141 )
= $false )
| ( ( ~ ( semiring @ SV141 ) )
= $true )
| ( ( ( times_times @ SV141 @ ( ti @ SV141 @ SV53 ) @ SV116 )
= ( times_times @ SV141 @ SV53 @ SV116 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1153]) ).
thf(1274,plain,
! [SV117: $i,SV54: $i,SV142: $i] :
( ( ( number @ SV142 )
= $false )
| ( ( ~ ( semiring @ SV142 ) )
= $true )
| ( ( ( times_times @ SV142 @ SV54 @ ( ti @ SV142 @ SV117 ) )
= ( times_times @ SV142 @ SV54 @ SV117 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1154]) ).
thf(1275,plain,
! [SV118: $i,SV55: $i,SV143: $i] :
( ( ( number @ SV143 )
= $false )
| ( ( ~ ( semiring @ SV143 ) )
= $true )
| ( ( ( ti @ SV143 @ ( times_times @ SV143 @ SV55 @ SV118 ) )
= ( times_times @ SV143 @ SV55 @ SV118 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1155]) ).
thf(1276,plain,
! [SV60: $i,SV156: $i,SV219: $i] :
( ( ( ~ ( ord_less_eq @ int @ pls @ SV219 ) )
= $true )
| ( ( ~ ( ord_less_eq @ int @ pls @ SV156 )
| ( ( times_times @ SV60 @ ( number_number_of @ SV60 @ SV219 ) @ ( number_number_of @ SV60 @ SV156 ) )
= ( number_number_of @ SV60 @ ( times_times @ int @ SV219 @ SV156 ) ) ) )
= $true )
| ( ( number_semiring @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1159]) ).
thf(1277,plain,
! [SV272: $i,SV62: $i] :
( ( ( ! [SY513: $i,SY514: $i] :
( ( times_times @ SV62 @ ( plus_plus @ SV62 @ SV272 @ SY513 ) @ ( number_number_of @ SV62 @ SY514 ) )
= ( plus_plus @ SV62 @ ( times_times @ SV62 @ SV272 @ ( number_number_of @ SV62 @ SY514 ) ) @ ( times_times @ SV62 @ SY513 @ ( number_number_of @ SV62 @ SY514 ) ) ) ) )
= $true )
| ( ( number @ SV62 )
= $false )
| ( ( semiring @ SV62 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1161]) ).
thf(1278,plain,
! [SV273: $i,SV63: $i] :
( ( ( ! [SY515: $i,SY516: $i] :
( ( times_times @ SV63 @ ( number_number_of @ SV63 @ SV273 ) @ ( plus_plus @ SV63 @ SY515 @ SY516 ) )
= ( plus_plus @ SV63 @ ( times_times @ SV63 @ ( number_number_of @ SV63 @ SV273 ) @ SY515 ) @ ( times_times @ SV63 @ ( number_number_of @ SV63 @ SV273 ) @ SY516 ) ) ) )
= $true )
| ( ( number @ SV63 )
= $false )
| ( ( semiring @ SV63 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1162]) ).
thf(1279,plain,
! [SV158: $i] :
( ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( number_number_of @ nat @ SV158 ) )
= $false )
| ( ( ord_less @ int @ pls @ SV158 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1163]) ).
thf(1280,plain,
! [SV159: $i] :
( ( ( ord_less @ int @ pls @ SV159 )
= $false )
| ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( number_number_of @ nat @ SV159 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1164]) ).
thf(1281,plain,
! [SV221: $i,SV160: $i] :
( ( ( ( SV160 = SV221 )
| ~ ( ord_less_eq @ int @ SV160 @ SV221 ) )
= $true )
| ( ( ord_less @ int @ SV160 @ SV221 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1165]) ).
thf(1282,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1166]) ).
thf(1283,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1167]) ).
thf(1284,plain,
! [SV161: $i] :
( ( ( ord_less @ int @ ( zero_zero @ int ) @ SV161 )
= $false )
| ( ( ord_less_eq @ int @ ( one_one @ int ) @ SV161 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1168]) ).
thf(1285,plain,
! [SV162: $i] :
( ( ( ord_less_eq @ int @ ( one_one @ int ) @ SV162 )
= $false )
| ( ( ord_less @ int @ ( zero_zero @ int ) @ SV162 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1169]) ).
thf(1286,plain,
! [SV222: $i,SV163: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( bit0 @ SV163 ) @ ( bit1 @ SV222 ) ) )
= $true )
| ( ( ord_less_eq @ int @ SV163 @ SV222 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1170]) ).
thf(1287,plain,
! [SV223: $i,SV164: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV164 @ SV223 ) )
= $true )
| ( ( ord_less_eq @ int @ ( bit0 @ SV164 ) @ ( bit1 @ SV223 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1171]) ).
thf(1288,plain,
! [SV224: $i,SV165: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( bit0 @ SV165 ) @ ( bit1 @ SV224 ) ) )
= $true )
| ( ( ord_less_eq @ int @ SV165 @ SV224 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1172]) ).
thf(1289,plain,
! [SV225: $i,SV166: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV166 @ SV225 ) )
= $true )
| ( ( ord_less_eq @ int @ ( bit0 @ SV166 ) @ ( bit1 @ SV225 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1173]) ).
thf(1290,plain,
! [SV65: $i] :
( ( ( ~ ! [SY344: $i,SY345: $i] :
( ~ ( ord_less_eq @ SV65 @ ( number_number_of @ SV65 @ SY344 ) @ ( number_number_of @ SV65 @ SY345 ) )
| ( ord_less_eq @ int @ SY344 @ SY345 ) )
| ~ ! [SY346: $i,SY347: $i] :
( ~ ( ord_less_eq @ int @ SY346 @ SY347 )
| ( ord_less_eq @ SV65 @ ( number_number_of @ SV65 @ SY346 ) @ ( number_number_of @ SV65 @ SY347 ) ) ) )
= $false )
| ( ( linordered_idom @ SV65 )
= $false )
| ( ( number_ring @ SV65 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1174]) ).
thf(1291,plain,
! [SV167: $i] :
( ( ( ord_less_eq @ int @ ( bit0 @ SV167 ) @ pls )
= $false )
| ( ( ord_less_eq @ int @ SV167 @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1175]) ).
thf(1292,plain,
! [SV168: $i] :
( ( ( ord_less_eq @ int @ SV168 @ pls )
= $false )
| ( ( ord_less_eq @ int @ ( bit0 @ SV168 ) @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1176]) ).
thf(1293,plain,
! [SV169: $i,SV226: $i] :
( ( ( ~ ( ord_less @ int @ SV226 @ pls ) )
= $true )
| ( ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV226 ) @ ( number_number_of @ nat @ SV169 ) )
= ( number_number_of @ nat @ SV169 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1177]) ).
thf(1294,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)],[1178]) ).
thf(1295,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)],[1179]) ).
thf(1296,plain,
! [SV227: $i,SV66: $i,SV274: $i] :
( ( ~ ( linordered_idom @ SV274 )
| ~ ( ord_less @ SV274 @ SV66 @ ( ti @ SV274 @ SV227 ) )
| ( ord_less @ SV274 @ SV66 @ SV227 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1180]) ).
thf(1297,plain,
! [SV228: $i,SV66: $i,SV275: $i] :
( ( ~ ( linordered_idom @ SV275 )
| ~ ( ord_less @ SV275 @ SV66 @ SV228 )
| ( ord_less @ SV275 @ SV66 @ ( ti @ SV275 @ SV228 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1181]) ).
thf(1298,plain,
! [SV229: $i,SV67: $i,SV276: $i] :
( ( ~ ( linordered_idom @ SV276 )
| ~ ( ord_less @ SV276 @ ( ti @ SV276 @ SV67 ) @ SV229 )
| ( ord_less @ SV276 @ SV67 @ SV229 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1182]) ).
thf(1299,plain,
! [SV230: $i,SV67: $i,SV277: $i] :
( ( ~ ( linordered_idom @ SV277 )
| ~ ( ord_less @ SV277 @ SV67 @ SV230 )
| ( ord_less @ SV277 @ ( ti @ SV277 @ SV67 ) @ SV230 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1183]) ).
thf(1300,plain,
! [SV231: $i,SV68: $i,SV278: $i] :
( ( ~ ( linordered_ring @ SV278 )
| ~ ( ord_less_eq @ SV278 @ ( ti @ SV278 @ SV68 ) @ SV231 )
| ( ord_less_eq @ SV278 @ SV68 @ SV231 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1184]) ).
thf(1301,plain,
! [SV232: $i,SV68: $i,SV279: $i] :
( ( ~ ( linordered_ring @ SV279 )
| ~ ( ord_less_eq @ SV279 @ SV68 @ SV232 )
| ( ord_less_eq @ SV279 @ ( ti @ SV279 @ SV68 ) @ SV232 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1185]) ).
thf(1302,plain,
! [SV233: $i,SV170: $i] :
( ( ( ( ( bit0 @ SV170 )
!= ( bit0 @ SV233 ) ) )
= $true )
| ( ( SV170 = SV233 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1186]) ).
thf(1303,plain,
! [SV234: $i,SV171: $i] :
( ( ( ( SV171 != SV234 ) )
= $true )
| ( ( ( bit0 @ SV171 )
= ( bit0 @ SV234 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1187]) ).
thf(1304,plain,
! [SV235: $i,SV69: $i,SV280: $i] :
( ( ~ ( linorder @ SV280 )
| ~ ( number @ SV280 )
| ~ ( ord_less_eq @ SV280 @ SV69 @ ( ti @ SV280 @ SV235 ) )
| ( ord_less_eq @ SV280 @ SV69 @ SV235 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1188]) ).
thf(1305,plain,
! [SV236: $i,SV69: $i,SV281: $i] :
( ( ~ ( linorder @ SV281 )
| ~ ( number @ SV281 )
| ~ ( ord_less_eq @ SV281 @ SV69 @ SV236 )
| ( ord_less_eq @ SV281 @ SV69 @ ( ti @ SV281 @ SV236 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1189]) ).
thf(1306,plain,
! [SV70: $i] :
( ( ( ! [SY364: $i,SY365: $i] :
( ( ( number_number_of @ SV70 @ SY364 )
!= ( ti @ SV70 @ SY365 ) )
| ( ( ti @ SV70 @ SY365 )
= ( number_number_of @ SV70 @ SY364 ) ) ) )
= $true )
| ( ( number @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1190]) ).
thf(1307,plain,
! [SV70: $i] :
( ( ( ! [SY366: $i,SY367: $i] :
( ( ( ti @ SV70 @ SY367 )
!= ( number_number_of @ SV70 @ SY366 ) )
| ( ( number_number_of @ SV70 @ SY366 )
= ( ti @ SV70 @ SY367 ) ) ) )
= $true )
| ( ( number @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1191]) ).
thf(1308,plain,
! [SV237: $i,SV172: $i] :
( ( ( ~ ( ord_less @ int @ SV172 @ SV237 ) )
= $true )
| ( ( ord_less_eq @ int @ ( bit1 @ SV172 ) @ ( bit0 @ SV237 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1192]) ).
thf(1309,plain,
! [SV238: $i,SV173: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( bit1 @ SV173 ) @ ( bit0 @ SV238 ) ) )
= $true )
| ( ( ord_less @ int @ SV173 @ SV238 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1193]) ).
thf(1310,plain,
! [SV174: $i] :
( ( ( twoSqu33214720sum2sq @ ( ti @ int @ SV174 ) )
= $false )
| ( ( twoSqu33214720sum2sq @ SV174 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1194]) ).
thf(1311,plain,
! [SV175: $i] :
( ( ( twoSqu33214720sum2sq @ SV175 )
= $false )
| ( ( twoSqu33214720sum2sq @ ( ti @ int @ SV175 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1195]) ).
thf(1312,plain,
! [SV239: $i,SV176: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( number_number_of @ int @ SV176 ) @ ( number_number_of @ int @ SV239 ) ) )
= $true )
| ( ( ord_less_eq @ int @ SV176 @ SV239 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1196]) ).
thf(1313,plain,
! [SV240: $i,SV177: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV177 @ SV240 ) )
= $true )
| ( ( ord_less_eq @ int @ ( number_number_of @ int @ SV177 ) @ ( number_number_of @ int @ SV240 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1197]) ).
thf(1314,plain,
! [SV178: $i] :
( ( ( ( number_number_of @ nat @ SV178 )
= ( zero_zero @ nat ) )
= $false )
| ( ( ord_less_eq @ int @ SV178 @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1198]) ).
thf(1315,plain,
! [SV179: $i] :
( ( ( ord_less_eq @ int @ SV179 @ pls )
= $false )
| ( ( ( number_number_of @ nat @ SV179 )
= ( zero_zero @ nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1199]) ).
thf(1316,plain,
! [SV241: $i,SV71: $i,SV282: $i] :
( ( ~ ( linorder @ SV282 )
| ~ ( number @ SV282 )
| ~ ( ord_less @ SV282 @ ( ti @ SV282 @ SV71 ) @ SV241 )
| ( ord_less @ SV282 @ SV71 @ SV241 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1200]) ).
thf(1317,plain,
! [SV242: $i,SV71: $i,SV283: $i] :
( ( ~ ( linorder @ SV283 )
| ~ ( number @ SV283 )
| ~ ( ord_less @ SV283 @ SV71 @ SV242 )
| ( ord_less @ SV283 @ ( ti @ SV283 @ SV71 ) @ SV242 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1201]) ).
thf(1318,plain,
! [SV243: $i,SV180: $i] :
( ( ( ( ( bit1 @ SV180 )
!= ( bit1 @ SV243 ) ) )
= $true )
| ( ( SV180 = SV243 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1202]) ).
thf(1319,plain,
! [SV244: $i,SV181: $i] :
( ( ( ( SV181 != SV244 ) )
= $true )
| ( ( ( bit1 @ SV181 )
= ( bit1 @ SV244 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1203]) ).
thf(1320,plain,
! [SV245: $i,SV182: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( bit1 @ SV182 ) @ ( bit1 @ SV245 ) ) )
= $true )
| ( ( ord_less_eq @ int @ SV182 @ SV245 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1204]) ).
thf(1321,plain,
! [SV246: $i,SV183: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV183 @ SV246 ) )
= $true )
| ( ( ord_less_eq @ int @ ( bit1 @ SV183 ) @ ( bit1 @ SV246 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1205]) ).
thf(1322,plain,
! [SV184: $i] :
( ( ( zprime @ ( ti @ int @ SV184 ) )
= $false )
| ( ( zprime @ SV184 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1206]) ).
thf(1323,plain,
! [SV185: $i] :
( ( ( zprime @ SV185 )
= $false )
| ( ( zprime @ ( ti @ int @ SV185 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1207]) ).
thf(1324,plain,
! [SV186: $i] :
( ( ( ord_less_eq @ int @ pls @ ( bit1 @ SV186 ) )
= $false )
| ( ( ord_less_eq @ int @ pls @ SV186 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1208]) ).
thf(1325,plain,
! [SV187: $i] :
( ( ( ord_less_eq @ int @ pls @ SV187 )
= $false )
| ( ( ord_less_eq @ int @ pls @ ( bit1 @ SV187 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1209]) ).
thf(1326,plain,
! [SV247: $i,SV188: $i] :
( ( ( ~ ( ord_less @ int @ ( bit0 @ SV188 ) @ ( bit1 @ SV247 ) ) )
= $true )
| ( ( ord_less_eq @ int @ SV188 @ SV247 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1210]) ).
thf(1327,plain,
! [SV248: $i,SV189: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV189 @ SV248 ) )
= $true )
| ( ( ord_less @ int @ ( bit0 @ SV189 ) @ ( bit1 @ SV248 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1211]) ).
thf(1328,plain,
! [SV249: $i,SV190: $i] :
( ( ( ~ ( ord_less @ int @ SV190 @ SV249 ) )
= $true )
| ( ( ord_less_eq @ int @ ( plus_plus @ int @ SV190 @ ( one_one @ int ) ) @ SV249 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1212]) ).
thf(1329,plain,
! [SV250: $i,SV191: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( plus_plus @ int @ SV191 @ ( one_one @ int ) ) @ SV250 ) )
= $true )
| ( ( ord_less @ int @ SV191 @ SV250 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1213]) ).
thf(1330,plain,
! [SV251: $i,SV72: $i,SV284: $i] :
( ( ~ ( linorder @ SV284 )
| ~ ( number @ SV284 )
| ~ ( ord_less_eq @ SV284 @ ( ti @ SV284 @ SV72 ) @ SV251 )
| ( ord_less_eq @ SV284 @ SV72 @ SV251 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1214]) ).
thf(1331,plain,
! [SV252: $i,SV72: $i,SV285: $i] :
( ( ~ ( linorder @ SV285 )
| ~ ( number @ SV285 )
| ~ ( ord_less_eq @ SV285 @ SV72 @ SV252 )
| ( ord_less_eq @ SV285 @ ( ti @ SV285 @ SV72 ) @ SV252 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1215]) ).
thf(1332,plain,
! [SV253: $i,SV73: $i,SV286: $i] :
( ( ~ ( linorder @ SV286 )
| ~ ( number @ SV286 )
| ~ ( ord_less @ SV286 @ SV73 @ ( ti @ SV286 @ SV253 ) )
| ( ord_less @ SV286 @ SV73 @ SV253 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1216]) ).
thf(1333,plain,
! [SV254: $i,SV73: $i,SV287: $i] :
( ( ~ ( linorder @ SV287 )
| ~ ( number @ SV287 )
| ~ ( ord_less @ SV287 @ SV73 @ SV254 )
| ( ord_less @ SV287 @ SV73 @ ( ti @ SV287 @ SV254 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1217]) ).
thf(1334,plain,
! [SV255: $i,SV192: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( bit1 @ SV192 ) @ ( bit1 @ SV255 ) ) )
= $true )
| ( ( ord_less_eq @ int @ SV192 @ SV255 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1218]) ).
thf(1335,plain,
! [SV256: $i,SV193: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV193 @ SV256 ) )
= $true )
| ( ( ord_less_eq @ int @ ( bit1 @ SV193 ) @ ( bit1 @ SV256 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1219]) ).
thf(1336,plain,
! [SV257: $i,SV194: $i] :
( ( ( ~ ( ord_less @ int @ SV194 @ SV257 ) )
= $true )
| ( ( ord_less_eq @ int @ ( bit1 @ SV194 ) @ ( bit0 @ SV257 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1220]) ).
thf(1337,plain,
! [SV258: $i,SV195: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( bit1 @ SV195 ) @ ( bit0 @ SV258 ) ) )
= $true )
| ( ( ord_less @ int @ SV195 @ SV258 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1221]) ).
thf(1338,plain,
! [SV259: $i,SV196: $i] :
( ( ( ~ ( ord_less @ int @ SV196 @ ( plus_plus @ int @ SV259 @ ( one_one @ int ) ) ) )
= $true )
| ( ( ord_less_eq @ int @ SV196 @ SV259 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1222]) ).
thf(1339,plain,
! [SV260: $i,SV197: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV197 @ SV260 ) )
= $true )
| ( ( ord_less @ int @ SV197 @ ( plus_plus @ int @ SV260 @ ( one_one @ int ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1223]) ).
thf(1340,plain,
! [SV74: $i] :
( ( ( ~ ! [SY380: $i,SY381: $i] :
( ~ ( ord_less_eq @ SV74 @ ( number_number_of @ SV74 @ SY380 ) @ ( number_number_of @ SV74 @ SY381 ) )
| ~ ( ord_less @ SV74 @ ( number_number_of @ SV74 @ SY381 ) @ ( number_number_of @ SV74 @ SY380 ) ) )
| ~ ! [SY382: $i,SY383: $i] :
( ( ord_less @ SV74 @ ( number_number_of @ SV74 @ SY383 ) @ ( number_number_of @ SV74 @ SY382 ) )
| ( ord_less_eq @ SV74 @ ( number_number_of @ SV74 @ SY382 ) @ ( number_number_of @ SV74 @ SY383 ) ) ) )
= $false )
| ( ( linorder @ SV74 )
= $false )
| ( ( number @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1224]) ).
thf(1341,plain,
! [SV75: $i] :
( ( ( ! [SY384: $i,SY385: $i] :
( ~ ( ord_less @ SV75 @ ( zero_zero @ SV75 ) @ ( plus_plus @ SV75 @ ( power_power @ SV75 @ SY384 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV75 @ SY385 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
| ( ( ti @ SV75 @ SY384 )
!= ( zero_zero @ SV75 ) )
| ( ( ti @ SV75 @ SY385 )
!= ( zero_zero @ SV75 ) ) ) )
= $true )
| ( ( linordered_idom @ SV75 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1225]) ).
thf(1342,plain,
! [SV75: $i] :
( ( ( ~ ( ~ ! [SY386: $i] :
( ( ( ti @ SV75 @ SY386 )
= ( zero_zero @ SV75 ) )
| ! [SY387: $i] : ( ord_less @ SV75 @ ( zero_zero @ SV75 ) @ ( plus_plus @ SV75 @ ( power_power @ SV75 @ SY386 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV75 @ SY387 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
| ~ ! [SY388: $i,SY389: $i] :
( ( ( ti @ SV75 @ SY389 )
= ( zero_zero @ SV75 ) )
| ( ord_less @ SV75 @ ( zero_zero @ SV75 ) @ ( plus_plus @ SV75 @ ( power_power @ SV75 @ SY388 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV75 @ SY389 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) ) )
= $true )
| ( ( linordered_idom @ SV75 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1226]) ).
thf(1343,plain,
! [SV76: $i] :
( ( ( ~ ! [SY390: $i] :
( ~ ( ord_less_eq @ SV76 @ ( one_one @ SV76 ) @ ( number_number_of @ SV76 @ SY390 ) )
| ( ord_less_eq @ int @ ( bit1 @ pls ) @ SY390 ) )
| ~ ! [SY391: $i] :
( ~ ( ord_less_eq @ int @ ( bit1 @ pls ) @ SY391 )
| ( ord_less_eq @ SV76 @ ( one_one @ SV76 ) @ ( number_number_of @ SV76 @ SY391 ) ) ) )
= $false )
| ( ( linordered_idom @ SV76 )
= $false )
| ( ( number_ring @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1227]) ).
thf(1344,plain,
! [SV77: $i] :
( ( ( ! [SY392: $i,SY393: $i] :
( ( ( ti @ SV77 @ SY392 )
!= ( zero_zero @ SV77 ) )
| ( ( ti @ SV77 @ SY393 )
!= ( zero_zero @ SV77 ) )
| ( ( plus_plus @ SV77 @ ( power_power @ SV77 @ SY392 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV77 @ SY393 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV77 ) ) ) )
= $true )
| ( ( linordered_idom @ SV77 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1228]) ).
thf(1345,plain,
! [SV77: $i] :
( ( ( ~ ( ~ ! [SY394: $i] :
( ! [SY395: $i] :
( ( plus_plus @ SV77 @ ( power_power @ SV77 @ SY394 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV77 @ SY395 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV77 ) )
| ( ( ti @ SV77 @ SY394 )
= ( zero_zero @ SV77 ) ) )
| ~ ! [SY396: $i,SY397: $i] :
( ( ( plus_plus @ SV77 @ ( power_power @ SV77 @ SY396 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV77 @ SY397 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV77 ) )
| ( ( ti @ SV77 @ SY397 )
= ( zero_zero @ SV77 ) ) ) ) )
= $true )
| ( ( linordered_idom @ SV77 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1229]) ).
thf(1346,plain,
! [SV78: $i] :
( ( ( ! [SY398: $i] :
( ( ( power_power @ SV78 @ SY398 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= ( zero_zero @ SV78 ) )
| ( ( ti @ SV78 @ SY398 )
= ( zero_zero @ SV78 ) ) ) )
= $true )
| ( ( ring_11004092258visors @ SV78 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1230]) ).
thf(1347,plain,
! [SV78: $i] :
( ( ( ! [SY399: $i] :
( ( ( ti @ SV78 @ SY399 )
!= ( zero_zero @ SV78 ) )
| ( ( power_power @ SV78 @ SY399 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SV78 ) ) ) )
= $true )
| ( ( ring_11004092258visors @ SV78 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1231]) ).
thf(1348,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ord_less @ int @ SX0 @ SX1 )
| ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ nat @ ( number_number_of @ nat @ SX0 ) @ ( number_number_of @ nat @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1232]) ).
thf(1349,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ pls @ SX1 )
| ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ nat @ ( number_number_of @ nat @ SX0 ) @ ( number_number_of @ nat @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1233]) ).
thf(1350,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ nat @ ( number_number_of @ nat @ SX0 ) @ ( number_number_of @ nat @ SX1 ) )
| ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ int @ pls @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1234]) ).
thf(1351,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ nat @ ( number_number_of @ nat @ SX0 ) @ ( number_number_of @ nat @ SX1 ) )
| ( ord_less @ int @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1235]) ).
thf(1352,plain,
! [SV79: $i] :
( ( ( ! [SY400: $i] :
( ( ( ti @ SV79 @ SY400 )
= ( zero_zero @ SV79 ) )
| ( ord_less @ SV79 @ ( zero_zero @ SV79 ) @ ( power_power @ SV79 @ SY400 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true )
| ( ( linordered_idom @ SV79 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1236]) ).
thf(1353,plain,
! [SV79: $i] :
( ( ( ! [SY401: $i] :
( ~ ( ord_less @ SV79 @ ( zero_zero @ SV79 ) @ ( power_power @ SV79 @ SY401 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ( ( ti @ SV79 @ SY401 )
!= ( zero_zero @ SV79 ) ) ) )
= $true )
| ( ( linordered_idom @ SV79 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1237]) ).
thf(1354,plain,
! [SV80: $i] :
( ( ( ~ ! [SY402: $i,SY403: $i] :
( ( ( number_number_of @ SV80 @ SY402 )
!= ( number_number_of @ SV80 @ SY403 ) )
| ( SY402 = SY403 ) )
| ~ ! [SY404: $i,SY405: $i] :
( ( SY404 != SY405 )
| ( ( number_number_of @ SV80 @ SY404 )
= ( number_number_of @ SV80 @ SY405 ) ) ) )
= $false )
| ( ( number_ring @ SV80 )
= $false )
| ( ( ring_char_0 @ SV80 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1238]) ).
thf(1355,plain,
! [SV198: $i] :
( ( ( ord_less_eq @ int @ pls @ ( bit0 @ SV198 ) )
= $false )
| ( ( ord_less_eq @ int @ pls @ SV198 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1239]) ).
thf(1356,plain,
! [SV199: $i] :
( ( ( ord_less_eq @ int @ pls @ SV199 )
= $false )
| ( ( ord_less_eq @ int @ pls @ ( bit0 @ SV199 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1240]) ).
thf(1357,plain,
! [SV81: $i] :
( ( ( ~ ! [SY406: $i] :
( ~ ( ord_less_eq @ SV81 @ ( number_number_of @ SV81 @ SY406 ) @ ( zero_zero @ SV81 ) )
| ( ord_less_eq @ int @ SY406 @ pls ) )
| ~ ! [SY407: $i] :
( ~ ( ord_less_eq @ int @ SY407 @ pls )
| ( ord_less_eq @ SV81 @ ( number_number_of @ SV81 @ SY407 ) @ ( zero_zero @ SV81 ) ) ) )
= $false )
| ( ( linordered_idom @ SV81 )
= $false )
| ( ( number_ring @ SV81 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1241]) ).
thf(1358,plain,
! [SV261: $i,SV200: $i] :
( ( ( ~ ( ord_less @ int @ ( number_number_of @ int @ SV200 ) @ ( number_number_of @ int @ SV261 ) ) )
= $true )
| ( ( ord_less @ int @ SV200 @ SV261 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1242]) ).
thf(1359,plain,
! [SV262: $i,SV201: $i] :
( ( ( ~ ( ord_less @ int @ SV201 @ SV262 ) )
= $true )
| ( ( ord_less @ int @ ( number_number_of @ int @ SV201 ) @ ( number_number_of @ int @ SV262 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1243]) ).
thf(1360,plain,
! [SV263: $i,SV202: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( bit0 @ SV202 ) @ ( bit0 @ SV263 ) ) )
= $true )
| ( ( ord_less_eq @ int @ SV202 @ SV263 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1244]) ).
thf(1361,plain,
! [SV264: $i,SV203: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV203 @ SV264 ) )
= $true )
| ( ( ord_less_eq @ int @ ( bit0 @ SV203 ) @ ( bit0 @ SV264 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1245]) ).
thf(1362,plain,
! [SV82: $i] :
( ( ( ! [SY408: $i,SY409: $i] :
( ( ( ti @ SV82 @ SY408 )
!= ( zero_zero @ SV82 ) )
| ( ( ti @ SV82 @ SY409 )
!= ( zero_zero @ SV82 ) )
| ( ( plus_plus @ SV82 @ ( times_times @ SV82 @ SY408 @ SY408 ) @ ( times_times @ SV82 @ SY409 @ SY409 ) )
= ( zero_zero @ SV82 ) ) ) )
= $true )
| ( ( linord581940658strict @ SV82 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1246]) ).
thf(1363,plain,
! [SV82: $i] :
( ( ( ~ ( ~ ! [SY410: $i] :
( ! [SY411: $i] :
( ( plus_plus @ SV82 @ ( times_times @ SV82 @ SY410 @ SY410 ) @ ( times_times @ SV82 @ SY411 @ SY411 ) )
!= ( zero_zero @ SV82 ) )
| ( ( ti @ SV82 @ SY410 )
= ( zero_zero @ SV82 ) ) )
| ~ ! [SY412: $i,SY413: $i] :
( ( ( plus_plus @ SV82 @ ( times_times @ SV82 @ SY412 @ SY412 ) @ ( times_times @ SV82 @ SY413 @ SY413 ) )
!= ( zero_zero @ SV82 ) )
| ( ( ti @ SV82 @ SY413 )
= ( zero_zero @ SV82 ) ) ) ) )
= $true )
| ( ( linord581940658strict @ SV82 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1247]) ).
thf(1364,plain,
! [SV265: $i,SV83: $i,SV288: $i] :
( ( ~ ( linordered_ring @ SV288 )
| ~ ( ord_less_eq @ SV288 @ SV83 @ ( ti @ SV288 @ SV265 ) )
| ( ord_less_eq @ SV288 @ SV83 @ SV265 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1248]) ).
thf(1365,plain,
! [SV266: $i,SV83: $i,SV289: $i] :
( ( ~ ( linordered_ring @ SV289 )
| ~ ( ord_less_eq @ SV289 @ SV83 @ SV266 )
| ( ord_less_eq @ SV289 @ SV83 @ ( ti @ SV289 @ SV266 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1249]) ).
thf(1366,plain,
! [SV84: $i] :
( ( ( ~ ! [SY418: $i] :
( ~ ( ord_less_eq @ SV84 @ ( number_number_of @ SV84 @ SY418 ) @ ( one_one @ SV84 ) )
| ( ord_less_eq @ int @ SY418 @ ( bit1 @ pls ) ) )
| ~ ! [SY419: $i] :
( ~ ( ord_less_eq @ int @ SY419 @ ( bit1 @ pls ) )
| ( ord_less_eq @ SV84 @ ( number_number_of @ SV84 @ SY419 ) @ ( one_one @ SV84 ) ) ) )
= $false )
| ( ( linordered_idom @ SV84 )
= $false )
| ( ( number_ring @ SV84 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1250]) ).
thf(1367,plain,
! [SV85: $i] :
( ( ( ~ ! [SY420: $i] :
( ~ ( ord_less_eq @ SV85 @ ( zero_zero @ SV85 ) @ ( number_number_of @ SV85 @ SY420 ) )
| ( ord_less_eq @ int @ pls @ SY420 ) )
| ~ ! [SY421: $i] :
( ~ ( ord_less_eq @ int @ pls @ SY421 )
| ( ord_less_eq @ SV85 @ ( zero_zero @ SV85 ) @ ( number_number_of @ SV85 @ SY421 ) ) ) )
= $false )
| ( ( linordered_idom @ SV85 )
= $false )
| ( ( number_ring @ SV85 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1251]) ).
thf(1368,plain,
! [SV204: $i] :
( ( ( ord_less @ int @ SV204 @ pls )
= $false )
| ( ( ord_less_eq @ int @ ( bit1 @ SV204 ) @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1252]) ).
thf(1369,plain,
! [SV205: $i] :
( ( ( ord_less_eq @ int @ ( bit1 @ SV205 ) @ pls )
= $false )
| ( ( ord_less @ int @ SV205 @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1253]) ).
thf(1370,plain,
! [SV86: $i] :
( ( ( ! [SY422: $i,SY423: $i] :
( ( ( ti @ SV86 @ SY422 )
!= ( zero_zero @ SV86 ) )
| ( ( ti @ SV86 @ SY423 )
!= ( zero_zero @ SV86 ) )
| ( ord_less_eq @ SV86 @ ( plus_plus @ SV86 @ ( times_times @ SV86 @ SY422 @ SY422 ) @ ( times_times @ SV86 @ SY423 @ SY423 ) ) @ ( zero_zero @ SV86 ) ) ) )
= $true )
| ( ( linord581940658strict @ SV86 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1254]) ).
thf(1371,plain,
! [SV86: $i] :
( ( ( ~ ( ~ ! [SY424: $i] :
( ! [SY425: $i] :
~ ( ord_less_eq @ SV86 @ ( plus_plus @ SV86 @ ( times_times @ SV86 @ SY424 @ SY424 ) @ ( times_times @ SV86 @ SY425 @ SY425 ) ) @ ( zero_zero @ SV86 ) )
| ( ( ti @ SV86 @ SY424 )
= ( zero_zero @ SV86 ) ) )
| ~ ! [SY426: $i,SY427: $i] :
( ~ ( ord_less_eq @ SV86 @ ( plus_plus @ SV86 @ ( times_times @ SV86 @ SY426 @ SY426 ) @ ( times_times @ SV86 @ SY427 @ SY427 ) ) @ ( zero_zero @ SV86 ) )
| ( ( ti @ SV86 @ SY427 )
= ( zero_zero @ SV86 ) ) ) ) )
= $true )
| ( ( linord581940658strict @ SV86 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1255]) ).
thf(1372,plain,
! [SV267: $i,SV206: $i] :
( ( ( ~ ( ord_less @ int @ ( bit0 @ SV206 ) @ ( bit1 @ SV267 ) ) )
= $true )
| ( ( ord_less_eq @ int @ SV206 @ SV267 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1256]) ).
thf(1373,plain,
! [SV268: $i,SV207: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV207 @ SV268 ) )
= $true )
| ( ( ord_less @ int @ ( bit0 @ SV207 ) @ ( bit1 @ SV268 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1257]) ).
thf(1374,plain,
! [SV269: $i,SV208: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( bit0 @ SV208 ) @ ( bit0 @ SV269 ) ) )
= $true )
| ( ( ord_less_eq @ int @ SV208 @ SV269 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1258]) ).
thf(1375,plain,
! [SV270: $i,SV209: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV209 @ SV270 ) )
= $true )
| ( ( ord_less_eq @ int @ ( bit0 @ SV209 ) @ ( bit0 @ SV270 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1259]) ).
thf(1376,plain,
! [SV210: $i] :
( ( ( ( zero_zero @ nat )
= ( number_number_of @ nat @ SV210 ) )
= $false )
| ( ( ord_less_eq @ int @ SV210 @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1260]) ).
thf(1377,plain,
! [SV211: $i] :
( ( ( ord_less_eq @ int @ SV211 @ pls )
= $false )
| ( ( ( zero_zero @ nat )
= ( number_number_of @ nat @ SV211 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1261]) ).
thf(1378,plain,
! [SV212: $i] :
( ( ( ord_less @ int @ pls @ ( bit1 @ SV212 ) )
= $false )
| ( ( ord_less_eq @ int @ pls @ SV212 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1262]) ).
thf(1379,plain,
! [SV213: $i] :
( ( ( ord_less_eq @ int @ pls @ SV213 )
= $false )
| ( ( ord_less @ int @ pls @ ( bit1 @ SV213 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1263]) ).
thf(1380,plain,
! [SV99: $i,SV28: $i,SV130: $i] :
( ( ( ord_less_eq @ int @ SV130 @ SV28 )
= $false )
| ( ( ord_less_eq @ int @ SV99 @ SV28 )
= $true )
| ( ( ord_less_eq @ int @ SV99 @ SV130 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1265]) ).
thf(1381,plain,
! [SV154: $i,SV133: $i,SV103: $i,SV35: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV35 @ SV103 ) )
= $true )
| ( ( ord_less @ int @ ( plus_plus @ int @ SV133 @ SV35 ) @ ( plus_plus @ int @ SV154 @ SV103 ) )
= $true )
| ( ( ord_less @ int @ SV133 @ SV154 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1268]) ).
thf(1382,plain,
! [SV44: $i,SV155: $i,SV218: $i] :
( ( ( ord_less_eq @ int @ pls @ SV218 )
= $false )
| ( ( ~ ( ord_less_eq @ int @ pls @ SV155 )
| ( ( plus_plus @ SV44 @ ( number_number_of @ SV44 @ SV218 ) @ ( number_number_of @ SV44 @ SV155 ) )
= ( number_number_of @ SV44 @ ( plus_plus @ int @ SV218 @ SV155 ) ) ) )
= $true )
| ( ( number_semiring @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1269]) ).
thf(1383,plain,
! [SV113: $i,SV50: $i,SV138: $i] :
( ( ( semiring @ SV138 )
= $false )
| ( ( number @ SV138 )
= $false )
| ( ( ( plus_plus @ SV138 @ ( ti @ SV138 @ SV50 ) @ SV113 )
= ( plus_plus @ SV138 @ SV50 @ SV113 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1270]) ).
thf(1384,plain,
! [SV114: $i,SV51: $i,SV139: $i] :
( ( ( semiring @ SV139 )
= $false )
| ( ( number @ SV139 )
= $false )
| ( ( ( plus_plus @ SV139 @ SV51 @ ( ti @ SV139 @ SV114 ) )
= ( plus_plus @ SV139 @ SV51 @ SV114 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1271]) ).
thf(1385,plain,
! [SV115: $i,SV52: $i,SV140: $i] :
( ( ( semiring @ SV140 )
= $false )
| ( ( number @ SV140 )
= $false )
| ( ( ( ti @ SV140 @ ( plus_plus @ SV140 @ SV52 @ SV115 ) )
= ( plus_plus @ SV140 @ SV52 @ SV115 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1272]) ).
thf(1386,plain,
! [SV116: $i,SV53: $i,SV141: $i] :
( ( ( semiring @ SV141 )
= $false )
| ( ( number @ SV141 )
= $false )
| ( ( ( times_times @ SV141 @ ( ti @ SV141 @ SV53 ) @ SV116 )
= ( times_times @ SV141 @ SV53 @ SV116 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1273]) ).
thf(1387,plain,
! [SV117: $i,SV54: $i,SV142: $i] :
( ( ( semiring @ SV142 )
= $false )
| ( ( number @ SV142 )
= $false )
| ( ( ( times_times @ SV142 @ SV54 @ ( ti @ SV142 @ SV117 ) )
= ( times_times @ SV142 @ SV54 @ SV117 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1274]) ).
thf(1388,plain,
! [SV118: $i,SV55: $i,SV143: $i] :
( ( ( semiring @ SV143 )
= $false )
| ( ( number @ SV143 )
= $false )
| ( ( ( ti @ SV143 @ ( times_times @ SV143 @ SV55 @ SV118 ) )
= ( times_times @ SV143 @ SV55 @ SV118 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1275]) ).
thf(1389,plain,
! [SV60: $i,SV156: $i,SV219: $i] :
( ( ( ord_less_eq @ int @ pls @ SV219 )
= $false )
| ( ( ~ ( ord_less_eq @ int @ pls @ SV156 )
| ( ( times_times @ SV60 @ ( number_number_of @ SV60 @ SV219 ) @ ( number_number_of @ SV60 @ SV156 ) )
= ( number_number_of @ SV60 @ ( times_times @ int @ SV219 @ SV156 ) ) ) )
= $true )
| ( ( number_semiring @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1276]) ).
thf(1390,plain,
! [SV290: $i,SV272: $i,SV62: $i] :
( ( ( ! [SY517: $i] :
( ( times_times @ SV62 @ ( plus_plus @ SV62 @ SV272 @ SV290 ) @ ( number_number_of @ SV62 @ SY517 ) )
= ( plus_plus @ SV62 @ ( times_times @ SV62 @ SV272 @ ( number_number_of @ SV62 @ SY517 ) ) @ ( times_times @ SV62 @ SV290 @ ( number_number_of @ SV62 @ SY517 ) ) ) ) )
= $true )
| ( ( number @ SV62 )
= $false )
| ( ( semiring @ SV62 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1277]) ).
thf(1391,plain,
! [SV291: $i,SV273: $i,SV63: $i] :
( ( ( ! [SY518: $i] :
( ( times_times @ SV63 @ ( number_number_of @ SV63 @ SV273 ) @ ( plus_plus @ SV63 @ SV291 @ SY518 ) )
= ( plus_plus @ SV63 @ ( times_times @ SV63 @ ( number_number_of @ SV63 @ SV273 ) @ SV291 ) @ ( times_times @ SV63 @ ( number_number_of @ SV63 @ SV273 ) @ SY518 ) ) ) )
= $true )
| ( ( number @ SV63 )
= $false )
| ( ( semiring @ SV63 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1278]) ).
thf(1392,plain,
! [SV221: $i,SV160: $i] :
( ( ( SV160 = SV221 )
= $true )
| ( ( ~ ( ord_less_eq @ int @ SV160 @ SV221 ) )
= $true )
| ( ( ord_less @ int @ SV160 @ SV221 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1281]) ).
thf(1393,plain,
! [SV292: $i] :
( ( ! [SY519: $i] :
( ~ ( ord_less @ int @ SV292 @ SY519 )
| ( SV292 != SY519 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1282]) ).
thf(1394,plain,
! [SV293: $i] :
( ( ! [SY520: $i] :
( ~ ( ord_less @ int @ SV293 @ SY520 )
| ( ord_less_eq @ int @ SV293 @ SY520 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1283]) ).
thf(1395,plain,
! [SV222: $i,SV163: $i] :
( ( ( ord_less_eq @ int @ ( bit0 @ SV163 ) @ ( bit1 @ SV222 ) )
= $false )
| ( ( ord_less_eq @ int @ SV163 @ SV222 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1286]) ).
thf(1396,plain,
! [SV223: $i,SV164: $i] :
( ( ( ord_less_eq @ int @ SV164 @ SV223 )
= $false )
| ( ( ord_less_eq @ int @ ( bit0 @ SV164 ) @ ( bit1 @ SV223 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1287]) ).
thf(1397,plain,
! [SV224: $i,SV165: $i] :
( ( ( ord_less_eq @ int @ ( bit0 @ SV165 ) @ ( bit1 @ SV224 ) )
= $false )
| ( ( ord_less_eq @ int @ SV165 @ SV224 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1288]) ).
thf(1398,plain,
! [SV225: $i,SV166: $i] :
( ( ( ord_less_eq @ int @ SV166 @ SV225 )
= $false )
| ( ( ord_less_eq @ int @ ( bit0 @ SV166 ) @ ( bit1 @ SV225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1289]) ).
thf(1399,plain,
! [SV65: $i] :
( ( ( ~ ! [SY344: $i,SY345: $i] :
( ~ ( ord_less_eq @ SV65 @ ( number_number_of @ SV65 @ SY344 ) @ ( number_number_of @ SV65 @ SY345 ) )
| ( ord_less_eq @ int @ SY344 @ SY345 ) ) )
= $false )
| ( ( linordered_idom @ SV65 )
= $false )
| ( ( number_ring @ SV65 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1290]) ).
thf(1400,plain,
! [SV65: $i] :
( ( ( ~ ! [SY346: $i,SY347: $i] :
( ~ ( ord_less_eq @ int @ SY346 @ SY347 )
| ( ord_less_eq @ SV65 @ ( number_number_of @ SV65 @ SY346 ) @ ( number_number_of @ SV65 @ SY347 ) ) ) )
= $false )
| ( ( linordered_idom @ SV65 )
= $false )
| ( ( number_ring @ SV65 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1290]) ).
thf(1401,plain,
! [SV169: $i,SV226: $i] :
( ( ( ord_less @ int @ SV226 @ pls )
= $false )
| ( ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV226 ) @ ( number_number_of @ nat @ SV169 ) )
= ( number_number_of @ nat @ SV169 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1293]) ).
thf(1402,plain,
! [SV294: $i] :
( ( ! [SY521: $i] :
( ( ord_less @ int @ SY521 @ pls )
| ~ ( ord_less @ int @ SV294 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SY521 ) @ ( number_number_of @ nat @ SV294 ) )
= ( number_number_of @ nat @ SY521 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1294]) ).
thf(1403,plain,
! [SV295: $i] :
( ( ! [SY522: $i] :
( ( ord_less @ int @ SY522 @ pls )
| ( ord_less @ int @ SV295 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SY522 ) @ ( number_number_of @ nat @ SV295 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SY522 @ SV295 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1295]) ).
thf(1404,plain,
! [SV227: $i,SV66: $i,SV274: $i] :
( ( ( ~ ( linordered_idom @ SV274 ) )
= $true )
| ( ( ~ ( ord_less @ SV274 @ SV66 @ ( ti @ SV274 @ SV227 ) )
| ( ord_less @ SV274 @ SV66 @ SV227 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1296]) ).
thf(1405,plain,
! [SV228: $i,SV66: $i,SV275: $i] :
( ( ( ~ ( linordered_idom @ SV275 ) )
= $true )
| ( ( ~ ( ord_less @ SV275 @ SV66 @ SV228 )
| ( ord_less @ SV275 @ SV66 @ ( ti @ SV275 @ SV228 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1297]) ).
thf(1406,plain,
! [SV229: $i,SV67: $i,SV276: $i] :
( ( ( ~ ( linordered_idom @ SV276 ) )
= $true )
| ( ( ~ ( ord_less @ SV276 @ ( ti @ SV276 @ SV67 ) @ SV229 )
| ( ord_less @ SV276 @ SV67 @ SV229 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1298]) ).
thf(1407,plain,
! [SV230: $i,SV67: $i,SV277: $i] :
( ( ( ~ ( linordered_idom @ SV277 ) )
= $true )
| ( ( ~ ( ord_less @ SV277 @ SV67 @ SV230 )
| ( ord_less @ SV277 @ ( ti @ SV277 @ SV67 ) @ SV230 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1299]) ).
thf(1408,plain,
! [SV231: $i,SV68: $i,SV278: $i] :
( ( ( ~ ( linordered_ring @ SV278 ) )
= $true )
| ( ( ~ ( ord_less_eq @ SV278 @ ( ti @ SV278 @ SV68 ) @ SV231 )
| ( ord_less_eq @ SV278 @ SV68 @ SV231 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1300]) ).
thf(1409,plain,
! [SV232: $i,SV68: $i,SV279: $i] :
( ( ( ~ ( linordered_ring @ SV279 ) )
= $true )
| ( ( ~ ( ord_less_eq @ SV279 @ SV68 @ SV232 )
| ( ord_less_eq @ SV279 @ ( ti @ SV279 @ SV68 ) @ SV232 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1301]) ).
thf(1410,plain,
! [SV233: $i,SV170: $i] :
( ( ( ( bit0 @ SV170 )
= ( bit0 @ SV233 ) )
= $false )
| ( ( SV170 = SV233 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1302]) ).
thf(1411,plain,
! [SV234: $i,SV171: $i] :
( ( ( SV171 = SV234 )
= $false )
| ( ( ( bit0 @ SV171 )
= ( bit0 @ SV234 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1303]) ).
thf(1412,plain,
! [SV235: $i,SV69: $i,SV280: $i] :
( ( ( ~ ( linorder @ SV280 )
| ~ ( number @ SV280 ) )
= $true )
| ( ( ~ ( ord_less_eq @ SV280 @ SV69 @ ( ti @ SV280 @ SV235 ) )
| ( ord_less_eq @ SV280 @ SV69 @ SV235 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1304]) ).
thf(1413,plain,
! [SV236: $i,SV69: $i,SV281: $i] :
( ( ( ~ ( linorder @ SV281 )
| ~ ( number @ SV281 ) )
= $true )
| ( ( ~ ( ord_less_eq @ SV281 @ SV69 @ SV236 )
| ( ord_less_eq @ SV281 @ SV69 @ ( ti @ SV281 @ SV236 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1305]) ).
thf(1414,plain,
! [SV296: $i,SV70: $i] :
( ( ( ! [SY523: $i] :
( ( ( number_number_of @ SV70 @ SV296 )
!= ( ti @ SV70 @ SY523 ) )
| ( ( ti @ SV70 @ SY523 )
= ( number_number_of @ SV70 @ SV296 ) ) ) )
= $true )
| ( ( number @ SV70 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1306]) ).
thf(1415,plain,
! [SV297: $i,SV70: $i] :
( ( ( ! [SY524: $i] :
( ( ( ti @ SV70 @ SY524 )
!= ( number_number_of @ SV70 @ SV297 ) )
| ( ( number_number_of @ SV70 @ SV297 )
= ( ti @ SV70 @ SY524 ) ) ) )
= $true )
| ( ( number @ SV70 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1307]) ).
thf(1416,plain,
! [SV237: $i,SV172: $i] :
( ( ( ord_less @ int @ SV172 @ SV237 )
= $false )
| ( ( ord_less_eq @ int @ ( bit1 @ SV172 ) @ ( bit0 @ SV237 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1308]) ).
thf(1417,plain,
! [SV238: $i,SV173: $i] :
( ( ( ord_less_eq @ int @ ( bit1 @ SV173 ) @ ( bit0 @ SV238 ) )
= $false )
| ( ( ord_less @ int @ SV173 @ SV238 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1309]) ).
thf(1418,plain,
! [SV239: $i,SV176: $i] :
( ( ( ord_less_eq @ int @ ( number_number_of @ int @ SV176 ) @ ( number_number_of @ int @ SV239 ) )
= $false )
| ( ( ord_less_eq @ int @ SV176 @ SV239 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1312]) ).
thf(1419,plain,
! [SV240: $i,SV177: $i] :
( ( ( ord_less_eq @ int @ SV177 @ SV240 )
= $false )
| ( ( ord_less_eq @ int @ ( number_number_of @ int @ SV177 ) @ ( number_number_of @ int @ SV240 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1313]) ).
thf(1420,plain,
! [SV241: $i,SV71: $i,SV282: $i] :
( ( ( ~ ( linorder @ SV282 )
| ~ ( number @ SV282 ) )
= $true )
| ( ( ~ ( ord_less @ SV282 @ ( ti @ SV282 @ SV71 ) @ SV241 )
| ( ord_less @ SV282 @ SV71 @ SV241 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1316]) ).
thf(1421,plain,
! [SV242: $i,SV71: $i,SV283: $i] :
( ( ( ~ ( linorder @ SV283 )
| ~ ( number @ SV283 ) )
= $true )
| ( ( ~ ( ord_less @ SV283 @ SV71 @ SV242 )
| ( ord_less @ SV283 @ ( ti @ SV283 @ SV71 ) @ SV242 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1317]) ).
thf(1422,plain,
! [SV243: $i,SV180: $i] :
( ( ( ( bit1 @ SV180 )
= ( bit1 @ SV243 ) )
= $false )
| ( ( SV180 = SV243 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1318]) ).
thf(1423,plain,
! [SV244: $i,SV181: $i] :
( ( ( SV181 = SV244 )
= $false )
| ( ( ( bit1 @ SV181 )
= ( bit1 @ SV244 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1319]) ).
thf(1424,plain,
! [SV245: $i,SV182: $i] :
( ( ( ord_less_eq @ int @ ( bit1 @ SV182 ) @ ( bit1 @ SV245 ) )
= $false )
| ( ( ord_less_eq @ int @ SV182 @ SV245 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1320]) ).
thf(1425,plain,
! [SV246: $i,SV183: $i] :
( ( ( ord_less_eq @ int @ SV183 @ SV246 )
= $false )
| ( ( ord_less_eq @ int @ ( bit1 @ SV183 ) @ ( bit1 @ SV246 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1321]) ).
thf(1426,plain,
! [SV247: $i,SV188: $i] :
( ( ( ord_less @ int @ ( bit0 @ SV188 ) @ ( bit1 @ SV247 ) )
= $false )
| ( ( ord_less_eq @ int @ SV188 @ SV247 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1326]) ).
thf(1427,plain,
! [SV248: $i,SV189: $i] :
( ( ( ord_less_eq @ int @ SV189 @ SV248 )
= $false )
| ( ( ord_less @ int @ ( bit0 @ SV189 ) @ ( bit1 @ SV248 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1327]) ).
thf(1428,plain,
! [SV249: $i,SV190: $i] :
( ( ( ord_less @ int @ SV190 @ SV249 )
= $false )
| ( ( ord_less_eq @ int @ ( plus_plus @ int @ SV190 @ ( one_one @ int ) ) @ SV249 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1328]) ).
thf(1429,plain,
! [SV250: $i,SV191: $i] :
( ( ( ord_less_eq @ int @ ( plus_plus @ int @ SV191 @ ( one_one @ int ) ) @ SV250 )
= $false )
| ( ( ord_less @ int @ SV191 @ SV250 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1329]) ).
thf(1430,plain,
! [SV251: $i,SV72: $i,SV284: $i] :
( ( ( ~ ( linorder @ SV284 )
| ~ ( number @ SV284 ) )
= $true )
| ( ( ~ ( ord_less_eq @ SV284 @ ( ti @ SV284 @ SV72 ) @ SV251 )
| ( ord_less_eq @ SV284 @ SV72 @ SV251 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1330]) ).
thf(1431,plain,
! [SV252: $i,SV72: $i,SV285: $i] :
( ( ( ~ ( linorder @ SV285 )
| ~ ( number @ SV285 ) )
= $true )
| ( ( ~ ( ord_less_eq @ SV285 @ SV72 @ SV252 )
| ( ord_less_eq @ SV285 @ ( ti @ SV285 @ SV72 ) @ SV252 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1331]) ).
thf(1432,plain,
! [SV253: $i,SV73: $i,SV286: $i] :
( ( ( ~ ( linorder @ SV286 )
| ~ ( number @ SV286 ) )
= $true )
| ( ( ~ ( ord_less @ SV286 @ SV73 @ ( ti @ SV286 @ SV253 ) )
| ( ord_less @ SV286 @ SV73 @ SV253 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1332]) ).
thf(1433,plain,
! [SV254: $i,SV73: $i,SV287: $i] :
( ( ( ~ ( linorder @ SV287 )
| ~ ( number @ SV287 ) )
= $true )
| ( ( ~ ( ord_less @ SV287 @ SV73 @ SV254 )
| ( ord_less @ SV287 @ SV73 @ ( ti @ SV287 @ SV254 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1333]) ).
thf(1434,plain,
! [SV255: $i,SV192: $i] :
( ( ( ord_less_eq @ int @ ( bit1 @ SV192 ) @ ( bit1 @ SV255 ) )
= $false )
| ( ( ord_less_eq @ int @ SV192 @ SV255 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1334]) ).
thf(1435,plain,
! [SV256: $i,SV193: $i] :
( ( ( ord_less_eq @ int @ SV193 @ SV256 )
= $false )
| ( ( ord_less_eq @ int @ ( bit1 @ SV193 ) @ ( bit1 @ SV256 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1335]) ).
thf(1436,plain,
! [SV257: $i,SV194: $i] :
( ( ( ord_less @ int @ SV194 @ SV257 )
= $false )
| ( ( ord_less_eq @ int @ ( bit1 @ SV194 ) @ ( bit0 @ SV257 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1336]) ).
thf(1437,plain,
! [SV258: $i,SV195: $i] :
( ( ( ord_less_eq @ int @ ( bit1 @ SV195 ) @ ( bit0 @ SV258 ) )
= $false )
| ( ( ord_less @ int @ SV195 @ SV258 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1337]) ).
thf(1438,plain,
! [SV259: $i,SV196: $i] :
( ( ( ord_less @ int @ SV196 @ ( plus_plus @ int @ SV259 @ ( one_one @ int ) ) )
= $false )
| ( ( ord_less_eq @ int @ SV196 @ SV259 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1338]) ).
thf(1439,plain,
! [SV260: $i,SV197: $i] :
( ( ( ord_less_eq @ int @ SV197 @ SV260 )
= $false )
| ( ( ord_less @ int @ SV197 @ ( plus_plus @ int @ SV260 @ ( one_one @ int ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1339]) ).
thf(1440,plain,
! [SV74: $i] :
( ( ( ~ ! [SY380: $i,SY381: $i] :
( ~ ( ord_less_eq @ SV74 @ ( number_number_of @ SV74 @ SY380 ) @ ( number_number_of @ SV74 @ SY381 ) )
| ~ ( ord_less @ SV74 @ ( number_number_of @ SV74 @ SY381 ) @ ( number_number_of @ SV74 @ SY380 ) ) ) )
= $false )
| ( ( linorder @ SV74 )
= $false )
| ( ( number @ SV74 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1340]) ).
thf(1441,plain,
! [SV74: $i] :
( ( ( ~ ! [SY382: $i,SY383: $i] :
( ( ord_less @ SV74 @ ( number_number_of @ SV74 @ SY383 ) @ ( number_number_of @ SV74 @ SY382 ) )
| ( ord_less_eq @ SV74 @ ( number_number_of @ SV74 @ SY382 ) @ ( number_number_of @ SV74 @ SY383 ) ) ) )
= $false )
| ( ( linorder @ SV74 )
= $false )
| ( ( number @ SV74 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1340]) ).
thf(1442,plain,
! [SV298: $i,SV75: $i] :
( ( ( ! [SY525: $i] :
( ~ ( ord_less @ SV75 @ ( zero_zero @ SV75 ) @ ( plus_plus @ SV75 @ ( power_power @ SV75 @ SV298 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV75 @ SY525 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
| ( ( ti @ SV75 @ SV298 )
!= ( zero_zero @ SV75 ) )
| ( ( ti @ SV75 @ SY525 )
!= ( zero_zero @ SV75 ) ) ) )
= $true )
| ( ( linordered_idom @ SV75 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1341]) ).
thf(1443,plain,
! [SV75: $i] :
( ( ( ~ ! [SY386: $i] :
( ( ( ti @ SV75 @ SY386 )
= ( zero_zero @ SV75 ) )
| ! [SY387: $i] : ( ord_less @ SV75 @ ( zero_zero @ SV75 ) @ ( plus_plus @ SV75 @ ( power_power @ SV75 @ SY386 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV75 @ SY387 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
| ~ ! [SY388: $i,SY389: $i] :
( ( ( ti @ SV75 @ SY389 )
= ( zero_zero @ SV75 ) )
| ( ord_less @ SV75 @ ( zero_zero @ SV75 ) @ ( plus_plus @ SV75 @ ( power_power @ SV75 @ SY388 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV75 @ SY389 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) )
= $false )
| ( ( linordered_idom @ SV75 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1342]) ).
thf(1444,plain,
! [SV76: $i] :
( ( ( ~ ! [SY390: $i] :
( ~ ( ord_less_eq @ SV76 @ ( one_one @ SV76 ) @ ( number_number_of @ SV76 @ SY390 ) )
| ( ord_less_eq @ int @ ( bit1 @ pls ) @ SY390 ) ) )
= $false )
| ( ( linordered_idom @ SV76 )
= $false )
| ( ( number_ring @ SV76 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1343]) ).
thf(1445,plain,
! [SV76: $i] :
( ( ( ~ ! [SY391: $i] :
( ~ ( ord_less_eq @ int @ ( bit1 @ pls ) @ SY391 )
| ( ord_less_eq @ SV76 @ ( one_one @ SV76 ) @ ( number_number_of @ SV76 @ SY391 ) ) ) )
= $false )
| ( ( linordered_idom @ SV76 )
= $false )
| ( ( number_ring @ SV76 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1343]) ).
thf(1446,plain,
! [SV299: $i,SV77: $i] :
( ( ( ! [SY526: $i] :
( ( ( ti @ SV77 @ SV299 )
!= ( zero_zero @ SV77 ) )
| ( ( ti @ SV77 @ SY526 )
!= ( zero_zero @ SV77 ) )
| ( ( plus_plus @ SV77 @ ( power_power @ SV77 @ SV299 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV77 @ SY526 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV77 ) ) ) )
= $true )
| ( ( linordered_idom @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1344]) ).
thf(1447,plain,
! [SV77: $i] :
( ( ( ~ ! [SY394: $i] :
( ! [SY395: $i] :
( ( plus_plus @ SV77 @ ( power_power @ SV77 @ SY394 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV77 @ SY395 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV77 ) )
| ( ( ti @ SV77 @ SY394 )
= ( zero_zero @ SV77 ) ) )
| ~ ! [SY396: $i,SY397: $i] :
( ( ( plus_plus @ SV77 @ ( power_power @ SV77 @ SY396 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV77 @ SY397 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV77 ) )
| ( ( ti @ SV77 @ SY397 )
= ( zero_zero @ SV77 ) ) ) )
= $false )
| ( ( linordered_idom @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1345]) ).
thf(1448,plain,
! [SV300: $i,SV78: $i] :
( ( ( ( ( power_power @ SV78 @ SV300 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= ( zero_zero @ SV78 ) )
| ( ( ti @ SV78 @ SV300 )
= ( zero_zero @ SV78 ) ) )
= $true )
| ( ( ring_11004092258visors @ SV78 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1346]) ).
thf(1449,plain,
! [SV301: $i,SV78: $i] :
( ( ( ( ( ti @ SV78 @ SV301 )
!= ( zero_zero @ SV78 ) )
| ( ( power_power @ SV78 @ SV301 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SV78 ) ) )
= $true )
| ( ( ring_11004092258visors @ SV78 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1347]) ).
thf(1450,plain,
! [SV302: $i] :
( ( ! [SY527: $i] :
( ( ord_less @ int @ SV302 @ SY527 )
| ~ ( ord_less @ int @ SV302 @ SY527 )
| ( ord_less @ nat @ ( number_number_of @ nat @ SV302 ) @ ( number_number_of @ nat @ SY527 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1348]) ).
thf(1451,plain,
! [SV303: $i] :
( ( ! [SY528: $i] :
( ~ ( ord_less @ int @ pls @ SY528 )
| ~ ( ord_less @ int @ SV303 @ SY528 )
| ( ord_less @ nat @ ( number_number_of @ nat @ SV303 ) @ ( number_number_of @ nat @ SY528 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1349]) ).
thf(1452,plain,
! [SV304: $i] :
( ( ! [SY529: $i] :
( ~ ( ord_less @ nat @ ( number_number_of @ nat @ SV304 ) @ ( number_number_of @ nat @ SY529 ) )
| ~ ( ord_less @ int @ SV304 @ SY529 )
| ( ord_less @ int @ pls @ SY529 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1350]) ).
thf(1453,plain,
! [SV305: $i] :
( ( ! [SY530: $i] :
( ~ ( ord_less @ nat @ ( number_number_of @ nat @ SV305 ) @ ( number_number_of @ nat @ SY530 ) )
| ( ord_less @ int @ SV305 @ SY530 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1351]) ).
thf(1454,plain,
! [SV306: $i,SV79: $i] :
( ( ( ( ( ti @ SV79 @ SV306 )
= ( zero_zero @ SV79 ) )
| ( ord_less @ SV79 @ ( zero_zero @ SV79 ) @ ( power_power @ SV79 @ SV306 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true )
| ( ( linordered_idom @ SV79 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1352]) ).
thf(1455,plain,
! [SV307: $i,SV79: $i] :
( ( ( ~ ( ord_less @ SV79 @ ( zero_zero @ SV79 ) @ ( power_power @ SV79 @ SV307 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ( ( ti @ SV79 @ SV307 )
!= ( zero_zero @ SV79 ) ) )
= $true )
| ( ( linordered_idom @ SV79 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1353]) ).
thf(1456,plain,
! [SV80: $i] :
( ( ( ~ ! [SY402: $i,SY403: $i] :
( ( ( number_number_of @ SV80 @ SY402 )
!= ( number_number_of @ SV80 @ SY403 ) )
| ( SY402 = SY403 ) ) )
= $false )
| ( ( number_ring @ SV80 )
= $false )
| ( ( ring_char_0 @ SV80 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1354]) ).
thf(1457,plain,
! [SV80: $i] :
( ( ( ~ ! [SY404: $i,SY405: $i] :
( ( SY404 != SY405 )
| ( ( number_number_of @ SV80 @ SY404 )
= ( number_number_of @ SV80 @ SY405 ) ) ) )
= $false )
| ( ( number_ring @ SV80 )
= $false )
| ( ( ring_char_0 @ SV80 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1354]) ).
thf(1458,plain,
! [SV81: $i] :
( ( ( ~ ! [SY406: $i] :
( ~ ( ord_less_eq @ SV81 @ ( number_number_of @ SV81 @ SY406 ) @ ( zero_zero @ SV81 ) )
| ( ord_less_eq @ int @ SY406 @ pls ) ) )
= $false )
| ( ( linordered_idom @ SV81 )
= $false )
| ( ( number_ring @ SV81 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1357]) ).
thf(1459,plain,
! [SV81: $i] :
( ( ( ~ ! [SY407: $i] :
( ~ ( ord_less_eq @ int @ SY407 @ pls )
| ( ord_less_eq @ SV81 @ ( number_number_of @ SV81 @ SY407 ) @ ( zero_zero @ SV81 ) ) ) )
= $false )
| ( ( linordered_idom @ SV81 )
= $false )
| ( ( number_ring @ SV81 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1357]) ).
thf(1460,plain,
! [SV261: $i,SV200: $i] :
( ( ( ord_less @ int @ ( number_number_of @ int @ SV200 ) @ ( number_number_of @ int @ SV261 ) )
= $false )
| ( ( ord_less @ int @ SV200 @ SV261 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1358]) ).
thf(1461,plain,
! [SV262: $i,SV201: $i] :
( ( ( ord_less @ int @ SV201 @ SV262 )
= $false )
| ( ( ord_less @ int @ ( number_number_of @ int @ SV201 ) @ ( number_number_of @ int @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1359]) ).
thf(1462,plain,
! [SV263: $i,SV202: $i] :
( ( ( ord_less_eq @ int @ ( bit0 @ SV202 ) @ ( bit0 @ SV263 ) )
= $false )
| ( ( ord_less_eq @ int @ SV202 @ SV263 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1360]) ).
thf(1463,plain,
! [SV264: $i,SV203: $i] :
( ( ( ord_less_eq @ int @ SV203 @ SV264 )
= $false )
| ( ( ord_less_eq @ int @ ( bit0 @ SV203 ) @ ( bit0 @ SV264 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1361]) ).
thf(1464,plain,
! [SV308: $i,SV82: $i] :
( ( ( ! [SY531: $i] :
( ( ( ti @ SV82 @ SV308 )
!= ( zero_zero @ SV82 ) )
| ( ( ti @ SV82 @ SY531 )
!= ( zero_zero @ SV82 ) )
| ( ( plus_plus @ SV82 @ ( times_times @ SV82 @ SV308 @ SV308 ) @ ( times_times @ SV82 @ SY531 @ SY531 ) )
= ( zero_zero @ SV82 ) ) ) )
= $true )
| ( ( linord581940658strict @ SV82 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1362]) ).
thf(1465,plain,
! [SV82: $i] :
( ( ( ~ ! [SY410: $i] :
( ! [SY411: $i] :
( ( plus_plus @ SV82 @ ( times_times @ SV82 @ SY410 @ SY410 ) @ ( times_times @ SV82 @ SY411 @ SY411 ) )
!= ( zero_zero @ SV82 ) )
| ( ( ti @ SV82 @ SY410 )
= ( zero_zero @ SV82 ) ) )
| ~ ! [SY412: $i,SY413: $i] :
( ( ( plus_plus @ SV82 @ ( times_times @ SV82 @ SY412 @ SY412 ) @ ( times_times @ SV82 @ SY413 @ SY413 ) )
!= ( zero_zero @ SV82 ) )
| ( ( ti @ SV82 @ SY413 )
= ( zero_zero @ SV82 ) ) ) )
= $false )
| ( ( linord581940658strict @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1363]) ).
thf(1466,plain,
! [SV265: $i,SV83: $i,SV288: $i] :
( ( ( ~ ( linordered_ring @ SV288 ) )
= $true )
| ( ( ~ ( ord_less_eq @ SV288 @ SV83 @ ( ti @ SV288 @ SV265 ) )
| ( ord_less_eq @ SV288 @ SV83 @ SV265 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1364]) ).
thf(1467,plain,
! [SV266: $i,SV83: $i,SV289: $i] :
( ( ( ~ ( linordered_ring @ SV289 ) )
= $true )
| ( ( ~ ( ord_less_eq @ SV289 @ SV83 @ SV266 )
| ( ord_less_eq @ SV289 @ SV83 @ ( ti @ SV289 @ SV266 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1365]) ).
thf(1468,plain,
! [SV84: $i] :
( ( ( ~ ! [SY418: $i] :
( ~ ( ord_less_eq @ SV84 @ ( number_number_of @ SV84 @ SY418 ) @ ( one_one @ SV84 ) )
| ( ord_less_eq @ int @ SY418 @ ( bit1 @ pls ) ) ) )
= $false )
| ( ( linordered_idom @ SV84 )
= $false )
| ( ( number_ring @ SV84 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1366]) ).
thf(1469,plain,
! [SV84: $i] :
( ( ( ~ ! [SY419: $i] :
( ~ ( ord_less_eq @ int @ SY419 @ ( bit1 @ pls ) )
| ( ord_less_eq @ SV84 @ ( number_number_of @ SV84 @ SY419 ) @ ( one_one @ SV84 ) ) ) )
= $false )
| ( ( linordered_idom @ SV84 )
= $false )
| ( ( number_ring @ SV84 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1366]) ).
thf(1470,plain,
! [SV85: $i] :
( ( ( ~ ! [SY420: $i] :
( ~ ( ord_less_eq @ SV85 @ ( zero_zero @ SV85 ) @ ( number_number_of @ SV85 @ SY420 ) )
| ( ord_less_eq @ int @ pls @ SY420 ) ) )
= $false )
| ( ( linordered_idom @ SV85 )
= $false )
| ( ( number_ring @ SV85 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1367]) ).
thf(1471,plain,
! [SV85: $i] :
( ( ( ~ ! [SY421: $i] :
( ~ ( ord_less_eq @ int @ pls @ SY421 )
| ( ord_less_eq @ SV85 @ ( zero_zero @ SV85 ) @ ( number_number_of @ SV85 @ SY421 ) ) ) )
= $false )
| ( ( linordered_idom @ SV85 )
= $false )
| ( ( number_ring @ SV85 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1367]) ).
thf(1472,plain,
! [SV309: $i,SV86: $i] :
( ( ( ! [SY532: $i] :
( ( ( ti @ SV86 @ SV309 )
!= ( zero_zero @ SV86 ) )
| ( ( ti @ SV86 @ SY532 )
!= ( zero_zero @ SV86 ) )
| ( ord_less_eq @ SV86 @ ( plus_plus @ SV86 @ ( times_times @ SV86 @ SV309 @ SV309 ) @ ( times_times @ SV86 @ SY532 @ SY532 ) ) @ ( zero_zero @ SV86 ) ) ) )
= $true )
| ( ( linord581940658strict @ SV86 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1370]) ).
thf(1473,plain,
! [SV86: $i] :
( ( ( ~ ! [SY424: $i] :
( ! [SY425: $i] :
~ ( ord_less_eq @ SV86 @ ( plus_plus @ SV86 @ ( times_times @ SV86 @ SY424 @ SY424 ) @ ( times_times @ SV86 @ SY425 @ SY425 ) ) @ ( zero_zero @ SV86 ) )
| ( ( ti @ SV86 @ SY424 )
= ( zero_zero @ SV86 ) ) )
| ~ ! [SY426: $i,SY427: $i] :
( ~ ( ord_less_eq @ SV86 @ ( plus_plus @ SV86 @ ( times_times @ SV86 @ SY426 @ SY426 ) @ ( times_times @ SV86 @ SY427 @ SY427 ) ) @ ( zero_zero @ SV86 ) )
| ( ( ti @ SV86 @ SY427 )
= ( zero_zero @ SV86 ) ) ) )
= $false )
| ( ( linord581940658strict @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1371]) ).
thf(1474,plain,
! [SV267: $i,SV206: $i] :
( ( ( ord_less @ int @ ( bit0 @ SV206 ) @ ( bit1 @ SV267 ) )
= $false )
| ( ( ord_less_eq @ int @ SV206 @ SV267 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1372]) ).
thf(1475,plain,
! [SV268: $i,SV207: $i] :
( ( ( ord_less_eq @ int @ SV207 @ SV268 )
= $false )
| ( ( ord_less @ int @ ( bit0 @ SV207 ) @ ( bit1 @ SV268 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1373]) ).
thf(1476,plain,
! [SV269: $i,SV208: $i] :
( ( ( ord_less_eq @ int @ ( bit0 @ SV208 ) @ ( bit0 @ SV269 ) )
= $false )
| ( ( ord_less_eq @ int @ SV208 @ SV269 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1374]) ).
thf(1477,plain,
! [SV270: $i,SV209: $i] :
( ( ( ord_less_eq @ int @ SV209 @ SV270 )
= $false )
| ( ( ord_less_eq @ int @ ( bit0 @ SV209 ) @ ( bit0 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1375]) ).
thf(1478,plain,
! [SV154: $i,SV133: $i,SV103: $i,SV35: $i] :
( ( ( ord_less_eq @ int @ SV35 @ SV103 )
= $false )
| ( ( ord_less @ int @ ( plus_plus @ int @ SV133 @ SV35 ) @ ( plus_plus @ int @ SV154 @ SV103 ) )
= $true )
| ( ( ord_less @ int @ SV133 @ SV154 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1381]) ).
thf(1479,plain,
! [SV218: $i,SV44: $i,SV155: $i] :
( ( ( ~ ( ord_less_eq @ int @ pls @ SV155 ) )
= $true )
| ( ( ( plus_plus @ SV44 @ ( number_number_of @ SV44 @ SV218 ) @ ( number_number_of @ SV44 @ SV155 ) )
= ( number_number_of @ SV44 @ ( plus_plus @ int @ SV218 @ SV155 ) ) )
= $true )
| ( ( ord_less_eq @ int @ pls @ SV218 )
= $false )
| ( ( number_semiring @ SV44 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1382]) ).
thf(1480,plain,
! [SV219: $i,SV60: $i,SV156: $i] :
( ( ( ~ ( ord_less_eq @ int @ pls @ SV156 ) )
= $true )
| ( ( ( times_times @ SV60 @ ( number_number_of @ SV60 @ SV219 ) @ ( number_number_of @ SV60 @ SV156 ) )
= ( number_number_of @ SV60 @ ( times_times @ int @ SV219 @ SV156 ) ) )
= $true )
| ( ( ord_less_eq @ int @ pls @ SV219 )
= $false )
| ( ( number_semiring @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1389]) ).
thf(1481,plain,
! [SV310: $i,SV290: $i,SV272: $i,SV62: $i] :
( ( ( ( times_times @ SV62 @ ( plus_plus @ SV62 @ SV272 @ SV290 ) @ ( number_number_of @ SV62 @ SV310 ) )
= ( plus_plus @ SV62 @ ( times_times @ SV62 @ SV272 @ ( number_number_of @ SV62 @ SV310 ) ) @ ( times_times @ SV62 @ SV290 @ ( number_number_of @ SV62 @ SV310 ) ) ) )
= $true )
| ( ( number @ SV62 )
= $false )
| ( ( semiring @ SV62 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1390]) ).
thf(1482,plain,
! [SV311: $i,SV291: $i,SV273: $i,SV63: $i] :
( ( ( ( times_times @ SV63 @ ( number_number_of @ SV63 @ SV273 ) @ ( plus_plus @ SV63 @ SV291 @ SV311 ) )
= ( plus_plus @ SV63 @ ( times_times @ SV63 @ ( number_number_of @ SV63 @ SV273 ) @ SV291 ) @ ( times_times @ SV63 @ ( number_number_of @ SV63 @ SV273 ) @ SV311 ) ) )
= $true )
| ( ( number @ SV63 )
= $false )
| ( ( semiring @ SV63 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1391]) ).
thf(1483,plain,
! [SV221: $i,SV160: $i] :
( ( ( ord_less_eq @ int @ SV160 @ SV221 )
= $false )
| ( ( SV160 = SV221 )
= $true )
| ( ( ord_less @ int @ SV160 @ SV221 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1392]) ).
thf(1484,plain,
! [SV312: $i,SV292: $i] :
( ( ~ ( ord_less @ int @ SV292 @ SV312 )
| ( SV292 != SV312 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1393]) ).
thf(1485,plain,
! [SV313: $i,SV293: $i] :
( ( ~ ( ord_less @ int @ SV293 @ SV313 )
| ( ord_less_eq @ int @ SV293 @ SV313 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1394]) ).
thf(1486,plain,
! [SV65: $i] :
( ( ( ! [SY344: $i,SY345: $i] :
( ~ ( ord_less_eq @ SV65 @ ( number_number_of @ SV65 @ SY344 ) @ ( number_number_of @ SV65 @ SY345 ) )
| ( ord_less_eq @ int @ SY344 @ SY345 ) ) )
= $true )
| ( ( linordered_idom @ SV65 )
= $false )
| ( ( number_ring @ SV65 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1399]) ).
thf(1487,plain,
! [SV65: $i] :
( ( ( ! [SY346: $i,SY347: $i] :
( ~ ( ord_less_eq @ int @ SY346 @ SY347 )
| ( ord_less_eq @ SV65 @ ( number_number_of @ SV65 @ SY346 ) @ ( number_number_of @ SV65 @ SY347 ) ) ) )
= $true )
| ( ( linordered_idom @ SV65 )
= $false )
| ( ( number_ring @ SV65 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1400]) ).
thf(1488,plain,
! [SV294: $i,SV314: $i] :
( ( ( ord_less @ int @ SV314 @ pls )
| ~ ( ord_less @ int @ SV294 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV314 ) @ ( number_number_of @ nat @ SV294 ) )
= ( number_number_of @ nat @ SV314 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1402]) ).
thf(1489,plain,
! [SV295: $i,SV315: $i] :
( ( ( ord_less @ int @ SV315 @ pls )
| ( ord_less @ int @ SV295 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV315 ) @ ( number_number_of @ nat @ SV295 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SV315 @ SV295 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1403]) ).
thf(1490,plain,
! [SV227: $i,SV66: $i,SV274: $i] :
( ( ( linordered_idom @ SV274 )
= $false )
| ( ( ~ ( ord_less @ SV274 @ SV66 @ ( ti @ SV274 @ SV227 ) )
| ( ord_less @ SV274 @ SV66 @ SV227 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1404]) ).
thf(1491,plain,
! [SV228: $i,SV66: $i,SV275: $i] :
( ( ( linordered_idom @ SV275 )
= $false )
| ( ( ~ ( ord_less @ SV275 @ SV66 @ SV228 )
| ( ord_less @ SV275 @ SV66 @ ( ti @ SV275 @ SV228 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1405]) ).
thf(1492,plain,
! [SV229: $i,SV67: $i,SV276: $i] :
( ( ( linordered_idom @ SV276 )
= $false )
| ( ( ~ ( ord_less @ SV276 @ ( ti @ SV276 @ SV67 ) @ SV229 )
| ( ord_less @ SV276 @ SV67 @ SV229 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1406]) ).
thf(1493,plain,
! [SV230: $i,SV67: $i,SV277: $i] :
( ( ( linordered_idom @ SV277 )
= $false )
| ( ( ~ ( ord_less @ SV277 @ SV67 @ SV230 )
| ( ord_less @ SV277 @ ( ti @ SV277 @ SV67 ) @ SV230 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1407]) ).
thf(1494,plain,
! [SV231: $i,SV68: $i,SV278: $i] :
( ( ( linordered_ring @ SV278 )
= $false )
| ( ( ~ ( ord_less_eq @ SV278 @ ( ti @ SV278 @ SV68 ) @ SV231 )
| ( ord_less_eq @ SV278 @ SV68 @ SV231 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1408]) ).
thf(1495,plain,
! [SV232: $i,SV68: $i,SV279: $i] :
( ( ( linordered_ring @ SV279 )
= $false )
| ( ( ~ ( ord_less_eq @ SV279 @ SV68 @ SV232 )
| ( ord_less_eq @ SV279 @ ( ti @ SV279 @ SV68 ) @ SV232 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1409]) ).
thf(1496,plain,
! [SV235: $i,SV69: $i,SV280: $i] :
( ( ( ~ ( linorder @ SV280 ) )
= $true )
| ( ( ~ ( number @ SV280 ) )
= $true )
| ( ( ~ ( ord_less_eq @ SV280 @ SV69 @ ( ti @ SV280 @ SV235 ) )
| ( ord_less_eq @ SV280 @ SV69 @ SV235 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1412]) ).
thf(1497,plain,
! [SV236: $i,SV69: $i,SV281: $i] :
( ( ( ~ ( linorder @ SV281 ) )
= $true )
| ( ( ~ ( number @ SV281 ) )
= $true )
| ( ( ~ ( ord_less_eq @ SV281 @ SV69 @ SV236 )
| ( ord_less_eq @ SV281 @ SV69 @ ( ti @ SV281 @ SV236 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1413]) ).
thf(1498,plain,
! [SV316: $i,SV296: $i,SV70: $i] :
( ( ( ( ( number_number_of @ SV70 @ SV296 )
!= ( ti @ SV70 @ SV316 ) )
| ( ( ti @ SV70 @ SV316 )
= ( number_number_of @ SV70 @ SV296 ) ) )
= $true )
| ( ( number @ SV70 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1414]) ).
thf(1499,plain,
! [SV297: $i,SV317: $i,SV70: $i] :
( ( ( ( ( ti @ SV70 @ SV317 )
!= ( number_number_of @ SV70 @ SV297 ) )
| ( ( number_number_of @ SV70 @ SV297 )
= ( ti @ SV70 @ SV317 ) ) )
= $true )
| ( ( number @ SV70 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1415]) ).
thf(1500,plain,
! [SV241: $i,SV71: $i,SV282: $i] :
( ( ( ~ ( linorder @ SV282 ) )
= $true )
| ( ( ~ ( number @ SV282 ) )
= $true )
| ( ( ~ ( ord_less @ SV282 @ ( ti @ SV282 @ SV71 ) @ SV241 )
| ( ord_less @ SV282 @ SV71 @ SV241 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1420]) ).
thf(1501,plain,
! [SV242: $i,SV71: $i,SV283: $i] :
( ( ( ~ ( linorder @ SV283 ) )
= $true )
| ( ( ~ ( number @ SV283 ) )
= $true )
| ( ( ~ ( ord_less @ SV283 @ SV71 @ SV242 )
| ( ord_less @ SV283 @ ( ti @ SV283 @ SV71 ) @ SV242 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1421]) ).
thf(1502,plain,
! [SV251: $i,SV72: $i,SV284: $i] :
( ( ( ~ ( linorder @ SV284 ) )
= $true )
| ( ( ~ ( number @ SV284 ) )
= $true )
| ( ( ~ ( ord_less_eq @ SV284 @ ( ti @ SV284 @ SV72 ) @ SV251 )
| ( ord_less_eq @ SV284 @ SV72 @ SV251 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1430]) ).
thf(1503,plain,
! [SV252: $i,SV72: $i,SV285: $i] :
( ( ( ~ ( linorder @ SV285 ) )
= $true )
| ( ( ~ ( number @ SV285 ) )
= $true )
| ( ( ~ ( ord_less_eq @ SV285 @ SV72 @ SV252 )
| ( ord_less_eq @ SV285 @ ( ti @ SV285 @ SV72 ) @ SV252 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1431]) ).
thf(1504,plain,
! [SV253: $i,SV73: $i,SV286: $i] :
( ( ( ~ ( linorder @ SV286 ) )
= $true )
| ( ( ~ ( number @ SV286 ) )
= $true )
| ( ( ~ ( ord_less @ SV286 @ SV73 @ ( ti @ SV286 @ SV253 ) )
| ( ord_less @ SV286 @ SV73 @ SV253 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1432]) ).
thf(1505,plain,
! [SV254: $i,SV73: $i,SV287: $i] :
( ( ( ~ ( linorder @ SV287 ) )
= $true )
| ( ( ~ ( number @ SV287 ) )
= $true )
| ( ( ~ ( ord_less @ SV287 @ SV73 @ SV254 )
| ( ord_less @ SV287 @ SV73 @ ( ti @ SV287 @ SV254 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1433]) ).
thf(1506,plain,
! [SV74: $i] :
( ( ( ! [SY380: $i,SY381: $i] :
( ~ ( ord_less_eq @ SV74 @ ( number_number_of @ SV74 @ SY380 ) @ ( number_number_of @ SV74 @ SY381 ) )
| ~ ( ord_less @ SV74 @ ( number_number_of @ SV74 @ SY381 ) @ ( number_number_of @ SV74 @ SY380 ) ) ) )
= $true )
| ( ( linorder @ SV74 )
= $false )
| ( ( number @ SV74 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1440]) ).
thf(1507,plain,
! [SV74: $i] :
( ( ( ! [SY382: $i,SY383: $i] :
( ( ord_less @ SV74 @ ( number_number_of @ SV74 @ SY383 ) @ ( number_number_of @ SV74 @ SY382 ) )
| ( ord_less_eq @ SV74 @ ( number_number_of @ SV74 @ SY382 ) @ ( number_number_of @ SV74 @ SY383 ) ) ) )
= $true )
| ( ( linorder @ SV74 )
= $false )
| ( ( number @ SV74 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1441]) ).
thf(1508,plain,
! [SV318: $i,SV298: $i,SV75: $i] :
( ( ( ~ ( ord_less @ SV75 @ ( zero_zero @ SV75 ) @ ( plus_plus @ SV75 @ ( power_power @ SV75 @ SV298 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV75 @ SV318 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
| ( ( ti @ SV75 @ SV298 )
!= ( zero_zero @ SV75 ) )
| ( ( ti @ SV75 @ SV318 )
!= ( zero_zero @ SV75 ) ) )
= $true )
| ( ( linordered_idom @ SV75 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1442]) ).
thf(1509,plain,
! [SV75: $i] :
( ( ( ~ ! [SY386: $i] :
( ( ( ti @ SV75 @ SY386 )
= ( zero_zero @ SV75 ) )
| ! [SY387: $i] : ( ord_less @ SV75 @ ( zero_zero @ SV75 ) @ ( plus_plus @ SV75 @ ( power_power @ SV75 @ SY386 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV75 @ SY387 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) )
= $false )
| ( ( linordered_idom @ SV75 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1443]) ).
thf(1510,plain,
! [SV75: $i] :
( ( ( ~ ! [SY388: $i,SY389: $i] :
( ( ( ti @ SV75 @ SY389 )
= ( zero_zero @ SV75 ) )
| ( ord_less @ SV75 @ ( zero_zero @ SV75 ) @ ( plus_plus @ SV75 @ ( power_power @ SV75 @ SY388 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV75 @ SY389 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) )
= $false )
| ( ( linordered_idom @ SV75 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1443]) ).
thf(1511,plain,
! [SV76: $i] :
( ( ( ! [SY390: $i] :
( ~ ( ord_less_eq @ SV76 @ ( one_one @ SV76 ) @ ( number_number_of @ SV76 @ SY390 ) )
| ( ord_less_eq @ int @ ( bit1 @ pls ) @ SY390 ) ) )
= $true )
| ( ( linordered_idom @ SV76 )
= $false )
| ( ( number_ring @ SV76 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1444]) ).
thf(1512,plain,
! [SV76: $i] :
( ( ( ! [SY391: $i] :
( ~ ( ord_less_eq @ int @ ( bit1 @ pls ) @ SY391 )
| ( ord_less_eq @ SV76 @ ( one_one @ SV76 ) @ ( number_number_of @ SV76 @ SY391 ) ) ) )
= $true )
| ( ( linordered_idom @ SV76 )
= $false )
| ( ( number_ring @ SV76 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1445]) ).
thf(1513,plain,
! [SV319: $i,SV299: $i,SV77: $i] :
( ( ( ( ( ti @ SV77 @ SV299 )
!= ( zero_zero @ SV77 ) )
| ( ( ti @ SV77 @ SV319 )
!= ( zero_zero @ SV77 ) )
| ( ( plus_plus @ SV77 @ ( power_power @ SV77 @ SV299 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV77 @ SV319 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV77 ) ) )
= $true )
| ( ( linordered_idom @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1446]) ).
thf(1514,plain,
! [SV77: $i] :
( ( ( ~ ! [SY394: $i] :
( ! [SY395: $i] :
( ( plus_plus @ SV77 @ ( power_power @ SV77 @ SY394 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV77 @ SY395 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV77 ) )
| ( ( ti @ SV77 @ SY394 )
= ( zero_zero @ SV77 ) ) ) )
= $false )
| ( ( linordered_idom @ SV77 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1447]) ).
thf(1515,plain,
! [SV77: $i] :
( ( ( ~ ! [SY396: $i,SY397: $i] :
( ( ( plus_plus @ SV77 @ ( power_power @ SV77 @ SY396 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV77 @ SY397 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV77 ) )
| ( ( ti @ SV77 @ SY397 )
= ( zero_zero @ SV77 ) ) ) )
= $false )
| ( ( linordered_idom @ SV77 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1447]) ).
thf(1516,plain,
! [SV300: $i,SV78: $i] :
( ( ( ( ( power_power @ SV78 @ SV300 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= ( zero_zero @ SV78 ) ) )
= $true )
| ( ( ( ti @ SV78 @ SV300 )
= ( zero_zero @ SV78 ) )
= $true )
| ( ( ring_11004092258visors @ SV78 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1448]) ).
thf(1517,plain,
! [SV301: $i,SV78: $i] :
( ( ( ( ( ti @ SV78 @ SV301 )
!= ( zero_zero @ SV78 ) ) )
= $true )
| ( ( ( power_power @ SV78 @ SV301 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SV78 ) )
= $true )
| ( ( ring_11004092258visors @ SV78 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1449]) ).
thf(1518,plain,
! [SV320: $i,SV302: $i] :
( ( ( ord_less @ int @ SV302 @ SV320 )
| ~ ( ord_less @ int @ SV302 @ SV320 )
| ( ord_less @ nat @ ( number_number_of @ nat @ SV302 ) @ ( number_number_of @ nat @ SV320 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1450]) ).
thf(1519,plain,
! [SV303: $i,SV321: $i] :
( ( ~ ( ord_less @ int @ pls @ SV321 )
| ~ ( ord_less @ int @ SV303 @ SV321 )
| ( ord_less @ nat @ ( number_number_of @ nat @ SV303 ) @ ( number_number_of @ nat @ SV321 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1451]) ).
thf(1520,plain,
! [SV322: $i,SV304: $i] :
( ( ~ ( ord_less @ nat @ ( number_number_of @ nat @ SV304 ) @ ( number_number_of @ nat @ SV322 ) )
| ~ ( ord_less @ int @ SV304 @ SV322 )
| ( ord_less @ int @ pls @ SV322 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1452]) ).
thf(1521,plain,
! [SV323: $i,SV305: $i] :
( ( ~ ( ord_less @ nat @ ( number_number_of @ nat @ SV305 ) @ ( number_number_of @ nat @ SV323 ) )
| ( ord_less @ int @ SV305 @ SV323 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1453]) ).
thf(1522,plain,
! [SV306: $i,SV79: $i] :
( ( ( ( ti @ SV79 @ SV306 )
= ( zero_zero @ SV79 ) )
= $true )
| ( ( ord_less @ SV79 @ ( zero_zero @ SV79 ) @ ( power_power @ SV79 @ SV306 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $true )
| ( ( linordered_idom @ SV79 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1454]) ).
thf(1523,plain,
! [SV307: $i,SV79: $i] :
( ( ( ~ ( ord_less @ SV79 @ ( zero_zero @ SV79 ) @ ( power_power @ SV79 @ SV307 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true )
| ( ( ( ( ti @ SV79 @ SV307 )
!= ( zero_zero @ SV79 ) ) )
= $true )
| ( ( linordered_idom @ SV79 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1455]) ).
thf(1524,plain,
! [SV80: $i] :
( ( ( ! [SY402: $i,SY403: $i] :
( ( ( number_number_of @ SV80 @ SY402 )
!= ( number_number_of @ SV80 @ SY403 ) )
| ( SY402 = SY403 ) ) )
= $true )
| ( ( number_ring @ SV80 )
= $false )
| ( ( ring_char_0 @ SV80 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1456]) ).
thf(1525,plain,
! [SV80: $i] :
( ( ( ! [SY404: $i,SY405: $i] :
( ( SY404 != SY405 )
| ( ( number_number_of @ SV80 @ SY404 )
= ( number_number_of @ SV80 @ SY405 ) ) ) )
= $true )
| ( ( number_ring @ SV80 )
= $false )
| ( ( ring_char_0 @ SV80 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1457]) ).
thf(1526,plain,
! [SV81: $i] :
( ( ( ! [SY406: $i] :
( ~ ( ord_less_eq @ SV81 @ ( number_number_of @ SV81 @ SY406 ) @ ( zero_zero @ SV81 ) )
| ( ord_less_eq @ int @ SY406 @ pls ) ) )
= $true )
| ( ( linordered_idom @ SV81 )
= $false )
| ( ( number_ring @ SV81 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1458]) ).
thf(1527,plain,
! [SV81: $i] :
( ( ( ! [SY407: $i] :
( ~ ( ord_less_eq @ int @ SY407 @ pls )
| ( ord_less_eq @ SV81 @ ( number_number_of @ SV81 @ SY407 ) @ ( zero_zero @ SV81 ) ) ) )
= $true )
| ( ( linordered_idom @ SV81 )
= $false )
| ( ( number_ring @ SV81 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1459]) ).
thf(1528,plain,
! [SV324: $i,SV308: $i,SV82: $i] :
( ( ( ( ( ti @ SV82 @ SV308 )
!= ( zero_zero @ SV82 ) )
| ( ( ti @ SV82 @ SV324 )
!= ( zero_zero @ SV82 ) )
| ( ( plus_plus @ SV82 @ ( times_times @ SV82 @ SV308 @ SV308 ) @ ( times_times @ SV82 @ SV324 @ SV324 ) )
= ( zero_zero @ SV82 ) ) )
= $true )
| ( ( linord581940658strict @ SV82 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1464]) ).
thf(1529,plain,
! [SV82: $i] :
( ( ( ~ ! [SY410: $i] :
( ! [SY411: $i] :
( ( plus_plus @ SV82 @ ( times_times @ SV82 @ SY410 @ SY410 ) @ ( times_times @ SV82 @ SY411 @ SY411 ) )
!= ( zero_zero @ SV82 ) )
| ( ( ti @ SV82 @ SY410 )
= ( zero_zero @ SV82 ) ) ) )
= $false )
| ( ( linord581940658strict @ SV82 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1465]) ).
thf(1530,plain,
! [SV82: $i] :
( ( ( ~ ! [SY412: $i,SY413: $i] :
( ( ( plus_plus @ SV82 @ ( times_times @ SV82 @ SY412 @ SY412 ) @ ( times_times @ SV82 @ SY413 @ SY413 ) )
!= ( zero_zero @ SV82 ) )
| ( ( ti @ SV82 @ SY413 )
= ( zero_zero @ SV82 ) ) ) )
= $false )
| ( ( linord581940658strict @ SV82 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1465]) ).
thf(1531,plain,
! [SV265: $i,SV83: $i,SV288: $i] :
( ( ( linordered_ring @ SV288 )
= $false )
| ( ( ~ ( ord_less_eq @ SV288 @ SV83 @ ( ti @ SV288 @ SV265 ) )
| ( ord_less_eq @ SV288 @ SV83 @ SV265 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1466]) ).
thf(1532,plain,
! [SV266: $i,SV83: $i,SV289: $i] :
( ( ( linordered_ring @ SV289 )
= $false )
| ( ( ~ ( ord_less_eq @ SV289 @ SV83 @ SV266 )
| ( ord_less_eq @ SV289 @ SV83 @ ( ti @ SV289 @ SV266 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1467]) ).
thf(1533,plain,
! [SV84: $i] :
( ( ( ! [SY418: $i] :
( ~ ( ord_less_eq @ SV84 @ ( number_number_of @ SV84 @ SY418 ) @ ( one_one @ SV84 ) )
| ( ord_less_eq @ int @ SY418 @ ( bit1 @ pls ) ) ) )
= $true )
| ( ( linordered_idom @ SV84 )
= $false )
| ( ( number_ring @ SV84 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1468]) ).
thf(1534,plain,
! [SV84: $i] :
( ( ( ! [SY419: $i] :
( ~ ( ord_less_eq @ int @ SY419 @ ( bit1 @ pls ) )
| ( ord_less_eq @ SV84 @ ( number_number_of @ SV84 @ SY419 ) @ ( one_one @ SV84 ) ) ) )
= $true )
| ( ( linordered_idom @ SV84 )
= $false )
| ( ( number_ring @ SV84 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1469]) ).
thf(1535,plain,
! [SV85: $i] :
( ( ( ! [SY420: $i] :
( ~ ( ord_less_eq @ SV85 @ ( zero_zero @ SV85 ) @ ( number_number_of @ SV85 @ SY420 ) )
| ( ord_less_eq @ int @ pls @ SY420 ) ) )
= $true )
| ( ( linordered_idom @ SV85 )
= $false )
| ( ( number_ring @ SV85 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1470]) ).
thf(1536,plain,
! [SV85: $i] :
( ( ( ! [SY421: $i] :
( ~ ( ord_less_eq @ int @ pls @ SY421 )
| ( ord_less_eq @ SV85 @ ( zero_zero @ SV85 ) @ ( number_number_of @ SV85 @ SY421 ) ) ) )
= $true )
| ( ( linordered_idom @ SV85 )
= $false )
| ( ( number_ring @ SV85 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1471]) ).
thf(1537,plain,
! [SV325: $i,SV309: $i,SV86: $i] :
( ( ( ( ( ti @ SV86 @ SV309 )
!= ( zero_zero @ SV86 ) )
| ( ( ti @ SV86 @ SV325 )
!= ( zero_zero @ SV86 ) )
| ( ord_less_eq @ SV86 @ ( plus_plus @ SV86 @ ( times_times @ SV86 @ SV309 @ SV309 ) @ ( times_times @ SV86 @ SV325 @ SV325 ) ) @ ( zero_zero @ SV86 ) ) )
= $true )
| ( ( linord581940658strict @ SV86 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1472]) ).
thf(1538,plain,
! [SV86: $i] :
( ( ( ~ ! [SY424: $i] :
( ! [SY425: $i] :
~ ( ord_less_eq @ SV86 @ ( plus_plus @ SV86 @ ( times_times @ SV86 @ SY424 @ SY424 ) @ ( times_times @ SV86 @ SY425 @ SY425 ) ) @ ( zero_zero @ SV86 ) )
| ( ( ti @ SV86 @ SY424 )
= ( zero_zero @ SV86 ) ) ) )
= $false )
| ( ( linord581940658strict @ SV86 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1473]) ).
thf(1539,plain,
! [SV86: $i] :
( ( ( ~ ! [SY426: $i,SY427: $i] :
( ~ ( ord_less_eq @ SV86 @ ( plus_plus @ SV86 @ ( times_times @ SV86 @ SY426 @ SY426 ) @ ( times_times @ SV86 @ SY427 @ SY427 ) ) @ ( zero_zero @ SV86 ) )
| ( ( ti @ SV86 @ SY427 )
= ( zero_zero @ SV86 ) ) ) )
= $false )
| ( ( linord581940658strict @ SV86 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1473]) ).
thf(1540,plain,
! [SV218: $i,SV44: $i,SV155: $i] :
( ( ( ord_less_eq @ int @ pls @ SV155 )
= $false )
| ( ( ( plus_plus @ SV44 @ ( number_number_of @ SV44 @ SV218 ) @ ( number_number_of @ SV44 @ SV155 ) )
= ( number_number_of @ SV44 @ ( plus_plus @ int @ SV218 @ SV155 ) ) )
= $true )
| ( ( ord_less_eq @ int @ pls @ SV218 )
= $false )
| ( ( number_semiring @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1479]) ).
thf(1541,plain,
! [SV219: $i,SV60: $i,SV156: $i] :
( ( ( ord_less_eq @ int @ pls @ SV156 )
= $false )
| ( ( ( times_times @ SV60 @ ( number_number_of @ SV60 @ SV219 ) @ ( number_number_of @ SV60 @ SV156 ) )
= ( number_number_of @ SV60 @ ( times_times @ int @ SV219 @ SV156 ) ) )
= $true )
| ( ( ord_less_eq @ int @ pls @ SV219 )
= $false )
| ( ( number_semiring @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1480]) ).
thf(1542,plain,
! [SV312: $i,SV292: $i] :
( ( ( ~ ( ord_less @ int @ SV292 @ SV312 ) )
= $true )
| ( ( ( SV292 != SV312 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1484]) ).
thf(1543,plain,
! [SV313: $i,SV293: $i] :
( ( ( ~ ( ord_less @ int @ SV293 @ SV313 ) )
= $true )
| ( ( ord_less_eq @ int @ SV293 @ SV313 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1485]) ).
thf(1544,plain,
! [SV326: $i,SV65: $i] :
( ( ( ! [SY533: $i] :
( ~ ( ord_less_eq @ SV65 @ ( number_number_of @ SV65 @ SV326 ) @ ( number_number_of @ SV65 @ SY533 ) )
| ( ord_less_eq @ int @ SV326 @ SY533 ) ) )
= $true )
| ( ( linordered_idom @ SV65 )
= $false )
| ( ( number_ring @ SV65 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1486]) ).
thf(1545,plain,
! [SV65: $i,SV327: $i] :
( ( ( ! [SY534: $i] :
( ~ ( ord_less_eq @ int @ SV327 @ SY534 )
| ( ord_less_eq @ SV65 @ ( number_number_of @ SV65 @ SV327 ) @ ( number_number_of @ SV65 @ SY534 ) ) ) )
= $true )
| ( ( linordered_idom @ SV65 )
= $false )
| ( ( number_ring @ SV65 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1487]) ).
thf(1546,plain,
! [SV294: $i,SV314: $i] :
( ( ( ord_less @ int @ SV314 @ pls )
= $true )
| ( ( ~ ( ord_less @ int @ SV294 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV314 ) @ ( number_number_of @ nat @ SV294 ) )
= ( number_number_of @ nat @ SV314 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1488]) ).
thf(1547,plain,
! [SV295: $i,SV315: $i] :
( ( ( ord_less @ int @ SV315 @ pls )
= $true )
| ( ( ( ord_less @ int @ SV295 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV315 ) @ ( number_number_of @ nat @ SV295 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SV315 @ SV295 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1489]) ).
thf(1548,plain,
! [SV227: $i,SV66: $i,SV274: $i] :
( ( ( ~ ( ord_less @ SV274 @ SV66 @ ( ti @ SV274 @ SV227 ) ) )
= $true )
| ( ( ord_less @ SV274 @ SV66 @ SV227 )
= $true )
| ( ( linordered_idom @ SV274 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1490]) ).
thf(1549,plain,
! [SV228: $i,SV66: $i,SV275: $i] :
( ( ( ~ ( ord_less @ SV275 @ SV66 @ SV228 ) )
= $true )
| ( ( ord_less @ SV275 @ SV66 @ ( ti @ SV275 @ SV228 ) )
= $true )
| ( ( linordered_idom @ SV275 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1491]) ).
thf(1550,plain,
! [SV229: $i,SV67: $i,SV276: $i] :
( ( ( ~ ( ord_less @ SV276 @ ( ti @ SV276 @ SV67 ) @ SV229 ) )
= $true )
| ( ( ord_less @ SV276 @ SV67 @ SV229 )
= $true )
| ( ( linordered_idom @ SV276 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1492]) ).
thf(1551,plain,
! [SV230: $i,SV67: $i,SV277: $i] :
( ( ( ~ ( ord_less @ SV277 @ SV67 @ SV230 ) )
= $true )
| ( ( ord_less @ SV277 @ ( ti @ SV277 @ SV67 ) @ SV230 )
= $true )
| ( ( linordered_idom @ SV277 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1493]) ).
thf(1552,plain,
! [SV231: $i,SV68: $i,SV278: $i] :
( ( ( ~ ( ord_less_eq @ SV278 @ ( ti @ SV278 @ SV68 ) @ SV231 ) )
= $true )
| ( ( ord_less_eq @ SV278 @ SV68 @ SV231 )
= $true )
| ( ( linordered_ring @ SV278 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1494]) ).
thf(1553,plain,
! [SV232: $i,SV68: $i,SV279: $i] :
( ( ( ~ ( ord_less_eq @ SV279 @ SV68 @ SV232 ) )
= $true )
| ( ( ord_less_eq @ SV279 @ ( ti @ SV279 @ SV68 ) @ SV232 )
= $true )
| ( ( linordered_ring @ SV279 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1495]) ).
thf(1554,plain,
! [SV235: $i,SV69: $i,SV280: $i] :
( ( ( linorder @ SV280 )
= $false )
| ( ( ~ ( number @ SV280 ) )
= $true )
| ( ( ~ ( ord_less_eq @ SV280 @ SV69 @ ( ti @ SV280 @ SV235 ) )
| ( ord_less_eq @ SV280 @ SV69 @ SV235 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1496]) ).
thf(1555,plain,
! [SV236: $i,SV69: $i,SV281: $i] :
( ( ( linorder @ SV281 )
= $false )
| ( ( ~ ( number @ SV281 ) )
= $true )
| ( ( ~ ( ord_less_eq @ SV281 @ SV69 @ SV236 )
| ( ord_less_eq @ SV281 @ SV69 @ ( ti @ SV281 @ SV236 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1497]) ).
thf(1556,plain,
! [SV316: $i,SV296: $i,SV70: $i] :
( ( ( ( ( number_number_of @ SV70 @ SV296 )
!= ( ti @ SV70 @ SV316 ) ) )
= $true )
| ( ( ( ti @ SV70 @ SV316 )
= ( number_number_of @ SV70 @ SV296 ) )
= $true )
| ( ( number @ SV70 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1498]) ).
thf(1557,plain,
! [SV297: $i,SV317: $i,SV70: $i] :
( ( ( ( ( ti @ SV70 @ SV317 )
!= ( number_number_of @ SV70 @ SV297 ) ) )
= $true )
| ( ( ( number_number_of @ SV70 @ SV297 )
= ( ti @ SV70 @ SV317 ) )
= $true )
| ( ( number @ SV70 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1499]) ).
thf(1558,plain,
! [SV241: $i,SV71: $i,SV282: $i] :
( ( ( linorder @ SV282 )
= $false )
| ( ( ~ ( number @ SV282 ) )
= $true )
| ( ( ~ ( ord_less @ SV282 @ ( ti @ SV282 @ SV71 ) @ SV241 )
| ( ord_less @ SV282 @ SV71 @ SV241 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1500]) ).
thf(1559,plain,
! [SV242: $i,SV71: $i,SV283: $i] :
( ( ( linorder @ SV283 )
= $false )
| ( ( ~ ( number @ SV283 ) )
= $true )
| ( ( ~ ( ord_less @ SV283 @ SV71 @ SV242 )
| ( ord_less @ SV283 @ ( ti @ SV283 @ SV71 ) @ SV242 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1501]) ).
thf(1560,plain,
! [SV251: $i,SV72: $i,SV284: $i] :
( ( ( linorder @ SV284 )
= $false )
| ( ( ~ ( number @ SV284 ) )
= $true )
| ( ( ~ ( ord_less_eq @ SV284 @ ( ti @ SV284 @ SV72 ) @ SV251 )
| ( ord_less_eq @ SV284 @ SV72 @ SV251 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1502]) ).
thf(1561,plain,
! [SV252: $i,SV72: $i,SV285: $i] :
( ( ( linorder @ SV285 )
= $false )
| ( ( ~ ( number @ SV285 ) )
= $true )
| ( ( ~ ( ord_less_eq @ SV285 @ SV72 @ SV252 )
| ( ord_less_eq @ SV285 @ ( ti @ SV285 @ SV72 ) @ SV252 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1503]) ).
thf(1562,plain,
! [SV253: $i,SV73: $i,SV286: $i] :
( ( ( linorder @ SV286 )
= $false )
| ( ( ~ ( number @ SV286 ) )
= $true )
| ( ( ~ ( ord_less @ SV286 @ SV73 @ ( ti @ SV286 @ SV253 ) )
| ( ord_less @ SV286 @ SV73 @ SV253 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1504]) ).
thf(1563,plain,
! [SV254: $i,SV73: $i,SV287: $i] :
( ( ( linorder @ SV287 )
= $false )
| ( ( ~ ( number @ SV287 ) )
= $true )
| ( ( ~ ( ord_less @ SV287 @ SV73 @ SV254 )
| ( ord_less @ SV287 @ SV73 @ ( ti @ SV287 @ SV254 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1505]) ).
thf(1564,plain,
! [SV328: $i,SV74: $i] :
( ( ( ! [SY535: $i] :
( ~ ( ord_less_eq @ SV74 @ ( number_number_of @ SV74 @ SV328 ) @ ( number_number_of @ SV74 @ SY535 ) )
| ~ ( ord_less @ SV74 @ ( number_number_of @ SV74 @ SY535 ) @ ( number_number_of @ SV74 @ SV328 ) ) ) )
= $true )
| ( ( linorder @ SV74 )
= $false )
| ( ( number @ SV74 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1506]) ).
thf(1565,plain,
! [SV329: $i,SV74: $i] :
( ( ( ! [SY536: $i] :
( ( ord_less @ SV74 @ ( number_number_of @ SV74 @ SY536 ) @ ( number_number_of @ SV74 @ SV329 ) )
| ( ord_less_eq @ SV74 @ ( number_number_of @ SV74 @ SV329 ) @ ( number_number_of @ SV74 @ SY536 ) ) ) )
= $true )
| ( ( linorder @ SV74 )
= $false )
| ( ( number @ SV74 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1507]) ).
thf(1566,plain,
! [SV318: $i,SV298: $i,SV75: $i] :
( ( ( ~ ( ord_less @ SV75 @ ( zero_zero @ SV75 ) @ ( plus_plus @ SV75 @ ( power_power @ SV75 @ SV298 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV75 @ SV318 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true )
| ( ( ( ( ti @ SV75 @ SV298 )
!= ( zero_zero @ SV75 ) )
| ( ( ti @ SV75 @ SV318 )
!= ( zero_zero @ SV75 ) ) )
= $true )
| ( ( linordered_idom @ SV75 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1508]) ).
thf(1567,plain,
! [SV75: $i] :
( ( ( ! [SY386: $i] :
( ( ( ti @ SV75 @ SY386 )
= ( zero_zero @ SV75 ) )
| ! [SY387: $i] : ( ord_less @ SV75 @ ( zero_zero @ SV75 ) @ ( plus_plus @ SV75 @ ( power_power @ SV75 @ SY386 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV75 @ SY387 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) )
= $true )
| ( ( linordered_idom @ SV75 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1509]) ).
thf(1568,plain,
! [SV75: $i] :
( ( ( ! [SY388: $i,SY389: $i] :
( ( ( ti @ SV75 @ SY389 )
= ( zero_zero @ SV75 ) )
| ( ord_less @ SV75 @ ( zero_zero @ SV75 ) @ ( plus_plus @ SV75 @ ( power_power @ SV75 @ SY388 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV75 @ SY389 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) )
= $true )
| ( ( linordered_idom @ SV75 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1510]) ).
thf(1569,plain,
! [SV330: $i,SV76: $i] :
( ( ( ~ ( ord_less_eq @ SV76 @ ( one_one @ SV76 ) @ ( number_number_of @ SV76 @ SV330 ) )
| ( ord_less_eq @ int @ ( bit1 @ pls ) @ SV330 ) )
= $true )
| ( ( linordered_idom @ SV76 )
= $false )
| ( ( number_ring @ SV76 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1511]) ).
thf(1570,plain,
! [SV76: $i,SV331: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( bit1 @ pls ) @ SV331 )
| ( ord_less_eq @ SV76 @ ( one_one @ SV76 ) @ ( number_number_of @ SV76 @ SV331 ) ) )
= $true )
| ( ( linordered_idom @ SV76 )
= $false )
| ( ( number_ring @ SV76 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1512]) ).
thf(1571,plain,
! [SV319: $i,SV299: $i,SV77: $i] :
( ( ( ( ( ti @ SV77 @ SV299 )
!= ( zero_zero @ SV77 ) )
| ( ( ti @ SV77 @ SV319 )
!= ( zero_zero @ SV77 ) ) )
= $true )
| ( ( ( plus_plus @ SV77 @ ( power_power @ SV77 @ SV299 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV77 @ SV319 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV77 ) )
= $true )
| ( ( linordered_idom @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1513]) ).
thf(1572,plain,
! [SV77: $i] :
( ( ( ! [SY394: $i] :
( ! [SY395: $i] :
( ( plus_plus @ SV77 @ ( power_power @ SV77 @ SY394 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV77 @ SY395 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV77 ) )
| ( ( ti @ SV77 @ SY394 )
= ( zero_zero @ SV77 ) ) ) )
= $true )
| ( ( linordered_idom @ SV77 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1514]) ).
thf(1573,plain,
! [SV77: $i] :
( ( ( ! [SY396: $i,SY397: $i] :
( ( ( plus_plus @ SV77 @ ( power_power @ SV77 @ SY396 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV77 @ SY397 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV77 ) )
| ( ( ti @ SV77 @ SY397 )
= ( zero_zero @ SV77 ) ) ) )
= $true )
| ( ( linordered_idom @ SV77 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1515]) ).
thf(1574,plain,
! [SV300: $i,SV78: $i] :
( ( ( ( power_power @ SV78 @ SV300 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SV78 ) )
= $false )
| ( ( ( ti @ SV78 @ SV300 )
= ( zero_zero @ SV78 ) )
= $true )
| ( ( ring_11004092258visors @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1516]) ).
thf(1575,plain,
! [SV301: $i,SV78: $i] :
( ( ( ( ti @ SV78 @ SV301 )
= ( zero_zero @ SV78 ) )
= $false )
| ( ( ( power_power @ SV78 @ SV301 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SV78 ) )
= $true )
| ( ( ring_11004092258visors @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1517]) ).
thf(1576,plain,
! [SV320: $i,SV302: $i] :
( ( ( ( ord_less @ int @ SV302 @ SV320 )
| ~ ( ord_less @ int @ SV302 @ SV320 ) )
= $true )
| ( ( ord_less @ nat @ ( number_number_of @ nat @ SV302 ) @ ( number_number_of @ nat @ SV320 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1518]) ).
thf(1577,plain,
! [SV303: $i,SV321: $i] :
( ( ( ~ ( ord_less @ int @ pls @ SV321 )
| ~ ( ord_less @ int @ SV303 @ SV321 ) )
= $true )
| ( ( ord_less @ nat @ ( number_number_of @ nat @ SV303 ) @ ( number_number_of @ nat @ SV321 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1519]) ).
thf(1578,plain,
! [SV322: $i,SV304: $i] :
( ( ( ~ ( ord_less @ nat @ ( number_number_of @ nat @ SV304 ) @ ( number_number_of @ nat @ SV322 ) ) )
= $true )
| ( ( ~ ( ord_less @ int @ SV304 @ SV322 )
| ( ord_less @ int @ pls @ SV322 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1520]) ).
thf(1579,plain,
! [SV323: $i,SV305: $i] :
( ( ( ~ ( ord_less @ nat @ ( number_number_of @ nat @ SV305 ) @ ( number_number_of @ nat @ SV323 ) ) )
= $true )
| ( ( ord_less @ int @ SV305 @ SV323 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1521]) ).
thf(1580,plain,
! [SV307: $i,SV79: $i] :
( ( ( ord_less @ SV79 @ ( zero_zero @ SV79 ) @ ( power_power @ SV79 @ SV307 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $false )
| ( ( ( ( ti @ SV79 @ SV307 )
!= ( zero_zero @ SV79 ) ) )
= $true )
| ( ( linordered_idom @ SV79 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1523]) ).
thf(1581,plain,
! [SV332: $i,SV80: $i] :
( ( ( ! [SY537: $i] :
( ( ( number_number_of @ SV80 @ SV332 )
!= ( number_number_of @ SV80 @ SY537 ) )
| ( SV332 = SY537 ) ) )
= $true )
| ( ( number_ring @ SV80 )
= $false )
| ( ( ring_char_0 @ SV80 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1524]) ).
thf(1582,plain,
! [SV80: $i,SV333: $i] :
( ( ( ! [SY538: $i] :
( ( SV333 != SY538 )
| ( ( number_number_of @ SV80 @ SV333 )
= ( number_number_of @ SV80 @ SY538 ) ) ) )
= $true )
| ( ( number_ring @ SV80 )
= $false )
| ( ( ring_char_0 @ SV80 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1525]) ).
thf(1583,plain,
! [SV334: $i,SV81: $i] :
( ( ( ~ ( ord_less_eq @ SV81 @ ( number_number_of @ SV81 @ SV334 ) @ ( zero_zero @ SV81 ) )
| ( ord_less_eq @ int @ SV334 @ pls ) )
= $true )
| ( ( linordered_idom @ SV81 )
= $false )
| ( ( number_ring @ SV81 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1526]) ).
thf(1584,plain,
! [SV81: $i,SV335: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV335 @ pls )
| ( ord_less_eq @ SV81 @ ( number_number_of @ SV81 @ SV335 ) @ ( zero_zero @ SV81 ) ) )
= $true )
| ( ( linordered_idom @ SV81 )
= $false )
| ( ( number_ring @ SV81 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1527]) ).
thf(1585,plain,
! [SV324: $i,SV308: $i,SV82: $i] :
( ( ( ( ( ti @ SV82 @ SV308 )
!= ( zero_zero @ SV82 ) )
| ( ( ti @ SV82 @ SV324 )
!= ( zero_zero @ SV82 ) ) )
= $true )
| ( ( ( plus_plus @ SV82 @ ( times_times @ SV82 @ SV308 @ SV308 ) @ ( times_times @ SV82 @ SV324 @ SV324 ) )
= ( zero_zero @ SV82 ) )
= $true )
| ( ( linord581940658strict @ SV82 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1528]) ).
thf(1586,plain,
! [SV82: $i] :
( ( ( ! [SY410: $i] :
( ! [SY411: $i] :
( ( plus_plus @ SV82 @ ( times_times @ SV82 @ SY410 @ SY410 ) @ ( times_times @ SV82 @ SY411 @ SY411 ) )
!= ( zero_zero @ SV82 ) )
| ( ( ti @ SV82 @ SY410 )
= ( zero_zero @ SV82 ) ) ) )
= $true )
| ( ( linord581940658strict @ SV82 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1529]) ).
thf(1587,plain,
! [SV82: $i] :
( ( ( ! [SY412: $i,SY413: $i] :
( ( ( plus_plus @ SV82 @ ( times_times @ SV82 @ SY412 @ SY412 ) @ ( times_times @ SV82 @ SY413 @ SY413 ) )
!= ( zero_zero @ SV82 ) )
| ( ( ti @ SV82 @ SY413 )
= ( zero_zero @ SV82 ) ) ) )
= $true )
| ( ( linord581940658strict @ SV82 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1530]) ).
thf(1588,plain,
! [SV265: $i,SV83: $i,SV288: $i] :
( ( ( ~ ( ord_less_eq @ SV288 @ SV83 @ ( ti @ SV288 @ SV265 ) ) )
= $true )
| ( ( ord_less_eq @ SV288 @ SV83 @ SV265 )
= $true )
| ( ( linordered_ring @ SV288 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1531]) ).
thf(1589,plain,
! [SV266: $i,SV83: $i,SV289: $i] :
( ( ( ~ ( ord_less_eq @ SV289 @ SV83 @ SV266 ) )
= $true )
| ( ( ord_less_eq @ SV289 @ SV83 @ ( ti @ SV289 @ SV266 ) )
= $true )
| ( ( linordered_ring @ SV289 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1532]) ).
thf(1590,plain,
! [SV336: $i,SV84: $i] :
( ( ( ~ ( ord_less_eq @ SV84 @ ( number_number_of @ SV84 @ SV336 ) @ ( one_one @ SV84 ) )
| ( ord_less_eq @ int @ SV336 @ ( bit1 @ pls ) ) )
= $true )
| ( ( linordered_idom @ SV84 )
= $false )
| ( ( number_ring @ SV84 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1533]) ).
thf(1591,plain,
! [SV84: $i,SV337: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV337 @ ( bit1 @ pls ) )
| ( ord_less_eq @ SV84 @ ( number_number_of @ SV84 @ SV337 ) @ ( one_one @ SV84 ) ) )
= $true )
| ( ( linordered_idom @ SV84 )
= $false )
| ( ( number_ring @ SV84 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1534]) ).
thf(1592,plain,
! [SV338: $i,SV85: $i] :
( ( ( ~ ( ord_less_eq @ SV85 @ ( zero_zero @ SV85 ) @ ( number_number_of @ SV85 @ SV338 ) )
| ( ord_less_eq @ int @ pls @ SV338 ) )
= $true )
| ( ( linordered_idom @ SV85 )
= $false )
| ( ( number_ring @ SV85 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1535]) ).
thf(1593,plain,
! [SV85: $i,SV339: $i] :
( ( ( ~ ( ord_less_eq @ int @ pls @ SV339 )
| ( ord_less_eq @ SV85 @ ( zero_zero @ SV85 ) @ ( number_number_of @ SV85 @ SV339 ) ) )
= $true )
| ( ( linordered_idom @ SV85 )
= $false )
| ( ( number_ring @ SV85 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1536]) ).
thf(1594,plain,
! [SV325: $i,SV309: $i,SV86: $i] :
( ( ( ( ( ti @ SV86 @ SV309 )
!= ( zero_zero @ SV86 ) )
| ( ( ti @ SV86 @ SV325 )
!= ( zero_zero @ SV86 ) ) )
= $true )
| ( ( ord_less_eq @ SV86 @ ( plus_plus @ SV86 @ ( times_times @ SV86 @ SV309 @ SV309 ) @ ( times_times @ SV86 @ SV325 @ SV325 ) ) @ ( zero_zero @ SV86 ) )
= $true )
| ( ( linord581940658strict @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1537]) ).
thf(1595,plain,
! [SV86: $i] :
( ( ( ! [SY424: $i] :
( ! [SY425: $i] :
~ ( ord_less_eq @ SV86 @ ( plus_plus @ SV86 @ ( times_times @ SV86 @ SY424 @ SY424 ) @ ( times_times @ SV86 @ SY425 @ SY425 ) ) @ ( zero_zero @ SV86 ) )
| ( ( ti @ SV86 @ SY424 )
= ( zero_zero @ SV86 ) ) ) )
= $true )
| ( ( linord581940658strict @ SV86 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1538]) ).
thf(1596,plain,
! [SV86: $i] :
( ( ( ! [SY426: $i,SY427: $i] :
( ~ ( ord_less_eq @ SV86 @ ( plus_plus @ SV86 @ ( times_times @ SV86 @ SY426 @ SY426 ) @ ( times_times @ SV86 @ SY427 @ SY427 ) ) @ ( zero_zero @ SV86 ) )
| ( ( ti @ SV86 @ SY427 )
= ( zero_zero @ SV86 ) ) ) )
= $true )
| ( ( linord581940658strict @ SV86 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1539]) ).
thf(1597,plain,
! [SV312: $i,SV292: $i] :
( ( ( ord_less @ int @ SV292 @ SV312 )
= $false )
| ( ( ( SV292 != SV312 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1542]) ).
thf(1598,plain,
! [SV313: $i,SV293: $i] :
( ( ( ord_less @ int @ SV293 @ SV313 )
= $false )
| ( ( ord_less_eq @ int @ SV293 @ SV313 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1543]) ).
thf(1599,plain,
! [SV340: $i,SV326: $i,SV65: $i] :
( ( ( ~ ( ord_less_eq @ SV65 @ ( number_number_of @ SV65 @ SV326 ) @ ( number_number_of @ SV65 @ SV340 ) )
| ( ord_less_eq @ int @ SV326 @ SV340 ) )
= $true )
| ( ( linordered_idom @ SV65 )
= $false )
| ( ( number_ring @ SV65 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1544]) ).
thf(1600,plain,
! [SV65: $i,SV341: $i,SV327: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV327 @ SV341 )
| ( ord_less_eq @ SV65 @ ( number_number_of @ SV65 @ SV327 ) @ ( number_number_of @ SV65 @ SV341 ) ) )
= $true )
| ( ( linordered_idom @ SV65 )
= $false )
| ( ( number_ring @ SV65 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1545]) ).
thf(1601,plain,
! [SV314: $i,SV294: $i] :
( ( ( ~ ( ord_less @ int @ SV294 @ pls ) )
= $true )
| ( ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV314 ) @ ( number_number_of @ nat @ SV294 ) )
= ( number_number_of @ nat @ SV314 ) )
= $true )
| ( ( ord_less @ int @ SV314 @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1546]) ).
thf(1602,plain,
! [SV315: $i,SV295: $i] :
( ( ( ord_less @ int @ SV295 @ pls )
= $true )
| ( ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV315 ) @ ( number_number_of @ nat @ SV295 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SV315 @ SV295 ) ) )
= $true )
| ( ( ord_less @ int @ SV315 @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1547]) ).
thf(1603,plain,
! [SV227: $i,SV66: $i,SV274: $i] :
( ( ( ord_less @ SV274 @ SV66 @ ( ti @ SV274 @ SV227 ) )
= $false )
| ( ( ord_less @ SV274 @ SV66 @ SV227 )
= $true )
| ( ( linordered_idom @ SV274 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1548]) ).
thf(1604,plain,
! [SV228: $i,SV66: $i,SV275: $i] :
( ( ( ord_less @ SV275 @ SV66 @ SV228 )
= $false )
| ( ( ord_less @ SV275 @ SV66 @ ( ti @ SV275 @ SV228 ) )
= $true )
| ( ( linordered_idom @ SV275 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1549]) ).
thf(1605,plain,
! [SV229: $i,SV67: $i,SV276: $i] :
( ( ( ord_less @ SV276 @ ( ti @ SV276 @ SV67 ) @ SV229 )
= $false )
| ( ( ord_less @ SV276 @ SV67 @ SV229 )
= $true )
| ( ( linordered_idom @ SV276 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1550]) ).
thf(1606,plain,
! [SV230: $i,SV67: $i,SV277: $i] :
( ( ( ord_less @ SV277 @ SV67 @ SV230 )
= $false )
| ( ( ord_less @ SV277 @ ( ti @ SV277 @ SV67 ) @ SV230 )
= $true )
| ( ( linordered_idom @ SV277 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1551]) ).
thf(1607,plain,
! [SV231: $i,SV68: $i,SV278: $i] :
( ( ( ord_less_eq @ SV278 @ ( ti @ SV278 @ SV68 ) @ SV231 )
= $false )
| ( ( ord_less_eq @ SV278 @ SV68 @ SV231 )
= $true )
| ( ( linordered_ring @ SV278 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1552]) ).
thf(1608,plain,
! [SV232: $i,SV68: $i,SV279: $i] :
( ( ( ord_less_eq @ SV279 @ SV68 @ SV232 )
= $false )
| ( ( ord_less_eq @ SV279 @ ( ti @ SV279 @ SV68 ) @ SV232 )
= $true )
| ( ( linordered_ring @ SV279 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1553]) ).
thf(1609,plain,
! [SV235: $i,SV69: $i,SV280: $i] :
( ( ( number @ SV280 )
= $false )
| ( ( linorder @ SV280 )
= $false )
| ( ( ~ ( ord_less_eq @ SV280 @ SV69 @ ( ti @ SV280 @ SV235 ) )
| ( ord_less_eq @ SV280 @ SV69 @ SV235 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1554]) ).
thf(1610,plain,
! [SV236: $i,SV69: $i,SV281: $i] :
( ( ( number @ SV281 )
= $false )
| ( ( linorder @ SV281 )
= $false )
| ( ( ~ ( ord_less_eq @ SV281 @ SV69 @ SV236 )
| ( ord_less_eq @ SV281 @ SV69 @ ( ti @ SV281 @ SV236 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1555]) ).
thf(1611,plain,
! [SV316: $i,SV296: $i,SV70: $i] :
( ( ( ( number_number_of @ SV70 @ SV296 )
= ( ti @ SV70 @ SV316 ) )
= $false )
| ( ( ( ti @ SV70 @ SV316 )
= ( number_number_of @ SV70 @ SV296 ) )
= $true )
| ( ( number @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1556]) ).
thf(1612,plain,
! [SV297: $i,SV317: $i,SV70: $i] :
( ( ( ( ti @ SV70 @ SV317 )
= ( number_number_of @ SV70 @ SV297 ) )
= $false )
| ( ( ( number_number_of @ SV70 @ SV297 )
= ( ti @ SV70 @ SV317 ) )
= $true )
| ( ( number @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1557]) ).
thf(1613,plain,
! [SV241: $i,SV71: $i,SV282: $i] :
( ( ( number @ SV282 )
= $false )
| ( ( linorder @ SV282 )
= $false )
| ( ( ~ ( ord_less @ SV282 @ ( ti @ SV282 @ SV71 ) @ SV241 )
| ( ord_less @ SV282 @ SV71 @ SV241 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1558]) ).
thf(1614,plain,
! [SV242: $i,SV71: $i,SV283: $i] :
( ( ( number @ SV283 )
= $false )
| ( ( linorder @ SV283 )
= $false )
| ( ( ~ ( ord_less @ SV283 @ SV71 @ SV242 )
| ( ord_less @ SV283 @ ( ti @ SV283 @ SV71 ) @ SV242 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1559]) ).
thf(1615,plain,
! [SV251: $i,SV72: $i,SV284: $i] :
( ( ( number @ SV284 )
= $false )
| ( ( linorder @ SV284 )
= $false )
| ( ( ~ ( ord_less_eq @ SV284 @ ( ti @ SV284 @ SV72 ) @ SV251 )
| ( ord_less_eq @ SV284 @ SV72 @ SV251 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1560]) ).
thf(1616,plain,
! [SV252: $i,SV72: $i,SV285: $i] :
( ( ( number @ SV285 )
= $false )
| ( ( linorder @ SV285 )
= $false )
| ( ( ~ ( ord_less_eq @ SV285 @ SV72 @ SV252 )
| ( ord_less_eq @ SV285 @ ( ti @ SV285 @ SV72 ) @ SV252 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1561]) ).
thf(1617,plain,
! [SV253: $i,SV73: $i,SV286: $i] :
( ( ( number @ SV286 )
= $false )
| ( ( linorder @ SV286 )
= $false )
| ( ( ~ ( ord_less @ SV286 @ SV73 @ ( ti @ SV286 @ SV253 ) )
| ( ord_less @ SV286 @ SV73 @ SV253 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1562]) ).
thf(1618,plain,
! [SV254: $i,SV73: $i,SV287: $i] :
( ( ( number @ SV287 )
= $false )
| ( ( linorder @ SV287 )
= $false )
| ( ( ~ ( ord_less @ SV287 @ SV73 @ SV254 )
| ( ord_less @ SV287 @ SV73 @ ( ti @ SV287 @ SV254 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1563]) ).
thf(1619,plain,
! [SV342: $i,SV328: $i,SV74: $i] :
( ( ( ~ ( ord_less_eq @ SV74 @ ( number_number_of @ SV74 @ SV328 ) @ ( number_number_of @ SV74 @ SV342 ) )
| ~ ( ord_less @ SV74 @ ( number_number_of @ SV74 @ SV342 ) @ ( number_number_of @ SV74 @ SV328 ) ) )
= $true )
| ( ( linorder @ SV74 )
= $false )
| ( ( number @ SV74 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1564]) ).
thf(1620,plain,
! [SV329: $i,SV343: $i,SV74: $i] :
( ( ( ( ord_less @ SV74 @ ( number_number_of @ SV74 @ SV343 ) @ ( number_number_of @ SV74 @ SV329 ) )
| ( ord_less_eq @ SV74 @ ( number_number_of @ SV74 @ SV329 ) @ ( number_number_of @ SV74 @ SV343 ) ) )
= $true )
| ( ( linorder @ SV74 )
= $false )
| ( ( number @ SV74 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1565]) ).
thf(1621,plain,
! [SV318: $i,SV298: $i,SV75: $i] :
( ( ( ord_less @ SV75 @ ( zero_zero @ SV75 ) @ ( plus_plus @ SV75 @ ( power_power @ SV75 @ SV298 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV75 @ SV318 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $false )
| ( ( ( ( ti @ SV75 @ SV298 )
!= ( zero_zero @ SV75 ) )
| ( ( ti @ SV75 @ SV318 )
!= ( zero_zero @ SV75 ) ) )
= $true )
| ( ( linordered_idom @ SV75 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1566]) ).
thf(1622,plain,
! [SV344: $i,SV75: $i] :
( ( ( ( ( ti @ SV75 @ SV344 )
= ( zero_zero @ SV75 ) )
| ! [SY539: $i] : ( ord_less @ SV75 @ ( zero_zero @ SV75 ) @ ( plus_plus @ SV75 @ ( power_power @ SV75 @ SV344 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV75 @ SY539 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true )
| ( ( linordered_idom @ SV75 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1567]) ).
thf(1623,plain,
! [SV345: $i,SV75: $i] :
( ( ( ! [SY540: $i] :
( ( ( ti @ SV75 @ SY540 )
= ( zero_zero @ SV75 ) )
| ( ord_less @ SV75 @ ( zero_zero @ SV75 ) @ ( plus_plus @ SV75 @ ( power_power @ SV75 @ SV345 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV75 @ SY540 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) )
= $true )
| ( ( linordered_idom @ SV75 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1568]) ).
thf(1624,plain,
! [SV330: $i,SV76: $i] :
( ( ( ~ ( ord_less_eq @ SV76 @ ( one_one @ SV76 ) @ ( number_number_of @ SV76 @ SV330 ) ) )
= $true )
| ( ( ord_less_eq @ int @ ( bit1 @ pls ) @ SV330 )
= $true )
| ( ( linordered_idom @ SV76 )
= $false )
| ( ( number_ring @ SV76 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1569]) ).
thf(1625,plain,
! [SV76: $i,SV331: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( bit1 @ pls ) @ SV331 ) )
= $true )
| ( ( ord_less_eq @ SV76 @ ( one_one @ SV76 ) @ ( number_number_of @ SV76 @ SV331 ) )
= $true )
| ( ( linordered_idom @ SV76 )
= $false )
| ( ( number_ring @ SV76 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1570]) ).
thf(1626,plain,
! [SV319: $i,SV299: $i,SV77: $i] :
( ( ( ( ( ti @ SV77 @ SV299 )
!= ( zero_zero @ SV77 ) ) )
= $true )
| ( ( ( ( ti @ SV77 @ SV319 )
!= ( zero_zero @ SV77 ) ) )
= $true )
| ( ( ( plus_plus @ SV77 @ ( power_power @ SV77 @ SV299 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV77 @ SV319 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV77 ) )
= $true )
| ( ( linordered_idom @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1571]) ).
thf(1627,plain,
! [SV346: $i,SV77: $i] :
( ( ( ! [SY541: $i] :
( ( plus_plus @ SV77 @ ( power_power @ SV77 @ SV346 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV77 @ SY541 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV77 ) )
| ( ( ti @ SV77 @ SV346 )
= ( zero_zero @ SV77 ) ) )
= $true )
| ( ( linordered_idom @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1572]) ).
thf(1628,plain,
! [SV347: $i,SV77: $i] :
( ( ( ! [SY542: $i] :
( ( ( plus_plus @ SV77 @ ( power_power @ SV77 @ SV347 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV77 @ SY542 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV77 ) )
| ( ( ti @ SV77 @ SY542 )
= ( zero_zero @ SV77 ) ) ) )
= $true )
| ( ( linordered_idom @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1573]) ).
thf(1629,plain,
! [SV320: $i,SV302: $i] :
( ( ( ord_less @ int @ SV302 @ SV320 )
= $true )
| ( ( ~ ( ord_less @ int @ SV302 @ SV320 ) )
= $true )
| ( ( ord_less @ nat @ ( number_number_of @ nat @ SV302 ) @ ( number_number_of @ nat @ SV320 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1576]) ).
thf(1630,plain,
! [SV303: $i,SV321: $i] :
( ( ( ~ ( ord_less @ int @ pls @ SV321 ) )
= $true )
| ( ( ~ ( ord_less @ int @ SV303 @ SV321 ) )
= $true )
| ( ( ord_less @ nat @ ( number_number_of @ nat @ SV303 ) @ ( number_number_of @ nat @ SV321 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1577]) ).
thf(1631,plain,
! [SV322: $i,SV304: $i] :
( ( ( ord_less @ nat @ ( number_number_of @ nat @ SV304 ) @ ( number_number_of @ nat @ SV322 ) )
= $false )
| ( ( ~ ( ord_less @ int @ SV304 @ SV322 )
| ( ord_less @ int @ pls @ SV322 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1578]) ).
thf(1632,plain,
! [SV323: $i,SV305: $i] :
( ( ( ord_less @ nat @ ( number_number_of @ nat @ SV305 ) @ ( number_number_of @ nat @ SV323 ) )
= $false )
| ( ( ord_less @ int @ SV305 @ SV323 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1579]) ).
thf(1633,plain,
! [SV307: $i,SV79: $i] :
( ( ( ( ti @ SV79 @ SV307 )
= ( zero_zero @ SV79 ) )
= $false )
| ( ( ord_less @ SV79 @ ( zero_zero @ SV79 ) @ ( power_power @ SV79 @ SV307 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $false )
| ( ( linordered_idom @ SV79 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1580]) ).
thf(1634,plain,
! [SV348: $i,SV332: $i,SV80: $i] :
( ( ( ( ( number_number_of @ SV80 @ SV332 )
!= ( number_number_of @ SV80 @ SV348 ) )
| ( SV332 = SV348 ) )
= $true )
| ( ( number_ring @ SV80 )
= $false )
| ( ( ring_char_0 @ SV80 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1581]) ).
thf(1635,plain,
! [SV80: $i,SV349: $i,SV333: $i] :
( ( ( ( SV333 != SV349 )
| ( ( number_number_of @ SV80 @ SV333 )
= ( number_number_of @ SV80 @ SV349 ) ) )
= $true )
| ( ( number_ring @ SV80 )
= $false )
| ( ( ring_char_0 @ SV80 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1582]) ).
thf(1636,plain,
! [SV334: $i,SV81: $i] :
( ( ( ~ ( ord_less_eq @ SV81 @ ( number_number_of @ SV81 @ SV334 ) @ ( zero_zero @ SV81 ) ) )
= $true )
| ( ( ord_less_eq @ int @ SV334 @ pls )
= $true )
| ( ( linordered_idom @ SV81 )
= $false )
| ( ( number_ring @ SV81 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1583]) ).
thf(1637,plain,
! [SV81: $i,SV335: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV335 @ pls ) )
= $true )
| ( ( ord_less_eq @ SV81 @ ( number_number_of @ SV81 @ SV335 ) @ ( zero_zero @ SV81 ) )
= $true )
| ( ( linordered_idom @ SV81 )
= $false )
| ( ( number_ring @ SV81 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1584]) ).
thf(1638,plain,
! [SV324: $i,SV308: $i,SV82: $i] :
( ( ( ( ( ti @ SV82 @ SV308 )
!= ( zero_zero @ SV82 ) ) )
= $true )
| ( ( ( ( ti @ SV82 @ SV324 )
!= ( zero_zero @ SV82 ) ) )
= $true )
| ( ( ( plus_plus @ SV82 @ ( times_times @ SV82 @ SV308 @ SV308 ) @ ( times_times @ SV82 @ SV324 @ SV324 ) )
= ( zero_zero @ SV82 ) )
= $true )
| ( ( linord581940658strict @ SV82 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1585]) ).
thf(1639,plain,
! [SV350: $i,SV82: $i] :
( ( ( ! [SY543: $i] :
( ( plus_plus @ SV82 @ ( times_times @ SV82 @ SV350 @ SV350 ) @ ( times_times @ SV82 @ SY543 @ SY543 ) )
!= ( zero_zero @ SV82 ) )
| ( ( ti @ SV82 @ SV350 )
= ( zero_zero @ SV82 ) ) )
= $true )
| ( ( linord581940658strict @ SV82 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1586]) ).
thf(1640,plain,
! [SV351: $i,SV82: $i] :
( ( ( ! [SY544: $i] :
( ( ( plus_plus @ SV82 @ ( times_times @ SV82 @ SV351 @ SV351 ) @ ( times_times @ SV82 @ SY544 @ SY544 ) )
!= ( zero_zero @ SV82 ) )
| ( ( ti @ SV82 @ SY544 )
= ( zero_zero @ SV82 ) ) ) )
= $true )
| ( ( linord581940658strict @ SV82 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1587]) ).
thf(1641,plain,
! [SV265: $i,SV83: $i,SV288: $i] :
( ( ( ord_less_eq @ SV288 @ SV83 @ ( ti @ SV288 @ SV265 ) )
= $false )
| ( ( ord_less_eq @ SV288 @ SV83 @ SV265 )
= $true )
| ( ( linordered_ring @ SV288 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1588]) ).
thf(1642,plain,
! [SV266: $i,SV83: $i,SV289: $i] :
( ( ( ord_less_eq @ SV289 @ SV83 @ SV266 )
= $false )
| ( ( ord_less_eq @ SV289 @ SV83 @ ( ti @ SV289 @ SV266 ) )
= $true )
| ( ( linordered_ring @ SV289 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1589]) ).
thf(1643,plain,
! [SV336: $i,SV84: $i] :
( ( ( ~ ( ord_less_eq @ SV84 @ ( number_number_of @ SV84 @ SV336 ) @ ( one_one @ SV84 ) ) )
= $true )
| ( ( ord_less_eq @ int @ SV336 @ ( bit1 @ pls ) )
= $true )
| ( ( linordered_idom @ SV84 )
= $false )
| ( ( number_ring @ SV84 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1590]) ).
thf(1644,plain,
! [SV84: $i,SV337: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV337 @ ( bit1 @ pls ) ) )
= $true )
| ( ( ord_less_eq @ SV84 @ ( number_number_of @ SV84 @ SV337 ) @ ( one_one @ SV84 ) )
= $true )
| ( ( linordered_idom @ SV84 )
= $false )
| ( ( number_ring @ SV84 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1591]) ).
thf(1645,plain,
! [SV338: $i,SV85: $i] :
( ( ( ~ ( ord_less_eq @ SV85 @ ( zero_zero @ SV85 ) @ ( number_number_of @ SV85 @ SV338 ) ) )
= $true )
| ( ( ord_less_eq @ int @ pls @ SV338 )
= $true )
| ( ( linordered_idom @ SV85 )
= $false )
| ( ( number_ring @ SV85 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1592]) ).
thf(1646,plain,
! [SV85: $i,SV339: $i] :
( ( ( ~ ( ord_less_eq @ int @ pls @ SV339 ) )
= $true )
| ( ( ord_less_eq @ SV85 @ ( zero_zero @ SV85 ) @ ( number_number_of @ SV85 @ SV339 ) )
= $true )
| ( ( linordered_idom @ SV85 )
= $false )
| ( ( number_ring @ SV85 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1593]) ).
thf(1647,plain,
! [SV325: $i,SV309: $i,SV86: $i] :
( ( ( ( ( ti @ SV86 @ SV309 )
!= ( zero_zero @ SV86 ) ) )
= $true )
| ( ( ( ( ti @ SV86 @ SV325 )
!= ( zero_zero @ SV86 ) ) )
= $true )
| ( ( ord_less_eq @ SV86 @ ( plus_plus @ SV86 @ ( times_times @ SV86 @ SV309 @ SV309 ) @ ( times_times @ SV86 @ SV325 @ SV325 ) ) @ ( zero_zero @ SV86 ) )
= $true )
| ( ( linord581940658strict @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1594]) ).
thf(1648,plain,
! [SV352: $i,SV86: $i] :
( ( ( ! [SY545: $i] :
~ ( ord_less_eq @ SV86 @ ( plus_plus @ SV86 @ ( times_times @ SV86 @ SV352 @ SV352 ) @ ( times_times @ SV86 @ SY545 @ SY545 ) ) @ ( zero_zero @ SV86 ) )
| ( ( ti @ SV86 @ SV352 )
= ( zero_zero @ SV86 ) ) )
= $true )
| ( ( linord581940658strict @ SV86 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1595]) ).
thf(1649,plain,
! [SV353: $i,SV86: $i] :
( ( ( ! [SY546: $i] :
( ~ ( ord_less_eq @ SV86 @ ( plus_plus @ SV86 @ ( times_times @ SV86 @ SV353 @ SV353 ) @ ( times_times @ SV86 @ SY546 @ SY546 ) ) @ ( zero_zero @ SV86 ) )
| ( ( ti @ SV86 @ SY546 )
= ( zero_zero @ SV86 ) ) ) )
= $true )
| ( ( linord581940658strict @ SV86 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1596]) ).
thf(1650,plain,
! [SV312: $i,SV292: $i] :
( ( ( SV292 = SV312 )
= $false )
| ( ( ord_less @ int @ SV292 @ SV312 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1597]) ).
thf(1651,plain,
! [SV340: $i,SV326: $i,SV65: $i] :
( ( ( ~ ( ord_less_eq @ SV65 @ ( number_number_of @ SV65 @ SV326 ) @ ( number_number_of @ SV65 @ SV340 ) ) )
= $true )
| ( ( ord_less_eq @ int @ SV326 @ SV340 )
= $true )
| ( ( linordered_idom @ SV65 )
= $false )
| ( ( number_ring @ SV65 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1599]) ).
thf(1652,plain,
! [SV65: $i,SV341: $i,SV327: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV327 @ SV341 ) )
= $true )
| ( ( ord_less_eq @ SV65 @ ( number_number_of @ SV65 @ SV327 ) @ ( number_number_of @ SV65 @ SV341 ) )
= $true )
| ( ( linordered_idom @ SV65 )
= $false )
| ( ( number_ring @ SV65 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1600]) ).
thf(1653,plain,
! [SV314: $i,SV294: $i] :
( ( ( ord_less @ int @ SV294 @ pls )
= $false )
| ( ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV314 ) @ ( number_number_of @ nat @ SV294 ) )
= ( number_number_of @ nat @ SV314 ) )
= $true )
| ( ( ord_less @ int @ SV314 @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1601]) ).
thf(1654,plain,
! [SV235: $i,SV69: $i,SV280: $i] :
( ( ( ~ ( ord_less_eq @ SV280 @ SV69 @ ( ti @ SV280 @ SV235 ) ) )
= $true )
| ( ( ord_less_eq @ SV280 @ SV69 @ SV235 )
= $true )
| ( ( linorder @ SV280 )
= $false )
| ( ( number @ SV280 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1609]) ).
thf(1655,plain,
! [SV236: $i,SV69: $i,SV281: $i] :
( ( ( ~ ( ord_less_eq @ SV281 @ SV69 @ SV236 ) )
= $true )
| ( ( ord_less_eq @ SV281 @ SV69 @ ( ti @ SV281 @ SV236 ) )
= $true )
| ( ( linorder @ SV281 )
= $false )
| ( ( number @ SV281 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1610]) ).
thf(1656,plain,
! [SV241: $i,SV71: $i,SV282: $i] :
( ( ( ~ ( ord_less @ SV282 @ ( ti @ SV282 @ SV71 ) @ SV241 ) )
= $true )
| ( ( ord_less @ SV282 @ SV71 @ SV241 )
= $true )
| ( ( linorder @ SV282 )
= $false )
| ( ( number @ SV282 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1613]) ).
thf(1657,plain,
! [SV242: $i,SV71: $i,SV283: $i] :
( ( ( ~ ( ord_less @ SV283 @ SV71 @ SV242 ) )
= $true )
| ( ( ord_less @ SV283 @ ( ti @ SV283 @ SV71 ) @ SV242 )
= $true )
| ( ( linorder @ SV283 )
= $false )
| ( ( number @ SV283 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1614]) ).
thf(1658,plain,
! [SV251: $i,SV72: $i,SV284: $i] :
( ( ( ~ ( ord_less_eq @ SV284 @ ( ti @ SV284 @ SV72 ) @ SV251 ) )
= $true )
| ( ( ord_less_eq @ SV284 @ SV72 @ SV251 )
= $true )
| ( ( linorder @ SV284 )
= $false )
| ( ( number @ SV284 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1615]) ).
thf(1659,plain,
! [SV252: $i,SV72: $i,SV285: $i] :
( ( ( ~ ( ord_less_eq @ SV285 @ SV72 @ SV252 ) )
= $true )
| ( ( ord_less_eq @ SV285 @ ( ti @ SV285 @ SV72 ) @ SV252 )
= $true )
| ( ( linorder @ SV285 )
= $false )
| ( ( number @ SV285 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1616]) ).
thf(1660,plain,
! [SV253: $i,SV73: $i,SV286: $i] :
( ( ( ~ ( ord_less @ SV286 @ SV73 @ ( ti @ SV286 @ SV253 ) ) )
= $true )
| ( ( ord_less @ SV286 @ SV73 @ SV253 )
= $true )
| ( ( linorder @ SV286 )
= $false )
| ( ( number @ SV286 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1617]) ).
thf(1661,plain,
! [SV254: $i,SV73: $i,SV287: $i] :
( ( ( ~ ( ord_less @ SV287 @ SV73 @ SV254 ) )
= $true )
| ( ( ord_less @ SV287 @ SV73 @ ( ti @ SV287 @ SV254 ) )
= $true )
| ( ( linorder @ SV287 )
= $false )
| ( ( number @ SV287 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1618]) ).
thf(1662,plain,
! [SV342: $i,SV328: $i,SV74: $i] :
( ( ( ~ ( ord_less_eq @ SV74 @ ( number_number_of @ SV74 @ SV328 ) @ ( number_number_of @ SV74 @ SV342 ) ) )
= $true )
| ( ( ~ ( ord_less @ SV74 @ ( number_number_of @ SV74 @ SV342 ) @ ( number_number_of @ SV74 @ SV328 ) ) )
= $true )
| ( ( linorder @ SV74 )
= $false )
| ( ( number @ SV74 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1619]) ).
thf(1663,plain,
! [SV329: $i,SV343: $i,SV74: $i] :
( ( ( ord_less @ SV74 @ ( number_number_of @ SV74 @ SV343 ) @ ( number_number_of @ SV74 @ SV329 ) )
= $true )
| ( ( ord_less_eq @ SV74 @ ( number_number_of @ SV74 @ SV329 ) @ ( number_number_of @ SV74 @ SV343 ) )
= $true )
| ( ( linorder @ SV74 )
= $false )
| ( ( number @ SV74 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1620]) ).
thf(1664,plain,
! [SV318: $i,SV298: $i,SV75: $i] :
( ( ( ( ( ti @ SV75 @ SV298 )
!= ( zero_zero @ SV75 ) ) )
= $true )
| ( ( ( ( ti @ SV75 @ SV318 )
!= ( zero_zero @ SV75 ) ) )
= $true )
| ( ( ord_less @ SV75 @ ( zero_zero @ SV75 ) @ ( plus_plus @ SV75 @ ( power_power @ SV75 @ SV298 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV75 @ SV318 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $false )
| ( ( linordered_idom @ SV75 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1621]) ).
thf(1665,plain,
! [SV344: $i,SV75: $i] :
( ( ( ( ti @ SV75 @ SV344 )
= ( zero_zero @ SV75 ) )
= $true )
| ( ( ! [SY539: $i] : ( ord_less @ SV75 @ ( zero_zero @ SV75 ) @ ( plus_plus @ SV75 @ ( power_power @ SV75 @ SV344 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV75 @ SY539 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true )
| ( ( linordered_idom @ SV75 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1622]) ).
thf(1666,plain,
! [SV345: $i,SV354: $i,SV75: $i] :
( ( ( ( ( ti @ SV75 @ SV354 )
= ( zero_zero @ SV75 ) )
| ( ord_less @ SV75 @ ( zero_zero @ SV75 ) @ ( plus_plus @ SV75 @ ( power_power @ SV75 @ SV345 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV75 @ SV354 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true )
| ( ( linordered_idom @ SV75 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1623]) ).
thf(1667,plain,
! [SV330: $i,SV76: $i] :
( ( ( ord_less_eq @ SV76 @ ( one_one @ SV76 ) @ ( number_number_of @ SV76 @ SV330 ) )
= $false )
| ( ( ord_less_eq @ int @ ( bit1 @ pls ) @ SV330 )
= $true )
| ( ( linordered_idom @ SV76 )
= $false )
| ( ( number_ring @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1624]) ).
thf(1668,plain,
! [SV76: $i,SV331: $i] :
( ( ( ord_less_eq @ int @ ( bit1 @ pls ) @ SV331 )
= $false )
| ( ( ord_less_eq @ SV76 @ ( one_one @ SV76 ) @ ( number_number_of @ SV76 @ SV331 ) )
= $true )
| ( ( linordered_idom @ SV76 )
= $false )
| ( ( number_ring @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1625]) ).
thf(1669,plain,
! [SV319: $i,SV299: $i,SV77: $i] :
( ( ( ( ti @ SV77 @ SV299 )
= ( zero_zero @ SV77 ) )
= $false )
| ( ( ( ( ti @ SV77 @ SV319 )
!= ( zero_zero @ SV77 ) ) )
= $true )
| ( ( ( plus_plus @ SV77 @ ( power_power @ SV77 @ SV299 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV77 @ SV319 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV77 ) )
= $true )
| ( ( linordered_idom @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1626]) ).
thf(1670,plain,
! [SV346: $i,SV77: $i] :
( ( ( ! [SY541: $i] :
( ( plus_plus @ SV77 @ ( power_power @ SV77 @ SV346 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV77 @ SY541 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV77 ) ) )
= $true )
| ( ( ( ti @ SV77 @ SV346 )
= ( zero_zero @ SV77 ) )
= $true )
| ( ( linordered_idom @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1627]) ).
thf(1671,plain,
! [SV355: $i,SV347: $i,SV77: $i] :
( ( ( ( ( plus_plus @ SV77 @ ( power_power @ SV77 @ SV347 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV77 @ SV355 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV77 ) )
| ( ( ti @ SV77 @ SV355 )
= ( zero_zero @ SV77 ) ) )
= $true )
| ( ( linordered_idom @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1628]) ).
thf(1672,plain,
! [SV320: $i,SV302: $i] :
( ( ( ord_less @ int @ SV302 @ SV320 )
= $false )
| ( ( ord_less @ int @ SV302 @ SV320 )
= $true )
| ( ( ord_less @ nat @ ( number_number_of @ nat @ SV302 ) @ ( number_number_of @ nat @ SV320 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1629]) ).
thf(1673,plain,
! [SV303: $i,SV321: $i] :
( ( ( ord_less @ int @ pls @ SV321 )
= $false )
| ( ( ~ ( ord_less @ int @ SV303 @ SV321 ) )
= $true )
| ( ( ord_less @ nat @ ( number_number_of @ nat @ SV303 ) @ ( number_number_of @ nat @ SV321 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1630]) ).
thf(1674,plain,
! [SV322: $i,SV304: $i] :
( ( ( ~ ( ord_less @ int @ SV304 @ SV322 ) )
= $true )
| ( ( ord_less @ int @ pls @ SV322 )
= $true )
| ( ( ord_less @ nat @ ( number_number_of @ nat @ SV304 ) @ ( number_number_of @ nat @ SV322 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1631]) ).
thf(1675,plain,
! [SV348: $i,SV332: $i,SV80: $i] :
( ( ( ( ( number_number_of @ SV80 @ SV332 )
!= ( number_number_of @ SV80 @ SV348 ) ) )
= $true )
| ( ( SV332 = SV348 )
= $true )
| ( ( number_ring @ SV80 )
= $false )
| ( ( ring_char_0 @ SV80 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1634]) ).
thf(1676,plain,
! [SV80: $i,SV349: $i,SV333: $i] :
( ( ( ( SV333 != SV349 ) )
= $true )
| ( ( ( number_number_of @ SV80 @ SV333 )
= ( number_number_of @ SV80 @ SV349 ) )
= $true )
| ( ( number_ring @ SV80 )
= $false )
| ( ( ring_char_0 @ SV80 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1635]) ).
thf(1677,plain,
! [SV334: $i,SV81: $i] :
( ( ( ord_less_eq @ SV81 @ ( number_number_of @ SV81 @ SV334 ) @ ( zero_zero @ SV81 ) )
= $false )
| ( ( ord_less_eq @ int @ SV334 @ pls )
= $true )
| ( ( linordered_idom @ SV81 )
= $false )
| ( ( number_ring @ SV81 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1636]) ).
thf(1678,plain,
! [SV81: $i,SV335: $i] :
( ( ( ord_less_eq @ int @ SV335 @ pls )
= $false )
| ( ( ord_less_eq @ SV81 @ ( number_number_of @ SV81 @ SV335 ) @ ( zero_zero @ SV81 ) )
= $true )
| ( ( linordered_idom @ SV81 )
= $false )
| ( ( number_ring @ SV81 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1637]) ).
thf(1679,plain,
! [SV324: $i,SV308: $i,SV82: $i] :
( ( ( ( ti @ SV82 @ SV308 )
= ( zero_zero @ SV82 ) )
= $false )
| ( ( ( ( ti @ SV82 @ SV324 )
!= ( zero_zero @ SV82 ) ) )
= $true )
| ( ( ( plus_plus @ SV82 @ ( times_times @ SV82 @ SV308 @ SV308 ) @ ( times_times @ SV82 @ SV324 @ SV324 ) )
= ( zero_zero @ SV82 ) )
= $true )
| ( ( linord581940658strict @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1638]) ).
thf(1680,plain,
! [SV350: $i,SV82: $i] :
( ( ( ! [SY543: $i] :
( ( plus_plus @ SV82 @ ( times_times @ SV82 @ SV350 @ SV350 ) @ ( times_times @ SV82 @ SY543 @ SY543 ) )
!= ( zero_zero @ SV82 ) ) )
= $true )
| ( ( ( ti @ SV82 @ SV350 )
= ( zero_zero @ SV82 ) )
= $true )
| ( ( linord581940658strict @ SV82 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1639]) ).
thf(1681,plain,
! [SV356: $i,SV351: $i,SV82: $i] :
( ( ( ( ( plus_plus @ SV82 @ ( times_times @ SV82 @ SV351 @ SV351 ) @ ( times_times @ SV82 @ SV356 @ SV356 ) )
!= ( zero_zero @ SV82 ) )
| ( ( ti @ SV82 @ SV356 )
= ( zero_zero @ SV82 ) ) )
= $true )
| ( ( linord581940658strict @ SV82 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1640]) ).
thf(1682,plain,
! [SV336: $i,SV84: $i] :
( ( ( ord_less_eq @ SV84 @ ( number_number_of @ SV84 @ SV336 ) @ ( one_one @ SV84 ) )
= $false )
| ( ( ord_less_eq @ int @ SV336 @ ( bit1 @ pls ) )
= $true )
| ( ( linordered_idom @ SV84 )
= $false )
| ( ( number_ring @ SV84 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1643]) ).
thf(1683,plain,
! [SV84: $i,SV337: $i] :
( ( ( ord_less_eq @ int @ SV337 @ ( bit1 @ pls ) )
= $false )
| ( ( ord_less_eq @ SV84 @ ( number_number_of @ SV84 @ SV337 ) @ ( one_one @ SV84 ) )
= $true )
| ( ( linordered_idom @ SV84 )
= $false )
| ( ( number_ring @ SV84 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1644]) ).
thf(1684,plain,
! [SV338: $i,SV85: $i] :
( ( ( ord_less_eq @ SV85 @ ( zero_zero @ SV85 ) @ ( number_number_of @ SV85 @ SV338 ) )
= $false )
| ( ( ord_less_eq @ int @ pls @ SV338 )
= $true )
| ( ( linordered_idom @ SV85 )
= $false )
| ( ( number_ring @ SV85 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1645]) ).
thf(1685,plain,
! [SV85: $i,SV339: $i] :
( ( ( ord_less_eq @ int @ pls @ SV339 )
= $false )
| ( ( ord_less_eq @ SV85 @ ( zero_zero @ SV85 ) @ ( number_number_of @ SV85 @ SV339 ) )
= $true )
| ( ( linordered_idom @ SV85 )
= $false )
| ( ( number_ring @ SV85 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1646]) ).
thf(1686,plain,
! [SV325: $i,SV309: $i,SV86: $i] :
( ( ( ( ti @ SV86 @ SV309 )
= ( zero_zero @ SV86 ) )
= $false )
| ( ( ( ( ti @ SV86 @ SV325 )
!= ( zero_zero @ SV86 ) ) )
= $true )
| ( ( ord_less_eq @ SV86 @ ( plus_plus @ SV86 @ ( times_times @ SV86 @ SV309 @ SV309 ) @ ( times_times @ SV86 @ SV325 @ SV325 ) ) @ ( zero_zero @ SV86 ) )
= $true )
| ( ( linord581940658strict @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1647]) ).
thf(1687,plain,
! [SV352: $i,SV86: $i] :
( ( ( ! [SY545: $i] :
~ ( ord_less_eq @ SV86 @ ( plus_plus @ SV86 @ ( times_times @ SV86 @ SV352 @ SV352 ) @ ( times_times @ SV86 @ SY545 @ SY545 ) ) @ ( zero_zero @ SV86 ) ) )
= $true )
| ( ( ( ti @ SV86 @ SV352 )
= ( zero_zero @ SV86 ) )
= $true )
| ( ( linord581940658strict @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1648]) ).
thf(1688,plain,
! [SV357: $i,SV353: $i,SV86: $i] :
( ( ( ~ ( ord_less_eq @ SV86 @ ( plus_plus @ SV86 @ ( times_times @ SV86 @ SV353 @ SV353 ) @ ( times_times @ SV86 @ SV357 @ SV357 ) ) @ ( zero_zero @ SV86 ) )
| ( ( ti @ SV86 @ SV357 )
= ( zero_zero @ SV86 ) ) )
= $true )
| ( ( linord581940658strict @ SV86 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1649]) ).
thf(1689,plain,
! [SV340: $i,SV326: $i,SV65: $i] :
( ( ( ord_less_eq @ SV65 @ ( number_number_of @ SV65 @ SV326 ) @ ( number_number_of @ SV65 @ SV340 ) )
= $false )
| ( ( ord_less_eq @ int @ SV326 @ SV340 )
= $true )
| ( ( linordered_idom @ SV65 )
= $false )
| ( ( number_ring @ SV65 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1651]) ).
thf(1690,plain,
! [SV65: $i,SV341: $i,SV327: $i] :
( ( ( ord_less_eq @ int @ SV327 @ SV341 )
= $false )
| ( ( ord_less_eq @ SV65 @ ( number_number_of @ SV65 @ SV327 ) @ ( number_number_of @ SV65 @ SV341 ) )
= $true )
| ( ( linordered_idom @ SV65 )
= $false )
| ( ( number_ring @ SV65 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1652]) ).
thf(1691,plain,
! [SV235: $i,SV69: $i,SV280: $i] :
( ( ( ord_less_eq @ SV280 @ SV69 @ ( ti @ SV280 @ SV235 ) )
= $false )
| ( ( ord_less_eq @ SV280 @ SV69 @ SV235 )
= $true )
| ( ( linorder @ SV280 )
= $false )
| ( ( number @ SV280 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1654]) ).
thf(1692,plain,
! [SV236: $i,SV69: $i,SV281: $i] :
( ( ( ord_less_eq @ SV281 @ SV69 @ SV236 )
= $false )
| ( ( ord_less_eq @ SV281 @ SV69 @ ( ti @ SV281 @ SV236 ) )
= $true )
| ( ( linorder @ SV281 )
= $false )
| ( ( number @ SV281 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1655]) ).
thf(1693,plain,
! [SV241: $i,SV71: $i,SV282: $i] :
( ( ( ord_less @ SV282 @ ( ti @ SV282 @ SV71 ) @ SV241 )
= $false )
| ( ( ord_less @ SV282 @ SV71 @ SV241 )
= $true )
| ( ( linorder @ SV282 )
= $false )
| ( ( number @ SV282 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1656]) ).
thf(1694,plain,
! [SV242: $i,SV71: $i,SV283: $i] :
( ( ( ord_less @ SV283 @ SV71 @ SV242 )
= $false )
| ( ( ord_less @ SV283 @ ( ti @ SV283 @ SV71 ) @ SV242 )
= $true )
| ( ( linorder @ SV283 )
= $false )
| ( ( number @ SV283 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1657]) ).
thf(1695,plain,
! [SV251: $i,SV72: $i,SV284: $i] :
( ( ( ord_less_eq @ SV284 @ ( ti @ SV284 @ SV72 ) @ SV251 )
= $false )
| ( ( ord_less_eq @ SV284 @ SV72 @ SV251 )
= $true )
| ( ( linorder @ SV284 )
= $false )
| ( ( number @ SV284 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1658]) ).
thf(1696,plain,
! [SV252: $i,SV72: $i,SV285: $i] :
( ( ( ord_less_eq @ SV285 @ SV72 @ SV252 )
= $false )
| ( ( ord_less_eq @ SV285 @ ( ti @ SV285 @ SV72 ) @ SV252 )
= $true )
| ( ( linorder @ SV285 )
= $false )
| ( ( number @ SV285 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1659]) ).
thf(1697,plain,
! [SV253: $i,SV73: $i,SV286: $i] :
( ( ( ord_less @ SV286 @ SV73 @ ( ti @ SV286 @ SV253 ) )
= $false )
| ( ( ord_less @ SV286 @ SV73 @ SV253 )
= $true )
| ( ( linorder @ SV286 )
= $false )
| ( ( number @ SV286 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1660]) ).
thf(1698,plain,
! [SV254: $i,SV73: $i,SV287: $i] :
( ( ( ord_less @ SV287 @ SV73 @ SV254 )
= $false )
| ( ( ord_less @ SV287 @ SV73 @ ( ti @ SV287 @ SV254 ) )
= $true )
| ( ( linorder @ SV287 )
= $false )
| ( ( number @ SV287 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1661]) ).
thf(1699,plain,
! [SV342: $i,SV328: $i,SV74: $i] :
( ( ( ord_less_eq @ SV74 @ ( number_number_of @ SV74 @ SV328 ) @ ( number_number_of @ SV74 @ SV342 ) )
= $false )
| ( ( ~ ( ord_less @ SV74 @ ( number_number_of @ SV74 @ SV342 ) @ ( number_number_of @ SV74 @ SV328 ) ) )
= $true )
| ( ( linorder @ SV74 )
= $false )
| ( ( number @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1662]) ).
thf(1700,plain,
! [SV318: $i,SV298: $i,SV75: $i] :
( ( ( ( ti @ SV75 @ SV298 )
= ( zero_zero @ SV75 ) )
= $false )
| ( ( ( ( ti @ SV75 @ SV318 )
!= ( zero_zero @ SV75 ) ) )
= $true )
| ( ( ord_less @ SV75 @ ( zero_zero @ SV75 ) @ ( plus_plus @ SV75 @ ( power_power @ SV75 @ SV298 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV75 @ SV318 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $false )
| ( ( linordered_idom @ SV75 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1664]) ).
thf(1701,plain,
! [SV358: $i,SV344: $i,SV75: $i] :
( ( ( ord_less @ SV75 @ ( zero_zero @ SV75 ) @ ( plus_plus @ SV75 @ ( power_power @ SV75 @ SV344 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV75 @ SV358 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true )
| ( ( ( ti @ SV75 @ SV344 )
= ( zero_zero @ SV75 ) )
= $true )
| ( ( linordered_idom @ SV75 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1665]) ).
thf(1702,plain,
! [SV345: $i,SV354: $i,SV75: $i] :
( ( ( ( ti @ SV75 @ SV354 )
= ( zero_zero @ SV75 ) )
= $true )
| ( ( ord_less @ SV75 @ ( zero_zero @ SV75 ) @ ( plus_plus @ SV75 @ ( power_power @ SV75 @ SV345 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV75 @ SV354 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true )
| ( ( linordered_idom @ SV75 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1666]) ).
thf(1703,plain,
! [SV299: $i,SV319: $i,SV77: $i] :
( ( ( ( ti @ SV77 @ SV319 )
= ( zero_zero @ SV77 ) )
= $false )
| ( ( ( ti @ SV77 @ SV299 )
= ( zero_zero @ SV77 ) )
= $false )
| ( ( ( plus_plus @ SV77 @ ( power_power @ SV77 @ SV299 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV77 @ SV319 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV77 ) )
= $true )
| ( ( linordered_idom @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1669]) ).
thf(1704,plain,
! [SV359: $i,SV346: $i,SV77: $i] :
( ( ( ( ( plus_plus @ SV77 @ ( power_power @ SV77 @ SV346 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV77 @ SV359 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV77 ) ) )
= $true )
| ( ( ( ti @ SV77 @ SV346 )
= ( zero_zero @ SV77 ) )
= $true )
| ( ( linordered_idom @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1670]) ).
thf(1705,plain,
! [SV355: $i,SV347: $i,SV77: $i] :
( ( ( ( ( plus_plus @ SV77 @ ( power_power @ SV77 @ SV347 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV77 @ SV355 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV77 ) ) )
= $true )
| ( ( ( ti @ SV77 @ SV355 )
= ( zero_zero @ SV77 ) )
= $true )
| ( ( linordered_idom @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1671]) ).
thf(1706,plain,
! [SV321: $i,SV303: $i] :
( ( ( ord_less @ int @ SV303 @ SV321 )
= $false )
| ( ( ord_less @ int @ pls @ SV321 )
= $false )
| ( ( ord_less @ nat @ ( number_number_of @ nat @ SV303 ) @ ( number_number_of @ nat @ SV321 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1673]) ).
thf(1707,plain,
! [SV322: $i,SV304: $i] :
( ( ( ord_less @ int @ SV304 @ SV322 )
= $false )
| ( ( ord_less @ int @ pls @ SV322 )
= $true )
| ( ( ord_less @ nat @ ( number_number_of @ nat @ SV304 ) @ ( number_number_of @ nat @ SV322 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1674]) ).
thf(1708,plain,
! [SV348: $i,SV332: $i,SV80: $i] :
( ( ( ( number_number_of @ SV80 @ SV332 )
= ( number_number_of @ SV80 @ SV348 ) )
= $false )
| ( ( SV332 = SV348 )
= $true )
| ( ( number_ring @ SV80 )
= $false )
| ( ( ring_char_0 @ SV80 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1675]) ).
thf(1709,plain,
! [SV80: $i,SV349: $i,SV333: $i] :
( ( ( SV333 = SV349 )
= $false )
| ( ( ( number_number_of @ SV80 @ SV333 )
= ( number_number_of @ SV80 @ SV349 ) )
= $true )
| ( ( number_ring @ SV80 )
= $false )
| ( ( ring_char_0 @ SV80 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1676]) ).
thf(1710,plain,
! [SV308: $i,SV324: $i,SV82: $i] :
( ( ( ( ti @ SV82 @ SV324 )
= ( zero_zero @ SV82 ) )
= $false )
| ( ( ( ti @ SV82 @ SV308 )
= ( zero_zero @ SV82 ) )
= $false )
| ( ( ( plus_plus @ SV82 @ ( times_times @ SV82 @ SV308 @ SV308 ) @ ( times_times @ SV82 @ SV324 @ SV324 ) )
= ( zero_zero @ SV82 ) )
= $true )
| ( ( linord581940658strict @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1679]) ).
thf(1711,plain,
! [SV360: $i,SV350: $i,SV82: $i] :
( ( ( ( ( plus_plus @ SV82 @ ( times_times @ SV82 @ SV350 @ SV350 ) @ ( times_times @ SV82 @ SV360 @ SV360 ) )
!= ( zero_zero @ SV82 ) ) )
= $true )
| ( ( ( ti @ SV82 @ SV350 )
= ( zero_zero @ SV82 ) )
= $true )
| ( ( linord581940658strict @ SV82 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1680]) ).
thf(1712,plain,
! [SV356: $i,SV351: $i,SV82: $i] :
( ( ( ( ( plus_plus @ SV82 @ ( times_times @ SV82 @ SV351 @ SV351 ) @ ( times_times @ SV82 @ SV356 @ SV356 ) )
!= ( zero_zero @ SV82 ) ) )
= $true )
| ( ( ( ti @ SV82 @ SV356 )
= ( zero_zero @ SV82 ) )
= $true )
| ( ( linord581940658strict @ SV82 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1681]) ).
thf(1713,plain,
! [SV309: $i,SV325: $i,SV86: $i] :
( ( ( ( ti @ SV86 @ SV325 )
= ( zero_zero @ SV86 ) )
= $false )
| ( ( ( ti @ SV86 @ SV309 )
= ( zero_zero @ SV86 ) )
= $false )
| ( ( ord_less_eq @ SV86 @ ( plus_plus @ SV86 @ ( times_times @ SV86 @ SV309 @ SV309 ) @ ( times_times @ SV86 @ SV325 @ SV325 ) ) @ ( zero_zero @ SV86 ) )
= $true )
| ( ( linord581940658strict @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1686]) ).
thf(1714,plain,
! [SV361: $i,SV352: $i,SV86: $i] :
( ( ( ~ ( ord_less_eq @ SV86 @ ( plus_plus @ SV86 @ ( times_times @ SV86 @ SV352 @ SV352 ) @ ( times_times @ SV86 @ SV361 @ SV361 ) ) @ ( zero_zero @ SV86 ) ) )
= $true )
| ( ( ( ti @ SV86 @ SV352 )
= ( zero_zero @ SV86 ) )
= $true )
| ( ( linord581940658strict @ SV86 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1687]) ).
thf(1715,plain,
! [SV357: $i,SV353: $i,SV86: $i] :
( ( ( ~ ( ord_less_eq @ SV86 @ ( plus_plus @ SV86 @ ( times_times @ SV86 @ SV353 @ SV353 ) @ ( times_times @ SV86 @ SV357 @ SV357 ) ) @ ( zero_zero @ SV86 ) ) )
= $true )
| ( ( ( ti @ SV86 @ SV357 )
= ( zero_zero @ SV86 ) )
= $true )
| ( ( linord581940658strict @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1688]) ).
thf(1716,plain,
! [SV328: $i,SV342: $i,SV74: $i] :
( ( ( ord_less @ SV74 @ ( number_number_of @ SV74 @ SV342 ) @ ( number_number_of @ SV74 @ SV328 ) )
= $false )
| ( ( ord_less_eq @ SV74 @ ( number_number_of @ SV74 @ SV328 ) @ ( number_number_of @ SV74 @ SV342 ) )
= $false )
| ( ( linorder @ SV74 )
= $false )
| ( ( number @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1699]) ).
thf(1717,plain,
! [SV298: $i,SV318: $i,SV75: $i] :
( ( ( ( ti @ SV75 @ SV318 )
= ( zero_zero @ SV75 ) )
= $false )
| ( ( ( ti @ SV75 @ SV298 )
= ( zero_zero @ SV75 ) )
= $false )
| ( ( ord_less @ SV75 @ ( zero_zero @ SV75 ) @ ( plus_plus @ SV75 @ ( power_power @ SV75 @ SV298 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV75 @ SV318 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $false )
| ( ( linordered_idom @ SV75 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1700]) ).
thf(1718,plain,
! [SV359: $i,SV346: $i,SV77: $i] :
( ( ( ( plus_plus @ SV77 @ ( power_power @ SV77 @ SV346 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV77 @ SV359 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV77 ) )
= $false )
| ( ( ( ti @ SV77 @ SV346 )
= ( zero_zero @ SV77 ) )
= $true )
| ( ( linordered_idom @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1704]) ).
thf(1719,plain,
! [SV355: $i,SV347: $i,SV77: $i] :
( ( ( ( plus_plus @ SV77 @ ( power_power @ SV77 @ SV347 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV77 @ SV355 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV77 ) )
= $false )
| ( ( ( ti @ SV77 @ SV355 )
= ( zero_zero @ SV77 ) )
= $true )
| ( ( linordered_idom @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1705]) ).
thf(1720,plain,
! [SV360: $i,SV350: $i,SV82: $i] :
( ( ( ( plus_plus @ SV82 @ ( times_times @ SV82 @ SV350 @ SV350 ) @ ( times_times @ SV82 @ SV360 @ SV360 ) )
= ( zero_zero @ SV82 ) )
= $false )
| ( ( ( ti @ SV82 @ SV350 )
= ( zero_zero @ SV82 ) )
= $true )
| ( ( linord581940658strict @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1711]) ).
thf(1721,plain,
! [SV356: $i,SV351: $i,SV82: $i] :
( ( ( ( plus_plus @ SV82 @ ( times_times @ SV82 @ SV351 @ SV351 ) @ ( times_times @ SV82 @ SV356 @ SV356 ) )
= ( zero_zero @ SV82 ) )
= $false )
| ( ( ( ti @ SV82 @ SV356 )
= ( zero_zero @ SV82 ) )
= $true )
| ( ( linord581940658strict @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1712]) ).
thf(1722,plain,
! [SV361: $i,SV352: $i,SV86: $i] :
( ( ( ord_less_eq @ SV86 @ ( plus_plus @ SV86 @ ( times_times @ SV86 @ SV352 @ SV352 ) @ ( times_times @ SV86 @ SV361 @ SV361 ) ) @ ( zero_zero @ SV86 ) )
= $false )
| ( ( ( ti @ SV86 @ SV352 )
= ( zero_zero @ SV86 ) )
= $true )
| ( ( linord581940658strict @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1714]) ).
thf(1723,plain,
! [SV357: $i,SV353: $i,SV86: $i] :
( ( ( ord_less_eq @ SV86 @ ( plus_plus @ SV86 @ ( times_times @ SV86 @ SV353 @ SV353 ) @ ( times_times @ SV86 @ SV357 @ SV357 ) ) @ ( zero_zero @ SV86 ) )
= $false )
| ( ( ( ti @ SV86 @ SV357 )
= ( zero_zero @ SV86 ) )
= $true )
| ( ( linord581940658strict @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1715]) ).
thf(1724,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[412,1723,1722,1721,1720,1719,1718,1717,1716,1713,1710,1709,1708,1707,1706,1703,1702,1701,1698,1697,1696,1695,1694,1693,1692,1691,1690,1689,1685,1684,1683,1682,1678,1677,1672,1668,1667,1663,1653,1650,1642,1641,1633,1632,1612,1611,1608,1607,1606,1605,1604,1603,1602,1598,1575,1574,1541,1540,1522,1483,1482,1481,1478,1477,1476,1475,1474,1463,1462,1461,1460,1439,1438,1437,1436,1435,1434,1429,1428,1427,1426,1425,1424,1423,1422,1419,1418,1417,1416,1411,1410,1401,1398,1397,1396,1395,1388,1387,1386,1385,1384,1383,1380,1379,1378,1377,1376,1369,1368,1356,1355,1325,1324,1323,1322,1315,1314,1311,1310,1292,1291,1285,1284,1280,1279,1267,1266,1264,1160,1158,1157,1156,1147,1146,1144,1141,1139,1138,1137,1136,1135,1134,1030,1028,1020,1019,1013,1012,905,904,902,899,898,892,889,888,885,884,876,875,871,788,774,765,764,754,752,745,681,675,655,654,652,639,638,631,618,617,616,615,548,547,546,545,544,527,526,525,524,523,522,521,520,519,518,517,516,515,514,513,512,511,496,495,478,477,476,459,446,435,432,431,430,429,413]) ).
thf(1725,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[1724]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : NUM924+5 : TPTP v8.1.0. Released v5.3.0.
% 0.07/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33 % Computer : n008.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 21:35:38 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.39 ...
% 0.19/0.45
% 0.19/0.45 No.of.Axioms: 154
% 0.19/0.45
% 0.19/0.45 Length.of.Defs: 0
% 0.19/0.45
% 0.19/0.45 Contains.Choice.Funs: false
% 0.19/0.48 .........
% 0.19/0.53 (rf:2,axioms:154,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:156,loop_count:0,foatp_calls:0,translation:fof_full)....................................................................................................................
% 0.91/1.15
% 0.91/1.15 ********************************
% 0.91/1.15 * All subproblems solved! *
% 0.91/1.15 ********************************
% 0.91/1.15 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:2,axioms:154,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:1724,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.52/1.69
% 1.52/1.69 %**** Beginning of derivation protocol ****
% 1.52/1.69 % SZS output start CNFRefutation
% See solution above
% 1.52/1.69
% 1.52/1.69 %**** End of derivation protocol ****
% 1.52/1.69 %**** no. of clauses in derivation: 1725 ****
% 1.52/1.69 %**** clause counter: 1724 ****
% 1.52/1.69
% 1.52/1.69 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:2,axioms:154,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:1724,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------