%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM924+5 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:35:35 AM UTC 2026
% Result : Theorem 11.03s 2.09s
% Output : CNFRefutation 11.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 141
% Syntax : Number of formulae : 1405 ( 759 unt; 0 typ; 0 def)
% Number of atoms : 8268 (3140 equ; 0 cnn)
% Maximal formula atoms : 7 ( 5 avg)
% Number of connectives : 22701 (2677 ~;2255 |; 60 &;17379 @)
% ( 138 <=>; 192 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 35 ( 32 usr; 9 con; 0-3 aty)
% Number of variables : 2886 ( 0 ^;2886 !; 0 ?;2886 :)
% 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_SX0,type,
sK1_SX0: $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(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(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(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(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(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(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,
( ( number @ nat )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(159,plain,
( ( semiring @ nat )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(160,plain,
( ( semiring_1 @ nat )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(161,plain,
( ( linorder @ nat )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(162,plain,
( ( number_semiring @ nat )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(163,plain,
( ( number @ int )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(164,plain,
( ( semiring @ int )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(165,plain,
( ( number_ring @ int )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(166,plain,
( ( ring_char_0 @ int )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(167,plain,
( ( semiring_1 @ int )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(168,plain,
( ( linorder @ int )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(169,plain,
( ( number_semiring @ int )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(170,plain,
( ( linordered_idom @ int )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(171,plain,
( ( linordered_ring @ int )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(172,plain,
( ( linord581940658strict @ int )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(173,plain,
( ( ring_11004092258visors @ int )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(174,plain,
( ( ( zero_zero @ int )
= ( number_number_of @ int @ pls ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(175,plain,
( ( ! [Z: $i,W: $i] :
( ( plus_plus @ int @ Z @ W )
= ( plus_plus @ int @ W @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(176,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(177,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(178,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(179,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(180,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(181,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(182,plain,
( ( ! [K: $i,L: $i] :
( ( ( bit0 @ K )
= ( bit0 @ L ) )
<=> ( K = L ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(183,plain,
( ( ! [K: $i,L: $i] :
( ( ( bit1 @ K )
= ( bit1 @ L ) )
<=> ( K = L ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(184,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(185,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(186,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(187,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(188,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(189,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(190,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(191,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(192,plain,
( ( ( one_one @ nat )
= ( number_number_of @ nat @ ( bit1 @ pls ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(193,plain,
( ( ( number_number_of @ nat @ ( bit1 @ pls ) )
= ( one_one @ nat ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(194,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(195,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(196,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(197,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(198,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(199,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(200,plain,
( ( ! [K: $i] :
( ( ord_less @ int @ pls @ ( bit1 @ K ) )
<=> ( ord_less_eq @ int @ pls @ K ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(201,plain,
( ( ! [K: $i] :
( ( ord_less_eq @ int @ ( bit1 @ K ) @ pls )
<=> ( ord_less @ int @ K @ pls ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(202,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(203,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(204,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(205,plain,
( ( ! [Z: $i] :
( ( times_times @ int @ ( one_one @ int ) @ Z )
= Z ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(206,plain,
( ( ! [Z: $i] :
( ( times_times @ int @ Z @ ( one_one @ int ) )
= Z ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(207,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(208,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(209,plain,
( ( ! [W: $i] :
( ( times_times @ int @ pls @ W )
= pls ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(210,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(211,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(212,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(213,plain,
( ( ( zero_zero @ nat )
= ( number_number_of @ nat @ pls ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(214,plain,
( ( ( number_number_of @ nat @ pls )
= ( zero_zero @ nat ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(215,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(216,plain,
( ( ! [K: $i] :
( ( ord_less_eq @ int @ pls @ ( bit0 @ K ) )
<=> ( ord_less_eq @ int @ pls @ K ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(217,plain,
( ( ! [K: $i] :
( ( ord_less_eq @ int @ ( bit0 @ K ) @ pls )
<=> ( ord_less_eq @ int @ K @ pls ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(218,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(219,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(220,plain,
( ( ! [K: $i] :
( ( ord_less_eq @ int @ pls @ ( bit1 @ K ) )
<=> ( ord_less_eq @ int @ pls @ K ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(221,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(222,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(223,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(224,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(225,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(226,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(227,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(228,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(229,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(230,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(231,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(232,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(233,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(234,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(235,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(236,plain,
( ( ord_less_eq @ int @ pls @ pls )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(237,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(238,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(239,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(240,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(241,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(242,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(243,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(244,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(245,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(246,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(247,plain,
( ( ! [Z: $i,W: $i] :
( ( times_times @ int @ Z @ W )
= ( times_times @ int @ W @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(248,plain,
( ( ! [K_1: $i] :
( ( number_number_of @ int @ K_1 )
= K_1 ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(249,plain,
( ( ! [W: $i] : ( ord_less_eq @ int @ W @ W ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(250,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(251,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(252,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(253,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(254,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(255,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(256,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(257,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(258,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(259,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(260,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(261,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(262,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(263,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(264,plain,
( ( ~ ( ord_less_eq @ int @ ( one_one @ int ) @ t ) )
= $true ),
inference(unfold_def,[status(thm)],[110]) ).
thf(265,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(266,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(267,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(268,plain,
( ( ord_less @ int @ t @ ( one_one @ int ) )
= $true ),
inference(unfold_def,[status(thm)],[114]) ).
thf(269,plain,
( ( ord_less @ int @ t @ ( zero_zero @ int ) )
= $true ),
inference(unfold_def,[status(thm)],[115]) ).
thf(270,plain,
( ( ( ti @ int @ t )
= t )
= $true ),
inference(unfold_def,[status(thm)],[116]) ).
thf(271,plain,
( ( ( ti @ int @ m )
= m )
= $true ),
inference(unfold_def,[status(thm)],[117]) ).
thf(272,plain,
( ( ! [B_1: $i] :
( ( twoSqu33214720sum2sq @ ( ti @ int @ B_1 ) )
<=> ( twoSqu33214720sum2sq @ B_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[118]) ).
thf(273,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(274,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(275,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(276,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(277,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(278,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(279,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(280,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(281,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(282,plain,
( ( ! [B_1: $i] :
( ( zprime @ ( ti @ int @ B_1 ) )
<=> ( zprime @ B_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[132]) ).
thf(283,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(284,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(285,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(286,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(287,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(288,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(289,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(290,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(291,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(292,plain,
( ( ( ti @ int @ s )
= s )
= $true ),
inference(unfold_def,[status(thm)],[149]) ).
thf(293,plain,
( ( ( ti @ int @ pls )
= pls )
= $true ),
inference(unfold_def,[status(thm)],[150]) ).
thf(294,plain,
( ( ! [B_1: $i] :
( ( ti @ int @ ( bit1 @ B_1 ) )
= ( bit1 @ B_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[151]) ).
thf(295,plain,
( ( ! [B_1: $i] :
( ( bit1 @ ( ti @ int @ B_1 ) )
= ( bit1 @ B_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[152]) ).
thf(296,plain,
( ( ! [B_1: $i] :
( ( ti @ int @ ( bit0 @ B_1 ) )
= ( bit0 @ B_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[153]) ).
thf(297,plain,
( ( ! [B_1: $i] :
( ( bit0 @ ( ti @ int @ B_1 ) )
= ( bit0 @ B_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[154]) ).
thf(298,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(299,plain,
( ( ! [B_1: $i] :
( ( bit0 @ ( ti @ int @ B_1 ) )
= ( bit0 @ B_1 ) ) )
= $true ),
inference(copy,[status(thm)],[297]) ).
thf(300,plain,
( ( ! [B_1: $i] :
( ( ti @ int @ ( bit0 @ B_1 ) )
= ( bit0 @ B_1 ) ) )
= $true ),
inference(copy,[status(thm)],[296]) ).
thf(301,plain,
( ( ! [B_1: $i] :
( ( bit1 @ ( ti @ int @ B_1 ) )
= ( bit1 @ B_1 ) ) )
= $true ),
inference(copy,[status(thm)],[295]) ).
thf(302,plain,
( ( ! [B_1: $i] :
( ( ti @ int @ ( bit1 @ B_1 ) )
= ( bit1 @ B_1 ) ) )
= $true ),
inference(copy,[status(thm)],[294]) ).
thf(303,plain,
( ( ( ti @ int @ pls )
= pls )
= $true ),
inference(copy,[status(thm)],[293]) ).
thf(304,plain,
( ( ( ti @ int @ s )
= s )
= $true ),
inference(copy,[status(thm)],[292]) ).
thf(305,plain,
( ( ! [X_a: $i] :
( ( semiring_1 @ X_a )
=> ( ( ti @ X_a @ ( one_one @ X_a ) )
= ( one_one @ X_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[291]) ).
thf(306,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)],[290]) ).
thf(307,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)],[289]) ).
thf(308,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)],[288]) ).
thf(309,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)],[287]) ).
thf(310,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)],[286]) ).
thf(311,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)],[285]) ).
thf(312,plain,
( ( ! [X_a: $i] :
( ( linordered_ring @ X_a )
=> ( ( ti @ X_a @ ( zero_zero @ X_a ) )
= ( zero_zero @ X_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[284]) ).
thf(313,plain,
( ( ! [X_a: $i] :
( ( semiring_1 @ X_a )
=> ( ( ti @ X_a @ ( zero_zero @ X_a ) )
= ( zero_zero @ X_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[283]) ).
thf(314,plain,
( ( ! [B_1: $i] :
( ( zprime @ ( ti @ int @ B_1 ) )
<=> ( zprime @ B_1 ) ) )
= $true ),
inference(copy,[status(thm)],[282]) ).
thf(315,plain,
( ( ! [B_1: $i,X_a: $i] :
( ( number @ X_a )
=> ( ( number_number_of @ X_a @ ( ti @ int @ B_1 ) )
= ( number_number_of @ X_a @ B_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[281]) ).
thf(316,plain,
( ( ! [B_1: $i,X_a: $i] :
( ( number @ X_a )
=> ( ( ti @ X_a @ ( number_number_of @ X_a @ B_1 ) )
= ( number_number_of @ X_a @ B_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[280]) ).
thf(317,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(copy,[status(thm)],[279]) ).
thf(318,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(copy,[status(thm)],[278]) ).
thf(319,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(copy,[status(thm)],[277]) ).
thf(320,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(copy,[status(thm)],[276]) ).
thf(321,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)],[275]) ).
thf(322,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)],[274]) ).
thf(323,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)],[273]) ).
thf(324,plain,
( ( ! [B_1: $i] :
( ( twoSqu33214720sum2sq @ ( ti @ int @ B_1 ) )
<=> ( twoSqu33214720sum2sq @ B_1 ) ) )
= $true ),
inference(copy,[status(thm)],[272]) ).
thf(325,plain,
( ( ( ti @ int @ m )
= m )
= $true ),
inference(copy,[status(thm)],[271]) ).
thf(326,plain,
( ( ( ti @ int @ t )
= t )
= $true ),
inference(copy,[status(thm)],[270]) ).
thf(327,plain,
( ( ord_less @ int @ t @ ( zero_zero @ int ) )
= $true ),
inference(copy,[status(thm)],[269]) ).
thf(328,plain,
( ( ord_less @ int @ t @ ( one_one @ int ) )
= $true ),
inference(copy,[status(thm)],[268]) ).
thf(329,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)],[267]) ).
thf(330,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)],[266]) ).
thf(331,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)],[265]) ).
thf(332,plain,
( ( ~ ( ord_less_eq @ int @ ( one_one @ int ) @ t ) )
= $true ),
inference(copy,[status(thm)],[264]) ).
thf(333,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)],[263]) ).
thf(334,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)],[262]) ).
thf(335,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(copy,[status(thm)],[261]) ).
thf(336,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(copy,[status(thm)],[260]) ).
thf(337,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)],[259]) ).
thf(338,plain,
( ( ! [X_a: $i] :
( ( linordered_idom @ X_a )
=> ! [A_2: $i] :
( ( ord_less @ X_a @ ( zero_zero @ X_a ) @ ( power_power @ X_a @ A_2 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
<=> ( ( ti @ X_a @ A_2 )
!= ( zero_zero @ X_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[258]) ).
thf(339,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)],[257]) ).
thf(340,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)],[256]) ).
thf(341,plain,
( ( ! [X_a: $i] :
( ( ring_11004092258visors @ X_a )
=> ! [A_2: $i] :
( ( ( power_power @ X_a @ A_2 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ X_a ) )
<=> ( ( ti @ X_a @ A_2 )
= ( zero_zero @ X_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[255]) ).
thf(342,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)],[254]) ).
thf(343,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)],[253]) ).
thf(344,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)],[252]) ).
thf(345,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(copy,[status(thm)],[251]) ).
thf(346,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)],[250]) ).
thf(347,plain,
( ( ! [W: $i] : ( ord_less_eq @ int @ W @ W ) )
= $true ),
inference(copy,[status(thm)],[249]) ).
thf(348,plain,
( ( ! [K_1: $i] :
( ( number_number_of @ int @ K_1 )
= K_1 ) )
= $true ),
inference(copy,[status(thm)],[248]) ).
thf(349,plain,
( ( ! [Z: $i,W: $i] :
( ( times_times @ int @ Z @ W )
= ( times_times @ int @ W @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[247]) ).
thf(350,plain,
( ( ! [Z: $i,W: $i] :
( ( ord_less_eq @ int @ Z @ W )
| ( ord_less_eq @ int @ W @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[246]) ).
thf(351,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)],[245]) ).
thf(352,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(copy,[status(thm)],[244]) ).
thf(353,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(copy,[status(thm)],[243]) ).
thf(354,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)],[242]) ).
thf(355,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)],[241]) ).
thf(356,plain,
( ( ! [Z: $i,W: $i] :
( ( ord_less_eq @ int @ Z @ W )
=> ( ( ord_less_eq @ int @ W @ Z )
=> ( Z = W ) ) ) )
= $true ),
inference(copy,[status(thm)],[240]) ).
thf(357,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)],[239]) ).
thf(358,plain,
( ( ! [K1: $i,K2: $i] :
( ( ord_less_eq @ int @ ( bit1 @ K1 ) @ ( bit1 @ K2 ) )
<=> ( ord_less_eq @ int @ K1 @ K2 ) ) )
= $true ),
inference(copy,[status(thm)],[238]) ).
thf(359,plain,
( ( ! [K: $i,L: $i] :
( ( ord_less_eq @ int @ ( bit1 @ K ) @ ( bit1 @ L ) )
<=> ( ord_less_eq @ int @ K @ L ) ) )
= $true ),
inference(copy,[status(thm)],[237]) ).
thf(360,plain,
( ( ord_less_eq @ int @ pls @ pls )
= $true ),
inference(copy,[status(thm)],[236]) ).
thf(361,plain,
( ( ! [K1: $i,K2: $i] :
( ( ord_less_eq @ int @ ( bit0 @ K1 ) @ ( bit0 @ K2 ) )
<=> ( ord_less_eq @ int @ K1 @ K2 ) ) )
= $true ),
inference(copy,[status(thm)],[235]) ).
thf(362,plain,
( ( ! [K: $i,L: $i] :
( ( ord_less_eq @ int @ ( bit0 @ K ) @ ( bit0 @ L ) )
<=> ( ord_less_eq @ int @ K @ L ) ) )
= $true ),
inference(copy,[status(thm)],[234]) ).
thf(363,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(copy,[status(thm)],[233]) ).
thf(364,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)],[232]) ).
thf(365,plain,
( ( ! [V_3: $i] :
( ( ( number_number_of @ nat @ V_3 )
= ( zero_zero @ nat ) )
<=> ( ord_less_eq @ int @ V_3 @ pls ) ) )
= $true ),
inference(copy,[status(thm)],[231]) ).
thf(366,plain,
( ( ! [V_3: $i] :
( ( ( zero_zero @ nat )
= ( number_number_of @ nat @ V_3 ) )
<=> ( ord_less_eq @ int @ V_3 @ pls ) ) )
= $true ),
inference(copy,[status(thm)],[230]) ).
thf(367,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)],[229]) ).
thf(368,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)],[228]) ).
thf(369,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)],[227]) ).
thf(370,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)],[226]) ).
thf(371,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)],[225]) ).
thf(372,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(copy,[status(thm)],[224]) ).
thf(373,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(copy,[status(thm)],[223]) ).
thf(374,plain,
( ( ! [V_3: $i] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( number_number_of @ nat @ V_3 ) )
<=> ( ord_less @ int @ pls @ V_3 ) ) )
= $true ),
inference(copy,[status(thm)],[222]) ).
thf(375,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(copy,[status(thm)],[221]) ).
thf(376,plain,
( ( ! [K: $i] :
( ( ord_less_eq @ int @ pls @ ( bit1 @ K ) )
<=> ( ord_less_eq @ int @ pls @ K ) ) )
= $true ),
inference(copy,[status(thm)],[220]) ).
thf(377,plain,
( ( ! [K1: $i,K2: $i] :
( ( ord_less_eq @ int @ ( bit0 @ K1 ) @ ( bit1 @ K2 ) )
<=> ( ord_less_eq @ int @ K1 @ K2 ) ) )
= $true ),
inference(copy,[status(thm)],[219]) ).
thf(378,plain,
( ( ! [K: $i,L: $i] :
( ( ord_less_eq @ int @ ( bit0 @ K ) @ ( bit1 @ L ) )
<=> ( ord_less_eq @ int @ K @ L ) ) )
= $true ),
inference(copy,[status(thm)],[218]) ).
thf(379,plain,
( ( ! [K: $i] :
( ( ord_less_eq @ int @ ( bit0 @ K ) @ pls )
<=> ( ord_less_eq @ int @ K @ pls ) ) )
= $true ),
inference(copy,[status(thm)],[217]) ).
thf(380,plain,
( ( ! [K: $i] :
( ( ord_less_eq @ int @ pls @ ( bit0 @ K ) )
<=> ( ord_less_eq @ int @ pls @ K ) ) )
= $true ),
inference(copy,[status(thm)],[216]) ).
thf(381,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)],[215]) ).
thf(382,plain,
( ( ( number_number_of @ nat @ pls )
= ( zero_zero @ nat ) )
= $true ),
inference(copy,[status(thm)],[214]) ).
thf(383,plain,
( ( ( zero_zero @ nat )
= ( number_number_of @ nat @ pls ) )
= $true ),
inference(copy,[status(thm)],[213]) ).
thf(384,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(copy,[status(thm)],[212]) ).
thf(385,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(copy,[status(thm)],[211]) ).
thf(386,plain,
( ( ( plus_plus @ nat @ ( one_one @ nat ) @ ( one_one @ nat ) )
= ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(copy,[status(thm)],[210]) ).
thf(387,plain,
( ( ! [W: $i] :
( ( times_times @ int @ pls @ W )
= pls ) )
= $true ),
inference(copy,[status(thm)],[209]) ).
thf(388,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)],[208]) ).
thf(389,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(copy,[status(thm)],[207]) ).
thf(390,plain,
( ( ! [Z: $i] :
( ( times_times @ int @ Z @ ( one_one @ int ) )
= Z ) )
= $true ),
inference(copy,[status(thm)],[206]) ).
thf(391,plain,
( ( ! [Z: $i] :
( ( times_times @ int @ ( one_one @ int ) @ Z )
= Z ) )
= $true ),
inference(copy,[status(thm)],[205]) ).
thf(392,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)],[204]) ).
thf(393,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)],[203]) ).
thf(394,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)],[202]) ).
thf(395,plain,
( ( ! [K: $i] :
( ( ord_less_eq @ int @ ( bit1 @ K ) @ pls )
<=> ( ord_less @ int @ K @ pls ) ) )
= $true ),
inference(copy,[status(thm)],[201]) ).
thf(396,plain,
( ( ! [K: $i] :
( ( ord_less @ int @ pls @ ( bit1 @ K ) )
<=> ( ord_less_eq @ int @ pls @ K ) ) )
= $true ),
inference(copy,[status(thm)],[200]) ).
thf(397,plain,
( ( ! [K1: $i,K2: $i] :
( ( ord_less_eq @ int @ ( bit1 @ K1 ) @ ( bit0 @ K2 ) )
<=> ( ord_less @ int @ K1 @ K2 ) ) )
= $true ),
inference(copy,[status(thm)],[199]) ).
thf(398,plain,
( ( ! [K: $i,L: $i] :
( ( ord_less_eq @ int @ ( bit1 @ K ) @ ( bit0 @ L ) )
<=> ( ord_less @ int @ K @ L ) ) )
= $true ),
inference(copy,[status(thm)],[198]) ).
thf(399,plain,
( ( ! [K1: $i,K2: $i] :
( ( ord_less @ int @ ( bit0 @ K1 ) @ ( bit1 @ K2 ) )
<=> ( ord_less_eq @ int @ K1 @ K2 ) ) )
= $true ),
inference(copy,[status(thm)],[197]) ).
thf(400,plain,
( ( ! [K: $i,L: $i] :
( ( ord_less @ int @ ( bit0 @ K ) @ ( bit1 @ L ) )
<=> ( ord_less_eq @ int @ K @ L ) ) )
= $true ),
inference(copy,[status(thm)],[196]) ).
thf(401,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(copy,[status(thm)],[195]) ).
thf(402,plain,
( ( ! [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)],[194]) ).
thf(403,plain,
( ( ( number_number_of @ nat @ ( bit1 @ pls ) )
= ( one_one @ nat ) )
= $true ),
inference(copy,[status(thm)],[193]) ).
thf(404,plain,
( ( ( one_one @ nat )
= ( number_number_of @ nat @ ( bit1 @ pls ) ) )
= $true ),
inference(copy,[status(thm)],[192]) ).
thf(405,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)],[191]) ).
thf(406,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(copy,[status(thm)],[190]) ).
thf(407,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(copy,[status(thm)],[189]) ).
thf(408,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)],[188]) ).
thf(409,plain,
( ( ! [V_1: $i,V: $i] :
( ( ( ord_less @ int @ V @ pls )
=> ( ( plus_plus @ nat @ ( number_number_of @ nat @ V ) @ ( number_number_of @ nat @ V_1 ) )
= ( number_number_of @ nat @ V_1 ) ) )
& ( ~ ( ord_less @ int @ V @ pls )
=> ( ( ( ord_less @ int @ V_1 @ pls )
=> ( ( plus_plus @ nat @ ( number_number_of @ nat @ V ) @ ( number_number_of @ nat @ V_1 ) )
= ( number_number_of @ nat @ V ) ) )
& ( ~ ( ord_less @ int @ V_1 @ pls )
=> ( ( plus_plus @ nat @ ( number_number_of @ nat @ V ) @ ( number_number_of @ nat @ V_1 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ V @ V_1 ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[187]) ).
thf(410,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)],[186]) ).
thf(411,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(copy,[status(thm)],[185]) ).
thf(412,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(copy,[status(thm)],[184]) ).
thf(413,plain,
( ( ! [K: $i,L: $i] :
( ( ( bit1 @ K )
= ( bit1 @ L ) )
<=> ( K = L ) ) )
= $true ),
inference(copy,[status(thm)],[183]) ).
thf(414,plain,
( ( ! [K: $i,L: $i] :
( ( ( bit0 @ K )
= ( bit0 @ L ) )
<=> ( K = L ) ) )
= $true ),
inference(copy,[status(thm)],[182]) ).
thf(415,plain,
( ( ! [X: $i,Y: $i] :
( ( ord_less @ int @ X @ Y )
| ( X = Y )
| ( ord_less @ int @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[181]) ).
thf(416,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(copy,[status(thm)],[180]) ).
thf(417,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)],[179]) ).
thf(418,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)],[178]) ).
thf(419,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)],[177]) ).
thf(420,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)],[176]) ).
thf(421,plain,
( ( ! [Z: $i,W: $i] :
( ( plus_plus @ int @ Z @ W )
= ( plus_plus @ int @ W @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[175]) ).
thf(422,plain,
( ( ( zero_zero @ int )
= ( number_number_of @ int @ pls ) )
= $true ),
inference(copy,[status(thm)],[174]) ).
thf(423,plain,
( ( ring_11004092258visors @ int )
= $true ),
inference(copy,[status(thm)],[173]) ).
thf(424,plain,
( ( linord581940658strict @ int )
= $true ),
inference(copy,[status(thm)],[172]) ).
thf(425,plain,
( ( linordered_ring @ int )
= $true ),
inference(copy,[status(thm)],[171]) ).
thf(426,plain,
( ( linordered_idom @ int )
= $true ),
inference(copy,[status(thm)],[170]) ).
thf(427,plain,
( ( number_semiring @ int )
= $true ),
inference(copy,[status(thm)],[169]) ).
thf(428,plain,
( ( linorder @ int )
= $true ),
inference(copy,[status(thm)],[168]) ).
thf(429,plain,
( ( semiring_1 @ int )
= $true ),
inference(copy,[status(thm)],[167]) ).
thf(430,plain,
( ( ring_char_0 @ int )
= $true ),
inference(copy,[status(thm)],[166]) ).
thf(431,plain,
( ( number_ring @ int )
= $true ),
inference(copy,[status(thm)],[165]) ).
thf(432,plain,
( ( semiring @ int )
= $true ),
inference(copy,[status(thm)],[164]) ).
thf(433,plain,
( ( number @ int )
= $true ),
inference(copy,[status(thm)],[163]) ).
thf(434,plain,
( ( number_semiring @ nat )
= $true ),
inference(copy,[status(thm)],[162]) ).
thf(435,plain,
( ( linorder @ nat )
= $true ),
inference(copy,[status(thm)],[161]) ).
thf(436,plain,
( ( semiring_1 @ nat )
= $true ),
inference(copy,[status(thm)],[160]) ).
thf(437,plain,
( ( semiring @ nat )
= $true ),
inference(copy,[status(thm)],[159]) ).
thf(438,plain,
( ( number @ nat )
= $true ),
inference(copy,[status(thm)],[158]) ).
thf(439,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)],[298]) ).
thf(440,plain,
( ( ! [SX0: $i] :
( ~ ( linordered_idom @ SX0 )
| ! [SX1: $i,SX2: $i] :
~ ( ~ ( ( ( plus_plus @ SX0 @ ( power_power @ SX0 @ SX1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SX0 @ SX2 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SX0 ) )
| ~ ( ( ( ti @ SX0 @ SX1 )
!= ( zero_zero @ SX0 ) )
| ( ( ti @ SX0 @ SX2 )
!= ( zero_zero @ SX0 ) ) ) )
| ~ ( ~ ~ ( ( ( ti @ SX0 @ SX1 )
!= ( zero_zero @ SX0 ) )
| ( ( ti @ SX0 @ SX2 )
!= ( zero_zero @ SX0 ) ) )
| ( ( plus_plus @ SX0 @ ( power_power @ SX0 @ SX1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SX0 @ SX2 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[336]) ).
thf(441,plain,
( ( ! [SX0: $i] :
( ~ ( number_semiring @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ~ ( ord_less_eq @ int @ pls @ SX2 )
| ~ ( ord_less_eq @ int @ pls @ SX1 )
| ( ( plus_plus @ SX0 @ ( number_number_of @ SX0 @ SX2 ) @ ( number_number_of @ SX0 @ SX1 ) )
= ( number_number_of @ SX0 @ ( plus_plus @ int @ SX2 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[408]) ).
thf(442,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( linordered_ring @ SX2 )
| ( ( ti @ SX2 @ ( plus_plus @ SX2 @ SX0 @ SX1 ) )
= ( plus_plus @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[311]) ).
thf(443,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ord_less_eq @ int @ ( plus_plus @ int @ SX0 @ ( one_one @ int ) ) @ SX1 )
| ( ord_less @ int @ SX0 @ SX1 ) )
| ~ ( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ ( plus_plus @ int @ SX0 @ ( one_one @ int ) ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[406]) ).
thf(444,plain,
( ( ! [SX0: $i] :
( ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SX0 )
| ( ord_less @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( one_one @ int ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[410]) ).
thf(445,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 ) )
| ~ ( ord_less @ int @ SX0 @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( 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(unfold_def,[status(thm)],[401]) ).
thf(446,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( semiring_1 @ SX2 )
| ( ( power_power @ SX2 @ SX0 @ ( ti @ nat @ SX1 ) )
= ( power_power @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[322]) ).
thf(447,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( number @ SX1 )
| ( ( ti @ SX1 @ ( number_number_of @ SX1 @ SX0 ) )
= ( number_number_of @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[316]) ).
thf(448,plain,
( ( ! [SX0: $i] :
( ~ ( linordered_ring @ SX0 )
| ( ( ti @ SX0 @ ( zero_zero @ SX0 ) )
= ( zero_zero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[312]) ).
thf(449,plain,
( ( ! [SX0: $i] :
( ~ ( linordered_idom @ SX0 )
| ! [SX1: $i] :
~ ( ord_less @ SX0 @ ( power_power @ SX0 @ SX1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( zero_zero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[337]) ).
thf(450,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( number_ring @ SX0 )
| ~ ( ring_char_0 @ SX0 ) )
| ! [SX1: $i,SX2: $i] :
~ ( ~ ( ( ( number_number_of @ SX0 @ SX1 )
!= ( number_number_of @ SX0 @ SX2 ) )
| ( SX1 = SX2 ) )
| ~ ( ( SX1 != SX2 )
| ( ( number_number_of @ SX0 @ SX1 )
= ( number_number_of @ SX0 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[411]) ).
thf(451,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( ord_less @ int @ pls @ ( bit1 @ SX0 ) )
| ( ord_less_eq @ int @ pls @ SX0 ) )
| ~ ( ~ ( ord_less_eq @ int @ pls @ SX0 )
| ( ord_less @ int @ pls @ ( bit1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[396]) ).
thf(452,plain,
( ( ! [SX0: $i] :
( ~ ( ring_11004092258visors @ SX0 )
| ! [SX1: $i] :
~ ( ~ ( ( ( power_power @ SX0 @ SX1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= ( zero_zero @ SX0 ) )
| ( ( ti @ SX0 @ SX1 )
= ( zero_zero @ SX0 ) ) )
| ~ ( ( ( ti @ SX0 @ SX1 )
!= ( zero_zero @ SX0 ) )
| ( ( power_power @ SX0 @ SX1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[341]) ).
thf(453,plain,
( ( ! [SX0: $i] :
( ~ ( number_ring @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ( times_times @ SX0 @ ( number_number_of @ SX0 @ SX1 ) @ ( number_number_of @ SX0 @ SX2 ) )
= ( number_number_of @ SX0 @ ( times_times @ int @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[369]) ).
thf(454,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( ord_less_eq @ int @ pls @ ( bit1 @ SX0 ) )
| ( ord_less_eq @ int @ pls @ SX0 ) )
| ~ ( ~ ( ord_less_eq @ int @ pls @ SX0 )
| ( ord_less_eq @ int @ pls @ ( bit1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[376]) ).
thf(455,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq @ int @ SX0 @ SX1 ) )
| ~ ( ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[358]) ).
thf(456,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less @ int @ SX0 @ SX1 ) )
| ~ ( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[397]) ).
thf(457,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ord_less @ int @ SX1 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SX1 ) @ ( number_number_of @ nat @ SX0 ) )
= ( number_number_of @ nat @ SX0 ) ) )
| ~ ( ~ ~ ( ord_less @ int @ SX1 @ pls )
| ~ ( ~ ( ~ ( ord_less @ int @ SX0 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SX1 ) @ ( number_number_of @ nat @ SX0 ) )
= ( number_number_of @ nat @ SX1 ) ) )
| ~ ( ~ ~ ( ord_less @ int @ SX0 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SX1 ) @ ( number_number_of @ nat @ SX0 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SX1 @ SX0 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[409]) ).
thf(458,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 ) )
| ~ ( ~ ( 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)],[352]) ).
thf(459,plain,
( ( ! [SX0: $i] :
( ~ ( number_semiring @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ~ ( ord_less_eq @ int @ pls @ SX2 )
| ~ ( ord_less_eq @ int @ pls @ SX1 )
| ( ( times_times @ SX0 @ ( number_number_of @ SX0 @ SX2 ) @ ( number_number_of @ SX0 @ SX1 ) )
= ( number_number_of @ SX0 @ ( times_times @ int @ SX2 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[367]) ).
thf(460,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_eq @ int @ SX0 @ SX1 ) )
| ~ ( ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[361]) ).
thf(461,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( linordered_ring @ SX2 )
| ( ( plus_plus @ SX2 @ ( ti @ SX2 @ SX0 ) @ SX1 )
= ( plus_plus @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[309]) ).
thf(462,plain,
( ( ! [SX0: $i] :
( ~ ( linordered_idom @ SX0 )
| ! [SX1: $i] :
~ ( ~ ( ~ ( ord_less @ SX0 @ ( zero_zero @ SX0 ) @ ( power_power @ SX0 @ SX1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ( ( ti @ SX0 @ SX1 )
!= ( zero_zero @ SX0 ) ) )
| ~ ( ~ ( ( ( ti @ SX0 @ SX1 )
!= ( zero_zero @ SX0 ) ) )
| ( ord_less @ SX0 @ ( zero_zero @ SX0 ) @ ( power_power @ SX0 @ SX1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[338]) ).
thf(463,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit0 @ SX0 ) @ pls )
| ( ord_less_eq @ int @ SX0 @ pls ) )
| ~ ( ~ ( ord_less_eq @ int @ SX0 @ pls )
| ( ord_less_eq @ int @ ( bit0 @ SX0 ) @ pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[379]) ).
thf(464,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( ( bit1 @ SX0 )
!= ( bit1 @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ( ( SX0 != SX1 )
| ( ( bit1 @ SX0 )
= ( bit1 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[413]) ).
thf(465,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( number @ SX0 )
| ~ ( semiring @ SX0 ) )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ( times_times @ SX0 @ ( number_number_of @ SX0 @ SX1 ) @ ( plus_plus @ SX0 @ SX2 @ SX3 ) )
= ( plus_plus @ SX0 @ ( times_times @ SX0 @ ( number_number_of @ SX0 @ SX1 ) @ SX2 ) @ ( times_times @ SX0 @ ( number_number_of @ SX0 @ SX1 ) @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[418]) ).
thf(466,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( linordered_idom @ SX2 )
| ~ ( ~ ( ~ ( ord_less @ SX2 @ ( ti @ SX2 @ SX0 ) @ SX1 )
| ( ord_less @ SX2 @ SX0 @ SX1 ) )
| ~ ( ~ ( ord_less @ SX2 @ SX0 @ SX1 )
| ( ord_less @ SX2 @ ( ti @ SX2 @ SX0 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[319]) ).
thf(467,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ ( plus_plus @ int @ SX0 @ ( one_one @ int ) ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[405]) ).
thf(468,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( linordered_idom @ SX2 )
| ~ ( ~ ( ~ ( ord_less @ SX2 @ SX0 @ ( ti @ SX2 @ SX1 ) )
| ( ord_less @ SX2 @ SX0 @ SX1 ) )
| ~ ( ~ ( ord_less @ SX2 @ SX0 @ SX1 )
| ( ord_less @ SX2 @ SX0 @ ( ti @ SX2 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[320]) ).
thf(469,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( number @ SX2 )
| ~ ( semiring @ SX2 ) )
| ( ( plus_plus @ SX2 @ SX0 @ ( ti @ SX2 @ SX1 ) )
= ( plus_plus @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[307]) ).
thf(470,plain,
( ( ! [SX0: $i] :
( ~ ( number @ SX0 )
| ! [SX1: $i,SX2: $i] :
~ ( ~ ( ( ( number_number_of @ SX0 @ SX1 )
!= ( ti @ SX0 @ SX2 ) )
| ( ( ti @ SX0 @ SX2 )
= ( number_number_of @ SX0 @ SX1 ) ) )
| ~ ( ( ( ti @ SX0 @ SX2 )
!= ( number_number_of @ SX0 @ SX1 ) )
| ( ( number_number_of @ SX0 @ SX1 )
= ( ti @ SX0 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[412]) ).
thf(471,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( ord_less_eq @ int @ ( one_one @ int ) @ SX0 )
| ( ord_less @ int @ ( zero_zero @ int ) @ SX0 ) )
| ~ ( ~ ( ord_less @ int @ ( zero_zero @ int ) @ SX0 )
| ( ord_less_eq @ int @ ( one_one @ int ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[402]) ).
thf(472,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( number @ SX2 )
| ~ ( semiring @ SX2 ) )
| ( ( plus_plus @ SX2 @ ( ti @ SX2 @ SX0 ) @ SX1 )
= ( plus_plus @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[306]) ).
thf(473,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( semiring_1 @ SX2 )
| ( ( ti @ SX2 @ ( power_power @ SX2 @ SX0 @ SX1 ) )
= ( power_power @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[323]) ).
thf(474,plain,
( ( ! [SX0: $i] :
( ~ ( number_ring @ SX0 )
| ! [SX1: $i] :
( ( plus_plus @ SX0 @ ( number_number_of @ SX0 @ SX1 ) @ ( one_one @ SX0 ) )
= ( number_number_of @ SX0 @ ( plus_plus @ int @ SX1 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[343]) ).
thf(475,plain,
( ( ! [SX0: $i] :
( ~ ( number_ring @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ( number_number_of @ SX0 @ ( times_times @ int @ SX1 @ SX2 ) )
= ( times_times @ SX0 @ ( number_number_of @ SX0 @ SX1 ) @ ( number_number_of @ SX0 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[370]) ).
thf(476,plain,
( ( ! [SX0: $i] :
( ~ ( linordered_idom @ SX0 )
| ! [SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( ord_less @ SX0 @ ( zero_zero @ SX0 ) @ ( plus_plus @ SX0 @ ( power_power @ SX0 @ SX1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SX0 @ SX2 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
| ( ( ti @ SX0 @ SX1 )
!= ( zero_zero @ SX0 ) )
| ( ( ti @ SX0 @ SX2 )
!= ( zero_zero @ SX0 ) ) )
| ~ ( ~ ( ( ( ti @ SX0 @ SX1 )
!= ( zero_zero @ SX0 ) )
| ( ( ti @ SX0 @ SX2 )
!= ( zero_zero @ SX0 ) ) )
| ( ord_less @ SX0 @ ( zero_zero @ SX0 ) @ ( plus_plus @ SX0 @ ( power_power @ SX0 @ SX1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SX0 @ SX2 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[335]) ).
thf(477,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( ( bit0 @ SX0 )
!= ( bit0 @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ( ( SX0 != SX1 )
| ( ( bit0 @ SX0 )
= ( bit0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[414]) ).
thf(478,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq @ int @ SX0 @ SX1 ) )
| ~ ( ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ( ord_less @ int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[400]) ).
thf(479,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq @ int @ SX0 @ SX1 ) )
| ~ ( ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[378]) ).
thf(480,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( number @ SX2 )
| ~ ( linorder @ SX2 ) )
| ~ ( ~ ( ~ ( ord_less @ SX2 @ SX0 @ ( ti @ SX2 @ SX1 ) )
| ( ord_less @ SX2 @ SX0 @ SX1 ) )
| ~ ( ~ ( ord_less @ SX2 @ SX0 @ SX1 )
| ( ord_less @ SX2 @ SX0 @ ( ti @ SX2 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[318]) ).
thf(481,plain,
( ( ! [SX0: $i] :
( ~ ( semiring_1 @ SX0 )
| ( ( power_power @ SX0 @ ( zero_zero @ SX0 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[340]) ).
thf(482,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ord_less @ int @ SX0 @ SX1 )
| ~ ( ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ~ ( ( SX0 != SX1 ) ) ) )
| ~ ( ~ ~ ( ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ~ ( ( SX0 != SX1 ) ) )
| ( ord_less @ int @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[363]) ).
thf(483,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( twoSqu33214720sum2sq @ ( ti @ int @ SX0 ) )
| ( twoSqu33214720sum2sq @ SX0 ) )
| ~ ( ~ ( twoSqu33214720sum2sq @ SX0 )
| ( twoSqu33214720sum2sq @ ( ti @ int @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[324]) ).
thf(484,plain,
( ( ! [SX0: $i] :
( ~ ( number_ring @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ( times_times @ SX0 @ ( number_number_of @ SX0 @ SX1 ) @ ( times_times @ SX0 @ ( number_number_of @ SX0 @ SX2 ) @ SX3 ) )
= ( times_times @ SX0 @ ( number_number_of @ SX0 @ ( times_times @ int @ SX1 @ SX2 ) ) @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[368]) ).
thf(485,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( number_ring @ SX0 )
| ~ ( linordered_idom @ SX0 ) )
| ! [SX1: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SX0 @ ( zero_zero @ SX0 ) @ ( number_number_of @ SX0 @ SX1 ) )
| ( ord_less_eq @ int @ pls @ SX1 ) )
| ~ ( ~ ( ord_less_eq @ int @ pls @ SX1 )
| ( ord_less_eq @ SX0 @ ( zero_zero @ SX0 ) @ ( number_number_of @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[373]) ).
thf(486,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( ord_less_eq @ int @ pls @ ( bit0 @ SX0 ) )
| ( ord_less_eq @ int @ pls @ SX0 ) )
| ~ ( ~ ( ord_less_eq @ int @ pls @ SX0 )
| ( ord_less_eq @ int @ pls @ ( bit0 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[380]) ).
thf(487,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( number_ring @ SX0 )
| ~ ( linordered_idom @ SX0 ) )
| ! [SX1: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SX0 @ ( number_number_of @ SX0 @ SX1 ) @ ( zero_zero @ SX0 ) )
| ( ord_less_eq @ int @ SX1 @ pls ) )
| ~ ( ~ ( ord_less_eq @ int @ SX1 @ pls )
| ( ord_less_eq @ SX0 @ ( number_number_of @ SX0 @ SX1 ) @ ( zero_zero @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[372]) ).
thf(488,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less_eq @ int @ SX0 @ SX1 ) )
| ~ ( ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[362]) ).
thf(489,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ ( number_number_of @ nat @ SX0 ) )
| ( ord_less @ int @ pls @ SX0 ) )
| ~ ( ~ ( ord_less @ int @ pls @ SX0 )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ ( number_number_of @ nat @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[374]) ).
thf(490,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( number_ring @ SX0 )
| ~ ( linordered_idom @ SX0 ) )
| ! [SX1: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SX0 @ ( number_number_of @ SX0 @ SX1 ) @ ( one_one @ SX0 ) )
| ( ord_less_eq @ int @ SX1 @ ( bit1 @ pls ) ) )
| ~ ( ~ ( 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)],[384]) ).
thf(491,plain,
( ( ! [SX0: $i] :
( ~ ( number_ring @ SX0 )
| ! [SX1: $i] :
( ( plus_plus @ SX0 @ ( one_one @ SX0 ) @ ( number_number_of @ SX0 @ SX1 ) )
= ( number_number_of @ SX0 @ ( plus_plus @ int @ ( bit1 @ pls ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[342]) ).
thf(492,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( number @ SX2 )
| ~ ( semiring @ SX2 ) )
| ( ( ti @ SX2 @ ( plus_plus @ SX2 @ SX0 @ SX1 ) )
= ( plus_plus @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[308]) ).
thf(493,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( zprime @ ( ti @ int @ SX0 ) )
| ( zprime @ SX0 ) )
| ~ ( ~ ( zprime @ SX0 )
| ( zprime @ ( ti @ int @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[314]) ).
thf(494,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( semiring_1 @ SX2 )
| ( ( power_power @ SX2 @ ( ti @ SX2 @ SX0 ) @ SX1 )
= ( power_power @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[321]) ).
thf(495,plain,
( ( ~ ! [SX0: $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 ) ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[345]) ).
thf(496,plain,
( ( ! [SX0: $i] :
( ~ ( semiring_1 @ SX0 )
| ( ( power_power @ SX0 @ ( one_one @ SX0 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( one_one @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[339]) ).
thf(497,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)],[331]) ).
thf(498,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( number @ SX0 )
| ~ ( linorder @ 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 ) ) )
| ~ ( ~ ~ ( 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)],[375]) ).
thf(499,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ord_less @ int @ SX0 @ ( plus_plus @ int @ SX1 @ ( one_one @ int ) ) )
| ( ord_less_eq @ int @ SX0 @ SX1 ) )
| ~ ( ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ( ord_less @ int @ SX0 @ ( plus_plus @ int @ SX1 @ ( one_one @ int ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[407]) ).
thf(500,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq @ int @ SX0 @ SX1 ) )
| ~ ( ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ( ord_less @ int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[399]) ).
thf(501,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ~ ( ord_less_eq @ int @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[356]) ).
thf(502,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ( ( zero_zero @ nat )
!= ( number_number_of @ nat @ SX0 ) )
| ( ord_less_eq @ int @ SX0 @ pls ) )
| ~ ( ~ ( ord_less_eq @ int @ SX0 @ pls )
| ( ( zero_zero @ nat )
= ( number_number_of @ nat @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[366]) ).
thf(503,plain,
( ( ! [SX0: $i] :
( ~ ( linordered_ring @ SX0 )
| ! [SX1: $i,SX2: $i] : ( ord_less_eq @ SX0 @ ( zero_zero @ SX0 ) @ ( plus_plus @ SX0 @ ( times_times @ SX0 @ SX1 @ SX1 ) @ ( times_times @ SX0 @ SX2 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[371]) ).
thf(504,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( linordered_ring @ SX2 )
| ( ( plus_plus @ SX2 @ SX0 @ ( ti @ SX2 @ SX1 ) )
= ( plus_plus @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[310]) ).
thf(505,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( number @ SX1 )
| ( ( number_number_of @ SX1 @ ( ti @ int @ SX0 ) )
= ( number_number_of @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[315]) ).
thf(506,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less @ int @ SX0 @ SX1 ) )
| ~ ( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[398]) ).
thf(507,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( number @ SX0 )
| ~ ( semiring @ SX0 ) )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ( times_times @ SX0 @ ( plus_plus @ SX0 @ SX1 @ SX2 ) @ ( number_number_of @ SX0 @ SX3 ) )
= ( plus_plus @ SX0 @ ( times_times @ SX0 @ SX1 @ ( number_number_of @ SX0 @ SX3 ) ) @ ( times_times @ SX0 @ SX2 @ ( number_number_of @ SX0 @ SX3 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[417]) ).
thf(508,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ( ( number_number_of @ nat @ SX0 )
!= ( zero_zero @ nat ) )
| ( ord_less_eq @ int @ SX0 @ pls ) )
| ~ ( ~ ( ord_less_eq @ int @ SX0 @ pls )
| ( ( number_number_of @ nat @ SX0 )
= ( zero_zero @ nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[365]) ).
thf(509,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( ord_less_eq @ int @ SX1 @ SX2 )
| ~ ( ord_less_eq @ int @ SX2 @ SX0 )
| ( ord_less_eq @ int @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[355]) ).
thf(510,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( number @ SX2 )
| ~ ( linorder @ SX2 ) )
| ~ ( ~ ( ~ ( ord_less @ SX2 @ ( ti @ SX2 @ SX0 ) @ SX1 )
| ( ord_less @ SX2 @ SX0 @ SX1 ) )
| ~ ( ~ ( ord_less @ SX2 @ SX0 @ SX1 )
| ( ord_less @ SX2 @ ( ti @ SX2 @ SX0 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[317]) ).
thf(511,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq @ int @ SX0 @ SX1 ) )
| ~ ( ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[359]) ).
thf(512,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( ord_less_eq @ int @ SX1 @ SX2 )
| ( ord_less_eq @ int @ ( plus_plus @ int @ SX0 @ SX1 ) @ ( plus_plus @ int @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[364]) ).
thf(513,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SX0 ) @ pls )
| ( ord_less @ int @ SX0 @ pls ) )
| ~ ( ~ ( ord_less @ int @ SX0 @ pls )
| ( ord_less_eq @ int @ ( bit1 @ SX0 ) @ pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[395]) ).
thf(514,plain,
( ( ! [SX0: $i] :
( ~ ( linordered_idom @ SX0 )
| ! [SX1: $i,SX2: $i] :
~ ( ord_less @ SX0 @ ( plus_plus @ SX0 @ ( power_power @ SX0 @ SX1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SX0 @ SX2 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( zero_zero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[334]) ).
thf(515,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ord_less @ int @ ( number_number_of @ int @ SX0 ) @ ( number_number_of @ int @ SX1 ) )
| ( ord_less @ int @ SX0 @ SX1 ) )
| ~ ( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ int @ ( number_number_of @ int @ SX0 ) @ ( number_number_of @ int @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[389]) ).
thf(516,plain,
( ( ! [SX0: $i] :
( ~ ( linord581940658strict @ 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 ) )
| ( ( ti @ SX0 @ SX2 )
!= ( zero_zero @ SX0 ) ) ) )
| ~ ( ~ ~ ( ( ( 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 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[416]) ).
thf(517,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( ord_less @ int @ SX2 @ SX3 )
| ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ( ord_less @ int @ ( plus_plus @ int @ SX2 @ SX0 ) @ ( plus_plus @ int @ SX3 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[381]) ).
thf(518,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( number_ring @ SX0 )
| ~ ( linordered_idom @ 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 ) )
| ~ ( ~ ( 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)],[353]) ).
thf(519,plain,
( ( ! [SX0: $i] :
( ~ ( semiring_1 @ SX0 )
| ( ( ti @ SX0 @ ( zero_zero @ SX0 ) )
= ( zero_zero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[313]) ).
thf(520,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less_eq @ int @ SX0 @ SX1 ) )
| ~ ( ~ ( ord_less_eq @ int @ SX0 @ SX1 )
| ( ord_less_eq @ int @ ( bit0 @ SX0 ) @ ( bit1 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[377]) ).
thf(521,plain,
( ( ! [SX0: $i] :
( ~ ( semiring_1 @ SX0 )
| ( ( ti @ SX0 @ ( one_one @ SX0 ) )
= ( one_one @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[305]) ).
thf(522,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( number_ring @ SX0 )
| ~ ( linordered_idom @ SX0 ) )
| ! [SX1: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SX0 @ ( one_one @ SX0 ) @ ( number_number_of @ SX0 @ SX1 ) )
| ( ord_less_eq @ int @ ( bit1 @ pls ) @ SX1 ) )
| ~ ( ~ ( 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)],[385]) ).
thf(523,plain,
! [SV1: $i] :
( ( ( bit0 @ ( ti @ int @ SV1 ) )
= ( bit0 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[299]) ).
thf(524,plain,
! [SV2: $i] :
( ( ( ti @ int @ ( bit0 @ SV2 ) )
= ( bit0 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[300]) ).
thf(525,plain,
! [SV3: $i] :
( ( ( bit1 @ ( ti @ int @ SV3 ) )
= ( bit1 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[301]) ).
thf(526,plain,
! [SV4: $i] :
( ( ( ti @ int @ ( bit1 @ SV4 ) )
= ( bit1 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[302]) ).
thf(527,plain,
( ( ord_less_eq @ int @ ( one_one @ int ) @ t )
= $false ),
inference(extcnf_not_pos,[status(thm)],[332]) ).
thf(528,plain,
! [SV5: $i] :
( ( ord_less_eq @ int @ SV5 @ SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[347]) ).
thf(529,plain,
! [SV6: $i] :
( ( ( number_number_of @ int @ SV6 )
= SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[348]) ).
thf(530,plain,
! [SV7: $i] :
( ( ! [SY223: $i] :
( ( times_times @ int @ SV7 @ SY223 )
= ( times_times @ int @ SY223 @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[349]) ).
thf(531,plain,
! [SV8: $i] :
( ( ! [SY224: $i] :
( ( ord_less_eq @ int @ SV8 @ SY224 )
| ( ord_less_eq @ int @ SY224 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[350]) ).
thf(532,plain,
! [SV9: $i] :
( ( ! [SY225: $i] :
( ( times_times @ int @ ( number_number_of @ int @ SV9 ) @ ( number_number_of @ int @ SY225 ) )
= ( number_number_of @ int @ ( times_times @ int @ SV9 @ SY225 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[351]) ).
thf(533,plain,
! [SV10: $i] :
( ( ! [SY226: $i,SY227: $i] :
( ( times_times @ int @ ( times_times @ int @ SV10 @ SY226 ) @ SY227 )
= ( times_times @ int @ SV10 @ ( times_times @ int @ SY226 @ SY227 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[354]) ).
thf(534,plain,
! [SV11: $i] :
( ( ! [SY228: $i,SY229: $i] :
( ( power_power @ int @ SV11 @ ( plus_plus @ nat @ SY228 @ SY229 ) )
= ( times_times @ int @ ( power_power @ int @ SV11 @ SY228 ) @ ( power_power @ int @ SV11 @ SY229 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[357]) ).
thf(535,plain,
! [SV12: $i] :
( ( ( times_times @ int @ pls @ SV12 )
= pls )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[387]) ).
thf(536,plain,
! [SV13: $i] :
( ( ! [SY230: $i] :
( ( times_times @ int @ ( bit0 @ SV13 ) @ SY230 )
= ( bit0 @ ( times_times @ int @ SV13 @ SY230 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[388]) ).
thf(537,plain,
! [SV14: $i] :
( ( ( times_times @ int @ SV14 @ ( one_one @ int ) )
= SV14 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[390]) ).
thf(538,plain,
! [SV15: $i] :
( ( ( times_times @ int @ ( one_one @ int ) @ SV15 )
= SV15 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[391]) ).
thf(539,plain,
! [SV16: $i] :
( ( ! [SY231: $i] :
( ( plus_plus @ int @ ( number_number_of @ int @ SV16 ) @ ( number_number_of @ int @ SY231 ) )
= ( number_number_of @ int @ ( plus_plus @ int @ SV16 @ SY231 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[392]) ).
thf(540,plain,
! [SV17: $i] :
( ( ! [SY232: $i,SY233: $i] :
( ( times_times @ int @ ( plus_plus @ int @ SV17 @ SY232 ) @ SY233 )
= ( plus_plus @ int @ ( times_times @ int @ SV17 @ SY233 ) @ ( times_times @ int @ SY232 @ SY233 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[393]) ).
thf(541,plain,
! [SV18: $i] :
( ( ! [SY234: $i,SY235: $i] :
( ( times_times @ int @ SV18 @ ( plus_plus @ int @ SY234 @ SY235 ) )
= ( plus_plus @ int @ ( times_times @ int @ SV18 @ SY234 ) @ ( times_times @ int @ SV18 @ SY235 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[394]) ).
thf(542,plain,
! [SV19: $i] :
( ( ! [SY236: $i] :
( ( ord_less @ int @ SV19 @ SY236 )
| ( SV19 = SY236 )
| ( ord_less @ int @ SY236 @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[415]) ).
thf(543,plain,
! [SV20: $i] :
( ( ! [SY237: $i,SY238: $i] :
( ( plus_plus @ int @ ( plus_plus @ int @ SV20 @ SY237 ) @ SY238 )
= ( plus_plus @ int @ SV20 @ ( plus_plus @ int @ SY237 @ SY238 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[419]) ).
thf(544,plain,
! [SV21: $i] :
( ( ! [SY239: $i,SY240: $i] :
( ( plus_plus @ int @ SV21 @ ( plus_plus @ int @ SY239 @ SY240 ) )
= ( plus_plus @ int @ SY239 @ ( plus_plus @ int @ SV21 @ SY240 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[420]) ).
thf(545,plain,
! [SV22: $i] :
( ( ! [SY241: $i] :
( ( plus_plus @ int @ SV22 @ SY241 )
= ( plus_plus @ int @ SY241 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[421]) ).
thf(546,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)],[439]) ).
thf(547,plain,
! [SV23: $i] :
( ( ~ ( linordered_idom @ SV23 )
| ! [SY242: $i,SY243: $i] :
~ ( ~ ( ( ( plus_plus @ SV23 @ ( power_power @ SV23 @ SY242 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV23 @ SY243 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV23 ) )
| ~ ( ( ( ti @ SV23 @ SY242 )
!= ( zero_zero @ SV23 ) )
| ( ( ti @ SV23 @ SY243 )
!= ( zero_zero @ SV23 ) ) ) )
| ~ ( ~ ~ ( ( ( ti @ SV23 @ SY242 )
!= ( zero_zero @ SV23 ) )
| ( ( ti @ SV23 @ SY243 )
!= ( zero_zero @ SV23 ) ) )
| ( ( plus_plus @ SV23 @ ( power_power @ SV23 @ SY242 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV23 @ SY243 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV23 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[440]) ).
thf(548,plain,
! [SV24: $i] :
( ( ~ ( number_semiring @ SV24 )
| ! [SY244: $i,SY245: $i] :
( ~ ( ord_less_eq @ int @ pls @ SY245 )
| ~ ( ord_less_eq @ int @ pls @ SY244 )
| ( ( plus_plus @ SV24 @ ( number_number_of @ SV24 @ SY245 ) @ ( number_number_of @ SV24 @ SY244 ) )
= ( number_number_of @ SV24 @ ( plus_plus @ int @ SY245 @ SY244 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[441]) ).
thf(549,plain,
! [SV25: $i] :
( ( ! [SY246: $i,SY247: $i] :
( ~ ( linordered_ring @ SY247 )
| ( ( ti @ SY247 @ ( plus_plus @ SY247 @ SV25 @ SY246 ) )
= ( plus_plus @ SY247 @ SV25 @ SY246 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[442]) ).
thf(550,plain,
! [SV26: $i] :
( ( ! [SY248: $i] :
~ ( ~ ( ~ ( ord_less_eq @ int @ ( plus_plus @ int @ SV26 @ ( one_one @ int ) ) @ SY248 )
| ( ord_less @ int @ SV26 @ SY248 ) )
| ~ ( ~ ( ord_less @ int @ SV26 @ SY248 )
| ( ord_less_eq @ int @ ( plus_plus @ int @ SV26 @ ( one_one @ int ) ) @ SY248 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[443]) ).
thf(551,plain,
! [SV27: $i] :
( ( ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV27 )
| ( ord_less @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( one_one @ int ) @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[444]) ).
thf(552,plain,
! [SV28: $i] :
( ( ! [SY249: $i] :
~ ( ~ ( ~ ( ord_less @ nat @ ( number_number_of @ nat @ SV28 ) @ ( number_number_of @ nat @ SY249 ) )
| ~ ( ~ ( ~ ( ord_less @ int @ SV28 @ SY249 )
| ( ord_less @ int @ pls @ SY249 ) )
| ~ ( ord_less @ int @ SV28 @ SY249 ) ) )
| ~ ( ~ ~ ( ~ ( ~ ( ord_less @ int @ SV28 @ SY249 )
| ( ord_less @ int @ pls @ SY249 ) )
| ~ ( ord_less @ int @ SV28 @ SY249 ) )
| ( ord_less @ nat @ ( number_number_of @ nat @ SV28 ) @ ( number_number_of @ nat @ SY249 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[445]) ).
thf(553,plain,
! [SV29: $i] :
( ( ! [SY250: $i,SY251: $i] :
( ~ ( semiring_1 @ SY251 )
| ( ( power_power @ SY251 @ SV29 @ ( ti @ nat @ SY250 ) )
= ( power_power @ SY251 @ SV29 @ SY250 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[446]) ).
thf(554,plain,
! [SV30: $i] :
( ( ! [SY252: $i] :
( ~ ( number @ SY252 )
| ( ( ti @ SY252 @ ( number_number_of @ SY252 @ SV30 ) )
= ( number_number_of @ SY252 @ SV30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[447]) ).
thf(555,plain,
! [SV31: $i] :
( ( ~ ( linordered_ring @ SV31 )
| ( ( ti @ SV31 @ ( zero_zero @ SV31 ) )
= ( zero_zero @ SV31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[448]) ).
thf(556,plain,
! [SV32: $i] :
( ( ~ ( linordered_idom @ SV32 )
| ! [SY253: $i] :
~ ( ord_less @ SV32 @ ( power_power @ SV32 @ SY253 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( zero_zero @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[449]) ).
thf(557,plain,
! [SV33: $i] :
( ( ~ ~ ( ~ ( number_ring @ SV33 )
| ~ ( ring_char_0 @ SV33 ) )
| ! [SY254: $i,SY255: $i] :
~ ( ~ ( ( ( number_number_of @ SV33 @ SY254 )
!= ( number_number_of @ SV33 @ SY255 ) )
| ( SY254 = SY255 ) )
| ~ ( ( SY254 != SY255 )
| ( ( number_number_of @ SV33 @ SY254 )
= ( number_number_of @ SV33 @ SY255 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[450]) ).
thf(558,plain,
! [SV34: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ int @ pls @ ( bit1 @ SV34 ) )
| ( ord_less_eq @ int @ pls @ SV34 ) )
| ~ ( ~ ( ord_less_eq @ int @ pls @ SV34 )
| ( ord_less @ int @ pls @ ( bit1 @ SV34 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[451]) ).
thf(559,plain,
! [SV35: $i] :
( ( ~ ( ring_11004092258visors @ SV35 )
| ! [SY256: $i] :
~ ( ~ ( ( ( power_power @ SV35 @ SY256 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= ( zero_zero @ SV35 ) )
| ( ( ti @ SV35 @ SY256 )
= ( zero_zero @ SV35 ) ) )
| ~ ( ( ( ti @ SV35 @ SY256 )
!= ( zero_zero @ SV35 ) )
| ( ( power_power @ SV35 @ SY256 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SV35 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[452]) ).
thf(560,plain,
! [SV36: $i] :
( ( ~ ( number_ring @ SV36 )
| ! [SY257: $i,SY258: $i] :
( ( times_times @ SV36 @ ( number_number_of @ SV36 @ SY257 ) @ ( number_number_of @ SV36 @ SY258 ) )
= ( number_number_of @ SV36 @ ( times_times @ int @ SY257 @ SY258 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[453]) ).
thf(561,plain,
! [SV37: $i] :
( ( ~ ( ~ ( ~ ( ord_less_eq @ int @ pls @ ( bit1 @ SV37 ) )
| ( ord_less_eq @ int @ pls @ SV37 ) )
| ~ ( ~ ( ord_less_eq @ int @ pls @ SV37 )
| ( ord_less_eq @ int @ pls @ ( bit1 @ SV37 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[454]) ).
thf(562,plain,
! [SV38: $i] :
( ( ! [SY259: $i] :
~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SV38 ) @ ( bit1 @ SY259 ) )
| ( ord_less_eq @ int @ SV38 @ SY259 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV38 @ SY259 )
| ( ord_less_eq @ int @ ( bit1 @ SV38 ) @ ( bit1 @ SY259 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[455]) ).
thf(563,plain,
! [SV39: $i] :
( ( ! [SY260: $i] :
~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SV39 ) @ ( bit0 @ SY260 ) )
| ( ord_less @ int @ SV39 @ SY260 ) )
| ~ ( ~ ( ord_less @ int @ SV39 @ SY260 )
| ( ord_less_eq @ int @ ( bit1 @ SV39 ) @ ( bit0 @ SY260 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[456]) ).
thf(564,plain,
! [SV40: $i] :
( ( ! [SY261: $i] :
~ ( ~ ( ~ ( ord_less @ int @ SY261 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SY261 ) @ ( number_number_of @ nat @ SV40 ) )
= ( number_number_of @ nat @ SV40 ) ) )
| ~ ( ~ ~ ( ord_less @ int @ SY261 @ pls )
| ~ ( ~ ( ~ ( ord_less @ int @ SV40 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SY261 ) @ ( number_number_of @ nat @ SV40 ) )
= ( number_number_of @ nat @ SY261 ) ) )
| ~ ( ~ ~ ( ord_less @ int @ SV40 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SY261 ) @ ( number_number_of @ nat @ SV40 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SY261 @ SV40 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[457]) ).
thf(565,plain,
! [SV41: $i] :
( ( ! [SY262: $i] :
~ ( ~ ( ~ ( ord_less_eq @ int @ ( number_number_of @ int @ SV41 ) @ ( number_number_of @ int @ SY262 ) )
| ( ord_less_eq @ int @ SV41 @ SY262 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV41 @ SY262 )
| ( ord_less_eq @ int @ ( number_number_of @ int @ SV41 ) @ ( number_number_of @ int @ SY262 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[458]) ).
thf(566,plain,
! [SV42: $i] :
( ( ~ ( number_semiring @ SV42 )
| ! [SY263: $i,SY264: $i] :
( ~ ( ord_less_eq @ int @ pls @ SY264 )
| ~ ( ord_less_eq @ int @ pls @ SY263 )
| ( ( times_times @ SV42 @ ( number_number_of @ SV42 @ SY264 ) @ ( number_number_of @ SV42 @ SY263 ) )
= ( number_number_of @ SV42 @ ( times_times @ int @ SY264 @ SY263 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[459]) ).
thf(567,plain,
! [SV43: $i] :
( ( ! [SY265: $i] :
~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit0 @ SV43 ) @ ( bit0 @ SY265 ) )
| ( ord_less_eq @ int @ SV43 @ SY265 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV43 @ SY265 )
| ( ord_less_eq @ int @ ( bit0 @ SV43 ) @ ( bit0 @ SY265 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[460]) ).
thf(568,plain,
! [SV44: $i] :
( ( ! [SY266: $i,SY267: $i] :
( ~ ( linordered_ring @ SY267 )
| ( ( plus_plus @ SY267 @ ( ti @ SY267 @ SV44 ) @ SY266 )
= ( plus_plus @ SY267 @ SV44 @ SY266 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[461]) ).
thf(569,plain,
! [SV45: $i] :
( ( ~ ( linordered_idom @ SV45 )
| ! [SY268: $i] :
~ ( ~ ( ~ ( ord_less @ SV45 @ ( zero_zero @ SV45 ) @ ( power_power @ SV45 @ SY268 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ( ( ti @ SV45 @ SY268 )
!= ( zero_zero @ SV45 ) ) )
| ~ ( ~ ( ( ( ti @ SV45 @ SY268 )
!= ( zero_zero @ SV45 ) ) )
| ( ord_less @ SV45 @ ( zero_zero @ SV45 ) @ ( power_power @ SV45 @ SY268 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[462]) ).
thf(570,plain,
! [SV46: $i] :
( ( ~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit0 @ SV46 ) @ pls )
| ( ord_less_eq @ int @ SV46 @ pls ) )
| ~ ( ~ ( ord_less_eq @ int @ SV46 @ pls )
| ( ord_less_eq @ int @ ( bit0 @ SV46 ) @ pls ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[463]) ).
thf(571,plain,
! [SV47: $i] :
( ( ! [SY269: $i] :
~ ( ~ ( ( ( bit1 @ SV47 )
!= ( bit1 @ SY269 ) )
| ( SV47 = SY269 ) )
| ~ ( ( SV47 != SY269 )
| ( ( bit1 @ SV47 )
= ( bit1 @ SY269 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[464]) ).
thf(572,plain,
! [SV48: $i] :
( ( ~ ~ ( ~ ( number @ SV48 )
| ~ ( semiring @ SV48 ) )
| ! [SY270: $i,SY271: $i,SY272: $i] :
( ( times_times @ SV48 @ ( number_number_of @ SV48 @ SY270 ) @ ( plus_plus @ SV48 @ SY271 @ SY272 ) )
= ( plus_plus @ SV48 @ ( times_times @ SV48 @ ( number_number_of @ SV48 @ SY270 ) @ SY271 ) @ ( times_times @ SV48 @ ( number_number_of @ SV48 @ SY270 ) @ SY272 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[465]) ).
thf(573,plain,
! [SV49: $i] :
( ( ! [SY273: $i,SY274: $i] :
( ~ ( linordered_idom @ SY274 )
| ~ ( ~ ( ~ ( ord_less @ SY274 @ ( ti @ SY274 @ SV49 ) @ SY273 )
| ( ord_less @ SY274 @ SV49 @ SY273 ) )
| ~ ( ~ ( ord_less @ SY274 @ SV49 @ SY273 )
| ( ord_less @ SY274 @ ( ti @ SY274 @ SV49 ) @ SY273 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[466]) ).
thf(574,plain,
! [SV50: $i] :
( ( ! [SY275: $i] :
( ~ ( ord_less @ int @ SV50 @ SY275 )
| ( ord_less_eq @ int @ ( plus_plus @ int @ SV50 @ ( one_one @ int ) ) @ SY275 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[467]) ).
thf(575,plain,
! [SV51: $i] :
( ( ! [SY276: $i,SY277: $i] :
( ~ ( linordered_idom @ SY277 )
| ~ ( ~ ( ~ ( ord_less @ SY277 @ SV51 @ ( ti @ SY277 @ SY276 ) )
| ( ord_less @ SY277 @ SV51 @ SY276 ) )
| ~ ( ~ ( ord_less @ SY277 @ SV51 @ SY276 )
| ( ord_less @ SY277 @ SV51 @ ( ti @ SY277 @ SY276 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[468]) ).
thf(576,plain,
! [SV52: $i] :
( ( ! [SY278: $i,SY279: $i] :
( ~ ~ ( ~ ( number @ SY279 )
| ~ ( semiring @ SY279 ) )
| ( ( plus_plus @ SY279 @ SV52 @ ( ti @ SY279 @ SY278 ) )
= ( plus_plus @ SY279 @ SV52 @ SY278 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[469]) ).
thf(577,plain,
! [SV53: $i] :
( ( ~ ( number @ SV53 )
| ! [SY280: $i,SY281: $i] :
~ ( ~ ( ( ( number_number_of @ SV53 @ SY280 )
!= ( ti @ SV53 @ SY281 ) )
| ( ( ti @ SV53 @ SY281 )
= ( number_number_of @ SV53 @ SY280 ) ) )
| ~ ( ( ( ti @ SV53 @ SY281 )
!= ( number_number_of @ SV53 @ SY280 ) )
| ( ( number_number_of @ SV53 @ SY280 )
= ( ti @ SV53 @ SY281 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[470]) ).
thf(578,plain,
! [SV54: $i] :
( ( ~ ( ~ ( ~ ( ord_less_eq @ int @ ( one_one @ int ) @ SV54 )
| ( ord_less @ int @ ( zero_zero @ int ) @ SV54 ) )
| ~ ( ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV54 )
| ( ord_less_eq @ int @ ( one_one @ int ) @ SV54 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[471]) ).
thf(579,plain,
! [SV55: $i] :
( ( ! [SY282: $i,SY283: $i] :
( ~ ~ ( ~ ( number @ SY283 )
| ~ ( semiring @ SY283 ) )
| ( ( plus_plus @ SY283 @ ( ti @ SY283 @ SV55 ) @ SY282 )
= ( plus_plus @ SY283 @ SV55 @ SY282 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[472]) ).
thf(580,plain,
! [SV56: $i] :
( ( ! [SY284: $i,SY285: $i] :
( ~ ( semiring_1 @ SY285 )
| ( ( ti @ SY285 @ ( power_power @ SY285 @ SV56 @ SY284 ) )
= ( power_power @ SY285 @ SV56 @ SY284 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[473]) ).
thf(581,plain,
! [SV57: $i] :
( ( ~ ( number_ring @ SV57 )
| ! [SY286: $i] :
( ( plus_plus @ SV57 @ ( number_number_of @ SV57 @ SY286 ) @ ( one_one @ SV57 ) )
= ( number_number_of @ SV57 @ ( plus_plus @ int @ SY286 @ ( bit1 @ pls ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[474]) ).
thf(582,plain,
! [SV58: $i] :
( ( ~ ( number_ring @ SV58 )
| ! [SY287: $i,SY288: $i] :
( ( number_number_of @ SV58 @ ( times_times @ int @ SY287 @ SY288 ) )
= ( times_times @ SV58 @ ( number_number_of @ SV58 @ SY287 ) @ ( number_number_of @ SV58 @ SY288 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[475]) ).
thf(583,plain,
! [SV59: $i] :
( ( ~ ( linordered_idom @ SV59 )
| ! [SY289: $i,SY290: $i] :
~ ( ~ ( ~ ( ord_less @ SV59 @ ( zero_zero @ SV59 ) @ ( plus_plus @ SV59 @ ( power_power @ SV59 @ SY289 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV59 @ SY290 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
| ( ( ti @ SV59 @ SY289 )
!= ( zero_zero @ SV59 ) )
| ( ( ti @ SV59 @ SY290 )
!= ( zero_zero @ SV59 ) ) )
| ~ ( ~ ( ( ( ti @ SV59 @ SY289 )
!= ( zero_zero @ SV59 ) )
| ( ( ti @ SV59 @ SY290 )
!= ( zero_zero @ SV59 ) ) )
| ( ord_less @ SV59 @ ( zero_zero @ SV59 ) @ ( plus_plus @ SV59 @ ( power_power @ SV59 @ SY289 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV59 @ SY290 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[476]) ).
thf(584,plain,
! [SV60: $i] :
( ( ! [SY291: $i] :
~ ( ~ ( ( ( bit0 @ SV60 )
!= ( bit0 @ SY291 ) )
| ( SV60 = SY291 ) )
| ~ ( ( SV60 != SY291 )
| ( ( bit0 @ SV60 )
= ( bit0 @ SY291 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[477]) ).
thf(585,plain,
! [SV61: $i] :
( ( ! [SY292: $i] :
~ ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SV61 ) @ ( bit1 @ SY292 ) )
| ( ord_less_eq @ int @ SV61 @ SY292 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV61 @ SY292 )
| ( ord_less @ int @ ( bit0 @ SV61 ) @ ( bit1 @ SY292 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[478]) ).
thf(586,plain,
! [SV62: $i] :
( ( ! [SY293: $i] :
~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit0 @ SV62 ) @ ( bit1 @ SY293 ) )
| ( ord_less_eq @ int @ SV62 @ SY293 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV62 @ SY293 )
| ( ord_less_eq @ int @ ( bit0 @ SV62 ) @ ( bit1 @ SY293 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[479]) ).
thf(587,plain,
! [SV63: $i] :
( ( ! [SY294: $i,SY295: $i] :
( ~ ~ ( ~ ( number @ SY295 )
| ~ ( linorder @ SY295 ) )
| ~ ( ~ ( ~ ( ord_less @ SY295 @ SV63 @ ( ti @ SY295 @ SY294 ) )
| ( ord_less @ SY295 @ SV63 @ SY294 ) )
| ~ ( ~ ( ord_less @ SY295 @ SV63 @ SY294 )
| ( ord_less @ SY295 @ SV63 @ ( ti @ SY295 @ SY294 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[480]) ).
thf(588,plain,
! [SV64: $i] :
( ( ~ ( semiring_1 @ SV64 )
| ( ( power_power @ SV64 @ ( zero_zero @ SV64 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SV64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[481]) ).
thf(589,plain,
! [SV65: $i] :
( ( ! [SY296: $i] :
~ ( ~ ( ~ ( ord_less @ int @ SV65 @ SY296 )
| ~ ( ~ ( ord_less_eq @ int @ SV65 @ SY296 )
| ~ ( ( SV65 != SY296 ) ) ) )
| ~ ( ~ ~ ( ~ ( ord_less_eq @ int @ SV65 @ SY296 )
| ~ ( ( SV65 != SY296 ) ) )
| ( ord_less @ int @ SV65 @ SY296 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[482]) ).
thf(590,plain,
! [SV66: $i] :
( ( ~ ( ~ ( ~ ( twoSqu33214720sum2sq @ ( ti @ int @ SV66 ) )
| ( twoSqu33214720sum2sq @ SV66 ) )
| ~ ( ~ ( twoSqu33214720sum2sq @ SV66 )
| ( twoSqu33214720sum2sq @ ( ti @ int @ SV66 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[483]) ).
thf(591,plain,
! [SV67: $i] :
( ( ~ ( number_ring @ SV67 )
| ! [SY297: $i,SY298: $i,SY299: $i] :
( ( times_times @ SV67 @ ( number_number_of @ SV67 @ SY297 ) @ ( times_times @ SV67 @ ( number_number_of @ SV67 @ SY298 ) @ SY299 ) )
= ( times_times @ SV67 @ ( number_number_of @ SV67 @ ( times_times @ int @ SY297 @ SY298 ) ) @ SY299 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[484]) ).
thf(592,plain,
! [SV68: $i] :
( ( ~ ~ ( ~ ( number_ring @ SV68 )
| ~ ( linordered_idom @ SV68 ) )
| ! [SY300: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV68 @ ( zero_zero @ SV68 ) @ ( number_number_of @ SV68 @ SY300 ) )
| ( ord_less_eq @ int @ pls @ SY300 ) )
| ~ ( ~ ( ord_less_eq @ int @ pls @ SY300 )
| ( ord_less_eq @ SV68 @ ( zero_zero @ SV68 ) @ ( number_number_of @ SV68 @ SY300 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[485]) ).
thf(593,plain,
! [SV69: $i] :
( ( ~ ( ~ ( ~ ( ord_less_eq @ int @ pls @ ( bit0 @ SV69 ) )
| ( ord_less_eq @ int @ pls @ SV69 ) )
| ~ ( ~ ( ord_less_eq @ int @ pls @ SV69 )
| ( ord_less_eq @ int @ pls @ ( bit0 @ SV69 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[486]) ).
thf(594,plain,
! [SV70: $i] :
( ( ~ ~ ( ~ ( number_ring @ SV70 )
| ~ ( linordered_idom @ SV70 ) )
| ! [SY301: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV70 @ ( number_number_of @ SV70 @ SY301 ) @ ( zero_zero @ SV70 ) )
| ( ord_less_eq @ int @ SY301 @ pls ) )
| ~ ( ~ ( ord_less_eq @ int @ SY301 @ pls )
| ( ord_less_eq @ SV70 @ ( number_number_of @ SV70 @ SY301 ) @ ( zero_zero @ SV70 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[487]) ).
thf(595,plain,
! [SV71: $i] :
( ( ! [SY302: $i] :
~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit0 @ SV71 ) @ ( bit0 @ SY302 ) )
| ( ord_less_eq @ int @ SV71 @ SY302 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV71 @ SY302 )
| ( ord_less_eq @ int @ ( bit0 @ SV71 ) @ ( bit0 @ SY302 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[488]) ).
thf(596,plain,
! [SV72: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ ( number_number_of @ nat @ SV72 ) )
| ( ord_less @ int @ pls @ SV72 ) )
| ~ ( ~ ( ord_less @ int @ pls @ SV72 )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ ( number_number_of @ nat @ SV72 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[489]) ).
thf(597,plain,
! [SV73: $i] :
( ( ~ ~ ( ~ ( number_ring @ SV73 )
| ~ ( linordered_idom @ SV73 ) )
| ! [SY303: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV73 @ ( number_number_of @ SV73 @ SY303 ) @ ( one_one @ SV73 ) )
| ( ord_less_eq @ int @ SY303 @ ( bit1 @ pls ) ) )
| ~ ( ~ ( ord_less_eq @ int @ SY303 @ ( bit1 @ pls ) )
| ( ord_less_eq @ SV73 @ ( number_number_of @ SV73 @ SY303 ) @ ( one_one @ SV73 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[490]) ).
thf(598,plain,
! [SV74: $i] :
( ( ~ ( number_ring @ SV74 )
| ! [SY304: $i] :
( ( plus_plus @ SV74 @ ( one_one @ SV74 ) @ ( number_number_of @ SV74 @ SY304 ) )
= ( number_number_of @ SV74 @ ( plus_plus @ int @ ( bit1 @ pls ) @ SY304 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[491]) ).
thf(599,plain,
! [SV75: $i] :
( ( ! [SY305: $i,SY306: $i] :
( ~ ~ ( ~ ( number @ SY306 )
| ~ ( semiring @ SY306 ) )
| ( ( ti @ SY306 @ ( plus_plus @ SY306 @ SV75 @ SY305 ) )
= ( plus_plus @ SY306 @ SV75 @ SY305 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[492]) ).
thf(600,plain,
! [SV76: $i] :
( ( ~ ( ~ ( ~ ( zprime @ ( ti @ int @ SV76 ) )
| ( zprime @ SV76 ) )
| ~ ( ~ ( zprime @ SV76 )
| ( zprime @ ( ti @ int @ SV76 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[493]) ).
thf(601,plain,
! [SV77: $i] :
( ( ! [SY307: $i,SY308: $i] :
( ~ ( semiring_1 @ SY308 )
| ( ( power_power @ SY308 @ ( ti @ SY308 @ SV77 ) @ SY307 )
= ( power_power @ SY308 @ SV77 @ SY307 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[494]) ).
thf(602,plain,
( ( ! [SX0: $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 ) ) @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[495]) ).
thf(603,plain,
! [SV78: $i] :
( ( ~ ( semiring_1 @ SV78 )
| ( ( power_power @ SV78 @ ( one_one @ SV78 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( one_one @ SV78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[496]) ).
thf(604,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)],[497]) ).
thf(605,plain,
! [SV79: $i] :
( ( ~ ~ ( ~ ( number @ SV79 )
| ~ ( linorder @ SV79 ) )
| ! [SY309: $i,SY310: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV79 @ ( number_number_of @ SV79 @ SY309 ) @ ( number_number_of @ SV79 @ SY310 ) )
| ~ ( ord_less @ SV79 @ ( number_number_of @ SV79 @ SY310 ) @ ( number_number_of @ SV79 @ SY309 ) ) )
| ~ ( ~ ~ ( ord_less @ SV79 @ ( number_number_of @ SV79 @ SY310 ) @ ( number_number_of @ SV79 @ SY309 ) )
| ( ord_less_eq @ SV79 @ ( number_number_of @ SV79 @ SY309 ) @ ( number_number_of @ SV79 @ SY310 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[498]) ).
thf(606,plain,
! [SV80: $i] :
( ( ! [SY311: $i] :
~ ( ~ ( ~ ( ord_less @ int @ SV80 @ ( plus_plus @ int @ SY311 @ ( one_one @ int ) ) )
| ( ord_less_eq @ int @ SV80 @ SY311 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV80 @ SY311 )
| ( ord_less @ int @ SV80 @ ( plus_plus @ int @ SY311 @ ( one_one @ int ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[499]) ).
thf(607,plain,
! [SV81: $i] :
( ( ! [SY312: $i] :
~ ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SV81 ) @ ( bit1 @ SY312 ) )
| ( ord_less_eq @ int @ SV81 @ SY312 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV81 @ SY312 )
| ( ord_less @ int @ ( bit0 @ SV81 ) @ ( bit1 @ SY312 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[500]) ).
thf(608,plain,
! [SV82: $i] :
( ( ! [SY313: $i] :
( ~ ( ord_less_eq @ int @ SV82 @ SY313 )
| ~ ( ord_less_eq @ int @ SY313 @ SV82 )
| ( SV82 = SY313 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[501]) ).
thf(609,plain,
! [SV83: $i] :
( ( ~ ( ~ ( ( ( zero_zero @ nat )
!= ( number_number_of @ nat @ SV83 ) )
| ( ord_less_eq @ int @ SV83 @ pls ) )
| ~ ( ~ ( ord_less_eq @ int @ SV83 @ pls )
| ( ( zero_zero @ nat )
= ( number_number_of @ nat @ SV83 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[502]) ).
thf(610,plain,
! [SV84: $i] :
( ( ~ ( linordered_ring @ SV84 )
| ! [SY314: $i,SY315: $i] : ( ord_less_eq @ SV84 @ ( zero_zero @ SV84 ) @ ( plus_plus @ SV84 @ ( times_times @ SV84 @ SY314 @ SY314 ) @ ( times_times @ SV84 @ SY315 @ SY315 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[503]) ).
thf(611,plain,
! [SV85: $i] :
( ( ! [SY316: $i,SY317: $i] :
( ~ ( linordered_ring @ SY317 )
| ( ( plus_plus @ SY317 @ SV85 @ ( ti @ SY317 @ SY316 ) )
= ( plus_plus @ SY317 @ SV85 @ SY316 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[504]) ).
thf(612,plain,
! [SV86: $i] :
( ( ! [SY318: $i] :
( ~ ( number @ SY318 )
| ( ( number_number_of @ SY318 @ ( ti @ int @ SV86 ) )
= ( number_number_of @ SY318 @ SV86 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[505]) ).
thf(613,plain,
! [SV87: $i] :
( ( ! [SY319: $i] :
~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SV87 ) @ ( bit0 @ SY319 ) )
| ( ord_less @ int @ SV87 @ SY319 ) )
| ~ ( ~ ( ord_less @ int @ SV87 @ SY319 )
| ( ord_less_eq @ int @ ( bit1 @ SV87 ) @ ( bit0 @ SY319 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[506]) ).
thf(614,plain,
! [SV88: $i] :
( ( ~ ~ ( ~ ( number @ SV88 )
| ~ ( semiring @ SV88 ) )
| ! [SY320: $i,SY321: $i,SY322: $i] :
( ( times_times @ SV88 @ ( plus_plus @ SV88 @ SY320 @ SY321 ) @ ( number_number_of @ SV88 @ SY322 ) )
= ( plus_plus @ SV88 @ ( times_times @ SV88 @ SY320 @ ( number_number_of @ SV88 @ SY322 ) ) @ ( times_times @ SV88 @ SY321 @ ( number_number_of @ SV88 @ SY322 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[507]) ).
thf(615,plain,
! [SV89: $i] :
( ( ~ ( ~ ( ( ( number_number_of @ nat @ SV89 )
!= ( zero_zero @ nat ) )
| ( ord_less_eq @ int @ SV89 @ pls ) )
| ~ ( ~ ( ord_less_eq @ int @ SV89 @ pls )
| ( ( number_number_of @ nat @ SV89 )
= ( zero_zero @ nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[508]) ).
thf(616,plain,
! [SV90: $i] :
( ( ! [SY323: $i,SY324: $i] :
( ~ ( ord_less_eq @ int @ SY323 @ SY324 )
| ~ ( ord_less_eq @ int @ SY324 @ SV90 )
| ( ord_less_eq @ int @ SY323 @ SV90 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[509]) ).
thf(617,plain,
! [SV91: $i] :
( ( ! [SY325: $i,SY326: $i] :
( ~ ~ ( ~ ( number @ SY326 )
| ~ ( linorder @ SY326 ) )
| ~ ( ~ ( ~ ( ord_less @ SY326 @ ( ti @ SY326 @ SV91 ) @ SY325 )
| ( ord_less @ SY326 @ SV91 @ SY325 ) )
| ~ ( ~ ( ord_less @ SY326 @ SV91 @ SY325 )
| ( ord_less @ SY326 @ ( ti @ SY326 @ SV91 ) @ SY325 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[510]) ).
thf(618,plain,
! [SV92: $i] :
( ( ! [SY327: $i] :
~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SV92 ) @ ( bit1 @ SY327 ) )
| ( ord_less_eq @ int @ SV92 @ SY327 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV92 @ SY327 )
| ( ord_less_eq @ int @ ( bit1 @ SV92 ) @ ( bit1 @ SY327 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[511]) ).
thf(619,plain,
! [SV93: $i] :
( ( ! [SY328: $i,SY329: $i] :
( ~ ( ord_less_eq @ int @ SY328 @ SY329 )
| ( ord_less_eq @ int @ ( plus_plus @ int @ SV93 @ SY328 ) @ ( plus_plus @ int @ SV93 @ SY329 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[512]) ).
thf(620,plain,
! [SV94: $i] :
( ( ~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SV94 ) @ pls )
| ( ord_less @ int @ SV94 @ pls ) )
| ~ ( ~ ( ord_less @ int @ SV94 @ pls )
| ( ord_less_eq @ int @ ( bit1 @ SV94 ) @ pls ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[513]) ).
thf(621,plain,
! [SV95: $i] :
( ( ~ ( linordered_idom @ SV95 )
| ! [SY330: $i,SY331: $i] :
~ ( ord_less @ SV95 @ ( plus_plus @ SV95 @ ( power_power @ SV95 @ SY330 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV95 @ SY331 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( zero_zero @ SV95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[514]) ).
thf(622,plain,
! [SV96: $i] :
( ( ! [SY332: $i] :
~ ( ~ ( ~ ( ord_less @ int @ ( number_number_of @ int @ SV96 ) @ ( number_number_of @ int @ SY332 ) )
| ( ord_less @ int @ SV96 @ SY332 ) )
| ~ ( ~ ( ord_less @ int @ SV96 @ SY332 )
| ( ord_less @ int @ ( number_number_of @ int @ SV96 ) @ ( number_number_of @ int @ SY332 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[515]) ).
thf(623,plain,
! [SV97: $i] :
( ( ~ ( linord581940658strict @ SV97 )
| ! [SY333: $i,SY334: $i] :
~ ( ~ ( ( ( plus_plus @ SV97 @ ( times_times @ SV97 @ SY333 @ SY333 ) @ ( times_times @ SV97 @ SY334 @ SY334 ) )
!= ( zero_zero @ SV97 ) )
| ~ ( ( ( ti @ SV97 @ SY333 )
!= ( zero_zero @ SV97 ) )
| ( ( ti @ SV97 @ SY334 )
!= ( zero_zero @ SV97 ) ) ) )
| ~ ( ~ ~ ( ( ( ti @ SV97 @ SY333 )
!= ( zero_zero @ SV97 ) )
| ( ( ti @ SV97 @ SY334 )
!= ( zero_zero @ SV97 ) ) )
| ( ( plus_plus @ SV97 @ ( times_times @ SV97 @ SY333 @ SY333 ) @ ( times_times @ SV97 @ SY334 @ SY334 ) )
= ( zero_zero @ SV97 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[516]) ).
thf(624,plain,
! [SV98: $i] :
( ( ! [SY335: $i,SY336: $i,SY337: $i] :
( ~ ( ord_less @ int @ SY336 @ SY337 )
| ~ ( ord_less_eq @ int @ SV98 @ SY335 )
| ( ord_less @ int @ ( plus_plus @ int @ SY336 @ SV98 ) @ ( plus_plus @ int @ SY337 @ SY335 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[517]) ).
thf(625,plain,
! [SV99: $i] :
( ( ~ ~ ( ~ ( number_ring @ SV99 )
| ~ ( linordered_idom @ SV99 ) )
| ! [SY338: $i,SY339: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV99 @ ( number_number_of @ SV99 @ SY338 ) @ ( number_number_of @ SV99 @ SY339 ) )
| ( ord_less_eq @ int @ SY338 @ SY339 ) )
| ~ ( ~ ( ord_less_eq @ int @ SY338 @ SY339 )
| ( ord_less_eq @ SV99 @ ( number_number_of @ SV99 @ SY338 ) @ ( number_number_of @ SV99 @ SY339 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[518]) ).
thf(626,plain,
! [SV100: $i] :
( ( ~ ( semiring_1 @ SV100 )
| ( ( ti @ SV100 @ ( zero_zero @ SV100 ) )
= ( zero_zero @ SV100 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[519]) ).
thf(627,plain,
! [SV101: $i] :
( ( ! [SY340: $i] :
~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit0 @ SV101 ) @ ( bit1 @ SY340 ) )
| ( ord_less_eq @ int @ SV101 @ SY340 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV101 @ SY340 )
| ( ord_less_eq @ int @ ( bit0 @ SV101 ) @ ( bit1 @ SY340 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[520]) ).
thf(628,plain,
! [SV102: $i] :
( ( ~ ( semiring_1 @ SV102 )
| ( ( ti @ SV102 @ ( one_one @ SV102 ) )
= ( one_one @ SV102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[521]) ).
thf(629,plain,
! [SV103: $i] :
( ( ~ ~ ( ~ ( number_ring @ SV103 )
| ~ ( linordered_idom @ SV103 ) )
| ! [SY341: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV103 @ ( one_one @ SV103 ) @ ( number_number_of @ SV103 @ SY341 ) )
| ( ord_less_eq @ int @ ( bit1 @ pls ) @ SY341 ) )
| ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ pls ) @ SY341 )
| ( ord_less_eq @ SV103 @ ( one_one @ SV103 ) @ ( number_number_of @ SV103 @ SY341 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[522]) ).
thf(630,plain,
! [SV104: $i,SV7: $i] :
( ( ( times_times @ int @ SV7 @ SV104 )
= ( times_times @ int @ SV104 @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[530]) ).
thf(631,plain,
! [SV105: $i,SV8: $i] :
( ( ( ord_less_eq @ int @ SV8 @ SV105 )
| ( ord_less_eq @ int @ SV105 @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[531]) ).
thf(632,plain,
! [SV106: $i,SV9: $i] :
( ( ( times_times @ int @ ( number_number_of @ int @ SV9 ) @ ( number_number_of @ int @ SV106 ) )
= ( number_number_of @ int @ ( times_times @ int @ SV9 @ SV106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[532]) ).
thf(633,plain,
! [SV107: $i,SV10: $i] :
( ( ! [SY342: $i] :
( ( times_times @ int @ ( times_times @ int @ SV10 @ SV107 ) @ SY342 )
= ( times_times @ int @ SV10 @ ( times_times @ int @ SV107 @ SY342 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[533]) ).
thf(634,plain,
! [SV108: $i,SV11: $i] :
( ( ! [SY343: $i] :
( ( power_power @ int @ SV11 @ ( plus_plus @ nat @ SV108 @ SY343 ) )
= ( times_times @ int @ ( power_power @ int @ SV11 @ SV108 ) @ ( power_power @ int @ SV11 @ SY343 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[534]) ).
thf(635,plain,
! [SV109: $i,SV13: $i] :
( ( ( times_times @ int @ ( bit0 @ SV13 ) @ SV109 )
= ( bit0 @ ( times_times @ int @ SV13 @ SV109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[536]) ).
thf(636,plain,
! [SV110: $i,SV16: $i] :
( ( ( plus_plus @ int @ ( number_number_of @ int @ SV16 ) @ ( number_number_of @ int @ SV110 ) )
= ( number_number_of @ int @ ( plus_plus @ int @ SV16 @ SV110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[539]) ).
thf(637,plain,
! [SV111: $i,SV17: $i] :
( ( ! [SY344: $i] :
( ( times_times @ int @ ( plus_plus @ int @ SV17 @ SV111 ) @ SY344 )
= ( plus_plus @ int @ ( times_times @ int @ SV17 @ SY344 ) @ ( times_times @ int @ SV111 @ SY344 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[540]) ).
thf(638,plain,
! [SV112: $i,SV18: $i] :
( ( ! [SY345: $i] :
( ( times_times @ int @ SV18 @ ( plus_plus @ int @ SV112 @ SY345 ) )
= ( plus_plus @ int @ ( times_times @ int @ SV18 @ SV112 ) @ ( times_times @ int @ SV18 @ SY345 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[541]) ).
thf(639,plain,
! [SV113: $i,SV19: $i] :
( ( ( ord_less @ int @ SV19 @ SV113 )
| ( SV19 = SV113 )
| ( ord_less @ int @ SV113 @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[542]) ).
thf(640,plain,
! [SV114: $i,SV20: $i] :
( ( ! [SY346: $i] :
( ( plus_plus @ int @ ( plus_plus @ int @ SV20 @ SV114 ) @ SY346 )
= ( plus_plus @ int @ SV20 @ ( plus_plus @ int @ SV114 @ SY346 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[543]) ).
thf(641,plain,
! [SV115: $i,SV21: $i] :
( ( ! [SY347: $i] :
( ( plus_plus @ int @ SV21 @ ( plus_plus @ int @ SV115 @ SY347 ) )
= ( plus_plus @ int @ SV115 @ ( plus_plus @ int @ SV21 @ SY347 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[544]) ).
thf(642,plain,
! [SV116: $i,SV22: $i] :
( ( ( plus_plus @ int @ SV22 @ SV116 )
= ( plus_plus @ int @ SV116 @ SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[545]) ).
thf(643,plain,
! [SV23: $i] :
( ( ( ~ ( linordered_idom @ SV23 ) )
= $true )
| ( ( ! [SY242: $i,SY243: $i] :
~ ( ~ ( ( ( plus_plus @ SV23 @ ( power_power @ SV23 @ SY242 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV23 @ SY243 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV23 ) )
| ~ ( ( ( ti @ SV23 @ SY242 )
!= ( zero_zero @ SV23 ) )
| ( ( ti @ SV23 @ SY243 )
!= ( zero_zero @ SV23 ) ) ) )
| ~ ( ~ ~ ( ( ( ti @ SV23 @ SY242 )
!= ( zero_zero @ SV23 ) )
| ( ( ti @ SV23 @ SY243 )
!= ( zero_zero @ SV23 ) ) )
| ( ( plus_plus @ SV23 @ ( power_power @ SV23 @ SY242 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV23 @ SY243 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV23 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[547]) ).
thf(644,plain,
! [SV24: $i] :
( ( ( ~ ( number_semiring @ SV24 ) )
= $true )
| ( ( ! [SY244: $i,SY245: $i] :
( ~ ( ord_less_eq @ int @ pls @ SY245 )
| ~ ( ord_less_eq @ int @ pls @ SY244 )
| ( ( plus_plus @ SV24 @ ( number_number_of @ SV24 @ SY245 ) @ ( number_number_of @ SV24 @ SY244 ) )
= ( number_number_of @ SV24 @ ( plus_plus @ int @ SY245 @ SY244 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[548]) ).
thf(645,plain,
! [SV117: $i,SV25: $i] :
( ( ! [SY348: $i] :
( ~ ( linordered_ring @ SY348 )
| ( ( ti @ SY348 @ ( plus_plus @ SY348 @ SV25 @ SV117 ) )
= ( plus_plus @ SY348 @ SV25 @ SV117 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[549]) ).
thf(646,plain,
! [SV118: $i,SV26: $i] :
( ( ~ ( ~ ( ~ ( ord_less_eq @ int @ ( plus_plus @ int @ SV26 @ ( one_one @ int ) ) @ SV118 )
| ( ord_less @ int @ SV26 @ SV118 ) )
| ~ ( ~ ( ord_less @ int @ SV26 @ SV118 )
| ( ord_less_eq @ int @ ( plus_plus @ int @ SV26 @ ( one_one @ int ) ) @ SV118 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[550]) ).
thf(647,plain,
! [SV27: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV27 ) )
= $true )
| ( ( ord_less @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( one_one @ int ) @ SV27 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[551]) ).
thf(648,plain,
! [SV119: $i,SV28: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ nat @ ( number_number_of @ nat @ SV28 ) @ ( number_number_of @ nat @ SV119 ) )
| ~ ( ~ ( ~ ( ord_less @ int @ SV28 @ SV119 )
| ( ord_less @ int @ pls @ SV119 ) )
| ~ ( ord_less @ int @ SV28 @ SV119 ) ) )
| ~ ( ~ ~ ( ~ ( ~ ( ord_less @ int @ SV28 @ SV119 )
| ( ord_less @ int @ pls @ SV119 ) )
| ~ ( ord_less @ int @ SV28 @ SV119 ) )
| ( ord_less @ nat @ ( number_number_of @ nat @ SV28 ) @ ( number_number_of @ nat @ SV119 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[552]) ).
thf(649,plain,
! [SV120: $i,SV29: $i] :
( ( ! [SY349: $i] :
( ~ ( semiring_1 @ SY349 )
| ( ( power_power @ SY349 @ SV29 @ ( ti @ nat @ SV120 ) )
= ( power_power @ SY349 @ SV29 @ SV120 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[553]) ).
thf(650,plain,
! [SV30: $i,SV121: $i] :
( ( ~ ( number @ SV121 )
| ( ( ti @ SV121 @ ( number_number_of @ SV121 @ SV30 ) )
= ( number_number_of @ SV121 @ SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[554]) ).
thf(651,plain,
! [SV31: $i] :
( ( ( ~ ( linordered_ring @ SV31 ) )
= $true )
| ( ( ( ti @ SV31 @ ( zero_zero @ SV31 ) )
= ( zero_zero @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[555]) ).
thf(652,plain,
! [SV32: $i] :
( ( ( ~ ( linordered_idom @ SV32 ) )
= $true )
| ( ( ! [SY253: $i] :
~ ( ord_less @ SV32 @ ( power_power @ SV32 @ SY253 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( zero_zero @ SV32 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[556]) ).
thf(653,plain,
! [SV33: $i] :
( ( ( ~ ~ ( ~ ( number_ring @ SV33 )
| ~ ( ring_char_0 @ SV33 ) ) )
= $true )
| ( ( ! [SY254: $i,SY255: $i] :
~ ( ~ ( ( ( number_number_of @ SV33 @ SY254 )
!= ( number_number_of @ SV33 @ SY255 ) )
| ( SY254 = SY255 ) )
| ~ ( ( SY254 != SY255 )
| ( ( number_number_of @ SV33 @ SY254 )
= ( number_number_of @ SV33 @ SY255 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[557]) ).
thf(654,plain,
! [SV34: $i] :
( ( ~ ( ~ ( ord_less @ int @ pls @ ( bit1 @ SV34 ) )
| ( ord_less_eq @ int @ pls @ SV34 ) )
| ~ ( ~ ( ord_less_eq @ int @ pls @ SV34 )
| ( ord_less @ int @ pls @ ( bit1 @ SV34 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[558]) ).
thf(655,plain,
! [SV35: $i] :
( ( ( ~ ( ring_11004092258visors @ SV35 ) )
= $true )
| ( ( ! [SY256: $i] :
~ ( ~ ( ( ( power_power @ SV35 @ SY256 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= ( zero_zero @ SV35 ) )
| ( ( ti @ SV35 @ SY256 )
= ( zero_zero @ SV35 ) ) )
| ~ ( ( ( ti @ SV35 @ SY256 )
!= ( zero_zero @ SV35 ) )
| ( ( power_power @ SV35 @ SY256 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SV35 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[559]) ).
thf(656,plain,
! [SV36: $i] :
( ( ( ~ ( number_ring @ SV36 ) )
= $true )
| ( ( ! [SY257: $i,SY258: $i] :
( ( times_times @ SV36 @ ( number_number_of @ SV36 @ SY257 ) @ ( number_number_of @ SV36 @ SY258 ) )
= ( number_number_of @ SV36 @ ( times_times @ int @ SY257 @ SY258 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[560]) ).
thf(657,plain,
! [SV37: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ pls @ ( bit1 @ SV37 ) )
| ( ord_less_eq @ int @ pls @ SV37 ) )
| ~ ( ~ ( ord_less_eq @ int @ pls @ SV37 )
| ( ord_less_eq @ int @ pls @ ( bit1 @ SV37 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[561]) ).
thf(658,plain,
! [SV122: $i,SV38: $i] :
( ( ~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SV38 ) @ ( bit1 @ SV122 ) )
| ( ord_less_eq @ int @ SV38 @ SV122 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV38 @ SV122 )
| ( ord_less_eq @ int @ ( bit1 @ SV38 ) @ ( bit1 @ SV122 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[562]) ).
thf(659,plain,
! [SV123: $i,SV39: $i] :
( ( ~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SV39 ) @ ( bit0 @ SV123 ) )
| ( ord_less @ int @ SV39 @ SV123 ) )
| ~ ( ~ ( ord_less @ int @ SV39 @ SV123 )
| ( ord_less_eq @ int @ ( bit1 @ SV39 ) @ ( bit0 @ SV123 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[563]) ).
thf(660,plain,
! [SV40: $i,SV124: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ int @ SV124 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV124 ) @ ( number_number_of @ nat @ SV40 ) )
= ( number_number_of @ nat @ SV40 ) ) )
| ~ ( ~ ~ ( ord_less @ int @ SV124 @ pls )
| ~ ( ~ ( ~ ( ord_less @ int @ SV40 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV124 ) @ ( number_number_of @ nat @ SV40 ) )
= ( number_number_of @ nat @ SV124 ) ) )
| ~ ( ~ ~ ( ord_less @ int @ SV40 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV124 ) @ ( number_number_of @ nat @ SV40 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SV124 @ SV40 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[564]) ).
thf(661,plain,
! [SV125: $i,SV41: $i] :
( ( ~ ( ~ ( ~ ( ord_less_eq @ int @ ( number_number_of @ int @ SV41 ) @ ( number_number_of @ int @ SV125 ) )
| ( ord_less_eq @ int @ SV41 @ SV125 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV41 @ SV125 )
| ( ord_less_eq @ int @ ( number_number_of @ int @ SV41 ) @ ( number_number_of @ int @ SV125 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[565]) ).
thf(662,plain,
! [SV42: $i] :
( ( ( ~ ( number_semiring @ SV42 ) )
= $true )
| ( ( ! [SY263: $i,SY264: $i] :
( ~ ( ord_less_eq @ int @ pls @ SY264 )
| ~ ( ord_less_eq @ int @ pls @ SY263 )
| ( ( times_times @ SV42 @ ( number_number_of @ SV42 @ SY264 ) @ ( number_number_of @ SV42 @ SY263 ) )
= ( number_number_of @ SV42 @ ( times_times @ int @ SY264 @ SY263 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[566]) ).
thf(663,plain,
! [SV126: $i,SV43: $i] :
( ( ~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit0 @ SV43 ) @ ( bit0 @ SV126 ) )
| ( ord_less_eq @ int @ SV43 @ SV126 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV43 @ SV126 )
| ( ord_less_eq @ int @ ( bit0 @ SV43 ) @ ( bit0 @ SV126 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[567]) ).
thf(664,plain,
! [SV127: $i,SV44: $i] :
( ( ! [SY350: $i] :
( ~ ( linordered_ring @ SY350 )
| ( ( plus_plus @ SY350 @ ( ti @ SY350 @ SV44 ) @ SV127 )
= ( plus_plus @ SY350 @ SV44 @ SV127 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[568]) ).
thf(665,plain,
! [SV45: $i] :
( ( ( ~ ( linordered_idom @ SV45 ) )
= $true )
| ( ( ! [SY268: $i] :
~ ( ~ ( ~ ( ord_less @ SV45 @ ( zero_zero @ SV45 ) @ ( power_power @ SV45 @ SY268 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ( ( ti @ SV45 @ SY268 )
!= ( zero_zero @ SV45 ) ) )
| ~ ( ~ ( ( ( ti @ SV45 @ SY268 )
!= ( zero_zero @ SV45 ) ) )
| ( ord_less @ SV45 @ ( zero_zero @ SV45 ) @ ( power_power @ SV45 @ SY268 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[569]) ).
thf(666,plain,
! [SV46: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( bit0 @ SV46 ) @ pls )
| ( ord_less_eq @ int @ SV46 @ pls ) )
| ~ ( ~ ( ord_less_eq @ int @ SV46 @ pls )
| ( ord_less_eq @ int @ ( bit0 @ SV46 ) @ pls ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[570]) ).
thf(667,plain,
! [SV128: $i,SV47: $i] :
( ( ~ ( ~ ( ( ( bit1 @ SV47 )
!= ( bit1 @ SV128 ) )
| ( SV47 = SV128 ) )
| ~ ( ( SV47 != SV128 )
| ( ( bit1 @ SV47 )
= ( bit1 @ SV128 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[571]) ).
thf(668,plain,
! [SV48: $i] :
( ( ( ~ ~ ( ~ ( number @ SV48 )
| ~ ( semiring @ SV48 ) ) )
= $true )
| ( ( ! [SY270: $i,SY271: $i,SY272: $i] :
( ( times_times @ SV48 @ ( number_number_of @ SV48 @ SY270 ) @ ( plus_plus @ SV48 @ SY271 @ SY272 ) )
= ( plus_plus @ SV48 @ ( times_times @ SV48 @ ( number_number_of @ SV48 @ SY270 ) @ SY271 ) @ ( times_times @ SV48 @ ( number_number_of @ SV48 @ SY270 ) @ SY272 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[572]) ).
thf(669,plain,
! [SV129: $i,SV49: $i] :
( ( ! [SY351: $i] :
( ~ ( linordered_idom @ SY351 )
| ~ ( ~ ( ~ ( ord_less @ SY351 @ ( ti @ SY351 @ SV49 ) @ SV129 )
| ( ord_less @ SY351 @ SV49 @ SV129 ) )
| ~ ( ~ ( ord_less @ SY351 @ SV49 @ SV129 )
| ( ord_less @ SY351 @ ( ti @ SY351 @ SV49 ) @ SV129 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[573]) ).
thf(670,plain,
! [SV130: $i,SV50: $i] :
( ( ~ ( ord_less @ int @ SV50 @ SV130 )
| ( ord_less_eq @ int @ ( plus_plus @ int @ SV50 @ ( one_one @ int ) ) @ SV130 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[574]) ).
thf(671,plain,
! [SV131: $i,SV51: $i] :
( ( ! [SY352: $i] :
( ~ ( linordered_idom @ SY352 )
| ~ ( ~ ( ~ ( ord_less @ SY352 @ SV51 @ ( ti @ SY352 @ SV131 ) )
| ( ord_less @ SY352 @ SV51 @ SV131 ) )
| ~ ( ~ ( ord_less @ SY352 @ SV51 @ SV131 )
| ( ord_less @ SY352 @ SV51 @ ( ti @ SY352 @ SV131 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[575]) ).
thf(672,plain,
! [SV132: $i,SV52: $i] :
( ( ! [SY353: $i] :
( ~ ~ ( ~ ( number @ SY353 )
| ~ ( semiring @ SY353 ) )
| ( ( plus_plus @ SY353 @ SV52 @ ( ti @ SY353 @ SV132 ) )
= ( plus_plus @ SY353 @ SV52 @ SV132 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[576]) ).
thf(673,plain,
! [SV53: $i] :
( ( ( ~ ( number @ SV53 ) )
= $true )
| ( ( ! [SY280: $i,SY281: $i] :
~ ( ~ ( ( ( number_number_of @ SV53 @ SY280 )
!= ( ti @ SV53 @ SY281 ) )
| ( ( ti @ SV53 @ SY281 )
= ( number_number_of @ SV53 @ SY280 ) ) )
| ~ ( ( ( ti @ SV53 @ SY281 )
!= ( number_number_of @ SV53 @ SY280 ) )
| ( ( number_number_of @ SV53 @ SY280 )
= ( ti @ SV53 @ SY281 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[577]) ).
thf(674,plain,
! [SV54: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( one_one @ int ) @ SV54 )
| ( ord_less @ int @ ( zero_zero @ int ) @ SV54 ) )
| ~ ( ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV54 )
| ( ord_less_eq @ int @ ( one_one @ int ) @ SV54 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[578]) ).
thf(675,plain,
! [SV133: $i,SV55: $i] :
( ( ! [SY354: $i] :
( ~ ~ ( ~ ( number @ SY354 )
| ~ ( semiring @ SY354 ) )
| ( ( plus_plus @ SY354 @ ( ti @ SY354 @ SV55 ) @ SV133 )
= ( plus_plus @ SY354 @ SV55 @ SV133 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[579]) ).
thf(676,plain,
! [SV134: $i,SV56: $i] :
( ( ! [SY355: $i] :
( ~ ( semiring_1 @ SY355 )
| ( ( ti @ SY355 @ ( power_power @ SY355 @ SV56 @ SV134 ) )
= ( power_power @ SY355 @ SV56 @ SV134 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[580]) ).
thf(677,plain,
! [SV57: $i] :
( ( ( ~ ( number_ring @ SV57 ) )
= $true )
| ( ( ! [SY286: $i] :
( ( plus_plus @ SV57 @ ( number_number_of @ SV57 @ SY286 ) @ ( one_one @ SV57 ) )
= ( number_number_of @ SV57 @ ( plus_plus @ int @ SY286 @ ( bit1 @ pls ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[581]) ).
thf(678,plain,
! [SV58: $i] :
( ( ( ~ ( number_ring @ SV58 ) )
= $true )
| ( ( ! [SY287: $i,SY288: $i] :
( ( number_number_of @ SV58 @ ( times_times @ int @ SY287 @ SY288 ) )
= ( times_times @ SV58 @ ( number_number_of @ SV58 @ SY287 ) @ ( number_number_of @ SV58 @ SY288 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[582]) ).
thf(679,plain,
! [SV59: $i] :
( ( ( ~ ( linordered_idom @ SV59 ) )
= $true )
| ( ( ! [SY289: $i,SY290: $i] :
~ ( ~ ( ~ ( ord_less @ SV59 @ ( zero_zero @ SV59 ) @ ( plus_plus @ SV59 @ ( power_power @ SV59 @ SY289 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV59 @ SY290 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
| ( ( ti @ SV59 @ SY289 )
!= ( zero_zero @ SV59 ) )
| ( ( ti @ SV59 @ SY290 )
!= ( zero_zero @ SV59 ) ) )
| ~ ( ~ ( ( ( ti @ SV59 @ SY289 )
!= ( zero_zero @ SV59 ) )
| ( ( ti @ SV59 @ SY290 )
!= ( zero_zero @ SV59 ) ) )
| ( ord_less @ SV59 @ ( zero_zero @ SV59 ) @ ( plus_plus @ SV59 @ ( power_power @ SV59 @ SY289 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV59 @ SY290 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[583]) ).
thf(680,plain,
! [SV135: $i,SV60: $i] :
( ( ~ ( ~ ( ( ( bit0 @ SV60 )
!= ( bit0 @ SV135 ) )
| ( SV60 = SV135 ) )
| ~ ( ( SV60 != SV135 )
| ( ( bit0 @ SV60 )
= ( bit0 @ SV135 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[584]) ).
thf(681,plain,
! [SV136: $i,SV61: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SV61 ) @ ( bit1 @ SV136 ) )
| ( ord_less_eq @ int @ SV61 @ SV136 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV61 @ SV136 )
| ( ord_less @ int @ ( bit0 @ SV61 ) @ ( bit1 @ SV136 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[585]) ).
thf(682,plain,
! [SV137: $i,SV62: $i] :
( ( ~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit0 @ SV62 ) @ ( bit1 @ SV137 ) )
| ( ord_less_eq @ int @ SV62 @ SV137 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV62 @ SV137 )
| ( ord_less_eq @ int @ ( bit0 @ SV62 ) @ ( bit1 @ SV137 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[586]) ).
thf(683,plain,
! [SV138: $i,SV63: $i] :
( ( ! [SY356: $i] :
( ~ ~ ( ~ ( number @ SY356 )
| ~ ( linorder @ SY356 ) )
| ~ ( ~ ( ~ ( ord_less @ SY356 @ SV63 @ ( ti @ SY356 @ SV138 ) )
| ( ord_less @ SY356 @ SV63 @ SV138 ) )
| ~ ( ~ ( ord_less @ SY356 @ SV63 @ SV138 )
| ( ord_less @ SY356 @ SV63 @ ( ti @ SY356 @ SV138 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[587]) ).
thf(684,plain,
! [SV64: $i] :
( ( ( ~ ( semiring_1 @ SV64 ) )
= $true )
| ( ( ( power_power @ SV64 @ ( zero_zero @ SV64 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SV64 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[588]) ).
thf(685,plain,
! [SV139: $i,SV65: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ int @ SV65 @ SV139 )
| ~ ( ~ ( ord_less_eq @ int @ SV65 @ SV139 )
| ~ ( ( SV65 != SV139 ) ) ) )
| ~ ( ~ ~ ( ~ ( ord_less_eq @ int @ SV65 @ SV139 )
| ~ ( ( SV65 != SV139 ) ) )
| ( ord_less @ int @ SV65 @ SV139 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[589]) ).
thf(686,plain,
! [SV66: $i] :
( ( ~ ( ~ ( twoSqu33214720sum2sq @ ( ti @ int @ SV66 ) )
| ( twoSqu33214720sum2sq @ SV66 ) )
| ~ ( ~ ( twoSqu33214720sum2sq @ SV66 )
| ( twoSqu33214720sum2sq @ ( ti @ int @ SV66 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[590]) ).
thf(687,plain,
! [SV67: $i] :
( ( ( ~ ( number_ring @ SV67 ) )
= $true )
| ( ( ! [SY297: $i,SY298: $i,SY299: $i] :
( ( times_times @ SV67 @ ( number_number_of @ SV67 @ SY297 ) @ ( times_times @ SV67 @ ( number_number_of @ SV67 @ SY298 ) @ SY299 ) )
= ( times_times @ SV67 @ ( number_number_of @ SV67 @ ( times_times @ int @ SY297 @ SY298 ) ) @ SY299 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[591]) ).
thf(688,plain,
! [SV68: $i] :
( ( ( ~ ~ ( ~ ( number_ring @ SV68 )
| ~ ( linordered_idom @ SV68 ) ) )
= $true )
| ( ( ! [SY300: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV68 @ ( zero_zero @ SV68 ) @ ( number_number_of @ SV68 @ SY300 ) )
| ( ord_less_eq @ int @ pls @ SY300 ) )
| ~ ( ~ ( ord_less_eq @ int @ pls @ SY300 )
| ( ord_less_eq @ SV68 @ ( zero_zero @ SV68 ) @ ( number_number_of @ SV68 @ SY300 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[592]) ).
thf(689,plain,
! [SV69: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ pls @ ( bit0 @ SV69 ) )
| ( ord_less_eq @ int @ pls @ SV69 ) )
| ~ ( ~ ( ord_less_eq @ int @ pls @ SV69 )
| ( ord_less_eq @ int @ pls @ ( bit0 @ SV69 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[593]) ).
thf(690,plain,
! [SV70: $i] :
( ( ( ~ ~ ( ~ ( number_ring @ SV70 )
| ~ ( linordered_idom @ SV70 ) ) )
= $true )
| ( ( ! [SY301: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV70 @ ( number_number_of @ SV70 @ SY301 ) @ ( zero_zero @ SV70 ) )
| ( ord_less_eq @ int @ SY301 @ pls ) )
| ~ ( ~ ( ord_less_eq @ int @ SY301 @ pls )
| ( ord_less_eq @ SV70 @ ( number_number_of @ SV70 @ SY301 ) @ ( zero_zero @ SV70 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[594]) ).
thf(691,plain,
! [SV140: $i,SV71: $i] :
( ( ~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit0 @ SV71 ) @ ( bit0 @ SV140 ) )
| ( ord_less_eq @ int @ SV71 @ SV140 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV71 @ SV140 )
| ( ord_less_eq @ int @ ( bit0 @ SV71 ) @ ( bit0 @ SV140 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[595]) ).
thf(692,plain,
! [SV72: $i] :
( ( ~ ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ ( number_number_of @ nat @ SV72 ) )
| ( ord_less @ int @ pls @ SV72 ) )
| ~ ( ~ ( ord_less @ int @ pls @ SV72 )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ ( number_number_of @ nat @ SV72 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[596]) ).
thf(693,plain,
! [SV73: $i] :
( ( ( ~ ~ ( ~ ( number_ring @ SV73 )
| ~ ( linordered_idom @ SV73 ) ) )
= $true )
| ( ( ! [SY303: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV73 @ ( number_number_of @ SV73 @ SY303 ) @ ( one_one @ SV73 ) )
| ( ord_less_eq @ int @ SY303 @ ( bit1 @ pls ) ) )
| ~ ( ~ ( ord_less_eq @ int @ SY303 @ ( bit1 @ pls ) )
| ( ord_less_eq @ SV73 @ ( number_number_of @ SV73 @ SY303 ) @ ( one_one @ SV73 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[597]) ).
thf(694,plain,
! [SV74: $i] :
( ( ( ~ ( number_ring @ SV74 ) )
= $true )
| ( ( ! [SY304: $i] :
( ( plus_plus @ SV74 @ ( one_one @ SV74 ) @ ( number_number_of @ SV74 @ SY304 ) )
= ( number_number_of @ SV74 @ ( plus_plus @ int @ ( bit1 @ pls ) @ SY304 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[598]) ).
thf(695,plain,
! [SV141: $i,SV75: $i] :
( ( ! [SY357: $i] :
( ~ ~ ( ~ ( number @ SY357 )
| ~ ( semiring @ SY357 ) )
| ( ( ti @ SY357 @ ( plus_plus @ SY357 @ SV75 @ SV141 ) )
= ( plus_plus @ SY357 @ SV75 @ SV141 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[599]) ).
thf(696,plain,
! [SV76: $i] :
( ( ~ ( ~ ( zprime @ ( ti @ int @ SV76 ) )
| ( zprime @ SV76 ) )
| ~ ( ~ ( zprime @ SV76 )
| ( zprime @ ( ti @ int @ SV76 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[600]) ).
thf(697,plain,
! [SV142: $i,SV77: $i] :
( ( ! [SY358: $i] :
( ~ ( semiring_1 @ SY358 )
| ( ( power_power @ SY358 @ ( ti @ SY358 @ SV77 ) @ SV142 )
= ( power_power @ SY358 @ SV77 @ SV142 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[601]) ).
thf(698,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_SX0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[602]) ).
thf(699,plain,
! [SV78: $i] :
( ( ( ~ ( semiring_1 @ SV78 ) )
= $true )
| ( ( ( power_power @ SV78 @ ( one_one @ SV78 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( one_one @ SV78 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[603]) ).
thf(700,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)],[604]) ).
thf(701,plain,
! [SV79: $i] :
( ( ( ~ ~ ( ~ ( number @ SV79 )
| ~ ( linorder @ SV79 ) ) )
= $true )
| ( ( ! [SY309: $i,SY310: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV79 @ ( number_number_of @ SV79 @ SY309 ) @ ( number_number_of @ SV79 @ SY310 ) )
| ~ ( ord_less @ SV79 @ ( number_number_of @ SV79 @ SY310 ) @ ( number_number_of @ SV79 @ SY309 ) ) )
| ~ ( ~ ~ ( ord_less @ SV79 @ ( number_number_of @ SV79 @ SY310 ) @ ( number_number_of @ SV79 @ SY309 ) )
| ( ord_less_eq @ SV79 @ ( number_number_of @ SV79 @ SY309 ) @ ( number_number_of @ SV79 @ SY310 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[605]) ).
thf(702,plain,
! [SV143: $i,SV80: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ int @ SV80 @ ( plus_plus @ int @ SV143 @ ( one_one @ int ) ) )
| ( ord_less_eq @ int @ SV80 @ SV143 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV80 @ SV143 )
| ( ord_less @ int @ SV80 @ ( plus_plus @ int @ SV143 @ ( one_one @ int ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[606]) ).
thf(703,plain,
! [SV144: $i,SV81: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SV81 ) @ ( bit1 @ SV144 ) )
| ( ord_less_eq @ int @ SV81 @ SV144 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV81 @ SV144 )
| ( ord_less @ int @ ( bit0 @ SV81 ) @ ( bit1 @ SV144 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[607]) ).
thf(704,plain,
! [SV145: $i,SV82: $i] :
( ( ~ ( ord_less_eq @ int @ SV82 @ SV145 )
| ~ ( ord_less_eq @ int @ SV145 @ SV82 )
| ( SV82 = SV145 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[608]) ).
thf(705,plain,
! [SV83: $i] :
( ( ~ ( ( ( zero_zero @ nat )
!= ( number_number_of @ nat @ SV83 ) )
| ( ord_less_eq @ int @ SV83 @ pls ) )
| ~ ( ~ ( ord_less_eq @ int @ SV83 @ pls )
| ( ( zero_zero @ nat )
= ( number_number_of @ nat @ SV83 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[609]) ).
thf(706,plain,
! [SV84: $i] :
( ( ( ~ ( linordered_ring @ SV84 ) )
= $true )
| ( ( ! [SY314: $i,SY315: $i] : ( ord_less_eq @ SV84 @ ( zero_zero @ SV84 ) @ ( plus_plus @ SV84 @ ( times_times @ SV84 @ SY314 @ SY314 ) @ ( times_times @ SV84 @ SY315 @ SY315 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[610]) ).
thf(707,plain,
! [SV146: $i,SV85: $i] :
( ( ! [SY359: $i] :
( ~ ( linordered_ring @ SY359 )
| ( ( plus_plus @ SY359 @ SV85 @ ( ti @ SY359 @ SV146 ) )
= ( plus_plus @ SY359 @ SV85 @ SV146 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[611]) ).
thf(708,plain,
! [SV86: $i,SV147: $i] :
( ( ~ ( number @ SV147 )
| ( ( number_number_of @ SV147 @ ( ti @ int @ SV86 ) )
= ( number_number_of @ SV147 @ SV86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[612]) ).
thf(709,plain,
! [SV148: $i,SV87: $i] :
( ( ~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SV87 ) @ ( bit0 @ SV148 ) )
| ( ord_less @ int @ SV87 @ SV148 ) )
| ~ ( ~ ( ord_less @ int @ SV87 @ SV148 )
| ( ord_less_eq @ int @ ( bit1 @ SV87 ) @ ( bit0 @ SV148 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[613]) ).
thf(710,plain,
! [SV88: $i] :
( ( ( ~ ~ ( ~ ( number @ SV88 )
| ~ ( semiring @ SV88 ) ) )
= $true )
| ( ( ! [SY320: $i,SY321: $i,SY322: $i] :
( ( times_times @ SV88 @ ( plus_plus @ SV88 @ SY320 @ SY321 ) @ ( number_number_of @ SV88 @ SY322 ) )
= ( plus_plus @ SV88 @ ( times_times @ SV88 @ SY320 @ ( number_number_of @ SV88 @ SY322 ) ) @ ( times_times @ SV88 @ SY321 @ ( number_number_of @ SV88 @ SY322 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[614]) ).
thf(711,plain,
! [SV89: $i] :
( ( ~ ( ( ( number_number_of @ nat @ SV89 )
!= ( zero_zero @ nat ) )
| ( ord_less_eq @ int @ SV89 @ pls ) )
| ~ ( ~ ( ord_less_eq @ int @ SV89 @ pls )
| ( ( number_number_of @ nat @ SV89 )
= ( zero_zero @ nat ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[615]) ).
thf(712,plain,
! [SV90: $i,SV149: $i] :
( ( ! [SY360: $i] :
( ~ ( ord_less_eq @ int @ SV149 @ SY360 )
| ~ ( ord_less_eq @ int @ SY360 @ SV90 )
| ( ord_less_eq @ int @ SV149 @ SV90 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[616]) ).
thf(713,plain,
! [SV150: $i,SV91: $i] :
( ( ! [SY361: $i] :
( ~ ~ ( ~ ( number @ SY361 )
| ~ ( linorder @ SY361 ) )
| ~ ( ~ ( ~ ( ord_less @ SY361 @ ( ti @ SY361 @ SV91 ) @ SV150 )
| ( ord_less @ SY361 @ SV91 @ SV150 ) )
| ~ ( ~ ( ord_less @ SY361 @ SV91 @ SV150 )
| ( ord_less @ SY361 @ ( ti @ SY361 @ SV91 ) @ SV150 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[617]) ).
thf(714,plain,
! [SV151: $i,SV92: $i] :
( ( ~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SV92 ) @ ( bit1 @ SV151 ) )
| ( ord_less_eq @ int @ SV92 @ SV151 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV92 @ SV151 )
| ( ord_less_eq @ int @ ( bit1 @ SV92 ) @ ( bit1 @ SV151 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[618]) ).
thf(715,plain,
! [SV93: $i,SV152: $i] :
( ( ! [SY362: $i] :
( ~ ( ord_less_eq @ int @ SV152 @ SY362 )
| ( ord_less_eq @ int @ ( plus_plus @ int @ SV93 @ SV152 ) @ ( plus_plus @ int @ SV93 @ SY362 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[619]) ).
thf(716,plain,
! [SV94: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SV94 ) @ pls )
| ( ord_less @ int @ SV94 @ pls ) )
| ~ ( ~ ( ord_less @ int @ SV94 @ pls )
| ( ord_less_eq @ int @ ( bit1 @ SV94 ) @ pls ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[620]) ).
thf(717,plain,
! [SV95: $i] :
( ( ( ~ ( linordered_idom @ SV95 ) )
= $true )
| ( ( ! [SY330: $i,SY331: $i] :
~ ( ord_less @ SV95 @ ( plus_plus @ SV95 @ ( power_power @ SV95 @ SY330 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV95 @ SY331 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( zero_zero @ SV95 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[621]) ).
thf(718,plain,
! [SV153: $i,SV96: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ int @ ( number_number_of @ int @ SV96 ) @ ( number_number_of @ int @ SV153 ) )
| ( ord_less @ int @ SV96 @ SV153 ) )
| ~ ( ~ ( ord_less @ int @ SV96 @ SV153 )
| ( ord_less @ int @ ( number_number_of @ int @ SV96 ) @ ( number_number_of @ int @ SV153 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[622]) ).
thf(719,plain,
! [SV97: $i] :
( ( ( ~ ( linord581940658strict @ SV97 ) )
= $true )
| ( ( ! [SY333: $i,SY334: $i] :
~ ( ~ ( ( ( plus_plus @ SV97 @ ( times_times @ SV97 @ SY333 @ SY333 ) @ ( times_times @ SV97 @ SY334 @ SY334 ) )
!= ( zero_zero @ SV97 ) )
| ~ ( ( ( ti @ SV97 @ SY333 )
!= ( zero_zero @ SV97 ) )
| ( ( ti @ SV97 @ SY334 )
!= ( zero_zero @ SV97 ) ) ) )
| ~ ( ~ ~ ( ( ( ti @ SV97 @ SY333 )
!= ( zero_zero @ SV97 ) )
| ( ( ti @ SV97 @ SY334 )
!= ( zero_zero @ SV97 ) ) )
| ( ( plus_plus @ SV97 @ ( times_times @ SV97 @ SY333 @ SY333 ) @ ( times_times @ SV97 @ SY334 @ SY334 ) )
= ( zero_zero @ SV97 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[623]) ).
thf(720,plain,
! [SV154: $i,SV98: $i] :
( ( ! [SY363: $i,SY364: $i] :
( ~ ( ord_less @ int @ SY363 @ SY364 )
| ~ ( ord_less_eq @ int @ SV98 @ SV154 )
| ( ord_less @ int @ ( plus_plus @ int @ SY363 @ SV98 ) @ ( plus_plus @ int @ SY364 @ SV154 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[624]) ).
thf(721,plain,
! [SV99: $i] :
( ( ( ~ ~ ( ~ ( number_ring @ SV99 )
| ~ ( linordered_idom @ SV99 ) ) )
= $true )
| ( ( ! [SY338: $i,SY339: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV99 @ ( number_number_of @ SV99 @ SY338 ) @ ( number_number_of @ SV99 @ SY339 ) )
| ( ord_less_eq @ int @ SY338 @ SY339 ) )
| ~ ( ~ ( ord_less_eq @ int @ SY338 @ SY339 )
| ( ord_less_eq @ SV99 @ ( number_number_of @ SV99 @ SY338 ) @ ( number_number_of @ SV99 @ SY339 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[625]) ).
thf(722,plain,
! [SV100: $i] :
( ( ( ~ ( semiring_1 @ SV100 ) )
= $true )
| ( ( ( ti @ SV100 @ ( zero_zero @ SV100 ) )
= ( zero_zero @ SV100 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[626]) ).
thf(723,plain,
! [SV155: $i,SV101: $i] :
( ( ~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit0 @ SV101 ) @ ( bit1 @ SV155 ) )
| ( ord_less_eq @ int @ SV101 @ SV155 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV101 @ SV155 )
| ( ord_less_eq @ int @ ( bit0 @ SV101 ) @ ( bit1 @ SV155 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[627]) ).
thf(724,plain,
! [SV102: $i] :
( ( ( ~ ( semiring_1 @ SV102 ) )
= $true )
| ( ( ( ti @ SV102 @ ( one_one @ SV102 ) )
= ( one_one @ SV102 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[628]) ).
thf(725,plain,
! [SV103: $i] :
( ( ( ~ ~ ( ~ ( number_ring @ SV103 )
| ~ ( linordered_idom @ SV103 ) ) )
= $true )
| ( ( ! [SY341: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV103 @ ( one_one @ SV103 ) @ ( number_number_of @ SV103 @ SY341 ) )
| ( ord_less_eq @ int @ ( bit1 @ pls ) @ SY341 ) )
| ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ pls ) @ SY341 )
| ( ord_less_eq @ SV103 @ ( one_one @ SV103 ) @ ( number_number_of @ SV103 @ SY341 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[629]) ).
thf(726,plain,
! [SV105: $i,SV8: $i] :
( ( ( ord_less_eq @ int @ SV8 @ SV105 )
= $true )
| ( ( ord_less_eq @ int @ SV105 @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[631]) ).
thf(727,plain,
! [SV156: $i,SV107: $i,SV10: $i] :
( ( ( times_times @ int @ ( times_times @ int @ SV10 @ SV107 ) @ SV156 )
= ( times_times @ int @ SV10 @ ( times_times @ int @ SV107 @ SV156 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[633]) ).
thf(728,plain,
! [SV157: $i,SV108: $i,SV11: $i] :
( ( ( power_power @ int @ SV11 @ ( plus_plus @ nat @ SV108 @ SV157 ) )
= ( times_times @ int @ ( power_power @ int @ SV11 @ SV108 ) @ ( power_power @ int @ SV11 @ SV157 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[634]) ).
thf(729,plain,
! [SV158: $i,SV111: $i,SV17: $i] :
( ( ( times_times @ int @ ( plus_plus @ int @ SV17 @ SV111 ) @ SV158 )
= ( plus_plus @ int @ ( times_times @ int @ SV17 @ SV158 ) @ ( times_times @ int @ SV111 @ SV158 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[637]) ).
thf(730,plain,
! [SV159: $i,SV112: $i,SV18: $i] :
( ( ( times_times @ int @ SV18 @ ( plus_plus @ int @ SV112 @ SV159 ) )
= ( plus_plus @ int @ ( times_times @ int @ SV18 @ SV112 ) @ ( times_times @ int @ SV18 @ SV159 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[638]) ).
thf(731,plain,
! [SV113: $i,SV19: $i] :
( ( ( ( ord_less @ int @ SV19 @ SV113 )
| ( SV19 = SV113 ) )
= $true )
| ( ( ord_less @ int @ SV113 @ SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[639]) ).
thf(732,plain,
! [SV160: $i,SV114: $i,SV20: $i] :
( ( ( plus_plus @ int @ ( plus_plus @ int @ SV20 @ SV114 ) @ SV160 )
= ( plus_plus @ int @ SV20 @ ( plus_plus @ int @ SV114 @ SV160 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[640]) ).
thf(733,plain,
! [SV161: $i,SV115: $i,SV21: $i] :
( ( ( plus_plus @ int @ SV21 @ ( plus_plus @ int @ SV115 @ SV161 ) )
= ( plus_plus @ int @ SV115 @ ( plus_plus @ int @ SV21 @ SV161 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[641]) ).
thf(734,plain,
! [SV23: $i] :
( ( ( linordered_idom @ SV23 )
= $false )
| ( ( ! [SY242: $i,SY243: $i] :
~ ( ~ ( ( ( plus_plus @ SV23 @ ( power_power @ SV23 @ SY242 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV23 @ SY243 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV23 ) )
| ~ ( ( ( ti @ SV23 @ SY242 )
!= ( zero_zero @ SV23 ) )
| ( ( ti @ SV23 @ SY243 )
!= ( zero_zero @ SV23 ) ) ) )
| ~ ( ~ ~ ( ( ( ti @ SV23 @ SY242 )
!= ( zero_zero @ SV23 ) )
| ( ( ti @ SV23 @ SY243 )
!= ( zero_zero @ SV23 ) ) )
| ( ( plus_plus @ SV23 @ ( power_power @ SV23 @ SY242 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV23 @ SY243 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV23 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[643]) ).
thf(735,plain,
! [SV24: $i] :
( ( ( number_semiring @ SV24 )
= $false )
| ( ( ! [SY244: $i,SY245: $i] :
( ~ ( ord_less_eq @ int @ pls @ SY245 )
| ~ ( ord_less_eq @ int @ pls @ SY244 )
| ( ( plus_plus @ SV24 @ ( number_number_of @ SV24 @ SY245 ) @ ( number_number_of @ SV24 @ SY244 ) )
= ( number_number_of @ SV24 @ ( plus_plus @ int @ SY245 @ SY244 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[644]) ).
thf(736,plain,
! [SV117: $i,SV25: $i,SV162: $i] :
( ( ~ ( linordered_ring @ SV162 )
| ( ( ti @ SV162 @ ( plus_plus @ SV162 @ SV25 @ SV117 ) )
= ( plus_plus @ SV162 @ SV25 @ SV117 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[645]) ).
thf(737,plain,
! [SV118: $i,SV26: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( plus_plus @ int @ SV26 @ ( one_one @ int ) ) @ SV118 )
| ( ord_less @ int @ SV26 @ SV118 ) )
| ~ ( ~ ( ord_less @ int @ SV26 @ SV118 )
| ( ord_less_eq @ int @ ( plus_plus @ int @ SV26 @ ( one_one @ int ) ) @ SV118 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[646]) ).
thf(738,plain,
! [SV27: $i] :
( ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ SV27 )
= $false )
| ( ( ord_less @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( one_one @ int ) @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[647]) ).
thf(739,plain,
! [SV119: $i,SV28: $i] :
( ( ~ ( ~ ( ord_less @ nat @ ( number_number_of @ nat @ SV28 ) @ ( number_number_of @ nat @ SV119 ) )
| ~ ( ~ ( ~ ( ord_less @ int @ SV28 @ SV119 )
| ( ord_less @ int @ pls @ SV119 ) )
| ~ ( ord_less @ int @ SV28 @ SV119 ) ) )
| ~ ( ~ ~ ( ~ ( ~ ( ord_less @ int @ SV28 @ SV119 )
| ( ord_less @ int @ pls @ SV119 ) )
| ~ ( ord_less @ int @ SV28 @ SV119 ) )
| ( ord_less @ nat @ ( number_number_of @ nat @ SV28 ) @ ( number_number_of @ nat @ SV119 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[648]) ).
thf(740,plain,
! [SV120: $i,SV29: $i,SV163: $i] :
( ( ~ ( semiring_1 @ SV163 )
| ( ( power_power @ SV163 @ SV29 @ ( ti @ nat @ SV120 ) )
= ( power_power @ SV163 @ SV29 @ SV120 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[649]) ).
thf(741,plain,
! [SV30: $i,SV121: $i] :
( ( ( ~ ( number @ SV121 ) )
= $true )
| ( ( ( ti @ SV121 @ ( number_number_of @ SV121 @ SV30 ) )
= ( number_number_of @ SV121 @ SV30 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[650]) ).
thf(742,plain,
! [SV31: $i] :
( ( ( linordered_ring @ SV31 )
= $false )
| ( ( ( ti @ SV31 @ ( zero_zero @ SV31 ) )
= ( zero_zero @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[651]) ).
thf(743,plain,
! [SV32: $i] :
( ( ( linordered_idom @ SV32 )
= $false )
| ( ( ! [SY253: $i] :
~ ( ord_less @ SV32 @ ( power_power @ SV32 @ SY253 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( zero_zero @ SV32 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[652]) ).
thf(744,plain,
! [SV33: $i] :
( ( ( ~ ( ~ ( number_ring @ SV33 )
| ~ ( ring_char_0 @ SV33 ) ) )
= $false )
| ( ( ! [SY254: $i,SY255: $i] :
~ ( ~ ( ( ( number_number_of @ SV33 @ SY254 )
!= ( number_number_of @ SV33 @ SY255 ) )
| ( SY254 = SY255 ) )
| ~ ( ( SY254 != SY255 )
| ( ( number_number_of @ SV33 @ SY254 )
= ( number_number_of @ SV33 @ SY255 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[653]) ).
thf(745,plain,
! [SV34: $i] :
( ( ~ ( ~ ( ord_less @ int @ pls @ ( bit1 @ SV34 ) )
| ( ord_less_eq @ int @ pls @ SV34 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[654]) ).
thf(746,plain,
! [SV34: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ pls @ SV34 )
| ( ord_less @ int @ pls @ ( bit1 @ SV34 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[654]) ).
thf(747,plain,
! [SV35: $i] :
( ( ( ring_11004092258visors @ SV35 )
= $false )
| ( ( ! [SY256: $i] :
~ ( ~ ( ( ( power_power @ SV35 @ SY256 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= ( zero_zero @ SV35 ) )
| ( ( ti @ SV35 @ SY256 )
= ( zero_zero @ SV35 ) ) )
| ~ ( ( ( ti @ SV35 @ SY256 )
!= ( zero_zero @ SV35 ) )
| ( ( power_power @ SV35 @ SY256 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SV35 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[655]) ).
thf(748,plain,
! [SV36: $i] :
( ( ( number_ring @ SV36 )
= $false )
| ( ( ! [SY257: $i,SY258: $i] :
( ( times_times @ SV36 @ ( number_number_of @ SV36 @ SY257 ) @ ( number_number_of @ SV36 @ SY258 ) )
= ( number_number_of @ SV36 @ ( times_times @ int @ SY257 @ SY258 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[656]) ).
thf(749,plain,
! [SV37: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ pls @ ( bit1 @ SV37 ) )
| ( ord_less_eq @ int @ pls @ SV37 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[657]) ).
thf(750,plain,
! [SV37: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ pls @ SV37 )
| ( ord_less_eq @ int @ pls @ ( bit1 @ SV37 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[657]) ).
thf(751,plain,
! [SV122: $i,SV38: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SV38 ) @ ( bit1 @ SV122 ) )
| ( ord_less_eq @ int @ SV38 @ SV122 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV38 @ SV122 )
| ( ord_less_eq @ int @ ( bit1 @ SV38 ) @ ( bit1 @ SV122 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[658]) ).
thf(752,plain,
! [SV123: $i,SV39: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SV39 ) @ ( bit0 @ SV123 ) )
| ( ord_less @ int @ SV39 @ SV123 ) )
| ~ ( ~ ( ord_less @ int @ SV39 @ SV123 )
| ( ord_less_eq @ int @ ( bit1 @ SV39 ) @ ( bit0 @ SV123 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[659]) ).
thf(753,plain,
! [SV40: $i,SV124: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV124 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV124 ) @ ( number_number_of @ nat @ SV40 ) )
= ( number_number_of @ nat @ SV40 ) ) )
| ~ ( ~ ~ ( ord_less @ int @ SV124 @ pls )
| ~ ( ~ ( ~ ( ord_less @ int @ SV40 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV124 ) @ ( number_number_of @ nat @ SV40 ) )
= ( number_number_of @ nat @ SV124 ) ) )
| ~ ( ~ ~ ( ord_less @ int @ SV40 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV124 ) @ ( number_number_of @ nat @ SV40 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SV124 @ SV40 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[660]) ).
thf(754,plain,
! [SV125: $i,SV41: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( number_number_of @ int @ SV41 ) @ ( number_number_of @ int @ SV125 ) )
| ( ord_less_eq @ int @ SV41 @ SV125 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV41 @ SV125 )
| ( ord_less_eq @ int @ ( number_number_of @ int @ SV41 ) @ ( number_number_of @ int @ SV125 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[661]) ).
thf(755,plain,
! [SV42: $i] :
( ( ( number_semiring @ SV42 )
= $false )
| ( ( ! [SY263: $i,SY264: $i] :
( ~ ( ord_less_eq @ int @ pls @ SY264 )
| ~ ( ord_less_eq @ int @ pls @ SY263 )
| ( ( times_times @ SV42 @ ( number_number_of @ SV42 @ SY264 ) @ ( number_number_of @ SV42 @ SY263 ) )
= ( number_number_of @ SV42 @ ( times_times @ int @ SY264 @ SY263 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[662]) ).
thf(756,plain,
! [SV126: $i,SV43: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( bit0 @ SV43 ) @ ( bit0 @ SV126 ) )
| ( ord_less_eq @ int @ SV43 @ SV126 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV43 @ SV126 )
| ( ord_less_eq @ int @ ( bit0 @ SV43 ) @ ( bit0 @ SV126 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[663]) ).
thf(757,plain,
! [SV127: $i,SV44: $i,SV164: $i] :
( ( ~ ( linordered_ring @ SV164 )
| ( ( plus_plus @ SV164 @ ( ti @ SV164 @ SV44 ) @ SV127 )
= ( plus_plus @ SV164 @ SV44 @ SV127 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[664]) ).
thf(758,plain,
! [SV45: $i] :
( ( ( linordered_idom @ SV45 )
= $false )
| ( ( ! [SY268: $i] :
~ ( ~ ( ~ ( ord_less @ SV45 @ ( zero_zero @ SV45 ) @ ( power_power @ SV45 @ SY268 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ( ( ti @ SV45 @ SY268 )
!= ( zero_zero @ SV45 ) ) )
| ~ ( ~ ( ( ( ti @ SV45 @ SY268 )
!= ( zero_zero @ SV45 ) ) )
| ( ord_less @ SV45 @ ( zero_zero @ SV45 ) @ ( power_power @ SV45 @ SY268 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[665]) ).
thf(759,plain,
! [SV46: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( bit0 @ SV46 ) @ pls )
| ( ord_less_eq @ int @ SV46 @ pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[666]) ).
thf(760,plain,
! [SV46: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ SV46 @ pls )
| ( ord_less_eq @ int @ ( bit0 @ SV46 ) @ pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[666]) ).
thf(761,plain,
! [SV128: $i,SV47: $i] :
( ( ~ ( ( ( bit1 @ SV47 )
!= ( bit1 @ SV128 ) )
| ( SV47 = SV128 ) )
| ~ ( ( SV47 != SV128 )
| ( ( bit1 @ SV47 )
= ( bit1 @ SV128 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[667]) ).
thf(762,plain,
! [SV48: $i] :
( ( ( ~ ( ~ ( number @ SV48 )
| ~ ( semiring @ SV48 ) ) )
= $false )
| ( ( ! [SY270: $i,SY271: $i,SY272: $i] :
( ( times_times @ SV48 @ ( number_number_of @ SV48 @ SY270 ) @ ( plus_plus @ SV48 @ SY271 @ SY272 ) )
= ( plus_plus @ SV48 @ ( times_times @ SV48 @ ( number_number_of @ SV48 @ SY270 ) @ SY271 ) @ ( times_times @ SV48 @ ( number_number_of @ SV48 @ SY270 ) @ SY272 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[668]) ).
thf(763,plain,
! [SV129: $i,SV49: $i,SV165: $i] :
( ( ~ ( linordered_idom @ SV165 )
| ~ ( ~ ( ~ ( ord_less @ SV165 @ ( ti @ SV165 @ SV49 ) @ SV129 )
| ( ord_less @ SV165 @ SV49 @ SV129 ) )
| ~ ( ~ ( ord_less @ SV165 @ SV49 @ SV129 )
| ( ord_less @ SV165 @ ( ti @ SV165 @ SV49 ) @ SV129 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[669]) ).
thf(764,plain,
! [SV130: $i,SV50: $i] :
( ( ( ~ ( ord_less @ int @ SV50 @ SV130 ) )
= $true )
| ( ( ord_less_eq @ int @ ( plus_plus @ int @ SV50 @ ( one_one @ int ) ) @ SV130 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[670]) ).
thf(765,plain,
! [SV131: $i,SV51: $i,SV166: $i] :
( ( ~ ( linordered_idom @ SV166 )
| ~ ( ~ ( ~ ( ord_less @ SV166 @ SV51 @ ( ti @ SV166 @ SV131 ) )
| ( ord_less @ SV166 @ SV51 @ SV131 ) )
| ~ ( ~ ( ord_less @ SV166 @ SV51 @ SV131 )
| ( ord_less @ SV166 @ SV51 @ ( ti @ SV166 @ SV131 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[671]) ).
thf(766,plain,
! [SV132: $i,SV52: $i,SV167: $i] :
( ( ~ ~ ( ~ ( number @ SV167 )
| ~ ( semiring @ SV167 ) )
| ( ( plus_plus @ SV167 @ SV52 @ ( ti @ SV167 @ SV132 ) )
= ( plus_plus @ SV167 @ SV52 @ SV132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[672]) ).
thf(767,plain,
! [SV53: $i] :
( ( ( number @ SV53 )
= $false )
| ( ( ! [SY280: $i,SY281: $i] :
~ ( ~ ( ( ( number_number_of @ SV53 @ SY280 )
!= ( ti @ SV53 @ SY281 ) )
| ( ( ti @ SV53 @ SY281 )
= ( number_number_of @ SV53 @ SY280 ) ) )
| ~ ( ( ( ti @ SV53 @ SY281 )
!= ( number_number_of @ SV53 @ SY280 ) )
| ( ( number_number_of @ SV53 @ SY280 )
= ( ti @ SV53 @ SY281 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[673]) ).
thf(768,plain,
! [SV54: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( one_one @ int ) @ SV54 )
| ( ord_less @ int @ ( zero_zero @ int ) @ SV54 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[674]) ).
thf(769,plain,
! [SV54: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV54 )
| ( ord_less_eq @ int @ ( one_one @ int ) @ SV54 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[674]) ).
thf(770,plain,
! [SV133: $i,SV55: $i,SV168: $i] :
( ( ~ ~ ( ~ ( number @ SV168 )
| ~ ( semiring @ SV168 ) )
| ( ( plus_plus @ SV168 @ ( ti @ SV168 @ SV55 ) @ SV133 )
= ( plus_plus @ SV168 @ SV55 @ SV133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[675]) ).
thf(771,plain,
! [SV134: $i,SV56: $i,SV169: $i] :
( ( ~ ( semiring_1 @ SV169 )
| ( ( ti @ SV169 @ ( power_power @ SV169 @ SV56 @ SV134 ) )
= ( power_power @ SV169 @ SV56 @ SV134 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[676]) ).
thf(772,plain,
! [SV57: $i] :
( ( ( number_ring @ SV57 )
= $false )
| ( ( ! [SY286: $i] :
( ( plus_plus @ SV57 @ ( number_number_of @ SV57 @ SY286 ) @ ( one_one @ SV57 ) )
= ( number_number_of @ SV57 @ ( plus_plus @ int @ SY286 @ ( bit1 @ pls ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[677]) ).
thf(773,plain,
! [SV58: $i] :
( ( ( number_ring @ SV58 )
= $false )
| ( ( ! [SY287: $i,SY288: $i] :
( ( number_number_of @ SV58 @ ( times_times @ int @ SY287 @ SY288 ) )
= ( times_times @ SV58 @ ( number_number_of @ SV58 @ SY287 ) @ ( number_number_of @ SV58 @ SY288 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[678]) ).
thf(774,plain,
! [SV59: $i] :
( ( ( linordered_idom @ SV59 )
= $false )
| ( ( ! [SY289: $i,SY290: $i] :
~ ( ~ ( ~ ( ord_less @ SV59 @ ( zero_zero @ SV59 ) @ ( plus_plus @ SV59 @ ( power_power @ SV59 @ SY289 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV59 @ SY290 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
| ( ( ti @ SV59 @ SY289 )
!= ( zero_zero @ SV59 ) )
| ( ( ti @ SV59 @ SY290 )
!= ( zero_zero @ SV59 ) ) )
| ~ ( ~ ( ( ( ti @ SV59 @ SY289 )
!= ( zero_zero @ SV59 ) )
| ( ( ti @ SV59 @ SY290 )
!= ( zero_zero @ SV59 ) ) )
| ( ord_less @ SV59 @ ( zero_zero @ SV59 ) @ ( plus_plus @ SV59 @ ( power_power @ SV59 @ SY289 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV59 @ SY290 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[679]) ).
thf(775,plain,
! [SV135: $i,SV60: $i] :
( ( ~ ( ( ( bit0 @ SV60 )
!= ( bit0 @ SV135 ) )
| ( SV60 = SV135 ) )
| ~ ( ( SV60 != SV135 )
| ( ( bit0 @ SV60 )
= ( bit0 @ SV135 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[680]) ).
thf(776,plain,
! [SV136: $i,SV61: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SV61 ) @ ( bit1 @ SV136 ) )
| ( ord_less_eq @ int @ SV61 @ SV136 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV61 @ SV136 )
| ( ord_less @ int @ ( bit0 @ SV61 ) @ ( bit1 @ SV136 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[681]) ).
thf(777,plain,
! [SV137: $i,SV62: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( bit0 @ SV62 ) @ ( bit1 @ SV137 ) )
| ( ord_less_eq @ int @ SV62 @ SV137 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV62 @ SV137 )
| ( ord_less_eq @ int @ ( bit0 @ SV62 ) @ ( bit1 @ SV137 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[682]) ).
thf(778,plain,
! [SV138: $i,SV63: $i,SV170: $i] :
( ( ~ ~ ( ~ ( number @ SV170 )
| ~ ( linorder @ SV170 ) )
| ~ ( ~ ( ~ ( ord_less @ SV170 @ SV63 @ ( ti @ SV170 @ SV138 ) )
| ( ord_less @ SV170 @ SV63 @ SV138 ) )
| ~ ( ~ ( ord_less @ SV170 @ SV63 @ SV138 )
| ( ord_less @ SV170 @ SV63 @ ( ti @ SV170 @ SV138 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[683]) ).
thf(779,plain,
! [SV64: $i] :
( ( ( semiring_1 @ SV64 )
= $false )
| ( ( ( power_power @ SV64 @ ( zero_zero @ SV64 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SV64 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[684]) ).
thf(780,plain,
! [SV139: $i,SV65: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV65 @ SV139 )
| ~ ( ~ ( ord_less_eq @ int @ SV65 @ SV139 )
| ~ ( ( SV65 != SV139 ) ) ) )
| ~ ( ~ ~ ( ~ ( ord_less_eq @ int @ SV65 @ SV139 )
| ~ ( ( SV65 != SV139 ) ) )
| ( ord_less @ int @ SV65 @ SV139 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[685]) ).
thf(781,plain,
! [SV66: $i] :
( ( ~ ( ~ ( twoSqu33214720sum2sq @ ( ti @ int @ SV66 ) )
| ( twoSqu33214720sum2sq @ SV66 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[686]) ).
thf(782,plain,
! [SV66: $i] :
( ( ~ ( ~ ( twoSqu33214720sum2sq @ SV66 )
| ( twoSqu33214720sum2sq @ ( ti @ int @ SV66 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[686]) ).
thf(783,plain,
! [SV67: $i] :
( ( ( number_ring @ SV67 )
= $false )
| ( ( ! [SY297: $i,SY298: $i,SY299: $i] :
( ( times_times @ SV67 @ ( number_number_of @ SV67 @ SY297 ) @ ( times_times @ SV67 @ ( number_number_of @ SV67 @ SY298 ) @ SY299 ) )
= ( times_times @ SV67 @ ( number_number_of @ SV67 @ ( times_times @ int @ SY297 @ SY298 ) ) @ SY299 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[687]) ).
thf(784,plain,
! [SV68: $i] :
( ( ( ~ ( ~ ( number_ring @ SV68 )
| ~ ( linordered_idom @ SV68 ) ) )
= $false )
| ( ( ! [SY300: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV68 @ ( zero_zero @ SV68 ) @ ( number_number_of @ SV68 @ SY300 ) )
| ( ord_less_eq @ int @ pls @ SY300 ) )
| ~ ( ~ ( ord_less_eq @ int @ pls @ SY300 )
| ( ord_less_eq @ SV68 @ ( zero_zero @ SV68 ) @ ( number_number_of @ SV68 @ SY300 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[688]) ).
thf(785,plain,
! [SV69: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ pls @ ( bit0 @ SV69 ) )
| ( ord_less_eq @ int @ pls @ SV69 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[689]) ).
thf(786,plain,
! [SV69: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ pls @ SV69 )
| ( ord_less_eq @ int @ pls @ ( bit0 @ SV69 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[689]) ).
thf(787,plain,
! [SV70: $i] :
( ( ( ~ ( ~ ( number_ring @ SV70 )
| ~ ( linordered_idom @ SV70 ) ) )
= $false )
| ( ( ! [SY301: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV70 @ ( number_number_of @ SV70 @ SY301 ) @ ( zero_zero @ SV70 ) )
| ( ord_less_eq @ int @ SY301 @ pls ) )
| ~ ( ~ ( ord_less_eq @ int @ SY301 @ pls )
| ( ord_less_eq @ SV70 @ ( number_number_of @ SV70 @ SY301 ) @ ( zero_zero @ SV70 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[690]) ).
thf(788,plain,
! [SV140: $i,SV71: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( bit0 @ SV71 ) @ ( bit0 @ SV140 ) )
| ( ord_less_eq @ int @ SV71 @ SV140 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV71 @ SV140 )
| ( ord_less_eq @ int @ ( bit0 @ SV71 ) @ ( bit0 @ SV140 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[691]) ).
thf(789,plain,
! [SV72: $i] :
( ( ~ ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ ( number_number_of @ nat @ SV72 ) )
| ( ord_less @ int @ pls @ SV72 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[692]) ).
thf(790,plain,
! [SV72: $i] :
( ( ~ ( ~ ( ord_less @ int @ pls @ SV72 )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ ( number_number_of @ nat @ SV72 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[692]) ).
thf(791,plain,
! [SV73: $i] :
( ( ( ~ ( ~ ( number_ring @ SV73 )
| ~ ( linordered_idom @ SV73 ) ) )
= $false )
| ( ( ! [SY303: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV73 @ ( number_number_of @ SV73 @ SY303 ) @ ( one_one @ SV73 ) )
| ( ord_less_eq @ int @ SY303 @ ( bit1 @ pls ) ) )
| ~ ( ~ ( ord_less_eq @ int @ SY303 @ ( bit1 @ pls ) )
| ( ord_less_eq @ SV73 @ ( number_number_of @ SV73 @ SY303 ) @ ( one_one @ SV73 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[693]) ).
thf(792,plain,
! [SV74: $i] :
( ( ( number_ring @ SV74 )
= $false )
| ( ( ! [SY304: $i] :
( ( plus_plus @ SV74 @ ( one_one @ SV74 ) @ ( number_number_of @ SV74 @ SY304 ) )
= ( number_number_of @ SV74 @ ( plus_plus @ int @ ( bit1 @ pls ) @ SY304 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[694]) ).
thf(793,plain,
! [SV141: $i,SV75: $i,SV171: $i] :
( ( ~ ~ ( ~ ( number @ SV171 )
| ~ ( semiring @ SV171 ) )
| ( ( ti @ SV171 @ ( plus_plus @ SV171 @ SV75 @ SV141 ) )
= ( plus_plus @ SV171 @ SV75 @ SV141 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[695]) ).
thf(794,plain,
! [SV76: $i] :
( ( ~ ( ~ ( zprime @ ( ti @ int @ SV76 ) )
| ( zprime @ SV76 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[696]) ).
thf(795,plain,
! [SV76: $i] :
( ( ~ ( ~ ( zprime @ SV76 )
| ( zprime @ ( ti @ int @ SV76 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[696]) ).
thf(796,plain,
! [SV142: $i,SV77: $i,SV172: $i] :
( ( ~ ( semiring_1 @ SV172 )
| ( ( power_power @ SV172 @ ( ti @ SV172 @ SV77 ) @ SV142 )
= ( power_power @ SV172 @ SV77 @ SV142 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[697]) ).
thf(797,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_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[698]) ).
thf(798,plain,
! [SV78: $i] :
( ( ( semiring_1 @ SV78 )
= $false )
| ( ( ( power_power @ SV78 @ ( one_one @ SV78 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( one_one @ SV78 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[699]) ).
thf(799,plain,
! [SV79: $i] :
( ( ( ~ ( ~ ( number @ SV79 )
| ~ ( linorder @ SV79 ) ) )
= $false )
| ( ( ! [SY309: $i,SY310: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV79 @ ( number_number_of @ SV79 @ SY309 ) @ ( number_number_of @ SV79 @ SY310 ) )
| ~ ( ord_less @ SV79 @ ( number_number_of @ SV79 @ SY310 ) @ ( number_number_of @ SV79 @ SY309 ) ) )
| ~ ( ~ ~ ( ord_less @ SV79 @ ( number_number_of @ SV79 @ SY310 ) @ ( number_number_of @ SV79 @ SY309 ) )
| ( ord_less_eq @ SV79 @ ( number_number_of @ SV79 @ SY309 ) @ ( number_number_of @ SV79 @ SY310 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[701]) ).
thf(800,plain,
! [SV143: $i,SV80: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV80 @ ( plus_plus @ int @ SV143 @ ( one_one @ int ) ) )
| ( ord_less_eq @ int @ SV80 @ SV143 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV80 @ SV143 )
| ( ord_less @ int @ SV80 @ ( plus_plus @ int @ SV143 @ ( one_one @ int ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[702]) ).
thf(801,plain,
! [SV144: $i,SV81: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SV81 ) @ ( bit1 @ SV144 ) )
| ( ord_less_eq @ int @ SV81 @ SV144 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV81 @ SV144 )
| ( ord_less @ int @ ( bit0 @ SV81 ) @ ( bit1 @ SV144 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[703]) ).
thf(802,plain,
! [SV145: $i,SV82: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV82 @ SV145 ) )
= $true )
| ( ( ~ ( ord_less_eq @ int @ SV145 @ SV82 )
| ( SV82 = SV145 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[704]) ).
thf(803,plain,
! [SV83: $i] :
( ( ~ ( ( ( zero_zero @ nat )
!= ( number_number_of @ nat @ SV83 ) )
| ( ord_less_eq @ int @ SV83 @ pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[705]) ).
thf(804,plain,
! [SV83: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ SV83 @ pls )
| ( ( zero_zero @ nat )
= ( number_number_of @ nat @ SV83 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[705]) ).
thf(805,plain,
! [SV84: $i] :
( ( ( linordered_ring @ SV84 )
= $false )
| ( ( ! [SY314: $i,SY315: $i] : ( ord_less_eq @ SV84 @ ( zero_zero @ SV84 ) @ ( plus_plus @ SV84 @ ( times_times @ SV84 @ SY314 @ SY314 ) @ ( times_times @ SV84 @ SY315 @ SY315 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[706]) ).
thf(806,plain,
! [SV146: $i,SV85: $i,SV173: $i] :
( ( ~ ( linordered_ring @ SV173 )
| ( ( plus_plus @ SV173 @ SV85 @ ( ti @ SV173 @ SV146 ) )
= ( plus_plus @ SV173 @ SV85 @ SV146 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[707]) ).
thf(807,plain,
! [SV86: $i,SV147: $i] :
( ( ( ~ ( number @ SV147 ) )
= $true )
| ( ( ( number_number_of @ SV147 @ ( ti @ int @ SV86 ) )
= ( number_number_of @ SV147 @ SV86 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[708]) ).
thf(808,plain,
! [SV148: $i,SV87: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SV87 ) @ ( bit0 @ SV148 ) )
| ( ord_less @ int @ SV87 @ SV148 ) )
| ~ ( ~ ( ord_less @ int @ SV87 @ SV148 )
| ( ord_less_eq @ int @ ( bit1 @ SV87 ) @ ( bit0 @ SV148 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[709]) ).
thf(809,plain,
! [SV88: $i] :
( ( ( ~ ( ~ ( number @ SV88 )
| ~ ( semiring @ SV88 ) ) )
= $false )
| ( ( ! [SY320: $i,SY321: $i,SY322: $i] :
( ( times_times @ SV88 @ ( plus_plus @ SV88 @ SY320 @ SY321 ) @ ( number_number_of @ SV88 @ SY322 ) )
= ( plus_plus @ SV88 @ ( times_times @ SV88 @ SY320 @ ( number_number_of @ SV88 @ SY322 ) ) @ ( times_times @ SV88 @ SY321 @ ( number_number_of @ SV88 @ SY322 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[710]) ).
thf(810,plain,
! [SV89: $i] :
( ( ~ ( ( ( number_number_of @ nat @ SV89 )
!= ( zero_zero @ nat ) )
| ( ord_less_eq @ int @ SV89 @ pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[711]) ).
thf(811,plain,
! [SV89: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ SV89 @ pls )
| ( ( number_number_of @ nat @ SV89 )
= ( zero_zero @ nat ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[711]) ).
thf(812,plain,
! [SV90: $i,SV174: $i,SV149: $i] :
( ( ~ ( ord_less_eq @ int @ SV149 @ SV174 )
| ~ ( ord_less_eq @ int @ SV174 @ SV90 )
| ( ord_less_eq @ int @ SV149 @ SV90 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[712]) ).
thf(813,plain,
! [SV150: $i,SV91: $i,SV175: $i] :
( ( ~ ~ ( ~ ( number @ SV175 )
| ~ ( linorder @ SV175 ) )
| ~ ( ~ ( ~ ( ord_less @ SV175 @ ( ti @ SV175 @ SV91 ) @ SV150 )
| ( ord_less @ SV175 @ SV91 @ SV150 ) )
| ~ ( ~ ( ord_less @ SV175 @ SV91 @ SV150 )
| ( ord_less @ SV175 @ ( ti @ SV175 @ SV91 ) @ SV150 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[713]) ).
thf(814,plain,
! [SV151: $i,SV92: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SV92 ) @ ( bit1 @ SV151 ) )
| ( ord_less_eq @ int @ SV92 @ SV151 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV92 @ SV151 )
| ( ord_less_eq @ int @ ( bit1 @ SV92 ) @ ( bit1 @ SV151 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[714]) ).
thf(815,plain,
! [SV93: $i,SV176: $i,SV152: $i] :
( ( ~ ( ord_less_eq @ int @ SV152 @ SV176 )
| ( ord_less_eq @ int @ ( plus_plus @ int @ SV93 @ SV152 ) @ ( plus_plus @ int @ SV93 @ SV176 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[715]) ).
thf(816,plain,
! [SV94: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SV94 ) @ pls )
| ( ord_less @ int @ SV94 @ pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[716]) ).
thf(817,plain,
! [SV94: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV94 @ pls )
| ( ord_less_eq @ int @ ( bit1 @ SV94 ) @ pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[716]) ).
thf(818,plain,
! [SV95: $i] :
( ( ( linordered_idom @ SV95 )
= $false )
| ( ( ! [SY330: $i,SY331: $i] :
~ ( ord_less @ SV95 @ ( plus_plus @ SV95 @ ( power_power @ SV95 @ SY330 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV95 @ SY331 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( zero_zero @ SV95 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[717]) ).
thf(819,plain,
! [SV153: $i,SV96: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( number_number_of @ int @ SV96 ) @ ( number_number_of @ int @ SV153 ) )
| ( ord_less @ int @ SV96 @ SV153 ) )
| ~ ( ~ ( ord_less @ int @ SV96 @ SV153 )
| ( ord_less @ int @ ( number_number_of @ int @ SV96 ) @ ( number_number_of @ int @ SV153 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[718]) ).
thf(820,plain,
! [SV97: $i] :
( ( ( linord581940658strict @ SV97 )
= $false )
| ( ( ! [SY333: $i,SY334: $i] :
~ ( ~ ( ( ( plus_plus @ SV97 @ ( times_times @ SV97 @ SY333 @ SY333 ) @ ( times_times @ SV97 @ SY334 @ SY334 ) )
!= ( zero_zero @ SV97 ) )
| ~ ( ( ( ti @ SV97 @ SY333 )
!= ( zero_zero @ SV97 ) )
| ( ( ti @ SV97 @ SY334 )
!= ( zero_zero @ SV97 ) ) ) )
| ~ ( ~ ~ ( ( ( ti @ SV97 @ SY333 )
!= ( zero_zero @ SV97 ) )
| ( ( ti @ SV97 @ SY334 )
!= ( zero_zero @ SV97 ) ) )
| ( ( plus_plus @ SV97 @ ( times_times @ SV97 @ SY333 @ SY333 ) @ ( times_times @ SV97 @ SY334 @ SY334 ) )
= ( zero_zero @ SV97 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[719]) ).
thf(821,plain,
! [SV154: $i,SV98: $i,SV177: $i] :
( ( ! [SY365: $i] :
( ~ ( ord_less @ int @ SV177 @ SY365 )
| ~ ( ord_less_eq @ int @ SV98 @ SV154 )
| ( ord_less @ int @ ( plus_plus @ int @ SV177 @ SV98 ) @ ( plus_plus @ int @ SY365 @ SV154 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[720]) ).
thf(822,plain,
! [SV99: $i] :
( ( ( ~ ( ~ ( number_ring @ SV99 )
| ~ ( linordered_idom @ SV99 ) ) )
= $false )
| ( ( ! [SY338: $i,SY339: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV99 @ ( number_number_of @ SV99 @ SY338 ) @ ( number_number_of @ SV99 @ SY339 ) )
| ( ord_less_eq @ int @ SY338 @ SY339 ) )
| ~ ( ~ ( ord_less_eq @ int @ SY338 @ SY339 )
| ( ord_less_eq @ SV99 @ ( number_number_of @ SV99 @ SY338 ) @ ( number_number_of @ SV99 @ SY339 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[721]) ).
thf(823,plain,
! [SV100: $i] :
( ( ( semiring_1 @ SV100 )
= $false )
| ( ( ( ti @ SV100 @ ( zero_zero @ SV100 ) )
= ( zero_zero @ SV100 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[722]) ).
thf(824,plain,
! [SV155: $i,SV101: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( bit0 @ SV101 ) @ ( bit1 @ SV155 ) )
| ( ord_less_eq @ int @ SV101 @ SV155 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV101 @ SV155 )
| ( ord_less_eq @ int @ ( bit0 @ SV101 ) @ ( bit1 @ SV155 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[723]) ).
thf(825,plain,
! [SV102: $i] :
( ( ( semiring_1 @ SV102 )
= $false )
| ( ( ( ti @ SV102 @ ( one_one @ SV102 ) )
= ( one_one @ SV102 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[724]) ).
thf(826,plain,
! [SV103: $i] :
( ( ( ~ ( ~ ( number_ring @ SV103 )
| ~ ( linordered_idom @ SV103 ) ) )
= $false )
| ( ( ! [SY341: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV103 @ ( one_one @ SV103 ) @ ( number_number_of @ SV103 @ SY341 ) )
| ( ord_less_eq @ int @ ( bit1 @ pls ) @ SY341 ) )
| ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ pls ) @ SY341 )
| ( ord_less_eq @ SV103 @ ( one_one @ SV103 ) @ ( number_number_of @ SV103 @ SY341 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[725]) ).
thf(827,plain,
! [SV113: $i,SV19: $i] :
( ( ( ord_less @ int @ SV19 @ SV113 )
= $true )
| ( ( SV19 = SV113 )
= $true )
| ( ( ord_less @ int @ SV113 @ SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[731]) ).
thf(828,plain,
! [SV178: $i,SV23: $i] :
( ( ( ! [SY366: $i] :
~ ( ~ ( ( ( plus_plus @ SV23 @ ( power_power @ SV23 @ SV178 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV23 @ SY366 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV23 ) )
| ~ ( ( ( ti @ SV23 @ SV178 )
!= ( zero_zero @ SV23 ) )
| ( ( ti @ SV23 @ SY366 )
!= ( zero_zero @ SV23 ) ) ) )
| ~ ( ~ ~ ( ( ( ti @ SV23 @ SV178 )
!= ( zero_zero @ SV23 ) )
| ( ( ti @ SV23 @ SY366 )
!= ( zero_zero @ SV23 ) ) )
| ( ( plus_plus @ SV23 @ ( power_power @ SV23 @ SV178 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV23 @ SY366 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV23 ) ) ) ) )
= $true )
| ( ( linordered_idom @ SV23 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[734]) ).
thf(829,plain,
! [SV24: $i,SV179: $i] :
( ( ( ! [SY367: $i] :
( ~ ( ord_less_eq @ int @ pls @ SY367 )
| ~ ( ord_less_eq @ int @ pls @ SV179 )
| ( ( plus_plus @ SV24 @ ( number_number_of @ SV24 @ SY367 ) @ ( number_number_of @ SV24 @ SV179 ) )
= ( number_number_of @ SV24 @ ( plus_plus @ int @ SY367 @ SV179 ) ) ) ) )
= $true )
| ( ( number_semiring @ SV24 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[735]) ).
thf(830,plain,
! [SV117: $i,SV25: $i,SV162: $i] :
( ( ( ~ ( linordered_ring @ SV162 ) )
= $true )
| ( ( ( ti @ SV162 @ ( plus_plus @ SV162 @ SV25 @ SV117 ) )
= ( plus_plus @ SV162 @ SV25 @ SV117 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[736]) ).
thf(831,plain,
! [SV118: $i,SV26: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( plus_plus @ int @ SV26 @ ( one_one @ int ) ) @ SV118 )
| ( ord_less @ int @ SV26 @ SV118 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[737]) ).
thf(832,plain,
! [SV118: $i,SV26: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV26 @ SV118 )
| ( ord_less_eq @ int @ ( plus_plus @ int @ SV26 @ ( one_one @ int ) ) @ SV118 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[737]) ).
thf(833,plain,
! [SV119: $i,SV28: $i] :
( ( ~ ( ~ ( ord_less @ nat @ ( number_number_of @ nat @ SV28 ) @ ( number_number_of @ nat @ SV119 ) )
| ~ ( ~ ( ~ ( ord_less @ int @ SV28 @ SV119 )
| ( ord_less @ int @ pls @ SV119 ) )
| ~ ( ord_less @ int @ SV28 @ SV119 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[739]) ).
thf(834,plain,
! [SV119: $i,SV28: $i] :
( ( ~ ( ~ ~ ( ~ ( ~ ( ord_less @ int @ SV28 @ SV119 )
| ( ord_less @ int @ pls @ SV119 ) )
| ~ ( ord_less @ int @ SV28 @ SV119 ) )
| ( ord_less @ nat @ ( number_number_of @ nat @ SV28 ) @ ( number_number_of @ nat @ SV119 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[739]) ).
thf(835,plain,
! [SV120: $i,SV29: $i,SV163: $i] :
( ( ( ~ ( semiring_1 @ SV163 ) )
= $true )
| ( ( ( power_power @ SV163 @ SV29 @ ( ti @ nat @ SV120 ) )
= ( power_power @ SV163 @ SV29 @ SV120 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[740]) ).
thf(836,plain,
! [SV30: $i,SV121: $i] :
( ( ( number @ SV121 )
= $false )
| ( ( ( ti @ SV121 @ ( number_number_of @ SV121 @ SV30 ) )
= ( number_number_of @ SV121 @ SV30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[741]) ).
thf(837,plain,
! [SV180: $i,SV32: $i] :
( ( ( ~ ( ord_less @ SV32 @ ( power_power @ SV32 @ SV180 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( zero_zero @ SV32 ) ) )
= $true )
| ( ( linordered_idom @ SV32 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[743]) ).
thf(838,plain,
! [SV33: $i] :
( ( ( ~ ( number_ring @ SV33 )
| ~ ( ring_char_0 @ SV33 ) )
= $true )
| ( ( ! [SY254: $i,SY255: $i] :
~ ( ~ ( ( ( number_number_of @ SV33 @ SY254 )
!= ( number_number_of @ SV33 @ SY255 ) )
| ( SY254 = SY255 ) )
| ~ ( ( SY254 != SY255 )
| ( ( number_number_of @ SV33 @ SY254 )
= ( number_number_of @ SV33 @ SY255 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[744]) ).
thf(839,plain,
! [SV34: $i] :
( ( ~ ( ord_less @ int @ pls @ ( bit1 @ SV34 ) )
| ( ord_less_eq @ int @ pls @ SV34 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[745]) ).
thf(840,plain,
! [SV34: $i] :
( ( ~ ( ord_less_eq @ int @ pls @ SV34 )
| ( ord_less @ int @ pls @ ( bit1 @ SV34 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[746]) ).
thf(841,plain,
! [SV181: $i,SV35: $i] :
( ( ( ~ ( ~ ( ( ( power_power @ SV35 @ SV181 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= ( zero_zero @ SV35 ) )
| ( ( ti @ SV35 @ SV181 )
= ( zero_zero @ SV35 ) ) )
| ~ ( ( ( ti @ SV35 @ SV181 )
!= ( zero_zero @ SV35 ) )
| ( ( power_power @ SV35 @ SV181 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SV35 ) ) ) ) )
= $true )
| ( ( ring_11004092258visors @ SV35 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[747]) ).
thf(842,plain,
! [SV182: $i,SV36: $i] :
( ( ( ! [SY368: $i] :
( ( times_times @ SV36 @ ( number_number_of @ SV36 @ SV182 ) @ ( number_number_of @ SV36 @ SY368 ) )
= ( number_number_of @ SV36 @ ( times_times @ int @ SV182 @ SY368 ) ) ) )
= $true )
| ( ( number_ring @ SV36 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[748]) ).
thf(843,plain,
! [SV37: $i] :
( ( ~ ( ord_less_eq @ int @ pls @ ( bit1 @ SV37 ) )
| ( ord_less_eq @ int @ pls @ SV37 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[749]) ).
thf(844,plain,
! [SV37: $i] :
( ( ~ ( ord_less_eq @ int @ pls @ SV37 )
| ( ord_less_eq @ int @ pls @ ( bit1 @ SV37 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[750]) ).
thf(845,plain,
! [SV122: $i,SV38: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SV38 ) @ ( bit1 @ SV122 ) )
| ( ord_less_eq @ int @ SV38 @ SV122 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[751]) ).
thf(846,plain,
! [SV122: $i,SV38: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ SV38 @ SV122 )
| ( ord_less_eq @ int @ ( bit1 @ SV38 ) @ ( bit1 @ SV122 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[751]) ).
thf(847,plain,
! [SV123: $i,SV39: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SV39 ) @ ( bit0 @ SV123 ) )
| ( ord_less @ int @ SV39 @ SV123 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[752]) ).
thf(848,plain,
! [SV123: $i,SV39: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV39 @ SV123 )
| ( ord_less_eq @ int @ ( bit1 @ SV39 ) @ ( bit0 @ SV123 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[752]) ).
thf(849,plain,
! [SV40: $i,SV124: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV124 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV124 ) @ ( number_number_of @ nat @ SV40 ) )
= ( number_number_of @ nat @ SV40 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[753]) ).
thf(850,plain,
! [SV40: $i,SV124: $i] :
( ( ~ ( ~ ~ ( ord_less @ int @ SV124 @ pls )
| ~ ( ~ ( ~ ( ord_less @ int @ SV40 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV124 ) @ ( number_number_of @ nat @ SV40 ) )
= ( number_number_of @ nat @ SV124 ) ) )
| ~ ( ~ ~ ( ord_less @ int @ SV40 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV124 ) @ ( number_number_of @ nat @ SV40 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SV124 @ SV40 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[753]) ).
thf(851,plain,
! [SV125: $i,SV41: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( number_number_of @ int @ SV41 ) @ ( number_number_of @ int @ SV125 ) )
| ( ord_less_eq @ int @ SV41 @ SV125 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[754]) ).
thf(852,plain,
! [SV125: $i,SV41: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ SV41 @ SV125 )
| ( ord_less_eq @ int @ ( number_number_of @ int @ SV41 ) @ ( number_number_of @ int @ SV125 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[754]) ).
thf(853,plain,
! [SV42: $i,SV183: $i] :
( ( ( ! [SY369: $i] :
( ~ ( ord_less_eq @ int @ pls @ SY369 )
| ~ ( ord_less_eq @ int @ pls @ SV183 )
| ( ( times_times @ SV42 @ ( number_number_of @ SV42 @ SY369 ) @ ( number_number_of @ SV42 @ SV183 ) )
= ( number_number_of @ SV42 @ ( times_times @ int @ SY369 @ SV183 ) ) ) ) )
= $true )
| ( ( number_semiring @ SV42 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[755]) ).
thf(854,plain,
! [SV126: $i,SV43: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( bit0 @ SV43 ) @ ( bit0 @ SV126 ) )
| ( ord_less_eq @ int @ SV43 @ SV126 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[756]) ).
thf(855,plain,
! [SV126: $i,SV43: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ SV43 @ SV126 )
| ( ord_less_eq @ int @ ( bit0 @ SV43 ) @ ( bit0 @ SV126 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[756]) ).
thf(856,plain,
! [SV127: $i,SV44: $i,SV164: $i] :
( ( ( ~ ( linordered_ring @ SV164 ) )
= $true )
| ( ( ( plus_plus @ SV164 @ ( ti @ SV164 @ SV44 ) @ SV127 )
= ( plus_plus @ SV164 @ SV44 @ SV127 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[757]) ).
thf(857,plain,
! [SV184: $i,SV45: $i] :
( ( ( ~ ( ~ ( ~ ( ord_less @ SV45 @ ( zero_zero @ SV45 ) @ ( power_power @ SV45 @ SV184 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ( ( ti @ SV45 @ SV184 )
!= ( zero_zero @ SV45 ) ) )
| ~ ( ~ ( ( ( ti @ SV45 @ SV184 )
!= ( zero_zero @ SV45 ) ) )
| ( ord_less @ SV45 @ ( zero_zero @ SV45 ) @ ( power_power @ SV45 @ SV184 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) )
= $true )
| ( ( linordered_idom @ SV45 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[758]) ).
thf(858,plain,
! [SV46: $i] :
( ( ~ ( ord_less_eq @ int @ ( bit0 @ SV46 ) @ pls )
| ( ord_less_eq @ int @ SV46 @ pls ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[759]) ).
thf(859,plain,
! [SV46: $i] :
( ( ~ ( ord_less_eq @ int @ SV46 @ pls )
| ( ord_less_eq @ int @ ( bit0 @ SV46 ) @ pls ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[760]) ).
thf(860,plain,
! [SV128: $i,SV47: $i] :
( ( ~ ( ( ( bit1 @ SV47 )
!= ( bit1 @ SV128 ) )
| ( SV47 = SV128 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[761]) ).
thf(861,plain,
! [SV128: $i,SV47: $i] :
( ( ~ ( ( SV47 != SV128 )
| ( ( bit1 @ SV47 )
= ( bit1 @ SV128 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[761]) ).
thf(862,plain,
! [SV48: $i] :
( ( ( ~ ( number @ SV48 )
| ~ ( semiring @ SV48 ) )
= $true )
| ( ( ! [SY270: $i,SY271: $i,SY272: $i] :
( ( times_times @ SV48 @ ( number_number_of @ SV48 @ SY270 ) @ ( plus_plus @ SV48 @ SY271 @ SY272 ) )
= ( plus_plus @ SV48 @ ( times_times @ SV48 @ ( number_number_of @ SV48 @ SY270 ) @ SY271 ) @ ( times_times @ SV48 @ ( number_number_of @ SV48 @ SY270 ) @ SY272 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[762]) ).
thf(863,plain,
! [SV129: $i,SV49: $i,SV165: $i] :
( ( ( ~ ( linordered_idom @ SV165 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( ord_less @ SV165 @ ( ti @ SV165 @ SV49 ) @ SV129 )
| ( ord_less @ SV165 @ SV49 @ SV129 ) )
| ~ ( ~ ( ord_less @ SV165 @ SV49 @ SV129 )
| ( ord_less @ SV165 @ ( ti @ SV165 @ SV49 ) @ SV129 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[763]) ).
thf(864,plain,
! [SV130: $i,SV50: $i] :
( ( ( ord_less @ int @ SV50 @ SV130 )
= $false )
| ( ( ord_less_eq @ int @ ( plus_plus @ int @ SV50 @ ( one_one @ int ) ) @ SV130 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[764]) ).
thf(865,plain,
! [SV131: $i,SV51: $i,SV166: $i] :
( ( ( ~ ( linordered_idom @ SV166 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( ord_less @ SV166 @ SV51 @ ( ti @ SV166 @ SV131 ) )
| ( ord_less @ SV166 @ SV51 @ SV131 ) )
| ~ ( ~ ( ord_less @ SV166 @ SV51 @ SV131 )
| ( ord_less @ SV166 @ SV51 @ ( ti @ SV166 @ SV131 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[765]) ).
thf(866,plain,
! [SV132: $i,SV52: $i,SV167: $i] :
( ( ( ~ ~ ( ~ ( number @ SV167 )
| ~ ( semiring @ SV167 ) ) )
= $true )
| ( ( ( plus_plus @ SV167 @ SV52 @ ( ti @ SV167 @ SV132 ) )
= ( plus_plus @ SV167 @ SV52 @ SV132 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[766]) ).
thf(867,plain,
! [SV185: $i,SV53: $i] :
( ( ( ! [SY370: $i] :
~ ( ~ ( ( ( number_number_of @ SV53 @ SV185 )
!= ( ti @ SV53 @ SY370 ) )
| ( ( ti @ SV53 @ SY370 )
= ( number_number_of @ SV53 @ SV185 ) ) )
| ~ ( ( ( ti @ SV53 @ SY370 )
!= ( number_number_of @ SV53 @ SV185 ) )
| ( ( number_number_of @ SV53 @ SV185 )
= ( ti @ SV53 @ SY370 ) ) ) ) )
= $true )
| ( ( number @ SV53 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[767]) ).
thf(868,plain,
! [SV54: $i] :
( ( ~ ( ord_less_eq @ int @ ( one_one @ int ) @ SV54 )
| ( ord_less @ int @ ( zero_zero @ int ) @ SV54 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[768]) ).
thf(869,plain,
! [SV54: $i] :
( ( ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV54 )
| ( ord_less_eq @ int @ ( one_one @ int ) @ SV54 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[769]) ).
thf(870,plain,
! [SV133: $i,SV55: $i,SV168: $i] :
( ( ( ~ ~ ( ~ ( number @ SV168 )
| ~ ( semiring @ SV168 ) ) )
= $true )
| ( ( ( plus_plus @ SV168 @ ( ti @ SV168 @ SV55 ) @ SV133 )
= ( plus_plus @ SV168 @ SV55 @ SV133 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[770]) ).
thf(871,plain,
! [SV134: $i,SV56: $i,SV169: $i] :
( ( ( ~ ( semiring_1 @ SV169 ) )
= $true )
| ( ( ( ti @ SV169 @ ( power_power @ SV169 @ SV56 @ SV134 ) )
= ( power_power @ SV169 @ SV56 @ SV134 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[771]) ).
thf(872,plain,
! [SV186: $i,SV57: $i] :
( ( ( ( plus_plus @ SV57 @ ( number_number_of @ SV57 @ SV186 ) @ ( one_one @ SV57 ) )
= ( number_number_of @ SV57 @ ( plus_plus @ int @ SV186 @ ( bit1 @ pls ) ) ) )
= $true )
| ( ( number_ring @ SV57 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[772]) ).
thf(873,plain,
! [SV187: $i,SV58: $i] :
( ( ( ! [SY371: $i] :
( ( number_number_of @ SV58 @ ( times_times @ int @ SV187 @ SY371 ) )
= ( times_times @ SV58 @ ( number_number_of @ SV58 @ SV187 ) @ ( number_number_of @ SV58 @ SY371 ) ) ) )
= $true )
| ( ( number_ring @ SV58 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[773]) ).
thf(874,plain,
! [SV188: $i,SV59: $i] :
( ( ( ! [SY372: $i] :
~ ( ~ ( ~ ( ord_less @ SV59 @ ( zero_zero @ SV59 ) @ ( plus_plus @ SV59 @ ( power_power @ SV59 @ SV188 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV59 @ SY372 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
| ( ( ti @ SV59 @ SV188 )
!= ( zero_zero @ SV59 ) )
| ( ( ti @ SV59 @ SY372 )
!= ( zero_zero @ SV59 ) ) )
| ~ ( ~ ( ( ( ti @ SV59 @ SV188 )
!= ( zero_zero @ SV59 ) )
| ( ( ti @ SV59 @ SY372 )
!= ( zero_zero @ SV59 ) ) )
| ( ord_less @ SV59 @ ( zero_zero @ SV59 ) @ ( plus_plus @ SV59 @ ( power_power @ SV59 @ SV188 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV59 @ SY372 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) ) )
= $true )
| ( ( linordered_idom @ SV59 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[774]) ).
thf(875,plain,
! [SV135: $i,SV60: $i] :
( ( ~ ( ( ( bit0 @ SV60 )
!= ( bit0 @ SV135 ) )
| ( SV60 = SV135 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[775]) ).
thf(876,plain,
! [SV135: $i,SV60: $i] :
( ( ~ ( ( SV60 != SV135 )
| ( ( bit0 @ SV60 )
= ( bit0 @ SV135 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[775]) ).
thf(877,plain,
! [SV136: $i,SV61: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SV61 ) @ ( bit1 @ SV136 ) )
| ( ord_less_eq @ int @ SV61 @ SV136 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[776]) ).
thf(878,plain,
! [SV136: $i,SV61: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ SV61 @ SV136 )
| ( ord_less @ int @ ( bit0 @ SV61 ) @ ( bit1 @ SV136 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[776]) ).
thf(879,plain,
! [SV137: $i,SV62: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( bit0 @ SV62 ) @ ( bit1 @ SV137 ) )
| ( ord_less_eq @ int @ SV62 @ SV137 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[777]) ).
thf(880,plain,
! [SV137: $i,SV62: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ SV62 @ SV137 )
| ( ord_less_eq @ int @ ( bit0 @ SV62 ) @ ( bit1 @ SV137 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[777]) ).
thf(881,plain,
! [SV138: $i,SV63: $i,SV170: $i] :
( ( ( ~ ~ ( ~ ( number @ SV170 )
| ~ ( linorder @ SV170 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( ord_less @ SV170 @ SV63 @ ( ti @ SV170 @ SV138 ) )
| ( ord_less @ SV170 @ SV63 @ SV138 ) )
| ~ ( ~ ( ord_less @ SV170 @ SV63 @ SV138 )
| ( ord_less @ SV170 @ SV63 @ ( ti @ SV170 @ SV138 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[778]) ).
thf(882,plain,
! [SV139: $i,SV65: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV65 @ SV139 )
| ~ ( ~ ( ord_less_eq @ int @ SV65 @ SV139 )
| ~ ( ( SV65 != SV139 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[780]) ).
thf(883,plain,
! [SV139: $i,SV65: $i] :
( ( ~ ( ~ ~ ( ~ ( ord_less_eq @ int @ SV65 @ SV139 )
| ~ ( ( SV65 != SV139 ) ) )
| ( ord_less @ int @ SV65 @ SV139 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[780]) ).
thf(884,plain,
! [SV66: $i] :
( ( ~ ( twoSqu33214720sum2sq @ ( ti @ int @ SV66 ) )
| ( twoSqu33214720sum2sq @ SV66 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[781]) ).
thf(885,plain,
! [SV66: $i] :
( ( ~ ( twoSqu33214720sum2sq @ SV66 )
| ( twoSqu33214720sum2sq @ ( ti @ int @ SV66 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[782]) ).
thf(886,plain,
! [SV189: $i,SV67: $i] :
( ( ( ! [SY373: $i,SY374: $i] :
( ( times_times @ SV67 @ ( number_number_of @ SV67 @ SV189 ) @ ( times_times @ SV67 @ ( number_number_of @ SV67 @ SY373 ) @ SY374 ) )
= ( times_times @ SV67 @ ( number_number_of @ SV67 @ ( times_times @ int @ SV189 @ SY373 ) ) @ SY374 ) ) )
= $true )
| ( ( number_ring @ SV67 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[783]) ).
thf(887,plain,
! [SV68: $i] :
( ( ( ~ ( number_ring @ SV68 )
| ~ ( linordered_idom @ SV68 ) )
= $true )
| ( ( ! [SY300: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV68 @ ( zero_zero @ SV68 ) @ ( number_number_of @ SV68 @ SY300 ) )
| ( ord_less_eq @ int @ pls @ SY300 ) )
| ~ ( ~ ( ord_less_eq @ int @ pls @ SY300 )
| ( ord_less_eq @ SV68 @ ( zero_zero @ SV68 ) @ ( number_number_of @ SV68 @ SY300 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[784]) ).
thf(888,plain,
! [SV69: $i] :
( ( ~ ( ord_less_eq @ int @ pls @ ( bit0 @ SV69 ) )
| ( ord_less_eq @ int @ pls @ SV69 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[785]) ).
thf(889,plain,
! [SV69: $i] :
( ( ~ ( ord_less_eq @ int @ pls @ SV69 )
| ( ord_less_eq @ int @ pls @ ( bit0 @ SV69 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[786]) ).
thf(890,plain,
! [SV70: $i] :
( ( ( ~ ( number_ring @ SV70 )
| ~ ( linordered_idom @ SV70 ) )
= $true )
| ( ( ! [SY301: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV70 @ ( number_number_of @ SV70 @ SY301 ) @ ( zero_zero @ SV70 ) )
| ( ord_less_eq @ int @ SY301 @ pls ) )
| ~ ( ~ ( ord_less_eq @ int @ SY301 @ pls )
| ( ord_less_eq @ SV70 @ ( number_number_of @ SV70 @ SY301 ) @ ( zero_zero @ SV70 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[787]) ).
thf(891,plain,
! [SV140: $i,SV71: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( bit0 @ SV71 ) @ ( bit0 @ SV140 ) )
| ( ord_less_eq @ int @ SV71 @ SV140 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[788]) ).
thf(892,plain,
! [SV140: $i,SV71: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ SV71 @ SV140 )
| ( ord_less_eq @ int @ ( bit0 @ SV71 ) @ ( bit0 @ SV140 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[788]) ).
thf(893,plain,
! [SV72: $i] :
( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ ( number_number_of @ nat @ SV72 ) )
| ( ord_less @ int @ pls @ SV72 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[789]) ).
thf(894,plain,
! [SV72: $i] :
( ( ~ ( ord_less @ int @ pls @ SV72 )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ ( number_number_of @ nat @ SV72 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[790]) ).
thf(895,plain,
! [SV73: $i] :
( ( ( ~ ( number_ring @ SV73 )
| ~ ( linordered_idom @ SV73 ) )
= $true )
| ( ( ! [SY303: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV73 @ ( number_number_of @ SV73 @ SY303 ) @ ( one_one @ SV73 ) )
| ( ord_less_eq @ int @ SY303 @ ( bit1 @ pls ) ) )
| ~ ( ~ ( ord_less_eq @ int @ SY303 @ ( bit1 @ pls ) )
| ( ord_less_eq @ SV73 @ ( number_number_of @ SV73 @ SY303 ) @ ( one_one @ SV73 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[791]) ).
thf(896,plain,
! [SV190: $i,SV74: $i] :
( ( ( ( plus_plus @ SV74 @ ( one_one @ SV74 ) @ ( number_number_of @ SV74 @ SV190 ) )
= ( number_number_of @ SV74 @ ( plus_plus @ int @ ( bit1 @ pls ) @ SV190 ) ) )
= $true )
| ( ( number_ring @ SV74 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[792]) ).
thf(897,plain,
! [SV141: $i,SV75: $i,SV171: $i] :
( ( ( ~ ~ ( ~ ( number @ SV171 )
| ~ ( semiring @ SV171 ) ) )
= $true )
| ( ( ( ti @ SV171 @ ( plus_plus @ SV171 @ SV75 @ SV141 ) )
= ( plus_plus @ SV171 @ SV75 @ SV141 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[793]) ).
thf(898,plain,
! [SV76: $i] :
( ( ~ ( zprime @ ( ti @ int @ SV76 ) )
| ( zprime @ SV76 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[794]) ).
thf(899,plain,
! [SV76: $i] :
( ( ~ ( zprime @ SV76 )
| ( zprime @ ( ti @ int @ SV76 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[795]) ).
thf(900,plain,
! [SV142: $i,SV77: $i,SV172: $i] :
( ( ( ~ ( semiring_1 @ SV172 ) )
= $true )
| ( ( ( power_power @ SV172 @ ( ti @ SV172 @ SV77 ) @ SV142 )
= ( power_power @ SV172 @ SV77 @ SV142 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[796]) ).
thf(901,plain,
! [SV79: $i] :
( ( ( ~ ( number @ SV79 )
| ~ ( linorder @ SV79 ) )
= $true )
| ( ( ! [SY309: $i,SY310: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV79 @ ( number_number_of @ SV79 @ SY309 ) @ ( number_number_of @ SV79 @ SY310 ) )
| ~ ( ord_less @ SV79 @ ( number_number_of @ SV79 @ SY310 ) @ ( number_number_of @ SV79 @ SY309 ) ) )
| ~ ( ~ ~ ( ord_less @ SV79 @ ( number_number_of @ SV79 @ SY310 ) @ ( number_number_of @ SV79 @ SY309 ) )
| ( ord_less_eq @ SV79 @ ( number_number_of @ SV79 @ SY309 ) @ ( number_number_of @ SV79 @ SY310 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[799]) ).
thf(902,plain,
! [SV143: $i,SV80: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV80 @ ( plus_plus @ int @ SV143 @ ( one_one @ int ) ) )
| ( ord_less_eq @ int @ SV80 @ SV143 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[800]) ).
thf(903,plain,
! [SV143: $i,SV80: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ SV80 @ SV143 )
| ( ord_less @ int @ SV80 @ ( plus_plus @ int @ SV143 @ ( one_one @ int ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[800]) ).
thf(904,plain,
! [SV144: $i,SV81: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SV81 ) @ ( bit1 @ SV144 ) )
| ( ord_less_eq @ int @ SV81 @ SV144 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[801]) ).
thf(905,plain,
! [SV144: $i,SV81: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ SV81 @ SV144 )
| ( ord_less @ int @ ( bit0 @ SV81 ) @ ( bit1 @ SV144 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[801]) ).
thf(906,plain,
! [SV145: $i,SV82: $i] :
( ( ( ord_less_eq @ int @ SV82 @ SV145 )
= $false )
| ( ( ~ ( ord_less_eq @ int @ SV145 @ SV82 )
| ( SV82 = SV145 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[802]) ).
thf(907,plain,
! [SV83: $i] :
( ( ( ( zero_zero @ nat )
!= ( number_number_of @ nat @ SV83 ) )
| ( ord_less_eq @ int @ SV83 @ pls ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[803]) ).
thf(908,plain,
! [SV83: $i] :
( ( ~ ( ord_less_eq @ int @ SV83 @ pls )
| ( ( zero_zero @ nat )
= ( number_number_of @ nat @ SV83 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[804]) ).
thf(909,plain,
! [SV191: $i,SV84: $i] :
( ( ( ! [SY375: $i] : ( ord_less_eq @ SV84 @ ( zero_zero @ SV84 ) @ ( plus_plus @ SV84 @ ( times_times @ SV84 @ SV191 @ SV191 ) @ ( times_times @ SV84 @ SY375 @ SY375 ) ) ) )
= $true )
| ( ( linordered_ring @ SV84 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[805]) ).
thf(910,plain,
! [SV146: $i,SV85: $i,SV173: $i] :
( ( ( ~ ( linordered_ring @ SV173 ) )
= $true )
| ( ( ( plus_plus @ SV173 @ SV85 @ ( ti @ SV173 @ SV146 ) )
= ( plus_plus @ SV173 @ SV85 @ SV146 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[806]) ).
thf(911,plain,
! [SV86: $i,SV147: $i] :
( ( ( number @ SV147 )
= $false )
| ( ( ( number_number_of @ SV147 @ ( ti @ int @ SV86 ) )
= ( number_number_of @ SV147 @ SV86 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[807]) ).
thf(912,plain,
! [SV148: $i,SV87: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SV87 ) @ ( bit0 @ SV148 ) )
| ( ord_less @ int @ SV87 @ SV148 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[808]) ).
thf(913,plain,
! [SV148: $i,SV87: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV87 @ SV148 )
| ( ord_less_eq @ int @ ( bit1 @ SV87 ) @ ( bit0 @ SV148 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[808]) ).
thf(914,plain,
! [SV88: $i] :
( ( ( ~ ( number @ SV88 )
| ~ ( semiring @ SV88 ) )
= $true )
| ( ( ! [SY320: $i,SY321: $i,SY322: $i] :
( ( times_times @ SV88 @ ( plus_plus @ SV88 @ SY320 @ SY321 ) @ ( number_number_of @ SV88 @ SY322 ) )
= ( plus_plus @ SV88 @ ( times_times @ SV88 @ SY320 @ ( number_number_of @ SV88 @ SY322 ) ) @ ( times_times @ SV88 @ SY321 @ ( number_number_of @ SV88 @ SY322 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[809]) ).
thf(915,plain,
! [SV89: $i] :
( ( ( ( number_number_of @ nat @ SV89 )
!= ( zero_zero @ nat ) )
| ( ord_less_eq @ int @ SV89 @ pls ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[810]) ).
thf(916,plain,
! [SV89: $i] :
( ( ~ ( ord_less_eq @ int @ SV89 @ pls )
| ( ( number_number_of @ nat @ SV89 )
= ( zero_zero @ nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[811]) ).
thf(917,plain,
! [SV90: $i,SV174: $i,SV149: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV149 @ SV174 ) )
= $true )
| ( ( ~ ( ord_less_eq @ int @ SV174 @ SV90 )
| ( ord_less_eq @ int @ SV149 @ SV90 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[812]) ).
thf(918,plain,
! [SV150: $i,SV91: $i,SV175: $i] :
( ( ( ~ ~ ( ~ ( number @ SV175 )
| ~ ( linorder @ SV175 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( ord_less @ SV175 @ ( ti @ SV175 @ SV91 ) @ SV150 )
| ( ord_less @ SV175 @ SV91 @ SV150 ) )
| ~ ( ~ ( ord_less @ SV175 @ SV91 @ SV150 )
| ( ord_less @ SV175 @ ( ti @ SV175 @ SV91 ) @ SV150 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[813]) ).
thf(919,plain,
! [SV151: $i,SV92: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SV92 ) @ ( bit1 @ SV151 ) )
| ( ord_less_eq @ int @ SV92 @ SV151 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[814]) ).
thf(920,plain,
! [SV151: $i,SV92: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ SV92 @ SV151 )
| ( ord_less_eq @ int @ ( bit1 @ SV92 ) @ ( bit1 @ SV151 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[814]) ).
thf(921,plain,
! [SV93: $i,SV176: $i,SV152: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV152 @ SV176 ) )
= $true )
| ( ( ord_less_eq @ int @ ( plus_plus @ int @ SV93 @ SV152 ) @ ( plus_plus @ int @ SV93 @ SV176 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[815]) ).
thf(922,plain,
! [SV94: $i] :
( ( ~ ( ord_less_eq @ int @ ( bit1 @ SV94 ) @ pls )
| ( ord_less @ int @ SV94 @ pls ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[816]) ).
thf(923,plain,
! [SV94: $i] :
( ( ~ ( ord_less @ int @ SV94 @ pls )
| ( ord_less_eq @ int @ ( bit1 @ SV94 ) @ pls ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[817]) ).
thf(924,plain,
! [SV192: $i,SV95: $i] :
( ( ( ! [SY376: $i] :
~ ( ord_less @ SV95 @ ( plus_plus @ SV95 @ ( power_power @ SV95 @ SV192 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV95 @ SY376 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( zero_zero @ SV95 ) ) )
= $true )
| ( ( linordered_idom @ SV95 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[818]) ).
thf(925,plain,
! [SV153: $i,SV96: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( number_number_of @ int @ SV96 ) @ ( number_number_of @ int @ SV153 ) )
| ( ord_less @ int @ SV96 @ SV153 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[819]) ).
thf(926,plain,
! [SV153: $i,SV96: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV96 @ SV153 )
| ( ord_less @ int @ ( number_number_of @ int @ SV96 ) @ ( number_number_of @ int @ SV153 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[819]) ).
thf(927,plain,
! [SV193: $i,SV97: $i] :
( ( ( ! [SY377: $i] :
~ ( ~ ( ( ( plus_plus @ SV97 @ ( times_times @ SV97 @ SV193 @ SV193 ) @ ( times_times @ SV97 @ SY377 @ SY377 ) )
!= ( zero_zero @ SV97 ) )
| ~ ( ( ( ti @ SV97 @ SV193 )
!= ( zero_zero @ SV97 ) )
| ( ( ti @ SV97 @ SY377 )
!= ( zero_zero @ SV97 ) ) ) )
| ~ ( ~ ~ ( ( ( ti @ SV97 @ SV193 )
!= ( zero_zero @ SV97 ) )
| ( ( ti @ SV97 @ SY377 )
!= ( zero_zero @ SV97 ) ) )
| ( ( plus_plus @ SV97 @ ( times_times @ SV97 @ SV193 @ SV193 ) @ ( times_times @ SV97 @ SY377 @ SY377 ) )
= ( zero_zero @ SV97 ) ) ) ) )
= $true )
| ( ( linord581940658strict @ SV97 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[820]) ).
thf(928,plain,
! [SV154: $i,SV98: $i,SV194: $i,SV177: $i] :
( ( ~ ( ord_less @ int @ SV177 @ SV194 )
| ~ ( ord_less_eq @ int @ SV98 @ SV154 )
| ( ord_less @ int @ ( plus_plus @ int @ SV177 @ SV98 ) @ ( plus_plus @ int @ SV194 @ SV154 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[821]) ).
thf(929,plain,
! [SV99: $i] :
( ( ( ~ ( number_ring @ SV99 )
| ~ ( linordered_idom @ SV99 ) )
= $true )
| ( ( ! [SY338: $i,SY339: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV99 @ ( number_number_of @ SV99 @ SY338 ) @ ( number_number_of @ SV99 @ SY339 ) )
| ( ord_less_eq @ int @ SY338 @ SY339 ) )
| ~ ( ~ ( ord_less_eq @ int @ SY338 @ SY339 )
| ( ord_less_eq @ SV99 @ ( number_number_of @ SV99 @ SY338 ) @ ( number_number_of @ SV99 @ SY339 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[822]) ).
thf(930,plain,
! [SV155: $i,SV101: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( bit0 @ SV101 ) @ ( bit1 @ SV155 ) )
| ( ord_less_eq @ int @ SV101 @ SV155 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[824]) ).
thf(931,plain,
! [SV155: $i,SV101: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ SV101 @ SV155 )
| ( ord_less_eq @ int @ ( bit0 @ SV101 ) @ ( bit1 @ SV155 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[824]) ).
thf(932,plain,
! [SV103: $i] :
( ( ( ~ ( number_ring @ SV103 )
| ~ ( linordered_idom @ SV103 ) )
= $true )
| ( ( ! [SY341: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV103 @ ( one_one @ SV103 ) @ ( number_number_of @ SV103 @ SY341 ) )
| ( ord_less_eq @ int @ ( bit1 @ pls ) @ SY341 ) )
| ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ pls ) @ SY341 )
| ( ord_less_eq @ SV103 @ ( one_one @ SV103 ) @ ( number_number_of @ SV103 @ SY341 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[826]) ).
thf(933,plain,
! [SV195: $i,SV178: $i,SV23: $i] :
( ( ( ~ ( ~ ( ( ( plus_plus @ SV23 @ ( power_power @ SV23 @ SV178 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV23 @ SV195 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV23 ) )
| ~ ( ( ( ti @ SV23 @ SV178 )
!= ( zero_zero @ SV23 ) )
| ( ( ti @ SV23 @ SV195 )
!= ( zero_zero @ SV23 ) ) ) )
| ~ ( ~ ~ ( ( ( ti @ SV23 @ SV178 )
!= ( zero_zero @ SV23 ) )
| ( ( ti @ SV23 @ SV195 )
!= ( zero_zero @ SV23 ) ) )
| ( ( plus_plus @ SV23 @ ( power_power @ SV23 @ SV178 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV23 @ SV195 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV23 ) ) ) ) )
= $true )
| ( ( linordered_idom @ SV23 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[828]) ).
thf(934,plain,
! [SV24: $i,SV179: $i,SV196: $i] :
( ( ( ~ ( ord_less_eq @ int @ pls @ SV196 )
| ~ ( ord_less_eq @ int @ pls @ SV179 )
| ( ( plus_plus @ SV24 @ ( number_number_of @ SV24 @ SV196 ) @ ( number_number_of @ SV24 @ SV179 ) )
= ( number_number_of @ SV24 @ ( plus_plus @ int @ SV196 @ SV179 ) ) ) )
= $true )
| ( ( number_semiring @ SV24 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[829]) ).
thf(935,plain,
! [SV117: $i,SV25: $i,SV162: $i] :
( ( ( linordered_ring @ SV162 )
= $false )
| ( ( ( ti @ SV162 @ ( plus_plus @ SV162 @ SV25 @ SV117 ) )
= ( plus_plus @ SV162 @ SV25 @ SV117 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[830]) ).
thf(936,plain,
! [SV118: $i,SV26: $i] :
( ( ~ ( ord_less_eq @ int @ ( plus_plus @ int @ SV26 @ ( one_one @ int ) ) @ SV118 )
| ( ord_less @ int @ SV26 @ SV118 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[831]) ).
thf(937,plain,
! [SV118: $i,SV26: $i] :
( ( ~ ( ord_less @ int @ SV26 @ SV118 )
| ( ord_less_eq @ int @ ( plus_plus @ int @ SV26 @ ( one_one @ int ) ) @ SV118 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[832]) ).
thf(938,plain,
! [SV119: $i,SV28: $i] :
( ( ~ ( ord_less @ nat @ ( number_number_of @ nat @ SV28 ) @ ( number_number_of @ nat @ SV119 ) )
| ~ ( ~ ( ~ ( ord_less @ int @ SV28 @ SV119 )
| ( ord_less @ int @ pls @ SV119 ) )
| ~ ( ord_less @ int @ SV28 @ SV119 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[833]) ).
thf(939,plain,
! [SV119: $i,SV28: $i] :
( ( ~ ~ ( ~ ( ~ ( ord_less @ int @ SV28 @ SV119 )
| ( ord_less @ int @ pls @ SV119 ) )
| ~ ( ord_less @ int @ SV28 @ SV119 ) )
| ( ord_less @ nat @ ( number_number_of @ nat @ SV28 ) @ ( number_number_of @ nat @ SV119 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[834]) ).
thf(940,plain,
! [SV120: $i,SV29: $i,SV163: $i] :
( ( ( semiring_1 @ SV163 )
= $false )
| ( ( ( power_power @ SV163 @ SV29 @ ( ti @ nat @ SV120 ) )
= ( power_power @ SV163 @ SV29 @ SV120 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[835]) ).
thf(941,plain,
! [SV180: $i,SV32: $i] :
( ( ( ord_less @ SV32 @ ( power_power @ SV32 @ SV180 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( zero_zero @ SV32 ) )
= $false )
| ( ( linordered_idom @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[837]) ).
thf(942,plain,
! [SV33: $i] :
( ( ( ~ ( number_ring @ SV33 ) )
= $true )
| ( ( ~ ( ring_char_0 @ SV33 ) )
= $true )
| ( ( ! [SY254: $i,SY255: $i] :
~ ( ~ ( ( ( number_number_of @ SV33 @ SY254 )
!= ( number_number_of @ SV33 @ SY255 ) )
| ( SY254 = SY255 ) )
| ~ ( ( SY254 != SY255 )
| ( ( number_number_of @ SV33 @ SY254 )
= ( number_number_of @ SV33 @ SY255 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[838]) ).
thf(943,plain,
! [SV34: $i] :
( ( ( ~ ( ord_less @ int @ pls @ ( bit1 @ SV34 ) ) )
= $true )
| ( ( ord_less_eq @ int @ pls @ SV34 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[839]) ).
thf(944,plain,
! [SV34: $i] :
( ( ( ~ ( ord_less_eq @ int @ pls @ SV34 ) )
= $true )
| ( ( ord_less @ int @ pls @ ( bit1 @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[840]) ).
thf(945,plain,
! [SV181: $i,SV35: $i] :
( ( ( ~ ( ( ( power_power @ SV35 @ SV181 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= ( zero_zero @ SV35 ) )
| ( ( ti @ SV35 @ SV181 )
= ( zero_zero @ SV35 ) ) )
| ~ ( ( ( ti @ SV35 @ SV181 )
!= ( zero_zero @ SV35 ) )
| ( ( power_power @ SV35 @ SV181 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SV35 ) ) ) )
= $false )
| ( ( ring_11004092258visors @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[841]) ).
thf(946,plain,
! [SV197: $i,SV182: $i,SV36: $i] :
( ( ( ( times_times @ SV36 @ ( number_number_of @ SV36 @ SV182 ) @ ( number_number_of @ SV36 @ SV197 ) )
= ( number_number_of @ SV36 @ ( times_times @ int @ SV182 @ SV197 ) ) )
= $true )
| ( ( number_ring @ SV36 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[842]) ).
thf(947,plain,
! [SV37: $i] :
( ( ( ~ ( ord_less_eq @ int @ pls @ ( bit1 @ SV37 ) ) )
= $true )
| ( ( ord_less_eq @ int @ pls @ SV37 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[843]) ).
thf(948,plain,
! [SV37: $i] :
( ( ( ~ ( ord_less_eq @ int @ pls @ SV37 ) )
= $true )
| ( ( ord_less_eq @ int @ pls @ ( bit1 @ SV37 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[844]) ).
thf(949,plain,
! [SV122: $i,SV38: $i] :
( ( ~ ( ord_less_eq @ int @ ( bit1 @ SV38 ) @ ( bit1 @ SV122 ) )
| ( ord_less_eq @ int @ SV38 @ SV122 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[845]) ).
thf(950,plain,
! [SV122: $i,SV38: $i] :
( ( ~ ( ord_less_eq @ int @ SV38 @ SV122 )
| ( ord_less_eq @ int @ ( bit1 @ SV38 ) @ ( bit1 @ SV122 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[846]) ).
thf(951,plain,
! [SV123: $i,SV39: $i] :
( ( ~ ( ord_less_eq @ int @ ( bit1 @ SV39 ) @ ( bit0 @ SV123 ) )
| ( ord_less @ int @ SV39 @ SV123 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[847]) ).
thf(952,plain,
! [SV123: $i,SV39: $i] :
( ( ~ ( ord_less @ int @ SV39 @ SV123 )
| ( ord_less_eq @ int @ ( bit1 @ SV39 ) @ ( bit0 @ SV123 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[848]) ).
thf(953,plain,
! [SV40: $i,SV124: $i] :
( ( ~ ( ord_less @ int @ SV124 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV124 ) @ ( number_number_of @ nat @ SV40 ) )
= ( number_number_of @ nat @ SV40 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[849]) ).
thf(954,plain,
! [SV40: $i,SV124: $i] :
( ( ~ ~ ( ord_less @ int @ SV124 @ pls )
| ~ ( ~ ( ~ ( ord_less @ int @ SV40 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV124 ) @ ( number_number_of @ nat @ SV40 ) )
= ( number_number_of @ nat @ SV124 ) ) )
| ~ ( ~ ~ ( ord_less @ int @ SV40 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV124 ) @ ( number_number_of @ nat @ SV40 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SV124 @ SV40 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[850]) ).
thf(955,plain,
! [SV125: $i,SV41: $i] :
( ( ~ ( ord_less_eq @ int @ ( number_number_of @ int @ SV41 ) @ ( number_number_of @ int @ SV125 ) )
| ( ord_less_eq @ int @ SV41 @ SV125 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[851]) ).
thf(956,plain,
! [SV125: $i,SV41: $i] :
( ( ~ ( ord_less_eq @ int @ SV41 @ SV125 )
| ( ord_less_eq @ int @ ( number_number_of @ int @ SV41 ) @ ( number_number_of @ int @ SV125 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[852]) ).
thf(957,plain,
! [SV42: $i,SV183: $i,SV198: $i] :
( ( ( ~ ( ord_less_eq @ int @ pls @ SV198 )
| ~ ( ord_less_eq @ int @ pls @ SV183 )
| ( ( times_times @ SV42 @ ( number_number_of @ SV42 @ SV198 ) @ ( number_number_of @ SV42 @ SV183 ) )
= ( number_number_of @ SV42 @ ( times_times @ int @ SV198 @ SV183 ) ) ) )
= $true )
| ( ( number_semiring @ SV42 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[853]) ).
thf(958,plain,
! [SV126: $i,SV43: $i] :
( ( ~ ( ord_less_eq @ int @ ( bit0 @ SV43 ) @ ( bit0 @ SV126 ) )
| ( ord_less_eq @ int @ SV43 @ SV126 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[854]) ).
thf(959,plain,
! [SV126: $i,SV43: $i] :
( ( ~ ( ord_less_eq @ int @ SV43 @ SV126 )
| ( ord_less_eq @ int @ ( bit0 @ SV43 ) @ ( bit0 @ SV126 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[855]) ).
thf(960,plain,
! [SV127: $i,SV44: $i,SV164: $i] :
( ( ( linordered_ring @ SV164 )
= $false )
| ( ( ( plus_plus @ SV164 @ ( ti @ SV164 @ SV44 ) @ SV127 )
= ( plus_plus @ SV164 @ SV44 @ SV127 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[856]) ).
thf(961,plain,
! [SV184: $i,SV45: $i] :
( ( ( ~ ( ~ ( ord_less @ SV45 @ ( zero_zero @ SV45 ) @ ( power_power @ SV45 @ SV184 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ( ( ti @ SV45 @ SV184 )
!= ( zero_zero @ SV45 ) ) )
| ~ ( ~ ( ( ( ti @ SV45 @ SV184 )
!= ( zero_zero @ SV45 ) ) )
| ( ord_less @ SV45 @ ( zero_zero @ SV45 ) @ ( power_power @ SV45 @ SV184 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $false )
| ( ( linordered_idom @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[857]) ).
thf(962,plain,
! [SV46: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( bit0 @ SV46 ) @ pls ) )
= $true )
| ( ( ord_less_eq @ int @ SV46 @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[858]) ).
thf(963,plain,
! [SV46: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV46 @ pls ) )
= $true )
| ( ( ord_less_eq @ int @ ( bit0 @ SV46 ) @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[859]) ).
thf(964,plain,
! [SV128: $i,SV47: $i] :
( ( ( ( bit1 @ SV47 )
!= ( bit1 @ SV128 ) )
| ( SV47 = SV128 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[860]) ).
thf(965,plain,
! [SV128: $i,SV47: $i] :
( ( ( SV47 != SV128 )
| ( ( bit1 @ SV47 )
= ( bit1 @ SV128 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[861]) ).
thf(966,plain,
! [SV48: $i] :
( ( ( ~ ( number @ SV48 ) )
= $true )
| ( ( ~ ( semiring @ SV48 ) )
= $true )
| ( ( ! [SY270: $i,SY271: $i,SY272: $i] :
( ( times_times @ SV48 @ ( number_number_of @ SV48 @ SY270 ) @ ( plus_plus @ SV48 @ SY271 @ SY272 ) )
= ( plus_plus @ SV48 @ ( times_times @ SV48 @ ( number_number_of @ SV48 @ SY270 ) @ SY271 ) @ ( times_times @ SV48 @ ( number_number_of @ SV48 @ SY270 ) @ SY272 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[862]) ).
thf(967,plain,
! [SV129: $i,SV49: $i,SV165: $i] :
( ( ( linordered_idom @ SV165 )
= $false )
| ( ( ~ ( ~ ( ~ ( ord_less @ SV165 @ ( ti @ SV165 @ SV49 ) @ SV129 )
| ( ord_less @ SV165 @ SV49 @ SV129 ) )
| ~ ( ~ ( ord_less @ SV165 @ SV49 @ SV129 )
| ( ord_less @ SV165 @ ( ti @ SV165 @ SV49 ) @ SV129 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[863]) ).
thf(968,plain,
! [SV131: $i,SV51: $i,SV166: $i] :
( ( ( linordered_idom @ SV166 )
= $false )
| ( ( ~ ( ~ ( ~ ( ord_less @ SV166 @ SV51 @ ( ti @ SV166 @ SV131 ) )
| ( ord_less @ SV166 @ SV51 @ SV131 ) )
| ~ ( ~ ( ord_less @ SV166 @ SV51 @ SV131 )
| ( ord_less @ SV166 @ SV51 @ ( ti @ SV166 @ SV131 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[865]) ).
thf(969,plain,
! [SV132: $i,SV52: $i,SV167: $i] :
( ( ( ~ ( ~ ( number @ SV167 )
| ~ ( semiring @ SV167 ) ) )
= $false )
| ( ( ( plus_plus @ SV167 @ SV52 @ ( ti @ SV167 @ SV132 ) )
= ( plus_plus @ SV167 @ SV52 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[866]) ).
thf(970,plain,
! [SV199: $i,SV185: $i,SV53: $i] :
( ( ( ~ ( ~ ( ( ( number_number_of @ SV53 @ SV185 )
!= ( ti @ SV53 @ SV199 ) )
| ( ( ti @ SV53 @ SV199 )
= ( number_number_of @ SV53 @ SV185 ) ) )
| ~ ( ( ( ti @ SV53 @ SV199 )
!= ( number_number_of @ SV53 @ SV185 ) )
| ( ( number_number_of @ SV53 @ SV185 )
= ( ti @ SV53 @ SV199 ) ) ) ) )
= $true )
| ( ( number @ SV53 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[867]) ).
thf(971,plain,
! [SV54: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( one_one @ int ) @ SV54 ) )
= $true )
| ( ( ord_less @ int @ ( zero_zero @ int ) @ SV54 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[868]) ).
thf(972,plain,
! [SV54: $i] :
( ( ( ~ ( ord_less @ int @ ( zero_zero @ int ) @ SV54 ) )
= $true )
| ( ( ord_less_eq @ int @ ( one_one @ int ) @ SV54 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[869]) ).
thf(973,plain,
! [SV133: $i,SV55: $i,SV168: $i] :
( ( ( ~ ( ~ ( number @ SV168 )
| ~ ( semiring @ SV168 ) ) )
= $false )
| ( ( ( plus_plus @ SV168 @ ( ti @ SV168 @ SV55 ) @ SV133 )
= ( plus_plus @ SV168 @ SV55 @ SV133 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[870]) ).
thf(974,plain,
! [SV134: $i,SV56: $i,SV169: $i] :
( ( ( semiring_1 @ SV169 )
= $false )
| ( ( ( ti @ SV169 @ ( power_power @ SV169 @ SV56 @ SV134 ) )
= ( power_power @ SV169 @ SV56 @ SV134 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[871]) ).
thf(975,plain,
! [SV200: $i,SV187: $i,SV58: $i] :
( ( ( ( number_number_of @ SV58 @ ( times_times @ int @ SV187 @ SV200 ) )
= ( times_times @ SV58 @ ( number_number_of @ SV58 @ SV187 ) @ ( number_number_of @ SV58 @ SV200 ) ) )
= $true )
| ( ( number_ring @ SV58 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[873]) ).
thf(976,plain,
! [SV201: $i,SV188: $i,SV59: $i] :
( ( ( ~ ( ~ ( ~ ( ord_less @ SV59 @ ( zero_zero @ SV59 ) @ ( plus_plus @ SV59 @ ( power_power @ SV59 @ SV188 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV59 @ SV201 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
| ( ( ti @ SV59 @ SV188 )
!= ( zero_zero @ SV59 ) )
| ( ( ti @ SV59 @ SV201 )
!= ( zero_zero @ SV59 ) ) )
| ~ ( ~ ( ( ( ti @ SV59 @ SV188 )
!= ( zero_zero @ SV59 ) )
| ( ( ti @ SV59 @ SV201 )
!= ( zero_zero @ SV59 ) ) )
| ( ord_less @ SV59 @ ( zero_zero @ SV59 ) @ ( plus_plus @ SV59 @ ( power_power @ SV59 @ SV188 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV59 @ SV201 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) ) )
= $true )
| ( ( linordered_idom @ SV59 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[874]) ).
thf(977,plain,
! [SV135: $i,SV60: $i] :
( ( ( ( bit0 @ SV60 )
!= ( bit0 @ SV135 ) )
| ( SV60 = SV135 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[875]) ).
thf(978,plain,
! [SV135: $i,SV60: $i] :
( ( ( SV60 != SV135 )
| ( ( bit0 @ SV60 )
= ( bit0 @ SV135 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[876]) ).
thf(979,plain,
! [SV136: $i,SV61: $i] :
( ( ~ ( ord_less @ int @ ( bit0 @ SV61 ) @ ( bit1 @ SV136 ) )
| ( ord_less_eq @ int @ SV61 @ SV136 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[877]) ).
thf(980,plain,
! [SV136: $i,SV61: $i] :
( ( ~ ( ord_less_eq @ int @ SV61 @ SV136 )
| ( ord_less @ int @ ( bit0 @ SV61 ) @ ( bit1 @ SV136 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[878]) ).
thf(981,plain,
! [SV137: $i,SV62: $i] :
( ( ~ ( ord_less_eq @ int @ ( bit0 @ SV62 ) @ ( bit1 @ SV137 ) )
| ( ord_less_eq @ int @ SV62 @ SV137 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[879]) ).
thf(982,plain,
! [SV137: $i,SV62: $i] :
( ( ~ ( ord_less_eq @ int @ SV62 @ SV137 )
| ( ord_less_eq @ int @ ( bit0 @ SV62 ) @ ( bit1 @ SV137 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[880]) ).
thf(983,plain,
! [SV138: $i,SV63: $i,SV170: $i] :
( ( ( ~ ( ~ ( number @ SV170 )
| ~ ( linorder @ SV170 ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ( ord_less @ SV170 @ SV63 @ ( ti @ SV170 @ SV138 ) )
| ( ord_less @ SV170 @ SV63 @ SV138 ) )
| ~ ( ~ ( ord_less @ SV170 @ SV63 @ SV138 )
| ( ord_less @ SV170 @ SV63 @ ( ti @ SV170 @ SV138 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[881]) ).
thf(984,plain,
! [SV139: $i,SV65: $i] :
( ( ~ ( ord_less @ int @ SV65 @ SV139 )
| ~ ( ~ ( ord_less_eq @ int @ SV65 @ SV139 )
| ~ ( ( SV65 != SV139 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[882]) ).
thf(985,plain,
! [SV139: $i,SV65: $i] :
( ( ~ ~ ( ~ ( ord_less_eq @ int @ SV65 @ SV139 )
| ~ ( ( SV65 != SV139 ) ) )
| ( ord_less @ int @ SV65 @ SV139 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[883]) ).
thf(986,plain,
! [SV66: $i] :
( ( ( ~ ( twoSqu33214720sum2sq @ ( ti @ int @ SV66 ) ) )
= $true )
| ( ( twoSqu33214720sum2sq @ SV66 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[884]) ).
thf(987,plain,
! [SV66: $i] :
( ( ( ~ ( twoSqu33214720sum2sq @ SV66 ) )
= $true )
| ( ( twoSqu33214720sum2sq @ ( ti @ int @ SV66 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[885]) ).
thf(988,plain,
! [SV202: $i,SV189: $i,SV67: $i] :
( ( ( ! [SY378: $i] :
( ( times_times @ SV67 @ ( number_number_of @ SV67 @ SV189 ) @ ( times_times @ SV67 @ ( number_number_of @ SV67 @ SV202 ) @ SY378 ) )
= ( times_times @ SV67 @ ( number_number_of @ SV67 @ ( times_times @ int @ SV189 @ SV202 ) ) @ SY378 ) ) )
= $true )
| ( ( number_ring @ SV67 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[886]) ).
thf(989,plain,
! [SV68: $i] :
( ( ( ~ ( number_ring @ SV68 ) )
= $true )
| ( ( ~ ( linordered_idom @ SV68 ) )
= $true )
| ( ( ! [SY300: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV68 @ ( zero_zero @ SV68 ) @ ( number_number_of @ SV68 @ SY300 ) )
| ( ord_less_eq @ int @ pls @ SY300 ) )
| ~ ( ~ ( ord_less_eq @ int @ pls @ SY300 )
| ( ord_less_eq @ SV68 @ ( zero_zero @ SV68 ) @ ( number_number_of @ SV68 @ SY300 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[887]) ).
thf(990,plain,
! [SV69: $i] :
( ( ( ~ ( ord_less_eq @ int @ pls @ ( bit0 @ SV69 ) ) )
= $true )
| ( ( ord_less_eq @ int @ pls @ SV69 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[888]) ).
thf(991,plain,
! [SV69: $i] :
( ( ( ~ ( ord_less_eq @ int @ pls @ SV69 ) )
= $true )
| ( ( ord_less_eq @ int @ pls @ ( bit0 @ SV69 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[889]) ).
thf(992,plain,
! [SV70: $i] :
( ( ( ~ ( number_ring @ SV70 ) )
= $true )
| ( ( ~ ( linordered_idom @ SV70 ) )
= $true )
| ( ( ! [SY301: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV70 @ ( number_number_of @ SV70 @ SY301 ) @ ( zero_zero @ SV70 ) )
| ( ord_less_eq @ int @ SY301 @ pls ) )
| ~ ( ~ ( ord_less_eq @ int @ SY301 @ pls )
| ( ord_less_eq @ SV70 @ ( number_number_of @ SV70 @ SY301 ) @ ( zero_zero @ SV70 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[890]) ).
thf(993,plain,
! [SV140: $i,SV71: $i] :
( ( ~ ( ord_less_eq @ int @ ( bit0 @ SV71 ) @ ( bit0 @ SV140 ) )
| ( ord_less_eq @ int @ SV71 @ SV140 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[891]) ).
thf(994,plain,
! [SV140: $i,SV71: $i] :
( ( ~ ( ord_less_eq @ int @ SV71 @ SV140 )
| ( ord_less_eq @ int @ ( bit0 @ SV71 ) @ ( bit0 @ SV140 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[892]) ).
thf(995,plain,
! [SV72: $i] :
( ( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ ( number_number_of @ nat @ SV72 ) ) )
= $true )
| ( ( ord_less @ int @ pls @ SV72 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[893]) ).
thf(996,plain,
! [SV72: $i] :
( ( ( ~ ( ord_less @ int @ pls @ SV72 ) )
= $true )
| ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( number_number_of @ nat @ SV72 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[894]) ).
thf(997,plain,
! [SV73: $i] :
( ( ( ~ ( number_ring @ SV73 ) )
= $true )
| ( ( ~ ( linordered_idom @ SV73 ) )
= $true )
| ( ( ! [SY303: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV73 @ ( number_number_of @ SV73 @ SY303 ) @ ( one_one @ SV73 ) )
| ( ord_less_eq @ int @ SY303 @ ( bit1 @ pls ) ) )
| ~ ( ~ ( ord_less_eq @ int @ SY303 @ ( bit1 @ pls ) )
| ( ord_less_eq @ SV73 @ ( number_number_of @ SV73 @ SY303 ) @ ( one_one @ SV73 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[895]) ).
thf(998,plain,
! [SV141: $i,SV75: $i,SV171: $i] :
( ( ( ~ ( ~ ( number @ SV171 )
| ~ ( semiring @ SV171 ) ) )
= $false )
| ( ( ( ti @ SV171 @ ( plus_plus @ SV171 @ SV75 @ SV141 ) )
= ( plus_plus @ SV171 @ SV75 @ SV141 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[897]) ).
thf(999,plain,
! [SV76: $i] :
( ( ( ~ ( zprime @ ( ti @ int @ SV76 ) ) )
= $true )
| ( ( zprime @ SV76 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[898]) ).
thf(1000,plain,
! [SV76: $i] :
( ( ( ~ ( zprime @ SV76 ) )
= $true )
| ( ( zprime @ ( ti @ int @ SV76 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[899]) ).
thf(1001,plain,
! [SV142: $i,SV77: $i,SV172: $i] :
( ( ( semiring_1 @ SV172 )
= $false )
| ( ( ( power_power @ SV172 @ ( ti @ SV172 @ SV77 ) @ SV142 )
= ( power_power @ SV172 @ SV77 @ SV142 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[900]) ).
thf(1002,plain,
! [SV79: $i] :
( ( ( ~ ( number @ SV79 ) )
= $true )
| ( ( ~ ( linorder @ SV79 ) )
= $true )
| ( ( ! [SY309: $i,SY310: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV79 @ ( number_number_of @ SV79 @ SY309 ) @ ( number_number_of @ SV79 @ SY310 ) )
| ~ ( ord_less @ SV79 @ ( number_number_of @ SV79 @ SY310 ) @ ( number_number_of @ SV79 @ SY309 ) ) )
| ~ ( ~ ~ ( ord_less @ SV79 @ ( number_number_of @ SV79 @ SY310 ) @ ( number_number_of @ SV79 @ SY309 ) )
| ( ord_less_eq @ SV79 @ ( number_number_of @ SV79 @ SY309 ) @ ( number_number_of @ SV79 @ SY310 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[901]) ).
thf(1003,plain,
! [SV143: $i,SV80: $i] :
( ( ~ ( ord_less @ int @ SV80 @ ( plus_plus @ int @ SV143 @ ( one_one @ int ) ) )
| ( ord_less_eq @ int @ SV80 @ SV143 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[902]) ).
thf(1004,plain,
! [SV143: $i,SV80: $i] :
( ( ~ ( ord_less_eq @ int @ SV80 @ SV143 )
| ( ord_less @ int @ SV80 @ ( plus_plus @ int @ SV143 @ ( one_one @ int ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[903]) ).
thf(1005,plain,
! [SV144: $i,SV81: $i] :
( ( ~ ( ord_less @ int @ ( bit0 @ SV81 ) @ ( bit1 @ SV144 ) )
| ( ord_less_eq @ int @ SV81 @ SV144 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[904]) ).
thf(1006,plain,
! [SV144: $i,SV81: $i] :
( ( ~ ( ord_less_eq @ int @ SV81 @ SV144 )
| ( ord_less @ int @ ( bit0 @ SV81 ) @ ( bit1 @ SV144 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[905]) ).
thf(1007,plain,
! [SV82: $i,SV145: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV145 @ SV82 ) )
= $true )
| ( ( SV82 = SV145 )
= $true )
| ( ( ord_less_eq @ int @ SV82 @ SV145 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[906]) ).
thf(1008,plain,
! [SV83: $i] :
( ( ( ( zero_zero @ nat )
!= ( number_number_of @ nat @ SV83 ) )
= $true )
| ( ( ord_less_eq @ int @ SV83 @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[907]) ).
thf(1009,plain,
! [SV83: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV83 @ pls ) )
= $true )
| ( ( ( zero_zero @ nat )
= ( number_number_of @ nat @ SV83 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[908]) ).
thf(1010,plain,
! [SV203: $i,SV191: $i,SV84: $i] :
( ( ( ord_less_eq @ SV84 @ ( zero_zero @ SV84 ) @ ( plus_plus @ SV84 @ ( times_times @ SV84 @ SV191 @ SV191 ) @ ( times_times @ SV84 @ SV203 @ SV203 ) ) )
= $true )
| ( ( linordered_ring @ SV84 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[909]) ).
thf(1011,plain,
! [SV146: $i,SV85: $i,SV173: $i] :
( ( ( linordered_ring @ SV173 )
= $false )
| ( ( ( plus_plus @ SV173 @ SV85 @ ( ti @ SV173 @ SV146 ) )
= ( plus_plus @ SV173 @ SV85 @ SV146 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[910]) ).
thf(1012,plain,
! [SV148: $i,SV87: $i] :
( ( ~ ( ord_less_eq @ int @ ( bit1 @ SV87 ) @ ( bit0 @ SV148 ) )
| ( ord_less @ int @ SV87 @ SV148 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[912]) ).
thf(1013,plain,
! [SV148: $i,SV87: $i] :
( ( ~ ( ord_less @ int @ SV87 @ SV148 )
| ( ord_less_eq @ int @ ( bit1 @ SV87 ) @ ( bit0 @ SV148 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[913]) ).
thf(1014,plain,
! [SV88: $i] :
( ( ( ~ ( number @ SV88 ) )
= $true )
| ( ( ~ ( semiring @ SV88 ) )
= $true )
| ( ( ! [SY320: $i,SY321: $i,SY322: $i] :
( ( times_times @ SV88 @ ( plus_plus @ SV88 @ SY320 @ SY321 ) @ ( number_number_of @ SV88 @ SY322 ) )
= ( plus_plus @ SV88 @ ( times_times @ SV88 @ SY320 @ ( number_number_of @ SV88 @ SY322 ) ) @ ( times_times @ SV88 @ SY321 @ ( number_number_of @ SV88 @ SY322 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[914]) ).
thf(1015,plain,
! [SV89: $i] :
( ( ( ( number_number_of @ nat @ SV89 )
!= ( zero_zero @ nat ) )
= $true )
| ( ( ord_less_eq @ int @ SV89 @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[915]) ).
thf(1016,plain,
! [SV89: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV89 @ pls ) )
= $true )
| ( ( ( number_number_of @ nat @ SV89 )
= ( zero_zero @ nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[916]) ).
thf(1017,plain,
! [SV90: $i,SV174: $i,SV149: $i] :
( ( ( ord_less_eq @ int @ SV149 @ SV174 )
= $false )
| ( ( ~ ( ord_less_eq @ int @ SV174 @ SV90 )
| ( ord_less_eq @ int @ SV149 @ SV90 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[917]) ).
thf(1018,plain,
! [SV150: $i,SV91: $i,SV175: $i] :
( ( ( ~ ( ~ ( number @ SV175 )
| ~ ( linorder @ SV175 ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ( ord_less @ SV175 @ ( ti @ SV175 @ SV91 ) @ SV150 )
| ( ord_less @ SV175 @ SV91 @ SV150 ) )
| ~ ( ~ ( ord_less @ SV175 @ SV91 @ SV150 )
| ( ord_less @ SV175 @ ( ti @ SV175 @ SV91 ) @ SV150 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[918]) ).
thf(1019,plain,
! [SV151: $i,SV92: $i] :
( ( ~ ( ord_less_eq @ int @ ( bit1 @ SV92 ) @ ( bit1 @ SV151 ) )
| ( ord_less_eq @ int @ SV92 @ SV151 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[919]) ).
thf(1020,plain,
! [SV151: $i,SV92: $i] :
( ( ~ ( ord_less_eq @ int @ SV92 @ SV151 )
| ( ord_less_eq @ int @ ( bit1 @ SV92 ) @ ( bit1 @ SV151 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[920]) ).
thf(1021,plain,
! [SV93: $i,SV176: $i,SV152: $i] :
( ( ( ord_less_eq @ int @ SV152 @ SV176 )
= $false )
| ( ( ord_less_eq @ int @ ( plus_plus @ int @ SV93 @ SV152 ) @ ( plus_plus @ int @ SV93 @ SV176 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[921]) ).
thf(1022,plain,
! [SV94: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( bit1 @ SV94 ) @ pls ) )
= $true )
| ( ( ord_less @ int @ SV94 @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[922]) ).
thf(1023,plain,
! [SV94: $i] :
( ( ( ~ ( ord_less @ int @ SV94 @ pls ) )
= $true )
| ( ( ord_less_eq @ int @ ( bit1 @ SV94 ) @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[923]) ).
thf(1024,plain,
! [SV204: $i,SV192: $i,SV95: $i] :
( ( ( ~ ( ord_less @ SV95 @ ( plus_plus @ SV95 @ ( power_power @ SV95 @ SV192 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV95 @ SV204 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( zero_zero @ SV95 ) ) )
= $true )
| ( ( linordered_idom @ SV95 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[924]) ).
thf(1025,plain,
! [SV153: $i,SV96: $i] :
( ( ~ ( ord_less @ int @ ( number_number_of @ int @ SV96 ) @ ( number_number_of @ int @ SV153 ) )
| ( ord_less @ int @ SV96 @ SV153 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[925]) ).
thf(1026,plain,
! [SV153: $i,SV96: $i] :
( ( ~ ( ord_less @ int @ SV96 @ SV153 )
| ( ord_less @ int @ ( number_number_of @ int @ SV96 ) @ ( number_number_of @ int @ SV153 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[926]) ).
thf(1027,plain,
! [SV205: $i,SV193: $i,SV97: $i] :
( ( ( ~ ( ~ ( ( ( plus_plus @ SV97 @ ( times_times @ SV97 @ SV193 @ SV193 ) @ ( times_times @ SV97 @ SV205 @ SV205 ) )
!= ( zero_zero @ SV97 ) )
| ~ ( ( ( ti @ SV97 @ SV193 )
!= ( zero_zero @ SV97 ) )
| ( ( ti @ SV97 @ SV205 )
!= ( zero_zero @ SV97 ) ) ) )
| ~ ( ~ ~ ( ( ( ti @ SV97 @ SV193 )
!= ( zero_zero @ SV97 ) )
| ( ( ti @ SV97 @ SV205 )
!= ( zero_zero @ SV97 ) ) )
| ( ( plus_plus @ SV97 @ ( times_times @ SV97 @ SV193 @ SV193 ) @ ( times_times @ SV97 @ SV205 @ SV205 ) )
= ( zero_zero @ SV97 ) ) ) ) )
= $true )
| ( ( linord581940658strict @ SV97 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[927]) ).
thf(1028,plain,
! [SV154: $i,SV98: $i,SV194: $i,SV177: $i] :
( ( ( ~ ( ord_less @ int @ SV177 @ SV194 ) )
= $true )
| ( ( ~ ( ord_less_eq @ int @ SV98 @ SV154 )
| ( ord_less @ int @ ( plus_plus @ int @ SV177 @ SV98 ) @ ( plus_plus @ int @ SV194 @ SV154 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[928]) ).
thf(1029,plain,
! [SV99: $i] :
( ( ( ~ ( number_ring @ SV99 ) )
= $true )
| ( ( ~ ( linordered_idom @ SV99 ) )
= $true )
| ( ( ! [SY338: $i,SY339: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV99 @ ( number_number_of @ SV99 @ SY338 ) @ ( number_number_of @ SV99 @ SY339 ) )
| ( ord_less_eq @ int @ SY338 @ SY339 ) )
| ~ ( ~ ( ord_less_eq @ int @ SY338 @ SY339 )
| ( ord_less_eq @ SV99 @ ( number_number_of @ SV99 @ SY338 ) @ ( number_number_of @ SV99 @ SY339 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[929]) ).
thf(1030,plain,
! [SV155: $i,SV101: $i] :
( ( ~ ( ord_less_eq @ int @ ( bit0 @ SV101 ) @ ( bit1 @ SV155 ) )
| ( ord_less_eq @ int @ SV101 @ SV155 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[930]) ).
thf(1031,plain,
! [SV155: $i,SV101: $i] :
( ( ~ ( ord_less_eq @ int @ SV101 @ SV155 )
| ( ord_less_eq @ int @ ( bit0 @ SV101 ) @ ( bit1 @ SV155 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[931]) ).
thf(1032,plain,
! [SV103: $i] :
( ( ( ~ ( number_ring @ SV103 ) )
= $true )
| ( ( ~ ( linordered_idom @ SV103 ) )
= $true )
| ( ( ! [SY341: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV103 @ ( one_one @ SV103 ) @ ( number_number_of @ SV103 @ SY341 ) )
| ( ord_less_eq @ int @ ( bit1 @ pls ) @ SY341 ) )
| ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ pls ) @ SY341 )
| ( ord_less_eq @ SV103 @ ( one_one @ SV103 ) @ ( number_number_of @ SV103 @ SY341 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[932]) ).
thf(1033,plain,
! [SV195: $i,SV178: $i,SV23: $i] :
( ( ( ~ ( ( ( plus_plus @ SV23 @ ( power_power @ SV23 @ SV178 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV23 @ SV195 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV23 ) )
| ~ ( ( ( ti @ SV23 @ SV178 )
!= ( zero_zero @ SV23 ) )
| ( ( ti @ SV23 @ SV195 )
!= ( zero_zero @ SV23 ) ) ) )
| ~ ( ~ ~ ( ( ( ti @ SV23 @ SV178 )
!= ( zero_zero @ SV23 ) )
| ( ( ti @ SV23 @ SV195 )
!= ( zero_zero @ SV23 ) ) )
| ( ( plus_plus @ SV23 @ ( power_power @ SV23 @ SV178 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV23 @ SV195 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV23 ) ) ) )
= $false )
| ( ( linordered_idom @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[933]) ).
thf(1034,plain,
! [SV24: $i,SV179: $i,SV196: $i] :
( ( ( ~ ( ord_less_eq @ int @ pls @ SV196 ) )
= $true )
| ( ( ~ ( ord_less_eq @ int @ pls @ SV179 )
| ( ( plus_plus @ SV24 @ ( number_number_of @ SV24 @ SV196 ) @ ( number_number_of @ SV24 @ SV179 ) )
= ( number_number_of @ SV24 @ ( plus_plus @ int @ SV196 @ SV179 ) ) ) )
= $true )
| ( ( number_semiring @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[934]) ).
thf(1035,plain,
! [SV118: $i,SV26: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( plus_plus @ int @ SV26 @ ( one_one @ int ) ) @ SV118 ) )
= $true )
| ( ( ord_less @ int @ SV26 @ SV118 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[936]) ).
thf(1036,plain,
! [SV118: $i,SV26: $i] :
( ( ( ~ ( ord_less @ int @ SV26 @ SV118 ) )
= $true )
| ( ( ord_less_eq @ int @ ( plus_plus @ int @ SV26 @ ( one_one @ int ) ) @ SV118 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[937]) ).
thf(1037,plain,
! [SV119: $i,SV28: $i] :
( ( ( ~ ( ord_less @ nat @ ( number_number_of @ nat @ SV28 ) @ ( number_number_of @ nat @ SV119 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( ord_less @ int @ SV28 @ SV119 )
| ( ord_less @ int @ pls @ SV119 ) )
| ~ ( ord_less @ int @ SV28 @ SV119 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[938]) ).
thf(1038,plain,
! [SV119: $i,SV28: $i] :
( ( ( ~ ~ ( ~ ( ~ ( ord_less @ int @ SV28 @ SV119 )
| ( ord_less @ int @ pls @ SV119 ) )
| ~ ( ord_less @ int @ SV28 @ SV119 ) ) )
= $true )
| ( ( ord_less @ nat @ ( number_number_of @ nat @ SV28 ) @ ( number_number_of @ nat @ SV119 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[939]) ).
thf(1039,plain,
! [SV33: $i] :
( ( ( number_ring @ SV33 )
= $false )
| ( ( ~ ( ring_char_0 @ SV33 ) )
= $true )
| ( ( ! [SY254: $i,SY255: $i] :
~ ( ~ ( ( ( number_number_of @ SV33 @ SY254 )
!= ( number_number_of @ SV33 @ SY255 ) )
| ( SY254 = SY255 ) )
| ~ ( ( SY254 != SY255 )
| ( ( number_number_of @ SV33 @ SY254 )
= ( number_number_of @ SV33 @ SY255 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[942]) ).
thf(1040,plain,
! [SV34: $i] :
( ( ( ord_less @ int @ pls @ ( bit1 @ SV34 ) )
= $false )
| ( ( ord_less_eq @ int @ pls @ SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[943]) ).
thf(1041,plain,
! [SV34: $i] :
( ( ( ord_less_eq @ int @ pls @ SV34 )
= $false )
| ( ( ord_less @ int @ pls @ ( bit1 @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[944]) ).
thf(1042,plain,
! [SV181: $i,SV35: $i] :
( ( ( ~ ( ( ( power_power @ SV35 @ SV181 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= ( zero_zero @ SV35 ) )
| ( ( ti @ SV35 @ SV181 )
= ( zero_zero @ SV35 ) ) ) )
= $false )
| ( ( ring_11004092258visors @ SV35 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[945]) ).
thf(1043,plain,
! [SV181: $i,SV35: $i] :
( ( ( ~ ( ( ( ti @ SV35 @ SV181 )
!= ( zero_zero @ SV35 ) )
| ( ( power_power @ SV35 @ SV181 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SV35 ) ) ) )
= $false )
| ( ( ring_11004092258visors @ SV35 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[945]) ).
thf(1044,plain,
! [SV37: $i] :
( ( ( ord_less_eq @ int @ pls @ ( bit1 @ SV37 ) )
= $false )
| ( ( ord_less_eq @ int @ pls @ SV37 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[947]) ).
thf(1045,plain,
! [SV37: $i] :
( ( ( ord_less_eq @ int @ pls @ SV37 )
= $false )
| ( ( ord_less_eq @ int @ pls @ ( bit1 @ SV37 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[948]) ).
thf(1046,plain,
! [SV122: $i,SV38: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( bit1 @ SV38 ) @ ( bit1 @ SV122 ) ) )
= $true )
| ( ( ord_less_eq @ int @ SV38 @ SV122 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[949]) ).
thf(1047,plain,
! [SV122: $i,SV38: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV38 @ SV122 ) )
= $true )
| ( ( ord_less_eq @ int @ ( bit1 @ SV38 ) @ ( bit1 @ SV122 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[950]) ).
thf(1048,plain,
! [SV123: $i,SV39: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( bit1 @ SV39 ) @ ( bit0 @ SV123 ) ) )
= $true )
| ( ( ord_less @ int @ SV39 @ SV123 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[951]) ).
thf(1049,plain,
! [SV123: $i,SV39: $i] :
( ( ( ~ ( ord_less @ int @ SV39 @ SV123 ) )
= $true )
| ( ( ord_less_eq @ int @ ( bit1 @ SV39 ) @ ( bit0 @ SV123 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[952]) ).
thf(1050,plain,
! [SV40: $i,SV124: $i] :
( ( ( ~ ( ord_less @ int @ SV124 @ pls ) )
= $true )
| ( ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV124 ) @ ( number_number_of @ nat @ SV40 ) )
= ( number_number_of @ nat @ SV40 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[953]) ).
thf(1051,plain,
! [SV40: $i,SV124: $i] :
( ( ( ~ ~ ( ord_less @ int @ SV124 @ pls ) )
= $true )
| ( ( ~ ( ~ ( ~ ( ord_less @ int @ SV40 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV124 ) @ ( number_number_of @ nat @ SV40 ) )
= ( number_number_of @ nat @ SV124 ) ) )
| ~ ( ~ ~ ( ord_less @ int @ SV40 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV124 ) @ ( number_number_of @ nat @ SV40 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SV124 @ SV40 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[954]) ).
thf(1052,plain,
! [SV125: $i,SV41: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( number_number_of @ int @ SV41 ) @ ( number_number_of @ int @ SV125 ) ) )
= $true )
| ( ( ord_less_eq @ int @ SV41 @ SV125 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[955]) ).
thf(1053,plain,
! [SV125: $i,SV41: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV41 @ SV125 ) )
= $true )
| ( ( ord_less_eq @ int @ ( number_number_of @ int @ SV41 ) @ ( number_number_of @ int @ SV125 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[956]) ).
thf(1054,plain,
! [SV42: $i,SV183: $i,SV198: $i] :
( ( ( ~ ( ord_less_eq @ int @ pls @ SV198 ) )
= $true )
| ( ( ~ ( ord_less_eq @ int @ pls @ SV183 )
| ( ( times_times @ SV42 @ ( number_number_of @ SV42 @ SV198 ) @ ( number_number_of @ SV42 @ SV183 ) )
= ( number_number_of @ SV42 @ ( times_times @ int @ SV198 @ SV183 ) ) ) )
= $true )
| ( ( number_semiring @ SV42 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[957]) ).
thf(1055,plain,
! [SV126: $i,SV43: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( bit0 @ SV43 ) @ ( bit0 @ SV126 ) ) )
= $true )
| ( ( ord_less_eq @ int @ SV43 @ SV126 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[958]) ).
thf(1056,plain,
! [SV126: $i,SV43: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV43 @ SV126 ) )
= $true )
| ( ( ord_less_eq @ int @ ( bit0 @ SV43 ) @ ( bit0 @ SV126 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[959]) ).
thf(1057,plain,
! [SV184: $i,SV45: $i] :
( ( ( ~ ( ~ ( ord_less @ SV45 @ ( zero_zero @ SV45 ) @ ( power_power @ SV45 @ SV184 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ( ( ti @ SV45 @ SV184 )
!= ( zero_zero @ SV45 ) ) ) )
= $false )
| ( ( linordered_idom @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[961]) ).
thf(1058,plain,
! [SV184: $i,SV45: $i] :
( ( ( ~ ( ~ ( ( ( ti @ SV45 @ SV184 )
!= ( zero_zero @ SV45 ) ) )
| ( ord_less @ SV45 @ ( zero_zero @ SV45 ) @ ( power_power @ SV45 @ SV184 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $false )
| ( ( linordered_idom @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[961]) ).
thf(1059,plain,
! [SV46: $i] :
( ( ( ord_less_eq @ int @ ( bit0 @ SV46 ) @ pls )
= $false )
| ( ( ord_less_eq @ int @ SV46 @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[962]) ).
thf(1060,plain,
! [SV46: $i] :
( ( ( ord_less_eq @ int @ SV46 @ pls )
= $false )
| ( ( ord_less_eq @ int @ ( bit0 @ SV46 ) @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[963]) ).
thf(1061,plain,
! [SV128: $i,SV47: $i] :
( ( ( ( bit1 @ SV47 )
!= ( bit1 @ SV128 ) )
= $true )
| ( ( SV47 = SV128 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[964]) ).
thf(1062,plain,
! [SV128: $i,SV47: $i] :
( ( ( SV47 != SV128 )
= $true )
| ( ( ( bit1 @ SV47 )
= ( bit1 @ SV128 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[965]) ).
thf(1063,plain,
! [SV48: $i] :
( ( ( number @ SV48 )
= $false )
| ( ( ~ ( semiring @ SV48 ) )
= $true )
| ( ( ! [SY270: $i,SY271: $i,SY272: $i] :
( ( times_times @ SV48 @ ( number_number_of @ SV48 @ SY270 ) @ ( plus_plus @ SV48 @ SY271 @ SY272 ) )
= ( plus_plus @ SV48 @ ( times_times @ SV48 @ ( number_number_of @ SV48 @ SY270 ) @ SY271 ) @ ( times_times @ SV48 @ ( number_number_of @ SV48 @ SY270 ) @ SY272 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[966]) ).
thf(1064,plain,
! [SV129: $i,SV49: $i,SV165: $i] :
( ( ( ~ ( ~ ( ord_less @ SV165 @ ( ti @ SV165 @ SV49 ) @ SV129 )
| ( ord_less @ SV165 @ SV49 @ SV129 ) )
| ~ ( ~ ( ord_less @ SV165 @ SV49 @ SV129 )
| ( ord_less @ SV165 @ ( ti @ SV165 @ SV49 ) @ SV129 ) ) )
= $false )
| ( ( linordered_idom @ SV165 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[967]) ).
thf(1065,plain,
! [SV131: $i,SV51: $i,SV166: $i] :
( ( ( ~ ( ~ ( ord_less @ SV166 @ SV51 @ ( ti @ SV166 @ SV131 ) )
| ( ord_less @ SV166 @ SV51 @ SV131 ) )
| ~ ( ~ ( ord_less @ SV166 @ SV51 @ SV131 )
| ( ord_less @ SV166 @ SV51 @ ( ti @ SV166 @ SV131 ) ) ) )
= $false )
| ( ( linordered_idom @ SV166 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[968]) ).
thf(1066,plain,
! [SV132: $i,SV52: $i,SV167: $i] :
( ( ( ~ ( number @ SV167 )
| ~ ( semiring @ SV167 ) )
= $true )
| ( ( ( plus_plus @ SV167 @ SV52 @ ( ti @ SV167 @ SV132 ) )
= ( plus_plus @ SV167 @ SV52 @ SV132 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[969]) ).
thf(1067,plain,
! [SV199: $i,SV185: $i,SV53: $i] :
( ( ( ~ ( ( ( number_number_of @ SV53 @ SV185 )
!= ( ti @ SV53 @ SV199 ) )
| ( ( ti @ SV53 @ SV199 )
= ( number_number_of @ SV53 @ SV185 ) ) )
| ~ ( ( ( ti @ SV53 @ SV199 )
!= ( number_number_of @ SV53 @ SV185 ) )
| ( ( number_number_of @ SV53 @ SV185 )
= ( ti @ SV53 @ SV199 ) ) ) )
= $false )
| ( ( number @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[970]) ).
thf(1068,plain,
! [SV54: $i] :
( ( ( ord_less_eq @ int @ ( one_one @ int ) @ SV54 )
= $false )
| ( ( ord_less @ int @ ( zero_zero @ int ) @ SV54 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[971]) ).
thf(1069,plain,
! [SV54: $i] :
( ( ( ord_less @ int @ ( zero_zero @ int ) @ SV54 )
= $false )
| ( ( ord_less_eq @ int @ ( one_one @ int ) @ SV54 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[972]) ).
thf(1070,plain,
! [SV133: $i,SV55: $i,SV168: $i] :
( ( ( ~ ( number @ SV168 )
| ~ ( semiring @ SV168 ) )
= $true )
| ( ( ( plus_plus @ SV168 @ ( ti @ SV168 @ SV55 ) @ SV133 )
= ( plus_plus @ SV168 @ SV55 @ SV133 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[973]) ).
thf(1071,plain,
! [SV201: $i,SV188: $i,SV59: $i] :
( ( ( ~ ( ~ ( ord_less @ SV59 @ ( zero_zero @ SV59 ) @ ( plus_plus @ SV59 @ ( power_power @ SV59 @ SV188 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV59 @ SV201 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
| ( ( ti @ SV59 @ SV188 )
!= ( zero_zero @ SV59 ) )
| ( ( ti @ SV59 @ SV201 )
!= ( zero_zero @ SV59 ) ) )
| ~ ( ~ ( ( ( ti @ SV59 @ SV188 )
!= ( zero_zero @ SV59 ) )
| ( ( ti @ SV59 @ SV201 )
!= ( zero_zero @ SV59 ) ) )
| ( ord_less @ SV59 @ ( zero_zero @ SV59 ) @ ( plus_plus @ SV59 @ ( power_power @ SV59 @ SV188 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV59 @ SV201 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) )
= $false )
| ( ( linordered_idom @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[976]) ).
thf(1072,plain,
! [SV135: $i,SV60: $i] :
( ( ( ( bit0 @ SV60 )
!= ( bit0 @ SV135 ) )
= $true )
| ( ( SV60 = SV135 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[977]) ).
thf(1073,plain,
! [SV135: $i,SV60: $i] :
( ( ( SV60 != SV135 )
= $true )
| ( ( ( bit0 @ SV60 )
= ( bit0 @ SV135 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[978]) ).
thf(1074,plain,
! [SV136: $i,SV61: $i] :
( ( ( ~ ( ord_less @ int @ ( bit0 @ SV61 ) @ ( bit1 @ SV136 ) ) )
= $true )
| ( ( ord_less_eq @ int @ SV61 @ SV136 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[979]) ).
thf(1075,plain,
! [SV136: $i,SV61: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV61 @ SV136 ) )
= $true )
| ( ( ord_less @ int @ ( bit0 @ SV61 ) @ ( bit1 @ SV136 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[980]) ).
thf(1076,plain,
! [SV137: $i,SV62: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( bit0 @ SV62 ) @ ( bit1 @ SV137 ) ) )
= $true )
| ( ( ord_less_eq @ int @ SV62 @ SV137 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[981]) ).
thf(1077,plain,
! [SV137: $i,SV62: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV62 @ SV137 ) )
= $true )
| ( ( ord_less_eq @ int @ ( bit0 @ SV62 ) @ ( bit1 @ SV137 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[982]) ).
thf(1078,plain,
! [SV138: $i,SV63: $i,SV170: $i] :
( ( ( ~ ( number @ SV170 )
| ~ ( linorder @ SV170 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( ord_less @ SV170 @ SV63 @ ( ti @ SV170 @ SV138 ) )
| ( ord_less @ SV170 @ SV63 @ SV138 ) )
| ~ ( ~ ( ord_less @ SV170 @ SV63 @ SV138 )
| ( ord_less @ SV170 @ SV63 @ ( ti @ SV170 @ SV138 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[983]) ).
thf(1079,plain,
! [SV139: $i,SV65: $i] :
( ( ( ~ ( ord_less @ int @ SV65 @ SV139 ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq @ int @ SV65 @ SV139 )
| ~ ( ( SV65 != SV139 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[984]) ).
thf(1080,plain,
! [SV139: $i,SV65: $i] :
( ( ( ~ ~ ( ~ ( ord_less_eq @ int @ SV65 @ SV139 )
| ~ ( ( SV65 != SV139 ) ) ) )
= $true )
| ( ( ord_less @ int @ SV65 @ SV139 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[985]) ).
thf(1081,plain,
! [SV66: $i] :
( ( ( twoSqu33214720sum2sq @ ( ti @ int @ SV66 ) )
= $false )
| ( ( twoSqu33214720sum2sq @ SV66 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[986]) ).
thf(1082,plain,
! [SV66: $i] :
( ( ( twoSqu33214720sum2sq @ SV66 )
= $false )
| ( ( twoSqu33214720sum2sq @ ( ti @ int @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[987]) ).
thf(1083,plain,
! [SV206: $i,SV202: $i,SV189: $i,SV67: $i] :
( ( ( ( times_times @ SV67 @ ( number_number_of @ SV67 @ SV189 ) @ ( times_times @ SV67 @ ( number_number_of @ SV67 @ SV202 ) @ SV206 ) )
= ( times_times @ SV67 @ ( number_number_of @ SV67 @ ( times_times @ int @ SV189 @ SV202 ) ) @ SV206 ) )
= $true )
| ( ( number_ring @ SV67 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[988]) ).
thf(1084,plain,
! [SV68: $i] :
( ( ( number_ring @ SV68 )
= $false )
| ( ( ~ ( linordered_idom @ SV68 ) )
= $true )
| ( ( ! [SY300: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV68 @ ( zero_zero @ SV68 ) @ ( number_number_of @ SV68 @ SY300 ) )
| ( ord_less_eq @ int @ pls @ SY300 ) )
| ~ ( ~ ( ord_less_eq @ int @ pls @ SY300 )
| ( ord_less_eq @ SV68 @ ( zero_zero @ SV68 ) @ ( number_number_of @ SV68 @ SY300 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[989]) ).
thf(1085,plain,
! [SV69: $i] :
( ( ( ord_less_eq @ int @ pls @ ( bit0 @ SV69 ) )
= $false )
| ( ( ord_less_eq @ int @ pls @ SV69 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[990]) ).
thf(1086,plain,
! [SV69: $i] :
( ( ( ord_less_eq @ int @ pls @ SV69 )
= $false )
| ( ( ord_less_eq @ int @ pls @ ( bit0 @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[991]) ).
thf(1087,plain,
! [SV70: $i] :
( ( ( number_ring @ SV70 )
= $false )
| ( ( ~ ( linordered_idom @ SV70 ) )
= $true )
| ( ( ! [SY301: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV70 @ ( number_number_of @ SV70 @ SY301 ) @ ( zero_zero @ SV70 ) )
| ( ord_less_eq @ int @ SY301 @ pls ) )
| ~ ( ~ ( ord_less_eq @ int @ SY301 @ pls )
| ( ord_less_eq @ SV70 @ ( number_number_of @ SV70 @ SY301 ) @ ( zero_zero @ SV70 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[992]) ).
thf(1088,plain,
! [SV140: $i,SV71: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( bit0 @ SV71 ) @ ( bit0 @ SV140 ) ) )
= $true )
| ( ( ord_less_eq @ int @ SV71 @ SV140 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[993]) ).
thf(1089,plain,
! [SV140: $i,SV71: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV71 @ SV140 ) )
= $true )
| ( ( ord_less_eq @ int @ ( bit0 @ SV71 ) @ ( bit0 @ SV140 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[994]) ).
thf(1090,plain,
! [SV72: $i] :
( ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( number_number_of @ nat @ SV72 ) )
= $false )
| ( ( ord_less @ int @ pls @ SV72 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[995]) ).
thf(1091,plain,
! [SV72: $i] :
( ( ( ord_less @ int @ pls @ SV72 )
= $false )
| ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( number_number_of @ nat @ SV72 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[996]) ).
thf(1092,plain,
! [SV73: $i] :
( ( ( number_ring @ SV73 )
= $false )
| ( ( ~ ( linordered_idom @ SV73 ) )
= $true )
| ( ( ! [SY303: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV73 @ ( number_number_of @ SV73 @ SY303 ) @ ( one_one @ SV73 ) )
| ( ord_less_eq @ int @ SY303 @ ( bit1 @ pls ) ) )
| ~ ( ~ ( ord_less_eq @ int @ SY303 @ ( bit1 @ pls ) )
| ( ord_less_eq @ SV73 @ ( number_number_of @ SV73 @ SY303 ) @ ( one_one @ SV73 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[997]) ).
thf(1093,plain,
! [SV141: $i,SV75: $i,SV171: $i] :
( ( ( ~ ( number @ SV171 )
| ~ ( semiring @ SV171 ) )
= $true )
| ( ( ( ti @ SV171 @ ( plus_plus @ SV171 @ SV75 @ SV141 ) )
= ( plus_plus @ SV171 @ SV75 @ SV141 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[998]) ).
thf(1094,plain,
! [SV76: $i] :
( ( ( zprime @ ( ti @ int @ SV76 ) )
= $false )
| ( ( zprime @ SV76 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[999]) ).
thf(1095,plain,
! [SV76: $i] :
( ( ( zprime @ SV76 )
= $false )
| ( ( zprime @ ( ti @ int @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1000]) ).
thf(1096,plain,
! [SV79: $i] :
( ( ( number @ SV79 )
= $false )
| ( ( ~ ( linorder @ SV79 ) )
= $true )
| ( ( ! [SY309: $i,SY310: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV79 @ ( number_number_of @ SV79 @ SY309 ) @ ( number_number_of @ SV79 @ SY310 ) )
| ~ ( ord_less @ SV79 @ ( number_number_of @ SV79 @ SY310 ) @ ( number_number_of @ SV79 @ SY309 ) ) )
| ~ ( ~ ~ ( ord_less @ SV79 @ ( number_number_of @ SV79 @ SY310 ) @ ( number_number_of @ SV79 @ SY309 ) )
| ( ord_less_eq @ SV79 @ ( number_number_of @ SV79 @ SY309 ) @ ( number_number_of @ SV79 @ SY310 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1002]) ).
thf(1097,plain,
! [SV143: $i,SV80: $i] :
( ( ( ~ ( ord_less @ int @ SV80 @ ( plus_plus @ int @ SV143 @ ( one_one @ int ) ) ) )
= $true )
| ( ( ord_less_eq @ int @ SV80 @ SV143 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1003]) ).
thf(1098,plain,
! [SV143: $i,SV80: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV80 @ SV143 ) )
= $true )
| ( ( ord_less @ int @ SV80 @ ( plus_plus @ int @ SV143 @ ( one_one @ int ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1004]) ).
thf(1099,plain,
! [SV144: $i,SV81: $i] :
( ( ( ~ ( ord_less @ int @ ( bit0 @ SV81 ) @ ( bit1 @ SV144 ) ) )
= $true )
| ( ( ord_less_eq @ int @ SV81 @ SV144 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1005]) ).
thf(1100,plain,
! [SV144: $i,SV81: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV81 @ SV144 ) )
= $true )
| ( ( ord_less @ int @ ( bit0 @ SV81 ) @ ( bit1 @ SV144 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1006]) ).
thf(1101,plain,
! [SV82: $i,SV145: $i] :
( ( ( ord_less_eq @ int @ SV145 @ SV82 )
= $false )
| ( ( SV82 = SV145 )
= $true )
| ( ( ord_less_eq @ int @ SV82 @ SV145 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1007]) ).
thf(1102,plain,
! [SV83: $i] :
( ( ( ( zero_zero @ nat )
= ( number_number_of @ nat @ SV83 ) )
= $false )
| ( ( ord_less_eq @ int @ SV83 @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1008]) ).
thf(1103,plain,
! [SV83: $i] :
( ( ( ord_less_eq @ int @ SV83 @ pls )
= $false )
| ( ( ( zero_zero @ nat )
= ( number_number_of @ nat @ SV83 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1009]) ).
thf(1104,plain,
! [SV148: $i,SV87: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( bit1 @ SV87 ) @ ( bit0 @ SV148 ) ) )
= $true )
| ( ( ord_less @ int @ SV87 @ SV148 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1012]) ).
thf(1105,plain,
! [SV148: $i,SV87: $i] :
( ( ( ~ ( ord_less @ int @ SV87 @ SV148 ) )
= $true )
| ( ( ord_less_eq @ int @ ( bit1 @ SV87 ) @ ( bit0 @ SV148 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1013]) ).
thf(1106,plain,
! [SV88: $i] :
( ( ( number @ SV88 )
= $false )
| ( ( ~ ( semiring @ SV88 ) )
= $true )
| ( ( ! [SY320: $i,SY321: $i,SY322: $i] :
( ( times_times @ SV88 @ ( plus_plus @ SV88 @ SY320 @ SY321 ) @ ( number_number_of @ SV88 @ SY322 ) )
= ( plus_plus @ SV88 @ ( times_times @ SV88 @ SY320 @ ( number_number_of @ SV88 @ SY322 ) ) @ ( times_times @ SV88 @ SY321 @ ( number_number_of @ SV88 @ SY322 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1014]) ).
thf(1107,plain,
! [SV89: $i] :
( ( ( ( number_number_of @ nat @ SV89 )
= ( zero_zero @ nat ) )
= $false )
| ( ( ord_less_eq @ int @ SV89 @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1015]) ).
thf(1108,plain,
! [SV89: $i] :
( ( ( ord_less_eq @ int @ SV89 @ pls )
= $false )
| ( ( ( number_number_of @ nat @ SV89 )
= ( zero_zero @ nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1016]) ).
thf(1109,plain,
! [SV149: $i,SV90: $i,SV174: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV174 @ SV90 ) )
= $true )
| ( ( ord_less_eq @ int @ SV149 @ SV90 )
= $true )
| ( ( ord_less_eq @ int @ SV149 @ SV174 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1017]) ).
thf(1110,plain,
! [SV150: $i,SV91: $i,SV175: $i] :
( ( ( ~ ( number @ SV175 )
| ~ ( linorder @ SV175 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( ord_less @ SV175 @ ( ti @ SV175 @ SV91 ) @ SV150 )
| ( ord_less @ SV175 @ SV91 @ SV150 ) )
| ~ ( ~ ( ord_less @ SV175 @ SV91 @ SV150 )
| ( ord_less @ SV175 @ ( ti @ SV175 @ SV91 ) @ SV150 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1018]) ).
thf(1111,plain,
! [SV151: $i,SV92: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( bit1 @ SV92 ) @ ( bit1 @ SV151 ) ) )
= $true )
| ( ( ord_less_eq @ int @ SV92 @ SV151 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1019]) ).
thf(1112,plain,
! [SV151: $i,SV92: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV92 @ SV151 ) )
= $true )
| ( ( ord_less_eq @ int @ ( bit1 @ SV92 ) @ ( bit1 @ SV151 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1020]) ).
thf(1113,plain,
! [SV94: $i] :
( ( ( ord_less_eq @ int @ ( bit1 @ SV94 ) @ pls )
= $false )
| ( ( ord_less @ int @ SV94 @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1022]) ).
thf(1114,plain,
! [SV94: $i] :
( ( ( ord_less @ int @ SV94 @ pls )
= $false )
| ( ( ord_less_eq @ int @ ( bit1 @ SV94 ) @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1023]) ).
thf(1115,plain,
! [SV204: $i,SV192: $i,SV95: $i] :
( ( ( ord_less @ SV95 @ ( plus_plus @ SV95 @ ( power_power @ SV95 @ SV192 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV95 @ SV204 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( zero_zero @ SV95 ) )
= $false )
| ( ( linordered_idom @ SV95 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1024]) ).
thf(1116,plain,
! [SV153: $i,SV96: $i] :
( ( ( ~ ( ord_less @ int @ ( number_number_of @ int @ SV96 ) @ ( number_number_of @ int @ SV153 ) ) )
= $true )
| ( ( ord_less @ int @ SV96 @ SV153 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1025]) ).
thf(1117,plain,
! [SV153: $i,SV96: $i] :
( ( ( ~ ( ord_less @ int @ SV96 @ SV153 ) )
= $true )
| ( ( ord_less @ int @ ( number_number_of @ int @ SV96 ) @ ( number_number_of @ int @ SV153 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1026]) ).
thf(1118,plain,
! [SV205: $i,SV193: $i,SV97: $i] :
( ( ( ~ ( ( ( plus_plus @ SV97 @ ( times_times @ SV97 @ SV193 @ SV193 ) @ ( times_times @ SV97 @ SV205 @ SV205 ) )
!= ( zero_zero @ SV97 ) )
| ~ ( ( ( ti @ SV97 @ SV193 )
!= ( zero_zero @ SV97 ) )
| ( ( ti @ SV97 @ SV205 )
!= ( zero_zero @ SV97 ) ) ) )
| ~ ( ~ ~ ( ( ( ti @ SV97 @ SV193 )
!= ( zero_zero @ SV97 ) )
| ( ( ti @ SV97 @ SV205 )
!= ( zero_zero @ SV97 ) ) )
| ( ( plus_plus @ SV97 @ ( times_times @ SV97 @ SV193 @ SV193 ) @ ( times_times @ SV97 @ SV205 @ SV205 ) )
= ( zero_zero @ SV97 ) ) ) )
= $false )
| ( ( linord581940658strict @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1027]) ).
thf(1119,plain,
! [SV154: $i,SV98: $i,SV194: $i,SV177: $i] :
( ( ( ord_less @ int @ SV177 @ SV194 )
= $false )
| ( ( ~ ( ord_less_eq @ int @ SV98 @ SV154 )
| ( ord_less @ int @ ( plus_plus @ int @ SV177 @ SV98 ) @ ( plus_plus @ int @ SV194 @ SV154 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1028]) ).
thf(1120,plain,
! [SV99: $i] :
( ( ( number_ring @ SV99 )
= $false )
| ( ( ~ ( linordered_idom @ SV99 ) )
= $true )
| ( ( ! [SY338: $i,SY339: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV99 @ ( number_number_of @ SV99 @ SY338 ) @ ( number_number_of @ SV99 @ SY339 ) )
| ( ord_less_eq @ int @ SY338 @ SY339 ) )
| ~ ( ~ ( ord_less_eq @ int @ SY338 @ SY339 )
| ( ord_less_eq @ SV99 @ ( number_number_of @ SV99 @ SY338 ) @ ( number_number_of @ SV99 @ SY339 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1029]) ).
thf(1121,plain,
! [SV155: $i,SV101: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( bit0 @ SV101 ) @ ( bit1 @ SV155 ) ) )
= $true )
| ( ( ord_less_eq @ int @ SV101 @ SV155 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1030]) ).
thf(1122,plain,
! [SV155: $i,SV101: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV101 @ SV155 ) )
= $true )
| ( ( ord_less_eq @ int @ ( bit0 @ SV101 ) @ ( bit1 @ SV155 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1031]) ).
thf(1123,plain,
! [SV103: $i] :
( ( ( number_ring @ SV103 )
= $false )
| ( ( ~ ( linordered_idom @ SV103 ) )
= $true )
| ( ( ! [SY341: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV103 @ ( one_one @ SV103 ) @ ( number_number_of @ SV103 @ SY341 ) )
| ( ord_less_eq @ int @ ( bit1 @ pls ) @ SY341 ) )
| ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ pls ) @ SY341 )
| ( ord_less_eq @ SV103 @ ( one_one @ SV103 ) @ ( number_number_of @ SV103 @ SY341 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1032]) ).
thf(1124,plain,
! [SV195: $i,SV178: $i,SV23: $i] :
( ( ( ~ ( ( ( plus_plus @ SV23 @ ( power_power @ SV23 @ SV178 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV23 @ SV195 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV23 ) )
| ~ ( ( ( ti @ SV23 @ SV178 )
!= ( zero_zero @ SV23 ) )
| ( ( ti @ SV23 @ SV195 )
!= ( zero_zero @ SV23 ) ) ) ) )
= $false )
| ( ( linordered_idom @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1033]) ).
thf(1125,plain,
! [SV195: $i,SV178: $i,SV23: $i] :
( ( ( ~ ( ~ ~ ( ( ( ti @ SV23 @ SV178 )
!= ( zero_zero @ SV23 ) )
| ( ( ti @ SV23 @ SV195 )
!= ( zero_zero @ SV23 ) ) )
| ( ( plus_plus @ SV23 @ ( power_power @ SV23 @ SV178 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV23 @ SV195 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV23 ) ) ) )
= $false )
| ( ( linordered_idom @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1033]) ).
thf(1126,plain,
! [SV24: $i,SV179: $i,SV196: $i] :
( ( ( ord_less_eq @ int @ pls @ SV196 )
= $false )
| ( ( ~ ( ord_less_eq @ int @ pls @ SV179 )
| ( ( plus_plus @ SV24 @ ( number_number_of @ SV24 @ SV196 ) @ ( number_number_of @ SV24 @ SV179 ) )
= ( number_number_of @ SV24 @ ( plus_plus @ int @ SV196 @ SV179 ) ) ) )
= $true )
| ( ( number_semiring @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1034]) ).
thf(1127,plain,
! [SV118: $i,SV26: $i] :
( ( ( ord_less_eq @ int @ ( plus_plus @ int @ SV26 @ ( one_one @ int ) ) @ SV118 )
= $false )
| ( ( ord_less @ int @ SV26 @ SV118 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1035]) ).
thf(1128,plain,
! [SV118: $i,SV26: $i] :
( ( ( ord_less @ int @ SV26 @ SV118 )
= $false )
| ( ( ord_less_eq @ int @ ( plus_plus @ int @ SV26 @ ( one_one @ int ) ) @ SV118 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1036]) ).
thf(1129,plain,
! [SV119: $i,SV28: $i] :
( ( ( ord_less @ nat @ ( number_number_of @ nat @ SV28 ) @ ( number_number_of @ nat @ SV119 ) )
= $false )
| ( ( ~ ( ~ ( ~ ( ord_less @ int @ SV28 @ SV119 )
| ( ord_less @ int @ pls @ SV119 ) )
| ~ ( ord_less @ int @ SV28 @ SV119 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1037]) ).
thf(1130,plain,
! [SV119: $i,SV28: $i] :
( ( ( ~ ( ~ ( ~ ( ord_less @ int @ SV28 @ SV119 )
| ( ord_less @ int @ pls @ SV119 ) )
| ~ ( ord_less @ int @ SV28 @ SV119 ) ) )
= $false )
| ( ( ord_less @ nat @ ( number_number_of @ nat @ SV28 ) @ ( number_number_of @ nat @ SV119 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1038]) ).
thf(1131,plain,
! [SV33: $i] :
( ( ( ring_char_0 @ SV33 )
= $false )
| ( ( number_ring @ SV33 )
= $false )
| ( ( ! [SY254: $i,SY255: $i] :
~ ( ~ ( ( ( number_number_of @ SV33 @ SY254 )
!= ( number_number_of @ SV33 @ SY255 ) )
| ( SY254 = SY255 ) )
| ~ ( ( SY254 != SY255 )
| ( ( number_number_of @ SV33 @ SY254 )
= ( number_number_of @ SV33 @ SY255 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1039]) ).
thf(1132,plain,
! [SV181: $i,SV35: $i] :
( ( ( ( ( power_power @ SV35 @ SV181 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= ( zero_zero @ SV35 ) )
| ( ( ti @ SV35 @ SV181 )
= ( zero_zero @ SV35 ) ) )
= $true )
| ( ( ring_11004092258visors @ SV35 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1042]) ).
thf(1133,plain,
! [SV181: $i,SV35: $i] :
( ( ( ( ( ti @ SV35 @ SV181 )
!= ( zero_zero @ SV35 ) )
| ( ( power_power @ SV35 @ SV181 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SV35 ) ) )
= $true )
| ( ( ring_11004092258visors @ SV35 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1043]) ).
thf(1134,plain,
! [SV122: $i,SV38: $i] :
( ( ( ord_less_eq @ int @ ( bit1 @ SV38 ) @ ( bit1 @ SV122 ) )
= $false )
| ( ( ord_less_eq @ int @ SV38 @ SV122 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1046]) ).
thf(1135,plain,
! [SV122: $i,SV38: $i] :
( ( ( ord_less_eq @ int @ SV38 @ SV122 )
= $false )
| ( ( ord_less_eq @ int @ ( bit1 @ SV38 ) @ ( bit1 @ SV122 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1047]) ).
thf(1136,plain,
! [SV123: $i,SV39: $i] :
( ( ( ord_less_eq @ int @ ( bit1 @ SV39 ) @ ( bit0 @ SV123 ) )
= $false )
| ( ( ord_less @ int @ SV39 @ SV123 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1048]) ).
thf(1137,plain,
! [SV123: $i,SV39: $i] :
( ( ( ord_less @ int @ SV39 @ SV123 )
= $false )
| ( ( ord_less_eq @ int @ ( bit1 @ SV39 ) @ ( bit0 @ SV123 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1049]) ).
thf(1138,plain,
! [SV40: $i,SV124: $i] :
( ( ( ord_less @ int @ SV124 @ pls )
= $false )
| ( ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV124 ) @ ( number_number_of @ nat @ SV40 ) )
= ( number_number_of @ nat @ SV40 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1050]) ).
thf(1139,plain,
! [SV40: $i,SV124: $i] :
( ( ( ~ ( ord_less @ int @ SV124 @ pls ) )
= $false )
| ( ( ~ ( ~ ( ~ ( ord_less @ int @ SV40 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV124 ) @ ( number_number_of @ nat @ SV40 ) )
= ( number_number_of @ nat @ SV124 ) ) )
| ~ ( ~ ~ ( ord_less @ int @ SV40 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV124 ) @ ( number_number_of @ nat @ SV40 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SV124 @ SV40 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1051]) ).
thf(1140,plain,
! [SV125: $i,SV41: $i] :
( ( ( ord_less_eq @ int @ ( number_number_of @ int @ SV41 ) @ ( number_number_of @ int @ SV125 ) )
= $false )
| ( ( ord_less_eq @ int @ SV41 @ SV125 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1052]) ).
thf(1141,plain,
! [SV125: $i,SV41: $i] :
( ( ( ord_less_eq @ int @ SV41 @ SV125 )
= $false )
| ( ( ord_less_eq @ int @ ( number_number_of @ int @ SV41 ) @ ( number_number_of @ int @ SV125 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1053]) ).
thf(1142,plain,
! [SV42: $i,SV183: $i,SV198: $i] :
( ( ( ord_less_eq @ int @ pls @ SV198 )
= $false )
| ( ( ~ ( ord_less_eq @ int @ pls @ SV183 )
| ( ( times_times @ SV42 @ ( number_number_of @ SV42 @ SV198 ) @ ( number_number_of @ SV42 @ SV183 ) )
= ( number_number_of @ SV42 @ ( times_times @ int @ SV198 @ SV183 ) ) ) )
= $true )
| ( ( number_semiring @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1054]) ).
thf(1143,plain,
! [SV126: $i,SV43: $i] :
( ( ( ord_less_eq @ int @ ( bit0 @ SV43 ) @ ( bit0 @ SV126 ) )
= $false )
| ( ( ord_less_eq @ int @ SV43 @ SV126 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1055]) ).
thf(1144,plain,
! [SV126: $i,SV43: $i] :
( ( ( ord_less_eq @ int @ SV43 @ SV126 )
= $false )
| ( ( ord_less_eq @ int @ ( bit0 @ SV43 ) @ ( bit0 @ SV126 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1056]) ).
thf(1145,plain,
! [SV184: $i,SV45: $i] :
( ( ( ~ ( ord_less @ SV45 @ ( zero_zero @ SV45 ) @ ( power_power @ SV45 @ SV184 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
| ( ( ti @ SV45 @ SV184 )
!= ( zero_zero @ SV45 ) ) )
= $true )
| ( ( linordered_idom @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1057]) ).
thf(1146,plain,
! [SV184: $i,SV45: $i] :
( ( ( ~ ( ( ( ti @ SV45 @ SV184 )
!= ( zero_zero @ SV45 ) ) )
| ( ord_less @ SV45 @ ( zero_zero @ SV45 ) @ ( power_power @ SV45 @ SV184 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true )
| ( ( linordered_idom @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1058]) ).
thf(1147,plain,
! [SV128: $i,SV47: $i] :
( ( ( ( bit1 @ SV47 )
= ( bit1 @ SV128 ) )
= $false )
| ( ( SV47 = SV128 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1061]) ).
thf(1148,plain,
! [SV128: $i,SV47: $i] :
( ( ( SV47 = SV128 )
= $false )
| ( ( ( bit1 @ SV47 )
= ( bit1 @ SV128 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1062]) ).
thf(1149,plain,
! [SV48: $i] :
( ( ( semiring @ SV48 )
= $false )
| ( ( number @ SV48 )
= $false )
| ( ( ! [SY270: $i,SY271: $i,SY272: $i] :
( ( times_times @ SV48 @ ( number_number_of @ SV48 @ SY270 ) @ ( plus_plus @ SV48 @ SY271 @ SY272 ) )
= ( plus_plus @ SV48 @ ( times_times @ SV48 @ ( number_number_of @ SV48 @ SY270 ) @ SY271 ) @ ( times_times @ SV48 @ ( number_number_of @ SV48 @ SY270 ) @ SY272 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1063]) ).
thf(1150,plain,
! [SV129: $i,SV49: $i,SV165: $i] :
( ( ( ~ ( ~ ( ord_less @ SV165 @ ( ti @ SV165 @ SV49 ) @ SV129 )
| ( ord_less @ SV165 @ SV49 @ SV129 ) ) )
= $false )
| ( ( linordered_idom @ SV165 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1064]) ).
thf(1151,plain,
! [SV129: $i,SV49: $i,SV165: $i] :
( ( ( ~ ( ~ ( ord_less @ SV165 @ SV49 @ SV129 )
| ( ord_less @ SV165 @ ( ti @ SV165 @ SV49 ) @ SV129 ) ) )
= $false )
| ( ( linordered_idom @ SV165 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1064]) ).
thf(1152,plain,
! [SV131: $i,SV51: $i,SV166: $i] :
( ( ( ~ ( ~ ( ord_less @ SV166 @ SV51 @ ( ti @ SV166 @ SV131 ) )
| ( ord_less @ SV166 @ SV51 @ SV131 ) ) )
= $false )
| ( ( linordered_idom @ SV166 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1065]) ).
thf(1153,plain,
! [SV131: $i,SV51: $i,SV166: $i] :
( ( ( ~ ( ~ ( ord_less @ SV166 @ SV51 @ SV131 )
| ( ord_less @ SV166 @ SV51 @ ( ti @ SV166 @ SV131 ) ) ) )
= $false )
| ( ( linordered_idom @ SV166 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1065]) ).
thf(1154,plain,
! [SV132: $i,SV52: $i,SV167: $i] :
( ( ( ~ ( number @ SV167 ) )
= $true )
| ( ( ~ ( semiring @ SV167 ) )
= $true )
| ( ( ( plus_plus @ SV167 @ SV52 @ ( ti @ SV167 @ SV132 ) )
= ( plus_plus @ SV167 @ SV52 @ SV132 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1066]) ).
thf(1155,plain,
! [SV199: $i,SV185: $i,SV53: $i] :
( ( ( ~ ( ( ( number_number_of @ SV53 @ SV185 )
!= ( ti @ SV53 @ SV199 ) )
| ( ( ti @ SV53 @ SV199 )
= ( number_number_of @ SV53 @ SV185 ) ) ) )
= $false )
| ( ( number @ SV53 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1067]) ).
thf(1156,plain,
! [SV185: $i,SV199: $i,SV53: $i] :
( ( ( ~ ( ( ( ti @ SV53 @ SV199 )
!= ( number_number_of @ SV53 @ SV185 ) )
| ( ( number_number_of @ SV53 @ SV185 )
= ( ti @ SV53 @ SV199 ) ) ) )
= $false )
| ( ( number @ SV53 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1067]) ).
thf(1157,plain,
! [SV133: $i,SV55: $i,SV168: $i] :
( ( ( ~ ( number @ SV168 ) )
= $true )
| ( ( ~ ( semiring @ SV168 ) )
= $true )
| ( ( ( plus_plus @ SV168 @ ( ti @ SV168 @ SV55 ) @ SV133 )
= ( plus_plus @ SV168 @ SV55 @ SV133 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1070]) ).
thf(1158,plain,
! [SV201: $i,SV188: $i,SV59: $i] :
( ( ( ~ ( ~ ( ord_less @ SV59 @ ( zero_zero @ SV59 ) @ ( plus_plus @ SV59 @ ( power_power @ SV59 @ SV188 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV59 @ SV201 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
| ( ( ti @ SV59 @ SV188 )
!= ( zero_zero @ SV59 ) )
| ( ( ti @ SV59 @ SV201 )
!= ( zero_zero @ SV59 ) ) ) )
= $false )
| ( ( linordered_idom @ SV59 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1071]) ).
thf(1159,plain,
! [SV201: $i,SV188: $i,SV59: $i] :
( ( ( ~ ( ~ ( ( ( ti @ SV59 @ SV188 )
!= ( zero_zero @ SV59 ) )
| ( ( ti @ SV59 @ SV201 )
!= ( zero_zero @ SV59 ) ) )
| ( ord_less @ SV59 @ ( zero_zero @ SV59 ) @ ( plus_plus @ SV59 @ ( power_power @ SV59 @ SV188 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV59 @ SV201 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) )
= $false )
| ( ( linordered_idom @ SV59 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1071]) ).
thf(1160,plain,
! [SV135: $i,SV60: $i] :
( ( ( ( bit0 @ SV60 )
= ( bit0 @ SV135 ) )
= $false )
| ( ( SV60 = SV135 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1072]) ).
thf(1161,plain,
! [SV135: $i,SV60: $i] :
( ( ( SV60 = SV135 )
= $false )
| ( ( ( bit0 @ SV60 )
= ( bit0 @ SV135 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1073]) ).
thf(1162,plain,
! [SV136: $i,SV61: $i] :
( ( ( ord_less @ int @ ( bit0 @ SV61 ) @ ( bit1 @ SV136 ) )
= $false )
| ( ( ord_less_eq @ int @ SV61 @ SV136 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1074]) ).
thf(1163,plain,
! [SV136: $i,SV61: $i] :
( ( ( ord_less_eq @ int @ SV61 @ SV136 )
= $false )
| ( ( ord_less @ int @ ( bit0 @ SV61 ) @ ( bit1 @ SV136 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1075]) ).
thf(1164,plain,
! [SV137: $i,SV62: $i] :
( ( ( ord_less_eq @ int @ ( bit0 @ SV62 ) @ ( bit1 @ SV137 ) )
= $false )
| ( ( ord_less_eq @ int @ SV62 @ SV137 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1076]) ).
thf(1165,plain,
! [SV137: $i,SV62: $i] :
( ( ( ord_less_eq @ int @ SV62 @ SV137 )
= $false )
| ( ( ord_less_eq @ int @ ( bit0 @ SV62 ) @ ( bit1 @ SV137 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1077]) ).
thf(1166,plain,
! [SV138: $i,SV63: $i,SV170: $i] :
( ( ( ~ ( number @ SV170 ) )
= $true )
| ( ( ~ ( linorder @ SV170 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( ord_less @ SV170 @ SV63 @ ( ti @ SV170 @ SV138 ) )
| ( ord_less @ SV170 @ SV63 @ SV138 ) )
| ~ ( ~ ( ord_less @ SV170 @ SV63 @ SV138 )
| ( ord_less @ SV170 @ SV63 @ ( ti @ SV170 @ SV138 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1078]) ).
thf(1167,plain,
! [SV139: $i,SV65: $i] :
( ( ( ord_less @ int @ SV65 @ SV139 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq @ int @ SV65 @ SV139 )
| ~ ( ( SV65 != SV139 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1079]) ).
thf(1168,plain,
! [SV139: $i,SV65: $i] :
( ( ( ~ ( ~ ( ord_less_eq @ int @ SV65 @ SV139 )
| ~ ( ( SV65 != SV139 ) ) ) )
= $false )
| ( ( ord_less @ int @ SV65 @ SV139 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1080]) ).
thf(1169,plain,
! [SV68: $i] :
( ( ( linordered_idom @ SV68 )
= $false )
| ( ( number_ring @ SV68 )
= $false )
| ( ( ! [SY300: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV68 @ ( zero_zero @ SV68 ) @ ( number_number_of @ SV68 @ SY300 ) )
| ( ord_less_eq @ int @ pls @ SY300 ) )
| ~ ( ~ ( ord_less_eq @ int @ pls @ SY300 )
| ( ord_less_eq @ SV68 @ ( zero_zero @ SV68 ) @ ( number_number_of @ SV68 @ SY300 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1084]) ).
thf(1170,plain,
! [SV70: $i] :
( ( ( linordered_idom @ SV70 )
= $false )
| ( ( number_ring @ SV70 )
= $false )
| ( ( ! [SY301: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV70 @ ( number_number_of @ SV70 @ SY301 ) @ ( zero_zero @ SV70 ) )
| ( ord_less_eq @ int @ SY301 @ pls ) )
| ~ ( ~ ( ord_less_eq @ int @ SY301 @ pls )
| ( ord_less_eq @ SV70 @ ( number_number_of @ SV70 @ SY301 ) @ ( zero_zero @ SV70 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1087]) ).
thf(1171,plain,
! [SV140: $i,SV71: $i] :
( ( ( ord_less_eq @ int @ ( bit0 @ SV71 ) @ ( bit0 @ SV140 ) )
= $false )
| ( ( ord_less_eq @ int @ SV71 @ SV140 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1088]) ).
thf(1172,plain,
! [SV140: $i,SV71: $i] :
( ( ( ord_less_eq @ int @ SV71 @ SV140 )
= $false )
| ( ( ord_less_eq @ int @ ( bit0 @ SV71 ) @ ( bit0 @ SV140 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1089]) ).
thf(1173,plain,
! [SV73: $i] :
( ( ( linordered_idom @ SV73 )
= $false )
| ( ( number_ring @ SV73 )
= $false )
| ( ( ! [SY303: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV73 @ ( number_number_of @ SV73 @ SY303 ) @ ( one_one @ SV73 ) )
| ( ord_less_eq @ int @ SY303 @ ( bit1 @ pls ) ) )
| ~ ( ~ ( ord_less_eq @ int @ SY303 @ ( bit1 @ pls ) )
| ( ord_less_eq @ SV73 @ ( number_number_of @ SV73 @ SY303 ) @ ( one_one @ SV73 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1092]) ).
thf(1174,plain,
! [SV141: $i,SV75: $i,SV171: $i] :
( ( ( ~ ( number @ SV171 ) )
= $true )
| ( ( ~ ( semiring @ SV171 ) )
= $true )
| ( ( ( ti @ SV171 @ ( plus_plus @ SV171 @ SV75 @ SV141 ) )
= ( plus_plus @ SV171 @ SV75 @ SV141 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1093]) ).
thf(1175,plain,
! [SV79: $i] :
( ( ( linorder @ SV79 )
= $false )
| ( ( number @ SV79 )
= $false )
| ( ( ! [SY309: $i,SY310: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV79 @ ( number_number_of @ SV79 @ SY309 ) @ ( number_number_of @ SV79 @ SY310 ) )
| ~ ( ord_less @ SV79 @ ( number_number_of @ SV79 @ SY310 ) @ ( number_number_of @ SV79 @ SY309 ) ) )
| ~ ( ~ ~ ( ord_less @ SV79 @ ( number_number_of @ SV79 @ SY310 ) @ ( number_number_of @ SV79 @ SY309 ) )
| ( ord_less_eq @ SV79 @ ( number_number_of @ SV79 @ SY309 ) @ ( number_number_of @ SV79 @ SY310 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1096]) ).
thf(1176,plain,
! [SV143: $i,SV80: $i] :
( ( ( ord_less @ int @ SV80 @ ( plus_plus @ int @ SV143 @ ( one_one @ int ) ) )
= $false )
| ( ( ord_less_eq @ int @ SV80 @ SV143 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1097]) ).
thf(1177,plain,
! [SV143: $i,SV80: $i] :
( ( ( ord_less_eq @ int @ SV80 @ SV143 )
= $false )
| ( ( ord_less @ int @ SV80 @ ( plus_plus @ int @ SV143 @ ( one_one @ int ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1098]) ).
thf(1178,plain,
! [SV144: $i,SV81: $i] :
( ( ( ord_less @ int @ ( bit0 @ SV81 ) @ ( bit1 @ SV144 ) )
= $false )
| ( ( ord_less_eq @ int @ SV81 @ SV144 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1099]) ).
thf(1179,plain,
! [SV144: $i,SV81: $i] :
( ( ( ord_less_eq @ int @ SV81 @ SV144 )
= $false )
| ( ( ord_less @ int @ ( bit0 @ SV81 ) @ ( bit1 @ SV144 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1100]) ).
thf(1180,plain,
! [SV148: $i,SV87: $i] :
( ( ( ord_less_eq @ int @ ( bit1 @ SV87 ) @ ( bit0 @ SV148 ) )
= $false )
| ( ( ord_less @ int @ SV87 @ SV148 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1104]) ).
thf(1181,plain,
! [SV148: $i,SV87: $i] :
( ( ( ord_less @ int @ SV87 @ SV148 )
= $false )
| ( ( ord_less_eq @ int @ ( bit1 @ SV87 ) @ ( bit0 @ SV148 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1105]) ).
thf(1182,plain,
! [SV88: $i] :
( ( ( semiring @ SV88 )
= $false )
| ( ( number @ SV88 )
= $false )
| ( ( ! [SY320: $i,SY321: $i,SY322: $i] :
( ( times_times @ SV88 @ ( plus_plus @ SV88 @ SY320 @ SY321 ) @ ( number_number_of @ SV88 @ SY322 ) )
= ( plus_plus @ SV88 @ ( times_times @ SV88 @ SY320 @ ( number_number_of @ SV88 @ SY322 ) ) @ ( times_times @ SV88 @ SY321 @ ( number_number_of @ SV88 @ SY322 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1106]) ).
thf(1183,plain,
! [SV149: $i,SV90: $i,SV174: $i] :
( ( ( ord_less_eq @ int @ SV174 @ SV90 )
= $false )
| ( ( ord_less_eq @ int @ SV149 @ SV90 )
= $true )
| ( ( ord_less_eq @ int @ SV149 @ SV174 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1109]) ).
thf(1184,plain,
! [SV150: $i,SV91: $i,SV175: $i] :
( ( ( ~ ( number @ SV175 ) )
= $true )
| ( ( ~ ( linorder @ SV175 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( ord_less @ SV175 @ ( ti @ SV175 @ SV91 ) @ SV150 )
| ( ord_less @ SV175 @ SV91 @ SV150 ) )
| ~ ( ~ ( ord_less @ SV175 @ SV91 @ SV150 )
| ( ord_less @ SV175 @ ( ti @ SV175 @ SV91 ) @ SV150 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1110]) ).
thf(1185,plain,
! [SV151: $i,SV92: $i] :
( ( ( ord_less_eq @ int @ ( bit1 @ SV92 ) @ ( bit1 @ SV151 ) )
= $false )
| ( ( ord_less_eq @ int @ SV92 @ SV151 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1111]) ).
thf(1186,plain,
! [SV151: $i,SV92: $i] :
( ( ( ord_less_eq @ int @ SV92 @ SV151 )
= $false )
| ( ( ord_less_eq @ int @ ( bit1 @ SV92 ) @ ( bit1 @ SV151 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1112]) ).
thf(1187,plain,
! [SV153: $i,SV96: $i] :
( ( ( ord_less @ int @ ( number_number_of @ int @ SV96 ) @ ( number_number_of @ int @ SV153 ) )
= $false )
| ( ( ord_less @ int @ SV96 @ SV153 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1116]) ).
thf(1188,plain,
! [SV153: $i,SV96: $i] :
( ( ( ord_less @ int @ SV96 @ SV153 )
= $false )
| ( ( ord_less @ int @ ( number_number_of @ int @ SV96 ) @ ( number_number_of @ int @ SV153 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1117]) ).
thf(1189,plain,
! [SV205: $i,SV193: $i,SV97: $i] :
( ( ( ~ ( ( ( plus_plus @ SV97 @ ( times_times @ SV97 @ SV193 @ SV193 ) @ ( times_times @ SV97 @ SV205 @ SV205 ) )
!= ( zero_zero @ SV97 ) )
| ~ ( ( ( ti @ SV97 @ SV193 )
!= ( zero_zero @ SV97 ) )
| ( ( ti @ SV97 @ SV205 )
!= ( zero_zero @ SV97 ) ) ) ) )
= $false )
| ( ( linord581940658strict @ SV97 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1118]) ).
thf(1190,plain,
! [SV205: $i,SV193: $i,SV97: $i] :
( ( ( ~ ( ~ ~ ( ( ( ti @ SV97 @ SV193 )
!= ( zero_zero @ SV97 ) )
| ( ( ti @ SV97 @ SV205 )
!= ( zero_zero @ SV97 ) ) )
| ( ( plus_plus @ SV97 @ ( times_times @ SV97 @ SV193 @ SV193 ) @ ( times_times @ SV97 @ SV205 @ SV205 ) )
= ( zero_zero @ SV97 ) ) ) )
= $false )
| ( ( linord581940658strict @ SV97 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1118]) ).
thf(1191,plain,
! [SV194: $i,SV177: $i,SV154: $i,SV98: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV98 @ SV154 ) )
= $true )
| ( ( ord_less @ int @ ( plus_plus @ int @ SV177 @ SV98 ) @ ( plus_plus @ int @ SV194 @ SV154 ) )
= $true )
| ( ( ord_less @ int @ SV177 @ SV194 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1119]) ).
thf(1192,plain,
! [SV99: $i] :
( ( ( linordered_idom @ SV99 )
= $false )
| ( ( number_ring @ SV99 )
= $false )
| ( ( ! [SY338: $i,SY339: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV99 @ ( number_number_of @ SV99 @ SY338 ) @ ( number_number_of @ SV99 @ SY339 ) )
| ( ord_less_eq @ int @ SY338 @ SY339 ) )
| ~ ( ~ ( ord_less_eq @ int @ SY338 @ SY339 )
| ( ord_less_eq @ SV99 @ ( number_number_of @ SV99 @ SY338 ) @ ( number_number_of @ SV99 @ SY339 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1120]) ).
thf(1193,plain,
! [SV155: $i,SV101: $i] :
( ( ( ord_less_eq @ int @ ( bit0 @ SV101 ) @ ( bit1 @ SV155 ) )
= $false )
| ( ( ord_less_eq @ int @ SV101 @ SV155 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1121]) ).
thf(1194,plain,
! [SV155: $i,SV101: $i] :
( ( ( ord_less_eq @ int @ SV101 @ SV155 )
= $false )
| ( ( ord_less_eq @ int @ ( bit0 @ SV101 ) @ ( bit1 @ SV155 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1122]) ).
thf(1195,plain,
! [SV103: $i] :
( ( ( linordered_idom @ SV103 )
= $false )
| ( ( number_ring @ SV103 )
= $false )
| ( ( ! [SY341: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV103 @ ( one_one @ SV103 ) @ ( number_number_of @ SV103 @ SY341 ) )
| ( ord_less_eq @ int @ ( bit1 @ pls ) @ SY341 ) )
| ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ pls ) @ SY341 )
| ( ord_less_eq @ SV103 @ ( one_one @ SV103 ) @ ( number_number_of @ SV103 @ SY341 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1123]) ).
thf(1196,plain,
! [SV195: $i,SV178: $i,SV23: $i] :
( ( ( ( ( plus_plus @ SV23 @ ( power_power @ SV23 @ SV178 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV23 @ SV195 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV23 ) )
| ~ ( ( ( ti @ SV23 @ SV178 )
!= ( zero_zero @ SV23 ) )
| ( ( ti @ SV23 @ SV195 )
!= ( zero_zero @ SV23 ) ) ) )
= $true )
| ( ( linordered_idom @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1124]) ).
thf(1197,plain,
! [SV195: $i,SV178: $i,SV23: $i] :
( ( ( ~ ~ ( ( ( ti @ SV23 @ SV178 )
!= ( zero_zero @ SV23 ) )
| ( ( ti @ SV23 @ SV195 )
!= ( zero_zero @ SV23 ) ) )
| ( ( plus_plus @ SV23 @ ( power_power @ SV23 @ SV178 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV23 @ SV195 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV23 ) ) )
= $true )
| ( ( linordered_idom @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1125]) ).
thf(1198,plain,
! [SV196: $i,SV24: $i,SV179: $i] :
( ( ( ~ ( ord_less_eq @ int @ pls @ SV179 ) )
= $true )
| ( ( ( plus_plus @ SV24 @ ( number_number_of @ SV24 @ SV196 ) @ ( number_number_of @ SV24 @ SV179 ) )
= ( number_number_of @ SV24 @ ( plus_plus @ int @ SV196 @ SV179 ) ) )
= $true )
| ( ( ord_less_eq @ int @ pls @ SV196 )
= $false )
| ( ( number_semiring @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1126]) ).
thf(1199,plain,
! [SV119: $i,SV28: $i] :
( ( ( ~ ( ~ ( ord_less @ int @ SV28 @ SV119 )
| ( ord_less @ int @ pls @ SV119 ) )
| ~ ( ord_less @ int @ SV28 @ SV119 ) )
= $false )
| ( ( ord_less @ nat @ ( number_number_of @ nat @ SV28 ) @ ( number_number_of @ nat @ SV119 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1129]) ).
thf(1200,plain,
! [SV119: $i,SV28: $i] :
( ( ( ~ ( ~ ( ord_less @ int @ SV28 @ SV119 )
| ( ord_less @ int @ pls @ SV119 ) )
| ~ ( ord_less @ int @ SV28 @ SV119 ) )
= $true )
| ( ( ord_less @ nat @ ( number_number_of @ nat @ SV28 ) @ ( number_number_of @ nat @ SV119 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1130]) ).
thf(1201,plain,
! [SV207: $i,SV33: $i] :
( ( ( ! [SY379: $i] :
~ ( ~ ( ( ( number_number_of @ SV33 @ SV207 )
!= ( number_number_of @ SV33 @ SY379 ) )
| ( SV207 = SY379 ) )
| ~ ( ( SV207 != SY379 )
| ( ( number_number_of @ SV33 @ SV207 )
= ( number_number_of @ SV33 @ SY379 ) ) ) ) )
= $true )
| ( ( number_ring @ SV33 )
= $false )
| ( ( ring_char_0 @ SV33 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1131]) ).
thf(1202,plain,
! [SV181: $i,SV35: $i] :
( ( ( ( power_power @ SV35 @ SV181 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= ( zero_zero @ SV35 ) )
= $true )
| ( ( ( ti @ SV35 @ SV181 )
= ( zero_zero @ SV35 ) )
= $true )
| ( ( ring_11004092258visors @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1132]) ).
thf(1203,plain,
! [SV181: $i,SV35: $i] :
( ( ( ( ti @ SV35 @ SV181 )
!= ( zero_zero @ SV35 ) )
= $true )
| ( ( ( power_power @ SV35 @ SV181 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SV35 ) )
= $true )
| ( ( ring_11004092258visors @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1133]) ).
thf(1204,plain,
! [SV40: $i,SV124: $i] :
( ( ( ord_less @ int @ SV124 @ pls )
= $true )
| ( ( ~ ( ~ ( ~ ( ord_less @ int @ SV40 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV124 ) @ ( number_number_of @ nat @ SV40 ) )
= ( number_number_of @ nat @ SV124 ) ) )
| ~ ( ~ ~ ( ord_less @ int @ SV40 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV124 ) @ ( number_number_of @ nat @ SV40 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SV124 @ SV40 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1139]) ).
thf(1205,plain,
! [SV198: $i,SV42: $i,SV183: $i] :
( ( ( ~ ( ord_less_eq @ int @ pls @ SV183 ) )
= $true )
| ( ( ( times_times @ SV42 @ ( number_number_of @ SV42 @ SV198 ) @ ( number_number_of @ SV42 @ SV183 ) )
= ( number_number_of @ SV42 @ ( times_times @ int @ SV198 @ SV183 ) ) )
= $true )
| ( ( ord_less_eq @ int @ pls @ SV198 )
= $false )
| ( ( number_semiring @ SV42 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1142]) ).
thf(1206,plain,
! [SV184: $i,SV45: $i] :
( ( ( ~ ( ord_less @ SV45 @ ( zero_zero @ SV45 ) @ ( power_power @ SV45 @ SV184 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true )
| ( ( ( ti @ SV45 @ SV184 )
!= ( zero_zero @ SV45 ) )
= $true )
| ( ( linordered_idom @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1145]) ).
thf(1207,plain,
! [SV184: $i,SV45: $i] :
( ( ( ~ ( ( ( ti @ SV45 @ SV184 )
!= ( zero_zero @ SV45 ) ) ) )
= $true )
| ( ( ord_less @ SV45 @ ( zero_zero @ SV45 ) @ ( power_power @ SV45 @ SV184 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $true )
| ( ( linordered_idom @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1146]) ).
thf(1208,plain,
! [SV208: $i,SV48: $i] :
( ( ( ! [SY380: $i,SY381: $i] :
( ( times_times @ SV48 @ ( number_number_of @ SV48 @ SV208 ) @ ( plus_plus @ SV48 @ SY380 @ SY381 ) )
= ( plus_plus @ SV48 @ ( times_times @ SV48 @ ( number_number_of @ SV48 @ SV208 ) @ SY380 ) @ ( times_times @ SV48 @ ( number_number_of @ SV48 @ SV208 ) @ SY381 ) ) ) )
= $true )
| ( ( number @ SV48 )
= $false )
| ( ( semiring @ SV48 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1149]) ).
thf(1209,plain,
! [SV129: $i,SV49: $i,SV165: $i] :
( ( ( ~ ( ord_less @ SV165 @ ( ti @ SV165 @ SV49 ) @ SV129 )
| ( ord_less @ SV165 @ SV49 @ SV129 ) )
= $true )
| ( ( linordered_idom @ SV165 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1150]) ).
thf(1210,plain,
! [SV129: $i,SV49: $i,SV165: $i] :
( ( ( ~ ( ord_less @ SV165 @ SV49 @ SV129 )
| ( ord_less @ SV165 @ ( ti @ SV165 @ SV49 ) @ SV129 ) )
= $true )
| ( ( linordered_idom @ SV165 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1151]) ).
thf(1211,plain,
! [SV131: $i,SV51: $i,SV166: $i] :
( ( ( ~ ( ord_less @ SV166 @ SV51 @ ( ti @ SV166 @ SV131 ) )
| ( ord_less @ SV166 @ SV51 @ SV131 ) )
= $true )
| ( ( linordered_idom @ SV166 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1152]) ).
thf(1212,plain,
! [SV131: $i,SV51: $i,SV166: $i] :
( ( ( ~ ( ord_less @ SV166 @ SV51 @ SV131 )
| ( ord_less @ SV166 @ SV51 @ ( ti @ SV166 @ SV131 ) ) )
= $true )
| ( ( linordered_idom @ SV166 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1153]) ).
thf(1213,plain,
! [SV132: $i,SV52: $i,SV167: $i] :
( ( ( number @ SV167 )
= $false )
| ( ( ~ ( semiring @ SV167 ) )
= $true )
| ( ( ( plus_plus @ SV167 @ SV52 @ ( ti @ SV167 @ SV132 ) )
= ( plus_plus @ SV167 @ SV52 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1154]) ).
thf(1214,plain,
! [SV199: $i,SV185: $i,SV53: $i] :
( ( ( ( ( number_number_of @ SV53 @ SV185 )
!= ( ti @ SV53 @ SV199 ) )
| ( ( ti @ SV53 @ SV199 )
= ( number_number_of @ SV53 @ SV185 ) ) )
= $true )
| ( ( number @ SV53 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1155]) ).
thf(1215,plain,
! [SV185: $i,SV199: $i,SV53: $i] :
( ( ( ( ( ti @ SV53 @ SV199 )
!= ( number_number_of @ SV53 @ SV185 ) )
| ( ( number_number_of @ SV53 @ SV185 )
= ( ti @ SV53 @ SV199 ) ) )
= $true )
| ( ( number @ SV53 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1156]) ).
thf(1216,plain,
! [SV133: $i,SV55: $i,SV168: $i] :
( ( ( number @ SV168 )
= $false )
| ( ( ~ ( semiring @ SV168 ) )
= $true )
| ( ( ( plus_plus @ SV168 @ ( ti @ SV168 @ SV55 ) @ SV133 )
= ( plus_plus @ SV168 @ SV55 @ SV133 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1157]) ).
thf(1217,plain,
! [SV201: $i,SV188: $i,SV59: $i] :
( ( ( ~ ( ord_less @ SV59 @ ( zero_zero @ SV59 ) @ ( plus_plus @ SV59 @ ( power_power @ SV59 @ SV188 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV59 @ SV201 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
| ( ( ti @ SV59 @ SV188 )
!= ( zero_zero @ SV59 ) )
| ( ( ti @ SV59 @ SV201 )
!= ( zero_zero @ SV59 ) ) )
= $true )
| ( ( linordered_idom @ SV59 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1158]) ).
thf(1218,plain,
! [SV201: $i,SV188: $i,SV59: $i] :
( ( ( ~ ( ( ( ti @ SV59 @ SV188 )
!= ( zero_zero @ SV59 ) )
| ( ( ti @ SV59 @ SV201 )
!= ( zero_zero @ SV59 ) ) )
| ( ord_less @ SV59 @ ( zero_zero @ SV59 ) @ ( plus_plus @ SV59 @ ( power_power @ SV59 @ SV188 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV59 @ SV201 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true )
| ( ( linordered_idom @ SV59 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1159]) ).
thf(1219,plain,
! [SV138: $i,SV63: $i,SV170: $i] :
( ( ( number @ SV170 )
= $false )
| ( ( ~ ( linorder @ SV170 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( ord_less @ SV170 @ SV63 @ ( ti @ SV170 @ SV138 ) )
| ( ord_less @ SV170 @ SV63 @ SV138 ) )
| ~ ( ~ ( ord_less @ SV170 @ SV63 @ SV138 )
| ( ord_less @ SV170 @ SV63 @ ( ti @ SV170 @ SV138 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1166]) ).
thf(1220,plain,
! [SV139: $i,SV65: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV65 @ SV139 )
| ~ ( ( SV65 != SV139 ) ) )
= $false )
| ( ( ord_less @ int @ SV65 @ SV139 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1167]) ).
thf(1221,plain,
! [SV139: $i,SV65: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV65 @ SV139 )
| ~ ( ( SV65 != SV139 ) ) )
= $true )
| ( ( ord_less @ int @ SV65 @ SV139 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1168]) ).
thf(1222,plain,
! [SV209: $i,SV68: $i] :
( ( ( ~ ( ~ ( ~ ( ord_less_eq @ SV68 @ ( zero_zero @ SV68 ) @ ( number_number_of @ SV68 @ SV209 ) )
| ( ord_less_eq @ int @ pls @ SV209 ) )
| ~ ( ~ ( ord_less_eq @ int @ pls @ SV209 )
| ( ord_less_eq @ SV68 @ ( zero_zero @ SV68 ) @ ( number_number_of @ SV68 @ SV209 ) ) ) ) )
= $true )
| ( ( number_ring @ SV68 )
= $false )
| ( ( linordered_idom @ SV68 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1169]) ).
thf(1223,plain,
! [SV210: $i,SV70: $i] :
( ( ( ~ ( ~ ( ~ ( ord_less_eq @ SV70 @ ( number_number_of @ SV70 @ SV210 ) @ ( zero_zero @ SV70 ) )
| ( ord_less_eq @ int @ SV210 @ pls ) )
| ~ ( ~ ( ord_less_eq @ int @ SV210 @ pls )
| ( ord_less_eq @ SV70 @ ( number_number_of @ SV70 @ SV210 ) @ ( zero_zero @ SV70 ) ) ) ) )
= $true )
| ( ( number_ring @ SV70 )
= $false )
| ( ( linordered_idom @ SV70 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1170]) ).
thf(1224,plain,
! [SV211: $i,SV73: $i] :
( ( ( ~ ( ~ ( ~ ( ord_less_eq @ SV73 @ ( number_number_of @ SV73 @ SV211 ) @ ( one_one @ SV73 ) )
| ( ord_less_eq @ int @ SV211 @ ( bit1 @ pls ) ) )
| ~ ( ~ ( ord_less_eq @ int @ SV211 @ ( bit1 @ pls ) )
| ( ord_less_eq @ SV73 @ ( number_number_of @ SV73 @ SV211 ) @ ( one_one @ SV73 ) ) ) ) )
= $true )
| ( ( number_ring @ SV73 )
= $false )
| ( ( linordered_idom @ SV73 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1173]) ).
thf(1225,plain,
! [SV141: $i,SV75: $i,SV171: $i] :
( ( ( number @ SV171 )
= $false )
| ( ( ~ ( semiring @ SV171 ) )
= $true )
| ( ( ( ti @ SV171 @ ( plus_plus @ SV171 @ SV75 @ SV141 ) )
= ( plus_plus @ SV171 @ SV75 @ SV141 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1174]) ).
thf(1226,plain,
! [SV212: $i,SV79: $i] :
( ( ( ! [SY382: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV79 @ ( number_number_of @ SV79 @ SV212 ) @ ( number_number_of @ SV79 @ SY382 ) )
| ~ ( ord_less @ SV79 @ ( number_number_of @ SV79 @ SY382 ) @ ( number_number_of @ SV79 @ SV212 ) ) )
| ~ ( ~ ~ ( ord_less @ SV79 @ ( number_number_of @ SV79 @ SY382 ) @ ( number_number_of @ SV79 @ SV212 ) )
| ( ord_less_eq @ SV79 @ ( number_number_of @ SV79 @ SV212 ) @ ( number_number_of @ SV79 @ SY382 ) ) ) ) )
= $true )
| ( ( number @ SV79 )
= $false )
| ( ( linorder @ SV79 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1175]) ).
thf(1227,plain,
! [SV213: $i,SV88: $i] :
( ( ( ! [SY383: $i,SY384: $i] :
( ( times_times @ SV88 @ ( plus_plus @ SV88 @ SV213 @ SY383 ) @ ( number_number_of @ SV88 @ SY384 ) )
= ( plus_plus @ SV88 @ ( times_times @ SV88 @ SV213 @ ( number_number_of @ SV88 @ SY384 ) ) @ ( times_times @ SV88 @ SY383 @ ( number_number_of @ SV88 @ SY384 ) ) ) ) )
= $true )
| ( ( number @ SV88 )
= $false )
| ( ( semiring @ SV88 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1182]) ).
thf(1228,plain,
! [SV150: $i,SV91: $i,SV175: $i] :
( ( ( number @ SV175 )
= $false )
| ( ( ~ ( linorder @ SV175 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( ord_less @ SV175 @ ( ti @ SV175 @ SV91 ) @ SV150 )
| ( ord_less @ SV175 @ SV91 @ SV150 ) )
| ~ ( ~ ( ord_less @ SV175 @ SV91 @ SV150 )
| ( ord_less @ SV175 @ ( ti @ SV175 @ SV91 ) @ SV150 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1184]) ).
thf(1229,plain,
! [SV205: $i,SV193: $i,SV97: $i] :
( ( ( ( ( plus_plus @ SV97 @ ( times_times @ SV97 @ SV193 @ SV193 ) @ ( times_times @ SV97 @ SV205 @ SV205 ) )
!= ( zero_zero @ SV97 ) )
| ~ ( ( ( ti @ SV97 @ SV193 )
!= ( zero_zero @ SV97 ) )
| ( ( ti @ SV97 @ SV205 )
!= ( zero_zero @ SV97 ) ) ) )
= $true )
| ( ( linord581940658strict @ SV97 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1189]) ).
thf(1230,plain,
! [SV205: $i,SV193: $i,SV97: $i] :
( ( ( ~ ~ ( ( ( ti @ SV97 @ SV193 )
!= ( zero_zero @ SV97 ) )
| ( ( ti @ SV97 @ SV205 )
!= ( zero_zero @ SV97 ) ) )
| ( ( plus_plus @ SV97 @ ( times_times @ SV97 @ SV193 @ SV193 ) @ ( times_times @ SV97 @ SV205 @ SV205 ) )
= ( zero_zero @ SV97 ) ) )
= $true )
| ( ( linord581940658strict @ SV97 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1190]) ).
thf(1231,plain,
! [SV194: $i,SV177: $i,SV154: $i,SV98: $i] :
( ( ( ord_less_eq @ int @ SV98 @ SV154 )
= $false )
| ( ( ord_less @ int @ ( plus_plus @ int @ SV177 @ SV98 ) @ ( plus_plus @ int @ SV194 @ SV154 ) )
= $true )
| ( ( ord_less @ int @ SV177 @ SV194 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1191]) ).
thf(1232,plain,
! [SV214: $i,SV99: $i] :
( ( ( ! [SY385: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV99 @ ( number_number_of @ SV99 @ SV214 ) @ ( number_number_of @ SV99 @ SY385 ) )
| ( ord_less_eq @ int @ SV214 @ SY385 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV214 @ SY385 )
| ( ord_less_eq @ SV99 @ ( number_number_of @ SV99 @ SV214 ) @ ( number_number_of @ SV99 @ SY385 ) ) ) ) )
= $true )
| ( ( number_ring @ SV99 )
= $false )
| ( ( linordered_idom @ SV99 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1192]) ).
thf(1233,plain,
! [SV215: $i,SV103: $i] :
( ( ( ~ ( ~ ( ~ ( ord_less_eq @ SV103 @ ( one_one @ SV103 ) @ ( number_number_of @ SV103 @ SV215 ) )
| ( ord_less_eq @ int @ ( bit1 @ pls ) @ SV215 ) )
| ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ pls ) @ SV215 )
| ( ord_less_eq @ SV103 @ ( one_one @ SV103 ) @ ( number_number_of @ SV103 @ SV215 ) ) ) ) )
= $true )
| ( ( number_ring @ SV103 )
= $false )
| ( ( linordered_idom @ SV103 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1195]) ).
thf(1234,plain,
! [SV195: $i,SV178: $i,SV23: $i] :
( ( ( ( plus_plus @ SV23 @ ( power_power @ SV23 @ SV178 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV23 @ SV195 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( zero_zero @ SV23 ) )
= $true )
| ( ( ~ ( ( ( ti @ SV23 @ SV178 )
!= ( zero_zero @ SV23 ) )
| ( ( ti @ SV23 @ SV195 )
!= ( zero_zero @ SV23 ) ) ) )
= $true )
| ( ( linordered_idom @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1196]) ).
thf(1235,plain,
! [SV195: $i,SV178: $i,SV23: $i] :
( ( ( ~ ~ ( ( ( ti @ SV23 @ SV178 )
!= ( zero_zero @ SV23 ) )
| ( ( ti @ SV23 @ SV195 )
!= ( zero_zero @ SV23 ) ) ) )
= $true )
| ( ( ( plus_plus @ SV23 @ ( power_power @ SV23 @ SV178 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV23 @ SV195 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV23 ) )
= $true )
| ( ( linordered_idom @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1197]) ).
thf(1236,plain,
! [SV196: $i,SV24: $i,SV179: $i] :
( ( ( ord_less_eq @ int @ pls @ SV179 )
= $false )
| ( ( ( plus_plus @ SV24 @ ( number_number_of @ SV24 @ SV196 ) @ ( number_number_of @ SV24 @ SV179 ) )
= ( number_number_of @ SV24 @ ( plus_plus @ int @ SV196 @ SV179 ) ) )
= $true )
| ( ( ord_less_eq @ int @ pls @ SV196 )
= $false )
| ( ( number_semiring @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1198]) ).
thf(1237,plain,
! [SV119: $i,SV28: $i] :
( ( ( ~ ( ~ ( ord_less @ int @ SV28 @ SV119 )
| ( ord_less @ int @ pls @ SV119 ) ) )
= $false )
| ( ( ord_less @ nat @ ( number_number_of @ nat @ SV28 ) @ ( number_number_of @ nat @ SV119 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1199]) ).
thf(1238,plain,
! [SV119: $i,SV28: $i] :
( ( ( ~ ( ord_less @ int @ SV28 @ SV119 ) )
= $false )
| ( ( ord_less @ nat @ ( number_number_of @ nat @ SV28 ) @ ( number_number_of @ nat @ SV119 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1199]) ).
thf(1239,plain,
! [SV119: $i,SV28: $i] :
( ( ( ~ ( ~ ( ord_less @ int @ SV28 @ SV119 )
| ( ord_less @ int @ pls @ SV119 ) ) )
= $true )
| ( ( ~ ( ord_less @ int @ SV28 @ SV119 ) )
= $true )
| ( ( ord_less @ nat @ ( number_number_of @ nat @ SV28 ) @ ( number_number_of @ nat @ SV119 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1200]) ).
thf(1240,plain,
! [SV216: $i,SV207: $i,SV33: $i] :
( ( ( ~ ( ~ ( ( ( number_number_of @ SV33 @ SV207 )
!= ( number_number_of @ SV33 @ SV216 ) )
| ( SV207 = SV216 ) )
| ~ ( ( SV207 != SV216 )
| ( ( number_number_of @ SV33 @ SV207 )
= ( number_number_of @ SV33 @ SV216 ) ) ) ) )
= $true )
| ( ( number_ring @ SV33 )
= $false )
| ( ( ring_char_0 @ SV33 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1201]) ).
thf(1241,plain,
! [SV181: $i,SV35: $i] :
( ( ( ( power_power @ SV35 @ SV181 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SV35 ) )
= $false )
| ( ( ( ti @ SV35 @ SV181 )
= ( zero_zero @ SV35 ) )
= $true )
| ( ( ring_11004092258visors @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1202]) ).
thf(1242,plain,
! [SV181: $i,SV35: $i] :
( ( ( ( ti @ SV35 @ SV181 )
= ( zero_zero @ SV35 ) )
= $false )
| ( ( ( power_power @ SV35 @ SV181 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ SV35 ) )
= $true )
| ( ( ring_11004092258visors @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1203]) ).
thf(1243,plain,
! [SV124: $i,SV40: $i] :
( ( ( ~ ( ~ ( ord_less @ int @ SV40 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV124 ) @ ( number_number_of @ nat @ SV40 ) )
= ( number_number_of @ nat @ SV124 ) ) )
| ~ ( ~ ~ ( ord_less @ int @ SV40 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV124 ) @ ( number_number_of @ nat @ SV40 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SV124 @ SV40 ) ) ) ) )
= $false )
| ( ( ord_less @ int @ SV124 @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1204]) ).
thf(1244,plain,
! [SV198: $i,SV42: $i,SV183: $i] :
( ( ( ord_less_eq @ int @ pls @ SV183 )
= $false )
| ( ( ( times_times @ SV42 @ ( number_number_of @ SV42 @ SV198 ) @ ( number_number_of @ SV42 @ SV183 ) )
= ( number_number_of @ SV42 @ ( times_times @ int @ SV198 @ SV183 ) ) )
= $true )
| ( ( ord_less_eq @ int @ pls @ SV198 )
= $false )
| ( ( number_semiring @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1205]) ).
thf(1245,plain,
! [SV184: $i,SV45: $i] :
( ( ( ord_less @ SV45 @ ( zero_zero @ SV45 ) @ ( power_power @ SV45 @ SV184 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $false )
| ( ( ( ti @ SV45 @ SV184 )
!= ( zero_zero @ SV45 ) )
= $true )
| ( ( linordered_idom @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1206]) ).
thf(1246,plain,
! [SV184: $i,SV45: $i] :
( ( ( ( ti @ SV45 @ SV184 )
!= ( zero_zero @ SV45 ) )
= $false )
| ( ( ord_less @ SV45 @ ( zero_zero @ SV45 ) @ ( power_power @ SV45 @ SV184 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $true )
| ( ( linordered_idom @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1207]) ).
thf(1247,plain,
! [SV217: $i,SV208: $i,SV48: $i] :
( ( ( ! [SY386: $i] :
( ( times_times @ SV48 @ ( number_number_of @ SV48 @ SV208 ) @ ( plus_plus @ SV48 @ SV217 @ SY386 ) )
= ( plus_plus @ SV48 @ ( times_times @ SV48 @ ( number_number_of @ SV48 @ SV208 ) @ SV217 ) @ ( times_times @ SV48 @ ( number_number_of @ SV48 @ SV208 ) @ SY386 ) ) ) )
= $true )
| ( ( number @ SV48 )
= $false )
| ( ( semiring @ SV48 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1208]) ).
thf(1248,plain,
! [SV129: $i,SV49: $i,SV165: $i] :
( ( ( ~ ( ord_less @ SV165 @ ( ti @ SV165 @ SV49 ) @ SV129 ) )
= $true )
| ( ( ord_less @ SV165 @ SV49 @ SV129 )
= $true )
| ( ( linordered_idom @ SV165 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1209]) ).
thf(1249,plain,
! [SV129: $i,SV49: $i,SV165: $i] :
( ( ( ~ ( ord_less @ SV165 @ SV49 @ SV129 ) )
= $true )
| ( ( ord_less @ SV165 @ ( ti @ SV165 @ SV49 ) @ SV129 )
= $true )
| ( ( linordered_idom @ SV165 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1210]) ).
thf(1250,plain,
! [SV131: $i,SV51: $i,SV166: $i] :
( ( ( ~ ( ord_less @ SV166 @ SV51 @ ( ti @ SV166 @ SV131 ) ) )
= $true )
| ( ( ord_less @ SV166 @ SV51 @ SV131 )
= $true )
| ( ( linordered_idom @ SV166 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1211]) ).
thf(1251,plain,
! [SV131: $i,SV51: $i,SV166: $i] :
( ( ( ~ ( ord_less @ SV166 @ SV51 @ SV131 ) )
= $true )
| ( ( ord_less @ SV166 @ SV51 @ ( ti @ SV166 @ SV131 ) )
= $true )
| ( ( linordered_idom @ SV166 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1212]) ).
thf(1252,plain,
! [SV132: $i,SV52: $i,SV167: $i] :
( ( ( semiring @ SV167 )
= $false )
| ( ( number @ SV167 )
= $false )
| ( ( ( plus_plus @ SV167 @ SV52 @ ( ti @ SV167 @ SV132 ) )
= ( plus_plus @ SV167 @ SV52 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1213]) ).
thf(1253,plain,
! [SV199: $i,SV185: $i,SV53: $i] :
( ( ( ( number_number_of @ SV53 @ SV185 )
!= ( ti @ SV53 @ SV199 ) )
= $true )
| ( ( ( ti @ SV53 @ SV199 )
= ( number_number_of @ SV53 @ SV185 ) )
= $true )
| ( ( number @ SV53 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1214]) ).
thf(1254,plain,
! [SV185: $i,SV199: $i,SV53: $i] :
( ( ( ( ti @ SV53 @ SV199 )
!= ( number_number_of @ SV53 @ SV185 ) )
= $true )
| ( ( ( number_number_of @ SV53 @ SV185 )
= ( ti @ SV53 @ SV199 ) )
= $true )
| ( ( number @ SV53 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1215]) ).
thf(1255,plain,
! [SV133: $i,SV55: $i,SV168: $i] :
( ( ( semiring @ SV168 )
= $false )
| ( ( number @ SV168 )
= $false )
| ( ( ( plus_plus @ SV168 @ ( ti @ SV168 @ SV55 ) @ SV133 )
= ( plus_plus @ SV168 @ SV55 @ SV133 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1216]) ).
thf(1256,plain,
! [SV201: $i,SV188: $i,SV59: $i] :
( ( ( ~ ( ord_less @ SV59 @ ( zero_zero @ SV59 ) @ ( plus_plus @ SV59 @ ( power_power @ SV59 @ SV188 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV59 @ SV201 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true )
| ( ( ( ( ti @ SV59 @ SV188 )
!= ( zero_zero @ SV59 ) )
| ( ( ti @ SV59 @ SV201 )
!= ( zero_zero @ SV59 ) ) )
= $true )
| ( ( linordered_idom @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1217]) ).
thf(1257,plain,
! [SV201: $i,SV188: $i,SV59: $i] :
( ( ( ~ ( ( ( ti @ SV59 @ SV188 )
!= ( zero_zero @ SV59 ) )
| ( ( ti @ SV59 @ SV201 )
!= ( zero_zero @ SV59 ) ) ) )
= $true )
| ( ( ord_less @ SV59 @ ( zero_zero @ SV59 ) @ ( plus_plus @ SV59 @ ( power_power @ SV59 @ SV188 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV59 @ SV201 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true )
| ( ( linordered_idom @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1218]) ).
thf(1258,plain,
! [SV138: $i,SV63: $i,SV170: $i] :
( ( ( linorder @ SV170 )
= $false )
| ( ( number @ SV170 )
= $false )
| ( ( ~ ( ~ ( ~ ( ord_less @ SV170 @ SV63 @ ( ti @ SV170 @ SV138 ) )
| ( ord_less @ SV170 @ SV63 @ SV138 ) )
| ~ ( ~ ( ord_less @ SV170 @ SV63 @ SV138 )
| ( ord_less @ SV170 @ SV63 @ ( ti @ SV170 @ SV138 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1219]) ).
thf(1259,plain,
! [SV139: $i,SV65: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV65 @ SV139 ) )
= $false )
| ( ( ord_less @ int @ SV65 @ SV139 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1220]) ).
thf(1260,plain,
! [SV139: $i,SV65: $i] :
( ( ( ~ ( ( SV65 != SV139 ) ) )
= $false )
| ( ( ord_less @ int @ SV65 @ SV139 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1220]) ).
thf(1261,plain,
! [SV139: $i,SV65: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV65 @ SV139 ) )
= $true )
| ( ( ~ ( ( SV65 != SV139 ) ) )
= $true )
| ( ( ord_less @ int @ SV65 @ SV139 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1221]) ).
thf(1262,plain,
! [SV209: $i,SV68: $i] :
( ( ( ~ ( ~ ( ord_less_eq @ SV68 @ ( zero_zero @ SV68 ) @ ( number_number_of @ SV68 @ SV209 ) )
| ( ord_less_eq @ int @ pls @ SV209 ) )
| ~ ( ~ ( ord_less_eq @ int @ pls @ SV209 )
| ( ord_less_eq @ SV68 @ ( zero_zero @ SV68 ) @ ( number_number_of @ SV68 @ SV209 ) ) ) )
= $false )
| ( ( number_ring @ SV68 )
= $false )
| ( ( linordered_idom @ SV68 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1222]) ).
thf(1263,plain,
! [SV210: $i,SV70: $i] :
( ( ( ~ ( ~ ( ord_less_eq @ SV70 @ ( number_number_of @ SV70 @ SV210 ) @ ( zero_zero @ SV70 ) )
| ( ord_less_eq @ int @ SV210 @ pls ) )
| ~ ( ~ ( ord_less_eq @ int @ SV210 @ pls )
| ( ord_less_eq @ SV70 @ ( number_number_of @ SV70 @ SV210 ) @ ( zero_zero @ SV70 ) ) ) )
= $false )
| ( ( number_ring @ SV70 )
= $false )
| ( ( linordered_idom @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1223]) ).
thf(1264,plain,
! [SV211: $i,SV73: $i] :
( ( ( ~ ( ~ ( ord_less_eq @ SV73 @ ( number_number_of @ SV73 @ SV211 ) @ ( one_one @ SV73 ) )
| ( ord_less_eq @ int @ SV211 @ ( bit1 @ pls ) ) )
| ~ ( ~ ( ord_less_eq @ int @ SV211 @ ( bit1 @ pls ) )
| ( ord_less_eq @ SV73 @ ( number_number_of @ SV73 @ SV211 ) @ ( one_one @ SV73 ) ) ) )
= $false )
| ( ( number_ring @ SV73 )
= $false )
| ( ( linordered_idom @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1224]) ).
thf(1265,plain,
! [SV141: $i,SV75: $i,SV171: $i] :
( ( ( semiring @ SV171 )
= $false )
| ( ( number @ SV171 )
= $false )
| ( ( ( ti @ SV171 @ ( plus_plus @ SV171 @ SV75 @ SV141 ) )
= ( plus_plus @ SV171 @ SV75 @ SV141 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1225]) ).
thf(1266,plain,
! [SV218: $i,SV212: $i,SV79: $i] :
( ( ( ~ ( ~ ( ~ ( ord_less_eq @ SV79 @ ( number_number_of @ SV79 @ SV212 ) @ ( number_number_of @ SV79 @ SV218 ) )
| ~ ( ord_less @ SV79 @ ( number_number_of @ SV79 @ SV218 ) @ ( number_number_of @ SV79 @ SV212 ) ) )
| ~ ( ~ ~ ( ord_less @ SV79 @ ( number_number_of @ SV79 @ SV218 ) @ ( number_number_of @ SV79 @ SV212 ) )
| ( ord_less_eq @ SV79 @ ( number_number_of @ SV79 @ SV212 ) @ ( number_number_of @ SV79 @ SV218 ) ) ) ) )
= $true )
| ( ( number @ SV79 )
= $false )
| ( ( linorder @ SV79 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1226]) ).
thf(1267,plain,
! [SV219: $i,SV213: $i,SV88: $i] :
( ( ( ! [SY387: $i] :
( ( times_times @ SV88 @ ( plus_plus @ SV88 @ SV213 @ SV219 ) @ ( number_number_of @ SV88 @ SY387 ) )
= ( plus_plus @ SV88 @ ( times_times @ SV88 @ SV213 @ ( number_number_of @ SV88 @ SY387 ) ) @ ( times_times @ SV88 @ SV219 @ ( number_number_of @ SV88 @ SY387 ) ) ) ) )
= $true )
| ( ( number @ SV88 )
= $false )
| ( ( semiring @ SV88 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1227]) ).
thf(1268,plain,
! [SV150: $i,SV91: $i,SV175: $i] :
( ( ( linorder @ SV175 )
= $false )
| ( ( number @ SV175 )
= $false )
| ( ( ~ ( ~ ( ~ ( ord_less @ SV175 @ ( ti @ SV175 @ SV91 ) @ SV150 )
| ( ord_less @ SV175 @ SV91 @ SV150 ) )
| ~ ( ~ ( ord_less @ SV175 @ SV91 @ SV150 )
| ( ord_less @ SV175 @ ( ti @ SV175 @ SV91 ) @ SV150 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1228]) ).
thf(1269,plain,
! [SV205: $i,SV193: $i,SV97: $i] :
( ( ( ( plus_plus @ SV97 @ ( times_times @ SV97 @ SV193 @ SV193 ) @ ( times_times @ SV97 @ SV205 @ SV205 ) )
!= ( zero_zero @ SV97 ) )
= $true )
| ( ( ~ ( ( ( ti @ SV97 @ SV193 )
!= ( zero_zero @ SV97 ) )
| ( ( ti @ SV97 @ SV205 )
!= ( zero_zero @ SV97 ) ) ) )
= $true )
| ( ( linord581940658strict @ SV97 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1229]) ).
thf(1270,plain,
! [SV205: $i,SV193: $i,SV97: $i] :
( ( ( ~ ~ ( ( ( ti @ SV97 @ SV193 )
!= ( zero_zero @ SV97 ) )
| ( ( ti @ SV97 @ SV205 )
!= ( zero_zero @ SV97 ) ) ) )
= $true )
| ( ( ( plus_plus @ SV97 @ ( times_times @ SV97 @ SV193 @ SV193 ) @ ( times_times @ SV97 @ SV205 @ SV205 ) )
= ( zero_zero @ SV97 ) )
= $true )
| ( ( linord581940658strict @ SV97 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1230]) ).
thf(1271,plain,
! [SV220: $i,SV214: $i,SV99: $i] :
( ( ( ~ ( ~ ( ~ ( ord_less_eq @ SV99 @ ( number_number_of @ SV99 @ SV214 ) @ ( number_number_of @ SV99 @ SV220 ) )
| ( ord_less_eq @ int @ SV214 @ SV220 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV214 @ SV220 )
| ( ord_less_eq @ SV99 @ ( number_number_of @ SV99 @ SV214 ) @ ( number_number_of @ SV99 @ SV220 ) ) ) ) )
= $true )
| ( ( number_ring @ SV99 )
= $false )
| ( ( linordered_idom @ SV99 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1232]) ).
thf(1272,plain,
! [SV215: $i,SV103: $i] :
( ( ( ~ ( ~ ( ord_less_eq @ SV103 @ ( one_one @ SV103 ) @ ( number_number_of @ SV103 @ SV215 ) )
| ( ord_less_eq @ int @ ( bit1 @ pls ) @ SV215 ) )
| ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ pls ) @ SV215 )
| ( ord_less_eq @ SV103 @ ( one_one @ SV103 ) @ ( number_number_of @ SV103 @ SV215 ) ) ) )
= $false )
| ( ( number_ring @ SV103 )
= $false )
| ( ( linordered_idom @ SV103 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1233]) ).
thf(1273,plain,
! [SV195: $i,SV178: $i,SV23: $i] :
( ( ( ( plus_plus @ SV23 @ ( power_power @ SV23 @ SV178 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV23 @ SV195 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV23 ) )
= $false )
| ( ( ~ ( ( ( ti @ SV23 @ SV178 )
!= ( zero_zero @ SV23 ) )
| ( ( ti @ SV23 @ SV195 )
!= ( zero_zero @ SV23 ) ) ) )
= $true )
| ( ( linordered_idom @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1234]) ).
thf(1274,plain,
! [SV195: $i,SV178: $i,SV23: $i] :
( ( ( ~ ( ( ( ti @ SV23 @ SV178 )
!= ( zero_zero @ SV23 ) )
| ( ( ti @ SV23 @ SV195 )
!= ( zero_zero @ SV23 ) ) ) )
= $false )
| ( ( ( plus_plus @ SV23 @ ( power_power @ SV23 @ SV178 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV23 @ SV195 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV23 ) )
= $true )
| ( ( linordered_idom @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1235]) ).
thf(1275,plain,
! [SV119: $i,SV28: $i] :
( ( ( ~ ( ord_less @ int @ SV28 @ SV119 )
| ( ord_less @ int @ pls @ SV119 ) )
= $true )
| ( ( ord_less @ nat @ ( number_number_of @ nat @ SV28 ) @ ( number_number_of @ nat @ SV119 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1237]) ).
thf(1276,plain,
! [SV119: $i,SV28: $i] :
( ( ( ord_less @ int @ SV28 @ SV119 )
= $true )
| ( ( ord_less @ nat @ ( number_number_of @ nat @ SV28 ) @ ( number_number_of @ nat @ SV119 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1238]) ).
thf(1277,plain,
! [SV119: $i,SV28: $i] :
( ( ( ~ ( ord_less @ int @ SV28 @ SV119 )
| ( ord_less @ int @ pls @ SV119 ) )
= $false )
| ( ( ~ ( ord_less @ int @ SV28 @ SV119 ) )
= $true )
| ( ( ord_less @ nat @ ( number_number_of @ nat @ SV28 ) @ ( number_number_of @ nat @ SV119 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1239]) ).
thf(1278,plain,
! [SV216: $i,SV207: $i,SV33: $i] :
( ( ( ~ ( ( ( number_number_of @ SV33 @ SV207 )
!= ( number_number_of @ SV33 @ SV216 ) )
| ( SV207 = SV216 ) )
| ~ ( ( SV207 != SV216 )
| ( ( number_number_of @ SV33 @ SV207 )
= ( number_number_of @ SV33 @ SV216 ) ) ) )
= $false )
| ( ( number_ring @ SV33 )
= $false )
| ( ( ring_char_0 @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1240]) ).
thf(1279,plain,
! [SV124: $i,SV40: $i] :
( ( ( ~ ( ~ ( ord_less @ int @ SV40 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV124 ) @ ( number_number_of @ nat @ SV40 ) )
= ( number_number_of @ nat @ SV124 ) ) ) )
= $false )
| ( ( ord_less @ int @ SV124 @ pls )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1243]) ).
thf(1280,plain,
! [SV124: $i,SV40: $i] :
( ( ( ~ ( ~ ~ ( ord_less @ int @ SV40 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV124 ) @ ( number_number_of @ nat @ SV40 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SV124 @ SV40 ) ) ) ) )
= $false )
| ( ( ord_less @ int @ SV124 @ pls )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1243]) ).
thf(1281,plain,
! [SV184: $i,SV45: $i] :
( ( ( ( ti @ SV45 @ SV184 )
= ( zero_zero @ SV45 ) )
= $false )
| ( ( ord_less @ SV45 @ ( zero_zero @ SV45 ) @ ( power_power @ SV45 @ SV184 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $false )
| ( ( linordered_idom @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1245]) ).
thf(1282,plain,
! [SV184: $i,SV45: $i] :
( ( ( ( ti @ SV45 @ SV184 )
= ( zero_zero @ SV45 ) )
= $true )
| ( ( ord_less @ SV45 @ ( zero_zero @ SV45 ) @ ( power_power @ SV45 @ SV184 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $true )
| ( ( linordered_idom @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1246]) ).
thf(1283,plain,
! [SV221: $i,SV217: $i,SV208: $i,SV48: $i] :
( ( ( ( times_times @ SV48 @ ( number_number_of @ SV48 @ SV208 ) @ ( plus_plus @ SV48 @ SV217 @ SV221 ) )
= ( plus_plus @ SV48 @ ( times_times @ SV48 @ ( number_number_of @ SV48 @ SV208 ) @ SV217 ) @ ( times_times @ SV48 @ ( number_number_of @ SV48 @ SV208 ) @ SV221 ) ) )
= $true )
| ( ( number @ SV48 )
= $false )
| ( ( semiring @ SV48 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1247]) ).
thf(1284,plain,
! [SV129: $i,SV49: $i,SV165: $i] :
( ( ( ord_less @ SV165 @ ( ti @ SV165 @ SV49 ) @ SV129 )
= $false )
| ( ( ord_less @ SV165 @ SV49 @ SV129 )
= $true )
| ( ( linordered_idom @ SV165 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1248]) ).
thf(1285,plain,
! [SV129: $i,SV49: $i,SV165: $i] :
( ( ( ord_less @ SV165 @ SV49 @ SV129 )
= $false )
| ( ( ord_less @ SV165 @ ( ti @ SV165 @ SV49 ) @ SV129 )
= $true )
| ( ( linordered_idom @ SV165 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1249]) ).
thf(1286,plain,
! [SV131: $i,SV51: $i,SV166: $i] :
( ( ( ord_less @ SV166 @ SV51 @ ( ti @ SV166 @ SV131 ) )
= $false )
| ( ( ord_less @ SV166 @ SV51 @ SV131 )
= $true )
| ( ( linordered_idom @ SV166 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1250]) ).
thf(1287,plain,
! [SV131: $i,SV51: $i,SV166: $i] :
( ( ( ord_less @ SV166 @ SV51 @ SV131 )
= $false )
| ( ( ord_less @ SV166 @ SV51 @ ( ti @ SV166 @ SV131 ) )
= $true )
| ( ( linordered_idom @ SV166 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1251]) ).
thf(1288,plain,
! [SV199: $i,SV185: $i,SV53: $i] :
( ( ( ( number_number_of @ SV53 @ SV185 )
= ( ti @ SV53 @ SV199 ) )
= $false )
| ( ( ( ti @ SV53 @ SV199 )
= ( number_number_of @ SV53 @ SV185 ) )
= $true )
| ( ( number @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1253]) ).
thf(1289,plain,
! [SV185: $i,SV199: $i,SV53: $i] :
( ( ( ( ti @ SV53 @ SV199 )
= ( number_number_of @ SV53 @ SV185 ) )
= $false )
| ( ( ( number_number_of @ SV53 @ SV185 )
= ( ti @ SV53 @ SV199 ) )
= $true )
| ( ( number @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1254]) ).
thf(1290,plain,
! [SV201: $i,SV188: $i,SV59: $i] :
( ( ( ord_less @ SV59 @ ( zero_zero @ SV59 ) @ ( plus_plus @ SV59 @ ( power_power @ SV59 @ SV188 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV59 @ SV201 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $false )
| ( ( ( ( ti @ SV59 @ SV188 )
!= ( zero_zero @ SV59 ) )
| ( ( ti @ SV59 @ SV201 )
!= ( zero_zero @ SV59 ) ) )
= $true )
| ( ( linordered_idom @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1256]) ).
thf(1291,plain,
! [SV201: $i,SV188: $i,SV59: $i] :
( ( ( ( ( ti @ SV59 @ SV188 )
!= ( zero_zero @ SV59 ) )
| ( ( ti @ SV59 @ SV201 )
!= ( zero_zero @ SV59 ) ) )
= $false )
| ( ( ord_less @ SV59 @ ( zero_zero @ SV59 ) @ ( plus_plus @ SV59 @ ( power_power @ SV59 @ SV188 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV59 @ SV201 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true )
| ( ( linordered_idom @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1257]) ).
thf(1292,plain,
! [SV138: $i,SV63: $i,SV170: $i] :
( ( ( ~ ( ~ ( ord_less @ SV170 @ SV63 @ ( ti @ SV170 @ SV138 ) )
| ( ord_less @ SV170 @ SV63 @ SV138 ) )
| ~ ( ~ ( ord_less @ SV170 @ SV63 @ SV138 )
| ( ord_less @ SV170 @ SV63 @ ( ti @ SV170 @ SV138 ) ) ) )
= $false )
| ( ( number @ SV170 )
= $false )
| ( ( linorder @ SV170 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1258]) ).
thf(1293,plain,
! [SV139: $i,SV65: $i] :
( ( ( ord_less_eq @ int @ SV65 @ SV139 )
= $true )
| ( ( ord_less @ int @ SV65 @ SV139 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1259]) ).
thf(1294,plain,
! [SV139: $i,SV65: $i] :
( ( ( SV65 != SV139 )
= $true )
| ( ( ord_less @ int @ SV65 @ SV139 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1260]) ).
thf(1295,plain,
! [SV139: $i,SV65: $i] :
( ( ( ord_less_eq @ int @ SV65 @ SV139 )
= $false )
| ( ( ~ ( ( SV65 != SV139 ) ) )
= $true )
| ( ( ord_less @ int @ SV65 @ SV139 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1261]) ).
thf(1296,plain,
! [SV209: $i,SV68: $i] :
( ( ( ~ ( ~ ( ord_less_eq @ SV68 @ ( zero_zero @ SV68 ) @ ( number_number_of @ SV68 @ SV209 ) )
| ( ord_less_eq @ int @ pls @ SV209 ) ) )
= $false )
| ( ( number_ring @ SV68 )
= $false )
| ( ( linordered_idom @ SV68 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1262]) ).
thf(1297,plain,
! [SV68: $i,SV209: $i] :
( ( ( ~ ( ~ ( ord_less_eq @ int @ pls @ SV209 )
| ( ord_less_eq @ SV68 @ ( zero_zero @ SV68 ) @ ( number_number_of @ SV68 @ SV209 ) ) ) )
= $false )
| ( ( number_ring @ SV68 )
= $false )
| ( ( linordered_idom @ SV68 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1262]) ).
thf(1298,plain,
! [SV210: $i,SV70: $i] :
( ( ( ~ ( ~ ( ord_less_eq @ SV70 @ ( number_number_of @ SV70 @ SV210 ) @ ( zero_zero @ SV70 ) )
| ( ord_less_eq @ int @ SV210 @ pls ) ) )
= $false )
| ( ( number_ring @ SV70 )
= $false )
| ( ( linordered_idom @ SV70 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1263]) ).
thf(1299,plain,
! [SV70: $i,SV210: $i] :
( ( ( ~ ( ~ ( ord_less_eq @ int @ SV210 @ pls )
| ( ord_less_eq @ SV70 @ ( number_number_of @ SV70 @ SV210 ) @ ( zero_zero @ SV70 ) ) ) )
= $false )
| ( ( number_ring @ SV70 )
= $false )
| ( ( linordered_idom @ SV70 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1263]) ).
thf(1300,plain,
! [SV211: $i,SV73: $i] :
( ( ( ~ ( ~ ( ord_less_eq @ SV73 @ ( number_number_of @ SV73 @ SV211 ) @ ( one_one @ SV73 ) )
| ( ord_less_eq @ int @ SV211 @ ( bit1 @ pls ) ) ) )
= $false )
| ( ( number_ring @ SV73 )
= $false )
| ( ( linordered_idom @ SV73 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1264]) ).
thf(1301,plain,
! [SV73: $i,SV211: $i] :
( ( ( ~ ( ~ ( ord_less_eq @ int @ SV211 @ ( bit1 @ pls ) )
| ( ord_less_eq @ SV73 @ ( number_number_of @ SV73 @ SV211 ) @ ( one_one @ SV73 ) ) ) )
= $false )
| ( ( number_ring @ SV73 )
= $false )
| ( ( linordered_idom @ SV73 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1264]) ).
thf(1302,plain,
! [SV218: $i,SV212: $i,SV79: $i] :
( ( ( ~ ( ~ ( ord_less_eq @ SV79 @ ( number_number_of @ SV79 @ SV212 ) @ ( number_number_of @ SV79 @ SV218 ) )
| ~ ( ord_less @ SV79 @ ( number_number_of @ SV79 @ SV218 ) @ ( number_number_of @ SV79 @ SV212 ) ) )
| ~ ( ~ ~ ( ord_less @ SV79 @ ( number_number_of @ SV79 @ SV218 ) @ ( number_number_of @ SV79 @ SV212 ) )
| ( ord_less_eq @ SV79 @ ( number_number_of @ SV79 @ SV212 ) @ ( number_number_of @ SV79 @ SV218 ) ) ) )
= $false )
| ( ( number @ SV79 )
= $false )
| ( ( linorder @ SV79 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1266]) ).
thf(1303,plain,
! [SV222: $i,SV219: $i,SV213: $i,SV88: $i] :
( ( ( ( times_times @ SV88 @ ( plus_plus @ SV88 @ SV213 @ SV219 ) @ ( number_number_of @ SV88 @ SV222 ) )
= ( plus_plus @ SV88 @ ( times_times @ SV88 @ SV213 @ ( number_number_of @ SV88 @ SV222 ) ) @ ( times_times @ SV88 @ SV219 @ ( number_number_of @ SV88 @ SV222 ) ) ) )
= $true )
| ( ( number @ SV88 )
= $false )
| ( ( semiring @ SV88 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1267]) ).
thf(1304,plain,
! [SV150: $i,SV91: $i,SV175: $i] :
( ( ( ~ ( ~ ( ord_less @ SV175 @ ( ti @ SV175 @ SV91 ) @ SV150 )
| ( ord_less @ SV175 @ SV91 @ SV150 ) )
| ~ ( ~ ( ord_less @ SV175 @ SV91 @ SV150 )
| ( ord_less @ SV175 @ ( ti @ SV175 @ SV91 ) @ SV150 ) ) )
= $false )
| ( ( number @ SV175 )
= $false )
| ( ( linorder @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1268]) ).
thf(1305,plain,
! [SV205: $i,SV193: $i,SV97: $i] :
( ( ( ( plus_plus @ SV97 @ ( times_times @ SV97 @ SV193 @ SV193 ) @ ( times_times @ SV97 @ SV205 @ SV205 ) )
= ( zero_zero @ SV97 ) )
= $false )
| ( ( ~ ( ( ( ti @ SV97 @ SV193 )
!= ( zero_zero @ SV97 ) )
| ( ( ti @ SV97 @ SV205 )
!= ( zero_zero @ SV97 ) ) ) )
= $true )
| ( ( linord581940658strict @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1269]) ).
thf(1306,plain,
! [SV205: $i,SV193: $i,SV97: $i] :
( ( ( ~ ( ( ( ti @ SV97 @ SV193 )
!= ( zero_zero @ SV97 ) )
| ( ( ti @ SV97 @ SV205 )
!= ( zero_zero @ SV97 ) ) ) )
= $false )
| ( ( ( plus_plus @ SV97 @ ( times_times @ SV97 @ SV193 @ SV193 ) @ ( times_times @ SV97 @ SV205 @ SV205 ) )
= ( zero_zero @ SV97 ) )
= $true )
| ( ( linord581940658strict @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1270]) ).
thf(1307,plain,
! [SV220: $i,SV214: $i,SV99: $i] :
( ( ( ~ ( ~ ( ord_less_eq @ SV99 @ ( number_number_of @ SV99 @ SV214 ) @ ( number_number_of @ SV99 @ SV220 ) )
| ( ord_less_eq @ int @ SV214 @ SV220 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV214 @ SV220 )
| ( ord_less_eq @ SV99 @ ( number_number_of @ SV99 @ SV214 ) @ ( number_number_of @ SV99 @ SV220 ) ) ) )
= $false )
| ( ( number_ring @ SV99 )
= $false )
| ( ( linordered_idom @ SV99 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1271]) ).
thf(1308,plain,
! [SV215: $i,SV103: $i] :
( ( ( ~ ( ~ ( ord_less_eq @ SV103 @ ( one_one @ SV103 ) @ ( number_number_of @ SV103 @ SV215 ) )
| ( ord_less_eq @ int @ ( bit1 @ pls ) @ SV215 ) ) )
= $false )
| ( ( number_ring @ SV103 )
= $false )
| ( ( linordered_idom @ SV103 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1272]) ).
thf(1309,plain,
! [SV103: $i,SV215: $i] :
( ( ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ pls ) @ SV215 )
| ( ord_less_eq @ SV103 @ ( one_one @ SV103 ) @ ( number_number_of @ SV103 @ SV215 ) ) ) )
= $false )
| ( ( number_ring @ SV103 )
= $false )
| ( ( linordered_idom @ SV103 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1272]) ).
thf(1310,plain,
! [SV195: $i,SV178: $i,SV23: $i] :
( ( ( ( ( ti @ SV23 @ SV178 )
!= ( zero_zero @ SV23 ) )
| ( ( ti @ SV23 @ SV195 )
!= ( zero_zero @ SV23 ) ) )
= $false )
| ( ( ( plus_plus @ SV23 @ ( power_power @ SV23 @ SV178 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV23 @ SV195 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV23 ) )
= $false )
| ( ( linordered_idom @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1273]) ).
thf(1311,plain,
! [SV195: $i,SV178: $i,SV23: $i] :
( ( ( ( ( ti @ SV23 @ SV178 )
!= ( zero_zero @ SV23 ) )
| ( ( ti @ SV23 @ SV195 )
!= ( zero_zero @ SV23 ) ) )
= $true )
| ( ( ( plus_plus @ SV23 @ ( power_power @ SV23 @ SV178 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV23 @ SV195 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV23 ) )
= $true )
| ( ( linordered_idom @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1274]) ).
thf(1312,plain,
! [SV119: $i,SV28: $i] :
( ( ( ~ ( ord_less @ int @ SV28 @ SV119 ) )
= $true )
| ( ( ord_less @ int @ pls @ SV119 )
= $true )
| ( ( ord_less @ nat @ ( number_number_of @ nat @ SV28 ) @ ( number_number_of @ nat @ SV119 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1275]) ).
thf(1313,plain,
! [SV119: $i,SV28: $i] :
( ( ( ~ ( ord_less @ int @ SV28 @ SV119 ) )
= $false )
| ( ( ~ ( ord_less @ int @ SV28 @ SV119 ) )
= $true )
| ( ( ord_less @ nat @ ( number_number_of @ nat @ SV28 ) @ ( number_number_of @ nat @ SV119 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1277]) ).
thf(1314,plain,
! [SV28: $i,SV119: $i] :
( ( ( ord_less @ int @ pls @ SV119 )
= $false )
| ( ( ~ ( ord_less @ int @ SV28 @ SV119 ) )
= $true )
| ( ( ord_less @ nat @ ( number_number_of @ nat @ SV28 ) @ ( number_number_of @ nat @ SV119 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1277]) ).
thf(1315,plain,
! [SV216: $i,SV207: $i,SV33: $i] :
( ( ( ~ ( ( ( number_number_of @ SV33 @ SV207 )
!= ( number_number_of @ SV33 @ SV216 ) )
| ( SV207 = SV216 ) ) )
= $false )
| ( ( number_ring @ SV33 )
= $false )
| ( ( ring_char_0 @ SV33 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1278]) ).
thf(1316,plain,
! [SV33: $i,SV216: $i,SV207: $i] :
( ( ( ~ ( ( SV207 != SV216 )
| ( ( number_number_of @ SV33 @ SV207 )
= ( number_number_of @ SV33 @ SV216 ) ) ) )
= $false )
| ( ( number_ring @ SV33 )
= $false )
| ( ( ring_char_0 @ SV33 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1278]) ).
thf(1317,plain,
! [SV124: $i,SV40: $i] :
( ( ( ~ ( ord_less @ int @ SV40 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV124 ) @ ( number_number_of @ nat @ SV40 ) )
= ( number_number_of @ nat @ SV124 ) ) )
= $true )
| ( ( ord_less @ int @ SV124 @ pls )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1279]) ).
thf(1318,plain,
! [SV124: $i,SV40: $i] :
( ( ( ~ ~ ( ord_less @ int @ SV40 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV124 ) @ ( number_number_of @ nat @ SV40 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SV124 @ SV40 ) ) ) )
= $true )
| ( ( ord_less @ int @ SV124 @ pls )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1280]) ).
thf(1319,plain,
! [SV201: $i,SV188: $i,SV59: $i] :
( ( ( ( ti @ SV59 @ SV188 )
!= ( zero_zero @ SV59 ) )
= $true )
| ( ( ( ti @ SV59 @ SV201 )
!= ( zero_zero @ SV59 ) )
= $true )
| ( ( ord_less @ SV59 @ ( zero_zero @ SV59 ) @ ( plus_plus @ SV59 @ ( power_power @ SV59 @ SV188 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV59 @ SV201 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $false )
| ( ( linordered_idom @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1290]) ).
thf(1320,plain,
! [SV201: $i,SV188: $i,SV59: $i] :
( ( ( ( ti @ SV59 @ SV188 )
!= ( zero_zero @ SV59 ) )
= $false )
| ( ( ord_less @ SV59 @ ( zero_zero @ SV59 ) @ ( plus_plus @ SV59 @ ( power_power @ SV59 @ SV188 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV59 @ SV201 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true )
| ( ( linordered_idom @ SV59 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1291]) ).
thf(1321,plain,
! [SV188: $i,SV201: $i,SV59: $i] :
( ( ( ( ti @ SV59 @ SV201 )
!= ( zero_zero @ SV59 ) )
= $false )
| ( ( ord_less @ SV59 @ ( zero_zero @ SV59 ) @ ( plus_plus @ SV59 @ ( power_power @ SV59 @ SV188 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV59 @ SV201 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true )
| ( ( linordered_idom @ SV59 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1291]) ).
thf(1322,plain,
! [SV138: $i,SV63: $i,SV170: $i] :
( ( ( ~ ( ~ ( ord_less @ SV170 @ SV63 @ ( ti @ SV170 @ SV138 ) )
| ( ord_less @ SV170 @ SV63 @ SV138 ) ) )
= $false )
| ( ( number @ SV170 )
= $false )
| ( ( linorder @ SV170 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1292]) ).
thf(1323,plain,
! [SV138: $i,SV63: $i,SV170: $i] :
( ( ( ~ ( ~ ( ord_less @ SV170 @ SV63 @ SV138 )
| ( ord_less @ SV170 @ SV63 @ ( ti @ SV170 @ SV138 ) ) ) )
= $false )
| ( ( number @ SV170 )
= $false )
| ( ( linorder @ SV170 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1292]) ).
thf(1324,plain,
! [SV139: $i,SV65: $i] :
( ( ( SV65 = SV139 )
= $false )
| ( ( ord_less @ int @ SV65 @ SV139 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1294]) ).
thf(1325,plain,
! [SV139: $i,SV65: $i] :
( ( ( SV65 != SV139 )
= $false )
| ( ( ord_less_eq @ int @ SV65 @ SV139 )
= $false )
| ( ( ord_less @ int @ SV65 @ SV139 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1295]) ).
thf(1326,plain,
! [SV209: $i,SV68: $i] :
( ( ( ~ ( ord_less_eq @ SV68 @ ( zero_zero @ SV68 ) @ ( number_number_of @ SV68 @ SV209 ) )
| ( ord_less_eq @ int @ pls @ SV209 ) )
= $true )
| ( ( number_ring @ SV68 )
= $false )
| ( ( linordered_idom @ SV68 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1296]) ).
thf(1327,plain,
! [SV68: $i,SV209: $i] :
( ( ( ~ ( ord_less_eq @ int @ pls @ SV209 )
| ( ord_less_eq @ SV68 @ ( zero_zero @ SV68 ) @ ( number_number_of @ SV68 @ SV209 ) ) )
= $true )
| ( ( number_ring @ SV68 )
= $false )
| ( ( linordered_idom @ SV68 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1297]) ).
thf(1328,plain,
! [SV210: $i,SV70: $i] :
( ( ( ~ ( ord_less_eq @ SV70 @ ( number_number_of @ SV70 @ SV210 ) @ ( zero_zero @ SV70 ) )
| ( ord_less_eq @ int @ SV210 @ pls ) )
= $true )
| ( ( number_ring @ SV70 )
= $false )
| ( ( linordered_idom @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1298]) ).
thf(1329,plain,
! [SV70: $i,SV210: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV210 @ pls )
| ( ord_less_eq @ SV70 @ ( number_number_of @ SV70 @ SV210 ) @ ( zero_zero @ SV70 ) ) )
= $true )
| ( ( number_ring @ SV70 )
= $false )
| ( ( linordered_idom @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1299]) ).
thf(1330,plain,
! [SV211: $i,SV73: $i] :
( ( ( ~ ( ord_less_eq @ SV73 @ ( number_number_of @ SV73 @ SV211 ) @ ( one_one @ SV73 ) )
| ( ord_less_eq @ int @ SV211 @ ( bit1 @ pls ) ) )
= $true )
| ( ( number_ring @ SV73 )
= $false )
| ( ( linordered_idom @ SV73 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1300]) ).
thf(1331,plain,
! [SV73: $i,SV211: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV211 @ ( bit1 @ pls ) )
| ( ord_less_eq @ SV73 @ ( number_number_of @ SV73 @ SV211 ) @ ( one_one @ SV73 ) ) )
= $true )
| ( ( number_ring @ SV73 )
= $false )
| ( ( linordered_idom @ SV73 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1301]) ).
thf(1332,plain,
! [SV218: $i,SV212: $i,SV79: $i] :
( ( ( ~ ( ~ ( ord_less_eq @ SV79 @ ( number_number_of @ SV79 @ SV212 ) @ ( number_number_of @ SV79 @ SV218 ) )
| ~ ( ord_less @ SV79 @ ( number_number_of @ SV79 @ SV218 ) @ ( number_number_of @ SV79 @ SV212 ) ) ) )
= $false )
| ( ( number @ SV79 )
= $false )
| ( ( linorder @ SV79 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1302]) ).
thf(1333,plain,
! [SV212: $i,SV218: $i,SV79: $i] :
( ( ( ~ ( ~ ~ ( ord_less @ SV79 @ ( number_number_of @ SV79 @ SV218 ) @ ( number_number_of @ SV79 @ SV212 ) )
| ( ord_less_eq @ SV79 @ ( number_number_of @ SV79 @ SV212 ) @ ( number_number_of @ SV79 @ SV218 ) ) ) )
= $false )
| ( ( number @ SV79 )
= $false )
| ( ( linorder @ SV79 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1302]) ).
thf(1334,plain,
! [SV150: $i,SV91: $i,SV175: $i] :
( ( ( ~ ( ~ ( ord_less @ SV175 @ ( ti @ SV175 @ SV91 ) @ SV150 )
| ( ord_less @ SV175 @ SV91 @ SV150 ) ) )
= $false )
| ( ( number @ SV175 )
= $false )
| ( ( linorder @ SV175 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1304]) ).
thf(1335,plain,
! [SV150: $i,SV91: $i,SV175: $i] :
( ( ( ~ ( ~ ( ord_less @ SV175 @ SV91 @ SV150 )
| ( ord_less @ SV175 @ ( ti @ SV175 @ SV91 ) @ SV150 ) ) )
= $false )
| ( ( number @ SV175 )
= $false )
| ( ( linorder @ SV175 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1304]) ).
thf(1336,plain,
! [SV205: $i,SV193: $i,SV97: $i] :
( ( ( ( ( ti @ SV97 @ SV193 )
!= ( zero_zero @ SV97 ) )
| ( ( ti @ SV97 @ SV205 )
!= ( zero_zero @ SV97 ) ) )
= $false )
| ( ( ( plus_plus @ SV97 @ ( times_times @ SV97 @ SV193 @ SV193 ) @ ( times_times @ SV97 @ SV205 @ SV205 ) )
= ( zero_zero @ SV97 ) )
= $false )
| ( ( linord581940658strict @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1305]) ).
thf(1337,plain,
! [SV205: $i,SV193: $i,SV97: $i] :
( ( ( ( ( ti @ SV97 @ SV193 )
!= ( zero_zero @ SV97 ) )
| ( ( ti @ SV97 @ SV205 )
!= ( zero_zero @ SV97 ) ) )
= $true )
| ( ( ( plus_plus @ SV97 @ ( times_times @ SV97 @ SV193 @ SV193 ) @ ( times_times @ SV97 @ SV205 @ SV205 ) )
= ( zero_zero @ SV97 ) )
= $true )
| ( ( linord581940658strict @ SV97 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1306]) ).
thf(1338,plain,
! [SV220: $i,SV214: $i,SV99: $i] :
( ( ( ~ ( ~ ( ord_less_eq @ SV99 @ ( number_number_of @ SV99 @ SV214 ) @ ( number_number_of @ SV99 @ SV220 ) )
| ( ord_less_eq @ int @ SV214 @ SV220 ) ) )
= $false )
| ( ( number_ring @ SV99 )
= $false )
| ( ( linordered_idom @ SV99 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1307]) ).
thf(1339,plain,
! [SV99: $i,SV220: $i,SV214: $i] :
( ( ( ~ ( ~ ( ord_less_eq @ int @ SV214 @ SV220 )
| ( ord_less_eq @ SV99 @ ( number_number_of @ SV99 @ SV214 ) @ ( number_number_of @ SV99 @ SV220 ) ) ) )
= $false )
| ( ( number_ring @ SV99 )
= $false )
| ( ( linordered_idom @ SV99 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1307]) ).
thf(1340,plain,
! [SV215: $i,SV103: $i] :
( ( ( ~ ( ord_less_eq @ SV103 @ ( one_one @ SV103 ) @ ( number_number_of @ SV103 @ SV215 ) )
| ( ord_less_eq @ int @ ( bit1 @ pls ) @ SV215 ) )
= $true )
| ( ( number_ring @ SV103 )
= $false )
| ( ( linordered_idom @ SV103 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1308]) ).
thf(1341,plain,
! [SV103: $i,SV215: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( bit1 @ pls ) @ SV215 )
| ( ord_less_eq @ SV103 @ ( one_one @ SV103 ) @ ( number_number_of @ SV103 @ SV215 ) ) )
= $true )
| ( ( number_ring @ SV103 )
= $false )
| ( ( linordered_idom @ SV103 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1309]) ).
thf(1342,plain,
! [SV195: $i,SV178: $i,SV23: $i] :
( ( ( ( ti @ SV23 @ SV178 )
!= ( zero_zero @ SV23 ) )
= $false )
| ( ( ( plus_plus @ SV23 @ ( power_power @ SV23 @ SV178 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV23 @ SV195 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV23 ) )
= $false )
| ( ( linordered_idom @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1310]) ).
thf(1343,plain,
! [SV178: $i,SV195: $i,SV23: $i] :
( ( ( ( ti @ SV23 @ SV195 )
!= ( zero_zero @ SV23 ) )
= $false )
| ( ( ( plus_plus @ SV23 @ ( power_power @ SV23 @ SV178 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV23 @ SV195 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV23 ) )
= $false )
| ( ( linordered_idom @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1310]) ).
thf(1344,plain,
! [SV195: $i,SV178: $i,SV23: $i] :
( ( ( ( ti @ SV23 @ SV178 )
!= ( zero_zero @ SV23 ) )
= $true )
| ( ( ( ti @ SV23 @ SV195 )
!= ( zero_zero @ SV23 ) )
= $true )
| ( ( ( plus_plus @ SV23 @ ( power_power @ SV23 @ SV178 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV23 @ SV195 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV23 ) )
= $true )
| ( ( linordered_idom @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1311]) ).
thf(1345,plain,
! [SV119: $i,SV28: $i] :
( ( ( ord_less @ int @ SV28 @ SV119 )
= $false )
| ( ( ord_less @ int @ pls @ SV119 )
= $true )
| ( ( ord_less @ nat @ ( number_number_of @ nat @ SV28 ) @ ( number_number_of @ nat @ SV119 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1312]) ).
thf(1346,plain,
! [SV119: $i,SV28: $i] :
( ( ( ord_less @ int @ SV28 @ SV119 )
= $true )
| ( ( ~ ( ord_less @ int @ SV28 @ SV119 ) )
= $true )
| ( ( ord_less @ nat @ ( number_number_of @ nat @ SV28 ) @ ( number_number_of @ nat @ SV119 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1313]) ).
thf(1347,plain,
! [SV119: $i,SV28: $i] :
( ( ( ord_less @ int @ SV28 @ SV119 )
= $false )
| ( ( ord_less @ int @ pls @ SV119 )
= $false )
| ( ( ord_less @ nat @ ( number_number_of @ nat @ SV28 ) @ ( number_number_of @ nat @ SV119 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1314]) ).
thf(1348,plain,
! [SV216: $i,SV207: $i,SV33: $i] :
( ( ( ( ( number_number_of @ SV33 @ SV207 )
!= ( number_number_of @ SV33 @ SV216 ) )
| ( SV207 = SV216 ) )
= $true )
| ( ( number_ring @ SV33 )
= $false )
| ( ( ring_char_0 @ SV33 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1315]) ).
thf(1349,plain,
! [SV33: $i,SV216: $i,SV207: $i] :
( ( ( ( SV207 != SV216 )
| ( ( number_number_of @ SV33 @ SV207 )
= ( number_number_of @ SV33 @ SV216 ) ) )
= $true )
| ( ( number_ring @ SV33 )
= $false )
| ( ( ring_char_0 @ SV33 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1316]) ).
thf(1350,plain,
! [SV124: $i,SV40: $i] :
( ( ( ~ ( ord_less @ int @ SV40 @ pls ) )
= $true )
| ( ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV124 ) @ ( number_number_of @ nat @ SV40 ) )
= ( number_number_of @ nat @ SV124 ) )
= $true )
| ( ( ord_less @ int @ SV124 @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1317]) ).
thf(1351,plain,
! [SV124: $i,SV40: $i] :
( ( ( ~ ~ ( ord_less @ int @ SV40 @ pls ) )
= $true )
| ( ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV124 ) @ ( number_number_of @ nat @ SV40 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SV124 @ SV40 ) ) )
= $true )
| ( ( ord_less @ int @ SV124 @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1318]) ).
thf(1352,plain,
! [SV201: $i,SV188: $i,SV59: $i] :
( ( ( ( ti @ SV59 @ SV188 )
= ( zero_zero @ SV59 ) )
= $false )
| ( ( ( ti @ SV59 @ SV201 )
!= ( zero_zero @ SV59 ) )
= $true )
| ( ( ord_less @ SV59 @ ( zero_zero @ SV59 ) @ ( plus_plus @ SV59 @ ( power_power @ SV59 @ SV188 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV59 @ SV201 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $false )
| ( ( linordered_idom @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1319]) ).
thf(1353,plain,
! [SV201: $i,SV188: $i,SV59: $i] :
( ( ( ( ti @ SV59 @ SV188 )
= ( zero_zero @ SV59 ) )
= $true )
| ( ( ord_less @ SV59 @ ( zero_zero @ SV59 ) @ ( plus_plus @ SV59 @ ( power_power @ SV59 @ SV188 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV59 @ SV201 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true )
| ( ( linordered_idom @ SV59 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1320]) ).
thf(1354,plain,
! [SV188: $i,SV201: $i,SV59: $i] :
( ( ( ( ti @ SV59 @ SV201 )
= ( zero_zero @ SV59 ) )
= $true )
| ( ( ord_less @ SV59 @ ( zero_zero @ SV59 ) @ ( plus_plus @ SV59 @ ( power_power @ SV59 @ SV188 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV59 @ SV201 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true )
| ( ( linordered_idom @ SV59 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1321]) ).
thf(1355,plain,
! [SV138: $i,SV63: $i,SV170: $i] :
( ( ( ~ ( ord_less @ SV170 @ SV63 @ ( ti @ SV170 @ SV138 ) )
| ( ord_less @ SV170 @ SV63 @ SV138 ) )
= $true )
| ( ( number @ SV170 )
= $false )
| ( ( linorder @ SV170 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1322]) ).
thf(1356,plain,
! [SV138: $i,SV63: $i,SV170: $i] :
( ( ( ~ ( ord_less @ SV170 @ SV63 @ SV138 )
| ( ord_less @ SV170 @ SV63 @ ( ti @ SV170 @ SV138 ) ) )
= $true )
| ( ( number @ SV170 )
= $false )
| ( ( linorder @ SV170 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1323]) ).
thf(1357,plain,
! [SV139: $i,SV65: $i] :
( ( ( SV65 = SV139 )
= $true )
| ( ( ord_less_eq @ int @ SV65 @ SV139 )
= $false )
| ( ( ord_less @ int @ SV65 @ SV139 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1325]) ).
thf(1358,plain,
! [SV209: $i,SV68: $i] :
( ( ( ~ ( ord_less_eq @ SV68 @ ( zero_zero @ SV68 ) @ ( number_number_of @ SV68 @ SV209 ) ) )
= $true )
| ( ( ord_less_eq @ int @ pls @ SV209 )
= $true )
| ( ( number_ring @ SV68 )
= $false )
| ( ( linordered_idom @ SV68 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1326]) ).
thf(1359,plain,
! [SV68: $i,SV209: $i] :
( ( ( ~ ( ord_less_eq @ int @ pls @ SV209 ) )
= $true )
| ( ( ord_less_eq @ SV68 @ ( zero_zero @ SV68 ) @ ( number_number_of @ SV68 @ SV209 ) )
= $true )
| ( ( number_ring @ SV68 )
= $false )
| ( ( linordered_idom @ SV68 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1327]) ).
thf(1360,plain,
! [SV210: $i,SV70: $i] :
( ( ( ~ ( ord_less_eq @ SV70 @ ( number_number_of @ SV70 @ SV210 ) @ ( zero_zero @ SV70 ) ) )
= $true )
| ( ( ord_less_eq @ int @ SV210 @ pls )
= $true )
| ( ( number_ring @ SV70 )
= $false )
| ( ( linordered_idom @ SV70 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1328]) ).
thf(1361,plain,
! [SV70: $i,SV210: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV210 @ pls ) )
= $true )
| ( ( ord_less_eq @ SV70 @ ( number_number_of @ SV70 @ SV210 ) @ ( zero_zero @ SV70 ) )
= $true )
| ( ( number_ring @ SV70 )
= $false )
| ( ( linordered_idom @ SV70 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1329]) ).
thf(1362,plain,
! [SV211: $i,SV73: $i] :
( ( ( ~ ( ord_less_eq @ SV73 @ ( number_number_of @ SV73 @ SV211 ) @ ( one_one @ SV73 ) ) )
= $true )
| ( ( ord_less_eq @ int @ SV211 @ ( bit1 @ pls ) )
= $true )
| ( ( number_ring @ SV73 )
= $false )
| ( ( linordered_idom @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1330]) ).
thf(1363,plain,
! [SV73: $i,SV211: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV211 @ ( bit1 @ pls ) ) )
= $true )
| ( ( ord_less_eq @ SV73 @ ( number_number_of @ SV73 @ SV211 ) @ ( one_one @ SV73 ) )
= $true )
| ( ( number_ring @ SV73 )
= $false )
| ( ( linordered_idom @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1331]) ).
thf(1364,plain,
! [SV218: $i,SV212: $i,SV79: $i] :
( ( ( ~ ( ord_less_eq @ SV79 @ ( number_number_of @ SV79 @ SV212 ) @ ( number_number_of @ SV79 @ SV218 ) )
| ~ ( ord_less @ SV79 @ ( number_number_of @ SV79 @ SV218 ) @ ( number_number_of @ SV79 @ SV212 ) ) )
= $true )
| ( ( number @ SV79 )
= $false )
| ( ( linorder @ SV79 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1332]) ).
thf(1365,plain,
! [SV212: $i,SV218: $i,SV79: $i] :
( ( ( ~ ~ ( ord_less @ SV79 @ ( number_number_of @ SV79 @ SV218 ) @ ( number_number_of @ SV79 @ SV212 ) )
| ( ord_less_eq @ SV79 @ ( number_number_of @ SV79 @ SV212 ) @ ( number_number_of @ SV79 @ SV218 ) ) )
= $true )
| ( ( number @ SV79 )
= $false )
| ( ( linorder @ SV79 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1333]) ).
thf(1366,plain,
! [SV150: $i,SV91: $i,SV175: $i] :
( ( ( ~ ( ord_less @ SV175 @ ( ti @ SV175 @ SV91 ) @ SV150 )
| ( ord_less @ SV175 @ SV91 @ SV150 ) )
= $true )
| ( ( number @ SV175 )
= $false )
| ( ( linorder @ SV175 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1334]) ).
thf(1367,plain,
! [SV150: $i,SV91: $i,SV175: $i] :
( ( ( ~ ( ord_less @ SV175 @ SV91 @ SV150 )
| ( ord_less @ SV175 @ ( ti @ SV175 @ SV91 ) @ SV150 ) )
= $true )
| ( ( number @ SV175 )
= $false )
| ( ( linorder @ SV175 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1335]) ).
thf(1368,plain,
! [SV205: $i,SV193: $i,SV97: $i] :
( ( ( ( ti @ SV97 @ SV193 )
!= ( zero_zero @ SV97 ) )
= $false )
| ( ( ( plus_plus @ SV97 @ ( times_times @ SV97 @ SV193 @ SV193 ) @ ( times_times @ SV97 @ SV205 @ SV205 ) )
= ( zero_zero @ SV97 ) )
= $false )
| ( ( linord581940658strict @ SV97 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1336]) ).
thf(1369,plain,
! [SV193: $i,SV205: $i,SV97: $i] :
( ( ( ( ti @ SV97 @ SV205 )
!= ( zero_zero @ SV97 ) )
= $false )
| ( ( ( plus_plus @ SV97 @ ( times_times @ SV97 @ SV193 @ SV193 ) @ ( times_times @ SV97 @ SV205 @ SV205 ) )
= ( zero_zero @ SV97 ) )
= $false )
| ( ( linord581940658strict @ SV97 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1336]) ).
thf(1370,plain,
! [SV205: $i,SV193: $i,SV97: $i] :
( ( ( ( ti @ SV97 @ SV193 )
!= ( zero_zero @ SV97 ) )
= $true )
| ( ( ( ti @ SV97 @ SV205 )
!= ( zero_zero @ SV97 ) )
= $true )
| ( ( ( plus_plus @ SV97 @ ( times_times @ SV97 @ SV193 @ SV193 ) @ ( times_times @ SV97 @ SV205 @ SV205 ) )
= ( zero_zero @ SV97 ) )
= $true )
| ( ( linord581940658strict @ SV97 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1337]) ).
thf(1371,plain,
! [SV220: $i,SV214: $i,SV99: $i] :
( ( ( ~ ( ord_less_eq @ SV99 @ ( number_number_of @ SV99 @ SV214 ) @ ( number_number_of @ SV99 @ SV220 ) )
| ( ord_less_eq @ int @ SV214 @ SV220 ) )
= $true )
| ( ( number_ring @ SV99 )
= $false )
| ( ( linordered_idom @ SV99 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1338]) ).
thf(1372,plain,
! [SV99: $i,SV220: $i,SV214: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV214 @ SV220 )
| ( ord_less_eq @ SV99 @ ( number_number_of @ SV99 @ SV214 ) @ ( number_number_of @ SV99 @ SV220 ) ) )
= $true )
| ( ( number_ring @ SV99 )
= $false )
| ( ( linordered_idom @ SV99 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1339]) ).
thf(1373,plain,
! [SV215: $i,SV103: $i] :
( ( ( ~ ( ord_less_eq @ SV103 @ ( one_one @ SV103 ) @ ( number_number_of @ SV103 @ SV215 ) ) )
= $true )
| ( ( ord_less_eq @ int @ ( bit1 @ pls ) @ SV215 )
= $true )
| ( ( number_ring @ SV103 )
= $false )
| ( ( linordered_idom @ SV103 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1340]) ).
thf(1374,plain,
! [SV103: $i,SV215: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( bit1 @ pls ) @ SV215 ) )
= $true )
| ( ( ord_less_eq @ SV103 @ ( one_one @ SV103 ) @ ( number_number_of @ SV103 @ SV215 ) )
= $true )
| ( ( number_ring @ SV103 )
= $false )
| ( ( linordered_idom @ SV103 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1341]) ).
thf(1375,plain,
! [SV195: $i,SV178: $i,SV23: $i] :
( ( ( ( ti @ SV23 @ SV178 )
= ( zero_zero @ SV23 ) )
= $true )
| ( ( ( plus_plus @ SV23 @ ( power_power @ SV23 @ SV178 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV23 @ SV195 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV23 ) )
= $false )
| ( ( linordered_idom @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1342]) ).
thf(1376,plain,
! [SV178: $i,SV195: $i,SV23: $i] :
( ( ( ( ti @ SV23 @ SV195 )
= ( zero_zero @ SV23 ) )
= $true )
| ( ( ( plus_plus @ SV23 @ ( power_power @ SV23 @ SV178 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV23 @ SV195 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV23 ) )
= $false )
| ( ( linordered_idom @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1343]) ).
thf(1377,plain,
! [SV195: $i,SV178: $i,SV23: $i] :
( ( ( ( ti @ SV23 @ SV178 )
= ( zero_zero @ SV23 ) )
= $false )
| ( ( ( ti @ SV23 @ SV195 )
!= ( zero_zero @ SV23 ) )
= $true )
| ( ( ( plus_plus @ SV23 @ ( power_power @ SV23 @ SV178 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV23 @ SV195 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV23 ) )
= $true )
| ( ( linordered_idom @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1344]) ).
thf(1378,plain,
! [SV119: $i,SV28: $i] :
( ( ( ord_less @ int @ SV28 @ SV119 )
= $false )
| ( ( ord_less @ int @ SV28 @ SV119 )
= $true )
| ( ( ord_less @ nat @ ( number_number_of @ nat @ SV28 ) @ ( number_number_of @ nat @ SV119 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1346]) ).
thf(1379,plain,
! [SV216: $i,SV207: $i,SV33: $i] :
( ( ( ( number_number_of @ SV33 @ SV207 )
!= ( number_number_of @ SV33 @ SV216 ) )
= $true )
| ( ( SV207 = SV216 )
= $true )
| ( ( number_ring @ SV33 )
= $false )
| ( ( ring_char_0 @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1348]) ).
thf(1380,plain,
! [SV33: $i,SV216: $i,SV207: $i] :
( ( ( SV207 != SV216 )
= $true )
| ( ( ( number_number_of @ SV33 @ SV207 )
= ( number_number_of @ SV33 @ SV216 ) )
= $true )
| ( ( number_ring @ SV33 )
= $false )
| ( ( ring_char_0 @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1349]) ).
thf(1381,plain,
! [SV124: $i,SV40: $i] :
( ( ( ord_less @ int @ SV40 @ pls )
= $false )
| ( ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV124 ) @ ( number_number_of @ nat @ SV40 ) )
= ( number_number_of @ nat @ SV124 ) )
= $true )
| ( ( ord_less @ int @ SV124 @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1350]) ).
thf(1382,plain,
! [SV124: $i,SV40: $i] :
( ( ( ~ ( ord_less @ int @ SV40 @ pls ) )
= $false )
| ( ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV124 ) @ ( number_number_of @ nat @ SV40 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SV124 @ SV40 ) ) )
= $true )
| ( ( ord_less @ int @ SV124 @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1351]) ).
thf(1383,plain,
! [SV188: $i,SV201: $i,SV59: $i] :
( ( ( ( ti @ SV59 @ SV201 )
= ( zero_zero @ SV59 ) )
= $false )
| ( ( ( ti @ SV59 @ SV188 )
= ( zero_zero @ SV59 ) )
= $false )
| ( ( ord_less @ SV59 @ ( zero_zero @ SV59 ) @ ( plus_plus @ SV59 @ ( power_power @ SV59 @ SV188 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV59 @ SV201 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $false )
| ( ( linordered_idom @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1352]) ).
thf(1384,plain,
! [SV138: $i,SV63: $i,SV170: $i] :
( ( ( ~ ( ord_less @ SV170 @ SV63 @ ( ti @ SV170 @ SV138 ) ) )
= $true )
| ( ( ord_less @ SV170 @ SV63 @ SV138 )
= $true )
| ( ( number @ SV170 )
= $false )
| ( ( linorder @ SV170 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1355]) ).
thf(1385,plain,
! [SV138: $i,SV63: $i,SV170: $i] :
( ( ( ~ ( ord_less @ SV170 @ SV63 @ SV138 ) )
= $true )
| ( ( ord_less @ SV170 @ SV63 @ ( ti @ SV170 @ SV138 ) )
= $true )
| ( ( number @ SV170 )
= $false )
| ( ( linorder @ SV170 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1356]) ).
thf(1386,plain,
! [SV209: $i,SV68: $i] :
( ( ( ord_less_eq @ SV68 @ ( zero_zero @ SV68 ) @ ( number_number_of @ SV68 @ SV209 ) )
= $false )
| ( ( ord_less_eq @ int @ pls @ SV209 )
= $true )
| ( ( number_ring @ SV68 )
= $false )
| ( ( linordered_idom @ SV68 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1358]) ).
thf(1387,plain,
! [SV68: $i,SV209: $i] :
( ( ( ord_less_eq @ int @ pls @ SV209 )
= $false )
| ( ( ord_less_eq @ SV68 @ ( zero_zero @ SV68 ) @ ( number_number_of @ SV68 @ SV209 ) )
= $true )
| ( ( number_ring @ SV68 )
= $false )
| ( ( linordered_idom @ SV68 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1359]) ).
thf(1388,plain,
! [SV210: $i,SV70: $i] :
( ( ( ord_less_eq @ SV70 @ ( number_number_of @ SV70 @ SV210 ) @ ( zero_zero @ SV70 ) )
= $false )
| ( ( ord_less_eq @ int @ SV210 @ pls )
= $true )
| ( ( number_ring @ SV70 )
= $false )
| ( ( linordered_idom @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1360]) ).
thf(1389,plain,
! [SV70: $i,SV210: $i] :
( ( ( ord_less_eq @ int @ SV210 @ pls )
= $false )
| ( ( ord_less_eq @ SV70 @ ( number_number_of @ SV70 @ SV210 ) @ ( zero_zero @ SV70 ) )
= $true )
| ( ( number_ring @ SV70 )
= $false )
| ( ( linordered_idom @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1361]) ).
thf(1390,plain,
! [SV211: $i,SV73: $i] :
( ( ( ord_less_eq @ SV73 @ ( number_number_of @ SV73 @ SV211 ) @ ( one_one @ SV73 ) )
= $false )
| ( ( ord_less_eq @ int @ SV211 @ ( bit1 @ pls ) )
= $true )
| ( ( number_ring @ SV73 )
= $false )
| ( ( linordered_idom @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1362]) ).
thf(1391,plain,
! [SV73: $i,SV211: $i] :
( ( ( ord_less_eq @ int @ SV211 @ ( bit1 @ pls ) )
= $false )
| ( ( ord_less_eq @ SV73 @ ( number_number_of @ SV73 @ SV211 ) @ ( one_one @ SV73 ) )
= $true )
| ( ( number_ring @ SV73 )
= $false )
| ( ( linordered_idom @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1363]) ).
thf(1392,plain,
! [SV218: $i,SV212: $i,SV79: $i] :
( ( ( ~ ( ord_less_eq @ SV79 @ ( number_number_of @ SV79 @ SV212 ) @ ( number_number_of @ SV79 @ SV218 ) ) )
= $true )
| ( ( ~ ( ord_less @ SV79 @ ( number_number_of @ SV79 @ SV218 ) @ ( number_number_of @ SV79 @ SV212 ) ) )
= $true )
| ( ( number @ SV79 )
= $false )
| ( ( linorder @ SV79 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1364]) ).
thf(1393,plain,
! [SV212: $i,SV218: $i,SV79: $i] :
( ( ( ~ ~ ( ord_less @ SV79 @ ( number_number_of @ SV79 @ SV218 ) @ ( number_number_of @ SV79 @ SV212 ) ) )
= $true )
| ( ( ord_less_eq @ SV79 @ ( number_number_of @ SV79 @ SV212 ) @ ( number_number_of @ SV79 @ SV218 ) )
= $true )
| ( ( number @ SV79 )
= $false )
| ( ( linorder @ SV79 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1365]) ).
thf(1394,plain,
! [SV150: $i,SV91: $i,SV175: $i] :
( ( ( ~ ( ord_less @ SV175 @ ( ti @ SV175 @ SV91 ) @ SV150 ) )
= $true )
| ( ( ord_less @ SV175 @ SV91 @ SV150 )
= $true )
| ( ( number @ SV175 )
= $false )
| ( ( linorder @ SV175 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1366]) ).
thf(1395,plain,
! [SV150: $i,SV91: $i,SV175: $i] :
( ( ( ~ ( ord_less @ SV175 @ SV91 @ SV150 ) )
= $true )
| ( ( ord_less @ SV175 @ ( ti @ SV175 @ SV91 ) @ SV150 )
= $true )
| ( ( number @ SV175 )
= $false )
| ( ( linorder @ SV175 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1367]) ).
thf(1396,plain,
! [SV205: $i,SV193: $i,SV97: $i] :
( ( ( ( ti @ SV97 @ SV193 )
= ( zero_zero @ SV97 ) )
= $true )
| ( ( ( plus_plus @ SV97 @ ( times_times @ SV97 @ SV193 @ SV193 ) @ ( times_times @ SV97 @ SV205 @ SV205 ) )
= ( zero_zero @ SV97 ) )
= $false )
| ( ( linord581940658strict @ SV97 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1368]) ).
thf(1397,plain,
! [SV193: $i,SV205: $i,SV97: $i] :
( ( ( ( ti @ SV97 @ SV205 )
= ( zero_zero @ SV97 ) )
= $true )
| ( ( ( plus_plus @ SV97 @ ( times_times @ SV97 @ SV193 @ SV193 ) @ ( times_times @ SV97 @ SV205 @ SV205 ) )
= ( zero_zero @ SV97 ) )
= $false )
| ( ( linord581940658strict @ SV97 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1369]) ).
thf(1398,plain,
! [SV205: $i,SV193: $i,SV97: $i] :
( ( ( ( ti @ SV97 @ SV193 )
= ( zero_zero @ SV97 ) )
= $false )
| ( ( ( ti @ SV97 @ SV205 )
!= ( zero_zero @ SV97 ) )
= $true )
| ( ( ( plus_plus @ SV97 @ ( times_times @ SV97 @ SV193 @ SV193 ) @ ( times_times @ SV97 @ SV205 @ SV205 ) )
= ( zero_zero @ SV97 ) )
= $true )
| ( ( linord581940658strict @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1370]) ).
thf(1399,plain,
! [SV220: $i,SV214: $i,SV99: $i] :
( ( ( ~ ( ord_less_eq @ SV99 @ ( number_number_of @ SV99 @ SV214 ) @ ( number_number_of @ SV99 @ SV220 ) ) )
= $true )
| ( ( ord_less_eq @ int @ SV214 @ SV220 )
= $true )
| ( ( number_ring @ SV99 )
= $false )
| ( ( linordered_idom @ SV99 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1371]) ).
thf(1400,plain,
! [SV99: $i,SV220: $i,SV214: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV214 @ SV220 ) )
= $true )
| ( ( ord_less_eq @ SV99 @ ( number_number_of @ SV99 @ SV214 ) @ ( number_number_of @ SV99 @ SV220 ) )
= $true )
| ( ( number_ring @ SV99 )
= $false )
| ( ( linordered_idom @ SV99 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1372]) ).
thf(1401,plain,
! [SV215: $i,SV103: $i] :
( ( ( ord_less_eq @ SV103 @ ( one_one @ SV103 ) @ ( number_number_of @ SV103 @ SV215 ) )
= $false )
| ( ( ord_less_eq @ int @ ( bit1 @ pls ) @ SV215 )
= $true )
| ( ( number_ring @ SV103 )
= $false )
| ( ( linordered_idom @ SV103 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1373]) ).
thf(1402,plain,
! [SV103: $i,SV215: $i] :
( ( ( ord_less_eq @ int @ ( bit1 @ pls ) @ SV215 )
= $false )
| ( ( ord_less_eq @ SV103 @ ( one_one @ SV103 ) @ ( number_number_of @ SV103 @ SV215 ) )
= $true )
| ( ( number_ring @ SV103 )
= $false )
| ( ( linordered_idom @ SV103 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1374]) ).
thf(1403,plain,
! [SV178: $i,SV195: $i,SV23: $i] :
( ( ( ( ti @ SV23 @ SV195 )
= ( zero_zero @ SV23 ) )
= $false )
| ( ( ( ti @ SV23 @ SV178 )
= ( zero_zero @ SV23 ) )
= $false )
| ( ( ( plus_plus @ SV23 @ ( power_power @ SV23 @ SV178 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV23 @ SV195 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ SV23 ) )
= $true )
| ( ( linordered_idom @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1377]) ).
thf(1404,plain,
! [SV216: $i,SV207: $i,SV33: $i] :
( ( ( ( number_number_of @ SV33 @ SV207 )
= ( number_number_of @ SV33 @ SV216 ) )
= $false )
| ( ( SV207 = SV216 )
= $true )
| ( ( number_ring @ SV33 )
= $false )
| ( ( ring_char_0 @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1379]) ).
thf(1405,plain,
! [SV33: $i,SV216: $i,SV207: $i] :
( ( ( SV207 = SV216 )
= $false )
| ( ( ( number_number_of @ SV33 @ SV207 )
= ( number_number_of @ SV33 @ SV216 ) )
= $true )
| ( ( number_ring @ SV33 )
= $false )
| ( ( ring_char_0 @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1380]) ).
thf(1406,plain,
! [SV124: $i,SV40: $i] :
( ( ( ord_less @ int @ SV40 @ pls )
= $true )
| ( ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV124 ) @ ( number_number_of @ nat @ SV40 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SV124 @ SV40 ) ) )
= $true )
| ( ( ord_less @ int @ SV124 @ pls )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1382]) ).
thf(1407,plain,
! [SV138: $i,SV63: $i,SV170: $i] :
( ( ( ord_less @ SV170 @ SV63 @ ( ti @ SV170 @ SV138 ) )
= $false )
| ( ( ord_less @ SV170 @ SV63 @ SV138 )
= $true )
| ( ( number @ SV170 )
= $false )
| ( ( linorder @ SV170 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1384]) ).
thf(1408,plain,
! [SV138: $i,SV63: $i,SV170: $i] :
( ( ( ord_less @ SV170 @ SV63 @ SV138 )
= $false )
| ( ( ord_less @ SV170 @ SV63 @ ( ti @ SV170 @ SV138 ) )
= $true )
| ( ( number @ SV170 )
= $false )
| ( ( linorder @ SV170 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1385]) ).
thf(1409,plain,
! [SV218: $i,SV212: $i,SV79: $i] :
( ( ( ord_less_eq @ SV79 @ ( number_number_of @ SV79 @ SV212 ) @ ( number_number_of @ SV79 @ SV218 ) )
= $false )
| ( ( ~ ( ord_less @ SV79 @ ( number_number_of @ SV79 @ SV218 ) @ ( number_number_of @ SV79 @ SV212 ) ) )
= $true )
| ( ( number @ SV79 )
= $false )
| ( ( linorder @ SV79 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1392]) ).
thf(1410,plain,
! [SV212: $i,SV218: $i,SV79: $i] :
( ( ( ~ ( ord_less @ SV79 @ ( number_number_of @ SV79 @ SV218 ) @ ( number_number_of @ SV79 @ SV212 ) ) )
= $false )
| ( ( ord_less_eq @ SV79 @ ( number_number_of @ SV79 @ SV212 ) @ ( number_number_of @ SV79 @ SV218 ) )
= $true )
| ( ( number @ SV79 )
= $false )
| ( ( linorder @ SV79 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1393]) ).
thf(1411,plain,
! [SV150: $i,SV91: $i,SV175: $i] :
( ( ( ord_less @ SV175 @ ( ti @ SV175 @ SV91 ) @ SV150 )
= $false )
| ( ( ord_less @ SV175 @ SV91 @ SV150 )
= $true )
| ( ( number @ SV175 )
= $false )
| ( ( linorder @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1394]) ).
thf(1412,plain,
! [SV150: $i,SV91: $i,SV175: $i] :
( ( ( ord_less @ SV175 @ SV91 @ SV150 )
= $false )
| ( ( ord_less @ SV175 @ ( ti @ SV175 @ SV91 ) @ SV150 )
= $true )
| ( ( number @ SV175 )
= $false )
| ( ( linorder @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1395]) ).
thf(1413,plain,
! [SV193: $i,SV205: $i,SV97: $i] :
( ( ( ( ti @ SV97 @ SV205 )
= ( zero_zero @ SV97 ) )
= $false )
| ( ( ( ti @ SV97 @ SV193 )
= ( zero_zero @ SV97 ) )
= $false )
| ( ( ( plus_plus @ SV97 @ ( times_times @ SV97 @ SV193 @ SV193 ) @ ( times_times @ SV97 @ SV205 @ SV205 ) )
= ( zero_zero @ SV97 ) )
= $true )
| ( ( linord581940658strict @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1398]) ).
thf(1414,plain,
! [SV220: $i,SV214: $i,SV99: $i] :
( ( ( ord_less_eq @ SV99 @ ( number_number_of @ SV99 @ SV214 ) @ ( number_number_of @ SV99 @ SV220 ) )
= $false )
| ( ( ord_less_eq @ int @ SV214 @ SV220 )
= $true )
| ( ( number_ring @ SV99 )
= $false )
| ( ( linordered_idom @ SV99 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1399]) ).
thf(1415,plain,
! [SV99: $i,SV220: $i,SV214: $i] :
( ( ( ord_less_eq @ int @ SV214 @ SV220 )
= $false )
| ( ( ord_less_eq @ SV99 @ ( number_number_of @ SV99 @ SV214 ) @ ( number_number_of @ SV99 @ SV220 ) )
= $true )
| ( ( number_ring @ SV99 )
= $false )
| ( ( linordered_idom @ SV99 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1400]) ).
thf(1416,plain,
! [SV212: $i,SV218: $i,SV79: $i] :
( ( ( ord_less @ SV79 @ ( number_number_of @ SV79 @ SV218 ) @ ( number_number_of @ SV79 @ SV212 ) )
= $false )
| ( ( ord_less_eq @ SV79 @ ( number_number_of @ SV79 @ SV212 ) @ ( number_number_of @ SV79 @ SV218 ) )
= $false )
| ( ( number @ SV79 )
= $false )
| ( ( linorder @ SV79 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1409]) ).
thf(1417,plain,
! [SV212: $i,SV218: $i,SV79: $i] :
( ( ( ord_less @ SV79 @ ( number_number_of @ SV79 @ SV218 ) @ ( number_number_of @ SV79 @ SV212 ) )
= $true )
| ( ( ord_less_eq @ SV79 @ ( number_number_of @ SV79 @ SV212 ) @ ( number_number_of @ SV79 @ SV218 ) )
= $true )
| ( ( number @ SV79 )
= $false )
| ( ( linorder @ SV79 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1410]) ).
thf(1418,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[303,1417,1416,1415,1414,1413,1412,1411,1408,1407,1406,1405,1404,1403,1402,1401,1397,1396,1391,1390,1389,1388,1387,1386,1383,1381,1378,1376,1375,1357,1354,1353,1347,1345,1324,1303,1293,1289,1288,1287,1286,1285,1284,1283,1282,1281,1276,1265,1255,1252,1244,1242,1241,1236,1231,1194,1193,1188,1187,1186,1185,1183,1181,1180,1179,1178,1177,1176,1172,1171,1165,1164,1163,1162,1161,1160,1148,1147,1144,1143,1141,1140,1138,1137,1136,1135,1134,1128,1127,1115,1114,1113,1108,1107,1103,1102,1101,1095,1094,1091,1090,1086,1085,1083,1082,1081,1069,1068,1060,1059,1045,1044,1041,1040,1021,1011,1010,1001,975,974,960,946,941,940,935,911,896,872,864,836,827,825,823,798,797,779,742,738,733,732,730,729,728,727,726,700,642,636,635,632,630,546,538,537,535,529,528,527,526,525,524,523,438,437,436,435,434,433,432,431,430,429,428,427,426,425,424,423,422,404,403,386,383,382,360,346,344,333,330,329,328,327,326,325,304]) ).
thf(1419,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[1418]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM924+5 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.18 % Computer : n015.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Oct 6 13:47:58 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.03/2.09 .
% 11.03/2.09
% 11.03/2.09 No.of.Axioms: 140
% 11.03/2.09
% 11.03/2.09 Length.of.Defs: 0
% 11.03/2.09
% 11.03/2.09 Contains.Choice.Funs: false
% 11.03/2.09 .................................................
% 11.03/2.09
% 11.03/2.09 ********************************
% 11.03/2.09 * All subproblems solved! *
% 11.03/2.09 ********************************
% 11.03/2.09 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:140,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:1418,loop_count:0,foatp_calls:1,translation:fof_full)
% 11.03/2.09
% 11.03/2.09 %**** Beginning of derivation protocol ****
% 11.03/2.09 % SZS output start CNFRefutation
% See solution above
% 11.03/2.11
% 11.03/2.11 %**** End of derivation protocol ****
% 11.03/2.11 %**** no. of clauses in derivation: 1405 ****
% 11.03/2.11 %**** clause counter: 1418 ****
% 11.03/2.11
% 11.03/2.11 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:140,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:1418,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------